Answers
Answer:
[tex]\huge\boxed{\sf {(5,2)}}[/tex]
Step-by-step explanation:
Given equations:6x - 3y = 24 ----------------(1)
8x + y = 42 -----------------(2)
Take Eq. (1)
6x - 3y = 24
Take 3 as a common factor3(2x - y) = 24
Divide both sides by 32x - y = 24/3
2x - y = 8 ----------------(3)
Add Eq. (2) and (3)8x + y + 2x - y = 42 + 8
8x + 2x = 50
10x = 50
Divide both sides by 10x = 50/10
x = 5Put x = 5 in Eq. (3)2(5) - y = 8
10 - y = 8
Add y to both sides10 = 8 + y
Subtract 8 from both sides10 - 8 = y
2 = y
y = 2Solution set:{(x,y)} = {(5,2)}
[tex]\rule[225]{225}{2}[/tex]
Related Questions
which of the following describes the type of sampling method in which a sample frame is divided into groups? question 1 options: simple random sampling. systematic sampling. cluster sampling. stratified sampling.
Answers
The type of sampling method in which a sample frame is divided into groups is called stratified sampling.
The sampling method that describes the division of a sample frame into groups is called cluster sampling. This method involves randomly selecting groups (or clusters) from the population and then selecting individuals within those clusters to be part of the sample. It is different from stratified sampling, which involves dividing the population into subgroups and then randomly selecting individuals from each subgroup, and simple random sampling, which involves randomly selecting individuals from the population without any grouping. Systematic sampling involves selecting every nth individual from a list of the population.
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**5. Eric can run 50 meters in 7 seconds while Samer can run 20 meters in 5 seconds. If Samer
get s 30-meter head start, when will Eric catch up? How far from the start will they be at that
point?
SOLVE USING SYSTEM OF EQUATIONS 13 PTS
Answers
They will be 50 meters from the start when Eric catches up to Samer.
How to determine How far from the start will they be at that pointTo solve this problem using a system of equations, we can use the following variables:
Let t be the time it takes for Eric to catch up to Samer
Let d be the distance from the start that Eric catches up to Samer
Using the given information, we can create two equations:
Eric's equation: d = 50t
Samer's equation: d - 30 = 20t
The first equation represents Eric's distance from the start after t seconds, while the second equation represents Samer's distance from the start after t seconds, with a 30-meter head start.
To solve for t, we can substitute the first equation into the second equation:
50t - 30 = 20t
Simplifying and solving for t:
30t = 30
t = 1
Therefore, Eric will catch up to Samer after 1 second.
To find the distance from the start that they will be at that point, we can substitute t = 1 into either equation:
d = 50t = 50(1) = 50
Therefore, they will be 50 meters from the start when Eric catches up to Samer.
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How do you find the linear transformation of a 2x2 matrix?
Answers
To find the linear Transformation of a 2x2 matrix, you can use the following steps:
Start with a 2x2 matrix in the form of:
[ a b ]
[ c d ]
Define a vector [x, y] that represents a point in the input space.
Multiply the matrix by the vector to get the output vector:
[ a b ] [ x ] [ ax + by ]
[ c d ] * [ y ] = [ cx + dy ]
This represents a linear transformation that maps the input vector [x, y] to the output vector [ax + by, cx + dy].
Alternatively, you can represent the matrix as a set of linear equations in the form:
x' = ax + by
y' = cx + dy
where (x', y') represents the output vector.
These equations represent the same linear transformation as the matrix-vector multiplication, and can be used to visualize the effect of the transformation on points in the input space.
Overall, finding the linear transformation of a 2x2 matrix involves multiplying the matrix by input vectors and observing the resulting output vectors, or using the matrix to define a set of linear equations that describe the transformation.
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let q denote the set of all(2×2)symmetric matrices with the usual matrix addition and scalar multiplication. verify that q is a vector space.
Answers
The set Q of all 2x2 symmetric matrices is a vector space as Q satisfies all the properties of a vector space, and is thus a vector space.
To verify that Q is a vector space, we need to check that it satisfies the following properties:
Closure under addition: If A and B are in Q, then A + B is also in Q. This is true since the sum of two symmetric matrices is also symmetric.Commutativity of addition: If A and B are in Q, then A + B = B + A. This is true since matrix addition is commutative.Associativity of addition: If A, B, and C are in Q, then (A + B) + C = A + (B + C). This is true since matrix addition is associative.Additive identity: There exists a matrix 0 in Q such that A + 0 = A for all A in Q. This is true since the zero matrix is symmetric.Additive inverse: For every A in Q, there exists a matrix -A in Q such that A + (-A) = 0. This is true since the negative of a symmetric matrix is also symmetric.Closure under scalar multiplication: If A is in Q and k is a scalar, then kA is also in Q. This is true since the product of a scalar and a symmetric matrix is also symmetric.Distributivity of scalar multiplication over vector addition: If A and B are in Q and k is a scalar, then k(A + B) = kA + kB. This is true since scalar multiplication distributes over matrix addition.Distributivity of scalar multiplication over field addition: If A is in Q and k and l are scalars, then (k + l)A = kA + lA. This is true since scalar multiplication distributes over field addition.Associativity of scalar multiplication: If A is in Q and k and l are scalars, then (kl)A = k(lA). This is true since scalar multiplication is associative.Multiplicative identity: If A is in Q and 1 is the multiplicative identity of the field, then 1A = A. This is true since multiplying a matrix by 1 does not change the matrix.Therefore, Q satisfies all the properties of a vector space and is thus a vector space.
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Find f. (Use C for the constant of the first antiderivative and D for the constant of the second antiderivative.) f ''(x) = 4 /5( x^4/5)
Answers
The function f(x) that satisfies [tex]f ''(x) = 4/5(x^{(4/5)})[/tex] is: f(x) =[tex](2/45) x^{(14/5)} + C_1 \times x + C_2[/tex]
Integration is a fundamental concept in calculus, which involves finding the antiderivative or the integral of a given function. The antiderivative of a function is the function whose derivative is the original function. Integration is often used to solve problems in physics, engineering, economics, and many other fields.
To find f, we need to integrate the given function twice.
First, we integrate[tex]f ''(x) = 4/5(x^{(4/5)})[/tex]with respect to x to find f '(x):
f '(x) = ∫ [tex](4/5)(x^{(4/5)}) dx = (4/5)\times (5/9)\times x^{(9/5)} + C_1 = (4/9) x^{(9/5)} + C_1[/tex]
where [tex]C_1[/tex]is a constant of integration.
Next, we integrate f '(x) to find f(x):
f(x) = ∫[tex][(4/9) x^{(9/5)} + C_1] dx = (4/9)\times (5/14) \times x^{(14/5)} + C_1 \times x + C_2[/tex]
=[tex](2/45) x^{(14/5)} + C_1 \times x + C_2[/tex]
where [tex]C_2[/tex] is another constant of integration
Therefore, the function f(x) that satisfies [tex]f ''(x) = 4/5(x^{(4/5)) }[/tex]is:
[tex]f(x) = (2/45) x^{(14/5) }+ C_1 \times x + C_2.[/tex]
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A trash bin has a capacity of 50 gallons. What percentage of its capacity is each amount?
1. 5 gallons is % of 50 gallons
2. 30 gallons is % of 50 gallons
3. 45 gallons is
% of 50 gallons
4. 100 gallons is
% of 50 gallons
Answers
The percentage of the trash bins with a capacity of 50 gallons for each amount is as follows:
5 gallons = 10%30 gallons = 60%45 gallons = 90%100 gallons = 200%.How the percentages are determined:The percentages can be determined by dividing one value or amount by the total capacity of the trash bin.
Percentages represents portions or relative values of the whole value.
To expression a number in percentage, the quotient of the division operation is multiplied by 100.
The total capacity of a trash bin = 50 gallons
5 gallons = 10% of 50 galloons (5 ÷ 50 × 100)30 gallons = 60% of 50 galloons (30 ÷ 50 × 100)45 gallons = 90% of 50 gallons (45 ÷ 50 × 100)100 gallons = 200% of 50 gallons (100 ÷ 50 × 100)Learn more about percentages at https://brainly.com/question/24877689.
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Help please!! Anything helps
Answers
The missing lengths of right triangles are listed below:
Case 1: AB = 3√3, AC = 6√3
Case 2: DE = √2, DF = 2
Case 3: GI = 5√2, GH = 5
Case 4: JL = 14, KL = 7√3
Case 5: OP = 10√3, MP = 20
How to calculate missing sides in special right triangles
In this problem we must determine the missing sides of special right triangles by means of Euclidean geometry. There are two special right triangles: (45 - 90 - 45), (30 - 60 - 90)
Right triangle 45 - 90 - 45
The length of the hypotenuse is √2 times the length of any leg.Right triangle 30 - 60 - 90
The length of the short leg is 0.5 times the length of the hypotenuse.The length of the long leg is 0.5√3 times the length of the hypotenuse.The length of the long leg is √3 times the length of the short leg.Now we proceed to find the missing lengths:
Case 1
AB = BC / √3
AB = 3√3
AC = BC / 0.5√3
AC = 6√3
Case 2
DE = √2
DF = 2
Case 3
GI = 5√2
GH = 5
Case 4
JL = 7 / 0.5
JL = 14
KL = 7√3
Case 5
OM = 10
MP = 20
OP = 10√3
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Let Σ = {0, 1} , and let B be the collection of strings that contain at least one 1 in their second half.
B={uv |u ∈ Σ ∗ , v ∈ Σ ∗ and |u|>=|v|}
Give a PDA that recognizes B.
Answers
The PDA recognizes the language B, which consists of all strings that contain at least one 1 in their second half.
To construct a PDA that recognizes B, we first need to define its states, input alphabet, and stack alphabet.The states of the PDA can be represented as q0, q1, q2, and q3, where q0 is the initial state and q3 is the final state. The input alphabet is Σ = {0, 1}, and the stack alphabet is Γ = {0, 1, Z}, where Z is the initial stack symbol. The PDA works as follows:
1. In state q0, the PDA reads the input symbol a and pushes Z onto the stack.
2. In state q1, the PDA reads the input symbol b and pushes it onto the stack. If the input symbol b is 1, the PDA transitions to state q2. Otherwise, it remains in state q1.
3. In state q2, the PDA reads the input symbol c and pops the top symbol from the stack. If the top symbol is b, the PDA transitions to state q3. Otherwise, it returns to state q2.
4. In state q3, the PDA accepts the input string if the stack is empty. Otherwise, it rejects the input string. In other words, the PDA reads the input string from left to right and pushes each symbol onto the stack until it reaches the middle of the string. If it encounters a 1 in the second half of the string, it transitions to state q2, which checks that there is at least one 1 in the second half of the string. If the condition is satisfied, the PDA transitions to state q3 and accepts the string. Otherwise, it returns to state q2 and continues checking the remaining symbols in the second half of the string. If the PDA reaches the end of the string and there is no 1 in the second half, it rejects the string.
Overall, the PDA recognizes the language B, which consists of all strings that contain at least one 1 in their second half.
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Andy stacked a pile of wooden logs. The bottom row contained 30 logs. The rows above it held 27 logs, 24 logs and so on. Determine the number of logs in the 9th row.
A- 3 Logs
B- 6 Logs
C- 9 Logs
D- 10 Logs
Answers
Answer:
B. 6
Step-by-step explanation:
You want the 9th term of the arithmetic sequence with first term 30 and common difference -3.
N-th termThe n-th term of an arithmetic sequence is given by ...
an = a1 -d(n -1 . . . . . . . first term a1, common difference d
ApplicationFor the given first term and difference, the formula for the n-th term is ...
an = 30 -3(n -1)
The 9th term is ...
a9 = 30 -3(9 -1) = 30 -24
a9 = 6
There are 6 logs in the 9th row.
__
Additional comment
Sometimes, the answer can be found quicker by simply listing the terms:
30 27 24 21 18 15 12 9 6
The 9th row has 6 logs.
What is the main factor used to judge the quality of a systematic reviews (SR)?
a. The reputation of the professional association that distributes it
b. The number of studies included in the analysis
c. Whether or not statistics were used to combine the findings
d. The soundness of the methodology used to conduct it
Answers
The main factor used to judge the quality of a systematic review (SR) is D. The soundness of the methodology used to conduct it.
A systematic review aims to provide a comprehensive synthesis of available evidence on a specific research question by identifying, evaluating, and summarizing all relevant studies. The quality of a systematic review is heavily dependent on the rigor and transparency of the methodology employed. A well-conducted SR follows a predefined protocol, which includes a clear research question, eligibility criteria for study inclusion, and a comprehensive search strategy.
While the reputation of the professional association that distributes the SR (option a) and the number of studies included in the analysis (option b) can provide some insights into the review's credibility and comprehensiveness, they are not the main factors in judging the SR's quality. Similarly, the use of statistics to combine the findings (option c) is an important aspect of a systematic review but is not the primary factor to determine its quality.
In conclusion, the soundness of the methodology used to conduct a systematic review is the most critical factor in determining its quality. A rigorous and transparent methodology ensures that the review's findings are reliable, valid, and can inform decision-making and policy development. Therefore, the correct option is D.
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find the volume of the solid by subtracting two volumes, the solid enclosed by the parabolic cylinder y = 16x2, and the planes z = 3y, z = 2 y.
Answers
The volume of the solid is (32/3) cubic units.
To find the volume of the solid, we need to calculate the volume enclosed by the parabolic cylinder y = 16x² and the planes z = 3y and z = 2y, and then subtract the smaller volume from the larger volume.
The intersection of the planes z = 3y and z = 2y is the line y = 0, so we can set z = 0 in the equation y = 16x² to find the bounds of integration for x. Solving for x, we get x = ±√(y/16), so the bounds of integration for y are 0 and 48.
The volume of the solid enclosed by the parabolic cylinder y = 16x² and the plane z = 3y can be calculated using the triple integral ∭ dV, where the bounds of integration are 0 ≤ x ≤ √(y/16), 0 ≤ y ≤ 48, and 0 ≤ z ≤ 3y. Evaluating this integral, we get a volume of 256 cubic units.
Similarly, the volume of the solid enclosed by the parabolic cylinder y = 16x² and the plane z = 2y can be calculated using the triple integral ∭ dV, where the bounds of integration are 0 ≤ x ≤ √(y/16), 0 ≤ y ≤ 48, and 0 ≤ z ≤ 2y. Evaluating this integral, we get a volume of (128/3) cubic units.
Subtracting the smaller volume from the larger volume, we get (256 - 128/3) cubic units, which simplifies to (768/3 - 128/3) cubic units, or (640/3) cubic units. Simplifying further, we get (32/3) cubic units. Therefore, the volume is (32/3) cubic units.
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The function in the graph below has a vertical asymptote
x = ____
Answers
Based on the graph provided, the vertical asymptote of the function appears to be x = -2.
What is function?Functions can be represented in different ways, such as algebraically with equations, graphically with curves, or numerically with tables of values. They are used to model relationships between quantities in a wide variety of applications, from physics and engineering to economics and social sciences.
Here,
As x approaches -2 from the left, the function appears to be approaching negative infinity, indicating a vertical asymptote. As x approaches -2 from the right, the function appears to be approaching positive infinity, further supporting the existence of a vertical asymptote at x = -2.
To calculate this mathematically, we can first analyze the function by factoring the numerator and denominator:
f(x) = (x+2)/(x²-4)
The denominator can be factored as the difference of squares:
f(x) = (x+2)/[(x+2)(x-2)]
Simplifying the expression, we can cancel out the common factor of (x+2) in the numerator and denominator:
f(x) = 1/(x-2)
Now, we can see that the denominator has a zero at x = 2, but there is no zero at x = -2. Therefore, there is a vertical asymptote at x = -2.
Thus, the vertical asymptote of the given function is x = -2.
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Costas and Sheila bought a raffle ticket for a charity. The grand prize is $1000.00. Costa contributed $3.50 and Sheila contributed $1.50 to the price of the ticket. If they win the grand prize, they will share the money in the same proportion that they paid for the ticket. How much of the money should each person receive?
Answers
Answer:
Step-by-step explanation:
$3.50+$1.50=$5.00
So proportion of the price money will be
divided in 3.5/5 and 1.5/5
To make a percentage, first lets multiply our fractions by 10/10
so our new fractions are 35/50 and 15/50.
Now multiply our new fractions by 2
70/100 and 30/100.
So if they win Costa is going to get 70% of the winnings and Sheila is going to get 30% of the winnings.
[tex]\frac{1000}{1}*\frac{70}{100} = \frac{70000}{100} = 700[/tex]
so Costa will get $700
and Sheila will get the rest $1000-$700 = $300
if roller a is moving to the right with velocity va. what is the correct expression for the angular velocity of the link?
Answers
The correct expression for the angular velocity of the link would depend on the specific configuration and geometry of the system.
Without additional information, it is not possible to provide a definitive answer. However, in general, the angular velocity of the link can be determined by relating the linear velocity of the roller to the radius of the link and the angular velocity of the link using the equation v = rω,
where v is the linear velocity, r is the radius, and ω is the angular velocity.
1. First, let's identify the variables:
- va = linear velocity of Roller A (moving to the right)
- r = radius of Roller A
- ω = angular velocity of the link
2. The relationship between linear velocity (va) and angular velocity (ω) can be described by the formula:
va = rω
3. To find the correct expression for the angular velocity (ω) of the link, we can rearrange the formula to solve for ω:
ω = va / r
So, the correct expression for the angular velocity of the link is ω = va / r.
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evaluate the integral. ∫ 5 4 (t^3i +t √t − 4 j + t sin πtk) dt
Answers
The integral ∫ 5 4 (t³i +t √t − 4 j + t sin πtk) dt is evaluated as (1/4)t⁴ + (10/3)i + (-5k cos(5πk))j + (-4/πk) sin(4)k + (1/πk) sin(5πk)k + C
To evaluate the given integral, we need to integrate each component of the vector function separately with respect to t.
∫_4⁵ (t³i + t√(t-4)j + t sin(πtk)k) dt
The integral of the first component t³ with respect to t is (1/4)t⁴.
The integral of the second component t√(t-4) with respect to t can be simplified by making a substitution. Let u = t-4, then du/dt = 1 and dt = du. So the integral becomes:
∫_0¹ ((u+4)√u du) = ∫_0¹ ([tex]u^{1/2[/tex] + 4[tex]u^{1/2[/tex]) du = (2/3)[tex]u^{3/2[/tex] + 8/3 [tex]u^{1/2[/tex] evaluated from 0 to 1
= (2/3)(1[tex]u^{3/2[/tex] - [tex]0^{(3/2)[/tex]) + 8/3 ([tex]1^{(1/2)[/tex] - [tex]0^{(1/2)[/tex]) = 2/3 + 8/3 = 10/3.
The integral of the third component t sin(πtk) with respect to t can be evaluated using integration by substitution. Let u = πtk, then du/dt = πk and dt = du/(πk). So the integral becomes:
(1/πk) ∫_[tex]4^{(5\pi k)[/tex] (u/π) sin(u) du
Using integration by parts, let u = (u/π), dv = sin(u) du, then du = du/π and v = -cos(u):
= (1/πk) [(u/π) (-cos(u)) - ∫_[tex]4^{(5\pi k)[/tex] (-cos(u) du/π)]
= (1/πk) [(u/π) (-cos(u)) + (1/π) sin(u)] evaluated from 4 to 5πk
= (1/πk) [(5πk/π) (-cos(5πk)) - (4/π) sin(4) + (1/π) sin(5πk)]
= (-5k cos(5πk)) - (4/πk) sin(4) + (1/πk) sin(5πk)
Therefore, the final answer for the integral is: (1/4)t⁴ + (10/3)i + (-5k cos(5πk))j + (-4/πk) sin(4)k + (1/πk) sin(5πk)k + C, where C is the constant of integration.
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Match the pairs of equivalent expressions.
(-14+3/2b)-(1+8/2b)
4b+13/2
8b-15
(5+2b)+(2b+3/2)
(-10+b)+(7b-5)
(7/2b-3)-(8+6b)
-15-5/2b
-5/2b-11
Answers
Solving the expressions, we can find their equivalent expressions as follows:
(5 + 2b) + (2b + 3/2) ⇔ 4b + 13/2
(-10 + b) + (7b - 5) ⇔ 8b - 15
(-14 + 3/2b) - (1 + 8/2b) ⇔ -15 - 5/2b
(7/2b - 3) - (8 + 6b) ⇔ -5/2b - 11
What does expression mean?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent criteria.
Mathematical statements that comprise either numbers, variables, or both and at least two terms associated by an operator are referred to as expressions. Mathematical operations including addition, subtraction, multiplication, and division are all feasible.
Here in the question,
In the 1st expression,
(5 + 2b) + (2b + 3/2)
Simplifying it:
= (10 + 2b + 2b + 3)/2
= (13+4b)/2
In the 2nd expression:
(-10 + b) + (7b - 5)
= -10 + b + 7b - 5
= 8b - 15
In the 3rd expression:
(-14 + 3/2b) - (1 + 8/2b)
= -14 - 1 + 3/2b - 8/2b
= -15 -5/2b
In the final expression:
(7/2b - 3) - (8 + 6b)
= 7/2b - 6b - 3 - 8
= -5/2b - 11
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The complete question is:
Drag the tiles to the boxes to form correct pairs. Match the pairs of equivalent expressions.
Between
(5 + 2b) + (2b + 3/2)
(-14 + 3/2b) - (1 + 8/2b)
(-10 + b) + (7b -5)
(7/2b - 3) - (8 + 6b)
And
8b - 15
4b + 13/2
-5/2b - 11
-15 - 5/2b
suppose a hypothesis test, using α = 0.05, is being conducted with the following null hypothesis: h0: μ = 2. which one of the following confidence intervals would lead to rejecting the null hypothesis
Answers
A confidence interval cannot instantly lead to rejecting the null hypothesis in a hypothesis test. In the given case the null hypothesis is either rejected or rejected based on test statistics.
α = 0.05
μ = 2
If the confidence interval is 1.0 or 2.0, then the null hypothesis value of 2 drops exceeds the interval, this makes the data contradict the null hypothesis and may reject the null hypothesis.
This alone would not be good to decline the null theory - the conclusion to reject or not reject the null hypothesis is determined by the test statistic and the alternate p-value.
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a numerical measure from a population, such as a population mean, is called _____.a. a sampleb. the mean deviationc. a statisticd. a parameter
Answers
A numerical measure from a population, such as a population mean, is called a statistic. This can be answered by the concept of Standard deviation.
A statistic refers to a numerical measure that is calculated from a sample, which is a subset of a larger population. It is commonly used to estimate or describe characteristics of a population based on the information obtained from a sample. Examples of statistics include sample mean, sample standard deviation, sample proportion, etc. These measures are used to provide insights and make inferences about the population from which the sample was drawn.
Therefore, the correct answer is C. a statistic.
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5. Determine if the given set is a subspace of P7. Justify your answer. All polynomials of degree at most 7, with negative real numbers as coefficients. Complete each statement below. The zero vector of P, (1) in the set because zero (2) — - a negative real number. The set (3) - - closed under vector addition because the sum of two negative real numbers (4) - a negative real number The set (5) closed under multiplication by scalars because the product of a scalar and a negative real number (6) a negative real number Is the set a subspace of P7? O O Yes No (1) Ois o is not (2) Ois 0 is not (3) O is not 0 is (4) O is not 0 in (5) Ois 0 is not (6) O is not necessarily is
Answers
(1) is not
(2) is not
(3) is not
(4) is
(5) is not
(6) is not necessarily
The given set is all polynomials of degree at most 7, with negative real numbers as coefficients. Let's analyze each statement:
1. The zero vector of P7 is in the set because zero is not a negative real number.
2. The set is not closed under vector addition because the sum of two negative real numbers is a negative real number.
3. The set is not closed under multiplication by scalars because the product of a scalar and a negative real number is not necessarily a negative real number.
Based on these findings, the set is not a subspace of P7. Here are the answers to fill in the blanks:
(1) is not
(2) is not
(3) is not
(4) is
(5) is not
(6) is not necessarily
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pls hlp thx your the best
Answers
Answer:
Jordan earns $10.6 an hour more than Dianelys
Step-by-step explanation:
As the graph reveals, we're dealing with linear functions where earnings (y) is a function of x:
y = mx + b
Because we want to know how much more Jordan earns per hour than Dianelys, we will need to find the slopes of both lines and subtract.
We can find the slopes of the lines modeling Dianelys and Jordan's earnings using the slope formula:
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex], were x1 and y1 are one point on the line and x2 and y2 are another point on the line
Dianelys' equation:
We can let (10, 171) be our x1 and y1 point and (20, 342) our x2 and y2 point:
[tex]m=\frac{342-171}{20-10}\\ m=\frac{171}{10}\\ m=17.1[/tex]
We know that our b is 0. As the graph shows, when no work is done, Dianelys earns $0. When you're given a graph of a linear function that intersects the y-intercept at (0, 0), you can either stop or verify your answer by plugging in the slope and solving for b and using either one of the points for x and y like (10, 171):[tex]171=17.1(10)+b\\171=171=b\\0=b[/tex]
Thus, the equation modeling Dianelys earnings per hour is y = 17.1x
Jordan's equation:
We can let (10, 277) represent our x1 and y1 point and let (20, 554) represent our x2 and y2 point:
[tex]m=\frac{554-277}{20-10}\\ m=\frac{277}{10}\\ m=27.7[/tex]
Like Dianelys equation, we can assume that Jordan's line intersects the y-axis at (0, 0) especially since we're not told something to indicate a b value other than 1 (e.g., "Jordan and Dianelys earn a bonus in addition to their regular wages"):. However, it's important to check by plugging in 27.7 for m and using the point (10, 277) for x and y:[tex]277=27.7(10)+b\\277=277+b\\0=b[/tex]
Thus, the equation modeling Jordan's earnings per hour is y = 27.7x
Finally, we can subtract Dianelys' slope from Jordan's to find how much Jordan earns per hour than Dianelys:
27.7 - 17.1 = 10.6
i need just the answer please!
Answers
Answer:
Step-by-step explanation:
According to Triangle Property: Angle A + Anlge B + Angle C = 180°
Solution:
1. ∠A = 119° ( ∵ ∠A > 90°. It is an Obtuse Angle )
2. ∠B = 38° ( ∵ ∠B < 90°. It is an Acute Angle )
3. ∠C = 23° ( ∵ ∠C < 90° . It is an Acute Angle
∴ The triangle is an Obtuse Triangle as it consists of an Obtuse
Angle.
What is the volume, in cubic in, of a cylinder with a height of Sin and a base radius of
2in, to the nearest tenths place?
Answers
This can be rounded to the nearest tenths place, giving us a final answer of V = 4πSin in³, rounded to the nearest tenths place.
What is area?Area is the size of a two-dimensional surface or shape. It is usually measured in square units such as square feet, square meters, or acres. Area can be used in a variety of ways, such as for measuring the size of a garden or calculating the amount of paint needed for a wall. Area can also be used to measure the area of a circle, triangle, or other shapes. Area is an important concept in mathematics, as it is used in a variety of formulas and equations.
The volume of a cylinder is calculated by multiplying the base area with the height. The base area is calculated by multiplying pi (π) with the square of the radius. Therefore, the volume of a cylinder with a height of h and a base radius of r is calculated by the formula V = πr2h. In this case, the height is h = Sin and the base radius is r = 2in. Applying these values to the formula, we get V = π(2in)2(Sin) = 4πSin in². This can be rounded to the nearest tenths place, giving us a final answer of V = 4πSin in3, rounded to the nearest tenths place.
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Please help me, and show all work
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The x-intercepts of the graph of the function are (-2, 0), (5, 0)
The midpoint of the x-intercept is 1.5.
The extremum of the function is a minimum and the value of x at which it occurs is k(1.5) = -61.25.
What is the x-intercept?In Mathematics, the x-intercept is the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).
In this exercise, we would use an online graphing calculator to plot the quadratic equation in order to determine the x-intercepts as shown in the graph attached below.
Therefore, the x-intercepts of the graph of the given quadratic equation k(x) = 5x² - 15x - 50 including the following:
x = (-2, 0).x = (5, 0).Since a line of symmetry must lie in the middle of the x-intercepts, the symmetry is given by;
x = (-2 + 5)/2
x = 3/2
x = 1.5
For the extremum, we have;
k(1.5) = 5(1.5)² - 15(1.5) - 50
k(1.5) = 11.25 - 22.5 - 50
k(1.5) = -61.25
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which triangle is ABC similar to and why?
Answers
The third one. They have the same angle measures (65, 65, 50)
Answer:
JEL
Step-by-step explanation:
ABC and JEL have the same angle measurements. The sum of the interior angles of a triangle add to 180
50 + 65 + 65 = 180
Helping in the name of Jesus.
Given: E is the midpoint of AB and CD
Prove: AAEC ABED
Statements
1. E is the midpoint of AB + CD
2. AEBE
3. CEDE
Reasons
1.
given
2. def. of midpoint
3. det. of midpoint.
4.
5.
4.
5. AAECABED
What should go in for reason #4 AND reason #5? (make sure you pick two answers)
# 4. Vertical Angles
#4. Definition of Congruent Angels
#4. Definition of Angle Bisector
#5. SSS
#5. SAS
#5. SSA
What should go in for reason #4 AND reason # 5? (make sure you pick two answers)
Select 2 correct answer(s)
Answers
5: SAS
Public health and safety officials have classified the Zika virus as a hazardous threat to pregnant women in Brazil. A study based in Rio found the virus to be more active near a body of water that was found to be polluted. A study of 20 water samples around areas that were heavily affected by the Zika virus found an average chemical waste of 126 g per mile with a standard deviation of 11.78 g. (a) What are the degrees of freedom for this study?(b) construct a 95onfidence interval (in g per mile) for the mean chemical waste of bodies of water for all areas where the zika virus was overly active. (round your answers to three decimal places.)____ ____ per mile
Answers
We need to determine the degrees of freedom and construct a 95% confidence interval for the mean chemical waste.
(a) Degrees of freedom: In this study, we have a sample size of 20 water samples (n = 20).
Degrees of freedom (df) for a sample is calculated as df = n - 1. In this case, df = 20 - 1 = 19.
(b) Construct a 95% confidence interval for the mean chemical waste:
First, we need to find the standard error (SE) of the mean, which is calculated as SE = standard deviation (SD) / sqrt(n).
In this case, SD = 11.78 g and n = 20, so SE = 11.78 / sqrt(20) = 2.634.
Next, we need to find the critical value (t*) for a 95% confidence interval with 19 degrees of freedom.
You can find this value using a t-table or calculator. For this case, t* ≈ 2.093. Now, we can calculate the margin of error (ME) using the formula ME = t* * SE.
In this case, ME = 2.093 * 2.634 = 5.513.
Finally, we can calculate the lower and upper bounds of the 95% confidence interval as follows:
Lower bound = mean - ME = 126 - 5.513 = 120.487 g/mile
Upper bound = mean + ME = 126 + 5.513 = 131.513 g/mile
So, the 95% confidence interval for the mean chemical waste in g per mile is (120.487, 131.513) per mile.
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Which measure of variation is the average distance between each data entry and the mean of the data set?
A. First quartile
B. Median
C. Range
D. Mean absolute value deviation
Answers
The measure of variation is the average distance between each data entry and the mean of the data set is mean absolute value deviation. Option D
What is mean absolute value deviation?The mean absolute deviation of a dataset is simply described as the average distance that exists between each given data point and the absolute mean.
This value gives us information about the variability in a dataset.
The steps in determining the value is;
Calculate the mean.Calculate how far away each data point is from the meanAdd those deviations together.Divide the sum by the number of data points.Read more about mean absolute deviation at: https://brainly.com/question/447169
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suppose you know σ and you want an 85onfidence level. what value would you use as z in formula (9–1)?
Answers
To find the value of z for an 85% confidence level when you know σ, you would use z = 1.44.
To find the z-value for an 85% confidence level, you need to determine the corresponding percentile in the standard normal distribution. The standard normal distribution is a bell-shaped curve where the mean is 0 and the standard deviation is 1.
To find the z-value, you need to find the area under the curve that corresponds to the middle 85% of the distribution. In this case, the area is split into two tails with 7.5% in each tail (100% - 85% = 15%, divided by 2).
You can use a standard normal table or calculator to find the z-value that corresponds to the 92.5th percentile (85% + 7.5%), which is approximately 1.44. This is the value you would use as z in formula (9-1) for an 85% confidence level.
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To obtain information on the corrosion-resistance properties of a certain type of steel conduit, 45 specimens were buried in soil for a 2-year period. The maximum penetration (in mils) for each specimen was measured, yielding a sample average of x =52.7, and a sample standard deviation of s=4.8. The conduits were manufactured with the specification that the true average penetration be less than 50 mils. The conduit will be used unless it can be demonstrated conclusively that the specification has not been met. What would you conclude? Clearly state your null and alternate hypotheses, your selected level of significance, and you conclusion.
Answers
We can conclude that the steel conduit does not meet the specified requirements for corrosion resistance.
Null hypothesis: The true average penetration of the steel conduit is less than or equal to 50 mils.
Alternative hypothesis: The true average penetration of the steel conduit is greater than 50 mils.
We will use a one-tailed t-test with a significance level of 0.05 to determine whether we can reject the null hypothesis.
The t-statistic can be calculated as:
t = (x - μ) / (s / √n)
where x is the sample mean (52.7), μ is the hypothesized true population mean (50), s is the sample standard deviation (4.8), and n is the sample size (45).
Plugging in the values, we get:
t = (52.7 - 50) / (4.8 / √45) = 4.09
Using a t-table with 44 degrees of freedom (df = n - 1), we find that the critical value for a one-tailed test at a significance level of 0.05 is 1.68.
Since our calculated t-value (4.09) is greater than the critical value (1.68), we can reject the null hypothesis and conclude that the true average penetration of the steel conduit is greater than 50 mils.
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the determinant of the matrix whose columns are vectors which define the sides of a parallelogram opposite one another is equal to the area of the parallelogram.
Answers
The area of the parallelogram is equal to the absolute value of the determinant of the matrix .
Explanation:
To demonstrate that the determinant of the matrix whose columns are vectors defining the sides of a parallelogram is equal to the area of the parallelogram, we can follow these steps:
1. Let's consider two vectors that define the sides of a parallelogram, A and B, opposite to each other.
2. Form a matrix M with the components of the vectors A and B as columns:
[tex]M=det \left[\begin{array}{ccc}A_{x} &B_{x} \\A_{y} &B_{y} \end{array}\right][/tex]
3. Calculate the determinant of matrix M:
[tex]det(M) = (A_{x} *B_{y} ) - (B_{x} *A_{y} )[/tex]
4. The area of a parallelogram can be found using the cross product of its side vectors:
Area = ||A x B||
5. The cross product of A and B is a vector with components:
A x B = (0, 0, A_x * B_y - A_y * B_x)
6. The magnitude of the cross-product is the area of the parallelogram:
Area = ||A x B|| = [tex]\sqrt{ (A_{x} *B_{y} ) - (B_{x} *A_{y} )^{2} }[/tex] = [tex](A_{x} *B_{y} ) - (B_{x} *A_{y} )[/tex]
Now, we can see that the area of the parallelogram is equal to the absolute value of the determinant of the matrix M:
Area = |det(M)|
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