a) When P is less than 5000, the population is increasing. When P is greater than 5000, the population is decreasing.
b) If the initial population is 5500, the limiting population is 5000.
c) If the initial population is 5500, the limiting population is 5000, and the equilibrium solutions are P = 0 and P = 5000.
(a) To determine when the population is increasing or decreasing, we can look at the sign of the derivative dP/dt. Using the given differential equation, we can write:
dP/dt = 1.2P (1 - P/5000)
The expression 1.2P is always positive, so the sign of dP/dt is determined by the factor (1 - P/5000). When P is less than 5000, (1 - P/5000) is positive, and the population is increasing. When P is greater than 5000, (1 - P/5000) is negative, and the population is decreasing.
(b) If the initial population is 5500, we can find the limiting population by solving for the equilibrium solution. The equilibrium solution is obtained by setting dP/dt = 0:
1.2P (1 - P/5000) = 0
This equation has two solutions: P = 0 and P = 5000. However, since the initial population is 5500, the population cannot reach 0. Therefore, the limiting population is 5000.
(c) The equilibrium solutions are the values of P where dP/dt = 0. We found these solutions in part (b): P = 0 and P = 5000. When P = 0, the population is extinct, and when P = 5000, the population is at its carrying capacity. These are the only two stable equilibrium solutions for this differential equation.
In conclusion, the given differential equation models a population that increases when P is less than 5000 and decreases when P is greater than 5000.
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A) Without eliminating the parameter, find dydx and d2ydx2 for the parametric equations x=√t,y=3t−7 at the point where t=4.B) Check your answers from part A) by eliminating the parameter.
A) Without eliminating the parameter of parametric equations x = √t, y = 3t−7:
dy/dx = 6√t and d²y/dx² = 0
B) By eliminating the parameter:
dy/dx = 6x and d²y/dx² = 6
Consider parametric equations x = √t, y = 3t−7
We find the derivative if above parametric equations with respect to t.
dx/dt = 1/2√t
and dy/dt = 3
Again find the derivative above equations with respect to t.
so, d²x/dt² = (1/2)(1/2t√t)
= 1/4t√t
and d²y/dt² = 0
So, dy/dx would be,
dy/dx
= (dy/dt)/(dx/dt)
= (3)/(1/2√t)
= 3(2√t)
= 6√t
And the value of d²y/dx² would be,
d²y/dx²
= (d²y/dt²) / (d²x/dt² )
= 0 / (1/4t√t)
= 0
B)
Here, x = √t, y = 3t−7
so, t = x²
⇒ y = 3x² - 7
Now differentiate above function with respect to x
dy/dx = 6x
And d²y/dx² = 6
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Federick chopin-nocturne Op. 9 revloutionary etude which peice conveys chopins passionate side?
A. Nocture Op. 9 No. 2
B. Revolutionary Etude
Federick chopin-nocturne Op. 9 revloutionary etude which peice conveys chopins passionate side, Nocturne Op. 9 No. 2 conveys Chopin's passionate side is the correct answer, so option B is correct.
The Nocturne Op. 9 No. 2 is generally considered to be the piece that conveys Chopin's passionate and emotional side, as it is a beautiful and expressive melody with a romantic character. The Revolutionary Etude, on the other hand, is known for its fiery and intense nature, as it was written to reflect Chopin's feelings about the political situation in his native Poland.
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Put the following equation of a line into slope-intercept form, simplifying all
fractions.
4x + y = 7
The equation of this line in slope-intercept form is equal to y = -4x + 7.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope or rate of change.x and y are the points.c represents the y-intercept or initial value.By making the variable "y" the subject of formula, we have the following:
4x + y = 7
y = -4x + 7
Therefore, the slope (m) is equal to -4.
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If f(x) = x3 – 4x^2 + 10, determine the concavity when x=1. Hint: First find the second derivative f(x) is neither concave up nor down when x=1 f(x) is concave up when x=1 f(x) is concave down when x=1
When x=1, the second derivative of f(x) is 6, indicating that f(x) is concave up.
To determine the concavity of a function at a given point, we need to look at the sign of the second derivative. The second derivative of [tex]f(x)=x^3-4x^2+10 is f''(x)=6x-8. When x=1, f''(1)=6(1)-8=-2.[/tex]
Since f''(1) is negative, this indicates that f(x) is concave down when x=1. This means that the graph of the function at x=1 has a downward curvature,
where the tangent line will lie below the curve. Intuitively, this means that the rate of change of slope is decreasing as we move towards the point x=1. In contrast, if f''(1) were positive,
it would indicate that f(x) is concave up at x=1, meaning that the graph would have an upward curvature and the tangent line would lie above the curve.
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Find dy/by implicit differentiation, given that x^2y– 7y7 =-5. Your answer could involve both I and y. Enclose numerators and denominators in parentheses. For example, (a - b)/(1+n). dy/dx = _____
To find dy/dx by implicit differentiation, we need to use the chain rule and product rule. Let's first differentiate both sides of the given equation with respect to x.
d/dx ([x^{2}[/y – 7y^7) = d/dx (-5)
Applying the product rule, we get:
(2xy + x^2(dy/dx)) - 7(7y^6)(dy/dx) = 0
Simplifying and rearranging, we get:
dy/dx = (-2xy)/(x^2 - 49y^6)
Therefore, dy/dx involves both x and y. To enclose numerators and denominators in parentheses, we can write the final answer as:
dy/dx = (-2xy)/((x^2) - (49y^6))
In simpler terms, the rate of change of y with respect to x is equal to -2xy divided by the difference between x squared and 49y to the power of 6.
Implicit differentiation is a useful tool when we cannot directly isolate y in terms of x in an equation. By using differentiation rules, we can still find the rate of change of y with respect to x. In this case, we have found the derivative of y with respect to x in terms of x and y, given an implicit equation.
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Can someone give some help on this please
1. The volume of the cylinder is 11309.73 in³
2. The volume of the cylinder is 74.22 m³
3. The maximum amount of water the water cooler will hold is 2787.38 in³
Calculating the volume of cylindersFrom the question, we are to determine the volume of each cylinder.
The volume of a cylinder is given by the formula,
V = πr²h
Where V is the volume of the cylinder
r is the radius of the cylinder
h is the height of the cylinder
1.
r = 20 in
h = 9 in
Volume = π × 20² × 9
Volume = 11309.73 in³
2.
Diameter, d = 3 m
Thus,
r = 1.5 m
h = 10.5 m
Volume = π × 1.5² × 10.5
Volume = 74.22 m³
3. To determine the maximum amount of water the cooler will hold, we will calculate the volume
Diameter, d = 13 in
Thus,
r = 6.5 in
h = 21 in
Volume = π × 6.5² × 21
Volume = 2787.38 in³
Hence, the maximum amount of water it will hold is 2787.38 in³
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A random sample of 107 observations produced a sample mean of 33. Find the critical and observed values of for the following test of hypothesis using a = 0.02. The population standard deviation is known to be S and the population distribution is normal. He: = 28 versus H: > 28. Round your answers to two decimal places
The observed value (z-score) is greater than the critical value (2.05), we would reject the null hypothesis (H₀) and conclude that there is sufficient evidence to support the alternative hypothesis (H₁) that μ > 28.
To find the critical value of t, we need to use the t-distribution with degrees of freedom (df) = n - 1 = 106 and alpha (α) = 0.02.
Using a t-table or calculator, the critical value of t for a one-tailed test with df = 106 and α = 0.02 is 2.366.
To find the observed value of t, we can use the formula:
t = (x - μ) / (S / √n)
where x = 33, μ = 28, S is the population standard deviation (not given), and n = 107.
Without knowing the population standard deviation, we cannot calculate the observed value of t.
To find the critical and observed values for the given hypothesis test, we will first need to use the provided information.
Given:
Sample size (n) = 107
Sample mean (x) = 33
Population mean (μ) = 28
Population standard deviation (σ) = S
Significance level (α) = 0.02
H₀: μ = 28
H₁: μ > 28
First, let's find the observed value (z-score):
z = (x - μ) / (σ / √n)
Now, we will find the critical value. Since this is a one-tailed test with α = 0.02, we need to find the z-score corresponding to the 0.98 quantile (1 - α) in the standard normal distribution.
Using a z-table or calculator, we find the critical value:
z(0.98) ≈ 2.05
So, the critical value is 2.05, and the observed value is calculated using the formula provided. Note that without knowing the population standard deviation (S), the observed value cannot be calculated.
If the observed value (z-score) is greater than the critical value (2.05), we would reject the null hypothesis (H₀) and conclude that there is sufficient evidence to support the alternative hypothesis (H₁) that μ > 28.
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Based on past musical productions, a theater predicts selling 400 - 8p tickets when each ticket is sold at p dollars.
We know this because the formula given in the problem statement predicts the number of tickets selling based on the ticket price, and the theater will only earn revenue when it sells more than 400 tickets.
a. It includes ticket price (dollars), number of tickets sold, revenue (dollars)
see image for table.
To complete the table, we start with the maximum expected number of tickets sold at a given price and subtract the expected decrease in ticket sales for every $1 increase in ticket price, until we reach the minimum expected number of tickets sold at a given price.
For example, at a ticket price of $5, the theater expects to sell 400-8(5) = 360 tickets. For every $1 increase in ticket price, the theater expects to sell 8 fewer tickets. Therefore, at a ticket price of $10, the theater expects to sell 400-8(10) = 320 tickets. Continuing in this manner, we can fill out the table as shown above.
b. The theater will earn no revenue when the ticket price is $50, because the expected number of tickets sold at that price is 50, which is less than the break-even point of 400 tickets.
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express the number as a ratio of integers. 0.1 = 0.1111
It can be expressed as a ratio of integers as 1111:10000
How to express the given number as a ratio?Hi! I'd be happy to help you express the given number as a ratio of integers. To express the number 0.1111 as a ratio of integers, follow these steps:
Step 1: Count the decimal places in the number.
In 0.1111, there are four decimal places.
Step 2: Remove the decimal point and write the number as a fraction.
To remove the decimal point, write 1111 over a denominator that has the same number of zeros as there are decimal places in the original number. In this case, that's four zeros, so the denominator is 10,000.
So, the fraction is 1111/10000.
Therefore, the number 0.1111 can be expressed as a ratio of integers as 1111:10000.
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c. using systematic random sampling, every fifth dealer is selected starting with the third dealer in the list. which dealers are included in the sample?
The dealers included in the sample are dealers 3, 8, 13, 18, 23, 28, 33, 38, 43, 48, 53, 58, 63, 68, 73, 78, 83, 88, 93, and 98.
How to find dealers that included in the sample?To use systematic random sampling, we need to choose a starting point and a sampling interval. In this case, we are starting with the third dealer in the list, so we need to skip the first two dealers.
Let's assume that the dealers are numbered 1 to 100 in the list. Since we are starting with the third dealer, our starting point is dealer 3. We also need to choose a sampling interval of 5, since we want to select every fifth dealer.
To find out which dealers are included in the sample, we can use the following formula:
Sampled Dealers = Starting Point + (Sampling Interval * Number of Samples)
Using the formula, we can calculate the dealers that are included in the sample as follows:
Sampled Dealers = 3 + (5 * n)
where n is the number of samples.
If we want to select a sample of 20 dealers, we can substitute n = 1 to 20 into the formula to get the following list of dealers:
3, 8, 13, 18, 23, 28, 33, 38, 43, 48, 53, 58, 63, 68, 73, 78, 83, 88, 93, 98
Therefore, the dealers included in the sample are dealers 3, 8, 13, 18, 23, 28, 33, 38, 43, 48, 53, 58, 63, 68, 73, 78, 83, 88, 93, and 98.
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determine the value k such that there are an infinite number of solutions to the system of linear equations. 521x - 17y = 13 kx + 5y = -353
If k = -2605/17, the two equations will be linearly dependent and have an infinite number of solutions.
To have an infinite number of solutions to the system of linear equations, the two equations must be linearly dependent, which means that one of the equations can be obtained by multiplying the other equation by a constant and adding or subtracting the result.
We can check if this is the case by dividing the coefficients of one of the variables in the first equation by the coefficients of the same variable in the second equation:
521/ k = -17/5
Solving for k, we get:
k = -2605/17
If k is any other value, the equations will be linearly independent and have either one unique solution or no solutions.
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X=______ CM PIz HeIp
Answer:
x=18
Step-by-step explanation:
11×11= 121
10×10=100
so, 5x+10=100
5x=90
x=18
saw a 1 star review so I decided to add my own answer
Answer:
20
Step-by-step explanation:
The top triangle has lengths 11, 10, and p ( unknown p ). We can form a larger triangle by including the bottom half. This now becomes a triangle with sides 132 and 5x + 20. Following ratios 11:10 must be equal to 132:5x+20. 132 = 11 * 12
By the ratio 5x+20 = 10 * 12
Or 5x + 20 = 120 or 5x = 100 or x = 20
find the average value of f(x,y)=4x^2 + y^2 over the rectangle rr with vertices (0,−2),(2,−2),(0,1),(0,−2),(2,−2),(0,1), and (2,1)
The average value of f(x, y) = 4x² + y² over the rectangle with vertices (0, -2), (2, -2), (0, 1), and (2, 1) is 17/3.
To find the average value of the function over the given rectangle, follow these steps:
1. Determine the area of the rectangle: A = (2 - 0) * (1 - (-2)) = 2 * 3 = 6.
2. Set up the double integral for the average value: (1/A) * ∬[f(x, y) dA], where dA = dx dy.
3. Integrate f(x, y) = 4x² + y² over the rectangle limits, x = 0 to 2 and y = -2 to 1: ∬[4x² + y² dx dy].
4. Perform the integration with respect to x and then y.
5. Multiply the result by (1/A), which is (1/6) in this case.
Following these steps, the average value of the function over the given rectangle is found to be 17/3.
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If a 5x8 matrix A has rank 5, find dim Nul A, dim Row A, and rank A^T. dim Nul A= ____ dim Row A= ____ rank A^T= ____
We find the following values:
dim(Nul A) = 3dim(Row A) = 5rank([tex]A^T[/tex]) = 5How to find the values of dim Nul A, Dim row A and Rank [tex]A^T[/tex]?Given that matrix A is a 5x8 matrix and has rank 5, we can use the rank-nullity theorem to find the dimensions of the null space and row space:
rank(A) + dim(Nul A) = number of columns of A
Since rank(A) = 5 and number of columns of A = 8, we have:
5 + dim(Nul A) = 8
Therefore, dim(Nul A) = 8 - 5 = 3.
This means that the null space of A is a subspace of [tex]R^8[/tex] with dimension 3.
To find the dimension of the row space, we use the fact that the row space and column space of a matrix have the same dimension:
dim(Row A) = dim(Col A)
Since the column space of A is a subspace of [tex]R^5[/tex]with dimension 5 (since rank(A) = 5), we have:
dim(Row A) = dim(Col A) = 5.
Therefore, the row space of A is a subspace of [tex]R^8[/tex] with dimension 5.
Finally, we can use the fact that the rank of a matrix is equal to the rank of its transpose to find the rank of [tex]A^T[/tex]:
rank(A) = rank([tex]A^T[/tex])
Since we know that rank(A) = 5, we have:
rank([tex]A^T[/tex]) = 5.
Therefore, the rank of [tex]A^T[/tex] is 5.
In summary:
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Helicopter Number Labor Hours
1 2000
2 1450
3 1238
4 1143
5 1073
6 1029
7 989
8 951
Determine the best curvilinear trendline that maximizes R2.
The best trendline is power with an R^2 value of( ) , The Equation is y=( )*^( )
Best curvilinear trendline for given data is a power trendline with an R² value of (insert calculated R² value here). The equation of trendline is y = (insert estimated value for a here) *[tex]x^(insert estimated value for b here).[/tex] This equation allows us to estimate labor hours for various helicopter number.
To find the best power trendline, we can use statistical techniques such as regression analysis to estimate the parameters that yield the highest R² value. R², also known as the coefficient of determination, measures the proportion of the total variation in the dependent variable that can be explained by the model. A higher R² value indicates a better fit of the trendline to the data.
The given power trendline equation is [tex]: y = a * x^b[/tex]. Here, 'y' represents the labor hours, 'x' denotes the helicopter number, and 'a' and 'b' are the constants to be determined. Once these constants are estimated, the resulting equation can be used to predict labor hours for different helicopter numbers with reasonable accuracy.
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Which represents the solution to x³ = 512?
3
x = √512
x=512³
x=512²
x = √512
Step-by-step explanation:
x^3 = 512 take cube root of both sides of the equation:
x = [tex]\sqrt[3]{512}[/tex] = 8
Answer:
8
Step-by-step explanation:
The researcher must decide on the level of significance after setting up the null hypothesis and alternate hypothesis, but before formulating a decision rule and collecting sample data. True or False
The statement, "Researcher must decide on "level-of-Significance" after setting up "null-hypothesis" and "alternate-hypothesis", but before formulating a "decision-rule" and collecting sample data" is True because it finds the critical value, which is then used to decide whether to reject or fail to reject "Null Hypothesis".
The "level-of-significance" is defined as a predetermined probability threshold which is used in hypothesis testing to determine if the results of a statistical test are statistically significant or not.
The level of significance is generally decided upon before conducting the hypothesis test. It denotes probability of rejecting the "null-hypothesis" when it is true.
The researcher generally sets this level before collecting any data and it is used to determine the critical value for the test statistic, which is used to decide whether to reject or "fail-to-reject" the null hypothesis.
The level of significance is generally set at 0.05 or 0.01 but can vary depending on the research question and the level of risk the researcher is willing to accept in making a Type I error which is rejecting the null hypothesis when it is true.
Therefore, the statement is True.
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Find the equation of the line shown.
I
У.
#&+
4
3
21
of du & u
4
2
3
-5
2 3 4 5
X
to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{1}-\stackrel{y1}{3}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{(-4)}}} \implies \cfrac{-2}{4 +4} \implies \cfrac{ -2 }{ 8 } \implies - \cfrac{ 1 }{ 4 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{- \cfrac{ 1 }{ 4 }}(x-\stackrel{x_1}{(-4)}) \implies y -3 = - \cfrac{ 1 }{ 4 } ( x +4) \\\\\\ y-3=- \cfrac{ 1 }{ 4 }x-1\implies {\Large \begin{array}{llll} y=- \cfrac{ 1 }{ 4 }x+2 \end{array}}[/tex]
Select whether the equation has a solution or not
roots
no roots
Answer:
The equation has no solution. It has no roots. Therefore the second option no roots is correct.
Step-by-step explanation:
Suppose there is a real number y that satisfies the equation.
Squaring both sides, we get:
2y-5 = 2y+6
Subtracting 2y from both the sides, we get:
-5=6
-5 can't be equal to 6, this is a contradiction.
Therefore, there is no real number y that satisfies the equation. Hence there are no roots for this equation.
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Find the area of the figure.
the answer is 154 mm²
we basically have to do the area for the first tri then the rectangle then the other tri and add them
Answer:
154
Step-by-step explanation:
I can't give the solution process, I just figure it out in my mind.
Given cot A = 9/4 and that angle A is in Quadrant III, find the exact value of sin A in simplest radical form using a rational denominator.
Step-by-step explanation:
In Q III both sin and cos are negative values
cot A = cos A / sin A = 9/4
Hypotenuse = sqrt ( 9^2 + 4^2) = sqrt 97
then cos A = - 9 / sqrt ( 97 )
and sin A = - 4 / sqrt 97 = - 4 sqrt (97) / 97
given that z is a standard normal variable, p(z > 1.61) is (rounding to two decimal places):
The probability that a standard normal variable z is greater than 1.61 is 0.0549.
This is derived from the standard normal table which gives the area under the normal curve between -∞ and the given value.
This area is equal to the probability of the variable falling between -∞ and the given value. For a standard normal variable, the area between -∞ and 1.61 is 0.9451, which is the probability of the variable falling between -∞ and 1.61.
The area between 1.61 and ∞ is 0.0549, which is the probability of the variable falling between 1.61 and ∞.
Therefore, the probability of z being greater than 1.61 is 0.0549.
Complete Question:
Given that z is a standard normal variable, what is the probability that z is greater than 1.61?
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we have a jar of coins, all dimes and nickels. all together, we have 250 coins, and the total value of all coins in the jar is $ 18.4. how many dimes are there in the jar?
Answer: there are 118 dimes in the jar.
Step-by-step explanation: Let's use a system of equations to solve the problem:
Let d be the number of dimes and n be the number of nickels.
We know that:
d + n = 250 (Equation 1) (The total number of coins is 250)
0.1d + 0.05n = 18.4 (Equation 2) (The total value of all coins is $18.4)
To solve for d, we need to eliminate n from the equations above. We can do this by multiplying Equation 1 by -0.05 and adding it to Equation 2:
-0.05d - 0.05n = -12.5
0.1d + 0.05n = 18.4
0.05d = 5.9
Dividing both sides by 0.05, we get:
d = 118
Therefore, there are 118 dimes in the jar.
Pre-Calclus! 95 Points! + [tex]Brainliest[/tex]
[tex]Question:[/tex]
Sam got an assignment in which questions on real numbers are given. He got some confusion between prime numbers and composite numbers. He is stuck in one question, please help him and make him understand this concept. Consider the numbers 1×29×107×2679+47 and 1×71. Help him to identify which of these two is composite number and which one is prime number. Also, find these numbers after multiplication.
[tex]Options[/tex] ↓↓
( In picture )
Expectations:
Correct
Explanation
Must not:
Incorrect
No explanation
Spam
( none of above = reported )
Answer: here is what I've got 8,312,984
I thank it is B.
Step-by-step explanation:
Given the following numbers 1×29×107×2679+47 and 1×71.
We are asked to determine which number is composite and which is prime.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
What is a composite number? A composite number is a number with more than two factors (ex: 10=>1,2,5,10).
What is a prime number? A prime number is a number with only two factors, the number "1" and itself (ex: 7=> 1,7).
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Right away we can recognize 1×71 will not be a composite number. No nice factors go into it rather than the number "1" and "71," so this is a prime number.
This leaves 1×29×107×2679+47 to be our composite number. I would simply just use a calculator to expand this number.
=> 1×29×107×2679+47= 8,312,984
Thus, the second option is correct.
If Tamara works 4x+7 total hours at her three jobs, where x represents how many
hours she worked at her first job, find the total hours she worked at her three jobs
assuming she works 12.5 hours per week at her first job.
Answer:
57 hours
Step-by-step explanation:
substitute the value 12.5 as x and solve
4(12.5)+7
50+7
57
so she works 57 hours
from a srs of 125 americans, 45 regularly use two or more pairs of eyeglasses. give a 95onfidence interval for the proportion of all americans who regularly use two or more pairs of eyeglasses.
With 95% confidence that the true proportion of all Americans who regularly use two or more pairs of eyeglasses is between 0.247 and 0.473.
To calculate the confidence interval, we need to determine the level of confidence we want to use. In this case, we are asked to provide a 95% confidence interval. This means that if we were to repeat this study many times, we would expect 95% of the confidence intervals calculated to contain the true proportion of Americans who regularly use two or more pairs of eyeglasses.
Next, we need to use a confidence level of 95% to find the critical value, which corresponds to the number of standard errors that we need to add and subtract from the sample proportion to obtain the interval. The critical value can be found using a standard normal distribution table or calculator, and for a 95% confidence level, it is 1.96.
Finally, we can use the formula for the confidence interval:
CI = p ± z x SE
where p is the sample proportion, z is the critical value, and SE is the standard error.
Plugging in the numbers, we get:
CI = 0.36 ± 1.96 x 0.057 = (0.247, 0.473)
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At a coffee shop, 80% of customers order coffee. Only 15% of customers order
coffee and a bagel. What is the probability that a customer who orders coffee also
orders a bagel?
The probability that a customer who orders coffee will also order a bagel would be = 3/20
How to calculate the probability of the given event?To calculate the probability, the formula that should be used would be as follows;
Probability = possible outcome/Sample space
The possible outcome = 15%
The sample space = 100%
Therefore the probability that a customer who orders coffee will also order a bagel would be;
= 15/100 = 3/20
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how many outcomes are possible if we know that amy finished ahead of bob and bob finished ahead of charlie?
There are only three possible outcomes that satisfy the condition that Amy finished ahead of Bob and Bob finished ahead of Charlie: Amy, Bob, Charlie or Amy, Charlie, Bob, and Bob, Amy, Charlie.
In a competition involving only three people, there are six possible ways they can finish: ABC, ACB, BAC, BCA, CAB, and CBA. However, in this particular scenario, we know that Amy finished ahead of Bob and Bob finished ahead of Charlie. This means that Amy cannot finish last and Charlie cannot finish first, since Bob is in the middle.
If Amy finished first, then there are only two possibilities for the order of finish: Amy, Bob, Charlie or Amy, Charlie, Bob.
If Bob finished first, then there is only one possibility for the order of finish: Bob, Amy, Charlie.
If Charlie finished first, then there are no possibilities that satisfy the condition that Amy finished ahead of Bob and Bob finished ahead of Charlie.
Therefore, there are only three possible outcomes that satisfy the condition that Amy finished ahead of Bob and Bob finished ahead of Charlie: Amy, Bob, Charlie or Amy, Charlie, Bob, and Bob, Amy, Charlie.
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Which of the following sets of ordered pairs represents a function?
{(−6, −5), (−4, −3), (−2, 0), (−2, 2), (0, 4)}
{(−5, −5), (−5, −4), (−5, −3), (−5, −2), (−5, 0)}
{(−4, −5), (−3, 0), (−2, −4), (0, −3), (2, −2}
{(−6, −3), (−6, −2), (−5, −3), (−3, −3), (0, 0)}
Answer:
The third set
Step-by-step explanation:
What is a function?A function, in simple terms, is a relationship between a set of inputs having one output each.
This means that a function is a relationship where there is a set of inputs that have one corresponding output, so if an input has multiple outputs its not a function. (this means the x value CANNOT repeat)
Which set of ordered pairs represents a function?If we look at each set of ordered pairs, the only set that doesn't have an x value that doesn't repeat is the third set.
In the first set, an x value of -2 has multiple outputs, making it not a function. (−2, 0), (−2, 2),
In the second set, the x value -5 has multiple outputs, making it not a function. (−5, −5), (−5, −4)
In the third set, each x value has its own corresponding output. This is the only function
In the last set, the x value -6 has multiple outputs, making it not a function. (−6, −3), (−6, −2)
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Please help me pick which ones they are. Thank you!
The correct answer for the transformation will be:
translation up π/4
vertical stretch by 2
translation right π/4
How to explain the informationThe parent function of g(x) is y = sin(x), and g(x) is obtained from the parent function by performing the following transformations:
Translation: The argument of sin(x) is shifted by π/4 units to the left, which results in a horizontal translation to the right by π/4 units.
Vertical stretch: The amplitude of the sine function is multiplied by 2, which results in a vertical stretch by a factor of 2.
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