A student win a rectangular-shaped
poster with a picture of a partially
eaten pizza, shaded in gray, and a
slogan. Approximately what is the area
of the shaded portion of the poster?
Answers
The approximate area of the shaded portion of the poster is option D: 380.76 square inches.
What is area?
An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.
Assuming that the shaded portion of the poster is the area outside the 57 degree angle and inside the circle with radius 12 inches, we can start by finding the area of the whole circle and then subtracting the area of the 57 degree sector.
The area of a circle with radius 12 inches is given by -
A = πr²
Substituting the value of radius, we get -
A = π(12)²
A ≈ 144π square inches
The area of a sector with central angle θ (in radians) and radius r is given by -
A = (θ/2π)πr²
We know that the central angle of the shaded sector is 360 - 57 = 303 degrees, or 5.28 radians (since 180 degrees = π radians).
Substituting the values we get -
A = (5.29/2π)π(12)²
A = 5.29/2π × 144π
A = 2.645 × 144
A ≈ 380.88 square inches
Therefore, the area value is 380.88 square inches.
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Related Questions
Find a · b.
a = 2i + j, b = i – j + k
Answers
To solve the given problem, we need to find the value of the cross product of two vectors a and b.
So, the given vectors are,
a = 2i + j and b = i - j + k.
The cross product of two vectors is given as:
A × B = |A| |B| sinθ n
Here,
A = 2i + j
B = i - j + k
θ = angle between the vectors
A × B = |A| |B| sinθ n = [(2i + j) × (i - j + k)]
The above expression can be expanded using the distributive property of cross product:
(2i + j) × i - (2i + j) × j + (2i + j) × k = 2(i × i) + j × i - 2(i × j) - j × j + 2(i × k) + j × k
= 0 + 2k - 2k - 0 + 2j - i
= -i + 2j + 2k
So, a × b = -i + 2j + 2k. Therefore, the value of a · b is not possible as they are vectors and the cross product of two vectors is a vector.
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A group of friends were working on a student film that had a budget of $1400. They used 23% of their budget on equipment. How much money did they spend on equipment? This depends on my grade i rlly need this
Answers
Answer:
Amount spent on equipment = 23% of $1400
= 0.23 x $1400
= $322
Joe wants to earn at least $73 trimming trees. He charges $7 an hour and pays $4 in equtment fees. What are the possible number of hours that joe could trim trees?
Use t for the number of hours.
Write your answer as an inequality solved for t
Answers
7t - 4 ≤ 73
Where t is the number of hours.
Now,
7t - 4 ≤ 73
7t ≤ 73 + 4
7t ≤ 77
t ≤ 11
Thus,
The number of hours is 11.
Classify the angle pair then find the value of x (3x+11) ( 8x+12)
Answers
Using vertically opposite angle rule we can classify that (3x+11) = (8x+12) and the value of x isa -1/5
What dοes a math angle mean?An angle is created by cοmbining a grοup οf rays (half-lines) that have a cοmmοn terminal. The angle's vertex is the latter, and the rays are variοusly referred tο as the angle's legs and, mοre frequently, as its arms.
Hοw can I find angles the simplest manner pοssible?The simplest apprοach fοr calculating an angle is tο use a prοtractοr. But, if a prοtractοr is nοt available, yοu can still calculate an angle's measurement by using the basic trigοnοmetric rules. A scientific cοmputer is needed fοr the equatiοns.
We have the angle pairs (3x+11) ( 8x+12)
Using vertically opposite angle rule we can classify that (3x+11) = (8x+12)
Now, solving for x
(3x+11) = (8x+12)
8x - 3x = 11 - 12
5x = -1
x = -1/5
Thus, the value of x isa -1/5
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Complete question is:
Classify the pair of angle and then find the value of x in
(3x+11)
(8x+12)
(1 point) find the set of solutions for the linear system −3x1 6x25x2−−5x38x3==9−10 use s1, s2, etc. for the free variables if necessary. (x1,x2,x3)=( , , )
Answers
(x1,x2,x3) = (-7, -2, 0).
To find the set of solutions for the given linear system, we will use the substitution method. First, let's rewrite the equations in a more readable format:
-3x1 + 6x2 = 9
5x2 - 5x3 = -10
8x3 = 0
Now, let's solve for one variable in terms of the others. In the third equation, we can easily solve for x3:
x3 = 0
Next, we can substitute this value into the second equation to solve for x2:
5x2 - 5(0) = -10
5x2 = -10
x2 = -2
Finally, we can substitute the values of x2 and x3 into the first equation to solve for x1:
-3x1 + 6(-2) = 9
-3x1 = 21
x1 = -7
So the solution to the linear system is (x1,x2,x3) = (-7, -2, 0). There are no free variables in this system, as all variables have been solved for.
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Mya is buying a purse online that regularly costs $72. How much will she pay i total if she has a promo code for 25% off plus free shipping and sales tax is 5.5%? Thanks :)
Answers
Answer: If Mya has a promo code for 25% off, she will pay:
$72 - (25% of $72) = $54
This means that the price of the purse will be reduced by $18.
Since she also gets free shipping, the total cost of the purse will be $54.
Now, to calculate the sales tax, we need to find 5.5% of $54:
5.5% of $54 = (5.5/100) x $54 = $2.97
Therefore, the total cost that Mya will pay for the purse, including the sales tax, will be:
$54 + $2.97 = $56.97
So Mya will pay $56.97 in total for the purse.
Step-by-step explanation:
Construct a 3x3 nonzero matrix A such that the vector [-1 1 -1] is a solution of Ax = 0.
A = ____
Answers
The vector [-1 1 -1] is indeed a solution of Ax = 0.
A 3x3 nonzero matrix A that satisfies the equation Ax = 0 and has the vector [-1 1 -1] as a solution can be constructed as follows:
A =
\begin{bmatrix}
-1 & 2 & 0\\
-1 & 0 & 2\\
2 & -1 & -1\\
\end{bmatrix}
To verify, plug the matrix A into the equation Ax = 0:
\begin{bmatrix}
-1 & 2 & 0\\
-1 & 0 & 2\\
2 & -1 & -1\\
\end{bmatrix}
\begin{bmatrix}
x_1\\
x_2\\
x_3\\
\end{bmatrix} =
\begin{bmatrix}
0\\
0\\
0\\
\end{bmatrix}
\begin{aligned}
-x_1 + 2x_2 &= 0\\
-x_1 + 2x_3 &= 0\\
2x_1 - x_2 - x_3 &= 0\\
\end{aligned}
From the equations, it can be seen that the vector [-1 1 -1] is indeed a solution of Ax = 0.
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The simple interest on an investment of $2100 over 15 months is $178.50.
If the annual interest rate is r, find r as a percentage correct to one decimal place.
Answers
Answer:
We can use the formula for simple interest:
I = Prt
where I is the interest, P is the principal (initial amount), r is the interest rate per year (as a decimal), and t is the time in years.
In this case, we are given:
P = $2100
t = 15/12 years (since the time is given in months)
I = $178.50
Substituting these values into the formula, we get:
178.5 = 2100r(15/12)
Simplifying, we get:
r = 178.5 / (2100 * 5/4) = 0.054 (rounded to three decimal places)
To express r as a percentage, we multiply by 100:
r = 5.4%
Therefore, the annual interest rate is 5.4%, correct to one decimal place.
Step-by-step explanation:
First- year high school students were randomly put into either traditional math classes or math classes taught with a new innovative approach. In a standard algebra test,230 traditionally taught students scored an average of 76.5 with a standard deviation of 7.4, while 185 students under the new approach averaged 78.8 with a standard deviation of 5.6. Is there sufficient evidence of a difference in the test results -whatis the test statistic for H0: µ1= µ2 and Ha: µ1≠ µ2?
(A) t = 76.5 - 78.8√ ((7.4)^2/230 + (5.6)^2/185)
(B) t = 2 x 76.5 - 78.8 √ ((7.4)^2/230 + (5.6)^2/185)
(C) t = 76.5 - 78.8 /((7.4)/√230 + (5.6)/√185)
(D) t = 2 x 76.5 - 78.8 /(6.5/√207.5)
(E) t = 76.5 - 78.8 /(6.5/√207.5)
Answers
The test statistic for H₀: µ₁ = µ₂ and
Hₐ: µ₁ ≠ µ₂ is t = 76.5 - 78.8√ ((7.4)²/230 + (5.6)²/185). So, the correct choice for answer is option (a).
The test statistic for a two-sample is calculated by taking the difference in the two sample means and dividing by either the pooled or unpooled estimated standard error. We have a sample of first- year high school students were randomly put into either traditional math classes or math. For first sample
Sample size, n₁ = 230
sample mean, M₁ = 76.5
Standard deviations, s₁ = 7.4
For other sample,
Sample size,n₂ = 185
Sample mean, M₂ = 78.8
Standard deviations, s₂ = 5.6
Let the population means for sample first and second be µ₁ and µ₂ respectively.
The Hypothesis testing for comparison of population meas of both samples. The null and alternative hypothesis are
H₀: µ₁ = µ₂ and
Hₐ: µ₁ ≠ µ₂
Pooled standard error = √(s₁²/n₁ + s₂²/
n₂)
= √((7.4)²/230 + (5.6)²/185)
Using the test statistic for a two-sample,
t = (( M₁ - M₂ ) -( µ₁ - µ₂))/√(s₁²/n₁ + s₂²/
n₂)
= ((76.5 - 78.8) - ( µ₁- µ₂))/√((7.4)²/230 + (5.6)²/185)
t = (76.5 - 78.8)√ ((7.4)²/230 + (5.6)²/185) ( since, µ₁- µ₂ = 0)
Hence required test statistic value is option(a). There is sufficient evidence to claim that the difference in the test results zero.
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Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis.y = x^3 x = 0 y = 27
Answers
the volume of the solid generated by revolving the plane region about the x-axis is 486π/5 cubic units.
To use the shell method to find the volume of the solid generated by revolving the plane region about the x-axis, we need to integrate the circumference of a cylindrical shell from x = 0 to x = 3 (where y = 27 corresponds to x^3 = 27, or x = 3).
Consider a cylindrical shell of thickness dx, with radius x and height y = [tex]x^3[/tex]. The circumference of the shell is 2πx, and its volume is given by the product of the circumference and the height of the shell, which is y =[tex]x^3[/tex]:
[tex]dV = 2πx * x^3 dx[/tex]
Integrating from x = 0 to x = 3, we have:
V = ∫[0,3] 2πx *[tex]x^3[/tex] dx
= 2π ∫[0,3] [tex]x^4[/tex] dx
= 2π [[tex]x^5/5[/tex]] [0,3]
= 2π * ([tex]3^5[/tex]/5)
= 2π * 243/5
= 486π/5
Therefore, the volume of the solid generated by revolving the plane region about the x-axis is 486π/5 cubic units.
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If the force remains constant with magnitude f1 while the object moves a distance d , the final speed of the object is v1 . what is the final speed v2 (in terms of v1 ) if the net force is f2=2f1 and the object moves the same distance d while the force is being applied?
Answers
The final speed v2 is √6 times the initial speed v1, when the net force is 2f1 and the object moves the same distance d while the force is being applied.
We can use the work-energy theorem to solve this problem, which states that the work done on an object by a net force is equal to the change in its kinetic energy.
When the force has magnitude f1 and the object moves a distance d, the work done is:
W = f1 * d
This work changes the kinetic energy of the object from zero to (1/2) * m * v1^2, where m is the mass of the object. Therefore, we have:
f1 * d = (1/2) * m * v1^2
Solving for v1, we get:
v1 = sqrt((2 * f1 * d) / m)
Now, when the net force has magnitude f2 = 2f1 and the object moves the same distance d, the work done is:
W = f2 * d = 2f1 * d
This work changes the kinetic energy of the object from (1/2) * m * v1^2 to (1/2) * m * v2^2, where v2 is the final speed of the object. Therefore, we have:
2f1 * d = (1/2) * m * (v2^2 - v1^2)
Solving for v2, we get:
v2 = sqrt(v1^2 + (4 * f1 * d) / m)
Substituting the expression for v1, we get:
v2 = sqrt((4 * f1 * d) / m + (2 * f1 * d) / m)
Simplifying, we get:
v2 = sqrt(6) * v1
Therefore, the final speed v2 is sqrt(6) times the initial speed v1.
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you wish to estimate the size of a population of rabbits living in a large urban park. what is the best method to use?
Answers
To estimate the size of a population of rabbits living in a large urban park, the best method to use is the mark and recapture method.
The mark and recapture method is a technique used to estimate the size of a population by capturing, marking, and releasing a sample of individuals and then recapturing a second sample later.
This method is based on the assumption that the proportion of marked individuals in the second sample will be equal to the proportion of marked individuals in the first sample.
To use the mark and recapture method to estimate the population size of rabbits in a large urban park, you would need to follow these steps:
Capture a sample of rabbits and mark them in a non-invasive way, such as using ear tags, tattoos, or fur dye.
Release the marked rabbits back into the park.
Wait for a period of time to allow the marked rabbits to mix back into the population.
Capture a second sample of rabbits from the park.
Count the number of marked and unmarked rabbits in the second sample.
Use the following formula to estimate the population size:
N = (M x n) / R
Where:
N is the estimated population
is the number of individuals in the first sample
n is the number of individuals in the second sample
R is the number of marked individuals recaptured in the second sample
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A bakery makes cylindrical mini muffins that measure 2 inches in diameter and one and one fourth inches in height. If each mini muffin is completely wrapped in paper, then at least how much paper is needed to wrap 6 mini muffins? Approximate using pi equals 22 over 7.
14 and 1 over 7 in2
23 and 4 over 7 in2
47 and 1 over 7 in2
84 and 6 over 7 in2
Answers
At least 84 and 6/7 square inches of paper are needed to wrap 6 mini muffins. The closest option is 84 and 6 over 7 in2.
Given that the diameter of each mini muffin is 2 inches, the radius r is 1 inch. Also, the height h is 1 and 1/4 inches.
So, the surface area of each mini muffin is:
SA = 2π(1)² + 2π(1)(1.25)
SA = 2π + 2.5π
SA = 4.5π
To wrap 6 mini muffins, we need to multiply the surface area of one mini muffin by 6:
Total surface area = 6 × 4.5π
Total surface area = 27π
Using π = 22/7 (approximate value), we get:
Total surface area ≈ 27 × 22/7
Total surface area ≈ 84.857 in²
Rounding to one decimal place, we get:
Total surface area ≈ 84.9 in²
Therefore, at least 84 and 6/7 square inches of paper are needed to wrap 6 mini muffins. The closest option is 84 and 6 over 7 in2.
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A bakery sells hollow chocolate spheres. The larger diameter of each sphere is 6 cm. The thickness of the chocolate between each sphere is 0.5 cm.
What is the volume of the chocolate sphere?
Answers
Rοunding tο twο decimal places, the vοlume οf the chοcοlate sphere is apprοximately 47.75 cubic centimetres.
Tο find the vοlume οf the chοcοlate sphere, we need tο first find the radius οf each sphere.
The diameter οf each sphere is 6 cm, sο the radius is half οf that:
r = 6 cm / 2 = 3 cm
Next, we need tο find the vοlume οf the entire sphere, including the chοcοlate and the hοllοw centre. The fοrmula fοr the vοlume οf a sphere is:
V = (4/3)πr³
Plugging in the value οf the radius, we get:
V = (4/3)π(3 cm)³
V = (4/3)π(27 cm³)
V = 36π cm³
This is the vοlume οf the entire sphere, including the hοllοw center. Tο find the vοlume οf the chοcοlate, we need tο subtract the vοlume οf the hοllοw center.
The diameter οf the hοllοw center is the diameter οf the sphere minus twice the thickness οf the chοcοlate:
d = 6 cm - 2(0.5 cm) = 5 cm
The radius οf the hοllοw center is half οf that:
r_h = 5 cm / 2 = 2.5 cm
The vοlume οf the hοllοw center is the vοlume οf a smaller sphere with radius 2.5 cm:
V_h = (4/3)π(2.5 cm)³
V_h = (4/3)π(15.625 cm³)
V_h = 20.833π cm³
Finally, the vοlume οf the chοcοlate is the vοlume οf the entire sphere minus the vοlume οf the hοllοw center:
V_chοcοlate = V - V_h
V_chοcοlate = 36π cm³ - 20.833π cm³
V_chοcοlate = 15.167π cm³
Rοunding tο twο decimal places, the vοlume οf the chοcοlate sphere is apprοximately 47.75 cubic centimeters.
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Please answer the question
Answers
Answer:
675 will be stuffed crust.
Step-by-step explanation:
The total number of pizzas sold initially is 1060 pizzas. Calculate the percentage of the stuffed crust pizzas within the 1060 pizzas.
[tex] \frac{1569}{1060} \times 100 \\ = 15\%[/tex]
Therefore the stuffed crust is 15% of the total sales.
To find how many pizzas she should expect to be stuffed crust pizzas in the next 4500, calculate 15% of 4500.
[tex] \frac{15}{100} \times4500 \\ = 675[/tex]
Therefore she should expect 675 pizzas of her next 4500 sales to be stuffed crust pizzas.
rewrite f(t)=0.4(1.16)^t-1 in exponential form
Answers
Therefore , the solution of the given problem of expressions comes out to be (1.16)t = 2.5(f(t) + 1) is the exponential version .
An expression is what?Once the variables are moving, it is preferable to make approximations that involve joining, pausing, and dividing rather than doing so at random. They might be able to help one another out with some information, software, or an answer to a problem. Formulas, elements, and mathematical equation notation such as addition, deduction, combination, but also combination can all be found in a declaration of truth.
Here,
f(t)=0.4(1.16)t-1 can be simplified by adding 1 to both sides of the equation before being rewritten in exponential form as follows:
=> f(t) + 1 = 0.4[tex](1.16)^{t}[/tex]
Then, to find the exponential component, divide both sides by 0.4:
=> [tex](1.16)^{t}[/tex] = (f(t) + 1)/0.4
Finally, using base 1.16, we can express the exponential form as follows:
=>[tex](1.16)^{t}[/tex] = 2.5(f(t) + 1)
As a result, (1.16)t = 2.5(f(t) + 1) is the exponential version of the expression f(t)=0.4(1.16)t-1).
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Write a formula that describes the value of an initial investment of $1200, growing at an interest rate of 4%, compounded monthly.
Answers
The formula describing the given situation is A = 1200 [tex]e^{0.04t}[/tex] . The solution has been obtained by using compound interest.
What is compound interest?
Compound interest considers the principal when determining the interest for the subsequent month, in contrast to simple interest, which does not. In the algebra, compound interest is sometimes denoted by the letter C.I.
We know that compound interest is given by
A = P[tex]e^{rt}[/tex]
In the question, we are given the values as
P = $1200
r = 0.04
So, from this we get
A = 1200 [tex]e^{0.04t}[/tex]
Hence, the formula describing the given situation is A = 1200 [tex]e^{0.04t}[/tex] .
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The graph shows point F located at (0, 3) and line d given by the equation y = -2.
Which point is equidistant from F and d?
Answers
Answer: (0,.5)
x is 0 because it is the value where point F and line D are the closest. And y = .5 because both 3 and -2 are 2.5 units away from (0,.5).
solve 2x+x+5=7x-4x+5
Answers
Answer:
x=All real numbers
Step-by-step explanation:
2x+x+5=7x-4x+5
3x+5=3x+5
3x=3x
0=0
Any value of x will make the equation a true statement, so it has an infinite number of solutions.
Matrix Algebra: Enter the following matrices: [ 5 2 -6 ] [ 3.8 0.6 1.8 ] [ -5 0 ]
A = [-6 3 -5 ] B = [ 0.9 -0.3 2.2 ] C = [ -5 -5 ]
[ 0 -4 4 ] [ 4.0 0.9 1.7 ] [ 3 3 ]
Compute the following: (i) AC (ii) A+B (iii) AB (iv) 4A + 4B
(v) A+ C
(vi) 1 + c (vii) CA (viii) BA (ix) B+A (x) 4(A + B) (a) Did MATLAB refuse to do any of the requested calculations? If so, which ones and why? (b) Does 4(A + B) = 4A + 4B ? (c) Does AB = BA? (d) What did 1+C do? (e) Does A + B = B+ A?
Answers
1+C is [-4 -4].
(i) AC = [13 -32 -40]
(ii) A + B = [-5.1 2.7 -2.8]
(iii) AB = [-13.3 10.3 -10.3]
(iv) 4A + 4B = [-20.4 10.8 -11.2]
(v) A + C = [-11 -9 -10]
(vi) 1 + C = [ -4 -4]
(vii) CA = [6 11 8]
(viii) BA = [-6.3 9.9 -9.9]
(ix) B + A = [-5.1 2.7 -2.8]
(x) 4(A + B) = [-20.4 10.8 -11.2]
(a) MATLAB may refuse to do some calculations if they are not mathematically valid. For example, the product of two matrices (AB) must have the same number of columns in the first matrix as the number of rows in the second matrix.
(b) Yes, 4(A + B) = 4A + 4B.
(c) No, AB ≠ BA.
(d) Adding a scalar to a matrix adds the scalar to each element of the matrix. In this case, 1+C is [-4 -4].
(e) Yes, A + B = B + A.
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Consider the value of t such that 0.1 of the area under the curve is to the right of t. Step 2 of 2 : Assuming the degrees of freedom equals 9, select the t value from the t table.
Answers
t is 1.383.
HTML tags cannot be used on the platform. However, the solution to the question is as follows:
Step 1: We must first find the t value such that 0.1 of the area under the curve is to the right of t.
For the given problem, the area to the left of t is 1 - 0.1 = 0.9.The value of t can be found using a t-table. This will give us the corresponding t-value for 0.9 area to the left of t.
Step 2: Assuming the degrees of freedom equals 9, select the t-value from the t table.Since we have 9 degrees of freedom and we need to find the t-value for 0.9 area to the left of t, we must look at the row that corresponds to 9 degrees of freedom in the t-table. In that row, we must look for the column that has a value closest to 0.9.
The t-value in that column will be the required value of t. The t-value that has a 0.9 area to the left of it is 1.383.So, the value of t such that 0.1 of the area under the curve is to the right of t is 1.383.
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10 records in her collection. Now she has 12 records. What is the percent increase of her collection?
Answers
10 records in her collection. Now she has 12 records. The percentage increase of her collection is by 20%.
Percentage:
In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is usually represented by the percent sign "%", although 'it is abbreviated "pct.", "pct.", and sometimes "pc". Percentage is a dimensionless number (pure number); it is unmeasured Unit.
Example :
If 50% of the total number of pupils in a class are boys, this means that 50 out of 100 pupils are boys. If there are 500 students, 250 of them are men.
According to the Question:
We can use the rule of three to solve this problem.
If 100% is 10 records, the percentage of 12 records:
= 12 × 100%/10
= 120%
Then if subtracted 120% -100%, there will be a difference of 20%, i.e. 12 is 20% more, i.e. his collection has increased by 20%.
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The line plot represents the sales of rose bouquets at a local market.
A horizontal line labeled Number of Rose Bouquets that starts at 1 with tick marks every one unit up to 10. There is one dot above 1 and 10. There are two dots above 6, 7 and 9. There are three dots above 8. The graph is titled Roses Purchased Per Day.
Which of the following describes the spread and distribution of the data represented?
The data is almost symmetric, with a range of 9. This might happen because the market offers a special price when 5 bouquets are purchased.
The data is skewed, with a range of 9. This might happen because the bouquets were purchased around a holiday when flowers are popular gifts.
The data is bimodal, with a range of 10. This might happen because the market offers a buy one get one free special if you purchase 4 or 8 bouquets.
The data is symmetric, with a range of 10. This might happen because the market has been having trouble getting bouquets in, due to the weather, and sales are low.
Answers
The data represented in the line plot is symmetric, with a range of 10. This means that the highest number of bouquets sold is 10, while the lowest number of bouquets sold is 1.
This indicates that the market offers a steady rate of sales, with a few special offers that increase the rate of sales.The range can be calculated using the formula Range = Maximum Value - Minimum Value. In this case, the range is 10 = 10 - 1.The symmetry can be seen by looking at the number of dots above each number. For the numbers 1, 6, 7, 9, and 10, there is one dot above each. For the number 8, there are three dots above it. This indicates that the number of bouquets sold over each number is almost the same, creating a balanced and symmetric distribution of the data. This suggests that the market offers steady sales, with a few promotional offers that increase the rate of sales.The data represented in the line plot is symmetric, with a range of 10. This means that the highest number of bouquets sold is 10, while the lowest number of bouquets sold is 1.
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Given A and b to the right, write the augmented matrix for the linear system that corresponds to the matrix equation Ax = b Then solve the system and write the solution as a vector. A= 1 2 3 3 5 2 -4 2 5 b= -13 11 8 Write the augmented matrix for the linear system that corresponds to the matrix equation Ax = b. Select the correct choice below and fill in any answer boxes within your choice.1 2 3 3 5 2 -4 2 5 -13 11 8 Solve the system and write the solution as a vector. Select the correct choice below and fill in any answer boxes within your choice. x =
Answers
The solution to the system of equations is x = [3, -10, 17/2].Thus, the required vector is x = [3, -10, 17/2].
The augmented matrix for the linear system corresponding to the matrix equation Ax = b is given by the matrix [A|b] as shown below.Augmented Matrix: [1 2 3|-13; 3 5 2|11; -4 2 5|8]Now we will reduce this augmented matrix into row echelon form.R1 <--> R2 (-3R1 + R2) R3 <--> R2 (2R1 + R3) R2/2 (-3R2 + R3) R3/(-17) We obtain the row echelon form of the augmented matrix as [1 2 3|-13; 0 -1/2 -7/2|20; 0 0 1|17/2]
Next, we will reduce the row echelon form of the augmented matrix into reduced row echelon form. R2 <--> R3 (-1/2R2 + R3) R1 <--> R2 (2R2 + R1) R3/1We obtain the reduced row echelon form of the augmented matrix as [1 0 0|3; 0 1 0|-10; 0 0 1|17/2]Therefore, the solution to the system of equations is x = [3, -10, 17/2].Thus, the required vector is x = [3, -10, 17/2].
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The 5 points plotted below are on the graph of y = log, x. Based only on these 5 points, plot the 5 corresponding points that must be on the graph of y = b by clicking on the graph.
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Therefore , the solution of the given problem of graphs comes out to be graph of y = 2ˣ .
What is graph?Graphs are used by theoretical physicists to visually or analytically vertices chart assertions rather than values. Typically, a graph point shows the relationship between several different objects. A graph is a particular kind of train assembly consisting of groups and lines. The networks, also known as the borders, should be joined with glue. The edges of this network had the digits 1, 2, 3, and 4, along with the numerals (2.5), (3.5),
Here,
y = logₐ(x); logarithmic function (x)
The matching points that must appear on the graph x = bx can be found using the procedure below.
Step 1: In the equation
=> x = bˣ
=> 2= b¹
=> b =2
replace (2,1) with the value of x and y.
Step 2: Now change the number of b in the equation to make
=> y = 2ˣ
Step 3: The above equation becomes y=2 at (x = 1).
Step 4 - The equation (2) becomes: at (x = 2)
Step 5 - The equation (2) becomes: y = 16 at (x = 4)
The graph of y = 2ˣ
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Determine whether or not the function f(x)=5⋅3x+3 is continuous everywhere. If it is continuous everywhere it is defined, enter the domain on which it is continuous in interval notation. To enter [infinity], type infinity. To enter ∪, type U.If it is discontinuous, state where it is discontinuous. Enter your answer as a list of numbers separated by semicolons (e.g. 2;4;6). The order of the list does not matter.
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The function f(x) = [tex]5(3)^x+3[/tex] is continuous everywhere on its domain, which is (-∞, ∞).
The function f(x) = [tex]5(3)^x+3[/tex] is continuous everywhere because it is an exponential function with a base of 3, which is a positive number. Exponential functions with positive bases are continuous over their entire domain.
To see why, consider the definition of continuity: a function f(x) is continuous at a point x = c if the limit of f(x) as x approaches c exists and is equal to f(c). For an exponential function with a positive base, as x approaches c, the function values either increase to infinity or decrease to 0, depending on whether the exponent is positive or negative, respectively. In either case, the limit exists and is equal to the function value at c, so the function is continuous at c. Since this holds for all points in the domain, the function is continuous everywhere it is defined.
The domain of f(x) is all real numbers, so the function is continuous on the interval (-infinity, infinity), or in interval notation, the domain is (-∞, ∞).
In summary, the function f(x) = 5(3)ˣ +3 is continuous everywhere on its domain, which is (-∞, ∞).
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Find the value of f(4)
Answers
4f
Step-by-step explanation:
f(4)Move 44 to the left of ff.4f
Answer:
f(4) = 5
Step-by-step explanation:
f(4) means what is the value of y when x = 4
locate x = 4 on the x- axis
go vertically up to meet the graph at (4, 5 )
then when x = 4 , y = 5 , so
f(4) = 5
let f(x)=ln(3x) domain of f is
Answers
The domain of the function f(x) = ln(3x) is x > 0.
How to determine domain of he functionGiven a function f(x) = ln(3x). We are to determine the domain of the function. Let's discuss the domain of the given function:
Domain: The domain of a function is the set of all possible values of x that makes the function defined. The natural logarithmic function ln(x) is defined only for positive real numbers.
That is, the expression inside the ln(x) must be greater than 0. This is because the logarithmic function is undefined for negative numbers and zero.
So, for the given function, we have:
3x > 0
Dividing both sides by 3 gives us:x > 0/3x > 0
Thus, the domain of the function f(x) = ln(3x) is x > 0.
Hence, the answer is x > 0.
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We want to know if there exists a difference in sleep between pregnant and non-pregnant Americans.
In a sample of 52 non-pregnant American adults, you find they average 7.14 hours of sleep per night, with a standard deviation of 1.14 hours.
In an independent sample of 58 pregnant American adults, you find they average 7.75 hours of sleep per night, with a standard deviation of 0.96 hours.
To a significance level of a=0.08, test whether there exists a difference in sleep between the two groups. Please write your answers to at least four places. Assume that all conditions necessary for inference are satisfied.
What will our hypotheses look like?
What is the standard error?
What is the test statistic?
What is the p-value?
Based on this p-value, at a significance level of a=0.08, would we reject the null hypothesis?
Answers
The standard error is 0.2021
The test statistic is - 2.95
The p-value is 0.0042.
Based on this p-value, at a significance level of a = 0.08, we can reject the null hypothesis.
The hypotheses for this test are:Null hypothesis: There is no significant difference in sleep between pregnant and non-pregnant Americans.
Alternative hypothesis: There is a significant difference in sleep between pregnant and non-pregnant Americans.
Here we have
In a sample of 52 non-pregnant American adults, the average was 7.14 hours of sleep per night, with a standard deviation of 1.14 hours.
In an independent sample of 58 pregnant American adults, the average was 7.75 hours of sleep per night, with a standard deviation of 0.96 hours.
To test these hypotheses, we will use a two-sample t-test with unequal variances, also known as a Welch's t-test. The standard error for this test is calculated as:
SE = √[(s₁²/n₁) + (s₂²/n₂)]
Where s₁ and s₂ are the sample standard deviations, n₁, and n₂ are the sample sizes
Substitute the values from the problem, we get:
SE = √[(1.14²/52) + (0.96²/58)]
SE = 0.2021
The test statistic is calculated as:
t = (x₁ - x₂) / SE
Where x₁ and x₂ are the sample means for the non-pregnant and pregnant groups, respectively.
Substitutes the values from the problem, we get:
t = (7.14 - 7.75) / 0.2068
t = - 2.95
Using a t-distribution with degrees of freedom calculated by the Welch-Satterthwaite method (df = 90.87), we can find the p-value for this test. The p-value for a two-tailed test at a significance level of 0.08 is approximately 0.0042.
Since the p-value (0.0042) is less than the significance level (0.08), we can reject the null hypothesis.
Therefore,
Conclude that there is a significant difference in sleep between pregnant and non-pregnant Americans.
Hence,
The standard error is 0.2021
The test statistic is - 2.95
The p-value is 0.0042.
Based on this p-value, at a significance level of a = 0.08, we can reject the null hypothesis.
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2. Let X have a geometric distribution with parameter p. Suppose, for all positive integers n, the conditional distribution of Y given X=n is binomial with parameters n and q. Calculate P(Y=0)
Answers
P(Y=0) = p*((1-q)n).
EXPLANATION:
We can calculate this by using the law of total probability. Since X has a geometric distribution, the probability of Y given X = n is binomial with parameters n and q. Therefore, P(Y = 0) can be calculated as the sum of the probability of Y = 0 given X = n multiplied by the probability of X = n.
P(Y = 0) = p*((1-q)n).
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