Answers
Answer:
the answer is 247.7 cm²
see the attachment photo!
Related Questions
Write an equation perpendicular to y = -2x - 7 that passes through the point (4,3)
Answers
y=1/2x+b
3=1/2(4)+b
3=2+b
b=1
the new equation is y=1/2x+1
You are shopping for single-use cameras to hand out at a party. The daylight cameras cost $2.75 and the flash cameras cost$4.25. You must buy exactly 20 cameras and you want to spend between $65 and$75, inclusive. Write and solve a compound inequality for this situation. Then list all the solutions that involve whole numbers of cameras.
Answers
The compound inequality for the given situation is $2.75x + $4.25y ≥ $65 and $2.75x + $4.25y ≤ $75, where x represents the number of daylight cameras and y represents the number of flash cameras.
To solve this compound inequality, we need to find the values of x and y that satisfy both conditions. The inequality $2.75x + $4.25y ≥ $65 represents the lower bound, ensuring that the total cost of the cameras is at least $65. The inequality $2.75x + $4.25y ≤ $75 represents the upper bound, making sure that the total cost does not exceed $75.
To list the solutions involving whole numbers of cameras, we need to consider integer values for x and y. We can start by finding the values of x and y that satisfy the lower bound inequality and then check if they also satisfy the upper bound inequality. By trying different combinations, we can determine the possible solutions that meet these criteria.
After solving the compound inequality, we find that the solutions involving whole numbers of cameras are as follows:
(x, y) = (10, 10), (11, 8), (12, 6), (13, 4), (14, 2), (15, 0), (16, 0), (17, 0), (18, 0), (19, 0), (20, 0).
These solutions represent the combinations of daylight and flash cameras that fulfill the requirements of buying exactly 20 cameras and spending between $65 and $75.
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A cookie recipe calls for 2 cups of sugar for every 1 cup of flour. If 6 cups of sugar
are used, how many cups of flour will be needed?
Answers
Answer:
3 cups of flour
Step-by-step explanation:
We know
2 cups of sugar = 1 cup of flour
1 cup of sugar = 0.5 cup of flour
To find how many cup of flour for 6 cups of sugar
We take 6 times 0.5 = 3 cups of flour
So, 3 cups of flour will be needed for 6 cups of sugar.
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Derek decides that he needs $184,036.00 per year in retirement to cover his living expenses. Therefore, he wants to withdraw $184036.0 on each birthday from his 66th to his 90.00th. How much will he need in his retirement account on his 65th birthday? Assume a interest rate of 5.00%.
Derek plans to retire on his 65th birthday. However, he plans to work part-time until he turns 71.00. During these years of part-time work, he will neither make deposits to nor take withdrawals from his retirement account. Exactly one year after the day he turns 71.0 when he fully retires, he will wants to have $2,742,310.00 in his retirement account. He he will make contributions to his retirement account from his 26th birthday to his 65th birthday. To reach his goal, what must the contributions be? Assume a 5.00% interest rate.
Answers
Derek needs to make contributions of approximately $21,038.34 per year from his 26th birthday to his 65th birthday in order to accumulate $2,742,310.00 in his retirement account by the time he fully retires.
To determine the amount Derek needs in his retirement account on his 65th birthday, we can use the concept of present value. Since he plans to withdraw $184,036.00 per year, starting from his 66th birthday until his 90th, the cash flows can be treated as an annuity. The interest rate is 5.00%, and the time period is 25 years (from 66 to 90). Using the formula for the present value of an annuity, we can calculate the required amount. The formula is:
PV = PMT * (1 - \((1 + r)^(-n)\)) / r
where PV is the present value, PMT is the annual withdrawal amount, r is the interest rate per period, and n is the number of periods.
Plugging in the values, we get:
PV = $184,036.00 * (1 - \((1 + 0.05)^(-25)\)) / 0.05 ≈ $2,744,607.73
Therefore, Derek needs approximately $2,744,607.73 in his retirement account on his 65th birthday to cover his desired annual withdrawals.
Moving on to the second part, Derek plans to make contributions to his retirement account from his 26th birthday to his 65th birthday. To reach his goal of having $2,742,310.00 in his retirement account after fully retiring, we can calculate the necessary contributions using the formula for the future value of an ordinary annuity:
FV = PMT * \(((1 + r)^n\) - 1) / r
Rearranging the formula, we can solve for the required contributions (PMT):
PMT = FV * (r / (\(((1 + r)^n\) - 1))
Plugging in the values, we get:
PMT = $2,742,310.00 * (\(\frac{0.05} {((1+0.05)^{39}-1 )}\))≈ $21,038.34
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PLEASE HELP!!!!!! The length of a rectangle is three times its width. If the perimeter of the rectangle is 56 cm, find its area.
Answers
Step-by-step explanation:
l = length
w = width
l = 3w
perimeter p = 2l + 2w = 56
using the identity of the first equation
p = 2(3w) + 2w = 56
6w + 2w = 56
8w = 56
w = 7 cm
l = 3w = 3×7 = 21 cm
so, the area is
l×w = 21×7 = 147 cm²
A fair, 6-sided dice is rolled 50 times. Predict how many times it will land on a number greater than 3.
A. 1/2
B. 5
C. 25
D. 50
Answers
reasoning:
there are three numbers greater than 3 (4, 5 and 6) so that gives it about an equal opportunity to rolling a 1, 2 or 3. Given that there are no advantages, if the dice is rolled fifty times, half of that would have to be 25. The likelihood of rolling a 4, 5 or 6 is 25.
Answer:
C. 25
Step-by-step explanation:
We Know
A fair, 6-sided dice is rolled 50 times.
Predict how many times it will land on a number greater than 3.
There are 3 numbers greater than the number 3 are 4, 5, 6.
So, the ratio is 3/6 = 1/2
Then we take 1/2 and multiply by the number of rolls which is 50
1/2 x 50 = 25
So, the answer is C. 25
A clothing store specializes in blue jeans. They run a regression and get the following results: Coefficients Intercept 200.0 Price -4.5 PriceKhakis 2.2 Advertising 6.5 Weekend 10.0 price is $40, price khakis (a substitute) are $50, advertising is $2, and Weekend is a dummy variable. If it IS the weekend, find price elasticity of the blue jeans. You MUST properly round out 2 decimals exactly and include a negative sign if needed.
Using the elasticity you found before, determine what will happen to the quantity demanded of blue jeans if they drop the price by 5%?
Answers
a. The price elasticity of blue jeans on the weekend is approximately -2.14, indicating that a 1% decrease in price will result in a 2.14% increase in quantity demanded.
b. The quantity demanded of blue jeans will increase by approximately 10.7%.
a. The price elasticity of demand measures the responsiveness of the quantity demanded to a change in price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price.
Given:
Price = $40
Price of khakis = $50
Advertising = $2
Weekend (dummy variable) = 1 (indicating it is the weekend)
To calculate the price elasticity of blue jeans on the weekend, we need to use the coefficient for the "Price" variable from the regression results.
Price elasticity of demand = (Coefficient for Price * Price) / Quantity demanded
Coefficient for Price = -4.5 (from regression results)
Price = $40 (given)
Quantity demanded can be calculated using the regression equation:
Quantity demanded = Intercept + (Coefficient for Price * Price) + (Coefficient for Price Khakis * Price of khakis) + (Coefficient for Advertising * Advertising) + (Coefficient for Weekend * Weekend)
Intercept = 200 (from regression results)
Coefficient for Price Khakis = 2.2 (from regression results)
Coefficient for Advertising = 6.5 (from regression results)
Coefficient for Weekend = 10.0 (from regression results)
Quantity demanded = 200 + (-4.5 * 40) + (2.2 * 50) + (6.5 * 2) + (10.0 * 1)
Quantity demanded = 200 - 180 + 110 + 13 + 10
Quantity demanded = 153
Now we can calculate the price elasticity of demand:
Percentage change in quantity demanded = (Quantity demanded - Quantity demanded with a 5% price decrease) / Quantity demanded
Percentage change in quantity demanded = (153 - Quantity demanded with a 5% price decrease) / 153
Percentage change in price = 5% (given)
Price elasticity of demand = (Percentage change in quantity demanded / Percentage change in price) * (Price / Quantity demanded)
Price elasticity of demand = ((153 - Quantity demanded with a 5% price decrease) / 153) / 0.05 * (40 / 153)
To find the quantity demanded with a 5% price decrease, we calculate:
New price = $40 - (5% of $40) = $40 - ($2) = $38
New quantity demanded = 200 + (-4.5 * 38) + (2.2 * 50) + (6.5 * 2) + (10.0 * 1)
New quantity demanded = 200 - 171 + 110 + 13 + 10
New quantity demanded = 162
Substituting the values into the formula:
Price elasticity of demand = ((153 - 162) / 153) / 0.05 * (40 / 153)
Price elasticity of demand = (-0.059 / 0.05) * (40 / 153)
Price elasticity of demand ≈ -2.14
The price elasticity of blue jeans on the weekend is approximately -2.14, indicating that a 1% decrease in price will result in a 2.14% increase in quantity demanded.
b. We already calculated the price elasticity of demand (-2.14). Now, we can use this elasticity to determine the percentage change in quantity demanded when the price is reduced by 5%.
Percentage change in price = -5% (given)
Percentage change in quantity demanded = Price elasticity of demand * Percentage change in price
Percentage change in quantity demanded = -2.14 * (-5%)
Percentage change in quantity demanded = 10.7%
Therefore, if the price of blue jeans is reduced by 5%, the quantity demanded will increase by approximately 10.7%.
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Examine these lyrics from "Fireflies" by Owl City:
You would not believe your eyes
If ten million fireflies
Lit up the world as I fell asleep
'Cause they fill the open air
And leave teardrops everywhere
You'd think me rude but I would just stand and stare
To ten million fireflies
I'm weird cause I hate goodbyes
I got misty eyes as they said farewell
Which of the following is true?
A.) The lyrics shared here have no rhyme scheme.
B.) The lyrics shared here are divided into three stanzas.
C.) The lyrics shared here could be considered a sonnet.
D.) The lyrics shared here end in a couplet.
*I know that A. Isn’t right.*
Answers
Answer:
They are divided into 3 stanzas so B.
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Songs are like poetry, they are written in stanzas. Pls mark brainliest
the penguin exhibit at a zoo has a raised circular island that is surrounded by water. the diameter of the island is 20 meters 20 meters20, start text, space, m, e, t, e, r, s, end text. one penguin swims half way around the island before hopping out. how far did the penguin swim?
Answers
The penguin swims half the circumference of the circular island, which is equivalent to half the distance around the circle.
The circumference of a circle can be calculated using the formula:
C = πd,
where C is the circumference and d is the diameter of the circle.
Given that the diameter of the island is 20 meters, the radius (r) of the island is half the diameter, which is 10 meters.
Substituting the value of the radius into the formula, we have:
C = π * 10 meters = 10π meters.
To find half the circumference, we divide the total circumference by 2:
Half circumference = (10π meters) / 2 = 5π meters.
Therefore, the penguin swims a distance of 5π meters.
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Which on is not a function
Answers
Answer:
D.
Step-by-step explanation:
Find bases for the four fundamental subspaces of the matrix A as follows. N(A) = nullspace of A N(AT) = nullspace of AT R(A) = column space of A R(AT) = column space of AT Then show that N(A) = R(AT)perpendicular and N(AT) = R(A)perpendicular.
Answers
If we can show that the dot product between any vector in N(A) and any vector in R(AT) is zero, then we have proved that N(A) = R(AT)⊥.
To find bases for the four fundamental subspaces of the matrix A, we have to follow the given fundamental subspaces.
N(A) = nullspace of AN(AT) = nullspace of ATR(A) = column space of AR(AT) = column space of ATWe can calculate the basis vectors for these subspaces using the row-reduced echelon form of A.
The basis for N(A) can be found by solving the equation Ax = 0. The basis for R(A) can be found by taking the pivot columns of A as the basis vectors.
Similarly, the basis for N(AT) can be found by solving the equation ATx = 0, and the basis for R(AT) can be found by taking the pivot columns of AT as the basis vectors.
Next, we have to show that N(A) = R(AT)⊥ and N(AT) = R(A)⊥.To show that N(A) = R(AT)⊥, we have to prove that every vector in N(A) is orthogonal to every vector in R(AT). Similarly, to show that N(AT) = R(A)⊥, we have to prove that every vector in N(AT) is orthogonal to every vector in R(A).
This can be done using the dot product between the vectors in each subspace. If the dot product is zero, then the vectors are orthogonal.
Similarly, if we can show that the dot product between any vector in N(AT) and any vector in R(A) is zero, then we have proved that N(AT) = R(A)⊥.
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A tidal wave caused by an earthquake off the Alaskan coast begins running toward Carmel, California. The water first goes down from its normal level, and then rises an equal distance above its normal level; the water then returns to normal. Assume that the depth of the water varies sinusoidally with time as the wave passes. Suppose the wave, with a period of 20 minutes and an amplitude of 12 meters, approaches a dock in Carmel where the normal depth is 8 meters.
Answers
y = 6 sin [(π/10)t] + 8; equation gives us the depth of the water at the dock as a function of time elapsed since the wave started passing the dock.
Define the sinusoidal function?A sinusoidal function is a mathematical function that oscillates or fluctuates in a periodic manner, following a sine or cosine curve.
If the wave approaches a dock in Carmel where the normal depth is 8 meters and varies sinusoidal with time, then we can use the equation for a sinusoidal function:
y = A sin (ωt + φ) + C
where: A is the amplitude of the wave, which is given as 12 meters
ω is the angular frequency, which can be calculated as 2π / T, where T is the period of the wave (20 minutes in this case)
t is the time elapsed since the wave started passing the dock
φ is the phase angle, which we can assume to be 0 since we are not given any information about it
C is the vertical displacement of the wave from the normal depth, which is 8 meters in this case
putting the given values into the equation,
y = 12 sin [(2π/20)t] + 8
Simplifying this equation,
y = 6 sin [(π/10)t] + 8
This equation gives us the depth of the water at the dock as a function of time elapsed since the wave started passing the dock.
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A net of a rectangular prism is show
What is the surface area of the prism?
550 1/4cm
412 3/4cm
275 1/8cm
137 9/16cm
Answers
The surface area of the rectangular prism is 1,355,531 cm2.
What is surface area?Surface area is a measure of the total area of the surface of an object. It is calculated by taking the total area of its faces, edges, and vertices and combining them into one figure. It is an important factor in determining the volume, mass, and other properties of a three-dimensional object. In the case of a cube, for example, the surface area is the sum of the areas of its six faces. It is also used to measure the total area of a two-dimensional object, such as a circle or a triangle.
The surface area of a rectangular prism is the sum of the areas of all of its faces. To find the surface area, one can use the formula A = 2lw + 2lh + 2hw, where l is the length, w is the width, and h is the height.
In this case, the length of the rectangular prism is 550 1/4 cm, the width is 412 3/4 cm, and the height is 275 1/8 cm. Using the formula, we can calculate the surface area of the prism as follows:
A = 2(550 1/4)(412 3/4) + 2(550 1/4)(275 1/8) + 2(412 3/4)(275 1/8)
A = 936,406 1/2 + 304,437 1/2 + 114,687 1/2
A = 1,355,531 cm2
Therefore, the surface area of the rectangular prism is 1,355,531 cm2.
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a function is a relation if and only if the x values do not repeat in a given set. true or false?
Answers
Answer:
true
Step-by-step explanation:
when the domain (x-values)is not repeated in the relation
Maths ice cream shop has 7 cups of sprinkles to use on Sundays for the rest of the day if each Sunday serves with one 8th cup of sprinkles how many Sundays can they serve
Answers
56 Sundays Maths Ice Cream Shop can serve with 7 cups of sprinkles using one-eighth (1/8) cup of sprinkles per Sunday.
Converting the cups of sprinkles into eighths:
7 cups × 8 eighths/cup
= 56 eighths
Dividing the total eighths by the eighths used per Sunday:
56 eighths / (1/8 cup per Sunday)
= 56 Sundays
So, Maths Ice Cream Shop can serve for 56 Sundays using 7 cups of sprinkles with each Sunday serving one-eighth cup of sprinkles.
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what i the width of a rectangle when the length is 19.6 and the diagonal length is 20
Answers
A piece of chocolate is 4/5 inch long. Meg lays 4 chocolate pieces end to end in a row. How many inches long is the row of chocolates ( please helpppppp) ( MAP test question)
Answers
Answer:
The length of row = 3.2 inches.
Step-by-step explanation:
The length of a chocolate = 4/5 inch
Total number of chocolate pieces placed = 4
Now we have given the length of one chocolate and it is required to find the total length of the row when four chocolates are placed end to end. So in order to find the length of the chocolate row we have to multiply the size of one chocolate by the number of chocolates.
The length of row = Length of one chocolate × number of chocolates
The length of row = 4/5 × 4
The length of row = 3.2 inches.
The piece of chocolate and the number of chocolates in a row can be represented using equations.
A row of chocolate is 3.2 inches long
Given that:
\(L = \frac 45\) ---- Length of a piece
\(n =4\) --- number of chocolate pieces
The length of the chocolate in a row is calculated as follows:
\(Length = n \times L\)
So, we have:
\(Length = 4 \times \frac 45\)
\(Length = 4 \times 0.8\)
\(Length = 3.2\)
Hence, a row of chocolate is 3.2 inches long
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Select all conditions for which it is possible to construct a triangle. Group of answer choices A. A triangle with angle measures 30, 40, and 100 degrees. B. A triangle with side lengths 4 cm, 5 cm, and 8 cm, C. A triangle with side lengths 4 cm and 5 cm, and a 50 degree angle. D. A triangle with side lengths 4 cm, 5 cm, and 12 cm. E. A triangle with angle measures 40, 60, and 80 degrees.
Answers
The options that allow for the construction of a triangle are:
Option B: A triangle with side lengths 4 cm, 5 cm, and 8 cm.
To determine if it is possible to construct a triangle, we need to consider the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's evaluate each option:
A. A triangle with angle measures 30, 40, and 100 degrees.
This option does not provide any side lengths, so we cannot determine if it satisfies the triangle inequality theorem. Insufficient information.
B. A triangle with side lengths 4 cm, 5 cm, and 8 cm.
We can apply the triangle inequality theorem to this option:
4 cm + 5 cm > 8 cm (True)
5 cm + 8 cm > 4 cm (True)
4 cm + 8 cm > 5 cm (True)
This set of side lengths satisfies the triangle inequality theorem, so it is possible to construct a triangle.
C. A triangle with side lengths 4 cm and 5 cm, and a 50-degree angle.
We don't have the length of the third side, so we cannot determine if it satisfies the triangle inequality theorem. Insufficient information.
D. A triangle with side lengths 4 cm, 5 cm, and 12 cm.
Applying the triangle inequality theorem:
4 cm + 5 cm > 12 cm (False)
5 cm + 12 cm > 4 cm (True)
4 cm + 12 cm > 5 cm (True)
Since the sum of the lengths of the two smaller sides (4 cm and 5 cm) is not greater than the length of the longest side (12 cm), it is not possible to construct a triangle with these side lengths.
E. A triangle with angle measures 40, 60, and 80 degrees.
This option does not provide any side lengths, so we cannot determine if it satisfies the triangle inequality theorem. Insufficient information.
Based on the analysis, the options that allow for the construction of a triangle are:
Option B: A triangle with side lengths 4 cm, 5 cm, and 8 cm.
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Helllllpppppppp!!!!!
Answers
Answer: The correct answer is C
Step-by-step explanation:The graph is horizontally stretched by a factor of 1/5 because you are literally multiplying x by 1/5. So, your answer is C. Hope it makes sense. mark me brainlest
For what value of the constant c is the function f continuous on (-infinity, infinity)?
f(x)= cx^2 + 2x if x < 3 and
x^3 - cx if x ≥ 3
Answers
The value of c that makes the function f continuous on (-∞, ∞) is 3.
To find the value of c that makes the function f continuous at x = 3, we should calculate the left and right-hand limits for the function at x = 3. If both the limits are equal, the function f will be continuous at x = 3. We will use this criterion to determine the value of c.
For x < 3,f(x) = cx² + 2x
For x ≥ 3,f(x) = x³ - cx
f(x) is continuous at x = 3, if
limx→3- f(x) = limx→3+ f(x)
limx→3- (cx² + 2x) = limx→3+ (x³ - cx)(3)²c(3) + 2(3) = 3³ - c(3)c = 3
Thus, the value of c that makes the function f continuous on (-∞, ∞) is 3.
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can someone help solve? will give brainliest
Answers
Answer:
Step-by-step explanation:
Your answer
About all the sides are equal so we can say (10x + 44) side's triagle is twice than another triangle
So, 10x + 44 = 2( 8x - 23)
..... 10x +44 = 16x -46
...... X = 15
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Structural and functional unit of life is what?
Answers
Cell is the Structural and functional unit of life.
Answer:
cells
hope this helps
have a good day :)
Step-by-step explanation:
I've been stuck on this for a bit, and I'm still figuring this out in the process. a little help?
Answers
Steps to solve:
4x + 1/3y^2 when x = 2 and y = 3
~Substitute
4(2) + 1/3(3)^2
~Simplify
8 + 1/3(9)
~Simplify
8 + 3
~Add
11
Best of Luck!
Consider the expression 16 - 4 × 3 + 7. Use parentheses to rewrite the
expression so that it equals 11.
Answers
Answer:
16 - (4 × 3) + 7
Step-by-step explanation:
Circle all statements that MUST be true
a. Diagonals of parallelograms bisect each other
b. Parallelograms have four congruent sides
c. Isosceles triangles have 3 congruent angles
d.
If the endpoints of a line segment are equidistant from a third point, that third point lies on the
perpendicular bisector of the line segment.
7. Find the value of X, Y. Show your work
Answers
Answer:
6) True, False, False, True;7) x = 135, y = 45.--------------------
Question 6a. Diagonals of parallelograms bisect each other
TRUEb. Parallelograms have four congruent sides
FALSE, it is true for rhombusc. Isosceles triangles have 3 congruent angles
FALSE, it has 2 congruent angles as two sides are congruent.d. If the endpoints of a line segment are equidistant from a third point, that third point lies on the perpendicular bisector of the line segment.
TrueQuestion 7Adjacent angles of a parallelogram are supplementary and opposite angles are congruent.
x + y = 180 and y = 45Find x:
x + 45 = 180x = 180 - 45x = 135The point at which a line intersects the Y axis when X = 0 is called the standard error of the estimate least squares criterion slope Intercept
Answers
The point at which a line intersects the Y-axis when X = 0 is called the intercept. It is denoted as the value of Y when X is zero.
The intercept represents the starting point of the line and indicates the value of the dependent variable (Y) when the independent variable (X) has no effect.
On the other hand, the standard error of the estimate is a measure of the variability or uncertainty in the predicted values of the dependent variable (Y) based on the regression model. It quantifies how well the regression line fits the observed data points. It represents the average amount by which the observed Y values deviate from the predicted values on average.
The least squares criterion is a principle used in linear regression to estimate the line that minimizes the sum of the squared differences between the observed Y values and the predicted values. The least squares criterion is used to find the best-fitting line by minimizing the overall error between the line and the observed data points.
To summarize:
The intercept is the point at which a line intersects the Y-axis when X = 0.
The standard error of the estimate measures the variability in the predicted Y values based on the regression model.
The least squares criterion is a principle used to estimate the line that minimizes the sum of squared differences between observed and predicted Y values.
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The radius of a circle is 65 centimeters.
Enter the circumference of the circle, in centimeters. Round your answer to the nearest hundredth.
Answers
circumference = 2 x pi x r
r = 65 cm
so C ≈ 2 x 3,14 x 65 ≈ 408,20
Answer: C=408.41 centimeters
Step-by-step explanation:
2 times pi times 65
130 pi
Approximately 408.41
If the mpc increases in value, what will happen to the slope of the consumption function?
Answers
If the mpc increases in value, the consumption function will become steeper.
What is MPC ?
MPC is an advanced method of process control that is used to control a process while satisfying a set of constraints. In economics, the marginal propensity to consume is a metric that quantifies induced consumption, the concept that the increase in personal consumer spending occurs with an increase in disposable income. The proportion of disposable income which individuals spend on consumption is known as propensity to consume. MPC is the proportion of additional income that an individual consumes.
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if f(x)=4x-1 and g(x)=x^2+7 ,find G(f(x))
Answers
Answer:
\(g(f(x))=(4x-1)^2+7=16\,x^2-8x+8\)
Step-by-step explanation:
Given:
\(f(x)=4x-1\\and \\g(x)=x^2+7\)
Then the composition of functions:
\(g(f(x))=g(4x-1)=(4x-1)^2+7= (16\,x^2-8x+1)+7=16\,x^2-8x+8\)
where we have written the final functional expression in its standard form.
The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 9.5 to 24 on the number line. A line in the box is at 15.5. The lines outside the box end at 2 and 30. The graph is titled Burger Quick.
Which drive-thru typically has more wait time, and why?
Burger Quick, because it has a larger median
Burger Quick, because it has a larger mean
Super Fast Food, because it has a larger median
Super Fast Food, because it has a larger mean
Question 2
The box plot represents the number of tickets sold for a school dance.
A horizontal line labeled Number of Tickets sold that starts at 8, with tick marks every one unit up to 30. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 21 on the number line. A line in the box is at 19. The lines outside the box end at 10 and 27.
Which of the following is the appropriate measure of center for the data, and what is its value?
The mean is the best measure of center, and it equals 19.
The median is the best measure of center, and it equals 4.
The median is the best measure of center, and it equals 19.
The mean is the best measure of center, and it equals 4.
Question 3
A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
5, 5, 6, 8, 10, 15, 18, 20, 20, 20, 20, 20, 20
A graph titled Donations to Charity in Dollars. The x-axis is labeled 1 to 5, 6 to 10, 11 to 15, and 16 to 20. The y-axis is labeled Frequency. There is a shaded bar up to 2 above 1 to 5, up to 3 above 6 to 10, up to 1 above 11 to 15, and up to 7 above 16 to 20.
Which measure of variability should the charity use to accurately represent the data? Explain your answer.
The range of 13 is the most accurate to use, since the data is skewed.
The IQR of 13 is the most accurate to use, since the data is skewed.
The range of 20 is the most accurate to use to show that they have plenty of money.
The IQR of 20 is the most accurate to use to show that they need more money.
Question 4
The circle graph describes the distribution of preferred transportation methods from a sample of 400 randomly selected San Francisco residents.
circle graph titled San Francisco Residents' Transportation with five sections labeled walk 40 percent, bicycle 8 percent, streetcar 15 percent, bus 10 percent, and cable car 27 percent
Which of the following conclusions can we draw from the circle graph?
Together, Streetcar and Cable Car are the preferred transportation for 168 residents.
Together, Walk and Streetcar are the preferred transportation for 55 residents.
Bus is the preferred transportation for 45 residents.
Bicycle is the preferred transportation for 50 residents.
Question 5
The line plot displays the number of roses purchased per day at a grocery store.
A horizontal line starting at 1 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 1 and 2. There are two dots above 8. There are three dots above 6, 7, and 9.
Which of the following is the best measure of variability for the data, and what is its value?
The range is the best measure of variability, and it equals 8.
The range is the best measure of variability, and it equals 2.5.
The IQR is the best measure of variability, and it equals 8.
The IQR is the best measure of variability, and it equals 2.5.
Question 7
At a recent baseball game of 5,000 in attendance, 150 people were asked what they prefer on a hot dog. The results are shown.
Ketchup Mustard Chili
63 27 60
Based on the data in this sample, how many of the people in attendance would prefer mustard on a hot dog?
900
2,000
2,100
4,000
Question 8
The number of milligrams of Vitamin C from 100 different gummy vitamins sold in the world was collected.
Which graphical representation would be most appropriate for the data, and why?
Box plot, because the median can easily be determined from the large set of data
Stem-and-leaf plot, because you can see the shape of the data
Histogram, because it shows each individual data point
Bar chart, because the data is categorical
Answers
Burger Quick, because it has a larger median.
How to explain the informationBurger Quick typically has more wait time because it has a larger range (30-2=28) compared to Super Fast Food (27-3=24) and also has a larger interquartile range (IQR) (24-9.5=14.5) compared to Super Fast Food (15.5-8.5=7), indicating more variability in the wait times. The fact that Burger Quick's median (15.5) is larger than Super Fast Food's median (12) reinforces this conclusion.
Therefore, the correct answer is: Burger Quick, because it has a larger median.
Answer 2: The appropriate measure of center for this data is the median, which is represented by the line in the box at 19. This is because the data is skewed, with a longer tail to the right, and the median is less sensitive to extreme values compared to the mean. Therefore, the correct answer is: The median is the best measure of center, and it equals 19.
Answer 3: The measure of variability that the charity should use to accurately represent the data is the IQR (Interquartile Range), which is the range of the middle 50% of the data. The reason for this is that the data is skewed to the right, with many values concentrated in the upper range of the data, and the IQR is less sensitive to outliers compared to the range.
The IQR for this data is 20-10=10, which represents the spread of the middle 50% of the data. Therefore, the correct answer is: The IQR of 20 is the most accurate to use, since the data is skewed.
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