the average house has 15 paintings on its walls. is the mean larger for houses owned by teachers? the data show the results of a survey of 12 teachers who were asked how many paintings they have in their houses. assume that the distribution of the population is normal. round your mean and standard deviation to three decimal places when doing these calculations.

Answer:

200 ft^3

Step-by-step explanation:

Volume of rectangular prism equation is

\(V=lwh\)

steps in attachment

A.Michel can buy 18 Fudge centres, 18 Nut clusters, and 18 Truffles. B.herefore, Michel will spend exactly $38.70. C.Total cost = (f * 0.60) + (n * 0.75) + (t * 0.80) Total cost = $38.70

a) To determine how many of each type of chocolate Michel can buy and stay within his budget, we need to divide his budget by the price of each type of chocolate and find the smallest whole number that satisfies all three conditions.

Price of Fudge centres: $0.60

Price of Nut clusters: $0.75

Price of Truffles: $0.80

Let's calculate the maximum quantity for each type of chocolate:

Fudge centres: $15.00 / $0.60 = 25 (rounded down)

Nut clusters: $15.00 / $0.75 = 20

Truffles: $15.00 / $0.80 = 18.75 (rounded down)

To stay within the budget and have an equal number of each type, Michel can buy 18 Fudge centres, 18 Nut clusters, and 18 Truffles.

b) To calculate exactly how much Michel will spend, we multiply the quantity of each type by their respective prices and sum them up:

Total cost = (Quantity of Fudge centres * Price of Fudge centres) + (Quantity of Nut clusters * Price of Nut clusters) + (Quantity of Truffles * Price of Truffles)

Total cost = (18 * $0.60) + (18 * $0.75) + (18 * $0.80)

Total cost = $10.80 + $13.50 + $14.40

Total cost = $38.70

Therefore, Michel will spend exactly $38.70.

c) The algebraic expression representing the total amount Michel will spend is:

Total cost = (f * 0.60) + (n * 0.75) + (t * 0.80)

Substituting the quantities from part (a):

Total cost = (18 * 0.60) + (18 * 0.75) + (18 * 0.80)

Total cost = $10.80 + $13.50 + $14.40

Total cost = $38.70

The amount obtained in part (b) is equal to the amount calculated using the algebraic expression, which confirms the accuracy of the calculations.

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The true statement about the function of area of by rectangle and width of rectangle are:

The correct answer option is options A and D

A rectangle is a quadrilateral having opposing sides parallel and four right angles.

At point (x, y) = (10, 100) the area is maximum.

This means that the area of the rectangle is maximum when width is 10m.

If the width of the rectangle is more than 10m, the area reduces or decreases.

Therefore, the statement Greater width relates to greater area as long as the width is more than 10 m is false.

The statement "To get the greatest area, the width should be 20" is false.

Complete question:

Simon has a certain length of fencing to enclose a rectangular area. The function A, models give the rectangles area (in square meters) as a function of its width (in meters).

Wlhich of these statements are true?

A. Greater width relates to greater area as long as the width is less than 10.

B. Greater width relates to greater area as long as the width is more than 10.

C. To get the greatest area, the width should be 10

D. To get the greatest area, the width should be 20

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The given statement, "Block designs result only from observing subjects several times, each time with a different treatment," is false because block designs can be created by observing subjects several times with the same treatment as well.

Block designs involve dividing subjects into homogeneous groups or blocks based on certain characteristics, and within each block, subjects receive different treatments.

By doing so, the effects of confounding variables can be minimized, allowing for more accurate analysis of treatment effects. Thus, block designs can be used to compare treatments within subjects observed multiple times, whether the treatments are the same or different.

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Answer:

5/3*1/5= 1/3

Step-by-step explanation:

change the mixed fraction into improper fraction which is 1*3+2=5

then multiply

The given expressions, when A=1, B=0, and C=1, X evaluates to 1.001; when A=B=C=1, X evaluates to 1.111; and when A=B=C=0, X evaluates to 0.000. These evaluations are based on the given values of A, B, and C, and the notation ¯¯¯¯¯¯BC represents the complement of BC.

To evaluate the expression X = A.¯¯¯¯¯¯BC, we substitute the given values of A, B, and C into the expression.

(a) For A = 1, B = 0, and C = 1:

X = 1.¯¯¯¯¯¯01

To find the complement of BC, we replace B = 0 and C = 1 with their complements:

X = 1.¯¯¯¯¯¯01 = 1.¯¯¯¯¯¯00 = 1.001

(b) For A = B = C = 1:

X = 1.¯¯¯¯¯¯11

Similarly, we find the complement of BC by replacing B = 1 and C = 1 with their complements:

X = 1.¯¯¯¯¯¯11 = 1.¯¯¯¯¯¯00 = 1.111

(c) For A = B = C = 0:

X = 0.¯¯¯¯¯¯00

Again, we find the complement of BC by replacing B = 0 and C = 0 with their complements:

X = 0.¯¯¯¯¯¯00 = 0.¯¯¯¯¯¯11 = 0.000

In conclusion, when A = 1, B = 0, and C = 1, X evaluates to 1.001. When A = B = C = 1, X evaluates to 1.111. And when A = B = C = 0, X evaluates to 0.000. The evaluation of X is based on substituting the given values into the expression A.¯¯¯¯¯¯BC and finding the complement of BC in each case.

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The  requried rationalized form of 1/(7-3√2) is (7+3√2)/31.

To rationalize the denominator, we need to eliminate the radical in the denominator. To do this, we can multiply the numerator and denominator by the conjugate of the denominator, which is 7+3√2:

1/(7-3√2) * (7+3√2)/(7+3√2) = (7+3√2)/(49-18) = (7+3√2)/31

Therefore, the rationalized form of 1/(7-3√2) is (7+3√2)/31.

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Using the binomial distribution, it is found that there is a 0.242 = 24.2% probability that exactly 2 are dressed inappropriately.

The formula is:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

The values of the parameters are given as follows:

n = 40, p = 0.07.

The probability that exactly 2 are dressed inappropriately is given by P(X = 2), hence:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 2) = C_{40,2}.(0.07)^{2}.(0.93)^{38} = 0.242\)

0.242 = 24.2% probability that exactly 2 are dressed inappropriately.

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Answer:

Option (3)

Step-by-step explanation:

Given: EF = 10x + 20

           FG = 43

           EG = 183

From the figure attached,

Length of segment EF + length of segment FG = length of segment EG

By substituting the values of each segment in the equation,

(10x + 20) + 43 = 183

10x + 20 = 183 - 43

10x = 140 - 20

x = \(\frac{120}{10}\)

x = 12

Therefore, x = 12 will be the answer.

Option (3) will be the correct option.

Based on the survey results, a typical parent would spend around $44 on their child's birthday gift, with a margin of error of approximately $2.9 at a 99% confidence level.

To estimate how much a typical parent would spend on their child's birthday gift, we use the sample mean and standard deviation as estimates of the population parameters. The sample mean of $44 serves as the point estimate for the population mean.

To determine the margin of error, we use the standard error, which is the standard deviation divided by the square root of the sample size. In this case, the standard error is approximately $2.5 (standard deviation of $10 divided by the square root of 20). Multiplying the standard error by the critical value corresponding to a 99% confidence level (z-value of 2.58 for a large sample size) gives us the margin of error.

Therefore, the typical amount spent on a child's birthday gift is estimated to be $44, with a margin of error of approximately $2.9. This means that we can be 99% confident that the true mean amount spent by parents falls within the range of $41.1 to $46.9.

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Answer:

7 and 5 are congruent

Step-by-step explanation:

which pair of angles is congruent meaning which pair of angles is the same when looking at the angles given angles 5 and 7 are the same

Using it's concept, it is found that the average rate of change of the function during the interval from 0 to 2 seconds is given by:

B. -32 ft/s; the average change in altitude of the ball each second over that interval.

The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:

\(r = \frac{f(b) - f(a)}{b - a}\)

In this problem, the function is given by:

f(t) = -16t² + 100.

The outputs are given as follows:

Hence the average rate of change is given by:

r = (36 - 100)/(2 - 0) = -32 ft/s.

And the correct option is:

B. -32 ft/s; the average change in altitude of the ball each second over that interval.

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Answer:

y=1

Step-by-step explanation:

you plug-2 in for x and then the problem looks like this y=-2(3)+7.

then you follow order of operations and multiply-2 and 3, and you get -6 so the problem now looks like y=-6+7.

you then add -6 and 7 and you get 1. now the problem looks like y=1 and you are finished.

Answer:

they only had one pair of trunks

Step-by-step explanation: i hope that helps you

Answer : C] 4√6

Thank you !

The condition for the first dark fringe through a single slit of width w is given by w sin(θ) = λ/2.

The condition for destructive interference at the first dark fringe can be found using the path difference between the two waves.

For the first dark fringe, the path difference between the two waves that pass through the edges of the slit must be half a wavelength:

Δx = λ/2

where Δx is the path difference and λ is the wavelength of the light.

The path difference Δx can be related to the width of the slit w and the angle θ that the diffracted wave makes with the central axis of the slit by:

Δx = w sin(θ)

Therefore, the condition for the first dark fringe can be expressed as:

w sin(θ) = λ/2

The condition for the first dark fringe through a single slit of width w is given by w sin(θ) = λ/2.

This means that if the width of the slit and the wavelength of the light are known, the angle θ at which the first dark fringe occurs can be calculated.

This condition arises due to the interference of the diffracted waves from the edges of the slit. When the path difference between these waves is equal to half a wavelength, the waves interfere destructively and produce a dark fringe.

The first dark fringe is observed at the angle θ for which the path difference between the waves passing through the edges of the slit is equal to λ/2.

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Answer:

The percentile rank of someone who earns $75,000 per year is the 85th percentile.

Step-by-step explanation:

Meaning of percentile:

When a value V is said to be in the xth percentile of a set, x% of the values in the set are lower than V and (100-x)% of the values in the set are higher than V.

In this question:

Working population of 10,500

8,925 people earn less than $75,000 per year.

8925/10500 = 0.85

0.85*100 = 85

The percentile rank of someone who earns $75,000 per year is the 85th percentile.

Answer:

1/2

Step-by-step explanation:

Answer: 12/2 i think

Step-by-step explanation:

Answer: a and b

Step-by-step explanation: lol it obvious

Answer: Quadrilateral, Parallelogram

Step-by-step explanation:

A Quadrilateral is any closed 4 sided figure

A Parallelogram is a quadrilateral with two sets of parallel and opposite sides.

Answer:

Step-by-step explanation:

x - 3y = -16

x + 2y = 4

-x + 3y = 16

x + 2y = 4

5y = 20

y = 4

x + 2(4) = 4

x + 8 = 4

x = -4

(-4, 4)

The amount of water dispensed, y, as a function of the number of minutes, x for Marty's new energy-saving showerhead is y = 1.5x.

Here's the equation of the amount of water dispensed, y, as a function of the number of minutes, x for Marty's new energy-saving shower head:

y = 1.5x

In Marty's house, a standard showerhead dispenses 7 gallons of water per minute. But after Marty changed his showerhead to an energy-saving one, the new showerhead dispenses 1.5 gallons per minute.

Therefore, the function that describes the amount of water dispensed by the energy-saving showerhead is given by:

y = 1.5x where x represents the number of minutes for which the showerhead is used.

Thus, in 1 minute, the energy-saving showerhead will dispense 1.5 gallons of water and in 10 minutes, it will dispense

1.5 x 10 = 15 gallons of water.

Therefore, the amount of water dispensed by the showerhead depends directly on the number of minutes it is used. This relationship is linear since the amount of water dispensed per minute is constant.

In general, the function can be represented as:

y = kx where k is the rate of water flow per minute.

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1.a.  The solution to the system of equations is (1, 6).

b. We know that the two lines in this system of equations are not parallel because their slopes are not equal

2. This tells us that the two lines are parallel and do not intersect.

3.a The system of equation that model the pproblem is 2.4x + 1.25y - 1.25x - 1.25y = 136.5 - 96.25 which can be solved as Mr. Perrins’s class sold 35 packs of peanut butter cookies and Mr. Woods’s class sold 42 bottles of milk.

b. Mr. Woods’s class earned less money.

c. Mr. Perrins’s class earned $31.50 more than Mr. Woods’s class.

1. (a) Using the substitution method, we can solve for y in terms of x from the second equation:

y - 4x = 2

y = 4x + 2

Substituting this into the first equation, we get:

3x + 2(4x + 2) = 15

11x = 11

x = 1

Substituting x = 1 into the equation y = 4x + 2, we get:

y = 6

Therefore, the solution to the system of equations is (1, 6).

(b) We know that the two lines in this system of equations are not parallel because their slopes are not equal. We also know that they are not the same line because their y-intercepts are different. Therefore, they intersect at a single point, which is the solution we found in part (a).

2. Using the linear combination (elimination) method, we can eliminate y by multiplying the first equation by 2 and adding it to the second equation:

4x - 16y = 12

-4x + 16y = -14

Adding the two equations, we get:

0 = -2

This is a contradiction, which means that the system of equations has no solution. This tells us that the two lines are parallel and do not intersect.

3 (a) Let x be the number of packs of peanut butter cookies sold by Mr. Perrins’s class, and y be the number of bottles of milk sold by Mr. Woods’s class. Then we can write a system of equations based on the information given:

2.4x + 1.25y = 136.5

x + y = 77

To solve this system, we can multiply the second equation by 1.25 and subtract it from the first equation:

2.4x + 1.25y - 1.25x - 1.25y = 136.5 - 96.25

1.15x = 40.25

x ≈ 35

Substituting x = 35 into the equation x + y = 77, we get:

35 + y = 77

y = 42

Therefore, Mr. Perrins’s class sold 35 packs of peanut butter cookies and Mr. Woods’s class sold 42 bottles of milk.

(b) To determine which class earned less money, we can calculate the total revenue for each class:

Total revenue for Mr. Perrins’s class = 2.4(35) = 84

Total revenue for Mr. Woods’s class = 1.25(42) = 52.5

Therefore, Mr. Woods’s class earned less money.

(c) The difference in revenue between the two classes is:

84 - 52.5 = 31.5

Therefore, Mr. Perrins’s class earned $31.50 more than Mr. Woods’s class.

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Answer:

\(\huge\boxed{\sf x = 60\°}\)

Step-by-step explanation:

So,

100 + x + 20 = 180

x + 120 = 180

x = 180 - 120

x = 60°

\(\rule[225]{225}{2}\)

The maintenance cost expected to be incurred during July is $9,400. This corresponds to option C in the given choices.

To determine the maintenance cost expected to be incurred during July, we need to substitute the planned machine time of 9,000 hours into the cost formula Y = $5,800 + $0.40X.

Plugging in X = 9,000 into the formula, we get:

Y = $5,800 + $0.40(9,000)

Y = $5,800 + $3,600

Y = $9,400

Therefore, the maintenance cost expected to be incurred during July is $9,400. This corresponds to option C in the given choices.

The cost formula Y = $5,800 + $0.40X represents the fixed cost component of $5,800 plus the variable cost component of $0.40 per machine-hour. By multiplying the planned machine time (X) by the variable cost rate, we can determine the additional cost incurred based on the number of machine-hours. Adding the fixed cost component gives us the total maintenance cost expected for a given level of machine-time. In this case, with 9,000 hours of planned machine time, the expected maintenance cost is $9,400.

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Answer:

$27.75 and c=6.50p-4.75

Answer:

median 6.5

mean 6.166

range 6

Step-by-step explanation: