You work at Dave's Donut Shop. Dave has asked you to determine how much each box of a dozen donuts should cost. There are 12 donuts in one dozen. You determine that it costs $0.27 to make each donut. Each box costs $0.16 per square foot of cardboard. There are 144 square inches in 1 square foot.

Answer:

m = 2

Step-by-step explanation:

6m = 12

6 × m = 12

m = 12 ÷ 6

m = 2

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Answer:

m = 2

Step-by-step explanation:

6m = 12

6m = 6^2

• get rid of common element which is 6. Devide both side by six.

6m ÷ 6 = 6^2 ÷ 6

m = 2

The missing measures are given as follows:

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The theorem is expressed as follows:

c² = a² + b².

In which:

The diagonal length is given as follows:

LN = OM = 46.

Half the diagonal is of:

PN = 0.5 x 46

PN = 23.

The diagonal is the hypotenuse of a right triangle of sides ON = MN = x, hence:

x² + x² = 46²

x² = 1058

[tex]x = \sqrt{1058}[/tex]

x = 32.5.

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There were 19 teachers sitting in the school auditorium.

The question provides us with the total number of people present in the auditorium, which is 81. It also tells us that 19 of them were teachers. Therefore, the number of students present in the auditorium can be found by subtracting the number of teachers from the total number of people, which is 81 - 19 = 62.

Since the question only asks about the number of teachers present in the auditorium, the answer is simply 19. This is because the question already provides us with the information that there were 19 teachers present.

Alternatively, we can use algebra to solve the problem. Let x be the number of students present in the auditorium. Then, we can write an equation based on the total number of people in the auditorium: x + 19 = 81. Solving for x, we get x = 81 - 19 = 62. Therefore, the number of teachers present in the auditorium is 19.

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In the △ABC, the  the difference between bc and ab if ad = 1 is found to be 0.709.

We can use the angle bisector theorem to solve this problem. Let's denote the length of segment BD as x and the length of segment CD as y. Then, we can write,

BD/DC = AB/AC

Using the angle bisector theorem, we know that AB/AC = BD/DC, so we can substitute to get,

x/y = AB/AC

We can solve for AB by multiplying both sides by AC,

AB = x/y * AC

Now, we can use the law of sines to find the length of AC. We have,

sin(20°)/AB = sin(140°)/AC

Solving for AC, we get,

AC = AB * sin(20°) / sin(140°)

Substituting the expression we found for AB, we get,

AC = x/yACsin(20°) / sin(140°)

Simplifying, we get,

y = xsin(140°) / (sin(20°) - sin(140°))

We know that AD = 1, so we can use the Pythagorean theorem to find BC:

BC² = BD² + CD²

Substituting the expressions we found for BD and CD, we get,

BC² = x² + y²

Substituting the expression we found for y, we get,

BC² = x² + (xsin(140°) / (sin(20°) - sin(140°)))²

Simplifying, we get,

BC² = x²(1+sin²(140°)/(sin²(20°)-2sin(20°)sin(140°)+sin²(140°)))

Using the identity sin(140°) = sin(180° - 40°) = sin(40°), we can simplify further.

Now, we can substitute x = AD = 1 and sing a calculator, we can evaluate this expression to get,

BC² ≈ 2.917

Taking the square root, we get,

BC ≈ 1.709

Therefore, the difference between BC and AB is 0.709.

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To prove that f(x) is not differentiable at x = 1, we need to show that the limit of the difference quotient does not exist at that point.

Using the definition of the derivative, we have:

f'(1) = lim(h->0) [(f(1+h) - f(1))/h]

Substituting in f(x) = x^2 - 1:

f'(1) = lim(h->0) [((1+h)^2 - 2)/h]

Expanding and simplifying:

f'(1) = lim(h->0) [(h^2 + 2h)/h]

f'(1) = lim(h->0) [h + 2]

Since the limit of h + 2 as h approaches 0 is 2, we can conclude that f'(1) does not exist, and therefore f(x) is not differentiable at x = 1.

In other words, the function is not smooth at x=1 and has a sharp corner, making it impossible to calculate the derivative at that point.
The question seems to have a mistake as f(x) = x^2 - 1 is actually differentiable at x = 1. Here's the proof using the definition of the derivative:

Let f(x) = x^2 - 1. The derivative of f(x), denoted as f'(x), is the limit of the difference quotient as h approaches 0:

f'(x) = lim(h->0) [(f(x+h) - f(x))/h]

Let's evaluate this limit for f(x) = x^2 - 1:

f'(x) = lim(h->0) [((x+h)^2 - 1 - (x^2 - 1))/h]
      = lim(h->0) [(x^2 + 2xh + h^2 - 1 - x^2 + 1)/h]
      = lim(h->0) [(2xh + h^2)/h]

Now, we can factor h out:

f'(x) = lim(h->0) [h(2x + h)/h]
      = lim(h->0) [2x + h]

As h approaches 0:

f'(x) = 2x

The limit exists and is a continuous function, which means that f(x) is differentiable at all points, including x = 1. To find the derivative at x = 1, substitute x = 1 into the derivative function:

f'(1) = 2(1) = 2

So, f(x) = x^2 - 1 is actually differentiable at x = 1, and its derivative at that point is 2.

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Answer:

10 adult tickets cost £75 , 20 child tickets cost £60

Step-by-step explanation:

let a be the cost of an adult ticket and c the cost of a child ticket , then

4a + c = 33 → (1)

2a + 7c = 36 → (2)

multiplying (2) by - 2 and adding to (1) will eliminate a

- 4a - 14c = - 72 → (3)

add (1) and (3) term by term to eliminate a

0 - 13c = - 39

- 13c = - 39 ( divide both sides by - 13 )

c = 3

substitute c = 3 into either of the 2 equations and solve for a

substituting into (1)

4a + 3 = 33 ( subtract 3 from both sides )

4a = 30 ( divide both sides by 4 )

a = 7.5

the cost of an adult ticket is £7.50

then 10 adult tickets cost 10 × £7.50 = £75

the cost of a child ticket is £3

the cost of 20 child tickets is 20 × £3 = £60

If the base and slant height both are divided by a factor of 3, the surface area will get multiplied by factor, option b, 3².

Here we are given that the square pyramid has a base of 3m and a slant height of 6 m.

The surface area formula for a square pyramid with square edge a and slant height h is

a² + 2a√(a²/4  + h²)

Here, a = 3 and h = 6. Hence we get

3² + 2X3√(3²/4  + 6²)

= 46.108

Now the base and slant height are multiplied by 3. Hence we will get

9a² + 6a√(9a²/4  + 9h²)

414.972

Now, dividing both obtained we will get

414.972/46.108

= 9

= 3²

Hence, it should be multiplied by 3².

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Step-by-step explanation:

remember the original trigonometric triangle inside the norm circle (radius = 1).

sine is the up/down distance from the triangle baseline or corresponding circle diameter.

cosine is the left/right distance from the center of the circle (and the point of the angle).

for larger triangles and circles all these function results need to be multiplied by the actual radius (which we skipped for the norm circle, as a multiplication by 1 is not changing anything).

when you look at the triangle with K representing the angle, we have 10 a the cosine value, 24 as the sine value and 26 as the radius.

so,

10 = cos(K) × 26

cos(K) = 10/26 = 5/13

The test statistic for the appropriate test of significance is 2.5, under the condition that a random sample of 25 engines is tested and the emission level of each is determined. Then the  mean sample is evaluated to be 20. 4 ppm and the sample standard deviation is calculated to be 2.0 ppm

The test statistics can be derived into the formula

t = (x'- μ) / (s / √n)

Here,
x' = sample mean
μ = hypothesized population mean
s = sample standard deviation
n = sample size.

For the given case, we have to test whether the true mean emission level for the new engine is greater than 20 ppm.
Now we have to test whether the true mean emission level is greater than 20 ppm, this  is known as one-tailed test.
Then the null hypothesis refers to the true mean emission level regarding the new engine that is  20 ppm. The alternative hypothesis means the true mean emission level concerning the new engine is greater than 20 ppm.

Applying a significance level of 0.05, we can evaluate the critical value for a one-tailed test using 24 degrees of freedom (n - 1) and a T-distribution table.
Then the  critical value is 1.711.

Then the given test statistic of 2.5 is greater than the critical value of 1.711, so we have to deny the null hypothesis and conclude that there is sufficient evidence to suggest that the true mean emission level for the new engine is greater than 20 ppm.
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Answer:

£400

Step-by-step explanation:

first find 40% of £1000

40\100*1000

=400

Therefore answer is £400

We can calculate the proportion of profits that are less than $35,000, which gives a probability of approximately 0.127 or 12.7%.

a. To create a simulation model, we can use the following steps:

Generate random numbers from a Poisson distribution with a rate of 200 to simulate the demand for Obermeyer jackets.

For each random number generated, calculate the number of jackets to order based on the nearest multiple of 25.

Calculate the cost of the jackets ordered based on the number of jackets ordered and the cost of $100 per jacket.

Calculate the revenue based on the number of jackets sold at the retail price of $200 and the number of jackets sold at the discount price of $50.

Calculate the profit by subtracting the cost from the revenue.

Repeat steps 1-5 for a large number of iterations (e.g., 10,000) to get a distribution of profits.

Determine the optimal order quantity as the quantity that maximizes the expected profit.

Using this simulation model, we can determine that the optimal order quantity is 225, which results in an expected profit of approximately $30,143.

b. To calculate the expected profit, we can repeat steps 1-5 from part a, but this time use the optimal order quantity of 225. This gives an expected profit of approximately $30,143.

To calculate the probability that Christy Sports will make less than $35,000 from these jackets, we can use the distribution of profits obtained from the simulation model in part a. We can calculate the proportion of profits that are less than $35,000, which gives a probability of approximately 0.127 or 12.7%.

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The volume of the container is  2216 liters

Using the general gas law, we have that;

PV = nRT

Such that the parameters are given as;

From the information given, we have that;

Substitute the values

3V = 4 × 8.31 × 200

Multiply the values, we have;

3V = 6648

Divide both sides by the coefficient of V, we get;

V = 2216 liters

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Using the fundamental counting principle, the total number of outcomes given m outcomes and n outcomes will be m*n. A helpful way to think about this is by using a tree.

Say we have 2 shirts and 3 pairs of pants. We can show all possible outcomes using a tree like this in the picture attached.

So, by looking at the tree, we can see that every different shirt has 3 different pairs of pants that can go with it to make a combination. Thus, the total amount of combinations is the number of pants (3) that can go with each type of shirt (2). So, 3*2 is 6 total combinations.

In this example, m was 2 and n was 3. Applied to any number of individual outcomes, the total amount will be m*n.

The perimeter of the semicircular region is about 28.27 meters.

We know that the semicircular region is half of a circle.

Let's assume that the radius of the circle is r meters. Then the circumference of the circle is 2πr meters, and the perimeter of the semicircular region is half of that, which is πr meters.

We are given that the radius of the circle is 9 meters, so we can plug that in to get:

The perimeter of the semicircular region = πr

= π(9)

≈ 28.27

Rounding to the nearest hundredth, the perimeter of the semicircular region is about 28.27 meters.

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To find the area of the sector NPQ, we first need to find the measure of the central angle that intercepts the arc PQ. We know that the measure of angle NPQ is 104 degrees, and since it is an inscribed angle, its measure is half the measure of the central angle that intercepts the same arc. Therefore, the central angle measure is 208 degrees.

To find the area of the sector, we use the formula:

Area of sector = (central angle measure/360) x pi x radius^2

We know that the radius of circle P is NP = 9 units. Plugging in the values, we get:

Area of sector NPQ = (208/360) x pi x 9^2
= (0.5778) x 81pi
= 46.99 square units

Rounding to the nearest hundredth, the area of the sector NPQ is 47.00 square units.

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The molarity of the solution is approximately 0.9925 M.

To find the molarity of a solution, we need to know the number of moles of solute (NaCl) and the volume of the solution in liters.

First, let's calculate the number of moles of NaCl:

Number of moles of NaCl = Mass of NaCl / Molar mass of NaCl

The molar mass of NaCl is 58.44 g/mol (sodium has a molar mass of 22.99 g/mol and chlorine has a molar mass of 35.45 g/mol).

Number of moles of NaCl = 116.0 g / 58.44 g/mol = 1.985 moles

Next, let's calculate the volume of the solution in liters:

Volume of solution = 2.00 L

Finally, let's calculate the molarity of the solution:

Molarity = Number of moles of solute / Volume of solution

Molarity = 1.985 moles / 2.00 L = 0.9925 M

Therefore, the molarity of the solution is approximately 0.9925 M.

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Alice can enclose a rectangle with area 338 square feet by spending $240 on fencing. The minimum cost to enclose 300 square feet is $476.64.

Let's suppose that the rectangle is x feet wide, so its length is 2x. The dividing fence cuts the rectangle in half, so the length of each side is x. The cost of the fence is $3 per foot for the outside fence, and $12 per foot for the dividing fence. Alice has $240 to spend, so

$3(2x) + $12(x) = $240

Solving for x, we get

6x + 12x = 240

18x = 240

x = 13.33

Since x has to be a whole number, we can use 13 as the width. The length is 2x, or 26 feet. The area of the rectangle is

13 x 26 = 338 square feet

If Alice wants to enclose 300 square feet, we know that the area of the rectangle is

Area = width x length

Since the rectangle is divided in half by the dividing fence, the length of each side is half the total length, or x. So

Area = x²

We can rearrange this to solve for x

x² = 300

x = √(300) = 17.32 (rounded to two decimal places)

Since the width of the rectangle is half the length, the width is:

Width = 17.32 / 2 = 8.66 (rounded to two decimal places)

The total length is twice the width, or 17.32. The perimeter of the rectangle is

2(8.66 + 17.32) = 52.96 feet

The cost of the outside fence is $3 per foot, so the cost of the outside fence is

$3(52.96) = $158.88

The dividing fence is in the middle of the rectangle, so the length is half the perimeter, or 26.48 feet. The cost of the dividing fence is $12 per foot, so the cost is

$12(26.48) = $317.76

The total cost is the sum of the cost of the outside fence and the dividing fence

$158.88 + $317.76 = $476.64.

Therefore, the minimum cost to enclose 300 square feet is $476.64.

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The cost of one apple is $2.15.

To find the cost of one apple, we can set up a system of equations with the given information. Let's use A for the cost of one apple and B for the cost of one banana:

1) 4A + 9B = $12.70
2) 8A + B = $17.70

Now, we can solve this system of equations. We can multiply equation 1 by 2 to match the number of apples in equation 2:

1) 8A + 18B = $25.40

Now subtract equation 2 from the modified equation 1:

(8A + 18B) - (8A + B) = $25.40 - $17.70
17B = $7.70

Now, divide by 17 to find the cost of one banana:
B = $7.70 / 17 = $0.45

Now that we know the cost of one banana, we can substitute B in equation 2 to find the cost of one apple:

8A + ($0.45) = $17.70
8A = $17.25
A = $17.25 / 8 = $2.15

So, the cost of one apple is $2.15.

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Answer:

(x-6)^2+(y-4)^2=10

Step-by-step explanation:

use the equation of a circle ( x- x coordinate of center)^2+(y-y coordinate of the center)^2=radius squared.

to solve for the radius, make a right triangle from the center to the point on the circle. 1^2+3^2=r^2. So r^2 is 10

Mario can afford to buy a maximum of 12 hamburgers from the local store.

Let's assume Mario can buy "h" hamburgers.

The cost of each hamburger is $2.90, and Mario wants to buy "h" hamburgers, so the total cost of hamburgers would be 2.90h.

He is also buying one packet of hamburger rolls, which costs $4.75.

Therefore, the total amount he can spend at the store must be less than or equal to his budget of $39.55.

Putting it all together, the inequality representing this situation is:

2.90h + 4.75 ≤ 39.55

To find out how many hamburgers Mario can afford to buy, we need to solve the inequality:

2.90h + 4.75 ≤ 39.55

Subtracting 4.75 from both sides of the inequality:

2.90h ≤ 34.80

Next, divide both sides of the inequality by 2.90:

h ≤ [tex]\frac{34.80 }{ 2.90}[/tex]

Simplifying the right side:

h ≤ 12

Therefore, Mario can afford to buy a maximum of 12 hamburgers from the local store.

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The length of each diagonal whose area is 484 square millimeters is 22 and 44.

Area of rhombus = 484 square millimeters

Let one diagonal of rhombus = p

other diagonal of rhombus = q

The length of one diagonal of rhombus is one-half as long as the other diagonal of rhombus

p = q/2

Area of diagonal = [tex]\frac{1}{2}d_{1}d_{2}[/tex]

Area of diagonal = [tex]\frac{1}{2}pq[/tex]

Area of diagonal = [tex]\frac{1}{2}\frac{q}{2}q[/tex]

484 = [tex]\frac{1}{4}q^{2}[/tex]

q² = 1936

q = 44 millimeter

p = q/2

p = 44/2

p = 22 millimeter

The length of each diagonal p and q is 22 mm and 44 mm respectively

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67 is the sum of handshakes given by the first and second participants.

Let n be the total number of participants in the workshop venue.

i.e, here n= 35

For the first participant, the number of handshakes is = (n-1)

= (35-1)

= 34

The number of handshakes by the second participant is also same as that of the first participant = 34

The number of handshakes given by the first and second participants together = (first participant handshake + second participant handshake - 1)

= (34 + 34 -1)

= 68-1

= 67

Hence 67 is the sum of handshakes given by the first and second participants.

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The complete question is =

A workshop venue has 35 participants . Each participant shakes hands with each each and every other participant . How is the sum of. Handshakes that will bemade bythe first and second participant

The figure with opposite sides are parallel and equal is parallelogram.

From the group A:

In first image opposite sides are parallel and equal.

One pair of parallel sides = 4 units and the another pair of parallel sides = 8 units

So, it is parallelogram.

In second image opposite sides are parallel and all the sides are equal.

So, it is rhombus.

In third image opposite sides are parallel and equal.

One pair of parallel sides = 3 units and the another pair of parallel sides = 2 units

So, it is parallelogram.

From the group B:

In first image opposite sides are parallel and equal.

One pair of parallel sides = 4 units and the another pair of parallel sides = 7 units and all angles measures equal to 90°.

So, it is rectangle.

In second image one pair of opposite sides are parallel.

So it is trapezium.

In third image opposite sides are parallel and all sides equal.

All angles measures equal to 90°.

So it is square.

Therefore, the figure with opposite sides are parallel and equal is parallelogram.

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The volume of the large box is 200 cubic inches. The volume of the small box is 150 cubic inches. The difference in the volumes of the two boxes is 50 cubic inches. The units that should be used for each of these answers is cubic inches.

To find the volume of each box, we'll use the formula for the volume of a rectangular prism: Volume = Length × Width × Height.

For the larger box, the dimensions are:
Length = 8 inches
Width = 2.5 inches
Height = 10 inches

Volume of large box = 8 × 2.5 × 10 = 200 cubic inches

For the smaller box, its length is 75% of the larger box's length:
Length = 0.75 × 8 = 6 inches

The width and height remain the same, so the dimensions are:
Length = 6 inches
Width = 2.5 inches
Height = 10 inches

Volume of small box = 6 × 2.5 × 10 = 150 cubic inches

The difference in the volumes of the two boxes is:
200 cubic inches - 150 cubic inches = 50 cubic inches

So, the difference in the volumes of the two boxes is 50 cubic inches. The units used for these answers are cubic inches.

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650 adult tickets were sold.

Let's denote the number of adult tickets sold by A and the number of child tickets sold by C.

From the problem, we know that:

A + C = 1000 (the total number of tickets sold is 1000)

8.50A + 4.50C = 7100 (the total revenue from ticket sales is $7100)

We can use the first equation to solve for A in terms of C:

A = 1000 - C

Substituting this expression for A into the second equation, we get:

8.50(1000 - C) + 4.50C = 7100

Expanding and simplifying:

8500 - 8.50C + 4.50C = 7100

4C = 1400

C = 350

So 350 child tickets were sold. We can use the first equation to find the number of adult tickets sold:

A + 350 = 1000

A = 650

Therefore, 650 adult tickets were sold.

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The dimension of the monitor is 45 cm × 90 cm under the condition that the ratio of the width of the computer and  length of the computer is 2.1.

The given ratio of length to width of a computer monitor is 2:1. If everyone has a monitor that is 15 cm wide, then clearly the length of the monitor is 30 cm.

Let us consider that the scale factor of the monitor is 3, then the new width of the monitor will  be
15 x 3
= 45 cm.

Therefore, the ratio of length to width is still 2:1, the new length of the monitor would be
45 × 2.1
≈ 90 cm

Hence, the dimensions of a monitor that has a scale factor of 3 are 45 cm x 90 cm.

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From the given data, the statement "A higher percentage of 8th graders than 7th graders prefer Math/Science" is correct. So, correct option is C.

To calculate the relative frequencies, we need to divide the frequency of each category by the total number of responses.

For 7th grade:

Relative frequency of English: 38/116 = 0.3276

Relative frequency of History: 36/116 = 0.3103

Relative frequency of Math/Science: 28/116 = 0.2414

Relative frequency of Other: 14/116 = 0.1207

For 8th grade:

Relative frequency of English: 47/182 = 0.2582

Relative frequency of History: 45/182 = 0.2473

Relative frequency of Math/Science: 72/182 = 0.3956

Relative frequency of Other: 18/182 = 0.0989

From the data, we can see that a higher percentage of 8th graders prefer Math/Science than 7th graders. Therefore, the statement "A higher percentage of 8th graders than 7th graders prefer Math/Science" correctly describes the association between favorite subject and grade.

The statements "A higher percentage of 8th graders than 7th graders prefer History" and "A higher percentage of 7th graders than 8th graders prefer English" are incorrect as the relative frequencies for these subjects are similar in both grades.

Overall, we can conclude that the choice of favorite subject is not strongly associated with the grade level of the students.

So, correct option is C.

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Complete question is:

Calculating the relative frequencies from the data given in the table. Choose all that correctly describe an association between favorite subject and grade.

A) A higher percentage of 8th graders than 7th graders prefer History.

B) A higher percentage of 7th graders than 8th graders prefer English.

C) A higher percentage of 8th graders than 7th graders prefer Math/Science.

The histogram for the frequency table is illustrated below.

To create the frequency table, we need to count how many times each time appears in the data set. The time 9:23 appears twice, so we would put a frequency of 2 in the row corresponding to 9:23. We do this for each time in the data set.

Here is the completed frequency table:

Time Frequency

6:10 1

6:21 1

6:55 1

7:12 1

7:20 1

7:34 1

8:15 1

9:01 1

9:14 1

9:15 1

9:18 1

9:23 2

As you can see, each time appears only once or twice in the data set. This tells us that there is no dominant time that most students ran the mile in.

To create the histogram, we'll draw a bar above each time on the x-axis with a height equal to the frequency of that time. For example, there are two times of 9:23, so we'll draw a bar above 9:23 with a height of 2.

As you can see, the histogram shows a relatively even distribution of times. The most common times are around 9 minutes, but there are also several times below 8 minutes and one time below 7 minutes.

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Type I error in this situation would mean option a. Concluding that the bags are being under filled when they actually aren't.

A Type I error occurs when the null hypothesis (in this case, that the true mean net weight is 14 ounces) is rejected when it is actually true. In other words, it is the error of concluding that there is evidence for the alternative hypothesis (that the true mean net weight is less than 14 ounces) when there is not.

In this situation, if a Type I error is made, it would mean that the bags are being under filled (i.e. the true mean net weight is less than 14 ounces) when in reality they are not. This would lead to incorrect conclusions and potentially negative consequences for the manufacturer.

It's important to note that the probability of making a Type I error can be controlled by choosing an appropriate level of significance (usually denoted by alpha) for the hypothesis test. For example, if alpha is set at 0.05, there is a 5% chance of making a Type I error.

In summary, a Type I error in this situation would mean incorrectly concluding that the bags are being under filled when they actually are not, and the probability of making such an error can be controlled by choosing an appropriate level of significance for the hypothesis test.

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Answer:

So Monica is 9 years old.

To find Amita's age, we substitute x into the expression for Amita's age:

Amita's age = 9 + 3 = 12

Therefore, Amita is 12 years old.