A college cafeteria is looking for a new dessert to offer its 4,000 students. The table shows the preference of 225 students.


Ice Cream Candy Cake Pie Cookies
81 9 72 36 27


Which statement is the best prediction about the number of cookies the college will need?
The college will have about 480 students who prefer cookies.
The college will have about 640 students who prefer cookies.
The college will have about 1,280 students who prefer cookies.
The college will have about 1,440 students who prefer cookies.

Question 14

A random sample of 100 middle schoolers were asked about their favorite sport. The following data was collected from the students.


Sport Basketball Baseball Soccer Tennis
Number of Students 17 12 27 44


Which of the following graphs correctly displays the data?
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44

Question 15

The line plots represent data collected on the travel times to school from two groups of 15 students.

A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4, 6, 14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.

A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9, 18, 20, and 22. There are two dots above 6, 10, 12, 14, and 16. The graph is titled Bus 18 Travel Times.

Compare the data and use the correct measure of center to determine which bus typically has the faster travel time. Round your answer to the nearest whole number, if necessary, and explain your answer.

Bus 18, with a median of 13
Bus 47, with a median of 16
Bus 18, with a mean of 13
Bus 47, with a mean of 16

Answer:

a=60 (12*5=60)

b=7 (45/9=5 5+2=7)

c=62

d=25 (11*5=55 55-30=25)

To rewrite the equation of the circle in graphing form, we need to complete the square for both the x and y terms.

x² + 6x + y² - 4y = -9

Step 1: Move the constant term to the right side of the equation.

x² + 6x + y² - 4y + 9 = 0

Step 2: Group the x terms and the y terms separately.

(x² + 6x) + (y² - 4y) + 9 = 0

Step 3: Complete the square for the x terms. To do this, take half of the coefficient of x (which is 6), square it, and add and subtract it inside the parentheses.

(x² + 6x + 9 - 9) + (y² - 4y) + 9 = 0

(x + 3)² - 9 + (y² - 4y) + 9 = 0

(x + 3)² + (y² - 4y) = 0

Step 4: Complete the square for the y terms. To do this, take half of the coefficient of y (which is -4), square it, and add and subtract it inside the parentheses.

(x + 3)² + (y² - 4y + 4 - 4) = 0

(x + 3)² + (y - 2)² - 4 = 0

Step 5: Move the constant term to the right side of the equation.

(x + 3)² + (y - 2)² = 4

The equation is now in graphing form, which is:

(x - h)² + (y - k)² = r²

where (h, k) is the center of the circle and r is the radius.

Comparing the equation to the graphing form, we see that the center of the circle is (-3, 2) and the radius is 2. Thus, the graph of the circle is centered at (-3, 2) with a radius of 2.

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After answering the presented question, we may conclude that  So the surface area of the ramp, including the front and sides, is 42 square feet.

The surface area of an object indicates the overall space occupied by its surface. The surface area of a three-dimensional form is the entire amount of space that surrounds it. The surface area of a three-dimensional form refers to its full surface area. By summing the areas of each face, the surface area of a cuboid with six rectangular faces may be computed. As an alternative, you may use the following formula to name the box's dimensions: 2lh + 2lw + 2hw = surface (SA). Surface area is a measurement of the total amount of space occupied by the surface of a three-dimensional object (a three-dimensional shape contains height, breadth, and depth).

To find the surface area of the ramp, we need to calculate the area of each face and add them up.

The front face is a rectangle with dimensions 6 ft by 4 ft, so its area is:

Area of front face = length * width = 6 ft * 4 ft = 24 ft²

The two side faces are right triangles with base 6 ft and height 3 ft. The area of each triangle is:

Area of one side face = 1/2 * base * height = 1/2 * 6 ft * 3 ft = 9 ft²

Since there are two side faces, the total area of the side faces is:

Area of side faces = 2 * Area of one side face = 2 * 9 ft² = 18 ft²

Therefore, the total surface area of the ramp is:

Surface area = Area of front face + Area of side faces = 24 ft² + 18 ft² = 42 ft²

So the surface area of the ramp, including the front and sides, is 42 square feet.

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The function has been solved, and f (t) = 15 - 3t, with n days equal to 5.

Given data ,

There were 15 inches of snow on the ground on Monday morning. As the temperature increased, 3 inches of snow had evaporated by Tuesday morning. By Wednesday morning, three more inches had melted, and the pattern persisted.

The following factors affect this situation:

Time: Indicates how many days have elapsed since Monday morning.

Measures how much snow is still on the ground in inches.

Given that the amount of snow is reducing by a given amount every day, the situation may be modelled using a linear function.

f(t)= 15-3t

when f ( t ) = 0

15 = 3t

Divide by 3 on both sides:

t = 5 days

Therefore, after 5 days, all of the snow will have melted.

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Answer:

1. The parameter of interest is the proportion of students in the school who think of their parents or guardians as “strict”. A statistic that the students could use to estimate the parameter is the proportion of students in their sample who think of their parents or guardians as “strict”.

2. The best design for this study is a sample survey. An experiment would involve manipulating the parents' behavior and observing the effect on the students, which is not ethical. An observational study would only observe the behavior without manipulation, but it is not clear what behavior to observe in this case.

3. Here are three questions that could provide objective data related to strictness:

4. An appropriate method for obtaining a sample of 100 students is random sampling. The students could assign each student in the school a number, and then use a random number generator to select 100 numbers. They could then survey the students corresponding to those numbers. Another method could be stratified sampling, where the students divide the school into groups based on grade level, and then randomly sample a proportionate number of students from each group.

Answer:

Step-by-step explanation:

18

A) The probability that the sample mean is within $500 of the population mean for a sample of size 60 is 0.6611

B) The probability that the sample mean is within $500 of the population mean for a sample of size 120 is 0.7362

The EAI (Error of the Estimate) sampling problem is a specific case of the Central Limit Theorem, which states that the distribution of sample means from a population with a finite variance will be approximately normally distributed as the sample size increases.

The formula for calculating the standard error of the mean is

SE = σ/√n

where SE is the standard error, σ is the population standard deviation, and n is the sample size.

For n = 30, SE = 4,000/√30 = 729.16

A. For a sample size of n = 60, SE = 4,000/√60 = 516.40

To find the probability that the sample mean is within $500 of the population mean, we need to calculate the z-score for a range of +/- $500

z = (x - μ) / SE

where x is the sample mean, μ is the population mean, and SE is the standard error.

For a range of +/- $500, the z-scores are

z = ($51,300 - $51,800) / 516.40 = -0.969

z = ($52,300 - $51,800) / 516.40 = 0.969

Using a standard normal distribution table, the area between z = -0.969 and z = 0.969 is 0.6611.

B. For a sample size of n = 120, SE = 4,000/√120 = 368.93

Following the same steps as above, the z-scores for a range of +/- $500 are

z = ($51,300 - $51,800) / 368.93 = -1.364

z = ($52,300 - $51,800) / 368.93 = 1.364

Using the standard normal distribution table, the area between z = -1.364 and z = 1.364 is 0.7362.

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A good prediction for the number of times a 5 will be rolled out of 50 rolls of a 6-sided number cube is 8 times.

Assuming the number cube is fair and each outcome has an equal probability of occurring, we can use the concept of probability to make a prediction for the number of times a 5 will be rolled.

Since there are six possible outcomes, each with a probability of 1/6, the expected frequency of rolling a 5 in one roll is:

1/6 x 50 = 8.33

This means that if the number cube is rolled 50 times, we would expect to see a 5 appear approximately 8.33 times. However, since we cannot roll a fraction of a time, we need to round this number to the nearest whole number.

Rounding 8.33 to the nearest whole number, we get:

8

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Complete question is:

A 6-sided number cube with sides labeled 1,2,3,4,5, and 6 is rolled 50 times. What is a good prediction for the number of times a 5 will be rolled?

Answer:

19.25

Step-by-step explanation:

You add up all three sides which would be 10+3.25+6 to get the awnser 19.25

The standard deviation of the sampling distribution of the sample mean is 0.02.

The standard deviation of the sampling distribution of the sample mean can be calculated using the formula:

σ/√n

Where σ is the population standard deviation and n is the sample size.

In this case, the population standard deviation (σ) is 0.2 and the sample size (n) is 100. Substituting these values in the formula gives:

0.2/√100

Simplifying, we get:

0.2/10 = 0.02

This means that if we were to take multiple random samples of size 100 from the population, the mean of each sample would vary around the population mean of 3.2, with a standard deviation of 0.02.

This is because the standard deviation of the sampling distribution represents the amount of variation in sample means around the population mean.

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The length of wire per unit length is 8.168 cm.

Its function is to produce a regulated magnetic field through a coil twisted into a compact helix. The solenoid is a sort of electromagnet.

The magnetic field inside a solenoid is given by:

B = u*n*I

where B is the magnetic field, u is the permeability of free space, n is the number of turns per unit length, and I is the current.

The number of turns in a solenoid is given by:

N = n*L

where N is the total number of turns, L is the length of the solenoid, and n is the number of turns per unit length.

Therefore, the magnetic field can be written as:

B = u*N*I/L

Rearranging this equation, we get:

L = u*N*I/B

Substituting the given values, we get:

L = (4*pi*10⁻⁷)*(N=?) * (I=18.0 A) / (B=23.0 mT)

The number of turns per unit length is not given, so we cannot determine the total number of turns N. However, we can calculate the length of wire per unit length by using the formula for the circumference of a circle:

C = 2*pi*r

where r is the radius of the solenoid.

Substituting the given values, we get:

C = 2*pi*(d/2) = pi*d = 8.168 cm

Therefore, the length of wire per unit length is 8.168 cm.

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Matching of the equation will be:

A) x= -7

B) x= 3

C) x= 9

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

A) 3(x-5) = 2(x-11) has x= -7 as the solution.

B) 4(3x+7) -5 = 12x +8 has x= 3 as the solution.

C) 3(x+1) -2x = x+3 has x= 9 as the solution.

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The incorrect measurements of the right triangle is 36² + 60² = 48²

Given data ,

Let the triangle be represented as ABC

Now , let the height of the triangle be AB = 36 miles north

Let the base of the triangle be BC = 48 miles east

Now , For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

So , 36² + 48² = 60²

So , the incorrect option from the data is 36² + 60² = 48²

Hence , the triangle is formed

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Answer: 0.5

Step-by-step explanation:

1/2% is equal to 50 out of 100, or 50/100.

So you turn that into a decimal (fifty one hundredths).

0.50

You can get rid of the 0 at the end.

0.5

Hope this helps!!! :)

The formula for the volume of a cylinder is:

V = πr^2h

where r is the radius and h is the height of the cylinder.

Substituting the given values, we get:

V = π(7^2)(13)

= 1274π

≈ 3993.87 cubic inches (rounded to the nearest hundredth)

Therefore, the volume of the cylinder is approximately 3993.87 cubic inches.

The inequality to find the number of tablespoons of flour actually used in a recipe is |t - 48| <= 4. The correct answer is D.

Since the recipe calls for 3 cups of flour with a variation of up to 4 tablespoons, the total amount of flour used can vary between 3 cups - 4 tablespoons and 3 cups + 4 tablespoons. Converting tablespoons to cups, this becomes 3 cups - 1/4 cup and 3 cups + 1/4 cup.

Thus, the range of cups of flour used is [3 - 1/4, 3 + 1/4], which is [2.75, 3.25]. Multiplying by 16 to convert back to tablespoons, we get the range [44, 52].

So, the inequality that could be used to find the number of tablespoons of flour actually used in the recipe is

|t - 48| <= 4

where t is the number of tablespoons of flour used. So, the correct option is D).

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Answer:

152.4 centimeters.

Step-by-step explanation:

1 inch = 2.54 centimeters

60 inches = x centimeters

Where x is the number of centimeters equivalent to 60 inches.

To solve for x, we can set up a proportion:

1 inch / 2.54 centimeters = 60 inches / x centimeters

Cross-multiplying, we get:

1 inch * x centimeters = 2.54 centimeters * 60 inches

Simplifying, we get:

x = (2.54 cm/in) * (60 in)

x = 152.4 cm

Therefore, 60 inches is equivalent to 152.4 centimeters.

A cone with a height of 9 in and a base diameter of 6 in has the volume 84.78 cubic inches.

The formula for the volume of a cone is:

V = (1/3)π[tex]r^{2}[/tex]h, where r is the radius of the base and h is the height.

In the question it is given height = 9 in and a base diameter = 6 in.

Radius = diameter/2

r = d/2 = 6/2 = 3 inches

Substituting the values in the formula:

V = (1/3)π[tex](3\ in)^2[/tex](9 in)

Simplifying the expression:

V ≈ 84.78 [tex]in^3[/tex]

Rounding to the nearest hundredth, we get:

V ≈ 84.78 [tex]in^3[/tex]

Therefore, the approximate volume of the cone is 84.78 cubic inches.

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The set of inequalities that expresses the given relationships are -6 < -2 and -2 > -4. The correction is second option -6 < -2 and -2 > -4

From the question, we are to determine the set of inequalities that expresses the relationships

From the given information,

The given relationships are:

A score of -6 is lower than a score of -2. A score of -2 is higher than a score of -4.

First, we will write the first relationship as an inequality

A score of -6 is lower than a score of -2

This means that -6 is less than -2.

Using inequalities symbols, we can write that

-6 < -2

Now,

For the second relationship :

A score of -2 is higher than a score of -4

This means, -2 is greater than -4

Using inequalities symbols, we can write that

-2 > -4

Hence,

The inequalities that express the relationships are -6 < -2 and -2 > -4

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Cash was paid for salaries during 2014 was $55,100. These are the formulas for calculating the cash salary received in 2014:

Salary paid in cash = Salary expense in 2014 - Reduction in salary payable

The difference between the balance due for salaries at the end of each year—that is, at December 31, 2013 and December 31, 2014—can be used to determine the decline in salaries payable:

Salaries payable at December 31, 2013, compared to salaries payable at December 31, 2014, are $3,700, $1,800, and $1,900, respectively.

The drop in the balance of salaries payable from 2013 to 2014 indicates that the business paid more compensation than it incurred for the year. As a result, the 2014 salary payments in cash are:

Cash paid for salaries equals salaries paid in 2014 less salaries payable, or $57,000 minus $1,900, or $55,100.

Hence, (A) $55,100 is the correct response.

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Answer:

240 tickets sold

Step-by-step explanation:

first, you would set up the proportion by writing [tex]\frac{228}{95} =\frac{x}{100}[/tex]

with "x" being the number of seats that needs to be sold

then, you would cross multiply

and you get

[tex]95x=228*100[/tex]    next, you simplify to get the inequality [tex]95x=22800[/tex]

then divide both sides by 95

[tex]x=240[/tex]

so 240 tickets to fill all the seats

hope this helps ;)

The time required to ring up the customer with 11 items is; 20 seconds

A linear equation is defined as an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.

We are given the linear equation:

t = p + 9

Where;

p is the variable that represents the number of items being purchased

t reprensts the time required to ring up the customer.

Thus:

When p = 11 items, we have:

t = 11 + 9

t = 20 seconds

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For the mean weight five boxes of cookies, the p-value is equals to 0.04189. If p-value is 0.233 > α, the conclusion is that mean weight of cookies is equals to 16.

We have total five boxes of cookies. Let population of weights is normally distributed, 15.91, 14.07 , 14.88, 16.07, 14.79. Use t.test to determine the p value and hypothesis testing for mean weight of product ( cookies). Let null and alternative hypothesis be defined as

[tex]H_0 : \mu = 16[/tex]

[tex]H_a : \mu<16[/tex]

degree of freedom, df = n - 1 = 5

Using the t-test formula, t value= -2.291,

Using t distribution table and the value p-value for t = -2.2907 and 4 degree of freedom is 0.04189. Hence, required value is 0.04189.

b) Now, p-value = 0.233 for mean weight varied from the specified value of 16.

Level of significance, [tex]\alpha[/tex] = 0.05

As we see p-value = 0.233 > 0.05 ( α), so, this is a significant region and null hypothesis can't be rejected. There is no enough evidence to conclude that the mean weight is actually less than 16 ounces.

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Complete question:

Following are the weights of 5 boxes of cookies, each of which is labeled as containing 16 ounces. Assume that the population of weights is normally distributed, 15.91, 14.07 , 14.88, 16.07, 14.79 . A quality control inspector wants to know whether the mean weight is actually less than 16 ounces. Compute the P-value of the test. Write down your P-value. Also, if he obtained a p-value of 0.233. which conclusion is appropriate?

Answer:

color cube

Step-by-step explanation:

Answer: 162

Step-by-step explanation:

so you will have to do 62+28+75=162

15 member enjoy both dancing and hiking.

The likelihood of the preceding event is multiplied by the probability of the subsequent, or conditional, occurrence to determine the conditional probability. Conditional probability examines the likelihood that one event will occur given the likelihood that a related event will occur beforehand.

We have,

Member enjoy dancing, n(D) = 62

Member enjoy hiking, n(H) = 28

Member enjoy dancing or hiking, n(D ∪ H) = 62

Using Conditional probability

n (D ∪ H) = n(D) + n(H) - n (D ∩ H)

75 = 62 + 28 - n (D ∩ H)

75 - 90 = - n (D ∩ H)

n (D ∩ H) = 15

Thus, 15 member enjoy both dancing and hiking.

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Answer:

152 cm, 161 cm, and 162 cm

Answer: The outlier is 93 is an outlier. Since an outlier exists, median and IQR are the best measures of center and variation to represent this data set

a) A recurrence relation, aₙ = aₙ₋₂ + aₙ₋₃

is for the different signals that can be sent in n microseconds.

b) Initial conditions are a₀ = 0, a₁ = a₂ = 1

c) The number of messages sent in 12 microseconds are equal to 16.

A recurrence relation is an equation form for nth term of a sequence of numbers which is equal to some combination of the previous terms. We have a messages are sent over a communications channel using two different signals. Let an be different number of messages that can be transmitted in n microseconds. In case of First signal, it required 2 microsecondes time to tramissmit the signals. So, the different number of signals that can be transmitted in 2 microseconds are [tex]a_{n - 2} [/tex]

In case of second signal , Time required by second signal to to transmit signal = 3

microsecondes

So, different number of messages that can be transmitted in 3 microseconds are

[tex]a_{n - 3} [/tex]

Each signal of a message is transmitted one by one.

a) A recurrence relation for the number of different signals that can be sent in n microseconds is written as

[tex]a_n = a_{n - 2} + a_{n - 3}[/tex]

hat is an us sum of different signals transmitted by each signals.

b) recurrence relation is

[tex]a_n = a_{n - 2} + a_{n - 3}[/tex]

so, the initial conditions of the recurrence relation in part (a) is n = 3 , [tex]a_3 = a_1 + a_0 [/tex]

a₀ = 0, a₁ = 1 , a₂ = 1

c) Different messages can be sent in 12 microseconds is determined by plugging the value in recurrence relation, a₃

= a₁ + a₀ = 1 + 0 = 1

a₄ = 1 + 1 = 2

a₅ = 1 + 1 = 2

a₆ = 2 + 1 = 3

a₇ = 2 + 2 = 4

a₈ = 3 + 2 =5

a₉= 4 + 3 = 7

a₁₀= 5 + 4 = 9

a ₁₁ = 7 + 5 = 12

a₁₂ = 9 + 7 = 16

Hence, required value is 16.

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