Question 14(Multiple Choice Worth 2 points)
(Creating Graphical Representations MC)

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(Multiple Choice Worth 2 points)

Step-by-step explanation:

2:3

sum =5

=2/5×500

=200 books in the children's section while

=3/5×500

=300 bks in other sections

Answer:

see image

Step-by-step explanation:

We need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit which is compounded semi-annually.

To solve this problem, we can use the formula for the future value of an annuity:

\(FV = P * ((1 + r)^n - 1) / r\)

Where:

FV is the future value of the annuity

P is the periodic payment or deposit amount

r is the interest rate per period

n is the number of periods

In this case, the deposit amount is $726.56, the interest rate is 6.45% compounded semi-annually, and the future value is $31,300. We need to find the number of deposits (n).

We can rearrange the formula and solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Substituting the given values:

n = log((31,300 * 0.03225) / (726.56 * 0.03225 + 31,300)) / log(1 + 0.03225)

Using a calculator or software, we find that n ≈ 9.989.

Therefore, we need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit.

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The instructional context can greatly impact learning with educational technology. In a study with a digital learning game, it was found that the instructional context influences student engagement and motivation. This, in turn, affects their learning outcomes.

The study examined the design of the game, the teacher's role, and the classroom environment. By optimizing these factors, the researchers found that students were more likely to be actively engaged and achieved better learning outcomes.

Therefore, the instructional context plays a crucial role in leveraging the potential of educational technology for effective learning.

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the Answer: t=18, - 18

The evaluated double Integral is:
(1/2) * e^(4) - (5/2)

Let's consider the given limits for integration and the function:

Function: f(x, y) = x * e^(xy)
Limits: 0 ≤ x ≤ 2, 0 ≤ y ≤ 1

To evaluate the double integral, we'll integrate with respect to y first, and then with respect to x:

∬(x * e^(xy)) dy dx

First, let's integrate with respect to y:

∫(x * e^(xy)) dy = x * ∫(e^(xy)) dy

To integrate e^(xy) with respect to y, we'll use substitution:

u = xy
du/dy = x
dy = du/x

Now, substitute u into the integral:

∫(x * e^(xy)) dy = x * ∫(e^u * (du/x))

The x terms cancel out, so we have:

∫(x * e^(xy)) dy = ∫(e^u) du

Now, integrate with respect to u:

∫(e^u) du = e^u + C = e^(xy) + C

Now, let's integrate with respect to x:

∫(∫(x * e^(xy)) dy) dx = ∫(e^(xy) + C) dx

Now, we apply the limits:

For y: [e^(xy) + C] from 0 to 1

= [(e^(2x) + C) - (e^(0) + C)]

= [e^(2x) - 1]

For x: ∫([e^(2x) - 1]) dx from 0 to 2

Now, integrate with respect to x:

= [(1/2) * e^(2x) - x] from 0 to 2

Apply the limits:

= [(1/2) * e^(4) - 2] - [(1/2) * e^(0) - 0]

= [(1/2) * e^(4) - 2] - (1/2)

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The value of x from the given expression is 5 and the property used are addition and division property

Given the equation below

2x - 30 = -20

Add 30 to both sides (Addition property)

2x - 30 + 30 = -20 + 30

2x = -20 + 30

2x = 10

Divide both sides by 2

2x/2 = 10/2

x = 5

Hence the value of x from the given expression is 5 and the property used are addition and division property

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Answer:

the common factor is b since it is divisible by both 2b and 5b

Step-by-step explanation:

The variance of the error anticipated value should therefore be constant when plotting each individual error against the expected value.

What is regression line?

A regression line is a line that in statistics best depicts the behavior of a set of data. It is, in other words, a line that best fits the trend of the data at hand.

The standard deviation and variance of the residuals are assumed to be constant for all values of independent variables in regression analysis under the concept of constant variance.

The variance of the error anticipated value should therefore be constant when plotting each individual error against the expected value.

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The ice cream no of tasters relative frequency. The correct option is B.

Strawberry                4 0.2

Choco Nuts              12 0.6

orange mints               4 0.2

Wagenlucht Ice Cream Company is always trying to create new flavors of ice cream. They are market-testing three kinds to find out which one has the best chance of becoming popular.

They give small samples of each to 20 people at a grocery store. 4 ice cream tasters preferred the Strawberry Cream, 12 preferred Choco- Nuts, and 4 loved the Orange Mint. Construct a Pareto chart to represent these preferences. Choose the vertical scale so that the relative frequencies are represented.

Ice cream no of tasters relative frequency.

Strawberry                4 0.2

Choco Nuts              12 0.6

orange mints               4 0.2

Relative frequency is frequency over the total frequency.

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The set A.{x | x R, x < 5} would have a graph with an open circle on 5 and a ray pointing left on the number line.

What exactly is a set?

In mathematics, a set is a collection of distinct objects or elements, which are considered as a single entity. The objects or elements in a set can be anything, such as numbers, letters, people, animals, or other things, depending on the context.

Now,

The set  A.{x | x R, x < 5}  would have a graph with an open circle on 5 and a ray pointing left on the number line.

This is because the symbol "<" means "less than," so the set A includes all real numbers less than 5. The open circle on 5 indicates that 5 is not included in the set, so the graph will have an open circle on 5. The ray pointing left indicates that the set extends infinitely to the left of 5.

In contrast, set B.{x | x R, x > 5} would have an open circle on 5 and a ray pointing to the right, since it includes all real numbers greater than 5. Set C.{x | x R, x ≤ 5} would have a closed circle on 5 and a ray pointing to the left, since it includes all real numbers less than or equal to 5.

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The answer is option B: 0.040. When Z is a standard normal random variable, it means that Z has a mean of 0 and a standard deviation of 1. Therefore, P(-1.75 < Z < -1.25) represents the area under the standard normal curve between -1.75 and -1.25 standard deviations from the mean.

Using a standard normal distribution table or calculator, we can find that the area under the curve between -1.75 and -1.25 is approximately 0.040. Hence, the answer is option B: 0.040.
 To solve your question, we need to find the probability P(-1.75 ≤ Z ≤ -1.25) where Z is a standard normal random variable.

Step 1: Identify the given values
Z1 = -1.75
Z2 = -1.25

Step 2: Look up the Z-values in a standard normal table or use a calculator to find the corresponding probabilities
P(Z ≤ -1.75) = 0.0401
P(Z ≤ -1.25) = 0.211

Step 3: Use the properties of probabilities to find the required probability
P(-1.75 ≤ Z ≤ -1.25) = P(Z ≤ -1.25) - P(Z ≤ -1.75)
P(-1.75 ≤ Z ≤ -1.25) = 0.211 - 0.0401
P(-1.75 ≤ Z ≤ -1.25) = 0.1709

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The number of soccer balls based on the given ratio will be 60.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

Suppose, the number of softballs balls is x while soccer  is y

Ratio x/y = 12/15

x = 48

48/y = 12/15

y = 48(15/12) = 60

Hence "The number of soccer balls based on the given ratio will be 60".

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Answer:

D

Step-by-step explanation:

since 3.14^2=9.86 which is between 9 and 10

Answer:

A.2

Step-by-step explanation:

1+1=2

THAT'S TOUGHEST ENGINEERING LEVEL QUESTION

To determine if there is significant evidence to suggest that the population of adolescents in a youth detention facility has a reading disability prevalence that is different from 9%, we need to conduct a hypothesis test. Let p be the proportion of adolescents in the population who have a reading disability. Our null hypothesis is that p=0.09, and the alternative hypothesis is that p is not equal to 0.09. We will use a significance level of 0.05.

Using the sample data, we can calculate the sample proportion, p-hat, which is 38/407=0.0933. To calculate the z-test value, we first need to calculate the standard error, which is sqrt(0.09*(1-0.09)/407)=0.0191. The z-test value is (0.0933-0.09)/0.0191=1.57. This z-test value can be compared to the critical value of the standard normal distribution at a significance level of 0.05/2=0.025. The critical value is 1.96. Since the calculated z-test value of 1.57 is less than the critical value of 1.96, we fail to reject the null hypothesis. Therefore, there is not significant evidence to suggest that the population of adolescents in a youth detention facility has a reading disability prevalence that is different than 9%.

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Mean for start of school year is 6.5; Mean for end of school year is 7.2.

Median for start of school year is 6.5; Median for end of school year is 7.

To find the means, list out each data value given for each dot plot and calculated the mean.

Mean for start of school year:

We have, 4, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 9

Mean = ( 4 + 5 + 5 + 6 + 6 + 6 + 6 + 7 + 7 + 7 + 7 + 8 + 8 + 9)/14

= 91/14

Mean ≈ 6.5

Mean for end of school year:

We have, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 8, 9, 9, 9

Mean = ( 5 + 5 + 6 + 6 + 7 + 7 + 7 + 7 + 8 + 8 + 8 + 9 + 9 + 9)/14

= 101/14

Mean ≈ 7.2

Median represents the middle data value in a data set, therefore:

Median for start of school year = ( 6 + 7)/2 = 6.5

Median for end of school year = ( 7 + 7)/2 = 7

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For equation 1;

For equation 2;

For equation 3;

The measurement that is closest to the value of x, in centimeters, is given as follows:

14.3.

In this problem, we have a right triangle, in which the legs, which are the sides between the angle of 90º, are of 11.9 cm and 7.9 cm.

Then the hypotenuse x, which is the segment connecting both legs, is obtained using the Pythagorean Theorem.

The Pythagorean Theorem states that the measure of the hypotenuse squared is equals to the sum of the squares of the measures of each side.

Then the length of x is calculated as follows:

x² = 11.9² + 7.9²

x = square root of (11.9² + 7.9²)

x = 14.28.

Closest to 14.3, rounding to the nearest tenth, meaning that the third option is correct.  

We suppose that 11.9 cm and 7.9 cm are the measures of the legs.

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Answer:

61

Step-by-step explanation:

Definition of conguency

*figure on the right is rotated a bit

Answer:

\(m=\frac{-5}{3}\)

Step-by-step explanation:

We want to find the slope between the points (-2,5) and (1,0).

The slope (m) can be found using the formula \(\frac{y_2-y_1}{x_2-x_1}\), where \((x_1,y_1)\) and \((x_2,y_2)\) are points.

We are already given the values of the points, but let's label their values to avoid any confusion and mistakes.

\(x_1=-2\\y_1=5\\x_2=1\\y_2=0\)

Now, substitute into the formula.

\(m=\frac{y_2-y_1}{x_2-x_1}\)

\(m=\frac{0-5}{1--2}\)

Simplify this to:

\(m=\frac{0-5}{1+2}\)

\(m=\frac{-5}{3}\)

The slope is -5/3.

Answer:

A positive standard score indicates that the original score is greater than the mean

Step-by-step explanation:

please mark as brainliest

A negative standard score indicates that the original score is lower than the mean.

A standard score, also known as a z-score, is a statistical measure that represents the number of standard deviations an individual score is away from the mean of a distribution. It provides a standardized way to compare and interpret individual scores within a dataset.

When the standard score is negative, it means that the original score is below the mean of the distribution. In other words, the value associated with the score is lower than the average value in the dataset.

For example, if we have a dataset with a mean of 50 and an individual score of 45, we can calculate the standard score (z-score) using the formula:

z = (x - μ) / σ

where x is the original score, μ is the mean, and σ is the standard deviation.

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Answer:

Postulates and conjectures are similar in that they are both used in mathematical proofs. The difference between them is that whilst a conjecture is a opinion that is put forward without proof, and that simply represents a belief, a postulate it something that is assumed true (but still does not have any proof behind it).

Step-by-step explanation:

Answer: Postulate – this is also called as axiom. This study is accepted without asking for any proof. This is considered as true without further proof. IT is simply considered as self-evident. It is usually agreed by anyone to be true and acceptable.

Example of postulate is to prove a simple triangle as congruent.

While conjecture – considered as proposition in which it needs to provide value proof or evident in order for it to be considered as true.

Examples of conjecture are four color theorems and Fermat’s Last theorem.

Step-by-step explanation:

The fraction of Anitra's hair ribbons is red is 1/2.

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

Given that, Anitra has 12 hair ribbons.

One fourth of the ribbons are pink.

So, number of pink ribbons = 1/4 ×12

= 3

Three are purple, and the rest are red.

So, number of red ribbons

= 12-3-3

= 6

Now, fraction = 6/12 = 1/2

Therefore, the fraction of Anitra's hair ribbons is red is 1/2.

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Answer:

Step-by-step explanation:

By using a maclaurin series to obtain the maclaurin series for the given function is  F(x) = x cos(5x) = \(1 - 25x^2/2! + 625x^4/4! - 15625x^6/6! + ...\)

To obtain the Maclaurin series for the function f(x) = x cos(5x), we need to write the Maclaurin series for cos(5x). The Maclaurin series for cos(x) is: \(cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + ...\)

Using this formula, we can substitute 5x for x and obtain the Maclaurin series for cos(5x): cos(5x) =\(1 - (5x)^2/2! + (5x)^4/4! - (5x)^6/6! + ...\)

\(= 1 - 25x^2/2! + 625x^4/4! - 15625x^6/6! + ...\)

We can substitute this series into the original function f(x) = x cos(5x) and obtain its Maclaurin series: f(x) = x cos(5x)

\(= x[1 - 25x^2/2! + 625x^4/4! - 15625x^6/6! + ...]\)

\(= x - 25x^3/2! + 625x^5/4! - 15625x^7/6! + ...\)

This is the Maclaurin series for the function f(x) = x cos(5x). It is obtained by substituting the Maclaurin series for cos(5x) into the original function and simplifying the resulting series. Maclaurin series are useful for approximating functions using polynomials. By truncating the series after a certain number of terms, we can obtain a polynomial that approximates the original function to a certain degree of accuracy. The accuracy of the approximation depends on the number of terms in the series that are used. The more terms we include, the more accurate the approximation will be.

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Hi,

28 - 23 = 5

23 - 18 = 5

18 - 13 = 5

The commun difference is 5

✅(•‿•)

The value of z if the area to the right of z is 0.0934 is -1.34.Answer: b. -1.32

We are given that Z is a standard normal random variable, and we need to find the value z if the area to the right of z is 0.0934 i.e. when P(Z ≥ z) = 0.0934.

What we know is that for the standard normal distribution, the area to the right of a value z is given by the expression: P(Z ≥ z) = 1 - P(Z < z)This is the same as the area to the left of negative z.

i.e. P(Z ≤ -z).Thus, for a given value of p, we can determine the corresponding z-value by finding the value of -z such that the area to the left of -z is equal to p.

We can then flip the sign of -z to get the value of z.We can find the z-value corresponding to P(Z ≥ z) = 0.0934 by finding the area to the left of the corresponding negative z-value using a standard normal distribution table or a calculator.

The closest value to 0.0934 in the standard normal distribution table is 0.09324, which corresponds to a z-value of 1.34 (rounded to two decimal places).To find the corresponding negative z-value, we flip the sign and get: -1.34.

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3 Answers

The correct box plot is shown below.

=====================================================

Explanation:

The first step when constructing a box plot is to sort the data from smallest to largest. That has already been done for us, so we can move to the next step.

For step 2, we need to find the median. This is the middle-most value. Write out all of the values on one horizontal line. Then cross off the first and last values. You'll end up with a smaller set, with two values tossed out. Repeat this process (cross off the first and last items) and keep doing this until you work your way toward the very middle position. There are 19 numbers in this list, which is an odd number, this means that the middle value is in slot 10 (note how 19/2 = 9.5 which rounds to 10). We have 9 values below the median and 9 values above the median. So 9+1+9 = 19 items total.

You should find that the value 55 is at slot 9, and at the very middle. So 55 is the median. Billy marked on the box plot that the median is at 50, so this is one mistake he made. Choice C is one of the answers

Note: the median is the vertical bar inside the box of the box-and-whisker-plot.

-----------------------------

Once you have the median, break the list into two halves like so:

L = {25,25,30,30,35,35,40,45,50}

U = {60,60,60,70,85,90,95,95,105}

L is the lower set of values smaller than the median, U is the upper set of values larger than the median. Set L and set U have 9 items each. Note the median of 55 is not part of set L nor is it part of set U either.

Repeat the process to find the median, but you'll do so on sets L and U separately. The median of set L is 35, so this is the value of Q1 or the first quartile.

The left edge of the box is the visual location of Q1. We can see that Billy marked Q1 at 30, but it should be at 35. So this is another mistake he made. Choice B is one of the answers

The median of set U is 85. We have four values below 85, and four values above 85 in set U. This makes Q3 to be 85. However, Billy marked the third quartile at 80 instead of 85. This is another mistake. Choice D is one of the answers.

--------------------------------

To summarize his 3 mistakes, they are:

The good news is that he got the minimum correct because 25 is the smallest value. The min value is the left-most tip of the left whisker. The max is also in the correct location since 105 is the largest item. As you can probably guess, the max is located at the right-most tip of the right whisker.

See the attached image below to see how Billy should have drawn the box plot.

The graph of the function is shown below:

a)

From the graph we notice that the vertex of the function is at the point:

b)

From the graph we notice that the axis of the function is the line:

C)

Since this is a polynomial its domain is all the real numbers, that is:

d)

From the graph we notice that the range is:

e)

The graph is increasing in the interval:

f)

The graph is decreasing in the interval: