The frequency of grades earned on a Spanish test are displayed in the histogram.

Which of the following best describes the shape of the data, and why?


The data is symmetric because the average test grade falls in the middle of the data.

The data is not symmetric because the grades are spread out in each of the intervals.

The data is skewed because there is a large amount of data, showing the average grade in the middle.

The data is bimodal because there is a low amount of data in the first and last intervals, showing that many students had low grades.

Answer:

<ABC = 17

Step-by-step explanation:

I'm going to make a guess. My guess is that you want the measure of angle B.  I didn't see that the diagram asks that very question.

If you join <ADC, that angle is also 34 degrees. By the property of angles touching the circumference of a circle, the angle touching the circumference is 1/2 the central angle

1/2 34 = 17

Answer:

18 cm

Step-by-step explanation:

Let X represent a square

For it to be a rectangle, needs to be:

X X X

X X X

X X X

(It's a giant square made of squares)

This works since a square is a rectangle, but a rectangle isn't always a square. No other arrangement of the squares lead to a rectangle.

For Example:

X X X X

X X X X X

It doesn't work because there is an odd number of squares, and only would work if it was a multiple of 3,5,7 etc.. and 3 is the only number that fits.

So if the length is 18cm, the width is also 18cm.

Answer:

Answer is 7:20

It's basically asking "what is the ratio of math teachers to total teachers?" assuming there are only math and science teachers at this school. For the sake of simplicity, let's just go with that. We have 14 math teachers and 14+26 = 40 teachers total. The ratio of math to total is 14:40 which reduces to 7:20 when we divide both parts of the ratio by the GCF 2.

Step-by-step explanation:

Answer:

the ratio is

14:26

but you can leave the answer like this the two numbers can be divided by 2 so

14/2=7 and 26/2=13

then the answer is 7:13.

Answer: -1 \(\frac{5}{12}\)

The volume of a stack of 9 books is 1368.75 cubic inches.

To find the volume of a stack of 9 books, we first need to find the height of the stack. Since each book is 3/4 inch thick, the height of the stack is 9 times 3/4 inch, which is 6 3/4 inches.

Now we need to find the area of the base of the rectangular prism formed by the stack of books. Since each book has an area of 22 1/2 square inches, the total area of the base of the stack is 9 times 22 1/2 square inches, which is 202 1/2 square inches.

Therefore, the volume of the stack of 9 books is:

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Answer:

\(12 + 12 + 12 = 36 \\ \\ \\ i \: hope \: it \: is \: helpfull\)

Answer:

14

Step-by-step explanation:

2÷1/7

Using copy dot flip

2 * 7/1

14

Answer:

14

Step-by-step explanation:

2/1 x 7/1 = 14

This method is called keep, change and flip.

Keep the first number. Change the division sign into multiplication. Flip 1/7.

Answer:

y =0.5x +4

Step-by-step explanation:

The gradient of the two lines are the same

thus m2 =1/2

(y-5)/(x-2) = 1/2

2y -10 = x-2

2y=x+8

y = o.5x+4

Step-by-step explanation:

15+10z=105

10z=105-15

10z=90

z=9

Answer:

Hii okay so the answer would be, 8

Step-by-step explanation:

So she spent $200 and got 2 pairs of jeans that costed $50 for both.

So we subtract 50 from 200 which would be 150. This is the total she has

left to spend on her shirts. So 150 divided by 18 (Remember each shirt cost $18) Would be 8.3, we round to the nearest number and it would be 8. Hope this helps!

Answer:

t ≥ 2

Step-by-step explanation:

3t ≥ 15-9

3t ≥ 6

t ≥ 6/3

t ≥ 2

Yes, the line given is a reasonably good fit. The given equation is y = 12.04x + 40.87.The data points on the table can be plotted on a graph as shown below: We can see that the points are relatively close to the line of best fit. In addition, the correlation coefficient (r) value can be calculated to determine the strength of the linear relationship between the two variables.

A correlation coefficient of 0.986 indicates a strong positive correlation, which further supports the conclusion that the line of best fit is a reasonably good fit for the data. content loaded one part of Clare's job at an environmental awareness organization is to answer the phone to collect donations. The table shows the number of hours she worked each week (x) and the amount of donations in dollars (y) that the organization collected each week for 10 weeks The data in the table suggests a linear relationship.

The line of best fit is y=12.04x+40.87Is the line given a reasonably good fit Using the given information, the amount of commission earned by the salesperson is calculated as follows: Amount of sales up to $5,000 = $5,000So, the amount of commission earned on the first $5,000 of sales is:$5,000 × 5% = $250Amount of sales above $5,000 = $8,000 − $5,000 = $3,000Therefore, the amount of commission earned on sales greater than $5,000 is:$3,000 × 7.5% = $225.

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To find the probability that at least 7 Coffleton residents recognize the brand name, we need to use the binomial distribution formula.

The binomial distribution formula is given by:P(X = k) = nCk * pk * (1 - p)n - kWhere,X = Number of successesk = Number of successes we want to findP(X = k) = Probability of finding k successesn = Total number of trialsp = Probability of successnCk = Combination of n and kThe question does not provide the values of n and p. Hence, let's assume that n = 10 and p = 0.6. Therefore, q = 0.4 (since p + q = 1).We need to find P(X ≥ 7).

This means we need to find the probability of getting 7 or more successes.P(X ≥ 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)Now, let's use the binomial distribution formula to calculate each of these probabilities.P(X = 7) = 10C7 * 0.6^7 * 0.4^3= 0.2668P(X = 8) = 10C8 * 0.6^8 * 0.4^2= 0.1209P(X = 9) = 10C9 * 0.6^9 * 0.4^1= 0.0282P(X = 10) = 10C10 * 0.6^10 * 0.4^0= 0.0060Therefore, P(X ≥ 7) = 0.2668 + 0.1209 + 0.0282 + 0.0060= 0.4220Therefore, the probability that at least 7 Coffleton residents recognize the brand name is 0.4220 (or approximately 42.20%).

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a. Jada is the input and 4 is output, the output is 4 because there are 4 letters in Jada word.

b. G(Diego) =5

A relation is a function if it has only One y-value for each x-value.

Given that a  Function G takes a student's first name for its input and gives the number of letters in the first name for its output.

a.

Given that G(Jada) = 4

In the above function Jada is the input and 4 is output, the output is 4 because there are 4 letters in Jada word.

b. We need to find the value of G(Diego)

In the above function Diego is the input and 5 will be output, the output is 5 because there are 5 letters in Diego word.

G(Diego) =5

Hence, a. Jada is the input and 4 is output, the output is 4 because there are 4 letters in Jada word.

b. G(Diego) =5

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Answer:

  (b)  Yes, they are congruent

Step-by-step explanation:

Given two triangles with a side length marked as 5 units, you want to know whether they are congruent. One triangle has marked angles 65° and 67° with the angle opposite the marked side being unmarked. The other triangle has angles marked 65° and 48°, with the latter being opposite the marked side.

In each case, the sum of angles is 180°, so the measure of the third angle is the value that makes that be the sum of all angles.

Triangle 1:

The third angle is 180° -65° -67° = 48°.

Triangle 2:

The third angle is 180° -65° -48° = 67°.

The measures of the angles in each triangle are 48°, 65°, and 67°. Since the angles are the same, the triangles are similar.

In each case, the marked side is opposite the smallest angle. This means we can claim congruence using either the ASA or AAS postulates.

Yes, they are congruent.

Answer:

\(x=-1\)

Step-by-step explanation:

The equation for slope is:

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

In this case, x would represent, \(y_2\). Therefore...

\(Slope=\frac{y_2-y_1}{x_2-x_1}\\1=\frac{x-(-8)}{5-(-2)}\\1=\frac{x+8}{5+2}\\1=\frac{x+8}{7}\\\\Multiply\ 7\ to\ both\ sides\\\\7=x+8\\\\\ Subtract\ 8\ from\ both\ sides\\\\x=-1\)

The best applicant to fill the only position available based on the test score is Vincent as he scored highest. The method for determining which applicant performed the best on the aptitude test is to use z-scores, which are measurements of how far from the mean a test score falls in standard deviation units.

Since the test is not on the same scale, it is impossible to compare raw test scores. What are Z-scores?A z-score, also known as a standard score, is a score that indicates the number of standard deviations from the mean a raw score is. In other words, a z-score tells you how far from the mean the score is in terms of standard deviations.

In other words, we can use the following formula to calculate the z-score for each person's test result.$$Z = \frac {x - \mu}{\sigma}$$where x is the test score, μ is the test mean, and σ is the standard deviation.The Z-scores for each of the candidates based on their test results are as follows: Demetria:$$Z = \frac {85.1 - 61.1}{12} = 2.00$$,Vincent:$$Z = \frac {299.2 - 264}{22} = 1.6$$,Tobias:$$Z = \frac {7.26 - 7.1}{0.4} = 0.4$$. From the calculations, Vincent has the highest z-score, indicating that he outperformed the other candidates. The candidate with the highest z-score is the best performer, thus Vincent is the best candidate for the job.

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The standard deviation of the sampling distribution can be calculated using the formula:  standard deviation = sqrt [p(1-p)/n] . Therefore, the mean of the sampling distribution is 0.5 and the standard deviation is 0.025.

The mean of the sampling distribution of possible sample proportions is equal to the population proportion, which is p = 0.5. The standard deviation of the sampling distribution can be calculated using the formula:

standard deviation = sqrt [p(1-p)/n]

Plugging in the values, we get:

standard deviation = sqrt [(0.5)(1-0.5)/400]

standard deviation = sqrt [(0.25)/400]

standard deviation = 0.025

Therefore, the mean of the sampling distribution is 0.5 and the standard deviation is 0.025.

To find the mean and standard deviation of the sampling distribution for sample proportions, you can use the following formulas:

Mean (μ) = p
Standard Deviation (σ) = √(p(1-p)/n)

Given the sample size (n) = 400 and population proportion (p) = 0.5, you can calculate the mean and standard deviation as follows:

Mean (μ) = 0.5
Standard Deviation (σ) = √(0.5(1-0.5)/400) = √(0.5*0.5/400) = √(0.125/100) = √(0.00125) ≈ 0.0354

So, the mean of the sampling distribution is 0.5 and the standard deviation is approximately 0.0354.

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Answer:

174 seconds or 2 minutes, 54 seconds

Step-by-step explanation:

you can set up a system up equations to solve this problem:

Keith:    y = 1x + 200

Erica:    y = -1x + 548

if you graph the above lines, their point of intersection is the solution

in this case, after 174 seconds both balloons will be 374 feet above the ground

If the mean cost of new books is the same as the median cost of new books in a small town library, the distribution of book costs is most likely normal with a symmetrical peak at the center.

In the library of a small town, the mean cost of new books is the same as the median cost of new books. The distribution of book costs is likely symmetrical with a single peak at the center, as in the normal distribution. In other words, the distribution of book costs is most likely to be normal when the median cost and the mean cost are the same. Therefore, if the mean cost of new books in the library of a small town is the same as the median cost of new books, it suggests that the distribution of book costs is normal. A normal distribution is one in which the median, mode, and mean are equal, as well as symmetrical. The median is the middle value in a sorted data set, whereas the mean is the average of all the data in the set. In conclusion, if the mean cost of new books is the same as the median cost of new books in a small town library, the distribution of book costs is most likely normal with a symmetrical peak at the center.

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The multiplicative inverse property of the questions that we have here are:

This is the term that is used in Mathematics to show that we are to multiply a fraction by the inverse of that fraction.

A good example of this would be the form that is written as:

1/a would have the inverse property written as a/1

such that 1/a *a/1 = 1

In the same way,

we have

9/7 * 7 / 9 = 1

4/3 * 3/4 = 1

5 1/3 = 16 / 3 * 3/ 16 = 1

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A Type I error is committed when the scientist concludes that the antipollution device is effective when it actually is not. This can happen if the scientist sets the significance level too low, or if there is a lot of random variation in the data.

The null hypothesis in this case is that the antipollution device is not effective. The alternative hypothesis is that the antipollution device is effective. If the scientist rejects the null hypothesis, they are saying that they have enough evidence to conclude that the antipollution device is effective. However, if the null hypothesis is actually true, then the scientist has made a Type I error.

The probability of making a Type I error is typically set at 5%. This means that if the null hypothesis is true, then there is a 5% chance that the scientist will reject it. The significance level can be set higher or lower, depending on how much risk the scientist is willing to take of making a Type I error.

Random variation in the data can also lead to a Type I error. If the data is very noisy, then it can be difficult to tell whether the results are due to the antipollution device or just random chance. This is why it is important to have a large sample size when conducting statistical tests.

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A Type I error is committed when the scientist concludes that the antipollution device is effective when it actually is not. This can happen if the scientist sets the significance level too low, or if there is a lot of random variation in the data.

The null hypothesis in this case is that the antipollution device is not effective. The alternative hypothesis is that the antipollution device is effective. If the scientist rejects the null hypothesis, they are saying that they have enough evidence to conclude that the antipollution device is effective. However, if the null hypothesis is actually true, then the scientist has made a Type I error.

The probability of making a Type I error is typically set at 5%. This means that if the null hypothesis is true, then there is a 5% chance that the scientist will reject it. The significance level can be set higher or lower, depending on how much risk the scientist is willing to take of making a Type I error.

Random variation in the data can also lead to a Type I error. If the data is very noisy, then it can be difficult to tell whether the results are due to the antipollution device or just random chance. This is why it is important to have a large sample size when conducting statistical tests.

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(a) For the given data set, the sample mean is approximately 159.43 and the median is 163.

(b) The 15% trimmed mean is calculated to be approximately 160.88.

(c) The quartiles for the initial data set are Q1 = 137, Q2 (median) = 163, and Q3 = 189.

(d) If the 6th observation had been 100 instead of 137, the mean would decrease to approximately 154.72, while the median would remain the same at 163.

(e) The sample variance is approximately 853.03 and the standard deviation is approximately 29.20.

(a) The sample mean is calculated by summing all the data points and dividing by the number of observations. In this case, the sum of the data is 2,869, and since there are 18 observations, the mean is 2,869/18 ≈ 159.43.

The sample mean represents the average value of the data set. The median is the middle value when the data set is arranged in ascending order. In this case, the data set is already sorted, and the middle value is the 9th observation, which is 163. The median represents the central tendency of the data set.

(b) The 15% trimmed mean involves removing a certain percentage of the smallest and largest values and then calculating the mean of the remaining values.

To calculate the 15% trimmed mean, we discard 15% of the lowest and highest values, which is approximately 0.15 * 18 = 2.7. Since we cannot discard a fraction of an observation, we remove the two smallest and two largest values. After removing them, we are left with 14 observations, and the mean of these values is approximately 160.88.

(c) The quartiles divide the data set into four equal parts. The first quartile (Q1) represents the 25th percentile, the median (Q2) represents the 50th percentile, and the third quartile (Q3) represents the 75th percentile.

To calculate the quartiles, we first need to arrange the data set in ascending order.

The sorted data set is:

126, 126, 127, 136, 137, 139, 146, 150, 163, 165, 167, 176, 184, 188, 189, 189, 194, 197.

Q1 is the median of the lower half of the data, which is the 9th observation, so Q1 = 137.

Q3 is the median of the upper half of the data, which is the 14th observation, so Q3 = 189.

(d) If the 6th observation had been 100 instead of 137, the mean would change. The sum of the data would be 2,833, and the new mean would be 2,833/18 ≈ 154.72.

However, the median would remain the same because it is the middle value of the sorted data set, which is 163.

(e) The sample variance measures the spread or dispersion of the data set. It is calculated by taking the average of the squared differences between each data point and the mean.

The sample variance for the given data set is approximately 853.03. The standard deviation is the square root of the variance and provides a measure of the average distance between each data point and the mean. The sample standard deviation for the given data set is approximately 29.20.

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Answer:

2.6 kilometers

Step-by-step explanation:

To find the circumference of a circle, we can use the formula:

Circumference = π * diameter

Given that the diameter of the volcanic crater is 840 meters, we can substitute this value into the formula:

Circumference = π * 840

Using the approximate value of π as 3.14159, we can calculate the circumference:

Circumference = 3.14159 * 840

Circumference ≈ 2643.1796 meters

To convert the circumference to kilometers, we divide the value by 1000:

Circumference in kilometers = 2643.1796 / 1000

Circumference ≈ 2.6432 kilometers

Therefore, the circumference of the rim of the volcanic crater is approximately 2.6 kilometers (rounded to 1 decimal place).

Use implicit differentiation to find ∂z/∂x and ∂z/∂y. yz = 8 ln(x + z) ∂z ∂x is ∂z/∂y = -z/y. To use implicit differentiation to find ∂z/∂x and ∂z/∂y for yz = 8 ln(x + z), we first need to differentiate both sides with respect to x and y separately.

For ∂z/∂x, we have:

yz = 8 ln(x + z)

Taking the partial derivative with respect to x on both sides:

y ∂z/∂x + z ∂y/∂x = 8/(x+z)

Now, we can solve for ∂z/∂x:

∂z/∂x = (8/(x+z) - z ∂y/∂x)/y

For ∂z/∂y, we have:

yz = 8 ln(x + z)

Taking the partial derivative with respect to y on both sides:

z ∂y/∂y + y ∂z/∂y = 0

Simplifying:

∂z/∂y = -z/y

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1) The value of an equation for y in terms of x is, y = 1/5x

And, y = 20 at x = 100

2) y = 184.8 , at x = 14

The value of an equation for y in terms of x is, y = 13.2x

Given that;

1) y is directly proportional to x.

2) y ∝ x and y=132 when x=10

Now, For 1;

1) Since, y is directly proportional to x.

Hence, We get;

y = kx

Plug y = 5 and x = 25

5 = 25k

k = 1/5

Hence, The value of an equation for y in terms of x is,

y = 1/5x

And, Plug x = 100,

y = 1/5 x 100

y = 20

2) Since,  y ∝ x and y=132 when x=10

y = kx

132 = 10k

k = 13.2

Hence, At x = 14;

y = 13.2 x 14

y = 184.8

Thus, The correct equation is,

y = 13.2x

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There are 1,207,084,032,000 ways for 6 CE majors and 10 CS majors to stand next to each other in the lines.

We use permutations and combinations for solving this problem. We fix the position of CS students so that they can stand in a fixed place by

= 10! ways (i)

Now, there are 11 places left for CE students so that no two CE students stand next to each other.

6 CE students in the rest of the 11 places can sit by = 11! / (11-6)! ways (ii)

Hence, using the values of (i) and (ii), we get -

= (10! * 11!) / (11-6)!

= 1,207,084,032,000

Therefore, we have 1,207,084,032,000 ways in which the six CE majors and ten CS majors can stand in a line so that no two CE majors stand next to each other.

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(b) The probability is 1/6.

(c) The probability is 1/6.

(a) The density curve for X, the number of minutes your friend is late, is a rectangle with a base of 30 (representing the range of possible values) and a height of 1/30 (since it follows a uniform distribution).

(b) The probability that your friend is between 15 and 20 minutes late can be calculated by finding the area under the density curve between those two values. In this case, it is (20-15) * (1/30) = 1/6.

(c) The probability that your friend is less than 5 minutes late can be calculated by finding the area under the density curve up to 5 minutes. Since it is a uniform distribution, the probability is (5-0) * (1/30) = 1/6.

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

Explanation:

x = radius of the circle

The vertical leg of the right triangle is also x. The horizontal leg is 99.

The hypotenuse is x+81

We have these triangle side lengths:

Use the pythagorean theorem to tie them all together, which will allow us to solve for x.

\(a^2+b^2 = c^2\\\\\text{x}^2+99^2 = (\text{x}+81)^2\\\\\text{x}^2+9801 = \text{x}^2+162\text{x}+6561\\\\9801 = 162\text{x}+6561\\\\9801-6561 = 162\text{x}\\\\3240 = 162\text{x}\\\\\text{x} = 3240/162\\\\\text{x} = 20\)

A tool like GeoGebra or WolframAlpha can be used to confirm the answer is correct.

Answer: If Sarah's total was $9.05 and the binder costs 7.25 then in order to find the price of the folders you must subtract the cost of the binder (7.25) from the total (9.05) which leaves $1.80 as the amount she paid in total for 6 folders.

Step-by-step explanation: