A rectangle has a perimeter of 46 inches. The length of the rectangle is 7 inches. What is the rectangle width?

Using the calculated value of test statistic and critical value correct option is ,

(A) There is not sufficient evidence which reject the dean's claim of showing 50% of undergraduate students reside in dormitories.

To test the claim that 50% of all undergraduate students reside in the college dormitories,

Use a hypothesis test ,

State the null and alternative hypotheses,

Null hypothesis (H₀),

The proportion of undergraduate students residing in the dormitories is equal to 50%.

Alternative hypothesis (Hₐ),

The proportion of undergraduate students residing in the dormitories is not equal to 50%.

Set the significance level,

The significance level (a) is given as 0.017.

Calculate the test statistic,

To calculate the test statistic, use the formula for a test of proportion, Test statistic (z) = (p₁ - p₀) / √((p₀(1-p₀))/n)

Where p₁ is the sample proportion, p₀ is the hypothesized proportion under the null hypothesis, and n is the sample size.

p₁ = 32/5 = 0.64 (proportion of students residing in the dormitories),

p₀ = 0.50 (hypothesized proportion of students residing in the dormitories),

and n = 5 (sample size).

Substituting these values into the formula, we get,

Test statistic (z)

= (0.64 - 0.50) / √((0.50(1-0.50))/5)

= 0.14 / √(0.25/5)

= 0.14 / √(0.05)

= 0.14 / 0.2236

≈ 0.626

Determine the critical value,

Since the alternative hypothesis is two-tailed (not equal to 50%),

The critical value corresponding to the significance level

a/2 = 0.017/2 = 0.0085.

Using a standard normal distribution calculator,

the critical value is approximately ±2.576.

Compare the test statistic to the critical value and make a decision,

Since the test statistic (0.626) does not exceed the critical value of ±2.576,

fail to reject the null hypothesis.

Therefore, as per test statistic and critical value ,

correct answer is (A) There is not sufficient evidence to reject the dean's claim that 50% of undergraduate students reside in dormitories.

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The ogive is a line graph that plots the cumulative relative frequency distribution.

An ogive, also known as a cumulative frequency polygon, is a line graph that shows the cumulative frequency distribution of a data set. The cumulative frequency is calculated by adding up the frequencies of each value up to a certain point in the data set.

The cumulative relative frequency is calculated by dividing the cumulative frequency by the total number of observations in the data set. The ogive plots these cumulative relative frequencies against the corresponding values in the data set, usually on the x-axis.

By plotting the cumulative relative frequencies, the ogive shows how the data is distributed over the entire range of values. It can be used to identify patterns in the data, such as whether it is skewed or symmetrical. It is also useful for determining percentiles, as the percentile for a given value can be read directly from the ogive.

Overall, the ogive is a helpful tool for summarizing and visualizing the distribution of a data set, particularly when dealing with large data sets or complex distributions.

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Answer:

.

Step-by-step explanation:

The simplified expression that represents the perimeter of the new triangle

is 72c² + 20c.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know the perimeter of any two-dimensional planer figure is the sum of the lengths of it's all the sides except the circle.

The given perimeter of the right angle triangle is,

= (4c + 6c + 4 + 8c + 1).

= 18c + 5.

Therefore, The new perimeter of the triangle will be,

= 4c(18c + 5).

= 72c² + 20c.

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The equation that represents the length of the square dining room in feet is (1/4)x - 5/6.

The area of a square is a product of it's any two sides or a product of diagonals divided by two. If a side has a length 'a' then the diagonal is a√2.

The perimeter of a square is the sum of the lengths of all the sides.

We know the perimeter of a square is 4×side.

We also know that 1 foot is equal 12 inches.

Given, A square dining room table has a perimeter of (12x - 40)".

Now if we factor out a 4 we'll have the side inside the bracket which is,

4(3x - 10)'', This is in inches to convert it to feet we have to divide what is inside the bracket by 12 which is,

= (3/12)x - 10/12 feet.

= (1/4)x - 5/6 feet.

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The scenario described above illustrates the Service Recovery Paradox, where a customer's satisfaction can actually increase after experiencing a service failure and receiving effective recovery efforts.

Dr. Amarkant Tripathi faced a delay and inconvenience with his suit order from B N Rao suits, but the store manager went above and beyond to rectify the situation, ultimately leading to Dr. Tripathi's increased satisfaction and loyalty.

The Service Recovery Paradox occurs when a customer's satisfaction and loyalty increase even after encountering a service failure. In the given context, Dr. Tripathi experienced a delay and fitting issue with his suit order. However, the store manager took prompt action to resolve the problem and ensure Dr. Tripathi's satisfaction.
Despite initial setbacks, the store manager exhibited proactive service recovery efforts. He communicated with Dr. Tripathi, apologized sincerely, and made efforts to rectify the situation promptly. The manager's willingness to listen, understand, and address the customer's concerns played a crucial role.
Furthermore, the store manager's personal involvement, contacting Dr. Tripathi's home, explaining the situation to his daughter, and arranging for the suit to be taken to the Domlur branch for repairs and express delivery showcased a high level of customer service and dedication to resolving the issue.
These service recovery efforts exceeded Dr. Tripathi's expectations and demonstrated B N Rao suits' commitment to customer satisfaction. As a result, when Dr. Tripathi received the suit, along with the apology note and additional handkerchiefs, he felt not only satisfied with the resolution but also impressed by the store's efforts to understand his needs and deliver a superior service experience.
The Service Recovery Paradox, in this case, highlights the importance of effective service recovery in building customer loyalty and turning a potentially negative experience into a positive one. B N Rao suits' commitment to resolving the issue and going the extra mile to deliver a satisfactory outcome ultimately strengthened the customer's trust and loyalty in the brand.

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Therefore, the probability that exactly 4 out of 20 randomly chosen college students are near-sighted is closest to 0.7988 or approximately 0.80.

To find the probability that exactly 4 out of 20 randomly chosen college students are near-sighted, we can use the binomial probability formula.

The formula for the probability of k successes in n trials, with a probability of success p in each trial, is given by:

\(P(X = k) = (n choose k) * p^k * (1 - p)^{(n - k)\)

In this case, n = 20, k = 4, and p = 0.28 (probability of a student being near-sighted).

Plugging in these values into the formula, we get:

\(P(X = 4) = (20 choose 4) * (0.28)^4 * (1 - 0.28)^{(20 - 4)\)

Calculating the values:

(20 choose 4) = 4845

\((0.28)^4\) ≈ 0.006859

\((1 - 0.28)^{(20 - 4)\) ≈ 0.19224

P(X = 4) ≈ 4845 * 0.006859 * 0.19224

≈ 0.7988

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The total amount given the original price and tax rate is $33.59

From the question, we have the following parameters:

Original price = $31.69

Sales tax rate = 6%

In order to determine the total sales amount, we make use of the following total sales equation

Total sales = original price + original price * sales tax rate

Substitute the known values in the above equation

So, we have the following equation

Total sales = 31.69 + 31.69 * 6%

Evaluate

Total sales = 33.59

Hence, the total amount is $33.59

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Step-by-step explanation:

using set notation

domain [-3,3]

range[-1,3]

The slope and y-intercept of the given equations of line are shown below.

When any equation is represented in the y = mx +c form, it is called the slope intercept from of the equation.

Here m is slope and c is constant.

(1)

y = 3x + 3

Slope m = 3

y intercept, at x =0,

y = 3

(2)

y = 3x - 3

Slope m = 3

y intercept, at x =0,

y = - 3

(3)

y = (1/3)x + 3

Slope m = 1/3

y intercept, at x =0,

y = 3

(4)

y = -(1/3)x + 3

Slope m = -1/3

y intercept, at x =0,

y = 3

(5)

y = (1/3)x - 3

Slope m = 1/3

y intercept, at x =0,

y = -3

(6)

y = -(1/3)x - 3

Slope m = -1/3

y intercept, at x =0,

y = -3

(7)

y = -3x + 3

Slope m = -3

y intercept, at x =0,

y = 3

(8)

y = -3x - 3

Slope m = -3

y intercept, at x =0,

y = - 3

The slope and y-intercept are shown above.

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Answer:

The amount of the markup is $2. The full price is $7

Step-by-step explanation:

%40 is 4/10, this can be simplified into 2/5

2/5 of 5 is 2

it is marked up so we add them together

5+2=7

Answer:

sin x° = Opposite / Hypotenuse

x = 3.38

Step-by-step explanation:

sin 70° = x / 3.6

sin 70° × 3.6 = x

x = 0.93969262079 × 3.6

x = 3.38289343483 ~ 3.38

Answer:

0.5

Step-by-step explanation:

Co-ordinate of the mid point of the segment whose co-ordinates are -6 & 7 is =

\( \frac{7 + ( - 6)}{2} = \frac{1}{2} = 0.5\)

The sixth term of the arithmetic progression is 94.

An arithmetic progression is a sequence of numbers such that the difference between any two successive members of the sequence is a constant.

Let's call the first term of the arithmetic progression "a" and the common difference "d". Then the nth term of the progression can be found using the formula:

an = a + (n-1)d

We know that the sum of the first four terms is 14, so we can set up the following equation:

a + (a+d) + (a+2d) + (a+3d) = 14

We also know that the sum of the first eight terms is 108, so we can set up another equation:

a + (a+d) + (a+2d) + (a+3d) + (a+4d) + (a+5d) + (a+6d) + (a+7d) = 108

Now we can use the first equation to substitute for the first four terms of the second equation:

14 + (a+4d) + (a+5d) + (a+6d) + (a+7d) = 108

This gives us:

a + 4d = 94

So the sixth term can be found by substituting n = 6 into the first formula:

a + (6-1)d = a + 5d = 94

Therefore, the sixth term of the arithmetic progression is 94.

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The expression given is 30 x [(9 x 2) - (4 + 3)]. In order to find which expression has a value of 1, we must simplify the expression. First, we must solve the parentheses by adding 4 and 3 together, which equals 7, and multiplying 9 and 2 together, which equals 18.

So, the expression now becomes 30 x [18 - 7]. Next, we must solve the brackets by subtracting 7 from 18, which equals 11. So, the expression now becomes 30 x 11. Finally, we must multiply 30 and 11 together to get the final answer, which is 330. Therefore, the given expression does not have a value of 1.
Hello! Let's solve the given expression and check if its value is 1.

Expression: 30 x [(9 x 2) - (4 + 3)]

Step 1: Perform operations within the parentheses first.
9 x 2 = 18
4 + 3 = 7

Step 2: Substitute these values back into the expression.
30 x (18 - 7)

Step 3: Perform subtraction inside the parentheses.
30 x (11)

Step 4: Perform the final multiplication.
30 x 11 = 330

The given expression has a value of 330, not 1.

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Using the formula of area of a circle, about 226.08in² has been eaten

The diameter of the pizza is given as 24 inches. To calculate the area of the entire pizza, we need to use the formula for the area of a circle:

Area = π * r²

where π is approximately 3.14 and r is the radius of the circle.

Given that the diameter is 24 inches, the radius (r) would be half of the diameter, which is 12 inches.

Let's calculate the area of the entire pizza first:

Area = 3.14 * 12²

Area = 3.14 * 144

Area ≈ 452.16 square inches

Now, if half of the pizza is consumed, we need to calculate the area of half of the pizza. To do that, we divide the area of the entire pizza by 2:

Area of half of the pizza = 452.16 / 2

Area of half of the pizza ≈ 226.08 square inches

Therefore, if half of the pizza is consumed, approximately 226.08 square inches of pizza would be eaten.

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The proportion of the 30 sampled bottles are more than 12 ounces is 0.30. The value is most affected by the error will be mean.

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency. A data set's mean (average) is calculated by adding all of the numbers in the set, then dividing by the total number of values in the set. When a data set is ranked from least to greatest, the median is the midpoint.

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Answer:The answer is x > -1

Step-by-step explanation:

Answer:

Can you give me any more context?

Answer:

81 degrees

Step-by-step explanation:

Because of exterior angles u=u-41+u-40

Solve:

u=2u-81

0=u-81

u=81

1. The mean of a dataset represents the average value of the entire set of numbers. It is calculated by adding up all the values and dividing by the number of values in the dataset. Knowing the standard deviation of a dataset adds information about how much the values deviate from the mean.

A high standard deviation indicates that the values are more spread out from the mean, while a low standard deviation indicates that the values are closer to the mean. It can help to identify outliers and the overall variability of the dataset.

2. A p-value is a statistical measure that helps to determine whether the null hypothesis (there is no significant difference between two groups) is true or false.

It is the probability of obtaining a result as extreme or more extreme than the observed result, assuming that the null hypothesis is true. A p-value of less than 0.05 (typically) is considered statistically significant, which means that there is strong evidence to reject the null hypothesis and accept the alternative hypothesis (there is a significant difference between the two groups).

3. Alpha is the level of significance that is set to determine whether a p-value is statistically significant or not. It is typically set at 0.05, which means that if the p-value is less than 0.05, then the result is considered statistically significant and the null hypothesis is rejected.

If the p-value is greater than 0.05, then the result is not statistically significant and the null hypothesis cannot be rejected. In summary, alpha and p-value are related because alpha sets the threshold for determining whether a p-value is statistically significant or not.

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Answer:

Step-by-step explanation:

(b) is correct.  x represents the bill and 0.15 represents the 15% tip on that bill.

Answer: 1/5

Step-by-step explanation:

The probability that a trip will be to either Nassau or Paris is 0.2 or 20%.

Given, a travel agency is giving away a free trip as part of a grand opening.

The trip will be to one of the ten locations listed. The 10 locations are London, Paris, Rome, Sydney, Athens, Nassau, Hong Kong, Madrid, Tokyo, and Rio De Janeiro.

To find the probability, we need to find how many outcomes are favorable to the event "the trip is to Nassau or Paris" and divide by the total number of possible outcomes.

So, favorable outcomes = 2 (Nassau, Paris)

Total possible outcomes = 10

Probability = (Favorable outcomes)/(Total possible outcomes)= 2/10= 0.2 or 20%.

Therefore, the probability that a trip will be to either Nassau or Paris is 0.2 or 20%.

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The solution and the answer are in the photograph.

The unknown angles when line BD bisect the angle ABC is as follows:\

An angle bisector divides and angle into 2 equal angles.

Therefore, line BD bisect angle ABC.

Hence,

let's find m∠ABD

if m∠ABD = 6x + 4

m∠DBC =  8x - 4

Therefore,

m∠ABD  = m∠DBC

6x + 4 = 8x - 4

6x - 8x = -4 - 4

-2x = -8

x = -8 / -2

x = 4

Therefore,

m∠ABD = 6x + 4 = 6(4) + 4  = 24 + 4 = 28°

let's find m∠ABC

If m∠ABD = 5y - 3

m∠DBC = 3y + 15

Hence,

m∠ABD = m∠DBC

5y - 3 = 3y + 15

5y - 3y = 15 + 3

2y = 18

y = 18 / 2

y = 9

Therefore,

m∠ABC = m∠ABD +  m∠DBC

m∠ABC = 5(9) - 3 + 3(9) + 15

m∠ABC = 45 - 3 + 27 + 15

m∠ABC = 84°

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The compound interest on birr 5006 at 5% for 4 years compounded annually​ is $1,078.82.

Compound interest is a type of interest that is calculated not only on the initial principal amount but also on the accumulated interest of previous periods.

In other words, the interest earned during each period is added to the principal amount, and the interest for the next period is calculated on the sum of the principal and the accumulated interest.

Given that:

First, convert R as a percent to r as a decimal

r = R/100

r = 5/100

r = 0.05 rate per year,

Then solve the equation for A

A = P(1 + r/n)^(nt)

A = 5,006(1 + 0.05/1)^(1*4)

A = 5,006(1 + 0.05)^(4)

A = $6,084.82

Compound interest =Amount - Principal

Compound interest = 6084.82 - 5006

Compound interest = $1,078.82

Therefore, The total amount accrued, principal plus interest, with compound interest on a principal of $5,006.00 at a rate of 5% per year compounded 1 time per year over 4 years is $6,084.82.

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The value of {x} for the given proportion is 853.4.

Given is the proportion as -

x : 8 : : 90120 : x

We know that -

Product of extremes = Product of means

x² = 90120 x 8

x² = 728160

x = 853.4

Therefore, the value of {x} for the given proportion is 853.4.

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