Which of the fractions are less than 5/8? select 3 a) 3/4 b)5/6 c)1/2 d)2/5 e)1/4​

Given Data:

The time taken to compleat one yard is: 1 hour.

The expression to calculate the total yard made in 1/4 hour is,

The five-number summary for the dataset are Minimum: 68, Q1: 69, Median: 78, Q3: 90 and Maximum: 94.

To create a box and whisker plot for the given dataset {69, 88, 94, 73, 78, 90, 68}, follow these steps:

Step 1: Arrange the data in ascending order:

68, 69, 73, 78, 88, 90, 94

Step 2: Find the five-number summary:

Minimum: The smallest value in the dataset, which is 68.

First quartile (Q1): The median of the lower half of the dataset. In this case, it's the median of {68, 69, 73}, which is 69.

Median (Q2): The middle value of the dataset. In this case, it's 78.

Third quartile (Q3): The median of the upper half of the dataset. In this case, it's the median of {88, 90, 94}, which is 90.

Maximum: The largest value in the dataset, which is 94.

Step 3: Create the box and whisker plot:

Draw a number line with a range from the minimum (68) to the maximum (94).

Mark the first quartile (Q1) at 69.

Mark the median (Q2) at 78.

Mark the third quartile (Q3) at 90.

Draw a box from Q1 to Q3.

Draw a vertical line (whisker) from the box to the minimum (68) and another vertical line from the box to the maximum (94).

The resulting box and whisker plot for the given dataset would look like this:

  |

 94|                 ▄

  |                ╱ ╲

 90|              ╱   ╲

  |             ╱     ╲

 88|            ▇       ▂

  |            ▇       ▂

 78|            ▇       ▂

  |            ▇       ▂

 73|          ╱         ╲

  |         ╱           ╲

 69|        ▃             ▃

  |       ╱               ╲

 68|      ╱                 ╲

  |_________________________________

    68     73     78     88     94

This plot represents the distribution of the given dataset, showing the minimum, maximum, first quartile (Q1), median (Q2), and third quartile (Q3).

The five-number summary for the dataset are Minimum: 68, Q1: 69, Median: 78, Q3: 90 and Maximum: 94.

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Answer:

720

Step-by-step explanation:

The lock requires that repetition is not allowed.

The possibles numbers are 0 - 9, that is, 10 digits.

The first number in the combination can be picked from the 10 digits.

This means that there are 10 possible choices.

The second number in the combination can now only be picked from 9 digits.

This means that there are 9 possible choices.

The third number in the combination can now only be picked from 8 digits.

This means that there are 8 possible choices.

Therefore, the number of possible outcomes in the combination is:

10 * 9 * 8 = 720 outcomes

If there is a 93% chance of it being cloudy in the afternoon, the odds of it not being cloudy can be calculated as 7:93.

To determine the odds of an event, we divide the probability of the event not occurring by the probability of the event occurring. In this case, the probability of it being cloudy is 93%, which means the probability of it not being cloudy is 100% - 93% = 7%.

To express the odds, we use a ratio. The odds of it not being cloudy can be represented as 7:93. This means that for every 7 favorable outcomes (not cloudy), there are 93 unfavorable outcomes (cloudy).

It's important to note that the odds are different from the probability. While probability represents the likelihood of an event occurring, odds compare the likelihood of an event occurring to the likelihood of it not occurring.

In this case, the odds of it not being cloudy are relatively low compared to the odds of it being cloudy, reflecting the high probability of cloudy weather as announced by the meteorologist.

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The factor of 144 - 49x² is (12 - 7x)(12 + 7x). (Options a, c )

To find the factor  of 144 - 49x², we can use the difference of squares formula, which states that a² - b² can be factored as (a + b)(a - b).

In this case, a is 12 and b is 7x. Therefore, we can express 144 - 49x² as (12)² - (7x)² and apply the difference of squares formula to get:

(12)² - (7x)² = (12 + 7x)(12 - 7x)

Therefore, the factor of 144 - 49x² is (12 - 7x)(12 + 7x), which is the product of the factors obtained using the difference of squares formula.

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Complete Question:

Which is a factor of 144 − 49x2?

a. 12 + 7x

b. 72 – 7x

c. 12 – 7x

d. 72 + 7x

Estimable functions can be calculated using linear algebra when a design matrix is presented. Thus, the statement is proved.

Suppose E(Y)=Xβ as usual and let x 1, …,x r denote the columns of the matrix X. We have to show that β k is not estimable if and only if x k can be expressed exactly as a linear

combination of the other columns of X.

An estimable function is a linear combination of the parameters in a model that can be estimated. Estimable functions can be calculated using linear algebra when a design matrix is presented.

A design matrix is a table that displays the explanatory variables for the dependent variables in a statistical model. Let us prove the above statement by splitting it into two parts:

(i) β k is not estimable ⇒ x k can be expressed exactly as a linear combination of the other columns of X. Suppose that β k is not estimable, which implies that Xβ = Pβ, where P is an n x n symmetric, idempotent matrix of rank r-1, and β has r components. Because P is idempotent, it follows that X is in the null space of (I-P), and thus any column of X can be represented as a linear combination of the other columns of X.

(ii) x k can be expressed exactly as a linear combination of the other columns of X ⇒ β k is not estimable. Suppose x k can be expressed exactly as a linear combination of the other columns of X, say x k = Σa i x i, where i ≠ k and a i are scalars. Then, it follows that the jth element of Pβ is Σ a i β i if j ≠ k and P jj β k if j = k. Since x k can be expressed as a linear combination of the other columns, it follows that P kk = 0, which means that β k is not estimable.

Thus, the above statement is proved.

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Answer:

y = -3/4x - 5

Slope: -3/4

y-intercept: -5

Answer:

4.29x + 6.99y ≤ 88

Step-by-step explanation:

x represents the number of pounds of chicken he can buy and y represents the number of pounds of ham he can buy. Multiplying the price per pound by the number of pounds he will buy will give you the amount of money he will spend and here he has only $88. Which means the amount of money he will spend should be less than or equal to $88 as shown in the inequality above.

Hope this helps.

We need approximately 44.33 cubic feet of mulch to cover the flower bed with three inches of mulch.

We first need to convert the dimensions of the flower bed from feet to inches, since the thickness of the mulch is given in inches.

The length of the flower bed is 8 ft = 96 in (since 1 ft equals 12 inches), and the width is 22 ft = 264 in.

To find the volume of mulch needed, we need to find the volume of the rectangular solid that fits over the flower bed with a height of 3 inches:

Volume = Length x Width x Height

Volume = 96 in x 264 in x 3 in

Volume = 76,608 cubic inches

However, we are asked for the answer in cubic feet, so we need to convert our answer from cubic inches to cubic feet, using the fact that 1 cubic foot equals 12 x 12 x 12 = 1728 cubic inches:

Volume = 76608/1728 cubic feet

Volume = 44.33 cubic feet (rounded to two decimal places)

Therefore, we need approximately 44.33 cubic feet of mulch to cover the flower bed with three inches of mulch.

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a) The probability that at least 12 components will fail in performance among 100 components is approximately: 0.3707

b) The probability that between 8 and 13 (inclusive) components will fail in performance among 100 components is approximately: 0.5888

c) The probability that exactly 9 components will fail in performance among 100 components is approximately: 0.3693

To solve this problem using the normal approximation to the binomial distribution, we can use the following formulas:

Mean (μ) = n * p

Standard Deviation (σ) = √(n * p * (1 - p))

Given:

Number of components (n) = 100

Probability of failure (p) = 0.1

(a) To find the probability that at least 12 components will fail in performance among 100 such components using the normal approximation to the binomial distribution, we can follow these steps:

1. Calculate the mean (μ) and standard deviation (σ) of the binomial distribution:

  Mean (μ) = n * p = 100 * 0.1 = 10

  Standard Deviation (σ) = √(n * p * (1 - p)) = √(100 * 0.1 * 0.9) ≈ 3.0

2. Convert the binomial distribution to a normal distribution:

  The binomial distribution can be approximated by a normal distribution when n is large and the success probability (p) is not too close to 0 or 1. In this case, with n = 100 and p = 0.1, the conditions for approximation are satisfied.

3. Calculate the z-score for the lower value of "at least 12" (11 components or fewer):

  z = (x - μ) / σ

  z = (11 - 10) / 3 ≈ 0.333

4. Find the probability of the lower tail of the standard normal distribution using the z-score:

  P(Z ≤ 0.333) = 0.6293 (approximately)

5. Subtract the probability from 1 to get the probability of at least 12 components failing:

  P(X ≥ 12) = 1 - P(X ≤ 11)

            = 1 - 0.6293

            ≈ 0.3707

Therefore, the probability that at least 12 components will fail in performance among 100 components, using the normal approximation to the binomial distribution, is approximately 0.3707.

(b) To find the probability that between 8 and 13 components (inclusive) will fail in performance among 100 components using the normal approximation to the binomial distribution, we can follow these steps:

1. Calculate the mean (μ) and standard deviation (σ) of the binomial distribution:

  Mean (μ) = n * p = 100 * 0.1 = 10

  Standard Deviation (σ) = √(n * p * (1 - p)) = √(100 * 0.1 * 0.9) ≈ 3.0

2. Convert the binomial distribution to a normal distribution:

  The binomial distribution can be approximated by a normal distribution when n is large and the success probability (p) is not too close to 0 or 1. In this case, with n = 100 and p = 0.1, the conditions for approximation are satisfied.

3. Calculate the z-scores for the lower value (8 components) and the upper value (13 components):

  For the lower value:

  z_lower = (x_lower - μ) / σ = (8 - 10) / 3 = -2/3 ≈ -0.667

  For the upper value:

  z_upper = (x_upper - μ) / σ = (13 - 10) / 3 = 1

4. Find the cumulative probabilities for the lower and upper values using the standard normal distribution:

  P(X ≤ 8) ≈ P(Z ≤ -0.667) ≈ 0.2525 (using a standard normal distribution table or statistical software)

  P(X ≤ 13) ≈ P(Z ≤ 1) = 0.8413

5. Calculate the probability between 8 and 13 components (inclusive) failing:

  P(8 ≤ X ≤ 13) = P(X ≤ 13) - P(X ≤ 8) = 0.8413 - 0.2525 ≈ 0.5888

Therefore, the probability that between 8 and 13 components (inclusive) will fail in performance among 100 components, using the normal approximation to the binomial distribution, is approximately 0.5888.

(c) To find the probability that exactly 9 components will fail in performance among 100 components using the normal approximation to the binomial distribution, we can follow these steps:

1. Calculate the mean (μ) and standard deviation (σ) of the binomial distribution:

  Mean (μ) = n * p = 100 * 0.1 = 10

  Standard Deviation (σ) = √(n * p * (1 - p)) = √(100 * 0.1 * 0.9) ≈ 3.0

2. Convert the binomial distribution to a normal distribution:

  The binomial distribution can be approximated by a normal distribution when n is large and the success probability (p) is not too close to 0 or 1. In this case, with n = 100 and p = 0.1, the conditions for approximation are satisfied.

3. Calculate the z-scores for the lower value (9 components) and the upper value (9 components):

  For the lower value:

  z = (x - μ) / σ = (9 - 10) / 3 ≈ -0.333

4. Find the probability of the lower value using the standard normal distribution:

  P(X = 9) ≈ P(9 ≤ X ≤ 9) ≈ P(-0.333 ≤ Z ≤ -0.333) (using the normal approximation)

  Using a standard normal distribution table or statistical software, we can find the probability associated with the z-score of -0.333. Let's assume it is approximately 0.3693.

  P(X = 9) ≈ 0.3693

Therefore, the probability that exactly 9 components will fail in performance among 100 components, using the normal approximation to the binomial distribution, is approximately 0.3693.

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Answer:

should be 4L

Step-by-step explanation:

there is 4 cups with 1L of water in them so you add them up to get the total amount .

Answer:

4 Liters

Step-by-step explanation:

1. Create Equation

1L+1L+1L+1L

2. Solve

1L+1L+1L+1L

1+1+1+1

2+1+1

2+2

4

3. Check

1+1+1+1=4

2+2=4

4=4

Correct

4. Answer

4L

(a)Probability that a person could give up cell phone = 0.48

(b)Probability that a person who could give up her cell phone also could give up television is 0.65

(c) Probability that a person who could not give up a cell phone could give up television is 0.73

What is Probability?

Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability. It is crucial to grasp this branch's most fundamental concepts in order to fully comprehend it, including the formula for computing probabilities in equiprobable sample spaces, the likelihood of two events joining together, the probability of the complementary event, etc.

According to  the given question:

a. Probability that a person could give up cell phone = 0.48

b. Probability that a person who could give up her cell phone also could give up television

= P(give up cell phone and TV)/p(give up cell phone)

= 0.31/0.48

= 0.6458

= 0.65

c. Probability that a person who could not give up a cell phone could give up television is

= P(could not give up cellphone and could give up TV)/P(could not give up cell phone)

= 0.38/0.52

= 0.73

d. The probability a person could give up television is higher for persons who couldn't give up cell phones than for those who could give up their cell phones.

Hence,

(a)Probability that a person could give up cell phone = 0.48

(b)Probability that a person who could give up her cell phone also could give up television is 0.65

(c) Probability that a person who could not give up a cell phone could give up television is 0.73

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Answer:

Step-by-step explanation:

first plug 362.50 in for y since that is our office supply expense

362.50 = 10.50x + 100

then we solve for x

362.50 = 10.50x + 100

262.50 = 10.50x

25 = x

so 25 are working in the office that month

hope this helps <3

Answer:

a) 10, 20, 30, ...
b) 2, 4, 6, ...
c) 10, 20, 30, ...
d) 61, 66, 71, 76, ...
e) 180, 280, 380, ...

i dont know if this is correct but hope it helps

Answer:

2.828

Step-by-step explanation:

Answer:

60 r 56

Step-by-step explanation:

The volume of the parallelopiped is 1 cubic units.

In this question,

A parallelepiped is a three-dimensional shape with six faces, that are all in the shape of a parallelogram. It has 6 faces, 8 vertices, and 12 edges. The volume of a parallelepiped is the space occupied by the shape in a three-dimensional plane.

Let the parallelepiped be PQRS.

The vertices of parallelepiped are P(0, 1, 0), Q(1, 1, 1), R(0, 2, 0), S(3, 1, 2).

The volume of parallelopiped can be found by using following steps.

PQ = Q - P = (1,0,1)

PR = R - P  = (0,1,0)

PS = S - P  = (3,0,2)

Now, the volume of parallelopiped is

\(v=\left\begin{vmatrix}1&0&1\\0&1&0\\3&0&2\end{vmatrix}\)

The determinant the matrix is

⇒ 1(2-0) - 0(0-0) + 1(0-3)

⇒ 1(2) - 0 + (-3)

⇒ 2 - 3

⇒ -1

Hence we can conclude that the volume of the parallelopiped is 1 cubic units.

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Answer:

Step-by-step explanation:

the ration of the 2 figures are 4/3 from the larger to the smaller one

this means that 4/3*6=8

x-1=8

x=9

choice c

The length on the map representing the 27 miles between the two cities is 18 inches.Therefore, the length on the map would be 18 inches.

To solve this problem, we can use the scale of the map to set up a proportion:

2 inches / 3 miles = x inches / 27 miles

We can then cross-multiply to solve for x:

3x = 2 * 27
3x = 54
x = 18

Therefore, the length on the map would be 18 inches.

To find the length on the map representing the actual distance between two cities, we'll use the given scale:

2 inches represents 3 miles.

First, we'll determine the ratio between inches and miles:

2 inches / 3 miles

The actual distance between the cities is 27 miles. To find the corresponding length on the map, we can set up a proportion:

Length on map (in inches) / 27 miles = 2 inches / 3 miles

Next, we'll solve for the length on the map (in inches):

Length on map (in inches) = (2 inches / 3 miles) * 27 miles

The miles cancel out, and we're left with:

Length on map (in inches) = (2 inches * 27) / 3

Length on map (in inches) = 54 inches / 3

Length on map (in inches) = 18 inches

So, the length on the map representing the 27 miles between the two cities is 18 inches.

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The required Matlab code to find the greatest common divisor of a number using the Euclidean algorithm is shown.

To find the greatest common divisor (GCD) of two numbers using the Euclidean algorithm in MATLAB, you can use the following code:

% Replace '12345678' with your actual student number

studentNumber = '12345678';

% Extract the first 4 digits as the first number

firstNumber = str2double(studentNumber(1:4));

% Extract the last 3 digits as the second number

secondNumber = str2double(studentNumber(end-2:end));

% Find the GCD using the Euclidean algorithm

gcdValue = gcd(firstNumber, secondNumber);

% Display the result

disp(['The GCD of ' num2str(firstNumber) ' and ' num2str(secondNumber) ' is ' num2str(gcdValue) '.']);

Make sure to replace '12345678' with your actual student number. The code extracts the first 4 digits as the first number and the last 3 digits as the second number using string indexing. Then, the gcd function in MATLAB is used to calculate the GCD of the two numbers. Finally, the result is displayed using the disp function.

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At least 7 people chosen at random are needed to make the probability greater than 1/2 (or 50%) that there are at least two people born on the same day of the week.

To find the number of people needed to make the probability greater than 1/2 (which is 50%) that there are at least two people born on the same day of the week, we can use the concept of the birthday paradox.
The probability of two people having the same birthday is calculated as follows:
P(same birthday) = 1 - P(different birthdays)

The probability of two people having different birthdays can be calculated by considering the first person's birthday (1/7 chance of being born on any particular day of the week) and then multiplying it by the probability that the second person has a different birthday (6/7 chance).

Therefore, P(different birthdays) = (1/7) * (6/7) = 6/49.

To calculate the probability of no two people having the same birthday, we can calculate the complement:
P(no same birthday) = 1 - P(same birthday)

Using the complement rule, we can calculate the probability of no two people having the same birthday for different numbers of people chosen at random. We want to find the minimum number of people needed to make this probability less than 1/2.

For 2 people: P(no same birthday) = (6/49) ≈ 0.122

For 3 people: P(no same birthday) = (6/49) * (5/49) ≈ 0.092

For 4 people: P(no same birthday) = (6/49) * (5/49) * (4/49) ≈ 0.071

As the number of people chosen at random increases, the probability of no two people having the same birthday decreases. To find the minimum number of people needed to make the probability greater than 1/2, we continue this calculation until we find a probability less than 1/2:

For 5 people: P(no same birthday) = (6/49) * (5/49) * (4/49) * (3/49) ≈ 0.052

For 6 people: P(no same birthday) = (6/49) * (5/49) * (4/49) * (3/49) * (2/49) ≈ 0.037

For 7 people: P(no same birthday) = (6/49) * (5/49) * (4/49) * (3/49) * (2/49) * (1/49) ≈ 0.026

Therefore, at least 7 people chosen at random are needed to make the probability greater than 1/2 (or 50%) that there are at least two people born on the same day of the week.

In conclusion, at least 7 people chosen at random are needed to make the probability greater than 1/2 (or 50%) that there are at least two people born on the same day of the week.

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Noote that the measure of angle R is 27°. Here is how we got that.

Since the largest triangle is right triangle, the vertical segment is the perpendicular bisector of right angle with vertex at the center of circle.

Then we have

m∠R + 18° = 90°/2

m∠R + 18° = 45°

m∠R = 45° - 18°

m∠R = 27°

Note that the angle on the top of the triangle is right angle, 90 deg. Its altitude is the vertical segment, which is also angle bisector. It bisects the right angle and each formed angle measures 90/2 = 45°

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Full Question:

Although part of your question is missing, you might be referring to this full question:

See the attached iamge.

Answer:

A

because it is a negative number and because it is less than -1/2

Answer:

Step-by-step explanation:

the answer is -1 as negative integers become smaller as they go to the left.

no problem

Answer:

Step-by-step explanation:

Which accurately shows how to use inverse operations to find the value of a in a + 5 = 14?

if a + 5 = 14 just subtract 5 from 14

a + 5 = 14

a = 14 - 5

a = 9

------------check

9+5=14

14=14

the answer is good

Salik and Maya are discussing a project that examines the relationship between the number of siblings someone has and their household income. Maya predicts that those with more siblings will have a higher household income. Salik questions whether the number of siblings is a categorical variable since it is a whole number. Our response can be : "In order to conduct this project, we need to choose two quantitative variables, which are variables that can be measured and expressed as numbers. The number of siblings is not a categorical variable because it is a continuous variable that can take on any whole number value."

The number of siblings is a quantitative variable because it can be expressed as a whole number. Household income is also a quantitative variable because it can be measured and expressed as a numerical value. Categorical variables are variables that can be divided into distinct categories or groups, such as gender, race, or occupation. The number of siblings is not a categorical variable because it is a continuous variable that can take on any whole number value.

To examine the relationship between the number of siblings and household income, Maya and Salik could use statistics to analyze their data. They could calculate descriptive statistics such as the mean and standard deviation for each variable, as well as the correlation coefficient to determine the strength and direction of the relationship between the two variables. They could also use probability theory to make predictions about the likelihood of certain outcomes, such as the probability that someone with more siblings will have a higher household income.

The complete question is:

Our classmates, Maya and Salik, are talking about the variables they want to study and how they plan to collect their samples. Here is part of their conversation. Respond in the places that say “your response.”

Double-check that both of their variables are quantitative.

Maya: I want to look at the relationship between the number of siblings someone has and the household income. I predict that those with more siblings have a higher household income.

Salik: We need two quantitative variables for this project. Wouldn’t number of siblings be categorical since it is whole numbers?

Your response:.........

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a. Present value of $400 per year for 14 years at 14%: $2,702.83
b. Present value of $200 per year for 7 years at 7%: $1,155.54
c. Present value of $400 per year for 7 years at 0%: $2,800
d. Present value of $400 per year for 14 years at 14% (annuity due): $2,943.07
  Present value of $200 per year for 7 years at 7% (annuity due): $1,233.24
  Present value of $400 per year for 7 years at 0% (annuity due): $2,800

To find the present values of the ordinary annuities, we can use the formula for the present value of an annuity:

PV = PMT * [(1 - (1 + r)^(-n)) / r]
Where:
PV = Present value
PMT = Payment per period
r = Interest rate per period
n = Number of periods

a. $400 per year for 14 years at 14%:
PV = $400 * [(1 - (1 + 0.14)^(-14)) / 0.14]

≈ $2,702.83

b. $200 per year for 7 years at 7%:
PV = $200 * [(1 - (1 + 0.07)^(-7)) / 0.07]

≈ $1,155.54

c. $400 per year for 7 years at 0%:
Since the interest rate is 0%, the present value is simply the total amount of payments over the 7 years:
PV = $400 * 7

= $2,800

d. Reworking previous parts assuming they are annuities due:
For annuities due, we need to adjust the formula by multiplying it by (1 + r):

a. Present value of $400 per year for 14 years at 14%:
PV = $400 * [(1 - (1 + 0.14)^(-14)) / 0.14] * (1 + 0.14)

≈ $2,943.07

b. Present value of $200 per year for 7 years at 7%:
PV = $200 * [(1 - (1 + 0.07)^(-7)) / 0.07] * (1 + 0.07)

≈ $1,233.24

c. Present value of $400 per year for 7 years at 0%:
Since the interest rate is 0%, the present value remains the same:
PV = $400 * 7

= $2,800

In conclusion:
a. Present value of $400 per year for 14 years at 14%: $2,702.83
b. Present value of $200 per year for 7 years at 7%: $1,155.54
c. Present value of $400 per year for 7 years at 0%: $2,800
d. Present value of $400 per year for 14 years at 14% (annuity due): $2,943.07
  Present value of $200 per year for 7 years at 7% (annuity due): $1,233.24
  Present value of $400 per year for 7 years at 0% (annuity due): $2,800

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The most unlikely value of the population correlation coefficient (p) in this case is 0.98.

A confidence interval provides a range of values within which the true population parameter is likely to fall. In this case, the confidence interval for the population correlation coefficient is given as (0.62, 0.98). This means that there is a high likelihood that the true population correlation coefficient falls within this interval.

Since the interval is (0.62, 0.98), any value within this range is more likely to be the true population correlation coefficient compared to values outside the range. Therefore, the value of 0.98 is the most likely value of p within the given confidence interval.

Conversely, values outside the confidence interval are less likely to be the true population correlation coefficient. In this case, the value of 0.98 is at the upper end of the interval, making it the least likely value within the given range. Therefore, the most unlikely value of p among the options provided is 0.98.

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Answer:

B. 4

Step-by-step explanation:

\(7 \sqrt{7x} = \sqrt{49 \times 7x} \)

49 × 7x = 343x

14√7 = √(1372)

1372 ÷ 343 = 4 this is the vaule of x.

The correct option is (D). Approximately 77.3% of new machine set ups are completed in less than 25 minutes.

Given a local manufacturing plant, employees must complete new machine set ups within 30 minutes.

The new machine set-up times can be described by a normal model with a mean of 22 minutes and a standard deviation of four minutes. The typical worker needs five minutes to adjust to their surroundings before beginning their duties.

To find the percentage of new machine set ups completed in less than 25 minutes, we need to calculate the z-score. For this, we will use the formula:

z = (X - μ) / σ

where X = 25 minutes, μ = 22 minutes, and σ = 4 minutes

z = (25 - 22) / 4z = 0.75

We can now look up the percentage of the area under the normal distribution curve that corresponds to z = 0.75. Using a standard normal distribution table, we find that the area to the left of z = 0.75 is approximately 0.7734.

So, the percentage of new machine set ups completed in less than 25 minutes is approximately 77.34%.

Therefore, the correct option is (D).Approximately 77.3% of new machine set ups are completed in less than 25 minutes.

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Answer:

Point B

Step-by-step explanation:

The square root of 38 is 6.164, and point B is closest to 6.164