A solution consisting of 70 mg of dopamine in 70 mL of solution is administered at a rate of 15 mL/hr. Complete parts (a) and (b)
below.

Answer:

1.04

$45,552

Step-by-step explanation:

new price = 1.04 * original price

new price = 1.04 * 43,800

newprice: $45,552

Answer:

x = 10.6

Step-by-step explanation:

Soh...

Sine = Opposite / Hypotenuse

...cah...

Cosine = Adjacent / Hypotenuse

...toa

Tangent = Opposite / Adjacent

sin(49) = 8/x

x = 8/sin(49)

x = 10.6

Therefore, the unique value of c for this case is 1/2, which does not depend on p.

The Mean Value Theorem is a fundamental result in calculus that relates

f(b) - f(a) = f'(c) (b - a).

by the question.

We have, f(x) = x², where p > 1 and [a, b] = [0, 1].

Then, f(a) = f(0) = 0 and f(b) = f(1) = 1.

Also, f'(x) = 2x.

Now, by the Mean Value Theorem, there exists at least one number c in (a, b) such that:

f(b) - f(a) = f'(c)(b-a)

Substituting the values, we get:

1 - 0 = f'(c)(1-0)

1 = 2c

c = 1/2

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Answer:

A. the degree is 4         11x^4-4x^2-12

B. The degree is 5        2x^5-3x^4+3x^3+7x+14

Step-by-step explanation:

The degree is always the highest or greatest exponent in the polynomial. To rearrange the polynomial put it in descending order from highest exponent to lowest exponent with x as an exponent of 1

There sould be 11 terms of the following convergent series must be summed to be sure that the remainder is less than 10⁻¹ in magnitude

We can use the formula for the remainder of a convergent series:

Rn = Sn - S

where Rn is the remainder after summing the first n terms, Sn is the sum of the first n terms, and S is the infinite sum. In this case, the series is

sum(k=0 to infinity) (3^k - 1) / k!

so the infinite sum is S = e³ - 1. We want to find n such that the remainder Rn is less than 0.1, or |Rn| < 0.1.

The remainder formula tells us that

|Rn| = |sum(k=n+1 to infinity) (3^k - 1) / k!| <= sum(k=n+1 to infinity) |(3^k - 1) / k!|

To make an estimate, we can use the fact that

|3^k / k!| <= 3^k / (k-1)!

So we can write

|Rn| <= sum(k=n+1 to infinity) (3^k / (k-1)!) = e³ / (n!)

We want this to be less than 0.1, so we solve for n:

e³ / (n!) < 0.1

n! > e³ / 0.1

n > ln(e³ / 0.1)

n > 10.026

Since we can't sum a fraction of a term, we need to sum at least n = 11 terms to be sure that the remainder is less than 0.1 in magnitude.

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Option B is correct. The volume of the solid created is approximately 2.356 cubic units.

We can use the disk method.

First, we need to find the equation of the line passing through the points (1,0) and (1,1), which is simply x=1.

Next, we can find the equation of the line passing through the points (3,1) and (1,1) using the slope-intercept form: y - 1 = (1-1)/(3-1)(x-3) => y = -x/2 + 2

Now, we can find the points of intersection of the two lines:

x = 1, y = -x/2 + 2 => (1, 3/2)

Using the disk method, we can find the volume of the solid as follows:

V = ∫[1,3] πy² dx

= ∫[1,3] π(-x/2 + 2)² dx

= π∫[1,3] (x²- 4x + 4)dx/4

= π[(x³/3 - 2x² + 4x)] [1,3]/4

= π(3/4)

= 0.75π

Hence, volume of the solid created is 2.356 cubic units. Answer is closest to option B.

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Answer:

-6, -4, -3, 0

Step-by-step explanation:

I just did this question and got it right.

-6, -4, -3, and 0 are the values which are within the range of the piecewise-defined function.

Correct options: a) y = -6, b) y = -4, c) y = -3, d) y = 0

Here, we have, to determine which values are within the range of the piecewise-defined function, we need to evaluate the function for each given value of y.

Given piecewise-defined function:

f(x) =

2x, x < -3

x, x = -3

-x - 2, x > -3

Let's evaluate the function for each value of y:

a) y = -6

For y = -6, we need to find x such that f(x) = -6.

-6 is in the range of the function if there exists an x such that f(x) = -6.

For x < -3: f(x) = 2x

2x = -6

x = -3

For x = -3: f(x) = x

x = -3

For x > -3: f(x) = -x - 2

-x - 2 = -6

x = 4

Since there is a value of x (-3) that satisfies f(x) = -6, option a) y = -6 is correct.

b) y = -4

For y = -4, we need to find x such that f(x) = -4.

-4 is in the range of the function if there exists an x such that f(x) = -4.

For x < -3: f(x) = 2x

2x = -4

x = -2

For x = -3: f(x) = x

x = -3

For x > -3: f(x) = -x - 2

-x - 2 = -4

x = 2

Since there is a value of x (-3) that satisfies f(x) = -4, option b) y = -4 is correct.

c) y = -3

For y = -3, we need to find x such that f(x) = -3.

-3 is in the range of the function if there exists an x such that f(x) = -3.

For x < -3: f(x) = 2x

2x = -3

x = -1.5

For x = -3: f(x) = x

x = -3

For x > -3: f(x) = -x - 2

-x - 2 = -3

x = 1

Since there is a value of x (-3) that satisfies f(x) = -3, option c) y = -3 is correct.

d) y = 0

For y = 0, we need to find x such that f(x) = 0.

0 is in the range of the function if there exists an x such that f(x) = 0.

For x < -3: f(x) = 2x

2x = 0

x = 0

For x = -3: f(x) = x

x = -3

For x > -3: f(x) = -x - 2

-x - 2 = 0

x = -2

Since there is a value of x (-3) that satisfies f(x) = 0, option d) y = 0 is correct.

e) y = 1

For y = 1, we need to find x such that f(x) = 1.

1 is in the range of the function if there exists an x such that f(x) = 1.

For x < -3: f(x) = 2x

2x = 1

x = 0.5

For x = -3: f(x) = x

x = -3

For x > -3: f(x) = -x - 2

-x - 2 = 1

x = -3

Since there is no value of x that satisfies f(x) = 1, option e) y = 1 is incorrect.

f) y = 3

For y = 3, we need to find x such that f(x) = 3.

3 is in the range of the function if there exists an x such that f(x) = 3.

For x < -3: f(x) = 2x

2x = 3

x = 1.5

For x = -3: f(x) = x

x = -3

For x > -3: f(x) = -x - 2

-x - 2 = 3

x = -5

Since there is no value of x that satisfies f(x) = 3, option f) y = 3 is incorrect.

Correct options: a) y = -6, b) y = -4, c) y = -3, d) y = 0

The correct values within the range of the piecewise-defined function are -6, -4, -3, and 0.

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The store manager can use the function f(g(x)) = 0.90x - 30 to find the final price of a bicycle after the 10% sale discount and the additional $30 discount.

The first discount is a 10% sale on all items which means the price will be reduced by 10%.

We can represent this discount as 0.10x, where x is the original price.

The second discount is an additional $30 off the sale price.

We subtract $30 from the sale price.

Now, let's define the functions:

f(x) = x - 30 represents the additional $30 discount to the sale price of any bicycle.

g(x) = 0.90x represents the 10% discount, which is equivalent to multiplying the original price (x) by 0.90 (1 - 0.10 = 0.90).

To find the final price of a bicycle after both discounts, we need to apply both functions.

We can do this by evaluating f(g(x)).

f(g(x)) = f(0.90x) = 0.90x - 30

Therefore, the store manager can use the function f(g(x)) = 0.90x - 30 to find the final price of a bicycle after the 10% sale discount and the additional $30 discount.

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The quadratic equation I(x)=50x-x² into a linear factor form is x - 25.

The formula for linear factors is ax + b, an x + b. A polynomial cannot be factorised further over the real numbers, and there are no actual zeros or x  values that would make an irreducible quadratic factor equal to 0. A linear factor model establishes a linear equation-based link between the return on an asset (such as a stock, bond, mutual fund, or other type of investment) and the values of a small number of variables.

50x- x²

=x(50-x)

= product of 2 linear factors

zeros are 0 and 50 = x intercepts or roots

You could rewrite it in vertex form

-(x² - 50x + 25²) + 25²

= -(x-25)² + 625

with vertex = (25,625) = max point of a downward opening parabola

= -(x-25)(x-25) + 624

where (x-25)² is the product or square of 2 linear factors x - 25 and x-25

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(a) | Masses (kg) | Frequency | Cumulative Frequency |

|-------------|-----------|---------------------|

| 15-24       | 14        | 14                  |

| 25-34       | 54        | 68                  |

| 35-44       | 24        | 92                  |

| 45-54       | 26        | 118                 |

| 55-64       | 2         | 120                 |

(b) The cumulative frequency curve starts from the origin (0, 0) and moves upward and to the right, indicating that the mass of logs is increasing as we move right on the x-axis.

To construct the cumulative frequency table for the distribution of masses of 120 logs of wood, we need to add up the frequencies of each class and all the classes before it.

(b) To draw a cumulative frequency curve, we plot the cumulative frequency values against the upper class limits. The plot shows how the cumulative frequency increases with the increase in the mass of the log.

We use the same class intervals as in part (a):

- x-axis = Masses (kg)

- y-axis = Cumulative frequency

To plot the cumulative frequency curve, we mark the upper limit of each class on the x-axis, and its corresponding cumulative frequency on the y-axis. Then, we join the plotted points with a smooth curve, as shown in the graph.

The steeper the curve, the more rapid the increase in cumulative frequency, indicating that a larger number of logs fall in higher mass categories.

In the given distribution, the plot of the cumulative frequency curve shows that the majority of logs fall in the mass range of 25-34 kg, closely followed by the range of 45-54 kg.

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Answer:

x means 10 sooooo

Step-by-step explanation:

hope it helps

Answer:

X < 4

Step-by-step explanation:

Your welcome

Answer:

B

Step-by-step explanation:

Answer:

\(a= 10,\:\: b=6\)

Step-by-step explanation:

Answer:

A. If a bird is a crow, then it is black.

Step-by-step explanation:

Answer:

if a bird is a crow, then it is black

Answer:

C. AB = 10.7

Step-by-step explanation:

Let's look through each option.

Option A

❌ AB = 2(AC)

It can't be that since AC isn't equivalent to BC. AC is 5.5 and CB is 5.2

Option B

❌ AB = 11

AB doesn't equal 11. AB equals to AB + AC.

If you put the numbers in, it gets to AB = 5.5 + 5.2.

If you add the numbers up, it would get to AB = 10.7. Since 10.7 is not 11, option B won't work.

Option C

Option C works as shown in Option B.

Option D

none of the above isn't true since option C works.

Hope this helped! If not, please let me know! <3

The average rate of change over an interval can be calculated by finding the difference in the function's values at the endpoints of the interval and dividing it by the difference in the input values of the endpoints.

To calculate the average rate of change over an interval, follow these steps:

1. Identify the two endpoints of the interval. Let's call them x1 and x2.

2. Evaluate the function at x1 and x2 to find the corresponding function values, let's call them y1 and y2.

3. Calculate the difference in the function values by subtracting y1 from y2: (y2 - y1).

4. Calculate the difference in the input values by subtracting x1 from x2: (x2 - x1).

5. Finally, divide the difference in the function values by the difference in the input values to find the average rate of change: (y2 - y1) / (x2 - x1).

Let's look at an example:

Suppose we have the function f(x) = 2x + 3 and we want to find the average rate of change over the interval [1, 4].

1. The endpoints of the interval are x1 = 1 and x2 = 4.

2. Evaluate the function at x1 and x2:
  - f(1) = 2(1) + 3 = 5
  - f(4) = 2(4) + 3 = 11

3. Calculate the difference in the function values: 11 - 5 = 6.

4. Calculate the difference in the input values: 4 - 1 = 3.

5. Divide the difference in the function values by the difference in the input values:
  - 6 / 3 = 2.

Therefore, the average rate of change of f(x) over the interval [1, 4] is 2. This means that, on average, for every unit increase in x, the function f(x) increases by 2.

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For each of the given , we need to use the Law of Sines to determine whether the given information results in two triangles, one triangle, or no triangles. The Law of Sines states that for any triangle, the ratio of the length of a side to the sine of the opposite angle is the same for all three sides:

a/sin A = b/sin B = c/sin C

Let's look at each scenario and apply the Law of Sines:

Scenario 1: a = 7, b = 10, A = 50°

Using the Law of Sines, we can find the value of angle B:

7/sin 50° = 10/sin B

sin B = 10*sin 50°/7

sin B = 0.918

B = sin^-1(0.918) = 66.4°

Since the sum of the angles in a triangle must equal 180°, we can find the value of angle C:

C = 180° - 50° - 66.4° = 63.6°

Since all three angles add up to 180° and are positive, we can conclude that this scenario results in one triangle.

Scenario 2: a = 5, b = 7, A = 120°

Using the Law of Sines, we can find the value of angle B:

5/sin 120° = 7/sin B

sin B = 7*sin 120°/5

sin B = 1.209

Since the sine of an angle cannot be greater than 1, this scenario does not result in a triangle.

Scenario 3: a = 9, b = 12, A = 30°

Using the Law of Sines, we can find the value of angle B:

9/sin 30° = 12/sin B

sin B = 12*sin 30°/9

sin B = 0.667

B = sin^-1(0.667) = 41.8°

Since the sum of the angles in a triangle must equal 180°, we can find the value of angle C:

C = 180° - 30° - 41.8° = 108.2°

Since all three angles add up to 180° and are positive, we can conclude that this scenario results in one triangle.

In conclusion, scenario 1 and scenario 3 result in one triangle, while scenario 2 does not result in a triangle. We can determine this by using the Law of Sines and checking whether the values of the angles are valid and add up to 180°.

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The word IRON can be arranged is 24 unique ways.

Given:

The word = IRON

The number of unique ways in which the letters in the word IRON can be arranged = ?

The number of letters in IRON = 4

The number of positions = 4

In the first position, any one of the 4 letters can be placed

In the second position any one of the remaining 3 letters can be placed

In the third position any one of the remaining 2 letters can be placed

The fourth position can be filled with the left over letter

So the total number arrangement in unique way

= (Number of ways to fill in 1st position)* (Number of ways to fill in 2nd position)* (Number of ways to fill in 3rd position)* (Number of ways to fill in 4th position)

=> 4 *3*2*1

= 24 ways

Hence, The word IRON can be arranged is 24 unique ways.

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Problem

write this as a conditional statement, converse inverse and counterpositive

Mrs.smith has a dog that is not a poodle.​

Solution

Conditional: If Mrs smith has a dog THEN is not a poodle

Converse Inverse: If a dog is a poodle then is from Mrs Smith

Counterpositive: If the dog is NOT a poodle then is NOT from Mrs Smith

a) X is an unbiased estimator of p. b) The Var(X) is p(1-p)/n. c) The E[X(1-X)] is (n-1)[p(1-p)/n]. d) The value of c is c = 1/(n-1).

(a) To show that X = Y/n is an unbiased estimator of p, we need to show that E[X] = p.

Since Y is a sum of n iid Bern(p) random variables, we have E[Y] = np.

Now, let's find the expected value of X:

E[X] = E[Y/n] = E[Y]/n = np/n = p.

Therefore, X is an unbiased estimator of p.

(b) To find the variance of X, we'll use the fact that Var(aX) = a^2 * Var(X) for any constant a.

Var(X) = Var(Y/n) = Var(Y)/n² = np(1-p)/n² = p(1-p)/n.

(c) To show that E[X(1-X)] = (n-1)[p(1-p)/n], we expand the expression:

E[X(1-X)] = E[X - X²] = E[X] - E[X²].

We already know that E[X] = p from part (a).

Now, let's find E[X²]:

E[X²] = E[(Y/n)²] = E[(Y²)/n²] = Var(Y)/n² + (E[Y]/n)².

Using the formula for the variance of a binomial distribution, Var(Y) = np(1-p), we have:

E[X²] = np(1-p)/n² + (np/n)² = p(1-p)/n + p² = p(1-p)/n + p(1-p) = (1-p)(p + p(1-p))/n = (1-p)(p + p - p²)/n = (1-p)(2p - p²)/n = 2p(1-p)/n - p²(1-p)/n = 2p(1-p)/n - p(1-p)²/n = [2p(1-p) - p(1-p)²]/n = [p(1-p)(2 - (1-p))]/n = [p(1-p)(1+p)]/n = p(1-p)(1+p)/n = p(1-p)/n.

Therefore, E[X(1-X)] = E[X] - E[X²] = p - p(1-p)/n = (n-1)p(1-p)/n = (n-1)[p(1-p)/n].

(d) To find the value of c such that cX(1-X) is an unbiased estimator of p(1-p)/n, we need to have E[cX(1-X)] = p(1-p)/n.

E[cX(1-X)] = cE[X(1-X)] = c[(n-1)[p(1-p)/n]].

For unbiasedness, we want this to be equal to p(1-p)/n:

c[(n-1)[p(1-p)/n]] = p(1-p)/n.

Simplifying, we have:

c(n-1)p(1-p) = p(1-p).

Since this should hold for all values of p, (n-1)c = 1.

Therefore, the value of c is c = 1/(n-1).

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Based on the information provided, it seems that you are encountering some issues with a module called "binary_finder."

The phrase "content loaded" suggests that you have loaded some content, possibly related to this module. "Binary not linear" indicates that the nature of the content or code you're dealing with is binary, which means it consists of zeros and ones.

You mentioned having two pictures, one showing the question code and another displaying an answer from Chegg, which you find insufficient. However, the actual content of those pictures was not provided. If you can share the code or describe the specific problem you're facing with the binary_finder module, I'll be happy to assist you further.

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The 95% confidence interval for the average cost of

accessories on Mini Cooper is between $4790.254 and $5219.746

The margin of error in estimating the average cost of accessories on Mini Coopers is $219.7459.

The required sample size should be 34574400 to reduce the

margin of error by 50%

Sample size, n = 179

Sample mean, x = 5,000

Population standard deviation, σ = 1,500

Confidence level, 1-α=0.95

⇒ Level of significance, α = 0.05

From the z-table, the tabulated value is given by

\(Z_{\alpha /2}\) / \(Z_{0.025}\)

=1.95

95% confidence interval for the average cost of accessories on Mini Cooper is

5,000±1.96×(1,500/√179)

= (5,000 ± 219.7459)

=($4790.254, $5219.746)

Therefore the 95% confidence interval for the average cost of

accessories on Mini Cooper is between $4790.254 and $5219.746.

Margin of error

= 1.96x(1,500/√179)

= 219.7459

Therefore, the margin of error in estimating the average cost of accessories on Mini Coopers is $219.7459.

The margin of error (E) is 0.50

⇒(0.50) √n=1.96(1500)

√n = 1.96(1500) /0.50

= n = (1.96(1500) /0.50)²

= n = (5880)²

= n = 34574400

Therefore, the required sample size should be 34574400 to reduce the

the margin of error by 50%

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The following statements that are true four years from now, in the year 2024 are the Thrift segment will demand 7,745 thousand units and the Core segment will demand 9,779 thousand units.

Demand in economics refers to a consumer's readiness to pay a particular price for goods and services as well as their desire to buy them. Demand for a good or service typically declines when its price goes up. Demand describes the consumer's desire and willingness to purchase a good or service at a specific time or over an extended period of time. Additionally, consumers must be able to afford the items they want or need based on their budgeted disposable income. Demand therefore has an impact on market expansion and economic growth.

Given

The following statements that are true four years from now, in the year 2024 are:

The Thrift segment will demand 7,745 thousand units.

The Core segment will demand 9,779 thousand units.

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There are 9,999 natural numbers that have no more than 4 digits.

To determine the number of natural numbers that have no more than 4 digits, we consider the range of numbers from 1 to 9,999.

The natural numbers with no more than 4 digits include all numbers from 1 to 9 (which form the single-digit numbers), all numbers from 10 to 99 (which form the two-digit numbers), all numbers from 100 to 999 (which form the three-digit numbers), and all numbers from 1,000 to 9,999 (which form the four-digit numbers).

To calculate the total count, we can add the number of single-digit numbers, two-digit numbers, three-digit numbers, and four-digit numbers:

Single-digit numbers: 9 (from 1 to 9)

Two-digit numbers: 90 (from 10 to 99)

Three-digit numbers: 900 (from 100 to 999)

Four-digit numbers: 9,000 (from 1,000 to 9,999)

Adding these counts together:

9 + 90 + 900 + 9,000 = 9,999

Therefore, there are 9,999 natural numbers that have no more than 4 digits.

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The area represented by g(x) is a triangular region with base 1 and height (7/3) x, where x is the variable along the horizontal axis. The resulting shape will be a right triangle with vertices at (0,0), (1,0), and (0, (7/3) x).

It seems like you are asking to sketch the area represented by the function g(x) given as the integral of x with respect to t from 1 to 2. However, there seems to be a typo in your question. I will assume that you meant g(x) = ∫[1 to x] t^2 dt. Please follow these steps to sketch the area represented by g(x):

1. Draw the function y = t^2 on the coordinate plane (x-axis: t, y-axis: t^2).

To sketch the area represented by g(x) = x t2 dt 1, we first need to evaluate the definite integral. Integrating x t2 with respect to t gives us (1/3) x t3 + C, where C is the constant of integration. Evaluating this expression from t=1 to t=2 gives us (1/3) x (2^3 - 1^3) = (7/3) x.

2. Choose an arbitrary x-value between 1 and 2 (e.g., x = 1.5).
3. Draw a vertical line from the x-axis to the curve of y = t^2 at x = 1.5. This line represents the upper limit of the integral.
4. Draw another horizontal axis from the x-axis to the curve of y = t^2 at x = 1. This line represents the lower limit of the integral.
5. The area enclosed by the curve y = t^2, the x-axis, and the vertical lines at x = 1 and x = 1.5 represents the area for the given value of x.

In conclusion, the area represented by g(x) = ∫[1 to x] t^2 dt can be sketched by plotting the curve y = t^2, choosing a specific x-value between 1 and 2, and then finding the enclosed area between the curve, x-axis, and the vertical lines at x = 1 and x = chosen x-value.

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Step-by-step explanation:

To convert a value from meters/seconds to kilometers/hour you multiply by 3,6.

example:

1,2 m/s => 1,2x3,6 = > 4,32 km/h

78 km/h => 78/3,6 => 21,67 m/s

Answer:

36 km/hr

Step-by-step explanation:

To convert meters/second to kilometers/hour, we need to multiply the value in meters/second by 3.6 (which is 3,600 seconds per hour) and divide it by 1,000 (which is the number of meters in a kilometer). So the formula is:

kilometers/hour = (meters/second) x 3.6 / 1,000

For example, if we want to convert a speed of 10 meters/second to kilometers/hour, we can use the formula as follows:

kilometers/hour = (10 meters/second) x 3.6 / 1,000 = 36 kilometers/hour

Therefore, a speed of 10 meters/second is equivalent to 36 kilometers/hour.

The 99 percent confidence interval for the mean score of all subjects lies greater than 63.464 and less than 78.936.

Given:

No. of samples (n)= 16

df = n-1 = 16 -1 = 15

The mean score is 71.2

The standard deviation = 10.5.

So, from the t-distribution of critical values table through the above-mentioned details. We get the values:

Alpha / 2 = 0.005

z = 99/100 + 0.005 = .99 + .005 = .995

Sample mean = xbar = 76.2

t = 2.947

The formula for standard error = E = value of t (at z, and df) / S.D./sqrt(n)

i.e. E = 2.947 x 10.5 / sqrt 16 = 7.736

I = 71.2 +/- E =  71.2 +/-  7.736

99 percent confidence interval - 71.2 +/- 7.736

Adding both sides 7.736 for range. We get,

63.464 < u < 78.936

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Answer:

12/5

Step-by-step explanation:

7 1/5=

Answer:

\( \frac{36}{5} \)

Step-by-step explanation:

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