7. As part of an environmental studies class project, students measured the circumferences of a random sample of 41 spruce trees in Colorado. The sample mean circumference was X = 29.8 inches with a sample standard deviation of 7.2 inches. Find a 95% confidence interval for the true mean circumference of all spruce trees. (round to three decimal places.) (12 pts) a. State n, x, o ors, and determine the model (t or Z) b. Check the conditions: a. Find the Margin of Error d. Find the confidence interval e State your conclusion

Answer:

9

Step-by-step explanation:

Just substitute -2 in for a and 5 in for b

\(a^2 + b\\-2^2 + 5\\4 + 5\\9\)

Whenever you square a negative number the result is positive

Answer:

The answer is 9 or 3squared

Step-by-step explanation:

Swap the -2 in for a and 5 in for b

When ever a negative number is squared the answer will be a postive number.

Answer:

Step-by-step explanation:

Center: The center of a circle is defined as the point in the middle of the circle. The points that make up the curve that is the circle are all equidistant from the center point.

Answer:

Center of the circle.

Step-by-step explanation:

8x + 7 = -25

=>  8x = -25 - 7 = -32

=> x = -32/8 = -4

Answer:

-4=x

Step-by-step explanation:

8x+7(-7)=-25(-7)

8x(/8)=-32(/8)

-4=x

Answer:

Answer is option D

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

Answer:

f should be multiplied by e

Step-by-step explanation:

\(\frac{d}{e}\) = f ( multiply both sides by e to clear the fraction

d = ef ← f is multiplied by e

The estimated current total cost for the installed and insulated tank is $12,065.73.

The first step is to calculate the surface area of the tank. The surface area of a cylinder is calculated as follows:

surface_area = 2 * pi * r * h + 2 * pi * r^2

where:

r is the radius of the cylinder

h is the height of the cylinder

In this case, the radius of the cylinder is 1 meter (half of the diameter) and the height of the cylinder is 1 meter. So the surface area of the tank is:

surface_area = 2 * pi * 1 * 1 + 2 * pi * 1^2 = 6.283185307179586

The insulation will add a thickness of 0.05 meters to the surface area of the tank, so the total surface area of the insulated tank is:

surface_area = 6.283185307179586 + 2 * pi * 1 * 0.05 = 6.806032934459293

The cost of the insulation is $40 per square meter and the cost of labor is $95 per square meter, so the total cost of the insulation and labor is:

cost = 6.806032934459293 * (40 + 95) = $1,165.73

The original cost of the tank was $10,900, so the total cost of the insulated tank is:

cost = 10900 + 1165.73 = $12,065.73

Therefore, the estimated current total cost for the installed and insulated tank is $12,065.73.

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Answer:

5

Step-by-step explanation:

1.5+5x

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax n is nax n−1

5x1−1

Subtract 1 from 1.

5x 0

For any term t except 0, t 0 =1.

5×1

For any term t, t×1=t and 1t=t.

5

This is how i would solve it :))

The coterminal angles with the angle of 45º are given as follows:

The angle for this problem is given as follows:

45º.

For the positive coterminal angle, we can obtain the equivalent angle on the second quadrant, subtracting 180 from the angle measure, as follows:

180 - 45 = 35º.

For the negative coterminal angle, we can just change the sign, as follows:

-45º.

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2,13,26,41,58,77,98,etc.

The difference between every two consecutive numbers is greater by 2 than between the two previous consecutive numbers, starting with it being 11 between the first two numbers.

This can be written as:

2 13 (2+11) 26 (13+13) 41 (26+15)

58 (41+17) 77 (58+17) 98 (77+21) 121 (98+23) 146 (121+25)

Odd numbers are added to obtain the next term, as explained above.

The sequence up to 10 terms would be:

2, 13, 26, 41, 58, 77, 98, 121, 146

The proportion of the variation in the dependent variable y that is explained by the estimated regression equation is measured by the coefficient of determination.

What is coefficient of determination?

The effectiveness of a statistical model in forecasting a result is shown by the coefficient of determination (R²). The dependent variable in the model is a representation of the result.

R² can have a value of 0 or 1, with 1 being the maximum achievable. Simply said, a model's R² will be closer to 1 the more accurate its predictions are.

R² is a more precise measure of goodness of fit. The amount of volatility in the dependent variable that the model can account for.

You can typically tell whether your linear regression data's R² is high or low by graphing it. The graphs below, for instance, display two sets of simulated data:

Dots represent the observations.

The line of best fit, or predictions of the model, is displayed as a black line.

Purple lines represent the deviations (the residuals) between the data and their expected values.

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The production rate of the assembly line is 6000 parts per month.The assembly line produces 6000 parts per month, with a weekly production rate of 1500 parts.

To calculate the production rate of the assembly line, we need to consider the number of weeks in a month. Since the plant operates for 4 weeks per month, we can divide the total production by the number of weeks to find the weekly production rate.

Given that the assembly operations are sequential, we can calculate the weekly production rate as follows:

6000 parts/month ÷ 4 weeks/month = 1500 parts/week.

Therefore, the assembly line produces 1500 parts per week.

The assembly line produces 6000 parts per month, with a weekly production rate of 1500 parts. This information can be used for planning and managing production schedules efficiently.

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Observe the pattern below. (The alternate numbers form a pattern)2, 3, 4, 6, 6, 9, 8, 12, 10, 15, 12, ….The next two numbers in the series:

18 , 14 ...

If A be a matrix with linearly independent columns, then the statement that must be true is (A) The equation Az=b always has a solution for all b.

Since the columns of A are linearly independent, the matrix A has full column rank, i.e., its column space is the entire space R^n. Here are the implications of this fact for each statement:

A. The equation Az=b always has a solution for all b.

This is true, because for any b in R^n, we can write it as a linear combination of the columns of A, say b=c_1a_1+c_2a_2+...+c_na_n. Then, the solution to Az=b is simply z=[c_1,c_2,...,c_n]^T.

B. The equation Ab has a solution for all b precisely when it has more rows than columns.

This statement is false. The equation Ab=b is always solvable, regardless of the dimensions of A and b. The solution is simply b expressed in the basis of the column space of A.

C. There is no easy way to tell if Ax-b has a solution for all b.

This statement is also false. Since the columns of A are linearly independent, the equation Ax=b has at most one solution for each b. Therefore, Ax=b has a solution for all b if and only if the columns of A span the entire space R^n. This can be checked by computing the rank of A.

D. The equation Az-b has a solution for all b precisely when it has more columns than rows.

This statement is false. The equation Az=b is always solvable, regardless of the dimensions of A and b, as we have seen in (A).

E. The equation Ax-b never has a solution for all b.

This statement is false. The equation Ax=b has at most one solution for each b, and it is solvable for all b if and only if the columns of A span the entire space R^n, as we have seen in (C).

F. The equation Az-b has a solution for all b precisely when it is a square matrix.

This statement is false. The equation Az=b is always solvable, regardless of whether A is square or not, as we have seen in (A).

Therefore, the only true statement among the given options is (A) The equation Az=b always has a solution for all b.

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The function f ″ changes sign at approximately x = 0.64 and x = 2.50. These are the x-coordinates of the inflection points. So, the smaller value of x is 0.64 and the larger value of x is 2.50.

(a) Graphing the function.The given function is

f(x) = (sin(x))sin(x)

Here is the graph of the function :

The given function is an odd function. So, it is symmetric with respect to origin.

(b) Explanation of shape of graph.

As x approaches 0 from the right side, the function value approaches 0. As we can see from the graph, the function has a local maxima at x = π / 2 and local minima at x = 3π / 2.

The function oscillates between 1 and -1 infinitely many times in the given interval.

Hence, the limit does not exist.

(c) Using calculus to find exact maximum and minimum values of f(x).Differentiating the given function, we get

f '(x) = 2sin²x cosx

Again differentiating, we get

f ''(x) = 2sinx(2cos²x − sin²x)

= 2sinx(3cos²x − 1)

= 6sinxcos²x − 2sinx

Therefore, critical points occur at

x = π/2, 3π/2, 5π/2, 7π/2, ...f has a critical point at x = π/2.

On the interval [0, π], the critical points are endpoints of the interval. f(0) = 0 and f(π) = 0.The maximum value is 1 and the minimum value is -1.

(d) Using a computer algebra system to compute f″ and then using a graph of f″ to estimate the x-coordinates of the inflection points.We know that the second derivative of the function is

f''(x) = 6sin(x)cos²(x) − 2sin(x).The graph of f ″ can be obtained as follows:

Here, the function f ″ changes sign at approximately x = 0.64 and x = 2.50. These are the x-coordinates of the inflection points. So, the smaller value of x is 0.64 and the larger value of x is 2.50.

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The volume of the given solid over the indicated region of integration, f(x,y) = 2x + 2y - 5 and R = {(x,y): -4 ≤ x ≤ 1, 3 ≤ y ≤ 6}, is 63 units³.

To find the volume, we will integrate the function f(x,y) over the region R. Follow these steps:

1. Set up the double integral: ∬R (2x + 2y - 5) dA

2. Set up the limits of integration: ∫(from -4 to 1) ∫(from 3 to 6) (2x + 2y - 5) dy dx
3. Integrate with respect to y: ∫(from -4 to 1) [(2xy + 2y²/2 - 5y)] (evaluated from 3 to 6) dx
4. Simplify and evaluate: ∫(from -4 to 1) [6x + 18 - 5(6-3)] dx
5. Integrate with respect to x: [3x² + 18x - 15x] (evaluated from -4 to 1)
6. Simplify and evaluate: (3 + 18 - 15) - (-12 + 72 + 60)
7. Calculate the final result: 6 - (-30) = 36

The volume of the region is 63 units³.

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Answer:

53 (seconds)

Step-by-step explanation:

Let's calculate each of the boy's time to reach the destination and subtract them from each other to get our answer.

Bill:
Using the Pythagorean Theorem, a^2 + b^2 = c^2
Plugging in:
300^2 + (500+150)^2 = c^2

90000 + 650^2 = c^2 (you're gonna want a calculator)

90000 + 422500 = c^2
512500= c^2

Take the square root of both sides, isolating the variable c:
c= 715.891053 m
round it off: 716 m
c stands for the distance that Bill has to walk. If he is walking at 3 meters per second, we can divide to get the number of seconds:

716 / 3 = 238.666667 seconds to get to the playground
round it off: 239

Ted:
Using the Pythagorean Theorem, a^2 + b^2 = c^2
Plugging in:
300^2 + 500^2 = c^2

90000 + 250000 = c^2

340000=c^2

Take the square root of both sides, isolating the variable c:
c= 583.095189 m
round it off: 583 m
c stands for the distance that Ted has to walk. If he is walking at 2 meters per second, we can divide to get the number of seconds:

583 / 2 = 291.5 seconds to get to the playground
round it off: 292

Lastly, subtract the number of seconds it took Ted to the number of seconds it took Bill because Ted took a longer amount of time, and that will be your answer:
292-239= 53

The shorter route 53 seconds faster

Answer:

-20

Step-by-step explanation:

2((-1)(3)-7) = x

-1•3 first, then subtract that by 7 = -10

then multiply by 2 = -20

Answer:

Step-by-step explanation:

Given two points on the line:

Use the slope equation:

Slope:-

\(\sf\longmapsto m=\dfrac{y_2-y_1}{x_2-x_1}\)

\(\sf\longmapsto m=\dfrac{-4-78}{90-86}\)

\(\sf\longmapsto m=\dfrac{-82}{4}\)

\(\sf\longmapsto m=-41/2\)

\(\sf\longmapsto m=20.5\)

The false statement is B. 50% of houses in Ames are smaller than 1,499.69 square feet.

Statistics uses both the mean and median as gauges of central tendency, although their definitions and methods of computation vary. A number's mean is determined by adding together all of the values and dividing by the total number of values. A group of numbers has a median, which is the midpoint value, with half of the values above and below.

The median size of a home in Ames is 1,499.69 square feet, thus this claim is untrue. Therefore, 50% of the homes are smaller and 50% are larger than 1,499.69 square feet. Thus, assertion B is untrue.

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Answer:

C

Step-by-step explanation:

Given the 2 equations

5x + 2y = 29 → (1)

x + 4y = 13 → (2)

Multiplying (1) by - 2 and adding to (2) will eliminate the y- term

- 10x - 4y = - 58 → (3)

Add (2) and (3) term by term to eliminate y

- 9x + 0 = - 45

- 9x = - 45 ( divide both sides by - 9 )

x = 5

Substitute x = 5 into either of the 2 equations and solve for y

Substituting into (2)

5 + 4y = 13 ( subtract 5 from both sides )

4y = 8 ( divide both sides by 4 )

y = 2

Solution is x = 5, y = 2 → C

Answer:

c) x = 5, y = 2

Step-by-step explanation:

Answer:

do u mean decimal to a fraction

Answer:

0.875

Step-by-step explanation:

7/8 in a decimal form is 0.875

The domain of the function \(f(x) = \sqrt{\frac{1}{3}x + 2\) is (d) x  ≥ -6

From the question, we have the following parameters that can be used in our computation:

\(f(x) = \sqrt{\frac{1}{3}x + 2\)

Set the radicand greater than or equal to 0

So, we have

1/3x + 2 ≥ 0

Next, we have

1/3x  ≥ -2

So, we have

x  ≥ -6

Hence, the domain of the function is (d) x  ≥ -6

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Answer:

2x + 3 = 3x + 1

x = 2

hope that helps ✌

Answer: d-20

Step-by-step explanation:

if Mia has $20 less than Brandi, it means Brandi has d dollars, so we subtract Brandi 's money from $20.hope you understood.

Answer:

Over 2 up 4

Step-by-step explanation: I just learned this so I am not a pro but, 5 would be X for A, So to the right, down 2, 3 right for B, down 6

Answer:

4x² - 57x + 206

Step-by-step explanation:

To evaluate (t ￮ s)(x), substitute x = s(x) into t(x) , that is

t(x - 7)

= 4(x - 7)² - (x - 7) + 3 ← expand (x - 7)² using FOIL

= 4(x² - 14x + 49) - x + 7 + 3

= 4x² - 56x + 196 - x + 10 ← collect like terms )

= 4x² - 57x + 206

To use the tangent ratio in a triangle, you need to know the lengths of two sides or the measures of two angles in the triangle. The tangent ratio relates the length of the side opposite an angle to the length of the side adjacent to that angle in a right triangle.

The tangent ratio is a trigonometric ratio that relates the length of one side of a right triangle to the length of another side. It is defined as the ratio of the length of the side opposite a given angle to the length of the side adjacent to that angle.

In order to use the tangent ratio, you must have knowledge of the triangle's sides or angles. If you know the lengths of two sides of a right triangle, you can use the tangent ratio to find the measure of one of the acute angles in the triangle. Conversely, if you know the measure of one of the acute angles, you can use the tangent ratio to find the ratio of the lengths of the sides in the triangle.

Essentially, to apply the tangent ratio, you need to have sufficient information about the triangle to identify the sides or angles involved in the ratio calculation. This information can be provided in terms of lengths of sides or measures of angles, allowing you to use the tangent ratio to solve for missing values or determine specific relationships within the triangle.

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