The mean of a normally distributed data set is 45, and its standard deviation is 7. for this data, the probability of which range of numbers is represented by the area of the shaded region in the given curve?

Answer:

120 trees

Step-by-step explanation:

4x10=40

40x3=120

120 trees will be planted

The probability of getting a 4 on the first roll, a 5 on the second roll, and a 6 on the third roll is,

⇒ 1/216

We have to given that,

A number cube is rolled three times.

Now, Let the number cube is fair and has six equally likely outcomes (1, 2, 3, 4, 5, or 6) on each roll,

Hence, The probability of getting a 4 on the first roll is,

⇒ 1 / 6

And, The probability of getting a 5 on the second roll is,

⇒ 1 / 6

And, The probability of getting a 6 on the third roll is,

⇒ 1 / 6

Thus, The probability of getting a 4 on the first roll, a 5 on the second roll, and a 6 on the third roll is,

⇒ 1/6 × 1/6 × 1/6

⇒ 1 / 216

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Answer: 47.5

Step-by-step explanation:

The measure of angle x is 140°

For given question,

We are given that a pair of parallel lines is cut by a transversal line .

Let a pair of parallel lines are PQ and RS and the transversal line AB cut the parallel lines PQ and RS.

We are given that an exterior angle on the left side of the transversal line is 40 degrees.

The interior angle on the right side of transversal line is x which is not vertical opposite to exterior angle = 40 degrees

We know that when two lines are parallel and cut by a transversal line then corresponding angles are congruent.

So, angle MNR = 40°

Also, ∠MNR + ∠MNS = 180°           ...............(linear pair of angles)

⇒ 40° + x = 180°

⇒ x = 140°

Therefore, the measure of angle x is 140°

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If Angle M is y then,

Step-by-step explanation:

(6y) + (3y -6) + y = 180°

10y - 6 = 180

10y = 186

y= 18.6

Angle O = 3(18.6) - 6 = 49.8

Answer 49.8

I hope this helps!!!

Answer:

$100

Step-by-step explanation:

The bottom row is how many mph the driver is over, the left row is how much it costs per mph over. Since 62mph in a 55mph zone is 7mph over, you go the 7 on the bottom, and go up until you get to the point, then see what the number on the left is. In this case, it would be 100. So therefore the fine is $100.

Answer:

Its C

Step-by-step explanation:

Im not sure if its correct but heres  the best i  explination I got!!

Ok so  first negatives would be least so ignore 13   and seven

now since  theres two that could be greater than the other ( -11 3/4 or -13) next would be  -7 after u and the 7 to 13! so ur best one is C since D and E make -11 behind 7 or scrambled in greatest

Answer:

x=26°, y=26°, z=26°

Step-by-step explanation:

x+74=100 (the sum of linear pair)

x=100-74

x=26

x=y=26 (alternate angle)

y=z=26 (vertically opposite angle V.O.A)

peacekeeper yesyklll

Answer:

1x + 2 = 13

1x = 13 - 2

1x = 11 (divide both sides by 1 to get x)

1x/1 = 11/1

x = 11

Step-by-step explanation:

:)

Answer:

x < 11

Step-by-step explanation:

By subtracting both sides of the equation by 2 via the subtraction property of equality, one can eliminate the positive 2 on the left side of the equation in order to simplify the inequality as much as possible.

If square based pyramid's perimeter is 18.5 ft and it's height is 7.6 ft, then volume of that pyramid is 54.4 cubic foot.

The "Volume" of a square pyramid is known as the space which is occupied by pyramid, and it is represented as : V = (1/3) × B × h, where V is volume, B is area of base, and h is height of pyramid,

The shape of "base-of-pyramid" is a square,

So, we find "base-area" by dividing perimeter by 4 and squaring it;

⇒ Perimeter of base of pyramid = 18.5 ft,

⇒ Length of "one-side" of base = 18.5/4 = 4.625 ft,

So, ⇒ Base area = (4.625 ft)² = 21.390625 sq ft,

Now, using the formula to find volume;

⇒ Volume = (1/3) × 21.390625 × 7.6 ,

⇒ Volume = 54.384375 cubic feet,

Rounding volume to "nearest-tenth" of a cubic foot,

We get,

⇒  Volume ≈ 54.4 ft³.

Therefore, Volume of pyramid is 54.4 ft³.

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The given question is incomplete, the complete question is

Find the volume of a pyramid with a square base, where the perimeter of the base is 18.5 ft and the height of the pyramid is 7.6 ft. Round your answer to the nearest tenth of a cubic foot.

Step-by-stepAnswer:

∠4 and ∠5

Step-by-step explanation:

Both angels seem to add up to 180°

Answer:

f^-1(4) = 2

f^-1(-5) = -4

f^-1(0) = 0

Step-by-step explanation:

To find the inverse of the function, we simply switch the places of x and y

You simply find the value given on the y-axis and trace to the x-axis

Thus, we have the following ;

f^-1(4) = 2

f^-1(-5) = -4

f^-1(0) = 0

Answer:

2

-4

0

Step-by-step explanation:

(a) Sample size: Increasing the sample size decreases the variance of the OLS estimator. (b) Variation in X: Greater variation in X leads to higher variance in the OLS estimator.

(a) Sample Size: Increasing the sample size tends to reduce the variance of the Ordinary Least Squares (OLS) estimator. As the sample size grows larger, the estimator becomes more precise and better captures the true underlying relationship between the variables. With more observations, the OLS estimator tends to average out random errors, leading to a decrease in variance. However, if there are influential outliers or systematic biases present in the data, increasing the sample size may not necessarily result in a significant reduction in the variance.

(b) Variation in X: The variance of the OLS estimator is influenced by the variation in the independent variable (X). When there is greater variation in X, the OLS estimator tends to have higher variance. This occurs because a wider range of X values can lead to a wider range of predicted Y values, resulting in larger deviations from the true regression line. In contrast, if there is less variation in X, the OLS estimator will have lower variance as the predicted Y values will be more tightly clustered around the regression line. Therefore, an increase in the variation of X tends to increase the variance of the OLS estimator.

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Step-by-step explanation:

\(f(x) = ln( \frac{1}{x} ) \)

To find the derivative, notice we have a function 1/x inside of another function, ln(x)

We use what we call the chain rule,

It states that

derivative of a '

\( \frac{d}{dx} f(g(x)) = f '(g(x)) \times \: g '(x)\)

Here f is ln(x)

f is 1/x

So first, we know that

\( \frac{d}{dx} ( ln(x) = \frac{1}{x} \)

so

\(f'(g(x)) = \frac{1}{ \frac{1}{x} } \)

We know that

\(g'(x) = - \frac{1}{ {x}^{2} } \)

So we have

\(x \times - \frac{1}{ {x}^{2} } = \frac{ - 1}{x} \)

The costs of carrying inventory do not include the interest on funds tied up in inventory. The firm's operating income at sales of 30,000 units will be $30,000. The correct answer is $30,000.

Calculate the firm's operating income at sales of 30,000 units, we first need to calculate the total contribution margin, which is the contribution margin per unit multiplied by the number of units sold:
Contribution margin per unit = $3.00
Number of units sold = 30,000
Total contribution margin = $3.00 x 30,000 = $90,000
Next, we can calculate the firm's total operating expenses, which are the fixed costs of $60,000:
Total operating expenses = $60,000
Finally, we can calculate the firm's operating income by subtracting the total operating expenses from the total contribution margin:
Operating income = Total contribution margin - Total operating expenses
Operating income = $90,000 - $60,000
Operating income = $30,000
Therefore, the firm's operating income at sales of 30,000 units will be $30,000. The correct answer is $30,000.

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Alessandra's statement corresponds to the alternative hypothesis (c) in a hypothesis test, suggesting a change or effect of the independent variable on the dependent variable.

The statement made by Alessandra regarding a hypothesis test suggests the use of an alternative hypothesis (c). In hypothesis testing, the alternative hypothesis represents the claim or belief that there will be a change or effect on the dependent variable due to the independent variable. It opposes the null hypothesis, which assumes no change or effect. In this case, Alessandra is proposing that there will be a difference or relationship between the independent and dependent variables.

To further elaborate, a hypothesis test is a statistical method used to make inferences about a population based on sample data. It involves formulating a null hypothesis (b), which assumes no significant difference or relationship between variables, and an alternative hypothesis (c), which asserts that there is a significant difference or relationship. The independent-measures t-test and repeated-measures t-test (d) are specific types of statistical tests used to compare means or differences between groups, but they are not directly related to the hypothesis statement provided by Alessandra.

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The distance bewteen the points (-3,5) and (3,1) in a simple radical form is 2√13.

The distance formula used in finding the distance between two points is expressed as;

d = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

From the graph;

Point A: (-3,5)

x₁ = -3

y₁ = 5

Point B: (3,1)

x₂ = 3

y₂ = 1

Plug the given values into the distance formula and simplify.

\(d = \sqrt{( x_2 - x_1)^2 + (y_2 -y_1 )^2} \\\\d = \sqrt{( 3-(-3))^2 + (1 -5)^2} \\\\d = \sqrt{( 3+ 3)^2 + (1 -5)^2} \\\\d = \sqrt{( 6)^2 + (-4)^2} \\\\d = \sqrt{36 + 16} \\\\d = \sqrt{52}\\\\d = 2\sqrt{13}\)

Therefore, the distance between the points is 2√13.

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Answer: 360

Step-by-step explanation:

done

The expression that fails to compute the area of a triangle correctly is option b: (1 / 2) * b * h.

The correct formula to compute the area of a triangle is one-half times the base multiplied by the height, which can be written as (1/2) * b * h. Option a, c, and d correctly represent this formula. However, option b is incorrect because it uses integer division instead of decimal division.

In option b, (1 / 2) is computed using integer division, which results in truncating the decimal part. Therefore, (1 / 2) evaluates to 0 instead of 0.5. As a result, the expression (1 / 2) * b * h would yield incorrect and significantly smaller results than the actual area of the triangle.

To accurately calculate the area of a triangle using this formula, it is essential to use decimal division or explicitly represent the fraction as a decimal. Options a, c, and d correctly account for this by using either 1.0/2.0 or 0.5, ensuring the proper calculation of the area.

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The equation of the line in point-slope form is: C. y − 5 = −(x − 2).

A line with a slope (m) and a point (a, b) is represented in point-slope form as, y - b = m(x - a).

Slopes of perpendicular lines are negative reciprocals of each other. Find the slope of the line in the graph given as follows:

Slope (m) = rise/run = 3 units/3 units = 1

Negative reciprocal of 1 is -1.

The slope of the line would be m = -1.

Substitute m = -1 and (a, b) = (2, 5) into y - b = m(x - a) to wrote the equation:

y - 5 = -1(x - 2)

y − 5 = −(x − 2)

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Answer:

(-5 , 6)

Step-by-step explanation:

f(x) = (x - (-5))² - 3     ... vertex (h , k) : (-5 , -3)     y = (x-h)² + k

g(x) = -f(x) + 3 = -((x+5)² - 3) + 3 = -(x + 5)² + 6

vertex of g(x) is : (-5 , 6)

The average speed of Renee over the last 2 hours of her trip is 9 miles/hour.

Let the average speed of Renee in 2 hours in between 6th and 8th hour be x miles / hours.

So the distance covered by Renee in 6 hours is = 6x

So the distance covered by Renee in 8 hours is = 8x

So the distance covered by Renee in this 2 hours in between 6th and 8th hours is = 8x - 6x

So according to the information the distance covered by Renee in this same 2 hours = 74 - 56 = 18 miles.

The equation best situated to the situation is,

8x - 6x = 18

2x = 18

x = 18/2

x = 9

Hence the average speed of Renee over the last 2 hours of her trip is 9 miles/hour.

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To solve the inequality −35x + 15 > 720, we need to find the value of x that satisfies the inequality. The solution to the inequality is x < -19.

To solve the inequality, we first subtract 15 from both sides to isolate the term with x. This gives us −35x > 705. Then, we divide both sides by -35. However, it's important to remember that when we divide an inequality by a negative number, we must reverse the direction of the inequality symbol. Therefore, we get x < -19 as the solution.

The inequality x < -19 represents all the values of x that make the original inequality −35x + 15 > 720 true. It means that any value of x less than -19 will satisfy the inequality. The solution set consists of all real numbers to the left of -19 on the number line.

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Answer:

The weight of the two goats is 2.08 kg

Step-by-step explanation:

Total avg

Avg of the two goats

Avg of one goat

Answer:

0.110

0.230

Step-by-step explanation:

Given :

In health :

Average salary, m = 51,541

Standard deviation, s = 11000

In Business :

Average salary, m = 53,901

Standard deviation, s = 15000

Since distribution is approximately normal ;

We can obtain the standardized scores and find the probability ;

Zscore = (x - mean) / standard deviation

Probability of earning salary if atleast $65,000

Health:

P(Z ≥ (65000 - 51541) / 11000) = P(Z ≥ 1.224) = 0.11048 (Z probability calculator)

Business :

P(Z ≥ (65000 - 53901) / 15000) = P(Z ≥ 0.740) = 0.22965 (Z probability calculator)

Hence, the probability of earning a starting salary of atleast $65,000 is :

Health = 0.11048

Business = 0.22965

The beta of the portfolio, considering $1 with a beta of 3% and $2 with a beta of 7% and a weight of 0.1 (w1), is 6.6%.


The beta of a portfolio measures its sensitivity to overall market movements. To calculate the beta of a portfolio, we need the individual asset weights and betas of each asset. Given that $1 has a beta of 3% and $2 has a beta of 7%, with a weight of 0.1 (w1), we can determine the beta of the portfolio.

To calculate the beta of the portfolio, we use the following formula:

β(portfolio) = (w1 * β1) + (w2 * β2) + ...

In this case, the portfolio contains two assets, so the formula becomes:

β(portfolio) = (w1 * β1) + (w2 * β2)

Substituting the given values:

β(portfolio) = (0.1 * 3%) + (0.9 * 7%)

β(portfolio) = 0.3% + 6.3%

β(portfolio) = 6.6%

Therefore, the beta of the portfolio is 6.6%.

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The length of one side of the box is 10 inches.

Suppose that: The side length of the considered cube is L units.

Then, we get the Volume of that cube = L³ cubic units.

The volume of a cube is of the form V =  L³, where L is the side length.

Given that the shipping box has a volume of 1,000 cubic inches.

Here, we know the volume V, but not the measure of length. So, we can plug in the value 1000 for V and solve for L:

1000 =  L³

Cube root both sides:

L = \(\sqrt[3]{1000}\)

Therefore, each side is 10 inches.

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Answer:

($3.189/gallon)(1 gallon/15 miles)(165 miles)

= $35.079 = $35.08

Answer:

It will cost $35.08 to go 165 miles.

Step-by-step explanation:

165/15 = 11

You will need 11 gallons

11 x 3.189 = 35.079

Helping in the name of Jesus.