In a large population of mesquite trees, 13% are infested with mistletoe. A biologist selects a random sample of 25 mesquite trees from this population. About how far do you expect the sample proportion of infested trees to vary from the true proportion, on average?
(a) 0.005
(b) 0.026
(c) 0.067
(d) 0.072
(e) 0.130

The function f(x) - g(x) is an illustration of a composite function

Leanne's end result of f(x) - g(x) = -1/2x + 9 is correct

The functions are given as:

f(x) = 1/2x + 6

g(x) = x - 3

The function f(x) - g(x) is calculated using:

f(x) - g(x) = 1/2x + 6 - x + 3

Collect like terms

f(x) - g(x) = 1/2x - x + 6  + 3

Evaluate the like terms

f(x) - g(x) = -1/2x + 9

By comparing the above solution to the students' response, we can see that:

Leanne's end result of f(x) - g(x) = -1/2x + 9 is correct

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Answer:

11) 6

12) 3

Step-by-step explanation:

2 log 2 8

so 2(log2 8)

Base 2 so 2^x=8 so 3.

2*3 is 6.

log a a cubed

base a so a^ x = a^3

x=3

so 3.

Hope this helps ;D

Answer:

6 and 3

Step-by-step explanation:

Using the rules of logarithms

log\(x^{n}\) ⇔ n log x

\(log_{b}\) x = n ⇒ x = \(b^{n}\)

\(log_{a}\) a = 1

(11)

let 2 \(log_{2}\)8 = n , then

\(log_{2}\) 8² = n

\(log_{2}\) 64 = n

\(log_{2}\) \(2^{6}\) = n

\(2^{6}\) = \(2^{n}\)

Since bases on both sides are equal, equate the exponents, that is

n = 6

(12)

\(log_{a}\) a³

= 3 \(log_{a}\) a

= 3 × 1

= 3

Answer:

the answer is 8

Step-by-step explanation:

the first step is to work whats in the brackets then you get 4.8 then you divide 4.8 into 0.6 and ur answer should be 8

Answer:

#14 - t = for each t-shirt(s) sold / h = hour(s) worked

8h + 0.50t

#15 - d = for hot dog(s) sold / h = hour(s) worked

8.50h + 0.35d

Is this what you needed?

Answer:

Question 14

let n = number of t-shirts sold

let h = number of hours worked

let y = total money earned

Given Adila earns $8.00 per hour plus $0.50 for each T-shirts she sells:

\(y = 8h + 0.5n\)

Question 15

let n = number of hot-dogs sold

let h = number of hours worked

let y = total money earned

Given Ramesh earns $8.50 per hour plus $0.35 for each hot-dog he sells:

\(y = 8.5h + 0.35n\)

the value of the variable newexample is -25.The given statement is a conditional (ternary) operator expression in the form:

condition ? expression1 : expression2

If the condition (50 <= 75) is true, then the value of newexample will be expression1 (50-75). If the condition is false, then the value of newexample will be expression2 (75-50).

Since 50 is indeed less than or equal to 75, the condition is true. Therefore, the value of newexample will be the result of expression1, which is 50-75.

Performing the subtraction, we get:

newexample = 50 - 75 = -25

Hence, the value of the variable newexample is -25.

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Answer:

4 miles

Step-by-step explanation:

24/6=4 He ran one miles every six minutes

Based on the given temperature data, the forecasted high temperature for today using a three-day moving average is 93°F, and using a two-day moving average is 89°F. The mean absolute deviation for the two-day moving average is 1°F, and the mean squared error is 1. The mean absolute percent error for the two-day moving average is approximately 1.13%.

These metrics provide a way to assess the accuracy of the temperature forecasts and the variability of the actual temperatures from the moving averages.

a) To forecast the high temperature today using a three-day moving average, we take the average of the temperatures from the last three days. So, (95 + 96 + 88) / 3 = 93°F.

b) To forecast the high temperature today using a two-day moving average, we take the average of the temperatures from the last two days. So, (88 + 90) / 2 = 89°F.

c) The mean absolute deviation (MAD) based on a two-day moving average is calculated by finding the absolute difference between each temperature and the two-day moving average, summing up those differences, and then dividing by the number of observations.

The two-day moving average is 89°F. The deviations from the moving average are: |88 - 89| = 1 and |90 - 89| = 1. The sum of these deviations is 1 + 1 = 2. Since we have two observations, the MAD is 2 / 2 = 1°F.

d) The mean squared error (MSE) for the two-day moving average is calculated by squaring the differences between each temperature and the two-day moving average, summing up those squared differences, and then dividing by the number of observations.

The differences are: (88 - 89)^2 = 1 and (90 - 89)^2 = 1. The sum of squared differences is 1 + 1 = 2. Since we have two observations, the MSE is 2 / 2 = 1.

e) The mean absolute percent error (MAPE) for the two-day moving average is calculated by finding the absolute difference between each temperature and the two-day moving average, dividing that difference by the actual temperature, summing up those absolute differences, and then dividing by the number of observations.

The two-day moving average is 89°F. The absolute percent differences are: |88 - 89| / 88 = 0.0114 and |90 - 89| / 90 = 0.0111. The sum of these absolute differences is 0.0114 + 0.0111 ≈ 0.0225. Since we have two observations, the MAPE is 0.0225 / 2 ≈ 0.0113 or 1.13%.

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The probable question may be:

A Canadian tourist travelling to Miami learned that the local temperatures in Fahrenheit for the last week were as follows: 93, 94, 93, 95, 96, 88, 90 (yesterday).

a) Forecast the high temperately today, using a three-day moving average.

b) Forecast the high temperature today, using a two-day moving average.

c) Calculate the mean absolute deviation based on a two-day moving average.

d) Compute the mean squared error for the two-day moving average.

e) Calculate the mean absolute percent error for the two-day moving average.

Answer:

Dimensions: 11 meters by 27 meters

2. \(76=2w+2(2w+5)\)

Step-by-step explanation:

Finding Dimensions:

The perimeter of a rectangle can be written as \(2l+2w\) where \(l\) is the length and \(w\) is the width. It is given that the length is 5 more than twice the length of width and the perimeter of the rectangle is 76 meters.

With this information we can write:

Length = \(2w+5\)

\(2(2w+5)+2w = 76\) (perimeter of the rectangle)

\(4w+10+2w=76\)

\(6w=66\)

\(w=11\)

Length = \(2(11)+5\)

Length = \(27\)

∴ The dimensions of the rectangle is 11 meters by 27 meters.

Perimeter

Since the length can be written as \(2w+5\), the equation that represents the perimeter of the rectangle is \(76=2w+2(2w+5)\)

The statement that is true is:

Statements 1 and 3

Let's examine each statement individually:

If n is a multiple of 8, then n is a multiple of 4. This statement is true because every number that is divisible by 8 is also divisible by 4. Since 8 is a multiple of 4, any multiple of 8 will have factors of both 8 and 4. If n is a multiple of 18, then n is a multiple of 2.

This statement is also true. Any number that is divisible by 18 is also divisible by 2 because 18 contains a factor of 2. Every multiple of 18 will have at least one factor of 2.

Statement 2 is not true. If n is a multiple of 18, then n is a multiple of 9.

This statement is false because there are numbers that are multiples of 18 but not multiples of 9. For example, 18 itself is a multiple of 18 but not a multiple of 9, as 18 divided by 9 is equal to 2.

Therefore, the correct answer is c) Statements 1 and 3.

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a. The formula B = 703w/h^2 can be solved for w by rearranging the equation as w = B * h^2 / 703.
b. For a person who is 64 inches tall and has a body mass index of 21.45, the weight can be calculated by substituting the values into the formula w = B * h^2 / 703, where B is 21.45 and h is 64 inches.

a. To solve the formula B = 703w/h^2 for w, we can rearrange the equation to isolate w on one side of the equation. Multiply both sides of the equation by h^2, then divide both sides by 703. The resulting equation is w = B * h^2 / 703.
b. To find the weight of a person who is 64 inches tall and has a body mass index of 21.45, we can substitute the values into the formula w = B * h^2 / 703. In this case, B is 21.45 and h is 64 inches. Plugging these values into the equation, we get w = 21.45 * 64^2 / 703. Evaluating this expression will give us the weight in pounds.

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Let X be the number of fixed points of a random permutation of n elements. A fixed point is an element that remains in the same position after the permutation. Thus, the probability that an element is fixed is 1/n, and the probability that it is not fixed is (n-1)/n.

Using the linearity of the expected value, we can calculate the expected value of X as:

E(X) = E(X1 + X2 + ... + Xn) = E(X1) + E(X2) + ... + E(Xn)

where Xi is the indicator random variable that is equal to 1 if the i-th element is fixed and 0 otherwise. Since the probability of an element being fixed is 1/n, we have E(Xi) = 1/n. Therefore,

E(X) = n * (1/n) = 1

To find the variance of X, we need to compute E(X^2) - E(X)^2. We can use the fact that X^2 = X1 + X2 + ... + Xn, where Xi is the indicator random variable that is equal to 1 if the i-th and j-th elements are both fixed and 0 otherwise. Then,

E(X^2) = E(X1 + X2 + ... + Xn)^2 = E(X1^2 + X2^2 + ... + Xn^2) + 2 E(X1X2 + X1X3 + ... + X(n-1)n)

Since there is only one way to fix two elements out of n, we have E(XiXj) = 1/(n(n-1)). Therefore,

E(X^2) = n * (1/n) + n(n-1) * (1/(n(n-1))) = 1 + 1/n

Finally, the variance of X is

Var(X) = E(X^2) - E(X)^2 = 1 + 1/n - 1^2 = 1/n

Therefore, the variance of the number of fixed elements of a randomly selected permutation of n elements is 1/n.

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Answer:

i think its C

Step-by-step explanation:

not really sure but have a good day

From the given information, cholesterol level X follows the N(222, 37) distribution.

The probability of having borderline high cholesterol (between 200 and 240 mg/dl) can be calculated by using the z-score formula as follows:

z = (x - μ) / σ

For lower limit x1 = 200, z1 = (200 - 222) / 37 = -0.595

For upper limit x2 = 240, z2 = (240 - 222) / 37 = 0.486

The probability of having borderline high cholesterol (between 200 and 240 mg/dl) can be computed as

P(200 ≤ X ≤ 240) = P(z1 ≤ Z ≤ z2) = P(Z ≤ 0.486) - P(Z ≤ -0.595) = 0.683 - 0.277 = 0.406

In this population, 90% of men have a cholesterol level that is at most X90.The z-score corresponding to a cholesterol level of X90 can be calculated as follows:

z = (x - μ) / σ

Since the z-score separates the area under the normal distribution curve into two parts, that is, from the left of the z-value to the mean, and from the right of the z-value to the mean.

So, for a left-tailed test, we find the z-score such that the area from the left of the z-score to the mean is 0.90.

By using the standard normal distribution table,

we get the z-score as 1.28.z = (x - μ) / σ1.28 = (X90 - 222) / 37X90 = 222 + 1.28 × 37 = 274.36 ≈ 274

The cholesterol level of 90% of men in this population is at most 274 mg/dl.

The distributions that we can consider to be approximately normal are the sampling distribution of mean BMI for random samples of 60 adults and the sampling distribution of mean BMI for random samples of 9 adults.

The reason for considering these distributions to be approximately normal is that according to the Central Limit Theorem, if a sample consists of a large number of observations, that is, at least 30, then its sample mean distribution is approximately normal.

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The statement is valid because the measure of the vertices located in the center of the pentagon is the quotient of 360 and 5, and the sum of two base angles in the given isosceles triangle is 108.

==========================================================

Explanation:

Check out the diagram below. I have added x and y such that

x = base angle

y = vertex angle (located adjacent to center of polygon)

The pentagon is sliced up like a cake into 5 equal portions. Each vertex angle is y = 360/5 = 72 degrees.

The two base angles x must add with the vertex angle y to get 180

(angle1)+(angle2)+(angle3) = 180

x+x+y = 180

2x+y = 180

2x+72 = 180

2x = 180-72

2x = 108

This is true for any one of the five triangles. Notice that for angle LMN, we can divide it into LMQ and QMN where Q is the center of the polygon. Both of these angles are x. Since we've shown 2x = 108, we can see that LMN must also be 108 as well.

Choice A is close, but we wouldn't use the exterior angle theorem. Choice B is the better answer.

Waterways should retain the old backhoes equipment.

To determine whether it is more favorable to purchase new backhoes or overhaul the old ones, we will evaluate the net present value (NPV), profitability index (PI), and internal rate of return (IRR) for both options.

Net Present Value (NPV):

For the new backhoes:

The initial cost of investment = Purchase cost when new - Salvage value now

= $199,994 - $15,200 = $184,794

The net cash flow generated each year for the new backhoes remains unspecified, so we cannot calculate its NPV.

For the old backhoes:

Initial investment = Cost of the overhaul = $41,400

Net cash flow generated each year = $15,200

Using the provided PV table, we can calculate the NPV for the old backhoes:

NPV = Net cash flow generated each year * PV factor for 8 years - Initial investment

= $15,200 * 5.76162 - $41,400 ≈ $55,689.69

Since the NPV for the old backhoes is positive, retaining the old equipment is favorable.

Profitability Index (PI):

The profitability index is calculated by dividing the present value of cash inflows by the initial investment.

For the new backhoes:

Since the net cash flow generated each year is unspecified, we cannot calculate the PI.

For the old backhoes:

PI = (Net cash flow generated each year * PV factor for 8 years) / Initial investment

= ($15,200 * 5.76162) / $41,400 ≈ 2.11

The profitability index for the old backhoes is 2.11.

Based on the PI, the old backhoes have a higher profitability index than the new backhoes, indicating that retaining the old equipment is more profitable.

Internal Rate of Return (IRR):

The IRR factor for the new and old backhoes is not provided, so we cannot calculate the exact IRR.

In summary, based on the net present value (NPV) and profitability index (PI), it is more favorable for Waterways to retain the old backhoes equipment.

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A major disadvantage of correlations is that they cannot make a cause-and-effect statement.

Correlations are statistical measures that describe the size and direction of a relationship between variables.

Correlations are expressed as numbers. Correlations establish that relationships exist but do not explain if the change in one variable is caused by the change in another variable's value.

The disadvantages of correlations include:

Thus, a major disadvantage of correlations is that they cannot make a cause-and-effect statement.

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Answer:

the answer is 41

Step-by-step explanation:

C. 41

Step-by-step explanation:

The given data is tabulated for conditional relative frequency table as follows.

Total male = 145, Total female = 139

Total male votes for Santiago = 68, Total female votes for Measha = 89

Total female votes for Santiago = 50, Total male votes for Measha = 77

Now total votes for Santiago = 68+50=118

Total votes for Measha = 166

Total votes casted = 284

The above data is formulated in tables attached below.

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We have found two positive and two negative coterminal angles for each given angle.

For 5pi/4, two positive angles that are coterminal would be 13pi/4 and 21pi/4. Two negative angles that are coterminal would be -3pi/4 and -11pi/4.
For 7pi/6, two positive angles that are coterminal would be 19pi/6 and 31pi/6. Two negative angles that are coterminal would be -5pi/6 and -17pi/6.
In general, to find angles that are coterminal with a given angle, add or subtract 2pi (or a multiple of 2pi) until the angle falls within the range of 0 to 2pi.
For the given angles, 5π/4 and 7π/6, we can find coterminal angles by adding or subtracting multiples of 2π.
For 5π/4:
Positive coterminal angles: (5π/4 + 2π) = 13π/4, (5π/4 + 4π) = 21π/4
Negative coterminal angles: (5π/4 - 2π) = -3π/4, (5π/4 - 4π) = -11π/4
For 7π/6:
Positive coterminal angles: (7π/6 + 2π) = 19π/6, (7π/6 + 4π) = 31π/6
Negative coterminal angles: (7π/6 - 2π) = -5π/6, (7π/6 - 4π) = -17π/6
Thus, we have found two positive and two negative coterminal angles for each given angle.

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Equation for a linear line is y=5x-5

What is linear line?

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, whereas B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.

slope of line passing through two points (-2,-15) and (2,5) is

\(m= (5-(-15))/(2-(-2))\\m=20/4\\m=5\)

Therefore, the slope of the line is 5

Now,finding the y-intercept now by using the slope and one of the two points.

\(y=m*x+b\\5=5*2+b\\b=-5\)

putting this value of b to find equation,

\(y=m*x+b\\y=5x-5\\\)

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Answer:22,000

Explanation:

21.933=21.930

21.930= 21.900

21.900 = 22,000

Answer:

Step-by-step explanation:

c =7

The length of the hypotenuse of a 45-45-90 triangle is √2x units.

To find the hypotenuse of a 45-45-90 triangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse).

Let's denote the length of each leg of the triangle as "x". Since the triangle is isosceles, both legs are of equal length. Therefore, we can write:

Leg 1 = Leg 2 = x

To find the length of the hypotenuse (which we'll call "h"), we can use the Pythagorean theorem as follows:

x² + x² = h²

Simplifying this equation, we get:

2x² = h²

To solve for h, we need to take the square root of both sides of the equation:

√(2x²) = √(h²)

√2 * x = h

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Answer:

I think the possible answer is C.12

hope its right but if its wrong please feel free to correct me.

Answer:

(2π + 28) mm²

Step-by-step explanation:

The Area of the Composite figure =

Area of the Trapezoid + Area of the Square + Area of the semicircle

a) Area of the Trapezoid

Trapezoid M D C K has base lengths of 8 millimeters and 4 millimeters

Diameter of the semicircle= length of 4 millimeters = height of the trapezoid

Area of trapezoid = 1/2 × h × (b + b)

= 1/2 × 4 × (8 + 4)

= 1/2 × 4 × 12

= 1/2× 48

= 24mm²

b) Area of the square

Square A B C D has side lengths of 2 millimeters.

Area of a square = Side length²

=(2mm)² = 4mm²

c) Area of the semicircle

Line A B is the diameter of the semicircle and has a length of 4 millimeters.

Formula for the Area of a semi circle: πr²/2

Radius = Diameter/2 = 4mm/2 = 2mm

= π × 2²/2

= 4π/2

= 2πmm²

The Area of the Composite figure =

Area of the Trapezoid + Area of the Square + Area of the semicircle

= 24mm² + 4mm² + 2πmm²

= 28mm² + 2πmm²

= (28 + 2π)mm²

Therefore, the Area of the Composite figure = (28 + 2π)mm² or (2π + 28) mm²

Answer:

A- (2π + 28) mm²

Step-by-step explanation:

edge

Answer:

5x-1

Step-by-step explanation:

f(x) = 3x-2

g(x) = 2x+1

(f+g) (x) = 3x-2 + 2x+1

Combine like terms

            = 5x -1

Answer:

C. 5x - 1

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

f(x) = 3x - 2

g(x) = 2x + 1

(f + g)(x) is f(x) + g(x)

Step 2: Find

Answer:

n=10

Step-by-step explanation:

6=3n/5

multiply both sides by 5

30=3n

divide both sides 3

10=n

The correct answer is b. we know the standard deviation of the population.

The Nearly Normal condition, also known as the Central Limit Theorem, states that the sampling distribution of the sample mean tends to be approximately normal, even if the population distribution is not normal, under certain conditions. One way to meet the Nearly Normal condition is by knowing the standard deviation of the population.

When the standard deviation of the population is known, the sample size does not have to be large for the sampling distribution of the sample mean to be approximately normal. This is because the standard deviation provides information about the variability of the population, allowing for a more accurate estimation of the sample mean distribution.

While the other options (a, c, and d) may be relevant in specific scenarios, they are not directly related to meeting the Nearly Normal condition as defined by the Central Limit Theorem.

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