please help with this math problem ​

Answer:

a) By the Central Limit Theorem, the mean is $142 and the standard deviation is $0.7488.

b) By the Central Limit Theorem, approximately normal.

c) 0.0901 = 9.01% probability that the average cable service paid by the sample of cable service customers will exceed $143

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The mean monthly fee is $142 and the standard deviation is $29.

This means that \(\mu = 142, \sigma = 29\)

Part a: what are the mean an standard deviation of the sample distribution of x hat show your work and justify your reasoning.

Sample of 1500(larger than 30).

By the Central Limit Theorem

The mean is $142

The standard deviation is \(s = \frac{29}{\sqrt{1500}} = 0.7488\)

Part b: what is the shape of the sampling distribution of x hat justify your answer.

By the Central Limit Theorem, approximately normal.

Part C: what is the probability that the average cable service paid by the sample of cable service customers will exceed $143?

This is 1 subtracted by the pvalue of Z when X = 143. So

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{143 - 142}{0.7488}\)

\(Z = 1.34\)

\(Z = 1.34\) has a pvalue of 0.9099

1 - 0.9099 = 0.0901

0.0901 = 9.01% probability that the average cable service paid by the sample of cable service customers will exceed $143

The central angle of Bathing = 108 degrees.

In the given pie chart,

Since we know,

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle possesses rotational symmetry around the center.

The whole circle is 360 degrees

which represents 100%.

It is given that,

Bathing = 30%

So have need to find 30% of 360 degrees.

Therefore,

Bathing = (30/100)x360

            =  (30/10) x 36

            = 3x36

            = 108

Hence,

The central angle = 108 degrees.

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The complete question is:

To the nearest degree, what is the measure of the central angle for bathing?

Answer:

90%

Explanation: 27/30 ÷ 3 = 9/10

9/10 ⇒ 9 x 10 = 90%

Answer: C. The classmate did not reverse the coordinates of (2, 1), so the inverse of s is wrong and it is not a function

The first two points in relation s are (3,1) and (2,1). Their coordinates swap to get (1,3) and (1,2) respectively which helps form the inverse relation.

We don't have a function with { (1,3), (1,2) } because the x coordinate repeats itself. Functions are only possible if any input x leads to exactly one output y.

Answer: c = 6

Step-by-step explanation:

%/100 = is/of

14/100 = 7/a. (14% of what number is 7) (cross multiplication)

(7*100)/14 = 50 (a)

6/100 = 18/b

(18*100)/6 = 300 (b)

b/a = 300/50 = 6

Pattern is a rule that guides the formation of a dataset. Based on the given patterns of a and b, the value of c is 6

Given that:

\(7 = 14\% \times a\)

\(18 = 6\% \times b\)

Make a the subject in \(7 = 14\% \times a\)

\(a=7 \div 14\%\)

\(a = 50\)

Make b the subject in \(18 = 6\% \times b\)

\(b = 18 \div 6\%\)

\(b = 300\)

Given that:

\(c = \frac ba\)

Substitute values for a and b

\(c = \frac{300}{50}\)

\(c = 6\)

Hence, the value of c is 6

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This question is incomplete, the complete question is;

Consider a set of data in which the sample mean is 73.4 and the sample standard deviation is 4.9. Calculate the z-score given that x  = 69.5.

Round your answer to two decimal places.

Answer: the z-score is -0.80

Step-by-step explanation:

Given that;

mean μ = 73.4

standard deviation σ = 4.9

x = 69.5

z-score = ?

z = (x - μ) / σ

we substitute

z =  (69.5 - 73.4) / 4.9

z = -3.9 / 4.9

z = - 0.7959 ≈ -0.80    { 2 decimal places }

Therefore, the z-score is -0.80

Answer:

-1/8x-22

Step-by-step explanation:

Insert 3 in the RHS bracket

Insert - in the RHS bracket

Simplify

Answer:

\(-\frac{x+176}{8}\)

Step-by-step explanation:

The Central tendency is typically located to the right of the tallest bar.

In a skewed left distribution, the central tendency is typically located to the right of the tallest bar. Skewed left distributions, also known as negatively skewed distributions, are characterized by a tail that extends towards the left side of the distribution.

The central tendency refers to the measure that represents the center or average of a distribution. It provides information about the typical or central value around which the data points tend to cluster. Common measures of central tendency include the mean, median, and mode.

In a skewed left distribution, the mean is usually influenced by the long tail on the left side of the distribution. This tail pulls the mean towards lower values, resulting in a lower mean compared to the median. Therefore, the mean will typically be located to the left of the tallest bar in a skewed left distribution.

On the other hand, the median is less affected by the skewness of the distribution and is relatively robust to extreme values. It represents the value that separates the lower 50% of the data from the upper 50%. In a skewed left distribution, the median will be located closer to the tallest bar or even slightly to the right of it.

The mode, which represents the most frequently occurring value in a distribution, may or may not be influenced by the skewness depending on the shape of the distribution. It can be located anywhere along the distribution, and its position is not necessarily tied to the location of the tallest bar.

To summarize, in a skewed left distribution, the central tendency is typically located to the right of the tallest bar. The median is usually closer to the tallest bar or slightly to the right, while the mean is influenced by the skewness and tends to be located to the left of the tallest bar.

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Answer:

r= negative 637 <my negative sign doesnt work sorry>

Step-by-step explanation:

The slope of the line passing through the points (5, 3) and (8, 2) is -1/3.

To find the slope of the line passing through the points (5, 3) and (8, 2), we can use the formula for slope:

slope = (y2 - y1) / (x2 - x1)

Let's substitute the coordinates of the given points into the formula:

x1 = 5, y1 = 3

x2 = 8, y2 = 2

slope = (2 - 3) / (8 - 5)

Calculating the numerator and denominator:

slope = -1 / 3

Therefore, the slope of the line passing through the points (5, 3) and (8, 2) is -1/3.

Note: The slope represents the rate of change between the y-coordinates and x-coordinates of two points on a line. In this case, for every 3 units increase in the x-coordinate, the y-coordinate decreases by 1 unit.

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Answer:

Less

Step-by-step explanation:

Interpreting this, total is 40, so if you are splitting that with multiple people, it can't be more than 40.

The surface area of the figure is approximately 997.5π cm².

We have,

The figure has two shapes:

Cone and a semicircle

Now,

The surface area of a cone:

= πr (r + l)

where r is the radius of the base and l is the slant height.

Given that

r = 15 cm and l = 19 cm, we can substitute these values into the formula:

= π(15)(15 + 19) = 885π cm² (rounded to the nearest whole number)

The surface area of a semicircle:

= (πr²) / 2

Given that r = 15 cm, we can substitute this value into the formula:

= (π(15)²) / 2

= 112.5π cm² (rounded to one decimal place)

The surface area of the figure:

To find the total surface area of the figure, we add the surface area of the cone and the surface area of the semicircle:

Now,

Total surface area

= 885π + 112.5π

= 997.5π cm² (rounded to one decimal place)

Therefore,

The surface area of the figure is approximately 997.5π cm².

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Answer:

B

Step-by-step explanation:

square units (units for all area)

Answer:

225 m^2

Step-by-step explanation:

2x + 2y = 60 m

x + y = 30

15 + 15 = 10 + 20 = 25 + 5 = 30

10 x 20 = 200 m^2

15 x 15 = 225 m^2

25 x 5 = 100 m^2

Answer:

28

Step-by-step explanation:

M/8 = 21/6

6M = 168

M = 28

The value for the function f(x) = z² + 3/z² for f(2) is 4.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range.

Given:

f(x) = z² + 3/z²

Also we have f(1)= 2 then

f(1) = z² + 3/z²

2 = z² + 3/z²

2z² = \(z^4\) + 3

-3 = \(z^4\) - 2z²

-3 = z²(z²-2)

So, z²= -3  or z²-2 = -3

z= ±√3i or z =i

Now, F(2) we get

F(2) = z² + 3/z²

      = (-1)² + 3/ (-1)²

      = 1 + 3

F(2) = 4

Hence, the value of F(2) is 4.

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Answer:

It's not there but you should be able to type it in

hold shift and press 5

edit: press tab or an arrow on the side and it should show you the %

Step-by-step explanation:

hope this helps<3

-liyah

Answer:

The roots of this function are at -4 and -1.

f(x) = (2x + 8)(-2x - 2)

= (2x + 8)(-2x + (-2))

The height of the kite from the ground when the angle is 50 degrees is 232 feet.

The study of the correlations between triangles' sides and angles is the focus of the mathematic branch known as trigonometry. To link the angles of a right triangle to the lengths of its sides, it makes use of trigonometric functions like sine, cosine, and tangent.

Numerous industries, including physics, engineering, and navigation, use trigonometry. It can be used, for instance, to determine a building's height or the separation between two locations on a map, as well as to examine how waves and oscillations behave.

To find the height of the kite above the ground we use the trigonometric identity of tangent.

Thus, we have:

tan(50°) = h/200

Now, using cross multiplication:

h = 200 tan(50°) ≈ 232 feet

Hence, the height of the kite from the ground when the angle is 50 degrees is 232 feet.

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Answer:

the value of x is equal to3.

The function is continuous in the domain x ≥ 3/4

Here we have a root function:

f(x) = ⁴√(4x - 3)

This is an even degree root function, so we have problems when the argument is negative.

Then the allowed values (where the function is defined, and thus, continuous) are:

4x - 3 ≥ 0

4x ≥ 3

x ≥ 3/4

There the function is continuous.

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The first semi-annual interest payment with a credit to in the amount of $109.556.15

Given that, a company issues $50,000 of 8%, 10-year bonds dated January 1 that pay interest semiannually on June 30 and December 31 each year.

We need to find the amount,

\(A = P(1+r/2)^{2t}\)

\(A = 50,000(1+0.08/2)^{2(10)\)

\(A = 50,000(1.04)^{20\)

\(A = 109,556.15\)

Hence, the first semi-annual interest payment with a credit to in the amount of $109.556.15

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Here are the correct matches to the expressions to their solutions.

The GCF of 28 and 60 is 4.

(-3/8)+(-5/8) = -4/4 = -1.

-1/6 DIVIDED BY 1/2 = -1/6 X 2 = -1/3.

The solution of 0.5 x = -1 is x = -2.

The solution of 1/2 m = 0 is m = 0.

-4 + 5/3 = -11/3.

-2 1/3 - 4 2/3 = -10/3.

4 is not a solution of -4 < x.

1. The GCF of 28 and 60 is 4.

The greatest common factor (GCF) of two numbers is the largest number that is a factor of both numbers. To find the GCF of 28 and 60, we can factor each number completely:

28 = 2 x 2 x 7

60 = 2 x 2 x 3 x 5

The factors that are common to both numbers are 2 and 2. The GCF of 28 and 60 is 2 x 2 = 4.

2. (-3/8)+(-5/8) = -1.

To add two fractions, we need to have a common denominator. The common denominator of 8/8 and 5/8 is 8. So, (-3/8)+(-5/8) = (-3 + (-5))/8 = -8/8 = -1.

3. -1/6 DIVIDED BY 1/2 = -1/3.

To divide by a fraction, we can multiply by the reciprocal of the fraction. The reciprocal of 1/2 is 2/1. So, -1/6 DIVIDED BY 1/2 = -1/6 x 2/1 = -2/6 = -1/3.

4. The solution of 0.5 x = -1 is x = -2.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate x by dividing both sides of the equation by 0.5. This gives us x = -1 / 0.5 = -2.

5. The solution of 1 m = 0 is m = 0.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate m by dividing both sides of the equation by 1. This gives us m = 0 / 1 = 0.

6. -4 + 5/3 = -11/3.

To add a fraction and a whole number, we can convert the whole number to a fraction with the same denominator as the fraction. In this case, we can convert -4 to -4/3. So, -4 + 5/3 = -4/3 + 5/3 = -11/3.

7. -2 1/3 - 4 2/3 = -10/3.

To subtract two fractions, we need to have a common denominator. The common denominator of 1/3 and 2/3 is 3. So, -2 1/3 - 4 2/3 = (-2 + (-4))/3 = -6/3 = -10/3.

8. 4 is not a solution of -4 < x.

The inequality -4 < x means that x must be greater than -4. The number 4 is not greater than -4, so it is not a solution of the inequality.

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Answer: B

Step-by-step explanation:

It is B Beacuse you cant say its A beacsuse that wrong to the question you asked.

The continuous function f is defined on the closed interval −6 ≤ x ≤ 5. The figure above shows a portion of the graph of f, consisting of two line segments and a quarter of a circle centered at the point (5, 3). It is known that the point (3, 3 −√5 ) is on the graph of f. 4.

In mathematics, a continuous function is a function such that a continuous variation (that is a change without jump) of the argument induces a continuous variation of the value of the function. This means that there are no abrupt changes in value, known as discontinuities. More precisely, a function is continuous if arbitrarily small changes in its value can be assured by restricting to sufficiently small changes of its argument. A discontinuous function is a function that is not continuous. Up until the 19th century, mathematicians largely relied on intuitive notions of continuity, and considered only continuous functions. The epsilon–delta definition of a limit was introduced to formalize the definition of continuity.

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Answer:

b & c

Step-by-step explanation: