Scores on a test are normally distributed with a mean of 81 and a standard deviation of 8. Find the probability that a randomly chosen score will be less than 70? Show your work.

Answer:32.9 m

Step-by-step explanation:

The amount of Dividends of $3,000, $5,000, $34,500, and $71,000 were distributed to the 20,000 preferred and 25,000 common shareholders of Lightfoot Inc. over the first four years of operations.

To calculate the dividend per share of the preferred and common stock of Lightfoot Inc., the total amount of dividends paid out over the first four years must first be determined. This can be done by adding the given amounts of $3,000, $5,000, $34,500, and $71,000 to get a total of $113,500. To find the dividend per share for the preferred stock, the total dividend is divided by the number of shares (20,000) which gives a dividend per share of $5.68. To find the dividend per share for the common stock, the total dividend is divided by the number of shares (25,000) which gives a dividend per share of $4.54.

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Answer: 6

Step-by-step explanation:

Answer:

Step-by-step explanation:

given in the question that what is the distance between the 2 points that are given in the question that is (-3,-7) and (-9,-7)

we know the formulae, that the distance between the points is

distance = \(\sqrt{x} 2-x1)2+(y2-y1)2\)

insert the values in the formula we get that  

             distance =\(\sqrt{-6^2 +0^2\)

                             = \(\sqrt{36\)

                             = 6

so therefore the distance between the point is 6

Here is the equation:

\(6(x-8)=72\)

In the equation, 6 is being multiplied by x - 8. There are two ways to solve this equation.

FIRST METHOD

You need to remove the parentheses by multiplying everything in the parentheses by 6.

\(6(x-8) = (6\times x) + (6 \times -8)\)

Multiply:

\(6 \times x = 6x\\6 \times -8 = -48\)

Remember:

NEGATIVES

POSITIVES

Now combine the two values and rewrite the equation:

\(6x+-48 \rightarrow 6x-48=72\)

Since you're looking for x alone, you will need to remove the -48. This can be done by adding 48 to both sides, -48+48=0, which cancels it out).

\(6x-48+48=72+48\\6x=120\)

Lastly, divide both sides by 6 to leave x alone.

\(\frac{6x}{6} = \frac{120}{6}\)

\(x=20\)

SECOND METHOD

While the first step is somewhat complicated, there is a much easier way.

\(6(x-8)=72\)

Start by dividing both sides by 6 to remove the number next to the parentheses.

\(\frac{6(x-8)}{6} =\frac{72}{6}\)

\(x-8=12\)

(The 6 is cancelled out since 6 divided by 6 equals 1, and 1 × any number is that number).

Now you need to leave the variable alone, which can be done by adding 8 to both sides(-8+8=0 and -8 is cancelled out).

\(x-8+8=12+8\\\)

\(x=20\)

Either method can be used, but the second one is definitely shorter!

The answer is x = 20.

Answer:

x=20

Step-by-step explanation:

In edge you will get it right.

I took the test.

Hope this helps ;)

Step-by-step explanation:

I just did in the other posting. how often did you post it ?

this is a trick question. the triangle at the top is not an isoceles triangle.

we use Pythagoras for an the steps.

so, the left part of the baseline (split by the height) is calculated by

12² = 10² + part²

144 = 100 + part²

part = sqrt(44) = 6.633249581... ft

the other part is then

20 - 6.633249581... = 13.36675042... ft

and the second leg of the large triangle is

leg² = 10² + 13.36675042...² = 278.6700168...

leg = 16.69341238... ft

P = 12 + 16.69341238... + 8 + 8 + 20 = 64.69341238... ft ≈

≈ 64.69 ft

please see the answer to the other posting for more details.

Answer:

A manufacturing corporation make tires with a probability 0.77 of lasting over 3,000 miles.

Step-by-step explanation:

The probability of exactly seven out of the next eight tires lasting over 3,000 miles will be 0.32.

Binomial distributions consist of n independent Bernoulli trials.

Bernoulli's trials are those trials which end up randomly either on success (with probability p) or on failures (with probability 1- p = q (say))

The probability that out of n trials, there'd be x successes is given by

\(\rm P(X =x) = \: ^nC_x \ p^x(1-p)^{n-x}\)

A manufacturing corporation make tires with a probability 0.79 of lasting over 3,000 miles.

The probability of exactly seven out of the next eight tires lasting over 3,000 miles will be

P(x = 7) = ⁸C₇ (0.79)⁷  (1 – 0.79)⁽⁸⁻⁷⁾

P(x = 7) = 0.32

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Answer:

b

Step-by-step explanation:

as 2.5 × 10-^5 is 250000 and b is 3100 and if you do 10-5 + 10-3 it is 10-8 which will give u 0.0008cm I think if my calculations r correct

Answer:

a

Step-by-step explanation:

just did it and got right

Answer:

Below

Step-by-step explanation:

(x-10)^2 = 90     sqrt both sides

x-10  =  ± sqrt (90)

x  =   10 ± sqrt (90)

Answer:

tectonic plate movements

Step-by-step explanation:

Answer:

add all the angles and equal with 180°

Answer:

SEE THE IMAGE FOR SOLUTION

Answer:

c. The period is 2π

Step-by-step explanation:

The period of a function is the smallest value of $p$ for which\( f(x+p) = f(x)\) for all x.

For the function f(x) = 2cos(x^2), we can see that f(x+2π) = f(x) for all x.

This is because the cosine function has a period of 2π. Therefore, the period of f(x) = 2cos(x^2) is \(\boxed{2\pi}\)

It is not accurate to make a blanket statement that the U.S. always has a lower unemployment rate than other countries. The unemployment rates can differ significantly based on specific circumstances, making it important to examine the relevant data and context before drawing conclusions.

The statement "The unemployment rate in the U.S. tends to be lower than in other countries" is subjective and cannot be definitively categorized as true or false without further context and data analysis.

Unemployment rates vary across countries due to a multitude of factors, such as economic conditions, labor market policies, demographics, and government interventions. While it is true that at certain times the unemployment rate in the U.S. may be lower than in some other countries, it is not universally true in all circumstances.

Comparing unemployment rates between countries requires a comprehensive analysis of various factors and data points, including the specific time period, the methodology used for calculating unemployment, and the demographic and socio-economic characteristics of each country. Additionally, economic conditions can fluctuate over time, leading to variations in unemployment rates.

Therefore, it is not accurate to make a blanket statement that the U.S. always has a lower unemployment rate than other countries. The unemployment rates can differ significantly based on specific circumstances, making it important to examine the relevant data and context before drawing conclusions.

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Answer:

\(\frac{3}{10}\)

Step-by-step explanation:

considering there is 10 slices each slice has a 1/10 peprcent chance of being landed on

since there is 3 blue slices there is a 3/10 percent chance of it landing on a blue slice

since there is 2 yellow slices there is a 2/10 percent chance of it landing on a yellow slice

since there is 5 red slices there is a 5/10 percent chance of it landing on a red slice

The complete expression is (2 × x) + (2 × 6). This is an equivalent expression to the given expression.

What is an expression?

A number, a variable, or a combination of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation.

Given expression is

2 (x+6)

Distributive property: The same outcome is obtained by multiplying the sum of two or more addends by a number as it is by multiplying each addend by the number separately and combining the resulting products.

The mathematical representation is a(b+c) = ab + ac.

Apply the Distributive property in the given expression:

(2×x) + (2×6)

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The solution of the equation is to the nearest ten-thousandth is x = 2.7712.

A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459. Typically, the natural logarithm of x is expressed as ln x, loge x, or, if the base e is implicit, just log x.

The given equation is \(3^{x-1} = 7\).

Take natural log on both sides of the equation:

\(\ln (3^{x-1} )=\ln( 7)\)

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

x - 1 = ln(7) / ln(3)

x = 1 +  ln(7) / ln(3)

x = 2.7712

Hence, the solution of the equation is to the nearest ten-thousandth is x = 2.7712.

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h(5) means the value of h(x) at x = 5. So what we have to do is to substitute x = 5 in the function.

We are given the function h(x) below:

\( \large{h(x) = \frac{6}{x - 3} }\)

Substitute x = 5 in the equation.

\( \large{h(5) = \frac{6}{5 - 3} \longrightarrow \frac{6}{2} }\)

Simplify in the simplest form.

\( \large{h(5) = \frac{3}{1} \longrightarrow 3}\)

Thus h(5) is 3.

Answer

Hope this helps! Let me know if you have any doubts.

Answer:

11

Step-by-step explanation:

26-15=11

Answer:    x=67

Step-by-step explanation:

All of the angles add up to 180 for a triangle

38 + 75 + x = 180               >combine like terms (the numbers)

113 + x = 180                       >subtract 113 from both sides

x=67

Answer:

Step-by-step explanation:

We know that,

\( \sf \: By \: Using \: Angle \: sum \: property \: of \: triangle\)

\( \large \sf \: → x +38° + 75° = 180°\)

\( \large \sf \: → x + 113 = 180°\)

\( \large \sf→ x = 180°- 113°\)

\( \boxed{\large \bf→ x = 67° }\)

The value of x from the venn diagram if P(T | V) = 1/5 is 16

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

The venn diagram

From the venn diagram, we have the following probability values

P(T | V) = (x - 4)/(3x + x - 4)

Evaluate the like terms

So, we have

P(T | V) = (x - 4)/(4x - 4)

From the question, we have

P(T | V) = 1/5

This means that

(x - 4)/(4x - 4) = 1/5

When evaluated, we have

x = 16

Hence, the value of x is 16

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For each statement for triangle SQP and SQR, Q is the midpoint of PR: No, ∠P ≅ ∠R: No, ∠PSQ ≅ ∠RSQ: Yes, m∠P = 33°, m∠RSQ = 57°: No, ∠P ≅ ∠R, ∠PSQ ≅ ∠RSQ: Yes.

What is triangle?

A triangle is a geometric shape that consists of three line segments connected end-to-end to form a closed shape. Triangles are one of the basic shapes studied in geometry and are used in a wide range of applications, from construction to computer graphics.

Here are the answers to whether each statement provides enough information to prove that △SQP ≅ △SQR:

Q is the midpoint of PR: No, this information alone is not sufficient to prove the triangles are congruent. We need additional information about the angles or sides.

∠P ≅ ∠R: No, this information alone is not sufficient to prove the triangles are congruent. We need additional information about the sides or other angles.

∠SQP is a right angle, ∠PSQ ≅ ∠RSQ: Yes, this information is sufficient to prove that the triangles are congruent by the angle-angle-side (AAS) congruence criterion.

∠SQP is a right angle, m∠P = 33°, m∠RSQ = 57°: No, this information alone is not sufficient to prove the triangles are congruent. We need additional information about the sides or other angles.

∠P ≅ ∠R, ∠PSQ ≅ ∠RSQ: Yes, this information is sufficient to prove that the triangles are congruent by the angle-angle-angle (AAA) congruence criterion.

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The perimeter of triangle ABC could be either approximately 27.98 cm or approximately 14.66 cm, depending on the length of AB.

What is the perimeter?

The perimeter is a mathematical term that refers to the total distance around the outside of a two-dimensional shape. It is the length of the boundary or the sum of the lengths of all the sides of a closed figure.

Let's call the length of AB x and the length of BC y.

First, we can use the fact that CD is the height of the triangle to find the area of triangle ABC:

Area of triangle ABC = 1/2 * CD * AB

Substituting the given values, we have:

1/2 * 12 * x = 6x

So the area of triangle ABC is 6x square centimeters.

We can also use the fact that angle BCD is 30 degrees to set up a trigonometric equation involving x and y:

tan(30) = x/y

Simplifying, we get:

y = x/tan(30) = x/(1/√(3)) = √(3) * x

Now we can use the formula for the area of a triangle in terms of its sides:

Area of triangle ABC = 1/2 * AB * BC * sin(B)

where B is the angle between sides AB and BC. In this case, we know that angle BCD is 30 degrees, so angle BCA is 60 degrees, and angle ABC is 90 degrees. Therefore, we have:

Area of triangle ABC = 1/2 * x * √3 * x * sin(60)

Simplifying, we get:

Area of triangle ABC = 1/4 * √3 * x²

Since we already found that the area of triangle ABC is 6x square centimeters, we can set these two expressions equal to each other and solve for x:

6x = 1/4 * √(3) * x²

Multiplying both sides by 4/√3, we get:

24/√(3) * x = x²

Simplifying, we get:

x² - 24/√(3) * x = 0

Using the quadratic formula, we get:

x = (24/√(3) ± √((24/√(3))² - 410)) / 2*1

Simplifying, we get:

x = 16√(3) / 3 or x = 8 √(3) / 3

Since we are looking for the perimeter of triangle ABC, we need to find y as well. Using the equation we derived earlier, we have:

y = √(3) * x

Therefore, we have two possible triangles:

Triangle ABC1: AB = 16 √(3) / 3, BC = 16, and AC = 8 √7 / 3

Triangle ABC2: AB = 8 √3 / 3, BC = 8, and AC = 4 √7 / 3

The perimeter of each triangle is the sum of its side lengths. Therefore:

Perimeter of triangle ABC1 = 16 √3/ 3 + 16 + 8 √7 / 3 ≈ 27.98 cm

Perimeter of triangle ABC2 = 8 √3 / 3 + 8 + 4 √7 / 3 ≈ 14.66 cm

hence, the perimeter of triangle ABC could be either approximately 27.98 cm or approximately 14.66 cm, depending on the length of AB.

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Answer:

Step-by-step explanation:

Answer:

Sin = -5/13

Cos = 12/13

Tan = -5/12

Step-by-step explanation:

Answer:

5.5%

Step-by-step explanation:

8453.50/153700 × 100

= 5.5%

The commission is 5.5%.

The ladder will reach a Height of approximately 43.46 meters on the building.

To find out how high on the building the ladder will reach, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the ladder forms a right triangle with the ground and the building. The base of the ladder is 7 meters, the height of the building is what we need to find, and the length of the ladder is given as 44 meters.

Using the Pythagorean theorem, we can set up the equation:

(Height of the building)^2 + 7^2 = 44^2

Simplifying the equation, we have:

(Height of the building)^2 + 49 = 1936

Subtracting 49 from both sides, we get:

(Height of the building)^2 = 1887

To find the height of the building, we take the square root of both sides:

Height of the building = √1887

Calculating the square root of 1887, we find that the height of the building is approximately 43.46 meters.

Therefore, the ladder will reach a height of approximately 43.46 meters on the building.

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The indicated measures in the given circle are:

a. m<A = 38°;   b. m(CE) = 56°;    c. m<C = 38°;   d. m<D = 39°;  

e. m<ABE = 67°

In order to find the indicated measures in the circle, recall that the measure of an inscribed angle is half of the measure of the intercepted arc based on the inscribed angle theorem.

Thus, we have:

a. m<A = 1/2(m(BD))

Substitute:

m<A = 1/2(76)

m<A = 38°

b. m(CE) = 2(m<CBE))

Substitute:

m(CE) = 2(28)

m(CE) = 56°

c. m<C = 1/2(m(BD))

Substitute:

m<C = 1/2(76)

m<C = 38°

d. m<D = 1/2(m(AC))

Substitute:

m<D = 1/2(78)

m<D = 39°

e. m<ABE = 1/2(m(ACE))

m<ABE = 1/2(m(AC) + m(CE))

Substitute:

m<ABE = 1/2(78 + 56)

m<ABE = 67°

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Answer:

∠ B = 60°

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

10x - 45 is an exterior angle of the triangle , then

10x - 45 = 3x + 4x = 7x ( subtract 7x from both sides )

3x - 45 = 0 ( add 45 to both sides )

3x = 45 ( divide both sides by 3 )

x = 15

Then

∠ B = 4x = 4 × 15 = 60°