1. SHADOWS George
in the middle of the day
George's shadow is 15 feet long, and
pole's shadow is 45 feet long
If George is 6 feet tall, how tall is the light pole ?

A set of statistics exam scores are normally distributed with a mean of 76. 5576. 5576, point, 55 points and a standard deviation of 555 points. 28.34% proportion of exam scores are between 797979 and 86. 586. 0586..

A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed. In contrast, a high or low standard deviation indicates that the data points are, respectively, above or below the mean. A standard deviation that is close to zero implies that the data points are close to the mean.

Given,

Mean = 76.55

Standard deviation = 5

To calculate this, we first need to get the Z score mathematically

Z = X - mean/standard deviation

For the 79,

Z = 79 - 76.55/5

Z = 0.49

For the 86.05

Z = X - mean/standard deviation

Z = 86.05 - 76.55/5

Z = 1.9

So, we have

P(0.49 < Z < 1.9)

P( Z < 1.9) - P( Z < 0.49)

Using the table of standard score probability

P(Z < 1.9) = 0.9713

P( Z < 0.49) = 0.6879

P( Z < 1.9) - P( Z < 0.49)

0.9713 - 0.6879

0.2834

In percentage,

0.2834 × 100%

28.34%

A set of statistics exam scores are normally distributed with a mean of 76. 5576. 5576, point, 55 points and a standard deviation of 555 points. 28.34% proportion of exam scores are between 797979 and 86. 586. 0586..

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Answer:

The correct answer is A. hire employees.

During a boom, or an economic expansion, businesses typically experience increased demand for their products and services. This often leads to higher profits and sales, and as a result, many businesses will choose to hire additional employees to help meet the increased demand. Hiring employees allows businesses to increase their production and sales, and it can also help them to capitalize on opportunities for growth and expansion.

The other answer choices, cutting jobs (B) and saving cash (C), are not typically associated with a boom. Cutting jobs would be more likely to occur during a recession or a downturn in the economy, when businesses are trying to reduce costs and improve their bottom line. Saving cash, on the other hand, is something that businesses might do during any economic conditions, as it can help them to build up a financial cushion and prepare for unexpected events. However, during a boom, businesses are more likely to focus on expanding their operations and taking advantage of the increased demand for their products and services.

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

It seems like the most logical answer, as boom usually means it's doing well. When a business is doing well I doubt they would want to cut jobs or have to be worried about saving their extra cash.

The solution to the given linear inequality is x > 1

From the question, we are to solve the given linear inequality.

The given linear inequality is

3x - 2 > 4 - 3x

Solving the inequality

3x - 2 > 4 - 3x

Add 3x to both sides

3x +3x - 2 > 4 - 3x + 3x

6x - 2 > 4

Add 2 to both sides

6x - 2 + 2 > 4 + 2

6x > 6

Divide both sides by 6

6x/6 > 6/6

x > 1

Hence, the solution is x > 1

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Answer:9

Step-by-step explanation:

18 times 2 =36

1 triangle is half of a square

36 divided by 4 is 9

The total mass of the paper clips in the box will be C. 2.226 × 10^1

Scientific notation is a method of displaying very large or very small numbers in a more simplified format. We know that entire numbers can be extended indefinitely, but such large numbers cannot be written on a piece of paper. Furthermore, the numbers in the millions place after the decimal required to be represented in a simpler format.

Since the mass of a paper clip is 7.0 x 10−4 mg and a box of paper clips has 3.18 x 104 paper clips, the total mass of the paper clips in the box will be:

= (7.0 × 20^-4) × 3.18 ÷ 10^4)

= 22.26

= 2.226 × 10^1

The correct option is C.

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Answer:

Step-by-step explanation:

65kilo

We need 42 minimum number integers from 0 to 80 that must be selected in order to be sure of getting at least one that is odd.

We need Pigeonhole Principle which states,

The pigeonhole principle is one of the simplest but most useful ideas in mathematics, and can rescue us here. A basic version says that if (N+1) pigeons occupy N holes, then some hole must have at least 2 pigeons. Thus if 5 pigeons occupy 4 holes, then there must be some hole with at least 2 pigeons.

We know that there are 40 odd integers 1, 3, 5, 7, ....79 and 41 even integers 0, 2, 4, 6, .....80 from 0 to 80 .

So, at most, 41 integers picked out of them. If we pick one more integer after picking all of these then it must be odd integer according to Pigeonhole  Principle. Therefore, we need to at least one more integer from 0 through 80 to be sure that there is at least one odd integer.

So, in total we need to pick at least 41 + 1 = 42 integers from 0 to 80 to be sure of getting at least one that is odd.

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Using PEDMAS to calculate the mathematical operation -4 + (6 + 8) ÷ (-2)  the value is -11

This is the use of mathematical operands to solve mathematical problems. This is involves the use of PEMDAS to solve mathematical expressions and equations.

In the given question,

-4 + (6 + 8) ÷ (-2)

Using PEMDAS;

The resultant operation will become

-4 + (6 + 8) ÷ (-2) = -11

The operation of -4 + (6 + 8) ÷ (-2) will give -11

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128 possible ways can the student answer the seven questions.

What is combinations?

We have 7 true-false questions.

Each question can be answered 2 different ways and the answer for one question has no effect on the answer for another.

They are independent events.

So, the number of different ways that 7 questions can be answered is

= 2⁷

= 128 ways

Hence, there are 128 possible ways can the student answer the seven questions.

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Answer:

Let us label the point where the two circles touch as point B. Since the two circles have the same size and are tangent to each other at point B, the radii of both circles must be equal. Let the radius of the circle be r.

Since triangle ACE is equilateral, all sides of the triangle must be equal in length. Since the circumference of each circle is 66 cm, the length of each side of triangle ACE must be 66/3 = 22 cm.

Since the radius of the circle is tangent to the side of the triangle at point B, the length of line segment EB must be equal to the radius of the circle. Since the length of line segment EB is 29.7 cm, the radius of the circle must be 29.7 cm.

The area of the shaded region can be found by subtracting the area of the smaller circle from the area of the larger circle. The area of a circle with radius r is given by the formula A = πr², where A is the area of the circle and r is the radius of the circle. Since the radius of the smaller circle is 29.7 cm, the area of the smaller circle is 29.7²π = 869.43π cm².

Since the radius of the larger circle is half the length of the side of the triangle, the radius of the larger circle must be 22/2 = 11 cm. The area of the larger circle is therefore 11²π = 121π cm².

The area of the shaded region is therefore 121π - 869.43π = -748.43π cm². Since the area of a region cannot be negative, the answer to the question must be 0 cm². The area of the shaded region is therefore 0 cm².

If PQ=3x+8 and QR=2x + 17, the value of x is 31.

When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°. The linear pair postulate or linear pair theorem in mathematics states the same thing mathematically. The sum of the measurements of two angles that make up a linear pair is 180°.

Given

Value of lines,

PQ = 3x + 8

QR = 2x + 17

Linear pair theorem,

3x + 2x + 8 + 17 = 180

5x + 25 = 180

5x = 180 - 25

5x = 155

x = 155/5

Value

x = 31

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Answer:

      I hoped this helped! Please give me brainliest :D

Slope is a measure of how much a line changes in the y-direction for every unit of change in the x-direction. It is typically represented by the m in the equation y = mx + b. The slope of (-1,2) is undefined because it has only one point.

Slope is calculated by taking the difference in the y-coordinates divided by the difference in the x-coordinates of two points on a line. Since we only have one point, we cannot calculate the slope.Slope is a measure of how steep a line is, and is calculated by taking the ratio of the change in the y-coordinate to the change in the x-coordinate. Since we only have one point, we don't have any changes and therefore cannot calculate the slope.

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Answer:

25 feet long and 16 feet wide

Step-by-step explanation:

16 x 2 = 32
32 - 7 = 25
25 x 16 = 400

The linear model equation for the given data is y = 2x  .

In the question ,

it is given that ,

a data table is given ,

from the table we can see that ,

when x is = 2 , the value of y = 4 ,

and when x is = 4 , the value of y = 8 .

So , we have two points as (2,4) and (4,8) .

the slope of the line is = (8-4)/(4-2)

= 4/2

= 2 .

So , the equation of the line with m = 2 and (x,y) = ( 2,4) will be

(y - 4) = 2(x - 2)

y - 4 = 2x - 4

Adding 4 in both sides of equation ,

we get ,

y = 2x

Therefore , the linear model equation of the line is y = 2x .

The given question is incomplete , the complete question is

How do you write a linear model equation for a data table given as ?

 x    y

2    4

4    8

6    12

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The approximate probability that the next 100 sunday customers will spend an average of at most $28 is 0.97725

This theorem limits the central value (mean) of a sample measure to the mean value of the population from which the sample was drawn. There are two versions of this set, average and ratio respectively. This is true only if each sample is the same size and that size matters.

We have given that,

Mean , μ = $32

Standard deviations, σ = $20

sample size, n = 100

The probability that the test 100 sunday customers will spend on average of at most $28.

Using formula,

Standard error = 20/Sqrt(100) = 2

Test- statistic, Z = (x -μ)/S.E

here we have, x = 28 , S.E = 2 , μ = 32

=> Z = ( 28 - 32)/2 = - 4/2 = -2

Now, the approximate probability value, P(X≤ x )

is P(X≤ 28) = P(X - μ / S.E < 28- 32/2) = P(Z≤ -2)

= 1 - P(Z>-2) = 1- P(Z< 2) = 1 - 0.02275 = 0.97725 To learn more about Central Limit Theorem, refer:

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The figure was rotated 270° counterclockwise and was translated 2 units to the left.

Translation moves a shape left, right, up, or down but does not turn. The translated shapes (or the image) appear to be the same size as the original shape, indicating that they are congruent.

if we pick a point on the shape with a coordinate (3,2) if we rotate that point 270° counterclockwise the new coordinates become ( 2, -3)

From the graph the final coordinates of that point i (0, -3)

Which means that point moved from point 2 to point 0 2 units to the left.

So then shape was translated 2 units to the left.

In conclusion, the shape was translated by 2 units to the left.

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Answer:

x = -8

Step-by-step explanation:

Step 1: Combine multiplied terms into a single fraction.

(-x / 5) - 1.4 = 2x + 16.2

Step 2: Find a common denominator.

(-x / 5) + [5(-1.4) / 5] = 2x + 16.2

Step 3: yeah this is boring idc about the explanation

The statement for the congruency of the triangles and the corresponding sides are as follows:

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal .

In other words, triangles that have exactly the same size and shape are called congruent triangles.

Let's write a congruency statement for the triangles and identify the pair of congruent corresponding side.

Therefore,

ΔPQR ≅ ΔCBA

Hence,

∠Q = ∠B

∠R = ∠A

∠P = ∠C

PQ = BC

QR = AB

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The speed of Ted is 08 mph  and the speed of Frank is 12 mph.

Given:

Ted runs 2/3 as fast as frank. In 2 hours frank runs 8 miles farther than ted.

Ted Data:

Distance = d;

Rate = (2/3)x;

Time = 2 hours

Candid Data:

Distance = d+8;

Rate = x;

Time = 2 hours

Formula: Distance = Speed*Time

Therefore,

Flank distance = ted distance + 8

2x = (4/3)x + 8

6x = 4x + 24

2x = 24

x = 12 mph

The speed of Flank is 12 mph.

Therefore, the speed of Ted is:

(2/3)x = 8 mph

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Answer:

The solution to this equation is x=4 (or A)

Step-by-step explanation:

First, you want to remove the parentheses from the equation and distribute 2 through the parentheses:

4x+2x+12=36

Then you collect like terms:

6x+12=36

Then you move the constant to the right-hand side and change its sign:

6x=36-12

Then you subtract the numbers:

6x=24

Then you divide both sides of the equation by 6, which gives you your solution:

x=4

Yes, 1 is the first square number.

What is a square number?

A square number, sometimes known as a perfect square, is an integer that is an integer squared; in other words, it is the result of multiplying an integer by itself. Because it equals 3² and can be represented as 3 *3, the number 9 is an example of a square number.

Given that 1 x 1 equals 1, the initial square number is 1.

Due to the fact that 3  x 3 = 9, the third square number is 9, and so forth. Following are the first fifteen square numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, and 225.

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The quadratic equation which satisfy all the condition is y= -(x+4) (x- 10)

What is the simple quadratic formula?

The quadratic formula is as follows. The equation Ax2+Bx+C=0 can be divided by A to get x2+B/Ax+C/A=0, and the procedure repeated to get the more generic version.

How do you square a number?

How to use the Quadratic Formula to solve a quadratic equation.

Ax2 + bx + c = 0 is the quadratic equation in standard form. Find the values of a, b, and c.

the quadratic formula in writing. Then enter the values for a, b, and c.

Simplify.

Verify the answers.

Given that :

Roots are (-4, 0) and (10, 0)

and goes through  the point (5,45)

So as we can see that that only second and third option satisfy the roots and the third one satisfy the point conditions.

hence the quadratic equation which satisfy all the condition is y= -(x+4) (x- 10)

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The measure of angle B is given as follows:

m < B = 19.12º.

The measure of angle B is obtained applying the law of sines, which states that the ratio between the sine of an angle and the length of the opposite side to the angle is equals for all three angles.

The angles for the triangles are given as follows:

Then the measure of angle C is calculated as follows:

sin(148º)/1950 = sin(C)/820

sin(C) = 820 x sin(148º)/1950

sin(C) = 0.22283784444

C = arcsin(0.22283784444)

C = 12.88º.

The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of angle B is obtained as follows:

148 + 12.88 + x = 180

x = 180 - (148 + 12.88)

x = 19.12º.

The figure is given by the image shown at the end of the answer.

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The football game was attended by 1250 teenagers out of 5000 people who attended the game.

The number of teenagers who calculated the game can be calculated by finding the percentage of people who were teenagers. The word formula for the calculation will be -

Number of teenagers in the game = 5000 × 25%

Writing the percentage as fraction

Number of teenagers in the game = 5000 × 25/100

Cancelling zero as common in numerator and denominator

Number of teenagers in the game = 50 × 25

Performing multiplication on Right Hand Side of the equation

Number of teenagers in the game = 1250

Hence, there are 1250 teenagers.

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The volume of the cone in cubic inches is 209.52 inches³.

Here we have to find the volume of the cone.

Data given:

diameter (d) = 10 inches

height(h) = 8 inches

radius (r) = 5 inches

The formula for the volume of the cone:

Volume = 1/3 πr²h

Now putting the values in the equation we have:

V = 1/3 π (5)² × 8

  = 209.52 inches³

Therefore the volume is 209.52 inches³.

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