Evaluate 150 - (2 + x) to the power of 3 when x = 2.

The height of the flagpole, found using the ratio of the sides of similar triangles is 12.975 meters

Similar triangles are triangles  in which two angles of one triangle  are congruent to two angles in the other triangle, such that they have the same shape.

The parameters that can be used to find the height of the flagpole are;

Distance of the mirror from the flagpole = 8.65 meters

Distance of Feng on the other side of the flagpole = 1.1 meters

The height from Feng's eyes to the ground = 1.65 meters

According to the law of reflection, the angle of incident and the angle of reflection are the same

The angle made by Feng and the ground = Angle made by the flagpole and the ground = 90°

The triangle formed by the Feng and the flagpole are therefore similar by AA similarity postulate

The ratio of corresponding sides of similar triangles are the same, therefore;

[tex]\dfrac{1.65}{Height\, of \, the \, flagpole} = \dfrac{1.1}{8.65}[/tex]

[tex]Height\, of \, the \, flagpole = \dfrac{1.65}{1.1} \times 8.65 = 12.975[/tex]

Height of the flagpole = 12.975  meters

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Half a mile every hour is equal to 1/5 mile every 4/10th of an hour.

Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.

Create a square on paper by using a pencil. Two dimensions make it up. A shape's area on paper is the space it takes up.

Imagine that your square is made up of smaller unit squares.

The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.

To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.

According to our question-

(1/5) / (4/10) = x / 1

Cross-multiplication yielding

1/5 * 1 = 4/10 * x

How to find x?

10 / 20 = x

x = 1 / 2

Half a mile every hour is equal to 1/5 mile every 4/10th of an hour.

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The value of the equation log(3 47) is about 4.235.

The power to which a number must be increased in order to obtain another number is known as a logarithm. For instance, since ten raised to the power of two equals 100, the base ten logarithm of 100 is 2: log 100 = 2.

Given that the approximate values of log(3) and log(47) are 1.1 and 3.85, respectively,

we must determine the approximate value of log(347).

log(a × b) = log(a) × log(b)

we get ,

log(3 × 47) = log(3) × log(47)

substituting , the values of log(3) and log(47) ,

we get ,

log(3 × 47) = 1.1 × 3.85

≈ 4.235

Therefore , The approximate value of log(3 × 47) is 4.235   .

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As the out comes are (3,6), (5,6), (5,3), (5,4), (5,5),(3,5) when you rolled an odd number first so the probability of rolling a sum greater than 7 is 1/6

The probability is equal to the variety of possible outcomes. the total number of outcomes that could occur. For instance, there is only one way to receive a head and there are a total of two possible outcomes, hence the probability of flipping a coin and getting heads is 1 in 2. (a head or tail). it will be written as P(heads) = 1/2.

Information about the possibility that something will happen is provided by probability. For instance, meteorologists use weather patterns to forecast the likelihood of rain. Probability theory is utilized in epidemiology to comprehend the connection between exposures and the risk of health outcomes.

There are total 36 possible outcomes of two dices when they are rolled.

N=36

now we have to consider the out comes having sum greater than 7

which are;

(2,6),(3,5),(3,6),(4,4) ,(4,5),(4,6),(5,3),(5,4),(5,5) ,(5,6),(6,2),(6,3),(6,4),(6,5),(6,6)

and now selecting only those having first number is odd

so they are:

(3,5),(3,6),(5,3),(5,4),(5,5),(5,6)

now using probability formula;

Probability = favorable outcomes /total outcomes

value putting;

probability = 6/36

probability =1/6

this is our required answer.

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Probability of rolling an odd number on a single die is 3/6, or 1/2. This is because there are three odd numbers (1, 3, and 5) on a standard six-sided die, and the probability of rolling any given number is 1/6.

Probability is a metric used to determine how likely an event or result is to occur. A decimal or fraction between 0 and 1 is typically used to express it, with 0 denoting that the event will not occur and 1 denoting that it will occur without a doubt. For instance, the likelihood of rolling a 6 on a conventional six-sided die is 1/6 since there is only one scenario out of the six conceivable events that will result in rolling a 6. By dividing the number of desired outcomes by the total number of potential possibilities, one may compute probability. In general, the more likely an event is to occur, the greater its probability.

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Lela is making peach pies. She uses 9 peaches for each pie. If she uses 18 peaches for 2 pies and 36 peaches for 4 pies, how many peaches will she need for 7 pies?

As, Lela is using 9 peaches for each pie.

Thus, she used 18 peaches for 2 pies, which is 2 times 9 and 36 peaches for 4 pies, which is 4 times 9. Therefore, to make 7 pies, she would need :

Peaches used for one pie = 9

=> Peaches used for 7 pies = 9 × 7

=> Peaches needed for 7 pies = 63

Hence, she will need 63 peaches to make 7 pies.

The option that is not a benefit of stretching is 1. Poor circulation

The option that is not in upper body stretch is 3. Straddle stretch

The benefits include:

The straddle stretch is one that is not considered an upper body stretch. Straddle stretch, also known as the middle split, requires a lot of leg flexibility. In conclusion, the correct option is C.

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Answer:

Step-by-step explanation:

=(37 * 45 ) + (63 * 45 )

=1665 + 2835

=4500

Answer:

Step-by-step explanation:

[tex]\tt 37\times 45\times63\times45[/tex]

[tex]\tt 1665\times63\times45[/tex]

[tex]\tt 104895\times 45[/tex]

[tex]\tt 4720275[/tex]

____________________

Hope this helps you!

Have a great day! :)

Answer:

x = 4

Step-by-step explanation:

5 x .8 = 4

Answer: the value of x is 4

Step-by-step explanation:

x=5*0.8=4

The LORD is faithful to all generations, and His loving kindness endures forever.

God Is Love, Therefore God Is Good God is light, and He is also love. God "is love." Because God loved the world so much that he gave his one and only Son, he ensured that everyone who trusted in him would not perish but have eternal life.

In the church, the adage "God is good, all the time, all the time" gained popularity a number of years ago. It is still in use today and was once used as a welcome and a response, frequently in a call-and-response pattern.

The Oxford English Dictionary describes omnibenevolence as unlimited or infinite compassion.

The complete question is,

Why is God so merciful all the time?

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Answer:

5 groups

Step-by-step explanation:

10/2=5

Answer:

x = 12.5

Step-by-step explanation:

The inside angles of a triangle should sum 180°

then

2x + (7x+5) + (180 - (11x-25)) = 180

2x + 7x + 5 + 180 - 11x -25 = 180

-2x - 25 = 0

2x = -25

x -25/2

x = 12.5

The equivalence of the expression 18⁺⁷ * 18⁵ is

Power or exponents as used in mathematics are number written on top of a base number. The power says how many times the base number multiplies itself.

The given expression 18⁺⁷ * 18⁵ is solved using the power rule, the power rule used is equation of bases> In equation of bases the base are kept constant and the mathematical operators act on the powers

This method is used as in this case as shown below

= 18⁺⁷ * 18⁵

= 18⁺⁷⁺⁵

= 18⁻²

= 1/18²

Therefore the equivalence of the expression is 1/18²

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Answer: 1

Step-by-step explanation:

Richard is 23years old and Thiago is 5years old

A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation.

From the question,

Let R stands for Richard

     T stands for Teo

we were told that the combined age of Richard and Teo is 28

i.e

R + T = 28 ......eqn (i)

we were also told that  Richard is 13 years older than twice Teo’s age

i.e

R = 2T + 13 .....eqn(ii)

substituting 2T + 13 for R in eqn (i)

(2T+13)+T = 28

expanding the bracket

3T + 13 = 28

collecting like terms

3T = 28 - 13

3T = 15

T = 15/3

T = 5

Teo age is 5years

From eqn (i)

R + T = 28

R + 5 = 28

R = 28 - 5

R = 23

Hence, Richard age is 23years

From eqn (ii)

R = 2T + 13

substituting for R in the eqn

23=2T+13

collecting like terms

23-13=2T

10=2T

T=10/2

T=5

Hence. Thiago age is 5years

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The  number of trucks and cars need by the class for the trip will be 3 and 2 respectively

Information from the question is used as follows

There are 22 people going on this trip.

total number = 22

There are four drivers and two types of vehicles, cars and trucks

drivers = 4

vehicle types = 2

The cars set four people, including the driver and the truck seats six people again including drive

cars = 4 people

truck = 6 people

Total number of people + drivers = 26

let the number of people in the truck be t and the number of people in the car be c

6t + 4c = 26

assuming the trucks were 3

6 * 3 + 4c = 26

4c = 26 - 18

4c = 8

c = 2

The class will need 3 trucks and 2 cars

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Answer: The square root of 169 is 13, so the two solutions for x are:

x = (13 + 13) / 4 = 3.25

x = (13 - 13) / 4 = -0.25

Since the quadratic expression 2x^2 - 13x - 5 equals 0 when x is either 3.25 or -0.25, the factors of this expression are (x - 3.25)(x + 0.25).

In summary, the factors of the first quadratic expression are (x + 1.056)(x + 5.937), the factors of the second expression are (x - 0.75)(x + 3.75), and the factors of the third expression are (x - 3.25)(x + 0.25).

Step-by-step explanation: To find the factors of a quadratic expression, we can use the quadratic formula. The quadratic formula states that for a quadratic expression of the form ax^2 + bx + c = 0, the solutions for x are given by the formula x = (-b ± sqrt(b^2 - 4ac)) / (2a).

In the first equation, a is 9, b is 31, and c is 20. Plugging these values into the quadratic formula, we get:

x = (-31 ± sqrt(31^2 - 4 * 9 * 20)) / (2 * 9)

This simplifies to:

x = (-31 ± sqrt(961 - 720)) / 18

This further simplifies to:

x = (-31 ± sqrt(241)) / 18

We can find the value of the square root by using a calculator or by remembering some common square roots. The square root of 241 is approximately 15.937, so the two solutions for x are:

x = (-31 + 15.937) / 18 = -1.056

x = (-31 - 15.937) / 18 = -5.937

Since the quadratic expression 9x^2 + 31x + 20 equals 0 when x is either -1.056 or -5.937, the factors of this expression are (x + 1.056)(x + 5.937).

We can use the same approach to find the factors of the other two quadratic expressions. For the second expression 2x^2 + 7x - 4, the values of a, b, and c are 2, 7, and -4, respectively. Plugging these values into the quadratic formula, we get:

x = (-7 ± sqrt(7^2 - 4 * 2 * -4)) / (2 * 2)

This simplifies to:

x = (-7 ± sqrt(49 + 32)) / 4

This further simplifies to:

x = (-7 ± sqrt(81)) / 4

The square root of 81 is 9, so the two solutions for x are:

x = (-7 + 9) / 4 = 0.75

x = (-7 - 9) / 4 = -3.75

Since the quadratic expression 2x^2 + 7x - 4 equals 0 when x is either 0.75 or -3.75, the factors of this expression are (x - 0.75)(x + 3.75).

For the third expression 2x^2 - 13x - 5, the values of a, b, and c are 2, -13, and -5, respectively. Plugging these values into the quadratic formula, we get:

x = (13 ± sqrt(13^2 - 4 * 2 * -5)) / (2 * 2)

This simplifies to:

x = (13 ± sqrt(169 + 40)) / 4

``

Answer:

1. no solution

2. one solution

3. infinitely many solutions

4. one solution

Step-by-step explanation:

1. same slope, different intercepts, parallel lines, no solution

2. different slopes, lines intersect at 1 point, one solution

3. same equation, infinitely many solutions

4. different slopes, lines intersect at 1 point, one solution

Answer:

2 1/4

Step-by-step explanation:

Subtract the whole numbers first:

8 - 6 = 2

To subtract the fractions, change 1/2 to 2/4 since they equal the same thing and 2/4 has the same denominator as 1/4:

2/4 - 1/4 = 1/4 <--- all we needed to do was subtract the numerators

Your final answer is 2 1/4.

It will be 38 feet long

The perimeter is the space surrounding a shape's edge.

The sum of the lengths of all the sides in a rectangular shape is its perimeter. P = 2( L+B)

Given that a rectangle's width is 17 feet and its perimeter is 110 feet, the length will be P = 2 (L + B)

110 = 2 (L + 17)

55 - 17 = L.

The pool is therefore 38 feet long.

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Answer: It would be 2.

Step-by-step explanation: The GCF of 10 and 6 would be 2 because that is the greatest number that 10 and 6 can be divided into. If we added them both to get 16. It would still be 2. I hope this helps!

Answer: To estimate the company's sales in 2026, we need to find the average increase in sales per year and then use that to predict the sales for 2026.

The total increase in sales from 2017 to 2020 was $14.5 million - $9 million = $<<14.5-9=5.5>>5.5 million.

The number of years from 2017 to 2020 is 2020 - 2017 = <<2020-2017=3>>3 years.

Therefore, the average increase in sales per year was $5.5 million / 3 years = $<<5.5/3=1.83>>1.83 million/year.

Since the average increase in sales per year was $1.83 million/year, we can estimate the sales in 2026 by adding that amount to the sales for each year from 2020 to 2026. For example, the estimated sales for 2021 would be $14.5 million + $1.83 million = $16.33 million. Similarly, the estimated sales for 2022 would be $16.33 million + $1.83 million = $18.16 million, and so on.

Using this method, we can estimate that the sales for 2026 will be $26.73 million.

Answer:

5 doors.

Step-by-step explanation:

10.5 times 2.7 is 28.35. 12 times 12 is 144. and 144 divided by 28.35 is 5.08 simplified to 5 doors

Answer:     0.26666667 (0.3)

Therefore the table values of which represents a linear function are table 2 and table 3

A linear equation is a first-order (linear) term and a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. A "linear equation of two variables" is what is sometimes referred to here, where y and x are the variables.

Here,

The values shown in table 2 have same constant rate of change of 3 units.

where as,

The values shown in table 3 have same constant rate of change of 5 units.

Therefore the table values of which represents a linear function are table 2 and table 3

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Answer:

B. 49

Step-by-step explanation:

21/3 = 7

7*7 = 49

On solving the provided question, we got that The 90% confidence interval for the population mean mu is (140.4, 147.6)

A measure of how far the data are from the mean is called standard deviation (or). Data that have a low standard deviation are more likely to be centered around the mean than those that have a high standard deviation.

xbar = 144 (sample mean)

s = 12 (sample standard deviation)

n = 30 (sample size)

z = 1.645 (critical value at 90% confidence; use a calculator or table to compute this value)

[tex]The lower limit of the confidence interval is L, which is found by\\\\L = xbar - z(s/sqrt(n))\\L = 144 - 1.645(12/sqrt(30))\\L = 140.395985571616\\L = 140.4\\[/tex]

Similarly the upper limit U is

U = xbar + z(s/sqrt(n))

U = 144 + 1.645(12/sqrt(30))

U = 147.604014428384

U = 147.6

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Indirectly we are asked for x and y intercepts because

Let us find out

Y intercept:-

put x=0

(0,-3)

X intercept

put y=0

(-3/5,0)