A pole 9 feet tall is used to support a guy wire for a tower, which runs from the tower to a metal stake in the ground. After placing the pole, Ella measures the distance from the pole to the stake and from the pole to the tower, as shown in the diagram below. Find the length of the guy wire, to the nearest foot.

The product of 1.0×[tex]10^{2}[/tex] and 1.8×[tex]10^{3}[/tex] expressed in scientific notation is 1.8×[tex]10^{5}[/tex]

Scientific notation is the notation that used to express a very large  number or very smaller number is the simplest form. In scientific notation there will be number between 1 to 10 times multiplied by the power of 10.

The first number = 1.0×[tex]10^{2}[/tex]

The second number = 1.8×[tex]10^{3}[/tex]

Multiply the first number by second number, then the result will be

( 1.0×[tex]10^{2}[/tex] )×(1.8×[tex]10^{3}[/tex] )= 100×1800

= 180000

Convert the result to the scientific notation

180000 = 1.8×[tex]10^{5}[/tex]

Hence, the product of 1.0×[tex]10^{2}[/tex] and 1.8×[tex]10^{3}[/tex] expressed in scientific notation is 1.8×[tex]10^{5}[/tex]

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Answer: x=3

Step-by-step explanation:

40-25=15

15 divided by the 5 movies is 3

so $3 per movie

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Answer:

14137167 liters approximately

Step-by-step explanation:

Total Volume of a cylinder

V = π R² H

where R - base radius

H = height

Given diameter of base = 30m, base radius R = 30/2 = 15

H  = 20m

Volume = π x 15² x 20 = 4500π m³ = 14,137.16694 m³

Since 1 m³ = 1000 liters

this works out to  14137.16694 x 1000 ≈ 14137167 liters

If Katie has [tex]5\frac{1}{3}[/tex] pounds of plotting soil to use in her flowerpots and it takes 1/4 pounds of soil to fill one flowerpot, then the number of flowerpot that she can fill is 21 pots

The total quantity of potting soil that she has =  [tex]5\frac{1}{3}[/tex] pounds

Convert  the mixed fraction to the simple fraction

[tex]5\frac{1}{3}[/tex] pounds = 16/3 pounds

The quantity of potting soil that required to fill one flowerpot = 1/4 pounds

Number of flowerpot that she can fill = The total quantity of potting soil that she has / The quantity of potting soil that required to fill one flowerpot

= 16/3 ÷ 1/4
= 16/3 × 4

= 64/3

= 21.33

≈ 21 flowerpot

Hence, if Katie has [tex]5\frac{1}{3}[/tex] pounds of plotting soil to use in her flowerpots and it takes 1/4 pounds of soil to fill one flowerpot, then the number of flowerpot that she can fill is 21 pots

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even if an independent variable has an effect on the dependent variable, it fail to reject the null hypothesis and make a type II error

Even if a treatment is effective in the real world (it has an effect), it is still possible to obtain a sample mean that is so similar to the population mean that the sample mean doesn't fall in the critical, or rejection, region. If this happens, you are likely to fail to reject the null hypothesis and make a type II error.

Since that sample mean is so similar to the population mean, the treatment effect may not be detected on analysis even though it is in fact significant, this will cause the research to erroneously concluded that the treatment effect is zero and accept the null hypothesis when it is actually not zero. This is a type II error. Type II error in statistics means the non-rejection of a false null hypothesis and type I error is the rejection of a correct null hypothesis.

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Answer:

The car will use 9 3/8 or 9.375(simple form) gallons of gasoline on the highway

Step-by-step explanation:

if a car uses 3 1/8 gollon per one hour

Multiply the gallon usage of the car by the hours the car will travel on the road

3 1/8(gallons) x 3(hours on the road)

9 3/8 or if you change it to simple form it will be equal to 9.375

Answer: 36

Step-by-step explanation:

The answer is 36 because if you multiply:

6 * 2 = 12

12 * 3 = 36

And so that equals 36 sq cm

OR:

6 * 2 * 3 = 36 sq cm

I hope this helped!

The equation of the perpendicular line that passes through (−10, 2) will be y = (5/4)x + 14.5.

If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.

The equation is given below.

4x + 5y = 15

5y = −4x + 15

y = −(4/5)x + 3

The slope of the equation is −4/5. Then the slope of the perpendicular line will be 5/4. Then the equation is given as,

y = (5/4)x + c

The equation that passes through (−10, 2) will be

2 = (5/4)(−10) + c

2 = −12.5 + c

c = 14.5

Then the equation of the perpendicular line that passes through (−10, 2) will be y = (5/4)x + 14.5.

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Answer:

[tex]-5x^2 + 3x+9[/tex]

Step-by-step explanation:

Let the polynomial be p(x).

[tex]p(x)+(5x^2 -3x-9)=0 \\ \\ p(x)=-(5x^2 -3x-9) \\ \\ =-5x^2 + 3x+9[/tex]

The number 3 will come 20 times in 1 to 100 .

In mathematics, a number serves as both a unit of measurement and a label.

We know that the number 3 will come up in 3 ,13 ,23,30 , 31, 32, 33, 34, 35, 36, 37, 38, 39, 43, 53, 63, 73, 83, 93.

Therefore the number 3 will come up 20 times.

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The quadratic equation will be; 3x² + 6x + 9

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

Given that roots are x = -3 and x = - 1, and whose leading coefficient is 3.

The factors are; (x + 3) and (x + 1)

f(x) = a(x + 3)(x + 1)

As, a = 3.

Then we get;

f(x) = 3(x + 3)(x + 1)

= 3(x² + 2x + 3)

= 3x² + 6x + 9

The quadratic equation will be; 3x² + 6x + 9

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The ratio of the number of words Li Zhen typed to the number of words Kara typed to the number of words Rose typed = 8 : 4 : 1

Total numbers of words Li Zhen, Kara and Rose typed = 156 words

What is Ratio ?

A ratio displays the multiplicity of two numbers. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.

Since, it's given that

    the number of words Kara typed = 48

number of words Li Zhen typed = 2 x 48

                                                      =96words

a)  The ratio of the number of words Kara typed to the number of words Rose typed = 4:1

Since, it's given that

    the number of words Kara typed = 48

let, the number of words Rose typed = x

then, by equating them we get,

4/1 = 48/x

       4x = 48

          x = 48/4

          x = 12

The ratio of the number of words Li Zhen typed to the number of words Kara typed to the number of words Rose typed :

=  96 : 48 : 12

= 8 : 4 : 1

b) Now we know that,

  The number of words Li Zhen typed = 96words

  The number of words Kara typed = 48words

  The number of words Rose typed = 12words

Then, the total numbers of words Li Zhen, Kara and Rose type altogether

                               = 96 + 48 + 12

                               = 156 words

Hence, the total numbers of words Li Zhen, Kara and Rose type altogether is 156 words

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In terms of x and y, Julia's withdrawal from her savings account was equal to y/4 + x/12.

An expression obtained by performing a finite number of algebraic fundamental operations on symbols representing numbers.

Both Ang and Julia have savings balances of x and y dollars, respectively.

Ang = x dollars

Julia = y dollars

Ang offers Julia a third of his savings, which she then transfers to her own savings account.

Amount in Julia's account = (1/3)x + y

Julia then spends a quarter of the total into her savings account.

Amount of money Julia spent = 1/4 × [(1/3)x + y]

                                                 = (1/12)x + (1/4)y

                                                 = y/4 + x/12

Therefore, in terms of x and y, the amount Julia spent from her savings account is y/4 + x/12.

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Answer: 100

Step-by-step explanation:

525/84 x 100= 625 total students

625 - 525 = 100

iq scores have a bell shape distribution with a mean of 100 and standard deviation of 15. 81.855%  of the population has an iq score between 70 and 115

What is z-score?

The z score, also referred to as the standard score, serves to calculate how far each data point place is from its mean. In other words, it calculates x's (data point's) deviation in terms of standard deviations.

Using z tables, you may calculate the proportion of the population that is either below or above the score.

Now, according to the question;

IQ scores follow a normal distribution, with a mean of 100 as well as a standard deviation = 15.

A z score is determined as follows:

z = (x - μ)/σ

μ = mean of the distribution

σ = standard distribution of the sampling.

Calculation for the z score for x = 70 and  115

z= (70-100)/15

= -30/15

=-2

and x=115

z = (115 - 100)/15

= 15/15

z = 1.0

Use z-score table, then likelihood that a randomly chosen person's IQ is more than 115 is,

P( -2 < z < 1)= P(z<1) - P(z< -2)

                   =  0.8413 - 0.02275

                  = 0.81855

Therefore, the percent of the population has an iq between 70and 115 is 81.855%.

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Answer:

k = 4

Step-by-step explanation:

Polynomials:

 p(x) = 2x³ - 3x² - kx - 17

  x - 3 = 0

       x = 3

It is given that when p(x) is divided by (x - 3), it leaves the remainder -2

                ⇒  p(3) = -2

 2(3)³ - 3(3)² - k *3 - 17 = -2

       2*27 -3*9 - 3k -17 = -2

           54 - 27 - 3k -17 = -2

                       -3k + 10 = -2

                             -3k  = -2 - 10

                             -3k = -12

                                 k = (-12) ÷ (-3)

                                  [tex]\sf \boxed{k = 4}[/tex]

Answer:

53 sets

Step-by-step explanation:

730 - 204 = 526

526 / 10 = 52 r 6

therefore he'd have to buy 53 sets to have enough knives.

There are 53 number of sets of knives Jordan could buy for the restaurant to have enough knives.

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The restaurant needs at least 730 knives.

There are currently 204 knives.

And, each set on sale contains 10 knives.

Now,

By the given condition, we formulate;

⇒ 730 ≤ 204 + 10x

Solve for x as;

⇒ 730 ≤ 204 + 10x

⇒ 730 - 204 ≤ 204 + 10x - 204

⇒ 529 ≤  10x

Divide by 10 as;

⇒ 52.9 ≤ x

After rounding, we get;

⇒ 53 ≤ x

Thus, There are 53 number of sets of knives Jordan could buy for the restaurant to have enough knives.

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the total price paid for a pair of shoes after tax is included is $37.1.

A sales tax is a tax paid to the government for sales of certain types of goods and services.

According to the question,

Cost of the shoes =  $35.             (given)

Total amount/price paid = cost + tax

As the tax percentage is not given in the question, we will assume it to be 6% for example. Then,

Tax amount = 6% of $35

= 6/100*35

= $2.1

Now, total price = cost + tax

= $35+$2.1

= $37.1

Therefore, we conclude that the total price paid for a pair of shoes after tax is included is $37.1.

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[tex]m=\frac{y_{2-y_{1} } }{x_{2} -x_{1} } \\m=\frac{8-4}{3-2} \\m=\frac{4}{1} \\m=4[/tex]

I also provided the formula on how to calculate the slope between the points

Answer:

Image result for the government

The Federal Government is composed of three distinct branches: legislative, executive, and judicial, whose powers are vested by the U.S. Constitution in the Congress, the President, and the Federal courts, respectively.

Step-by-step explanation:

The correct option c: Subjective Probability, defined by teacher estimated that 95% of the Senior class would attend the prom.

For the given question,

As the probability estimated by the teacher that 95% of the Senior class would attend the prom, is the personal opinion.

Thus, the given case is of Subjective Probability.

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We can conclude that 30 inches of wood is needed to make 120 pins by solving some mathematical operations.

So, the wood we need to make 120 pins:

Therefore, we can conclude that 30 inches of wood is needed to make 120 pins by solving some mathematical operations.

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Damien score on the fourth day is 86.

Damien played golf on each of the four days of his vacation and the average for the four days of was 90.

so, his score on the fourth day.

so firstly let, X, be his score on the fourth day. then, the other four day's score is already given so, by using the formula for average.

the average for four numbers is given by, the sum of all numbers divided by the total numbers. so, by using this formula we have

=>(93+92+89+X)/4=90.and ,

on solving this we got,

X=86.

that is our answer.

so, His score on the fourth day is 86

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The expression in term numerator and denomerator of P the write answer would be

25.

Sol-

we have a deal an arrangement where, at the end of 5 years, the value of the car is going to be a fifth, the original price. So that's what i have written here after 5 years, the value of the car will be the price, the original price divided by 5 point. What we also know is that at 0 years, our initial value, the output here- should be the price of the car. So what we're going to do is when we use these 2 values to find the slope of this line, so we're going to do y 2, minus 1 y 1 over x, 2 minus x 1. It doesn't matter which 1 is y 2 and which 1 is y 1 as long as you're consistent here, i'm going to do p minus p over 5, and since i started here in the numerator, i need to start there in the denominator.

So we know here that x equals 4 we're doing that in the problem. So i'm goin t go ahead and replace this right here. We'Re gonna have y equals 16 p over negative 25 plus p, and if we get a common denominator here to add this, we have y equals 16 p plus 25 over 25. With this p right here, because it's gonna be 25 p over 25 here and then i recognize that are y value here, that was that was v or value here. All right and, let's see 25 p minus 16 p is going to give us 9 p. All right, so 9 p over 25 is going to be the value of the car, giving the original price p after 4 years.

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Answer:

The pattern the sequence follows is a perfect square, minus 2

Step-by-step explanation:

esentially use ( n^2 - 2 ) to find the nth number in the sequence.

the 5th number ( n = 5 ), would look like ( 5^2 - 2 ), simplfiying to ( 25 - 2 ), then being 23.

The same applies to all numbers listed in the sequence.

Ann must bowl 119 in the sixth game to have an average score of 120.

What is average?

Average is defined as the mean value that is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.

According to question,

155+121+125+118+112+x= 6(120)

601+x=720

x= 720-601

x= 119

Hence, she must bowl 119 in the sixth game.

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Answer: -0.875

Step-by-step explanation:

Answer: -1 1/8

Step-by-step explanation:

6 - 4 3/4 = 1 1/4

1 1/4 - 2 1/8 = -1 1/8

The force created by the object is 3.75 Newton.

Given

Mass of the object (m)  = 1250 grams

Convert 1250 grams to kilograms by dividing it by 1000.

Mass (m) = 1.25 kg

Acceleration of the body (a) = 3 [tex]m/s^{2}[/tex]

From Newton's second law we know [tex]F= m *a[/tex]

By Substituting in the above equation we get

Force = 1.25 x 3

Force = 3.75 [tex]kg/m /s^{2}[/tex]

It can also be written as force = 3.75 N

Hence Force created by the body is 3.75 Newton.

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They plant a total number of 480 seeds.

In the given question, Chrystal and her grandmother plant seeds in the garden. They plant a total of 4 types of seeds: Squash, Corn, Sunflower, and Tomato. They plant 6 rows of each type of seed. Also, each row has 20 seeds. We have to calculate the total number of seeds that they plant.

Given that,

=> Total number of types of seeds, T = 4

=> Number of rows, R = 6

=> Number of seeds in each row, S = 20

To calculate the Total Number of seeds planted we use the formula:

=> Total = T * R * S, Putting values we get:

=> Total = 4 * 6 * 20

=> Total = 480

Hence, the Total number of seeds planted is 480.

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The approximate side length of a square game board with an area of 160in² is equal to 12.6 inches.

As given in the question,

Area of the square game board is equal to 160in².

Let 'x' inches be the side length of the square game board.

Area of the square game board = (side length)²

⇒ 160 = ( x )²

Take square root both the sides we get,

    x = √160

⇒ x = 12.649 inches

⇒ x = 12.6 inches( approximately)

Therefore, the approximate side length of a square game board with an area of 160in² is equal to 12.6 inches.

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