A 35 foot ladder is set against the side of a house so that it reaches up 21 feet. If Elijah
grabs the ladder at its base and pulls it 4 feet farther from the house, how far up the
side of the house will the ladder reach now? (The answer is not 17 ft.) Round to the
nearest tenth

If a street that is 270 ft long is covered in snow. City workers are using a snowplow to clear the street. The diameter of the tire is: 3.2 meters.

First step is to determine the circumference of the tire

Circumference of the tire =  (270 m / 27)

Circumference of the tire = 10 meters

Second step is to make use of  3.14 for π to determine the diameter of the tire using this formula

Diameter of the tire = Circumference of the tire /  π

Let plug in the formula

Diameter of the tire = 10 / 3.14

Diameter of the tire = 3.18 meters

Diameter of the tire = 3.2 meters (Approximately)

Therefore 3.2 meters is the diameter.

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Given the normal distribution, the following can be illustrated:

1. The number of people who have an IQ between 70 and 130 is 1024.

2. The number of people who have an IQ between 85 and 115 is 1024.

The number of people who have an IQ over 145 is 3.

1. The The number of people who have an IQ between 70 and 130 will be:

z(115) = (130-100)/15 = 2

z(85) = (70-100)/15 = -2

P(-2< z < 2) = 0.6827

The number of 1500 that have IQ between 70 and 130 will be:

= 0.6827 × 1500

= 1024

2. The number of people who have an IQ between 85 and 115 will be:

z(115) = (115-100)/15 = 1

z(85) = (85-100)/15 = -1

We need to consult Z-table to find P value with this Z value

P(85< x < 115) = P(-1< z < 1) = 0.6827

Number of people of 1500 that have IQ between 85 and 115:

= 0.6827 × 1500

= 1024

3. The number of people who have IQ over 145?

Z(>145)

=( 145-100)/15

=3

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The number of customers surveyed is 499.

UESTION A

ehe age ranges that fall within the required one for this question are 20-29, 30-39, and 40-49.

The number of people in these groups in total will be:

Therefore, the probability of this occurring is calculated to be:

he probability is 0.4449.

QUESTION B

he age ranges for this question are >≥60, <20, and 20-29.

The number of people in these groups in total will be:

he probability is 0.4850.

QUESTION C

is ≥60.

The number of people in this group is 84.

Answer:

[tex]\sqrt{8}[/tex]

We use the process of elimination to solve:

When we solve [tex](\sqrt{10})^{2}[/tex] we get 10 and we know that 10 is a integer and we know all integers are rational numbers, therefore, this is rational.

When we solve [tex]\sqrt{196}[/tex] we get 14 and we know its a rational number because it can be expressed as the quotient of two integers: 14 ÷ 1. Therefore this one is, rational.

0.63, The decimal 0.6 is a rational number. It is the decimal form of the fraction 6/10. A rational number is, by definition, any number that results when one integer is divided by another. Since both 6 and 10 are integers, or whole numbers, 0.6 is a rational number.

And lastly this leaves is with [tex]\sqrt{8}[/tex]  and It is a non-terminating decimal with non-repeating digits. The number 2.828427125... can't be written in p/q form. Hence, the square root of 8 is a irrational number.

Evaluate (-2) (-2) . 2

For this problem, we are given the zeros of a polynomial, we need to determine its expression.

The zeros are:

Therefore we can write:

The correct answer is option A.

According to the given information, the sum of the calories of a bag of popcorn and a juice box is 518. Taking x as the number of calories of a bag of popcorn and y as the number of calories of a juice box, we have that:

Then, 2 bags of popcorn (it means 2x) and 6 juice boxes (it means 6y) have a total of 1456 calories, this is:

Use this system of equations and solve the problem, this way:

Solve the first equation for x:

Use this expression and replace for x in the second equation:

Use this value to find the value of x:

It means that there are 413 calories in each bag of popcorn and 105 calories in each juice box.

x represents the amount of gas in the tank, has a domain described by which inequality

[tex]0 \leq x \leq 3[/tex]

This is further explained below.

Generally, A typical 3-gallon lawnmower requires 0.6 gallons of petrol per hour.

This circumstance is modeled by a function, where x is the volume of gas in the tank.

The lawnmower's gas tank has a maximum capacity of gallons and may be completely empty (having 0 gallons of gas).

In conclusion, a function's domain is

[tex]0 \leq x \leq 3[/tex]

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The sum and the difference in the amount saved in the accounts will be 180 + 50w and 20 + 30w respectively.

From the information, I have have $100 in a savings accoun and save an additional $40 each week.

Let the number of weeks be represented by w. The expression to represent this will be:

= 100 + 40w

My friend has $80 in a savings account and saves and addtional $10 each week. This will be:

= 80 + 10w

The sum will be:

= 100 + 40w + 80 + 10w

= 180 + 50w

The difference in the amount will be:

= 100 + 40w - (80 + 10w)

= 20 + 30w

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The equation of a circle with center (a, b) and radius r is

We are given the center as

To find the radius, we can use the formula to find the distance between two points, that is, the point on the circle and the center.

where (x₁, y₁) = (-14, 9)

(x₂, y₂) = (-11, 12)

Thus, we have

Therefore, inputting all the values into the equation for a circle, we have

Solution:

Thus;

Given;

FINAL ANSWER: Associative Property.

The statement is true. This is an example of Factorization being correct as it takes the factors of the quadratic equation set them equal to 0 and then calculates the value of x.

In the given question, an example of factorization is taken for the equation x²+4x-21 which is factorized using the Middle-Term split rule. We have to find out if the example is conducted correctly.

Factorization is the rule to factorize an equation such that its factors if multiplied together form the equation itself.

We will verify the factorization, for equation x²+4x-21

=> x² + 4x - 21

=> x² + 7x -3x -21

=> x(x + 7) -3(x + 7)

=> (x + 7)(x - 3) = 0

=> x = -7, x = 3

Hence, the statement is True.

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The Compound Interest would be $1104.895

What is Compound Interest ?

The interest charged on a loan or deposit is known as compound interest. It is the idea that we use the most frequently on a daily basis. Compound interest is calculated for an amount based on both the principal and cumulative interest. The main distinction between compound and simple interest is this. If we examine our bank statements, we will typically see that our account is credited with interest on a yearly basis. Even though the principal remains the same, the interest changes annually. We can observe that interest rises over time. As a result, we can infer that the interest the bank charges is compound interest, or CI, rather than simple interest.

Number of quarters in 5years =5×4=20

Quarterly rate of compound interest

r=24=0.5%

Initial amount

P=$1000

hence the total amount after 5years

=  P(1+r/100)n

=1000(1+0.5/100)^20

=1000(1.005)^20

=$1104.895

Hence, The Interest will be $1104.895

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Answer:

d ≈ 11.40

Step-by-step explanation:

K: (-4, -6); L: (5, 1)

    (x₁, y₁)     (x₂, y₂)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(5 - (-4))² + (1 - (-6))²

d = √(5 + 4)² + (1 + 6)²

d = √(9)² + (7)²

d = √81 + 49

d = √130 ≈ 11.40

I hope this helps!

Answer: The Y intercept is B) 3.

Step-by-step explanation:

you just have to see where the line crosses the y axis which in this case is it crosses the y axis on 3

Answer:

Step-by-step explanation:

5 over 12 is 5/17

Answer:

x=1/3k-y-z

Step-by-step explanation:

3x+3y+3z=k

Move the variables to the right

3x= -3y-3z+k

Divide both sides of the equation by 3

x=1/3k-y+z

Step-by-step explanation:

You will want to divide the cost of $4.99 by 100, this will give you the cost per yard.

Answer:

$4.99 / 100 = $0.0499

About 5 cents per yard.

Please give thanks, 5 stars, and brainliest answer :)

Answer:

$500

Step-by-step explanation:

Startup cost: $200

Cost of 1 car: $3

Cost of 100 cars: $3 × 100 = $300

$200 + $300 = $500

P( A and B) is [tex]\frac{1}{15}[/tex].

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is accurate. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Given Data

P(A) = [tex]\frac{1}{3}[/tex]

P(B) = [tex]\frac{1}{5}[/tex]

P (A or B) = [tex]\frac{1}{2}[/tex]

1) No, events are not mutually exclusive. as P(A) + p(B) is not equal to P(A or B)

2) P( A and B) = P(A) × P (B)

P( A and B) = [tex]\frac{1}{3}[/tex] ×[tex]\frac{1}{5}[/tex]

P( A and B) = [tex]\frac{1}{15}[/tex]

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yes

yes

yes

yes

yes

yes

no

The weight of the elephant on planet B given the ratio of the weights on planet A an B is 72 pounds.

Ratio is used to compare two or more quantities together. It shows the number of times that one quantity is contained in another quantity. In this question, the weight of the elephant on Planet B is 100/3 times that of Planet A.

In order to determine the weight of the elephant on Planet B, multiply the ratio of the weight in planet B by the weight in Planet A and divide by the ratio of weight in planet A.

Weight in Planet B = (3 x 2400) / 100 = 72 pounds

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Answer:

we need more info than this

Step-by-step explanation:

a) An equation to model the problem of determining the birth year when the average life expectancy will be 71 years is y = 55 + 0.2x.

b) From the equation above, from 1980 or in the 80th birth, the average life expectancy will be 71 years.

The average life expectancy refers to the average time in years that a person is expected to live after birth.

The average life expectancy has been a statistical tool for understanding a person's lifespan on earth based on some demographics.

An equation is a mathematical statement that equates two or more variables, numbers, or values or regards them as equivalent or equal.

For this situation, we can use the formed equation to predict a person's life expectancy average in the future, given the current years and increasing rate of life expectancy.

Life expectancy in 1900 = 55 years

Life expectancy increase for each birth year after 1900 = 0.2

Life expectancy = y

Year = x

y = 55 + 0.2x ... Equation

71 = 55 + 0.2x

0.2x = 16

x = 16/0.2

= 80 birth year

1980 = (1900 + 80)

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If y = -3 cos (2x), then derivative d²y / dx² is 12 cos (2x)

Given,

y = -3 cos (2x)

We have to find derivative d²y / dx²

d²y / dx² = -3 (d² cos x / dx²) = -3 d/dx (d cos 2x / dx)

According to the concept:

d cos x / dx = - sin x

Here,

d cox 2x / dx = - sin 2x

So,

d²y / dx² = (- 3 × 2) d/dx (- sin 2x)

d²y / dx² = -6 (d sin 2x / dx)

d²y / dx² = 2 × 6 cos 2x

d²y / dx² = 12 cos (2x)

That is, if y = -3 cos (2x), then derivative d²y / dx² is 12 cos (2x)

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The non-real solutions of the polynomial expression are x = (1 + 2√-5)/3 and x = (1 - 2√-5)/3

The equation of the polynomial expression is given as:

3x5 + 25x4 + 26x3 – 82x2 + 76x = 48

Rewrite the equation as

3x^5 + 25x^4 + 26x^3 – 82x^2 + 76x - 48 = 0

The points on the graph are given as

(-6, 0), (-5, 500), (-2.5, -450), (0, - 50), (1, 0), (2, 400).

Write out the x-intercepts

(-6, 0) and (1, 0)

This means that

Real solution = -6

Real solution = 1

Rewrite the above as

x = -6 and x = 1

So, we have

x + 6 = 0 and x - 1 = 0

Multiply

(x + 6)(x - 1) = 0

The next step is to divide the polynomial equation 3x^5 + 25x^4 + 26x^3 – 82x^2 + 76x - 48 = 0 by (x + 6)(x - 1) = 0

This is represented as

3x^5 + 25x^4 + 26x^3 – 82x^2 + 76x - 48/(x + 6)(x - 1)

Using a graphing calculator, we have

3x^5 + 25x^4 + 26x^3 – 82x^2 + 76x - 48/(x + 6)(x - 1) = 3x^3 + 10x^2 - 6x + 8

So, we have

3x^3 + 10x^2 - 6x + 8

Factorize

(x + 4)(3x^2 - 2x + 2)

Next, we determine the solution of the quadratic expression 3x^2 - 2x + 2 using a quadratic formula

So, we have

x = (-b ± √(b² - 4ac))/2a

This gives

x = (2 ± √((-2)² - 4 * 3 * 2))/2 * 3

So, we have

x = (2 ± √-20)/6

This gives

x = (2 ± 4√-5)/6

Divide

x = (1 ± 2√-5)/3

Split

x = (1 + 2√-5)/3 and x = (1 - 2√-5)/3

So, the conclusion is that

Using the polynomial expression, the non-real solutions are x = (1 + 2√-5)/3 and x = (1 - 2√-5)/3

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It is found that the displacement between t= 0  and t = 1 second is of 0.536 m.

The equation of motion is given by:

x(t) = 4 sin(πt + π/2)

The displacement between t= 0  and t = 1 second is given by:

d = x(1) - x(0)

Hence,

position of the object when t = 1

x(1) = 4sin(π(1) + 1 (π/2))

= 4 sin (π + π/2)

= 4 sin (3π/2)

= 4 x √3/2

= 2√3

= 3.464

position of the object when t = 0

x(0) = 4sin(π(0) + (π/2))

= 4 sin (0 + π/2)

= 4 x 1

= 4

Then,

d = x(1) - x(0)

= 4 - 3.464

= 0.536(approx)

Therefore, the displacement of the object between t = 0 and t = 1 is 0.536.

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Answer:

Step 6: Subtraction Property of =

Step-by-step explanation:

The ratio value of multiplication problems to division problems is 1:2.

The ratio value compares two quantities or values.

The ratio value shows the quantity of one variable contained in another.

Ratios are depicted by the ratio sign (:) or in fractions, decimals, or percentages.

The number of multiplications problems in the math test = 12

The number of division problems in the math test = 24

The ratio value of their relationship = 12:24 or 1:2

Thus, the math test shows that there are twice as many division problems as multiplication problems.

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FOR EQUATION INVERSES IT MEANS ... x and y swap positions.

[tex]x = (f(x))^{2} - 9 \\ (f(x))^{2} = x + 9 \\ \sqrt{(f(x))^{2} } = \sqrt{x + 9} \\ f(x) = \sqrt{x + 9} [/tex]

ATTACHED IS THE SOLUTION.