Find the length of the third side of a right triangle with a hypotenuse of 17 and a leg of 10.

The parameter 2,400 in the depreciation function represents the initial value of Amy's printer. The printer depreciates by a factor of 0.86 each year. After calculations, the first printer has more value ($1,004.40) after 5 years compared to the second printer ($949.24).

Part A: The parameter 2,400 represents the initial purchase price or the original value of the printer that Amy owns in her graphic design store.

Part B: The factor by which the printer depreciates each year is 0.86 (which is calculated as 1 - 0.14, meaning the value retains 86% of its worth each subsequent year).

Part C: To compare which printer will have more value in 5 years, we need to calculate the future value of both printers using their respective depreciation rates:

After calculating:

Therefore, the first printer will have more value after 5 years.

ANSWER

True

EXPLANATION

According to the Rational Roots Theorem,the rational roots of a polynomial function F(x) can be written in the form

[tex] \frac{p}{q} [/tex]

,

where p is a factor of the constant term of the polynomial, and q is a factor of the leading coefficient.

The polynomial must be written in standard form.

This means the polynomial must be written in descending powers of x.

The leading term is the first term of a polynomial written in standard form.

The constant term is the term independent of x.

Answer:

4 days

Step-by-step explanation:

Final answer:

The probability of picking a second black marble, given that the first marble picked was black, is 1.

Explanation:

To find the probability of picking a second black marble, given that the first marble picked was black, we can use the formula for conditional probability: P(A|B) = P(A and B)/P(B).

In this case, A represents the event of picking a black marble on the second draw, and B represents the event of picking a black marble on the first draw.

We are given that P(B) = 514, and the probability of picking two black marbles without replacement is 1091. Therefore, P(A and B) = P(A|B) * P(B) = (1091/514) * (514/1091) = 1.

So, the probability of picking a second black marble, given that the first marble picked was black, is 1.

The correct answer is:

gas prices

Explanation:

As the number of people driving for pleasure goes down, the sales of electric cars go up. This is likely due to gas prices. As gas prices go up, fewer people drive for pleasure and more people purchase electric cars. Both are ways to reduce the amount of money spent on gasoline.

The option 'gas prices' variable is most likely the lurking variable that explains the correlation.

Given that a researcher finds a negative correlation between the total number of people driving for pleasure and the sales of electric cars.

It is required to find which variable is most likely the lurking variable that explains the correlation.

It is defined as the relation between two variables which is a quantitative type and gives an idea about the direction of these two variables.

We have a negative correlation between:

The total number of people driving for pleasure and the sales of electric cars.

We know that the negative correlation means one variable decreases and as the other increases and vice versa.

If the sales of electric cars increase the total number of people driving for pleasure goes down.

This can happen if the gas prices go up fewer people drive for pleasure and more people buy an electric car.

Thus, the option 'gas prices' is correct.

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The solution of the given trigonometric expression is x = 2π/3.

Use the concept of trigonometric ratio defined as:

Trigonometric ratios depend on the value of the ratio of sides of a triangle which is right-angled and contains the values of all trigonometric functions.

The ratios of a right-angled triangle's sides with regard to a certain acute angle are known as it's trigonometric ratios.

The given expression is:

2 cos x + 1 = 0

Where,

0 ≤ x ≤ 2π

To solve it,

Subtract  both sides,

2 cos x  = - 1

Divide by 2 on both sides,

cos x = -1/2

Take cos inverse on both sides,

[tex]x = cos^{-1} (\frac{1}{2})[/tex]

Since  cos(2π/3) = -1

x = 2π/3

Now since 2π/3 lies between  0 ≤ x ≤ 2π

Hence,

The solution of the given expression is x = 2π/3

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Answer:

7

Step-by-step explanation:

Answer:

Step-by-step explanation:

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The sum in sigma notation for the sequence as follows:

From

5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 + 45 + 50

first term=5

common difference=5

number of terms=10

n=nth term

therefore the total will be:

(i=2 to 10)∑(5(n-1)+5

Answer

Find out the  volume of a cylinder .

To prove

Formula

[tex]Volume\ of\ cylinder = \pi r^{2}h[/tex]

Where r is the radius and h is the height.

As given

Diameter of 12 in. and a height of 7 in.

[tex]Radius = \frac{Diameter}{2}[/tex]

[tex]Radius = \frac{12}{2}[/tex]

Radius = 6 in

[tex]\pi = 3.14[/tex]

put all the values in the formula

[tex]Volume\ of\ cylinder = 3.14\times 6\times 6\times 7[/tex]

                                          = 791.28 in³

Therefore the volume of the cylinder is 791 .28 in³ .

The answer provides the experimental probability of selecting green or purple marbles, predicts the occurrences of rolling 3 or 5 on a number cube, and estimates the total number of people who enjoyed the movie.

Experimental Probability Calculation: In the given scenario, there are 8 green marbles and 2 purple marbles, making a total of 10 marbles. The probability of selecting a green or purple marble is the sum of the individual probabilities, which is (8/10) + (2/10) = 0.8.

Expected Outcome of Rolling a Number Cube: Since a standard number cube has numbers 1 to 6, each number has an equal probability of 1/6. Predicting how many times 3 or 5 will be rolled out of 180 rolls can be calculated by (1/6 + 1/6) x 180 = 60 times each for 3 and 5.

Total Number of People Who Enjoyed the Movie: Based on the sample data, 4,200 out of 8,000 people enjoyed the movie. Extrapolating this to the total viewers, the predicted number of people who enjoyed the movie would be: (4,200/8,000) x 500,000 = 262,500 people.

The solution is: these have a subtraction operation, the exact opposite ellipse.

The parabola is a plane curve which is mirror symmetrical and is approximately U-shaped. It fits several superficial different mathematical descriptions.

here, we have,

The equation of a circle is:

(x - h)² + (y - k)² = r²

The equation of a parabola is:

(x - h)² = 4p(y - k)

The equation of an ellipse is:

(x - h)²/ a² + (y - k)²/ b² = 1

where variables a and b and the two different measurements of the vertices

The equation of a hyperbola is:

(x - h)²/ a² - (y - k)²/ b² = 1 if it is with a horizontal transverse axis

(y - k)²/ b² - (x - h)²/ a²  = 1 if it is with a vertical transverse axis

Notice these have a subtraction operation, the exact opposite ellipse.

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[tex] |\Omega|=2^3=8\\
|A|=1\\\\
P(A)=\dfrac{1}{8}=12.5\% [/tex]

Answer:

The dolphin is at height 5 feet after 1.40 seconds or 0.228 seconds.

Step-by-step explanation:

Given : The function [tex]h=-16t^2+26t[/tex]models the height h (in feet) of the dolphin after t seconds.

To Find: After how many seconds is the dolphin at a height of 5 feet?

Solution:

Function: [tex]h=-16t^2+26t[/tex]

h is the height

t is the time

Now we are supposed to find After how many seconds is the dolphin at a height of 5 feet

Substitute h = 5

So, [tex]5=-16t^2+26t[/tex]

[tex]16t^2-26t+5=0[/tex]

[tex]16t^2-26t+5=0[/tex] ---1

Using quadratic formula : [tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

General quadratic equation: [tex]ax^2+bx+c=0[/tex]   ---A

On Comparing equation 1 with A

a = 16

b = -26

c=5

Substitute the values in the quadratic formula.

[tex]x = \frac{-(-26)\pm\sqrt{(-26)^2-4(16)(5)}}{2(16)}[/tex]

[tex]x = \frac{26\pm 18.86796}{32}[/tex]

[tex]x = \frac{26+18.86796}{32},\frac{26-18.86796}{32}[/tex]

[tex]x = 1.4021,0.2228[/tex]

Thus the dolphin is at height 5 feet after 1.40 seconds or 0.228 seconds.

The dolphin is at a height of 5 feet at 0.2 second and 1.4 seconds.

Polynomial is an expression that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

Let h represent the height of dolphin at t seconds.

Given the function:

For a height of 5 ft.:

5 = −16t² + 26t

16t² - 26t + 5 = 0

t = 0.2 or t = 1.4

The dolphin is at a height of 5 feet at 0.2 second and 1.4 seconds.

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The solution is A = 11/25

The value of the equation A = ( 2x + 1 ) / x² is 11/25

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

A =  ( 2x + 1 ) / x²

when x = 5 , substitute the value of x as 5 in the equation , we get

A = ( 2 ( 5 ) + 1 ) / 5²

The value of A = ( 10 + 1 ) / 25

The value of A = 11/25

Therefore , the value of A = 11/25

Hence , The value of the equation A = ( 2x + 1 ) / x² is 11/25

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