When the temperature is 68 F, the speed of the sound in air is approximately 343 meters per second. Approximately how many kilometers dose sound travel in five seconds?

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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

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:

Step-by-step explanation:

The probability of selecting a blue marble followed by a purple marble from a jar containing 120 marbles with different colors is approximately 2.2%.

The probability of grabbing a blue marble and then a purple marble is determined by multiplying the probability of grabbing a blue marble first and the probability of grabbing a purple marble second. Here's the calculation:

Probability of selecting a blue marble first: 17/120

Probability of selecting a purple marble second (after one blue marble is already taken out): 18/119

Multiplying the probabilities: (17/120) * (18/119) ≈ 0.022, or 2.2%

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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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:

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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Answer:

4 days

Step-by-step explanation:

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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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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The line of symmetry for the parabola is x = 1.

The line of symmetry for the parabola is x = 1. In the given equation (x-1)^2 = 4(y-1)^2, the x-coordinate of the vertex is 1, which means the line of symmetry is a vertical line passing through x = 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 given equation of parabola is

[tex] \frac{1}{32} (y-2)^2 = x-1 [/tex]

Which can also be written as

[tex] x = \frac{1}{32} (y-2)^2 +1 [/tex]

Here vertex (h,k) is (1,2)

And value of a is

[tex] a = \frac{1}{32} [/tex]

Formula of focus is

[tex] (h+ \frac{1}{4a} , k) [/tex]

Substituting the values of h,k and a, we will get

[tex] (1+ \frac{1}{4*(1/32) } , 2} = (1+ 8,2) = (9,2) [/tex]

Therefore the correct option is the last option .

Answer:  The correct option is (D) (9, 2).

Step-by-step explanation:  We are given to find the co-ordinates of the focus for the following parabola:

[tex]\dfrac{1}{32}(y-2)^2=x-1~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We know that the standard form equation of a parabola is

[tex](y-k)^2=4p(x-h),[/tex]

where the co-ordinates of the focus are (h+p, k).

From equation (i), we have

[tex]\dfrac{1}{32}(y-2)^2=x-1\\\\\\\Rightarrow (y-2)^2=32(x-1)\\\\\Rightarrow (y-2)^2=4\times 8(x-1).[/tex]

Comparing the above equation with the standard form equation of the parabola, we get

h = 1, k = 2, and p = 8.

Therefore, the co-ordinates of the focus are

[tex](h+p,k)=(1+8,2)=(9,2).[/tex]  

Thus, option (D) is CORRECT.