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2 years ago

T had 53,790 miles onit. They had the car for 8.25 years. On average, how many miles did they drive per year?

Mathematics

1 answer:

liq [111]2 years ago

7 0

Answer: ‭6,520‬ miles per year

Step-by-step explanation:

They had driven the car for 53,790 miles in 8.25 years.

The average number of number of miles driven per year is:

= 53,790 / 8.25 years

= ‭6,520‬ miles per year

They drove an average of ‭6,520‬ miles per year.

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10. A bag contains 4 red balls, 6 green balls and some white balls. If the probability of not drawing a white ball in one draw b

klasskru [66]

Answer:

No of white balls = 5

Step-by-step explanation:

Given that,

Total no of red balls = 4

Total no of green balls = 6

The probability of not drawing a white ball in one draw be, $P=\dfrac{2}{3}$

We need to find the number of white balls. Let there are x balls.

The probability of drawing a white ball = 1 - the probability of not drawing a white ball

= 1 -2/3

= 1/3

Using the formula for solving probability of having a white ball.

$P=\dfrac{\text{favorable outcome}}{\text{total no of outcomes}}\\\\\dfrac{1}{3}=\dfrac{x}{4+6+x}\\\\\dfrac{1}{3}=\dfrac{x}{10+x}\\\\10+x=3x\\\\10=2x\\\\x=5$

Hence, there are 5 white balls.

3 0

2 years ago

Find the equation of the sphere centered at (-9,9, -9) with radius 5. Normalize your equations so that the coefficient of x2 is

olganol [36]

<h2>Answer:</h2>

(a) x² + y² + z² + 18(x - y + z) + 218 = 0

(b) (x + 9)² + (y - 9)² + 56 = 0

<h2>Step-by-step explanation:</h2>

The general equation of a sphere of radius r and centered at C = (x₀, y₀, z₀) is given by;

(x - x₀)² + (y - y₀)² + (z - z₀)² = r² ------------------(i)

From the question:

The sphere is centered at C = (x₀, y₀, z₀) = (-9, 9, -9) and has a radius r = 5.

Therefore, to get the equation of the sphere, substitute these values into equation (i) as follows;

(x - (-9))² + (y - 9)² + (z - (-9))² = 5²

(x + 9)² + (y - 9)² + (z + 9)² = 25 ------------------(ii)

Open the brackets and have the following:

(x + 9)² + (y - 9)² + (z + 9)² = 25

(x² + 18x + 81) + (y² - 18y + 81) + (z² + 18z + 81) = 25

x² + 18x + 81 + y² - 18y + 81 + z² + 18z + 81 = 25

x² + y² + z² + 18(x - y + z) + 243 = 25

x² + y² + z² + 18(x - y + z) + 218 = 0 [equation has already been normalized since the coefficient of x² is 1]

Therefore, the equation of the sphere centered at (-9,9, -9) with radius 5 is:

x² + y² + z² + 18(x - y + z) + 218 = 0

(2) To get the equation when the sphere intersects a plane z = 0, we substitute z = 0 in equation (ii) as follows;

(x + 9)² + (y - 9)² + (0 + 9)² = 25

(x + 9)² + (y - 9)² + (9)² = 25

(x + 9)² + (y - 9)² + 81 = 25 [subtract 25 from both sides]

(x + 9)² + (y - 9)² + 81 - 25 = 25 - 25

(x + 9)² + (y - 9)² + 56 = 0

The equation is therefore, (x + 9)² + (y - 9)² + 56 = 0

6 0

3 years ago

Which equation could generate the curve in the graph below

Setler79 [48]

The curve has been attached and the answer choices are:

y = 3x² – 2x + 1

y = 3x² – 6x + 3

y = 3x² – 7x + 1

The attached graph has a vertex in the first quadrant. Therefore, the coordinates of the vertex would be both positive.

Let's start with first equation:

y = 3x² – 2x + 1

using the equation of axis:
x = -b/2a
x = 2/6
x = 1/3
SUbstituting the value of x in the main equation to get the y-coordinate of the vertex.
y = 3(1/3)² – 2(1/3) + 1
y = 3/9 – 2/3 + 1
y = 1/3 – 2/3 + 1
y = (1 - 2 + 3)/3
y = 2/3

Hence, the vertex would be:
(h,k) = (1/3 , 2/3)

Also, the leading coefficient is positive, so the parabola would be concave up.

Thus the final answer choice will be:

y = 3x² – 2x + 1