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4 years ago

Solve for a! 264=π×a×(20-a) Thank you!

Mathematics

1 answer:

jasenka [17]4 years ago

4 0

Answer:

a ≈ 14 or 6

Step-by-step explanation:

264 = π × a × (20 - a)

a(20 - a) = $\frac{264}{Pi}$ ≈ 84 (rounded off to nearest whole number)

Opening the brackets we get;

a² - 20a + 84 = 0

Applying the quadratic formula we get:

a ≈ 14 or 6

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4 years ago

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3 years ago

1. Maryann is tracking the change in her vertical jump over 6 months. Use the table to write a linear function that models her j

ArbitrLikvidat [17]

Answer:

Part 1) Option A. f of x equals one half times x plus 16

Part 2) Option A. x = 5

Part 3) Option C. x − 4y = −9

Part 4) Option A. The number of rides is the independent variable, and the total cost is the dependent variable.

Step-by-step explanation:

Part 1)

Let

x -----> the number of months

y ----> vertical jump in inches

step 1

Find the slope

we have the points

(0,16) and (2,17)

$m=(17-16)/(2-0)=\frac{1}{2}$

The equation of the line in slope intercept form is

$y=mx+b$

we have

$m=\frac{1}{2}$

$b=16$ -----> the point (0,16) is the y-intercept

substitute

$y=\frac{1}{2}x+16$

convert to function notation

f(x)=y

$f(x)=\frac{1}{2}x+16$

Part 2) What is the equation of a line that contains the points (5, 0) and (5, −2)?

step 1

Find the slope

we have the points

(5, 0) and (5, −2)

$m=(-2-0)/(5-5)=\frac{-2}{0}$

the slope is undefined

This is a vertical line (parallel to the y-axis)

therefore

The equation is

x=5

Part 3) Choose the equation that represents a line that passes through points (−1, 2) and (3, 1)

step 1

Find the slope

we have the points

(−1, 2) and (3, 1)

$m=(1-2)/(3+1)=-\frac{1}{4}$

step 2

Find the equation of the line into point slope form

$y-y1=m(x-x1)$

we have

$m=-\frac{1}{4}$

$point\ (3, 1)$

substitute

$y-1=-\frac{1}{4}(x-5)$

Convert to standard form

Multiply by 4 both sides to remove the fraction

$4y-4=-(x-5)$

$4y-4=-x+5$

$x-4y=-4-5$

$x-4y=-9$

Part 4) Jewels has $6.75 to ride the ferry around Connecticut. It will cost her $0.45 every time she rides. Identify the dependent variable and independent variable in this scenario

we know that

The <u>independent variable</u> is the variable whose change isn’t affected by any other variable (An example the age and time)

The <u>dependent variable</u> it’s what changes as a result of the changes to the independent variable (An example of a dependent variable is how tall you are at different ages. The dependent variable (height) depends on the independent variable (age))

Let

x ----> the number of rides

y ----> the total cost in dollars

In this problem

The independent variable or input is the number of rides

The dependent variable or output is the total cost

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3 years ago

Adimas found the mean of her 11 math test scores for the first semester. X = StartFraction (76 87 65 88 67 84 77 82 91 85 90) Ov

Reika [66]

To find the solution we will first find the difference between each number and mean, and then substitute the value in the formula of standard deviation.

The standard deviation is 8.4477 and the variance is 71.40.

Given to us

Test scores of Adimas = (76, 87, 65, 88, 67, 84, 77, 82, 91, 85, 90)
Mean = 81

<h3>Standard Deviation</h3>

difference between each number and mean,

$x_1 -\mu= 76-81 = -5\\
x_2-\mu = 87-81 = 6\\
x_3-\mu = 65-81 = -16\\
x_4-\mu = 88 -81 = 7\\
x_5-\mu = 67-81 = -14\\
x_6 -\mu= 84-81 = 3\\
x_7 -\mu= 77-81 = -4\\
x_8 -\mu= 81-81 = 1\\
x_9 -\mu= 91-81 = 10\\
x_{10}-\mu=85-81 = 4\\
x_{11} -\mu= 90-81 = 9$

$\sum(x-\mu)^2 = x_1^2+x_2^2+x_3^2+x_4^2+x_5^2+x_6^2+x_7^2+x_8^2+x_9^2+x_{10}^2+x_{11}^2$

= 25 + 36 + 256 + 49 + 196 + 9 + 16 + 1 + 100 +16 + 81

= 785

$\rm{ Standard\ Deviation = \sqrt{\dfrac{\sum{(X-\mu)^2}} {n}$

$\sigma= \sqrt{\dfrac{785}{11}}\\\\
\sigma = 8.4477$

<h3>Variance</h3>

Variance = $\sigma ^2$

= 71.40

Hence, the standard deviation is 8.4477 and the variance is 71.40.

Learn more about Standard Deviation:

brainly.com/question/12402189

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3 years ago

The mean temperature change is −3.2°f−3.2°f per day for 5 days. what is the total change over the 5-day period?the total change

Fiesta28 [93]

The mean temperature change per day is - 3.2° F.
For 5 days:
5 * ( -3.2° F ) = - 16° F.
Answer:
The total change over the 5-day period is - 16° F.

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4 years ago

Read 2 more answers