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3 years ago

Solve the equation. x+7=−8

2 answers:

4 0

X+7=-8
You are trying to get x on its own so you will subtract 7 from both sides.
x+7-7=-8-7
This simplifies to x= -8-7
A negative plus a negative equals a negative. So -8-7 equals -15
Your final answer is x=-15

Andrei [34K]3 years ago

3 0

Solution

1) Subtract 7 from each side
x=−8−7

2) Simplify −8−7 to −15
x=−15

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The volume of a sphere is 36π cubic feet. What is the radius of the sphere? (V = 4 3 πr3)

MrRa [10]

radius = 3 feet

rearrange the formula making r the subject

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4πr³ = 3V ( divide both sides by 4π )

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3 years ago

Find a formula for the transformation of reflection across the line l with equation y = -x.

Julli [10]

Answer:

The rule or formula for the transformation of reflection across the line l with equation y = -x will be:

P(x, y) ⇒ P'(-y, -x)

Step-by-step explanation:

Considering the point

$P(x, y)$

If we reflect a point $P(x, y)$ across the line $l$ with equation $y = -x$ , the coordinates of the point P flips their places and the sign of the coordinates reverses.

Thus, the rule or formula for the transformation of reflection across the line l with equation y = -x will be:

P(x, y) ⇒ P'(-y, -x)

For example, if we reflect a point, let suppose A(1, 3), across the line $l$ with equation $y = -x$ , the coordinates of point A flips their places and the sign of the coordinates reverses.

Hence,

A(1, 3) ⇒ A'(-3, -1)

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3 years ago

The latest poll from ESPN asked fans what their favorite sport was, considering pro, college and highschool levels. Out of 1000

shepuryov [24]

Answer:

Confidence interval is $0.2911$

Step-by-step explanation:

Given that 32% of fans sport is basketball as favorite sport. So total number of fans is,

$32\%\times 1000$

$= \dfrac{32}{100}\times 1000$

$=320$

So 320 fans favorite sport is basket ball.

Now find sample proportion ,

$\widehat{p}=\dfrac{number\:of\:people\:in\:the\:sample}{total\:number\:of\:people}$

Substituting the value,

$\widehat{p}=\dfrac{320}{1000}$

$\widehat{p}=0.320$

Formula for confidence interval is,

$CI=\widehat{p}\pm z\sqrt{\dfrac{\widehat{p}\left (1-\widehat{p}\right )}{n}}$

To calculate the z value.

$Confidence Level=1-\alpha$

$0.95=1-\alpha$

$0.05=\alpha$

Now divide above value by 2,

$\dfrac{0.05}{2}=\dfrac{\alpha}{2}$

$0.025=\dfrac{\alpha}{2}$

To find the value of z score calculate the area under the curve as follows

$A=\dfrac{1+CL}{2}$

$A=\dfrac{1+0.95}{2}$

$A=\dfrac{1.95}{2}$

$A=0.975$

On z table, find the value of 0.975. So the row corresponding to 0.975 is 1.9 and column corresponding to 0.975 is 0.06. Adding these two values the z score is 1.96.

or find the value from excel by using command as follows,

=NORM.S.INV(0.025)= -1.959963985

Now substituting the value,

$CI=0.320\pm 1.96\sqrt{\dfrac{0.320\left (1-0.320\right )}{1000}}$