Simplify 4(2+3/4n(3n))=8

which is the equation of a line that has a slope of 1 and passes through the point (5,3)? y=x-2 , y=x+2 , y=x+2 , y=x-1

Margarita [4]

Answer:

y=x-2

Step-by-step explanation:

if x: 5, x-2=3

y=x-2

therefore:

y=3

x=5

4 0

3 years ago

Find the outlier in the data: 32, 40, 34, 31, 20, 36, 40, 31. How does the outlier affect the mean?

Inessa [10]

The outlier is 20

it affect the mean because

1)32 +40+34+ 31 +20+ 36 +40+31=264

2) 264 divided by 8= 33

so it gives you an odd number

8 0

3 years ago

A line passes through the point (9,1) and has a slope of 2.Write an equation in slope-intercept form for this line.

bogdanovich [222]

Answer:

y = 2x-17

Step-by-step explanation:

We have a point and a slope, we can write the equation in point slope form and then convert to slope intercept form

y-y1 = m(x-x1) where m is the slope and (x1,y1) is the point

y-1 = 2(x-9)

Distribute

y-1=2x-18

Add 1 to each side

y-1+1 = 2x-18+1

y = 2x-17

This is slope intercept form

4 0

3 years ago

If you are offered one slice from a round pizza (in other words, a sector of a circle) and the slice must have a perimeter of 24

VARVARA [1.3K]

Answer:

A 12 in diameter will reward you with the largest slice of pizza.

Step-by-step explanation:

Let $r$ be the radius and $\theta$ be the angle of a circle.

According with the graph, the area of the sector is given by

$A=\frac{1}{2}r^2\theta$

The arc lenght of a circle with radius $r$ and angle $\theta$ is $r \theta$

The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches. Thus the perimeter has length

$2r+r\theta=24 \:in$

We need to express the area as a function of one variable, to do this we use the above equation and we solve for $\theta$

$2r+r\theta=24\\r\theta=24-2r\\\theta=\frac{24-2r}{r}$

Next, we substitute this equation into the area equation

$A=\frac{1}{2}r^2(\frac{24-2r}{r})\\A=\frac{1}{2}r(24-2r)\\A=12r-r^2$

The domain of the area is

$0$

To find the diameter of pizza that will reward you with the largest slice you need to find the derivative of the area and set it equal to zero to find the critical points.

$\frac{d}{dr} A=\frac{d}{dr}(12r-r^2)\\A'(r)=\frac{d}{dr}(12r)-\frac{d}{dr}(r^2)\\A'(r)=12-2r$

$12-2r=0\\-2r=-12\\\frac{-2r}{-2}=\frac{-12}{-2}\\r=6$

To check if $r=6$ is a maximum we use the Second Derivative test

if $f'(c)=0$ and $f''(c)$ , then f(x) has a local maximum at x = c.

The second derivative is

$\frac{d}{dr} A'(r)=\frac{d}{dr} (12-2r)\\A''(r)=-2$

Because $A''(r)=-2$ the largest slice is when r = 6 in.

The diameter of the pizza is given by

$D=2r=2\cdot 6=12 \:in$

A 12 in diameter will reward you with the largest slice of pizza.

3 0

3 years ago

The weights of newborn baby boys born at a local hospital are believed to have a normal distribution with a mean weight of 4016

hodyreva [135]

Answer:

Required Probability = 0.97062

Step-by-step explanation:

We are given that the weights of newborn baby boys born at a local hospital are believed to have a normal distribution with a mean weight of 4016 grams and a standard deviation of 532 grams.

Let X = weight of the newborn baby, so X ~ N( $\mu=4016 , \sigma^{2} = 532^{2}$ )

The standard normal z distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

Now, probability that the weight will be less than 5026 grams = P(X < 5026)

P(X < 5026) = P( $\frac{X-\mu}{\sigma}$ < $\frac{5026-4016}{532}$ ) = P(Z < 1.89) = 0.97062

Therefore, the probability that the weight will be less than 5026 grams is 0.97062 .

5 0

3 years ago