How many times does 73 go into 141

Find the center-radius form of the equation of the circle described.

Kitty [74]

Answer:

Correct answer: (x-√2)² + (y-√5)² = 3

Step-by-step explanation:

Given data: Center (x,y) = (√2,√5) and r = √3

The canonical or cartesian form of the equation of the circle is:

( x-p )² + ( y-q )² = r²

Where p is the x coordinate of the center, q is the y coordinate of the center and r is the radius of the circle.

God is with you!!!

8 0

3 years ago

The length of a rectangle is 5 more than the width. Find the length and width of a rectangle if the area of the rectangle is 36

harkovskaia [24]

Answer:

width = 4 in

length = 9 in

Step-by-step explanation:

To solve this problem, write an expression for the length and use the area of a rectangle formula.

The formula for area of a triangle is A = lw

"A" is the area.

"l" is the length.

"w" is the width.

"The length of a rectangle is 5 more than the width". It is represented in an expression:

l = w + 5 The width plus 5 is the length.

We also know the area is 36 in². Using information we know, replace variables in the formula for area of a rectangle.

Substitute l = w + 5 and A = 36

A = lw

36 = (w + 5)w Expand by multiplying w by the terms in the brackets.

36 = w² + 5w Since the equation is quadratic, make it equate to 0.

36 - 36 = w² + 5w - 36 Subtract 36 from both sides

0 = w² + 5w - 36 Factor this. Use group factoring, which is when you replace the middle term (5w) with two terms that add to make 5w, and multiply to get the last term (-36).

0 = w² + 9w - 4w - 36 9w times -4w is -36. They also add to get 5w.

0 = (w² + 9w) + (-4w - 36) Group the factors

0 = w(w + 9) + -4(w + 9) Take out the common factor in each group.

0 = w(w + 9) + -4(w + 9) Take out the new common factor binomial w+9

0 = (w + 9) (w - 4) Fully factored equation.

w + 9 = 0 w - 4 = 0 Set each binomial to equal 0.

w = -9 w = 4 Chose what makes sense to be the width.

The width cannot be a negative number, so the width is 4.

Since we know the width, we can find the length because the length is 5 more than the width.

l = w + 5

l = 4 + 5

l = 9 Length of the rectangle

Don't forget to include the units, inches.

Therefore the length is 9 inches and the width is 4 inches.

8 0

3 years ago

To decrease the impact on the environment, factory chimneys must be high enough to allow pollutants to dissipate over a larger a

Komok [63]

Answer:

The probability hat the sample mean height for the 40 chimneys is greater than 102 meters is 0.1469.

Step-by-step explanation:

Let the random variable X be defined as the height of chimneys in factories.

The mean height is, μ = 100 meters.

The standard deviation of heights is, σ = 12 meters.

It is provided that a random sample of n = 40 chimney heights is obtained.

According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample means will be approximately normally distributed.

Then, the mean of the distribution of sample means is given by,

$\mu_{\bar x}=\mu$

And the standard deviation of the distribution of sample means is given by,

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}$

Since the sample selected is quite large, i.e. n = 40 > 30, the central limit theorem can be used to approximate the sampling distribution of sample mean heights of chimneys.

$\bar X\sim N(\mu_{\bar x},\ \sigma^{2}_{\bar x})$

Compute the probability hat the sample mean height for the 40 chimneys is greater than 102 meters as follows:

$P(\bar X>102)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}})>\frac{102-100}{12/\sqrt{40}})$

$=P(Z>1.05)\\=1-P(Z$

*Use a z-table fr the probability.

Thus, the probability hat the sample mean height for the 40 chimneys is greater than 102 meters is 0.1469.

8 0

3 years ago

FAST ANSWER PLEASE!!! What is the measure of ZPSQ in degrees? 9º 24° 45° 54°

iragen [17]

Answer:

C, 45 degrees

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

3x+5y-4=0 what is the slope and y-intercept?

zaharov [31]

Answer:

$3x + 5y - 4 = 0 \\ 3x + 5y = 4 \\ 5y = 4 - 3x \\ y = \frac{4}{5} - \frac{3}{5} x \\ y = mx + c \\ slope = m = \frac{ - 3}{5} \\ y \: intersept = c = \frac{4}{5} \\ thank \: you$

5 0

3 years ago