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4 years ago

If the equation of a circle is (x + 5)2 + (y - 7)2 = 36, its radius is:

Mathematics

1 answer:

andrey2020 [161]4 years ago

5 0

Answer:

Step-by-step explanation:

The number on the right side of the equal side represents the radius, HOWEVER, it is squared, therefore you must square root it to get 6

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Two feet is what percent of one yard

Mashcka [7]

1 yard = 3 feet
2 feet = 2/3 of 1 yard

If you can't figure it out from there, and if you want to get really specific, it's 66.67%

3 0

3 years ago

Evaluate the difference quotient for the given function. Simplify your answer.

IgorC [24]

Answer:

-5 - h

Step-by-step explanation:

ƒ(x) = 1 + 5x - x²

[f(5 + h) -f(5)]/h

= [1 + 5(5 + h) - (5 + h)² - 1 - 5(5) +5²]/h

= (25 + 5h - 25 - 10h - h² - 25 + 25)/h

= (-5h - h²)/h

= -5 - h

The difference quotient is -5 - h.

7 0

3 years ago

The ages of a random sample of five university professors are 39, 54, 61, 72, and 59. Using this information, find a 99% confide

kondor19780726 [428]

Answer:

99% confidence interval for the population standard deviation = (74.97 , 635.20).

Step-by-step explanation:

We are given that the ages of a random sample of five university professors are 39, 54, 61, 72 and 59. Also, it is provided that the ages of university professors are normally distributed.

So, firstly the pivotal quantity for 99% confidence interval for the population standard deviation is given by;

P.Q. = $\frac{(n-1)s^{2} }{\sigma^{2} }$ ~ $\chi^{2} __n_-_1$

where, s = sample standard deviation

$\sigma$ = population standard deviation

n = sample of university professors = 5

Also, $s^{2}$ = $\frac{\sum (X-\bar X)^{2} }{n-1}$ = 144.5

So, 99% confidence interval for population standard deviation, $\sigma$ is;

P(0.2070 < $\chi^{2} __5_-_1$ < 14.86) = 0.99 {As the table of $\chi^{2}$ at 4 degree of freedom

gives critical values of 0.2070 & 14.86}

P(0.2070 < $\frac{(n-1)s^{2} }{\sigma^{2} }$ < 14.86) = 0.99

P( $\frac{ 0.2070}{(n-1)s^{2} }$ < $\frac{1 }{\sigma^{2} }$ < $\frac{ 14.86}{(n-1)s^{2} }$ ) = 0.99

P( $\frac{ (n-1)s^{2}}{14.86 }$ < $\sigma^{2}$ < $\frac{ (n-1)s^{2}}{0.2070 }$ ) = 0.99

99% confidence interval for $\sigma^{2}$ = ( $\frac{ (n-1)s^{2}}{14.86 }$ , $\frac{ (n-1)s^{2}}{0.2070 }$ )

= ( $\frac{ (5-1) \times 144.5^{2}}{14.86 }$ , $\frac{ (5-1) \times 144.5^{2}}{0.2070 }$ )

= (5620.525 , 403483.092)

99% confidence interval for $\sigma$ = ( $\sqrt{5620.525}$ , $\sqrt{403483.092}$ )

= (74.97 , 635.20)

Therefore, 99% confidence interval for the population standard deviation of the ages of all professors at the university is (74.97 , 635.20).

8 0

4 years ago

18) mZVST -37.8 +2 T. +20 -27x-3

Burka [1]

Answer:

m∠VST = 105°

Step-by-step explanation:

Two central angles are marked as having the same measure. The measure of the corresponding arcs are the same. The sum of all arc measures is 360°.

(-37x +2) +2(-27x -3) = 360

-91x -4 = 360

-91x = 364

x = -4

m∠VST = (-27(-4) -3) = 105 . . . . degrees

3 0

4 years ago

Calculate the following:

miskamm [114]

Answer:

bghj767yh6bbbbbbbbbn

Step-by-step explanation:

bgtgvcxcvb mjnhgtrfedxdcfvgbtgewr3234323rq

7 0

3 years ago