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Genrish500 [490]
3 years ago
15

The number of visits to public libraries increased from 1.3 billion in 1998 to 1.5 billion in 2002. Find the average rate of cha

nge in the number of public library visits from 1998 to 2002.
Mathematics
1 answer:
9966 [12]3 years ago
4 0

Answer: The average rate of change in the number of public library visits from 1998 to 2002 = 0.05 billion per year.

Step-by-step explanation:

Given: Number of visits in 1998 = 1.3 billion

Number of visits in 2002 = 1.5 billion

The average rate of change in the number of public library visits from 1998 to 2002 = \dfrac{\text{Number of visits in 2002 - Number of visits in 1998}}{2002-1998}

=\dfrac{1.5-1.3}{4}\\\\=\dfrac{0.2}{4}\\\\= 0.05 \text{ billion per year.}

Hence, the average rate of change in the number of public library visits from 1998 to 2002 = 0.05 billion per year.

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Find the limit, if it exists (picture below)
valentinak56 [21]

Answer:

c. \frac{1}{2 \sqrt{7} }

Step-by-step explanation:

When plugging in zero into the given equation:

\lim_{x \rightarrow 0}    \frac{\sqrt{x + 7} -  \sqrt{7}  }{x} =  \frac{0}{0}

Answer is in indeterminate form = use L'Hospital's Rule:

(Derivative of the top / Derivative of the bottom)

\lim_{x \rightarrow 0}  \frac{ \frac{1}{2} (x + 7)^{ \frac{-1}{2}} - 0 }{1}

Rearranged equation:

\lim_{x \rightarrow 0}  \frac{1}{2 \sqrt{x + 7} }

Plug zero back into equation:

\lim_{x \rightarrow 0}  \frac{1}{2 \sqrt{x + 7} }  =  \frac{1}{2 \sqrt{0 + 7} } =  \frac{1}{2 \sqrt{7} }

Answer:

\lim_{x \rightarrow 0}    \frac{\sqrt{x + 7} -  \sqrt{7}  }{x} = \frac{1}{2 \sqrt{7} }

5 0
2 years ago
What is ST?<br> S<br> 30<br> V<br> Q<br> 17 T<br> 19<br> R 5<br> ST=
Stella [2.4K]

Step-by-step explanation:

PQR=STV

angPQR=angSTV

angPRQ=angSVQ

Both triangle are similar by AA test

therefore,

PQ/ST=QR/TV

30/ST=36/24

ST=36*30/24

<h3>ST= 45</h3>

<h2><u>MARK ME AS BRAINLIST</u> </h2>

5 0
2 years ago
What is the endpoint formula given midpoint?
zysi [14]

Answer:

  B = 2M -A

Step-by-step explanation:

For given endpoint A and midpoint M, the other endpoint B can be found using the definition of the midpoint:

  M = (A+B)/2

  2M = A+B . . . . . multiply by 2

  2M-A = B . . . . . subtract A

The second endpoint can be found by subtracting the given endpoint from twice the midpoint:

  B = 2M -A

7 0
3 years ago
The heights of women aged 20 to 29 are approximately Normal with mean 64 inches and standard deviation 2.7 inches. Men the same
masha68 [24]

Answer: The z-scores for a woman 6 feet tall is 2.96 and the z-scores for a a man 5'10" tall is 0.25.

Step-by-step explanation:

Let x and y area the random variable that represents the heights of women and men.

Given : The heights of women aged 20 to 29 are approximately Normal with mean 64 inches and standard deviation 2.7 inches.

i.e. \mu_1 = 64   \sigma_1=2.7

Since , z=\dfrac{x-\mu}{\sigma}

Then, z-score corresponds to  a woman 6 feet tall (i.e. x=72 inches).

[∵  1 foot = 12 inches , 6 feet = 6(12)=72 inches]

z=\dfrac{72-64}{2.7}=2.96296296\approx2.96

Men the same age have mean height 69.3 inches with standard deviation 2.8 inches.

i.e. \mu_2 = 69.3   \sigma_2=2.8

Then, z-score corresponds to a man 5'10" tall (i.e. y =70 inches).

[∵  1 foot = 12 inches , 5 feet 10 inches= 5(12)+10=70 inches]

z=\dfrac{70-69.3}{2.8}=0.25

∴ The z-scores for a woman 6 feet tall is 2.96 and the z-scores for a a man 5'10" tall is 0.25.

6 0
3 years ago
The quotient of 2 times a number and 19
Reptile [31]
This one is worded oddly, but I think it's going to be:
(2x)/19
3 0
3 years ago
Read 2 more answers
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