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2 years ago

Which of the following is written in scientific notation correctly?

Mathematics

1 answer:

snow_lady [41]2 years ago

8 0

Answer:

The answer is B.thus 7.4*10^9

Step-by-step explanation:

This is because,in scientific notation, we deal with numbers which are in the standard form

And from alt A-D , only the alt B is in the standard form. the rest are not in the standard form hence cannot be considered them as written In scientific notation.

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A simple random sample of size nequals81 is obtained from a population with mu equals 83 and sigma equals 27. (a) Describe the

Ivanshal [37]

Answer:

a) $\bar X \sim N (\mu, \frac{\sigma}{\sqrt{n}})$

With:

$\mu_{\bar X}= 83$

$\sigma_{\bar X}=\frac{27}{\sqrt{81}}= 3$

b) $z= \frac{89-83}{\frac{27}{\sqrt{81}}}= 2$

$P(Z>2) = 1-P(Z$

c) $z= \frac{75.65-83}{\frac{27}{\sqrt{81}}}= -2.45$

$P(Z$

d) $z= \frac{89.3-83}{\frac{27}{\sqrt{81}}}= 2.1$

$z= \frac{79.4-83}{\frac{27}{\sqrt{81}}}= -1.2$

$P(-1.2$

Step-by-step explanation:

For this case we know the following propoertis for the random variable X

$\mu = 83, \sigma = 27$

We select a sample size of n = 81

Part a

Since the sample size is large enough we can use the central limit distribution and the distribution for the sampel mean on this case would be:

$\bar X \sim N (\mu, \frac{\sigma}{\sqrt{n}})$

With:

$\mu_{\bar X}= 83$

$\sigma_{\bar X}=\frac{27}{\sqrt{81}}= 3$

Part b

We want this probability:

$P(\bar X>89)$

We can use the z score formula given by:

$z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And if we find the z score for 89 we got:

$z= \frac{89-83}{\frac{27}{\sqrt{81}}}= 2$

$P(Z>2) = 1-P(Z$

Part c

$P(\bar X$

We can use the z score formula given by:

$z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And if we find the z score for 75.65 we got:

$z= \frac{75.65-83}{\frac{27}{\sqrt{81}}}= -2.45$

$P(Z$

Part d

We want this probability:

$P(79.4 < \bar X < 89.3)$

We find the z scores:

$z= \frac{89.3-83}{\frac{27}{\sqrt{81}}}= 2.1$

$z= \frac{79.4-83}{\frac{27}{\sqrt{81}}}= -1.2$

$P(-1.2$

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2 years ago

What is the measure of 165 15 82.5 97.5

Zina [86]

Answer:

15°

Step-by-step explanation:

L MLP = 180-165=15°

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2 years ago

I need to find the area of both of these rectangles and add them up to find the compound shape .

Citrus2011 [14]

For a problem 1 the answer is 3×6+6×9.
for a problem 3 the answer is 9×10+8×7
for problem 4 the answer is 4×8+8×4+8×4.

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2 years ago

What does it mean to say that a figure has slide or translational symmetry?

vredina [299]

Answer:

Step-by-step explBanation:

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2 years ago

The coordinates of the vertices of △RST are R(−3, −1) , S(−1, −1) , and T(−4, −5) .

Tatiana [17]

Given coordinates of △RST are R(−3, −1) , S(−1, −1) , and T(−4, −5) .

and coordinates of the vertices of △R′S′T′ are R′(1, −2) , S′(1, 0) , and T′(5, −3) .

Solution : We know the rule for the new coordinates of rotatation 90°counterclockwise about the origin.The rule is (h, k) ---> (-k,h).

Where (h,k) are the coordinates of original image on axes and (-k,h) are the coordinates of rotated image.

In resulting coordinates of the image first swap the x and y coordinates of the original image and then make the sign opposite of each x-coordinate.

On applying rule (h, k) ---> (-k,h), we get

R(−3, −1) --> R′(1, -3).

S(−1, −1) --> S′(1, -1).

T(−4, −5) --> T′(5, −4).

Let us apply another rule, each of the y-coordinate is getting reduced by 1 by adding 1 to the new coordinates.

Adding 1 to y-coordinates, we get

(1, -3) --> (1,-3+1) --> R'(1,-2)

(1, -1) --> (1,-1+1) --> S'(1,0) and

(5, −4) --> (5,-4+1) --> T' (5,-3).

So, the transformations steps would be:

1) Translation 1 unit up

2) Rotation of 90 degrees counterclockwise.

4 0

2 years ago

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