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3 years ago

Point T has coordinates (-1,3). Point M is symmetric to point T with respect to the line y=1

1 answer:

6 0

T (-1, 3) is vertically 2 units away from the line y = 1.
When finding the ordered pair for the new point, M, it must also be 2 units from the line y = 1, but on the opposite of the line. The x-value will not change only the y-value.
Counting two units BELOW the line we get M(-1, -1)

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Rewrite the exponent as a fraction with postive a positive exponent.<br><br> (-2)^-3

Stella [2.4K]

Answer:

Step-by-step explanation:

The sign minus indicates that the power is located on the denominator

$\frac{1}{2^{3} }$

4 0

3 years ago

A simple random sample of size nequals=8181 is obtained from a population with mu equals 77μ=77 and sigma equals 27σ=27. (a) De

ivanzaharov [21]

Answer:

a) $P(\bar X>81.5)=1-0.933=0.067$

b) $P(\bar X$

c) $P(73.4$

Step-by-step explanation:

1) Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Let X the random variable that represent interest on this case, and for this case we know the distribution for X is given by:

$X \sim N(\mu=77,\sigma=27)$

And let $\bar X$ represent the sample mean, the distribution for the sample mean is given by:

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

On this case $\bar X \sim N(77,\frac{27}{\sqrt{81}})$

Part a

We want this probability:

$P(\bar X>81.5)=1-P(\bar X$

The best way to solve this problem is using the normal standard distribution and the z score given by:

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

If we apply this formula to our probability we got this:

$P(\bar X >81.5)=1-P(Z$

$P(\bar X>81.5)=1-0.933=0.067$

Part b

We want this probability:

$P(\bar X\leq 69.5)$

If we apply the formula for the z score to our probability we got this:

$P(\bar X \leq 69.5)=P(Z\leq \frac{69.5-77}{\frac{27}{\sqrt{81}}})=P(Z$

$P(\bar X\leq 69.5)=0.0062$

Part c

We are interested on this probability

$P(73.4$

If we apply the Z score formula to our probability we got this:

$P(73.4$

$=P(\frac{73.4-77}{\frac{27}{\sqrt{81}}}$

And we can find this probability on this way:

$P(-1.2$

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.

$P(-1.2$

3 0

4 years ago

A soda can has a diameter of 6 cm. What is the circumference of the can? (C = πD) will giv e 50 pts

kvasek [131]

We know, Circumference = π × Diameter
C = 3.14 * 6
C = 18.84

In short, Your Answer would be 18.84 cm

Hope this helps!

8 0

3 years ago

Read 2 more answers

Anybody know what the answer is?

Rudik [331]

Side b is adjacent to the 30° angle so use cosine to solve. (soh cah toa)

cos(30°) = b/12

12*cos(30°) = b

cos(30°) is √(3)/2

12*(√(3)/2 ) = b

6√(3) = b

3 goes in the box

8 0

4 years ago

Jon has $5,000 to invest in a savings account that has interest compounded annually. If he wants his money to double in eight ye

Sergio [31]

Answer:

Rate=9.05%

Step-by-step explanation:

Let P represent the Principal ,t the time = 8 years and r be the rate of interest.

It is given money doubles in 8 years so A=2P.

The compound interest is given by the formula :

$A= P(1+r^{)t}$