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Sophie [7]
3 years ago
6

Given an angle, draw the opposite ray of one of its sides to form a linear pair. Find the measure of the angle formed by the ang

le bisector of the given angle and the drawn opposite ray if the measure of the given angle is: 50°, 90°, and 150°.
Mathematics
1 answer:
Andrej [43]3 years ago
4 0
<span>For 50°, answer is 65° For 90°, answer is 45° For 150°, answer is 15° A linear pair of angles adds up to 180° by definition. So the new angle drawn by the ray will have an angle of 180°-a where a is the measure of the original angle. And the bisector of that new angle will be (180°-a)/2. So with that in mind, let's calculate the new measures of the described construction. 50°: (18° - 50°)/2 = 130°/2 = 65° 90°: (180° - 90°)/2 = 90°/2 = 45° 150°: (180° - 150°)/2 = 30°/2 =15°</span>
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the trailer cost one-fourth as much as the boat. the total cost of both is 4,000 how much did each cost
Katarina [22]

Answer: Boat  cost $ 3200

Trailer cost $ 800

Step-by-step explanation:  From the statement , the coat of Trailer (t) = 1/4 of the coat of the boat ( b)

i.e t = 1/4b

multiply through by 4

4t = b

both cost 4,000

i.e t + b = 4000

recall: b = 4t

therefore

t + 4t = 4000

5t      = 4000

       t = 4000/5

       t = 800

       b = 4000 - 800

       b = 3200

4 0
3 years ago
The histograms below show the heights (in meters) of the tallest buildings in China and the United States.
gregori [183]

Answer:

A and B

Step-by-step explanation:

This is correct on khan academy!

8 0
3 years ago
Read 2 more answers
Write a function number_of_pennies() that returns the total number of pennies given a number of dollars and (optionally) a numbe
seraphim [82]
Ok, first of all, it is important to understand that this function would depend on 2 variables; the number of dollars (x) and the number of pennies (y). Every dollar is equivalent to 100 pennies. So, if we are given x dollars, we have 100*x pennies. If we also have y pennies, we still get y pennies. We need to add these two to get the total amount of pennies. Thus, the correct function is:
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7 0
3 years ago
Suppose we are interested in analyzing the weights of NFL players. We know that on average, NFL players weigh 247 pounds with a
tigry1 [53]

Answer:

SE= \frac{\sigma}{\sqrt{n}} = \frac{47}{\sqrt{30}}= 8.58

ME= 1.64 *\frac{\sigma}{\sqrt{n}} = 1.64*\frac{47}{\sqrt{30}}= 14.073

\bar X - ME = 237- 14.073 = 222.927

\bar X + ME = 237+ 14.073 = 251.073

n=(\frac{1.640(47)}{5})^2 =237.65 \approx 238

So the answer for this case would be n=238 rounded up to the nearest integer

Null hypothesis:\mu \geq 247  

Alternative hypothesis:\mu  

z=\frac{237-247}{\frac{47}{\sqrt{30}}}=-1.165  

p_v =P(z  

If we compare the p value and the significance level given \alpha=0.1 we see that p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can't conclude that the true mean is lower than 247 at 10% of significance.

Step-by-step explanation:

For this case we have the following data given:

\bar X =237 represent the sample mean

\sigma = 47 represent the population deviation

n =30 represent the sample size selected

\mu_0 = 247 represent the value that we want to test.

The standard error for this case is given by:

SE= \frac{\sigma}{\sqrt{n}} = \frac{47}{\sqrt{30}}= 8.58

For the 90% confidence the value of the significance is given by \alpha=1-0.9 = 0.1 and \alpha/2 = 0.05 so we can find in the normal standard distribution a quantile that accumulates 0.05 of the area on each tail and we got:

z_{\alpha/2}= 1.64

And the margin of error would be:

ME= 1.64 *\frac{\sigma}{\sqrt{n}} = 1.64*\frac{47}{\sqrt{30}}= 14.073

The confidence interval for this case would be given by:

\bar X - ME = 237- 14.073 = 222.927

\bar X + ME = 237+ 14.073 = 251.073

The margin of error is given by this formula:

ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}    (a)

And on this case we have that ME =5 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

n=(\frac{z_{\alpha/2} \sigma}{ME})^2   (b)

Replacing into formula (b) we got:

n=(\frac{1.640(47)}{5})^2 =237.65 \approx 238

So the answer for this case would be n=238 rounded up to the nearest integer

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the true mean is lower than 247 pounds, the system of hypothesis would be:  

Null hypothesis:\mu \geq 247  

Alternative hypothesis:\mu  

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:  

z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}} (1)  

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic  

We can replace in formula (1) the info given like this:  

z=\frac{237-247}{\frac{47}{\sqrt{30}}}=-1.165  

P-value  

Since is a left tailed test the p value would be:  

p_v =P(z  

Conclusion  

If we compare the p value and the significance level given \alpha=0.1 we see that p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can't conclude that the true mean is lower than 247 at 10% of significance.

5 0
2 years ago
A triangle has side lengths of (3.76 + 1.7) centimeters, (1.36 + 1.1) centimeters,
pychu [463]

Answer:

Step-by-step explanation:

our triangle has one length:     3.76+1.7=5.46

                           another side: 1.36+1.1=2.46

                            last side:        7.1+5.1=12.20

Perimeter is=5.46+2.46+12.20=20.12 cm

7 0
3 years ago
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