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3 years ago

Determine the unknown angle measures in the figure.HELP NOW!!! please

Mathematics

1 answer:

maw [93]3 years ago

8 0

Answer:

m∠1=80°

m∠2=112°

m∠3=131°

m∠4=80°

m∠5=37°

Step-by-step explanation:

First you have to find m∠2

To do that find m∠6 (I created this angle shown in pic below)

Find m∠6 by using the sum of all ∠'s in a Δ theorem

m∠6=180°-(63°+49°)

m∠6=68°

Now you can find m∠2 with the supplementary ∠'s theorem

m∠2=180°-68°

m∠2=112°

Then you find m∠5 using the sum of all ∠'s in a Δ theorem

m∠5=180°-(112°+31°)

m∠5=37°

Now you can find m∠1

m∠1=180°-(63°+37°)

m∠1=180°-100°=80°

m∠4 can easily be found too now:

m∠4=180°-(63°+37°)

m∠4=80°

m∠3=180°-49°

m∠3=131°

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3 years ago

The lengths of text messages are normally distributed with a population standard deviation of 6 characters and an unknown popula

ryzh [129]

Answer:

The 80% confidence interval for the population mean is between 28.32 characters and 31.68 characters.

Step-by-step explanation:

We have the standard deviation for the population, so we can use the normal distribution. If we had the standard deviation for the sample, we would have to use the t-distribution.

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.8}{2} = 0.1$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.5 = 0.9$ , so $z = 1.282$

Now, find the margin of error M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 1.282*\frac{6}{\sqrt{21}} = 1.68$

The lower end of the interval is the sample mean subtracted by M. So it is 30 - 1.68 = 28.32 characters.

The upper end of the interval is the sample mean added to M. So it is 30 + 1.68 = 31.68 characters.

The 80% confidence interval for the population mean is between 28.32 characters and 31.68 characters.

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3 years ago

Question

Ahat [919]

Answer:

4 minutes.

Step-by-step explanation:

There are three trains that Rachel has to take to go to her job. The total time is taken by her, on average, 1 hour and 20 minutes i.e. (60 + 20) = 80 minutes.

In his journey, she walks for 15 minutes and a train journey for about 53 minutes.

Then the total waiting time for the trains is (80 - 53 - 15) = 12 minutes.

Therefore, the average waiting time, in minutes, at each of the three train stations will be $\frac{12}{3} = 4$ minutes. (Answer)

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4 years ago

Solve the following system. x2 + y 2= 25 2x + y = 10 The solution set

anzhelika [568]

Answer: {(5,0), (3,4)}

Step-by-step explanation:

You can apply the Substitution method:

- Solve for y from the second equation.

- Substitute into the first equation and solve for x.

Then:

$y=10-2x$

$x^2+y^2=25\\x^2+(10-2x)^2=25\\$

(Remember that: $(a\±b)^2=a^2\±2ab+b^2$ )

$x^2+(10^2-2(10)(2x)+(2x)^2)=25\\x^2+100-40x+4x^2=25\\5x^2-40x+75=0\\x^2-8x+15=0\\(x-5)(x-3)=0\\\\x=5\\x=3$

Substitute the values obtained into one of the original equation and solve for y:

$2(5)+y=10\\10+y=10\\y=0\\\\2(3)+y=10\\6+y=10\\y=4$

The solution set is: {(5,0), (3,4)}

8 0

3 years ago

15. Jim had 103 red and blue marbles. After giving of his blue marbles and 15 of his red marbles

sesenic [268]

This question above is incomplete

Complete Question

Jim had 103 red and blue marbles. After giving 2/5 of his blue marbles and 15 of his red marbles to Samantha, Jim had 3/7 as many red marbles as blue marbles. How many blue marbles did he have originally?

Answer:

70 Blue marbles

Step-by-step explanation:

Let red marbles = R

Blue marbles = B

Step 1

Jim had 103 red and blue marbles.

R + B = 103.......Equation 1

R = 103 - B

Step 2

After giving 2/5 of his blue marbles and 15 of his red marbles to Samantha, Jim had 3/7 as many red marbles as blue marbles

2/5 of B to Samantha

Jim has = B - 2/5B = 3/5B left

He also gave 15 red marbles to Samantha

= R - 15

The ratio of what Jim has left

= Red: Blue

= 3:7

= 3/7

Hence,

R - 15/(3/5)B = 3/7

Cross Multiply

7(R - 15) = 3(3/5B)

7R - 105 = 3(3B/5)

7R - 105 = 9B/5

Cross Multiply

5(7R - 105) = 9B

35R - 525 = 9B............ Equation 2

From Equation 1, we substitute 103 - B for R in Equation 2

35(103 - B) - 525 = 9B

3605 - 35B - 525 = 9B

Collect like terms

3605 - 525 = 9B + 35B

3080 = 44B

B = 3080/44

B = 70

Therefore, Jim originally had 70 Blue marbles.

4 0

3 years ago