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Harlamova29_29 [7]
3 years ago
6

Determine the measure of the indicated angle (in degrees).

Mathematics
1 answer:
ohaa [14]3 years ago
4 0

Answer:

  105°

Step-by-step explanation:

Same-side interior angles are supplementary, so angle 4 and the one marked 75° are supplementary.

  ∠4 = 180° -75°

  ∠4 = 105°

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Paul has $20,000 to invest. His intent is to earn 11% interest on his investment. He can invest part of his money at 8% interest
hjlf

Answer:

In the 8% option , $5,000 should be invested

In the 12% option, $15,000 should be invested

Step-by-step explanation:

Let’s start with the total return.

Since the total return expected is 11%, the amount expected to be returned will be;

11/100 * 20,000 = $2,200

Now, let the amount invested at 8% interest be $x while the amount invested at 12% interest be $y

Mathematically;

x + y = 20,000 ••••••(i)

Now let’s work with the interest part;

On the 8% part, amount of interest expected is 8/100 * x

on the 12% part, amount of interest expected is 12/100 * x

8% of $x + 12% of $y = 2,200

Writing this fully mathematically, we have;

(8/100 * x) + (12/100 * y) = 2,200

8x/100 + 12y/100 = 2,200

Multiply through by 100

8x + 12y = 220,000 ••••••(ii)

Now we have two equations to solve simultaneously;

x + y = 20,000

8x + 12y = 220,000

From i, x = 20,000-y

Substitute this into ii

8(20,000-y) + 12y = 220,000

160,000-8y + 12y = 220,000

4y = 220,000 - 160,000

4y = 60,000

y = 60,000/4

y = $15,000

x = 20,000 -y

x = 20,000 - 15,000

x = $5,000

8 0
3 years ago
In a recent year, team 1 made 191 out of 238 free- throw attempts and team 2 made 106 out of 160 free- throw attempts. Copy and
ivann1987 [24]
Cross multiply and divide Put 191 over 238 (like a fraction) the put another fraction bar right next to your first fraction and put 100 on bottom (this equals a whole in % and it's right across from the total of 238 free throws) then multiply 191 by 100 then divide by 238 and that answer should be your the percent you need.
5 0
3 years ago
Read 2 more answers
How many FIVES are equal in value to £7?
OLga [1]
<span>£1 equals to 1.43 us dollars.

7 </span>× 1.43 = <span>10.01

</span>10.01 ÷ 5 = <span>2.002
</span>
2 fives are equal to <span>£7. </span>
5 0
3 years ago
Anyone solve this pls
Bingel [31]
X = -3.5 or -7/2 or -3 1/2
8 0
2 years ago
Read 2 more answers
A phone manufacturer wants to compete in the touch screen phone market. He understands that the lead product has a battery life
alisha [4.7K]

Answer:

a)

The null hypothesis is H_0: \mu \leq 10

The alternative hypothesis is H_1: \mu > 10

b-1) The value of the test statistic is t = 1.86.

b-2) The p-value is of 0.0348.

Step-by-step explanation:

Question a:

Test if the battery life is more than twice of 5 hours:

Twice of 5 hours = 5*2 = 10 hours.

At the null hypothesis, we test if the battery life is of 10 hours or less, than is:

H_0: \mu \leq 10

At the alternative hypothesis, we test if the battery life is of more than 10 hours, that is:

H_1: \mu > 10

b-1. Calculate the value of the test statistic.

The test statistic is:

We have the standard deviation for the sample, so the t-distribution is used to solve this question

t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}

In which X is the sample mean, \mu is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.

10 is tested at the null hypothesis:

This means that \mu = 10

In order to test the claim, a researcher samples 45 units of the new phone and finds that the sample battery life averages 10.5 hours with a sample standard deviation of 1.8 hours.

This means that n = 45, X = 10.5, s = 1.8

Then

t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}

t = \frac{10.5 - 10}{\frac{1.8}{\sqrt{45}}}

t = 1.86

The value of the test statistic is t = 1.86.

b-2. Find the p-value.

Testing if the mean is more than a value, so a right-tailed test.

Sample of 45, so 45 - 1 = 44 degrees of freedom.

Test statistic t = 1.86.

Using a t-distribution calculator, the p-value is of 0.0348.

5 0
2 years ago
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