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3 years ago

The measure of _A is 18° greater than the measure of _B. The two angles are complementary. Find the

Mathematics

1 answer:

kozerog [31]3 years ago

4 0

Answer:

angle A=54 degree

angle B =36 degree

Step-by-step explanation:

let angle B be x

angle A=x+18

since they are complementary angles sum of these two angles will be 90 degree

x+x+18=90

2x=90-18

2x=72

x=72/2

x=36 degree

substitute the value of x to find angle A and angle B

for angle A

x+18

36+18

54 degree

for angle B

angle B =x

=36 degree

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If there were 125 students in 5 buses what is the ratio of students to buses

enot [183]

Answer:

125:5

Step-by-step explanation:

obvious.

6 0

3 years ago

Dividin a number by 10 exponent, how is the decimal point moved

Tanzania [10]

Decimal moves towards right!

6 0

3 years ago

6/10+6/100= how do i do this problem

olya-2409 [2.1K]

Answer:

0.66

Step-by-step explanation:

As division is always done before addition you would divide the 6 by 10 and then divide the 6 by 100. 6 divided by 10 is equal to 0.6 as you move the decimal point to the left once. 6 divided by 100 is equal to 0.06 as you move the decimal point to the left twice. Addition is always done after division so you would add 0.6 and 0.06 together. This will give you 0.66 as your answer.

8 0

3 years ago

A programmer plans to develop a new software system. In planning for the operating system that he will use, he needs to estimat

Vedmedyk [2.9K]

Using the z-distribution, we have that:

a) A sample of 601 is needed.

b) A sample of 93 is needed.

c) A. Yes, using the additional survey information from part (b) dramatically reduces the sample size.

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which z is the z-score that has a p-value of $\frac{1+\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

95% confidence level, hence $\alpha = 0.95$ , z is the value of Z that has a p-value of $\frac{1+0.95}{2} = 0.975$ , so $z = 1.96$ .

For this problem, we consider that we want it to be within 4%.

Item a:

The sample size is n for which M = 0.04.

There is no estimate, hence $\pi = 0.5$

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.04 = 1.96\sqrt{\frac{0.5(0.5)}{n}}$

$0.04\sqrt{n} = 1.96\sqrt{0.5(0.5)}$

$\sqrt{n} = \frac{1.96\sqrt{0.5(0.5)}}{0.04}$

$(\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.5(0.5)}}{0.04}\right)^2$

$n = 600.25$

Rounding up:

A sample of 601 is needed.

Item b:

The estimate is $\pi = 0.96$ , hence:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.04 = 1.96\sqrt{\frac{0.96(0.04)}{n}}$

$0.04\sqrt{n} = 1.96\sqrt{0.96(0.04)}$

$\sqrt{n} = \frac{1.96\sqrt{0.96(0.04)}}{0.04}$

$(\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.96(0.04)}}{0.04}\right)^2$

$n = 92.2$

Rounding up:

A sample of 93 is needed.

Item c:

The closer the estimate is to $\pi = 0.5$ , the larger the sample size needed, hence, the correct option is A.

For more on the z-distribution, you can check brainly.com/question/25404151

8 0

2 years ago

Tom and his best friend are going to join a gym. Tom saw that Platinum gym has a sale with a one time fee of $90 and a monthly f

worty [1.4K]

Answer:

Part 1:

For Platinum Gym:

90 + 30x

For Super Fit Gym:

200 + 20x

Part 2: $270

Part 3: $320

Part 4: 11 months

Part 5: See explanation below

Step-by-step explanation:

Part 1:

Let "x" be the number of months:

For Platinum Gym:

90 + 30x

For Super Fit Gym:

200 + 20x

Part 2:

We put x = 6 in platinum gym's equation and get our answer.

90 + 30x

90 + 30(6)

90 + 180

=$270

Part 3:

We put x = 6 into super fit's equation and get our answer.

200 + 20x

200 + 20(6)

200 + 120

=$320

Part 4:

To find the number of months for both gyms to cost same, we need to equate both equations and solve for x:

90 + 30x = 200 + 20x

10x = 110

x = 11

So 11 months

Part 5:

We know for 11 months, they will cost same. Let's check for 10 months and 12 months.

In 10 months:

Platinum = 90 + 30(10) = 390

Super Fit = 200 + 20(10) = 400

In 12 months:

Platinum = 90 + 30(12) = 450

Super Fit = 200 + 20(12) = 440

Thus, we can see that Platinum Gym is a better deal if you want to get membership for months less than 11 and Super Fit is a better deal if you want to get membership for months greater than 11.

4 0

4 years ago