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3 years ago

A ladder is leaning against the side of a building. The

Mathematics

1 answer:

cupoosta [38]3 years ago

8 0

Answer:

16 ft

Step-by-step explanation:

Based on the situation above, it forms into a right triangle. Therefore we can apply the Pythagorean Theorem. We will use the formula below:

c = √( a² + b²)

In the problem above, the ladder acts as the hypotenuse denoted by c. It has a length of 20 ft. While the base denoted by b is 12 ft. Therefore, we need to solve for a. We will derive the formula above.

c² = a² + b²

a² = c² - b²

a = √( c² - b² )

a = √( 20² - 12² )

a = 16

The unit is in ft.

Correct me if I'm wrong. I hope it helps.

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Donna read 18 out of 30 pages in her book.What percent of the book did she read?

inysia [295]

Answer:

Step-by-step explanation:

18 /30 is .6. So the answer would be 60 percent

6 0

3 years ago

Read 2 more answers

Determine if (-1,9) and (-2,6) are solutions to the system of equations: x + y = 8 x2 + y = 10 A) Both are solutions B) Neither

Dahasolnce [82]

Answer:

D) Only (-1,9) is a solution.

Step-by-step explanation:

x+y =8

x^2 + y = 10

Lets check the first point (-1,9)

Put in x =-1 y =9

x+y =8

-1+9 = 8

8 =8

This works

x^2 + y = 10

(-1)^2 +9 =10

1+9 = 10

10 = 10

This works

Lets check the second point (-2,6)

Put in x =-2 y =6

x+y =8

-2+6 = 8

4=8

This does not work

We can stop now. (-2,6) cannot be a solution

7 0

3 years ago

F(x)=6x-18 sub in f(x/3), f(x)/3

arlik [135]

These are two separate problems: in the first we will have to substitute in a new value for x into the original equation and in the second we will manipulate the preexisting equation for f(x).

To begin, we will sub in f(x/3). To do this, we will substitute each variable x in the equation (in this case there is only one) with x/3, and then simplify the resulting equation.

f(x) = 6x - 18

f(x/3) = 6(x/3) - 18

To simplify, we should distribute the 6 on the right side of the equation.

f(x/3) = 6x/3 - 18

Now, we can divide the first term on the right side to finalize our simplification.

f(x/3) = 2x -18

Secondly, we are asked to find f(x)/3. To do this, we will take our original value for f(x), and then simplify divide that entire function by 3.

f(x) = 6x - 18

f(x)/3 = (6x-18)/3

This means that we must divide each term of the binomial by 3, so we are really computing

f(x)/3 = 6x/3 - 18/3

We can simplify by dividing both of the terms.

f(x)/3 = 2x - 6

Therefore, your answer is that f(x/3) = 2x - 18, but f(x)/3 = 2x - 6. It is important to recognize that these are two similar, yet different, answers.

Hope this helps!

8 0

3 years ago

The table below shows the number of cameras made when an assembly line runs at a constant rate for a certain number of hours. Nu

jeka57 [31]

Computing the rate we get:

$\frac{300}{10}\frac{cameras}{\text{hour}}=30\frac{cameras}{\text{hour}}$

Then, when the assembly line runs at the same rate for 24 hours they will produce:

$24\text{hour}\cdot30\frac{cameras}{\text{hour}}=720\text{ cameras}$

Answer: Option C) 720.

7 0

1 year ago

From a large number of actuarial exam scores, a random sample of scores is selected, and it is found that of these are passing s

Mnenie [13.5K]

<u>Supposing 60 out of 100 scores are passing scores</u>, the 95% confidence interval for the proportion of all scores that are passing is (0.5, 0.7).

The lower limit is 0.5.
The upper limit is 0.7.

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 $\frac{1+\alpha}{2}$ .

60 out of 100 scores are passing scores, hence $n = 100, \pi = \frac{60}{100} = 0.6$

95% confidence level

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

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6 - 1.96\sqrt{\frac{0.6(0.4)}{100}} = 0.5$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6 + 1.96\sqrt{\frac{0.6(0.4)}{100}} = 0.7$

The 95% confidence interval for the proportion of all scores that are passing is (0.5, 0.7).

The lower limit is 0.5.
The upper limit is 0.7.

A similar problem is given at brainly.com/question/16807970

5 0

3 years ago