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3 years ago

Use the pythagorean theorem to solve the problem. Round your answer to the nearest tenth if necessary.

Mathematics

1 answer:

zmey [24]3 years ago

4 0

Answer:

11.31 ft

Step-by-step explanation:

Here in this problem ladder forms a right triangle with the wall of the house and it is acts as hypotenuse, length of one leg of right triangle given to be 4 feet.

Let the ladder reaches x ft height of the house.

Hence, by Pythagoras theorem:

${12}^{2} = {4}^{2} + {x}^{2} \\ 144 = 16 + {x}^{2} \\ {x}^{2} = 144 - 16 \\ {x}^{2} = 128 \\ x = \sqrt{128} \\ x = 11.3137085 \\ x = 11.31 \: ft$

Hence, the ladder reaches 11.31 ft height of the house.

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Does the amount of hazardous material absorbed by the bodies of hazardous waste workers depend on gender? The level of lead in t

Eva8 [605]

Answer:

Correct option is (A).

Step-by-step explanation:

A two-sample t-test can be performed to determine whether the amount of hazardous material absorbed by the bodies of hazardous waste workers depend on gender or not.

Th hypothesis will be:

H₀: The amount absorbed by men is same as the amount absorbed by women, i.e. μ₁ = μ₂.

Hₐ: The amount absorbed by men is greater than the amount absorbed by women, i.e. μ₁ > μ₂.

The test statistic used is:

$t=\frac{\bar x_{1}-\bar x_{2}-(\mu_{1}-\mu_{2})}{\sqrt{\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}}}}$

The decision rule to reject the null hypothesis based on the p-value is:

If the p-value of the test is less than the significance level α then the null hypothesis will be rejected. And if the p-value of the test is greater than the significance level α then the null hypothesis will not be rejected.

The p-value of the test is,

p - value = 0.0032

The commonly used significance levels are:

α = 0.01, 0.05 and 0.10.

The p-value of this test is less than all these α's.

Thus, the null hypothesis will be rejected.

Conclusion:

As the null hypothesis is rejected, it can be concluded that the amount of leas absorbed by men is significantly greater than the amount absorbed by women.

Thus, the correct option is (A).

4 0

3 years ago

C(x) = 15x + 75,000 B(x) = 55x

iVinArrow [24]

Answer:

Step-by-step explanation:

C(x) = 15x + 75,000

8 0

3 years ago

Explain why 58 can be rounded to the nearest hundred even though there is not a digit in the hundreds place?

Mrac [35]

Because 58 is closer to 100 than 0
another example you can see is if it was 10058 and you were asked to round to the nearest hundred you can say 10100

8 0

3 years ago

Read 2 more answers

Maria put trim around a banner that is the shape of a triangle. Each side is 21 inches long. Maria has 3 4 foot of trim left. Wh

Sergio039 [100]

We have been given that Maria put trim around a banner that is the shape of a triangle. Each side is 21 inches long.

The amount of trim will be equal to perimeter of triangle. The perimeter of given triangle will be 3 times each side length that is $3\times 21=63$ inches.

Now we need to convert 63 inches into feet.

12 inches = 1 feet

63 inches = $\frac{63}{12}$ feet = 5.25 feet.

We are also told that Maria has $\frac{3}{4}$ foot of trim left, so total length of trim would be trim used plus trim left that is $5.25+\frac{3}{4}=5.25+0.75=6$ feet.

Since we need to find length of trim in yards, so we will convert 6 feet into yards.

3 feet = 1 yard

6 feet = $\frac{6}{3}$ yards = 2 yards

Therefore, the length of the trim was 2 yards.

5 0

3 years ago

Please help and good night

lana66690 [7]

Answer:

(7) n = ⁴/₃

(8) x = -5

(9) d = ³/₂

(10) v = -20

Step-by-step explanation:

(7) $n-\frac{8}{9} = \frac{4}{9}$

$n-\frac{8}{9} = \frac{4}{9} \\\\Collect \ similar \ terms \ together\\\\n = \frac{4}{9} + \frac{8}{9} \\\\n = \frac{4+8}{9} \\\\n = \frac{12}{9} \\\\n = \frac{4}{3}$

(8)

$\frac{3}{2} + \ x = -\frac{7}{2}\\\\collect \ similar \ terms \ together\\\\x = -\frac{7}{2} -\frac{3}{2} \\\\x = \frac{-7-3}{2} \\\\x = \frac{-10}{2} \\\\x = -5$

(9)

$\frac{6}{5} = \frac{d}{(\frac{5}{4} )} \\\\cross \ and \ multiply\\\\5d = 6(\frac{5}{4} )\\\\5d = \frac{30}{4} \\\\d = \frac{30}{4\times 5} \\\\d = \frac{30}{20} \\\\d = \frac{3}{2} \\\\d = 1\frac{1}{2}$

(10)

$-\frac{1}{8} v = \frac{5}{2} \\\\\frac{-v}{8} = \frac{5}{2} \\\\cross \ and \ multiply\\\\-2v = 40\\\\-v = \frac{40}{2} \\\\-v = 20\\\\v = -20$

6 0

2 years ago