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3 years ago

As part of his math assignment, Santos has to estimate the height

Mathematics

1 answer:

ycow [4]3 years ago

5 0

Answer:

105.46 feet

Step-by-step explanation:

We know all three angles (60, 90, and 30), as well as one side, which is adjacent to the 60 degrees. We want to find the side opposite to the 60 degree angle. To do this, we can use tangent, utilizing both opposite and adjacent.

Using tan, we can say that tan(60) = x/58, with x representing the height of the lighthouse (minus 5, because Santos is 5 feet tall and he is measuring the angle from the top of his head). Multiplying both sides by 58, we can get that 58 *tan(60) = x = 100.46. Add 5 to that to get 105.46 feet as your answer.

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Simplify the expression. Write your answer without negative exponents.

Phoenix [80]

Answer:

-5/ (x^19 * y^12)

Step-by-step explanation:

-15x^-10 * y ^ -3 * x^-9 * y^-9/3 (It's writing it like this.)

15 and 3 have a GCF of 3.

-5x^-10 * y^-3 * x^-9 * y^-9/1

Reduce similar occurrences. *twice in a row*

-5x^(-10 + (-9)) * y^(-3 + (-9))/1

Remove extra signs *twice in a row*

-5x^(-10 - 9) * y^(-3 - 9)/1

Remove extraneous 1.

-5x^(-10 - 9) * y^(-3 - 9)

Add integers.

-5x^-19 * y^-12

Negative powers change multiplication to division.

-5 / (x^19 * y^12) is the final answer.

Even with that, the simplified answer wouldn't have negative exponents because of the negative powers rule.

8 0

2 years ago

What is the solution to 5x+9-3x=18+15 A.x=8 B.x=12 C.x=21 D.x=3

Vlad [161]

Your answer will be B) x=12

1)5x-3x
2) move 9 to the other side (change signs)
3)18+15-9
4) 2x= 24 (divide 2 from both sides
5)x=12

hope this helps

7 0

3 years ago

Read 2 more answers

What is the value of n in the equation shown below? 2²×2n=(2

pychu [463]

Answer:

Step-by-step explanation:

$2^2 \times 2n= (2)\\\\\mathrm{Simplify\:}2^2\times\:2n:\quad 8n\\\\\mathrm{Simplify\:}\left(2\right):\quad 2\\\\8n=2\\\\\mathrm{Divide\:both\:sides\:by\:}8\\\\\frac{8n}{8}=\frac{2}{8}\\\\Simplify\\\\n=\frac{1}{4}$

4 0

3 years ago

What is the difference between a linear pair and angles on a straight line

expeople1 [14]

Answer:

Linear pair is two adjacent angles whose non-common side from opposite rays. the line through points A., B and C is straight line. if two angles from a linear pair the angle are supplementary.

7 0

2 years ago

A true/false test has 40 questions. Suppose a passing grade is 30 or more correct answers. Test the claim that a student knows m

Angelina_Jolie [31]

Answer:

z≈3.16

p≈0.001

we reject the null hypothesis and conclude that the student knows more than half of the answers and is not just guessing in 0.05 significance level.

Step-by-step explanation:

As a result of step 2, we can assume normal distribution for the null hypothesis

step 3:

z statistic is computed as follows:

z= $\frac{X-M}{\frac{\sqrt{p*(1-p)} }{\sqrt{N} } }$ where

X is the proportion of correct answers in the test ( $\frac{30}{40}$ )
M is the expected proportion of correct answers according to the null hypothesis (0.5)

p is the probability of correct answer (0.5)
N is the total number of questions in the test (40)

z= $\frac{0.75-0.50}{\frac{\sqrt{0.5*(0.5)} }{\sqrt{40} } }$ ≈ 3.16

And corresponding p value for the z-statistic is p≈0.001.

Since p<0.05, we reject the null hypothesis and conclude that the student knows more than half of the answers and is not just guessing in 0.05 significance level.

7 0

3 years ago