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2 years ago

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A portion of a hiking trail slopes upward at about a 6 angle. To the nearest tenth of a foot, what is the value of x, the distan

ce the hiker traveled along the path, if he has traveled a horizontal distance of 120 feet?

1 answer:

Virty [35]2 years ago

6 0

The distance covered by the hiker if he traveled a horizontal distance of 120 ft at and angle of 6° will be given by:
cos θ=adjacent/hypotenuse
let the hypotenuse be h, adjacent =120 ft, θ=6°, thus plugging in the values we shall have:
cos 6=120/h
h=120/cos 6
h=120.661 ft
Answer: 120.661 ft

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Divide 12x 4 y 4 by 3x 2 y. A. 4x 6y 5 B. 4x 2y 3 C. 9x 6 D. 9x 2y 3

andrew-mc [135]

Answer:

$\frac{12x^4y^4}{3x^2y}=4x^2y^3$

Step-by-step explanation:

Consider an element $a\neq 0$

We know that $\frac{a^m}{a^n}=a^{m-n}$

Here, m and n are exponents and a is a base. Exponent refers to the no. of times a term is multiplied by itself. Another word for exponents is powers.

Other Properties of exponents:

$a^m\times a^n=a^{m+n}\\a^0=1\\\left ( a^m \right )^n=a^{mn}$

Here, we are required to divide $12x^4y^4$ by $3x^2y$ .

Consider $\frac{12x^4y^4}{3x^2y}$

We will solve $\frac{12}{3}\,,\,\frac{x^4}{x^2}\,,\,\frac{y^4}{y}$ separately.

Here,

$\frac{12}{3}=4\\\frac{x^4}{x^2}=x^{4-2}=x^2\\\frac{y^4}{y}=y^3$

So, $\frac{12x^4y^4}{3x^2y}=4x^2y^3$

8 0

2 years ago

Laura's school is holding an outdoor activities celebration event for its 20th anniversary. Laura decides to participate in the

Pachacha [2.7K]

Probabilities are used to determine the chances of Laura winning an activity

The value of p is 1/12
The expected score of the game is -1/6
The probability that she has a total score of 5 after two rounds is 0

<h3>How to calculate the value of p</h3>

To calculate the value of p, we make use of the following probability formula

$\sum P(x) = 1$

So, we have:

$\frac 3{12} + \frac 1{12} + \frac 4{12} + \frac 2{12} + p + \frac 1{12} = 1$

Collect like terms

$\frac 3{12} + \frac 1{12} + \frac 4{12} + \frac 2{12} + \frac 1{12} + p= 1$

Evaluate the sums, on the left-hand side

$\frac{11}{12} + p = 1$

Subtract 11/12 from both sides

$p = \frac 1{12}$

Hence, the value of p is 1/12

<h3>(b) How to calculate the expected score</h3>

This is calculated using the following expected value formula

$E(x) = \sum x * P(x)$

So, we have:

$E(x) = -3 * \frac{3}{12} -1 * \frac 1{12} + 0 * \frac 4{12} + 1 * \frac 2{12} + 2 * \frac 1{12} + 4 * \frac 1{12}$

Evaluate the products

$E(x) = -\frac{9}{12} - \frac 1{12} + \frac 2{12} + \frac 2{12} + \frac 4{12}$

$E(x) = -\frac 2{12}$

Simplify

$E(x) = -\frac 1{6}$

Hence, the expected score of the game is -1/6

<h3>(c) The probability that she has a total score of 5 after two rounds</h3>

From the table, we have:

$P(5) = 0$

For after two rounds, we make use of the following equation

$P(5) * P(5) = 0 * 0$

$P(5) * P(5) = 0$

Hence, the probability that she has a total score of 5 after two rounds is 0

Read more about probabilities at:

brainly.com/question/25870256

4 0

2 years ago

What type of polynomial is this? 6x + 3

victus00 [196]

Answer:

Binomial

Step-by-step explanation:

A binomial has two terms. Each term consists of a coefficient, and a variable with an exponent. We can see the two terms:

6x (the exponent would be 1) + 3 (the variable and exponent would be x to the 0. Any variable to the power of 0 is equal to 1, which is why it's not shown)

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3 years ago

When h has the value 6 calculate 5h + 9

vova2212 [387]

You multiply 5 and 6 =30 then you add 9 and that's 39

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3 years ago

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Find a number which decreased by 18 is 5 times its opposite

Harrizon [31]

Firzt set up an equation.
x-18=-5x
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3 years ago