(−5) + 4 2) 6 + (−2)

A girl is on the beach and the angle of elevation from her feet to the top of a lighthouse is 62' If the lighthouse is 30ft tall

soldi70 [24.7K]

Answer:

15.95 feets

Step-by-step explanation:

Given that:

Angle of elevation = 62°

Using trigonometric relation :

Tanθ = opposite / Adjacent

From the drawing attached :

Opposite = 30 feets

Distance between girl and lighthouse = d

Tan 62 = 30 / d

1.8807264 * d = 30

d = 30 / 1.8807264

d = 15.951283

d = 15.95 feets

3 0

3 years ago

The triangles are similar. What is the value of x? Enter your answer in the box. x =

notsponge [240]

Answer:

Value of x is used to consider unknown value. The letter “x” is commonly used in algebra to indicate an unknown value. It is referred to as a “variable” or, in some cases, a “unknown.” In x + 2 = 7, x is a variable. ... A variable need not be “x,” but might be “y,” "w," or any other letter, name, or symbol.

6 0

3 years ago

The temperature at 9 a.m. is 2 degrees. The temperature rises 3 more degrees by noon. Which expression describes the temperature

Advocard [28]

Answer:

2 + 3

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

What is the solution to the system of equations below? y = negative one-third x + 9 and y = two-thirds x minus 12 (21, 2) (21, –

lora16 [44]

Answer:

(21, 2 )

Step-by-step explanation:

Given the 2 equations

y = - $\frac{1}{3}$ x + 9 → (1)

y = $\frac{2}{3}$ x - 12 → (2)

Substitute (2) into (1)

$\frac{2}{3}$ x - 12 = - $\frac{1}{3}$ x + 9 ( add $\frac{1}{3}$ x to both sides )

x - 12 = 9 ( add 12 to both sides )

x = 21

Substitute x = 21 into either of the 2 equations and evaluate for y

Substituting into (2)

y = $\frac{2}{3}$ × 21 - 12 = 14 - 12 = 2

Solution is (21, 2 )

6 0

4 years ago

A journal published a study of the lifestyles of visually impaired students. Using diaries, the students kept track of several v

Serga [27]

Answer:

a) $P(X$

b) $P(8 \leq X\leq 10) = 0.3640$

c) $x = 8.89 -0.842(2.11)=7.11$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Let X the random variable that represent interest on this case, and for this case we know the distribution for X is given by:

$X \sim N(\mu=8.89,\sigma=2.11)$

And let $\bar X$ represent the sample mean, the distribution for the sample mean is given by:

$\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})$

a. Find P(x < 6). P(x < 6) = (Round to four decimal places as needed.)

In order to find this probability we can use the z score given by this formula

$z=\frac{x-\mu}{\sigma}$

And if we use this we got this:

$P(X$

b. Find P(8 < x < 10) = (Round to four decimal places as needed.)

$P(8 \leq X\leq 10) = P(\frac{8-8.89}{2.11} \leq Z< \frac{10-8.89}{2.11})=P(-0.422 \leq Z\leq 0.526)=P(Z$

c. Find the value a for which P(x < a) = 0.2. (Round to two decimal places as needed.)

For this case we can use the definition of z score given by:

$z=\frac{x-\mu}{\sigma}$

First we need to find a z score that accumulates 0.2 of the area on the left tail, and the z score on this case is z=-0.842. and using this z score we can solve for x like this:

$-0.842=\frac{x-8.89}{2.11}$

And if we solve for x we got:

$x = 8.89 -0.842(2.11)=7.11$

And that would be the value required for this case.

6 0

4 years ago