8/k = -12/30 solve the proportion

Marianna [84]

Look at the rectangle. The bottom side measures 8 miles, so the top side also measures 8 miles.

Now look at the upper right triangle. For the angle of 32 deg, the top side of the triangle is the adjacent leg of the triangle. The air distance, marked x, is the hypotenuse of the triangle.

The trig ratio that relates the adjacent leg and the hypotenuse is the cosine.

$\cos \theta = \dfrac{adj}{hyp}$

$\cos 32^\circ = \dfrac{8~miles}{x}$

$x = \dfrac{8~miles}{\cos 32^\circ}$

$x = 9.4 ~miles$

6 0

3 years ago

Review

Iteru [2.4K]

Answer:

300 meters

Step-by-step explanation:

250+150+50+x=750

450+x=750

x=750-450=300

3 0

3 years ago

Find the equation of the line parallel to y=5x+1 that contains the point (4,8)

astraxan [27]

The equation of a parallel line will have the same x-term, but a different constant (y-intercept). The required value can be found by putting the given point values in to the equation to see what it needs to be.

... y = 5x + ___

... 8 = 5·4 + ___

... 8 - 20 = -12 = ___

Your equation is ...

... y = 5x -12

4 0

3 years ago

Listed below are the number of years it took for a random sample of college students to earn bachelor's degrees (based on data f

schepotkina [342]

Answer:

a) Mean = 6.5, sample standard deviation = 3.50

b) Standard error = 0.7826

c) Point estimate = 6.5

d) Confidence interval: (5.1469 ,7.8531)

Step-by-step explanation:

We are given the following data set for students to earn bachelor's degrees.

4, 4, 4, 4, 4, 4, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 6, 6, 8, 9, 9, 13, 13, 15

a) Formula:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{130}{20} = 6.5$

Sum of squares of differences = 6.25 + 6.25 + 6.25 + 6.25 + 6.25 + 6.25 + 4 + 4 + 4 + 4 + 4 + 4 + 0.25 + 0.25 + 2.25 + 6.25 + 6.25 + 42.25 + 42.25 + 72.25 = 233.5

$S.D = \sqrt{\frac{233.5}{19}} = 3.50$

b) Standard Error

$= \displaystyle\frac{s}{\sqrt{n}} = \frac{3.50}{\sqrt{20}} = 0.7826$

c) Point estimate for the mean time required for all college is given by the sample mean.

$\bar{x} = 6.5$

d) 90% Confidence interval:

$\bar{x} \pm t_{critical}\displaystyle\frac{s}{\sqrt{n}}$

Putting the values, we get,

$t_{critical}\text{ at degree of freedom 19 and}~\alpha_{0.10} = \pm 1.729$

$6.5 \pm 1.729(\frac{3.50}{\sqrt{20}} ) = 6.5 \pm 1.3531 = (5.1469 ,7.8531)$

e) No, the confidence interval does not contain the value of 4 years. Thus, confidence interval is not a good estimator as most of the value in the sample is of 4 years. Most of the sample does not lie in the given confidence interval.

5 0

4 years ago

Daniel is looking over some data regarding the temperatures of countries and how the temperature relates to the number of mosqui

Doss [256]

The logarithmic function when the temperature is 64 degrees is given as
ln f(x) = x ln 2.

<h3>What is a logarithmic function?</h3>

A logarithmic function is the inverse of an exponential function. It is to be noted that all exponential functions can be written as logarithmic functions.

Hence, to convert the mathematical statement above into a logarithmic function we say:

f(x) = 2ˣ

ln f(x) = ln 2ˣ

ln f(x) = x ln 2

Ln 64 = x Ln 2

Let f(x) = 64;

Hence,

Ln 64 = x ln 2

Divide both sides by ln 2 to get x

ln 64/ln 2 = x

Hence,

x = ln 64/ln 2

= 6

Learn more about Logarithmic Functions at:
brainly.com/question/1695836

#SPJ1

7 0

2 years ago