Beth and Amy are trading marbles. Beth has three times more marbles than her sister, Amy.

In math class, James, Hadley, and Gwen were challenged to go stand on the field in a random location and find the distance betwe

o-na [289]

The interior angles of the triangle of 61°, 73°, and 46°, and the distance from James to Hadley of 15 meters gives;

Gwen to Hadley ≈ 18.24 meters

Gwen to James ≈ 19.94 meters

<h3>How can the distances between the students be found?</h3>

The given angles are;

At James's location; 61°

At Hadley's location; 73°

At Gwen's location; 46°

The distance between James and Hadley = 15 meters

The angle facing the distance between James and Hadley is the angle at Gwen, 46°

The angle facing the distance between Gwen and James is the angle at Hadley, 73°

The angle facing the distance between Gwen and Hadley is the angle at James, 61°

The angle that faces the 15 meter length is the angle at Gwen, which is 46°

By the rule of sines, the distance from Gwen to Hadley is therefore;

$\frac{15}{sin( 46 ^ \circ)} = \frac{Gwen \: to \: Hadley}{sin( 61 ^ \circ)}$

Which gives;

$Gwen \: to \: Hadley= \frac{15 \times sin( 61 ^ \circ) }{sin( 46 ^ \circ)} \approx 18.24$

Gwen to Hadley ≈ 18.24 meters

Similarly, we have;

$\frac{15}{sin( 46 ^ \circ} = \frac{Gwen \: to \: James}{sin( 73 ^ \circ)}$

Therefore;

$Gwen \: to \: James = \frac{15 \times sin( 73 ^ \circ) }{sin(46 ^ \circ)} \approx 19.94$

Gwen to James ≈ 19.94 meters

Learn more about the rule of sines here:

brainly.com/question/4372174

#SPJ1

4 0

2 years ago

9×27+2×31-28=n what is the value of n

patriot [66]

(9)(27)+(2)(31)−28=n

Simplify:

(9)(27)+(2)(31)−28=n

243+62+−28=n

(243+62+−28)=n(Combine Like Terms)

277=n

Flip the equation.

n=277

6 0

3 years ago

At a large university, the mean amount spent by students for cell phone service is $58.90 per month with a standard deviation of

zhenek [66]

Answer:

2.28% probability that the mean amount of their monthly cell phone bills is more than $60

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

$\mu = 58.90, \sigma = 3.64, n = 44, s = \frac{3.64}{\sqrt{44}} = 0.54875$

What is the probability that the mean amount of their monthly cell phone bills is more than $60?

This is 1 subtracted by the pvalue of Z when X = 60. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{60 - 58.90}{0.54875}$

$Z = 2$

$Z = 2$ has a pvalue of 0.9772

1 - 0.9772 = 0.0228

2.28% probability that the mean amount of their monthly cell phone bills is more than $60

4 0

3 years ago

Elaina Kicks A Soccer Ball With An Initial Velocity Of

VladimirAG [237]

By using the motion equations, we conclude that she will make the goal.

First, we know that the goal is 20ft away, and the position in x is given by:

$x = 28*cos(58)*t$

Let's find the time in which the ball will travel these 20 ft.

$20 = 28*cos(58)*t$

$(20)/(28*cos(58)) = t = 1.35$

So the horizontal distance is covered in 1.35 seconds, now let's see which is the height of the ball at that time.

The height equation is:

$y = -16*t^2 +28*sin(58)*t$

Evaluating in t = 1.35 we get:

$y = -16*(1.35)^2 +28*sin(58)*1.35\\\\y = 2.9$

And the goal is 5ft tall, so we can conclude that she will make the goal.

If you want to learn more about motion equations:

brainly.com/question/19365526

#SPJ1

5 0

2 years ago

PLEASE, ANSWER WILL GIVE BRAINLIEST

balu736 [363]

0.30 • 18 = 5.4
0.30 • 40 = 12
0.30 • 9 = 2.7
0.30 • 70 = 21
0.30 • 48 = 14.4
0.30 • 26 = 7.8
0.30 • 14 = 4.2
Add the sums together which would be 67.5
Subtract $100 from $67.5 and that would be $32.5

Answer: $32.50 change

7 0

3 years ago