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suter [353]
3 years ago
14

An arc of length 8 in. is intersected by a central angle in a circle with a radius of 3 in. What is the measure of the angle? Ro

und your answer to the nearest tenth.
Mathematics
1 answer:
krok68 [10]3 years ago
7 0
Using the formula
L=rx  (x=angle)
x=L/r
x=8/3
x=2.6 radians
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Suppose monthly rental prices for a one-bedroom apartment in a large city has a distribution that is skewed to the right with a
omeli [17]

Answer:

a) Nothing, beause the distribution of the monthly rental prices are not normal.

b) 1.43% probability that the sample mean rent price will be greater than $900

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 random variable X, with mean \mu and standard deviation \sigma, the sample means with size n of at least 30 can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}

(a) Suppose a one-bedroom rental listing in this large city is selected at random. What can be said about the probability that the listed rent price will be at least $930?

Nothing, beause the distribution of the monthly rental prices are not normal.

(b) Suppose a random sample 30 one-bedroom rental listing in this large city will be selected, the rent price will be recorded for each listing, and the sample mean rent price will be computed. What can be said about the probability that the sample mean rent price will be greater than $900?

Now we can apply the Central Limit Theorem.

\mu = 880, \sigma = 50, n = 30, s = \frac{50}{\sqrt{30}} = 9.1287

This probability is 1 subtracted by the pvalue of Z when X = 900.

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

By the Central Limit Theorem

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

Z = \frac{900 - 880}{9.1287}

Z = 2.19

Z = 2.19 has a pvalue of 0.9857

1 - 0.9857 = 0.0143

1.43% probability that the sample mean rent price will be greater than $900

8 0
3 years ago
Mark dropped an object from a bridge 400 feet above the ground level with an initial velocity of 0. He knows that the gravitatio
lisabon 2012 [21]

Answer:

The first listed equation is the correct equation to solve

The correct answer is: t = 5 seconds

Step-by-step explanation:

Let me mention first that there is an error in the statement that the gravitational pull of the Earth is 16 ft/s^2. It is in fact 32 ft/s^2, and the actual equation uses half of the acceleration multiplied by the square of the variable time, so it gives as final expression :

y(t)=-16\,t^2+ 0 \,t +400

and we want to find the value/s for "t" that make this equation equal zero (when it reaches the ground and the object just touches the ground. This makes the equation we want to solve:

0=-16\,t^2+ 0 \,t +400\\16\,t^2+0\,t -400=0

which solving for "t" becomes:

16\,t^2-400 =0\\16\,t^2=400\\t^2=\frac{400}{16} \\t^2=25\\t= +/- 5\,\,sec

So we adopt the positive answer (positive time) since the negative value has no physical meaning for this problem.

That is: t = 5 seconds

6 0
3 years ago
Given: Q = 7m + 3n, R = 11 - 2m, S = n + 5, and T = -m - 3n + 8.
Oxana [17]

Answer:

6m + n + 2

Step-by-step explanation:

[7m + 3n - 11 - 2m] + [n + 5 - -m - 3n + 8]

[5m + 3n - 11] + [n + 5 + m - 3n + 8]

5m + 3n - 11 + (-2n + 13 + m)

5m + 3n - 11 - 2n + 13 + m

6m + n + 2

3 0
3 years ago
3x - 5y = -35 <br> please solve and show your work
scoray [572]
You use the formula y=mx+b, therefore you have to isolate the y
First you subtract 3x to both sides.
3x - 5y = -35
-3x -3x
Then it would be
-5y = -3x -35
Then you divide -5 on both sides to isolate the y
-5y = -3x -35
/-5 /-5 /-5
Two negatives cancel out and make a positive so it would be
Y = 3/5x + 7
(:
8 0
2 years ago
1)2{18-(5+3^2)÷7] <br>2) 1+(-2-5)^2+-3*4<br>PEMDAS<br>​
stira [4]

Answer:

I think these are the right answers. The answer to one is 32. The answer to two is 38.

1: 2[18-(5+3^2)/7]

2[18-(5+9)/7]

2[18-14/7]

2[18-2]

2 times 16 = 32

2: I used a calculator for this one.

3 0
2 years ago
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