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MAVERICK [17]
3 years ago
9

Solve the following inequalities a) algebraically AND b) graphically.

Mathematics
1 answer:
STALIN [3.7K]3 years ago
4 0

Answer:

Step-by-step explanation:

2x-x-5

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Can someone solve this?
aleksley [76]

Answer:

Considering the Law of Cosines:

c^2=a^2+b^2-2ab*cosC

a=14mi; b=24mi; c=CA; C=91degrees

\cos \left(91^{\circ \:}\right)=-0.01745\dots

c^2=14^2+24^2-2(14)(24)*\cos \left(91^{\circ \:}\right)\\c^2=196+576-672*\cos \left(91^{\circ \:}\right)\\c^2=772-672*\cos \left(91^{\circ \:}\right)\\c^2=772-672*(-0.01745)\\c^2=772+11.7264\\c=\sqrt{772+11.7264} \\c=\sqrt{783.7264}\\c=27.99mi

4 0
3 years ago
What is the value of x for which m || n?<br> x = 40<br> x = 5<br> x = 105<br> x = 30
QveST [7]

Answer:

(A) x=40

Step-by-step explanation:

Given: It is given that m is parallel to n.

To find: The value of x.

Proof: It is given that m is parallel to n, from the figure it can be seen that 105° and (3x-15)° forms alternate exterior angles which are equal in measure because m is parallel to n.

Thus, 105^{\circ}=3x-15^{\circ}

⇒105^{\circ}+15^{\circ}=3x

⇒120^{\circ}=3x

⇒\frac{120}{3}=x

⇒x=40

Thus, the value of x is 40, hence option A is correct.

4 0
3 years ago
Read 2 more answers
Stephanie and alejandro
Elena-2011 [213]

Answer:

Stephanie saved

Step-by-step explanation:

x+4x=15600

5x=15600

divide by 5 on both sides

you get 3120

since stephanie got 4 times more, you multiply 3120*4 and get 12480

therefore, Alejandro saved 3120

: )

4 0
2 years ago
Assume the average height for American women is 64 inches with a standard deviation of 2 inches. A sorority on campus wonders if
satela [25.4K]

Answer:

a) s = 0.4

b) Z = 2.5

c) 99th percentile.

d) The larger sample size would lead to a smaller margin of error, which would lead to a higher z-score and a increased percentile.

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 normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes 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.

Assume the average height for American women is 64 inches with a standard deviation of 2 inches

This means that \mu = 64, \sigma = 2

A) Calculate the standard error for the distribution of means.

Sample of 25 means that n = 25, so s = \frac{2}{\sqrt{25}} = 0.4.

B) Calculate the z statistic for the sorority group.

Sample mean of 65 means that X = 65.

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

By the Central Limit Theorem

Z = \frac{X - \mu}{0.4}

Z = \frac{65 - 64}{0.4}

Z = 2.5

C) What is the approximate percentile for this sample? Enter as a whole number.

Z = 2.5 has a p-value of 0.9938, so 0.99*100 = 99th percentile.

D) If the sorority actually had 36 members (still with an average of 65 inches), would you expect the percentile value to increase or decrease? why?

The larger sample size would lead to a smaller margin of error, which would lead to a higher z-score and a increased percentile.

3 0
2 years ago
An investment account plays 3.7% annual interest compound weekly. If $370 is invested in this account, what will be the balance
MAXImum [283]

Answer: 358

Explanation:  370 - 12 = 358

3 0
2 years ago
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