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3 years ago

What is the slope of the line that passes through the points (-5, -7) and (4,-1)?

Mathematics

2 answers:

joja [24]3 years ago

5 0

Answer:

$m=\frac{2}{3}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Slope Formula: $m=\frac{y_2-y_1}{x_2-x_1}$

Step-by-step explanation:

Step 1: Define

Point (-5, -7)

Point (4, -1)

Step 2: Find slope m

Substitute [Slope Formula]: $m=\frac{-1+7}{4+5}$
Add: $m=\frac{6}{9}$
Simplify: $m=\frac{2}{3}$

Ann [662]3 years ago

4 0

Answer:

2/3

Step-by-step explanation:

-7 - -1 = -6

-5 - 4 = -9

-6/-9= 2/3

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Together, two apples have 1/5 gram of fat. How many apples have a total of 4 grams of fat?

4vir4ik [10]

20 apples

1/5=0.2

0.2×20=4

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3 years ago

Read 2 more answers

The elevation E, in meters, above sea level at which the boiling point of a certain liquid is t degrees Celsius is given by th

const2013 [10]

For T = 89.5 degrees C:
E(t) = 1100(90 - 89.5) + 520(90 - 89.5)^2= 1100(0.5) + 520(0.5)^2= 550 + 130= 680 m
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E(t) = 1100(90 - 90) + 520(90 - 90)^2= 0 + 0= 0 m (meaning that boiling point is 90 degrees C at ground level)

3 0

3 years ago

How can a ratio's number can be changed without changing the ratio itself

eimsori [14]

<h2>Answer:</h2>

The ratio is a fraction that tells us how many times longer a thing is compared to another thing. In mathematics, we express a ratio as the relationship between two numbers, namely $a \ and \ b$ , so the ratio can be written as:

$r=\frac{a}{b}$

If we can change this number without changing the ration we need to multiply both the numerator and the denominator by the same number. For instance, if we have the following ratio:

$r=\frac{2}{3}$

We can multiply both the numerator and denominator, say, by 7. Then:

$r=\frac{7\times 2}{7 \times 3}=\frac{14}{21}$

As you can see, the ratio's number has changed but without changing the ratio itself because:

$\frac{2}{3}=\frac{14}{21}$

8 0

3 years ago

The CPA Practice Advisor reports that the mean preparation fee for 2017 federal income tax returns was $273. Use this price as t

skad [1K]

Answer:

a) 0.6212 = 62.12% probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean.

b) 0.7416 = 74.16% probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean.

c) 0.8804 = 88.04% probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean.

d) None of them ensure, that one which comes closer is a sample size of 100 in option c), to guarantee, we need to keep increasing the sample size.

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.

The CPA Practice Advisor reports that the mean preparation fee for 2017 federal income tax returns was $273. Use this price as the population mean and assume the population standard deviation of preparation fees is $100.

This means that $\mu = 273, \sigma = 100$

A) What is the probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean?

Sample of 30 means that $n = 30, s = \frac{100}{\sqrt{30}}$

The probability is the p-value of Z when X = 273 + 16 = 289 subtracted by the p-value of Z when X = 273 - 16 = 257. So

X = 289

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

By the Central Limit Theorem

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

$Z = \frac{289 - 273}{\frac{100}{\sqrt{30}}}$

$Z = 0.88$

$Z = 0.88$ has a p-value of 0.8106

X = 257

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

$Z = \frac{257 - 273}{\frac{100}{\sqrt{30}}}$

$Z = -0.88$

$Z = -0.88$ has a p-value of 0.1894

0.8106 - 0.1894 = 0.6212

0.6212 = 62.12% probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean.

B) What is the probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean?

Sample of 30 means that $n = 50, s = \frac{100}{\sqrt{50}}$

X = 289

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

By the Central Limit Theorem

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

$Z = \frac{289 - 273}{\frac{100}{\sqrt{50}}}$

$Z = 1.13$

$Z = 1.13$ has a p-value of 0.8708

X = 257

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

$Z = \frac{257 - 273}{\frac{100}{\sqrt{50}}}$

$Z = -1.13$

$Z = -1.13$ has a p-value of 0.1292

0.8708 - 0.1292 = 0.7416

0.7416 = 74.16% probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean.

C) What is the probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean?

Sample of 30 means that $n = 100, s = \frac{100}{\sqrt{100}}$

X = 289

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

By the Central Limit Theorem

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

$Z = \frac{289 - 273}{\frac{100}{\sqrt{100}}}$

$Z = 1.6$

$Z = 1.6$ has a p-value of 0.9452

X = 257

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

$Z = \frac{257 - 273}{\frac{100}{\sqrt{100}}}$

$Z = -1.6$

$Z = -1.6$ has a p-value of 0.0648

0.9452 - 0.0648 =

0.8804 = 88.04% probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean.

D) Which, if any of the sample sizes in part (a), (b), and (c) would you recommend to ensure at least a .95 probability that the same mean is withing $16 of the population mean?

None of them ensure, that one which comes closer is a sample size of 100 in option c), to guarantee, we need to keep increasing the sample size.

6 0

2 years ago

Solving two-step equations:

aleksklad [387]

Answer:

Mia scored 6 baskets Last Saturday.

Step-by-step explanation:

Let:

Mia made score of baskets on Last Saturday = x

Mia made score of baskets yesterday = 3x (Mia made three times as many baskets in yesterday’s basketball game as she did last Saturday. three times means multiply 3 with score of Last Saturday baskets, i.e. x)

Total score of baskets = 24

We need to find How many baskets did Mia score last Saturday?

We can write:

Total Score = Score on Last Saturday + Score yesterday

$24=x+3x$

Solving this equation we can find value of x:

$24=x+3x\\24=4x\\=>4x=24\\x=\frac{24}{4}\\x=6$

So, we get value of x = 6

Mia made score of baskets on Last Saturday = x = 6

Mia scored 6 baskets Last Saturday.

4 0

2 years ago