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konstantin123 [22]
3 years ago
14

Write an equation of the line parallel to y=3x−7 that passes through point (2, 4).

Mathematics
1 answer:
MrRissso [65]3 years ago
6 0
Parallel lines share the same slope. y=3x+7 has a slope of 3, so that is the slope of the parallel line. Then use y=mx+b an plug in (2,4).
y=3x+b
4=3(2)+b
4=6+b
b=-2

So the equation is y=3x-2
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For a particular diamond mine, 81% of the diamonds fail to qualify as "gemstone grade". A random sample of 92 diamonds is analyz
Fed [463]

Answer:

68.79% probability that more than 79% of the sample diamonds fail to qualify as gemstone grade

Step-by-step explanation:

We use the binomial approximation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

Normal probability distribution

Problems of normally distributed samples can be 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.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

In this problem, we have that:

n = 92, p = 0.81

So

\mu = E(X) = np = 92*0.81 = 74.52

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{92*0.81*0.19} = 3.76

Find the probability that more than 79% of the sample diamonds fail to qualify as gemstone grade.

This is 1 subtracted by the pvalue of Z when X = 0.79*92 = 72.68. So

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

Z = \frac{72.68 - 74.52}{3.76}

Z = -0.49

Z = -0.49 has a pvalue of 0.3121

1 - 0.3121 = 0.6879

68.79% probability that more than 79% of the sample diamonds fail to qualify as gemstone grade

4 0
3 years ago
3. Elena can make 15 pizzas in 3 hours. If the number of pizzas is represented by p and time is represented by t, Write an equat
zhuklara [117]

Answer:

Your answer is 3x = 15

Step-by-step explanation:

3x = 15

Since 3 is being multiplied by x, we divide both sides by 3.  3x/3 cancels out, and you're left with x.

15/3 = 5

x = 5

This is my take using algebraic methods.

6 0
3 years ago
What is value of x?<br><br><br><br> Enter your answer in the box.
Kryger [21]

Answer:

A number

Step-by-step explanation:

4 0
3 years ago
ANWSER these three questions show ur work, if u can is somewhat optional
Airida [17]

Answer:

1. 35            2. 565.5         3. 12.28

Step-by-step explanation:

1. Triangle 1 & 2: 7x3=21    

You do not have to divide by 2 is since there are two triangles.

 Semi-circle: 14.13

2. Trinagle: 29x19/2 = 275.5

Rectangle: 29x10 = 290

3. Triangle: 3x4/2 = 6

Semi-circle: 3.14x4/2 = 6.28

<em>Took a long time- Please give Brainliest and points!</em>

7 0
3 years ago
Write 0.4 as a fraction
scoundrel [369]
0.4 / 2 = 0.2

1/0.2 = 5

2/5 is the answer
4 0
3 years ago
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