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Cerrena [4.2K]
2 years ago
11

Identify the equation in slope-intercept form for the line containing the point (0,7) and perpendicular to y=−5/4x+11/4.

Mathematics
1 answer:
g100num [7]2 years ago
4 0

Answer:

4/5x + 7

Step-by-step explanation:

the slope-intercept form is y = ax+b

a is the slope, to figure it out the line is perpendicular to y = -5/4x+11/4

There is a rule said if two lines are perpendiculars, the multiplication of their slopes = -1, so -5/4 * a = 1, solve for a = 4/5

b is the intercept to get it use the point (0,7)

so y = 4/5x+b, 7 = 4/5 * 0 + b,  then b = 7

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Answer:

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Step-by-step explanation:Well we know that for two angles A , B

it holds that cos ( A + B ) = cos A cos B − sin A ⋅ sin B hence for A = B you get cos ( 2 A ) = cos 2 A − sin 2 A But sin 2 A = 1 − cos 2 A


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3 years ago
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If the factors of quadratic function g are (x − 7) and (x + 3), what are the zeros of function g?
MArishka [77]

Answer: B. -3 and 7

Step-by-step explanation:

To find the zeros, just move the constants to the other side,

x - 7 ⇒ x = 7

x + 3 ⇒ x = -3

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Hope it helps!

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2 years ago
Which function is equivalent to y = 3(x + 2)2 + 7?
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Step-by-step explanation:

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2 years ago
Andrew fish tank holds 144 gallons of water. To clean the tank, he drains the water at a rate the water at a rate of 6 gallons p
Kobotan [32]

Answer:

8 minutes

Step-by-step explanation:

Since the level of the tank needs to be at two-thirds its original level, then this means that Andrew needs to drain only one-third of the fish tank. Therefore the amount of time it would take can easily be solved with this 2-step equation...

6t = 144 * \frac{1}{3} .... first multiply the right side of the equation

6t = 48   ... next divide both sides by 6

t = 8

Finally, we can see that it will take Andrew 8 minutes to drain the tank to two-thirds of its original level.

4 0
3 years ago
Suppose the weights of Farmer Carl's potatoes are normally distributed with a mean of 8.0 ounces and a standard deviation of 1.1
svet-max [94.6K]

Answer:

a) 0.9959 = 99.59% probability that the mean weight is less than 9.3 ounces

b) 0.0129 = 1.29% probability that the mean weight is more than 9.0 ounces

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 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.

Mean of 8.0 ounces and a standard deviation of 1.1 ounces.

This means that \mu = 8, \sigma = 1.1

(a) If 5 potatoes are randomly selected, find the probability that the mean weight is less than 9.3 ounces?

n = 5 means that s = \frac{1.1}{\sqrt{5}} = 0.4919

This probability is the pvalue of Z when X = 9.3. So

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

By the Central Limit Theorem

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

Z = \frac{9.3 - 8}{0.4919}

Z = 2.64

Z = 2.64 has a pvalue of 0.9959

0.9959 = 99.59% probability that the mean weight is less than 9.3 ounces

(b) If 6 potatoes are randomly selected, find the probability that the mean weight is more than 9.0 ounces?

n = 6 means that s = \frac{1.1}{\sqrt{6}} = 0.4491

This probability is 1 subtracted by the pvalue of Z when X = 9. So

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

Z = \frac{9 - 8}{0.4491}

Z = 2.23

Z = 2.23 has a pvalue of 0.9871

1 - 0.9871 = 0.0129

0.0129 = 1.29% probability that the mean weight is more than 9.0 ounces

8 0
3 years ago
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