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3 years ago

A circle is centered at the point (7,1) and passes through the point (8,7). what is the radius

1 answer:

7 0

Easy

the radius is the distance from the center to a point on the circle

we are given
center=(7,1)
a point=(8,7)
find the distance
distance formula
D= $\sqrt{(x2-x1)^2+(y2-y1)^2}$

so the distance between point and center is radius
D= $\sqrt{(8-7)^2+(7-1)^2}$
D= $\sqrt{(1)^2+(6)^2}$
D= $\sqrt{1+36}$
D=√37 units

radius is √37 units

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Some scientists say, happiness, when measured on a scale of 0 (super unhappy) to 100 (super happy), is a function of the number

ololo11 [35]

Answer:

f(x) = 60-2x

Step-by-step explanation:

Suppose that f(x) = y is a happiness function. It is a function of the number of hours you spend on Instagram per day. That means that the output of the function will be a "happiness score",i.e. the value between 0 and 100, and the variable <em>x </em>will be an output value, the hours spent on Instagram daily.

We know that if we spend 0 hours on Instagram per day the happiness score will be 60, which means that:

f(0) = 60

If we spend 1 hour per day on Instagram our level of happiness will be decreased by 2, i.e. 60-2 = 58. Therefore,

f(1) = 58

If we spend 2 hours on Instagram per day our level of happiness will be decreased even more, i.e. 58-2 = 56. Therefore,

f(2) = 56

Notice that 56 = 60-4 = 60-2*2

If we spend 3 hours on Instagram per day our level of happiness will be decreased even more, i.e. 56-2 = 54. Therefore,

f(3) = 54

Notice that 54 = 60-6 = 60-3*2

Now we can see the pattern from which the level of happiness can be calculated. It is 60 decreased by the number of hours multiplied by 2.

Hence, the "happiness function" is:

f(x) = 60-x*2 = 60-2x, where x is a number of hours spent on Instagram.

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3 years ago

Nina's car exponentially depreciates at a rate of 7% per year. If Nina bought the car when it was six year old for $12,000 what

Maksim231197 [3]

<span>$18,547.42, hope it works!

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7 0

3 years ago

Convert 2/50 to percent

vodomira [7]

Answer: 4%

Step-by-step explanation: 50 x 2 = 100

2x2=4 4/100 or 4%

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3 years ago

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Suppose that the national average for the math portion of the College Board's SAT is 515. The College Board periodically rescale

nasty-shy [4]

Answer:

a) 16% of students have an SAT math score greater than 615.

b) 2.5% of students have an SAT math score greater than 715.

c) 34% of students have an SAT math score between 415 and 515.

d) $Z = 1.05$

e) $Z = -1.10$

Step-by-step explanation:

To solve this question, we have to understand the normal probability distribution and the empirical rule.

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.

Empirical rule

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

$\mu = 515, \sigma = 100$

(a) What percentage of students have an SAT math score greater than 615?

615 is one standard deviation above the mean.

68% of the measures are within 1 standard deviation of the mean. The other 32% are more than 1 standard deviation from the mean. The normal probability distribution is symmetric. So of those 32%, 16% are more than 1 standard deviation above the mean and 16% more then 1 standard deviation below the mean.

So, 16% of students have an SAT math score greater than 615.

(b) What percentage of students have an SAT math score greater than 715?

715 is two standard deviations above the mean.

95% of the measures are within 2 standard deviations of the mean. The other 5% are more than 2 standard deviations from the mean. The normal probability distribution is symmetric. So of those 5%, 2.5% are more than 2 standard deviations above the mean and 2.5% more then 2 standard deviations below the mean.

So, 2.5% of students have an SAT math score greater than 715.

(c) What percentage of students have an SAT math score between 415 and 515?

415 is one standard deviation below the mean.

515 is the mean

68% of the measures are within 1 standard deviation of the mean. The normal probability distribution is symmetric, which means that of these 68%, 34% are within 1 standard deviation below the mean and the mean, and 34% are within the mean and 1 standard deviation above the mean.

So, 34% of students have an SAT math score between 415 and 515.

(d) What is the z-score for student with an SAT math score of 620?

We have that:

$\mu = 515, \sigma = 100$

This is Z when X = 620. So

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

$Z = \frac{620 - 515}{100}$

$Z = 1.05$

(e) What is the z-score for a student with an SAT math score of 405?

We have that:

$\mu = 515, \sigma = 100$

This is Z when X = 405. So

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

$Z = \frac{405 - 515}{100}$

$Z = -1.10$

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3 years ago

Consider the following incomplete deposit ticket:

boyakko [2]

Answer:

B) 105.20

Step-by-step explanation:

491.60 + 157.68 - 68.44 = 581.20

6 0

3 years ago

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