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luda_lava [24]
1 year ago
6

The center of a circle is at the origin on a coordinate grid. A line with a positive slope intersects the circle at (0, 7). Whic

h statement must be true?
Mathematics
1 answer:
denis23 [38]1 year ago
3 0

The true statement is the circle has the radius equal to 7.

<h3>What is Equation of circle?</h3>

The general equation for a circle is (x-h)² + (y-k)² = r², where ( h, k ) is the center and r is the radius.

As, standard form of equation of circle is

(x-h)² + (y-k)² = r²

At origin, equation of circle will be

(0-h)² + (0-k)² = r²

r² = x² + y²

Now, The line intersects the circle at (0,7)

r² = 0² + 7²

r² =49

r=7.

Hence, the circle has the radius equal to 7.

Learn more about this concept here:

brainly.com/question/11702700

#SPJ1

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A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose pe
soldier1979 [14.2K]

Using the normal distribution, it is found that:

a) 0.8599 = 85.99% probability that x is more than 60.

b) 0.1788 = 17.88% probability that x is less than 110.

c) 0.6811 = 68.11% probability that x is between 60 and 110.

d) 0.0643 = 6.43% probability that x is greater than 125.

In a normal distribution with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

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

  • It 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, which is the percentile of X.

In this problem:

  • The mean is of 87, thus \mu = 87.
  • The standard deviation is of 25, thus \sigma = 25.

Item a:

This probability is <u>1 subtracted by the p-value of Z when X = 60</u>, thus:

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

Z = \frac{60 - 87}{25}

Z = -1.08

Z = -1.08 has a p-value of 0.1401.

1 - 0.1401 = 0.8599

0.8599 = 85.99% probability that x is more than 60.

Item b:

This probability is the <u>p-value of Z when X = 110</u>, thus:

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

Z = \frac{110 - 87}{25}

Z = 0.92

Z = 0.92 has a p-value of 0.8212.

1 - 0.8212 = 0.1788.

0.1788 = 17.88% probability that x is less than 110.

Item c:

This probability is the <u>p-value of Z when X = 110 subtracted by the p-value of Z when X = 60</u>.

From the previous two items, 0.8212 - 0.1401 = 0.6811.

0.6811 = 68.11% probability that x is between 60 and 110.

Item d:

This probability is <u>1 subtracted by the p-value of Z when X = 125</u>, thus:

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

Z = \frac{125 - 87}{25}

Z = 1.52

Z = 1.52 has a p-value of 0.9357.

1 - 0.9357 = 0.0643.

0.0643 = 6.43% probability that x is greater than 125.

A similar problem is given at brainly.com/question/24863330

7 0
3 years ago
The price of an item has been reduced by 30%. The original price was $30. What is the price of the item now ?
Anit [1.1K]

Answer:

9

Step-by-step explanation:

30 multiply by 30 and divide by 100

6 0
3 years ago
What is the relationship among proportional relationships lines, rates of change, and slope?
sdas [7]
<span><span>
It introduces the relationship between two variables and is called correlation. Proportionality or variation is state of relationship or correlation between two variables It has two types: </span>direct variation or proportion which states both variables are positively correlation. It is when both the variables increase or decrease together. On the contrary, indirect variation or proportion indicates negative relationship or correlation. Elaborately, the opposite of what happens to direct variation. One increases with the other variables, you got it, decreases. This correlations are important to consider because you can determine and identify how two variables relates with one another. Notice x = y (direct), y=1/x (indirect)</span>
3 0
3 years ago
Read 2 more answers
The following figure shows A ABC with side lengths to the nearest tenth.
xz_007 [3.2K]

Answer:

17.7

Step-by-step explanation:

angle B = 180 - 81 - 65 = 34 degrees

as the sum of all angles in any triangle is always 180 degrees.

a/sin(A) = b/sin(B) = c/sin(C)

the sides are always on the opposite side of the angle.

so,

10/sin(34) = AB/sin(81)

AB = 10×sin(81) / sin(34) = 17.7

3 0
2 years ago
State whether the following statement is true or​ false, and explain why. If the statement is​ false, state the true change. A h
katovenus [111]

Answer:

False

Step-by-step explanation:

Given that a high school reports that its​ students' SAT scores were down by 12​% in one year. The next​ year, however, the test scores rose by 20​%.

Let score initially be 100

Down by                     12

Next year score         88

For succeedingyear

increase is 20%        =20% of 88=17.6\\

Score in the 2nd year = 88+17.6 = 105.6

Hence overall scores improvement is 5.6% and not 8%

5 0
2 years ago
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