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2 years ago

Find KL and show work

Mathematics

2 answers:

MissTica2 years ago

6 0

Answer:

Secant: a straight line that intersects a circle at two points.

Intersecting Secants Theorem

If two secant segments are drawn to the circle from one exterior point, the product of the measures of one secant segment and its external part is equal to the product of the measures of the other secant segment and its external part.

From inspection of the given diagram:

M = Exterior point
MK = secant segment and ML is its external part
MS = secant segment and MN is its external part

Therefore:

⇒ ML · MK = MN · MS

Given:

MK = (x + 15) + 6 = x + 21
ML = 6
MS = 7 + 11 = 18
MN = 7

Substituting the given values into the formula and solving for x:

⇒ ML · MK = MN · MS

⇒ 6(x + 21) = 7 · 18

⇒ 6x + 126 = 126

⇒ 6x = 0

⇒ x = 0

Substituting the found value of x into the expression for KL:

⇒ KL = x + 15

⇒ KL = 0 + 15

⇒ KL = 15

Scilla [17]2 years ago

6 0

Let's see

LM(KL+LM)=NM(NM+NS)
6(6+x+15)=7(7+11)
6(x+21)=7(18)
6(x+21)=126
x+21=21
x=0

KL=0+15=15

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The mean annual premium for automobile insurance in the United States is $1503 (Insure website, March 6, 2014). Being from Penns

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Answer:

If we compare the p value and the significance level for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can conclude that the mean annual premium in Pennsylvania is significantly lower than the national mean annual premium of 1503 at 5% of significance.

Step-by-step explanation:

1) Data given and notation

$\bar X=1440$ represent the mean annual premium value for the sample

$s=165$ represent the sample standard deviation for the sample

$n=25$ sample size

$\mu_o =1503$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean annual premium in Pennsylvania is lower than the national mean annual premium, the system of hypothesis would be:

Null hypothesis: $\mu \geq 1503$

Alternative hypothesis: $\mu < 1503$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{1440-1503}{\frac{165}{\sqrt{25}}}=-1.909$