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Eduardwww [97]
2 years ago
13

Triangle J K L is shown. Point N is the midpoint of side J L and point M is the midpoint of side K L. The length of J K is 19.6

meters. The lengths of J N and N L are 7.4 meters. The lengths of K M and M L are 10.7 meters.
What is the distance between points M and N?

meters
Mathematics
1 answer:
Kruka [31]2 years ago
7 0

The distance between points M and N according to the task content is; 9.8 meters.

<h3>What is the distance between points M and N?</h3>

From observation of the task content information; it can be deduced for a fact that the line segment MN which joins points M and N is parallel to the line JK. This follows from the fact that M and N are midpoints KL and JL respectively.

Hence, it follows that triangles NLM and JLK are congruent and by the ratio of corresponding sides equality;

NM/19.6 = 7.4/(2×7.4)

NM = 19.6/2 = 9.8 meters.

This follows from congruence theorems in which case, the ratio of corresponding sides of congruent triangles are equal.

Read more on congruent triangles;

brainly.com/question/1675117

#SPJ1

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A politician estimates that 61% of his constituents will vote for him in the coming election. How many constituents are required
Katyanochek1 [597]

Using the z-distribution, as we are working with a proportion, it is found that 1016 constituents are required.

<h3>What is a confidence interval of proportions?</h3>

A confidence interval of proportions is given by:

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which:

  • \pi is the sample proportion.
  • z is the critical value.
  • n is the sample size.

The margin of error is given by:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

In this problem, we have a 95% confidence level, hence\alpha = 0.95, z is the value of Z that has a p-value of \frac{1+0.95}{2} = 0.975, so the critical value is z = 1.96.

The estimate is of \pi = 0.61, while the margin of error is of M = 0.03, hence solving for n we find the minimum sample size.

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.03 = 1.96\sqrt{\frac{0.61(0.39)}{n}}

0.03\sqrt{n} = 1.96\sqrt{0.61(0.39)}

\sqrt{n} = \frac{1.96\sqrt{0.61(0.39)}}{0.03}

(\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.61(0.39)}}{0.03}\right)^2

n = 1015.5

Rounding up, 1016 constituents are required.

More can be learned about the z-distribution at brainly.com/question/25890103

8 0
2 years ago
there is a college student who wants to buy apples from the local store. the store generally sells about 5 apples for every 2 cu
myrzilka [38]
125 apples sold after 6 hours
3 0
3 years ago
Compare 6 ⋅ 108 to 3 ⋅ 106.
djverab [1.8K]

Answer:

6*10^8  is 200 times larger than  3*10^6

Step-by-step explanation:

6*10^8\ and \ 3*10^6

To compare both values we divide the exponents

\frac{6*10^8}{3*10^6}

6 divide by 3 is 2

for simplify exponents we use exponential property

a^m / a^n = a^(m-n)

\frac{10^8}{10^6}=10^2

\frac{6*10^8}{3*10^6}=2*10^2= 200

6*10^8  is 200 times larger than  3*10^6

4 0
3 years ago
Read 2 more answers
Write the ratio of the area of a circle with radius r to the circumference of the same circle
Goshia [24]

Answer:

\frac{r}{2\pi r} =\frac{1}{2\pi }

Step-by-step explanation:

A ratio is a comparison of two quantities and can be written in several forms including fractions. It is most commonly written in fraction form or a:b.

To write a ratio, we count the number of each quantity we are comparing or use the variable for that quantity. We write radius:circumference. Recall, the circumference of a circle can be found using \pi d or 2\pi r.

We write r: \pi d  or r:2\pi r.

We can also write in fraction form:

\frac{r}{\pi d} or \frac{r}{2\pi r} =\frac{1}{2\pi }


6 0
3 years ago
What's is 1 + 1 please help idk this
alexandr402 [8]

Answer:

One plus one is two.

Step-by-step explanation:

3 0
3 years ago
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