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Masja [62]
3 years ago
7

Based only on the information given in the diagram, it is guaranteed that

Mathematics
1 answer:
Alona [7]3 years ago
3 0

Answer:

True

Step-by-step explanation:

Given

In JKL, we have:

\angle J = 27

\angle K = 90

In WXY, we have:

\angle Y = 63

\angle X = 90

Required

Is JKL ~ WXY?

In both triangles, we already have one similar angle (90)

Next, is to determine the third angles in both triangles.

In JKL

\angle J + \angle K + \angle L = 180

We have that:

\angle J = 27 and \angle K = 90

The expression becomes:

27 + 90 + \angle L = 180

117 + \angle L = 180

\angle L = 180-117

\angle L = 63

In WXY

\angle W + \angle X + \angle Y = 180

We have that:

\angle Y = 63 and \angle X = 90

The expression becomes:

\angle W + 63 + 90 = 180

\angle W + 153 = 180

\angle W = 180-153

\angle W = 27

The three angles in JKL are:

\angle J = 27    \angle K = 90   \angle L = 63

The three angles in WXY are:

\angle W = 27   \angle X = 90   \angle Y = 63

<em>By comparing the angles, we can conclude that  both triangles are similar because of AAA postulate (Angle-Angle-Angle)</em>

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After the closing of the mill, the town of Sawyerville experienced a decline in its population.
vfiekz [6]

Step-by-step explanation:

P(t) = 12,000 (2)^(-t/15)

9,000 = 12,000 (2)^(-t/15)

0.75 = 2^(-t/15)

ln(0.75) = ln(2^(-t/15))

ln(0.75) = (-t/15) ln(2)

-15 ln(0.75) / ln(2) = t

t = 6.23

4 0
3 years ago
The length of a rectangle is 4 yards less than 2 times the width. If the perimeter is 34 yards, find the length and the width of
tamaranim1 [39]

Answer:

21 yards

Step-by-step explanation:

4 0
2 years ago
Which graph represents 2x − 5y ≥ − 20
DENIUS [597]

Answer:

Go to desmos and it will answer literally all of your graphing questions. Just type in desmos graphing calculator.

Step-by-step explanation:

3 0
3 years ago
The heights of a random sample of 50 college students showed a mean of 174.5 centimeters and a standard deviation of 6.9 centime
Minchanka [31]

Answer:

Step-by-step explanation:

Hello!

For me, the first step to any statistics exercise is to determine what is the variable of interest and it's distribution.

In this example the variable is:

X: height of a college student. (cm)

There is no information about the variable distribution. To estimate the population mean you need a variable with at least a normal distribution since the mean is a parameter of it.

The option you have is to apply the Central Limit Theorem.

The central limit theorem states that if you have a population with probability function f(X;μ,δ²) from which a random sample of size n is selected. Then the distribution of the sample mean tends to the normal distribution with mean μ and variance δ²/n when the sample size tends to infinity.

As a rule, a sample of size greater than or equal to 30 is considered sufficient to apply the theorem and use the approximation.

The sample size in this exercise is n=50 so we can apply the theorem and approximate the distribution of the sample mean to normal:

X[bar]~~N(μ;σ2/n)

Thanks to this approximation you can use an approximation of the standard normal to calculate the confidence interval:

98% CI

1 - α: 0.98

⇒α: 0.02

α/2: 0.01

Z_{1-\alpha /2}= Z_{1-0.01}= Z_{0.99} =2.334

X[bar] ± Z_{1-\alpha /2} * \frac{S}{\sqrt{n} }

174.5 ± 2.334* \frac{6.9}{\sqrt{50} }

[172.22; 176.78]

With a confidence level of 98%, you'd expect that the true average height of college students will be contained in the interval [172.22; 176.78].

I hope it helps!

4 0
3 years ago
What is the smallest integer greater than square root of 92?
vovikov84 [41]

sqrt(81) = 9

sqrt(100) = 100

sqrt(92) is between 9 and 10.

Answer: 10

5 0
3 years ago
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