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3 years ago

Find the value of each variable

Mathematics

1 answer:

vaieri [72.5K]3 years ago

6 0

Answer:

x=67 y=113 x=52

Step-by-step explanation:

85+28= 113

180-113=67

67= x

67+28=95

95+85=180

y= 28+ 85 =113

113+15= 128

180-128=52

52=x

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kobusy [5.1K]

I hope this helps, sorry for my messy handwriting. If you have any questions feel free to ask me!

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4 years ago

Triangle J K L is shown. Angle J L K is 105 degrees. The length of J K is 4.7 and the length of J L is 2.7.

cluponka [151]

Answer:

The approximate measure of angle K is 34°

Step-by-step explanation:

In ΔJKL

∠L = 105°

JK = 4.7

JL = 2.7

Sine Rule:

$\frac{SinA}{a} = \frac{SinB}{b}= \frac{SinC}{c}$

So, $\frac{SinL}{JK} = \frac{SinK}{JL}\\\frac{SinL}{4.7} = \frac{SinK}{2.7}\\\frac{Sin 105}{4.7} = \frac{SinK}{2.7}\\\frac{Sin 105 \times 2.7}{4.7} = SinK\\\frac{(0.9659 \times 2.7)}{4.7} = Sin K\\\frac{2.60793}{4.7} = Sin K\\0.5549 = Sin K\\Sin^{-1}(0.5549)= K\\K = 33.70$

K ≈ 34°

So, Option B is true

Hence The approximate measure of angle K is 34°

5 0

3 years ago

Write 36.7 decimal out in words.

Scrat [10]

Answer:

thirty-six and seven tenths

Step-by-step explanation:

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3 years ago

Read 2 more answers

In a study, 43% of adults questioned reported that their health was excellent. A researcher wishes to study the health of people

marishachu [46]

Answer:

13.44% probabilith that at most 3 are in excellent health.

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either they are in excellent health, or they are not. The probability of an adult being in excellent health is independent of other adults. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

43% of adults questioned reported that their health was excellent.

This means that $p = 0.43$

13 adults randomly selected

This means that $n = 13$

Find the probability that when 13 adults are randomly selected, at most 3 are in excellent health.

$P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)$

In which:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{13,0}.(0.42)^{0}.(0.58)^{13} = 0.0008$

$P(X = 1) = C_{13,1}.(0.42)^{1}.(0.58)^{12} = 0.0079$

$P(X = 2) = C_{13,2}.(0.42)^{2}.(0.58)^{11} = 0.0344$

$P(X = 3) = C_{13,3}.(0.42)^{3}.(0.58)^{10} = 0.0913$

$P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0008 + 0.0079 + 0.0344 + 0.0913 = 0.1344$

13.44% probabilith that at most 3 are in excellent health.

6 0

3 years ago

Techside Real Estate, Inc. is a research firm that tracks the cost of apartment rentals in Southwest Virginia. In mid-2002, the

maks197457 [2]

Answer:

1) we will fail to reject the null hypothesis and conclude that the population mean apartment rental rate does not exceed the level reported in 2002

2) P - value = 0.116435

Step-by-step explanation:

We are given;

Population mean; μ = $895

Sample mean; x' = $915

Population standard deviation; σ = $225

Sample standard deviation; s = $227.50

Sample size; n = 180

Let's state the hypothesis;

Null hypothesis;H0: μ ≤ $895

Alternative hypothesis;Ha: μ > $895

Now, the z-score formula is;

z = (x' - μ)/(σ/√n)

Thus, we are making use of the population standard deviation

z = (915 - 895)/(225/√180)

z = 20/16.7705

z = 1.193

From online p-value from z-score calculator attached, with α = 0.10, one tail, we have;

The P-Value is 0.116435

This is more than the significance level of 0.1, thus we will fail to reject the null hypothesis and conclude that the population mean apartment rental rate does not exceed the level reported in 2002

3 0

3 years ago