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1 year ago

Triangles IJK and LMN are similar. Find y using proportions. Explain and show all your steps.

Mathematics

1 answer:

Deffense [45]1 year ago

4 0

Triangles IJK and LMN are similar. Then, the proportion between their similar sides must be equal. That is:

IJ/ML = JK/MN = IK/LN

where:

IJ = x

JK = 54

IK = y

MN = 42

ML = 28

NL = 35

In order to find the value of y, you consider the equation JK/MN = IK/LN, and solve for y, just as follow

JK/MN = IK/LN replace by the values

54/42 = y/35 multiply both sides by 35

(54/42)(35) = y

45 = y

Hence, y = 45

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The mean height of women in a country (ages 20-29) is 64 4 inches A random sample of 50 women in this age group is selected What

Simora [160]

Answer:

0.0721 = 7.21% probability that the mean height for the sample is greater than 65 inches.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

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

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

The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 64.4 inches, standard deviation of 2.91

This means that $\mu = 64.4, \sigma = 2.91$

Sample of 50 women

This means that $n = 50, s = \frac{2.91}{\sqrt{50}}$

What is the probability that the mean height for the sample is greater than 65 inches?

This is 1 subtracted by the p-value of Z when X = 65. So

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

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{65 - 64.4}{\frac{2.91}{\sqrt{50}}}$

$Z = 1.46$

$Z = 1.46$ has a p-value of 0.9279

1 - 0.9279 = 0.0721

0.0721 = 7.21% probability that the mean height for the sample is greater than 65 inches.

8 0

2 years ago

Please help! Its due today!

Helga [31]

Answer:

don't know if this is the right way butttt i'm going to give it a shot

Step-by-step explanation:

Cost: I'm guessing this is for the rent for the shoes or is the total cost?

Bowler World: 5 + 1.1g = c | c + 1.1g = t {(this is the other option) probs not correct}

Lucky Spares: 3 + 1.5g = c | c + 1.5g = t

K so personally you should choose option 1 (for example: 5 + 1.1g = c), i have no idea how the proper format is supposed to be

either i hope this helps :)

7 0

2 years ago

Could you please help me with number 6 thank you sm !!

ololo11 [35]

Answer:

A) a = 4, b = 3

Step-by-step explanation:

Given equation:

4/(x - 3) + 2/(x - 2) = 2

Multiply all terms by (x - 3)(x - 2):

4(x - 2) + 2(x - 3) = 2(x - 3)(x - 2)
2(x - 2) + (x - 3) = (x - 3)(x - 2)
2x - 4 + x - 3 = x² - 5x + 6
x² - 5x - 3x + 6 + 7 = 0
x² - 8x + 13 = 0
x = (8 ± √(8² - 4*13))/2 = (8 ± √12)/2 = (8 ± 2√3)/2 = 4 ± √3

Compare this to the given form to get:

a = 4, b = 3

Correct choice is A

6 0

2 years ago

The marginal cost of producing x units of a certain product is 72 + 1.1x − 0.007x2 + 0.00004x3 (in dollars per unit). Find the i

Rzqust [24]

Answer:

The increase in cost is $81620.

Step-by-step explanation:

Given:

The marginal cost of producing 'x' units of a certain product is given as:

$C= 72+1.1x-0.007x^2 + 0.00004x^3$

Where, 'C' is the marginal cost.

Now, when $x=1800\ units$ , the marginal cost is given as:

$C_1=72+1.1(1800)-0.007(1800)^2+0.00004(1800)^3\\\\C_1=72+1980-22680+233280\\\\C_1=\$212652$

Again, when $x=2000\ units$ , the marginal cost is given as:

$C_2=72+1.1(2000)-0.007(2000)^2+0.00004(2000)^3\\\\C_2=72+2200-28000+320000\\\\C_2=\$294272$

Now, increase in cost is equal to the difference of the above two costs calculated. Therefore,

$\Delta C= C_2-C_1=\$294272-\$212652=\$81620$

Therefore, the increase in cost is $81620.

6 0

3 years ago

Multiply 6⁄5 × 25⁄24 . A. 144⁄125 B. 4⁄5 C. 125⁄144 D. 5⁄4

Tju [1.3M]

6/5 * 25/24 = (6 * 25) / (5 * 24) = 150/120 = 15/12 = 5/4

8 0

3 years ago

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