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Katena32 [7]
3 years ago
7

Triangle ABC

Mathematics
1 answer:
Virty [35]3 years ago
5 0

Answer:

15 cm

Step-by-step explanation:

Similar triangles are triangles which have the same shape but not the same size. This means their angle measures are equal but their side lengths are not instead they are proportional. To solve, we will set up a proportion and solve.

A proportion is two equal ratios set equal to each other. We form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). Out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

\frac{BC}{EF} =\frac{AC}{DF}.

\frac{18}{x}=\frac{12}{10}

To solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.

\frac{18}{x}=\frac{12}{10}\\ 18*10 = x*12 \\ 180 = 12x \\ 15 = x

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The mean number of English courses taken in a two–year time period by male and female college students is believed to be about t
prisoha [69]

Answer:

Step-by-step explanation:

This is a test of 2 independent groups. The population standard deviations are not known. it is a two-tailed test. Let m be the subscript for the number of English courses taken by male students and f be the subscript for the number of English courses taken by female students.

Therefore, the population means would be μm and μf.

The random variable is xm - xf = difference in the sample mean number of English courses taken by male and female students.

We would set up the hypothesis.

The null hypothesis is

H0 : μm = μf H0 : μm - μf = 0

The alternative hypothesis is

H1 : μm ≠ μf H1 : μm - μf ≠ 0

Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is

(xm - xf)/√(sm²/nm + sf²/nf)

From the information given,

xm = 3

xf = 4

sm = 0.8

sf = 1

nm = 29

nf = 16

t = (3 - 4)/√(0.8²/29 + 1²/16)

t = - 11.82

The formula for determining the degree of freedom is

df = [sm²/nm + sf²/nf]²/(1/nm - 1)(sm²/nm)² + (1/nf - 1)(sf²/nf)²

df = [0.8²/29 + 1²/16]²/[(1/29 - 1)(0.8²/29)² + (1/16 - 1)(1²/16)²] = 0.00715/0.00027781093

df = 25.7

Approximately, df = 26

We would determine the probability value from the t test calculator. It becomes

p value = 0.00001

Assuming a level of significance of 0.05, we would reject the null hypothesis because the p value, 0.00001 is < 0.05

Therefore, we can conclude that the means are not statistically the same.

3 0
3 years ago
Find each missing angle of the trapezoid
zimovet [89]

Answer:

∠J = 107°

∠K =107°

∠L = 73°

∠M = 73°

Step-by-step explanation:

Angle J + angle M = 180°

(10x - 33) + (4x+17) = 180

simplify:

14x -16 = 180

14x = 196

x = 14

∠J = 10(14) - 33 = 107°

∠M = 4(14) + 17 = 73°

7 0
2 years ago
The dogs at a shelter are housed in 4 different rooms. If there are 10 dogs in each room, how many dogs are housed at the shelte
frozen [14]
If there are 10 dogs in each room there are 40 dogs
6 0
3 years ago
What is the distance of -a and a?
melamori03 [73]

Step-by-step explanation:

Distance = positive value

a + a = 2a

6 0
3 years ago
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The scale in the drawing is 2 inches : 3 feet. What are the length and width of the actual room? *
patriot [66]

drawing isn't shown, pls take a screenshot or photograph the exercise

5 0
3 years ago
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