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3 years ago

What Is The Length Of RT?

Mathematics

1 answer:

Ulleksa [173]3 years ago

6 0

Answer:

Step-by-step explanation:

AS is an angle bisector, thus the ratio of the sides of the triangle is equal to the ratio of the corresponding parts of RT, that is

$\frac{SR}{ST}$ = $\frac{RA}{TA}$ , substituting values

$\frac{7.5}{9}$ = $\frac{3.5}{x}$ ( cross- multiply )

7.5x = 31.5 ( divide both sides by 7.5 )

x = 4.2

Thus

RT = 3.5 + x = 3.5 + 4.2 = 7.7 → B

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Brian deposits $7000 into an account that pays simple interest at an annual rate of 3%. He does not make any more deposits. He m

Andre45 [30]

Answer:

A)1050

B)8050

Step-by-step explanation:

to find interest we use the formula A= P(1+rt) where P is the initial investment, r is the rate percent, and t is the time interval

for this question we have A=7000(1+3(5)) which gives 8,050 dollars which is the answer to part B

for part A we simply subtract the answer from B from the initial investment so 8050 - 7000 = 1050 made from interest

4 0

2 years ago

Assortative mating is a nonrandom mating pattern where individuals with similar genotypes and/or phenotypes mate with one anothe

scZoUnD [109]

Answer:

a) P(male=blue or female=blue) = 0.71

b) P(female=blue | male=blue) = 0.68

c) P(female=blue | male=brown) = 0.35

d) P(female=blue | male=green) = 0.31

e) We can conclude that the eye colors of male respondents and their partners are not independent.

Step-by-step explanation:

We are given following information about eye colors of 204 Scandinavian men and their female partners.

Blue Brown Green Total

Blue 78 23 13 114

Brown 19 23 12 54

Green 11 9 16 36

Total 108 55 41 204

a) What is the probability that a randomly chosen male respondent or his partner has blue eyes?

Using the addition rule of probability,

∵ P(A or B) = P(A) + P(B) - P(A and B)

For the given case,

P(male=blue or female=blue) = P(male=blue) + P(female=blue) - P(male=blue and female=blue)

P(male=blue or female=blue) = 114/204 + 108/204 − 78/204

P(male=blue or female=blue) = 0.71

b) What is the probability that a randomly chosen male respondent with blue eyes has a partner with blue eyes?

As per the rule of conditional probability,

P(female=blue | male=blue) = 78/114

P(female=blue | male=blue) = 0.68

c) What is the probability that a randomly chosen male respondent with brown eyes has a partner with blue eyes?

As per the rule of conditional probability,

P(female=blue | male=brown) = 19/54

P(female=blue | male=brown) = 0.35

d) What is the probability of a randomly chosen male respondent with green eyes having a partner with blue eyes?

As per the rule of conditional probability,

P(female=blue | male=green) = 11/36

P(female=blue | male=green) = 0.31

e) Does it appear that the eye colors of male respondents and their partners are independent? Explain

If the following relation holds true then we can conclude that the eye colors of male respondents and their partners are independent.

∵ P(B | A) = P(B)

P(female=blue | male=brown) = P(female=blue)

or alternatively, you can also test

P(female=blue | male=green) = P(female=blue)

P(female=blue | male=blue) = P(female=blue)

But

P(female=blue | male=brown) ≠ P(female=blue)

19/54 ≠ 108/204

0.35 ≠ 0.53

Therefore, we can conclude that the eye colors of male respondents and their partners are not independent.

7 0

3 years ago

½ is the same as 0.5 and the ratio of _____.

Crazy boy [7]

1:2

Similar to the 1/2 fraction, 1:2 is a simplified ratio of a half.

6 0

3 years ago

-4x - 6y = 6<br> 4x + 6y = -4

Sloan [31]

Step-by-step explanation:

$-4x - 6y = 6$

$4x + 6y = -4$

To solve a system of equations, we can add the two equations and solve for one of the remaining variables -- let's try to eliminate the $x$ variable when we add the two equations together.

Right now, there's a $-4x$ term in the first equation, and a $4x$ term in the second equation, so if we add those together, we'll be able to eliminate the $x$ variable altogether and solve for $y$ .

However, when we also have a $-6y$ term in the first equation and $6y$ term in the second equation, so adding these together will also eliminate the $y$ term, leaving a $0$ on the left-hand side of the equation.

If we add the two numbers on the right side of the equation, we get $-2$ , which does not equal $0$ , meaning there are no solutions to this system of equations.

3 0

3 years ago

Read 2 more answers

Raw scores on a certain standardized test one year were normally distributed, with a mean of 156 and a standard deviation of 23.

s344n2d4d5 [400]

Answer:

About 220 of the students scored less than 96

Step-by-step explanation:

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.

Mean of 156 and a standard deviation of 23.

This means that $\mu = 156, \sigma = 23$

Proportion that scored less than 96:

p-value of Z when X = 96. So

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

$Z = \frac{96 - 156}{23}$

$Z = -2.61$

$Z = -2.61$ has a p-value of 0.00453.

About how many of the students scored less than 96?

0.00453 out of 48592.

0.00453*48592 = 220.1.

Rounding to the closest integer:

About 220 of the students scored less than 96

3 0

3 years ago