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1 year ago

Explain how complex fractions can be used to solve problems involving ratios

1 answer:

8 0

When you have ratios and some unknowns you can create complex fractions from them.Bring them to the same denominator and solve for X.

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Find the indicated values: <br> Given: OA=AC=2<br> AB is a tangent line<br> Find: AB

nlexa [21]

Step-by-step explanation:

OA=AC=OC=2 (equal triangle)

which means angle O =60 degree

tan 60 = AB / 2

AB = 2 tan 60 =

$2 \sqrt{3}$

3 0

1 year ago

A local cable company claims that the proportion of people who have Internet access is less than 63%. To test this claim, a rand

MaRussiya [10]

Answer:

Step-by-step explanation:

For the null hypothesis,

H0 : p = 0.63

For the alternative hypothesis,

Ha : p < 0.63

This is a left tailed test

Considering the population proportion, probability of success, p = 0.63

q = probability of failure = 1 - p

q = 1 - 0.63 = 0.37

Considering the sample,

Sample proportion, P = x/n

Where

x = number of success = 478

n = number of samples = 800

P = 478/800 = 0.6

We would determine the test statistic which is the z score

z = (P - p)/√pq/n

z = (0.6 - 0.63)/√(0.63 × 0.37)/800 = - 1.76

From the normal distribution table, the area below the test z score in the left tail 0.039

Thus

p = 0.039

7 0

1 year ago

What is the value of b and the missing symbol in Jamilla’s inequality?

Sindrei [870]

Answer:

$b=1, \geq$

Step-by-step explanation:

we know that

The absolute value function has two solutions

Observing the graph

the solutions are

$x\geq 1$ and $x\leq -3$

First solution (case positive)

assume the symbol of the first solution and then compare the results

$\left|x+b\right|\ge2$

$(x+b)\ge2$

$x\ge2-b$

$2-b=1\\b=2-1\\ b=1$

Second solution (case negative)

$-(x+b)\ge2$

Multiply by -1 both sides

$(x+b)\leq-2$

substitute the value of b and compare the results

$(x+1)\leq-2$

$x\leq-2-1$

$x\leq-3$ -------> is correct

4 0

2 years ago

Read 2 more answers

According to a human modeling project, the distribution of foot lengths of women is approximately Normal with a mean of 23.3 ce

Yakvenalex [24]

Answer:

26.11% of women in the United States will wear a size 6 or smaller

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 23.3, \sigma = 1.4$

In the United States, a woman's shoe size of 6 fits feet that are 22.4 centimeters long. What percentage of women in the United States will wear a size 6 or smaller?

This is the pvalue of Z when X = 22.4. So

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

$Z = \frac{22.4 - 23.3}{1.4}$

$Z = -0.64$

$Z = -0.64$ has a pvalue of 0.2611

26.11% of women in the United States will wear a size 6 or smaller

8 0

2 years ago

△ABC has vertices A(−1, 6), B(2, 10), and C(7, −2) . Find the measure of each angle of the triangle. Round decimal answers to th

kolbaska11 [484]

Answer:

<A = 90°, <B = 71.6° <C = 18.4°

Step-by-step explanation:

Given the vertices of a △ABC to be A(−1, 6), B(2, 10), and C(7, −2)

Before we can get each angle of the triangle, we need to get its sides first.

Using the formula fie finding the distance between two points

D = √(x2-x1)²+(y2-y1)²

For side AB:

Given A(−1, 6), B(2, 10)

AB = √{2-(-1)}²+(10-6)²

AB =√3²+4²

AB = √25

AB = 5

For side AC:

Given A(-1,6) and C(7, −2)

AC = √{7-(-1)}²+(-2-6)²

AC = √8²+8²

AC = √128

AC = √64×2

AC = 8√2

For side BC:

Given B(2,10) and C(7, −2)

BC = √(7-2)²+(-2-10)²

BC = √5²+12²

BC = √25+144

BC = √169

BC = 13

First we need to get theta using cosine rule

|AC|² = |AB|+|BC| - 2|AB||AC| cos theta

(8√2)² = 5²+13²-2(5)(13)cos theta

128 = 169-130costheta

128-169 = -130costheta

-41= -130costheta

Costheta = -41/-130

Cos theta = 0.315

theta = arccos 0.315

theta = 71.64°

<B = 71.6°

Using sine rule to get <A,

BC/sin A = AC/sinB

13/sinA = 8√2/sin71.6°

8√2sinA = 13sin71.6°

SinA = 12.34/8√2

SinA = 1.09°

A = arcsin1

<A = 90.0°

<C = 180°-(71.6+90)

< C = 180-161.6

<C = 18.4°

3 0

2 years ago