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2 years ago

Find the value of x. please explain and show your work.

Mathematics

1 answer:

iris [78.8K]2 years ago

3 0

Answer:

Step-by-step explanation:

use Pythagoras theorem

hypothenuse of bottom triangle =√24^2+32^2 = 40

x =√50^2-40^2 = 30

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Factor completely.

Serga [27]

Factor the polynomial:

4u² – 20u + 25

Rewrite – 20u as – 10u – 10u, and then factor it by grouping:

= 4u² – 10u – 10u + 25

= 2u * (2u – 5) – 5 * (2u – 5)

= (2u – 5) * (2u – 5)

= (2u – 5)² <––– this is the answer.

I hope this helps. =)

5 0

3 years ago

In a random sample of males, it was found that 28 write with their left hands and 210 do not. In a random sample of females, it

Drupady [299]

Answer:

a) Null hypothesis: $p_{M} \geq p_{W}$

Alternative hypothesis: $p_{M} < p_{W}$

b) $z=\frac{0.118-0.125}{\sqrt{0.122(1-0.122)(\frac{1}{238}+\frac{1}{497})}}=-0.271$

c) $p_v =P(Z$

d) If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the the proportion of men that write with their left hand is NOT significant lower than the proportion of female that write with their left hand

Step-by-step explanation:

1) Data given and notation

$X_{M}=28$ represent the number of men that write with their left hand

$X_{W}=62$ represent the number of women that write with their left hand

$n_{M}=210+28=238$ sample of male selected

$n_{W}=62+435=497$ sample of female selected

$p_{M}=\frac{28}{238}=0.118$ represent the proportion of men that write with their left hand

$p_{W}=\frac{62}{497}=0.125$ represent the proportion of women that write with their left hand

$\alpha=0.05$ represent the significance level

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to check if the rate of left-handedness among males is less than that among females , the system of hypothesis would be:

Null hypothesis: $p_{M} \geq p_{W}$

Alternative hypothesis: $p_{M} < p_{W}$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{M}-p_{W}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{M}}+\frac{1}{n_{W}})}}$ (1)

Where $\hat p=\frac{X_{M}+X_{W}}{n_{M}+n_{W}}=\frac{28+62}{238+497}=0.122$

3) Calculate the statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.118-0.125}{\sqrt{0.122(1-0.122)(\frac{1}{238}+\frac{1}{497})}}=-0.271$

4) Statistical decision

We have a significance level provided $\alpha=0.05$ , and now we can calculate the p value for this test.

Since is a one left side test the p value would be:

$p_v =P(Z$

If we compare the p value and the significance level given $\alpha=0.05, 0,1,0.15$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the the proportion of men that write with their left hand is NOT significant loer than the proportion of female that write with their left hand .

6 0

2 years ago

What is the equation of the line perpendicular to 3x+y=6 that passes through the point (0,8)

Alekssandra [29.7K]

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$3x + y = 6$

$y = - 3x + 6$

The coefficient of x is the slope of the line , So the slope of the above equation is -3 .

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

Remember from now on ,

Product of multiplying the slopes of two lines which are perpendicular to each other , is -1 .

Thus ;

$( - 3) \times (m) = - 1$

m is the slope of the line which we want.

$- 3m = - 1$

Negatives simplifies

$3m = 1$

Divide sides by 3

$\frac{3m}{3} = \frac{1}{3} \\$

$m = \frac{1}{3} \\$

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

We have following equation to find the point-slope form of the linear functions :

$y - y(0) = m(x - x(0))$

x(0) and y(0) are the coordinates of the point which the line passed through.

$y - 8 = \frac{1}{3} (x - 0) \\$

$y - 8 = \frac{1}{3} x \\$

Add sides 8

$y = \frac{1}{3} x + 8 \\$

Done....

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

6 0

2 years ago

Consider the sequence of numbers: 3/8, 3/4, 1 /18, 1 1/2, 1 7/8

vredina [299]

Question:

Consider the sequence of numbers: $\frac{3}{8}, \frac{3}{4}, 1\frac{1}{8}, 1\frac{1}{2}, 1\frac{7}{8}$

Which statement is a description of the sequence?

(A) The sequence is recursive, where each term is 1/4 greater than its preceding term.

(B) The sequence is recursive and can be represented by the function

f(n + 1) = f(n) + 3/8 .

(D) The sequence is arithmetic and can be represented by the function

f(n + 1) = f(n)3/8.

Answer:

Option B:

The sequence is recursive and can be represented by the function

$f(n + 1) = f(n) + \frac{3}{8} .$

Explanation:

A sequence of numbers are

$\frac{3}{8}, \frac{3}{4}, 1\frac{1}{8}, 1\frac{1}{2}, 1\frac{7}{8}$

Let us first change mixed fraction into improper fraction.

$\frac{3}{8}, \frac{3}{4}, \frac{9}{8}, \frac{3}{2}, \frac{15}{8}$

To find the pattern of the sequence.

To find the common difference between the sequence of numbers.

$\frac{3}{4}-\frac{3}{8}=\frac{6}{8}-\frac{3}{8}= \frac{3}{8}$

$\frac{9}{8}-\frac{3}{4}=\frac{9}{8}-\frac{6}{8}= \frac{3}{8}$

$\frac{3}{2}-\frac{9}{8}=\frac{12}{8}-\frac{9}{8}= \frac{3}{8}$

$\frac{15}{8}-\frac{3}{2}=\frac{15}{8}-\frac{12}{8}= \frac{3}{8}$

Therefore, the common difference of the sequence is 3.

That means each term is obtained by adding $\frac{3}{8}$ to the previous term.

Hence, the sequence is recursive and can be represented by the function $f(n + 1) = f(n) + \frac{3}{8} .$

3 0

2 years ago

Caleb made a scale drawing of a neighborhood park. The scale of the drawing was

WITCHER [35]

Answer:

2:1 =36mm: x m

2/1 = 36mm/ m......(Criss cross)

36mm x 1M/2mm = 18 Meter

5 0

3 years ago