A right triangle has a hypotenuse of 15 cm. What is the length for the missing leg if one of the two legs of the triangle is 5?

Answer:

B. Z= -2.55

Step-by-step explanation:

To solve this question, first we need to understand the central limit theroem and subtraction of normal variables.

Central Limit Theorem

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

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

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction of normal variables:

When two normal variables are subtracted, the mean is the subtraction of the means while the standard deviation is the square root of the sum of the variances.

11 of 50 men believe that sexual discrimination is a problem:

This means that:

[tex]p_M = \frac{11}{50} = 0.22, s_M = \sqrt{\frac{0.22*0.78}{50}} = 0.0586[/tex]

19 of 40 women believe that sexual discrimination is a problem:

This means what:

[tex]p_W = \frac{19}{40} = 0.475,  s_W = \sqrt{\frac{0.475*0.525}{40}} = 0.079[/tex]

Difference between the proportion of men and women:

[tex]p_D = p_M - p_W = 0.22 - 0.475 = -0.255[/tex]

[tex]s_D = \sqrt{s_M^2+s_W^2} = \sqrt{0.0586^2+0.079^2} = 0.0984[/tex]

A powerful women's group has claimed that men and women differ in attitudes about sexual discrimination.

This means that the null hypothesis is that they do not differ, than is, the difference is 0. So

[tex]H_0: p_D = 0[/tex]

At the alternate hypothesis, we test that they differ, that is, the difference is different of 0. So

[tex]H_a: p_D \neq 0[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{s}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis and s is the standard error.

0 is tested at the null hypothesis:

This means that [tex]\mu = 0[/tex]

For the sample, we calculated that:

[tex]X = -0.255, s = 0.0984[/tex]

The value of the test-statistic is:

[tex]z = \frac{X - \mu}{s}[/tex]

[tex]z = \frac{-0.255 - 0}{0.0984}[/tex]

[tex]z = -2.59[/tex]

Closes answer is Z = -2.55, option B.

Answer:

Step-by-step explanation:

Use SOH CAH TOA to recall how the trig functions fit on a triangle

SOH: Sin(Ф)= Opp / Hyp

CAH: Cos(Ф)= Adj / Hyp

TOA: Tan(Ф) = Opp / Adj

Let's use CAH  1st  , on the Lenovo building,  b/c we  have they Hypotenuse (Hyp)  and an angle and we want to know the other side of the Lenovo building

Cos(30) = x/294

294*Cos(30) = x

254.611 = x

Sin(30) = y / 294

294*Sin(30) = y

147 = y

perimeter = 147+254.611+294

perimeter Lenovo = 695.611 feet

For Asus building

hyp = sqrt [ ( 144.5*[tex]\sqrt{2}[/tex])^2 +  144.5*[tex]\sqrt{2}[/tex])^2 )]

hyp = 289

perimeter = 289+144.5*[tex]\sqrt{2}[/tex]+144.5*[tex]\sqrt{2}[/tex]

perimeter Asus = 697.7077

The difference of the two buildings is

697.7077 -  695.611 =2.09671 feet

the difference is 2.10 feet ( rounded to nearest 100th)

Answer:45

Step-by-step explanation:

The value of x by the given data is 190/3 or 63.33

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We are given that;

The angles between the lines

Now,

To find the value of x, you need to use the fact that the sum of angles in a triangle is equal to 180°1. This means that:

30° + (3x)° + (-40)° = 180°

Simplifying, we get:

(3x)° - 10° = 180°

Adding 10° to both sides, we get:

(3x)° = 190°

Dividing both sides by 3, we get:

x = 190/3

Therefore, by algebra the answer will be 190/3 or 63.33.

More about the Algebra link is given below.

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The volume in cubic inches of the prism is 528 cubic inches.

Volume is defined as the space occupied by any object in the three-Dimensions. All three parameters are required for the volume like length, width and height of the Cuboid.

The volume is calculated as:-

V = L  x  W  x  H

V = 6  x  11  x   8  

V = 528 cubic inches

Therefore the volume in cubic inches of the prism is 528 cubic inches.

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Answer:

The third graph

Step-by-step explanation:

y intecepts at (0, 4) and (0, 12)

the slopes are up 1 over 3 and up 3 over 1

Answer:

1,500.00

Step-by-step explanation:

Assuming 52 weeks in a year, you would make $1,500.00 per week.

Answer:

$1500

Step-by-step explanation:

Here, the question asks what hector's income per week is.

- Keep in mind that if you are asked what something is per unit, you will most likely need to divide. Example: This problem. See below for answer and explanation.

- If a question asks what something is of  a unit, you will most likely need to multiply. Example: 1/4 of a pizza with 4 slices (1 slice). To solve this, you will have to multiply 1/4 to 4. But never mind this, let's focus at this problem.

The bullet points above essentially explain what you have to do here. To find Hector's income, you have to do 78000/52. The answer to this is 1,500 ($1500).

I hope this helped :)

Answer:

x^2 +7

Step-by-step explanation:

1/2×(x+7)(2x)

2x^2 + 14x/2

2(x^2+7)/2

=x^2 +7

Answer:

The answer would be C. It is 6% higher than the theoretical probability.

Answer:

The correct answer is C. It is 6% higher than the theoretical probability.

Step-by-step explanation:

This is correct, I took the test.

Answer:

Step-by-step explanation:

first term (a) = 4

last term (b) = 9

Arithmetic mean (AM)

= ( a + b) / 2

= ( 4 + 9 ) / 2

= 13/2

= 6.5

Geometric mean (GM)

= √a *b

=√4 * 9

=√36

= 6

hope it helps :)

Answer:

A, B, and E are the correct options.

Step-by-step explanation:

You can see by the table shown, 12+25 people biked (37). The total of people that were surveyed would be 55 (the bottom right of the graph). Twelve people run but don't bike (down the first column to the left). Just follow the graph and you've got your answers!

Answer:

y+4=2(x-4)

Step-by-step explanation:

y-y1=m(x-x1)

y-(-4)=2(x-4)

y+4=2(x-4)   point slope form

Answer:

Sorry about last time I didnt answer correct hopefully you can forgive me but this one I know 100% its C hope that helps.

Answer:

45

Step-by-step explanation:

1/2×9×10

since the formula says half base times height, so therefore

Area =45

Answer:

384

Step-by-step explanation:

I just went to my calculator and did 24×16 and I got 384

Step-by-step explanation:

(o, -2) is the correct answer because in -90°

P [x,y] =P' [y,-x ]

hope it is helpful to you

Answer:

31.5 units.

Step-by-step explanation:

Area = BC * distance from BC extended to A/2

A to BC extended and the line is vertical from A to BC extended = 7+2 units

A to BC extended and the line is vertical from A to BC extended = 9 units This becomes the height

h = 9 units

BC = 7 units

Area  = 1/2 * h * BC

Area = 1/2 * 9 * 7

Area = 1/2 * 63

Area = 31.5

Answer:

D

Step-by-step explanation:

6(g + 4)

we distribute the 6 to the terms in the parenthesis.

(6 × g) + (6 × 4)

(6g) + (24)

6g + 24

Answer:

one million eight hundred ninety-six thousand twenty-five

The approximate measure of angle Q will be 93.2°. Then the correct option is B.

Let there is a triangle ABC such that |AB| = a units, |AC| = b units, and |BC| = c units and the internal angle A is of θ degrees, then we have:

a² + b² – 2ab cos C = c²

In a triangle QRS, the length of QR is 21, the length of RS is 32, and the length of SQ is 23.

Then the approximate measure of angle Q will be given as,

RQ² + SQ² – 2 × SQ × RQ × cos Q = RS²

    21² + 23² – 2 × 23 × 21 × cos Q = 32²

                 441 + 529 – 966 cos Q = 1024

                           970 – 966 cos Q = 1024

                                      966 cos Q = – 54

                                              cos Q = – 54 / 966

                                              cos Q = – 0.0559

                                                     Q = 93.2°

The approximate measure of angle Q will be 93.2°.

Then the correct option is B.

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Yes, 23 has an inverse mod 1000 because gcd(23, 1000) = 1 (i.e. they are coprime).

Let x be the inverse. Then x is such that

23x ≡ 1 (mod 1000)

Use the Euclidean algorithm to solve for x :

1000 = 43×23 + 11

23 = 2×11 + 1

→   1 ≡ 23 - 2×11   (mod 1000)

→   1 ≡ 23 - 2×(1000 - 43×23)   (mod 1000)

→   1 ≡ 23 - 2×1000 + 86×23   (mod 1000)

→   1 ≡ 87×23 - 2×1000 ≡ 87×23   (mod 1000)

→   23⁻¹ ≡ 87   (mod 1000)

Answer:

in all about 70

Step-by-step explanation:

Step-by-step explanation:

math is all about repetition. the more you do it and use it, the easier it gets. but burning yourself out by putting in to much time is no good either.

there is not a one sized fits all answer, do what's best for you.

Answer:

I'd say 20 minutes to 4 hours, but it really depends on what you're learning. For example, if you're having trouble with a math subject, you may want to divide it in half and practice a little each day.

Step-by-step explanation:

Answer:

3:6

3x2=6

Scale factor = 2

Step-by-step explanation:

Answer:

A  

Step-by-step explanation:

x = -3 goes straight through -3, 7 vertically