Which solution finds the value of x in the triangle below?

A right triangle is shown. The hypotenuse has a length of 8. Another side has a length of x. The angle between the hypotenuse and the other side is 60 degrees.

Kindly find complete question attached below

Answer:

Kindly check explanation

Step-by-step explanation:

Given a normal distribution with ;

Mean = 36

Standard deviation = 4

According to the empirical rule :

68% of the distribution is within 1 standard deviation of the mean ;

That is ; mean ± 1(standard deviation)

68% of subjects :

36 ± 1(4) :

36 - 4 or 36 + 4

Between 32 and 40

2.)

95% of the distribution is within 2 standard deviations of the mean ;

That is ; mean ± 2(standard deviation)

95% of subjects :

36 ± 2(4) :

36 - 8 or 36 + 8

Between 28 and 44

3.)

99% is about 3 standard deviations of the mean :

That is ; mean ± 3(standard deviation)

99% of subjects :

36 ± 3(4) :

36 - 12 or 36 + 12

Between 24 and 48

[tex]V = 864\pi[/tex]

Step-by-step explanation:

Since one of the boundaries is y = 0, we need to find the roots of the function [tex]f(x)=-2x^2+6x+36[/tex]. Using the quadratic equation, we get

[tex]x = \dfrac{-6 \pm \sqrt{36 - (4)(-2)(36)}}{-4}= -3,\:6[/tex]

But since the region is also bounded by [tex]x = 0[/tex], that means that our limits of integration are from [tex]x=0[/tex] (instead of -3) to [tex]x=6[/tex].

Now let's find the volume using the cylindrical shells method. The volume of rotation of the region is given by

[tex]\displaystyle V = \int f(x)2\pi xdx[/tex]

[tex]\:\:\:\:\:\:\:= \displaystyle \int_0^6 (-2x^2+6x+36)(2 \pi x)dx[/tex]

[tex]\:\:\:\:\:\:\:= \displaystyle 2\pi \int_0^6 (-2x^3+6x^2+36x)dx[/tex]

[tex]\:\:\:\:\:\:\:= \displaystyle 2\pi \left(-\frac{1}{2}x^4+2x^3+18x^2 \right)_0^6[/tex]

[tex]\:\:\:\:\:\:\:= 864\pi [/tex]

Answer:

50% i believe

Step-by-step explanation:

because in every scenario theres 2 teams and if they are well matched it be half and half on every game assuming they're the same level of comp

Answer:

108801

Step-by-step explanation:

Palindrome as defined in the given question as a number which reads the same forward and backward. Examples are: 1001, 20202, 1331 etc.

Thus, to determine the smallest 6-digit palindrome divisible by 99 without a remainder, the digits should be in the form of abccba.

Therefore, the smallest 6-digit palindrome that can be divided by 99 is 108801.

So that,

108801 ÷ 99 = 1099

Solution :

Given :

[tex]f(x) = \left\{\begin{matrix}\frac{1}{450}(x^2-x) & \text{if } 6 < x < 12 \\ 0 & \text{otherwise}\end{matrix}\right.[/tex]

1. Cumulative distribution function

[tex]$P(X \leq x) = \int_{- \infty}^x f(x) \ dx$[/tex]

              [tex]$=\int_{- \infty}^6 f(x) dx + \int_{6}^x f(x) dx $[/tex]

             [tex]$=0+\int_6^x \frac{1}{450}(x^2-x) \ dx$[/tex]

             [tex]$=\frac{1}{450} \int_6^x (x^2-x) \ dx$[/tex]

             [tex]$=\frac{1}{450}\left[\frac{x^3}{3}-\frac{x^2}{2}\right]_6^x$[/tex]

             [tex]$=\frac{1}{450}\left[ \left( \frac{x^3}{3} - \frac{x^2}{2}\left) - \left( \frac{6^3}{3} - \frac{6^2}{2} \right) \right] $[/tex]

            [tex]$=\frac{1}{450}\left[\frac{x^3}{3} - \frac{x^2}{2} - 54 \right]$[/tex]

2.  Mean [tex]$E(x) = \int_{- \infty}^{\infty} \ x \ f(x) \ dx$[/tex]

                       [tex]$=\int_{6}^{12}x . \left( \frac{1}{450} \ (x^2-x)\right)\ dx$[/tex]

                     [tex]$=\frac{1}{450} \int_6^{12} \ (x^3 - x^2) \ dx$[/tex]

                     [tex]$=\frac{1}{450} \left[\frac{x^4}{4} - \frac{x^3}{3} \right]_6^{12} \ dx$[/tex]

                     [tex]$=\frac{1}{450} \left[ \left(\frac{(12)^4}{4} - \frac{(12)^3}{3} \right) - \left(\frac{(6)^4}{4} - \frac{(6)^3}{3} \right) $[/tex]

                     [tex]$=\frac{1}{450} [4608 - 252]$[/tex]

                    = 17.2857

Answer:

x < -10

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

Identify

x/-2 > 5

Step 2: Solve for x

[tex]\large {\mathsf {\red{\underbrace {\overbrace{\blue{ {\pink}{Answєr}}}}}}} \: [/tex]

x > - 10

[tex] \large \mathtt \green{Step-by-step \: explanation : }[/tex]

[tex] \small \sf \frac{x}{ - 2} > 5 \\ [/tex]

Solve for x

[tex] \small \sf \frac{x}{ - 2} > 5 \\ [/tex]

common denominator is 2

[tex]\small \sf ➪ \frac{2x}{ - 2} >2 \times 5 \\ [/tex]

[tex]\small \sf ➪ \frac{ \cancel{2}x}{ - \cancel{ 2}} >2 \times 5 \\ [/tex]

➪ - x > 2 × 5

➪ - x > 10

multiply by - 1

➪ - x × - 1 > 10 × - 1

x > - 10

Answer:

C

Step-by-step explanation:

Start by simplifying what you can in each radicalfor example, the

∛(xy⁵)= y∛(xy²)

and

∛(x⁷y¹⁷)=x²y⁵∛(xy²)

So know our equation looks like

y∛(xy²)*x²y⁵∛(xy²)

Now because what's inside the radical is the same we can combine them

y⁶x²∛(xy²)²

distribute the square

so

∛(xy²)²=  ∛(x²y⁴)= y∛(x²y)

and finally,

y⁶x²*y∛(x²y)= y⁷x²∛(x²y)

this is equal to option C

Answer: -9x-1y-9/

Step-by-step explanation:

Answer: b

Step-by-step explanation:

I really dont like edge

Answer:

[tex]\sqrt{49}[/tex]

Step-by-step explanation:

Define a rational number by a number able to expressed a fraction where the denominator is not 0 or 1.

Non-terminating (never-ending) decimals cannot be expressed as a fraction and therefore are irrational. However, recall that [tex]\sqrt{49}=7[/tex], which can be expressed as a fraction (e.g. [tex]\frac{14}{2}[/tex], etc). Thus, the answer is [tex]\boxed{\sqrt{49}}[/tex].

Answer:

(d) 7

Step-by-step explanation:

The total number of subsets that can be derived from a set with n elements is given by;

2ⁿ

Out of these subsets, there is one empty set. Therefore, the total number of non-empty subsets is given by;

2ⁿ - 1

Given:

A = {x, y, z}

Set A has 3 elements. This means that n = 3

Therefore, the total number of subsets that can be derived from set A is

2ⁿ = 2³ = 8

One of these 8 subsets is an empty set, therefore, the total number of non-empty subsets of A is;

2ⁿ - 1 = 2³ - 1

8 - 1 = 7

This can be checked by writing all the possible subsets of A as follows;

∅

{x}

{y}

{z}

{x, y}

{y, z}

{x, z}

{x, y, z}

Removing the empty set ∅, the non-empty subsets of A are;

{x}

{y}

{z}

{x, y}

{y, z}

{x, z}

{x, y, z}

Answer:

53.06°F

Step-by-step explanation:

Given the equation of best fit :

y=-3.32x +97.05.

The average temperature for a month with 13.25 inches of Rainfall

Amount of Rainfall = x

Average temperature = y

To make our prediction ; put x = 13.25 in the equation and solve for y ;

y = -3.32x +97.05

Put x = 13.25

y = -3.32(13.25) +97.05

y = - 43.99 + 97.05

y = 53.06°F

Answer:

15m

Step-by-step explanation:

Use Pythagoras

Folow the steps in the image

Answer:

:] brainlist me friends

The y-intercept is the y value where the blue line crosses the Y axis which is the vertical black line.

The line crosses at the number 4, so the y-intercept is 4

Answer: D. 4

Answer:

D. <S, <R, <T

Step-by-step explanation:

Recall: On a triangle, the bigger an angle measure the longer the side opposite it and vice versa.

In ∆RST,

The longest side, SR = 22, is opposite to <T

Therefore, <T is the biggest angle.

Medium side, ST = 21, is opposite to <R, therefore,

<R is the medium angle measure

The smallest angle measure <S is opposite to the shortest side, RT.

Angels I'm order form the smallest to largest will be:

<S, <R, <T

Answer:

ya the equation divides y as a function of x

Answer:

y - 1 = -6(x - 1)

General Formulas and Concepts:

Algebra I

Point-Slope Form: y - y₁ = m(x - x₁)

Step-by-step explanation:

Step 1: Define

Identify

Point (1, 1)

Slope m = -6

Step 2: Find Equation

9514 1404 393

Answer:

Step-by-step explanation:

There are a couple of relations that are applicable to these questions.

__

The segment lengths relation tells us ...

  10x = 8×7 . . . . . . products of segment lengths are equal

  x = 56/10 = 5.6 . . . . divide by 10

__

The value of y° is the average of the intercepted arcs:

  y° = (85° +45°)/2 = 65°

_____

Additional comment

This diagram does not have enough information to allow computation of z. We would need to know the intercepted arc, or the length of the secant that meets tangent z.

Answer:

6, 15, 24, 33

Step-by-step explanation:

Basically, the number on top of the sigma represents the number of terms total in that sequence, and on the right you have the equation in which you can plug in whichever value that falls into what the top number says to find the output. In other words, just plug in 1 for k to find a1, 2 for k to find a2, etc.

Hope that helps!

Answer:

a. 8.95

b. it is

c. yes it belongs

d. males are 2.574 taller than females on average.

Step-by-step explanation:

GIven the regression outpuit that we have in this question, the value of the t test statistics for the shoe size can be solved as

a. test statistic = 1.164/0.13

t test = 8.95

b. the regression coefficient of shoe size is 1.164, this is statistically significant

c. Yes the variable shoe size does belong to the model.

d. The regression coefficient of gender shows that on the average, while holding other variables constant, males are 2.574 inches taller than the their female counterparts.

Answer:

[tex](a)\ P(White) = \frac{1}{2}[/tex]

(b) 10 additional white balls

(c) 10 additional black balls

Step-by-step explanation:

Given

[tex]White = 5[/tex]

[tex]Black =3[/tex]

[tex]Red = 2[/tex]

Solving (a): P(White)

This is calculated as:

[tex]P(White) = \frac{White}{Total}[/tex]

[tex]P(White) = \frac{5}{5+3+2}[/tex]

[tex]P(White) = \frac{5}{10}[/tex]

[tex]P(White) = \frac{1}{2}[/tex]

Solving (b): Additional white balls, if [tex]P(White) = \frac{3}{4}[/tex]

Let the additional white balls be x

So:

[tex]P(White) = \frac{White+x}{Total+x}[/tex]

This gives:

[tex]\frac{3}{4} = \frac{5+x}{10+x}[/tex]

Cross multiply

[tex]30+3x = 20 + 4x[/tex]

Collect like terms

[tex]4x - 3x = 30 - 20[/tex]

[tex]x = 10[/tex]

Hence, 10 additional white balls must be added

Solving (c): Additional black balls, if [tex]P(White) = \frac{1}{4}[/tex]

Let the additional black balls be x

So:

[tex]P(White) = \frac{White}{Total+x}[/tex]

So, we have:

[tex]\frac{1}{4} = \frac{5}{10+x}[/tex]

Cross multiply

[tex]10+x = 5 * 4[/tex]

[tex]10+x = 20[/tex]

Collect like terms

[tex]x = 20 -10[/tex]

[tex]x = 10[/tex]

Hence, 10 additional black balls must be added

Answer:

C: 44

Step-by-step explanation:

Answer:

gradient = 2

line: y = 2x - 4

Step-by-step explanation:

Find the slope from the slope intercept formula

y = mx + b

b is the y intercept

b = -4 and the point is (0,-4)

So far the equation looks like this.

y = mx - 4

Use the other intercept (x intercept) to find m

x = 2

y = 0

0 = m*2 - 4                Add 4 to both sides

4 = 2m                      Divide by 2

4/2 = m

m = 2

So the gradient or slope is 2

Answer:

))

Step-by-step explanation:

just place your decimal once to the left I think

Answer:

9

Step-by-step explanation:

Answer:

hello there here are your answers:

1) a- 12, 18, 24, 30, 36

2) b- 31

3) a-communitive property of addition

4) a- 6a

Step-by-step explanation:

1: go through all the numbers and add 6 like 12+6=16 etc.

2: the common difference is 4 so 27+4 =31

3: communitive property because you can change the number in any order and still get the same sum

4: 6a because only 24ab has a b in it

Answer:

0.0070 = 0.70% probability that the proportion of smokers in a sample of 664 males would differ from the population proportion by greater than 3%

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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.

Central Limit Theorem

The Central Limit Theorem establishes 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]

A researcher believes that 9% of males smoke cigarettes.

This means that [tex]p = 0.09[/tex]

Sample of 664

This means that [tex]n = 664[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.09[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.09*0.91}{664}} = 0.011[/tex]

What is the probability that the proportion of smokers in a sample of 664 males would differ from the population proportion by greater than 3%?

Proportion below 9 - 3 = 6% or above 9 + 3 = 12%. Since the normal distribution is symmetric, these probabilities are equal, so we find one of them and multiply by 2.

Probability the proportion is below 6%

P-value of Z when X = 0.06. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

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

[tex]Z = \frac{0.06 - 0.09}{0.011}[/tex]

[tex]Z = -2.7[/tex]

[tex]Z = -2.7[/tex] has a p-value of 0.0035

2*0.0035 = 0.0070

0.0070 = 0.70% probability that the proportion of smokers in a sample of 664 males would differ from the population proportion by greater than 3%

Answer:

Step-by-step explanation:

The solution triangle attached below :

Since we have a right angled triangle, we can make use of Pythagoras rule to obtain the vertical distance, x

Recall :

Hypotenus² = opposite² + adjacent²

Hence,

x² = 61² - 60²

x² = 3721 - 3600

x² = 121

x = √121

x = 11

Vertical distance equals 11 inches

Step-by-step explanation:

2nd number = x

1st number = x - 7

5 (x - 7) = 6x + 9

5x - 35 = 6x + 9

- x = 44

x = - 44

1st number = -51

2nd number = -44

Proof: 5 (-51) = 6(-44) + 9

-255 = -264 + 9

-255 = -255

hope it helps.

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