Find the probability of each event. A class has five boys and nine girls. If the teacher randomly picks six students, what is the probability that he will pick exactly four girls?

Answer:

3 and 8

Step-by-step explanation:

Given the proportion:

[tex] \frac{3}{4} = \frac{6}{8}[/tex]

Required:

Find the extreme values.

When given an equation like the one we have here, there is always a very easy way to find the extreme value.

First make rewrite to a ratio form:

Example:

a:b = c:d

Just know that extreme values are the values on the outside of the ratio(a & d)

Therefore,

3:4 = 6:8

When it is written this way extreme values are 3 & 8

Extreme values = 3 and 8

Answer:

[tex]\boxed{Area\ of\ sector = 141.4\ cm^2}[/tex]

Step-by-step explanation:

Radius = r = 9 cm

Angle = θ = 200° = 3.5 radians

Now,

[tex]Area \ of \ sector = \frac{1}{2} r^2 \theta[/tex]

Area = 1/2 (9)²(3.5)

Area = 1/2 (81)(3.5)

Area = 282.7 / 2

Area of sector = 141.4 cm²

Answer:

45 pi cm^2 or 141.3 cm^2

Step-by-step explanation:

First find the area of the circle

A = pi r^2

A = pi (9)^2

A = 81 pi

A circle has 360 degrees

The shaded part has 200

The fraction that is shaded is

200/360 =5/9

Multiply by the total area

5/9 * 81 pi

45 pi

Using 3.14 for pi

141.3

45 pi cm^2 or 141.3 cm^2

Answer:

[tex]\dfrac{21}{10}\text{ km}[/tex].

Step-by-step explanation:

It is given that,

Area of rectangular plot [tex]=\dfrac{7}{10}\text{ km}^2[/tex]

Width of rectangular plot [tex]=\dfrac{1}{3}\text{ km}[/tex]

We need to find the length of the parking lot.

We know that,

[tex]\text{Area of rectangle}=length\times width[/tex]

[tex]\dfrac{7}{10}=length\times \dfrac{1}{3}[/tex]

[tex]\dfrac{7\times 3}{10}=length[/tex]

[tex]length=\dfrac{21}{10}[/tex]

Therefore, length of the parking lot is [tex]\dfrac{21}{10}\text{ km}[/tex].

Answer:

Step-by-step explanation:

Assuming the colon between 40 and 8 is a mistype...

PEMDAS(Parenthesis, Exponents, Multiplication + Division, Addition + Subtraction)

[tex]40-8+3^2+(15-7)*2\\\\Parenthesis\\\\40-8+3^2+8*2\\\\Exponents\\\\40-8+9+8*2\\\\Multiplication\\\\40-8+9+16\\\\Subtraction\\\\32+9+16\\\\Addition\\\\41+16\\\\Addition\\\\57[/tex]

Hope it helps <3

━━━━━━━☆☆━━━━━━━

▹ Answer

57

▹ Step-by-Step Explanation

You need to follow PEMDAS:

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

40 - 8 + 3² + (15 - 7)* 2

40 - 8 + 9 + (15 - 7) * 2

40 - 8 + 9 + 8 * 2

40 - 8 + 9 + 16

= 57

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

1 3/8

Step-by-step explanation:

Well to find the average or the mean we need to add all the numbers,

3/8 + 2/4 + 5/8 + 7/8 + 1 1/8 + 1 5/8 + 1 7/8 + 4

= 11

Then we divide t by the number of numbers in the set.

11 ÷ 8 = 1 3/8

Thus,

the average in the set is 1 3/8.

Hope this helps :)

Answer:

84π mm^2

Step-by-step explanation:

formula for circumference is 2πr where r is the radius of circle

Given,The circumference of the base of a cylinder is 24π mm

Thus,

2πr= 24π mm

=> r = 24π mm/2π = 12 mm

________________________________________

A similar cylinder has a base with circumference of 60π mm.

radius for this cylinder will be

2πr= 60π mm

r =   60π mm/2π = 30mm

______________________________________________

Given

The lateral area of the larger cylinder is 210π mm2

lateral area of cylinder is given by  2πrl

where l is the length of cylinder

thus,

r for larger cylinder = 30mm

2π*30*l  = 210π mm^2

=> l = 210π mm^2/2π*30 = 3.5 mm

___________________________________________

the lateral area of the smaller cylinder

r = 12 mm

l = 3.5 mm as both larger and smaller cylinder are same

2πrl  =  2π*12*3.5 mm^2 = 84π mm^2 answer

Answer:

33.6pi mm2 is the correct answer

edge 2021

Step-by-step explanation:

The circumference of the base of a cylinder is 24π mm. A similar cylinder has a base with circumference of 60π mm. The lateral area of the larger cylinder is 210π mm2.

What is the lateral area of the smaller cylinder?

17.1π mm2

33.6π mm2

60π mm2

84π mm2

Answer:

Problem 1: We conclude that less than or equal to 50% of adult Americans without a high school diploma are worried about having enough saved for retirement.

Problem 2: We conclude that the volume of Google stock has changed.

Step-by-step explanation:

Problem 1:

We are given that in a recent survey conducted by Pew Research, it was found that 156 of 295 adult Americans without a high school diploma were worried about having enough saved for retirement.

Let p = proportion of adult Americans without a high school diploma who are worried about having enough saved for retirement

So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\leq[/tex] 50%    {means that less than or equal to 50% of adult Americans without a high school diploma are worried about having enough saved for retirement}

Alternate Hypothesis, [tex]H_A[/tex] : p > 50%     {means that a majority of adult Americans without a high school diploma are worried about having enough saved for retirement}

This is a right-tailed test.

The test statistics that would be used here is One-sample z-test for proportions;

                       T.S.  =  [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of adult Americans who were worried about having enough saved for retirement = [tex]\frac{156}{295}[/tex] = 0.53

           n = sample of adult Americans = 295

So, the test statistics =  [tex]\frac{0.53-0.50}{\sqrt{\frac{0.50(1-0.50)}{295} } }[/tex]

                                    =  1.03

The value of z-test statistics is 1.03.

Also, the P-value of the test statistics is given by;

              P-value = P(Z > 1.03) = 1 - P(Z [tex]\leq[/tex] 1.03)

                           = 1 - 0.8485 = 0.1515

Now, at a 0.05 level of significance, the z table gives a critical value of 1.645 for the right-tailed test.

Since the value of our test statistics is less than the critical value of z as 1.03 < 1.645, so we insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that less than or equal to 50% of adult Americans without a high school diploma are worried about having enough saved for retirement.

Problem 2:

We are given that a random sample of 35 trading days in 2014 resulted in a  sample mean of 3.28 million shares with a standard deviation of 1.68 million shares.

Let [tex]\mu[/tex] = mean daily volume in Google stock

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 5.44 million shares    {means that the volume of Google stock has not changed}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 5.44 million shares     {means that the volume of Google stock has changed}

This is a two-tailed test.

The test statistics that would be used here is One-sample t-test statistics because we don't know about the population standard deviation;

                       T.S.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean volume in Google stock = 3.28 million shares

            s = sample standard deviation = 1.68 million shares

           n = sample of trading days = 35

So, the test statistics =  [tex]\frac{3.28-5.44}{\frac{1.68}{\sqrt{35} } }[/tex]  ~ [tex]t_3_4[/tex]

                                    =  -7.606

The value of t-test statistics is -7.606.

Also, the P-value of the test statistics is given by;

              P-value = P([tex]t_3_4[/tex] < -7.606) = Less than 0.05%

Now, at a 0.05 level of significance, the t table gives a critical value of -2.032 and 2.032 at 34 degrees of freedom for the two-tailed test.

Since the value of our test statistics doesn't lie within the range of critical values of t, so we sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the volume of Google stock has changed.

Answer:

[tex]120^o,\,120^o,\,60^o,\,\,\,and\,\,\,60^o[/tex]

which agrees with the first answer in the list of possible options.

Step-by-step explanation:

We can use the fact that the addition of all four internal angles of a quadrilateral must render [tex]360^o[/tex]. Then we can create the following equation and solve for the unknown "h":

[tex]2h+2h+h+h = 360^o\\6h=360^o\\h=60^o[/tex]

Therefore the angles of this quadrilateral are:

[tex]120^o,\,120^o,\,60^o,\,\,\,and\,\,\,60^o[/tex]

Answer:60,60,120,120

Step-by-step explanation:All qualdrilaterals equal to 360, so if you add all of the different numbers you should get 360

Stokes' theorem equates the surface integral of the curl of F to the line integral of F along the boundary of the hemisphere. The boundary itself is a circle C (the intersection of the hemisphere with the plane y = 0) with equation

[tex]x^2+z^2=16[/tex]

Parameterize this circle by

[tex]\mathbf r(t)=4\cos t\,\mathbf i+4\sin t\,\mathbf k[/tex]

with [tex]0\le t\le2\pi[/tex].

The surface is oriented such that its normal vector points in the positive y direction, which corresponds to the curve having counterclockwise orientation. The parameterization we're using here already takes this into account.

Now compute the line integral of F along C :

[tex]\displaystyle\iint_S\mathrm{curl}\mathbf F(x,y,z)\cdot\mathrm d\mathbf S=\int_C\mathbf F(x,y,z)\cdot\mathrm d\mathbf r[/tex]

[tex]=\displaystyle\int_0^{2\pi}\mathbf F(4\cos t,0,4\sin t)\cdot\frac{\mathrm d\mathbf r}{\mathrm dt}\,\mathrm dt[/tex]

[tex]=\displaystyle\int_0^{2\pi}(4\sin t\,\mathbf i+4\cos t\,\mathbf j)\cdot(-4\sin t\,\mathbf i+4\cos t\,\mathbf k)\,\mathrm dt[/tex]

[tex]=\displaystyle\int_0^{2\pi}-16\sin^2t\,\mathrm dt[/tex]

[tex]=-8\displaystyle\int_0^{2\pi}(1-\cos(2t))\,\mathrm dt=\boxed{-16\pi}[/tex]

Line integral of F along C is,

[tex]\rm \int \int_S curl F(x,y,z) dS = -16\pi[/tex]

Step-by-step explanation:

Given :

Hemisphere -   [tex]x^2 +y^2+z^2=16[/tex]

Calculation :

Accordind to Stoke's theorem the surface integral of the curl of F to the line integral of F along the boundary of the hemisphere. The boundary itself is a circle C (the intersection of the hemisphere with the plane y = 0) with equation

[tex]x^2+z^2=16[/tex]

then parameterize the circle,

[tex]\rm r(t) = 4 cos(t) \;\hat{i} + 4 sin(t)\;(\hat{k})[/tex]

with , [tex]0\leq t\leq 2\pi[/tex]

Line integral of F along C is,

[tex]\rm \int \int_S curl F(x,y,z) dS = \int_{C}^{} F(x,y,z) \;dr[/tex]

[tex]= \int_{0}^{2\pi} F(4cos(t),0,4sin(t)) \;\dfrac{dr}{dt}.dt[/tex]

[tex]= \int_{0}^{2\pi}(4sin(t)i+4cos(t) j).(-4sin(t)i+4cos(t)k) \;dt[/tex]

[tex]= \int_{0}^{2\pi} -16sin^2tdt[/tex]

[tex]=-8 \int_{0}^{2\pi} (1-cos(2t))dt[/tex]

[tex]= -16\pi[/tex]

For more information, refer the link given below

https://brainly.com/question/8130922?referrer=searchResults

Answer:

Step-by-step explanation:

We assume you are not interested in five infinite sets of translations. Rather, we assume you want to pick 5 translations from the infinite set of possibilities.

The attached graph shows f(x), g(x), and 5 lines (dashed or dotted) that represent possible reflections and shifts of the function f(x).

The function f1 represents a reflection of f(x) about the x-axis, followed by a left-shift of 6 units. To make it match g(x), we need to shift it upward 4 units. Then the set if translations is ...

  g(x) = f(x) ... {reflected over the x-axis, shifted left 6, shifted up 4}

Along the same lines, other possibilities are ...

  g(x) = f(x) ... {reflected over the x-axis, shifted left 3, shifted up 3}

  g(x) = f(x) ... {reflected over the x-axis, shifted left 0, shifted up 2}

  g(x) = f(x) ... {reflected over the x-axis, shifted right 3, shifted up 1}

  g(x) = f(x) ... {reflected over the x-axis, shifted right 9, shifted down 1}

___

Additional comment

All of the transformations listed above use reflection in the x-axis. Reflection could use the y-axis, as well. Reflection of the basic function f(x) in the y-axis will have the identical effect as reflection in the x-axis. The listed translations would apply unchanged.

Answer:

The correct answer for the best line of fit is C: y = 1/3x+12

Step-by-step explanation:

So our goal here is to find the best equation that matches the line of fit.

So right away we can already eliminate two of the options because in the scatter point it shows that the starting y-intercept is 12 and two of the options have a y-intercept of 15. So we are able to tell that Option B and Option D isn't the equation for the lien of fit.

Now we are left with Option A and Option C, which both have a y-intercept of 12. To find the right equation that best matches the line of fit we look at the slope. Option A has a slope of 3x while Option C has a slope of 1/3x, to tell what slope the line of has we applied both option's slope and see which one matches it.

When we match Option A's slope which is 3x it doesn't match because a slope of 3x is going first going up the y-axis 3 times then moving through the x-axis 1 time. Which would had made the line of fit more steep.

Next we match Option C's slope which is 1/3x this slope matches the line of fit because in the scatter plot it clearly shows  it going up 1 time on the y=axis and 3 times through the x-axis. Which made the line of fit not that steep.

So the correct answer to this question is C:  y = 1/3x+12.

Here a picture of the line of fit if it has a slope of 3x.

Answer:

correct answer  C: y = 1/3x+12

Step-by-step explanation:

i just did the problem

Answer:

y=9x

Step-by-step explanation:

rise over run the rise is the y=9 and run is x=1.

9/1=9x

Answer:

Option (D)

Step-by-step explanation:

Zero of any function is defined by the x-value of the function when y = 0.

Let the equation of the line given in the graph is,

y = mx + b

where m = slope of the line

b = y-intercept of the line

Slope of a line passing through [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is defined by the formula,

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

If the passes through (0, -3) and (-2, 0)

m = [tex]\frac{-3-0}{0+2}[/tex]

m = [tex]-\frac{3}{2}[/tex]

Fro the graph,

y-intercept 'b' = -3

Therefore, equation of the line is,

[tex]y=-\frac{3}{2}x-3[/tex]

For y = 0,

[tex]0=-\frac{3}{2}x-3[/tex]

[tex]\frac{3}{2}x=-3[/tex]

x = -2

Therefore, option (D) will be the answer.

Answer:

d- -2

Step-by-step explanation:

Answer:

A. 1.812

B. 1.753

C. 2.602

D. 3.747

E. 2.069

F. 2.453

Step-by-step explanation:

A. 95% confidence level, the level of significance = 5% or 0.05

Using t-table, the critical value for a lower or an upper confidence bound at 0.05 significance level with 10 degrees of freedom = 1.182

B. 95% confidence interval = 0.05 level of significance

Using t-table, the critical value for a lower or an upper confidence bound at 0.05 significance level with 15 degrees of freedom = 1.753

C. 99% confidence interval = 0.01 level of significance

Using t-table, the critical value for a lower or an upper confidence bound at 0.01 significance level with 15 degrees of freedom = 2.602

D. 99% confidence interval = 0.01 level of significance; DF (n - 1) = 5- 1 = 4

Using t-table, the critical value for a lower or an upper confidence bound at 0.01 significance level with 4 degrees of freedom = 3.747

E. 98% confidence interval = 0.02 level of significance

Using t-table, the critical value for a lower or an upper confidence bound at 0.02 significance level with 23 degrees of freedom = 2.069

F. 99% confidence interval = 0.01 level of significance; df (n - 1) = 32 - 1 = 31

Using t-table, the critical value for a lower or an upper confidence bound at 0.01 significance level with 31 degrees of freedom = 2.453

Answer:

2/7

Step-by-step explanation:

Joseph bought a cheese and cut it into 7 equal pieces, so the denominator is 7.

Saved 5 pieces for cooking.

Gave 2 pieces to Omar.

Hope this helps :) ❤❤❤

Answer:

Step-by-step explanation:

if he gives to Omar 2 pieces of 7

2/7 = 28.57% for Omar rest of is for himself

hii

Step-by-step explanation:

length-10x

width-x

perimeter-2(l+b)

66=2(10x+x)

66-2=10x+x

64=11x

x=11/64

lenght-11

width-64

Answer:

Step-by-step explanation:

3(−2a - 4)+3a

=-6a - 12 +3a

A: -6a - 12 +3a

[tex]hope \: this \: helps[/tex]

Answer:

the answer is A

Step-by-step explanation:

you have to distribute the number 3 throughout the parentheses so (3*-2a-3*4)+3a = -6a-12+3a

Answer:

clearly the value of the test statistics shows that there are no enough evidence to support the claim that the proportion of the grads are the same.

Step-by-step explanation:

lets prove the statement by counter example, where if we have found the statement to be false for one then we conclude that it is false for all.

first lets explain what proportion is all about; proportion can be explained as the numerical relationship that compares things together.

in particular lets take grade A proportional to grade B which implies that 18:20

clearly if we observe here grade A is not same proportion with grade B. hence we conclude that there are no enough evidence to support the professor's claim.

Answer:

0

Step-by-step explanation:

Solution:-

We are given two functions as follows:

                      [tex]f ( x ) = x^2 - 15\\\\g ( x ) = 2x[/tex]

We need to determine the composite function defined as ( g - f ) ( x ). To determine this function we need to make sure that both function exist for all real positive value of x.

The function f ( x ) is a quadratic function which has real values for all values of x. Similarly, function g ( x ) is a linear line that starts from the origin. Hence, both functions are defined over the domain ( -∞, ∞ )

We will perform arithmetic operation of subtracting function f ( x ) from g ( x ) as follows:

                       [tex][ g - f ] ( x ) = g ( x ) - f ( x )\\\\\\( g - f ) ( x ) = x^2 - 15 - 2x\\\\[/tex]

Now evaluate the above determined function at x = -3 as follows:

                       [tex]( g - f ) ( -3 ) = ( -3 )^2 - 2 ( -3 ) - 15\\\\( g - f ) ( -3 ) = 9 + 6 - 15\\\\( g - f ) ( -3 ) = 0[/tex]

Answer:

m∠N = 51°

m∠M = 31°

m∠O = 98°

Step-by-step explanation:

It is given that ΔMNO is an isosceles triangle with base NM.

m∠N = (4x + 7)° and m∠M = (2x + 29)°

By the property of an isosceles triangle,

Two legs of an isosceles triangle are equal in measure.

ON ≅ OM

And angles opposite to these equal sides measure the same.

m∠N = m∠M

(4x + 7) = (2x + 29)

4x - 2x = 29 - 7

2x = 22

x = 11

m∠N = (4x + 7)° = 51°

m∠M = (2x + 9)° = 31°

m∠O = 180° - (m∠N + m∠M)

         = 180° - (51° + 31°)

         = 180° - 82°

         = 98°

Answer:

vertex(-2,4)

Step-by-step explanation:

f(x)=-3(x+2)^2+4

f(x)=-3(x²+4x+4)+4

f(x)=-3x²-12x-12+4

    = -3x²-12x-8

v(h,k)

h=-b/2a=-(12/-6)==2

substitute for x=-2

k=-3(2)²-12(-2)-8=-12+24-8=4

Answer:

54.5 years.

Step-by-step explanation:

From the above question, we are asked to find the time

The formula for Time(t) =

t = log(A/P) / n[log(1 + r/n)]

A = Amount accumulated after a particular interest and period of time = $80,000

P = Principal (Money invested) = $4,000

r = rate = 5.5% = 0.055

n = compounding frequency = compounding continuously

n = number of days in a year × number of hours in a day

= 365 days × 24 hours = 8760

t = log(A/P) / n[log(1 + r/n)]

t = log(80,000/4,000) /8760[log(1 + 0.055/8760)]

t = log(80000 ÷ 4000) ÷ (8760 × [log(1 + 0.0000062785)]

t = 54.468367222 years

Approximately to the nearest tenth of a year, therefore, the length of time it will it take for his money to reach $80,000 is 54.5 years

Answer:

54.5

Step-by-step explanation:

Answer:

72°

Step-by-step explanation:

Given two vectors a and b, The vector i+3j will form a right angled triangle with the x-axis (i.e the horizontal axis).

The opposite side of the triangle on the Cartesian plane will be 3units along the y axis while the adjacent will be 1 unit along the x axis.

The angle between thus two vectors is expressed as tan (theta) = opp/adj

tantheta = 3/1

theta = tan^-1(3)

Theta = 71.57° ≈ 72° to nearest degree

The true statement about the given transformation is; B: It is a dilation because the transformation is not isometric.

An isometric transformation is a shape-preserving transformation in the plane or in space. They include reflection, rotation and translation.

Now, from the given attachment showing the two figures, we can see that there is a dilation which means that it can't be isometric as the definition of Isometric transformation does not include Dilation.

Read more about Transformation at; https://brainly.com/question/4289712

#SPJ5

Answer:

b

Step-by-step explanation:

just took the test

Answer: 0.045 is the growth rate.

Step-by-step explanation:

A generic exponential growth function can be written as:

f(t) = A*(1 + r)^t

where A is the initial amount.

t is the unit of time.

r is the rate of growth.

For example if we have an increase of 10% per year, with an initial population of 100 we have that:

A = 100, r = 10%/100% = 0.10, t = number of years.

the equation will be:

f(t) = 100*(1 + 0.10)^t

Now, in this case the equation is:

S(t) = 152*(1.045)^t

We can write this as:

S(t) = 152*(1 + 0.045)^t

Then 152 is the initial amount and 0.045 is the growth rate.

Answer:

the value of c is  20.155 such that 99% of all parcels are under the surcharge weight.

Step-by-step explanation:

Given that :

The mean value [tex]\mu[/tex] = 12

The standard deviation [tex]\sigma[/tex] = 3.5

Let Consider Q to be the weight of the parcel that is normally distributed .

Then;

Q [tex]\sim[/tex] Norm(12,3.5)

The objective is to determine thewight  value of c under which there is a surcharge

Also, let's not that 99% of all the parcels are below the surcharge

However ;

From the Percentiles table of Standard Normal Distribution;

At 99th percentile; the value for Z = 2.33

The formula for the Z-score is:

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

[tex]2.33 = \dfrac{X - 12}{3.5}[/tex]

2.33 × 3.5 = X - 12

8.155 = X - 12

- X = - 12 - 8.155

- X = -20.155

 X = 20.155

the weight  value of c under which there is a surcharge = X + 1 (0) since all the  pounds are below the surcharge

c = 20.155 + 1(0)

c = 20.155

Thus ; the value of c is  20.155 such that 99% of all parcels are under the surcharge weight.

Answer:

11 + Mai's Score = 59

Step-by-step explanation:

You need to add 11 and Mai's score together to get 59, so with the values given we can make the equation 11 + Mai's Score = 59.

*depending on the question, Mai's score may need to be said as a letter variable, so:

If m = mai's score,

11 + m = 59

I hope this helped! :)

Answer:

30

Step-by-step explanation:

We can call the number of boys 4x and girls 6x so we can write:

4x + 6x = 50

10x = 50

x = 5, therefore the number of girls is 6x = 6 * 5 = 30.

Answer:

30

Step-by-step explanation:

In the ratio 4:6, we can think of this like 4 boys and 6 girls out of 10 team members.

We can find how many girls play by multiplying 6 by 5, since 50 divided by 10 is 5.

6(5) = 30, so 30 girls play in the soccer league.

Answer:

x=8

Step-by-step explanation:

[tex]\sqrt{x+8}-\sqrt{x-4}=2\\\sqrt{x+8}=2+\sqrt{x-4}\\\left(\sqrt{x+8}\right)^2=\left(2+\sqrt{x-4}\right)^2\\x+8=x+4\sqrt{x-4}\\8=4\sqrt{x-4}\\8^2=\left(4\sqrt{x-4}\right)^2\\64=16x-64\\x=8[/tex]

Answer:

Y = 40

Step-by-step explanation:

First find the measure of V

The sum of the angles of a triangle equal 180

U+V+W =180

70+Y+70 =180

140+U =180

U = 180-140

U = 40

Since the triangles are similar

V = Y

40 = Y