Simplify.
Remove all perfect squares from inside the square roots.
Assume a and b are positive.

Answer:

x = 10

Step-by-step explanation:

We know x = 6

asked: x + 4

Plus it in =>

6 + 4

=> 10

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:

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:

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

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:

work is shown and pictured

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.

Explanation:

1. CS ≅ HR, ∠CHS ≅ ∠HCR, ∠CSH ≅ ∠HRC — given

2. ∆CRH ~ ∆HSC — AA similarity theorem

3. ∠SCH ≅ ∠RHC — corresponding angles of similar triangles are congruent

4. CH ≅ HC — reflexive property of congruence

5. ∆CRH ≅ ∆HSC — SAS congruence theorem

6. CR ≅ HS — CPCTC

Answer:

x= 1 + or - sr37/4 got it from a sitr

Here you go.

I really hope I helped. Good luck.

Answer:

AGE = 129 degrees

Step-by-step explanation:

Two angles whose sum is 180° are called supplementary angles. The measure of ∠AGE in the given figure is 129°.

Two angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, that if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.

In the given figure, line segment CE is a straight line. Therefore, the sum of the angles formed on the same side of the line will be a linear pair.

Thus, the measure of the angles can be rewritten as,

∠AGC + ∠AGE = 180°

51° + ∠AGE = 180°

∠AGE = 180° - 51°

∠AGE = 129°

Learn more about Supplementary Angles:

https://brainly.com/question/2882938

#SPJ2

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:

3.54%

Step-by-step explanation:

This question represents a binomial distribution. A binomial distribution is given by:

[tex]P(x)=\frac{n!}{(n-x)!x!} p^xq^{n-x}[/tex]

Where n is the total number of trials, p is the probability of success, q is the probability of failure and x is the number of success.

Given that:

A basketball player scores 70% of his shots on average, therefore p = 70% = 0.7. Also q = 1 - p = 1 - 0.7 = 0.3.

The total number of trials (n) = 20 shots

The probability that he scores at least 18 successful shots tonight if he gets 20 shots = P(x = 18) + P(x = 19) + P(x = 20)

P(x = 18) = [tex]\frac{20!}{(20-18)!18!}*0.7^{18}*0.3^{20-18}=0.0278[/tex]

P(x = 19) = [tex]\frac{20!}{(20-19)!19!}*0.7^{19}*0.3^{20-19}=0.0068[/tex]

P(x = 20) = [tex]\frac{20!}{(20-20)!20!}*0.7^{20}*0.3^{20-20}=0.0008[/tex]

The probability that he scores at least 18 successful shots tonight if he gets 20 shots = P(x = 18) + P(x = 19) + P(x = 20) = 0.0278 + 0.0068 + 0.0008 = 0.0354 = 3.54%

Answer:

8.4ft

Step-by-step explanation:

Formula for calculating the length of an arc is expressed as [tex]L = \frac{\theta}{360} * 2\pi r\\[/tex]

[tex]\theta[/tex] is the central angle = π/3 rad

r is the radius of the circle = 8ft

Substituting the values into the formula above we have;

[tex]L =[/tex] [tex]\frac{(\frac{\pi}{3} )}{2 \pi} * 2\pi (8)\\\\[/tex]

[tex]L = \frac{\pi}{6 \pi} * 2\pi(8) \\\\L = 1/6 * 16\pi\\\\L = 8\pi/3\\\\L = \frac{8(22/7)}{3} \\\\L = \frac{8*22}{7*3}\\ \\L = 176/21\\\\L = 8.4 ft (to\ the\ nearest\ tenth)[/tex]

Hence, the length of the arc s is approximately 8.4 ft.

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:

A

Step-by-step explanation:

When subtracting 7 on the left of the equation, he also needs to subtract 7 from the right of the equation.

Step 2 should be:

⅓X +7 -7= 15 -7

What he is trying to do here by subtracting 7 is to move all the constants, that is numbers without any variables such as x, to one side of the equation.

⅓X= 8

X= 8 ×3

X= 24

Answer:

x=10.

Step-by-step explanation:

Answer:

Probability of orange hat = 0.0833

Step-by-step explanation:

We have to find the probability of getting an orange hat while we randomly choose from 444 pieces of clothing and 333 colors.

So we have to get hat from the clothing and we have to get orange color from the colors. All shirts , pants , socks and hats are in equal numbers and are 111 each. Also purple, blue and orange are 111 each in number.

The probability of getting hats =

                                                   = 0.25

The probability of getting orange =  = 0.333

Final probability = 0.25 0.333

                          = 0.0833

Answer: 1/12

Step-by-step explanation:

I just had khan academy

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:

2.28% of babies born in the United States having a low birth weight.

Step-by-step explanation:

The complete question is: In the United States, birth weights of newborn babies are approximately normally distributed with a mean of μ = 3,500 g and a standard deviation of σ = 500 g. What percent of babies born in the United States are classified as having a low birth weight (< 2,500 g)? Explain how you got your answer.

We are given that in the United States, birth weights of newborn babies are approximately normally distributed with a mean of μ = 3,500 g and a standard deviation of σ = 500 g.

Let X = birth weights of newborn babies

The z-score probability distribution for the normal distribution is given by;

                          Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean = 3,500 g

            [tex]\sigma[/tex] = standard deviation = 500 g

So, X ~ N([tex]\mu=3500, \sigma^{2} = 500[/tex])

Now, the percent of babies born in the United States having a low birth weight is given by = P(X < 2500 mg)

   P(X < 2500 mg) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{2500-3500}{500}[/tex] ) = P(Z < -2) = 1 - P(Z [tex]\leq[/tex] 2)

                                                                 = 1 - 0.97725 = 0.02275 or 2.28%

The above probability is calculated by looking at the value of x = 2 in the z table which has an area of 0.97725.

Answer:

The z-score for 2,500 is -2. According to the empirical rule, 95% of babies have a birth weight of between 2,500 g and 4,500 g. 5% of babies have a birth weight of less than 2,500 g or greater than 4,500 g. Normal distributions are symmetric, so 2.5% of babies weigh less than 2,500 g.

Step-by-step explanation:

did the assignment on edge:)

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.

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:

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:

See below

Step-by-step explanation:

Alex finally understands how Bob was trying to trick him into winning the bet because of how he puts in the condition for probability being less than 10%. Whichever way the outcome of the coin toss turns out to be, it will be in Bob's favor and Alex will lose the bet. If the coin is flipped 3 times, the probability of having heads exactly twice is [tex]\frac{4}{9}[/tex]

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.

Looks like the series is

[tex]\displaystyle\sum_{k=1}^\infty\left(\frac4{\sqrt{k+5}}-\frac4{\sqrt{k+6}}\right)[/tex]

This series has n-th partial sum

[tex]S_n=\displaystyle\sum_{k=1}^n\bullet[/tex]

(where [tex]\bullet[/tex] is used as a placeholder for the summand)

[tex]S_n=\displaystyle\left(\frac4{\sqrt6}-\frac4{\sqrt7}\right)+\left(\frac4{\sqrt7}-\frac4{\sqrt8}\right)+\cdots+\left(\frac4{\sqrt{n+4}}-\frac4{\sqrt{n+5}}\right)+\left(\frac4{\sqrt{n+5}}-\frac4{\sqrt{n+6}}\right)[/tex]

In each grouped term, the last term is annihilated by the first term of the next group; that is, for instance,

[tex]\displaystyle\left(\frac4{\sqrt6}-\frac4{\sqrt7}\right)+\left(\frac4{\sqrt7}-\frac4{\sqrt8}\right)=\frac4{\sqrt6}-\frac4{\sqrt8}[/tex]

Ultimately, all the middle terms will vanish and we're left with

[tex]S_n=\dfrac4{\sqrt6}-\dfrac4{\sqrt{n+6}}[/tex]

As [tex]n\to\infty[/tex], the last term converges to 0 and we're left with

[tex]\displaystyle\sum_{k=1}^\infty\bullet=\lim_{n\to\infty}S_n=\frac4{\sqrt6}=\boxed{2\sqrt{\dfrac23}}[/tex]

Answer:

LL

Step-by-step explanation:

We have two right triangles

The two legs are congruent

We can use the LL congruence theorem

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

The depth of hole is 0.609 inches.

Given, the total depth of the block of  wood is  [tex]\frac{13}{16}[/tex] inches.

Since the hole is [tex]\frac{3}{4}[/tex] of the total depth, so the depth of the hole will be,

[tex]D=\frac{3}{4} \times\frac{13}{16}[/tex]

Or, [tex]D=\frac{39}{64}[/tex]

[tex]D=0.609375 \ in[/tex]

Hence the depth of hole is 0.609 inches.

For more details follow the link:

https://brainly.com/question/2263981