HELP SOMEONE FOR 20 POINTS

[tex]\\ \sf\longmapsto \frac{5}{ \sqrt{7} - \sqrt{3} } + \frac{1}{ \sqrt{7} + \sqrt{3} } \\ \\ \sf\longmapsto \frac{5( \sqrt{7} + \sqrt{3} ) + 1 (\sqrt{7} - \sqrt{3} )}{( \sqrt{7} - \sqrt{3} )( \sqrt{7} + \sqrt{3} )} \\ \\ \sf\longmapsto \frac{5 \sqrt{7} + 5 \sqrt{3} + \sqrt{7} - \sqrt{3} }{( { \sqrt{7} )}^{2} - ( \sqrt{3}) {}^{2} } \\ \\ \sf\longmapsto \frac{5 \sqrt{7} + \sqrt{7} + 5 \sqrt{3} - \sqrt{3} }{7 - 3} \\ \\ \sf\longmapsto \frac{6 \sqrt{7} + 4 \sqrt{3} }{4} [/tex]

Answer:

0.9922 = 99.22% probability that the mean monitor life would be greater than 81.2 months in a sample of 146 monitors.

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.

The production manager claims they have a mean life of 83 months with a variance of 81.

This means that [tex]\mu = 83, \sigma = \sqrt{81} = 9[/tex]

Sample of 146:

This means that [tex]n = 146, s = \frac{9}{\sqrt{146}}[/tex]

What is the probability that the mean monitor life would be greater than 81.2 months in a sample of 146 monitors?

This is 1 subtracted by the p-value of Z when X = 81.2. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{81.2 - 83}{\frac{9}{\sqrt{146}}}[/tex]

[tex]Z = -2.42[/tex]

[tex]Z = -2.42[/tex] has a p-value of 0.0078.

1 - 0.0078 = 0.9922.

0.9922 = 99.22% probability that the mean monitor life would be greater than 81.2 months in a sample of 146 monitors.

Answer:

(123)(62)=x

Step 1: Simplify both sides of the equation.

7626=x  

Step-by-step explanation:

Have a good day.

Answer:7,626

Step-by-step explanation:The easiest way I do it is by taking the numbers and putting them under each other like this

123

 62

then take the number 2 for example and multiply it by 3 then 20 then 100 and do the same with the 6=60 and heres how I solve it

2 x 3=6      2 x 20=40     2 x 100=200       60 x 3=180     60 x 20=1,200    60 x 100=6,000 now take all the numbers and add them

6+40+200=246

180+1,200+6,000=7,380

7,380+246=7,626

(if this helps in anyway feel free to put brainiest but thats your choice) :) happy to help.

9514 1404 393

Answer:

  undefined

Step-by-step explanation:

A rational expression is undefined when its denominator is zero.

Answer:

ask in English then I can help

Answer:

[tex]here \: the \: two \: sides \: are \: equal \: so \: \\ the \: triangle \: is \: issosceles \\ then \: x = 40 \\ thank \: you[/tex]

Answer:

C. 10,080

Step-by-step explanation:

We can multiply to find how many minutes there are in 1 day.

24 * 60 = 1,440

Now, we can multiply that value by 7 to find out how many minutes there are in 1 week.

1,440 * 7 = 10,080

Best of Luck!

Answer:

A) children attended=98 b) students attended=60 c)adults attended=49

Step-by-step explanation:

system%28a%2Bc%2Bx=207%2Cc%2Fa=2%2C5c%2B7x%2B12a=1498%29

Simplify and solve the system.

-

a%2B2a%2Bx=207

3a%2Bx=207

x=207-3aandc=2a

-

The revenue equation can be written in terms of just one variable, a.

10a%2B7%28207-3a%29%2B12a=1498

Solve for a;

use it to find x and c.

FURTHER STEPS

-

10a%2B1449-21a%2B12a=1498

a%2B1449=1498

a=98-49

highlight%28a=49 -------adults

-

c=2a

c=2%2A49

highlight%28c=98 -------children

-

x=207-a-c

x=207-49-98

highlight%28x=60 ---------students

Answer:

0.0079 = 0.79% probability that she randomly plants the trees so that all 5 sycamores are next to each other and all 5 palm trees are next to each other.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The trees are arranged, so, to find the number of outcomes, the arrangements formula is used.

Arrangements formula:

The number of possible arrangements of n elements is given by:

[tex]A_n = n![/tex]

Desired outcomes:

5 sycamores(5! possible ways) and then the 5 palm trees(5! possible ways)

5 palm trees(5! possible ways) then the 5 sycamores(5! possible ways).

[tex]D = 2*5!*5![/tex]

Total outcomes:

Arrangements of 10 plants, so:

[tex]T = 10![/tex]

What is the probability that she randomly plants the trees so that all 5 sycamores are next to each other and all 5 palm trees are next to each other?

[tex]p = \frac{D}{T} = \frac{2*5!*5!}{10!} = 0.0079[/tex]

0.0079 = 0.79% probability that she randomly plants the trees so that all 5 sycamores are next to each other and all 5 palm trees are next to each other.

Answer: D

"Separating the students on the list into boys and girls and choosing a sample from each group that is proportional to the size of the group."

Step-by-step explanation:

You are sampling an equal amount of boys and girls since your getting an equal sample of each gender. (Not random)

The option that is not a random sample is:

Separating the students on the list into boys and girls and choosing a sample from each group that is proportional to the size of the group.

Option D is the correct answer.

It is the way of choosing a number of required items from a population given.

Each item has an equal probability of being chosen.

We have,

We will see which option is a sample that is not random.

A. Going through the list and choosing the first 25 names on the list.

Going through the list means every name has an equal chance of getting chosen.

This is a random sample.

B. Writing each student’s name on a card and then drawing out 25 names without looking.

Since we are drawing out 25 names without looking, all the students' names have an equal chance of getting drawn.

This is a random sample.

C. Choosing one student at random from the list and going through the list and choosing every fifth student until she has 25 names.

Choosing one student at random means every student has an equal chance of getting chosen.

This is a random sampling.

D. Separating the students on the list into boys and girls and choosing a sample from each group that is proportional to the size of the group.

The students are separated into boys and girls and the sample is chosen from each group so we are selecting the sample from the separated group.

This can not be a random sampling.

Thus,

The option that is not a random sample is:

Separating the students on the list into boys and girls and choosing a sample from each group that is proportional to the size of the group.

Option D is the correct answer.

Learn more about random sampling here:

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Answer:

(-16.494 ; -3.506)

Step-by-step explanation:

student Prob A Prob B difference, d (A-B)

1 20 35____ - 15

2 30 40 ___ - 10

3 15 20 ___ - 5

4 40 50 __ - 10

Difference, d = -15, -10, -5, -10

Xd = Σd/ n = - 40 / 4 = - 10

Standard deviation of d ; Sd = 4.082

The confidence interval for the difference is given as :

Xd ± Tcritical*(Sd/√n)

Tcritical at 95%; df = n - 1 ; 4 - 1 = 3

Tcritical(0.05, 3)). = 3.182

C.I = -10 ± 3.182(4.082/√4)

C.I = -10 ± 6.494462

C. I = (-16.494 ; -3.506)

Answer:

75 inches

Step-by-step explanation:

with this we use change of subject

V=1/3

Pie=3.14

radius =3

height =8

so therefore

V=1/3 ×3.14×3×3×8

V=75.36

Answer:

a = 9

Step-by-step explanation:

The given trinomial is :

[tex]x^2-6x+\_\_\__[/tex]

let the blank is a.

So, we need to find the value of a so that it results in a perfect square trinomial.

We know that, [tex](m-n)^2=m^2-2mn+n^2[/tex]

So,

[tex]x^2-6x+a=x^2-2(1)(3)+3^2\\=(x-3)^2[/tex]

So, the value of a is 9. If a is 9, then only it would be a perfect square trinomial.

Answer:

36 is the answer

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

72: 2×2×2×3×3

108: 2×2×3×3×3

180: 2×2×3×3×5

here, common factors are 2,2,3 and 3 ..

so.. HCF: 2×2×3×3

•°•HCF=36 ..

Answer:

D.

Step-by-step explanation:

The required inequality is given as x ≥ 100 as the water boils at 100°C and above, Option B is correct.

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

here,
As given in the question,
Water boils at 100°C and above,
So let x be the temperature of the water,
And according to the condition,
x ≥ 100° C

Thus, the inequality x ≥ 100 is shown in option B.

Thus, the required inequality is given as x ≥ 100 as the water boils at 100°C and above, and Option B is correct.

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Answer:

  (3t -7)²

Step-by-step explanation:

We know that the square of a binomial is ...

  (a -b)² = a² -2ab +b²

So, when we see the first and last terms are both perfect squares, we suspect that the trinomial is a perfect square trinomial.

  9t² = (3t)²

  49 = 7²

  -42t = -2(3t)(7) . . . . confirming we have a perfect square

The factorization is ...

  (3t -7)²

z -5 =4

neutralize the left -5 by adding 5 on both sides

z -5 (+5) = 4 (+5)

z = 9

Answer:

B

Step-by-step explanation:

5³.5^×

simply means

5³×5^×

using indices rule,

multiplication is addition

5 is common

so 5(³+×)

hence 5^3+×

Step-by-step explanation:

area=length×width

2.4=x×1.2

1.2x=2.4

x=2.4÷1.2

x=2

therefore width = 2cm

The length of the rectangle is 2 meters.

We have,

Width of rectangle= 1.2m

Area of rectangle = 2.4 m²

To find the length of a rectangle when given its width and area, you can use the formula:

Length = Area / Width

So, the length rectangle

Length = 2.4 m² / 1.2 m

Length = 2 meters

Therefore, the length of the rectangle is 2 meters.

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Answer:

17.3

Step-by-step explanation:

14.4 x 1.2

= 17.28

= 17.3 ( approximately )

Answer:

Mabel's score = s

2s-59

Step-by-step explanation:

I HOPE MABEL HAS A NICE GRADE

Is it Mabel from Gravity Falls?

lol

Correct option is "multiplying a fraction by a repeating decimal."

Explanation:

Since multiplying a fraction is a rational and repeating decimal is also rational, therefore, it's result is also rational.

Hope it helps you... pls mark brainliest if it helped you

Answer:

the ans is 45⁰ BC it is a right angle

Step-by-step explanation:

Is this a trigonometry ratio

Differentiating both sides of

xy = 99

with respect to t yields

x dy/dt + y dx/dt = 0

When x = 11, we have

11y = 99   ==>   y = 9

and we're given that dy/dt = -4 at this point, which means

11 (-4) + 9 dx/dt = 0   ==>   dx/dt = 44/9

Here we have a problem of maximization and quadratic equations.

The unit prize that maximizes the revenue is $1,500, and the maximum revenue is $18,000.

We know that the revenue equation is:

R(P) = - 8p^2 + 24,000p

Where the variable p is the price.

Now we want to find the value of p that maximizes the revenue.

To do it, we can see that the revenue equation is a quadratic equation with a negative leading coefficient.

This means that the arms of the graph will go downwards, then the maximum point of the graph will be at the vertex.

Remember that for an equation like:

y = a*x^2 + b*x+ c

The x-value of the vertex is at:

x = -b/(2*a)

Then for the equation:

R(P) = - 8p^2 + 24,000p

The vertex is at:

p = -(24,000)/(2*-8) = 1,500

The value of p that maximizes the revenue is p = $1,500

To get the maximum revenue, we need to evaluate the revenue equation in that p value.

R(1,500) =  - 8*(1,500)^2 + 24,000*1,500 = 18,000

And the revenue equation is in dollars, then the maximum revenue is 18,000 dollars.

If you want to learn more, you can read:

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p = 1500  $    the unit price

R(p) = 18000000 $ maximum revenue

We will use two different procedures to calculate the maximum revenue.

That is equivalent to solve the problem and after that to test the solution

The first one is:

R(p) = - 8*p² + 24000*p

we realize that R(p) is a quadratic function ( a parabola) of the form:

y = a*x² + b*x + c    ( c = 0 in this case)

We also know that  as the coefficient of p² is negative the parabola opens downwards then the vertex is a maximum value for R(p), and the x coordinate of p is:

x = p =  - b/2*a   then by substitution

p = - ( 24000)/ 2 ( - 8)

p = 1500  $   and for that value of p

R(p) = - 8 ( 1500)² + 24000* (1500)  = - 18000000 + 36000000

R(p) = 18000000 $

The second procedure is solving with the help of derivatives.

R(p) =  - 8*p² + 24000*p

Tacking derivatives on both sides of the equation we get:

R´(p) = -16p  +  24000

If R´(p) = 0    then    -16p  +  24000 = 0

p = 24000/ 16         p  =  1500

if we check for the second derivative

R´´(p) = -16          -16 < 0  therefore there is a maximum value for R(p) when p = 1500, and that value is:

By substitution in R(p)

R(p) = -8 *(1500)² + 24000* 1500

R(p) =  - 18000000 + 36000000

R(p) = 18000000 $

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Answer:

  A = 108.78°

  a = 11 mi

  b = 7 mi

Step-by-step explanation:

The sum of angles in a triangle is 180°, so the third angle is ...

  A = 180° -38.71° -32.51°

  A = 108.78°

__

The remaining sides can be found from the law of sines.

  a/sin(A) = c/sin(C)

  a = sin(A)·c/sin(C) ≈ 0.946762 × 11.163896

  a ≈ 11 mi

  b = sin(B)·11.163896 ≈ 0.625379 × 11.163896

  b ≈ 7 mi

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Answer:

  491,400 ft·lb

Step-by-step explanation:

The mass of the water is ...

  M = Vρ = LWHρ = (25 ft)(15 ft)(7 ft)(62.4 lb/ft³) = 163,800 lb

The average depth is 3 ft, so the work required is equivalent to that required to raise this mass 3 ft.

  W = (3 ft)(163,800 lb) = 491,400 ft·lb

Step-by-step explanation:

A=140sq. units

Step-by-step explanation:

ABCD

A=13

B=15

C=14

D=20

C=14×14

=196sqr.units

NA = A + W

By adding one unit to length, we increase the overall area by the width of the rectangle. This is because the formula for the area of a rectangle is A = l x w. So, NA = (l + 1) x w = (l x w) + w = A + w.