Use the distributive property to remove the parentheses.
7c^2(9c^5 +10c)
Simplify your answer as much as possible.

Answer:

Part A:

Probability that average single manager beat the index= [tex](0.5)^7=0.0078125=0.0078 (4\ decimals)[/tex]

Part B:

Fund Managers to beat index 7 years=78.125≅78 managers.

Step-by-step explanation:

Part A:

Given data:

Since there are equal chances for delivering equal better performance and of under performance so

Probability of better performance =0.5

Required:

Probability that the average single fund managers beats the index 7 years in a row (before fees)=?

Solution:

Since there is 7 year index:

Probability that average single manager beat the index= [tex](0.5)^7=0.0078125=0.0078 (4\ decimals)[/tex]

Part B:

Given Data:

Number of mutual fund managers=10,000

Probability that average single manager beat the index= 0.0078125 (Calculated in part A)

Required:

How many fund managers would you expect to beat the index 7 years in a row if only luck and no skill was involved?

Solution:

Fund Managers to beat index 7 years=Total number of managers*probability  average single member beat the index

Fund Managers to beat index 7 years=10,000*0.0078125

Fund Managers to beat index 7 years=78.125≅78 managers.

Answer:

Step-by-step explanation:

The area of the rectangular floor is the product of its length and width:

  A = LW = (21 ft)(9 ft) = 189 ft²

The volume of the pod is the product of that floor area and the height:

  V = Bh = (189 ft²)(7 ft) = 1323 ft³

The area of the floor is 189 ft²; the volume of the pod is 1323 ft³.

Answer:

26 and 36.

Step-by-step explanation:

Let the two whole numbers be a and b. Thus, the product of them is 936 while their sum is 62. In equations, this is:

[tex]ab=936\\a+b=62[/tex]

This is a system of equations. To solve, subtract either a or b from the second equation and substitute it into the first.

For instance, subtract b from both sides in the second equation:

[tex]a+b=62\\a=62-b[/tex]

Substitute this into the first equation:

[tex](62-b)(b)=936[/tex]

Distribute:

[tex]62b-b^2=936[/tex]

Rearrange:

[tex]-b^2+62b=936[/tex]

Divide everything by -1 to make the leading coefficient positive:

[tex]b^2-62b=-936[/tex]

Add 936 to both sides:

[tex]b^2-62b+936=0[/tex]

This is now a quadratic. Solve for b.

To do so, we can factor.

After a bit of testing, we can see that -36 and -26 are possible. Thus:

[tex](b-26)(b-36)=0[/tex]

For for b:

[tex]b=26\text{ or } b=36[/tex]

Thus, b is 26 or 36.

Now, plug these back into the isolated equation to solve for a:

[tex]a=62-b\\a=62-(26) \text{ or } a=62-(36)\\a=36\text{ or } a=26[/tex]

It doesn't really matter which one we choose since they're the same.

Thus, the answer is 26 and 36.

Answer:

[tex]\Huge \boxed{\mathrm{60 \ cm^2 }}[/tex]

Step-by-step explanation:

Area of a rectangle is length × width.

The length of the rectangle is 10 cm.

The width of the rectangle is 6 cm.

[tex]\Rightarrow 10 \cdot 6 \\\\\\ \Rightarrow 60[/tex]

The area of the rectangle is 60 cm².

Answer:

60cm is the answer

Step-by-step explanation:

Area of a rectangle is length × width.

so..... The length of the rectangle is 10 cm.

And the width of the rectangle is 6 cm.

so... 10x6=60 cm

Answer:

the probability that the rack ends up in alphabetical order is 0.0001984

Step-by-step explanation:

Given that:

You own 24 CDs. You want to randomly arrange 7 of them in a CD rack.

Th probability that the rack ends up in alphabetical order can be determined by taking note of the permutations and combinations.

From above; all possible permutations of size 7 we can derive from 24 is

24P7

Similarly,we are meant  to estimate  all the possible ways a unique set of 7 things can be gotten from a total of 24

i.e

24 C7

∴

The probability = [tex]\dfrac{^{24}{C}_7}{^{24}{P}_7}[/tex]

= [tex]\dfrac{\dfrac{24!}{7!(24-7)!} }{ \dfrac{24!}{(24-7)!} }[/tex]

=[tex]\dfrac{\dfrac{24!}{7!(17)!} }{ \dfrac{24!}{(17)!} }[/tex]

= [tex]\dfrac{346104}{ 1.74436416 \times 10^9}[/tex]

= 0.0001984

the probability that the rack ends up in alphabetical order is 0.0001984

The probability that the rack ends up in alphabetical order is 0.0001984

The total number of CD is given as:

[tex]\mathbf{n = 24}[/tex]

The number of CDs to select is given as:

[tex]\mathbf{r = 7}[/tex]

The number of arrangement of 7CDs in 24 is represented as 24P7

So, we have:

[tex]\mathbf{^{24}P_7 = \frac{24!}{(24 - 7)!}}[/tex]

[tex]\mathbf{^{24}P_7 = \frac{24!}{17!}}[/tex]

Simplify

[tex]\mathbf{^{24}P_7 =1744364160}[/tex]

The number of selecting 7 CDs from 24 is represented as 24C7

So, we have:

[tex]\mathbf{^{24}C_7 = \frac{24!}{(24 - 7)!7!}}[/tex]

[tex]\mathbf{^{24}C_7 = \frac{24!}{17!!7}}[/tex]

Simplify

[tex]\mathbf{^{24}C_7 =346104}[/tex]

So, the probability is:

[tex]\mathbf{Pr = \frac{346104}{1744364160}}[/tex]

Divide

[tex]\mathbf{Pr = 0.0001984}[/tex]

Read more about permutation and probability at:

https://brainly.com/question/14767366

Answer:

1/3

Step-by-step explanation:

√2 is irrational because radicals are irrational. π is also an irrational number. The third option, 1.3985624785461.... is obviously not a terminating decimal, hence, it is also irrational. Therefore, the answer is 1/3. We know this because 1/3 can be written in the form a / b where a and b are rational numbers, in this case, a = 1 and b = 3.

Answer:

2

Step-by-step explanation:

Pretend there is no decimal point. We can do this by multiplying both numbers by 10.

After that, it becomes 68/34. You then divide those two, and you get 2 as your answer.

Answer:

2

Step-by-step explanation:

its easy you can do it with calculator or paper -__-

Answer:

Step-by-step explanation:

[tex]\left(6^2\right)^x=1\\\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc}\\\left(6^2\right)^x=6^{2x}\\\\6^{2x}=1\\\mathrm{If\:}f\left(x\right)=g\left(x\right)\mathrm{,\:then\:}\ln \left(f\left(x\right)\right)=\ln \left(g\left(x\right)\right)\\\ln \left(6^{2x}\right)=\ln \left(1\right)\\\\\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)\\\ln \left(6^{2x}\right)=2x\ln \left(6\right)\\2x\ln \left(6\right)=\ln \left(1\right)\\[/tex]

[tex]\mathrm{Solve\:}\:2x\ln \left(6\right)=\ln \left(1\right):\\\quad x=0[/tex]

Answer:

x = 0

Simplified: [tex]36^{x} = 1[/tex]

Step-by-step explanation:

How to simplify:

Answer: im pretty sure its exponential decay?

Step-by-step explanation:

Answer:

L = A÷W

Step-by-step explanation:

The area of a rectangle (A) is related to the length (L) and width (W) of its sides by the following relationship: A = L ⋅ W. If you know the width, it's easy to find the length by rearranging this equation to get L = A ÷ W.

Answer:

Time travelled each day = 8 hours

Step-by-step explanation:

total distance of 2-day trip = 880 miles

half the distance each day = 880 ÷ 2 = 440 miles

velocity travelled each day = 55 miles per hour

time travelled each day = ???

velocity = (distance trvaelled) ÷ (Time)

55 = 440 ÷ Time

[tex]55=\frac{440}{Time} \\cross-multiplying\\55\ \times\ Time = 440\\Time = \frac{440}{55} \\Time = 8\ hours[/tex]

∴ Time travelled each day = 8 hours

Answer:

9 hours

Step-by-step explanation:

Total distance for the two days = 880 miles

If half of the distance is to be traveled each day, then;

distance each day = 440 miles

speed of the automobile = 55 miles per hour.

Now, let's calculate the number of hours that will be driven each day.

Remember that;

speed = distance / time

=> time = distance / speed           [substitute the values of distance and speed]

=> time = (440 miles) / (55 miles/hour)

=> time = 9 hours.

Therefore, the number of hours that will be driven each day is 9

Answer:

t^2 -4t + 4

Step-by-step explanation:

(2t-4)(2t-4) Use the FOIL Method (first, outside, inside, last)

2t*2t =4t^2 First

2t*-4 = -8t Outside

-4*2t = -8t Inside

-4*-4 = 16 Last

4t^2 -8t -8t + 16 (simplify/add like terms)

(4t^2 -16t + 16)/4 (you can further simplify by dividing each value by 4)

t^2 -4t + 4

Answer:

[tex] x = \pm \sqrt{19} [/tex]

[tex] x = \pm 4.36 [/tex]

Step-by-step explanation:

[tex] x^2 = 19 [/tex]

[tex] x = \pm \sqrt{19} [/tex]

[tex] x = \pm 4.36 [/tex]

The exact solution is 4.36.

Squares are the numbers, generated after multiplying a value by itself. Whereas square root of a number is value which on getting multiplied by itself gives the original value. Hence, both are vice-versa methods. For example, the square of 2 is 4 and the square root of 4 is 2.

Given:

x² = 19

On taking root on both side

√x² = √19

x= √19

x = 4.3588

Hence, the exact solution and its approximation rounded to two decimal places is 4.36.

Learn more about square root here:

https://brainly.com/question/3120622

#SPJ2

Answer:

x > 5

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Write out equation

8x - 6(x + 1) < 4(2x - 9)

Step 2: Distribute parenthesis

8x - 6x - 6 < 8x - 36

Step 3: Combine like terms

2x - 6 < 8x - 36

Step 4: Subtract 2x on both sides

-6 < 6x - 36

Step 5: Add 36 on both sides

30 < 6x

Step 6: Divide both sides by 6

5 < x

Step 7: Rewrite

x > 5

Answer:

A) ¬(¬q) ≡ q

B) ≡ ( эx) (¬p(x) ∧ ¬q(x)

C) ≡ ( зx ) (p(x) ∧ (¬ q(x) ∨ r(x)) )

Step-by-step explanation:

using De Morgan's law for quantified statements and the laws of propositional logic to show the equivalent of the following

from De -Morgan law

¬(A ∨ B ) = ¬ A ∧¬ B

ATTACHED BELOW IS THE COMPLETE SOLUTION

Answer:

32100

Step-by-step explanation:

hope this helps

sorry if its wrong

Options :

a mean - 40, median - 50, mode - 60

b. mean-60, median - 50, mode - 40

c. mean - 40, median-60, mode - 50

d. mean - 50, median - 50, mode - 50

Answer: mean - 40, median - 50, mode - 60

Step-by-step explanation: A negatively skewed distribution is characterized by it long tail being positioned to the left(negative direction) with its peak positioned to the right (positive direction) of the distribution. On a general note, the mean is always positioned towards the left or negative side if the peak, with the median coming next and usually positioned to the right of the mean and the mode positioned to the right side of the median.

Hence, for a negatively skewed distribution, the mean has the least value followed by the median, with the mode boasting the highest.

That is : mean < median < mode

Answer:

The standard error is 0.033.

Step-by-step explanation:

We are given that Sukie interviewed 125 employees at her company and discovered that 21 of them planned to take an extended vacation next year.

Let [tex]\hat p[/tex] = proportion of employees who planned to take an extended vacation next year

[tex]\hat p[/tex] = [tex]\frac{X}{n}[/tex] = [tex]\frac{21}{125}[/tex] = 0.168

n = number of employees at her company = 125

Now, the standard error is calculated by the following formula;

       Standard error, S.E. =  [tex]\sqrt{\frac{\hat p(1-\hat p)}{n} }[/tex]

                                         =  [tex]\sqrt{\frac{0.168(1-0.168)}{125} }[/tex]

                                         =  [tex]\sqrt{\frac{0.168 \times 0.832}{125} }[/tex]  = 0.033

Hence, the standard error is 0.033.

Answer:

.10 - .23

Step-by-step explanation:

.168 +/- 1.96 ( sqrt ((.168 * .832)/125))

Answer:

A month at the very least

Step-by-step explanation:

Answer:

One brother says of his younger brother: “Two years ago, I was three times as old as my brother was. In three years’ time, I will be twice as old as my brother.” How old are they each now?

Step-by-step explanation:

Let us suppose two years ago my brother's age was x years

Then, my age was 3x

Three years from now, my brother's age will be (x +2+3) = (x+5) years

And my age will be (3x+2+3) = (3x+5) years

But it is given that i will be twice as old as my brother.

So, 2(x+5)= (3x+5)

or, x= 5 years

So my brother's present age is 5+2= 7 years

And my age is 5*3+2= 17 years

The age of the older brother is 13 and the age of the younger brother is 5.

Two simultaneous equations can be determined from this question:

y = 3x - 2 equation 1

y = 2x + 3 equation 2

Where:

y = older brother's age

x = younger brother's age

Equate equation 1 and equation 2

3x - 2 = 2x + 3

Combine similar terms

3x - 2x = 3 + 2

x = 5

Substitute for x in equation 1

3(5) - 2

15 - 2

y =13

To learn more about simultaneous equations, please check: https://brainly.com/question/25875552

Answer:

24 - 16x

Step-by-step explanation:

8(3 - 2x)

Distribute

8*3 - 8*2x

24 - 16x

Answer:

34416

Step-by-step explanation:

.72(percentage) × 47800(people)

34416

Answer:

24

Step-by-step explanation:

Assuming you want to find a mean, the answer is: 24 (sum of all values/number of values)

Range is largest-smallest

Median is middle value

Answer:

i think b is answer. i think this is useful to you

Answer:

1) W₁ is a subspace of Pₙ (R)

2) W₂ is not a subspace of Pₙ (R)

4) W₃ is a subspace of Pₙ (R)

Step-by-step explanation:

Given that;

1.Let W₁ be the set of all polynomials of the form p(t) = at², where a is in R

2.Let W₂ be the set of all polynomials of the form p(t) = t² + a, where a is in R

3.Let W₃ be the set of all polynomials of the form p(t) = at² + at, where a is in R

so

1)

let W₁ = { at² ║ a∈ R }

let ∝ = a₁t² and β = a₂t²  ∈W₁

let c₁, c₂ be two scalars

c₁∝ + c₂β = c₁(a₁t²) + c₂(a₂t²)

= c₁a₁t² + c²a₂t²

= (c₁a₁ + c²a₂)t² ∈ W₁

Therefore c₁∝ + c₂β ∈ W₁ for all ∝, β ∈ W₁  and scalars c₁, c₂

Thus, W₁ is a subspace of Pₙ (R)

2)

let W₂ = { t² + a ║ a∈ R }

the zero polynomial 0t² + 0 ∉ W₂

because the coefficient of t² is 0 but not 1

Thus W₂ is not a subspace of Pₙ (R)

3)

let W₃ = { at² + a ║ a∈ R }

let ∝ = a₁t² +a₁t  and β = a₂t² + a₂t ∈ W₃

let c₁, c₂ be two scalars

c₁∝ + c₂β = c₁(a₁t² +a₁t) + c₂(a₂t² + a₂t)

= c₁a₁t² +c₁a₁t + c₂a₂t² + c₂a₂t

= (c₁a₁ +c₂a₂)t² + (c₁a₁t + c₂a₂)t ∈ W₃

Therefore c₁∝ + c₂β ∈ W₃ for all ∝, β ∈ W₃ and scalars c₁, c₂

Thus, W₃ is a subspace of Pₙ (R)

Answer:

D.13-2x

Step-by-step explanation:

[tex]10-\left(2x-3\right)\\\\-\left(2x-3\right):\quad -2x+3\\=10-2x+3\\\\\mathrm{Simplify}\:10-2x+3:\\\quad -2x+13[/tex]

Answer:

13 -2x

Step-by-step explanation:

10-(2x-3)

Distribute the minus sign

10 -2x +3

Combine like terms

13 -2x

Answer:

Step-by-step explanation:

When you work addition and subtraction problems, it is often easier to do them if you can "make a 10" or "make a 100", because adding or subtracting 10 or 100 is easier than with non-zero digits.

__

Here, you are steered toward noticing that there are two elements of the sum that have a total of -100. Those elements are -65 and -35. With the above in mind, you can use the commutative property to rearrange the sum to ...

  -65 +(-35) +(-150) . . . . . . . last two terms were swapped

Then the first step is to add -65 and -35:

  [tex]\text{It is easier to add }\boxed{-65}\,+\,\boxed{(-35)}\text{ first to get $-100$.}[/tex]

Now, the sum reduces to ...

  -100 +(-150) = -250

So, the final sentence becomes ...

  [tex]\text{Then add }\boxed{-100+(-150)}\text{ to get }\boxed{-250}\,.[/tex]

Answer:

[tex] \boxed{ \bold{ \huge{\boxed{ \sf{ \: 12.9 \: \: dollars}}}}}[/tex]

Step-by-step explanation:

Given,

Cost without tax = $ 12

Tax percent = 7.5 %

Cost including tax = ?

First, finding the tax amount :

[tex] \sf{tax \: amount \: = \: 7.5 \: \% \: of \: 12}[/tex]

⇒[tex] \sf{tax \: amount = \frac{7.5}{100} \times 12} [/tex]

⇒[tex] \sf{tax \: amount = 0.9}[/tex] dollars

Finding the total cost of the lunch including tax :

⇒[tex] \sf{total \: cost \: = \: 12 + 0.9}[/tex]

⇒[tex] \sf{total \: cost \: = \: 12.9}[/tex] dollars

Hope I helped!

Best regards ! :D