Which expression is equivalent to
R^9/r^3?

Answer:

192

Step-by-step explanation:

geometric mean theorem :

with p and q being the segments of the Hypotenuse, then

h = x = sqrt(p×q)

p = 144

q = 400-144 = 256

h = x = sqrt(144×256) = 12×16 = 192

Answer:

[tex]n = 8[/tex]

Step-by-step explanation:

Given

[tex]3(^nP_2 + 24) = ^{2n}P_2[/tex]

Required

Find n

To do this, we simply apply permutations formula

[tex]nP_r = \frac{n!}{(n -r)!}[/tex]

So, we have:

[tex]3 * [\frac{n!}{(n -2)!} + 24] = \frac{2n!}{(2n -2)!}[/tex]

Expand

[tex]3 * [\frac{n * (n - 1) * (n - 2)!}{(n -2)!} + 24] = \frac{2n * (2n - 1) * (2n - 2)}{2n - 2}[/tex]

[tex]3 * [n * (n - 1) + 24] = 2n * (2n - 1)[/tex]

[tex]3 * [n^2 - n + 24] = 4n^2 - 2n[/tex]

Open bracket

[tex]3n^2 - 3n + 72 = 4n^2 - 2n[/tex]

Collect like terms

[tex]3n^2 - 4n^2- 3n+2n + 72 = 0[/tex]

[tex]-n^2- n + 72 = 0[/tex]

Expand

[tex]-n^2 -9n + 8n + 72 = 0[/tex]

Factorize

[tex]-n(n +9) - 8(n + 9) = 0[/tex]

Factor out n + 9

[tex](-n -8)(n + 9) = 0[/tex]

Split

[tex](-n -8)= 0 \ or\ (n + 9) = 0[/tex]

Solve for n

[tex]n =8\ or\ n = -9[/tex]

The positive value is [tex]n = 8[/tex]

Answer:

cannot understand the language man

but please follow

Answer:

37/43

Step-by-step explanation:

6+12+14+11=43

Males: 6+14=20

Females: 11+12=23

If the selected person is a teaching assistant or a female, then the probability is 11+12+14=37. 37/43

Answer:

-0.54

Step-by-step explanation:

Hope it helped.

• • •

Answer:

Force need F2 = 2000 N

Step-by-step explanation:

Given:

Weight F1 = 25 kg = 25 x 10 = 250 N

Length L1 = 32 cm

Add new length = 4 cm

Net momentum = 0

Find:

Force need F2

Computation:

F2L2 - F1L1 = 0

F2(4) - (250)(32) = 0

F2(4) - 8000 = 0

F2(4) = 8000

F2 = 8000 / 4

F2 = 2000

Force need F2 = 2000 N

Answer:C

Step-by-step explanation:

A correlation of -0.97 is a strong negative correlation while a correlation of 0.10 would be a weak positive correlation

Answer:

C) strong negative.

Step-by-step explanation:

According to Chebyshev,

P(|X - µ| ≤ 2.9σ) ≥ 1 - 1/2.9² ≈ 0.8811

Answer:

The function will be exist if and only if :

[tex] \frac{ - x + 3}{2} > 0 \\ = > - x + 3 > 0 \\ = > - x > - 3 \\ = > x < 3 \\ \\ \therefore \bf \: domain \: \: \green{x < 3}[/tex]

Answer:

8 cm^2

Step-by-step explanation:

If the triangle is isosceles the sides are the same

Let the sides be x

We know that we can use the Pythagorean theorem

a^2+b^2 = c^2 where a and b are the sides and c is the hypotenuse

x^2+x^2 = (4 sqrt(2))^2

2x^2 =16(2)

2x^2 = 32

Divide by 2

2x^2/ 32/2

x^2 = 16

Taking the square root of each side

sqrt(x^2) = sqrt(16)

x = 4

The area of the triangle is

A =1/2 bh

A = 1/2 (4) (4)

A = 1/2(16)

A = 8

Answer:

8

Step-by-step explanation:

a^2 + b^2 = c^2

c = [tex]4\sqrt{2}[/tex]

[tex]c^{2} = 32[/tex]

a^2 + b^2 = 32

a=b (isosceles triangle)

a=b=4

base = 4

height = 4

area = 1/2 bh = 1/2(4)(4) = 8

Answer: 275 adults and 130 children

Step-by-step explanation:

First, find the value of one variable by rearranging a equation:

[tex]a+c=405\\c=405-a[/tex]

Substitute it into the other equation and solve for a:

[tex]12a+5c=3950\\12a+5(405-a)=3950\\12a+2025-5a=3950\\12a-5a=3950-2025\\7a=1925\\a=\frac{1925}{7} =275[/tex]

Use the a-value to find b by substituting it into the rearranged equation:

[tex]c=405-a=405-275=130[/tex]

Therefore, the answer would be:

[tex]\left \{ {{a=275} \atop {c=130}} \right.[/tex]

Answer:

B the range, the x- and y-intercept

Step-by-step explanation:

the domain stays the same : all values of x are possible out of the interval (-infinity, +infinity).

but the range changes, as for the original function y could only have positive values - even for negative x.

the new function has a first term (with b) that can get very small for negative x, and then a subtraction of 2 makes the result negative.

the y-intercept (x=0) of the original function is simply y=1, as b⁰=1.

the y-intercept of the new function is definitely different, because the first term 3×(b¹) is larger than 3, because b is larger than 1. and a subtraction of 2 leads to a result larger than 1, which is different to 1.

the original function has no x-intercept (y=0), as this would happen only for x = -infinity. and that is not a valid value.

the new function has an x-intercept, because the y-values (range) go from negative to positive numbers. any continuous function like this must therefore have an x-intercept (again, y = the function result = 0)

[tex] 3 {b}^{x + 1} = 2[/tex]

[tex] {b}^{x + 1} = 2 \div 3[/tex]

[tex] log_{b}(2 \div 3) = x + 1[/tex]

[tex]x = log_{b}(2 \div 3) - 1[/tex]

Answer:

The answer is "0.6368 and 0.773".

Step-by-step explanation:

The manufacturer of organic compounds guarantees that its clients have at least 100 lbs. of solvent in every fluid drum they deliver. [tex]X\ is\ N(101.8, 3.76)\\\\P(X>100) =P(Z> \frac{100-101.8}{3.76}=P(Z>-0.47))[/tex]

For point a:

Therefore the Probability =0.6368  

For point b:

[tex]P(Z\geq \frac{100-101.8}{\sigma})=0.99\\\\P(Z\geq \frac{-1.8}{\sigma})=0.99\\\\1-P(Z< \frac{-1.8}{\sigma})=0.99\\\\P(Z< \frac{-1.8}{\sigma})=0.01\\\\z-value =0.01\\\\area=-2.33\\\\ \frac{-1.8}{\sigma}=-2.33\\\\ \sigma= \frac{-1.8}{-2.33}=0.773[/tex]

Answer:

The number is 16

Step-by-step explanation:

Number : x

Procedure and resolution:

6x = 96

x = 96/6

x = 16

Answer:

Degree of freedom = 2

Expected frequency = 80%

Critical value, = 5.991

χ² statistic = 3.5

Step-by-step explanation:

Given the data :

Hong Kong New York Paris

Yes 86% 76% 78%

No 14% 24% 22%

The degree of freedom for the Chisquare statistic is given as :

(no of rows - 1) * (number of columns - 1)

Number of rows = 2

Number of columns = 3

. Degree of freedom = (2-1) * (3-1) = 1*2 = 2

Expected frequency = (Row total * column total) / grand total

The expected frequency of Hong Kong / Yes cell :

Row total = (86+76+78) = 240

Column total = (86+14) = 100

Grand total, N = (14+24+22)+240 = 300

Expected frequency = (240*100)/300 = 80%

The critical value :

At α - level = 0.05 ; df = 2

Critical value = 5.991

χ² = Σ(observed - Expected)² / Expected

The expected values :

80 80 80

20 20 20

Hence,

χ² = Σ(86-80)²/80 + (76-80)²/80 + (78-80)²/80 + (14-20)²/20 + (24-20)²/20 + (22-20)²/20

χ² statistic = 3.5

Answer:

[tex]T=812[/tex]

Step-by-step explanation:

From the question we are told that:

No. Committee Members [tex]n=6[/tex]

Pool of : 5 students and 7 faculty members

At least 2 student members and at least 1 faculty member

Generally the committee is mathematically given by

The Total Events are

[tex]T=(^5C_2*^7C_4)+(^5C_3)*(^7C_3)+(^5C_4)*(^7C_2)+(^5C_5)*(^7C_1)[/tex]

[tex]T=350+350+105+7[/tex]

[tex]T=812[/tex]

Answer:

78 yards

Step-by-step explanation:

The perimeter of a rectangle is given by

P = 2(l+w)

346 = 2(95+w)

Divide each side by 2

346/2 = 2/2(95+w)

173 = 95+w

Subtract 95 from each side

173-95 = 95+w-95

78 = w

Answer:

x = 8

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Step-by-step explanation:

Step 1: Define

Identify

6x - 6 = 42

Step 2: Solve for x

Answer: -6

Step-by-step explanation:

We can create an equation based on the info given.

6-6x=42 Now you solve for x, the unknown number.

-6      -6      Subtract 6 on both sides

-6x=36

/-6   /-6       Divide by -6 on both sides

x=-6

The number is -6.

Answer:

The probability is: 0.8889.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Approved

Event B: Qualified

Probability of a person being approved:

80% of 75%(qualified)

30% of 25%(not qualified). So

[tex]P(A) = 0.8*0.75 + 0.3*0.25 = 0.675[/tex]

Probability of a person being approved and being qualified:

80% of 75%, so:

[tex]P(A \cap B) = 0.8*0.75[/tex]

Find the probability that a person is qualified if he or she was approved by the manager.

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.8*0.75}{0.675} = 0.8889[/tex]

The probability is: 0.8889.

Answer:

The correct answer is - $720 or 20%.

Step-by-step explanation:

Given:

Total expense = 3600

Electric=30%

Heating and gas=50%

Water and sewer=X%

Solution:

For electric: 3600*30/100 = 1080

for heating and gas: 3600*50/100 = 1800

Left money for expense of water and shower = total - (electric and heating)

= 3600-1880

= 720

Percentage of water and shower = 720*100/3600

= 20%

Answer:

Correct!

Step-by-step explanation:

Thank you this is correct :) I took the test

( x - 2 )( x - 8 )( x + 5 ) =

( x^2 - 10x + 16 )( x + 5 ) =

x^3 - 10x^2 + 16x + 5x^2 - 50x + 80 =

x^3 + ( - 10 + 5 )x^2 + ( 16 - 50)x + 80 =

x^3 - 5x^2 - 34x + 80

Answer:

x=13.2

Step-by-step explanation:

cos(43)=x/18

x=18×cos(43)

x=13.2

Answered by GAUTHMATH

Answer: A)  4√2 units

Step-by-step explanation:

Use the distance formula to find the distance(d) between Point D and Point C:

[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]

[tex]d=\sqrt{(8-4)^{2}+(2-(-2))^{2}}=\sqrt{(4)^{2}+(4)^{2}}=\sqrt{16+16} =\sqrt{32} =4\sqrt{2}[/tex]

Answer:

[tex]\displaystyle\frac{19,683}{200,000}\text{ or }\approx 9.84\%[/tex]

Step-by-step explanation:

For each planted seed, there is a 90% chance that it grows into a healthy plant, which means that there is a [tex]100\%-90\%=10\%[/tex] chance it does not grow into a healthy plant.

Since we are planting 6 seeds, we want to choose 2 that do not grow and 4 that do grow:

[tex]\displaystyle \frac{1}{10}\cdot \frac{1}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}[/tex]

However, this is only one case that meets the conditions. We can choose any 2 out of the 6 seeds to be the ones that don't grow into a healthy plant, not just the first and second ones. Therefore, we need to multiply this by number of ways we can choose 2 things from 6 (6 choose 2):

[tex]\displaystyle \binom{6}{2}=\frac{6\cdot 5}{2!}=\frac{30}{2}=15[/tex]

Therefore, we have:

[tex]\displaystyle\\P(\text{exactly 2 don't grow})=\frac{1}{10}\cdot \frac{1}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \binom{6}{2},\\\\P(\text{exactly 2 don't grow})=\frac{1}{10}\cdot \frac{1}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot 15,\\\\P(\text{exactly 2 don't grow})=\boxed{\frac{19,683}{200,000}}\approx 9.84\%[/tex]

Answer:

[tex] {?}^{?} However, this is only one case that meets the conditions. We can choose any 2 out of the 6 seeds to be the ones that don't grow into a healthy plant, not just the first and second ones. Therefore, we need to multiply this by number of ways we can choose 2 things from 6 (6 choose 2):

\displaystyle \binom{6}{2}=\frac{6\cdot 5}{2!}=\frac{30}{2}=15(26)=2!6⋅5=230=15

Therefore, we have:

\begin{gathered}\displaystyle\\P(\text{exactly 2 don't grow})=\frac{1}{10}\cdot \frac{1}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \binom{6}{2},\\\\P(\text{exactly 2 don't grow})=\frac{1}{10}\cdot \frac{1}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot 15,\\\\P(\text{exactly 2 don't grow})=\boxed{\frac{19,683}{200,000}}\approx 9.84\%\end{gathered}P(exactly 2 don’t grow)=101⋅101⋅109⋅109⋅109⋅109⋅(26),P(exactly 2 don’t grow)=101⋅101⋅109⋅109⋅109⋅109⋅15,P(exactly 2 don’t grow)=200,00019,683≈9.84%

[/tex]

Answer:

qualitative

Step-by-step explanation:

bcos it is in quality format

Answer:

أنت مجنون ، هل تعرف ذلك؟

Step-by-step explanation:

بنسلفانيا

Answer:

Choice B.

[tex]4x - 2y = 0[/tex]

Step-by-step explanation:

Has integer coefficients and equal to 0.

Answer:

$3

Step-by-step explanation:

7 rands for $1

7×3=21

21 rands for $3

Answer:

$3

Step-by-step explanation:

7 rand = 1 dollar

Divide both sides by 7 rand.

1 = (1 dollar)/(7 rand)

Notice that the fraction (1 dollar)/(7 rand) equals 1, so multiplying by it will not change the amount, just the units.

21 rand * (1 dollar)/(7 rand) =

= 21/7 dollar

= 3 dollar = $3

Answer:

the graph would cut the y-axis 11 units below y=f(x)

Answer:

71

Step-by-step explanation:

The reference angle is always the smallest angle  with the x-axis.

The nearest x axis is at 0 or another name for 0 is 360

360 -289 = 71

The reference angle is 71