given g(x)=3/x^2+2x find g^-1(x)

Answer:

2 cm

Step-by-step explanation:

If x is the length of the sides of the squares, then the height of the box is also x.  The length and width of the base are 10−2x and 20−2x.  The area of the base is the length times the width.

96 = (10 − 2x) (20 − 2x)

96 = 200 − 20x − 40x + 4x²

0 = 4x² − 60x + 104

0 = x² − 15x + 26

0 = (x − 2) (x − 13)

x = 2 or 13

Since x < 5, x = 2.

So the length of the sides of the squares is 2 cm.

Answer:

0.6127 = 61.27% probability of guessing 6 or more questions correctly.

Step-by-step explanation:

For each question, there are only two possible outcomes. Either you guess the correct answer, or you do not. The probability of guessing the correct answer of a question is independent of other questions. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

12 questions:

This means that [tex]n = 12[/tex]

True-false:

Two options, one of which is correct. So [tex]p = \frac{1}[2} = 0.5[/tex]

Find the probability of guessing 6 or more questions correctly.

[tex]P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 6) = C_{12,6}.(0.5)^{6}.(0.5)^{6} = 0.2256[/tex]

[tex]P(X = 7) = C_{12,7}.(0.5)^{7}.(0.5)^{5} = 0.1934[/tex]

[tex]P(X = 8) = C_{12,8}.(0.5)^{8}.(0.5)^{4} = 0.1208[/tex]

[tex]P(X = 9) = C_{12,9}.(0.5)^{9}.(0.5)^{3} = 0.0537[/tex]

[tex]P(X = 10) = C_{12,10}.(0.5)^{10}.(0.5)^{2} = 0.0161[/tex]

[tex]P(X = 11) = C_{12,11}.(0.5)^{11}.(0.5)^{1} = 0.0029[/tex]

[tex]P(X = 12) = C_{12,12}.(0.5)^{12}.(0.5)^{0} = 0.0002[/tex]

[tex]P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) = 0.2256 + 0.1934 + 0.1208 + 0.0537 + 0.0161 + 0.0029 + 0.0002 = 0.6127[/tex]

0.6127 = 61.27% probability of guessing 6 or more questions correctly.

Answer:

P

Step-by-step explanation:

Count the line endings in each letter as you write it down.

Answer:

I agree with tonb .Ace,he's/she's right

Answer:

B. [tex] \frac{7x^2 + 11x}{x^2 + 6x + 5} [/tex]

Step-by-step explanation:

The sum is worked as shown below:

[tex] \frac{x}{x + 1} + \frac{6x}{x + 5} [/tex]

Use the common denominator to divide each denominator, then use the result to multiply the numerator, you'd have the following:

[tex] \frac{x(x + 5) + 6x(x + 1)}{(x + 1)(x + 5)} [/tex]

Use the distributive property of multiplication to solve

[tex] \frac{x(x) + x(5) + 6x(x) + 6x(1)}{(x(x + 5) + 1(x + 5)} [/tex]

[tex] \frac{x^2 + 5x + 6x^2 + 6x}{x^2 + 5x + x + 5} [/tex]

Pair like terms

[tex] \frac{x^2 + 6x^2 + 5x + 6x}{x^2 + 6x + 5} [/tex]

[tex] \frac{7x^2 + 11x}{x^2 + 6x + 5} [/tex]

The answer is B.

Answer:

A) v = f(x) = 96 -32x

B)the velocity when x = 0

V = 96 ft/s

The velocity when x =4

V = -32 ft/s

C). Time when v= 0

3 seconds = x

Step-by-step explanation:

f(x) = 96x -16x^2

The above equation represents the position of the object at x time along the x axis.

The velocity will be determined by differentiating the equation with respect with x

f(x) = 96x -16x^2,

D f(x)/Dx= 96 -2(16x)

D f(x)/Dx= 96 -32x

v = f(x) = 96 -32x

The velocity when x = 0

v = f(x) = 96 -32x

V = f(0) = 96-32(0)

V = 96 ft/s

The velocity when x = 4

v = f(x) = 96 -32x

V = f(4) = 96-32(4)

V = 96 - 128

V = -32 ft/s

Time when v= 0

v = f(x) = 96 -32x

0= 96 -32x

-96= -32x

-96/-32=x

3 seconds = x

Answer:

These payments will be worth $11,332.94.

Step-by-step explanation:

We can calculate this as an annuity but with monthly periods and monthly interest rates.

Then, we have:

C = cash flow per period = $210

n = number of payments = 48

i = interest rate = 0.49% = 0.0049

Then, we can calculate the future value of this stream of deposits as:

[tex]FV=C\left[\dfrac{(1+i)^n-1}{i}\right]\\\\\\FV=210\left[\dfrac{(1.0049)^{48}-1}{0.0049}\right]=210\left[\dfrac{1.2644-1}{0.0049}\right]=210\left[\dfrac{0.2644}{0.0049}\right]\\\\\\FV=210\cdot 53.966\\\\\\FV=11332.94[/tex]

Answer:

Step-by-step explanation:

Question:

4(y - 3) = 48

1. Distribute

4y - 12 = 48

2. Simplify Like terms

4y - 12 = 48

    + 12 + 12

4y = 60

3. Solve

4y = 60

/4       /4

y = 15

4. Check:

4(y - 3) = 48

4((15) - 3) = 48

4(12) = 48

48 = 48     Correct!

Hope this helped,

Kavitha

Answer:

[tex]y=15\\[/tex]

Step 1:

To find y, we first have to multiply [tex]4(y-3)[/tex]. When we do that (4 * y, 4 * - 3), we get [tex]4y-12[/tex].

Step 2:

Our equation looks like this now:

[tex]4y-12=48[/tex]

To solve this equation, we have to add 12 on both sides so we can cancel out the -12 on the left side of the equation.

[tex]4y-12(+12)=48(+12)[/tex]

[tex]4y=60[/tex]

Now, we can divide 4 on both sides to get y  by itself.

[tex]4y/4\\60/4[/tex]

[tex]y=15[/tex]

Answer:

[tex]\boxed{\mathrm{view \: explanation}}[/tex]

Step-by-step explanation:

A) 3x²c² + 5xc² - 2c²

Factor c² from all terms in the expression.

c²(3x² + 5x - 2)

Factor 3x² + 5x - 2

c²(3x-1)(x+2)

B) x² + 6x + 9

x² + 3x + 3x + 9

Factor common terms.

x(x+3)+3(x+3)

Take x+3 common.

(x+3)(x+3)

C) x² - 9

x² -3²

Apply formula : a² - b² = (a+b)(a-b)

(x+3)(x-3)

Answer:

A) [tex]c^2(3x-1)(x+2)[/tex]

B) [tex](x+3)(x+3)[/tex]

C) [tex](x+3)(x-3)[/tex]

Step-by-step explanation:

Part A:

[tex]3x^2c^2+5xc^2-2c^2[/tex]

Taking [tex]c^2[/tex] common

[tex]c^2(3x^2+5x-2)[/tex]

Using mid term break formula

[tex]c^2 (3x^2+6x-x-2)[/tex]

[tex]c^2[3x(x+2)-1(x+2)][/tex]

[tex]c^2(3x-1)(x+2)[/tex]

Part B:

[tex]x^2 + 6x + 9.[/tex]

[tex](x)^2+2(x)(3)+(3)^2[/tex]

[tex](x+3)^2[/tex]

[tex](x+3)(x+3)[/tex]

Part C:

[tex]x^2-9[/tex]

[tex](x)^2-(3)^2[/tex]

[tex](x+3)(x-3)[/tex]

Answer:

If we have a function f(x) = y.

the set of possible values of x is called the domain

the set of possible values of y is called the range.

In this case, we have:

Blood alcohol content vs Reflex time,

The possible values of alcohol in blood content depend on the particular person, but we can have a minimum of 0.0 (no alcohol in blood) and a maximum of .51 (for a 90 lb person) because at this range the person enters the risk of death.

So the domain is: D = [0.0, 0.51]

But, we actually can have higher values of alcohol in blood, so we actually can use a domain:

D = [0.0, 1.0]

For the range, we need to see at the possible values of the reflex time.

And we know that the human reflex time is in between 100ms and 500ms

So our range can be:

R = [100ms, 500ms]

Answer:

672

Step-by-step explanation:

If we call the number of non-fiction books as x, the number of fiction books would be 3x. Therefore: we can write the following equation:

3x - 120 = 2(x - 24)  ← the 3x - 120 and x - 24 represents the new number of books

3x - 120 = 2x - 48

x - 120 = 48

x = 168 which means 3x = 3 * 168 = 504, therefore the total number of books is 168 + 504 = 672.

Answer:

Step-by-step explanation:

Given : In a circle O,

AB is a diameter and CD⊥AB,

To Prove :

ΔADC ~ ΔACB

Solution :

In ΔADC and ΔACB,

m∠ADC = 90° [Given]

m∠ACB = 90° [Angle subtended by the diameter = 90°]

m∠ADC ≅ m∠ACB ≅ 90°

∠A ≅ ∠A [Reflexive property]

Therefore, ΔADC ~ ΔACB [By AA postulate of similarity]

Answer:

L = [tex]\frac{V}{HW}[/tex]

Step-by-step explanation:

Given

V = LHW ( isolate L by dividing both sides by HW )

[tex]\frac{V}{HW}[/tex] = L

Answer:

[tex]l = \frac{v}{w \times h} [/tex]

Step-by-step explanation:

[tex]v = l \times w \times h = \frac{v}{w \times h} = \frac{l \times h \times w}{w\times h} = l = \frac{v}{w \times h} [/tex]

Hope this helps ;) ❤❤❤

Answer:

C

Step-by-step explanation:

It is the graph of f(x) translated 3 units down. Think about in numerical terms,

if      y = 5     y-1  = 5- 1 = 4, so that's what is happening with all numbers on the y axis. You have y = f(x) and you do y-3 = f(x)-3, so, all "y" points are translated 3 units down

Answer:

x = 8

Step-by-step explanation:

x + 4 = 12

x=12-4

x=8

Answer:

8

Step-by-step explanation:

x+4=12, so 12-4=x (if you use an the inverse operation of addition, subtraction.)

12-4=x, so all you have to do is subtract and, there you have it, 8. It makes sense, 8+4=12. :)

Answer:

16.97 Units

Step-by-step explanation:

From the graph

Point W is located at (-6,4)

Point X is located at (6,-8)

To determine the distance between points W and X, we use the distance formula.

[tex]\text{Distance Formula}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex](x_1,y_1)=(-6,4)\\(x_2,y_2)=(6,-8)[/tex]

So,

[tex]WX=\sqrt{(6-(-6))^2+(-8-4)^2} \\=\sqrt{(6+6)^2+(-12)^2}\\=\sqrt{(12)^2+(-12)^2}\\=\sqrt{288}\\=16.97$ units (correct to the nearest hundredth)[/tex]

Answer:

The answer is option B

Step-by-step explanation:

To solve for x we use tan

tan ∅ = opposite / adjacent

From the question

The adjacent is x

The opposite is 19

So we have

tan 29 = 19/ x

x = 19/ tan 29

x = 34.276

Hope this helps

Answer:

x ≈ 34.28

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan29° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{19}{x}[/tex] ( multiply both sides by x )

x × tan29° = 19 ( divide both sides by tan29° )

x = [tex]\frac{19}{tan29}[/tex] ≈ 34.28 ( to the nearest hundredth )

Answer:

0.11

Step-by-step explanation:

Hello,

[tex]P(A|B)=\dfrac{P(A\cap B)}{P(B)} \ \ \text{ so ...}\\\\P(A\cap B)=P(A|B)\cdot {P(B)= 0.55 * 0.2 = 0.11\\[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

a. Total amount after 65 years = $1179415.39

b. The total contribution to the account  = $288000

Step-by-step explanation:

Given annuity amount = $1800

Total number of years for contribution = 65 – 25 = 40 years

Interest rate  = 6%

a. Total amount after 65 years = Annuity[((1+r)^n -1) / r]

Total amount after 65 years = 1800×((1+.06/4)^(4 × 40) - 1)/(.06/4)

Total amount after 65 years = $1179415.39

b. The total contribution to the account =1800 × 4 Quarter × 40 Years

        The total contribution to the account  = $288000

Answer:

C. [tex]\Rightarrow \bold{8x = 16}[/tex]

Step-by-step explanation:

Given the two equations:

[tex]y=2x ........ (1)\\ 2x+3y=16.......(2)[/tex]

To find:

The correct option when value of y is substituted to 2nd equation using the 1st equation.

Solution:

First of all, let us learn about the substitution method.

Substitution method is the method to provide solutions to two variables when we have two equations and two variables.

In substitution method, we find the value of one variable in terms of the other variable and put this value in the other equation.

Now, the other equation becomes only single variable and then we solve for the variable's value.

Here, we have two equations and value of one varible is:

[tex]y=2x[/tex]

Let us put value of y in 2nd equation:

[tex]2x+3y=16\\\Rightarrow 2x + 3(2x) = 16\\\Rightarrow 2x + 6x = 16\\\Rightarrow \bold{8x=16}[/tex]

So, the correct answer is option C. [tex]\Rightarrow \bold{8x = 16}[/tex]

Answer: 8x=16

Step-by-step explanation:a pex

Hey there! I'm happy to help!

First, let's multiply this thickness by one million to see how many inches this  pile is.

0.0043*×1,000,000=4,300 inches

We know that there are 12 inches in a foot and 3 feet in a yard, so there must be 36 inches in a yard.

So, we divide our 4,300 inches by 36 to find how many yards high this pile is.

4300÷36=119 4/9

Therefore, a pile of a million $1 bills is 119 4/9 yards high.

Have a wonderful day! :D

Answer:

-$2.63

Step-by-step explanation:

Calculation for the expected profit for one spin of the roulette wheel with this bet

Based on the information given you bet $50 on 00 while the standard roulette has 38 possible outcomes which means that the probability or likelihood of getting 00 will be 1/38.

Therefore when we get an 00, we would get the amount of $1,750 with a probability of 1/38 and in a situation where were we get something other than 00 this means we would lose $50 with a probability of 37/38.

Now let find the Expected profit using this formula

Expected profit = sum(probability*value) -sum(probability*value)

Let plug in the formula

Expected profit =($1,750 * 1/38) - ($50 * 37/38)

Expected profit=($1,750*0.026315)-($50×0.973684)

Expected profit= 46.05 - 48.68

Expected profit = - $2.63

Therefore the expected profit for one spin of the roulette wheel with this bet will be -$2.63

Answer:

-2/9

Step-by-step explanation:

When you multiply a number by its multiplicative inverse, you should get 1. So, the multiplicative inverse (or reciprocal) of -9/2 is 1/(-9/2) which is -2/9. You can get the answer by simply flipping the numerator and denominator.

Answer:

C = 31.4 cm

Step-by-step explanation:

C = pi * d where d is the diameter

C = 3.14 * 10

C = 31.4 cm

Circumference = pi x diameter

                         = 3.14 x 10

                         = 31.4 cm

The answer is D. 31.4 cm.

Answer:

140

Step-by-step explanation:

2{ 2[24 + 4(9)-25]}

2{ 2[24 + 36-25]}

2{ 2[35]}

2(70)

140

Answer:

B)Gift shop

pls mark me as BRAINLIEST

hope the answer helped you

Answer: sample required n = 18

Step-by-step explanation:

Given that the value under under null hypothesis is 40 while the value under the alternative is less than 40, specifically 35.9

∴ H₀ : u = 40

  H₁  : u = 35.9

therefore β = ( 35.9 - 40 ) = -4.1

The level of significance ∝ = 0.05

Probability of committing type 11 error P = 0.1

standard deviation α = 5.8

Therefore our z-vales (z table)

Z₀.₅ = 1.645

Z₀.₁ = 1.282

NOW let n be sample size

n = {( Z₀.₅ + Z₀.₁ )² × α²} / β²

n = {( 1.645 + 1.282 )² × 5.8²} / (- 4.1)²

n = 17.14485

Since we are talking about sample size; it has to be a whole number

therefore

sample required n = 18

Answer:

 P [ Z >  24,1 ] =  72,24 %

Step-by-step explanation:

P [ Z > 24,1 ]  =  1  - P [ Z < 24,1 ]

P [ Z < 24,1 ] = ( Z - μ₀ ) / σ

P [ Z < 24,1 ] = ( 24,1 - 25,4) / 2,1

P [ Z < 24,1 ] = - 1,3/ 2,1

P [ Z <  24,1 ] = - 0,6190  ≈ - 0,62

We look in z-table and find for  z(score) -0,6190

P [ Z <  24,1 ] = 0,27763

Then

P [ Z >  24,1 ] = 1 - 0,27763

P [ Z >  24,1 ] = 0,72237    ⇒    or       P [ Z >  24,1 ] =  72,24 %

Answer:

X= 50°

Y= 70°

Z= 30°

BDE= 30°

2BDE= 60°

Step-by-step explanation:

(2x -70 )+z+(2x+20)=180...(sum of angle on a straight line)

2x -70 = BDE... alternate angles

Y + (2x-70)+(50+x-20) = 180...(sum of angles in a triangle)

X-20 = z ... alternate and opposite angles

(2x -70 )+z+(2x-+20)=180

2x-70 + x-20 +2x +20= 180

5x -70= 180

5x = 250

X= 50°

X-20 = z

50-20= z

30° = z

2x -70 = BDE

2(50) -70 = BDE

100-70 = BDE

30°= BDE

Y + (2x-70)+(50+x-20)

Y + 100-70 +50 +50 -20 = 180

Y + 200-90=180

Y= 70°

2BDE = 2*30

2BDE= 60°

Answer:

12

Step-by-step explanation:

The second diagram is most helpful for finding the surface area.

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