find the probability of the event given the odds. express your answer as a simplified fraction. against

If G(x) or H(x) is the inverse of F(x) for the domain x2 then Option B. H(x) is the inverse of F(x) is correct

To determine if G(x) or H(x) is the inverse of F(x), we need to perform function composition and check if it results in the identity function.

Let's start by finding the composition of F(x) and G(x):

(F ∘ G)(x) = F(G(x))

= F((x + 2)²)

= √((x + 2)² - 2)

= √(x² + 4x + 4 - 2)

= √(x² + 4x + 2)

Now let's find the composition of F(x) and H(x):

(F ∘ H)(x) = F(H(x))

= F(x² + 2)

= √(x² + 2 - 2)

= √(x²)

= x

To determine if either G(x) or H(x) is the inverse of F(x), we need to check if the composition results in the identity function.

The identity function is defined as f(x) = x.

Comparing the composition results:

(F ∘ G)(x) = √(x² + 4x + 2)

(F ∘ H)(x) = x

Since (F ∘ H)(x) equals x, we can conclude that H(x) is the inverse of F(x) for the given domain x² ≥ 2.

Therefore, the correct answer is: Option B. H(x) is the inverse of F(x).

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Rounded to the whole number: 6

The required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let 'a' be the cost per gallon of fuel in the year 2000, and 'b' be the inflation rate per year. If the rate of inflation is constant then
After 7 year inflation = 7b
Cost of fuel in 2007 = a + 7b

Now,
according to the question
Change in cost of fuel
= cost in 2007 - cost in 2000
= a + 7b - a
= 7b

Thus, the required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

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Answer:

2x³ + x² - 11x - 15

Step-by-step explanation:

Step 1: Write out expression

2x³ + x² + 7x - 6 - (-2x + 10x + 10x + 9)

Step 2: Distribute negative

2x³ + x² + 7x - 6 + 2x - 10x - 10x - 9

Step 3: Combine like terms (x)

2x³ + x² + 9x - 10x - 10x - 9 - 6

2x³ + x² - x - 10x - 9 - 6

2x³ + x² - 11x - 9 - 6

Step 4: Combine like terms (constants)

2x³ + x² - 11x - 15

Answer:

Im here can u do it now?

Step-by-step explanation:

Answer:

here we have to divide the number of words per hour to the number of minutes per hour.

Step-by-step explanation:

5400÷60

=90.

therefore in a minute she types 90 words.

\(\text{Larger angle} =x\\\\\text{Smaller angle} =y\\ \\\text{According to the condition,}\\\\x=10y+15\\\\\text{The two angles are supplementary, so their sum is}~ 180^{\circ} \\\\x+y=180\\\\\implies 10y+15 +y = 180\\\\\implies 11y = 180-15\\\\\implies 11y=165\\\\\implies y = \dfrac{165}{11}\\\\\implies y = 15\\\\\text{So,} ~x =180-15 = 165\\\\\text{Hence the larger angle is}~ 165^{\circ}~ \text{and the smaller angle is }15^{\circ}\)

A. The Total cost of producing 10 units is $300.

B. The price charged by a monopolist is higher than that charged by firms in an oligopoly market. As a result, some firms will exit the market, supply will shift left, and prices will rise.

C. The MC (Marginal Cost) is $20.

D. The MC is $20.

E. The competitive firm's profit by producing and selling 30 units of output is zero (no profit or loss).

F. Some firms will exit the market, supply will shift right, and prices will fall.

G. The Total cost of producing 30 units is $300.

H. The competitive firm's profit by producing and selling 30 units of output is negative (a loss)

A. If the average total cost (ATC) of producing 10 units is $30, then the total cost of producing 10 units is calculated by multiplying the ATC by the number of units: $30 * 10 = $300.

B. In a monopolistic market, the monopolist has the ability to set higher prices compared to firms in an oligopoly market, where there is some degree of competition. As a result, in an oligopoly market, some firms may find it unprofitable to compete and exit the market. This leads to a decrease in supply, causing prices to rise.

C. and D. The marginal cost (MC) is the additional cost incurred when producing one additional unit of output. If the total cost (TC) increases from $175 to $225 when the firm increases output from 5 to 6 units, the change in TC is $225 - $175 = $50. Since the firm is producing one additional unit, the MC is calculated by dividing the change in TC by the change in output: $50 / 1 = $50.

E. In a competitive market, firms aim to maximize their profits. If the price is $10 and the average total cost (ATC) is $58, the firm's profit per unit is $10 - $58 = -$48 (a loss). By producing and selling 30 units of output, the total profit is calculated by multiplying the profit per unit by the number of units: -$48 * 30 = -$1,440. Therefore, the competitive firm's profit is zero (no profit or loss).

F. When firms in a competitive market are making losses, some firms may find it unsustainable to continue operating and choose to exit the market. As a result, the overall supply in the market decreases, leading to a leftward shift in the supply curve. This reduction in supply can eventually lead to an increase in prices.

G. The total cost of producing 30 units can be calculated by multiplying the ATC by the number of units: $10 * 30 = $300.

H. In a competitive market, if the firm's profit is negative (a loss), it means that the firm's costs exceed its revenue. Therefore, the competitive firm's profit by producing and selling 30 units of output would be negative (a loss).

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Answer:

jjjhhvvbjkknnnnmknnmkkkjnnnnnnnnnnnn

The return on assets (ROA) for Harley-Davidson, Inc. in 2016 can be calculated using the given information.

Return on assets (ROA) is a financial ratio that measures a company's profitability by comparing its net income to its total assets. It indicates how efficiently a company is utilizing its assets to generate profit. The formula for ROA is: ROA = Net Income / Total Assets. From the given information, the net income for 2016 is $692 million, and the total assets are $9,890 million. Plugging these values into the formula, we can calculate the ROA for 2016: ROA = 692 / 9,890

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From the figure, the coordinates center of the circle is (x, y)=(-1, -2).

The horizontal distance from the center of the circle to one point of the circle gives the radius of the circle.

So, the radius of the circle is r=4.

Now, the circumference of the circle can be calculated as,

Therefore, the approximate circumference of the circle is 25.1 units.

Option B is correct.

The probability of rolling an even number, then the number 3 is 1/12.

Given that Jeremy will roll a number cube, numbered 1-6, twice.

Now, the possible outcomes are {1,2,3,4,5,6} and out of this the number of even numbers choices are {2,4,6}. Therefore, the probability of getting an even number will be,

Probability(Even)

= Number of Even outcomes possible/Number of outcomes possible

= 3/6

Further, the probability of getting the number 3 will be,

Probability(x=3)

= Number of outcomes possible/Number of outcomes possible

= 1/6

Therefore, the probability of rolling an even number, then the number 3 is,

Probability

= Probability(Even) × Probability(x=3)

= (3/6) × (1/6)

= 3/36

= 1/12

Hence, the correct option is D.

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Answer:

Step-by-step explanation:

5) 121/11 = 11 meals / day

6) 50/10 = 5 min/call

7) 91/7 = 13 books / week

8) 1275 ants/5 ant holes = 255 ants / ant hole

The number of subs in the order is 8 or 9

Let's call the number of subs in the order "x".

Since the cost of 3 subs is $20, the cost per sub is $20 / 3 = $6.67.

And since the cost of 4 subs is $26, the cost per sub is $26 / 4 = $6.50.

So the cost per sub is between $6.50 and $6.67.

If the total cost is $56, then the cost per sub must be $56 / x.

So:

x = 56/6.5 or x = 56/6.67

Evalutate

x = 8.6 or x = 8.4

Approximate

x = 9 or 8

Hence, the subs is 8 to 9

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Answer:

yes, after 7 weeks they will have the same amount of money. 46 dollars.

Step-by-step explanation:

First start of by writing an expression to represent this problem

11 + 5x = 60 - 2x

combine like terms. and find value of x.

subtract 11 from the 60

5x = 49 - 2x

move the 2x over to the other side. So + 2x

7x = 49

divide 7 from 49

49/7

x = 7

x=7 amount of weeks they will have the same amount of money

Answer:

21.78

Step-by-step explanation:

87.13/4=21.78

Answer:

A. Juan wins the race

B. At about 7 minutes J(t )= A(t)

C. 2 minutes

Step-by-step explanation:

A. Juan wins the race. This is because she covers the distance in a shorter time interval than Antonio

B. At about 7 minutes J(t )= A(t). to get this, just look at the point that the two curves intersect on the graph, and trace it down to the time axis to read off the time.

C. J(t) is greater than A(t) with about 2 minutes. To get this, we just subtract the time Juan arrived at the finish line from the time Antonio arrived, this is = 15 -13 = 2 minutes

Answer:

6.55 miles

Step-by-step explanation:

26.2 miles in 4 hours means 6.55 each hour adds up to the total.

Do ---> 26.2 divided by 4 to get hourly miles = 6.55

The increase in the average movie theater ticket price from 2015 to 2016 is $1.22 and 14.97% in percentage terms

What is the average price increase between 2016 and 2015?

The increase in the average movie theater ticket price from 2015 to 2016 can be determined as the difference between 2016 and 2015 prices divided by the 2015 price, bearing in mind that movie theater ticket price is the base price

increase in price in 2016=$9.37- ​$8.15

increase in price in 2016=$1.22

% increase in  movie theater ticket price=$1.22/$8.15

% increase in  movie theater ticket price=14.97%

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Answer:

To determine the amount of oil needed per cup of water, we need to find the ratio between the oil and water quantities given in the recipe.

According to the recipe:

1/4 cup of oil is required for every 2/3 cup of water.

To find the amount of oil needed per cup of water, we can set up a proportion:

1/4 cup of oil / 2/3 cup of water = x cups of oil / 1 cup of water

To solve for x, we can cross-multiply and then divide:

(1/4) * (1 cup of water) = (2/3) * (x cups of oil)

1/4 = (2/3) * (x cups of oil)

To isolate x, we can multiply both sides of the equation by the reciprocal of (2/3), which is (3/2):

(1/4) * (3/2) = (2/3) * (x cups of oil) * (3/2)

3/8 = (2/3) * (x cups of oil) * (3/2)

Now, let's simplify the equation:

3/8 = x/1

x = 3/8

Therefore, per cup of water, you would need approximately 3/8 cups of oil.

Step-by-step explanation:

The amount of work done on the system during the isothermal and reversible expansion of 1.742 moles of the gas from an initial volume of 8.253 L to a final volume of 41.81 L is approximately -1,204.7 J.

To find the amount of work done on the system, we can use the equation for work done during an isothermal and reversible expansion of a gas:

W = -∫PdV

In the given equation of state, P + \(V^2\)(an²) /\(V^n^R^T\), we can solve for P in terms of V and substitute it into the work equation:

P = \(V^n^R^T\) / (\(V^n\) - \(V^2\)(an²))

Now we can calculate the work done by integrating this expression with respect to V over the given range of volumes:

W = -∫(\(V^n^R^T\) / (\(V^n\) -\(V^2\)(an²))) dV

Integrating this expression gives us the amount of work done on the system. Plugging in the values: n = 1.742 moles, V1 = 8.253 L, V2 = 41.81 L, R = 0.0821 L·atm/(mol·K), T = 20.3 + 273.15 K, and a = 4.1702 atm/\(mol^2\), we can evaluate the integral and find the result to be approximately -1,204.7 J.

Therefore, the amount of work done on the system is -1,204.7 J.

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The remainder when x³ - 1 is divided by (x + 3) is  -28

The functions are given as

x 3 1 is divided by x 3

Rewrite them as

f(x) = x³ - 1 is divided by (x + 3)

Set the divisor to 0

So, we have

x + 3 = 0

Determine the value of x

This gives

x = -3

By the remainder theorem

Substitute x = -3 in the function f(x)

So, we have

f(-3) = (-3)³ - 1

Evaluate the expression

f(-3) = -28

By the remainder theorem, this represents the remainder

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Answer:

Step-by-step explanation:

If 25 new born babies are randomly selected, what is the probability that the 25 babies

are born that their mean weigh less than 3100g?

a. What are the parameters?

b. Construct the normal distribution density curve, then shade your seeking area.

c. Find the Z-score, and construct the standard normal distribution density curve,

then shade your seeking area.

H. Find the probability.

Answer:



Step-by-step explanation:



If 25 new born babies are randomly selected, what is the probability that the 25 babies

are born that their mean weigh less than 3100g?

a. What are the parameters?

b. Construct the normal distribution density curve, then shade your seeking area.

c. Find the Z-score, and construct the standard normal distribution density curve,

then shade your seeking area.

H. Find the probability.

Answer:



Step-by-step explanation:



If 25 new born babies are randomly selected, what is the probability that the 25 babies

are born that their mean weigh less than 3100g?

a. What are the parameters?

b. Construct the normal distribution density curve, then shade your seeking area.

c. Find the Z-score, and construct the standard normal distribution density curve,

then shade your seeking area.

H. Find the probability.

Answer:



Step-by-step explanation:



If 25 new born babies are randomly selected, what is the probability that the 25 babies

are born that their mean weigh less than 3100g?

a. What are the parameters?

b. Construct the normal distribution density curve, then shade your seeking area.

c. Find the Z-score, and construct the standard normal distribution density curve,

then shade your seeking area.

H. Find the probability.

Answer:



Step-by-step explanation:



Question

If 25 new born babies are randomly selected, what is the probability that the 25 babies

are born that their mean weigh less than 3100g?

a. What are the parameters?

b. Construct the normal distribution density curve, then shade your seeking area.

c. Find the Z-score, and construct the standard normal distribution density curve,

then shade your seeking area.

H. Find the probability.Question

If 25 new born babies are randomly selected, what is the probability that the 25 babies

are born that their mean weigh less than 3100g?

a. What are the parameters?

b. Construct the normal distribution density curve, then shade your seeking area.

c. Find the Z-score, and construct the standard normal distribution density curve,

then shade your seeking area.

H. Find the probability.

Answer:

I think it's 34.12 inches

Step-by-step explanation:

Use the Phythagorean Theorem, because bisecting a rectangle using the diagonal will produce 2 triangles. The diagonal represents the hypotenuse of the triangle so to solve for it you'd use the formula c² = a²+b²

The box measures 100.79 cm by 100.79 cm by 50.40 cm in size, which minimizes the quantity of material used.

Given,

Let the side of the square base be x

h be the height of the box

Volume V = x²h

512000 = x²h

h = 512000/x² ..... 1

Surface area =  x² + 2xh + 2xh

Surface area S =  x² + 4xh  ...... 2

Substitute 1 into 2;

From 2;

S =  x² + 4xh

S = x² + 4x(512000/x²)

S = x² + 2048000/x

To minimize the amount of material used;

dS/dx = 0

dS/dx = 2x - 2048000/x²

0 = 2x - 2048000/x²

0 = 2x³ - 2048000

2x³ = 2048000

x³ = 1024000

x = ∛1024000

x = 100.79 cm

Since Volume = x²h

512000 = 100.79²h

h = 512000/10158.62

h = 50.40 cm

Hence the dimensions of the box that minimize the amount of material used is 100.79 cm by 100.79 cm by 50.40 cm

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If a system of two linear equations has one solution, the two lines will intersect at exactly one point on the graph.

A linear equation is the one in which the variables are raised to power 1 or -1.

The solution of an equation refers to all the possible values of the variable that can satisfy the equation.

Linear equations can be solved graphically by plotting the lines of the given equations and the point of intersection of lines gives the solution.

The lines will intersect as many times as there are solutions to the given system of linear equations.

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The pieces of cloth are beyond the standard at 0.05 level of significance.

We can use a one-sample t-test to determine if the mean length of the 35 pieces of cloth is significantly different from the standard length of 3.25 meters.

The null hypothesis is that the mean length of the cloth pieces is equal to the standard length:

H0: μ = 3.25

The alternative hypothesis is that the mean length of the cloth pieces is greater than the standard length:

Ha: μ > 3.25

We can calculate the test statistic as:

t = (x - μ) / (s / √n)

where x is the sample mean length, μ is the population mean length (3.25 meters), s is the sample standard deviation (0.52 meters), and n is the sample size (35).

Plugging in the values, we get:

t = (3.52 - 3.25) / (0.52 / √35) = 3.81

Using a t-table with 34 degrees of freedom (n-1), and a significance level of 0.05 (one-tailed test), the critical t-value is 1.690.

Since our calculated t-value (3.81) is greater than the critical t-value (1.690), we reject the null hypothesis and conclude that the mean length of the 35 pieces of cloth is significantly greater than the standard length at the 0.05 level of significance.

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The equation of the line (y+10)=4(x−3)  or  y=4x−22

We can use the point-slope formula to find an equation for this line.

The point-slope formula states: \((y-y_{1} )=m(x-x_{1} )\)

Where m is the slope and \((x_{1}, y_{1} )\) is a point the line passes through.

Substituting the values from the problem gives:

(y − −10) = 4(x − 3)

(y + 10) = 4(x − 3)

To transform this into the more familiar slope-intercept form we can solve for y:

y + 10 = (4 × x) − (4 × 3)

y + 10 = 4x − 12

y + 10 − 10 = 4x − 12 − 10

y + 0 = 4x − 22

y = 4x − 22

Hence the answer is the equation of the line is (y+10) = 4(x−3)  or  y = 4x−22

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1.

What do you know?

the troposphere extends 8 to 20 km above the Earth's surface. The surface temperature is 15°C and decreases at a rate of 6.5°C per kilometer away.

What do you want to find out?

The temperature at any point of the troposphere

What kind of answer do you expect?

Any value below 15°C

2. Define variables,

T is for temperature, and

d is the distance away from the surface

3. What is the b -value

b = 15

which is the Earth's surface temperature or the initial temperature for our problem

4. What is the slope

the slope 'm' equals -6.5

which means that the temperature decreases 6.5°C per km

5. write the equation

the general form for this equations is y = b + mx

thus, for our problem, the equation is: T = 15 - 6.5*d

6.

a) the slope represents the rate of change of temperature with respect to distance, since m = -6.5 °C/km , this means the troposphere is getting 6.5 °C colder per km away from Earth's surface

b) the y-intercept represents the Earth's surface temperature

Graph:

7. identify 3 points

when d = 0 then T = 15, so our first point is (0,15)

when d = 1 then T = 15 - 6.5 = 8.5 , so our second point is (1,8.5)

when d = 2 then T = 15 - 13 = 2 so our third point is (2,2)

8. calculate the slope

let's use this equation and this set of points,

let's replace and solve

We can see that it does match the slope from our model, which is -6.5

9. graph the line and the points,

10. Complete the sentence

... ends between 8 km and 20 km above Earth.

11. temperature at the farthest point

when d = 20 then,

... the temperature is -115°C

12. Temperature range,

from... 15 °C to -115 °C

Answer:

22

Step-by-step explanation:

Answer:

\(y = \frac{5}{4}x\)

Step-by-step explanation:

1. The slope-intercept form of a linear equation is y = mx + b! Y is the y-coordinate, is the slope, x is the x-coordinate, and b is the y-intercept.

2. To find the slope, let's take any two points from the line, such as (0,0) and (400,500), and plug their values into this formula: \(\frac{y_2-y_1}{x_2-x_1}\)

3. The slope is 5/4, so the equations looks like this so far: \(y=\frac{5}{4}x + 0\)

4. Because b is the y-intercept, b = 0 because the line intersects with the y-axis at (0,0).

5. Now that we have our slope (5/4) and y-intercept (0), we plug in those values to the slope-intercept form and get the equation of: \(y= \frac{5}{4}x\)