Hello can somebody help me with this problem (Funcitons). Thank you in advance.

If we select three balls, the probability of selecting exactly one white one is 16.

There are 6 balls in a box.

2 white and 4 black.

If we select three balls, then we have to determine the probability of selecting exactly one white.

First we determine the number of ways of selecting three balls in total of 6 balls. So

[tex]^{6}C_{3} = \frac{6!}{3!(6-3)!}[/tex]

[tex]^{6}C_{3} = \frac{6!}{3!3!}[/tex]

[tex]^{6}C_{3} = \frac{6\times5\times4\times3!}{3\times2\times1\times3!}[/tex]

Simplify

[tex]^{6}C_{3}[/tex] = 5 × 4

[tex]^{6}C_{3}[/tex] = 20

Now determining the probability of selecting the 3 balls out of non white balls.

[tex]^{4}C_{3}=\frac{4!}{3!(4-3)!}[/tex]

[tex]^{4}C_{3}=\frac{4!}{3!1!}[/tex]

Simplify

[tex]^{4}C_{3}=\frac{4\times3!}{3!\times1}[/tex]

[tex]^{4}C_{3}[/tex] = 4

Now, the probability of selecting exactly one white one = The number of ways of selecting three balls in total of 6 balls - The probability of selecting the 3 balls out of non white balls

The probability of selecting exactly one white one = 20 - 4

The probability of selecting exactly one white one = 16

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Answer:

19) x=10⁰ 20) x=17⁰

Step-by-step explanation:

19) angles in a straight line add upto 180⁰

 6x-10⁰+4x⁰+6+7x+14⁰=180⁰

collect like terms

 17x+10⁰=180⁰

 17x=1170⁰

x=10⁰

20)58⁰ alternates with 4x-10 therefore;

4x-10⁰=58⁰

4x=58⁰+10⁰

4x=68⁰

x= 17⁰

Answer: (-3, -1/2)

Step-by-step explanation: Search math w ay on the internet for any further math questions :)

The scalar projection of vector b onto vector a is 57/289 and the vector projection of vector b onto vector a is (0.38, 0.92).

A quantity or phenomena with independent qualities for both magnitude and direction is called a vector. The term can also refer to a quantity's mathematical or geometrical representation. Velocity, momentum, force, electromagnetic fields, and weight are a few examples of vectors in nature.

The scalar projection of vector b onto vector a is given by:

(b . a) / ||a||^2

= (3 * -8 + 5 * 15) / ( -8^2 + 15^2)

= 165 / 289

= (57/289)

The vector projection of vector b onto vector a is given by:

proj(b onto a) = (b . a) / ||a||^2 * (a / ||a||)

= (57/289) * (-8/√(-8^2 + 15^2), 15/√(-8^2 + 15^2))

= (0.38, 0.92)

Note: sqrt(-8^2 + 15^2) = sqrt(289) = 17

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When the sample size is decreased from 39 to 29 , the impact on confidence interval will be (c) It would become wider due to using the t distribution.

we know that , in general, as the sample size decreases, the variability of the estimate increases and the width of the confidence interval becomes larger.

The t distribution is used when the sample size is small, which increases the width of the confidence interval to account for the greater uncertainty in the estimate.

When the sample size is large, the t distribution approaches the standard normal (z) distribution, which results in a narrower confidence interval.

Therefore, a decrease in sample size would result in a larger t distribution and a wider confidence interval.

The given question is incomplete , the complete question is

In a situation where the sample size was decreased from 39 to 29, what would be the impact on the confidence interval ?

(a) It would become narrower with fewer values.

(b) It would remain the same as sample size does not impact confidence intervals.

(c) It would become wider due to using the t distribution.

(d) It would become narrower due to using the z distribution.

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By thoroughly reacting a 2.2g zinc nail with an excess of hydrochloric acid, 0.0075 L of hydrogen gas is created.

The force per unit area on an item in the fluid or on the surface of a closed container is measured as fluid pressure. Gravity, acceleration, or forces outside a closed container can all create this pressure. Because a fluid has no fixed structure, its pressure is applied in all directions.

Here,

The reaction between zinc and hydrochloric acid produces hydrogen gas according to the following equation:

Zn + 2HCl -> ZnCl2 + H2

From the equation, we can see that 1 mole of zinc reacts with 2 moles of hydrochloric acid to produce 1 mole of hydrogen gas. The volume of a gas is proportional to the number of moles at constant temperature and pressure, so if we can determine the number of moles of zinc that were reacted, we can calculate the volume of hydrogen produced.

The moles of zinc can be calculated using the molar mass of zinc:

moles = mass / molar mass

moles = 2.2 g / 65.38 g/mol = 0.0337 mol

Since 1 mole of zinc reacts with 2 moles of hydrochloric acid, the number of moles of hydrogen produced is 0.0337 mol * 1 mol H2/1 mol Zn = 0.0337 mol H2.

Finally, the volume of hydrogen produced at standard temperature and pressure (STP) is calculated using the Ideal Gas Law:

PV = nRT

V = nRT / P

V = (0.0337 mol) * (0.08206 L atm / K mol) * (273.15 K) / (1 atm)

V = 0.0075 L

0.0075 L of hydrogen gas are produced by completely reacting a zinc nail with a mass of 2.2g with an excess of hydrochloric acid.

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Complete question:

What volume of hydrogen gas are produced by completely reacting a zinc nail with a mass of 2.2g with an excess of hydrochloric acid?

The total number of ways are 225, 225.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up.

Given:

There are 11 kittens and 15 puppies.

so, we have to select 3 kittens from 11 kittens and 4 puppies from 15 puppies.

Then, the number of ways can be

= C(11, 3) x C(15, 4)

= 990 / 6 x 32,760/ 24

= 165 x 1365

= 225, 225.

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x=-10, 2

you would have to factor it.

refer to picture

In total, there are 192 + 144 + 144 = 480 different starting lineups that can be created.

There are 3 centers to choose from, and for each center there are 4 choices for each of the two guard positions and 4 choices for each of the two forward positions. So, there are:

3 * 4 * 4 * 4 = 192

different starting lineups without x.

Lineups with x as guard: There are 3 centers, 3 choices for the first guard (since x can play either guard or forward), 4 choices for the second guard, and 4 choices for each forward. So, there are

3 * 3 * 4 * 4 = 144

different lineups with x as guard.

Lineups with x as forward: There are 3 centers, 4 choices for each guard, 3 choices for the first forward (since x can play either guard or forward), and 4 choices for the second forward. So, there are 3 * 4 * 3 * 4 = 144 different lineups with x as forward.

In total, there are 192 + 144 + 144 = 480 different starting lineups that can be created.

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The X value for the boundary for the lowest 2.5% of a normal distribution with a mean of 50 and a standard deviation of 4 is 43.04.

The lowest 2.5% boundary for a normal distribution with a mean of 50 and standard deviation of 4 can be calculated using the Z-score formula.

Z = (X - mean) / standard deviation

We want to find the X value for which Z = -1.96 since -1.96 represents the boundary for the lowest 2.5% of a standard normal distribution.

Plugging in the mean and standard deviation:

-1.96 = (X - 50) / 4

Solving for X:

X = 50 - 1.96 × 4

X = 43.04

So, the X value for the boundary for the lowest 2.5% of a normal distribution with a mean of 50 and a standard deviation of 4 is 43.04.

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An equation for Windy Kite's total cost, y, in terms of the number of kites purchased, x, is y = 2x + 20.

An equation for Kites-R-Fun's total cost, y, in terms of the number of kites purchased, x, is y = 4x + 8.

Based on the table, if the Alaskan customer wants to buy 4 kites, Kites-R-Fun charges the least.

If the Alaskan customer wants to buy 10 kites, Windy kites charges the least.

The solution to the system of equations is (6, 32).

The meaning of the solution is that 6 kites would cost a total of $32 at both Windy kites and Kites-R-Fun.

In order to write a linear equation to describe this situation, we would a assign variable to the number of kites purchased and the total cost respectively, and then translate the word problem into a linear equation as follows:

Since Wendy charges $2 per kite and a flat rate of $20 for shipping, a linear equation that models the total cost is given by:

y = 2x + 20

When x = 4, the total cost for Windy kites is given by:

y = 2(4) + 20

y = $28.

When x = 7, the total cost for Windy kites is given by:

y = 2(7) + 20

y = $34.

When x = 10, the total cost for Windy kites is given by:

y = 2(10) + 20

y = $40.

For Kites-R-Fun, a linear equation that models the total cost is given by:

y = 4x + 8

When x = 4, the total cost for Kites-R-Fun is given by:

y = 4(4) + 8

y = $24.

When x = 7, the total cost for Kites-R-Fun is given by:

y = 4(7) + 8

y = $36.

When x = 10, the total cost for Kites-R-Fun is given by:

y = 4(10) + 8

y = $48.

Lastly, we would use an online graphing calculator to plot the system of linear equations as shown in the graph attached below.

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The lateral surface area of the rectangular prism given in the picture is 36 cm ²

The lateral surface area of a rectangular prism can be found by the formula :

= 2 x height x ( Length + Breadth )

Height = 2 cm

Length = 3 cm

Breadth = 6 cm

The lateral surface area is therefore:

= 2 x 2  x ( 3 + 6 )

= 4 x 9

= 36 cm ²

In conclusion, the lateral surface area is 36 cm ².

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The midpoint of the  1/3 and 6/11 as a fraction is, 29/33

The midpoint of two numbers can be found by taking the average of the two numbers. To find the average of two fractions, you need to find a common denominator, add the numerators, and divide the sum by the denominator.

Given that,

Two fractions,

1/3 and 6/11

To find the common denominator for 1/3 and 6/11, you can find the least common multiple (LCM) of the denominators:

LCM(3, 11) = 33

Next, convert each fraction to an equivalent fraction with a denominator of 33:

1/3 = 11/33

6/11 = 18/33

Finally, add the numerators and divide the sum by the denominator to find the average:

(11 + 18) / 33 = 29/33

The midpoint of 1/3 and 6/11 as a fraction is 29/33.

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This indicates that the cutoff value for the amount of minutes before contacting the consumer is 674 minutes, rounded to the closest minute.

Quartiles are three numbers that divide sorted data into four equal portions with an equal amount of observations each. A quantile is a sort of quantile. The first quartile is sometimes known as the lower quartile or Q1. Second quartile: Also known as the median or Q2. Third quartile: Also known as the higher quartile or Q3.

Here,

To find the upper fence, we need to calculate the following statistics:

Q1 (first quartile), Q2 (median), and Q3 (third quartile) of the data

Interquartile range (IQR), which is the difference between Q3 and Q1

Upper fence, which is Q3 + 1.5 * IQR

First, we need to order the data in ascending order:

339, 350, 358, 388, 430, 458, 458, 463, 480, 489, 501, 536

Next, we can find the quartiles:

Q1 = 388

Q2 = 458

Q3 = 501

IQR = Q3 - Q1 = 501 - 388 = 113

Finally, we can calculate the upper fence:

Upper fence = Q3 + 1.5 * IQR = 501 + 1.5 * 113 = 674

This means that the cutoff point for the number of minutes at which the customer should be contacted is 674 minutes, rounded to the nearest minute.

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(C) $563,700 in cash was received from customers during the year.

Accounting lingo for partial payment of an amount outstanding is "on the account."

The phrase "on account" can also refer to buying or selling anything on credit.

On credit is another way to say "on the account."

Simply changing a sales representative's job title won't make them an account manager.

The needed abilities are varied.

Account managers require abilities in project management, financial control, consultative/value selling, and planning, some of which may require training.

So, gross sales of $560,000.

Accounts receivable decreased ($22,500 - $18,800). $3,700.

Money obtained from clients. $563,700.

Note that the further details provided in the question are not necessary to determine the total amount of money received from customers for the year.

Therefore, (C) $563,700 in cash was received from customers during the year.

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Profit function is P(x) = 3.1x - 0.05x² - 181

The profit a business makes is equal to the revenue it takes in minus what it spends as costs. To obtain the profit function, subtract costs from revenue.

P(x) = R(x) - C(x)

Given,

Cost C(x) = 181 +2.9x

Revenue R(x) = 6x -0.05x²

Profit P(x) = R(x) - C(x)

                = 6x - 0.05x² - (181 +2.9x)

                = 6x - 0.05x² - 181 - 2.9x

         P(x) = 3.1x - 0.05x² - 181

Hence,  P(x) = 3.1x - 0.05x² - 181 is the profit function.

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Answer:

Below

Step-by-step explanation:

You cannot 'solve' this equation..... you have only one equation and TWO unknowns p and x      you will need another equation relating p and x to solve this

The quadratic regression equation for the data-set in this problem is given as follows:

y = 0.96x² - 5.77x + 1.38.

Regression equations are obtained inserting the points of a data-set into a calculator.

In this problem, we want to find the quadratic regression equation, hence a quadratic regression calculator is used.

The points are given as follows:

(-1,8), (5,-4), (7,8), (2,-6).

Inserting these points into a calculator, the regression equation is given as follows:

y = 0.96x² - 5.77x + 1.38.

Meaning that the second option is the correct option.

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Equation used to represent the amount of interest that was paid​ is S.I = 900 × 0.11 × 0.5 and the amount is $49.5.

Simple interest is defined as the interest obtained over the principal amount on a certain rate.

Simple interest amount can be calculated using the formula,

S.I = Prt

Here P is the principal amount, r is the rate of interest and t is the time in years.

Given a loan of $900 at a rate of 11% with paid off in 6 months.

P = $900,

r = 11% = 0.11 and

t = 6 months = 0.5 year

S.I = 900 × 0.11 × 0.5

    = 49.5

Hence the amount of simple interest is $49.5.

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The speed of the slower boat is 15 mph and the speed of the faster boat is 35 mph.

The problem involves using the formula for distance, speed, and time, which is:

distance = speed × time

In this case, we are given the distance between two boats (400 miles) and the time it takes for them to meet (8 hours), and we need to find the speed of each boat. This involves solving a linear equation to find the unknown speed. The problem also involves the concept of finding the rate of change of distance, which is the sum of the speeds of the two boats.

Let's call the speed of the slower boat = x mph.

The speed of the faster boat would be = x + 20 mph.

The distance between the two boats decreases at a rate = x + x + 20 = 2x + 20 mph.

The time it takes for the two boats to meet is 8 hours, so the distance between the two boats when they meet is:

400 = (2x + 20) × 8

Solving for x:

400 = 16x + 160

16x = 240

x = 15

So, the speed of the slower boat is 15 mph and the speed of the faster boat is x + 20 = 35 mph.

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Answer:

-1/3

Step-by-step explanation:

multiply across

1/2 * -2/3

-2/6

-1/3

The inverse of the functions y = x + 3 and y = 2x - 4 are y = x - 3 and

y = (x + 4)/2 respectively.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, A function y = x + 3 or f(x) = x + 3.

Now, To find the inverse of f(x) we'll solve for 'x' in terms of 'y'.

y = x + 3.

x = y - 3.

y = x - 3.

f⁻¹(x) = x - 3.

Again,

y = 2x - 4.

2x = y + 4.

x = (y + 4)/2.

y = (x + 4)/2.

f⁻¹(x) = (x + 4)/2.

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The new coordinate of the points after the dilation will be (3, 5).

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.

The point is (6, 10). And the scale factor is 1/2. Then the new coordinate of the points after the dilation is given as,

⇒ (1/2)(6, 10)

⇒ (1/2 x 6, 1/2 x 10)

⇒ (3, 5)

The new coordinate of the points after the dilation will be (3, 5).

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The number of times both services left the interchange together from 9am to 12 noon is 0.

Let's call the number of 15-minute intervals that have passed since 9 am "t".

So, the time that bus number 801 leaves the interchange after t intervals is 9am + 15t minutes.

Similarly, the time that bus number 802 leaves the interchange after t intervals is 9 am + 20t minutes.

For both services to leave the interchange at the same time, the number of 15-minute intervals that have passed since 9 am must be the same for both buses.

In other words, 15t must equal 20t.

Dividing both sides of this equation by 5, we get 3t = 4t.

This equation has no solution, which means that bus number 801 and bus number 802 never leave the interchange at the same time from 9am to 12 noon.

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Answer:

the probability becomes less

Step-by-step explanation:

There is 700 number of $5 bills and 200 number of $10 bills

An equation is an expression that shows the relationship between numbers and variables using mathematical expressions. Equations are classified based on degree as linear, quadratic, cubic

Let x represent the number of $5 bills and y represent the number of $10 bills.

There is a total of 900 $5, $10 dollar bills, hence:

x + y = 900        (1)

The value of all the bills is $5500, hence:

5x + 10y = 5500     (2)

From both equation, solving simultaneously:

x = 700, y = 200

There are 700 $5 bills and 200 $10 bills

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The required angle is 26.5°, line y=1/2x + 1 made with an x-axis.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,
Given the equation of the line,
y = 1/2x + 1

Compare the above equation with equation y = max +c
m = 1/2

tanФ = 1/2   [since m = tanФ]
Ф = tan⁻¹[1/2]
Ф = 26.5°

Thus, the required angle is 26.5°.

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The area of the surface generated when the given curve is revolved about the x-axis with y=8√x on [9,20] is approximately 764.26 square units.

The area of the surface generated when the given curve is revolved about the x-axis is calculated using the formula:

A = 2 * π * ∫[a,b] y * √(1 + (dy/dx)²) dx,

where y = 8√x, and a and b are the limits of integration, i.e., a = 9, and b = 20.

First, we'll find the derivative of y with respect to x:

dy/dx = 8 / (2 * √x)

Now, we can substitute the values into the formula:

A = 2 * π * ∫[9,20] 8√x * √(1 + (8 / (2 * √x))²) dx

Using the change of variable u = √x, the above equation becomes:

A = 16π * ∫[3,4.472] u² * √(1 + (8 / u)²) du

Evaluating the definite integral, we get:

A = 16π * (u³ / 3) * √(1 + (8 / u)²) |[3,4.472]

A = 16π * [(4.472³ / 3) * √(1 + (8 / 4.472)²) - (3³ / 3) * √(1 + (8 / 3)²)]

A = 16π * [(4.472³ / 3) * √(1 + (8 / 4.472)²) - (27 / 3) * √(1 + (8 / 3)²)]

A ≈ 764.26

So, the area of the surface generated when the given curve is revolved about the x-axis is approximately 764.26 square units.

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The equation represents the relationship between the independent variable, x, and the dependent variable is y= 2x

From the question, we have the following parameters that can be used in our computation:

The table of values

On the yable of values, we can see that

y is twice of x

When represented as an equation, we have

y = 2x

Hence, the equation is y = 2x

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The rate of change of the volume of the cone at the given instant is 1 238 768 66.67 cm^3/s.

The volume of a cone can be calculated using the formula V = (πr^2h)/3, where r is the radius and h is the height of the cone.

At the given instant, radius = 8 88 cm and height = 10 1010 cm.

Substituting these values in the formula we get,

[tex]V = (π(8 88 cm)^2(10 1010 cm))/3 = 2 477 537 33.33 cm^3[/tex]

The rate of change of the volume of the cone at that instant can be calculated as follows:

Let dV/dt be the rate of change of the volume at that instant.

[tex]dV/dt = (dV/dr)*(dr/dt) + (dV/dh)*(dh/dt) \\dr/dt = 3 33 cm/s \\dh/dt = -4 44 cm/s[/tex]

Differentiating the volume of a cone formula with respect to r and h, we get

[tex]dV/dr = (πr^2h) dV/dh = (πr^2h)/3[/tex]

Substituting these values in the equation for dV/dt, we get

[tex]dV/dt = (π(8 88 cm)^2(10 1010 cm)) + (π(8 88 cm)^2(10 1010 cm))/3 * (-4 44 cm/s) = 1 238 768 66.67 cm^3/s[/tex]

Therefore, the rate of change of the volume of the cone at the given instant is [tex]1 238 768 66.67 cm^3/s[/tex].

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