let f(x) = x 4 and g(x) = x – 3. if g is a vertical translation of f, how many units and in what direction is f translated to form g?

The solution to all parts are given below:

The experimental probability of an event occurring is the number of times that it occurred when the experiment was conducted as a fraction of the total number of times the experiment was conducted.

1. The experiment is to spin the wheel and get the number and related to that number reward will be there.

2. The outcomes will be,

{1, 2, 3, 4, 5, 6, 7, 8}

3. Sample space

{1, 2, 3, 4, 5, 6, 7, 8}

4. Event of red with even number

= 2 , 6

5.  Event of red with odd number

= 3,7

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True. Deducting a polynomial from itself generally brings about another polynomial since 0 is a steady monomial is true.

A polynomial is a numerical articulation comprising of factors and coefficients, which are consolidated utilizing just the tasks of expansion, deduction, and duplication. On the off chance that we deduct a polynomial from itself, the outcome will be one more polynomial articulation since deduction of two polynomials is characterized as adding the main polynomial to the nullification of the subsequent polynomial. The refutation of a polynomial is likewise a polynomial. The deduction of a polynomial from itself brings about a polynomial articulation equivalent to nothing, which is a steady monomial. Consequently, the deduction of a polynomial from itself generally brings about another polynomial since 0 is a steady monomial.

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None of the options (A, B, C, D) can be determined as the cost of the sand.

To determine the volume of the container, we need to multiply the height, width, and depth of the container.

Given that the height of the gate is 3 feet, the width is 5 feet, and the depth is not specified, we cannot calculate the volume accurately without knowing the depth.

Therefore, none of the options provided (A, B, C, D) can be determined as the volume of the container.

Regarding Part B, since we don't have the volume of the container, we cannot accurately calculate the cost of the sand either.

Hence, none of the options (A, B, C, D) can be determined as the cost of the sand.

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The area of a regular octagon with sides 1/3 the length of sides of the larger octagon is 173.82 ft sq.

The area of a polygon = n side^2 / (4 tan(180/n))

where "n" is the number of sides

To calculate area for side = 2

area = 8 x 2^2 / (4  tan(180/8))

area = 32 / (4  tan(22.5))

area = 32 / 4 x 0.41421

area = 19.3138746047

To calculate area for side = 6

area = 8*6^2 / (4 * tan(180/8))

area = 288 / 1.65684

area = 173.824871442

173.824871442 / 19.3138746047 =  9

So, the area would be 9 times larger.

Therefore, if we increase the side length is increased by 1/3, then the area increases by 1/9.

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To translate figure ABCD into A'B'C'D' rotate 90° about D and then reflect across AB.

When a figure is relocated from one place to another without changing its size, shape, or orientation, a transition known as translation takes place.

If we know which way the figure is moving and how much, we can draw the translation in the coordinate plane.

Every point of the object must be translated by the same amount and in the same direction.

To translate figure ABCD into A'B'C'D' rotate 90° about D and then reflect across AB.

option (d)

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There are 98,280 ways to select a bowl of 5 scoops of ice cream from 28 available flavors if each scoop is a different flavor.

To solve this problem, we can use the formula for combinations, which is nCr = n! / r! (n-r)!, where n is the total number of items, r is the number of items we want to select, and ! means factorial (multiply all numbers from 1 to n together).
In this case, we have 28 flavors of ice cream and we want to select 5 scoops.

So we can plug in n = 28 and r = 5:
28C5 = 28! / 5!(28-5)!
= 28! / 5!23!
= (28x27x26x25x24) / (5x4x3x2x1)
= 98,280
Therefore, there are 98,280 ways to select a bowl of 5 scoops of ice cream from 28 available flavors if each scoop is a different flavor.

Summary: There are 98,280 ways to select 5 scoops of ice cream from 28 flavors if each scoop is a different flavor, using the formula for combinations.

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Answer:

y-4 = 5(x+2)

y-4=5x+10

y=5x+14

Step-by-step explanation:

The double points of the following conic section x' + 4xy + 3y - 2xz - 4yz + 2 = 0 is  x = 1, y = 0, z = 1

The equation that represents double points of the conic section x" + 2xy + y - 8xz - 8yz + 16 = 0 is x + y - 4z = 0

The equation of the tangent line at point P(2,0) is x - 2y - 2z = 0

The first question asks to calculate the double points of a given conic section. The conic section is represented by the equation:

x' + 4xy + 3y - 2xz - 4yz + 2 = 0

To find the double points, we need to solve the equation for the variables x, y, and z. The solution is:

x = 1, y = 0, z = 1

These values represent the double points of the conic section.

In the second question, we are again asked to calculate the double points of a conic section. The equation is:

x" + 2xy + y - 8xz - 8yz + 16 = 0

To find the double points, we need to solve the equation for the variables x, y, and z. The solution is:

x + y - 4z = 0

This equation represents the double points of the conic section.

Finally, in the third question, we are asked to calculate the tangent line at the point P(2,0) of a conic section. The equation of the conic section is:

x - 4xy - y' + 2x - 4y - 8 = 0

To find the tangent line at point P(2,0), we need to differentiate the equation with respect to x. The derivative is:

1 - 4y + 2 - 4 = -2 - 4y

At point P(2,0), the value of y is 0. Plugging in this value, we get:

-2 - 4(0) = -2

Therefore, the equation of the tangent line at point P(2,0) is:

x - 2y - 2z = 0

This equation represents the tangent line at point P(2,0) of the conic section.


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Answer:

133

Step-by-step explanation:

Answer is 133

\(answer \\ = 133 \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps\)

Answer:

the answer is (0,-1,-2,-3)

Answer:

I need the answer too g

Step-by-step explanation:

The inequality that represents all the solutions of -2(3x + 6) ≥ 4(x + 7) is x ≤ -4

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

-2(3x + 6) ≥ 4(x + 7)

Divide both sides of the inequality by -2

So, we have the following representation

3x + 6 ≤ -2(x + 7)

Open the brackets

This gives

3x + 6 ≤ -2x - 14

Add 2x to both sides of the inequality

So, we have the following representations

5x + 6 ≤ -14

Subtract 6 from both sides of the inequality

So, we have the following representations

5x ≤ -20

Divide both side of the inequality

x ≤ -4

Hence, the solution is x ≤ -4

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Answer:

Donald earnings = 3(s + k)

Step-by-step explanation:

Susan earnings = s

Kurt earnings = k

Combined salary = s + k

Donald earns earns three times as much as the combined salary of his two vice presidents,

Donald earnings = 3(s + k)

= 3s + 3k

Answer:

8x= -16

x=-2

Step-by-step explanation:

1. add 4x+4x=8x

2. subtract -7y+7y=0

3. subtract 13-29= -16

4. divide -16 by 8x= -2

you basically align the variables and solve down.

Answer: 48 pupils get the bus to the cinema and 36 pupils walk to the cinema.

Step-by-step explanation:

Let's suppose that there are a total of N pupils.

We know that N/4 walk to the cinema.

We know that N/3 get the bus to the cinema.

And the remainder is equal to 60 people.

Then:

N - N/4 - N/3 = 60

N*(1 - 1/4 - 1/3) = 60

N( 12/12 - 3/12 - 4/12) = 60

N*( 5/12) = 60

N = (12/5)*60 = 144

Then the number of pupils that walk to the cinema is N/4, or:

144/4 = 36

And the number of pupils that get the bus is N/3, or:

144/3 = 48.

The procedure used to analyze the given data is intention-to-treat analysis.

The procedure to analyze data according to the original assignment of the treatment regardless of the actual treatment received is called the intention-to-treat (ITT) analysis. It is considered the gold standard in clinical trial analysis because it preserves the randomization and avoids bias that may arise from differential dropouts or non-compliance. By analyzing all patients according to their randomized group, the ITT analysis provides an unbiased estimate of the treatment effect and better reflects the real-world effectiveness of the intervention.

The intention-to-treat (ITT) analysis is different from other types of analyses because it includes all patients according to their original randomized group, regardless of whether they received the assigned treatment or not. This is in contrast to per-protocol analysis, where only patients who completed the study without any major protocol deviations are included, or as-treated analysis, where patients are analyzed according to the actual treatment received.

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Answer:

subtract 3 each time

Step-by-step explanation:

hope it helps

Answer:

.7456

Step-by-step explanation:

The question is asking for the area under the curve from 1 to 2 ....see diagram.....this is approx .75

To find the points on the surface 4x^2+3y^2+z^2=1 at which the tangent plane is parallel to the plane -2x+5y+4z = 9, we need to find the gradient vector of the surface and the normal vector of the given plane.

The gradient vector of the surface 4x^2+3y^2+z^2=1 is given by:

grad(f) = <8x, 6y, 2z>

So, at any point (x, y, z) on the surface, the tangent plane has a normal vector equal to the gradient vector:

N1 = <8x, 6y, 2z>

Now, we need to find the normal vector of the plane -2x+5y+4z = 9. This is simply the coefficients of x, y, and z in the equation:

N2 = <-2, 5, 4>

For the two planes to be parallel, their normal vectors must be proportional. So, we need to find a point (x, y, z) on the surface such that:

N1 = k*N2

where k is some scalar. Equating the components, we get:

8x = -2k
6y = 5k
2z = 4k

Solving for x, y, and z, we get:

x = -k/4
y = 5k/6
z = 2k

Substituting these values into the equation of the surface, we get:

4(-k/4)^2 + 3(5k/6)^2 + (2k)^2 = 1

Simplifying, we get:

25k^2 = 36

So, k = +/-6/5.

Therefore, the points on the surface at which the tangent plane is parallel to the plane -2x+5y+4z = 9 are:

(-3/5, 2, 12/5) and (3/5, -2, -12/5).
To find the points on the surface 4x^2 + 3y^2 + z^2 = 1 where the tangent plane is parallel to the plane -2x + 5y + 4z = 9, we need to compare the gradients of the surfaces.

The gradient of the surface F(x, y, z) = 4x^2 + 3y^2 + z^2 is given by the gradient vector (∇F) = (8x, 6y, 2z).

The normal vector of the plane -2x + 5y + 4z = 9 is (-2, 5, 4).

Two planes are parallel if their normal vectors are proportional. So, we need to find the points (x, y, z) such that:

(8x, 6y, 2z) = k(-2, 5, 4), for some scalar k.

From this, we get the equations:
8x = -2k,
6y = 5k,
2z = 4k.

Now, substitute these equations back into the original surface equation:

4(-2k/8)^2 + 3(5k/6)^2 + (4k/2)^2 = 1.

Solve this equation for k, and then use the values of k to find the corresponding x, y, and z values. Those points (x, y, z) are the points on the surface where the tangent plane is parallel to the given plane.

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Answer:

70 s

Step-by-step explanation:

24 L = 20s

84 L = 20×84/ 24

= 70 s

Answer:

the number of children = 156

the number of adults = 183

Step-by-step explanation:

let x be the number of children

    y be the number of adults

We have to solve this system:

\(\begin{cases}x+y=339&\\ 1.75x + 2.50y = 730.50&\end{cases}\)

\(\Longleftrightarrow \begin{cases}y=339-x&\\ 1.75x + 2.50(339-x) = 730.50&\end{cases}\)

\(\Longleftrightarrow \begin{cases}y=339-x&\\ -0.75x + 847.5 = 730.50&\end{cases}\)

\(\Longleftrightarrow \begin{cases}y=339-x&\\ -0.75x =-117&\end{cases}\)

\(\Longleftrightarrow \begin{cases}y=339-156=183&\\ x =156&\end{cases}\)

Answer:

Step-by-step explanation:

if in the bank account is 1600 dollars

the rate is 5%

1600*5%=80 dollars

Answer:

20-24

Step-by-step explanation:

you can see that when you find the middle of the total data the data set left is in the 20-24 category

hope this helps! :)

The expression representing the amount of ore sold is 2t - 12, and the mine can sell 12 metric tons of ore after extracting for 12 hours.

The mine extracts 2 metric tons of coal every hour, but it uses 1 metric ton of coal to generate electricity for the mine, leaving the remaining amount to be sold. Since t represents the number of hours spent mining, the expression 2t - 12 represents the amount of ore sold. The 12 is subtracted because for every hour of mining, 1 metric ton is used for generating electricity.

After mining for 12 hours, the value of t would be 12. Substituting t = 12 into the expression 2t - 12, we get 2(12) - 12 = 24 - 12 = 12 metric tons. Therefore, the mine can sell 12 metric tons of ore after extracting for 12 hours.

Hence, option A is incorrect, option B is incorrect, option C is incorrect, and the correct answer is option D.

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As per the unitary method, the number of dimes is 4.35 and the number of quarters is 30.55

Here we have given that Tabitha has $4.35 in dimes and quarters. if the quantity of dimes is three more than twice the number of quarters.

And we need to find how many of each coin does she have.

Here let us consider x be the number of dimes and y be the number of quarters.

And we also consider that there are hundred coins in total, so

=> x + y = 100 -------------------(Equation 1)

Now, here he has x dimes, each dime is 10¢ =  $0.10 and in total he has $ 0.10x in dimes.

Then if he has y quarters, each quarter is 25¢ = $0.25, then in total he has $ 0.25y in quarters.

While we adding the above two quantities,  

Then he has 0.1x + 0.25y in dimes and quarters,

Here we know the total amount of money he has is $4.35,

Then it can be written as

=> 0.10x + 0.25y = 4.35 ---------------------------- (Equation 2).

Then we have to solve these two simultaneously for x and y

By multiply equation 2 by 10 on the left and right hand sides, which gives

=> x + 2.5y = 43.5 (Equation 3).

Then subtract equation (1) from equation (3) to eliminate x.

=> 1.5y = 56.5

=> 3.77

Then the value of x is

=> x = 43.5 - 12.95

=> x = 30.55

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Answer:

the second and 3rd one

Step-by-step explanation:

The exact values of the six trigonometric functions of the angle (8, 18)

sin α = y/r = 18/√388, cos α = x/r = 8/√388, tan α = y/x = 18/ 8  

cot α = x/y = 8/18, secα = r/x =√388/8 & cosec α = r/y =√388/18

Trigonometric angles are angles given by the ratios of trigonometric functions. Trigonometry is the study of the relationship between the sides and angles of a triangle. Angle values ​​range from 0 to 360 degrees. Important angles in trigonometry are 0°, 30°, 45°, 60°, 90°, 180°, 270° and 360°.

According too the Question:

If a point is given on one side of the endpoint of an angle, then:

Calculates the distance from the given point to the origin:

\(r =\sqrt{x^2+y^2}\)

Here it is:

\(r =\sqrt{8^2 +18^2}\)

  = \(\sqrt{64+324}\)

  = \(\sqrt{388} =19.69\)

Now,

we can calculate all 6 trigonometric functions:

sin α = y/r = 18/√388

cos α = x/r = 8/√388

tan α = y/x = 18/ 8

cot α = x/y = 8/18

secα = r/x =√388/8

cosec α = r/y =√388/18

Complete Question:

The point is on the terminal side of an angle in standard position. Determine the exact values of the six trigonometric functions of the angle.

(?8, 18)

sinθ =?

cosθ =?

tanθ =?

cscθ =?

secθ =?

cotθ =?

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-0.85 is the strongest correlation coefficient which represents the strongest correlation as compared to others.

What is Correlation coefficients ?

Correlation coefficients are used to measure how strong a relationship is between two variables. There are several types of correlation coefficients, but the most popular is Pearson’s. Pearson’s correlation is a correlation coefficient commonly used in linear regression. Generally, correlation coefficients range between -1.00 to +1.00.

According to the rule of correlation coefficients, the strongest correlation is considered when the value is closest to +1 (positive correlation) or -1 (negative correlation).

A positive correlation coefficient indicates that the value of one variable depends on the other variable directly.

A zero-correlation coefficient indicates that there is no correlation between both variables.

A negative correlation coefficient indicates that the value of one variable depends on the other variable inversely.

Hence, according to the options, we know that -0.85 is the closest to -1, and none of the values is closer than that to either of -1 or +1. Hence, it is more negatively correlated.

Hence, -0.85 is the strongest correlation coefficient which represents the strongest correlation as compared to others.

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To calculate the discharge through the circular channel, we can use Manning's equation, which relates the flow rate (Q) to the channel properties and flow conditions. Manning's equation is given by:

Q = (1/n) * A * R^(2/3) * S^(1/2)

where:

Q is the discharge (flow rate)

n is Manning's coefficient (0.014 in this case)

A is the cross-sectional area of the channel

R is the hydraulic radius of the channel

S is the slope of the channel bed

First, let's calculate the cross-sectional area (A) of the circular channel. The diameter of the channel is given as 6m, so the radius (r) is half of that, which is 3m. Therefore, the area can be calculated as:

A = π * r^2 = π * (3m)^2 = 9π m^2

Next, let's calculate the hydraulic radius (R) of the channel. For a circular channel, the hydraulic radius is equal to half of the diameter, which is:

R = r = 3m

Now, we can calculate the slope (S) of the channel bed. The given slope is 1 in 600, which means for every 600 units of horizontal distance, there is a 1-unit change in vertical distance. Therefore, the slope can be expressed as:

S = 1/600

Finally, we can substitute these values into Manning's equation to calculate the discharge (Q):

Q = (1/0.014) * (9π m^2) * (3m)^(2/3) * (1/600)^(1/2)

Using a calculator, the discharge can be evaluated to get the final result.

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