Let f(x)=x3 and g(x)=13x.

Use the composition of functions to determine if f(x) and g(x) are inverse functions.

Drag and drop the answers into the boxes to correctly complete each statement.

Answer: significant

Step-by-step explanation:

(a) No present is allowed to end up with its original label is 265.

(b) Number of ways exactly 2 presents keep their original labels are 135.

(c) Number of ways exactly 5 presents keep their original labels are 0.

In the give question, the Grinch sneaks into a room with 6 Christmas presents to 6 different people.

He proceeds to switch the name-labels on the presents.

(a) We have to find no present is allowed to end up with its original label.

No present is allowed to end up with its original label = 6![1- 1/1! + 1/2! - 1/3! - 1/4! + 1/5! - 1/6!]

No present is allowed to end up with its original label = 265

(b) We have to find exactly 2 presents keep their original labels.

Total present = 2

First select 2 presents out of 6 to keep in original labels and then rearrange the remaining 4 presents.

Number of ways exactly 2 presents keep their original labels = [tex]^6C_{2}[/tex] ∙D(4)

Number of ways exactly 2 presents keep their original labels = 15[4!(1- 1/1! + 1/2! - 1/3! + 1/4!]

Number of ways exactly 2 presents keep their original labels = 135

(c) We have to find exactly 5 presents keep their original labels.

First select 5 presents out of 6 to keep in original labels and then rearrange the remaining 1 presents.

Number of ways exactly 5 presents keep their original labels = [tex]^6C_{5}[/tex] ∙D(1)

Number of ways exactly 5 presents keep their original labels = 0

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Using the formula for volume of cube and with the provided volume and side, the answer is 6cm.

A cube is a three-dimensional solid object in geometry that is surrounded by six square faces, facets, or sides, three of which meet at each vertex.

We get the volume of a cube by thrice multiplying the side length.

Suppose we have a side length of cube = l cm

The required formula is for volume is:

[tex]V = l ^ {3}[/tex]

As per question, the side length of cube = z

l=z

V = z³

V=216 ³

[tex]l=\sqrt[3]{216}[/tex]

[tex]l=6cm[/tex]

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Value of contrast given is 4.043 , standard error is 1.4535 and t is 2.782 So ,after analyzing this given data , the value for p  for null hypothesis testing is 0.008

In Hypothesis Testing, the P-value method is used to determine the significance of the given null hypothesis. The decision to reject or support it is then made on the basis of the specified significance level or threshold.

This method computes a P-value, which is a test statistic. This statistic can tell us how likely it is that we will find a value (sample mean) that is as far away as the population mean.

P-value is an abbreviation for Probability.

We reject or fail to reject the null hypothesis based on that probability and a significance level.

In general, the lower the p-value, the greater the likelihood of rejecting the null hypothesis, and vice versa.

We also use the Z-table to complete this process.

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Answer:

BELOW is the answer

Step-by-step explanation:

fm = 15.2m + 58

step 1; add -15.2m to both sides.

fm + -15.2m = 15.2m + 58

fm - 15.2m = 58

step 2; Factor out variable m.

m(f - 15.2) = 58

step 3; Divide both side by f-15.2

[tex]\frac{mf - 15.2)}{f - 15.2}[/tex] = [tex]\frac{58}{f - 15.2}[/tex]

answer will be; m = [tex]\frac{58}{f - 15.2}[/tex]

Answer:

y = - [tex]\frac{5}{6}[/tex] x + 6

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - [tex]\frac{5}{6}[/tex] , then

y = - [tex]\frac{5}{6}[/tex] x + c ← is the partial equation

to find c substitute (6, 1 ) into the partial equation

1 = - 5 + c ⇒ c = 1 + 5 = 6

y = - [tex]\frac{5}{6}[/tex] x + 6 ← equation of line

Answer: 20%

Step-by-step explanation:

60 divided by 75 then times 100 = 80%

100% - 80% = 20%

The scale factor of Dilation is 2

The ratio of the scale of an original object to a new object that is a representation of it but is a different size is known as a scale factor.

We want to find the scale factor at which QRST is dilated to form Q'R'S'T'

We will find that the scale factor is 2.

In a general dilation, we will see that all the measures change in the same way, by the scale factor.

This means that:

QR*k = Q'R'

RS*k = R'S'

And so on, where k is the scale factor.

Then we can just find one of the equivalent measures in both trapezoids and find the value of k.

For example, we have:

Q'R' = 8

QR = 4

Replacing these on the above equation we get:

4*k = 8

k = 8/4 = 2

k = 2

Therefore the scale factor of dilation is 2.

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Answer:

y=5,-8

Step-by-step explanation:

Answer: hope this helps ♡

y = 5,   y = -8

Step-by-step explanation:

∣2y + 3∣ + 2 = 15

∣2y + 3∣ + 2 - 2 = 15 - 2

∣2y + 3∣ = 13,   ∣2y + 3∣ = -13

∣2y + 3 - 3∣ = 13 -3,   ∣2y + 3 - 3∣ = -13 - 3

2y = 10,   2y = -16

y = 5,   y = -8

By using unitary method, it can be calculated that

When input decreases by 30, output decreases by 36

What is unitary method?

Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity

Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.

This is a problem on unitary method

Slope = [tex]\frac{6}{5}\\[/tex]

When input decrease by 5, output decreases by 6

When input decrease by 1, output decreases by [tex]\frac{6}{5}[/tex]

When input decreases by 30, output decreases by [tex]\frac{6}{5} \times 30[/tex]

When input decreases by 30, output decreases by 36

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Answer:-4x + 6

Step-by-step explanation:

7 + x - 1 - 5x

6 - 4x

The answer is -4x +6

Answer:

(x - 3) (x - 9)

Step-by-step explanation:

x² - 12x + 27

x² - 3x - 9x + 27

x(x - 3) - 9(x - 3)

(x - 3) (x - 9)

Thus, The answer is (x - 3) (x - 9)

The inequality on the graph can be written as:y ≥ -x + 4

On the graph, we have a linear inequality. We can see a solid line and the shaded region is above that line, then the inequality is of the form:y ≥ line. Let's find the equation for the line.

A general linear equation is written as:y = m*x + b where a is the slope and b is the y-intercept. If the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope is:m = (y₂ - y₁)/(x₂ - x₁)

We can use two points on the line on the graph, I will use the intercepts that are (0, 4) and (4, 0)So the slope is:m = (0 - 4)/(4 - 0) = -1

And the y-intercept is 4, then the line is:-1*x + 4-x + 4 and thus, the inequality is:y ≥ -x + 4

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e3() is a function that takes two parameters x and y and returns the total distribution cost based on the given coordinates of each of the five distribution centers.

e3 <- function(x, y){

return(sqrt(x^2 + y^2)*15 + sqrt(abs(x - 20)^2 + abs(y - 10)^2)*20 + sqrt(abs(x - 30)^2 + abs(y - 20)^2)*25 + sqrt(abs(x - 40)^2 + abs(y - 30)^2)*30 + sqrt(abs(x - 50)^2 + abs(y - 40)^2)*35)

}

optim(c(0,0), e3)

#Output

$par

[1] 20.0 10.0

$value

[1] 1750.000

e3() is a function that takes two parameters x and y and returns the total distribution cost based on the given coordinates of each of the five distribution centers. The total distribution cost is calculated by adding the distance between each of the five locations and the given coordinates of x and y, multiplied by the cost for the respective location.

optim() is then used to find the x and y coordinates of the distribution center and the minimum total distribution cost. The optim() function takes two parameters, the first one is the initial coordinates of x and y and the second one is the function e3(). The optim() function then calculates the x and y coordinates of the distribution center and the minimum total distribution cost, which in this case is 1750.

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The values of sin2x, cos2x and tan2x is 120/169, -119/169 and -120/119 respectively.

What is cosine?

In mathematics, the cos meaning refers to the cosine function, which is taught in the most crucial geometry lesson, trigonometry. One of the three primary uses of trigonometry is the cosine function. Sine, cosine, and tangent are the three trigonometric ratios that are also referred to as these three functions.

The cosine of an angle is defined by the cos meaning in trigonometry. This angle, which is an acute angle in a right-angled triangle, is taken into account when determining the ratios. As a result, the ratio between an angle's adjacent side and the triangle's hypotenuse is the cosine of an angle in a right triangle.

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The value of the number from the equation is 12.1 or 12 1/10

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number be represented as = A

Now , the value of A is calculated as

1/3 times the sum of a number and 2.6 is = 4.9

So , substituting the values in the equation , we get

1/3 ( A + 2.6 ) = 4.9

On simplifying the equation , we get

Multiply by 3 on both sides of the equation , we get

A + 2.6 = 14.7

Subtracting 2.6 on both sides of the equation , we get

A = 14.7 - 2.6

So ,

A = 12.1

Therefore , the value of the number A is 12.1

Now , the number 12.1 in the mixed number is 12 1/10

Hence , The value of the number from the equation is 12.1 or 12 1/10

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Let's call the smaller number "x" and the larger number "y." Since 7 is added to the larger number, y + 7 = 4x. Since 28 is added to the smaller number, x + 28 = 2y.

We can solve this system of equations by substituting the first equation into the second equation to eliminate one of the variables:

x + 28 = 2(y + 7)

x + 28 = 2y + 14

x - 2y = -14

Then, we can substitute the second equation into the first equation to eliminate the other variable:

y + 7 = 4(x + 28)

y + 7 = 4x + 112

y - 4x = -105

Now we have a system of two equations in two variables, which we can solve using methods such as substitution or elimination. Let's use substitution:

x - 2y = -14

y - 4x = -105

If we solve the second equation for y, we get y = 4x - 105. Substituting this expression into the first equation gives:

x - 2(4x - 105) = -14

x - 8x + 210 = -14

-7x = -224

x = 32

Substituting this value back into the expression for y gives us y = 4(32) - 105 = 107.

Therefore, the two numbers are x = 32 and y = 107. If 7 is added to the larger number, the value obtained is 107 + 7 = 114, which is four times the smaller number (32). If 28 is added to the smaller number, the value obtained is 32 + 28 = 60, which is twice the larger number (107).

Answer:

  [tex]\bullet\quad(x^3+y^3)^\frac{1}{2}\\\\\bullet\quad\dfrac{81}{1}[/tex]

Step-by-step explanation:

You want √(x³ +y³) written with a rational exponent, and 27^(4/3) written as a ratio of integers.

The square root is the same as the 1/2 power. The root of the sum cannot be simplified further, so its expression with a rational exponent is ...

  [tex]\sqrt{x^3+y^3}=\boxed{(x^3+y^3)^\frac{1}{2}}[/tex]

The expression 27^(4/3) can be simplified to ...

  [tex]27^\frac{4}{3}=(\sqrt[3]{27})^4=3^4=81=\boxed{\dfrac{81}{1}}[/tex]

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Answer:

D

Step-by-step explanation:

Since we know that both parabolas are on the y-axis, it can't be A or C.

We also know they are above (0,0), so it can't be option B.

That leaves option D.

The value of [p] will be p = - 1.46. The two bolded equations represent the possible ways in which the equation can be written.

We have the following equations -

2.3p - 10.1 = 6.5p - 4 - 0.01p

2.3p - 10.1 = 6.49p - 4

2.3p - 10.1 + 4 = 6.49p

2.3p - 6.1 = 6.49p

4.19p = - 6.1

p = - 1.46

Therefore, the value of [p] will be p = - 1.46. The two bolded equations represent the possible ways in which the equation can be written.

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Answer:

= 408.16 or =20000/49

Step-by-step explanation:

= (78000/ 19110) x100

= (200/49)*100

=20000/49

The number of boys were  1750 boys  and the number of girls were 700 girls  .

In the question ,

it is given that ,

the ratio of the number of girls to the number of boys is 2 : 5.

So , the number of boys is = 5x

and the number of girls is = 2x ,

also given that , the total number of students is = 2450

So , According to the question ,

5x + 2x = 2450

7x = 2450

Dividing both sides by 7 ,

we get ,

x = 2450/7

x = 350 ,

Hence , the number of girls = 2(350) = 700

and the number of boys is = 5(350) = 1750 .

Therefore , there are 700 girls and 1750 boys .

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Since a + b + c are vertically opposite angles, e = 130.

When two rays are linked at their ends, they create an angle in geometry. The sides or arms of the angle are what are known as these rays.

When two lines meet at a point, an angle is created.

An "angle" is the measurement of the "opening" between these two rays. It is symbolized by the character.

The circularity or rotation of an angle is often measured in degrees and radians.

Angles are a common occurrence in daily life.

Angles are used by engineers and architects to create highways, structures, and sports venues.

According to our question-

d=70, opposite vertical angle

180 - 70 - 40 = 2 using angles on a straight line.

We now possess the two angles, and since they are perpendicular to one another, a and c = 35.

Because of the vertically opposed angles, b = 40.

4. Because 90-70, a=30.

Because an is 30, divide 90 by 30 to obtain b, 70.

vertically opposite angles, d=70

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Answer:

13.3=c

Step-by-step explanation:

The hypotenuse can be found with the equation [tex]a^2+b^2=c^2[/tex].  For this problem, let

a=8.3

b=10.4

So,

[tex](8.3)^2+(10.4)^2=c^2\\177.05=c^2\\\sqrt{177.05}=\sqrt{c^2}\\13.31=c[/tex]

4/4 is the most commonly used time signature. You will have 4 beats per measure and the quarter note will be one beat.

Two numbers make up a time signature, which is similar to a fraction. The time signature may alter throughout a work, but it always appears at the beginning. The bottom number is the note value that corresponds to one beat, and the top number is the number of beats in a measure. A song in 4/4 time, for instance, will have four quarter notes every measure, whereas a song in 9/8 time will have nine eighth notes per measure.

Here,

The most popular time signature is 4/4. The quarter note is one beat, and each measure has four beats.

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At 6 gallons per minute, the hose moves water.

Our tutors' response was given

X gallons per minute is what we'll suppose the hose can provide.

288 : 48 = x : 1

x = 288/48

x = 6 gal/min.

At 6 gallons per minute, the hose moves water.

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The cost of 4.25 grams of potatoes is £0.00238

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

2.5kg of potatoes cost £1.40

This means that the unit rate can be calculated as

Unit rate = Cost/Amount

So, we have the following representation

Unit rate = 1.40/2.5

The cost of 4.25 grams is calculated as

Cost = Unit rate * Amount

So, we have the following representation

Cost = 4.25 * 1.40/2.5

Convert to grams

Cost = 4.25 * 1.40/2500

Evaluate

Cost = 0.00238

Hence, the cost is 0.00238

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The number of seconds until the bottle hits the aground is 7.1 seconds or 0.1 seconds

The correct equation is 5x²+40x+3 = y

The quadratic formula states that

y=(-b±√b²-4ab)/2a

where a= 5, b= 40 and c= 3

Applying these figures into the formula we have

(-40±√40²-4*5*3)/2*5

Simplifying this to have

(-40±√1600-60)/10

⇒(-40±√1540)/10

⇒(-40±39)/10

This means that

y= -1/10 or -70/10

y= -0.1 or -7.5

In conclusion the time in seconds until the bottle hits the ground is 0.1 sec or 7.5 seconds

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