For the given functions f and g, find the indicated composition.
f(x)=−4x+7,g(x)=3x+9
(g∘f)(x)
​

−12x+43
−12x−12
−12x+30
12x+30
​

Answer:

1a)12 b)1296 2a)6 b)6

Step-by-step explanation:

1a)a*b=3a^2b

(2*1)=3*2^2*1

=3*4*1

=12.

b)(2*1)*3=12*3

=3*12^2*3

=3*144*3

=1296.

2a)n#m=√3mn

2#6=√3*2*6

=√36

=6.

b)(4#3)#2

(4#3)=√3*4*3

=√36

=6

6#2= √3*6*2

= √36

=6

By answering the presented question, we may conclude that As a result, the probability of not receiving a factor of two is 4/7, or "four-sevenths."

Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% since there are two equally likely outcomes. (Heads or tails). Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many disciplines, including statistics, economics, science, and engineering.

There are seven potential results from the spinner: 1, 2, 3, 4, 5, 6, and 7.

The numbers that are factors of two are 2, 4, and 6. As a result, the numbers 1, 3, 5, and 7 are not factors of 2.

The likelihood of receiving a number that is not a factor of two is:

P(not factor of 2) = total number of outcomes / number of outcomes that are not factors of 2.

P(without the factor of 2) = 4/7

As a result, the likelihood of not receiving a factor of two is 4/7, or "four-sevenths."

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Answer:

the answer is 4818 pls give me brainliest

Step-by-step explanation:

Answer:

16 inches

Step-by-step explanation:

The variables in this equation are miles and inches. You're given the ration 2 inches: 75 miles. Take the other factor that you are given, which for this problem would be 600 miles, and divide it by the number with the same variable, which would be 75 miles. This comes out to be 8, to which you then multiply that by the number with the variable that you are trying to find, which is two. Therefore, the length of the highway on the map would be 16 inches.

To find the optimal level of production for this product, we need to set the marginal cost equal to the marginal revenue and solve for x. So, 3x + 20 = 34 - 4x. 7x = 14 x = 2. Therefore, the optimal level of production for this product is 2 goods.
To find the optimal level of production for this product, you should set the marginal cost (MC) equal to the marginal revenue (MR), since the profit is maximized when these two values are equal.

MC = MR
3x + 20 = 34 - 4x

Now, solve for x:

3x + 4x = 34 - 20
7x = 14
x = 2

So, the optimal level of production for this product is 2 goods. This is the number of goods that should be produced and sold in order to maximize the profit achieved.

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The solution is, a)Range

The range is the difference between the highest and the lowest value of a set, so it is sensitive to extreme values. That is, you can have two sets with the same mean, but with very different spacings.

For example, two grades:

set A = {40, 50, 50, 60}

set B = {0, 50, 50, 100}

The set B has a way higher range(100) than set A(20), that is, the range is sensitive to extreme values.

So the correct answer is:

a)Range

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Answer:

96/95

Step-by-step explanation:

8/5 /  ( 3/4 + 5/6 )

8/5 / 19/12

= 96/95

Answer:

wrong

Step-by-step explanation:

(a+b)^2=(a+b)(a+b)

=a(a+b)b(a+b)

=a^2+ab+ab+b^2

=a^2+2ab+b^2

i hope it helps you

Probability that selected chip is white: 1/2

Probability that the other chip in the bowl is red given if the selected chip is white: 1/3

Let A be the event that bowl A is randomly selected; let B be the event that bowl B is randomly selected; and let C be the event that bowl C is randomly selected. All these three bowls are equally likely to be selected:

P(A) = P(B) = P(C) = 1/3

The probability of selecting a white chip from a bowl depends on from which bowl the chip is selected.

Let W be the event that a white chip is randomly selected.

Attached is the picture solution.

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Answer:

Step-by-step explanation:

Hope this Helps ;)

Answer:

18.445

Step-by-step explanation:

Multiply

Step-by-step explanation:

the diameter of a circle is 2 times the radius.

the area of a circle is

pi × r²

r being the radius.

so,

1519.76 = pi × r²

r² = 1519.76/pi = 483.7546326...

r = 21.99442276... in

diameter = 2r = 43.98884552... in ≈ 44 in

If 96 people divide into groups of eight, the following expression indicates that 12 groups are created.

Eight persons form groups made up of multiple people. a expression for how many groups made up of p people there are.

P = the number of groups.

12 groups out of 96

If there are 96 individuals, 12 groups are created.

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Answer:

63

Step-by-step explanation:

John's percentage:

36 and 48 have a common factor of 12 so divide both of them by 12.

36/12= 3 and 48/12=4 therefore

so 36/48= 3/4 which is 75% but we don't need to focus on the percent.

Don's no. of shirts:

we know Don has 84 shirts so we say

3/4 of 84= no. of shirts that Don put in his closet

84/4=21 21x3=63

Don put 63 shirts in his closet.

Hope that helped! Anymore questions just ask! :)

In the given equation which is 3 + 2n = 7, the value of n = 2.

For, further explanation to find the value of the variable in the given equation, we can solve the given equation by transferring the non-variable digits to one side either to L.H.S or R.H.S.

Given equation = 2n + 3 =7

In the above equation, the variable is 'n' and the non-variable digits are '3' and '7'. To find the value of 'n', we can transfer the non-variable digits to the R.H.S (Right Hand Side) as shown below:

2n + 3 = 7

2n = 7 - 3

2n = 4

n = \(\frac{4}{2}\)

n = 2.

So, from the above solution the value of 'n' is 2.

Given question is incomplete/incorrect, I assume the given question was to "obtain the value of n from the linear equation 3 + 2n = 7"

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The arclength of the curve r(t) = ⟨4sin t, 3t, 4cos t⟩ from t = -4 to t = 4 is approximately 25.1327 units.

To find the arclength of the curve, follow these steps:

1. Calculate the derivative of r(t): r'(t) = ⟨4cos t, 3, -4sin t⟩.
2. Find the magnitude of r'(t): |r'(t)| = √((4cos t)² + 3² + (-4sin t)²) = √(16cos² t + 9 + 16sin² t).
3. Simplify |r'(t)|: |r'(t)| = √(16(cos² t + sin² t) + 9) = √(16 + 9) = √25 = 5.
4. Integrate |r'(t)| from t = -4 to t = 4: ∫(-4 to 4) 5 dt = 5∫(-4 to 4) dt = 5(t)|(-4 to 4) = 5(4 - (-4)) = 5(8) = 40.

Note: There was an error in the main answer. The correct arclength is 40 units.

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Answer:

The last one (-2,-6),(-1,2),(-2,-7),(6,6)

Step-by-step explanation:

Because there are no pairs with the same x value

Answer:

(D) { (-2, -6), (-1,2), (-2, -7), (6,6)}

Step-by-step explanation:

functions do not have the same x

Answer : D

{ (-2, -6), (-1,2), (-2, -7), (6,6)}

Because the set has two the same x, i.e. -2

(-2,-6) and (-2, -7)

____________________

Jim rode for 5.5 hours

The given parameters are:

\(Distance = 189miles\) -- the total distance

\(Time= 6hours\) --- the total time

The rates are given as:

\(w = 4mi/hr\) ---- walks

\(r = 34mi/hr\) --- ride

So, we have the following equation

\(t_w + t_r = 6\) --- the sum of time walking and riding the bicycle

\(d_w + d_r = 189\) --- the sum of distance walked and riding the bicycle

Make dr and tr the subjects in the above equations

\(t_r = 6 - t_w\)

\(d_r = 189 - d_w\)

The equation for distance walked is:

\(w = \frac{d}{t}\)

So, we have:

\(4 = \frac{d}{t}\)

Make d the subject

\(d = 4t\)

Rewrite as:

\(d_w = 4t_w\)

For riding the bicycle, we have:

\(r = \frac{d}{t}\)

So, we have:

\(34 = \frac{189 - d_w}{6 -t_w}\)

Open brackets

\(204 - 34t_w = 189 - d_w\)

Rewrite as:

\(d_w =34t_w + 189 - 204\)

\(d_w =34t_w-15\)

Substitute \(d_w =34t_w-15\) in \(d_w = 4t_w\)

\(34t_w - 15 = 4t_w\)

Collect like terms

\(34t_w - 4t_w = 15\)

\(30t_w = 15\)

Divide both sides by 30

\(t_w = 0.5\)

Recall that:

\(t_r = 6 - t_w\)

So, we have:

\(t_r = 6 - 0.5\)

\(t_r = 5.5\)

Hence, Jim rode for 5.5 hours

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Answer:

hey hey hey

Step-by-step explanation:

blackpink in your area !

Henry could only see one line since both lines had the same slope, which means that the graphs of both equations will be identical and hence overlap.

Linear equations in a system 3x + 2y = 4, and 9x + 6y = 12

We must demonstrate why Henry could only make out one line when he plotted the equations 3x-2y=4 and 9x-6y=12 on a graph.

Take the provided linear equation system into consideration.

3x - 2y = 4 ................(1)

9x - 6y = 12 ..................(2)

Due to the fact that equation (2) is a multiple of equation (1), 3 (3x - 2y = 4) = 9x - 6y = 12

The slopes of the provided equations are also same.

Difference with regard to x for equation (1) yields,

additional to equation (2),

With regard to x, we can differentiate to get,

The graphs of both equations will overlap since both lines have the same slope and hence have the same appearance on the graph.

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The value of p(10) we get as  123.

What is Quadratic polynomial ?

A quadratic polynomial is a polynomial of degree 2, which means that it is a polynomial expression in one variable (usually written as x) that contains only terms of the form ax² + bx + c, where a, b, and c are constants. The highest exponent of the variable x in a quadratic polynomial is 2.

We are given a table of values for the quadratic polynomial p. Since p is a quadratic polynomial, it can be written in the form:

p(x) = ax² + bx + c

where a, b, and c are constants.

To find the value of p(10), we need to substitute x = 10 in the above equation and simplify:

p(10) = a(10)² + b(10) + c

p(10) = 100a + 10b + c

We don't know the values of a, b, and c, but we can use the values in the table to set up a system of equations.

From the table, we can see that:

p(0) = c = 3

p(1) = a + b + c = 6

p(2) = 4a + 2b + c = 11

Solving this system of equations, we get:

a = 1

b = 2

c = 3

Therefore, the quadratic polynomial p is:

p(x) = x² + 2x + 3

To find p(10), we substitute x = 10 in the above equation:

p(10) = (10)² + 2(10) + 3

p(10) = 100 + 20 + 3

p(10) = 123

Therefore, the value of p(10) is 123.

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The probability that Brandon ordered a pepperoni pizza is 1/6.

To find the probability that Brandon ordered a pepperoni pizza, we need to first determine the fraction of pizzas sold that were pepperoni.

We know that 1/6 of the pizzas sold were cheese, which means that 5/6 of the pizzas sold were not cheese. So, if we let x be the total number of pizzas sold in the week, then (5/6)x is the number of pizzas sold that were not cheese.

Of those non-cheese pizzas, 1/5 were pepperoni. So the total number of pepperoni pizzas sold would be (1/5)(5/6)x = (1/6)x.

Therefore, the probability that Brandon ordered a pepperoni pizza is (1/6)x / x = 1/6.

So the answer is: The probability that Brandon ordered a pepperoni pizza is 1/6.

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No, the sample standard deviation of differences (sd) is not equal to the difference of the sample standard deviations (s1 - s2).

The sample standard deviation of differences is a measure of the dispersion or spread of the differences between two sets of data. It is calculated by taking the square root of the average of the squared differences between each paired observation. On the other hand, s1 and s2 represent the individual sample standard deviations of two separate data sets. Simply subtracting these values (s1 - s2) does not give you the correct measure of the dispersion of the differences between the two sets of data.

The sample standard deviation of differences (sd) cannot be obtained by merely subtracting the sample standard deviations of the individual data sets (s1 - s2). Instead, the proper method for calculating the sample standard deviation of differences should be used.

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The equation of the tangent would be y = -4x/3 - 25/3 and the equation of the normal would be y = 3x/4.

What is a parabola?

A parabola is a plane curve that is mirror-symmetrical and roughly U-shaped in mathematics. It fits several seemingly disparate mathematical descriptions, all of which can be shown to define the same curves. A point and a line are two ways to describe a parabola.

The given equation is x² + y² = 25 ; (4, 3)

Now when we put x = 4 and y = 3

then LHS = RHS.

Now find the slope:

      2x + yy' = 0

       ⇒ y' = -x/y

Now at (4, 3) slope would be y' = -4/3.

The equation of the tangent would be

      y - y1 = m(x - x1)

      y - 3 = (-4/3)(x-4)

     3y - 9 = -4x + 16

     4x + 3y = 25

     y = -4x/3 - 25/3

Now equation of the normal is:

  y - y1 = (-1/m)(x - x1)

  y - 3 = 3/4(x - 4)

  y = 3x/4

Hence, the equation of the tangent would be y = -4x/3 - 25/3 and the equation of the normal would be y = 3x/4.

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According to the given statement The faster computer will take 2 minutes to send out the company's email on its own.

To solve this problem, let's assign variables to the given information. Let "x" represent the time it takes the slower computer to send out the company's email on its own, and let "y" represent the time it takes both computers working together to send out the email.

According to the problem, it takes two computers "y" minutes to send out the email, and it takes the slower computer "x" minutes to do the job on its own.

Since the two computers are working together, we can set up the following equation: 1/x + 1/y = 1/t, where "t" represents the time it takes the faster computer to do the job on its own.

Substituting the given values into the equation, we have: 1/x + 1/y = 1/2y

To find the value of "t", we need to solve for "y" in terms of "x". Multiply both sides of the equation by 2xy to eliminate the denominators:

2y + 2x = xy

Rearranging the equation, we get:

xy - 2y - 2x = 0

Now, let's factor the equation:

y(x - 2) - 2(x - 2) = 0

Simplifying further:

(x - 2)(y - 2) = 0

Since we are looking for the time it takes the faster computer to do the job on its own, we disregard the solution (y - 2) = 0, which gives us y = 2.

Therefore, the faster computer will take 2 minutes to send out the company's email on its own.

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Part A:

For a normally distributed data, population mean = sample mean

From the question, population mean = 34.82

Hence the sample mean = 34.82

The sample standard deviation is given by;

where n = 6, and

Therefore, the sample standard deviation is 2.05.

Part B

The interpretation of the standard deviation of the sampling distribution is that, since the square root of the sample size appears at the denominator, the standard deviation decreases as the sample size increases.

Part C

Hence, the probability is 0.0111.

Answer:

Step-by-step explanation:

11

15

1/2

144

81

4/9

We need AC ≅ XZ to show that triangle ABC ≅ triangle XYZ by ASA congruence of triangle.

What is ASA congruence of triangle?

The two triangles are considered to be congruent according to the ASA rule if any two angles and the side located between the angles of one triangle are equal to the corresponding two angles and side located between the angles of the second triangle.

We are given the following:

1. ∠A ≅ ∠X

2. ∠C ≅ ∠Z

Now, in order to show the triangles as congruent by ASA congruence of triangle, we need the side which is in between both the angles.

The sides in between both the angles are AC and XZ.

Hence, we need AC ≅ XZ to show that triangle ABC ≅ triangle XYZ by ASA congruence of triangle.

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