How would the domain of the function y = 4(12)^x be affected if it were to be changed to y = 4(24)^x?

Answer:

24.5%

Step-by-step explanation:

Given

P(Off-Campus) = 0.30

P(Part-Time Job | Off-Campus) = 0.62

P(Part-Time Job | On-Campus) = 0.65

Inferred

P(On-Campus) = 0.70

P(No Part-Time Job | Off-Campus) = 0.38

P(No Part-Time Job | On-Campus) = 0.35

Calculation

P(No Part-Time Job | On-Campus) = P(No Part-Time Job ∩ On-Campus)/P(On-Campus)

0.35 = P(No Part-Time Job ∩ On-Campus)/0.70

0.245 = P(No Part-Time Job ∩ On-Campus)

Therefore, 24.5% of students that live on campus do not have a part-time job.

Answer:

x = 4

Step-by-step explanation:

\(f(x)=3x-1\\g(x)=2x-3\)

substitute x = 2 into f(x):

\(f(2)=(3 \times2)-1=5\)

equate g(x) with found value for f(2) and solve for x:

\(g(x)=f(2)\\2x-3=5\\2x=8\\x=4\)

The mean of brothers and sisters = 3

From the attached data set of brothers and sisters we can write the data values (frequency) as:

1, 5, 4, 2

We need to find the mean of brothers and sisters,

We know that the formula for the mean of data.

mean(\(\bar{x}\)) = sum of all data values / total number of data values

First we find the sum of all data values.

1 + 5 + 4 + 2 = 12

and the total number of data values = 4

Using above formula of mean,

mean(\(\bar{x}\)) = sum of all data values / total number of data values

mean(\(\bar{x}\)) = 12 / 4

mean(\(\bar{x}\)) = 3

Therefore, the required mean is: 3

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Find the complete question below.

Multiplying each outcome by it's respective probability, and adding them, it is found that the expected value of the game is -€0.25.

-------------------------

The probabilities of each outcome are:

The expected earnings are:

\(E = 0.5(2) + 0.25(4) + 0.125(14) + 0.125(8) = 4.75\)

Subtracting the cost to play:

\(4.75 - 5 = -0.25\)

The expected value of this game is of -€0.25.

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Answer:

The values of b that satisfy the equation are:

b = (2√3 - 3) / 2

b = (-2√3 - 3) / 2

In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.

Step-by-step explanation:

To find the values of b that satisfy the equation 3(2b + 3)² = 36, we can solve for b by following these steps:

1. Divide both sides of the equation by 3:

  (2b + 3)² = 12

2. Take the square root of both sides:

  √[(2b + 3)²] = √12

  Simplifying further:

  2b + 3 = ±√12

3. Subtract 3 from both sides:

  2b = ±√12 - 3

4. Divide both sides by 2:

  b = (±√12 - 3) / 2

  Simplifying further:

  b = (±√4 * √3 - 3) / 2

  b = (±2√3 - 3) / 2

Therefore, the values of b that satisfy the equation are:

b = (2√3 - 3) / 2

b = (-2√3 - 3) / 2

In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.

Answer:

Step-by-step explanation:

Given that

X1, X2, X3....... X18 are the volume of beverages in 18 bottles. These volumes have the same distribution and are independent of each other.

E.X(i) = 2.013L, while the Standard Deviation is given as

S D = X(i) = 0.005L

The average volume per bottle = X bar

E.X bar = E.X(i) = 2.013L

S D X bar = [S D X(i)]/√n = 0.005 /√18 = 0.005 / 4.24 = 1.18*10^-3L

She can either have 24 people since there are more slices of pizza there will be extras

The answer as a result of the numerical expression above is B) 1/36

This expression is rank number:

\(( {6}^{ - 4} ) {}^{ \frac{1}{2} } = 6 {}^{ - 2} = \frac{1}{ {6}^{2} } = \frac{1}{36}.

So the answer as a result of the numerical expression above is 1/36.

From these calculations it can be seen that the rank between what is inside the brackets and what is outside it can be multiplied.

In the question above the power of -4 multiplied by the power of ½ ( (-4×½) the result is -2.

So all that's left is 6⁻². Another form of 6⁻² is 1/6² or 1/36.

This refers to the exponential rule in mathematics, namely a⁻ⁿ can be written as 1/aⁿ.

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A. True.

In a two-column proof, the left column consists of statements, which are the facts or assumptions that lead to the proof of the theorem, while the right column consists of the reasons or justifications that explain how each statement logically follows from the previous one. Therefore, the left column states your reasons is a true statement.

The answer to the student's question is True. In a two-column proof, the left column contains the statements (steps) and the right column contains the corresponding reasons (justifications).

The answer to the question, 'True or false? In a two-column proof, the left column states your reasons', is A. True.

A two-column proof is organized into two columns. The left column contains the 'Statements' and the right column contains the corresponding 'Reasons'. The 'Statements' are the steps that lead to the conclusion of the proof, while the 'Reasons' justify each of those steps according to rules or laws of mathematics.

For example, if we want to prove that the opposite angles of a parallelogram are equal. The left column (Statements) could contain the first step 'ABCD is a parallelogram' and the right column (Reasons) would give the explanation 'Given'. Therefore, in a two-column proof, the left column does represent statements, not reasons.

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Answer:

1.68 hours

Step-by-step explanation:

Answer;  one divided by 7......14 percent

Step-by-step explanation:

Hello!

surface area

= 2(4 x 2) + 2(12 x 4) + 2(12 x 2)

= 160cm²

Answer:

10/40 were men, or simplified the amount is 1/4 of the total is men

The solution to the equation sqrt 2-3x / sqrt 4x = 2 is x = -2/3.

To solve the equation, we must first clear the denominators and simplify the equation. We can do this by multiplying both sides by sqrt(4x) and then squaring both sides. This gives us:
sqrt 2-3x = 4sqrt x
2 - 6x + 9x² = 16x
9x² - 22x + 2 = 0
Using the quadratic formula, we can find that x = (-b ± sqrt(b² - 4ac)) / 2a. Plugging in a = 9, b = -22, and c = 2, we get:
x = (-(-22) ± sqrt((-22)² - 4(9)(2))) / 2(9)
x = (22 ± sqrt(352)) / 18
x = (22 ± 4sqrt22) / 18
Simplifying this expression, we get:
x = (11 ± 2sqrt22) / 9
Therefore, the solution to the equation is x = -2/3.
To solve the equation sqrt 2-3x / sqrt 4x = 2, we must clear the denominators and simplify the equation. This involves multiplying both sides by sqrt(4x) and then squaring both sides.

After simplifying, we end up with a quadratic equation. Using the quadratic formula, we can find that the solutions are x = (11 ± 2sqrt22) / 9.

However, we must check that these solutions do not result in a division by zero, as the original equation involves square roots. It turns out that the only valid solution is x = -2/3.

Therefore, this is the solution to the equation.

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Answer: C) (1, -1)

Step-by-step explanation:

\(\boldsymbol{\sf{\underline{\diamond System \ of \ equations \ by \ the \ reduction \ method:} }}\)

   \(\boldsymbol{\sf{We\:have\:the\:system\:of\:equations \ --\to \ \left \{ {{x+2y=1 \ } \atop {2x-3y=5 }} \right. }}\)

Multiply the first equation by 2, and the second equation by -1, then both equations must be added.

             \(\boldsymbol{\sf{\star \ 2(x+2y=-1) }}\\ \boldsymbol{\sf{\star -1(2x-3y=5) }}\)

We add these equations to eliminate x.

             \(\boldsymbol{\sf{\star \ 7y=-7 }}\)

Then we solve 7y=-7 for y (divide by 7).

               \(\boldsymbol{\sf{\star \ \dfrac{7y}{7}=\dfrac{-7}{7} }}\\ \\ \boxed{\boldsymbol{\sf{\star \ y=-1}}}\)

We place the found value of y, in one of the original equations y to solve for x.

                  \(\boldsymbol{\sf{\star \ x+2y=-1}} \\ \\ \boldsymbol{\sf{\star \ x+2(-1)=-1}}\\ \\ \boldsymbol{\sf{\star \ 0=-x+1 }}\)

Simplify (We add x to both sides.)

                  \(\boldsymbol{\sf{\star \ 0+(x)=-x+1+(x) }}\\ \\ \boldsymbol{\sf{\star \ x=1}}\\ \\ \boldsymbol{\sf{\star -2=-1-x}}\)

Add (2) to both sides.

                   \(\boldsymbol{\sf{\star \ -2+(2)=-x-1+(2) }}\\ \\ \boldsymbol{\sf{\star \ 0=-x+1 }}\)

We divide by 1.

                      \(\boldsymbol{\sf{\star \ \dfrac{x}{1}=\dfrac{1}{1} }}\\ \\ \boxed{\boldsymbol{\sf{\star \ x=1}}}\)

                                     \(\underline{\bf{ \ \ x,y \ answer\ \ \ \ }}\\\boxed{\boldsymbol{\sf{x=1,y=-1 }}}\)

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According to the concept of algebraic expression and arithmetic, the correct answers are A) Number of adults = N - 25. B) Number of adults when N = 124: 124 - 25 = 99

A) Let's denote the number of children as N. Since there are 25 fewer adults than children, the number of adults can be expressed as N - 25.

B) If there are 124 children, we substitute N with 124 in the expression from part A. Thus, the number of adults would be 124 - 25 = 99.

To arrive at these answers, we used the given information that there are "N" children and 25 fewer adults than children. By substituting the value of N, we determined the number of adults in terms of N and then calculated the specific number of adults when N is equal to 124.

Note: The given question is incomplete. The complete question is:

Some adults and children are watching a musical. there are 'N' number of children. There are 25 fewer adults than children.

A) find the number of adults in terms of 'N'.

B) if there are 124 children how many adults are there?​

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a) There are 2^6 = 64 subsets total.

b)  There are 2^3 = 8 subsets total

c) There are 2^5 = 32 subsets total

d) There are 32^4 = 48 subsets total

e)  There are (6 choose 4) = 15 subsets total

f)   There are 32 = 6 subsets total

g) There are is (6 choose 4) - (3 choose 4) = 15 - 0 = 15 subsets total

h) There are (3 choose 1) * (3 choose 3) = 3  subsets total

a) There are 2^6 = 64 subsets total.

b)  Since we need to include elements 2, 3, and 5 in a subset, we have 3 elements fixed, and we need to choose 1, 2, or 3 elements from the remaining 3 elements (1, 4, and 6). Therefore, there are 2^3 = 8 subsets that contain the elements 2, 3, and 5.

c) There are 2^5 = 32 subsets that contain at least one odd number. This can be seen by noticing that if a subset does not contain any odd numbers, then it must be {2,4,6}, which is not a valid subset since it does not satisfy the condition that it be a subset of S.

d) There are 32^4 = 48 subsets that contain exactly one even number. To see why, notice that there are 3 choices for which even number to include (2, 4, or 6), and then there are 2^4 = 16 choices for which of the remaining 4 odd numbers to include in the subset.

e) There are (6 choose 4) = 15 subsets of cardinality 4. This is the number of ways to choose 4 elements from a set of 6.

f) Since we need to include elements 2, 3, and 5 in a subset of cardinality 4, we have 3 elements fixed, and we need to choose 1 element from the remaining 3 even elements, and 1 element from the remaining 2 odd elements. Therefore, there are 32 = 6 subsets of cardinality 4 that contain the elements 2, 3, and 5.

g) The number of subsets of cardinality 4 that contain at least one odd number is equal to the total number of subsets of cardinality 4 minus the number of subsets of cardinality 4 that contain only even numbers. This is (6 choose 4) - (3 choose 4) = 15 - 0 = 15.

h) The number of subsets of cardinality 4 that contain exactly one even number is equal to the number of ways to choose 1 even number out of 3, and then the number of ways to choose 3 odd numbers out of 3. This is (3 choose 1) * (3 choose 3) = 3.

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Answer:

70

Step-by-step explanation:

Given:

Total number of students = 38

From the given Venn diagram, let's determine how many students have been only to Spain.

From the venn diagram, we have the following:

Number of students that have only been to Germany = 2

Number of students that have only been to France = 6

Number of students that have only been to Spain = 8

We can see in the circle that represents Spain, the number that is alone is 8.

Therefore, we can say that 8 students have been only to Spain.

ANSWER:

8

Answer:

quadratic

Step-by-step explanation:

This graph has a parabola form wich is a propertie for qaudratic functions

Answer:

A

Step-by-step explanation:

Answer:

\( V = \pi r^2 h\)

For this case we know that \( r=5m\) represent the radius, \( h = 10m\) the height and the rate given is:

\( \frac{dV}{dt}= \frac{100 L}{min}\)

\( Q = 100 \frac{L}{min} *\frac{1m^3}{1000L}= 0.1 \frac{m^3}{min}\)

And replacing we got:

\( \frac{dh}{dt}=\frac{0.1 m^3/min}{\pi (5m)^2}= 0.0012732 \frac{m}{min}\)

And that represent \( 0.127 \frac{cm}{min}\)

Step-by-step explanation:

For a tank similar to a cylinder the volume is given by:

\( V = \pi r^2 h\)

For this case we know that \( r=5m\) represent the radius, \( h = 10m\) the height and the rate given is:

\( \frac{dV}{dt}= \frac{100 L}{min}\)

For this case we want to find the rate of change of the water level when h =6m so then we can derivate the formula for the volume and we got:

\( \frac{dV}{dt}= \pi r^2 \frac{dh}{dt}\)

And solving for \(\frac{dh}{dt}\) we got:

\( \frac{dh}{dt}= \frac{\frac{dV}{dt}}{\pi r^2}\)

We need to convert the rate given into m^3/min and we got:

\( Q = 100 \frac{L}{min} *\frac{1m^3}{1000L}= 0.1 \frac{m^3}{min}\)

And replacing we got:

\( \frac{dh}{dt}=\frac{0.1 m^3/min}{\pi (5m)^2}= 0.0012732 \frac{m}{min}\)

And that represent \( 0.127 \frac{cm}{min}\)

Answer:

y = 1/4x + 3

Step-by-step explanation:

m= slope

1) Find the slope

y1-y2 divided by x1-x2

2-6 divided by -4 - 12 = -4/-16= 1/4

The slope of the line is 1/4

m= 1/4

2) Plug it in to find b. (12,6) is easier

6= 1/4(12)+b

6= 3 +b

b= 3

3) Check

2= 1/4 (-4) + 3

2= -1 +3

4) The answer is y = 1/4x + 3

Answer:

\(f(-3)=-27\)

Step-by-step explanation:

So we have the function:

\(f(x)=-4x^2+9\)

And we want to find f(-3).

So, let's substitute -3 for x. Therefore:

\(f(-3)=-4(-3)^2+9\)

Square:

\(f(-3)=-4(9)+9\)

Multiply:

\(f(-3)=-36+9\)

Add:

\(f(-3)=-27\)

And we're done!

Answer:

-27

Step-by-step explanation:

Answer:

16777216

Step-by-step explanation:

1) \(\frac{8^{10} }{8^2} = 8^{10-2}\)

2) \(8^{10-2} = 8^8\)

3) \(8^8\) = 16777216

Step-by-step explanation:

it seems you solved the tricky part yourself already.

just to be sure, let's do the first derivative here again.

the easiest way would be for me to simply multiply the functional expression out and then do a simple derivative action ...

f(t) = (t² + 6t + 7)(3t² + 3) = 3t⁴ + 3t² + 18t³ + 18t + 21t² + 21 =

= 3t⁴ + 18t³ + 24t² + 18t + 21

f'(t) = 12t³ + 54t² + 48t + 18

and now comes the simple part (what was your problem here, don't you know how functions work ? then you are in a completely wrong class doing derivatives; for that you need to understand what functions are, and how they work). we calculate the function result of f'(2).

we simply put the input number (2) at every place of the input variable (t).

so,

f'(2) = 12×2³ + 54×2² + 48×2 + 18 = 96 + 216 + 96 + 18 =

= 426

The equation of the line through the point (3,5) that cuts off the least area from the first quadrant is 5x +3y -30 = 0.

An intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+c, where m is the slope and c is the y-intercept.

There are basically two intercepts, x-intercept and y-intercept. The point where the line crosses the x-axis is the x-intercept and the point where the line crosses the y-axis is the y-intercept.

The equation of the line, which intersects the y-axis at a point is given by:

                           y = mx + c

Suppose the line passes through (t,0) and (3,5), where t>3. Then the y-intercept is at (0, 5t/t-3).

So the area of the triangle is:

\(\frac{1}{2}\)×\(t\)×\(\frac{5t}{t-3}\) \(=\)\(\frac{5(t^{2} )}{3(t-3)}\)

Then:

d(5t²/2(t-3))/dt = (5t/t-3) - 5t²/2(t-3)²

=  5t²(2(t-3)-t)/2(t-3)²

=5t(t-6)/2(t-3)²

Since we require t >3, the zero of the derivative that we see is when t=6.

We can write the equation of this line as: 5x +3y -30 = 0

Thus, the equation of the line through the point (3,5) that cuts off the least area from the first quadrant is 5x +3y -30 = 0.

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Based on the data, the estimated number of lemon candies in the bag of 100 assorted candies is about 19.

In mathematics, proportion refers to the relationship between two quantities that are equivalent or have a constant ratio. It is usually expressed as a fraction or a ratio. For example, if a recipe calls for 2 cups of flour and 1 cup of water, the proportion of flour to water is 2:1 or 2/1. Proportions are used in a variety of mathematical and real-world situations, such as solving problems involving ratios, rates, and percentages.

In the given question,

We can use a simple proportion to estimate the number of lemon candies in the bag. We know that Ridgette handed out a total of 6 lemon candies out of a total of candies. Therefore, the proportion of lemon candies in the bag is:

6/total candies = number of lemon candies/100

We can cross-multiply to solve for the number of lemon candies:

number of lemon candies = 6 x 100 / total candies

We can also use the information about the other flavors to estimate the total number of candies in the bag. The total number of candies is:

total candies = lemon + orange + grape + cherry

Using the information from the table, we can estimate the total number of candies:

total candies = 6 + 5 + 8 + 13 = 32

Therefore, the estimated number of lemon candies in the bag is:

number of lemon candies = 6 x 100 / 32 = 18.75

We can round this to the nearest whole number to estimate that there were about 19 lemon candies in the bag of 100 assorted candies.

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