Maggie earns $20 each time she babysits. If she babysits 8 times, how much money did she earn?
The solution is

Step-by-step explanation:

Multiply each number in the parentheses by the number to the left;

\(-2(-4)-3(+2)\)

Simplify and combine like terms;

\(8-6\)

\(2\)

Answer:

\(\boxed{12u^3+8u^2-6u+9}\)

Step-by-step explanation:

\((8u^3+8u^2+6)+(4u^3-6u+3) = 8u^3+8u^2+6+4u^3-6u+3\)

Once

\(8x+4x = 12x, \text{ as } x = u^3\)

\(8u^3+8u^2+6+4u^3-6u+3 = 12u^3+8u^2+6-6u+3 = \boxed{12u^3+8u^2-6u+9}\)

You don't need to factor.

Answer:

Step-by-step explanation:

The correct answer is a. A larger sample size was used.As per the Law of Large Numbers, the more times an experiment is repeated, the closer the actual results will be to the expected probability. In this case, rolling the cube 100 times provides a larger sample size than rolling it only 20 times. The more rolls that are made, the greater the likelihood that the actual results will converge towards the expected probability of 1/2 for rolling an even number.Option b, The 100 tosses were controlled better, is not relevant to this scenario since the fairness of the cube is assumed.Option c, The expected probability changed when the cube was rolled 100 times, is not true. The expected probability of rolling an even number on a fair six-sided die is always 1/2, regardless of the number of times it is rolled.Option d, The thrower considered only the even rolls, and disregarded the odd rolls, is not a valid assumption. The question states that the number of even rolls was recorded, but it does not imply that odd rolls were disregarded.

Answer: B

Step-by-step explanation:

multiply the 1/2 of a mile by 3 (to complete the full hour)

You are already correct.

Answer:

B

Step-by-step explanation:

P(AUB)=P(A)+P(B)-P(A∩B)

191/400=7/20+P(B)-49/400

P(B)=191/400+49/400-7/20=240/400-7/20=12/20-7/20=5/20=1/4

The value of P(B) is 1/4.

The probability is defined as the possibility of an event is equal to the ratio of the number of favorable outcomes and the total number of outcomes.

For an experiment having q number of outcomes, the number of favorable outcomes can be denoted by p. The formula to calculate the probability of an event is as follows:

Probability(Event) = Favorable Outcomes/Total Outcomes = p/q

Given data as :

P(A) = 7/20,

P(A∪B) = 191/400,

P(A∩B) = 49/400 ,

P(AUB) = P(A) + P(B) - P(A∩B)

Substitute the values of P(A), P(A∪B) and P(A∩B) in formula,

191/400 = 7/20 + P(B) - 49/400

Rearrange the terms in the equation,

P(B) = 191/400 + 49/400 - 7/20

P(B) = 240/400 - 7/20

P(B) = 12/20 - 7/20

P(B) = 5/20

P(B) = 1/4

Hence, the value of P(B) is 1/4.

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The expression to model the problem is \(\frac{2}{3}\) ÷ 12, and the solution is 1/18.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Total fraction of grains Alexis has = 2/3 pounds

Grains used to feed 12 chickens = 2/3

Grains used to feed 1 chicken = (2/3) / 12

                                                  = \(\frac{2}{3}\) ÷ 12

Using the reciprocal rule,

Grains used to feed 1 chicken = \(\frac{2}{3}\) × \(\frac{1}{12}\)

                                                  = 1/18

Hence the amount of grains for 1 chicken is 1/18.

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Answer:

  A Volvo

Step-by-step explanation:

A "good" is something you can touch. Song rights and dog training are not "goods". It is durable if it has a long life.

A Twinkie may have a shelf life approaching that of a Volvo, but food (or what passes for food) is not considered durable, in general. Rather, it is considered consumable.

A Volvo is an example of a durable good.

Answer:

[6, 8).

Step-by-step explanation:

When we are looking for the range of a function by just looking at the graph, we have to define from what point to what point the graph move vertically. On the other hand, if we were looking for the domain, we would state from where to where the graph moves horizontally.

In this case we have to analyze the graph vertically, since we are looking for the range of the function. Therefore, if we take a look at the line we can notice that it goes from y=6 to y=8. Therefore the range should be from 6 to 8.

Now, this result must be expressed in interval notation, meaning that we have to state whether the values of each end are contained or not by the function. The graph already tells us about it., because it marks it with the closed or open dots. In the case of the number 6, we have a closed dot, means that the function contains the number 6. For the other end we have an open dot, means that the function doesn't contain the number 8.

Applying internal notation, the range of this function is:

[6, 8).

Learn more about interval notation here:

1. https://web.nmsu.edu/~kberver/Unit1/Unit18.html#:~:text=An%20interval%20is%20closed%20if,used%20for%20an%20open%20endpoint.

2. https://brilliant.org/wiki/interval-notation/#:~:text=Interval%20notation%20is%20a%20way,inequality%20or%20system%20of%20inequalities.

The product and the quotient of the functions are as follows:

(rs)(4) =8

(r / s)(3) = 2

A function relates input and output. It relates an independent variable with a dependent variable.

Therefore, let's solve the function as follows:

r(x) = 2√x

s(x) = √x

Therefore, let's find

(rs)(4) = r(4) × s(4) = 2√4 × √4 = 4 × 2 = 8

Let's find

(r / s)(3) = r(3) / s(3) = 2√3 / √3 = 2

Therefore,

(rs)(4) =8

(r / s)(3) = 2

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Answer:

h = 6 feet

Step-by-step explanation:

It is given that,

Area of a triangle, A = 18 sq feet

Base of the triangle, b = 6 feet

We need to find the height of the triangle. The area of a triangle can be given by the formula as follows :

\(A=\dfrac{1}{2}\times b\times h\)

h is height

\(h=\dfrac{2A}{b}\\\\h=\dfrac{2\times 18}{6}\\\\h=6\ \text{feet}\)

So, the height of the triangle is 6 feet.

Answer:

B

Step-by-step explanation:

using the recursive rule \(a_{n}\) = 3\(a_{n-1}\) and a₁ = 10, then

a₁ = 10

a₂ = 3a₁ = 3 × 10 = 30

a₃ = 3a₂ = 3 × 30 = 90

the first 3 terms are 10 , 30 , 90

Answer:

they will only have 16 dollars left

Answer:

The bigger number is 56

Step-by-step explanation:

\(\frac{x}{y}\) = \(\frac{7}{5}\)  cross multiply

5x = 7y

y = x -16  substage x-16 in the equation above for y

5x = 7( x - 16)

5x = 7x - 112  Subtract 7x from both sides

-2x = -112  Divide both sides by -2

x = 56

Check:

y = x - 16

y = 56 - 16

y = 40

5x = 7y

5(56) = 7(40)

280 = 28

y = x - 16

40 = 45-16

40 = 40

Answer:

3 songs

Step-by-step explanation:

25% more songs: 12 x 1.25 = 15

80% removed: 15 x 0.2 = 3

The length of the third side is 14.4 units.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We find the third side of a triangle by using Pythagoras theorem.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides

8²+12²=x²

64+144=x²

208=x²

Take square root on both sides

x=14.4

Hence, the length of the third side is 14.4 units.

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Answer:

\(Q(-2,3) \longrightarrow Q'(-1/3, 1/2) \\ \\ R(-3,1) \longrightarrow R'(-1/2, 1/6) \\ \\ T(2,-1) \longrightarrow T'(1/3, -1/6) \\ \\ W(2,4) \longrightarrow W'(1/3, 2/3)\)

Step-by-step explanation:

For a dilation at the origin, multiply each of the coordinates by the scale factor.

\(Q(-2,3) \longrightarrow Q'(-1/3, 1/2) \\ \\ R(-3,1) \longrightarrow R'(-1/2, 1/6) \\ \\ T(2,-1) \longrightarrow T'(1/3, -1/6) \\ \\ W(2,4) \longrightarrow W'(1/3, 2/3)\)

This is a linear programming problem with three constraints and two variables, where the objective is to minimize the expression 3x + 2y subject to the following constraints:

5x + y = 10

x + y = 6

x + 4y = 12

The first constraint represents a straight line in the x-y plane, the second constraint represents another straight line, and the third constraint represents yet another straight line. The feasible region is the region where all three constraints are satisfied simultaneously, which is the intersection of the three lines.

To solve this problem, you can use the method of substitution or elimination to solve for one variable in terms of the other in two of the equations, and then substitute this expression into the third equation to obtain a single equation in one variable. You can then solve for that variable, and use back-substitution to find the values of the other variable.

For example, using the first and second equations, you can solve for x in terms of y as follows:

x = 6 - y (from the second equation)

y = 10 - 5x (from the first equation)

Substituting y = 10 - 5x into the third equation, you get:

x + 4(10 - 5x) = 12

Simplifying this equation, you get:

-19x + 40 = 0

Solving for x, you get:

x = 40/19

Using x = 40/19 and the equation x + y = 6, you can solve for y as:

y = 6 - x = 6 - 40/19 = 94/19

Therefore, the minimum value of 3x + 2y subject to the given constraints is:

3(40/19) + 2(94/19) = 222/19

And the values of x and y that minimize this expression are:

x = 40/19 and y = 94/19.

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This is a linear programming problem with three constraints and two variables, where the objective is to minimize the expression 3x + 2y subject to the following constraints:

5x + y = 10

x + y = 6

x + 4y = 12

The first constraint represents a straight line in the x-y plane, the second constraint represents another straight line, and the third constraint represents yet another straight line. The feasible region is the region where all three constraints are satisfied simultaneously, which is the intersection of the three lines.

To solve this problem, you can use the method of substitution or elimination to solve for one variable in terms of the other in two of the equations, and then substitute this expression into the third equation to obtain a single equation in one variable. You can then solve for that variable, and use back-substitution to find the values of the other variable.

For example, using the first and second equations, you can solve for x in terms of y as follows:

x = 6 - y (from the second equation)

y = 10 - 5x (from the first equation)

Substituting y = 10 - 5x into the third equation, you get:

x + 4(10 - 5x) = 12

Simplifying this equation, you get:

-19x + 40 = 0

Solving for x, you get:

x = 40/19

Using x = 40/19 and the equation x + y = 6, you can solve for y as:

y = 6 - x = 6 - 40/19 = 94/19

Therefore, the minimum value of 3x + 2y subject to the given constraints is:

3(40/19) + 2(94/19) = 222/19

And the values of x and y that minimize this expression are:

x = 40/19 and y = 94/19.

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Answer:

A.

Step-by-step explanation:

The vertical line test is a way of finding out if a relation is a function.

Graph the relation.

Then imagine a vertical line moving from left to right over the graph of the relation.

If the vertical line intersects at most one point of the graph in any position you place the vertical line, then the relation is a function.

This function passes the vertical test since it never intersects more than one point on the vertical line at a time.

Answer: A.

The mean is  2,071,798.33

The Median is 1,485,552

The range is 7,425,310

The standard deviation is given as 1961105.68

Mean = (Sum of all populations) / (Number of cities)

= (8,336,817 + 979,576 + 2,693,976 + 2,320,268 + 1,680,992 + 1,584,064 + 1,547,253 + 1,423,851 + 1,343,573 + 1,021,795 + 978,908 + 911,507) / 12

= 24,861,580 / 12

= 2,071,798.33

To find the median, we need to arrange the populations in increasing order and find the middle value. If we arrange these values, we get:

911,507, 978,908, 979,576, 1,021,795, 1,343,573, 1,423,851, 1,547,253, 1,584,064, 1,680,992, 2,320,268, 2,693,976, 8,336,817

Since there are 12 cities (an even number), the median would be the average of the 6th and 7th values:

Median = (1,423,851 + 1,547,253) / 2

= 1,485,552

The mode isn't applicable here as no city population repeats.

The range is the highest population minus the lowest population:

Range = 8,336,817 - 911,507

= 7,425,310

Standard deviation  =  (911507- 2068548.3333333)² +  (978908 - 2068548.3333333)² + (979576  - 2068548.3333333)²  + ( 1021795 -  2068548.3333333)² +  (1343573- 2068548.3333333)²  +( 1423851- 2068548.3333333)² + (1547253- 2068548.3333333)² +( 1584064- 2068548.3333333)² + (1680992- 2068548.3333333)² + ( 2320268- 2068548.3333333)²  +(2693976- 2068548.3333333)² +( 8336817 - 2068548.3333333)² / 12

= 46151226311869 / 12

=  3845935525989.1

\(standard deviation = \sqrt{ 3845935525989.1}\)

=  1961105.6896529

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Answer:

128 miles

Step-by-step explanation:

The number of miles Amy's parents drove altogether is 128 miles.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Amy's dad drove 3 miles for every 5 miles her mom

drove.

So, the ratio is 3:5

Amy's mom drove 32 more miles than her dad

Let number mile Amy's father drove be x and then the number of miles Amy's mom drove will be x+32

Here, x/(x+32) =3/5

5x=3(x+32)

5x=3x+96

2x=96

x=48

So, x+32=80

Then, total distance is 80+48=128 miles

Therefore, the number of miles Amy's parents drove altogether is 128 miles.

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Answer:

6

Step-by-step explanation:

4

Answer:

B) approximately normal with mean 2.3 and standard deviation 2

Step-by-step explanation:

Given the following :

Mean crimes per day = 2.3

Standard deviation = 2

Number of samples = 100

Sampling distribution of the mean:

According to the central limit theorem:

Sample mean = population mean

2.3 = 2.3

The standard deviation of the sample (s) : ratio of the population standard deviation and square root of the sample size.

s = population standard deviation / √sample size

s = 2 / √100

s = 2 / 10

s = 0.2

The central limit theorem also posits that once ths sample size is large enough, the sampling of the sample mean will be approximately normal.

Hence, the distribution is approximately normal, with mean of 2.3 and standard deviation of 0.2

Answer:

250

Step-by-step explanation:

The equation of a line in the slope intercept form is expressed as

y = mx + c

Where

m represents slope

c represents y intercept

The equation of the given line is

3x + 5y = 7

5y = 7 - 3x

5y = - 3x + 7

y = - 3x/5 + 7/5

By comparing with the equation of the given line, slope of the given line is - 3/5

If two lines are parallel, it means that they have the same slope. This means that the slope of the line passing through (5, - 6) is - 3/5

We would determine the y intercept, c by substituting m = - 3/5, x = 5 and y = - 6 into the slope intercept equation. It becomes

- 6 = - 3/5 * 5 + c

- 6 = - 3 + c

c = - 6 + 3

c = - 3

By substituting m = - 3/5 and c = - 3, into the slope intercept equation, the equation of the line would be

y = - 3x/5 - 3

9514 1404 393

Answer:

  a) -13

  b) -22

Step-by-step explanation:

It can be convenient to compute the function values first:

  f(1) = 1² -14·1 = -13

  g(1) = 1 +8 = 9

Then the compositions are ...

(a) (f+g)(1) = f(1) +g(1) = -13 +9 = -4

(b) (f-g)(1) = f(1) -g(1) = -13 -9 = -22