a couple has 3 children. they sit in 5 adjacent seats in the same row while watching a movie. if the mother must sit in between the two youngest children, how many seating arrangements are possible?

Answer:

12a + 13b

Step-by-step explanation:

3(5a + 4b) - 3a + b

multiply 3 by 5a and 4b

15a + 12b - 3a + b

Now add the a terms together and b terms together

15a - 3a + 12b + b

12a + 13b

Answer:

12a + 13b

Step-by-step explanation:

3(5a+4b)-3a+b

To simplify the expression, we need to distribute the 3 to all terms inside the parentheses

3*5a+3*4b-3a+b

15a+12b-3a+b

Combine like terms

12a + 13b

Answer:

20800 dollars

Step-by-step explanation:

15600*(1/0.75)

=20800

the original price was 20800 dollars.

weirdly expensive computer though

Answer:

picture it to pixilated

Step-by-step explanation:

The x-intercept and y-intercept of the equation will be (-1, 0) and (0, 2). The graph is given below.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

x/a + y/b = 1

Where 'a' is the x-intercept of the line and ‘b’ is the y-intercept of the line.

The linear equation is given below.

y = 2x + 2

Convert the equation into intercept form, then we have

y = 2x + 2

y - 2x = 2

y / 2 - x / 1 = 1

The x-capture and y-block of the situation will be (- 1, 0) and (0, 2). The chart is given beneath.

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Answer:

[tex]-4x^2-4x+20[/tex]

Step-by-step explanation:

Since we're subtracting the entire quadratic, we can place the second equation in parentheses and distribute the subtraction sign.

[tex]2x^2-9x+8-(6x^2-5x-12)\\2x^2-9x+8-6x^2+5x+12\\2x^2-6x^2-9x+5x+8+12\\-4x^2-4x+20[/tex]

Answer:

[tex]-4x^2-4x+20[/tex]

Step-by-step explanation:

To find the difference of the two quadratic expressions, subtract the second expression from the first expression:

[tex]\implies (2x^2-9x+8)-(6x^2-5x-12)[/tex]

Remove the parentheses and apply the distributive law
[tex]-\left(a-b\right)=-a+b[/tex]

[tex]\implies 2x^2-9x+8-6x^2+5x+12[/tex]

Collect like terms:

[tex]\implies 2x^2-6x^2+5x-9x+8+12[/tex]

Combine like terms:

[tex]\implies -4x^2-4x+20[/tex]

Therefore, the difference of the two quadratic expressions is:

[tex]\large \boxed{-4x^2-4x+20}[/tex]

Dr. Ellison's equation that f(2) = 5/3 is wrong

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

y = -3x + 7

This equation can be expressed as a function

So, we have

f(x) = -3x + 7

In Dr. Ellison's equation, we have

f(2) = 5/3

This means that

x = 2

So, we have

f(2) = -3 * 2 + 7

Evaluate

f(2) = 1

The calculated value is different from Dr. Ellison's equation

Hence, the solution is wrong

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Answer:

-1.1

Step-by-step explanation:

:)

Answer:

Step-by-step explanation: 34

Answer:

x = [tex]\frac{11}{26}[/tex]

Step-by-step explanation

Expand 2(9x - 1):  18x - 2

Expand - ( x - 9 - 7x:     -8 + 9

Add 2 to both sides 18x - 2 +2 =  -8x + 9 + 2

Simplify

18x = -8x + 11

Add 8x to both sides

18x + 8x =  -8x + 11 + 8x

Simplify

26x = 11

Divide both sides by 26

[tex]\frac{26x}{26}[/tex] = [tex]\frac{11}{26}[/tex]

Simplify

x = [tex]\frac{11}{26}[/tex]

Answer:

Angle 6 is 78 degrees Angle 7 is 102 degrees

Step-by-step explanation:

Since both lines are parallel, you can assume that Angle 6 plus Angle 7 are a linear pair. Angle 1 corresponds to Angle 5 by the corresponding parts. Angle 5 is congruent to Angle 7 by Vertical angles so therefore Angle 7 is 102. Since Angle 6 + Angle 7 equal 180 degrees, you can put the equation like this,

[tex]Angle 6 + 102 = 108. Angle 6 = 78.[/tex]

Therefore you get your two answers

Answer: Slope=7/9

Step-by-step explanation:

m=[tex]y_{2} - y_{1} / x_{2} - x_{1}[/tex]

We can insert your equation to get:

m=8-1/10-1

Simplify:

m=7/9

A. The equation that can be used to determine the number of weeks is $999=225+42w

B. The number of weeks it will take Hannah to repay is 18weeks

An equation is a mathematical statement, which has an equal sign (=) between the algebraic expression. Linear equations are the equations of degree 1. It is the equation for the straight line. The solutions of linear equations will generate values, which when substituted for the unknown values, make the equation true. In the case of one variable, there is only one solution. For example, the equation x + 3 = 0 has only one solution as x = -2.

the total amount of money Hannah repaid is $225+$43×w, where w is the number of weeks to repay $43.

therefore $999= $225+$43w

$43w=$ (999+225)

$43w= $1224

divide both side by $43

w= $1224/$43

w= 18 weeks

therefore it will take Hannah 18weeks to repay the money.

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Answer:

-6 is the y-intercept, as in the point that crosses the y axis

The linear model that represents the total cost of recording is f(x) = 75x + 50.

The initial fee is $50 for recording an album.

There is an additional cost per hour i.e. $75.

number of hours = x

Now based on the above information, the linear model should be f(x)=75x+50

Here 50 represent the initial fee i.e. equivalent to y-intercept

And, 75 represent the slope

Therefore we can conclude that the linear model that represents the total cost of recording is f(x) = 75x + 50.

The ball hits the ground after x = 6 seconds.

Two or more expressions with an equal sign are defined as an equation.

The given equation is h(x) = -2x² + 8x + 24.

(a) when the ball is thrown, the time is t = 0 sec.

Therefore, the height of the ball when it is thrown is,

h(0) = -2(0)² +8(0) +24

h(0) = 24

(b) The derivative of the function is,

h'(x) = -4x + 8

Substitute h'(x) = 0 into the above equation,

0 = -4x +8

4x = 8

x = 2

The second derivative of the function is,

h''(x) = -4

Since the second derivative of the function is negative, the function is maximum at x = 2.

(c) The maximum height of the ball is,

h(2) = -2(2)² + 8(2) +24

h(2) = -8 +16 +24

h(2) = 32

(d) The ball hits the ground when h(x)= 0, therefore,

0 = -2x² +8x +24

0 = -2x² +12x - 4x + 24

0 = -2x(x - 6) - 4(x - 6)

0 = (x - 6)(-2x - 4)

(x - 6) = 0 or (-2x-4) = 0

x = 6 or x = -2

Since time cannot be negative, it follows, x = 6 seconds.

Hence, the ball hits the ground after x = 6 seconds.

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The correct numbers from the box below are 5/6 - 1/3 = 1/2.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, A table with five different fractions.

Now, 5/6 - 1/3 we will check and the result must fall in the fractions given in the table.

5/6 - 1/3.

= (5 - 2)/6.

= 3/6.

= 1/2.

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Answer:

the exact form is 419/104

decimal for:4.02884615...

mixed number form: 4 3/104

Step-by-step explanation:

calculator

Answer:

y = 8/5

Step-by-step explanation:

Formula we use,

→ y = kx

Then the value of y will be,

→ y = kx

→ y = (-2/5) × (-4)

→ y = (-2 × -4)/5

→ [ y = 8/5 ]

Hence, the value of y is 8/5.

Answer:

the is 20 because you need to multiple

For the given fees charged by two fitness clubs , number of months required by two fitness clubs to pay the same total amount is equal to      10 months.

As given in the question,

Number of fitness club  = 2

Let 'x' represents the number of months

Charges for a month membership charged by Mike's Fitness center is equal to $30.

Charges for a month membership charged by All-Day Fitness club is equal to $22 plus $80 initiation fee.

Required equation when two clubs have same amount of charges is given by:

30x = 22x + 80

⇒ 30x -22x = 80

⇒ 8x = 80

⇒ x = 10 months

Therefore, number of months required by two fitness clubs to pay the same total amount is equal to 10 months.

The complete question is:

Mikes fitness center charges $30 per month for a membership. All-Day fitness club charges $22 per month plus an $80 initiation fee for a membership. After how many months will the total amount paid to the two fitness clubs be the same?

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Answer: x=1    x=-2   x=-1/3

Step-by-step explanation:

[tex]f(x)=3x^3+4x^2-5x-2\\\\3x^3+4x^2-5x-2=0\\\\3x^3+(-3x^2+7x^2)-5x-2=0\\\\(3x^3-3x^2)+7x^2-5x-2=0\\\\3x^2(x-1)+7x^2+(-7x+2x)-2=0\\\\3x^2(x-1)+(7x^2-7x)+(2x-2)=0\\\\3x^2(x-1)+7x(x-1)+2(x-1)=0\\\\(x-1)(3x^2+7x+2)=0\\\\x-1=0\\\\x=1\\\\3x^2+7x+2=0\\\\3x^2+(6x+x)+2=0\\\\(3x^2+6x)+(x+2)=0\\\\3x(x+2)+(x+2)=0\\\\(x+2)(3x+1)=0\\\\x+2=0\\\\x=-2\\\\3x+1=0\\\\3x=-1\\\\[/tex]

Divide both parts of the equation by 3:

[tex]\displaystyle\\x=-\frac{1}{3}[/tex]

The number of pounds of chamomile tea that cost $9 per pound that must be mixed with 8 pounds of orange tea that cost $6 per pound to make a mixture that costs $7.80 from the algebraic equation is; 12 pounds

Let x represent the number of pounds of Chamomile tea needed.

We are told to find the number of pounds of chamomile tea that cost $9 per pound that must be mixed with 8 pounds of orange tea that cost $6 per pound to make a mixture that costs $7.80.

Therefore,

9x + 6(8) = 7.8(8 + x)

9x + 48 = 62.4 + 7.8x

9x - 7.8x = 62.4 - 48

1.2x = 14.4

x = 14.4/1.2

x = 12

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Answer:

There are two solutions. The parabola and the line intersect at two different points.

Answer:

Two

Step-by-step explanation:

there are two slope lines, so you need two equations for each lines.

Answer: 44.35

Step-by-step explanation:

0.07x20=1.4

45.75-1.4

The interest rate that would be required for Emma to end up with $2440 in her bank account is 6.8%

Given,

P = $720

A = $2440

t = 18 years.

r = n[(A/P)^1/nt - 1]

r = 12 × [(2440/720)¹/⁽¹²⁾¹⁸ - 1]

r = 0.06799764

Then convert r to R as a percentage.

R = r × 100

R = 0.06799764 × 100

R = 6.8%/year

Hence the rate of interest is 6.8%

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a) Continuous random variable

b) Discrete variable

c) Discrete random variable

d) Continuous random variable

e) Continuous random variable

f) Continue random variables

A variable is something whose value changes.

A discrete variable is a variable whose value can be obtained by counting.

Example: Number of students in attendance

Number of red marbles in a jar

A continuous variable is a variable whose value is determined by measurements.

Example: Height of a student in a class

Weight of a student in a class

Random variable : A random variable is a variable whose value is the numerical result of a random phenomenon.

Random variables can be discrete or continuous.

A discrete random variable X has a countable number of possible values.

Example: Let X be the sum of two dice.

A continuous random variable X takes all values at a specific number interval.

On the basis of above definition we can easily evaluate that the given examples are random variable, continuous random variable or Discrete variable.

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There are 33 numbers that are less than 200 and divisible 4 but not divisible 12. this can be solved with the help of simplification.

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Main body:

Given that,

To determine how many natural numbers less than 200 are divisible by 4, but not divisible by 12.

Here,

Let the largest number divisible by 4 less than 200 is 198

The total numbers divisible by 4 and less than 200 is,

= 198 / 4 = 49

Similarly

The total number divisible by 12 and less than 200 is,

= 192/ 12 = 16

So the numbers that are less than 200 but divisible 4 not by 12 is,

= 49 - 16

= 33

Hence, there are 33 numbers that are less than 200 and divisible 4 but not divisible 12.

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Answer:

Assuming w=2 and r=3, we plug in these values

2+5*3 = 2+15 = 17

Step-by-step explanation:

Watkins family should install a chlorine pool because it is more cost effective because the y-value at 10 years is less on graph B than it is on graph A.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

If the family plans to move to their retirement home in 10 years, We need to find which pool would be more cost effective to install.

As in the given graph, the x-axis denotes the year while the y-axis denotes the cost of maintaining the pool in that year.

When we compare the two of the given graph we will find the cost of maintaining a chlorine pool is less as compared to a salt water pool at x=10, therefore, after 10 years.

Hence, the Watkins family should install a chlorine pool because it is more cost effective because the y-value at 10 years is less on graph B than it is on graph A.

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Answer:

a

Step-by-step explanation:edge

A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.