Taylor is curious to know how different types of music will impact how long it takes someone to finish their homework. She gathers a group of 12 year olds and breaks them into groups of 3. The first group listens to nothing. The 2nd group listens to classical, the 3rd listens to pop music, and the 4th listens to heavy metal. Each group needs to read 20 pages of the same book and answer the same set of 20 math questions. She times each group and compares.

a) Find the Independent Variable
b) Find the dependent variable
c) Find the Control Group
d) Find the experimental group
e) Find 3 constants

There are 2 pictures.

1. The equation 4x=7(x-3) is x=7.

2. Given ∠2≅∠4 and ∠2 and ∠3 are supplementary. we have proved ∠1≅∠3.

Given that,

There are 2 pictures.

1st picture is

We have to solve the given equation.

Equation is 4x=7(x-3)------> given

4x=7x-21 ---------> multiplying 7 to x and -3

4x-7x=-21

-3x=-21 --------> taking 7x to right side and subtracting 4x and 7x

x=-21/-3

x=7--------> taking -3 to left we get divided by 21, after division we got 7

Therefore, the equation 4x=7(x-3) is x=7.

2nd picture is

We have to prove the statement.

∠2≅∠4 --------> given

m ∠2=m ∠4 --------> angle congruence postulate

∠2 and ∠3 are supplementary ----------> given

m ∠2+m ∠3=180° ---------> Definition of supplementary angles

∠1 and ∠4 are supplementary ------> ∠2 ≅∠4 and ∠2 and ∠3 are supplementary then ∠2 and ∠1 also supplementary then ∠1 and ∠4 are supplementary.

m ∠1+m ∠4=180° --------> Definition of supplementary

m ∠1+m ∠4=m ∠2+m ∠3 ------> from step 4 we can write

m ∠1+m ∠4=m ∠4+m ∠3 -------> we know ∠2≅∠4

m ∠1=m ∠3 --------> ∠4 is remove from both sides.

∠1≅∠3 --------> definition of midpoint

Therefore, the statement is proved.

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Part 1

∠FBA = 42° (alternate interior angles)

Part 2

∠FDC = 23° (linear pair)

∠BAD = 23° (alternate interior angles)

Part 3

∠AFBA = 115° (sum of angles in a triangle)

1. The number of people who carried a cell phone or a tablet is 128.

2. The probability that a person carries a cell phone or a tablet is 78.5%.

3. The number of people who carried neither a cell phone nor a tablet is 35.

4. The probability that a person carried neither a cell phone nor a tablet is 21.5%.

5. The number of people who carried a cell phone only is 43.

6. The probability that a person carried a cell phone only is 26.4%.

7. The number of people who carried a tablet but not a cell phone is 38.

8. The probability that a person carried a tablet but not a cell phone is 23.3%.

The sample size of the survey = 163

The number of persons who carried a cell phone = 90

The number of persons who carried a tablet computer = 81

The number of persons who carried both a cell phone and a tablet = 43

1. The number of people who carried a cell phone or a tablet is 128 (90 + 81 - 43).

2. The probability that a person carries a cell phone or a tablet is 78.5%. (128/163).

3. The number of people who carried neither a cell phone nor a tablet is 35 (163 - 128).

4. The probability that a person carried neither a cell phone nor a tablet is 21.5% (35/163).

5. The number of people who carried a cell phone only is 43.

6. The probability that a person carried a cell phone only is 26.4%(43/163).

7. The number of people who carried a tablet but not a cell phone is 38 (81 - 43).

8. The probability that a person carried a tablet but not a cell phone is 23.3% (38/163).

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1. How many people carried a cell phone or a tablet?

2. What is the probability that a person carries a cell phone or a tablet?

3. How many people carried neither a cell phone nor a tablet?

4. What is the probability that a person carried neither a cell phone nor a tablet?

5. How many people carried a cell phone only?

6. What is the probability that a person carried a cell phone only?

7. How many people carried a tablet but not a cell phone?

8. What is the probability that a person carried a tablet but not a cell phone?

Answer:

42

Step-by-step explanation:

because its 42

The lengths of AB and CD are 12 and 26.5 units

The given parameters are

AB = 2x + 3

BC = 21

CD = 7x - 5

AD = 11x + 10

The points are on line AD

So, we have

AD = AB + BC + CD

This gives

11x + 10 = 2x + 3 + 21 + 7x - 5

Evaluate the like terms

2x = 9

Divide by 2

x  = 4.5

Substitute x  = 4.5 in AB = 2x + 3 and CD = 7x - 5

AB = 2 * 4.5 + 3 = 12

CD = 7 * 4.5 - 5 = 26.5

Hence, the lengths of AB and CD are 12 and 26.5 units

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Answer:

$507 958.20

Step-by-step explanation:

11 100 x   table value for 20 years , 8%

11,100 x 45.762 = $ 507,958.20

Answer: n=38/3

Step-by-step explanation:

4*(n-10)=(n-2)

4*(n-10)=n-2

4n-40=n-2

3n-40=-2

3n=38

n=38/3

The number n is four times as close to 10 as it is to 2 would be 38/3.

A number pattern is a pattern in a series of numbers that represents the common relationship between the numbers.

The equation form here;

4*(n-10)=(n-2)

4*(n-10)=n-2

4n-40=n-2

3n-40=-2

3n=38

n=38/3

Therefore, The number n is four times as close to 10 as it is to 2 would be 38/3.

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Therefore, the value for the algebraic expression 5 / 6 ( 1 / 2 (x) + 6 ) - 3x for x = 12 is -26.

Given algebraic expression is 5/6(1/2 (x) + 6 )-3x

As we know An algebraic expression in mathematics is an expression that consists of variables and constants, along with algebraic operations such as addition, subtraction, etc., and are made up of terms

Solve the expression for x = 12

To solve this algebraic expression we have to substitute the value of x = 12 in an expression as below

= 5 / 6 ( 1 / 2 (x) + 6 ) - 3x

Substitute the value of x in the given expression as below

= 5 / 6 ( 1 / 2 * 12 + 6 ) - 3 * 12

= 5 / 6 ( 6 + 6 )) - 36

= 5 / 6 ( 12 ) - 36

= 5 * 2 - 36

= 10 - 36

= -26

Therefore, the value  for the expression 5 / 6 ( 1 / 2 (x) + 6 ) - 3x for x = 12 is -26.

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We need to know about the perimeter of a rectangle to solve this problem.The length of the field is 131 yards and width is 46 yards.

The perimeter of a rectangle is the summation of it's length and breadth, the longer side of a rectangle is called length and the shorter side is called breadth. The perimeter of a rectangle is given by the formula 2(l+b) where l is the length of the rectangle and b is the breadth of the rectangle. In this question we have been told the perimeter of the rectangular field is 354 yards. The length of the field is 7 yards less than triple the width. Let the width of the field be x yard, then the length is

length=3x-7

Then perimeter in terms of x= 2(l+b)=2((3x-7)+x)=2(4x-7)=8x-14

8x-14=354

8x=368

x=46

Then breadth=46 yards

length =3x-7=138-7=131 yards

Therefore we found out the dimensions of the field to be, the length is 131 yards and breadth is 46 yards.

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Answer:

16

Step-by-step explanation:

Difference means subtract

Let the two numbers be x and y

x-y = 6

Let y be the smaller number

2y = x+4

Using substitution

x = 6+y

2y = 6 +y +4

2y = y+10

Subtract y from each side

2y-y = y+10-y

y = 10

Now we need to find x

x-y = 6

x-10 = 6

Add 10 fo each side

x-10+10 =6+10

x = 16

The lengths can be used since it's more than the tightrope.

It should be noted that the the length of the tightrope is 15 feet long and the lengths given are 2,6 and 8 feet.

The addition of the lengths will be:

= 2 + 6 + 8

= 16 feet

Therefore, the lengths can be used since it's more than the tightrope. In this case, 26 feet is more than 15 feet.

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Answer:

x=1 and 4

suppose t=x1.5

Answer:

14[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

Make equivalent fractions with all the same denominator.  Let's us 12 as our common denominator

[tex]\frac{1}{3}[/tex] x [tex](\frac{4}{4})[/tex] = [tex]\frac{4}{12}[/tex]  Another name for [tex]\frac{4}{4}[/tex] is 1.  (4 divided by 4 is 1)  I am just making an equivalent fraction of [tex]\frac{1}{3}[/tex]

[tex]\frac{3}{4}[/tex] x [tex](\frac{3}{3})[/tex] = [tex]\frac{9}{12}[/tex] another name for [tex]\frac{3}{3}[/tex] is 1 (3 divided by 3 is 1)  I am just making an equivalent fraction of [tex]\frac{3}{4}[/tex].

Now that my denominators are all the same size I can see how many 12's I have.

6 [tex]\frac{4}{12}[/tex] + 4 [tex]\frac{9}{12}[/tex] + 3 [tex]\frac{7}{12}[/tex]  I can rearrange this to add all the whole numbers together and all of the fractions together.

6 + 4 + 3 = 13

[tex]\frac{4}{12}[/tex] + [tex]\frac{9}{12}[/tex] + [tex]\frac{7}{12}[/tex] = [tex]\frac{20}{12}[/tex]  I have 20 12ths.  every [tex]\frac{12}{12}[/tex] makes another whole, so

[tex]\frac{20}{12}[/tex]  1 whole with [tex]\frac{8}{12}[/tex] Left over.  If we put this all together, we have

13 + 1  + [tex]\frac{8}{12}[/tex]

14 [tex]\frac{8}{12}[/tex]  To simplify this.  I will divide [tex]\frac{8}{12}[/tex] ÷ [tex]\frac{4}{4}[/tex] = [tex]\frac{2}{3}[/tex].

the final answer is 14 [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

so, what's the question ?

I don't need to "assume" that both machines have the same rate. it is clearly written there :

A produces in 22 hours 3 cockpits and 5 propulsion systems.

and B produces in twice the time (44 hours) twice the results (6 cockpits, 10 propulsion systems).

that means they have exactly the same production rate for both products.

so, this is confirmed. but what should we do now with this information ?

Answer:

C - No; the system has many solutions

Step-by-step explanation:

I just got it right on khan.

Answer:

x = s/(1/q + 1/p)

Step-by-step explanation:

Solve for x:

x/p + x/q = s

Collect in terms of x:

x (1/q + 1/p) = s

Divide both sides by 1/q + 1/p:

Answer: x = s/(1/q + 1/p)

The function represents a continuous function because it can be measured and not counted.

The domain is; x ≤ 19 gallons

The range is ; d(x) ≤ 323 miles

We are given the function that represents the distance d(x) in miles that the car can travel with x gallons of gasoline as;

d(x) = 17x

A) The Independent Variable is Number of gallons of gasoline used while the dependent variable is the distance that the car travels.

B) Discrete data is a numerical type of data that includes whole, concrete numbers with specific and fixed data values determined by counting. Continuous data includes complex numbers and varying data values measured over a particular time interval.

Thus, the situation represents a continuous function because it can be measured and not counted.

C) The domain is the set of all possible input values. You have 19 gallons and so the domain is; x ≤ 19 gallons

The range is the set of all possible output values. Thus, the range is;

d(x) ≤ (19 * 17)

d(x) ≤ 323 miles

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The best estimation of the current of the jeans is $39.

Percentage is the value per hundredth.Fractions and decimas can be converted into percentage by multiplying them with 100.

According to the given question a pair of jeans was 31 dollars but due to an increase the price went up to 129% of what it was originally.

Let us assume that the new price of the jeans be x dollars.

So, 129% of 31 which is (129/100) is the new price.

∴ (129/100)×31 = x

1.29×31 = x.

x = 39.99 dollars.

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a) The lowest cost per tiger is $2.74, according to Company C. (Divide the costs by how many stuffed animals there are; in this case, it's $41.10/15).

b) They would make $2.26 profit for each tiger sold.

You must divide the pricing by the anticipated number of sales to determine how much money customers must pay for each plush toy. For Company C, the calculation would be $41.10 divided by 15. You'll discover that Company C is the least expensive of all the companies when you do that.

By deducting $2.74 from $5, you can calculate their profit.

Although they had to spend $2.74 to purchase the plush animals, they are selling it for $5. $5 - $2.74 = $2.26

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Answer:

1,171 miles

Step-by-step explanation:

The trip is 1792 miles.

They have driven (58857 - 58236) miles of the trip so far (because the odometer change is equal to the distance driven).

(58857 - 58236) = 621

They still need to drive 1792 - 621 miles

1792 - 621 = 1171

So they have 1171 miles left until they complete the trip.

Answer:

15(16+3) is the right answer

Step-by-step explanation:

mark me brainliest PLS

[tex]\frac{3}{y}=18 \\ \\ 3=18y \\ \\ y=1/6 \\ \\ \implies y+2=\boxed{13/6}[/tex]

Answer: -2√10

Step-by-step explanation:

-1√10 - 1√10 = -2√10.

Since they are like terms, you'd simply just collect the two together. Think of it as just doing -1 - 1 = -2 and adding the radical behind the two.

You'd also leave it as √10 because you're unable to break it down or simplify it further than that.

Hope I was able to help you out.

Answer:  E

Step-by-step explanation:

[tex]\frac{5}{6}(18x^{2} -3x)-\frac{6}{5} (5x^{3} -10x-30x^{2} )[/tex]

[tex]=\frac{5}{6}(18x^{2}) + \frac{5}{6} (-3x) - \frac{6}{5} (5x^{3} )-\frac{6}{5} (-10x)-\frac{6}{5} (-30x^{2} )[/tex]

[tex]= 15x^{2} -\frac{5}{2} x-6x^{3} +12x+36x^{2}[/tex]

[tex]=-6x^{3} + (15x^{2} +36x^{2} )+(-\frac{5}{2}x+12x)[/tex]

[tex]=-6x^{3} + 51x^{2} -\frac{5}{2}x+12x[/tex]

Therefore, the answer is E.

Answer: E.

Step-by-step explanation:

[tex]\displaystyle\\\frac{5}{6} (18x^2-3x)-\frac{6}{5} (5x^3-10x-30x^2)=\\\\\frac{5}{6}(18)(x^ 2)-\frac{5}{6} (3)(x)-\frac{6}{5} (5)(x^3)+\frac{6}{5}(10)(x)+\frac{6}{5} (30)(x^2)=\\\\ \frac{5*18}{6} x^2-\frac{5*3}{6}x -\frac{6*5}{5} x^3+\frac{6*10}{5}x+\frac{6*30}{5} x^2=\\\\5*3*x^2-\frac{5}{2} x-6x^3+6*2*x+6*6*x^2=\\\\15x^2-\frac{5}{2}x-6x^3+12x+36x^2=\\ -6x^3+51x^2-\frac{5}{2} x+12x[/tex]

Answer:

1/27 in^3.

Step-by-step explanation:

1/3 * 1/3 * 1/3

the recommended range of water consumption is defined by the compound inequality:

14.84  ≤  x ≤ 38.28

The water utility charges a fixed amount of $38 plus $1.28 per hundred cubic feet of water. So, if you consume x hundred cubic feet of water, the cost is given by the linear relation:

$38 + $1.28*x

Now, this needs to be between $57 and $87 (values included) so we can write the inequality:

$57 ≤  $38 + $1.28*x ≤ $87

Now we just need to solve this for x. If you subtract $38 in both sides you will get:

$57 - $38  ≤  $1.28*x ≤ $87 - $38

$19  ≤  $1.28*x ≤ $49

Now we divide by $1.28 so we get:

$19/$1.28  ≤  x ≤ $49/$1.28

14.84  ≤  x ≤ 38.28

So to be in the recommended range of water consumption, your water consumption x must be in the range:

[14.84, 38, 28]

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Answer:

The y-intercept is (0, 4/3) and the equation of is y = -1/6x + 4/3. if the y-coordinate of point c is 13, its x-coordinate is -70

The equation of a line in slope-intercept form is y = mx + b

where;

m is the slope

b is the y-intercept

Given the coordinate points (14, -1) and (2, 1)

Slope = 1-(-1)/2-14

Slope = 2/-12

Slope = -1/6

Determine the y-intercept

1 = -1/6(2) + b

1 = -1/3 + b

b = 1 + 1/3

b = 4/3

The given equation of the line is y = -1/6x + 4/3

For the y-intercept

y = -1/6(0) + 4/3

y = 4/3

Hence the y-intercept is (0, 4/3)

For the x-intercept

0 = -1/6(x) + 4/3

1/6x = 4/3

24x = 3

x = 1/8

Hence the x-intercept is (1/8, 0)

If the y-coordinate of point C is 13, hence;

y = -1/6x + 4/3

13 = -1/6x + 4/3

-1/6x = 13 - 4/3

-1/6x = 35/3

-1/2 x = 35

x = -70

The y-intercept is (0, 4/3) and the equation of is y = -1/6x + 4/3. if the y-coordinate of point c is 13, its x-coordinate is -70

The correct answer is option c.

Jasmine gave a negative answer for distance.

The number line is the main visual base in statistics and we often want to look at two points on the number line and determine the distance between them. This is used to find the base of a rectangle or another figure that lies above the number line. By the end of this section, you will be able to determine the distance between any two points on a number line that comes from a statistics application.

The absolute value of 5 is 5, because it is 5 units away from 0. A negative number is a number that is less than zero. On a horizontal number line, negative numbers are usually shown to the left of 0. Two numbers are opposites if they are the same distance from 0 and on different sides of the number line.

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Answer:

 14

Step-by-step explanation:

Given the points (-2,1), (3,1), (3,-1), and (-2,-1) that are the vertices of a quadrilateral, you want to find the perimeter.

The perimeter of a plane figure is the sum of the lengths of its sides. When you plot these points, you see they define a rectangle with horizontal sides of length (3-(-2)) = 5, and vertical sides of length (1 -(-1)) = 2. There are two sides of each of these lengths, so the perimeter is ...

  P = 2(L+W) = 2(5 +2) = 2(7)

  P = 14

The perimeter of the figure is 14 units.

__

Additional comment

When trying to work out measures associated with a set of points, it is often useful to graph those points.