5. The table below shows the number of people (in millions) who voted in U.S. Presidential elections.
Year
Voters
1984 1988 1992 1996 2004
91.6 104.4 96.3
92.7
122.3
a. Find the line of best fit.
1980
86.5
b. Predict the number of voters in 2012.
Find line of best fit
Predict the number of voters in 2012

The probability of getting at least one head is 15/16.

What is probability?

The ratio of positive outcomes to all possible outcomes of an event is known as the probability.

Formula for probability = favourable outcomes/ total outcomes

Main body:

if 4 coins are tossed , total no. of outcomes = 2⁴ = 16

In a toss there are 2 outcomes T or H

so, Probability of getting Head = 1/2

The probability of getting at least 1 head = 1- probability of getting no heads

⇒1 - Probability of getting tail in 4 tosses

⇒ 1 - (1/2)⁴

⇒ 1 - 1/16

⇒ 15/16

So the probability of getting at least one head is 15/16.

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Considering the parallel and triangle sum properties and the isosceles triangle properties the only correct part option is 2

Option 1

The angle 52 degrees is base angle of isosceles triangle therefore say angle at the third angle is x such that

x + 52 + 52 = 180 (triangle sum property)

x + 104 = 180

x = 76

The figure shows that the base angle of the triangle at the base is equal to 76 too

32 + 2x = 180 (triangle sum property for isosceles triangle)

x = 74

The two angles 74 and 76 are not equal - wrong option

Option 2

x + 2 * 76  = 180  (triangle sum property for isosceles triangle)

x = 28

The figure shows that the base angle of the triangle at the base is equal to 28

124 + 2x = 180 (triangle sum property for isosceles triangle)

x = 28

The two angles 28 and 28 are equal  hence a right option

Option 3

wood you believe it, I past plain geometry -  wrong

would you believe it, I passed plain geometry - correct

Option 4

The triangle in the parallelogram the isosceles triangle with base angle 27

The alternate interior angle is showing same base angle as 29

and the two angles 27 and 29 are not equal

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The answer choice which represents the location of any unit rate, m as graphed on a coordinating plane is; Choice 1; (1, m).

It follows from the task content that the answer choice which represents the location of any unit rate, m on a coordinate plane.

Hence, since the slope is defined as the rate of change on a graph such that slope = ∆y/∆x.

In this case, when the change in y with respect to x is to be equal to m.

Therefore, the location as required is the point defined by; (1, m).

Such that; Unit rate = (m - 0)/(1 - 0)

Ultimately, the required location of the unit rate is; Choice 1; (1, m).

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The ratio for the length of grey to red to bule is 4:9:3.

Ratio is the relation between two numbers which shows how much bigger one quantity than another. Ratio show how many times one contain show the other one.

According to the question

The given data are -

Grey = 0.8m

Red = 1.8 m

Bule = 0.6 m

By solving these we can get -

=0.8:1.8:0.6

=0.8×10:1.8×10: 0.6×10

=8:18:6

By simplifying it we can get

4:9:3.

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a) Relation of recurrence for the number of bacteria remaining after n hours is   [tex]a_{n} = a_{n-1} + 2a_{n-1} - a_{n-2} = 3a_{n-1}-a_{n-2}[/tex]

b) the solution to this recurrence relationship is [tex]a_{n} = (50 + 30\sqrt{5}) [(3 + \sqrt{5}) / 2]^{n} - (30\sqrt{5} - 50) [(3 - \sqrt{5}) / 2]^{n}[/tex]

c) There will be more than a million microorganisms after 7 hours.

A recurrence relation is an equation that states that some combination of the previous terms and the nth term in a series of numbers equals 1.

a) a₀ = 100, a₁ = 300 Every hour the bacteria - bacteria before two hours, and every hour the bacteria + 2(existing bacteria). Consequently, the corresponding recurrence relationship is [tex]a_{n} = a_{n-1} + 2a_{n-1} - a_{n-2} = 3a_{n-1}-a_{n-2}[/tex]  where n is an hour reference.

(b) The associated difference equation is

r² - 3r + 1 = 0

⇒ r = [3 ± (√9 - 4)] / 2 = (3 ± √5) / 2

hence, the answer is [tex]a_{n} = a[(3 + \sqrt{5}) / 2] ^{n} + b [(3 - \sqrt{5}) / 2] ^{n}[/tex]

Using n = 0 as the initial condition, we have a₀ = 100 = a + b → (1)

putting n = 1,

⇒ √5 (a - b) = 300 → (2)

(1) ⇒ √5 (a + b) = 100√5

By combining these relationships, we have

a = [(300 + 100√5) / 2√5] = 50 + 30√5

therefore, b = 50 - 30√5

Consequently, the answer to the equation is [tex]a_{n} = (50 + 30\sqrt{5}) [(3 + \sqrt{5}) / 2]^{n} - (30\sqrt{5} - 50) [(3 - \sqrt{5}) / 2]^{n}[/tex]

c) if there are more than one million bacteria, i.e.

[tex]a_{n} = (50 + 30\sqrt{5}) [(3 + \sqrt{5}) / 2]^{n} - (30\sqrt{5} - 50) [(3 - \sqrt{5}) / 2]^{n} > 1,000,000[/tex]

⇒ log (50 + 30√5) + n {log (3 + √5)} - log2} - log {30√5 - 50} - n {log (3 - √5) - log2} > log 1,000,000

⇒ 2.06849 + n {0.719 - 0.3010} - 1.2325 - n {-0.41797} > 6

⇒ 0.835975n > 5.16401

⇒ n > (5.16401 / 0.83975)

Therefore, n > 6.177, or after 7 hours, there will be more than 1 million bacteria.

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The probability that at least one of the next three babies is a boy is 0.875.

Probability turned into added into arithmetic to are expecting the possibility of an occasion occurring. Probability essentially approach how in all likelihood it's miles that some thing will happen. This is the fundamental principle of possibility and is likewise utilized in possibility distributions to examine feasible consequences of random experiments.

Probability of the complement of event B:

The probability of the complement of event B is computed as follows:

P(B* )=1-P(B) P(B)=14(1-(0.5x0.5)) = 0.25

The probability of the complement of event B is B) 0.25.

Probability that at least one of the next three babies is a boy:

The probability that at least one of the next three babies is a boy is computed as follows:

at least one of the next three babies is a boy =1-(0.5x0.5x0.5) =1-0.125 = 0.875

The probability that at least one of the next three babies is a boy is D) 0.875.

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Given that a photocopier takes 8s to make 20 copies and we need to find out how long would it take to make 45 copies .

This can be solved using Unitary Method as ,

To make 20 copies it takes 8 s.

To make 1 copy it would take 8/20 s

Hence to make 45 copies it would take 8/20*45 = 18s

And we are done!

Answer:

45 copies = 18 seconds

Step-by-step explanation:

Time taken to make 1 copy,

→ Total time ÷ Total copies

→ 8 ÷ 20

→ 8/20 seconds

Then the time taken for 45 copies,

→ 45 × (8/20)

→ (45 × 8)/20

→ 360/20

→ 18 seconds

Hence, time taken is 18 seconds.

Area of semicircle is 76.93 [tex]units^{2}[/tex].

Given,

Diameter = 14 units

Radius = r = 14/2

                 = 7 units

Area of semicircle = [tex]\frac{1}{2}\pi r^{2}[/tex]

                               = (3.14*7*7)/2

                               = 153.86/2

                               = 76.93

Hence, Area of semicircle is 76.93 [tex]units^{2}[/tex].

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The correct value of x = 23.

Each interior angle of an n-sided regular polygon is given by 180 (n-2)/n degrees.

Given that:

n = 9

Therefore, each interior angle＝180 x (9-2)/9 degrees

Each interior angle = 180 x 7/9

Each interior angle = 140°

Each internal angle of a regular polygon having 9 sides is 140°.

Also, given that:

A 9-sided regular polygon with one angle equals 7x-21.

For the polygon to be a 9-sided regular polygon, the angles must equal 140°.

Checking the value of x from the given option which one satisfies the value of interior angle = 140°.

Option 1, x= 17

=> 7 x 17 - 21 = 98° which is wrong.

Option 2, x= 23

=> 7 x 23 - 21 = 161-21 = 140° which is correct.

Option 3, x= 29

=> 7 x  29 - 21 = 203-21 = 182° which is wrong.

Option 4, x= 140

=> 7 x 140 - 21 = 980- 21 = 959° which is wrong.

Only, the value of x = 23 satisfies the value of a 9-sided regular polygon with one angle equal to 7x-21.

Hence, the correct value of x = 23

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Answer:

The correct value of x = 23.

Step-by-step explanation:

The break-even point in unit sales of the company is $7,625.

According to the question,

Thus,

Break-even point =  fixed costs/margin per unit

Break-even point = $305,000/$40

Break-even point = $7,625

Thus, the break-even point in unit sales of the company is $7,625.

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The value that lie above 25% of the data of the box plot is: 31.

Lower quartile (Q1) = 14

Upper quartile (Q3) = 31

A box plot tells us the following values of a data set as shown in the diagram attached:

Using the box plot that shows the information given about the data collected on the number of points scored, we can conclude that:

Lower quartile (Q1) = 14

Upper quartile (Q3) = 31

25% of the data lie above 31, which is the upper quartile.

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Answer:

4

Step-by-step explanation:

1.) Create an equation. If we let the number be x, we get x+8=3x

2.) Solve. If you move x to the other side, we get 2x=8. Finally, by dividing by 2 on each side, we get x=4. Therefore, the number is 4.

Answer:

4

Step-by-step explanation:

create an equation thus 8+x =3x

8+X=3x

collect like terms

8=3x-x

8=2x

divide both sides by 2

8/2=2x/2

X=4

Only y = - 2x - 3...(iv) and y = (1/2)x...(v) are perpendicular to each other as the negative reciprocal of - 2 is 1/2.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

We know lines that are perpendicular to each other have a slope that is negative reciprocal of each other.

The given lines are,

y = 2x + 8...(i)

y = 2x...(ii)

2y = (1/2)x + 4.

y = (1/4)x + 2...(iii)

y = - 2x - 3...(iv).

y = (1/2)x...(v)

3y = 2x - 4.

y = (2/3)x - 4/3...(vi)

So, only y = - 2x - 3...(iv) and y = (1/2)x...(v) are perpendicular to each other as the negative reciprocal of - 2 is 1/2.

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Type - I error states that the training program actually raised the score but statistically, it is not.

Type-II error states that the training program does not actually raise the score but statistically, it raised the scores.

Given statement is

"A random sample of test-takers who had completed the training showed a mean increase smaller than 30 points."

Hypothesis is,

Null hypothesis H0 :μ ≥ 30 (claim)

Alternate hypothesis H1 :μ < 30  (actual result)

in the null hypothesis, we have to consider the claim and the other in the alternate hypothesis.

In the given context of the problem, the Type-1 error will be stated below

" If in reality, the training program raises the SAT score by more than or equal to 30 points and statistically the claim is rejected".

The training program actually raised the score but statistically, it is not.

Type-II error

" If in reality, the training program does not raise the SAT score by more than or equal to 30 points and statistically the claim is failed to reject".

The training program does not actually raise the score but statistically, it raised the scores.

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Answer:

Y=5X-7

Step-by-step explanation:

(2,3)

Y-Yo=m(X-Xo)

Y-3=m(X-2)

Y-3=mX-2m

Y=mX-2m+3

(5,18)

18=m(5)-2m+3

18=5m-2m+3

18=3m+3

18-3=3m

15=3m

15/3=m

5=m

Y=5X-2(5)+3

Y=5X-10+3

Y=5X-7

Area of the other square is 7/20 cm²

Let side of the larger square be 'b' and side of the smaller square be 'a'.

Given the perimeter of the smaller square = 2 cm

⇒ 4a = 2

⇒ a = 2/4 = 1/2 cm

Given, ratio of the areas of squares = 5 : 7

⇒ area of smaller square/ area of larger square = 5 : 7

⇒ a²/b² = 5/7

⇒ (1/4)/b² = 5/7

⇒ b² = 7/(5×4) = 7/20

Therefore, area of the larger square = 7/20 cm²

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Answer:

x = -2, y = 9

Step-by-step explanation:

x + y = 7 --1

2x² + y² = 35 - 3xy --2

For 1, make y the subject.

y = 7 - x

Substitute y = 7 - x into 2.

2x² + (7 - x)² = 35 - 3x(7 - x)

Simplify and solve for x.

2x² + (49 - 14x + x²) = 35 - 21x + 3x²

3x² - 14x + 49 = 3x² - 21x + 35

7x = -14

x = -2

Substitute x = -2 into y = 7 - x.

y = 7 - (-2)

= 9

Thus, x = -2, y = 9

The side and angle is in the right angle triangle respectively x = 3,  68°.

What is a right angle triangle?

A right triangle, also known as a right-angled triangle, is a triangle with one angle that is a right angle (i.e., a 90-degree angle) and two perpendicular sides.

We have,

            [tex]1) Opposite = x, \ Adjustment = 12, \ \theta = 18.\\\\2) Opposite = 25, \ Adjustment = 10, \ \theta = ?.[/tex]

How to determine the angle in a right angled triangle,

                                        [tex]Tan (\theta ) = \frac{opposite}{adjacent}[/tex]

                                        [tex]cos(\theta) = \frac{Adjacent}{Hypotenuse}[/tex]

[tex]1) \ Opposite = x, Adjustment = 12, \ \theta = 18.[/tex]

                   [tex]cos(\theta) = \frac{Adjacent}{Hypotenuse}[/tex]

                  [tex]Hypotenuse = \frac{Adjacent}{cos(\theta)}[/tex]

                 [tex]Hypotenuse = \frac{Adjacent}{cos(18)}[/tex]

                                 [tex]= 12.61755[/tex]

           [tex]Opposite = \sqrt{Hypotenuse^{2} - Adjacent^{2} }[/tex]

                          [tex]= \sqrt{12.6175466908592 - 122}[/tex]

                         [tex]= \sqrt{15.202484496012}[/tex]

         ∴  [tex]Opposite(x) = 3.89904[/tex]  

[tex]2) \ Opposite = 25, \ Adjustment = 10, \ \theta = ?.[/tex]

                  [tex]Hypotenuse = \sqrt{{Opposite^{2} - Adjacent^{2} }[/tex]

                               [tex]= \sqrt{25^{2} + 10^{2} }[/tex]

                               [tex]= \sqrt{725} \\\\= \ 26.92582 \ = \ 5\sqrt{29}[/tex]

                    [tex]\theta =\ sin^{-1} {\frac{Opposite }{Hypotenuse} }[/tex]

                    [tex]\theta = \ sin^{-1} (\frac{25}{26.92} )[/tex]

                    [tex]\theta = \ sin^{-1} (\frac{25}{26.92} )[/tex]

                     [tex]= sin^{-1} (0.92847669088526)[/tex]

                    [tex]\theta = \ 68[/tex]°

Hence, The side and angle is in the right angle triangle respectively x = 3,  68°.

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Answer:

  D  1,078.5 ft^2

Step-by-step explanation:

You want the area of a figure composed of a rectangle 100 ft long and 10 ft wide with semicircles of diameter 10 ft at each end.

The area of the rectangle is ...

  A = LW

  A = (100 ft)(10 ft) = 1000 ft²

The two half-circles have the area of a whole circle with radius 5 ft.

  A = πr²

  A = π(5 ft)² = 25π ft² ≈ 78.5 ft²

The area of the figure is the sum of the areas of its parts:

  total area = rectangle area + circle area

  total area = 1000 ft² +78.5 ft² = 1078.5 ft²

The total area of the figure is about 1078.5 ft².

Answer:

 1

 52

+ 19

____

  71

Step-by-step explanation:

add 2+9 and get 11

carry the one

add 1+1+5 and get 7

71

The number of blue tiles is 68.

Given:

Red tiles = 1/5 of the total

Total tiles = 85

Red tiles = 1/5*85

= 17.

Number of blue tiles = total tiles - red tiles

= 85 - 17

= 68.

Therefore the number of blue tiles is 68.

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The winner of the race finished the race in eleven twenty-fourths(11/24) minutes which is option B

A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.

Kyla finished her race in 1 3/8 minutes.

converting this to improper fraction, we have 11/8 minutes

The winner of the race finished in 1/3 of Kyla's time which is 1/3 x 11/8

= 11/24 minute

The winner of the race finished in 11/24 minute.

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After forming the algebraic equation, he equation of the given statement is 7x+80=3x−50.

In the given question,

Yvonne is thinking of a number.

Fifty decreased by three times the number is the same as seven times the number increased by 80.

We have to set it up in a equation.

To set it up in a equation we divide the step in small steps.

Firstly the statement is saying that fifty decreased by three times the number.

Let the number be x.

So three times of a number is 3x and 50 decreased means 3x−50.

Next statement is saying that seven times the number increased by 80.

As the number is x so seven times of a number is 7x and increased by 80 means 7x+80.

The both statement is equal to each other.

So 7x+80=3x−50

So the equation of the given statement is 7x+80=3x−50.

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0.5852  is the process capability for the index when  standard deviation. is 0.14 mm .

What is standard deviation in math?

Cpk = minimum of [(23.0 - 22.8)/(3 *0.15),(22.8 - 22.6)/(3 * 0.15)]

=  (0.2/0.45) , ( 0.6/0.45)

=  (0.44 )( 1.33)

= 0.5852

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Answer:

1 1/4 cup of flour

Step-by-step explanation:

1/4 × 5 = 1 1/4

Answer:

     6\sqrt3

Step-by-step explanation:

Since 30-60-90 tri, small side is 6.

This means x=[tex]6\sqrt3[/tex]

Answer:

[tex]x = 6\sqrt{3}[/tex]

Step-by-step explanation:

Utilize the trigonometric ratio cosine.

[tex]\cos(30\textdegree ) = \dfrac{x}{12}[/tex]

Solve for x by multiplying both sides by 12.

[tex]12\cos(30\textdegree ) = x[/tex]

[tex]12\left(\dfrac{\sqrt{3}}{2} \right) = x[/tex]

[tex]x = 6\sqrt{3}[/tex]

Elevator 1 is 18 feet above ground level, and Elevator 2 is 20 feet below ground level.

Option B is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Elevator 1 in a hotel moved from ground position to a final position of +18 feet.

+18 means the elevator is 18 feet above the ground floor.

Elevator 2 in the same building moved from the ground to a final position of −20 feet.

-20 feet means the elevator is 20 below the ground floor.

Thus,

Elevator 1 is 18 feet above ground level, and Elevator 2 is 20 feet below ground level.

Option B is the correct answer.

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Answer:

Step-by-step explanation:

(x 2 y) 4 = x2*4 y 1*4  = x 8 y4

An exponent raised to another exponent means to multiply the exponents. If a number does not have a visible exponent, then it is an implied 1.

The required simplified form of the expression is 1 / (x² · y⁴) which is the correct answer would be an option (D).

When multiplying similar bases, keep the base and add the exponents the same. When comparing one power to another, keep the base constant and multiply the exponents. Keep the base constant when dividing like bases and subtract the denominator exponent from the numerator exponent.

Simplify x raised to the negative second power over y raised to the fourth power.

The expression is given in the question below as:

x⁻² / y⁴

The expression can be simplified as follows:

⇒ x⁻² / y⁴

⇒ (1 / x²) / (y⁴)

⇒ 1 / (x²) · y⁴)

⇒ 1 / (x² · y⁴)

Therefore, the simplified form of the expression is 1 / (x² · y⁴).

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The height of lighthouse is 72.54

Given,

In the question:

To see the figure:

To find the height of lighthouse.

Now, According to the question:

In Triangle ABD

tan 20° = [tex]\frac{h}{20 + x}[/tex]

0.36  = [tex]\frac{h}{20 + x}[/tex]

=> (20 + x)0.36 = h

=> 0.72 + 0.36x = h

=> x = [tex]\frac{h - 72}{0.36}[/tex] .....(1)

In Triangle ABC

tan 34° = h/x

=> 0.67 = [tex]\frac{h}{\frac{h-72}{0.36} }[/tex]

=> 0.67 = 0.36/h - 72

=> 0.67 (h - 72) = 0.36

=> h - 72 = 0.54

=> h = 0.54 + 72

=> h = 72.54

Hence, The height of lighthouse is 72.54

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