Write each proof. Finish the table.

Note that the answer to the expression {96 ÷ [36÷3-(18 x 2 - 30)]} ÷ (31-16+1) Is: one (1). This problem is solved using PEMDAS.

PEMDAS is the acronym for parenthesis, exponents, multiplication, division, addition, and subtraction. These operators must be solved exactly in the order given above. Thus:

{96 ÷ [36÷3-(18 x 2 - 30)]} ÷ (31-16+1)

⇒ {96 ÷ [36÷3-(6)]} ÷ (31-16+1)

⇒ {96 ÷ [12-6]} ÷ (31-16+1)

⇒ {96 ÷ 6} ÷ (31-16+1)

⇒ 16 ÷ 16

⇒ 1

Thus, it is correct to state that the answer to the mathematical expression  {96 ÷ [36÷3-(18 x 2 - 30)]} ÷ (31-16+1) is 1 or

{96 ÷ [36÷3-(18 x 2 - 30)]} ÷ (31-16+1) = 1

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7/6 = 28/x

To solve for x, you can cross-multiply:

7 * x = 6 * 28

Simplifying:

x = 6*28/7

x = 24

So, you would need 24 cups of milk.

Answer:

28 cups of sugar / 7 parts of sugar = 4 cups

If 4 cups is 1 part, 6 parts of milk would be 4 x 6

4 x 6

= 24

You would need 24 cups of milk.

Answer: 4.53

Step-by-step explanation:

10 times less than 45.3 means that you will be looking for an answer that is the solution to 45.3 / 10, which equals 4.53.

Based on the given percentages, the number of adult American men who think the federal government should fund stem cell research is 67,860,000.

The percentage is the ratio of a value in relation to another.

The percentage is determined as the quotient of the numerator divided by the denominator, multiplied by 100.

The percentage of men who approve of stem cell research = 58%

The percentage of men who do not approve of the research = 39%

The percentage of men who have no opinion on the research = 3%

The estimated number of adult American men = 117,000,000

Thus, based on the percentage of men who approve of stem cell research, the number is 67,860,000. (117,000,000 x 58%).

Federal Government Funding of Stem Cell Research

                          Total      Men     Women

Should fund       55%       58%        52%

Should not fund 41%       39%         44%

No opinion          4%          3%           4%

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Answer:

Step-by-step explanation:

The formula of the area of a triangle is equal to Length multiply by Width[A = L * W]

Answer:

A.

Step-by-step explanation:

4x² is a perfect square because it is (2x)²

9 is a perfect square with a value of 3

so if we factor 4x² - 9 we can use the difference of two squares to get:

(2x+3)(2x-3)

This data's linear regression equation is y = mx + b, where y is the quantity of chicken feed, x is the number of months since March, m is the line's slope (or the rate at which y changes with respect to x), and b is the y-intercept (or the value of y at x = 0).

The pace at which the amount of chicken feed has been decreasing over time is seen by the slope of the line. The beginning quantity of chicken feed in the barn in March is represented by the y-intercept.

Based on the rate of reduction and beginning quantity for each month since March, the linear regression equation may be used to forecast the amount of chicken feed in the barn in the issue situation.

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Answer:

$709.58

Step-by-step explanation:

The total cost is 100% plus the tax rate of 8.5%, it will be 108.5%

To find the cost of the camera with the sales tax included, we take

$653.99 divided by 100, then times 108.5 = $709.58

So, the cost of the camera with sales tax is $709.58

x^-4/x^3 times x^-7 in equivalent expression is x⁻¹⁴

The index form of a number can be defined as the number that is written as an exponential expression.

It is also seen as the single number that is raised to another number.

The rules of index forms are;

From the information given, we have that;

x⁻⁴/x³ × x⁷

Since the denominators are of the same base, add the powers

x⁻⁴/x³⁺⁷

Add the values

x⁻⁴/x¹⁰

Now, subtract the powers

x⁻¹⁴

Hence, the value is x⁻¹⁴

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Answer:  Timo is correct; the hypotenuse rounds to 11

Work Shown:

[tex]a^2+b^2 = c^2\\\\c = \sqrt{a^2+b^2}\\\\c = \sqrt{6^2+9^2}\\\\c = \sqrt{36+81}\\\\c = \sqrt{117}\\\\c \approx 10.81665\\\\c \approx 11\\\\[/tex]

This confirms Timo is correct.

It appears Lucy mistakenly added the side lengths 6 and 9 to get 6+9 = 15, which is not the correct way to get the hypotenuse.

Annie mentioning the 117 seems to suggest that she might have forgotten about the square root, since we got [tex]\sqrt{117}[/tex] earlier in the steps shown above.

If Annie said [tex]\text{The hypotenuse is } \sqrt{117} \text{ units long}[/tex], then she would be correct. Though it's probably better to go with the decimal form (rounding however you want) to get a better sense of how long the hypotenuse is.

Answer:

[tex]\sf x=11+11i\\x=11-11i[/tex]

Step-by-step explanation:

Given quadratic equation:

[tex]\sf -108=(x-11)^2+13[/tex]

Subtract 13 from both sides:

[tex]\implies \sf -108-13=(x-11)^2+13-13[/tex]

[tex]\implies \sf -121=(x-11)^2[/tex]

Switch sides:

[tex]\implies \sf (x-11)^2=-121[/tex]

[tex]\textsf{For $(g(x))^2=f(a)$ the solutions are $g(x)=\pm\sqrt{f(a)}$}[/tex]

[tex]\implies \sf x-11=\pm \sqrt{-121}[/tex]

Rewrite -121 as 11² · -1 :

[tex]\implies \sf x-11=\pm \sqrt{11^2 \cdot-1}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]

[tex]\implies \sf x-11=\pm\sqrt{11^2} \sqrt{-1}[/tex]

[tex]\implies \sf x-11=\pm11\sqrt{-1}[/tex]

[tex]\textsf{Apply\;imaginary\;number\;rule}:\quad \sqrt{-1}=i[/tex]

[tex]\implies \sf x-11=\pm11i[/tex]

Add 11 to both sides:

[tex]\implies \sf x=11\pm11i[/tex]

Therefore, the solutions are:

[tex]\implies \sf x=11+11i[/tex]

[tex]\implies \sf x=11-11i[/tex]

The value of x and y in the equation are 1 and 4 respectively

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 14 , 4x − 4y = 4.

7x-3y=-5 equation 1

3x+2y=11 equation 2

using elimination method, we multiply the coefficient of x by both equations

21x- 9y = -15 equation 3

21x +14y = 77 equation 4

subtract equation 3 from 4

23y = 92

y = 92/23

y = 4

substitute 4 for y in equation 1

7x -3(4) = -5

7x -12 = -5

7x = -5+12

7x = 7

x= 7/7= 1

therefore the value of x and y are 1 and 4 respectively

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The points for the inequality are plotted on the graph attached below.

What is inequality?

A linear inequality is one that, if the equals relation were used in place of the inequality, would provide a linear equation. When multiplying or dividing both sides by a negative number, the direction of the inequality is reversed when the problem is solved. The solution set for an inequality is the set of all solutions.

We are given an inequality as y ≤ 6x/5 - 6

Now, in order to plot the points, we need to find x and y

So, let y be 0, then

⇒0 ≤ 6x/5 - 6

⇒6 ≤ 6x/5

⇒6 ≤ 6x/5

⇒5 ≤ x

So, we get first point as (5,0).

Now, let x=0, then

⇒y ≤ 6(0)/5 - 6

⇒y ≤ -6

So, we get second point as (-6,0).

From these two points, the graph is plotted which is shown below.

Hence, the graph for the inequality is plotted.

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So, there are 52 ways to draw two cards such that the first card is a spade and the second card is a queen.

In a standard 52-card deck, there are 13 cards of each suit: spades, hearts, diamonds, and clubs. Each suit has 4 face cards (Jack, Queen, King, and Ace) and 9 numbered cards (2 through 10).

To find the number of ways to draw two cards such that the first card is a spade and the second card is a queen, we first need to determine the number of spades in the deck, and then the number of queens.

There are 13 spades in a standard 52-card deck, so there are 13 ways to draw a spade as the first card.

There are 4 queens in a standard 52-card deck (one from each suit), so there are 4 ways to draw a queen as the second card.

To find the total number of ways to draw two cards such that the first card is a spade and the second card is a queen, we multiply the number of ways to draw each card: 13 * 4 = 52 ways.

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Below is the answer

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Answer:

Answer is in attached photo.

Step-by-step explanation:

Solution is in attached photo, this question is testing on function substitution. (Substituting an input to get an output.)

The coordinates of upper R prime are  (-2, 4).

Now, According to the question:

Rotation describes the circular motion of an object around its center. There are different ways things can rotate. Rotation of the Earthre. A very familiar kind of rotation is when a spherical, three-dimensional object turns around an invisible line inside its center.

The sails center of rotation is the origin (0,0)

The top of one sails point R(2, -4).

A 180 degree rotation make you turn (x, y) into (-x, -y),

So, the point  turn (2,-4 ), into (-2, 4).

Therefore the coordinates of R are  (-2, 4).

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The mode of each data-set is given by the input that has the most dots in the dot plot.

After obtaining the mode, the difference is obtained subtracting the mode from the MAD of 1.4 for each data-set.

A dot plot shows the number of times that each observation appears in the data-set.

The mode of a data-set is the observation that appears the most times in the data-set, hence it will be given by the observation with the most dots in the dot plot.

The mean absolute deviation is of 1.4, then for each data-set the mode is subtracted by 1.4.

The problem is incomplete, hence the answer was given in general terms.

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The number of occupied rooms is 140 rooms

Percentage can be defined as a ratio or number that is expressed as a fraction of the number, 100.

It is denoted the the percent sign, "%"

Percentage is known as a dimensionless number. This means that is it has no unit of measurement.

They can also be represented in fraction or decimal forms, like 0.3%, 0.5%, etc

From the information given, we have that;

The number of occupied rooms is;

= 16/100 × 875

Find the fraction

=0. 16 × 875

multiply the values

= 140 rooms

Hence, the value is 140 rooms

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The train travels an average 12 miles/hr

We always need to be working in the same units, so lets convert the trains speed to minutes since the time traveled is in minutes.

12 miles / 60 min = 0.2 miles/min

Answer:

False

Step-by-step explanation:

Answer come only two

The part containing the sum of two terms in the given expression can be found to be as (3 + 4) and (6 + 8) respectively.

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

here, we have,

The given expression is 2(3 + 4).

It can be rewritten as follows,

2(3 + 4)

=2 × 3 + 2 × 4

=6 + 8

or, 2 × 7

Thus, in order to find the expression for sum of two terms in the given expression, there can be two possible ways, the first is (3 + 4) and the other is (6 + 8).

Hence, the sum of two terms in the given expression is found to be as (3 + 4) and (6 + 8) respectively.

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If Katy wants to wrap a present that is 15cm wide, 18cm deep and 4cm high , then amount of wrapping paper that she need to use is 804 cm² .

Katy is wrapping a gift ,

the dimensions of the box that needs to be wrapped is ⇒

length(l) is = 15cm , width(w) is = 18cm and height(h) is = 4cm .

the present is in shape of cuboid ,

we know that Total Surface Area of cuboid is = 2(lw + wh + hl) ;

substituting values of length , width and height ,

we get ;

Area is = 2(15×18 + 18×4 + 4×15)

= 2( 270 + 72 + 60)

= 2( 402 )

= 804 cm² .

Therefore , Katy will need 804 cm² of wrapping paper to wrap the gift .

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Answer: A decline of 10% per year means that the number of landlines will be multiplied by 0.9 (100% - 10%) every year.

So, in 12 years the number of landlines will be multiplied by 0.9^12 = 0.531441

So, in 12 years there will be 86,652 * 0.531441 = 46,115.69 landlines.

Rounded to the nearest whole number there will be 46,116 landlines in 12 years.

Step-by-step explanation:

Answer: 24,473

Step-by-step explanation: This is the formula for exponential decay:

y=a(1–r)t

In this formula, a is the initial amount, r is the rate of decrease expressed as a decimal, t is the elapsed time, and y is the final amount.

solve

Plug in 86,652 landlines for the initial amount, 0.1 for the rate of decrease, and 12 years for the time elapsed.

y

= a(1–r)t

y

= 86,652(1–0.1)12 Plug in values

y

= 86,652(0.9)12 Subtract

y

= 86,652(0.28242…) Simplify

y

= 24,473.08419… Multiply

Round to the nearest whole number.

24,473.08419… → 24,473

To the nearest whole number, there will be 24,473 landlines.

You need to drive 122.86 km/ h to driving from Vegas to los Angeles in 3.5 hours

It is a physical quantity that indicates the displacement of a mobile per unit of time, it is expressed in units of distance per time, for example (miles/h, km/h).

The formula and procedure we will use to solve this exercise is:

v = x /t

Where:

Information about the problem:

Applying the velocity formula, we get:

v = x /t

v = 430 km / 3.5 h

v = 122.86 km/ h

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The equation in slope-intercept form as required is; y = 240x + 500

This is when the value of the dependent variable depends partly on the value of the independent variable and partly on an initial value that is not 0

According to the statements in the task content;

One employee sells 5 cars and makes $1,700 that week.

A second employee sells 6 cars and makes $1,940 that week.

Hence, it follows from partial variation that;

1700 = 5a + b

1940 = 6a + b

Hence, by solving simultaneously, it follows that;

a = 240

b = 500

Hence, the equation in slope-intercept form as required is; y = 240x + 500

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The probability of landing on purple is equal to the probability of landing on yellow. Therefore, option D is the correct answer.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes

Given that, a spinner divided into eight equal colored sections, with one orange, two purple, two yellow, and three blue.

Here,

Probability of landing on orange is 1/8

Probability of landing on purple is 2/8 =1/4

Probability of landing on yellow is 2/8 =1/4

Probability of landing on blue is 3/8

Therefore, option D is the correct answer.

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Answer:

112.8 hours / 12 days

112.8/12 = average of 9.4 hours per day

As an alternative, we could contend that the probability of the first coin coming up heads or tails is 1/2, the probability of the second coin coming up heads or tails is 1/2, and so on for the third and fourth coins.

This would reduce the probability of any given sequence of heads and tails to (1/2)x(1/2)x(1/2)x(1/2)=(1/16).

The curve achieves its greatest value for N=2 heads, which is the case where the outcome is most likely. This is exactly what you would anticipate: if each coin has an equal chance of landing heads or tails, then in four flips, half of the results should be heads, making N = 4x(1/2) = 2 the most likely result.

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