Translate each sentence into an equation.
1. One fourth of m minus six is equal to two times the sum of m and 9.
4. MARBLES Drew has 50 red, green, and blue marbles. He has six more red marbles than blue marbles
and four fewer green marbles than blue marbles. Write and solve an equation to determine how many blue
marbles Drew has.

Answer:

[tex]-4\leq x[/tex] is what it looks like simplifed. In word form this means x is greater than all values equal to or greater than four. This means that the FOURTH graph is correct.

Step-by-step explanation:

[tex]13-2x\leq 37+4x = -24\leq 6x.[/tex]

Simplify this into [tex]-4\leq x[/tex] or [tex]x\geq -4[/tex]

This in words translates into x is greater than or equal to the value of four. Meaning all values larger than 4 and 4 are equal to x

Meaning the 4th graph is correct because it shows exactly what the word form says.

-------------------------

Have a great day,

Nish

The percentage of the whole school that plays soccer is 35.5%

The percentage of the boys is given as

Percentage boys = 45%

This means that the percentage of the girls is given as

Percentage girls = 55%

Also, from the question, we have:

30% of the boys and 40% of the girls play soccer

So, the percentage of the whole school that plays soccer is

P = Boys * Percentage Boys + Girls * Percentage Girls

This gives

P = 45% * 30% + 55% * 40%

Evaluate the product

P = 13.5% + 22%

Evaluate the sum

P = 35.5%

Hence, the percentage of the whole school that plays soccer is 35.5%

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Answer:

2.57

Step-by-step explanation:

The mean absolute deviation(MAD) of a data set is given by the formula

[tex]$ MAD =\frac{1}{n} \sum_{i=1}^n |x_i-\bar{x}|$[/tex]

n = number of data set values. Here n=7

[tex]\bar{x}=[/tex]mean of the data set values   = [tex](20+16+21+16+22+16+ 15)/7 = 126/7 = 18[/tex]

[tex]x_{i}[/tex] are the n individual values

Substituting in the summation we get

MAD = [tex]\frac{1}{7} |20-18| + |16-18| + |21-18| + |16-18| + |22-18| + |16-18| + |15-18|\\= (2 + 2 + 3 + 2 + 4+ 2 + 3)/7\\= 18/7 = 2.571428 \\[/tex]

Rounded to the nearest hundredth, the answer is 2.57

When one organism gains a benefit at the expense of a second organism and causes them harm is called:

A. Parasitism

B. Mutualism

C. Commensalism

D. Predation

Answer:

Step-by-step explanation:

a

Answer:  [tex]\frac{1}{4}[/tex]

Work Shown:

[tex]\left(\frac{1}{2}\right)^2 = \left(\frac{1}{2}\right)*\left(\frac{1}{2}\right) = \frac{1*1}{2*2} = \frac{1}{4}[/tex]

Answer:

The answer is

→ 91.5 feet

Step-by-step explanation:

Given:

183 feet

What were supposed to find:

The radius of the SkyWheel

183 / 2 = 91.5

How to find the radius:

To find the radius, you must divide 183 with 2, giving 91.5

Hence, the answer you are looking for is 91.5

The sum of the convergent series [tex]\sum_{n=1}^{\infty}~(sin(1))^n[/tex] is 5.31

For given question,

We have been given a series [tex]\sum_{n=1}^{\infty}~(sin(1))^n[/tex]

[tex]\sum_{n=1}^{\infty}~(sin(1))^n=sin(1)+(sin(1))^2+...+(sin(1))^n[/tex]

We need to find the sum of given convergent series.

Given series is a geometric series with ratio r = sin(1)

The first term of the given geometric series is [tex]a_1=sin(1)[/tex]

So, the sum is,

= [tex]\frac{a_1}{1-r}[/tex]

= sin(1) / [1 - sin(1)]

This means, the series converges to sin(1) / [1 - sin(1)]

[tex]\sum_{n=1}^{\infty}~(sin(1))^n[/tex]

= [tex]\frac{sin(1)}{1-sin(1)}[/tex]

= [tex]\frac{0.8415}{1-0.8415}[/tex]

= [tex]\frac{0.8415}{0.1585}[/tex]

= 5.31

Therefore, the sum of the convergent series [tex]\sum_{n=1}^{\infty}~(sin(1))^n[/tex] is 5.31

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Answer:

2000

Step-by-step explanation:

let the sum of the two terms be,x

Then,

x/100=20

where

100=no. of terms

20=mean

Then,

x/100=20

x=20×100

x=2000

So,

Sum of terms=2000

Answer:

The airspeed is 201.17 mph and bearing is  and this can be determined by using the vector form of velocity

Plane to fly 700 miles due north in 3.5 hours if the wind is blowing from a direction of 338 degrees at 10 ​mph

The Area of the composite figure as shown in the image below is: 105.57 km².

Referring to the diagram given below, the shape can be decomposed into one rectangle, one square, and one quarter circle.

The area of the composite figure = area of rectangle + area of square + area of quarter circle.

Area of the Rectangle = length × width

Length = 12 km

Width = 7 km

Area of the Rectangle = 12 × 7

Area of the Rectangle = 84 km²

Area of the square = (s)²

s = 3 km

Area of the square = 3²

Area of the Rectangle = 9 km²

Area of the quarter circle = 1/4(πr²)

r = 4 km

Area of the quarter circle = 1/4(π × 4²)

Area of the quarter circle = 12.57 km²

Area of the composite figure = 84 + 9 + 12.57

Area of the composite figure = 105.57 km².

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3 ways of computing the sum on the number line are:

Here we have the sum:

8 + (-3) + (-2)

The first way of doing the sum in a number line is starting on the first number, which is 8.

Now, we also can think the sum as:

(-3) + 8 + (-2)

So now we can start at the value -3, then move 8 units to the right, and then 2 units to the left.

Or think the sum as:

(-2) + (-3) + 8

So we start at -2, then we move 3 units to the left, and finally 8 units to the right.

So the different ways of computing the sum on a number line depends on where we start.

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The answer is 40

you just times 23 by the number of photocopies you need with is 20

so 23x20 which is 460

500-460 is 40

The number of sheets of papers remain unused are 40.

Given that, Jean loads a ream of paper 500 sheets into the tray of her photocopier she has 23 sheets and need 20 copies each sheet.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Number of sheets used = 23×20

= 460

Remaining sheets = 500-460

= 40

Therefore, the number of sheets of papers remain unused are 40.

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Answer: 4.0 * 10^0 kg = 4.0 kg essentially

Step-by-step explanation:

No need to convert these to numbers...

Weight of 1 bee: 1 * 10^-4 = (0.0001 kg)

Number of bees: 4 * 10^4 = (40000 bees)

(1 * 10^-4) * (4 * 10^4) =

(1 * 4) * (10^-4 * 10^4) =

(10^0 because when multiply exponential numbers, you add the exponents)

4 * 10^0 =

4 * 1 = 4 kg

The product of the given expression is 7x/24y²

Given the product of the fractions below

3x/6y * 7/12y

Simplify

x/2y * 7/12y

Multiply the numerator and denominator to have:

7x/24y²

Hence the product of the given expression is 7x/24y²

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Answer:

Midpoints are (-1/2 , - 3)

Step-by-step explanation:

Given P (-4, - 2) and Q (3, - 4)

[tex]x1 = - 4 \\ x2 = 3 \\ y1 = - 2 \\ y2 = - 4[/tex]

[tex]midpoints = (\frac{x1 + x2}{2})( \frac{y1 + y2}{2}) \\ = ( \frac{ - 4 + 3}{2})( \frac{ - 2 + ( - 4)}{2}) \\ = ( \frac{ - 1}{2})( \frac{ - 2 - 4}{2}) \\ = ( \frac{ - 1}{2})( \frac{ - 6}{2}) \\ = ( \frac{ - 1}{2})( - 3)[/tex]

[tex]e-\frac{1}{e} +\frac{4}{3} 0r 3.687[/tex]  is the value when the equation is to integrate with respect to x or y

we integrate with respect to x

Area = [tex]\int\limits^b_a{(f(x)-g(x))} \, dx[/tex]

       = [tex]\int\limits^1_-1{e^{x}-x^{2} +1 } \, dx[/tex]

        =[tex]e^{x} -\frac{x^{3} }{3} +x[/tex]

   substitute 1 and -1 in place of x

  = [tex](e-\frac{1}{3}+1-\frac{1}{e} -\frac{1}{3} +1)[/tex]

  = [tex]e-\frac{1}{e} + \frac{4}{3} or 3.6837[/tex]

The diagram was attached in the given below.

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Answer:

NONE of these statements are true

[tex] \frac{d}{dx} (f(x).g(x)) = f'(x).g(x) + g'(x).f(x)[/tex]

[tex] \frac{d}{dx} ( \sqrt{x {}^{2} + x} ) {}^{2} = \frac{2x + 1}{2 (\sqrt{x {}^{2} + x}) {}^{2} } = \frac{2(2x + 1)(x {}^{2} + x) }{2|x²+x|} = \frac{(2x + 1)(x { }^{2} +x)}{|x²+x|} [/tex]

[tex] \frac{d}{dx} ( \sqrt{f(x)} ) = \frac{f'(x)}{2 \sqrt{f(x)} } [/tex]

The restricted values in (x^2 - 3x - 2)/-4y * (2x - 2)/(-xy^2 + 2y^2) are x ≠2 and y ≠ 0

The complete question is added as an attachment

The equation is given as:

(x^2 - 3x - 2)/-4y * (2x - 2)/(-xy^2 + 2y^2)

Set the products of the denominators to 0

-4y * (-xy^2 + 2y^2) = 0

Split the equation

-4y = 0 or (-xy^2 + 2y^2) = 0

Remove the bracket

-4y = 0 or -xy^2 + 2y^2 = 0

Divide both sides by -4 in -4y = 0

y = 0

Factor out y^2 in -xy^2 + 2y^2 = 0

y^2(-x + 2) = 0

This means that y^2 = 0 or -x + 2= 0

This gives y = 0 or -x + 2 = 0

Solve for x in -x + 2 = 0

x = 2

Hence, the restricted values in (x^2 - 3x - 2)/-4y * (2x - 2)/(-xy^2 + 2y^2) are x ≠2 and y ≠ 0

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The rate of change for the function on the table is; 15 grapes eaten per minute.

It follows from the complete question that the table given indicates that;

On this note, it is conclusive that the rate of change of the function represented by the table is; 15 grapes eaten per minute.

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You will need 3 cans of paint to cover the two walls

We know that 1 can will cover 200 square feet of wall.

And here we have 2 walls, let's find the total area of these walls.

wall 1 is 20ft by 8ft, then its area is:

A = 20ft*8ft = 160ft^2

wall 2 is 40t by 8 ft, then its area is:

A'  = 40ft*8ft = 320ft^2

The total area is:

160ft^2 +  320ft^2 = 480ft^2

The number of cans of paint needed is given by the quotient between the total area and the area that each can cover.

N = 480ft^2/200ft^2 = 2.4

But we can't have a 0.4 of a can, so we should round to the next whole number, which is 3.

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Minimum: 59

Lower Quartile: 67

Median: 76

Upper Quartile: 86

Maximum: 92

Interquartile Range: 19

Answer:

it can be use in equation

An irrational number is a number that cannot be expressed as a fraction for any integers and. . Irrational numbers have decimal expansions that neither terminate nor become periodic.

Answer: Vertical: angles ABF and DBE. Adjacent: angles ABC and CBD

Step-by-step explanation:

vertical angles are angles that share a common point. they are right across from each other, and in this case, share point B. adjacent angles are angles that are directly next to each other, and share a line or segment. in this case, the two angles share the segment BC. hope this helps.

Answer:

5B; 7B; 1,024; see answer

Step-by-step explanation:

5.

We can see from the table that

a1 = 5

a2= 5·2 = 10

a3= 5·2·2 = 5·2² = 20

a4 = 5·2·2·2 = 5·2³ = 40

...

[tex]a_{n} = 5*2^{n-1}[/tex]

7.

Is given that the filter removes 90% of contaminated air

after run 1 :

100% air

90% contamination removed for 100% air

100% is 10%+10%+10%+10%+10%+10%+10%+10%+10%+10%

10% is still contaminated air

after run 2:

10% air

90% contamination removed for 10% air

10% is 1%+1%+1%+1%+1%+1%+1%+1%+1%+1%

1% is still contaminated air

after run 3:

1% air

90% contamination removed for 1% air

1% is .1%+.1%+.1%+.1%+.1%+.1%+.1%+.1%+.1%+.1%

.1% is still contaminated air

11.

Figure 1 = 1 piece

Figure 2 = 4 pieces

Figure 3 = 4² = 16

...

[tex]Figure 6 = 4^{(6-1)} = 4^{5} = 1024[/tex]

12.

[tex](c+d)^{6} \\[/tex]

-we know that the coefficients should be 1, 6, 15, 20, 15, 6, 1

-we start with c to the lowest power 0 and d to the highest power 6  and end with  d to the lowest power 0 and c to the highest power 6

[tex](c+d)^{6} = 1*c^{0} d^{6} +6*c^{1} d^{5} +15*c^{2} d^{4} +20*c^{3} d^{3} +15*c^{4} d^{2} +6*c^{5} d^{1} +1*c^{6} d^{0}[/tex]

-we simplify to have the final answer:

[tex](c+d)^{6 } = d^{6} +6cd^{5} +15c^{2} d^{4} +20c^{3} d^{3} +15c^{4} d^{2} +6c^{5} d+c^{6}[/tex]

The perimeter of quadrilateral ABCD will be 26 units.

It should be noted that we want to measure the length of each side of ABC, and use those lengths to calculate the perimeter of ABC.

This will be 10, 5, 5, and 6. Therefore the perimeter will be the addition. This will be:

= 10 + 5 + 5 + 6

= 26 units.

This also was identical to the result gotten. This is attached below.

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Answer:

343.608 million to nearest thousand.

Step-by-step explanation:

Projected annual percent of growth = 3%  ( from the values 1.03 in the equation)

Worth is 2012 ( 12 years after 2000) is:

241(1.03)^12

= 343.608 million

The option B is correct. APR is important tool because It allows consumers to compare the full cost of loans from different lenders.

According to the statement

we have to explain all about the APR and tel that why it is important for the consumers.

So, For this purpose,

We know that the

The term annual percentage rate of charge, corresponding sometimes to a nominal APR and sometimes to an effective APR.

It is the interest rate for a whole year, applied on the loan etc. It is a finance charge expressed as an annual rate

APR is the important tool for the consumers because of some reasons which are written below:

APR is important because it can give you a good idea of how much you'll pay to take out a loan.

APR helps a customer determine the true cost of the loan, allowing them to compare many loans and choose the most advantageous one.

So, The option B is correct. APR is important tool because It allows consumers to compare the full cost of loans from different lenders.

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Answer:

168 square inches

Step-by-step explanation:

A = BH

or

Area = Base x Height

In other words multiply 12 and 14.