Express using exponents and simplify any numerical coefficients: 4 · 4 · 4 · b · b · c · c · c

Answer:a

Step-by-step explanation

let me know if this helps

The dimensions of the tank with minimum weight are 24*24*12 ft

What is rectangular tank?

There is a benefit to employing vertical cylindrical stores that are put behind the double glass as in the Trombe wall system because a rectangular tank that extends from floor to ceiling is relatively expensive to construct and must be constructed to withstand quite high hydraulic pressures.

The tank with minimum weight is the one with minimum surface area.

Let x= base width and base height

     h= height of the tank

The volume of tank is :

  v=hx²

substitute v=6912 ft³

 6912=hx²

  h= 6912/x²............(1)

Formula for the tank surface area is:

A=x²+4xh

On substituting h value and simplifying,

A=x²+(27.648/x)

Differentiate with respect to x and equate to zero

2x-(27.648/x²)=0

On simplifying,

x³=27648/2 = [tex]\sqrt[^3]{13824}[/tex]

x= 24

substitute x=24 into the equation 1

h= 6912/(24)²= 12 ft

So, the dimensions of the tank with minimum weight are 24*24*12 ft

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Answer:

Step-by-step explanation:

the numerical coefficient of x2 here is 3.

Answer: 500 W (watt)

Step-by-step explanation:

Power = P = Work / time = W/t

W = Fd = Force x distance = 400N x 5m = 2000J

P = 2000J/4s = 500 W

p=4n+2 equation describes the relationship between n and p

How to find a function?

To ascertain whether a graph accurately depicts a function, use the vertical line test. The graph is a function if a vertical line drawn across it is moved and hits it only once at any given time. If there are multiple points where the vertical line intersects the graph, the graph is not a function.

Here the coordinates are (1,6),(2,10),(3,14),(4,18)

take two coordinates arbitrarily

ie. (1,6) and (3,14)

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

[tex]m=\frac{14-6}{3-1}\\ = \frac{8}{2}[/tex]

=4

we know the equation

[tex]y-y_{0} = m(x-x_{0} )[/tex]

where [tex](x_{0},y_{0})= (1,6)[/tex]

y-6 = 4(x-1)

y-6 = 4x-4

y = 4x-4+6

y = 4x+2

here y is the profit and x is the number of shirts

∴p=4n+2

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Answer:

Slope: -2

Step-by-step explanation:

(This answer is if you meant to write 6y = 3x - 9)

First, change the standard equation form into a linear equation form, y=mx+b. To do this, divide both sides by 6 to get:

[tex]y=\frac{3}{6} x-\frac{9}{6}[/tex]

This can then simplify to:

[tex]y=\frac{1}{2} x-\frac{3}{2}[/tex]

In order to find the equation of a perpendicular line, you need to find the opposite reciprocal of the current slope:

[tex]y=-2x-\frac{3}{2}[/tex]

The slope is m, meaning that the slope of the perpendicular equation is -2.

Hope this helps!

The miles that Jude needs to run on Thursday is 1 3/5 miles.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

Total fraction = 7 3/15

Monday race = 2 3/15

Tuesday race = 1 1/15

Wednesday race = 2 1/3

The miles remaining will be:

= 7 3/15 - (2 3/15 + 1 1/15 + 2 1/3)

= 7 3/15 - 5 9/15

= 1 9/15

= 1 3/5 miles

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The centripetal acceleration is 15.625 m/s²

From the question, we have

centripetal acceleration (a) = v²/r

where,

v is the velocity in m./s

r is the radius in m

a = v²/r

= 2.5²/0.4

=15.625 m/s²

Divide:

Divide, in its simplest form, means to divide into two or more equivalent portions, spaces, groups, or divisions. Divide, in plain English, means to provide the entire thing to a group in equal portions or to divide it into equal pieces. Let's say a square is divided into two triangles with equal areas by a diagonal. A division operation may or may not provide an integer as the outcome. The outcome may occasionally take the form of decimal numbers.

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The required position of the -2.25 lies above the -2.25 on the vertical number line.

Given that,
If -2.5 < -2.25, how are the positions of the two numbers related on the vertical number line is to be determined.

A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.

Here,
Since -2.5 is 0.25 lower than -2.25, and also the -2.25 is greater than -2.5.
So on the vertical number line, -2.25 lies 0.25 units above the number -2.5.

Thus, the required position of the -2.25 lies above the -2.25 on the vertical number line.

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Answer:

On the vertical number line, -2.5 is located below -2.25.

Step-by-step explanation:

edmentum answer. have a good day

Answer:

  (d)  (x, y) ⇒ (x -6, y -6)

Step-by-step explanation:

You want to know the transformation rule that translates A(2, -6) to A'(-4, -12).

The amount of translation is the difference between the image coordinates and the original coordinates:

  A' -A = (-4, -12) -(2, -6) = (-4 -2, -12 -(-6)) = (-6, -6)

The amount is added to the original coordinates to give the translated coordinates:

  (x, y) ⇒ (x -6, y -6)

Answer: she donated 25%

Step-by-step explanation:

Answer:

54.54

Step-by-step explanation:

30x100 then divided by 55

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Answer:

x = 84

Hope this helped! If you need to know the steps, just let me know and I'll add it :)

Answer:

Step 1: Simplify both sides of the equation.

x/4−10=11

1/4x+−10=11

1/4x−10=11

Step 2: Add 10 to both sides.

1/4x−10+10=11+10

1/4x=21

Step 3: Multiply both sides by 4.

4*(1/4x)=(4)*(21)

x=84

Answer:

x=84

The fourth integer is 16.

Key skills needed: Casework, Mean, Median, and Mode

1) We start with 4 numbers _ _ _ _

2) We can determine two of the numbers by using the fact that the median is 14 and the mode is 14.

3) The numbers would have to be:

   _ 14 14 _

   _ 14 14 14

The 2nd one does not work because the last number would have to be a 6 to have a mean of 14, but the range would not be 14.

4) So, our numbers are _ 14 14 _

5) The two numbers add up to 20 (in order to have a mean of 14. If you subtract the bigger one by the smaller one, it will be 14.

6) We can make a system: saying x is the bigger number and y is the smaller number.

x + y = 20

x - y = 14

Add both and you will get 2x = 32 (since the y values cancel out).

7) divide by on both sides, and x = 16.

8) To find y, we can plug x back in to one equation:

16 + y = 20

y = 4

Our smaller number is 4 and our bigger number is 16.

9) Therefore the numbers are: 4, 14, 14, 16

Hence the answers is, the fourth integer is 16.

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The ratios for each pair of the data are the same, so the download time and the file size are proportional.

A proportional relationship is a linear function that has the following features.

Hence the output variable y is given by the multiplication of the input variable x and the constant of proportionality k, hence the equation is:

y = kx.

A set of data is only proportional if the division of the output by the input is the same for all pairs of values.

For this set of data, this division is given as follows:

Same ratios, hence the measures are proportional.

The data is given by the image at the end of the answer.

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The least number of miles she would have to drive per year to make leasing no more expensive than purchasing is 48500 miles.

Given:

She can lease a car for $420 per month (on an annual basis). Under this plan, the cost per mile (gas and oil) is $0.06. If she were to purchase the car, the fixed annual expense would be $4700, and other costs would amount to $0. 08 per mile.

Let x be the least miles.

420 * 12 + 0.06x < > 4700 + 0.08x

multiply by 100 on both sides.

504000+6x < > 470000+8x

97000 < > 2x

48500=x

Therefore the least number of miles she would have to drive per year to make leasing no more expensive than purchasing is 48500 miles.

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The expression that represents the perimeter is 8.6b  and the expression that represents the area of the exercise mat is  3.3b²  .

In the question ,

it is given that ,

the exercise mat is is 3.3 times as long as it is wide .

let the width of the exercise mat be = "b" .

So , the length of the exercise mat will be = 3.3b

The Perimeter of the exercise mat = 2( length + width)

= 2(3.3b + b)

= 2(4.3b)

= 8.6b

the perimeter is = 8.6b

The Area of the exercise mat = length × width

= 3.3b × b

= 3.3b²

the area is = 3.3b²

Therefore , The expression that represents the perimeter is 8.6b  and the expression that represents the area of the exercise mat is  3.3b²  .

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keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]y=1+2x\implies y=\stackrel{\stackrel{m}{\downarrow }}{2}x+1\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{2\implies \cfrac{2}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{2}}}[/tex]

so we're really looking for the equation of a line whose slope is -1/2 and that it passes through (4 , -4)

[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{1}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{- \cfrac{1}{2}}(x-\stackrel{x_1}{4}) \implies y +4= -\cfrac{1}{2} (x -4) \\\\\\ y+4=-\cfrac{1}{2}x+2\implies {\Large \begin{array}{llll} y=-\cfrac{1}{2}x-2 \end{array}}[/tex]

Total triangles on all the quilt are 672.

What is quilt?

Quilts are often made of two or more layers of cloth or fibre and are multi-layered textiles. Three layers and a filler substance are frequently employed. These layers are often made up of a woven top, a batting or wadding layer, and a woven back that are all connected using quilting techniques.

Main Body:

Number of triangles on 1 quilt = 32

Total number of quilt = 21

So total triangles can be calculated by simply multiplying the two values,

Total triangles = 32*21

                        = 672 quilts

Hence total number of triangles = 672

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Answer:

0.76 hits / per inning.

Step-by-step explanation:

Comment

Nor very many.

You are using a double ratio question.

Givens

5 hits

33 innings

x

5 innings

Formula

5 hits                 x

====           =     =====

33 innings         5 innings                 Cross multiply

Solution

5 * 5 = 33* x                                       Combine

25 = 33*x                                           Divide by 33

25/33 = x

x = 0.760                                

Less than 1 hit per inning.

The area of the triangle PQX is 9.8 cm².

Given,

on this circle

∠PQX = ∠SXR

since vertical angles are equal.

∠PQX = ∠XRS and ∠QPX = ∠XSR

since the angle is the same as the angle opposite the arc.

so triangle PQX is similar to triangle SRX

three angles are equal.

since two triangles are similar:

so, RX/QX = SX/PX = SR/PQ = 10/7

and since S Δ PQX = 1/2 . QX . PX . sin∠PXQ

SΔSRX = 1/2 . RX . SX . sin∠SXR

= 10/7 × 10/7

= 100/49

S Δ PQX = 49.SΔSRX/100

= 9.8 cm²

Hence we get the area as 9.8 cm²

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Option (C) is the correct one and the sum of all four-digit positive integers greater than 2019 that can be formed in the given way is 476,661.

Given, the integer 2019 can be formed by placing two consecutive two-digit positive integers, 19 and 20, in decreasing order.

We have to find the sum of all four-digit positive integers greater than 2019 that can be formed in this way.

First number that can be formed in the given way is,

2120

and the last number that can be formed in the given way is,

9998

As, we can observe that the last two digits of all the numbers will make an A.P and in similar way the first two digits also make an A.P

So, first finding the sum of last two digits which is forming an A.P

first term be, 20 and last term be, 98

also, the number of terms be, 79

Sum = 79/2(20 + 98)

Sum = 79×59

Sum = 4661

So, the last two digits of the final answer will be 61 and 46 will add as carry.

Now, similarly finding the sum of first two digit numbers be

Sum = 79/2(21 + 99)

Sum = 79×60

Sum = 4740

on adding the carry of 46, we get

4740 + 46 = 4786

So, the sum of all four-digit positive integers greater than 2019 that can be formed in the given way is 476,661

Hence, option (C) is the correct one and the sum of all four-digit positive integers greater than 2019 that can be formed in the given way is 476,661.

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The student's having a sister is 0.4827 likely. And a random student is chosen who has a brother. Therefore, the probability that this student has a sister is 0.3636.

The fundamental assumption that something will almost certainly occur is known as probability. the percentage of positive occurrences to all occurrences.

Next, the probability is given as

P = (a favorable event) / (Total event)

The letters £ stand for the 29 students in the class, B for those who have brothers, and S for those who have sisters.

Next, the equation will be presented.

7 + 4 + 2x + x + 3 = 29

3x = 29 - 14

3x = 15

x = 5

2x will then have the value

2x = 2(5)

2x = 10

After that, x + 3 will have the value.

x + 3 = 5 + 3 = 8

The probability of the student having a sister is

P = (10 + 4) / 29

P = 14 / 29

P = 0.4827

If a student with a brother is randomly selected, the probability that this student also has a sister will be

P = 4/11

P = 0.3636

As a result, the probability that the student has a sister is 0.4827. And at random, one of the students with a brother is chosen. The likelihood that this student has a sister is then 0.3636.

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Answer:

In algebra class, we are learning about the commutative property. We are also learning about coefficients and how to evaluate expressions. Another thing we are learning about is the order of operations where you have to simplify at the end, and in each problem there are terms and variables.

Answer:

0

Step-by-step explanation:

f(x) is basically y (or in this case k(x))

to find the k(6) we find the y value when x is 6

we look and the graph and see that it is 0

that is your answer

Answer:

$64.00

Step-by-step explanation:

4(9) + 2(6.5) + 4(3.75)

36 + 13 + 15

64

The quantity of fruit left is 2 pounds which is the difference between the quantity bought by Delon and the quantity eaten by the class.

Subtraction is a mathematical operation that deducts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

The quantity of fruit has left the difference between the quantity bought by Delon and the quantity eaten by the class.

The quantity bought by Delon = 2.9 pounds

The quantity eaten by the class =  0.9 pounds

The quantity of fruit left = 2.9 pounds - 0.9 pounds  

Apply the subtraction operation,

The quantity of fruit left = 2 pounds

Thus, the quantity of fruit left is 2 pounds

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The Equation of the graph in slope-intercept form is 3y = 1350 - 100x

Misty will travel 150 miles after 9 hours

It will take misty 12 hours to cover 50 miles

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.

Equation of line in slope-intercept form is y = mx + c

let y be the distance in miles and x be the time in hours.

from the graph when x = 0, y = 450

substituting into the equation,

450 = 0(m) + c

c = 450 which is the intercept

Also from the graph, taking the point (3, 350)

when x = 3, y = 350

350 = 3m + 450

3m = 350 - 450

3m = -100

m = -100/3

SO the equation of straight line becomes

y = -100x/3 + 450

multiply through by 3

3y = -100x + 1350

if misty travel 9 hours that is x = 9, then y =

3y = -100(9) + 1350

3y = 450

y = 450/3

y = 150 miles

If there are 5o miles remaining,

y = 50, x =

3(50) = -100x +1350

100x = 1350 -150

100x = 1200

x = 1200/100

x = 12 hours.

The Equation of the graph is 3y = 1350 - 100x

Misty will travelled 150 miles after 9 hours

It will take misty 12 hours to cover 50 miles

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