Rewrite the radical expression as an expression with rational exponents four square root X to the fifth

Answer:

A. Drusilla

Step-by-step explanation:

The line of random numbers is used for numbered population.

As we can see that the students are already labelled we have to divide the random number line in pairs of 2 digits

59,78,44,43,12,15,95,40,92,33,00,04,67,43,18,02,61,05,73,96,16,84,33,84,54

We have to keep in mind that our serial numbers are till 29.

So read the pair of numbers one by one

59 can't be used as it is greater than 29. Similarly 78,44,43 cannot be used.

The first student will be: 12 Kiefer

Then 15 and 00 will be second and third.

So the fourth student will be: 04 Drusilla

Hence option A is correct ..

Answer:

At (4, 0), (6, 0)

Step-by-step explanation:

[tex]x^2 - 10x + 24 = 0\\(x-6)(x-4) = 0\\x_1 = 6\\x_2 = 4[/tex]

Answer:

C) 2744 cm

Step-by-step explanation:

To find the volume of a cube you have to use this equation:

V = a^3

Now plug in the number:

V = 14^3

14^3 or 14*14*14 = 2,744

The volume is 2,744 cm

Answer:

1) 2744cm^3

2)1176cm^2

Step-by-step explanation:

1)Since it's a square, the sides are all equal length. And volume=base×width×height

thus we can multiply 14×14×14=14^3=2744cm^3

2)for surface area we can find the area of on side and multiply it by 6 because the square has six equal sides. thus, area=base×height so, area=14×14=14^2=196cm^2

Now we multiply it by 6 which is equal to 1176cm^2

Answer:

answer C:  (x - 1) is also a factor of P(x).

Step-by-step explanation:

Synthetic division is the best approach here.  Given that one factor is x - 9, we know that 9 is the appropriate divisor in synthetic division:

9    )    5    -51      k       -9

                 45    -54      (9k - 486)

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

           5     -6   (k - 54)  (-9 + 9k - 486)

and this remainder must = 0.  Find k:  -9 + 9k - 486 = 0, or

                                                                      9k = 486 + 9 = 495

                                                                      Then k = 495/9 = 55

Look at the last line of synthetic division, above:

5   -6   (k - 54)    0

Substituting 55 for k, we get:

5   -6     1          

These are the coefficients of the quotient obtained by

dividing P(x) by (x - 9).    They correspond to 5x^2 - 6x + 1.

We must factor this result.

Let's start with 5x + 1, and check whether this is a factor of 5x^2 - 6x + 1 or not.  If 5x + 1 is a factor, then the related root is -1/5.  Let's use -1/5 as the divisor in synthetic div.:

-1/5    )       5       -6        1

                           -1        7/5

         ----------------------------

                 5        -7       12/5       Here the remainder is not zero, so -1/5 is

                                                    not a root and 5x + 1 is not a factor.

Now try x - 5.  Is this a factor of 5x^2 - 6x + 1?  Use 5 as divisor in synth. div.:

5    )     5      -6      1

                    25    95

     ------------------------

         5         19     96  Same conclusion:  x - 5 is not a factor.

Try x = -1:

-1     )    5     -6     1

                    -5     11

        ----------------------

            5       -11     12.  The remainder is not zero, so (x + 1) is not a factor.

Finally, try x = 1:

1     )    5    -6     1

                  5    -1

      --------------------

          5     -1      0

Finally, we get a zero remainder, and thus we know that x - 1 is a factor of P(x)

Answer C is correct:  x - 1 is a factor of P(x)

To solve this question, we can apply the Remainder Theorem. According to the Remainder Theorem, if a polynomial \( P(x) \) is divided by \( x - c \), the remainder of the division is \( P(c) \).
Given:
\( P(x) = 5x^3 − 51x^2 + kx − 9 \)
We are told that when \( P(x) \) is divided by \( x − 9 \), the remainder is 0. Therefore, according to the Remainder Theorem:
\( P(9) = 5(9)^3 − 51(9)^2 + k(9) − 9 = 0 \)
Let's compute \( P(9) \):
\( P(9) = 5(729) − 51(81) + 9k − 9 \)
\( P(9) = 3645 − 4131 + 9k − 9 \)
\( P(9) = 9k − 495 = 0 \)
To solve for \( k \):
\( 9k = 495 \)
\( k = 495 / 9 \)
\( k = 55 \)
Now, we know that P(x) with \( k = 55 \) has no remainder when divided by \( x − 9 \).
The updated polynomial \( P(x) \) is:
\( P(x) = 5x^3 − 51x^2 + 55x − 9 \)
To determine which of the given options is a factor of \( P(x) \), we will test each option by plugging in the roots of these factors into the polynomial \( P(x) \) and checking if it yields zero.
A) For \( x − 5 \), the root is \( x = 5 \):
\( P(5) = 5(5)^3 − 51(5)^2 + 55(5) − 9 \)
\( P(5) = 5(125) − 51(25) + 275 − 9 \)
\( P(5) = 625 − 1275 + 275 − 9 \)
\( P(5) = 625 − 1009 \)
\( P(5) ≠ 0 \) (This factor does not yield zero, so it is not a factor of \( P(x) \).)
B) For \( x + 1 \), the root is \( x = -1 \):
\( P(-1) = 5(-1)^3 − 51(-1)^2 + 55(-1) − 9 \)
\( P(-1) = -5 − 51 − 55 − 9 \)
\( P(-1) = -120 \)
\( P(-1) ≠ 0 \) (This factor does not yield zero, so it is not a factor of \( P(x) \).)
C) For \( x − 1 \), the root is \( x = 1 \):
\( P(1) = 5(1)^3 − 51(1)^2 + 55(1) − 9 \)
\( P(1) = 5 − 51 + 55 − 9 \)
\( P(1) = 60 − 60 \)
\( P(1) = 0 \) (This factor yields zero, so it is a factor of \( P(x) \).)
D) For \( 5x + 1 \), the root is \( x = -1/5 \):
\( P(-1/5) = 5(-1/5)^3 − 51(-1/5)^2 + 55(-1/5) − 9 \)
\( P(-1/5) = -1/25 − 51/25 − 55/5 − 9 \)
Since the coefficients add up to a non-zero value, we can tell that it's not going to be zero; therefore, it is not worth computing the whole expression.
\( P(-1/5) ≠ 0 \) (Hence, this is also not a factor of \( P(x) \).)
The only option that gives a remainder of zero when its root is substituted into \( P(x) \) is C, \( x - 1 \). Therefore, the correct answer is:
C- x − 1

Answer:

a^15 * 2^9

Step-by-step explanation:

(a^5 * 2^3)^3 =

= (a^5)^3 * (2^3)^3

= a^(5 * 3) * 2^(3 * 3)

= a^15 * 2^9

Answer: the second choice 3.

Answer:

3. a^15*2^9

Step-by-step explanation:

We know that (a * b) ^c = a^c * b^c

(a^5 * 2^3)^3

a^5^3 * 2^3^3

And we know that a^b^c = a^(b*c)

a^(5*3) * 2^(3*3)

a^15 * 2^9

Answer:

101

Step-by-step explanation:

3^4 = 81

4 x 5  20

81 +20 = 101

Answer:

101

Step-by-step explanation:

[tex]3^{4}[/tex] = 81 and 4 x 5 =20, so 20+81= 101.

Answer:

the answer is -2 and would be plotted on -2 on a number line

Circumference is 62.8

To find the circumference, the formula is 2πr

The radius is half so we must multiply by 2 which is 20.

And finally, you multiply by π (3.14) and you will get 62.8 cm.

In conclusion, the answer is 62.8 cm.

The Circumference of the Circle is 62.8 cm

The Circumference (or) perimeter of circle = 2πr

where, r is the radius of the circle. π is the mathematical constant

Given:

Radius- 10 cm

Now, the Circumference of Circle

= 2πr

=2 x 3.14 x 10

= 2 x 31.4

= 62.8 cm

Hence, the Circumference of the Circle is 62.8 cm

Learn more about Circumference of Circle here:

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Answer:

Part 1) The equation tells us that Terry started at an elevation of 2,600 ft

Part 2) The elevation is decreasing by 50 feet each second

Step-by-step explanation:

we have

[tex]E(t)=2,600-50t[/tex]

where

E(t) is Terry's elevation in feet

t is the time in seconds

Part 1) Find the E intercept of the equation

The E-intercept is the value of E when the value of t is equal to zero

so

For t=0

substitute

[tex]E(0)=2,600-50(0)[/tex]

[tex]E(0)=2,600\ ft[/tex]

therefore

The equation tells us that Terry started at an elevation of 2,600 ft

Part 2) Find the slope of the equation

we have

[tex]E(t)=2,600-50t[/tex]

This is the equation of the line into slope intercept form

The slope m is equal to

[tex]m=-50\ ft/sec[/tex]

The slope is negative, because is decreasing

therefore

The elevation is decreasing by 50 feet each second

The subject of this question is Physics. The given equation represents Terry's elevation while skiing down a steep hill.

The subject of this question is Physics. The given equation E(t) = 2600 - 50t represents Terry's elevation in feet after t seconds while skiing down a steep hill.

To better understand the equation, let's break it down step-by-step:
- The constant term 2600 represents Terry's initial elevation at t = 0 seconds.
- The coefficient of t, -50, represents the rate at which Terry's elevation decreases as time passes. This means that Terry's elevation decreases by 50 feet for every second that goes by.

Based on this equation, Terry's elevation will progressively decrease as time passes.

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Answer:

Option A.) 1.30

Step-by-step explanation:

we know that

The secant of x is 1 divided by the cosine of x:

so

sec(40°)=1/cos(40°)

using a calculator

sec(40°)=1.30

Answer:

A.) 1.30

Step-by-step explanation:

If the cosine value is 40*, the secant value to the hundredths degree is 1.30.

sec(40°)=1.30

Answer:

12

Step-by-step explanation:

The number 144 can be factorized as = 2*2*2*2*3*3= (4^2)* (3^2)

Therefore, sqrt(144)= sqrt((4^2)* (3^2))= sqrt{(4*3)^2= sqrt{12^2}=12

To graph the equation y > 2x, start by graphing the line y = 2x and shading the region above it.

To graph the equation y > 2x, we start by graphing the line y = 2x. This line has a positive slope (b > 0) and passes through the origin (0, 0). Since we want to graph y > 2x, we need to shade the region above the line.

Draw the line y = 2x as a solid line. Then, shade the region above the line to indicate that y is greater than 2x.

Answer: Graph (a) matches the given inequality y > 2x.

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Step-by-step explanation:

In ∆ABC, if <A is 90° and <B is 45° then hypotenuse is BC.

Now,

Cos B= base/height

Cos B= AB/ BC

BC= AB/cos 45°.

Answer:

17 sqrt 2

Step-by-step explanation:

trust me the length is 24.04163 which equals 17√2

www.calculator.net has a triangle calculator if u think im wrong just look up triangle calculator

Answer:

12.5

Step-by-step explanation:

divide 25 by 2

To find the area of the painted part, subtract the area of the missing sector from the area of the entire circle.

The area of the painted part of the figure can be found by subtracting the area of the missing sector from the area of the entire circle. To find the area of the missing sector, we need to know the central angle of the sector. Once we have the central angle, we can use the formula for the area of a sector to calculate the area of the missing sector. Finally, we subtract the area of the missing sector from the area of the entire circle to find the area of the shaded part.

Example:

If the circle has a radius of 5 units and the central angle of the missing sector is 60 degrees, we can calculate:

Area of missing sector = (60/360) * π * 5^2

Area of the shaded part = π * 5^2 - (60/360) * π * 5^2

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Answer:

30 inches

Step-by-step explanation:

By definition,

volume of a pyramid = (Base Area x height ) / 3

or

500 = (50 x h ) / 3

50h = (500) (3)

h = (500)(3) / (50) = 30 inches

Answer:

h=30in

Step-by-step explanation:

The height of a pyramid whose volume is 500 cubic inches and whose area base is 50 square inches is 30inches.

Formula: V = Ab h/3

h=3 V/Ab = 3 ⋅ 500/50 = 30 inches

Question 2

Answer: 1.20

---------

To get this answer, you divide the total amount of royalties (300) over the number of books (250) to get 300/250 = 1.20

Another way to see this is through the ratio of

300 dollars: 250 books

then you divide both parts of that ratio by 250 so that the "250 books" turns into "1 book" like so...

300 dollars: 250 books

300/250 dollars: 250/250 books

1.20 dollars: 1 book

Indicating that his royalties per book is 1.20 dollars. The rate of change is often expressed as a unit rate, meaning that we want the royalties for 1 book (which then scales up).

=========================================================

Question 3

Answer: slope is -1/10 or -0.1; slope tells us how much the candle height is decreasing each minute, y intercept is the starting candle height (see below for further explanation)

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

Explanation:

The y intercept is at 25, as this is where the diagonal line crosses the vertical y axis. Similarly, the x intercept is 250. The y and x intercept lead to the two points (0,25) and (250,0). Let's use the slope formula to find the slope of the line through these two points

m = (y2 - y1)/(x2 - x1)

m = (0 - 25)/(250 - 0)

m = -25/250

m = -1/10

m = -0.1

The slope of the line is -1/10 or the decimal equivalent -0.1

What does the slope tell us? It tells us how much of the candle's height is changing as each minute ticks by. Specifically, the slope -0.1 means that the candle height is going down by 0.1 cm for each minute gone by. A shorter way to say this is to say "the height is decreasing by 0.1 cm per minute" (think of it like a speed such as miles per hour)

The y intercept is the starting height of the candle due to the fact that x = 0 here. Therefore, the starting height of the candle is 25 cm.

Side note: the x intercept of 250 tells us how long the candle burns for, which in this case is 250 minutes (4 hrs, 10 min) because y = 0 for the x intercept, and y is the height of the candle at time x. Anything beyond x = 250 is not possible in realistic sense as we can't have a negative y height value.

Step-by-step explanation:

The first polygon, ABCD, should be rotated around DA' axis and then create a function f'(x)=f(x) +5 to transpose ABCD poligon into A'B'C'D' position

The second polygon, MNOP, rotate around MP axis and half the size ( Area)

Step-by-step explanation:

1b) First, reflect ABCDE over the x-axis.

(x, y) → (x, -y)

Then, translate 5 units to the right and 3 units down.

(x, -y) → (x+5, -y-3)

1c) Instead of reflecting over the x-axis, we can reflect ABCDE over the y-axis.

(x, y) → (-x, y)

Then, rotate about the origin 180 degrees.

(-x, y) → (x, -y)

Finally, translate 5 units to the right and 3 units down.

(x, -y) → (x+5, -y-3)

2b) First, rotate MNOP 90 degrees clockwise about the origin.

(x, y) → (y, -x)

Then, scale by 1/2.

(y, -x) → (y/2, -x/2)

Finally, translate 3.5 units to the left and 2.5 units down.

(y/2 - 3.5, -x/2 - 2.5)

2c) We can form a second method by changing the order of transformations.

First translate MNOP 5 units to the right and 7 units down.

(x, y) → (x + 5, y - 7)

Then scale by 1/2.

(x + 5, y - 7) → (x/2 + 2.5, y/2 - 3.5).

Finally, rotate 90 degrees about the origin.

(y/2 - 3.5, -x/2 - 2.5)

3b) First, rotate EFGH 45 degrees counterclockwise about the origin.

(x, y) → (½√2 (x - y), ½√2 (x + y))

Then scale by ⅓√2.

(½√2 (x - y), ½√2 (x + y)) → (⅓ (x - y), ⅓ (x + y))

Finally, translate 13/3 units to the right and 1 units down.

(⅓ (x - y), ⅓ (x + y)) → (⅓ (x - y) + 13/3, ⅓ (x + y) - 1)

3c) Again, we can form a second method by changing the order of the transformations.

Let's keep the first step the same, rotating EFGH 45 degrees counterclockwise about the origin:

(x, y) → (½√2 (x - y), ½√2 (x + y))

Then translate 13/√2 units to the right and 3/√2 units down.

(½√2 (x - y), ½√2 (x + y)) → (½√2 (x - y) + 13/√2, ½√2 (x + y) + 3/√2)

Finally, scale by ⅓√2.

(½√2 (x - y) + 13/√2, ½√2 (x + y) + 3/√2) → (⅓ (x - y) + 13/3, ⅓ (x + y) + 1)

4b) First, rotate XYZ 45 degrees clockwise about the origin.

(x, y) → (½√2 (x + y), ½√2 (y - x))

Then translate 5-√2 units to the right and 4√2 units up.

(½√2 (x + y), ½√2 (y - x)) → (½√2 (x + y) + 5 - √2, ½√2 (y - x) + 4√2)

4c) Instead, let's translate XYZ 5 units to the left and 3 units up.

(x, y) → (x - 5, y + 3)

Then rotate 45 degrees clockwise about the origin:

(x - 5, y + 3) → (½√2 (x + y - 2), ½√2 (y - x + 8))

Finally, translate 5 units to the right.

(½√2 (x + y - 2), ½√2 (y - x + 8)) → (½√2 (x + y - 2) + 5, ½√2 (y - x + 8))

Answer:

[tex]f(2)=\frac{37}{4}[/tex]  or [tex]f(2)=-(-\frac{37}{4})[/tex]

Step-by-step explanation:

we have

[tex]f(x)=2x^{2} +\frac{5}{x+2}[/tex]

Find f(2)

we know that

f(2) is the value of f(x) when the value of x is equal to 2

so

For x=2

substitute

[tex]f(2)=2(2)^{2} +\frac{5}{2+2}[/tex]

[tex]f(2)=8 +\frac{5}{4}[/tex]

[tex]f(2)=\frac{37}{4}[/tex]

or

[tex]f(2)=-(-\frac{37}{4})[/tex]

Answer:

y + 3 = -6(x + 9) or y = -6x - 57

Step-by-step explanation:

We can use the point-slope form for this situation.

Point-slope form: y - y₁ = m(x - x₁), where m = slope and (x₁, y₁) are given coordinates.

Plug in: y + 3 = -6(x + 9)

This can be changed to the more common slope-intercept form.

Multiply: y + 3 = -6x - 54

Subtract: y = -6x -57

Answer:

y=-6x-57 (this answer is in slope-intercept form)

I don't know what your choices are and if you can select multiple answers or not.

Step-by-step explanation:

y=mx+b is an equation for a line with slope m and y-intercept b.

We are given m=-6 so we will plug this in giving us: y=-6x+b.

Now we need to find b, the y-intercept.  Let's use a point (x,y) we know is on the line of y=-6x+b to find b.

We know (x,y)=(-9,-3) is on that line.  So our line should satisfy this point.  We must pick a b so that happens.  Plug (x,y)=(-9,-3) into the equation now.

-3=-6(-9)+b

-3=54+b

-3-54=b

-57=b

So the equation is y=-6x-57

Answer:

x is 50 degrees

Step-by-step explanation:

If you subtract 65 twice from 180 you get this answer. The line is a straight line making it equal 180 degrees

The correct answer is 50

To find the average, you add all of the numbers and divide by the number of numbers (If that makes sense)

We can use variables (x) to solve for the last number.

268+258+271+x/4 = 266

Multiply both sides by 4

268+258+271+x = 266*4

268+258+271+x = 1064

Add the three numbers together

797+x = 1064

Subtract both sides by 797

x = 267

Her fourth pregnancy must last 267 days.

Answer:

267

Step-by-step explanation:

So we want to find the average of 4 numbers:

268, 258, 271, and x

The average of those 4 numbers is represented by the fraction:

[tex]\frac{268+258+271+x}{4}[/tex]

Now we also wanting this average to be equal to 266.  We need to find x such that that happens.

So we have the following equation to solve:

[tex]\frac{268+258+271+x}{4}=266[/tex]

Multiply both sides by 4:

[tex]268+258+271+x=4(266)[/tex]

Do any simplifying on both sides:

[tex]797+x=1064[/tex]

Subtract 797 on both sides:

[tex]x=1064-797[/tex]

Simplify:

[tex]x=267[/tex]

Answer:

Option B k > 0

Step-by-step explanation:

we know that

Observing the graph

The slope of the line is positive

The y-intercept is negative

we have

[tex]3y-2x=k(5x-4)+6\\ \\3y=5kx-4k+6+2x\\ \\3y=[5k+2]x+(6-4k)\\ \\y=\frac{1}{3}[5k+2]x+(2-\frac{4}{3}k)[/tex]

The slope of the line is equal to

[tex]m=\frac{1}{3}[5k+2][/tex]

Remember that the slope must be positive

so

[tex]5k+2> 0\\ \\k > -\frac{2}{5}[/tex]

The value of k is greater than -2/5

Analyze the y-intercept

[tex](2-\frac{4}{3}k) < 0\\ \\ 2 < \frac{4}{3}k\\ \\1.5 < k\\ \\k > 1.5[/tex]

1.5 is greater than zero

so

the solution for k is the interval ------> (1.5,∞)

therefore

must be true

k > 0

Answer:

The length is 5 times the width

Step-by-step explanation:

Let

W ----> the width of the rectangle

L ----> the length of the rectangle

we know that

The area of rectangle is equal to

[tex]A=LW[/tex]

In this problem we have

[tex]L=5x[/tex] ----> equation A

[tex]W=x[/tex] ----> equation B

substitute equation B in equation A

[tex]L=5W[/tex]

therefore

The length is 5 times the width

Answer:

Final answer: a-2b+3c

Step-by-step explanation:

5ab/5b= a

-10b^2/5b= -2b

15bc/5b= 3c  

Answer:

a - 2b + 3c

Step-by-step explanation:

Factor the numerator by factoring out 5b from each term, that is

[tex]\frac{5b(a-2b+3c)}{5b}[/tex]

Cancel the 5b on the numerator/ denominator, leaving

a - 2b + 3c

Answer:

temperature of city a=5

temperature of city b=4

Step-by-step explanation:

Given:

Let temperature of city A= a

temperature of city B=b

As given:

4a=8+3b

a-2b=-3

rearranging 2nd equation we get:

a=-3+2b

substituting above in 1st equation we get:

4(-3+2b)-3b=8

8b - 12 = 3b + 8

8b-3b=12+8

5b = 20

b = 4

Now substituting b=4 in 4a = 8 + 3b , we get

4a = 8 + 3b

4a = 8 + 3(4)

4a = 8 + 12

4a = 20

a = 20/4

a = 5

temperature of city a and city b on that day is 5C and 4C respectively!

Answer:

The temperature of the city a was 5 °C and b was 4 °C.

Step-by-step explanation:

First we have to write the equations based on the description, this is:

[tex]4a=8+3b\\a-2b=-3[/tex]

Now that we have the equations, we can replace the second in the first:

[tex]4(2b-3)=8+3b[/tex]

Now we can find the value of b:

[tex]8b-12=8+3b[/tex]

[tex]8b-3b=8+12[/tex]

[tex]5b=20[/tex]

[tex]b=\frac{20}{5}[/tex]

[tex]b=4\\[/tex]

Now with the value of b and the second equation we can get the value of a:

[tex]a-2(4)=-3[/tex]

[tex]a-8=-3[/tex]

[tex]a=8-3[/tex]

[tex]a=5[/tex]

The temperature of the city a was 5 °C and b was 4 °C.

Answer:

1873

Step-by-step explanation:

just add them up

The restaurant sold a total of 1837 orders of eggs.

To calculate the total number of orders of eggs sold by the breakfast restaurant, we need to add up all the individual orders for each type of eggs.

Scrambled eggs: 889 orders

Poached eggs: 313 orders

Fried eggs: 594 orders

Hard-boiled eggs: 41 orders

Now, let's add these numbers together:

889 + 313 + 594 + 41 = 1837 orders

Therefore, the restaurant sold a total of 1837 orders of eggs.

Answer: 364.7 pounds

Step-by-step explanation: Multiply the number of kilograms, 165, by the number of pounds per kilogram, 2.21.

165 x 2.21 = 364.65

Round to the nearest tenth.

364.7 pounds in 165 kilograms.

The number of pounds in 165 kilograms is approximately 363.2 pounds. Rounding to the nearest tenth, the number of pounds in 165 kilograms is approximately 363.2 pounds.

To find the number of pounds in 165 kilograms, we can use the conversion rate of 1 kilogram is approximately equal to 2.21 pounds. We can set this up as a proportion: 1 kilogram / 2.21 pounds = 165 kilograms / x pounds. Cross-multiplying, we get x pounds = (165 kilograms * 2.21 pounds) / 1 kilogram. Simplifying, x pounds = 363.15 pounds. Rounding to the nearest tenth, the number of pounds in 165 kilograms is approximately 363.2 pounds.

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Answer:

There are 32 words total on the list.

Step-by-step explanation:

24*4=96;  

96÷3=32;  

There are 32 words total on the list.

Answer:

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Step-by-step explanation:

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