Randy does 200 Newton-meters of work moving a 100 pound piano a distance of 5 meters. How much force did he use?

Answer:

a) 4 - [tex]vt - d = \frac{1}{2} at^{2}[/tex]

b) 1 - [tex]2(vt - d) = at^{2}[/tex]

c) 6 - [tex]\frac{2(vt - d)}{t^{2}} = a[/tex]

Step-by-step explanation:

It simply asks the steps to go from the original displacement formula to isolate a (the acceleration).  It's just a matter of moving items around.

We start with:

[tex]d = vt - \frac{1}{2} at^{2}[/tex]

We then move the vt part on the left side, then multiply each side by -1 (to get rid of the negative on the at side and to match answer choice #4):

[tex]vt - d = \frac{1}{2} at^{2}[/tex]

Then we multiply each side by 2 to get rid of the 1/2, answer #1:

[tex]2(vt - d) = at^{2}[/tex]

Finally, we divide each side by t^2 to isolate a (answer #6):

[tex]\frac{2(vt - d)}{t^{2}} = a[/tex]

Answer:

Step-by-step explanation:

The first and fourth answer choices are the correct one:  $2.20/0.65 lb, $2.20 for 0.65 lb of almonds.

Answer:

i) True

ii) Not True

iii) Cannot be Determined

iv) True

Step-by-step explanation:

From the given graph, we infer the following information.

Cost of 0.65 Almonds is $2.2

Therefore,

i) The price per one pound of almonds equals [tex]\frac{2.20}{0.65lb}[/tex]---TRUE

ii) 2.2 pounds of almonds cost $0.65 ---------> Not True.

iii) Each bag of almonds weighs 2.2 pounds -----> Cannot be Determined (Because we don't have any information about bag)

iv) 0.65 pound of almonds costs $2.20 -----------> True

Answer:

[tex]\frac{4}{5}[/tex]

Step-by-step explanation:

Using the Pythagorean identity

sin²x + cos²x = 1, then

sin²x = 1 - cos²x

sinx = [tex]\sqrt{1-cos^2x}[/tex]

note that cosΘ = [tex]\frac{6}{10}[/tex] = [tex]\frac{3}{5}[/tex]

sinΘ = [tex]\sqrt{1-(3/5)^2}[/tex]

        = [tex]\sqrt{1-\frac{9}{25} }[/tex]

        = [tex]\sqrt{\frac{16}{25} }[/tex] = [tex]\frac{4}{5}[/tex]

Answer:

f-1(x)=x-7/3

Step-by-step explanation:

The inverse of f(x) is, [tex]f^{-1}(x)=\frac{x-7}{3}[/tex]

Given function is, [tex]y=f(x)=3x+7[/tex]

Solve for x.

                 [tex]y=3x+7\\\\3x=y-7\\\\x=\frac{y-7}{3}[/tex]

Therefore, inverse function of f(x) is,

                     [tex]f^{-1}(x)=\frac{x-7}{3}[/tex]

Learn more about the Inverse function here:

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Answer:

335.5 sq ft.

Step-by-step explanation:

Let's start with the 2 straight 10-feet long walls, it's easier.

Each of those two wall sections are 10 feet long by 9 feet high...  They're rectangles, so their area is their base (10) by their height (9).

Wall 1 = 10 x 9 = 90 sq ft

Wall 2 = 10 x 9 = 90 sq ft

Now the half-circle portion.

The trick here is to calculate half of the circumference. The circumference of a circle is given by C = 2 π r, but we only want half of it... so C/2 = π r

We have the radius (r = 5.5 ft).

So, the half circle has a (half) perimeter of: 5.5 π r = 17.28 ft

Then we multiply this by the height of 9 feet: 17.28 = 155.52 sq ft

Then we add the two other walls:

Total area = 90 + 90 + 155.52 = 335.52, which we round down to 335.5 sq ft.

Answer:

x = 2

Step-by-step explanation:

2 + 4x = 10

4x = 10 - 2

x = 8

x = 8 ÷ 4

x = 2

Answer:

r = 1/2

Step-by-step explanation:

Each entry is diminished by a factor of 1/2 times the previous entry.

so r = 1/2

The next number in the series is 1 and then the one after that is 1/2 and then 1/4 ...

Answer:

(13.8,1.42) (18,3.7)(16.7,3.21) and so on REMEMBER ITS (X,Y)

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

There is a rather simple method to this.

The factor given is ( x - 2 ) and the dividend is ( 2x⁵ - 7x³ - x² + 4x - 1)

To find the remainder, we will take it as x - 2 = 0

We will get x as 2

Now, substitute the value.

2 ( 2 )⁵ - 7 ( 2 )³ - ( x )² + 4 ( 2 ) - 1

2 ( 32 ) - 7 ( 8 ) - ( 4 ) + 8 - 1

64 - 56 - 4 + 8 - 1

8 - 4 + 8 - 1

16 - 4 - 1

16 - 5

11

Hence, the remainder is 11.

Answer:

The rule for finding a reflection of a point across the y-axis is that the y-coordinate will stay the same but the x-coordinate will become its opposite. Thus, in the context of the problem, point (3,6) would become (-3,6) if reflected across the y-axis.

Step-by-step explanation: If you were going to reflect a point across the x-axis, the x-coordinate would stay the same. You're not moving it and it shouldn't change signs. The y-coordinate, however, would become its opposite because it'd be joining a new quadrant. Think of it like this:

Y-AXIS = Y remains the same and gains a neighbor; X changes because it isn't the center of attention.

X-AXIS = X remains the same and gains a neighbor; Y changes because it isn't the center of attention.

Basically, the letter of the axis is the number that doesn't change.

I hope I helped!

Answer:

First option: True.

Step-by-step explanation:

To know if the volume of this cylinder is 496.21 ft³, you need to use the formula for calculate the volume of a cylinder:

[tex]V=\pi r^2h[/tex]

Where "r" is the radius and "h" is the height.

You can observe in the figure that the radius of the cylinder is 4.5 feet and the height is 7.8 feet.

Then, knowing this, you can substitute these values into the formula.

Therefore, the volume of this cylinder is:

[tex]V=\pi (4.5ft)^2(7.8ft)\\V=496.21ft^3[/tex]

Then the answer is: True.

There are [tex]2^{10}[/tex] possible outcomes when flipping 10 coins.  Of those  [tex] {10 \choose 8} [/tex]  have exactly 8 heads.   So the probability is

[tex]p = \dfrac{ {10 \choose 8} }{ 2^{10} } = \dfrac{10(9)/2}{2^{10}}=\dfrac{45}{1024}[/tex]

Answer: 45/1024

There are 25 marbles: (12 red, 7 yellow, 5 blue, 1 white)

The probability of the first marble being red is 12/25 because there are 12 red marbles still available and no marbles are missing

The probability of the second marble being red is 11/24 because only 11 red marbles are available and 1 marble has already been selected from the pile

The probability of the third marble being red is 10/23 because only 10 red marbles are available and 2 marbles have already been selected from the pile

The probability of the fourth marble being red is 9/22 because only 9 red marbles are available and 3 marbles have already been selected from the pile

Since we are interested in all of these events occurring simultaneously, we must multiply the probability of all 4 events, like so:

[tex] \frac{12}{25} \times \frac{11}{24} \times \frac{10}{23} \times \frac{9}{22} [/tex]

Solving for this we are left with:

[tex] \frac{9}{230} \: \: or \: \: 0.0391[/tex]

Answer:

4.782608696  x  10^10

Step-by-step explanation:

47.83.

To find the result of 330 billion divided by 6.9 billion, we can simplify the question by dividing both numbers by a billion, which gives us 330 divided by 6.9. Now, we perform the division: 330 \/ 6.9 = 47.8260869565. However, since we're dealing with significant figures usually present in population data, we might want to round the answer to a reasonable number of significant digits. So the result would be approximately 47.83.

Answer:

D

Step-by-step explanation:

There are 4 colors to choose from, so use numbers 1-4 to represent each color.

The remainder is non-zero, so [tex]x-3[/tex] is not a factor of [tex]2x^3-4x^2-8[/tex] (or whatever the given polynomial is supposed to be)

The Remainder Theorem suggests that if you substitute '3' into the polynomial equation [tex]2x^3 - 4x^2 - 8x + 1[/tex], the result is -5, which is the same as the remainder of that polynomial equation divided by x - 3.

Eric used the Remainder Theorem in his calculation, which is a mathematical principle in algebra. It states that the remainder of a polynomial f(x), when divided by a linear divisor x - a, is equal to f(a). In this scenario, when he plugged '3' (the value of 'a') into the equation [tex]2x^3 - 4x^2 - 8x + 1[/tex], he obtained a resultant value of -5.

This indicates that when the polynomial [tex]2x^3 - 4x^2 - 8x + 1[/tex] is divided by x - 3, the remainder is -5. This remainder would also be the result if 3 substituted for x in the original polynomial equation, as per the Remainder Theorem.

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Answer:

The maximum number of rides is 5

Step-by-step explanation:

Let

x----> the number of rides

we know that

The inequality that represent this situation is

[tex]2.75x\leq 15[/tex]

Solve for x

Divide by 2.75 both sides

[tex]x\leq 15/2.75[/tex]

[tex]x\leq 5.45[/tex]

Round down

The maximum number of rides is 5

Answer:

The maximum number of rides is 5

answer is 5 i took the test

Answer:

f(t) = 5(4)^t

f(3) = 5(4^3) = 5 * 64 = 320

Answer:

True

Step-by-step explanation:

we know that

sin(-360°)=sin(360°)=0

therefore

y=sin(-360°)=0

Answer:

144 π  or 452.4 sq inches, for each dot

Step-by-step explanation:

We are given the perimeter of the circle (24π), and we are asked to find the area of the circle basically.

The Circumference of a circle is given by C = 2 * π * r

while its area is given by A = π r²

So, having the circumference, we can isolate r to use it in the area calculation.

C = 2  * π * r

24π = 2 * π * r  (now dividing both sides by 2π)

12 = r

The radius is 12 inches.

That means the area of one dot is:

A = π r² = π 12² = 144 π sq inches

The amount of blue glass needed for each dot is 144 π  or 452.4 sq inches

Answer: 144

Step-by-step explanation:

Answer:

yes, 6

Step-by-step explanation:

The given sequence is −34, −28, −22, −16, . . .

We check to see if there is a constant difference among the terms.

[tex]d=-28--34=-22--28=-16--22=6[/tex]

Since there is a constant difference of 6 among the consecutive terms, the sequence is arithmetic.

The correct choice is yes, 6

Answer: OPTION C

Step-by-step explanation:

Remember that:

[tex]\sqrt[n]{a^n}=a[/tex]

And the Product of powers property establishes that:

[tex]a^m*a^n=a^{(mn)}[/tex]

Rewrite the expression:

[tex]\frac{\sqrt{18x} }{\sqrt{32} }[/tex]

Descompose 18 and 32 into their prime factors:

[tex]18=2*3*3=2*3^2\\32=2*2*2*2*2=2^5=2^4*2[/tex]

Substitute into the expression, then:

[tex]\frac{\sqrt{(2*3^2)x} }{\sqrt{2^4*2} }[/tex]

Finally,simplifying, you get:

[tex]\frac{3\sqrt{(2)x} }{2^2\sqrt{2} }=\frac{3\sqrt{2x}}{4\sqrt{2}}=\frac{(3)(\sqrt{x})(\sqrt{2})}{(4)(\sqrt{2})}= \frac{3\sqrt{x}}{4}[/tex]

You can use the Pythagorean theorem to solve.

Distance = √(650^2 + 150^2)

Distance = √(422500 + 22500)

Distance = √(445000)

Distance = 667.08 miles

Rounded to the nearest whole mile = 667 miles.

The calculated distance is approximately 667.08 miles.

Calculating the Distance of the Eagle from Its Nest

To determine the distance of the eagle from its nest after flying 650 miles east and 150 miles south, we can use the Pythagorean theorem, which is applicable for right-angled triangles.

The eagle's eastward flight of 650 miles and southward flight of 150 miles form the two perpendicular sides of a right triangle, while the hypotenuse represents the straight-line distance from the nest.

The formula for the Pythagorean theorem is:

a² + b² = c²

Where:
a = 650 miles
b = 150 miles
c = the distance from the nest

Therefore, the distance of the eagle from his nest is approximately 667.08 miles.

Answer:

-18

Step-by-step explanation:

A geometric sequence has a common ratio.  So the second term divided by the first term is the same as the third term divided by the second.

6 / -2 = -3

x / 6 = -3

x = -18

Answer:

  √33 cm ≈ 5.745 cm

Step-by-step explanation:

Let b represent the third side. If the third side is not the hypotenuse, then the longest of the given sides must be the hypotenuse. The Pythagorean theorem tells us ...

  4^2 + b^2 = 7^2

  b^2 = 49 -16 = 33 . . . . . . . . subtract 16

  b = √33 ≈ 5.745 . . . . . . . . . take the square root

The third side is √33 cm long, about 5.745 cm.

To find the length of the third side of a right triangle, apply the Pythagorean theorem by squaring the given sides and calculating the square root of their sum. In this case, the third side would be approximately 5.74 cm.

To find the length of the third side of a right triangle when the other two sides are 4 cm and 7 cm, you can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

Given sides are 4 cm and 7 cm

Let's assume the third side is x

Applying the Pythagorean theorem: 4² + x² = 7²

Solving for x: 16 + x² = 49 => x² = 33 => x = √33 cm

Therefore, the length of the third side is approximately 5.74 cm

Answer:

1/4 ft vertically per 1 ft horizontally, or 3inches per foot

Step-by-step explanation:

Translate these words into symbols:  One point is at (4 ft, 12 in) and the other is at (6 ft, 18 in).  Now find the slope of the line connecting these two points:

As we move from (4 ft, 12 in) to (6 ft, 18 in), x increases by 2 ft and y increases by (1/2) ft.

Thus, the slope of this line is m = rise / run = (1/2 ft) / (2 ft) = (1/4) ft per ft

Answer:

D) 3 inches up per foot across

Step-by-step explanation:

Pretty sure its right

Answer:

range= 20   median= 38   lower quartile and upper quartile= 29 and 42.5

interquartile range= 13.5

Step-by-step explanation:

range= you take the biggest number and subract it from the smallest number.

median= you set the numbers to smallest to biggest then go in from the left and right moving both fingures at once till you get to the middle.

Lower quartile= exclude the medain and average the 4 numbers

Upper quartile= exclude the medain and average the 4 numbers

interquartile range= subract 29 from 42.5

range (i think)

Final answer:

The price of a CD that sells for 21% more than the amount (m) needed to manufacture the CD is 2/5m.

Explanation:

The price of a CD that sells for 21% more than the amount (m) needed to manufacture the CD can be calculated as follows:

Therefore, the correct answer is D. 2/5m.

Answer:

169 : 289

Step-by-step explanation:

Since the figures are similar then

linear ratio of sides = a : b, then

ratio of areas = a² : b²

ratio of sides = 52 : 68 = 13 : 17

ratio of areas = 13² : 17² = 169 : 289

If Willie ends up with only 20CDs that would be half of what he had at first and 20 plus 20 which would be the other half would be 40. 6 minus 40 would be 34 which he started with.

Answer:34

Step-by-step explanation: