The distance, d, an object travels is represented by the equation d = rt, where r represents the average rate of speed and t represents time. Determine the units of t if d is measured in feet and r is measured in feet per second.

A.
square feet

B.
seconds

C.
feet per second

D.
feet per second squared

Using the combination formula, it is found that you can select 2 boys and 5 girls in 2,520 ways.

In this problem, Joao and Elisa would be the same team as Elisa and Joao, hence the order is not important and the combination formula is used to solve this question.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem:

Hence:

[tex]T = C_{5,2}C_{10,5} = \frac{5!}{3!2!} \times \frac{10!}{5!5!} = 2520[/tex]

You can select 2 boys and 5 girls in 2,520 ways.

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Answer:

30 ants are in the ant farm.

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

If there are 40 ants on the second part of the scale,

multiply 5 by 8 to get 40 because there are 5 ants for each row, and 8 rows total

and there are 10 ants visible on the first side of the scale, the second part of the scale would have the majority and there would be a big inbalance. To fix that, we could say there are 30 ants in the ant farm, because there are 10 ants on the scale. [tex]10 + 30 = 40[/tex], so that would make the scale balanced.

The spinner of Maddi's game is an illustration of probability, and it is expected that the number of spins is 28

The number of sections in the spinner is given as:

Sections = 4

The letter C is given as:

Letter C = 1

The expected appearance of letter C is given as:

Expected appearance = 7

The expected number of letter C is calculated using

Expected = Letter C/Sections * Number of spins (n)

So, we have:

7 = 1/4 * (n)

Multiply both sides by 4

n = 28

Hence, it is expected that the number of spins is 28

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Answer:

8/x = x/20

x^2=160

x=sqrt(160)

x=sqrt(16*10)

x=sqrt(16)*sqrt(10)

x=4*sqrt(10)

Step-by-step explanation:

The geometric mean of 8 and 20 in the simplest radical form is 2√10.

The Geometric Mean is a unique kind of average in which the numbers are multiplied together and then their square, cube, or other root is taken (for two numbers, three numbers, etc.).

To calculate the geometric mean of two numbers:

You would multiply the numbers together and take the square root of the result.

First, multiply 8 and 20.

That equals 160.

Then you take the square root of 160;

√160

= 12.65,

which doesn't result in a whole number.

So you factor 160 and removing perfect squares.

√160

= √ (4 x 10)

= 2√(10)

Therefore, the geometric mean is 2√10.

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Answer:

  a)  V = (8 -4/3π)r³

  b)  2048(2 -π/3) cm³ ≈ 1951.34 cm³

Step-by-step explanation:

When a sphere is placed in a box the empty space volume is the difference between the box volume and the sphere volume. Here, the box is a cube with the same outside dimensions as the sphere.

__

The side length of the cube is 2r, where r is the radius of the sphere. So, the volume of the cube is ...

  V = s³ = (2r)³ = 8r³

The volume of the sphere is given by the formula ...

  V = 4/3πr³

The volume of the empty space is the difference of these:

  V = (8r³) -(4/3πr³)

  V = (8 -4/3π)r³ . . . . . . . formula for the empty volume

__

For r=8 cm, the empty volume is ...

  V = (8 -4/3π)(8 cm)³ = 4(2 -π/3)(512 cm³)

  V = 2048(2 -π/3) cm³ ≈ 1951.34 cm³ . . . . empty volume

[tex]\bull\:[/tex][tex]\sf{x^2+y^2 -10x+8y + 1= 0}[/tex]

[tex]\\[/tex]

The general form of circle is given by the equation by the equation -

[tex]\green{ \underline { \boxed{ \sf{x^2+y^2 + 2gx+2fy + c = 0}}}}[/tex]

in which

❀ Comparing given equation with general form of circle -

So, Center of Circle = (-(-5), -4)

➥ (5, -4)

[tex]\\[/tex]

Also, radius of circle = [tex]\sqrt{(-5)^2+4^2-1}[/tex]

➥ [tex]\sqrt{25+16-1}[/tex]

➥ [tex]\sqrt{40}[/tex]

➥ [tex]2\sqrt{10}[/tex] units .

Applying the inscribed angle theorem, since x and 31° are subtended by the same arc in the given circle, then x = 31°.

The inscribed angle theorem states that if two inscribed angles are subtended by the same arc, the measure of both inscribed angles are equal.

Inscribed angle = 1/2(measure of intercepted arc)

Based on the inscribed angle theorem, x = 31° because they are both subtended by the same arc.

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Answer:

17157.28

Step-by-step explanation:

If we know that the volume of a sphere is equal to V=4/3πr3, then we can assume this.

The radius of the sphere is 16, so 16 cubed is 4096. 4096 x pi is 12867.96

12867.96 x 4/3 is 17157.28

The expression shown in the cattle on the lazy circle will be 22m + 42 and 17m + 3.

From the complete information, the first expression is given as:

= 7(2m + 6) + 8m

= 14m + 42 + 8m

= 22m + 42

The second expression is given as:

= 3(1 + 4m) + 5m

= 3 + 12m + 5m

= 17m + 3

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Answer:

Step-by-step explanation:

Remark

The circumference of a circle is given by

C = 2*pi*r

C is the circumference

r is the radius.

Givens

r = 11.8

pi = 3.14

Solution and answer

C = 2 * 3.14 * 11.8

C = 74.10

answer C = 74.10

Note:If you are called  upon to round to the nearest hundredth, then 74.1 is not the answer. You must add the zero to show that it occupies the hundredths place.

Step-by-step explanation:

As the cards are being drawn with replacement, the events are independent. Thus we can find the probability by multiplying the probability of individual events.

There are 4 queens in a pack of 52 cards. So, probability of drawing a queen= 4/52=1/13

There are 26 red cards. So, probability of drawing a red card= 26/52=12

Required probability= 1/13×1/2=1/26

Answer:

1/26

Step-by-step explanation:

For probability, the numerator is the number of options for the specified property (red card/drawing a queen) and the denominator is the total number of options (in this case 52).

There are 26 red cards in a deck, the the probability of choosing a red card is [tex]\frac{26}{52}[/tex] or [tex]\frac{1}{2}[/tex].

There are 4 queens in a deck, so the probability of choosing a queen is [tex]\frac{4}{52}[/tex] or [tex]\frac{1}{13}[/tex].

To find the probability of getting these both, multiply the results, giving [tex]\frac{1}{26}[/tex].

Step-by-step explanation:

(y-(-5))/(x-2) = 4

(y+5)/(x-2) = 4

y+5 = 4x - 8

y = 4x - 13

Answer:

8064cm.

Step-by-step explanation:

When trying to find volume,All you have to do is multiply all the numbers.

Answer:

3 x 2=6 x 6 = 36 x 4 = 144 x 4 = 576 x 2 = 1152 x 7 = 8064

Step-by-step explanation:

Answer:

To graph a linear inequality in two variables (say, x and y ), first get y alone on one side. Then consider the related equation obtained by changing the inequality sign to an equality sign. The graph of this equation is a line.

If the inequality is strict ( < or > ), graph a dashed line. If the inequality is not strict ( ≤ or ≥ ), graph a solid line.

Finally, pick one point that is not on either line ( (0,0) is usually the easiest) and decide whether these coordinates satisfy the inequality or not. If they do, shade the half-plane containing that point. If they don't, shade the other half-plane.

Graph each of the inequalities in the system in a similar way. The solution of the system of inequalities is the intersection region of all the solutions in the system.

Example 1:

Solve the system of inequalities by graphing:

y≤x−2y>−3x+5

First, graph the inequality y≤x−2 . The related equation is y=x−2 .

Since the inequality is ≤ , not a strict one, the border line is solid.

Graph the straight line.

Consider a point that is not on the line - say, (0,0) - and substitute in the inequality y≤x−2 .

0≤0−20≤−2

This is false. So, the solution does not contain the point (0,0) . Shade the lower half of the line.

Similarly, draw a dashed line for the related equation of the second inequality y>−3x+5 which has a strict inequality. The point (0,0) does not satisfy the inequality, so shade the half that does not contain the point (0,0) .

The solution of the system of inequalities is the intersection region of the solutions of the two inequalities.

Example 2:

Solve the system of inequalities by graphing:

2x+3y≥128x−4y>1x<4

Rewrite the first two inequalities with y alone on one side.

3y≥−2x+12y≥−23x+4−4y>−8x+1y<2x−14

Now, graph the inequality y≥−23x+4 . The related equation is y=−23x+4 .

Since the inequality is ≥ , not a strict one, the border line is solid.

Graph the straight line.

Consider a point that is not on the line - say, (0,0) - and substitute in the inequality.

0≥−23(0)+40≥4

This is false. So, the solution does not contain the point (0,0) . Shade upper half of the line.

Similarly, draw a dashed line of related equation of the second inequality y<2x−14 which has a strict inequality. The point (0,0) does not satisfy the inequality, so shade the half that does not contain the point (0,0) .

Draw a dashed vertical line x=4 which is the related equation of the third inequality.

Here point (0,0) satisfies the inequality, so shade the half that contains the point.

The solution of the system of inequalities is the intersection region of the solutions of the three inequalities.

Step-by-step explanation:

I got it right

Answer:

Option1 : Domain and range for both functions are all real numbers

Step-by-step explanation:

[tex]\large\bold{{Question :-}}[/tex]The sum of the Squares of three consecutive number is 110. Then determine the Three Numbers.

[tex]\large\bold\red{\underline{Answer :-}}[/tex]

So, First of all The Question is to find out three consecutive Numbers .

First of all let's learn a little about Consecutive Numbers. So, Consecutive Numbers are the Numbers which follows each other. For example :- 1,2,3,4 are consecutive Numbers.

Let's start with Our Question :-

So,

[tex]:\pink\implies[/tex] [tex]\bold{{(x)^{2}}}[/tex] + [tex]\bold{{(x + 1)^{2}}}[/tex] + [tex]\bold{{(x + 2)^{2}}}[/tex] = [tex]\bold{{110}}[/tex]

[tex]:\pink\implies[/tex] [tex]\bold{{(x)^{2}}}[/tex] + [tex]\bold{{(x)^{2}}}[/tex] + [tex]\bold{{(1)^{2}}}[/tex]+ [tex]\bold{{2x}}[/tex] +[tex]\bold{{(x)^{2}}}[/tex] + [tex]\bold{{(4)}}[/tex]+ [tex]\bold{{(4x)}}[/tex] = [tex]\bold{{110}}[/tex]

[tex]:\pink\implies[/tex] [tex]\bold{{3x^{2}}}[/tex] + [tex]\large\bold{{6x}}[/tex] + [tex]\bold{{5}}[/tex] - [tex]\large\bold{{110}}[/tex] = [tex]\bold{{0}}[/tex]

[tex]:\pink\implies[/tex] [tex]\bold{{3x^{2}}}[/tex] + [tex]\bold{{6x}}[/tex] - [tex]\bold{{105}}[/tex] = [tex]\bold{{0}}[/tex]

By taking 3 Out as Common, we are left with the Quadratic Equation :—

[tex]:\pink\implies[/tex] [tex]\large\bold{{1x^{2}}}[/tex]+ [tex]\large\bold{{2x}}[/tex] - [tex]\large\bold{{35}}[/tex] = [tex]\large\bold{{0}}[/tex]

x = -b ± √(b)^2— 4 × a × c / 2a

x = -2 ± √(2)^2— 4 × 1 × -35 / 2×1

x = -2 ± √144/2

[ As we know that "144" is square of 12 ]

x = -2 ± 12/2

Hence, x = +5

x +1 = 5+1 = +6

x+2 = 5+2 = +7

Hence, x = -7

x+1 = -7+1 = -6

x+2 = -7+2 = -5

Answer:

Step-by-step explanation:

Let the three consecutive numbers be denoted as :

Identity

It is given that the sum of the squares of these numbers add up to 110.

Taking x = 5

Taking x = -7

Solution

Answer:

$138.00

Step-by-step explanation:

The original price of the shelf is $345.00.  The new sale price is the original price of  100% less the 60% of the original price.  That means the sales price is 40% of the original price.

You can do this 2 ways:

1.  $345 x 60% or .60 = $207

   $345-207 = $138

or

2.  $345 x 40% or .40 = $138

Answer:$138

Step-by-step explanation:

Since the store is on sale 60% out of a whole 100%

= 100% - 60% = 40%

40% is [tex]\frac{40}{100}[/tex] = 0.4

0.4 x 345 = $138

Answer:

(3, 11), because both lines pass through this point

Step-by-step explanation:

x = y - 8

y = 3(y -8) + 2

y = 3y - 24 + 2

y - 3y = -22

-2y = -22

y = 11

11 = x + 8

x = 11 - 8

x = 3

Answer :- (3,11)

Answer:

7) graphing, because they are in the y=mx+b format.

8) substitution, because it tells you what y equals.

9) substitution, because it tells you what y equals.

10) elimination, because you can subtract the x's to equal 0.

11) graphing, because they are in the y=mx+b format.

12) substitution, because it tells you what y equals.

Step-by-step explanation:

Answer:

The closest answer is C) After 6 months, the outstanding balance on the credit card will be approximately $281.54.

Step-by-step explanation:

First we figure out the amount of interest.

0.02 x 250 = 5

5 x 6 = 30

30 + 250 = 280

keeping in mind that a function does not have any X-Repeats, that is, the 1st coordinate in every pair never repeats, well, in this case, all of them have no X-repeats, that means all of them are functions.  However, only one-to-one functions have an inverse that is also a function.

A one-to-one function is one that has no X-repeats as well as no Y-repeats, so each pair in the set has no coordinate repeats, Check the picture below.

For an ordered pairs to represent has an inverse a that is function, It shouldn't show one-to-many relation in the pairs. The answer is   {(-4, 3), (-2, 7), (-1, 0), (4, -3), (11, -7)} represents a function.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

The set of all potential values that the function would be return when the domain is provided as input is the definition of range.

The one-to-one function has inverse where the inverse is the function.

That is, should be unique output for each input values.

{(-4, 3), (-2, 7), (-1, 0), (4, -3), (11, -7)} in this option, There are no one-to-many relations. So, It is a function.

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Answer: 3x + 28 > 200

Step-by-step explanation:

[tex]$$Let $x$ be the amount each friend received. Since there are 3 friends, then $3 x$ is the amount of money they split evenly. The amount of money they split evenly was the amount left over after paying their parent's $\$ 28$. Therefore $3 x+28$ is the total amount they earned.[/tex]

Answer:

y'= 5x^4 + 5^x In(5)

Step-by-step explanation:

Differentiate with Respect to x

f(x)'=5x^4 + In(5^x)

f(x)'= 5x^4 + x In(5)

with respect to x, we have

y'= 5x^4 + y In(5)

y'= 5x^4 + 5^x In(5)

Answer:

Parallelogram

Step-by-step explanation:

Answer:parallelogram

Step-by-step explanation:

Answer:

Reflection over the x-axis, shift up 5 units

Step-by-step explanation:

Given Parent Function:

Transformed function:

In transformed function:

then in transformed function,

represent that after reflection function is shifted 5 unit in upward direction.

Answer:

Reflection over the x-axis, shirt up 5 units

Step-by-step explanation:

It's a reflection because the x axis is a negative, and +5 moves up 5 units on the y axis

Answer:

8470 people are at the second show

Answer:

13 sheep, 19 chicken

Step-by-step explanation:

You can start to solve this problem by assigning variables. First, let's assign the number of sheep there are as [tex]x[/tex] and the number of chickens there are as [tex]y[/tex].

Because each sheep has 4 legs, the number of legs for each sheep would be [tex]4x[/tex]. Similarly, because each chicken has 2 legs, the number of legs for each chicken would be [tex]2y[/tex]. Each animal would have 1 head, so the number of heads would just be [tex]x[/tex] and [tex]y[/tex]. Because the number of legs in total are 90, [tex]4x + 2y=90[/tex]. Because the number of heads in total are 32, [tex]x+y=32.[/tex]

There is now a system of equations with two unknown variables and two equations. There are many ways to solve this, but for me, the easiest would be elimination. First, I would double the second equation, [tex]2x+2y=64[/tex]. Then, I would subtract that from the first equation, eliminating [tex]y[/tex]. [tex]2x=26[/tex]. Solving for x gives 13. We can then plug that value into the second equation, making y be [tex]32-13=19[/tex]. This means that [tex]x=13[/tex] and [tex]y=19[/tex], meaning that there are 13 sheep and 19 chicken.

Answer:

2In4x= 2In8 ln(16x^2) = ln64 Multiply e by both sides.

Step-by-step explanation:

Answer:

value of x is y to the nearest tenth. is 6.0 is equal to 8.3 to 5.8. 6.2