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Answer:

8 cups

Step-by-step explanation:

The number of cups of Gatorade served to the players during the last game was 8 cups.

To solve the problem, we need to determine how many cups are in half a gallon, given that 1 cup is equal to 1/16 of a gallon.

First, we establish the conversion factor between cups and gallons:

1 cup = 1/16 gallon

Now, we need to find out how many cups are in 1/2 gallon. To do this, we multiply the amount of Gatorade used in the last game by the conversion factor:

Cups served = (1/2 gallon) * (16 cups / 1 gallon)

Performing the multiplication:

Cups served = 1/2 * 16

Cups served = 8 cups

Therefore, 8 cups of Gatorade were served to the players during the last game.

Answer:

After 7.5 seconds and a height of 0

Step-by-step explanation:

The time taken for the bolt to hit the elevator is 3 seconds, at a height of 60 feet.

Given that the elevator height is h(t)=20t while the bolt height is given by h(t)=-16t² + 200.

At the point when the bolt hit the elevator, they would be at the same height, hence:

-16t² + 200 = 20t

16t² + 20t - 200 = 0

t = -4.2 or t = 3

Therefore the time taken for the bolt to hit the elevator is 3 seconds, the height is:

h(3) = 20(3) = 60 feet

The time taken for the bolt to hit the elevator is 3 seconds, at a height of 60 feet.

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Answer:

11,499 cm^3

Step-by-step explanation:

The volume of a sphere is given by the formula  [tex]V=\frac{4}{3}\pi r^3[/tex]

The radius is given as 14, we plug it into the formula and find the volume:

[tex]V=\frac{4}{3}\pi r^3\\V=\frac{4}{3}(\frac{22}{7}) (14)^3\\V=11498.66[/tex]

rounded to nearest integer, the volume is 11,499

Answer:

r=14 cm

V=11499 cubic cm

Step-by-step explanation:

If the radius of the sphere is r cm, then the perimeter of the largest cross section is the circumference of the circle qith radius r. Thus,

[tex]88=2\pi r,\\ \\r=\dfrac{88}{2\pi}=\dfrac{44}{\pi}=\dfrac{44}{\frac{22}{7}}=\dfrac{44}{1}\cdot \dfrac{7}{22}=14\ cm.[/tex]

Thvolume of the sphere can be calculated using formula

[tex]V=\dfrac{4}{3}\pi r^3.[/tex]

Since r=14 cm, we get

[tex]V=\dfrac{4}{3}\cdot \dfrac{22}{7}\cdot 14^3=\dfrac{4\cdot 22\cdot 2\cdot 14^2}{3}=\dfrac{34496}{3}\approx 11499\ cm^3.[/tex]

Answer: 6 meters per second

Step-by-step explanation:

Ben's average speed from Post A to Post C is 6 meters per second, calculated by dividing the total distance cycled (420 meters) by the total time taken (70 seconds).

The subject of the problem is calculating average speed. In this context, Ben's average speed can be calculated by dividing the total distance cycled by the total time taken.

Total distance is the sum of the distance from Post A to Post B and from Post B to Post C, which is 120 meters + 300 meters = 420 meters.

Total time is the sum of the time taken from Post A to Post B and from Post B to Post C, which is 15 seconds + 55 seconds = 70 seconds.

So, Ben's average speed=Total Distance/Total Time.
This equals 420 meters/70 seconds= 6 meters/second.

Therefore, Ben’s average speed for the entire distance from Post A to Post C is 6 meters per second.

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Answer:

Final answer is [tex]80x^2[/tex].

Step-by-step explanation:

Given expression is [tex]\frac{16x^3}{y}\cdot\frac{5y^2}{xy}[/tex].

Now we need to simplify this expression as shown below:

[tex]\frac{16x^3}{y}\cdot\frac{5y^2}{xy}[/tex]

[tex]=\frac{80x^3\cdot y^2}{y\cdot xy}[/tex]

[tex]=\frac{80x^3\cdot y^2}{xy^2}[/tex]

[tex]=\frac{80x^3}{x}[/tex]

[tex]=80x^2[/tex]

Hence final answer is [tex]80x^2[/tex].

Answer:

[tex]\left(gof\right)\left(0\right)=16[/tex]

Step-by-step explanation:

Given functions are [tex]f\left(x\right)=-3x+4[/tex] and [tex]g\left(x\right)=x^2[/tex].

Using both functions we need to find about what is the value of [tex]\left(gof\right)\left(0\right)[/tex]. That can be done as shown below:

[tex]\left(gof\right)\left(0\right)[/tex]

[tex]=g\left(f\left(0\right)\right)[/tex]

[tex]=g\left(-3\left(0\right)+4\right)[/tex]

[tex]=g\left(0+4\right)[/tex]

[tex]=g\left(4\right)[/tex]

[tex]=4^2[/tex]

[tex]=16[/tex]

Hence final answer is [tex]\left(gof\right)\left(0\right)=16[/tex].

Answer:

Thus, the fourth answer choice is the correct one

Step-by-step explanation:

Let's check this, using the Pythagorean Theorem:

"Yes, the distance from (0, 0) to (2, square root 6 ) is 3 units."

Does 2² + (√6)² = 3²?

Does 4 + 6 = 9?  NO.   .

Answer: D) 13y+15y^2

Step-by-step explanation:

(4y+9y)+(-8y^2-7y^2)=13y-15y^2

4y-8y^2+9y−7y^2

=4y+ −8y^2+9y+ −7y^2

Combine Like Terms:

=4y+ −8y^2+9y+ −7y^2

=(−8y^2+ −7y^2)+(4y+9y)

= −15y^2+13y

Answer:

the answers are B, C, and D.

The given item soup can is a cylinder.

The volume of the cylinder is given as :

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

Here 'h' is the height and 'r' is the radius.

So, the true statements are:

B) The volume is the area of the base times the height - The base of the cylinder is circular and the area of the circle is [tex]\pi r^{2}[/tex], so the volume is the area of base multiplied by height.

C) Given the radius or the diameter, you can calculate the area of the base of a cylinder - Yes as the area is [tex]\pi r^{2}[/tex] where 'r' is the radius.

D) The height of a cylinder is the distance between the 2 parallel bases. Yes this is right.

For this case we must build a quotient that multiplied by the divisor, is eliminating the terms of the dividend until you reach the remainder of the division. It must be fulfilled that:

Dividend = Quotient * Divider + Remainder

Answer:

See attached image

Option D

Answer:

14

Step-by-step explanation:

Mean = (5+10+10+20+20+5+20+20+15+15)÷10

= 140÷10

= 14

there would be 12 combinations

Answer:

12

Step-by-step explanation:

We are given that tent hold 2,3,5,6 or 12 people.

We have to find the combinations of tents are possible to sleep 32 all tents are fully occupied and exactly one 12 person tent is used.

If one 12 person tents is used then remaining people=32-12=20

Therefore, 20 people that must be in other tents.

To place 20 persons in combination of 2,3,5 and 6.

20=5+5+5+5

20=5+5+5+2+3

20=6+6+6+2

20=2(10)=2+2+....+2(10 times)

20=5+5+2(5)(5 times add 2)

20=6+6+2(4) (4 times add 2)

20=3+3+3+3+3+3+2

20=3+3+3+3+3+5

20=3+2+6+5+2+2

20=3+3+3+3+6+2

20=3+3+5+5+2+2

20=6+6+3+5

Hence, there are 12 possible combination of tents  to sleep 32  all tents are fully occupied and exactly one 12 person tents is used.

Answer:

B

Step-by-step explanation:

B). RA and NY are perpendicular segments

Answer:

The correct answer option is B. Perpendicular segments.

Step-by-step explanation:

We are given two segments RA and NY and we are to determine whether which of the given answer options describe them the best.

Since the angles ∠RDA and ∠NDY are perpendicular angles and they lines RA and NY intersect each other at point D so the formed segments are also perpendicular.

Therefore, the option which best describes this is B. Perpendicular segments.

ANSWER

[tex]\frac{ {y}^{2} }{49} + \frac{ {x}^{2} }{ 16 } = 1[/tex]

EXPLANATION

The given ellipse has a vertex at (0, -7), a co-vertex at (4,0), and a center at the origin.

The equation of an ellipse with vertex on the y-axis and center at the origin is given by

[tex]\frac{ {y}^{2} }{a ^{2} } + \frac{ {x}^{2} }{ {b}^{2} } = 1[/tex]

[tex]\frac{ {y}^{2} }{( - 7) ^{2} } + \frac{ {x}^{2} }{ {4}^{2} } = 1[/tex]

[tex]\frac{ {y}^{2} }{49} + \frac{ {x}^{2} }{ 16 } = 1[/tex]

The equation of the ellipse with a vertex at (0, -7), a co-vertex at (4,0), and a center at the origin is x^2/16 + y^2/49 = 1.

To find the equation of the ellipse in standard form, we need to identify the lengths of the major and minor axes. The given vertex at (0, -7) indicates that the semi-major axis length, a, is 7 because the distance from the center to a vertex measures the semi-major axis. Similarly, the co-vertex at (4, 0) represents the semi-minor axis length, b, which is 4.

Since the center is at the origin (0, 0), the standard form of the ellipse equation is given by x^2/b^2 + y^2/a^2 = 1. Plugging the values of a and b, we get x^2/4^2 + y^2/7^2 = 1. So, the equation of the ellipse is x^2/16 + y^2/49 = 1.

The probability of drawing the number 14 is 1/10 (because there are 10 different numbers to pick from). The probability of drawing a number less than 12 is 8/10 (or 4/5 simplified). Multiply the fractions: 1/10 *4/5 = 4/50. Simplify to 2/25. The probability of drawing 14 and then a number less than 12 is 2/25.

Answer:

The area of rhombus = 195 yd²

Step-by-step explanation:

Points to remember

Area of rhombus = d₁d₂/2

Where d₁ and d₂ are the diagonals of the rhombus

To find the area of given rhombus

Here diagonals of rhombus are given

From the figure we get,

d₁ = 13 + 13 = 26 yd and

d₂ = 7.5 + 7.5 = 15 yd

Area = d₁d₂/2 = (26 * 15 )/2 = 13 * 15 = 195 yd²

Therefore the area of rhombus = 195 yd²

Each person in the Vale family will drink a total of 339.5 ounces of water over the course of 7 days.

The student is asking how much water in ounces each person in the Vale family will drink over the span of 7 days if each person drinks 48.5 ounces of water daily.

To find the total amount of water consumed by one person in 7 days, we multiply the daily intake by the number of days:

48.5 ounces/day imes 7 days = 339.5 ounces

So, each person will drink a total of 339.5 ounces of water in 7 days.

The equation of a circle is written as (x-h)^2 +(y-k)^2 = r^2

h and K are the center points of the circle and r is the radius.

replace the letters with the provided center and radius:

(x- (-7))^2 + (y- (-3))^2 = 2^2

Simplify:

(x+7)^2 + (y+3)^2 = 4

Answer:

Part 1) The system is solved using elimination

The cost  per can of grape juice is [tex]\$1.19[/tex] and the cost per can of apple juice is [tex]\$1.49[/tex]

Part 2) The system is solved using substitution

The cost  per can of grape juice is [tex]\$1.19[/tex] and the cost per can of apple juice is [tex]\$1.49[/tex]

Part 3) The system is solved by graphing

The graph in the attached figure

Step-by-step explanation:

Part 1) Solve the system by elimination

Let

x----> the cost per can of grape juice

y----> the cost per can of apple juice

we know that

[tex]6x+4y=13.10[/tex] -----> equation A

[tex]4x+6y=13.10+0.60[/tex]

[tex]4x+6y=13.70[/tex]  -----> equation B

Solve the system by elimination

Multiply the equation A by -6 both sides

[tex]-36x-24y=-78.6[/tex] -------> equation C

Multiply the equation B by 4 both sides

[tex]16x+24y=54.8[/tex] -------> equation D

Adds equation C and equation D

[tex]-36x-24y=-78.6\\16x+24y=54.8\\----------\\-36x+16x=-78.6+54.5\\-20x=-23.8\\x=1.19[/tex]

Substitute the value of x in the equation A

[tex]6(1.19)+4y=13.10[/tex]

[tex]4y=5.96[/tex]

[tex]y=1.49[/tex]

therefore

The cost  per can of grape juice is [tex]\$1.19[/tex]

The cost per can of apple juice is [tex]\$1.49[/tex]

Part 2) Solve the system by substitution

Let

x----> the cost per can of grape juice

y----> the cost per can of apple juice

we know that

[tex]6x+4y=13.10[/tex]    

[tex]4y=-6x+13.10[/tex]

[tex]y=-1.5x+3.275[/tex] -----> equation A

[tex]4x+6y=13.10+0.60[/tex]

[tex]4x+6y=13.70[/tex]  

[tex]6y=-4x+13.70[/tex]

[tex]y=-(4/6)x+13.70/6[/tex]

[tex]y=--0.67x+2.28[/tex] -----> equation B

Substitute equation B in equation A and solve for x

[tex]-0.67x+2.28=-1.5x+3.275[/tex]

[tex]1.5x-0.67x=3.275-2.28[/tex]

[tex]0.83x=0.995[/tex]

[tex]x=1.19[/tex]

Find the value of y

Substitute the value of x in the equation A

[tex]y=-1.5(1.19)+3.275=1.49[/tex]

therefore

The cost  per can of grape juice is [tex]\$1.19[/tex]

The cost per can of apple juice is [tex]\$1.49[/tex]

Part 3) Solve the system by graphing

we have

[tex]y=-1.5x+3.275[/tex] -----> equation A

[tex]y=-(4/6)x+13.70/6[/tex] -----> equation B

Remember that

The solution of the system of equations is equal to the intersection point both lines

The solution is the point [tex](1.19,1.49)[/tex]

see the attached figure

therefore

The cost  per can of grape juice is [tex]\$1.19[/tex]

The cost per can of apple juice is [tex]\$1.49[/tex]

Rounded Answer: 256

Exact Answer : 255.6

Answer:

[tex]V=120\ units^3[/tex]

Step-by-step explanation:

we know that

The volume of a prism is equal to

[tex]V=BL[/tex]

where

B is the area of the base of the prism (triangular base in this problem)

L is the length of the prism (perpendicular distance between the top and the bottom)

Find the area of the triangular base B

[tex]B=\frac{1}{2}(3)(4)=6\ units^2[/tex] ---> area of a triangle

we have

[tex]L=20\ units[/tex]

substitute in the formula of volume

[tex]V=6(20)=120\ units^3[/tex]

Note The problem does not specify whether the measurements are in centimeters or in units, so I assume they are in units.

Answer:

p = 1/6

Step-by-step explanation:

5/6 - 1/3 n = p(5-2n)

Multiply each side by 6 so we do not have any fractions

6(5/6 - 1/3 n) = 6*p(5-2n)

5 - 2n = 6p (5-2n)

Divide each side by (5-2n) to isolate 6p

(5-2n)/(5-2n) = 6p (5-2n)/ (5-2n)

1 = 6p

Now divide by 6 to get p alone

1/6 = 6p/6

1/6 = p

your answer would be $405.60

The answer is 709.8 You would do 8.45 times 40 = 338 now since he did overtime you multiply it by 2. 338*2= 676. He also did another 4 hours 8.45*4=33.8 now you add these together 33.8+676 = 709.8

Answer:

x² + 2x + [3\x - 1]

Step-by-step explanation:

Since the divisor is in the form of x - c, use what is called Synthetic Division. Remember, in this formula, -c gives you the OPPOSITE terms of what they really are, so do not forget it. Anyway, here is how it is done:

1| 1 1 -2 3

↓ 1 2 0

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

1 2 0 3 → x² + 2x + [3\x - 1]

You start by placing the c in the top left corner, then list all the coefficients of your dividend [x² + 5x - 36]. You bring down the original term closest to c then begin your multiplication. Now depending on what symbol your result is tells you whether the next step is to subtract or add, then you continue this process starting with multiplication all the way up until you reach the end. Now, when the last term is 0, that means you have no remainder, which in this case is a 3, so what you is set the divisor underneath the remainder of 3. Finally, your quotient is one degree less than your dividend, so that 1 in your quotient can be an x², 2 becomes 2x, and the remainder of 3 is set over the divisor, giving you the other factor of x² + 2x + [3\x - 1].

If you are ever in need of assistance, do not hesitate to let me know by subscribing to my channel [USERNAME: MATHEMATICS WIZARD], and as always, I am joyous to assist anyone at any time.

Answer:

12, 18.

Step-by-step explanation:

2x-5 < 33

2x < 38

x < 38/2

x < 19

Answer:

2 2/3+ 3 1/3 = 6. Multiply 6 by 4 weeks. 24 as your whole number.

Step-by-step explanation:

Final answer:

Mary spends a total of 24 hours on math and art homework combined over a period of 4 weeks.

Explanation:

Mary spends 2 2/3 hours on math homework and 3 1/3 hours on art homework each week.

To find out how much time she spends on both subjects over 4 weeks, first, we add the weekly hours:

2 2/3 + 3 1/3 = 6 hours per week.

Next, we multiply this weekly total by 4 to determine the monthly total: 6 hours/week × 4 weeks = 24 hours.

Therefore, Mary spends a total of 24 hours on math and art homework over 4 weeks.

Answer:

Step-by-step explanation:

The log is basically saying: 13/5 to what exponent gives you 50 000/3.

and the exponent is approximated at 10.17378.

the answer is b and f

Answer:

b f

Step-by-step explanation:

Answer:

4.64

Step-by-step explanation:

s = 6a^3

600=6a^3

100 = a^3

solve for a which would be 4.64

Answer:

[tex]\left[\begin{array}{ccc}7\\4\\2\end{array}\right][/tex]

The answer is a single-column matrix (7,4,2)

Step-by-step explanation:

In such multiplication of matrices, you have to proceed by multiplying each ROW of the first matrix by the COLUMN of the second matrix.  So,

[tex]\left[\begin{array}{ccc}3&6&1\end{array}\right] * \left[\begin{array}{ccc}2\\0\\1\end{array}\right] = (3 * 2) + (6 * 0) + (1 * 1) = 6 + 0 + 1 = 7[/tex]

then...

[tex]\left[\begin{array}{ccc}2&4&0\end{array}\right] * \left[\begin{array}{ccc}2\\0\\1\end{array}\right] = (2 * 2) + (4 * 0) + (0 * 1) = 4 + 0 + 0 = 4[/tex]

and

[tex]\left[\begin{array}{ccc}0&6&2\end{array}\right] * \left[\begin{array}{ccc}2\\0\\1\end{array}\right] = (0 * 2) + (6 * 0) + (2 * 1) = 0 + 0 + 2= 2[/tex]

I hope it helps.