A sphere with a diameter of 9 units fits exactly in the clear glass cube as shown.

A sphere is inside of a cube. The cube has side lengths of 9 units.

Which expression represents the volume, in cubic units, of empty space in the cube?

Four-thirdsπ(4.53) – (4.5)3
(9)3 – Four-thirdsπ(4.52)
Four-thirdsπ(4.53) – (9)3
(9)3 – Four-thirdsπ(4.53)

Answer: B

Step-by-step explanation: I hope I am good at math if not sorry

The combination of 8 large cabinets and 8 small cabinets maximizes the objective function, resulting in a value of 640. Option b is correct.

To maximize the objective function P = 50x + 30y, where x represents the number of large cabinets and y represents the number of small cabinets.

Need to determine the combination of x and y that results in the highest value for P.

For 0 large and 10 small:

P = 50(0) + 30(10)

= 0 + 300

= 300

For 8 large and 8 small:

P = 50(8) + 30(8)

= 400 + 240

= 640

For 4 large and 4 small:

P = 50(4) + 30(4)

= 200 + 120

= 320

For 4 large and 5 small:

P = 50(4) + 30(5)

= 200 + 150

= 350

Based on these calculations, 8 large cabinets and 8 small cabinets maximizes the objective function, resulting in a value of 640.

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Answer: 11

Step-by-step explanation:

[tex]48=4x+4[/tex] (angles opposite congruent sides in a triangle are congruent)

This gives that x = 11

Answer:

C

Step-by-step explanation:

Answer:

pretty sure the answer is electrons  so D

Step-by-step explanation:

Electrons are particles that surround the nucleus of an atom like a cloud

Answer:

C - 100

Step-by-step explanation:

9514 1404 393

Answer:

  C.  100°

Step-by-step explanation:

Consecutive (same-side) exterior angles are supplementary.

  ∠1 = 180° -∠7 = 180° -80°

  ∠1 = 100°

Answer:

D

Step-by-step explanation:

Find the slope by picking two ordered pairs in the table and using the slope formula( y2-y1/x2-x1) to get the slope. The smallest numbers are easiest to work with. (-1,1), (0,-2)

-2-1/0-(-1) = 3/0+1 = -3/1 = m=-3

Use one of the points you used and plug in the x and y values of the ordered pair into the equation with the slope to find your b( y-intercept). (0,-2)

-2= -3(0) +b

-2= 0+b

b=-2

The final equation will only have your slope and b( y-intercept). That should be your answer. Hope this helps!

Final Equation: y=-3x-2

Answer: C

Step-by-step explanation:

5 × 3.5 = 17.5 > 16 .

Answer:

40

Step-by-step explanation:

if 20% were Caesar and 20 divided by 5 is 4, then every four salads sold is five percent.

Answer:

No

Step-by-step explanation:

Two triangles are  similar if their corresponding angles are congruent and the corresponding sides are in proportion  They  are the same shape, but not necessarily the same size

Triangle ABC  54 +68 +  58 = 180

Triangle EFG    68 +63 +49 = 180

In this case their corresponding angles are nor congruent

Answer:

V = 114.75 Volts

Step-by-step explanation:

Ohm's Law   V = IR

I = 4.5 A

R = 25.5 Ω

V = (4.5)(25.5)

V = [4×25.5] + [0.5×25.5]

V =  102 + 12.75

V = 114.75 Volts

Answer:

120.08

Step-by-step explanation:

15.8 x 7.6

-> 120.08 [tex]m^2\\[/tex]

9514 1404 393

Answer:

  y = -(x -7)² +6

Step-by-step explanation:

Replacing x with (x-h) translates the graph h units to the right. You want h=7.

Replacing f(x) with f(x)+k translates the graph k units upward. You want k=6.

These transformations make the new equation be ...

  y = -(x -7)² +6

Answer:

the center of the data set is 7 so probably 7

7 is the best representation of the center of given data set.

The correct answer is an option (C).

"It is the average of the given numbers."

"I is the middle value of a sorted list of numbers."

For given question,

We have been given a dot plot of the number of letters in each students first name.

From the given dot plot,

We have data as 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6,6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 9, 10, 10, 11, 11, 11

From above data,

the total number of students in the class are n = 30

We write 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6,6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 9, 10, 10, 11, 11, 11 as 3, (4 × 2), (5 × 4), (6 × 7), (7 × 7), (8 × 3), 9, (10 × 2), (11 × 3)

So, the mean of the above data would be,

[tex]\Rightarrow \bar{X}=\frac{3+ (4\times 2)+(5\times 4)+(6\times 7)+(7\times 7)+(8\times 3)+9+(10\times 2)+(11\times 3)}{30}\\\\\Rightarrow \bar{X}=\frac{208}{30}\\\\\Rightarrow \bar{X}=6.93\\\\\Rightarrow \bar{X}\approx 7[/tex]

From above data we can observe that there are two numbers in middle of the data 6 and 7.

So, the median would be,

[tex]\Rightarrow M=\frac{6+7}{2}\\\\\Rightarrow M=6.5\\\\\Rightarrow M\approx 7[/tex]

Therefore, 7 is the best representation of the center of given data set.

The correct answer is an option (C).

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Answer:

176

Step-by-step explanation:

8+8+64+64+16+16

Answer:

11.55 years

Step-by-step explanation:

Given data

Principal= $3000

Rate= 6%

Final Amount= $6000

expression for the time is given as

t = ln(A/P) / r

Substitute

t= ln(6000/3000)/0.06

t= ln(2)/0.06

t= 0.693/0.06

t= 11.55 years

Hence the time is 11.55 years

Answer and Step-by-step explanation:

The first step in solving for x is to square both sides.

8x = 4 + 2x

Now, subtract 2x from both sides.

6x = 4

Now, divide each side by 6.

x = [tex]\frac{4}{6} = \frac{2}{3}[/tex]

x = [tex]\frac{2}3}[/tex] is the answer.

#teamtrees #PAW (Plant And Water)

Answer:

$346.5

Step-by-step explanation:

10% of $550 is 55

3*55 = 165

550 - 165 = $385

10% of $385 is 38.5

385 - 38.5 = $346.5

Have a nice day! :-)

Answer:

sin∅=3/4

Step-by-step explanation:

sin²x+cos²x=1

sin²x+(√7/4)²=1

sin²x+7/16=1

sin²x=9/16

sinx=3/4

Therefore, sin∅=3/4

Answer:

The area of the shaded region is:

Step-by-step explanation:

First, we're gonna find the area of the whole rectangle and next we can subtract the area of the triangles in the corners, we use the next formula:

And we replace the measurements in the picture (32 ft and 16 ft):

Now, we must calculate the area of a triangle, this can be made by this formula:

We can replace the values we have in the picture (4 ft and 6 ft), then:

As you can see in the picture, we have to subtract two triangles with the same measurements, by this reason, we multiply the area of the triangle by two and we'll obtain the area we must subtract:

At last, we take the area of the whole rectangle and subtract the area of the triangles:

The area of the shaded region is 488 ft^2.

Answer:

1.5 feet

Step-by-step explanation:

V = base area x height

divide the two members by the base area

height = V/ base area

height = 13.5 / 9 = 1.5 feet

Answer:

A

Step-by-step explanation:

2 3/8=19/8=2.375

Answer:

Circumference is 18.84956

Area: 28.27433

Step-by-step explanation:

(Circumference) C=2πr=2·π·3≈ 18.84956

(Area) A=πr2=π·32≈ 28.27433

Answer:

Step-by-step explanation:

x-4/4=x/6+1

x-4 =4/6x+4

x-2/3x =8

1/3x =8

x=24

Answer:

the probability of rolling any single digit on a 6-sided fair cube is 1/6

Answer:

C. 360°

Step-by-step explanation:

I calculated it logically

Answer:

Answer is C) 360°

Step-by-step explanation:

Answer: 125.6 inches cubed.

Step-by-step explanation:

Formula for cylinder volume: Volume=(pi times radius cubed) times height

3.14 x 4(radius)=12.56

12.56 x 10 (height) = 125.6

Hope this helps