The base of a pyramid is a rectangle with a length of 3 centimeters and a width of 6 centimeters. If the height of the pyramid is 12 centimeters, what is the volume of the pyramid?

Answer:

84 units²

Step-by-step explanation:

v = 8 * 5 1/4 * 2

v = 84 units²

The volume of the rectangular prism is 42 cubic units.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

To find the volume of a rectangular prism, you need to multiply the height of the prism by the base area.

The height of the prism is given as 8 units.

The base area is given as 5 1/4 units².

To convert the mixed fraction to an improper fraction, we multiply the whole number (5) by the denominator (4), then add the numerator (1).

5 1/4 = (5 x 4 + 1) / 4 = 21/4

Now, we can calculate the volume of the rectangular prism:

Volume = height x base area

Volume = 8 x 21/4

Volume = 168/4

Volume = 42

Therefore, the volume of the rectangular prism is 42 cubic units.

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Answer:

She has to get a score of 88 on that test

Step-by-step explanation:

Take the average of the other grades, and that gives you 84.25. So she has to think about what rating she gives it is 85, and the rating is 88.

Hailey needs to score an 88 on the last exam in order to get an average of 85.

The overall average is the mean and the mean is calculated by adding up all the scores and then dividing by the number of exams.

There are 5 exams but only 4 scores. The 5th score will be denoted, "x" and the average we are looking for is 85.

The fifth score should therefore be:

Overall score = Sum of 5 exams / 5

85 = (86 + 94 + 76 + 81 + x) / 5

85 x 5 = 337 + x

425 = 337 + x

x = 425 - 337

= 88

In conclusion, Hailey needs a score of 88 on the fifth exam.

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Answer:

BCD = 60

ABD - 90

Step-by-step explanation:

BCD)

BC and CD are the same length on in the circle, they are the radius. Therefor,  all angles will be the same at 60

ABD)

All angles together are 180

You know 2 Angles, A at 30 and D at 60

180 - 30 - 60 = Angle B

90 = Angle B

Probability is simply how likely something is to happen.

Whenever we’re unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

The best example for understanding probability is flipping a coin:

There are two possible outcomes—heads or tails.

What’s the probability of the coin landing on Heads? We can find out using the equation P(H) = ?P(H)=?P, left parenthesis, H, right parenthesis, equals, question mark.You might intuitively know that the likelihood is half/half, or 50%.  

Tips

The probability of an event can only be between 0 and 1 and can also be written as a percentage.

Answer:

The Probability that the spinner landed on the colors blue and green in any order = 2/9

Step-by-step explanation:

Given - Azul spun a tri-color spinner twice.

To find - What is the probability that the spinner landed on the colors blue and green in any order?

Solution -

Given that,

A tri-color spinner spun twice

So,

The Sample Space, S = {BB, BG, BY, GB, GG, GY, YB, YG, YY}

⇒n(S) = 9

Now,

Let A be an event that the spinner landed on the colors blue and green

So,

A = {BG, GB}

⇒n(A) = 2

Now,

Probability that the spinner landed on the colors blue and green in any order = n(A) ÷ n(S)

         = 2 ÷ 9

∴ we get

The Probability that the spinner landed on the colors blue and green in any order = 2/9

Answer:

91in^2

Step-by-step explanation:

SA of base =  7x7 = 49in^2

SA of each triangle = 1/2 x 7 x 3 = 10.5in^2

SA of all 4 triangles = 10.5 x 4 = 42in^2

SA Total = 49 + 42.= 91inch^2

Step-by-step explanation:

[tex]midpoint = ( \frac{4.9 + - 5.2}{2} , \: \frac{ - 1.3 + - 0.6}{2} ) \\ = ( - 0.15, \: - 0.95)[/tex]

Answer:

2/10 (A)

Step-by-step explanation:

Answer:

z (max) = 96

x₁  = 2

x₂ = 0

x₃ = 1

Step-by-step explanation:

Fromproblem statement:

                                    weight (lb) .          Profit $

Denim jeans                    2.1                         40

CD players                       3.2                        48

Compact Discs                0.8                        16

Objective Function z is:

z = 40*x₁  + 48*x₂ + 16*x₃             to maximize

Subject to:

Weight constrain:    5 lb

2.1*x₁  +   3.2*x₂   + 0.8*x₃

x₁≥ 0   x₂  ≥ 0        x₃ ≥ 0      All integers

Using AtomZmath on-line solver and after 2 iterations

Solution:

z (max) = 96

x₁  = 2

x₂ = 0

x₃ = 1

The maximized profit is the highest profit Juan can get by selling his items.

The maximized profit is $96

Let x represents the Denim jeans, y represents the CD players and z represent the compact discs.

So, we have the following parameters

Weights

[tex]x = 2.1[/tex]

[tex]y = 3.2[/tex]

[tex]z = 0.8[/tex]

The weight cannot exceed 5 pounds.

So, the constraint is

[tex]2.1x + 3.2y + 0.8z \le 5[/tex]

The profit is given as:

[tex]x = 40[/tex]

[tex]y = 48[/tex]

[tex]z = 16[/tex]

So, the objective function to maximize is

[tex]Max\ Z = 40x + 48y + 16z[/tex]

The integer programming model is then represented as:

[tex]Max\ Z = 40x + 48y + 16z[/tex]

Subject to:

[tex]2.1x + 3.2y + 0.8z \le 5[/tex]

[tex]x,y,z \ge 0[/tex]

Using a graphing calculator, the values that maximize the objective function are:

[tex]x = 2[/tex]

[tex]y = 0[/tex]

[tex]z = 1[/tex]

Substitute these values in the objective function

[tex]Max\ Z = 40x + 48y + 16z[/tex]

[tex]Z = 40 \times 2 + 48 \times 0 + 16 \times 1[/tex]

[tex]Z = 80 + 0 + 16[/tex]

[tex]Z = 96[/tex]

Hence, the maximized profit is $96

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Answer:

C

Step-by-step explanation:

This can come from process of elimination, 1 shift is not enough. 2 shifts, 3 1/2 + 3 1/2 is 7, meaning it still isn't enough. 4 shifts 7 + 7 is 14, making it to much.

5 servings looked It up

Alex has 5 1/5cups of dog food. A serving of dog food is 4/5cup. Therefore, Alex has 4 servings.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Alex has 5 1/5 cups of dog food. A serving of dog food is 4/5 cup.

[tex]5\dfrac{1}{5} = \dfrac{26}{5}\\\\= \dfrac{26}{5}/ \dfrac{4}{5} \\\\= \dfrac{26}{5}\times \dfrac{5}{4} \\\\=\dfrac{26}{4}[/tex]

Therefore, Alex has 4 servings.

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Answer:

142.5 cm2

Step-by-step explanation:

The small markings create a new height, so that would be 9.5 cm.

Multiply:

9.5x15=142.5

Therefore, the area is 142.5 cm2

2yrds/8= 9 inches

9 inches are needed to make 1 bag

:)

The equation represents the yards of fabric, x, needed to make a certain number of bags, y will be y = 4x.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

As per the given,

2 yards of fabric for 8 bags,

y/x = 8/2 = 4

y = 4x

Hence "The equation represents the yards of fabric, x, needed to make a certain number of bags, y will be y = 4x".

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Answer:

3/4 of the area of the circle is of [tex]48\pi[/tex] squared units.

Step-by-step explanation:

Equation of a circle:

The equation of a circle has the following format:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

In which the center is [tex](x_0,y_0)[/tex] and r is the radius.

Area of a circle:

The area of a circle of radius r is given by:

[tex]A = \pi r^2[/tex]

Circle (x+2)² + (y-5)² = 64

Comparing with the standard equation, we have that:

[tex]r^2 = 64[/tex]

Area of the circle:

[tex]A = \pi r^2 = 64\pi[/tex]

What is 3/4 of its area?

[tex]\frac{3A}{4} = \frac{3*64\pi}{4} = 3*16\pi = 48\pi[/tex]

3/4 of the area of the circle is of [tex]48\pi[/tex] squared units.

Answer:

B. No

Step-by-step explanation:

I calculated it logically

Answer:

(2,4)

Step-by-step explanation:

3x-2(-2)=x

3x-4=x

-4= -2x

x=2

y=3(2)-2

y=6-2

y=4

(2,4)

Answer:

sin D = 28/53

sin E =45/53

cos D =45/53

cos E =28/53

Answer: I got ~17% (It's 17% as the problem asked for the answer to be rounded)

Step-by-step explanation:

I added the 12 possible chances from the spinner with the 6 sided die chances. This gets me 18. Since the problem is asking the probability of rolling an 8 or 10 alongside a 3, I did 3/18 and got 16.66% (repeating). I'm not entirely sure if I did this right, but I hope this helped somehow. Let me know if it's not the correct answer.

Answer:

The answer would be 2. Which means that your answer would be option 1 I believe.

Step-by-step explanation:

Answer:

There is a 33.3% chance you will pull a red marble after pulling a blue one.

Step-by-step explanation:

There are a total of 10 marbles in the sack. A blue marble is removed from the bag without being replaced, leaving 9 in the sack. 3 of the marbles left are red. To find the probability of pulling a red marble, we divide the number of red marbles by the number of total marbles.

3/9 = 1/3 = 0.333 = 33.3%

Answer:

[tex] - 17y−16z+4[/tex]

Step-by-step explanation:

[tex] - y+9z−16y−25z+4[/tex]

[tex] - 17y+9z−25z+4[/tex]

[tex] - 17y−16z+4[/tex]

Answer:

13 feet

Step-by-step explanation:

This is a right triangle problem

Use the Pythagorean Theorem

c² = a² + b²

c² = 12² + 5²

c² = 144 + 25

c² = 169

Take the square root of both sides

c = 13

Answer:

The number of red pencils is 2 times the number of yellow pencils

Answer:

Option B is correct

Step-by-step explanation:

[tex] \sf \longmapsto \: \frac{{x}^{3} - {y}^{3} }{4} \\ \sf \longmapsto \: \frac{ {4}^{3} - {2}^{3} }{4} \\ \sf \longmapsto \: \frac{64 - 8}{4} \\ \sf \longmapsto \: \frac{56}{4} \: \: \: \: \: \: \: \: \\ \sf \longmapsto \: 14[/tex]

Answer:

Step-by-step explanation:

Percy Jakcson maybe?

Answer:

The egg hits the ground after 2.5 seconds.

Step-by-step explanation:

Height of the egg:

The height of the egg after t seconds is given by:

[tex]h(t) = 100 - 16t^2[/tex]

After how many seconds does the egg hit the ground?

This is t for which [tex]h(t) = 0[/tex]. So

[tex]h(t) = 100 - 16t^2[/tex]

[tex]16t^2 - 100 = 0[/tex]

[tex]16t^2 = 100[/tex]

[tex]t^2 = \frac{100}{16}[/tex]

[tex]t = \sqrt{\frac{100}{16}}[/tex]

[tex]t = \frac{10}{4}[/tex]

[tex]t = 2.5[/tex]

The egg hits the ground after 2.5 seconds.

Answer:

5?

Step-by-step explanation:

9514 1404 393

Answer:

  500 cm³

Step-by-step explanation:

The diameter of the sphere is shown as 10 cm, so its radius is 5 cm. Using the given numbers in the given formula, you find the volume to be ...

  V = (4/3)(3)(5 cm)³ = 4(125 cm³) = 500 cm³