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liberstina [14]
3 years ago
11

The first cube has a side length of 3 units. The second cube has a side length of 5 units. Write an expression that you can use

to find the total volume of ice you can make.
Mathematics
1 answer:
andrey2020 [161]3 years ago
3 0

Answer:

152 cubic units

Step-by-step explanation:

Volume of a cube = L³ where;

L is the side length of a cube

For the cube of side length of 3 units

Volume of the cube = 3³

Volume of the cube = 27 cubic units

For the cube of side length of 5 units

Volume of the cube = 5³

Volume of the cube = 125 cubic units

Total volume the ice can make = (125 + 27)cubic units

Total volume the ice can make = 152 cubic units

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Use the formula 4/3(pi)r^3
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3 years ago
Slope is 3/7,and (4,9) is on the line
TiliK225 [7]

Answer:

y-9=\frac{3}{7}(x-4)

or

y=\frac{3}{7}x+\frac{51}{7}

Step-by-step explanation:

To write the equation of the line using a slope and a point, use the point-slope formula y-y_1 = m(x-x_1). Here m is 3/7. And the point (x_1,y_1) is (4,9). Substitute the values and simplify.

y-y_1=m(x-x_1)\\y-9=\frac{3}{7}(x-4)\\y-9=\frac{3}{7}x - \frac{12}{7}\\y=\frac{3}{7}x -\frac{12}{7} + 9\\y=\frac{3}{7}x + \frac{51}{7}

Both the point slope form and the final simplified form are considered equations of the line.

3 0
3 years ago
The ELISA test was an early test used to screen blood donations for antibodies to HIV. A study (Weiss et al. 1985) found that th
patriot [66]

Answer:

0.057258

Step-by-step explanation:

From the statement of the problem, the following information were given:

  • P(Positive|HIV)=0.979
  • P(Negative|No HIV)=0.919
  • P(HIV)=0.005

The following can be derived:

  • P(Positive|No HIV)=1-P(Negative|No HIV)=1-0.919=0.081
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We are to determine the probability that a person has HIV given that they test positive. [P(HIV|Positive)]

Using Baye's theorem for Conditional Probability

P(HIV|Positive)=\dfrac{P(Positive|HIV)P(HIV)}{P(Positive|HIV)P(HIV)+P(Positive|No HIV)P(No HIV)}=\dfrac{0.979*0.005}{0.979*0.005+0.081*0.995}

P(HIV|Positive)=0.057258

The probability that a random person tested has HIV given that they tested positive is 0.057258.

5 0
4 years ago
The point (–5, 6) is located in which quadrant?
kolbaska11 [484]
Quadrant 1 is the answer. quadrant 2 is to the right of quadrant 1 and quadrant 3 is below quadrant 1
5 0
4 years ago
A track and field playing area is in the shape of a rectangle with semicircles at each end. See the figure. The inside perimeter
Schach [20]

Answer:

Step-by-step explanation:

Let x be the track straights lengths

Let y be the track ends diameter and the other rectangle side lengths.

1800 = 2x + πy

y = (1800 - 2x) / π

A = xy

A = x((1800 - 2x) / π

A = (1/π)(1800x - 2x²)

dA/dx = (1/π)(1800 - 4x)

       0 = (1/π)(1800 - 4x)

       0 = 1800 - 4x

     4x = 1800

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        y = (1800 - 2(450)) / π

        y = 900/π or approximately 286.5 m

8 0
3 years ago
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