MATHEMATICS HIGH SCHOOL

Find two numbers with a sum of 20 and a difference of 14.a. 4 and 18
b. –3 and –17
c. 2 and 16
d. 3 and 17

Answers

Answer 1
Answer: D is the right option. 3 and 17 make 20. Difference is 17- 3= 14.

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23 means 3 · 2

True or false

Answers

False I'm pretty sure buddy

What is the probability (rounded to the nearest whole percent) that a randomly selected gym member would buy passion fruit vitamin water but not tropical grape vitamin water?54%
21%
17%
39%

Answers

The probability (rounded to the nearest whole percent) that a randomly selected gym member would buy passion fruit vitamin water but not tropicalgrape vitamin water is 17 percent.

The work of a student to solve a set of equations is shown:Equation A: y = 4 − 2z
Equation B: 4y = 2 − 4z
Step 1: −4(y) = −4(4 − 2z) [Equation A is multiplied by −4.]
4y = 2 − 4z [Equation B]
Step 2: −4y = 4 − 2z [Equation A in Step 1 is simplified.]
4y = 2 − 4z [Equation B]
Step 3: 0 = 6 − 6z [Equations in Step 2 are added.]
Step 4: 6z = 6
Step 5: z = 1
In which step did the student first make an error?
Step 1
Step 3
Step 4
Step 2

Answers

in step 2 .. because when you multiple by -4 in step 1 , the equation in step 2 will be ( -4y =-16 + 8z)

What is the slope of the line whose equation is 2y=5×+4?

Answers

2y=5x+4

Transforms into:

y=5/2x+2

Therefore the slope is: 5/2
2y=5x+4\ny=(5)/(2)+2\n\n\boxed{m=(5)/(2)}

Will you help me with these?

Answers

1's answer: 3rd one

2nd one answer: -25

3rd one answer: 1st one

4th one answer: --3

5th one answer: 3rd one.

Hope this helps.

(OFFERING ALL THE POINTS I HAVE) Word Problem. Please help!! Part 1 of problem: The main tank has a radius of 70 feet. What is the volume of the quarter-sphere sized tank? Round your answer to the nearest whole number and use 3.14 for Pi. (Use sphere volume formula) Part 2: The theme park company is building a scale model of the killer whale stadium main show tank for an investor's presentation. Each dimension will be made 6 times smaller to accommodate the mock-up in the presentation room. How many times smaller than the actual volume is the volume of the mock-up? Part 3: Using the information from part 2, answer the following question by filling in the blank: The volume of the actual tank is __% of the mock-up of the tank.

Answers

Answer:

Part 1: 359,007 ft³

Part 2: 216 times smaller

Part 3: 21600%

Step-by-step explanation:

Part 1:

The parameters for the tank are;

The radius of the tank = 70 feet

The volume of a sphere = 4/3·π·r³

Therefore, the volume of a quarter sphere = 1/4×The volume of a sphere

The volume of a quarter sphere = 1/4×4/3·π·r³ = π·r³/3

Plugging in the value for the radius gives

Volume = π×70³/3 = 114,333.33×3.14 = 359,006.7≈ 359,007 ft³.

Part 2:

The dimension of the scale model  = 1/6 × Actual dimension

Therefore, we have the radius of the sphere of the scale model = 1/6 × 70

Which gives;

The radius of the sphere of the scale model = 35/3 = 11.67 feet

The volume of the scale model = π·r³/3 = (3.14×11.67³)/3 = 1662.07 ≈ 1662 ft³

The number of times smaller the scale model is than the actual volume = (Actual volume)/(Scale model) = (359,007 ft³)/(1662 ft³) = 216 times

The number of times smaller the scale model is than the actual volume =  216 times = (1/Scale of model)³ = (1/(1/6))³ = 6³.

Part 3:

The percentage of the mock-up, x, to the volume of the actual tank is given as follows

x/100 ×  1662  = 359,007

∴ x = 216 × 100 = 21600%

The percentage of the mock-up, to the volume of the actual tank is 21600%.

Answer:

Part 1: 359,007 ft³

Part 2: 216 times smaller

Part 3: 21600%

Step-by-step explanation:

Part 1:

The parameters for the tank are;

The radius of the tank = 70 feet

The volume of a sphere = 4/3·π·r³

Therefore, the volume of a quarter sphere = 1/4×The volume of a sphere

The volume of a quarter sphere = 1/4×4/3·π·r³ = π·r³/3

Plugging in the value for the radius gives

Volume = π×70³/3 = 114,333.33×3.14 = 359,006.7≈ 359,007 ft³.

Part 2:

The dimension of the scale model  = 1/6 × Actual dimension

Therefore, we have the radius of the sphere of the scale model = 1/6 × 70

Which gives;

The radius of the sphere of the scale model = 35/3 = 11.67 feet

The volume of the scale model = π·r³/3 = (3.14×11.67³)/3 = 1662.07 ≈ 1662 ft³

The number of times smaller the scale model is than the actual volume = (Actual volume)/(Scale model) = (359,007 ft³)/(1662 ft³) = 216 times

The number of times smaller the scale model is than the actual volume =  216 times = (1/Scale of model)³ = (1/(1/6))³ = 6³.

Part 3:

The percentage of the mock-up, x, to the volume of the actual tank is given as follows

x/100 ×  1662  = 359,007

∴ x = 216 × 100 = 21600%

The percentage of the mock-up, to the volume of the actual tank is 21600%.
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