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Vikki [24]
4 years ago
13

A boat travels upstream for 96 miles in 4 hours and returns in 3 hours traveling downstream in a river. What is the rate of the

boat in still water and what is the rate of the current?
Mathematics
1 answer:
Dahasolnce [82]4 years ago
6 0

Answer:

Speed of boat in still water = 28 miles/hr

Speed of current = 4 miles/hr

Step-by-step explanation:

Speed upstream, u = 96/4 = 24 miles/hr

Speed downstream, v = 96/3 = 32 miles/hr

Speed of boat in still water = ½(v+u)

= ½ (24 + 32) = 28 miles/hr

Speed of the current = ½ ( v - u)

= ½ (32 - 24) = 4 miles/hr

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What is the value of x <br><br> A. 20<br> B. 34<br> C. 60<br> D. 69
Grace [21]

Answer:

A

Step-by-step explanation:

The given angles are vertical and thus congruent, so

3x = x + 40 ( subtract x from both sides )

2x = 40 ( divide both sides by 2 )

x = 20 → A

4 0
4 years ago
The figure is made up of a cylinder and a hemisphere. To the nearest whole number, what is the approximate volume of this figure
Novosadov [1.4K]

Hello!

The figure is made up of a cylinder and a hemisphere. To the nearest whole number, what is the approximate volume of this figure?  

Use 3.14 to approximate π .  


Enter your answer in the box.  in.³

Data: (Cylinder)

h (height) = 7 in

r (radius) = 2.5 in (The diameter is 5 being twice the radius)

Adopting: \pi \approx 3.14

V (volume) = ?

Solving: (Cylinder volume)

V = \pi *r^2*h

V = 3.14 *2.5^2*7

V = 3.14*6.25*7

V = 137.375 \to \boxed{V_{cylinder} \approx 137.38\:in^3}

Note: Now, let's find the volume of a hemisphere.

Data: (hemisphere volume)

V (volume) = ?

r (radius) = 2.5 in (The diameter is 5 being twice the radius)

Adopting: \pi \approx 3.14

If: We know that the volume of a sphere is V = 4* \pi * \dfrac{r^3}{3} , but we have a hemisphere, so the formula will be half the volume of the hemisphere V = \dfrac{1}{2}* 4* \pi * \dfrac{r^3}{3} \to \boxed{V = 2* \pi * \dfrac{r^3}{3}}

Formula: (Volume of the hemisphere)

V = 2* \pi * \dfrac{r^3}{3}

Solving:

V = 2* \pi * \dfrac{r^3}{3}

V = 2*3.14 * \dfrac{2.5^3}{3}

V = 2*3.14 * \dfrac{15.625}{3}

V = \dfrac{98.125}{3}

\boxed{ V_{hemisphere} \approx 32.70\:in^3}

Now, to find the total volume of the figure, add the values: (cylinder volume + hemisphere volume)

Volume of the figure = cylinder volume + hemisphere volume

Volume of the figure = 137.38 in³ + 32.70 in³

Volume\:of\:the\:figure =170.08 \to \boxed{\boxed{\boxed{Volume\:of\:the\:figure = 170\:in^3}}}\end{array}}\qquad\quad\checkmark

_______________________

I Hope this helps, greetings ... Dexteright02! =)

5 0
3 years ago
Read 2 more answers
Assume that adults have IQ scores that are normally distributed with a mean of and a standard deviation . Find the probability t
Tcecarenko [31]

Answer:

the probability when the IQ is lower than 136 is 0.9641

Step-by-step explanation:

Given that

The mean is 100

The standard deviation is 20

We need to find out the probability when the IQ is lower than 136

So,

z value equivalent to 136 = (136 - 100)  ÷ 20 = 1.8

Now  

p (z < 1.8) = 0.9641

hence, the probability when the IQ is lower than 136 is 0.9641

3 0
3 years ago
1 (4 x 12) + (4 x 8) 2 4 x (12 - 8) 3 (4 x 12) - ( 4 x 8) 4 4 x (12 + 8)
jenyasd209 [6]

Answer: 4 x (12 - 8)

Step-by-step explanation:

the word difference really means exactly what it is saying. it is the quantity difference between two numbers. like, if someone would say, "what's the difference between 4 and 2?' then you would just subtract 2 from 4 to find the difference between the two numbers.

so, we now know that we are going to be subtracting 8 from 12.

plus, it tells us to show 4 times 12 - 8. that means that we will be multiplying (12 - 8) by 4.

so, our only viable option is 4 x (12 - 8).

4 0
3 years ago
Recognizing the no-solution case algebraically <br> need geometry help!!
Dmitrij [34]

Answer:

"The values for y are square roots of negative numbers"

Step-by-step explanation:

The steps shown are correct. But at the end we can see that we have to <em><u>"take the negative square roots"</u></em>.

This means we have to take the square root of -1. In the real number system, we CANNOT take the square root of any negative number. Hence, there is NO SOLUTION to the system.

2nd answer choice, "The values for y are square roots of negative numbers", is right.

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3 years ago
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