MATHEMATICS MIDDLE SCHOOL

What is the value of x?

5.6/8=x/24

Answers

Answer 1
Answer: Cross \ Multiply: \n\ 8x = 134.4 \n\ x = 16.8
Answer 2
Answer: The answer is 16.8. Do you need to know how?

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The speed of a stream is 4 mph. A boat travels 8 miles upstream in the same time it takes to travel 16 miles downstream. what is the speed of the boat in still water

Answers

Answer

Find out the speed of the boat in still water .

To proof

Let us assume that the speed of the boat in still water be u .

As given

The speed of a stream is 4 mph

hence

speed upstream = u - 4

speed downstream = u + 4

Formula

Time = (Distance)/(speed)

As given

A boat travels 8 miles upstream in the same time it takes to travel 16 miles downstream.

First case for the upstream

Time = (8)/(u - 4)

Second case for the downstream

Time = (16)/(4 + u)

now compare the equations

(8)/(u - 4) = (16)/(u + 4)

simplify the equation

8( u +4 ) = 16 (u -4)

8u +32 = 16u - 64

8u = 96

u = (96)/(8)

u = 12 mph is the speed of the boat in still water .

Hence proved





   

   

The speed of the stream = 4 mph.

Let us assume speed of the boat in still water = x mph.

Total speed upstream = (x-4) mph.

Total speed downstream = (x+4) mph.

We know,  time, speed and distance relation.

Time = Distance / Speed.

Total time taken upstream = 8 / (x-4)

Total time taken downstream = 16/(x+4).

Time taken upstream = time taken downstream.

Therefore,

8 / (x-4)  =  16/(x+4).

On cross multiplication, we get

16(x-4) = 8(x+4).

16x - 64 = 8x +32.

Adding 64 on both sides, we get

16x - 64+64 = 8x +32+64

16x = 8x + 96.

Subtracting 8x from both sides, we get

16x-8x = 8x-8x + 96.

8x = 96.

Dividing both sides by 8, we get

x = 12.

Therefore, 12 mph is the speed of the boat in still water.

ms tao flies roundtrip twice yearly between jacksonville and los angeles on business the distance between the two cities is 2,150 miles. estimate the distance she flies for both trips. then find the exact distance

Answers

The answer is about 4,300 miles because from Jacksonville to Los Angles is 2,150 miles plus,going back another 2,150 miles.

2 13/18 −z=1 19/36

Answer

Answers

Answer:

Answer is z= 43/36

Step-by-step explanation:

We have given,

2 13/18 - z = 1 19/36

Since 2 13/18 = 49/18  and 1 19/36 = 55/36

So we can write,

2 13/18 - z = 1 19/36

or 49/18 - z = 55/36

or 49/18 - 55/36 = z

or (98 -55)/36 = z

or 43/36 = z

Hence we got z = 43/36

The Gonzalez family is taking a cruise that costs $3,082.24 for a family of four. How much does it cost perperson?

Answers

$770.56 per person. You take the total cost of the cruise and divide it by 4. 

Find the variance and standard deviation of the given set of data to the nearest tenth.{440, 130, 280, 500, 150, 640, 760}


A) variance = 222.7, standard deviation = 49,595.9

B) variance = 49,595.9, standard deviation = 24,798

C) variance = 49,595.9, standard deviation = 222.7

D) variance = 57,861.9, standard deviation = 240.5

Answers

Answer:

Part 1) variance = 49,595.9

Part 2) standard deviation = 222.7

Option C

Step-by-step explanation:

we have

set of data [440,130,280,500,150,640,760]

step 1  

Find the mean  

Adds the values and divide by the number of values

In this problem the number of values is 7

[440+130+280+500+150+640+760]/7

[2,900]/7=414.3

step 2  

for each number: subtract the Mean and square the result  

(440-414.3)^(2)=660.49\n (130-414.3)^(2)= 80,826.49\n (280-414.3)^(2)= 18,036.49\n (500-414.3)^(2)= 7,344.49\n (150-414.3)^(2)= 69,854.49\n (640-414.3)^(2)= 50,940.49\n (760-414.3)^(2)=119,508.49

step 3  

work out the mean of those squared differences  

[660.49+80,826.49+18,036.49+7,344.49+69,854.49+50,940.49+119,508.49]/7=347,171.43/7=49,595.9 ----> this value is called the "Variance"  

step 4

The standard deviation is the square root of the variance

so

The standard deviation is equal to

√(49,595.9)=222.7

If you flip three fair coins what is the probability that the two first flips will both be heads, and the third flip will be either heads or tales?

Answers

Answer:

The probability that a coin flip is a head or a tail is 0.5. The probability that a coin flip is either a head or a tail is 1. The probability that a three-coin-flip is two heads and a head or a tail is 0.25.

Step-by-step explanation:
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