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2 years ago

What is the rate of the boat in still water and what is the rate of the current?

Mathematics

1 answer:

Alekssandra [29.7K]2 years ago

4 0

Answer: 2mp

Step-by-step explanation: Let "b" represent the speed of the boat in still water

Let "c" represent the speed of the current

Let "t" represent time

Downstream(same direction) =(b+c)*t

Upstream(against current)=(b-c)*t

(b+c)*3=24

(b-c)*4=16

3b+3c=24....all sides can be divided by 3 =b+c=8

4b-4c=16.....all sides can be divided by 4 =b-c=4

Use Elimination method

b+c=8

b-c= 4 Subtracting

=====

2c=4

find c by dividing both sides by 2. c=2

if c=2, substitute to get b

b+2=8

-2=-2

======

b=6

Speed of boat in still water =6mph

rate of current=2mp

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Imagine that the intelligence test score (M=100, SD =15) is perfectly correlated with SAT score. Your Z score on SAT is +1.0, yo

Oksanka [162]

Answer:

115

Step-by-step explanation:

Given :

Mean of intelligence score = 100

Standard deviation of intelligence score = 15

Since both are perfectly correlated,

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Using the standard normal interpretation, Xcore on SAT of +1.0 means 1 standard deviation to the right

This means :

Mean + 1 standard deviation

100 + 1*15

= 115

We could use the Zscore formula directly too:

Zscore = (x - mean) / standard deviation

Zscore = +1 ; x = score

Hence, we have

1 = (x - 100) / 15

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3 years ago

Is 0.2971 irrational?

Vladimir [108]

Answer:

Yes

Step-by-step explanation:

An irrational number can be written as a decimal, but not as a fraction. An irrational number has endless non-repeating digits to the right of the decimal point.

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3 years ago

In the clip from the Simpsons, Ralph charges Bart twice the fair from Tucson to Flagstaff, minus 2/3 the fair from Albuquerque t

cluponka [151]

Answer:

$20.

Step-by-step explanation:

Given:

In the clip from the Simpsons, Ralph charges Bart twice the fair from Tucson to Flagstaff, minus 2/3 the fair from Albuquerque to El Paso.

It costs $40 to travel from Tucson to Flagstaff,

And $90 to travel from Albuquerque to El Paso.

Question asked:

How much does Bart need to pay ?

Solution:

Fair to travel from Tucson to Flagstaff = $40

Fair to travel from Albuquerque to El Paso = $90

<u>As Ralph charges Bart twice the fair from Tucson to Flagstaff, minus 2/3 the fair from Albuquerque to El Paso. </u>

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3 years ago

For how many three digit numbers (100 to 999) is the sum of the digits even? (For example, 343 has an even sum of digits: 3 + 4

n200080 [17]

Answer:

there are 425 numbers of three digits whose the sum of the digits is even.

Step-by-step explanation:

Option 1:

It is necessary to accomplish one of the next conditions:

(1) all of the digits are even.

(2) exactly 2 of the digits are odd

Then, for the first condition:

4x5x5 = 100 -> this is because the first digit can not be 0.

for the second condition:

(3C1)*5*5*5-1*5*5 =3*125-25=350

where 3C1 is a combination. The 3C1 determines which of the three digits is even, and it is necessary to subtract the numbers under 100 with the other 2 digits odd.

So, there are 450 numbers of three digits whose the sum of the digits is even.

Option 2:

there are 900 three digit number and 5*5*5 =125 has 3 odd numbers and 5*5*5+4*5*5+4*5*5=325 has 1 odd number, so there are 450 numbers of three digits whose the sum of the digitis is odd, so 900-450 whose the sum of the digits is even.

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3 years ago

The function f(x) = x2 - 6x + 9 is shifted 5 units to the left to create g(x). What is g(x)?

creativ13 [48]

Answer:

g(x) = x^2 + 4x + 4

Step-by-step explanation:

In translation of functions, adding a constant to the domain values (x) of a function will move the graph to the left, while subtracting from the input of the function will move the graph to the right.

Given the function;

f(x) = x2 - 6x + 9

a shift 5 units to the left implies that we shall be adding the constant 5 to the x values of the function;

g(x) = f(x+5)

g(x) = (x+5)^2 - 6(x+5) + 9

g(x) = x^2 + 10x + 25 - 6x -30 + 9

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3 years ago