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3 years ago

A boat makes a 120-mile trip downstream in 3 hours but makes the return trip in 4 hours. What is the rate of the current?

2 answers:

8 0

With the current 40 miles per hour
Against the current 30 miles per hour
bv means boat velocity with NO current
cv means current velocity
A) bv + cv = 40 mph
B) bv - cv = 30 mph
Adding both equations:
2bv = 70
boat velocity with NO CURRENT = 35 miles per hour

Using equationA
bv + cv = 40
35 + cv = 40

current velocity = 5 miles per hour

Alchen [17]3 years ago

5 0

Answer:

Speed of current = 5 mph

Step-by-step explanation:

Let u be the speed of boat and v be the speed of current.

A boat makes a 120-mile trip downstream in 3 hours.

120 = 3(u+v)

u + v = 40

It makes the return trip in 4 hours.

120 = 4(u-v)

u - v= 30

Adding both equations

u + v + u - v = 40+30

2u = 70

u = 35 mph

35 + v = 40

v = 5 mph

Speed of current = 5 mph

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What is the answer to (x + 7) + 3y

Oduvanchick [21]

Answer:

4y+7

Step-by-step explanation:

there is no way of knowing what y is

3 0

3 years ago

(2) Using the distance formula, d = √(x2 - x1)2 + (y2 - y1)2, what is the distance between point (-2, 2) and point (4, 4) rounde

monitta

Using the distance formula, $d = \sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2 } \\$ , what is the distance between point (-2, 2) and point (4, 4) rounded to the nearest tenth?

Using the points given, plug them into the equation.

$d = \sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2 } \\d = \sqrt{((4) - (-2))^2 + ((4) - (2)^2 } \\d=\sqrt{(4+2)^2 + (4-2)^2}\\d=\sqrt{(6)^2 + (2)^2} \\d=\sqrt{36+4} \\d=\sqrt{40} \\$

Plug this into a calculator and you get 6.32455532

Since you only need it up to the tenth (0.1), round up 6.32

Since two is lower than four, we drop it.

Therefore, the distance between points (-2, 2) and (4, 4) is 6.3

Hope this helps ^w^

8 0

3 years ago

Solve the inequality <br> x-2>15

creativ13 [48]

Answer:

Inequality Form: x > 17

Interval Notation: (17, ∞)

7 0

1 year ago

Justin has $7.50 more than Eva, and Emma has $12 less than Justin. Together , they have a total of 63.00. How much money does ea

Setler [38]

Since no value is given to Eva, we'll call her x. Justin, then, is 7.50+x. That leaves Emma, who would be Justin (7.50+x) -12. If we add them all together we get 63. So our equation is

x + (7.50+x) + (7.50+x)-12 = 63

Combine like terms

x+x+x + 7.50+7.50-12 = 63
3x + 3 = 63
3x = 60
x = 20

Since we said Eva is x then Eva has 20 dollars.

Justin is 7.50 + x so 7.50+20=
$27.50

Emma is Justin - 12 so 27.50-12= $15.50

Let's check our answer...

15.50+27.50+20 = 63
63=63

It checks!

4 0

4 years ago

A simple random sample from a population with a normal distribution of 98 body temperatures has x =98.90 °F and s =0.68°F. Const

Ludmilka [50]

Answer:

$0.609 \leq \sigma \leq 0.772$

And the best conclusion would be:

D. This conclusion is safe because 1.40 °F is outside the confidence interval.

Step-by-step explanation:

1) Data given and notation

s=0.68 represent the sample standard deviation

$\bar x =98.90$ represent the sample mean

n=98 the sample size

Confidence=90% or 0.90

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population mean or variance lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

The Chi Square distribution is the distribution of the sum of squared standard normal deviates .

2) Calculating the confidence interval

The confidence interval for the population variance is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

$df=n-1=98-1=97$

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical values.