a boat travels upstream for 108 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 in the current?

Answer:

Step-by-step explanation:

f(7) = 32

f(-9) = 32

f(s) = 32

f(s-t) = 32

g(7) = 10·7+4 = 74

g(-9)  = 10(-9)+4 = -86

Answer:

1) The expected value of the number of moving violations for which the individual was cited during the last 3 years is 1

2) The expected amount of surcharges is $250

Step-by-step explanation:

Given that;

Y      0           1       2        3         4

p(y) 0.50   0.20   0.15   0.10   0.05

1)

Value of E(Y)

E(Y) = (0×0.50) + ( 1×0.20) + ( 2×0.15) + (3×0.10) + (4×0.05)

= 0 + 0.20 + 0.3 + 0.3 + 0.2

E(Y) = 1

Therefore, The expected value of the number of moving violations for which the individual was cited during the last 3 years is 1

b)

Suppose an individual with Y violations incurs a surcharge of $100Y² , the expected amount of the surcharge is given by,

E($100Y²) = 100E(Y)²

= 100∑Y²P(y)

= 100(0²×0.50) + ( 1²×0.20) + ( 2²×0.15) + (3²×0.10) + (4²×0.05)

= 100( 0 + 0.2 + 0.6 + 0.9 + 0.8 )

= 100(2.5)

= $250

Therefore; The expected amount of surcharges is $250

Answer:

-4 and any number above.

Answer:

3/24 + 4/24 = 7/24

Step-by-step explanation:

Find a common denominator then multiply the numerator by how many times you multiplied the denominator and add them to get your answer and you may simplify.

Answer:

5.5%

Step-by-step explanation:

Given data

Simple interest =  $137.50

Principal= $500

time = 5 years

We want to find the rate  R

Simple interest= PRT/100

137.50 = 500*R*5/100

137.50=2500R/100

cross multiply

137.5*100= 2500R

13750= 2500R

divide both sides by 2500

R= 13750/2500

R=5.5%

Hence the rate is 5.5%

Answer:

s e([tex]p^{-} _{1} - p^{-} _{2}[/tex] ) =  0.07576

Step-by-step explanation:

Step(i):-

The  proportion of the first sample

      [tex]p^{-} _{1} = \frac{x_{1} }{n_{1} } = \frac{23}{53} = 0.43396[/tex]

The proportion of the second sample

      [tex]p^{-} _{2} = \frac{x_{2} }{n_{2} } = \frac{48}{178} = 0.2696[/tex]

Step(ii):-

Standard Error of ([tex]p^{-} _{1} - p^{-} _{2}[/tex]) is determined by

[tex]se(p^{-} _{1} - p^{-} _{2}) = \sqrt{\frac{p^{-} _{1} (1-p^{-} _{1} )}{n_{1} }+\frac{p^{-} _{2}(1-p^{-} _{2} ) }{n_{2} } }[/tex]

[tex]se(p^{-} _{1} - p^{-} _{2}) = \sqrt{\frac{0.43396) (1-0.43396 )}{53 }+\frac{0.2696(1-0.2696 ) }{178} }[/tex]

on simplification, we get

s e([tex]p^{-} _{1} - p^{-} _{2}[/tex] ) =  0.07576

Answer:

I think it's the 3 one if in wrong I'm sorry

Answer:

A(n) = a + (n - 1)d is the correct formula for an arithmetic sequence.

Step-by-step explanation:

Answer:

90

Step-by-step explanation:

This is an increasing sequence, with -9 as its first term. The first increase is +3, then +5, +7, and +9. The differences increase by 2 each time. The sixth term will be 15 + 11, and the seventh would be 15 + 11 + 13. We can follow this pattern to get to the tenth term. 15 + 11 + 13 + 15 + 17 + 19 = 90

Answer:

60 + 2 + 0.8 +0.03 +0.007

Step-by-step explanation:

Add these up and yo get the same number: 62.837.

Answer:

The answer is below

Step-by-step explanation:

Given that the length of the plastic string is 3 3/4 feet = 15 / 4 feet.

Bracelets of 5/8 foot long is needed to be made. To determine the maximum number of bracelets that can be made; using the number line, 5/8 is subtracted repeated times from 15/4.

We can see that when 5/8 is subtracted 6 times from 15/4, the result is 0.

15/4 ÷ 5/8 = 6

Hence Tara can make 6 bracelets from the plastic sting.

Answer: 8x+2

explanation:

i just solved it

Answer:

8x - 15

Step-by-step explanation:

(2x + 5)(4x -3)

distribute ur numbers

2x * 4x = 8x

5 * -3 = -15

now ur left with 8x - 15 and that is ur answer

Answer:

Step-by-step explanation:

9514 1404 393

Answer:

  468

Step-by-step explanation:

Men:

  (3/4)(2/5)(600) = (6/20)(600) = 6(30) = 180 men over 30

Women:

  (4/5)(3/5)(600) = (12/25)(600) = 48(6) = 288 women over 30

The total number of members over 30 is ...

  180 +288 = 468 . . . members over 30

Answer:

The volume is: [tex]V = \frac{\pi}{3}[/tex] cubic units

Step-by-step explanation:

Volume of a solid:

The volume of a solid, given by the function f(x), over an interval between a and b, is given by:

[tex]V = \pi \int_{a}^{b} (f(x))^2 dx[/tex]

y = x, y =1, x = 0

This means that the upper function is y = 1, and the lower function is y = x. So

[tex]f(x) = (1 - x)[/tex]

The lower limit of integration is x = 0.

The upper limit is y = x when y = 1, so x = 1.

Then

[tex]V = \pi \int_{a}^{b} (f(x))^2 dx[/tex]

[tex]V = \pi \int_{0}^{1} (1-x)^2 dx[/tex]

[tex]V = \pi \int_{0}^{1} (1-2x+x^2) dx[/tex]

[tex]V = \pi (x-x^2+\frac{x^3}{3})|_{0}^{1} dx[/tex]

[tex]V = \pi(1 - (1^2) + \frac{1^3}{3})[/tex]

[tex]V = \frac{\pi}{3}[/tex]

Answer:

2

Step-by-step explanation:

Answer:

Volume of the cylinder = 602.88 square centimeters

Step-by-step explanation:

Given that:

Radius of cylinder = 4 cm

Height of cylinder = 12 cm

Volume of a cylinder is given by the following formula;

Volume = πr²h

Putting π = 3.14, r = 4 and h = 12 in the formula

Volume = 3.14 * (4)² * 12

Volume = 3.14 * 16 * 12

Volume = 602.88 square centimeters

Hence,

Volume of the cylinder = 602.88 square centimeters

Answer:

216 m

Step-by-step explanation:

12/4= x/6

3=x/6

x=3x6

length= 18

area=length x width

12x18=216

The required measure of the radius inscribed in the triangle RST is 11.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

Here,
The incenter of the triangle will be the center of the circle inscribed in the triangle. and radius will be the perpendicular distance from the incenter to the sides.
So,
XU = XW,
-2y + 15 = 3y +5
5y = 10
y = 2

Now,
Radius = XU
          = -2(2) + 15
          = 11

Thus, the required measure of the radius inscribed in the triangle RST is 11.

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1n=n Answer:

Step-by-step explanation:

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Answer:

A) 1000/1 = x/2500 is the answer

Answer:

[tex]\Large \boxed{-3, \ 5,\ 13,\ 21}[/tex]

Step-by-step explanation:

A function is given

[tex]f\left(x\right)=4x+1[/tex]

Plug values of x and evaluate

[tex]f\left(x\right)=4\left(-1\right)+1=-3[/tex]

[tex]f\left(x\right)=4\left(1\right)+1=5[/tex]

[tex]f\left(x\right)=4\left(3\right)+1=13[/tex]

[tex]f\left(x\right)=4\left(5\right)+1=21[/tex]

Answer:

Solution given:

f(x)=4x+1

f(-1)=-4+1=-3

f(1)=3+1=5

f(3)=4×3+1=13

f(5)=4×5+1=21

Answer:

The amount of sale is approximately 5714.

Step-by-step explanation:

Let x be the sales made that will result to the same salary and let y be the same weekly salary.

We can represent both salaries as follows:

300 + 0.04x = y

100 + 0.075x = y

Subtracting the second equation from the first, we have:

200 – 0.035x = 0

0.035x= 200

x = 200/0.035

x ≈ 5714.

Therefore, the amount of sale is approximately 5714.

Answer:

abc

Step-by-step explanation:

Answer:

Step-by-step explanation:

it a

Dave’s commission be for the month for sales worth $7000 is $900.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, Dave receives 10% commission on his first $5000 and receives 20% commission on any sales beyond the first $5000.

He made sales worth $7000 this month,

Therefore, For the first $5000 he receives,

= (10/100)×5000.

= $500.

And for the rest (7000 - 5000) = $2000 he receives,

= (20/100)×2000.

= $400.

So, In total, he received (500 + 400) = $900

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Answer:

0.32

Step-by-step explanation:

just divide

Answer:

$6

Step-by-step explanation:

25%= 1/4

8 divided by 4 =2

$2 is what is taken off

$8-$2 which is $6

answer is 13

I hope it helpful

Answer:

The value of p² + r³, when p = 2 & r = 3

(2)²+(3)³=4+27=31