A motorboat travels 116 kilometers in 4 hours going upstream. It travels 164 kilometers going downstream in the same amount of time. What is the rate of the
boat in still water and what is the rate of the current?
Rate of the boat in still water:
Rate of the current:

Answer:

1 7/8

Step-by-step explanation:

Answer:

[tex] - 4x + 5 - (6x + 7) = 0\\ - 4x + 5 - 6x - 7 = 0 \\ - 10x - 2 = 0 \\ 10x + 2 = 0 \\ 10x = - 2 \\ x = \frac{ - 2}{10} \\ x = - .2 \\ thank \: you[/tex]

Answer:

5 ft

Step-by-step explanation:

Using the formula,

A = 6a²

a² = A/6

a = √(A/6)

a =√(150/6)

a = √25

a = 5

The area of a 2D form is the amount of space within its perimeter. The length of the edge of the cube is 5 ft. The correct option is B.

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

The total surface area of a cube is 6 times the area of a face which is equal to the square of side of the cube. Therefore, the total surface area of the cube is,

Total surface area of cube = 6a²

Given that the total surface area of the cube is 150 square feet. Therefore,  the length of the side of the cube can be written as,

Total surface area of cube = 6a²

150 square feet = 6a²

150 square feet / 6 = a²

25 ft² = a²

a = √(25 ft²)

a = 5 ft

Hence, the length of the edge of the cube is 5 ft.

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Answer:

D. (x+2)(-8x+70)​

Step-by-step explanation:

-8x^2+54x+140

Factor out -2

-2(4x^2+27x+70)

Factor

-2(x+2)(4x-35)

Option D is the same answer if we multiply -2 in the second term

(x+2) (-8x+70)

Answer:

12.7 m

Step-by-step explanation:

use pythagorean theorem

[tex]13^{2} + b^{2} = 18.2^{2}[/tex]

rounds to 12.73735

not fully sure if that's right

Answer:

105+105+2x=360 and x=75

Step-by-step explanation:

z=75

Answer:

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

(2 x 6) - 9 = 12 - 9 = 3

Answer:

25

Step-by-step explanation:

Answer:

21 answers.

Step-by-step explanation:

First, change the percentage into a decimal point. Move the decimal point to the left two place values and drop the percentage sign:

70% = 70/100 = 0.70

Next, multiply 0.70 with the total amount of questions (30):

30 x 0.70 = 21

21 answers must be correct.

Check:

Divide 21 with 30:

21/30 = 0.70 = 70%

~

Answer:

1they are 15 kilometers apart

Answer:

Step-by-step explanation:

[tex](-\frac{1}{3} \sqrt{\frac{7}{2} } )^2+(\frac{1}{3} \sqrt{\frac{13}{2} } )^2\\=\frac{1}{9} (\frac{7}{2} +\frac{13}{2} )\\=\frac{1}{9} (\frac{7+13}{2} )\\=\frac{1}{9} \times10\\=\frac{10}{9} \neq 1[/tex]

not a unit vector.

b.

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

it is a unit vector.

c.

[tex](\frac{1}{2} \sqrt{\frac{5}{3} } )^2+(-\frac{1}{2} \sqrt{\frac{7}{3} } )^2\\=\frac{1}{4} (\frac{5}{3} +\frac{7}{3} )\\=\frac{1}{4} (\frac{5+7}{3} )\\=\frac{1}{4} (\frac{12}{3} )\\=\frac{1}{4} (4)\\=1[/tex]

it is a unit vector.

d.

[tex](\frac{3}{\sqrt{7} } )^2+(-\frac{2}{\sqrt{7} } )^2\\=\frac{9}{7} +\frac{4}{7} \\=\frac{9+4}{7} \\=\frac{13}{7} \neq 1[/tex]

it is not a unit vector.

Step-by-step explanation:

2t/r=d cross multiply

2t=rd

t=rd/2

3250 mL = 3.25 L

* 1 mL = 0.001 L

I hope I helped you^_^

Answer:

26) 1/2 b×h

= 1/2(8×9)

=1/2(72)

=36

27)1/2b×h

=1/2(12×15)

=1/2(180)

=90

28)a÷b×2

=(60÷8)×2

=15

29)1/2b×h

=1/2(16×1/2)

=1/2(8)

=4

30)1/2b×h

=1/2(18×12)

=1/2(216)

=108

Answer:

10 3/5

Step-by-step explanation:

6 4/5 + 3 4/5

First convert to improper fraction,

34/5 + 19/5

Then add the improper fractions,

=>53/5

Then convert improper fraction to mixed fraction,

=> 53/5 = 10 3/5

Answer:

d

Step-by-step explanation:

It is a 1/13 chance but even if you shuffle and replace it, its still a 1/13 chance.

The probability that John draws a jack on the first try is 1/13. If John replaces the card, re-shuffles, and draws again, the probability that he will pull another jack stays the same. Hence, statement d is correct.

The probability of an event is the ratio of the number of favorable outcomes to the event to the total number of outcomes for the experiment.

If we have an event A, the number of favorable outcomes to event A is n, and the total number of outcomes in the experiment is S, then the probability of the event A is given by,

P(A) = n/S.

We are given that John is playing a game with a standard deck of playing cards.

We are said that he wants to try to draw a jack on the first try.

Let the event of drawing a jack be A.

The number of outcomes favorable to the event A (n) = 4 (number of jacks)

The total number of outcomes in the experiment of drawing a card (S) = 52 (the total number of cards)

∴ The probability of the event A is given by,

P(A) = n/S = 4/52 = 1/13.

∴ The probability of drawing a jack on the first try is 1/13.

When he replaces the card and re-shuffles it, the probability will be the same as the number of favorable outcomes and the total number of outcomes remains the same.

∴ The probability that John draws a jack on the first try is 1/13. If John replaces the card, re-shuffles, and draws again, the probability that he will pull another jack stays the same. Hence, statement d is correct.

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9514 1404 393

Answer:

  multiple solutions, see the attachment

Step-by-step explanation:

If you allow any digits 0-9, there are 11 possible solutions. Of these, two have the leading digit O = 0, so you may not agree that is an allowable solution.

Each row in the attachment is a possible solution. (Rows 4 and 10 have O=0.)

__

Found by exhaustive search using a computer program. Note that E=7 and N=1 are not hard to find by hand.

Answer:

Step-by-step explanation:

Start by calculating the effective rate of interest:

.09/52= .0017307

(we divide by 52 because there are 52 weeks in a year)

Then just use the annuity formula

[tex]1600(\frac{1-(1+.0017307)^{-(20*52)}}{.0017307})=771396.864393[/tex]

9514 1404 393

Answer:

  (c)  y = 3|x| + 5

Step-by-step explanation:

The vertex is at (0, 5), so the basic function has been translated up 5 units.

The slope of each line has a magnitude of 3, so the basic function has been scaled vertically by a factor of 3.

The transformation ...

  g(x) = c·f(x) +h

is a vertical scaling by a factor of c, and a translation upward by h units. Here, we have c=3 and h=5. The basic function is f(x) = |x|, so the transformed function shown on the graph is ...

  y = 3|x| +5

Answer:

C. $11.55

Step-by-step explanation:

First, multiply 4 by $0.85 to get an answer of $3.40. Next, multiply 6 by $1.25 to get an answer of $7.50. Add up the cost of the pencils and pens by adding $3.40 and $7.50 to get $10.90. Next, we have to add the tax. Multiply $10.90 by 0.06 to get $.65. Add the $.65 to the $10.90 for a grand total of $11.55. Hope this helps!

Step-by-step explanation:

For TU is it -2x-4 or 2x-4 cause the question and what on your paper are different

Answer:

20

Step-by-step explanation:

ST= SU - TU

=24 - (2x-4)

=24-2x+4=28-2x

but. 2x-4+3x+8 = 5x+4 = 24

5x=24-4=20

x=20/5=4

so ST=28-2x= 28-2(4)

ST=20

Answer:

x = 1

Step-by-step explanation:

2/x = 2^(x)

x = 1

hope that helps

Answer:

The choose A.

y= – | x+1|–4

I hope I helped you^_^

9514 1404 393

Answer:

  19.3 g/cm³

Step-by-step explanation:

There are 2.54 cm in one inch, so the weight of 1 cm³ is ...

   (316 g/in³) ÷ (2.54 cm/in)³ = 19.3 g/cm³

Answer:

The coordinates of a point are a pair of numbers that define its exact location on a two-dimensional plane.

Answer:

Step-by-step explanation:

Start a little more generally. Carefully find k

distance = k * speed ^2      

112 = k*40^2

112 = k * 1600                     Divide by 1600

112/1600 = k

k = 0.07

Now do the question you are asked to do.

distance = k * speed^2

distance = 0.07 * 65^2

distance = 295.75

Now having done that, you can set up a proportion.

d1 / d2 = k speed1^2/kspeed2^2      Cancel the ks

112/d2 = 40^2 / 65^2                         Cross multiply

112 * 65^2 = 40^2 * d2                      Divide by 40^2

112 * 65^2/40^2 = d2                        Expand the squares

112 * 4225 / 1600 = d2

295.75 = d2    

The second way is shorter, but I suggest the long way until you get comfortable with it.

Answer:

-35

Step-by-step explanation:

-(18+17)

-35

that should be the answer but don't quote me on it