A motor boat travels 60 miles down a river in 3 hours but takes 5 hours to return upstream. Find the rate of the boat in still water and the rate of the current.

Answer:

84 Passengers

Step-by-step explanation:

30/100(280)

= 3/10(280)

= 84

Answer:

84

Step-by-step explanation:

30/100x280

So 84 is the answer

A negative x is to the left of the y axis and a negative y value is below the x axis. Any value to the left and below the axis’ will be in the 3rd quadrant.

Answer: 3rd quadrant

Answer:

48

Step-by-step explanation:

the answer is 48 I got this answer by multiplying 5 by 10 and subtracting is from 2 which gives me 50 - 2 which is 48

Answer:

48

Step-by-step explanation:

5×10-2=50-2

=48

hope it helps!!

Answer:

P(A or B) = 1.16

Step-by-step explanation:

Given probability:

Probability of event A = P(A) = 0.46

Probability of event B = P(B) = 0.7

P(A and B) = 0.43

Find:

P(A or B)

Computation:

If A is an incident and B is a separate event, P(A or B) is the possibility of either A, B, or both events occurring.

P(A or B) = P(A) + P(B)

P(A or B) = 0.46 + 0.7

P(A or B) = 1.16

Answer:

54 m^3

Step-by-step explanation:

this is the answer = 54 m^3

Volume of the rectangular pyramid will be 54[tex]m^{3}[/tex].

Rectangular pyramid has 5 faces where one face is rectangular which is at bases and other 4 faces are triangular which is connected at the one point .

If we assume that l is the length of the base and b is the width of the base and h is height of the rectangular pyramid then we can calculate the volume of the rectangular pyramid using the formula stated below

                 Volume of the rectangular pyramid = V=  (1/3)×l×b×h

According to the asked question

l = 6m

b = 3m

h = 9m

then we can calculate the volume of the rectangular pyramid by using the above formula

= V=  (1/3)×l×b×h

= (1/3)×6m×3m×9m

= 54[tex]m^{3}[/tex]

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Answer:

The equation of the line is [tex]y + 7 = -\frac{1}{3}(x - 9)[/tex]

Step-by-step explanation:

Equation of a line:

The equation of line, in point-slope form, is given by:

[tex]y - y_0 = m(x - x_0)[/tex]

In which m is the slope and the point is [tex](x_0, y_0)[/tex]

Perpendicular lines:

If two lines are perpendicular, the multiplication of their slopes is -1.

Through (9,-7)

This means that [tex]x_0 = 9, y_0 = -7[/tex]

So

[tex]y - y_0 = m(x - x_0)[/tex]

[tex]y - (-7) = m(x - 9)[/tex]

[tex]y + 7 = m(x - 9)[/tex]

Perpendicular to y = 3x + 4

This line has slope 3, so:

[tex]3m = -1[/tex]

[tex]m = -\frac{1}{3}[/tex]

Thus

[tex]y + 7 = m(x - 9)[/tex]

[tex]y + 7 = -\frac{1}{3}(x - 9)[/tex]

Answer:

[tex]\sqrt{\left(4-1\right)^2}+\left(3+1\right)^2[/tex]

[tex]\longmapsto \sqrt{(4-1)^2} =3[/tex]

[tex]\longmapsto (3+1)^2=4^2[/tex]

[tex]\hookrightarrow 3+4^2[/tex]

[tex]\hookrightarrow 4^2=16[/tex]

[tex]\hookrightarrow 3+16[/tex]

[tex]\hookrightarrow 19\checkmark[/tex]

hope it helps

Answer:

5

Step-by-step explanation:

Given :

[tex]\sqrt{(4-1)^{2} +(3+1)^{2} }[/tex]

Now,

[tex]\sqrt{(3^{2} )+4^{2} } \\\sqrt{9+16}\\\sqrt{25} \\5[/tex]

Answer of the given expression will be 5.

Answer:

Step-by-step explanation:

Answer:

option B

Step-by-step explanation:

[tex]f(x) = 2x^2 + 6x -4\\\\g(x) = 5x^3 - 6x^2 - 3\\\\(f + g)(x) = f(x) + g(x) \\\\[/tex]

               [tex]= (2x^2 + 6x - 4) + ( 5x^3 -6x^2 - 3) \\\\= 2x^2 + 6x - 4 + 5x^3 - 6x^2 - 3\\\\= 5x^3 + 2x^2 - 6x^2 + 6x - 4 - 3 \\\\= 5x^3 - 4x^2 + 6x - 7[/tex]

Answer:

the answer is b

Step-by-step explanation:

hope this helps :)

Answer:

s = 4.28 cm (Answer A)

Step-by-step explanation:

1) The formula for the circumference of a circle of radius r is C = 2(pi)r, and this corresponds to a full circle, with central angle 360 degrees.  

2) Here the circumference is 28 cm.  Therefore, solving for the radius involves the following calculation:   28 cm = 2(pi)r, or

r = (28 cm) / (2 pi), or (28 cm) / 6.28 = 4.46 cm.  

3) The arc length s = r(theta), when the central angle (theta) is 55 degrees, is (55/360) times the circumference of the circle:  (55/360)(28 cm), or

s = 4.28 cm (Answer A)

Answer:

He traveled at 72km/hr during the rain

Step-by-step explanation:

Question is not well formatted. See comment

Given

[tex]d=400km[/tex] --- distance

[tex]t = 11hrs[/tex] --- total time

Let his speed from city A till the rain starts on his return trip be [tex]s_1[/tex]

Let his speed from city during the rain be [tex]s_2[/tex]

So:

[tex]s_2 = s_1 -20[/tex]

Required

Calculate [tex]s_2[/tex]

From the question, we understand that; he drives the whole 400 km and 2/5 of 400 km at [tex]s_1[/tex]

The distance covered during this period is:

[tex]d_1 = 400 + \frac{2}{5} * 400[/tex]

[tex]d_1 = 400 + 160[/tex]

[tex]d_1 = 560[/tex]

And the time during this period is:

[tex]t_1 = \frac{2}{5} * 11[/tex]

[tex]t_1 = 4.4[/tex]

So, the distance during the rain is:

[tex]d_2 = 2 * 400 - d_1[/tex]

[tex]d_2 = 2 * 400 - 560[/tex]

[tex]d_2 = 800 - 560[/tex]

[tex]d_2 = 240[/tex]

And the time during the rain is:

[tex]t_2 = 11 - t_1[/tex]

[tex]t_2 = 11 - 4.4[/tex]

[tex]t_2 = 6.6[/tex]

So, we have:

[tex]d_1 = 560[/tex] --- distance covered before the rain

[tex]d_2 = 240[/tex] --- distance covered when raining

[tex]s_2 = s_1 -20[/tex]

[tex]t_1 = 4.4[/tex] ---- time spent before the rain

[tex]t_2 = 6.6[/tex] --- time spent in the rain

Speed is calculated as:

[tex]Speed = \frac{distance}{time}[/tex]

Make distance the subject

[tex]distance = speed * time[/tex]

So:

[tex]d_1 + d_2 = s_1 * t_1 + s_2 * t_2[/tex]

Recall that:

[tex]s_2 = s_1 -20[/tex]

Make [tex]s_1[/tex] the subject

[tex]s_1 = s_2 + 20[/tex]

The expression [tex]d_1 + d_2 = s_1 * t_1 + s_2 * t_2[/tex] becomes:

[tex]560 + 240 = (s_2 + 20) * 4.4 + s_2 * 6.6[/tex]

[tex]800 = 4.4s_2 + 88+ 6.6s_2[/tex]

Collect like terms

[tex]6.6s_2 + 4.4s_2 = 880 - 88[/tex]

[tex]11s_2 = 792[/tex]

Solve for [tex]s_2[/tex]

[tex]s_2= \frac{792}{11}[/tex]

[tex]s_2=72km/h[/tex]

The distance and time 400 km and 11 hours as well as the speed

reduction gives the speed during the rainy part as 60 km/h.

Based on the comment in the question, we have;

Given:

Distance between City A and City B = 400 km

Distance travelled at the same speed on his way back = [tex]\mathbf{\frac{2}{5}}[/tex] of the distance

Amount by by which his speed is reduced in the remaining [tex]\frac{3}{5}[/tex] of the distance because of rain = 20 km/h

The duration of the trip = 11 hours

Required:

How fast Mr. Jones was driving during the rainy part of his trip from City

B to City A?

Solution:

Let v represent the constant speed, we have;

[tex]Time = \mathbf{ \dfrac{Distance}{Speed}}[/tex]

The distance for which his speed is v = ([tex]\frac{2}{5}[/tex] + 1) × 400 km = 560 km

Total distance of the round trip = 400 km + 400 km = 800 km

The distance for which the speed = v - 20 = 800 km - 560 km = 240 km

Therefore, we have;

[tex]\mathbf{\dfrac{560}{v} + \dfrac{240}{v - 20}}= 11[/tex]

Which gives;

[tex]\mathbf{\dfrac{560 \times (v - 20) + 240 \cdot v}{v\times (v - 20) } } = 11[/tex]

11 × (v² - 20·v) = 560·v - 20 × 560 + 240·v

11·v² - 220·v - 560·v - 240·v + 11200

11·v² - 1020·v + 11,200 = 0

Using the quadratic formula, to solve the above quadratic equation we have;

[tex]v = \dfrac{1020 \pm\sqrt{(-1020)^2 - 4 \times 11 \times 11200} }{2 \times 11} = \dfrac{1020 \pm740 }{22} = \mathbf{ \dfrac{1020 \pm740 }{22}}[/tex]

v = 80 or v = [tex]12 . \overline{72}[/tex]

The possible value for the constant speed is therefore;

v = 80 km/h

The speed during the rain = v - 20, which gives;

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Answer:

294 in

Step-by-step explanation:

set a ratio w/l

11/14

set it equal to 231/x

x = length

[tex]\frac{11}{14}[/tex] = [tex]\frac{231}{x}[/tex]

cross multiply

11x = 3234

divide by 11

x = 294

Answer:

Faces = 6

Vertices = 8

Edges = 12

Step-by-step explanation:

In a solid geometric shape :

         A face is a flat surface : faces = 6

         A vertex (plural: vertices) is a Corner : vertices = 8

         An edge is a particular type of line segment joining

                                                          two vertices : Edges = 12

Answer:

See below.

Step-by-step explanation:

Problem 3.

1. <3, <4

Given

2. <1, <2

Given

3. KG

Congruence of segments is reflexive.

4. HKG, LKG

ASA

Problem 4.

1. MR, OR

Given

2. PR, NR

Given

3. <2

Vertical angles are congruent.

4. MPR, ONR

SAS

Answer:

The width of the rectangle lies between 12 and 20.

Step-by-step explanation:

Let the width of the rectangle is w.

length of the rectangle,

L = 8 w + 20

116 < L < 180

So,

116 < 8 w + 20 < 180

96 < 8 w < 160

12 < w < 20

So, the width of the rectangle lies between 12 and 20.

Answer:

45) 35.75 sq km

46) 24.5 sq km

Step-by-step explanation:

Area of Square:

A= [tex]\frac{(base)(height)}{2}[/tex]

45) A = (11)(6.5) ÷ 2 =

46) A = (10)(4.9) ÷ 2 =

Answer:

45) [tex]35.75[/tex] [tex]km^2[/tex]

46) [tex]24.5[/tex] [tex]km^2[/tex]

Step-by-step explanation:

------------------------------

The formula to find the area of a triangle is  [tex]A=\frac{1}{2}bh[/tex] where [tex]b[/tex] stands for the base and [tex]h[/tex] stands for the height.

So, let's solve and find out the answer.

--------------->>>>

45)

[tex]A=\frac{1}{2}(11)(6.5)[/tex]

[tex]A=\frac{1}{2}(71.5)[/tex]

[tex]A=35.75[/tex]

The area of this triangle is [tex]35.75[/tex] [tex]km^2[/tex]

--------------->>>>

46)

[tex]A=\frac{1}{2} (10)(4.9)[/tex]

[tex]A=\frac{1}{2} (49)[/tex]

[tex]A=24.5[/tex]

The area of this triangle is [tex]24.5[/tex] [tex]km^2[/tex]

------------------------------

Hope this is helpful

Answer:

5 hours.

Step-by-step explanation:

let they meet after t hours.

310t+380t=3450

690t=3450

69t=345

t=345/69=5

Answer:

a. Cookbooks

b. 50%

c. 30%

Step-by-step explanation:

According To the Question,

a. Now, Approximately Cookbooks & Textbooks revenue Form 180°, but textbook revenue is more than cookbooks as clearly visible in the diagram

Thus, cookbooks are less than 90°.

Now, we have to find 1/5th of total publisher revenue which is 360°/5= 72°. & the Cookbooks is nearest to 72° ( less than 90°)

So, Answer For (a) is Cookbooks  

b. Here in Diagram Clearly Visible that The Cookbooks & Textbooks Revenue Form 180° which is Approximately 50% of total Publisher's Revenue.

So, the Total Revenue Comes From Textbooks & Cookbooks is 50%.

c. Now We know the Cookbooks + Textbooks Revenue form 180° Approximately & Cookbook is approximately equal to 72° (as we solve above)

So, textbooks are 180°-72° = 108°, which is 30% of 360° ∴ 30% Revenue Come From Textbooks.

Answer:

here is your answer

Step-by-step explanation:

b

c

a answer

Answer:b

Step-by-step explanation:

Answer:

About 135.

Step-by-step explanation:

As the sample is random the number of monkeys likely to be in the zoo

=  (22/65) * 400

= 135.38

9514 1404 393

Answer:

Step-by-step explanation:

The 3+4 = 7 ratio units represent the total of 490 snacks, so each ratio unit represents 490/7 = 70 snacks.

The number of soda cans is 3·70 = 210.

The number of candy bars is 4·70 = 280.

Marvin bought 210 soda cans and 280 candy bars.

Answer:

4m - 15

Step-by-step explanation:

a( x + y) = ax + ay

[tex]3( m - 5 ) + m\\\\3m - 15 + m \\\\4m - 15[/tex]

Answer:

4m-15

Step-by-step explanation:

Distrubite 3 through the parentheisis

3m-15+m

Collect like terms

4m-15

Answer:

21 < x

Step-by-step explanation:

4 > 11 -x/3

Subtract 11 from both sides

4 - 11 > -x/3

-7 > -x/3

Multiply both sides by 3

-7*3 > -x

-21 > -x

Multiply both sides by (-1)  

21 < x

When we are multiplying by negative, then inequality sign changes.

Answer:

Step-by-step explanation:

X * (1.065) = $633.68

X = $633.68/1.065

X= $595.00

The price of the handbag before the sales tax was added is $595

A sales tax is a tax paid to a governing body for the sales of certain goods and services. Usually laws allow the seller to collect funds for the tax from the consumer at the point of purchase.

Given that, Christine paid $633.68 for a handbag the sales tax in her state is 6.5%

Let the cost of the handbag before sales tax be x,

Therefore,

x + 6.5% of x = 633.68

x + 6.5 / 100 × x = 633.68

x(1 + 6.5 / 100) = 633.68

x(106.5 / 100) = 633.68

x = 633.68 × 100 / 106.5

x = 595

Hence, the price of the handbag before the sales tax was added is $595

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Answer:

Santino rented the canoe for 8 hours.

Step-by-step explanation:

The total bill is represented by the formula r(h) = $10 + ($7.50/hour)h,

where h is the number of hours over which the canoe is rented.

If the total bill is $70, then $70 = $10 +  ($7.50/hour)h.

Solve this for h.  Start by subtracting $10 from both sides, obtaining:

$60 =  ($7.50/hour)h.

Dividing both sides by ($7.50/hour), we get:

           $60

h = --------------------- = 8 hours

      ($7.50/hour)

Santino rented the canoe for 8 hours.

Answer:

1. f= 3/5

2. t= 3/5

Step-by-step explanation:

FYI you can use the app photo math, you just take a pic of the problem and it gives you the answer and explains the steps and it is free.

Answer:

Below in bold.

Step-by-step explanation:

2(f - 9) = -28

2f - 18 = -28

2f = -28 + 18

2f = -10

f = -5.

-3(2t + 3) = -21

2t + 3 = -21/-3

2t + 3 =  7

2t = 4

t = 2.

Câu trả lời:

0,7

Giải thích từng bước:

Xác suất để một sự kiện xảy ra = 0,3

Cho sự kiện = A

P (A) = 0,3

Xác suất mà sự kiện không xảy ra có thể thu được bằng cách sử dụng quy tắc bổ sung;

P (A ') = 1 - P (A)

Vì thế,

P (A ') = 1 - 0,3 = 0,7