going down the river a boat went 13 km/h. going up the river it only 1 km/h. Find the speed of the boat in still water and the speed of the current.

Answer:

The net force is 8N.

Step-by-step explanation:

Consider the provided information.

Two forces cancel each other if they are in opposite direction and the forces are equal, the net force is zero in this case.

Now consider the figure 1:

Here, vertical forces (up and down) cancel each other and horizontal forces do not cancel each other, thus the force is unbalanced.

Calculate the net force as shown:

[tex]F_{net} = F_g + F_n + F_f + F_a[/tex]

Substitute [tex]F_g=-20, F_n=20, F_f =-14, F_a=22[/tex] in above  formula.

[tex]F_{net}= -20 + 20 -14 + 22 = 8 N[/tex]

Hence, the net force is 8N.

The prime factors of the given number 220 in index form are [tex]2^2 \times 5 \times 11[/tex]

The prime factors of a number are the factors that have only two factors, 1 and the number itself.

Index form is defined as that number represented as an exponential expression or as a single number raised to another number.

An algebraic expression or a number that divides another number without leaving any remainder and the quotient is a whole number is called a factor.

The prime factors of 220 in ascending order are,

[tex]220 = 2 \times 2 \times \ 5 \times 11[/tex]

The prime factors of 220 in index form can be written as:

[tex]220 = 2^2 \times 5 \times 11[/tex]

Thus, the prime factor of 220 in the index form is [tex]2^2 \times 5 \times 11[/tex].

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The number is 19.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

The sum of twice a number and 17 is 55.

So, let the number be x

2x+ 17= 55

2x = 55 - 17

2x = 38

x= 19

Hence, the number is 19.

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Answer:

[tex]F'(15,\ 30),\ U'(25,\ 10),\ T'(10,\ -15),\ B'(-15,\ -10),\ O'(-25,\ 5),\ L'(-10,\ 25)[/tex]

Step-by-step explanation:

We known that ,

When a figure (with coordinate (x,y)) gets dilated by a scale factor k from origin (0,0) , then the coordinate of the new image will become :-

[tex](x,y)\to(kx,ky)[/tex]

Given : Hexagon FUTBOL has coordinates F(3,6), U(5,2), T(2,-3), B(-3,-2), O(-5,1) and L(-2,5), and it is dilated by scale factor of 5 centered at origin.

Then, the coordinates of F'U'T'B'O'L' will be :-

[tex]F(3,6)\toF'(5(3),\ 5(6))=F'(15,\ 30)[/tex]

[tex]U(5,2)\toU'(5(5),\ 5(2))=U'(25,\ 10)[/tex]

[tex]T(2,-3)\toT'(5(2),\ 5(-3))=T'(10,\ -15)[/tex]

[tex]B(-3,-2)\toB'(5(-3),\ 5(-2))=B'(-15,\ -10)[/tex]

[tex]O(-5,1) \toO'(5(-5),\ 5(1))=O'(-25,\ 5)[/tex]

[tex]L(-2,5) \toL'(5(-2),\ 5(5))=L'(-10,\ 25)[/tex]

Hence, the coordinates of F'U'T'B'O'L' will be :-

[tex]F'(15,\ 30),\ U'(25,\ 10),\ T'(10,\ -15),\ B'(-15,\ -10),\ O'(-25,\ 5),\ L'(-10,\ 25)[/tex]

Answer:

c 35+0.05m=50+0.01

Step-by-step explanation:

because the person who commented said

The quotient of the expression (48a³bc²) ÷  (3abc) will be 16a²bc.

Division means the separation of something into different parts, sharing of something among different people, places, etc.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ (48a³bc²) ÷  (3abc)

Simplify the expression, then we have

⇒ (48a³bc²) ÷  (3abc)

⇒ 16a²bc

The quotient of the expression (48a³bc²) ÷  (3abc) will be 16a²bc.

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it is 19. i just took the test.

Answer:

Part A:The total cost can then be estimated as 20 × 30 = $600

Part B:  Estimating the total cost with compatible number = 25 × 20 = $500

Step-by-step explanation:

Part A

Rounding off a number simply means making the number simpler but the rounded value should be close to the actual number. The number could be rounded to the nearest ten, hundred or thousand. The field trip to the zoo involved 22 student and the cost for each student is $26. The question ask to round each factor before estimating the total cost of the student's field trip. The number of student rounded to the nearest ten is 20 and the cost for each student rounded to the nearest ten is $30. The total cost can then be estimated as 20 × 30 = $600

Part B

Part B request we use compatible numbers to estimate the total cost of the field trip. Compatible numbers are numbers that are easy to calculate mentally. This pairs of numbers are easy to add, subtract, divide and multiply mentally. Using compatible numbers the cost can be 25 and the number of student can be 20. Estimating the total cost = 25 × 20 = $500

Note the actual total cost is 26 × 22 = $572

Answer: The number of books in Jason's collection is 21 , and the number of books in Nathan's collection is 24 .

Step-by-step explanation:

Let x represent the number of books Jason has and y represents the number of books Nathan has .

Then , According to the question , we have

[tex]6x+\dfrac{1}{3}y=134..........................(1)\\\\\dfrac{1}{3}x+y=31.....................................(2)[/tex]

Multiply 9 in equation (1) and and 3 in equation (2), we get

[tex]54x+3y=1206..................................(3)\\\\x+3y=93.............................................(4)[/tex]

Subtract equation (4) from equation (3), we get

[tex]53x=1113[/tex]

Divide 53 on both sides, we get

[tex]x=21[/tex]

Put the value of x in (2), we get

[tex]\dfrac{1}{3}(21)+y=31\\\\\Rightarrow\ 7+y=31\\\\\Righarrow\ y=24[/tex]

Hence, The number of books in Jason's collection is 21 , and the number of books in Nathan's collection is 24 .

Answer:

Sample Response: Divide the number of hits, 102, by the times at bat, 300. Then move the decimal 2 places to the right and add the percent sign to get 34%.

Step-by-step explanation:

Sample Response: Divide the number of hits, 102, by the times at bat, 300. Then move the decimal 2 places to the right and add the percent sign to get 34%.

The percent of times the baseball player got a hit out of the number of times at bat will be 34%.

The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.

A baseball player got 102 hits in the last 300 times at bat.

Then the percent of times the baseball player got a hit out of the number of times at bat will be

P = (102 / 300) x 100

P = 0.34 x 100

P = 34%

The percent of times the baseball player got a hit out of the number of times at bat will be 34%.

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Answer:

B. The graph has two y-intercepts.

Step-by-step explanation:

Answer:

Option (B) is correct.

The mass of the reactants equals the mass of the products.

Step-by-step explanation:

According to law of conservation of mass :

In a balanced chemical equation, the mass of reactants is always equal to the mass of products.

Here, Water [tex]2H_{2}O[/tex] is the reactant which has 4 units of Hydrogen and 2 units of oxygen.

and [tex]2H_2+O_2[/tex] are products which also has 4 units 4 units of Hydrogen and 2 units of oxygen.

Thus, The mass of the reactants equals the mass of the products.

Thus, option (B) is correct.

When 32 is divided by opposite of 4 then result is - 8.

Here,

The statement is;

''thirty two divided by the opposite of 4''.

What is additive inverse ?

Additive inverse of a number is such a number when the original number and it's additive inverse is added we get zero.

Now,

Since, 4 + ( - 4 ) = 0.

So, the additive inverse of 4 is - 4.

Hence, According to the given question we have to obtain the result when 32 is divided by opposite of 4.

Here, opposite of 4 means additive inverse of 4 which is -4.

⇒ 32 ÷ -4 = - 8.

Hence, When 32 is divided by opposite of 4 then result is - 8.

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To calculate the total amount Zuma spent on a snowboard, first determine the sale price by subtracting the discount from the original price, then add the sales tax to the sale price. Zuma spent a total of $238.95 on the snowboard after a 25% discount and an additional 8% sales tax.

To find out how much Zuma spent to buy the snowboard, we have to first calculate the discounted price of the snowboard and then add the sales tax to it.

Step 1: Calculate the discount amount by multiplying the original price by the discount rate in decimal form.

Discount = Original Price × Discount Rate

Discount = $295 × 0.25 = $73.75

Step 2: To find the sale price, subtract the discount amount from the original price.

Sale Price = Original Price - Discount

Sale Price = $295 - $73.75 = $221.25

Step 3: Calculate the sales tax by multiplying the sale price by the tax rate in decimal form.

Sales Tax = Sale Price × Tax Rate

Sales Tax = $221.25 × 0.08 = $17.70

Step 4: To find the total amount spent, add the sales tax to the sale price.

Total Spent = Sale Price + Sales Tax

Total Spent = $221.25 + $17.70 = $238.95

Zuma spent $238.95 to buy the snowboard.

The solution of the expression 7x2y is 112.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is 7x2y and the values x = 4 and y = 2.

The expression will be solved as:-

E = 7x2y

E = ( 7 x 4 x 2 x 2)

E = 28 x 4

E = 112

Therefore, the solution will be 112.

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Final answer:

Mr. Young has 60 pencils, and the whole school has 400 pencils, calculated by multiplying Jack's 2 pencils by 30 and 200 respectively.

Explanation:

Mr. Young has 30 times as many pencils as Jack. If Jack has 2 pencils, then to find out how many pencils Mr. Young has, we simply multiply Jack's number of pencils by 30:

Mr. Young's pencils = Jack's pencils × 30

Mr. Young's pencils = 2 × 30 = 60 pencils.

Similarly, the whole school has 200 times as many pencils as Jack. To find out how many pencils the whole school has, we multiply Jack's number of pencils by 200:

The whole school's pencils = Jack's pencils × 200

The whole school's pencils = 2 × 200 = 400 pencils.

Answer:

45 feet of lace is not enough, because the tablecloth would need 50.24 feet of lace to go around the outside.

Step-by-step explanation:

Solve

You know that  

C

d

 = π for all circles.

C

2 × r

 =  

3.14

1

C

2 × 8

 =  

3.14

1

C

16

 =  

3.14

1

C

16

 =  

3.14 × 16

1 × 16

Since 1 times 16 is 16, multiply 3.14 by 16 to find the value of C.

C

16

 =  

50.24

16

C = 50.24  

The circumference of the expanded tablecloth is 50.24 feet.

45 feet of lace is not enough, because the tablecloth would need 50.24 feet of lace to go around the outside.