Mathematics High School

What is the rate and unit rate of 16 dollars for 9 books?

Answers

Answer 1

the rate is 16 dollars for 9 books and the unit rate is $1.777777778 per book.

Related Questions

(0.2,3),(0.4,6) what is the slope? 10,15,20,25

HELP PLEASE

Answers

Answer:

Step-by-step explanation:

Use the slope formula to find the slope m.

m= y2-y1 / x2-x1

m= 6-3/0.4-0.2

m=15

Rico is making 4 batches of salsa.EAxh batch needs 2/3 cup of corn.He only had a 1/3 cup measure.How many times must rico measure 1/3 cup of corn to have enough for all of the salsa

Answers

He would need to measure the 1/3 cup of corn 2 times

Shannon collects charms for her charm bracelet. her charm bracelet had 4 charms when she bought it. each year on her vacation she buys 2 more charms to add to her bracelet. assume that shannon continues to buy the same number of charms each year. write an equation that can be used to find how many charms shannon will have on her bracelet after 5 years.

Answers

I think it should be y=4+2*5

2x + 4 = the number of charms that Shannon has

x = the number of years that Shannon has had the bracelet

Replace x with 5 to find the total number of charms after 5 years

2*5 + 4 = 14 charms after 5 years.

If the state sales tax is 6% and a city adds an additional 1 1/4% tax,
What will the tax be on a purchase of $146.00? (Round the answer to the nearest cent.)

A. $10.59
B. $8.76
C. $10.80
D. $18.25

Answers

Your answer is A. 10.59 is the tax.

Point A is located at (0, 4) and point B is located at (−2, −3). Find the x value for the point that is 1/4 the distance from point A to point B.

−1

−0.75

−0.5

−0.25,

Answers

- First thing, find the distance between A and B:

AB =[tex] \sqrt{( x_{2} - x_{1})^{2} + ( y_{2} - y_{1})^{2} } [/tex] =
=[tex] \sqrt{(0-(-2))^{2} + (4-(-3))^{2} } [/tex] =
= [tex] \sqrt{4+49} [/tex] =
= √53

- Hence, we know that the distance between point A and the point C to be found is:
AC = √53 / 4

- The only other thing we know about point C is that it lays on the line that connects A and B. Let's use the point-slope formula to find the equation of this line:

y - y₂ = [tex] \frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex] (x - x₂)
y - (-3) = (7/2)(x - (-2))
y + 3 = (7/2)(x + 2)
y = (7/2)x + 7 - 3
y = (7/2)x + 4

This is the equation that ties the coordinates of every point laying on it, therefore it is vaid for A, B and, above all, C which will be:
C (x , (7/2)x + 4)

- Now let's find the distnce between A and C:
AC =[tex] \sqrt{( x_{2} - x_{1})^{2} + ( y_{2} - y_{1})^{2} } [/tex]=
=[tex] \sqrt{(x-0)^{2} + ((7/2)x+4-4)^{2} } [/tex] =
=[tex]\sqrt{x^{2} + (49/4)x^{2} }[/tex] =
=[tex] \sqrt{(53/4) x^{2} } [/tex] =
=+/-(√53/2)x
- Lastly, we know this distance must be equal to √53 / 4, therefore you need to set and solve the equation:
+/-(√53/2)x = √53 / 4
(1/2)x = +/-(1/4)
x = +/-(1/2)

Since point C is towards point B, we have to take the negative answer:
x = -(1/2)

- Therefore the correct answer is C: -0.5

A $50,000 investment earns 18% annually. If B represents the balance and t represents the number of years, determine an expression that gives the account balance, B, after t years. Also, determine an equivalent expression that displays the effective monthly interest rate.

Answers

Using the compound interest formula;
FV=P(1+r/100)^t

FV is the future value
P is the principle
r is the rate
t is the time

the formula that gives the account balance after t years will be:

FV=50000(1+18/100)^t
FV=50000(1.18)^t

The formula for effective monthly interest rate will be:
monthly interest rate=(annual rate)/(number of months)
annual rate=18%
number of months in a year=12 months
rate=18/12=1.5%

Answer:

usa test prep its B

Step-by-step explanation:

How many real number solutions does the equation have?
0=5x^2+2x-12
A- one solution
B- two solution
C-infinity many solutions
D-no solutions

Answers

b is the answer to this

5x^2+2x-12=0 is a quadratic equation. For any ax^2 + bx + c = 0, the solution can be found by completing the square to find the equations
x=(-b+sqrt(b^2-4ac))/2a and x=(-b-sqrt(b^2-4ac))/2a
Substituting using the equation 0=5x^2+2x-12
x=(-2+sqrt(2^2-4(5)(-12)))/(2(5)) and x=(-2+sqrt(2^2-4(5)(-12)))/(2(5))
Since the sqrt(244) is a real number, there are two real solutions.

5 times the sum of p and r

A.5(p+r)
B.5p+r
C.5pr
D.5+p+r

Answers

The answer would be 5(p+r) because p+r means the sum of those two variables and 5 would times the numbers in the parenthesis.

Answer:

Option: A is the correct answer.

The mathematical representation of the given statement is:

[tex]5(p+r)[/tex]

Step-by-step explanation:

We are asked to represent the given expression in words to numerical expression.

The statement is:

5 times the sum of p and r

The sum of p and r is: (p+r)

and now 5 times the sum of p and r i.e. 5 is multiplied to the sum of p and r.

i.e.

[tex]5(p+r)[/tex]

Justin lives in saint paul and goes to school in minneapolis. in the morning, he has 333 transportation options (bus, cab, or train) to school, and in the evening he has the same 333 choices for his trip home. if justin randomly chooses his ride in the morning and in the evening, what is the probability that he'll use both the bus and the train?

Answers

To answer this question you will multiply the probability of the first event happening by the probability of the second event happening. He has a one in three chance of taking the bus on the way to school, and a one in three chance of taking the train home. 1/3 x 1/3= 1/9 chance of both of these occurring at the time he is indicating.

Answer:

2/9

Step-by-step explanation:

TRUST ME THIS GUY ABOVE ME IS A DING DONG

Triangle ABC and Triangle DEF are similar. For triangle ABC, AB = 2x , AC = 24 inches and BC = 20. For triangle DEF, EF = 5 and DF = x - 2 . What is the value of x?

Answers

x=8.

Following the similarity statement, we know that AC is to DF as BC is to EF. The ratio would be:

24/(x-2) = 20/5

Cross multiply:
24*5 = 20(x-2)

Use the distributive property:
120 = 20x - 40

Add 40 to both sides:
120+40 = 20x - 40 + 40
160 = 20x

Divide both sides by 20:
160/20 = 20x/20
8 = x

Suppose that a system has 5000 grasshoppers. how many hawks would be expected?

Answers

Probably 2500 or less because they dont need that much hawks.

which do you think would seat more people a 4ft by 6 ft rectangular table or a circular table with a diameter of 6 ft? How many people would sit at each table? Explain your reasoning.

Answers

To determine which seating arrangement would be able to seat more people you will find the distance around each table.

For the rectangle, you will find the perimeter:

P = 2l + 2w
2 x 6 + 2 x 4
P = 20 feet

For the circle you will find the circumference:

C = pi x d
3.14 x 6
C = 18.84 feet

The rectangle would seat more people because the distance around the table is longer.

You would be able to fit about 7-8 people around the rectangular table and 6-7 people around the circular table.

Final answer:

Comparing a 4ft by 6ft rectangular table and a circular table with a 6ft diameter, the circular table can seat more people (approximately 9) due to more efficient use of its perimeter, compared to the rectangular table which can seat 6 people.

Explanation:

The question asks which table would seat more people: a 4ft by 6ft rectangular table or a circular table with a diameter of 6ft. To answer this, we need to compare the arrangements and sizes of the two tables.

The rectangular table measures 4 feet by 6 feet. Typically, a person needs about 2 feet of space at a dining table to sit comfortably. Therefore, on the longer sides (6 feet), you can seat 3 people on each side, for a total of 6. On the shorter sides (4 feet), it's not practical to seat anyone due to space constraints and leg room. So, the rectangular table can seat 6 people.

The circular table has a diameter of 6 feet. Placing chairs around a circle often allows for more efficient use of space. If we assume each person requires the same 2 feet of space, roughly, the circumference of the table (which is π * diameter) dictates how many people can sit around it. The circumference of a 6-foot diameter table is about 18.85 feet (π * 6). Dividing this by 2 feet per person, you can seat approximately 9 people around the circular table.

In conclusion, a circular table with a diameter of 6 ft would seat more people, approximately 9, compared to a 4ft by 6ft rectangular table, which would seat 6 people. This is due to the circular table's ability to more efficiently use the perimeter for seating.

Ben walks at a rate of 3 miles per hour. he runs at a rate of 6 miles per hour. in one week, the combined distance that he walks and runs is 210 miles.
b. (using 3x + 6y = 210 with x representing walk and y representing run) ben runs for 25 hours. for how many hours does he walk?

Answers

25 x 6 is 150 out of 210 miles therefore Ben ran for 150 miles and walked for 60 miles

Find the zeros of the function. f(x)=9x^2-12x-5

Answers

x=5/3, -1/3

You can use the quadratic formula or you can do any method that your teacher teaches you (box, etc.)

Answer: 5/3 and - 1/3

Explanation:

1) Set the given function equal to 0: 9x^2 - 12x - 5 = 0

2) make 9x^2 = (3x)^2 and 12x = 4(3x)

=> (3x)^2 - 4(3x) - 5 = 0

3) Factor the polynomial:

(3x - )(3x + ) first stept of factoring.

Now find two numbers that sum - 4 and their product of - 5, those are -5 and + 1: =>

(3x - 5) (3x + 1) = 0

4) Set the two factors equal to 0:

3x - 5 = 0 => 3x = 5 => x = 5/3 ↔ one root

3x + 1 = 0 => 3x = - 1 => x = - 1/3 ↔ the other root.

Please help me please

Answers

The 1st selection is appropriate.

_____
The other selections are nonsense.

Find the simple interest. $7,064 at 6.5% for 8 months

Answers

the answer is 57.395

Simple Interest can be calculated using the formula I=Pr t

Here I= interest earned ,P= Principal ,R= rate of interest ,t= time in years.

It is given Principal P=$7,064

Rate r=6.5% =0.065

Time t= 8 months =[tex] \frac{8}{12} =\frac{2}{3} [/tex] years

Substituting these values in I = P r t

I =(7064)(0.065)([tex] \frac{2}{3} [/tex])

Solving for I

I=306.11

interest earned on $7,064 at 6.5% for 8 months is $306.11

75 less than twice a number

Answers

I think the number is 75 because 75 x 2 = 150 - 75 = 75.

What is 5% in a decimal and a fraction?

Answers

5/100 or .05 would be the answers I believe.

It can be helpful to understand that the "%" is a sort of fancy or short-hand way to write "/100".

That is, 5% means 5/100. This is your fraction. It can be reduced to 1/20.

As a decimal, of course, 5/100 = .05, a number with 5 in the hundredths place.

find the area of the circle .Leave your answer in terms of pie (3.14) the area is 4.1m .I need help on this question

Answers

The area of a circle = pi x radius^2. If the area is 4.1m, then to transfer that into terms of pi you would simply divide 4.1 by pi. Pi is infinite, but is typically simplified to 3.14, 4.1/3.14 = 1.31. So the area in terms of pi is 1.31 x pi.

Answer:

Area of the circle = 1.3π m²

Step-by-step explanation:

Area of the circle is given by the formula A = πr²

It is given that area of the circle is 4.1 m² and we have to convert it in the terms of π.

Now to convert the area in terms of π we will multiply the area by π and divide the area by 3.14.

⇒ Area×π / 3.14 = 4.1 × π/3.14 = 1.30π

Therefore answer is area of the circle = 1.30π m²

PLEASE HELP ASAP! BRAINLIEST TO BEST/RIGHT ANSWER!

Answers

In this problem, we are dealing with simplifying expressions with exponents in the denominator. When we have exponents in the denominator, one thing that we want to be sure of is that there are not any negative exponents and that the numerators and denominators are completely simplified.

Our expression is 5/x^-2y^5

The first thing we notice is that we have a negative exponent in the denominator. This is easily solved if we switch the term with the negative exponent into the numerator.

Our expression now looks like this: 5x^2/y^5

Now, there aren't any other terms that cancel out, so our simplified expression is 5x^2/y^5.

Which fraction is NOT equivalent to 8 1/2 ? A) 2 3 B) 24 36 C) 4 6 D) 6 10

What is 5 x 2/3?

A) 3 1/3

B) 3 2/5

C) 5 2/3

D) 10/15

Answers

None of the fractions are equivalent on the first one.

The answer for the second question is A. 3 1/3. 5/1 x 2/3 =10/3 10/3=3 1/3

Please explain it and tell me how u got the answer
Thx

Answers

The y-intercept of a function is that function's value when x=0.
.. f(0) = 4
.. g(0) = 0
These y-intercepts differ by 4.

If you want them to differ by zero (be the same), you have to move them to the same point.

Selection 1. Moves f(0) down 3 (to 1) and g(0) up 1 (to 1), so moves the y-intercepts to the same point. This is what you want, so this is an appropriate answer selection.

Selection 2. Moves f(0) up 4 (to 8) and g(0) down 1 (to -1). 8 and -1 are not the same point, so this is not the answer.

Selection 3. Moves f(0) down 2 (to 2) and g(0) up 1 (to 1). 2 and 1 are not the same point, so this is not the answer.

Selection 4. Moves f(0) up 3 (to 7) and g(0) down 6 (to -6). 7 and -6 are not the same point, so this is not the answer.

___
The appropriate choice is the 1st one.
  f(x) - 3 and
  g(x) + 1

What is the best first step in solving the equation 3 +3 square root 6x = 5? A.)Subtract 3 from both sides.
B.)Find the cube of 3 square root 6x .
C.)Cube both sides of the equation.
D.) Subtract 5 from both sides.

Answers

Final answer:

The best initial step in solving the equation 3 + 3√(6x) = 5 is to subtract 3 from both sides, simplifying the equation to 3√(6x) = 2, which lays a clear path towards isolating and solving for x.So,option A.)Subtract 3 from both sides. is correct.

Explanation:

The best first step in solving the equation 3 + 3√(6x) = 5 is to simplify the equation by isolating the square root term. This can be done by following option A: Subtract 3 from both sides of the equation. This action makes the equation easier to manage step-by-step as you move toward isolating x, which is the ultimate goal of solving for x. The resulting equation after subtracting 3 from both sides is 3√(6x) = 2. This simplified equation can then be further manipulated to solve for x, primarily by squaring both sides to eliminate the square root, and then solving the resulting simple algebraic equation.

What needs to happen before you can use the reason CPCTC?

Answers

Answer: before you can use the reason CPCTC it must be stated that the triangles are congruente.

Explanation:

1) CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent.

2) Therefore, to use that reason you first need to prove that the the triangles are congruent.

3) Once, it has been stated that the triangles are congruent, then you can use the reason to state the the corresponding segments are congruent which will let you to state the length of any side of one triangle known the corresponding side of the other triangle, because they are congruent (have the same length).

How do you decide which variable to isolate in order to use the substitution method to solve a system of linear equations?

Answers

Find a variable with no coefficient.If there is more than one variable with no coefficient,it dose not matter which one you isolate.Isolate the variable and then use substitution to solve the system of equations.

The way to decide which variable to isolate in order to use the substitution method to solve a system of linear equations is;

to look for the variable with no coefficient or least coefficient and then isolate it and use substitution to solve the simultaneous equation.

A system of linear equations can be solved by three major methods which are;

- Elimination method

- Substitution method

- Graph method

Now, in this question we want to know how substitution method is done.

Let us say we have two simultaneous equations which are;

2x + 3y = 8 ----(eq 1)

x + 5y = 11 ----(eq 2)

Now, in this method, we need to first isolate a variable in one of the equations by making it the subject of formula there. Usually, we go with the variable that has no coefficient first.

In this case, it is x that has no coefficient in eq 2 and as such, we will isolate it to get;

x = 11 - 5y

In conclusion, the way we decide which variable to isolate in substitution method of simultaneous equations is to look for the variable with no coefficient or least coefficient.

Read more at;https://brainly.com/question/19770914

What context clue in the paragraph best helps in understanding the meaning of the word native?

Question 2 options:

"much in America"

"lived in Nantes, France"

"first in France"

"born in Louisiana"

Answers

What was the Answer?

A roped off area of width x is created around a 4-foot by 6-foot rectangular museum of display of Native American artifacts. The combined area of the display and the roped-off is 120 square feet. Find the width.

Answers

Let
x----------> width a roped off area

we know that
(4+2x)*(6+2x)=120
then
4*6+4*2x+2x*6+2x*2x=120 ---> 24+8x+12x+4x²=120 -------> 4x²+20x+24=120
4x²+20x-96=0

using a graph tool---------> to calculate the quadratic equation
see the attached figure

the solution is
x=3 ft

the answer is
the width a roped off area is 3 ft

The width of the roped off area around the museum display is 4 feet.

To find the width of the roped off area around the museum display of Native American artifacts, we need to solve for x in the area equation. The area of just the display is 4 feet by 6 feet, which is 24 square feet. Since we know the combined area of the display and the roped-off area is 120 square feet, the equation is:

Area of display + Area of roped-off region = Total Area

(4)(6) + ((4 + 2x)(6 + 2x) - (4)(6)) = 120

24 + (24 + 4x + 12x + 4x2) - 24 = 120

Simplifying, we get:

4x² + 16x - 96 = 0

Divide by 4:

x² + 4x - 24 = 0

Factor the quadratic equation:

(x + 6)(x - 4) = 0

Setting each factor equal to zero gives us two potential solutions:

x + 6 = 0
or
x - 4 = 0

Therefore, x can be -6 or 4. Since a width can't be negative, the only logical solution is:

x = 4 feet

The width of the roped-off area is 4 feet.

Perform the indicated operation. (r + s)(r2 - rs + s2)

Answers

Final answer:

The operation in the equation, (r + s)(r2 - rs + s2), is solved by distributing the multiplication of the binomial across each term in the trinomial. When the multiplications are complete and the terms are added, the resulting solution is r3 + s3.

Explanation:

The indicated operation in the question is the multiplication of the binomial, (r + s), and the trinomial, (r2 - rs + s2). This can be performed by using the distributed property of multiplication over addition. In this case, you would multiply each term in the binomial by each term in the trinomial, then add the products. So the solution will be:

r3 - r2s + rs2 + r2s - rs2 + s3 = r3 + s3

Note: the terms -r2s and r2s cancel each other out, as do the terms rs2 and -rs2, which is why the final result is r3 + s3.

Learn more about Polynomial Multiplication here:

https://brainly.com/question/20121808

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Will mark brainliest ⭐️⭐️⭐️⭐️⭐️

Answers

is a hope this helped

Answer:

answer is d

Step-by-step explanation:

Phil is a commercial fisherman. He keeps 5 salmon for every 8 cod he catches. If Phil keeps 15 salmon, how many cod will he keep?

Answers

15 / 5 = 3

3 * 8 = 24 cod

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