Mathematics College

Bennett tried to solve exercise 1 a few different ways. Which of his methods are correct? Of the other methods, which makes the most sense to you? Explain

A. 5% sales tax means that for every dollar you spend, you need to pay a nickel in tax. If you buy a nickel tax. If you buy something for $21, you need to pay 21 nickels in tax.
B. You can set up a promotion and solve for the missing value.
$.05 = x <-- (These are fractions)
___ __
$1.00 $21.00

C. If you know that 10% of $21 is $2.10, so 5% should be half of $2.10
D. 5% is equal to 1/20. To find the amount of tax on $21, find $21 ÷ 20
E. 1% of $21.00 is $0.21 so 5% of $21.00 is 5 x $ 0.2

Answers

Answer 1
the answer is e beac=use it fits

Related Questions

The complex number z = –1 + 3i can be expressed in trigonometric form as:

Answers

[tex]\bf z=\stackrel{a}{-1}\stackrel{b}{+3}i\qquad \begin{cases} r=\sqrt{a^2+b^2}\\ \theta =tan^{-1}\left( \frac{b}{a} \right) \end{cases}\qquad \qquad z=r[cos(\theta )i~sin(\theta )]\\\\ -------------------------------\\\\ r=\sqrt{(-1)^2+3^2}\implies r=\sqrt{10} \\\\\\ \theta =tan^{-1}\left( \frac{3}{-1} \right)\implies \theta \approx -71.57\implies \theta \approx\stackrel{360-71.57}{288.43^o}\\\\ -------------------------------\\\\ z=\sqrt{10}\left[ cos(288.43^o)+i~sin(288.43^o) \right][/tex]

now, the calculation in the choices, show 289.5°, which I take it is due some early rounding up.

The price of a calculator has decreased from $200 to $150. What is the percent of decrease?

Answers

The percent of the decrease is 25%.

50 because 200-150=50
Hope this helps!

Is m=0.75d-2 proportional?

Answers

no, a proportion will have a constant for the ratio m/d

If m = 0.75d, then ratio m/d = (0.75d)/d = 0.75

In this example, the ratio is (.75d-2)/d = 0.75 - (2/d).

Therefore, it is not proportional.

Answer:

No, the equation m=0.75d-2 does not represent proportional relationship.

Step-by-step explanation:

The given equation is

[tex]m=0.75d-2[/tex]

We need to check whether the given equation represents proportional relationship or not.

If variable y is proportional to variable x, then

[tex]y\propto x[/tex]

[tex]y=kx[/tex]

where, k is the constant of proportionality.

At x=0 the value of y is 0. It means, if a linear equation represents proportional relationship then it must be passes though the origin.

Substitute d=0 in the given equation.

[tex]m=0.75(0)-2[/tex]

[tex]m=-2[/tex]

The line passes through the point (0,-2).

Since the line does not pass through the origin, therefore it does not represent proportional relationship.

What is the average rate of change of f(x) = −2x + 1 from x = −5 to x = 1?

Answers

by calculating the slope, the average rate of change is -2
-1-11
---------
1--5

Answer:-2

Step-by-step explanation:

On st. Patrick's day, 3/5 of the students in Ms. pikes band class are wearing green . If there are 60 students in her class , how many of them are wearing green?

Answers

36 students I believe is the answer
60 divided by 5 = 12
12 x 3 = 36

The answer is 36 

Hope this helps!

The number of Adult tickets is the same as the number of Child (age 5-12) tickets. A total of 38 tickets was purchased. What is the total cost of the tickets? Explain.


Data: Adult Tickets $23
Child Tickets $17
Under 5 $8

Answers

A+C = 38
A=C=19
A*19 +C*17 = cost
19*19+19*17=684

What is the measure of the smallest angle?



52°
61°
67°
69°

Answers

52 Degrees is the smallest measure :)

Answer:

52° is ur answer

Step-by-step explanation:

I just did the quiz so i know

A disc jockey must allow time for 24 minutes of commercials every hour, along with 4 minutes for news, 3 minutes for weather, and 2 minutes for public-service announcements. If each record lasts and average of 3 minutes, how many records per hour can the DJ play?

Answers

about 11 records per hour

What are the answers for both drop downs the first one is asking for 3.113 and the second is asking for 1.2795

Answers

[tex]\bf \qquad \textit{Amount for Exponential Growth}\\\\ A=I(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{elapsed time}\\ \end{cases}\\\\ -------------------------------\\\\ P(x)=3.113(1.2795)^x\implies \stackrel{A}{P(x)}=\stackrel{I}{3.113}(1+\stackrel{r}{0.2795})^{\stackrel{t}{x}}[/tex]

usually, the "r" above, is used as a "rate of increase".

but 1+r combined, can be referred as the "rate for the new size".

so, for example, if something is increasing at a rate of 25%, 1+0.25 or 1.25, the new size wil be 1.25 or 125% of the old size.

1.A system of two linear equations is graphed on a coordinate plane. If the system of equations has infinitely many solutions, which statement must be true?

A.On the graph, there is exactly one point (x,y) that satisfies both equations.


B.On the graph, any point (x,y) that satisfies one of the equations cannot satisfy the other equation.


C.On the graph, there are no points (x,y) that satisfy both equations.


D.On the graph, any point (x,y) that satisfies one of the equations must also satisfy the other equation.

2.Mark drank a total of 10 glasses of water and iced tea yesterday.

Each glass of water contained 8 ounces. Each glass of iced tea contained 12 ounces.

All together, he drank 96 ounces. The system of equations below models this situation.

x + y = 10
8 x + 12 y = 96

How many glasses of water did Mark drink yesterday?

A.3 glasses


B.4 glasses


C.5 glasses


D.6 glasses

Answers

You dint know what going to tell me Abe's and you can tell that she's hitting in the shower now I know I will ince and but 7. C is the answer

Mark drank 6 classes of water. :) im probably late on answering this, sorry

A hollow ball is made of rubber that is 1 centimeter thick. The ball has a radius of 5 centimeters at the outside surface.

What is the approximate volume of rubber used to make the ball?

Answers

Given that the ball has a thickness of 1 cm and the radius at the outside is 5 cm, thus the radius from inside is 5 - 1 = 4cm.

The approximate volume of rubber used to make the ball is given by the volume of the ball at the outside surface minus the volume of the ball at the inside surface.

i.e.

[tex]Volume\ of\ rubber= \frac{4}{3} \pi\left(5^3-4^3\right) \\ \\ = \frac{4}{3} \pi(61)= \frac{244}{3} \pi\approx255.5\ cm^3[/tex]

Answer: I got the same answer. It's 255.4 cm3

Step-by-step explanation:

A Pitcher of fruit punch holds 2 gallons , If 9 people share the entire pitcher equally how much punch does ecah person get

Answers

You would do 2 divided by 9 to get that each person would have 2/9 of a gallon or .22 of a gallon. I hope this helps.

Rachel and Sabrina belong to different local gyms. Rachel pays $35 per month and a one-time registration fee of $15. Sabrina pays only $25 a month with a one-time registration fee of $75. Write an equation to represent Rachel's total cost, T, as a function of the number of months, m.

Answers

I believe it would be:
T= 35m+ 15

Maxine bought items costing $5.25, $18.99, $2.99, and $17.50. She used a coupon worth $5.50. If Maxine had $60.00 before she went into the store, how much did she have when she left?

Answers

The answer should be $20.77

A water tank holds 24000 gallons. How many hours will it take for 2/3 of the water to be used if the water is used at an average rate of 650 gallons a day?

Answers

First, determine what 2/3 of 24000 gallons is.  That's 18000 gallons.

Next, divide this   18000 gallon amount by 650 gallons/da:

 18000 gal
----------------- =  27.69 days, or about 28 days.
650 gal/day
24000 Gallons / 650(gallons per day) =36.92 days to fill it fully. Now take 36.92 and multiply by (2/3)=24.61 days. (.61 days = 14 Hours and 36 minutes)

Help me asap!!! :) please


Mark you a brainly!

Answers

30 /10 = 3

 so multiply 9 by 3

9*3 = 27

9/10 = 27/30

a = 27

You are standing above the point (5,4)(5,4) on the surface z=15−(2x2+3y2)z=15−(2x2+3y2). (a) in which direction should you walk to descend fastest? (give your answer as a unit 2-vector.)

Answers

The direction you'll walk to descend fastest is obtained as follows:

[tex]u= \frac{-\nabla z(5,\ 4)}{||\nabla f(5,\ 4)||} \\ \\ = \frac{-\ \textless \ -4x,\ -6y\ \textgreater \ |_{(5,\ 4)}}{||\ \textless \ -4x,\ -6x\ \textgreater \ ||_{(5,\ 4)}} \\ \\ = \frac{\ \textless \ 20,\ 24\ \textgreater \ }{\sqrt{(-20)^2+(-24)^2}} = \frac{\ \textless \ 20,\ 24\ \textgreater \ }{\sqrt{400+576}} \\ \\ = \frac{\ \textless \ 20,\ 24\ \textgreater \ }{\sqrt{976}} = \frac{\ \textless \ 20,\ 24\ \textgreater \ }{4\sqrt{61}} = \frac{\ \textless \ 5,\ 6\ \textgreater \ }{\sqrt{61}} [/tex]
Final answer:

To descend fastest from the point (5,4) on the surface z=15-(2x^2+3y^2), you should walk in the direction of the negative gradient vector, normalized to be a unit vector, which is approximately <0.640, 0.768>.

Explanation:

To determine the direction in which you should walk to descend fastest from the point (5,4) on the surface z=15-(2x^2+3y^2), we can find the gradient of the surface at that point. The gradient vector will point in the direction of the steepest ascent, so the direction of the steepest descent is the opposite direction of the gradient vector.

First, calculate the partial derivatives of z with respect to x and y:
∂z/∂x = -4x
∂z/∂y = -6y
Next, evaluate these derivatives at the point (5,4):
∂z/∂x(5,4) = -4(5) = -20
∂z/∂y(5,4) = -6(4) = -24
The gradient vector at (5,4) is <-20, -24>. To get the direction of steepest descent, we take the negative of the gradient vector, which is <20, 24>.

Finally, normalize this vector to make it a unit vector (so it has a length of 1):
Length of gradient vector = √(20^2 + 24^2) = √(400 + 576) = √976 ≈ 31.24
The unit vector in the direction of steepest descent is <20/31.24, 24/31.24> ≈ <0.640, 0.768>.

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peter walks 40 meters in 1 minute what is his walking rate in meters per second

Answers

Incorrect, I apologize.

there is a 20% markup on a tv if the tv is $450 before the markup what is the cost after the markup

Answers

Hello!
If the markup is 20% you would multiply $450 by .20 to get $90. Then you add $90 to $450

Here's a simpler version...
$450x.20=$90
$450+$90=$540

The answer would equal $540.

Hope this helped!
The answer is 540 multiply 20 by 450 then divide by 100 and add 90

Subtract 9 from z. 9-Z, Or Z-9

Answers

It would be Z-9 since you are subtracting 9 from Z

Which equation can be used to find the number of wolves in the state on January 1? A zoologist is recording the loss of wolves in her state. She notes the number of wolves, w, in the state on January 1. One year later, there were 84 wolves in the state, which is 23 fewer wolves than were in the state a year earlier. What is the number of wolves in the state on January 1? w−84=−23 w−23=84 23−w=84 w + 23 = 84

Answers

There were 23 fewer wolves, and there were 84 left after one year

w - 23 = 84

is your answer

because there were 107 wolves the previous year

hope this helps

Answer: w - 23 = 84

Step-by-step explanation:

write an equation of the line given its slope,m=3,and it's y-intercept b=10

Answers

y = mx + b

plug in m and b

y = (3)x + (10)

hope this helps

What does −2/3(12c−9)+14c simplify to?

Answers

Answer:

The simplified form of the provided expression is [tex]6c+6[/tex] or [tex]6(c+1)[/tex]

Step-by-step explanation:

Consider the provided expression.

[tex]\frac{-2}{3}(12c-9)+14c[/tex]

Use the distributive property:

[tex]a(b+c)=ab+ac[/tex]

By using the above property we can simplify it as shown:

[tex]\frac{-2}{3}\times 12c-\frac{-2}{3}\times 9+14c[/tex]

[tex]-2\times 4c+2\times 3+14c[/tex]

[tex]-8c+6+14c[/tex]

Add or subtract the like terms.

[tex]6c+6[/tex] or [tex]6(c+1)[/tex]

Thus, the simplified form of the provided expression is [tex]6c+6[/tex] or [tex]6(c+1)[/tex]

The simplest form of expression by applying distributive property would be, 6 (c + 1)

Given that,

The expression is,

[tex]\dfrac{- 2}{3} (12c - 9) + 14c[/tex]

Now, used the concept of distributive property to simplify the expression,

[tex]\dfrac{- 2}{3} (12c - 9) + 14c[/tex]

Apply distributive property,

[tex][\dfrac{- 2}{3} \times 12c - (\dfrac{- 2}{3} )\times 9] + 14c[/tex]

[tex][- 2 \times 4c + 2 \times 3] + 14c[/tex]

[tex][- 8c + 6] + 14c[/tex]

Combine like terms,

[tex]- 8c + 14c + 6[/tex]

[tex]6c + 6[/tex]

Take 6 as a common term,

[tex]6 (c + 1)[/tex]

So, the solution of expression 6 (c + 1).

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he average distance between Jupiter and the sun is 7.8 × 108 kilometers, and the average distance between the sun and Neptune is 4.51 × 109 kilometers. What is the approximate difference between these average distances?

Answers

Final answer:

The approximate difference between the average distances from the Sun to Jupiter and from the Sun to Neptune is approximately [tex]-3.71 * 10^9 km.[/tex]

Explanation:

The approximate difference between the average distances from the Sun to Jupiter and from the Sun to Neptune can be found by subtracting the average distance to Neptune from the average distance to Jupiter.

Average distance to Jupiter: 7.8 × 108 km

Average distance to Neptune: 4.51 × 109 km

Subtract the average distance to Neptune from the average distance to Jupiter:

[tex]= 7.8 * 10^8 km - 4.51 * 10^9 km[/tex]

= [tex]-3.71 * 10^9[/tex]

The approximate difference between the average distances is [tex]-3.71 * 10^9 km.[/tex]

Name all sets of numbers to which each real number belongs

Answers

heres a chart hope this helps

Final answer:

A real number can belong to several sets of numbers, including the integers, rationals, irrationals, and reals. Integers are the set of whole numbers and their negatives, rationals can be expressed as a fraction of two integers, irrationals cannot be expressed as a fraction, and reals represent all possible numbers on the number line.

Explanation:

A real number can belong to several sets of numbers, including the integers, rationals, irrationals, and reals.



Integers are the set of whole numbers and their negatives, including zero. They don't include fractions or decimals.



Rationals are the set of numbers that can be expressed as a fraction of two integers, like 3/4 or -5/2.



Irrationals are the set of numbers that cannot be expressed as a fraction, like √2 or π.



Reals represent all possible numbers on the number line, including integers, rationals, and irrationals.

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For integer values of a and b, b^a = 8. The ratio of a to b is equivalent to the ratio of c to d, where c and d are integers. What is the value of c when d = 10?

Answers

the only integer values to fit b^a = 8 would be 2^3, knowing this you can set up  a proportion where 
3:2  =  c:10
c is then equal to 10/2 *3 
15

To find the value of c when d = 10, we first need to determine the values of a and b. Given that b^a = 8, we know that 8 is the result of raising b to the power of a.

Since the question states that a and b are integers, there are a limited number of possibilities to consider. Let's examine the possible combinations of a and b that satisfy this equation: [tex]1^3 = 1 2^3 = 8 3^2 = 9[/tex](which is not 8) [tex]4^2 = 16[/tex] (which is not 8) [tex]5^1 = 5 6^1 = 6 7^1 = 7 8^1 = 8[/tex]From these calculations, we find that the only combination that satisfies the equation is a = 3 and b = 2. Now, let's consider the ratio of a to b and the ratio of c to d.

The ratio of a to b is a/b = 3/2. The question states that the ratio of a to b is equivalent to the ratio of c to d, which means: a/b = c/d Given that d = 10, we can substitute the value into the equation: [tex]3/2 = c/10[/tex] Next, we can cross-multiply to solve for c: [tex]3 * 10 = 2 * c 30 = 2[/tex] c Dividing both sides by 2, we get: c = 15 Therefore, when d = 10, the value of c is 15. In conclusion, when d = 10, the value of c is 15 based on the given equation and calculations.

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callie spent 3/4 hour on a science report and 1/3 hour on a social studies report. What fraction of an hour longer did she spend on the science report ?

Answers

3/4+1/3=9/12+4/12=13/12  of an hour

13/12= 1 1/12

What's the radius of a circle with an area of 123 square feet? A. 6.26 ft. B. 39.17 ft. C. 26.32 ft. D. 3.14 ft.

Answers

the correct answer is A) 6.26

what is 4 1/2 divided by 3

Answers

You divide 4.5 by 3. The answer is 1.5.

What is the factored form of 6x2 + 11x – 10? (2x + )( x – )

Answers

Answer:

[tex]6x^2+11x-10=(2x+5)(3x-2)[/tex]

Step-by-step explanation:

we are given

[tex]6x^2+11x-10[/tex]

We can factor it

[tex]6x^2+11x-10=6x^2+15x-4x-10[/tex]

we can use grouping method

[tex]6x^2+11x-10=(6x^2+15x)-(4x+10)[/tex]

now, we can take out common terms

[tex]6x^2+11x-10=3x(2x+5)-2(2x+5)[/tex]

we can take 2x+5 from both terms

[tex]6x^2+11x-10=(2x+5)(3x-2)[/tex]

so, we get factor terms as

[tex]6x^2+11x-10=(2x+5)(3x-2)[/tex]


The factored form of 6x² + 11x - 10 is: (2x + 5)(3x - 2)

Factorization of Algebraic Expressions

Given the algebraic expression, 6x² + 11x - 10, it can be factorized as shown in the steps below:

6x² + 11x - 10

6x² + 15x - 4x - 10

(6x² + 15x) - (4x - 10)

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

6x² + 11x - 10 = (2x + 5)(3x - 2)

Therefore, the factored form of 6x² + 11x - 10 is: (2x + 5)(3x - 2).

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