Goran's gas tank is 1/3
full. After he buys 3 gallons of gas, it is 1/2
full. How many gallons can Goran's tank hold?

Answer:

$960.95

Step-by-step explanation:

The question is about finding the final amount after 4 years of a $700 investment with 8% interest, compounded quarterly. This can be solved using the compound interest formula.

The subject of your question pertains to compound interest in mathematics. Given the parameters, we want to find the amount after 4 years when $700 is invested at an interest rate of 8%, compounded quarterly. To solve this, we can use the compound interest formula, A = P(1 + r/n)^(nt), where 'A' is the amount of money accumulated after n years, including interest, 'P' is the principal amount (the initial amount of money), 'r' is the annual interest rate (in decimal form), 't' is the time the money is invested for in years, and 'n' is the number of times that interest is compounded per year. Plugging the values in, we get A = $700(1 + 0.08/4)^(4*4) which gives us the total amount after 4 years.

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The annual rate of interest per year is 8%

Solution:

Given:- Principal (p) = 4600 rupees, Time –Period (t) = 5 years, Total amount(A) = 6440 rupees

First we will calculate the Interest and then using formula of simple interest we will calculate the rate of interest

Interest = Amount – Principal

Interest = 6440  – 4600 = 1840

Now using the formula of simple Interest and on putting values we get,

[tex]\text {Simple Interest }=\frac{P \times R \times T}{100}[/tex]

Where "P" is the principal and "R" is the rate of interest per annum and "T" is the time period

[tex]1840=\frac{4600 \times R \times 5}{100}[/tex]

[tex]\begin{aligned} \mathrm{R} &=\frac{1840 \times 100}{4600 \times 5} \\\\ \mathrm{R} &=\frac{1840}{230} \\\\ \mathrm{R} &=8 \% \end{aligned}[/tex]

Hence, the required rate of interest per year is 8%

Answer:

The annual rate of interest per year is 8%

Solution:

Given:- Principal (p) = 4600 rupees, Time –Period (t) = 5 years, Total amount(A) = 6440 rupees

First we will calculate the Interest and then using formula of simple interest we will calculate the rate of interest

Interest = Amount – Principal

Interest = 6440  – 4600 = 1840

Now using the formula of simple Interest and on putting values we get,

Where "P" is the principal and "R" is the rate of interest per annum and "T" is the time period

Hence, the required rate of interest per year is 8%

Let me know if it is correct! Thank you. :)

Step-by-step explanation:

The expression for the nth term of the given sequence -7, -12, -17, -22, -27 is -7 - 5(n-1).

The given sequence is -7, -12, -17, -22, -27. In this sequence, each term is obtained by subtracting 5 from the previous term. So, we can write the expression for the nth term as:

-7 - 5(n-1)

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The puppy's weight increased by 60%.

Answer:

Step-by-step explanation:

60

Eric collected 18 green gems and 7 blue gems.

Step-by-step explanation:

Let,

Green gems = x

Blue gems = y

One green gem = 5 points

One blue gem = 10 points

According to given statement;

x+y=25   Eqn 1

5x+10y=160   Eqn 2

Multiplying Eqn 1 by 5;

[tex]5(x+y=25)\\5x+5y=125\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 2;

[tex](5x+10y)-(5x-5y)=160-125\\5x+10y-5x-5y=35\\5y=35[/tex]

Dividing both sides by 5;

[tex]\frac{5y}{5}=\frac{35}{5}\\y=7[/tex]

Putting y=7 in Eqn 1;

[tex]x+7=25\\x=25-7\\x=18[/tex]

Eric collected 18 green gems and 7 blue gems.

Keywords: linear equations, subtraction

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Eric collected 18 green gems and 7 blue gems. This conclusion is reached by forming and solving a system of linear equations based on the problem's conditions related to the total number of gems and their respective point values.

This question deals with a system of equations, defined by the value of the gems and the total number of gems. Here, let's represent green gems as 'g' and blue gems as 'b'.

The two equations formed from the problem are as follows: g + b = 25 (since Eric collected 25 gems) and 5g + 10b = 160 (since green gems are worth 5 points each and blue ones 10, yielding a total score of 160).

To solve it, we need to isolate one of the variables: first, multiply the first equation by 5: 5g + 5b = 125. Then subtract this equation from the second equation, so we get 5b = 35, which simplifies to b = 7.

Substitute b = 7 into the first equation to get g = 25 - 7 = 18. Therefore, Eric collected 18 green gems and 7 blue gems.

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Answer:

65%

Step-by-step explanation:

Cross, multiply and divide method has saved my life with these problems, heres how to do it.

Set up like this:

143 x

------- = -------

220 100

Multiply 143 by 100, then divide that by 220.

x= 65, so she has read 65%

Final answer:

Olivia has read approximately 65% of her 220-page novel by reading 143 pages.

Explanation:

To calculate the percent of the novel that Olivia has read, we use the formula: (number of pages read ÷ total number of pages) × 100%. Olivia has read 143 pages of a 220-page novel. Therefore, the calculation is (143 ÷ 220) × 100%, which simplifies to approximately 65%.

The steps to solve the problem are given below:

Step 1: 143 / 220 = 0.65

Step 2: 0.65 x 100 = 65%

So, Olivia has read about 65% of the novel.

Answer:

wheres the answer choices

Answer:

38/3 km per hour

Step-by-step explanation:

3 1/6=19/6

1/4=0.25

(19/6)*4=38/3

Answer:

a is 7.5

b is 67.5

c is 100

d is let me think on d

Answer:

a is 7.5

b is 67.5

c is 100

d is for every 7.5

[tex]h^{-1}(x) = \frac{2x-8}{5}[/tex]

Step-by-step explanation:

Given function is:

[tex]h(x) = \frac{5}{2}x+4[/tex]

In order to find the inverse:

Replacing h(x) with y

[tex]y = \frac{5}{2}x+4[/tex]

Replacing x with y and y with x

[tex]x = \frac{5}{2}y+4[/tex]

Solving for y

[tex]x = \frac{5}{2}y+4\\x - 4 = \frac{5}{2}y+4-4\\x-4 = \frac{5}{2}y\\y = \frac{2}{5}(x-4)\\y = \frac{2x-8}{5}[/tex]

Replace y with h^(-1)(x)

[tex]h^{-1}(x) = \frac{2x-8}{5}[/tex]

Hence,

[tex]h^{-1}(x) = \frac{2x-8}{5}[/tex]

Keywords: Inverse, Functions

Learn more about functions at:

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The ratio of Erin's tennis trophies to soccer trophies is 3/7.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

As per the given,

She has earned 333 tennis trophies, 444 basketball trophies, 777 soccer trophies, and 111 volleyball trophies.

The ratio of tennis trophies to soccer = 333/777

3/7(111/111) = 3/7

Hence "The ratio of Erin's tennis trophies to soccer trophies is 3/7".

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This is an incomplete question, here is a complete question.

Debnil has 6 teaspoons of salt. The ratio of teaspoons to tablespoons is 3:1 How many tablespoons does Debnil have?

A. 1/18

B. 1/2

C. 2

D.18​

Answer : The correct option is, (C) 2

Step-by-step explanation :

As we are give that Debnil has 6 teaspoons of salt.

The ratio of teaspoons to tablespoons is 3 : 1.

It means,

if he has 3 teaspoons then he has 1 tablespoons

if he has 1 teaspoons then he has [tex]\frac{1}{3}[/tex] tablespoons

So,

if he has 6 teaspoons then he has [tex]6\times \frac{1}{3}=2[/tex] tablespoons

Therefore, Debnil have 2 tablespoons of salt.

The number of tablespoons that debnil has is;

C: 2

We are told that;

Thus, if the total spoons is x. Then;

¾x = 6

Thus;

x = (4 × 6)/3

x = 8 spoons

Thus, number of tablespoons she has = 8 - 6 = 2

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Answer:

x = -10

Step-by-step explanation:

-16 = 8x/5

-80 = 8x

x = -10

Answer:

The function f(x) has a hole at point x = - 5.

Step-by-step explanation:

We are given a function as

[tex]f(x) = \frac{x^{2} + 7x + 10}{x^{2} + 9x + 20}[/tex]

Now, we have to describe where the function has a hole.

Now, [tex]f(x) = \frac{x^{2} + 7x + 10}{x^{2} + 9x + 20}[/tex]

⇒ [tex]f(x) = \frac{(x + 5)(x + 2)}{(x + 4)(x + 5)}[/tex]

Therefore, the common factor of the numerator and denominator is (x + 5).

Now, (x + 5) = 0

⇒ x = - 5

Therefore, the function f(x) has a hole at point x = - 5. (Answer)

By factoring and simplifying the function f(x)=(x^2+7x+10)/(x^2+9x+20), we find a hole at x=-5. This is because -5 was an excluded value in the original function, but does not cause the denominator to be zero in the simplified function.

The given function is f(x) = (x^2+7x+10) / (x^2+9x+20). To find where the function has a hole, we need to factor both the numerator and the denominator. We also must exclude any values of x that would cause the denominator to be zero as these are undefined in the function.

The numerator factors into (x+2)(x+5), and the denominator into (x+4)(x+5). If we simplify, the x+5 term will cancel out, leaving us with f(x) = (x+2)/(x+4).

Originally, x could not be equal to -4 or -5, as these would make the denominator zero. In the simplified function, only x=-4 causes the denominator to be zero. But since x=-5 was an excluded value in the original function, that indicates there is a 'hole' at x=-5 on the function.

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Answer:

20,236.32

Step-by-step explanation:

because (-282) * (-71.76) = 20,236.32

Answer:

20236.32 feet

Step-by-step explanation:

-282*-71.76=20236.32

I can't really give an explanation, since it's just multiplication, so here are the answers:

1. 32

2. 12

3. 24

4. 40

5. 20

6. 12

7. 12

Answer:

h=11.3 and c=8(or 8.1 depending on what you do first)

Step-by-step explanation:

so we do the same thing like last time and 8√2 rounded is 11.3, and 7/√3, or 7√3/3 is 4( 4.04 gets rounded down). now we multiply by two because of the theorems and get 8(if this is wrong then try 8.1 because the answer differs depending on what you do first.)

Answer:

$0.5

Step-by-step explanation:

formula ; y = kx

where ; y = $1.5

             x = 3 pounds of bananas

             k = constant of proportionality

Step 1. Do the equation based on the data given

y = kx

$1.5 = k3

Step 2. Compute the mathematical equation. Divide both sides by the coefficient of 3.

$1.5 = k3

  3      3

k = .5

Answer; $0.5 is the constant of proportionality cost in dollars per pound of banana.

Answer:

0.25

Step-by-step explanation:

Have a nice day <3

Answer:

L=15  W=12   15*12 = 180

Step-by-step explanation:

W*L = area

W*(W+3) = 180

Do the distributive

W^+3 W-180=0

Find 2 numbers that when multiplied ,the result is -180

and when added the result is 3

      - 12* 15  = -180

        -12 +15 = 3

Answer:

The slope is 1/2.

Step-by-step explanation:

m=(-2-(-4))/(7-3)=(-2+4)/4=1/2

Last year's salary is $32000

Step-by-step explanation:

We will use the linear equations to solve the given problem

Let x be the last years salary

then

0.06x will be the raise in the salary

This year's salary is $33920

So,

[tex]x+0.06x=33920\\1.06x=33920[/tex]

Dividing both sides by 1.06

[tex]\frac{1.06x}{1.06}=\frac{33920}{1.06}\\=32000[/tex]

Hence,

Last year's salary is $32000

Keywords: Percentage, Linear equations

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Answer:

50, 62

The drawing will help

Answer:

Step-by-step explanation:

[tex]a(1)=2\\\\a(2)=a(1)+12=2+12=14\\\\a(3)=a(2)+12=14+12=26\\\\a(4)=a(3)+12=26+12=38\\\\a(5)=a(4)+12=38+12=50\\\\a(5)=a(5)+12=50+12=62[/tex]

If you want the formula.

It's an arithmetic sequence with the first term 2 and common difference 12.

The explicit formula of an arithmetic sequence:

[tex]a(n)=a(1)+(n-1)d[/tex]

d - common difference

Substitute:

[tex]a(n)=2+(n-1)(12)[/tex]        use the distributive property

[tex]a(n)=2+12n-12[/tex]

[tex]a(n)=12n-10[/tex]

Answer:

t=3

Step-by-step explanation:

Answer:

I would marry Ino from Naruto

Step-by-step explanation:

Plz mark brainliest

Answer:

my bestfriend jaheim

Step-by-step explanation:

Answer:

Step-by-step explanation:

Wheres the picture?

The equation (5 x 2) + (5 x 4) = 5 x (2 + 4) showcases the distributive property in mathematics where two different expressions yield the same result.

The equation (5 x 2) + (5 x 4) = 5 x (2 + 4) is a demonstration of the distributive property in mathematics.

(5 x 2) + (5 x 4) can be simplified as 10 + 20 = 30.

5 x (2 + 4) can be simplified as 5 x 6 = 30.

Hence, both sides of the equation result in the same value, displaying the equality of the expression.

Answer:

The volume in liters is 2.041165665 liter.

Step-by-step explanation:

Given : Clare wants to mail a package that weighs [tex]4\frac{1}{2}[/tex] pounds.

To find : What could be its volume in liters ?

Solution :

We know that,

Pound (lb) is a unit of Weight used in Standard system.

Liter (l) is a unit of Volume used in Metric system.

To convert 1 pound into liter is

1 pound (lb) = 0.45359237 liter (l)

[tex]4\frac{1}{2}[/tex] pounds in simpler fraction is [tex]\frac{9}{2}[/tex]

Converting into liter,

[tex]\frac{9}{2}[/tex] pound (lb)=[tex]\frac{9}{2}\times 0.45359237[/tex] liter (l)

[tex]\frac{9}{2}[/tex] pound (lb) = 2.041165665 liter (l).

Therefore, the volume in liters is 2.041165665 liter.

Answer:

[tex]\cos x=-\dfrac{\sqrt{21}}{5}\\ \\\tan x =-\dfrac{2}{\sqrt{21}}\\ \\\cot x=-\dfrac{\sqrt{21}}{2}[/tex]

Step-by-step explanation:

Given

[tex]\sin x=\dfrac{2}{5}\\ \\\cos x<0[/tex]

Use formula:

[tex]\cos^2x+\sin ^2x=1\\ \\\cos^2x+\left(\dfrac{2}{5}\right)^2=1\\ \\\cos^2x=1-\dfrac{4}{25}\\ \\cos^2x=\dfrac{21}{25}\\ \\\cos x=\pm \dfrac{\sqrt{21}}{5}[/tex]

Since [tex]\cos x<0,[/tex] then

[tex]\cos x=-\dfrac{\sqrt{21}}{5}[/tex]

By definition,

[tex]\tan x =\dfrac{\sin x}{\cos x}=\dfrac{\frac{2}{5}}{-\frac{\sqrt{21}}{5}}=-\dfrac{2}{\sqrt{21}}\\ \\ \\\cot x=\dfrac{1}{\tan x}=\dfrac{1}{-\frac{2}{\sqrt{21}}}=-\dfrac{\sqrt{21}}{2}[/tex]

Answer:

y=x

Step-by-step explanation:

Answer:

y = x

because it's at 1y axsis, and 1x axsis

Answer:

f(x) = |x| or f(x) = x² etc.

Step-by-step explanation:

There are several functions that gives positive value for entire interval [-3,-2].

Like the function, y = |x| , where if you put any negative value of x, the resulting output of the value of y is always positive. Therefore, for domain of [-3,-2] the range of the function will be [3,2]

Again, the function y = x², where if you put any negative number as a value of x, the corresponding value of y will be always positive.

Therefore, for domain of [-3,-2] the range of the function will be [9,4] (Answer)