Last week, Sally bought 8 ½ gallons of
gas at $2.30 per
gallon. This week, she bought 4 ½ gallons at $2.20 per
gallon. What was her total cost?

Answer:

  2 2/3 hours

Step-by-step explanation:

You want to know the time it would take Elon, Jeff, and Bruce working together, if Elon and Jeff can complete the work in 3 hours, Jeff and Bruce take 6 hours, and Elon and Bruce take 4 hours.

Job completion time problems like this one are more easily understood in terms of rate of completion. If we let e, j, and b represent the rates of job completion in jobs per hour for each of Elon, Jeff, and Bruce, respectively, then the given relations can be written ...

  e +j = 1/3

  j +b = 1/6

  e +b = 1/4

Adding these equations together gives ...

  (e +j) +(j +b) +(e +b) = (1/3) +(1/6) +(1/4)

  2(e +j +b) = 3/4 . . . . . . . simplify

  e + j + b = 3/8 . . . . . . . . divide by 2

The total rate of job completion when Elon, Jeff, and Bruce work together is 3/8 job per hour. The hours it takes them to do one job is the reciprocal of this:

  1/(3/8 job/hour) = 8/3 hour/job

It would take Elon, Jeff, and Bruce 2 2/3 hours to complete the work if they worked together.

__

Additional comment

For this problem, we don't need to know the individual completion times. If we were to figure them we'd find them to be (working alone) ...

The amount in Mrs. Piazza's account after 4 years is 8960 dollars.

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time. In simple interest, the principal amount is always the same, unlike compound interest where we add the interest of previous years principal to calculate the interest of the next year.

Principal(P) = 8000

time(T) = 4 years

rate(R) = 3%

simple interest = PRT/100

Simple interest = 8000 x 3 x 4 / 100

simple interest is 960 dollars

Amount after 4 years = principal + interest

                                    = 8000 + 960

                                    = 8960 dollars

In conclusion, the Amount after 4 years is 8960 dollars

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Answer: w=6

Step-by-step explanation: 1. Simplify. Distribute the -4 to the w and the -3. -4*w is -4w and -4*-3 is +12, so your left with 3w-4w+12=6.

2. simplify again. 3w-4w is -w.

3. -w+12=6. Subtract w to both sides, so its -w=-6. The negatives cancel out, so w just equals 6.

The last function having the greatest rate of change.

What is rate of change?

The pace at which one quantity changes in relation to another quantity is known as the rate of change function. Simply said, the rate of change is calculated by dividing the amount of change in one item by the equal amount of change in another.

Consider the first function,

From this function we get two points (2, 1) and (-2, -1).

To find rate using this points.

Rate = [tex]\frac{y_2-y_1}{x_2-x_1} = \frac{-1-1}{-2-2} = \frac{-2}{-4}=\frac{2}{4} =\frac{1}{2}[/tex]

Consider the second function,

The second function is a vertical line of x = -3.

Since the rate of vertical line is undefined.

Consider the third function,

The third function is a horizontal line y =  4.

Since two points having the same y - value.

Hence, the rate is zero.

Consider, the last function,

From last function we get two points (1, 5) and (-3, -3).

So,

Rate = [tex]\frac{-3-5}{-3-1} = \frac{-8}{-4} = \frac{8}{4} = 2[/tex]

Hence, the last function having the greatest rate.

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Answer:

Please be more specific

Step-by-step explanation:

Answer: It should be 33.5%

The total amount  will have in the account in 15 years is $900.47

What is compound interest?

Compound Interest is the interest calculated on the cumulative amount, rather than being calculated on the principal amount only.

Amount,[tex]A=P[1+(\frac{R}{100})^{T}][/tex], where P is the principal, R is the rate of interest per unit time period and n is the time period.

Compound Interest, CI = Amount – Principal

Using the formula,

                     [tex]A=P[1+(\frac{R}{100})^{T}][/tex]

Where,

             A=Total Amount(To be calculated)

             P=Principal of money deposited=$500

             R=Annual interest rate=4%

             T=Time in years=15 years

⇒[tex]A=500(1+\frac{4}{100}[/tex][tex])^{15}[/tex]

⇒A=500(1+0.04[tex])^{15}[/tex]

⇒A=500(1.04[tex])^{15}[/tex]

⇒A=500*1.80094351

⇒A=$900.47

Hence,the total amount will have in account in 15 years is $900.47

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Markup adds an increase in the original price of an item, and tips or taxes add money to a bill. Hence, the connection between markups and tips or taxes.

Discounts are given in order to lower the price of an item from its original price, and markdown is the price that is reduced from an item's original price.

What is the difference between Markup and Markdown?
Markup price is the increase in an item (by a certain percentage) over the original price.

Markdown prices are reductions in an item's selling price from its initial selling price expressed as a rate (markdown percentage).

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The correct option for the given function is (D) g(-13) = 20.

Given that:

The function g has domain -20 ≤ x ≤ 5, range -5 ≤ g(x) ≤ 45, g(0) = -2, g(-9) = 6.

Let's analyze each option to see if it fits the given domain.

A. g(7) = -1

At the beginning of the problem, it is said that the domain is restricted to the range [-20, 5]. The input x = 7 here is outside this domain. That is, it cannot be true for function g without being in the domain. So g(7) is not possible.

B. g(-4) = -11

Similarly, it is said that the domain is restricted to the range [-20, 5]. The input x = -4 here is outside this domain. That is, it cannot be true for function g without being in the domain.

C. g(0) = 2

We know in the question that g(0) = -2. So, this is also the wrong option.

D. g(-13) = 20

Unlike the other options, x= -13 is in the range of -20 to 5. g(-13) = 20 is also in the range of -5 to 45. Option D is true for a function g.

x= -13 is in range and 20 is also in range. So this applies to g.

From the statement given,

g(-13) = 20 is true for the value of g.

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Answer:

x = - 8

Step-by-step explanation:

7(4 - x) = 84 ( divide both sides by 7 )

4 - x = 12 ( subtract 4 from both sides )

- x = 8 ( multiply both sides by - 1 )

x = - 8

As a check

substitute x = - 8 into the left side of the equation and if equal to the right side then it is the solution.

7(4 - (- 8) )

= 7(4 + 8)

= 7(12)

= 84 = right side

Then x = - 8 is the solution to the equation

The third coordinate of the equilateral triangle is [tex](\sqrt3a,0)[/tex]. Ir can be obtained by distance formula.

What is distance formula?

It gives the distance between two coordinates.

Distance formula is given by the following expression:

[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Consider the third cordinate is (x,0) and x is positive because it is on tight side on the x axis.

Now, since the triangle is equilateral hence, the distance of (x,0) from (0, -a) and (0, a) should be equal to distance between (0, -a) and (0, a).

Now, caculate the distance between (0,-a) and (0, a).[tex]\sqrt{(0-0)^2+(-a-a)^2}=2a[/tex]

Now, distance between (x,0) and (0, a) should be 2a.

[tex]\sqrt{(x-0)^2+(0-a)^2}=2a\\\sqrt{x^2+a^2}=2a[/tex]

Now, square on both the sides.

[tex]x^2+a^2=4a^2\\x^2=3a^2\\x=\sqrt3a[/tex]and [tex]-\sqrt3a[/tex]

But the negative value of x is not possible because the coordinate lies on the right side.

Hence, the third coordinate of equilateral triangle is [tex](\sqrt3a,0)[/tex].

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Answer:

x = 10

Step-by-step explanation:

The angles are supplemental

100 -2x + 10x = 180  Combine like terms

100 + 8x = 180  Subtract 100 from both sides of the equation

8x = 80  Divide both sides by 8

x = 10

The x value is 12, length is 14 feet and breath is 9 feet when the area of rectangle is 126 square feet.

Given that,

The rectangle has a surface area of 126 square feet.

The length is x+2 and the breath is x-3.

We have to find the x value, length and breath.

We know that,

The area of the rectangle is length × breath.

126=(x+2)(x-3)

126= x²-3x+2x-6

126= x²-x-6

x²-x-6-126=0

x²-x-132=0

x²-12x+11x-132=0

x(x-12)+11(x-12)=0

(x-12)(x+11)=0

x-12=0     or   x+11=0

x=12        or    x=-11

We take the x as positive so its 12.

Length is x+2=12+2=14

Breath is x-3=12-3=9

Therefore, The x value is 12, length is 14 feet and breath is 9 feet when the area of rectangle is 126 square feet.

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a) The total amount in the account after the last deposit is $26755.96.

b) A total of $16900 was deposited.

c) Amount of each withdrawal is $517.

d) The total amount withdrawn is $31020.

The worth of a present asset at some point in the future based on an estimated rate of growth is known as future value (FV). For investors and financial planners, the future value is crucial because they use it to predict how much an investment made now will be worth in the future.

FV of a single deposit of $ 2800 can be computed as

FV₁ = PV(1+r)ⁿ

PV = $ 2800

r = 6% = 0.06/12

r = 0.005

n= number of periods

= 12 yr × 12 months = 144

FV₁ = 2800 (1 + 0.005)¹⁴⁴

= 2800 (1.005)¹⁴⁴

= 2800(2.0507)

= 5741.96

The FV of monthly deposits can be computed using the formula for the FV of the annuity:

FV₂ = C x [(1+r) n -1/r]

Periodic cash deposit, C = $100

So,

FV = 100 × [((1.055)¹⁴⁴ - 1)/0.005]

= 100 × [(2.0507 - 1)/0.005]

= 100 × [1.0507/0.005]

= 100 × 210.14

= $21014

The total future value of the account is given by

= $5741.96 + $21014

= $26755.96

b) Total deposit = Initial investment amount + amount of monthly deposits

= 2800 + (100 × 144)

= 2800 +14400

= 16900

c) Formula for PV of an annuity can be used to compute monthly withdrawals as:

PV = A x [1-(1+r)⁻ⁿ/r]

So, A = PV/[1-(1+r)⁻ⁿ/r]

PV = $26755.96

n= number of periods = 5 × 12 = 60

r = 0.005 per month

A = 26755.96/ [1- (1+0.005)⁻⁶⁰/0.005]

A = 26755.96/ [1- (1.005)⁻⁶⁰/0.005]

A = 26755.96/ [1- (0.7413)/0.005]

= 26755.96/ [0.2587/0.005]

= 26755.96/(51.74)

= 517.12

So, the amount of each withdrawal for five years is $517.

d) Total amount withdrawn is

= number of withdrawals × amount of each withdrawal

= 60 × 517

=31020

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The answer, the money needs to be deposited each month is $557.47.

What is simple interest?

A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,

The future money plan to have 500000

Retirement in 35 years.

The interest 4%.

number of time periods = 35 years * 12 months per year = 420

interest will be .4166666667% per month

The formula = [tex]p(\frac{(1+r/n)^{r/n} -1 }{\frac{r}{n} } )[/tex]

⇒500000*(.014/12) = d(3.98-1)

⇒d = 1666.7/2.98 = 557.47

Hence the money needs to be deposited each month is $557.47

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The triangle with all sides is are given below

What is a triangle?

Triangles are three-sided closed polygon formed by the intersection of three lines. It is encountered a lot in everyday life. It is one of the basic shapes of geometry. It has three sides, three angles, and three vertices.

Given, angle A =30, b=6

we know cos 30 = √3/2

√3/2 = b/c

√3/2=6/c

c =6/√3/2= 6.9

Similarly for a=13, b =13

using pythagoras theorem,

c^2=a^2+b^2

=18.38

Hence, we can write the rest part

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Answer:

3

Step-by-step explanation:

2.64 rounded to the nearest whole number would be 3. This is because if a number is 5 or greater than 5, it rounds up, but if a number is under 5, it would round down. Since we are looking at the number to the right of the 2 in 2.64, and because we are looking for the nearest whole number, it would round up to 3. 6 is greater than 5, so we automatically know that we round up.

The expression of logarithm will be -In4 x k .

Given,

In the question:

The expression of the logarithms is:

In[tex](\frac{1}{4^k} )[/tex]

To solve the above expression:

Now, According to the question:

In([tex]\frac{1}{4^k}[/tex])

Apply laws of logarithm to simplify the expression

-In[tex]4^k[/tex]

Express the logarithm of a power of an expression as the power times the logarithm of the expression

-k x In4

Multiply the monomials :

-In 4 x k

Hence, The expression of logarithm will be -In4 x k .

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Answer: It is C

Step-by-step explanation:

The slop for Kitten A is 1/4 or 4

Kitten B has a slop of 2/6 or 3 so the answer is,

If the six teams of a baseball league , and each team plays seven games with each other , then the number of games to be played is 105  .

in the question ,

it is given that

the number of teams in the baseball league = 6

number of matches that each team plays with each other = 7 .

Number of ways two teams can be selected out of 6 teams = C(6,2)

and they need to play 7 games with each other ,

so the number of games required to complete the schedule is

= 7 × C(6,2)

= 7 × 15

= 105

Therefore , the number of matches that is needed to complete the schedule is 105 .

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The value of b is 405 in the given polynomial (a+3)⁵=a⁵+15a⁴+90a³3²+270a²+ba+243

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

Given,

(a+3)⁵=a⁵+15a⁴+90a³3²+270a²+ba+243,

We need to find the value of b

The binomial formula for (a+b)⁵=a⁵+5a⁴b+10a³b²+10a²b³+5ab⁴+b⁵

Now let us find (a+3)⁵

We just need to replace b with 3 in above formula.

(a+3)⁵=a⁵+5a⁴3+10a³3²+10a²3³+5a3⁴+3⁵

=a⁵+15a⁴+90a³3²+270a²+405a+243

Hence the value of b is 405 in the given polynomial a⁵+5a⁴b+10a³b²+10a²b³+5ab⁴+b⁵

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There is only 1 way for all 5 selected calculators to be defective.

There are 792 different ways for all 5 selected calculators to be non-defective.

Given, that a box contains 17 calculators, 5 of which are defective.

So, there are 12 non-defective calculators.

Now, five calculators are selected randomly from the box.

We are asked the number of ways in which all the selected calculators are defective.

So, the number of ways in which all selected 5 calculators be defective is,

C(5 , 5) i.e. we only select 5 defective calculators.

C(5 , 5) = 1.

So, there is only 1 way for all 5 selected calculators to be defective.

Now, we are asked the number of ways in which all the selected calculators are non-defective.

So, the number of ways in which all selected 5 calculators be non-defective is,

C(12 , 5) i.e. we select 5 calculators from the 12 non-defective calculators.

C(12 , 5) = (12×11×10×9×8)/(5×4×3×2×1)

C(12 , 5) = 792

So, there are 792 different ways for all 5 selected calculators to be non-defective.

Hence, there is only 1 way for all 5 selected calculators to be defective.

There are 792 different ways for all 5 selected calculators to be non-defective.

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Answer:

126.72m

Step-by-step explanation: 1.32 x 96 = 126.72, I struggled with that stuff too no shame

Answer:

100%?

Step-by-step explanation:

Answer:

below

Step-by-step explanation:

point -1,-4

y - -4  = 3 ( x - -1)

y + 4 = 3 ( x+1)     <====== I think this is a far as they want you to take it

y = 3x -1          slope - intercept form

Answer: 49476

Step-by-step explanation:

The solution of the system equation is (-4,-11).

What is system equation?

One or more equations involving a number of variables make up a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations cross, are the solutions of systems of equations.

Here the given system equation is,

=> y = 5/2x-1------->1

=> t=2x-3---------->2

Put 1 into 2 then

=> 5/2x-1=2x-3

=>1/2 x=-2

=> x=-4

Put x=-4 into 2 then,

=> y=-8-3=-11.

Hence the solution of the system equation is (-4,-11).

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Answer:

the third one is the answer.

Step-by-step explanation:

take 0 at the x value, the greatest integer function of 0 is 0 its self. so when you take 0, Y=[x]-2 become -2. so the y-axis Crosses in (0,-2).