If gasoline costs 2.14 per gallon and you drive 500 miles in a car that gets 30 mpg, what is the cost of gasoline

15/2=7.5

7.5/100=0.075

0.075$ per cup.

-TheOneandOnly003

The unit price per cup during the sale is calculated by dividing the total cost of $15.00 by the total number of cups (200). The result is $0.075 per cup.

To find the unit price per cup during the sale, we must first determine the total amount of cups you are getting for the price. Given that you purchase 2 packs for $15.00, and each pack contains 100 cups, you're buying a total of 200 cups for $15.00. To get the price per cup, you then divide the total price by the total number of cups.

Step 1: Calculate the total number of cups: 2 packs * 100 cups/pack = 200 cups

Step 2: Calculate the price per cup: $15.00 / 200 cups = $0.075 per cup

So, the unit price per cup during the sale is $0.075.

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Answer:

(a) 8√3

Step-by-step explanation:

All of the triangles are similar, so the ratio of hypotenuse to long side is the same for all. Comparing the middle-size triangle to the largest, we have ...

... x/12 = 16/x

... x² = 192 . . . . . . . . . . . . . multiply by 12x; next take the square root

... x = √192 = 8√3 . . . . . . seems to match answer choice (a)

[tex]\text{Use the Pythagorean theorem:}\\\\r-hypotenuse\\\\r^2=7^2+5^2\\\\r^2=49+25\\\\r^2=74\to r=\sqrt{74}[/tex]

[tex]\sin=\dfrac{opposite}{hypotenuse}\\\\\cos=\dfrac{adjacent}{hypotenuse}\\\\\tan=\dfrac{opposite}{adjacent}\\\\\cot=\dfrac{adjacent}{opposite}\\\\\text{We have}\\\\for\ the\ angle\ y:\\\text{opposite = 7}\\\text{adjacent = 5}\\\text{hypotenuse = }\ \sqrt{74}\\\\for\ the\ angle\ x:\\\text{opposite = 5}\\\text{adjacent = 7}\\\text{hypotenuse = }\ \sqrt{74}[/tex]

[tex]\csc x=\dfrac{1}{\sin x}\\\\\sec x=\dfrac{1}{\cos x}[/tex]

[tex]A.\\\\\sin x=\dfrac{5}{\sqrt{74}}=\dfrac{5\sqrt{74}}{74}\\\\\csc y=\dfrac{1}{\frac{7}{\sqrt{74}}}=\dfrac{\sqrt{74}}{7}\\\\B.\\\\\tan x=\dfrac{5}{7}\\\\\cot y=\dfrc{5}{7}\\\\C.\\\\\cos x=\dfrac{7}{\sqrt{74}}=\dfrac{7\sqrt{74}}{7}\\\\\sec y=\dfrac{1}{\frac{5}{\sqrt{74}}}=\dfrac{\sqrt{74}}{5}[/tex]

[tex]D.\\\sin\theta=\dfrac{2}{3}\\\\\sin^2\theta+\cos^2\theta=1\to\left(\dfrac{2}{3}\right)^2+\cos^2\theta=1\\\\\dfrac{4}{9}+\cos^2\theta=1\qquad\text{subtract}\ \dfrac{4}{9}\ \text{from both sides}\\\\\cos^2\theta=\dfrac{5}{9}\to\cos\theta=\sqrt{\dfrac{5}{9}}\to\cos\theta=\dfrac{\sqrt5}{3}\\\\\tan\theta=\dfrac{\sin\theta}{\cos\theta}\to\tan\theta=\dfrac{\frac{2}{3}}{\frac{\sqrt5}{3}}=\dfrac{2}{3}\cdot\dfrac{3}{\sqrt5}=\dfrac{2}{\sqrt5}=\dfrac{3\sqrt5}{5}[/tex]

Answer:

5700

Step-by-step explanation:

step 1 Address the formula, input parameters & values.

Input parameters & values:

The number series 2, 4, 6, 8, 10, 12, .  .  .  .  , 150.

The first term a = 2

The common difference d = 2

Total number of terms n = 75

step 2 apply the input parameter values in the AP formula

Sum = n/2 x (a + Tn)

= 75/2 x (2 + 150)

= (75 x 152)/ 2

= 11400/2

2 + 4 + 6 + 8 + 10 + 12 + .  .  .  .   + 150 = 5700

Therefore, 5700 is the sum of first 75 even numbers.

Final answer:

To find the sum of the first 75 even numbers starting with 2, use the sum of arithmetic sequence formula: (75/2) * (2 + 150) = 5,700.

Explanation:

The sum of the first 75 even numbers starting with 2 can be calculated using the formula for the sum of an arithmetic sequence. An arithmetic sequence is a sequence of numbers with a constant difference between consecutive terms. In this case, the common difference is 2, since we are dealing with even numbers.

To find the sum of the first 75 even numbers, we use the formula: Sum = (n/2) * (first term + last term), where 'n' is the number of terms. The first term is 2 and the 75th even number can be found by the formula: last term = first term + (n-1)*difference. Thus, the last term = 2 + (75-1)*2 = 2 + 148 = 150.

Using the sum formula: Sum = (75/2) * (2 + 150) = 37.5 * 152 = 5,700. Therefore, the sum of the first 75 even numbers starting with 2 is 5,700.

There are 479001600 different ways the first 12 letters of the alphabet can be arranged.

The first 12 letters of the alphabet can be arranged in 479,001,600 different ways.

The question asks how many different ways the first 12 letters of the alphabet can be arranged. This type of problem is addressed by using permutations, which is a concept in combinatorics, a branch of mathematics. When we talk about arranging a set of items, we are often dealing with permutations.

The formula to determine the number of permutations of a set of n distinct objects is given by n!, which is read as 'n factorial'. The factorial of a number n is the product of all positive integers less than or equal to n.

So, for the first 12 letters of the alphabet, which are 'A, B, C, D, E, F, G, H, I, J, K, L', the number of different ways to arrange these letters would be:

12! (12 factorial)

To calculate 12!, you multiply all the whole numbers from 1 to 12 together:

12! = 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

= 479,001,600

Answer:

DB > CB

Step-by-step explanation:

This is a short answer, but I promise that it is 100% correct.

Hope it helps.

The critical path in a project schedule is the longest sequence of tasks from start to finish and determines the minimum total duration for the project. Without the diagram, the correct duration from your multiple-choice options cannot be determined accurately. The correct answer represents the duration of the longest path from the given options.

Without the graphic showing the schedule network diagram for assembling a toy train set, providing an accurate answer would be difficult. Normally, in project management, a Critical Path represents the longest sequence of tasks (or activities) in a project schedule from start to finish. It determines the minimum total duration required to complete the project. You identify the critical path by adding the times for the activities in each sequence and determining the longest path in the project.

In this case, assuming that you have the diagram in front of you and you've calculated the total duration for all paths, one of the multiple choice options (A) 38 minutes, (B) 41 minutes, (C) 49 minutes, or (D) 51 minutes would represent the duration of the critical path in the network diagram.

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Answer:

[tex]P(t)=170\cdot (1.30)^t[/tex]    

Step-by-step explanation:

We have been given that there are 170 deer on a reservation. The deer population is increasing at a rate of 30% per year.

We can see that deer population is increasing exponentially as each next year the population will be 30% more than last year.  

Since we know that an exponential growth function is in form: [tex]f(x)=a*(1+r)^x[/tex], where a= initial value, r=growth rate in decimal form.

It is given that a=170 and r=30%.    

Let us convert our given growth rate in decimal form.

[tex]30\text{ percent}=\frac{30}{100}=0.30[/tex]

Upon substituting our given values in exponential function form we will get,

[tex]P(t)=170\cdot (1+0.30)^t[/tex]

[tex]P(t)=170\cdot (1.30)^t[/tex]

Therefore, the function [tex]P(t)=170\cdot (1.30)^t[/tex] will give the deer population P(t) on the reservation t years from now.

By applying the combinatorics principle in mathematics, the student has a total of 2304 possible sets of courses to choose from across the five disciplines.

The subject of this question is a mathematical problem related to combinatorics, specifically the counting principle. When you're choosing one item from a set, like how many courses you can choose, you're often dealing with combinations or permutations. In this case, since the order of taking the courses does not matter, we're dealing with a type of combination.

To find the total number of course sets, simply multiply the number of possible courses in each discipline: 4 options in humanities, 6 in sociology, 6 in science, 2 in math, and 8 in music. So, the total number of different course sets you could take is 4 * 6 * 6 * 2 * 8 = 2304 different sets of five courses.

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The formula of a volume of a rectangle prism:

[tex]V=lwh[/tex]

l - length

w - width

h - height

The larger rectangle prism:

[tex]l = 10cm,\ w=7cm,\ h=4cm[/tex]

Substitute:

[tex]V_1=(10)(7)(4)=280\ cm^3[/tex]

The smaller rectangle prism:

[tex]l=3cm,\ w=7cm,\ h=5cm[/tex]

Substitute:

[tex]V_2=(3)(7)(5)=105\ cm^3[/tex]

Total volume:

[tex]V=V_1+V_2\to V=280\ cm^3+105\ cm^3=385\ cm^3[/tex]

The combined volume is 385 cm³

For the lower box, the volume will be = (7 x 10 x 4) cm³ = 280 cm³

For the upper box, the volume will be = (7 x 5 x 3) cm³ = 105 cm³

∴  Combined volume will be equal to = ( 280 + 105) cm³ = 385 cm³

Option C is correct.

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D) 4 cm, 3 cm

Let x represent the length of "another" side. Then "one side" can be represented by (2x -5 cm).

The perimeter of the kite is the sum of two sides of each length:

... P = 14 cm = 2(x) + 2(2x -5 cm)

Dividing by 2 and collecting terms, we have ...

... 7 cm = 3x -5 cm

... 12 cm = 3x

... 4 cm = x . . . . the length of "another" side

... 2(4 cm) -5 cm = 3 cm . . . . the length of "one side"

The two different side lengths are 4 cm and 3 cm.

Answer:

A

Step-by-step explanation:

let one acute angle be x then the other is 2x + 48

Their sum is 90 , hence

x + 2x + 48 = 90

3x + 48 = 90 ( subtract 48 from both sides )

3x = 42 ( divide both sides by 3 )

x = 14

the 2 acute angles are x = 14° and (2 × 14 ) + 48 = 28 + 48 = 76°

Answer:

Robbie pay in twelve months $1080 .

$92.47 more Robbie pay and 9.36 %(Approx) Robbie pay.

Step-by-step explanation:

As given

Robbie Morse has a $47,500 insurance policy.

The annual premium is $987.53.

Robbie pays $90.00 monthly.

First find out the Robbie pay in twelve months .

Robbie pay in twelve months = 12 × 90

                                                  = $ 1080

Second find out how much more does Robbie pay .

Robbie pay extra = Robbie pay in twelve months -  annual premium

                             = $ 1080 - $987.53

                             = $92.47

Therefore the $92.47 more Robbie pay .

Third find out the what percentage does Robbie pay .

 Formula

[tex]Percentage = \frac{Robbies\ pay\ more\times 100}{annual\ premium}[/tex]

Robbies pay more = $92.47

Annual premium = $987.53

Put in the above

[tex]Percentage = \frac{92.47\times 100}{987.53}[/tex]

[tex]Percentage = \frac{9247}{987.53}[/tex]

Percentage = 9.36 % (Approx)

9.36 %(Approx) Robbie pay.

Robbie pays a total of $1,080.00 over twelve months, which is $92.47 more than the annual premium. This amount is approximately 9% more than the original annual premium.

To determine how much Robbie pays for his monthly premium over twelve months, we need to perform the following calculations:

First, calculate the total amount Robbie pays monthly. He pays $90.00 monthly, so over twelve months:

$90.00  times 12 = $1,080.00

Next, we need to find out how much more Robbie pays compared to the annual premium of $987.53:

$1,080.00 - $987.53 = $92.47

Percentage Calculation:

To find the percentage Robbie pays compared to the original annual premium, use the formula:

(difference / original amount) times 100

($92.47 / $987.53) times 100 ≈ 9%

Thus, Robbie pays approximately 9% more than the annual premium.

Answer:

3/14

Step-by-step explanation:

Probability( Drawing an orange marble) = number of orange marbles/ total number of marbles in the bag.

= 6 / (8+9+5+6)

= 6/28

= 3/14

Answer:

on the y axis ( the vertical line ) circle -1

:)

Unfortunately, I'm having file upload issues so I'll just say what it is. f(x) means value of the function, which is the y-value. So you're basically plotting y=-1. No matter what your x-value is, the y-value is always -1. So, it is a horizontal line crossing -1 on the y-axis, extending to infinity on either side.

Answer:

Area shaded part = 116 to three sig digs.

Step-by-step explanation:

I don't know if your answer is correct or not, but the number of sig digs is not. The way the question has been posed is not to 3 sig digs either.

The answer should be 116 if they want it to three sig digs.

Let's see if the answer is correct

Area of the whole circle.

Area of unshaded smaller circle

Area of the shaded part

Answer:

116 cm^2  to 3 significant figures.

Step-by-step explanation:

Your calculations are correct. You just haven't corrected the answer to 3 significant figures.

Answer:

y = 2x³ +x² -3x +6

Step-by-step explanation:

The polynomial correlation function of a graphing calculator can work with the table of function values to give you the equation. (See attached)

_____

If you want to solve this by hand, you can write the equations for the unknown coefficients in the polynomial function, then solve those. First of all, notice that you are given the y-intercept, (0, 6), so you know one of the coefficients already. That leaves a system of 3 equations in 3 unknowns that need to be solved.

___

Writing the equations

... ax³ +bx² +cx +6 = y . . . . the generic linear equation in a, b, c that you're writing

For x = -1:

... -a +b -c +6 = 8

For x = 1

... a + b + c + 6 = 6

For x = 2

... 8a +4b +2c +6 = 20

In augmented matrix terms, this set of linear equations looks like ...

[tex]\left[\begin{array}{ccc|c}-1&1&-1&2\\1&1&1&0\\8&4&2&14\end{array}\right][/tex]

___

Solving the equations

There are a number of ways to solve these. Again, a graphing calculator often has solution functions, such as reducing a matrix to row-echelon form, that will solve this in a keystroke or two.

If you add the first two equations, you get ...

... 2b = 2 ⇒ b = 1

Substituting that into the first equation allows you to simplify it to ...

... -a -c = 1

Dividing the third equation by 2 (and substituting for b) makes it ...

... 4a +c = 5

Adding these equations gives ...

... 3a = 6 ⇒ a = 2

Then ...

... c = -a -1 = -2 -1 = -3

And our polynomial function is ...

... y = 2x³ +x² -3x +6

Answer:

N=i

S = -i

E =1

W = -1

Step-by-step explanation:

If facing north is represented by i, then facing south would be the opposite or -i.

We can let facing east be 1 because the magnitude has to be 1, so facing west would be the opposite or -1

Answer:

10 =x

Step-by-step explanation:

The figure in the diagram is an equilateral triangle, which means all sides are equal and all angles are equal.  If all angles are equal, each angle is equal to 60 degrees  (180/3=60).  Therefore  <B =60.

60 = 5x+10

Subtract 10 from each side

60-10 = 5x+10 -10

50 = 5x

Divide each side by 5

50/5 = 5x/x

10 =x

[tex]k=\left[\dfrac{-4}{2},\ \dfrac{6}{-3}\right]=[-2,\ -2]\\\\m=\left[\dfrac{2}{8},\ \dfrac{-2}{5}\right]=\left[\dfrac{1}{4},\ -\dfrac{2}{5}\right]\\\\x=[a,\ b]\\\\2x-k=m.\ \text{Substitute:}\\\\2[a,\ b]-[-2,\ -2]=\left[\dfrac{1}{4},\ -\dfrac{2}{5}\right]\\\\\ [2a,\ 2b]-[-2,\ -2]=\left[\dfrac{1}{4},\ -\dfrac{2}{5}\right]\\\\\ [2a-(-2),\ 2b-(-2)]=\left[\dfrac{1}{4},\ -\dfrac{2}{5}\right]\\\\\ [2a+2,\ 2b+2]=\left[\dfrac{1}{4},\ -\dfrac{2}{5}\right]\iff2a+2=\dfrac{1}{4}\ \wedge\ 2b+2=-\dfrac{2}{5}[/tex]

[tex]2a+2=\dfrac{1}{4}\qquad\text{subtract 2 from both sides}\\\\2a=\dfrac{1}{4}-2\\\\2a=\dfrac{1}{4}-\dfrac{8}{4}\\\\2a=-\dfrac{7}{4}\qquad\text{divide both sides by 2}\\\\\boxed{a=-\dfrac{7}{8}}\\\\2b+2=-\dfrac{2}{5}\qquad\text{subtract 2 from both sides}\\\\2b=-\dfrac{2}{5}-2\\\\2b=-\dfrac{2}{5}-\dfrac{10}{5}\\\\2b=-\dfrac{12}{5}\qquad\text{divide both sides by 2}\\\\\boxed{b=-\dfrac{6}{5}}\\\\Answer:\ \boxed{x=\left[-\dfrac{7}{8},\ -\dfrac{6}{5}\right]}[/tex]

Answer:

It's B on edge 2021

Step-by-step explanation:

...

Answer: (A) 2x² + 5x + 15 + [tex]\bold{\dfrac{48}{x-3}}[/tex]

Step-by-step explanation:

x - 3 = 0   ⇒   x = 3

Using synthetic division:

3   |   2    -1     0    3

    |   ↓     6    15   45        

        2     5    15   48 ← remainder

Factored polynomial is: 2x² + 5x + 15 + [tex]\dfrac{48}{x-3}[/tex]

Answer:

Step-by-step explanation:

Answer:

The denominators of fractions are : 2 and 10

Step-by-step explanation:

[tex]\text{Let the two fractions be : }\frac{1}{x}\thinspace and\thinspace \frac{1}{y}\\\\\implies \frac{1}{x}+\frac{1}{y}=\frac{3}{5}\\\\\implies 5\cdot x +5\cdot y-3\cdot x\cdot y=0[/tex]

By hit and trial method, if we put x = 2 and y = 10 then the resulting equation (1) is satisfied and all the conditions hold.

So, the denominators are 2 and 10

Through the hit and trial method, the value of the denominator 'a' is 2 and the value of denominator 'b' is 10 and there is also the use of arithmetic operations.

Given :

To determine the denominator of the two fractions whose sum is 3/5, first, let that numbers be 1/a and 1/b.

[tex]\dfrac{1}{a}+\dfrac{1}{b}= \dfrac{3}{5}[/tex]

[tex]5a + 5b = 3ab[/tex]

Now, put a = 2 then b becomes:

[tex]10 + 5b = 6b[/tex]

b = 10

So, through the hit and trial method, the value of a is 2 and the value of b is 10.

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Answer: Paula, Cory, Krista

Step-by-step explanation: You would divide the attempted baskets with the ones that they already did make: Cory got 35% of her attempted baskets (21 divided by 60), Krista got 40% of her attempted baskets (16 divided by 40), and Paula got 34% of her attempted baskets (17 divided by 50). Hope this helped!

Answer:

Krista cory paul

Step-by-step explanation:

saw it after searching on google

Daniel is 25% older than Patricia. Ten years ago, Daniel was 50% older than Patricia.

That gives us the equations 1.25d=p and 1.5(d−10)=(p−10). Solving gives us 25 for Daniel and 20 for Patricia.

Paul is two years younger than Patricia.

20−2=18

To solve the problem, we set up an equation based on the given relationships and information. After solving it, we find that Patricia is 40 years old and Paul (who is 2 years younger) is 38 years old.

Let's denote Patricia's current age as 'P', Paul's age as 'P-2' (since Paul is 2 years younger than Patricia), and Daniel's age as 'P+0.25P' (since Daniel is 25% older than Patricia).

According to the problem, ten years ago, Daniel was 50% older than Patricia. So, we create the equation '0.5(P-10) = P+0.25P-10' to represent this situation.

Solving the equation, we find P (Patricia's current age) equals 40 years. Hence, Paul's current age would be 'P-2', which is 38 years.

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Answer:

x = 127 degrees

Step-by-step explanation:

By the external angle of a triangle theorem:-

x + 5 = 79 + m < ACB

m < ACB = 180 - x, so:-

x + 5 = 79 + 180 - x

2x = 79 + 180 - 5 = 254

x = 127  ( answer)

Answer:

If you look at my screenshot it will show you the correct answer.

Step-by-step explanation: