A gallon of gas last summer was $2.28. This week, a gallon costs $3.48.
What is the percent change?

Answer:

[tex] \frac{1}{2} {x}^{2} + 10 + \frac{1}{4} x[/tex]

Step-by-step explanation:

[tex] \frac{1}{2} {x}^{2} + 2 + \frac{1}{4} x + 8[/tex]

[tex]2 + 8 = 10[/tex]

[tex] \frac{1}{2} {x}^{2} + 10 + \frac{1}{4} x[/tex]

9514 1404 393

Answer:

  23, 49

Step-by-step explanation:

Let s represent the smaller of the two numbers. Then the larger is s+26, and the sum is ...

  s + (s+26) = 72

  2s = 72 -26

  s = (72 -26)/2 = 23

Then the larger number is

  s +26 = 49

The two numbers are 23 and 49.

_____

The reason we wrote the solution this way is to show you that the smaller number is half the difference between the given sum (72) and difference (26). This is the generic solution to a "sum and difference" problem. The smaller number is always half the difference of the give sum and difference. (Similarly, the larger is always half the sum of the given sum and difference.)

That is, the two numbers are always half the sum ± half the difference:

  72/2 ± 26/2 = {36+13, 36-13} = {49, 23}

Using the z-distribution, as we are working with a proportion, it is found that the 95% confidence interval for the difference of the proportions is (-0.052, -0.0038).

For each sample, the mean and the standard error are given by:

[tex]p_C = 0.0256, s_C = \sqrt{\frac{0.0256(0.9744)}{586}} = 0.0065[/tex]

[tex]p_H = 0.0535, s_H = \sqrt{\frac{0.0535(0.9465)}{467}} = 0.0104[/tex]

Hence, for the distribution of differences, the mean and the standard error are given by:

[tex]p = p_C - p_H = 0.0256 - 0.0535 = -0.0279[/tex]

[tex]s = \sqrt{s_C^2 + s_H^2} = \sqrt{0.0065^2 + 0.0104^2} = 0.0123[/tex]

It is given by:

[tex]p \pm zs[/tex]

In which z is the critical value.

95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so [tex]z = 1.96[/tex].

Then, the bounds of the interval are given as follows:

[tex]p - zs = -0.0279 - 1.96(0.0123) = -0.052[/tex]

[tex]p + zs = -0.0279 + 1.96(0.0123) = -0.0038[/tex]

The 95% confidence interval for the difference of the proportions is (-0.052, -0.0038).

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Answer:

.00035453808

Step-by-step explanation

Answer:

Step-by-step explanation:

if you draw the situation you get a right triangle with

hypothenuse Edelton Walton and the Park City as the vertex of the right angle

Michael went 38+25= 63 miles

Landon went the length of the hypothenuse so use Pythagorean theorem

√38²+25² ≅45.49miles

Michael went 63-45.5 ≅17.5 further

Answer:

1/3 is eaten and 2/3 is left

Step-by-step explanation:

Answer:

Step-by-step explanation:

5x-(x-18)=6-2(x+15)

5x-x+18=6-2x-30

6x=-42

x=-7

The equivalent value of the expression is x = -7

Given data ,

Let the equation be represented as A

Now , the value of A is

5x - ( x - 18 ) = 6 - 2 ( x + 15 )

On simplifying the equation , we get

5x - ( x - 18 ) = 6 - 2 ( x + 15 )

So , the left hand side of the equation is equated to the right hand side by the value of 6 - 2 ( x + 15 )

Opening the parenthesis on both sides , we get

5x - x + 18 = 6 - 2x - 30

From the distributive property , we get

5x - x + 18 = 6 - 2x - 30

On further simplification , we get

4x + 18 = -2x - 24

Adding 2x on both sides , we get

6x + 18 = -24

Subtracting 18 on both sides , we get

6x = -24 - 18

6x = -42

Divide by 6 on both sides , we get

x = -42/6

x = -7

Therefore , the value of x = -7

Hence , the expression is x = -7

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Answer:

ehjrbbvhbvebvuhbdhvhdhsduhsdbrhw

Step-by-step explanation:

Answer:

4n ≥ 5/6

Step-by-step explanation:

Hope this helps!!!

Answer:

9

Step-by-step explanation:

simplify both sides of the equation then isolate the variables. hope this helps

Answer: A) The only zero of the function is 3 which is where the graph of the function intersects the x-axis

Step-by-step explanation:

Remember, a quadratic function which has roots x = a, and x = b, can be written as:

p(x) = A*(x - a)*(x - b)

Where A is the leading coefficient. This is the factorized form of a quadratic.

We have the function:

f(x) = (x - 3)^2

Now, we could rewrite this as:

f(x) = (x - 3)*(x - 3) = 1*(x - 3)*(x - 3)

Then we wrote f(x) in its factorized form, from this, we can see that the roots of the function are x = 3, and x = 3 (we have the same root two times)

Then the only root of f(x) is x = 3.

Remember that a root (also called a zero) is the value of x where the function intersects the x-axis. then the correct option here is:

A) The only zero of the function is 3 which is where the graph of the function intersects the x-axis

Answer:

Which one?

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

di ko po alam kung tama ba

(sana po makatulong po)

Answer:

prime factors of 900 are 2,2,3,3,5,5

which is the same as 2^2×3^2×5^2

Answer:

45°

Step-by-step explanation:

abcdefghijklmnopqrstuvwxyz

Answer:

1: 90 degrees

2: 45 degrees

3: 8

Step-by-step explanation:

This is the only reasonable answer

Answer:

X = 5

Step-by-step explanation:

Answer:

1. 258 square meters

2. 180 square meters

3. 286 square feet

Step-by-step explanation:

1. Find the surface area of each side:

9 * 5 + 5 * 6 + 9 * 5 + 6 * 5 + 9 * 6 + 9 * 6

45 + 30 + 45 + 30 + 54 + 54

75 + 75 + 108

150 + 108

258

2. Base: 5 * 5 = 25

Top: 5 * 5 = 25

Sides: each 5 * 6.5 = 32.5

Altogether: 32.5 * 4 = 130

130 + 25 + 25 = 180

3. Base and top: both 8 * 10 = 80, together 80 * 2 = 160

Front and back sides: both 8 * 3.5 = 28, together 28 * 2 = 56

Left and right sides: both 10 * 3.5 = 35, together 35 * 2 = 70

Altogether: 160 + 56 + 70 = 286 sq feet

Answer:

Step-by-step explanation:

x is the amount of the bill

tax = 8.25% of x = 0.0825x

tip = 20% of x = 0.20x

total payment = x + 0.0825x + 0.20x = 1.2825x

The total cost of the meal is given by the equation A = x + 0.2x + 0.0825x and A = 1.2825x , where x is the initial cost of the meal

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let total cost of the meal be represented as A

Now , the equation will be

Let the cost of the meal be x

Let the tip percentage be = 20 %

Now , the sales tax percentage of the meal = 8.25 %

So , the total cost of the meal A = cost of the meal + ( tip percentage x cost of the meal ) + ( sales tax percentage of the meal x cost of the meal )

Substituting the values in the equation , we get

The total cost of the meal A = x + ( 20/100 )x + ( 8.25/100 )x

On simplifying the equation , we get

The total cost of the meal A = x + 0.2x + 0.0825x

The total cost of the meal A = 1.2825x

Hence , the equation is A = 1.2825x

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Answer:

60cm³

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

The agency's commission was ...

  0.046 × $311,000 = $14,306

The agent's commission was ...

  0.25 × $14,306 = $3,576.50

__

The agency made $14,306; the agent earned $3,576.50.

Answer:

28

Step-by-step explanation:

7C2

The 3rd term of 7th row of the Pascals triangle is 21.

We have a Pascal's triangle.

We have to determine the 3rd term of 7th row of this triangle.

A pascal's triangle is an arrangement of numbers in a triangular array such that the numbers at the end of each row are 1 and the remaining numbers are the sum of the nearest two numbers in the above row. The pascals triangle is shown below -

[tex]\begin{tabular}{rccccccccc}$n=0$:& & & & & 1\\\noalign{\smallskip\smallskip}$n=1$:& & & & 1 & & 1\\\noalign{\smallskip\smallskip}$n=2$:& & & 1 & & 2 & & 1\\\noalign{\smallskip\smallskip}$n=3$:& & 1 & & 3 & & 3 & & 1\\\noalign{\smallskip\smallskip}$n=4$:& 1 & & 4 & & 6 & & 4 & & 1\\\noalign{\smallskip\smallskip}\end{tabular}[/tex]

If we have to find the element or term at position - m in row number - n, than the element will be -

[n] C [m-1] = [n-1] C [m-2] + [n-1] C [m-1]

According to the question, we have to find the 3rd term of 7th row of this triangle. It can be found out using the formula -

[n] C [m-1] = [n-1] C [m-2] + [n-1] C [m-1]

We have - n = 7 and m = 3

[7] C [2] = [6] C [1] + [6] C [2]

[tex]$\frac{7!}{(7-2)!2!} = \frac{6!}{(6-1)!1!} + \frac{6!}{(6-2)!2!} = 6 + 15 = 21[/tex]

Hence, the 3rd term of 7th row of the Pascals triangle is 21.

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Those look hard

But maybe someone can help

9514 1404 393

Answer:

  5 miles

Step-by-step explanation:

It may get a bit messy, but we can solve for the desired value directly. Let d = the distance walked (in miles). Then 20-d is the distance traveled in the car. The relevant relation is ...

  time = distance / speed

The total travel time is 9:00 -6:50 = 2:10 = 2 1/6 hours = 13/6 hours. Here is the equation for total travel time.

  total time = time spent walking + time spent riding

  13/6 = (d/3) + (20-d)/30

Multiplying by 30 gives ...

  65 = 10d + 20 -d

  45 = 9d . . . . . . . . . . subtract 20

  5 = d . . . . . . . . . . . . divide by 9

The girl walked 5 miles.

_____

Check

Her walking time was (5 mi)/(3 mph) = 5/3 h = 1:40.

Her riding time was (15 mi)/(30 mph) = 1/2 h = 0:30.

Her total travel time was 1:40 +0:30 = 1:70 = 2:10, as required.

Answer:

The length of the actual wall is 405 inches or 33.75 feet