Suppose that you drive 40,000 miles per year and gas averages $4 per gallon what will you save in annual fuel expenses by owning a hybrid car averaging 40 miles per gallon rather than an SUV averaging 16 miles per gallon?

The amount paid with discount for the laptop is $ 660.

Discount is the amount of money removed from the price of an object being sold.

Amount paid is the total cost of an item.

Since laptop computer that you want to purchase was originally priced at $750. You will receive a 20% student discount, and the sales tax rate is 8%.

First, we need to know how much discount is given.

Since there is a 20 % discount, the amount of discount removed is 20% × $750 = 0.2 × % 750 = $ 150

Also, there is a sales tax rate of 8%. So, the amount of sales tax added is 8% × $750 = 0.08 × $ 750 = $ 60

So, the total amount paid is T =  price - discount + tax

= $ 750 - $ 150 + $ 60

=  $ 660

So, the amount paid is $ 660.

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Answer:

n = 14

Step-by-step explanation:

Theorem:

In a triangle, the measure of an exterior angle equals the sum of the measures of the two remote interior angles.

12n - 8 = 8n - 4 + 52

4n = 56

n = 14

A quadratic equation in standard form to represent the data in the table is as follows;

y = 0.5x² - 4x + 9

In order to determine a quadratic equation in standard form for the line of best fit that models the data points described above, we would use a scatter plot (graphing calculator).

On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display a quadratic equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the data set, a quadratic equation for the line of best fit is given by:

y = 0.5x² - 4x + 9

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Answer:

Step-by-step explanation:

$1.49 = 149 cents

149 / 42 = ~4

4 cents per fork

Answer:

the Rhine River is approximately 1216 km long

Step-by-step explanation:

a) If the Mississippi River is 19% longer than the Indus River, we can find its length by multiplying the length of the Indus River by 1.19:

Length of Mississippi River = 3200 km x 1.19 = 3808 km

Therefore, the Mississippi River is approximately 3808 km long.

b) If the Rhine River is 62% shorter than the Indus River, we can find its length by multiplying the length of the Indus River by 0.38 (100% - 62% = 38%):

Length of Rhine River = 3200 km x 0.38 = 1216 km

Therefore, the Rhine River is approximately 1216 km long.

Answer:

Examples below

Step-by-step explanation:

How many milliseconds are in 3.25 days?  

How many grams are in 12.6 ounces ?

How many meters are in 2 3/4 miles ?

This means that if at most one household is tuned to Pretty Betty, it is not unusual and does not necessarily indicate that the 26% share value is wrong.

What is probability ?

Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.

This is a binomial distribution problem, where the probability of success (a household tuned to Pretty Betty) is p = 0.26 and the number of trials is n = 14.

The probability that none of the households are tuned to Pretty Betty is:

P(none) = (1 - p)ⁿ = (1 - 0.26)¹⁴≈ 0.031

The probability that at least one household is tuned to Pretty Betty is:

P(at least one) = 1 - P(none) = 1 - 0.031 ≈ 0.969

The probability that at most one household is tuned to Pretty Betty is:

P(at most one) = [tex]P(0) + P(1) = (1 - p)^n + np(1 - p)^{(n-1)[/tex] ≈ 0.500

However, if more than one household is tuned to Pretty Betty, it may indicate that the share value is inaccurate.

Therefore, This means that if at most one household is tuned to Pretty Betty, it is not unusual and does not necessarily indicate that the 26% share value is wrong.

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To determine the height of the rock at a specific time, we need to substitute the time value into the equation y = 20t - 1.87t². For example, to find the height of the rock after 3 seconds, we substitute t = 3 into the equation:

y = 20(3) - 1.87(3)²

y = 60 - 16.83

y = 43.17

Therefore, the height of the rock after 3 seconds is 43.17 meters.

Answer:

So we have two possible values for the width: W = 16 or W = 7.5.

If W = 16, then L = 130/16 ≈ 8.125. This gives us a perimeter of 2(8.125) + 2(16) = 48.25, which is too much fencing.

If W = 7.5, then L = 130/7.5 ≈ 17.333. This gives us a perimeter of 2(17.333) + 2(7.5) ≈ 46.666, which is close enough to 46. Therefore, the dimensions of the field are approximately L = 17.333 m and W = 7.5 m.

Step-by-step explanation:

Let the length of the rectangular plot be L, and let the width be W. Then we have:

The perimeter of the plot is 2L + 2W, and this must equal the length of fencing that Morgan has, which is 46 m. So we have the equation:

2L + 2W = 46

The area of the plot is LW, and we know that this equals 130 square meters. So we have the equation:

LW = 130

We can solve for one variable in terms of the other from the second equation, so let's solve for L:

L = 130/W

Now we can substitute this expression for L into the first equation:

2(130/W) + 2W = 46

Simplifying this equation, we get:

260/W + 2W = 46

260 + 2W^2 = 46W

2W^2 - 46W + 260 = 0

Dividing by 2, we get:

W^2 - 23W + 130 = 0

This is a quadratic equation that we can solve using the quadratic formula:

W = [23 ± √(23^2 - 4(1)(130))] / (2(1))

W = [23 ± 9] / 2

So we have two possible values for the width: W = 16 or W = 7.5.

If W = 16, then L = 130/16 ≈ 8.125. This gives us a perimeter of 2(8.125) + 2(16) = 48.25, which is too much fencing.

If W = 7.5, then L = 130/7.5 ≈ 17.333. This gives us a perimeter of 2(17.333) + 2(7.5) ≈ 46.666, which is close enough to 46. Therefore, the dimensions of the field are approximately L = 17.333 m and W = 7.5 m.

Answer:

Length = 13

Width = 10

Step-by-step explanation:

Let L = length and W = width of the plot

The area is given by LW and is given as 130 square meters

LW = 130   (1)

The perimeter = 2(L + W) and given as 46 meters(length of fencing)
2(L + W) = 46
L+W = 23        (2)

In equation 1, isolate L by dividing both sides by W
LW/W = 130/W
L = 130/W

Substitute this value for L in equation (2)
L + W = 23
130/W + W = 23

Multiply throughout by W:
130/W x W + W x W = 23x W
130 + W² = 23W

Subtract 130W from both sides:
130 + W² - 23W= 0

Rewrite as

W² - 23W + 130 = 0

This is a quadratic equation which can be solved by factoring

Factoring W² - 23W + 130 = 0
(W - 13)(W-10) = 0

This means W = 13 or W = 10
If W = 13, L = 130/W = 120/13 = 10
If W = 10, L = 130/W= 130/10 = 13

So the possible values for L, W are
L = 13, W = 10

or

L = 10, W =13

Choosing the larger value for L gives us:
L = 13, W = 10

A function that decreases by 12% every time x increases by 1 is,

y = 100(1 -0.12)ˣ.

An exponential function's curve is created by a pattern of data called exponential decay, which exhibits higher decreases over time.

The exponential decay function:

Aₙ = A₀(1-r)ˣ, where y = Final amount, A₀ = Initial amount, r = Rate of decay in decimal form, x = Time.

An exponential decay function is represented by the following equation,

y = a(1 -r)ˣ.

Here, a = 100.

And the function decreases by 12%.

So,

100 - 12 = 88

In decimals, 88 = 0.88.

So, y = 100(1 -0.12)ˣ.

Therefore, the function is y = 100(1 -0.12)ˣ.

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Answer:

Area = 380 square inch

Volume = 697 cubic inch

Step-by-step explanation:

Diameter = 11

=> radius = 11/2 = 5.5

A = 4πr^2 =4·π·(5.5^2) ≈ 380 square inch

V=4/3πr^3=4/3·π·(5.5^3) ≈ 697 cubic inch

The inequalities solution is given below as

[tex]8 x-y \leq 32 \\\\&-3 x+5 y \leq 25 \\\\& \Rightarrow {[8 x-y \leq 32] \times 5 } \\\\& {[-3 x+5 y \leq 25] \times 1 } \\\\& \Rightarrow 40 x-5 y \leq 160 \\\\&-3 x+5 y \leq 25 \\\\& 37 x \leq 185 \\\\& x \leq \frac{185}{37} \leq 5[/tex]

substitute $x=5$ into eqn(11)

[tex]-3 x+5 y \leq 25\\\\$-3(5)+5 y \leq 25\\\\& -15+5 y \leq 25 \\\\\& 5 y \leq 25+15 \\\\& 5 y \leq 450 \\\\& y \leq \frac{40}{5} \\\\& -y \leq 8 \\\\[/tex]

(5,8)

z=-4 x+5 y

[tex]& \frac{\partial z}{\partial x}=-4(i)-5 y \\[/tex]

=-4-5 y

when y=8

[tex]\frac{\partial z}{\partial x} & =-4-5(8)[/tex]

=-4-40

=-4-40

=-44

[tex]& \frac{\partial z}{\partial y}=-4 x-5(i) \\[/tex]

when x=5

[tex]\frac{\partial z}{\partial y}=-4 x-5 \\[/tex]

[tex]\frac{\partial z}{\partial y} & =-4(5)-5 \\[/tex]

=-20-5

=-25

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The perimeter of the triangle is 24 units.

what is perimeter ?

Perimeter is the total distance around the boundary of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape. For example, the perimeter of a rectangle is found by adding the length of all four sides, while the perimeter of a circle is the distance around the circle. Perimeter is typically measured in units such as centimeters, meters, feet, or miles.

Given by the question:

To find the perimeter of the triangle, we need to find the distance between each pair of vertices and then add them up.

Distance between (-4, -2) and (2, -2):

[tex]d = sqrt[(2-(-4))^2 + (-2-(-2))^2] = sqrt[6^2 + 0^2] = 6[/tex]

Distance between (2, -2) and (2, 6):

[tex]d = sqrt[(6-(-2))^2 + (2-2)^2] = sqrt[8^2] = 8[/tex]

Distance between (2, 6) and (-4, -2):

[tex]d = sqrt[(-4-2)^2 + (-2-6)^2] = sqrt[(-6)^2 + (-8)^2] = sqrt[36 + 64] = sqrt[100][/tex]= 10

Now we add up the distances:

Perimeter = 6 + 8 + 10 = 24

Therefore, the perimeter of the triangle is 24.

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Therefore , the solution of the given problem of fraction comes out to be the restaurant could make 48 cups of pudding from the 8 quarts they have.

An whole can be represented by any set of related sums or fractions. In standard English, a percentage is used to represent the quantity of a specific size. 8, 3/4. Also wholes are fractions. Numbers are expressed in mathematics using the ratio of it's own portion to the bottom. These fractions are all made up of basic numbers. Due to variances in actual percentage calculations, numerators, and numerators, a difficult fraction contains a fraction. A measurement that reflects a portion of the whole is a percentage.

Here,

There are different ways to approach this problem, but one possible method is to use unit conversions to find how many cups are in 8 quarts, and then divide by 1/6 of a quart per cup.

1 quart = 4 cups (by definition of quart)

Therefore, 8 quarts = 8 x 4 cups = 32 cups

1/6 of a quart = 1/6 x 4 cups = 2/3 cups

Therefore, the number of cups of pudding that could be made is:

32 cups / (2/3 cups) = 48 cups

Therefore, the restaurant could make 48 cups of pudding from the 8 quarts they have.

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The minimum number of trips needed to haul 20,000 cubic feet of dirt is B) 17.

What is capacity?

The ability to hold or contain something. The maximum amount or number that can be contained in a room's seating capacity.

The capacity of the dump bin is:

21 feet (length) x 8 feet (width) x 6 feet (height) = 1,008 cubic feet

The dump bin can hold dirt equivalent to 1.2 times its capacity, which is:

1.2 x 1,008 cubic feet = 1,209.6 cubic feet

To haul 20,000 cubic feet of dirt, you need:

20,000 cubic feet / 1,209.6 cubic feet per load = 16.52 loads

Since you can't have a fraction of a load, you need to round up to the nearest whole number, which is 17 loads.

Therefore, the minimum number of trips needed to haul 20,000 cubic feet of dirt is B) 17.

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Answer:

R=47/pi

Step-by-step explanation:

If the of circumference of the circle is 94 cm, the diameter is 94/pi makin the radius 47/pi.

When Aldo and Lena are standing on a riverside 220 meters apart at certain points, the distance between Lena and the home is 240.8 meters.

Displacement is the overall, purposeless movement of an object. Speed can be characterized as the amount of area an object has covered, disregarding of the origin or ending location. Distance has characterized by the extent or size of the distance between two places. The gap between adjacent positions and the distance moved between them are not exactly the same thing, it should be emphasized. The travelled is the entire length of a path that join different places. Distance is the average trip distance of a body. It is also known as distance. For instance, OP = 360 m would indicate the length of the path for an object traveling from 0 ° to point P.

given

BC/sin 53 = 250/sin 56

BC = 250 * sin 53 /sin 56

=240.8 m

When Aldo and Lena are standing on a riverside 220 meters apart at certain points, the distance between Lena and the home is 240.8 meters.

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Answer:

Step-by-step explanation:

If the generation time of bacteria is 30 minutes, it means that in every 30 minutes, the number of cells will double. Let No = 100 be the initial number of cells, and n be the number of generations at that point.

Using the given formula N1 = N x 2^n, we can find the number of cells at any given time t, in minutes.

For t = 30 minutes:

The number of generations in 30 minutes is 1 (since generation time is also 30 minutes)

N1 = 100 x 2^1 = 200 cells

For t = 60 minutes:

The number of generations in 60 minutes is 2 (since generation time is 30 minutes)

N1 = 100 x 2^2 = 400 cells

For t = 90 minutes:

The number of generations in 90 minutes is 3 (since generation time is 30 minutes)

N1 = 100 x 2^3 = 800 cells

For t = 120 minutes:

The number of generations in 120 minutes is 4 (since generation time is 30 minutes)

N1 = 100 x 2^4 = 1600 cells

Therefore, after 30 minutes, the number of cells will be 200, after 60 minutes it will be 400, after 90 minutes it will be 800, and after 120 minutes it will be 1600.

Therefore, the length of diagonal A'C' is also 2 units after the polygon translates 3 units further to the left and 4 units down.

A polygon is any form having three sides. Although a circle is curved and devoid of sides and angles, it is not categorised as a polygon even if it is a plane figure.

If the polygon translates 3 units to the left and 1 unit down, the coordinates of the new vertices would be:

A' (0, 3)

B' (2, 2)

C' (0, 1)

D' (-2, 2)

To find the length of diagonal AC, we can use the distance formula:

AC = √[(3-3)^2 + (2-4)^2] ≈ 2 units

If the polygon translates 3 units further to the left and 4 units down, the coordinates of the new vertices would be:

A'' (-3, -1)

B'' (-1, -2)

C'' (-3, -3)

D'' (-5, -2)

To find the length of diagonal A'C', we can use the distance formula:

A'C' = √[(0-0)^2 + (1-3)^2] ≈ 2 units

Therefore, the length of diagonal A'C' is also 2 units after the polygon translates 3 units further to the left and 4 units down.

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Answer:

0.1369

Step-by-step explanation:

(37/100)^2=0.1369

Answer:

Below

Step-by-step explanation:

See the image below :

Area of the ENTIRE rectangle would be: Area = Base * Height

I think you can see that  the triangle is 1/2 of the rectangle. so the

     Area of the right triangle would be: Area = 1/2 * base * height

Answer:

The expected growth rate for the company's stock price is 9.7%. This is calculated by subtracting the dividend yield (3.40/53.50 = 0.0635) from the required return (13%).

The runners can finish in 362880 possible results

What is Permutation?

Permutation is the different number of arrangements that can be formed by taking r things from the n available things.

The formula  n! = 1 × 2 × 3 × 4 × .......× n.

To get the order the runners could possibly finish,

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

= 326880

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Vera's location after three hours is thus 2,100 feet above sea level.

Division is a basic arithmetic operation used to find how many times one number (the divisor) is contained within another number (the dividend). The result of a division operation is the quotient. Division is often represented using the symbol "÷" or "/".  Sometimes division results in a remainder, which is the amount left over after dividing as much as possible.  Division is one of the four basic arithmetic operations, along with addition, subtraction, and multiplication. It is used in a wide variety of mathematical and real-world contexts, such as sharing equally, calculating rates, and solving equations.

Here,

To find Vera's location after three hours of climbing down the mountain, we first need to convert three hours into minutes. There are 60 minutes in one hour, so three hours is:

3 hours x 60 minutes/hour = 180 minutes

Vera descends at a rate of five feet per minute, so after 180 minutes, she will have descended:

180 minutes x 5 feet/minute = 900 feet

3,000 - 900 = 2,100

Therefore, Vera's location after three hours is 2,100 feet above sea level.

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Answer:

181

Step-by-step explanation:

To simplify this expression, we need to apply the order of operations (PEMDAS):

First, we evaluate the expression inside the parentheses: 9 ÷ 3 = 3.

Then, we add 6 + 3 = 9.

Finally, we divide 1,629 by 9 to get the answer:

1,629 ÷ 9 = 181.

Therefore, 1,629 ÷ (6 + 9 ÷ 3) simplifies to 181.

Using the table and definition of inverse functions we will get:

f ⁻¹ (6) = 10.

Remember how inverse functions work, we know that for two inverse functions f(x) and f ⁻¹ (x)?

if f(x) =y

Then:

f ⁻¹ (y) = x

So now we want to find  f ⁻¹ (6), then if:

f ⁻¹ (6) = k

f(k) = 6

Looking at the table we can see that f(10) = 6, then f ⁻¹ (6) = 10.

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The standard error tells us how much we can expect the sample proportion to vary from the true proportion in repeated samples of the same size. Option (d) correctly states that "In samples of size 100 from this school, the sample proportion of students who bring a reusable water bottle from home typically varies by about 0.048 from the true proportion." This means that if we were to take many samples of 100 students from the same school and calculate the proportion of students who bring a reusable water bottle from home in each sample, about 95% of the sample proportions would fall within +/-0.048 of the true proportion.

The correct option is (d) "In samples of size 100 from this school, the sample proportion of students who bring a reusable water bottle from home typically varies by about 0.048 from the true proportion."

The standard error of the sample proportion can be calculated using the formula:

SE = √[p*(1-p) / n]

where p is the sample proportion and n is the sample size.

In this case, the sample proportion is 37/100 = 0.37 and the sample size is 100. Plugging in these values, we get:

SE = sqrt[0.37*(1-0.37) / 100] = 0.048

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The description corresponds to an experiment.

Mathematics is the sciences and study of quality, structure, space, and change. Mathematician's are seek out patterns, formulate new conjectured, and establish truth by the  rigorous seduction from appropriately choden axioms and definitions.

An experiment is a type of scientific research method in which a researcher manipulates one or more variables and measures the effects of the manipulation on other variables. In this example, the researcher divided the thirty university students into two groups and manipulated one variable (free tutoring in mathematics) to measure the effects on another variable (final mathematical examination scores). Therefore, this is an experiment.

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Answer:

are you trying to find the derivative if so the answer will be 0

Step-by-step explanation:

Answer:

A≈50.27in²

Step-by-step explanation:

A=πr2=π·42≈50.26548in²