A car has a 16-gallon fuel tank. when driven on a highway, it has a gas mileage of 30 miles. how many gallons are left in the tank when the car has traveled the following distances on the highway? 90 miles 246 miles per gallon. the gas mileage (also called "fuel efficiency") tells us the number of miles the car can travel for a particular amount of fuel (one gallon of gasoline, in this case). after filling the gas tank, the driver got on a highway and drove for a while. how many gallons are left in the tank when the car has traveled the following distances on the highway?

a. 90 miles

b. 246 miles

a property has a back yard 125 x 150 feet and a side yard of 195 x 25 feet. then 23625  is the combined square footage of the side and back yard

125*150 and 195*25

total 23625

The area covered with grass, in square feet, is the area of the shape of the yard.

What is the Area of a Yard?

The area of a yard can be calculated by determining the shape of the yard, and using the appropriate area formula of the shape to find the area of the yard.

Image of the yard is missing. However, assuming the yard is a rectangular shape with a dimension of 10 ft by 6 ft, therefore:

The square feet of grass Russell has = area of rectangle = (10)(6) = 60 ft²

In summary, the area covered with grass, in square feeet, is the area of the shape of the yard.

a property has a back yard 125 x 150 feet and a side yard of 195 x 25 feet. then 23625  is the combined square footage of the side and back yard

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By algebra properties, the rational equation 1 / [1 / (x + 2) + 1 / (x + 3)] is equivalent to the rational expression (x² + 5 · x + 6) / (2 · x + 5). (Correct choice: B)

In this problem we find a rational equation, whose simplified form has to be found by means of algebra properties. First, write the entire expression:

1 / [1 / (x + 2) + 1 / (x + 3)]

Second, expand the denominator by addition of fractions with distinct denominator:

1 / [[(x + 3) + (x + 2)] / [(x + 2) · (x + 3)]]

Third, use division of fractions:

[(x + 2) · (x + 3)] / [(x + 3) + (x + 2)]

Fourth, simplify both numerator and denominator:

(x² + 5 · x + 6) / (2 · x + 5)

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I would recommend taking this bet, as the expected value of the bet is Positive.

The expected value of a bet is the sum of the product of each possible outcome and its corresponding probability. In this case, the probability of getting two heads is 0.25, and the payout for that outcome is $10. The probability of not getting two heads is 0.75, and the payout for that outcome is -$2. When you multiply each outcome by its corresponding probability and sum them together, the expected value of the bet is $1.0. Because the expected value of the bet is positive, it is  a good bet to take. It is more likely that you will gain money .

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Answer:

To the nearest tenth of an inch, the length of the arc is 54.0 inches

Step-by-step explanation:

To determine the length of the arc, x, we need to use the formula for arc length, which is:

arc length = radius * angle (in radians)

Therefore,

arc length = 30 inches * 1.8 radians = 54 inches

The scatter plot shows the number of hats and scarves each knitter sold at a knitting show. 02 hats did the knitter who sold 9 scarves sell.

Scatterplot:

A scatterplot  is a graph or mathematical graph that displays the values ​​of usually two variables of a data set using Cartesian coordinates. is a kind of Additional variables can be displayed if the points are coded (color/shape/size). The data is displayed as a set of points, where each point has the value of one variable that determines its position on the horizontal axis and the value of another variable that determines its position on the vertical axis.

According to the Question:

I need to find out how many hats were sold when the knitter sold his 09 scarves.

To find this out, in the scatterplot he needs to find the x-values ​​corresponding to the y-values ​​of the 9 scarves.

Corresponding to 9 on the y-axis, there is a point with a corresponding value of 02.

Therefore, when the weaver sold 09 scarves, he sold two(02) hats.

Option B) 02 is correct.

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The central angle of the arc in degrees is 162 degrees.

The circumference of the circle is 10 units. The length of the arc is 9 / 2 units. The central angle can be calculated as follows;

We can find the central angle by comparing it to the length of the arc.

Therefore, we know the circle has a circumference of 10. We also know a circle is 360°.  The length of the arc is given as 9 / 2 units(4.5 units).

To determine the degrees of the central angle, we have to set up a ratio and set the unknown angle as x.

Hence,

length of the arc / circumference = angle of the arc / angle of the circle

4.5 / 10 = x / 360

cross multiply

360 × 4.5 = 10x

1620 = 10x

divide both sides by 10

x = 1620 / 10

x = 162 degrees

Hence,

central angle = 162 degrees.

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Answer:

-8

Step-by-step explanation:

(-2)^3 X (-2)^7 / 3X 4^6

= (-8) X (-128) / (3 X 4096)

= 1024 X -128 / 12288

= -128/12

= -8/1

So the final answer is -8

Answer:

1.398101×10^6

Step-by-step explanation:

(-2)^3×(-2)^7/3 ×4^6

=4194304/3

=1.398101×10^6

Answer:

[tex]\frac{3}{16}[/tex] f - [tex]\frac{3}{2}[/tex] g

Step-by-step explanation:

[tex]\frac{3}{8}[/tex] ( [tex]\frac{1}{2}[/tex] f - 4g )

multiplying each of the terms inside the parenthesis by [tex]\frac{3}{8}[/tex]

[tex]\frac{3}{8}[/tex] × [tex]\frac{1}{2}[/tex] f

= [tex]\frac{3(1)}{8(2)}[/tex] f

= [tex]\frac{3}{16}[/tex] f

and

[tex]\frac{3}{8}[/tex] × - 4g ( cancel 4 and 8 by 4 )

= [tex]\frac{3}{2}[/tex] × - g

= - [tex]\frac{3}{2}[/tex] g

combining the 2 products, gives

[tex]\frac{3}{16}[/tex] f - [tex]\frac{3}{2}[/tex] g

Answer:

[tex]\textsf{Orange partial product}=\dfrac{3}{16}\;f[/tex]

[tex]\textsf{Pink partial product}=-\dfrac{3}{2} \;g[/tex]

[tex]\textsf{Product}=\dfrac{3}{16}\;f-\dfrac{3}{2} \;g[/tex]

Step-by-step explanation:

Given expression:

[tex]\dfrac{3}{8}\left(\dfrac{1}{2}f-4g\right)[/tex]

Calculate the partial products then add these together to find the product of the given expression.

Orange partial product

[tex]\implies \dfrac{3}{8} \times \dfrac{1}{2}f[/tex]

[tex]\implies \dfrac{3 \times 1}{8\times 2}\;f[/tex]

[tex]\implies \dfrac{3}{16}\;f[/tex]

Pink partial product

[tex]\implies \dfrac{3}{8} \times (-4g)[/tex]

[tex]\implies \dfrac{3 \times -4}{8} \;g[/tex]

[tex]\implies \dfrac{-12}{8} \;g[/tex]

[tex]\implies -\dfrac{\diagup\!\!\!\!4 \times 3}{\diagup\!\!\!\!4 \times 2} \;g[/tex]

[tex]\implies -\dfrac{3}{2} \;g[/tex]

Product:

[tex]\implies \dfrac{3}{8}\left(\dfrac{1}{2}f-4g\right)=\dfrac{3}{16}\;f-\dfrac{3}{2} \;g[/tex]

Answer:

(2x-7)(9x+2)

Step-by-step explanation:

Find The Least Common Multiplier of 9x+2, 2x-7

There are two solutions for equation [tex]3x^2-6x+2=0[/tex] are [tex]1+\frac{1}{\sqrt{3}} , 1-\frac{1}{\sqrt{3}}[/tex].

and solutions are irrational solutions.

Every nth degree equation has a total of 'n' real or hypothetical roots. The polynomial [tex]f (x)[/tex] is exactly divisible by ([tex]x -a[/tex] ), which means that ([tex]x -b[/tex] ) is the factor of the provided polynomial [tex]f(x)[/tex].

The theory of equations in algebra refers to the study of algebraic equations, which are equations defined by polynomials. Any expression with one or more terms is considered to be a polynomial. Knowing when an algebraic problem has an algebraic solution was a major challenge in the theory of equations.

Here solution of equation:

[tex]3x^2-6x+2=0\\3x^2-6x+2+1-1=0\\3x^2-6x+3=1\\3(x^2-2x+1)=1\\3(x-1)^2=1\\x=1+\frac{1}{\sqrt{3}} , 1-\frac{1}{\sqrt{3}}[/tex]

So here two solutions are presented for given equation.

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The difference between Georgina's total stock earnings and her real return is $119.70. he difference between Georgina's total stock earnings and her real return is $119.70.

What is the difference?

The term "difference" refers to the amount by which one quantity is greater or less than another.

The difference between Georgina's total stock earnings and her real return can be calculated as follows:

Difference = Total stock earnings - Real return

Difference = $395.50 - $275.80

Difference = $119.70

Hence, the difference between Georgina's total stock earnings and her real return is $119.70.

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The graph of the proportional relation is the one in the second option.

"a graph of a line that passes through the points 0 comma 0 and 4 comma negative 1"

A general linear equation can be written as:

y = a*x +b

Where a is the slope and b is the y-intercept.

Particularly, if the y-intercept is 0, then we have:

y = a*x

We have a proportional relationship.

Notice that when x = 0 we have:

y = a*0

y = 0

So the proportional relationships always pass through the point (0, 0).

Then the correct option is the second one:

"a graph of a line that passes through the points 0 comma 0 and 4 comma negative 1"

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Answer:

Francesca

Step-by-step explanation:

The object hits the ground after 17.5 seconds.

f(x) = ax2 + bx + c, where a, b, and c are integers and an is not equal to zero, is a quadratic function. A parabola is the shape of a quadratic function's graph. Although the "width" or "steepness" of a parabola can vary as well as its direction of opening, they always have the same fundamental "U" form.

The height of an object modeled by the function:

h(t) = −16t^2 + 4900

The object hits the ground when h(t) = 0

The equation becomes:

0 = −16t^2 + 4900

-16t² = -4900

t² = 4900/16

t² = 306.25

t = √306.25

t = 17.5 secs

Thus, the object hits the ground after 17.5 seconds.

Complete question: An object is 4900 ft above the ground. The object falls, and its height is given by the quadratic function: h(t) = −16t 2 + 4900. The height of the object above the ground is in feet and the time, t, is in seconds. Determine when the object hits the ground.

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a. The sample mean for U is 21.55 and the sample mean for F is 8.39.

b. sample median for U is 17 and the sample median for F is 8.

c. trimmed mean for U is 17 and the trimmed mean for F is 7.95.

d. trimmed percentage for U is 18.18% and the trimmed percentage for F is 13.33%.

a) Sample mean can be calculated by adding values and dividing the sum by the number of the values.

< Strong > Mean(U) < / Strong > =

[tex]\frac{6.0 +5.0 + 11.0 + 33.0 + 4.0+5.0+80.0+18.0 + 35.0+17.0+23.0}{11}[/tex] = 21.55

< Strong > Mean(F) < / Strong > =  [tex]\frac{2.0 + 15.0 + 12.0 + 8.0 + 8.0 + 7.0 + 6.0 + 19.0 + 3.0+9.8+22.0+9.6+2.0+2.0+0.5}{15}[/tex] = 8.39

b) Sample median is the middle value of a sorted sample:

Sorted(U)= [ 4.,  5.,  5.,  6., 11., 17., 18., 23., 33., 35., 80.]

Sorted(F)=[ 0.5,  2. ,  2. ,  2. ,  3. ,  6. ,  7. ,  8. ,  8. ,  9.6,  9.8, 12. , 15. , 19. , 22.]

Median(U)=17, which is the 6th (middle) value

Median(F)=8, which is the 8th (middle) value

c) If we delete the smallest and largest observation, we have:

U= [  5.,  5.,  6., 11., 17., 18., 23., 33., 35., ]

F= [ 2. ,  2. ,  2. ,  3. ,  6. ,  7. ,  8. ,  8. ,  9.6,  9.8, 12. , 15. , 19. ]

Using the above equation for the new samples, we have:

TrimmedMean(U)= 17

TrimmedMean(F)=7.95

d) Trimming percentages can be found by dividing the number of removed values by the old sample size

That is, for U: [tex]\frac{2}{11} = 0.18[/tex] 18.18%

for F: [tex]\frac{2}{15} = 0.13[/tex] ,13.33%

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The required interval of the given normal distribution using the empirical rule is [100, 140].

The empirical rule formula (also known as a 68 95 99 rule formula) uses data from a normal distribution to determine the first, second, and third standard deviations, which, respectively, differ from the mean value by 68%, 95%, and 99%. Additionally, it shows that 99.9% of the data fall inside the third standard deviation range (either above or below the mean value). The empirical rule formula is described below with cases that have been resolved.

In the question, we are given that IQ scores for adults aged 20 to 34 years are normally distributed according to N(120, 20), and are asked for the range in which the middle 68% of people in this group score on the test.

N(120, 20) signifies a normal distribution with mean, μ = 120, and the standard deviation, σ = 20.

By the empirical formula, 68% of the data lies within one standard deviation from the mean.

Thus, the required interval is [μ - σ, μ + σ] = [120 - 20, 120 + 20] = [100, 140].

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They tend to satisfice, meaning they settle on a satisfactory solution rather than searching for the optimal solution.

This type of decision making is known as bounded rationality. Bounded rationality acknowledges that people often make decisions based on incomplete and imperfect information but seek the best possible outcome. People use heuristics and mental shortcuts to make decisions and tend to satisfice, which means they settle on a satisfactory solution rather than searching for the optimal solution. This type of decision making is often used when the complexity of a problem is too great to be solved analytically.

Bounded rationality is a type of decision making which acknowledges that people often make decisions based on incomplete and imperfect information, and seek the best possible outcome using heuristics and mental shortcuts. They tend to satisfice, meaning they settle on a satisfactory solution rather than searching for the optimal solution.

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On solving the provided question we can say that by unitary method number of extra copies made by machine 2 = 192 – 180 = 12

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen.

In 8 minutes, Machine 1 produces 240 copies. In 5 minutes, machine 2 produces 240 copies. The rates of operation for each machine are constant.

machine 1 makes 240 = 8 mins

[tex]1 min = 240/8 = 30\\6 min = 3 X 6 = 180[/tex]

In 5 minutes, machine 2 produces 240 copies.

[tex]1 min = 240/5 = 48\\4 min = 192[/tex]

number of extra copies made by machine 2

[tex]= 192 – 180\\ = 12[/tex]

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The square that must be cut from each corner of the cardboard to form a box with a volume of 288 cubic inches is 2.4 inches on each.

Square is a two-dimensional shape with four equal sides and four right angles. It is one of the most common shapes in geometry. Squares have many practical uses, such as in forming grids, creating patterns, and making tiling. Squares are also used in art and architecture, as well as in construction, mathematics, and science.
To solve this problem, we will use the formula for the volume of a rectangular box, V = lwh. We can substitute the given values to solve for x. First, we will find the length and width of the box after the square corners are cut out:

Length = 20 - 2x

Width = 14 - 2x

Now, substituting these values into the volume formula, we get:

288 = (20 - 2x)(14 - 2x)h

Expanding and simplifying, we get:

288 = 280 - 56x + 4x^2

Subtracting 280 from both sides, we get:

8 = -56x + 4x^2

Solving for x, we get:

4x^2 - 56x + 8 = 0

Using the quadratic equation, we get x = 2.4 or x = 0.4

Since x must represent a length, we can discard the negative solution, x = 0.4. Therefore, the square that must be cut from each corner of the cardboard to form a box with a volume of 288 cubic inches is 2.4 inches on each.

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Domain: [-2, 2]

Range: [-4, 3]

Answer: In any triangle, the sum of the three angles is always 180 degrees. This is known as the triangle angle sum theorem.

So in triangle efg, we can use this theorem to find angle g in terms of x:

angle e + angle f + angle g = 180

5x+6 + 4x-6 + 5x-2 = 180

14x = 180 + 8

14x = 188

angle g = 5x-2 = 5(188/14) - 2 = 5(13.4285714) - 2 = 67.1428571 degrees

So angle g = 67.1428571 degrees

It's important to note that the values of x are the unknowns.

Step-by-step explanation:

The slope of the line in 1. is -3/4 and the slope of 2. is 9/10.

Understanding what slope is is among the most crucial things to know about lines. The line's slope, also referred to as rise over run, is how "steep" it is. By dividing the difference between the y-values at two points by the difference between the x-values, we can determine slope. Understanding how to interpret graphs and create equations is necessary in order to comprehend the significance of the definition of slope.

The slope of the line = m in y = mx + b

−3x−4y=6

4y = -3x -6

y = (-3x -6)/4

y = -3x/4 -6/4

y = -3/4(x) -3/2

2. Slope formula = y₂ - y₁ = m(x₂ -x₁)

points (6, -1) and (-4, -10)

Substitute

-10 -(-1)= m(-4 -6)

m = 9/10

Thus, the slope of the line in 1. is -3/4 and the slope of 2. is 9/10.

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The empirical probability that there are more than 5 left-handed students  in a class of 30 is 0.06.

Empirical probability is a sort of experimental probability that is based on historical data. Empirical probability is, then, an illustration of  the likelihood of an occurrence occurring based on prior data.

The formula of the empirical probability is:

Experimental probability  = number of times an event occurs / total number of outcomes.

In the problem, total number of classes = 50

From the graph, we can read that:

- number of classes with 6 left-handed students = 2

- number of classes with 7 left-handed students = 1

Hence, the empirical probability that there are more 5 left-handed students in a class of 30 is:

Empirical probability = 3/50 = 0.06

Your question is incomplete. Most likely it was:

Casey read a report that said the probability that a randomly selected America is left handed is 14%. she was curious how many left handed students to expect in a class of 30 seconds. she simulated 50 classes of 30 students where each student had a 0.14 probability of being left handed. Casey counted how many left handed students were in each simulated class. here are her results: use her results to estimate the probability that there are more than 5 left handed students in a class of 30 students. (The graph is attached)

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As, the moon has an elliptical orbit around a planet, the maximum distance between the planet and its moon is 88.54 Mm.

What is an elliptical orbit?

When an object moves around another object in an oval shaped path (ellipse), it is known to be revolving in an elliptical orbit.

The standard form of the equation of an ellipse with center at the origin (0,0) and x - axis major axis is given by

x²/a² + y²/b² = 1

Now,

Given that a moon's elliptical orbit around a planet is modeled by the equation 225x² + 576y² = 176,400, where distance is measured in megameters (Mm). and the planet is the center of the orbit's path.

Since the equation of the path is the equation of an ellipse, we write it in standard form

As standard form of the equation of an ellipse with center at the origin (0,0) and x - axis major axis is

x²/a² + y²/b² = 1  (1) where

a = vertex of major axis and

b = vertex of minor axis

So, converting 225x² + 576y² = 176,400 into standard form, we have

225x² + 576y² = 176,400

225x²/1764,000 + 576y²/1764,000 = 176,400/1764,000

x²/7840 + y²/3062.5 = 1  (2)

Comparing equation (2) with (1), we have that

a² = 7840 and b² = 3062.5

⇒ a = √7840 = 88.54 and

⇒ b = √3062.5 = 55.34

Since a = 88.54 is greater than b = 55.34, so, a is the major axis, and the maximum distance between the planet and its moon is 88.54 Mm

So, the maximum distance between the planet and its moon is 88.54 Mm

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Since the moon's has an elliptical orbit around a planet, the maximum distance between the planet and its moon is 88.54 Mm

How to find the maximum distance between the planet and its moon?

x²/a² + y²/b² = 1  (1) where

a = vertex of major axis and

b = vertex of minor axis

o, converting 225x² + 576y² = 176,400 into standard form, we have

225x² + 576y² = 176,400

225x²/1764,000 + 576y²/1764,000 = 176,400/1764,000

x²/7840 + y²/3062.5 = 1  (2)

Comparing equation (2) with (1), we have that

a² = 7840 and b² = 3062.5

⇒ a = √7840 = 88.54 and

⇒ b = √3062.5 = 55.34

Since a = 88.54 is greater than b = 55.34, so, a is the major axis, and the maximum distance between the planet and its moon is 88.54 Mm

So, the maximum distance between the planet and its moon is 88.54 Mm

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The number of Canadians who are at least 100 years old in 2001 is 3793.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Percentage of Canadians who live in British Columbia are at least 100 years old = 14%

The number of Canadians who live in British Columbia who are at least 100 years old in the 2001 census = 531

This means,

14% = 531

Now,

The number of Canadians who are at least 100 years old.

14% = 531

Multiply 100/14 on both sides.

100% = 100/14 x 531

100% = 3792.8

100% = 3793

Thus,

The number of Canadians who are at least 100 years old is 3793.

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At point, the parametric curves cross (4, 1, 32).

t functions expressed as x = f(y) = y = f(x) = (some function of the variable x) (some function of the variable y).

It is frequently more easier to view functions of two or more variables (although we'll keep it at two here) as parametric functions, particularly in physical science.

The introduction of the idea of time makes parametric functions the most simple to understand.

Imagine tracing a parabola-like function from left to right as time passes.

Then, it is simple to begin considering how the x-coordinate and the y-coordinate change as a function of time: x = f(t), y = g. (t). In this sense, time is actually referred to as the parameter.

We will investigate functions for which a point exists in this section.

Hence, At point, the parametric curves cross (4, 1, 32).

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Answer:

6700

Step-by-step explanation:

6.7*10³ to ordinary form. You simply move the decimal point three steps back because it's positive and put zeros before the decimal point which you have moved

The amount of money Ryan will have in his account in 6 years is $3668.71.

Compound interest is calculated using the exponential formula y = P(1+r)ⁿ. P is for "Present" or Principal value; r stands for interest rate; n stands for time (in years), and y stands for future value after the amount compounds annually

Given:

Principal Amount = $2500

Rate of interest = 6.25%

Time = 6 years

The exponential equation can be given as:

y = P(1+r)ⁿ where n is the number of years.

y = 2500(1 + 0.0625)ⁿ

The money Ryan will have in his account in 6 years can be calculated as by putting n's value as 6 years.

y = 2500(1 + 0.0625)⁶

y = $3668.71

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The required dimensions of the given rectangle are a breadth of 21 meters and a length of 63 meters.

The homes we live in and the items we use on a daily basis all have three dimensions: height, length, and width.

The minimal set of coordinates required to specify any point within a mathematical space is known as the dimension of the space in physics and mathematics.

So, the dimensions of the rectangle are:

Let the dimensions of this rectangle be x for the width and 3x for the length.

2(Length + Breadth) =perimeter of rectangular park.

2( 3x + x ) = 168 metres.

6x + 2x = 168 metres.

8x = 168 metres.

x = (168/8) metres.

x = 21 metres.

Now,

Breadth: x = 21 metres

Length: 3x = 3× 21 = 63 metres

Therefore, the required dimensions of the given rectangle are a breadth: of 21 meters and a length of 63 meters.

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Correct question:

The length of a rectangular park is thrice its breadth and if the perimeter of the park is 168 meters, find its dimensions.