The Fuel Economy In Miles Per Gallon For 2015 Model Cars In The U.S.is Summarized In The Table Below. (2024)

29 mins will that take. 116 yards will Kyle have to hop.

What is the rate?

A rate is a broader measure that involves dividing one quantity by another, where neither quantity necessarily needs to have the same unit of measurement as the other. It is capable of being equal to any value, even a negative one. It can be expressed as a number or a percentage, just like proportions.

Given that, Lester is younger, so he is given a head start of 29 yards.

The rate of hops of Lester is 3 yards per second.

The rate of hops of Kyle is 4 yards per second.

The equation that represents the distance covered by Lester is

L = 3t + 29 ......(i)

The equation that represents the distance covered by Kyle is

K = 4t ......(ii)

Kyle will overtake Lester. Then the time of overtaking L = K

Equate equations (i) and (ii)

4t = 3t + 29

t = 29

After 29 mins, Kyle will overtake Lester.

Putting t = 29 in equation (ii):

K = 4×29

K = 116 yards

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Answer:

A = 9π m²

Step-by-step explanation:

the area (A) of a circle is calculated as

A = πr² ( r is the radius )

= π × 3²

= 9π m²

The linear equation will be y=535+4.75x where y is distance climbed and x is time in minutes and average rate of climbing the remaining distance will be 4.75 feet/minute.

What exactly is a linear equation?

A linear equation is one in which the variable's maximum power is always 1. A one-degree equation is another name for it. A linear equation in one variable has the following standard form:

Ax + B = 0

e.g. x-10=0. In this equation, x is a variable, A is a coefficient, and B is constant.

A linear equation in two variables has the following standard form:

Ax + By = C

e.g. 2x-4y=10. The variables x and y are variables, the coefficients A and B are coefficients, and the constant C is a constant.

Now,

Total distance to climb=1200 feet in 4 hours or 240 minutes

Climbed 535 feet in 100 minutes and left distance=1200-535=665

and time left =240-100=140 minutes

average rate with which remaining distance will be covered in time=665/140

=4.75 feet/minute

and linear equation for the graph will be

y=535+4.75x where where y is distance climbed and x is time in minutes

Hence,

The linear equation will be y=535+4.75x and average rate of climbing the remaining distance will be 4.75 feet/minute.

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The volume of the solid obtained by rotating the region in the first quadrant bounded by x=0, y=1, x=y^4 about the line y=10 is 678.53 units cubed.

Here we can use the formula for the area of the circle which is A = pi*r^2 to calculate the area of the cylindrical shell. since the volume of the solid formed by rotating the given region about the line y=10 can be found by using the method of cylindrical shells, it states that the volume of the solid of revolution is equal to the integral of the cross-sectional area of the solid with respect to the axis of rotation.

in order to calculate the volume, we first need to find the radius of the cylindrical shell, this can be done by subtracting the distance from the line of rotation. in this case, the distance from the line of rotation to the axis of rotation is 10, thus the radius of the cylindrical shell is y-10.

while using the formula for the area of the circle, here subsituting the radius of the cylindrical shell into this formula will give us the area of the sylindrical shell, then integrate the area of the cylindrical shell with respect to the axis of rotation, which will given us the volume of the solid, so the volume of the solid by rotating the region in the first quadrant bounded by v about the line y=10 given by the integral of the I*(y-10)^2 from y=1 to y=10, which gives us the aprroximately 678.54

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The equations that are equal to the given equation are 56 + 8x = 80 and 2x = 6.

How to find the equations

From the question,

We are to determine the equations that are equal to the given equation

The given equation is 1/4 (8x + 56) = 20

Multiply both sides of the equation by 4,

We get

4 x 1/4 (8x + 56) = 20

This gives

8x + 56 = 80

OR

56 + 8x = 80

∴ Option a. 56 + 8x = 80 is equal to the given equation

Simplifying further

56 + 8x = 80 becomes

8x = 80 - 56

8x = 24

Now, divide both sides by 4

This gives

2x = 6

Therefore, 2x = 6 is equal to the given equation

Hence, the equations that are equal to the given equation are 56 + 8x = 80 and 2x = 6.

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The correct statement is d. X has a comparative advantage in food production, whereas Y has a comparative advantage in clothing production.

Comparative advantage refers to a country's ability to produce a good at a lower opportunity cost than another country. Opportunity cost is the next best alternative that must be given up in order to produce a certain good. In this case, we can compare the opportunity cost of producing food and clothing in both countries.

In Country X, the opportunity cost of producing one unit of food is 50/20 = 2.5 units of clothing. This means that in order to produce one unit of food, 2.5 units of clothing must be given up. In Country Y, the opportunity cost of producing one unit of food is 20/10 = 2 units of clothing.

Thus, in Country Y, the opportunity cost of producing food is lower compared to that in Country X. Hence, Y has a comparative advantage in clothing production.

On the other hand, the opportunity cost of producing one unit of clothing in Country X is 20/50 = 0.4 units of food. In Country Y, the opportunity cost of producing one unit of clothing is 10/20 = 0.5 units of food.

In this case, Country X has a lower opportunity cost of producing clothing compared to Country Y, and therefore, X has a comparative advantage in food production.

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The distance around the given figure above which is its perimeter would be = 17.6cm.

How to calculate the distance around the given figure?

The distance around the given figure can be calculated using the formula for perimeter= addition of all the sides of the shape which is made up of three different figures.

That is =

Figure 1 = a+a+d+d

= 0.3+0.3+1.8+1.8

= 4.2cm.

figure 2 = 3a + 3a + 2e

=6(0.3) + 1.0(2)

= 1.8+2 =2.8cm

figure 3 = 2c + 2f

= 2(1.7) + 2(3.6)

= 3.4 + 7.2 = 10.6cm.

Therefore the perimeter of the figure = 4.2+2.8+10.6 = 17.6cm.

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Answer:

13. ∠N < ∠R < ∠Q

14. ∠G < ∠H < ∠J

Step-by-step explanation:

In a triangle:

The largest angle is opposite the longest side.The smallest angle is opposite the shortest side.

Question 13

From inspection of triangle NQR:

As ∠N is opposite the shortest side, it is the smallest angle.As ∠Q is opposite the longest side, it is the largest angle.

Therefore, the angles in order from least to greatest are:

∠N < ∠R < ∠Q

Question 14

From inspection of triangle GHJ:

As ∠G is opposite the shortest side, it is the smallest angle.As ∠J is opposite the longest side, it is the largest angle.

Therefore, the angles in order from least to greatest are:

∠G < ∠H < ∠J

Answer:

Step-by-step explanation:

The number of partial products in this calculation will be equal to the number of digits in the 4-digit number being multiplied by 36. Since 36 has two digits, there will be 2 partial products for each digit in the 4-digit number, for a total of 2 * 4 = 8 partial products.

Multiply 2.5 and 8.25 which equals 20.65

Answer: he had 17/5 over 3 times 2

Step-by-step explanation:

Answer:Its 54

Step-by-step explanaon:

y = 2/3x +6 for x < -3

y = 2/3x +1 for x > 3.

This can be solved using the concept of slope-intercept form.

What is slope-intercept form?

The equation for a straight line is y = mx + b, where m stands for the slope and b for the y-intercept of the line. The slope-intercept formula, y = mx + b, is used when the slope of the line under study is known and the specified point also serves as the y-intercept (0, b). The y value of both the y-intercept point is represented by b in the formula.

The graph is a line for x < -3

(-6,2) and ( -3,4)

The slope is m= ( y₂ - y₁)/(x₂-x₁)

m = ( 4-2)/(-3 - -6)

m = 2/ ( -3+6)

m = 2/3

∴ The slope is 2/3

Using point slope form:

y-y₁ = m (x-x₁) and the point ( -6,2)

y -2 = 2/3 (x - -6)

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

y-2 = 2/3 x + 6

y = 2/3x +6 x< -3

The graph is a line for x > 3

(3,3) and ( 6,5)

The slope is m= ( y₂-y₁)/(x₂-x₁)

m = ( 5-3)/(6-3) = 2/ (3) = 2/3

The slope is 2/3

Using point slope form:

y-y₁ = m(x-x₁) and the point (6,5)

y -5 = 2/3(x - 6)

y-5 = 2/3 (x -4)

y = 2/3x +1 x> 3

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The proportional relationship that defines the graphed function is given as follows:

y = 40x.

What is a proportional relationship?

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

A proportional relationship is a special case of a linear function, with an intercept of zero.

For this problem, when x = 2, y = 80, hence the constant k is given as follows:

k = y/x

k = 80/2

k = 40.

Meaning that the equation is given as follows:

y = 40x.

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[tex]\qquad \qquad \textit{combined proportional variation} \\\\ \begin{array}{llll} \textit{\underline{y} varies directly with \underline{x}}\\ \textit{and inversely with }\underline{z^5} \end{array} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}x}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{array}{llll} \textit{"t" varies directly}\\ \textit{with "s" and}\\ \textit{inversely with }r^2 \end{array}\qquad t=\cfrac{ks}{r^2}\hspace{5em}\textit{we also know that} \begin{cases} s=48\\ t=8\\ r=3 \end{cases} \\\\\\ 8=\cfrac{k(48)}{(3)^2}\implies 8=\cfrac{16k}{3}\implies \cfrac{3}{16}\cdot 8=k\implies \cfrac{3}{2}=k~\hfill \boxed{t=\cfrac{ ~~ \frac{3}{2}s ~~ }{r^2}} \\\\\\ \textit{when t=12 and r=5, what's "s"?}\qquad 12=\cfrac{\frac{3}{2}s}{5^2}\implies 300\cdot \cfrac{2}{3}=s\implies 200=s[/tex]

Answer:

Step-by-step explanation:

15 inch

The volume of the rectangular, prism-shaped speaker is 455 cubic inches.

What is a prism?

In three-dimensional space, prisms is a polyhedron where two ends are similar.

Given:

A stereo speaker in the shape of a rectangular prism has a height of 10 inches the length of the base of the stereo speaker is 6.5 inches and the width of the base is 7 inches.

The volume of the rectangular prism-shaped speaker,

= Length x width x height

= 10 x 6.5 x 7

= 455 cubic inches.

Therefore, the volume is 455 cubic inches.

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The required volume of disinfectant is 34.

To calculate the required volume of disinfectant, we need to use the simple dilution method.

To make a 1:29 dilution, we need one part disinfectant for every 29 parts water.

Since we want to make 1.0 L of the solution, we need to find out how many parts of the solution are water. We can calculate this by dividing 1.0 L by 29, which gives us 0.0345 L of water.

Now we need to figure out how many parts of disinfectant we need to get a 1:29 dilution. To do this, we can simply multiply 0.0345 L of water by 29, which gives us 1.0055 L of disinfectant.

Finally, we need to convert this to milliliters. We can do this by multiplying 1.0055 L of disinfectant by 1,000 to get 1,005.5 mL of disinfectant.

Rounding the answer to one decimal place, the required volume of disinfectant is 34.5 mL.

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On solving the provided question, we can say that the expression 826 + 27³, value is = 826 + 27*27*27 = 20509

what is expression ?

In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted. Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated by the arithmetic sign +.

the expression 826 + 27³

value is = 826 + 27*27*27 = 20509

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Answer:

Option B.

Step-by-step explanation:

Their growth rate is more proportional to their value and exponential functions are mainly characterized by the fact that their rate of growth is proportional to their own value.

To Construct the frequency and relative frequency distributions to summarize the data, and determine the answers to the rest of the problem, let's go straight to the analysis below.

Step by step analysis of the problem

(a)

Frequency:

Pitcher: 21

Catcher: 11

1st Base: 5

2nd Base: 5

3rd Base: 3

Shortstop: 7

Left Field: 5

Center Field: 3

Right Field: 5

Relative Frequency:

Pitcher: 0.382

Catcher: 0.200

1st Base: 0.091

2nd Base: 0.091

3rd Base: 0.055

Shortstop: 0.127

Left Field: 0.091

Center Field: 0.055

Right Field: 0.091

(b) The position that provides the most Hall of Famers is Pitcher.

(c) The position that provides the fewest Hall of Famers is 3rd Base.

(d) The outfield position that provides the most Hall of Famers is Right Field.

(e) There are more infielders than outfielders.

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The standard form of the equation of the quadratic function is y = 1/169x² + 20/169² - 5.41.

What is quadratic form of equation?

A polynomial with all terms of degree two is known as a quadratic form in mathematics ("form" is another termfor a hom*ogeneous polynomial). It is common to refer to a quadratic form over K when the coefficients are typically members of an external factors K, such as the real or complicated numbers.

The vertex form of the quadratic equation is given as:

y = a(x - h)² + k

Substitute the value of the vertex and the point to find the value of a:

-5 = a(3 + 10)² - 6

-5 = a(169) - 6

1 / 169 = a

Substitute the value of a in the equation along with the vertex:

y = 1/169(x + 10)² - 6

y = 1/169(x² + 20x + 100) - 6

y = 1/169x² + 20/169² + 100/169 - 6

y = 1/169x² + 20/169² - 5.41

Hence, the standard form of the equation of the quadratic function is y = 1/169x² + 20/169² - 5.41.

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Answer:

Step-by-step explanation:

The department of designing the Death Star originally had 62,000 dollars in the bank account.

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

Let's call the original amount of money in the department's bank account as "A".

After receiving the donation of 13,000, the total amount of money in the account became A + 13,000.

Each project received (A + 13,000) / 3 dollars.

And since each project was funded with 25,000 dollars, we can write an equation to solve for M:

(A + 13,000) / 3 = 25,000

A + 13,000 = 75,000

A = 75,000 - 13,000

A = 62,000

Hence, the department of designing the Death Star originally had 62,000 dollars in the bank account.

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The volume of this required figure is 190m³.

What is volume, exactly?

Volume is a term used in mathematics to describe the volume of three-dimensional space inhabited by an object or a closed surface.

Volume is measured in cubic units like m3, cm3, in3, etc. Volume and capacity may be used interchangeably.

Volume of a rectangular prism is the space inside the prism. It is calculated by multiplying its base area by its height.

Volume (v) = l × b × h, where l is the length, b is the breadth, and h is the height of the prism.

so volume of both the rectangular prism are to be found.

Volume of first rectangular prism = l×b×h = 5 × 4 × 5 = 100 m³.

volume of second prism = 2 × 9 × 5 = 90m³.

∴ the volume of the figure

= volume of first rectangular prism +volume of second prism

= 100m³ + 90m³

=190m³.

Thus, the volume of this required figure is 190m³.

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The required expression is x = 4z/√a that the subject is x.

What is the expression?

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

The expression is given in the question, as follows:

√a/z = 4/x

We have to make x the subject,

As per the question, we have

√a/z = 4/x

Apply the cross-multiplication,

(√a)x = 4z

Isolate the term of variable x, and we get

x = 4z/√a

This is the required expression that the subject is x.

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Given the polynomial Q(x)=2x^3+3x^2+3x+1, and knowing the only real zero is x= -1/2, the complex zeros are:

z1 = -3/4 + (√(3) / 2)i

z2 = -3/4 - (√(3) / 2)i

How to find the complex zeros?

Since the polynomial Q(x) has degree 3 and only one real zero, we know that it must have two complex zeros in the form of a complex conjugate pair, let's call them z1 and z2.

From Vieta's Formulas, we know that the sum of the zeros of a polynomial is equal to the negation of the coefficient of the linear term divided by the leading coefficient. So, in this case:

z1 + z2 = -3/2

Also, the product of the zeros of a polynomial is equal to the negation of the constant term divided by the leading coefficient. So, in this case:

z1 * z2 = -1/2

Since z1 and z2 are complex conjugates, they have the same magnitude and opposite phases. Hence, we can represent them in the form:

z1 = a + bi

z2 = a - bi

where a and b are real numbers and "i" is the imaginary unit.

Using the two equations above, we can find the value of "a" and "b":

a = -3/4

b = √(1/4 - (-1/2)) = √(3/4) = √(3) / 2

So, the complex zeros are:

z1 = -3/4 + (√(3) / 2)i

z2 = -3/4 - (√(3) / 2)i

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Answer:

Step-by-step explanation:

Given the polynomial Q(x)=2x^3+3x^2+3x+1, and knowing the only real zero is x= -1/2, the complex zeros are:

z1 = -3/4 + (√(3) / 2)i

z2 = -3/4 - (√(3) / 2)i

The value of x in the circle is x = 15

How to solve for the value of x in the circle?

Since the measure of angle BAC is m∠BAC = 3x-6. The measure of arc BC will be:

arc BC = 2 *(3x-6) (inscribed angle theorem)

arc BC = 6x-12

In a semicircle, the intercepted arc measures 180°. Thus:

27+5x + 6x-12 = 180°

11x + 15 = 180

11x = 180 - 15

11x = 165

x = 165/11

x = 15

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