Keith drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 12 hours. When Keith drove home, there was no traffic and the trip only took 8 hours. If his average rate was 20 miles per hour faster on the trip home, how far away does Keith live from the mountains?
Do not do any rounding.

The surface area of the frustum is 1744 square units

The volume of the pyramid is 2031.33 cube units.

What is a frustum of a pyramid?

By cutting the top of a typical pyramid, the frustum is created, which is a pyramid. Because of this, it is known as a truncated pyramid. The frustum of the pyramid is that portion of a pyramid that is cut through by a plane parallel to its base and lies between the vertex and the base.

a) First, we calculate the height of the frustum.

Let height be H

The base length be L1=24

Base width be W1=12

Top length is L2=14

To width be W2=13

Side height be C=13

Using the formula, H

[tex]H=\sqrt{ C^{2} - \frac{(L1-L2)^{2}}{2}}\\H=\sqrt{ 13^{2} - \frac{(24-14)^{2}}{2}}\\H=\sqrt{ 169 -50}\\H=\sqrt{119} \\H=11[/tex]

Now, the surface area of the frustum is LSA+area of bases of a frustum

Here, P1= perimeter of the base1 of the frustum

P2 is the perimeter of the base 2 of the frustum

[tex]L.S.A=\frac{1}{2} .(P1+P2).L \\=\frac{1}{2} .(72+42).24 \\=\frac{1}{2} .(114).24 \\=1368[/tex]

Now, S1 =area of base1 of frustum =288

S2= area of base 2 of frustum=98

TSA is given by LSA+area of bases of a frustum

=1368+288+98

=1724.

Therefore the surface area is 1724 square units.

b) Volume is given by

[tex]V=\frac{1}{3}.H.(S1+S2+\sqrt{S1S2} )\\ V=\frac{1}{3} . 11.(386+168)\\V=2031.33[/tex]

Therefore the volume is 2031.33 cube units.

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Answer:

The slope is -1

Step-by-step explanation:

To find the slope using two points, you must do this:

(y2-y1) divided by (x2-x1) which is -1-4 divided by 2+3 and the answer will be -5/5 or just simply -1

Explanation:

Choices A and B are ruled out because they are cube root functions, which have a domain and range of "all real numbers".

Choice C is ruled out because the domain is [tex][a, \infty)[/tex]

To determine this domain, we set the radicand (aka stuff under the square root) to be greater than or equal to zero.

[tex]x-a \ge 0 \ \ \text{ solves to } \ \ x \ge a[/tex]

[tex]x \ge a \ \ \text{ turns into the interval notation } \ \ [a, \infty)[/tex]

The square bracket is used to include the value 'a' as part of the interval. This is the interval from x = a to positive infinity.

The domain of choice D is [tex][b, \infty)[/tex] found using similar steps as shown above.

The range is [tex](-\infty, a][/tex] since this square root function is decreasing, due to the negative out front, which means y = a the largest output possible. I recommend graphing it out using a tool like desmos or geogebra. These tools offer a way to use parameters.

Answer:

y=3x-4

Step-by-step explanation:

-9x+3y=-12

3y=12-9x

y=3x-4

Answer:

Here,

the length=8x

the width =3y-2

We know that,

Area of rectangle=l×b

or, 8x × 3y-2

8x(3y-2)

24xy-16x

Hence, the correct answer is 24xy-16x

ax + by = 6000 and a + 5 = b are two equations that might be used to calculate how many soup cans and frozen dinners were purchased.

There are several methods to define a formula. A mathematical statement that establishes the equivalence of two mathematical expressions is the definition of an equation in algebra.

This is best shown by the formula 3x + 5 = 14. In this instance, the word equal comes between the phrases 3x + 5 and 14. Even the most basic algebraic equations include the usage of mathematical variables.

Let frozen supper be y and soup cans be x.

X now has 300 mg of sodium in it.

x = 300

Y also has 450 mg of sodium in it.

y = 450

Samuel reportedly buys five more frozen dinners than soup cans, and they all have a combined salt content of 6000 mg.

Let the number of frozen dinners be "b," and the number of soup cans be "a."

ax + by = 6000

⇒ a(300) + b(450) = 6000 ...1

Samuel bought 5 more frozen dinners than soup cans, according to the inquiry, which results in equation

a + 5 = b ...2

Now, by changing the value of b in equation 1 we obtain,

⇒ a(300) + (a + 5)(450) = 6000

⇒ 300a + 450a = 6000 - 2250

⇒ 750a = 3750

⇒ a = 3750/750

⇒ a = 5

By changing the value of an in equation 2, we obtain

⇒ 5 + 5 = b

⇒ b = 10

So, ax + by = 6000 and a + 5 = b are two equations that might be used to calculate how many soup cans and frozen dinners were purchased, respectively, where x and y stand for soup cans and frozen dinners, respectively, and a and b stand for the quantity of soup cans and frozen dinners.

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Answer:

x = -2

Step-by-step explanation:

hope this will help you

Answer:

Bachelor's Degree: $55,000
Master's Degree: $61,000

Step-by-step explanation:

First start defining variables for each of the salaries

Let M be the salary of the master's individual

Let B be the salary of the bachelor's individual

Given:
Average yearly salary of an individual whose final degree is a master's is $49 thousand less than twice that of an individual whose final degree is a bachelor's

can be translated into the equation

M = 2B - 49,000

Subtract M from both sides and add 49,000 to both sides:

49,000 = 2B - M

Switch sides:

2B - M = 49,000   [1]

Together they earned 116,000 becomes

B + M = 116,000   [2]

Add equations [1] and [2] to eliminate M
2B - M + B + M = 49,000 +116000
3B = 165000

B = 165000/3 = 55,000

Using equation 2, B + M = 116000 we get

55000 + M = 116000

M = 116000 - 55000 = 61,000

Solution
Bachelor's Degree: $55,000
Master's Degree: $61,000

The length of x in the similar quadrilateral is 1.5 units.

Quadrilaterals are polygons with 4 sides. The sum of the interior angles of a quadrilateral is 360 degrees.

Two quadrilaterals are similar quadrilaterals when the three corresponding angles are the same and two adjacent sides have equal ratios.

Therefore, quadrilaterals ABCD and JKLM are similar.

Hence, let's find the side x of the quadrilaterals.

Therefore,

CD / LM = BC / KL

CD = 5

LM = 2.5

BC = 3

KL = x

Hence,

5 / 2.5 = 3 / x

cross multiply

5x = 2.5 × 3

5x = 7.5

x = 7.5 / 5

x = 1.5

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The collection of all logical values for each independent variable under consideration.

The set of all independent variable values that are logical in the particular circumstance. the collection of every possible value for the dependent variable the collection of all feasible dependent variable values that are appropriate in the situation.

Let y = f(x) represent a function where x and y are independent variables. The chosen x-value is said to fall within the domain of f if a function f offers a means of successfully producing a single value y while using a value for x to that end.

The set of possible input values is referred to as the domain, and the domain of a graph is made up of all the input values displayed on the x-axis. The set of potential output values that make up the range is represented by the y-axis.

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to get the slope of any straight line, we simply need two points off of it, let's use those in the picture below.

[tex]\stackrel{\textit{\LARGE line of reflection}}{(\stackrel{x_1}{-1}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-2})} \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{(-4)}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-1)}}} \implies \cfrac{-2 +4}{1 +1} \implies \cfrac{ 2 }{ 2 } \implies \text{\LARGE 1}[/tex]

now, keeping in mind that perpendicular lines have negative reciprocal slopes, there are three dotted lines, each one of them, hits the line of reflection perpendicularly, so their slope must be

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{1\implies \cfrac{\boxed{1}}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{\boxed{1}}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{\boxed{1}}\implies \text{\LARGE -1}}}[/tex]

Using the interest rates formula, we know that an automobile that costs $24588.44 is within our means.

The amount of interest due each period expressed as a percentage of the amount lent, deposited, or borrowed is known as an interest rate.

The total interest on a loaned or borrowed sum is determined by the principal amount, the interest rate, the frequency of compounding, and the period of time the loan, deposit, or borrowing took place.

So, let's say the car's affordable price is P:

The entire payback is equal to P r/100 T + P.

In this case, P, r = 4.75, and T = 9 years.

$351,00 = P × (4.75/100 × 9 + 1)

$351,00 = P × ( 0.4275 + 1)

$351,00 = P × 1.4275

P = 351,00 / 1.4275

When you use the division operation, we receive:

P = $24588.44

Therefore, using the interest rates formula, we know that an automobile that costs $24588.44 is within our means.

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By solving a linear equation, we will see that they sold a total of 288 cookies.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

We know that Phil and Matt sell cookies for $0.25 each, so, if they sell x cookies, the total revenue is: R(x) = $0.25*x

Now, we know that they made a total of $72.00, so now we need to solve the linear equation:

$0.25*x = $72.00x

= $72.00/$0.25 = 288

They sold 288 cookies.

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The recursive formula for the arithmetic succession will be written as aₙ = 25 - 5n.

A series of integers called an arithmetic succession or arithmetic chain of events has a fixed difference between the terms.

Let a₁ be the first term and d be a common difference.

Then the nth term of the arithmetic sequence is given as,

aₙ = a₁ + (n - 1)d

The sequence is given below.

20, 15, 10, 5, .....

The first term is 20 and the common difference is given as,

d = 15 - 20

d = - 5

Then the recursive formula given the following sequence is given as,

aₙ = a₁ + (n - 1)d

aₙ = 20 + (n - 1) × (-5)

aₙ = 20 - 5n + 5

aₙ = 25 - 5n

The formula for the arithmetic sequence will be written as aₙ = 25 - 5n.

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Answer:

x = 79

Step-by-step explanation:

To find the value of x we first need to find the missing angle of the triangle in the image.

101 + 29 + missing angle = 180

130 + missing side = 180

missing side = 50

Now, the sum of two interior angles in a triangle is equal to an exterior angle that is supplementary to the third interior angle.

So the value of x:

29 + 50 = 79

The answer is true, if radius OP intersects chord AC in point B and AB=8 units, BC=8 units.

The length of the line segments from a circle's center to its perimeter is referred to as the radius of a circle or sphere in more contemporary use. Radius has two possible plurals: the traditional English plural radiuses or radii. R or r is the most common radius abbreviation and mathematical variable name. Consequently, the diameter D is equal to double the radius.

Given,

In circle radius OP intersects chord AC in point B.

And AB=8 units, BC=8 units

So, OP is perpendicular to AC.

Due to the fact that OA and OC have equal sides and a base length of AC, OAC forms a triangle (the radius of the circle)

When you trace AC, you discover that O, a line perpendicular to AC, intersects the circle's center.

So, the answer is true.

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Answer: The correct answer is D, Lines are skew if and only if they are non-coplanar.

In geometry, lines are said to be skew if they are non-coplanar, meaning they do not lie in the same plane. They also do not intersect.

Option A is incorrect because angles can be supplementary (add up to 180 degrees) even if they do not form a linear pair (meaning they do not share a common vertex and a common side).

Option B is incorrect because Valentine's Day does not always fall in February. It is February 14th, but it could fall on a different month in a different year.

Option C is correct because a number is even if and only if it is divisible by 2. An even number can be divided evenly by 2, while an odd number cannot.

The system of equations has infinite solutions, actually, any pair (x, y) is a solution.

To solve a system by elimination, we just need to add/subtract the equations in such a way that we can remove one of the variables.

Here the system of equations is:

-2x-3y = -9

-2x-3y = -9

If we subtract the two equations we will get:

(-2x-3y) - (-2x-3y) = -9 - (-9)

0 = 0

This is a trivial equation, that happens because both equations of the system are the same one.

So the system is true for all real values of x and y.

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Answer:

See below

Step-by-step explanation:

I would start off writing the equation in the slope intercept form of a line

y + 4 = 1/4(x + 10)  Distribute the 1/4

y + 4 = 1/4x + 10/4    Simplify 10/4

y + 4 = 1/4 x + 5/2  Subtract 4 from both sides

y = 1/4 x + 5/2 -4

y = 1/4 x + 5/2 - 8/2

y = 1/4 x - 3/2

Then I used the free graphing calculator Desmos to graph.

Answer:

24-3-32233'2]/2

Step-by-step explanation:

Nancy can buy maximum 8 video games.

Steps to solve inequality:

The inequality will not change if the coefficient is positive.

The inequality will be the other way around if the coefficient is negative.

If Nancy wants to keep at least $120 in her account and at present, she is having $240

So, she can spend = 240-120= $120

And, one video game price= $15

Let us consider she can buy maximum 'X' games

15×X=$120

X = 8 units

Hence, she can buy a maximum of 8 video games.

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In differentiation , qA = 13/5  , qB = 11/5 are  values of qA and qB maximize the revenue .

What does mathematics differentiation serve?

In mathematics, differentiation is used to compute rates of change. For instance, in mechanics, velocity is the amount at which a displacement changes over time.

                   The acceleration is the speed at which velocity is changing with respect to time.

R = 40qA + 50qB − 6qA2 − 9qB2 − 4qAqB

Let aA = x , qB = y

so,

 R= 40x + 50y - 6x² - 9y² - xy

Partially differentiate above equation with respect to x and y .

Rx = 40 - 12x - 4y

Ry = 50 - 18y - 4y

Set Rx = 0 and Ry = 0 solve x and y .

40 - 12x - 4y = 0

50 - 18y - 4x = 0

Solving above questions

 x = 13/5 , y = 11/5

therefore,

      qA = 13/5  , qB = 11/5

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Answer:

thanks.

0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Answer:

the digit 1 is less than 5, so we round 54.71 down to 54.7.

Step-by-step explanation:

To find the two points having an x-coordinate of 3 whose distance from the point (-2, -1) is 13, you can use the distance formula:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) is the coordinates of the first point, and (x2, y2) is the coordinates of the second point.

In this case, you can use the distance formula to find the y-coordinates of the two points having an x-coordinate of 3:

Distance = √((3 - (-2))^2 + (y - (-1))^2)

= √(5^2 + (y + 1)^2)

= √(25 + y^2 + 2y + 1)

= √(26 + y^2 + 2y)

= 13

If you set the distance equal to 13 and simplify the equation, you get:

y^2 + 2y + 12 = 0

This is a quadratic equation, which means it can be solved using the quadratic formula:

y = (-b ± √(b^2 - 4ac)) / (2a)

where a, b, and c are the coefficients of the quadratic equation.

Substituting the values into the quadratic formula, you get:

y = (-2 ± √(-2^2 - 4 * 1 * 12)) / (2 * 1)

= (-2 ± √(-4 - 48)) / 2

= (-2 ± √(-52)) / 2

Since the square root of a negative number is not a real number.

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Total percentage of students in each department, to the whole of Lee Business School is 85.5298308   11.48709 0 2.983081     100.

What is percentage ?

A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. A dimensionless connection between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals. The sign "%" is frequently put after the number to indicate percentages.

Department Undergrad Master Doctoral Total

 Total % Total % Total % Numbers %

Accounting 390 17.364203 83 3.695459 0 0 473 21.05966

Economics 467 20.79252 20 0.890472 0 0 487 21.68299

Finance 215 9.5725735 7 0.311665 0 0 222 9.884239

Management, E&T 590 26.268923 75 3.33927 1 0.044524 666 29.65272

Marketing and I.B. 259 11.531612 10 0.445236 1 0.044524 270 12.02137

MBA 0 0 63 2.804987 65 2.894034 128 5.69902

Total 1921   258   67   2246  

Percentage of total students 85.5298308   11.48709 0 2.983081     100

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Answer:

x=9.8

Step-by-step explanation:

So each friend will get by dividing  3*10 + 5 + 6/2 = 30 + 5 + 3 =38 blueberries.

One of the fundamental mathematical operations is division, which involves breaking a bigger number into smaller groups with the same number of components. How many groups will be created, for instance, if 30 students need to be separated into groups of five for a sporting event? The division operation may be used to quickly and simply fix such issues. In this case, we must divide 30 by 5. 30 x 5 = 6 will be the outcome. There will thus be 6 groups with 5 students each. The initial number, 30, which is obtained by multiplying 6 by 5 may be used to confirm this figure.

The names of the phrases connected with the division process are referred to as division parts. The division is made up of the following four components: dividend, divisor, quotient, and remainder.

Two friends can divide 76 blueberries by dividing 76 divided by 10 .

The value we get is Divisor is 10 , Dividend is 76

So, The Quotient is 7 and Remainder is 6

So there will be 7 box of 10 blueberries and 1 box with 6 berries.

Pictorial Representation is :

(10), (10), (10), (10), (10), (10), (10), (06).

Now since there are 7 bowls of 10 berries so 7 divide by 2 is 3 as quotient and 1 as remainder so 1 box will be split apart into 10 divided by 2 is 5 berries each.

So each friend will get 3*10 + 5 + 6/2 = 30 + 5 + 3 =38 blueberries.

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So each friend will get by dividing  3*10 + 5 + 6/2 = 30 + 5 + 3 =38 blueberries.

What is Division ?

One of the fundamental mathematical operations is division, which involves breaking a bigger number into smaller groups with the same number of components. How many groups will be created, for instance, if 30 students need to be separated into groups of five for a sporting event? The division operation may be used to quickly and simply fix such issues. In this case, we must divide 30 by 5. 30 x 5 = 6 will be the outcome. There will thus be 6 groups with 5 students each. The initial number, 30, which is obtained by multiplying 6 by 5 may be used to confirm this figure.

The names of the phrases connected with the division process are referred to as division parts. The division is made up of the following four components: dividend, divisor, quotient, and remainder.

Two friends can divide 76 blueberries by dividing 76 divided by 10 .
The value we get is Divisor is 10 , Dividend is 76
So, The Quotient is 7 and Remainder is 6
So there will be 7 box of 10 blueberries and 1 box with 6 berries.
Pictorial Representation is :
(10), (10), (10), (10), (10), (10), (10), (06).
Now since there are 7 bowls of 10 berries so 7 divide by 2 is 3 as quotient and 1 as remainder so 1 box will be split apart into 10 divided by 2 is 5 berries each.
So each friend will get 3*10 + 5 + 6/2 = 30 + 5 + 3 =38 blueberries.

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