3
A 15-foot tree casts a shadow 20 feet long at the same time a nearby building casts a shadow
4
166 feet long. How tall is the building?

Answer:

.20x = 72, so x = 360

.30(360) = 108

Answer:

36 units squared

Step-by-step explanation:

Since this is kind of a weird shape, we can split it into two smaller shapes, a triangle, and a rectangle.  

The rectangle is 6 units wide, and 4 units long.  Multiply the length and width to get 24 units squared.  

The triangle has a base of 6 and a height of 4, so multiply the base and height, then divide by 2.  6 times 4 is 24 and that divided by 2 is 12.  

Finally add the two areas together.  24+12=36 units squared.

Answer:

36

Step-by-step explanation:

Since the two triangles on the bottom are the same, we can flip one of them over onto the other, and they will make a square. Then the top rectangle is 24, and the bottom new square would be 12 and 24 plus 12 is  36

The step that Inga could use to solve the quadratic equation is;

2(x² + 6x + 9) = 18 + 3.

The solution to the quadratic equation is calculated as follows;

2x² + 12x - 3 = 0

Add 3 to both sides to get;

2x² + 12x = 3

Divide through by 2 which is the coefficient of x² to get;

x² + 6x = ³/₂

Square half of the coefficient of x, and then add it both sides of the equation to get;

(x + 3)² = ³/₂ + 3²

x² + 6x + 9 = 9 + ³/₂

2(x² + 6x + 9) = 18 + 3

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Answer:

x = 11

Step-by-step explanation:

3x+1 = 2x+12 (subtract 2x from both sides)

x+1 = 12 (subtract 1 from both sides)

x = 11

So x is equal to 11

Answer:

To determine the crossover point, we need to find the production volume at which the total cost of each process is equal. Let's denote the production volume as "x."

For Process A:

Fixed cost = $50,000

Variable cost = $10 per unit

Total cost for Process A = Fixed cost + (Variable cost * x)

For Process B:

Fixed cost = $30,000

Variable cost = $15 per unit

Total cost for Process B = Fixed cost + (Variable cost * x)

The selling price for the product is $25 per unit.

To find the crossover point, we'll equate the total costs of both processes and solve for "x."

Total cost for Process A = Total cost for Process B

$50,000 + ($10 * x) = $30,000 + ($15 * x)

Now, let's solve this equation to find the crossover point:

$50,000 + $10x = $30,000 + $15x

$10x - $15x = $30,000 - $50,000

-$5x = -$20,000

x = -$20,000 / -$5

x = 4,000

Therefore, the crossover point occurs at a production volume of 4,000 units.

To determine which process should be chosen above that volume, we'll compare the total costs of each process at a production volume greater than 4,000 units.

For Process A:

Total cost for Process A = $50,000 + ($10 * x)

Total cost for Process A = $50,000 + ($10 * 4,000)

Total cost for Process A = $50,000 + $40,000

Total cost for Process A = $90,000

For Process B:

Total cost for Process B = $30,000 + ($15 * x)

Total cost for Process B = $30,000 + ($15 * 4,000)

Total cost for Process B = $30,000 + $60,000

Total cost for Process B = $90,000

At a production volume greater than 4,000 units, both Process A and Process B have the same total cost of $90,000. Therefore, either process can be chosen above that volume without any cost advantage.

The measure of ∠T is:

∠T = 42°

In geometry, an angle is the figure formed by two rays (i.e. the sides of the angle) sharing a common endpoint (i.e. vertex).

Angles formed by two rays lie in the plane that contains the rays. Angles are also formed by the intersection of two planes.

In the given figure, ∠S is vertically opposite ∠T. We know that vertically opposite angles are equal. Thus, we can say:

∠T = ∠S

Since ∠S = 42°

Thus, the measure of ∠T is:

∠T = 42°

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The number of times the group need to fill the measuring spoon in order to perform the experiment is 12 times

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 the equation be represented as A

Now , the value of A is

Let the amount of teaspoon of salt added to the solution be = ( 3/8 ) of spoon

Let the number of students = 4 students

The group only has ( 1/8 ) teaspoon measuring spoon

Substituting the values in the equation , we get

So , the amount of teaspoon of salt added to the solution by one student = amount of teaspoon of salt added to the solution / ( 1/8 )

On simplifying the equation , we get

The amount of teaspoon of salt added to the solution by one student = ( 3/8 ) / ( 1/8 )

The amount of teaspoon of salt added to the solution by one student = 3 times

And , the number of times the salt is added by 4 students = 4 x 3 = 12 times

Hence , the number of times is 12

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Answer:

3x=12

Step-by-step explanation:

3 times X with x being 4 making it 12 so X=4 and 3x=12

The Nth term rule for the quadratic sequence is 5n² + 10n.

We have,

To find the Nth term rule for a quadratic sequence, we first need to determine the second difference, which is the difference between consecutive first differences.

The first differences are:

20 - 5 = 15

45 - 20 = 25

80 - 45 = 35

125 - 80 = 45

The second differences are:

25 - 15 = 10

35 - 25 = 10

45 - 35 = 10

Since the second differences are constant, the sequence is quadratic.

We can use the formula for the Nth term of a quadratic sequence:

Nth term = an² + bn + c

To find the values of a, b, and c, we can use the first three terms of the sequence:

5 = a(1)² + b(1) + c

20 = a(2)² + b(2) + c

45 = a(3)² + b(3) + c

Simplifying each equation, we get:

5 = a + b + c

20 = 4a + 2b + c

45 = 9a + 3b + c

Solving for a, b, and c, we get:

a = 5

b = 10

c = 0

Thus,

The Nth term rule for the quadratic sequence is 5n² + 10n.

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Answer:

57.1 years

Step-by-step explanation:

multiply the money put into savings by the interest rate 6000×.035=210

divide the total earned by the annual interest earned

12000÷210=57.1428571428

rounded to the nearest tenth is 57.1

Step-by-step explanation:

(8+(-2)-4)

=8-2-4

=2

(3-5)

=-2

Answer:

x= -5/9

That is the answer, try it.

Step-by-step explanation:

the average score would be 3 i think

Answer:

B.1/100 is your answer for your question

Answer:

Opposite numbers

Step-by-step explanation:

Opposite numbers are defined as numbers that have the same distance from zero but are on opposite sides of zero. So opposite numbers have the same absolute values. Another word for opposite numbers is additive inverses because when opposite numbers are added together the sum is always zero.

Answer: $1.75

Step-by-step explanation:

Increase 1.25 by 4.25

5.31

Presently increase 1.25 by 2.85

3.56

Take away 3.56 from 5.31

1.75

Answer:

Beef= 5.75

Turkey=4.35

Beef cost is $1.40 more than turkey.

Step-by-step explanation:

Answer:

x<-35

Step-by-step explanation:

ŷ= 6.45x + 31.5 is the equation of the regression line for the given data

Construct the table of the data as follows:

x    >>>>     y  >>>>  x²  >>>>  y²  >>>>   xy

1                39            1            1521         39

2               45            4           2025       90

3               52             9          2704       156

4               49            16          2401        196

5               61             25         4096       305

5               72            25          5184        360

................................................................................................

20             318           80          17931       1146

.................................................................................................

∑x = 20,  ∑y = 318, ∑x²= 80, ∑xy = 1146,  n = 6 (number data points)

The linear regression equation is of the form:

ŷ = ax + b

where a and b are the slope and y-intercept respectively

a = ( n∑xy -(∑x)(∑y) ) / ( n∑x² - (∑x)² )

a = (6×1146 - 20×318) / ( 6×80-20² )

a = 6876-6360 / 480-400

a = 516 / 80

a = 6.45

x' =  ∑x/n

x' = 20/6 = 10/3

y' = ∑y/n

y' = 318/6 = 53

b = y' - ax'

b = 53 - 6.45×(10/3)

b = 53 - 21.5

b = 31.5

ŷ = ax + b

ŷ= 6.45x + 31.5

Thus,  the equation of the regression line for the given data is ŷ= 6.45x + 31.5. (The scatter plot of the data is shown in the attached image)

(a) x=3 hours

ŷ= 6.45(3) + 31.5 = 50.85

(b) x=4.5 hours

ŷ= 6.45(4.5) + 31.5 = 60.525

(c) x=13 hours

ŷ= 6.45(13) + 31.5 = 115.35

(d) x=1.5 hours

ŷ= 6.45(1.5) + 31.5 = 41.175

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\(\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=5\\ h=3 \end{cases}\implies V=\pi (5)^2(3)\implies V\approx 236~ft^3\)

Answer:

236 ft^3

Step-by-step explanation:

Base radius = 5 ft

Height = 3 ft

Volume =   πr^2h

              =  π × 5^2 × 3

              =  75π

               =  235.61944901923 feet^3

Nearest Cubic Foot = 236 ft^3

Nearest Cubic Foot:

Hence Answer is:

236 ft^3

Hope this helps!

Answer:

3,068

Step-by-step explanation:

you add $541 and $270 and your end answer you add it to $2,457 and you can get your end answer after you add everything to together

I think that the answer

We get the cost of the system and cost of the games  as $126 and $378 respectively.

Given, the price of the video game and several games are sold for $504.

The cost of the game is 3 times as much as the cost of the system.

we need to determine the cost of the system and the cost of the game = ?

Let x = the cost of the games.

Let y = the cost of the system.

therefore, x+y=504

and y = 3x

substitute the value of y.

⇒ x + y = 504

⇒ x + 3x = 504

combine like terms.

⇒ 4x = 504

Divide both sides by 4.

⇒ x = 504/4

⇒ x = 126

The cost of the system is $126.

Use y = 3x substituting 126 for x.

g = 3(126)

g = 378

The cost of the games is $378.

Hence we get the cost of the system and cost of the games as $126 and $378 respectively.

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Answer:

The other two angles are 22° , 22°

Step-by-step explanation:

To find the other angles, we can use angle sum property of triangle.

      The given angle 136° cannot be base angles. Let the base angles be x.

x + x + 136 = 180°

   2x + 136 = 180°

Subtract 136 from both sides,

            2x = 180 - 136

            2x = 44°

Divide both sides by 2,

              x = 44 ÷ 2

                \(\sf \boxed{x = 22^\circ}\)

Answer:42

Step-by-step explanation:

Answer:

The answer is 1/3x-1

Step-by-step explanation:

Let's simplify step-by-step.

5/6x−7−(1/2x−6)

Distribute the Negative Sign:

=5/6x−7+−1(1/2x−6)

=5/6x+−7+−1(1/2x)+(−1)(−6)

=5/6x+−7+−1/2x+6

Combine Like Terms:

=5/6x+−7+−1/2x+6

=(5/6x+−1/2x)+(−7+6)

=1/3x+−1

Answer:

=1/3x−1

The equation is y =  \(\frac{1}{4}\)x + 37

74.5 warm is it when the crickets are chirping 150 times a minute.

Let

x = chirps, y = degrees

When crickets chirp 124 times a minute, it is about 68 degrees Fahrenheit.

So when x = 124, y = 68.  So the graph of the equation contains the point

(124,68)

When they chirp 172 times a minute, it is about 80 degrees Fahrenheit.

So when x = 172, y = 80.  So the graph of the equation contains the point

(172,80)

We assume the graph of the equation is a straight line.

So we use the slope formula to find the slope of the line

m = \(\frac{y2 - y1}{x2 - x1}\)

m = \(\frac{80-68}{172-124}\)

m = \(\frac{12}{48}\)

m = \(\frac{1}{4}\)

We use the point-slope equation:

y - y1 = m(x - x1)

y - 68 =  \(\frac{1}{4}\)(x - 124)

y - 68 =  \(\frac{1}{4}\)x -  \(\frac{1}{4}\)(124)

y - 68 = \(\frac{1}{4}\)x - 31

y =  \(\frac{1}{4}\)x + 37

Substitute x = 150:

y =  \(\frac{1}{4}\)(150) + 37

y = 37.5 + 37

y = 74.5

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Answer:

' =9 93/107 days

Step-by-step explanation:

1/11+1/24

one day =35/264

35/264 -1/32

=107/ 1056- fraction of rem in a day

1 day= 107/1056

x = 1

=107/1056x=1

x=1÷107/1056

1056÷107

=9 93/107 days

Jim did not buy any tickets (n_Jim = 0).

Larry bought 7 more tickets than Jim.

To determine the number of tickets Larry bought more than Jim, we need to find the values of n for Larry and Jim's ticket purchases.

For Larry:

Let's substitute C = $170 into the equation C = 24n + 2 and solve for n:

$170 = 24n + 2

Subtracting 2 from both sides:

$168 = 24n

Dividing both sides by 24:

n = 7

For Jim:

We can calculate the number of tickets Jim bought by subtracting 12 from Larry's number of tickets:

n_Jim = n_Larry - 12

n_Jim = 7 - 12

n_Jim = -5

Since we cannot have a negative number of tickets, we can conclude that Jim did not buy any tickets (n_Jim = 0).

To find the difference in the number of tickets bought, we subtract the number of tickets Jim bought from the number of tickets Larry bought:

n_difference = n_Larry - n_Jim

n_difference = 7 - 0

n_difference = 7

Therefore, Larry bought 7 more tickets than Jim.

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Question

The equation C=24n+2 represents the cost, C, in dollars, of buying n tickets to a play. J $170. How many more tickets did Larry buy than Jim? 12

Answer:

$14500

Step-by-step explanation:

For a car with an initial value \(A_0\), its value, A(t) after time t for which it depreciates by period k with a decay rate of r is given is:

\(A(t)=A_0 \cdot r^{t/k}\)

If the value of the car depreciated by \(\dfrac{1}{2}\) every four years, then the value of the car at any time t is defined by the function:

\(A(t)=41000(0.5)^{t/4}\)

We want to determine the value of the car 6 years after it was purchased.

When t=6

\(A(6)=41000(0.5)^{6/4}\\=\$14495\\\approx \$14500 $(to the nearest hundred dollars)\)

Answer:

brown

Step-by-step explanation:

it might be brown because it compelled

Answer:

Clean and Bright

Step-by-step explanation:

For soapy suds, you would do 13×12, would would give you only 156 sq inches. However, with Clean and Bright, you would do 9×13×8 since it is three dimensional. This would give you 936 cubic inches, meaning it holds the most detergent.