Tyrone went to a basketball game and bought a jersey that was on sale at a 30% discount. He also bought a hat that cost $37.89. Tyrone spent a total of $83.39. Write an equation to find the original cost of the jersey.

Answer:

$10,224.30

Step-by-step explanation:

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{19})\hspace{10em} \stackrel{slope}{m} ~=~ 7 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{19}=\stackrel{m}{ 7}(x-\stackrel{x_1}{2}) \\\\\\ y-19=7x-14\implies {\Large \begin{array}{llll} y=7x+5 \end{array}}[/tex]

Answer: [tex]2\sqrt{13}-\sqrt{697}[/tex]

Step-by-step explanation:

Since ABD is a right triangle, 14^2 = 12^2 + BD^2

196 = 144 + BD^2

52 = BD^2

BD = [tex]\sqrt{52} = 2\sqrt{13}[/tex]

ADC is also a right triangle, so 29^2 = 12^2 + DC^2

841 = 144 + DC^2

DC^2 = 697

DC = [tex]\sqrt{697}[/tex]

Since x = BD + DC,

x = [tex]2\sqrt{13} +\sqrt{697}[/tex] :>

there exists an integer that is greater than 5 and whose square is smaller than 40, express as a mathematical quantifiers ∃x∈ℤ: x > 5 ∧ x² < 40

1.  Start by writing down the equation: x² < 40

2.  Take the square root of both sides of the equation to isolate the variable x: √x² < √40

3.  Simplify both sides of the equation: x < √40

4.  Check that the result makes sense: x < 6.3

5.  Take the integer part of the result: x < 6

6.  Since the requirement is that x is greater than 5, the answer is x = 6.

We start by writing the equation x² < 40 and then take the square root of both sides to get x < √40. We check that the result is reasonable and then take the integer part of the result to get x < 6. Since the requirement is that x is greater than 5, the answer is x = 6. To confirm, we can calculate that x² = 36 which is smaller than 40, and indeed, 6 is greater than 5. Therefore, the integer that is greater than 5 and whose square is smaller than 40 is 6. This can be expressed mathematically as ∃x∈ℤ: x > 5 ∧ x² < 40 which translates to: There exists an integer x such that x is greater than 5 and the square of x is smaller than 40.

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Yes, it is possible to offer a discount to customers who order two dozen cookies.

What is Discount ?

The discount equals the difference between the price paid for and it's par value. Discount is a kind of reduction or deduction in the cost price of a product.

1 dozen=12 pieces

Yes, it's possible to offer a reduction to guests who order two dozen eyefuls. Depending on the capacity of the company, offering a reduction could help to increase the number of orders and potentially increase the company's capacity. still, it's important to consider the cost of offering a reduction and the implicit increase in profit that could be generated from the fresh orders.

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Yes, it is possible to offer a discount to customers who order two dozen cookies.

What is Discount ?

The discount equals the difference between the price paid for and it's par value. Discount is a kind of reduction or deduction in the cost price of a product.

1 dozen=12 pieces

Yes, it's possible to offer a reduction to guests who order two dozen eyefuls. Depending on the capacity of the company, offering a reduction could help to increase the number of orders and potentially increase the company's capacity. still, it's important to cocost nsider the of offering a reduction and the implicit increase in profit that could be generated from the fresh orders.

So ,Yes it is possible to offer a discount to customers who order two dozen cookies.

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The sample has 3.33% of defective bulbs so, B. The shipment will not be replaced.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, If a shipment has at least 5% defective light bulbs, it will be replaced.

Now, A sample of 60 light bulbs has 2 that are defective.

Therefore, The percentage of defective bulbs is,

= (2/60)×100%.

= (1/30)×100%.

= 3.33%, So, the shipment will not be replaced.

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Answer:

490 adults at the museum!

hope that helps :)

mark brainly please.

Use the intercepts to graph the equation y = 18-2x

What is meant by graph ?

Interpret What real-life quantities do the x- and y-intercepts

represent in this situation:

when x = 0, y = 18,  when y = 0 x = 9

The x intercept is 9,  y intercept is 18.

After 9 hours the gas is run not .

The amount of gas in a car when it is not running

18 × 1/4 = 4.5

4.5 = 18-2x

x= 6.75 hours

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The solution of the equation x/6 + 2 = 15 will be 78 by using the property of subtraction and multiplication of equality.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The equation is given below.

x/6 + 2 = 15

Subtract 2 on both sides. Then we have

x / 6 + 2 - 2 = 15 - 2

x / 6 = 13

Multiply the equation by 6, then we have

x/6 × 6 = 6 × 13

x = 78

The solution of the equation x/6 + 2 = 15 will be 78 by using the property of subtraction and multiplication of equality.

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The height in meters is 19.75 meters

The rocket hit the ground after 8.06 sec

The maximum height in seconds is 81 meters

we would have to use 0.5 as the value for t in the formula

h(t) = -5t² + 40t + 1

h(0.5) = -5(0.5)² + 40(0.5) + 1

= -1.25 + 20 +1

= 19.75

To find when the rocket hit the ground, we need to find when the height of the rocket is equal to 0. So we will set h(t) = 0 and solve for t:

-5t² + 40t + 1 = 0

by using Quadratic equation formula we get t = (-b ± √(b²-4ac))/2a

we solve this using the calculator

so t1 = (40 + 40.6)/10 = 80.6/10 = 8.06 sec

Since the time of the rocket hit the ground should be positive, so the rocket hit the ground after 8.06 seconds after launch.

To find the rocket's maximum height, we need to find the vertex of the parabola. The vertex of the parabola can be found by using the formula x = -b/2a,

where x is time and a, b, c are from equation.

so, x = -b/2a

= -40/2*-5

= -40/ -10

= 4 sec

and by using the above formula of x, we get the

h(4) = -5(4)² + 40(4) + 1

= -80 + 160 + 1

= 81 meters

Therefore, the rocket's maximum height is 81 meters.

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We have to find solutions for the given differential equation when

y = 0,  y = 1/(k-x) and y(a) = b using ordinary differential equations.

We have dy / dx = y^2

a. let's define the given y = 1/(k-x)

derive the above equation with respect to x :

                                  dy / dx = y' = 1/(k-x)^2

So this is the general solution.

b) We would want a singular solution that is not included in the general form. Here we could use y = 0

dy / dx = 0 = 0^2

so,this is a trivial singular solution.

c) If we have y(a) = b,

then, y = 1(k-a) = b

To find the value of k we use the other condition: y'(^2) = 4 x y(2)

           1/(k-a)^2 = 4 x  1/(k-a)

              k - 2 = 1/4

              therefore, k = 9/4

hence we got, y = 1/(9/4 - a) = b

So the points (a, b) are of the form: (a, 1/(9/4 - a))

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The complete question is :

Find a general solution of the differential equation dy/dx=y2

b. Find a singular solution that is not included in the general solution.

c. Inspect a sketch of typical solution curves to determine the points (a,b) for which the initial value problem (y′)2=4y,y(a)=b

Answer:  -1 7/20

Step-by-step explanation:

hope this helps

These points (-1,-8), (0,-6), (1,-4), and (2,-2) are the set of ordered pairs made up of points on the graph of the function y = 2x – 6.

What is the linear system?

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

The linear function is given below.

y = 2x – 6

The points (-1,-8), (0,-6), (1,-4), and (2,-2) lies on the equation.

As when the put the given points in the equation , than it satisfies the given condition.

Hence, these points (-1,-8), (0,-6), (1,-4), and (2,-2) are the set of ordered pairs made up of points on the graph of the function y = 2x – 6.

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Answer:

c (72)

Step-by-step explanation:

since there are four wheels to every bike, you just have to multiply the number of bikes to the amount of wheels per bike. given this, 18 * 4=72.

a) The probability of a student living within walking distance of campus is 0.1521.

To find the probability of a student living within walking distance of the campus, we can use the formula for conditional probability:

P(A and B) = P(A) * P(B|A).

For this situation, An is "living within walking distance to campus" and B is "living with parents."

Thus, P(A and B) = (0.23)(0.67) + (0.06)(0.33) = 0.1521.

Hence, the probability of a student living within walking distance of campus is 0.1521.

b)  The probability given a student living within walking distance of campus they experience with their parents is 0.67.

To find the probability given a student day to day routines within walking distance to campus they experience with their parents, we can use the formula for conditional probability:

P(A|B) = P(A and B)/P(B).

In this situation, A is "living with parents" and B is "living within walking distance to campus."

Thus, P(A|B) = P(A and B)/P(B) = (0.23)(0.67)/0.1521 = 0.67.

Subsequently, the probability gave a student living within walking distance of campus experience with their parents is 0.67.

c) Living with parents and living within walking distance are independent events.

To decide whether living with parents and living within walking distance are independent events, we can analyze P(A|B) with P(A).

On the off chance that P(A|B) = P(A), the events are independent. For this situation, P(A|B) = 0.67 and P(A) = 0.67, so living with parents and living within walking distance are independent events.

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The value of 3h(2) + 4g(1) is 39

You can simply replace those variables in function with the value you know of them and then operate on those values to get a final value. This is the result of that expression at those values of the considered variables.

Given;

h(x)= 3x        x<2

     = 4x+1     x>2

g(x)= x^2+2   x<3

     = x^3        x>3

Now, substituting the values;

3h(2)= 3*(4*2+1)

=3*9

=27

4g(1)= 4(1^2 + 2)

=4(3)

=12

3h(2)+4g(1)=27+12

=39

Therefore, the answer of the function will be 39

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This problem is designed to minimize the cost of feeding students in the dorms while providing a minimum of 1800 calories. The objective function is to minimize the cost of the diet, which is calculated by multiplying the pounds of each food by its cost and adding them together. The constraints of the problem are that A must be greater than or equal to 0, B must be greater than or equal to 2, and C must be less than or equal to 0.75.

1. 2.25A + 2B + 3C

2. A >= 0

3. B >= 2

4. C <= 0.75

The objective of this problem is to minimize the cost of feeding students in the dorms, while the diet must contain a minimum of 1800 calories. To achieve this, three decision variables were defined: A, B, and C, which represent the pounds of food A, B, and C respectively. The objective function is to minimize the cost of the diet, which is calculated by multiplying the pounds of each food by its cost, and adding them together. There are three constraints in the problem: A must be greater than or equal to 0, B must be greater than or equal to 2, and C must be less than or equal to 0.75. These constraints ensure that the diet contains the desired amount of each food and that the total calories meet the minimum requirements.

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Analyze the diagram of the trapezoid gives BA = 10.5 units

A trapezoid (also known as a trapezium) is a four-sided geometric shape that has two parallel sides (the bases) and two non-parallel sides (the legs). The bases of a trapezoid can have different lengths, but the legs must be congruent and parallel to each other.

Let's analyze the diagram below and complete the instructions:

Since CB / CA = DE / DF

where CB = 6, DE = 4, EF = 7

We can say:

DF = DE + EF = 4 + 7 = 11

CA = CB + BA = 6 + BA

CB / CA = DE / DF

6/(6 + BA) = 4/11

6 × 11 = 4(6 + BA)

66 = 24 + 4BA

24 + 4BA = 66

4BA = 66 - 24

4BA = 42

BA = 42/4

BA = 10.5 units

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The average salary for college graduates is 53% higher than that of high school graduates.

Mathematically, percentage increase can be calculated by using this mathematical expression:

Percentage increase = [Final value - Initial value]/Initial value × 100

Substituting the given parameters into the percentage increase formula, we have the following;

Percentage increase = [62,047 - 40,626]/40,626 × 100

Percentage increase = 21,421/40,626 × 100

Percentage increase = 0.527 × 100

Percentage increase = 52.7 ≈ 53%.

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Answer:

Option 3. Look at my screenshot so you can see the circled one

Step-by-step explanation:

The reasoning behind this is slope is rise over run (rise/run)
Graph 3 goes down 3 so -3 and runs 1 over so (-3/1)
This is simplified as -3.

I hope this helps you out :D

As per the cone surface, the general direction in which the shatter cone ridges converge is south.

The term cone in math is defined as a three-dimensional shape in geometry that narrows smoothly from a flat base  to a point called the apex or vertex.

Here we have given that Shatter cones are key features that uniquely characterize impact structures

In this one their presence provides evidence that an impact occurred. Here we also know that the Shatter cone surfaces exhibit a texture with a series of intersecting ridges that produce its conical geometry.

Based on the definition of cone surface we have identified that the the correct  option is (a) that is the south.

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The reflection of point G across the x-axis would be at (-3, 2).

A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.

The coordinates of point G in the question are (-3,-2)

When a point is reflected across the x-axis, the x-coordinate remains the same, but the sign of the y-coordinate is changed.

Therefore, the reflection of point G, which is located at (-3, -2), across the x-axis would be at (-3, 2).

The x-coordinate is the same, but the y-coordinate has changed from negative to positive.

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The question seems incomplete, the completed question would be as:

The coordinates of point G are (-3,-2)

What would be the reflection point G across the x-axis?

The equation will be 4(x + 2) = 40. Then the value of the variable 'x' will be 8.

The sum of all the sides of the square or the product of the four and the edge length of the square is known as the perimeter of the square. For a square with a side length of a unit, we get:

Perimeter of the square = 4a unit

The perimeter of the square is 40 cm. And the sides length of the square is (x + 2) cm. Then the perimeter of the square is given as,

4(x + 2) = 40

Simplify the equation, then we have

4(x + 2) = 40

(x + 2) = 10

x = 10 - 2

x = 8

The equation will be 4(x + 2) = 40. Then the value of the variable 'x' will be 8.

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The complete question is given below.

Solve it to find the value of x. Also, find the actual length of each square perimeter of the square is 40 cm and side length is (x + 2).

The angle whose supplement is 30 degrees greater than 4 times the supplement is 30°

Two angles are called supplementary when their measures add up to 180 degrees.

For example:- 120° and 60°, 110° and 70°, 140° and 40°, 90° and 90°, 20° and 160°, 135° and 45° are some example of supplementary angles.

Given that, an angle whose supplement is 30 degrees greater than 4 times the supplement.

Let the angle asked be x,

Therefore, the supplement of x, will be = 180°-x

According to the question, Its supplement is 30 degrees greater than 4 times the supplement.

Therefore, establishing the equation,

So, for solving for x, we have,

180°-x = 30°+4x

4x+x = 180°- 30°

5x = 150°

5x/5 = 150°/5

x = 30°

As, we considered the angle asked be x,

Hence, the angle whose supplement is 30 degrees greater than 4 times the supplement is 30°

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The speed of the bicycle is 381 meters per minutes

we know that,

revolutions per minute = speed in meters per minute / circumference in meters.

Diameter = 32 inches

Circumference of the wheel = 2πr

r = Diameter/2 = 32/2 = 16

Circumference = 2 × π × 16

=  100.5714 inches

Approximately = 100 inches

we know that,

1 inch = 0.0254 meter

100 inches = x

x = 100 × 0.0254 meters

x = 2.54 meters

Hence:

Revolutions per minute = Speed in meters per minute / circumference in meters.

Speed = Revolutions per minute × circumference in meters.

Speed = 150 RPM × 2.54 meters

Speed = 381  meters per minutes

so, the speed of the bicycle is 381 meters per minutes.

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Answer:

v^2+4v+4

Step-by-step explanation:

To do this we have to know that (2+v)^2 is the same as (2+v) (2+v)

Next, use the distributive property and add like variables to get the final answer of v2+4v+4

I hope this was able to help you out :D

Answer:hie

hie

Step-by-step explanation:hie

The surface area of the container is 62 square inches.

The correct option is D.

In three-dimensional space,

a prism is a polyhedron where two ends are similar.

Given:

A student draws the net below to show the dimensions of a container that is shaped like a right rectangular prism.

We have H = 2 inches

L = 5 inches

W = 3 inches

Surface area of the rectangular prism,

A = 2(W×L + H×L + H×W)

A = 2(3×5+2×5+2×3)

A = 2(15+10+6)

A = 2(31)

A = 62 square inches

Therefore, the surface area is 62 square inches.

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Answer:

I believe it's BC

Step-by-step explanation:

I can't really give an explanation but I've done this before and struggled but learned it, hope I'm right