MATHEMATICS COLLEGE

The value of a particular rookie baseball card was $2.00 when it was first printed. Five years later, when the player was at his peak, the card was valued at $25.00. Ten years after printing, the card was valued at $8.00. Model the above scenario, showing the value of the card, y, with respect to years since it was printed, x. Write the equation in standard form, y = ax2 + bx + c, where a, b, and c are real numbers rounded to the nearest tenth.

Answers

Answer 1

Answer:

Let t be the time passed in years and y be the value of baseball card.

You know that

when x=0, then y=2;
when x=5, then y=25;
when x=10, y=8.

The equation in standard form is $y=ax^2+bx+c.$ Substitute given data into the equation:

$a\cdot 0^2+b\cdot 0+c=2,\n\na\cdot 5^2+b\cdot 5+c=25,\n\na\cdot 10^2+b\cdot 10+c=8.$

Solve the system of equations:

$\left\{\begin{array}{l}c=2\n25a+5b+c=25\n100a+10b+c=8\end{array}\right.\Rightarrow \left\{\begin{array}{l}c=2\n25a+5b=23\n100a+10b=6\end{array}\right.\Rightarrow$

$\left\{\begin{array}{l}c=2\na=-0.76\approx -0.8\nb=8.4\end{array}\right.$

Then the parabola equation is

$y=-0.8x^2+8.4x+2.$

Answer 2

Answer: thirty four
$25 + 2 + 8$

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Answers

An equation is something with a = sign btw and it’s C because it’s the only one with the = sign

6. Jefferson has $30,000 property damage insurance and comprehensive/collision insurance with adeductible of $1,000. He crashes into a house causing $40,000 damage to the house. Jefferson's car needs
$4,500 worth of repairs? How much will Jefferson have to pay total to fix the house and his car?

Answers

Answer: Since Jefferson has a $1,000 deductible on his comprehensive/collision insurance, he will have to pay the first $1,000 of his car repairs himself. The insurance will cover the remaining amount, which is $4,500 - $1,000 = $3,500.

For the damage to the house, Jefferson's property damage insurance will cover up to $30,000. Since the damage to the house is $40,000, Jefferson will have to pay the difference out of his own pocket. The amount he will have to pay is $40,000 - $30,000 = $10,000.

Therefore, the total amount Jefferson will have to pay to fix the house and his car is $1,000 + $3,500 + $10,000 = $14,500.

Step-by-step explanation:

The employees of a firm that manufactures insulation are being tested for indications of asbestos in their lungs. The firm is requested to send 4 employees who have positive indications of asbestos on to a medical center for further testing. If 55% of the employees have positive indications of asbestos in their lungs, find the probability that 11 employees must be tested in order to find 4 positives. If each test costs 300 Swedish kronor, find the expected value of the total cost of conducting the tests necessary to locate the 4 positives. Swedish kronor Find the variance of the total cost necessary to locate the 4 positives.

Answers

Answer:

attached below

Step-by-step explanation:

Solve the equation for the value of x-6=x/-4

Please show your work, thank you.

Answers

Answer: x=24

x=-6*-4=24

Rylen hiked 3/4 of a mile in 2/3 of an hour . What was his hiking speed in miles per hour?1/8 miles per hour

1 1/8 miles per hour

8/9 miles per hour

1 5/12 miles per hour

Answers

Answer:

The hiking speed in miles per hour is 1 1/8.

Step-by-step explanation:

This can be solved by a simple rule of three.

In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.

When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too.

When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease.

In this problem, the measures are the time spent hiking and the distance hiked. As the the time spent hiking increases, so will the distance hiked. So their relationship is direct.

So:

3/4 - 2/3 hour

x miles - 1 hour

$(2x)/(3) = (3)/(4)$

$x = (9)/(8)$

x can also be written in this format

$x = (9)/(8) = (8)/(8) + (1)/(8) = 1 + (1)/(8)$

So the hiking speed in miles per hour is 1 1/8.

In the coordinate plane, triangle ABC has vertices A(1,-2), B(1,0.5), and C(2,1) and triangle DEF has vertices D(4,-3), E(4,2), and F(6,3). The triangles are similar because DEF is the image of ABC under a dilation with center (_,_) and scale factor ___.PLEASE HELPP