For question 5, use elimination or substitution.
5) x + 2y = 16
X- y = -2

a) The approximate sports league salary cap in 1995 was $35.17 million. b) According to the model, the salary cap reached $65 million in the year 2001.

To approximate the sports league salary cap in millions of dollars for a given year using the quadratic model, we substitute the corresponding value of x into the equation \(y = 0.2313x^2 + 2.600x + 35.17\).

a) To approximate the sports league salary cap in a particular year, we need to determine the value of y when x represents that year. Let's calculate:

For the year 1995 (x = 0):

\(y = 0.2313(0)^2 + 2.600(0) + 35.17\)

y ≈ 35.17 million dollars

Therefore, the sports league salary cap in 1995 was approximately 35.17 million dollars.

b) We can use the quadratic equation to determine the year when the salary cap reached 65 million dollars. Let's solve the equation for y = 65:

\(65 = 0.2313x^2 + 2.600x + 35.17\)

To solve this quadratic equation, we can rearrange it to:

\(0.2313x^2 + 2.600x + 35.17 - 65 = 0\)

\(0.2313x^2 + 2.600x - 29.83 = 0\)

To solve this equation, we can use the quadratic formula:

x = (-b ± √(b²- 4ac)) / 2a

where a = 0.2313, b = 2.600, and c = -29.83.

Substituting these values into the quadratic formula, we get:

x = (-2.600 ± √(2.600² - 4 * 0.2313 * (-29.83))) / (2 * 0.2313)

Calculating the expression within the square root:

x = (-2.600 ± √(6.76 + 27.4376)) / 0.4626

x = (-2.600 ± √(34.1976)) / 0.4626

x = (-2.600 ± 5.8456) / 0.4626

Now we can calculate the two possible values for x:

x1 = (-2.600 + 5.8456) / 0.4626 ≈ 6.22

x2 = (-2.600 - 5.8456) / 0.4626 ≈ -14.09

The value of x represents the number of years since 1995. Therefore, -14.09 is not a valid solution in this context.

According to the model, the salary cap reached 65 million dollars approximately 6.22 years after 1995. Adding this to 1995, we find:

1995 + 6.22 ≈ 2001.22

Therefore, according to the model, the salary cap reached 65 million dollars around the year 2001.

Learn more about quadratic equation here: https://brainly.com/question/30098550

#SPJ11

The complete question is:

In 1995, the sports league introduced a salary cap that limits the amount of money spent on players' salaries. The quadratic model y=0.2313x2+2.600x+35.17 approximates this cap in millions of dollars for the years 1995-2006, where x=0 represents 1995, x=1 represents 1996, and so on. Complete parts a and b.

a) Approximate the sports league salary cap in .

b) According to the model, in what year did the salary cap reach 65 million dollars?

C) f is decreasing for x<0 because f′(x)<0 for x<0. , we can conclude that the function f is decreasing for x<0 because f′(x)<0 for x<0.

The derivative of f is f′(x)=x2−a2=(x−a)(x+a).

This implies that f′(x)<0 when x<−a or x>a. From the derivative, we can deduce that f is decreasing for x<0 because f′(x)<0 for x<0.

The derivative of the function f is f′(x)=x2−a2=(x−a)(x+a), where a is a positive constant. This means that the derivative is negative when x<−a or x>a. We can use this information to determine the behavior of the function. Since the derivative is negative when x is less than zero, we can conclude that the function f is decreasing for x<0 because f′(x)<0 for x<0.

Learn more about function here

https://brainly.com/question/29633660

#SPJ4

the formula by using x=-2 in the other direction.

Reversing equation is what?

The goal of equation solving is to get the variable by itself on one side of the equation and a number on the other side. To isolate the variable, we must turn around the processes that effect it. To achieve this, w, we carry out each operation's inverse on both sides of the equation.

based on the provided statement;

Eliminate the biggest shared variable on both sides of the equation:

3x+2=-4

Unknown terms should be moved to the left side of the equation:

3x=-4-2

Determine the total or difference:

3x=-6

Add the variable's coefficient to both sides of the equation, then subtract it:

x=-6/3

x=-2

Calculate the product or quotient x=-2

to know more about Reversing equation visit;

https://brainly.com/question/15705398

#SPJ9

According to the question, the given parameters of a triangle Δ IJK is given below:

j = 960 inches, i = 200 inches and ∠I = 68 degree.

As we know, the sum of the angle of a triangle is 180 degree.

Therefore, ∠I + ∠J + ∠K = 180 degree

Substituting above values in the given expression, we get:

∠J + ∠K = 180 - 68 = 112 degree

For isosceles triangle, two sides are equal. Therefore, ∠J = 56 degree

Hence, the calculated value for the ∠J is 56 degree.

What is triangle?

In the geometry of mathematics, the triangle can be defined as a polygon shape which has three edges as well as three vertices. There are three different forms of triangle which are known as scalene, isosceles and equilateral triangle.

To learn more about the triangle from the given link:

https://brainly.com/question/17335144

#SPJ1

a. The population in this situation is the group of all individuals who are interested in Seattle Mariners and its performance in the upcoming baseball season.b. The sampling strategy described here is a voluntary response sampling strategy. c. The type of bias that is present in this situation is voluntary response bias.Explanation:Voluntary Response SamplingVoluntary response sampling is a type of non-probability sampling that involves participants who voluntarily choose to participate in a survey or study. In other words, individuals are not randomly selected to participate. Instead, they choose to participate on their own. Voluntary response sampling is considered an easy and inexpensive way to gather data, but it is often biased because those who choose to participate may not be representative of the population as a whole.In this situation, a Mariners fan website published a survey asking for predictions about the Mariners' performance in the upcoming baseball season. Nearly 3000 different individuals responded. So, the sampling strategy described here is a voluntary response sampling strategy. The population in this situation is the group of all individuals who are interested in Seattle Mariners and its performance in the upcoming baseball season. The type of bias that is present in this situation is voluntary response bias.

to know more about population visit :

https://brainly.com/question/15889243

#SPJ11

The radius of the cone is 3 times the radius of the cylinder, given that they have equal volumes and radii of equal length.

The height of the cylinder is also 24 centimeters since the radii are equal.

To find the volume of the cylinder, use the formula V = πr^2h, where r is the radius and h is the height.

To find the volume of the cone, use the formula V = (1/3)πr^2h, where r is the radius and h is the height.

Since the volumes are equal, you can set up the equation (1/3)πr^2(24) = πr^2(24) and solve for r.

Simplifying the equation, you get (1/3) = 1.

This means that the radius of the cone is 3 times the radius of the cylinder.

Therefore, the radius of the cone is 3 times the radius of the cylinder, given that they have equal volumes and radii of equal length.
To know more about cone visit:

https://brainly.com/question/29767724

#SPJ11

answer is 60 degrees

The variables of farmer are independent variables and dependent variables.

In this scenario, the farmer is testing the impact of different amounts of nitrogen on corn plant height. Her variables are as follows:

1. Independent variable: The amount of nitrogen infused in the soil (one pot has nitrogen-infused soil and the other has regular soil).

2. Dependent variable: The height of the corn plants (measured in feet).

However, it's important to note that the experimental setup has a potential confounding variable, which is the location of the pots (one is outside and the other is in the bathroom). This might influence the results and make it difficult to solely attribute the differences in height to the nitrogen content in the soil.

Learn more about "variables ":

https://brainly.com/question/28248724

#SPJ11

The random variable has an expected value of 16, an E(x²) value of 288, a mean of 16, a variance of 32, and a standard deviation of 4√2.

To find the expected value (E), mean (μ), variance (σ²), and standard deviation (σ) of the random variable with the probability density function f(x) = (1/288)x on the interval [0, 24], we need to perform the necessary calculations.

Expected value (E):

E(x) is calculated by integrating x * f(x) over the given interval:

E(x) = ∫[0, 24] x * (1/288)x dx

Simplifying:

E(x) = (1/288) ∫[0, 24] x² dx

E(x) = (1/288) [x³/3] evaluated from 0 to 24

E(x) = (1/288) [(24³/3) - (0³/3)]

E(x) = (1/288) [(13824/3) - 0]

E(x) = (1/288) * 4608

E(x) = 16

Therefore, E(x) = 16.

E(x²):

E(x²) is calculated by integrating x² * f(x) over the given interval:

E(x²) = ∫[0, 24] x² * (1/288)x dx

Simplifying:

E(x²) = (1/288) ∫[0, 24] x³ dx

E(x²) = (1/288) [x⁴/4] evaluated from 0 to 24

E(x²) = (1/288) [(24⁴/4) - (0⁴/4)]

E(x²) = (1/288) [(331776/4) - 0]

E(x²) = (1/288) * 82944

E(x²) = 288

Therefore, E(x²) = 288.

Mean (μ):

The mean (μ) is the same as the expected value E(x). So, μ = 16.

Variance (σ²):

Variance (σ²) is calculated as E(x²) - (E(x))^2:

σ² = E(x²) - (E(x))^2

σ² = 288 - (16)^2

σ² = 288 - 256

σ² = 32

Therefore, σ² = 32.

Standard Deviation (σ):

The standard deviation (σ) is the square root of the variance:

σ = √(σ²)

σ = √32

σ = 4√2

Therefore, σ = 4√2.

To summarize:

E(x) = 16

E(x²) = 288

μ = 16

σ² = 32

σ = 4√2

To know more about standard deviation,

https://brainly.com/question/20892773

#SPJ11

Answer:

y= -2x^2+4x+126

Step-by-step explanation:

Answer:

yes 1/6 is a rational number.

Answer:

B

Step-by-step explanation:

2x+3y=12

3y=12-2x

y=-2/3x+4

B

Hope this helps plz hit the crown :D

Answer:

19.0

Step-by-step explanation:

19.0 is the correct answer.

Hello, hope you are having a nice day.

e=2.718281828...

e^7 means e times e times e times e times e times e times e.

The approximate answer is

1096.6

I hope it helps. Please mark brainliest!

~An emotional teen who helps others with joy

Good luck.

The value of m for the given equation is 18. The solution has been obtained by solving the linear equation.

What is a linear equation?

A linear equation is the one with the highest degree of one. This demonstrates that there are no variables in a linear equation with an exponent bigger than one. On the graph, such an equation yields a straight line.

We are given an equation as 2 = m/2 - 7

On solving the equation for m, we get

⇒2 = m/2 - 7

⇒2 = (m - 14)/2

⇒2*2 = (m - 14)

⇒4 = m - 14

⇒m = 18

Hence, the value of m for the given equation is 18.

Learn more about linear equation from the given link

https://brainly.com/question/30092358

#SPJ1

Answer:

Step-by-step explanation:

P(t) = K / (1 + (K/P0 - 1) * e^(-rt))

In this equation, P(t) is the population at time t, P0 is the initial population at time t=0, K is the carrying capacity, r is the intrinsic growth rate, and e is the base of the natural logarithm ( approximately 2.71828).

To find the carrying capacity, you can set P(t) equal to K and solve for t. This will give you the time at which the population reaches its carrying capacity.

To find the value of k, you can plug in the values for P(t), P0, and r and solve for K.

To write the solution of the equation, you can solve for t by rearranging the equation and taking the natural logarithm of both sides.

To find the population after 10 weeks, you can plug in the values for P0, K, r, and t=10 into the equation and solve for P(t).

I hope this helps! Let me know if you have any further questions.

Answer:

Step-by-step explanation:

Here you go mate

Step 1

mp-(m+2)

Step 2

(-6)(3)-((-6)+2)  Substitute m for -6 and p for 3

Step 3

(-6)(3)-((-6)+2)  Simplify

answer

-14

Hope this helps

Answer:

-17/10

Step-by-step explanation:

you have to find a common denomentaor first wich would be 10

then you have to mutiply -4/5 by 2 which would be -8/10

and then you would do regular subtraction

but since its a negative number your gonna actually add but then the final answer will be negative

-17/10

hope this helps I really suck with fractions

An equation is two expressions that are equal to each other

2x + 5 = 10

The above is an example of an equation

From the given picture, we can see a cylinder in option A. Strictily speaking, a cylinder is not a prism as the other options because a prism has edges, vertices and faces and the cylinder has not faces in the circular shape. Therefore, the answer is option A (cylinder)

Answer:

see below

Step-by-step explanation:

sqrt(77)

8^2 = 64

9^2 = 81

It is closer to 9

We know it is between 8.5 and 9

8.8^2 = 77.44

This is a good approximation

The y-axis intercept of the total cost curve is 100.

The y-axis intercept represents the value of the dependent variable when the independent variable is zero. In this case, the y-axis intercept represents the total cost when the quantity of units is zero.

Given the total cost curve c = 100 + 2q, we can find the y-axis intercept by setting q to zero:

c = 100 + 2(0)

c = 100

Therefore, the y-axis intercept of the total cost curve is 100.

To know more about y-axis intercept , refer here:

https://brainly.com/question/12716308

#SPJ4

Answer:

12000

Step-by-step explanation:

sqrt144*1000000= sqrt144*sqrt10^6= 12*10^3=12000

Blocks that can be accommodated are 66,199 blocks

\(2cm * 4 cm * 3 cm = 24 cm^{3}\)

\(24 cm^3 / 1,832 = 0.0131 cm^3\)

To find out how many blocks can fit in a cylinder with a height of 11 cm and a radius of 5 cm, we need to calculate the volume of the cylinder first.

\(V = \pi r^2h\)

Where,

r is the radius

h is the height

π is a mathematical constant approximately equal to 3.14.

\(V = \pi * 5^2 * 11\)

\(V = 865.7 cm^3\)

Now, to find out how many blocks can fit in this cylinder, we need to divide the volume of the cylinder by the volume of each block:

\(865.7 cm^3 / 0.0131 cm^3\) = 66198.5 blocks (rounded to the nearest whole number)

Therefore, a cylinder with a height of 11 cm and a radius of 5 cm can hold approximately 66,199 blocks.

Learn more about volume here:

https://brainly.com/question/17636933

#SPJ1

Earned over the 35 years is $179,494.

The annuity formula is used to calculate the present value of a stream of fixed payments over a specified period of time. It is a formula that takes into account the time value of money and can be used to determine how much an annuity is worth today. The formula is PV = PMT(1-1/((1+r)^n))/r, where PV is the present value, PMT is the payment amount, r is the interest rate, and n is the number of payments.

To calculate this, use the annuity formula:

A = P[((1+r)^n-1)/r]. Where P is the periodic deposit, r is the interest rate,

and n is the time. In this case,

A is 219,494, P is 40, r is 0.07/12,

and n is 420 (35 years x 12 months).

To know more about annuity formula click-
https://brainly.com/question/25792915
#SPJ4

Step-by-step explanation:

1-2cos²c.

> (cos²c+sin²c)-2cos²c. (cos²c+sin²c=1)

> cos²c+sin²c-2cos²c

> sin²c-cos²c.

is your correct answer.

hope this helps you.

The word that best describes the degree of overlap between the two data sets is C. low

In statistics, data overlap refers to the situation where two or more groups being compared have some individuals or data points that have similar or identical values. When this happens, it can make it more difficult to accurately distinguish between the groups and to draw meaningful conclusions from the data.

From the given data, we can see that one data set is positively skewed while the other is negative. This shows that the data overlap is quite low.

Find out more on data overlap at https://brainly.com/question/3369918

#SPJ1

The probability that the first child of Clara and Charles will be a boy with hemophilia is 1/4.

It shouldbe noted the dominant and recessive alleles is given as H and h. It should be noted that A and a also represent the tyrosinase alleles.

The father of Clara had hemophilia.

Therefore, the probability that the first child of Clara and Charles will be a boy with hemophilia will be:

= 1/2 × 1/2

= 1/4.

Therefore, the probability is 1/4.

Learn more about probability on:

brainly.com/question/24756209

#SPJ1

In humans, hemophilia (OMIM 306700) is an X-linked recessive disorder. The dominant and recessive alleles represented by H and h . Albinism is an autosomal recessive condition . A and a represent the tyrosinase alleles. A healthy woman named Clara (II-2), whose father (I-1) has hemophilia and whose brother (II-1) has albinism, is married to a healthy man named Charles (II-3), whose parents are healthy. Charles's brother (II-5) has hemophilia, and his sister (II-4) has albinism. The pedigree is shown.

Determine the probability that the first child of clara and charles will be a boy with hemophilia.