if you had to express a typical NBA player's salary with a single number (round to the nearest 100000) you would use

Answer:

y intercept when x is 0, so the answer is 3

(i) The first term (a) is 24 and the common difference (d) is -2.

(ii) The sum of the progression is 2520.

i) Finding the first term and common difference:

Given that the number of terms in the arithmetic progression is 40 and the last term is -54, we can use the formula for the nth term of an arithmetic progression to find the first term (a) and the common difference (d).

The nth term formula is: An = a + (n-1)d

Using the given information, we can substitute the values:

-54 = a + (40-1)d

-54 = a + 39d

We also know that the sum of the first 15 terms added to the sum of the first 30 terms is zero:

S15 + S30 = 0

The sum of the first n terms of an arithmetic progression can be calculated using the formula:

Sn = (n/2)(2a + (n-1)d)

Substituting the values for S15 and S30:

[(15/2)(2a + (15-1)d)] + [(30/2)(2a + (30-1)d)] = 0

Simplifying the equation:

15(2a + 14d) + 30(2a + 29d) = 0

30a + 210d + 60a + 870d = 0

90a + 1080d = 0

a + 12d = 0

a = -12d

Substituting this value into the equation -54 = a + 39d:

-54 = -12d + 39d

-54 = 27d

d = -2

Now we can find the value of a by substituting d = -2 into the equation a = -12d:

a = -12(-2)

a = 24

Therefore, the first term (a) is 24 and the common difference (d) is -2.

ii) Finding the sum of the progression:

The sum of the first n terms of an arithmetic progression can be calculated using the formula:

Sn = (n/2)(2a + (n-1)d)

Substituting the values:

S40 = (40/2)(2(24) + (40-1)(-2))

S40 = 20(48 - 39(-2))

S40 = 20(48 + 78)

S40 = 20(126)

S40 = 2520

Therefore, the sum of the arithmetic progression is 2520.

for such more question on common difference

https://brainly.com/question/25731911

#SPJ8

Answer:

x = 7

Step-by-step explanation:

\(x + 4 \div 8 = 30 \div 4\)

\(x + 0.5 = 7.5\)

\(x = 7.5 - 0.5\)

\(x = 7\)

Answer:

56

Step-by-step explanation:

x+4=30*2

x=60-4

x=56

Answer:

Step-by-step explanation:

x=22.5 degrees

\(\frac{y}{x} =4\)

\(\frac{z}{x} =3\)

\(y = 4x\)

\(z=3x\)

\(x +3x+4x=180\)

\(8x=180\)

\(\frac{8x}{8} =\frac{180}{8}\)

\(x=22.5\)

Solving the provided question, we can say that Not exponential growth or decay (no exponent) G(x)=1.3(x)

The process of quantity growth over time is called exponential growth. occurs when the rate at which a quantity changes instantaneously with time is proportionate to the quantity itself. A data pattern that shows bigger increases with time is known as exponential growth. Compound interest yields exponential rewards in the world of finance. Savings accounts with compound interest sometimes see exponential growth. characterized by an extremely fast exponential growth rate rise (in size or extent). exponentially.

The base of the exponentiation is the strongest indicator of whether an equation exhibits an exponential growth or decline.

It will be an exponential growth if the base is greater than 1.

It will be an exponential decay if the base is less than 1.

There won't be any exponential growth or decay if the function's exponent is zero.

Therefore: Decay exponential (base less than 1:

W = 9/8(3/5)t

f(t) = (3/4)t

L = 4.2(0.6)t

Exponential Growth (base larger than 1:

L = 0.25(12)t

W = 0.5(2.1)t

f(t) = 2/3(6)t

Not exponential growth or decay (no exponent):

G(x)=1.3(x)

To know more about exponential growth visit:

https://brainly.com/question/12490064

#SPJ1

Answer:

3.33 but he cant buy 3 and 1/3 of a bag of chips so 4

Step-by-step explanation:

It would take Fran and Denise (working together) approximately \(\frac{24}{7}\) hours to paint the living room.

To solve this problem, we can use the concept of "work rates."

Let's find out how much work Fran and Denise can do individually in one hour.

If Fran takes 6 hours to paint the living room alone, her work rate is \(\frac{1}{6}\) of the room per hour \((\frac{1 room}{6 hours } = \frac{1}{6}room/hour )\).

Similarly, if Denise takes 8 hours to paint the living room alone, her work rate is \(\frac{1}{8}\) of the room per hour \((\frac{1 room}{8 hours } =\frac{1}{8}room/hour )\).

When they work together, their work rates are additive.

So, their combined work rate would be:

\(\frac{1}{6} room/hour+\frac{1}{8} room/hour\)

\(=(\frac{4}{24} )room/hour + (\frac{3}{24} )room/hour\)

\(=\frac{7}{24} room/hour\)

This means that working together, Fran and Denise can paint \(\frac{7}{24}\) of the living room in one hour.

To determine the total time required for them to paint the entire room, we can invert their combined work rate:

\(\frac{(1 room) }{(\frac{7}{24}room/hour) } =\frac{24}{7}hour\)

Therefore, it would take Fran and Denise (working together) approximately \(\frac{24}{7}\) hours to paint the living room.

For such more questions on living room

https://brainly.com/question/31126272

#SPJ8

The present value (PV) of the investment today is approximately $2,965.05.

To find the present value (PV) of the investment today, we need to calculate the present value of each individual contribution and then sum them up. We can use the formula for the present value of an annuity to do this calculation.

The formula for the present value of an annuity is given by:

PV = C * [(1 - (1 + r)^(-n)) / r]

Where:

PV = Present Value

C = Cash flow per period

r = Interest rate per period

n = Number of periods

In this case, the cash flow per period (C) is $500, the interest rate per period (r) is 10.5% (or 0.105), and the number of periods (n) is 20 years.

Let's plug in these values into the formula and calculate the present value (PV):

PV = $500 * [(1 - (1 + 0.105)^(-20)) / 0.105]

Using a calculator, we can evaluate the expression inside the brackets:

PV = $500 * [(1 - 0.376889) / 0.105]

Simplifying further:

PV = $500 * [0.623111 / 0.105]

PV = $500 * 5.930105

PV = $2,965.05

Therefore, the present value (PV) of the investment today is approximately $2,965.05.

​for such more question on present value

https://brainly.com/question/28256489

#SPJ8

Answer:

x = 4, -2

Step-by-step explanation:

x^2-2x=8

Move the constant term to the right side of the equation.

x^2 - 2x = 8

Take half of the coefficient of x and square it.

(-2/2)^2 = 1

Add the square to both sides of the equation.

x^2 - 2x + 1 = 8 + 1

Factor the perfect square trinomial.

(x - 1)^2 = 9

Take the square root of both sides of the equation.

x-1=\(\sqrt{9}\)
x-1=±3

Isolate x to find the solutions.

Taking positive

x=3+1=4

x=4

Taking negative

x=-3+1

x=-2

The solutions are:

x = 4, -2

Answer:

\(x = -2,\;\;x=4\)

Step-by-step explanation:

To solve the quadratic equation x² - 2x = 8 by factoring, subtract 8 from both sides of the equation so that it is in the form ax² + bx + c = 0:

\(x^2-2x-8=8-8\)

\(x^2-2x-8=0\)

Find two numbers whose product is equal to the product of the coefficient of the x²-term and the constant term, and whose sum is equal to the coefficient of the x-term.

The two numbers whose product is -8 and sum is -2 are -4 and 2.

Rewrite the coefficient of the middle term as the sum of these two numbers:

\(x^2-4x+2x-8=0\)

Factor the first two terms and the last two terms separately:

\(x(x-4)+2(x-4)=0\)

Factor out the common term (x - 4):

\((x+2)(x-4)=0\)

Apply the zero-product property:

\(x+2=0 \implies x=-2\)

\(x-4=0 \implies x=4\)

Therefore, the solutions to the given quadratic equation are:

\(\boxed{x = -2,\;\;x=4}\)

Subtract the difference form the total:

717 - 67 = 650

Divide the remaining amount by 2:

650/2 = 375

The bench cost$375

If the certain truck traveled 7,605 miles in 15 days. The average number of miles traveled per day will be 507.

It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.

It is given that, a certain truck traveled 7,605 miles in 15 days.

The average number of miles traveled per day is obtained by dividing the total distance traveled by the total time taken as,

Suppose the average number of miles traveled per day is x,

x=76015 / 15

x=507 miles per day.

Thus, if the certain truck traveled 7,605 miles in 15 days. The average number of miles traveled per day will be 507.

Learn more about the average here:

brainly.com/question/24057012

#SPJ1

With 99% confidence that the true difference lies between 0.1316 and 0.2694.

A 99% confidence interval for the difference in average SAT scores between coached and uncoached students can be constructed using the data above.

The confidence interval is calculated as (mean of coached students - mean of uncoached students) +/- (2 * standard error of the difference in means).

The mean of coached students is (0.3098 + 0.3399 + 0.219 + 0.0798) / 4 = 0.2155, and the mean of uncoached students is (0.0046 + 0.0248) / 2 = 0.0147. The standard error of the difference in means can be calculated as the square root of ((0.2155(1-0.2155)/4) + (0.0147(1-0.0147)/2)).

The confidence interval is then (0.2155 - 0.0147) +/- (2 * 0.0347) = 0.201 +/- 0.0694, or (0.1316, 0.2694). This indicates that, on average, coached students gain 0.201 points more than uncoached students, with 99% confidence that the true difference lies between 0.1316 and 0.2694.

Learn more about The confidence interval:

https://brainly.com/question/20309162

#SPJ4

\(\pink{\bigstar}\) The measure if ∠x \(\large\leadsto\boxed{\tt\purple{43^{\circ}}}\)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• To Find:-

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

The given angles are made by a straight line. We know that the total angle made by a straight line is 180°.

Therefore, all the angles should sum upto 180°.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• Working:-

➪ \(\sf (x + 31^{\circ}) + (x + 20^{\circ}) + (x) = 180^{\circ}\)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪ \(\sf x + 31^{\circ} + x + 20^{\circ} + x = 180^{\circ}\)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪ \(\sf 3x + 51^{\circ} = 180^{\circ}\)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪ \(\sf 3x = 180^{\circ} - 51^{\circ}\)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪ \(\sf 3x = 129^{\circ}\)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪ \(\sf x = \dfrac{129}{3}\)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

★ \(\large{\bold\red{x = 43^{\circ}}}\)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Therefore, the measure of the ∠x is 43°.

Step-by-step explanation:

\(we \: know \: that \: sum \: of \: angles \: in \: a \: line \: = 180 \\ so \\ x + 31 + x + 20 + x = 180 \\ 3x + 51 = 180 \\ 3x = 180 - 51 \\ 3x = 129 \\ x = \frac{129}{3} \\ x = 43degree \\ thank \: you\)

Answer:

(2). -4

(4). 8

Step-by-step explanation:

The opposite of a negative or positive number will always be it's absolute value.

Answer:

2(x² + 5)

Step-by-step explanation:

To factor 2x² + 10, we can first factor out the greatest common factor of the terms, which is 2:

2x² + 10 = 2(x² + 5)

We can't factor anymore, so the answer is:

2(x² + 5)

Answer:

2(x² + 5)

Step-by-step explanation:

To factorise this, do the distributive property backwards. In other words:

2x² + 10

2x² ÷ 2 + 10 ÷ 2

x² + 5

2(x² + 5)

∴ 2(x² + 5) is the answer

Answer:

$406

Step-by-step explanation:

The formula for simple interest is I=prtI=prt where II is the amount of interest earned, pp is the initial deposit, rr is the annual interest rate, and tt is the number of years.

It is given that he deposits p=$400p=$400, the bank pays r=1.5%= 0.015r=1.5%=0.015 in annual interest, and t=1t=1 year. The amount of interest he will earn is then I=prt=400(0.015)(1)=$6I=prt=400(0.015)(1)=$6.

His total balance after one year will then be p+i=$400+$6=$406p+i=$400+$6=  

$406

​  

.

The distance between two points in three-dimensional space is a measure of the separation between the two points. In this case, the two points are the center of a sphere and a point that the sphere passes through.

To find the distance, we can use the distance formula in three dimensions, which is an extension of the distance formula in two dimensions. The distance formula is:

d = √((x1 - x2)^2 + (y1 - y2)^2 + (z1 - z2)^2)

where (x1, y1, z1) is the center of the sphere and (x2, y2, z2) is the point that the sphere passes through. The square root of the sum of the squares of the differences between the corresponding coordinates gives the distance between the two points.

In this problem, the center of the sphere is not given, so it is not possible to calculate the distance between the sphere and the point. The center of the sphere is a crucial piece of information needed to solve this problem.

to know more about Geometry

https://brainly.com/question/24375372

#SPJ4

The value of such that = k * 180, where k is an integer, is the value at which cotangent is undefinable.

Cotangent, or cot, is one of the six standard trigonometric functions. Cotangent of an angle is defined as the ratio of the adjacent side to the opposite side of a right-angled triangle.

The value of cotangent is undefined when the denominator is zero. This implies that cotangent is undefined at angles where the value of sine is zero.

Since the sine function is periodic and has a period of 360 degrees, the values of sine repeat themselves after every 360 degrees.

For this reason, cotangent is undefined at angles such that θ = k * 180, where k is an integer.

That is, cotangent is undefined at 0°, 180°, 360°, and so on. It is also important to note that cotangent is a periodic function, and its values repeat every 180 degrees.

Therefore, cotangent is undefined at 0° + k * 180°, where k is an integer.

To summarize, the value of Θ at which cotangent is undefined is such that θ = k * 180, where k is an integer.

For more questions on integer

https://brainly.com/question/929808

#SPJ8

Answer:

A. Nonlinear function

Step-by-step explanation:

It is not a linear function because :-

x and y have the values 7 and 7√2, respectively.

The sides of a right triangle with 45-degree acute angles have a unique ratio of 1:1:2.

We can use this information to determine the values of x and y because the base is specified as being 7.

Let's give the perpendicular side the value of x, and the hypotenuse the value of y.

The perpendicular side (x) and the base (7) have the same length because the acute angles are both 45 degrees.

Consequently, x = 7.

We can determine that x:y:2x using the ratio of 1:1:2.

When we enter the value of x, we may calculate y:

7:y:√2(7)

Simplifying even more

7:y:7√2

Given that the hypotenuse (y) equals 72, we can write:

y = 7√2

Thus, x and y have the values 7 and 7√2, respectively.

Learn more about right triangle click;

https://brainly.com/question/30966657

#SPJ1

Randy's error is in the first step of the division, where he subtracts 4x² instead of adding it. The correct subtraction should be: x³ + 2x² + 5x - 3

Randy made an error in the step where he subtracted (2x² - 2x + 1) from (2x² - 3x³ - 3x² + 7x - 3).

Instead of getting -x³ + 4x² + 6x - 4 as the result, he got 2x⁴ - 4x³ + 2x². This error occurred because he forgot to change the sign of all the terms in (x² - 2x + 1) when subtracting it from the polynomial.

It should be (3x³ - 2x² + 7x - 3) divided by (x² - 2x + 1).

Let me proceed with this corrected version of the question.

Randy divides (3x³ - 2x² + 7x - 3) by (x² - 2x + 1) as,
2x² + x + 3
____________
x² - 2x + 1) 3x³ - 2x² + 7x - 3
2x³ - 4x² + 2x
_____________
x³ - 2x² + 5x
x³ - 2x² + x
____________
-3x² + 4x - 3
-3x² + 6x - 3
___________
\(-2x^2\) + x - 3

3x³ - 2x² + 7x - 3
-(2x³ - 4x² + 2x)
______________
x³ + 2x² + 5x - 3

For more related questions on Randy's erro:

https://brainly.com/question/11536711

#SPJ11

Randy made an error while dividing (2x⁴ - 3x³ - 3x² + 7x - 3) by (x² - 2x + 1). He mistakenly subtracted intermediate results from zero instead of the original polynomial, leading to an incorrect division.

Randy made an error in his division of the polynomial (2x⁴ - 3x³ - 3x² + 7x - 3) by (x² - 2x + 1). Let's go through the division process step by step to identify the mistake:

Randy correctly started by dividing 2x⁴ by x², which gives him 2x² as the first term of the quotient.

He then multiplied (x² - 2x + 1) by 2x², which resulted in 2x⁴ - 4x³ + 2x². So far, so good.

Randy should have subtracted this result from the original polynomial (2x⁴ - 3x³ - 3x² + 7x - 3), but he mistakenly subtracted it from 0. The correct step should have been to subtract 2x⁴ - 4x³ + 2x² from (2x⁴ - 3x³ - 3x² + 7x - 3).

Here's the corrected division:

(2x⁴ - 3x³ - 3x² + 7x - 3) - (2x⁴ - 4x³ + 2x²) = -3x³ - 5x² + 7x - 3

Now, Randy should have continued the division by bringing down the next term, which is -3x², and repeated the process. However, he incorrectly moved to the next step without subtracting -3x³ - 5x² + 7x - 3 from (x² - 2x + 1).

So, Randy's error is that he failed to properly subtract the intermediate result from the original polynomial, causing the division process to go awry.

For more such information on: polynomial

https://brainly.com/question/1496352

#SPJ2

Answer: I think it's Sporting Life:)

hope this help!

Answer:

66

Step-by-step explanation:

added and dont stop untill the end

The maximum that the couple can spend on the meal is $40.63

Let's say that the couple spends a total of X.

Then we know that we need to add a tax of 7%, then we need to add a factor of (1.07) to the total cost.

And we also know that they want to pay a tip of 15%, then we need to add a factor of (1.15) to the total cost.

Then the total cost for the meal will be:

C = x*(1.15)*(1.07)

The maximum that the spend is 50, then let's solve this for C = 50

50 = X*(1.15)*(1.07)

50/(1.15)*(1.07) = X

40.63 = X

The maximum that they can spend is $40.63

Learn more about taxes at.

https://brainly.com/question/1775528

#SPJ1

Answer:

Conclusion

   There is no sufficient evidence to conclude that the mean of the home prices from Ascension parish is higher than the EBR mean

Step-by-step explanation:

From the question we are told that

   The population mean for EBR is  \(\mu_ 1 = \$239,000\)

    The sample mean for Ascension parish  is \(\= x_2 = \$246,000\)

   The  p-value  is  \(p-value = 0.045\)

     The level of significance is  \(\alpha = 0.01\)

The null hypothesis is  \(H_o : \mu_2 = \mu_1\)

The  alternative hypothesis is  \(H_a : \mu_2 > \mu_1\)

Here \(\mu_2\) is the population mean for Ascension parish

   From the data given values we see that  

          \(p-value > \alpha\)

So we fail to reject the null hypothesis

So we conclude that there is no sufficient evidence to conclude that the mean of the home prices from Ascension parish is higher than the EBR mean

Answer:

Step-by-step explanation:

A  = 2π +πrl                

A - 2π = πrI                  subtract by 2π

(A- 2π)/(πr) = I               divide by πr to isolate I

Answer: Therefore, the value of x is 4√5 meters.

Step-by-step explanation:

To solve for x, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, we can see that side a is the hypotenuse, so we have:

a^2 = b^2 + c^2

Substituting the given values, we get:

(6m)^2 = (3m)^2 + (2m)^2

Simplifying:

36m^2 = 9m^2 + 4m^2

36m^2 = 13m^2

Dividing both sides by 13m^2:

36/13 = (4√5)^2/x^2

Simplifying:

x^2 = (4√5)^2 / (36/13)

x^2 = (16513) / 36

x^2 = 260/9

Taking the square root of both sides (and simplifying the surd):

x = 4√(65/9) = 4√5 X m

Answer:

Step-by-step explanation:

See attachment.