The 12th term of an arithmetic sequence is 36, and the common difference is 3. What is the first term of the sequence?

Find the percent of change from $40 to $50.

andrezito [222]

Answer:

125%

Step-by-step explanation:

so you are increasing by $10, and $10 is 25% of $40, so the percent change is 125%

3 0

3 years ago

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Jennifer is leasing a car from a local auto retailer. The terms of the lease include a 9% interest rate for 36 months with a res

katrin [286]

1. The problem gives the residual value in percentage, and you need it in dollars. So, if the MSRP for the car Jennifer is leasing is $ 17,500, you have:

57%/100=0.57

residual value=$17,500*0.57= $9,975

2. Then, you need to substract the residual value and the lease term, to calculate the value of the car, as below:

car value=$17,500-$9,975=$7,525

3. You need to calculate the money factor, which is the interest rate divided by 2400. Then, you have:

Interest rate=9%/100=0.09

Money factor=0.09x2400
Money factor=0.00375

4. The interest is:

I=($17,500+$9,975)(0.00375)
I=$103.03

5. Therefore, the monthly payment is:

Monthly payment=(car value/36 months)+Interest
Monthly payment=($7,525/36)+$103.03
Monthly payment=$209.02+$103.03
Monthly payment=$312.06

What will Jennifer’s monthly lease payment be?

The answer is: d. $312.06

6 0

3 years ago

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What is the value of x?

charle [14.2K]

Answer:

72

Step-by-step explanation:

RQS + KLM = 180 degrees, because RQS = QLK, and QLK + KLM = 180 degrees (because they are on the same line).

Substitute the values for RQS and KLM:

x-36 + x = 180 -->

2x-36=180 -->

2x = 144 -->

x=72

5 0

3 years ago

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Solve and round answer to nearest hundredth please.

MA_775_DIABLO [31]

Answer:

Step-by-step explanation:

Solve this by using natural logs. Taking the natural log of both sides:

$ln(7*16^{8x-8})=ln(3)$

To undo the multiplication, we use addition:

$ln(7)+ln(16)^{8x-8}=ln(3)$

The rule says we can now bring the exponent down in front of the ln:

$ln(7)+(8x-8)ln(16)=ln(3)$

Now we will subtract ln(7) from both sides:

(8x - 8)ln(16) = ln(3) - ln(7)

Now we will divide both sides by ln(16):

$8x-8=\frac{ln(3)-ln(7)}{ln(16)}$ then add 8 to both sides:

$8x=\frac{ln(3)-ln(7)}{ln(16)}+8$ which simplifies to

8x = 7.694401895 so

x = .9618002368 or, rounded,

x = .96

(Rest assured I did the math and checked the answer and it checked out perfectly!) I recommend you learn the laws of natural and common logs cuz they're kinda important!! :)

5 0

3 years ago

The cost and revenue functions for producing and selling x units of a product are given. Cost and revenue are expressed in dolla

Flauer [41]

Answer:

(A) the number of units produced and sold at break-even point is the value of X and that is 1.126 units.

(B) the dollar amount coming in and going out at this point/level is the price of X and that is 0.37 dollars

(C) the profit function for X units produced and sold is: π(x) = R(x) - C(x)

where pie (the symbol "π") represents PROFIT.

Step-by-step explanation:

(A) C(x) = 75x + 84 ...(equation 1)

660R(x) = 245x

R(x) = 245x ÷ 660 = 0.3712x

So R(x) = 0.3712x ...(equation 2)

To find X, equate the cost function to the revenue function

75x + 84 = 0.3712x

X = -1.126units

Since quantity cannot be negative in real life situation, we use the modulus of X in place of the above value.

|X| = 1.126 hence X = 1.126 now

Since we equated cost to revenue in order to get this quantity X, X is the quantity produced and sold at break even point.

Break-even point is the point where cost = revenue

This is also the point where profit is zero because profit = revenue - cost

(B) Revenue = Price × Quantity

R = P×Q

Our revenue here is 0.3712x

Which is equal to 0.418 dollars

So P = R÷Q

Price = 0.418÷1.126 = 0.37 dollars

(C) This is the profit function from producing and selling X units of the product: π(x) = R(x) - C(x)

4 0

3 years ago