Answer:
x=-16/3
Step-by-step explanation:
9x-8(-8)=16
9x+64=16
9x=-48
x=-48/9
x=-16/3
A car depreciates at a rate of 15% of its value annually. Carl purchased a new car for $25,000 and wants to know how many years it
will take until the car is worth a specific amount.
a) Formulate a logarithmic function that would find the number of years t it will take for the car to be worth x dollars.
Then
b) How many years will Carl have until he new car is worth about $5000?
Answer:
(a) (log X - log 25000)/log 0.85 = t
(b) about 9.9 years
Step-by-step explanation:
(a) Let X = value and t = elapsed years since purchase; X in dollars
X = 25000 x 0.85 x 0.85 x 0.85 ... with a factor of 0.85 for every year
(If you lose 15% of value, you have 85% left, right?)
So if you do it for t years, you have t as the exponent on the 0.85 factor.
[tex]X = 25000(0.85)^t[/tex] is a good equation, but not logarithmic like they ask.
[tex]log X = log 25000 + log [(0.85)^t][/tex] because the log of a product is the sum of the logs of the factors
log X = log 25000 + t*log 0.85 because the log of a power is power times log
log X - log 25000 = t* log 0.85 just algebra, subtracting from both sides
(log X - log 25000)/log 0.85 = t just algebra, dividing both sides
(b) If we let X = $5000
t = (log 5000 - log 25000)/log 0.85
= (3.69897 - 4.39794)/-0.07058
= 9.90
So t = 9.9 years is a good estimate
Carl will have approximately 5.06 years until his new car is worth about $5000.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let V(t) be the value of the car t years after it was purchased.
We know that the car depreciates at a rate of 15% annually, so the value of the car after t years can be expressed as:
[tex]V(t) = 25000 \times (1 - 0.15)^t[/tex]
Simplifying this equation, we get:
[tex]V(t) = 25000 \times 0.85^t[/tex]
Now suppose Carl wants to know how many years it will take for the car to be worth x dollars.
We can set V(t) equal to x and solve for t:
[tex]25000 \times 0.85^t = x[/tex]
log0.85(25000) +[tex]log0.85(0.85^t)[/tex] = log0.85(x)
Since log0.85(25000) is a constant, we can subtract it from both sides of the equation:
[tex]log0.85(0.85^t)[/tex]= log0.85(x) - log0.85(25000)
Divide both sides of the equation by log0.85(0.85) = 1:
t = [log0.85(x) - log0.85(25000)] / log0.85(0.85)
Therefore, the logarithmic function that would find the number of years t it will take for the car to be worth x dollars is:
t = [log0.85(x) - log0.85(25000)] / log0.85(0.85)
b) We want to find the number of years it will take for the car to be worth $5000.
Substituting x = 5000 into the formula derived in part (a), we get:
t = [log0.85(5000) - log0.85(25000)] / log0.85(0.85)
t = 5.06
Therefore, Carl will have approximately 5.06 years until his new car is worth about $5000.
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A study was conducted to investigate whether a new drug could significantly reduce pan in people with arthritis. From a group of 500 people with arthritis 250 were randomly assigned to receive the drug (group 1) and the remaining people were assigned a placebo (group 2). After one month of treatment, 225 people in group 1 reported pain relief and 150 people in group 2 reported pain relief Let Pe represent the combined (or pooled) sample proportion for the two samples. Have the conditions for inference for testing the difference in population proportions been mel? (A) No. The people in the study were not selected at random (6) (B) No. The number of people in the study was too large compared with the size of the population (C) No. The normality of the sampling distribution cannot be assumed because Pe times each sample size is not sufficiently large (D) No. The normality of the sampling distribution cannot be assumed because I - Pe times each sample size is not sufficiently large 6 (E) Yes. All conditions for inference have been met
Answer:
(C) No. The normality of the sampling distribution cannot be assumed because Pe times each sample size is not sufficiently large
Step-by-step explanation:
The above happens to be the true statement to the question asked about the new drug study which was carried out just to know its effect with those patients suffering from arthrities.
3x-2y=10. 4x-y=6. solve each of the pair of simultaneous linear equation by substitution method
Answer:
x = 2/5, y= -22/5
Step-by-step explanation:
4x−y=6;3x−2y=10
Step: Solve4x−y=6for y:
4x−y+−4x=6+−4x(Add -4x to both sides)
−y=−4x+6
-y/-1 = -4x +6 over -1 (Divide both sides by -1)
y=4x−6
Step: Substitute4x−6for y in 3x−2y=10:
3x−2y=10
3x−2(4x−6)=10
−5x+12=10(Simplify both sides of the equation)
−5x+12+−12=10+−12(Add -12 to both sides)
−5x=−2
-5x/-5 = -2/5 (Divide both sides by -5)
x= 2 /5
Step: Substitute 2/ 5 for x in y=4x−6:
y=4x−6
y=4 ( 2/ 5 ) −6
y= −22 /5
(Simplify both sides of the equation)
x = 2/5, y= -22/5
cause yo hair nappy........
Answer:
what do you mean?
Step-by-step explanation:
Given that 5x - 8y = 33 find x when y = 1
Answer:
x = ⁴¹⁄₅ or 8.2Explanation:
5x - 8y = 33
y = 1
Insert 1 for 'y' in the equation
5x - 8(1) = 33
Remove parenthesis: (a) = a
5x - 8 · 1 = 33
Multiply 8 · 1: 8
5x - 8 = 33
Add 8 to both sides
5x - 8 + 8 = 33 + 8
Simplify
5x = 41
Divide both sides by 5
5x / 5 = 41 / 5
x = ⁴¹⁄₅
Turn the fraction into a decimal
x = 8.2
I need help with this
Answer:
look at the picture i sent.......
What is the area of one trapezoidal face of the figure
QUESTION IS IN THE PICTURE, PLEASE HELP!!
Answer:
The median is 5, mode is 5, and range is 12
Step-by-step explanation:
Answer:
MEDIAN - 5
MODE - 2 (4times)
RANGE - 13-1=12 (12 is the range)
Step-by-step explanation:
MEDIAN - Arrange the data in an ascending order and the median is the middle value. If the number of values is an even number, the median will be the average of the two middle numbers.
MODE - The mode is the element that occurs most in the data set. In this case, 2 occurs 4 times.
RANGE - Subtract the minimum data value from the maximum data value to find the data range. In this case, the data range is 13-1=12
Help please if you know the answer
Answer:
180-140=a
180-90=b
180-a-b= your ans
Than Nguyen opened a business called Nguyen engineering and recorded the following transactions in its first month of operations.
June 1: Than Nguyen, the owner, invested $158,000 cash, office equipment with a value of $19,500, and $89,000 of drafting equipment to launch the company in exchange for common stock.
June 2: the company purchased land worth $63,500 for an office by paying $26,000 cash and signing a long-term note payable for $36,900.
June 2: The company purchased a portable building with $40,500 cash and moved it onto the land acquired on June 2.
June 2: The company paid $11,700 cash for the premium on a 15-month insurance policy.
June 7: The company completed and delivered a set of plans for a client and collected $17,800 cash.
June 12: The company purchased $37,400 of additional drafting equipment by paying $24,000 cash and signing a long-term note payable for $13,400.
June 14: The company completed $37,200 of engineering services for a client. This amount is to be received in 30 days.
June 15: The company purchased $2,600 of additional office equipment on credit.
June 17: The company completed engineering services for $27,000 on credit.
June 18: The company revived a bill for rent of equipment that was used on a recently completed job. The $2,750 rent cost must be paid within 30 days.
June 20: The company collected $18,600 cash in partial payment from the client billed on June 14.
June 21: The company paid $2,000 cash for wages to a drafting assistant.
June 23: The company paid $2,600 cash to settle the account payable created on June 15.
June 24: The company paid $1,650 for minor maintenance of its drafting equipment.
June 26: The company paid $10,060 cash in dividends.
June 28: The company paid $2,000 cash for wages to a drafting assistant.
June 30: The company paid $3,660 cash for advertisements on the web during June.
Description of items that require adjusting entries on June 30, follow:
A.) The company has completed, but not yet billed, $17,600 of engineering services for a client.
B.) straight-line depreciation on the office equipment, assuming a 5 year life and a $2,300 salvage value, is $330 per month.
C.) straight-line depreciation on the drafting equipment, assuming a 5 year life and a $12,400 salvage value, is $1,900 per month.
D.) straight-line depreciation on the building, assuming a 25 year life and a $1,500 salvage value, is $130 per month.
E.) the balance in prepaid insurance represents a 15 month policy that went into effect on June 1.
F.) Accrued interest on the long-term note payable is $190.
G.) the drafting assistant is paid $2,000 for a 5 day work week. 2 days’ wages have been incurred but are unpaid as of month end.
Please answer please thank you
Based on the transactions made by Than Nguyen, the following journal entries are true:
Date Account Title Debit Credit
June 1 Cash $158,000
Office equipment $ 19,500
Drafting equipment $89,000
Nguyen, Captal account $266,500
June 2 Land $63,600
Cash $ 26,600
Note Payable $36,900
June 2 Building $40,500
Cash $40,500
June 2 Prepaid insurance $11,700
Cash $11,700
June 7 Cash $17,800
Service Revenue $17,800
What journal entries should be made?The amount that Than Nguyen put up for capital should be credited to the capital account and then debited to the various asset accounts.
The purchased land should also be debited to land, and the cash that was spent to buy the land should be credited along with the note payable.
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How to figure out diameter
Answer:
If you are given the area of a circle, the diameter is equal to the square root of four times the area divided by pi (diameter = √ (4 x area) / pi).
Answer:
A diameter of a circle is twice its radius!
Hope that helps!
Step-by-step explanation:
Question 1 of 10
Which of the following is most likely the next step in the series?
Answer:
The second one.
Step-by-step explanation:
The pattern is red with 0 arrows, blue with 1 arrow, red with 2 arrows, so it would be blue with 3 arrows.
including zero) depending on your answer
The taco truck sells tacos for $3 and burritos for $4. The number of items sold on a Tuesday is 125 with a total income of $430. How
many tacos were sold?
The solution is
Answer: here b
Step-by-step explanation:
http://bigtrucktacos.com/menu/
Answer:
2
Step-by-step explanation:
[tex]\frac{28}{54} = \frac{2x+8}{5x-4}[/tex]
Step-by-step explanation:
step 1. what is the question? solve for x? okay.
step 2. 28/54 = (2x+ 8)/(5x - 4)
step 3. 28(5x - 4) = 54(2x + 8) (cross multiplication)
step 4. 14(5x - 4) = 27(2x + 8) (divide both sides by 2)
step 5. 70x - 56 = 54x + 216 (distributive property)
step 6. 16x = 272 (group x's and add 56 to both sides)
step 7. x = 17 (divide both sides by 16).
Solve the equation by balancing 3n+2=17
Answer:
3n=17-2
3n=15
n=15/3
n=5
Step-by-step explanation:
therefore putting the value of n=5 the equation can be balance
1. Mike’s rectangular dining room is 8 feet wide and 6 feet long. Mike wants to install a new wood floor and new base boards. It will cost $10.00 per square foot for the new flooring.
a. How many square feet of flooring does Mike need to purchase? SHOW YOUR WORK
b. Use the information from part a to answer, how much will it cost Mike for the new flooring? SHOW YOUR WORK
c. How much base board would Mike need to purchase to go around the perimeter of the dining room? SHOW YOUR WORK
Answer:
a:
to find area we need to multiply width by length
so lets multiply 8×6
so we will get 48 feet
b:
the area is 48 feet, and we know that it costs 10$ per
square foot
so we will multiply 48×10
so we will get 480$
c:
the premiter = all sides added to gather
in a rectangle we have 4 sides, 2 width and 2 length
so the answer will be (8×2)+(6×2)
so the answer will be 16+12=30
The scatter plot shows Leanna's elevation above sea level during a hike. The trend line passes
through the points (30,1070) and (75,1680). If Leanna starts at 663 feet above sea level and
maintains the same rate, how far above sea level will she be after one hour?
Answer:
The y-intercept is 663 and the slope is 13.56.Thus, the equation for the trend line is y = 13.56x + 663
Step-by-step explanation:
After one hour, her altitude will be
1476.60 feet above sea level. that was only if u get a part b
help me on my geometry homework? :/
Answer:
You could use a graphing calculator I just used Desmos. Origin is (0, 0). Rotate 90 degrees about the origin.
I used triangles
The rotated point would be at (1, 2)
ANSWER: the question mark = 1
Test test 123 123 12345678
Answer:
test test 9101112131415
Answer:
Answer answer 233 234 23456789
Step-by-step explanation:
is that right.......:)
Jeremy bought 3 pairs of pants for $68.25. Each pair of pants cost the same amount. How much will he pay for 5 pairs of pants at the same price per pair?
$170.63
$341.25
$113.75
$22.75
Answer:
113.75
Step-by-step explanation:
Please help and explain if you can cuz im confused
Answer:
B. 664 square inches
Step-by-step explanation:
14 * 10 =140
140 * 2 = 280
8 * 10 = 80
80 * 2 = 160
14 * 8 =112
112 * 2 = 224
280 + 160 + 224 = 664
Therefore, your answer would be B. 664 square inches.
I need help, Please help me.
Answer:
Yes, SSS
Step-by-step explanation:
Well they are congruent since well the triangles are from a square which means that the sides will all be equal so therefore it is the SSS rule which stands for "side, side, side" meaning all of the sides are equal.
Landen has his daily video gaming time each day for 7 days. But one day he plays and extra 50 minutes. His total video playing time for the week was 540 minutes. How long is his daily video playing time? Choose the equation that describes this word problem.
Answer:
im thinking 25 or 24
Step-by-step explanation:
sorry if i made you get it wrong
Market researchers selected a random sample of people from region A and a random sample of people from region B. The researchers asked the people in the samples whether they had tried a new product. The difference between the sample proportions (B minus A) of people in the regions who indicated they had tried the new product was 0.15. Under the assumption that all conditions for inference were met, a hypothesis test was conducted with the alternative hypothesis being that the population proportion of B is greater than that of A. The p-value of the test was 0.34.Which of the following is the correct interpretation of the pp-value?If the difference in proportions of people who have tried the new product between the two populations is actually 0.15, the probability of observing that difference is 0.34.A. If the difference in proportions of people who have tried the new product between the two populations is actually 0.34, the probability of observing that difference is 0.15.B. If the proportions of all people who have tried the new product is the same for both regions, the probability of observing a difference of at least 0.15 is 0.34.C. If the proportions of all people who have tried the new product is the same for both regions, the probability of observing a difference of at most 0.15 is 0.34.D. If the proportions of all people who have tried the new product is the same for both regions, the probability of observing a difference equal to 0.15 is 0.34.
Answer:
B. If the proportions of all people who have tried the new product is the same for both regions, the probability of observing a difference of at least 0.15 is 0.34.
Step-by-step explanation:
Null hypothesis:
H0: The population proportion B = population proportion A
Alternative hypothesis:
H1: The population proportion of B > population proportion A
The P value, also called calculated probability, is that of getting test results which are at least as extreme as the results which were observed in a Statistical test. We assume the null hypothesis to be true.
Therefore if the population proportion of B = A (H0 is true), then we conclude that the probability of observing a difference of at least 0.15 is = 0.34.
What are the terms or 8x+6
Answer:
14x. ....................
which inequality has the same solution set as 3(q + 6) > 11?
3q + 18 < 11
3q + 6 > 11
q + 18 > 11
q + 18 > 11
Given:
The inequality is
[tex]3(q+6)>11[/tex]
To find:
The inequality that has the same solution set as the given inequality.
Solution:
We have,
[tex]3(q+6)>11[/tex]
Using distributive property, we get
[tex]3(q)+3(6)>11[/tex]
[tex]3q+18>11[/tex]
Since the given inequality can be rewritten as [tex]3q+18>11[/tex], therefore the inequality [tex]3q+18>11[/tex] has the same solution set as [tex]3(q+6)>11[/tex].
Hence, all options are incorrect. The required inequality is [tex]3q+18>11[/tex].
Answer:
3q+18 > 11
Step-by-step explanation:
What property is used to show that 3(4 – 6) = 12 – 18?
Distributive Property
Associative Property
Commutative Property
Subtraction Property
Answer:
Distributive Property
Step-by-step explanation:
Answer:
Distributive property
Step-by-step explanation:
a(b-c)= (a×b) - (a×c)
3(4-6)=(3×4) - (3×6)
= 12 - 18
Use synthetic substitution to find |(3) for f(x) = x2 - 9x +5.
Oa. 41
Ob.-23
Oc. -13
Od. -16
Answer:
-13
Step-by-step explanation:
In ΔWXY, x = 1.2 cm, ∠X=45° and ∠Y=108°. Find the length of w, to the nearest 10th of a centimeter.
Answer:
w = 0.8cm
Step-by-step explanation:
Evaluate x1 - x1 + x0 for x = 2.
0
1/2
1 1/2
2 1/2
Answer:
the answer is 0
Step-by-step explanation:
hoped I helped:)
Answer: 2 1/2
Step-by-step explanation: