Answer: EXPONENTIAL GROWTH AND DECAY a = starting or initial value ADD = Growth y=a(1Ær)* amount r = percent of change SUBTRACT-Decay Basic Equation Statements: Determine growth decay, the percent of change, and initial value. EQUATION Initial Value Growth or Decay? Percent of Change 1) y = 7500(1 +.03) 2)y = (0.85) 3)y=900 (1.27) 4) y = 24000(1-.08) 5)y = 750(1.15) 6) y = 250,000(0.65) 7) y = 11,275(1.1) 8)y = 673 (2.2) Exponential Growth and Decay Word Problems: Evaluate all answers exactly and then round when necessary 9. The price of a car that was bought for $10,000 and has depreciated 10% yearly. Find the price of the car 8 years later, PRICE: The equation for the price of a baseball card that was bought for 5 dollars and has appreciated 5% yearly. Find the value of the card 25 years later. VALUE: !!. A town of 3200, grows at a rate of 25% every year. Find the size of the city in 10 years. Population: 12 Acity of 100,000 is having pollution problems and is decreasing in size 2% annually (every year). Find the population of this city in 100 years. Population: In 1982, the number of Starbucks was shops. It has exponentially grown by 21% yearly. Let the number of years since 1982. Find an equation for this growth and find the number of Starbucks predicted in 2015
Step-by-step explanation:
Find the product of 2x2(x 6). 8x3 2x3 12x2 3x3 12x2 2x2 x 6.
Product of two polynomials can be done by distribution of multiplication over addition. The product of [tex]-2x^2(x+6)[/tex] is [tex]-2x^3 - 12x^2[/tex]
What is distributive property of multiplication over addition?Suppose a, b and c are three numbers. Then we have:
[tex]a(b + c) = a\times b + a\times c[/tex]
(a(b+c) means a multiplied to (b+c). The sign of multiplication is usually hidden when using symbols and both quantities which are in multiplication are written together without space)
The product result of the given expression is
[tex]-2x^2(x+6) = -2x^{2+1} -12x^2 =-2x^3 -12x^2[/tex]
It is because when bases are same and there is multiplication, then powers add up, so we have: [tex]a^b \times a^c = a^{b+c}[/tex]
Also, we've
[tex](-ve \times (+ve) = -ve\\(-ve) \times (-ve) = +ve\\(+ve) \times (+ve) = +ve\\(+ve) \times (-ve) = -ve[/tex]
where -ve, +ve are sign of operands and result.
That's why [tex]-2 \times 6 = -12[/tex]
Thus,
The product of [tex]-2x^2(x+6)[/tex] is [tex]-2x^3 - 12x^2[/tex]
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There is a bag with only milk and dark chocolates.
The probability of randomly choosing a dark chocolate is
5
12
.
There are 25 dark chocolates in the bag and each is equally likely to be chosen.
Work out how many milk chocolates there must be.
Answer:
35 milk chocolates
Step-by-step explanation:
5/12 for first bag
5 x 5 = 25
12 x 5 = 60
25/60
25 of the total chocolate are dark and there are only two types of chocolate in the bag (milk and dark)
60 - 25 = 35
Here are the monthly charges of Jim’s mobile phone
Monthly charge £20
100 free minutes then 9p per minute
200 free texts, then 11p per text
During one month,Jim makes 140 minutes of calls and sends 261 texts
Workout the total charge for the month
For the given data the monthly charges for Jim’s mobile phone will be £31.31.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that, Monthly charge of £20,100 for free minutes then 9p per minute for 200 free texts, then 11p per text. During one month, Jim makes 140 minutes of calls and sends 261 texts.
If there are 100 free minutes then it cost 9p per minute as a result, The charge is applied for calls,
40x9=£3.60
If there are 200 free texts, then it cost 11p per text as a result, The charge is applied for text,
61x11=£6.71
The total charge for the text and call is,
£6.71+£3.60=£10.31
If the monthly charge is £20. The total charge for the month,
£20+£10.31=£31.31
Thus, for the given data the monthly charges for Jim’s mobile phone will be £31.31.
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Calvin’s credit card computes finance charges using the daily balance method. His card has a billing cycle of 30 days and an APR of 14. 75%. The following table details Calvin’s transactions in the month of September. Date Amount ($) Transaction 9/1 716. 54 Beginning balance 9/7 84. 94 Purchase 9/12 15. 69 Purchase 9/20 200. 00 Payment What will Calvin’s starting balance be next month? a. $617. 17 b. $624. 74 c. $625. 91 d. $623. 52.
Answer:
c. $625. 91
Step-by-step explanation:
The average daily balance totals each day's balance for the billing cycle and divides by the total number of days in the billing cycle. Then, the balance is multiplied by the monthly interest rate to assess the customer's finance charge—dividing the cardholder's APR by 12 calculates the monthly interest rate.
How many lines are
perpendicular to AB?
A. 1
B. 2
C. 3
Archie cycled for 12 hours at an average speed of 23 km/h.
Jade travelled the same route as Archie but it took her 2 hour 45 minutes.
What is Jade's average speed to 1 dp?
Answer:
100.4 km/h (1 dp)
Step-by-step explanation:
If Archie cycled for 12 hours at an average speed of 23 km/h, then the total distance he cycled is:
total distance = 12 x 23 = 276 kmconvert 2 hours 45 mins to decimal:
2 hours 45 mins = 2 + 45/60 = 2.75 hoursTherefore, if Jade took 2.75 hours to travel 276 km, her average speed is:
average speed = 276 ÷ 2.75 = 100.4 km/h (1 dp)For Archie
Avg speed=23km/hTime=12hDistance=23(12)=276kmNow
for Jade
Time=2h 45min=2+3/4h=2+0.75h=2.75hAvg speed:-
[tex]\\ \tt\Rrightarrow \dfrac{276}{2.75}[/tex]
[tex]\\ \tt\Rrightarrow 100.4km/h[/tex]
Help!!!! Its A Math Problem What is the number that goes in the blanks?
Solve each system of linear equations by elimination.
3x-2y=3
-x+y=1
Answer:
x=5, y=6
Step-by-step explanation:
Double the second equation to give you:
-2x+2y=2
Now we add the 2 equations to eliminate the y:
3x-2y=3
+
-2x+2y=2
x=5
Now we substitute this value to give us:
3(5)-2y=3
15-2y=3
-12=-2y
y=6
You can substitute both these values in equation 2 to see if it works:
-x+y=1
-(5)+6=1 ✅
Given a fair six-sided number cube. What is the probability of the complement of rolling a 3 or 4?
Question 8 options:
2/6
1/3
1/2
2/3
Hannah earned $1536 in 8 years on an investment at a 4% annual simple interest rate. How much was Hannah’s investment? $4800 $3072 $768 $491. 52.
Simple interest calculates interest on initial amount only. The investment by Hannah was : Option A: $4800
How to calculate simple interest amount if rate of interest is R% annually?Suppose that the initial amount of investment is P
And the rate of simple interest is R% annually,
And the time of investment is T years.
Then, the amount of simple interest is calculated as:
[tex]I = \dfrac{P \times R \times T}{100}[/tex]
For the given case, let the initial investment Hannah made was of $P
Then, the time of investment is T = 8 years, R% = 4%, and given that Hannah earned interest I = $1536
Putting values in the above formula, we get;
[tex]I = \dfrac{P \times R \times T}{100}\\\\1536 = \dfrac{P \times 8 \times 4}{100}\\\\P = \dfrac{153600}{32} = 4800[/tex]
Thus,
The investment by Hannah was : Option A: $4800
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6 3/4 as a decimal number
Answer:
6.75.Step-by-step explanation:
Remember:
Numbers, 2, 4, 5, 8, 10, 100, and 1,000 can only be decimals.So, we do division:
(Without the whole number).3 ÷ 4= 0.75.6 + 0.75= 6.75.6 3/4 = 6.75.
Answer :
[tex]6\frac{3}{4}[/tex]
= 6.75
PLEASE HELP ME!!!!!!!!!!!
Answer:
3y
Step-by-step explanation:
Sqrt of 9 = ±3
-±3[tex]\sqrt{y^{2} }[/tex]
the square and sqrt cancel leaving you with -±3y
Since y < 0, the sqrt of 9 should be -3 to cancel out the - sign in front.
Hope that helps
Two questions about equivalent fractions
Answer:
first photo Answer12-4m secend 2.3/8y+6
Mr and mrs Boyden take their 3 children to a leisure park.
they buy tickets for the whole family
the cost of an adult ticket is £6 more than the cost of a child ticket
the total of the cost of the five of the tickets is £82
work out the cost of an adult ticket
Answer:
The Answer Should Be 20
explanation:
Hope This Helps :)
What comes next in the following pattern?
12, 11, 15, 14, __
Hi!
I will help you with joy!
Let's take a look at our pattern.
12, 11, 15, 14, _
Here, we subtract 1, then add 4, then subtract 1, then add 4.
Thus, the next number in the pattern will be 18.
12, 11, 15, 14, 18
The next number will be 17, and so on...
I hope it helps!
Ask me if you have any queries.
Misty ~
[tex]\bf{Grace}\sf{ful\rm{Teen[/tex]
Enjoy your day!
As the heart beats, blood pressure increases and decreases. This happens cyclically at the rate of the person’s heart beat. A doctor is monitoring the blood pressure of a patient whose heart rate is 70 beats per minute. The maximum blood pressure over the course of a 10-minute period is 120 mm/Hg and the minimum is 60 mm/Hg. Find a sine function that models the person’s blood pressure as a function of time (in minutes). F(x) = 30 sin(140πt) 90 f(x) = 60 sin(70πt) 30 f(x) = 60 sin(140πt) 90 f(x) = 30 sin(70πt) -60.
Sin function goes up and down, standard amplitude is 1 unit. The sin function modelling the given situation is [tex]f(x) = 30\sin(\dfrac{\pi x}{5}) + 90[/tex]
How does sine function works?Suppose that we've got
[tex]f(x) = a\sin(bx + c) + d[/tex]
It has got
Amplitude or maximum height from average motion horizontal axis = a+dAnd thus, the minimum low from horizontal axis is -a (sin ranges from -1 to 1, and multiplying a to it make it range from -a + d to a).Period of wave: [tex]\dfrac{2\pi}{b}[/tex]Phase shift (horizontal left shift) = c/bHorizontal line around which wave moves is: y = dThe situation given has:
Maximum blood pressure as 120 mm/Hg = a + d
Minimum blood pressure as 60 mm/Hg = -a + d
Thus, adding both will give:
[tex](a+d) + (-a + d) = 120 + 60\\2d = 180\\d = 90[/tex]
Thus, as a + d = 120, thus, a = 120-d = 120 - 90 = 30
Now, The period is given to be 10 minutes, or we get:
[tex]\dfrac{2\pi}{b} = 10\\\\b = \dfrac{\pi}{5}[/tex]
Since count started from 0, thus, c= 0
Therefore, the sine function modelling the given situation is:
[tex]f(x) = a\sin(bx + c) + d \\\\f(x) = 30\sin(\dfrac{\pi x}{5}) + 90[/tex]
Here x is the number of minutes passed.
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Answer:
A
Step-by-step explanation:
Im giving brainleist lol
Which sampling would be appropriate to survey 280,000 people?
A. 28,000
B. 2,800
C. 280
D. 28
Answer:
Option C
Step-by-step explanation:
280 sampling would be appropriate to survey 280,000 people
Please mark as Brainliest!!
Simplify This Equation!
Answer:
[tex]=5^{\frac{5}{6} }[/tex]
Step-by-step explanation:
[tex](\sqrt{5} )(\sqrt[3]{5} )=(5^{\frac{1}{2} } )(5^{\frac{1}{3} } )=5^{\frac{1}{2}+\frac{1}{3} } =5^{\frac{5}{6} }[/tex]
Hope this helps
Step-by-step explanation:
any root of a number can be written as fraction in the exponent of that number.
so, here, the square root of 5 is 5^1/2.
and the cubic root of 5 is 5^1/3.
what happens, when we multiply the same base number with exponents ?
a^n × a^m = a^(n+m)
and so we get here
5^1/2 × 5^1/3 = 5^(1/2 + 1/3)
how do we add fractions with different denominators ?
we bring them to the same denominator, usually by using the smallest (or least) common multiple of the existing denominators, which is 6 for 2 and 3.
so,
1/2 + 1/3 = 3/6 + 2/6 = 5/6
therefore, the simplified solution is
5^5/6
the first answer option is correct.
Marty has $110 and is spending it at a rate of $3 per day. How much money does he have left after 14 days? Write your answer in the box.
3x14=42
110-42=68
So, Matry will have 68 dollars after 14 days. If you dont mind, mark me brainliest?
Answer:
$58
Step-by-step explanation:
Per day- $3
14 days- 14($3)
so, 14 days he spends $52
Then, He had $110 originally, so to find how much he has left:
110-52=58
So, he has $58 now.
A trucking company operates in three regions of the country. The table below depicts the probability that each company truck is in the region and the fuel prices per gallon. What amount should the company budget on average for a gallon of fuel across its operations? Round your answer to the nearest cent. Probability and Fuel Cost by Region Region Probability in Region Fuel Cost per Gallon Southeast 20% $3. 10 Southwest 30% $3. 50 California 50% $4. 05 $3. 53 $3. 55 $3. 68 $3. 70.
The cost the company budget on average for a gallon of fuel across its operations is given by: Option D: $3.70
What does the expectation of a random variable tells about?A random variable is usually taking some numerical information of each elementary event of the sample space . (map from sample space to real numbers). Its expected value is the best prediction value in most of the cases. It is the mean or average value of that random variable.
How to find the mean (expectation) of a random variable?Supposing that the considered random variable is discrete, we get:
[tex]Mean = E(X) = \sum_{\forall x_i} f(x_i)x_i\\\\[/tex]
where [tex]x_i; \: \: i = 1,2,.. , n[/tex] is its n data values
and [tex]f(x_i)[/tex] probability of [tex]X = x_i[/tex]
How to convert percent to probability?Percent counts the number compared to 100 whereas probability counts it compare to 1.
So, if we have a%, that means for each 100, there are 'a' parts. If we divide each of them with 100, we get:
For each 1, there are a/100 parts.
Thus, 50% = 50/100 = 0.50 (in probability)
If assuming that X = Fuel cost per gallon, then
E(X) = Average fuel cost per gallon that the company should budget (its per gallon, means for a gallon)
Using the tabulated value given in the problem, we get:
[tex]Mean = E(X) = \sum_{\forall x_i} f(x_i)x_i\\\\\\\\E(X) = 3.10 \times 0.2 + 3.5 \times 0.3 + 4.05 \times 0.5 = 3.695 \approx 3.70[/tex] (in dollars)
(we converted percentage to probability).
Thus, the cost the company budget on average for a gallon of fuel across its operations is given by: Option D: $3.70
Learn more about expectation of a random variable here:
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Answer:
D is the correct answer! ~Hope this helps!
Step-by-step explanation:
Work:
A four-letter code uses the letters Z and X. Either letter can be repeated in the code. How many
different codes are possible?
Answer:
Step-by-step explanation:
10? i believe so if not then one or two more
what do you get when you times 30 by 56
Answer:
we divide both 30 and 56 by the greatest common factor to get the following simplified fraction: 15/28 Therefore, this equation is true:
MARK AS BRAINLIESTSAY THANKS ON AVATAR SAY THANKS ON ANSWERRATE AT LEAST 3 -- 5DONT HAVE A GOOD DAY HAVE A GREAT DAY
Plot the image point P under the translation (x,y)→(x-4,y-6).
An eighth-grade teacher wants to improve how the students function in small groups. What is the best strategy for improving the functionality of the small groups
Answer:
I don't think you are asking a math question, but in my opinion you should choose a leader that you think would be responsible in a group, then tell them what the group needs to do.
Step-by-step explanation:
I domt understand how to solve
Answer:
The answer is---
x=10
Step-by-step explanation:
(4x+9)+(7x+4)+57=180
11x+13+57=180
11x=110
x=10
Two trains, Train A and Train B weigh a total of 349 tons. Train A is heavier than Train B. The difference in their weights is 249 tons. What is the weight of each train?
Answer:
Train A = 299 tons Train B = 50 tons
Step-by-step explanation:
Train A = x
Train B = y
x+y = 349
x= y +249
Plug in one equation into another
y+249+y= 349
Simplify
2y+249=349
Subtract 249 from both sides
2y=100
Divide both sides by 2
y=50
Plug it into the x equation to solve for x
x+50=349
-50 from both sides
x=299
3x+x+x+x-3-2=7+x+x
What is the value of x
Answer:
x = 3
Step-by-step explanation:
3x+x+x+x-3-2=7+x+x
3x+x+x+x-x-x= 7 + 3 +2
3x+x = 12
4x = 12
x = 3
(6x+7) (3x-1) - (5x+3) (2x+1)
Answer:
8x² + 4x - 10
Step-by-step explanation:
We will use the order of PEMDAS to solve
-> See attached
(6x+7) (3x-1) - (5x+3) (2x+1)
(6x+7) (3x-1) becomes 18x² - 6x + 21x - 7 which is equal too 18x² + 15x - 7
(5x+3) (2x+1) becomes 10x² + 6x + 5x + 3 which is equal too 10x² + 11x + 3
(18x² + 15x - 7) - (10x² + 11x + 3)
18x² - 10x² = 8x²
15x - 11x = 4x
-7 - 3 = -10
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly.
- Heather
Find the integer $n$ such that\[10^n = 10^{3}\sqrt{\dfrac{10^{31}}{0.001}}.\]
Please help :(
The value of n is 20 from the given indices
How to determine the variable in an exponential functionGiven the exponential function expressed as:
[tex]\[10^n = 10^{3}\sqrt{\dfrac{10^{31}}{0.001}}.\][/tex]
This can be further expressed as:
[tex]\[10^n = 10^{3}\sqrt{\dfrac{10^{31}}{10^{-3}}}.\\\[10^n = 10^{3}\sqrt{10^{34}\\10^n = 10^3\cdot 10^{17}[/tex]
Since the use are equal, add the exponents
[tex]10^n= 10^{3+17}\\10^n=10^{20}\\n=20[/tex]
Hence the value of n is 20 from the given indices
Learn more on indices here: https://brainly.com/question/10339517
Answer:
20
Step-by-step explanation:
3x²-4x-7=0 find out b and c
Answer: there is no b and c so you cant find b and c
Step-by-step explanation: