Answer:
Answer is f(x)=245(4^1/12)^12x
Step-by-step explanation:
The general formula for the growth of population in years is:
f(x) =P0(1+r)^x
where 1+r is the rate of growth in this case 4 and x is time in years. To take it to months we do not change initial population , this doesn't vary by changing time scale (there are 45 fruit flies in time 0 )
we change the time period x to 12 x because we want our formula to remain equivalent to the original one so if x = 1 year in months this would be equivalent to twelve months (12x = 12 with x =1 ) taht is the same
However we need to reescale our growth rate to a value that calculates it by month growth. After 12 time periods of a month our grow rate should be equivalent to the growth rate of a year. So For that reason we elevate to a 1/12 because of exponent rules
(4^1/12)^12x =(4^12x/12) because of exponent of an exponent is multiplying exponents
= (4)^x we arrive to the same expression. So
Find two consecutive even integers whors sum is 86. Which of the following could be used to solve the problem?
Answer:
42 and 44
Step-by-step explanation:
The even numbers are numbers which can be written as 2n where n is any integer number.
Therefore, two consecutive numbers would be "2n" and "2n + 2"
We then have that
2n + (2n+2) = 86
4n + 2 = 86
4n = 84
n = 21
And the even number 2n is 2(21) = 42.
(We can verify this answer by doing 42 + 44 = 86)
Stuart's best golf score is 4 under par or -4. He wants to beat this score by an additional 3 strokes under par. With one hole remaining, stuart is 5 under par, or -5. What must his score be on the last hole to beat his best score
Answer:
-2
Step-by-step explanation:
he wants to get -7 because -4 + -3 = -7
he has -5 currently, so to get to -7 I added -2 which is the amount he needs.
I hope this helps you :)
Stuart requires a score of atleast - 2 on his last hole in other to beat his best score.
Best score = - 4
Required score < Best score + (-2)
Required score < - 4 + (-2)
Current score = - 5
Therefore, the least score required to beat his best score is - 7
Therefore, the required score on last hole will be :
-7 - (-5) = - 7 + 5 = - 2Therefore, a score of - 2 is required on last hole in other to beat his best score.
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The volume of a rectangular prism is 655.2 Ft cubed. If the base of the prism is 9 ft by 5.2 ft, find the height of the prism.
Answer:
Step-by-step explanWe can easily calculate for the height of the prism since all needed measurements are given. Volume of a rectangular prism is expressed by the equation:
V = lwh
where l is the length, w is the width and h is the height of the prism.
655 = 9 (5.2) hation:
h=14ft
Michael starting a savings account with $300. After 4 weeks he had $350 and after 9 weeks he had $400. What is the rate of change in his savings account per week
Answer:
$12.5 per week
Step-by-step explanation:
(300)+12.5 +12.5+12.5+12.5=350
The rate of change in Michael's savings account per week is $12.50.
Explanation:To find the rate of change in Michael's savings account per week, we need to determine how much the account balance increased per week. We can subtract the initial balance from the final balance and divide that by the number of weeks:
Rate of change per week = (Final balance - Initial balance) / Number of weeks
Using the given information, the rate of change per week is:
(350 - 300) / 4 = 50 / 4 = 12.5
Therefore, the rate of change in Michael's savings account per week is $12.50.
A small toy car costs $3.A large toy car costs 5 times as much as the small one.Aaron wants to buy one of each.Which equation can he use to find the cost (a) of the two cars?
Answer:$18.00
Step-by-step explanation:5×3=15
$3+$15=$18
Answer:
Step-by-step explanation:
To
kenya plans to make a down payment plus monthly payments in order to buy a motorcycle. at one dealer she would pay 2,500 down and 150 each month. at another dealer she would pay 3,000 down and 125 each month after how many months would the total amount paid be the same for both dealers? what would that amount be?
Answer:
20 months
Step-by-step explanation:
Let the number of months be denoted by x.
Then, we shall form two equations to represent the total cost from each dealer. Thus,
2500 + 150x is the cost of the motorcycle from the first dealer.
3000 + 125x is the cost of the motorcycle from the second dealer.
If the costs from the dealers are equal, then
2500 + 150x =3000 +125x
150x- 125x = 3000-2500
25x = 500
x = 500/ 25
x =20 months
You can buy 5 cans for green beans at the vilage market for $2.80 .You can buy 10 of the same cans of beans at sam club for $7.50.Which place is the better buy?
Recall that the symbol z represents the complex conjugate of z. If z = a + bi, show that the statement is true. Z − z is a pure imaginary number. Use the definition of complex conjugates to simplify the expression.
Answer:
Step-by-step explanation:
z = a + bi
the complex conjugate is : Z = a-bi
so : Z-z = (a-bi) - ( a + bi ) = a-bi -a -bi
Z-z = -2bi ...is a pure imaginary number (the statement is true)
The statement is true, Z-z is a pure imaginary number = -2bi.
What is conjugate complex?
A conjugate of a complex number is another complex number which has the same real part as the original complex number and the imaginary part has the same magnitude but opposite sign.
Here, given that, z = a+ib,
Let, Z be the complex conjugate of z, then, Z=a-ib
Now, Z-z = (a-ib)-(a+ib)
=a-ib-a-ib
=-i2b (which is purely imaginary)
Hence, proved. The given statement is true.
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PLEASE!!! HELP NEEDED!!!
Given the following equation, x^4 - x^3 - 3x - 2. Use synthetic division to test the following 3 points and show which one is a root. Must show synthetic division for all 3 of the following test points. Test these 3 possible root points also called possible zeros using synthetic division: (x,y) = (-1, 0) (-3, 0) (2, 0).
PLEASE SHOW YOUR WORK!!!
Answer:
(x, y) = (-1, 3), (-3, 115), (2, 0)
Step-by-step explanation:
The first two test points are not roots. The last one is a root.
The price of one share of Starbucks declined five dollars per day for four days in a row. How much did the price of one share change in total after the four days?
Answer:
Each share lost $20 in value over 4 days time
Step-by-step explanation:
$5 loss for 4 days
5 x 4 = 20
$20 loss in 4 days.
Colton and gage were building a castle together. Colton was 3 times as fast at building the castle than gage. If it takes 80 blocks to build the castle, how many blocks did colton build on the castle?
Answer:
60
Step-by-step explanation:
For each 3 blocks Colton placed, Gage place 1, so Colton placed 3/4 of the total number blocks.
3/4 × 80 = 60
Colton placed 60 blocks on the castle.
Answer:
60
Step-by-step explanation:
A cable service provider charges $40 per month for its basic package plus an additional $5.35 for each premium channel chosen. The average cost for cable per additional channel is given by the expression 5.35x + 40 / x, where x is the number of premium channels added to the basic package. What does the quotient 40/x represent?
Answer:
the answer will be d.PLATO users
find an equation of the line through (5,-9) and perpendicular to x=7
Answer:
y = - 9
Step-by-step explanation:
x = 7 is the equation of a vertical line parallel to the y- axis and passing through all points with an x- coordinate of 7
A line perpendicular to it is a horizontal line parallel to the x- axis with equation y = c
Where c is the value of the y- coordinates the line passes through.
The line passes through (5, - 9) with y- coordinate - 9, thus
equation of line is y = - 9
The first hill on a roller coaster is 155 feet tall. The first drop on a second roller coaster is about 11/20 as tall as the first coaster. Find the height of the hill on the second roller coaster
Answer:
85.25
Step-by-step explanation:
155 x (11/20) =85.25 feet
In terms of paying less in interest, which is more economical for a $150,000 mortgage: a 30-year fixed-rate at 8% or a 20-year fixed-rate at 7.5%? How much is saved in interest?
Answer:
20-year fixed-rate at 7.5%$106,219.32Step-by-step explanation:
The shorter the term, the lower the amount of interest.
The lower the interest rate, the lower the amount of interest.
The loan that has both a shorter term and a lower interest rate will cost less in interest.
___
The total of payments for the 30-year loan is 396,232.87.
The total of payments for the 20-year loan is 290,013.55.
The amount saved by taking the shorter loan is the difference of these amounts: $106,219.32.
_____
You can use an amortization formula, spreadsheet, or a financial calculator to compute the payments for each loan. The total repayment amount is the product of the monthly payment and the number of them, 360 for the 30-year loan; 240 for the 20-year loan.
The distance from Earth to the sun is about 9.3 × 107 miles. The distance from Earth to the Moon is about 2.4 × 105 miles. About how many times greater is the distance from Earth to the Sun than Earth to the Moon?
Answer:
The answer to your question is: 387.5 times distance from earth to the sun than distance from the earth to the moon
Step-by-step explanation:
Data
distance from earth to the sun = 9.3 x 10⁷ miles
distance from the earth to the moon = 2.4 x 10⁵ miles
distance ES to EM
Then we need to divide
distance from earth to the sun / distance from the earth to the moon
9.3 x 10⁷ miles / 2.4 x 10⁵ miles
= 387.5 times is greater.
The distance from Earth to the Sun is about 387.5 times greater than the distance from Earth to the Moon. This is calculated by dividing the distance from Earth to the Sun by the distance from Earth to the Moon.
Explanation:To determine how many times greater the distance from Earth to the Sun is than the distance from Earth to the Moon, we need to divide the distance from Earth to the Sun by the distance from Earth to the Moon. So, we have 9.3 × 107 miles (distance to the Sun) divided by 2.4 × 105 miles (distance to the Moon).
When you perform this calculation, you get a value of approximately 387.5. Therefore, the distance from Earth to the Sun is about 387.5 times greater than the distance from Earth to the Moon.
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Correct answers only please! If you don't know the answer, then please don't guess or say what you think it is.
Mike recently increased the size of his truck tires from the original P215/60R16 to the larger P235/7016. If Mike didn't recalibrate his speedometer, how fast is really going on the new tires when his speedometer shows he is traveling 60 mph?
A. 54.2 mph
B. 63.8 mph
C. 66.4 mph
D. 69.7 mph
Final answer:
When Mike increased the size of his truck tires from the original P215/60R16 to the larger P235/70R16 without recalibrating his speedometer, the actual speed he was going on the new tires when his speedometer showed 60 mph was approximately 54.2 mph.
Explanation:
When Mike increased the size of his truck tires without recalibrating his speedometer, his speedometer reading would be inaccurate. To determine how fast he is going on the new tires when his speedometer shows 60 mph, we can use the concept of tire revolutions per mile.
The original tire size, P215/60R16, has a diameter of approximately 25.7 inches, while the larger tire size, P235/70R16, has a diameter of approximately 29.0 inches. The new tires cover a greater distance in one revolution compared to the original tires.
To calculate the actual speed, we can use the equation:
Actual Speed = Speedometer Reading * (Original Tire Diameter / New Tire Diameter)
Substituting the given values:
60 mph * (25.7 inches / 29.0 inches)
By simplifying this calculation, the actual speed is approximately 54.2 mph. Therefore, the correct answer is A. 54.2 mph.
Mike is actually traveling approximately 64.4 mph. Hence the correct option is c.
Calculate the difference in tire circumference:
Original circumference: 2 * π * radius = 2 * π * (215 mm / 25.4 mm/inch) * (60 + 30%) = 79.3 inches (assuming 30% aspect ratio)
New circumference: 2 * π * (235 mm / 25.4 mm/inch) * (70 + 30%) = 85.1 inches
Difference: 85.1 inches - 79.3 inches = 5.8 inches
Calculate the percentage increase in circumference:
(5.8 inches / 79.3 inches) * 100% = 7.3%
Apply the percentage increase to the speedometer reading:
Actual speed = Speedometer reading * (1 + % increase)
Actual speed = 60 mph * (1 + 7.3%) = 60 mph * 1.073
Actual speed ≈ 64.4 mph
Therefore, when the speedometer shows 60 mph, Mike is actually traveling approximately 64.4 mph. Hence the correct option is c.
A contestant on a game show is given $250 and is ask five questions the contestant loses $50 for every wrong answer determine the domain and range
Answer:
The domain is (all possible values of x) [tex]\{0,1,2,3,4,5\}[/tex]
The range is (all possible values of f(x)) [tex]\{250,200,150,100,50,0\}[/tex]
Step-by-step explanation:
A contestant on a game show is given $250. He is asked five questions and loses $50 for every wrong answer.
If he answer all 5 questions correct, then he will still have $250;If he answers 4 questions correct and 1 question incorrect, he will have $200; If he answers 3 questions correct and 2 questions incorrect, he will have $150; If he answers 2 questions correct and 3 questions incorrect, he will have $100; If he answers 1 question correct and 4 questions incorrect, he will have $50; If he answers 5 questions incorrect, he will have $0.Let x be the number of wrong answers. Then you get a relationship
[tex]\begin{array}{cc}x&f(x)\\ 0&250\\1&200\\2&150\\3&100\\4&50\\5&0\end{array}[/tex]
The domain is (all possible values of x) [tex]\{0,1,2,3,4,5\}[/tex]
The range is (all possible values of f(x)) [tex]\{250,200,150,100,50,0\}[/tex]
Answer:
down below(hope this helps
Step-by-step explanation:
25 POINTS AND BRAINLIEST PLZ HELP!!!
Given f(x) and g(x) = f(k⋅x), use the graph to determine the value of k.
A. 5
B. 1/5
C. -1/5
D. −5
Answer:
Step-by-step explanation:
B is the answer
Tony loves to put stickers on his papers. Tony has 15 shark stickers. Tony has 21 whale sticker. Tony has 47 dolphi Stickers. Tony has 40 papers. Tony puts a dolphine sticker on every paper. Tony puts a shark sticker on every fourth paper. Tony puts a whale sticker on every fifth paper. When tony finishes putting all the stickers on the papers, how many papers will all three kinds of stickers on them.
Answer:
2 papers
Step-by-step explanation:
shark stickers : 15
whale stickers : 21
dolphin stickers : 47
papers:40
papers with dolphin stickers: 47
papers with shark stickers: 4, 8 , 12, 16, 20,24,28,32,36, 40 (every fourth paper, multiples of 4 till 40)
40/4 = 10 papers with shark stickers
papers with whale stickers: 5, 10,15, 15, 20, 25,30,35,40 (multiples of 5 till 40)
Papers with the three kinds of stickers : 2 (paper 20 and 40 )
Answer:
2 papers
Step-by-step explanation:
What is the multiplicative rate of change for the exponential function f(x) = f start bracket x end bracket equals two start bracket five-halves end bracket superscript negative x
Answer:
a) 0.4
Step-by-step explanation:
Got it right on quiz
The multiplicative rate of change for the exponential function is 5/2, indicating that the function increases by a factor of 5/2 for each unit increase in x.
The multiplicative rate of change for an exponential function
[tex]\( f(x) = a \times b^x \)[/tex]
is given by the base of the exponential term, b .
In the function
[tex]\( f(x) = 2 \left(\frac{5}{2}\right)^{-x} \),[/tex]
the base of the exponential term is 5/2.
So, the multiplicative rate of change is 5/2
What is X if X + R = S?
Answer:
The correct answer is the second option.
Step-by-step explanation:
If X + R = S, then X = S - R. You need to subtract each pair:
-2 - 0 = -2
-8 - 3 = -11
0 - (-4) = 4
2 - 5 = -3
Answer:
B
Step-by-step explanation:
Edge2020
show that (f o g)(x) = (g o f)(x) = x
f(x)= [tex]\frac{3}{x-1}[/tex]
g(x)= [tex]\frac{2}{x}[/tex]
Answer:
[tex] - \frac{2[1 - x]}{3} = g[f(x)] \\ \\ \frac{3x}{2 - x} = f[g(x)][/tex]
Step-by-step explanation:
They are not.
For the g[f(x)] function, you substitute ³/ₓ ₋ ₁ from the f(x) function in for x in the g(x) function to get this:
[tex] \frac{2}{ \frac{3}{x - 1}} [/tex]
Then, you bring x - 1 to the top while changing the expression to its conjugate [same expressions with opposite symbols]:
[tex] - \frac{2[1 - x]}{3}[/tex]
You could also do this [attaching another negative would make that positive].
For the f[g(x)] function, ²/ₓ from the g(x) function for x in the f(x) function to get this:
[tex] \frac{3}{ \frac{2}{x} - 1}[/tex]
Now, if you look closely, ²/ₓ is written as 2x⁻¹, and according to the Negative Exponential Rule, you bring the denominator to the numerator while ALTERING THE INTEGER SYMBOL FROM NEGATIVE TO POSITIVE:
[tex] \frac{3x}{2 - x} [/tex]
When this happens, x leaves the two and gets attached to the three, and 1 gets an x attached to it.
I am joyous to assist you anytime.
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11+4-3/4
Answer:
57/4
Step-by-step explanation:
Answer:
11 + 4 = 15
Rewrite the problem:
15-3/4= ?
15-3= 12
the divide it by 4:
12 / 4 = 3
ANSWER: 3
Step-by-step explanation:
I WILL GIVE BRAINLYIST!
Which graph shows a system of equations with exactly one solution?
Answer:
The last graph, where the functions intersect at only one point.
Step-by-step explanation:
A system of equations with only one solution is the one that in some point the solutions of each ecuation is exactly the same. In the graphs 1 and 3, where the equations does not intersect each other, the system of equations have no solution. In the second graph, the equations intersect 2 times, so the system of equations have 2 solutions.
Answer:
The last graph:/ D
Step-by-step explanation:
i got it right on the test
Please help I keep getting it wrong and I can't move on to the next part! You need to look at both pictures to answer this.
Explanation:
3. ∠2 and ∠3 are a linear pair → definition of a linear pair
4. ∠3 and ∠4 are a linear pair → definition of a linear pair
5. m∠2 +m∠3 = 180° → definition of a linear pair (or angle addition postulate)
6. m∠3 +m∠4 = 180° → definition of a linear pair (or angle addition postulate)
7. m∠2 +m∠3 = m∠3 +m∠4 → substitution property
8. m∠2 = m∠4 → subtraction property
9. ∠2 ≅ ∠4 → definition of congruent angles
_____
A pair of angles is a "linear pair" if they are adjacent and supplementary. ∠2 and ∠3 are adjacent and the non-common legs form a straight line. It isn't clear what your definition of linear pair is and what you need to do to claim that the angles sum to 180°. Above, we have assumed a definition of "linear pair" that includes the facts that → they sum to 180°; → non-adjacent sides form a straight line.
Which expression shows the sum of the polynomials with like terms grouped together? 10x2y + 2xy2 - 4x2 - 4x2y
A. [9-4x2) + (-4x2y) + 10x2y] + 2xy2
B. 10x2y + 2xy2 + [(-4x2) + (-4x2y)]
C. (-4x2) + 2xy2 + [10x2y + (-4x2y)]
D. [10x2y + 2xy2 + (-4x2y)] + (-4x2)
Answer:
The answer to your question is letter C
Step-by-step explanation:
A. [9-4x2) + (-4x2y) + 10x2y] + 2xy2 : in this polynomial the first term is not a like term, then this is incorrect.
B. 10x2y + 2xy2 + [(-4x2) + (-4x2y)] : in this polynomial, the terms that are grouped, are not like terms, then is incorrect.
C. (-4x2) + 2xy2 + [10x2y + (-4x2y)] ; This polynomial is the right answer because the like terms are grouped.
D. [10x2y + 2xy2 + (-4x2y)] + (-4x2): This polynomial is incorrect because one of the terms that are grouped is not a like term.
We have two coins, A and B. For each toss of coin A, we obtain Heads with probability 1/2 ; for each toss of coin B, we obtain Heads with probability 1/3 . All tosses of the same coin are independent. We toss coin A until Heads is obtained for the first time. We then toss coin B until Heads is obtained for the first time with coin B. The expected value of the total number of tosses is:
Answer:
The expected value is 5.
Step-by-step explanation:
Let X represent the number of tosses until the event described in the question happens. Let Y represent the number of tosses with coin A until Heads is obtained.Let Z represent the number of tosses with coin B until Heads is obtained.As we can see, X=Y+Z. Then, by the linearity of the expected value operator, we have that
[tex]E(X)=E(Y)+E(Z).[/tex]
We will compute E(Y) and E(Z).Observe that Y and Z have countable sets of outcomes (1,2,3,....) then,
[tex]E(X)=\sum^\infty_{n=1}nP(Y=n)[/tex],
[tex]E(Z)=\sum^\infty_{n=1}nP(Z=n)[/tex],
Then:
for each [tex]n\in \mathbb{N}[/tex], the probability of Y=n is given by [tex](0.5)^{n-1}(0.5)=(0.5)^{n}[/tex] (because the first n-1 tosses must be Tails and the n-th must be Heads). Therefore[tex]E(Y)=\sum^\infty_{n=1}nP(Y=n)=\sum^\infty_{n=1}n(\frac{1}{2} )^n=\\\\\sum^\infty_{m=1}\sum^\infty_{n=m}(\frac{1}{2} )^n=\sum^\infty_{m=1}(\frac{1}{2} )^{m-1}=\sum^\infty_{m=0}(\frac{1}{2} )^{m}=2.[/tex]
For each [tex]n\in \mathbb{N}[/tex], the probability of Z=n is given by [tex](\frac {2}{3})^{n-1}(\frac {1}{3})[/tex] (because the first n-1 tosses must be Tails and the n-th must be Heads). Therefore[tex]E(Z)=\sum^\infty_{n=1}nP(Z=n)=\frac{1}{3}\sum^\infty_{n=1}n(\frac{2}{3} )^{n-1}=\frac{1}{3}\sum^\infty_{m=1}\sum^\infty_{n=m}(\frac{2}{3} )^{n-1}[/tex]
Observe that, by the geometric series formula:
[tex]\sum^\infty_{n=m}(\frac{2}{3} )^{n-1}=\sum^\infty_{n=1}(\frac{2}{3} )^{n-1}-\sum^{m-1}_{n=1}(\frac{2}{3} )^{n-1}=3-\sum^{m-1}_{n=1}(\frac{2}{3} )^{n-1}=\\\\3-\sum^{m-2}_{n=0}(\frac{2}{3} )^{n}=3-\frac{1-(\frac{2}{3})^{m-1} }{1-\frac{2}{3}}=3(\frac{2}{3})^{m-1}[/tex]
Therefore
[tex]E(Z)=\frac{1}{3}\sum^\infty_{m=1}\sum^\infty_{n=m}(\frac{2}{3} )^{n-1}=\frac{1}{3}\sum^\infty_{m=1}3(\frac{2}{3})^{m-1} =\\\\ \sum^\infty_{m=1}(\frac{2}{3})^{m-1} = \sum^\infty_{m=0}(\frac{2}{3})^{m} =3.[/tex]
Finally, E(X)=E(Y)+E(Z)=2+3=5.
Using the binomial distribution, it is found that the expected value of the total number of tosses is of 5.
For each coin, there are only two possible outcomes, either it is heads, or it is tails. The outcome of a coin is independent of any other coin, hence the binomial distribution is used to solve this question.
What is the binomial probability distribution?It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The expected number of trials until q successes is:
[tex]E_s(X) = \frac{q}{p}[/tex]
For coin A, we obtain Heads with probability 1/2, hence:
[tex]E_{sA}(X) = \frac{1}{\frac{1}{2}} = 2[/tex]
For coin B, we obtain Heads with probability 1/3, hence:
[tex]E_{sB}(X) = \frac{1}{\frac{1}{3}} = 3[/tex]
2 + 3 = 5, hence, the expected value of the total number of tosses is of 5.
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First, rewrite 16//21 and 7/9 so that they have a common denominator.
(I'm so confused on how to do this, someone please help me out a bit)
Answer:
Step-by-step explanation:
Janelle is planning to rent a car while on vacation. The equation C=0.32m+15 models the relation between the cost in dollars, C, per day and the number of miles, m, she drives in one day. Interpret the slope of the equation.
Select the correct answer below:
The slope, 15, means that the cost for renting the car on a particular day increases by 15 dollars for every 15 miles she drives on that day.
The slope, 15, means that the cost for renting the car on a particular day increases by 15 dollars for each mile she drives on that day.
The slope, 0.32, means that the cost for renting the car on a particular day increases by 0.32 of a dollar for each mile she drives on that day.
The slope, 0.32, means that the cost for renting the car on a particular day increases by 0.32 of a dollar for each 0.32 of a mile she drives on that day.
Answer:
The C-intercept, 15, means that if Janelle drove 0 miles on a particular day it would cost her 15 dollars to rent the car for that day.
Step-by-step explanation:
The slope, 0.32, means that the cost for renting the car on a particular day increases by 0.32 of a dollar for each mile she drives on that day.
Explanation:The slope of the equation C=0.32m+15 is 0.32. The slope represents the rate of change in the cost per day for each unit increase in the number of miles Janelle drives. In this case, for every additional mile Janelle drives, the cost of renting the car increases by 0.32 dollars.