Answer:
Step-by-step explanation:
your doing the calculation wrong
Type the correct answer in each box. Round your answers to two decimal places. Find the average rate of change of f(x) = log2(3x − 6) on [3, 4], [4, 5], and [5, 6].
Answer:
on [3, 4] = 0.30
on [4, 5] = 0.18
on [5, 6] = 0.12
Step-by-step explanation:
The average rate of change f, of a function f(x) on an interval [a, b] is given by;
[tex]f = \frac{f(b) - f(a)}{b - a}[/tex] -------------(i)
In our case,
f(x) = log 2(3x - 6)
Now let's get the average rate of change of f(x) on;
(i) [3, 4]
Here, a = 3 and b = 4
f(a) = f(3) [This is f(x) at x = 3]
=> f(3) = log[2(3(3) - 6)]
=> f(3) = log[2(9 - 6)]
=> f(3) = log[2(3)]
=> f(3) = log[6]
Also,
f(b) = f(4) [This is f(x) at x = 4]
=> f(4) = log[2(3(4) - 6)]
=> f(4) = log[2(12 - 6)]
=> f(4) = log[2(6)]
=> f(4) = log[12]
Now substitute the values of a, b, f(a) and f(b) into equation (i) as follows;
[tex]f = \frac{log 12 - log 6}{4 - 3}[/tex] [Remember that log m - log n = log (m / n)]
[tex]f = \frac{log (12 / 6)}{4 - 3}[/tex]
[tex]f = \frac{log (2)}{1}[/tex]
f = log 2 = 0.3010
f = 0.30 [to two decimal places]
∴ The average rate of change on [3, 4] = 0.30
(ii) [4, 5]
Here, a = 4 and b = 5
f(a) = f(4) [This is f(x) at x = 4]
=> f(4) = log[2(3(4) - 6)]
=> f(4) = log[2(12 - 6)]
=> f(4) = log[2(6)]
=> f(4) = log[12]
Also,
f(b) = f(5) [This is f(x) at x = 5]
=> f(5) = log[2(3(5) - 6)]
=> f(5) = log[2(15 - 6)]
=> f(5) = log[2(9)]
=> f(5) = log[18]
Now substitute the values of a, b, f(a) and f(b) into equation (i) as follows;
[tex]f = \frac{log 18 - log 12}{5 - 4}[/tex] [Remember that log m - log n = log (m / n)]
[tex]f = \frac{log (18 / 12)}{5 - 4}[/tex]
[tex]f = \frac{log (1.5)}{1}[/tex]
f = log 1.5 = 0.176
f = 0.18 [to two decimal places]
∴ The average rate of change on [4, 5] = 0.18
(iii) [5, 6]
Here, a = 5 and b = 6
f(a) = f(5) [This is f(x) at x = 5]
=> f(5) = log[2(3(5) - 6)]
=> f(5) = log[2(15 - 6)]
=> f(5) = log[2(9)]
=> f(5) = log[18]
Also,
f(b) = f(6) [This is f(x) at x = 6]
=> f(6) = log[2(3(6) - 6)]
=> f(6) = log[2(18 - 6)]
=> f(6) = log[2(12)]
=> f(6) = log[24]
Now substitute the values of a, b, f(a) and f(b) into equation (i) as follows;
[tex]f = \frac{log 24 - log 18}{6 - 5}[/tex] [Remember that log m - log n = log (m / n)]
[tex]f = \frac{log (24 / 18)}{6 - 5}[/tex]
[tex]f = \frac{log (1.33)}{1}[/tex]
f = log 1.33 = 0.124
f = 0.12 [to two decimal places]
∴ The average rate of change on [5, 6] = 0.12
Answer:CORRECT ANSWER ON PLATO
[3,4]= 1
[4,5]=0.59
[5,6]= 0.41
Sara and Jenny can both do flips in the air. The ratio of the number of flips Sara can
do to the number of flips Jenny can do is 3:8. Jenny can do 120 more flips than Sara.
If Sara increases the number of her flips by 3 and Jenny decreases the number of her
flips by 12, what will be the new ratio of the number of flips Sara can do to the
number of flips Jenny can do?
Answer:
The ratio will be 48/109
Step-by-step explanation:
What are the Division Properties of Zero?
You cannot divide any number by zero since it is meaningless to say that we are dividing a number or object in zero groups or in 0 size parts
We hat does (-9) mean
Answer:
(-9) still means -9 it doesn't really mean anything thou....but if u have another number besides it then it means to multiply like maybe 2(-9)then it will be -18...... but if it is just (-9) then it doesn't mean anything.....
If x = 9, then x is between
15 and 20
02 and 3
80 and 90
0 4 and 5
Find the surface area of the rectangular prism
2mi 2mi
4mi
Answer:
the SA is 40
Step-by-step explanation:
the formula for SA of a rectangular prism is 2(lw + lh + wh)
so it would be: 2(2x2+2x2+4x2)
can i get brainliest please? i only need two more
2) the quotient of 14 and 7
Answer:
The quotient of 7 and 14 is 2..
Evaluate f(x) = 6x - 2 for x = 3 Group of answer choices 7 16 10 61
Solve the initial value problem where y′′+4y′−21 y=0, y(1)=1, y′(1)=0 . Use t as the independent variable.
Answer:
[tex]y = \frac{7}{10} e^{3(t - 1)} + \frac{3}{10}e^{-7(t - 1)}[/tex]
Step-by-step explanation:
y′′ + 4y′ − 21y = 0
The auxiliary equation is given by
m² + 4m - 21 = 0
We solve this using the quadratic formula. So
[tex]m = \frac{-4 +/- \sqrt{4^{2} - 4 X 1 X (-21))} }{2 X 1}\\ = \frac{-4 +/- \sqrt{16 + 84} }{2}\\= \frac{-4 +/- \sqrt{100} }{2}\\= \frac{-4 +/- 10 }{2}\\= -2 +/- 5\\= -2 + 5 or -2 -5\\= 3 or -7[/tex]
So, the solution of the equation is
[tex]y = Ae^{m_{1} t} + Be^{m_{2} t}[/tex]
where m₁ = 3 and m₂ = -7.
So,
[tex]y = Ae^{3t} + Be^{-7t}[/tex]
Also,
[tex]y' = 3Ae^{3t} - 7e^{-7t}[/tex]
Since y(1) = 1 and y'(1) = 0, we substitute them into the equations above. So,
[tex]y(1) = Ae^{3X1} + Be^{-7X1}\\1 = Ae^{3} + Be^{-7}\\Ae^{3} + Be^{-7} = 1 (1)[/tex]
[tex]y'(1) = 3Ae^{3X1} - 7Be^{-7X1}\\0 = 3Ae^{3} - 7Be^{-7}\\3Ae^{3} - 7Be^{-7} = 0 \\3Ae^{3} = 7Be^{-7}\\A = \frac{7}{3} Be^{-10}[/tex]
Substituting A into (1) above, we have
[tex]\frac{7}{3}B e^{-10}e^{3} + Be^{-7} = 1 \\\frac{7}{3}B e^{-7} + Be^{-7} = 1\\\frac{10}{3}B e^{-7} = 1\\B = \frac{3}{10} e^{7}[/tex]
Substituting B into A, we have
[tex]A = \frac{7}{3} \frac{3}{10} e^{7}e^{-10}\\A = \frac{7}{10} e^{-3}[/tex]
Substituting A and B into y, we have
[tex]y = Ae^{3t} + Be^{-7t}\\y = \frac{7}{10} e^{-3}e^{3t} + \frac{3}{10} e^{7}e^{-7t}\\y = \frac{7}{10} e^{3(t - 1)} + \frac{3}{10}e^{-7(t - 1)}[/tex]
So the solution to the differential equation is
[tex]y = \frac{7}{10} e^{3(t - 1)} + \frac{3}{10}e^{-7(t - 1)}[/tex]
10 degrees above 0?
100 points + brainliest! Simple math
Answer:
The cordinates are:
y = 3
x = 4
Step-by-step explanation:
If you draw a line in the middle of the triangle
It Will go through the base at point V
point V can be marked at y=3 and x=4 the line drawn will intersect 0
Can you please help me with this I’ll give a brain list
Answer: opposite
Step-by-step explanation:
Answer:
opposite
Step-by-step explanation:
the opposite of -4 is 4.
the absolute value of -4 is 4.
the reciprocal of -4 is -1/4.
The table below gives the numbers of protons, electrons, and neutrons in four atoms. Atom Number of protons Number of electrons Number of neutrons 1 39 39 52 2 40 40 50 3 39 39 54 4 40 40 51 Based on the information that is given, which atom in the table has the highest mass? 1 2 3 4
Answer:
3
Step-by-step explanation:
As per table, the mass is:
1 | 39 + 39 + 52 = 1302 | 40 + 40 + 50 = 1303 | 39 + 39 + 54 = 1324 | 40 + 40 + 51 = 131So the atom 3 has the highest mas of 132
Answer choice 3 is correct
Answer:
3
Step-by-step explanation:
Add protons and neutrons.
If the base is 8 in. and the height is 7 in. What is the area?
Answer:
The formula of area is Pi×R×R
and then you add all sides and answer of your question is 30cm
Answer:
a = 28
Step-by-step explanation: First you would have to multiply 7 x 8 which equals =56. Then you would have to divide 56 by 2 which is =28 and that would be your area if you are solving for a triangle.
A man has 12 different colored shirts and 20 different ties in his closet. How many shirts and tie combinations can he select to take on a trip if he only takes 3 shirts and 5 ties?
The 100th term of 50, 80, 110 is??
In class, there are 9 boys and 13 girls. If half of the class has a cold, how many girls must have a cold?
Answer: a or c one of those
Step-by-step explanation:
how many numbers lie between 101 the square and 102 the square
Answer:
203
Step-by-step explanation:
Square of 101 = 101^2= 10201
Square of 102 = 102 ^2=10404
No. of numbers between both of them =10404-10201=203
Answer:
203
Step-by-step explanation:
✓101 kare = 10.201
✓102 kare = 10.404
✓ 10.404- 10.201 = 203
#Başarılar
#Türkiye
Beverly has a backyard that is square. One of the sides is 10 feet long. What is the area of her back yard?
Answer: all of the sides are 10ft long
Step-by-step explanation:
Clark and Lana take a 30-year home mortgage of $128,000 at 7.8%, compounded monthly. They make their regular monthly payments for 5 years, then decide to pay $1300 per month.
A) Find their regular monthly payment.
B) Find the unpaid balance when they begin paying the $1400.
C) How many payments of $1400 will it take to pay off the loan?
D) How much interest will they save by paying the loan using the number of payments from part (c)?
Answer:
Step-by-step explanation:
From the given information:
The present value of the house = 128000
interest rate compounded monthly r = 7.8% = 0.078
number of months in a year n= 12
duration of time t = 30 years
To find their regular monthly payment, we have:
[tex]PV = P \begin {bmatrix} \dfrac{1 - (1 + \dfrac{r}{n})^{-nt}}{\dfrac{r}{n}} \end {bmatrix}[/tex]
[tex]128000 = P \begin {bmatrix} \dfrac{1 - (1 + \dfrac{0.078}{12})^{- 12*30}}{\dfrac{0.078}{12}} \end {bmatrix}[/tex]
128000 = 138.914 P
P = 128000/138.914
P = $921.433
∴ Their regular monthly payment P = $921.433
To find the unpaid balance when they begin paying the $1400.
when they begin the payment ,
t = 30 year - 5years
t= 25 years
[tex]PV= 921.433 \begin {bmatrix} \dfrac{1 - (1 - \dfrac{0.078}{12})^{25*30}}{\dfrac{0.078}{12}} \end {bmatrix}[/tex]
PV = $121718.2714
C) In order to estimate how many payments of $1400 it will take to pay off the loan, we have:
[tex]121718.2714 = \begin {bmatrix} \dfrac{1300 (1 - \dfrac{12.078}{12}))^{-nt}}{\dfrac{0.078}{12}} \end {bmatrix}[/tex]
[tex]121718.2714 = 200000 \begin {bmatrix} (1 - \dfrac{12.078}{12}))^{-nt} \end {bmatrix}[/tex]
[tex]\dfrac{121718.2714}{200000 } = \begin {bmatrix} (1 - \dfrac{12.078}{12}))^{-nt} \end {bmatrix}[/tex]
[tex]0.60859 = \begin {bmatrix} (1 - \dfrac{12}{12.078}))^{nt} \end {bmatrix}[/tex]
[tex]0.60859 = (0.006458)^{nt}[/tex]
[tex]nt = \dfrac{0.60859}{0.006458}[/tex]
nt = 94.238 payments is required to pay off the loan.
How much interest will they save by paying the loan using the number of payments from part (c)?
The total amount of interest payed on $921.433 = 921.433 × 30(12) years
= 331715.88
The total amount paid using 921.433 and 1300 = (921.433 × 60 )+( 1300 + 94.238)
= 177795.38
The amount of interest saved = 331715.88 - 177795.38
The amount of interest saved = $153920.5
Find the standard form of the equation of the ellipse with the given characteristics. Center: (1, 2); vertex: (−7, 2); minor axis of length 12
Answer:
(x-1)²/64 + (y-2)²/ 144= 1
Step-by-step explanation:
Given that
The standard form for an ellipse is
(x-h)/a² + ( y-k)/b²=1
So
h, k
is the centre of the ellipse, and
a is the distance from the centre to the vertices and c is the distance from the centre to the foci.
b is the minor axis.
So b² + c²= a²
In this example
a= -7-1= -8
When solving this problem, what is the first step you would need to do? 3 (4x - 5) = 10 Add 5 Divide by 4 Distribute the 3 Subtract 4x - 5
Answer:
Distribute the 3
Step-by-step explanation:
order of operations mate
Tyra bought 4.5 pounds of strawberries. They cost $2.60 a pound. How much did
she spend?
can some one please help me with this.
3 1⁄8 − 1 7⁄8 =
Answer:
1 2/8
Step-by-step explanation:
3 1/8 = 25/8
25/8 - 15/8 = 10/8 = 1 2/8
A sheet of paper is cut into 3 same size pieces and then cut 3 more and so on..... after the 4th cut, how many pieces? after the nth cut, how many pieces?
Round to the nearest dollar $7,563.27
Answer:
$7,563
Step-by-step explanation:
We will round to the nearest whole number to round to the nearest dollar
$7,563.27
since we have 27 cents ( .27), that is less than 50 cents, we leave it alone
$7,563.00 or $7,563
Answer:
$7,563
Step-by-step explanation:
Rounding to the nearest dollar is just like rounding to the nearest whole number.
The number we are given is:
$7,563.27
To round to the nearest dollar, look to the tenths place. If it is less than or equal to 4, round down. If it is greater than or equal to 5, round up.
The tenths place has a 2. Therefore, we leave the number as is.
$7, 563
$7,563 rounded to the nearest dollar is $7,563.00
If the volume of a cube is increased by a factor of 10, by what factor does the surface area per unit volume change
Answer:
(1/10)∛100 ≈ 0.4642
Step-by-step explanation:
For a cube of volume V, the edge length is ...
s = ∛V
and the area is ...
A = 6s² = 6V^(2/3)
Then the ratio of area to volume is ...
r1 = A/V = 6V^(2/3)/V = 6V^(-1/3)
If the value of V is increased by a factor of 10, the ratio of area to volume is now ...
r2 = 6(10V)^(-1/3)
The factor by which the ratio changed is ...
r2/r1 = (6(10V)^(-1/3))/(6V^(-1/3)) = 10^(-1/3) = (1/10)∛100
The surface area per unit volume changes by a factor of (∛100)/10.
___
Example
For a cube of side length 2, the volume is 2³ = 8 and the surface area is 6·2² = 24. The ratio of surface area to volume is 24/8 = 3.
Multiplying the edge length by ∛10, we now have a volume of (2∛10)³ = 80, and a surface area of 6(2∛10)² = 24(10^(2/3)). The ratio of surface area to volume is ... 24(10^(2/3))/80 = 0.3∛100.
The ratio of area to volume changed by a factor of (0.3∛100)/3 = (∛100)/10, as above.
Cassius drives his boat upstream for 45 minutes. It takes him 30 minutes to return downstream. His speed going upstream is 3 miles per hour slower than his speed going downstream. Find his upstream and downstream speed
Answer:
Upstream speed= 6 mile per hour
Downstream speed= 9 miles per hour
Step-by-step explanation:
Distance traveled during upstream
= x miles
Distance traveled during downstream
= y
Time traveling upstream
= 45 minutes.
Time traveling downstream
= 30 minutes
Speed traveling upstream
= a miles/hour
Speed traveling downstream
= b miles/hour
But
b = a+3
Distance= speed*time
X=45a
a= x/45
Y= 30(a+3)
Y= 30a +90
a= (y-90)/30
Equating both a
X/45= (y-90)/30
30x= 45(y-90)
X= 1.5y-135
But x= y
Y= 1.5y-135
135= 0.5y
270 miles = y
Y= x= 270 miles
X= 45a
270/45= a
6 mile/hour = a
b = a+3
b= 6+3
b = 9 miles/hour
Suppose we play the following game based on tosses of a fair coin. You pay me $10, and I agree to pay you $n 2 if heads comes up first on the nth toss. If we play this game repeatedly, how much money do you expect to win or lose per game over the long run
Answer:
In the long run, ou expect to lose $4 per game
Step-by-step explanation:
Suppose we play the following game based on tosses of a fair coin. You pay me $10, and I agree to pay you $n^2 if heads comes up first on the nth toss.
Assuming X be the toss on which the first head appears.
then the geometric distribution of X is:
X [tex]\sim[/tex] geom(p = 1/2)
the probability function P can be computed as:
[tex]P (X = n) = p(1-p)^{n-1}[/tex]
where
n = 1,2,3 ...
If I agree to pay you $n^2 if heads comes up first on the nth toss.
this implies that , you need to be paid [tex]\sum \limits ^{n}_{i=1} n^2 P(X=n)[/tex]
[tex]\sum \limits ^{n}_{i=1} n^2 P(X=n) = E(X^2)[/tex]
[tex]\sum \limits ^{n}_{i=1} n^2 P(X=n) =Var (X) + [E(X)]^2[/tex]
[tex]\sum \limits ^{n}_{i=1} n^2 P(X=n) = \dfrac{1-p}{p^2}+(\dfrac{1}{p})^2[/tex] ∵ X [tex]\sim[/tex] geom(p = 1/2)
[tex]\sum \limits ^{n}_{i=1} n^2 P(X=n) = \dfrac{1-p}{p^2}+\dfrac{1}{p^2}[/tex]
[tex]\sum \limits ^{n}_{i=1} n^2 P(X=n) = \dfrac{1-p+1}{p^2}[/tex]
[tex]\sum \limits ^{n}_{i=1} n^2 P(X=n) = \dfrac{2-p}{p^2}[/tex]
[tex]\sum \limits ^{n}_{i=1} n^2 P(X=n) = \dfrac{2-\dfrac{1}{2}}{(\dfrac{1}{2})^2}[/tex]
[tex]\sum \limits ^{n}_{i=1} n^2 P(X=n) =\dfrac{ \dfrac{4-1}{2} }{{\dfrac{1}{4}}}[/tex]
[tex]\sum \limits ^{n}_{i=1} n^2 P(X=n) =\dfrac{ \dfrac{3}{2} }{{\dfrac{1}{4}}}[/tex]
[tex]\sum \limits ^{n}_{i=1} n^2 P(X=n) =\dfrac{ 1.5}{{0.25}}[/tex]
[tex]\sum \limits ^{n}_{i=1} n^2 P(X=n) =6[/tex]
Given that during the game play, You pay me $10 , the calculated expected loss = $10 - $6
= $4
∴
In the long run, you expect to lose $4 per game
Below is the table of values of a function. Write the output when the input is n. input 3 8 72 ñ
output 6 11 12 []
Answer:
n + 3
Step-by-step explanation:
6 is 3 + 3, 11 is 8 + 3 and 12 is 9 + 3 so the output seems to be the input plus 3. Therefore, when the input is n, the output is n + 3.
Answer:
output = n+3
Step-by-step explanation:
When the input changes by 5 units (from 3 to 8), the output changes by 5 unis (from 6 to 11). So the rate of change of the output with respect to the input is 1. However, each output is 3 more than the input, so ...
for input n
output = n+3