Answer:
5+k
Step-by-step explanation:
Since k is Kathy's height and we know Jo is 5+ cm than Kathy. That makes Jo = 5+k
Mrs. Kleim bought 5 boxes of 15 pencils to give to her students. If she has 26 students in her class, how many pencils can she give each student? How many pencils will she have left over?
Answer:2
Step-by-step explanation: 15x5=75
75/26=2.886
If x = 9, then x is between
15 and 20
02 and 3
80 and 90
0 4 and 5
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
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
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]
State the domain and the range of each relation. Then determine whether the relation is a function. Write yes or no. {(2,7), (3,10), (1,6)}
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
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:
(3x ^3 + 4x^2)+(3x3-4x^2-9x)=
Answer:=6x3−9c
Step-by-step explanation:
3x3+4x2+3x3−4x2−9c
=3x3+4x2+3x3+−4x2+−9c
Combine Like Terms:
=3x3+4x2+3x3+−4x2+−9c
=(3x3+3x3)+(4x2+−4x2)+(−9c)
=6x3+−9c
Tyra bought 4.5 pounds of strawberries. They cost $2.60 a pound. How much did
she spend?
The 100th term of 50, 80, 110 is??
10 degrees above 0?
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
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 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.
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?
PLEASE HELP ME SOLVE THIS QUESTION(PLS CHECK IMAGE)
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?
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
Find the 7th term in the
sequence
-1, -3, -9,...
Answer:
The answer is 729
Step-by-step explanation:
to get the next term, the sequence multiples the previous number by -3
1 * -3 = -3
-3 * -3 = 9
and so on.
To get the 7th term:
-27 * -3 = 81 (5th term)
81 * -3 = -243 (6th)
-243 * -3 = 729 (7th)
Answer:
The seventh term in the sequence is -729.
Step-by-step explanation:
Notice that the sequence is not increasing linearly. Therefore, this is a geometric sequence.
Recall that the explicit formula for a geometric sequence is given by:
[tex]x_n=a(r)^{n-1}[/tex]
Where a is the first term, r is the common ratio, and n denotes the nth term.
From the sequence, we can see that our first term a is -1.
Because each term is thrice the previous, our common ratio r is 3.
By substitution:
[tex]x_n=-(3)^{n-1}[/tex]
Hence, the seventh term is:
[tex]\displaystyle \begin{aligned} x_7 & = -(3)^{(7)-1} \\ \\ & = -(3)^{6} \\ \\ & = -729\end{aligned}[/tex]
In conclusion, the seventh term is -729.
What is the area of the parallelogram?
Answer:
A = 60 cm^2
Step-by-step explanation:
The area of a parallelogram is
A = bh
A = 14*5
A = 60 cm^2
[tex] area \: of \: parallelogram \: = \: base \times height[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: a \: \: \: \: \: \: \: \: \: \: \: \: = \: \: \: \: \: \: \: \: \: \: \: 14cm \times 5cm[/tex]
[tex]a \: \: \: \: \: \: \: \: \: \: \: \: \: = \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 70 {cm}^{2} [/tex]
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
Find the missing variable and indicated angle measure. pls help lol
Answer:
see below (I hope this helps!)
Step-by-step explanation:
∠VZY and ∠VXW form a linear pair and are supplementary, and since m∠VZY = 90°, m∠VXW = 180 - 90 = 90°. Since m∠WXU + m∠UXV = ∠VXW, we can write the following equation:
44 + 5x - 4 = 90
5x + 40 = 90
5x = 50
x = 10°
Therefore, m∠UXV = 5 * 10 - 4 = 46°
Answer:
x = 10 m(UXV)=46°
Step-by-step explanation:
m(UXV) + m(UXW) = 90° because m(VXY)= 90°
m(UXW) = 44°
m(UXV) + 44° = 90°
m(UXV) = 46°
5x - 4 = 46°
5x = 50
5x/5 = 50/5
x = 10
Hope this helps ^-^
A collection of nickels,dimes,and quarters consist of 9 coins with a total of $1.20. If the number of dimes is equal to the number of nickels, find the number of each type of coins.
Answer:
129
Step-by-step explanation:
120 +9 =129
because it is total and total means add
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.
my hw write find an equation of the line passing through (-2,3) and (4,-5) I have to write the equation in slope-intercept form I need help
Answer:
The line passing through the given points is:
[tex]y=-\frac{4}{3}x+\frac{1}{3}[/tex]
in its slope-intercept form
Step-by-step explanation:
Start by finding the slope of the segment that joins the two given points using the slope formula:
[tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
which for our case renders:
[tex]slope=\frac{3-(-5)}{-2-4}=\frac{8}{-6} =-\frac{4}{3}[/tex]
Now we can find the y-intercept by using any one of the given points in the general slope-intercept form of a line with this slope:
[tex]y=-\frac{4}{3} x+b\\3=-\frac{4}{3} (-2)+b\\3=\frac{8}{3}+b\\b=3-\frac{8}{3} \\b=\frac{9-8}{3} \\b=\frac{1}{3}[/tex]
Therefore, the equation of the line becomes:
[tex]y=-\frac{4}{3}x+\frac{1}{3}[/tex]
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
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
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
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
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