Answer:
12
Step-by-step explanation:
12 is the coefficient
The graph represents function 1, and the equation represents function 2: A coordinate plane graph is shown. A horizontal line is graphed passing through the y-axis at y = 4. Function 2 y = 8x + 12 How much more is the rate of change of function 2 than the rate of change of function 1? (4 points) Select one: a. 3 b. 4 c. 5 d. 8
Answer:
A
Step-by-step explanation:
Annual windstorm losses, X and Y, in two different regions are independent, and each is uniformly distributed on the interval [0, 10]. Calculate the covariance of X and Y, given that X+ Y < 10.
Answer:
[tex]Cov(X,Y) = -\frac{ 25}{9}[/tex]
Step-by-step explanation:
Given
[tex]Interval =[0,10][/tex]
[tex]X + Y < 10[/tex]
Required
[tex]Cov(X,Y)[/tex]
First, we calculate the joint distribution of X and Y
Plot [tex]X + Y < 10[/tex]
So, the joint pdf is:
[tex]f(X,Y) = \frac{1}{Area}[/tex] --- i.e. the area of the shaded region
The shaded area is a triangle that has: height = 10; width = 10
So, we have:
[tex]f(X,Y) = \frac{1}{0.5 * 10 * 10}[/tex]
[tex]f(X,Y) = \frac{1}{50}[/tex]
[tex]Cov(X,Y)[/tex] is calculated as:
[tex]Cov(X,Y) = E(XY) - E(X) \cdot E(Y)[/tex]
Calculate E(XY)
[tex]E(XY) =\int\limits^X_0 {\int\limits^Y_0 {\frac{XY}{50}} \, dY} \, dX[/tex]
[tex]X + Y < 10[/tex]
Make Y the subject
[tex]Y < 10 - X[/tex]
So, we have:
[tex]E(XY) =\int\limits^{10}_0 {\int\limits^{10 - X}_0 {\frac{XY}{50}} \, dY} \, dX[/tex]
Rewrite as:
[tex]E(XY) =\frac{1}{50}\int\limits^{10}_0 {\int\limits^{10 - X}_0 {XY}} \, dY} \, dX[/tex]
Integrate Y
[tex]E(XY) =\frac{1}{50}\int\limits^{10}_0 {\frac{XY^2}{2}}} }|\limits^{10 - X}_0 \, dX[/tex]
Expand
[tex]E(XY) =\frac{1}{50}\int\limits^{10}_0 {\frac{X(10 - X)^2}{2} - \frac{X(0)^2}{2}}} }\ dX[/tex]
[tex]E(XY) =\frac{1}{50}\int\limits^{10}_0 {\frac{X(10 - X)^2}{2}}} }\ dX[/tex]
Rewrite as:
[tex]E(XY) =\frac{1}{100}\int\limits^{10}_0 X(10 - X)^2\ dX[/tex]
Expand
[tex]E(XY) =\frac{1}{100}\int\limits^{10}_0 X*(100 - 20X + X^2)\ dX[/tex]
[tex]E(XY) =\frac{1}{100}\int\limits^{10}_0 100X - 20X^2 + X^3\ dX[/tex]
Integrate
[tex]E(XY) =\frac{1}{100} [\frac{100X^2}{2} - \frac{20X^3}{3} + \frac{X^4}{4}]|\limits^{10}_0[/tex]
Expand
[tex]E(XY) =\frac{1}{100} ([\frac{100*10^2}{2} - \frac{20*10^3}{3} + \frac{10^4}{4}] - [\frac{100*0^2}{2} - \frac{20*0^3}{3} + \frac{0^4}{4}])[/tex]
[tex]E(XY) =\frac{1}{100} ([\frac{10000}{2} - \frac{20000}{3} + \frac{10000}{4}] - 0)[/tex]
[tex]E(XY) =\frac{1}{100} ([5000 - \frac{20000}{3} + 2500])[/tex]
[tex]E(XY) =50 - \frac{200}{3} + 25[/tex]
Take LCM
[tex]E(XY) = \frac{150-200+75}{3}[/tex]
[tex]E(XY) = \frac{25}{3}[/tex]
Calculate E(X)
[tex]E(X) =\int\limits^{10}_0 {\int\limits^{10 - X}_0 {\frac{X}{50}}} \, dY} \, dX[/tex]
Rewrite as:
[tex]E(X) =\frac{1}{50}\int\limits^{10}_0 {\int\limits^{10 - X}_0 {X}} \, dY} \, dX[/tex]
Integrate Y
[tex]E(X) =\frac{1}{50}\int\limits^{10}_0 { (X*Y)|\limits^{10 - X}_0 \, dX[/tex]
Expand
[tex]E(X) =\frac{1}{50}\int\limits^{10}_0 ( [X*(10 - X)] - [X * 0])\ dX[/tex]
[tex]E(X) =\frac{1}{50}\int\limits^{10}_0 ( [X*(10 - X)]\ dX[/tex]
[tex]E(X) =\frac{1}{50}\int\limits^{10}_0 10X - X^2\ dX[/tex]
Integrate
[tex]E(X) =\frac{1}{50}(5X^2 - \frac{1}{3}X^3)|\limits^{10}_0[/tex]
Expand
[tex]E(X) =\frac{1}{50}[(5*10^2 - \frac{1}{3}*10^3)-(5*0^2 - \frac{1}{3}*0^3)][/tex]
[tex]E(X) =\frac{1}{50}[5*100 - \frac{1}{3}*10^3][/tex]
[tex]E(X) =\frac{1}{50}[500 - \frac{1000}{3}][/tex]
[tex]E(X) = 10- \frac{20}{3}[/tex]
Take LCM
[tex]E(X) = \frac{30-20}{3}[/tex]
[tex]E(X) = \frac{10}{3}[/tex]
Calculate E(Y)
[tex]E(Y) =\int\limits^{10}_0 {\int\limits^{10 - X}_0 {\frac{Y}{50}}} \, dY} \, dX[/tex]
Rewrite as:
[tex]E(Y) =\frac{1}{50}\int\limits^{10}_0 {\int\limits^{10 - X}_0 {Y}} \, dY} \, dX[/tex]
Integrate Y
[tex]E(Y) =\frac{1}{50}\int\limits^{10}_0 { (\frac{Y^2}{2})|\limits^{10 - X}_0 \, dX[/tex]
Expand
[tex]E(Y) =\frac{1}{50}\int\limits^{10}_0 ( [\frac{(10 - X)^2}{2}] - [\frac{(0)^2}{2}])\ dX[/tex]
[tex]E(Y) =\frac{1}{50}\int\limits^{10}_0 ( [\frac{(10 - X)^2}{2}] )\ dX[/tex]
[tex]E(Y) =\frac{1}{50}\int\limits^{10}_0 [\frac{100 - 20X + X^2}{2}] \ dX[/tex]
Rewrite as:
[tex]E(Y) =\frac{1}{100}\int\limits^{10}_0 [100 - 20X + X^2] \ dX[/tex]
Integrate
[tex]E(Y) =\frac{1}{100}( [100X - 10X^2 + \frac{1}{3}X^3]|\limits^{10}_0)[/tex]
Expand
[tex]E(Y) =\frac{1}{100}( [100*10 - 10*10^2 + \frac{1}{3}*10^3] -[100*0 - 10*0^2 + \frac{1}{3}*0^3] )[/tex]
[tex]E(Y) =\frac{1}{100}[100*10 - 10*10^2 + \frac{1}{3}*10^3][/tex]
[tex]E(Y) =10 - 10 + \frac{1}{3}*10[/tex]
[tex]E(Y) =\frac{10}{3}[/tex]
Recall that:
[tex]Cov(X,Y) = E(XY) - E(X) \cdot E(Y)[/tex]
[tex]Cov(X,Y) = \frac{25}{3} - \frac{10}{3}*\frac{10}{3}[/tex]
[tex]Cov(X,Y) = \frac{25}{3} - \frac{100}{9}[/tex]
Take LCM
[tex]Cov(X,Y) = \frac{75- 100}{9}[/tex]
[tex]Cov(X,Y) = -\frac{ 25}{9}[/tex]
3. Find the length of X (in the picture) plssss I need help.
Answer:
imagine the upper triangle as the same as the lower one, but rotated by 180° around the corner point they share, and resized.
the base of the smaller triangle is resized by a factor of 3/4.5, or reduced: 1/1.5
we just take the length from the hypotenuse of the bigger triangle and resize it to, either by multiplying with 1/1.5 or by dividing by 1.5
personally, I find the latter easier.
x = 7.5/1.5 = 5
Find the missing length indicated
x = 65
Step-by-step explanation:
cos theta = 25/x
cos theta = x/169
25/x = x/169
x² = 169 x 25
x = 65
The missing length x = 65, using the Pythagoras Theorem.
What is the Pythagoras Theorem?
According to the Pythagoras Theorem, in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs.
How to solve the question?In the question, we are asked to find the value of x.
In the right triangle ABC, by Pythagoras' Theorem,
AC² + BC² = AB²,
or, x² + BC² = (144 + 25)²,
or, BC² = 169² - x² ... (i).
In the right triangle ACD, by Pythagoras Theorem,
AD² + DC² = AC²,
or, 25² + DC² = x²,
or, DC² = x² - 25² ... (ii).
In the right triangle BCD, by Pythagoras Theorem,
BD² + DC² = BC²,
or, 144² + x² - 25² = 169² - x² {Substituting BC² = 169² - x² from (i) and DC² = x² - 25² from (ii)},
or, x² + x² = 169² + 25² - 144² {Rearranging},
or, 2x² = 28561 + 625 - 20736,
or, 2x² = 8450,
or, x² = 4225,
or, x = √4225 = 65.
Thus, the missing length x = 65, using the Pythagoras Theorem.
Learn more about the Pythagoras Theorem at
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An American tourist visits South Africa with $3000. The exchange rate when she arrives is
$1 = 12.90. She changes all her dollars into rands and then spends R900 per day for seven
days. She changes the rands she has left back into dollars at a rate of $1 = R12.93. How much
does she get in dollars? show your working.
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Answer:
$2505.80
Step-by-step explanation:
After the first exchange, the tourist has ...
$3000(12.90 R/$) = R38,700
After 7 days, she has ...
R38,700 -7(R900) = R32,400
After the second exchange, she has ...
R32,400 × ($1/R12.93) = $2505.80
She gets $2505.80 at the second exchange.
A bus travels at a constant speed. The following table shows the distance the bus travels (in kilometers) over a period of
time (in hours):
distance (d) 42 252 378
time (9 0.5 3
4.5
a. Use complete sentences to describe the relationship represented in the table.
b. Write an equation using variables that represents the relationship shown in the table.
c. Use your equation to find how far the bus travels in 6 hours.
Answer:
question is not clear
specify the table
Line t has an equation of y = -8x + 7. Line u includes the point (-1, 7) and is parallel to line
t. What is the equation of line u?
Write the equation in slope-intercept form. Write the numbers in the equation as proper
fractions, improper fractions, or integers.
Use y=mx+b.
1
2 3 4
5.
12
Answer:
y = -8x - 1
Step-by-step explanation:
y = mx + b
7 = -8 (-1) + b Substitute in points for x and y. Substitute -8 for m (parallel)
7 = 8 + b
-1 = b
find the equation of the line perpendicular to the given line, through the given point x=-3; (1,8)
Answer:
y = 8
General Formulas and Concepts:
Algebra I
Coordinates (x, y)
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
Step 1: Define
Identify
[Line] x = -3
Point (1, 8)
Step 2: Find Perpendicular Line
A vertical line's slope is undefined.
The negative reciprocal of an undefined slope is 0.
Define perpendicular slope: m = 0Substitute in m [Slope-Intercept Form]: y = 0x + bSimplify: y = bGiven point (1, 8), our y-value is equal to 8.
∴ the perpendicular line is y = 8.
In a math class, there are 6 students with brown hair, 8 students with black hair, and 9 students with blonde hair? One student is selected at random. What is the sample space? *
Brown, black .
Black, blonde.
Brown, black, blonde.
Brown, blonde.
Explanation:
The sample space is simply the list of possible outcomes. We list all the hair colors possible in this class.
help? write down the answer with an explanation I give brainiest
so we'll go backwards.
emily ended with $6.00.
6×2 at the music store = $12
12×2 at the bakery = $24
24 × 2 at the grocery store = $48
she started with a total of $48.00
to check answer:
48 ÷ 2 = 24 at bakery
24 ÷ 2 = 12 at music
12 ÷ 2 =6 at lunch
PLS HELP ASAP!!!
THANK YOU.
9514 1404 393
Answer:
rectangular prism: 288 ft³triangular prism: 72 ft³total: 360 ft³Step-by-step explanation:
The volume of a rectangular prism is given by the formula ...
V = LWH . . . . . the product of length, width, height
This rectangular prism has a volume of ...
V = (12 ft)(6 ft)(4 ft) = 288 ft³ . . . . rectangular prism volume
__
The volume of a triangular prism is found from the formula ...
V = Bh
where B is the area of the triangular base, and h is the height of the prism (distance between the triangular bases). The triangular base area is found from ...
A = 1/2bh . . . . .where b is the base of the triangle, and h is its height.
Here, we have ...
B = 1/2(6 ft)(4 ft) = 12 ft²
V = Bh = (12 ft²)(6 ft) = 72 ft³ . . . . triangular prism volume
__
The total volume of the given geometry is the sum of the volumes of the parts:
aquarium volume = 288 ft³ +72 ft³ = 360 ft³
What is the domain and range of the relation [(1, -8), (-7,8), (-3, 7). (-3, -5]?
Step-by-step explanation:
domain = {-7, -3, 1}
range ={-8, -5, 7, 8}
Which is shown by the map
Answer:
A
Step-by-step explanation:
Answer: A
Step-by-step explanation: Different colours show different parts of africa and the general language spoken by individuals. From the map show, there are a lot of languages in Africa.
how do i simplify 81^5 = 3x
Step-by-step explanation:
81/5=3x
x=81×1/5×3
x=81/15
The time, t, required to drive a fixed distance varies inversely as the speed, r. It takes 2 hr at a speed of 15 km/h to drive a fixed distance. How long will it take to drive the same distance at a speed of 29 km/h?
The time taken to drive the same distance at a speed of 29km/h is
Answer:
1.03h
Step-by-step explanation:
S=vt
S= 15km/h*2h
S= 30km
Distance same, S=30km
v= 29km/h
t = 30/29
t = 1.03 h
Wayne is picking out some movies to rent, and he is primarily interested in dramas and horror films. He has narrowed down his selections to 7 dramas and 16 horror films. How many different combinations of 3 movies can he rent if he wants at least two dramas
Answer:
The number of selections is 49.
Step-by-step explanation:
drama = 7
horror films = 16
Select 3 movies at least two dramas
For 2 drama and 1 horror film
(3 C 2) x (16 C 1) = 48
For 3 drama
(3 C 3) = 1
So, total number of selections is 48 + 1 = 49.
I need help on this question
Which statement is true regarding the graphed functions?
Answer:
I am pretty sure that it's the second one
One card is selected from a deck of cards. Find the odds against drawing a 5
Please help kdkeoeieiei
Answer:
NEGATIVE
Step-by-step explanation:
Answer:
positive
Step-by-step explanation:
positive
can anyone help me in this questions
Answer:
Step-by-step explanation:
If I have 46 $ and the taxi cab charges 0.60$ plus 7$ fee how far can I ride
Answer:
65 miles
Step-by-step explanation:
costs = flat fee + cost per mile * miles
46 = 7+ .60m
Subtract 7 from each side
46-7 = 7+.6m-7
39 = .6m
Divide each side by .6
39/.6 = m
65 miles
Una librería consta de 5400 libros repartidos en 3 estanterías
En la estanteria A ahi el triple de libros que en la B y en la B la mitad que en la C calcular cuantos libros ahi en cada estanteria
Construir la ecuacion que plantea el problema
Answer:
B = 900 Libros
A = 2700 Libros
C = 1800 Libros
Step-by-step explanation:
A = 3B
2B = C
A + B + C = 5400
3B + B + 2B = 5400
6B = 5400
B = 5400 / 6
B = 900 Libros
A = 3B
A = 3(900)
A = 2700 Libros
C = 2B
C = 2(900)
C = 1800 Libros
What is 4+1 lets see how smart u sre
Answer:
its legit 5
Step-by-step explanation:
Answer:
Very tricky question..
4 + 1 is 5 because you have written 4+1 not 4 1
so 5 is correct answer
Step-by-step explanation:
hope it helps
Solve the inequality.
y-6 < -13
y< 19
O
y<7
y<-7
y < -19
Answer:
y < -7.
Step-by-step explanation:
y - 6 < -13
Add 6 to both sides:
y - 6 + 6 < -13 + 6
y < -7.
Use the tax table to help answer the following question.
If the wages are. And the number of withholding allowances dalmedish
0 1
But less
2 3 4 5 6 7 8 9 10+
At least
than
The amount of income tax withheld is
80
26
14
1
0
0
0
0
0
83
820
720
740
6244
740 760
47 28 16 3 0 0 0 0 0
760 780 86 68 50 31 18 5 o o o o o
780 800 89 71 53 34 20 . . . .
800
92 74 56 37 22 9 . a . o o
820 840 95 77 59 40 24 11 oo
840 860 98 80 62 43 26
Luce is single and making $763 biweekly. She claims no federal withholding
allowances. If the state tax is 19% of the federal tax, how much in state tax de
Luce contribute?
a.
$12.92
0
0
13
1
0
0
0
0
b.
$15.13
c.
$15.77
d.
$16.34
1
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Answer:
d. $16.34
Step-by-step explanation:
Luce's income of 763 is between 760 and 780, so the third row of the table applies. Her allowances are 0, so the first column applies, indicating her federal tax withholding is $86.
Her state tax withholding is 19% of that amount, so is ...
19% × $86 = $16.34 . . . . matches choice D
The amount in state tax that Lucy will contribute is D. $16.34.
How to calculate the tax?Tax simply means a compulsory levy that's paid to the government by individuals and organizations.
In this case, the tax amount that will be paid will be:
= 19% × $86
= $16.34
In conclusion, the correct option is $16.34.
Learn more about tax on:
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In rectangle ABCD shown below, CD = 24 and m angle ABD = 35º. Determine the length of diagonal line BD to the nearest tenth. Show the work that leads to your answer.
Answer:
BD = 29.3
Step-by-step explanation:
Each half of the rectangle is a right triangle.
The diagonal is the hypotenuse of each right triangle.
Let's focus on right triangle ABD
Reference angle = m<ABD = 35°
AB = CD = 24
Adjacent length = AB = 24
Diagonal = Hypotenuse = BD
To find BD, apply CAH:
Cos 35° = Adj/Hyp
Substitute
Cos 35° = 24/BD
BD × Cos 35° = 24
BD = 24/Cos 35°
BD = 29.3 (nearest tenth)
The exponential regression equation y=307.60(1.11)^x models the dollar value of a retirement fund after x years. Which is best estimate for the value of the retirement fund after 6 years, if no additional deposits or withdrawals are made. ?
A. $310
B. $580
C. $1,880
D. $2,050
Answer:
B. $580
Step-by-step explanation:
Value of the retirement fund after x years:
The value of the retirement fund after x years is given by the following function:
[tex]y(x) = 307.6(1.11)^x[/tex]
Which is best estimate for the value of the retirement fund after 6 years, if no additional deposits or withdrawals are made?
This is y(6). So
[tex]y(6) = 307.6(1.11)^6 = 575.34[/tex]
Close to $580, and thus, the correct answer is given by option B.
Answer:
B. $580 is best estimate for the value of the retirement fund after 6 years, if no additional deposits or withdrawals are made.
Thus it is little close to answer because actual answer is $575.34.
Byron is working in a lab testing bacteria populations. After starting out with a population of 288 bacteria, he observes the change in population and notices that the population triples every 16 minutes. Step 1 of 2 : Find the equation for the population P in terms of time t in minutes. Round values to three decimal places.
Answer:
[tex]P = 288 * 3^{(\frac{t}{16}) }[/tex]
Step-by-step explanation:
According to the Question,
Given that, Byron is working in a lab testing bacteria populations. After starting out with a population of 288 bacteria, he observes the change in population and notices that the population triples every 16 minutes.Therefore, the equation for the population P in terms of time t in minutes is[tex]P = 288 * 3^{(\frac{t}{16}) }[/tex] .
Which expression is equivalent to:
-(4a-4b)
-4a-4b
-8a+4b
-8ab
-4a+4b
Step-by-step explanation:
-4a+4b is equivalent to -(4a-4b).hope it helpsstay safe healthy and happy..