Answer:
The correct answer is "0.3410, 0.4990".
Step-by-step explanation:
Given values are:
[tex]n=150[/tex]
[tex]p=\frac{63}{150}[/tex]
[tex]=0.42[/tex]
At 95% confidence interval,
C = 95%
z = 1.96
As we know,
⇒ [tex]E=z\sqrt{\frac{p(1-p)}{n} }[/tex]
By substituting the values, we get
[tex]=1.96\sqrt{\frac{0.42\times 0.58}{150} }[/tex]
[tex]=1.96\sqrt{\frac{0.2436}{150} }[/tex]
[tex]=0.0790[/tex]
hence,
The confidence interval will be:
= [tex]p \pm E[/tex]
= [tex]0.42 \pm 0.079[/tex]
= [tex](0.3410,0.4990)[/tex]
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]
Should I get my nose pierced??
Answer:
no...you can just use a clip on
Answer:
it's absolutely worth it. The pain of getting one isn't that bad, at least for me. It's just a quick pinch. It'll look so good. Just make sure you are also cleaning it.
Step-by-step explanation:
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..I need help on this question
The measures of the angles of the triangle are 32°, 53º,
950. Based on the side lengths, what are the measures
of each angle?
m2A = 95°, mZB = 53º, mZC = 32°
MZA= 32º, mzB = 53º, mZC = 95°
MZA= 43º, mZB = 32°, m2C = 95°
OmZA= 53º, m B = 95°, m2C = 32°
Answer:
m∠A = 32°
Step-by-step explanation:
8^2 = 12^2 + 15^2 - 2*12*15*cosA
Answer:
B
Step-by-step explanation:
did it on edge
Please help kdkeoeieiei
Answer:
NEGATIVE
Step-by-step explanation:
Answer:
positive
Step-by-step explanation:
positive
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)
put these numbers in order of size, smallest to largest 4.5,-1,-3,-3.5,3
Answer:
-3.5, -3, -1, 3, 4.5
Step-by-step explanation:
Answer:
-3.5, -3, -1, 3, 4.5 because the higher the negative is, the lower the number.
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.
Jerry borrow $35,00 for 3 years at 7 1/2% simple interest rate how much interest rate he have to pay
Answer:
787.50
Step-by-step explanation:
interest=principle*rate*time/100
interest=3500*7.5*3/100
interest=35*7.5*3
interest=787.50
Solve the system of equations by substitution:
3n + 5m = 7
m - 4n = 6
Answer:
m=2, n=-1 or (2,-1)
Step-by-step explanation:
Hi there!
We're given this system of equations:
3n+5m=7
m-4n=6
we want to solve by substitution; in one equation, we'll set one variable to equal an expression containing the other variable, substitute that expression as the variable into the other equation, solve for the variable substituted, and use the value of that variable to find the other variable
First, let's get the expression we'll substitute into the other
let's use m-4n=6 as it has 1m (m by itself)
add 4n to both sides
m=4n+6
now substitute 4n+6 as m into 3n+5m=7 to solve for n
3n+5(4n+6)=7
do the distributive property
3n+20n+30=7
combine like terms
23n+30=7
subtract 30 from both sides
23n=-23
divide both sides by 23
n=-1
we found the value of n
now let's substitute -1 as n in m=4n+6 to find the value of m
m=4(-1)+6
multiply
m=-4+6
add
m=2
so the answer is m=2, n=-1. As a point, it's (2,-1)
Hope this helps! :)
Pleeeeeeeese help me I will mark you as brainliest
[tex] \orange{\underline{\huge{\bold{\textit{\green{\bf{QUESTION}}}}}}} [/tex]
FIND THE NUMBER THAT MAKE EQUIVALENT FRACTION.
[tex] \huge\mathbb{\red A \pink{N}\purple{S} \blue{W} \orange{ER}}[/tex]
[tex] \red{solved} \\ \frac{4}{ \cancel{5}} = \frac{x}{ \cancel{40}^{ \: \: \: \tiny{8}} } \\ 8 \times 4 = x \\ 32 = x[/tex]
[tex] \blue{Part - 1} \\ \frac{4}{ \cancel{6}} = \frac{x}{ \cancel{24}^{ \: \: \: \tiny{4}} } \\ 4\times 4 = x \\ 16 = x[/tex]
[tex] \green{Part - 2} \\ \frac{1}{ 2} = \frac{6}{ x } \\ 6 \times 2 = x \\ 12 = x[/tex]
SOLVE LIKE THIS FOR ALL
PART - 3 --> 12
PART - 4--> 40
PART - 5 --> 6
PART - 6--> 4
PART - 7 --> 54
PART - 8 --> 12
PART - 9--> 36
PART - 10 --> 28
PART - 11--> 20
PART - 12 --> 28
PART - 13 --> 16
PART - 14 --> 20
PART - 15 --> 12
PART - 16 --> 6
PART - 17 --> 32
PART - 18--> 30
PART - 19 --> 27
PART - 20 --> 36
PLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ HELP MEEEEEEEEEEEEE OUTTTTTTTTTTTTTTTTTTTT I DO ANYTHING
Emma and Zeke own an on-line business, EZ Coasters, that sells cork beverage coasters, which can be bought plain or with logos. The price for both types of coasters is $3.00 each. There is also a one-time set-up charge of $25 for coasters with a logo.
1) Write an equation describing the relationship between:
a) The number of plain coasters bought and the cost of the coasters.
b) The number of coasters with a logo bought and the price of the coasters.
c) Is either coaster relationship proportional? Explain in writing how you know.
d) Explain what the unit rate of the line described by each equation means in the context of the coasters.
2) EZ Sales also sells plain natural sandstone coasters for $4.00 each.
a) Write the equation describing this relationship.
b) Indicate whether or not it is a proportional relationship and explain why?
c) Will the graph of this equation ever intersect the graph of the equations for either of the other two EZ Coasters? Explain in typing how you made your decision.
Answer:
6
Step-by-step explanation:
Answer:
Q1.
a. y = 3x + 0
b. y = 3x + 25
c. Plain is proportional because the y-intercept is zero.
d. It shows the cost of each coaster.
Q2
a. y = 4x + 0
b. It is proportional since the y-intercept is zero.
c. No the graph will never intersect because the equations in combination will result in parallel lines since there is a slight variation in the cost of EZ Coaters
What is the radius of a sphere with a volume of 11411 m ^3 to the nearest tenth of a meter
Answer:
r = 22.5
Step-by-step explanation:
[tex]V=\frac{4}{3} \pi r^{3}[/tex]
[tex]11411=\frac{4}{3} \pi r^{3}[/tex]
[tex]r^{3}=3(\frac{11411}{3})[/tex]
[tex]r^{3}=11411[/tex]
∛r³ = ∛11411
r = 22.5134076467
22.5134076467 rounded to the nearest tenth is 22.5
Answer:
its 14
Step-by-step explanation:
Gỉaỉ pt
2x^2×(2x^2+3)=2-x^2 ai giải giúp vs
2x²×(2x²+3)=2-x²
[tex]x = \frac{1}{2} , - \frac{1}{2} ,i \sqrt{2} , - i \sqrt{2} [/tex]
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.
9514 1404 393
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.
What is the period of the graph of y = 5 sin (πx) + 4?
Answer:
I think it’s 2 hope my answer was good have a nice day as well
Step-by-step explanation:
The period of the given function y = 5 sin (πx) + 4 is π.
We have given that,
y = 5 sin (πx) + 4
We have to determine the period
What is the period?
The period of the sine curve is the length of one cycle of the curve. The natural period of the sine curve is 2π.
Therefore the period of the given function is π.
To learn more about the period visit:
https://brainly.com/question/13753522
#SPJ2
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] .
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
https://brainly.com/question/231802
#SPJ2
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:
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.
One card is selected from a deck of cards. Find the odds against drawing a 5
Pls solve this question:
it is about Square and square roots
if u answer, then I will mark you as brilliant
Answer:
2.3
Step-by-step explanation:
A number when squarerooted squared will be come that number.
In formula terms, it is something like that:
[tex]\sqrt{x} X \sqrt{x} =x[/tex]
So…
[tex]\sqrt{2.3} X \sqrt{2.3} = 2.3[/tex]
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.
can anyone help me in this questions
Answer:
Step-by-step explanation:
Suppose that you have a square pyramid like the one pictured. Which plane section will produce a triangle?
Question 7 options:
A)
A cut parallel to the vertical axis, directly through the vertical axis
B)
A cross section cut parallel with the bottom
C)
A cut parallel to the vertical axis, but off the vertical axis
D)
Cutting off one of the bottom corners
18 = [(-2) + (-1)] =
6
(-24)
(-6)
giving out brainliest
Answer:
[tex]x = -6[/tex]
Step-by-step explanation:
[tex]18 = [(-2) + (-1)]x[/tex]
Required
Find x
Remove the inner brackets
[tex]18 = [-2-1]x[/tex]
[tex]18 = [-3]x[/tex]
Remove the square bracket
[tex]18 = -3x[/tex]
Divide both sides by -3
[tex]\frac{18}{-3} = x[/tex]
[tex]x = -6[/tex]
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}
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
9514 1404 393
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:
https://brainly.com/question/25783927
Find a mathematical model for the below statement. (Use k for the constant of proportionality.) The gravitational attraction F between two objects of masses m1 and m2 is jointly proportional to the masses and inversely proportional to the square of the distance r between the objects.
Answer:
[tex]F = k\frac{m_1m_2}{r^2}[/tex]
Step-by-step explanation:
Direct proportional:
Multiplication
Inverse proportional:
Division
The gravitational attraction F between two objects of masses m1 and m2 is jointly proportional to the masses
This means that:
[tex]F = k\frac{m_1m_2}{}[/tex]
Inversely proportional to the square of the distance r between the objects.
Denominator is [tex]r^2[/tex]. Thus:
[tex]F = k\frac{m_1m_2}{r^2}[/tex]