Answer:
f(x,y) = 5x⁴(2y³ +y ) 0<x<1 , 0<y<1 , 0 otherwise
Step-by-step explanation:
Given
F(x) = 5x⁴ for 0<x<1 and 0 otherwise
f(y)= 2y³ +y for 0<y<1 and 0 otherwise
the joint p.d.f is given by
f(x,y) = f(x) * f(y)= 5x⁴(2y³ +y ) 0<x<1 , 0<y<1 , 0 otherwise
The joint pdf is found by multiplying the marginal pdfs.
The two random variables are said to be statistically independent if the joint probability function can be expressed as the product of two marginal functions.
The heights of women aged 20 to 29 are approximately Normal with mean 64.3 inches and standard deviation 2.7 inches. Men the same age have mean height 69.9 inches with a standard deviation 3.1 inches. Describe in lay terms what information the z scores give that the original nonstandardized heights do not.
Answer:
In a lay term; The z-score gives us information concerning how many percentages of data lie between the given data interval. The z-score gives us an overview of the distance from the mean a data point is. In addition to that, it measures the degree of standard deviations below or above the population mean a raw score. We can place a z-score on a normal distribution curve.
Step-by-step explanation:
Given that:
Height of woman between age 20 -29 are approximately normal with:
population mean = 64.3 inches &;
standard deviation = 2.7
For men:
population mean = 69.9 inches
Standard deviation = 3.1 inches
In a lay term; The z-score gives us information concerning how many percentages of data lie between the given data interval. The z-score gives us an overview of the distance from the mean a data point is. In addition to that, it measures the degree of standard deviations below or above the population mean a raw score. We can place a z-score on a normal distribution curve.
Please help y < 5 inequality
Answer:
Step-by-step explanation:
F is directly proportional to a . If F = 42 when a = 7 find, F when a = 3
Answer:
24?
Step-by-step explanation:
A company plans to sell a new type of vacuum cleaner for $280 each. The company’s financial planner estimates that the cost, y, of manufacturing the vacuum cleaners is a quadratic function with a y-intercept of 11,000 and a vertex of (500, 24,000). Which system of equations can be used to determine how many vacuums must be sold for the company to make a profit?
StartLayout Enlarged Left-Brace 1st Row y = 280 x 2nd Row y = negative 0.052 (x minus 500) squared + 24,000 EndLayout
StartLayout Enlarged Left-Brace 1st Row y = 280 x 2nd Row y = 0.052 x squared + 11,000 EndLayout
StartLayout Enlarged Left-Brace 1st Row y = 280 x 2nd Row y = 0.052 (x minus 500) squared + 24,000 EndLayout
StartLayout Enlarged Left-Brace 1st Row y = 280 x 2nd Row y = negative 0.052 (x minus 500) squared + 11,000 EndLayout
Answer:
StartLayout Enlarged Left-Brace 1st Row y = 280 x 2nd Row y = negative 0.052 (x minus 500) squared + 24,000 EndLayout
Step-by-step explanation:
Given that:
Cost per cleaner = $280
The cost of x vacuum cleaners will be :
Cost per cleaner * number of cleaners
$280 * x
= $280x
The general vertex firm equation :
y-k = a(x-h)^2
Vertex = (500, 24000) ; Vertex = (h, k)
h = 500 ; k =24000 y= 11000, x = 0
y intercept = 11000
Plugging the values :
11000 - 24000 = a(0 - 500)^2
- 13000 = a(-500)^2
-13000 = a * 250000
a = - 13000 / 250000
a = - 0.052
Hence,
y - 24000 = a(0 - 500)^2
y = - 0.052(0 - 500)^2 + 24000
Answer:
A on edge
Step-by-step explanation:
i took the test
If you do not see a number next to a variable, what is it understood to be?
Math is hard.
Whats 9 + 10 = ????
Answer:
19
Step-by-step explanation:
im jumping off a bridge
Answer:
the answer in 19
Step-by-step explanation:
use Ur brain
Marla needs 115 square feet of tile to cover the floor of her
square sunroom. What is the length of one wall to the nearest
foot?
Answer:
11 feet
hope this helps
A personnel manager has found that, historically, the scores on aptitude tests given to applicants for entry-level positions follow a normal distribution with standard deviation 21.73 points. A random sample of 14 test scores from the current group of applicants had a mean score of 74.57 points. Based on these sample results, a statistician found for the population mean a confidence interval extending from 65.7425 to 83.3975 points. Find the confidence level of this interval. Round off your answer to two decimal places.
Answer:
The value is [tex]C = 85\%[/tex]
Step-by-step explanation:
From the question we are told that
The standard deviation is [tex]\sigma = 21.73[/tex]
The sample size is n = 14
The mean score is [tex]\= x = 74.57[/tex]
The confidence interval is 65.7425 to 83.3975
Generally the degree of freedom is mathematically represented as
[tex]df = n -1[/tex]
=> [tex]df = 14 -1[/tex]
=> [tex]df = 13[/tex]
Generally the margin of error is mathematically evaluated as
[tex]E = \frac{83.3975 -65.7425 }{2}[/tex]
=> [tex]E = 8.828[/tex]
Generally this margin of error is mathematically represented as
[tex]E = t_{\frac{\alpha }{2} , df} * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]8.828 = t_{\frac{\alpha }{2} , df} * \frac{21.73 }{\sqrt{14} }[/tex]
=> [tex]t_{\frac{\alpha }{2} , df} = 1.520[/tex]
From the t distribution table the probability of [tex]( t> 1.520 )[/tex] at a degree of freedom of 13 is
[tex]\frac{\alpha }{2} = P( t > 1.52 ) = 0.076[/tex]
=> [tex]\alpha = 2 * 0.076[/tex]
=> [tex]\alpha = 1.52[/tex]
So the confidence level is evaluated as
[tex]C = 1- \alpha[/tex]
=> [tex]C = 1- 0.152[/tex]
=> [tex]C = 0.85[/tex]
Converting to percentage
=> [tex]C = 0.85 * 100[/tex]
=> [tex]C = 85\%[/tex]
17. The sum of three consecutive integers is three times the second integer.
Show that this is true for the three consecutive integers 7, 8, and 9.
I
twork being lat
Set up an equation that models this statement.
Show, by solving the equation, that this equation will always be true for any three consecutive integers.
Answer:
By using Carl Gauss's clever formula, (n / 2)(first number + last number) = sum, where n is the number of integers, we learned how to add consecutive numbers quickly. We now know that the sum of the pairs in consecutive numbers starting with the first and last numbers is equal.
Step-by-step explanation:
Answer:
Step-by-step explanation:
7+8+9=24.
8 is the second integer and 8*3=24.
Which decimal is the best best estimate of the fraction 29/40
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Answer:
C
Step-by-step explanation:
I hope this helps!!!!
The best estimate of the fraction 29/40 would be; 0.7
How can we interpret the division?When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get. Division can be interpreted as equally dividing the number that is being divided into total x parts, where x is the number of parts the given number is divided.
We need to find the decimal that best best estimate of the fraction 29/40
A negative divided by a negative is positive, then;
29/40 = 0.72
Therefore, The best estimate of the fraction 29/40 would be; 0.7
Learn more about division here:
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Katie Perry is standing 30 feet away from the entrance to a store. She sees Taylor Swift walk out of the store, and Katie keeps walking away from her at speed of 4 feet each second. Write an equation that represents Katie's distance from the store's entrance.
PLEASE HELP MEMEMEMEME
Answer:
y=4x+30
Step-by-step explanation:
y is distance, x is time
5 4/5-3 1/3,whoever can help I will mark brainleist
Answer:
[tex] \huge{ \boxed{ \bold{ \tt{2 \: \frac{7}{15} }}}}[/tex]
Step-by-step explanation:
[tex] \tt{5 \frac{4}{5} - 3 \frac{1}{3} }[/tex]
Convert the mixed number into improper fraction
[tex] \tt{↦ \: \frac{5 \times 5 + 4}{5} - \frac{3 \times 3 + 1}{3} }[/tex]
[tex] \tt{↦ \: \frac{25 + 4}{5} - \frac{9 + 1}{3}} [/tex]
[tex] \tt{ ↦ \: \frac{29}{5} - \frac{10}{3} }[/tex]
While performing the addition or subtraction of unlike fractions , you have to express the given fractions into equivalent fractions of common denominator and add or subtract as we do with like fractions. Thus, obtained fractions should be reduced into lowest terms if there are any common on numerator and denominator. But in case of improper fraction, it needs to be deduced on mixed fraction. Now,
Take the L.C.M of 5 and 3
prime factors of 5 = 1 × 5
prime factors of 3 = 1 × 3
L.C.M = Common factors × Remaining factors
= 1 × 5 × 3
= 15
[tex] \tt{↦ \frac{29 \times (15 \div 5)}{15} - \frac{10 \times (15 \div 3)}{15} }[/tex]
[tex] \tt{↦ \: \frac{29 \times 3}{15} - \frac{10 \times \: 3 }{15} }[/tex]
[tex] \tt{↦ \: \frac{87}{15} - \frac{30}{15}} [/tex]
While performing the addition or subtraction of like fractions , you just have to add or subtract the numerator respectively in which the denominator is retained same.
[tex] \tt{ ↦ \: \frac{87 - 30}{15} }[/tex]
[tex] \tt{↦ \: \frac{37}{15} }[/tex]
Convert the improper fraction into mixed fraction.
[tex] \tt{↦ \boxed{ \tt{ 2 \frac{7}{15} }}}[/tex]
And we're done!
Hope I helped!
Best regards! :D
~[tex] \text{TheAnimeGirl}[/tex]
After knee surgery, your trainer tells you to return to your jogging program slowly. He suggests jogging for 12 minutes each day for the first week. Each week thereafter, he suggests that you increase that time by 6 minutes per day. How many weeks will it be before you are up to jogging 60 minutes per day?
Answer:
8 weeks
Step-by-step explanation:
1. Write out the equation
12+6x=60
2. Subtract 12 from both sides
6x = 48
isolate the variable (divide 6 on both sides)
x= 8
The region bounded by y = − 1x^2 + 3x + 18 , x = 0 and y = 0 is rotated about the y -axis. Find the volume of this solid of revolution:
Answer:
The volume of the solid V = 41601.6 π
Step-by-step explanation:
From the given information:
The volume of the shaded region bounded by rotating the shaded region about the y-axis is: dV
[tex]dV = \pi (-1x^2 +3x+18)^2 ((x+dx)^2 -(x)^2)[/tex]
[tex]dV =2 \pi x (-1x^2 +3x+18)^2 \ . dx[/tex]
[tex]dV =2 \pi x (-1x^2 +3x+18) ( -1x^2 +3x + 18). dx[/tex]
[tex]dV =2 \pi x (1x^4 -3x^3 -18x^2 -3x^3 +9x^2 +54x -18x^2 +54x + 324 ) \ .dx[/tex]
[tex]dV =2 \pi x (1x^4 -3x^3-3x^3 -18x^2 +9x^2 -18x^2 +54x +54x +324) \ .dx[/tex]
[tex]dV =2 \pi x (1x^4 -6x^3 -27x^2 +9x^2+ 108x +324) \ .dx[/tex]
[tex]\implies \int ^V_o \ dv = 2 \pi \int ^6_0 (1x^5 -6x^4 -27x^3+108x^2 +324x) \ dx[/tex]
[tex]V = 2 \pi \begin {bmatrix} \dfrac{1x^6}{6} - \dfrac{6x^6}{5} - \dfrac{27x^4}{4}+ \dfrac{108x^3}{3}+ \dfrac{324x^2}{2} \end {bmatrix}^6_0[/tex]
[tex]V = 2 \pi \begin {bmatrix} \dfrac{1(6)^6}{6} - \dfrac{6(6)^6}{5} - \dfrac{27(6)^4}{4}+ \dfrac{108(6)^3}{3}+ \dfrac{324(6)^2}{2} -0\end {bmatrix}[/tex]
V = 2π (20800.8)
V = 41601.6 π
Coach Manzer ran 6 laps in 360 seconds. Which of the following is an equivalent ratio?
Group of answer choices
1 lap in 30 seconds
2 laps in 120 seconds
4 laps in 300 seconds
14 laps in 1400 seconds
Answer:
2 laps in 120 seconds is correct
3(4x - 6) - 2x + 1 = 3 - (3x - 6)?
Convert the following degree measure to radians and round to the nearest thousandth:
72.5° = ? π radians
Answer:
0.403 π rad
or
1.265 rad
Hope this helps! I used both variations just to be safe but it seems you only need the one with Pi in it.
Determine the values of m, a, p, q and r.
Answer:
m= 68 degrees
a= 68 degrees
p= 68 degrees
q= 112 degrees
r= 68 degrees
Step-by-step explanation:
Hope this helps, if so mark me brainliest???
Who started with the greatest initial value of Halloween candy? Jeremy, Josh, Rachel, or Lydia?
Answer: Rachael Ray.
Step-by-step explanation: Have a blessed day hopefully this helped!
TIME REMAINING
54:32
Tom would like to take out a secured loan to help pay for a vacation this summer. He has offered his car as collateral.
His car is worth $3,500. His bank can offer loans for 80% of collateral value. The vacation he has planned will cost
$4,750. Approximately how much additional collateral will Tom need to offer in order to borrow enough to go on his
vacation as planned?
$1,000.00
b. $1,362.50
c. $2,437.50
d. $2,800.00
a.
Please select the best answer from the choices provided
A
B.
ОООО
D
Tom will need to offer additional collateral of C. $2,437.50 to borrow enough for his planned vacation.
What is collateral?Collateral refers to a valued property or financial security offered by the borrower to the lender to guarantee repayment of a loan.
Lenders sell collaterals when the borrowers fail to comply with their loan terms.
How is the additional collateral determined?Car's value = $3,500
Collateral value in percentage = 80%
Car's collateral value = $2,800 ($3,500 x 80%)
Planned cost of vacation = $4,750
Additional cost to meet vacation cost = $1,950 ($4,750 - $2,800)
Additional collateral value to meet target = $2,437.50 ($1,950/80%)
Total collateral that Tom needs to offer = $5,937.50 ($3,500 + $2,437.50)
80% of $5,937.50 = $4,750
Another way is to work with the planned cost and the collateral percentage offered by Tom's bank:
Planned cost of vacation = $4,750
Collateral value in percentage = 80%
Total collateral to be offered by Tom = $5,937.50 ($4,750/80%)
Car's collateral value = $3,500
Additional collateral value = $2,437.50 ($5,937.50 - $3,500)
Thus, Tom needs additional collateral of C. $2,437.50.
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How many oz. of mixed nuts that contain
30% peanuts must Abhasra add to 6.9 oz.
of mixed nuts that contain 20% peanuts to
make a mixture with 27% peanuts?
Answer:
77
Step-by-step explanation:
P(t) model the number of people at the beach
in Rio de Janeiro, Brazil, when it's t hours after
midnight on a certain day. When did the
number of people increase faster? *
Answer:
A, Between 9 and 10 am
Step-by-step explanation:
The math is simple. between 9 and 10 theres 1 hour, and between 28 and 67 there are 39 P(t).
Between 10 and 15 there are 5 hours, and between 67 and 212 there are 145 P(t), which divided by 5 is 29.
You divide by 5 to get the same amount of hours to compare both
9-10 am= 39
10-15am/pm= 29
Therefore, the number of people increased faster between 9 and 10 am.
The rate of increase of population is faster between t = 9 to t = 10.
What is the ratio of two numbers?The ratio of two numbers a and b can be written as a : b = a/b.
The ratio of two quantities is the unit rate of one quantity with respect to the other.
The table for the population and time can be formed as follows,
Population Time in hours
28 9
67 10
212 15
Now, the increase in population can be obtained by taking the ratios as follows,
Increase in population between t = 9 to t = 10 is given as,
(67 - 28) ÷ (10 - 9)
⇒ 39
And, between t = 10 to t = 15, it is given as,
(212 - 67) ÷ (15 - 10)
⇒ 145 ÷ 5 = 29
Thus, the rate of increase is more from t = 9 to t = 10.
Hence, the faster increase is given in time interval of t = 9 to t = 10.
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factor 49x^2-7^2
and please explain how
Answer:
[tex]49x^2-7^2=49(x-1)(x+1)[/tex]
Step-by-step explanation:
Factoring
We need to recall this property of binomials:
[tex](a-b)(a+b)= a^2-b^2[/tex]
It allows us to factor the difference between two squares as follows.
[tex]a^2-b^2=(a-b)(a+b)[/tex]
The given expression is
[tex]49x^2-7^2[/tex]
Comparing with the above expression:
[tex]a^2=49x^2[/tex]
Taking square root:
[tex]a = 7x[/tex]
[tex]b^2=7^2[/tex]
Taking square root:
b=7
Factoring:
[tex]49x^2-7^2=(7x-7)(7x+7)[/tex]
Now we can see each factor can be taken out the common factor 7:
[tex]49x^2-7^2=7(x-1)*7(x+1)[/tex]
Multiplying:
[tex]\boxed{49x^2-7^2=49(x-1)(x+1)}[/tex]
This is hard I’d love help
can someone help me plz
28 PLEASE GIVE BRAINLIEST
An angle is 6 more than five times it’s supplement. What is the measure of the smaller angle
solve for x SOMEONE PLS!
71+49+7x+11=180
12x+5??????????????pls help
Answer:
17
Step-by-step explanation:
How can you solve an equation with a variable on both sides? Complete the explanation.
You can solve the equation by using ____ operations to get the variable terms on one side of the equal sign and the constant terms on the ____ side. Then ____ both sides by the
coefficient of the resulting variable term.
Answer:
order of operations, right?, divide
Step-by-step explanation:
sorry if this is wrong :)
The GCF of 35 and 50 is
Answer: The greatest common factor of the two is 5.
Step-by-step explanation:
The greatest common factor is something that can be seen between the two as relation.
