Answer:
(c) [tex]f_{X}(x)=\left \{ {{\frac{1}{35-25}=\frac{1}{10};\ 25<X<35} \atop {0;\ Otherwise}} \right.[/tex]
(b) The probability that time taken by Ayesha to prepare breakfast exceeds 33 minutes is 0.20.
(c) The probability that cooking or preparation time is within 2 mins of the mean time is 0.40.
Step-by-step explanation:
The random variable X follows a Uniform (25, 35).
(a)
The probability density function of an Uniform distribution is:
[tex]f_{X}(x)=\left \{ {{\frac{1}{B-A};\ A<X<B} \atop {0;\ Otherwise}} \right.[/tex]
Then the probability density function of the random variable X is:
[tex]f_{X}(x)=\left \{ {{\frac{1}{35-25}=\frac{1}{10};\ 25<X<35} \atop {0;\ Otherwise}} \right.[/tex]
(b)
Compute the value of P (X > 33) as follows:
[tex]P(X>33)=\int\limits^{35}_{33} {\frac{1}{10}} \, dx \\\\=\frac{1}{10}\cdot\int\limits^{35}_{33} {1} \, dx \\\\=\frac{1}{10}\times [x]^{35}_{33}\\\\=\frac{35-33}{10}\\\\=\frac{2}{10}\\\\=0.20[/tex]
Thus, the probability that time taken by Ayesha to prepare breakfast exceeds 33 minutes is 0.20.
(c)
Compute the mean of X as follows:
[tex]\mu=\frac{A+B}{2}=\frac{25+35}{2}=30[/tex]
Compute the probability that cooking or preparation time is within 2 mins of the mean time as follows:
[tex]P(30-2<X<30+2)=P(28<X<32)[/tex]
[tex]=\int\limits^{32}_{28} {\frac{1}{10}} \, dx \\\\=\frac{1}{10}\cdot\int\limits^{32}_{28}{1} \, dx \\\\=\frac{1}{10}\times [x]^{32}_{28}\\\\=\frac{32-28}{10}\\\\=\frac{4}{10}\\\\=0.40[/tex]
Thus, the probability that cooking or preparation time is within 2 mins of the mean time is 0.40.
Will give brainliest answer
Answer:
9π or 28.3 units²
Step-by-step explanation:
A = πr²
A = π(3)²
A = 9π
or
A= 28.3 units²
Hope this helps. :)
Two bond funds pay interest at rates that differ by 4%. Money invested for one year in the first fund earns $550 interest. The same amount invested in the other fund earns $770. Find the lower rate of interest. _________ %
Answer:
10% interest.
Step-by-step explanation:
Interest I = PRT/100
If the rate R = x% we have
550 = P*x *1 / 100
and
770 = P*(x + 4) * 1 / 100
so From first equation
Px = 55000 and from the second
Px + 4P = 77000
So Px = 77000 - 4P
Therefore 77000 - 4P = 55000
4P = 22000
P = 5,500
So x = 55000/5500 = 10%.
And the rate for the other fund is 10 + 4 = 14%.
What is the difference?
StartFraction x Over x squared + 3 x + 2 EndFraction minus StartFraction 1 Over (x + 2) (x + 1) EndFraction
StartFraction x minus 1 Over 6 x + 4 EndFraction
StartFraction negative 1 Over 4 x + 2 EndFraction
StartFraction 1 Over x + 2 EndFraction
StartFraction x minus 1 Over x squared + 3 x + 2 EndFraction
Answer:
The answer is option D.Step-by-step explanation:
First we must first find the LCM
The LCM of x² + 3x + 2 and (x + 2)(x + 1 ) is
x² + 3x + 2
So we have
[tex] \frac{x}{ {x}^{2} + 3x + 2 } - \frac{1}{(x + 2)(x + 1)} \\ \\ = \frac{x - 1}{ {x}^{2} + 3x + 2 } [/tex]
Hope this helps you
Answer:
The answer is OPTION D!
Step-by-step explanation:
HoPe ThIs HeLpS!
Basic kinematics. Please help! Will give brainliest! Show all work!
Answer: 3.5 m/s
Step-by-step explanation:
[tex]v=\frac{vf+vi}{2}[/tex]
[tex]v=\frac{5+2}{2}[/tex]
5+2=7
7/2= 3.5
E = { x l x is a perfect square <36}
Answer:
E = { x l x is a perfect square <36}
And we can rewrite it taking in count the list of all the perfect squares less than 36 and we have:
1= 1*1
4= 2*2
9 = 3*3
16 =4*4
25= 5*5
And we can rewrite the set on this way:
E= {1,4,9,16,25}
Step-by-step explanation:
For this problem we have the following set:
E = { x l x is a perfect square <36}
And we can rewrite it taking in count the list of all the perfect squares less than 36 and we have:
1= 1*1
4= 2*2
9 = 3*3
16 =4*4
25= 5*5
And we can rewrite the set on this way:
E= {1,4,9,16,25}
When plotting points on the coordinate plane below, which point would lie on the y-axis? A coordinate plane. (0, 1) (7, 0) (6, 8) (8, 2)
Answer:
Numbers 1,0,8,2 would lie on y-axis.
Step-by-step explanation:
This is because for example, (0,1)
we must prefer 0 as x-axis and 1 as y-axis. That's means left number or side will always be x-axis and right side will always be y-axis.
Answer: (0, 1)
Step-by-step explanation:
When the x is 0 is lies on the y axis.
PLEASE HELP ME!!!!!!!!!! What polygon is tesellated to form this image?
Answer:
Pentagon
Step-by-step explanation:
the head is the closest I see
15. A zoo is building a glass cylindrical tank
for the small sharks. The tank is 10 feet
high and has a diameter of 16 feet. How
much water is needed to fill the tank?
(The volume of a right circular cylinder is
V = Tr?h, where r is the radius, h is the
height, and a = 3.14.)
Answer:
2009.6
Step-by-step explanation:
As we know, volume of a right cylinder is πr²h.
here, diameter is mentioned, which gives that the radius is half of the diameter.
r= 1/2*16=8 feet
height= 10 feet
π=3.14
volume= 3.14*8²*10
= 3.14*64*10
=3.14*640
= 2009.6
so, that much water is needed to fill the tank
Answer:
2,010.6192982
Step-by-step explanation:
Please help me I will mark BRAINLIEST THANK YOUUUUU
Answer:
33%
Step-by-step explanation:
The multiples of 3 are 3,6,9,12
Sum is 6+14+12+1 = 33
The total is 3+6+8+11+14+16+15+12+9+5+1=100
The experimental probability is number of multiples of 3 over the total
33/100 = 33%
When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained. Do you support capital punishment? Number of individuals Yes 40 No 60 No Opinion 50 We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. The calculated value for the test statistic equals a. 20. b. 4. c. 2. d. -2.
Answer:
[tex]\chi^2 = \sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}[/tex]
The expected values for all the categories is :
[tex] E_i =\frac{150}{3}=50[/tex]
And then the statistic would be given by:
[tex]\chi^2 = \frac{(40-50)^2}{50}+\frac{(60-50)^2}{50}+\frac{(50-50)^2}{50}=4[/tex]
And the best option would be:
b. 4
Step-by-step explanation:
For this problem we have the following observed values:
Yes 40 No 60 No Opinion 50
And we want to test the following hypothesis:
Null hypothesis: All the opinions are uniformly distributed
Alternative hypothesis: Not All the opinions are uniformly distributed
And for this case the statistic would be given by:
[tex]\chi^2 = \sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}[/tex]
The expected values for all the categories is :
[tex] E_i =\frac{150}{3}=50[/tex]
And then the statistic would be given by:
[tex]\chi^2 = \frac{(40-50)^2}{50}+\frac{(60-50)^2}{50}+\frac{(50-50)^2}{50}=4[/tex]
And the best option would be:
b. 4
Find the mass and center of mass of the lamina that occupies the region D and has the given density function rho. D is the triangular region with vertices (0, 0), (2, 1), (0, 3); rho(x, y) = 2(x + y)
The mass of the lamina is 6 units.
The center of mass of the lamina is (X,Y) = (-3/2, 9/2).
Here,
To find the mass and center of mass of the lamina, we need to integrate the density function ρ(x, y) over the triangular region D.
The mass (M) of the lamina is given by the double integral of the density function over the region D:
M = ∬_D ρ(x, y) dA
where dA represents the differential area element.
The center of mass (X,Y) of the lamina can be calculated using the following formulas:
X = (1/M) ∬_D xρ(x, y) dA
Y = (1/M) ∬_D yρ(x, y) dA
Now, let's proceed with the calculations:
The triangular region D has vertices (0, 0), (2, 1), and (0, 3). We can define the limits of integration for x and y as follows:
0 ≤ x ≤ 2
0 ≤ y ≤ 3 - (3/2)x
Now, let's calculate the mass (M):
M = ∬_D ρ(x, y) dA
M = ∬_D 2(x + y) dA
We need to set up the double integral over the region D:
M = ∫[0 to 2] ∫[0 to 3 - (3/2)x] 2(x + y) dy dx
Now, integrate with respect to y first:
M = ∫[0 to 2] [x(y²/2 + y)] | [0 to 3 - (3/2)x] dx
M = ∫[0 to 2] [x((3 - (3/2)x)²/2 + (3 - (3/2)x))] dx
M = ∫[0 to 2] [(3x - (3/2)x²)²/2 + (3x - (3/2)x²)] dx
Now, integrate with respect to x:
[tex]M = [(x^3 - (1/2)x^4)^2/6 + (3/2)x^2 - (1/4)x^3)] | [0 to 2]\\M = [(2^3 - (1/2)(2^4))^2/6 + (3/2)(2^2) - (1/4)(2^3)] - [(0^3 - (1/2)(0^4))^2/6 + (3/2)(0^2) - (1/4)(0^3)]\\M = [(8 - 8)^2/6 + 6 - 0] - [0]\\M = 6[/tex]
So, the mass of the lamina is 6 units.
Next, let's calculate the center of mass (X,Y):
X = (1/M) ∬_D xρ(x, y) dA
X = (1/6) ∬_D x * 2(x + y) dA
We need to set up the double integral over the region D:
X = (1/6) ∫[0 to 2] ∫[0 to 3 - (3/2)x] x * 2(x + y) dy dx
Now, integrate with respect to y first:
X = (1/6) ∫[0 to 2] [x(y² + 2xy)] | [0 to 3 - (3/2)x] dx
X = (1/6) ∫[0 to 2] [x((3 - (3/2)x)² + 2x(3 - (3/2)x))] dx
X = (1/6) ∫[0 to 2] [x(9 - 9x + (9/4)x² + 6x - (3/2)x²)] dx
X = (1/6) ∫[0 to 2] [(9/4)x³ - (3/2)x⁴ + 15x - (3/2)x³] dx
Now, integrate with respect to x:
[tex]X = [(9/16)x^4 - (3/8)x^5 + (15/2)x^2 - (3/8)x^4] | [0 to 2]\\X = [(9/16)(2)^4 - (3/8)(2)^5 + (15/2)(2)^2 - (3/8)(2)^4] - [(9/16)(0)^4 - (3/8)(0)^5 + (15/2)(0)^2 - (3/8)(0)^4]\\X = [9/2 - 12 + 15 - 0] - [0]\\X = 15/2 - 12\\X = -3/2[/tex]
Next, let's calculate Y:
Y = (1/M) ∬_D yρ(x, y) dA
Y = (1/6) ∬_D y * 2(x + y) dA
We need to set up the double integral over the region D:
Y = (1/6) ∫[0 to 2] ∫[0 to 3 - (3/2)x] y * 2(x + y) dy dx
Now, integrate with respect to y first:
Y = (1/6) ∫[0 to 2] [(xy² + 2y²)] | [0 to 3 - (3/2)x] dx
Y = (1/6) ∫[0 to 2] [x((3 - (3/2)x)²) + 2((3 - (3/2)x)²)] dx
Y= (1/6) ∫[0 to 2] [x(9 - 9x + (9/4)x²) + 2(9 - 9x + (9/4)x²)] dx
Y = (1/6) ∫[0 to 2] [(9x - 9x² + (9/4)x³) + (18 - 18x + (9/2)x²)] dx
Now, integrate with respect to x:
[tex]Y= [(9/2)x^2 - 3x^3 + (9/16)x^4) + (18x - 9x^2 + (9/6)x^3)] | [0 to 2]\\Y = [(9/2)(2)^2 - 3(2)^3 + (9/16)(2)^4) + (18(2) - 9(2)^2 + (9/6)(2)^3)] - [(9/2)(0)^2 - 3(0)^3 + (9/16)(0)^4) + (18(0) - 9(0)^2 + (9/6)(0)^3)]\\Y = [18 - 24 + 9/2 + 36 - 36 + 12] - [0]\\Y= 9/2[/tex]
So, the center of mass of the lamina is (X,Y) = (-3/2, 9/2).
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the table shows the time it took a group of students to complete a puzzle
Answer:
Where is the table because I dont see it up here?
6x^2-2x=20 use ac method
Answer:
Cannot be factored
Step-by-step explanation:
Triangle L M N is shown. Angle L M N is a right angle. Angles N L M and L M N are 45 degrees. The length of L N is x. Which statements are true regarding triangle LMN? Check all that apply. NM = x NM = LM = x StartRoot 2 EndRoot tan(45°) = StartFraction StartRoot 2 EndRoot Over 2 EndFraction tan(45°) = 1
Answer:
A.) NM= x
C.) LM = x√2
E.) tan (45°) = 1
Step-by-step explanation:
If the legs are both x, then the hypotenuse is equal to [tex]x\sqrt{2[/tex]
Therefore, LM= [tex]x\sqrt{2[/tex] is correct and MN= x
Disclaimer: The sum is done according to the picture attached as the question given is wrong.
The true statements regarding the given isosceles right triangle ΔLMN are:
NM = xLM = x√2tan 45° = 1.What are isosceles right triangles?An isosceles triangle is a triangle where two sides and their corresponding angles are equal.
A right triangle is a triangle with one angle = 90°.
An isosceles right triangle is a right-angled triangle with two legs including the right angle are equal. Their corresponding angles are equal and each of them = 45°. So, the three angles of an isosceles right triangle are 45°, 45°, and 90°, always.
How do we solve the given question?In the figure, we can see that we have a ΔLMN, with ∠L = 45°, ∠M = 45°, and ∠N = 90°. Also, we can see that LN = x.
The given angles of ΔLMN determine that it is an isosceles right triangle with a right angle at N.
Since, the two legs involving the right angle, that is N, are equal, we can say that, NM = LN = x.
The hypotenuse of the ΔLMN, that is the side opposite to ∠N, that is LM, can be found using the Pythagoras theorem, by which in a right-angled triangle,
Hypotenuse² = Base² + Perpendicular².
∴ LM² = LN² + NM² = x² + x² = 2x².
or, LM = √(2x²) = x√2.
The tangent of an angle ∅, that is, tan ∅ is computed using the formula,
tan ∅ = Perpendicular/Base.
To calculate tan 45°, that is, tangent to ∠L, we take Perpendicular = NM and Base = LN.
∴ tan 45° = NM/LN = x/x = 1.
Now, we check all the given options:
NM = x. TRUE (computed)NM = x√2. FALSE (∵ NM = x)LM = x√2. TRUE (computed)tan 45° = √2/2. FALSE (∵ tan 45° = 1)tan 45° = 1. TRUE (computed)∴ The true statements regarding the given isosceles right triangle ΔLMN are:
NM = xLM = x√2tan 45° = 1.Learn more about isosceles right triangle at
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Use the properties of logarithms to prove log81000= log210.
Answer:
Step-by-step explanation:
Given the expression [tex]log_81000 = log_210[/tex], to prove this expression is true using the properties of logarithm, we will follow the following steps.
Starting from the Left Hand Side:
[tex]log_81000\\[/tex]= log₈ 10³= log_ 2^3 (10³)= log₂10Which expression is not requivalent to
3x - 2?
Answer:
anything that is not -2+3x or x=2/3 is wrong
Step-by-step explanation:
John is going for a walk. He walks for 6.4 miles at a speed of 2 miles per hour. For how many hours does he walk?
Answer:
t = d/s
t = 6.4 / 2 miles
t = 3.2 miles
Step-by-step explanation:
follow me plzzz
Help pls any kind soul pls help
Answer:
3x
Step-by-step explanation:
If Dan is x years old and Olly is 3 times as old, that means that Olly's age is 3 * x or 3x for short.
Answer:
3x
Step-by-step explanation:
If Dan is x years old and Olly is 3 times old as Dan, then the expression is 3x.
The larger of two numbers is 33 more than the smaller. When added together, the sum of the larger number and five times the smaller number is 129. What are the two numbers? larger number = ___ smaller number = ____ Please Help!
Step-by-step explanation:
let the larger number be x and smaller number be y
according to this question
x=y+33----------(1)
y+33+5y=129----------(2)
6y+33=129
y=16
x=16+33(takimg equation (1)
x=49
Answer:
Larger number: 49.
Smaller number: 16.
Step-by-step explanation:
Let's say that the larger number is represented by y, and the smaller is represented by x.
y = 33 + x
y + 5 * x = 129
(33 + x) + 5x = 129
6x + 33 = 129
6x = 96
x = 16
y = 33 + 16
y = 49
Check our work...
49 + 5 * 16 = 49 + 80 = 129
49 = 33 + 16 = 49
Since it all works out, the larger number is 49 and the smaller number is 16.
Hope this helps!
Any help would be greatly appreciated
Answer: (-3, -2)
Step-by-step explanation:
Plug in -2 for y to find x
x - 5(-2) = 7
Multiply -5 and -2
x + 10 = 7
Subtract 10 from both sides
x = -3
The first ordered pair is (-3, -2)
David and Tina share their profit in a ratio of 5:7. Tina gets £70 more than David. How much money did David receive?
Answer:
Amount of money David received = £ 175
Step-by-step explanation:
Both of them share their profit in a ratio of 5:7 . Tina got £70 more than David. Let
the amount David received = a
amount Tina received = 70 + a
the total profit = 70 + 2a
Amount David received = 5/12 × 70 + 2a = a
Therefore,
5/12 × 70 + 2a = a
350 + 10a/12 = a
cross multiply
350 + 10a = 12a
collect like terms
350 = 12a - 10a
350 = 2a
divide both sides by 2
a = 350/2
a = 175
Amount of money David received = £ 175
what is the answer for 8=22x+1
Answer:
x = 22/7Step-by-step explanation:
22x + 1 = 8
Send 1 to the right side of the equation
22x = 8 - 1
22x = 7
Divide both sides by 22
x = 7/22
Hope this helps you
Please answer this correctly
Answer:
12.5%
Step-by-step explanation:
There is only 1 seven card from the 8 total cards.
1 out of 8.
1/8 = 0.125
P(7) = 12.5%
Answer:
12.5%
Step-by-step explanation:
Total Cards = 8
Number 7 = 1
P(7) = 1/8
In %age:
=> 12.5%
please help pleaseeeeeeeee
━━━━━━━☆☆━━━━━━━
▹ Answer
#3. 1.89/100
▹ Step-by-Step Explanation
1.89 → hundreths place so..
1.89/100 is the correct answer
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Divide and answer in simplest form: 1/5 ÷ 7
Answer: 1/35
Step-by-step explanation:
1/5 = 0.2
0.2/7= 1/35
Answer:
[tex] \frac{1}{35} [/tex]Step by step explanation
[tex] \frac{1}{5} \div 7[/tex]
Dividing is equivalent to multiplying with the reciprocal:
[tex] \frac{1}{5} \times \frac{1}{7} [/tex]
Multiply the fraction
[tex] \frac{1 \times 1}{5 \times 7} [/tex]
[tex] = \frac{1}{35} [/tex]
Hope this helps...
Good luck on your assignment.
Find two paths of approach from which one can conclude that the function has no limit as (x, y) approaches (0, 0).
Answer:
for us to be able to ascertain whether a function has no limit we approach from two points which are from zero and infinity.
Step-by-step explanation:
the two best path to approach a function is to approach from zero and approach from infinity, literary what we are trying to do is approach from the smallest to the greatest and it each point we can conclude with certainty whether the function has a limit or not.
mohsin is writing a 2400 words essay for his school project he writes 1/5 of the essay on the first day 2/3 of the remainder on the second day 220 words on third day now he has to write the conclusion how long was his conclusion
Answer: 420 words
Step-by-step explanation:
First find how much he did the first day by doing 1/5*2400=480.
Then find out how much he did the second day by doing 2400-480=1920, then doing 1920*(2/3)=1280.
Then, because he did 220 words the third day, simply do 2400-480-1280-220=420.
Hope it helps <3
Ans420 words per min
Step-by-step explanation:
Less than 51% of workers got their job through networking. Express the null and alternative hypotheses in symbolic form for this claim (enter as a percentage). H0 : p H1 : p
Use the following codes to enter the following symbols:
≥≥ enter >=
≤≤ enter <=
≠≠ enter !=
Answer:
Null Hypothesis, [tex]H_0[/tex] : p [tex]\geq[/tex] 51%
Alternate Hypothesis, [tex]H_A[/tex] : p < 51%
Step-by-step explanation:
We are given that less than 51% of workers got their job through networking. We have to express the null and alternative hypotheses in symbolic form for this claim.
Let p = population proportion of workers who got their job through networking
So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\geq[/tex] 51%
Alternate Hypothesis, [tex]H_A[/tex] : p < 51%
Here, the null hypothesis states that greater than or equal to 51% of workers got their job through networking.
On the other hand, the alternate hypothesis states that less than 51% of workers got their job through networking.
Hence, this is the appropriate hypothesis that can be used.
Consider the two savings plans below. Compare the balances in each plan after 14 years. Which person deposited more money in the plan? Which of the two investment strategies is better? Yolanda deposits $100 per month in an account with an APR of 5%, while Zach deposits $1200 at the end of each year in an account with an APR of 5%.
Step-by-step explanation:
It is not specified the compounding period, which in general is a month these days. So we will assume money is compounded each month, otherwise there is no point depositing monthly.
1. Yolanda:
APR=5% is equivalent to
Monthly interest = 5%/12 = 5/12% = 5/1200 = 1/240 = i
Monthly deposit = 100 = A
Future value after 14 years = 14*12 months = 168 months = n
FV1 = A((1+i)^n-1)/i
=100*((1+1/240)^168-1)/(1/240)
= $24259.83
2. Zach
He deposits 1200 at the end of the year. The last payment does not benefit from interest.
Since it is a yearly payment, each amount earns interest over a year, giving an annual interest of
(1+i)^12 -1 = 1.051161897881733 -1 =0.051161897881733 = j
Thus for 13 annual payments with annual interest j gives a compounded amount after 14 years, plus the last payment which does not earn interest
FV2 = A((1+j)^n-1)/j
= 1200((1.051161897881733)^13-1)/(0.051161897881733)+1200
= 22613.34
Summary
Total investments:
Yolanda = 12*100*14 = 16800
Zach = 1200 * 14 = 16800
So both investors have invested $16800 over the 14 year period.
Since Yolanda achieves a higher future value after 14 years ($24259.83) over that of Zach ($22613.34), financially Yolanda has a better strategy.
Note:
If zach had invested annually at the beginning of the year, he would have obtained:
A((1+j)^n-1)/j
= 1200((1.051161897881733)^14-1)/(0.051161897881733)
= 24908.88
which is superior over Yolanda's return.
The double cone is intersected by a vertical plane passing through the point where the tips of the cones meet. What is the shape of the cross section formed? HELP PLEASE ITS FOR PLATO
Answer:
B.
Step-by-step explanation:
The double cone is a cone on top of another cone. The bottom cone has the circular base on the bottom and the tip on top. The upper cone is upside down, and the two tips touch. Since the vertical plane goes through the tips of both cones, the cross section must have a shape that gets to a point at the middle of the height.
Answer: B. One triangle with the tip on top and an inverted triangle above it with the tips touching.
Answer:
B.
Step-by-step explanation:
answer: B. one triangle tip on top and invert above it with the top touching