The solution of the expression is (55z + 6 ) / 20.
What is an expression?Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.
Given that the expression is 3/4(z+2/5)+2z. The expression will be solved as below,
E = 3/4(z+2/5)+2z
E = 3/4( z + 2 / 5 ) + 2z
E = 3/4 ( 5z + 2) / 5 + 2z
E = ( 15z + 6 + 40z ) /20
E = (55z + 6 ) / 20
Therefore, the solution of the expression is (55z + 6 ) / 20.
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Let X1, X1, ..., X64 be a i.i.d. random sample of size 64 from a distribution with probability density function: f(x) = 6x(1 − x), 0 < x < 1 Approximate P(0.45 < X <¯ 0.5). Hint: find µ and σ 2
Answer:
The approximate value of [tex]P(0.45<\bar X<0.50)[/tex] is 0.3686.
Step-by-step explanation:
The pdf of X is:
[tex]f(x) = 6x(1-x), 0 < x < 1[/tex]
Compute the mean as follows:
[tex]\mu=\int\limits^{1}_{0} {x\times 6x(1-x)} \, dx \\\\=\int\limits^{1}_{0} {6x^{2}-6x^{3}} \, dx\\\\=[\frac{6x^{3}}{3}]-[\frac{6x^{4}}{4}]|^{1}_{0}\\\\=2-\frac{3}{2}\\\\=0.50[/tex]
Compute the variance as follows:
[tex]\sigma^{2}=E(X^{2})-(\mu)^{2}[/tex]
[tex]E(X^{2})=\int\limits^{1}_{0} {x^{2}\times 6x(1-x)} \, dx \\\\=\int\limits^{1}_{0} {6x^{3}-6x^{4}} \, dx\\\\=[\frac{6x^{4}}{4}]-[\frac{6x^{5}}{5}]|^{1}_{0}\\\\=\frac{3}{2}-\frac{6}{5}\\\\=0.30[/tex]
[tex]\sigma^{2}=E(X^{2})-(\mu)^{2}\\\\\sigma=\sqrt{E(X^{2})-(\mu)^{2}}\\\\=\sqrt{0.30-(0.50)^{2}}\\\\=0.2236[/tex]
According to the Central Limit Theorem if an unknown population is selected with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from this population with replacement, then the distribution of the sample means will be approximately normally.
Then, the mean of the sample means is given by,
[tex]\mu_{\bar x}=\mu[/tex]
And the standard deviation of the sample means is given by,
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
The sample selected is of size n = 64 > 30. Thus a central limit theorem can be applied to approximate the sampling distribution of sample mean.
Compute the value of [tex]P(0.45<\bar X<0.50)[/tex] as follows:
[tex]P(0.45<\bar X<0.50)=P(\frac{0.45-0.50}{0.2236/\sqrt{64}}<\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{0.50-0.50}{0.2236/\sqrt{64}})[/tex]
[tex]=P(-1.12<Z<0)\\\\=P(Z<0)-P(Z<-1.12)\\\\=0.50-0.13136\\\\=0.36864\\\\\approx 0.3686[/tex]
Thus, the approximate value of [tex]P(0.45<\bar X<0.50)[/tex] is 0.3686.
Sophia has a lemon drink made by mixing 70ml of concentrate with 180ml of water. Tommy has a lemon drink made by mixing 90ml of concentrate with 270ml of water. Who has the strongest drink, sophia or Tommy. Show your working.
Answer: Tommy has More
Step-by-step explanation: just add and you hey who has the highest song trust me if not
Which of the following lists is ordered from least to greatest?
A. -4 1/2 , -1.6, -1, , 3.2
B. -4 1/2 , -1, -1.6, , 3.2
C. -4 1/2, -1, -1.6, 3.2, 3/4
D. -1, -1.6, -4 1/2 , 3/4 , 3.2
Answer:
the answer is a
Step-by-step explanation:
-4 1/2 is the least number, then negative 1.6, then negative 1, then a positive 3.2
Zarika earns the same amount each week by walking her neighbor's dogs. When she started this job, she had $300 in her savings account.
The table shows Zarika's savings account balance for her first month of work.
Week 0 1 2 3 4
Balance $300 $550 $800 $1050 $1300
Let x represent the number of weeks Zarika has been working and let y represent Zarika's account balance.
Which equation, expressed in Slope-Intercept Form, represents the amount of money in Zarika's bank account over time?
y=250x+300
y=300x+250
y=300x−250
y=250x−300
Answer
y=250x+300
Step-by-step explanation:
An athlete runs 8 miles in 50 minutes on a treadmill. At this rate: How long will it take the athlete to run 9 miles?
Answer:
56.25min or 56min and 15 sec
Step-by-step explanation:
First find how long it will take to run 1 mile, 6.25 mins, then multiply 6.25 by 9
Evaluate the expression when w=-
=-14, x=-10.7, and y=1.2
w-x+y
Х
?
A
Answer:
- 2.1
Step-by-step explanation:
Given
w - x + y ← substitute given values
= - 14 - (- 10.7) + 1.2
= - 14 + 10.7 + 1.2
= - 2.1
3.) Write your answer as an improper fraction.
Find the quotient.
.
5/4 divided by 1 1/12
Answer:
5/4=15/13=1
Step-by-step explanation:
hope that helps
I need help asap. Please help.
Answer:
kjhjbhjn h
Step-by-step explanation:
PLEASE HELP QUICK Which of these mappings is a function
Answer:
z
Step-by-step explanation:
bcause that what it is
The price of apples can be determined by the equation P=0.17n, where P is the price and n is the number of apples. What is the constant of proportionality (unit rate)?
Answer:
.17 is the constant of proportionality (unit rate).
Water is being drained from a container which has the shape of an inverted right circular cone. The container has a radius of 5.00 inches at the top and a height of 6.00 inches. At the instant when the water in the container is 4.00 inches deep, the surface level is falling at a rate of 0.7 in./sec. Find the rate at which water is being drained from the container.
The rate at which water is being drained from the container is;
dV/dt = 24.4 in³/s
I've attached an image showing this inverted cone with the corresponding letters to represent the height and radius.
We are given;
Radius of Cone; R = 5 inches
Height of cone; H = 6 inches
h = 4 inches
Height rate of change; dh/dt = 0.7 in/s
Looking at the image attached, we can use similar triangle property to derive the relationship;
r/R = h/H
Where r is the radius at the instant where dh/dt = 0.7 in/s
Thus;
r/5 = 4/6
r = (5 × 4)/6
r = 3.33 inches
Now, from r/R = h/H
We can write with initial values of cone and differentiate;
r/5 = h/6
6r = 5h
6(dr/dt) = 5(dh/dt)
Since dh/dt = 0.7 in/s
Thus;
dr/dt = (5/6) × 0.7
dr/dt = 0.5833
Volume of cone is given by;
V = ⅓πr²h
We can find the rate at which the rate at which water is being drained from the container using partial differentiation on the volume equation.
Thus;
dV/dt = ⅓π((2rh × dr/dt) + (r² × dh/dt))
Plugging in the relevant values, we have;
dV/dt = ⅓π((2 × 3.33 × 4 × 0.5833) + (3.33² × 0.7))
dV/dt = 24.4 in³/s
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1. Use synthetic division to find the quotient and the remainder. Label both answers.
(x4 - 2x + x + 5) + (x + 1)
Write is 8.517 in expanded form
Answer: (8 x 1) + (5/10) + (1/100) + (7/1000)
Step-by-step explanation: Have a blessed day hopefully this helped!
Answer:
8 tens, 5 tenths, 1 hundredth, 7 thousandths
Step-by-step explanation:
Hope I helped give brainliest if right :D
T'he dwarf sea horse swims at a rate of 53 feet per hour. Convert this speed to inches per minute.
Answer:
10.6
Step-by-step explanation:
divide the speed value by 5
Find the area of the figure shown below and choose the appropriate result.
4 cm
2 cm
5 cm
6 cm
A 34 cm2
B 44 cm
54 cm
D 46 cm
Answer:
the answer is D 46 cm
Step-by-step explanation:
first you need to find the missing side measurements cutting in two separate figures. if one side is 2 you know the other side is also 2 same with the 4 if the top is 4 the bottom is 4 too so now you have the measurements for the first figure now you finder the area applying the formula
A=bxh
A= 4*2=8
second figure you know that one part of the rectangle top is 5 and if you add the 4 of the first figure give you the measurement of the top
5+4=9 so if the top is 9 the bottom is also 9
finally to find the other side you know the side is 6 and since you know one part of the first figure is 2 you need to subtract 6-2=4
A=bxh
A=9*4=28
once you have both you can add it 28+8=46
A pound has 60 German Shepherds and 40 Great Danes of both sexes. If they breed with each other randomly, what is the probability that the puppies are: (i) pure breed German Shepherds, (ii) pure breed Great Danes, (iii) German Shepherd-Great Danes
Answer:
(i) pure breed German Shepherds,= 0.6
(ii) pure breed Great Danes,= 0.4
(iii) German Shepherd-Great Danes= 0.24
Step-by-step explanation:
The probability of success for the German shepherd is 60/100 0r 6/10 0r 0.6
The probability of failure for the German shepherd is 40/100 0r 4/10 0r 0.4
The probability of success for the Great Danes is 40/100 0r 4/10 0r 0.4
The probability of failure for the Great Danes is 60/100 0r 6/10 0r 0.6
The probability that it is a pure German shepherd is 60/100 0r 6/10 0r 0.6
The probability that it is a pure the Great Danes is 40/100 0r 4/10 0r 0.4
The probability that the puppies are: German Shepherd-Great Danes is given by since the events are independent
P (GS ∩ GD) = 0.6* 0.4= 0.24
HELP WILL GIVE BRANLIEST! Please give an explanation
It’s the fourth one all the fractions on 4 are equal to -2/3
11/8=k/4 what’s k?!!
11/2
Step-by-step explanation:
chloe is buying a mixed nuts at a grocery store. she can either spend $7.93 on a 15.25 ounce bag or 11.75 on a 25 ounce bag. which is a better buy?
Answer:
25 ounce bag
Step-by-step explanation:
The data in which table represents a linear function that has a slope of zero? X -5 -4 -3 -2 -1 у 5 5 5 5 5 w х 1 2 3 4 5 y -5 -4 -3 -2 -1 X -5 -4 -3 -2 y 5 4 3 2
Answer: the answer is choice b
Step-by-step explanation:
The data in the first table represents a linear function that has a slope of zero
Linear equation
A linear equation is in the form:
y = mx + b
where y, x are variables, m is the slope of the line and b is the y intercept.
Slope (m) = change in y / change in x
From the first table, using the point (-5, 5) and (-1, 5), hence:
Slope = (5 - 5)/(-1 - (-5)) = 0
The data in the first table represents a linear function that has a slope of zero
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The grades of an exam whose mean is 82 and whose standard deviation is 14 are normally distributed. Anyone who scores below 55 will be retested. What percentage does this represent
Answer:
This represents 2.6803%
Step-by-step explanation:
We start by calculating the z-score
Mathematically;
z-score = (x - mean)/SD
here our x is 55
mean = 82
SD = 14
z-score = (55-82)/14
z-score = -1.93
So the probability that a test taker will be retested will be;
P( x < -1.93)
We use the standard normal distribution table for this
P( x < -1.93) = 0.026803
If we convert this to percentage, we have 2.6803%
15% of $9 is $_________________.
Answer: $1.35
Step-by-step explanation:
4x+6y=48 where x is the number of cars of vans?
Answer:
-3/2 y+12
or 12- 3y/2
Step-by-step explanation:
the lines are the line for a fraction not dividing
Answer:
the x- intercept shows they can take 12 cars and 0 vans.
the y intercept shows they can take 0 cars and 8 vans.
Step-by-step explanation:
35 points! Find the slope between the two points:
(2, 5) and (-2, 5)
Answer:
The slope is 0, since it is a horizontal line
35 points omgggggggggggggggggg
Once a month, Eddie cashes his paycheck at a check cashing service that charges a 1% fee. If Eddie gets paid $500 per month, which of the following will be true?
Answer:
He should be paying $5 monthly.
Step-by-step explanation:
500*0.01=5, I think this was a question from flocabulary, next time, try to also add the answer choices.
The true statement is that the amount of money which Eddie would be charged for each monthly withdrawal is equal to $5.
What is a paycheck?A paycheck refers to a financial document issued to an employee by an employer, as payment for the work done over a specific period of time.
How to calculate the service charge.Since the interest on Eddie's monthly withdrawal is 1% (0.01), it simply means that the service charge would be calculated by multiplying his wages by the interest rate.
Service charge = 500 × 0.01
Service charge = $5.
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Find the solution to the system of equations.
You can use the interactive graph below to find the solution.
Y =-5x + 6
Y = 3x -2
X= ___
Y= ___
(Please be descriptive, and if possible graph both lines on a website and send a picture)
Answer:
5x6=y=−5
2x3=y=23
Step-by-step explanation:
i hope i helped im not very good at this stuff but i hope i helped-Sgee4
f (x) = 5x - 1, find f (4) - show work
Answer:
f(4) = 19
Step-by-step explanation:
Plug in 4 for x in the given equation:
f(x) = 5x - 1
f(4) = 5(4) - 1
Simplify. Remember to follow the order of operations, PEMDAS. First multiply, then subtract:
f(4) = (5 * 4) - 1
f(4) = 20 - 1
f(4) = 19
f(4) = 19 is your answer.
~
Which of the following is a true statement about proportional?
A. The graph of a proportional relationship is only a straight line.
B. The graph of a proportional relationship includes the origin.
C. Neither
Answer:
A
Step-by-step explanation:
TAMa dahil kung wala ang graph of a relationship ano pa ba?
Which number line can be used to find the distance between (-1,2) and (-5,2)
Answer:
The number line is y = 2.
Step-by-step explanation:
We are given the points (-1,2) , (-5,2) and we have to find the number line that can be used find the distance between them.
The y coordinate of the two points is
same (equal to 2) , so the number line that can be used to find the distance between them is y = 2.
Distance between the points = |-5+1| = 4
Study the Venn diagram.
A Venn diagram. A large box is labeled rational numbers. A box inside the rational numbers box is labeled integers. A box inside the integers box is labeled whole numbers.
Which statement is correct?
–5 cannot be written as a fraction, so it is not rational.
–5 is a rational number, but not an integer.
–5 is a counting number, so it is also a whole number.
–5 is an integer, but not a whole number.
5 is an integer, but not a whole number.
A Venn diagram is a widely sued diagram and shows a logical relationships within the sets.
As per the Venn diagram the large box is labeled by a rational number. The numbers are integers and the box and them are labeled by the while numbers. Hence 5 number is an integer, but not the whole number. Thus option D is correct.Learn more about the Study the Venn diagram.
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