Step-by-step explanation:
If a fraction [tex]f(x)[/tex] is defined as
[tex]f(x) = \dfrac{g(x)}{h(x)}[/tex]
then the derivative [tex]f'(x)[/tex] is given by
[tex]f'(x) = \dfrac{g'(x)h(x) - g(x)h'(x)}{h^2(x)}[/tex]
So the derivative can be calculated as follows:
[tex]f'(x) = \dfrac{d}{dx}\left(\dfrac{4x^3 - 7x + 8}{x} \right)[/tex]
[tex]=\dfrac{(12x^2 - 7)x - (4x^3 - 7x + 8)}{x^2}[/tex]
[tex]= \dfrac{12x^3 - 7x - 4x^3 + 7x - 8}{x^2}[/tex]
[tex]= \dfrac{8x^3 - 8}{x^2}[/tex]
The number of hurricanes that will hit a certain house in the next ten years is Poisson distributed with mean 4. Each hurricane results in a loss that is exponentially distributed with mean 1000. Losses are mutually independent and independent of the number of hurricanes. Calculate
Answer:
The variance of total loss is 8000000
Step-by-step explanation:
Let
[tex]X \to[/tex] Number of hurricane
Poisson [tex]E(X) = 4[/tex]
[tex]Y \to[/tex] Loss in each hurricane
Exponential [tex]E(Y) = 1000[/tex]
[tex]T \to[/tex] Total Loss
Required
The variance of the total loss
This is calculated as:
[tex]Var(T) = Var(E(T|X)) + E(Var(T|X))[/tex]
Where:
[tex]E(T|X) \to[/tex] Expected total loss given X hurricanes
And it is calculated as:
[tex]E(T|X) = E(Y) *N[/tex] --- Expected Loss in each hurricane * number of loss
[tex]Var(T|X) \to[/tex] Variance of total loss given X hurricanes
And it is calculated as:
[tex]Var(T|X) = Var(Y) * N[/tex] ---- --- Variance of loss in each hurricane * number of loss
So, we have:
[tex]Var(T) = Var(E(T|X)) + E(Var(T|X))[/tex]
[tex]Var(T) = Var(E(Y) * N) + E(Var(Y) * N)[/tex]
For exponential distribution;
[tex]Var(Y) = E(Y)^2[/tex]
So, we have:
[tex]Var(T) = Var(E(Y) * X) + E(E(Y)^2 * X)[/tex]
Substitute values
[tex]Var(T) = Var(1000 * X) + E(1000^2 * X)[/tex]
Simplify:
[tex]Var(T) = Var(1000 * X) + 1000^2E(X)[/tex]
Using variance formula, we have:
[tex]Var(T) = 1000^2Var(X) + 1000^2E(X)[/tex]
For poission distribution:
[tex]Var(X) = E(X)[/tex]
So, we have:
[tex]Var(X) = E(X) = 4[/tex]
The expression becomes:
[tex]Var(T) = 1000^2*4 + 1000^2*4[/tex]
[tex]Var(T) = 1000000*4 + 1000000*4[/tex]
[tex]Var(T) = 4000000 + 4000000[/tex]
[tex]Var(T) = 8000000[/tex]
How to find B?
what type of angle is it?
Answer:
Obtuse angle; 57°
Step-by-step explanation:
b and 43° form a right angle. A right angle is 90°. Solution: 90°-43°=57°
43° is acute, so angle b must be obtuse.
Số táo của An Bình Chi là như nhau. An cho đi 17 quả, Chi cho đi 19 quả thì lúc đó số táo của Chi gấp 5 lần tổng số táo của An và Bình. Hỏi lúc đầu mỗi bạn có bao nhiêu quả táo?( Giải bài toán trên bằng phương trình hoặc hệ phương trình )
Answer:
please write in english i cannot understand
Step-by-step explanation:
Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 5?
Select one:
a. 420
4
20
b. 320
3
20
c. 520
5
20
d. 120
1
20
Answer:
4 / 20 = 1/5
Step-by-step explanation:
Given that:
Ticket numbering is from 1 - 20
Hence, total possible number of tickets : (1, 2, 3, 4, 5, 6, 7, 8,9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20)
Total possible outcomes = 20
Required outcome = multiples of 5 ; the multiples of 5 from the entire ticket numbers are : 5, 10, 15, 20
Required outcome = 4
P(multiple of 5) = Required outcome / Total possible outcomes
P(multiple of 5) = 4 / 20 = 1 / 5
Which system of equations below has no solution
Answer:
Step-by-step explanation:
y= 4x + 5
y = 4x - 5
4x + 5 = 4x - 5
0 ≠ -10
no solution
Determine which diagram could be used to prove triangle ABC is congruent to triangle EDC using similarity transformations
Answer:
A
Step-by-step explanation:
edge 2021
Question 2
A force F=5i+3j-2k is applied to move a block of cement from A(0,1,1) to B(4.-1,3).
Determine the work done by the force.
The work is simply the dot product of the force and displacement (which I assume are given in Newtons and meters, respectively):
W = F • d
W = (5i + 3j - 2k) N • ((4i - j + 3k) m - (j + k) m)
W = (5i + 3j - 2k) • (4i - 2j + 2k) Nm
W = (20 - 6 - 4) Nm
W = 10 J
Based on the following construction which statement below must NOT be true?
Answer:
I think C, sorry if I am wrong
Which expression is equivalent to (6x5z)3/4x4z2?
Hello!
(6x⁵z)³/4x⁴z² =
= 216x¹⁵z³/4x⁴z² =
= 54x¹¹z
Good luck! :)
please answer
Find the area of the polygon.
6 cm6 cm10 cm
Answer:
Area: 360 cm
Perimeter: 44 cm
Step-by-step explanation:
To calculate the area, you must multiply the length x width.
If you need help calculating the perimeter too, just add all your lengths and widths together twice.
Question 1
Assume that a procedure yields a binomial distribution.
n = 48 p = 0.44. Find the mean.
Answer:
The mean is 21.12.
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
In this question:
[tex]n = 48, p = 0.44[/tex]
Mean:
[tex]E(X) = np = 48(0.44) = 21.12[/tex]
The mean is 21.12.
if an orange weighs 570 grams what is the weight of an apple
Answer:
THE SAME
Step-by-step explanation:
2.6.67
Two cylindrical cans of soup sell for the same price. One can has a diameter of 6 inches and a height of 7 inches. The other has a diameter of 7 inches and a height
of 6 inches. Which can contains more soup and, therefore, is the better buy?
Which can contains more soup and therefore, is the better buy?
Please help :)
Answer:
second can
Step-by-step explanation:
The radius is half of the diameter.
The radius is squared in the formula for the volume of the cylinder.
A diameter of 7 and height of 6 will make a larger can than a diameter of 6 and height of 7.
The vertical test line
Step-by-step explanation:
The vertical line test is a graphical method of determining whether a curve in the plane represents the graph of a function by visually examining the number of intersections of the curve with vertical lines. and, as a result, any vertical line in the plane can intersect the graph of a function at most once.hope it helpsstay safe healthy and happy....Answer:
It is a graphical method
A pizza dough recipe calls for 6 1/2 cups of flour. The recipe makes 37 1/2 ounces of dough. How many ounces of dough does 1 cup of flour make?
Answer:
[tex]n = 5\frac{10}{13}[/tex]
Step-by-step explanation:
Given
[tex]Call = 6\frac{1}{2}[/tex] cups
[tex]Recipe = 37\frac{1}{2}[/tex] ounce
Required
Number of ounces per cup (n)
To do this, we simply divide the Recipe by the call
So, we have:
[tex]n = \frac{Recipe}{Call}[/tex]
[tex]n = 37\frac{1}{2} \div 6\frac{1}{2}[/tex]
Express as improper fraction
[tex]n = \frac{75}{2} \div \frac{13}{2}[/tex]
Rewrite as:
[tex]n = \frac{75}{2} * \frac{2}{13}[/tex]
[tex]n = \frac{75}{13}[/tex]
[tex]n = 5\frac{10}{13}[/tex]
The graph shows the solution of the following system of equations. y = –5∕3x + 3 y = 1∕3x – 3
Answer:
So whats your question ??
Step-by-step explanation:
11 Emilio makes metal fences.
He is making a fence using this design.
1.44 m
DO NOT WRITE IN THIS AREA
1.8 m
.
The fence will need
3 horizontal metal pieces of length 1.8m
2 tall metal pieces of length 1.44 m
5 medium metal pieces
6 short metal pieces as shown on the diagram.
The heights of the tall, medium and short metal pieces are in the ratio 9:8:7
.
How many metres of metal in total does Emilio need to make the fence?
Answer:
21.4 m
Step-by-step explanation:
Let x represent the sum of the tall metal, medium metal and short metal heights. Since the tall metal has a length of 1.44 m, and the ratio is in 9:8:7, hence:
(9/24) * x = 1.44
x = 3.84 m
For the medium metal pieces:
(8/24) * 3.84 = medium metal height
medium metal height = 1.28 m
For the short metal pieces:
(7/24) * 3.84 = short metal height
short metal height = 1.12 m
Total horizontal metal piece length = 3 * 1.8 m = 5.4 m
Total tall metal piece length = 2 * 1.44 m = 2.88 m
Total medium metal piece length = 5 * 1.28 m = 6.4 m
Total short metal piece length = 6 * 1.12 m = 6.72 m
Total length of metal = 5.4 + 2.88 + 6.4 + 6.72 = 21.4 m
Find the direction cosines and direction angles of the vector. (Give the direction angles correct to the nearest degree.) c, c, c , where c > 0
Answer:
cos(∝) = 1/√3
cos(β) = 1/√3
cos(γ) = 1/√3
∝ = 55°
β = 55°
γ = 55°
Step-by-step explanation:
Given the data in the question;
vector is z = < c,c,c >
the direction cosines and direction angles of the vector = ?
Cosines are the angle made with the respect to the axes.
cos(∝) = z < 1,0,0 > / |z|
so
cos(∝) = < c,c,c > < 1,0,0 > / √[c² + c² + c²] = ( c + 0 + 0 ) / √[ 3c² ]
cos(∝) = c / √[ 3c² ] = c / c√3 = 1/√3
∝ = cos⁻¹( 1/√3 ) = 54.7356° ≈ 55°
cos(β) = < c,c,c > < 0,1,0 > / √[c² + c² + c²] = ( 0 + c + 0 ) / √[ 3c² ]
cos(β) = c / √[ 3c² ] = c / c√3 = 1/√3
β = cos⁻¹( 1/√3 ) = 54.7356° ≈ 55°
cos(γ) = < c,c,c > < 0,0,1 > / √[c² + c² + c²] = ( 0 + 0 + c ) / √[ 3c² ]
cos(γ) = c / √[ 3c² ] = c / c√3 = 1/√3
γ = cos⁻¹( 1/√3 ) = 54.7356° ≈ 55°
Therefore;
cos(∝) = 1/√3
cos(β) = 1/√3
cos(γ) = 1/√3
∝ = 55°
β = 55°
γ = 55°
State the final conclusion in simple nontechnical terms.
Original claim: The proportion of male golfers is less than 0.6.
Initial conclusion: Fail to reject the null hypothesis.
Which of the following is the correct conclusion?
A. There is suffficient evidence to support the claim that the proportion of male golfers is less than 0.6.
B. There is not sufficient evidence to support the claim that the proportion of male golfers is less than 0.6.
Answer:
B. There is not sufficient evidence to support the claim that the proportion of male golfers is less than 0.6.
Step-by-step explanation:
The proportion of male golfers is less than 0.6.
At the null hypothesis, we test if the proportion is of at least 0.6, that is:
[tex]H_0: p \geq 0.6[/tex]
At the alternative hypothesis, we test if the proportion is of less than 0.6, that is:
[tex]H_1: p < 0.6[/tex]
Fail to reject the null hypothesis.
This means that there is not sufficient evidence to conclude that the proportion is less than 0.6, and thus the correct answer is given by option B.
A student ran out of time on a multiple choice exam and randomly guessed the answers for two problems. Each problem had 5 answer choices - a, b, c, d, e- and only one correct answer. What is the probability that she answered neither of the problems correctly? Do not round your answer. (If necessary, consult a list of formulas.)
Answer:
there is a 64% chance that the student got both problems wrong
a 32% chance that they got only 1 correct
and a 4% chance that they got both correct
Step-by-step explanation:
There are 25 total possible combinations of answers, with 8 possible combinations where the student would get 1 answer right, and 1 combination where the student would get both answers correct.
[tex]25-9=16[/tex]
[tex]\frac{16}{25} =\frac{x}{100}[/tex]
[tex]\frac{64}{100}[/tex]
[tex]64[/tex]%
[tex]\frac{8}{25} =\frac{y}{100}[/tex]
[tex]\frac{32}{100}[/tex]
[tex]32[/tex]%
[tex]\frac{1}{25} =\frac{z}{100}[/tex]
[tex]\frac{4}{100}[/tex]
[tex]4[/tex]%
what tearm means per hundred
a.base b.percent c.percentage d.rate
the term per hundred means percent
hope it helps
Answer:
C. Percent
Explanation:
per hundred means 1 in 100. percent is referring to the unit that is 1 in 100 of another value
1ex. 1% of 100 (1 percent of 100)
2ex. 49% of 235 (49 percent of 235)
help pls, stuck on this
Answer:
Step-by-step explanation:
what is a value between 1/4 and 1/3 is
9514 1404 393
Answer:
2/7
Step-by-step explanation:
Any unit fraction with a denominator between 3 and 4 will be between 1/3 and 1/4. For example, ...
1/3.5 = 2/7 . . . . is between 1/3 and 1/4
__
You can also go at this considering decimal equivalents.
1/4 = 0.25
1/3 = 0.333... (repeating)
So, decimal numbers like 0.26, 0.295, 0.3330 are all values that are between 1/4 and 1/3.
There are 100 sheets of paper on table. It takes 10 seconds to count 10 sheets. How many seconds will you need to count 80 sheets?
Answer:
80 seconds
Step-by-step explanation:
10/10 = 1
now it takes 1 seconds to count 1 sheet
80 x 1 = 80 seconds to count 80 sheets
Step-by-step explanation:
10sheets=10seconds
1sheet=1sheet÷10sheets x 10seconds
=1second
80sheets=80sheets÷1sheet x 1second
80seconds
hope this is helpful
SCALCET8 3.9.003. Each side of a square is increasing at a rate of 4 cm/s. At what rate is the area of the square increasing when the area of the square is 9 cm2
Answer: [tex]24\ cm^2/s[/tex]
Step-by-step explanation:
Given
Each side of square is increasing at a rate of 4 cm/s
Side of a square when area is [tex]9\ cm^2[/tex]
Suppose a is side of the square
[tex]\Rightarrow a=\sqrt{9}\\\Rightarrow a=3\ cm[/tex]
Area is given by
[tex]\Rightarrow A=a^2\\\text{Differentiate area w.r.t time}\\\\\Rightarrow \dfrac{dA}{dt}=2a\dfrac{da}{dt}\\\\\Rightarrow \dfrac{dA}{dt}=2\times 3\times 4\\\\\Rightarrow \dfrac{dA}{dt}=24\ cm^2/s[/tex]
Area is increasing at a rate of [tex]24\ cm^2/s[/tex]
Answer:
24cm^2/ s
Step-by-step explanation:
Can someone please help me
Answer:
sorry I can't help you sorry
Answer:
c
Step-by-step explanation:
A reflection in the x- axis of the parent function is - [tex]\sqrt{x}[/tex]
Given f(x) then f(x) + c is a vertical translation of f(x)
• If c > 0 then a shift up of c units
• If c < 0 then a shift down of c units
Here the shift is 3 units up , then
g(x) = - [tex]\sqrt{x}[/tex] + 3
Evaluate -6-2x when x=-4
Answer:
2
Step-by-step explanation:
Given [tex]-6-2x[/tex] where [tex]x=-4[/tex], substitute [tex]x=-4[/tex] to find the value of the given equation.
Substituting [tex]x=-4[/tex]:
[tex]-6-2(-4)[/tex]
Multiply [tex]-2\cdot -4[/tex]:
[tex]-6+8[/tex]
Combine like terms:
[tex]-6+8=\boxed{2}[/tex]
Therefore, the value of [tex]-6-2x[/tex] when [tex]x=-4[/tex] is [tex]\boxed{2}[/tex].
Solve the given system by the substitution method
5x + y 19
7x-2y = 13
Answer:
x = 3 , y = 4
Step-by-step explanation:
5x + y = 19 --------- ( 1 )
=> y = 19 - 5x
7x - 2y = 13 ------------ ( 2 )
Substitute y in ( 2 ) :
7x - 2( 19 - 5x ) = 13
7x - 38 + 10x = 13
17x = 13 + 38
17x = 51
x = 3
Substitute x in ( 1 ) :
5x + y = 19
5( 3 ) + y = 19
15 + y = 19
y = 19 - 15
y = 4
Which of the following statements are true?
Answer:
D
Step-by-step explanation:
i think it's correct if not I'm sorry
Joanne's monthly salary is $2400.she spend's ⅒ of it on food and ⅜ of it on leisure activities.How much does she have left?
Answer:
1200$
please mark me as brain liest
