Explanation:
It looks like you're trying to make the coherent statement ...
The average rate of change over the interval [a, x] is ...
[tex]\dfrac{f(x)-f(a)}{x-a}[/tex]
The limit ...
[tex]\lim\limits_{x \to a}{\dfrac{f(x)-f(a)}{x-a}}[/tex]
is the slope of the line. It is also the limit of the average rate of change, which is the instantaneous rate of change at x=a.
Suppose that, in an experimental setting, 100 students are asked to choose between Gamble A and Gamble B, where: Gamble A: The student will receive $5,100 with a 70 percent probability and $200 with a 30 percent probability. Gamble B: The student will receive $5,100 with a 50 percent probability, $200 with a 25 percent probability, and $0 (nothing) with a 25 percent probability. What is the expected value (EV) of Gamble B
Focus on Gamble B only. Multiply each winnings with their corresponding probabilities.
5100*0.50 = 2550
200*0.25 = 50
0*0.25 = 0
Add up those results: 2550+50+0 = 2600
The expected value of gamble B is $2600
Engineers want to design passenger seats in commercial aircraft so that they are wide enough to fit 95 percent of adult men. Assume that adult men have hip breadths that are normally distributed with a mean of 14.4 inches and a standard deviation of 1.1 inches. Find the 95th percentile of the hip breadth of adult men. Round your answer to one decimal place; add a trailing zero as needed. The 95th percentile of the hip breadth of adult men is [HipBreadth] inches.
Answer:
[tex]z=1.64<\frac{a-14.4}{1.1}[/tex]
And if we solve for a we got
[tex]a=14.4 +1.64*1.1=16.204[/tex]
The 95th percentile of the hip breadth of adult men is 16.2 inches.
Step-by-step explanation:
Let X the random variable that represent the hips breadths of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(14.4,1.1)[/tex]
Where [tex]\mu=14.4[/tex] and [tex]\sigma=1.1[/tex]
For this part we want to find a value a, such that we satisfy this condition:
[tex]P(X>a)=0.05[/tex] (a)
[tex]P(X<a)=0.95[/tex] (b)
We can find a quantile in the normal standard distribution who accumulates 0.95 of the area on the left and 0.05 of the area on the right it's z=1.64
Using this value we can set up the following equation:
[tex]P(X<a)=P(\frac{X-\mu}{\sigma}<\frac{a-\mu}{\sigma})=0.95[/tex]
[tex]P(z<\frac{a-\mu}{\sigma})=0.95[/tex]
And we have:
[tex]z=1.64<\frac{a-14.4}{1.1}[/tex]
And if we solve for a we got
[tex]a=14.4 +1.64*1.1=16.204[/tex]
The 95th percentile of the hip breadth of adult men is 16.2 inches.
Determine the value(s) of h such that the matrix is the augmented matrix of a consistent linear system. [Start 2 By 3 Matrix 1st Row 1st Column negative 15 2nd Column 21 3rd Column h 2nd Row 1st Column 5 2nd Column negative 7 3rd Column negative 3 EndMatrix ]
Answer: h = 9
Step-by-step explanation: A system of linear equations is consistent when it has at least one solution.
The matrix given is:
[tex]\left[\begin{array}{ccc}-15&21&h\\5&-7&-3\end{array}\right][/tex]
Transform this matrix in a row-echelon form:
[tex]\left[\begin{array}{ccc}-15&21&h\\5&-7&-3\end{array}\right][/tex] [tex]R_{2} = 3R_{2}+R_{1}[/tex] [tex]\left[\begin{array}{ccc}-15&21&h\\0&0&-9+h\end{array}\right][/tex]
For this row-echelon form to have solutions:
-9 + h = 0
h = 9
For this system to be consistent: h = 9.
Laure
Lauren made a shopping list of things she could buy
with $100.
Answer:
The shoes and purse each take up 1/4th of the circle (since 25 is 1/4th of 100) so we can eliminate the top 2 choices. Since the dress costs more than the bracelet it will take up more room leaving us with the bottom right circle as the answer.
Answer: The fourth one, or the bottom right hand corner one
Step-by-step explanation:
Shoes: 25 --> 25%
Purse: 25 --> 25%
Bracelet: 15 --> 15%
Dress: 35 --> 35%
Since the circle graph are not exact percentages, you have to estimate on how which values are larger.
The perimeter of a triangle is 39 feet one side of the triangle is 1 foot longer than the second side the third is 2 feet longer than the second side find the length of each side
Answer:
second side = s first side = s +1 third side = s +2
39 feet = s + (s+1) + (s +2)
39 feet = 3s +3
36 feet = 3s
s = second side = 12 feet
first side = 13 feet
third side = 14 feet
Step-by-step explanation:
A product is introduced to the market. The weekly profit (in dollars) of that product decays exponentially as function of the price that is charged (in dollars) and is given by P ( x ) = 95000 ⋅ e − 0.05 ⋅ x Suppose the price in dollars of that product, x ( t ) , changes over time t (in weeks) as given by x ( t ) = 53 + 0.95 ⋅ t 2 Find the rate that profit changes as a function of time, P ' ( t ) dollars/week How fast is profit changing with respect to time 7 weeks after the introduction. dollars/week
Answer:
1). [tex]P'(t) = (-9025t).e^{-0.05(53+0.95t^2)}[/tex]
2). (-435.36) dollars per week
Step-by-step explanation:
Weekly price decay of the product is represented by the function,
P(x) = [tex]95000.e^{-0.05x}[/tex]
And the price of the product changes over the period of 't' weeks is represented by,
x(t) = [tex]53+0.95t^2[/tex]
Function representing the rate of change in the profit with respect to the time will be represented by,
1). P'(t) = [tex]\frac{dP}{dx}.\frac{dx}{dt}[/tex]
Since, P(x) = [tex]95000.e^{-0.05x}[/tex]
P'(x) = [tex]95000\times (-0.05).e^{-0.05x}[/tex]
= [tex](-4750).e^{-0.05x}[/tex]
Since, x(t) = 53 + 0.95t²
x'(t) = 1.9t
[tex]\frac{dP}{dx}.\frac{dx}{dt}=(-4750).e^{-0.05x}\times (1.9t)[/tex]
By substituting x = 53 + 0.95t²
[tex]\frac{dP}{dx}.\frac{dx}{dt}=(-4750).e^{-0.05(53+0.95t^2)}\times (1.9t)[/tex]
P'(t) = [tex](-9025t).e^{-0.05(53+0.95t^2)}[/tex]
2). For t = 7 weeks,
P'(7) = [tex](-9025\times 7).e^{-0.05(53+0.95(7)^2)}[/tex]
= [tex](-63175).e^{-4.9775}[/tex]
= (-63175)(0.006891)
= (-435.356) dollars per week
≈ (-435.36) dollars per week
The exchange rate at a post office is £1 = 1.77 euros How many euros will you get with £280
Answer:
495.6 Euros
Step-by-step explanation:
If 1 pound equals 1.77 euros we can set up a proportion that;
[tex] \frac{1 pound}{1.77 euros} [/tex]
This proportion would be equal to the new amount;
[tex] \frac{280 pounds}{x euros} [/tex]
This means that
[tex] \frac{1 pound}{1.77 euros} = \frac{280 pounds}{ x euros} [/tex]
So;
[tex]280 pounds*1.77 euros / 1 pound[/tex]
Pounds cancel out; and so you have
[tex]280 * 1.77 euros[/tex]
giving you as performed on a calculator;
495.6 euros.
Hope this helps
Answer:
495.6 euros.
Step-by-step explanation:
For each pound we get 1.77 euros so:
it is 280 * 1.77
= 495.6 euros.
A test consists of 580 true or false questions. If the student guesses on each question, what is the standard deviation of the number of correct answers? Round the answer to the nearest hundredth.
Answer:
12.04
Step-by-step explanation:
Because the questions are true and false, that is, there are only two answer options, therefore, you have a success probability = 1/2 = 0.5
The standard deviation can be calculated as follows:
Standard Deviation = (n*p* (1-p)] ^ (1/2)
replacing we have:
SD = (290 * (1-0.5)] ^ (1/2) = 12.04
That is, the standard deviation is 12.04
Find all solutions of the equation in the interval [0, 2π). cos x + sin x tan x = 2
Answer:
The solutions of the equation in the interval [0,2π )
={ [tex]\frac{\pi }{3}[/tex] }
General solution θ = 2 nπ +α
θ = [tex]2n\pi + \frac{\pi }{3}[/tex]
Step-by-step explanation:
Step(i):-
Given equation
cos x + sin x tan x = 2
⇒ [tex]cos x + sin x \frac{sin x}{cos x} = 2[/tex]
On simplification , we get
⇒ [tex]\frac{sin^{2} x+ cos^2x}{cos x} = 2[/tex]
we know that trigonometry formula
[tex]sin^{2} x+ cos^2 x = 1[/tex]
now we get
[tex]\frac{1}{cos x} = 2[/tex]
⇒ [tex]cos x = \frac{1}{2}[/tex]
⇒ cos x = cos 60°
Step(ii):-
General solution of cosθ = cosα
General solution θ = 2 nπ +α
θ = 2 nπ +60°
θ = [tex]2n\pi + \frac{\pi }{3}[/tex]
put n = 0 ⇒ θ = 60°
Put n =1 ⇒ θ = 360°+60°= 420°
.....and so on
The solutions of the equation in the interval =[tex]\frac{\pi }{3}[/tex]
Final answer:-
The solutions of the equation in the interval [0,2π )
={ [tex]\frac{\pi }{3}[/tex] }
General solution θ = 2 nπ +α
θ = [tex]2n\pi + \frac{\pi }{3}[/tex]
Deanna's Quiz Scores
Use the dot plots to answer the question
has quiz scores that are less variable and
typically higher
80 82 84 86 88 90 92 94 96 98 100
Amy's Quiz Scores
.
.
.
..
80 82 84 86 88 90 92 94 96 98 100
Answer:
1.90.93
2.90.27
Step-by-step explanation:
Answer:
one above correct
Step-by-step explanation:
1st - 90.93
2nd-90.27
Please answer this correctly. I want genius,expert or ace people to answer this correctly
Answer:
6 times.
Step-by-step explanation:
There is a 1/9 chance you pick the orange one. If you pick 54 times, you can expect to pick the orange marble 6 times.
Prove With Diagram Which fraction is larger, 5/8 or 3/4 Brainliest
Answer:
3/4
Step-by-step explanation:
Convert the fractions into decimals.
5/8 = 0.625
3/4 = 0.75
0.75 is greater than 0.625.
What is the general formula for an parallelogram
Answer:
A = bh
Step-by-step explanation:
Area = base × height
Area = base · height
A = bh
Solve the linear equality 4x-7 <5
Answer:
X<3
Step-by-step explanation:
4x-7 <5
4x < 5+7
4x < 12
X < 12/4
X < 3
Hope this helps..
Good Luck!
Simplify this radical.
V84
2/21
242
4/21
4/42
Answer:
2√21
Step-by-step explanation:
√81 is √4 times √21
Since √4 is a perfect square, √4 = 2
We are left with 2 times √21
2√21
Answer:
2√21
Step-by-step explanation:
√84
84 can be written as 4 × 21.
√(4 × 21)
Distribute the square root to both terms.
√4 × √21
4 is a perfect square.
2 × √21
g Consider a 1 × n floor to be covered by 1 × 1 tiles that come in three different colors(Blue, Red, Green) and 1 × 2 tiles that come in 2 different colors (orange, white). Find a recurrence relation for the number of the ways the floor can be tiled. (Just find the recurrence relation together with an appropriate number of initial terms. Do not solve the recurrence)
Answer:
[tex]f(n) = 3f(n - 1) + 2f(n - 2)[/tex], if [tex]n \geq 2[/tex].
[tex]f(0) := 1[/tex], [tex]f(1) := 3[/tex]
Step-by-step explanation:
Let [tex]f(n)[/tex] be the number of different tiling of [tex]1 \times n[/tex] floor. We can divide all possible tiling of floor [tex]1 \times n[/tex] into five not overlapping groups by color of last cell in the row (Blue, Red, Green, Orange, White).
The number of tiling [tex]1\times n[/tex] floor such that last cell in row is Blue is exactly f(n - 1) because we can throw away last [tex]1\times 1[/tex] tile and cover the rest [tex]1\times (n - 1)[/tex] cells in f(n - 1) ways. Similarly for Red and Green.
The number of tiling [tex]1\times n[/tex] floor such that last cell in row is Orange is exactly f(n - 2) because we can throw away last [tex]1\times 2[/tex] tile and cover the rest [tex]1\times (n - 2)[/tex] cells in f(n - 2) ways. Similarly for White.
So we get recurrent relation:
[tex]f(n) = 3f(n - 1) + 2f(n - 2)[/tex], if [tex]n \geq 2[/tex].
Now we should define the initial conditions.
[tex]f(0) := 1[/tex] because there is only one empty tiling.
[tex]f(1) := 3[/tex] because we can place Blue, Red or Green tile.
This completely define our recurent sequence because the depth of reccurence is 2.
Which of the following is NOT a collinear point in the image below?
Which statements are true? Check all that apply. All rectangles are squares. All rhombi are parallelograms. All squares are rhombi. All trapezoids are parallelograms. No trapezoid is a rectangle.
Answer:
All rhombi are parallelograms.
All squares are rhombi.
No trapezoid is a rectangle.
Help needed ASAP please !!!!
Answer:I believe that it is A but i am not fully sure
Step-by-step explanation:
what is the midpoint of the horizontal (-2,3) and (10,3)
Brian invests £8300 into his bank account. He receives 1.4% per year compound interest. How much will Brian have after 7 years? Give your answer to the nearest penny where appropriate.
Answer:
The nearest penny will be £9146.6
Step-by-step explanation:
A = P[1 + (r/n)]^(nt)
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
A = 8300 [ 1 + {1.4 / (7*100)}]^(7*7)
A = 8300 [ 1 + {0.002}]^(49)
A= 8300 [ 1.002 ]^(49)
A = 8300 [ 1.102 ]
A = £9146.6
What is Compound Interest (CI) ?
Compound Interest is all about adding interest to principal amount of loan , deposit .
What is the slope of the line below
Answer:
C. [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
You can use the formula to find the slope: [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
(-1.5, 1.5) & (1.5, 0)
[tex]\frac{0-(-1.5)}{1.5-(-1.5)} =\\\\\frac{0+1.5}{1.5+1.5} =\\\\\frac{1.5}{3} =\\\\\frac{1}{2}[/tex]
The slope is [tex]\frac{1}{2}[/tex]
A tree that is 40 feet tall casts a 30 foot shadow. At the same time another tree casts a 20 foot shadow. How tall is the second tree?
Answer:26 2/3 feet
Step-by-step explanation:40/30 = 4/3
(26 2/3) / 20= 4/3
Determine the dimension of the vector space.
M2,4
STEP 1:Determine the number of linearly independent vectors needed to span M2,4.
The basis for M2,4 has _________ linearly independent vectors.
STEP 2:Using the result from Step 1, determine the dimension of M2,4.
_________
Answer:
a
The number of linearly independent vectors needed to span M2,4. N =8
b
The dimension of [tex]M_{2,4}[/tex] is 8
Step-by-step explanation:
From the question we are told that
The vector space is an [tex]M_{2,4}[/tex] matrix
Now the number of linear linearly independent vectors needed to span M2,4.
is evaluated as
[tex]N = 2 * 4 = 8[/tex]
this is due to the fact that each entry of the matrix is independent
Given that there are eight independent in the vector space the dimension of
[tex]M_{2,4}[/tex] is 8
a The number of linearly independent vectors needed to span M2,4. N =8
b The dimension of M2, 4 is 8.
Calculation of the number of linearly independent vectors and dimensions:Since there is vector space i.e. M2, 4
So, here n be = 2(4) = 8
Also, each entry of the matrix should be considered independent. Therefore, the dimension should also be 8.
Hence,
a The number of linearly independent vectors needed to span M2,4. N =8
b The dimension of M2, 4 is 8.
Learn more about vector here: https://brainly.com/question/12623333
The height of seaweed of all plants in a body of water are normally distributed with a mean of 10 cm and a standard deviation of 2 cm. Which length separates the lowest 30% of the means of the plant heights in a sampling distribution of sample size 15 from the highest 70%? Round your answer to the nearest hundredth. Use the z-table below:
0.00 0.01 0.02 0.030.04 0.05 0.06 0.08 0.09 0.07 -0.8 0.212 0.209 0.206 0.203 0.201 0.198 0.195 0.192 0.189 0.187 -0.7 0.242 0.239 0.236 0.233 0.230 0.227 0.224 0.221 0.218 0.215 -0.6 0.274 0.271 0.268 0.264 0.261 0.258 0.255 0.251 0.248 0.245 -0.5 0.309 0.305 0.302 0.298 0.295 0.291 0.288 0.284 0.281 0.278 -0.4 0.345 0.341 0.337 0.334 0.330 0.326 0.323 0.319 0.316 0.312 -0.3 0.382 0.378 0.374 0.3710.367 0.363 0.359 0.356 0.352 0.348
Round the z-score and i to two decimal places. Provide your answer below: Z-Score =
Answer:
Step-by-step explanation:
Hello!
The variable of interest is:
X: height of seaweed.
X~N(μ;σ²)
μ= 10 cm
σ= 2 cm
You have to find the value of the variable X that separates the bottom 0.30 of the distribution from the top 0.70
P(X≤x)= 0.30
P(X≥x)= 0.70
Using the standard normal distribution you have to find the value of Z that separates the bottom 0.30 from the top 0.70 and then using the formula Z= (X-μ)/σ translate the Z value to the corresponding X value.
P(Z≤z)= 0.30
In the body of the table look for the probability of 0.30 and reach the margins to form the Z value. The mean of the distribution is "0" so below 50% of the distribution you'll find negative values.
z= -0.52
Now you have to clear the value of X:
Z= (X-μ)/σ
Z*σ= X-μ
X= (Z*σ)+μ
X= (-0.52*2)+10= 8.96
The value of seaweed height that divides the bottom 30% from the top 70% is 8.96 cm
I hope this helps!
Answer:-0.53 and 9.72
Step-by-step explanation:
i need help Hurry!!!
Step-by-step explanation:
WX is parallel to YZ and WZ is also parallel to XY
Option C,D and E are correct.
Explanation:
In Euclidean geometry,a parallelogram is a simple quadrilateral with two pairs of parallel sides.The opposite or facing sides of a parallelogram are of equa length and the opposite angles of a parallelogram are of equal measure.
Hope this helps...
Good luck on your assignment..
Which system of inequalities is graphed below?
-5
Please help !! Correct and first answer I will give you brainesttttt!!!!! What is the equation of the line ?
Answer:
y = 3x + 5
Have a good day! :)
Answer:
y=2x+4
Step-by-step explanation:
the line has equation like this y=ax+b
x=0 then y=4 so 4=a*0+b so b=4
y=0, then x=-2, 0=a*(-2)+4 so -2a+4=0,-2a=-4, a=2
so the equation of the line is y=2x+4
verify
x=-1, y=2*(-1)+4=-2+4=2 so the equation is correct
An aircraft seam requires 30 rivets. The seam will have to be reworked if any of these rivets is defective. Suppose rivets are defective independently of one another, each with the same probability. (Round your answers to four decimal places.)
(a) If 21% of all seams need reworking, what is the probability that a rivet is defective?
(b) How small should the probability of a defective rivet be to ensure that only 11% of all seams need reworking?
Answer:
a. 0.00783
b. 0.003876
Step-by-step explanation:
The computation is shown below;
a. The probability for the rivet to be defective is
Let us assume A is the event for seam failure and B would be event for rivets failure
Now
a) [tex]P[A] = 1 - P[B']^{30}[/tex]
[tex]0.21 = 1 - P[B']^{30}[/tex]
[tex]0.79 = P[B']^{30}[/tex]
[tex]P[B'] = 0.79^{\frac{1}{30}}[/tex]
P[B'] = 0.99217
P[B] = 1 - P[B']
= 0.00783
b) Now the Next one is
[tex]0.08 = 1 - P[B']^{25}[/tex]
[tex]0.89 =P[B']^{30}[/tex]
[tex]P[B'] = 0.89^{(\frac{1}{30})}[/tex]
= 0.99612
So,
P[B] is
= 1 - P[B']
= 0.003876
We simply applied the above formula so that each one part could be calculated i.e the probabilities of the given question
What type of number can be written as an a fraction a/b where a and b are Integres and b is not equal to zero?
Answer:
Integers, Terminating Decimals, Recurring Decimals, Proper and Improper Fractions.
Step-by-step explanation:
The following subset of the real number system can be written in the form [tex]\dfrac{a}{b}[/tex], b≠0.
Integers(ℤ): These are positive and negative whole numbers. For example, 5 can be written as [tex]\dfrac{5}{1}[/tex]
Terminating Decimals: These are fractions that when converted to decimal numbers have an end.
e.g. [tex]\dfrac{5}{2}=2.5[/tex]
Recurring Decimals: These are fractions that when converted to decimal numbers do not have an end.
e.g. [tex]\dfrac{8}{11}=0.727272...=0.\overline{72}[/tex]
Proper Fractions: These are fractions of the form [tex]\dfrac{a}{b}[/tex] where a<b. An examples is [tex]\dfrac{4}{5}[/tex]
Improper Fractions: These are fractions of the form [tex]\dfrac{a}{b}[/tex] where a>b. An examples is [tex]\dfrac{5}{4}[/tex]