Aa. 8x2 - 2
i
Step-by-step explanation:
4x2 = 8
8-3 = 5
5 + 4 =
Answer:
c. 2x2+6x−2
Step-by-step explanation:
The age of Noelle's dad is 6 less than 3 times Noelle's age. The sum of their ages is 74 . Find their ages. Provide your answer below: $$ Noelle: , Noelle's Dad
Answer:
The age of Noelle = 20 years
Age of Noelle's dad = 54 years
Step-by-step explanation:
Here, Let us assume:
The age of Noelle's age = m years
So, the age of Noelle's dad = 3 x ( Age of Noelle) - 6 = 3(m) - 6
Also, sum of both the ages = 74
So, sum of (Noelle's age + Noelle's dad's) age = 74 years
⇒ m + ( 3 m - 6) = 74
or, 4 m = 74+ 6 = 80
or,m = 80 / 4 = 20
⇒ m = 20
Hence, the age of Noelle = m - 3 = 20 years
Age of Noelle's dad = 3 m - 6 = 3(20) - 6 = 54 years
The doubling time of a population of flies is 4 hours . By what factor does the population increase in 48 hours?
Answer:
4096
Step-by-step explanation:
The population doubles 12 times in that period, so is multiplied by 2^12 = 4096.
Which graph represents a quadratic function with a vertex at (0, 0)? On a coordinate plane, a parabola opens up. It goes through (negative 5, 6), has a vertex of (0, 1), and goes through (5, 6). On a coordinate plane, a parabola opens up. It goes through (negative 6, 6), has a vertex of (0, negative 1), and goes through (6, 6). On a coordinate plane, a parabola opens up. It goes through (negative 5, 6), has a vertex of (0, 0), and goes through (5, 6). On a coordinate plane, a parabola opens up. It goes through (negative 2.5, 6), has a vertex of (3, 0), and goes through (7.5, 4).
Answer:
On a coordinate plane, a parabola opens up. It goes through (negative 5, 6), has a vertex of (0, 0), and goes through (5, 6).
Step-by-step explanation:
Since you want a graph with a vertex of (0, 0), choose the one that is described as having a vertex of (0, 0).
Answer:
Option C.
Step-by-step explanation:
We need to find the graph which represents a quadratic function with vertex at (0,0).
The graph of quadratic function is a parabola (either upward or downward) and the extreme point of the parabola is know as vertex.
All graphs represent different parabolas.
Vertex of first parabola = (0,1)
Vertex of second parabola = (0,-1)
Vertex of third parabola = (0,0)
Vertex of fourth parabola = (3,0)
In option C, a parabola opens up on a coordinate plane. It goes through (-5, 6), has a vertex of (0, 0), and goes through (5, 6).
Only third graph represents a quadratic function with a vertex at (0, 0).
Therefore, the correct option is C.
Farmer bob's square plot ofland is slowly eroding away. Worried about the future of his farm. Farmer Bob measures the rate of erosion and finds that the length of each side of his square plot is decreasing at the constant rate of 2 feet/year. If he currently owns 250,000 square feet of land, what is the current rate of change of the area of Farmer Bob's land?
a) Farmer bob is losing 2,000 square feet of land per year
b) losing 1,000,000 square feet of land per year
c) losing 1,000 square feet of land per year
d) losing 4 square feet of land per year
Answer:
Option A.
Step-by-step explanation:
Area of a square is
[tex]A=x^2[/tex] .... (1)
where, x is side length.
The length of each side of his square plot is decreasing at the constant rate of 2 feet/year.
[tex]\dfrac{dx}{dt}=2[/tex]
It is given that bob currently owns 250,000 square feet of land.
Fist find the length of each side.
[tex]A=250000[/tex]
[tex]x^2=250000[/tex]
Taking square root on both sides.
[tex]x=500[/tex]
Differentiate with respect to t.
[tex]\dfrac{dA}{dt}=2x\dfrac{dx}{dt}[/tex]
Substitute x=500 and [tex]\frac{dx}{dt}=2[/tex] in the above equation.
[tex]\dfrac{dA}{dt}=2(500)(2)[/tex]
[tex]\dfrac{dA}{dt}=2000[/tex]
Farmer bob is losing 2,000 square feet of land per year.
Therefore, the correct option is A.
The average hourly wage of workers at a fast food restaurant is $6.75 with a standard deviation of $0.25. If the distribution is normal, what is the probability that a worker selected at random earns more than $7.00 an hour?
Answer:
25% would be the answer
Step-by-step explanation:
An insurance agent receives 16% commission on every premium paid. how much commission is paid on a policy with a premium of $497.69? $31.10 $79.63 $311.06 $796.30
Answer:
$79.63
Step-by-step explanation:
You can figure this by estimating. 16% is a little less than 20%, which is 1/5. $497.69 is almost $500. So, 1/5 of that is almost $100, and a little less than that is about $80. The closest answer choice is $79.63.
__
If you want to figure it exactly, you can do the multiplication ...
16% of $497.69 = 0.16 × $497.69 = $79.6304 ≈ $79.63
According to a candy company, packages of a certain candy contain 24% orange candies. Find the approximate probability that the random sample of 200 candies will contain 26% or more orange candies.
Final answer:
To find the approximate probability that the random sample of 200 candies will contain 26% or more orange candies, we can use the binomial distribution.
Explanation:
To find the approximate probability that the random sample of 200 candies will contain 26% or more orange candies, we need to use the binomial distribution.
The probability of selecting an orange candy is 24%. Let's define success as selecting an orange candy.
Using the binomial distribution formula, we can calculate the probability:
P(X ≥ k) = 1 - P(X < k)
where X is the random variable representing the number of orange candies in the sample, and k is the number of orange candies we want to have (26% of 200 is 52).
First, let's calculate P(X < 52). We can use a binomial probability table, or a binomial calculator to find this value. Once we have P(X < 52), we can find P(X ≥ 52) by subtracting it from 1.
A certain car depreciates such that its value at the end of each year is p % less than its value at the end of the previous year. If that car was worth a dollars on December 31, 2010 and was worth b dollars on December 31, 2011, what was the car worth on December 31, 2013 in terms of a and b ?
Answer:
b(b/a)^2
Step-by-step explanation:
Given that the value of the car depreciates such that its value at the end of each year is p % less than its value at the end of the previous year and that car was worth a dollars on December 31, 2010 and was worth b dollars on December 31, 2011, then
b = a - (p% × a) = a(1-p%)
b/a = 1 - p%
p% = 1 - b/a = (a-b)/a
Let the worth of the car on December 31, 2012 be c
then
c = b - (b × p%) = b(1-p%)
Let the worth of the car on December 31, 2013 be d
then
d = c - (c × p%)
d = c(1-p%)
d = b(1-p%)(1-p%)
d = b(1-p%)^2
d = b(1- (a-b)/a)^2
d = b((a-a+b)/a)^2
d = b(b/a)^2 = b^3/a^2
The car's worth on December 31, 2013 = b(b/a)^2 = b^3/a^2
The exponential model Upper A equals 104.8 e Superscript 0.001 t describes the population, A, of a country in millions, t years after 2003. Use the model to determine when the population of the country will be 106 million.
Answer: The population of the country will be 106 millions in 2014.
Step-by-step explanation:
The exercise gives you the following exponential model, which describes the population "A" (in millions) of a country "t" years after 2003:
[tex]A=104.8 e^{0.001 t}[/tex]
In this case you must determine when the population of that country will be 106 millions, so you can identify that:
[tex]A=106[/tex]
Now you need to substitute this value into the exponential model given in the exercise:
[tex]106=104.8 e^{0.001 t}[/tex]
Finally, you must solve for "t", but first it is important to remember the following Properties of logarithms:
[tex]ln(a)^b=b*ln(a)\\\\ln(e)=1[/tex]
Then:
[tex]\frac{106}{104.8}=e^{0.001 t}\\\\ln(\frac{106}{104.8})=ln(e)^{0.001 t}\\\\ln(\frac{106}{104.8})=0.001 t(1)\\\\\frac{ln(\frac{106}{104.8})}{0.001}}=t\\\\t=11.38\\\\t\approx11[/tex]
Notice that in 11 years the population will be 106 millions, then the year will be:
[tex]2003+11=2014[/tex]
The population of the country will be 106 millions in 2014.
Given: dp/dt = k(M- P)
where P(t) measures the performance of someone learning a skill after a training time t, M is the maximum level of performance, and k is a positive constant. Solve this differential equation to find an expression for P(t). (Use P for P(t). Assume that P(0) = 0.)
Answer:
[tex]P=M(1-e^{-kt})[/tex]
Step-by-step explanation:
The relation between the variables is given by
[tex]\frac{dP}{dt} = k(M- P)[/tex]
This is a separable differential equation. Rearranging terms:
[tex]\frac{dP}{(M- P)} = kdt[/tex]
Multiplying by -1
[tex]\frac{dP}{(P- M)} = -kdt[/tex]
Integrating
[tex]ln(P-M)=-kt+D[/tex]
Where D is a constant. Applying expoentials
[tex]P-M=e^{-kt+D}=Ce^{-kt}[/tex]
Where [tex]C=e^{D}[/tex], another constant
Solving for P
[tex]P=M+Ce^{-kt}[/tex]
With the initial condition P=0 when t=0
[tex]0=M+Ce^{-k(0)}[/tex]
We get C=-M. The final expression for P is
[tex]P=M-Me^{-kt}[/tex]
[tex]P=M(1-e^{-kt})[/tex]
Keywords: performance , learning , skill , training , differential equation
The differential equation dp/dt = k(M - P) can be solved via separating variables, integrating and applying the initial condition. Result provides the equation for performance over time: P(t) = M(1 - e-kt).
Explanation:The subject of the question is around a differential equation. Firstly, you will rewrite the given equation dp/dt = k(M - P) in the form necessary for separation of variables: dp/(M - P) = k dt. Then, integrate both sides: ∫dp/(M - P) = ∫k dt. The left-hand side integral results in -ln|M - P|, and the right side is k*t + C, where C is the constant of integration. Finally, solve for P(t) by taking the exponential of both sides, and rearranging. The procedure results in the performance level equation.
P(t) = M - Ce-kt
Since we're given P(0) = 0, we can determine that C = M. Hence, we finally have the solution:
P(t) = M(1 - e-kt)
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Express each statement using an inequality involving absolute value: The height of the plant must be within 2 inches of the standard 13-inch show size
Answer:
|h-13| ≤ 2
Step-by-step explanation:
The difference between the height of the plant (h) and show size (13 in) can be written as ...
h - 13
This value is allowed to be positive or negative, but its absolute value must not exceed 2 inches. Thus, the desired inequality is ...
|h -13| ≤ 2
To express the statement using an Inequality involving absolute value, use |height - 13| ≤ 2. This means the difference between the height of the plant and 13 inches must be less than or equal to 2 inches.
To express the statement using an inequality involving absolute value, we can use the inequality |height - 13| ≤ 2. This means that the difference between the height of the plant and 13 inches must be less than or equal to 2 inches.
For example, if the height of the plant is 12 inches, then |12 - 13| = |-1| = 1, which is less than 2, so it satisfies the inequality. However, if the height of the plant is 16 inches, then |16 - 13| = |3| = 3, which is not less than 2, so it does not satisfy the inequality.
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Complete the sentence below The _____ _____, denoted Modifying Above p with caret, is given by the formula Modifying Above p with caret equals_____, where x is the number of individuals with a specified characteristic in a sample of n individuals. The _____ _____ mean proportion error variance deviation , denoted Modifying Above p with caret, ________is given by the formula Modifying Above p with caretequals Start Fraction n Over x End Fraction xn Start Fraction x Over n End Fraction , where x is the number of individuals with a specified characteristic in a sample of n individuals.
Answer:down t
Step-by-step explanation: j this is world. Theo t sit with this
An Izod impact test was performed on 20 specimens of PVC pipe. The sample mean is and the sample standard deviation is s = 0.22. Find a 99% lower confidence bound on the true Izod impact strength. Assume the data are normally distributed.
For a 99% lower confidence bound, we use the Z-score of -2.33 with the formula for a confidence interval. The lower bound will be: 'Sample Mean - (-2.33) * (Sample Standard Deviation/√Sample Size).'
Explanation:The solution to this problem involves using concepts of statistics, primarily regarding normal distribution and confidence intervals. Given that we're finding a 99% lower confidence bound, we're interested only in the lower range of the spectrum, not the upper.
We need to look at the Z-score associated with a 99% confidence interval in a standard normal distribution. The Z-score for 99% is approximately 2.33 (meaning it cuts off the lowest 0.5% and highest 0.5% of the curve). However, since we're only interested in the lower bound, we will be using a Z-score of -2.33.
The formula for a confidence interval is: µ = X ± Z(s/√n), where µ is the population mean, X is the sample mean, Z is the Z-score, s is the sample standard deviation, and n is the size of the sample. In our question, X is unspecified, s = 0.22, and n = 20. So, assuming 'Xbar' is your sample mean, your lower bound would be: Xbar - (-2.33) * (0.22/√20)
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To find a 99% lower confidence bound on the true Izod impact strength, use the formula: Lower Confidence Bound = Sample Mean - (Critical Value × (Sample Standard Deviation / √n)). Substitute the given values into the formula and perform the necessary calculations.
Explanation:To find a 99% lower confidence bound on the true Izod impact strength, we can use the formula:
Lower Confidence Bound = Sample Mean - (Critical Value × (Sample Standard Deviation / √n))
Given that the sample mean is ______ and the sample standard deviation is s = 0.22, we need to calculate the critical value for a 99% confidence level. The critical value for a 99% confidence level is approximately 2.576. Plug in the values into the formula, substituting n = 20:
Lower Confidence Bound = ______ - (2.576 × (0.22 / √20))
Perform the necessary calculations to find the lower confidence bound.
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A certain list consists of 21 different numbers. If n is in the list and n is 4 times the average(arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list?
(A) 1/20
(B) 1/6
(C) 1/5
(D) 4/21
(E) 5/21
Answer:
B. [tex]\frac{1}{6}[/tex]
Step-by-step explanation:
Let x be the sum of the 21 numbers,
In which n is one of the numbers,
Since,
[tex]\text{Average}=\frac{\text{Sum of the observations}}{\text{Number of observations}}[/tex]
So, the average of 20 numbers excluded n = [tex]\frac{x-n}{20}[/tex]
According to the question,
[tex]n = 4\times \frac{x-n}{20}[/tex]
[tex]n = \frac{x-n}{5}[/tex]
[tex]5n = x - n[/tex]
[tex]6n = x[/tex]
[tex]\imples n = \frac{1}{6}x = \frac{1}{6}\text{ of the sum of the 21 numbers}[/tex]
Hence, OPTION 'B' is correct.
find one positive and one negative angle coterminal with an angle of 166 Question 4 options:
526°, –194°
516°, –14°
526°, –76
256°,-76
Answer: Choice A) 526 degrees, -194 degrees
==============================
Work Shown:
A coterminal angle points in the same exact direction as the original angle.
Because there are 360 degrees in a circle, this means we can add 360 to the original angle to get 166+360 = 526, which is one positive coterminal angle to 166 degrees.
Subtract 360 from the original angle and we'll get a negative coterminal angle
166 - 360 = -194
A bakery decided to expand since business was going so well. Originally, the width was five times the length. Now they are adding 5 feet to the length. If the length was originally 15 feet, what will be the area of the new bakery?
Step-by-step explanation:
We need to find new area of bakery.
Old length = 15 feet
Old width = New width = 5 x Old length = 5 x 15 = 75 feet
New length = Old length + 5 feet = 15 + 5 = 20 feet
New area = New length x New width
New area = 75 x 20 = 1500 square feet.
New area of bakery = 1500 square feet.
A submarine was stationed 700 feet below sea level. It ascends 259 feet every hour. If the submarine continues to ascend at the same rate when will the submarine be at the surface?
Answer: it will take 2.7 hours to get to the surface
Step-by-step explanation:
A submarine was stationed 700 feet below sea level. It means that the height of the submarine from the surface is 700 feet.
It ascends 259 feet every hour.
If the submarine continues to ascend at the same rate, the time it will take for it to get to the surface will be the distance from the surface divided by its constant speed.
Time taken to get to the surface
700/259 = 2.7 hours
A government's congress has 376 members, of which 44 are women. An alien lands near the congress building and treats the members of congress as as a random sample of the human race. He reports to his superiors that a 95% confidence interval for the proportion of the human race that is female has a lower bound of 0.085 and an upper bound of 0.149. What is wrong with the alien's approach to estimating the proportion of the human race that is female?
Answer:
Alien does not take the sample because alien choose the data of a Government's congress and congress contain less women.
On the other hand general population contain women greater than congress
So as compared to general population confidence interval is not representative.
Answer: The sample is not a simple random sample
Step-by-step explanation:
A bag contains 222 red marbles, 222 green marbles, and 444 blue marbles.
If we choose a marble, then another marble without putting the first one back in the bag, what is the probability that the first marble will be red and the second will be green?
Answer:
1/14
Step-by-step explanation:
Assuming you mean that there are 2 red, 2 green, and 4 blue marbles, there are a total of 8 marbles.
On the first draw, the probability the marble is red is 2/8.
On the second draw, there's one less marble, so the probability of selecting a green marble is 2/7.
The total probability is:
2/8 × 2/7 = 1/14
The probability that the first marble is red and the second is green is approximately 0.0626 or 6.26%.
To find the probability we need to follow these steps:
Calculate the total number of marbles: 222 (red) + 222 (green) + 444 (blue) = 888 marbles.Determine the probability of drawing a red marble first.The probability of drawing a red marble first is:
P(Red) = Number of Red Marbles / Total Number of Marbles = 222 / 888 = 1/4 or 0.25.
After drawing a red marble, there are now 887 marbles left and still 222 green marbles in the bag.Calculate the probability of then drawing a green marble.The probability of drawing a green marble after a red one has been drawn is:
P(Green | Red) = Number of Green Marbles / Remaining Marbles = 222 / 887.
Finally, multiply these probabilities together to find the overall probability.The overall probability is:
P(Red then Green) = P(Red) * P(Green | Red) = (222 / 888) * (222 / 887) = (1/4) * (222 / 887).
Therefore, the probability that the first marble is red and the second is green is approximately 0.0626 or 6.26%.
The bill is $330. We want to split it but a friend gave us $50 for it. Therefore we each owe $140 after the $50. Since I have the $50 in my possession I wok give him $165 since were splitting the $50. Correct?
I don't think that's correct
Step-by-step explanation:
Why are you splitting the $50? you'd end up paying more than the bill and he'd be getting back more money than he put in. Sounds like a rip off. If he had given you each $50 than maybe you'd each owe $140. I assume there is 3 friends, the original bill price would have been $110 for each of you. But then one friend gave $50 to help pay the bill, if you had split the $50 you'd still not be paying back that much. Also why are YOU paying so much more? Everyone else is paying $140 and you're paying $165? You would not be giving him that much, all of you would not be paying an extra $30 either. you'd be splitting it to where it equals $50 all around, so instead it'd be around $93.00. Not $140 or $165. $16.7 multipled by 3 = $50.1
But at the end of the day, just tell him to take his money back. He really didn't help pay the bill that much with his $50, he still owes you $60 if he too had participated in whatever you guys were doing. So instead of going through the trouble, just tell him to take back his money.
Twenty-four blue socks and twenty-four red socks are lying in a drawer in a dark room. What is the minimum number of socks you need to pull out of the drawer so that you are sure to have at least two blue socks
Answer:
26 socks
Step-by-step explanation:
There are a total of 48 socks here. Let us assume you pulled out 24 socks at a go and all are red. Now, you would have exhausted the number of red socks here. You would be left with only blue socks which you can pull one after the other to give a total of 26 socks pulled out to have 2 blue socks at least.
Combine like terms to create an equivalent expression. 4\left(1.75y-3.5\right)+1.25y4(1.75y−3.5)+1.25y4, left parenthesis, 1, point, 75, y, minus, 3, point, 5, right parenthesis, plus, 1, point, 25, y
Answer:
8.25y-14
Step-by-step explanation:
The simplified expression is 8.25y - 14, which is obtained by combining the like terms 7y and 1.25y and adding the constant term -14.
How to combine like terms?Break down the expression step by step.
4(1.75y - 3.5): This is a product of a number and a sum. Distribute the 4 to get 4 × 1.75y + 4 × (-3.5).
4 × 1.75y: This is multiplication of a number and a variable. The product is 7y.
4 × (-3.5): This is multiplication of a number and a constant. The product is -14.
1.25y: This is a single term.
Now, combine the like terms. Like terms are terms that have the same variable and the same exponent. In this case, the like terms are 7y and 1.25y.
When combined, the like terms are, 7y + 1.25y = 8.25y.
Add the constant term, -14.
Therefore, the simplified expression is 8.25y - 14.
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A jogger runs around a circular track of radius 55 ft. Let (x,y) be her coordinates, where the origin is the center of the track. When the jogger's coordinates are (33, 44), her x-coordinate is changing at a rate of 15 ft/s. Find dy/dt.
Using related rates and the Pythagorean theorem, we can find that dy/dt, the rate of change of the y-coordinate, is 0 ft/s.
Explanation:To find dy/dt, we need to determine the rate of change of the y-coordinate of the jogger. Since the jogger is running on a circular track, we can use the concept of related rates to solve this problem.
Let's assume that the jogger completes a full lap around the track in a time interval of Δt. During this time interval, the x-coordinate of the jogger changes by Δx, the y-coordinate changes by Δy, and the distance traveled along the track is Δs.
Since the jogger is running at a constant speed, the distance Δs is equal to the distance traveled in a straight line, which is the hypotenuse of a right triangle with legs Δx and Δy. Using the Pythagorean theorem, we have:
Δs^2 = Δx^2 + Δy^2
Taking the derivative with respect to time, we have:
2Δs(dΔs/dt) = 2Δx(dΔx/dt) + 2Δy(dΔy/dt)
Substituting the given values, Δx is 15 ft/s, Δy is 0 (since the y-coordinate is not changing), and Δs is the distance around the circular track, which is equal to the circumference of the circle:
2π(55ft) = 2(15ft)(dΔx/dt) + 2(0)(dΔy/dt)
Simplifying, we have:
dΔx/dt = π(55ft)/15s = 11π/3 ft/s
Therefore, dy/dt = dΔy/dt = 0 ft/s, since the y-coordinate is not changing.
Please find the center of dialation given the information in the link. Real answers only.
Answer:
(-4, 0)
Step-by-step explanation:
The scale factor of 1/2 means each "dilated" point is 1/2 the distance from the center of dilation that the original point is. That is, the dilated point is the midpoint between the original and the dilation center.
If O is the origin of the dilation, then ...
(O + X)/2 = P . . . . . P is the dilation of point X
O +X = 2P
O = 2P -X = 2(0, 2) -(4, 4)
O = (-4, 0)
The center of dilation is (-4, 0).
_____
Another way to find the center of dilation is to realize that dilation moves points along a radial line from the center. Hence the place where those radial lines converge will be the center of dilation. See the attachment for a solution that way.
Please help with these! I don't know how they work.
Answer:
1. all real numbers
2. y ≥ -8
3. It is all of the possible values of a function
4. Domain:{-4,-2,0,2,4} and Range:{-2,0,1,2,3}
Step-by-step explanation:
Let f:A→B be a function. In general sets A and B can be any arbitary non-empty sets.
Values in set A are the input values to the function and values in set B are the output values
Hence Set A is called the domain of the function f.
Set B is called co-domain or range of function f.
Now coming back to problem,
In first picture,
Given function is a straight line ⇒it can take any real number as its input
and for each value it gives a unique output value.
Hence output value is set of all real numbers, i.e. range of the function represented by the graph is set of all real numbers.
In the second picture,
The graph is x values are extending from -∞ to ∞ but the y values is the set of values of real numbers greater than -8 since we can see that the graph has global minimum of -8
Therefore range of the graph is y≥-8
in the third picture,
as we have already discussed the range of a function is the set of all possible output values of the function
In the fourth picture,
Let the function be 'f'.
from question we can tell that we can take only -4,-2,0,2,4 as the values for x and for corresponding x values we get 1,3,2,-2,0 as y values which are the output values.
hence we can tell that domain, which is set of input values, is {-4,-2,0,2,4}
and range, which is the of possible output values, is {-2,0,1,2,3}
The workers at Sandbachian, Inc. took a random sample of 800 manhole covers and found that 40 of them were defective. What is the 95% CI for p, the true proportion of defective manhole covers, based on this sample?a) (37.26, 42.74)b) (.035, .065)c) (.047, .053)d) (.015, .085)
Answer: b) [tex](0.035,\ 0.065)[/tex]
Step-by-step explanation:
The confidence interval for proportion (p) is given by :-
[tex]\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
, where[tex]\hat{p}[/tex] = Sample proportion
n= sample size.
z* = Critical z-value.
Let p be the true proportion of defective manhole covers, based on this sample.
Given : The workers at Sandbachian, Inc. took a random sample of 800 manhole covers and found that 40 of them were defective.
Then , n= 800
[tex]\hat{p}=\dfrac{40}{800}=0.05[/tex]
Confidence interval = 95%
We know that the critical value for 95% Confidence interval : z*=1.96
Then, the 95% CI for p, the true proportion of defective manhole covers will be :-
[tex]0.05\pm (1.96)\sqrt{\dfrac{0.05(1-0.05)}{800}}\\\\=0.05\pm (1.96)(0.0077055)\\\\=0.05\pm0.01510278\\\\=(0.05-0.01510278,\ 0.05+0.01510278)\\\\=(0.03489722,\ 0.06510278)\approx(0.035,\ 0.065) [/tex]
Hence, the required confidence interval : b) [tex](0.035,\ 0.065)[/tex]
Rita purchased a prepaid phone card for $30. Long distance cost 16 cents a minute using the card. Rita used her card only once to make a long distance call. If the remaining credit on her card if $26.48, how many minutes did her call last?
Answer: her call lasted for 22 minutes
Step-by-step explanation:
Rita purchased a prepaid phone card for $30. This means that the total credit on her card is $30. Long distance cost 16 cents a minute using the card. Converting to dollars, it costs 16/100 = $0.16
Rita used her card only once to make a long distance call. If the number of minutes if long distance call that she made is x, total cost of x minutes long distance calls will be 0.16 × x = $0.16x
The remaining credit on her card would be 30 - 0.16x
If the remaining credit on her card if $26.48, it means that
30 - 0.16x = 26.48
0.16x = 30 - 26.48 = 3.52
x = 3.52/0.16 = 22 minutes.
A 3 by 3 matrix Bis known to have eigenvalues 0, 1, 2. This information is enough to find three of these (give the answers where possible) : (a) the rank of B (b) thedeterminantofBTB (c) theeigenvaluesofBTB (d) the eigenvalues of (B2 + J)-1.
Answer with Step-by-step explanation:
We are given that a matrix B .
The eigenvalues of matrix are 0, 1 and 2.
a.We know that
Rank of matrix B=Number of different eigenvalues
We have three different eigenvalues
Therefore, rank of matrix B=3
b.
We know that
Determinant of matrix= Product of eigenvalues
Product of eigenvalues=[tex]0\times 1\times 2=0[/tex]
After transpose , the value of determinant remain same.
[tex]\mid B^TB\mid=\mid B^T\mid \mid B\mid =0\times 0=0[/tex]
c.Let
B=[tex]\left[\begin{array}{ccc}0&-&-\\-&1&-\\-&-&2\end{array}\right][/tex]
Transpose of matrix:Rows change into columns or columns change into rows.
After transpose of matrix B
[tex]B^T=\left[\begin{array}{ccc}0&-&-\\-&1&-\\-&-&2\end{array}\right][/tex]
[tex]B^TB=\left[\begin{array}{ccc}0^2&-&-\\-&1^2&-\\-&-&2^2\end{array}\right][/tex]
[tex]B^TB=\left[\begin{array}{ccc}0&-&-\\-&1&-\\-&-&4\end{array}\right][/tex]
Hence, the eigenvalues of [tex]B^TB[/tex] are 0, 1 and 4.
d.Eigenvalue of Identity matrix are 1, 1 and 1.
Eigenvalues of [tex]B^2+I=(0+1),(1+1),(2^2+1)=1,2,5[/tex]
We know that if eigenvalue of A is [tex]\lambda[/tex]
Then , the eigenvalue of [tex]A^{-1}[/tex] is [tex]\frac{1}{\lambda}[/tex]
Therefore, the eigenvalues of [tex](B^2+I)^{-1}[/tex] are
[tex]\frac{1}{1},\frac{1}{2},\frac{1}{5}[/tex]
The eigenvalues of [tex](B^2+I)^{-1}[/tex] are 1,[tex]\frac{1}{2}[/tex] and [tex]\frac{1}{5}[/tex]
21. The parent function of the following graph is f(x) = 2^x. What is the equation of the following graph?
Answer:
5
Step-by-step explanation:
Plug x = 0 into f(x) to get
f(x) = 2^x
f(0) = 2^0
f(0) = 1
The y intercept (0,1) is on the graph of f(x).
The y intercept for the red curve shown is (0,3). It has been moved up two units compared to (0,1)
Therefore, g(x) = f(x)+2 where g(x) represents the red curve.
g(x) = f(x) + 2
[tex]g(x) = 2^x + 2[/tex] is the answer
Please Help!!
Create two radical equations: one that has an extraneous solution, and one that does not have an extraneous solution. Use the equation below as a model:
[tex]a\sqrt{x+b} +c=d[/tex]
Given
[tex]a\sqrt{x+b}+c=d[/tex]
we have
[tex]\sqrt{x+b}=\dfrac{d-c}{a}[/tex]
Squaring both sides, we have
[tex]x+b=\dfrac{(d-c)^2}{a^2}[/tex]
And finally
[tex]x=\dfrac{(d-c)^2}{a^2}-b[/tex]
Note that, when we square both sides, we have to assume that
[tex]\dfrac{d-c}{a}>0[/tex]
because we're assuming that this fraction equals a square root, which is positive.
So, if that fraction is positive you'll actually have roots: choose
[tex]a=1,\ b=0,\ c=2,\ d=6[/tex]
and you'll have
[tex]\sqrt{x}+2=6 \iff \sqrt{x}=4 \iff x=16[/tex]
Which is a valid solution. If, instead, the fraction is negative, you'll have extraneous roots: choose
[tex]a=1,\ b=0,\ c=10,\ d=4[/tex]
and you'll have
[tex]\sqrt{x}+10=4 \iff \sqrt{x}=-6[/tex]
Squaring both sides (and here's the mistake!!) you'd have
[tex]x=36[/tex]
which is not a solution for the equation, if we plug it in we have
[tex]\sqrt{x}+10=4 \implies \sqrt{36}+10=4 \implies 6+10=4[/tex]
Which is clearly false