Find the union and interesection of each of the following A={3,6,9,12}, B ={6,8,9}
Answers
Answer:
Hello,
The answer would be,
A union B = {3,6,9,12}
and A intersection B= {6,9}
Answer:
[tex]\huge\boxed{ A\ union \ B = \{3,6,8,9,12\}}[/tex]
[tex]\huge\boxed{A\ intersection \ B = \{6,9\}}[/tex]
Step-by-step explanation:
A = {3,6,9,12}
B = {6,8,9}
A∪B = {3,6,9,12} ∪ { 6,8,9} [Union means all of the elements should be included in the set of A∪B]
=> A∪B = {3,6,8,9,12}
Now,
A∩B = {3,6,9,12} ∩ {6,8,9} [Intersection means common elements of the set]
=> A∩B = {6,9}
Related Questions
Write down the name of the shape for question D. Please help!
Answers
Step-by-step explanation:
thats shape is a delta
:)
Answer:
arrow head
Step-by-step explanation:
in the diagram, find the values of a and b.
Answers
Answer:
m∠a = 67° , m∠b = 42°Step-by-step explanation:
∠a is alternate interior angle to ∠ECD
∠b is alternate interior angle to ∠BCD
so:
If AB || CD then:
m∠a = m∠ECD = 25° + 42° = 67°
m∠b = 42°
A planet rotates on an axis through its poles and 1 revolution takes 1 day 1 day is 24 hours. The distance from the axis to a location the planet 30 degrees north latitude is about 3387.5 miles. Therefore, a location on the planet at 30 degrees north latitude is spinning on a circle of radius 3387.5 miles.
Compute the linear speed on the surface of the planet at 30 degrees north latitude.
Answers
Answer:
The velocity is [tex]v = 886.96 \ m/s[/tex]
Step-by-step explanation:
From the question we are told that
The period of each revolution is [tex]T = 1\ day = 24 \ hours[/tex]
The angle is [tex]\theta = 30^o[/tex]
The radius is [tex]r = 3387.5 \ miles[/tex]
Generally the linear speed is mathematically represented as
[tex]v = w * r[/tex]
Where [tex]w[/tex] is the angular speed which is mathematically represented as
[tex]w = \frac{2 \pi }{T}[/tex]
substituting values
[tex]w = \frac{2 *3.142 }{24}[/tex]
[tex]w = 0.2618 \ rad/s[/tex]
Thus
[tex]v = 0.261833 * 3387.5[/tex]
[tex]v = 886.96 \ m/s[/tex]
Even though the population standard deviation is unknown, an investigator uses z rather than the more appropriate t to test a hypothesis at the .01 level of significance. In this situation the true level of significance of this test is
Answers
Answer:
The true true level of significance of this test is more than 0.01.
Step-by-step explanation:
No standard deviation and we are told that the investigator still used z rather than the more appropriate t - distribution.
This method of using the z-distribution when standard deviation is unknown will definitely result in a smaller critical value and this in turn simply means that the p-value will be smaller than what it should really be.
Thus, it means the critical value is getting closer to the mean value than the way it should be.
Therefore, means that for a given significance of 0.01 and using the z-distribution under this no standard deviation situation, the true true level of significance of this test is more than 0.01.
A type of related samples design in which participants are observed more than once is called a
A. repeated measures design
B. matched pairs design
C. matched samples design
D. both matched pairs design and matched samples design
Answers
Answer:
Option A (repeated measures design) is the correct option.
Step-by-step explanation:
Researchers as well as statisticians vary in terms of methods used mostly for repetitive measurements. Besides illustration, repeated models of measurements are however recognized as repeated analyzes of variance measurements, standardized considerations of measurements, or layouts of objects throughout them.The other three options are not related to the given instance. So that alternative A would be the correct choice.
Yelena needs to swim a total of 8 miles this
week. So far, she swam 5 miles. Use the
equation 5 + m=8 to find how many more
miles Yelena needs to swim.
Answers
Answer:
3 miles
Step-by-step explanation:
5 + m=8
Subtract 5 from each side
5-5 + m=8-5
m = 3
She needs to swim 3 more miles
Answer:
Yelena needs to swim 3 more miles
Step-by-step explanation:
You need to solve for the variable "m", which represents the miles. Based on the information, Yelena swam 5 miles and she needs to swim 8. Solve:
[tex]5+m=8[/tex]
To find the value of m, you need to isolate it on one side of the equation. To do this, you need to get the 8 and 5 on the same side of the equal operation. For this, you need to use reverse operations. This undoes the value from one side and does the same on the other, keeping the equation balanced. Since we have a "positive 5", we take the opposite, which would be a "negative 5". So subtract 5 from both sides of the equation:
[tex]5-5+m=8-5[/tex]
Simplify. The 5's cancel each other out, leaving 0. 8-5 is 3:
[tex]m=3[/tex]
The total miles left that Yelena needs to swim is 3 miles.
:Done
Use the probability distribution table to answer the question.
What is P(1 < X < 5)?
Enter your answer, as a decimal, in the box.
Answers
Add up the P(x) values that correspond to x = 2 through x = 4
0.07+0.22+0.22
So we have a 51% chance of getting an x value such that 1 < x < 5
By using the probability distribution table, the value of P(1<x<5) is 0.51
What is Probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true
What is Probability distribution?A probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events
Given,
We have to find the value of P(1<x<5)
P(1<x<5) = P(2)+P(3)+P(4)
P(2)=0.07
P(3)=0.22
P(4)=0.22
P(1<x<5) = 0.07+0.22+0.22 =0.51
Hence, the value of P(1<x<4)= 0.51
Learn more about Probability and Probability distribution here
https://brainly.com/question/14210034
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5/7 minus 2/9 please
Answers
Answer:
[tex]\large \boxed{31/63}[/tex]
Step-by-step explanation:
5/7 - 2/9
Make denominators equal by LCM.
(5 × 9)/(7 × 9) - (2 × 7)/(9 × 7)
45/63 - 14/63
Subtract fractions since denominators are equal.
(45 - 14)/63
31/63
Answer:
[tex]\frac{31}{63}[/tex]
Step-by-step explanation:
Find the LCM of 7 and 9: 63Find how much we increased each number to get to 63: we increased 7 by 9, and we increased 9 by 7Multiply the numerators by the corresponding increase numbers: 5 × 9 = 45, and 2 × 7 = 14Put the new numerators over the new denominators, so it looks like this: [tex]\frac{45}{63}[/tex] and [tex]\frac{14}{63}[/tex] Finally, subtract one from the other and here's what you get: [tex]\frac{31}{63}[/tex]Therefore, the answer is [tex]\frac{31}{63}[/tex].
36x7 please EXPLAIN the process of the multiplication plse
Answers
36×7
=252
Explaination :
First Multiply 6 and 7 we get 42 !
Write 2 and 4 will be added to the product of 3×7
We get 21 and add 4 here
So we get 252
Answer:
[tex]36 \times 7 = 252[/tex]
Step-by-step explanation:
Firstly multiply 6 with 7 you have to write 2 and take 4 carry and then multiply 7 with 3 u get 21 now add the number u carry in 21 u get ur answer. 252.
Hope it helps u mate
Nala can spend no more than $150 per month on gasoline. She has already purchased $60 in gas this month. Which inequality can be used to find the maximum number of fill-ups she can purchase during the rest of the month, assuming each fill-up costs $30? 30n + 60 > 150 30n + 60 150
Answers
Answer:
150<60+30n
Step-by-step explanation:
150 is the maximum amount that she can spend on gas. (which is the total)
she already spend $60
each fill up (n) costs 30
Answer:
the answer is B)
Step-by-step explanation:
Chloe wants to wrap a present in a box for Sarah. The top and bottom of the box is 8 in. by 3 in., the sides are both 3 in by 2 in. and the front and back are 8 in by 2 in. How much wrapping
paper will Chloe need to wrap the present?
Answers
Answer:
92 inches squared
Step-by-step explanation:
T/P = 8 * 3
L/R = 3 * 2
F/B = 8 * 2
Solving for surface area!
2(24) + 2(6) + 2(16) = 92
Question 15 please and i will mark the brainliest!!! And thank you to whoever answers
Answers
Explanation:
We have 4 options for the first choice and 3 options for the next. So there are 4*3 = 12 different combos possible. The tree diagram below shows 12 different paths to pick from. For instance, the right-most path has us pick the number 4 and the color yellow.
Solve x2 + 9x + 8 = 0 by completing the square. What are the solutions?
O (1.-8)
O (1.8)
O (-1-8)
Answers
Explanation:
x^2 + 9x + 8 = 0
x^2 + 9x = -8
Add (9/2)^2 to both sides
x^2 + 9x + (9/2)^2 = -8 + (9/2)^2
(x + 9/2)^2 = -8 + 81/4
(x + 9/2)^2 = -32/4 + 81/4
(x + 9/2)^2 = 49/4
Square root both sides
Sqrt (x + 9/2)^2 = sqrt 49/4
x + 9/2 = plus or minus 7/2
Set x + 9/2 = 7/2:
x + 9/2 = 7/2
x = 7/2 - 9/2
x = -2/2 = -1
Set x + 9/2 = -7/2:
x + 9/2 = -7/2
x = -7/2 - 9/2
x = -16/2 = -8
Find an exact value of sin(17pi/12)
Answers
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
[tex]\frac{(17)(3.141593)}{12}[/tex]
= [tex]\frac{53.407075}{12}[/tex]
= [tex]4.45059[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
If this helped you, could you maybe give brainliest..?
Also Have a great day/night!
❀*May*❀
I have an answer and explanation but I can't type so search up the question you asked and you should get an answer and explanation from s0cratic.
Marine ecologists estimate the reproduction curve for swordfish in a fishing ground to be f(p) = −0.01p2 + 9p, where p and f(p) are in hundreds. Find the population that gives the maximum sustainable yield, and the size of the yield.
Answers
Answer:
The population that gives the maximum sustainable yield is 45000 swordfishes.
The maximum sustainable yield is 202500 swordfishes.
Step-by-step explanation:
Let be [tex]f(p) = -0.01\cdot p^{2}+9\cdot p[/tex], the maximum sustainable yield can be found by using first and second derivatives of the given function: (First and Second Derivative Tests)
First Derivative Test
[tex]f'(p) = -0.02\cdot p +9[/tex]
Let equalize the resulting expression to zero and solve afterwards:
[tex]-0.02\cdot p + 9 = 0[/tex]
[tex]p = 450[/tex]
Second Derivative Test
[tex]f''(p) = -0.02[/tex]
This means that result on previous part leads to an absolute maximum.
The population that gives the maximum sustainable yield is 45000 swordfishes.
The maximum sustainable yield is:
[tex]f(450) = -0.01\cdot (450)^{2}+9\cdot (450)[/tex]
[tex]f(450) =2025[/tex]
The maximum sustainable yield is 202500 swordfishes.
Century Roofing is thinking of opening a new warehouse, and the key data are shown below. The company owns the building that would be used, and it could sell it for $100,000 after taxes if it decides not to open the new warehouse. The equipment for the project would be depreciated by the straight-line method over the project's 3-year life, after which it would be worth nothing and thus it would have a zero salvage value. No new working capital would be required, and revenues and other operating costs would be constant over the project's 3-year life. What is the project's NPV? (Hint: Cash flows are constant in Years 1-3.)
Answers
Question Completion:
WACC = 10.0%
Opportunity cost = $100,000
Net equipment cost (depreciable basis) = $65,000
Straight-line deprec. rate for equipment = 33.333%
Sales revenues, each year = $123,000
Operating costs (excl. deprec.), each year = $25,000
Tax rate = 35%
Answer:
Century Roofing
Project's NPV is: ($6,578)
Step-by-step explanation:
a) Data and Calculations:
WACC = 10.0%
Opportunity cost = $100,000
Net equipment cost (depreciable basis) = $65,000
Straight-line deprec. rate for equipment = 33.333%
Sales revenues, each year = $123,000
Operating costs (excl. deprec.), each year = $25,000
Tax rate = 35%
Cash outflow in year 0 = $165,000 (Opportunity and new equipment costs)
Annual Cash inflow = $123,000 - $25,000 - $34,300 = $63,700
PV of annuity for 3 years at 10% = $158,422 ($63,700 x 2.487)
NPV = Cash inflow minus Cash outflow
= $158,422 - $165,000
= ($6,578)
Negative NPV
b) Since Century Roofing could have realized $100,000 from the sale of the building if it decides not to open the new warehouse, this opportunity cost is factored into the calculation of the Net Present Value. It becomes a present cash outflow. Century Roofing's opportunity cost is defined as the loss of $100,000 being the future return from the best alternative project when it chooses to build the new warehouse instead of selling off the building.
as
8
3) The volume of
a wall, 5 times
high as it is board and 8
times as long as it is high, 12.8
(a.metors) Find The Breadth of the
Wall
Answers
Answer:
0.4 meters
Step-by-step explanation:
The volume is ...
V = LHB
12.8 m³ = (8(5B))(5B)(B) = 200B³ . . . fill in given values
0.064 m³ = B³ . . . . . simplify
∛0.064 m = B = 0.4 m
The breadth of the wall is 0.4 meters.
Enter an expression that is equivalent to (6x2−1)+(x2+3)−2(x2−5)−15x2, combining all like terms. Use the on-screen keyboard to type the correct polynomial in the box below.
Answers
Answer:
Its 10x^2+12
Step-by-step explanation:
Answer:
-10X^2+12
Step-by-step explanation:
Scores on a college entrance examination are normally distributed with a mean of 500 and a standard deviation of 100. What percent of people who write this exam obtain scores between 350 and 650?
Answers
Answer:
The percentage is [tex]P(350 < X 650 ) = 86.6\%[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 500[/tex]
The standard deviation is [tex]\sigma = 100[/tex]
The percent of people who write this exam obtain scores between 350 and 650
[tex]P(350 < X 650 ) = P(\frac{ 350 - 500}{ 100} <\frac{ X - \mu }{ \sigma } < \frac{650 - 500}{ 100} )[/tex]
Generally
[tex]\frac{X - \mu }{\sigma } = Z (The \ standardized \ value \ of \ X )[/tex]
[tex]P(350 < X 650 ) = P(\frac{ 350 - 500}{ 100} <Z < \frac{650 - 500}{ 100} )[/tex]
[tex]P(350 < X 650 ) = P(-1.5<Z < 1.5 )[/tex]
[tex]P(350 < X 650 ) = P(Z < 1.5) - P(Z < -1.5)[/tex]
From the z-table [tex]P(Z < -1.5 ) = 0.066807[/tex]
and [tex]P(Z < 1.5 ) = 0.93319[/tex]
=> [tex]P(350 < X 650 ) = 0.93319 - 0.066807[/tex]
=> [tex]P(350 < X 650 ) = 0.866[/tex]
Therefore the percentage is [tex]P(350 < X 650 ) = 86.6\%[/tex]
Suppose that 11% of all steel shafts produced by a certain process are nonconforming but can be reworked (rather than having to be scrapped). Consider a random sample of 200 shafts, and let X denote the number among these that are nonconforming and can be reworked.Required:a. What is the (approximate) probability that X is at most 30?b. What is the (approximate) probability that X is less than 30?c. What is the (approximate) probability that X is between 15 and 25 (inclusive)?
Answers
Answer:
(a) The probability that X is at most 30 is 0.9726.
(b) The probability that X is less than 30 is 0.9554.
(c) The probability that X is between 15 and 25 (inclusive) is 0.7406.
Step-by-step explanation:
We are given that 11% of all steel shafts produced by a certain process are nonconforming but can be reworked. A random sample of 200 shafts is taken.
Let X = the number among these that are nonconforming and can be reworked
The above situation can be represented through binomial distribution such that X ~ Binom(n = 200, p = 0.11).
Here the probability of success is 11% that this much % of all steel shafts produced by a certain process are nonconforming but can be reworked.
Now, here to calculate the probability we will use normal approximation because the sample size if very large(i.e. greater than 30).
So, the new mean of X, [tex]\mu[/tex] = [tex]n \times p[/tex] = [tex]200 \times 0.11[/tex] = 22
and the new standard deviation of X, [tex]\sigma[/tex] = [tex]\sqrt{n \times p \times (1-p)}[/tex]
= [tex]\sqrt{200 \times 0.11 \times (1-0.11)}[/tex]
= 4.42
So, X ~ Normal([tex]\mu =22, \sigma^{2} = 4.42^{2}[/tex])
(a) The probability that X is at most 30 is given by = P(X < 30.5) {using continuity correction}
P(X < 30.5) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{30.5-22}{4.42}[/tex] ) = P(Z < 1.92) = 0.9726
The above probability is calculated by looking at the value of x = 1.92 in the z table which has an area of 0.9726.
(b) The probability that X is less than 30 is given by = P(X [tex]\leq[/tex] 29.5) {using continuity correction}
P(X [tex]\leq[/tex] 29.5) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{29.5-22}{4.42}[/tex] ) = P(Z [tex]\leq[/tex] 1.70) = 0.9554
The above probability is calculated by looking at the value of x = 1.70 in the z table which has an area of 0.9554.
(c) The probability that X is between 15 and 25 (inclusive) is given by = P(15 [tex]\leq[/tex] X [tex]\leq[/tex] 25) = P(X < 25.5) - P(X [tex]\leq[/tex] 14.5) {using continuity correction}
P(X < 25.5) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{25.5-22}{4.42}[/tex] ) = P(Z < 0.79) = 0.7852
P(X [tex]\leq[/tex] 14.5) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{14.5-22}{4.42}[/tex] ) = P(Z [tex]\leq[/tex] -1.70) = 1 - P(Z < 1.70)
= 1 - 0.9554 = 0.0446
The above probability is calculated by looking at the value of x = 0.79 and x = 1.70 in the z table which has an area of 0.7852 and 0.9554.
Therefore, P(15 [tex]\leq[/tex] X [tex]\leq[/tex] 25) = 0.7852 - 0.0446 = 0.7406.
coefficient of 8x+7y
Answers
Answer:
8
Step-by-step explanation:
Identify the exponents on the variables in each term, and add them together to find the degree of each term.
8x→1
7y→1
The largest exponent is the degree of the polynomial.
1
The leading term in a polynomial is the term with the highest degree.
8x
The leading coefficient of a polynomial is the coefficient of the leading term.
____________________________________________________________
The leading term in a polynomial is the term with the highest degree.
8x
The leading coefficient in a polynomial is the coefficient of the leading term.
8
List the results.
Polynomial Degree: 1
Leading Term: 8x
Leading Coefficient: 8
Hope This Helps!!!
A human factor expert recommends that there be atleast 9 square ft of floor space in a classroom for every student in the class. Find the min space required for 49 students
Answers
13,226 divided by 29
Answers
13226/29= 456.068965517
A new fast-food firm predicts that the number of franchises for its products will grow at the rate dn dt = 6 t + 1 where t is the number of years, 0 ≤ t ≤ 15.
Answers
Answer:
The answer is "253"
Step-by-step explanation:
In the given- equation there is mistype error so, the correct equation and its solution can be defined as follows:
Given:
[tex]\bold{\frac{dn}{dt} = 6\sqrt{t+1}}\\[/tex]
[tex]\to dn= 6\sqrt{t+1} \ \ dt.....(a)\\\\[/tex]
integrate the above value:
[tex]\to \int dn= \int 6\sqrt{t+1} \ \ dt \\\\\to n= \frac{(6\sqrt{t+1} )^{\frac{3}{2}}}{\frac{3}{2}}+c\\\\\to n= \frac{(12\sqrt{t+1} )^{\frac{3}{2}}}{3}+c\\\\[/tex]
When the value of n=1 then t=0
[tex]\to 1= \frac{12(0+1)^{\frac{3}{2}}}{3}+c\\\\ \to 1= \frac{12(1)^{\frac{3}{2}}}{3}+c\\\\\to 1-\frac{12}{3}=c\\\\\to \frac{3-12}{3}=c\\\\\to \frac{-9}{3}=c\\\\\to c=-3\\[/tex]
so the value of n is:
[tex]\to n= \frac{(12\sqrt{t+1} )^{\frac{3}{2}}}{3}-3\\\\[/tex]
when we put the value t= 15 then,
[tex]\to n= \frac{(12\sqrt{15+1} )^{\frac{3}{2}}}{3}-3\\\\\to n= \frac{(12\sqrt{16} )^{\frac{3}{2}}}{3}-3\\\\\to n= \frac{(12\times 64)}{3}-3\\\\\to n= (4\times 64)-3\\\\\to n= 256-3\\\\\to n= 253[/tex]
name all the pairs of angles which are vertical angles , alternate interior angles , alternate exterior angles , co interior angles , co exterior angles , and corresponding angles from the given figure . (co interior - interior angles on the same side of transversal)
Answers
Answer:
Step-by-step explanation:
Since m and k are the parallel lines and a transverse 'l' is intersecting these lines at two different points.
- Opposite angles at the point of intersection of parallel lines and the transverse will be the vertical angles.
∠1 ≅ ∠3, ∠2 ≅ ∠4, ∠5 ≅ ∠8 and ∠6 ≅ ∠7 [Vertical angles]
- Pair of angles between parallel lines 'k' and 'm' but on the opposite side of the transversal are the alternate interior angles.
∠4 ≅ ∠6 and ∠3 ≅ ∠5 [Alternate interior angles]
- Angles having the same relative positions at the point of intersection are the corresponding angles.
∠2 ≅ ∠6, ∠3 ≅ ∠8, ∠4 ≅ ∠7 and ∠1 ≅ ∠5 [Corresponding angles]
- Co interior angles are the angles between the parallel lines located on the same side of the transversal.
∠4 and ∠5, ∠3 and ∠6 [Co interior angles]
- Co exterior angles are the angles on the same side of the transverse but outside the parallel lines.
∠2 and ∠8, ∠1 and ∠7 [Co exterior angles]
Find the work W done by a force of 7pounds acting in the direction 30 degreesto the horizontal in moving an object 7feet from (0 comma 0 )to (7 comma 0 ).
Answers
Answer:
The work done by the force is 42.4 Joules
Step-by-step explanation:
The force F = 7 pounds
angle to the horizontal that the force acts ∅ = 30°
The object is moved a distance d = 7 feet
The coordinate (0 comma 0 )to (7 comma 0 ), indicates that the movement started from the origin, and is along the x-axis.
The work done by this force = F cos ∅ x d
==> 7 cos 30° x 7
==> 7 x 0.866 x 7 = 42.4 Joules
A parent increases a child’s monthly allowance by 20% each year. If the allowance is $8 per month now, in about how many years will it take to reach $20 per month? Use the equation 20 = 8(1.2)x to solve the problem. Round to the nearest year. 1 year 5 years 2 years 16 years
Answers
Answer:
6 years
Step-by-step explanation:
A parent increases a child’s monthly allowance by 20% each year. If the allowance is $8 per month now. This is an exponential function, An exponential function is given by:
[tex]y=ab^x[/tex]
Let x be the number of years and y be the allowance. The initial allowance is $8, this means at x = 0, y = 8
[tex]y=ab^x\\8=ab^0\\a=8[/tex]
Since it increases by 20% each year, i.e 100% + 20% = 1 + 0.2 = 1.2. This means that b = 1.2
Therefore:
[tex]y=ab^x\\y=8(1.2^x) \\[/tex]
To find the number of years will it take to reach $20 per month, we substitute y = 20 and find x
[tex]20=8(1.2)^x\\20/8=1.2^x\\1.2^x=2.5\\Taking \ natural\ log\ of \ both\ sides:\\ln(1.2^x)=ln2.5\\xln(1.2)=0.9163\\x=0.9163/ln(1.2)\\x=5.026[/tex]
x = 6 years to the nearest year
Answer:
5 years
Step-by-step explanation:444
Given the following hypotheses: H0: μ = 490 H1: μ ≠ 490 A random sample of 15 observations is selected from a normal population. The sample mean was 495 and the sample standard deviation 9. Using the 0.01 significance level:
a.) State the decision rule.
b.) Compute the value of the test statistic.
c.) What is your decision regarding the null hypothesis?
Answers
Answer:
We conclude that the population mean is equal to 490.
Step-by-step explanation:
We are given that a random sample of 15 observations is selected from a normal population. The sample mean was 495 and the sample standard deviation 9.
Let [tex]\mu[/tex] = population mean.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 490 {means that the population mean is equal to 490}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 490 {means that the population mean is different from 490}
The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_1_4[/tex]
where, [tex]\bar X[/tex] = sample mean = 495
s = sample standard deviation = 9
n = sample of observations = 15
So, the test statistics = [tex]\frac{495-490}{\frac{9}{\sqrt{15} } }[/tex] ~ [tex]t_1_4[/tex]
= 2.152
The value of t-test statistics is 2.152.
Now, at a 0.01 level of significance, the t table gives a critical value of -2.977 and 2.977 at 14 degrees of freedom for the two-tailed test.
Since the value of our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as the test statistics will not fall in the rejection region.
Therefore, we conclude that the population mean is equal to 490.
3
BO
Evaluate the function f(x) = x2 + 4x + 1 at the given values of the independent variable and simplify.
a. f(6)
b. f(x +9)
c. f(-x)
Answers
Answer:
a) f(6)=(6)^2+4(6)+1=65
b)f (x+9)=(x+9)^2+4 (x+9)+1=(x^2+18x+81)+(4x+36)+1=x^2+22x+117
f (-x)=(-x)^2-4x+1
Determine if the process appears to be within statistical control. If not, state the reason why not.
a. It does not appear to be within statistical control because there is an upward shift.
b. It appears to be within statistical control.
c. It does not appear to be within statistical control because there is an upward trend.
d. It does not appear to be within statistical control because there is increasing variation.
Answers
Answer:
c. It does not appear to be within statistical control because there is an upward trend.
Step-by-step explanation:
Statistical process control is a method for quality control which employs statistical method to monitor and control process. It ensures operation efficiency and ensuring required specification to reduce wastes in production lines. Here the process variation is out of control because the statistical control has an upward trend.
