Answer:
7x-1
Step-by-step explanation:
f(x)+g(x)5x-2+(2x+1) 5x-2+2x+17x-1The solution is : If f(x) = 5x – 2 and g(x) = 2x + 1, then the value of (f+g)(x) is : 7x-1.
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
given that,
If f(x) = 5x – 2 and g(x) = 2x + 1,
now, we have to find (f+g)(x).
so, we have,
f(x) = 5x – 2
and g(x) = 2x + 1
now,
(f+g)(x)
=f(x)+g(x)
=5x-2+(2x+1)
=5x-2+2x+1
=7x-1
Hence, The solution is : If f(x) = 5x – 2 and g(x) = 2x + 1, then the value of (f+g)(x) is : 7x-1.
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Which sentence in this excerpt from Common Sense by Thomas Paine supports the claim that the American colonies could thrive independently from Britain? I have heard it asserted by some, that as America hath flourished under her former connection with Great Britain that the same connection is necessary towards her future happiness, and will always have the same effect. Nothing can be more fallacious than this kind of argument. We may as well assert that because a child has thrived upon milk that it is never to have meat, or that the first twenty years of our lives is to become a precedent for the next twenty. But even this is admitting more than is true, for I answer roundly, that America would have flourished as much, and probably much more, had no European power had any thing to do with her. The commerce, by which she hath enriched herself, are the necessaries of life, and will always have a market while eating is the custom of Europe.
Answer:
A
Step-by-step explanation:
Answer:
"But even this is admitting more than is true, for I answer roundly, that America would have flourished as much, and probably much more, had no European power had any thing to do with her."
Step-by-step explanation:
Checked 2021
Which of the following points is NOT a solution of the inequality y ≥ Ixl + 3?
A. (-3, 0)
B. (-3, 6)
C. (0, 4)
Hey there!
To solve this, we need to plug each of our answer options into the inequality and see if it is true. Which ever one doesn't make the inequality true when plugged in is the answer.
OPTION A
(x,y)=(-3,0)
We plug our values into the inequality.
0≥ I-3I+3
You may have noticed the bars surrounding the negative three.. If you didn't know, this is called absolute value. Absolute value is how far the number is from 0 on the number line. -7 is 7 away from 0 on a number line, so the absolute value of -7 is 7. The absolute value of 7 is 7. The absolute value of 0 is 0. Absolute value is signified by these bars. Le'ts finish evaluating.
0≥6
As you can see, zero is not greater than or equal to six. So, option A is false.
Since A is not a solution, we already know that that is the answer, so we don't even need to check B and C. But, we can still evaluate them if you want.
OPTION B
6≥I-3I+3
6≥6
This is true.
OPTION C
4≥I0I+3
4≥3
This is also true.
Therefore, the answer is A. (-3,0)
Have a wonderful day!
11- In
how many ways 3 mathematics books, 4 history books ,3
chemisidy books and a biology books can be arranged
on an Shelf so thet all books of the same subjects are
together!
Answer: 20,736
Step-by-step explanation:
Math and History and Chemistry and Biology and Subjects
3! x 4! x 3! x 1! x 4! = 20,736
Simplfy the following expressions:
Answer:
1st one = d y^27
2nd one = b 2x^9
Step-by-step explanation:
1st one: since the power is being raised to the power of 3 you multiply the numbers
2nd one: the powers aren't being raised so you add the powers together.
12x^13y^10/6X^4y^10
then dividing for exponents is subtracting them so
2x^9 since y gets canceled out
A rectangle measures 18 cm x 3 cm what is its area
Answer:
Six
Step-by-step explanation:
The answer could be shown in multiple forms, but if I'm correct, the answer to this problem would be six.
Given the figure below, find the values of x and Z.
Please explain step by step how to solve, this is a guide for a test.
Answer:
(x, z) = (7, 69)
Step-by-step explanation:
Easy first: 69° and z° are vertical angles, so congruent:
z = 69
__
The angle marked with an expression in x is supplementary to either of the other two:
(6x +69)° +69° = 180°
6x = 42 . . . . . . . . . . . . divide by °, subtract 138
x = 7 . . . . . . . . . . . . . . divide by 6
In this problem, y = c1ex + c2e−x is a two-parameter family of solutions of the second-order DE y'' − y = 0. Find a solution of the second-order IVP consisting of this differential equation and the given initial conditions. y(−1) = 9, y'(−1) = −9
Answer:
[tex]y(x)=\frac{9}{e^{1} } e^{-x} =3.310914971e^{-x}[/tex]
Step-by-step explanation:
This problem is very simple, since they give the solution for the differential equation from the start. So basically, you need to evaluate the initial conditions into the solution, and the derivative of the solution in order to find the value of the constants [tex]c_1[/tex] and [tex]c_2[/tex].
So, first of all, let's find the derivative of [tex]y(x)[/tex]:
[tex]y'(x)=c_1 e^{x} -c_2e^{-x}[/tex]
Now, let's evaluate the first initial condition:
[tex]y(-1)=c_1e^{-1} +c_2e^{-(-1)} =9\\\\c_1e^{-1} +c_2e^{1}=9\hspace{10}(1)[/tex]
Now, the second initial condition:
[tex]y'(-1)=c_1 e^{-1} -c_2e^{-(-1)}=-9\\\\c_1 e^{-1} -c_2e^{1}=-9\hspace{10}(2)[/tex]
Combining (1) and (2) we have a 2x2 System of Equations. Let's use elimination method in order to solve it:
[tex](1)+(2):\\\\c_1e^{-1} +c_2e^{1} +c_1e^{-1} -c_2e^{1}=9-9\\\\2c_1e^{-1} =0\\\\Hence\\\\c_1=0[/tex]
Replacing [tex]c_1[/tex] into (1)
[tex](0)e^{-1} +c_2e^{1}=9\\\\c_2e^{1}=9\\\\Hence\\\\c_2=\frac{9}{e^{1} } =3.310914971[/tex]
Therefore the solution of the second-order IVP is:
[tex]y(x)=\frac{9}{e^{1} } e^{-x} =3.310914971e^{-x}[/tex]
PLZZZ I NEED HELP I’ll give 20 POINTS
What is the median of the following data set?
(6,3, 9, 1,7)
03
06
08
09
Answer:
6
Step-by-step explanation:
Arrange the data from smallest to largest
1,3,6,7,9
The median is the middle number
1,3 ,6, 7, 9
The middle number is 6
Classify the following triangle. Check all that apply.
A. Isosceles
B. Right
C. Obtuse
D. Equilateral
E. Scalene
F. Acute
Answer:
Equilateral
Acute
Step-by-step explanation:
The sides are all equal as indicated by the lines on each side - Equilateral
The angles are all equal by the angle marks 180/3 = 60 which is less than 90 degrees. This makes the angles acute
Suppose that we don't have a formula for g(x) but we know that g(3) = −1 and g'(x) = x2 + 7 for all x.
(a) Use a linear approximation to estimate g(2.95) and g(3.05).
g(2.95) =
g(3.05) =
(b) Are your estimates in part (a) too large or too small? Explain.
A) The slopes of the tangent lines are positive and the tangents are getting steeper, so the tangent lines lie below the curve. Thus, the estimates are too small.
B) The slopes of the tangent lines are positive but the tangents are becoming less steep, so the tangent lines lie below the curve. Thus, the estimates are too small.
C) The slopes of the tangent lines are positive and the tangents are getting steeper, so the tangent lines lie above the curve. Thus, the estimates are too large.
D) The slopes of the tangent lines are positive but the tangents are becoming less steep, so the tangent lines lie above the curve. Thus, the estimates are too large.
Answer:
g(2.95) ≈ -1.8; g(3.05) ≈ -0.2A) tangents are increasing in slope, so the tangent is below the curve, and estimates are too small.Step-by-step explanation:
(a) The linear approximation of g(x) at x=b will be ...
g(x) ≈ g'(b)(x -b) +g(b)
Using the given relations, this is ...
g'(3) = 3² +7 = 16
g(x) ≈ 16(x -3) -1
Then the points of interest are ...
g(2.95) ≈ 16(2.95 -3) -1 = -1.8
g(3.05) ≈ 16(3.05 -3) -1 = -0.2
__
(b) At x=3, the slope of the curve is increasing, so the tangent lies below the curve. The estimates are too small. (Matches description A.)
How many meters are in 18,200 milliliter
Answer:
18.2 :)
Have a great day!!!
PLEASE HELP SOLVE THIS!!!!!
Answer:
20) -43
21) 25
22)-9
Step-by-step explanation:
20) -6 (-6 + 49)/6 = -43
21) 10 - (-10 - (-1 + 6)) = 25
22) 1 - 10/2 - 5 = -9
Step-by-step explanation:
22Let's calculate the expression khowing that m= 1 and n = 5
m-[tex]\frac{m+m}{2}[/tex] -nm- [tex]\frac{2m}{2}[/tex]-n m-m-n0-n0-5-520Let's calculate the expression khowing that n= -7 and p= - 6
[tex]\frac{p(p+n^{2}) }{6}[/tex] [tex]\frac{-6(-6+(-7)^{2}) }{6}[/tex][tex]\frac{-6(-6+49)}{2}[/tex] [tex]\frac{-6*43}{6}[/tex] -1*43-4321Let's calculate the expression khowing that n = -6 and m = -1 and p = -10
mp-(p-(m-n))mp-(p-m+n)mp-p+m-n(-1)*(-10)-(-10)+(-1)-(-6)10+10-1+620-1+619+625What is the radius of a circle what circumference is 44cm
A. 42cm
D. 24cm
B. 48cm
C. 12cm
Hello!!
Circumference of a circle = 2πr
and
Given, 2πr = 44cm
So,
πr = 44/2 = 22
r = 22 × 7/22
r = 7cm is the answer.
Stay safe and God bless!
- eli <3
Answer:
7 cm
Step-by-step explanation:
Circumference of a circle is 2 π r
2πr = 44
Solve for radius.
r = 44/(2π)
r = 7.002817
Simplify: |4-5| / 9 × 3³ - 2/5 a.61/10 b.13/5 c.11/10 d.-2/15
━━━━━━━☆☆━━━━━━━
▹ Answer
Answer = b. 13/5
▹ Step-by-Step Explanation
|4 - 5| ÷ 9 × 3³ - 2/5
|-1| ÷ 9 × 3³ - 2/5
1 ÷ 9 × 3³ - 2/5
1/9 × 3³ - 2/5
1/3² × 3³ - 2/5
3 - 2/5
Answer = 13/5
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Answer:
[tex] \boxed{\sf b. \ \frac{13}{5}} [/tex]
Step-by-step explanation:
[tex] \sf Simplify \: the \: following: \\ \sf \implies \frac{ |4 - 5| }{9} \times {3}^{3} - \frac{2}{5} \\ \\ \sf 4 - 5 = - 1 : \\ \sf \implies \frac{ | - 1| }{9} \times {3}^{3} - \frac{2}{5} \\ \\ \sf Since \: - 1 \: is \: a \: negative \: constant, \: |-1| = 1: \\ \sf \implies \frac{1}{9} \times {3}^{3} - \frac{2}{5} \\ \\ \sf {3}^{3} = 3 \times {3}^{2} : \\ \sf \implies \frac{ \boxed{ \sf 3 \times {3}^{2}} }{9} - \frac{2}{5} \\ \\ \sf {3}^{2} = 9 : \\ \sf \implies \frac{3 \times 9}{9} - \frac{2}{5} \\ \\ \sf \frac{9}{9} = 1 : \\ \sf \implies 3 - \frac{2}{5} [/tex]
[tex] \sf Put \: 3 - \frac{2}{5} \: over \: the \: common \: denominator \: 5 : \\ \sf \implies 3 \times \frac{5}{5} - \frac{2}{5} \\ \\ \sf \implies \frac{3 \times 5}{5} - \frac{2}{5} \\ \\ \sf 3 \times 5 = 15 : \\ \sf \implies \frac{ \boxed{ \sf 15}}{5} - \frac{2}{5} \\ \\ \sf \implies \frac{15 - 2}{5} \\ \\ \sf 15 - 2 = 13 : \\ \sf \implies \frac{13}{5} [/tex]
Tublu buys a cylindrical water tank of height 1.4m and diameter 1.1 to catch rainwater off his roof.he has a full 2 liters tin of paint in his store and decides to paint the tank (not the base) If he uses 25ml to cover 1m^2 will he have enough paint to cover the tank with one layer of paint
Answer:
yes
Step-by-step explanation:
The lateral area of a cylinder is ...
LA = πdh
Putting in the given numbers, we find the area to be ...
LA = π(1.1 m)(1.4 m) ≈ 4.838 m²
At 25 mL per m², the amount of paint Tublu needs is ...
(4.838 m²)(25 mL/m²) = 120.95 mL
2 liters is 2000 mL, so Tublu easily has enough paint for one layer.
___
The amount he has is enough for more than 16 coats of paint, so he could paint inside and out with the paint he has.
Answer:
he should.
Step-by-step explanation:
Use the standard normal table to find P(z ≥ 1.06). Round to the nearest percent.
Answer:
14%
Step-by-step explanation:
On edge 2020
Which of the following cannot have a Discrete probability distribution? a. The number of customers arriving at a gas station in Christmas day b. The number of bacteria found in a cubic yard of soil. c. The number of telephone calls received by a switchboard in a specified time period. d. The length of a movie
Answer:
d. The length of a movie
Step-by-step explanation:
A discrete random variable is a variable which only takes on integer values.
A discrete distribution is used to describe the probability of the occurrence of each value of a discrete random variable.
From the given options, the length of a movie is not a discrete variable as it can have decimal values.
It therefore cannot have a Discrete probability distribution.
The correct option is D.
Brainliest to whoever gets this correct This word problem has too much information. Which fact is not needed to solve the problem? Tanisha tried to sell all her old CDs at a garage sale. She priced them at $2 each. She put 80 CDs in the garage sale, but she sold only 35 of them. How many did she have left? A. All of the information is needed. B. Tanisha sold the CDs for $2 each. C. Tanisha put 80 CDs in the sale. D. Tanisha sold 35 of the CDs.
Answer:
B. Tanisha sold the CDs for $2 each.
Step-by-step explanation:
Hurry!! Determine the intervals for which the function shown below is decreasing.
Answer:
everywhere except between 2 and 5
(between -inf and 2 and between 5 and inf)
Step-by-step explanation:
A production facility employs 20 workers on the day shift, 15 workers on the swing shift, and 10 workers on the graveyard shift. A quality control consultant is to select 7 of these workers for in-depth interviews. Suppose the selection is made in such a way that any particular group of 7 workers has the same chance of being selected as does any other group (drawing 7 slips without replacement from among 45).
1. How many selections result in all 7 workers coming from the day shift?
2. What is the probability that all 7 selected workers will be from the day shift?
3. What is the probability that all 7 selected workers will be from the same shift?
4. What is the probability that at least two different shifts will be represented among the selected workers?
5. What is the probability that at least one of the shifts will be un-represented in that sample of workers?
Answer:
1. 77520
2. [tex]P_1[/tex] = 0.0017
3. [tex]P_2[/tex] = 0.0019
4. [tex]P_3[/tex] = 0.9981
5. [tex]P_4[/tex] = 0.2036
Step-by-step explanation:
The number of ways or combinations in which we can select x elements from a group of n can be calculated as:
[tex]nCx = \frac{n!}{x!(n-x)!}[/tex]
So, there are 77520 selections that result in all 7 workers coming from the day shift. It is calculated as:
[tex]20C7 = \frac{20!}{7!(20-7)!}=77520[/tex]
At the same way, the total number of selections of 7 workers from the 45 is 45C7, so the probability that all 7 selected workers will be from the day shift is:
[tex]P_1=\frac{20C7}{45C7} =0.0017[/tex]
The probability that all 7 selected workers will be from the same shift is calculated as:
[tex]P_2=\frac{20C7+15C7+10C7}{45C7} =0.0019[/tex]
Because the consultant can select all workers from the day shift (20C7) or can select all workers from the swing shift (15C7) or can select all workers from the graveyard shift (10C7).
On the other hand, the probability that at least two different shifts will be represented among the selected workers is the complement of the probability that all 7 selected workers will be from the same shift. So it is calculated as:
[tex]P_3 = 1- P_2=1 - 0.0019 = 0.9981[/tex]
Finally, the probability that at least one of the shifts will be un-represented in that sample of workers is:
[tex]P_4=\frac{25C7+30C7+35C7}{45C7} =0.2036[/tex]
Where 25C7 is the number of ways to select all 7 workers from swing or graveyard shift, 30C7 is the number of ways to select all 7 workers from day or graveyard shift and 35C7 is the number of ways to selects all 7 workers from day shift and swing shift.
Simplify. Remove all perfect squares from inside the square root. \sqrt{30b^5}= 30b 5
Answer:
The answer is b=0 or b=9.085603
The equation is solved and the perfect squares are removed from the square root and A = b²√( 30b )
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
A = √( 30b⁵ )
On simplifying the equation , we get
We can simplify the given expression by breaking down the number inside the square root into its prime factors:
30b⁵ = 2 x 3 x 5 x b⁵
Since we are looking to remove all perfect squares, we can remove the factors of 2 and 3, which are the only perfect squares present in the prime factorization of 30. This leaves us with:
30b⁵ = 2 x 3 x 5 x b⁵
= 2 x 3 x 5 x b⁴ x b
= 30b⁴ x b
Therefore, we can simplify the original expression as:
√(30b⁵) = √(30b⁴ x b) = √(30b⁴) x √b
A = b²√30 x √b
Hence , the expression √(30b⁵) simplifies to A = b²√30 x √b
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The route used by a certain motorist in commuting to work contains two intersections with traffic signals. The probability that he must stop at the first signal is 0.36, the analogous probability for the second signal is 0.51, and the probability that he must stop at least one of the two signals is 0.67.What is theprobability that he must stop.
a) At both signals?
b) At the first signal but not at the second one?
c) At exactly on signal?
Answer:
a) P(X∩Y) = 0.2
b) [tex]P_1[/tex] = 0.16
c) P = 0.47
Step-by-step explanation:
Let's call X the event that the motorist must stop at the first signal and Y the event that the motorist must stop at the second signal.
So, P(X) = 0.36, P(Y) = 0.51 and P(X∪Y) = 0.67
Then, the probability P(X∩Y) that the motorist must stop at both signal can be calculated as:
P(X∩Y) = P(X) + P(Y) - P(X∪Y)
P(X∩Y) = 0.36 + 0.51 - 0.67
P(X∩Y) = 0.2
On the other hand, the probability [tex]P_1[/tex] that he must stop at the first signal but not at the second one can be calculated as:
[tex]P_1[/tex] = P(X) - P(X∩Y)
[tex]P_1[/tex] = 0.36 - 0.2 = 0.16
At the same way, the probability [tex]P_2[/tex] that he must stop at the second signal but not at the first one can be calculated as:
[tex]P_2[/tex] = P(Y) - P(X∩Y)
[tex]P_2[/tex] = 0.51 - 0.2 = 0.31
So, the probability that he must stop at exactly one signal is:
[tex]P = P_1+P_2\\P=0.16+0.31\\P=0.47[/tex]
A triangle on a coordinate plane is translated according to the rule T-3,5(x, y). Which is another way to write this rule?
(x, y) - (x - 3, y + 5)
(x, y) - (x-3, y-5)
(x,y) - (x + 3, y-5)
(x, y) = (x + 3, y + 5)
Explanation:
The notation [tex]T_{-3,5}(x,y)[/tex] or means to move any point (x,y) along the vector <-3,5>. Put another way, it says to shift (x,y) three units to the left and five units up. The x portion deals with left or right shifting, the y portion deals with up or down shifting. Since the x portion is negative, we go in the negative direction on the x axis. Y being positive means we move up rather than down.
This all means we end up with the translation rule [tex](x,y) \to (x-3,y+5)[/tex]
Question 3 of 10
2 Points
If h(x) =(fºg)(x) and h(x) = 3(x + 2), find one possibility for f (x) and g(x).
Answer:
[tex]\boxed{\sf \ \ \ \text{one possibility is } f(x)=3x \ and \ g(x)=x+2 \ \ \ }[/tex]
Step-by-step explanation:
hello
h(x)=f(g(x))=3(x+2)
if we have f(x)=3x and g(x)=x+2 then
f(g(x))=f(x+2)=3(x+2)
hope this helps
In an aquarium, there are 7 large fish and 6 small fish. Half of the small fish are red.
One fish is selected at random. Find the probability that it is a small, red fish.
Write your answer as a fraction in simplest form.
Answer:
3/13
Step-by-step explanation:
There are a total of 13 fish (6+ 7 = 13). There are 3 small, red fish. (1/2 · 6 = 3). Put the number of small, red fish over the total number of fish because the small, red fish is being selected from the entire tank of fish. 3/13 cannot be simplified any further.
As an example, 15,000 Men 18-34 watched program X at 7-8 pm on Monday night. 32,000 Men 18-34 had their TV on during the same time period. There are 200,000 Men 18-34 in the television households in the market. What would be the rating for Men 18-34 for program X? Group of answer choices 47 rating points 7.5 rating points 16 rating points 23.5 rating points
Answer:
7.5 rating points
Step-by-step explanation:
The computation of the rating for Men 18-34 for program X is shown below:
Given that
Number of men 18 -34 watched a program X = 15,000 = X
Number of men 18 - 34 watched in a same time = 32,000
And, the total households in the market = 200,000 = Y
So, the rating for men 18-34 for program x is
[tex]= \frac{X}{Y}[/tex]
[tex]= \frac{15,000}{200,000}[/tex]
= 7.5 rating points
We simply applied the above formula
i need this fast plz
Answer:
180-130 = 50 degrees because its same side angle
m<2 = 50
Step-by-step explanation:
the second one m<1 is 105 for the same reason
If we express $2x^2 + 6x + 11$ in the form $a(x - h)^2 + k$, then what is $h$? (ignore the $)
Answer:
h = - [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Given
y = 2x² + 6x + 11 ( factor out 2 from the first 2 terms )
= 2(x² + 3x) + 11
Using the method of completing the square
add/subtract ( half the coefficient of the x- term )² to x² + 3x
y = 2(x² + 2([tex]\frac{3}{2}[/tex] )x + [tex]\frac{9}{4}[/tex] - [tex]\frac{9}{4}[/tex] ) + 11
= 2(x + [tex]\frac{3}{2}[/tex] )² - [tex]\frac{9}{2}[/tex] + 11
= 2(x + [tex]\frac{3}{2}[/tex] )² + [tex]\frac{13}{2}[/tex] ← in vertex form
with h = - [tex]\frac{3}{2}[/tex]
Of 1000 randomly selected cases of lung cancer, 823 resulted in death within 10 years.
a. Calculate a 95% two-sided confidence interval on the death rate from lung cancer.
b. Using the point estimate of p obtained from the preliminary sample, what sample size is needed to be 95% confident that the error in estimating the true value of p is less than 0.03?
c. How large must the sample be if you wish to be at least 95% confident that the error in estimating p is less than 0.03, regardless of the true value of p?
Answer:
a) [tex]0.823 - 1.96\sqrt{\frac{0.823(1-0.823)}{1000}}=0.799[/tex]
[tex]0.823 + 1.96\sqrt{\frac{0.823(1-0.823)}{1000}}=0.847[/tex]
The 95% confidence interval would be given by (0.799;0.847)
b) [tex]n=\frac{0.823(1-0.823)}{(\frac{0.03}{1.96})^2}=621.79[/tex]
And rounded up we have that n=622
c) [tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11[/tex]
And rounded up we have that n=1068
Step-by-step explanation:
Part a
[tex]\hat p=\frac{823}{1000}=0.823[/tex]
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. And the critical value would be given by:
[tex]z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96[/tex]
The confidence interval for the mean is given by the following formula:
[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]
If we replace the values obtained we got:
[tex]0.823 - 1.96\sqrt{\frac{0.823(1-0.823)}{1000}}=0.799[/tex]
[tex]0.823 + 1.96\sqrt{\frac{0.823(1-0.823)}{1000}}=0.847[/tex]
The 95% confidence interval would be given by (0.799;0.847)
Part b
The margin of error for the proportion interval is given by this formula:
[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)
And on this case we have that [tex]ME =\pm 0.03[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex] (b)
And replacing into equation (b) the values from part a we got:
[tex]n=\frac{0.823(1-0.823)}{(\frac{0.03}{1.96})^2}=621.79[/tex]
And rounded up we have that n=622
Part c
[tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11[/tex]
And rounded up we have that n=1068
Identify the correct HYPOTHESIS used in a hypothesis test of the following claim and sample data: Claim: "The average annual household income in Warren County is $47,500." A random sample of 86 households from this county is obtained, and they have an average annual income of $48,061 with a standard deviation of $2,351. Test the claim at the 0.02 significance level.
Answer:
We accept H₀
Step-by-step explanation:
Population mean μ₀ = 47500
Population standard deviation unknown
Sample size n = 86 degree of freedom df = 86 - 1 df = 85
Sample mean μ = 48061
Sample standard deviation 2,351
The claim implies a two tail test with t-studend distributon
Null Hypothesis H₀ μ = μ₀
Alternative Hypothesis Hₐ μ ≠ μ₀
Confidence Interval mean α = 0,02 and α/2 = 0,01
With α/2 and df = 85, from t-table we find t(c) critical value
t(c) = 2,3710
We compute t(s) as
t(s) = ( μ - μ₀ ) / s /√n
t(s) = ( 48061 - 47500 )/ 2351/√86
t(s) = 561 * 9,273 / 2351
t(s) = 2,212
Now we compare t(s) and t(c)
t(s) < t(c) 2,212 < 2,371
Then we are in the acceptance region. We accept H₀