Answer:
Step-by-step explanation:
The question is incomplete. The complete question is:
A consumer rights advocate wants to determine the lifetime of a certain type of tablet computer. She randomly selects a sample of 29 of these tablets, and calculates the mean and standard deviation to be x = 6.7 years and s = 2.3 years. Find a 95% confidence interval for the true mean lifetime (in years) of this type of tablet.
Solution:
Confidence interval is written in the form,
(Sample mean - margin of error, sample mean + margin of error)
The sample mean, x is the point estimate for the population mean.
Margin of error = z × s/√n
Where
s = sample standard deviation = 2.3
n = number of samples = 29
x = 6.7
From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the t score
In order to use the t distribution, we would determine the degree of freedom, df for the sample.
df = n - 1 = 29 - 1 = 28
Since confidence level = 95% = 0.95, α = 1 - CL = 1 – 0.95 = 0.05
α/2 = 0.05/2 = 0.025
the area to the right of z0.025 is 0.025 and the area to the left of z0.025 is 1 - 0.025 = 0.975
Looking at the t distribution table,
t = 2.048
Margin of error = 2.048 × 2.3/√29
= 0.87
the lower limit of this confidence interval is
6.7 - 0.87 = 5.83
the upper limit of this confidence interval is
6.7 + 0.87 = 7.57
Therefore, we are 95% confident that true mean lifetime of a certain type of tablet computer lies between 5.83 years and 7.57 years
A baby’s t-shirt requires 2/9 yards of fabric. How many t-shirts can be made from 38 yards?
Answer:
8 and 4/9 i think... i am sorry if i am wrong
Step-by-step explanation:
(1)(a) Use the generalized binomial expansion to expand (1 + x)ā up to the x® and hence
determine (1.05). to 5 decimal places
10 marks
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
Use the generalized binomial expansion to expand (1 + x)^a up to the a = 5 and hence determine (1.05)^5. to 5 decimal places.
Answer:
Using the binomial theorem
[tex](1 .05)^5 = 1.27628[/tex]
Step-by-step explanation:
The binomial theorem is given by
[tex](a +b)^n = \binom{n}{0} a^nb^0 + \binom{n}{1} a^{n-1}b^1....+ \binom{n}{n} a^0b^n[/tex]
For the given case, we have
[tex]a = 1 \\\\b = 0.05 \\\\n = 5 \\\\[/tex]
So,
[tex](1 +0.05)^5 = \binom{5}{0} (1)^5(0.05)^0 + \binom{5}{1} (1)^4(0.05)^1 + \binom{5}{2} (1)^3(0.05)^2 + \binom{5}{3} (1)^2(0.05)^3 + \binom{5}{4} (1)^1(0.05)^4 + \binom{5}{5} (1)^0(0.05)^5[/tex]
[tex](1 +0.05)^5 = (1)(1)^5(0.05)^0 + (5) (1)^4(0.05)^1 + (10) (1)^3(0.05)^2 + (10) (1)^2(0.05)^3 + (5) (1)^1(0.05)^4 + (1) (1)^0(0.05)^5[/tex]
[tex](1 +0.05)^5 = 1 + 0.25 + 0.025 + 0.00125 + 0.00003125 + 0.0000003125[/tex]
[tex](1 + 0.05)^5 = 1.27628[/tex]
Therefore, using the binomial theorem
[tex](1 .05)^5 = 1.27628[/tex]
Determine whether the sequence converges or diverges. If it converges, find the limit. an = 9 + 14n2 n + 15n2 Step 1 To find lim n → [infinity] 9 + 14n2 n + 15n2 , divide the numerator and denominator by the highest power of n that occurs in the fraction. This is n .
Answer:
The sequence ConvergesStep-by-step explanation:
Given the sequence [tex]a_n = \frac{9+14n^{2} }{n+15n^{2} }[/tex]
To find the limit of the sequence, we will first divide the numerator and the denominator through by the highest power of n which is n² as shown;
[tex]\lim_{n \to \infty} \frac{9/n^{2} +14n^{2}/n^{2} }{n/n^{2} +15n^{2}/n^{2} }\\ \lim_{n \to \infty} \frac{9/n^{2} +14 }{1/n +15n^{2}/n^{2 }}\\[/tex]
As [tex]n[/tex] tends to [tex]\infty[/tex], [tex]\frac{a}{n}[/tex] tends to zero where n is any constant, The limit of tyhe sequence as n tends to infinity becomes;
[tex]= \frac{9/\infty+14 }{1/\infty+15 }\\= \frac{0+14}{0+15} \\= 14/15\\[/tex]
Therefore [tex]\lim_{n \to \infty} \frac{9+14n^{2} }{n+15n^{2} } = 14/15[/tex]
Since the limit of the sequence gave a finite number , the sequence converges.
Note that the only case when the sequence diverges id when the limit of the sequence is infinite
A model for consumers' response to advertising is given by the equation N(a)=2600 + 470ln (a) Where N(a) is the number of units sold, a is the amount spent on advertising, in thousands of dollars, & a≥1.
Required:
a. How many units were sold after spending $1,000 on advertising?
b. Find N′(a).
c. Find the maximum value, if it exists.
d. Find lim a→[infinity] N′(a).
Answer:
a. [tex]N(1)=2600[/tex]
b. [tex]N'(a) = 470/a[/tex]
c. N(a) has no maximum value, max N'(a) = 470 (when a = 1)
d. lim a→[infinity] N′(a) = 0
Step-by-step explanation:
a.
the variable 'a' is the amount spent in thousands of dollars, so $1,000 is equivalent to a = 1. Then, we have that:
[tex]N(1)=2600 + 470ln(1)[/tex]
[tex]N(1)=2600 + 470*0[/tex]
[tex]N(1)=2600[/tex]
b.
To find the derivative of N(a), we need to know that the derivative of ln(x) is equal (1/x), and the derivative of a constant is zero. Then, we have:
[tex]N'(a) = 2600' + (470ln(a))'[/tex]
[tex]N'(a) = 0 + 470*(1/a)[/tex]
[tex]N'(a) = 470/a[/tex]
c.
The value of 'ln(a)' increases as the value of 'a' increases from 1 to infinity, so there isn't a maximum value for N(a).
The maximum value of N'(a) is when the value of a is the lower possible, because 'a' is in the denominator, so the maximum value of N'(a) is 470, when a = 1.
d.
When the value of 'a' increases, the fraction '470/a' decreases towards zero, so the limit of N'(a) when 'a' tends to infinity is zero.
Describe the surface of Cone, ellipsoid, Hyperboloid, elliptic Cylinder, Hyperbolic Cylinder, parabolic Cylinder, elliptic paraboloid, hyperbolic paraboloid.
Answer:
a surface of a cone looks like an hyperbolic cylinder
Which graph shows the system StartLayout Enlarged left-brace 1st row x squared + y = 2 2nd row x squared + y squared = 9 EndLayout?
Answer: Hope this helps <3
Step-by-step explanation:
Graphs can be used to represent functions.
See attachment for the graphs of [tex]\mathbf{x^2 + y = 2}[/tex] and [tex]\mathbf{x^2 + y^2 = 9}[/tex]
The functions are given as:
[tex]\mathbf{x^2 + y = 2}[/tex]
[tex]\mathbf{x^2 + y^2 = 9}[/tex]
Rewrite [tex]\mathbf{x^2 + y^2 = 9}[/tex] as:
[tex]\mathbf{x^2 + y^2 = 3^2}[/tex]
The above equation represents a circle of radius 3, and that has its center as the origin.
Similarly, we have:
[tex]\mathbf{x^2 + y = 2}[/tex]
Make y the subject
[tex]\mathbf{y = 2 -x^2}[/tex]
Rewrite as:
[tex]\mathbf{y = -x^2 + 2 }[/tex]
The above is a square function, that is reflected over the y-axis, and then shifted up by 2 units.
See attachment for the graphs of [tex]\mathbf{x^2 + y = 2}[/tex] and [tex]\mathbf{x^2 + y^2 = 9}[/tex]
Read more about graphs and functions at:
https://brainly.com/question/18806107
In 4 days, the price of a share of stock rose 3/4 of a point. On a average, what was the change in stock each day?
Answer:
0.15 or 15%
Step-by-step explanation:
If the price of a stock rose 3/4 on a point, it means that 1x became 1,75x (x + 3/4x). X is the price of the stock here.
To calculate how much the price went up each day on average, we will create exponential equation.
x = price of the stock
y = average daily change
[tex]x*y^{4} =1.75x[/tex] divide by x
[tex]y^{4} = 1.75[/tex]
We will calculate it using logarithms.
y = 1.15016, rounded to 1.15
We see that the stock goes up 0.15 points every day.If we multiply it by 100%, we get 15%
A store accidentally priced an item at $20 instead of $30 and honored the mispricing.
Where should the store attribute the $10 difference?
Is it considered a loss or operating expense?
Thanks
Answer:
Sales
Step-by-step explanation:
Since it is mentioned that the store mistakenly priced an item at $20 instead of $30 so there is a difference of $10 so the price of sales is increased by $10 due to mispricing the value of the item so that it would be recorded at $30 rather than $20
Therefore in the given case neither it is considered as a loss nor an operating expense but as a sales and the same is to be relevant
Hence, the given options are incorrect
What is the inverse of f(x) = 2x − 8?
Step-by-step explanation:
firstly firstly we have to suppose f(X) as y and then solve it by interchanging X and y.
hope this is helpful
Answer:
B
Step-by-step explanation:
To find inverse you switch f(x) and x use y for f(x) then solve for y.
1. x = 2y - 8
2. x + 8 = 2y
3. (x + 8) / 2 = y
4. 1/2x + 4 = y
I NEED HELP PLEASE, THANKS! :)
Makya was conducting a physics experiment. He rolled a ball down a ramp and calculated the distance covered by the ball at different times. The ball rolled a distance of 1 foot during the first second, 3 feet during the next second, and so on. If the distances the ball rolled down the ramp each second form an arithmetic sequence, determine the distance the ball rolled down during the fifteenth second. (Show work)
Hey there! :)
Answer:
f(15) = 29 ft.
Step-by-step explanation:
We can write an arithmatic equation for this pattern:
Where:
[tex]n_{1}[/tex] = 1, [tex]n_{2}[/tex] = 3
Find the rate of change. This is constant because this is an arithmatic sequence.
3 - 1 = 2.
We can begin to write an explicit function for this situation:
f(n) = [tex]n_{1}[/tex] + d(n-1) where d is the rate of change:
f(n) = 1 + 2(n-1)
Substitute 15 for n to solve for the distance traveled after 15 seconds:
f(15) = 1 + 2(15-1)
f(15) = 1 + 2(14)
f(15) = 1 + 28
f(15) = 29 ft.
Therefore, the distance traveled after 15 seconds is 29 ft.
Graph each of the following lines without using a table of values. a. y = 2⁄3x - 5 b. 6x - 2y + 5 = 0
Answer:
(See explanation below for further details).
Step-by-step explanation:
The procedure for plotting each line consists in creating a table with at least two different points, given that Euclidean Geometry states that any line can be created with only two points, and plotting the lines with the help of graphing tools:
(a) [tex]y = \frac{2}{3}\cdot x - 5[/tex]
(i) Table of values
x y
-2 -6.333
-1 -5.667
0 -5
1 -4.333
2 -3.667
(ii) Plotting the line
The line is presented below in the attachment "line_1".
(b) [tex]6\cdot x - 2\cdot y + 5 = 0[/tex]
[tex]2\cdot y = 6\cdot x +5[/tex]
[tex]y = 3\cdot x +\frac{5}{2}[/tex]
(i) Table of values
x y
-2 -3.5
-1 -0.5
0 2.5
1 5.5
2 8.5
(ii) Plotting the line
The line is presented below in the attachment "line_2".
{1, 2, 3, 4, 5} {2, 4, 6, 8, 10} Please Help Which of the following shows the union of the sets?
Answer:
Step-by-step explanation:
hello
{1,2,3,4,5} ∪ {2,4,6,8,10} = {1,2,3,4,5,6,8,10}
hope this helps
Answer:
{1, 2, 3, 4, 5, 6, 8, 10}
Step-by-step explanation:
Union of the sets is the combination of the elements in the two sets.
{1, 2, 3, 4, 5} ∪ {2, 4, 6, 8, 10}
{1, 2, 3, 4, 5, 6, 8, 10}
PLEASE HURRY DONT HAVE MUCH TIME WILL GIVE BRAINLIEST
(SEE PICTURE)
Find the value of x for m(arc AB) = 46 and m(arc CD) = 25. (The figure is not drawn to
scale.)
Find the first four iterates of the function f(z)=z^2-2-2i with an initial value of z0=2+i
Obtain the next iterate by plugging the previous iterate into the function.
First iterate:
[tex]z_0=2+i\implies z_1=f(z_0)=(2+i)^2-2-2i=1+2i[/tex]
Second iterate:
[tex]z_2=f(z_1)=(1+2i)^2-2-2i=-5+2i[/tex]
Third iterate:
[tex]z_3=f(z_2)=(-5+2i)^2-2-2i=19-22i[/tex]
Fourth iterate:
[tex]z_4=f(z_3)=(19-22i)^2-2-2i=-125-838i[/tex]
Which of the following shows the union of the sets? {3, 6, 9, 12, 15} {1, 6, 12, 18, 24}
Answer:
A ∪ B = {1,3,6,9,12,15,18,24}
Step-by-step explanation:
Let A = {3,6,9,12,15}
B = {1,6,12,18,24}
So,
A ∪ B = {3,6,9,12,15} ∪ {1,6,12,18,24}
A ∪ B = {1,3,6,9,12,15,18,24}
Answer:
{1,3,6,9,12,15,18,24}
Step-by-step explanation:
The union is joining of the elements of the sets
{3, 6, 9, 12, 15}U {1, 6, 12, 18, 24}
= {1,3,6,9,12,15,18,24}
identify whether each phrase is an expression, equation, or inequality. PLEASE I NEED HELP!
Answer:
1st one is a expression, 2nd is a inequality, 3rd is a eqaution
Step-by-step explanation:
an equation has two expressions on each side of the equal sign, which is shown in 4j-3=j; An expression has only one side and is a string of variables and numbers with signs(multiply, add, etc.); An inequality is a comparison of two expressions
p is a rectangle with lengths 60cm and width x cm q is a rectangle with width y cm. the length of q is 20% more than the length of p the area of p is 15% less than the area of q work out the ratio x:y
Answer:
The ratio of x to y is
1.02/1 = x/y
1.02:1= x:y
Step-by-step explanation:
Rectangle p
Length = 60 cm
Width = x cm
Area = length* breadth
Area = 60 *x
Rectangle q
Length = 20% more than length of rectangle p
Length = (60*0.2) + 60
Length = 12 +60
Length = 72cm
Width = y cm
Area = 72*y
(72*y)-(72*y *0.15)= 60*x
72y - 10.8y = 60x
61.2y = 60x
61.2/60 = x/y
15.3/15= x/y
5.1/5 = x/y
1.02/1 = x/y
In a clinical study of an allergy drug, 108 of the 200 subjects reported experiencing significant relief from their symptoms. Test the claim that more than half of all those using the drug experience relief. Using a 0.01 significance level, what is your decision
Answer:
The decision is to not reject the null hypothesis.
At a significance level of 0.01, there is not enough evidence to support the claim that the proportion of all those using the drug that experience relief is significantly higher than 50% (P-value = 0.1443).
Step-by-step explanation:
This is a hypothesis test for a proportion.
The claim is that the proportion of all those using the drug that experience relief is significantly higher than 50%.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.5\\\\H_a:\pi>0.5[/tex]
The significance level is 0.01.
The sample has a size n=200.
The sample proportion is p=0.54.
[tex]p=X/n=108/200=0.54[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.5*0.5}{200}}\\\\\\ \sigma_p=\sqrt{0.00125}=0.035[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.54-0.5-0.5/200}{0.035}=\dfrac{0.038}{0.035}=1.061[/tex]
This test is a right-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z>1.061)=0.1443[/tex]
As the P-value (0.1443) is greater than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
At a significance level of 0.01, there is not enough evidence to support the claim that the proportion of all those using the drug that experience relief is significantly higher than 50%.
x+4 if x <5
f(x)= 8
if 5
2x-1 if 7
For Ax), evaluate the following:
a. 10)
b. 46)
Answer:
f(0) = 4 , f(6) = 8
Step-by-step explanation:
Since
[tex]0 < 5[/tex] then f(0) = 0+4 = 4
5 < 6 < 7 therefore f(6) = 8
Help me answer this question for 5.b)
Answer:
The provement is below
Step-by-step explanation:
z^(1/2)=x^(1/2)+y^(1/2) => (z^(1/2))^2= (x^(1/2)+y^(1/2))^2
=> z=x+y+2*x^(1/2)*y^(1/2) => z-x-y= 2*x^(1/2)*y^(1/2)
=> (z-x-y)^2= (2*x^(1/2)*y^(1/2) )^2 => (z-x-y)^2=4*x*y (1)
Pls note that (z-x-y)^2= ((-1)*(-1)*(z-x-y))^2= ((-1)*(x+y-z))^2= (-1)^2*(x+y-z)^2=
=(x+y-z)^2
So (z-x-y)^2= (x+y-z)^2 !!! Substitute in (1) (z-x-y)^2 by (x+y-z)^2 and will get
the required equality (x+y-z)^2=4*x*y
A store buys sneakers for $20.00 and marks them up 250%. What is the selling price?
Answer:
[tex]\$45[/tex]
Step-by-step explanation:
[tex]20+(2.5*20)=45[/tex]
Marking up means that the new value is added onto the original value.
As we are increasing the original price by 250% of the price, we need to multiply it by 2.5, as that is equal to 250%
Answer:
20*2.5 = $50 Gross margin $70 Selling price
Step-by-step explanation:
What is the pattern for 360,60,10
Step-by-step explanation: Begin by studying the pattern.
Notice that if we divide the first term,
360, by 6, we get the second term, 60.
Similarly, if we divide the second term,
60, by 6, we get the third term, 10.
So each new term is equal to the previous term
divided by 2, so we use this idea to find any missing terms.
WILL MARK BRAINLIEST! NEED HELP!
How does the graph of f(x) = (x + 2)4 + 6 compare to the parent function g(x) = x4?
Answer:
left 2 units and up 6 units
Step-by-step explanation:
f(x) = (x + 2)^4 + 6
y = f(x) + C C > 0 moves it up
So this moves it up 6 units
y = f(x + C) C > 0 moves it left
So this moves it to the left 2 units
The parent function g(x) is shifted to the left 2 units and up 6 units to get the function f(x).
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
Given function;
f(x) = (x + 2)^4 + 6
y = f(x) + C
C > 0 moves it up
So, this moves it up 6 units.
y = f(x + C)
C > 0 moves it left
So, this moves it to the left 2 units.
Learn more about function here:
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A couple plans to invest money into an account that earns 9% interest, compounded quarterly, for their child's college education. What principal must be deposited by the parents in order to have $25,000 after 13 years?
Answer:
$282.98
Step-by-step explanation:
For computing the principal amount we need to apply the present value function i.e to be shown in the attachment below:
Data provided that in question
Future value = $25,000
Rate of interest = 9%
NPER = 13 years × 4 quarters = 52 quarters
PMT = $0
The formula is shown below:
= -PV(Rate;NPER;PMT;FV;type)
So, after applying the above formula, the present value is $282.98
Determine the point estimate of the population proportion, the margin of error for the following confidence interval, and the number of individuals in the sample with the specified characteristic, x, for the sample size provided. Lower bound equals 0.345, upper boundequals0.895, nequals1000
Answer:
For this case we have the following confidence interval given:
[tex] 0.345 \leq p \leq 0.895 [/tex]
And for this case we want to find the estimated proportion like this:
[tex]\hat p= \frac{0.345 +0.895}{2}= 0.62[/tex]
And the margin of error for this case would be given by:
[tex] ME= \frac{0.895-0.345}{2}= 0.275[/tex]
Step-by-step explanation:
For this case we have the following confidence interval given:
[tex] 0.345 \leq p \leq 0.895 [/tex]
And for this case we want to find the estimated proportion like this:
[tex]\hat p= \frac{0.345 +0.895}{2}= 0.62[/tex]
And the margin of error for this case would be given by:
[tex] ME= \frac{0.895-0.345}{2}= 0.275[/tex]
Which best describes the structure outlined in the bridge.
Answer:D
Step-by-step explanation:
The red line in the figure is an altitude of triangle HJL. Using right angle trigonometry, write an equation involving sinL
Answer:
B.
Step-by-step explanation:
According to SohCahToa, when using Sin to find a side value, you must use opposite over hypotenuse.
So in this case to find x, you would do the Sin(L)=x/y
Answer:
B. Sin(L)=x/y indeed!
Step-by-step explanation:
Consider a data set containing the following values:
70 65 71 78 89 68 50 75
The mean of the preceding values is:
70.75.
The deviations for the mean have been calculated as follows:
-0.75, -5.75, 0.25,7.25,18.25,-2.75,-20.75, and 4.25
a. If this is the sample data, the sample variance is _____ and the sample standard deviation is ___
b. If this is a population data, the population variance is_____ and the population standard deviation is_____
Answer:
a. 125.0714; 11.1835.
b. 109.4375; 10.4612.
Step-by-step explanation:
Given the following data;
70, 65, 71, 78, 89, 68, 50, 75.
Mean = 70.75
The deviation for the mean of the data is -0.75, -5.75, 0.25,7.25,18.25,-2.75,-20.75, and 4.25.
We would then find the square of this deviation;
[tex]=(-0.75)^2+(-5.75)^2+( 0.25)^2+(7.25)^2 +(18.25)^2+(-2.75)^2+(-20.75)^2 +(4.25)^2[/tex]
[tex]=0.5625+33.0625+0.0625+52.5625+333.0625+7.5625+430.5625+18.0625[/tex]
= 875.5
Next is to find the population variance;
[tex]V = \frac{875.5}{8}[/tex]
Variance, V = 109.4375
The population standard deviation is the square root of the population variance;
[tex]Sd = \sqrt{109.4375}[/tex]
Standard deviation, Sd = 10.4612
To find the sample variance;
[tex]V = \frac{875.5}{8-1}[/tex]
[tex]V = \frac{875.5}{7}[/tex]
Variance, V = 125.0714
The sample variance is;
[tex]Sd = \sqrt{125.0714}[/tex]
Standard deviation, Sd = 11.1835
Therefore,
a. The sample variance is 125.0714 and the sample standard deviation is 11.1835.
b. If this is a population data, the population variance is 109.4375 and the population standard deviation is 10.4612.
Answer:
C. 20.67
Step-by-step explanation:
I got it right on edge :)
Matt wants to plot a garden. He was 48 meters to work with. He wants the length of the garden to be 3 times the width of the garden because he has many types of vegetables to grow. What is the width of the garden.
Answer: The width of the garden is 6 Meters
Step-by-step explanation:
3x + x = 24
The length is 3x and the width is x
24 / 4 = 6
x= 6
The width of the garden is 6 Meters
Answer:
x = 6
Step-by-step explanation:
3x + x = 24
24 / 4 = 6
x = 6
how are the values of the eights related in 880
Answer:
8 is in the hundreds place as well as in the tens place.
Step-by-step explanation:
We use the base 10 system. 880 would represent eight hundred and eighty. So our 0 would be the ones place, 8 in the tens place, and 8 also in the hundreds place.