Answer:
Step-by-step explanation:
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
H0: µ = 305
For the alternative hypothesis,
H1: µ > 305
This is a right tailed test
Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is
z = (x - µ)/(σ/√n)
Where
x = sample mean
µ = population mean
σ = population standard deviation
n = number of samples
From the information given,
µ = 305
x = 306.2
σ = 3.57
n = 55
z = (306.2 - 305)/(3.57/√55) = 2.49
Test statistic = 2.49
The calculated test statistic is 2.49 for the right tail and - 2.49 for the left tail
Since α = 0.05, the critical value is determined from the normal distribution table.
For the left, α/2 = 0.05/2 = 0.025
The z score for an area to the left of 0.025 is - 1.96
For the right, α/2 = 1 - 0.025 = 0.975
The z score for an area to the right of 0.975 is 1.96
In order to reject the null hypothesis, the test statistic must be smaller than - 1.96 or greater than 1.96
Since - 2.49 < - 1.96 and 2.49 > 1.96, we would reject the null hypothesis.
Therefore, at 5% level of significance, there is sufficient evidence to conclude that the average depth has increased.
{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}
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:
https://brainly.com/question/2253924
#SPJ2
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%.
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:
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:
To increase and increase an amount by 70%
what single multiplier would you use?
Answer:
Increase: 1.7
Decrease: 0.3
Step-by-step explanation:
Increase:
100% + 70% = 117%
117/ 100 = 1.7 (multiplier)
Decrease:
100% - 70%= 30%
30/ 100 = 0.3 (multiplier)
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
Find the missing length to the nearest tenth.
Right Triangle
6 m
C
16 m
Answer:
17.1 meters
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean Theorem.
[tex]a^2+b^2=c^2[/tex]
where a and b are the legs and c is the hypotenuse.
6 and 16 are the legs, because they form the right angle. c is the hypotenuse because it is opposite the right angle.
[tex]6^2+16^2=c^2[/tex]
Evaluate the exponents.
6^2= 6*6= 36
16^2= 16*16= 256
[tex]36+256=c^2[/tex]
Add 36 and 256.
[tex]292=c^2[/tex]
Since c is being squared, take the square root of both sides of the equation. The exponent and square root will cancel and leave c by itself
[tex]\sqrt{292} =\sqrt{c^2}[/tex]
[tex]\sqrt{292}=c[/tex]
[tex]17.0880075=c[/tex]
Round to the nearest tenth. The 8 in the hundredeth place tells us to roung the 0 in the tenth place up to a 1.
[tex]17.1=c[/tex]
c= 17.1 m
The missing length, or the hyptenuse is 17.1 meters.
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".
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.)
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}
Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.) f(x) = 8x3/5 + 3x−4/5
Answer:
[tex]\dfrac{8x^{4}}{20}+\dfrac{3x^{2}}{2}-\dfrac{4}{5}x+C[/tex]
Step-by-step explanation:
Given the function: [tex]f(x)=\dfrac{8x^3}{5}+3x-\dfrac{4}{5}[/tex]
To take the antiderivative (or integral) of a function, we follow the format below.
[tex]f(x)=x^n\\$Then its antiderivative\\Antiderivative of f(x)$=\dfrac{x^{n+1}}{n+1}[/tex]
Therefore, the antiderivative of f(x) is:
[tex]=\dfrac{8x^{3+1}}{5(3+1)}+\dfrac{3x^{1+1}}{2}-\dfrac{4}{5}x+C\\=\dfrac{8x^{4}}{20}+\dfrac{3x^{2}}{2}-\dfrac{4}{5}x+C[/tex]
We want to check our result by differentiation.
[tex]\dfrac{d}{dx}\left(\dfrac{8x^{4}}{20}+\dfrac{3x^{2}}{2}-\dfrac{4}{5}x+C\right)\\=\dfrac{d}{dx}\left(\dfrac{8x^{4}}{20}\right)+\dfrac{d}{dx}\left(\dfrac{3x^{2}}{2}\right)-\dfrac{d}{dx}\left(\dfrac{4}{5}x\right)+\dfrac{d}{dx}\left(C\right)\\\\=\dfrac{32x^{3}}{20}+\dfrac{6x}{2}-\dfrac{4}{5}+0\\\\=\dfrac{8x^{3}}{5}+3x-\dfrac{4}{5}[/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
Which ordered pair is in the solution set of the system of linear inequalities?
4
2
y> x-1
y
(-5, 2)
(2, 2)
(5.2)
Answer:
Step-by-step explanation:
y>3/2 x-1
y<3/2 x-1
graphs do not intersect any point.
so no solution.
Answer:
D
Step-by-step explanation:
no solution
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
Part A: The polynomial in standard form is Select a Value
Answer:
2nd Option
Step-by-step explanation:
Standard Form: ax² + bx + c
This can be modified to fit any degree polynomial, as long as the highest degree is first, and then decreasing. So our answer is B.
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.
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
Which best describes the structure outlined in the bridge.
Answer:D
Step-by-step explanation:
g Determine the area of the region between the two curves by integrating over the x-axis. y = x2 − 24 and y = 1
Answer:
A = 166.66
Step-by-step explanation:
You have the following functions:
[tex]y_1=x^2-24\\\\y_2=1[/tex]
In order to calculate the area of the given region, you first calculate the points at which the function y = x^2-24 intersects the line y=1:
[tex]1=x^2-24\\\\0=x^2-25\\\\x=\sqrt{25}=\pm 5[/tex]
Next, you take into account that the area between the two function is given by:
Where you have used the fact that y2 is above the y1 function.
Next, you calculate the following integral:
[tex]A=\int_{-5}^{5}(1-(x^2-24))dx=\int_{-5}^{5}(25-x^2)dx\\\\A=(25x-\frac{1}{3}x^3)|_{-5}^{5}\\\\A=(25(5)-\frac{1}{3}(125))-(25(-5)-\frac{1}{3}(-125))\\\\A=166.66[/tex]
Then, the area of the bounded region is 166.66
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 :)
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]
The claim that the mean amount of sleep for adults is less than 7 hours. Choose the correct statement about null and alternative hypothesis.
a) H0: µ > 7 hours (null hypothesis)
H1: µ < 7 hours (alternative hypothesis and original claim)
b) H0: µ = 7 hours (null hypothesis)
H1: µ < 7 hours (alternative hypothesis and original claim)
H2: µ > 7 hours (second alternative hypothesis and original claim)
c) H0: µ = 7 hours (null hypothesis)
H1: µ < 7 hours (alternative hypothesis and original claim)
d) H0: µ < 7 hours (null hypothesis)
H1: µ ≥≥ 7 hours (alternative hypothesis and original claim)
Answer:
c) H0: µ = 7 hours (null hypothesis)
H1: µ < 7 hours (alternative hypothesis and original claim)
Step-by-step explanation:
The hypothesis test is performed in order to see if a sample outcome gives evidence to reject a null hypothesis and support the researchers claim.
In this case, the claim is that the mean amount of sleep for adults is less than 7 hours.
For this claim, the alternative hypothesis will state the researcher's claim: the mean amount of sleep for adults is significantly less than 7 hours.
The null hypothesis will state the opposite: the mean amount of sleep for adults is not significantly less than 7 hours. In this case, it is the same to claim that the mean amount is 7 hours.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=7\\\\H_a:\mu< 7[/tex]
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.
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.
A die is rolled 8 times. Find the probability. P(getting even numbers 7 times)
Answer:
The probability of getting even 7 times out of 8 is 1/256. Hope this helps!!
Step-by-step explanation:
21/7 = 3 is the answer of your question
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
help me pls i need to graduatE
Answer:
The answer is option D.
LJ = 3.5Step-by-step explanation:
To find LJ we use the sine rule
From the picture
LK / sin J = LJ / sin K
LK = 9
J = 89°
K = 23°
So now LJ is
9 / sin 89° = LJ / sin 23°
Make LJ the subject
That's
LJ = 9 sin 23° / sin 89°
LJ = 3.51
The final answer is
LJ = 3.5Hope this helps you.
(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]