Answers
Answer:
x=4 and y = 12
Step-by-step explanation:
A diagonal of a parallelogram cuts the other diagonal in exactly 2 equal parts. So, we can say that x+12 = 16. That would give us x=4. And, we can say that 3y-14 = 22. If we solve for y, we get y = 12.
Related Questions
Many smartphones, especially those of the LTE-enabled persuasion, have earned a bad rap for exceptionally bad battery life. Battery life between charges for the Motorola Droid Razr Max averages 20 hours when the primary use is talk time and 7 hours when the Internet applications (The wall Street Journal, March 7, 2012).
Since the mean hours for talk time usage is greater than the mean hours for Internet usage, the question was raised as to whether the variance in hours of usage is also greater when the primary use Sample data showing battery hours of use for the two applications follows:
Primary use talking:
35.8 22.2 4.0 32.6 3.5 42.5
8.0 3.8 30.0 12.8 10.3 35.5
Primary use Internet:
24.0 12.5 36.4 1.9 9.9
5.4 1.0 15.2 4.0 4.7
a. Formulate hypotheses about the two population variances that can be used to determine if the population variance in battery hours of use is greater for the talk time application.
H1:σ21_____
Ha:σ22_____
b. What are the standard deviations of battery hours of use for the two samples? Round your answers to two decimal places.
S1_____
S2_____
c. Conduct the hypothesis test and compute the p-value.
- The value of _____
- P-value is _____
Answers
Answer:
Null hypothesis: the variance in hours of usage for talking is not greater than the the variance in hours of usage for internet.
[tex]H_o[/tex]: [tex]\sigma _1 ^2 \leq \sigma _2^2[/tex]
Alternative hypothesis: the variance in hours of usage for talking is greater than the the variance in hours of usage for internet.
[tex]H_a : \sigma_1^2 > \sigma_2^2[/tex]
[tex]\mathbf{s_ 1 =16.11}[/tex]
[tex]\mathbf{s_2 = 7.98}[/tex]
Step-by-step explanation:
Let [tex]x_1[/tex] and [tex]x_2[/tex] be the two variables that represents the battery life in hours for talking usage and battery life in hours for internet usage respectively.
The hypothesis can be formulated as:
Null hypothesis: the variance in hours of usage for talking is not greater than the the variance in hours of usage for internet.
[tex]H_o[/tex]: [tex]\sigma _1 ^2 \leq \sigma _2^2[/tex]
Alternative hypothesis: the variance in hours of usage for talking is greater than the the variance in hours of usage for internet.
[tex]H_a : \sigma_1^2 > \sigma_2^2[/tex]
The standard deviation for the battery usage for talking is :
[tex]\bar x_1 = \dfrac{1}{n_1} \sum x_i \\ \\ \bar x_1 = \dfrac{1}{12}(35.8 +22.4+...+35.5) \\ \\ \bar x_1 = \dfrac{241.2}{12} \\ \\ \bar x_1 =20.1[/tex]
The standard deviation Is:
[tex]s_ 1 = \sqrt{\dfrac{1}{n_1-1}\sum (x{_1i}-\bar x_i)^2}[/tex]
[tex]s_ 1 = \sqrt{\dfrac{1}{12-1}\sum (35.8- 20.1)^2+ (35.5-20.1)^2}[/tex]
[tex]s_ 1 = \sqrt{259.568}[/tex]
[tex]\mathbf{s_ 1 =16.11}[/tex]
The standard deviation for the battery life usage for the internet is :
[tex]\bar x_2 = \dfrac{1}{n_2} \sum x_{2i}[/tex]
[tex]\bar x_2 = \dfrac{1}{10} (24.0+12.5+36.4+...+4.7})[/tex]
[tex]\bar x_2 = \dfrac{115}{10}[/tex]
[tex]\bar x_2 = 11.5[/tex]
Thus; the standard deviation is:
[tex]s_2 = \sqrt{\dfrac{1}{n_2-1}(x_{2i}- \bar x_2)^2}[/tex]
[tex]s_2 = \sqrt{\dfrac{1}{10-1}(24-11.5)^2+(4.7-11.5)^2}[/tex]
[tex]s_2 = \sqrt{63.60}[/tex]
[tex]\mathbf{s_2 = 7.98}[/tex]
hiii guys i need help with my homewrok [tex]-9\leq 7-8x[/tex]
Answers
Answer:
The answer is x ≤ 2.
Step-by-step explanation:
Firstly, you have to move the unrelated term to the other side :
[tex] - 9 \leqslant 7 - 8x[/tex]
[tex] - 9 - 7 \leqslant - 8x[/tex]
[tex] - 16 \leqslant - 8x[/tex]
Next you can solve it :
[tex] - 8x \geqslant - 16[/tex]
[tex]x \leqslant - 16 \div - 8[/tex]
[tex]x \leqslant 2[/tex]
*Remember to change the symbol, when it is dividing by a negative value
Question 6
An experiment consists of rolling a single die 12 times and the variablex is the number of times that the outcome is 6. Use binomial distribution to find the probability that the
outcome of 6 occurs exactly 3 times
Answers
Answer:
[tex] P(X=3)[/tex]
And using the probability mass function we got:
[tex] P(X=3)= (12C3)(\frac{1}{6})^3 (1-\frac{1}{6})^{12-3}=0.1974[/tex]
Step-by-step explanation:
Let X the random variable of interest "number of times that 6 appears", on this case we now that:
[tex]X \sim Binom(n=12, p=1/6)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
And we want to find this probability:
[tex] P(X=3)[/tex]
And using the probability mass function we got:
[tex] P(X=3)= (12C3)(\frac{1}{6})^3 (1-\frac{1}{6})^{12-3}=0.1974[/tex]
Find the point estimate for the true difference between the given population means.
Weights (in Grams) of Soap Bar A: 121, 122, 124, 123, 120, 124, 121, 121, 121, 123, 120
Weights (in Grams) of Soap Bar B: 121, 120, 122, 119, 121, 122, 122, 120, 120, 121, 122, 123, 119
Answers
Answer:
0.9 grams
Step-by-step explanation:
The point estimate for the average weight of Soap Bar A is:
[tex]A=\frac{121+122+124+ 123+ 120+ 124+ 121+ 121+ 121+ 123+ 120}{11}\\A=121.82\ grams[/tex]
The point estimate for the average weight of Soap Bar B is:
[tex]B=\frac{121+120+122+ 119+ 121+ 122+ 122+ 120+ 120 +121+ 122+123+119}{13}\\B=120.92\ grams[/tex]
Therefore, the point estimate for the true difference between the given population means is:
[tex]Dif = A-B\\Dif = 121.82-120.92\\Dif=0.9\ grams[/tex]
The point estimate for the difference is 0.9 grams.
The ratio of boys to girls in a club is 4:3. If there are 48 boys, how many members of the club are there?
Answers
Answer:
84
Step-by-step explanation:
Basically the ratio was multiplied by 12 to get the number of boys so you do the same to the other one.
Answer:
number of boys+number of girls=48boys+36girls=84members
Step-by-step explanation:
FIRST WE FIND THE NUMBER OF GIRLS BY STATISTICAL METHOD
4:3=48:x
4/3=48/x
By cross multiplication
4×x=48×3
4x=144
Dividing 4 on both sides
4x/4=144/4
x=36=number of girls
Find the mean of the data summarized in the given frequency distribution. Compare the computed mean to the actual mean of 50.7 degrees. Low Temperature (circleF) 40 minus 44 45minus49 50 minus 54 55 minus 59 60 minus 64 Frequency 2 7 9 5 1 The mean of the frequency distribution is nothing degrees. (Round to the nearest tenth as needed.)
Answers
Answer:
51.2°FStep-by-step explanation:
Find the exact frequency table in the diagram attached. x is the midpoint of the interval f is the frequency. Using the formula below to find the mean;
[tex]\overline x = \frac{\sum fx}{\sum f} \\[/tex]
[tex]\sum fx = (42*2)+(47*7)+(52*9)+(57*5)+(62*1)\\\sum fx = 84+329+468+285+62\\\sum fx = 1,228\\\sum f = 24\\\\\overline x = \frac{1,228}{24} \\\overline x = 51.17^{0} F[/tex]
The mean of the frequency distribution compare to the actual mean of 50.7°F is 51.2°F(to nearest tenth)
Can someone help me figure out the steps to get the answer:)
Answers
Answer:
c = ± 8.363277
Step-by-step explanation :
[tex]5.72^{2} = 32.49\\\\6.12^{2} = 37.4544\\3.49 + 37.4544 = 69.9444\\\\c^{2} = \sqrt{69.9444} \\= 8.363277[/tex]
Select the correct expression and value.
Ray has 3 boxes of chocolates. Each box has 4 layers of chocolates. Each layer has 4 rows of 4 chocolates each. He distributes all the chocolates equally among 16 friends. Identify the expression and the value that give the number of chocolates that each of Ray’s friends gets.
Answers
Answer:
Total chocolates= 48
Each friend get 3 chocolates
Step-by-step explanation:
Ray has 3 boxes of chocolates = 3
Each box has 4 layers of chocolates
= 4
Each layer has 4 rows of 4 chocolates each= 4
Total number of chocolates = 3*4*4
Total number of chocolates
= 48 chocolates
He shares 48 chocolates among 16 friends.
They Will all obtain 48/16= 3 chocolates each
Answer: the correct answer is 12
A University of Florida economist conducted a study of Virginia elementary school lunch menus During the state-mandated testing period, school lunches average 863 calories The economist claims that after the testing period ends, the average caloric content of Virginia school lunches drops significantly They collected a random sample of 500 students' school lunches around Virginia
a). What null and alternative hypotheses should you test?
b). Set up the rejection region for this study using alpha = 0.05 Interpret alpha = 0.05 in the words of the problem
c). Suppose the sample data yielded the test statistic z = -2.17 What conclusion can you draw for the test?
d). Calculate the observed p-value for the test statistic z = -2.17 Interpret the p-value and draw the conclusion based on it
Answers
Answer:
a) Null hypothesis: [tex] \mu \geq 863[/tex]
Alternative hypothesis: [tex] \mu >863[/tex]
b) For this case using the significance level of [tex]\alpha=0.05[/tex] we can use the normal standard distirbution in order to find a quantile who accumulates 0.05 of the area in the left and we got:
[tex] z_{\alpha}=-1.64[/tex]
And the rejection zone would be:
[tex] z<-1.64[/tex]
c) For this case since the statistic calculated is lower than the critical value we have enough evidence to reject the null hypothesis at 5% of significance
d) [tex] p_v = P(z<-2.17) =0.015[/tex]
Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis at the significance level provided
Step-by-step explanation:
Part a
We want to test for this case if the true mean is significantly less than 863 calories so then the system of hypothesis are:
Null hypothesis: [tex] \mu \geq 863[/tex]
Alternative hypothesis: [tex] \mu >863[/tex]
Part b
For this case using the significance level of [tex]\alpha=0.05[/tex] we can use the normal standard distirbution in order to find a quantile who accumulates 0.05 of the area in the left and we got:
[tex] z_{\alpha}=-1.64[/tex]
And the rejection zone would be:
[tex] z<-1.64[/tex]
Part c
For this case since the statistic calculated is lower than the critical value we have enough evidence to reject the null hypothesis at 5% of significance
Part d
For this case the p value would be given by:
[tex] p_v = P(z<-2.17) =0.015[/tex]
Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis at the significance level provided
Acar traveled 63 miles on 3 gallons of gas. What proportion can you set up to determine how many miles, m, the car can
Tavel on 7 gallons of gas?
637
m
633
m
63
m
Nnjkkk
Answers
Answer:
63 miles x miles
----------- = -------------
3 gallons 7 gallons
Step-by-step explanation:
We will use proportions. the number of miles over the gallons of gas
63 miles x miles
----------- = -------------
3 gallons 7 gallons
Answer: 147 miles
Step-by-step explanation:
On 3 gallons, he travelled 63 miles
On 7 gallons, he travels
7/3 x 63 = 147 miles
The spinner at the right is divided into eight equal parts. Find the theoretical probability of landing on the given section(s) of the spinner.
P(not less than 5)
Answers
Answer:
P(not less than 5) = 0.5
Step-by-step explanation:
Given
Parts of spinner = 8 equal parts
Required
P(not less than 5)
First, it'll be assumed that the parts of the spinner is numbered 1 - 8.
This gives the following sample space (S)
S = {1,2,3,4,5,6,7,8}
Total = 8
To calculate PP(not less than 5), the number of parts not less than 5 is needed.
Parts not less than 5 = {5,6,7,8}
Number of parts = 4
So, P(not less than 5) = Number of parts not less than 5 divided by total number of parts
Mathematically, P(not less than 5) = 4/8
P(not less than 5) = 4/8
P(not less than 5) = ½
P(not less than 5) = 0.5
Hence, the theoretical probability of PP(not less than 5) is 0.5.
The circumference of a circle is 15 pi centimeters what is the area of the circle in terms of pi
Answers
Answer:
[225(pi)]/4
Step-by-step explanation:
circumference = pi(diameter)
area = pi (radius)^2
Diameter = 2(radius)
15pi cm = pi(diameter)
divide both sides by pi
diameter = 15
radius = 7.5
Area = pi (7.5)^2
A = 56.25 pi
most teachers prefer fractions so
225pi/4
What is the decimal equivalent of 23/9
Answers
Answer:
2.555555
Step-by-step explanation: Nine times 2 is 18. When we subtract 18 from 23 we get 5. In the quotient we add a decimal point and add a zero to 5 which is 50. Nine times 5 is 45. When we subtract 45 from 50 we get 5 again and again and again . In decimal form it is 2.5555555.
Answer:
2.55 Hope this helps!
Each of four tables at a party is set bowl with a bowl of grapes each Bowl contains 5/8 of a pound of grapes how many pounds of grapes are there altogether show your work
Answers
Answer:
2.5 pounds
Step-by-step explanation:
Which statement describes the graph of this polynomial function?
f(x) = x5-6x4+9x3
The graph crosses the x-axis at x = 0 and touches the x-axis at x = 3.
O The graph touches the x-axis at x = 0 and crosses the x-axis at x = 3.
O The graph crosses the x-axis at x = 0 and touches the x-axis at x = -3.
O The graph touches the x-axis at x = 0 and crosses the x-axis at x = -3.
Answers
Answer:
The graph crosses the x-axis at x = 0 and touches the x-axis at x = 3.
Step-by-step explanation:
When you graph this equation, you should see the zeros it passes and touches.
Answer:
A. The graph crosses the x-axis at x = 0 and touches the x-axis at x = 3.
Step-by-step explanation:
The hypotenuse of a 45°-45°-90° triangle measures 128 cm. A right triangle is shown. The length of the hypotenuse is 128 centimeters and the lengths of the other 2 sides are congruent. What is the length of one leg of the triangle? 64 cm 64 StartRoot 2 EndRoot cm 128 cm 128 StartRoot 2 EndRoot cm
Answers
Answer:
64√2 or 64 StartRoot 2 EndRoot
Step-by-step explanation:
A 45-45-90 traingle is a special traingle. Let's say one of the leg of the triangle is x. The other one is also x because of the isosocles triangle theorem. Therefore, using the pytagorean theorem, you find that x^2+x^2=c^2. 2(x)^2=c^2. You then square root both sides and get c= x√2.
Therefore, the two legs are x and the hypotenuse is x√2. x√2=128 because the question says that the hypotenuse is 128. Solve for x by dividing both sides by √2. X=128/√2. You rationalize it by multiplying the numberator and denominator of the fraction by √2. √2*√2= 2.
X=(128√2)/2= 64√2 cm.
Since X is the leg, the answer would be 64√2
Answer:
B.
Step-by-step explanation:
A graphic designer wants to translate rectangle DEFG using T–1, 2(x, y). The pre-image has coordinates D(–1, 3),
E(4, 3), F(4, 1), and G(–1, 1). What is the image of DEFG?
Answers
Answer:
D'(-2, 5), E'(3, 5), F'(3, 3), G'(-2, 3)
Step-by-step explanation:
Adding (-1, 2) to each of the coordinates gives ...
D +(-1, 2) = (-1-1, 3+2) = D'(-2, 5)
E +(-1, 2) = (4-1, 3+2) = E'(3, 5)
F +(-1, 2) = (4-1, 1+2) = F'(3, 3)
G +(-1, 2) = (-1-1, 1+2) = G'(-2, 3)
Answer:
The answer is B.
Step-by-step explanation:
I got it correct on Edge 2020
What’s the correct answer for this?
Answers
｡☆✼★ ━━━━━━━━━━━━━━ ☾
Tangents that meet at a point are equal in length so DB = CB
Let's form an equation:
10x + 16 = 5x + 20
- 16 from both sides
10x = 5x + 4
- 5x from both sides
5x = 4
/5 on both sides
x = 4/5
Sub this value into the expression for CB
5(4/5) + 20 = 24
Thus, the answer is option D. 24
Have A Nice Day ❤
Stay Brainly! ヅ
- Ally ✧
｡☆✼★ ━━━━━━━━━━━━━━ ☾
Answer:
4TH OPTION
Step-by-step explanation:
IN A CIRCLE , TANGENT DRAWN FROM AN EXTERNAL POINT TO THE CIRCLE ARE EQUAL.
ie BD = BC
ie 10x +16 = 5x+20
10x - 5x = 20 -16
5x = 4
x = 4/5
therfore BC = 5x+20 = 5*4/5 +20
BC= 4+20
BC = 24
HOPE IT HELPS...
A typist can type 45 words per minute. How many minutes will it take him the type a 2500 word report?
Answers
Answer:
55.56 or 55 5/9
Step-by-step explanation:
To find the time it takes to type a report, you need to divide the number of words in the report by the words the typist can type in a minute.
2500/45 = 55.56
It takes 55.56 minutes or 55 5/9 minutes to type a 2500 word report.
Answer:
55 minutes and 33 seconds.
Step-by-step explanation:
To solve this we can set up a proportion.
1/45=x/2500
Cross multiply.
1*2500=45*x
45x=2500
Divide both sides by 45.
x=55.5*
.5* minutes is about 33 seconds. (0.55555*60)
So, it will take him around 55 minutes and 33 seconds.
Sarah Wiggum would like to make a single investment and have $1.7 million at the time of her retirement in 34 years. She has found a mutual fund that will earn 7 percent annually. How much will Sarah have to invest today
Answers
Answer:
Sarah has to invest $502,958.58 today.
Step-by-step explanation:
This is a simple interest problem.
The simple interest formula is given by:
[tex]E = P*I*t[/tex]
In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.
After t years, the total amount of money is:
[tex]T = E + P[/tex]
In this question:
[tex]t = 35, I = 0.07, T = 1700000[/tex]
She has to invest P today.
[tex]T = E + P[/tex]
[tex]1700000 = E + P[/tex]
[tex]E = 1700000 - P[/tex]
So
[tex]E = P*I*t[/tex]
[tex]1700000 - P = P*0.07*34[/tex]
[tex]3.38P = 1700000[/tex]
[tex]P = \frac{1700000}{3.38}[/tex]
[tex]P = 502958.58[/tex]
Sarah has to invest $502,958.58 today.
value of 2 to the 3 power
Answers
Answer:
two to the thrid power is 8.
Step-by-step explanation:
2^3= 8
Answer:
I'm not sure what exactly the question is but it should be 8
Step-by-step explanation:
2^3
2×2×2=8
Answer the question above?
Answers
Answer:
m>n
Step-by-step explanation:
The value of m
The sum of the angles of a triangle are 180
50+30 + m = 180
m = 180-50-30
m = 100
The value of n
The sum of the angles of a triangle are 180
28 + 58+n = 180
n = 180-58-28
n=94
m>n
Suppose the high tide in Seattle occurs at 1:00 a.m. and 1:00 p.m. at which time the water is 10 feet above the height of the low tide. Low tides occur 6 hours after high tides. Suppose there are two high tides and two low tides every day and the height of the tide varies sinusoidally.
a) Find a formula for the function y = h(t) that computes the height of the tide above low tide at time t. (In other words, y = 0 corresponds to low tide)
b) What is the tide height at 11:00 am?
Answers
Answer:
The low tide, when it is 10 feet below the high tide would be at 7am and 7pm
Step-by-step explanation:
What’s the correct answer for this?
Answers
Answer:
ED = 26
Step-by-step explanation:
Using tangent-secant theorem
(12)²=(8)(x+10)
144=8x+80
144-80=8x
8x = 64
x=8
Now
ED = 8+8+10
ED = 26
Answer:
26
Step-by-step explanation:
Applying the tangent-secant theorem, we get:
12^2 = 8 * (x + 10)
144 = 8x + 80
= 8x = 144 - 80
8x = 64
x = 8
Putting x = 8 in ED, which is x + x + 10, we get:
= 8 + 8 + 10
= 26
Hope this helps!
Given a triangle ABC such that AB = 4. AC = squareroot (41) and BC = 5.
Find the measures of the interior angles of ABC.
Answers
Answer:
A = 51.3°, B = 90°, C = 38.7°
Step-by-step explanation:
The given lengths satisfy the Pythagorean theorem:
(√41)² = 4² +5² ⇒ 41 = 16 +25
so we know the triangle is a right triangle. The right angle is opposite the longest side, so is angle B, opposite side AC.
The remaining angles can be found using trig functions. For example, we know ...
tan(A) = BC/AB = 5/4
A = arctan(5/4) ≈ 51.3°
Then the other acute angle is ...
C = 90° -51.3° = 38.7°
Angles A, B, C are ...
(A, B, C) = (51.3°, 90°, 38.7°)
Let X and Y be independent normal random variables with distributions X „ Np1, 3q and Y „ Np0, 4q. Let W " 1 2X ´ Y ` 6. (a) Identify the distribution W. (b) Find the probability PpW ą 6q.
Answers
Answer:
Step-by-step explanation:
Here we have,
E(X) = 1, var(X) = 3, E(Y) = 0, var(Y) = 4
Since X and Y has normal distribution so W will also have normal distribution with mean
E(W) = E(05X-Y+6)
= 0.5E(X) - E(Y) +6
= 0.5* 1 -0+ 6
= 6.5
and variance
Var(W) = Var(0.5X-Y+6)
= 0.25Var(X)+Var(Y)
= 0.25 * 3 + 4
= 4.75
(b)
The z-score for W = 6 is
[tex]z=\frac{6-6.5}{\sqrt{4.75} } \\\\=-0.23[/tex]
The required probability is:
P(W>6) = P(z > -0.23)
= 0.5910
Please answer this correctly
Answers
Answer:
7.07
Step-by-step explanation:
The area of the whole circle is given by the formula ...
A = πr^2
For the given values, the area of the circle is ...
A = 3.14(3 in)^2 = 28.26 in^2
One-quarter of that area is ...
(28.26 in^2)/4 = 7.065 in^2
The area of the quarter-circle is about 7.07 square inches.
Answer:
[tex] = 7.065 {in}^{2} [/tex]
Step-by-step explanation:
[tex] area = \frac{90}{360} \times \pi {r}^{2} \\ \frac{1}{4} \times 3.14 \times 3 \times 3 \\ = \frac{28.26}{4} \\ = 7.065 \: \: {in}^{2} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
how do you solve 6 1/4 x 2 7/11 =
Answers
Answer:
16 and 21/44 or 725/44
Step-by-step explanation:
convert 6 and 1/4 into an improper fraction; 25/4
convert 2 and 7/11 into an improper fraction; 29/11
multiply them together. [tex]\frac{25}{4}[/tex] × [tex]\frac{29}{11}[/tex]
you can do 25 × 29 to get 725
you can also do 4 × 11 to get 44.
725/44 simplifies to 16 and 21/44.
Which point satisfies both ƒ(x) = 2x and g(x) = 3x?
Answers
Answer:
(0,0)
Step-by-step explanation:
If a point satisfies both functions, they must be equal to each other. Thus, we have:
[tex]f(x)=g(x)[/tex]
[tex]2x=3x[/tex]
The only x that satisfies this is 0.
Therefore, the y is also zero.
The point is (0,0).
Alternatively, you can also visualize the graphs. The only point where the graphs will touch is the origin point or (0,0).
Rainwater was collected in water collectors at thirty different sites near an industrial basin and the amount of acidity (pH level) was measured. The mean and standard deviation of the values are 4.9 and 1.5 respectively. When the pH meter was recalibrated back at the laboratory, it was found to be in error. The error can be corrected by adding 0.2 pH units to all of the values and then multiply the result by 1.3. Find the mean and standard deviation of the corrected pH measurements.
Answers
Answer:
The mean and standard deviation of the corrected pH measurements are 6.63 and 3.8025 respectively.
Step-by-step explanation:
We can correct the values of the mean and standard deviation using the properties of the mean and the variance.
To the original value X we have to add 0.2 and multiply then by 1.3 to calculate the new and corrected value Y:
[tex]Y=1.3(X+0.2)[/tex]
The mean and standard deviation of the original value X are 4.9 and 1.5 respectively.
Then, we can apply the properties of the mean as:
[tex]E(Y)=E(1.3(X+0.2))=1.3E(X+0.2)=1.3E(X)+1.3*0.2\\\\E(Y)=1.3E(X)+0.26\\\\E(Y)=1.3*4.9+0.26=6.37+0.26=6.63[/tex]
For the standard deviation, we apply the properties of variance:
[tex]V(Y)=V(1.3(X+0.2))\\\\V(Y)=1.3^2\cdot V(X+0.2)\\\\V(Y)=1.69\cdot V(X)\\\\V(Y)=1.69\cdot 1.5^2=1.69\cdot 2.25=3.8025[/tex]
The properties that have been applied are:
[tex]1.\,E(aX)=aE(X)\\\\ 2.\,E(X+b)=E(X)+b\\\\3.\,V(aX)=a^2V(X)\\\\4.\,V(X+b)=V(X)+0[/tex]
