Answer:
220 ft^3
Step-by-step explanation:
Assuming a rectangular tank,
V = l*w*h
= 8*5*5.5
=220 ft^3
The vertex form of a function is g(x)=(x-3)^2+9. How does the graph of g(x) compare toe the graph of the function f(x)=x^2
The graph of g(x) compare to the graph of the function[tex]f(x)=x^2[/tex] is; identical.
What is a solution to a system of equations? (SOLUTION GRAPHICALLY)For a solution to be the solution to a system, it must satisfy all the equations of that system, and as all points satisfying an equation are in their graphs, the solution to a system is the intersection of all its equation at a single point.
We are given that;
[tex]g(x)=(x-3)^2+9[/tex] and [tex]f(x)=x^2[/tex]
The vertex form of a quadratic function is given by:
[tex]g(x) = a(x - h)^2 + k[/tex]
where (h, k) is the vertex of the parabola.
Now Comparing [tex]g(x)=(x-3)^2+9[/tex] to [tex]f(x)=x^2[/tex]we can see that g(x) is the result of translating the graph of f(x) horizontally by 3 units to the right and vertically by 9 units upward.
The vertex of g(x) is (3, 9), that is obtained by shifting the vertex of f(x) at the origin (0, 0) to the right by 3 units and up by 9 units.
Since the coefficient is positive in both functions, both parabolas open upwards.
The shape of the parabolas is the same since both have the same coefficient [tex]x^2[/tex].
Therefore, the graph of g(x) is identical to the graph of f(x), its shape, but it is shifted horizontally and vertically with respect to f(x).
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Find the median, range, and interquartile range of both sets:
Set 1: 65, 66, 77, 79, 81, 93, 104, 105
Set 2: 56, 1, 29, 72, 67, 59, 74, 60
Which is true about the two sets?
Set 1 has a range of 40 and a median of 85.
Set 2 has a range of 74 and a median of 62.
Both sets have an interquartile range of 27.
Set 2 has data that is closer to its median than Set 1.
Answer:
C) Both sets have an interquartile range of 27.
Step-by-step explanation:
Sorted data
Set 1: 65, 66, 77, 79, 81, 93, 104, 105
Set 2: 1, 29, 56, 59, 60, 67, 72, 74
Median position: (8+1)/2 = 4.5th value
Ranges:
Set 1: 105 - 65 = 40
Set 2: 74 - 1 = 73
Medians:
Set 1: (79+81)/2 = 80
Set 2: (59+60)/2 = 59.5
IQR:
Set 1: (93+104)/2 - (66+77)/2
= 27
Set 2: (67+72)/2 - (29+56)/2
= 27
Answer:
c
Step-by-step explanation:
temperatures in f can be converted in c using the formula c=5(f-32)/9
Make F the subject of the formula.
give your answer in the form aC+b/c where a, b and c are all positive intergers.
To make F the subject of the formula in the Celsius to Fahrenheit conversion, multiply by 9, divide by 5, and then add 32, resulting in F = (9/5)C + 32.
Explanation:To make F the subject of the formula when given the Celsius to Fahrenheit conversion formula c = 5(f - 32)/9, we start by isolating Fahrenheit on one side of the equation. Here's a step-by-step process:
Multiply both sides of the equation by 9: 9c = 5(f - 32).Divide both sides by 5: (9/5)c = f - 32.Add 32 to both sides to isolate f: f = (9/5)c + 32.Now the formula for F in terms of C is in the form aC + b with a = 9/5, b = 32, and there's no c as in the denominator since the conversion is direct.
[tex]\( F = \frac{9c + 160}{5} \).[/tex] In form [tex]\( aC + \frac{b}{c} \), \( a = 9 \), \( b = 160 \),[/tex] and [tex]\( c = 5 \).[/tex]
Let's break down the process of rearranging the formula step by step.
Given formula: [tex]\( c = \frac{5(F - 32)}{9} \)[/tex]
We want to isolate [tex]\( F \)[/tex] on one side of the equation.
1. Multiply both sides by [tex]\( \frac{9}{5} \):[/tex]
[tex]\[ \frac{9}{5} \cdot c = \frac{9}{5} \cdot \frac{5(F - 32)}{9} \][/tex]
This cancels out the fraction on the right side.
[tex]\[ \frac{9}{5} \cdot c = F - 32 \][/tex]
2. Add 32 to both sides to isolate [tex]\( F \):[/tex]
[tex]\[ \frac{9}{5} \cdot c + 32 = F \][/tex]
Now, [tex]\( F \)[/tex] is isolated on the right side of the equation.
3. Rewrite [tex]\( F \)[/tex] in the required form [tex]\( aC + \frac{b}{c} \):[/tex]
[tex]\[ F = \frac{9}{5}c + 32 \][/tex]
To express [tex]\( F \)[/tex] in the required form, we can rewrite [tex]\( \frac{9}{5}c \) as \( \frac{9c}{5} \),[/tex]so the form becomes [tex]\( aC + \frac{b}{c} \).[/tex]
So, [tex]\( a = 9 \), \( b = 32 \), and \( c = 5 \).[/tex]
4. Final Form:
[tex]\[ F = \frac{9c + 160}{5} \][/tex]
So, in the form [tex]\( aC + \frac{b}{c} \),[/tex] we have [tex]\( a = 9 \), \( b = 160 \), and \( c = 5 \).[/tex]
The area of a regular polygon is 216cm2. The perimeter is 48cm, what is the
length of the apothem?
Answer:
The answer to your question is Apothem = 9 cm
Step-by-step explanation:
Data
Area = 216 cm²
Perimeter = 48 cm
Formula
Area = Perimeter x apothem / 2
Perimeter = length of the side x number of sides
Process
Substitute the values in the area formula and simplify it.
1.- Substitution
216 = 48a/2
-Solve for a
216 x 2 = 48a
432 = 48a
a = 432 / 48
-Result
a = 9 cm
Researchers studying the acquisition of pronunciation often compare measurements made on the recorded speech of adults and children. One variable of interest is called "voice onset time" (VOT), the length of time between the release of a consonant sound (such as "p") and the beginning of an immediately following vowel (such as the "a" in "pat"). For speakers of English, this short time lag can be heard as a period of breathiness between the consonant and the vowel. Here are the results for some randomly selected 4-year-old children and adults asked to pronounce the word "pat". VOT is measured in milliseconds and can be either positive or negative.
Children: n = 10, mean = 60.67, standard deviation = 39.89
Adults: n = 20, mean = 88.17, standard deviation = 24.74
You are interested in whether there is a difference in the VOT of adults and children, so you plan to test H0:μa−μc=0 against Ha:μa−μc≠0, where μa and μcare the population mean VOT for adults and children, respectively.
A. What additional information would you need to confirm that the conditions for this test have been met?
B. Assuming the conditions have been met, calculate the test statistic and p-value for this test.
C. Interpret the p-value in the context of this study and draw the appropriate conclusion at
α = 0.05.
D. Given your conclusion in part C, which type error, Type I or Type II, is it possible to make? Describe that error in the context of this study.
Answer:
(A) The additional information that is needed to confirm about the conditions for this test have been met is ‘Population is approximately normal.
(B) The test statistic = 1.9965
(C1) P-value = 0.0556
(C2) There is no significant difference between mean VOT for children and adults.
D1) It is possible to make type II error.
(D2) There should be a difference in the VOT of adults and children.
Step-by-step explanation:
Let na be the number of adults = 20
xa mean VOT for adults = 88.17
sa standard deviatiation of VOT for adults = 24.74
Let nc be the number of children = 10
xc mean VOT for children =60.67
sc standard deviatiation of VOT for children = 39.89
(A) From the information the population variances are unknown and the two sample are assumed to be independent and the sample the sample size are smaller that is (n<30).
This indicates that the additional information that is required for the conditions of the test to be satisfied is 'distribution of the population'. the addition assumption to be made is, that the population distribution is normal.
(b) Calculating the test statistics using the formula;
t = (xa -xc)/SE - d
where SE = standard deviation , d= hypothesized difference = 0
But SE = √sa²/na +sc²/nc
= √24.74 ²/20 + 39.89²/10
= √189.72559
= 13.774
Substituting into test statistics equation, we have
t = (xa -xc)/SE - d
= (88.17 - 60.67/13.774
= 1.9965
Therefore the test statistic is 1.9965
(c) Calculating the p-value, we have;
Degree of freedom = na + nc -2
= 10+ 20 -2
= 28
The p-value for t=1.9965 at 28 degrees of freedom and 0.05 level of significance is 0.0556.
The p-value 0.0556 is greater than given level of significance 0.05 hence we fail to reject the null hypothesis and conclude that there is no significant difference between mean VOT for children and adults.
(D1) From the information in part (C) the null hypothesis is not rejected.
Since the null hypothesis is not rejected, there might be a chance that not rejecting null hypothesis would be wrong. In this type of situation the error that can occur would be type II error.
(D2) The type of error describe in the context of this study is obtained by the concept of the type II error which tells that the null hypothesis is not rejected when it is actually false.
Paul observes that AB=AC and concludes that AB abd AC must be tangent to the circle. What is wrong with pauls reasoning?
Answer:
C
Step-by-step explanation:
Answer:
The answer should be C
Step-by-step explanation:
we know that
the triangle AOB is congruent with triangle AOC
because
AB=AC
OB=OC-----> the radius of the circle
The OB side is common
but
there is no additional information that allows me to calculate the OBA angle to determine if it is a right angle
therefore
the answer is the option
C.There is no indication that AB and AC are perpendicular to the radii at the points of intersection with the circle.
Thanks (4)
What is the measure of
Answer:
C: 107
Step-by-step explanation:
135-28 = 107
Answer:
it would have to be 107 bro
Step-by-step explanation:
The two cones are congruent
Determine the unknown measures of the cones.
A= units
B = units
C = units
Du units
5.2/B
6.2
V.42 units
Va
units
Answer:
3.1
4.2
5.2
42
Step-by-step explanation: They’re congruent so just copy what the other triangle has all you had to do was find the radius.
(4 × 6) ÷ (2 + 4) ÷ (8 ÷ 4) =
Answer:
2
Step-by-step explanation:
24÷ 6÷ 2=2
2.6-,2.061,2.601,2.34,2.7 order the following from least to greatest
Answer:
2.061, 2.34, 2.6, 2.601, 2.7
Step-by-step explanation:
Hello!
This is a bit hard to explain! If you want me to try, just comment.
I have arranged the sequence in ascending order below:
[tex]2.061,\:2.34,\:2.6,\:2.601,\:2.7[/tex].
Hope this helps!
Answer:
2.061, 2.34, 2.6, 2.601, 2.7
Step-by-step explanation:
Because the numbers all have a 2 in the ones place, you need to evaluate the numbers in the tenths place and the numbers with the lowest go first and so on :)
Find the unit price of 60lbs of honey for $123.99. Round your answer to the nearest cent if necessary.
Answer:
$2.07 per pound
Step-by-step explanation:
price divided by amount will get you the unit price. $123.99/60 equals 2.0665.
MaryJo is considering investing in 2 different mutual funds. Option A has an annual interest rate of 7% and requires a principal of $10,000 with monthly deposits of $200 for 10 years. Option B has an annual interest rate of 9% and requires a principal of $10,000 with monthly deposits of $200 for 5 years.
The option A mutual funds will be more effective.
Step-by-step explanation:
Option A:
Principal amount = $10000
Monthly deposit = $200
Time = 10 years
Rate of interest = 7%
Total deposit = (200 x 12 x 10) + 10000
= 24000 + 10000
= $34000
Interest = (34000 x 7 ) /100
= 340 x 7
= $2380
Total amount = 34000 + 2380
= $36380
Option B:
Principal amount = $10000
Monthly deposit = $200
Time = 5 years
Rate of interest = 9%
Total deposit = (200 x 12 x 5) + 10000
= 12000 + 10000
= $22000
Interest = (22000 x 9 ) /100
= $1980
Total amount = 22000+1980
= $23980
The option A mutual funds will be more effective.
Answer:
What is the difference in the final balances of the two mutual funds?
Step-by-step explanation:
The difference is $12,400.
Solve for a and d
6x^2+14x+4=(ax+b)(cx+d)
b=1 and c=2
Answer:
a = 3
d = 4
Step-by-step explanation:
6x^2+14x+4 = (ax+1)(2x+d)
6x^2+2x+12x+4
2x(3x+1)+4(3x+1)
(3x+1)(2x+4)
3 = a
4 = d
Answer:
Step-by-step explanation:
a=3, d=4
Determine the zeroes of 10x2−5=35
Answer:
x = +2, x = -2
Step-by-step explanation:
The equation to solve in this problem is
[tex]10x^2-5=35[/tex]
The first step we do is to subtract 35 on both sides of the equation, so we get:
[tex]10x^2-5-35=0\\10x^2-40=0[/tex]
Now we simplify the equation by dividing both terms by 10:
[tex]\frac{10x^2-40}{10}=0\\x^2-4=0[/tex]
Now we observe that the term on the left is the difference between two squares, so it can be rewritten using the property:
[tex]a^2-b^2=(a+b)(a-b)[/tex]
Where here,
a = x
b = 2
So we can rewrite the equation as:
[tex]x^2-4=0\\(x+2)(x-2)=0[/tex]
And this equation is zero when either one of the two factors is zero, so the two solutions are:
[tex]x+2=0\rightarrow x=-2\\x-2=0 \rightarrow x=+2[/tex]
wyatt bought a jacket that cost 12 dollers and a scarf that costs 18 dollers he recived a discount at the counter if he only paid 21 dollers total how many dollers was the discount?
Answer:
$9
Step-by-step explanation:
12 + 18 = $30 Total
30 - 21 = $9 Discount
30 - 9 = $21 After discount
Create a list of steps, in order, that will solve the following equation.
5(x-3)^2+4=1295(x−3)
2
+4=129
Answer:
subtract 4 from both sides
divide both sides by 5
take the square roots of both sides
add 3 to both sides
Step-by-step explanation:
Each wall in Keith's room is 12 meters long and seven and 7 7/8 meters wide. He plans to paint one wall blue. Each can of paint covers 15 square meters. How many cans of paint does kids need to cover the bedroom wall?
Answer:
7 cans
Step-by-step explanation:
6 cans of paint kids need to cover the bedroom wall.
What is area of a rectangle?The formula for calculating the area of a rectangle with dimensions l and w is: A = lw (rectangle). In other words, the length times the width equals the area of a rectangle.
Given
length = 12 m
width = 7.875 m
area = 12 * 7.875 = 94.5 sq. m
area 1 can can fill = 15 sq. m
no. of cans that can fill 94.5 = 6
therefore, 6 cans of paint kids need to cover the bedroom wall.
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select all of the ratios that are equivalent to 4 to 7.
5/8
12/10
8.14
5 to 10
16/28
9 to 16
Answer:
[tex]\frac{16}{28}[/tex]
Step-by-step explanation:
Question asked:
Select all of the ratios that are equivalent to 4 to 7.
1) 5/8
2) 12/10
3) 8.14
4) 5 to 10
5) 16/28
6) 9 to 16
Solution:
To know the ratios are equivalent to [tex]\frac{4}{7}[/tex] or not, we have to check each by cross multiplication:-
1) [tex]\frac{5}{8}[/tex]
[tex]\frac{4}{7} =\frac{5}{8} \\ \\[/tex]
By cross multiplication:
[tex]4\times8=5\times7\\ \\ 32=35[/tex]
Not equivalent.
2) [tex]\frac{12}{10}[/tex]
[tex]\frac{4}{7} =\frac{12}{10} \\ \\[/tex]
By cross multiplication:
[tex]4\times10=12\times7\\ \\ 40=84[/tex]
Not equivalent.
3) 8.14 = [tex]\frac{814}{100} \ eliminating\ decimal[/tex]
[tex]\frac{4}{7} =\frac{814}{100} \\ \\[/tex]
By cross multiplication:
[tex]4\times100=814\times7\\ \\ 400=5698[/tex]
Not equivalent.
4) [tex]\frac{5}{10}[/tex]
[tex]\frac{4}{7} =\frac{5}{10} \\ \\[/tex]
By cross multiplication:
[tex]4\times10=5\times7\\ \\ 40=35[/tex]
Not equivalent.
5)[tex]\frac{16}{28}[/tex]
[tex]\frac{4}{7} =\frac{16}{28} \\ \\[/tex]
By cross multiplication:
[tex]4\times28=16\times7\\ \\ 112=112[/tex]
Yes, this is equivalent.
6) [tex]\frac{9}{16}[/tex]
[tex]\frac{4}{7} =\frac{9}{16} \\ \\[/tex]
By cross multiplication:
[tex]4\times16=9\times7\\ \\ 64=63[/tex]
Not equivalent.
Thus, only [tex]\frac{16}{28}[/tex] is equivalent.
Solve negative 7 over 3, the whole multiplied by x minus 3 equals negative 52.
Answer:
x= [tex]\frac{135}{7}[/tex]
Step-by-step explanation:
1. [tex]-\frac{7}{3} (x-3)=-52[/tex]
2. combine -7/3(x - 3)
= [tex]-\frac{7}{3}x-7 = -52[/tex]
3. Do combine like terms on both sides
= -52 + -7 = -45
4. left with, [tex]-\frac{7}{3}x = -45[/tex]
5. divide -45 by -7/3
6. left with, [tex]x = \frac{135}{7}[/tex]
Answer:
21
Step-by-step explanation:]
plz mark me the Brainliest
70 points- help ASAP, please.
1. Is a^2 - 39 prime...
a. Over the set of polynomials with rational coefficients?
b. over the set of polynomials with real coefficients?
c. Explain your answers to Parts a and b
2. The Discriminant Theorem Factoring Quadratics applies to quadratics with ___ coeffecients.
Answer:
1) a) yes
b) no
c) a² - 39
(a)² - (sqrt(39))²
(a - sqrt(39))(a + sqrt(39))
This quadratic can be split into real factors, but not rational
sqrt(39) is a real number, but not rational
2) real
what are the two sides of a ray called??
The equation of a line is y=8x+2 and the point (3,q) lies on this line. What is the value of q?
Answer:
q = 26
Step-by-step explanation:
Given that (3, q ) lies on the line, then the coordinates of the point make the equation true.
Substitute x = 3, y = q into the equation
q = 8(3) + 2 = 24 + 2 = 26
Final answer:
To determine the value of q for the point (3, q) on the line y=8x+2, substitute x with 3 to get y=26. Hence, q is 26, and the point is (3, 26).
Explanation:
To find the value of q for the point (3, q) that lies on the line with the equation y=8x+2, we substitute the x-coordinate of the point, which is 3, into the equation and solve for y. This gives us:
y = 8(3) + 2
y = 24 + 2
y = 26
Therefore, the value of q is 26, and the point is (3, 26). This demonstrates how to use a line's equation to find a specific point on the line. The question illustrates the algebraic relationship between the coordinates of a point on a line and the equation of the line itself.
A random poll of 800 working men found that 11% had taken on a second job to help pay the bills. a) Estimate the true percentage of men that are taking on second jobs by constructing a 95% confidence interval. b) A pundit on a TV news show claimed that only 8% of working men had a second job. Use your confidence interval to test whether his claim is plausible given the poll data.
Answer:
a) 95% Confidence Interval = (8.832%, 13.168%)
b) The 8% claim for the pundit falls outside the range of the confidence interval, hence, it isn't a very plausible claim given the poll data.
Step-by-step explanation:
Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample proportion) ± (Margin of error)
Sample proportion = 11% = 0.11
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error of the sample proportion)
Critical value will be obtained using the z-distribution. This is because the sample size is large enough for the t-distributoon valur to approximate the z-distribution value
Critical value for 95% confidence = 1.960 (from the z-tables)
Standard error = σₓ = √[p(1-p)/n]
where
p = sample proportion = estimated to be 11% = 0.11
n = Sample size = 800
σₓ = √[p(1-p)/n]
σₓ = √[0.11×0.89/800]
σₓ = 0.0110623234 = 0.01106
95% Confidence Interval = (Sample proportion) ± [(Critical value) × (standard Error)]
CI = 0.11 ± (1.960 × 0.01106)
CI = 0.11 ± 0.02168
95% Confidence Interval = (0.08832, 0.13168)
95% Confidence Interval = (8.832%, 13.168%)
b) The 8% claim for the pundit falls outside the range of the confidence interval, hence, it isn't a very plausible claim given the poll data.
Hope this Helps!!!
Hurry late work! Consider the reduction of the rectangle. Rounded to the nearest 10th, what is the value of X?
Answer:
0.6 feet
Step-by-step explanation:
The first rectangle to scaled down. Therefore, the scale factor will be less than 1.
[tex]\frac{4.5}{16.8}=\frac{15}{56}[/tex]
Therefore, the scale factor is [tex]\frac{15}{56}[/tex].
[tex]\frac{15}{56}*2.3=\frac{69}{112}[/tex]
[tex]\frac{69}{112}[/tex] ≈ 0.6, so the value of x is 0.6 feet.
For what values of x and y must the figure have in order to be a parallelogram
Given:
Given that the parallelogram with the lengths 5x, 3x + 1, 2y - 5 and y.
We need to determine the values of x and y.
Values of x and y:
We know the property that the opposite sides of a parallelogram are congruent.
Thus, we have;
[tex]5x=2y-5[/tex] ------- (1)
[tex]3x+1=y[/tex] ------- (2)
The value of x and y can be determined using the substitution method.
Substituting equation (2) in equation (1), we have;
[tex]5x=2(3x+1)-5[/tex]
[tex]5x=6x+2-5[/tex]
[tex]5x=6x-3[/tex]
[tex]-x=-3[/tex]
[tex]x=3[/tex]
Thus, the value of x is 3.
Substituting x = 3 in equation (2), we have;
[tex]3(3)+1=y[/tex]
[tex]9+1=y[/tex]
[tex]10=y[/tex]
Thus, the value of y is 10.
Who knows the answer?
Answer:
t
Step-by-step explanation:
Line [tex] \purple{\boxed{\bold{t}}} [/tex] is the transversal.
*ignore selected answer haha* just need help answering
Answer:
[tex]x^2+8x+15[/tex]
Step-by-step explanation:
[tex]f(x)=x+4\\g(f(x))=g(x+4)\\g(x+4)=(x+4)^2-1\\(x+4)^2-1=x^2+8x+15[/tex]
Power +, Inc. produces AA batteries used in remote-controlled toy cars. The mean life of these batteries follows the normal probability distribution with a mean of 38 hours and a standard deviation of 5.8 hours. As a part of its quality assurance program, Power +, Inc. tests samples of 9 batteries.a. What can you say about the shape of the distribution of the sample mean?
b. What is the standard error of the distribution of the sample mean? (Round your anser to 4 decimals places.)
c. What proportion of the samples will have a mean useful life of more than 39.5 hours? (Round z value to 2 decimal places and final answer to 4 decimal places)
d. What proportion of the sample will have a mean useful life greater than 37.5? (Round z value to 2 decimal places and final answer to 4 decimal places.)
Answer:
a) For this case we select a sample size of n=9. And we know that the distribution of X is normal so then the distribution for the sample mean is given by:
[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]
b) [tex] SE = \frac{\sigma}{\sqrt{n}} =\frac{5.8}{\sqrt{9}} =1.9333[/tex]
c) [tex] P\bar X >39.5)[/tex]
And we can use the z score given by:
[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And if we find the z score for 39.5 we got:
[tex] z = \frac{39.5-38}{\frac{5.8}{\sqrt{9}}}= 0.78[/tex]
And using the complement rule we got:
[tex] P(z >0.78) =1-P(Z<0.78) = 1-0.7823= 0.2177[/tex]
d) [tex] P\bar X >37.5)[/tex]
And we can use the z score given by:
[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And if we find the z score for 37.5 we got:
[tex] z = \frac{37.5-38}{\frac{5.8}{\sqrt{9}}}= -0.26[/tex]
And using the complement rule we got:
[tex] P(z >-0.26) =1-P(Z<-0.26) = 1-0.3974= 0.6026[/tex]
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the life of batteries of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(38,5.8)[/tex]
Where [tex]\mu=38[/tex] and [tex]\sigma=5.8[/tex]
Part a
For this case we select a sample size of n=9. And we know that the distribution of X is normal so then the distribution for the sample mean is given by:
[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]
Part b
The standard error is given by:
[tex] SE = \frac{\sigma}{\sqrt{n}} =\frac{5.8}{\sqrt{9}} =1.9333[/tex]
Part c
We want this probability:
[tex] P\bar X >39.5)[/tex]
And we can use the z score given by:
[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And if we find the z score for 39.5 we got:
[tex] z = \frac{39.5-38}{\frac{5.8}{\sqrt{9}}}= 0.78[/tex]
And using the complement rule we got:
[tex] P(z >0.78) =1-P(Z<0.78) = 1-0.7823= 0.2177[/tex]
Part d
We want this probability:
[tex] P\bar X >37.5)[/tex]
And we can use the z score given by:
[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And if we find the z score for 37.5 we got:
[tex] z = \frac{37.5-38}{\frac{5.8}{\sqrt{9}}}= -0.26[/tex]
And using the complement rule we got:
[tex] P(z >-0.26) =1-P(Z<-0.26) = 1-0.3974= 0.6026[/tex]
The distribution of the mean life of Batteries produced by Power+, Inc. follows Normal distribution. The standard error is calculated to be 1.9333. Using Z scores, it's discovered that approximately 21.77% of samples will have a mean life more than 39.5 hours while around 60.26% samples will have a mean useful life more than 37.5 hours.
Explanation:Understanding the Distribution of the Mean Life of Batteries
a. The distribution of the sample mean should approximate a normal distribution because we know the distribution of the population (life of the batteries) is normal. The expectation is that the sample mean should also follow normal distribution, based on the Central Limit Theorem.
b. The standard error of the distribution of the sample mean, is calculated as the standard deviation divided by the square root of the number of samples. Therefore, the standard error is 5.8 / sqrt(9), that is approximately 1.9333.
c. To find the proportion of samples with a mean useful life of more than 39.5 hours, we first find the Z score for 39.5. The Z score is calculated by (sample mean - population mean) / standard error. Therefore, Z = (39.5 - 38) / 1.9333 = approximately 0.78 (rounded to 2 decimal places). Looking this up on a Z table gives us 0.7823. However, because we want the proportion where it is more than 39.5 hours, we need to subtract this from 1. So, 1-0.7823 = 0.2177 (i.e., 21.77% samples will have a mean useful life more than 39.5 hours).
d. Following the same procedure, the Z score for a sample mean of 37.5 is approx negative -0.26 (rounded to 2 decimal places) using the same calculation as above. Looking this up on a Z table gives us 0.3974. But, because we want the proportion greater than 37.5 hours, we need to subtract this from 1. So, 1-0.3974 = 0.6026 (i.e., 60.26% samples will have a mean useful life more than 37.5 hours).
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The equation h(t)=-16t^2+32t+12 gives the height of a baseball, in feet, t seconds after it is thrown from a platform. What is the height of the platform? What is the initial velocity when the baseball is thrown?
Answer:
(a) 12 m
(b) 32 m/s
Step-by-step explanation:
(a) The height of the platform is h(0) i.e. the height, h, at time t = 0 secs, since the ball would not have been thrown at that time.
Therefore, h(0) is:
[tex]h(0) = -16(0^2) + 32(0) + 12\\\\\\h(0) = 0 + 0 + 12\\\\\\h(0) = 12 m[/tex]
The height of the platform is 12 m.
(b) The initial velocity when the baseball is thrown will be v(0) that is velocity when t = 0 secs.
We obtain velocity, v, by differentiating height, h, with respect to time:
[tex]v(t) = \frac{dh}{dt} = -32t + 32[/tex]
Therefore, at time t = 0 secs:
[tex]v(0) = -32(0) + 32\\\\\\v(0) = 32 m/s[/tex]
The initial velocity of the baseball when it is thrown is 32 m/s.
Jacob wants to enlarge a triangle with sides 7, 12, and 12 inches to create a similar triangle. If the shortest side of the enlarged triangle is 24.5 inches, how long will each of the other two sides be?
Answer:
42
Step-by-step explanation:
If the shortest side is 7 and it is enlarged to be 24.5.
It is enlarged by a scale of 3.5.
so if you scale 12 by 3.5
then you get 42