Answer:
a) The p-value of the test is 0.2076 > 0.05, which means that the sample indicates that the resistors are conforming.
b) The 95% confidence interval for the average resistance is (0.147, 0.153). 0.152 is part of the confidence interval, which means that as the test statistic in item a), it indicates that the resistors are conforming.
Step-by-step explanation:
Question a:
The resistors produced by a manufacturer are required to have an average resistance of 0.150 ohms.
At the null hypothesis, we test if this is the average resistance, that is:
[tex]H_0: \mu = 0.15[/tex]
We are interested in testing the hypothesis that the resistors conform to the specifications.
At the alternative hypothesis, we test if it is not conforming, that is, the mean is different of 0.15, so:
[tex]H_1: \mu \neq 0.15[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.15 is tested at the null hypothesis:
This means that [tex]\mu = 0.15[/tex]
Sample mean of 0.152, sample of 10, population standard deviation of 0.005.
This means that [tex]X = 0.152, n = 10, \sigma = 0.005[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.152 - 0.15}{\frac{0.005}{\sqrt{10}}}[/tex]
[tex]z = 1.26[/tex]
P-value of the test and decision:
The p-value of the test is the probability of the sample mean differing from 0.15 by at least 0.152 - 0.15 = 0.002, which is P(|z| > 1.26), given by two multiplied by the p-value of z = -1.26.
Looking at the z-table, z = -1.26 has a p-value of 0.1038.
2*0.1038 = 0.2076
The p-value of the test is 0.2076 > 0.05, which means that the sample indicates that the resistors are conforming.
Question b:
We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a p-value of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96\frac{0.005}{\sqrt{10}} = 0.003[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 0.15 - 0.003 = 0.147.
The upper end of the interval is the sample mean added to M. So it is 0.15 + 0.003 = 0.153.
The 95% confidence interval for the average resistance is (0.147, 0.153). 0.152 is part of the confidence interval, which means that as the test statistic in item a), it indicates that the resistors are conforming.
Find a polynomial function of degree 4 with - 3 as a zero of multiplicity 3 and 0 as a zero of multiplicity 1.
The polynomial function in expanded form is f(x) =
(Use 1 for the leading coefficient.)
Answer:
[tex]f(x) = x^4 + 9x^3 + 27x^2 + 27x[/tex]
Step-by-step explanation:
Zeros of a function:
Given a polynomial f(x), this polynomial has roots [tex]x_{1}, x_{2}, x_{n}[/tex] such that it can be written as: [tex]a(x - x_{1})*(x - x_{2})*...*(x-x_n)[/tex], in which a is the leading coefficient.
- 3 as a zero of multiplicity 3
So
[tex]f(x) = (x - (-3))^3 = (x + 3)^3 = x^3 + 9x^2 + 27x + 27[/tex]
0 as a zero of multiplicity 1.
So
[tex]f(x) = x(x^3 + 9x^2 + 27x + 27) = x^4 + 9x^3 + 27x^2 + 27x[/tex]
(Use 1 for the leading coefficient.)
Multiply the polynomial by 1, so it stays the same. The polynomial in expanded form is:
[tex]f(x) = x^4 + 9x^3 + 27x^2 + 27x[/tex]
A parent is buying two types of chocolate truffles for their family. The oldest child can eat twice as much as their younger siblings and prefers white chocolate (W), the younger three like dark chocolate (D) and the spouse likes white chocolate (W). Five white chocolate truffles (W) cost the same as three dark chocolate truffles (D). If the parent bought 6 white chocolate truffles(W) and 10 dark chocolate truffles (D), and spent $34.00, how much was each dark chocolate truffle
Answer:
Each chocolate truffle is $2.125
Step-by-step explanation:
Honestly, I'm not 100% sure if this is correct, and I am truly sorry if this is wrong, but its worth a try :)
What is the distance between the following points?
Will give brainliest
Answer:
√65
Step-by-step explanation:
(-6,4) (-5,-4)
√(x2 - x1)² + (y2 - y1)²
√[-5 - (-6)]² + (-4 - 4)²
√(1)² + (-8)²
√1 + 64
√65
PLEASE HELPPPPP!!!! (answer in decimal)
Answer:
[tex]\approx 0.482659[/tex]
Step-by-step explanation:
The experimental probability is the chance of an event happening based on data, or rather the experiment results, and not on a theoretical calculation. In essence, a theoretical calculation can be described by the following formula:
[tex]\frac{desired}{total}[/tex]
However, the experimental probability can be described with the following formula:
[tex]\frac{number\ of\ desired\ outcomes}{number\ of \ trials}[/tex]
The number of trials is the sum of the number of outcomes. In this case, the desired outcome is tails. Therefore, the experimental probability can be described using the following formula:
[tex]\frac{tails}{total}[/tex]
One can also rewrite the formula as the following. This is because the total is the sum of the number of the two outcomes:
[tex]\frac{tails}{heads+tails}[/tex]
Substitute,
[tex]\frac{167}{167+179}[/tex]
Simplify,
[tex]\frac{167}{346}[/tex]
Rewrite as a decimal:
[tex]\approx 0.482659[/tex]
Find the equation of the line through points (-5,-6) and (4,12)
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Answer:
y = 2x +4
Step-by-step explanation:
The slope can be found using the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (12 -(-6))/(4 -(-5)) = 18/9 = 2
The y-intercept can be found from ...
b = y -mx
b = 12 -(2)(4) = 4
Then the slope-intercept equation for the line is ...
y = mx +b
y = 2x +4
Answer:
y=2x+4
Step-by-step explanation:
Hi there!
We want to find the equation of the line that passes through the points (-5, -6) and (4, 12)
The most common way to write the equation of the line is in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept
First, let's find the slope of the line
The formula for the slope calculated from two points is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where ([tex]x_1[/tex], [tex]y_1[/tex]) and ([tex]x_2[/tex], [tex]y_2[/tex]) are points
We have everything needed to calculate the slope, but let's label the values of the points to avoid any confusion
[tex]x_1[/tex]=-5
[tex]y_1[/tex]=-6
[tex]x_2[/tex]=4
[tex]y_2[/tex]=12
Now substitute into the formula (remember: the formula has SUBTRACTION in it)
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{12--6}{4--5}[/tex]
Simplify
m=[tex]\frac{12+6}{4+5}[/tex]
Add
m=[tex]\frac{18}{9}[/tex]
Divide
m=2
So the slope of the line is 2
Here is the equation so far:
y=2x+b
We need to find b
As the line will pass through both (-5, -6) and (4, 12), we can use the values of either one to solve for b
Let's take (4, 12) for instance
Substitute 4 as x and 12 as y
12=2(4)+b
Multiply
12=8+b
Subtract 8 from both sides
4=b
Substitute 4 as b in the equation
y=2x+4
Hope this helps!
letter A represents the decimal
Answer:
answer is 0.4
Step-by-step explanation:
I don’t understand these 3 questions and I need help.
Answer:
1: A=1
2: -3
3: C
Step-by-step explanation:
1: If 3x+4 is a factor, then -4/3 is equal to x. Substitute it in for x and solve for a. This gives us A=1.
For the commenter not understanding how I got -4/3: 3x+4 being a factor means that it equals 0. It might help you understand this if you remember that after factoring, like I did for 38 in my photo, we take expressions like x-4 and set them equal to 0 to get x=4, a solution. So, subtract 4 from both sides to get 3x=-4, then divide both sides by 3 to get x alone. Thus, x=-4/3.
2: To find the sum, we first need to find the two solutions. We can factor to get (x+7)(x-4). This gives us x=-7 and x=+4. The solution of these two would be (-7)+4 is -3.
3: B is a close answer, but the signs are wrong on the bottom. Factoring the question would give us 2(x-2) / 2(x^2-x-2). Factoring that equation is 2(x-2) / 2(x+1)(x-2). Simplifying this gives us 1 / x+1.
Sorry for the bad penmanship, I wanted to make it a little clearer for you! I really hope I helped! :)
Solve the initial-value problem using the method of undetermined coefficients.
y'' − y' = xe^x, y(0) = 6, y'(0) = 5
First check the characteristic solution. The characteristic equation to this DE is
r ² - r = r (r - 1) = 0
with roots r = 0 and r = 1, so the characteristic solution is
y (char.) = C₁ exp(0x) + C₂ exp(1x)
y (char.) = C₁ + C₂ exp(x)
For the particular solution, we try the ansatz
y (part.) = (ax + b) exp(x)
but exp(x) is already accounted for in the second term of y (char.), so we multiply each term here by x :
y (part.) = (ax ² + bx) exp(x)
Differentiate this twice and substitute the derivatives into the DE.
y' (part.) = (2ax + b) exp(x) + (ax ² + bx) exp(x)
… = (ax ² + (2a + b)x + b) exp(x)
y'' (part.) = (2ax + 2a + b) exp(x) + (ax ² + (2a + b)x + b) exp(x)
… = (ax ² + (4a + b)x + 2a + 2b) exp(x)
(ax ² + (4a + b)x + 2a + 2b) exp(x) - (ax ² + (2a + b)x + b) exp(x)
= x exp(x)
The factor of exp(x) on both sides is never zero, so we can cancel them:
(ax ² + (4a + b)x + 2a + 2b) - (ax ² + (2a + b)x + b) = x
Collect all the terms on the left side to reduce it to
2ax + 2a + b = x
Matching coefficients gives the system
2a = 1
2a + b = 0
and solving this yields
a = 1/2, b = -1
Then the general solution to this DE is
y(x) = C₁ + C₂ exp(x) + (1/2 x ² - x) exp(x)
For the given initial conditions, we have
y (0) = C₁ + C₂ = 6
y' (0) = C₂ - 1 = 5
and solving for the constants here gives
C₁ = 0, C₂ = 6
so that the particular solution to the IVP is
y(x) = 6 exp(x) + (1/2 x ² - x) exp(x)
Find the area of the circle. Use 3.14 for it. E d = 10 cm A = [?] cm2 A=7tr2
Answer:
A=(78.5)cm²
Step-by-step explanation:
d=10
r=10/2=5
A=πr²
A=3.14*5²
A=3.14*25
A=78.5cm²
Answer: d=10cm
According to the formula i.e. A=πr²
first we need 'r'
as r=d/2
hence, r= 10cm/2
r=5cm
put r=5 in formula
=3.14(5cm)²
=3.14×25cm²
=78.5cm²
For spring break you and some friends plan a road trip to a sunny destination that is 2215 miles away. If you drive a car that gets 38 miles per gallon and gas costs $3.119/gal, about how much will it cost to get to your destination
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Answer:
$181.81
Step-by-step explanation:
(2215 mi)/(38 mi/gal)×($3.119/gal) = $181.8048
We round this up so that we have enough gas to get there. We don't want to have to walk the last 309 feet to the destination.
It will cost $181.81 to get to the destination.
Plot the following equation using the x- and y-intercepts.
2y+6=0
If both intercepts are zero, find at least one other point. Identify the graph of this equation.
Answer:
option 2
Step-by-step explanation:
factorise: 30x^5+15x²y²+xy
Answer:
your answer calculated would be: x(30x^4 + 15xy^2 + y)
Step-by-step explanation:
i used math-way it's a really useful online calculator
I want to know how to solve this equation
Answer:
your answer will be Option D
Step-by-step explanation:
log 10
Find the value of x.
A. 85
B. 131
C. 73
D. 95
Answer:
b
Step-by-step explanation:
The value of x 85.
What is the arc of the circle?The arc period of a circle can be calculated with the radius and relevant perspective using the arc period method.
⇒angle= arc/radius
⇒ 107°=arc/7
⇒ arc =1o7°*7
⇒arc=107π/180° *7
⇒arc = 85
Learn more about circle here:-brainly.com/question/24375372
#SPJ2
m∠AFD=90° . m∠AFB=31°. Find m∠DFE.
A. 87
B. 29.5
C. 31
D. 28
Answer:
D. 28
Step-by-step explanation:
Given:
m∠AFD = 90°
m∠AFB = 31°
Required:
m∠DFE
Solution:
m<AFB = m<CFD (both angles are marked as congruent angles)
Since m<AFB = 31°, therefore,
m<CFD = 31°
m<AFB + m<CFD + m<BFC = m<AFD
Plug in the known values
31° + 31° + m<BFC = 90°
62° + m<BFC = 90°
Subtract 62° from each side
m<BFC = 90° - 62°
m<BFC = 28°
m<BFC = m<DFE = 28° (both angles are marked congruent to each other)
Therefore,
m<DFE = 28°
f(x)=4(2)^x
what would a graph of this look like?
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Answer:
see attached
Step-by-step explanation:
A graphing calculator can do a nice job of showing you what the graph looks like.
The initial factor of 4 is the value when x=0, the y-intercept. The base of 2 tells you the function value is multiplied by 2 for each unit of x to the right, and divided by 2 for each unit of x to the left. (The curve quickly goes off the top of the graph.)
The horizontal asymptote is y=0, as it is for all exponential functions (that have not been translated).
Jose saves $22.45 a week which is 37% of his weekly pay. How much is Jose's weekly pay?
Use the ratio of a 45-45-90triangle to solve for the variables. Make sure to simplify radicals. Leave your answers as radicals in simplest form.
Answer:
Step-by-step explanation:
in this specific case the two legs are congruent:
b = 18
For the Pythagorean theorem
a = √ 2 * 18^2 = 18√2
Given that f(x) = 2x + 9, find the value that makes f(x) = 27.
Answer:
9
Step-by-step explanation:
f(x) = 2x+9
f(x) = 27
so, you get:
2x+9=27
2x=18
x=9
The question is in the screenshot
Answer:
AC is about 4.29
Step-by-step explanation:
we need to use simple trigonometry for this problem
the tangent of an angle is the ratio between the opposite side and the adjacent side
so the tangent of the angle 35º is BC / AC
tan(35) is about 0.7
this means that BC / AC = 0.7
we know BC is 3
so 3 / AC = 0.7
3 = 0.7(AC)
AC is about 4.29
Based on a random sample of 50, a 95% confidence interval for the population proportion was computed. Holding everything else constant, which of the following will reduce the length of the confidence interval by half? (CHECK ALL THAT APPLY): A. Quadruple the sample size. B. Change the confidence level to 68%. C. Double the sample size. D. Change the confidence level to 99.7%. E. Decrease the sample proportion by half.
The length of the confidence interval is the margin of error, which is the ratio of the standard deviation and the square root of sample size. Hence, to reduce the length of confidence interval by half, Quadruple the sample size.
Recall :
Margin of Error = σ/√nEvaluating an hypothetical scenario :
Let standard deviation, σ = 2
Sample size = 50
Margin of Error = 2/√50 = 0.554
Using Quadruple of the sample size : (50 × 4) = 200 samples
Margin of Error = 2/√200 = 0.277(0.227 ÷ 0.554) = 0.5
Therefore, increasing the sample size, reduces the margin of error. Hence, using quadruple the sample size, will reduce the margin of error by half.
Learn more : https://brainly.com/question/13403969
What is the surface area of this figure in square centimeters?
A.96
B.75
C.84
D.60
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Answer:
A. 96
Step-by-step explanation:
The surface area is the sum of the areas of the two triangular bases and the areas of the three rectangular lateral faces.
A = 2(1/2)bh + PH
where b is the base of the triangle, h is its height, P is the perimeter of the triangle, and H is the height of the prism.
A = (3 cm)(4 cm) +(3 +4 +5 cm)(7 cm) = 12 cm² +84 cm²
A = 96 cm²
The surface area of the triangular prism is 96 square cm.
The ratio of the volumes of two similar solid polyhedra is equal to the square root of the ratio between their edges. True or False? HELP QUICK PLSSSSS
Answer:
FALSE.The ratio of the volumes of two similar solid polyhedra is equal to the square of the ratio between their edges. This statement is false. A polyhedron is a shape that has no gaps between their edges or vertices.
Answer:
it's false
~~~~~~~~~~~
The physical plant at the main campus of a large state university recieves daily requests to replace fluorescent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 45 and a standard deviation of 3. Using the empirical rule, what is the approximate percentage of lightbulb replacement requests numbering between 42 and 45?
Do not enter the percent symbol.
ans = %
Answer:
34%
Step-by-step explanation:
Given that the distribution of daily light bulb request replacement is approximately bell shaped with ;
Mean , μ = 45 ; standard deviation, σ = 3
Using the empirical formula where ;
68% of the distribution is within 1 standard deviation from the mean ;
95% of the distribution is within 2 standard deviation from the mean
Lightbulb replacement numbering between ;
42 and 45
Number of standard deviations from the mean /
Z = (x - μ) / σ
(x - μ) / σ < Z < (x - μ) / σ
(42 - 45) / 3 = -1
This lies between - 1 standard deviation a d the mean :
Hence, the approximate percentage is : 68% / 2 = 34%
Algebra help needed. Overwhelmed with other papers. See attached
Answer:
Step-by-step explanation:
whitch answer how do you want us to answer
Write the equation in slope-intercept form of a line is parallel to y=2x+5 and has a y-intercept of -7
Answer:
y = 2x - 7
Step-by-step explanation:
Parallel lines have the same slope so only the y-intercept is different. Therefore nothing is changed between the two equations except the y-intercept is -7.
Solve the following system of equations using the elimination method
8x + 2y= 30
7x+2y= 24
A) (3.-12)
B) (-53)
C) 1-6,-5)
D) 16,9)
Answer:
(6, -9)
Step-by-step explanation:
let: 8x + 2y = 30 be equation (a).
7x + 2y = 24 be equation (b).
[tex]{ \bf{equation \: (a) - equation \: (b) : }}[/tex]
[tex] (8 - 7)x + (2 - 2)y = (30 - 24) \\ x + 0y = 6 \\ x = 6[/tex]
substitute for x in equation (a):
[tex] (8 \times 6) + 2y = 30 \\ 48 + 2y = 30 \\ y = - 9[/tex]
Which is equivalent to 10’6
Answer:
35/5 (if you mean 10.6)
1000000 (if you mean 10 to the sixth power)
0.000001 (if you mean 10/6)
Answer:
There are 126 inches in 10'6
Step-by-step explanation:
take our feet and multiply the value by 12
f(x)=(2x+4)/(x^(2)+5x+6)
Step-by-step explanation:
Download gauthmath it will help
w^2+2w-42=0
what is the width and the length
Answer:
answers in the explanation cz I'm too lazy to type :(
not entirely sure tho
Step-by-step explanation:
w²+2w-42=0
*quadratic formula*
w= -1+ square root 43 m
or w= -1- square root 43 m
then since the length is 2m more than w
add 2 to both answers
l= 1+ square root 43 m
l=1- square root 43 m
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Answer:
width: 5.557 mlength: 7.557 mStep-by-step explanation:
Given:
a rectangular patio of width w meters, length w+2 meters, and area 42 m²
Find:
width and length
Solution:
The area is ...
A = LW
42 = w(w +2)
43 = w² +2w +1 . . . . . . add 1 to complete the square
√43 = w+1
w = √43 -1 ≈ 5.557 . . . meters
l = w+2 = √43 +1 ≈ 7.557 . . . meters
The width and length of the patio are 5.557 m and 7.557 m, respectively.
