Answer:
"The probability that the mean battery life would be greater than 948.8 minutes" is 0.1446.
Step-by-step explanation:
In this case, the quality control expert takes a sample of batteries. From these batteries, we want to find "the probability that the mean battery life would be greater than 948.8 minutes".
Different concepts needed to take into account to solve this question
Sampling Distribution of the Means
For doing this, we need to use the sampling distribution of the means, which results from taking the mean for each possible sample coming from a random variable [tex] \\ x[/tex]. Roughly speaking, each sample will have a different mean, [tex] \\ \overline{x}[/tex], and the probability distribution for any of these means is called the sampling distribution of the means.
The sampling distribution of the means has a mean that equals the population's mean for the random variable [tex] \\ x[/tex], i.e., [tex] \\ \mu[/tex], and its standard deviation is [tex] \\ \frac{\sigma}{\sqrt{n}}[/tex]. We can express this mathematically as:
[tex] \\ \overline{x} \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex] [1]
Standardized Values for [tex] \\ \overline{x}[/tex]
We can standardized the values for [tex] \\ \overline{x}[/tex] using z-scores:
[tex] \\ Z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex] [2]
This random variable [tex] \\ Z[/tex] follows a standard normal distribution, that is, [tex] \\ Z \sim N(0,1)[/tex], and it is easier to find probabilities since the values for them are tabulated in the standard normal table (available in any Statistics book or on the Internet.)
What type of distribution follows the sampling distribution of the means?
A general rule of thumb is that this distribution (the sampling distribution of the means) follows a normal distribution if the sample size, [tex] \\ n[/tex], is bigger than or equal to 30 observations, or [tex] \\ n \geq 30[/tex]. In this case, [tex] \\ n = 109[/tex] batteries. This is a result from the Central Limit Theorem, fundamental in Statistical Inference.
Standard Deviation
We have to remember that the standard deviation is the square root of the variance [tex] \\ \sigma^2[/tex], or [tex] \\ \sqrt{\sigma^2}[/tex].
[tex] \\ \sigma^{2} =5929[/tex][tex] \\ \sigma = \sqrt{5929} = 77[/tex]Therefore, the standard deviation in this case is [tex] \\ \sigma = 77[/tex] minutes.
In sum, we have the following information to answer this question:
[tex] \\ \sigma = 77[/tex] minutes.[tex] \\ \mu = 941[/tex] minutes.[tex] \\ n = 109[/tex] batteries (the sample size is large enough to assume that the sampling distribution of the means follows a normal distribution).[tex] \\ \overline{x} = 948.8[/tex] minutes.What is the probability that the mean battery life would be greater than 948.8 minutes?
Well, having all the previous information, we can use [2] to solve this question (without using units):
[tex] \\ z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex] \\ z = \frac{948.8 - 941}{\frac{77}{\sqrt{109}}}[/tex]
[tex] \\ z = \frac{7.8}{\frac{77}{\sqrt{109}}}[/tex]
[tex] \\ z = \frac{7.8}{7.37526}[/tex]
[tex] \\ z = 1.05758 \approx 1.06[/tex]
This result is the standardized value or z-score for [tex] \\ \overline{x}[/tex], considering [tex] \\ \mu = 941[/tex] and [tex] \\ \sigma = 77[/tex].
We round z to two decimals digits since standard normal table only uses it as an entry to find probabilities.
With [tex] \\ z = 1.06[/tex], we can consult the cumulative standard normal table. First, we need to find with [tex] \\ z = 1.0[/tex] in the first column in the table. Then, in its first raw, we need to find +0.06. The intersection for these two values determines the cumulative probability for [tex] \\ P(z<1.06)[/tex].
It is important to recall that [tex] \\ P(z<1.06) = P(\overline{x}<948.8)[/tex] because [tex] \\ z = 1.06[/tex] is the standardized value for [tex] \\ \overline{x} = 948.8[/tex] minutes.
Then, [tex] \\ P(z<1.06) = 0.8554[/tex]
However, the question is about [tex] \\ P(\overline{x} > 948.8) = P(z>1.06)[/tex]
And
[tex] \\ P(\overline{x} > 948.8) + P(\overline{x} < 948.8) = 1 [/tex]
Or
[tex] \\ P(z>1.06) + P(z<1.06) = 1[/tex]
Then
[tex] \\ P(z>1.06) = 1 - P(z<1.06)[/tex]
[tex] \\ P(z>1.06) = 1 - 0.8554[/tex]
[tex] \\ P(z>1.06) = 0.1446[/tex]
Therefore, "the probability that the mean battery life would be greater than 948.8 minutes" is 0.1446.
Which is equivalent to (9 y squared minus 4 x)(9 y squared + 4 x), and what type of special product is it?
Answer:
[tex](9y^2-4x)\,(9y^2+4x)=81y^4-16x^2[/tex]
and it is the special factor product that leads to a difference of squares
Step-by-step explanation:
The product: [tex](9y^2-4x)\,(9y^2+4x)[/tex]
is a product of the form:
[tex](a-b)\,(a+b) = a^2-b^2[/tex]
which leads as shown to a difference of squares. So they binomials [tex](a-b)[/tex] and [tex](a+b)[/tex] are the factors of the difference of squares [tex]a^2-b^2[/tex].
In our case, the product:
[tex](9y^2-4x)\,(9y^2+4x)= (9y^2)^2-(4x)^2=81y^4-16x^2[/tex]
Answer:
B
Step-by-step explanation:
Find the 96th term of the arithmetic sequence -16, -28, -40, ...
Answer:
1124.
Step-by-step explanation:
The common difference (d) is -16 - (-28) = 12, ( also -28 - (-40) = 12).
The nth term of an A.S. is a1 + d(n - 1) where a1 = first term, d=common difference.
so the 96th term of the given A.S. is:
-16 + 12(96 - 1)
= -16 + 12*95
= 1124.
-1156Answer:
Step-by-step explanation:
Which angles form a linear pair?
Answer:
b. is correct
PlZzzzz follow me guys...
Can I have help plz ASAP
Answer:
A: 4
B: -2
Step-by-step explanation:
calculate dy/dx:
A: 1 to the right and 4 up: gradient is 4/1 = 4
B: 2 to the right and 4 down: gradient is 4/-2 = -2
4x + 16 less than or equal to 18
Answer:
x≤1/2
Step-by-step explanation:
4x+16 ≤18
Subtract 16 from each side
4x+16-16 ≤18-16
4x≤2
Divide by 4
4x/4 ≤2/4
x≤1/2
anybody please help me :( I don’t know the answer ??
elimination means to get rid of one variable by altering the coefficients of variable (by multiplying and diving by some constant number)
in this case, if you just add the two equation, y gets cancelled you get 5x=20 or x=4
put it in any equation to get y (this works because both lines pass through the same point, so they must satisfy that point) to get y=2
Answer: (4,2)
Step-by-step explanation:
You can solve this systems of equation by substitution, graphing, and elimination
Solving by Elimination was found to be the easiest for me.
3x+2y=16
2x-2y=4
eliminate 2y because a positive and a negative will equal zero.
3x+2x=5x, 16+4=20
5x=20, divide 5 on both sides
x=4
Now we solve for y
You can plug in 4 for x in either equations
I did the first equation
3(4) +2y=16
3*4=12
12+2y=16
-12 -12
2y=4
divide 2 on both sides
y=2
Answer is (4,2)
Mark brainlist please
HELP ME ASAP! PLS!!!!
Which triangle’s unknown side length measures StartRoot 53 EndRoot units?
(A)A right triangle with side length of 6 and hypotenuse of StartRoot 91 EndRoot.
(B)A right triangle with side length of StartRoot 47 EndRoot and hypotenuse of 10.
(C)A right triangle with side length of StartRoot 19 EndRoot and hypotenuse of StartRoot 34 EndRoot.
(D)A right triangle with side length StartRoot 73 EndRoot and hypotenuse 20.
Answer:
(B) A right triangle with side length of StartRoot 47 EndRoot and hypotenuse of 10
Step-by-step explanation:
I just took the quiz on edge
Answer:
B
Step-by-step explanation:
Which statement is true regarding the graphed functions?
f(4) = g(4)
f(4) = g(-2)
f(2)= g(-2)
f(-2)=g(-2)
When x^3 + 2x^2 - 7x + a is divided by (x-2) the remainder is 4. Find the value of a. Please help
Answer:
a = - 8
Step-by-step explanation:
A polynomial divided by factor (x - h) has a remainder given by f(h)
Here the divisor is (x - 2), thus f(2) gives the remainder, that is
2³ + 2(2)² - 7(2) + a = 4 ← 4 being the remainder
8 + 8 - 14 + a = 4, that is
12 + a = 4 ( subtract 12 from both sides )
a = - 8
The sides of ∆ABC inscribed in a circle are equidistant from the center. Tricia says that ∆ABC must be equilateral. Which explains whether Tricia is correct?
Answer:
Tricia is correct because the sides of the triangle are congruent since they are equidistant from the center of the circle.
Step-by-step explanation:
Given that the sides of ΔABC inscribed in a circle are equidistant from the center. This implies the triangle is drawn within the circumference of the circle with a center.
Bisecting the three sides of the triangle shows that the three bisectors intersect at a point which is the center of the circle, and the lines are equidistant to this point. This proves that the length of the sides of the triangle are equal, so that the triangle is an equilateral triangle. Therefore, Tricia's statement is correct.
I NEED HELP PLEASE, THANKS! :)
Answer:
Graph A
Step-by-step explanation:
You can use symmetry to find the inverse of a function because you know that the inverse of a function will be that function reflected across the line y=x. This is a line that has a slope of 1 and runs through the origin. Taking a look at the graph choices given, the only one that appears to have been reflected across y=x is graph A, since all of the points of pre-image and the corresponding points on the image are equally distant from y=x. Hope this helps!
Answer: A (the first graph)
Step-by-step explanation:
Inverse is when you swap the x's and y's
A = (x, y) → A⁻¹ = (y, x)
I took three points from the graph (labeled A, B, C) and found their inverse.
A = (-7, 0) → A⁻¹ = (0, -7)
B = (0, 7) → B⁻¹ = (7, 0)
C = (9, 9) → C⁻¹ = (9, 9)
see graph below
Solve for the missing side of the triangle. 9.03 11.98 18.78 24.92
Answer:
11.98
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp/ hyp
sin 53 = x/15
15 sin 53 = x
11.97953265 = x
What is the y-coordinate of the point that divides the
directed line segment from J to k into a ratio of 5:1?
O -8
O -5
O 0
O 6
Answer:
[tex]y = 0[/tex]
Step-by-step explanation:
Given
Line segment JK
[tex]J = (1,-10)[/tex]
[tex]K = (7,2)[/tex]
Ratio; [tex]m:n= 5:1[/tex]
Required
Find the coordinates of y
From the question; the formula to use is
[tex]y = (\frac{m}{m+n})(y_2 - y_1) + y_1[/tex]
We have that; m = 5; n = 1
[tex]J =(x_1, y_1) = (1,-10)[/tex]
Hence, [tex]y_1 = -10[/tex]
[tex]K = (x_2,y_2)= (7,2)[/tex]
Hence, [tex]y_2 =2[/tex]
Substitute the above values in the given formula;
[tex]y = (\frac{m}{m+n})(y_2 - y_1) + y_1[/tex] becomes
[tex]y = (\frac{5}{5+1})(2 - (-10)) + (-10)[/tex]
Solve brackets
[tex]y = (\frac{5}{6})(2 +10)) - 10[/tex]
[tex]y = (\frac{5}{6})(12)) - 10[/tex]
Open bracket
[tex]y = \frac{5}{6} * 12 - 10[/tex]
[tex]y = \frac{5*12}{6}- 10[/tex]
[tex]y = \frac{60}{6}- 10[/tex]
[tex]y = 10 - 10[/tex]
[tex]y = 0[/tex]
Answer: 0
Step-by-step explanation:
Can somebody PLEASE help me with this :) ??
Answer:
Ab, De
Step-by-step explanation:
You need the base and the height in order to find out if the triangles are similar
what are the exact values of a and b?
The exact value of a and b is 5 and 5√3 respectively. Thus option D) is correct
From triangle ABC
We have AB = 10 ; And angle A = 30°
Trigonometry is the branch of mathematics that deal with study of triangles.
Now,
cos30= AC/AB
√3/2=b/10
b=5√3
Sin30 = BC/AB
1/2 = a/10
a = 5
Thus, the required value is a = 5, b = 5√3
Learn more about trigonometry here:
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Answer:
its the last option
Step-by-step explanation:
What is the numerical solution to the equation five less than three times a number equals four more than eight times the numbers?
A. -9/5
B. 1/11
C. -1/5
D. 1/5
Answer:
Option A
Step-by-step explanation:
Let us first consider the equation at hand. We are given that this equation is as follows, five less than three times a number equals four more than eight times the numbers. Convert this into a numerical format;
[tex]3x - 5 = 4 + 8x[/tex]
where x = " the number "
[tex]3x - 5 = 4 + 8x,\\- 5 = 4 + 5x,\\- 9 = 5x,\\\\x = - 9 / 5 \\\\Solution - Option A[/tex]
If you wish, take a look at this verbal explanation. To solve the equation 3x - 5 = 4 + 8x, one would first subtract 3x on either side of the equation, resulting in the simplified equation - 5 = 4 + 5x. Subtracting - 4 from either side, - 5 - 4 = - 9, and so we receive - 9 = 5x. Dividing 5 on either side, x = - 9 / 5, Option A.
Read the following statement: x + 6 = 6 + x. This statement demonstrates:
Answer:
See below.
Step-by-step explanation:
This statement demonstrates the commutative property (of addition). This is because even though the order is switched, the result will remain unchanged and they are equal to each other.
Answer:
Commutative Property of addition
Step-by-step explanation:
This statement demonstrates the commutative property (of addition). means that no. After the order of your calculation, the end result will always be the same.
This is only applicable to addition and multiplication.
Hope this helps
Please help me find the answer to this sequence? :)
Answer:
2....6......10........14.......18
Step-by-step explanation:
Add 4 each time
If f(x) = 6x -4, what is f(x) when x = 8?
A.2
B.16
C.44
D.52
Step-by-step explanation:
[tex] f(x) = 6x -4 \\ f(8) \\ f(x) = 6(8) - -4 \\ f(x) = 48 - 4 \\ f(x) = 44
[/tex]
Answer:
C.44
Step-by-step explanation:
Basically, the question is asking for you to plug in 8 for x into the equation, since the function of x is represented by the equation. Therefore, plug in 8 into the equation like this: 6(8)-4
Multiply 6 and 8, then subtract 4 from the product to get your answer
Haley’s work evaluating (-2)8 squared is shown below.
Which statement best describe Haley’s first error?
A.She used the wrong number as a repeated factor and should have
B.She used the wrong number as a repeated factor and should have evaluated
C.She misinterpreted the exponential form and should have multiplied –2 and 8.
D.She made a sign error when multiplying and should have had 256 as a final answer. its D on edge
Answer:
D
Step-by-step explanation:
she made a sign error when multiplying and should have had 256 as an answer
Answer:
the answer is D
Step-by-step explanation:
I'm taking the test now
a = 7cm, b = 14cm
Q1. Calculate the area and perimeter of the following ring where
(i)
Area of Ring:
(ii)
Perimeter of Ring:
Answer:
A =7 B=14
Step-by-step explanation:
AREA OF RING
PERIMETER OF RING
When solving, you took the square root of both
sides of the equation. Consider this step when
completing the following statements.
The roots are imaginary because of the
1) negative radicand.
2) non perfect square radicand
3) need to identify + and - roots of the radicand
Answer:
Step-by-step explanation:
Negative Radicand
The roots of the equation are imaginary because of negative radicand.
What is an imaginary number?An imaginary number is a number that, when squared, has a negative result. Essentially, an imaginary number is the square root of a negative number and does not have a tangible value.
According to the given question.
We have to take square root both sides of the equation.
Then we get imaginary roots only when there is some negative number under the radical symbol. That is when the radicand is negative.
Hence, the roots of the equation are imaginary because of negative radicand.
Thus, option 1 is correct.
Find out more information about imaginary roots here:
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14
[tex]14 \geqslant x - 8[/tex]
Answer:
Inequality form
x </ 22
Interval Notation
(-∞,22]
Step-by-step explanation:
Solve for x by simplifying both sides of the inequality, then isolating the varible
What is the length of segment GH?
Answer:
4√5
Step-by-step explanation:
Distance formula: [tex]d = \sqrt{(x2-x1)^2 + (y2-y1)^2}[/tex]
Coordinates given:
H(8, 1)
G(0, -3)
d = [tex]\sqrt{(8-0)^2 + (1+3)^2}[/tex] = 4√5
Answer:
StartRoot 80 EndRoot
80 square root is the answer
Step-by-step explanation:
|GH|² = (8 - 0)² + (1 - (-3))²
|GH|² = 64 + 16
|GH|² = 80
GH = sqrt(80)
pls mark as brainliest
Write -1/19, 7/4, -4/7 from least to greatest
Answer:
-4/7, -1/19, 7/4
Step-by-step explanation:
The fractions converted into decimals would be -0.05, 1.75, -0.57
MY LAST QUESTION WILL FOREVER BE GRATEFUL PLS HELP WILL GIVE BRANLIEST!! AT LEAST TAKE A LOOK!!!! PLS I AM BEGGING!!!
Given the diagram below, what statement can you NOT make?
A) m∠2 + m∠3 = 90
B) ∠5=∠3
C) ∠2=∠5
D) m∠4=90
Answer:
B
Step-by-step explanation:
∠ 2 + ∠ 3 = 90° ← True
∠ 5 = ∠ 3 ← False
∠ 2 = ∠ 5 ← True ( vertical angles )
∠ 4 = 90° ← True
Thus the statement that you cannot make is ∠ 5 = ∠ 3 → B
Given the function f(x) = –0.5|2x + 2| + 1, for what values of x is f(x) = 6? x = 6, x = –5 x = 5, x = –5 x = 7, x = –6 no solution
Answer:
Step-by-step explanation:
This is our absolute function for which we are tasked with finding the values of x that make the whole thing equal 6:
-.5 | 2x + 2 | + 1 = 6. Subtracting 1 from both sides gives us
-.5 | 2x + 2 | = 5. Dividing both sides by -.5 gives us
| 2x + 2 | = -10.
Because absolute value is in fact a distance measure, and one of the 2 things in math that will NEVER be negative is distance, there is no solution to this equation.
Answer:
no solution
Step-by-step explanation:
This is our absolute function for which we are tasked with finding the values of x that make the whole thing equal 6:
-.5 | 2x + 2 | + 1 = 6. Subtracting 1 from both sides gives us
-.5 | 2x + 2 | = 5. Dividing both sides by -.5 gives us
| 2x + 2 | = -10.
Because absolute value is in fact a distance measure, and one of the 2 things in math that will NEVER be negative
Write the equation of the line that is parallel to the given segment and that passes through the point (-3,0).
A. y=-3x + 9
B.
-1
y = -X-1
3
C.
1
y=-x+1
D. y = 3x - 1
Answer:
Option (B)
Step-by-step explanation:
In the figure attached,
A straight line is passing through two points (0, 2) and (3, 1).
Slope of this line ([tex]m_1[/tex]) = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{2-1}{0-3}[/tex]
= [tex]-\frac{1}{3}[/tex]
Let the slope of a parallel to the line given in the graph = [tex]m_2[/tex]
By the property of parallel lines,
[tex]m_1=m_2[/tex]
[tex]m_2=-\frac{1}{3}[/tex]
Equation of a line passing through a point (x', y') and slope 'm' is,
y - y' = m(x - x')
Therefore, equation of the parallel line which passes through (-3, 0) and having slope = [tex]-\frac{1}{3}[/tex] will be,
[tex]y-0=-\frac{1}{3}(x+3)[/tex]
[tex]y=-\frac{1}{3}x-1[/tex]
Option (B). will be the answer.
If f(x) = 2x, then f -1(x) =
0-2x
O 12x
OX-2
Answer:
What am I supposed to do
Step-by-step explanation:
if the perimeter of regular hexagon is 10 cm, what is the radius of the circle curcumscribing the polygon?
Answer:
60
Step-by-step explanation:
hexagon is 6 sided shape. 10 * 6=60