Answer:
The p-value of the test is 0.004 < 0.02, which means that there is sufficient evidence at the 0.02 level to support the company's claim.
Step-by-step explanation:
The company's promotional literature claimed that over 32% do not fail in the first 1000 hours of their use.
At the null hypothesis, we test if the proportion is of at most 32%, that is:
[tex]H_0: p \leq 0.32[/tex]
At the alternative hypothesis, we test if the proportion is more than 32%, that is:
[tex]H_1: p > 0.32[/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.
0.32 is tested at the null hypothesis:
This means that [tex]\mu = 0.32 \sigma = \sqrt{0.32*0.68}[/tex]
A sample of 1700 computer chips revealed that 35% of the chips do not fail in the first 1000 hours of their use.
This means that [tex]n = 1700, X = 0.35[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.35 - 0.32}{\frac{\sqrt{0.32*0.68}}{\sqrt{1700}}}[/tex]
[tex]z = 2.65[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample proportion above 0.35, which is 1 subtracted by the p-value of z = 2.65.
Looking at the z-table, z = 2.65 has a p-value of 0.9960.
1 - 0.9960 = 0.004.
The p-value of the test is 0.004 < 0.02, which means that there is sufficient evidence at the 0.02 level to support the company's claim.
Hi so sorry this is so long, would rlly appreciate an answer
Answer:
Step-by-step explanation:
Factor 64a^3 -8b^3 Explain all steps.
Answer:
[tex]8(2a- b)(4a^2+ 2ab+ b^2)[/tex]
Step-by-step explanation:
factor out the 8
then you have the sum/difference of cubes..
look that up SOAP: same opposite, always a plus
[tex]64a^3 -8b^3\\8(8a^3 -b^3)[/tex]
[tex]8(2a- b)(4a^2+ 2ab+ b^2)[/tex]
The job Andrew has this summer paid 7.25 an hour and the job he had last Summer paid 6.50 an hour. how much more does Andrew earn in a 40 hour week this summer than he did in a 40 hour week last summer
Answer:
30 Dollars more
Step-by-step explanation:
This summer he earned = 7.25 X 40 = 290
Last summer he earned = 6.5 X 40 = 260
How much more he earned in 40 hours = 290-260= 30 dollars more
Answer from Gauthmath
The sample size needed to estimate the difference between two population proportions to within a margin of error E with a significance level of ? can be found as follows. In the expression
E=z?p1(1?p1)n1+p2(1?p2)n2?????????????????????????
we replace both n1 and n2 by n (assuming that both samples have the same size) and replace each of p1, and p2, by 0.5 (because their values are not known). Then we solve for n, and get
n=(z?)22E2.
Finally, increase the value of n to the next larger integer number.
Use the above formula and Table C to find the size of each sample needed to estimate the difference between the proportions of boys and girls under 10 years old who are afraid of spiders. Assume that we want a 99% confidence level and that the error is smaller than 0.07.
n=______.
Answer:
n= (z)22E2
n=10× 99%÷ 0.07
If Jan can weed the garden in 2 hours and her husband can weed it in 1 hour and 30 minutes, find how long it takes them to weed the garden together.
Answer:
3 hours 30 minutes
Step-by-step explanation:
Jan :2 hours
her husband : 1 hour 30 minutes
2hr + 1 ½ hrs = 3 ½ hrs...that is 3 hours 30 minutes....?
Form a union for the following sets.
M = {1, 2, 4, 8)
N = (2,5,8)
Answer:
Step-by-step explanation:
When you are asked to find the union of sets you find numbers that are present in both sets.
So a number that appears in both the sets of M and N are 2 and 8.
So M U N = { 2,8} where U is the symbol for union.
the line parallel to 2x – 3y = 6 and containing (2,6)
what is the equation of the line ?
First, write out the equation in slope intercept form.
-3y= -2x+6
y= 2/3x -2
The slope of the equation is 2/3, m.
Substitute the slope and coordinate into y=mx+b. Since it’s parallel, the slope remains the same.
6= 2/3(2)+b
6= 4/3+b
14/3=b
y= 2/3x + 14/3
Use the substitution methed to solve the system of equations. Choose the correct ordered pair.
2y+5x=13
2y+3x=5
Solve both equations for 2y :
2y + 5x = 13 ==> 2y = 13 - 5x
2y + 3x = 5 ==> 2y = 5 - 3x
Solve for x :
13 - 5x = 5 - 3x
8 = 2x
x = 4
Solve for y :
2y = 13 - 5×4
2y = -7
y = -7/2
As an ordered pair, the solution is then the point (x, y) = (4, -7/2).
Calculate the Standard Deviation of the following set of data. 14, 15, 16, 16, 9, 3, 16, 20, 29, 12
Answer:
6,78
Step-by-step explanat
ion:data size :10
Sample mean:15
Standard sample deviation :6,782
Answer:
6,78
Step-by-step explanation:
Which key correctly represents the information below? A. 11 | 2 = 12 B. 1 | 2 = 12 C. 11 | 2 = 112 D. 11 | 2 = 13
Answer:
The answer is (B) 1/2=12
y = 95°, find the measure of x
9514 1404 393
Answer:
x = 100°
y = 95°
Step-by-step explanation:
It is probably easier to find y first. Opposite angles of an inscribed quadrilateral are supplementary, so ...
y = 180° -85° = 95°
The measure of an arc is double the measure of the inscribed angle subtending it. The arc subtended by angle y is ...
90° +x = 2y
x = 190° -90° = 100°
_____
Additional comment
The rule cited above regarding opposite angles of an inscribed quadrilateral comes from the theorem regarding inscribed angles. In the given diagram, the diagonal from the bottom vertex to the top one is a chord that divides the circle into two arcs. Their sum is 360°. The inscribed angle theorem tells you ...
2y +2(85°) = 360°
y + 85° = 180° . . . . . . . divide by 2; opposite angles are supplementary
My friend needs help on this sorry!
A group of 6 children and 6 adults are going to the zoo. Child tickets cost $10, and adult tickets cost $14. How much will the zoo tickets cost in all?
9514 1404 393
Answer:
$144
Step-by-step explanation:
Multiplication is used to simplify repeated addition. To find the total cost, add up the costs of each of the tickets.
6 child tickets will cost $10 +10 +10 +10 +10 +10 = 6×$10 = $60
6 adult tickets will cost $14 +14 +14 +14 +14 +14 = 6×$14 = $84
Then the total cost of all of these tickets will be ...
$60 +84 = $144 . . . . cost of zoo tickets in all
Write an absolute value equation to satisfy the given solution set shown on a number line.
Answer:
|x + 6| = 2
Step-by-step explanation:
For a general absolute value equation:
| f(x) | = b
We can rewrite it as:
f(x) = b
f(x) = -b
with b > 0.
Because in the number line we have only two points graphed, this means that our absolute value equation has two solutions.
And we can conclude that one solution comes from the equation:
f(x) = b
And the other solution comes from the equation:
f(x) = -b
And thus, f(x) is a linear equation, that we can simply write as:
x - c
Then our equations can be rewritten as:
x - c = b
x -c = -b
Now let's look at the graph, we can see that the two solutions are:
x = -8
and
x = -4
Let's input each one of these in one of our above equations (the order does not matter).
-4 - c = b
-8 - c = -b
The larger value of x, (x = -4) needs to be in the equation with the positive value of b.
From the first equation we can get:
b = -4 - c
now we can replace the variable "b" in the second equation by "-4 - c" to get:
-8 - c = -(-4 - c)
-8 - c = 4 + c
-8 - 4 = c + c
-12 = 2c
-12/2 =c
-6 = c
Now that we know the value of c, we can input it in the equation:
b = -4 - c
to find the value of b
b = -4 - (-6) = -4 + 6 = 2
b = 2
Then the absolute value equation is:
|x - (-6) | = 2
|x + 6| = 2
?
What is the equation of a parabola whose focus is (-4, -1)
and whose directrix is
y = -5?
x²
y = + x – 1
8
o
y = -
x²
--X+1
8
y?
x =
+ у - 1
8
y2
X = -
8 Y+1
Answer:
1st option,
y = x²/8 + x - 1
Answered by GAUTHMATH
Resistors for electronic circuits are manufactured on a high-speed automated machine. The machine is set up to produce a large run of resistors of 1,000 ohms each. Use Exhibit 10.13. To set up the machine and to create a control chart to be used throughout the run, 15 samples were taken with four resistors in each sample. The complete list of samples and their measured values are as follows: Use three-sigma control limits. SAMPLE NUMBER READINGS (IN OHMS) 1 1027 994 977 994 2 975 1013 999 1017 3 988 1016 974 997 4 998 1024 1006 1010 5 990 1012 990 1000 6 1016 998 1001 1030 7 1000 983 979 971 8 973 982 975 1030 9 992 1028 991 998 10 997 1026 972 1021 11 990 1021 1028 992 12 1021 998 996 970 13 1027 993 996 996 14 1022 981 1014 983 15 977 993 986 983 a. Calculate the mean and range for the above samples.
Answer:
See explanation
Step-by-step explanation:
Given
See attachment for proper presentation of question
Required
Mean and Range
To do this, we simply calculate the mean and the range of each row.
[tex]\bar x = \frac{\sum x}{n}[/tex] ---- mean
Where:
[tex]n = 4[/tex] ---- number of rows
[tex]R = Highest - Lowest[/tex] --- range
So, we have:
Sample 1
[tex]\bar x_1 = \frac{1027+ 994 +977 +994 }{4}[/tex]
[tex]\bar x_1 = 998[/tex]
[tex]R_1 = 1027- 994[/tex]
[tex]R_1 = 33[/tex]
Sample 2
[tex]\bar x_2 = \frac{975 +1013 +999 +1017}{4}[/tex]
[tex]\bar x_2 = 1001[/tex]
[tex]R_2 = 1017 - 975[/tex]
[tex]R_2 = 42[/tex]
Sample 3
[tex]\bar x_3 = \frac{988 +1016 +974 +997}{4}[/tex]
[tex]\bar x_3 = 993.75[/tex]
[tex]R_3 = 1016-974[/tex]
[tex]R_3 = 42[/tex]
Sample 4
[tex]\bar x_4 = \frac{998 +1024 +1006 +1010}{4}[/tex]
[tex]\bar x_4 = 1009.5[/tex]
[tex]R_4 = 1024 -998[/tex]
[tex]R_4 = 26[/tex]
Sample 5
[tex]\bar x_5 = \frac{990 +1012 +990 +1000}{4}[/tex]
[tex]\bar x_5 = 998[/tex]
[tex]R_5 = 1012 -990[/tex]
[tex]R_5 = 22[/tex]
Sample 6
[tex]\bar x_6= \frac{1016 + 998 +1001 +1030}{4}[/tex]
[tex]\bar x_6= 1011.25[/tex]
[tex]R_6= 1030-998[/tex]
[tex]R_6= 32[/tex]
Sample 7
[tex]\bar x_7 = \frac{1000 +983 +979 +971}{4}[/tex]
[tex]\bar x_7 = 983.25[/tex]
[tex]R_7 = 1000-971[/tex]
[tex]R_7 = 29[/tex]
Sample 8
[tex]\bar x_8 = \frac{973 +982 +975 +1030}{4}[/tex]
[tex]\bar x_8 = 990[/tex]
[tex]R_8 = 1030-973[/tex]
[tex]R_8 = 57[/tex]
Sample 9
[tex]\bar x_9 = \frac{992 +1028 +991 +998}{4}[/tex]
[tex]\bar x_9 = 1002.25[/tex]
[tex]R_9 = 1028 -991[/tex]
[tex]R_9 = 37[/tex]
Sample 10
[tex]\bar x_{10} = \frac{997 +1026 +972 +1021}{4}[/tex]
[tex]\bar x_{10} = 1004[/tex]
[tex]R_{10} = 1026 -972[/tex]
[tex]R_{10} = 54[/tex]
Sample 11
[tex]\bar x_{11} = \frac{990 +1021 +1028 +992}{4}[/tex]
[tex]\bar x_{11} = 1007.75[/tex]
[tex]R_{11} = 1028 -990[/tex]
[tex]R_{11} = 38[/tex]
Sample 12
[tex]\bar x_{12} = \frac{1021 +998 +996 +970}{4}[/tex]
[tex]\bar x_{12} = 996.25[/tex]
[tex]R_{12} = 1021 -970[/tex]
[tex]R_{12} = 51[/tex]
Sample 13
[tex]\bar x_{13} = \frac{1027 +993 +996 +996}{4}[/tex]
[tex]\bar x_{13} = 1003[/tex]
[tex]R_{13} =1027 -993[/tex]
[tex]R_{13} =34[/tex]
Sample 14
[tex]\bar x_{14} = \frac{1022 +981 +1014 +983}{4}[/tex]
[tex]\bar x_{14} = 1000[/tex]
[tex]R_{14} = 1022 -981[/tex]
[tex]R_{14} = 41[/tex]
Sample 15
[tex]\bar x_{15} = \frac{977 +993 +986 +983}{4}[/tex]
[tex]\bar x_{15} = 984.75[/tex]
[tex]R_{15} = 993-977[/tex]
[tex]R_{15} = 16[/tex]
PLEASE HELP!!!
Find the equation of the line with an x intercept of 4 and a y intercept of -1.5
Answer:
y = 4x - 1.5
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = 4x - 1.5
What is the area of this figure?
Answer:
22
Step-by-step explanation:
(5x2) + (3x2) + (3x2)
22 square units
Answer from Gauthmath
A concert promoter sells tickets and has a marginal-profit function given below, where P'(x) is in dollars per ticket. This means that the rate of
change of total profit with respect to the number of tickets sold, x, is P'(x). Find the total profit from the sale of the first 380 tickets, disregarding any
fixed costs.
P'(x) = 2x - 1198
The total profit is $
Answer:
The answer is "-310840".
Step-by-step explanation:
[tex]\begin{array}{l} P'(x) = 2x - 1198\\ \\ \frac{{dP}}{{dx}} = 2x - 1198\\ \\ dP = \left( {2x - 1198} \right)dx\\ \\ \int {dP} = \int\limits_0^{380} {\left( {2x - 1198} \right)dx} \\ \\ P = \left( {2\frac{{{x^2}}}{2} - 1198x} \right)_0^{380}\\ \\ P = {380^2} - 1198 \times 380 = 144400-455240=-310840\\ \end{array}[/tex]
PLEAZE HELPPPPPPPSPPSPAP
Answer:
Step-by-step explanation:
345ftyfthftyft.plk,k,
Answer:
Hello,
Anwser is C
Step-by-step explanation:
[tex]y=log_9(12x)\\\\9^y=12x\\\\9^x=12y\ inverting \ x \ and \ y \\\\y=\dfrac{9^x}{12} \\[/tex]
9. Find the value of the trigonometric ratio tan C
Hi there!
[tex]\large\boxed{tanC = 40/9}[/tex]
tan = O / A, or the opposite side over the adjacent side.
From the diagram, we can see that the opposite side = 40 and the adjacent side = 9, so:
tan C = 40 / 9
Answer:
tan C = 40/9
Step-by-step explanation:
According to SOH - CAH - TOA, tan = opposite over adjacent.
In the picture, the opposite of tan C is 40 and the adjacent is 9.
So, tan C = 40/9
P.S. - Answer above is also correct.
Need help!
given rectangle ABCD find m<CAB
Answer:
∠ CAB = 60°
Step-by-step explanation:
∠ CAD and ∠ BCA are alternate angles and congruent , so
∠ CAD = 30°
∠ BAD = 90° ( angle in a rectangle ) , then
∠ CAB = 90° - ∠ CAD = 90° - 30° = 60°
The measure of the angle m∠CAB is 60.
What is a rectangle?A rectangle is a 2-D shape with length and width.
The length and width are different.
If the length and width are not different then it is a square.
The area of a rectangle is given as:
Area = Length x width
We have,
The rectangle has 90 degrees on all the vertices.
So,
In ΔABC,
The sum of the angles = 180
So,
30 + 90 + m∠CAB = 180
m∠CAB = 180 - 120
m∠CAB = 60
Thus,
The measure of the angle m∠CAB is 60.
Learn more about rectangles here:
https://brainly.com/question/15019502
#SPJ2
The manager of a juice bottling factory is considering installing a new juice bottling machine which she hopes will reduce the amount of variation in the volumes of juice dispensed into 8-fluid-ounce bottles. Random samples of 10 bottles filled by the old machine and 9 bottles filled by the new machine yielded the following volumes of juice (in fluid ounces).
Old machine: 8.2, 8.0, 7.9, 7.9, 8.5, 7.9, 8.1,8.1, 8.2, 7.9
New machine: 8.0, 8.1, 8.0, 8.1, 7.9, 8.0, 7.9, 8.0, 8.1
Required:
Use a 0.05 significance level to test the claim that the volumes of juice filled by the old machine vary more than the volumes of juice filled by the new machine
Answer:
Reject H0 and conclude that volume filled by old machine varies more than volume filled by new machine
Step-by-step explanation:
Given the data:
Old machine: 8.2, 8.0, 7.9, 7.9, 8.5, 7.9, 8.1,8.1, 8.2, 7.9
New machine: 8.0, 8.1, 8.0, 8.1, 7.9, 8.0, 7.9, 8.0, 8.1
To test if volume filled by old machine varies more than volume filled by new machine :
Hypothesis :
H0 : s1² = s2²
H1 : s1² > s2²
Using calculator :
Sample size, n and variance of each machine is :
Old machine :
s1² = 0.37889
n = 10
New machine :
s2² = 0.006111
n = 9
Using the Ftest :
Ftest statistic = larger sample variance / smaller sample variance
Ftest statistic = 0.37889 / 0.006111
Ftest statistic = 62.001
Decision region :
Reject H0 ; If Test statistic > Critical value
The FCritical value at 0.05
DFnumerator = 10 - 1 = 9
DFdenominator = 9 - 1 = 8
Fcritical(0.05, 9, 8) = 3.388
Since 62 > 3.388 ; Reject H0 and conclude that volume filled by old machine varies more than volume filled by new machine
What fraction is equivalent to 0.46464646...
A)
46∕999
B)
46∕99
C)
23∕50
D)
46∕100
Answer:
Hello,
answer is B
Step-by-step explanation:
[tex]0.\overline{46}=\dfrac{46}{99}[/tex]
The answer is a fraction with numerator is the period (46) and the denominator is a number made with 9 as longer that there are digits in the periode (here 2 digits ==> 99)
Explain how the given graph is deceptive.
Complete the statements based on the bar graph.
By not starting the horizontal axis at 0, the
bar appears to be about one-fourth the height of the Pecan bar. The
bar appears to be about one-half the height of the Pecan bar. The
bar appears to be less than one-half the height of the Pecan bar. This misleads the viewer to
the number of each type of nut used
Ans:
Pine Nut
Walnut
Almond
Understimate
Answer:
In the picture below.
Step-by-step explanation:
From the commenter and answer above, confirmed on edge 2022.
If the graph of f(x)=x^2, how will the graph be affected if it is changed to f(x)=1/3x^2?
Answer:
The graph would be compressed vertically by a factor of 1/3.
Step-by-step explanation:
Multiplying a function by some constant is a way to stretch or compress that function. If the magnitude of the constant is greater than 1, you are vertically stretching, if the magnitude of the constant is less than one but greater than 0 you are vertically compressing your function.
Let A be an nxn matrix. Determine whether the statement below is true or false. Justify the answer. The determinant of a triangular matrix is the sum of the entries on the main diagonal Choose the correct answer below.
A. The statement is true. Cofactor expansion along the row (or column) with the most zeros of a triangular matrix produces a determinant equal to the son of the tries to the radar
B. The statement is true. The determinant of A is the following finite series. n det A= (-1)* laj, det A1 J = 1 In a triangular matrix, this series simplifies to the sum of the entries along the main diagonal.
C. The statement is false. The determinant of a matrix is the arithmetic mean of the entries along the main diagonal OD The statement is false. The determinant of a triangular matrix is the product of the entries along the main diagonal
8 ^ 3 −9⋅2÷3 can someone please help me quickly
Answer:
506
Step-by-step explanation:
8³-9×2÷3
= 512 - 9 × 2 ÷3
= 512 - 9 × ⅔
= 512 - 3 × 2
= 512 - 6
= 506
PEDMAS rule
P: Parentheses
E: Exponent
D: Division
M: Multiplication
A: Addition
S: Substraction
To win at LOTTO in one state, one must correctly select numbers from a collection of numbers (1 through ). The order in which the selection is made does not matter. How many different selections are possible?
Answer: If order does not matter then we can use following formula to find different combinations of 6 numbers out of 46 numbers
Step-by-step explanation: Use following Combination formula
nCr = n! / r!(n-r)!
n=46
r=6
=46!/6!(46-6)!
=46!/[6!(40)!]
=(46*45*44*43*42*41*40!)/(6*5*4*3*2*1)(40!)
Cancel out 40!
=46*45*44*43*42*41/(6*5*4*3*2*1)
=6744109680/720
=9366819
3/5x - 1/2x= 1, please help me to solve this
Answer:
x = - 10
Step-by-step explanation:
(6x -5x) / 10 = - 1
x = - 10
Jean can swim 100 meters in 1.86 minutes. Sean can swim the same distance in 2.12 minutes.
please where is the question
