Answer:
The p-value of the test is 0.0764 > 0.05, which means that there is not enough evidence to reject the null hypothesis that the proportion is of at most 0.009, and thus we can conclude that the supplier has met the guarantee.
Step-by-step explanation:
Your overseas supplier of engines guarantees that no more than 0.9% of the new engines shipped to you will fail a simple electrical test.
At the null hypothesis, we test if the proportion is of at most 0.9% = 0.009, that is:
[tex]H_0: p \leq 0.009[/tex]
At the alternative hypothesis, we test if the proportion is of more than 0.009, that is:
[tex]H_1: p > 0.009[/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.
0.009 is tested at the null hypothesis:
This means that [tex]\mu = 0.009, \sigma = \sqrt{0.009*0.991}[/tex]
50 of these engines, and you find that 1 is defective.
This means that [tex]n = 50, X = \frac{1}{50} = 0.02[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.02 - 0.009}{\frac{\sqrt{0.009*0.991}}{\sqrt{50}}}[/tex]
[tex]z = 1.43[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample proportion above 0.02, which is 1 subtracted by the p-value of z = 1.43.
Looking at the z-table, z = 1.43 has a p-value of 0.9236.
1 - 0.9236 = 0.0764.
The p-value of the test is 0.0764 > 0.05, which means that there is not enough evidence to reject the null hypothesis that the proportion is of at most 0.009, and thus we can conclude that the supplier has met the guarantee.
Find the missing side lengths
Answer:
x = 11√3
y = 11
Step-by-step explanation:
Let 60 be the reference angle
sin 60 = p/h
√3/2 = x/22
or, 22√3 = 2x
or, x = (22√3)/2
so, x = 11√3
now
[tex]h^2 = p^2 + b^2\\or, 22^2 = (11\sqrt{3} )^2+y^2\\or, 484 = 363 + y^2\\or, 484-363 = y^2\\or, 121 = y^2\\or, \sqrt{121} = y\\so, y = 11[/tex]
The battery standby duration (in hours) of a new model of cell phone is known to be normally distributed. Ten pieces of such new model of cell phone supplied from the manufacturer are randomly chosen and the actual standby durations are recorded as below:
48.2 47.8 45.6 47.2 49.3
51.2 44.2 45.4 49.2 43.6
(a) Calculate the unbiased estimates of population mean and standard deviation of battery standby duration (in hours) of the new cell phone.
Answer:
[tex]\mu = 47.17[/tex]
[tex]\sigma = 2.31[/tex]
Step-by-step explanation:
Solving (a): The population mean
This is calculated as:
[tex]\mu = \frac{\sum x}{n}[/tex]
So, we have:
[tex]\mu = \frac{48.2+ 47.8 +45.6 +47.2 +49.3+51.2 +44.2 +45.4 +49.2 +43.6}{10}[/tex]
[tex]\mu = \frac{471.7}{10}[/tex]
[tex]\mu = 47.17[/tex]
Solving (b): The population standard deviation
This is calculated as:
[tex]\sigma = \sqrt{\frac{\sum (x - \mu)^2}{n}}[/tex]
So, we have:
[tex]\sigma = \sqrt{\frac{(48.2-47.17)^2 + (47.8-47.17)^2 +.........+(43.6-47.17)^2}{10}}[/tex]
[tex]\sigma = \sqrt{\frac{53.521}{10}}[/tex]
[tex]\sigma = \sqrt{5.3521[/tex]
[tex]\sigma = 2.31[/tex]
Can someone help me with this math homework please!
(–6s2 + 12s – 8) – (3s2 + 8s – 6) =
Answer:
[tex]{ \tt{( - 6 {s}^{2} + 12s - 8) - (3 {s}^{2} + 8s - 6) }} \\ = { \tt{ - 9 {s}^{2} + 4s - 2 }}[/tex]
Answer:
4s - 2 - 9s²
Step-by-step explanation:
(–6s2 + 12s – 8) – (3s2 + 8s – 6)
= -6s²+ 12s - 8 - 3s²- 8s + 6
= 12s - 8s - 8 + 6 - 6s² -3s²
= 4s - 2 - 9s²
HELPPPP me I need help don’t know the answer
Answer:
All, if you're not defining the angles.
Step-by-step explanation:
The angle ACB/BCA is 55 degrees, ACE/ECA is 125 degrees, DCE/ECD is the same as ACB/BCA, and BCD/DCB is the same as ACE/ECA
Which equation represents a line which is perpendicular to the line y = -4x - 5
A) x + 4y = -32
B) 4x - y = -4
C) 4x + y = 3
D) 4y - x = 4
What is the length of
each leg of the triangle below?
Answer:
11 sqrt(2)
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp / hypotenuse
sin 45 = x /22
22 sin 45 = x
22 ( sqrt(2)/2) =x
11 sqrt(2)
The legs are equal since the base angles are equal
A basketball team received a care package and split it evenly among
5 players. If each player received 9 candy bars, how many candy bars
were in the care package?
Help please
Answer:
45
Step-by-step explanation:
9x5
The formula for the force between two objects is
F=GMm/r^2
,
where M and m are the masses of the two objects, G is a constant, and r is the distance between them. Solve the formula for G.
Here are the multiple-choice answers...
Answer:
G = Fr² / Mm
Step-by-step explanation:
Given:
F = GMm / r²
Where,
F = Force of the two objects
M = mass of object 1
m = mass of object 2
G = constant
r = distance between the objects
Solve the formula for G.
F = GMm / r²
Cross product
F * r² = GMm
Fr² = GMm
Divide both sides by Mm
G = Fr² / Mm
Do you remember how to solve a multistep linear equation with variables on both sides? Review with a Quick Check.
Solve:
5(a−1)−15=3(a+2)+4
Answer:
Step-by-step explanation:
5(a-1) -15 = 3(a+2) +4, distribute multiplication over subtraction and addition
5a -5 -15 = 3a +6 + 4, isolate the variable on one side
5a -3a = 6 +4 +5 +15, combine like terms
2a = 30, divide both sides by 2
a= 15
Suzy has some stickers and a sticker album. if she pastes 7 stickers on each page, she will need 21 more stickers. If she pastes 11 stickers on each page, she will need 81 more stickers. how many pages are there in Suzy's sticker album
Answer:
15 pages
Step-by-step explanation:
let x be the number of pages
7x-21 = 11x-81
4x = 60
x = 15
2.The school chess club is selling T-shirts for a profit of $4 each and baseball caps for a profit of $5 eac The club wants to sell 50 items and make a profit of $230. Calculate how many of each item the chess club needs
Step-by-step explanation
They sold $480 of tshirts, the ratio is 480;20, simplified to 24:1.
One shirt is $20, but $4 is the amount taken from 20 for the equipment.
Multiply $24 by the $4 taken for the equipment. (Equals $96)
They make 4/20 (1/5) of the the sales as a profit for equipment.
Multiply 1/5 by 480 and you will get $96 as the club's profits.
I hope this helped ya
The chess club needs 20 T-shirts and 30 baseball caps.
What is Profit?Profit is a term that often refers to the financial gain that a company receives when revenue exceeds costs and expenses. A child at a lemonade stand, for example, spends one quarter to make one cup of lemonade. She then charges $2 for the drink. Her profit on a cup of lemonade is $1.75.
Given :
Total no. of items to be sold = 50
Total profit to be made = $230
Profit on each T-shirt = $4
Profit on each Baseball cap = $5
Let no. of t-shirts be x
Let no. of t-shirts be y
Forming equations according to given problem :
Eq 1 : x + y = 50
Eq 2 : 4x + 5y = 230
Multiplying Eq 1 with 4 we get : 4x + 4y = 200
Subtracting Eq 1 from Eq 2
Solving Eq1 and Eq2 we get x = 20 and y = 30.
Therefore, The chess club needs 20 T- shirts and 30 baseball caps.
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I NEED JUSTIFICATION AND WORK ON PART A AND B
Part A: The sun produces 3.9 ⋅ 1033 ergs of radiant energy per second. How many ergs of radiant energy does the sun produce in 1.55 ⋅ 107 seconds? (5 points)
Part B: Which is the more reasonable measurement of the diameter of a human hair:
1.8 ⋅ 10−2 mm or 1.8 ⋅ 102 mm? Justify your answer. (5 points)
Answer:
6.045 * 10 ^40 ergs
1.8 * 10^-2 mm
Step-by-step explanation:
3.9 ⋅ 10^33 erg per second * 1.55 * 10 ^7 seconds
3.9 * 1.55 * 10^(33+7)
6.045 * 10 ^40 ergs
Human hair is around .1 mm thick
.1 = 1 * 10 ^ -1
This is closer to 1.8 * 10^-2
1.8 *10^2 = 180 mm which is too thick This is approximately 18 cm
Answer:
6.045 * 10 ^40 ergs
1.8 * 10^-2 mm
Step-by-step explanation:
3.9 ⋅ 10^33 erg per second * 1.55 * 10 ^7 seconds
3.9 * 1.55 * 10^(33+7)
6.045 * 10 ^40 ergs
Human hair is around .1 mm thick
.1 = 1 * 10 ^ -1
This is closer to 1.8 * 10^-2
1.8 *10^2 = 180 mm which is too thick This is approximately 18 cm
Step-by-step explanation:
Round 74.164 to the nearest whole.
Answer: [tex]\bf 7\underline4 . 164 \approx 74[/tex]
Step-by-step explanation:
Answer:
74
Step-by-step explanation:
Keep in mind you're rounding rules!
Can someone help me with this task please? !!
Answer:
we need to get your brain thinking in this way. that you begin to understand how to do these things.
airways to say that your brain is not working that way, is not a valid excuse. we need to change that. your brain needs to get used to this way of thinking.
so, please, please, PLEASE go through the explanations below and tell me, where exactly in these explanations you stopped understanding what I was saying. so that I can better explain to you what is happening.
1. (0, -2)
2. 4
3. a geometric sequence. the common ratio is -2.0
4. the third option
5. the fourth option
Step-by-step explanation:
1. as x increases, y decreases. until, suddenly after x=0, this tendency reverses, and with increasing x also y increases. so, this is a turning point.
2. look at the line. it only starts with x>0 (it looks like x is around 1).
"input" is all the values of x the function has a defined result for (y = result values).
so, as there is no line for negative x, we can eliminate the first 2 answers.
x=0 is no valid answer either (as mentioned above, the line only starts well after x=0).
in the answer options the only x value having an y value above or below this x value is x=4.
3. look at the difference between 2 numbers next to each other in the sequence.
2.4 to -4.8
-4.8 to 9.6
and so on.
what do we need to do to get from the left to the right ?
we need to multiply by -2.
so, the relationship between "sequence item n" (an) to "sequence item n-1" (an-1) is a ratio, a multiplication factor :
an/an-1 = -2
4. it is completely simple. a function can be many things. on an x/y coordinate grid it can have gaps, it can have sharp direction changes,...
but there us one thing a function can never have : multiple different y values for one x value.
in the first graph x=2 has two different y values (-1 and -3). so, it is not clear what the result for x=2 would be. and that means, it is not a function.
in the second graph x=4 has two different y values.
in the third graph all is OK.
in the fourth graph x=-2 has two different y values.
so, only the third option is a function.
5. this function calculates the height of the thrown rock after t seconds of flight.
therefore, only the fourth answer makes sense.
Help Please!!!
Find volume of the sphere
Answer:
Step-by-step explanation:
Hey GurpTheDestoyer! Find the volume of the sphere. Round to the nearest whole number. Radius= 8 what is the volume? The Volume = 2,144.660585 cm3. Hope this helped! <3
Please help me answer this question thank you :)
Answer:
A.
[tex]f(x) = \frac{ \sqrt[3]{x} }{5} \: { \bf{and}} \: g(x) = 5 {x}^{3} [/tex]
Step-by-step explanation:
Consider f(x) as the original function:
[tex]{ \tt{f(x) = \frac{ \sqrt[3]{x} }{5} }}[/tex]
Let the inverse be m:
[tex]{ \tt{g(x) = f {}^{ - 1} (x) = m}} \\ { \tt{m = \frac{ \sqrt[3]{x} }{5} }} \\ { \tt{5m = \sqrt[3]{x} }} \\ { \tt{x = 5m {}^{3} }} \\ therefore : \\ { \tt{g(x) = 5 {x}^{3} }}[/tex]
the graph of a linear function is given below
Answer:
The "zero" is where it crosses the x axis which is -2 in this graph
Step-by-step explanation:
If today is Tuesday, May 6, this year July 4 will fall on a _____
(A) Sunday
(B) Monday
(C) Thursday
(D) Friday
Answer:
July 4th will fall on Sunday
The date, July 4 will be Friday, the correct option is D.
What are Calendars?Calendars represent an year of 12 months, each month has 30 or 31 days, exceptionally February has 28 days.
If today is Tuesday, May 6,
Every 7th day is going to be a Tuesday .
From May 6 to July 4, the number of days is 59
Hence we divide 59 by 7. Quotient = 8 Remainder = 3
7 x 8 = 56
56 th day is Tuesday
57 th day is Wednesday
58th day vis Thursday
59th day is Friday
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limx²-9x+20
x->4 x-4?
Answer:
-1
Step-by-step explanation:
lim x tends to 4 (x^2-9x+20)/(x-4). (x^2-9x+20)(x-4)=x-5.
So the limit is 4-5=-1
Can someone explain and give an example of spurious correlation?
Answer:
A spurious correlation wrongly implies a cause and effect between two variables. For example, the number of astronauts dying in spacecraft is directly correlated to seatbelt use in cars: Use your seatbelt and save an astronaut life!
Interesting correlations are easy to find, but many will turn out to be spurious. Three examples are the skirt length theory, the Super Bowl indicator, and a suggested correlation between race and college completion rates.
Step-by-step explanation:
A rectangle has an area of 72 swaure units. The width of the rectangle is 9 units. The length of the rectangle is 2x + 4. What is the rectangle's length?
Answer:
8 units
Step-by-step explanation:
Area of a rectangle = Width multiplied by Length
Substitute in all the known numbers into this formula to get
72 = (9) × [tex](2x+4)[/tex]
Solve the equation for x, to find out the length
[tex]9(2x+4)=72[/tex]
[tex]2x+4=72/9[/tex]
[tex]2x+4=8[/tex]
[tex]2x=8-4[/tex]
[tex]2x=4[/tex]
[tex]x=4/2[/tex]
[tex]x=2[/tex]
Length of the rectangle = [tex](2x+4)[/tex]
[tex]2(2)+4[/tex]
[tex]4+4=8[/tex]
Can someone please just help me fill in those three boxes I’ve been struggling
I need help on this question 5=7+x/5
Answer:
-10 = x
Step-by-step explanation:
5=7+x/5
Subtract 7 from each side
5-7=7-7+x/5
-2 = x/5
Multiply each side by 5
-2 *5 = x/5 *5
-10 = x
Use the graph, the equations, or a table of values to support a logical argument that the linear functions
are inverses.
(please help)
Step-by-step explanation:
one line has the slope of -3 (-3/1 meaning that when x increases by 1 unit, y decreases by 3 units).
and this line has the offset of y=-5 for x=0
so, the line equation is
y = -3x - 5
inverse means that we exchange x and y and then solve for y again :
x = -3y - 5
3y = -x - 5
y = -x/3 - 5/3
when we look at the second line, we see its slope is -1/3 (when x increases by 3 units, y decreases by 1 unit).
and while we cannot read the offset on the y-axis precisely, we can use a clearly readable point to prove or disprove the equation above.
for example (-2, -1)
-1 = -(-2/3) - 5/3 = 2/3 - 5/3 = -3/3 = -1
correct.
so, the equation we got for the inverse function fits exactly with the second line in the graph.
therefore, yes, they are both inverse functions to each other.
The two given graphs are inverse functions of each other.
What is a graph?A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
One line has the slope of -3 (-3/1 meaning that when x increases by 1 unit, y decreases by 3 units).and this line has the offset of y=-5 for x=0
The line equation is
y = -3x - 5
Inverse means that we exchange x and y and then solve for y again :
x = -3y - 5
3y = -x - 5
y = -x/3 - 5/3
When we look at the second line, we see its slope is -1/3 (when x increases by 3 units, y decreases by 1 unit).and while we cannot read the offset on the y-axis precisely, we can use a clearly readable point to prove or disprove the equation above.
for example (-2, -1)
-1 = -(-2/3) - 5/3 = 2/3 - 5/3 = -3/3 = -1
The equation we got for the inverse function fits exactly with the second line in the graph.
Therefore the two given graphs are inverse functions of each other.
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A ladder is placed 8 feet away from a wall. The distance from the ground straight to the top of the wall is 16 feet. What is the height of the ladder?
Answer:
17.89 ft
Step-by-step explanation:
This is a right triangle so we can use the Pythagorean theorem
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
8^2 +16^2 = c^2
64+ 256 = c^2
320 =c^2
Taking the square root of each side
sqrt(320) = sqrt(c^2)
sqrt(64*5) = c
sqrt(64) sqrt(5) =c
8 sqrt(5) = c
17.88854382=c
17.89 ft
[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]
Given:-A ladder is placed 8 feet away from a wall. The distance from the ground straight to the top of the wall is 16 feet. Find:-What is the height of the ladder?solution:-A ladder is placed 8 feet away from a wall. The distance from the ground straight to the top of the wall is 16 feet.
so it is a right angle triangle
we know that,in a right angle triangle, According to the Pythagorean theorom,
[tex]\boxed{\sf{l^2+b^2=h^2 }}[/tex]
where
l= legs b=baseh=hypotenuse According to the question, [tex]\sf{8^2+16^2=h^2 }[/tex] [tex]\sf{64+256=h^2 }[/tex] [tex]\sf{ h^2=320 }[/tex] [tex]\sf{h=\sqrt{320} }[/tex] [tex]\sf{h=8\sqrt{5} }[/tex] Therefore:-The height of the ladder is [tex]\sf{8\sqrt{5} }[/tex]
2. What are the last 2 digits of 1 + 2 + 3 + + 2005 2006
Let S be the sum. So you have
S = 1 + 2 + 3 + … + 2004 + 2005 + 2006
as well as
S = 2006 + 2005 + 2004 + … + 3 + 2 + 1
Then
2S = (1 + 2006) + (2 + 2005) + … + (2005 + 2) + (2006 + 1)
2S = 2007 + 2007 + … + 2007 + 2007
2S = 2006 × 2007
S = (2006 × 2007)/2
S = 2,013,021
which makes the last two digits 21.
PLEASE HELP ME! I REALLY NEED HELP
Answer:
a)
(i) 5.8 hours
(ii) 6.5 hours
(iii) 6 hours
(iv) 6 hours
b) 180 hours
Final
Lines L and M are parallel.
34
2/5
16
38° 7
-L
>M
Find : m_6
Cotor the
Answer:
38
Step-by-step explanation:
Angle 6 is alternate to the angle that is given as 38 degrees because line L is parallel to line M so their measure is equal.
Is the last question correct? If not then what is the answer? (Last question is the first pic..)
9514 1404 393
Answer:
K+1 ⇒ (K+1)² = K² +2K +1
Step-by-step explanation:
Your first answers are correct. The sum of K odd numbers is K². Replacing K with K+1 in this statement gives you ...
The sum of K+1 odd numbers is (K+1)² = K² +2K +1.
