Answer:
0.9884 = 98.84% probability that the proportion of flops in a sample of 469 released films would be greater than 6%.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
A film distribution manager calculates that 9% of the films released are flops.
This means that [tex]p = 0.09[/tex]
Sample of 469
This means that [tex]n = 469[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.09[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.09*0.91}{469}} = 0.0132[/tex]
What is the probability that the proportion of flops in a sample of 469 released films would be greater than 6%?
1 subtracted by the p-value of Z when X = 0.06. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.06 - 0.09}{0.0132}[/tex]
[tex]Z = -2.27[/tex]
[tex]Z = -2.27[/tex] has a p-value of 0.0116
1 - 0.0116 = 0.9884
0.9884 = 98.84% probability that the proportion of flops in a sample of 469 released films would be greater than 6%.
convert the fraction 3/8 to a decimal WITHOUT the use of a calculator. Show your method clearly. SHOW ALL STEPS!
here you go it's too easy
Step-by-step explanation:
Explanation is in the attachment .
Hope it is helpful to you ❣️☪️❇️
Find the distance between the two points.
(3,-9) and (-93,-37)
Answer:
100
Step-by-step explanation:
√(x2 - x1)² + (y2 - y1)²
√(-93 - 3)² + [-37 - (-9)]
√(-96)² + (-28)²
√9216 + 784
√10000
= 100
A cardboard box without a lid is to have a volume of 4,000 cm3. Find the dimensions that minimize the amount of cardboard used. (Let x, y, and z be the dimensions of the cardboard box.)
When P(x) is divided by (x - 1) and (x + 3), the remainders are 4 and 104 respectively. When P(x) is divided by x² - x + 1 the quotient is x² + x + 3 and the remainder is of the form ax + b. Find the remainder.
Answer:
The remainder is 3x - 4
Step-by-step explanation:
[Remember] [tex]\frac{Dividend}{Divisor} = Quotient + \frac{Remainder}{Divisor}[/tex]
So, [tex]Dividend = (Quotient)(Divisor) + Remainder[/tex]
In this case our dividend is always P(x).
Part 1
When the divisor is [tex](x - 1)[/tex], the remainder is [tex]4[/tex], so we can say [tex]P(x) = (Quotient)(x - 1) + 4[/tex]
In order to get rid of "Quotient" from our equation, we must multiply it by 0, so [tex](x - 1) = 0[/tex]
When solving for [tex]x[/tex], we get
[tex]x - 1 = 0\\x - 1 + 1 = 0 + 1\\x = 1[/tex]
When [tex]x = 1[/tex],
[tex]P(x) = (Quotient)(x - 1) + 4\\P(1) = (Quotient)(1 - 1) + 4\\P(1) = (Quotient)(0) + 4\\P(1) = 0 + 4\\P(1) = 4[/tex]
--------------------------------------------------------------------------------------------------------------
Part 2
When the divisor is [tex](x + 3)[/tex], the remainder is [tex]104[/tex], so we can say [tex]P(x) = (Quotient)(x + 3) + 104[/tex]
In order to get rid of "Quotient" from our equation, we must multiply it by 0, so [tex](x + 3) = 0[/tex]
When solving for [tex]x[/tex], we get
[tex]x + 3 = 0\\x + 3 - 3 = 0 - 3\\x = -3[/tex]
When [tex]x = -3[/tex],
[tex]P(x) = (Quotient)(x + 3) + 104\\P(-3) = (Quotient)(-3 + 3) + 104\\P(-3) = (Quotient)(0) + 104\\P(-3) = 0 + 104\\P(-3) = 104[/tex]
--------------------------------------------------------------------------------------------------------------
Part 3
When the divisor is [tex](x^2 - x + 1)[/tex], the quotient is [tex](x^2 + x + 3)[/tex], and the remainder is [tex](ax + b)[/tex], so we can say [tex]P(x) = (x^2 + x + 3)(x^2 - x + 1) + (ax + b)[/tex]
From Part 1, we know that [tex]P(1) = 4[/tex] , so we can substitute [tex]x = 1[/tex] and [tex]P(x) = 4[/tex] into [tex]P(x) = (x^2 + x + 3)(x^2 - x + 1) + (ax + b)[/tex]
When we do, we get:
[tex]4 = (1^2 + 1 + 3)(1^2 - 1 + 1) + a(1) + b\\4 = (1 + 1 + 3)(1 - 1 + 1) + a + b\\4 = (5)(1) + a + b\\4 = 5 + a + b\\4 - 5 = 5 - 5 + a + b\\-1 = a + b\\a + b = -1[/tex]
We will call [tex]a + b = -1[/tex] equation 1
From Part 2, we know that [tex]P(-3) = 104[/tex], so we can substitute [tex]x = -3[/tex] and [tex]P(x) = 104[/tex] into [tex]P(x) = (x^2 + x + 3)(x^2 - x + 1) + (ax + b)[/tex]
When we do, we get:
[tex]104 = ((-3)^2 + (-3) + 3)((-3)^2 - (-3) + 1) + a(-3) + b\\104 = (9 - 3 + 3)(9 + 3 + 1) - 3a + b\\104 = (9)(13) - 3a + b\\104 = 117 - 3a + b\\104 - 117 = 117 - 117 - 3a + b\\-13 = -3a + b\\(-13)(-1) = (-3a + b)(-1)\\13 = 3a - b\\3a - b = 13[/tex]
We will call [tex]3a - b = 13[/tex] equation 2
Now we can create a system of equations using equation 1 and equation 2
[tex]\left \{ {{a + b = -1} \atop {3a - b = 13}} \right.[/tex]
By adding both equations' right-hand sides together and both equations' left-hand sides together, we can eliminate [tex]b[/tex] and solve for [tex]a[/tex]
So equation 1 + equation 2:
[tex](a + b) + (3a - b) = -1 + 13\\a + b + 3a - b = -1 + 13\\a + 3a + b - b = -1 + 13\\4a = 12\\a = 3[/tex]
Now we can substitute [tex]a = 3[/tex] into either one of the equations, however, since equation 1 has less operations to deal with, we will use equation 1.
So substituting [tex]a = 3[/tex] into equation 1:
[tex]3 + b = -1\\3 - 3 + b = -1 - 3\\b = -4[/tex]
Now that we have both of the values for [tex]a[/tex] and [tex]b[/tex], we can substitute them into the expression for the remainder.
So substituting [tex]a = 3[/tex] and [tex]b = -4[/tex] into [tex]ax + b[/tex]:
[tex]ax + b\\= (3)x + (-4)\\= 3x - 4[/tex]
Therefore, the remainder is [tex]3x - 4[/tex].
M H To determine the number of deer in a game preserve, a conservationist catches 412 deer, tags them and lets them loose. Later, 316 deer are caught, 158 of them are tagged. How many deer are in the preserve?
Answer:
There are 824 deer in the preserve.
Step-by-step explanation:
Since to determine the number of deer in a game preserve, a conservationist catches 412 deer, tags them and lets them loose, and later, 316 deer are caught, 158 of them are tagged, to determine how many deer are in the preserve you must perform the following calculation:
316 = 100
158 = X
158 x 100/316 = X
50 = X
50 = 412
100 = X
824 = X
Therefore, there are 824 deer in the preserve.
Find the volume (in cubic feet) of a cylindrical column with a diameter of 6 feet and a height of 28 feet. (Round your answer to one decimal place.)
Answer:
[tex]791.7\:\mathrm{ft^3}[/tex]
Step-by-step explanation:
The volume of a cylinder with radius [tex]r[/tex] and height [tex]h[/tex] is given by [tex]A_{cyl}=r^2h\pi[/tex].
By definition, all radii of a circle are exactly half of all diameters of the circle. Therefore, if the diameter of the circular base of the cylinder is 6 feet, the radius of it must be [tex]6\div 2=3\text{ feet}[/tex].
Now we can substitute [tex]r=3[/tex] and [tex]h=28[/tex] into our formula [tex]A_{cyl}=r^2h\pi[/tex]:
[tex]A=3^2\cdot 28\cdot \pi,\\A=9\cdot28\cdot \pi,\\A=791.681348705\approx \boxed{791.7\:\mathrm{ft^3}}[/tex]
is y=3x^2-x-1 a function
Answer: Yes it is a function.
This is because any x input leads to exactly one y output.
The graph passes the vertical line test. It is impossible to draw a single vertical line through more than one point on the parabolic curve.
Which choice is equivalent to √3 *√8*√5
A. 2√30
B. 4√30
C. 10√12
D. 24√5
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { A. \:2 \sqrt{30} }}}}}}[/tex]
[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:EXPLANATION:}}}[/tex]
[tex] = \sqrt{3} \times \sqrt{8} \times \sqrt{5} [/tex]
[tex] = \sqrt{3 \times 2 \times 2 \times 2 \times 5} [/tex]
[tex] = \sqrt{ ({2})^{2} \times 2 \times 3 \times 5} [/tex]
[tex] = 2 \sqrt{2 \times 3\times 5} [/tex]
[tex] = 2 \sqrt{30} [/tex]
Note:[tex] \sqrt{ ({a})^{2} } = a[/tex]
[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]
Answer:
A. 2√30
Step-by-step explanation:
[tex] \small \sf \: \sqrt{3} \times \sqrt{8} \times \sqrt{5} \\ [/tex]
split √8
[tex] \small \sf \leadsto \sqrt{3 × 2 × 2 × 2 × 5} [/tex]
[tex] \small \sf \leadsto \: 2 \sqrt{2 \times 3 \times 5} [/tex]
[tex] \small \sf \leadsto \: 2 \sqrt{30} [/tex]
2 (m+n) +m=9
3m-3n = 24
Answer:
m=5
n=-3
Step-by-step explanation:
3m+2m=9
3m-3n=24
3(5)+2(-3)=9
15-6=9 correct
Evaluate 12 sin 85° correct to two decimal places.
Answer:
12 x sin(85)
12x 0.99619
155.40
Solution:
12 x sin (85) = 11.95 (Since sin85 is 0.996194)
So, the answer is 11.95.
Which number is located to the right of on the horizontal number line?
A. -1 1/3
B. -2 1/3
C. -2 2/3
D. -3 1/3
Please help me
Answer:
A
Step-by-step explanation:
since it's negative so it will get smaller
A student sees a newspaper ad for an apartment that has 1330. How many square meters of area are there
Answer:
[tex]Area = 123.55 m^2[/tex]
Step-by-step explanation:
Given
[tex]Area = 1330ft^2[/tex]
Required
Convert to [tex]m^2[/tex]
To convert from square feet to square meter, we simply divide by 3.281^2
So, we have:
[tex]Area = \frac{1330}{3.281^2}m^2[/tex]
[tex]Area = \frac{1330}{10.765}m^2[/tex]
[tex]Area = 123.55 m^2[/tex]
Simplify (6 + 4i) + (3 - 3i)
Answer:
9 + i
Step-by-step explanation:
You just simplify by combining the real and imaginary parts of each expression.
Hope this helps you!!
The systolic blood pressure of adults in the USA is nearly normally distributed with a mean of 120 and standard deviation of 18 . Someone qualifies as having Stage 2 high blood pressure if their systolic blood pressure is 160 or higher. a. Around what percentage of adults in the USA have stage 2 high blood pressure
Answer:
The percentage of adults in the USA have stage 2 high blood pressure=98.679%
Step-by-step explanation:
We are given that
Mean, [tex]\mu=120[/tex]
Standard deviation, [tex]\sigma=18[/tex]
We have to find percentage of adults in the USA have stage 2 high blood pressure.
[tex]P(x\geq 160)=P(Z\geq \frac{160-120}{18})[/tex]
[tex]P(x\geq 160)=P(Z\geq \frac{40}{18})[/tex]
[tex]P(x\geq 160)=P(Z\geq 2.22)[/tex]
[tex]P(x\geq 160)=1-P(Z\leq 2.22[/tex]
[tex]P(x\geq 160)=0.98679[/tex]
[tex]P(x\geq 160)=98.679[/tex]%
Hence, the percentage of adults in the USA have stage 2 high blood pressure=98.679%
Please answer & number. Thank you! <33
Answer:
2）=2
4）=3
5）=5
8）=-1
Step-by-step explanation:
just divide the number by the number with variable
The square root of the variance is called the: standard deviation beta covariance coefficient of variation
Answer:
standard deviation
Step-by-step explanation:
Movie genres. The pie chart summarizes the genres of 120 first-run movies released in 2005. a) Is this an appropriate display for the genres
Answer:
Yes, it is appropriate
Step-by-step explanation:
Given
See attachment for pie chart
Required
Is the pie chart appropriate
The attached pie chart displays the distribution of each of the 4 genre. The partition occupied represents the measure of each genre.
Please I need help!!!!!!!!
Answer:
10 is the correct answer
Answer:
Go with the third option 10!
i hope this helped!
Which expression is equivalent to…
Answer:
D
Step-by-step explanation:
Which one is the correct answer? help pls!!
Answer:
(2k, k)
Step-by-step explanation:
x + y = 3k
x - y = k
Add the equations.
2x = 4k
x = 2k
2k + y = 3k
y = k
Answer: (2k, k)
a/b=2/5 and b/c=3/8 find a/c
Answer:
[tex]\frac{a}{c}[/tex] = [tex]\frac{3}{20}[/tex]
Step-by-step explanation:
[tex]\frac{a}{c}[/tex] = [tex]\frac{a}{b}[/tex] × [tex]\frac{b}{c}[/tex] = [tex]\frac{2}{5}[/tex] × [tex]\frac{3}{8}[/tex] = [tex]\frac{6}{40}[/tex] = [tex]\frac{3}{20}[/tex]
When Claire chooses a piece of fruit from a fruit bowl, there is a 22% chance that it will be a plum, an 18%
chance that it will be an orange, and a 60% chance that it will be an apple. Which type of fruit is she least likely
to choose?
Answer:
Orange
Step-by-step explanation:
As the chance of choosing orange is 18% which is the least.
5.
Tax: The property taxes on a house were
$1050. What was the tax rate if the house was
valued at $70,000?
Answer:
1.5%
Step-by-step explanation:
house value x property tax rate = property taxes
70,000 x property tax rate = 1050
property tax rate = 1050/70000
property tax rate = .015 0r 1.5%
x °
68°
26 °
Find the measure of x (Hint: The sum of the measures
of the angles in a triangle is 180°
Answers:
6 °
86 °
90 °
180 °
Answer:
86°
Step-by-step explanation:
180° is the sum of all angles in a triangle
The two angles given are 68° and 26°
The equation is : 180° - 68° - 26° = x°
180° - 68° - 26° = 86°
x° = 86°
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
How do I find the image after it’s been rotated 270 degrees about the point (-2,-1)?
Answer: (-1, 2)
Step-by-step explanation:
It's a counter-clockwise rotation, that means (x, y) changes to (y, -x).
(-2, -1) ⇒ (-1, -(-2)) ⇒ (-1, 2)
If it's a clockwise rotation, then (x, y) will change to (-y, x)
(-2, -1) ⇒ (-(-1), -2) ⇒ (1, -2)
Find the domain.
p(x) = x^2+ 2
Answer:
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Interval Notation:
( − ∞ , ∞ )
Set-Builder Notation:
{ x | x ∈ R }
Step-by-step explanation:
hope that helps bigger terms
Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 5?
Answer:
1/5
Step-by-step explanation:
Probability calculates the likelihood of an event occurring. The likelihood of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.
For example, the probability that it would rain on Friday is between o and 1. If it rains, a value of one is attached to the event. If it doesn't a value of zero is attached to the event.
probability that the ticket drawn has a number which is a multiple of 5 =
Number of tickets that are a multiple of 5 / total number of tickets
Multiple of 5 = 5, 10, 15, 20
there would be 4 tickets that would be a multiple of 5
= 4/20
To transform to the simplest form. divide both the numerator and the denominator by 4
= 1/5
answer please I’m dying from math
Answer:
B
substract the variables
How do you complete the other two?
I know how to complete the first one but 3D Pythag confuses me so much
For now, I'll focus on the figure in the bottom left.
Mark the point E at the base of the dashed line. So point E is on segment AB.
If you apply the pythagorean theorem for triangle ABC, you'll find that the hypotenuse is
a^2+b^2 = c^2
c = sqrt(a^2+b^2)
c = sqrt((8.4)^2+(8.4)^2)
c = 11.879393923934
which is approximate. Squaring both sides gets us to
c^2 = 141.12
So we know that AB = 11.879393923934 approximately which leads to (AB)^2 = 141.12
------------------------------------
Now focus on triangle CEB. This is a right triangle with legs CE and EB, and hypotenuse CB.
EB is half that of AB, so EB is roughly AB/2 = (11.879393923934)/2 = 5.939696961967 units long. This squares to 35.28
In short, (EB)^2 = 35.28 exactly. Also, (CB)^2 = (8.4)^2 = 70.56
Applying another round of pythagorean theorem gets us
a^2+b^2 = c^2
b = sqrt(c^2 - a^2)
CE = sqrt( (CB)^2 - (EB)^2 )
CE = sqrt( 70.56 - 35.28 )
CE = 5.939696961967
It turns out that CE and EB are the same length, ie triangle CEB is isosceles. This is because triangle ABC isosceles as well.
Notice how CB = CE*sqrt(2) and how CB = EB*sqrt(2)
------------------------------------
Now let's focus on triangle CED
We just found that CE = 5.939696961967 is one of the legs. We know that CD = 8.4 based on what the diagram says.
We'll use the pythagorean theorem once more
c = sqrt(a^2 + b^2)
ED = sqrt( (CE)^2 + (CD)^2 )
ED = sqrt( 35.28 + 70.56 )
ED = 10.2878569196893
This rounds to 10.3 when rounding to one decimal place (aka nearest tenth).
Answer: 10.3==============================================================
Now I'm moving onto the figure in the bottom right corner.
Draw a segment connecting B to D. Focus on triangle BCD.
We have the two legs BC = 3.7 and CD = 3.7, and we need to find the length of the hypotenuse BD.
Like before, we'll turn to the pythagorean theorem.
a^2 + b^2 = c^2
c = sqrt( a^2 + b^2 )
BD = sqrt( (BC)^2 + (CD)^2 )
BD = sqrt( (3.7)^2 + (3.7)^2 )
BD = 5.23259018078046
Which is approximate. If we squared both sides, then we would get (BD)^2 = 27.38 which will be useful in the next round of pythagorean theorem as discussed below. This time however, we'll focus on triangle BDE
a^2 + b^2 = c^2
b = sqrt( c^2 - a^2 )
ED = sqrt( (EB)^2 - (BD)^2 )
x = sqrt( (5.9)^2 - (5.23259018078046)^2 )
x = sqrt( 34.81 - 27.38 )
x = sqrt( 7.43 )
x = 2.7258026340878
x = 2.7
--------------------------
As an alternative, we could use the 3D version of the pythagorean theorem (similar to what you did in the first problem in the upper left corner)
The 3D version of the pythagorean theorem is
a^2 + b^2 + c^2 = d^2
where a,b,c are the sides of the 3D block and d is the length of the diagonal. In this case, a = 3.7, b = 3.7, c = x, d = 5.9
So we get the following
a^2 + b^2 + c^2 = d^2
c = sqrt( d^2 - a^2 - b^2 )
x = sqrt( (5.9)^2 - (3.7)^2 - (3.7)^2 )
x = 2.7258026340878
x = 2.7
Either way, we get the same result as before. While this method is shorter, I think it's not as convincing to see why it works compared to breaking it down as done in the previous section.
Answer: 2.7Answer:
Qu 2 = 10.3 cm
Qu 3. = 2.7cm
Step-by-step explanation:
Qu 2. Shape corner of a cube
We naturally look at sides for slant, but with corner f cubes we also need the base of x and same answer is found as it is the same multiple of 8.4^2+8/4^2 for hypotenuse.
8.4 ^2 + 8.4^2 = sq rt 141.42 = 11.8920141 = 11.9cm
BD = AB = 11.9 cm Base of cube.
To find height x we split into right angles
formula slant (base/2 )^2 x slope^2 = 11.8920141^2 - 5.94600705^2 = sq rt 106.065
= 10.2987863
height therefore is x = 10.3 cm
EB = 5.9cm
BC = 3.7cm
CE^2 = 5.9^2 - 3.7^2 = sqrt 21.12 = 4.59565012 = 4.6cm
2nd triangle ED = EC- CD
= 4.59565012^2- 3.7^2 = sq rt 7.43000003 =2.72580264
ED = 2.7cm
x = 2.7cm
I didn't understand this to be honest I thought I had to find what jm and lm were together and then subtract from the whole total...but ended up being wrong. whats the correct answer?
Answer:
The correct answer is 3x-2
Step-by-step explanation:
It gives you the expression for JM and LM, and it asks for JL. Therefore, if you take away LM from JM, you are left with JL. You must subtract 2x-6 from 5x-8.
∴5x-8-(2x-6)
Do not forget to distribute the negative since you are subtracting, so instead of subtracting 6 from 8, you will be adding 6 to 8 because two negatives make a positive.
