Answer:
Explained below.
Step-by-step explanation:
According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
The mean of this sampling distribution of sample proportion is:
[tex]\mu_{\hat p}= p[/tex]
The standard deviation of this sampling distribution of sample proportion is:
[tex]\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}[/tex]
(a)
The sample selected is of size n = 450 > 30.
Then according to the central limit theorem the sampling distribution of sample proportion is normally distributed.
The mean and standard deviation are:
[tex]\mu_{\hat p}=p=0.75\\\\\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.75(1-0.75)}{450}}=0.0204[/tex]
So, the sampling distribution of sample proportion is [tex]\hat p\sim N(0.75,0.0204^{2})[/tex].
(b)
Compute the probability that the sample proportion will be within 0.04 of the population proportion as follows:
[tex]P(p-0.04<\hat p<p+0.04)=P(\frac{-0.04}{0.0204}<\frac{\hat p-p}{\sigma_{\hat p}}<\frac{0.04}{0.0204})[/tex]
[tex]=P(-1.96<Z<196)\\=P(Z<1.96)-P(Z<-1.96)\\=0.975-0.025\\=0.95[/tex]
Thus, the probability that the sample proportion will be within 0.04 of the population proportion is 0.95.
(c)
The sample selected is of size n = 200 > 30.
Then according to the central limit theorem the sampling distribution of sample proportion is normally distributed.
The mean and standard deviation are:
[tex]\mu_{\hat p}=p=0.75\\\\\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.75(1-0.75)}{200}}=0.0306[/tex]
So, the sampling distribution of sample proportion is [tex]\hat p\sim N(0.75,0.0306^{2})[/tex].
(d)
Compute the probability that the sample proportion will be within 0.04 of the population proportion as follows:
[tex]P(p-0.04<\hat p<p+0.04)=P(\frac{-0.04}{0.0306}<\frac{\hat p-p}{\sigma_{\hat p}}<\frac{0.04}{0.0306})[/tex]
[tex]=P(-1.31<Z<196)\\=P(Z<1.31)-P(Z<-1.96)\\=0.9049-0.0951\\=0.8098\\\approx 0.81[/tex]
Thus, the probability that the sample proportion will be within 0.04 of the population proportion is 0.81.
(e)
The probability that the sample proportion will be within 0.04 of the population proportion if the sample size is 450 is 0.95.
And the probability that the sample proportion will be within 0.04 of the population proportion if the sample size is 200 is 0.81.
So, there is a gain in precision on increasing the sample size.
I don’t understand this
Answer:
9 to the 5th power
Step-by-
Answer:
n=5 I think...
Step-by-step explanation:
9^7/9^n = 9^2
Multiply by (n)
9^7-n = 9^2
7-n=2
7-n=2: n=5
-n=-5
Simplify:
n=5
Helpppp!!!! Plzzzzzzzzz
Answer:
false
Step-by-step explanation:
Answer:
false
Step-by-step explanation:
the intersection of two planes is a line. Planes are like grids so if you have a 3d model, they'd create a line
Practice Makes Perfect
This practice exercise should be done by the students independently, after
completing the chapter.
1. Discover the pattern and extend it.
ABC
CBA
DEF
FED
b.
18A
20B
22C
24D
D001
001
0001
C.
460
4400
4200
40000
d.
9Z
15Y
21X
27W
Answer:
A.
ABC
CBA
DEF
FED
Step-by-step explanation:
I hope it's help
#lets_help_each_other
also this one! :( pls help again! thanks.
Answer:
9 is the answer
An "extreme" pogo stick utilizes a spring whose uncompressed length is 46 cm and whose force constant is 1.4 x 104 N/m. A 60-kg person is jumping on the pogo stick, compressing the spring to a length of only 5.0 cm at the bottom of their jump. Which is the upward acceleration of the person at the moment the spring reaches its greatest compression at the bottom of their jump?
a. 96 m/s^2
b. 86 m/s^2
c. 976 m/s^2
d.860 m/s^2
Answer:
B. [tex]86\,\frac{m}{s^{2}}[/tex]
Step-by-step explanation:
From Newton's Laws of Motion, the spring is compressed against effects of weight of the person and as sping force is a restitutive force, the net force experimented by person is different from zero. By applying Second Newton's Law, we get this equation of equilibrium on person:
[tex]\Sigma F = k\cdot \Delta x -m\cdot g = m\cdot a[/tex] (Eq. 1)
Where:
[tex]k[/tex] - Spring constant, measured in newtons per meter.
[tex]\Delta x[/tex] - Change in the length of spring, measured in meters.
[tex]m[/tex] - Mass of the person, measured in meters.
[tex]g[/tex] - Gravitational acceleration, measured in meters per square second.
[tex]a[/tex] - Net acceleration of the person, measured in meters per square second.
Now we proceed to clear net acceleration:
[tex]a = \frac{k}{m}\cdot \Delta x -g[/tex]
If we know that [tex]k = 1.4\times 10^{4}\,\frac{N}{m}[/tex], [tex]m = 60\,kg[/tex], [tex]\Delta x = 0.41\,m[/tex] and [tex]g = 9.807\,\frac{m}{s^{2}}[/tex], the acceleration of the person when spring reaches its greatest compression at the bottom of their jump is:
[tex]a = \frac{1.4\times 10^{4}\,\frac{N}{m} }{60\,kg} \cdot (0.41\,m)-9.807\,\frac{m}{s^{2}}[/tex]
[tex]a = 85.859\,\frac{m}{s^{2}}[/tex]
Which corresponds to option B.
Suppose that you roll a die 8 times. What is the probability that you roll a six three or fewer times
Answer:
0.96
Step-by-step explanation:
Given that the a die is rolled 8 number of times.
[tex]n[/tex] = 8
Probability of getting a 6 on roll of a die, [tex]p=\frac{1}{6}[/tex]
Probability of not getting a 6 on roll of a die, [tex]q=1-p=1-\frac{1}{6}=\frac{5}{6}[/tex]
Probability of getting 6 three or fewer times:
[tex]P(r \le 3)=P(r=0)+P(r=1)+P(r=2)+P(r=3)[/tex]
Formula:
[tex]P(r=k)=_nC_k.p^k.q^{n-k}[/tex]
Putting the values using this formula:
[tex]P(r \le 3)=_8C_0.\frac{1}{6}^0.\frac{5}{6}^{8-0}+_8C_1.\frac{1}{6}^1.\frac{5}{6}^{8-1}+_8C_2.\frac{1}{6}^2.\frac{5}{6}^{8-2}+_8C_3.\frac{1}{6}^3.\frac{5}{6}^{8-3}\\\Rightarrow P(r \le 3)=1.\frac{5}{6}^{8}+8.\frac{1}{6}.\frac{5}{6}^{7}+28.\frac{1}{36}^2.\frac{5}{6}^{6}+56.\frac{1}{216}.\frac{5}{6}^{5}\\\Rightarrow P(r \le 3)=0.23+0.37+0.26+0.1=\bold{0.96}[/tex]
There are approximately 330,000,000 cubic miles of water on Earth. A cubic mile is approximately 147,200,000,000 cubic feet. How much water is on Earth? Estimate using scientific notation
Answer: 4.8576 × 10^19 cubic feet of water.
Step-by-step explanation:
330m * 147.2b = 48 quintillion feet.
Answer:
5 x 10^19 ft^3
Step-by-step explanation:
is this a equation or expression 4r+3=12
Answer:
Equation
Step-by-step explanation:
Because there is only one unknown term in it
I hope it helps
Thank U
For w(x)=-2x+7, find the value of x which w(x)=-3
Answer:
x = 5
Step-by-step explanation:
-3 = -2x+7
-10 = -2x
5 =x
The value of x from the given function is 5.
The given function is w(x)=-2x+7..
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Now, put w(x)=-3 in the function and simplify.
That is, -3=-2x+7
⇒ 2x=7+3
⇒ 2x=10
⇒ x=5
Therefore, the value of x from the given function is 5.
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i need help plz 4z+2=34
Answer:
It's 8.
Step-by-step explanation:
I have a calculator from my school and I solved it on the calculator.
Which of the following statements describes the value of the expression 35 – 2x, when x = 6?
A) It is a prime number
B) It is a composite number
C) It is a whole number that is neither prime nor composite
D) It is not a whole number.
Answer: B
Step-by-step explanation: 3x3=9 1x9 equals 9 if a number has 2 or more sets, it's a composite number. It would not become prime because 9 does not have 1 set.
Answer:
Step-by-step explanation:
b
What are reasons A, B, and C in the proof?
Prove: (4 · 3)l + (2 · 4)l = 20l
Statements Reasons
(4 · 3)l + (2 · 4)l = (4 · 3)l + (4 · 2)l A. _________________
= 4(3l + 2l) B. _________________
= 4(5l) Addition
= (4 · 5)l C. _________________
= 20l Multiplication
Answer:
A. Commutative property
B. Associative and distributive properties.
C. Associative property.
Step-by-step explanation:
We proceed to present which reason are utilized by supporting procedure:
1) [tex](4\cdot 3) \cdot i +(2\cdot 4)\cdot i[/tex] Given
2) [tex](4\cdot 3)\cdot i +(4\cdot 2)\cdot i[/tex] A. Commutative property
3) [tex]4\cdot (3\cdot i+2\cdot i)[/tex] B. Associative and distributive properties.
4) [tex]4\cdot (5\cdot i)[/tex] Addition.
5) [tex](4\cdot 5)\cdot i[/tex] C. Associative property.
6) [tex]20\cdot i[/tex] Multiplication/Result.
Help out asap please!
Answer:1<x_<6 and the third line thing w the open circle (1) connecting to closed circle (6)
Step-by-step explanation:subtract 5 from both sides,
please help my geometry assginment, brainly if answer properly
Answer:
Please mark me brainliest :) Hope it helps
Step-by-step explanation:
So basically, since CD and AB are parallel, that means that angle2 and angle3 are similar, due to the corresponding angle postulate. Furthermore, it is given that AG and CE are similar, so angle1 and angle2 are similar on the same principle.
This means that angle3 and angle4 are similar, since it is given that angle1 and angle4 are similar. A bisecting line divides a whole angle into two, equal value angles, and since ECF is composed of angle3 and angle4, and angle3 and angle4 are the same value, that means the line that forms angle3 and angle4 is bisecting the ECF, therefore CD bisects ECF.
FOR EXAMPLE:
Christa and her family went out for pizza and it cost $28. In Tennessee we have a sales tax that is 7% which has to be paid along with $28. What is the sales tax on $28?
I need help please
Which one of these relationships is different than the other three?
Group of answer choices
A
B
C
D
help!!!1
Answer:
B
Step-by-step explanation:
I got this by looking at the graph and the numbers that I got vertically and horizontally I divided them .
what is the slope of a line parallel to the line whose equation is 3x - 2y = 18
Answer:
3/2
Step-by-step explanation:
3x - 2y = 18
y=(3/2)x-9
Slope of the given line=3/2
As parallel lines have same slope, slope of the line parallel to the line 3x - 2y = 18 is 3/2.
Hope it helps :)
Slope of a line parallel to the line whose equation is 3x - 2y = 18 is 3/2.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
Two lines are said to be parallel when their slopes are same.
To find the slope of parallel line, we need to find slope of 3x - 2y = 18
3x-2y=18
-2y=18-3x
y=-18/2+3/2x
y=3/2x-18/2
Slope of line is 3/2
Hence, slope of a line parallel to the line whose equation is 3x - 2y = 18 is 3/2.
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Consider the line -7x - 5y=4.
A cartographer creates a map of Bucks County with a scale factor of 1 inch = 10 miles. The distance between Quakertown and Sellerville is 2.92 inches on the map. Determine the actual distance between the two boroughs.
what are the slopes of the two lines?
green has two yellow dots.
Answer:
-7(1/7) = -1
Step-by-step explanation:
GIVING 75 POINTS
Solve the equation from Part C so that y is by itself on one side of the equation. How are this equation and the equation of the line related? What does this relationship mean about any triangle created using this line?
Part C ---- For similar triangles, the side lengths are proportional. So, you can write a proportion relating the two pairs of vertical and horizontal side lengths. For the line y = 2x, a triangle can be drawn 2 units up and 1 unit right from the origin.
Write a proportion relating the side lengths of the triangle to any other triangle that has the line as a hypotenuse, a horizontal length of x units, and a vertical length of y units.
Answer:
This is my answer,
Step-by-step explanation:
The equation is y=2x, and the horizontal line will always be half of the vertical line (1:2). We can prove this by plugging in y or x. For example, if y is 12, 12=2x. X would equal six.
11.0.
Number o
In 6-card poker, played with a standard 52-card deck, 52Cg, or 20,358,520, different
hands are possible. The probability of being dealt various hands is the number of
different ways they can occur divided by 20,358,520. Shown to the right is the number
of ways a particular type of hand can occur and its associated probability. Find the
probability of not being dealt this type of hand.
The probability is (Round to six decimal places as needed.)
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and then click Check Answer
Using it's concept, it is found that there is a 0.999409 = 99.9409% probability of not being dealt this type of hand.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, there are 20,358,520 different outcomes. The given outcome can happen in 1024 ways, and we want to find the probability of it's complement, hence those are the non-desired outcomes and the probability is:
p = (20,358,520 - 1,2024)/20,358,520 = 0.999409.
0.999409 = 99.9409% probability of not being dealt this type of hand.
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Research shows that many banks are unwittingly training their online customers to take risks with their passwords and other sensitive account information, leaving them more vulnerable to fraud (Yahoo, July 23, 2008). Even web-savvy surfers could find themselves the victims of identity theft because they have been conditioned to ignore potential signs about whether the banking site they are visiting is real or a bogus site served up by hackers. Researchers at the University of Michigan found design flaws in 78% of the 214 U.S. financial institution websites they studied.
Required:
Is the sample evidence sufficient to conclude that more than three out of four financial institutions that offer online banking facilities are prone to fraud? Use a 5% significance level for the test.
Answer:
Decision rule
Fail to reject the null hypothesis
Conclusion
The sample evidence is not sufficient to conclude that more than three out of four financial institutions that offer online banking facilities are prone to fraud.
Step-by-step explanation:
From the question we are told that
The sample size is n = 214
The sample proportion is p = 0.78
The level of significance is [tex]\alpha = 0.05[/tex]
Generally the population proportion is mathematically represented as
[tex]p = \frac{3}{4} =0.75[/tex] (gotten from the statement ''three out of four'' in the question)
The null hypothesis is [tex]H_o : p = 0.75[/tex]
The alternative hypothesis [tex]H_a : p > 0.75[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{\^{p} - p}{ \sqrt{\frac{p(1-p)}{n} } }[/tex]
=> [tex]z = \frac{0.78- 0.75}{ \sqrt{\frac{ 0.75(1-0.75)}{214} } }[/tex]
=> [tex]z = 1.01[/tex]
Generally the p-value is mathematically represented as
[tex]p-value = P(Z > z )[/tex]
=> [tex]p-value = P(Z > 1.01 )[/tex]
From the z-table
[tex]P(Z > 1.01 ) = 0.15625[/tex]
So
[tex]p-value = 0.15625 [/tex]
From the obtained values we see that [tex]p-value > \alpha[/tex] hence we fail to reject the null hypothesis
Therefore we can conclude that the sample evidence is not sufficient to conclude that more than three out of four financial institutions that offer online banking facilities are prone to fraud.
How can a transformed quadratic equation be used real life situation?
Answer:
Quadratic equations are actually used in everyday life, as when calculating areas, determining a product's profit or formulating the speed of an object. Quadratic equations refer to equations with at least one squared variable, with the most standard form being ax² + bx + c = 0.
Step-by-step explanation:
Parker invests $1000 for 5 years at a simple rate of 10%.
A. How much interest will Parker earn after 5 years?
B. What will be the total amount that Parker will have after 5 years?
Answer:
SI=PTR/100
= 1000×5×10/100
=$500
Parker will receive $500 as interest.
Amount=$500+$1000
=$1500
Parker will have $1500 altogether.
A car sharing service offers a membership plan with a $50 per month fee that includes 10 hours of driving each month and charges $9 for each additional hour
(A) Write a piecewise definition of the cost F(x) for a month in which a member uses a car for x hours
(B) Graph F(x) for 0 < x s 15
(C) Find lim x--->10 F(x), lim x--->10F(x), and lim x--->10F(x), which- ever exist.
Answer:
A) F(x) = 50 + ( x - 10 )*9
B) Graph
C) lim ( x ⇒ 10) F(x) = 50
Step-by-step explanation:
A) F(x) = 50 + ( x - 10 )*9 since the first 10 hours are included in initial fee
B) In Annex
C) lim (x ⇒ 10) F(x) = 50 + ( 10 -10)*9
lim ( x ⇒ 10) F(x) = 50 + 0
lim ( x ⇒ 10) F(x) = 50
please i need in under 20 mintute quick
Answer:
its been over twenty minutes. did you figure it out ?
The low temperatures for three consecutive days were -5F, 3F, and 4F.Which temperature has the greatest absolute value
Answer: -5°F
Step-by-step explanation:
Absolute value makes any number positive, regardless of signs.
Therefore, -5°F has the highest absolute value because it will equal 5 which is greater than 3°F and 4°F.
Hope this helps!
a. For what values of k does the function y = cos(kt) satisfy the differential equation 25y'' = −16y?
b. For those values of k, verify that every member of the family of functions y = A sin(kt) + B cos(kt) is also a solution.
Answer:
Step-by-step explanation:
Given y = coskt
y' = -ksinkt
y'' = -k²coskt
Substitute this y'' into the expression 25y'' = −16y
25(-k²coskt) = -16(coskt)
25k²coskt = 16(coskt)
25k² = 16
k² = 16/25
k = ±√16/25
k = ±4/5
b) from the DE 25y'' = −16y
Rearrange
25y''+16y = 0
Expressing using auxiliary equation
25m² + 16 = 0
25m² = -16
m² = -16/25
m = ±4/5 I
m = 0+4/5 I
Since the auxiliary root is complex number
The solution to the DE will be expressed as;
y = Asinmt + Bsinmt
Since k = m
y = Asinkt+Bsinkt where A and B are constants