Answer:
B) Approximately normal, with mean -0.05 and standard deviation 0.083
Step-by-step explanation:
The correct answer is (B). The shape is approximately normal since the expected number of makes and misses for both Daren and Josh are all greater than 10.
The distribution of pD = pJ is given by: Option B: Approximately normal, with mean -0.05 and standard deviation 0.083
What is the distribution of population proportion?For large enough sample, let the population proportion of a quantity be denoted by random variable [tex]p[/tex]
Then, we get:
[tex]p \sim N(\hat{p}, \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}})[/tex]
where
[tex]\hat{p}[/tex] = estimated(mean value) proportion of that quantity, and n = size of sample drawn.Suppose that a random variable X is formed by n mutually independent and normally distributed random variables such that:
[tex]X_i = N(\mu_i , \sigma^2_i) ; \: i = 1,2, \cdots, n[/tex]
And if
[tex]X = X_1 + X_2 + \cdots + X_n[/tex]
Then, its distribution is given as:
[tex]X \sim N(\mu_1 + \mu_2 + \cdots + \mu_n, \: \: \sigma^2_1 + \sigma^2_2 + \cdots + \sigma^2_n)[/tex]
Here, we're specified that:
For proportion of correct free throw attempts by Daren:
Sample size = n = 50Estimated proportion = [tex]\hat{p}_D = 75\% = 0.75[/tex]Let the population proportion be represented by variable [tex]p_D[/tex]For proportion of correct free throw attempts by Josh:
Sample size = n = 50Estimated proportion = [tex]\hat{p}_J = 80\% = 0.8[/tex]Let the population proportion be represented by variable [tex]p_J[/tex]And therefore, we have:
[tex]p_D \sim N\left (0.75, \sqrt{\dfrac{0.75 \times 0.25}{50}}\right )\\\\p_J \sim N\left (0.80, \sqrt{\dfrac{0.8 \times 0.2}{50}}\right )[/tex]
And therefore, we get:
[tex]-p_J \sim N\left (-0.80, \sqrt{\dfrac{0.8 \times 0.2}{50}}\right )[/tex] (standard deviation doesn't get affected by change of sign of the considered random variable, and mean gets affected linearly, so mean became negative 0.80 and standard deviation stays same).
Adding [tex]p_D[/tex] and [tex]-p_J[/tex], we get:
[tex]p_D + (-p_J) = p_D - p_j \sim N\left (0.75 -0.80, \sqrt{\dfrac{0.8 \times 0.2}{50} + \dfrac{0.75 \times 0.25}{50}}\right )\\\\p_D - p_J \sim N\left( -0.05, 0.0837\right)[/tex]
Thus, the distribution of pD = pJ is given by: Option B: Approximately normal, with mean -0.05 and standard deviation 0.083
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In selecting a sulfur concrete for roadway construction in regions that experience heavy frost, it is important that the chosen concrete has a low value of ther- mal conductivity in order to minimize subsequent damage due to changing temperatures. Suppose two types of concrete, a graded aggregate and a no-fines aggregate, are being considered for a certain road. The table below summarizes data on thermal conductivity from an experiment carried out to compare the two types of concrete.
Ğ¢ÑÑеп ni xi si
Graded 42 0.486 0.187
No-fines Ñ 42 0.359 0.158
Assume that the conductivity for each sample of concrete is independent of that of all the others. Our interest is in determining if the mean conductivity for the graded concrete is significantly different than the mean conductivity for the no-fines concrete?
Required:
a. Formulate the above in terms of a hypothesis testing problem.
b. Give the test statistic and its reference distribution (under the null hypothesis).
c. Report the p-value of the test statistic and use it to assess the evidence that this sample provides on the scientific question of difference in mean conductivity of the two materials at the 5% level of significance.
Step-by-step explanation:
Given - In selecting a sulfur concrete for roadway construction in regions that experience heavy frost, it is important that the chosen concrete has a low value of thermal conductivity in order to minimize subsequent damage due to changing temperatures. Suppose two types of concrete, a graded aggregate and a no-fines aggregate, are being considered for a certain road. The table below summarizes data on thermal conductivity from an experiment carried out to compare the two types of concrete.
Type ni xi si
Graded 42 0.486 0.187
No-fines 42 0.359 0.158
To find - a. Formulate the above in terms of a hypothesis testing problem.
b. Give the test statistic and its reference distribution (under the null hypothesis).
c. Report the p-value of the test statistic and use it to assess the evidence that this sample provides on the scientific question of difference in mean conductivity of the two materials at the 5% level of significance.
Proof -
a.)
Hypothesis testing problem :
H0 : There is significant difference between mean conductivity for the graded concrete and mean conductivity for the no fines concrete.
H1 : There is no significant difference between mean conductivity for the graded concrete and mean conductivity for the no fines concrete.
b)
Test statistic :
[tex]Z = \frac{x_{1} - x_{2} }{\sqrt{\frac{s_{1} ^{2} }{n_{1}} + \frac{s_{2}^{2} }{n_{2}} } }[/tex]
[tex]Z = \frac{0.486 - 0.359 }{\sqrt{\frac{0.03496 }{42} + \frac{0.02496 }{42} } }[/tex]
[tex]Z = \frac{0.127 }{\sqrt{0.001468}}[/tex]
[tex]Z = \frac{0.127 }{0.0377}[/tex]
⇒Z(cal) = 3.3687
Z(tab) = 1.96
As Z (cal) > Z(tab)
So, we reject H0 at 5% Level of significance
p-value = 0.99962
Hence
There is significant difference in mean conductivity at the two materials.
A sample of a radioactive isotope had an initial mass of 450 mg in the year 2005 and decays exponentially over time. A measurement in the year 2012 found that the sample's mass had decayed to 310 mg. What would be the expected mass of the sample in the year 2017, to the nearest whole number?
Answer: 238
Step-by-step explanation:
please help me find the answer
Step-by-step explanation:
put 8 in both boxes
then it's
40-2(7)
40-14 = 26
In a clothing store, 65% of the customers buy a shirt, 30% of the customers buy a pair of pants, and 20% of the customers buy both a shirt and a pair of pants. I’m f a customer is chosen at random, what is the probability that he or she buys a shirt or a pair of pants?
Answer:
The Answer will be (0.75)
Are these 4 questions correct? If anything is wrong, let me know and tell me what is correct.
Answer:
they're all correct
Step-by-step explanation:
I think, if it's wrong I'm very sorry, but I'm fairly sure they're right
hope this helps:)
HELP!!! FIRST TO ANSWER GETS BRAINIEST!!!Which of the following equations was used to graph the line shown?
Answer:
Which Equations???
Step-by-step explanation:
Also for coordinates its
([tex]6,6[/tex])
And I think I answer is A
Hope this helps.. Have a nice day :)
Answer:
y=-x+6
Step-by-step explanation:
A negitive line faces down so this becomes y=-x. so in y=mx+b, b is the point where the line crosses the y axis. So that crosses at 6, so your eqation is y=-x+6
Question
Given matrix A shown below, find 6 A
Answer:
-6 18
-30 30
Step-by-step explanation:
Multiply each number in the matrix by the 6.
Christie's Auction sold a painting for
$24,500. It charges all buyers a 15%
premium of the final bid price. How much
did the bidder pay Christie's?
The price that bidder pays to Christie's is $2130.4.
What is percentage?A percentage is a value that indicates 100th part of any quantity.
A percentage can be converted into a fraction or a decimal by dividing it by 100.
And to convert a fraction or a decimal into percentage, they are multiplied by 100.
Given that,
The price for which painting is sold is $24,500.
The percentage of premium price of the final bid is 15%.
Suppose the price paid by the bidder be x.
Then, as per the question the following equation can be written for the price of painting,
x + 15% of x = 24500
=> x + (15/100)x = 24500
=> 115x/100 = 24500
=> x = (24500 × 100) ÷ 115
=> x = 2130.43
Hence, the amount paid to Christie's is $2130.4.
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Which of the following is the quotient of the rational expressions shown
below? Make sure your answer is in reduced form.
7x²/2x + 6/
3х - 5/X +3
Option (E) 7x^2/(6x-10) is the reduced form of the rational expression is the correct answer.
What is a rational expression?A rational expression is the ratio of two polynomials. It looks like fractions that have variables in their denominators. A rational expression is considered simplified if there are no common factors in its numerator and denominator.
For the given situation,
The rational expression is
7x²/(2x + 6) ÷ (3х - 5)/(x +3)
⇒ [tex]\frac{\frac{7x^{2} }{2x+6} }{\frac{3x-5}{x+3} }[/tex]
In conversion of division to multiplication, we need to change the division sign to multiplication sign and reciprocal the rational expression for simplification.
⇒ [tex](\frac{7x^{2} }{2x+6} )(\frac{x+3}{3x-5} )[/tex]
⇒ [tex](\frac{7x^{2} }{2(x+3)} )(\frac{x+3}{3x-5} )[/tex]
⇒ [tex](\frac{7x^{2} }{2(1)} )(\frac{1}{3x-5} )[/tex]
⇒ [tex]\frac{7x^{2} }{6x-10}[/tex]
Hence we can conclude that option (E) 7x^2/(6x-10) is the reduced form of the rational expression is the correct answer.
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Rewrite 2/5 and 4/11 so that they have a common denominator
Answer:
22/55 and 20/55
Step-by-step explanation:
multiply 2 and 5 by 11 to get 22/55, and multiply 4 and 11 by 5 to get 20/55
The radius of a cylindrical construction pipe is 1.5 ft. If the pipe is 15 ft long whats the volume
Answer:
Step-by-step explanation:
r = 1.5 ft
h = 15 ft
π = 3.14
Volume = πr²h
= 3.14 * 1.5 *1.5 *15
= 1.5.975 cubic feet
The radius of a cylindrical construction pipe is 1.5 ft. If the pipe is 15 ft long, what's the volume ?
Answer:-Given:-[tex] \bullet [/tex] Radius (r) of a cylindrical construction pipe is 1.5 ft.
[tex] \bullet [/tex] Height (h) of a cylindrical construction pipe is 15 ft.
To Find:-Volume of a cylindrical construction pipe.
Solution:-We know,
Formula of Volume of cylinder is πr²h.
So, Volume = 3.14 × (1.5)² × 15
Volume = 3.14 × 1.5 × 1.5 × 15
Volume = 105.975 cubic ft.
The volume of a cylindrical construction pipe is 105.975 cubic ft. [Answer]The base figure in a mandala design is a nine-pointed star. Find the measure of each arc of the circle circumscribed about the star.
Which of the following is a true statement?
o & >
o = }
Os <
Answer:
the last one Denise, is the only one that is true
Step-by-step explanation:
Answer:
last one
Step-by-step explanation:
can anyone help me with this please! Serious plz lol
I hope this helps you
I need help with my math assignment
The weekly average earnings of his drivers in a city is $980 with a standard deviation of $47. Assume that we select a random sample of 81 bus drivers. Compute the standard error of the mean
Answer: do the math, and after that know the definition of what the mean is and it will help you, its best to understand something.
Step-by-step explanation:
Suppose you have a right triangle with congruent legs and a hypotenuse that measure (12√5)/5. What is the length of the smaller leg? Round to the nearest hundredth
Answer:
5.4 is the length
Step-by-step explanation:
5.333 - (12√5)/5 - round to nearest hundreth (5.4)
length total 5.4
Thanks and Rate my Answer Please!
The length of the smaller leg is 3.8 unit.
What is Pythagoras theorem?Pythagoras theorem states that "the sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c)" i.e.
[tex]c^{2} = a^{2} + b^{2}[/tex]
Let the length of the leg be b and a.
According to the given question.
We have a rigth triangle which have congruent legs.
And hypotenuse, c = [tex]\frac{12\sqrt{5} }{5}[/tex]
Since, the legs are congruent.
Therefore,
a = b
Now, according to the Pythagoras theorem.
[tex]c^{2} = a^{2} + b^{2}[/tex]
[tex]\implies c^{2} = a^{2} + a^{2}[/tex]
[tex]\implies c^{2} = 2a^{2}[/tex]
[tex]\implies (\frac{12\sqrt{5} }{5} )^{2} = 2a^{2}[/tex]
[tex]\implies \frac{144\times 5}{25} = 2a^{2}[/tex]
[tex]\implies \frac{144}{5} = 2a^{2}[/tex]
[tex]\implies \frac{72}{5} = a^{2}[/tex]
[tex]\implies a = \sqrt{\frac{74}{5} }[/tex]
[tex]\implies a = \sqrt{14.8}[/tex]
[tex]\implies a = 3.84[/tex]
[tex]\implies a = 3.8[/tex] unit
Hence, the length of the smaller leg is 3.8 unit.
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Solve the equation using the method of completing the square.
Answer:
D) x = ± 2√5 - 4
Step-by-step explanation:
2x² + 16x - 8 = 0
Yah, i plugged this into m a t h w a y
(all of ur questions pretty much can use this app or website)
Answer:
D
Step-by-step explanation:
Given
2x² + 16x - 8 = 0 ( divide through by 2 )
x² + 8x - 4 = 0 ( add 4 to both sides )
x² + 8x = 4
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(4)x + 16 = 4 + 16
(x + 4)² = 20 ( take the square root of both sides )
x + 4 = ± [tex]\sqrt{20}[/tex] = ± [tex]\sqrt{4(5)}[/tex] = ± 2[tex]\sqrt{5}[/tex] ( subtract 4 from both sides )
x = - 4 ± 2[tex]\sqrt{5}[/tex] → D
DO NOT PRANK!! I NEED HELP PLS (will give brainly)
Use the diagram below for this question. The angle bisectors of triangle ABC meet at G.
If m∠ ABC = (4x + 12) degrees and m∠ GBA = (3x – 4) degrees , find m∠ GBC.
A.26 degrees
B.44 degrees
C.52 degrees
D.36 degrees
Answer:
b
Step-by-step explanation:
hiiii
Write the form of the partial fraction decomposition of the rational expression.
11x - 10/ (x-6)(x+7)
Answer:
x+7x2+3x+2=6x+1+−5x+2
Step-by-step explanation:
Simplify the expression: x+7x2+3x+2=x+7(x+1)(x+2)
The form of the partial fraction decomposition is
x+7(x+1)(x+2)=Ax+1+Bx+2
Write the right-hand side as a single fraction:
x+7(x+1)(x+2)=(x+1)B+(x+2)A(x+1)(x+2)
The denominators are equal, so we require the equality of the numerators:
x+7=(x+1)B+(x+2)A
Expand the right-hand side:
x+7=xA+xB+2A+B
Collect up the like terms:
x+7=x(A+B)+2A+B
The coefficients near the like terms should be equal, so the following system is obtained:
{A+B=12A+B=7
Solving it (for steps, see system of equations calculator), we get that A=6, B=−5
Therefore,
x+7(x+1)(x+2)=6x+1+−5x+2
Answer: x+7x2+3x+2=6x+1+−5x+2
Phyllis snow borrowed 3200 to pay for a new roof. She signed a 6-month promissory note at 12% interest. find the amount
PAST DUE DATE NEED DONE NOW! NO LINKS! HELP ME FIND THE EQUATION
To write an equation for this line, you first need to understand how to derive it.
Let's utilize slope-intercept form, as it's the easiest to understand compared to any other form for line functions:
y = mx + b
m: The slope of the line
b: The y-intercept (The point where the line is at the y-axis)
Now that we've defined our variables, how do we go about making the actual equation? Let's start off with the slope, m.
The slope is a measure of how high or low the line is. The number is a ratio between the rise and run of a slope. In other words, it is essentially [tex]\frac{rise}{run}[/tex]
Let's look back at the graph. In the time interval from 1 to 2 seconds, we see that the line rises by 22 feet. Because the time interval is only 1 second, the run is 1 second.
Therefore:
m = [tex]\frac{rise}{run}[/tex]
m = [tex]\frac{22}{1}[/tex]
m = 22
We now have the first variable of the equation.
y = 22x + b
What about b? As we established earlier, b is the value of coordinate y at the y-intercept. Essentially, to find b we need to know what the value of y is when the coordinate x is 0.
As you can see from the graph you made, the value of y when x is 0 is also 0. This makes sense, too. How can the cheetah travel distance at 0 seconds when it obviously hasn't started moving? We now know b = 0. Now, we have gotten all of the variables we need to make a full equation:
y = 22x + 0
y = 22x
If you'd like me to explain how I did anything, just ask!
- breezyツ
Answer:
Equation: y=22x + 0 (you can put 0 if you want)
Step-by-step explanation:
Okay, so this is set up as a y=mx+b equation meaning that m=rate of change and b=y-intercept. If a cheetah runs 22 feet per second which is x, that means that m=22. And if 1 second is equal to 22 feet then in 0 seconds they run 0 feet, which is your y-intercept. Another way to find the rate of change (m) is by using the equation y2-y1/x2-x1 or 44-22/1 in this case. This equation is usually written as y=22x. Hope this helps!
Please help me fast i need help please
Answer:
30
Step-by-step explanation:
because I find the lcm for each number
Ariel takes 3 pages of notes during each hour of class. In all, how many hours will Ariel
have to spend in class before she will have a total of 36 pages of notes in her notebook?
Answer:
12 hours
Step-by-step explanation:
36 divide that by 12 and she has 12 hours to write on 36 pages
Which is not a true statement about the disadvantages of certain methods of payment?
Answer:
I dont know explaining more its not clear plz explaining ore
The mixed number 2 5/6 is equivalent to a fraction with a
denominator of 6.
What is the missing numerator in the equivalent
fraction?
Answer:
6 x 2 = 12 then add 5, answer is 17
GIVING BRAINLIEST PLS HELP
(x + 3)^2 – 3 = 0
lesser x =
greater x=
This angle cuts out 1/4 of the circle. Find the measure of the angle.
Answer:
90 degrees
Step-by-step explanation:
Circle P has a circumference of approximately 75
inches.
What is the approximate length of the radius, r? Use 3.14
for y. Round to the nearest inch,
12 inches
D24 inches
38 inches
46 inches
Answer:
12 in
Step-by-step explanation:
C=2pi *r
75/2(3.14)=r
r=75/6.28
~11.94~12 inches
if my answer helps please mark as brainliest
Answer:
12 in
Step-by-step explanation:
Circumference:
C = 2πr
75 = 2(3.14)r
75 = 6.28r
r = 75/6.28
r = 11.95 ≈ 12
answer of the question
Answer:
The number of milk chocolate pieces is between 115 and 120 pieces.
Step-by-step explanation: