The table shows the results of an experiment in which subjects taking either a drug or a placebo either reported fatigue or did not report fatigue.
Which calculation shows that selecting a subject who took the drug and selecting a subject who reported fatigue are dependent events?
Choose all answers that are correct.
— P(drug) = 0.6
P(drug | fatigue) ≈ 0.727
0.6 ≠ 0.727
— P(fatigue) = 0.44
P(fatigue | drug) ≈ 0.533
0.44 ≠ 0.533
— P(drug) = 0.6
P(fatigue) ≈ 0.44
0.6 ≠ 0.44
—P(drug and fatigue) = 0.32
P(drug) • P(fatigue) = 0.264
0.33 ≠ 0.264
Answers
Answer:
Therefore, the correct options are;
-P(fatigue) = 0.44
[tex]P(fatigue \left | \right drug)[/tex] = 0.533
--P(drug and fatigue) = 0.32
P(drug)·P(fatigue) = 0.264
Step-by-step explanation:
Here we have that for dependent events,
[tex]P(A \, and \, B)= P(A)\times P(B\left | \right A )[/tex]
From the options, we have;
[tex]P(fatigue \left | \right drug)[/tex] = 0.533
P(drug) = 0.6
P(drug and fatigue) = 0.32
Therefore
P(drug and fatigue) = P(drug)×[tex]P(fatigue \left | \right drug)[/tex]
= 0.6 × 0.533 = 0.3198 ≈ 0.32 = P(drug and fatigue)
Therefore, the correct options are;
-P(fatigue) = 0.44
[tex]P(fatigue \left | \right drug)[/tex] = 0.533
--P(drug and fatigue) = 0.32
P(drug)·P(fatigue) = 0.264
Since P(fatigue) = 0.44 ∴ P(drug) = 0.264/0.44 = 0.6.
Related Questions
What is the area of a rectangle with vertices (2, 3), (9, 3), (9, Negative 2), and (2, Negative 2)? square units
Answers
Answer:
Area of the rectangle = [tex]35\,\,units^2[/tex]
Step-by-step explanation:
Area of the Rectangle= Product of the two Unequal sides
Finding the two unequal sides of the rectangle using the distance formula:
For the coordinates:
A(2,3) B(9,3) C(9,-2) D(2,-2)
Using Distance formula:
AB=
[tex]=\sqrt{(9-2)^2+(3-3)^2} \\\\=\sqrt{7^2+0} \\\\=\sqrt{49}\\\\ =7\,\,units[/tex]
Similarly, BC= 5 units
Area of the rectangle is:
[tex]=7\times 5\\\\=35\,\,units^2[/tex]
Answer:
The answer is definitely 35
If angle 1 is 70°, what is the measure of angle 3?
7
4
2
.
3
Answers
Answer:2
Step-by-step explanation:
What is the area of triangle MNO?
Answers
Answer:
30 [tex]ft^2[/tex]
Step-by-step explanation:
To find the area of a triangle, you must use the formula:
[tex]\frac{1}{2} bh[/tex]
The "[tex]b[/tex]," is the base (12), and the "[tex]h[/tex]," is the height (5).
Plug in the numbers accordingly:
[tex]\frac{1}{2} (12)(5)[/tex]
[tex]\frac{1}{2} (60)[/tex]
30
A worker at an automobile assembly plant checks new cars for defects. Of the first 280 cars
he checks, 4 have defects. If 10,500 cars will be checked this month, predict the total number of cars that will have
defects.
Answers
Answer:
i predict the 150 will have defects
Step-by-step explanation:
you do 280 divided by 4 which gives you 70
then 10,500 divided by 70 which gives you
There is a probability that 150 total autos will have defects if 10,500 vehicles are inspected this month.
What is Possibility?A chance that something might exist, happen, or be true: the state or fact of being possible.
Given, A worker at an automobile assembly plant checks new cars for defects. Of the first 280 cars he checks, 4 have defects.
Out of 280 cars defected = 4
out of 10500 cars defected = (4* 10500) / 280
out of 10500 cars defected = 150
therefore, If 10,500 cars will be checked this month there is a possibility of getting a total number of cars that will have defects of 150.
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Please help I am stuck
Answers
Please help me in these simple equations
Answers
Answer:
1. [tex]225cm^2[/tex]
2. [tex]544mm^2[/tex]
3. [tex]405mm^2[/tex]
4. [tex]67.50cm^2[/tex]
5. [tex]495mm^2[/tex]
6. [tex]480cm^2[/tex]
Step-by-step explanation:
1. Square
[tex]A=s^2[/tex]
s = 15 cm
[tex]A=(15cm)^2\\A=225cm^2[/tex]
------------------------------------------------------------------------------
2. Rectangle
[tex]A=l*w\\A=(32mm)(17mm)\\A=544mm^2[/tex]
------------------------------------------------------------------------------
3. Rectangle
[tex]A=l*w\\A=(45mm)(9mm)\\A=405mm^2[/tex]
------------------------------------------------------------------------------
4. Triangle
[tex]A=\frac{hb}{2}\\ A=\frac{(9cm)(15cm)}{2}\\ A=\frac{135cm^2}{2}\\ A=67.50cm^2[/tex]
------------------------------------------------------------------------------
5. Triangle
[tex]A=\frac{hb}{2}\\ A=\frac{(30mm)(33mm)}{2}\\ A=\frac{990mm^2}{2}\\ A=495mm^2[/tex]
------------------------------------------------------------------------------
6. Rectangle
[tex]A=l*w\\A=(34cm)(20cm)\\A=480cm^2[/tex]
A Pew Research Center poll asked independent random samples of working women and men how much they value job security. Of the 798 women, 702 said job security was very or extremely important, compared with 802 of the 940 men surveyed. Construct and interpret a 95% confidence interval for the difference in the proportion of all working women and men who consider job security very or extremely important
Answers
Final answer:
To construct a 95% confidence interval for the difference in the proportion of all working women and men who consider job security very or extremely important, calculate the sample proportions for women and men, calculate the standard error, calculate the margin of error, and calculate the lower and upper bounds of the confidence interval.
Explanation:
To construct a 95% confidence interval for the difference in the proportion of all working women and men who consider job security very or extremely important, we can use the formula for calculating the confidence interval for a difference in proportions.
Calculate the sample proportions for women and men who consider job security very or extremely important. For women, this would be 702/798 = 0.8797, and for men, this would be 802/940 = 0.8532.Calculate the standard error using the formula: sqrt((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)), where p1 and p2 are the sample proportions, and n1 and n2 are the sample sizes. In this case, the standard error would be sqrt((0.8797 * (1 - 0.8797) / 798) + (0.8532 * (1 - 0.8532) / 940)).Calculate the margin of error using the formula: z * standard error, where z is the z-score for the desired confidence level. For a 95% confidence level, the z-score is 1.96. In this case, the margin of error would be 1.96 * standard error.Calculate the lower and upper bounds of the confidence interval by subtracting and adding the margin of error to the difference in sample proportions. In this case, the lower bound would be (0.8797 - 0.8532) - margin of error, and the upper bound would be (0.8797 - 0.8532) + margin of error.The resulting 95% confidence interval for the difference in the proportion of all working women and men who consider job security very or extremely important would be interpreted as follows: We are 95% confident that the true difference in proportions lies between the lower and upper bounds calculated above. This means that there is a high likelihood that women place a higher value on job security compared to men, but there is still some uncertainty due to sampling variability.
We are 95% confident that the difference in the proportion of working women and men who consider job security very or extremely important is between -0.0043 and 0.0595. This indicates there is no statistically significant difference between the proportions at the 95% confidence level.
To construct a 95% confidence interval for the difference in the proportion of working women and men who consider job security very or extremely important, we will follow these steps:
1. Determine the sample proportions:
For women:
[tex]\[ \hat{p}_1 = \frac{702}{798} = 0.8797 \][/tex]
For men:
[tex]\[ \hat{p}_2 = \frac{802}{940} = 0.8521 \][/tex]
2. Calculate the difference in sample proportions:
[tex]\[ \hat{p}_1 - \hat{p}_2 = 0.8797 - 0.8521 = 0.0276 \][/tex]
3. Calculate the standard error (SE) for the difference in proportions:
[tex]\[ SE = \sqrt{\frac{\hat{p}_1 (1 - \hat{p}_1)}{n_1} + \frac{\hat{p}_2 (1 - \hat{p}_2)}{n_2}} \][/tex]
Plugging in the values:
[tex]\[ SE = \sqrt{\frac{0.8797 (1 - 0.8797)}{798} + \frac{0.8521 (1 - 0.8521)}{940}} \][/tex]
[tex]\[ SE = \sqrt{\frac{0.1059}{798} + \frac{0.1260}{940}} \][/tex]
[tex]\[ SE = \sqrt{0.0001327 + 0.0001340} \][/tex]
[tex]\[ SE = \sqrt{0.0002667} = 0.0163 \][/tex]
4. Determine the critical value (z*) for a 95% confidence interval:
The critical value for a 95% confidence interval (using a standard normal distribution) is approximately 1.96.
5. Calculate the margin of error (ME):
[tex]\[ ME = z^* \cdot SE = 1.96 \cdot 0.0163 = 0.0319 \][/tex]
6. Construct the confidence interval:
[tex]\[ \text{Lower limit} = (\hat{p}_1 - \hat{p}_2) - ME = 0.0276 - 0.0319 = -0.0043 \][/tex]
[tex]\[ \text{Upper limit} = (\hat{p}_1 - \hat{p}_2) + ME = 0.0276 + 0.0319 = 0.0595 \][/tex]
So, the 95% confidence interval for the difference in the proportion of all working women and men who consider job security very or extremely important is:
[tex]\[ -0.0043 \text{ to } 0.0595 \][/tex]
Interpretation:
We are 95% confident that the true difference in the proportion of all working women and men who consider job security very or extremely important is between -0.0043 and 0.0595. This interval includes 0, which suggests that there is no statistically significant difference between the proportions of women and men who value job security at the 95% confidence level.
2+2= ???
pleaae herp houme whork
Answers
Answer:
Goodness, hard question... I believe it is, uh 4?
2+2=4
for eg: if u buy 2 pencils and 2 erasers then,you have total 4 stationery items
hope it will help you
26 Can anyone help!!!
Answers
Ok, first let's find how much a nickle is worth, a nickle is worth $0.05.
0.05 x 27 = $1.35
0.05 x 32 = $1.60
0.05 x 39 = $1.95
0.05 x 47 ≠ $2.45 (It's equal to $2.35)
I hope this helps!
The area of a square is (4x2 − 12x + 9) square units. Determine the length of each side of the square by factoring the area expression completely. Show your work
Answers
Answer:
Length of each side 3/2 or 1.5 square units
Step-by-step explanation:
(4^2 − 12x + 9)
=(2x-3)(2x-3)
2x-3=0
2x=3
x=3/2
The length of each side of the square by factoring in the area expression completely is 3/2.
We have given that,
The area of a square is (4x^2 − 12x + 9) square units.
We have to determine the,
Determine the length of each side of the square by factoring in the area expression completely.
Length of each side 3/2 or 1.5 square units
(4^2 − 12x + 9)
=(2x-3)(2x-3)
2x-3=0
2x=3
x=3/2
The length of each side of the square by factoring in the area expression completely is 3/2.
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Hermina cut a 10" by 20" piece of cardboard down the diagonal. What is the length c of the cut, in inches?
Answers
The length of the diagonal of the rectangular cardboard Hermina cut
is 10√5''.
What is Pythagoras's theorem?In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.
Given, Hermina cut a 10" by 20" piece of cardboard down the diagonal.
So, The diagonal can be thought of as the hypotenuse of a right-angle triangle with a base 20'' and a height of 10''.
Therefore,
Hypotenuse² = Base² + Height².
Hypotenuse² = 20² + 10².
Hypotenuse² = 400 + 100.
Hypotenuse² = 500.
Hypotenuse = √(500).
Hypotenuse = 10√5''.
So, The length of the diagonal is 10√5''.
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The length of the cut (c) is 5 times the square root of 20 inches, which is approximately 22.36 inches when rounded to two decimal places.
When Hermina cuts a 10" by 20" piece of cardboard down the diagonal, she essentially creates two right triangles. The diagonal of a rectangle splits it into two congruent right triangles. This diagonal acts as the hypotenuse of each right triangle.
In a right triangle, we can use the Pythagorean theorem to find the length of the hypotenuse (c) if we know the lengths of the other two sides (a and b).
The Pythagorean theorem states: c^2 = a^2 + b^2, where c is the length of the hypotenuse.
In this case, one side (a) is 10 inches long, and the other side (b) is 20 inches long. Plugging these values into the formula:
c^2 = 10^2 + 20^2
c^2 = 100 + 400
c^2 = 500
Now, to find c, we take the square root of both sides to isolate c:
c = √500
To simplify the square root:
c = √(25 * 20)
c = 5√20
In summary, Hermina's diagonal cut creates two right triangles, and the length of the cut (c) can be found using the Pythagorean theorem. The calculated length is approximately 22.36 inches.
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Use the graph to estimate the solution of the system.
X+2y=5, -x+3y=6
Which integers is the x-value between? What is the x-value to the nearest tenth?
Which integers is the y-value between?
What is the y-value to the nearest tenth?
Answers
Answer:.
Step-by-step explanation: Answer:
1. 0 and 1
2. about 0.6
3. 2 and 3
4. about 2.2
For the graph the solution of the system, X+2y=5, -x+3y=6
1. The integer values of x in between -6 and 5 are (-5, -4, -3, -2, -1, 0, 1, 2, 3, 4)
2. The x-value to the nearest tenth is 1
3. The integer values of y in between 0 and 3 are (1, 2)
4. The y-value to the nearest tenth is 2
What is the equation of line?The equation of a straight line is a relationship between x and y coordinates, The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.
Given that,
system of lines , X+2y=5, -x+3y=6
by plotting graph of it,
we get following conclusions,
Point of intersection is (0.6, 2.2)
1. both the lines are intersecting x axis at (-6, 0) & (5, 0)
So, integers will be (-5, -4, -3, -2, -1, 0, 1, 2, 3, 4)
2. The coordinate of x is, 0.6
The x-value to the nearest tenth is 1
3. both the lines are intersecting y axis at (0, 2) & (0, 2.5)
So, integers will be ( 0, 1, 2)
4. The coordinate of y is, 2.2
The y-value to the nearest tenth is 2
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A theme park has a ride that is located in a sphere. The ride goes around the widest circle of the sphere which has a circumference of 489.84 yd. What is the surface area of the sphere? Use 3.14 for pi.
BRAINLIEST FOR FIRST CORRECT ANSWER!
NEED HELP ASAP!!!!
Answers
Answer:
The surface area of the sphere is about [tex]97,264.64 yd^{2}[/tex]
Step-by-step explanation:
Answer:
76,415.04
Step-by-step explanation:
What is the slope of the line defined by the equation y = -2x + 3?
A)
-2
B)
- 2 / 2
2
D
3
Answers
The answer is A
In the formula for slope intercept it is y= mx+b
The m in the formula is the slope
Answer:
The answer is -2
Step-by-step explanation:
The slope is m.
In an equation, it's shown as y=mx+b, where m is the slope and b is the y intercept.
Find the area of the figure.
Answers
What is the answer or this Equation. ‑1/2+(3/4•4/9) =
Answers
Reduce the numbers with the GCF which in this case is 4
3/4•4/9=1/3
-1/2+1/3= -1/6
Answer:
4/25 would be the answer as;
-1/2 + 1/3 = -0.16666666666
Step-by-step explanation:
‑1/2+(3/4•4/9) =
-1/2 + (1/3) = -4/25
-0.16
However true answer is 16666666666/100000000000. = 0.1666666666
The rule is when fractions reoccur, we show closest and -4/25 is closer than -1/6
What is the output of the function f(p) = 3p – 2 when the input is 2? A. 0 B. 2 C. 4 D. 6 E. 8
Answers
Step-by-step explanation:
Step 1: Find f(2)
[tex]f(p) = 3p - 2[/tex]
[tex]f(2) = 3(2) - 2[/tex]
[tex]f(2) = 6 - 2[/tex]
[tex]f(2) = 4[/tex]
Answer: Option C, 4
Answer:
C. 4
Step-by-step explanation:
f(p) = 3p - 2
Is a function with:
Input: p
Output: 3p - 2
p = 2
f(2) = 3(2) - 2 = 6 - 2 = 4
What is the distance between –3 and 2 on the number line? A number line going from negative 5 to positive 5. –5 –1 1 5
Answers
Answer:
The distance is 5.
Step-by-step explanation:
As you want distance, the best approach is to subtract.
My advice when you're dealing with a number line, and a negative and a positive number, is to subtract the negative from the positive, so that you get a positive distance.
Therefore:
[tex]2 - ( - 3) = 2 + 3 = 5[/tex]
Brian has a piece of yarn that 4 centimeters long how many millimeters long is his piece of yarn
Answers
Answer:
40mm.
there are 10 mm. in a cm, so if there are 4 cm, then there are 40 mm.
Hope this helps :)
HELLLPPP ME QUICKKKKK What do the following four equations have in common: -4x - 18 = 27,
1/2g + 14 = 13, -36 = 3/4n, and -3/7y - 9 = 11
A. All of the solutions are positive. B. All of the solutions are negative.
C. All of the solutions are odd numbers. D. All of the solutions are even numbers
Answers
Answer:
A
Step-by-step explanation:
i did the questions already
(2/3)^4= please help thanks
Answers
Answer:
2/3 x 2/3 x 2/3 x 2/3 = 16/81
Then show decimal form = 0.19753086...
Step-by-step explanation:
Felicia pays for $3000.00 in home repairs using a credit card with a 17% APR. She makes $200.00 monthly payments.
How much will she pay in interest and fees?
Answers
Answer:
262.96 Dollars is for interest
271.91 Dollars is the monthly charged price monthly with the interest included
3262.96 Dollars is the total cost with APR
Question 3:
Point Q is
units from Point R.
Point R is
units from Point T.
Point T is
units from Point S.
Question 4:
What is the area of polygon QRSU?
square units.
Answers
Answer:
Point Q is 6 units from Point R.
Point R is 7 units from Point T.
Point T is 3 units from Point S.
The area of polygon QRSU is 42 square units.
Please mark my answer brainliest so I can move up to the next rank.
Step-by-step explanation:
Water has a “bent” geometry. Which explanation does not explain why? Water’s oxygen has unbonded electron pairs that repel each other. Water can form hydrogen bonds. Electrons are evenly distributed in the water molecule.
Answers
Answer: c, electrons are eventlyg distributed in the water molecules.
Step-by-step explanation:
Answer:
its c on edge
Step-by-step explanation:
did the assignment
Angle 3 and Angle 6 are examples of which type of angle pair?
Answers
Answer:
They look like they are 90° angles
Step-by-step explanation:
(What are the options?)
What is the inverse function of dx) = 2x - 4?
Answers
Answer:
y = x/2 + 2
Step-by-step explanation:
y = 2x - 4
swap y and x
x = 2y - 4
x + 4 = 2y
x/2 + 2 = y
Answer:
d(x) = 1/2x + 2 or d(x) = (x + 4)/2
Step-by-step explanation:
y = 2x - 4
y + 4 = 2x
(y + 4)/2 = x
y = (x + 4)/2 or y = 1/2x + 2
Claudia buys 12 postcards, 12 stamps, and 1 pen . The postcards cost twice as much as the stamps. The pen costs $1.50. The total cost is $ 14.10. How much does each postcard cost? Show your work.
Answers
Answer:
Each postcard cost $0.7.
Step-by-step explanation:
In this problem we have two variables, the price of the postcard and the price of the stamp, since the price for the pain is known. We also have the total cost of the purchase that is $14.1. So we can create an equation as shown:
12*postcards + 12*stamps + pen = 14.1
This represents the total amount spent by Claudia, but we know that each pen costs $1.5, therefore:
12*postcards + 12*stamps + 1.5 = 14.1
12*postcards + 12*stamps = 14.1 - 1.5
12*postcards + 12*stamps = 12.6
We also know that the postcards cost twice as much as the stamps, so we have:
postcards = 2*stamps
Using this info we can solve for stams as shown below:
12*(2*stamps) + 12*stamps = 12.6
24*stamps + 12*stamps = 12.6
36*stamps = 12.6
stamps = 12.6/36
stamps = 0.35
postcards = 2*stamps = 2*0.35 = 0.7
Each postcard cost $0.7.
Answer:
the cost of a post card is $0.7
Step-by-step explanation:
Given
Number of postcard = 12
Number of stamp = 12
Number of pen = 1
Cost of a pen = $1.5
Required
Cost of each postcard..
Let P represent postcards, S represent stamps,Sp represented Pen.
Since there's a total of 12 postcard and 12 staffs, we have:
12P + 12S + 1.50 = $14.10
From the question, we have that the postcards cost twice as much as the stamps.
So, P = 2S.
Substitute 2S for P
12 * 2S+ 12S + 1.5 = 14.10
24S + 12S + 1.5. = 14.10
36S + 1.5 = 14.10
Collect like terms
36S = 14.10 - 1.5
36S = 12.6
Divide through by 36
S = 0.35
Recall that P = 2S.
So, p = 2 * 0.35
P = 0.7
Hence, the cost of a post card is $0.7
Jane wants to share her pizza with two friends. She wants to make sure they all get the same amount. How should she cut the pizza?
Answers
Answer:
Into 1/3 pieces
Step-by-step explanation:
1/3 + 1/3 + 1/3 = 1 the whole pizza pie, yum
Answer:
Hello there the Correct answer is Jane should cut 2 equal pieces, as a diameter of a pizza.
Hope it helps!
From ItsNobody
Bette has a life insurance policy that will pay her family $40,000 per year if
she dies. Bette's insurance company expects that it would have to put
$2,500,000 into a bank account so that it could make the payments. What
does Bette's insurance company expect the interest rate to be?
O A. 0.4%
O B. 2%
O C. 2.3%
O D. 1.6%
Answers
Divide the yearly payout by the amount in the bank:
40,000 / 2,500,000 = 0.016
Multiply by 100 to get the percentage:
0.016 x 100 = 1.6%
The answer is D. 1.6%
The insurance company expects an interest rate of 1.6% to provide the yearly payment of $40,000, calculated by dividing the annual payment by the principal amount deposited.
The student's question asks to calculate the interest rate expected by Bette's insurance company in order to provide a yearly payment of $40,000 to her family, given that the company needs to deposit $2,500,000 into a bank account.
To find the interest rate, we can use the formula for simple interest: Interest = Principal times Rate times Time. Since we are looking for the rate and are given the annual interest (the yearly payment) and the principal (the amount deposited), we can rearrange the formula to solve for the rate: Rate = Interest / Principal / Time. Here, Interest is $40,000, Principal is $2,500,000, and Time is 1 year.
Plugging in the values gives us: Rate = $40,000 / $2,500,000 / 1 = 0.016 or 1.6%. Therefore, the expected interest rate is 1.6%, which corresponds to option D.
pls help with this asap
Answers
Answer:
B
Step-by-step explanation:
Answer:
C. 540
Step-by-step explanation:
A=2(wl+hl+hw)