Answer:
P = 0.232
Step-by-step explanation:
In the cooler, we have 12 bottles of apple juice and 18 bottles of orange juice.
This adds up to a total of 30 bottles.
Now we want to find the probability of pulling a bottle of apple juice after you pulled one bottle of apple juice.
The probability of pulling a bottle of apple juice at the beginning is equal to the quotient between the number of apple juice bottles in the cooler and the total number of bottles in the cooler,
This means that 12 out of 30 are apple juice, then the probability of getting first a bottle of apple juice is:
p = 12/30
Now, we want to find the probability of getting another, we will do the same calculation than above, but now the number of bottles of apple juice is 11 (because we took one) and the total number of bottles is 29.
In this case, the probability is:
q = 11/29
The joint probability (the probability of both events happening) is equal to the product of the individual probabilities.
Then the probability of pulling apple juice and then pulling another apple juice is:
P = p*q = (12/30)*(11/29) = 0.232
A psychologist is interested in whether hypnosis affects brain dominance. Twelve college students from the freshmen class are randomly sampled for an experiment. The experiment has two conditions which are given on different days. In condition 1, the students are hypnotized and then given a test which measures the relative dominance of the right and left hemispheres. The higher the score, the more dominant is the right hemisphere. In condition 2, the same students are given the test again, only this time they are not hypnotized but are in their normal state of consciousness. The following scores are obtained:
Student 1 2 3 4 5 6 7 8 9 10 11
Condition 1 26 15 22 19 23 37 16 17 14 16 21
Condition 2 12 13 18 17 21 22 11 22 10 14 15
Answer the following questions and show your work for each mathematical question:
a. What is the (non-directional) alternative hypothesis?
b. What is the null hypothesis?
c. What is the p value?
Answer:
[tex](a)\ H_a : d_1 - d_2 \ne 0[/tex]
[tex](b)\ H_0 : d_1 - d_2 = 0[/tex]
[tex](c)\ p\ value = 0.0216[/tex]
Step-by-step explanation:
Given
The above data
The question says 12 college students were sampled. However, data for 11 students were provided.
So, I will solve this question using 11 students i.e. n = 11
Solving (a): The alternative hypothesis
Let the relative dominance of the hypnotized students (condition 1) be [tex]d_1[/tex] and the relative dominance of the non-hypnotized students (condition 2) be [tex]d_2[/tex], respectively
The alternative hypothesis is the difference between these relative dominance not equal to 0.
So:
[tex]H_a : d_1 - d_2 \ne 0[/tex]
Solving (b): The null hypothesis
The null hypothesis is the difference between these relative dominance equal to 0.
Using the same notation as (a), the null hypothesis is:
[tex]H_0 = d_1 - d_2 = 0[/tex]
Solving (c): The p value
Using paired samples t test:
First, calculate the difference in scores
[tex]i.e.\ Condition\ 1 - Condition\ 2[/tex]
The difference (d) is as follows:
[tex]d: 14, 2, 4,2, 2, 15, 5, -5, 4, 2, 6[/tex]
Next, calculate the mean of the differences:
This is calculated as:
[tex]\mu = \frac{\sum x}{n}[/tex]
[tex]\mu = \frac{14+ 2+ 4+2+ 2+ 15+ 5 -5+ 4+ 2+ 6}{11}[/tex]
[tex]\mu = \frac{51}{11}[/tex]
[tex]\mu = 4.6364[/tex]
Next, calculate the standard difference of the differences.
This is calculated as:
[tex]\sigma = \sqrt{\frac{\sum(x - \mu)^2}{n-1}}[/tex]
So:
[tex]\sigma = \sqrt{\frac{(14 - 4.6364)^2+ (2- 4.6364)^2+ (4- 4.6364)^2+ ............ (6- 4.6364)^2}{11-1}}[/tex]
[tex]\sigma = \sqrt{\frac{318.54545456}{10}}[/tex]
[tex]\sigma = \sqrt{31.854545456}[/tex]
[tex]\sigma = 5.64398[/tex]
Next, calculate the standard error of the mean difference.
This is calculated as:
[tex]SE = \frac{\sigma}{\sqrt{n}}[/tex]
[tex]SE = \frac{5.64398}{\sqrt{11}}[/tex]
[tex]SE = \frac{5.64398}{3.3166}[/tex]
[tex]SE = 1.70173[/tex]
Next, calculate the degree of freedom (df)
[tex]df = n -1[/tex]
[tex]df = 11 -1[/tex]
[tex]df = 10[/tex]
Lastly, calculate the test statistics (t)
This is calculated as:
[tex]t = \frac{\mu}{SE}[/tex]
[tex]t = \frac{4.6364}{1.70173}[/tex]
[tex]t = 2.72452[/tex]
[tex]t \approx 2.72[/tex]
From the t distribution table:
Where [tex]df = 10[/tex] and [tex]t = 2.72[/tex]
We have:
[tex]P(t > 2.72) = 0.0108[/tex]
For a two-tailed test, the p value is
[tex]p\ value = 2 * P(t > 2.72)[/tex]
[tex]p\ value = 2 * 0.0108[/tex]
[tex]p\ value = 0.0216[/tex]
In the equation below, variables X and Y represent two matrices. Which property of matrix addition is illustrated below?
Answer:commutative property
Step-by-step explanation:
Did it on edge
y''+2y'+y=e^2x how to solve it?
Answer:
[tex]y=C_1e^{-x}+C_2xe^{-x}+\frac{1}{5}e^{2x}.[/tex]
Step-by-step explanation:
all the details see in the attached picture.
CAN BOTS JUST PLEASE STOP REPOSTING THE SAME RESPONSE AND SOMEONE PLEASE HELP ME
Answer:
y=-5x+-3
Step-by-step explanation:
the slope is negative and its rise over run so 5/1 which is five and the y intercept is -3
I need work shown as well
Answer:
A
Step-by-step explanation:
area of the triangle is 5 x 2/ 2 which is 5
area of the square is 25
area of the semi circle is 1/2 * 3.14 * 2.5^2 which is 9.8125
9.8125. + 25 + 5 = 39.8125
please i’ve gotten two wrong and i need to pass this
Answer:5 and 92
Step-by-step explanation:
Answer:
Step-by-step explanation:
what's the answer choices ??
Find the area in square inches of the figure shown.
Answer:
96 [tex]in^2[/tex]
Step-by-step explanation:
48+12+36 (I divided it into 3 rectangles and added them up)
= 96 [tex]in^2[/tex]
Feel free to mark it as brainliest :D
State the change from the parent function in dotted black to the transformed function in blue.
A. The transformed function shifted 2 units down.
B. The transformed function shifted 2 units up.
C. The transformed function shifted 1 unit to the right.
D The transformed function did not shift.
Answer:
transformed function did not shift
Find the equation of the line with the given properties: passes
through (0,-9) and (-2,-9).
Answer:
I WRITE THE STEPS
Step-by-step explanation:
Find the Equation of a Line Given That You Know a Point on the Line And Its Slope. The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept. If you a point that a line passes through, and its slope, this page will show you how to find the equation of the line.
THE TOPIC IS: AREA OF CIRCLES!! PLEASE HELP ME WITH THIS QUESTION!!! WHATS THE ANSWER?? I WILL GIVE YOU BRAINLIEST AND A THANKS!!! AND PLS PUT AN EXPLANATION!! THANK YOU GUYS SO MUCHHHH!! CAN U PLS DO BOTH OF THESE!! :))
Answer:
8) 78.5 in.
11) 28.26 m
Step-by-step explanation:
The formula for area of a circle is πr^2 (pi ⋅ radius ⋅ radius).
Here, only the diameter is shown.
To find the radius, we must divide the diameter (10) by 2.
10/2 = 5.
So, 5 is the radius.
Now, we plug in the numbers.
pi ⋅ radius ⋅ radius
(3.14 is commonly used for pi)
3.14 ⋅ 5 ⋅ 5 = 78.5
78.5 is the area of this circle.
Now, to find the area of this circle, we simply repeat the steps.
6/2 = 3
pi ⋅ radius ⋅ radius
3.14 ⋅ 3 ⋅ 3 = 28.26
Calculator display for
1/9
Answer:
Here ya go :)
Step-by-step explanation:
Hope this helps!
Have a nice day <3
Of nine executives in a business firm, four are married, three have never married and two are divorced. Three of the executives are to be selected for a promotion. Let Y1 denote the number of married executives and Y2 be the number of never-married executives among the three selected for promotion. Assuming that the three are randomly selected from the nine available.
a. Find the joint PMF for y1 and y2
b. Find the marginal probability distribution of y1
c. If we let y3 denote the number of divorced executives among the three selected for promotion. Find P(y3 =1 | y2 = 1)
d. Are Y1 and Y2 independent? Why?
e. Find cov(Y1,Y2). Does the sign surprise you? Why?
Answer:
werere
Step-by-step explanation:
were
Each face of a small cube has a surface area of 0.25 square meters. A larger cube has edges that are six times as long as the edges of the small cube. What is the volume of the larger cube?
Answer:
1534
Step-by-step explanation:
34 35 baby you might need a seatbelet
Answer Choices
A. -0.01
B. 2
C. 0.01
D. 10,000
Answer:I hink its B if its not im sorry
Step-by-step explanation:
what is the probability that Sonny rolls a number on the number cube that is greater or equal to 5 and the spinner lands on Section labeled a
Answer:
your mom and do it yourself iinstead of getting it online
Step-by-step explanation:
btw im Purp
David invests $7000 in two different accounts. The first account paid 2 %, the second account paid 5
% in interest. At the end of the first year he had earned $182 in interest. How much was in each
account?
Answer:
3,990
Step-by-step explanation:
Find the length of are ab
Answer:
20.97?
Step-by-step explanation:
Use the Sine rule!
pls help help me plssss i need real answers :( asap its maths I will give the brainliest whoever's answer the real question pls
Answer:
13.34 pm
22.43 pm
16.22 pm
i cant see the last one clearly
What is the probability the spinner will land on red or white?
Answer:
I think either 1/10 or 2/5
Step-by-step explanation:
The game of Scrabble has 100 tiles. The diagram shows the number of tiles for each letter and the letter's point value. One tile is drawn from Scrabble's 100 tiles. Find the probability of selecting an O or a V.
Answer:
10%
Step-by-step explanation:
In the image attached below, we can see that there are
8 tiles of letter O
2 tiles of letter V
This means that there are 10 total tiles of the letters that you want to get (O and V). Since there are a total of 100 tiles we need to divide this value by 100 to get the probability of getting one of these tiles.
10 / 100 = 0.10 or 10%
Finally, we can see that the probability of selecting a O or a V is 10%
Answer: 8% of O, 2% of V
Step-by-step explanation: There are 8 O tiles and 2 V tiles
A kite flying in the air has a 78-string attached to it, and the string is pulled taut. The angle of elevation of the kite is 52°. Find the height of the kite. Round
your answer to the nearest tenth.
Answer:
sine 52 degrees = height / 78
height = 78 * sine 52
height = 78 * 0.78801
height = 61.46478 feet
rounded to nearest tenth 61.5 feet
Step-by-step explanation:
There are 230 calories in 4 ounces of ice cream. How many calories are in 6 ounces of that ice cream?
Answer:
345 calories
Step-by-step explanation:
The easiest way to do this is to find out how many calories there are for 1 ounce. So 230 divided by 4, equals 57.5. So if 57.5 calories are in one ounce, then you just multiply by 6 to get your answer.
57.5 x 6 = 345 calories
What type of quadrilateral is quadrilateral ABCD if AB=4x-2, BC=2x+12, DC=3x+5, AD=6x-16, AC=4x+12, DB=8x-10, and x=7? Explain and use the properties of the types of quadrilaterals as proofs.
Answer:
The quadrilateral ABCD is a square.
Step-by-step explanation:
According to the statement, AB, BC, CD and DA are the sides of the quadrilateral, whereas DB and AC are its diagonals. If we know that [tex]x = 7[/tex], [tex]AB = 4\cdot x - 2[/tex], [tex]BC = 2\cdot x + 12[/tex], [tex]DC = 3\cdot x +5[/tex], [tex]AD = 6\cdot x -16[/tex], [tex]AC = 4\cdot x + 12[/tex] and [tex]DB = 8\cdot x -10[/tex], the lengths of each line segment are respectively:
Sides
[tex]AB = 4\cdot (7) -2[/tex]
[tex]AB = 26[/tex]
[tex]BC = 2\cdot (7) +12[/tex]
[tex]BC = 26[/tex]
[tex]DC = 3\cdot (7) +5[/tex]
[tex]DC = 26[/tex]
[tex]AD = 6\cdot (7) -16[/tex]
[tex]AD = 26[/tex]
Diagonals
[tex]AC = 4\cdot (7) +12[/tex]
[tex]AC = 40[/tex]
[tex]DB = 8\cdot (7) - 10[/tex]
[tex]DB = 40[/tex]
This information indicates that this quadrilateral is a square because of these characteristics:
1) All sides have the same length.
2) The ratio of any diagonal to any side is [tex]\sqrt{2}[/tex].
Geometry help!! I don’t know how to do this
9514 1404 393
Answer:
659.52 cm^2
Step-by-step explanation:
In order to find the surface area of this figure, we need to know the dimensions of the base. If we assume the base is square, then the distance from its center to the center of one edge is half the dimension of one side of the base.
That center-to-edge distance (x) can be found from the given dimensions using the Pythagorean theorem.
x^2 + (15.4 cm)^2 = (17 cm)^2
x^2 = (289 -237.16) cm^2 = 51.84 cm^2
x = √51.84 cm = 7.2 cm
This means the edge length of the prism base is 2×7.2 cm = 14.4 cm.
__
The total surface area of the square prism is ...
A = b^2 +2bs . . . where b is the edge length of the base, s is the slant height
A = (14.4 cm)^2 + 2(14.4 cm)(17 cm) = 659.52 cm^2
The total surface area of this square pyramid is 659.52 cm^2.
Which shape have both parallel and perpendicular sides?
Answer:
a square
Step-by-step explanation:
all the sides are either perpendicular or parallel
First grey box options:
1)reflection
2) rotation
3)translation
Second grey box options:
1) reflection
2) rotation
3) translation
Answer:
1) reflection
2) translation
Step-by-step explanation:
Figure 0 is first reflected across the x-axis, and then moved 4 spaces to the left, although it could also be seen the other way around.
The only options that aren't possible are any influcing rotation, since the two shapes aren't translated, and rotation-rotation and translation-translation.
On Mother’s Day, 86 children were interviewed, and 15 said they were going to buy a chocolates for their mother, 25 said they were going to take their mother for vacation and 18 said they were going to buy their mother roses. Of these, 8 said they were going to buy a chocolate and take their mother for vacation. Five said they were going to buy both chocolate and roses, and eleven said they were going to buy their mother roses and take their mother for vacation. Only two children said they were going to treat their mother to all three, but chocolates, roses and take for vacations.
i. Illustrate the situation above with the Venn diagrams.
ii. How many children are going to buy chocolates and take their mother for vacation but not
buy them roses.
Answer:
do you need the answer?
Step-by-step explanation:
?
What expression is equivalent to 5(4x+3)-2x
Answer:
18x+15
Step-by-step explanation:
This is basically asking you to simplify the expression.
5(4x+3)-2x
Distribute the 5
20x+15-2x
Combine like terms (x values)
18x+15
Find the slope, or rate of change, from the following ordered pair: (-2, 17) and (-1,5)
Answer:
Slope, m = -12
Step-by-step explanation:
Given the following data;
Points on the x-axis (x1, x2) = (-2, -1)
Points on the y-axis (y1, y2) = (17, 5)
To find the slope, m;
Mathematically, slope is given by the formula;
[tex] Slope = \frac{Change \; in \; y \; axis}{Change \; in \; x \; axis} [/tex]
[tex] Slope, m = \frac {y_{2} - y_{1}}{x_{2} - x_{1}} [/tex]
Substituting into the equation, we have;
[tex] Slope, m = \frac {5 - 17}{-1 - (-2)} [/tex]
[tex] Slope, m = \frac {-12}{-1 + 2} [/tex]
[tex] Slope, m = \frac {-12}{1} [/tex]
Slope, m = -12
Pleaseeeeee helpppppp meeeeeee
Below is the graph of equation y=−|x−2|+2. Use this graph to find all values of x such that
1. y > 0
2. y < 0
3. y = 0
