There are 7 bottles of milk, 5 bottles of apple juice and 3 bottles of lemon juice in
a refrigerator. A bottle of drink is chosen at random from the refrigerator. Find the
probability of choosing a bottle of
a. Milk or apple juice
b. Milk or lemon
There are 48 families in a village, 32 of them have mango trees, 28 has guava
trees and 15 have both. A family is selected at random from the village. Determine
the probability that the selected family has
a. mango and guava trees
b. mango or guava trees.
Answers
For the first question, the probability of choosing a bottle of milk or apple juice is 4/5, and the probability of choosing a bottle of milk or lemon is 2/3. For the second question, the probability that a selected family has mango and guava trees is 15/48, and the probability that a selected family has mango or guava trees is 15/16.
a. The probability of choosing a bottle of milk or apple juice, we need to add the probabilities of choosing each separately and subtract the probability of choosing both.
Number of bottles of milk = 7
Number of bottles of apple juice = 5
Total number of bottles = 7 + 5 + 3 = 15
P(Milk) = Number of bottles of milk / Total number of bottles = 7 / 15
P(Apple juice) = Number of bottles of apple juice / Total number of bottles = 5 / 15
P(Milk or apple juice) = P(Milk) + P(Apple juice) - P(Milk and apple juice)
Since there are no bottles that contain both milk and apple juice, P(Milk and apple juice) = 0
P(Milk or apple juice) = P(Milk) + P(Apple juice) = 7 / 15 + 5 / 15 = 12 / 15
= 4 / 5
Therefore, the probability of choosing a bottle of milk or apple juice is 4/5.
b. The probability of choosing a bottle of milk or lemon, we need to add the probabilities of choosing each separately and subtract the probability of choosing both.
P(Milk) = 7 / 15
P(Lemon) = 3 / 15
P(Milk or lemon) = P(Milk) + P(Lemon) - P(Milk and lemon)
Since there are no bottles that contain both milk and lemon, P(Milk and lemon) = 0
P(Milk or lemon) = P(Milk) + P(Lemon) = 7 / 15 + 3 / 15 = 10 / 15 = 2 / 3
Therefore, the probability of choosing a bottle of milk or lemon is 2/3.
For the second question:
a. The probability that a selected family has mango and guava trees, we need to subtract the number of families that have both types of trees from the total number of families.
Number of families with mango trees = 32
Number of families with guava trees = 28
Number of families with both mango and guava trees = 15
P(Mango and guava trees) = Number of families with both / Total number of families = 15 / 48
b. The probability that a selected family has mango or guava trees, we need to add the number of families with mango trees, the number of families with guava trees, and subtract the number of families with both types of trees to avoid double counting.
P(Mango or guava trees) = (Number of families with mango + Number of families with guava - Number of families with both) / Total number of families
= (32 + 28 - 15) / 48
= 45 / 48
= 15 / 16
Therefore, the probability that a selected family has mango or guava trees is 15/16.
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Related Questions
Figure ABCD has vertice A (5,9) B (7,5) C (5,1) D (3,5)
Which names describe ABCD?
Answers
"Derive the demand function
Endowment (1,0)
U(x,y) = -e⁻ˣ — e⁻ʸ
Answers
To derive the demand function from the given utility function and endowment, we need to determine the optimal allocation of goods that maximizes utility. The utility function is U(x, y) = -e^(-x) - e^(-y), and the initial endowment is (1, 0).
To derive the demand function, we need to find the optimal allocation of goods x and y that maximizes the given utility function while satisfying the endowment constraint. We can start by setting up the consumer's problem as a utility maximization subject to the budget constraint. In this case, since there is no price information provided, we assume the goods are not priced and the consumer can freely allocate them.
The consumer's problem can be stated as follows:
Maximize U(x, y) = -e^(-x) - e^(-y) subject to x + y = 1.
To solve this problem, we can use the Lagrangian method. We construct the Lagrangian function L(x, y, λ) = -e^(-x) - e^(-y) + λ(1 - x - y), where λ is the Lagrange multiplier.
Taking partial derivatives of L with respect to x, y, and λ, and setting them equal to zero, we can find the values of x, y, and λ that satisfy the optimality conditions. Solving the equations, we find that x = 1/2, y = 1/2, and λ = 1. These values represent the optimal allocation of goods that maximizes utility given the endowment.
Therefore, the demand function derived from the utility function and endowment is x = 1/2 and y = 1/2. This indicates that the consumer will allocate half of the endowment to each good, resulting in an equal distribution.
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Hudson is blocking off several rooms in a hotel for guests coming to his wedding. The
hotel can reserve small rooms that can hold 3 people, and large rooms that can hold 4
people. Hudson reserved twice as many large rooms as small rooms, which altogether
can accommodate 66 guests. Write a system of equations that could be used to
determine the number of small rooms reserved and the number of large rooms
reserved. Define the variables that you use to write the system.
Check picture for full question.
Answers
Answer:
The picture won't show. are there answer options?
Step-by-step explanation:
Small room (S) - hold 3 people
Large room (L)- hold 4 people
Hudson reserved twice as many large rooms = 2x Large room #
2L + S = 66
So,
Let S = Small room
Let L = Large room
I hope this can make things slightly easier for you. I tried to make it more visible for you. Please comment if you need more help.
Is the triangle with leg lengths of 8 mm and 8 mm and a hypotenuse of length 12 mm a right triangle?
Answers
Answer:
No
Step-by-step explanation:
Use the Pythagorean Theorem to check on this.
Does 8^2 + 8^2 = 12^2? Does 64 + 64 = 144? NO. So this is not a right triangle.
Suppose an item cost $6.99 in 1977. What would have been the equivalent cost in 2017?
Answers
Explanation:
In 1977, the cpi value is
\(60.600\)In 2017 the cpi value is
\(245.120\)To figure out the cost of the value in 2017, we will interpolate below
\(\begin{gathered} 60.600=245.120 \\ 6.99=x \\ cross\text{ multiply, we will have} \\ 60.6x=6.99\times245.120 \\ \frac{60.6x}{60.6}=\frac{1713.3888}{60.6} \\ x=28.27 \end{gathered}\)Hence,
The final answer is
\(\Rightarrow\text{ \$}28.27\)Can someone explain this me..
Is 27.5 and 11.5 irritation or rational and why
Answers
Answer:
rational because they end
Step-by-step explanation:
Answer:
27.5 and 11.5 are both rational numbers.
Step-by-step explanation:
This is because they do not continue on forever. You know what they are. So numbers like 1, 1.5, 1.234, and 100 are rational. Numbers like pi, 1/3 (1.33333 forever) are irrational.
a pole that is 2.8m tall casts a shadow that is 1.49m long. at the same time, a nearby building casts a shadow that is 37.5m long. how tall is the building? round your answer to the nearest meter.
Answers
The height of the building is 71 meters.
We can solve this problem using the similar triangles. The height of the building can be determined by setting up the following proportion:
(the height of pole) / (length of pole's shadow) = (height of building) / (length of building's shadow)
Substituting the given values:
2.8 / 1.49 = (height of building) / 37.5
To find the height of the building, we can cross-multiply and solve for it:
(2.8 * 37.5) / 1.49 = height of building
Calculating the expression on the right side:
(2.8 * 37.5) / 1.49 ≈ 70.7013
Rounding to the nearest meter, the height of the building is approximately 71 meters.
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Expand & Simplify
(3x-3)^2 + (x+4)(x-1)
Please help... I have no clue what I'm doing and it's due in tomorrow. Thanks :)
Answers
Answer:
\( {(3x - 3)}^{2} + (x + 4)(x - 1) \\ = {(3x)}^{2} - 2 \times 3x \times 3 + {3}^{2} + ( {x}^{2} - x + 4x - 4) \\ = {(3x)}^{2} - 18x + 9 + {x}^{2} + 3x - 4 \\ = 9 {x}^{2} + {x}^{2} - 18x + 3x + 9 - 4 \\ = 10 {x}^{2} - 15x + 5 \\ thank \: you\)
Answer:
10x^2-15x-5
Step-by-step explanation:
(3x-3)^2 + (x+4)(x-1)
9x^2-18x+9+x^2+3x-4
10x^2-15x+5
Given f(x)=6x+2, find f(x+3).
Answers
Answer:
f(x+3) is 6x + 20
Step-by-step explanation:
\({ \sf{f(x) = 6x + 2}} \\ { \sf{f(x + 3) = 6(x + 3) + 2}} \\ = { \sf{6x + 20}}\)
You measure 41 textbooks' weights, and find they have a mean weight of 78 ounces. Assume the population standard deviation is 12 ounces. Based on this, construct a 95% confidence interval for the true population mean textbook weight.Give your answers as decimals, to two places < μ <
Answers
To construct the confidence interval, we first need to determine which distribution we need to use. Since the sample size is 41 (this is the number of books) and the standard deviation of the population is known we will use the normal distribution to construct our interval, that is, the interval is given by:
\(\bar{x}\pm z\sigma_{\bar{x}}\)where:
\(\begin{gathered} \bar{x}\text{ is the mean of the sample} \\ \sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}\text{ is the standard deviation of the mean} \\ z\text{ is the z-value for the given confidence interval } \end{gathered}\)We know that the point estimate of the mean is 78 ounces. The standard deviation of the mean is:
\(\sigma_{\bar{x}}=\frac{12}{\sqrt{41}}=1.874\)The z-value for a 95% confidence interval is 1.96, then we have:
\(\begin{gathered} \bar{x}-z\sigma_{\bar{x}}=78-(1.96)(1.874)=74.33 \\ \bar{x}+z\sigma_{\bar{x}}=78+(1.96)(1.874)=81.68 \end{gathered}\)Therefore, the confidence interval of the mean is:
\(74.33<\mu<81.68\)
Lynette has a metal doorstop with the dimensions shown.
Each cubic centimeter of the metal in the doorstop has a mass
of about 8.3 grams. Find the volume of the metal in the
doorstop. Then find the mass of the doorstop.
Answers
Volume = 105in³
Mass = 871.5g
To find the volume of the metal we can find the area of a base, and multiply it by the prism's width.
The base is 30cm in area, and the width is 3.5cm, which makes the volume 105in³
The mass of the doorstop can be found by just multiplying the grams per cubic centimeter by the volume, which would be 871.5g
two vectors are linearly dependent if and only if they are collinear.
Answers
The given statement "two vectors are linearly dependent if and only if they are collinear." is True, because these vectors lie on same plane.
Two vectors are linearly dependent if and only if one of them can be expressed as a scalar multiple of the other. In other words, if there exist scalars a and b such that av + bw = 0, where v and w are the two vectors in question, and at least one of a and b is not zero, then the vectors are linearly dependent.
If the vectors are collinear, it means that they lie on the same line and can be expressed as scalar multiples of each other. In this case, a and b can be chosen to be the coefficients of the vector components along the line, and the equation av + bw = 0 holds. Therefore, if two vectors are collinear, they are linearly dependent.
Conversely, if two vectors are linearly dependent, then one of them can be expressed as a scalar multiple of the other, which means that they lie on the same line and are collinear. Therefore, if two vectors are linearly dependent, they are also collinear.
Hence, we can conclude that two vectors are linearly dependent if and only if they are collinear.
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Complete question is:
Two vectors are linearly dependent if and only if they are collinear.
True/False.
if the tangent line to y = f(x) at (4, 3) passes through the point (0, 2), find f(4) and f '(4).
Answers
f(4) = 3 and f '(4) = 1/4, Given that the tangent line to y = f(x) at (4, 3) passes through the point (0, 2), we can find f(4) and f '(4) using the slope-point formula.
Since the tangent line passes through (4, 3) and (0, 2), we can calculate the slope (m) as:
m = (y2 - y1) / (x2 - x1)
m = (3 - 2) / (4 - 0)
m = 1 / 4
Now, we know that the slope of the tangent line at (4, 3) is equal to the derivative f '(4). Therefore: f '(4) = 1/4
Since the tangent line touches the curve at (4, 3), we have:
f(4) = 3.
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A class trip is planned for a cinema visit.
1/4 of the people walk to it.
1/3 of the people, get the bus.
The remaining 60 people get a lift in a car.
Calculate the number of pupils who get the bus and who walk to the cinema.
Answers
Answer: 48 pupils get the bus to the cinema and 36 pupils walk to the cinema.
Step-by-step explanation:
Let's suppose that there are a total of N pupils.
We know that N/4 walk to the cinema.
We know that N/3 get the bus to the cinema.
And the remainder is equal to 60 people.
Then:
N - N/4 - N/3 = 60
N*(1 - 1/4 - 1/3) = 60
N( 12/12 - 3/12 - 4/12) = 60
N*( 5/12) = 60
N = (12/5)*60 = 144
Then the number of pupils that walk to the cinema is N/4, or:
144/4 = 36
And the number of pupils that get the bus is N/3, or:
144/3 = 48.
on the map , from Denver to Chicago is 3 in . if the scale is 1 inch = 300 miles , find the actual distance
Answers
900 miles
1) Since when we talk about linear scale drawings, Then we must consider the following ratio:
\(Scale=\frac{\text{measure in the drawing}}{\text{Actual measure}}\)2) So let's pug into that the given data:
\(\begin{gathered} \frac{1}{300}=\frac{3}{x} \\ x=3\cdot300 \\ x=900 \end{gathered}\)3) So the actual distance from Denver to Chicago is 900 miles
The tables represent the points earned in each game for a season by two football teams.
Eagles
3 24 14
27 10 13
10 21 24
17 27 7
40 37 55
Falcons
24 24 10
7 30 28
21 6 17
16 35 30
28 24 14
Which team had the best overall record for the season? Determine the best measure of center to compare, and explain your answer.
Eagles; they have a larger median value of 21 points
Falcons; they have a larger median value of 24 points
Eagles; they have a larger mean value of about 22 points
Falcons; they have a larger mean value of about 20.9 points
Answers
Falcons had a more effective overall record because of the higher median. Thus, the answer is option B.
The median is usually used for the comparison of two data sets instead of the mean, as it is not affected by outliers.
Compare the total points earned by each team.
The Eagles data set is given below:
3, 7, 10, 10, 13, 14, 17, 21, 24, 24, 27, 27, 37, 40, 55.
As the data set has an odd cardinality, the median is the middle element, therefore it is for:
21.
For the Falcons, we use the same approach and obtain a median about:
24.
Therefore, we can say that the Falcons had a more effective overall record because of the higher median and the best measure of center to compare would be mean.
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Triangle LMN has vertices at L(0, 0), M(0,4), and N(-3,0). The triangle will be rotated 270° counterclockwise about the origin. What will
be the coordinates for point N'?
A (-3,0)
B. (0,-3)
C (0, 3)
D (3, 0)
Answers
\(\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}\)
Actually Welcome to the Concept of the mirror reflection.
Since the image of triangle is reflected along Y-axis,hence the coordinates of N after 270° rotation are
N ==> ( 3,0)
===> Option D.) is correct
Answer:(3,0)
Step-by-step explanation:
D
Find the slope of the line that passes through (99, -12) and (98, 57). How do I do this step by step
Answers
Answer:
-69. Nice!
Step-by-step explanation:
The slope of a line between two points is defined as the ration between the vertical distance and the horizontal distance - note that it doesn't matter if you go from the first to the second point, or the opposite, signs will end up fixed anyways. Let's get calculating!
\(\Delta y = -12 -57 = -69 \\ \Delta x = 99 - 98 = 1\)
Your slope is \(m = {\Delta y \over \Delta x}={-69 \over 1 } = -69\)
How many quart of pure antifreeze mut be added to 5 quart of a 10% antifreeze olution to obtain a 30% antifreeze olution?
Answers
The amount of pure antifreeze that needs to be added = 1.429 quarts
What is antifreeze ?
A colored liquid called antifreeze, often known as engine coolant, is combined with water to assist regulate your engine in extremely hot weather.
Let x be the amount of pure antifreeze that needs to be added
The amount of pure antifreeze added (x) plus the amount of pure antifreeze in the 5 quart of 10% antifreeze solution [ 0.1*5] should be equal to the amount of pure antifreeze in the final mixture [ 0.3*(5+x) ]
The equation obtained is:
x+[0.10*5]=0.30(5+x)
x+0.5=1.5+0.30x
x-0.30x =1.5-0.5 = 1
0.70x=1
divide each side by 0.70
x=1.429 quarts
So, the amount of pure antifreeze that needs to be added = 1.429 quarts
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Which of the following is the slope-intercept form of 9x + 3y – 15 = 0?
Answers
Answer:
y = -3x + 5
Step-by-step explanation:
slope-intercept form means it should look like
y = mx + b
9x + 3y – 15 = 0
3y = -9x + 15
y = -3x + 5
Determine if the following triangles are similar. If they are similar, choose their justification. If they are not similar, choose not similar.
Answers
Answer:AA~
Step-by-step explanation:
Go step by step to reduce the radical.
√216
Answers
Answer: 6√6
Step-by-step explanation:
√216=
√(36*6)=6√6
How far does judy travel in 2 3/4 hours if she travels at the rate of 5 1/2 miles per hour
Answers
Judy travel's 15.125 miles or 15\(\frac{1}{8}\) miles in 2 3/4 hours
How to solve such time related questions?
The key concept for solving such questions is the relationship between speed, distance and time.
The relationship between them is Distance = Speed x Time
Given:
Speed = 5 1/2 miles per hour Time = 2 3/4 hoursSubstituting it in the relationship we get,
Distance = Speed x Time
Distance = 5 1/2 miles per hour x 2 3/4 hours
Distance = \(\frac{11}{2} X \frac{11}{4}\) miles
Distance = \(\frac{121}{8}\) miles or 15\(\frac{1}{8}\) miles
Thus Judy travel's 15.125 miles or 15\(\frac{1}{8}\) miles in 2 3/4 hours
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If a+b+c = 9 and ab+bc+ca = 40, find a^2 + b^2 + c^2
Answers
Explanation
By definition.
\(\begin{gathered} (a+b+c)^2=a^2+b^2+c^2+2((ab)+(bc)+(ac)) \\ \end{gathered}\)so
Let
\(\begin{gathered} (a+b+c)=9 \\ ab+bc+ac=40 \\ \text{now, replace} \end{gathered}\)\(\begin{gathered} (a+b+c)^2=a^2+b^2+c^2+2((ab)+(bc)+(ac)) \\ 9^2=a^2+b^2+c^2+2(40) \\ 81=a^2+b^2+c^2+80 \\ \text{subtract 80 in both sides} \\ 81-80=a^2+b^2+c^2+80-80 \\ 1=a^2+b^2+c^2 \end{gathered}\)hence
\(a^2+b^2+c^2=1\)I hope this helps you
Select the solutions of the equation.(select all that apply)
x2+4= 0
A.-2i
B.-2
C. 2i
D.2
Answers
This is because it is the sqrt(-4)
Three hundred fifty seniors attended
the spring prom. If this number repre-
sents of the total senior class, then
how many seniors are in the class?
7
Answers
Answer:
there would be three hundred and fifty.
expand and simplyfy 4(2x+3) +4(3x+2)
Answers
Answer:
x=1 I'm not sure if I'm correct
Step-by-step explanation:
4x2x=8x
4x3=12
4x3x=12x
4x2=8
8x+12=12x+8
8x-12x= 8-12
-4x=-4 divide -4x in both side so the answer should be x=1
7 dived by 297 and round it off
Answers
The solution is 42.43.
What is Division method?
Division method is used to distributing a group of things into equal parts.
Given that;
The expression is;
'7 divided by 297'
Now, After divide we get;
7 ) 297 ( 42.428
28
--------
17
14
--------
30
28
-------
20
14
-----
60
56
------
4
Hence, 297 ÷ 7 = 42.428
After rounding we get;
297 ÷ 7 = 42.43
Thus, The solution is 42.43.
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PLS HELPPPPPPPPPPPPP
Answers
Answer:
Step-by-step explanation:
I see three equations that represents the first step. All the others (I think) have flaws of one kind or another.
Third
The third one divides both sides of the equation by 3. All that remains on the left is what is inside the brackets. 24/3 becomes 8 which what equation 3 says.
x + 6 = 24/3
x + 6 = 8
Fourth
Shows how the distributive property is performed. It does this with great care. The right side is not affected.
3*x + 6*3 = 24 is what is the result. It is a good first step.
Five
This one is a little iffy. It is more like the second step. You have taken the fourth choice and removed the brackets. If you can do this in your head, I think it counts. I'm not sure how to answer what you should do. You're darned if you do and darned if you don't. My opinion is that it is perfectly OK but your marker may not agree.
3. You are selling hot cocoa at an
amazing price of $0.80 a cup. You
want to make(earn) $ 48. How many
cups do you need to sell?
Answers
Answer:
you need to sell 60 cups
Step-by-step explanation:
48÷0.80= 60 cups
hope it helps!
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