Probability lies at the heart of this mathematics question, involving the selection of two students at random from a college. The calculations involve determining the joint probability for the two students being of the same sex, either both male or both female, from the given student population distribution.
Explanation:The subject of this problem is probability. Here, in this liberal arts college, we've been given that 40% of 10,000 students, i.e., 4000 students are males; hence, 60% i.e., 6000 students are females.
When selecting two students at random, there are two possibilities: (1) both students are male or (2) both students are female.
The probability of both students being male can be calculated by multiplying: the probability of the first student being male (which is 4000/10000 = 0.4) by the probability of the second student also being male (which, after the first extraction, would be 3999/9999 since the total number of students and the number of male students both decrease by 1). Hence, the joint probability for two male students is: 0.4 * (3999/9999).
Similarly, we can calculate the joint probability for two female students using the same approach: 0.6 * (5999/9999).
The total probability that the two selected students are of the same gender would be the sum of these two probabilities.
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I'm not quite sure where to start, help and answers would be appreciated !:)
Yesterday, Jack drove 44 1/2 miles. He used 1 1/4 gallons of gasoline. What is the unit rate for miles per gallon?
6.5x – 14.5 = 7.75x – 12
Find the exact volume of a waffle ice cream cone with a 15 -in. diameter and a height of 19 inches.
Find the average rate of exchange for the function. x=-6 and x=0
[tex]f(x)= \frac{1}{x-1} [/tex]
Please help me Estimate 476-269
What expression is equal to (3x^2yz) (5xy^3z^2)
find the distance between two points. Round answers to the nearest tenth (1,5), (7,9)
To find the distance between two points (1,5) and (7,9), you can use the distance formula sqrt((x2 - x1)^2 + (y2 - y1)^2). Rounding to the nearest tenth, the distance is approximately 7.2.
Explanation:To find the distance between two points, we can use the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using the given points (1,5) and (7,9), we substitute the values into the formula:
d = sqrt((7 - 1)^2 + (9 - 5)^2) = sqrt(36 + 16) = sqrt(52)
Rounding to the nearest tenth, the distance between the two points is approximately 7.2.
Simplify -(-7y+12) and explain
I got the question wrong :(
A survey of 240 families showed that.. 91 had a dog 70 had a cat 31 had a dog and a cat 91 had neither a cat nor a dog nor a parakeet 7 had a cat and a dog and a parakeet how many had a parakeet
There were 30 families that had a parakeet.
By using the concept of Sets :
- Total number of families surveyed (denoted as N) = 240.
- Number of families with dogs (denoted as D) = 91.
- Number of families with cats (denoted as C) = 70.
- Number of families with both dogs and cats (denoted as D ∩ C) = 31.
- Number of families with neither cats nor dogs nor parakeets (denoted as neither) = 91.
- Number of families with cats, dogs, and parakeets
(denoted as D ∩ C ∩ P) = 7.
We want to find the number of families that had parakeets
(denoted as P).
To find the number of families with parakeets, we can use the principle of inclusion-exclusion. It states that:
N(D ∪ C ∪ P) :
= N(D) + N(C) + N(P) - N(D ∩ C) - N(C ∩ P) - N(D ∩ P) + N(D ∩ C ∩ P).
Substitute the given values:
240 = 91 + 70 + P - 31 - N(C ∩ P) - N(D ∩ P) + 7.
Now, we can calculate the number of families with both cats and parakeets (C ∩ P) and the number of families with both dogs and parakeets (D ∩ P):
C ∩ P + D ∩ P = (C + D + P) - (N(D) + N(C) + N(P)) = 240 - 91 - 70 - P = 79 - P.
From the given information, we also know that the number of families with neither cats nor dogs nor parakeets is 91. Therefore, we can write:
neither + N(D ∩ P) + N(C ∩ P) + N(D ∩ C ∩ P) = 91.
Substitute the values:
91 + N(D ∩ P) + C ∩ P + 7 = 91.
Now, we can solve for C ∩ P:
C ∩ P = 91 - N(D ∩ P) - 7.
Substitute the value of C ∩ P we found earlier:
79 - P = 91 - N(D ∩ P) - 7.
Now, we can find N(D ∩ P):
N(D ∩ P) = 79 - P - 91 + 7 = -P - 5.
However, we know that the number of families cannot be negative. So, we ignore this solution. Instead, we use the previously calculated value of C ∩ P:
C ∩ P = 91 - N(D ∩ P) - 7.
91 - (79 - P) - 7 = 91 - 79 + P - 7 = P - 7.
P - 7 = 30.
Finally, we get the value of P:
P = 30.
Therefore, there were 30 families that had a parakeet.
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Write a for loop that assigns summedvalue with the sum of all odd values from 1 to usernum. assume usernum is always greater than or equal to 1.
Firstly, define a variable `usernum` and let's use 10 as an example. Then, define another variable `summedvalue` and set it as 0 initially. This variable will hold the sum of all odd numbers up to `usernum`.
Next, we start a for loop. This loop will go through each number in the range from 1 to `usernum` inclusive. That's why in the range function we provide `usernum + 1` as the second parameter.
Now, for every number `i` in this range, we check whether it is odd. A number is odd if it gives a remainder of 1 when divided by 2. In other words, we're checking if `i % 2` is not equal to 0 (`i % 2 != 0`).
If the current number `i` is indeed odd, we add it to `summedvalue` (`summedvalue += i`). Then, the loop goes to the next number and the process repeats itself until we've considered all numbers from 1 to `usernum`.
Finally, when the loop ends, the value of `summedvalue` is the sum of all odd numbers from 1 up to (and including) `usernum`. Return this `summedvalue`.
In the case of `usernum = 10`, the odd numbers between 1 to `usernum` are 1, 3, 5, 7, and 9. When you add them together, you get 25. That's why in this case, the result will be 25.
F(x)=5(3-x)^2 What is f(-4)
Use technology to find the p-value for a right-tailed test about a mean with nequals=66 and test statistic t equals 3.624 .
PLEASE HELP! DUE in 4 hours!
calculate the slopes
3-0 / -2 - 2 = 3/-4 = -3/4
3 - -4 / -2 - -1 = 7/-1 = -7/1
0 - -4 / 2 - -1 = 4/3
-3/4 and 4/3 are negative reciprocals so this is a right triangle
Answer is A
how many 3/8 are in 6
The number of the fraction 3/8 that we can get in 6, is: 16.
We are asked to find how many of the fraction, 3/8, we will have in 6.
This implies that, what number would we need to multiply with 3/8 to get 6?
To determine this, all we need to do is to divide 6 by the fraction, 3/8.
Thus:[tex]6 \div \frac{3}{8}[/tex]
To solve this, multiply 6 by the reciprocal of 3/8, which is 8/3[tex]6 \times \frac{8}{3} \\\\= \frac{6 \times 8}{3} \\\\= \frac{48}{3} \\\\\mathbf{= 16}[/tex]
Therefore, the number of the fraction 3/8 that we can get in 6 is: 16.
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Eric estimated 28*48 by finding 30*50. He estimated the product to be 1,500. Eric thinks the actual product wil be greather. Is eric correct. Explain.
Suppose 4-year-olds in a certain country average 3 hours a day unsupervised and that most of the unsupervised children live in rural areas, considered safe. Suppose that the standard deviation is 1.8 hours and the amount of time spent alone is normally distributed. We randomly survey one 4-year-old living in a rural area. We are interested in the amount of time the child spends alone per day. What percent of the children spend over 10 hours per day unsupervised?
A Z-score helps us to understand how far is the data from the mean. The percentage of children who spend over 10 hours per day unsupervised is 0.005%.
What is Z-score?A Z-score helps us to understand how far is the data from the mean. It is a measure of how many times the data is above or below the mean. It is given by the formula,
[tex]Z = \dfrac{X- \mu}{\sigma}[/tex]
Where Z is the Z-score,
X is the data point,
μ is the mean and σ is the standard variable.
Given that the average time that is unsupervised is 3 hours and the standard deviation is 1.8 hours. The percentage of children who spend over 10 hours per day unsupervised is,
P(X>10) = 1 - P(X<10)
[tex]= 1 - P(Z < \dfrac{10-3}{1.8})[/tex]
= 1 - P(Z< 3.889)
= 1 - 0.99995
= 0.00005
Hence, The percentage of children who spend over 10 hours per day unsupervised is 0.005%.
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Less than 0.01% of rural 4-year-olds spend over 10 hours unsupervised per day based on mean, standard deviation, and normal distribution.
To find the percentage of children spending over 10 hours per day unsupervised, we can use the z-score formula to standardize the value and then find the area under the normal distribution curve.
The formula for the z-score is:
[tex]\[ z = \frac{x - \mu}{\sigma} \][/tex]
Where:
[tex]- \( x \) is the value we're interested in (10 hours per day)\\- \( \mu \) is the mean (3 hours per day)\\- \( \sigma \) is the standard deviation (1.8 hours)[/tex]
Let's calculate the z-score:
[tex]\[ z = \frac{10 - 3}{1.8} = \frac{7}{1.8} \approx 3.89 \][/tex]
Now, we'll find the area to the right of this z-score in the standard normal distribution table (or using a calculator). This represents the percentage of children spending over 10 hours per day unsupervised.
From the standard normal distribution table or calculator, a z-score of 3.89 corresponds to approximately 0.9999.
This means that approximately 99.99% of the children spend less than 10 hours per day unsupervised.
However, if you're looking for the percentage of children spending over 10 hours per day unsupervised, you'd subtract this from 100%:
100% - 99.99% =approx 0.01%
So, only about 0.01% of the children spend over 10 hours per day unsupervised.
Mr. Li records the measures of the lengths of his students’ handprints. The lengths, in centimeters, are shown in the table.
14.0 , 11.5 , 12.1 , 16.2 , 13.5 , 14.3 , 16.8
12.4 , 13.7 , 12.0 , 14.7 , 15.2 , 11.9 , 15.6
13.8 , 14.2 , 12.5 , 15.0 , 16.0 , 13.1 , 11.7
If the class creates a histogram of the data in the table, how many students are in the range 12 cm to 13.9 cm?
1) 3
2) 4
3) 7
4) 8
In the given data set, there are 7 values in the given range.
What is data set?A data set is a collection of data. In the case of tabular data, a data set corresponds to one or more database tables, where every column of a table represents a particular variable, and each row corresponds to a given record of the data set in question.
Given is a set of data we need to determine how many students are in the range 12 cm to 13.9 cm,
So,
Here we just need to find the number of values between 12cm and 13.9 cm, from the given table, these are:
12.1 cm, 13.5 cm, 12.4 cm, 13.7 cm, 13.8 cm, 12.5 cm, 13.1 cm
So, there are 7 values in the given range, which means that 7 students are in the range of 12cm and 13.9cm.
Then the correct option is 7.
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BRAINLEIEST!!! To make 112 dozen muffins, a recipe uses 312 cups of flour. How many cups of flour are needed for every dozen muffins made? Enter your answer in the box as a mixed number in simplest form.
To find out the number of cups of flour needed for each dozen muffins, you need to divide the total quantity of flour used by the total number of dozens. Therefore, about 2 11/14 cups of flour are required for each dozen muffins.
Explanation:To find out how many cups of flour are needed for every dozen muffins made, we need to divide the total amount of flour used by the total number of dozens of muffins. The recipe used 312 cups of flour to make 112 dozens of muffins. So, we divide 312 by 112:
312 ÷ 112 = 2.78571428571429
To convert this to a mixed number in simplest form, you can say that approximately 2 11/14 cups of flour are needed for every dozen muffins made.
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For every dozen muffins made, the recipe requires [tex]\(2 \frac{11}{14}\)[/tex] cups of flour. This is determined by simplifying the ratio of 312 cups of flour needed for 112 dozen muffins to its simplest form.
To find the cups of flour needed for every dozen muffins, we can set up a ratio between the cups of flour and the number of dozens of muffins.
[tex]\[ \text{Cups of Flour} : \text{Dozens of Muffins} \][/tex]
Given that 112 dozen muffins require 312 cups of flour, the ratio becomes:
[tex]\[ \frac{312 \text{ cups}}{112 \text{ dozens}} \][/tex]
Now, simplify this ratio by dividing both the numerator and the denominator by the greatest common factor, which is 8.
[tex]\[ \frac{39 \text{ cups}}{14 \text{ dozens}} \][/tex]
Now, express this ratio as a mixed number in simplest form. Since 39 and 14 share no common factors other than 1, the mixed number is [tex]\(2 \frac{11}{14}\).[/tex]
Therefore, the answer is [tex]\(2 \frac{11}{14}\)[/tex] cups of flour for every dozen muffins made.
Three consecutive vertices of a parallelogram are points (2, 4), (0, 0), and (6, 0). The fourth vertex is point
1.)(2, -1)
2.)(10, 2)
3.)(8, 4)
Answer:
Option 3 - (8,4)
Step-by-step explanation:
Given : Three consecutive vertices of a parallelogram are points (2, 4), (0, 0), and (6, 0).
To find : The fourth vertex is point ?
Solution :
We have given that points are forming a parallelogram.
Let the fourth coordinate is (x,y)
Now, we draw a rough image of the given situation.
Refer the attached figure below.
Draw a parallelogram ABCD with mid point O.
Applying the mid point between two points (2,4) and (6,0).
[tex]O=\frac{2+6}{2}, \frac{4+0}{2}\\\\ O=4,2[/tex]
Now, Applying mid point between points (0,0) and (x,y)
[tex](4,2)=\frac{x+0}{2}, \frac{y+0}{2}[/tex]
[tex]\frac{x+0}{2}=4, \frac{y+0}{2}=2[/tex]
[tex]x=8 ,y=4[/tex]
Therefore, The fourth vertex point is (8,4).
Hence, Option 3 is correct.
If f(x) is discontinuous, determine the reason.
f(x) = {x^2 -4, x<1
{ x+4, x>1
f(x) is continuous for all real numbers
The limit as x approaches 1 does not exist
f(1) does not equal the limit as x approaches 1
f(1) is not defined
Answer:
F(1) is not defined
Step-by-step explanation:
is a relation a function if it passes through the y-axis twice
A relation that passes through the y-axis twice is not considered a function. A function, by definition, can only output one 'y' value for each unique 'x' value. This relation fails the 'vertical line test' which checks that each 'x' value only connects to a single 'y' value.
Explanation:In mathematical terms, a relation is a set of ordered pairs, where each first element is related to the second element. A function, on the other hand, is a special type of relation where every input (or 'x' value) corresponds to exactly one output (or 'y' value).
Now, if a relation passes through the y-axis twice, it means that there are two 'y' values for a single 'x' value (which in this case, is zero). This violates the definition of a function. Hence, a relation that passes through the y-axis twice is not a function. It is simply a relation because it doesn't pass the 'vertical line test' (a vertical line passing through more than one point on the graph of a relation means that the relation is not a function).
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what is m<4? I tryed to do the work but I just can't get it can someone help me plz
The ____ property allows you to regroup terms using parentheses when adding or multiplying, without changing the answer.
Answer:
The Answer is Associative
Step-by-step explanation:
DONT PUT PROPERTY YOU WILL GET IT WRONG...
There are currently 3 students signed up for a trip. The van can transport only 7 students.
Which graph shows all the possible values for the extra number of students that need to sign up so that more than one van is needed to transport them?
Number line with closed circle on 4 and shading to the right.
Number line with closed circle on 4 and shading to the left.
Number line with open circle on 4 and shading to the right.
Number line with open circle on 4 and shading to the left.
Answer:
Answer:
Number line with an open circle on 4 and shading to the right.
Explanation:
Call x the number of students that need to sign up so that more than one van is needed to transport them =>
x + 3 > 7
=> x > 7 - 3
=> x > 4
That is the number greater than 4, without including the number 4.
That is the number line is the set of numbers to the right of 4, and the open circle is used to indicate that the number 4 is not included (a closed circle would indicate that the number 4 is included, which is not the case).
Step-by-step explanation:
Jackrabbits are capable of reaching speeds up to 40 miles per hour. How fast is this in feet per second? (Round to the nearest whole number.)
5,280 feet = 1 mile
40 miles x 5280 = 211200 feet per hour
1 hour = 3600 seconds
211200 / 3600 = 58.67 feet per second
Answer:
The answer is 59 feet per second (B)
Step-by-step explanation:
edge hope ya do well
A kite on a 160-foot string is caught on a pole. When the full length of the string is stretched in a straight line to the ground, it touches the ground a distance of 50 feet from the bottom of the pole. The string forms an angle of _______° with the ground when it is stretched like this.
Answer:
String form an angle of 18.2° with the ground.
Step-by-step explanation:
Given: Length of the string of a kite = 160 ft.
Kite stuck on pole at height of = 50 ft.
We need to find: Measure of angle formed by string of kite with ground.
Attached figure showing the given situation.
let α be the required angle.
In ΔABC,
using trigonometric ratio,
[tex]sin\,\aplha=\frac{AB}{AC}[/tex]
[tex]sin\,\aplha=\frac{50}{160}[/tex]
[tex]sin\,\aplha=\frac{5}{16}[/tex]
[tex]sin\,\aplha=0.3125[/tex]
[tex]\aplha=sin^{-1}(0.3125)[/tex]
[tex]\alpha=18.20995686428301[/tex]
[tex]\alpha=18.21[/tex]
Therefore, String form an angle of 18.2° with the ground.
The Hampton family has a fish tank holding 10450 ml of water. The water is leaking at a rate of 270ml per minute. Write a function to model this situation
The average polar bear weighs 1,200 pounds. The average grizzly bear weighs 800 pounds. The average black bear weighs 400 pounds. The average polar bear weighs how many times more than the average black bear?
The average polar bear weighs is 800 times more than the average black bear.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We have given that the average polar bear weighs 1,200 pounds.
Average grizzly bear weighs is 800 pounds.
The average black bear weighs is 400 pounds.
To find the average polar bear weighs of x times more than the average black bear.
We need to subtract ;
1,200 - 400 = 800
That is 800
Hence, The average polar bear weighs is 800 times more than the average black bear.
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