Answer:
0.07 -The probability that a randomly chosen team has 3 girls and 7 boys.
0.12 -The probability that a randomly chosen team includes all 6 girls in the class.
0.44 -The probability that a randomly chosen team has 5 girls and 5 boys.
0.49-The probability that a randomly chosen team has either 4 or 6 boys.
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When a team of 10 players is to be selected from a class of 6 girls and 7 boys the probability of each scenario occurring is:
0.07 = The probability that a randomly chosen team has 3 girls and 7 boys.
0.12 = The probability that a randomly chosen team includes all 6 girls in the class.
0.44 = The probability that a randomly chosen team has 5 girls and 5 boys.
0.49 = The probability that a randomly chosen team has either 4 or 6 boys.
What is probability?
In simple words, it refers to a numerical guess of how likely an event is to occur. Hence, when it comes to probability we believe there is no guarantee the event would occur.
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Name the properties that were used to derive the properties of logarithms.
The properties that were used to derive the properties of logarithms are the properties of exponent because logarithms are exponents. The properties of exponents are: product of powers, power to a power, quotient of powers, power f a product and power of a quotient.
As an example, the log property log(a^k) = k log (a) can be derived from the exponential property (b^a)^k = b^(ak).
Likewise,
log (ab) = log (a) + log (b) comes from c^(a+b) = c^a*c^b
Proof:
Let x = c^a and y=c^b
Then,
log (x) = a and log (y) =
b (base c)
log (xy) = log (c^a * c^b) = log (c^(a+b)) = a+b = log(x) + log (y)
Aurora earns a salary of $25,000 per year. Her benefits are equal in value to 30 percent of her salary. What is the value of Aurora's benefits?
Value of Aurora's benefits as 30percent of her salary is equals to $7500.
What is percentage?" Percentage is defined as the hundredth part of the given whole number."
According to the question,
Salary amount of Aurora = $25,000
Benefit value = 30 percent of ( $25,000)
Therefore,
30 percent of ( $25,000) = 30% of 25,000
= [tex]\frac{(30) * (25,000)}{100}[/tex]
= $7,500
Hence, value of Aurora's benefits as 30percent of her salary is equals to $7500.
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jack is mowing a lawn that has a shed. needs to know area of lawn to mow. dimensions of yard are 5x by 13 x-4 . she'd are 2x by 2x+4. " find polynomial that describes area of lawn needed to mow. Polynomial in answer should have two terms.
please help.
Simplifying expressions with exponents
The distribution of the number of occurrences of the letter t on the pages of a book is found to be a normal distribution with a mean of 44 and a standard deviation of 18. If there are 500 pages in the book, which sentence most closely summarizes the data?
The data represents a normal distribution where approximately 68 percent of the pages will have a number of occurrences of the letter t within one standard deviation of the mean, 95 percent within two standard deviations, and more than 99 percent within three standard deviations.
Explanation:The sentence that most closely summarizes the data is: For data having a distribution that is bell-shaped and symmetric, the following are true:
Approximately 68 percent of the data is within one standard deviation of the mean.Approximately 95 percent of the data is within two standard deviations of the mean.More than 99 percent of the data is within three standard deviations of the mean. This is known as the Empirical Rule.Using this information, we can conclude that approximately 68 percent of the pages in the book will have a number of occurrences of the letter t within one standard deviation of the mean, which is 44. Approximately 95 percent of the pages will have a number of occurrences within two standard deviations, and more than 99 percent will have a number of occurrences within three standard deviations.
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Angle θ is in standard position. If (8, -15) is on the terminal ray of angle θ, find the values of the trigonometric functions.
Answer with explanation:
It is given that, Angle θ is in standard position.
A line from origin O to point , P(8,-15) is joined and then perpendicular to x and y axis, is drawn cutting X axis at Point M and Y axis at point N.
OM= 8 units
ON=P M=15 units
By Pythagorean Theorem
[tex]OM^2 + PM^2=OP^2\\\\ 8^2 +15^2=OP^2\\\\ OP^2=64 +225\\\\OP^2=289\\\\OP^2=17^2\\\\OP=17\\\\ Sin (\theta)=\frac{\text{Perpendicular}}{\text{Hypotenuse}}=\frac{-15}{17}\\\\Cos(\theta)=\frac{\text{Base}}{Hypotenuse}=\frac{8}{17}\\\\Tan(\theta)=\frac{\text{Perpendicular}}{Base}=\frac{-15}{8}\\\\ Cosec(\theta)=\frac{1}{Sin(\theta)}=\frac{-17}{15}\\\\ Sec(\theta)=\frac{1}{Cos(\theta)}=\frac{17}{8}\\\\ Cot (\theta)=\frac{1}{Tan(\theta)}=\frac{-8}{15}[/tex]
Point(8,-15), lies in Quadrant four. In Quadrant four Cosine and Secant Function are positive and all other trigonometric functions, Sine,Cosecant, Tangent,and Cotangent are Negative.
Divide the decimal numbers 12.012÷6
Ava wants to wash one load of laundry at a local laundromat. At laundromat A, it costs $6.35 to wash and $1.25 to dry one load of laundry. At laundromat B, it costs $5.95 to wash and $0.85 to dry one load of laundry. Which laundromat has the better price for doing one load of laundry, and by how much?
Laundromat A = 6.35 +1.25 = 7.60 for one load
Laundromat B = 5.95 +0.85 = 6.80 for one load
7.60-6.80 = 0.80
Laundromat B is has the better price by 0.80 cents
Solve l=14j+3k for j.
To solve the equation l = 14j + 3k for j, subtract 3k from both sides and then divide by 14, giving j = (l - 3k) / 14.
Explanation:To solve the equation l=14j+3k for j, you need to isolate j on one side of the equation. Here's how it is done step by step:
Start with the original equation: l = 14j + 3k Subtract 3k from both sides of the equation to isolate the term with j in it: l - 3k = 14j Divide both sides of the equation by 14 to solve for j: j = (l - 3k) / 14Therefore, the solution to the equation for j is: j = (l - 3k) / 14.
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Mr. Pham wrote the equation below on the board. 18 - 7x = -20.5 What is the value of x?
Answer: The answer should be D(x=5 1/2)
Step-by-step explanation:
Trust me I did the equation and work.
Josh estimates the height of his desk. Which is the best estimate?
EASY 5 POINTS!!!!! You have a 1-gallon paint can in the shape of a cylinder. One gallon is 231 cubic inches. The radius of the can is 3 inches. What is the approximate height of the paint can? Use 3.14 for pi.
A.) 5 inches
B.) 25 inches
C.) 8 inches
D.) 26 inches
Answer:
The height of the cylinder shaped can = 8.17 inches
Step-by-step explanation:
Volume of the cylinder shaped can = 1 gallon
1 gallon = 231 cubic inches
So, Volume of the cylinder shaped can = 231 cubic inches
Radius of the can = 3 inches
[tex]\text{Now, Volume of the cylinder = }\pi\times radius^2\times height\\\\\implies 231=3.14\times 3^2\times height\\\\\implies height=\frac{231}{3.14\times 9}\\\\\implies height\approx 8.17\text{ inchjes}[/tex]
Hence, The height of the cylinder shaped can = 8.17 inches
Jim has three times as many comic books as Charles Charles has two thirds as many as Bob Bob has 27 books how many comic books does Jim have
Charles has 2/3 of bob
bob has 27
so 2/3*27 = 27 *2 = 54/3 = 18
Charles has 18
Jim has 3 times as many as Charles so he has 3 x 18 = 54
jim has 54 comic books
Under what circumstance are two non right triangles congruent
What is the largest possible value of y, if y = - | 3 - x | + 5
what's 6 3/4 divided by 1 7/8
The value of 6 (3/4) divided by 1 (7/8) is 3 (3/5).
What is a fraction?A fraction is a part of the whole represented by a/b, where a and b are any integers
The given numbers are 6 (3/4) and 1 (7/8).
Simplify the mixed fractions:
6(3/4) = 27/4 and 1 (7/8) = 15/8
Now, divide 27/4 by 15/8:
27/4 ÷ 15/8
= 27/4 × 8/15
= 18/5
= 3 (3/5)
Hence, The value of 6 (3/4) divided by 1 (7/8) is 3 (3/5).
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"4. Suppose y varies directly with x. Write a direct variation equation that relates x and y. Then find the value of y when x= 12. y = -10 when x = 2 "
Answer:
5/ 2 x
Step-by-step explanation:
If prices Increase at a monthly rate of 1.4
%, by what percentage do they increase in a year?
The value of a car decreases by 20% per year Mr. Singh for purchase is a $22,000 automobile what is the value of the car the end of the second year
Answer: the answer is $26,400
Step-by-step explanation:
The Panthers, a high school basketball team, charges $6 for adult tickets and $3 for children’s tickets. If 120 people went to the most recent game, and the total earnings for ticket sales was $612, how many children went to the game?
There were 36 children at the game.
There were 50 children at the game.
There were 84 children at the game.
There were 108 children at the game.
Answer:
The answer is 36 children
Step-by-step explanation:
There were 36 children at the game
The number of children who went to the game was 36
What is Linear Equation in 2 variables?
An equation is said to be linear equation in two variables if it is written in the form of ax + by + c = 0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.
Given data ,
Let the number of children be = x
Let the number of adults be = y
Cost of ticket for 1 child = $ 3
Cost of ticket for 1 adult = $ 6
Total number of people who went to the game = 120
So , x + y = 120
Total earnings for the ticket sales = $ 612
Total earnings =
( Cost of one child x Number of children ) + ( Cost of one adult x Number of adult)
Total earnings = 3x + 6y
Now , we have 2 equations to solve
x + y = 120 be equation (1)
3x + 6y = 612 be equation (2)
Multiply equation (1) by 3 , we get
3x + 3y = 360 be equation (3)
Subtract equation (3) from equation (2)
3x + 6y - ( 3x + 3y ) = 612 - 360
3y = 252
Divide by 3 on both sides , we get
y = 84
So , the number of children who went to the game will be
x + y = 120
x + 84 = 120
Subtract 84 on both sides , we get
x = 36
Hence , the number of children who were at the game was 36
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A square with an area of 169 cm^2 is rotated to form a cylinder. What is the height of the cylinder?
Answer:
13 cm
Step-by-step explanation:
Area of the square is [tex]169 \:\:cm^{2}[/tex]
The square is rotated to form a cylinder. Now, we first need to find the side of the square, the cylinder is formed by rotating along its side.
Now area of square [tex]169 \:\:cm^{2}[/tex]
We know that area of square is [tex]\text{side}\times\text{side}[/tex]
So, [tex]\text{side}\times\text{side}=169[/tex]
[tex]\text{side}\times \text{side}=13\times13[/tex]
[tex]\text{side}=13 \:\text{cm}[/tex]
Now, as the cylinder is formed by rotating along its length, and we know that all the sides of a square is equal.
So, one side becomes the height of the cylinder and the other becomes the circumference.
Hence, the height of the cylinder is 13 cm.
Rita attends school 180 days out of the 365 days in a year. For what fraction of the year is Rita in school? Write your answer in simplest form.
the fraction is 180/365
this can get reduced to 36/73
(05.02 MC)
Trevor solved the system of equations below. What mistake did he make in his work?
2x + y = 5
x − 2y = 10
y = 5 − 2x
x − 2(5 − 2x) = 10
x − 10 + 4x = 10
5x − 10 = 10
5x = 0
x = 0
2(0) + y = 5
y = 5
His work should have looked like this.
2x + y = 5
x − 2y = 10
y = 5 − 2x
x − 2(5 − 2x) = 10
x − 10 + 4x = 10
5x − 10 = 10 When he added in both sides, he subtracted 10 from 10,
5x = 20 instead of adding 10 from 10 to make 20.
x = 4
2(4) + y = 5
8 + y = 5
y = -3
(08.03 MC)
A system of equations is shown below:
y = 3x – 7
y = 2x + 1
What is the solution to the system of equations? (1 point)
A. (8, 17)
B. (–8, 17)
C. (–8, –17)
D. (8, –17)
Answer:
(8, 17)
Step-by-step explanation:
Here you have two functions equalling y.
To find x, we set these two functions equal to one another, which eliminates y:
3x - 7 = 2x + 1.
Find x. To do this, subtract 2x from both sides, obtaining x - 7 = 1.
Next, add 7 to both sides: x = 8.
Finally, find y. Do this by subbing 8 for x in either of the two given equations.
Working with the 2nd equation: y = 2(8) + 1 = 17
Thus, the solution is (8, 17).
I believe the answer is (8 , 17)
Samantha loves to download new music. She originally had 52 songs but plans to purchase 2 new songs each week. She wants to know how many songs she will have after 93 weeks. Which equation should she use
The price of a calculator dropped from $32.88 to $25.95. What was the percent decrease in price
Using the formula in model 1, choose the correct answers for the new balance and amount of interest earned in the following compound interest problem. $1,050 at 6%, for 25 years, compounded annually. Total Amount = $ Interest Amount =$
Can anyone please solve the attached file?
Jane noticed as she was doing her morning run that a 12 m flagpole cast a 18 m shadow. A tree was casting a 36 m shadow. The tree was __? ___ m tall.
Factor completely 2x3 + 14x2 + 4x + 28.