Using the theories of probability, we got that 5/9 is the probability that one letter is from each sister's name if the letters from their names are placed on identical cards so that each of cards contains one letter. without replacement.
We know very well that if we want to count number of ways by which r object can be chosen from n objects ,this can be done in [tex]^nC_r[/tex] ways which is equivalent to =(n!/(r!.(n-r)!)
Here are the same case, we have 10 cards, in each of the card there is letter written on it. So number of ways to choose two cards such that it contains any letter is can be done in [tex]^1^0C_2[/tex] ways which is equivalent to 45 ways.
Similarly, number of ways of choosing card which contains only Cybil`s name =[tex]^5C_2[/tex] ways=10 ways.
Similarly, number of ways of choosing card which contains only Ronda`s name =[tex]^5C_2[/tex] ways=10 ways.
So the number of ways containing one letter from each name = 45 - 10 - 10 = 25
So....the probability of choosing one of these sets = 25 / 45 = 5 / 9 =0.55
Hence, Cybil and Ronda are sisters. the letters from their names are placed on identical cards so that each of cards contains one letter. without replacement, two cards are selected at random from the cards. the probability that one letter is from each sister's name is = 5/9.
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(Complete question) is:
cybil and ronda are sisters. the 10 letters from their names are placed on 10 identical cards so that each of cards contains one letter. without replacement, two cards are selected at random from the 10 cards. what is the probability that one letter is from each sister's name? express your answer as a common fraction.
Piper invested $4,700 in an account paying an interest rate of 4. 8% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 19 years?.
Assuming no deposits or withdrawals are made, the amount in the account after 19 years is: 11,454. 133.
How to find the amount in the account?Using this formula
A = P(1+r/100)ⁿ
Where:
A = Amount =?
P = Principal = $4700
r = Interest rate =4.8%
n = the number of periods =19 years
Let plug in the formula
A = 4,700 (1 + 4.8/100)¹⁹
A = 4,700 (1 + 0.048)¹⁹
A = 4,700 (1.048)¹⁹
A = $11,454. 133
Therefore the amount is $11,454. 133.
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9. Emily measured the depth of water in a bathtub at two-minute intervals after the tap was turned off and the
stopper released. The table shows her data.
a) Make a scatter plot for the data.
b) Describe the correlation of the scatter plot.
c) What will the approximate depth be at 15 seconds?
From the data in the table relating time and depth, we have that:
a) The scatter plot is graphed at the end of the answer.
b) The scatter plot has negative correlation.
c) The estimate for the depth at a time of 15 seconds is of 50.37 cm.
How to built the scatter plot?The scatter plot is built inserting all the points of the table in a graph, which are in the following format:
(Time in seconds, Depth in cm).
Hence the scatter plot will be composed by a set of points, without an image, as is shown at the end of the answer.
The points from the table are listed as follows:
(2, 47), (4, 41), (6, 38), (8, 37), (10, 32), (12, 24), (14, 20), (16, 19).
As the input variable time increases, the output variable depth decreases, meaning that the points in the scatter plot also follow the format of a decreasing line, hence there is negative correlation in the scatter plot.
These points are also inserted into a linear regression calculator to built the line of best fit, which is defined as follows:
y = -2.07x + 50.89.
At 15 seconds, the estimate is obtained replacing the lone instance of x in the equation by 15, hence:
y = -2.07 x 0.25 + 50.89 = 50.37 cm.
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a stats 10 test has 4 multiple choice questions with four choices with one correct answer each. if we just randomly guess on each of the 4 questions, what is the probability that you get exactly 1 question correct? find the nearest answer.
if we just randomly guess on each of the 4 questions, Then the probability that you get exactly 1 question correct is 1/4.
Probability formula: P(E) = favourable outcomes/Total outcomes
The number of questions is 10
The options for each question are 4.
Possible answers are 1.
Then,
favourable events = 1 × 10= 10
Total events = 4× 10= 40
Now, find the probability by putting the values as follows:
P(E) = favourable outcomes/Total outcomes
P(E) = 10/40
P(E) = 1/4
Therefore, the probability of doing all questions correct is 1/4
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Correct answer get's free 50 points
The correct statement regarding the solution of the inequality 8x - 6 < 3x + 19 is given as follows:
D. She knows that the solution must be either all the values less than 5 or all the values greater than 5.
What is the solution to the inequality?The inequality is presented as follows:
8x - 6 < 3x + 19.
Lin finds the value of x = 5 for which the two sides of the inequality are equal. Then, there are only two cases for the solution, which are listed as follows:
All values that are less than 5.All values that are greater than 5.Thus option D gives the correct option regarding how to find the solution.
The justifications for the other options being wrong are given as follows:
Options A, C and D: an inequality gives a range of values as a solution, not a single value, hence substituting the value on the inequality you verify if the value is a solution, but you do not solve, that is, you do not find all the values that are solutions to the inequality.Option E: The inequality is an open inequality, meaning that x = 5 is not a solution to the inequality.More can be learned about inequalities at https://brainly.com/question/25275758
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Answer:
I think its D.... id/k I think it is.
Step-by-step explanation:
Can anyone please help me with this? I don't get it.
Answer:
739
Step-by-step explanation:
2217 (weight) / 3 ( # of blocks)
Write 36 a product of it' prime factor. Write the factor in order, from mallet to larget
The factor of 36 in order from smallest to largest is 2 × 2× 3× 3.
Prime factor:
Factors are the numbers you multiply together to get another number. In simple words, a prime factor is finding which prime numbers multiply together to make the original number.
Here we have to find the prime factor 36.
That is we have to find the smallest multiplication of digits to get the value.
36 = 2 × 2 × 3 × 3
Therefore the prime factor is 2 × 2×3×3.
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There are 50 tudent in cla. Boy make up 20% of the cla. 60% of the boy wear glae. How many boy in the cla wear glae?
The boys in the class that wear glae are 6 people.
The boys in the class that wear glae can be calculated as follows:
First we should calculate how many boys there are in the class. We can calculate it by multiplying the percent of the boys to the total students.
Boys in the class = [tex]\frac{20}{100} X 50[/tex] = 10 people.
Thus, we can calculate the boys who wear the glae by multiplying the percent of the boys wearing glae of the boys in the class.
Boys wear glae = [tex]\frac{60}{100} X 10[/tex] = 6 people.
Hence, The boys in the class that wear glae are 6 people.
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Can someone please help
After solving the value of x is 2.
From the figure:
Let ABCDE be the figure such that:
AB = 6x , BC = 6 , CD = 4,and DE = CE - CD = 12 - 4 = 8.
BD and AE are parallel lines such that:
AB/BC = ED/CD
6x/6 = 8/4
x = 8/4
x = 2.
Therefore After solving the value of x is 2.
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Other than itself, which angle is congruent to ∠DEA?
Please help!!!
Answer:
Angle CEB
Step-by-step explanation:
They are vertical angles
:]
Below, the two-way table is given for a class
of students.
Sophomore
Freshmen
Male
4
Female 3
Total
6
4
17
Juniors Seniors Total
2
6
2
3
If a female student is selected at random, find the
probability that the student is a senior.
P(Senior | Female ) = [? ]%
Round to the nearest whole number.
Enter
Answer:
19%
Step-by-step explanation:
Of the female students, there are:
3 freshmen4 sophomores6 juniors3 seniorsOut of 16 total students, 3 are juniors, so the probability is [tex]\frac{3}{16} \approx 19\%[/tex]
There are 5 player on a baketball team. In a game 4 player cored 6 point each. The team cored a Tell how to make ene of the problem total of 34 point. How many point did the other player core?
Points scored by the last player is 10 points. this can be calculated by using BODMAS rule by forming equation.
What is an equation ?
A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
Main body:
Points scored by 4 players = 6 each
Total points scored by 4 players = 4*6
= 24
Total points scored by team = 34
Points scored by last player or 5th player = total points - points scored by 4 players
Points scored by 5th player = 34-24
= 10
Hence point scored by last player is 10.
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Nolan has five more quarters and dimes and seven fewer nickels and dimes. He has 25 coins. How many of each coin does he have? How much money in dollars and cents is it worth?
Answer:
9 dimes, 4 nickels, 12 quarters
90 cents + 20 cents + 300 cents = 410 cents = $6.83
Step-by-step explanation:
q=5+d
n=d-7
q+n+d=25
5 + d + d - 7 + d = 25
3d-2=25
3d=27
d=9
25 - 9 = 16 nickels and quarters
q + n = 16 ---> q=16-n
n=d-7 ---> d=n+7
q=5 + n + 7
q=n+12
n+12 = 16-n
2n=4
n=4
25-(9+4)= 12 quarters
He has 2 nickels, 9 dimes, and 14 quarters, with a total value of $4.50
Step-by-step explanation:I am going to assume that the "and" in "five more quarters and dimes" and the "and" in "seven fewer nickels and dimes" is actually "than" because otherwise, there is no context in this question. If my answer is incorrect, please tell me how to correctly interpret this question.
In this scenario, the "and" in "five more quarters and dimes" and the "and" in "seven fewer nickels and dimes" is actually "than."
Amount of nickels - x
If there are seven fewer nickels than dimes, the amount of dimes is x + 7. There are five more quarters than dimes, so the amount of quarters is x + 7 + 5, which equals x + 12.
x + x + 7 + x + 12 = 253x + 19 = 253x = 6x = 2
Therefore, there are 2 nickels. Now we must figure out the number of quarters and dimes.
x + 7 = 9
x + 12 = 14
There are 9 dimes and 14 quarters.
Nickels are each worth 5 cents. 2 times 5 is 10 cents.
Dimes are each worth 10 cents. 9 times 10 is 90 cents.
Quarters are each worth 25 cents. 14 times 25 is 350 cents.
Now, we add. 10 + 90 + 350 = 100 + 350 = 450.
REMEMBER, THIS IS IN CENTS. WE MUST STILL CONVERT IT INTO DOLLARS.
450 divided by 100 is $4.50
On November 1st, Halloween costumes
were off their original price. If a bat
costume usually costs $28, how much
will it cost on November 1st?
$21.00
25% off 28= 7
28-7=21
-0.6a^2b * (-10ab^2)
please help :)
Answer:
evaluation or perhaps difference
Step-by-step explanation:
ex: 6b 2a 2b+1
diff: 6(2b+1)b 2 a 2b
Keilantra has a toy car collection of 400 toy cars. She keeps 268 of the toy cars on her wall. What percentage of Keilantra's toy car collection does she keep on her wall?
Answer:
67%
Step-by-step explanation:
[tex]\frac{268}{400}[/tex] X 100
Answer:
67%
Step-by-step explanation:
268 ÷ 400 = 0.67 = 67%
A number is raised to the third power, then subtracted from 15 to get 7. What is the number squared?
Answer:
4
Step-by-step explanation:
Let x be the unknown number.
[tex]\begin{aligned}&\textsf{A number is raised to the third power}: & x^3&\\&\textsf{Subtracted from 15}: & 15-x^3&\\&\textsf{To get 7}: & 15-x^3&=7\end{aligned}[/tex]
Solve the found equation for x:
[tex]\begin{aligned}&\textsf{Given}: & 15-x^3&=7\\&\textsf{Subtract $15$ from both sides}: & -x^3&=-8\\&\textsf{Divide both sides by $-1$}: & x^3&=8\\&\textsf{Rewrite $8$ as $2^3$}: &x^3&=2^3\\&\textsf{Cube root both sides}: & x&=2\end{aligned}[/tex]
Therefore, the number squared is:
[tex]\implies x^2=2^2=4[/tex]
What is the rectangular form of 12(cos(π) + i sin(π))?
12
-12
12 + i
–12 + i
Answer:
12-12-12+i-12+i =0-i
.
.
.
,
Which of the following are two-dimensional shapes? Select three options.
circle
cube
cylinder
hexagon
oval
pyramid
Answer:
Circle, hexagon, and oval
Step-by-step explanation:
They are all 2d.
The tap can fill up the bathtub in 22 minutes. The capacity of the bathtub is 176 L
How much water is added to the tub per minute?
Answer:
8.8 L
Step-by-step explanation:
volume/time
176/22
=8.8
Write 8128 as the sum of consecutive odd cubes.
The sum of consecutive odd cubes of 8128 is 1³+3³+5³+7³+9³+11³+13³+15³
Therefore, 1+27+125+343+729+1331+2197+3375=8128
What are consecutive numbers?Consecutive numbers are those that come after each other in descending order from the smallest to the largest. The difference between consecutive numbers is always fixed and follows a predictable pattern. For example, the first three consecutive natural numbers are 1, 2, 3. The simplest way to find consecutive numbers is to look at the number set and find the number that is either before or after the term of interest.
We know that consecutive odd numbers are 1,3,5,7,9,11,13,15,17..
Here 8128 is a perfect square
And it can be written as the sum of consecutive odd cubes as follows:
1³=1
3³=27
5³=125
7³=343
9³=729
11³=1331
13³=2197
15³=3375
The sum of consecutive odd cubes of 8128 is
=1³+3³+5³+7³+9³+11³+13³+15³
=1+27+125+343+729+1331+2197+3375
=8128
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5. Gabi will graph f(x) = x and m(x) = f(x). Mark each statement as true or false. If false,
rewrite as true in the space below.
a. The slope of m(x) will be steeper than f(x).
_b. The y-intercept of m(x) will be units up from f(x).
d. g(x) = f(x − 3)
The Slope of the first function is greater than the slope of the second function. We can say that the function f(x) =x is steeper than the second function
What is a Slope?
A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.
A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, m = y/x, where m is the slope, can be used to express the change in the y coordinate with regard to the change in the x coordinate.
Take notice that tan = y/x.
In the given question, we have: two functions:
So, finding the slope of each of the functions;
The slope of the first function; f(x) =x is 1;
The slope of the second function: m(x) =[tex]\frac{3}{5} f(x)[/tex];
Since the Slope of the first function is greater than the slope of the second function. We can say that the function f(x) =x is steeper than the second function because the graph depends on the slope.
Hence,
the Slope of the first function is greater than the slope of the second function. We can say that the function f(x) =x is steeper than the second function.
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13. At Greenville High School 1/3 of the students
are involved in sports. Of the students
involved in sports 20% play football. If there
are 3,000 students at the school, how
many play football? (Example 5)
Out of 3000 students at the school , 200 student plays foot ball .
In the question ,
it is given that ,
fraction of students that are involved in sports at Greenville High School = 1/3 of total students ,
percent of students that plays football = 20% of sports students .
given that the total number of students present at the school = 3000
So , the number of students involved in sports = (1/3) × 3000
= 1000
number of students who plays football = 20% of 1000
= 0.20 × 1000 ....because 20% = 0.20
= 200
Therefore , Out of 3000 students at the school , 200 student plays foot ball .
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2.025 as a mixed number
a dog breeder is planning to buy more dog food. he makes a table showing how many pounds of food he will have after shopping the table is based on.how much he spends and how much food he already has which equation generates the table
The linear function that models the data-set is given as follows:
v = 4 + 0.4x.
What is a linear function?The slope-intercept representation of a linear function is presented as follows:
y = mx + b
The coefficients of the function and their meaning are obtained as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x increases by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the output y of the function when the input variable x assumes a value of 0.For this problem, the values of these parameters are given as follows:
Slope of m = 0.4, as when the input increases by 20, the output increases by 8, hence m = 8/20 = 0.4.Intercept of b = 4, as when the input is of zero, the output is of 4.Hence the equation is given as follows:
v = 4 + 0.4x.
Missing InformationThe table is given by:
Money Spent (x) $0 $20 $40 $60
Pounds of Food (v) 4 12 20 28
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what is the value of x in the equation 0.5x+3=4.5?
Answer:
x = 3
Step-by-step explanation:
Collect like terms
0.5x = 4.5 - 3
0.5x = 1.5
Divide both sides by 0.5
0.5x/0.5 = 1.5/0.5
x = 3
Using fractions,
1/2x = 9/2 - 3
1/2x = 3/2
Divide both sides by 1/2
x = 3/2÷1/2
Reciprocate
x = 3/2 × 2/1
x = 6/2
x = 3
The velocity, V, of a specific object being dropped from a particular height, h, can be found by the radical function V equals the square root of the quantity 2 times h times a end quantity where a represents the acceleration in ft/sec2. If the acceleration due to gravity is 32.2 ft/sec2, at what height should you drop an object in order for it to have a velocity of 60 ft/sec?
0.9 feet
55.6 feet
55.9 feet
3,864 feet
The height should you drop an object in order for it to have a velocity of 60 ft/sec is 55.9 feet
How to find the heightThe equation given in the problem is written below
v = √2ha
velocity, v = 60 ft/sec
height, h = ?
acceleration due to gravity, a = 32.2ft/sec^2
The problem asks for height hence we make h the subject of the formula
v = √2ha
v^2 = 2ha
h = v^2 / 2a
substituting the values in to the equation
h = 60^2 / (2 * 32.2)
h = 3600 / 64.4
h = 55.9 feet
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……………………………………………………..
Answer:
-11, -2, 3, 6
-16, -5, 19, 21
Step-by-step explanation:
Find the LCM of 2 and 3 using lists of multiples.
Answer:
Multiples of 2 = 2, 4, 6, 8, 10, 12
Multiples of 3 = 3, 6, 9, 12, 15,18
The LCM is 6.
Step-by-step explanation:
21. A basket holds n apples. You pick (2n - 3) apples, and your friend picks
(n+4) apples. How many apples do you and your friend pick together?
How many baskets do you need to carry all the apples? Justify your answer.
Answer:
21. A basket holds n apples. You pick (2n - 3) apples, and your friend picks
(n+4) apples. How many apples do you and your friend pick together?
How many baskets do you need to carry all the apples? Justify your answer.
Step-by-step explanation:
(2n - 3)(n + 4) binomial times a binomial equals
2n^2 + 5n - 12
Meshea sold 12 dresses in 120 minutes at this rate how many hours will it take her to sell 144 dresses
Answer: 144 dresses in 1440 minutes.
Step-by-step explanation:
Divide 144 and 12 you get 12. So you multiply 12 and 120 and you get 1440.
The rate is 120min/12dresses. Let's simplify it.
12/120 = 10min/1dress (or just 10)
Lets use this rate for 144 dresses
10 x 144 = 1140
It will take 1440 minutes to sell 144 dresses.