Answer:
a)
the probability that Celia is first in line is 1/n.
b)
the probability that Celia is first in line and Felicity is last in line is 1/n(n-1)
c)
the probability that Celia and Felicity are next to each other in the line is 2/n
Step-by-step explanation:
Given the data in question;
a) Celia is first in line?
the total ways are; n! to place n kids in n places in orderly fashion.
now, if Celia is the first kid, we have to order remaining n-1 kids
(n-1)! / n! = 1/n
therefore, the required probability is 1/n.
b) Celia is first in line and Felicity is last in line?
the total ways are; n! to place n kids in n places in orderly fashion,
now, if Celia is the first and Felicity is the last kid, we order the remaining n - 2 kids, which can be done in (n-2)!
(n-2)! / n! = 1 / n(n-1)
therefore, the required probability is 1 / n(n-1)
c) Celia and Felicity are next to each other in the line
the total ways are; n! to place n kids in n places in orderly fashion,
now, if Celia and Felicity as single object, so that they can be put together, we arrange n-1 objects which can be done in (n-1)! ways.
But also these 2 can change the place so in total there are 2(n-1)! ways.
2(n-1)! / n! = 2/n
Therefore, the required probability is 2/n
Create a model to show that 2(2x + 3y) = 4x + 6y
Pls
Answer:
0=0
Step-by-step explanation:
2(2x + 3y)=4x+6y
4x+6y=4x+6y
4x+6y-6y=4x+6y-6y
4x=4x
4x-4x=4x-4x
0=0
True for all
Greg feeds his dog 2/3 pounds of dog food for each meal. Greg has just bought 18 pounds of dog food. For how many meals will the food last? Write your answer in simplest form
please show all work i’ll mark brainliest
Answer:
Step-by-step explanation:
Draw a picture to see that the radius must be 7.
What is the length of side a?
Answer:
do provide the figure dude.
Paula made this model to show the sum of two mixed numbers. Write the addition equation shown by the model and solve it.
You can write out the fraction names or use the forward slash (/) on your keyboard to represent the fraction bars.
A number line from zero to one partitioned into thirds. There is a gray rectangle above the number line stretching from zero to three and two thirds. To the right is a darker gray rectangle above the number line stretching from three and two thirds to six and one third.
Your answer:
Answer:
[tex]3\frac{2}{3} + 2\frac{2}{3} = 6\frac{1}{3}[/tex]
Step-by-step explanation:
Given
See attachment for number line
Required
Determine the model
From the attachment, we can see that each partition is 1/3
The gray rectangle covers 11 partitions.
So:
[tex]Gray = 11 * \frac{1}{3}[/tex]
[tex]Gray = \frac{11}{3}[/tex]
Express as a mixed number
[tex]Gray = 3\frac{2}{3}[/tex]
The black rectangle covers 8 partitions
So:
[tex]Black= 8 * \frac{1}{3}[/tex]
[tex]Black= \frac{8}{3}[/tex]
Express as a mixed number
[tex]Black= 2\frac{2}{3}[/tex]
So, the model is:
[tex]Gray + Black = Total[/tex]
Where Total is the point where the black rectangle stops
[tex]3\frac{2}{3} + 2\frac{2}{3} = 6\frac{1}{3}[/tex]
Gustavo also went to the same store and has a 30% off
coupon. He bought a hoodie and saved $8.10 after
using the coupon. What is the original price of the
hoodie?
Answer:
Original Price was $27.00
Step-by-step explanation:
27*.30=8.10
HELP PLEASE PLEASE PLEASE
please please help me figure this out!!
Answer:
154
Step-by-step explanation:
180-26= 154
Supplementary angles equal 180
Number 3 answered please
Answer:
Step-by-step explanation:
n=3p, d=p-2
10d+5n+p=110 using n and d from above makes this become
10(p-2)+5(3p)+p=110
10p-20+15p+p=110
26p-20=110
26p=130
p=5
n=3p=3(5)=15
d=p-2=5-2=3
So she has 3 dimes, 15 nickels, and 5 pennies.
If m= 3 in the equation 2m=4-n, find the value of n.
Answer:
-2
Step-by-step explanation:
Which of the lists of letters all have rotational symmetry?
C,H, N, X
N.O.S. Z
H.J.N.S
F.H. X. Z
Answer:
N, O, S, Z, which will be B
Step-by-step explanation:
4x + y=7
2x - 7y=1
If (x,y) is the solution to the given system of equations, what is the Value of X?
Answer:
[tex]x = \frac{5}{3} [/tex]
The human resources department of an engineering company gives IQ tests to a randomly selected group of new hires every year. They claimed that the mean IQ score of new hires, , from this year is greater than or equal to the mean IQ score of new hires, , from last year. This year, 95 new hires took the test and scored an average of 112.2 points with a standard deviation of 14.0 . Last year, 70 new hires took the IQ test and they scored an average of 117.8 points with a standard deviation of 14.5 . Assume that the population standard deviation of the IQ scores from the current year and the last year can be estimated by the sample standard deviations, since the samples that are used to compute them are quite large. Is there enough evidence to reject the claim of the human resources department, at the 0.01 level of significance
Answer:
Step-by-step explanation:
Null hypothesis: [tex]\mathbf{H_o: \mu_1 \ge \mu_2}[/tex]
Alternative hypothesis: [tex]\mathbf{H_o: \mu_1< \mu_2}[/tex]
This type of test statistic is a z test statistics
1st 2nd
Sample mean x = 112.2 117,8
Standard deviation σ = 14.0 14.5
Sample size n = 95 70
Point estimate [tex]\bar x_1 - \bar x_2[/tex] = -5.60
Standard error [tex]\sigma_{x_1-x_2}= \sqrt{\dfrac{\sigma_1^2}{n_1} +\dfrac{\sigma_2^2}{n_2} }[/tex]
[tex]= \sqrt{\dfrac{14.0^2}{95} +\dfrac{14.5^2}{70} }[/tex] = 2.2509
Test statistics [tex]z=\dfrac{x_1 - x_2}{\sigma_{x_1-x_2}}[/tex] [tex]=\dfrac{112.2- 117.8}{2.2509}[/tex] = - 2.4878
P-value = 0.012
No, there is no enough evidence Since p-value is greater than 0.01.
Fran’s snowmobile weighs 0.8 ton. The weight of the snowmobile is
pounds
Answer: 0.8 ------ 1,600
Step-by-step explanation:
Jessie started a record collection with 8 records. Each week he added 3 records to his collection. Riley started her record collection with 23 records. Each week she gave away 2 records.
a) Write an equation to represent the number of records in Jessie's collection based on the number of weeks he has been collecting records.
3 per week + blank=8 Step-by-step explanation: brainly plz
1) The diameter of a circle is 7.5. Find the circumference to the nearest
tenth. Show all work *
Your answer
Answer:
Step-by-step explanation:circumference = pi x diameter.
Using 3.14 for pi
Circumference = 3.14 x 7.5 = 23.55
Rounded to the nearest tenth = 23.6
The circumference of the circle with a diameter of 7.5 is, C = 23.6
Used the concept of the circumference of the circle that states,
The circumference of the circle or perimeter of the circle is the measurement of the boundary of the circle. The formula used to calculate the circumference of the circle with radius 'r' is,
C = 2πr
Given that,
The diameter of a circle is 7.5.
Hence, The radius of a circle is,
7.5/2 = 3.75
So, The circumference of the circle with a radius of 3.75 is,
C = 2 × 3.14 × 3.75
C = 23.55
Rounded to the nearest tenth,
C = 23.6
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x2-12x-3=10 please help
Answer:
x= 13, -1
Step-by-step explanation:
Greg spent $47.45 on five books. If each book cost the same amount, how much does one book cost?
Answer:
Greg spent 9.49 cents on the book
The cost of one book is A = $ 9.49
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
Let the cost of 5 books be = $ 47.45
Now , the cost of one book is A
where A = 47.45 / 5
On simplifying the equation , we get
A = $ 9.49
Hence , the cost is A = $ 9.49
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Stefan sells Jin a bicycle for 135 and a helmet and a helmet for 19 the total cost for Jin is 140% of Stefan spent originally to buy the bike and helmet how much did Stefan spend originally how much money did he make by selling the bicycle and helmet to Jin
Answer:
Originally Stefan spent $ 110, and made $ 30 selling the bike and helmet to Jin.
Step-by-step explanation:
Given that Stefan sells Jin a bicycle for $ 135 and a helmet for $ 19, and the total cost for Jin is 140% of what Stefan spent originally to buy the bike and helmet, to determine how much did Stefan spend originally and how much money did he make by selling the bicycle and helmet to Jin, the following calculation must be performed:
100 + 140 = 240
140 = 135 + 19
100 = X
(100 x (135 + 19)) / 140 = X
100 x 154/140 = X
15,400 / 140 = X
110 = X
So originally Stefan spent $ 110, and made $ 30 selling the bike and helmet to Jin.
Which of the following examples has a unit rate of 70 miles per hour? Select all
that apply.
A) 210 miles in 3 hours
B) 420 miles in 6 hours
C) 280 miles in 5 hours
D) 560 miles in 8 hours
E) 560 miles in 7 hours
Answer:
A, B and D are the answers.
Answer:
A, B, D.
Step-by-step explanation:
Find the slope of the line 8x-2y=11
A farmer recently sold a large plot of land. The sale decreased his total acreage by 10%.
Lett be the original acreage. Find two equivalent expressions that will give the new acreage.
Answer: t - 0.1t and 0.9t
Step-by-step explanation:
Let the original acreage be represented by t.
Since there was a sale which ended up reducing the acreage by 10%, the expression for the new acreage will be:
= t - (10% × t)
= t - (0.1 × t)
= t - 0.1t
= 0.9t
Therefore, the equivalent expressions will be "t - 0.1t" and 0.9t
Determine if the following statements are true or false. If true give a reason or cite a theorem and if false, give a counter example.
a. If {a _n} is bounded, then it converges.
b. If {a _n} is not bounded, then it diverges.
c. If {a _n} diverges, then it is not bounded
Give an example of divergent sequences {a _n} and {b _n} such that {a _n + b _n} converges
Answer:
a. False the series [tex]\sum\limits_{i=1}^\infty (-1)^n[/tex]is bounded but does not converge
b. False, xₙ = n + (-1)ⁿ⁻¹(n - 1) does not diverge to infinity but it is not bounded for n ≥ 1
c. False some bounded sequences are divergent
An example of divergent sequences, aₙ, and bₙ, such that aₙ + bₙ converges is [tex]a_n = \sum\limits_{n} \dfrac{1}{n} , \, b_n = \sum\limits_{n} \dfrac{-1}{n}[/tex]
[tex]\sum\limits_{n} \dfrac{1}{n} + \sum\limits_{n} \dfrac{-1}{n}[/tex] is convergent
Step-by-step explanation:
a copy machine prints 10 copies per 1/4 at what rate in copies per minute does the copy machine print?
assistance with trying to figure out how to solve this question.
Answer:
137.24 mm²
Step-by-step explanation:
Big square = 9x9=81
Small rectangle at bottom = 2x3=6
Quarter Circle = 1/4(3.14)(8)(8)=50.24
81+6+50.24=137.24
Which function is shown in the graph below?
10
8
.
.4
0.5, 0.4(1.0)
ᎨᎲᎢ
4
0
8
-2
1-4
1-3
-10
Answer:
square root function is the correct answer
The solution is, y = 2 ^ (x + 2) +3, is the function is shown in the graph below.
What is graph?In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.
here, we have,
For this case we observe the cut point with the y axis in:
(0, 7)
The function that complies with this is:
y = 2 ^ (x + 2) +3
We have then:
y = 2 ^ (0 + 2) +3
y = 2 ^ (2) +3
y = 4 + 3
y = 7
Answer:
The answer for this case is given by:
y = 2 ^ (x + 2) +3
option 2
Hence, The solution is, y = 2 ^ (x + 2) +3, is the function is shown in the graph below.
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Consider the inequality x > −1.5.
Determine a value of x makes this inequality true.
Step-by-step explanation:
all intiger which is greater than-1.5
(2x -3) + (4c + 20) i need help
Answer:
=2x+4c+17
Step-by-step explanation:
(2x-3)+(4c+20)
=2x-3+4c+20
=2x+4c-3+20
=2x+4c+17
Which of the following figures shows a 1/4 -turn in the clockwise direction?
what is the H.C.F of 2³×3²
