There are 65,800,850,944,000 ways to divide the 40 students into 8 discussion groups, each consisting of 5 students.
To find the number of ways to divide 40 students into 8 discussion groups of 5 students each, we'll use a combination formula.
The number of ways to choose 5 students out of 40 for the first group is given by C(40, 5).
After choosing 5 students for the first group, there will be 35 students left for the second group.
The number of ways to choose 5 students out of these 35 for the second group is C(35, 5).
We continue this process until all 8 groups are formed.
The total number of ways to divide the students into groups is the product of the combinations for each group. So, the total number of ways is:
Total ways [tex]=^{40}C_5 \times ^{35}C_5 \times^{30}C_5 \times ^{25}C_5 \times ^{20}C_5 \times ^{15}C_5 \times ^{10}C_5 \times ^{5}C_5[/tex]
Total ways = 65800850944000
Hence, there are 65,800,850,944,000 ways to divide the 40 students into 8 discussion groups, each consisting of 5 students.
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janesa has 24 coins in her pocket worth exactly $1.00. she tells her younger brother jackson that he can have the coins if he correctly guesses how many of each coin she has. she gives him the hint that there are only nickels and pennies. complete the equation that represents the total value of the nickels and p pennies 5( blank ) + p = 100
Answer:
Number of Nickels = 19
Number of pennies = 5
Step-by-step explanation:
The type of coins that Janessa has = nickels and pennies.
Janessa has a total number of 24 coins
The sum of the nickels and pennies = $1.00
Let us represent the number of nickels as x
The number of pennies as y
Hence, our system of equations is :
x + y = 24..... Equation 1
x = 24 - y
A nickel is worth 5 cents.
1 nickel = $0.05
A penny is worth 1 cent.
1 penny = $0.01
Therefore,
$0.05× x + $0.01 × y= $1.00
0.05x + 0.01y = 1.00........Equation 2
Substitute 24 - y for x in Equation 1
0.05(24 - y) + 0.01y = 1
1.2 - 0.05y + 0.01y = 1
1.2 - 1 = 0.05y - 0.01y
0.2 = 0.04y
y = 0.2/0.04
y = 5
We have 5 pennies
x = 24 - y
x = 24 - 5
x = 19
We have 19 nickels
y< 4x – 1
y>-8x + 5
Answer:
m=4
m: 8
Step-by-step explanation:
Translate the sentence into an equation.
Seven times the sum of a number and 2 is 6.
Use the variable y for the unknown number.
Answer:
7(y+2)=6
Step-by-step explanation:
its right
Taylor buys dog food for $1.25 a pound. How much will he pay for 8.6 pounds of dog?
Answer:
Taylor will pay $10.75
Step-by-step explanation:
If 1.25 PER/for each/for one pound that means you would multiply. So the equation is 8.6 x 1.25 = 10.75
Hope that helps and have a great day!
Answer:
10.75
Step-by-step explanation: 1.25 times 8.6 is 10.75 so that is the answer.
Please help me ...............,..
Answer:
Angle A and H are Alternate exterior angles and they are congruent.
andre has x dollars. He buys lunch using 1/6 of his money and earns 8$ by doing chores after school
A newspaper is launching a new advertising campaign in order to increase the number of daily subscribers. The newspaper currently (t0) has 26,000 daily subscribers and management expects that number, S(t), to grow at the rate of subscribers per day, where t is the number of days since the campaign began. How long (to the nearest day) should the campaign last if the newspaper wants the number of daily subscribers to grow to 49,000?
Answer:
57 days
Step-by-step explanation:
Given that:
t(0) = 26000
Growth rate (S'(t)) = 80t^1/2
Targeted number of subscribers = 49000
Take the integral of the growth rate :
∫80t^1/2dt = [(80t^(1/2 + 1)) / 1/2 + 1] + C
[(80t^(1/2 + 1)) / 1/2 + 1] + C = (80t^3/2) / 3/2 + C
(80t^3/2) * 3/2 + C = (160/3)t^3/2 + C
(160/3)t^3/2 + C
Let C = t(0)
(160/3)t^3/2 + 26000 = 49000
(160/3)t^3/2 = 49000 - 26000
(160/3)t^3/2 = 23000
Multiply both sides by 3/160
t^3/2 = 23000* 3/160
t^3/2 = 69000/160
t^3/2 = 431.25
t^(3/2 * 2/3) = 431.25^2/3
t = 57.080277
t = 57 days (approx.)
A gallon of gas costs an average of two dollars is Betty spends $144 a month on gas determine how many gallons of gas she uses a month
Answer:
she uses 72 gallons
Step-by-step explanation:
just do 144/2 and the answer is 72
if you wanna check your answer just do 72x2 and it equals 144
4,378 divided by 15help
Answer:
291
Step-by-step explanation:
Answer:291.87
Step-by-step explanation:
You have 8 donuts and you want to give 1/4 of them to a friend. How many donuts would your friend get?
Answer: pretty sure the friend would get 2 donuts
Step-by-step explanation:
your job requires that you work at least 40 hours a week you have already worked 15 and there are 4 more days left in the week how many hours do you have to work each day to get at least 40 hours: inequality and solution
Answer:
6.25 hours
Step-by-step explanation:
this is rather simple really,
first, you have to work 40 hours a week
you have already worked 15 so now you can subtract that
40-15= 25hrs
if you have 4 more days of the week you divide the remaining hours by the days left
25/4= 6.25hrs
that would be the bare minimum of hours for you to work a 40 hour week.
A number is divided by 4, and the quotient is added to 3. The result is 24. What is the number? (Please show how you got it)
(n/4) + 3 = 24
Answer:
84
Step-by-step explanation:
(x/4) + 3 = 24
so in this case try and make x the subject or in other words try to leave x on one side of the equation.
(x/4) = 24 - 3
(x/4) = 21
now multiply 21 by 4 using cross multiplication
so x= 84
2)If a $100 deposit is made at a bank that pays 12% per year, compounded annually, determine how long it will take for the investment to reach $2000.
Answer:
It will take 26.4 years for investment to reach $2000
Step-by-step explanation:
2000=100(1+.12)^x
20=1.12^x
㏒_{20} 1.12=x
log 1.12/ log 20=x
x= 26.434
The number of years that should be taken for reaching $2,000 is 26.40 years.
Given that,
The deposit made at the bank is $100.The interest rate per year is 12%.And, the reaching amount is $2,000.Based on the above information, the calculation is as follows:
[tex]2000=100(1+.12)^x\\\\20 = 1.12^x[/tex]
Now apply log to both sides
[tex]\frac{log1.12}{log20} = x[/tex]
x = 26.4 years
Therefore we can conclude that the number of years that should be taken for reaching $2,000 is 26.40 years.
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estimate the answer for 1 2/3 x 5 1/10 (type a whole number
Answer:
Exact Form:
17/2
Decimal Form:
8.5
Mixed Number Form:
8 1/2
Given a normal distribution with a mean of 125 and a standard deviation of 14, what percentage of values is within the interval 111 to 139?
A. 32%
B. 50%
C. 68%
D. 95%
E. 99.7%
Answer:68%
Step-by-step explanation:
just took this test
The percentage of values is within the interval 111 to 139 will be "68%".
ProbabilityAccording to the question,
Mean = 125
Standard deviation = 14
Let,
The random variable be "X".
Now, the probability:
→ P(111 < X < 139) = P (111 - 125 < X - 125 < 139 - 125)
= P(-14 < X - 125 < 14)
= P(-[tex]\frac{14}{14}[/tex] < [tex]\frac{(X-125)}{14}[/tex] < [tex]\frac{14}{14}[/tex])
= P(-1 < Z < 1)
When, Distribution function "[tex]\phi[/tex]" now,
= [tex]\phi[/tex](1) - [tex]\phi[/tex](-1)
= [tex]\phi[/tex](1) - 1 + [tex]\phi[/tex](1)
= 2 × [tex]\phi[/tex](1) - 1
= 2 × 0.8413 -1
= 1.6826 - 1
= 0.6826 or,
= 68%
Thus the above answer i.e., "option C" is correct.
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What is the coefficient of determination for this data set?
Answer:
0.91
explanation:
Xis normally distributed with mean 1,000 and standard deviation 250. What is the probability that X lies between 800 and 1, 100?
Answer:
0.4435
Step-by-step explanation:
Given that :
X is normally distributed:
mean(m) = 1,000
standard deviation (s) = 250
probability that X lies between 800 and 1,100?
Using the relation :
X = 800
Zscore = (x - m) / s
Zscore = (800 - 1000) / 250
Zscore = - 200 / 250
Zscore = - 0.8
P(Z ≤ - 0.8) = 0.2119
X = 1100
Zscore = (x - m) / s
Zscore = (1100 - 1000) / 250
Zscore = 100 / 250
Zscore = 0.4
P(Z ≤ 0.4) = 0.6554
P(Z ≤ 0.4) - P(Z ≤ - 0.8)
0.6554 - 0.2119
= 0.4435
find the sum of 2x ÷ x-1 and x÷x-1
Answer with step-by-step explanation:
First of all, ORDER OF OPERATIONS!! 2x/x is 2/1, which is 2. Then, subtract 1, which is 1.
2x ÷ x - 1 = 1
Same thing: x/x = 1. Subtract 1 from 1, which is 0.
x ÷ x - 1 = 0
1 + 0 = 1
Hope this helped!
Based on the survey results from 300 selected students in the Burbank School District (BSD), the 98% confidence interval used to estimate the population proportion of all BSD students who have access to a working computer at home was computed to be 48% to 60%. The following 2 subquestions require a numeric input, no work is necessary. [2 points] What number of students (out of the 300 sampled) have access to a working computer at home
Answer:
follows are the solution to this question:
Step-by-step explanation:
Please find the correct question in the attached file:
The formula for calculating the Confidence interval of proportion:
[tex]\to CI=\hat{p} \pm Z_{\frac{\alpha}{2}} \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\\\\\to \hat{p}=\frac{\text{lower limit +upper limit}}{2}\\[/tex]
[tex]=\frac{0.48+0.60}{2}\\\\=\frac{1.08}{2}\\\\=0.54[/tex]
The number of learners with access to working at home on a computer:
[tex]= 0.54 \times 300 \\\\=162[/tex]
Lower limit =0.48
upper limit = 0.60
[tex]\to margin \ error = \frac{\text{upper limit - lower limit}}{2}\\[/tex]
[tex]=\frac{0.60-0.48}{2}\\\\=\frac{0.12}{2}\\\\= 0.06[/tex]
find the first 3 powers of 7
Answer:
7, 49, 343
Step-by-step explanation:
Just do it
5 divided 5/6 helpabacon hair please
Answer:
what? expalint the question
Step-by-step explanation:
Solution of the equation
Answer:
B
Step-by-step explanation:
The sides are not equal. You substitute the coordinates into the equation which gives you -11=-4 x 3
which solves to -11 = -12
therefore the sides are not equal
Use Symbolab for math problems, it helps alot especially on tests.
Can someone please help?
Answer:
<IJL and <IJG
Step-by-step explanation:
<IJL and <IJG
the polynomial p(x) has factors of x-5 and x-8. Which must be correct ?
Answer:
Find an answer to your question The polynomial p(x) has factors of x – 5 and x + 8. Which MUST be correct?
Step-by-step explanation:
If x – a is indeed a factor of p(x), then the remainder after division by x – a will be ... the polynomial (courtesy of the Remainder Theorem), but x – a is also a factor ... completed division: 2 2 5 0 7 ... x + 4 is a factor of 5x4 + 16x3 – 15x2 + 8x + 16.
PLEASE HELP I AM STUCK
12,049=-58,642+y
Answer:
70,691
Step-by-step explanation:
I need help please thanks
find x when y = 18, if y = 9 when x = 8
ASAP PLEASE
so
y=9 -> y=18
*2
x=8 -> x=16
*2
so x = 16
Answer:
the only logical way solving this question is:
if y=9 then x=8
if y=18 then x should be 16
Step-by-step explanation:
I cant find any other way to solve
what are factors of 7
Answer:
1 and 7
Step-by-step explanation:
Your new car drives 220 miles on 8 gallons of gas,
The car's MPG is
Will mark brainliest Simone please help
Answer:27.5
hope it helped can I have brainliest?
Step-by-step explanation:
The distance between Point P and Point Q was 3600 m. Beng Leong started jogging
at 08 35 from Point P and reached Point Q at 08 50. At the same time, Sam started
jogging from Point P at a speed of 200 m/min. Who jogged at a faster speed?
How much faster was his speed?
Answer:
Ben ran at a speed of 240m/min and Sam ran at a speed of 200m/min So Ben is faster by a rate of 40/min
Step-by-step explanation:
Ben's miles per minutes
[tex] \frac{3600}{15} = 240[/tex]
Sam's miles per minute
Given
What is the slope of the line perpendicular to y = 4x + 2
Answer:
slope is -1/4
Step-by-step explanation:
y = 4 x + 2
Use the equation y = m x + b
So m=4
And MPerpendicular=-1/4
Hope this helps!!