The number of collections of 7 books can you take is 1685.
What is Algebra?
Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We are given that;
Total books= 15
n = 15 (the number of possible books) and r = 7 (the number of books to be taken).
Now,
To find the number of different collections of 7 books, we can use the formula for combinations. Combinations are ways of selecting items from a collection, such that the order of selection does not matter.
The formula for combinations is:
nCr = n! / (r! (n - r)!)
where n is the number of items in the collection, r is the number of items to be selected, and ! is the factorial operator.
We can plug these values into the formula:
15C7 = 15! / (7! (15 - 7)!)
= 15! / (7! 8!)
= (15 x 14 x 13 x 12 x 11 x 10 x 9 x 8!) / (7! 8!)
= (15 x 14 x 13 x 12 x 11 x 10 x 9) / (7 x 6 x 5 x 4 x 3 x 2 x 1)
= (6435 x 1320) / (5040)
= 8491770 / 5040
= 1685.25
Since we cannot have a fraction of a collection, we round down to get the final answer:
15C7 = 1685
Therefor, by algebra the answer will be 1685.
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A Geiger counter registers a count rate of 7,600 counts per minute from a sample of a radioisotope. Eighteen minutes later, the count rate is 1,900 counts per minute. What is the half-life of the radioisotope?
Answer:
9 minutes is the half life of the radioisotope.
Step-by-step explanation:
Given;
initial count rate = 7,600 counts per minute
final count rate = 1,900 counts per minute
elapsed time, t = 18 minutes
The half life of the radioisotope is calculated as;
Time (half life) --------------------------remaining count rate
0 ------------------------------7,600 counts per minute
x ------------------------------3,800 counts per minute
2x----------------------------- 1,900 counts per minute
thus, 2x = 18 minutes
x = 18 / 2
x = 9 minutes
Therefore, 9 minutes is the half life of the radioisotope.
plzz anwser ill give brainlest simplify 16- 8/15
Answer:
232/15 [as an improper fraction] or 15 7/15 [as a mixed fraction]
Explanation:
16 - 8 / 15 =
(16) - (8 / 15) =
((16 × 15) / 15) - ((8) / 15) =
((240) / 15) - ((8) / 15) =
(240 - 8) / 15 =
232 / 15 =
15 7/15
please help me I'm going to fail if you don't help me
Answer:
B
Step-by-step explanation:
Shigaraki told me
I desperately need the answers to this, it’s about compound interests
Answer:
quarterly is n = 4semiannually is n = 2monthly is n = 12annually is n = 1Step-by-step explanation:
n is the number of times the interest is compounded, so just figure out stuff like monthly and annually mean. (ex. since annually means once a year, n = 1)
A firm is concerned with variability in hourly output at several factories and shifts. Here are the results of an ANOVA using output per hour as the dependent variable (some information is missing). Source Sum of Squares df Mean Square F Ratio Factory 19012.5 1 19012.5 26.427 Supplier 258.333 2 129.167 0.180 Factory*Shift 80908.333 2 40454.167 56.230 Error 8633.333 12 719.444 Total 108812.5 17 6400.735 The number of observations in each treatment cell (row-column intersection) is
Answer:
The number of observations is 3
Step-by-step explanation:
According to the given situation, The computation of the number of observations in each cell treatment via intersecting row-column is shown below
Here
N represents the number of observations
So from the given data, the number of observations is 3
i.e.
N = 3
The same is to be considered and relevant too
The number of adult Americans from a random sample of n adults who support a bill proposing to extend daylight savings time is a binomial random variable. Assume that its probability will be approximated using the normal distribution. Describe the area under the normal curve that will be computed in order to determine the probability that more than Americans support the bill.
Answer:
Right of X = 635.5
Step-by-step explanation:
By using the normal approximation to the Binomial random variable, we usually make use of continuity correction.
According to the rule of continuity;
P(X ≤ k) becomes P( X ≤ K + 0.5)
P(X < K) becomes P(X < K - 0.5)
P(X ≥ K) becomes P(X ≥ K - 0.5)
P(X > K) becomes P(X > K + 0.5)
P(X = K) becomes P(K - 0.5 ≤ X ≤ K + 0.5)
From the given question, Assume that we are to determine the probability that more than 635 Americans support the bill.
Then we use the > sign.
∴
P(X > K ) becomes P(X > K + 0.5)
P(X > 635) becomes P(X > 635 + 0.5)
⇒ P(X > 635.5) tot the right.
Right of X = 635.5
Bill bought a shirt for $35.80 plus he paid an additional 7% in sales tax. What was the final cost?
Answer:
$38.66
Step-by-step explanation:
Examine the figure below. Determine which of the following angel measures are correct . Select all that apply
Answer:
bhnnjn
Step-by-step explanation:
Solve y=3x-4 and y=2/5x+ 9
using systems of linear eqautions
Answer:
(5 , 11)
Step-by-step explanation:
[tex]Equation\ 1\\\\\y=3x-4\\\\Equation\ 2\\\\\y=\frac{2}{5}x+9[/tex]
There are three ways to solve the systems of linear equations
1) Elimination method - where we add/subtract the equations to eliminate the variable
2) Substitution method - where we substitute one variable in the form of another variable
3) Graphing method - where we sketch the graphs of both the equations and if they intersect that point would be the solution and if they don't there is no solution
We use the second method the Substitution method which is the easiest in my opinion.
Here we got two equations so lets just substitute equation 1 with equation 2 meaning insert equation 1 into equation 2 like here:
[tex]3x-4=\frac{2}{5}x+9[/tex]
as you can see here we eliminated the variable y by substituting y in terms of x.
Now we just solve the equation algebraically
[tex]3x-4=\frac{2}{5}x+9\\3x-\frac{2}{5}x=9+4\\\frac{15x-2x}{5} =13\\\\\frac{13x}{5}=13\\\\13x=65\\x=65/13\\x=5\\[/tex]
The value of x is 5 now to find the value of y we insert the value of x in any two equations lets insert the value of x into equation 1
[tex]y=3x-4\\y=3(5)-4\\y=15-4\\y=11[/tex]
so the solution of the system of linear equations is (5 , 11)
please hepl???
I will mark brainliest
Answer:
x = 59
Step-by-step explanation:
180 = 73 + x + (x-11)
180 - 73 + 11 = 2x
118 = 2x
x = 118/2
x = 59
Which of the following is equal to 4 2/3 divided by 3 1/2 ? (2 points)
a.
4 2/3 times 3 1/2
b.
14/3 times 2/7
c.
14/3 times 7/2
d.
42/3 times 2/31
Answer:
c I'm to 100 percent sure but if not it's b it's around 14 for sure
Explain how you know that segment de is not parallel to segment bc
Line segments DE and BC are not parallel because they divide the opposite side of the triangle at different ratios.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
Given, Line segment AD is 4 units and line segment DB is 2 units.
∴ Line segment AD is (4/2) = 2 times greater.
On the other hand line segment, AE is 9 units and line segment EC is 5 units.
∴ Line segment AE is (9/5) = 1.8 times greater.
Line segments BC and DE should have been parallel if they had the same ratios.
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1) A school has 1600 students and they are going to vote as to whether they will completely convert the school completely off fossil fuels. How many students would you have to poll to be 95% confident of the outcome within /- 2% of the vote
Answer:
Standard deviation of the students = 0.408
The students would you have to poll to be 95% confident of the outcome within /- 2% of the vote
= 0.408 X 1600
= 652.8
Step-by-step explanation:
Step(i):-
Given sample size 'n' = 1600
95% confidence interval of the margin error is determined by
[tex]M.E = \frac{Z_{0.05} S.D}{\sqrt{n} }[/tex]
Level of significance = 0.05
Z₀.₀₅ = 1.96
Given Margin of error = 2% = 0.02
[tex]M.E = \frac{Z_{0.05} S.D}{\sqrt{n} }[/tex]
[tex]0.02 = \frac{1.96 X S.D}{\sqrt{1600} }[/tex]
0.02 X √1600 = 1.96 X S.D
[tex]S.D = \frac{0.02X\sqrt{1600} }{1.96} = 0.408[/tex]
Standard deviation of the students = 0.408
The students would you have to poll to be 95% confident of the outcome within /- 2% of the vote
= 0.408 X 1600
= 652.8
Using the z-distribution, it is found that you would have to poll 2401 students.
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which z is the z-score that has a p-value of [tex]\frac{1+\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so [tex]z = 1.96[/tex].
There is no prior estimate, hence [tex]\pi = 0.5[/tex] is used.
The sample size is n for which M = 0.02, hence:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.02 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.02\sqrt{n} = 1.96(0.5)[/tex]
[tex]\sqrt{n} = \left(\frac{1.96(0.5)}{0.02}\right)[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96(0.5)}{0.02}\right)^2[/tex]
[tex]n = 2401[/tex]
You would have to poll 2401 students.
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6th grade hw help! Please and ty.
Answer: I cant see the pic clearly
Step-by-step explanation:
Answer:
i can't see pic clearly
HELP ASAP QUESTION IN PHOTO
1. What's the fraction 18/24 reduced to its lowest terms?
A. 12
B.24 18
C.34
D. 1824
Answer:
answer is 3 upon 4
Step-by-step explanation:
because if we reduce 18/24 to its lowest term so first we have to reduce 18 to and then 24 --- 18 is factor of 9x2 and 24 is factor of 12x2 then we have to cut 2 in both and there is answer 9 upon 12 still it is reducing so 3x3 is 9 and 3x4 is 12 so now we have to cut 3 in both the answer is 3 upon 4
Ripley’s Aquarium charges $29.95 for (a) adults and $13.95 for (c) children. Write an expression to represent admission pricing
Answer:
T=29.95a + 13.95c
Step-by-step explanation:
For this equation let a=amount of adult tickets, c=amount of children tickets, and T=the total cost. Since each adult ticket costs 29.95 dollars that needs to be multiplied by the number of adult tickets to see how much was spent on adults, the same goes for the price and number of children tickets. Finally, both of those totals need to be added together to see how much is spent overall for all of the guests.
What is the answer?????
Answer:
0.25
Step-by-step explanation:
What is this expression?
Answer:
2) 4/3
Step-by-step explanation:
(4^-3 * 3^4 * 4^2)/(3^5 * 4^-2)
4^-3 * 3^4 * 4^2 = 4^-1 * 3^4
(4^-1 * 3^4)/(4^-2 * 3^5)
(3^4)/(3^5) = 1/(3^5-4)
(4^(-1))/(4^-2 * 3^(5-4)
(4^-1)/(4^-2 * 3)
4^(-1 - (-2)) / (3)
-1 - (-2) = 1
4/3
1 A parallelogram has base 7.3 mi and height 3.1 mi. What is its area? A 22.63 mi? B 1116 mi? C 26.28 mi? D 21.8 mi?
Answer:
A) 22.63
Step-by-step explanation:
Well as we all know to find the area of a parallelogram u have to multiply Base by Height = Area ; Base×Height=Area
As so: 7.3×3.1=22.63
Final answer 22.63
Factor the expression using the GFC 70+95=
Answer:
165
Step-by-step explanation:
Answer: 165
Step-by-step explanation:
Aleena expands 2xx+3-5(x-2) as 2x2+3-5x-10. Has she expanded it correctly? Please identify the mistakes and write the correct way in which 2xx+3-5(x-2) should be expanded.
The given expression is :
2xx+3-5(x-2)
We know that, [tex]x{\cdot}x=x^2[/tex]
[tex]=2x^2+3-5(x-2)\\\\=2x^2+3+(-5)(x)+(-5)(-2)\\\\=2x^2+3-5x+10[/tex]
Aleena expands 2xx+3-5(x-2) as 2x²+3-5x-10. She is mistaken because the sign before 10 should be +10 instead of -10. Hence, the correct expanded form is 2x²+3-5x+10. Hence, this is the required solution.
A teacher administers a standardized math test to his class of 75 students. The mean score (out of 300 possible points) is 235. From previous studies, you know the population standard deviation is 28. Using the sample data given, calculate a 95% confidence interval for the population mean.
Answer:
(228.663 ; 241.337)
Step-by-step explanation:
Given that:
Mean (m) = 235
Standard deviation (s) = 28
α = 95%
Zcritical at 95% = 1.96
Sample size (n) = 75
The confidence interval of the population mean can be obtained using the relation :
Mean ± Error
Error = Zcritical * (s/sqrt(n))
Error = 1.96 * (28/sqrt(75))
Error = 1.96 * 3.2331615
Error = 6.33699654
Error = 6.337
Lower boundary = 235 - 6.337 = 228.663
Upper boundary = 235 + 6.337 = 241.337
(228.663 ; 241.337)
Aisha has 8 coins worth 50¢. If the coins are all dimes and nickels, how many dimes and nickels does she have?
Answer:
4 dimes
2 nickels
Step-by-step explanation:
Answer:
4 dimes 2 nickels
Step-by-step explanation:
I need some help please
Answer:
The awnser is A or -7/5
Step-by-step explanation:
you have to put the points into the formula y²-y¹/x²-x¹ (this is a fraction the y part is on top and the x part is on the bottom) then you need to plug in the numbers so it would look like 5-(-2)/-2-3. then you would add 5+2 since that is what -(-) means. then you would take 2+3 as -2-3. so the awnser would be -7/5.
Hope this helps
124 – 70 = n – 35 I need the answer i please this is very importend
Answer:
N=89
59 = n - 35
54+35 = n
89=n
n=89
Monica went shopping for holiday presents. She bought boxes of chocolates and boxes of ornaments for her
coworkers. Boxes of chocolate cost $10 each and boxes of ornaments cost $12 each. She buys a total of 14
boxes and spends $156. How many boxes of chocolates and how many boxes of ornaments does she buy?
Use C for number of chocolate boxes and for number of ornament boxes.
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The number of chocolate boxes is 6.
The number of ornament boxes is 8.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 5 is an equation.
We have,
Number of chocolate boxes = C
Number of ornaments boxes = B
The total cost of 14 boxes = $156
Cost of one box of chocolate = $10
Cost of one box of ornaments = $!2
Now,
C + B = 14 ______(1)
10C + 12B = 156 _______(2)
From (1) we get,
C = 14 - B ______(3)
Putting (3) in (2) we get,
10 (14 - B) + 12B = 156
140 - 10B + 12B = 156
140 + 2B = 156
2B = 156 - 140
2B = 16
B = 16/2
B = 8
Now,
C = 14 - B
C = 14 - 8
C = 6
Thus,
The number of chocolate boxes is 6.
The number of ornament boxes is 8.
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halp meer............
Answer:
D
Step-by-step explanation:
Well, 1/3 is in between 0 and 1. Only D is in between 0 and 1.
Help me I’ll give you stars
Answer:answer choice 2
Step-by-step explanation:
given that (ax^2 + bx + 3) (x + d) = x^3 + 6x^2 + 11x + 12
a + 2b - d = ?
Answer:
Let's solve for a.
(ax2+bx+3)(x+d)=x3+6x2+11x+12a+2b−d
Step 1: Add -12a to both sides.
adx2+ax3+bdx+bx2+3d+3x+−12a=x3+6x2+12a+2b−d+11x+−12a
adx2+ax3+bdx+bx2−12a+3d+3x=x3+6x2+2b−d+11x
Step 2: Add -bdx to both sides.
adx2+ax3+bdx+bx2−12a+3d+3x+−bdx=x3+6x2+2b−d+11x+−bdx
adx2+ax3+bx2−12a+3d+3x=−bdx+x3+6x2+2b−d+11x
Step 3: Add -bx^2 to both sides.
adx2+ax3+bx2−12a+3d+3x+−bx2=−bdx+x3+6x2+2b−d+11x+−bx2
adx2+ax3−12a+3d+3x=−bdx−bx2+x3+6x2+2b−d+11x
Step 4: Add -3d to both sides.
adx2+ax3−12a+3d+3x+−3d=−bdx−bx2+x3+6x2+2b−d+11x+−3d
adx2+ax3−12a+3x=−bdx−bx2+x3+6x2+2b−4d+11x
Step 5: Add -3x to both sides.
adx2+ax3−12a+3x+−3x=−bdx−bx2+x3+6x2+2b−4d+11x+−3x
adx2+ax3−12a=−bdx−bx2+x3+6x2+2b−4d+8x
Step 6: Factor out variable a.
a(dx2+x3−12)=−bdx−bx2+x3+6x2+2b−4d+8x
Step 7: Divide both sides by dx^2+x^3-12.
a(dx2+x3−12)
dx2+x3−12
=
−bdx−bx2+x3+6x2+2b−4d+8x
dx2+x3−12
a=
−bdx−bx2+x3+6x2+2b−4d+8x
dx2+x3−12
Answer:
a=
−bdx−bx2+x3+6x2+2b−4d+8x/
dx2+x3−12
Step-by-step explanation:
