To find out the number of ways the mice can be assigned to receive the two different drugs or no drug, we use the combination formula. The total number of ways is given by the product of the combinations C(60, 21) * C(39, 21) * 1.
Explanation:In this problem, we are given a group of 60 mice and we need to find the number of ways the mice can be assigned to receive drug A, drug B, or no drug. This is a problem of combinatorics, specifically a problem of combinations.
We have 60 mice and we want to choose 21 for the drug A. The number of ways to do this is given by the combination formula C(n, k) = n! / [k!(n-k)!], where 'n' is the total number of items, 'k' is the number of items to choose, and '!' represents the factorial function. So for drug A, it will be C(60, 21).
Then, from the remaining 39 mice, we need to choose 21 for drug B. The number of ways we can do this is C(39, 21).
Finally, the remaining 18 mice will serve as the control group. Given that there's no need to specifically choose which mice are in the control group (since all the remaining ones default to it), we only have 1 way for this selection.
Therefore, the total number of ways the assignment can be made is the product of the number of ways we can form each group, which is C(60, 21) * C(39, 21) * 1.
Learn more about Combinations here:https://brainly.com/question/30646507
#SPJ11
The number of ways the assignment of treatments to the mice can be made is 10278857927713471414080000.
To determine how many ways the treatments can be assigned to the 60 laboratory mice (21 for drug A, 21 for drug B, and 18 as controls), we need to calculate the number of permutations of the assignments.
The total number of mice is 60, consisting of:
- 21 mice for drug A
- 21 mice for drug B
- 18 mice as controls
The number of ways to assign treatments is the number of permutations of these groups within the total set of mice. This can be calculated using the multinomial coefficient:
[tex]\[ \frac{60!}{21! \times 21! \times 18!} \][/tex]
Where:
- 60! is the factorial of 60 (total number of mice)
- 21! is the factorial of 21 (number of mice for drug A)
- 21! is again the factorial of 21 (number of mice for drug B)
- 18! is the factorial of 18 (number of control mice)
Let's compute this step-by-step:
1. Calculate 60!:
[tex]\[ 60! = 60 \times 59 \times 58 \times \ldots \times 2 \times 1 \][/tex]
2. Calculate 21!:
[tex]\[ 21! = 21 \times 20 \times \ldots \times 2 \times 1 \][/tex]
3. Calculate 18!:
[tex]\[ 18! = 18 \times 17 \times \ldots \times 2 \times 1 \][/tex]
Now, plug these into the formula:
[tex]\[ \frac{60!}{21! \times 21! \times 18!} = \frac{60 \times 59 \times \ldots \times 2 \times 1}{(21 \times 20 \times \ldots \times 2 \times 1) \times (21 \times 20 \times \ldots \times 2 \times 1) \times (18 \times 17 \times \ldots \times 2 \times 1)} \][/tex]
[tex]\[ \frac{60!}{21! \times 21! \times 18!} = \frac{83209871127413901442763411832233643807541726063612459524492776964096000000000000000}{51090942171709440000} \][/tex]
[tex]\[ \frac{60!}{21! \times 21! \times 18!} = 10278857927713471414080000 \][/tex]
Chris uncle from japan promised to give him 42 g of gold .The local jewelry exchange will buy gold for $1286 per once.How much money can Chris get for selling the gold?
Answer:
Chris will make $1905.22 by selling gold.
Step-by-step explanation:
Amount of gold Chris will have = 42 g
Current rate of gold = $1286 per ounce
We need to find the amount Chris will make after selling the gold.
Now we will first find Current rate of gold in grams.
We know that 1 ounce = 28.3495 grams.
So we can say that
28.3495 g = $1286
So 1 g = Rate of gold for 1 gram.
By Using Unitary method we get;
Rate of gold for 1 gram = [tex]\frac{1286}{28.3495} \approx \$45.3624[/tex]
Now we will find the amount for 42 g of gold
if 1 g = $45.3624
so 42 g = Amount of money for 42 g
Again by using Unitary method we get;
Amount of money for 42 g = [tex]42 \times 45.3624 \approx \$1905.22[/tex]
Hence Chris will make $1905.22 by selling gold.
Chris can get $1,736.10 by selling 42 grams of gold.
Chris's uncle from Japan has promised to give him 42 grams of gold. The local jewellery exchange will buy gold for $1286 per ounce. To find out how much money Chris can get for selling the gold, we need to convert grams to ounces and then multiply by the price per ounce. There are approximately 31.1035 grams in an ounce. So, to convert grams to ounces we use the following formula:
Divide the amount of gold in grams by the number of grams per ounce. 42 grams ÷ 31.1035 grams/ounce = 1.35 ounces.
Multiply the amount of gold in ounces by the current price of gold per ounce. 1.35 ounces × $1286/ounce = $1,736.10.
At a movie theater, the ticket prices to see a movie in 3-D are $18 for an adult and $12 for a child. The owner of the theater wants to make at least $300 when a movie is shown in 3-D. Choose the inequality that shows the numbers of tickets that must be sold.
Answer:
[tex]18x+12y\geq 300[/tex]
Step-by-step explanation:
Let
x ---> the number of an adult tickets
y ---> the number of a child tickets
Remember that the word "at least" means "greater than or equal to"
so
The number of an adult tickets multiplied by its price ($18) plus the number of a child tickets multiplied by its price ($12) must be greater than or equal to $300
The inequality that represent this situation is
[tex]18x+12y\geq 300[/tex]
using a graphing tool
the solution is the shaded area
Remember that the number of tickets cannot be a negative number
see the attached figure
. Jane is practicing solving systems of equations by inspection. She thinks that y = 5 6 x + 2 and y = 5 6 x – 2 would have exactly one solution. Is she correct? Why or why not?
Answer:
No solution , The line's are parallel
Step-by-step explanation:
Given set of equations are y = 56x + 2 and y = 56x - 2
If we observe carefully these lines are in the form of y=mx+c where m is the slope of the line and c is the y-intercept
Here both the line's have slope m = 56
We also know that two lines are parallel only if their slopes are equal ie m1=m2
Here the two line's have same slope, so the giventwo line's are parallel And they don't have a solution So jane is wrong.
Andrew and Sarah are tracking the number of steps they walk. Andrew records that he can walk 6000 steps in 50 minutes. Sarah writes the equation y=118x where y is the number of steps and x is the number of minutes she walks, to describe her step rate.
Answer:
Andrew walks more steps than Sarah.
Step-by-step explanation:
The question is incomplete. The complete question is :
Andrew and Sarah are tracking the number of steps they walk. Andrew records that he can walk 6000 steps in 50 minutes. Sarah writes the equation y=118x, where y is the number of steps and x is the number of minutes she walks, to describe her step rate. This week, Andrew and Sarah each walk for a total of 5 hours. Who walks more steps?
Solution:
Given:
Andrew walks 6000 steps in 50 minutes.
Number of steps Sarah walks is given by the equation :
[tex]y=118x[/tex]
where [tex]y[/tex] is the number of steps and [tex]x[/tex] is the number of minutes she walks.
Finding the number of steps each walks in 5 hours.
Total number of minutes in 5 hours = [tex]5\times 60 = 300\ min[/tex]
For Andrew:
Using unitary method:
If in 50 minutes Andrew walks = 6000 steps.
In 1 minute he will walk = [tex]\frac{6000}{50}[/tex] = 120 steps
In 300 minutes he will walk = [tex]120\times 300 = 36000[/tex] steps
Thus, Andrew will walk 36,000 steps in 5 hours.
For Sarah:
We will plugin [tex]x=300[/tex] in the equation and solve for [tex]y[/tex].
We have:
[tex]y=118(300)[/tex]
∴ [tex]y=35400[/tex]
Thus, Sarah will walk 35,400 steps in 5 hours.
Therefore, Andrew walks more steps than Sarah as [tex]36,000>35,400[/tex].
An employee earns $7.00 an hour for the first 35 hours worked in a week and $10.50 for any hour over 35. One week's paycheck (before deduction) was for $308.00. How many hours did the employee work
Answer: the employee worked for 41 hours
Step-by-step explanation:
Let x represent the total number of hours that the employee worked. An employee earns $7.00 an hour for the first 35 hours worked in a week and $10.50 for any hour over 35. Let y represent the amount earned for x hours. Therefore
y = 7×35 + 10.5(x - 35)
y = 245 + 10.5x - 367.5
One week's paycheck (before deduction) was for $308.00. This means that y = $308.00. Therefore,
308 =245 + 10.5x - 367.5
308 = 10.5x - 122.5
10.5x = 308 + 122.5 = 430.5
x = 430.5/10.5
x = 41
If 2, 4, 6, and 9 are the digits of two 2-digit integers, what is the least possible positive difference between the integers? A28 B27
Answer: 13
Step-by-step explanation: first we have to know what an integer, which is a single whole number without fractions or decimal numbers e.g. 1,2,3,4,5,6,7,8,9
So now we are to find the least possible positive difference between two digit integers with combination of 2,4,6,9
So first, since it has to be the lowest difference, we have to look between these numbers for the lowest difference between the given integers, 6-4 = 2, 4-2 = 2, now the rest of the combination will give numbers higher that 2, e.g. 9-6 = 3, 6-2 = 4, 9-4 = 5, 9-2 = 7, so we can say our two digit integers can start with either 4 and 2, or 6 and 4, which is the tens in the two digit integers, so to get the least difference in this values, the units number of the bigger two digit integer will be smaller than the units number of the smaller two digit integers
So let's take the number 2, and 4
The bigger two digit integer will obviously start will 4, and since it's supposed to have the smaller units number, the two digit integer will be 46, and the second two digit integer will be 29, the finding the difference
We have 46-29=17
The taking the other combination of integer to give the smallest value, which was 2, (6 and 4) then giving the units number of the bigger integer which will be the smaller units number value (2), that two digit integer will be 62, and the other 49, finding the difference
62-49= 13
So therefore the least possible positive difference = 13
Indra baked and frosted a rectangular cake to sell at a bake sale for the Model UN club. The cake, including frosting, was 4 inches high, 16 inches wide, and 12 inches long. She centered the cake on a circular tray. The circular tray had a radius of 10 inches. What is the area, to the nearest square inch, of the tray that is not covered by the cake?
A. 100
B. 114
C. 122
D. 314
E. 192
Answer:
C. 122
Step-by-step explanation:
Given,
Dimension of the cake:
Length = 12 in Width = 16 in Height = 4 in
We have to find out the area of the tray that is not covered by the cake.
Indra centered the cake on a circular tray.
Radius of the tray = 10 in.
So area of the tray is equal to π times square of the radius.
Framing in equation form, we get;
Area of tray =[tex]\pi\times r^2=3.14\times{10}^2=3.14\times 100=314\ in^2[/tex]
Since the cake is placed in circular tray.
That means only base area of cake has covered the tray.
Base Area of cake = [tex]length\times width=12\times 16=192\ in^2[/tex]
Area of the tray that is not covered by the cake is calculated by subtracting area of base of cake from area of circular tray.
We can frame it in equation form as;
Area of the tray that is not covered by the cake = Area of tray - Base Area of cake
Area of the tray that is not covered by the cake =[tex]314-192=122\ in^2[/tex]
Hence The area of the tray that is not covered by the cake is 122 sq. in.
K12: Graph the image of this triangle after a dilation with a scale factor of 3 centered at the origin.
Use the polygon tool to graph the triangle.
The points after Dilation are (0,0), (9,-3), and (9,9).
Step-by-step explanation:
The given points are A(0,0), B(3,-1), and C(3,3).
The scale factor is 3.
[tex]D_{new}[/tex]([tex]p_{x} , p_{y}[/tex]) = scale factor × ([tex]p_{x} , p_{y}[/tex]) .
If the triangle starts form the origin (0,0) retains the same after the dilation.
[tex]D_{Anew}(p_{x} , p_{y})[/tex]= (0,0).
For point B(-1,3),
[tex]D_{Bnew}(p_{x} , p_{y})[/tex] = 3 × (3,-1).
[tex]D_{Bnew}(p_{x} , p_{y})[/tex] = (9,-3).
For Point C(3,3),
[tex]D_{Cnew}(p_{x} , p_{y})[/tex] = 3 × ( 3,3).
[tex]D_{Cnew}(p_{x} , p_{y})[/tex] = ( 9,9).
Refer the graph for dilated triangle.
in triangle abc shown below side ab is 6 and side ac is 4
which statement is needed to prove that segment DE is parallel to segment BC and half its length?
Question is Incomplete, Complete question is given below:
In Triangle ABC shown below, side AB is 6 and side AC is 4.
Which statement is needed to prove that segment DE is parallel to segment BC and half its length?
Answer
Segment AD is 3 and segment AE is 2.
Segment AD is 3 and segment AE is 4.
Segment AD is 12 and segment AE is 4.
Segment AD is 12 and segment AE is 8.
Answer:
Segment AD is 3 and segment AE is 2.
Step-by-step explanation:
Given:
side AB = 6
side AC = 4
Now we need to prove that segment DE is parallel to segment BC and half its length.
Solution:
Now AD + DB = AB also AE + EC = AC
DB = AB - AD also EC = AC - AE
Now we take first option Segment AD is 3 and segment AE is 2.
Substituting we get;
DB = 6-3 = 3 also EC = 4-2 =2
From above we can say that;
AD = DB and EC = AE
So we can say that segment DE bisects Segment AB and AC equally.
Hence From Midpoint theorem which states that;
"The line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side."
Hence Proved.
Find the midpoint of the line segment with the given points, (3, -7), (-2, 3)
Answer:
The answer to your question is Midpoint ( [tex]\frac{1}{2} , -2)[/tex]
Step-by-step explanation:
Data
A (3, -7)
B (-2, 3)
Formula
[tex]Xm = \frac{x1 + x2}{2}[/tex]
[tex]Ym = \frac{y1 + y2}{2}[/tex]
Substitution and simplification
[tex]Xm = \frac{3 - 2}{2}[/tex]
[tex]Xm = \frac{1}{2}[/tex]
[tex]Ym = \frac{-7 + 3}{2}[/tex]
[tex]Ym = \frac{-4}{2}[/tex]
[tex]Ym = -2[/tex]
Solution
Midpoint ( [tex]\frac{1}{2} , -2)[/tex]
In the graduating class of a certain college, 48 percent of the students are male and 52 percent are female. In this class 40 percent of the male and 20 percent of the female students are 25 years old or older. If one student in the class is randomly selected, approximately what is the probability that he or she will be less than 25 years old?A. 0.9B. 0.7C. 0.45D. 0.3E. 0.25
Answer:
Option B is right
Step-by-step explanation:
Given that in the graduating class of a certain college, 48 percent of the students are male and 52 percent are female. In this class 40 percent of the male and 20 percent of the female students are 25 years old or older.
Males Females
48% 52%
25 or more
age 40% 20%
One student in the class is randomly selected,
to find the probability that he or she will be less than 25 years old
= Prob (male and less than 25 years old)+Prob (female and less than 25 years old)
(since mutually exclusive and exhaustive)
= [tex]0.48(1-0.4) + 0.52(1-0.20)\\= 0.288+ 0.416\\= 0.704\\[/tex]
After rounding off to 1 one decimal
we get 0.7
Option B is right
Explain how the law of superposition was used to determine your findings.
Answer:sdxfrcgtvyhujikokjhgfdsasdfghjknbv 6yujhgtrfgb srry .\.
(5-4i)-(2-4i)
Complex numbers
Need to show work
Answer:
3
Step-by-step explanation:
Simplify :
(5-4i)-(2-4i)
5-4i-(2-4i)
=3
The sum of the circumference of two circles is 38π cm and the sum of their areas is 193π cm². Calculate the radii of the circles.
Answer:
The radii of the circles are 12 cm and 7cm.
Step-by-step explanation:
Let the radii of the circles be [tex]r_{1}\ and\ r_{2}[/tex]
Given:
Sum of circumference of two circles= 38π cm
Formula for circumference of a circle with radius r = 2πr
[tex]2\pi r_{1}+2\pi r_{2}=38\pi \\r_{1}+r_{2}=19[/tex]------------1
Sum of areas of two circles= 193π cm²
Area of circle with radius r = πr²
[tex]\pi r_{1}^{2}+\pi r_{2}^{2}=193\pi \\r_{1}^{2}+r_{2}^{2}=193[/tex]-------2
Substituting r2 = 19 - r1 in equation 2 we get:
[tex]r_{1}^{2}+(19-r_{1})^{2}=193\\2r_{1}^{2}-38r_{1}+168=0\\r_{1}^{2}-19r_{1}+84=0\\(r_{1}-12)(r_{1}-7)=0\\r_{1}=12\ or\ 7[/tex]
Then r2 = 19 - r1
[tex]r_{2}=12\ or\ 7[/tex]
The length of a string is L inches. Samantha cuts it into two unequal pieces such that the length of the small piece is 35% of L.
If the length of the big piece is 24 inches longer than the length of the small piece, what is the ratio of the length of the small piece to the length of the big piece as a fraction in its lowest terms?
Answer:
The shorter piece x = 8.4 in
The longer one y = 15.6 in
Step-by-step explanation:
If we cut a string length L in to unequal pieces we get two pieces
first one with length x and the other one with length y
Let call x the smaller piece, then y = L - x will be the longer one
If x = 35 % then
x = 0,35* L and
y = L - x = L - 0,35*L ⇒ y = 0,65 L ⇒ y = 0.65*24
Now if L = 24 in
x = 0,35*24 ⇒ x = 8.4 in
and
L - x = 0.65*L ⇒ L - x = 0.65*24 y = L - x = 15.6 in
as way of verification you can add the length of the two pieces and find:
8.4 + 15.6 = 24 in
Final answer:
The ratio of the length of the small piece to the big piece is found to be 7/13 after calculating the lengths of each piece, with the small piece being 28 inches and the big piece being 52 inches.
Explanation:
Given that the length of the small piece is 35% of the total length L, we can denote the length of the small piece as 0.35L. The big piece is 24 inches longer than the small piece, so the length of the big piece is 0.35L + 24 inches. Since the string is cut into only two pieces, the total length L is the sum of the lengths of the two pieces, which means L = 0.35L + (0.35L + 24).
Simplifying, we have L = 0.7L + 24. Subtracting 0.7L from both sides gives 0.3L = 24 inches. Therefore, the total length of the string is L = 24 / 0.3 = 80 inches. So the small piece is 0.35L = 0.35 * 80 = 28 inches, and the big piece is 28 + 24 = 52 inches.
To find the ratio of the lengths of the small piece to the big piece, we divide the length of the small piece by the length of the big piece: 28/52. Simplifying this ratio by dividing both the numerator and denominator by 4 gives us 7/13. Therefore, the ratio of the length of the small piece to the big piece in its lowest terms is 7/13.
Mandy is building a rectangular garden pond with the area on 12ft^2. The length of the pool needs to be 2ft more than twice that width. What are the dimensions of the pool
Answer: the length is 6 feet. The width is 2 feet
Step-by-step explanation:
The garden pool is rectangular in shape.
Let L represent the length of the rectangular garden.
Let W represent the width of the rectangular garden.
The area of a rectangle is expressed as L× W. The area of the rectangular garden pond is 12ft^2. It means that
L× W = 12 - - - - - - - - - - 1
The length of the pool needs to be 2ft more than twice that width. This means that
L = 2W + 2 - - - - - - - - - - - 2
Substituting equation 2 into equation 1, it becomes
W(2W + 2) = 12
2W^2 + 2W = 12
2W^2 + 2W - 12 = 0
W^2 + W - 6 = 0
W^2 + 3W - 2W - 6 = 0
W(W + 3) - 2(W + 3) = 0
W - 2 = 0 or W + 3 = 0
W = 2 or W = - 3
Since the Width cannot be negative, then the width is 2 feet
Substituting W = 2 into equation 2. It becomes
L = 2×2 + 2 = 6 feet
If you draw 2 cards from a shuffled 52 card deck, what is the probability that you'll have a pair?
Answer:
78/2,652, or 0.0294, or 2.94%.
Write an algebraic expression for the verbal expression, "17 less than k and 12"
Answer:
k-5
Step-by-step explanation:
"k and 12" : (k + 12)
"17 less than k and 12" : (k + 12) - 17
simplifying:
(k + 12) - 17
= k + 12 - 17
= k-5
A combination lock uses a 3-digit code. Each digit can be any one of the ten available integers 0-9. How many different combinations are possible?
Answer:
1000
Step-by-step explanation:
Each value of the first digit can be paired with any value of the second digit, so there are 10×10 = 100 possible pairs of the first two digits. Each of those can be combined with any third digit to give a total of ...
10×10×10 = 1000
possible combinations.
Final answer:
A combination lock with a 3-digit code where each digit can be 0-9 allows for 1000 different combinations, as calculated by 10 x 10 x 10, which equals 10³ or 1000.
Explanation:
The question asks how many different 3-digit combinations are possible with a combination lock where each digit can range from 0-9. Each digit of the code is independent and can take any of the ten possible values (0-9), leading to a total combination of possibilities calculated by multiplying the number of choices for each digit position. Given that there are three digit positions and each can be any of the ten digits, the calculation is as follows:
10 (choices for first digit) × 10 (choices for second digit) × 10 (choices for third digit) = 10³
Therefore, there are 1000 different possible combinations for the lock, ranging from 000 to 999.
And international calling plan charges a rate per minute plus a flat fee. A 10 minute call to France costs $4.29. Right and solve a linear equation to find the cost of a 12 minute call to France
Answer:
The cost of a 12 minute call to France is $ 3.63
Step-by-step explanation:
given:
The cost of 15 minute call to France = $ 4.29
The cost of 10 minute call to France = $ 3.19
To Find :
The cost of a 12 minute call to France = ?
Solution:
Let the flat fee be X
and the cost per minute be Y
so the 15 minute call to France will be
X + 15(Y) = 4.29---------------------------(1)
the 10 minute call to France will be
X + 10(X) = 3.19----------------------------(2)
Subtracting (2) from (1)
X + 15(Y) = 4.29
X + 10(Y) = 3.19
- - -
---------------------------------
5Y = 1.10
--------------------------------
[tex]Y =\frac{1.10}{5}[/tex]
Y = 0.22
So the cost per minute of a call = $0.22
substituting the values in (1)
X + 15(0.22) = 4.29
X + 3.3 = 4.29
X = 4.29 -3.3
X = 0.99
Now the cost of 12 minute call is
=>X + 12(Y)
=> 0.99 + 12(0.22)
=> 0.99 + 2.64
=> 3.63
Suppose the time required for an auto shop to do a tune-up is normally distributed, with a mean of 102 minutes and a standard deviation of 18 minutes. What is the probability that a tune-up will take more than 2hrs? Under 66 minutes?
Answer:
Step-by-step explanation:
Suppose the time required for an auto shop to do a tune-up is normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - u)/s
Where
x = points scored by students
u = mean time
s = standard deviation
From the information given,
u = 102 minutes
s = 18 minutes
1) We want to find the probability that a tune-up will take more than 2hrs. It is expressed as
P(x > 120 minutes) = 1 - P(x ≤ 120)
For x = 120
z = (120 - 102)/18 = 1
Looking at the normal distribution table, the probability corresponding to the z score is 0.8413
P(x > 120) = 1 - 0.8413 = 0.1587
2) We want to find the probability that a tune-up will take lesser than 66 minutes. It is expressed as
P(x < 66 minutes)
For x = 66
z = (66 - 102)/18 = - 2
Looking at the normal distribution table, the probability corresponding to the z score is 0.02275
P(x < 66 minutes) = 0.02275
If A, B, and C are integers between 1 and 10 (inclusive), how many different combinations of A, B, and C exist such that A
[tex]\fontsize{18}{10}{\textup{\textbf{The number of different combinations is 120.}}}[/tex]
Step-by-step explanation:
A, B and C are integers between 1 and 10 such that A<B<C.
The value of A can be minimum 1 and maximum 8.
If A = 1, B = 2, then C can be one of 3, 4, 5, 6, 7, 8, 9, 10 (8 options).
If A = 1, B = 3, then C has 7 options (4, 5, 6, 7, 8, 9, 10).
If A = 1, B = 4, then C has 6 options (5, 6, 7, 8, 9, 10).
If A = 1, B = 5, then C has 5 options (6, 7, 8, 10).
If A = 1, B = 6, then C has 4 options (7, 8, 9, 10).
If A = 1, B = 7, then C has 3 options (8, 9, 10).
If A = 1, B = 8, then C has 2 options (9, 10).
If A = 1, B = 9, then C has 1 option (10).
So, if A = 1, then the number of combinations is
[tex]n_1=1+2+3+4+5+6+7+8=\dfrac{8(8+1)}{2}=36.[/tex]
Similarly, if A = 2, then the number of combinations is
[tex]n_2=1+2+3+4+5+6+7=\dfrac{7(7+1)}{2}=28.[/tex]
If A = 3, then the number of combinations is
[tex]n_3=1+2+3+4+5+6=\dfrac{6(6+1)}{2}=21.[/tex]
If A = 4, then the number of combinations is
[tex]n_4=1+2+3+4+5=\dfrac{5(5+1)}{2}=15.[/tex]
If A = 5, then the number of combinations is
[tex]n_5=1+2+3+4=\dfrac{4(4+1)}{2}=10.[/tex]
If A = 6, then the number of combinations is
[tex]n_6=1+2+3=\dfrac{3(3+1)}{2}=6.[/tex]
If A = 7, then the number of combinations is
[tex]n_7=1+2=\dfrac{2(2+1)}{2}=3.[/tex]
If A = 3, then the number of combinations is
[tex]n_8=1.[/tex]
Therefore, the total number of combinations is
[tex]n\\\\=n_1+n_2+n_3+n_4+n_5+n_6+n_7+n_8\\\\=36+28+21+15+10+6+3+1\\\\=120.[/tex]
Thus, the required number of different combinations is 120.
Learn more#
Question : ow many types of zygotic combinations are possible between a cross AaBBCcDd × AAbbCcDD?
Link : https://brainly.in/question/4909567.
x, y, a, and b are positive integers. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9. Which of the following is NOT a possible value for y + b?
Answer:
y + b > 15
Step-by-step explanation:
given data
positive integers = x, y, a, b
x divided by y then remainder = 6
a divided by b then remainder = 9
to find out
possible value for y + b
solution
we know that here when x divided by y then remainder is 6
its mean y is greater than 6 and when a divided by b then remainder is 9
so its mean b is greater than 9
and we know remainder is less than divisor
so here y + b must be greater than = 6 + 9
y + b > 15
What is the slope of the line through (-10,1)(−10,1)left parenthesis, minus, 10, comma, 1, right parenthesis and (0,-4)(0,−4)left parenthesis, 0, comma, minus, 4, right parenthesis?
Answer:
-1/2
Step-by-step explanation:
Slope is calculated as ...
(change in y)/(change in x) = (y2 -y1)/(x2 -x1)
= (-4 -1)/(0 -(-10)) = -5/10 = -1/2
The slope of the line is -1/2.
Rachel is collecting donations for the local animal shelter. So far she has collected $245, which is 70% of what she hopes to collect. How much money does Rachel plan to collect for the shelter? Show your work.
Answer:
The money Rachael plan to collect for the shelter is $350.
Step-by-step explanation:
Given:
Rachel is collecting donations for the local animal shelter.
So far she has collected $245, which is 70% of what she hopes to collect.
Now, to find the money Rachael plan to collect for the shelter.
Let the total amount Rachael plan to collect be [tex]x[/tex].
Amount she collected = $245.
Percentage of amount she collected = 70%.
Now, to get the amount Rachael plan to collect we put an equation:
[tex]70\%\ of\ x=\$245.[/tex]
⇒ [tex]\frac{70}{100} \times x=245[/tex]
⇒ [tex]0.70\times x=245[/tex]
⇒ [tex]0.70x=245[/tex]
Dividing both sides by 0.70 we get:
⇒ [tex]x=\$350.[/tex]
Therefore, the money Rachael plan to collect for the shelter is $350.
HELP PLEASE:
Sketch the graph of the given function. Then state the function’s domain and range. f(x)= (1/3)^x+2
Answer:
Domain: set of all real numbers; (-∞, ∞)
Range : {y | y f > 2}
Check the attached figure to visualize the graph.
Step-by-step explanation:
The graph of the given function is attached. Please check the attached figure.
As the function is given as:
[tex]f(x) = (\frac{1}{3})^{x} +2[/tex]
As the table of some of the values of x and y values for [tex]f(x) = (\frac{1}{3})^{x} +2[/tex] is given as follows:
x y-2 11
-1 5
0 3
1 2.33
2 2.111
Hence, it is clear that the function is defined for every input value of x. So, domain is the set of all real numbers.
Domain: set of all real numbers; (-∞, ∞)
If we carefully analyze the graph of this function, it is clear that no matter what input value of x we put, range or y-value of this function would always be be greater than 2. Check the attached graph figure to better visualize the range of the function.
Range can also be denoted as: Range : {y | y f > 2}
Keywords: graph, function, domain and range
Learn more about domain and range from brainly.com/question/1581653
#learnwithBrainly
Do men and women differ, on average, in terms of the amount of television that they watch each day? A researcher conducted a hypothetical study in which he randomly selected 50 men and 50 women and recorded the number of minutes of television watched during the previous day. The researcher wanted to determine whether there is a difference in mean number of minutes of television viewing between men and women. What hypothesis testing technique should the researcher use to analyze the data?
Answer: Two-sample t-test
Step-by-step explanation:
The Two-sample t-test is used to test the difference between two random and distinct population means. It help test whether the difference between the two populations is statistically significant.
In the case above the researcher wants to determine whether there is a difference in mean number of minutes of television viewing between men and women which makes it a Two-sample t-test.
the length of a rectangle increases at a rate of 0.5 cm/sec and the width decreases at a rate of 0.5 cm/sec at the time when the length is 10cm and the width is 7 cm what is the rate of change in the area of the rectangle?
Answer:
Step-by-step explanation:
let length=x
width=y
area A=xy
[tex]\frac{dA}{dt}=x\frac{dy}{dt}+y\frac{dx}{dt}\\ \frac{dx}{dt}=0.5 ~cm/sec\\\frac{dy}{dt}=-0.5~cm/sec\\\frac{dA}{dt}=10*(-0.5)+7(0.5)=-5+3.5=-1.5[/tex]
area is decreasing at the rate of 1.5 cm^2/sec
The rate of change in the area of the rectangle when the length is 10 cm and the width is 7 cm, with their rates of change being 0.5 cm/sec and -0.5 cm/sec respectively, is -1.5 cm²/sec.
Explanation:To determine the rate of change in the area of a rectangle where the length is increasing at 0.5 cm/sec and the width is decreasing at 0.5 cm/sec, we can use the concept of derivatives from calculus.
Let L be the length and W be the width of the rectangle. The area A of the rectangle is given by A = L * W. Given that the length is increasing at 0.5 cm/sec (dL/dt = 0.5 cm/sec) and the width is decreasing at 0.5 cm/sec (dW/dt = -0.5 cm/sec) the rate of change of the area with respect to time can be found using the product rule for derivatives: dA/dt = (dL/dt) * W + L * (dW/dt).
At the moment when the length L is 10 cm and the width W is 7 cm, we can plug these values into the formula: dA/dt = (0.5 cm/sec) * 7 cm + 10 cm * (-0.5 cm/sec). This simplifies to dA/dt = 3.5 cm2/sec - 5 cm2/sec, giving us the rate of change in the area as dA/dt = -1.5 cm2/sec.
What is the value of secant theta given the diagram below? A unit circle is shown. A ray intersects point (negative 3, 6) in quadrant 2. Theta is the angle formed by the ray and the x-axis in quadrant 1. Negative StartRoot 5 EndRoot Negative StartFraction StartRoot 5 EndRoot Over 2 EndFraction StartFraction StartRoot 5 EndRoot Over 2 EndFraction StartRoot 5 EndRoot
Answer:
- √5
Step-by-step explanation:
Given that, a ray intersects point (negative 3, 6) in quadrant 2 and we are told to find the value of secant theta.
To get the answer to the question,
The first step is to find the hypotenuse, we have to use the Pythagoras theorem where, Hypotenuse = opposite raise to power two + adjacent raise to power.
(I.e. h= O² + A²)
H = 6² + (-3)2
H = 36 + 9
H = 45
We then convert the answer to surds form.
H = 3√5
The next step is to find the value of secant theta.
To get the value of secant theta we will have to divide the hypotenuse by adjacent with a negative sign because of the negative sign in the second quadrant
We have
Sec ø = - (hypotenuse/adjacent)
Sec ø = - (3√5/ 3)
Sec ø = - √5
Answer:
-√5
Step-by-step explanation:
Suppose an oligopoly consists of two firms. Firm A lowers price and Firm B responds by lowering its price by the same amount. If average costs and industry output remain the same, which of the following will occur?
Answer:
The profits for firma A and B will decrease.
Step-by-step explanation:
Oligopoly by definition "is a market structure with a small number of firms, none of which can keep the others from having significant influence. The concentration ratio measures the market share of the largest firms".
If the costs remain the same for both companies and both firms decrease the prices then we will have a decrease of profits, we can see this on the figure attached.
We have an equilibrium price (let's assume X) and when we decrease a price and we have the same level of output the area below the curve would be lower and then we will have less profits for both companies.