in how many different ways can 4 letters of the word "INDIRECTLY" be chosen
a. 50 b. 100 c. 35 d. 70
Answers
hi brainly user! ૮₍ ˃ ⤙ ˂ ₎ა
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\(\large \bold {ANSWER}\)
\(\large \boxed { \large \sf \green{d. \: 70}}\)\(\large \bold {SOLUTION}\)
Well, the first thing we have to do is see if we have any repeated letters and count how many letters the word has.
The word has 10 letters, the letters "i" is repeated once. So we need to exclude the repetitions.
\(10 - 2 = 8\)
Once this is done, we will use the combinatorial analysis, we will use this formula:
\({C}^{p}_{n} = \frac{n!}{p!(n- p)!}\)
The n is the number of letters and the o will be the number of elements we want to know how many groups are possible. Which will be the 4. The symbol of ! means factorial.
Substituted:\(\begin{gathered}{C}^{4}_{8} = \frac{8!}{4!(8 - 4)!} \\ \\ {C}^{4}_{8} = \frac{8 \times 7 \times 6 \times 5 \times \not4 !}{4! \times \not4!} \\ \\ {C}^{4}_{10} = \frac{8 \times 7 \times 6 \times 5}{4 \times 3 \times 2 \times 1} \\ \\ {C}^{4}_{10} = \frac{1680}{24} = 70\end{gathered}\)
Related Questions
Given the following polynomials
x = (a + b + c)^2
y= a^2 + b^ 2 + C^2
z = ab + bc + ac
Which identity is true?
A. x=y-z
B. x=y+z
C. x=y-2z
D. x=y+2z
Answers
Answer:
D. x=y+2z
Step-by-step explanation:
if you expand out the first equation (x) you will get: a^2+b^2+c^2+2ab+2bc+2ac
then looking at all of the choices, it can be seen that the third equation (z) needs to be multiplied by to get 2ab+2bc+2ac and then added to the second equation (y) which would result in D being the correct answer.
D. x=y+2z
I NEED HELP!! I'll give you brainliest!! A high school wants to expand its P.E. schedule. To better understand the needs of the students, the principal looked at which forms of exercise are preferred by the 18 students in the sample group.The Venn Diagram shows this information be gathered.a. How many students preferred swimming over running or walking?b. How many students choose running or walking?c. Which students preferred swimming and walking, but not running
Answers
Answer:
a. Three students preferred swimming over running and walking.
b. Fourteen students chose running or walking.
c. Alex and Jose preferred swimming and walking, but not running.
What is the ration thats simplest for is 8:7
Answers
Answer:
16:14
Step-by-step explanation:
Answer:
16:14
Answer. The ratio can be 16:14 whose simplest form is 8/7.
Please answer this correctly
Answers
There are 6 total cards. There is one 5 and one 7
You have a 1/6 probability of picking each number.
The probability of picking the 5 then the 7 would be 1/6 x 1/6 = 1/36
what is the sum of the 5th cube number an the 2nd cube number
Answers
Answer:
i think it is :
5×5×5=125
2×2×2=8
What is the range of function g if g(x)=-2f(x)+1
Answers
The range of g is bounded between 1 - 2M and 1, but it may not include all values in that interval, depending on the range of f.
The range of function g depends on the range of the function f.
Let's start by assuming that we know the range of f.
If the range of f is Rf, then the range of -2f is the set {-2y | y ∈ Rf}, which is just the set of all numbers that can be obtained by multiplying an element of Rf by -2.
Finally, we add 1 to each of these values to get the range of g. Therefore, the range of g is:
Rg = {1 - 2y | y ∈ Rf}
In other words, the range of g is obtained by taking the range of f, multiplying each element by -2, and adding 1 to each result.
If we don't know the range of f, we can still say something about the range of g. Specifically, we know that g(x) can never be greater than 1 (since the largest value that -2f(x) can take is 0, and adding 1 to 0 gives us 1), and g(x) can never be less than 1 - 2M, where M is the largest possible value that f(x) can take on. In other words, the range of g is bounded between 1 - 2M and 1, but it may not include all values in that interval, depending on the range of f.
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brainly really struggles with math especially graphs
Answers
The sinusoidal function y = 3 · cos 4x represents the graph. (Correct choice: C)
How to derive the trigonometric function behind a graph
In this question we find the graph of a trigonometric function. By direct inspection, we notice that function is continuous and bounded between - 3 and 3. Then, the trigonometric function is a sinusoidal function of the form:
y = A · cos (2π · x / T) + M
Where:
A - AmplitudeM - MidpointT - Periodx - Independent variable.y - Dependent variable.Now we proceed to determine the complete parameters of the sinusoidal function:
Amplitude
A = [3 - (- 3)] / 2
A = 3
Midpoint
M = [3 + (- 3)] / 2
M = 0
Period
T = π / 2
Finally, the trigonometric equation is the sinusoidal function y = 3 · cos 4x.
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1. A drama club earned $662.50 from a production where 85 adult tickets were sold and 65
student tickets were sold. An adult ticket costs $2.50 more than a student ticket. Which
system of equations can be used to find a, the cost of an adult ticket, and s, the cost of a
student ticket?
Answers
Answer: The cost of adult ticket is $6.1 and that of student ticket is $2.44
Step-by-step explanation:
Let the cost of adult ticket be 'x' and cost of student ticket be 'y'
From the question, the equations formed are:
\(662.5=85x+65y\) .....(1)
\(x=2.5y\) ......(2)
Putting value of 'y' from equation 2 to equation 1:
\(662.5=85(2.5x)+65y\\\\662.5=271.5y\\\\y=\frac{662.5}{271.5}=\$ 2.44\)
Now, solving for 'x', we get:
\(x=2.5(2.44)=\$ 6.1\)
Hence, the cost of adult ticket is $6.1 and that of student ticket is $2.44
The diagram shows a right-angled triangle.
24 cm
18 cm
_Not to scale
Calculate the value oft. Give your answer correct to 1 decimal place.
Answers
Answer:
can i have a photo, please?
Step-by-step explanation:
The Bainters want to know how much they would pay on their
loan each year as well as how much they would pay on their loan
after 5 years, 10 years, 15 years, and 30 years. They also want to
determine how much they would pay in interest on their loan
when they repay the entire loan.
What are the amounts?
Your answer should include (remember to show or explain your
calculations)
the total amount paid in loan payments after 1 year
the total amount paid in loan payments after 5 years
the total amount paid in loan payments after 10 years
the total amount paid in loan payments after 15 years
the total amount paid in loan payments after 30 years
the total amount of interest paid on the loan when it is
repaid
Answers
The total amounts paid are displayed in the image below:
What is an Interest Rate?The amount of interest due each period expressed as a percentage of the amount lent, deposited, or borrowed is known as an interest rate.
The total interest on a loaned or borrowed sum is determined by the principal amount, the interest rate, the frequency of compounding, and the period of time the loan, deposit, or borrowing took place.
How to calculate interest rates
Using S.I:
Simple Interest: The formula for simple interest is I = P x R x T, where I is the interest, P is the principal amount, R is the rate of interest, and T is the time period.
For example, if you borrow $1,000 at a simple interest rate of 5% per year for 3 years, the interest would be calculated as follows: I = $1,000 x 5% x 3 = $150.
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Use the Rational Root Theorem to list all of the possible Rational Zeros of the following equation: t^(3)-13t^(2)+65t-105=0
Answers
The possible rational zeros of the the given equation are ±1, ±3, ±5, ±7, ±15, ±21, ±35, ±105.
The given equation is (t)^3-13(t)^2+65t-105=0
According to Rational Root theorem, the possible rational zeros are the divisors of the constant term and leading coefficient that can be expressed in the form p/q.
The leading coefficient of the given equation = 1
It's divisors (q) = ±1
The constant term = 105
It's divisors (p) = ±1, ±3, ±5, ±7, ±15, ±21, ±35, ±105
The possible rational zeros of the given equation in the p/q form: ±1, ±3, ±5, ±7, ±15, ±21, ±35, ±105.
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What is the next value?
2 3 E 4 5 I 6 8
options: O 8 M N
Answers
Answer:
The correct answer is a.
Step-by-step explanation:
The sequence is: 2 3 E 4 5 I 6 8 We can notice that there are numbers and letters alternating in the sequence. The numbers are increasing, and the letters seem to be vowels in alphabetical order. So, the next value should be a letter (vowel) after I, which is O. The correct answer is a.
A bagel shop sells coffee in a container shaped like a rectangular prism. A graphic designer who works for the bagel shop drew the net below to create a design for the container.
Answers
1598 cm square is the area of the container.
According to the statement
we have given that the container is rectangular prism
And Length of rectangular prism is 34cm
Width of rectangular prism is 17 cm
Height of rectangular prism is 20 cm
we use the below written formula to find the surface area
Surface area formula A=(wl+hl+hw)
To find the surface area of the container.
Substitute the values of Length, width and height in the formula then
A=(wl+hl+hw)
A=((17)(34)+(20)(34)+(20)(17))
After solving the values
A=(578+680+340)
A= 1598
So, 1598 cm square is the area of the container.
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36 is what percent of 48?
Answers
36/48 x 100/100 = 75/100
NAW I NEED MORE HELP PLEASE
Answers
Answer:
-4
Step-by-step explanation:
We can use the slope formula: \(m=\frac{y_1-y_2}{x_1-x_2}\)
this formula is really just representing: \(\frac{\Delta y}{\Delta x}\\\) or in other words, change in y/change in x
The slope formula is calculating that difference by subtracting the y and x-values.
By just looking at the tables we can easily see that from x=6 to x=8 there is a change in 2
and from y=-16 to y=-24 there is a change in -8
So plugging this into the slope formula we get \(\frac{-8}{2}=-4\)
The line graph shows the time spent by people visiting the
Department of Motor Vehicles to renew their driver's license during
their birth month. To the nearest minute, what is the average waiting
time for all the months shown on the graph?
A)
18 minutes
B)
29 minutes
C)
37 minutes
D)
41 minutes
Answers
Answer:
Option (B)
Step-by-step explanation:
Average waiting time in the month of October = 20 minutes
Average waiting time in the month of November = 30 minutes
Average waiting time in the month of December = 60 minutes
Average waiting time in the month of January = 40 minutes
Average waiting time in the month of February = 10 minutes
Average waiting time in the month of March = 10 minutes
Average waiting time in the month of April = 30 minutes
Average waiting time in the month of May = 40 minutes
Average waiting time in the month of June = 20 minutes
Total waiting period from October to June = 20 + 30 + 60 + 40 + 10 + 10 + 30 + 40 + 20 = 260
Average waiting period = \(\frac{260}{9}\)
= 28.89
≈ 29 minutes
Option (B) is the answer.
A recipe requires 3 cups of flour to make 15 servings and 7 cups of flour to make 35 servings how many cups of flour are needed to make 20 servings?
Answers
Answer:
a = 8
b = 2
c = 48
Step-by-step explanation:
3 cups of flour is needed to make 24 servings.
3:24
Simplify. First, divide 3 from both sides of the ratio.
(3)/3 : (24)/3
1:8
Next, solve for b. You multiply 2 to 8 to get 16. Next, multiply 2 to 1
1 x 2 = b = 2
Finally, multiply 8 to 6 to get c.
8 x 6 = c = 48
~
True or false? The ½ in the function g(x)=½ sqrt x-1 is x>-1
Answers
Answer:
true
Step-by-step explanation:
100 POINTS
Find the error(s) and solve the
problem correctly in the picture below
Answers
Change the third line only .
<TFS\(\cong \)<PFQReason--(Opposite angles are same )Amd at 4th line
\(\\ \tt\Rrightarrow ∆TFS\cong∆PFQ(ASA)\)
ProvedEach of the counting problems below can be solved with stars and bars. For each, say what outcome the diagram
∗∗∗|∗||∗∗|
represents, if there are the correct number of stars and bars for the problem. Otherwise, say why the diagram does not represent any outcome, and what a correct diagram would look like.
a.) How many ways are there to select a handful of 6 jellybeans from a jar that contains 5 different flavors?
b.) How many ways can you distribute 5 identical lollipops to 6 kids?
c.) How many 6-letter words can you make using the 5 vowels in alphabetical order?
d.) How many solutions are there to the equation. show bars and stars.
x1+x2+x3+x4=6.
Answers
Question 2: Benjamin rolls an ordinary six-sided dice and flips a coin. List all the possible outcomes.
Answers
Answer:
Step-by-step explanation:
Calculus, derivatives. Please help! Show work, if possible. Thanks! :)
Answers
Answer:
a. y=4
b. graph the given and y=4
Step-by-step explanation:
The given is y= 8 sin(x) cos(x)
to get y' which is the slope of the tangent line we take the derivative
for this problem, the derivative involves the constant rule (which states that the derivative a constant times a value is just the constant times the derivative of said value) and the multiplication rule (assuming that the two parts in question are represented by the variables a and b then the derivative of a*b = a*b'+b*a')
thus we get 8*(sin(x)*-sin(x)+cos(x)*cos(x))
-8sin^2(x)+8cos^2(x)
You can also leave the 8 differentiated out depending on the form you need.
Now that we have the derivative we can plug pi/4 into this equation to get the slope of the tangent line at that point
=8sin^2(pi/4)+8cos^2(pi/4)
this would equal -8*1/2 +8*1/2 which equals 0
the slope of the tangent at this point would be zero
To get the point for point slope form we plug the pi/4 into the given equation to get a y value and get the point (pi/4, 4)
this means the point slope equation would be
y-4=0(x-pi/4)
y-4=0
y=4
To graph you would just enter the given equation and the equation for the tangent line into a graphing software or calculator and see if the line is tangent at the point (pi/4, 4)
if a plate of car consists of two letters and four digits and one car is chosen at random, then find the probability that the car has the letters at the beginning and at the end.
Answers
Answer:
if u take 1 degree to 78 its answer is 79
Step-by-step explanation:
got it?
The probability that the car has the letters at the beginning and at the end is 1/15.
What is probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
We have,
The plate of car consists of two letters and four digits.
So, there are
= 6!/(4!*2!)
=(6 x 5 x 4!)/4! x 2
= 3 x 4
= 15 ways of arranging
Then, the probability that the car has the letters at the beginning and at the end is 1/15.
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The net of a rectangular prism.
What is the surface area in square inches of the figure shown in the net
Answers
The answer of the given question based on finding the surface area of a rectangular prism the answer is ,60 square inches.
What is a Prism?A prism is polyhedron with two parallel, congruent faces called the bases, which are typically polygons, and rectangular sides connecting corresponding sides of bases.
To find the surface area of the rectangular prism shown in the net, we need to find the area of each of its six faces and then add them together.
Looking at the net, we can see that the rectangular prism has three pairs of identical faces. The dimensions of the rectangular prism are given by the labels on the net as follows:
The length of the rectangular prism is 6 inches (labeled L on the net).
The width of the rectangular prism is 3 inches (labeled W on the net).
The height of the rectangular prism is 2 inches (labeled H on the net).
The six faces of the rectangular prism and their areas are:
Front face: 3 x 2 = 6 square inches
Back face: 3 x 2 = 6 square inches
Top face: 6 x 2 = 12 square inches
Bottom face: 6 x 2 = 12 square inches
Left face: 6 x 2 = 12 square inches
Right face: 6 x 2 = 12 square inches
To find the total surface area, we add the areas of all six faces:
Total surface area = 6 + 6 + 12 + 12 + 12 + 12 = 60 square inches
Therefore, the surface area of the rectangular prism shown in the net is 60 square inches.
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For the function f(x) = 3 logx, estimate ƒ' (1) using a positive difference quotient. From the graph of f(x), would you expect you
estimate to be greater than or less than f' (1)?
Round your answer to three decimal places.
f' (1) =
Answers
To estimate \(\sf f'(1) \\\) using a positive difference quotient for the function \(\sf f(x) = 3\log(x) \\\), we can use the following formula:
\(\sf f'(1) \approx \frac{f(1+h) - f(1)}{h}\\\)
where \(\sf h \\\) is a small positive value. Let's choose \(\sf h = 0.001 \\\) for our estimation.
First, let's evaluate \(\sf f(1) \\\):
\(\sf f(1) = 3\log(1) = 3\cdot 0 = 0 \\\)
Next, let's evaluate \(\sf f(1+h) \\\):
\(\sf f(1+h) = 3\log(1+h) \\\)
Substituting \(\sf h = 0.001 \\\):
\(\sf f(1+0.001) = 3\log(1.001) \\\)
Now, we can calculate the positive difference quotient:
\(\sf f'(1) \approx \frac{f(1+h) - f(1)}{h} = \frac{3\log(1.001) - 0}{0.001} \\\)
Using a calculator, we find:
\(\sf f'(1) \approx 0.434 \\\)
Therefore, \(\sf f'(1) \approx 0.434 \\\) (rounded to three decimal places).
From the graph of \(\sf f(x) = 3\log(x) \\\), we would expect the estimate \(\sf f'(1) \\\) to be greater than \(\sf f'(1) \\\) since the graph of \(\sf f(x) \\\) is increasing at \(\sf x = 1 \\\).
Three companies offer swim lessons by the hour. Their information is shown in the tables below.
Which company has a signup fee of $11 and a cost per hour of $6
Answers
The answer is B because 6*2 = 12 + 11 = 23 !
A = {1, 2, 3, 4}
B = {3, 4, 5}
vertical line A intersection B vertical line =
Answers
The intersection of vertical lines A and B is 3 and 4.
How to find the intersection of the vertical linesWe are going to apply the sets theory here. In sets theory, the intersection of two elements means the values those elements have in common.
So given: A = {1, 2, 3, 4} and B = {3, 4, 5}
The intersection of A = {1, 2, 3, 4} and B = {3, 4, 5} is {3,4} since they both have 3 and 4 common.
Therefore, vertical lines A and B have intersection of 3 and 4.
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Write the equation of the line, in slope-intercept form, passing through the points (-2,5) and (3,6)
Answers
Answer:
y= 3/7x + 5 6/7
Step-by-step explanation:
6-3/5--2 = 3/7
y=3/7x+b
6=1/7+b
b=5 6/7
How do I solve 7x^2 + 8x = x^2
Answers
Answer:
x1=-4/3 x2=0
Step-by-step explanation:
1 cm (map)= 5 km (actual)