Evaluate 7!4!/3!6! Simplyfy your answer
Answer:
28
Step-by-step explanation:
Steps 1 : for the top numerator 7!4! =
7! = 7×6×5×4×3×2×1
4!=4×3×2×1
step 2 : for the bottom denominator 3!6!
3!= 3×2×1
6!=6×5×4×3×2×1
step 3 : is to cancel out all number that looks like on numerator over denominator
it will leave you with 7 × 4 only on the numerator = 28
because all the number in the denominator will cancel out with some on the numerator .
I hope it helps
The simplified solution of the factorial expression (7!4!)/(3!6!) is 14/3.
The given expression is
(7!4!)/(3!6!)
We can simplify it using properties of factorials.
First, let's expand each factorial:
7! = 7 x 6 x 5 x 4 x 3 x 2 x 1
4! = 4 x 3 x 2 x 1
3! = 3 x 2 x 1
6! = 6 x 5 x 4 x 3 x 2 x 1
Now, we can substitute these factorials into the original expression:
(7!4!)/(3!6!) = (7 x 6 x 5 x 4 x 3 x 2 x 1 x 4 x 3 x 2 x 1) / (3 x 2 x 1 x 6 x 5 x 4 x 3 x 2 x 1)
Next, we can cancel out common factors from the numerator and denominator:
(7 x 4)/(3 x 2 x 1) = 28/6
Simplifying:
28/6 = 14/3
Therefore, the simplified solution to (7!4!)/(3!6!) is 14/3.
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WILL MARK BRAINLEST AND THANKS Area: 28.67 sq m and the side is 4.7 m The missing side length is equal to:??? m
Answer:
The area of this is 28.67 meters squared
Step-by-step explanation:
You must use division in order to complete the question
Need help I’m on a timer
Answer:
b. 59
Step-by-step explanation:
cosΘ = 42/82
Θ ~= 59.1898
Sorry, you guys I put the subject in Math its english! But have a nice day! and please help me!
Answer:
disappoint
recall
disgusted
reunited
prepare
The rate of change of the number of students at a high school in Naples is the same from 2005 to 2013 as it is from 2013 to 2021. Is function f constant, linear, quadratic, or exponential?
A. Linear
B. Quadratic
C. Exponential
Answer:
Step-by-step explanation:
Linear
Shirley's water bottle is half full. She pours it into another bottle that is
one-third full, and it fills that bottle. If the second bottle holds 2 quarts,
how much did the first bottle hold? *
pls be right, im on rush time guys
Answer:
Step-by-step explanation:
She poured ⅔×2 = 4/3 qt into the second bottle.
Her bottle holds 2×4/3 = 8/3 qt
Consider this right triangle.
o
13
M
N
12
Select the ratio equivalent to tan(O).
Answer:
5/13
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
About 40% of athletes at a gym use a professional trainer. The proportion of successes is when p = 0.4. You choose a random sample of 50 athletes at the gym.
Answer: 0.089
Step-by-step explanation:
Math
helpp it due in 10 min!!!
the answer for that should be C
Answer:
I think its c
Step-by-step explanation:
4 is the initial cost and 55 is the amount per ticket
Carl has 50 apps on his phone. Of these apps, 12 are music apps. What percent of Carl’s apps are music apps?
AANNSSWWEER
AASSAAPP
Answer:
12 50 I don't know
Step-by-step explanation:
Show how to approximate the required work by a Riemann sum. Then express the work as an integral and evaluate it. A spherical water tank, 24 ft in in diameter, sits atop a 60 ft tower. The tank is filled by a hose attached to the bottom of the sphere. If a 1.5 horsepower pump is used to deliver water up to the tank, how long
Answer:
The time it will take is approximately 104,128 seconds
Step-by-step explanation:
The given parameters are;
The diameter of the tank, D = 24 ft.
Therefore, the tank radius, R = D/2 = 24 ft./2 = 12 ft.
The height of the tower on which the tank sits, h = 60 ft.
The hose through which the tank is filled is attached at the bottom of the tank
The radius of a slice of sphere, r = √(R² - y²) = √(12² - y²)
The power of the pump which is used to deliver the water = 1.5 horsepower
The volume of a slice of water in the tank, V = π·r²·Δx = π·(√(12² - y²))²·Δx ft³ = (144 - y²)·π·Δx ft³
The force of the slice, F = V·g·ρ = (144 - x²)·π·Δx ft³ × 62.5 lb/ft³
Let '[tex]y_i[/tex]' represent the height to which each slice is pumped in the tank, we have;
y = R - (√(R² - x²)) = 12 - (√(144 - x²)
[tex]\lim\limits_{n \to \infty}\ \sum\limits_{i=0}^n (144 - x^2) \cdot \pi \times 62.5 \cdot y_i\ \Delta x \ lb[/tex]
The work done is therefore;
[tex]W = 62.5\times\pi \times \int\limits^{12}_{-12} {(144 - x^2) \cdot(12-(\sqrt{144-x^2} ) \ } \, dx = 632044.366475 \ ft. \cdot lb[/tex]
The work done in filling the tank, W = 632,044.366475 ft·lb
The work done in lifting the water to the base of the tank, W₂ = V·ρ·g×h
[tex]\therefore W_2 = 60 \times 62.5\times\pi \times \int\limits^{12}_{-12} {(144 - x^2) \ } \, dx = 632044.366475 \ ft. \cdot lb = 85273382.0257[/tex]
Therefore, W₂ = 85,273,382.0257 ft.lb
The total work done by the pump,
W = 85,273,382.0257 ft.lb + 632,044.366475 ft·lb = 85,905,426.3922 ft.lb
The time it will take the pump to fill the tank, 't', is given as follows;
1
Power, P = Work, W/(Time, t)
∴ t = W/P
P = 1.5 HP = 550 × 1.5 ft·lb/s = 825 ft·lb/s
t = 85,905,426.3922 ft.lb/(825 ft·lb/s) = 104,127.789566 s
The time it will take, t ≈ 104,128 seconds
I WILL GIVE BRAINERLEST ABD LIKE AND 5 STARS IF YOU ANSWER
How many people n would be seated in
each section if there were 27 total
people in the gym?
Answer:
IT SAYS IT 27 PEOPLE WOULD BE SEATED
Step-by-step explanation:
a culture of bacteria has an initial population of 2100 bacteria and doubles every 4hours. using the formula Pt = P0 • 2 t/d, where Pt is the population after t hours, P0 is the initial population, t is the time in hours and d is the doubling time, what is the population of bacteria in the culture after 11hours, to the nearest whole number?
Answer:14127
Step-by-step explanation:
Po=2100
T=11
D=4
Pt=po•2 t/d
Pt=2100•2 11/4
Pt=14127.0598=14127
Find the capacity of the tanks with the following internal dimensions. Express the capacity in cubic meters and liters for each tank.
Step-by-step explanation:
i) Capacity(Volume) = length x breadth x depth
= 3.2 x 2.9 x 1.5
= 13.92 m³
In litres, 13.92 x 1000 = 139,20 litres
ii) Capacity(Volume) = length x breadth x depth
= 2.5 x 1.6 x 1.3
= 5.2 m³
In litres, 5.2 x 1000 = 5200 litres
iii) Capacity(Volume) = length x breadth x depth
= 7.3 x 3.6 x 1.4
= 36.792 m³
In litres, 36.792 x 1000 = 36,792 litres
What is the area surface of the pyramid please do not do any files or links just say the answer and do not guess
Answer:
448
Step-by-step explanation:
ill mark brainlist plss help
Answer:
25 in²
Step-by-step explanation:
formula for area of a triangle:
1/2(bxh)
1/2(5x10)
1/2(50)
25
Answer:
D. [tex]25^{2}[/tex]
Step-by-step explanation:
"K Co.'s" bonds currently sell for $1,150. They have a 6.75% semi-annual coupon rate and a 15-year maturity and are callable in 6 years at $1,067.50. Assume that no costs other than the call premium would be incurred to call and refund the bonds, and also assume that the yield curve is horizontal, with rates expected to remain at current levels on into the future. Under these conditions, what rate of return should an investor expect to earn if he or she purchases these bonds, the YTC or the YTM? Why?
Ans.......
YTC ...................................
Step-by-step explanation:
A market research company employs a large number of typists to enter data into a computer. The time taken for new typists to learn the computer system is known to have a normal distribution with a mean of 90 minutes and a standard deviation of 18 minutes. The proportion of new typists that take at most two hours to learn the computer system is
Answer:
The proportion of new typists that take at most two hours to learn the computer system is 0.9525 = 95.25%.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Normal distribution with a mean of 90 minutes and a standard deviation of 18 minutes.
This means that [tex]\mu = 90, \sigma = 18[/tex]
The proportion of new typists that take at most two hours to learn the computer system is
This is the pvalue of Z when X = 120 minutes = 2 hours. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{120 - 90}{18}[/tex]
[tex]Z = 1.67[/tex]
[tex]Z = 1.67[/tex] has a pvalue of 0.9525.
The proportion of new typists that take at most two hours to learn the computer system is 0.9525 = 95.25%.
Rita has a sister named Gabriela who is 4 years older than she is. The product of their ages is 21. Write an equation to find their ages.
Step-by-step explanation:
let Rita = R
Let Gabriela = G
so we have
G ×R = 21
G= R + 4
(R+4)(R) = 21
R^2+4R -21=0
At a Dance Team fundraiser, there is a pie toss going on and Claudia is
tossing pies at her coach.
The path of a pie models a quadratic, and the height is shown in this table.
What is the maximum height of the pie?
Probability is the likelihood of an event happening and is expressed as a number between ____ and ____.
-1 and 2
-1 and 100
-0 and 1
-0 and 100
Answer:
0 and 1
Step-by-step explanation:
"The probability ot an event lies between 0 and 1"
Solve for x. Enter the solutions from least to greatest. (x + 3)^2 - 4 = 0
The solutions of x in the equation are -5 and -1
What are quadratic equations?Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
How to determine the solution of x?The equation is given as
(x + 3)^2 - 4 = 0
Add 4 to both sides of the equation
So, we have
(x + 3)^2 = 4
Take the square root of both sides
x + 3 = ±2
Subtract 3 from both sides
x = - 3 ± 2
Evaluate
x = (-3 - 2, -3 + 2)
This gives
x = (-5, -1)
Hence, the solutions of x in the equation are -5 and -1
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Find the value of x in the picture below.
Answer:
I think that the answer is 2.5 , the second item .
HELP!!!
Determine whether the sequence converges or diverges. If it converges, give the limit.
36, - 6, 1, - , ...
a. Converges;
b. Converges;
c. Converges; 6660
d. Diverges
Answer:
c
Step-by-step explanation:
i just took a test on it
The sequence converges to 0.
What is geometric sequence?"It is a type of sequence where the ratio of every two consecutive terms is a constant."
Formula to find the nth term of geometric sequence:"[tex]a_n=a_1\times r^{n-1}[/tex]
where [tex]a_1[/tex] is the first term, and r is the common ratio."
What is the convergent sequence?"If [tex]\lim_{n \to \infty} a_n[/tex] exists and is finite we say that the sequence is convergent.
where [tex]a_n[/tex] is the n-th term of the sequence."
What is the divergent sequence?" If [tex]\lim_{n \to \infty} a_n[/tex]doesn't exist or is infinite we say the sequence diverges.
where [tex]a_n[/tex] is the n-th term of the sequence."
For given question,
We have been given a sequence.
36, - 6, 1, - , . . .
The first term of the sequence is [tex]a_1=36[/tex]
[tex]\frac{-6}{36}=-\frac{1}{6}\\\\ \frac{1}{-6}=-\frac{1}{6}[/tex]
The ratio of every two consecutive terms is a constant.
⇒ [tex]r=-\frac{1}{6}[/tex]
So, the n-th term of given geometric sequence would be,
[tex]a_n=36\times (-\frac{1}{6})^{n-1}[/tex]
Now we determine whether the sequence is convergent or divergent.
[tex]\lim_{n \to \infty} a_n \\\\= \lim_{n \to \infty}36\times (-\frac{1}{6} )^{n-1}\\\\=36\times \lim_{n \to \infty} (-\frac{1}{6} )^{n-1}\\\\=36\times 0\\\\=0[/tex]
Since [tex]\lim_{n \to \infty} a_n[/tex] exists and is finite we say that the sequence is convergent.
Therefore, the sequence converges to 0.
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Write the equation for a line with a slope of 1/3 that passes through the point 6,12
Answer:
y-12=1/3(x-6)
Step-by-step explanation:
Using the slope intercept form:
[tex]y - yo = m(x - xo) [/tex]
We can see from the given point (6,12) that yo = 12 and xo = 6. The slope, m, is 1/3. Plugging in the values gives us this equation in slope-intercept form that can then be converted to any other form.
Given you select a female, what probability will they prefer playing NBA2K20? Round your answer to the nearest thousandth. __________A. 0.609 B. 0.463 C. 0.185 D.0.398
Answer:
B
Step-by-step explanation:
just divide 152 by 328 and youll get 0.463
I need help with this
Answer:
i need help with this so you can ready
If Matrix A is 3 x 4, and Matrix B is 4 x 2, what is the size of matrix BA? If BA is undefined, please state so.
Answer:
Joe Mok
Step-by-step explanation:
Joe MAMA
5. What type of quadrilateral is DEFG?
A square
B rhombus
trapezoid
D parallelogram
Answer:
parallelogram
options D
I took the test and got it right.
determine the value of X, and the measure of angle E
Answer:
y = 55
x = 6
∠E = 70
Step-by-step explanation:
Hello There!
Segment DE and segment EF are congruent meaning that there opposite angles are congruent
So angle D and angle F are congruent
Because ∠D = 55 ∠F also equals 55
now we can solve for x
Remember all of the angles in a triangle add up to equal 180 so we use this equation to solve for x
180=55+55+11x+4
step 1 combine like terms
55+55+4=114
now we have
180=11x+114
step 2 subtract 114 from each side
180-114=66
now we have
66=11x
step 3 divide each side by 11
66/11=6
11x/11=x
we´re left with
x=6
Now we can plug in 6 to x to find the measure of angle E
6x11=66
66+4=70 so angle E = 70