Answer:
[tex]10!\:\times \:20!=\:8.82851\:\times\:10^{24}[/tex]
[tex]17!\:\times \:9!\:=\:1.29072\:\times \:10^{20}[/tex]
Step-by-step explanation:
1)
Given the expression
[tex]10!\times \:20![/tex]
[tex]\mathrm{Apply\:factorial\:rule}:\quad \:n!=1\times 2\times 3\times \ldots \times \:n[/tex]
[tex]10!=1\times \:2\times \:3\times \:4\times \:5\times \:6\times \:7\times \:8\times \:9\times \:10[/tex]
[tex]20!=1\times \:2\times \:3\times \:4\times \:5\times \:6\times \:7\times \:8\times \:9\times \:10\times \:11\times \:12\times \:13\times \:14\times \:15\times \:16\times \:17\times \:18\times \:19\times \:20[/tex]
Now, multiplying the result
[tex]10!\times \:20!= 1\times \:2\times \:3\times \:4\times \:5\times \:6\times \:7\times \:8\times \:9\times \:10\times \:1\times \:2\times \:3\times \:4\times \:5\times \:6\times \:7\times \:8\times \:9\times \:10\times \:11\times \:12\times \:13\times \:14\times \:15\times \:16\times \:17\times \:18\times \:19\times \:20[/tex]
so
[tex]10!\:\times \:20!=\:8.82851\:\times\:10^{24}[/tex]
Thus, we conclude that:
[tex]10!\:\times \:20!=\:8.82851\:\times\:10^{24}[/tex]
2)
Given the expression
[tex]17!\:\times \:9![/tex]
[tex]\mathrm{Apply\:factorial\:rule}:\quad \:n!=1\times 2\times 3\times \ldots \times \:n[/tex]
[tex]17!=1\times \:2\times \:3\times \:4\times \:5\times \:6\times \:7\times \:8\times \:9\times \:10\times \:11\times \:12\times \:13\times \:14\times \:15\times \:16\times \:17[/tex]
[tex]9!=1\times \:2\times \:3\times \:4\times \:5\times \:6\times \:7\times \:8\times \:9[/tex]
Now, multiplying the result
[tex]17!\:\times \:9!=1\times \:2\times \:3\times \:4\times \:5\times \:6\times \:7\times \:8\times \:9\times \:10\times \:11\times \:12\times \:13\times \:14\times \:15\times \:16\times \:17\times \:1\times \:2\times \:3\times \:4\times \:5\times \:6\times \:7\times \:8\times \:9[/tex]
so
[tex]17!\:\times \:9!\:=\:1.29072\:\times \:10^{20}[/tex]
Thus, we conclude that:
[tex]17!\:\times \:9!\:=\:1.29072\:\times \:10^{20}[/tex]
what I the range of f(x)=4^x?
A. all positive real numbers
B. all real numbers
C. all real numbers grater that or equal to 4
D. all real numbers grater than 4
Answer:
We conclude that the range of the function is 'all positive real numbers'.
Thus, option (A) is true.
Step-by-step explanation:
Given the expression
[tex]f\left(x\right)=4^x[/tex]
Determining the domain:
The domain of a function is the set of input values for which the function is real and defined.
It is clear that the given function has no undefined points nor domain constraints.
Therefore, the domain is: -∞ < x < ∞
Thus,
[tex]\mathrm{Domain\:of\:}\:4^x\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<x<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}[/tex]
Determining the range:
The range is the set of values of the dependent variable for which a function is defined.
We know that the range of an exponential function of the form
[tex]c\cdot \:n^{ax+b}+k\:\mathrm{is}\:\:f\left(x\right)>k[/tex]
[tex]k=0[/tex]
In other words, the range is all positive real numbers.
Thus,
[tex]\mathrm{Range\:of\:}4^x:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)>0\:\\ \:\mathrm{Interval\:Notation:}&\:\left(0,\:\infty \:\right)\end{bmatrix}[/tex]
Therefore, we conclude that the range of the function is 'all positive real numbers'.
Thus, option (A) is true.
A subway car travels at a rate of 32 meters per second. How far does it travel in 16 seconds?
What is the sum of 2x-5y+x+y
Answer:
3x - 4y
Step-by-step explanation:
2x + -5y + x + y
Group Like terms:
2x + x + -5y + y
2x + x = 3x
-5y + y = -4y
3x - 4y
What is this please help
find 24% of 165.........................................
Answer:
39.6
Step-by-step explanation:
Answer:
39.6
Step-by-step explanation:
If you need an explanation i can edit the answer and give you one.
Use the ALEKS graphing calculator to solve the system of equations.
y=-2x² - 4x-1
y = 3x+10
Round to the nearest hundredth.
If there is more than one solution, use the "or" button.
If applicable, click on "No solution".
(x, y) = (0
or
No
Solution
X
$
?
Answer:
This system has no solution in the set of real numbers.
Answer:
No solution
Step-by-step explanation:
The equations given are ;
y=-2x² - 4x-1
y = 3x+10
Using a graphing tool, the graphs of the equations are as shown in the attached.
From the graph, a solution occurs where the two graphs intersect. However, in this case, the graphs do not intersect hence there is no solution.
When you expand 2 (6x + 12), you get an answer of 12x + 24. How many other ways can
you use brackets so you get the answer of 12x + 24 when you expand them?
Answer:
3(4x+8) or 4(3x+6) or 12(x+2)
Step-by-step explanation:
Answer:
3(4x+8) or 4(3x+6) or 12(x+2)
Step-by-step explanation:
Elizabeth ate lunch and wanted to leave her waitress a 15% TIP. Her meal cost $8.95. How much money should Elizabeth leave total?
Answer:
$10.2925, Rounded up: 10.30
Step-by-step explanation:
First, you find what 15% is in a decimal. so you do 15 x 100 to get 0.15
Then you multiply that by 8.95 to get 1.3425
Finally, you add up the numbers and get 10.30 as a rounded answer :D
what does this mean?
Answer:
That means you finished.
Step-by-step explanation:
what's the area of the quadillateral
Answer:
The area of the quadillateral is 360 degree.
Step-by-step explanation:
Hope this helped!
Have an amazing day!
Laura bought some books. She spent a total of $71 after a discount of $5 off of her total purchase. Each book cost $4. How many books did she buy?
Answer:
4b-5=71
19 books
Step-by-step explanation:
b represents books, and 4 is the cost, so the cost (4•19) minus the discount (-5) equals 71 and solves the equation
On Monday, Byron spent $8.00 on lunch to purchase two tacos and one burrito. On Wednesday, he purchased one enchilada, one taco, and one burrito and spent $8.50. On Friday, it cost Byron $10.00 for two enchiladas and two tacos. If t represents the cost of a taco, b represents the cost of a burrito, and e represents the cost of an enchilada, which system of equations can be used to find the cost of each?
Answer:
2t+b=8.00
e+t+b=8.50
2e+2t=10.00
Step-by-step explanation:
Which number line shows Point A at −4, Point B at 2.5, Point C at −2 and 1 over 2, and point D, which is the opposite of point A?
Answer:
the answer is D
Step-by-step explanation:
Answer:
Your answer would be D
Step-by-step explanation:
:)
What is 3×7×7×7×7 using index notation
Answer: 3 x 7^4
Because there's one 3 & four 7's .
Step-by-step explanation:
2xsquared . 6 =
What does 2xsquared times 6 equal?
Answer:
24x
Step-by-step explanation:
Select all the expressions that are equivalent to y'.
Answer:
A, B, D
Step-by-step explanation:
A) y squared times y squared you just add the exponents
B) y^6/y^2 write it out as (y)(y)(y)(y)(y)(y)/(y)(y) then u cancel out two "y" from numerator and denominator and is left with y^4
C) is just 0 so its wrong
D) is the same process as B just cancel out 5 "y" from numerator and denominator and is left with y^4
E) is incorrect bc you need to add the exponents and you will get y^5 which is not equal to y^4 so yeah its wrong
what is a preimage and image of triangle in a translation
Answer:
translation to what language?
Step-by-step explanation:
9514 1404 393
Explanation:
The preimage is the original triangle, the figure before any transformation is done to it.
The image is the result of applying a transformation to the preimage.
__
When the transformation is translation, the image is congruent to the preimage, but is located in a different place. It is not rotated or reflected if the only transform is translation.
What is the answer to this?
Answer:
dfgv nm./
Step-by-step explanation:
A textbook store sold a combined total of 392 physics and psychology textbooks in a week. The number of physics textbooks sold was three times the number of psychology textbooks sold. How many textbooks of each type were sold?
Answer:
Psychology textbooks = 98 and physics textbooks = 294
Step-by-step explanation:
Let there are x psychology textbooks sold.
No of physics textbooks sold = 3x
ATQ,
A textbook store sold a combined total of 392 physics and psychology textbooks in a week.
x + 3x = 392
4x = 392
x = 98
It means there are 98 psychology textbooks sold and 3x = 3(98) = 294 physics textbooks sold.
2(2.5x+8)=26
what does x=?
plz help
Answer:
x=2
Step-by-step explanation:
Hope this helps!
Answer:
simplifying x = 2
Step-by-step explanation:
reordering the terms then solving + 5x =26
add -16 to each side of the equation
16 = -16 + 5x = 26+ -16
4t + 2u
w;t= 2 and u= 1
15
Step-by-step explanation:
4t + 2u²- u³
4×2=8
2×1=2²=8
1³=1
8+8-1
16-1=15
Jake had 42 frogs and gave the same number of frogs to each of his & cousins. If each cousin receives 14 frogs, did Jake have 2, 3, or 6 cousins?
pleas answer 100% honestly
Answer: 3 cousins
Step-by-step explanation:
Each of his cousins gets the same number of frogs, which is 14. To find the number of cousins Jake has, you need to divide 42 by 14, which is 3. Thus, Jake has 3 cousins.
CosA-[1+sin2A]1/2
_______________=TanA
SinA-[1+sin2A]1/2
Answer:
[tex]\frac{cosA-(1+sin2A)^{\frac{1}{2} } }{sinA-(1+sin2A)^{\frac{1}{2} } } =tanA[/tex]
Step-by-step explanation:
Step(I):-
Given
[tex]\frac{cosA-(1+sin2A)^{\frac{1}{2} } }{sinA-(1+sin2A)^{\frac{1}{2} } }[/tex]
By using sin²x+cos²x =1
now
= [tex]\frac{cosA-(1+sin2A)^{\frac{1}{2} } }{sinA-(1+sin2A)^{\frac{1}{2} } }[/tex]
= [tex]\frac{cosA-(sin^{2} +cos^{2}x +2sinAcosA)^{\frac{1}{2} } }{sinA-(sin^{2}x+cos^{2} x +s2sinAcosA){\frac{1}{2} } }[/tex]
= [tex]\frac{cosA-(sinx +cosx)^{2} )^{\frac{1}{2} } }{sinA-(sinx+cos x)^2){\frac{1}{2} } }[/tex]
After simplification , we get
= [tex]\frac{cosA-(sinA+cosA)}{sinA-(sinA+cosA)}[/tex]
= [tex]\frac{-sinA}{-cosA}[/tex]
= tanA
Ashley and her four friends went trick-or-treating. Each one of them got 4/5 of a bag of treats. How many bags of treats did they have in total?
Answer:
4 bags
Step-by-step explanation:
Since there were five in total, and each got 4/5 evenly, it's just basic adding while subtracting the amount from the other bags.
So to get 5/5, which is a full bag, you take portions out of the others to create a full one. Write out 4/5, five times, and then subtract the needed portions from a separate bag to combine a full one.
HELP!!! ASAP MARKING BRAINLIEST!!!!
Answer:
A. y=1/2x-4
Step-by-step explanation:
maths
A rancher decreased the number of his
herd from 150 head to 120 head of cattle.
What was the percent of decrease in the
number of cattle?
Please hurry
Answer:
20%
Step-by-step explanation:
150-120 is 30
30 is 1/5 of 150
1/5 is .2, which is 20%
Hope that helps~
Consider the following functions below.
f (x) = 2x² + 3x - 5
g(x) = 5x2 + 4x – 1
Which of the following represents g
g(x) – f(x)?
o - 3x² – x-4
o – 3x² + 7x - 6
3x²+x+4
3x² + 7x - 6
Samantha invested $670 in an account paying an interest rate of 5.5% compounded daily. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $1,740?
Answer:
17 years
Step-by-step explanation:
The formula for the value of an account earning compound interest can be used to find the number of years. That formula is ...
A = P(1 +r/n)^(nt)
where P is the principal invested at annual rate r compounded n times per year for t years.
__
Solving for t, we find ...
A/P = (1 +r/n)^(nt) . . . . . . divide by P
log(A/P) = nt·log(1 +r/n) . . . . take logarithms
t = log(A/P)/(n·log(1 +r/n)) . . . . . divide by the coefficient of t
For the given values, the time required is ...
t = log(1740/670)/(365·log(1 +0.055/365)) ≈ 17.353
It would take about 17 years for the account value to reach $1740.
_____
Additional comment
The time-value-of-money (TVM) apps of your calculator or spreadsheet can be used to find the time period of interest. Here, setting P/Y = 1 gives N in years.
Solve each equation for 0< theta < 2pi
3-2sin theta=5
Step-by-step explanation:
3 - 2sinθ = 5
2sinθ = -2
sinθ = -1
Therefore θ = 3π/4.
multiply 4-6i and -4+2i
Answer:
-4 + 32i
Step-by-step explanation:
use the distributive property to multiply
remember: i^2 = 1
(4 - 6i)(-4 + 2i)
-16 + 8i + 24i - 12i^2
-16 + 32i - 12(- 1)
-16 + 32i +12
-4 + 32i
Answer:
4 - (6 * i)) * ((-4) + (2 * i)) =
-4 + 32 i
Step-by-step explanation: