Step-by-step explanation:
2^400=2^(2×200)
2^(2×200) =[2^(2) ]^200
Now, [2^(2) ]^200=4^200
The power of 2 in 400! is 397.
What is the method of determination of power of prime in Factorial ?Let p is the prime number whose power is to be found
Let n is the factorial number then
p in n! = (n /p) + (n/p²) +(n/p³) + .......
until Numerator < Denominator
and after division only the integer part is taken
Therefore to determine the power of 2 in 400!
2 in 400! = (400 /2) + ( 400 /2²) + (400 /2³) +(400 /2⁴) +(400 /2⁵) +(400 /2⁶) +(400 /2⁷) +(400 /2⁸) + above this N < D
2 in 400! = 200 +100 +50+25+12+6+3+1
2 in 400 = 397
Therefore the power of 2 in 400! is 397.
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What is the value of 4 + 23. 3? Show your work.
Answer:
27.3
Step-by-step explanation:
4
23.3 +
27.3
You can align the numbers over each other and simply add them.
Find the 37th term of the arithmetic sequence: -38,-8,22,52
Answer:
1042
Step-by-step explanation:
-38,-8,22,52
The common difference is 52 - 22 = 30
a_1 = -38
a_2 = -38 + 30
a_3 = -38 + 2 * 30
a_4 = -38 + 3 * 30 (notice that the common difference is multiplied by 1 less than the term number)
a_n = -38 + (n - 1)30 (since the term number is n, we multiply the common difference by n - 1)
a_n = -38 + 30(n - 1)
a_37 = -38 + 30(37 - 1)
a_37 = 1042
(((please answer asap!!))).
25 gallons!have a nice day
Answer:
25 gallons of water
Step-by-step explanation:
1 minute= 2.5 gallons
10 minutes = 2.5 x 10
= 25 gallons
20. (01.03 MC)
What is the simplified expression
? (1 point)
Answer:
[tex]\displaystyle 3^2[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Exponential Rule [Multiplying]: [tex]\displaystyle b^m \cdot b^n = b^{m + n}[/tex]Exponential Rule [Dividing]: [tex]\displaystyle \frac{b^m}{b^n} = b^{m - n}[/tex]Step-by-step explanation:
Step 1: Define
[tex]\displaystyle \frac{3^3 \cdot 3^3}{3^4}[/tex]
Step 2: Simplify
[ER] Multiply: [tex]\displaystyle \frac{3^{3+3}}{3^4}[/tex]Add Exponents: [tex]\displaystyle \frac{3^6}{3^4}[/tex][ER] Divide: [tex]\displaystyle 3^{6 - 4}[/tex]Subtract Exponents: [tex]\displaystyle 3^2[/tex]4. a. Write a story to represent the equation 15 ÷ 1/9 : _______. Solve the equation and complete the story.
b. What multiplication equation shows that your division is correct?_________________________. This is due tomorrow. I need your help.
Answer:
4555
Step-by-step explanation:
32233x222213456765x345665434565
Devi rides the bus to her grandmother's house every day. She tracked how many minutes the bus rides took for one week: 24 32 25 24 30 30 24 calculate the mean, median, range, and mid range of the bus ride times for a week
Answer:
Mean: 27
Median: 25
Range: 8
Mid Range: 28
Step-by-step explanation:
The value of mean, median, range and mid range will be 27 , 24 , 8 and 28 respectively.
It is given that the time in minutes for which Devi rides the bus in a week is 24, 32, 25, 24, 30, 30, 24.
We have to find out the value of mean, median, range and mid range.
What is mean of numbers ?
The mean of numbers is the ratio of sum of all numbers to the total no. of numbers.
As per the question ;
The time in minutes for which Devi rides the bus in a week is ;
24, 32, 25, 24, 30, 30, 24.
So ;
The mean will be ;
= [tex]\frac{24 + 32 + 25 + 24 + 30 + 30 +24}{7}[/tex]
= [tex]\frac{189}{7}[/tex]
= 27
and
We know that when n is odd number then ; Median is ;
= [tex]\frac{n+1}{2}th[/tex] term
= [tex]\frac{8}{2}th[/tex] term
= 4th term
= 24
and
Range will be ;
= largest number - smallest number
= 32 - 24
= 8
and
Mid range will be ;
= (largest number + smallest number) / 2
= [tex]\frac{32 + 24}{2}[/tex]
= 56 / 2
= 28
Thus , the value of mean, median, range and mid range will be 27 , 24 , 8 and 28 respectively.
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WILL DO ABSOLUTELY ANYTHING FOR THIS ONE HELP ASAP TIMES
9514 1404 393
Answer:
A) -1 < x < 0
Step-by-step explanation:
The horizontal line that is the x-axis is also the line y = 0. The curve is above that line when x < 0, and when x > 3.6.
The only interval that overlaps either of these regions is ...
(A) -1 < x < 0
pls help i don’t get it , ill mark brainlist
Answer:
2 Radical 50
Step-by-step explanation:
Now we need to reduce the 100,since 2 is not reducible its automatically goes outside the radical. To reduce the 100 we can multiply 50 times 2.You can see now that the 2 in the radical is also not reducible so that also has to go outside the radical. When you get two numbers that are alike you don't necessarily combine them but only use one of them.
in the problem find m<1
Answer:
m∠1 = 124°
Step-by-step explanation:
If this is the case then m∠1 and m∠2 are congruent to each other with the same angle in which m∠2 is also 124°, if m∠3 is said to be 56°. Also, a straight angle has to equal to 180° in which the first angle is classified as obtuse.
Help I’m being timed!!
Answer:
Area of circular trail = 7.1 square miles
Step-by-step explanation:
Given that:
Distance covered by Mr. Baker = 6 miles
As this distance is of both sides, we will divide it by 2 which will give us the diameter of the circle.
Distance of one side = 6/2 = 3 miles
Diameter = 3 miles
Radius = 3/2 = 1.5 miles
Area of circle = [tex]\pi r^2[/tex]
Area of circle = [tex]3.14*(1.5)^2[/tex] = 3.14 * 2.25
Area of circle = 7.065 = 7.1 square miles
Hence,
Area of circular trail = 7.1 square miles
Solve for a: b − 2a = c
Answer:
[tex]a=-\frac{c-b}{2}[/tex]
Step-by-step explanation:
Solving for the variable [tex]a[/tex], given that :
[tex]b-2a=c[/tex]
We can first start start by subtracting [tex]b[/tex] from both sides of the equation:
[tex]-2a=c-b[/tex]
Now, we can divide both sides of the equation by the coefficient of [tex]a[/tex], which would be [tex]-2[/tex]:
[tex]a=\frac{c}{-2}-\frac{b}{-2}[/tex]
Applying the fraction rule [tex]\frac{a}{c}\pm\frac{b}{c} =\frac{a\pm b}{c}[/tex]:
[tex]a=\frac{c-b}{-2}[/tex]
Then, apply the fraction rule [tex]\frac{a}{-b} =-\frac{a}{b}[/tex]
[tex]a=-\frac{c-b}{2}[/tex]
30-60-90 please help me find the long side and short side Urgent
Answer:
just download conects
Step-by-step explanation:
You are taking a test in math. There are 20 questions and 30 minutes.
How many questions do you have for 12 minutes?
______questions
How much time do you have for 15 questions?
_________minutes
How much time do you have for 5 questions?
________minutes
Answer:
8, 10, 3.3333
Step-by-step explanation:
look at the picture for an explanation,
use the same method for all 3
A cabinetmaker is asked to build a cabinet with dimensions of 8 inches wide by 14 inches long by 40 inches tall. He is then asked to reduce the size of the cabinet by a scale factor of 3/4. What are the new dimensions of the cabinet?
Answer:
6 inches by 10 1/2 inches by 30 inches
Step-by-step explanation: To find this answer you have to multiply the old dimensions by the scale factor which is 3/4. You would do 8 times 3/4 which is 6 inches. Then 14 inches times 3/4 which is 10 1/2. And then 40 inches times 3/4 and that answer is 30 inches. Those are the new dimensions for the cabinet.
g(x) = 2x² +16x+35
(a) Write the equation in the form g (x)= a (x - h)2 + k.
Answer:
The equation g(x) = 2(x+4)² +3
(h,k) = (-4,3) and a = 2
Step-by-step explanation:
Step(i):-
Given equation g(x) = 2 x² + 16 x +35
g(x) = 2(x² +8 x ) +35
g(x) = 2(x² +2(4) (x ) +(4)² -(4)²)+35
we know that (a+b)² = a²+2ab+b²
Step(ii):-
g(x) = 2( x+4)² - 2(16) +35
⇒ g(x) = 2(x+4)² - 32 +35
⇒ g(x) = 2(x+4)² +3
comparing g(x) = a (x-h)² +k
(h,k) = (-4,3) and a = 2
Final answer:-
The equation g(x) = 2(x+4)² +3
(h,k) = (-4,3) and a = 2
cos ( 3 x )
sin ( 3 x )
tan ( 3 x )
A scuba diver was at a depth of −8012 feet. How many feet did the scuba diver ascend if the diver traveled to the surface of the ocean?
The scuba driver traveled to the sea level which is 8012 feet
what is sea level?Sea level is measured in relation to the adjacent land. Just like the ocean, the elevation of land may rise and fall over time. For example, the tremendous weight of a glacier on land pushes the land down, closer to sea level. And the sea level at the surface of the ocean is considered to be zero.
Given here, he dived to a depth -8012 feet so he has to ascend again by + 8012 feet to reach the surface of the ocean .
Hence, he traveled 8012 feet.
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High School Advice Situation:
I am in Engineering 1 rn and I am a freshman and my semester 1 grade is a C and I am struggling, so I am thinking of withdrawing from my elective and go to a different elective which I know I can get an A+ in, but should I, because when I withdrawal I think it shows as an F. Help Please!
Step-by-step explanation:
Which do you enjoy the most?
triangle abc is an isosceles triangle in which ab=ac what is the perimeter of abc
Answer:
C. 10 + squareroot10 units
Step-by-step explanation:
show equation has a slope of -3 and a y-intercept of 8
Answer:
y=-3x+8
Step-by-step explanation:
: Discuss the continuity of the function f(x)=xtan(1/x) at x = 0 given that x≠0 and f(0)=0.
Answer:
Left hand Limit = Right Hand Limit = f(a)
it is a continuous function.
Step-by-step explanation:
Solution:
In order to find out the continuity of the function, we need to keep in mind following things:
Left hand Limit = Right Hand Limit = f(a)
Where, f(x) = exists and f(a) = defined.
Data Given:
f(x) = x tan(1/x) x [tex]\neq[/tex] 0 (this function is used when x > 0 and x<0)
f(x) = 0 when x = 0
First we have to check the Left hand Limit.
L.H.L = f(0-h) (x<0)
Lim[tex]_{x-->0^{-} }[/tex] f(x)
Lim[tex]_{x-->0^{-} }[/tex] x tan (1/x)
Put x = 0-h
Lim[tex]_{x-->0^{-} }[/tex] (0-h) tan (1/(0-h))
Lim[tex]_{x-->0^{-} }[/tex] h tan (1/h)
Putting h = 0
(0) x (tan(1/0)))
As we know, for tanx value is a finitely oscillatory between -∞ to +∞
Hence, 0 x finite number then,
L.H.L = 0
Similarly,
R.H.L = f(0+h)
Lim[tex]_{x-->0^{+} }[/tex] (0+h) tan (1/(0+h))
Lim[tex]_{x-->0^{+} }[/tex] (h) tan (1/(h))
R.H.L = 0
Now, as we know, when x = 0
f(x) = 0
f(0) = 0
Left hand Limit = Right Hand Limit = f(a)
Hence, it is a continuous function.
Raul wants to buy a new collar for each of his 5 dogs. The collars come in a choice of 10 different colors. Step 1 of 2 : How many selections of collars for the 5 dogs are possible if repetitions of colors are allowed
Answer:
100,000
Step-by-step explanation:
Calculation for How many selections of collars for the 5 dogs are possible if repetitions of colors are allowed
Based on the information given since he has 5 dogs that he want to purchase a collar for, which means that if the collar has 10 choice of variety of colors, then the selection of collars for the 5 dogs if repetitions of colors are allowed will be calculated as:
Selections of collars=10*10*10*10*10
Selections of collars=100,000
Therefore the numbers of selections of collars for the 5 dogs that are possible if repetitions of colors are allowed is 100,000
PLZ I NEED ANSWERS. THIS IS MIDDLE SCHOOL LEVEL NOT COLLEGE
Determine whether the given statement is true or false.
13 € {1, 2, 3,..., 23}
Choose the correct answer below.
O True
False
Answer:
true, because 13 is belong to 1 to 23 between number so,
Companies A and B produce phone chargers. Company A makes 15 phone chargers when Company B makes 20 phone chargers. When Company A makes 30 phone chargers, how many phone chargers does Company B make? Write your answers in the blanks.
Answer:
40
Step-by-step explanation:
How do i do these problems? please answer what you can
Answer:
5)85+63=148
180 is how much a reingle add up to so you do
180-148=32
x=32
6)the right angle means 90°
so 90+61=151
180-151=29
x=29
hope it helps
Evaluate the expression (25)=
Answer:
?? im really confused sorry i dont think you finished the question
What is 147.5% as a decimal?
Answer:
1.475
Step-by-step explanation:
When we have a percentage and want to convert it to the decimal, we want to move the decimal 2 places to the left (away from the percentage) or divide by 100.
147.5/100 = 1.475
what is the measurement of 40.382052 degrees in minutes, degrees and seconds
Answer:
40 degrees
22 min's
55.39 sec's
Step-by-step explanation:
Keshon's mother drives Keshon to his grandmother's house to visit. First she drives 60 minutes at a constant speed of 40 mph. Then they reach the highway. She speeds up and drives for another 30 minutes at a constant speed of 70 miles mph
1) How long did the trip take?
2) How far did Keshon and his mother drive together?
Answer:
60+40+30+70=200 this an answer of a and B is 200
Answer:
A. 60+40+30+70=200
B. 200
Step-by-step explanation:
Hope this helps have an amazing day/month/year!
If the measure of ABC is 57º, what is the measure of AB?
Answer:
114°
Step-by-step explanation:
The measure of an arc is double the measure of the angle between the chord and the tangent line.