The largest possible value of n is approximately equal to 331.
What is the largest possible value of the integer n behind a power equation?
In this problem we find a factorial number as the result of a power with a base of 3. First, we need to estimate the maximum possible value of n (as a real number) by using logarithm properties:
3ⁿ = 100!
3ⁿ = 1 · 2 · 3 · ... · 99 · 100
㏒₃ 3ⁿ = ㏒₃ (1 · 2 · 3 · ... · 99 · 100)
n · ㏒₃ 3 = ㏒₃ 1 + ㏒₃ 2 + ㏒₃ 3 + ... + ㏒₃ 99 + ㏒₃ 100
n ≈ 331.090
Second, find the maximum possible integer n related to 100! is found by truncating the result found in the previous section. Hence, the largest possible value of n is approximately equal to 331.
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An epidemiological study of the spread of a certain influenza strain that hit a small school population found that the total number of students, P, who contracted the flu t days after it broke out is given by the model P = -2²+ 17t + 180, where 1 st≤ 6. Find the day that 210 students had the flu. Recall that the restriction on this at most 6.
Submit Answer
Answer:
At the 3rd day 160 students caught flu.
Step-by-step explanation:
Consider the provided model P = − t ² + 13t + 130 where 1 ≤ t ≤ 6
The total number of students is represents by P.
We need to find the day that 160 students had the flu.
Substitute the value of P=160 in above formula.
Hence the value of t=10 or t=3
But it is given that 1 ≤ t ≤ 6, Therefore select t=3
Hence, at the 3rd day 160 students caught flu.
the sum of two numbers is 51, five times the larger number decreased by 7 equals one, more than 8 times the smaller number. find the numbers
Answer: A=32 B=19
Step-by-step explanation:
11 = −5+y
Solve for Y
Answer:
y=16
Step-by-step explanation:
11 = −5+y
Solve for Y
Add 5 to each side
11+5 = -5+y+5
16 = y
y=16
Solve the quadratic equation by completing the square.
x²+18x+79=0
Step-by-step explanation:
completing the square means finding an expression
(x + a)² = b²
or
(x - a)² = b²
(x + a)² = x² + 2ax + a²
(x - a)² = x² - 2ax + a²
because of the "+ 18x" in the original equation we know that we are looking for (x + a)².
now, let's compare the different terms :
x² = x²
18x = 2ax
18 = 2a
a = 9
so, the complete square would look like
(x + 9)² = x² + 18x + 81
but we have only "+ 79" in the original equation.
so, we add the missing 2 (to both sides to keep the equation true)
x² + 18x + 79 + 2 = 0 + 2
x² + 18x + 81 = 2
(x + 9)² = 2
x + 9 = ±sqrt(2)
x1 = sqrt(2) - 9
x2 = -sqrt(2) - 9
x = sqrt(2) - 9, -sqrt(2) - 9
yes, every quadratic equation has 2 solutions.
as every cubic equation has 3 solutions.
and so on.
I neeeddd the answer
Answer: 80 degrees because a line is 180°.
So if you subtract
180 - 100 = 80°
Answer:
x=80°
Step-by-step explanation:
The measures of angle x and the 100° angle form a straight angle.
This straight angle is 180°.
You can subtract the measure of one angle from the whole to find the measure of the other angle.
180°-100°=80°
This means angle x is 80°.
Need help badly, I also need to know how you got the answer.
Answer:
-1/5
y=-1/5 x-8
-1/5 is the slope
Step-by-step explanation:
-1/5
Formula- y=mx+b
The slope-intercept form is
y=mx+b, where m is the slope and b is the y-intercept.
y=mx+b
Rewrite in slope-intercept form.
Simplify the left side
Simplify each term.
Combine 1/8 and x.
x/9+5y/8=-5
Subtract x/8 from both sides of the equation.
5y/8=-5-x/8
Multiply both sides of the equation by8/5.
8/5.5y/8=8/5(-5-x/8)
Simplify both sides of the equation.
Simplify the left side.
Simplify 8/5.5y/8
y=-x/5-8
y=-1/5 x-8
Step-by-step explanation:
Given equation:
1/8x + 5/8y =-5
Now write it in standard form like ax+by+c=0
1/8x + 5/8y + 5= 0
Now,slope of line (m) = -a/b
here value of a is 1/8 and value of b is 5/8
now by formula..
-(1/8)÷(5/8) = m(slope)
-1/8 × 8/5 = m
-1/5 = m
here ia your answer
darcy has a summer job painting houses. he is asked to paint the wooden siding on a house that is 28 feet wide and 35 feet long. the siding extends 6 feet up the side of the house. a) what is the total surface are he must paint? b) a one gallon can of the stain that darcy is using covers approximately 225 ft squared. if darcy applies 2 coats of stain, how many cabs of stain should he buy?
Darcy requires 24.14 gallons of paint to cover an area of 2716 feet².
Length of the house = 35 feet
width of the house = 28 feet
Height of the house = 6 feet
Total surface area = 2 l b + 2 b h + 2 h l
A = 2 (35) (28) + 2 (28) (6) + 2 (6) (35)
A = 1960 + 336 + 420
A = 2716 feet²
If he uses 2 coats of stain, the area he need to cover = 2 (2716) = 5432 feet²
Gallon of paint required = 5432 / 225 = 24.14 gallons.
Therefore, Darcy requires 24.14 gallons of paint to cover an area of 2716 feet².
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solve by completing the square
2x^2-12x-20=0
The square of the equation 2[tex]x^{2}[/tex] – 12x – 20=0 is
What is a quadratic equation?
A quadratic equation is any equation that can be rearranged in standard form as where x represents an unknown, and a, b, and c represent known numbers, where a ≠ 0.
a[tex]x^{2}[/tex]+bx+c , a, b, c are integers .
formula: −b±√b2−4ac/2a
Given equation ,
2[tex]x^{2}[/tex] -12x-20=0
By comparing with the quadratic equation
Here, a=2, b= -12, c= -20.
X=−b±[tex]\sqrt{b^2-4ac}[/tex]/2a
X= -(-12) + [tex]\sqrt{(-12)2-4(2)(20)}[/tex] /2(2)
X=12+- [tex]\sqrt{144-160}[/tex]/4
X=12+- [tex]\sqrt{-16}[/tex]/4,
X=12+- (-4)/4
X=12+(-4)/4 and x=12-(-4)/4
X= 12-4/4 and x=12+4/4
X=8/4 and x= 16/4
X=2 and x= 4
Therefore, the square of the equation 2x2-12x-20=0 is x= 2 and x=4.
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find the length of each segment with the given endpoints
(3, -2) and (-4, 7)
Exact Distance: [tex]\sqrt{130}[/tex] units
Approximate Distance: 11.4018 units
===================================================
Explanation:
Use the distance formula to have the following steps
[tex](x_1,y_1) = (3,-2) \text{ and } (x_2, y_2) = (-4,7)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-(-4))^2 + (-2-7)^2}\\\\d = \sqrt{(3+4)^2 + (-2-7)^2}\\\\d = \sqrt{(7)^2 + (-9)^2}\\\\d = \sqrt{49 + 81}\\\\d = \sqrt{130}\\\\d \approx 11.4018\\\\[/tex]
The exact distance is [tex]\sqrt{130}[/tex] units
This approximates to about 11.4018 units.
POWER TO A POWER
(ax) y =
When raising a base with an exponent to
another exponent, keep the
and
the exponents.
A number raised to a power represents a product where the same number is used as a repeated factor. The number is called the base and the power is given by the exponent. The base is the repeated factor and the exponent counts the number of factors. An exponent is that we are dealing with products and multiplication.
In the expression bn, b is the base and n is the exponent.
The Power Rule for Exponents: (am)n = am*n.
To raise a number with an exponent to a power, multiply the exponent times the power.
Negative Exponent Rule: x–n = 1/xn.
Invert the base to change a negative exponent into a positive.
Zero Exponent Rule: x0 = 1, for .
Any non-zero number raised to the zeroth power is 1.
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Iron has a density of 7.9 g/cm³. Gold has a density of 19.3 g/cm³.
I have a piece of metal that has a volume of 200 cm³ and a mass of 3.86 kg. Is it gold or iron?
I need help please!!
Answer:
9.6*10^-12
Step-by-step explanation:
To calculate this, you will do the mass of 2 times 10^(-12) gram. So, 2*(10)^-12. Then we know 30 hours = 480,000,000 bacteria.
So now now you calculate the mass, 480,000,000 * 2(10)^-12 which gives you 9.6*10^-4.
Sorry if it sounds confusing! I hope this helps, have a good day! :D
Find the value of x in the given diagram.
Answer:
The value of x is 125°.==================================
We see the exterior angle measures given with one unknown.
Recall the sum all exterior angles of a polygon is 360°.
Set up equation and find the unknown value:
70 + 65 + 60 + 40 + x = 360235 + x = 360x = 360 - 235x = 125(a) What was the maximum height the rocket reached?
After how many seconds?
Answer:
Can you provide more info? Like is there a graph that comes along with this question?
Step-by-step explanation:
robert spends 30.45$, before tax, at the store.
The cost of Robert purchase of books after the paid tax is $32.66.
What is defined as the percentage increase?The percentage increase would be the difference between both the final and initial values expressed as a percentage. For other sayings, it is the difference here between final and initial values divided by the original value and multiplied by 100.For the given question;
The original cost of the book purchased by the Robet = $30.45.
The tax of 7.25% is applied on the original cost of the book.
7.25% of $30.45 = (7.25×30.45)/100
7.25% of $30.45 = $2.21
The final cost of the book = original cost + tax
The final cost of the book = $30.45 + %2.21
The final cost of the book = 32.66
Therefore, the total price paid by the Robert for the book after 7.5% of the tax is applied is $36.66.
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The complete question is-
Robert spends $30.45 before tax at the bookstore. If the sales tax rate in his city is 7.25%, what is the total cost of his purchase?
A delivery person uses a service elevator to bring boxes of books up to an office. The delivery person weighs 160 lb and each box of books weighs 50 lb. The maximum capacity of the elevator is 1000 lb. How many boxes of books can the delivery person bring up at one time?
If a delivery person uses a service elevator to bring boxes of books up to an office. The delivery person weighs 160 lb and each box of books weighs 50 lb. The maximum capacity of the elevator is 1000 lb. The number of boxes of books that the delivery person can bring up at one time is: 16.8 boxes.
Number of boxes of booksGiven:
Weight of the delivery person=160 lb
Weight of box of book=50 lb
Maximum capacity=1,000lb
Let b represent the number of boxes of books
Hence,
160+50b=1,000
Collect like terms
50b=1000-160
50b=840
Divide both side by
b=840/50
b=16.8 boxes of books
Therefore the maximum capacity of the elevator is 1000 lb. The number of boxes of books that the delivery person can bring up at one time is: 16.8 boxes.
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Can someone explain why this is a false equation
Step-by-step explanation:
I think the answer is just no solution to begin with since the value of an absolute value will never be a negative number or in this case less than -2. therefore the equation is false
Jack takes 10 minutes to ride his stakeboard down the hill to his friend's house and 20 minutes to ride up the hill from his friend's house. he goes to his friend's house monday through friday. how many minutes does he spend riding his stakeboard to and from his friend's house in two weeks? write an equation to model your work.
Jack spends 300 minutes in two weeks riding his skateboard to and from his friend's house Monday through Friday.
Time taken by Jack to ride his skateboard down the hill to his friend's house = 10 minutes
Time taken by Jack to ride his skateboard up the hill to his friend's house = 20 minutes
Total time combined = 30 minutes
Total days in a week Monday through Friday= 5 days
Total days in 2 weeks = 10 days
Therefore, time spent by jack riding his skateboard up and down the hill to his friend's house in two weeks Monday through Friday = 10*30 = 300 minutes
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I do not understand UPSE what am I so sapouse to do and how?
First of all let me tell you UPSC is the body which conducts the civil services examination in our country. To prepare for the civil services you must know it is the highest offered post by the government to an citizen of India.
You have many subjects in order to complete the syllabus of civil services.
The examination takes place in two parts. In the first part there are multiple choice questions and in the second part there are subjective questions which must be answered in a descriptive format.
The candidate also has to face interview after clearing both the examinations.
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Please find the value of each variable
Step-by-step explanation:
I assume these are all angles.
4x is the arc angle (at the center of the circle) between the 2 endpoints of the short triangle side (baseline).
the trials itself is isoceles, so both legs have the same length, bedclothes the arc angles between their endpoints are equal.
now, when we move the reference point of an arc angle back, back, back to the circle arc, the angle is cut in half.
so, the inner top angle of the triangle is therefore 4x/2 = 2x.
because of the isoceles nature, the second triangle inner angle at the baseline is also x.
the sum of the triangle angles is therefore
2x + x + x = 4x
and we know the sum of all angles in a triangle is always 180°.
so,
4x = 180
x = 180/4 = 45°
4x is then again 180°, and 2× 8y are then the remaining 180° of the full circle 360°.
2× 8y = 180
8y = 90
y = 90/8 = 11.25
x = 45
y = 11.25
If the polynomial function f(x)=(x+1)(x+3)9x-4) is rewritten in standard form, the degree would be ______ and the constant term would be _______.
.
If the polynomial function f(x)=(x+1)(x+3)9x-4) is rewritten in standard form, the degree would be 3 and the constant term would be 12 .
What is polynomial function?
In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.A quadratic, cubic, quartic, and other functions involving only non-negative integer powers of x are examples of polynomial functions. We can define a polynomial's degree and provide a generic definition for it.f(x)=(x+1)(x+3)9x-4)
f(x ) = 3x³ + 36x² + 27x - 4x² - 16x - 12
f(x) = 3x³ + 32 x² + 11x - 12
in above function highest degree would be 3 and constant -12 .
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.
Children shorter than 48 inches get into the water park free. Howard is currently 32 inches tall. He grows approximately 3 inches per year. Write an inequality to represent the number of years, y, that he can get in free.
Answer:
5 year
3 inches every year 48 minus 32 equals 16 3 Inches divided into 16 equal 5.333333 round it equals 5 years y = 5 years
Evaluate
4(x+3)(x+1)
(x+5)(x-5)
for x = 3.
Answer: -1536
Step-by-step explanation:
1: 4(3+3) (3+1) (3+5) (3-5)
2: 4(6) (4) (8) (-2)
3: 24 (4) (8) (-2)
4: 96 (8) (-2)
5: 768 (-2)
= -1536
d= √(7₂ (x2 − ₁)² + (Y2 − ₁)² Evaluate d if (x1, y₁) = (-3, 4) and (x2, Y2) = (−2, 4).
Sasha has c green notebooks. she has 6 fewer red notebooks then green notebooks. how many notebooks does sasha have in all.
The total number of notebooks on Sasha's notebook is 2c - 6.
Unitary method:
The unitary method is used to solve problems by first determining the value of a single unit and then multiplying that value by the required value.
So, this method is basically used to find the value of a unit and then the value of a required number of units.
Given,
Sasha has c green notebooks.
She has 6 fewer red notebooks then green notebooks.
So, here we need to find how many notebooks does Sasha have in all.
We know that.
Sasha has c green notebooks.
The number of red notebooks on her is
=> c − 6.
Here Sasha has either green or red notebooks.
The total number of notebooks on Sasha's notebook is
=> c + c − 6
=> 2c - 6
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What is the solution (x,y) to the system of equations above?
Answer:
B
Step-by-step explanation:
what is this i need help ASAP
Answer:
The first and fourth statement.
Step-by-step explanation:
1. - 3 - 12/3 + 5
= - 3 - 4 + 5
= - 7 + 5
= - 2
- 2 < 0
4. 4 - 2 - 3/2
= 2 - 3 / 2
= 1 / 2
1 / 2 > 0
Hope this helped! ^^
Sidenote: If you need me to explain for 2, 3 and 5, comment below this and I'll explain.
1. The total length of the stage is 76 feet.
If the trap doors are centered across the
stage, what is the distance from the left
side of the stage to the first trap door?
3. Anna is 26 feet high on a rock-climbing
wall. She descends to the 15-foot mark,
rests, and then climbs down until she
reaches her friend, who is 8 feet from
the ground. How many feet has Anna
descended?
2. An actor starts at point A, walks across
the stage, and then stops at point B
before disappearing through the trap door.
How far does he walk across the stage?
Choose the best answer.
5. Jordan wants to adjust the shelves in his bookcase so that
there is twice as much space on the bottom shelf as on the
top shelf, and one and a half times more space on the
middle shelf as on the top shelf. If the total height of
the bookcase is 0.9 meter, how much space is the
middle shelf on?
A 0.2 m
B 0.3 m
C 0.4 m.
D 0.5 m
6. In a rowing race, the distance between
the teams in first and second place is 5.7
meters. The distance between the teams
in second and third place is one-third that
distance. How much farther ahead is the
team in first place than the team in third?
F 7.6 m
H 2.5 m
G 5.7 m
J 1.9 m
4. Jamilla has a piece of ribbon that is
48.5 centimeters long. For her scrapbook,
she cuts it into two pieces so that one
piece is 4 times as long as the other.
What are the lengths of the pieces?
7. On a subway route, station C is located
at the midpoint between stations A and D. Station B is located at the
midpoint between stations A and C. If the distance between stations A and D
is 2.4 kilometers, what is the distance
between stations B and D?
A 0.3 km
C 1.2 km
B 0.6 km
D 1.8 km
The distance from the left side of the stage to the first trap door is 24 3/4.
given;
total lenght of the stage is 76 feet.
Anna is 26 feet high on a rock-climbing.
here we have to substract 76-26 1/2.
=76-26 1/2
=49 1/2/2
=24 3/4
Distance is a scalar quantity. The distance of an object can be defined as the complete path travelled by an object. For example. if a car travels east for 5 km and takes a turn to travel north for another 8 km, the total distance travelled by car shall be 13 km.the space between the two points are called distance
Distance is a scalar quantity. The distance of an object can be defined as the complete path travelled by an object. For example. if a car travels east for 5 km and takes a turn to travel north for another 8 km, the total distance travelled by car shall be 13 km..
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The pie chart represents the proportions of how Henry spent the £720 he took on holiday.
What fraction of his money did he spend on drink?
Give your answer in its simplest form.
Answer:
£124
Step-by-step explanation:
first of all, you're meant to add all the figures given on the pie chart, which is 29+137+58+62+74 and that will give you a total of 360 degrees
so, you say 360 degrees is equal to the total amount of money he spent, which is £720, what about 62 degrees
therefore, you just do (62×720)÷360
that will give you £124
Evaluate the function.
f(x) = x² + 2x + 6
Find f(-7)
Answer: f(-7)=41
Step-by-step explanation:
f(x) = x² + 2x + 6
f(-7)=(-7)² + 2(-7) + 6
f(-7)=49-14 + 6
f(-7)=35 + 6
f(-7)=41
Answer:
f(-7) = 41
Step-by-step explanation:
f(x) = x² + 2x + 6
In order to find f(-7) ,we just need to substitute x in the expression of the function f by -7.
Then
f(-7) = (-7)² + 2(-7) + 6
= 49 - 14 + 6
= 35 + 6
= 41
