3⁴⁰+ 7⁴⁰is a multiple of 10
Answers
ANSWER :
It will be false , it is not the multiple of 10
Answer: False. The number \(3^{40}+7^{40}\) is not a multiple of 10
========================================================
Explanation:
Let's look at a fairly small table of powers of 3 and 7. Check out the diagram below.
Notice that the units digits for each power involve the items from this set: {1,3,7,9}.
Furthermore, note that in each blue row we have the units digits add to 3+7 = 10 or 7+3 = 10. In order to be a multiple of 10, we need to have 0 as the units digit. Eg: 90 is a multiple of 0 for this reason.
So \(3^1 + 7^1 = 3+7 = 10\) is one multiple of 10
And so is \(3^3+7^3 = 27+343 = 370\)
and so on. As the table shows, we have \(3^n+7^n\) as some multiple of 10 as long as n is an odd positive integer. This contradicts the fact that 40 is an even integer for \(3^{40}+7^{40}\). So there's no way that this expression (whatever the massive number happens to be) is a multiple of 10. The units digit for this sum is not zero.
----------------------
You can use modular arithmetic as an alternative pathway to show that the given number isn't a multiple of 10
\(3^{40} \equiv 3^{2*20} \ (\text{ mod }10)\\\\3^{40} \equiv (3^2)^{20} \ (\text{ mod }10)\\\\3^{40} \equiv (9)^{20} \ (\text{ mod }10)\\\\3^{40} \equiv (-1)^{20} \ (\text{ mod }10)\\\\3^{40} \equiv 1 \ (\text{ mod }10)\\\\\)
This shows that the units digit of \(3^{40}\) is 1
Also,
\(7^{40} \equiv 7^{2*20} \ (\text{ mod }10)\\\\7^{40} \equiv (7^2)^{20} \ (\text{ mod }10)\\\\7^{40} \equiv (49)^{20} \ (\text{ mod }10)\\\\7^{40} \equiv (-1)^{20} \ (\text{ mod }10)\\\\7^{40} \equiv 1 \ (\text{ mod }10)\\\\\)
which looks very similar to the steps of \(3^{40}\). This produces the same units digit. The two units digits add to 1+1 = 2, which is not zero and this is sufficient proof to show that \(3^{40}+7^{40}\) is not a multiple of 10.
Going back to the table below, we see that the units digit of 1 show ups for both 3^n and 7^n whenever n is a multiple of 4. This applies to 40 because 40 = 4*10.
Related Questions
is the word addition a collective, abstract or concrete noun?
Answers
Answer:
Should be a collective noun.
For example: In addition to those...
Put this graph into slope intercept form, FIRST CORRECT ANSWER GETS BRAINLIEST
Answers
Answer:
y = x + (-5)
Hope this helps.
Which equation is equivalent to the given equation? 7m + 11 = -4 (2m +3)
Answers
Answer:
15m=-23
Step-by-step explanation:
equivalent of 100 sqrt 2
Answers
Answer:
141.421356237
Determine the length of the interior bathroom wall(excluding the door) that is not goven if the door takes a take space of 860mm 2.The kitchen and the bathroom should be tiled .The floor tile dimension is 500mm by 500mm .when purchasing tiles you need to buy 5% more to cater for breakages .A tiling company charges R 8180.00 for labour and can supply the tiles for R 249.00 per box NOTE::area=l×width ..all items like the bath ,stives,cupboard are movable items and tiling will be done on the spaces where they will be placed 1.calculate the total area that must be tiled in metres (length=6030mm inner dimension excluding the bedroom but also calculate it and outer is 12330 mm and width =4680mm and 5130 mm excluding the bath area outer is 13680mm 3.2.2 the building manager made a statement that 150 tiles are needed to complete the tiling for the kitchen and bathroom .verify with calculations whether this statement is valid or not(Length=6030mm width=5130 mm for kitchen....bathroom =l 2250 mm width =13680 outer dimension including 4680 mm for bedroom 1 and 5130 mm for bedroom 2
Answers
A total number of 59.6001 tiles (approximately 60 tiles) are needed to complete the tiling for the kitchen and bathroom.
To calculate the total area that needs to be tiled, we'll start by converting the given dimensions from millimeters to meters:
Bathroom Inner Dimensions:
Length = 6030 mm = 6.03 m
Width = 5130 mm = 5.13 m
Bathroom Outer Dimensions (including bedroom areas):
Length = 12330 mm = 12.33 m
Width = 4680 mm = 4.68 m
Kitchen Dimensions:
Length = 6030 mm = 6.03 m
Width = 5130 mm = 5.13 m
Total area to be tiled in the bathroom (excluding the bath area):
Area = Length x Width = 6.03 m x (5.13 m - 0.86 m) = 6.03 m x 4.27 m = 25.7701 m²
Total area to be tiled in the kitchen:
Area = Length x Width = 6.03 m x 5.13 m = 30.9919 m²
Total area to be tiled (bathroom + kitchen):
Total Area = 25.7701 m² + 30.9919 m² = 56.762 m²
To account for breakages, we need to purchase 5% more tiles. So, the total number of tiles needed is:
Total Number of Tiles = Total Area x 1.05 (to account for 5% extra)
Total Number of Tiles = 56.762 m² x 1.05 = 59.6001 tiles
The building manager stated that 150 tiles are needed. Comparing this with our calculation:
150 tiles < 59.6001 tiles
Therefore, the statement made by the building manager is not valid. According to our calculations, a total of 59.6001 tiles (approximately 60 tiles) are needed to complete the tiling for the kitchen and bathroom.
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IPlz I need help I have 5 minutes left
Answers
Answer: 12.6
Step-by-step explanation:
Area= bh
4.2×3
Answer:
B) 6.3 ft^2
Step-by-step explanation:
Area of triangle: height*base/2
4.2*3=12.6
12.6/2= 6.3
If p is inversely proportional to the square of q and p is 13 when q is 4, what is p when q is 2?
Answers
Answer:
52
Step-by-step explanation:
Here it's given that p is inversely proportional to the square of q. We can write this mathematically as ,
\(\longrightarrow p \propto \dfrac{1}{q^2} \)
Let k be the constant of proportionalality .
\(\longrightarrow p = \dfrac{k}{q^2}\)
Again it's given that when p is 13 , q is 4 . On substituting this in the above equation we can find out the value of k , as ;
\(\longrightarrow 13 =\dfrac{k}{4^2}\)
Solve out for k ,
\(\longrightarrow k = 13 (16)\)
Multiply ,
\(\longrightarrow k = 208 \)
Again when the value of q is 2 , we need to find out the value of p . So ,
\(\longrightarrow p =\dfrac{k}{q^2}\)
Substitute ,
\(\longrightarrow p =\dfrac{208}{2^2}\\ \)
\(\longrightarrow p = \dfrac{208}{4}\)
Simplify,
\(\longrightarrow p = 52 \)
This is the required answer.
4) Sue is playing darts. So far, she has hit the bullseye 4 times and missed the bullseye 10 times. What
is the experimental probability that Sue will hit the bullseye on her next toss?
Answers
The probability that Sue will hit the bullseye on her next toss is approximately 0.29 or 29%.
What is probability?
The experimental probability of an event is defined as the ratio of the number of times the event occurs to the total number of trials or observations. In this case, Sue hit the bullseye 4 times out of 14 total trials (4 hits + 10 misses).
Therefore, the experimental probability that Sue will hit the bullseye on her next toss is:
4 hits / 14 total trials = 0.2857 or approximately 0.29
So the probability that Sue will hit the bullseye on her next toss is approximately 0.29 or 29%.
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Complete question is: Sue is playing darts. So far, she has hit the bullseye 4 times and missed the bullseye 10 times. the probability that Sue will hit the bullseye on her next toss is approximately 0.29 or 29%.
Answer: 2/7
Step-by-step explanation: i did this question, trust me
However, does these questions will be marked as brantliest !!!!
Answers
Answer:
i don't see questions but I'll go download the app on your picture:))
4.79 × 10^-6
0.0000000734
Hope this helps! :)
Given the point (2.-4) scale the point to a factor of 3
Answers
Hey there! I'm happy to help!
To increase a point by a certain scale factor, you multiply each number inside the point by that scale factors. Ours is 3.
2(3)=6
-4(3)=-12
So, our final point is (6,-12).
Have a wonderful day! :D
Gabriel deposits $660 every month into an account earning a monthly interest rate of
0.475%. How much would he have in the account after 16 months, to the nearest
dollar? Use the following formula to determine your answer.
Answers
The future value of the monthly deposit which earns 0.475 monthly interest will be $10,944.67 after 16 months.
How the future value is determined:The future value can be determined using the future value annuity formula or an online finance calculator.
The future value represents the periodic deposits compounded periodically at an interest rate.
N (# of periods) = 16 months
I/Y (Interest per year) = 5.7% (0.475% x 12)
PV (Present Value) = $0
PMT (Periodic Payment) = $660
Results:
Future Value (FV) = $10,944.67
The sum of all periodic payments = $10,560.00
Total Interest = $384.67
Thus, using an online finance calculator, the future value of the monthly deposits is $10,944.67.
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a frozen yogurt factory makes 100 quarts of frozen yogurt in 5 hours. how many quarts could be made in 36 hours
Answers
The required quarts of frozen yogurt made in 36 hours as per the given information is equal to 720 quarts.
Quarts of frozen yogurt made by factory is equal to 100 quarts
Time required to make 100 quarts of frozen yogurt is equal to 5 hours
Let 'x' quarts of frozen yogurt made in 36 hours
5 hours = 100 quarts of frozen yogurt
⇒ 1hour = ( 100 / 5 ) quarts of frozen yogurt
⇒ 36 hours = ( 100 / 5 ) × ( 36 ) quarts of frozen yogurt
⇒ 36 hours = ( 20 ) × ( 36 ) quarts of frozen yogurt
⇒ 36 hours = ( 720 ) quarts of frozen yogurt
Therefore, the quarts of frozen yogurt made in 36 hours is equal to 720 quarts.
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Help me on this math questionnn
Answers
*extra points* solve \(\sqrt[3]{64}\)
Answers
Answer: The answer is 4.
Step-by-step explanation: You'll need to simplify the radical by breaking the radicand up into a product of known factors, assuming real numbers: \(4^{3}=64\).
Please someone do this for me
Answers
Answer:
A = -12
Step-by-step explanation:
A put in -2 for 'x' in the equation to find value
2(-2) - y = 8 add 4 to both sides
-y = 12
y = -12
I think YOU can now find B and C with this method !
B= -8
C= -4
2x-y = 8 so reformatting by getting the y to be alone on the right side,
then 2x-8 = y
Just plug the value if x in and you find y
Have a nice day!
Marcy wants to paint the sides of the wooden storage chest shown below gray except the white lid. What is the surface area?
Answers
Answer:
Surface area = 2,160 in²
Step-by-step explanation:
Given:
Length of box = 15 in
Width of box = 30 in
Height of box = 24 in
Find:
Surface area
Computation:
Surface area = 2h[l+b]
Surface area = 2(24)[30 + 15]
Surface area = 48 x 45
Surface area = 2,160 in²
Cameron collects old books, and they convinced their friend Kenji to start collecting as well. Every month, they go to the store together, and they each buy a book. This table shows how many books they each have: Month 1 11 2 22 3 33 4 44 Kenji 1 11 2 22 3 33 4 44 Cameron 12 1212 13 1313 14 1414 15 1515 They both want an equation they can use to find how many books Cameron will have ( � cc) when Kenji has � kk books. Complete their equation. � = c=c, equals
Answers
The linear equation that describe the relationship between the book collection by Cameron, c and Kenji, c each month is represented as c = k - 11.
Linear equations are defined as the equations of degree one. It is represents equation for the straight line. The standard form of linear equation is written as, ax + by + c = 0, where a ≠ 0 and b ≠ 0. We have specify that Cameron collects and his friend Kenji start collecting the old books. The above table figure which contains data of books collected by both in different months. We have to determine the equation many books Cameron will have (c) when Kenji has k books. Let c and k denotes the books collected by Cameron and Kenji respectively. We see there is always increase in old book collection by one in case of both of them (Cameron and Kenji) each month. So, there exits a linear equation. Also, from the table, the Kenji's book collection is always 11 units less from Cameron's book collection. So, the required equation is written by c = k - 11 for each month. Hence, the required equation is equal to c = k - 11.
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Complete question:
The above figure complete the question.
Cameron collects old books, and they convinced their friend Kenji to start collecting as well. Every month, they go to the store together, and they each buy a book. This table shows how many books they each have: They both want an equation they can use to find how many books Cameron will have (c) when Kenji has k books. Complete their equation.
Answer:
c=k+11
Step-by-step explanation:
HELP BEFORE THE TIMES RUNS OUT!!!
Answers
The answer is B.14
Step-by-step explanation:
14
Your welcome
Answer: B=14
Step-by-step explanation:
9 2/3+ 4 1/5= 208/15 rounded to the nearest whole number is 14
Write a story that can be represented by the following equation: x + 16 = 42
Answers
Answer:
Amanda bought 42 apples and gave 16 away how many are left.
Step-by-step explanation:
X=26
Answer:
Renee runs a dogwalking business. She walked 42 dogs over the weekend. On Saturday she walked 16 dogs but Renee can't remember how many she walked on Sunday. Write and equation to find how many dogs Renee walked on Sunday where x is the number of dogs she walked on Sunday.
please help thx
calculate the value of x
calculate the value of y
calculate the value of z
Answers
Solve the system of linear equations below by substitution.
y = -2x + 6
-4x - 6y = 4
Group of answer choices
(-2, 10)
(5, -4)
(3, 0)
(0, 6)
Answers
Answer:
(5, -4)
Step-by-step explanation:
Substitute y from the first equation into the second equation:
-4x - 6(-2x + 6) = 4
Simplify:
-4x + 12x - 36 = 4
8x = 40
x = 5
The only answer choice where x = 5 is (5, -4).
Answer:
\(\boxed {\boxed {\sf (5, -4)}}\)
Step-by-step explanation:
We are given the two equations:
\(y= -2x+6 \\-4x-6y=4\)
We are asked to solve by substitution. Since we know that y is equal to -2x+6, so we can substitute the expression in for y in the second equation.
\(-4x-6y=4\)
\(-4x-6(-2x+6)=4\)
Now, solve for x by isolating the variable on one side of the equation.
First, distribute the -6 into the expression. Multiply each term in the parentheses by -6.
\(-4x+ (-6*-2x)+(-6*6)=4\)
\(-4x+12x+(-6*6)=4\)
\(-4x+12x-36=4\)
Combine like terms. There are 2 x terms that can be added.
\((-4x+12x)-36=4\)
\(8x-36=4\)
36 is being subtracted from 8x. The inverse of subtraction is addition, so add 36 to both sides of the equation.
\(8x-36+36=4+36\)
\(8x=40\)
x is being multiplied by 8. The inverse of multiplication is division, so divide both sides by 8.
\(\frac{8x}{8} =\frac{40}{8}\)
\(x=5\)
x is known, so we can find y using the first equation.
\(y=-2x+6\)
x is equal to 5, so substitute the value in.
\(y=-2(5)+6\)
Multiply first.
\(y=-10+6\)
Add.
\(y=-4\)
A solution is written as (x,y). So, the solution to this equation is (5, -4).
What's the mode of this set?
-7, -9, -3, 4, 6, 4, 1, -9, 4
Answers
Answer:
4 is the mode.
Explanation:
set: { -7, -9, -3, 4, 6, 4, 1, -9, 4 }
We can see that 4 has appeared 3 times.It has appeared a lot in this set and much more frequently.Thus 4 is the mode.To find mode, we first place all the numbers in order, least to greatest.
Mode is whichever number is repeated the most.
-9, -9, -7, -3, 1, 4, 4, 4,
Since 4 is repeated more then any other number, that's our mode!
A company uses a new machine and an old machine to print booklets. Each
machine prints booklets at a constant rate. The graph and the equation represent the relationships between x, the number of minutes the machines print, and y, the number of booklets printed.
The company uses both machines to print a total of 1,250 booklets. Both
machines start printing at the same time. During printing, the old machine breaks down and stops printing. The new machine continues printing for an additional 14 minutes and completes the order
What is the total number of minutes the new machine prints? Show or explain all
your work. Write your answer and your work below.
Answers
By solving a linear equation, it can be calculated that
Time for which new machine prints = 64 minutes
What is linear equation?
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
For the new machine
The line passes through (0, 0) and (6, 75)
Slope = \(\frac{75 - 0}{6-0}\) = 12.5
Equation of line for new machine
y - 0 = 12.5(x - 0)
y = 12.5x
Equation of line for old machine
y = 9x
Now,
During the 14 minutes, the number of pages printed = 12.50 \(\times\) 14 = 175
Number of pages printed earlier = 1250 - 175 = 1050
By the problem,
12x + 9x = 1050
21x = 1050
x = \(\frac{1050}{21}\)
x = 50
Time for which new machine prints = 50 + 14 = 64 minutes
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7p-5=6p+8 what is the answer to that
Answers
Answer:
p=13
Step-by-step explanation:
P=13
Explanation:
First you move one of the p to combine with the other p. I choose the 6p to be the moving. Since 6p is a positive number, you subtract it when you move it. 7p-6p= 1p
Next you move the constants which are -5 and 8. Since we already move the ps to the left side, we should move the constants to the right side. Since -5 is a negative number, we need to add it when we move it. 5 + 8 =13
So p equals to 13
The approximate weights of two animals are 5.36 x 10^4 lbs. and 6.2 x 10^4 lbs. Find the total weight of the two animals. Write the final answer in scientific notation with the correct number of significant digits.
Answers
Answer: The total weights of the two animals is 11. 92 × 10² Ibs
Step-by-step explanation:
Helppppp PLZZZZZZZZZZZZZZZZZZZZZZ i need help
Answers
Answer/Step-by-step explanation:
A) The temperature in Chicago could be -10*F because -10 is to the right of -13 on the number line.
Higher Temperatures -->
o----------->I
I---I---I---I---I---I---I---I---I---I---I---I---I---I---I---I---I---I---I---I---I---I---I---I---I
-13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
\(\sf\:Q.\:Show \: that \: there \: is \: no \: positive\:integer\)
\(\sf\:n \: for \: which \:\sqrt{n - 1} \: + \:\sqrt{n + 1}\:is\)
\(\sf\: rational.\)
Decide if the situation involves permutations, combinations, or neither. Explain your reasoning?
The number of ways 20 people can line up in a row for concert tickets.
Does the situation involve permutations, combinations, or neither? Choose the correct answer below.
A) Combinations, the order of 20 people in line doesnt matter.
B) permutations. The order of the 20 people in line matter.
C) neither. A line of people is neither an ordered arrangment of objects, nor a selection of objects from a group of objects
Answers
The situation described involves permutations because the order of the 20 people in line matters when lining up for concert tickets.
In this situation, the order in which the 20 people line up for concert tickets is important. Each person will have a specific place in the line, and their position relative to others will determine their spot in the queue. Therefore, the situation involves permutations.
Permutations deal with the arrangement of objects in a specific order. In this case, the 20 people can be arranged in 20! (20 factorial) ways because each person has a distinct position in the line.
If the order of the people in line did not matter and they were simply being selected without considering their order, it would involve combinations. However, since the order is significant in determining their position in the line, permutations is the appropriate concept for this situation.
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A line passes through the point (-6,-9) and has a slope of 5/2. Write an equation in slope-intercept form for this line.
Answers
Answer:
An equation in slope-intercept form for this line is \(y=\frac{5}{2}x-19\)
Step-by-step explanation:
Slope intercept form :
We are given that A line passes through the point (4, −9) and has a slope of 5/2.
So,
Substitute the value in the equation :
So,
So, an equation in slope-intercept form for this line is \(y=\frac{5}{2}x-19\)
At Freddy's Eatery, three steak burgers and two orders of fries cost $18. Two steak
burgers and three orders of fries cost $15.75. What is the cost of one steak burger?
A) $5
B) $4.50
D) $6.50
C)
$2.25
Answers
To solve this problem, we can set up a system of equations to represent the given information. Let x represent the cost of one steak burger. Then we can set up the following system of equations:
3x + 2(f) = 18
2x + 3(f) = 15.75
Where f represents the cost of one order of fries.
Subtracting the second equation from the first equation gives us:
x = 18 - 2(f) - 15.75 + 3(f)
= 18 - 15.75
= 2.25
Therefore, the cost of one steak burger is $2.25, which is answer choice C.
What number multiplied by itself is equal to the product of 6 and 150.
Answers
Answer:
30Step-by-step explanation:
What number multiplied by itself is equal to the product of 6 and 150?
30
30 x 30 = 900
6 * 150 = 900