Answer:
Step-by-step explanation:
Prove that for any natural number 3^(n+4)-3n is divisible by 16.
(I'm going to assume that you mean 3^(n+4)-3^n.)
1. We can break up 3^(n+4)-3n into 3^n * 3^4-3^n (by the rule a^b*a^c = a^b+c).
2. Solve to get 3^n * 81 - 3^n
3. Factor out the 3^n, and you'll get 3^n(81-1), and simplify: 3^n(80)
You may notice that 80 is divisible by 16.
4. Rewrite what we got from the last step as: 3^n*5(16).
Hope this helped you!
The proof that any natural number n in (3ⁿ⁺⁴ - 3ⁿ) is divisible by 16 is; it was simplified to 3ⁿ × 5
What is the proof that the number is divisible?
We want to show that show that 3ⁿ⁺⁴ - 3ⁿ is divisible by 16.
This is; (3ⁿ⁺⁴ - 3ⁿ)/16
From laws of indices, we know that;
aᵐ⁺ⁿ = aᵐ × aⁿ.
Thus; 3ⁿ⁺⁴ can be expressed as 3ⁿ × 3⁴.
Thus; (3ⁿ⁺⁴ - 3ⁿ)/16 is;
((3ⁿ × 3⁴) - 3ⁿ) = 3ⁿ((81 - 1)/16)
3ⁿ(80/16) = 3ⁿ × 5
The expression has been fully simplified to show that any natural number n in (3ⁿ⁺⁴ - 3ⁿ) is divisible by 16.
Read more about proof of numbers at; https://brainly.com/question/10657323
x-y+z for x= 1,y=6,z=1
Answer:
-4
Step-by-step explanation:
1-6+1=-4
Answer:
The answer is (2, -1, 3)
Step-by-step explanation:
Hope this helped.
What is the answer to this 8-(-8)=
Answer:
16
Step-by-step explanation:
the two negatives cancel out so if you are subtracting -8 from 8 you would actually end up adding them.
hope it helps!
Answer:
16
Step-by-step explanation:
personally I learned that when I see " -(- " in a equation it just means addition.
furniture maker used 1/2 of a can of paint to paint some chairs. She used 1/6 of a can of paint for each chair. How many chairs did she paint?
Answer:
3 chairs
Step-by-step explanation:
1/2 is the same as 3/6
There are three 1/6 in 3/6.
(3/6) ÷ (1/6) = 3
The requried, she painted 3 chairs as of the given proportion.
What is proportionality?Proportionality is the relationship between two or more sets of values, and it describes how these values are related to each other.
Here,
Let's assume that the number of chairs she painted is represented by the variable 'c'.
We know that she used 1/6 of a can of paint for each chair. So, the total amount of paint used for all the chairs can be expressed as:
1/6 x c = c/6
We also know that she used 1/2 of a can of paint in total. So we can set up the equation:
c/6 = 1/2
To solve for 'c', we can multiply both sides of the equation by 6:
c = 3
Therefore, she painted 3 chairs.
Learn more about proportionality here: https://brainly.com/question/22620356
#SPJ3
A red bus and a yellow bus are both driving on the same road, in the same direction They start driving from the same place and are traveling at a constant speed. The red bust started driving 0.5 hours after the yellow bus started driving. If the red bus drives 50 miles per hour and the yellow bus drives 40 miles per hour, how many miles will each bus have to traveled when the red bus catches up to the yellow bus?
Answer:
100 miles
Step-by-step explanation:
lets find out how much the yellow bus drove before red bus started
40*0.5=20
20 miles
50x=40x+20
10x=20
x=2
they traveled for two hours until red bus caught up with yellow bus
yellow:
2*40+20=80+20=100 miles
red:
2*50=100 miles
can anyone help me plz and I need the person to explain it for me
Answer:
1 cm = 100 mi
28.9/1=28.9
28.9 x 100 = 2890 miles distance
2890 / 65 miles per hour = 44.4615 hours to drive
44.461/24 hours in a day = 1.85 rounded up is 2 days
About two days
If you have any questions you can ask
Step-by-step explanation:
Answer:
a) 2900
b) about 44 hours
2 days
Step-by-step explanation:
- Mrs. Ward found 80-ounce packages of hamburger on sale. If she needs to make
2 of each size hamburger, how many packages of meat will she need to buy?
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
The Whispering Lakes Neighborhood Association is having a hamburger cookout. Each family can choose whether to order the hamburgers or bring their own. Use the information in the table to solve the number stories. Use drawings, tables, or equations to show what you did.
Mrs. Ward found 80-ounce packages of hamburger on sale. If she needs to make 2 of each size hamburger, how many packages of meat will she need to buy?
Answer:
The number of meat packages is
100/80 = 1.25 = 5/4
Assuming that the number of packages cannot be in fraction, then she would need at least 2 packages of meat.
Number of meat packages = 2
Step-by-step explanation:
Please refer to the attached table where we are given size of hamburgers and the weight of corresponding hamburger patty in pounds.
small = 1/8 lb
medium = 1/4 lb
large = 1/2 lb
jumbo = 3/4 lb
king of burgers = 1 1/2 lb = 3/2 lb
To make 1 of each hamburger we need
Total weight of patty = 1/8 + 1/4 + 1/2 + 3/4 + 3/2
Total weight of patty = 25/8 = 3.125 lb
But she needs to make 2 of each size hamburger so,
Total weight of patty = (25/8)×2 = 25/4 = 6.25 lb
Mrs. Ward found 80-ounce packages of hamburger on sale
first we have to convert pounds into ounces
We know that 1 pound has 16 ounces
6.25×16 = 100 ounces
So the number of meat packages required is
100/80 = 1.25 = 5/4
Assuming that the number of packages cannot be in fraction, then she would need at least 2 packages of meat.
Number of meat packages = 2
Evaluate 5 ÷ 4/6 Give your answer as a mixed number in its simplest form.
Answer:
15/2
Step-by-step explanation:
5*6/4=30/4=15/2
Answer: 7 1/2
Step-by-step explanation:
5 ÷ 4/6 = 7.5
7.5 as a mixed number is 7 1/2
7 1/2 simplified is 7 1/2
A physics test is normally distributed. The class average was 79.3, and the standard deviation was 7.5. What percent of students scored between a 68 and 86.8?
Answer:97.275% or 97.5%
Step-by-step explanation:
Help!!!
An employee at a factory is paid $9.25 per hour plus an $8.00 bonus for every 20 transformers assembled. Last week an employee worked 36 hours and assembled 380 transformers. How much money did the factory employee actually earn per hour last week rounded to the nearest cent?
Answer: $13.47 per hour.
Step-by-step explanation:
Hi, to answer this question we have to write an equation:
Total earnings = 9.25 (h) + 8 (t/20)
Where h is the number of hours and t is the number of transformers.
Since he worked for 36 hours and assembled 380 transformers:
Total earnings = 9.25 (36) + 8 (380/20)
Total earnings = 333+152 = $485
Finally, to find how much he earned per hours, we simply have to divide the result by the number of hours worked (36):
485/36 = $13.47 per hour.
Leah drives her truck 270KM in the same time Deborah drives her car 250KM. If Leah drives 4km/h faster than Deborah. What is each of their driving speeds?
Answer:
Leah: 54km/h
Deborah: 50 km/h
Step-by-step explanation:
250+4x=270
4x=20
x=5
both drove 5 hours
Deborah:
250/5=50km/h
Leah:
270/5=54km/h
To create an image, Figure B is going to be rotated 90° around the point indicated in the figure, translated horizontally across the y-axis and reflected across the x-axis. What must be true about Figure B and its image?
Answer: D. They are both congruent
Step-by-step explanation:
The only difference in the two shapes is the locations. One shape is located in the 4th (-x, +y) quadrant, while the other shape is located in the 2nd quadrant (+x, -y)
They two shapes are the same size with the same area, so they are both congruent.
Answer:
The answer on Imagine Math is...
-They are congruent
Step-by-step explanation:
I got the answer right on Imagine Math. Hope my answer can help those who need it. God bless you all!!
Based on the graphic, which three-dimensional figure has the greatest volume?
A) the cylinder
B) the rectangular prism
C) the oblique rectangular prism
D) all three have the same volume
At 4 p.m., the temperature started to change drastically. Each hour, for three hours, the temperature decreased by 7°F. Which word in the problem indicates that a negative integer should be used? change each decreased drastically
Answer:
Decreased.
Step-by-step explanation:
Decrease means to go down or take away, therefore in a mathematical equation, it would be represented by a negative integer.
Change could be positive or negative
each is a singular description word
and drastically is just describing how fast.
have a good day!
Answer:
decreased :^)
Step-by-step explanation:
Help me please !!!!!!!!!
Answer:
756.5 =x
Step-by-step explanation:
To find the perimeter of a rectangle
P = 2 (l+w)
4533 = 2 ( x+3 + 2x-6)
Combine like terms
4533 = 2 ( 3x -3)
Distribute
4533 = 6x -6
Add 6 to each side
4533+6 = 6x
4539 = 6x
Divide by 6
4539/6 =x
756.5 =x
Could someone help what is the variable in “8y3”?
Answer:
y
Step-by-step explanation:
The variable in 8y^3 is y because a variable is a number that we don't know yet, and that is the only one.
find four rational numbers between 2/3 and 3/4
Answer:
17/24
Step-by-step explanation:
(a+b)÷2
a= 2÷3
b= 3÷4
=(2/3 + 3/4)÷2
=(8+9/12)÷2
=17/24
if F(x)=2x^2-5 and g(x)=3x+3, find (f-g)(x)
A.2x^2-3x-8
B.-x^2-8
C.3x-2x^2-2
D.2x^2-3x-2
Answer:
work is pictured and shown
If it is on sale for 20% OFF and the sale price is $68; what was the original price?
Answer:
85
Step-by-step explanation:
The discount is original price times the percent off
The sale price is the original price minus the discount
original price - original price * 20 % = 68
Factor out the original price and change the percent to a decimal
original price ( 1 - .20) = 68
original price ( .80) = 68
Divide each side by .80
original price = 68/.80
original price = 85
Answer:
$13.60
Step-by-step explanation:
($68 x 20%) / 100
1360 / 100 = 13.6
A sprinter travels a distance of 300 m in a time of 28.22 seconds. What is the sprinter's average speed rounded to 4 sf?
Answer:
[tex]10.6 \: m/s[/tex]
Step-by-step explanation:
Average speed = distance covered divided by the time taken.
[tex]S=\frac{d}{t}[/tex]
[tex]\frac{300}{28.22}[/tex]
[tex]=10.63075[/tex]
Answer:
10.63m/s
Step-by-step explanation:
distance traveled=s=300m
time taken=t=28.22s
average speed=v=?
average speed=[tex]\frac{distance covered}{time taken}[/tex]
average speed=[tex]\frac{300m}{28.22s}[/tex]
average speed=10.63075m/s
now in the question it is said that round to 4 significant figures so will write only first four digits
average speed=10.63m/s
Find the number that makes the ratio equivalent to 2:3.
6: ___
Answer:
Step-by-step explanation:
2:3 = 6: ___
[tex]\frac{2*3}{3*3}=\frac{6}{9}[/tex]
2:3 = 6 :_9___
Answer:2:3=6:9
Step-by-step explanation:
2×3/3×3=6/9
2:3=6:9 !!!!!!!!
Find the domain and range of the relation. {(−7,−18),(−23,21),(4,13),(−17,22),(2,−10)}
Answer: Domain = all x values and Range = all y values
Step-by-step explanation:
The domain of a function is all the allowed x values that make the function true. Luckily you were already given the domain. Its all the x values.
The range of a function is pretty much all the allowed y values of a function. Or, what y values the function can be equal to. So that's just all the y values
When listing the domain and range, you generally want to do it from least to greatest and you do not want to repeat any values
Answer:
D:{ -23,-17,-7,2,4}
R:{-18,-10,13,21,22}
Step-by-step explanation:
The domain is the input
D:{ -7,-23,4,-17,2}
We normally put them in numerical order
D:{ -23,-17,-7,2,4}
The range is the output
R:{-18,21,13,22,-10}
We normally put them in numerical order
R:{-18,-10,13,21,22}
The diagram shows two sets of vectors that result in a single vector. What are the first two steps for finding the magnitude of the resultant vector?
A. Find the square of the first horizontal vector and the square root of the first vertical vector
B. Find the square root of the first horizontal vector and the square root of the second horizontal vector
C. Find the sum of the two horizontal vectors in the summer for two vertical vectors
D. Find the difference between the two horizontal vectors and the difference between the two vertical vectors
C. Find the sum of the two horizontal in the summer for two vertical vectors.
Answer:
Can confirm C is right i got 100 on the unit test
Step-by-step explanation:
I NEED HELP PLEASE 30 points
Select the correct paint
One linear equation is defined by the points (2, 4) and (1, 1), while the other is defined by the points (2.-2) and (-5). Which point represents
the solution to this system of equations?
What is the median of the data displayed in the box and whisker plot?
Answer:
The median is the middle number in a you box/whisker plot. The median is sometimes used as opposed to the mean when there are outliers in the sequence that might skew the average of the values
Step-by-step explanation:
The median is "the middle number" in short...
ex: 1,5,8,9,8648
the middle number would be 8
Brainliest plz
Answer:
median is where the middle line in the box is
Step-by-step explanation:
The Figure below shows a rectangular prism and a cube:
How many such cubes are required to completely pack the prism without any gap or overlap?
A. 288
B. 576
C. 1,152
D. 1,636
A group of 9 friends went bowling. Each person pays the same amount to bowl several games and a $3 fee to rent shoes. The total cost for the friends to bowl and rent shoes is $162. How much does it cost each friend to bowl ( not counting the shoe rental fee)?
Answer:
Each friend payed $15
Step-by-step explanation:
( 9 x 3 - 162 ) divide that answer by 9 to get the amount of how much each friend payed.
3. If f(x)=2x+3 then what is f(x+1)? Plzzz answer ASAP
Answer:
=2x+5
Step-by-step explanation:
f(x)=2x+3
Replace x with x+1
f(x+1)=2(x+1)+3
=2x+2+3
Combine like terms
=2x+5
Which algebraic expression represents the phrase "four times a number"?
4 + c
C-4
4-0
4c
Answer:
4c
Step-by-step explanation:
it pretty much means 4*c
Answer:
= 4c
Step-by-step explanation:
4×(c) . I hope it helps
Sara is moving into a new apartment. The Resort complex charges a $600 security
deposit and costs $950 a month for rent. The Uptown Suites Duplex charges a $300
security deposit and costs $1100 a month for rent. After how many months would the
apartments cost the same amount? Which apartment would you recommend Sara move
to if she plans on staying for 6 months? Please show work!
Answer:
1) 2 months
Step-by-step explanation:
y = 950x + 600
y = 1100x + 300
950x + 600 = 1100x + 300
-950x -950x
____________________ subtract slope from both sides
600 = 150x + 300 ( doesn't matter which one)
-300 - 300
____________________ subtract
300 = 150x
_________ Divide each # with the slope
150 = 150
2 = x
____________Answer 2_____________
Answer:
The Resort Complex would save you 300.
step-by-step solution:
you have to do is plug in the number of months.
then multiply
then subtract both Complexes
and compare
The Resort Complex. : y = 950(6) + 600 - 6300
The uptown suite duplex : y = 1100(6) + 300 - 6900
HOPE THIS HELPS!
Eva can type 320 words in 4 minutes. How many words per minute can Eva type?
words per minute
Answer:
80 words per minute
Step-by-step explanation:
320/4
80 wpm
Answer:80 wpm
Step-by-step explanation:
Divide 320 by 4.
That should give you 80.
Hope i helped :)))
