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
Rick is deciding what to wear to school. He has two different shirts, two different pants and two different pairs of shoes to choose from. How many different outfit combinations does he have to choose from?
Answer:
a total of 8 outfits
Step-by-step explanation:
shoes: L1, L2
shirts: S1, S2
pants: P1, P2
1: S1, P1, L1
2: S1, P1, L2
3: S1, P2, L1
4: S1, P2, L2
5: S2, P1, L1
6: S2, P1, L2
7: S2, P2, L1
8: S2, P2, L2
I hope that makes sense, since I couldnt figure out how to show the diagram.
Select the correct answer.
Shareese has a credit line of $3,000 on her credit card. Review the summary of her latest credit card statement.
Previous
Balance
Payments/Credits
Summary
New
Finance New
Purchases Charge Balance
$1,299.00 $18.00 $1,567.25
$1,250.25
$1,000.00
What is the available credit on Shareese's card?
O A $1,432.75
B. $1,299.00
$317.00
Reset
Net
reserved.
Answer:
the answer is A)1,432.75.
a certain Forest covers an area of 2000 square kilometers. Suppose that each year this area, decreases by 6%. What is the equation that best represents the area of the forest each year?
Which correlation coefficient indicated the strongest linear relationship between the variables?
A: 0.65
B: -0.87
C: -0.52
D: 0.8
Answer:
B
Step-by-step explanation:
since the strongest correlation is either 1 or negative 1, and weakest is closer to 0,
now, lets order from weakest to strongest:
-0.52,0.65, 0.8, -0.87
Since -0.87 is closest to negative one than others to -1 or 1, it has the strongest linear relationship
The applicants for a soccer coaching position were asked how many years of
coaching experience they had. Here are the results:
1, 2, 2, 2, 2, 4, 4, 5, 6, 6, 8, 8, 8, 10
On a piece of paper, draw a dot plot to represent the data. Then determine
which answer choice matches the dot plot you drew.
The 10 years experience applicant.
What is a dot plot?A dot plot, also known as a strip plot or dot chart, is a simple form of data visualization that consists of data points plotted as dots on a graph with an x- and y-axis.
The applicants for a soccer coaching position were asked how many years of coaching experience they had. Here are the results:
1, 2, 2, 2, 2, 4, 4, 5, 6, 6, 8, 8, 8, 10
Thus the 10 years experience applicant.
To know more about dot plot click here
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Angie has a box that is 3/4 of a foot long What fraction is equal to the length, in feet, of the box?
A. 6/12
B. 8/12
C. 9/12
D. 11/12
EXPLAIN AS WELL WHY YOU PICK THAT ANSWER!
Answer:
C.
3 x 3 = 9
4 x 3 = 12
3/3 = 1 so it is equal
3/4 = 9/12
Step-by-step explanation:
Why is partitioning a directed line segment into a ratio of 1:3 not the same as finding 1/3 the length of the directed line segment?
Answer:
The answer is C on Edge or "The ratio given is part to part. The total number of parts in the whole is 1 + 3 = 4."
Step-by-step explanation:
Find the area of a regular hexagon with a perimeter of 72 inches. *
1 point
360.055 square inches
374.112 square inches
381.489 square inches
The area of the hexagon is the amount of space on it
The area of the hexagon is 374.112 square inches
How to detemine the area of the hexagpon?The perimeter is given as:
P = 72 inches
The length of the hexagon is calculated using:
L = P/6
So, we have:
L =72/6 = 12
The area is then calculated as:
A = 1.5[tex]\sqrt 3[/tex] * L^2
This gives
A = 1.5[tex]\sqrt 3[/tex] * 12^2
Evaluate the product
A = 374.112
Hence, the area of the hexagon is 374.112 square inches
Read more about areas at:
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The fabric for Isabella’s new dress is sold by the yard. The pattern for the dress requires 8 feet of fabric. How many yards of fabric does Isabella need to purchase if 1 yard is equal to 3 feet?
1 third yard
2 2 over 3 yards
6 yards
24 yards
Answer:
2 2/3 yd
Step-by-step explanation:
Let's convert from feet to yards. See how the feet cancel, because feet is in the denominator and the numerator?
8 ft x 1 yd/3 ft = 8/3 yd
As a mixed number:
8/3 = 2 2/3 yd of fabric
answer options : 120, 60, 180 or 90
need help asap!
15 points
Answer:
D
Step-by-step explanation:
8*320=2560
(2560)^1/3=8*5^1/3
Answer:
It's D (8[tex]\sqrt[3]{5}[/tex])
I won't do step-by-step because it's multiple choice.
Goodluck :)
PLS HELP it is urgent and my homework due soon
Answer:
a) (1 , 4)
b) (-1 , 0) and (3 , 0)
Step-by-step explanation:
The turning point also call the vertex of the function is shown by in this case the maximum which is at the point (1 , 4). The roots, also known as zeros, are the values at which the graph crosses the x-axis. In this case it is at points: (-1 , 0) and (3 , 0)
Can someone help me on this?
Answer:
the triangle PQR is similar to RTS
Step-by-step explanation:
QR : RT
2 : 6
this 1:3 ratio is also seen in PR (4) with RS (12)
PLEASE HELP! A survey was done that asked people to indicate whether they preferred pool swimming or ocean swimming. The results of the survey are shown in the two-way table.
Chantal is making a relative frequency table from this data.
What operation should Chantal perform to determine the relative frequency of a person over 30 years old who prefers ocean swimming?
Divide 239 by 609.
Subtract 185 from 609, then divide by 609.
Divide 185 by 609.
Add 239 to 609, then divide by 609.
Answer:
C
Step-by-step explanation:
I think the answer is C,
since to find the relative frequency, you divide the specific frequency
(in this case people over 30 who prefer ocean swimming, 185 people)
by the # of values total
(all values recorded, which in this case is the 609 peoples' surveys)
so, divide 185 by 609, which is C
Which expression is equivalent to the given expression?
(6n-5)(3n-3)?
A.36n11
B.54n30
C. 36n30
D.54n11
Answer:
The answer is C = 36n30
Step-by-step explanation:
Does the equation represent a direct variation? If so, find the constant of variation.
4x -5y = 0
a. yes; k = -5 b. no c. yes; k = 4/5 d. yes; k = - 4
Answer:
4/5
Step-by-step explanation:
4x-5y=0
subtract 4x on both the sides
4x-4x-5y = 0-4x
-5y = -4x
divide by -5 on both the sides
-5y/-5 = -4x/-5
y =( 4/5 )x
QUICKLY ITS REALLY APPRECIATED RN IF U WOULD ANSWER!
THE IMAGE IS THE QUESTION PLS ANSWER PROPERLY I Will GIVE U BRAINLIESTTTT!
Answer:
3,-2/3,infinity
Step-by-step explanation:
Slope is change in y over change in x. Just find the changes in the coordinates y and x values. Pretty simple once you've got the hang of it!
PLEASE HELP ME WITH MY PROBLEM!!!CHECK MY ACCAnswer:
Step-by-step explanation:
1. y = 3x-12 m =3
2. y = -2/3x + 8 m = -2/3
3. m = infinity
Sam has three identical tennis balls with a diameter of 2.7 inches. Determine the volume of all three tennis balls?
Your answer would be approximately 30.93
Volume of a sphere is V=4 /3πr^3
Directions write 1/3 -3 (-3 is the exponet) without the exponet
Answer:
27
Step-by-step explanation:
I guess this would just be basically the same as 1/3 to the power of 3
Answer:
27
Step-by-step explanation:
The volume of a cylinder is 576, cubic inches. The radius of the circular base is 4 inches. What is the height of the cylinder?
Answer:
36 / pi = h
Using 3.14 for pi
h =11.46496815 inches
Using the pi button
h =11.45691559 inches
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h
We know the volume and the radius
576 = pi ( 4)^2 h
576 = pi 16 h
Divide each side by 16 pi
576/16 pi = pi 16 h/ 16 pi
36 / pi = h
Using 3.14 for pi
h =11.46496815 inches
Using the pi button
h =11.45691559 inches
Which rule will find the nth term of the arithmetic sequence
-58,-65, -72. -86,...?
Answer:
-85n - 7 = -92
Step-by-step explanation:
The sum of two consecutive numbers is 89. What are the two numbers? A. 43 and 46 B. 44 and 45 C. 38 and 51 D. 45 and 46
Answer:
C
Step-by-step explanation:
Its C
what is the discriminant of f(x)=-x^2-x+5?
a.-21
b.0
c.2
d.21
Answer: d. 21
Step-by-step explanation:
The formula to find a discriminant is b^2-4ac.
ax^2+bx+c is the quadratic equation. In your equation, -1 is a, -1 is b, and 5 is c. Now we can plug in the numbers into the discriminant formula b^2-4ac!
(-1)^2-4(-1)(5)=
1-4(-5)
1+20
21
The discriminant is 21.
Hope this helps!
Identify and explain the error.
Answer:
Step-by-step explanation:
Strictly speaking, 15% isn't precisely the same as 0.15; 0.15 is the decimal fraction used to calculate 15% of some quantity.
15% of 52 is indeed 7.8. $7.80 is the discount that is to be SUBTRACTED from the regular price ($52). Adding $7.80 to $52 is incorrect.
Also, 52 + 7.8 - 59.8 is incorrect: it's not an equation (but should be one), and we should be subtracting $7.80 from $52.
Use the distributive property to write the expression without parentheses. Then simplify the result, if possible.
1/3(6x+23)+1/3
please see the attached picture
hope it helps
good luck on your assignment
A museum opened at 8:00 a.m. In the first hour, 350 people purchased admission tickets. In the second hour, 20% more people purchased admission tickets than in the first hour. Each admission ticket cost $17.50.What was the total amount of money paid for all the tickets purchased in the first two hours? Show your work.
Answer: $13,475
Step-by-step explanation:
1st hour = 350
2nd hour = 420
Total 770 x $17.50 = $13475
Find the areas of the trapezoids.
Answer:
30 square units
Step-by-step explanation:
i did this problem before.
helpppp plleaassseee
Answer:
the answer is 1/2
explanation:
the answer is 1/2 because 3 is in the middle of 1 through 6 so it would be 1/2
question: if angle 1 measure 120 degrees what other angles would have the same 120 degrees?
Answer:
4,5, and 8
Step-by-step explanation:
corresponding angles
Answer:
Angle 4 coz vertical angle of angle 1
Angle 5 coz corresponding angle
Angle 8 coz vertical angle of angle 5
in the equation y=4x which is greater? explain answer
Answer:
If x is greater than 0, then y is greater than x
For example:
x = 2 => y = 4(2) = 8, 8 > 2
x = 3 => y = 4(3) = 12, 12 > 3
If x is = 0, then y is equal to x, because x = 0 => y = 4x = 4(0) = 0 => x = y = 0
If x is less than 0, then y is smaller than x
For example:
x = -2 => y = 4(-2) = -8, -8 < -2
x = -3 => y = 4(-3) = -12, -12 < -3
Hope this helps!