Answer:
n² ≤ 2ⁿ , ∀ n ≥ 4
Step-by-step explanation:
[tex]4^{2}=16 \leq16=2^{4}[/tex]
Then ,For n = 4 the inequality is true.
For n ≥ 4 , suppose n² ≤ 2ⁿ and prove that (n+1)² ≤ 2ⁿ⁺¹
(n+1)² = n² + 2n + 1
Since n² ≤ 2ⁿ (according to the hypothesis) and we know that 2n + 1 ≤ 2ⁿ
Then
(n+1)² = n² + 2n + 1 ≤ 2ⁿ + 2ⁿ
Then
(n+1)² ≤ 2ⁿ + 2ⁿ
Then
(n+1)² ≤ 2×2ⁿ
Then
(n+1)² ≤ 2ⁿ⁺¹
Conclusion:
n² ≤ 2ⁿ , ∀ n ≥ 4
How many feet are in 2,241 inches? (1 foot = 12 inches)
-186.75 feet
-62.25 feet
-747.00 feet
-189.25 feet
Please help me with this I would give you 50 points.
Answer:
15d=165
Step-by-step explanation:
15 dollars per dough (d)= 165 dollars
Hope this helps! ;-)
~Master Chief
Let's solve this problem step by step:
So we know that Isaac sold 'x' number of tubs of dough
⇒ and that each tub of dough is worth 15 dollars
⇒ means he made '[tex]15*x'[/tex] dollars from selling 'x' tubs of dough
⇒ coincidently, we know that he made a total of $165
⇒ So the equation is: [tex]15x = 165[/tex]
Answer: 15x = 165
Hope that helps!
14.30:A haunted house has six windows. In how many ways can Georgie the Ghost enter the house by one window and leave by a different window?
Answer:
30 waysStep-by-step explanation:
Possible ways to enter
6 windowsPossible ways to exit
5 windows, since same window entered is not usedTotal number of ways is
6*5 = 30The principal observes 8th grade the following day. Of the 120 students, 42 brought their lunch from home, 72 purchased lunches, and 6 brought a lunch from home and purchased an ice cream.
Explain how the principal could use the numbers from 7th grade to predict the 8th grade possibilities.
I think
Step-by-step explanation:
by finding each chart such as if there are 120 7th graders and 180 8th graders he can use the same numbers from the 7th graders and compare each percentage to the 8th-grade kids and get a close enough answer
Can anyone help with this problem?!
Answer:
1) 24 2) 65
Step-by-step explanation:
1) 40-8x when x=2
8*2=16
40-16=24
2) 65/p*3 when p=5
65/5= 13
13*5= 65
Hope this helps ^^
6) a. 40-8x
= 40-8(2) ← [8 x 2]
=40-16
=24
27. Find a polar equation of the conic with focus at the pole that has the given eccentricity and equation of directrix.
e=\frac{4}{3}, r \cos \theta=-3
The polar equation will be [tex]r=\dfrac{4}{1+cos\theta}[/tex]
What is the polar equation?A polar equation is any equation that expresses the relationship between r and theta, where r is the distance between the pole (origin) and a point on a curve, and theta is the counterclockwise angle formed by a point on a curve, the pole, and the positive x-axis.
From the equation, we are told that
The Eccentricity: e = 1
The Directrix is y = 4
Generally, the polar equation for e = 1 and y = + c is mathematically represented as
[tex]r =\dfrac{e\times c}{1+ecos\theta}[/tex]
[tex]r =\dfrac{1\times 4}{1+1\times cos\theta}[/tex]
[tex]r=\dfrac{4}{1+cos\theta}[/tex]
Therefore the polar equation will be [tex]r=\dfrac{4}{1+cos\theta}[/tex]
To know more about the polar equation follow
https://brainly.com/question/9363127
#SPJ1
Ricardo paid for 3 pounds of oranges with a $10 bill. He got back $8.20. What was the cost of 1 pound of oranges?
Answer:
6 cents
Step-by-step explanation:
10 - 8.20 = 1.8
1.8 / 3 = 0.6
Hope this helps you :D
Answer: $0.60
Step-by-step explanation:
Facts
got 3 lbs of oranges
paid with $10, got 8.20 in change.
Step 1: Find how much the 3lbs of oranges actually cost (actual total)
10-8.20= 1.8
Step 2: Find the unit rate (cost per lb)
Cost per lb. Divide the cost by the number of pounds, as shown:
1.8/3= 0.6
Step 3: Checks
[hypothetically], each pound costs 0.60.
Buying 3 pounds of oranges, multiply 0.6x3= 1.8.
Now, you pay with $10.
To find how much change you get, subtract 10-1.8= 8.20
These computations are correct, and the resulting facts match those given in the question. This is how I double check the answer is accurate.
Hence, each pound costs $0.60, or 60 cents.
Hope this helps :)) brainiest would be appreciated :D
Please help!
A net of a rectangular prism is shown below. The surface area of each face is labeled.
Problem
Which values represent the dimensions, in meters, of the rectangular prism?
A.3, 4, 10
B. 12, 30, 40
C. 2, 6, 8
D. 2, 5, 6
Answer:
b i think
Step-by-step explanation:
because if you make it into a prism, the dimensions are basically the same
the shoes department is offering a sale of 15% off all shoes. if mrs. jefferey saved $12.30, how much were the shoes full price?
Answer: $82
Step-by-step explanation:
F - .15F = 12.30
F = 12.3/.85 =$14.47 for full shoe price rounded down a fraction of a cent
Full Price minus 15% discount = $12.30
F - 0.15F = 12.30
F(1-0.15) = 12.30
0.85F = 12.30
Overall answer --->F = 12.30/.85 = 14.47058824
69. If four coins are flipped, find the probability and the odds of obtaining one head and three tails.
Answer:
The probability is 4/16 = 1/4
Step-by-step explanation:
I also need help on this one
2. The radius of a circle is 11 inches. Find the diameter. (Section 13.1)
Answer:
22
Step-by-step explanation:
diameter = radius x 2
11 x 2 = 22
Desmos
Is it Fair?
Explain your answer.
please helppppp me i need it
A rectangle is drawn on a coordinate plane. Three vertices of the rectangle are points A(−4,3), B(2,3), and C(2,−1). Point D is the fourth vertex of the rectangle.
What is the distance from point C to point D?
Enter your answer in the box.
units
Answer:
6 units
Step-by-step explanation:
D is at (-4, -1). 2 + 4 = 6.
First Question: Screenshot the following image and attach a photo after you dilate by a scale factor of 2.
Second Question: Screenshot the following image and attach a photo after you dilate by a scale factor of 1/3.
Please help! If you help with this please do my other questions!! (They are very similar!)
Answer: See in the explanation, screenshot attached
Step-by-step explanation:
SQUARE QRTS
Step 1: Label all of the coordinates
Step 2: Find the coordinates of the points
Q: (-2, 1)
R: (2, 1)
T: (-2, -2)
S: (2, -2)
Step 3: Know what it means to dilate
To dilate is to make a shape bigger or smaller. For example, when it says to dilate by a scale factor of 2, you multiply each coordinate by 2 to get coordinate pairs that are twice the original amount (in this case you make it bigger). However, if it says to dilate by a scale factor of a fraction, for example 1/2, you'd multiply the coordinates by 1/2 and hence make it smaller (1/2 its size).
Step 4: Dilate by a scale factor of 2--multiply by 2
*x stands for the x coordinate, and y stands for the y coordinate*
Q: -2, 1
x: -2x2= -4
y: 1x2= 2
[Dilated] Q: -4, 2
R: 2, 1
x :2x2= 4
y: 1x2= 2
[Dilated] R: 4, 2
T: -2, -2
x: -2x2= -4
y: -2x2=-4
[Dilated] T: -4, -4
S: 2, -2
x: 2x2= 4
y: -2x2= -4
[Dilated] S: 4, -4
Step 5: Plot the new pairs
(See screenshot)
SQUARE ABCD
Step 1: Label all the coordinates
Step 2: Find the coordinate pairs of the points
A: -3, 3
B: 3, 3
C: 3, -3
D: -3, -3
Step 3: Remember what it means to dilate
(See 1st explanation)
Step 4: Dilate by a scale factor of 1/3
**Since 1/3 is a fraction, we are making the square smaller, or making it ⅓ of its original size. You will see that the numbers of the coordinates get smaller once you dilate them.**
A: -3, 3
x: -3x1/3= -1
y: 3x1/3= 1
[Dilated] A: -1, 1
B: 3, 3
x: 3x1/3 = 1
y: 3x1/3= 1
[Dilated] B; 1, 1
C: 3, -3
x: 3x1/3= 1
y: -3x1/3= -1
[Dilated] C: 1, -1
D: -3, -3
x: -3x1/3= -1
y: -3x1/3= -1
[Dilated] D: -1, -1
Step 5: Plot the new pairs
(see screenshot)
Hope this helps :))
Also I worked pretty hard on this so brainiest would be appreciated :D
PLEASE HURRY AND FAST Raul's soccer team enters a tournament. He estimates that
his team has a 50% chance of winning each of the three
games they play. If they win all three games, they move to
the championship. To model his team's chance of going to
the championship, Raul performs a simulation using a
coin.
Let heads (H) represent a win.
• Let tails (T) represent a loss.
The results of the simulation were:
HTH HHH TTT HTT HHT
TTT HTT HTT HTT HHH
НHТ HTT ТTТ TTT HTH
Answer:
A. There were NOT 3 successes . there were only two.
Step-by-step explanation:
Answer: there were only two success
How do I do this? I'm so confused
Answer:
The answer is 67.5
Step-by-step explanation:
1. How can you describe the likelihood of an event?
Answer:
It could be the probability or this for an example: 1/2 = an equal chance of getting 1 or 2, 3/4 = likely, 1/4 is going to be unlikely since you have a lower chance of something, and 4/4 = 1 = a certain chance of something happening.
Step-by-step explanation:
well it could be the probability.
You randomly choose one of the tiles. Without replacing the first tile, you randomly choose a second tile. Find the probability of the compound event. Write your answer as a fraction or percent rounded to the nearest tenth. The probability of choosing a red tile and then a vowel is
Answer:
You randomly choose one of the tiles. Without replacing the first tile, you randomly choose a second tile. Find the probability of the compound event. Write your answer as a fraction or percent rounded to the nearest tenth. The probability of choosing a red tile and then a vowel is
Step-by-step explanation:
You randomly choose one of the tiles. Without replacing the first tile, you randomly choose a second tile. Find the probability of the compound event. Write your answer as a fraction or percent rounded to the nearest tenth. The probability of choosing a red tile and then a vowel is
please help 50 point will be given!!
Answer:
12
Step-by-step explanation:
Count how many there are per meat mixed with all three different veggies, sounds weird in writing but makes sense if clarified by speech. anyways hope this helped have a great night!
The two dot plots below compare the forearm lengths of two groups of schoolchildren:
Based on visual inspection of the dot plots, which of the following groups appears to have the longer average forearm length?
A. Group B, because a child in the group has the least forearm length of 11 inches
B. Group A, because three children in the group have the least forearm length of 11 inches
C. Group B, because four children have a forearm length longer than 13 inches
D. Group A, because no child in the group has a forearm length longer than 13 inches
So, The dots represent the children.
And the numbers represent the length in.
I wouldnt say its D.
I would say its C. Group B, because 4 kids have forearm length longer then 13 in.
Answer:
So, The dots represent the children.
And the numbers represent the length in.
I wouldnt say its D.
I would say its C. Group B, because 4 kids have forearm length longer then 13 in.
Step-by-step explanation:
bc
PLEASE HELP !!!!!!
find the missing number on the number line
What is the scale factor of ABC to A'B'C'?
Please help!! ASAP if you help with this PLEASE HELP WITH MY LAST QUESTION I ASKED!!! (it’s worth a lot of points!)
2. The radius of a circle is 9 yards. Find the diameter.
Answer:
18
Step-by-step explanation:
9 x 2 = 18
radius x 2 = diameter
I NEED HELP PLEASE I LOVE YOU!!!!! What is the mean absolute deviation (MAD) for the set of data?
{21, 18, 14, 23, 34, 40}
Answer: 8
Step-by-step explanation:You Take each number in the data set, subtract the mean, and take the absolute value. Then take the sum of the absolute values. Now compute the mean absolute deviation by dividing the sum above by the total number of values in the data set.
Select all the relationships with a constant of proportionality of 12.
A parallelogram has an area of 120 square feet and a height of 6 feet.
What is the length of the base of the parallelogram?
Enter your answer in the box.
*box*
Answer:
20 feet
Step-by-step explanation:
1. We know from here that A = bh (Area = Base x Height).
We are given:
A = 120 ft^2
h = 6 ft
b = ?
2. Let's rearrange our formula (A = bh) so that we find what "b" equals."
Our new formula will be: b = A/h (base = Area / height).
3. Let's apply it to the question and do the required math!
b = A/h
b = 120/6
b = 20 ft
Answer:
b = 20 ft
Step-by-step explanation:
The area of a parallelogram is given by:
A = b*h
where,
A: area = 120 ft^2
b: base = ?
h: height = 6 ft
From the equation for A, solve for b, replace the values of A and h and simplify:
b = A/h
b = 120ft^2/6ft
b = 20ft
Hence, the length of the base of the parallelogram is 20 ft
can someone help me? i need my math grade to go up
Answer:
59
Step-by-step explanation:
do it piece of paper or ask someone to help you.
Mr. Jackson is ordering kazoos for his second, third, and fourth grade music classes.
The kazoos come in boxes of 8. There are 26 second graders, 24 third graders, and 30 fourth graders.
How many boxes of kazoos does Mr. Jackson need to order so that every student will receive a kazoo?
Enter your answer in the box.
Answer:
The boxes of kazoos Mr. Jackson needs to order (26 + 24 + 30) ÷ 8.
We have given that,
There are 26-second graders, 24 third graders, and 30 fourth graders.
What is the expression?
An expression, in math, is a sentence with a minimum of two numbers and at least one math operation contain in it.
The amount of kazoos needed is 1 for every student
26 + 24 + 30
Since 8 come in each box, you divide by 8
To get your answer of (26 + 24 + 30) ÷ 8.