Identify a counterexample to disprove n3 ≤ 3n2, where n is a real number.

Answers

Answer 1

[tex]n^3\le3n^2\iff n^3-3n^2\le0\iff n^2(n-3)\le0[/tex]

The quantity on the left hand side will be positive for any [tex]n>3[/tex], so suppose consider [tex]n=4[/tex].

Now,

[tex]4^3=64[/tex]

but

[tex]3(4)^2=48[/tex]

and [tex]64\not\le48[/tex]

Answer 2

"The correct counterexample to disprove the inequality [tex]$ n^3 \leq 3n^2 $[/tex]for real numbers [tex]$ n $[/tex]is any real number[tex]$ n $[/tex]greater than 3.

To find a counterexample, we need to show that there exists at least one real number[tex]$ n $[/tex] for which the inequality [tex]$ n^3 \leq 3n^2 $[/tex] does not hold. Let's solve the inequality to find the values of[tex]$ n $[/tex] that satisfy it:

[tex]\[ n^3 \leq 3n^2 \][/tex]

[tex]\[ n^3 - 3n^2 \leq 0 \][/tex]

[tex]\[ n^2(n - 3) \leq 0 \][/tex]

The critical points of this inequality are [tex]$ n = 0 $ and $ n = 3 $[/tex]. We can divide the real number line into three intervals:[tex]$ n < 0 $, $ 0 \leq n \leq 3 $[/tex], and[tex]$ n > 3 $.[/tex]Let's test each interval:

1. For[tex]$ n < 0 $, $ n^2 $[/tex] is positive, but [tex]$ n - 3 $[/tex] is negative, so the product [tex]$ n^2(n - 3) $[/tex]is negative, and the inequality holds.

2. For [tex]$ 0 \leq n \leq 3 $[/tex], both [tex]$ n^2 $ and $ n - 3 $[/tex] are non-negative, so the product [tex]$ n^2(n - 3) $[/tex]is non-positive, and the inequality holds.

3. For [tex]$ n > 3 $[/tex], both [tex]$ n^2 $[/tex] and [tex]$ n - 3 $[/tex] are positive, so the product[tex]$ n^2(n - 3) $[/tex] is positive, and the inequality does not hold.

Therefore, any real number [tex]$ n $[/tex] greater than 3 will serve as a counterexample to the inequality[tex]$ n^3 \leq 3n^2 $[/tex]. For instance, if we take [tex]$ n = 4 $,[/tex] we get:

[tex]\[ 4^3 \leq 3 \cdot 4^2 \][/tex]

[tex]\[ 64 \leq 48 \][/tex]

This statement is false, as 64 is not less than or equal to 48. Thus, $ n = 4 $[tex]$ n = 4 $[/tex] is a valid counterexample."

Related Questions

If a polynomial function f(x) has roots 3 and mc001-1.jpg, what must also be a root of f(x)?

Answers

Final answer:

The Complex Conjugate Root Theorem dictates that if -4 is a root of f(x), then 4 must also be a root. This theorem applies to polynomials with real coefficients, ensuring non-real complex roots appear in conjugate pairs.

Explanation:

If a polynomial function f(x) has roots 3 and -4, then by the Complex Conjugate Root Theorem (also known as the Conjugate Pairs Theorem), if the polynomial has real coefficients, which is the usual assumption unless stated otherwise, the complex roots must come in conjugate pairs. Therefore, if -4 is a root, its complex conjugate 4 must also be a root of f(x). This applies to all non-real complex roots of a polynomial with real coefficients.

The Complex Conjugate Root Theorem is essential for understanding the behavior of polynomial functions with complex roots. In general, if a polynomial has a complex root a + bi, where a and b are real numbers and i is the imaginary unit (the square root of -1), its conjugate a - bi is also a root. This is true because polynomial equations with real coefficients have the property that their roots are either real or occur in complex conjugate pairs.

Answer:

A: -5 - √3i

This should be correct on edge

paige mows 1/6 acre in 1/4 hour.How many acres does paige mow per hour?

Answers

1 4 4 2
---- x ----- = ------- = ------ acres
6 1 6 3

Hope this helps! :)

You're finding a "unit rate" here: acres per hour, or acres/hour.

Divide 1/6 acre by 1/4 hour. I noticed right away that multiplying "1/4 hour" by 4 results in 1. So, I multiplied both sides of this rate by 4, obtaining

4/6 acre per 1 hour, or 2/3 acre per hour, or 2/3 acre/hr.

Evaluate the line integral, where c is the given curve. (x + 9y) dx + x2 dy, c c consists of line segments from (0, 0) to (9, 1) and from (9, 1) to (10, 0)

Answers

[tex]\displaystyle\int_C(x+9y)\,\mathrm dx+x^2\,\mathrm dy=\int_C\langle x+9y,x^2\rangle\cdot\underbrace{\langle\mathrm dx,\mathrm dy\rangle}_{\mathrm d\mathbf r}[/tex]

The first line segment can be parameterized by [tex]\mathbf r_1(t)=\langle0,0\rangle(1-t)+\langle9,1\rangle t=\langle9t,t\rangle[/tex] with [tex]0\le t\le1[/tex]. Denote this first segment by [tex]C_1[/tex]. Then

[tex]\displaystyle\int_{C_1}\langle x+9y,x^2\rangle\cdot\mathbf dr_1=\int_{t=0}^{t=1}\langle9t+9t,81t^2\rangle\cdot\langle9,1\rangle\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^1(162t+81t^2)\,\mathrm dt[/tex]
[tex]=108[/tex]

The second line segment ([tex]C_2[/tex]) can be described by [tex]\mathbf r_2(t)=\langle9,1\rangle(1-t)+\langle10,0\rangle t=\langle9+t,1-t\rangle[/tex], again with [tex]0\le t\le1[/tex]. Then

[tex]\displaystyle\int_{C_2}\langle x+9y,x^2\rangle\cdot\mathrm d\mathbf r_2=\int_{t=0}^{t=1}\langle9+t+9-9t,(9+t)^2\rangle\cdot\langle1,-1\rangle\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^1(18-8t-(9+t)^2)\,\mathrm dt[/tex]
[tex]=-\dfrac{229}3[/tex]

Finally,

[tex]\displaystyle\int_C(x+9y)\,\mathrm dx+x^2\,\mathrm dy=108-\dfrac{229}3=\dfrac{95}3[/tex]

Final answer:

To evaluate the given line integral, you need to parameterize the curve composed of two segments. Then, you solve the integrals along the two separate segments and take the sum.

Explanation:

To evaluate the line integral where the curve c consists of line segments from (0, 0) to (9, 1) and from (9, 1) to (10, 0) for the function (x + 9y) dx + x² dy, we need to parameterize the curve and solve the integral.

First, we parametrize the line segments. For the segment from (0, 0) to (9, 1), we have x = 9t and y = t for t in [0, 1]. For the segment from (9, 1) to (10, 0) let x = 9 + s and y = 1 - s for s in [0, 1].

Then, we integrate along the first and second segments separately with respect to t. For the first segment, the integral is ∫(9t + 9t) d(9t) + ∫(81t²) dt = ∫18t dt + ∫81t² dt. For the second segment, the integral is ∫(9 + s + 9(1 - s)) ds + ∫(81 + 2 * 9 * s + s²) d(1 - s) = ∫ds + ∫s² ds.

We then evaluate these integrals over the respective bounds, sum them up and that gives the line integral along the path described.

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find two possible factors for the estimated product 2,800

Answers

28 x 100 and 280 x 10

Marisol is preparing a care package to send to her brother. The package will include a board game that weighs 4 lb and several 14 lb snack packs. The total weight of the care package must be less than 25 lb.

Drag and drop the answer into the box.
Question Answer
Which statement describes the solution to this inequality?

Marisol must send less than 1 snack pack.Marisol must send fewer than 21 snack packs.Marisol must send fewer than 84 snack packs.Marisol must send fewer than 100 snack packs.

Answers

4 + 1/4s < 25
1/4s < 25 - 4
1/4s < 21
s < 21 / (1/4)
s < 21 * 4/1
s < 84

Marisol must send fewer then 84 snack packs <=

So what we gotta do is isolate the variable by
writing it out like this
4 1/4 25 those are the numbers where those go are like this
4x - 1/4 < 25 then move on to the next line on here we write out
4x + 1/4 - 1/4 < 25 + 1/4 (The reason why i put + 1/4 is because you have to isolate the variable by doing addition as well And i always find it easier to convert the fractions to decimals then after you make that line you make the next one like this you have to add 1/4 to 4x then take it away (which is 4x) then put that to the side like this 4x ? ? then we need to find those two ?s by adding 25 and 1/4 (or o.25) which is 25.25 then we need to add that to the second answer 4x ? 25.25 when you have this you need to find out which one is bigger so it is 4x<25.25 (or 25 1/4) then we need to divide 4 and 25.25 to get 6.25 so
the answer is x < 6.25 so c is your awnser

HELP ASAP PLEASE!!!!!!!!!!!!!!

Answers

Refer to the image attachment Figure 1 for the letter references. Hopefully the reference image is handy to keep track of all of the empty boxes.
The answers are given in Figure 2 which is also attached.
===================================================================================================================
Focus on the first Magic Square for now (the one in the top row, left side).
The middle row has 9+6+3 = 18 as the magic constant (aka magic sum). Every row, column and diagonal must add to this constant
A = 7 because the first column of values must add to 18
A+9+2 = A+11 = 18 leads to A = 7
----------
C = 10 since that solves 2+6+C = 18 (northeast diagonal)
----------
Solve the equation A+6+E = 18 for E to get E = 5 (plug in A = 7)
As a check, note how C+3+E = 10+3+5 = 18
----------
We know that A = 7 and C = 10 so B must be B = 1 since A+B+C = 7+1+10 = 18
----------
Similarly, 2+D+E = 18 and E = 5, so D must be 11.
As a check, note how B+6+D = 1+6+11 = 18
----------
----------
In summary we have
A = 7
B = 1
C = 10
D = 11
E = 5
See Figure 2 for the completed magic square
----------
Check:
Row1: 7+1+10 = 18
Row2: 9+6+3 = 18
Row3: 2+11+5 = 18
Column1: 7+9+2 = 18
Column2: 1+6+11 = 18
Column3: 10+3+5 = 18
NorthEast Diagonal: 2+6+10 = 18
NorthWest Diagonal: 7+6+5 = 18
As you can see, we get the same magic constant of 18
===================================================================================================================
Second Magic Square (Top Right)
For this magic square, the magic constant isn't known. So this is mainly a guess and check type of problem. This is what I got
F = 9
G = 6
H = 10
J = 12
K = 5
See Figure 2 for the completed magic square
----------
Check:
Row 1: 11+4+9 = 24
Row 2: 6+8+10 = 24
Row 3: 7+12+5 = 24
Column 1: 11+6+7 = 24
Column 2: 4+8+12 = 24
Column 3: 9+10+5 = 24
NorthEast Diagonal: 7+8+9 = 24
NorthWest Diagonal: 11+8+5 = 24
===================================================================================================================
Third Magic Square at the very bottom
The magic constant is 12+6+7+9 = 34
----------
Bottom row: 13+3+S+16 = 34 which solves to S = 2
----------
Northeast Diagonal: 13+Q+7+4 = 34 which solves to Q = 10
----------
Second Column: 3+Q+6+M = 34 turns into 3+10+6+M = 34 after substitution and that solves to M = 15
----------
For values R, P, L and N, I couldn't figure out an algebraic way to solve for them. So I had to resort to trial and error (guess and check). This is what I got
R = 11
P = 8
L = 1
N = 14
----------
----------
In summary we have
L = 1
M = 15
N = 14
P = 8
Q = 10
R = 11
S = 2
See Figure 2 for the completed magic square
----------
Check:
Row 1: 1+15+14+4 = 34
Row 2: 12+6+7+9 = 34
Row 3: 8+10+11+5= 34
Row 4: 13+3+2+16 = 34
Column 1: 1+12+8+13 = 34
Column 2: 15+6+10+3 = 34
Column 3: 14+7+11+2 = 34
Column 4: 4+9+5+16 = 34
NorthEast Diagonal: 13+10+7+4 = 34
NorthWest Diagonal: 1+6+11+16 = 34

Product of prime factors for 60 = 2x2x3x5
How do i write this in index form?
I have tried by simplifying so it is 2 to the power of 2 x 3 x 5
It stills says it is incorrect, anyone know?

Answers

The prime factors of 60
60 = 2,2,3,5
Index Form = [tex]2^2 \times 3 \times 5[/tex]
They might want something like below for the index form
[tex]2^2 \times 3^1 \times 5^1[/tex]

Final answer:

The correct index form for the product of prime factors of 60, which is 2x2x3x5, is 2^2 x 3 x 5.

Explanation:

The product of prime factors for 60 is indeed 2x2x3x5. To write this in index form, we group the same numbers together and count how many there are. Then we use the base and exponent form to write it. Here, 2 is repeated twice. So, 2x2 can be written as 2^2. The primes 3 and 5 are each given once, so, we do not write powers for them. Therefore, the correct index form is 2^2 x 3 x 5.

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Please help.. I got stuck on this question please help and explain

Sam earned $150 last week. Jay earned $130 last week. They combined their money and decided to donate ¼ of their total amount to a charity. Then, they spent 40% of the remaining amount at an amusement park. Jay claims that they only have 35% of their original combined total left.

Is jay right or wrong?

Answers

Jay is wrong about his claim

150 + 130 = 280 combined
they donated 1/4 of the total amount....1/4(280) = 280/4 = 70....so now they have 280 - 70 = 210
then they spent 40%.....210 - 0.4(210) = 210 - 84 = 126..what they have left

35% of 280 = 0.35(280) = 98

Jay is not correct

You have 2/3 of a pizza. You divide the remaining pizza into 4 equal pieces. What fraction of the pizza is each piece?

Answers

1/4? I feel like this is a trick question

Hi there!

Keep in mind that when you divide by a number, you are actually multiplying by its reciprocal.

The reciprocal of 4 is 1/4.

2/3 * 1/4 = 2/12

2/12, when simplified, is equal to 1/6.

So each remaining slice is equal to 1/6.

Hope this helps.

:)

A number cube is rolled with these results: 64 ones, 67 twos, 73 threes, 59 fours, 72 fives, and 71 sixes. What is the experimental probability of rolling an even number?

Write your answer as a percent, to the nearest tenth of a percent.

A. 51.9%

B. 48.5%

C. 53.6%

D. 46.8%

Answers

the answer to the question is B.48.5%

Answer: B. [tex]48.5\%[/tex]

Step-by-step explanation:

Given : A number cube is rolled with these results:

64 ones, 67 twos, 73 threes, 59 fours, 72 fives, and 71 sixes.

Even numbers : 2,4,6

The number of times of rolling even number = [tex]67+59+71=197[/tex]

Total outcomes = [tex]64+67+73+59+72+71=406[/tex]

Now, the experimental probability of rolling an even number :-

[tex]\dfrac{197}{406}[/tex]

In percent, [tex]\dfrac{197}{406}\times100=48.52216748\approx48.5\%[/tex]

Hence, the experimental probability of rolling an even number = [tex]48.5\%[/tex]

John and Jeremy are the local names for two lighthouses that guard a particularly dangerous part of the coast. John blinks every 6 seconds and Jeremy blinks every 4 seconds. They blink together at midnight. How many seconds will pass before they blink together again?

Answers

John blinks every 6 seconds, Jeremy every 4 seconds, so they both will blink next on a common factor of 6 and 4, or an LCD, that'd be 12 seconds later, so at 00:00:12.

6578 divided 34

20\5

Answers

You have apparently shared two different problems. In one case you divide
6578 by 34, and in the other you divide 6589 by 25.

I arbitrarily choose to focus on the second:

______________
25 / 6589

25 goes into 65 twice, with a remainder of 15:

______2_____
25 / 6589
50
-------------
158 25 goes into 158 6 times, with a remainder of 8.

Can you now finish this long division?

commutative
property of addition of 93+ (68+7)

Answers

93 + (68 + 7)

(93 + 68) + 7

= 168

hope this helps

the average marks of shahid first four papers is 88 how much mark should he get in the fifth paper so that the average of five papers becom 90?
a.92
b.94
c.96
d.98

Answers

your answer is D. 98
88*4=352
90*5=450
hence 450-352=98

Answer with Step-by-step explanation:

The average marks of Shahid first four papers is 88.

Let a,b,c and d be the marks in first four papers

⇒ [tex]\dfrac{a+b+c+d}{4}=88[/tex]

⇒ a+b+c+d=88×4

=352

Let marks in fifth paper be x

The average of five papers become 90

⇒ [tex]\dfrac{a+b+c+d+x}{5}=90[/tex]

⇒ a+b+c+d+x=90×5

⇒ 352+x=450 (since a+b+c+d=352)

⇒ x=450-352

⇒ x=98

Hence, Correct option is:

d.98

A theater group made appearances in two cities. The hotel charge before tax in the second city was $500 lower than in the first. The tax in the first city was 3.5% , and the tax in the second city was 7.5% . The total hotel tax paid for the two cities was $347.50 . How much was the hotel charge in each city before tax?

Answers

is pretty much the same as before, so without much fuss

a = charges before tax on first city

b = charges before tax on second city

how much is 3.5% of a? (3.5/100) * a, 0.035a.

how much is 7.5% of b? (7.5/100) * b, 0.075b.

the taxes for both cities, summed up to 347.50

so, 0.035a + 0.75b = 347.50

we also know that, whatever "a" may be, the second city charged $500 less, so b = a - 500.

[tex]\bf \begin{cases} \boxed{b}=a-500\\ 0.035a+0.075b=347.5\\ --------------\\ 0.035a+0.075\left( \boxed{a-500} \right)=347.5 \end{cases} \\\\\\ 0.035a+0.075a-37.5=347.5\implies 0.110a=385 \\\\\\ a=\cfrac{385}{0.11}\implies a=3500[/tex]

how much did the second city charge? well, b = a - 500.

It costs $2.80 to make a sandwich at the local deli shop. To make a profit, the deli sells it at a price that is 170% of the cost. The sandwich sells for $ .

Answers

namely, what is 170% of 2.80? well, if we take 2.80 to be the 100%, what is the 170%?

[tex]\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 2.80&100\\ x&170 \end{array}\implies \cfrac{2.80}{x}=\cfrac{100}{170}\implies \cfrac{2.80\cdot 170}{100}=x[/tex]

A two year degree that focuses on natural science, engineering, and mathematics is called an

Answers

Associate of science

Answer:

Assosiate in science

Step-by-step explanation:

An Associate of Science (AS) is a 2-year degree offered by most community colleges. Most AS degrees are transfer degrees and provide an academic foundation, but not specific career training. The A.S. degree is intended for students planning to pursue a bachelor’s degree in the areas of math or science.

I hope you find this information useful and interesting! Good luck!

A bottle of medicine contains 40 doses. How many doses are in 3 1/3 bottles?

Answers

Hi there! So, there are 40 doses in 1 bottle. To find out the number of doses in 3 1/3 bottles, we have to multiply both numbers together. 3 1/3 as an improper faction is 10/3. 40/1 * 10/3 is 400/3 or 133 1/3 in simplest form. There are 133 1/3 doses of medicine in 3 1/3 bottles.

Final answer:

To calculate the total number of doses in 3 1/3 bottles of medicine, multiply the fraction of bottles (10/3) by the number of doses per bottle (40). The result is 133 1/3 doses.

Explanation:

The student is asking how many doses are in 3 1/3 bottles of medicine if one bottle contains 40 doses. To find the answer, we need to multiply the number of bottles by the number of doses per bottle.

Here is the step-by-step calculation:

First, convert 3 1/3 bottles to an improper fraction: 3 1/3 = (3 × 3 + 1)/3 = 10/3 bottles.Next, multiply this value by the number of doses in one bottle to find the total number of doses: (10/3) × 40 doses = 400/3 doses.Finally, simplify the fraction: 400/3 doses = 133 1/3 doses.

So, there are 133 1/3 doses in 3 1/3 bottles of medicine.

Translate “the perimeter of a rectangle is equal to 2 times the length plus twice the width

Answers

perimeter (p)= 2l+2w

The required translated string of “the perimeter of a rectangle is equal to 2 times the length plus twice the width" is,
Perimeter = 2 * length + 2 * width.

Given that,
To translate “the perimeter of a rectangle is equal to 2 times the length plus twice the width."

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

What is the perimeter?

Perimeter is the measure of the figure on its circumference.

Here, the given string, “the perimeter of a rectangle is equal to 2 times the length plus twice the width" can be translated in the mathematical form is,
Perimeter = 2 * length + 2 * width.

Thus, the required translated string of “the perimeter of a rectangle is equal to 2 times the length plus twice the width" is,
Perimeter = 2 * length + 2 * width.

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If it snows on game day there is a 32% chance the Jets will win. If it does not snow on game day there is a 41% chance the jets will win. There is a 29% chance that it will snow on game day.

a. What is the probability the Jets will win?

b. What is the probability that it snows on game day and the Jets win?

c. What is the probability that it snows on game day given that the Jets win?

Answers

a) It is Win with snowfall OR Win without snowfall = 32% + 41% = 73% b) It is Snowfall on game day AND Win = 29% * 32% = 9.28% c) It is 32% * 29% / 73% = 12.71 %

Final answer:

To find the probability the Jets will win, we use the Law of Total Probability. The probability that it snows on game day and the Jets win is found using the definition of conditional probability. Lastly, to find the probability that it snows on game day given that the Jets win, Bayes' theorem is used.

Explanation:

To solve this problem, we can use the concept of conditional probability. Let's define the following events:

A = it snows on game day

B = the Jets win

We are given:

P(B|A) = 0.32 (the probability of the Jets winning if it snows)

P(B|A') = 0.41 (the probability of the Jets winning if it doesn't snow)

P(A) = 0.29 (the probability of it snowing on game day)

To find the probability of the Jets winning, we can use the Law of Total Probability:

P(B) = P(B|A)P(A) + P(B|A')P(A')

P(B) = 0.32 * 0.29 + 0.41 * (1 - 0.29)

P(B) = 0.0928 + 0.1059

P(B) ≈ 0.1987

To find the probability that it snows on game day and the Jets win, we can use the definition of conditional probability:

P(A and B) = P(A) * P(B|A)

P(A and B) = 0.29 * 0.32

P(A and B) ≈ 0.0928

To find the probability that it snows on game day given that the Jets win, we can use Bayes' theorem:

P(A|B) = (P(B|A) * P(A)) / P(B)

P(A|B) = (0.32 * 0.29) / 0.1987

P(A|B) ≈ 0.4643

The table shows the amount of money in your bank account over a period of 5 weeks. The account does not pay interest. You plan to keep saving at the same rate until you have $650 in the account. Which equation could you use to find the number of weeks, n, it would take to reach your goal?

Answers

Answer:

35*n+100=650

Step-by-step explanation:

I got the question right on TTM

A number, one-third of that number , and one-fourth of that number are added. The result is 19 what is the original number

Answers

x + 1/3x + 1/4x = 19...multiply by common denominator of 12
12x + 4x + 3x = 228
19x = 228
x = 228/19
x = 12 <=== ur original number

Hi, your original number is 12... hoped I helped!

Marko currently has 20 tulips in his yard. Each year he plants 5 more. Write an explicit formula for the number of tulips Marko has.

Predict the number of tulips Marko will have in 7 years.

Answers

The number of tulips that Marko has in his yard can be represented by the following formula: x = 20 + 5(y) where "x" is the number of tulips Marko has, and "y" is the number of years that have passed. If 7 years have passed, we substitute this number for "y" so, x = 20 + 5(7) = 20 + 35 = 55 Therefore, Marko will have 55 tulips in 7 years.

Final answer:

To write an explicit formula for the number of tulips Marko has, use the formula n = a + (x-1)d, where n represents the number of tulips, a is the initial number of tulips, x is the number of years, and d is the change in number of tulips each year. The explicit formula for Marko's tulips is n = 20 + 5(x-1). To predict the number of tulips Marko will have in 7 years, substitute x = 7 into the formula and solve for n, giving Marko will have 50 tulips in 7 years.

Explanation:

To write an explicit formula for the number of tulips Marko has, we can use the formula: n = a + (x-1)d. Here, n represents the number of tulips, a is the initial number of tulips (20), x is the number of years, and d is the change in number of tulips each year (5). So, the explicit formula is n = 20 + 5(x-1).

To predict the number of tulips Marko will have in 7 years, we can substitute x = 7 into our formula: n = 20 + 5(7-1). Solving this equation, we get n = 20 + 5(6) = 20 + 30 = 50. Therefore, Marko will have 50 tulips in 7 years.

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Can someone explain this a little better?

Answers

Answer:

1. 76,000

2. 8050

3. 240000

Step-by-step explanation:

We know that

1 tens = 10 ones

1 hundreds = 100 ones

1 thousand = 1000 ones

10 thousands = 10000 ones

Using these conversions we get,

1 : [tex]760\text{ hundreds}=760\times 100=76,000[/tex]

2 : [tex]805\text{ tens}=805\times 10=8050[/tex]

3 : [tex]24\text{ ten thousands}=24\times 10000=240000[/tex]

Table can be filled as shown below:

Thousands Ones

Q. no. Hundreds Tens Ones Hundreds Tens Ones

1. 7 6 0 0 0

2. 8 0 5 0

3. 2 4 0 0 0 0

In a sample of 200 students, what is the probability that over 31% of the sample has ap credit?

Answers

20 peppers and green tea and a few of my

As sand leaks out of a hole in a contaimer, it forms a conical pile whose altitude is always the same as its radius. If the height of the pile is increasing at a rate of 6in/min, find the rate at which sand is leaking out when the altitude is 10 inches.

Answers

the rate at which the sand is leaking, is the same rate at which the volume of the cone is increasing, so the rate of the sand leak is then the same as dv/dt of the cone.

now, we know the height is always the same length as the radius, thus h = r.

[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}\qquad \boxed{h=r}\qquad V=\cfrac{\pi h^2 h}{3}\implies V=\cfrac{\pi h^3}{3} \\\\\\ \cfrac{dV}{dt}=\cfrac{\pi }{3}\cdot 3h^2\cdot \cfrac{dh}{dt}\implies \cfrac{dV}{dt}=\pi h^2\cfrac{dh}{dt}\qquad \begin{cases} h=10\\ \frac{dh}{dt}=6 \end{cases} \\\\\\ \cfrac{dV}{dt}=\pi \cdot 10^2\cdot 6\implies \cfrac{dV}{dt}=600\pi ~\frac{in^3}{min}[/tex]

The rate at which sand is leaking out when the altitude is 10 inches is

600π inches³ / min.

What is a cone?

It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.

The volume of a cone is (1/3)πr²h.

We have,

A conical pile formed due to a leak out of a hole whose radius is equal to its height.

dh/dt = 6 in/min

The rate at which the sand is leaking when height is 10 inches.

We have,

Volume = (1/3)πr²h and h = 10 inches

V = 1/3 πh²h

V = 1/3 πh³

Differentiating both sides.

dV/dt = 1/3 x π x 3 x h² (dh/dt)

dV/dt = π x h² x 6

dV/dt = π x 10² x 6

dV/dt = 600π inches³ / min

Thus,

The rate at which sand is leaking out when the altitude is 10 inches is

600π inches³ / min.

Learn more about cones here:

https://brainly.com/question/13798146

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The school theater department made $2142 and the department sold the same number of tickets each night and each ticket cost $7. How many tickets did the theater department sell each night?

Answers

They sold 306 tickets each night. In order to get the answer, you just divide $2142 by $7 and then you should get 306.

Since the theater department made $2142 and sold a ticket each night for $7, then you have to divide.Now, you divide $2142/7.

You should get your answer of 306 :)

[tex]\sqrt[7]{2142}[/tex]

^online division .-.

Gina wrote the number 43,628. Then she used the same digits to write a new number. In the new number, she moved the digit 6 one place to the left. Which is the value of 6 in Gina's new number?

Answers

moving the number 6 one place to the left would put it where the 3 is, which is the thousands place

Amy Jo found that the perimeter of a square was 53.2 square inches. What is the side length of the square?

Answers

perimeter of a square is 4 times side length (4s)

to find the length of a side divide the perimeter by 4

53.2 / 4 = 13.3

so each side is 13.3 inches

The wall in the family room is exactly 12 feet long. Your couch is 10 feet and 6 inches long. Once the couch is placed, how much room is left for your end table?
inches

Answers

18 inches, 10 feet times 12 inches is 120 + 6 inches is 126 inches - 144 inches which is 12 inches times 12 inches, 144 - 126 inches is 18 inches.

well you still got the other wall homie g, but not including that you got like a foot and 6 inches

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