Q8) [6A, 2C] A cylindrical can is to have a volume of 2000 cm?
Determine the height and radius that will minimize the surface area. [Round approximate answers to 2 decimal places.] V = π r^2 h
SA = 2 π r^2 + 2 π r h

Since w is not connected to u or v by a path, it must be connected to some other vertex in the graph. Let's call this vertex x. Since x is connected to w and not connected to u or v, the path from u to v must pass through x and w. this creates a cycle in the graph, which contradicts our assumption that the graph is circuit-free.



The graph is circuit-free, there is no cycle that includes both u and v. Therefore, the only way to reach vertex v from vertex u is to go through other vertices in the graph. Let's assume that the shortest path between u and v has length k.
Since the graph is simple and has n vertices, the maximum degree of any vertex in the graph is n-1. This means that there are at most n-1 vertices adjacent to vertex u.

Therefore, we have shown that if a graph is circuit-free, simple, and has n vertices and at least n-1 edges, then it must be connected.

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Explanation:

There are 6 blocks across the width, 3 blocks along the height, and 2 blocks along the depth.

The volume is 6*3*2 = 18*2 = 36 cubic inches. In other words, there are 36 small blocks that make up this bigger 3D solid.

Answer:

a = -1 and 6

Step-by-step explanation:

\( \frac{a(a - 5)}{6} = 1\)

\(a(a - 5) = 6\)

\( {a}^{2} - 5a = 6\)

\( {a}^{2} - 5a - 6 = 0\)

\((a + 1)( a- 6)\)

a = -1 and a = 6

The worth of the investment after 4 years is approximately $13,953.95.

The formula accrued amount in a compounded interest is expressed as;

A = P( 1 + r/n )^( n × t )

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given that the data in the question;

First, convert R as a percent to r as a decimal.

r = R/100

r = 13.6/100

r = 0.136

Now, plug the given values into the above formula and solve for A.

A = P( 1 + r/n )^( n × t )

A = $8,100( 1 + 0.136/365 )^( 365 × 4 )

A = $8,100( 1 + 0.136/365 )^( 1460 )

A = $13,953.95.

Therefore, the accrued amount is $13,953.95.

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The dimensions of the column and row spaces of A are:

dim Col A = 3

dim Row A = 3

The nullity of a matrix A is the dimension of the null space of A. By the rank-nullity theorem, the rank of A plus the nullity of A equals the number of columns of A. Since A is a 4 x 6 matrix, it has 6 columns. Therefore, the rank of A is 6 - 3 = 3.

The dimension of the column space of A is equal to the rank of A, which is 3. This is because the column space is spanned by the columns of A, and the rank of A is the maximum number of linearly independent columns.

The dimension of the row space of A is also 3. This is because the row space is the orthogonal complement of the null space, and the null space has dimension 3. Therefore, the row space has dimension 6 - 3 = 3.

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Answer:

greater than

Step-by-step explanation:

Answer:

3X +ky=8 eqn 1

X-2ky=5 eqn 2

but we want to eliminate ky to get our X.

So let's multiply eqn 1 by 2.

We will have 6x +2ky=16 now eqn 3

now we add eqn 1 and 2

We will have 7x=21

divide by 7

x=3

Answer:

We need 45 cups on onion

Step-by-step explanation:

green pepper : onion: tomato: total

1                          5              7        13

We have 117 total so divide by 13

117/13 = 9

Multiply each number by 9

green pepper : onion: tomato: total

1*9                        5*9        7*9        13*9

9                            45         63           117

We need 45 cups on onion

The volume of the solid obtained by rotating the region bounded by the curves y = x², x = 5, and y = 0 about the x-axis is 125π cubic units.

The volume of the solid obtained by rotating the region bounded by the curves y = x², x = 5, and y = 0 about the x-axis is given by the formula for the volume of a solid of revolution:

        V = (π/3) * ∫[0,5] (R² - r²) dx

        V = (π/3) * ∫[0,5] (x²) dx

           = (π/3) * [x³/3]⁵_0

           = (π/3) * (125/3 - 0)

           = (π/3) * 41.67

           = 125π cubic units.

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- You can notice that from week 8 you have that the number of infected people is lower than 6 thousands. Then, from week 9 onwards you can travel. If the epidemic began on November, 9 weeks later, you are on January. Hence, in the following months, is it possible to travel:

- January

- February

- March

- You can notice that the maximum number of people infected during the epidemic was greater than 8 thousands.

- You can notice that from week 4 until 16, the total number of infected people were decreasing.

-

Answer:

Answer:

The anwser is 2

Step-by-step explanation:

1 for each person

Answer:

The answers are B, D, and E.

Step-by-step explanation:

After I got it wrong the first two times on edge, It showed me the answer.

Have a good morning/afternoon/evening!

\(dr/dt\)= speed of the wave = 100 sec/ft,We are to find how fast the volume within the spherical compression wave is increasing in t = 4 seconds. The formula for the volume of a sphere is given by:
\(V = (4/3)πr³\)
r = speed of the wave × time taken We are given that the speed of the wave is 100 sec/ft and the time taken is 4 seconds.
So,r = 100 × 4 = 400ft

The volume of the sphere with radius 400ft is given by:
\(V = (4/3)π(400)³= (4/3) × π × 256000000≈ 1073741824.926 cubic feet\)

Now, we need to find the rate of change of volume with respect to time.

For this, we differentiate the volume formula with respect to time.
We can use the chain rule here:dV/dt = dV/dr × dr/dt

The derivative of V with respect to r is:
dV/dr = 4πr²Now, we need to find dr/dt.

We know that\(r = 400ft and t = 4 seconds.\)
Therefore,\(dV/dt = dV/dr × dr/dt= 4πr² × 100= 400πr²= 400π(400)²= 64,000,000π\)
The value of dV/dt is approximately equal to 200960811.7 cubic feet per second.

Accurate to four decimals, the volume within the spherical compression wave is increasing at a rate of 200960811.7 cubic feet per second.

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Answer:

The answer would be 21.25

so it would just stay the same because the number

2 is in the tens place

1 is in the ones place

.

2 is in the tenths place

5 is in the hundreths place

Answer:

A = bh + L(s1 + s2 + s3)

Step-by-step explanation:

The formula for finding surface area of triangular prism is A = bh + L(s1 + s2 + s3).

The next time all three lights will flash at the same time will be in 210 seconds, or 3 minutes and 30 seconds.

To find the time at which all three lights will flash at the same time, we need to find the LCM (Least Common Multiple) of the given times.

Prime factorizing each time, we get:

6 = 2 x 3

15 = 3 x 5

21 = 3 x 7

To find the LCM, we take the highest power of each prime factor that appears in any of the numbers:

2 x 3 x 5 x 7 = 210

Therefore, the next time all three lights will flash at the same time will be in 210 seconds, or 3 minutes and 30 seconds.

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Answer:

first graph the y-intercept start at 0 and go up 2 plot that. Then, go up 7 from 2 and to the right 1

Step-by-step explanation:

The value of g(x) where g(x) is the translation 4 units up of \(f(x) = x^2 is (x + 2)^2.\)

To find g(x), the translation 4 units up of \(f(x) = x^2\), we need to add 4 to the function f(x).

g(x) = f(x) + 4

\(g(x) = x^2 + 4\)

To write the answer in the form \(a(x - h)^2 + k\), where a, h, and k are integers, we need to complete the square for g(x).

\(g(x) = x^2 + 4\)

\(g(x) = 1(x^2) + 4\\g(x) = 1(x^2) + 2(2x) + (2^2) - (2^2) + 4\\g(x) = (x^2 + 2(2x) + 2^2) - 4 + 4\\g(x) = (x^2 + 2(2x) + 2^2) + 0\\g(x) = (x + 2)^2 + 0\\\)

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The value of the function g(x) when  is the translation 4 units up of f(x) = x^2 is g(x) = (x - 0)^2 + 4

The function g(x) is obtained by translating the function f(x) = x^2 four units up.

To achieve this translation, we add 4 to the original function f(x).

g(x) = f(x) + 4

= x^2 + 4

Now, let's write the expression x^2 + 4 in the form a(x - h)^2 + k.

To do this, we complete the square:

g(x) = x^2 + 4

= (x^2 + 0x) + 4

= (x^2 + 0x + 0^2) + 4 - 0^2

= (x^2 + 0x + 0^2) + 4

Now, we can rewrite it as a perfect square:

g(x) = (x^2 + 0x + 0^2) + 4

= (x + 0)^2 + 4

Simplifying further, we have:

g(x) = (x - 0)^2 + 4

= (x - 0)^2 + 4

Therefore, g(x) = (x - 0)^2 + 4 is the desired form, where a = 1, h = 0, and k = 4.

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Answer:

your answer is correct

but in the third line 4.5×0 is wrong

it's 4.5×1

The amount A earned at the end of a given period t for an interest compounded annually is expressed as

Account 1:

Amount deposited = 10000. thus, P = 10000

r = 4% = 0.04

Since the interest is compounded annually, n= 1

t = 3.

Thus, the amount in account 1 after 3 years is evaluated as

The amount earned at the end of 3 years in account 1 is $ 11248.64

Account 2:

P =10000

r = 3% = 0.03

n =1

t = 3

Thus, the amount in account 2 after 3 years is evaluated as

The amount earned at the end of 3 years in account 2 is $ 10927.27

How much more will be in account 1 than account 2:

Hence, there will be $ 321.37 in account 1 than account 2.

To find the probability for different scenarios, we can use the binomial probability formula since we are dealing with a situation where there are only two possible outcomes (majoring in STEM or not) and the selection of students is independent.

The binomial probability formula is given by:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

where n is the number of trials, k is the number of successful outcomes, p is the probability of success, and (n choose k) represents the binomial coefficient.

In this case, n = 32 (the number of college students selected) and p = 0.25 (the probability of majoring in STEM).

a. Exactly 9 of them major in STEM:

P(X = 9) = (32 choose 9) * (0.25)^9 * (0.75)^(32 - 9)

b. At most 7 of them major in STEM:

P(X <= 7) = P(X = 0) + P(X = 1) + ... + P(X = 7)

= Σ [(32 choose k) * (0.25)^k * (0.75)^(32 - k)] for k = 0 to 7

c. At least 7 of them major in STEM:

P(X >= 7) = 1 - P(X < 7)

= 1 - [P(X = 0) + P(X = 1) + ... + P(X = 6)]

= 1 - Σ [(32 choose k) * (0.25)^k * (0.75)^(32 - k)] for k = 0 to 6

d. Between 4 and 8 (including 4 and 8) of them major in STEM:

P(4 <= X <= 8) = P(X = 4) + P(X = 5) + ... + P(X = 8)

= Σ [(32 choose k) * (0.25)^k * (0.75)^(32 - k)] for k = 4 to 8

You can calculate the values for each scenario using the given formulas.

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Answer:

∅=30°

Step-by-step explanation:

\(sin\)∅\(=\frac{1}{\sqrt{3} }sin60^{0}\)

sin∅=\(\frac{\frac{\sqrt{3} }{2} }{\sqrt{3} } =\frac{\sqrt{3} }{2\sqrt{3} }=\frac{1}{2}\)

∅=\(sin^{-1}(\frac{1}{2})= 30^{0}\)

I hope this help you

Answer:

blue i think good luck

In a right triangle, one of the interior angles measures exactly 90 degrees, which is called the right angle.

This right angle is formed by the intersection of the two non-hypotenuse sides of the triangle, and it is located at the vertex where these sides meet. The "right angle vertex" or "vertex of the right angle" are other names for this vertex. The right angle vertex is an important feature of right triangles, and it is used in many geometric and trigonometric calculations. For example, the Pythagorean Theorem, which relates the lengths of the sides of a right triangle, depends on the location of the right angle vertex.

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The number of students in each bus is 21

Given data

Total number of students on the trip = 172

25 students traveled in cars

7 buses were filled

let the number students on each bus be x

number of students on the bus is gotten by

172 - 25 = 147

so 147 students travelled by bus and the total number of buses is 7.

to get the number of students in each bus we solve as follows

147 / 7 = 21

Hence each bus contains 21 students.

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Answer:

The answer is 231.56.

Step-by-step explanation:

To solve this problem, we can use the following steps:

Align the numbers by their decimal points and write them one below the other.

Add zeros to the right of the decimal point if needed to make the numbers have the same number of digits after the decimal point.

Subtract each pair of digits starting from the rightmost column and write the result below the line. If the top digit is smaller than the bottom digit, borrow 1 from the next column to the left and add 10 to the top digit.

Write a decimal point in the answer directly below the decimal points in the numbers.

Simplify the answer if possible by removing any trailing zeros after the decimal point.

Using these steps, we can solve the problem as follows:

 543.73

- 312.17

-------

 231.56

The answer is C. 1/10 of a centimeter.

Answer:

a) m∠1 = 15°

b) m∠2 = 90°

c) m∠3 = 66°

d) m∠4 = 75°

e) m∠5 = 24°

f) m∠ITE = 132°

Hope this helps!

Answer:

Population(year x) = 120*(1.09)^x

Step-by-step explanation:

Let x be the number of years from the time the population is 120 (year 0).

Population(year x) = 120*(1.09)^x

The 1.09 represents the growth for 1 year added to the initial population.  E.g., year 1 would have a population of 120*(1.09)^1 or 140.8 (141).  Year 2 would be 120*(1.09)^2 or 142.5 (143).  And so on.

Each new year bilds on the prior year's ending population.  In longhamd, this would be:

Year   Pop.

 0       120   120*(1.09)^0

 1         141   120*(1.09)

 2                120*(1.09)(1.09) or 120*(1.09)^2

 3                120*(1.09)(1.09)(1.09) or 120*(1.09)^3

and so on.