a spherical snowball is melting in such a manner that its radius is changing at a constant rate, decreasing from 27 cm to 17 cm in 30 minutes. at what rate, in cm3 per minute, is the volume of the snowball changing at the instant the radius is 1 cm?

Answer:

The answer would be 87^2

Step-by-step explanation:

The solution is, Area of a sector is 138.23 cm².

Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

here, we have,

The formula for the area of a sector is given as:

θ/360 × πr²

θ = 110°

Radius = r = 12 cm

Hence

Area of a sector = 110/360 × π × 12²

= 138.23007676 cm²

Approximately, Area of a sector = 138.23 cm²

Hence, The solution is, Area of a sector is 138.23 cm².

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9514 1404 393

Answer:

  put the value into the equation and do the arithmetic

Step-by-step explanation:

As with any checking, you put the value where the variable is and do the arithmetic.

  7(2x +5) = 11x -9 -x

For x = -11

  7(2(-11) +5) = 11(-11) -9 -(-11)

  7(-22 +5) = -121 -9 +11

  7(-17) = -119

  -119 = -119

The value x = -11 makes the equation true.

Answer:

Hey there!

X+Y=0.

For example, two numbers that are equally far from the 0 on a number line are -2 and 2.

-2+2=0

Hope this helps :)

Answer:

x + y = 0

Step-by-step explanation:

Since the two values are the same distance from zero on the number line (i.e., they are equivalent in distance) and one is in the negative direction, and the other is in the positive direction, then the sum of both will be zero.

Since they are the same distance, just opposite in direction, it requires the same amount of "hops" for both values to reach zero, hence they will cancel each other out when added together.

Consider, -1 and 1.  Both are the same distance from 0; however, if you add them together (-1 + 1) you'll get the sum to be 0.

Cheers.

Answer:

Step-by-step explanation:

=5^-3 X 2^-1

= 1/5³ X 1/2

=1/(5³X 2)

=1/250 (Answer)

OR

=0•004 (Answer)

Answer:

1/250 or 0.004.

Step-by-step explanation:

5^-3 x 2^-1

= 1/5^3 * 1/2

= 1/125 * 1/2

= 1/250.

Answer:

4x + 2x would be 6x

Step-by-step explanation:

Yes, there is sufficient evidence at the 0.05 level to support the company's claim that less than 34% of computer chips fail in the first 1000 hours of their use.

To determine if there is sufficient evidence to support the claim, we can perform a hypothesis test. Let's set up the null and alternative hypotheses:

Null hypothesis (H0): The proportion of chips that fail in the first 1000 hours is equal to or greater than 34%.

Alternative hypothesis (Ha): The proportion of chips that fail in the first 1000 hours is less than 34%.

We can use the sample data to calculate the test statistic and compare it to the critical value at the 0.05 significance level.

Given that the sample of 1200 computer chips revealed that 31% of the chips failed, we can calculate the test statistic using the formula for the z-score:

z = (p - P) / √(P(1-P) / n)

Where p is the sample proportion, P is the hypothesized proportion, and n is the sample size.

In this case, p = 0.31, P = 0.34, and n = 1200. Plugging in these values, we can calculate the test statistic.

After calculating the test statistic, we compare it to the critical value from the standard normal distribution. At the 0.05 significance level, the critical value for a one-tailed test is approximately -1.645.

If the test statistic falls below the critical value, we reject the null hypothesis and conclude that there is sufficient evidence to support the company's claim. Otherwise, if the test statistic is greater than the critical value, we fail to reject the null hypothesis.

Performing the calculations, we find that the test statistic is approximately -5.76, which is much lower than the critical value of -1.645. Therefore, we reject the null hypothesis and conclude that there is sufficient evidence to support the company's claim that less than 34% of computer chips fail in the first 1000 hours of their use.

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The formula for the surface area of the box, in terms of the length of one side of the square base (s), is A = s^2 + 4s^2 = 5s^2.

The derivative of the surface area function with respect to s, denoted as dA/ds, gives us the rate of change of the surface area with respect to the length of one side of the base.

1. The surface area of the box consists of the area of the square base and the four equal sides. The area of the square base is s^2, and each side has a length of s. Therefore, the total surface area is given by A = s^2 + 4s^2 = 5s^2.

2. To find the derivative of the surface area function, we differentiate 5s^2 with respect to s using the power rule of differentiation. The power rule states that if we have a function f(x) = cx^n, then the derivative is f'(x) = cnx^(n-1).

  Applying the power rule, we have dA/ds = d(5s^2)/ds = 10s.

3. The derivative, dA/ds = 10s, represents the rate of change of the surface area with respect to the length of one side of the square base. This means that for every unit increase in s, the surface area increases by 10s units.

  The derivative does not provide information about minimizing the amount of material used. To find the dimensions of the box that minimize the amount of material used, we need to set up an optimization problem and solve for the critical points. This involves setting the derivative equal to zero and finding the values of s that satisfy this equation. However, since the problem statement does not provide a specific volume constraint or objective function, we cannot proceed with the optimization process.

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Answer:

29/150

Step-by-step explanation:

Probability is the number of times a certain value is obtained out of the total number of attempts.

If Carol got 6 29 times out of 150, then the probability of getting a 6 = 29/150.

This can be written as a percent or decimal too = 0.193 = 19.3%

Hope this helps.

Good Luck

To visualize it, imagine a rectangular box where the length is 4 ft., the width is 2 ft. and the height is 3 ft.

Each of the six faces of the prism would be a rectangle, with the two bases being identical and parallel to each other.

A right rectangular prism with a height of 3 ft and bases that are 2 ft by 4 ft would have the following characteristics:

The prism would have a rectangular shape as its bases, with one base measuring 2 ft by 4 ft.

The height of the prism would be perpendicular to the bases and would measure 3 ft.

All the faces of the prism would be rectangular, with the same dimensions as the bases.

The top and bottom faces of the prism would be congruent and have dimensions of 2 ft by 4 ft.

The front and back faces of the prism would also be congruent and have dimensions of 2 ft by 3 ft.

The left and right faces of the prism would be congruent and have dimensions of 4 ft by 3 ft.

To get a better visualization, you can try drawing a rectangular shape (base) measuring 2 ft by 4 ft.

Then, draw another rectangle of the same size directly above or below it and connect the corresponding vertices with vertical lines to represent the height of 3 ft.

This will give you an idea of what the right rectangular prism would look like.

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The simplified form of the rational expression is given as follows:

[(x - 5)/(x² - 3x - 10)] x [(x + 2)/(x² + x - 12)] = 1/[(x + 4)(x - 3)]

The rational expression for this problem is defined as follows:

[(x - 5)/(x² - 3x - 10)] x [(x + 2)/(x² + x - 12)].

To simplify the rational expression, first we must factor the quadratic equations at the denominator of each of the fractions, hence:

The simplification of the first quadratic function, x² - 3x - 10 = (x - 5)(x + 2), means that the numerators of each of the fractions can be simplified.

As the numerators of each of the fractions are simplified along with x² - 3x - 10, the remaining part is x² + x - 12, hence the simplified expression is given as follows:

[(x - 5)/(x² - 3x - 10)] x [(x + 2)/(x² + x - 12)] = 1/[(x + 4)(x - 3)]

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Euclid made significant contributions to our understanding and practice of geometry by compiling and organizing the principles of the subject into a systematic and logical framework known as Euclidean geometry. His work, "Elements," became the cornerstone of mathematical education for over two thousand years, shaping the way we approach geometry.

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Answer:

This is done by stating descriptions of these terms.

Step-by-step explanation:

Undefinable terms are terms with no formal definitions. Formal definitions are obtained when specific words are used to define a term. In mathematics, specifically, Geometry words like line, point, and plane have no definite definition, So descriptions are used to identify them.

For example, in describing a point, we note that a point has no dimensions, it is usually denoted with a capital letter, and it indicates a position. Also in a coordinate plane, it is denoted with descriptions such as  (u,v). Corresponding descriptions are given of other undefinable terms.

Triangles ABC and triangle PQR are congruent triangles based on angle-side-angle congruency theorem.

Two triangles are said to be congruent if they have the same shape and their corresponding sides are congruent to each other. Also, their corresponding angles are congruent to each other.

Triangles ABC and triangle PQR are congruent triangles based on angle-side-angle congruency theorem.

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Step-by-step explanation:

p/x + z = y

p/x = y-z/1

p = x (y-z)

The equation of the perpendicular bisector of the segment with the endpoints located at D(-2  ,-4) and E(2 , 1) is y = -4/5x - 3/2.

A perpendicular bisector of a segment is a line that divides the segment into two equal parts forming right angles at the point of intersection.

To get the perpendicular bisector of a segment, get the point of intersection of the two lines which is the midpoint of the segment.

midpoint (x , y) = [(x1 + x2)/2 , (y1 + y2)/2]

midpoint (x , y) = [(-2 + 2)/2 , (-4 + 1)/2]

midpoint (x , y) = (0 , -3/2)

Get the slope of the perpendicular bisector of a segment by taking the negative reciprocal of the slope of the segment.

slope of segment = (y2 - y1)/(x2 - x1)

slope of segment = (1 - -4)/(2 - -2)

slope of segment = 5/4

slope of the perpendicular bisector = -4/5

Solving for the y-intercept, b, plug in the point (0 , -3/2) and the slope -4/5 to the slope-intercept form of the equation, y = mx + b.

y = mx + b

-3/2 = -4/5(0) + b

b = -3/2

Setting up the equation in slope-intercept form, where m = -4/5 and b = -3/2.

y = mx + b

y = -4/5x - 3/2

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Answer: 3. Natural, whole, integer, rational, real

Answer:

Answer 3: Natural, whole, integer, rational, real

Step-by-step explanation:

Answer- 9 shelves

In order to find out how many shelves are need we must divided 175 into 20. 175 divided by 20 is 8.75. But, because you cannot have have .75 of a shelf, you have to round this to a whole. This means that 9 shelves will be the least needed number of shelves need to store 175 books. To check this answer 20 books X 8 shelves is 160 books, which means eight shelves can only store 160 books, we will need and additional shelf to store the last 15 books.

HOPE THIS HELPS & GOOD LUCK!

Total stockholders’ equity 7,800,000

Statement of stockholders’ equity for CC for the year ended December 31, 2012:Particulars Amount ($)
Common Stock 100,000

Additional Paid-in Capital 4,100,000
Retained Earnings (Opening Balance) 3,000,000
Add: Net Income for the year ended December 31, 2012 800,000
Total retained earnings 3,800,000

Less: Cash Dividend Declared on July 1 and paid on July 31 (200,000)
Retained earnings (Closing balance) 3,600,000
Total stockholders’ equity 7,800,000

Explanation:The given information is as follows:Common Stock on January 1, 2012 = $100,000Additional Paid-in Capital on January 1, 2012 = $4,100,000

Retained Earnings on January 1, 2012 = $3,000,000Net Income for the year ended December 31, 2012 = $800,000Cash Dividend Declared on July 1 and paid on July 31 = $200,000

To prepare the statement of stockholders’ equity for the year ended December 31, 2012, we will begin by preparing the opening balances of each of the equity accounts. We will then add the net income to the retained earnings account.

The closing balance for retained earnings is then computed by subtracting the cash dividend declared and paid from the total retained earnings. Finally, the total stockholders' equity is calculated by adding the balances of all the equity accounts.

Calculations:Opening balance of common stock = $100,000

Opening balance of additional paid-in capital = $4,100,000

Opening balance of retained earnings = $3,000,000

Net Income for the year ended December 31, 2012 = $800,000

Retained earnings (Opening Balance) = $3,000,000

Add: Net Income for the year ended December 31, 2012 = $800,000

Total retained earnings = $3,800,000Less: Cash Dividend Declared on July 1 and paid on July 31 = $200,000Retained earnings (Closing balance) = $3,600,000

Total stockholders’ equity = Common Stock + Additional Paid-in Capital + Retained Earnings (Closing balance) = $100,000 + $4,100,000 + $3,600,000 = $7,800,000

Therefore, the statement of stockholders’ equity for CC for the year ended December 31, 2012, is as follows:Particulars Amount ($)
Common Stock 100,000
Additional Paid-in Capital 4,100,000

Retained Earnings (Opening Balance) 3,000,000
Add: Net Income for the year ended December 31, 2012 800,000
Total retained earnings 3,800,000

Less: Cash Dividend Declared on July 1 and paid on July 31 (200,000)
Retained earnings (Closing balance) 3,600,000
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Answer:

Both of them are functions...

Step-by-step explanation:

Both of them are functions because neither A nor B has a repeated X value in their sets.

Answer:

C

Step-by-step explanation:

They both have different input and output

let's recall that d = rt, namely distance = rate * time.

d = distance from one pier to another

c = speed of the current

b = speed of the boat

now, let's notice something, on the way over the boat travelled "d" kilometers in 4 hrs, and back the same "d" kilometers in 5 hours.

when going with the current, the boat is not really going at "b" km/s, is really going faster, at "b + c" km/s, because the current is adding to it.

now, when going against the current, the boat is not really going "b" fast, is really going slower, at "b - c", because the current is subtracting from it.

from the above, we can conclude that the 4hrs trip was with the current, since it took less time, and the 5hrs trip was against the current, and we also know that the boat does 70 km with the current in 3.5 hrs, ok hmmm let's put all that in a table.

\(\begin{array}{lcccl} &\stackrel{km}{distance}&\stackrel{km/h}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ \textit{on the way over}&d&b+c&4\\ \textit{on the way back}&d&b-c&5\\\cline{1-4} \textit{we also know}&70&b+c&3.5 \end{array}~\hfill \begin{cases} d=(b+c)4\\\\ d = (b-c)5 \end{cases} \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{(b+c)4~~ = ~~(b-c)5}\implies 4b+4c=5b-5c \\\\\\ 4c=b-5c\implies \boxed{9c=b} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{we know that}}{70~~ = ~~(b+c)3.5}\implies 70=(b+c)\cfrac{7}{2}\implies \stackrel{\textit{substituting "b"}}{70=(9c+c)\cfrac{7}{2}} \\\\\\ 70=10c\cdot \cfrac{7}{2}\implies 70=\cfrac{70c}{2}\implies 140=70c\implies \cfrac{140}{70}=c\implies \blacktriangleright 2=c \blacktriangleleft \\\\\\ \stackrel{\textit{the speed of the boat in still water is then}}{9c=b\implies 9(2)=b}\implies \blacktriangleright 18=b\blacktriangleleft\)

The correct exponents for the gcd are: p^n for n = 1, q^n for n = 0, and r^n for n = 0 and the correct exponents for the lcm are: p^n for n = 2, q^n for n = 1, and r^n for n = 1.

The greatest common divisor (gcd) of two numbers is the largest number that divides both of them. The least common multiple (lcm) of two numbers is the smallest number that is a multiple of both of them.

To find the gcd and lcm of a and b, we need to look at the prime factorization of each number. For a, we have a = p^2. For b, we have b = p. Q. R.

For the gcd, we take the lowest exponent for each prime factor. So for p, we have p^1, for q, we have q^0, and for r, we have r^0. This gives us gcd(a,b) = p^1. Q^0. R^0 = p.

For the lcm, we take the highest exponent for each prime factor. So for p, we have p^2, for q, we have q^1, and for r, we have r^1. This gives us lcm(a,b) = p^2. Q^1. R^1 = p^2. Q. R.

So the correct exponents for the gcd are:

p^n for n = 1

q^n for n = 0

r^n for n = 0

And the correct exponents for the lcm are:

p^n for n = 2

q^n for n = 1

r^n for n = 1

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Answer: to get 1/2 of a number, simply divide it by 2

Step-by-step explanation: the denominator, or the second digit after the numerator, is the one you use to divide a number. for example 1/3 of 33 = 11, as you divide 33 by 3, or 1/2 of 500 = 250.

Answer:

tin of beans = .70 pound

Step-by-step explanation:

 10 =  1.90  + 2 * 3.10  +  .50   + 2b

b = .70

Answer:

Step-by-step explanation:

Plot 213, −56, and −312 on the number line.

Answer:22:2x10x10x10x10x10x10x10x10x10x10... 23:3.4x10 divided by 2.... 24:1.5x10 divided by 9...... 25:5.9x10x10x10x10x10x10x10x10x10x10.... 26: 4.8 x 10 divided by 3..... 27: 6.25x10x10x10x10x10.

Step-by-step explanation:I divide because on some of them it's a negative power so instead of multiplying I'll divide. Hope this helps

Answer:

27f + 59

Step-by-step explanation:

Answer:

12.57 or 12.56

Step-by-step explanation:

Surface area for a sphere is \(4\pi r^{2}\)

so assuming pi is 3.14

4*(3.14)*1^2

so..

4*(3.14)*1

4*3.14=12.56

12.56*1=12.56 rounds up to 12.57

Im sorry if this does't help much :I

Answer:

I think it would be Maxine's, since they did more tests.

To answer this question, we can proceed as follows:

We have that the complete way to obtain this division is that the quotient is equal to 1.38.

However, in a division in which we have the remainder, we can express this division as:

D = d * C + R

Where

D is the dividend (69)

d is the divisor (50)

C is the quotient.

R is the remainder

So having the remainder, and not having decimals part in the division, we can say that this division is equal to:

69 = 50 * 1 + 19.

We can express this as follows:

69 is the Dividend, 50 is the divisor, 1 is the quotient, and 19 is the remainder.

Therefore, the division 69 / 50 = 1 + 19. We can divide the number 69 by 50 and we have that we can divide it in 1, but we have 19 as the remainder, then we have:

69 = 50 * 1 + 19