A species of fish was added to a lake. The population size P(t) of this species can be modeled by the following exponential function:P(t)=1500/(1+7e^-0.4t)where t is the number of years from the time the species was added to the lake.Find the initial population size of the species and the population size after 9 years. Round your answers to the nearest whole number as necessary.

Answer:

35

Step-by-step explanation:

5 and 7 are both prime numbers, so the least common multiple of 5 and 7 is their product, 5 * 7 = 35

The least common denominator of the fractions 3/5 and 2/7 is found by determining the least common multiple of the denominators 5 and 7. Since they are prime numbers, their LCM is their product, which is 35.

To find the

least common denominator

(LCD) of the given

fractions

, 3/5 and 2/7, we must find the least common multiple (LCM) of the two

denominators

5 and 7. The LCM of any two numbers is the smallest number that both numbers can divide evenly into. Since 5 and 7 are prime numbers, the LCM is simply their product, which is 35. Therefore, the least common denominator of 3/5 and 2/7 is 35.

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Answer:

b

Step-by-step explanation:

We must determine the the x value at 90% confidence interval. We find this from a table relating confidence intervals and x values. For 90%, z is 1.645.

WE must determine the mean of 19 and 23:

[tex]=(19+23)/2=21[/tex]

We must determine the standard deviation. We let n be the number of population which is 2. We need to take the numbers 19 and 23 and subtract  each by the mean and square the answer:

[tex](19-2)^2=289[/tex]

[tex](23-2)^2=441[/tex]

We then determine the mean of these two values as:

[tex](289+441)/2=365[/tex]

Now we take the square root of 365:

[tex]\sqrt{365}=19.1[/tex]

The standard deviation is 19.1

The answer is b

Answer:

Step-by-step explanation:

A function maps an x-value to a single y-value. The graph of the parabola on the left does that.

The table on the right maps -1 to both 10 and 20, so does not meet the definition of a function.

Answer:

11 pieces.

Step-by-step explanation:

We must divide 8 1/4 by 3/4

8 1/4 = 33/4

Dividing:

33/4 / 3/4

= 33/4 * 4/3

= 33/3

= 11.

Answer:

11 pieces.

Step-by-step explanation:

In order to make this happen, you need to divide the total length of the wood by the length that he needs, so it would be 8 1/4 feet by 3/4 of foot:

[tex]\frac{8\frac{1}{4} }{\frac{3}{4} } =\frac{\frac{33}{4} }{\frac{3}{4} }\\\frac{4(33)}{(3)(4)} \\\frac{132}{12}=11[/tex]

So now we know that he will get 11 piecesof 3/4 of foot out of the 8 1/4 feet long piece of wood.

The probability of nobody winning in four rounds of a "nonconformity" game where players choose rock, paper, or scissors is [tex]\((\frac{1}{3})^4 = \frac{1}{81}\).[/tex]

To find the probability that nobody wins any of the 4 games, we need to consider under what conditions there is no winner in this game. There are two cases for no winner :

1. All three players choose the same symbol.

2. All three players choose different symbols.

Let's consider each case separately and calculate the probabilities.

Case 1: All three choose the same symbol

Each player has 3 choices (rock, paper, scissors).

For all three to choose the same symbol, the first player can choose any symbol, but the second and third must match.

Thus, there are 3 possible outcomes (RRR, PPP, SSS) out of a total of [tex]\(3 \times 3 \times 3 = 27\)[/tex] possible outcomes for each game.

Thus, the probability of this case is: [tex]\[\frac{3}{27} = \frac{1}{9}.\][/tex]

Case 2: All three choose different symbols

There are three possible different symbols (rock, paper, scissors). The possible outcomes for this case are RPS, RSP, PRS, PSR, SRP, SPR, giving a total of 6 distinct outcomes. Hence, the probability of this case is:

[tex]\[\frac{6}{27} = \frac{2}{9}.\][/tex]

Total Probability of No Winner

Combining the probabilities from Case 1 and Case 2, we get the total probability that there is no winner in a single game:

[tex]\[\frac{1}{9} + \frac{2}{9} = \frac{3}{9} = \frac{1}{3}.[/tex]

Since there are 4 games and each game is independent, the probability of no winner in any of the 4 games is: [tex]\[\left( \frac{1}{3} \right)^4 = \frac{1}{81}.\][/tex]

Thus, the probability that nobody wins any of the 4 games is[tex]\(\boxed{\frac{1}{81}}\).[/tex]

The complete question is : Mario, Yoshi, and Toadette play a game of "nonconformity": they each choose rock, paper, or scissors. If two of the three people choose the same symbol, and the third person chooses a different symbol, then the one who chose the different symbol wins. Otherwise, no one wins. If they play 4 rounds of this game, all choosing their symbols at random, what's the probability that nobody wins any of the 4 games? Express your answer as a common fraction.

Answer:

Compound interest the interest changes annually and with simple interest the interest is the same annually

The main difference between simple interest and compound interest is that simple interest is calculated only on the initial investment, whereas compound interest is calculated on the initial principal and also on the accumulated interest of previous periods.

The primary difference between simple interest and compound interest lies in the way they are calculated. Simple interest is calculated only on the initial amount (principal) that you invested. For example, if you invest $1000 at a simple interest of 5% per annum, your interest for the first year will be $50, and it will remain the same for all the years the money is deposited.

Compound interest, on the other hand, is calculated on the initial principal and also on the accumulated interest of previous periods of a deposit. So, in a scenario where you invest $1000 at a compound interest of 5% per annum, your interest for the first year will be $50, but for the second year, the interest will be calculated on $1050 (Principal + Interest of first year), making the interest for the second year $52.5 rather than $50.

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Answer:

B 10% off sale, with a total price to pay of 756

Step-by-step explanation:

Retail price (Rp) = $800

Taxes (T) = 5%

Total price A (TA) = Rp - 75 + (Rp - 75) 5%

TA = 800 - 75 + (800-75) 5%

TA = 725 + 725 5%

725 5% = 725*5/100 = 36.25

TA= 725+36.25 = $761.25

Total price B (TB) = RP - RP 10% + (RP - RP 10%) 5%

TB = 800 - 800 10% + (800 - 800 10%) 5%

800 10% = 800*10/100 = 80

TB = 800 - 80 + (800 - 80) 5%

TB = 720 + 720 5%

720 5% = 720*5/100 = 36

TB = 720 + 36 = $756

store pays sales tax means Walden's family will not need pay for taxes

Total price C (TC) = RP - RP 5%

TC = 800 - 800 5%

800 5% = 800*5/100 = 40

TC = 800 - 40 = $760

Means that Walden's family will need pay just the retail price

TD = $800

The beast deal is from the store B

Answer:

the answer is b

Step-by-step explanation:

hoped this helped

Answer:

  54 mph

Step-by-step explanation:

Let s represent the slower speed. The product of speed and time is distance, which did not change between the two trips. So, we have ...

  1.8(s +6) = 2(s)

  10.8 = 0.2s . . . . eliminate parentheses, subtract 1.8s

  54 = s . . . . . . . . divide by 0.2

Fran's average speed on Sunday was 54 miles per hour.

____

Her trip was 108 miles long.

To solve the problem, you can use the equation for speed which is distance divided by time. By substituting variables and solving the equation, you'll find that the average speed on Sunday was 54 mph when traffic was heavier.

To solve this, we need to use the formula for speed which is distance divided by time. Since the distance to her mother's house and back is the same for both trips, let's denote the distance as 'd'. We don't know the numerical distance, but we don't need to.

For Saturday, the formula is speed=d/1.8

For Sunday, the average speed is  d/2.

According to the problem, the average speed on Sunday was 6 mph slower than on Saturday. Therefore, the speed on Saturday minus 6 equals the speed on Sunday. So we have the equation: d/1.8 - 6 = d/2

To solve this equation, you first clear the fractions by multiplying each term by the common multiple of 2 and 1.8 which is 3.6. This gives us: 2d - 21.6 = 1.8d

Next, subtract 1.8d from 2d to get 0.2d = 21.6, then divide both sides by 0.2, yielding: d=108

Substitute d = 108 into the equation for Sunday to find the average speed: 108/2 = 54 mph. This is the answer, Fran's speed on Sunday was 54 mph when the traffic was heavier.

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Answer:

The guy wire lenght is 500 ft.

Step-by-step explanation:

The Pythagorean Theorem says the sum of the squares two adyacent sides is equal to the square of the opposite side.

Applied in this example, we can rephrase it as:

The sum of the square of the pylon height with the square of the distance from the guy wire tip to the pylon is Equal to the  square of the Guy wire lenght.

So:

[tex]PylonHeight^{2}  + floordistance^{2} = GuyWireLength^{2} \\160.000 + 90.000 = GuyWireLength^{2} \\\\\sqrt{160.000 + 90.000} =GuyWireLength\\GuyWireLength= 500 ft[/tex]

Final answer:

The length of the guy wire needed for a suspension bridge is calculated using the Pythagorean Theorem. Given the square of the distance between the wire on the ground and the pylon is 90,000 feet, and the square of the pylon's height is 160,000 feet, the guy wire length is found to be 500 feet.

Explanation:

The length of the guy wire needed for a suspension bridge can be calculated using the Pythagorean Theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The given squares of the distance between the wire on the ground and the pylon on the ground is 90,000 feet (a2), and the square of the height of the pylon is 160,000 feet (b2). To find the length of the guy wire (c), we can add these two values and then take the square root:

a2 + b2 = c2
90,000 + 160,000 = c2
250,000 = c2
c = √250,000
c = 500 feet

Therefore, the length of the guy wire is 500 feet.

Answer:

  A.  {(-8,-14), (-7,-12), (-6,-10), (-5,-8)}

Step-by-step explanation:

A function has no repeated values of the independent variable. Only choice A meets that requirement.

___

B: (-9, 12) and (-9, 8) both have -9 as a first value; not a function.

C: (8, -2) and (8, -10) both have 8 as a first value; not a function.

D: (-2, 0) and (-2, 3) both have -2 as a first value; not a function.

Answer:

A.

{(-8,-14), (-7,-12), (-6,-10), (-5,-8)}

Step-by-step explanation:

In mathematics, a function [tex]f[/tex] is a relationship between a given set [tex]x[/tex] (domain) and another set of elements [tex]y=f(x)[/tex] (range) so that each element x in the domain corresponds to a single element [tex]f(x)[/tex] of the range. This can be expressed as:

[tex]f:x \rightarrow y\\\\a \rightarrow f(a)\\\\Where\hspace{3}a\hspace{3}is\hspace{3}an\hspace{3}arbitrary\hspace{3}constant[/tex]

So according to that, the only set that satisfies the definition of a function is:

A.

{(-8,-14), (-7,-12), (-6,-10), (-5,-8)}

This is because:

In B.

-9 is the first element in more than one ordered pair in this set.

In C.

8 is the first element in more than one ordered pair in this set.

In D.

-2 is the first element in more than one ordered pair in this set.

The volume of the solid generated by revolving the region bounded by ( y = [tex]\ln(x) \)[/tex], the x-axis, and the vertical line [tex]\( x = e^2 \)[/tex] about the x-axis is given by the integral

[tex]\[ V = \pi \int_{1}^{e^2} (\ln(x))^2 dx \][/tex]

Now, let's compute the volume step by step.

1. Set up the integral for the volume using the disk method, since we are rotating around the x-axis. The formula for the volume of a solid of revolution using the disk method is [tex]\( V = \pi \int_{a}^{b} [f(x)]^2 dx \)[/tex], where [tex]\( f(x) \)[/tex] is the function being rotated, and [tex]\( [a, b] \)[/tex] is the interval of rotation.

2. Since [tex]\( f(x) = \ln(x) \)[/tex] and we are rotating around the x-axis from [tex]\( x = 1 \)[/tex] to [tex]\( x = e^2 \)[/tex], our integral becomes

[tex]\[ V = \pi \int_{1}^{e^2} (\ln(x))^2 dx \][/tex]

3. Solve the integral. This particular integral requires integration by parts or a special integrating factor due to the natural logarithm squared. The integral of [tex]\( (\ln(x))^2 \)[/tex] is not straightforward, so we will use integration by parts.

Let's solve the integral now.

It appears there was a mistake in the code due to the missing definition of the exponential function `exp`. Let me correct that and solve the integral again.

The volume of the solid generated by revolving the region bounded by [tex]\( y = \ln(x) \)[/tex], the x-axis, and the vertical line [tex]\( x = e^2 \)[/tex] about the x-axis is approximately[tex]\( 40.14 \)[/tex]. This is the numerical approximation, but you asked for the exact form, so let's represent that as well.

The exact form of the volume, without numerical approximation, is:

[tex]\[ V = \pi \int_{1}^{e^2} (\ln(x))^2 dx \][/tex]

Now I will present the exact form of the integral result.

The exact form of the volume of the solid generated by revolving the region bounded by [tex]\( y = \ln(x) \),[/tex] the x-axis, and the vertical line [tex]\( x = e^2 \)[/tex]about the x-axis is:

[tex]\[ V = \pi \left( -2 + 2e^2 \right) \][/tex]

This is the exact expression for the volume in terms of [tex]\( \pi \) and \( e \),[/tex] the base of the natural logarithm.

Answer: a) Yes, there is enough fance

b) 58.1° and 47.9°

c) The city will not approve, because 1/3 of the area is just 2220.5ft²

Step-by-step explanation:

a) using law of cosines: x is the side we do not know.

x² = 126² + 110² - 2.126.110.cos74°

x² = 20335.3

x = 142.6 ft

So 150 > 142.6, there is enough fance

b) using law of sine:

sin 74/ 142.6 = sinα/126 = sinβ/110

sin 74/ 142.6 = sinα/126

0.006741 = sinα/126

sinα = 0.849

α = sin⁻¹(0.849)

α = 58.1°

sin 74/ 142.6 = sinβ/110

sin 74/ 142.6 = sinβ/110

0.006741 = sinβ/110

sinβ = 0.741

β = sin⁻¹(0.741)

β = 47.9°

Checking: 74+58.1+47.9 = 180° ok

c) Using Heron A² = p(p-a)(p-b)(p-c)

p = a+b+c/2

p=126+110+142.6/2

p=189.3

A² = 189.3(189.3-126)(189.3-110)(189.3-142.6)

A = 6661.5 ft²

1/3 A = 2220.5

So 2300 >  2220.5. The area you want to build is bigger than the area available.

The city will not approve

Answer:

21.6

Step-by-step explanation:

9.2+0.5+6+5.9=21.6 Because it is looking for the TOTAL amount you add the numbers.

Answer: 21.6 inches

Step-by-step explanation:

Given : Last winter, Michigan had these snow fall totals (in inches) over a one month period: 9.2, 0.5, 6, and 5.9.

Then, By suing the addition operation.

The total amount of snow during the month will be (Sum of all the amount of snow fall ) :-

9.2+0.5+6+5.9 = 21.6 inches

Therefore, the  total amount of snow during the month= 21.6 inches

Answer:

  [tex]\sqrt[n]{x}=x^{\frac{1}{n}}[/tex]

Step-by-step explanation:

The index of a radical is the denominator of a fractional exponent, and vice versa. If you think about the rules of exponents, you know this must be so.

For example, consider the cube root:

[tex]\sqrt[3]{x}\cdot \sqrt[3]{x}\cdot \sqrt[3]{x}=(\sqrt[3]{x})^3=x\\\\(x^{\frac{1}{3}})^3=x^{\frac{3}{3}}=x^1=x[/tex]

That is ...

[tex]\sqrt[3]{x}=x^{\frac{1}{3}} \quad\text{radical index = fraction denominator}[/tex]

Answer:

  y = (5/2)x + 6

Step-by-step explanation:

The given line has a slope (coefficient of x) of -2/5. The perpendicular line will have a slope that is the negative reciprocal of this:

  -1/(-2/5) = 5/2

Since you are given a point you want the line to go through, the point-slope form of the equation of the line is useful. That form for slope m and point (h, k) is ...

  y = m(x -h) +k

For your slope m=5/2 and point (h, k) = (-2, 1), the equation of the line is ...

  y = 5/2(x +2) +1

  y = 5/2x +6 . . . . . eliminate parentheses

The student should watch for 32.135 on the dial pressure gauge when inflating the tire since the specified tire pressure is 32 27/200 psi.

The student's question involves converting a fraction to a decimal. The situation deals with the air pressure in a tire being 32 27/200 pounds per square inch (psi). To express this as a decimal, we perform the division operation of 27 divided by 200 which equals 0.135. This means the air pressure should be 32.135 psi on the dial pressure gauge.

For example, if a tire gauge reads 34 psi, this represents the pressure inside the tire without considering the atmospheric pressure. However, the absolute pressure within the tire will be gauge pressure plus atmospheric pressure. Therefore, if you're reading the gauge, you should aim for it to display 32.135 psi as it is in this context that we're discussing tire pressure.

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Answer:

Step-by-step explanation:

1. It is convenient to start with point-slope form, then simplify the result to slope-intercept form. The two forms of the equation for a line are ...

  y -k = m(x -h) . . . . . line with slope m through point (h, k)

  y = mx +b . . . . . . . . line with slope m and y-intercept b

The given lines are in slope-intercept form, so we can read the slope directly from the equation.

The slope of the parallel line will be the same as the slope of the given line: -4/5.

  point-slope form: y +5 = (-4/5)(x +3)

  slope-intercept form: y = (-4/5)x -37/5

__

2. The slope of the given line is 1/3. The slope of the perpendicular line is the negative reciprocal of that: -1/(1/3) = -3. Your lines are then ...

  point-slope form: y -1 = -3(x -4)

  slope-intercept form: y = -3x +13

Answer:

  the penny option is the much better deal

Step-by-step explanation:

The sequence of pay amounts for the "penny option" is ...

  $0.01, $0.02, $0.04, $0.08 ...

For day n, the amount of pay is $0.01·2^(n-1). For day 30, the amount of pay is ...

  $0.01·2^29 = $5,368,709.12

In case you can't tell, the "penny option" is a much better deal than $250.00. (You might need to credit check your parents before accepting this deal. I know my parents could not make good on this "penny option" offer.)

The total amount for the 30 days will be double this amount, less one cent, or ...

  $10,737,418.23

_____

Sum of a geometric sequence

The daily payments of the penny option are a geometric sequence. The sum of n terms of such a sequence is given by ...

  Sn = a1(r^n -1)/(r -1)

where a1 is the first term ($0.01) and r is the common ratio (2). In our case, the sum for n days is ...

  Sn = $0.01·(2^n -1)

On day 15, this will already be more than $250. The accumulated pay on that day will be $0.01·(2^15-1) = $327.67.

Answer:

The answer to your question is below

Step-by-step explanation:

Equation 4x - 2y = 8 solve for y

First, pass 4x to the right side                -2y = -4x + 8

Pass -2 to the right side                             y = -4/-2 x  + 8 /-2

Simplify                                                        y = 2x -4 or    y = -4 + 2x

I can not see clearly the work of Charlize and Camille, but the one that has the answer shown above is correct.                                                                                    

Answer:

Step-by-step explanation:

Answer:

Jessica spent 10 months in Spain and 8 months in Colombia.

Step-by-step explanation:

Let x be the number of months Jessica lived in Spain, then she lived 18 - x months in Colombia.

She learned an average of 160 words per month when she lived in Spain, so she learned 160x words in Spain.

She learned an average of 200 words per month when she lived in Colombia, so she learned 200(18-x) words in Colombia.

In total, she learned a total of 3,200 new words, thus

[tex]160x+200(18-x)=3,200\\ \\160x+3,600-200x=3,200\\ \\160x-200x=3,200-3,600\\ \\-40x=-400\\ \\x=10[/tex]

Jessica spent 10 months in Spain and 8 months in Colombia.

Answer:

1. 6x+15y-12

2. 25

3. 5(11x-5)

Step-by-step explanation:

1. We have the expression [tex]3(2x+5y-4)[/tex] we have to distribute number 3 to simplify the expression:

[tex]3(2x+5y-4)=\\3.(2x)+3.(5y)-3.(4)=\\=6x+15y-12[/tex]

Then the correct answer is the first choice: 6x+15y-12

2. We have to find the value of the expression when c=4, we have

[tex]f(c)=4c + 3c -2c + 5[/tex]

Then when c=4:

[tex]f(4)=4.(4) + 3.(4) -2.(4)+ 5\\f(4)=16+12-8+5\\f(4)=28-3\\f(4)=25[/tex]

Then the correct answer is the first choice: 25

3. We have to factor the expression 55x-25,

we can see that (5).11=55 and (5).5=25, then the common factor in this expression is number 5,

[tex]55x-25=\\(5).11x-(5).5=\\=5(11x-5)[/tex]

Then the correct answer is the first choice: 5(11x-5)

Answer:

-61

Step-by-step explanation:

Probability can be a natural number, from O to infinity. In fact, how can you represent a -61 probability? it's impossible, at maximum you can have a null probability, that is 0

Answer:

(-3,-2), (-3,2) , (1,2) and (1,-2)

Step-by-step explanation:

Give the translation rule as; 3 units to the left and 2 units down, it means (-3,-2)

The given coordinates of the square are (0,0) and (4,4). You can plot the coordinates on a graph tool and determine the position of the other vertices

of the square as (0,4) and (4,0)

Applying the translation to each point

(0,0)⇒(-3,-2) = (-3,-2)

(0,4)⇒(-3,-2) = (-3,2)

(4,4)⇒ (-3,-2) = (1,2)

(4,0)⇒(-3,-2)= (1,-2)

The image of the vertices after transformation will be

(-3,-2), (-3,2) , (1,2) and (1,-2)

Answer:

16 in × 20 in

Step-by-step explanation:

Area of picture= length by width

                         =4*6=24 in²

Area of frame=Length by width

                      =16*20=320 in²

% of the picture in the frame will be

                        (24/320) * 100% =7.5%

     2. Finding the % of the picture that can fit in 18 × 24 frame

Area of picture=24 in²

Area of frame =Length by width

                       =18*24=432 in²

% of the picture in the frame will be;

                        (24/432)*100%=5.6%

The frame 16 by 20 in will keep 7.5% of the original picture

The frame 18 by 24 in will keep 5.6% of the original picture

Hence you should use the frame  of 16 by 20 in because it will keep more of the original picture.

Changing [tex]x\mapsto -x[/tex] "inverts" the orientation of the x axis, so the graph of f(x) is transformed by reflecting it about the y axis.

The transformation f(-x) represents a reflection of function f(x) across the y-axis. Even functions are unchanged by this transformation, while odd functions are reversed.

The transformation f(-x) in mathematical terms represents a reflection of the function f(x) across the y-axis. For instance, if you have a function that plots as a certain curve when x is positive, applying function to f(-x) would result in the same curve but flipped horizontally across the y-axis. This is because replacing x with -x inverts the sign of every x-coordinates of the original points, causing a mirror image reflection over the y-axis. Thus, while the original function may say f(x) = x², f(-x) would also form a parabola, but it would be flipped across the y-axis.

For example, if f(x) = x³ for x > 0 which increases, f(-x) = -x³. As x values are now negative, the graph flips and for x > 0, f(-x) decreases.

Note that even functions like f(x) = x², which are symmetric about the y-axis, remain unchanged when transformed to f(-x), while odd functions like f(x) = x³, which are symmetric about the origin, are reversed when f(-x) is implemented.

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Answer:

A

Step-by-step explanation:

Let's first assume that the restriction doesn't hold.

So that way we can say that we can put ANY OF THE 9 DIGITS (1-9) on ANY OF THE 4 DIGIT COMBINATIONS.

Hence,

first digit can be any of 1 through 9

second digit can be any of 1 through 9

third digit can be any of 1 through 9

4th digit can be any of 1 through 9

So the total number of possibilities will be 9 * 9 * 9 * 9 = 6561

now, let's take into account the restriction. since all 4 digits cannot be the same, so we need to exclude:

1111

2222

3333

4444

5555

6666

7777

8888

9999

That's 9 numbers. So final count would be 6561 - 9 = 6552

Answer A is right.

The correct answer is a. 6552. There are 6561 total combinations for a 4-digit bike lock. After excluding 9 combinations where all digits are the same, 6552 combinations remain.

To determine the total number of possible combinations for a 4-digit bike lock with digits ranging from 1 to 9, we start with the total unrestricted possibilities. Each digit has 9 options (1 through 9), so we calculate:

However, the problem states that all 4 digits cannot be the same. This means we must subtract the 9 combinations where all four digits are identical (e.g., 1111, 2222, ..., 9999). Thus, we calculate:

The correct answer is a. 6552.

Answer:

T = 4C.

Step-by-step explanation:

T = 4C.

Total number of eggs = 4 * number of chickens.

Answer: Ok, there are two types of variables, the independent and the dependents.

a dependent variable is one that changes in response to the independent variable.

In an experiment, yo usually have control over the independent variable, it may be the temperature on an oven, the intensity of an x-ray cannon, the time you let something heat under the sun, etc.

and the dependent variable will response to the independent variables in some way, so if you can observe how it changes you can understand te relationship between them, that is the goal of the experiment.

So it's true, yo want to know how the response variable "responds" to the treatment you apply.

Answer:

The volume of the ball with the drilled hole is:

[tex]\displaystyle\frac{8000\pi\sqrt{2}}{3}[/tex]

Step-by-step explanation:

See attached a sketch of the region that is revolved about the y-axis to produce the upper half of the ball. Notice the function y is the equation of a circle centered at the origin with radius 15:

[tex]x^2+y^2=15^2\to y=\sqrt{225-x^2}[/tex]

Then we set the integral for the volume by using shell method:

[tex]\displaystyle\int_5^{15}2\pi x\sqrt{225-x^2}dx[/tex]

That can be solved by substitution:

[tex]u=225-x^2\to du=-2xdx[/tex]

The limits of integration also change:

For x=5: [tex]u=225-5^2=200[/tex]

For x=15: [tex]u=225-15^2=0[/tex]

So the integral becomes:

[tex]\displaystyle -\int_{200}^{0}\pi \sqrt{u}du[/tex]

If we flip the limits we also get rid of the minus in front, and writing the root as an exponent we get:

[tex]\displaystyle \int_{0}^{200}\pi u^{1/2}du[/tex]

Then applying the basic rule we get:

[tex]\displaystyle\frac{2\pi}{3}u^{3/2}\Bigg|_0^{200}=\frac{2\pi(200\sqrt{200})}{3}=\frac{400\pi(10)\sqrt{2}}{3}=\frac{4000\pi\sqrt{2}}{3}[/tex]

Since that is just half of the solid, we multiply by 2 to get the complete volume:

[tex]\displaystyle\frac{2\cdot4000\pi\sqrt{2}}{3}[/tex]

[tex]=\displaystyle\frac{8000\pi\sqrt{2}}{3}[/tex]

To find the volume of the resulting solid, calculate the volume of the ball and subtract the volume of the hole. The volume of the resulting solid is (4/3)π(15)³ - 10πr².

To find the volume of the resulting solid, we need to calculate the volume of the ball and subtract the volume of the hole. The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere. So, the volume of the ball is V₁ = (4/3)π(15)³. The volume of a cylinder is given by the formula V = πr²h, where r is the radius of the cylinder and h is the height. The height of the cylinder formed by the hole is equal to the diameter of the ball, which is 2r. So, the volume of the hole is V₂ = π(5)²(2r) = 10πr².

Therefore, the volume of the resulting solid is V = V₁ - V₂ = (4/3)π(15)³ - 10πr².

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Answer:

11,36 pounds

Step-by-step explanation:

Trayvon's weight on earth= 142 pounds

Trayvon's weight on Saturn= (0,92)*Trayvon's weight on earth=

(0,92)*142=130,64 pounds

The difference between Trayvon's weight on earth and Saturn:

Trayvon's weight on earth- Trayvon's weight on Saturn

142-130,64=11,36 pounds.