If 10,000 catfish can be accommodated by a pond with an area of 30 square meters, how large a pond is needed if the number of catfish is 20,000?

The x- and y-components of the vector [tex]\mathbf{\hat a}}[/tex] are 8.9 m/s² and -6.4 m/s², respectively.

In mathematics, components are the parts or elements that make up a larger structure or object. In the context of vectors, components refer to the parts of a vector that describe its direction and magnitude in a particular coordinate system.

To find the x-components and y-components of the vector [tex]\mathbf{\hat a}}[/tex] = (11 m/s², 36 degrees left of -y-axis), we need to determine the direction of the vector. The notation "left of -y-axis" means that the vector makes an angle of 36 degrees with the negative y-axis, as measured counterclockwise from the negative y-axis.

The magnitude (or length) of the vector is given by the first component, which is 11 m/s².

The x-component of the vector can be found by multiplying the magnitude by the cosine of the angle:

x-component = magnitude x cos(angle) = 11 m/s² x cos(36°) = 8.9 m/s²

The y-component of the vector can be found by multiplying the magnitude by the sine of the angle:

y-component = magnitude x sin(angle) = 11 m/s² x sin(36°) = -6.4 m/s²

The negative sign indicates that the y-component is in the opposite direction of the negative y-axis.

Therefore, the x- and y-components of the vector [tex]\mathbf{\hat a}}[/tex] are 8.9 m/s² and -6.4 m/s², respectively.

Expressed as an ordered pair, the components are (8.9 m/s², -6.4 m/s²).

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The correct transformation is, a dilation with a scale factor less than 1 and then a reflection.

A transformation is a process that manipulates a polygon or other two-dimensional object on a plane or coordinate system.

Given that, a transformation that maps polygon ABCD to polygon A'B'C'D',

We are asked to select the correct composition of similarity transformations,

According to the graph, there is a scale factor of 1/2 which is smaller than 1,

Also, the polygon is dilating and then reflected.

Hence, the correct transformation is, a dilation with a scale factor less than 1 and then a reflection.

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Answer:

Mrs. Morris drove a total of 1989 miles in June. This can be calculated by adding 873 miles (the amount she drove in May) to 1116 miles (the amount she drove more in June). Therefore, 873 + 1116 = 1989 miles.

The probability that more than 2 students will attend is 0.9179.

Part (a) List the values that X may take on.

X may take on the values 0, 1, 2, 3, ..., 13.

Part (b) Give the distribution of X.

The distribution of X can be represented as follows: X-0:0, 1:0.23, 2:0.23, 3:0.23, 4:0.23, 5:0.23, 6:0.23, 7:0.23, 8:0.23, 9:0.23, 10:0.23, 11:0.23, 12:0.23, 13:0.23

Part (c) How many of the 13 students do we expect to attend the festivities? (Round your answer to the nearest whole number.)

We can expect 3 students to attend the festivities.

Part (d) Find the probability that at most 3 students will attend. (Round your answer to four decimal places.)

The probability that at most 3 students will attend is 0.6923.

Part (e) Find the probability that more than 2 students will attend. (Round your answer to four decimal places.)

The probability that more than 2 students will attend is 0.9179.

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To get the cash flows from operating activities, we subtract this from the change in total cash, which is $0.01 billion, to get -$0.39 billion. Rounding to two decimal places, we get -$1.01 billion).

What is algebraic expression ?

An algebraic expression is a combination of variables, numbers, and mathematical operations, such as addition, subtraction, multiplication, and division. It can be used to represent a mathematical relationship or formula and can be simplified or evaluated using algebraic rules.

The change in total cash of Rectangle is $0.02 billion (3.59 - 0.59 - 4.18 = -0.98, which is rounded to -$1.00 billion, and then added to the beginning cash amount of $0.69 billion to get $0.69 - $1.00 = -$0.31 billion or -$0.31/100 = -$0.02 billion).

The ending cash amount of Circle is $0.72 billion (1.39 - 0.29 - 1.38 = -0.28, which is added to the beginning cash amount of $0.69 billion to get $0.41 billion or $0.41/100 = $0.72 billion).

The amount of cash flows from financing activities of Pentagon is -$0.55 billion (the change in total cash of $0.05 billion is the sum of the operating cash flows and investing cash flows, which is $0.08 billion + $0.62 billion = $0.70 billion. To get the cash flows from financing activities, we subtract this from the change in total cash, which is $0.05 billion, to get -$0.65 billion. Rounding to two decimal places, we get -$0.55 billion).

The amount of cash flows from investing activities of Square is -$0.40 billion (the change in total cash of $0.01 billion is the sum of the operating cash flows and financing cash flows, which is $0.59 billion + $0.41 billion = $1.00 billion. To get the cash flows from investing activities, we subtract this from the change in total cash, which is $0.01 billion, to get -$0.99 billion. Rounding to two decimal places, we get -$0.40 billion).

The amount of cash flows from operating activities of Hexagon is -$1.01 billion (the change in total cash of $0.01 billion is the sum of the investing cash flows and financing cash flows, which is -$1.40 billion + $1.02 billion = -$0.38 billion.

Therefore,  To get the cash flows from operating activities, we subtract this from the change in total cash, which is $0.01 billion, to get -$0.39 billion. Rounding to two decimal places, we get -$1.01 billion).

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Answer:

To find the probability of Miko taking a red marble first, then a white marble, we can use the formula for joint probability:

P(red, then white) = P(red) * P(white | red)

Where P(red) is the probability of Miko taking a red marble first and P(white | red) is the probability of Miko taking a white marble second, given that he took a red marble first.

P(red) = 3/12 = 1/4

P(white | red) = 4/12 = 1/3

So,

P(red, then white) = 1/4 * 1/3 = 1/12

Therefore, the probability of Miko taking a red marble first, then a white marble is 1/12.

Answer:

what is that maybe l can be of help to u

On solving the provided question, we can say that the slope intercept equation is 12x + 3y = -3 and slope, m = -4

In mathematics, the intersection point is the place on the y-axis where the slope of the line crosses. a place where the y-axis crosses on a line or curve. Y = mx+c, where m stands for the slope and c for the y-intercept, is used as the equation for the straight line to show this. The slope (m) of the line and its y-intercept (b) are emphasised in the equation's intercept form. When an equation has the intercept form (y=mx+b), the slope is m and the y-intercept is b. Some equations can also be rewritten such that they seem to be slope intercepts. If y=x is rewritten as y=1x+0, for instance, the slope and y-intercept are both changed to 1.

the slope intercept equation is

12x + 3y = -3

3y = -12x - 3

y = -4x - 1

also, y = mx + c

so, slope, m = -4

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Hi there, here's your answer:

Given:

The quotient of twice the difference of five less than a number and six.

Let the number be x.

By this, it is understood that the algebraic equation is in a fractional form, with the numerator being

Twice the difference of five less than a number, i.e.

2(x - 5)

And the denominator is 6.

Therefore, we get the algebraic equation to be:

[tex]\frac{2(x-5)}{6}[/tex]

Hope it helps! Please mark as brainliest!

Answer:

Step-by-step explanation:

Since Joe bought six bunches of seedless black grapes for $15, the cost per bunch of grapes is $15 / 6 = $2.50.

Since Anjali has $7.50, she can buy $7.50 / $2.50 = 3 bunches of seedless black grapes.

The percentage decrease for the sale of the house is 0.27%.

What are the nearest two places?

The second place to the right of the decimal point, or the hundredth place, is used to round a decimal number to two decimal places. For instance, you can round 2.83620364 to two decimal places as 2.84 and 0.7035 to two decimal places as 0.70.

Given that the initial cost of a home is  369,000.

The cost of a house decreases from 369,000 to 368,000.

The formula of percentage change is

(Final value - initial value)/ initial value × 100

= [(368,000 - 369,000)/369,000] × 100

= (-1000)/369,000 × 100

= 0.27

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d. The logarithmic model can be expressed as y1~alog(x1)+k or y1~aln(x1)+k.

The best fit curve for the given data would be: y1 = 0.2 * log(x1) + k or y1 = 0.2 * ln(x1) + k

a. If you wanted to find a station with a frequency of 93.3 on your radio dial, you would need to use the formula Frequency = 88 + 0.2 * (Channel Number). Using this formula, we can calculate that the channel number for a frequency of 93.3 is:

Channel Number = (Frequency - 88) / 0.2

Channel Number = (93.3 - 88) / 0.2

Channel Number = 5.3

Therefore, a station with a frequency of 93.3 can be found on channel 5.3 on your radio dial.

b. If you turned the radio dial to be 4 centimeters from the left end of the radio, the channel number would be:

Channel Number = 4 / 0.2

Channel Number = 20

Using the formula Frequency = 88 + 0.2 * (Channel Number), we can calculate that the frequency for channel 20 is:

Frequency = 88 + 0.2 * (Channel Number)

Frequency = 88 + 0.2 * (20)

Frequency = 96.0

Therefore, turning the radio dial to be 4 centimeters from the left end of the radio, you will pick up a station with a frequency of 96.0.

The scaled dimensions of a kitchen with dimensions 6.3m by 4.8m, if the kitchen plan is drawn to a scale of 1:500, are given as follows:

1.26 cm and 0.96 cm.

The scaled dimensions are obtained applying the proportions in the context of the problem.

The scale is of 1:500, meaning that each dimension is divided by 500, as follows:

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The area of the shape given which is a circle is; 38.465 in²

The area of a circle is π multiplied by the square of the radius. The area of a circle(A) when the radius 'r' is given is πr².

Area = πr²

The parameters are;

radius; r = 3¹/₂ inches = ⁷/₂ inches

Thus;

Area = π * (⁷/₂)²

Area = π * 49/4

Area = 3.14 * 49/4

Area = 38.465 in²

That's the area of the circle shape given.

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The positive angle which is less than 360 degrees and is co-terminal with -305 as required is; 55°.

It follows from the task content that the position angle which is co-terminal with -305° as required is to be determined.

Let the positive angle in discuss be; x.

Therefore, the angle x = 360 + (-305)

Consequently, it can be calculated as follows;

x = 360 - 305.

x = 55°

Hence, the required value of the positive co-terminal angle is; 55°.

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Answer:

  EF = 7

Step-by-step explanation:

You want to know the length of midsegment EF in the triangle with it labeled 43-4x and the parallel base segment labeled 32-2x.

The midsegment is half the length of the base segment, so we have ...

  (43 -4x) = 1/2(32 -2x)

  43 -4x = 16 -x . . . . . simplify

  27 = 3x . . . . . . . . add 4x-16

  9 = x . . . . . . . . divide by 3

  EF = 43 -4x = 43 -4(9) = 43 -36

  EF = 7

Step-by-step explanation:

(a) To convert feet to fathoms, we can use the conversion factor 1 fathom = 6 feet. Hence, we can divide the depth in feet by 6 to find the depth in fathoms:

36,078 feet / 6 feet/fathom = 6,013 fathoms

So the depth of the seabed is 6,013 fathoms.

(b) To convert feet to leagues (marine), we can use the conversion factor 1 league (marine) = 5,556 feet. Hence, we can divide the depth in feet by 5,556 to find the depth in leagues (marine):

36,078 feet / 5,556 feet/league (marine) = 6.52 leagues (marine)

So the depth of the seabed is approximately 6.52 leagues (marine).

To find the weight of 2.2 cubic feet of water in pounds, we can use the following formula:

Weight in pounds = Volume in cubic feet x Density of water in pounds per cubic foot

The density of water is 62.4 pounds per cubic foot, so we can substitute the values into the formula:

Weight in pounds = 2.2 x 62.4 = 138.08

So, 2.2 cubic feet of water weighs 138.08 pounds.

To convert this weight to tons, we can divide by 2000, as there are 2000 pounds in a ton:

Weight in tons = 138.08 / 2000 = 0.06904 tons

So, 2.2 cubic feet of water weighs 0.06904 tons.

Answer:

Step-by-step explanation:

First, we need to find how many gallons of water 2.2 cubic feet hold:

2.2 cubic feet * 7.48 gallons per cubic foot = 16.456 gallons

Next, we'll find the weight of the water in pounds:

16.456 gallons * 8.33 pounds per gallon = 136.08 pounds

Finally, we'll convert the weight to tons:

136.08 pounds / 2000 pounds per ton = 0.0680 tons

So 2.2 cubic feet of water weigh 136.08 pounds and 0.0680 tons.

The expression "log[a * b.c]" can be rewritten as 2 * log a + log b + log c.

The expression "log[a*b.c]" can be rewritten using the properties of logarithms as follows:

Use the logarithmic property log(a * b) = log a + log b:

log[a * b.c] = log (a * b) + log c

Apply logarithmic property log(a^n) = n * log a:

log[a * b.c] = log (a^2 * b) + log c = 2 * log a + log b + log c

So, the expression "log[a * b.c]" can be rewritten as 2 * log a + log b + log c.

Therefore, the correct answer is as given above. It could then be concluded that the rewritten expression will then be 2 * log a + log b + log c.

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The derivative formula for the division of two functions is equal to d [θ(x)] / dx = [g(x) · f'(x) - f(x) · g'(x)] / [g(x)]², where θ(x) = f(x) / g(x).

In this problem we need to derive the formula for the derivative of the division of two functions, that is, the expression θ(x) = f(x) / g(x). First, we write the definition of the derivative for the given expression:

[tex]\frac{d}{dx} [\theta (x)] = \lim_{h \to 0} \frac{\theta(x + h) - \theta (x)}{h}[/tex]

Second, substitute and expand the expression by algebra properties:

[tex]\frac{d}{dx} [\theta (x)] = \lim_{h \to 0} \frac{\frac{f(x + h)}{g(x + h)} - \frac{f(x)}{g(x)} }{h}[/tex]

[tex]\frac{d}{dx}[\theta (x)] = \lim_{h \to 0} \frac{f(x + h) \cdot g(x) - f(x) \cdot g(x + h)}{h\cdot g(x + h)\cdot g(x)}[/tex]

Third, expand and simplify the expression one more time by algebra properties and limit properties:

[tex]\frac{d}{dx} [\theta (x)] = \lim_{h \to 0} \frac{f(x + h) \cdot g(x) - f(x) \cdot g(x) + g(x) \cdot f(x) -f(x) \cdot g(x + h)}{h \cdot g(x + h) \cdot g(x)}[/tex]

[tex]\frac{d}{dx}[\theta (x)] = \lim_{h \to 0} g(x) \cdot \frac{f(x + h) - f(x)}{h\cdot g(x+h)\cdot g(x)} - \lim_{h \to 0} f(x) \cdot \frac{g(x + h) - g(x)}{h\cdot g(x+h)\cdot g(x)}[/tex]

[tex]\frac{d}{dx}[\theta (x)] = \lim_{h \to 0} \frac{g(x)}{g(x + h) \cdot g(x)} \cdot \lim_{h \to 0} \frac{f(x + h) - f(x)}{h} - \lim_{h \to 0} \frac{f(x)}{g(x+ h) \cdot g(x)} \cdot \lim_{h \to 0} \cdot \frac{g(x + h) - g(x)}{h}[/tex]

Fourth, simplify the resulting expression by evaluating the limits:

d [θ(x)] / dx = [g(x) / [g(x)]²] · f'(x) - [f(x) / [g(x)]²] · g'(x)

d [θ(x)] / dx = [g(x) · f'(x) - f(x) · g'(x)] / [g(x)]²

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Answer:

27,64,216,64,243

Step-by-step explanation:

Any number raise to power 3

Answer:

Let's call the number of white boards that Mr. Kelso purchased "W", the number of sharpies "S", and the number of glue sticks "G". We know the following information:

W = 5G

S = G + 10

And we also know the total cost of the items:

0.79W + 1.56S + 0.85G = 91.92

We can use the first equation to substitute for W in the second equation:

0.79(5G) + 1.56(G + 10) + 0.85G = 91.92

Expanding and simplifying the equation:

4.95G + 1.56G + 16.6 + 0.85G = 91.92

7.36G + 16.6 = 91.92

7.36G = 75.32

G = 10.25

So Mr. Kelso purchased 10 glue sticks. Using the first equation, we can find that he purchased 5 * 10.25 = 51 white boards. And using the second equation, we can find that he purchased 10.25 + 10 = 20.25 sharpies.

Since the number of each item must be a whole number, we round up or down to the nearest integer. In this case, it would make sense to round up the number of sharpies to 21. So Mr. Kelso purchased 51 white boards, 21 sharpies, and 10 glue sticks.

Answer:

Bryce is 10 years old

Step-by-step explanation:

The age of Brice is given by B = 10 years old

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as B

Now , the value of B is

Substituting the values in the equation , we get

The age of Aida = 15 years

The age of Brice = 5 years younger than Aida

On simplifying the equation , we get

So , age of Brice = 15 - 5 = 10 years

The age of Henry = three years younger than Aida

So , the age of Henry = 15 - 3 = 12 years

Hence , the age of Brice is 10 years old

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Answer:

f-g= 3x²+1-(1-x)

3x²+1-1+x

3x²+x=0

x(3x+1)=O

x=0, 3x+1=0

So, x=0 or -1/3

Answer:The range rule of thumb states that the standard deviation (s) is approximately equal to the range (R) divided by 4, where the range is the difference between the maximum and minimum values of a data set.

Using this formula, we can estimate the standard deviation of the heights as:

s = R / 4 = (192.5 - 152.0) / 4 = 20.625 / 4 = 5.156 cm

Comparing this estimate to the actual standard deviation of 12.22 cm, we see that the estimate is off by a factor of approximately 2.37.

Since the estimate is not within 1.7 cm of the actual standard deviation, it suggests that the range rule of thumb is not a very accurate way to estimate the standard deviation of this data set. The standard deviation calculated using the full set of data is much larger than the estimate, which means that the spread of the data is greater than what would be expected based on the range rule of thumb.

Answer:13

Step-by-step explanation:

r = circumference/2pi

81.64/6.28 = 13

The radius of the garden is 13 units.

The solution to the complex number in rectangular form is; -2 + 2i

The complex number is given as;

2√2(cos 135° + i sin 135°)

The standard form is a + bi.

The value of cos 135° is; -(√2)/2

The value of sin 135° is; (√2)/2

Plugging these values into the given equation is;

2√2(-(√2)/2 + ((√2)/2)i)

Expanding the bracket gives;

-2 + 2i

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