Un padre está usando una manguera de jardín para llenar una pequeña piscina inflable para su hijo pequeño. La piscina tiene una capacidad de 90 galones. Apaga el agua después de 5 minutos, pero deja la manguera en la piscina durante otros 3 minutos antes de guardarla. En esta situación, la relación entre los galones de agua en la piscina y los 8 minutos desde que el padre comenzó a llenar la piscina puede verse como una función. 1. En esa función, ¿qué variable es independiente? ¿Cuál es dependiente?

Answer:

If you're asking how long it will take for them to meet again, it will take 60 minutes.

Step-by-step explanation:

Answer:

7+2+3=12 pounds in totak

12÷6=2 pounds in each bag

Answer:

25 phone calls

Step-by-step explanation:

Create a proportion where x is the number of phone calls for 50 minutes on the phone:

\(\frac{34}{17}\) = \(\frac{50}{x}\)

Cross multiply and solve for x:

34x = 850

x = 25

So, Nick would have to make 25 phone calls

The result of ANDing 11001111 with 10010001 is 10000001. Option C

To find the result from ANDing (bitwise AND operation) the binary numbers 11001111 and 10010001, we compare each corresponding bit of the two numbers and apply the AND operation.

The AND operation returns a 1 if both bits are 1; otherwise, it returns 0. Let's perform the operation:

11001111

AND 10010001

10000001

By comparing each corresponding bit, we can see that:

The leftmost bit of both numbers is 1, so the result is 1.

The second leftmost bit of both numbers is 1, so the result is 1.

The third leftmost bit of the first number is 0, and the third leftmost bit of the second number is 0, so the result is 0.

The fourth leftmost bit of the first number is 0, and the fourth leftmost bit of the second number is 1, so the result is 0.

The fifth leftmost bit of both numbers is 0, so the result is 0.

The sixth leftmost bit of both numbers is 1, so the result is 1.

The seventh leftmost bit of both numbers is 1, so the result is 1.

The rightmost bit of both numbers is 1, so the result is 1.

Option C

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To calculate the line integral of the given vector field, we will use the formula of line integral. For the given function, the formula will be:∫CF.v dlWhere v = (x²+2yz)i + y²j and dl = dx i + dy j + dz kTherefore,∫CF.(x²+2yz) dx + y² dy … (1)Here, C is the curve from point (0,0,0) to (1,1,1) along the given route, that is, (0,0,0) + (1,0,0) + (1,1,0) + (1,1,1).∴

The above line integral is the required value. So, we need to evaluate this integral. To calculate the line integral of the given vector field, we will use the formula of line integral. For the given function, the formula will be:

∫CF.v dl

Where

v = (x²+2yz)i + y²j

and

dl = dx i + dy j + dz k

Therefore,

∫CF.(x²+2yz) dx + y² dy … (1)

Here, C is the curve from point (0,0,0) to (1,1,1) along the given route, that is, (0,0,0) + (1,0,0) + (1,1,0) + (1,1,1).∴ The above line integral is the required value. So, we need to evaluate this integral.The integral is a line integral of a vector field, with the curve path of integration is given by C as follows: C: (0,0,0) + (1,0,0) + (1,1,0) + (1,1,1)In other words, we need to evaluate the integral of the dot product of the vector field v with the differential of the curve:

∫CF.v dl...

where

v = (x²+2yz)i + y²j

and

dl = dx i + dy j + dz k

We must split the curve C into three distinct segments before we can start evaluating the integral. The segments will be from (0,0,0) to (1,0,0), from (1,0,0) to (1,1,0), and from (1,1,0) to (1,1,1).Let's start with the first segment, from (0,0,0) to (1,0,0). We can set x = t, y = 0, z = 0, with t varying from 0 to 1, to parametrize this segment. Then dx = dt, dy = 0, dz = 0. We have:∫(0,0,0)to(1,0,0)

vdl = ∫0to1(x²+2yz)dx + y²dy + 0dz= ∫0to1(t²+0)dt + 0 + 0= [t³/3]0to1= 1/3

Now, let's evaluate the second segment, from (1,0,0) to (1,1,0). We can set x = 1, y = t, z = 0, with t varying from 0 to 1, to parametrize this segment. Then dx = 0, dy = dt, dz = 0. We have:

∫(1,0,0)to(1,1,0)vdl = ∫0to1(x²+2yz)dx + y²dy + 0dz= ∫0to1(1²+0)dx + t²dy + 0dz= 1∫0to1(t²)dt= [t³/3]0to1= 1/3

Finally, let's evaluate the third segment, from (1,1,0) to (1,1,1). We can set x = 1, y = 1, z = t, with t varying from 0 to 1, to parametrize this segment. Then dx = 0, dy = 0, dz = dt. We have:

∫(1,1,0)to(1,1,1)vdl = ∫0to1(x²+2yz)dx + y²dy + 0dz= ∫0to1(1²+2(1)(t))dx + 1²dy + 0dz= ∫0to1(1+2t)dt + 1(0to1)+ 0= [t²+t]0to1+ 1= 3/2

Therefore, the line integral is the sum of the integrals along the three segments:

∫CF.v dl= 1/3+ 1/3+ 3/2= 2

Thus, the value of the line integral of the given function v = x²+2yzi + y²j from (0,0,0) the point (1,1,1) by the route (0,0,0) + (1,0,0) + (1,1,0) + (1,1,1) is equal to 2.

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Answer:

18/25

Step-by-step explanation:

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Answer:18/25

Step-by-step explanation:

2. 9. 2x9. = 18

- X. - = ————- It cannot be simplified

5. 5. 5x5=25

10 weeks

50 cans+additional 5 per week

5×10=50

100

10 per week

10×10=100

The equation of a line that is perpendicular to y=-(3)/(4)x+9 and goes through the point (6,4) is y = 4x/3 - 14/3.

Given line is y = -(3)/(4)x+9

We know that if two lines are perpendicular to each other, the product of their slopes is equal to -1.Let the required equation of the line be y = mx+c.

Therefore, the slope of the line is m.To find the slope of the given line:y = -(3)/(4)x+9

Comparing it with the general equation of a line:y = mx+c

We can say that slope of the given line is -(3/4).

Therefore, slope of the line perpendicular to the given line is: -(1/(-(3/4))) = 4/3

Let the equation of the perpendicular line be y = 4/3x+c.

Therefore, we have:4 = 4/3 * 6 + c4

= 8 + cC

= 4 - 8

= -4

Therefore, the equation of the required line is:y = 4x/3 - 14/3.

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If you can earn 8 percent on your money, the prize worth to you is: $76,812.50. To calculate the present value of the prize, we need to determine the current worth of receiving $1000 per month for 9 years, given an 8 percent annual interest rate.

This situation can be evaluated using the concept of the present value of an annuity. The present value of an annuity formula is used to find the current value of a series of future cash flows. In this case, the future cash flows are the $1000 monthly payments for 9 years. By applying the formula, which involves discounting each cash flow back to its present value using the interest rate, we find that the present value of the prize is $76,812.50.

This means that if you were to receive $1000 per month for 9 years and could earn an 8 percent return on your money, the equivalent present value of that prize, received upfront, would be $76,812.50.

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By using Taylor series, the limit does not exist, since the third term does not converge as x approaches 0.

To evaluate the limit using series, we can use the Taylor series expansion of each term in the limit as x approaches 0. A Taylor series is an infinite sum of terms that are expressed in terms of the derivatives of a function at a single point.

Starting with the first term:

lim x→0 (1/3) * x^3 = 0

Next, for the second term, we have:

lim x→0 ((x^3 - 1)/(2x^2)) = lim x→0 (x^3/2x^2) = lim x→0 (x/2) = 0

For the third term, we have:

lim x→0 (x - ln(1 + x))/x^4

= lim x→0 [(x - (x - x^2/2 + x^3/3 - ...))/x^4] (using the Taylor series expansion of ln(1+x))

= lim x→0 [x^2/2 - x^3/3 + ...]/x^4

= lim x→0 [1/2x^2 - 1/3x^3 + ...]

= ∞

Therefore, the limit does not exist, since the third term does not converge as x approaches 0.

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Answer: 0.75

Step-by-step explanation:

The evaluated lateral surface area is 261.8 square meters, under the condition that the base length is 20 m and height is 13 m.

The lateral surface area of a cylinder is given by the formula 2πrh
Here,
r = radius of the base
h = height of the cylinder.
For the given case, the base length is 20 m and height is 13 m. Then the base length is stated  instead of the radius, we have  to evaluate the radius first.
The radius of a cylinder can be found applying the formula r = l/2π
Here,
l = base length.
So, staging l = 20 m
, we get
r = 20/(2π)
≈ 3.18 m
Now that we have received the radius and height, we can evaluate the lateral surface area applying the formula mentioned above.
Staging
r = 3.18 m
h = 13 m,
we get:
Lateral surface area
= 2πrh
≈ 261.8 m²
Then, the lateral surface area of the given cylinder is approximately 261.8 square meters.
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The equation of the line perpendicular to the tangent to the curve y=x^3-4x+1 at the point (2,1) is y = (-1/8)x + 9/8.

To find the equation of the line perpendicular to the tangent to the curve at (2,1), we need to first find the slope of the tangent line at that point.

The derivative of y=x^3-4x+1 is y'=3x^2-4, so the slope of the tangent line at (2,1) is y'(2) = 3(2)^2-4 = 8.

Since we want the line perpendicular to the tangent, we know that its slope will be the negative reciprocal of the tangent's slope. Therefore, the slope of the line we're looking for is -1/8.

Next, we use the point-slope form of the equation of a line to write the equation of the line with the slope we found and passing through the point (2,1):

y - 1 = (-1/8)(x - 2)

Simplifying and putting the equation in slope-intercept form:

y = (-1/8)x + 9/8

Therefore, the equation of the line perpendicular to the tangent to the curve y=x^3-4x+1 at the point (2,1) is y = (-1/8)x + 9/8.

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The antiderivative of the function is F(x) = 4x + 5x^3 + 3x^5 - 12.

To find the antiderivative F(x) for F′(x) = f(x) = 4 + 15x^2 + 15x^4, and given F(1) = 0, follow these steps,
1. Find the antiderivative of f(x) with respect to x:
F(x) = ∫(4 + 15x^2 + 15x^4) dx

2. Integrate each term separately:
F(x) = ∫4 dx + ∫15x^2 dx + ∫15x^4 dx

3. Calculate the antiderivatives:
F(x) = 4x + (15/3)x^3 + (15/5)x^5 + C

4. Simplify:
F(x) = 4x + 5x^3 + 3x^5 + C

5. Use the given condition F(1) = 0 to find the value of C:
0 = 4(1) + 5(1)^3 + 3(1)^5 + C

6. Solve for C:
C = -12

7. Substitute the value of C back into F(x):
F(x) = 4x + 5x^3 + 3x^5 - 12

The antiderivative is F(x) = 4x + 5x + 3x - 12 as a result.

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Sarah's final position would be negative. Therefore, option B is the correct answer.

Given that, Sarah starts at a positive position along the x-axis. She then undergoes a negative displacement.

A negative displacement means that Sarah has moved backward along the x-axis, so her final position would be negative.

Therefore, option B is the correct answer.

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The initial flounder population in millions is 1 million. The derivative of the population function at t = 10 is 1.4000 million flounder per year.

(a) To find the initial flounder population, we substitute t = 0 into the population function P(t). Given that t is measured in years, we have:

P(0) = 7(0) + 5 - 0.2(0^2) + 1 = 0 + 5 - 0 + 1 = 6 million flounder.

Therefore, the initial flounder population is 6 million.

(b) To determine P'(10), we need to find the derivative of the population function P(t) and evaluate it at t = 10. Taking the derivative of P(t) with respect to t, we have:

P'(t) = 7 + 0.4t.

Now, substituting t = 10 into the derivative equation:

P'(10) = 7 + 0.4(10) = 7 + 4 = 11 million flounder per year.

Rounded to four decimal places, P'(10) is approximately 11.0000 million flounder per year.

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The change in the advertising budget necessary to maintain a monthly profit of $93,500 if the insurance company hires 5 new sales associates is estimated to be an increase of $2,308.

To estimate the change in advertising budget necessary to maintain a monthly profit of $93,500 with the addition of 5 new sales associates, we need to consider the potential impact of these new hires on the company's revenue and expenses.

Assuming that each new sales associate is expected to generate $10,000 in revenue per month, the total increase in revenue would be $50,000 (5 sales associates x $10,000).

However, there may also be additional expenses associated with the new hires, such as salaries and benefits. Let's assume that the total cost of adding 5 new sales associates is $30,000 per month.

Therefore, the net increase in monthly profit due to the new hires would be $20,000 ($50,000 in revenue - $30,000 in expenses).

To maintain a monthly profit of $93,500, the company would need to increase its advertising budget by an amount that would generate an additional $20,000 in profit. Assuming that the company's profit margin on its products is 20%, this would require an additional $100,000 in revenue per month ($20,000 / 0.20).

Based on the historical data and market conditions, the company could estimate the additional advertising budget required to generate this amount of revenue.

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The hiker plans a trip in two sections, with her destination being 18 km away on a bearing of N63'E from her starting position. The first leg of the trip is on a bearing of N13E. We need to find the length of the first leg.

To find the length of the first leg, we can use trigonometry. Since the bearing is given as an angle relative to the North direction, we can break it down into its components using the right-angled triangle formed by the bearing and the North direction.
In this case, the bearing of N13E can be broken down into a North component (opposite to the angle) and an East component (adjacent to the angle). The North component can be found using the formula: North component = length of leg * sin(bearing angle). The East component can be found using the formula: East component = length of leg * cos(bearing angle).
Once we have the North and East components, we can use them to find the length of the first leg using the Pythagorean theorem: Length of first leg = sqrt((North component)^2 + (East component)^2).
Therefore, to find the length of the first leg, we can follow these steps:
1. Calculate the North component: North component = length of leg * sin(bearing angle).
2. Calculate the East component: East component = length of leg * cos(bearing angle).
3. Calculate the length of the first leg using the Pythagorean theorem: Length of first leg = sqrt((North component)^2 + (East component)^2).
By substituting the given values, we can find the length of the first leg.

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The statement 'the expressions (-3) to the 2nd power and -3 to the second power have the same value' is True.

For given question,

We have been given a statement '(-3) to the 2nd power'

This statement can be written in expression form as,

(-3)²

Now we find the value of above expression.

(-3)² = (-3) × (-3)

       = 9                        .................(1)

Also, we have been given a statement '-3 to the second power'

This statement can be written in expression form as,

(-3)²

Now we find the value of above expression.

(-3)² = (-3) × (-3)

       = 9                        .................(2)

From (1) and (2),

We can say that the value of expressions '(-3) to the 2nd power' and '-3 to the second power' is same.

Therefore, the statement 'the expressions (-3) to the 2nd power and -3 to the second power have the same value' is True.

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Answer:

It's Arrives

Step-by-step explanation:

You can open those brackets and distribute one brackets content with multiplication to other bracket contents.

The products which result in a sum or difference of cubes is given by:

Option D: \((x+4)(x^2 -4x + 16)\)

If there are two terms which are with power 3 (ie cubed), and they both are in addition or subtraction, then that is called sum or difference of cubes for two terms.

Example: \(a^3 - b^3\) is difference of cubes.

There is a formula too which you can use in case if you need it which goes like this:

\(a^3 + b^3 = (a+b)(a^2 - ab + b^2)\\ \\ a^3 - b^3 = (a-b)(a^2 + ab + b^2)\)

Option A: \((x-4)(x^2 + 4x - 16)\)

\((x-4)(x^2 + 4x - 16) = x^3 + 64 -4x^2 + 4x^2 -16x - 16x = x^3 +4^3 -32x\)

Thus, not a sum or difference of cubes

Option B: \((x-1)(x^2 - x+ 1)\)

\((x-1)(x^2 - x+ 1) = x^3 - 1 + x + x -x^2 - x^2 = x^3 - 1 + 2x - 2x^2\)

Thus, not a sum or difference of cubes

Option C: \((x + 1) (x - 1)\)

\((x + 1) (x - 1) = x^2 - 1 + x - x = x^2 - 1\)

It is difference of squares but not of cubes.

Option D: \((x+4)(x^2 -4x + 16)\)

\((x+4)(x^2 -4x + 16) = x^3 + 64 -4x^2 + 16x + 4x^2 - 16x = x^3 + 64 = x^3 + 4^3\\ (x+4)(x^2 -4x + 16) = x^3 + 4^3\)

Thus, it is sum of cubes.

Thus, only Option D: \((x+4)(x^2 -4x + 16)\) is expressible as sum or product of cubes (here it is expressible as sum of cubes \(x^3\) and \(4^3\).

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Answer:

c and e

Step-by-step explanation:

Answer:

3.6

Step-by-step explanation:

Answer:

3.6

Step-by-step explanation:

1) cos α = 0.8, cos β = 0.6, cos γ = 0. The triangle exists and is right.

2) cos α ≈ 0.882, cos β ≈ 0.471, cos γ ≈ 0.441. The triangle exists and is acute.

3) cos α ≈ 0.977, cos β ≈ 0.324, cos γ ≈ -0.115. The triangle exists and is obtuse.

4) cos α = 1, cos β = 1, cos γ = -1. The triangle does not exist.

Triangles are geometric figures formed by three line segments and internal angles, whose sum is equal to 180°, which can be three acute angles or an obtuse angle and two acute angles or a right angle and two acute angles. The possibility is determined by applying the law of cosine:

\(\cos \theta = -\frac{x^{2}-y^{2}-z^{2}}{2\cdot y\cdot z}\)   (1)

The triangle if and only if the cosine of each angle is between -1 and 1 with the following characteristics:

Now we proceed to determine the existence of each triangle:

1) cos α = 0.8, cos β = 0.6, cos γ = 0. The triangle exists and is right.

2) cos α ≈ 0.882, cos β ≈ 0.471, cos γ ≈ 0.441. The triangle exists and is acute.

3) cos α ≈ 0.977, cos β ≈ 0.324, cos γ ≈ -0.115. The triangle exists and is obtuse.

4) cos α = 1, cos β = 1, cos γ = -1. The triangle does not exist.

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Answer: We on da same question i do not know

Step-by-step explanation:

Answer: a. 95%

In a normal distribution, about 95% of the distribution lies within two standard deviations of the mean.

Answer:

2996

Step-by-step explanation:

5x + 4x = 6741

9x = 6741

x = 6741/9

x = 749

to get the no votes,

4x i.e 4*749

=>  4*749 = 2996

hope this helps :)

Answer:

2996

Step-by-step explanation:

Answer: 15 minutes

Step-by-step explanation:

60 / 4 = 15

15 * 3 = 45

45 / 3 = 15

Answer:

Step-by-step explanation:

Time spent on jump rope = 1/3 of 3/4

                                           \(= \dfrac{1}{3}*\dfrac{3}{4}=\dfrac{1}{4} \ hour\) or 15 minutes

we have

15!12!(4−1)!

15!12!(3!)=3,758,268,687,305,932,800,000

therefore

the answer is

Find the x- and y-intercepts of the graph of each ... CCSS REASONING The equation 5x + 10y = 60 ... 20. SOLUTION: The x-intercept is the point at which the y-coordinate is 0, or the line ... charges $50 for admission before 6 p.m. and $20 for ... (90, 70). 100 f (100) = 160 – (100). 60. (100, 60). 130 f (130) = 160 – (130). 30.

Answer:

its the first one and here is some advice go to the website m a t h w a y and enter the equation and click graph!

Step-by-step explanation: