HELP ASAP!!!! HELP FAST PLEASE!!

For a vertical cylindrical water tank where the rate of flowing is 5 cubic metre per minute. The rate at which the height of the water is rising is equals to the \( \frac{5}{9π }\) metre per minute.

We have, water flowing into a vertical cylinder. Let the radius, height and volume of cylindrical tank be r metre, h metre and V cubic metre respectively. Now, Rate of water flow in tank, \( \frac{dV}{dt}\) = 5 cubic m /min

Radius of cylindrical tank, r = 3 m

We have to determine rate at which height of the water is rising, i.e., dh/dt. As we know, Volume of cylindrical water tank, V = πr²h --(2)

Differentiating equation (2) with respect to time t,

=> \( \frac{ dV}{dt }= π(r)²\frac{dh}{dt}\)( since, radius of cylinder is constant)

=> \(5 = π(3)² \frac{ dh}{dt}\)

=> \(5 = 9π \frac{dh}{dt}\)

=> \( \frac{ dh}{dt} = \frac{5}{9π }\)

Hence, the required rate is \( \frac{5}{9π }\)m/min.

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the x-coordinates of all local minima of the function g(x) are x = -√2.45.

To find the x-coordinates of all local minima of the function g(x), we need to find all the critical points and then determine which of them are local minima.

The critical points of g(x) are the values of x where the derivative of g(x) is equal to zero or undefined. To find the derivative, we can use the power rule and the chain rule:

g'(x) = 11x^10 - 27x^8

Setting g'(x) = 0 to find the values of x where the derivative is equal to zero, we get:

11x^10 - 27x^8 = 0

11x^8(x^2 - 2.45) = 0

This equation has two solutions: x = 0 and x = ±√2.45.

To determine which of these critical points are local minima, we need to look at the sign of the second derivative of g(x) at each critical point. The second derivative is:

g''(x) = 110x^9 - 216x^7

For x = 0, we have:

g''(0) = 0 - 0 = 0

Therefore, we cannot determine whether x = 0 is a local minimum using the second derivative test.

For x = √2.45, we have:

g''(√2.45) = 110(√2.45)^9 - 216(√2.45)^7 ≈ -20.76

Since g''(√2.45) is negative, x = √2.45 is a local maximum.

For x = -√2.45, we have:

g''(-√2.45) = 110(-√2.45)^9 - 216(-√2.45)^7 ≈ 20.76

Since g''(-√2.45) is positive, x = -√2.45 is a local minimum.

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So the coefficient of determination is 0.476 or 47.6%. This means that 47.6% of the total variation in the dependent variable can be explained by the independent variable(s) in the regression model.

The coefficient of determination (R-squared) is the proportion of the total variance in the dependent variable that is explained by the independent variable(s). It is calculated as the ratio of the sum of squares due to regression (SSR) to the total sum of squares (SST).

R-squared = SSR / SST

In this case, SSR = 11.06 and SST = 23.22. Therefore,

R-squared = SSR / SST = 11.06 / 23.22 = 0.476

The remaining 52.4% is due to other factors not included in the model.

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Answer:

yes

Step-by-step explanation:

The factor of the polynomial is option (D) (2x+5)^2 is the correct answer.

In this question,

Factorization is the breaking or decomposition of an entity (i.e.,) a number, a matrix, or a polynomial into a product of another entity, or factors, which when multiplied together give the original number. Factorize an expression involves take out the greatest common factor (GCF) of all the terms.

The polynomial is \(4x^{2} +20x+25\)

The above polynomial can be factored as

⇒ \(4x^{2} +20x+25=0\)

⇒ \((2x)^{2}+2(2x)(5)+5^{2}\)

⇒ \((2x+5)^{2}\)

Hence we can conclude that the factor of the polynomial is option (D)(2x+5)^2 is the correct answer.

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Answer:

−2±13−−√

Step-by-step explanation:  one answer for sure

Answer:

−2±13−−√

Step-by-step explanation:

The factor that influences loan’s interest rate is D. the federal funds rate.

The interest rate can be regarded as the amount  that us been charged by lender on a borrower which is usually some percentage of the principal.

One of the factor that influences loan’s interest rate is the federal funds rate because this can make loan to easy to access.

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Answer:

the domain will be all real #'s bc the arrows are continuous/never ending. The range would be y<4 because the line starts at 4 and goes down.

Hope this helped you :)

Answer:

In general, the formulas for these expressions are:

Answer:

C. 4,4,\(\sqrt{32}\)

Step-by-step explanation:

a^2 + b^2 = c^2

4,4,\(\sqrt{32}\)

4^2 + 4^2 = \(\sqrt{32}\)^2

16 + 16 = 32

32 = 32

Answer:

darnnnnn the person beat me to it. it is c. 4,4,√32

Step-by-step explanation:

The marginal revenue in the interval between six and seven jet skis is $300.

Here we are given that total revenue from six jet skis is $2,400

and total revenue from seven jet skis is $2,700

Now, marginal revenue is defined as the revenue gained or lost by producing one more additional unit of a good.

Here, the total revenue increases from $2,400 to $2,700 as we go from producing 6 jet skis to 7 jet skis.

Thus, the change in total revenue will be-

2700 - 2400

= 300

This means that the gain in revenue is $300.

Thus, the marginal revenue in the interval between six and seven jet skis is $300.

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Step-by-step explanation:

Straight line = 180 °

5x + 78 = 180

5x = 180 - 78

5x = 102

x = 20.4

and y = 78 ° because y is an opposite angle of 78 °

the answer is C. Because all your doing is counting how many numbers you see in the parentheses and seeing if it matches the numbers on the graph

Answer:

No the she should have been charged $203.88 the reason is if you times 12 by 16.99 you will get 203.88 not 220.87

The amount in credit card is enough to pay 12 months gym charge.

Given that, the charge for one month  is $16.99.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Number of months = 12

Let the total charge for 12 months be x.

Now, x = 16.99×12

= $203.88

Therefore, the amount in credit card is enough to pay 12 months gym charge.

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9514 1404 393

Answer:

  3) payday loan

Step-by-step explanation:

An loan in the amount of an upcoming paycheck is a payday loan.

__

Comment

It usually comes with an incredibly high interest rate.

Answer:

127.2

Step-by-step explanation:

The area of a semicircle is:

\(\frac{\pi r^{2} }{2}\)

So to figure it out we first find the diameter:

18÷2=9

Then we plug it into the equation

\(\frac{9^{2}\pi }{2} = \frac{81\pi}{2}\) Which we can put into a calculator to get 127.2345... so we round to 1 d.p to get our answer, 127.2 (the fifth digit, 3, rounds down)

The number of elements of order 15 in Z30 ⊕ Z20 is 8, and the number of cyclic subgroups of order 15 is 8.

In Z30 ⊕ Z20, the elements can be represented as pairs (a, b) where a belongs to Z30 and b belongs to Z20. The order of an element (a, b) in Z30 ⊕ Z20 is determined by the least common multiple (LCM) of the orders of a and b.

To find the elements of order 15, we need to consider pairs (a, b) where the LCM of the orders of a and b is 15. Since the order of any element in Z30 is a divisor of 30 and the order of any element in Z20 is a divisor of 20, we need to find pairs (a, b) where the LCM of a divisor of 30 and a divisor of 20 is 15.

There are 8 such pairs: (0, 15), (0, 5), (10, 0), (10, 15), (20, 0), (20, 5), (20, 10), and (20, 15). Each of these pairs represents an element of order 15 in Z30 ⊕ Z20.

The number of cyclic subgroups of order 15 is equal to the number of elements of order 15, which is also 8. Each element of order 15 generates a cyclic subgroup of order 15.

Therefore, in Z30 ⊕ Z20, there are 8 elements of order 15 and 8 cyclic subgroups of order 15.

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The scale factor from the scale drawing to the actual triangle is; 1/3

The area of a triangle is calculated using the formula;

A = ¹/₂bh

Where;

A is area.

b is base.

h is height.

The two sides of the rectangle are 6 units and 3 units. Use the measurements in the formula. "u" is for units.

Thus;

A = ¹/₂(6)(3)  

A = 9 square units

The scale factor, represented by the variable "k", tells you how much a shape enlarged or reduced. If "k" is greater than 1, the shape enlarged. If "k" is greater than 0 and less than 1, the shape reduced

In this case, since the drawing is smaller than the actual triangle, the scale factor will be a fraction less than 1 and greater than 0.

The scale factor is used for side length. When it's used to find a side length, we use "k" multiplied by a side. Since the information we know is area, we find k² first, then isolate "k".

Divide the depicted triangle area by the actual area.

k² = 9 ÷ 81

k² = 1/9

√k² = √(1/9)

k = 1/3

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The sampling distribution of x is E) approximately normal with mean 10 and standard deviation 0.5.

The sampling distribution of the sample mean, based on random samples of size n, tends to follow a normal distribution regardless of the shape of the population distribution, as long as the sample size is sufficiently large (by the Central Limit Theorem).

In this case, we have a random variable X with a skewed distribution. However, the question states that we are taking random samples of size 400. With a sample size of 400, we can assume that the sampling distribution of the sample mean will be approximately normal.

Therefore, the correct answer is:

E. approximately normal with mean 10 and standard deviation 0.5

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Answer:

(x + 2)^2-9

How to find answer:

Use the formula (b/2)^2 in order to complete the square.

Hope this helps :)

Answer:

y=mx+b

Step-by-step explanation:

To find the area between the curves, we need to first find the points of intersection between the two curves. So the area between the curves is also 54/5 square units.

To find the area between the curves, we need to first find the points of intersection between the two curves. We can do this by setting the two equations equal to each other:

\(x^2 + 2x + 1 = -x^2 - 3x + 4\)

Simplifying this equation, we get:

\(2x^2 + 5x - 3 = 0\)

We can solve for x using the quadratic formula:

\(x = (-5 ±\sqrt{ (5^2 - 4(2)(-3)))} / (2*2))\)

\(x = (-5 ± \sqrt{(49)} ) / 4\)

\(x = (-5 + 7) / 4 or x = (-5 - 7) / 4\)

x = 1/2 or x = -3

So the curves intersect at x = 1/2 and x = -3. Now we can integrate with respect to x to find the area between the curves:

∫[x=-3 to x=1/2] [(x^2 + 2x + 1) - (-x^2 - 3x + 4)] dx

Simplifying this equation, we get:

\(\int\[[x=-3 to x=1/2] [(x^2 + 2x + 1) - (-x^2 - 3x + 4)] dx\)

Integrating, we get:

\((2/3)x^3 + (5/2)x^2 - 3x\) evaluated from x=-3 to x=1/2

= \([(2/3)(1/2)^3 + (5/2)(1/2)^2 - 3(1/2)] - [(2/3)(-3)^3 + (5/2)(-3)^2 - 3(-3)]\)

= (7/12 + 5/8 - 3) - (-18 + 45/2 + 9)

= 53/24

So the area between the curves is 53/24 square units.

Alternatively, we could integrate with respect to y. To do this, we need to solve each equation for x:

\(x = \sqrt{(y - 2x - 1)}\)

\(x = -\sqrt{(y + 3x - 4)}\)

We can then set these two equations equal to each other and solve for y:

\(\sqrt{y-2x-1}\) = \(-\sqrt{y+3x-4}\)

Squaring both sides, we get:

y - 2x - 1 = y + 3x - 4

Simplifying, we get:

5x = 3

x = 3/5

We can then integrate with respect to y:

∫[y=1 to y=10] [(3/5) - (-3/5)] dy

= ∫[y=1 to y=10] (6/5) dy

= (6/5)(y) evaluated from y=1 to y=10

= (6/5)(10 - 1)

= 54/5

So the area between the curves is also 54/5 square units.

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Answer:

21.4

Step-by-step explanation:

13^2 + 17^2 = c^2

169 + 289 = c^2

458 = c^2

The square root of 458 is 21.4.

Answer:

D;

Step-by-step explanation:

In the Cartesian system and coordinates, we have the 2 dimensional plane and also the 3 dimensional plane.

The two dimensional plane is the more popular one within this level of education where we have one of the coordinates denoting the horizontal distance with the other coordinate denoting the vertical distance.

The one that denotes the horizontal distance is referred to as the x-coordinate with its plane called the x-axis while the one they represents the vertical distance is referred to the y-coordinate and its plane is called the y-axis

In the three dimensional space however, we have the third side which is the z part and it’s called the z-coordinate which is for the z axis

Answer:

d

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There are 41 ways to distribute five distinguishable objects into three indistinguishable boxes.

The boxes are indistinguishable, there are 5 different ways to arrange the number of balls in each box: (5,0,0), (4,1,0), (3,2,0), (3,1,1), or (2,2,1).

There is 1 way to put all 5 balls in one box i.e (5,0,0)

(4,1,0): There are 5 choices for the 4 balls in one of the boxes.

(3,2,0): There are 10 choices for the 3 balls in the boxes.

(3,1,1): There are 10 choices for the 3 balls in one of the boxes, and we can simply split the last two among the other indistinguishable boxes.

(2,2,1): There are 10 options for one of the boxes with two balls, then 3 options for the second box with two balls, and one for remaining for the third.

Therefore the boxes with two balls are indistinguishable, we are counting each pair of balls twice so we have to divide by two.

So there are (10×3)/2=15 arrangements of balls as (2,2,1).

Hence the total number of arrangements for 3 indistinguishable boxes and 5 distinguishable balls is 1+5+10+10+15=41.

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Answer:

-2

Step-by-step explanation:

9g-4-5=-27

9g-9=-27

Add 9 to both sides

9g=-18

g=-2

Answer:

-18

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In perspective of this, the function that degrades as input values go closer to both negative and positive infinity is \(g(x) = -2x^3 - 4x^2 +9\) and the appropriate response is (2).

Functions are the central idea of calculus in mathematics. The functions are special types of relations. A function seems to be a rule that generates a unique outcome one per input x in mathematical. A mapping as well as transformation in mathematics represents a function.

(1) \(f(x) = x^3 - 4x^2 + x\)

x3 and -4x2 become extremely big negative numbers as x approaches negative infinity, and x becomes a very large negative number. As a result, f(x) approaches infinity. \(x^3\) and \(-4x^{2}\) become extremely big positive values as x approaches positive infinity, and x becomes a very large positive number. As a result, f(x) approaches infinity. As a result, f(x) does not decrease when the input values approach negative and positive infinity.

(2) \(g(x) = -2x^3 - 4x^2 +9\)

When x approaches negative infinity, the negative integers -2x3 and \(-4x^{2}\) grow very big, and 9 becomes negligible. As a result, g(x) approaches infinity. When x approaches positive infinity, the negative integers -\(2x^3\) and \(-4x^{2}\) grow very big, and 9 becomes negligible. As a result, g(x) approaches infinity. As a result, g(x) diminishes as the input values approach negative and positive infinity.

(3) \(h(x) = x^4 - 4x^3 + 2x + 8\)

When x approaches negative infinity, the negative integers \(x^4\) and \(-4x^3\) grow very big, whereas 2x and 8 become unimportant. As a result, h(x) approaches infinity. When x approaches positive infinity, the positive integers \(x^4\) and \(-4x^3\) grow very big, whereas 2x and 8 become unimportant. As a result, h(x) approaches infinity. As a result, h(x) does not decrease when the input values approach negative and positive infinity.

(4) \(r(x) = -x^4 + 9x^3 + x^2 + 8x + 2\)

When x approaches negative infinity, the negative numbers \(x^4\) and \(9x^3\) grow quite big, whereas \(x^2\), 8x, and 2 become unimportant. As a result, r(x) approaches infinity. When x approaches positive infinity, the negative integers  \(-x^{4}\) and \(9x^{3}\) grow quite big, whereas \(x^2\), 8x, and 2 become unimportant. As a result, r(x) approaches infinity. As a result, r(x) diminishes as the input values approach negative and positive infinity.

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Her employer's contribution to the 401(k) was $2,500.

Given that for the first 3% of Pam's salary, her employer matches 100% of her 401(k) contributions, and from 3% to 12%, Pam's employer matches 50% of her 401(k) contributions, and Pam's salary is $30,000 , and last year, she contributed $4000 to her 401(k) plan, to determine what was her employer's contribution to the 401(k) the following calculation must be made:

Therefore, her employer's contribution to the 401(k) was $2,500.

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Answer: C. $2250

Step-by-step explanation: took the quiz.

Answer: 188in^2

Step-by-step explanation:

You can break the figure into 3 smaller shapes

15 x 5

10 x 5

and 9 x 7

The areas of these smaller shapes are 75, 59 and 63

adding these areas together would get you 188 in squared.