Choose the statement that is correct about the word “GIGGLING”

a) The rate of people leaving the health club, L(t), can be calculated as:

L(11) = 0.013(11)^2 - 0.25(11) + 8

b) To find the number of people, we integrate the net rate of change over the time interval:

Number of People at t=20 = Integral of (E(t) - L(t)) dt, from t=0 to t=20

c) This can be done by finding the critical points of the net rate of change and evaluating them to determine whether they correspond to maximum or minimum values.

To determine whether the number of people in the facility is increasing or decreasing at time t=11, we need to compare the rates of people entering and leaving the health club at that time.

a) At time t=11 hours:

The rate of people entering the health club, E(t), can be calculated as:

E(11) = -0.018(11)^2 + 11

Similarly, the rate of people leaving the health club, L(t), can be calculated as:

L(11) = 0.013(11)^2 - 0.25(11) + 8

By comparing the rates of people entering and leaving, we can determine if the number of people in the facility is increasing or decreasing. If E(t) is greater than L(t), the number of people is increasing; otherwise, it is decreasing.

b) To find the number of people in the health club at time t=20, we need to integrate the net rate of change of people over the time interval 0≤t≤20 hours.

The net rate of change of people can be calculated as:

Net Rate = E(t) - L(t)

To find the number of people, we integrate the net rate of change over the time interval:

Number of People at t=20 = Integral of (E(t) - L(t)) dt, from t=0 to t=20

c) To determine the time t at which the number of people in the health club is a maximum, we need to find the maximum value of the number of people over the interval 0≤t≤20.

This can be done by finding the critical points of the net rate of change and evaluating them to determine whether they correspond to maximum or minimum values.

Let's calculate these values and solve the problem.

Note: Since the calculations involve a series of mathematical steps, it would be best to perform them offline or using appropriate computational tools.

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I think the answer is

300

Answer: 5X^12

Step-by-step explanation: 5*x3*x4*x5

=5*x12

=5x12

Answer:

Step-by-step explanation:

Given the expression (2 + i)(3 - i)(1 + 2i)(1 - i)(3 + i), we are to take the product of all the complex values. We must note that i² = -1.

Rearranging the expression [(3 - i)(3 + i)] [(2 + i)(1 - i)](1 + 2i)

On expansion

(3 - i)(3 + i)

=  9+3i-3i-i²

= 9-(-1)

= 9+1

(3 - i)(3 + i) = 10

For the expression (2 + i)(1 - i), we have;

(2 + i)(1 - i)

= 2-2i+i-i²

= 2-i+1

= 3-i

Multiplying 3-i with the last expression (1 + 2i)

(2 + i)(1 - i)(1 + 2i)

= (3-i)(1+2i)

= 3+6i-i-2i²

= 3+5i-2(-1)

= 3+5i+2

= 5+5i

Finally,  [(3 - i)(3 + i)] [(2 + i)(1 - i)(1 + 2i)]

= 10(5+5i)

= 50+50i

Hence,  (3 - i)(3 + i)(2 + i)(1 - i)(1 + 2i) is equivalent to 50+50i

Answer:

im trying to figure out the same thing

Step-by-step explanation:

Answer:

Hey dude, sry about earlier.

Anyways, 24%=24/100

24/100 simplified is 6/25

There we go :)

*

The other angle of the triangle is 65°.

We know that

Exterior Angle = Sum of two angles opposite to the exterior angle

Here, 145° = 80° + x°

=> x° = (145 – 80)°

=> x° = 65°

Therefore, the value of x in the given figure is 65°

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Complete question:

After the 6-for-1 stock split, the stock price will be $16.41 per share, assuming no market imperfections or tax effects.

A stock split is a process in which a company increases the number of shares outstanding while proportionally reducing the price per share. In this case, the company plans a 6-for-1 stock split, which means that for every existing share, shareholders will receive six new shares.

To determine the post-split stock price, we divide the original stock price by the split ratio. The original stock price is $98.48, and the split ratio is 6-for-1. Therefore, we calculate:

$98.48 / 6 = $16.41

Hence, after the 6-for-1 stock split, the stock price will be $16.41 per share. This means that each shareholder will now hold six times more shares, but the value of their investment remains the same.

It is important to note that in practice, market imperfections, investor sentiment, and other factors can influence the stock price after a split. However, assuming no market imperfections or tax effects, the calculated value of $16.41 represents the theoretical post-split stock price.

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To determine the number of high fives that will be exchanged, we need to find the total number of unique pairs of students in Ronnie's class Since there are 20 people in the class, each person .

To calculate the number of unique pairs, we can use the formula for combinations, which is nC2, where n is the number of people .So, for Ronnie's class with 20 people, the number of high fives exchanged is:20C2 = (20 * 19) / (2 * 1) = 190.Therefore, a total of 190 high fives will be exchanged in Ronnie's class on National High Five Day. we need to find the total number of unique pairs of students in Ronnie's class Since there are 20 people in the class, each person needs to give a high five to every other person, excluding themselves.

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The value of x , y and z in the parallel line is 50 degrees.

When parallel lines are crossed by a transversal line, angle relationships are formed such as vertically opposite angles, alternate interior angles, alternate exterior angles, adjacent angles, corresponding angles etc.

Therefore, let's use the angle relationships to find the angle, x, y and z as follows:

Therefore,

x = 360 - 310(sum of angles in a point)

x = 50 degrees

Therefore,

x = y(alternate interior angles)

Alternate interior angles are congruent.

Hence,

y = 50 degrees

Therefore,

x = z(alternate interior angles)

z = 50 degrees.

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Answer:

12 = x^2 + y^2

PLEASE BRAINLIEST?!

The equation of the circle centered at the origin has a radius of 12 is x² + y² - 144 = 0.

The circle has a diameter, the whole circumference of the circle, so the radius is the half of the diameter.

The radius of the circle given 12.

All the points on the circle you're looking for have a distance from the origin of 12/ A point's distance from the center is

The equation will be

\(\rm d = \sqrt{x^2 + y^2} \\\\ 12 = \sqrt{x^2 + y^2}\\\\12^2 = x^2 + y^2\\\\x^2 + y^2 - 144 = 0\)

Thus, the equation will be \(\rm x^2 + y^2 - 144 = 0\)

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The Remainder when dividing f(x) by x - 3 is 840

The remainder when dividing the polynomial f(x) = 3x^5 + 4x^3 + 3 by the binomial x - 3, we can use the polynomial remainder theorem. According to the theorem, if we substitute the divisor, x - 3, into the polynomial f(x) and evaluate it at x = 3, the resulting value will be the remainder.

Let's calculate the remainder using this approach:

Substituting x = 3 into the polynomial f(x), we have:

f(3) = 3(3)^5 + 4(3)^3 + 3

    = 3(243) + 4(27) + 3

    = 729 + 108 + 3

    = 840

Therefore, when f(x) = 3x^5 + 4x^3 + 3 is divided by x - 3, the remainder is 840.

In summary, the remainder when dividing f(x) by x - 3 is 840.

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The diameter of his circular field is 18miles

What is sprinkler?

A sprinkler irrigation system is a tool used to irrigate (water) lawns, gardens, golf courses, and other areas. They are also utilised for cooling and dust control in the air. Sprinkler irrigation is a technique for applying water in a way that is similar to rainfall: it is controlled. Pumps, valves, pipes, as well as sprinklers are just a few of the possible components of the network used to distribute the water. Sprinklers for irrigation can be used in residential, commercial, and agricultural settings. Both sandy soil and uneven terrain with insufficient water supply can benefit from it. The rotating nozzle-topped perpendicular pipes are linked to the main pipeline at regular intervals. Water leaks from the rotating nozzles when it is pressurised and forced through the main pipe.

The irrigation sprinkler in this instance is angled.

θ = 50 = 50 π/ 180 rad.

It mists a sphere-shaped area.

A = 2/(2 miles).

If the sprinkler's length is

miles, L. It will be watered within the circle's radius.

Hence,

L^2 = A when divided by two in radians.

⇒ L = √ (2 A / θ)

= √ [(2 x 2 x 180) /40 π]

≈ 18 miles

Hence, The diameter of his circular field is 18 miles

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Given equation is Z−1= BP/RT.To show that Gᴿ/RT = p∫0 (Z-1) dp/p - Z-1-ln Z.As we know that Gibbs free energy is defined asG = H - TSwhere, H is the enthalpy, T is the temperature, and S is the entropy.This equation is valid for all types of systems, irrespective of the process.However, for a chemical reaction that involves gaseous substances, the ideal gas equation can be used in conjunction with the above equation. In other words,G = H - TS + Gᴿwhere, Gᴿ is the gas constant. The ideal gas equation can be written asPV = nRTFrom this, Z can be defined as the compressibility factor Z = PV/nRTThe definition of Z is given byZ−1= BP/RTDifferentiating this equation w.r.t pressure we get,dZ/dP = B/RTAs we know,Gibbs free energy = G = H - TS + Gᴿ= U + PV - TS + GᴿDifferentiating this equation w.r.t pressure we get,dG/dP = V - T(dS/dP) + (dGᴿ/dP)Using Maxwell’s equation, we know that(dS/dP) = (dV/dT)Now, let us substitute the values of dG/dP and dS/dP in the above equation, we get,dG/dP = V - T(dV/dT) + (dGᴿ/dP)Now, substituting the values of V and dV/dT in terms of Z, we get,dG/dP = RT/(PZ) - RT(dZ/dP) + (dGᴿ/dP)We know thatdG/dP = V - T(dS/dP) + (dGᴿ/dP)= nRTZ/P - nR ln P + (dGᴿ/dP)where, nRT/P = V, and dV/dT = 0Now, equating the above two equations, we get,nRTZ/P - nR ln P + (dGᴿ/dP) = RT/(PZ) - RT(dZ/dP) + (dGᴿ/dP)Thus, we getnRTZ/P - nR ln P = RT/(PZ) - RT(dZ/dP)Gᴿ/RT = p∫0 (Z-1) dp/p - Z-1-ln Z, where Z−1= BP/RT. Hence, it is proved that Gᴿ/RT = p∫0 (Z-1) dp/p - Z-1-ln Z when Z−1= BP/RT.

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As integers, proper or improper fractions in simplest form, or decimals

rounded to the nearest hundredth is \(u=-13+\sqrt{218}, u=-13-\sqrt{218}\)

What is fractions?

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

\(u^2+26 u-49=0\)

Solve with the quadratic formula

\(u_{1,2}=\frac{-26 \pm \sqrt{26^2-4 \cdot 1 \cdot(-49)}}{2 \cdot 1}\)

\(\sqrt{26^2-4 \cdot 1 \cdot(-49)}=2 \sqrt{218}\)

\(u_{1,2}=\frac{-26 \pm 2 \sqrt{218}}{2 \cdot 1}\)

Separate the solutions

\($$u_1=\frac{-26+2 \sqrt{218}}{2 \cdot 1}, u_2=\frac{-26-2 \sqrt{218}}{2 \cdot 1}$$\)

\(u=\frac{-26+2 \sqrt{218}}{2 \cdot 1}: \quad-13+\sqrt{218}\)

The solutions to the quadratic equation are:

\($$u=-13+\sqrt{218}, u=-13-\sqrt{218}$$\)

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The probability that 5 messages are received in 1 hour is is 0.1755 ,the probability that 10 messages are received in 1.5 hours is 0.0858 and the probability that less than 2 messages are received in 1/2 hour is 0.2873

Let X shows the number of messages received per hour. The pdf of X is

\(P(X=x)=\) \(\frac{e^{-5}\cdot 5^{x}}{x!},x=0,1,2,3,....\)

Therefore, the probability that 5 messages are received in a single hour is

\(P(X=5)=\frac{e^{-5}\cdot 5^{5}}{5!}=0.1755\)

(b) Number of message received in 1 hour is 5 so number of message received in 1.5 hour is 7.5. So the probability that 10 messages are received in 1.5 hours is

\(P(X=10)=\frac{e^{-7.5}\cdot 7.5^{10}}{10!}=0.0858\)

(c) Number of message received in 1 hour is 5 so number of message received in 1/2 hour is 2.5. So the probability that less than 2 messages are received in 1/2 hour is

\(P(X < 2)=\frac{e^{-2.5}\cdot 2.5^{0}}{0!}+\frac{e^{-2.5}\cdot 2.5^{1}}{1!}=0.2873\)

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The given equation is I = -2OD where I is the intensity of light, O is the aperture of the lens and D is the distance between the lens and the object. This equation is known as the Inverse Square Law of Light.

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to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below

\((\stackrel{x_1}{1}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{24}) ~\hfill~ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{24}-\stackrel{y1}{8}}}{\underset{\textit{\large run}} {\underset{x_2}{3}-\underset{x_1}{1}}} \implies \cfrac{ 16 }{ 2 } \implies 8\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8}=\stackrel{m}{ 8}(x-\stackrel{x_1}{1}) \\\\\\ y-8=8x-8\implies {\Large \begin{array}{llll} y=8x \end{array}}\)

Answer:

\(y=8x\)

Step-by-step explanation:

We can see that this line has a constant of proportionality. That is — x is proportional to y and vice versa. This means that the equation for the line's equation will be in the form:

\(y = mx\)

where \(m\) is the ratio of x to y.

This ratio is also known as the line's slope. We can solve for the slope using the equation:

slope = rise / run

slope = \(\Delta\)y / \(\Delta\)x

slope = 8 / 1

slope = 8

\(m=8\)

So, the equation of the line is:

\(y=mx\)

\(\boxed{y=8x}\)

Answer:

Step-by-step explanation:

\(\frac{1}{2}-4\frac{1}{5}=\frac{1}{2}-\frac{21}{5}\\\\\)

Find least common denominator of 2 and 5 = 10

\(=\frac{1*5}{2*5}-\frac{21*2}{5*2}\\\\=\frac{5}{10}-\frac{42}{10}\\\\=\frac{5-42}{10}\\\\=\frac{-37}{10}\\\\=-3\frac{7}{10}\)

Kaleb and Gage are standing approximately 12.72 feet apart from each other based on their angles of elevation to a basketball hoop that is 10 feet high.

Let's assume that Kaleb and Gage are standing on the same line perpendicular to the basketball hoop. Let's also assume that the distance between Kaleb and the hoop is x, and the distance between Gage and the hoop is y.

Using trigonometry, we can set up two equations based on the angles of elevation:

tan(40) = 10/x

tan(30) = 10/y

Solving for x and y:

x = 10/tan(40) ≈ 12.72 feet

y = 10/tan(30) ≈ 17.32 feet

Therefore, Kaleb and Gage are standing approximately 12.72 feet apart.

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The equation in standard form for the circle with diameter endpoints (1,17) and (1,-1) is (x - 1)^2 + (y - 8)^2 = 81.

To write the equation of a circle in standard form, we need to use the formula: (x - h)^2 + (y - k)^2 = r^2 Where (h,k) is the center of the circle and r is the radius.

We can use the midpoint formula to find the center of the circle, which is the midpoint of the diameter: Midpoint = ((x1 + x2)/2 , (y1 + y2)/2) Substituting the given endpoints, we get: Midpoint = ((1 + 1)/2 , (17 + (-1))/2) = (1, 8) So the center of the circle is (1,8).

Now we need to find the radius, which is half the length of the diameter: Length of diameter = sqrt((1-1)^2 + (17-(-1))^2) = sqrt(18^2) = 18 Radius = 18/2 = 9 Substituting the center and radius in the standard form equation, we get: (x - 1)^2 + (y - 8)^2 = 9^2 Simplifying, we get: (x - 1)^2 + (y - 8)^2 = 81

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The value of x in the given figure of parallel lines is x = 0.89.

When two parallel lines are sliced by a transversal, alternating interior angles and alternate exterior angles result in the shape "Z".

From the figure we observe that according to alternate interior angle, the angle adjacent to x + 94 is 95x.

Thus, the two angles form a straight line.

The angle of a straight line is 180 degrees.

Thus,

x + 94 + 95x = 180

96x + 94 = 180

x = 0.89

Hence, the value of x in the given figure of parallel lines is x = 0.89.

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The probability of a bulb lasting for between 557 and 561 hours is roughly 0.0382 or 3.82%

Able to utilize the standard ordinary dissemination to discover the likelihood of a bulb enduring for between 557 and 561 hours. To do this, we ought to standardize the values utilizing the equation:

z = (x - μ) / σ

where x is the bulb lifetime we're fascinated by

, μ is the cruel(mean) lifetime,

and σ is the standard deviation.

For 557 hours:

z1 = (557 - 530) / 15 = 1.8

For 561 hours:

z2 = (561 - 530) / 15 = 2.07

Employing a standard ordinary conveyance table or a calculator with a typical dissemination work, we are able to discover the probabilities corresponding to these z-scores:

P(z1 < Z < z2) = P(1.8 < Z < 2.07)

This speaks to the likelihood of a bulb enduring between 557 and 561 hours, where Z could be a standard ordinary variable.

Employing a standard ordinary dispersion table or a calculator, we discover:

P(1.8 < Z < 2.07) ≈ 0.0382

Therefore, the likelihood of a bulb enduring for between 557 and 561 hours is roughly 0.0382 or 3.82% (adjusted to four decimal places). 

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89 divided by 4.

4 goes into 80, 20 times with none left over.

4 goes into 9, 2 times with 1 left over.

Answer: 22 1/4

Hope this helps!! :)

Answer:

$135

Step-by-step explanation:

15-12=3/2=1.5

12+1.5=13.5

13.5*10=135

Answer:

$1620

Step-by-step explanation:

The area of the lawn is a trapezoid.

Area of a trapezoid = \(\dfrac12(a+b)h\)

where a and b are the parallel sides (bases) and h is the height

Therefore,

\(area=\dfrac12(15+12) \times 10 = 135 \ m^2\)

If the price of sod is $12 per square metre, then

total cost = 135 x 12 = $1620

Answer:

On day 26, both girls should be on page 60.

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

You have 7, and you take away five, which leaves you with 2

here is a drawing:

l  l  l  l  l  l  l

x x x x x l  l

Answer:  hope this helps, love. have a good day

Step-by-step explanation:

Answer:48 outfits.

Step-by-step explanation:

Number of outfits that Juan can wear

N =number of ties x number of pants x number of pants

N =4 x 3 x 4

N =48 outfits

Statement is true: If A is an invertible nxn matrix, then the equation\(Ax=b\) is consistent for each b in R. The correct option is (B).Why is it true?Proof: Suppose A is an invertible nxn matrix.

Let b be any vector in R. Since A is invertible, it has an inverse matrix A-1. Then, A-1b exists.Now, define\(x=A-1b\). Then we can write\(b=Ax\). We have shown that a solution x exists for each b. To show that this solution is unique, suppose x1 and x2 both satisfy\(Ax=b\). Then\(Ax1=Ax2=b, and so A(x1 - x2)=0\). Since A is invertible, it has a trivial nullspace.

Thus,\(x1 - x2=0\), and hence x1=x2. Therefore, the solution to \(Ax=b\) is unique. Since the solution exists for every b, the system \(Ax=b\) is consistent for every b. Therefore, the statement is true.Hence, option (B) is correct.

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