Your committee is voting on their logo. There are 7 possible logos and
you are to rank your top 3 logos. How many different combinations of 3 logos can you create?

Step-by-step explanation:

First find 28% of $19.50:

($19.50) / (100) × (28) = $5.46

Now minus the 285 from the original price:

($19.50) - ($5.46) = $14.04

The answer is $14.04

Hope it helped :)

The length of the arc CD is 3.84 units

Arc length formula is used to calculate the measure of the distance along the curved line making up the arc.

The length of an arc is expressed as;

l = θ/360 × 2πr

where r is radius of the circle and θ is the angle substended by the arc.

2πr is the circumference of the circle so we can also say that the length of an arc is

θ/360 × circumference of circle

Therefore;

l = 20/360 × 2 × 22/7 × 11

l = 9680/2520

l = 3.84 units

Therefore length of the arc CD is 3.84units

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Answer:

- 5√2 / 2   ,   - √2

Step-by-step explanation:

√2 x² + 7x + 5√2 = 0

√2          5

1              √2

(√2 x + 5) (x + √2) = 0

√2 x + 5 =0            x = - 5/√2 = - 5√2 / 2

or x + √2 = 0          x = -√2

The two column proof is written as follows

Statement                                                           Reason

line LQ || Line NP                                   given

< Q is congruent to < N                         Alternate interior angles

< L is congruent to < P                           Alternate interior angles

< LMQ is congruent to < PMN               Vertical angle theorem

Δ LMQ similar Δ PMN                            Definition of similar triangles

Similar triangles are triangles that have the same shape but may differ in size. In other words, they have the same angles but their sides may be of different lengths.

If two triangles are similar, it means that their corresponding angles are equal, and their corresponding sides are in proportion to each other.

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Using proportions, it is found that it's value before the 2-day drop was of 264 points.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, the value dropped by 25%, that is, it was 75% of the original amount, and the dropped value was of 198 points, hence the original amount was:

0.75x = 198

x = 198/0.75

x = 264

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Answer:

14 dimes and 17 quarters

Step-by-step explanation:

d and q are the number of dimes and quarters, respectively.

"31 coins, all of which are dimes and quarters."

d+q = 31

d = 31-q

"the value of the coins is $5.65"

0.10d + 0.25q = 5.65

substitution

0.10(31-q) + 0.25q = 5.65

3.10-0.10q + 0.25q = 5.65

0.15q = 2.55

q = 17

d = 31-q = 14

14 dimes and 17 quarters

The coordinates of the centroid are the average values of the \(x\)- and \(y\)-coordinates of the points \((x,y)\) that belong to the region. Let \(R\) denote the bounded region. These averages are given by the integral expressions

\(\dfrac{\displaystyle \iint_R x \, dA}{\displaystyle \iint_R dA} \text{ and } \dfrac{\displaystyle \iint_R y \, dA}{\displaystyle \iint_R dA}\)

The denominator is just the area of \(R\), given by

\(\displaystyle \iint_R dA = \int_0^8 \int_{\min(8\sin(2x), 8\cos(2x))}^{\max(8\sin(2x),8\cos(2x))} dy \, dx \\\\ ~~~~~~~~ = \int_0^8 |8\sin(2x) - 8\cos(2x)| \, dx \\\\ ~~~~~~~~ = 8\sqrt2 \int_0^8 \left|\sin\left(2x-\frac\pi4\right)\right| \, dx\)

where we rewrite the integrand using the identities

\(\sin(\alpha + \beta) = \cos(\alpha)\cos(\beta) + \sin(\alpha)\sin(\beta)\)

Now, if

\(8(\cos(2x) - \sin(2x)) = R \sin(2x + \alpha) = R \sin(2x) \cos(\alpha) + R \cos(2x) \sin(\alpha)\)

with \(R>0\), then

\(\begin{cases} R\cos(\alpha) = 8 \\ R\sin(\alpha) = -8 \end{cases} \implies \begin{cases}R^2 = 128 \\ \tan(\alpha) = -1\end{cases} \implies R=8\sqrt2\text{ and } \alpha = -\dfrac\pi4\)

Find where this simpler sine curve crosses the \(x\)-axis.

\(\sin\left(2x - \dfrac\pi4\right) = 0\)

\(2x - \dfrac\pi4 = n\pi\)

\(2x = \dfrac\pi4 + n\pi\)

\(x = \dfrac\pi8 + \dfrac{n\pi}2\)

In the interval [0, 8], this happens a total of 5 times at

\(x \in \left\{\dfrac\pi8, \dfrac{5\pi}8, \dfrac{9\pi}8, \dfrac{13\pi}8, \dfrac{17\pi}8\right\}\)

See the attached plots, which demonstrates the area between the two curves is the same as the area between the simpler sine wave and the \(x\)-axis.

By symmetry, the areas of the middle four regions (the completely filled "lobes") are the same, so the area integral reduces to

\(\displaystyle \iint_R dA \\\\ ~~~~ = 8\sqrt2 \left(-\int_0^{\pi/8} \sin\left(2x-\frac\pi4\right) \, dx + 4 \int_{\pi/8}^{5\pi/8} \sin\left(2x-\frac\pi4\right) \, dx \right. \\\\ ~~~~~~~~~~~~~~~~~~~~ \left. - \int_{17\pi/8}^8 \sin\left(2x-\frac\pi4\right) \, dx\right)\)

The signs of each integral are decided by whether \(\sin\left(2x-\frac\pi4\right)\) lies above or below axis over each interval. These integrals are totally doable, but rather tedious. You should end up with

\(\displaystyle \iint_R dA = 40\sqrt2 - 4 (1 + \cos(16) + \sin(16)) \\\\ ~~~~~~~~ \approx 57.5508\)

Similarly, we compute the slightly more complicated \(x\)-integral to be

\(\displaystyle \iint_R x dA = \int_0^8 \int_{\min(8\sin(2x), 8\cos(2x))}^{\max(8\sin(2x),8\cos(2x))} x \, dy \, dx \\\\ ~~~~~~~~ = 8\sqrt2 \int_0^8 x \left|\sin\left(2x-\frac\pi4\right)\right| \, dx \\\\ ~~~~~~~~ \approx 239.127\)

and the even more complicated \(y\)-integral to be

\(\displaystyle \iint_R y dA = \int_0^8 \int_{\min(8\sin(2x), 8\cos(2x))}^{\max(8\sin(2x),8\cos(2x))} y \, dy \, dx \\\\ ~~~~~~~~ = \frac12 \int_0^8 \left(\max(8\sin(2x),8\cos(2x))^2 - \min(8\sin(2x),8\cos(2x))^2\right) \, dx \\\\ ~~~~~~~~ \approx 11.5886\)

Then the centroid of \(R\) is

\((x,y) = \left(\dfrac{239.127}{57.5508}, \dfrac{11.5886}{57.5508}\right) \approx \boxed{(4.15518, 0.200064)}\)

the volume in the first octant bounded by\(y^2=4−x\) and y=2z is pi/36 sqrt(3).

(1) To find the volume in the first octant bounded by the surfaces \(y^2 = 4 - x\) and y = 2z, we can set up a triple integral in cylindrical coordinates.

First, we need to determine the bounds for our variables. Since we are working in the first octant, we know that 0 <= z, 0 <= theta <= pi/2, and 0 <= r.

Next, we need to find the equation for the upper and lower bounds of z in terms of r and theta. We can start with the equation \(y^2 = 4 - x\) and substitute y = 2z to get:

\((2z)^2 = 4 - x\)

\(4z^2 = 4 - x\)

\(x = 4 - 4z^2\)

We can then use this equation along with the equation z = y/2 to get the bounds for z:

\(0 < = z < = (4 - x)^(1/2)/2 = (4 - 4z^2)^(1/2)/2\)

Squaring both sides, we get:

\(0 < = z^2 < = (1 - z^2)/2\)

\(0 < = 2z^2 < = 1 - z^2\)

\(z^2 < = 1/3\)

So the bounds for z are:

\(0 < = z < = (1/3)^(1/2)\)

Finally, we can set up the triple integral in cylindrical coordinates:

V = ∫∫∫ r dz dtheta dr

with bounds:

0 <= r

0 <= theta <= pi/2

\(0 < = z < = (1/3)^(1/2)\)

and integrand:

r

So the volume in the first octant bounded by y^2=4−x and y=2z is:

V = ∫∫∫ r dz dtheta dr

= ∫ from 0 to\((1/3)^(1/2) ∫ from 0 to pi/2 ∫ from 0 to r r dz dtheta dr\)

= ∫ from 0 to\((1/3)^(1/2) ∫ from 0 to pi/2 r^2/2 dtheta dr\)

= ∫ from 0 to\((1/3)^(1/2) r^2 pi/4 dr\)

\(= pi/12 (1/3)^(3/2)\)

= pi/36 sqrt(3)

Therefore, the volume in the first octant bounded by\(y^2=4−x\) and y=2z is pi/36 sqrt(3).

(2) To find the volume bounded by z = x^2 + y^2 and z = 4, we can use a triple integral in cylindrical coordinates.

First, we need to determine the bounds for our variables. Since we are working in the region where z is bounded by \(z = x^2 + y^2\) and z = 4, we know that 0 <= z <= 4.

Next, we can rewrite the equation \(z = x^2 + y^2\) in cylindrical coordinates as \(z = r^2.\)

So the bounds for r and theta are:

0 <= r <= 2

0 <= theta <= 2pi

And the bounds for z are:

\(r^2 < = z < = 4\)

Finally, we can set up the triple integral in cylindrical coordinates:

V = ∫∫∫ r dz dtheta dr

with bounds:

0 <= r <= 2

0 <= theta <= 2pi

\(r^2 < = z < = 4\)

and integrand: 1

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The probability that the mean amount of cereal per box in a case is less than 18 ounces is 0.2743 for a random variable following a normal distribution.

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. The normal distribution appears as a “bell curve” on a graph.

Given,

X is a random variable denoting the actual amount of cereal in each box.

Mean, \(\mu\)=18.03 ounces

Standard deviation, \(\sigma\)=0.05 ounces

To determine the probability that the mean amount of cereal per box in a case is less than 18 ounces= P(X<18)

\(P(\frac{X-\mu}{\sigma} < \frac{18-\mu}{\sigma})\)

\(P(z < 18-18.03/0.05)=P(z < -0.6)\)

\(P(z < -0.6)=0.2743\)

Thus, the probability that the mean amount of cereal per box in a case is less than 18 ounces is 0.2743

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The expression for the volume of the cylinder is πB.

The cylinder is a three-dimensional figure that has a radius and a height.

The volume of a cylinder is πr²h.

Example:

The volume of a cup with a height of 5 cm and a radius of 2 cm is

Volume = 3.14 x 2 x 2 x 5 = 62.8 cubic cm

We have,

Volume = πr²h

Base area = πr²

Now,

B = πr²

r² = B/h

r = √(B/h)

Now,

Volume.

= πr²h

= π x B/h x h

= πB

Thus,

The volume of the cylinder is πB.

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The correct answer is Bh

Answer:

Around 22200 dollars

Step-by-step explanation:

Firstly, it was depreciating 20% per year for 17 years. So, if we were to go back in time, it would be appreciating by 25%. Therefore, after doing the plugging in, it is 500 * 1.25^17. The initial value is around 22200. It is around 22204, to be exact.

Answer:

2688 cm³

Step-by-step explanation:

2058×704/539 = 2688 cm³

Given

Answer

Since it is given

KJ=KL

HK=HK (Common)

The only condition to show SSS congruency is HJ = HL

Answer:

To determine the greatest number of books and magazines Julie can put on each shelf without mixing them, we need to find the highest common factor (HCF) of the given numbers.

The prime factorization of 36 is 2^2 * 3^2.

The prime factorization of 54 is 2 * 3^3.

To find the HCF, we take the highest power of each common prime factor. In this case, the HCF would be 2^2 * 3^2, which is 4 * 9 = 36.

Therefore, Julie can put a maximum of 36 books and 36 magazines on each shelf without mixing them.

HOPE I HELPED

Answer:

15

Step-by-step explanation:

According to propagation rule,

\(\frac{9}{3} =\frac{x}{5} \\45=3x\\x=15\)

Therefore, option (B) is correct

Answer:

8. Because if you add the degree of angle 7 to angle 8, then it makes a 180 degree angle, which is supplementary. Hope this helped

Answer:

DNA from multiple beings have been found all over the world, this is also a theory because of the ability for the continents to be formed together, they almost click together like puzzle pieces!

Step-by-step explanation:

Answer:

Another piece of evidence that could support the idea that continents were once joined together could be that mountain ranges can be found on multiple continents even though now they are very far apart. For example, the Appalachian Mountains can be connected to mountains in Europe.  This supports the idea that continents were once joined together.

Let me know if this helps!

This is the closed-form expression for the summation, which can be directly computed from k.

The expression "3 + 5 + 7 + 9 + ... + 2k+1" is a finite arithmetic series, which can be expressed in closed form using the formula:

Sn = n/2 * (2a + (n-1)d)

where:

n = number of terms

a = first term

d = common difference

In this case, we have:

n = k

a = 3

d = 2

Substituting the values in the formula, we get:

Sn = k/2 * (2 * 3 + (k-1) * 2)

= k/2 * (6 + 2k - 2)

= k/2 * (2k + 4)

Thus, This is the closed-form expression for the summation, which can be directly computed from k.

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The time it takes the ball to strike the ground after it is thrown, found using the kinematic equation, H = -16·t² - 24·t + 200 is approximately 2.86 seconds

A kinematic equation is an equation of the motion of an object moving with a constant acceleration.

The direction in which the ball is thrown = Downwards

Height of the building = 200 foot

Initial velocity of the ball = 24 ft./s

The kinematic equation that indicates the height of the ball after t seconds is, H = -16·t² - 24·t + 200

At ground level, H = 0, therefore;

H = 0 = -16·t² - 24·t + 200

-16·t² - 24·t + 200 = 0

-2·t² - 3·t + 25 = 0

t = (3 ± √((-3)² - 4 × (-2)×25))/(2×(-2))

t = (3 ± √(209))/(-4)

t =  (3 + √(209))/(-4) ≈ -4.36 and t =  (3 - √(209))/(-4)) ≈ 2.86

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\(2x - 8y = - 16\)

Subtract sides 2x

\( - 2x + 2x - 8y = - 2x - 16\)

\( - 8y = - 2x - 16\)

Negatives simplifies

\(8y = 2x + 16\)

Divide sides by 8

\( \frac{8y}{8} = \frac{2x + 16}{8} \\ \)

\(y = \frac{2}{8} x + \frac{16}{8} \\ \)

\(y = \frac{1}{4} x + 2 \\ \)

Done...

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

We have ST=5x, TU=3x+32 and they're equal if T is the midpoint:

5x = 3x + 32

2x = 32

x = 16

ST = 5x = 80

So TU = 80 and SU=160

Answer: Second choice

Step-by-step explanation:

I do not understand .____.

The computation illustrates that the rebate fraction is 0.18

Given that : the total number of payments = 36

The number of payments made = 21

Remaining payments = 36-21 =15

We know that the sum of the digits for n payments

S = (n(n+1))/2

sum of the digits payments remaining = 15*(15+1)/2

= (15*16)/2

= 240/2

= 120

Sum of the digits number of payments = 36*(37)/2

= 1332

= 666

Rebate fraction = 120/666 =0.18

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Complete question

Calculate the missing information for the installment loan that is being paid off early.

Number of payment = 36

Payment made = 21

Payment remaining = ?

Rebate fraction = ?

a) Situations when an observer needs to be introduced and the role of each matrix: In order to observe the state of a system in practice, an observer must be introduced. The observer's role is to assess the system's state variables based on the system's input and output values, as well as the system's dynamics. The observer consists of three matrices:L: State feedback gain matrix M: Determines the observer's internal dynamics N: Maps the output signal to the observer's inputThe purpose of the observer is to estimate the system's states so that they can be fed back into the control loop.

b) Det[s1 - L] discussion: When designing an observer, the choice of observer poles has a significant impact on the system's efficiency. If the observer poles are placed far too close to the system poles, the observer may become unstable and diverge from the true state values. Alternatively, if the observer poles are placed far too far from the system poles, the observer may not be sensitive enough to changes in the system's states.In this context, det[s1 - L] refers to the determinant of the system's matrix minus the state feedback gain matrix. To ensure that the observer's poles are not too close or too far from the system's poles, this determinant must be non-zero.

c) Designing state observer: The observer's gain matrix L can be determined using the Ackerman formula.

By using Ackerman formula, the observer gain matrix is:L = acker(A', C', [s1, s2])L = [21 12]s1 = -4; s2 = -5 The observer's matrix M is given by:M = A - LC = [0 1;-1 -2] - [21; 12][1 0]M = [-21 -12;-21 -8]

The observer's matrix N is given by:N = B - LD = [0] - [21; 12][0]N = [0]d) Observer block diagram with matrices:Based on the information given above, the observer's block diagram with matrices L, M, and N can be presented in the following diagram:state observer block diagram

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the answer is 1/8. Because you divide how many pieces there are by that same number.

Answer: 0.9

Step-by-step explanation: First, divide 18 by 19. The exact answer to the fraction is 0.94736842105. To round to the nearest tenth, check if the answer directly to the right of the number after the decimal point is above or below five. In this case, it is below, rounding the answer to 0.9. Hope that helps!

Answer:

13

\(FC + CB = \frac{DC}{2} +\frac{AB}{2}\)

Step-by-step explanation:

Line CB is half of Line AB, which the questions says line AB is the length of 20. 20/2 = 10.

Line CB is 10.

The question also says that point F is the midpoint of line DC. Line DE is 12. Line DC is half of 12, which means its 6. F is the midpoint of Line DC which means it's also half of Line DC, which is 3.

Line FC is 3.

The question asks you to find the value of Line FC PLUS Line CB. So 10 + 3 = 13.

Your answer is 13.

Answer:

13

Step-by-step explanation:

AB and DE split each other equally in half so

if AB = 20 then CB = 10

and if DE = 12 then DC = 6

meaning that FC = 3

3+10=13