what is (13X + 9k)+(17x +6k), simplified?

\(m\angle E=\sin \dfrac{\sqrt{10}}{2\sqrt5}=\sin \dfrac{\sqrt2}{2}=45^{\circ}\)

Answer:

12

Step-by-step explanation:

There would be 12 girl students in a class of 21 students.

"A proportion is a mathematical statement where two or more ratios are equivalent."

We have been given that, the ratio of girls to the total number of students in class is 4:7

We need to find the number of girl students if the class has 21 students in all.

Let 'n' represents the number of girl students.

⇒ \(\frac{4}{7} = \frac{n}{21}\)

⇒ \(4\times 21 = n\times 7\)                        ......................(cross product)

⇒ \(84 = n\times 7\)

⇒ \(n=\frac{84}{7}\)                                    ......................(Divide each side by 7)

⇒ \(n=12\)

Hence, there would be 12 girls if class has 21 students in all.

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Answer:

A. $0

B. 0

Step-by-step explanation:

A. If you deposit $10 in an empty bank account and you withdraw $10 from the account, the amount of money left in the account will be:

10 - 10 = $0

B. If you start at 0, add 7 and subtract 7, you'll end up at:

0 + 7 - 7 = 0

Even though the table appears to have varied shapes depending on the angle from which it is seen, Baby Mary recognizes the table as having the same shape. Shape constancy can be seen in this situation.

             Shape constancy is the ability of an object to retain its shape, size, and orientation even when viewed from different perspectives or angles. In essence, when the shape of an object is known, this allows an individual to recognize the object as a whole.

           It's an important part of perception, and it's what allows us to recognize objects even when they're partially obscured or viewed from a different angle. A child can recognize objects as having the same shape, regardless of the angle from which they are viewed. As the object is observed from a variety of angles, its proportions and the shapes of its edges and sides change. Even so, the child perceives the object as having a consistent shape, size, and orientation.

          This can be attributed to the ability of a child's brain to maintain a mental image of the object's actual shape, even when presented with an altered image.

            As a result, a child may perceive an object as having a consistent shape, even if it appears to be different from one angle to another.

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Your answer: A  −14 × {23 + (−47)} = [−14 × 23] + [−14 × (−47)]  This example demonstrates the distributive property of multiplication over addition for rational numbers, which states that for any rational numbers a, b, and c: a × (b + c) = (a × b) + (a × c).

The correct answer is A: −14 × {23 + (−47)} = [−14 × 23] + [−14 × (−47)]. This is an example of the distributive property of multiplication over addition for rational numbers because we are multiplying −14 by the sum of 23 and −47, and we can distribute the multiplication to each term inside the parentheses by multiplying −14 by 23 and −14 by −47 separately, and then add the two results together. This is the basic definition of the distributive property of multiplication over addition. Option B shows the distributive property of multiplication over subtraction, option C shows the product of multiplication and addition, and option D is not a valid equation.

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The dimensions of the base are 180 feet in length and 165 feet in width.

The whole length of any closed shape's boundary is known as its perimeter. Let's use an illustration to try to comprehend this. You may have a sizable square-shaped farm, for instance. You now decide to fence your farm in order to protect it from stray animals. Finding the entire length of the farm's boundary is as simple as multiplying the length of one side of the farm by 4. There are a lot of situations like this when we can be applying the perimeter-finding notion without even realizing it.

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Value of r is different for every series

let

a , b , c , d ..... be geometric series then

r = b/a or d/c and so on

where r is common ratio

Answer:

c = 45 + 3m

c = cost

m = # of movies

Step-by-step explanation:

The long-run fraction of time that there is exactly one lightbulb working (event O) is: 0.228.

Let's use the following notation:

Let W denote the event that both lightbulbs are working,

let O denote the event that one lightbulb is working, and

let B denote the event that both lightbulbs are burnt out.

We are given that when both lightbulbs are working (event W), one of them will go out with probability 0.03.

Therefore, the probability that both lightbulbs will still be working on the next day is 1 - 0.03 = 0.97.

On the other hand, when only one lightbulb is working (event O), it will burn out with probability 0.07, and the other lightbulb is already burnt out.

Hence, the probability of moving from O to B is 1.

We can set up the following system of equations to model the probabilities of being in each state on the next day:

P(W) = 0.97P(W) + 0.5P(O)

P(O) = 0.03P(W) + 0.93P(O) + 1P(B)

P(B) = 0.07P(O)

Note that in the first equation, we use 0.97 because the probability of staying in W is 0.97, and the probability of moving to O is 0.5 (because there are two ways for one of the lightbulbs to go out).

Simplifying the system of equations, we get:

0.03P(W) - 0.5P(O) = 0

-0.03P(W) + 0.07P(O) - 1P(B) = 0

0P(W) - 0.07P(O) + 1P(B) = 0

Solving for P(O), we get:

P(O) = 0.3P(W)

Substituting this into the second equation, we get:

-0.03P(W) + 0.07(0.3P(W)) - P(B) = 0

Simplifying, we get:

P(B) = 0.004P(W)

We also know that the sum of the probabilities of being in each state must be 1:

P(W) + P(O) + P(B) = 1

Substituting the expressions for P(O) and P(B), we get:

P(W) + 0.3P(W) + 0.004P(W) = 1

Solving for P(W), we get:

P(W) = 0.762

Therefore, the long-run fraction of time that there is exactly one lightbulb working (event O) is:

P(O) = 0.3P(W) = 0.228.

Approximately 22.8% of the time, there will be exactly one lightbulb working.

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The magnitude of the final velocity of the cue ball is (B) 0.56m/s.

How to calculate the magnitude of the final velocity?

The magnitude of the final velocity can be calculated by following the steps:

Assuming all pool balls have the same mass: 0.4kg

Let the final velocity of the cue ball be x.

Now, To find the final velocity:

Therefore, the magnitude of the final velocity of the cue ball is (B) 0.56m/s.

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The correct question is given below:

In a game of pool, a 0.4 kg cue ball is traveling at +0.80 m/s when it hits a slower striped ball moving at +0.38 m/s. After the collision, the striped ball moves off at +0.62 m/s. What is the magnitude of the final velocity of the cue ball? Assume all pool balls have the same mass.

A. 0.20 m/s

B. 0.56 m/s

C. 1.0 m/s

D. 1.8 m/s

Answer: 0.56m/s

Step-by-step explanation:

Answer: the coefficient is 5

Answer: New line = 4AB

Step-by-step explanation:

if AB a line through center of parallelogram RSTU is drawn , then, after dealation with scale factor k= 4 , the length of new line through center = 4 x AB or 4AB.

The relationship will the new line have with line AB :

New line = 4AB

The diver collected water samples at every 3 meters, starting from 5 meters below the water surface, up to a final depth of 35 meters.

We can find the number of samples collected by dividing the total depth range by the distance between each sample and then adding 1 to include the first sample.

The total depth range is:

35 m - 5 m = 30 m

The distance between each sample is 3 m, so the number of samples is:

(30 m) / (3 m/sample) + 1 = 10 + 1 = 11

Therefore, the diver collected a total of 11 water samples.

Answer:

A,C and D are true

Step-by-step explanation:

∆EFG

∆RST

∆LMN

Answer: The answer is A EFG I took the quiz and got it right hope this helps

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

3% = 3/100

So we can eliminate the first answer.

The proportions have to match each other so the number nine should be above and thus the x has only the option of being under it.

As a result, we eliminate the third answer and remain with one reasonable answer

The area of the square is changing at 12√2 + 2√2t square inches/minute when the circle is increasing at 1 in/min.

Let us find the relationship between r and s using the Pythagorean theorem. Since the square is inscribed in the circle, the diameter of the circle is equal to the diagonal of the square.

2r = s√2
Squaring both sides, we get:
4r² = 2s²or s² = 2r²
Dividing by 2 on both sides, we get:
s²/2 = r²
Differentiating both sides with respect to t, we get:
ds²/dt = 2r (dr/dt)
Dividing both sides by 2s, we get:
ds/dt = r (dr/dt) / s

Substituting r² = s²/2,

\(ds/dt = r (dr/dt) / √2s2s ds/dt = r (dr/dt)s ds/dt = (r/2) (dr/dt)2s ds/dt = r (dr/dt) or dA/dt = 2s ds/dt = 2r (dr/dt)\)

Now, substituting r² = s²/2,

dA/dt = 2s ds/dt = 2(√2 s) (dr/dt) = 2(√2) r (dr/dt)

Now, substituting dr/dt = 1 in/min and r = 6 in (since the circle is increasing at 1 in/min, the radius after t minutes is 6 + t),

dA/dt = 2(√2) (6 + t) (1) = 12√2 + 2√2t square inches/minute

Therefore, the area of the square is changing at a rate of 12√2 + 2√2t square inches/minute.

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The volume under the elliptic paraboloid \(z = 3x^2 + 6y^2\) and over the rectangle R = [-4, 4] x [-1, 1] is 256/3 cubic units.

To calculate the volume under the elliptic paraboloid z = 3x^2 + 6y^2 and over the rectangle R = [-4, 4] x [-1, 1], we need to integrate the height of the paraboloid over the rectangle. That is, we need to evaluate the integral:

\(V =\int\limits\int\limitsR (3x^2 + 6y^2) dA\)

where dA = dxdy is the area element.

We can evaluate this integral using iterated integrals as follows:

V = ∫[-1,1] ∫ \([-4,4] (3x^2 + 6y^2)\) dxdy

= ∫[-1,1] [ \((x^3 + 2y^2x)\) from x=-4 to x=4] dy

= ∫[-1,1] (128 + 16\(y^2\)) dy

= [128y + (16/3)\(y^3\)] from y=-1 to y=1

= 256/3

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The function f(x) = 1/x^2 is defined for all x except x = 0. To find the nth degree Taylor approximation of f(1.02) about x = 1, we need to calculate the nth derivative of f(x) and evaluate it at x = 1.

The function f(x) = 1/x^2 can be written as f(x) = x^(-2). Taking the derivatives of f(x), we have:

f'(x) = -2x^(-3)

f''(x) = 6x^(-4)

f'''(x) = -24x^(-5)

...

The nth derivative of f(x) can be written as f^n(x) = (-1)^(n+1) * (2n)! * x^(-(n+2)). To find the nth degree Taylor approximation, we evaluate the nth derivative at x = 1 and multiply it by (x - 1)^n/n!. The nth degree Taylor approximation Tn of f(1.02) about x = 1 is given by:

Tn = f(1) + f'(1)(x - 1) + f''(1)(x - 1)^2/2! + f'''(1)(x - 1)^3/3! + ... + f^n(1)(x - 1)^n/n!

Substituting the derivatives at x = 1, we have: Tn = 1 + (-2)(1.02 - 1) + 6(1.02 - 1)^2/2! + (-24)(1.02 - 1)^3/3! + ... + (-1)^(n+1) * (2n)! * (1.02 - 1)^n/n!. This expression represents the nth degree Taylor approximation of f(1.02) about x = 1.

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Answer:

There were 120 marbles to start

Step-by-step explanation:

Let x be the number of marbles at the start

x* 5/12 = number of marbles given away

1 -5/12 = 7/12 = fraction of marbles left

x * 7/12 = number of marbles left

x * 7/12 = 70

Multiply each side by 12/7

x *7/12 * 12/7 = 70 * 12/7

x =120

There were 120 marbles to start

we get that\($$\phi=\sin^{-1}\left(\frac{15}{34}\right)\approx 26.1^{\circ}$$\) Hence,  option (B) is correct.

We know that the length of member BC in the figure is 60 mm. So, the correct option among the given options is option (B) that is,  \(ϕ=sin−1[20 mm⋅sin15∘60 mm].\)

Now, let us solve the problem.To find the value of ϕ, we can use the sine law, which states that:\($$\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$$\)

Now, from the given figure, we can see that the triangle ABC is a right-angle triangle, and we can find the value of angle BAC using trigonometric ratios.

So, \($$\tan(\angle BAC)=\frac{20\text{ mm}}{60\text{ mm}}$$$$\\)

Rightarrow \(\angle BAC=\tan^{-1}\left(\frac{1}{3}\right)\approx 18.4^{\circ}$$\)

Now, let us use the sine rule to find the value of \($\phi$.\)

According to the sine rule,\($$\frac{\sin\phi}{20\text{ mm}}=\frac{\sin(180^{\circ}-18.4^{\circ}-\phi)}{60\text{ mm}}$$$$\\)

Rightarrow \frac{\sin\phi}{20\text{ mm}}=\frac{\sin(161.6^{\circ}-\phi)}{60\text{ mm}}$$

Now, cross-multiplying and simplifying, we get:\($$\sin\phi=\frac{20\text{ mm}\cdot\sin(161.6^{\circ}-\phi)}{60\text{ mm}}$$$$\\)

Rightarrow \(\sin\phi=\frac{1}{3}\cdot\sin(161.6^{\circ}-\phi)$$\)

Now, we can use the identity:\($$\sin(A-B)=\sin A\cos B-\cos A\sin B$$\)

to simplify the equation.\($$3\sin\phi=\sin(161.6^{\circ})\cos\phi-\cos(161.6^{\circ})\sin\phi$$$$\\)

Rightarrow \((3+\sin(161.6^{\circ}))\sin\phi=\sin(161.6^{\circ})\cos(161.6^{\circ})$$$$\\)

Rightarrow\(\sin\phi=\frac{\sin(161.6^{\circ})\cos(161.6^{\circ})}{3+\sin(161.6^{\circ})}$$$$\Rightarrow \sin\phi=\frac{\frac{1}{2}\cdot(-\frac{3}{5})}{3+\frac{1}{2}\cdot(-\frac{3}{5})}=\frac{15}{34}$$\)

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The complete question is :The length of member BC in the Figure below is 60 mm.

Determine the angle ϕ.

A. ϕ=sin−1[20 mm⋅sin115∘60 mm]

B. ϕ=sin−1[20 mm⋅sin15∘60 mm]

C. ϕ=sin−1[20 mm⋅sin115∘70.81 mm]

D. ϕ=sin−1[60 mm⋅sin65∘70.81 mm]

E. ϕ=sin−1[70.81 mm⋅sin15∘20 mm]

The probability of Angela rolling another three on her next roll, after rolling nine consecutive threes, is still 1/6.

If Angela rolls a fair die nine times and each time she rolls a three, it means that she has already rolled nine consecutive threes. Each roll of a fair die is an independent event, which means the outcome of one roll does not affect the outcome of another roll.

The probability of rolling a three on any given roll of a fair die is 1/6, as there are six possible outcomes (numbers 1 to 6) and only one favorable outcome (rolling a three).

Therefore, the probability of Angela rolling another three on her next roll, after rolling nine consecutive threes, is still 1/6. The previous rolls do not influence the probability of rolling a three on the next roll, as each roll is independent of the others.

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Answer:

The answer is 2

Step-by-step explanation:

The slope of Abha's climb is given by the equation

Slope m = 2

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be A

Now , let the point be P ( x , y )

And , the equation is given by

The horizontal distance covered by Abha x = 20 yards

The vertical distance covered by Abha y = 40 yards

Now , the slope of the point is given by the equation

Slope m = vertical distance covered by Abha  / horizontal distance covered by Abha

Substituting the values in the equation , we get

Slope m of Abha's climb = y/x

Slope m of Abha's climb = 40 / 20

Slope m of Abha's climb = 2

Therefore , the slope of the line is m = 2

Hence , The slope of Abha's climb is given by the equation Slope m = 2

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Answer:

Step-by-step explanation:

4x+4=4

-4 to get 4x alone

4x=0

therefore x=0

Find the value of x :-

4x + 4 = 4

x = 0

=> 4x + 4 = 4

=> 4x = 4 - 4

=> 4x = 0

=> x = 0/4

=> x = 0

Answer:

\(2abcosC = 37\)

Step-by-step explanation:

Given

\(a^2 + b^2 - 2abcosC = c^2\)

Required

\(2abcosC\)

\(a^2 + b^2 - 2abcosC = c^2\)

Add \(2abcosC\) to both sides

\(a^2 + b^2 - 2abcosC+2abcosC = c^2+2abcosC\)

\(a^2 + b^2 = c^2+2abcosC\)

Subtract \(c^2\) from both sides

\(a^2 + b^2 -c^2= c^2 -c^2+2abcosC\)

\(a^2 + b^2 -c^2= 2abcosC\)

From the attachment:

\(a = 4\) \(b = 5\) and \(c = 2\)

So, we have:

\(4^2 + 5^2 -2^2= 2abcosC\)

\(16 + 25 -4= 2abcosC\)

\(37= 2abcosC\)

i.e.

\(2abcosC = 37\)

Answer:

A. 37

Step-by-step explanation:

Let's assume Eric's height before summer is x cm. After summer, he became 5% taller, which means his new height is 1.05x cm. We also know that his new height is 151.2 cm. So we can set up an equation:

1.05x = 151.2

To solve for x, we can divide both sides by 1.05:

x = 151.2 / 1.05

x = 144 cm

Therefore, Eric's height before summer was 144 cm.

The trigonometric ratio for sin Z is 3/5 in the given right triangle.

Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.

The right triangle is given in the question, as shown.

As we know the cosine ratio, is as follows:

cos Z = base/hypotenuse

cos Z = YZ/XZ

cos Z = 32/40

cos Z = 4/5

Now, as we know the sine ratio, is as follows:

sin Z = √(1 - cos² Z)

sin Z = √(1 - (4/5)²)

sin Z = √(1 - 16/25)

sin Z = √(9/25)

sin Z = 3/5

Thus, the trigonometric ratio for sin Z is 3/5.

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There are 11 zeros in the given fraction's terminating decimal representation.

To determine the number of zeros to the right of the decimal point and before the first non-zero digit in the terminating decimal representation of  \($\frac{1}{2^5\cdot5^8}$\) , we need to simplify the fraction.

\($\frac{1}{2^5\cdot5^8}$\)  can be rewritten as \($\frac{1}{32\cdot390625}$\) .

To find the decimal representation of this fraction, we divide 1 by the product of the denominators: \($32\cdot390625$\) .

Performing the division, we get:

\($0.000000000000512$\)

In this decimal representation, there are 11 zeros located to the right of the decimal point and before the first non-zero digit, which is 5. Therefore, there are 11 zeros in the given fraction's terminating decimal representation.

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The mean absolute deviation for the group of household incomes is approximately 14.8 (rounded to the nearest tenth).

To calculate the mean absolute deviation (MAD) for a group of data, we follow these steps:

Find the mean (average) of the data set.

Subtract the mean from each data point, obtaining the deviations.

Take the absolute value of each deviation.

Find the mean of the absolute deviations.

Given the household incomes for 10 different households:

38, 45, 76, 93, 50, 54, 29, 44, 62, 31

Let's calculate the MAD step by step:

Find the mean (average):

Mean = (38 + 45 + 76 + 93 + 50 + 54 + 29 + 44 + 62 + 31) / 10

Mean = 482 / 10

Mean = 48.2

Calculate the deviations:

Deviation for each data point = Data point - Mean

Deviation for 38 = 38 - 48.2 = -10.2

Deviation for 45 = 45 - 48.2 = -3.2

Deviation for 76 = 76 - 48.2 = 27.8

Deviation for 93 = 93 - 48.2 = 44.8

Deviation for 50 = 50 - 48.2 = 1.8

Deviation for 54 = 54 - 48.2 = 5.8

Deviation for 29 = 29 - 48.2 = -19.2

Deviation for 44 = 44 - 48.2 = -4.2

Deviation for 62 = 62 - 48.2 = 13.8

Deviation for 31 = 31 - 48.2 = -17.2

Take the absolute value of each deviation:

Absolute deviation for each data point = |Deviation|

Absolute deviation for -10.2 = 10.2

Absolute deviation for -3.2 = 3.2

Absolute deviation for 27.8 = 27.8

Absolute deviation for 44.8 = 44.8

Absolute deviation for 1.8 = 1.8

Absolute deviation for 5.8 = 5.8

Absolute deviation for -19.2 = 19.2

Absolute deviation for -4.2 = 4.2

Absolute deviation for 13.8 = 13.8

Absolute deviation for -17.2 = 17.2

Find the mean of the absolute deviations:

Mean Absolute Deviation (MAD) = (10.2 + 3.2 + 27.8 + 44.8 + 1.8 + 5.8 + 19.2 + 4.2 + 13.8 + 17.2) / 10

MAD = 148 / 10

MAD = 14.8

To the nearest tenth, this means that the mean absolute deviation for the group of household incomes is around 14.8.

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