Sally has seen four movies. The ticket prices were: $13, $8, $10, $10 The next movie she plans to see in is 3D and the ticket price is $34. Circle one of the following that will not change after Sally sees the next movie

The general solution of the equation y' + ay = 0, where a is any constant, is y = Ce^(-ax), where C is an arbitrary constant.

To find the general solution of the given first-order linear homogeneous differential equation, y' + ay = 0, we can use the method of separation of variables.

Step 1: Rewrite the equation in the standard form:

y' = -ay

Step 2: Separate the variables:

dy/y = -a dx

Step 3: Integrate both sides:

∫(1/y) dy = -a ∫dx

Step 4: Evaluate the integrals:

ln|y| = -ax + C1, where C1 is an integration constant

Step 5: Solve for y:

|y| = e^(-ax + C1)

Step 6: Combine the constants:

|y| = e^C1 * e^(-ax)

Step 7: Combine the constants into a single constant:

C = e^C1

Step 8: Remove the absolute value by considering two cases:

(i) y = Ce^(-ax), where C > 0

(ii) y = -Ce^(-ax), where C < 0

The general solution of the differential equation y' + ay = 0 is given by y = Ce^(-ax), where C is an arbitrary constant.

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Using the Law of Cosines, we can find the value of CE when given the lengths of AE, DE, and BE. Specifically, we can use the equation:

CE^2 = AE^2 + BE^2 - 2(AE)(BE)cos(C), where C is the angle between AE and BE. To solve for CE, we first need to find the value of cos(C).

To do this, we can use the Law of Cosines again, but this time to find the measure of angle C. Using the equation:

DE^2 = AE^2 + BE^2 - 2(AE)(BE)cos(C)

we can solve for cos(C) as:

cos(C) = (AE^2 + BE^2 - DE^2) / (2(AE)(BE))

Substituting the given values, we get:

cos(C) = (14^2 + 6^2 - 7^2) / (2(14)(6)) = 85 / 168 ≈ 0.506

Now that we have found the value of cos(C), we can substitute it back into the original equation to solve for CE:

CE^2 = 14^2 + 6^2 - 2(14)(6)(0.506) ≈ 124.84

Taking the square root, we get:

CE ≈ 11.17

Therefore, the value of CE is approximately 11.17 when AE = 14, DE = 7, and BE = 6.

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\( \sin(x - 20°) = \cos(42°) \)

\( \sin(x - 20°) = \sin(90° - 42°) \)

\( \sin(x - 20°) = \sin 48°\)

\(x - 20° = 48°\)

\(x = 48° + 20°\)

\(x = 68°\)

Answer:68

Step-by-step explanation:

Answer:

5/6

Step-by-step explanation:

The slope of a perpendicular line is the negative reciprocal of the other.

Given: m = -6/5

Negative: m = 6/5

Reciprocal: m = 5/6

Answer:

\( x = 20 \)

Step-by-step explanation:

\( \frac{3}{5}x - \frac{1}{4}x = 7 \)

The LCD is 20, so multiply both sides of the equation by 20.

\( 20(\frac{3}{5}x - \frac{1}{4}x) = 20 \times 7 \)

\( 4 \times 3x - 5 \times x = 140 \)

\( 12x - 5x = 140 \)

\( 7x = 140 \)

\( x = 20 \)

Answer:

7 & 5

Step-by-step explanation:

7+5=12
7-5=2
5-7=-2

Answer:

5 and 7

Step-by-step explanation:

5 + 7 = 12

5 - 7 = -2

C, figure C

hope this helps, and have a good day! :)

The angle measures of the polygon are 60°, 120°, 120°, and 60°.
To find the value of a, we can use the fact that the sum of the interior angles of a polygon with n sides is (n-2) times 180 degrees. In this case, we have a polygon with 4 sides, so the sum of its interior angles is (4-2) times 180 degrees, which is 360 degrees.
Using this information, we can set up the equation:
a + 2a + 2a + a = 360
Simplifying, we get:
6a = 360
Dividing both sides by 6, we get:
a = 60
So the value of a is 60.
To find the angle measures of the polygon, we can use the fact that each angle in a regular polygon with n sides has a measure of (n-2)/n times 180 degrees. In this case, we have a polygon with 4 sides, so each angle has a measure of (4-2)/4 times 180 degrees, which is 90 degrees.
Therefore, the angle measures of the polygon are:
90 degrees, 90 degrees, 90 degrees, and 90 degrees.
a + 2a + 2a + a = 360
Now, we can simplify and solve for 'a':
6a = 360
a = 360 / 6
a = 60
Now that we have the value of 'a', we can find the angle measures of the polygon:
1st angle: a = 60 degrees
2nd angle: 2a = 2 * 60 = 120 degrees
3rd angle: 2a = 120 degrees (same as the 2nd angle)
4th angle: a = 60 degrees (same as the 1st angle)

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Tracey paid approximately 29.8% of the original price for the item.

To find the percentage of the original price that Tracey paid, we can use the formula:

Percentage = (Amount Paid / Original Price) * 100

Let's plug in the given values:

Percentage = (155 / 520) * 100

Percentage = 0.2980769230769231 * 100

Percentage ≈ 29.8%

So, Tracey paid approximately 29.8% of the original price for the item.

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Trade discount is the discount given to a retailer or wholesaler in the list price of a product for purchasing a specific amount or achieving a certain volume of sales.

It is a discount given to traders to encourage them to buy products in bulk. Here is the calculation of trade discount amount for a product with a list price of $440 and a trade discount rate of 30%

:Given, list price of the product = $440Trade discount rate = 30%Discount amount = Trade discount rate × List price

Discount amount = 30% × $440Discount amount = 0.3 × $440Discount amount = $132Therefore, the trade discount amount for the product with a list price of $440 and a trade discount rate of 30% is $132.

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Using Euler's Method with a step size of h = 0.1, the approximate values of the solution at t = 0.1, 0.2, 0.3, 0.4, and 0.5 are:

t = 0.1: y ≈ 1.1

t = 0.2: y ≈ 1.22

t = 0.3: y ≈ 1.34

t = 0.4: y ≈ 1.47

t = 0.5: y ≈ 1.61

To use Euler's Method, we start with an initial condition. In this case, the given initial condition is y(0) = 1. We can then iteratively calculate the approximate values of the solution at each desired time point using the formula:

Yn = Yn-1 + h * F(Xn-1, Yn-1)

Here, h represents the step size (0.1 in this case), Xn-1 is the previous time point (t = Xn-1), Yn-1 is the solution value at the previous time point, and F(Xn-1, Yn-1) represents the derivative of the solution function.

For the given differential equation +2y = 2 - ey, we can rearrange it to the form y' = (2 - ey) / 2. The derivative function F(Xn-1, Yn-1) is then (2 - eYn-1) / 2.

Using the initial condition y(0) = 1, we can proceed with the calculations:

t = 0.1:

Y1 = Y0 + h * F(X0, Y0)

= 1 + 0.1 * [(2 - e^1) / 2]

≈ 1 + 0.1 * (2 - 0.368) / 2

≈ 1 + 0.1 * 1.316 / 2

≈ 1 + 0.1316

≈ 1.1

Similarly, we can calculate the approximate values of the solution at t = 0.2, 0.3, 0.4, and 0.5 using the same formula and previous results.

Using Euler's Method with a step size of h = 0.1, we found the approximate values of the solution at t = 0.1, 0.2, 0.3, 0.4, and 0.5 to be 1.1, 1.22, 1.34, 1.47, and 1.61, respectively.

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The number of days spent or taken by assistant with work efficiency of 2 units per day to do the work alone is equals to the 7.5 days.

We have provide that there is a carpenter and his assistant can do a piece of work.

Number of days taken by both carpenter and his assistant to do a piece of work = 3 days.

Number of days taken by carpenter and to do the same piece of work alone = 5 days.

We have to determine number of taken by assistant and to do the same piece of work alone.

Let the required number of days that the assistant take to do the work alone be 'x days'. As we know, total available work units = LCM (3,5) = 15 units

Ability or efficiency of a person or man is calculated by dividing the total work units to the number of working days spent to do the work.

Now, Ability or efficiency of both carpenter and his assistant work together = 15/5

= 3 units/day

Similarly, Ability or efficiency of carpenter = 15/3

= 5 units/day

So, Ability or efficiency of assistant= 5 - 3 = 2 -(1)

Using efficiency formula, efficiency of assistant

= 15/x --(2)

from (1) and(2), 15/x = 2

=> 2x = 15

=> x = 7.5

Hence, required number of days are 7.5 days.

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Correct option is   -1,3,4,7 ,, More the data , more is the variance. Observe the range of each data set. Range = Maximum - Minimum  So it has largest variance among given data sets.

\(3,5,8,9,10\)

\(mu = (3+5+8+9+10)/5 = 7\)

\(x\\\) \(x-mu = x-7\) \((x-mu)2\)

3        -4                             16

5        -2                              4

8        1                               1

9        2                              4

10        3                              9

35         0                              34

\(Variance = sum of (x - mu)2 / N\)

\(= 34/5\)

\(= 6.8\)

Correct option is

\(6.8\)

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Answer:

its b -4 and 2 the line is inthe x axis

Answer:

42 cubic units

Step-by-step explanation:

2x3x7

Step-by-step explanation:

4x+6+7x-9=12x-7-×

4x-3+7x=12x-7

11x-3=12x-7

add the numbers

11x=12x-4

x=4

Answer:

Yes

Step-by-step explanation:

Yes because if you insert -39 for x and 42 for y then your equation is:

42 = -39 + 81

If you were to solve this equation it would be true.

Answer:

its 16  

i had this question on edge

Answer:

c

Step-by-step explanation:

Each piece of the nylon is 30 feet long.

Let's assume the length of each shorter piece is x feet.

We know that the sum of the lengths of the three pieces is equal to the length of the original rope, which is 60 feet.

Therefore, we can write the equation:

x + x + 2x = 60

Combining like terms, we have:

4x = 60

To solve for x, we divide both sides of the equation by 4:

x = 60/4

x = 15

So, each shorter piece is 15 feet long.

The longer piece is twice as long, so its length is:

2x = 2 * 15 = 30

Therefore, the longer piece is 30 feet long.

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Answer:

grouping is the answer

The amount 20% more than 1500 is 1800.

The amount 20% of 1500 is

=20/100 × 1500

=300

NOW,

The amount 20% more than 1500 is

=300 + 1500

=1800

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Answer :(10 * m) / 7

m is an unknown number.

Step-by-step explanation:

The quotient of 10 times m divided by 7 is given by:

(10 * m) / 7

So, this expression represents the result of dividing 10 times m by 7.

Answer:(10 * m) / 7

Step-by-step explanation:

The amount of cash Liz received is; 458 dollars and 57 cents.

The amounts deposited were as follows;

The subtotal is therefore; 1346 dollars and 75 cents.

Since, the total after cash received is; 888 dollars and 18 cents.

The amount of cash received by Liz is;

1346 dollars and 75 cents - 888 dollars and 18 cents.

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Answer:

A) 1145.39 on Edge

Step-by-step explanation:

Just took test :)

The equation representing the relationship between dy/dt and dx/dt that is rate at which the length of the woman's shadow is changing is equal to option C. dy/dt =4× (dx/dt).

Woman is walking towards the street lamp.

Rate at which the length of her shadow is changing as she walks.

Let us consider the height of the street lamp as h = 20 feet.

Height of the woman be w = 5 feet.

And the distance between the woman and the street lamp be x.

Length of the woman's shadow be y.

Triangles formed by the woman, the street lamp, and their shadows are similar.

Sides of similar triangles are in proportion,

This implies,

h / y = (h + w) / (x + y)

Solving for y we get,

⇒h(x + y) = y(h + w)

⇒hx + hy = hy + wy

⇒y = hx / w

Rate at which the length of the woman's shadow is changing by differentiating both sides of this equation with respect to time,

⇒ dy/dt = h(dx/dt) / w

Substitute in the values for dx/dt = 3 ft/s, h and w we get,

⇒dy/dt = (20)(3) / 5

⇒dy/dt = 60 /5

⇒dy/dt =12

⇒dy/dt = 4(3)

⇒dy/dt =4× (dx/dt)

Therefore, the rate at which the length of the woman's shadow is changing is given by option C. dy/dt =4× (dx/dt) .

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Step-by-step explanation:

wapsi ki Vidya kya hai Hindi mein

The probability that three or more defective bowling balls are found in the first 25 examined can be calculated using the binomial distribution formula, specifically P(X ≥ 3) = 1 - P(X < 3).

To calculate the probability that three or more defective bowling balls are found in the first 25 examined, we would use the binomial distribution formula. This formula calculates the probability of a certain number of successes (in this case, finding a defective bowling ball) in a given number of trials (25 examinations) with a known probability of success (the overall proportion of defective bowling balls).

The mathematical expression we would use is:

P(X ≥ 3) = 1 - P(X < 3)

Where X is the number of defective bowling balls found in the first 25 examinations. To calculate P(X < 3), we would use the binomial probability formula:

P(X = x) = (n choose x) * p^x * (1-p)^(n-x)

Where n is the number of trials (25), p is the probability of success (the proportion of defective bowling balls), and x is the number of successes (in this case, 0, 1, or 2).

Once we have calculated P(X < 3), we can subtract this value from 1 to find P(X ≥ 3), which is the probability of finding three or more defective bowling balls in the first 25 examinations.

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Answer:

11.8%

Step-by-step explanation:

Here in this question, we want to find the probability of no success in the binomial experiment for 6 trials.

Let p = probability of success = 30% = 30/100 = 0.3

q = probability of failure = 1-p = 1-0.3 = 0.7

Now to calculate the probability, we shall need to use the Bernoulli approximation of the binomial theorem.

That would be;

P(X = 0) = 6C0 p^0 q^6

6C0 is pronounced six combination zero

= 6 * 0.3^0 * 0.7^6 = 1 * 1 * 0.117649 = 0.117649

This is approximately 0.1176

If we convert this to percentage we have 11.76%

But we want our answer rounded to the nearest tenth of a percent and that is 11.8%