Marlene went shopping and bought a bunch of candy for her swim team. She bought packs of Skittles for $1.50 each and packs of M&Ms for $2 each. She spent a total of $39 and bought 24 items. How many of each item did she buy?

a) The solution to the given problem isL(F) = f(t) = 0 + (-(10 + 7C)/6)[tex]e^{-2t}[/tex]) + C[tex]e^{-3t}[/tex]+ D[tex]e^{-3t}[/tex]

b) The solution to the given problem isL(F) = [tex]e^{-2t}[/tex] [sin t + cos t](c)

c) The solution to the given problem is L(F) = 1/9 [[tex]e^{2t}[/tex] sin 9t - 3[tex]e^{2t}[/tex]) cos 9t]

(a)The inverse Laplace transform of F(s) = 10/s(s + 2)(s + 3)² can be found as follows:

L(F) = L{10/[s(s + 2)(s + 3)²]}

= 10 ∫∞₀[tex]e^{-st}[/tex]) /[s(s + 2)(s + 3)²] dt

L{F} = L⁻¹{10/[s(s + 2)(s + 3)²]}

By using partial fractions, we can simplify the equation and get it in a form that can be integrated easily.

L(F) = 10 ∫∞₀ {1/s - 2/(s + 2) + 3/(s + 3) - 2/(s + 3)² + 1/(s + 2)(s + 3)} [tex]e^{-st}[/tex]dt

L{F} = L⁻¹{1/s} - 2L⁻¹{1/(s + 2)} + 3L⁻¹{1/(s + 3)} - 2L⁻¹{d/ds[1/(s + 3)]} + L⁻¹{1/(s + 2)}

As the inverse Laplace transform of L{F} is given by L(F)

= L⁻¹{1/s} - 2L⁻¹{1/(s + 2)} + 3L⁻¹{1/(s + 3)} - 2L⁻¹{d/ds[1/(s + 3)]} + L⁻¹{1/(s + 2)}

Thus, the solution to the given problem isL(F) = f(t) = 0 + (-(10 + 7C)/6)[tex]e^{-2t}[/tex]) + C[tex]e^{-3t}[/tex]+ D[tex]e^{-3t}[/tex]

(b)

The inverse Laplace transform of F(s) = s/[s² + 4s + 5] can be found as follows:

L(F) = L{s/[s² + 4s + 5]}

= ∫∞₀ s e^(–st) / (s² + 4s + 5) dt

L{F} = L⁻¹{s/[s² + 4s + 5]}

By using partial fractions, we can simplify the equation and get it in a form that can be integrated easily. L(F) = ∫∞₀ [s/(s² + 4s + 5)] [tex]e^{-st}[/tex]) dt

L{F} = L⁻¹{s/(s² + 4s + 5)}

The solution to the given problem isL(F) = [tex]e^{-2t}[/tex] [sin t + cos t](c)

c) The inverse Laplace transform of F(s) = ([tex]e^{-3s}[/tex]) s/[(s - 2)² + 81] can be found as follows:

L(F) = L{([tex]e^{-3s}[/tex]) s/[(s - 2)² + 81]}= ∫∞₀ ([tex]e^{-st}[/tex]) s/[(s - 2)² + 81] dt

L{F} = L⁻¹{([tex]e^{-3s}[/tex])) s/[(s - 2)² + 81]}

So, The solution to the given problem is L(F) = 1/9 [([tex]e^{2t}[/tex]) sin 9t - 3([tex]e^{2t}[/tex]) cos 9t]

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Answer:

the cost of the replacement window will be $1501.44.

Step-by-step explanation:

area of an equilateral triangle:

[tex]A = \frac{\sqrt{3}}{4} a^{2}[/tex]

A = (√3)/4 * (17)^2

A = 125.12 in^2

125.12 * 12 = $1501.44

The equation for the cosine function is given as;cos(x) = 3 cos(π/2 x) + 5

A cosine function is defined as follows;cos(x) = a cos(b(x - h)) + kwhere a is the amplitude, period is 2π/b, and k is the midline. The amplitude, period, and midline of a cosine function can be used to find its equation.In this case,

we have a cosine function that has a midline of y=5, an amplitude of 3 and a period of 4/π. Thus, the amplitude of the function is given as 3, the midline is given as 5, and the period is 4/π.

The amplitude is the vertical distance from the midline to the highest point on the curve and also to the lowest point on the curve. The period is the distance over which the cosine function completes one full oscillation, or cycle.

In this case, we have a period of 4/π, so we can find b by the formula b = 2π/period = 2π/(4/π) = π/2.To find the phase shift, h, we use the formula h = x₀ - (π/b), where x₀ is the x-coordinate of the maximum or minimum value of the cosine function.

Since the midline is y=5, the maximum value of the cosine function occurs when y=8 and the minimum value occurs when y=2. The maximum and minimum values occur when cos(b(x - h)) = 1 and cos(b(x - h)) = -1, respectively.

Therefore, we have;8 = 5 + 3, cos(b(x - h)) = 1when x - h = 0, so x₀ = h2 = 5 - 3, cos(b(x - h)) = -1when x - h = π/b

Thus, h = 0 for the maximum value, and h = π/2 for the minimum value. We choose the value of h that corresponds to the maximum value of the cosine function, so h = 0.

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Answer:

Option 4

Step-by-step explanation:

The smaller sides must add up to be greater than the largest side so:

1) 6 + 8 < 15

1) No

2) 6 + 9 = 15

2) No

3) 9 + 6 < 16

3) No

4) 9 + 8 > 16

4) Yes

A) 12 and 33 can be divided by 3 so 12:33 = 4:11

B= 20 and 5 can be divided by 5 so 20mm:5mm = 4mm:1mm

Answer:

A. 4: 11

B. 4: 1

Step-by-step explanation:

What are these? These are ratios, which show proportion. For example, for every two dogs, there is one cat. They can be written as words, fractions, or with colons, such as in these problems.

How to simplify: To simplify, think of the highest common factor. If you can't think of the highest, just think of a factor both numbers have in common and keep going until the numbers don't have any factors in common.

In this case, for A, the common factor was 3. 12/3=4 and 33/3=11. This cannot be simplified further because 11 is prime, which means it has no factors besides 1 and 11.

For B, the common factor was 4, so it is 4:1.

Answer:

One pair of socks is $370.

Step-by-step explanation:

Sean bought three pairs of the same socks and a shoe polish for $1450. If the

polish cost $340, how much is the cost of one pair of socks.

6x - 340 = 1450

6x = 1450 -340

6x = 1110

2x = 1110 / 3

2x = 370

a)  Bryan is 1,168 meters away from the base of the watchtower

b) The nearest meter, Bryan and Lily are 315

a) To the nearest meter, Bryan is 1,168 meters away from the base of the watchtower.

Let AB be the watchtower. From B, the angle of elevation to the top of the tower is 20°.

We have to find BC.

BC/AB = tan 20°

BC = AB tan 20°

BC = 90 tan 20°

BC = 32.3

Therefore, BC = 32 meters

Now we have to find AC. AC is the distance between the foot of the watchtower and Bryan's position.

To do that, let BD = h be the height of the tower and AD = x be the distance between A and D.

From the information given, we know that tan 85° = h/x.

Rearranging the formula, x = h/tan 85°

x = 90/tan 85°

x = 418.55 meters

Therefore, AC = x + BC

AC = 418.55 + 32.3

AC = 450.85 meters

So, to the nearest meter, Bryan is 1,168 meters away from the base of the watchtower.

b) To the nearest meter, Bryan and Lily are 315 meters apart.

Let E be the position of Lily and AD be the distance from the foot of the watchtower to the position of Bryan. We have already found that AD = 418.55 meters.

Bryan and Lily are along the same horizontal line.

So, BE is the distance between them. We have to find BE.

From triangle AEB, tan 20° = h/AE.

Rearranging the formula, AE = h/tan 20°

AE = 90/tan 20°

AE = 267.9 meters

From triangle DEC, tan 85° = h/DE.

Rearranging the formula, DE = h/tan 85°

DE = 90/tan 85°

DE = 3,442.97 meters

Therefore, EC = DE - DC = 3,442.97 - 350 = 3,092.97 meters

Now, BE = AC - EC

BE = 450.85 - 3,092.97

BE = -2,642.12 meters (negative value means Bryan is to the left of Lily)So, to the nearest meter,

Bryan and Lily are 315 meters apart. Answer: (a) 1168m and (b) 315m

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Answer:

15

Step-by-step explanation:

the height of the person is y = 6 and the distance from the ladder is also 6 = x. To find the angle formed by the ladder we use [tex]arctan(\frac{y}{x})[/tex] which in this case is

[tex]arctan\frac{6}{6} = arctan(1)\\= 45 degrees[/tex]

now we know that the person is 9 feet away from wall and 6 feet away from the ladder so the total x distance is 9+6 = 15 = x

to find y we use tan(45) = [tex]\frac{y}{x}[/tex]

multiply both sides by x = 15 and simplify to get y = 15

Answer:

80

Step-by-step explanation:

Answer:

2 6/7 units

Step-by-step explanation:

You substitute 5/7 in for x

4(5/7) = 20/7 = 2 6/7 units

You can also add 5/7 + 5/7 + 5/7 + 5/7 to check your work

A)the required formula is r(x) = -3x² + 24x + 15.B)the worker will be assembling 36 units per hour at 10:00 A.M.C)the worker will assemble 70 units between 10:00 A.M. and 11:00 A.M.

a) Derive a formula for the rate at which the worker will be assembling units after x hours. The worker assembles f(x)= −x³ + 12x² + 15x units in x hours.

To determine the formula for the rate at which the worker will be assembling units after x hours, we can differentiate the given function with respect to time t.

We can write this function as:f(x) = -x³ + 12x² + 15xf'(x) = -3x² + 24x + 15

On differentiating the given function, we get the rate at which the worker will be assembling units after x hours is:r(x) = -3x² + 24x + 15

Therefore, the required formula is r(x) = -3x² + 24x + 15.

b)The worker arrives at 9:00 A.M. and we want to determine the rate at which the worker will be assembling units at 10:00 A.M, which means the worker will be assembling units after 1 hour.

We can use the formula:r(x) = -3x² + 24x + 15

To find the answer:r(1) = -3(1)² + 24(1) + 15r(1) = -3 + 24 + 15r(1) = 36 units per hour

Therefore, the worker will be assembling 36 units per hour at 10:00 A.M.

c)To find the number of units assembled by the worker between 10:00 A.M. and 11:00 A.M., we need to integrate the function r(x) = -3x² + 24x + 15 with limits 1 and 2.

We can use the formula:Integral of r(x)dx = f(x)

Using the formula, we get:f(2) - f(1) = Integral of r(x)dx between 1 and 2f(x) = -x³ + 12x² + 15x

Substituting the limits, we get:

f(2) - f(1) = [-2³ + 12(2²) + 15(2)] - [-1³ + 12(1²) + 15(1)]f(2) - f(1) = [−8 + 48 + 30] - [−1 + 12 + 15]f(2) - f(1) = 70

Therefore, the worker will assemble 70 units between 10:00 A.M. and 11:00 A.M.

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The expected number of matchings goes to infinity as N › [infinity].

Matching in Graph Theory:A matching in Graph Theory is a set of edges of a graph where no two edges share a common vertex. In other words, a matching is a set of independent edges of a graph. A perfect matching in a Graph Theory is a matching of size equal to half the number of vertices in a graph.The expected number of matchings goes to 0 as N › [infinity]:The expected number of matchings goes to zero as N › [infinity] when |E| = 3/N. It is because 3/N is a relatively dense number of edges that are independent of the number of vertices that can exist between A and B. The expected number of matchings is thus very small in comparison to the total number of matchings possible as N › [infinity].The expected number of matchings goes to infinity as N › [infinity]:The expected number of matchings goes to infinity as N › [infinity] when |E| = 4.V. It is because 4.V is a relatively large number of edges that are independent of the number of vertices that can exist between A and B. The expected number of matchings is thus very large in comparison to the total number of matchings possible as N › [infinity]. Hence the expected number of matchings goes to infinity as N › [infinity].

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Answer:

A.

Step-by-step explanation:

Answer:

A. 4,000,000 + 600,000 + 10,000 + 2,000 + 200 + 50 + 8 + 9

Step-by-step explanation:

Answer:

It is based on history

Step-by-step explanation:

Answer: the answer is based on history

Step-by-step explanation:

The correct option to the statements "1st statement: In an experimental study we can examine the association between the independent and dependent variable, and 2nd statement: In an experimental study we can examine the temporal relationship between the independent and dependent variable" is: a. Both statements are true.

An experimental study can be used to determine the relationship between two variables. It is also used to determine whether there is a cause-and-effect connection between two variables.

In an experimental study, two groups are compared. One group receives the independent variable, and the other group receives the dependent variable.

In an experimental study, the following two statements are true:

In an experimental study, we can examine the association between the independent and dependent variable. It is the correlation or connection between the two variables we are interested in exploring

In an experimental study, we can examine the temporal relationship between the independent and dependent variable. It refers to the timing or sequence of events that occurs between the two variables in question.

The study must include a time element that describes the order in which the dependent and independent variables were introduced to the subjects.

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Answer:

23

Step-by-step explanation:

please mark me as brainliest

Answer:

18 in

Step-by-step explanation:

len = y

width= y - 6

the area of rectangle is len x width

(Y) x (Y-6) = 216

Y^2 - 6Y = 216, Y^2 - 6y -216 = 0

y = (36 /2) or (-24 /2)

len couldn't be negative so 18

Answer:

Your question is Incomplete....

(a) The probability that a single randomly selected value is greater than 19.4. P(X> 19.4) = 0.6965.

(b) The probability that a sample of size n = 20 is randomly selected with a mean greater than 19.4. P(M> 19.4) =  0.9883.

To solve these probability questions, we can utilize the properties of the standard normal distribution since we know the mean and standard deviation of the population.

(a) Find the probability that a single randomly selected value is greater than 19.4.

To calculate this probability, we need to standardize the value 19.4 using the formula: z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.

z = (19.4 - 42.3) / 44.6 = -22.9 / 44.6 ≈ -0.51498

Using the standard normal distribution table or a calculator, we can find the corresponding probability for z > -0.51498, which is approximately 0.6965.

Therefore, P(X > 19.4) ≈ 0.6965.

(b) Find the probability that a sample of size n = 20 is randomly selected with a mean greater than 19.4.

For this question, we need to consider the sampling distribution of the sample mean. The mean of the sampling distribution is equal to the population mean (μ = 42.3), and the standard deviation of the sampling distribution, also known as the standard error, is equal to σ / √n, where σ is the population standard deviation and n is the sample size.

Standard error = 44.6 / √20 ≈ 9.9766

To find the probability that the sample mean is greater than 19.4, we need to standardize the sample mean using the formula: z = (x - μ) / (σ / √n), where x is the value (19.4 in this case), μ is the mean, σ is the standard deviation, and n is the sample size.

z = (19.4 - 42.3) / (44.6 / √20) ≈ -22.9 / 9.9766 ≈ -2.2972

Using the standard normal distribution table or a calculator, we can find the corresponding probability for z > -2.2972, which is approximately 0.9883.

Therefore, P(M > 19.4) ≈ 0.9883.

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Answer:

I NEED HELP ON THE SAME QUESTION

Step-by-step explanation:

NO ONE INDERSTANDS JT FOR SOME REASON AND NEITHER DO I

The ratio of the lateral area of the cone to the cylinder will be √(h²+r²)/2h.

The solid formed by two congruent closed curves in parallel planes along with the surface created by line segments connecting the corresponding points of the two curves is known as a cylinder.

A cylinder with a circular base is known as a circular cylinder. Based on the form of its base, a cone is given a name.

It is given that a cone and a cylinder have equal radii,r, and equal altitudes, h. The ratio of the lateral surface area of the cone to the cylinder will be calculated as below:-

The lateral area of the cone = πr√(h²+r²)

The lateral area of the cylinder = 2πrh

The ratio will be calculated as:-

R = πr√(h²+r²)  /   2πrh

R = √(h²+r²) / 2h

Therefore, the ratio of the lateral area of the cone to the cylinder will be √(h²+r²)/2h.

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The zeros of the polynomial function f(x) = x^2 - 9x - 70 can be found by factoring or using the quadratic formula. The zeros are -5 and 14.

To find the zeros of the polynomial function f(x) = x^2 - 9x - 70, we can factor the expression or use the quadratic formula. Let's factor the expression:

f(x) = x^2 - 9x - 70

= (x - 14)(x + 5)

Setting each factor equal to zero, we get:

x - 14 = 0 --> x = 14

x + 5 = 0 --> x = -5

Therefore, the zeros of the polynomial function are x = -5 and x = 14. These values represent the x-coordinates where the function intersects the x-axis, indicating the points where the function equals zero.

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Answer:

148 feet squared

Step-by-step explanation:

Hope it's correct!<D

A = 2 (wl+hl+hw) = 2 x (4x6+5x6+5x4) = 148

Answer:

10

Step-by-step explanation:

Answer:

what do you mean?

Step-by-step explanation:

The equation c₁ · a · c · x / b₁ · d · iₙ can have a solution for x if and only if the matrices a, b, and c are compatible and satisfy certain conditions.

Further information about the matrices and their properties is required to determine the specific solution.

To determine if the equation c₁ · a · c · x / b₁ · d · iₙ has a solution, we need to consider the compatibility and properties of the matrices involved.

Let's break down the equation:

c₁: The first column of matrix c.

a: Matrix a.

c: Matrix c.

x: The solution vector.

b₁: The first row of matrix b.

d: Matrix d.

iₙ: The identity matrix of size n.

For the equation to have a solution, the matrices a, b, and c need to be compatible, meaning their dimensions align appropriately for matrix multiplication. Specifically, the number of columns in matrix a should match the number of rows in matrix c.

Additionally, certain conditions or properties of the matrices may be required to ensure a solution exists. Without additional information about the specific matrices a, b, c, and d, it is not possible to determine the solution for x.

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