y" + 16y = 48(t – 7), y(0) = -1, y'(0) = 0 (a) Convert above ODE to a subsidiary equation and find its solution Y. (b) Find the solution above ODE. (c) Graph the solution.

Answer:

Step-by-step explanation:

The answer I believe is $5.44

The change that would she receive if she paid with bills totaling $80 is $11.

Given that, Lulu bought two blouses for $24 each, tax included, and three pairs of socks for $7 each.

She paid 24 for each of the two blouses,

Therefore 24 * 2 = 48.

The blouses cost her 48.

3 pairs of socks, each costing $7, for a total of 21 socks which she paid.

By simple math,

Add the two together because the total includes tax,

which is = 48 + 21 = 69.

She paid 80 and

Has change of $11 =$80-$69.

Therefore, the change she should expect is $11.00

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c)  It will have less variation.

Decreasing the sample size will generally result in more variation in the distribution of sample means. This is because with a smaller sample size, there is less information available to estimate the population mean, which means that the sample mean will be less precise and will vary more from one sample to the next.

For example, if you take a sample of 10 individuals from a population and calculate the mean of their heights, the sample mean will likely be a good estimate of the population mean height. However, if you take a sample of just 2 individuals and calculate the mean of their heights, the sample mean will be less precise and will be a less reliable estimate of the population mean height. This is because the sample of 2 individuals may not be representative of the overall population, and the sample mean will be more influenced by extreme values or outliers.

In general, as the sample size decreases, the distribution of sample means will become more spread out and will have more variation. This is because with a smaller sample size, there is more uncertainty about the population mean, and the sample means will be more likely to deviate from the true population mean.

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Answer:the sub goes down 32.81ft per min

Step-by-step explanation:

2100

2hours

1050ft

1hour

525ft

30min

262.5ft

15min

262.5 ft

7.5min

131.25

4min

65.625ft

2min

32.81ft

1mins

Answer:

4²+b² = 5²

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem to find the length of the missing side.

The Pythagorean theorem states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.  Algebraically, this is represented as

a²+b² = c²

We have the measure of one leg, 4 in.  We also have the measure of the hypotenuse, 5 in.  This gives us

4²+b² = 5²

I hope this helps <3

Reason: The line goes downhill when moving to the right, and when we're between x = -1 and x = 1. You can think of it like a roller coaster.

Answer:

12

Step-by-step explanation:

The minimum percentage of recent graduates who have salaries between $22,800 and $27,000 is 75%

What is chebyshev's theorem ?

The minimum percentage of observations that are within a given range of standard deviations from the mean is calculated using Chebyshev's Theorem. Numerous other probability distributions can be applied with this theorem. Chebyshev's Inequality is another name for Chebyshev's Theorem.

Given that

μ=24900,σ = 1050

From above we have

μ-2σ = 24900 -2. 1050 = 22800

μ+2σ = 24900 + 2. 1050 = 27000

That is k =2 and

1- 1/k^2 = 1 - 1/4 = 3/4 = 75%

So according to Chebyshev's Theorem, at least  75.0% of recent graduates who have salaries between $22,800 and $27,000.

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To write Acos(?0t) + Bsin(?0t) in the form r*sin(?0t - ?), we can use the identities. The relationship among R, r, ? and ? is:
R^2 = r^2 (1 + (A/B)^2), tan? = r/R = B/A

r = sqrt(A^2 + B^2)
tan? = B/A

Therefore, r = sqrt(A^2 + B^2) and tan? = B/A.

To determine the relationship among R, r, ? and ?, we can use the identity:

R^2 = r^2 + (tan?)^2

Therefore, R = sqrt(r^2 + (tan?)^2) and tan? = r/R. Substituting the expression for tan? from earlier, we get:

tan? = B/A = r/R

Solving for R, we get:

R = r/tan? = r/(B/A) = rA/B

And substituting the expression for R in terms of r and tan?, we get:

R = sqrt(r^2 + (r/R)^2) * A/B

Simplifying this expression, we get:

R^2 = r^2 + (A/B)^2 * r^2

R^2 = r^2 (1 + (A/B)^2)

Therefore, the relationship among R, r, ? and ? is:

R^2 = r^2 (1 + (A/B)^2)
tan? = r/R = B/A

To show that Acos(ω₀t) + Bsin(ω₀t) can be written in the form r*sin(ω₀t - θ), we can use trigonometric identities. We know that:

sin(a - b) = sin(a)cos(b) - cos(a)sin(b)

Comparing this to the given expression, we have:

Acos(ω₀t) + Bsin(ω₀t) = r*sin(ω₀t - θ) = r[sin(ω₀t)cos(θ) - cos(ω₀t)sin(θ)]

Now, let's equate the coefficients of sin(ω₀t) and cos(ω₀t):

A = -r*sin(θ)
B = r*cos(θ)

To find r and θ in terms of A and B, we can use the Pythagorean identity:

A² + B² = (-r*sin(θ))² + (r*cos(θ))² = r²(sin²(θ) + cos²(θ)) = r²

Therefore, r = √(A² + B²).

Now, to find θ, we can use the tangent function:

tan(θ) = -A/B

Now, for the second part, if Rcos(ω₀t - θ) = r*sin(ω₀t - θ), we can use the sine-to-cosine transformation:

Rcos(ω₀t - θ) = Rsin(ω₀t - θ + π/2)

This implies that:

R = r
θ + π/2 = θ'

So, the relationship among R, r, θ, and θ' is:

R = r
θ' = θ + π/2

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=======================================================

Explanation:

The given equation y = (-2/3)x+1 is in the form y = mx+b

m = -2/3 is our slope

b = 1 is the y intercept

The y intercept is where the line crosses the vertical y axis. Because b = 1, this location is (0,1). So that's one point we can use to graph this equation.

Another point can be found using the slope

Recall that slope = rise/run

Since slope = -2/3, this means rise/run = -2/3 leading to rise = -2 and run = 3. The "rise = -2" portion tells us to go down 2 and then "run = 3" portion means we go to the right 3 units.

The "down 2, right 3" motion has us go from (0,1) to (3,-1). So (3,-1) is another point we can use. We only need two points to graph a straight line.

The diagram below provides a visual summary. It shows plotting point A as the y intercept, and then you move to point B using the "down 2, right 3" movement rule.

Answer:

x=16

Step-by-step explanation:

because it's a equilateral triangle and its features are

it has three equal side and

every angle has 60°

So

x=16

The value of x is equal to 16

A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.

The sum of the internal angles of a triangle is equal to 180

so, 60 + 60 + m = 180

m = 180 - 120

m = 60

Since it's a equilateral triangle and its features that it has three equal side and every angle has 60°

So the three side are also equal to each other

x=16

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Your Answer is $0.5 or 1/2

Answer:

the answer for your question is "It's a cuboid"

Answer: Rectangular Prism

Step-by-step explanation:

Rectangular faces ✔️

8 vertices (4 on each side) ✔️

Solid figure ✔️

The narrator suggests that she now lives her life by striving to find optimism in even the worst circumstances when she adds, "I too have planted marigolds," at the conclusion of the story.

Because the narrator characterized the marigolds in the story as "Dazzling strips of bright petals bunch together in gigantic mounds warm and passionate in sun golden," the narrator's description of and response to seeing the marigolds is rather favorable.

The ability to comprehend and appreciate others as fully human beings serves as the story's central subject and marks the start of adulthood. Lizabeth felt ashamed when she realized she had wronged a genuine human being instead of a "witch" when she vented her anger at the marigolds and turned to look at Miss Lottie.

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The volume of a tennis ball is about 8.65 cubic inches

The volume of the space within the cylinder not taken up by the tennis balls is about 25.44 cubic inches

From the question, we are to determine the volume of a tennis ball

From the given information,

The circumference of a tennis ball is 8 inches

That is,

C = 2πr (C is circumference)

8 = 2πr

∴ r = 8/2π

r = 4/π inches

This the radius of a tennis ball

Now, for the volume of a tennis ball

Using the formula for calculating the volume of a sphere

\(V = \frac{4}{3}\pi r^{3}\)

Then, the volume of a tennis is

\(V = \frac{4}{3}\pi \times (\frac{4}{\pi})^{3}\)

\(V = \frac{4}{3}\pi \times \frac{64}{\pi^{3}}\)

\(V = \frac{256}{3\pi^{2}}\)

V = 8.64607 cubic inches

V ≅ 8.65 cubic inches

Hence, the volume of a tennis ball is about 8.65 cubic inches

b. To find the amount of space within the cylinder not taken up by the tennis balls

First, we will calculate the volume of the cylinder

Using the formula for calculating the volume of a cylinder

V = πr²h

Where V is the volume

r is the radius

and h is the height

From the given information,

r = 1.43 inches

h = 8 inches

Putting the parameters into the formula, we get

V = π × 1.43² × 8

V = 16.3592π

V = 51.39 cubic inches

This is the volume of the cylinder

Now, for the amount of space within the cylinder not taken up by the tennis balls

Since there are three tennis balls,

The amount of space not taken up will be

51.39 cubic inches - 3(8.65 cubic inches)

51.39 cubic inches - 25.95 cubic inches

= 25.44 cubic inches

Hence, the volume of the space within the cylinder not taken up by the tennis balls is about 25.44 cubic inches

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Answer: answer 199

Step-by-step explanation:

1.99/100 is 199

the following rules:

A) We round the number up to the nearest hundred if the last two digits in the number are 50 or above.

B) We round the number down to the nearest hundred if the last two digits in the number are 49 or below.

C) If the last two digits are 00, then we do not have to do any rounding, because it is already to the hundred.

In this case, Rule A applies and 199 rounded to the nearest hundred is:

200

After closely analyzing the line graph, it can be seen that the number of pygmy marmosets weighing more than 1/2 ounce are 8.

To create a line plot, we plot each weight of the each pygmy marmosets on the y-axis and the pygmy marmoset number on the x-axis, which will be ultimately being connected using the points with a line.

After ploting the each mentioned weights (in ounces ) and taking a close study of the plotted line graph,  we can see that there are total 8 pygmy marmosets which are weighing more than 1/2 ounce.

Therefore, the total number of pygmy marmosets with weight more than 1/2 ounces are 8.

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The complete question is :

The table shows the weights of 10 newborn pygmy marmosets make a line plot to display the data. How many pygmy marmosets weigh more than 1/2 ounce ?

Pygmy Marmoset      Weight (ounces)

1                                 0.4

2                                 0.5

3                                 0.6

4                                 0.7

5                                 0.8

6                                 0.9

7                                 1.0

8                                 1.1

9                                 1.2

10                                 1.3

Answer:

D

Step-by-step explanation:

Using the Cosine rule to find AC

AC² = BC² + AB² - (2 × BC × AB × cosB )

      = 18² + 12² - ( 2 × 18 × 12 × cos75° )

      = 324 + 144 - 432cos75°

      = 468 - 111.8

      = 356.2 ( take the square root of both sides )

AC = \(\sqrt{356.2}\) ≈ 18.9

-----------------------------------------

Using the Sine rule to find ∠ A

\(\frac{18}{sinA}\) = \(\frac{18.9}{sin75}\) ( cross- multiply )

18.9 sinA = 18 sin75° ( divide both sides by 18.9 )

sinA = \(\frac{18sin75}{18.9}\) , then

∠ A = \(sin^{-1}\) ( \(\frac{18sin75}{18.9}\) ) ≈ 66.9°

Answer:

Step-by-step explanation:

-Distance traveled is always the magnitude of the displacement vector. ... A car travels around a circular track clockwise (as viewed from above) at constant speed. ... Select all of the position versus time graphs below that could possibly correspond to this ... A straight line with a slope of 10 m/s that passes though the origin

Formula:

Shape =  Cone

Radius (R) =  1

Height (H) = 4

Formula of surface area (cone) = A=πr(r+h2+r2)

How to find a surface area of a cone?

Using the formula of the cone (A=πrl+πr2) We add the formula so the radius and the height (l=r2+h2). Since we are solving for a our formula will end up looking like (A=πr(r+h2+r2)=π·1·(1+42+12)≈16.09471). Which will equal our answer which is 16.09471. Round to the nearest tenth will be 16.09.

Answer: 16.09

Hope this helps.

Answer:

16.09

Step-by-step explanation:

16.09

This is a quadratic equation in terms of y. By solving this equation, we can find the value of y.

Let's solve this problem step by step.

The probability of picking the first white ball is the number of white balls divided by the total number of balls in the bag. Since we pick without replacement, there will be y - 1 balls left in the bag after picking the first white ball.

So, the probability of picking the second white ball, given that the first ball was white, is the number of remaining white balls divided by the remaining total number of balls.

Since we want to find the probability of picking two white balls, we can multiply the probabilities of picking the first and second white balls:

P(First white ball) * P(Second white ball|First white ball) = 1/3

A/y * (A - 1)/(y - 1) = 1/3

Now, we can solve this equation for y. By cross-multiplying and simplifying, we get:

3A(A - 1) = y(y - 1)

Expanding and rearranging the terms:

3A^2 - 3A = y^2 - y

Simplifying further

y^2 - y - 3A^2 + 3A = 0

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The Maclaurin series for f(x) is:

f(x) = sigma ^infinity _n = 1 (-1)^(n+1) * (x^(9n)) / (9n)

The function is f(x) = ln(1 + x^9). To find its Maclaurin series, we can use the power series for the natural logarithm of (1 + u), which is:

ln(1 + u) = Σ((-1)^(n+1) * u^n) / n, for n = 1 to infinity

In our case, u = x^9. So we substitute x^9 for u:

f(x) = ln(1 + x^9) = Σ((-1)^(n+1) * (x^9)^n) / n, for n = 1 to infinity

Now, simplify the expression:

f(x) = Σ((-1)^(n+1) * x^(9n)) / n, for n = 1 to infinity

So, the Maclaurin series for the given function f(x) = ln(1 + x^9) is:

f(x) = Σ((-1)^(n+1) * x^(9n)) / n, for n = 1 to infinity

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Answer:

Domain: -9, -6, 0, 9  I put them in ascending order

Range: -7, -6, 0, 3  I put them in ascending order.

Step-by-step explanation:

The domain is the inputs or the x values.

The range is the outputs or the y values.

The No Of ways are there to distribute the donuts = 34650

What is Probability?

Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

Number of ways to distribute 12 donuts in 12 kids so that each kid got one donut = 12!

Though, there are 4 chocolate, 4 jelly and 4 glazed donuts.

Hence,

Total number of ways to distribution the donuts

= 12/4*4*4

= 34650

Total number of ways = 34650

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The No Of ways there to distribute the donuts = 34650

What is Probability?

Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

Number of ways to distribute 12 donuts in 12 kids so that each kid got one donut = 12!

Though, there are 4 chocolate, 4 jelly and 4 glazed donuts.

Hence,

Total number of ways to distribute the donuts

= 12/4*4*4

= 34650

Total number of ways = 34650

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Answer:

C. \(\frac{1}{2}\)

Skills needed: Slope Formula

Step-by-step explanation:1

1) The slope is an important concept in algebra, and is also known as the rate of change, or growth rate.

- When graphing a linear equation, the slope determines how steep the line is. Slope can also be negative.

- To find slope, there is a formula you can use. In order to use the formula, you need to be given 2 coordinate points.

- This formula is not that hard to use, and should be remembered as it is a pretty important formula.

------------------------------------------------------------------------------------------------------------- 2) The formula for slope is:

Given two coordinate pairs: \((x_1, y_1)\) and \((x_2, y_2)\)

The formula is:

---> \(\frac{y_2-y_1}{x_2-x_1}\) also known as \(\frac{\triangle y}{\triangle x}\) (change of y over the change of x)

Let's use this formula for this problem (since we are given two coordinate points)

---> \((-9, 6)\) is the first point, \((-3, 9)\) is the second point

Let's plug it in below:

\(\frac{y_2-y_1}{x_2-x_1}=\frac{9-6}{-3-(-9)} \)

\(-3-(-9)\) can be made into \(-3+9\) since subtracting by a negative number is the same as adding a positive

\(9-6 = 3\)

\(-3+9=6\)

---> \(\frac{9-6}{-3-(-9)}=\frac{3}{6} = \frac{1}{2}\)

In most simplified form, it should be one-half, which is answer choice C.

Answer:

\(2x^3-3x^2-10x+15\\\)

Step-by-step explanation:

To find (fg)(x), we have to look at f(x) and g(x) and multiply the two quantities together. We are already given the two quantities individually so all that is left is the multiplication:

\((fg)(x)=(-2x+3)(5-x^2)=-10x+2x^3+15-3x^2\\\)

If we reorder the terms to go from highest degree to lowest, we get our final answer to be the following:

\(2x^3-3x^2-10x+15\)

The probability of selecting two Harry Potter DVDs at random, one after the other, is 1/110.

The probability of selecting a Harry Potter DVD at random is dependent on the total number of DVDs and the number of Harry Potter DVDs in the collection. Let's assume there are a total of 100 DVDs and 10 of them are Harry Potter films.

When selecting the first DVD, the probability of picking a Harry Potter film is 10/100 = 1/10.

After selecting the first DVD, there are 99 DVDs left, with 9 Harry Potter films remaining.

When selecting the second DVD, the probability of picking another Harry Potter film, while keeping the first one in hand, is 9/99 = 1/11.

To find the probability of both DVDs being Harry Potter films, we multiply the probabilities: (1/10) * (1/11) = 1/110.

Therefore, the probability that both DVDs will be Harry Potter films is 1/110.

In conclusion, the probability of selecting two Harry Potter DVDs at random, one after the other, is 1/110.

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There is sufficient evidence at the 0.02 level of significance that the percentage is over 62% for hypothesis.

Given that,

Over 62% of a newsletter publisher's subscribers, in their estimation, own a Rolls-Royce. A potential advertiser wants to verify this claim for marketing purposes. The advertiser decides to reject the null hypothesis following a test with a significance threshold of 0.02 after executing the analysis.

We have to find what is the verdict in relation to the publisher's assertion.

We know that,

First we have to write the null hypothesis and alternative hypothesis for the hypothesis test.

H₀:P=0.62

H₁:P>0.62

At 0.02 level of significance, rejecting H₀ then accepting H₁.

That is sufficient evidence that percentage over 62%.

Therefore, there is sufficient evidence at the 0.02 level of significance that the percentage is over 62% for hypothesis.

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