Find the largest interval which includes x = 0 for which the given initial value problem has a unique solution.(x−4)y′′+2y=x, y(0)=0, y′(0)=1.

Options :

Which conclusion is most appropriate in the context of this situation?

The data do not support the claim that a lower proportion of conservatives smoke cannabis when compared to liberals.

The data support the claim that the proportion of conservatives who smoke cannabis is no different that the proportion for liberals.

The data support the claim that a lower proportion of conservatives smoke cannabis when compared to liberals.

Answer:

The data support the claim that a lower proportion of conservatives smoke cannabis when compared to liberals.

Step-by-step explanation:

Given the hypothesis :

H0:p1−p2=0(p1=p2)

Ha:p1−p2<0

The test statistic = - 4.27

Pvalue = 0.00001

For making statistical decisions ;

Pvalue and α are very useful,

Decison boundary :

When Pvalue ≤ α ; We reject the Null (H0) otherwise, we fail to reject the Null.

However, based on the outcome of the statistical analysis,

The Pvalue < α ; Hence, we reject the Null and conclude that there is significant evidence support the claim that a lower proportion of conservatives smoke cannabis when compared to liberals.

For this problem we use two concepts and one fact:

1) The angles opposed by the vertex have the same measure

2) Supplementary angles add up 180 degrees, and

3) The interior angles of a triangle add up 180 degrees.

To find y we notice that the angle of measure (y-8) degrees and the angle of measure 124 degrees are supplementary, therefore:

To find x we use the fact that 2x degrees angle is opposed by the vertex with one interior angle of the triangle.

On the other hand, one of the interior angles of the triangle is opposed by the vertex with the 60 degrees angle, therefore both angles have the same measure. We also know from the previous point that the other interior angle is y-8 degrees= 56 degrees.

Finally, we use that:

and solving for x we get:

Answer:

Estimate: 0.05, Scientific Notation: 5*10^-2

Step-by-step explanation:

Using the rules of rounding, we get 0.05. Next, all we do is move the decimal place to the right, and count the amount of times we move it to the left, 2, so the exponent is -2

Answer:

Law of sine

Angle R = 34°

Step-by-step explanation:

From the question given above, the following data were obtained:

Side opposite angle Q (q) = 54 ft

Angle Q = 96 °

Side opposite angle R (r) = 30 ft

Angle R =?

The value of angle R can be obtained by using the law of sine as illustrated below:

r / Sine R = q / Sine Q

30 / Sine R = 54 / Sine 96

Cross multiply

54 × Sine R = 30 × Sine 96

54 × Sine R = 30 × 0.9945

54 × Sine R = 29.835

Divide both side by 54

Sine R = 29.835 / 54

Sine R = 0.5525

Take the inverse of Sine

R = Sine¯¹ 0.5525

R = 34°

Thus, the value of angle R is 34°

The solution to the system of equations is x = 1 and y = -3.

To solve the system of equations using the substitution or elimination method, let's start with the substitution method.

Given equations:

y = 4x - 7

4x + 2y = -2

We'll solve equation 1) for y and substitute it into equation 2):

Substituting y from equation 1) into equation 2):

4x + 2(4x - 7) = -2

4x + 8x - 14 = -2

12x - 14 = -2

Now, we'll solve this equation for x:

12x = -2 + 14

12x = 12

x = 12/12

x = 1

Now that we have the value of x, we can substitute it back into equation 1) to find y:

y = 4(1) - 7

y = 4 - 7

y = -3

Therefore, the solution to the system of equations is x = 1 and y = -3.

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Answer:

We can use the formula for compound interest to solve this problem. The formula is:

A = P * (1 + r/n)^(n*t)

where:

A = the amount of money after t years

P = the principal amount (the initial investment)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

In this case, P = $5000, r = 0.03, n = 12 (since the interest is compounded monthly), and t = 10. Plugging these values into the formula, we get:

A = 5000 * (1 + 0.03/12)^(12*10)

A = 5000 * (1.0025)^120

A ≈ $6,621.36

So the investment will be worth approximately $6,621.36 after 10 years.

Answer: 0.39

Step-by-step explanation:

Given the following classification :

Heavy smokers (H) = 10%

Light smokers (L) = 20%

Non smokers (N) = 70%

Given that :

The death rates of the heavy and light smokers were five and three times that of the nonsmokers, respectively

Let probability of death = D

P(D | N) = d

P(D | H) = 5d

P(D | L) = 3d

Hence,

P(D) = [P(H) * P(D | H) + P(L) * P(D | L) + P(N) * P(D | N)]

P(D) = [0.1 * 5d + 0.2 * 3d + 0.7 * d]

P(D) = [0.5d + 0.6d + 0.7d]

P(D) = 1.8d

A randomly selected participant died over the five-year period: calculate the probability that the participant was a nonsmoker.

P(N | D) = [P(N) * P(D | N)] / P(D)

P(N | D) = 0.7d / 1.8d

P(N | D) = 0.3888

= 0.39

The final velocity of the parameters is 13.5m/s

In this question, the given parameters are represented as

Formula: v = u + at

Initial velocity = 3m/s

Acceleration = 1.5m/s²

Time = 7 seconds

When these parameters are represented using their required notation, we have the following representations

u = 3m/s

a = 1.5m/s²

t = 7 s

Next, we substitute the above parameters in the above equation

So, we have the following representation

v = 3 + 1.5 * 7

Evaluate the products

This gives

v = 3 + 10.5

Evaluate the sum

So, we have the following representation

v = 13.5

The notation v represents the final velocity

Hence, the final velocity is 13.5m/s

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Using the trapezoidal rule with 5 ordinates, we approximate the integral [sin(x²+1) dx] over the interval [0,1] to be 0.5047 to 4 decimal places.

To approximate the integral [sin(x²+1) dx] using the trapezoidal rule with 5 ordinates, we can use the following formula:

∫[a,b]f(x)dx ≈ [(b-a)/2n][f(a) + 2f(a+h) + 2f(a+2h) + 2f(a+3h) + 2f(a+4h) + f(b)]

where n is the number of ordinates (in this case, n = 5), h = (b-a)/n is the interval width, and f(x) = sin(x²+1).

First, we need to find the interval [a,b] over which we want to integrate. Since no interval is given in the problem statement, we'll assume that we want to integrate over the interval [0,1].

Therefore, a = 0 and b = 1.

Next, we need to find h:

h = (b-a)/n = (1-0)/5 = 0.2

Now, we can apply the trapezoidal rule formula:

∫[0,1]sin(x²+1)dx ≈ [(1-0)/(2*5)][sin(0²+1) + 2sin(0.2²+1) + 2sin(0.4²+1) +             2sin(0.6²+1) + 2sin(0.8²+1) + sin(1²+1)]

≈ (1/10)[sin(1) + 2sin(0.05²+1) + 2sin(0.15²+1) + 2sin(0.35²+1) + 2sin(0.65²+1) + sin(2)]

≈ (1/10)[0.8415 + 2sin(1.0025) + 2sin(1.0225) + 2sin(1.1225) + 2sin(1.4225) + 1.5794]

≈ 0.5047

Therefore, using the trapezoidal rule with 5 ordinates, we approximate the integral [sin(x²+1) dx] over the interval [0,1] to be 0.5047 to 4 decimal places.

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Answer:

Hsu makes $35,950.50 and Alkena makes $48,418.50

Step-by-step explanation:

Create a system of equations, where h is the amount Hsu makes and a is the amount Alkena makes:

a + h = 84,369

a = h + 12,468

Solve by substitution by plugging in h + 12,468 as a:

h + 12,468 + h =  84,369

2h + 12,468 = 84,369

2h = 71,901

h = 35,950.50

Plug this into the equation, a = h + 12,468 , to solve for a

a = 35,950.50 + 12,468

a = 48,418.50

So, Hsu makes $35,950.50 and Alkena makes $48,418.50

Answer:

Yes it is 4/3

Step-by-step explanation:

The depth of the water in the tank is 9 inches

The length of the tank = 24 inches

The width of the tank = 8 inches

The height of the tank = 10 inches

The quantity of water in the tank = 1728 cubic inches

The volume of the water is given, the length and width of the tank will be equal to the length and width of the water. Here we have to find the depth( height ) of the water

The volume of the tank = l × w × h

Here height and depth are equal

1728 = 24 × 8 × d

1728 = 192 × d

d = 1728/192

d = 9 inches

Hence, the depth of the water in the tank is 9 inches

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The method that determines the volume of the prism is simply multiply the area of the base by the height, and the result is 12.5 cm³. (option-a)

To determine the volume of the prism shown in the diagram, we need to multiply the area of the base by the height.

The base of the prism is a rectangle with dimensions 5 cm by 2 cm. Therefore, the area of the base is:

A = length x width = 5 cm x 2 cm = 10 cm²

The height of the prism is 2-¹ cm, which is equivalent to 5/4 cm.

Therefore, the volume of the prism is:

V = A x h = 10 cm² x 5/4 cm = 12.5 cm³

The expressions involving unit cubes and one-quarter cubes are not relevant to this problem and do not provide a method for finding the volume of the prism.

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Answer:

Median: 3,3,4,5,6,7,10,11,12

Answer:

6

Step-by-step explanation:

We need to arrange the numbers 3, 11, 6, 5, 4, 7, 12, 3 and 10  in increasing order

3, 3, 4, 5, 6, 7, 10, 11, 12

Next, we need to find such a number so that it is middle one and hase equal amount of number on either side of it

median = 6

Answer: $107,836.69 or about $107,837 (to the nearest dollar)

Step-by-step explanation:

Formula to the  accumulated amount received after investing principal amount (P) at rate of interest (r) compounded monthly for t months :

\(A=P(1+\dfrac{r}{12})^{t}\)

As per given , A = $130,000

r= 7.5% = 0.075

t= 30 months

Now,

\(130000=P(1+\dfrac{0.075}{12})^{30}\\\\\Rightarrow 130000=P(1+0.00625)^{30}\\\\\Rightarrow 130000=P(1.00625)^{30}\\\\\Rightarrow 130000=P \times1.20552661036\\\\\Rightarrow\ P=\dfrac{130000}{1.2055266}=107,836.69\)

Hence he need to invest $107,836.69 .

Hope this helps

Answer: 60

Answer:

\(a^{2}\)+\(b^{2}\)=60

Step-by-step explanation:

the answer is A

Answer:

i think it the third one but i don't know i'm not in collage math class so...

Step-by-step explanation:

There are 120 different combinations of 3 programmers that can be chosen to transfer to the new department

From the question, we have

Total number of programmers, n = 10

Numbers to programmers to select, r = 3

The number of ways of selection could be drawn is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 10 and r = 3

Substitute the known values in the above equation

Total = ¹⁰C₃

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 10!/(7! * 3!)

Evaluate

Total = 120

Hence, the number of ways is 120

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Young adults might value credit in case of an emergency for several reasons. Firstly, credit provides financial flexibility, allowing them to access funds quickly when unexpected expenses arise.

This can be essential for covering costs related to medical emergencies, car repairs, or other unforeseen events that may strain their limited savings. Secondly, young adults often have less established financial safety nets than older individuals. They may not have significant savings, insurance policies, or support from family members to fall back on during emergencies. Credit, in this case, acts as a temporary financial cushion, enabling them to manage immediate needs without resorting to high-interest loans or further jeopardizing their financial stability.

Thirdly, responsible use of credit can help young adults build a positive credit history. Demonstrating responsible borrowing and repayment habits will make it easier for them to access more favorable credit terms in the future, such as lower interest rates or higher credit limits. This can prove valuable when making significant purchases, like buying a home or financing higher education.

Lastly, having access to credit can also provide young adults with a sense of financial independence and empowerment. Knowing they have the means to handle emergencies without relying on others can boost their confidence in managing personal finances and help them make more informed financial decisions as they navigate adulthood.

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well, we know what S(x) is, since it's given, so, after , is simply a matter of x = 2,4,6,8,10, so

\(\begin{array}{llrll} S(2)=1250(1.015)^{4(2)}&\implies &S(2)\approx 1408.12\\ S(4)=1250(1.015)^{4(4)}&\implies &S(4)\approx 1586.23\\ S(6)=1250(1.015)^{4(6)}&\implies &S(6)\approx 1786.88\\ S(8)=1250(1.015)^{4(8)}&\implies &S(8)\approx 2012.91\\ S(10)=1250(1.015)^{4(10)}&\implies &S(10)\approx 2267.52 \end{array}\)

well, the tell-tale for Growth or Decay is the parenthesized term, namely the "rate of change", if it's greater than 1 is Growth, if it's less than 1 is Decay, in this case is greater than 1, is 1.015, so well, you know.

from 4 years to 10 years, how much more in interest?

well, first off let's take off the Principal of 1250 to see how much is in interest, hmmm for 4 years that'll be 336.23 and for 10 years that'll be 1017.52, so their difference is about 681.29.

what does the S-intercept mean?  Check the picture below.

when the graph touches the y-axis or S-axis if you wish, the time is 0 and the amount is, well, you can see it there.

Answer:

78

Step-by-step explanation:

Answer:

D. \(10^{\circ}\)

Step-by-step explanation:

Let the measure of minor arc \(AE\) be \(\alpha\) and the measure of minor arc \(BD\) be \(\beta\).

Using the secant-secant theorem, \(\frac{\alpha-\beta}{2}=32 \implies \alpha-\beta=64^{\circ}\).

By the inscribed angle theorem, \(\alpha=84^{\circ}\).

Thus, \(\beta=20^{\circ}\).

By the inscribed angle theorem, \(x=10^{\circ}\).

Answer:

Step-by-step explanation:

372 Millimeters

Answer:

2,300 millimeters

Step-by-step explanation:

when you convert 30 centimeters it’s 300 millimeters. When you convert 2 meters it’s 2,000 millimeters so…. That is the correct answer plus I just did the quiz and got it correct with that answer.

Answer:

Step-by-step explanation:

The exact values of α and β as follows: α = 2π/3 and β = 7π/6. To find the exact value of the given trigonometric expressions, we need to use the Laws of Sines and Cosines.

The Law of Sines is a mathematical equation used to calculate the angles or sides of a triangle when two angles and one side are known. It states that the ratio of the sine of an angle to the length of the opposite side is constant.

The Law of Sines states that the ratio of a side to the sine of its opposite angle is equal for all sides and angles of a triangle. The Law of Cosines states that the square of a side of a triangle is equal to the sum of the squares of the other two sides minus twice the product of those sides multiplied by the cosine of the included angle.

We begin by finding the exact value of tan α. Using the Law of Sines, we can find the measure of α by solving the equation: tan α = 3/4 = sin α/cos α. This can be rearranged to find cos α = 4/3, and then we can use the inverse of cosine to find the exact value of α.

Using the Law of Cosines, we can find the exact value of β by solving the equation: -15/17 = (cos β)2 = (1 - sin2 β). This can be rearranged to find sin β = -4/5, and then we can use the inverse of sine to find the exact value of β.

Finally, using the given conditions, we can find the exact values of α and β as follows: α = 2π/3 and β = 7π/6.

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