help ASAP ill mark brainliest

(a) The improper integral ∫[0,∞] [tex](xe^(-2x)dx)[/tex] converges.

(b) To evaluate the integral ∫[0,1] [tex](4\sqrt{1-x^2}dx)[/tex], we can use the trigonometric substitution x = sin(θ).

(c) The general solution to the given differential equation is y = ln|x + 2| - ln|x - 1| + C.

(a) To determine if the improper integral ∫[0,∞] [tex](xe^{-2x}dx)[/tex] converges or diverges, we can use the limit comparison test.

Let's consider the function f(x) = x and the function g(x) = [tex]e^{-2x}[/tex].

Since both f(x) and g(x) are positive and continuous on the interval [0,∞], we can compare the integrals of f(x) and g(x) to determine the convergence or divergence of the given integral.

We have ∫[0,∞] (x dx) and ∫[0,∞] [tex](e^(-2x) dx)[/tex].

The integral of f(x) is ∫[0,∞] (x dx) = [[tex]x^2/2[/tex]] evaluated from 0 to ∞, which gives us [∞[tex]^2/2[/tex]] - [[tex]0^2/2[/tex]] = ∞.

The integral of g(x) is ∫[0,∞] [tex](e^{-2x} dx)[/tex] = [tex][-e^{-2x}/2][/tex] evaluated from 0 to ∞, which gives us [[tex]-e^{-2\infty}/2[/tex]] - [[tex]-e^0/2[/tex]] = [0/2] - [-1/2] = 1/2.

Since the integral of g(x) is finite and positive, while the integral of f(x) is infinite, we can conclude that the given integral ∫[0,∞] ([tex]xe^{-2x}dx[/tex]) converges.

(b) To evaluate the integral ∫[0,1] (4√([tex]1-x^2[/tex])dx), we can make the trigonometric substitution x = sin(θ).

When x = 0, we have sin(θ) = 0, so θ = 0.

When x = 1, we have sin(θ) = 1, so θ = π/2.

Differentiating x = sin(θ) with respect to θ, we get dx = cos(θ) dθ.

Now, substituting x = sin(θ) and dx = cos(θ) dθ in the integral, we have:

∫[0,1] (4√([tex]1-x^2[/tex])dx) = ∫[0,π/2] (4√(1-[tex]sin^2[/tex](θ)))cos(θ) dθ.

Simplifying the integrand, we have √(1-[tex]sin^2[/tex](θ)) = cos(θ).

Therefore, the integral becomes:

∫[0,π/2] (4[tex]cos^2[/tex](θ)cos(θ)) dθ = ∫[0,π/2] (4[tex]cos^3[/tex](θ)) dθ.

Now, we can integrate the function 4[tex]cos^3[/tex](θ) using standard integration techniques:

∫[0,π/2] (4[tex]cos^3[/tex](θ)) dθ = [sin(θ) + (3/4)sin(3θ)] evaluated from 0 to π/2.

Plugging in the values, we get:

[sin(π/2) + (3/4)sin(3(π/2))] - [sin(0) + (3/4)sin(3(0))] = [1 + (3/4)(-1)] - [0 + 0] = 1 - 3/4 = 1/4.

Therefore, the value of the integral ∫[0,1] (4√([tex]1-x^2[/tex])dx) is 1/4.

(c) To find the general solution to the differential equation ([tex]x^2 + x - 2[/tex])(dy/dx) = 3, for x ≠ -2, 1, we need to separate the variables and integrate both sides.

(dy/dx) = 3 / ([tex]x^2 + x - 2[/tex]).

∫(dy/dx) dx = ∫(3 / ([tex]x^2 + x - 2[/tex])) dx.

Integrating the left side gives us [tex]y + C_1[/tex], where [tex]C_1[/tex] is the constant of integration.

To evaluate the integral on the right side, we can factor the denominator:

∫(3 / ([tex]x^2 + x - 2[/tex])) dx = ∫(3 / ((x + 2)(x - 1))) dx.

Using partial fractions, we can express the integrand as:

3 / ((x + 2)(x - 1)) = A / (x + 2) + B / (x - 1).

Multiplying both sides by (x + 2)(x - 1), we have:

3 = A(x - 1) + B(x + 2).

Expanding and equating coefficients, we get:

0x + 3 = (A + B)x + (-A + 2B).

Equating the coefficients of like terms, we have:

A + B = 0,

- A + 2B = 3.

Solving this system of equations, we find A = -3 and B = 3.

3 / ((x + 2)(x - 1)) = (-3 / (x + 2)) + (3 / (x - 1)).

∫(3 / ([tex]x^2 + x - 2[/tex])) dx = -3∫(1 / (x + 2)) dx + 3∫(1 / (x - 1)) dx.

-3ln|x + 2| + 3ln|x - 1| + C2,

where C2 is another constant of integration.

Therefore, the general solution to the differential equation is:

y = -3ln|x + 2| + 3ln|x - 1| + C,

where C = C1 + C2 is the combined constant of integration.

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Answer:

3/4

Step-by-step explanation:

Make a common denominator and multiply the many times the denominator had to get to the common denominator to the numerator.

Answer:

3+(p.6)

Step-by-step explanation:

Answer:

3 + (p • 6)

Step-by-step explanation:

Answer:

The value for partners savings bank at the end of 1 year is $12,362.70. The value for Selwyn's at the end of 1 year is $12,334.58. The future value obtained by investing in Partners Saving Bank is more as compared to Selwyn’s Saving Bank. Hence Joseph is recommended to choose Partners Saving Bank.

Step-by-step explanation:

The value of the interest rate and the compounding applied, gives the

value in the account after one year.

Reasons:

The amount Joseph receives as gift, A₀ = $12,000

Amount interest from Partner's Savings Bank, r = 3% compounded semiannually

Interest rate offered by Selwyn's, r = 2.75% compounded continuously

Required:

The value of the two account at the end of one year.

Solution:

[tex]A_t = A_0 \cdot \left(1 + \dfrac{r}{2} \right)^{2 \times t}[/tex]

The amount at the end of one year (t = 1) in Partner's Savings Bank is therefore;

[tex]A_t = 12,000 \times \left(1 + \dfrac{0.03}{2} \right)^{2 \times 1} = 12,362.7[/tex]

The value of an account at Selwyn's is therefore;

The interest rate compounded continuously is presented as follows;

[tex]A(t) = \mathbf{A_0 \cdot e^{r \cdot t}}[/tex]

A₀ = The original amount invested = $12,000

Which gives;

[tex]A(t) = 12,000 \times e^{0.0275 \times 1} \approx \mathbf{12,334.58}[/tex]

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Answer: 3 red marbles, 3 blue marbles, 6 yellow marbles, 8 black marbles, 4 silver marbles

Step-by-step explanation:

I know these are the correct number of marbles because I set up these numbers as fractions and solved for x.

For examples, 2/16 of the marbles are red. 2/16=x/24

You would do this because we are trying to find the number of marbles that are red out of the 24 marbles.

Next, we would do 24 divided by 16= 1.5 Then 1.5 times 2=3

You would follow this rule for each fraction of marbles in order to find the true number of marbles out of 24.

Answer:

c

Step-by-step explanation:

Answer:

18. $11

19. $1.40

20. 31

21. 4.05

22. 8.2

23. 31

24. 5.05

25. $14.99 per month

26. 3.7 oz

27. 16 miles ???

28. $6 each

Step-by-step explanation:

Hope that helps. That took a long time sorry. Also I am not a hundred percent sure on 27. If someone else has a different answer just check both

The integral of the given form 1 = $* $(d, where f(x) = ln(x)h(x) and b>0, where h(0) exists but is not equal to zero, is divergent.

This is because the function f(x) is unbounded in the limit x + 0.The integral 1 = $* $(d, where f(x) = ln(x)h(x) and b>0, is divergent because the function f(x) is unbounded in the limit x + 0. The integral of the given form can be represented as∫ba ln(x)h(x) dx, which can be evaluated by using integration by parts.Using u = ln(x), dv = h(x) dx, v = ∫h(x) dx, and du = dx/x, we get the integral as∫ba ln(x)h(x) dx = ln(x) ∫ba h(x) dx - ∫ba (∫ba h(x) dx/x) dx= ln(b) ∫ba h(x) dx - ∫ba (∫xba h(t) dt/x^2) dx.Since h(0) exists but is not equal to zero, ln(x)h(x) goes to infinity as x approaches 0. Therefore, the integral diverges as x approaches 0.

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Explanation:

The type of test to be performed to test the hypothesis with the following data: Họ: H = 27, HA: μ< 27, X = 33, o= 2.5, and n= 77 is a left-tailed Z-test.

Hypothesis testing is a statistical technique that allows us to evaluate the validity of the hypothesis or assumptions regarding a population parameter. The hypothesis testing is based on several assumptions that must be met to test whether the null hypothesis is true or false.In this case, we will use the left-tailed Z-test since we have a sample size n > 30 and the population standard deviation is known as o= 2.5.Here are the steps for performing the left-tailed Z-test:

Step 1: State the null hypothesis and alternative hypothesis. H0: μ = 27 vs. Ha: μ < 27 (left-tailed test)

Step 2: Determine the level of significance (α). Assume α = 0.05

Step 3: Calculate the test statistic, which is given by: Z = (X - μ) / (o / √n)Where X is the sample mean, μ is the population mean, o is the population standard deviation, and n is the sample size.Z = (33 - 27) / (2.5 / √77)Z = 3.354

Step 4: Determine the p-value associated with the test statistic.Using a Z-distribution table or calculator, we find that the p-value is less than 0.001.

Step 5: Compare the p-value with the level of significance.Compare the p-value with α (0.05). Since the p-value is less than α, we reject the null hypothesis.Hence, the conclusion is that there is sufficient evidence to support the alternative hypothesis that the population mean is less than 27 at the 0.05 significance level.

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Answer:

A multiply by 5

Step-by-step explanation:

x/5-12=10

x/5=10+12

x/5=22

multiple each side by 5

x=22*5

The measure of the third interior angle, given that this is a triangle and the other two measures are known, is 100 degrees.

The sum of the interior angles of a triangle is always 180 degrees.

Given that the two of the interior angles are 45 degrees and 35 degrees, it is possible to find the measure of the third angle by subtracting the sum of these two angles from 180 degrees.

Third angle:

= 180 - ( 45 + 35 )

= 180 - 80

= 100 degrees

In conclusion, the measure of the third interior angle is 100 degrees.

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a. The value of the swap to firm XYZ is -$23,225.33.

b. This would help to protect the firm against an increase in interest rates.

a. Calculation of the value of the swap to firm XYZ

The value of the swap to firm XYZ can be calculated using the following formula:

Value of Swap = Value of Fixed Leg - Value of Floating Leg

Where Value of Fixed Leg = VFL = (Coupon Rate * Principal * (1 - (1 + r)-n / r))

Value of Floating Leg = VFL = (Interest Rate * Principal * (1 - (1 + r)-n / r))

Where, Coupon Rate = 4% p.a. Principal = $20 million

Interest Rate = LIBOR + Spread, Spread = 0, therefore,

Interest Rate = 4.5% p.a.

Time to Maturity, n = 15 months

Remaining Time to Next Payment = 6 - 2 = 4 months

Therefore, the current six-month LIBOR rate is required to calculate the value of the swap as follows:

Current six-month LIBOR rate = 4.5% * (4/6) + x% * (2/6)x = ((Value of Swap/Principal + (1 - (1 + r)-n / r)) * r) / (1 - (1 + r)-n / r) = 0.0251%

Value of Fixed Leg = VFL = (0.04 * 20,000,000 * (1 - (1 + 0.05/2)-30 / (0.05/2))) = $1,328,816.76

Value of Floating Leg = VFL = (0.0451 * 20,000,000 * (1 - (1 + 0.05/2)-10 / (0.05/2))) = $1,352,042.09

Value of Swap = $1,328,816.76 - $1,352,042.09 = -$23,225.33

Therefore, the value of the swap to firm XYZ is -$23,225.33.

b. Suggest a reason why XYZ entered into the swap in the first place

Firm XYZ might have entered into the swap in the first place to mitigate the risk of a rise in interest rates in the future. By entering into a fixed-for-floating interest rate swap, the firm has fixed its borrowing cost for the duration of the swap at 4%, regardless of the future interest rate changes.

Therefore, this would help to protect the firm against an increase in interest rates.

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The required probabilities are:(a) P(-1.721 < Z < k) = P(Z < k) - P(Z < -1.721) = 0.8531 - 0.0429 = 0.8102(b) P(k < Z) = 1 - P(Z < k) = 1 - 0.8531 = 0.1469(c) P(-k < Z) = P(Z < k) = 0.8531.

Given a random sample of size 22 from a normal distribution, the required probabilities are to be found. Therefore, the following is the solution to the problem.

Let X1, X2, ..., X22 be a random sample of size n = 22 from a normal distribution with µ = mean and σ = standard deviation.1. P(-1.721 -1.721).

We can find k using the standard normal distribution table as follows:

Using the table, we find that P(Z < k) = P(Z < 1.05) = 0.8531. Therefore, the value of k is 1.05. Hence, P(-k < Z < k) = P(-1.05 < Z < 1.05) = 0.8531 - 0.1469 = 0.7062. Therefore, the required probabilities are:(a) P(-1.721 < Z < k) = P(Z < k) - P(Z < -1.721) = 0.8531 - 0.0429 = 0.8102(b) P(k < Z) = 1 - P(Z < k) = 1 - 0.8531 = 0.1469(c) P(-k < Z) = P(Z < k) = 0.8531

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The values of k for the given probabilities are as follows:(a) k = 1.72(b) k = 1.96(c) k = -1.645. Given a random sample of size 22 from a normal distribution, to find k we will use the following steps:

Step 1: Write down the given probabilities. Using the standard normal table, we find the following probabilities: P(-1.721  = 0.0426 (rounding off to four decimal places)

Step 2: Find the value of k for (a)We need to find k such that P(-1.721  = 0.0426.From the table, we get the area between the mean (0) and z = -1.72 as 0.0426. Therefore,-k = -1.72k = 1.72Therefore, k = 1.72

Step 3: Find the value of k for (b)We need to find k such that P(k < Z) = 0.975From the standard normal table, we get the area between the mean (0) and z = 1.96 as 0.975. Therefore,k = 1.96Therefore, k = 1.96

Step 4: Find the value of k for (c)We need to find k such that P(-k < Z) = 0.90For a two-tailed test with an area of 0.10, the z-value is 1.645. Therefore,-k = 1.645k = -1.645Therefore, k = -1.645

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Answer:

These types of finance charges include things such as annual fees for credit cards, account maintenance fees, late fees charged for making loan or credit card payments past the due date, and account transaction fees.

Answer:

3.79

Step-by-step explanation:

took the test and got the answer. Hope this helps!

Answer: I think it’s 4

Step-by-step explanation: count the squares surrounding the triangle, 4 times 2 is eight 1/2 of that is 4

Answer:

D

Step-by-step explanation:

In a busy amusement park the number of people entering always increases as time goes on. I’m sure you know this if you ever been to one and had to wait in those long lines at the entrance or at any of the rides.

Answer:

D

Step-by-step explanation:

ifunny is dankreloaded

Answer:

6

Step-by-step explanation:

Formula for area A=0.5(bh)

12=0.5(4h)

12=2h

6=h

Answer:

6

Step-by-step explanation:

Area of triangle equation:

A=[tex]\frac{1}{2}[/tex] base * height

For this triangle...

12=[tex]\frac{1}{2}[/tex] (4) (x)

we need to figure out what x is to find the height.

To get x alone in this equation we can first divide both sides by 4

12/4=[tex]\frac{1}{2}[/tex] (x) ---> 3= [tex]\frac{1}{2}[/tex] (x) Then multiply by the reciprocal of 1/2 which is 2/1

x=6

Answer:

Let x be the number of hours Jose worked washing cars last week and y be the number of hours Jose worked waking dogs last week.

10x + 9y = 122

x + y = 13

Answer:

-4x - 16y

Step-by-step explanation:

Given:

-4(3x - 2x + 4y)

Required:

Simplify

Solution:

To simplify, apply the distributive property by multiplying every term that is inside the brackets by -4

Thus:

-4*3x -4*-2x -4*+4y

-12x + 8x - 16y

Add like terms

-4x - 16y

Answer:

3.8

Step-by-step

Got it wrong so you could get it right

5. The independent variable is the period of time.

6. The dependent variable is the distance traveled by the car.

5. The independent variable is the period of time because it is the variable that is controlled or manipulated in this scenario. The car's speed remains constant at 60 miles per hour, and the time is the factor that can be changed or adjusted.

6. The dependent variable is the distance travelled by car because it is the variable that is influenced or affected by the independent variable. In this case, the distance traveled depends on the period of time for which the car maintains a constant speed of 60 miles per hour.

The longer the period of time, the greater the distance traveled, and vice versa. The relationship between the independent variable (time) and the dependent variable (distance) is determined by the constant rate of 60 miles per hour. As time increases, the car covers more distance, while as time decreases, the car covers less distance.

Therefore, the distance traveled is dependent on the period of time for which the car maintains its constant speed.

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Answer:

(√3·x - 1)(√3·x + 1)(4x - 3)

Step-by-step explanation:

Note that the last two coefficients are -4 and +3, and the associated factor is (4x - 3).

The first two terms are

12x^3 - 9x^2, which become 3x(4x^2 - 3x) through factoring and then 3x^2(4x - 3).  

Therefore, 12x3 – 9x2 – 4x + 3 can be rewritten as:

                   (4x - 3)(3x^2 - 1).  

It's possible to factor 3x^2 - 1, even though 3 is not a perfect square.  Write 3x^2 - 1 as (√3·x - 1)(√3·x + 1)    

Then 12x3 – 9x2 – 4x + 3 = (√3·x - 1)(√3·x + 1)(4x - 3)

Answer:

( 3 x2 –  1 )( 1  ⇒ 4x –  3 )

Step-by-step explanation:

I did it lol

Answer:

10.1g+3.52x+16y+43.7

Step-by-step explanation:

Answer:

It would be the last choice. Base= 8 in; height= 3 in

Step-by-step explanation:

It gives you the measurement for the height you just have to read what the ruler says at the bottom. When does the shape stop on the ruler? That number would be the answer in this case it would be the last choice.

Answer:

i dont know lol

Step-by-step explanation:

The statement as it has been written can be shown as false.

There is often a trade-off between specificity and sensitivity when changing the cutoff criterion for a classification algorithm. Sensitivity relates to the classifier's capacity to accurately identify the positive cases, while specificity refers to the classifier's capacity to do so.

You can modify the ratio of true positive to false positive rates by setting the cutoff value. By identifying more occurrences as positive, lowering the threshold may boost sensitivity, but it can also result in an increase in false positives, which lowers specificity.

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The length of the arc on a circle with radius 10 cm intercepted by a 20° angle is,

Lenght of arc = 3.48 cm

We have to given that,

In a circle,

Radius = 10 cm

And, Angle = 20 degree

Since, We know that,

Lenght of arc = 2πr (θ/360)

Where, θ is central angle and r is radius.

Substitute all the values,

Lenght of arc = 2πr (θ/360)

Lenght of arc = 2 x 3.14 x 10 (20/360)

Lenght of arc = 3.48 cm

Therefore, the length of the arc on a circle with radius 10 cm intercepted by a 20° angle is,

Lenght of arc = 3.48 cm

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Answer: a = 3x

b = 2x+25

180 = a + b

180 = 3x + 2x + 25

180 = 5x + 25

155 = 5x

x = 31

a = 3*31 = 93

b = 2*31 + 25 = 87

Step-by-step explanation: pls mark as branlyest

The Bank of Cheerton now holds $1,200 in excess reserves. So, correct option is A.

To determine the quantity of excess reserves that the Bank of Cheerton holds, we first need to calculate the required reserves. The required reserves are the portion of the deposits that the bank is required to hold as reserves based on the reserve requirement set by the Federal Reserve.

The reserve requirement is given as 5 percent, and the Bank of Cheerton has deposits of $60,000. Therefore, the required reserves can be calculated as follows:

Required Reserves = Deposits * Reserve Requirement

= $60,000 * 0.05

= $3,000

Next, we can calculate the excess reserves, which are the reserves held by the bank in excess of the required reserves. Excess reserves can be calculated as the difference between the total reserves (reserves held by the bank) and the required reserves:

Excess Reserves = Reserves - Required Reserves

= $4,200 - $3,000

= $1,200

Therefore, correct option is A.

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