Leo deposited $1,472 in an account that earned 2.5% interest compounded annually for 7 years. After 7 years, what was Leo's account balance?

Answer:

2(11*9) + 2(11*h) + 2(9*h) = 558

h = 9 in.

Step-by-step explanation:

2(11*9) + 2(11*h) + 2(9*h) = 558

198 + 22h + 18h = 558

40h = 558-198

40h = 360

h = 9 in.

The particular solution to the differential equation with the initial condition y(0) = 1 is:

[tex]y = 1 + cos(t) + 1 - e^{(cos(t))[/tex]

To solve the given differential equation:

dy/dt + sin(t) = 1

We can rewrite it in the standard form of a first-order linear homogeneous differential equation:

dy/dt = 1 - sin(t)

The integrating factor for this equation is [tex]e^{(\int(-sin(t))dt)} = e^{(-cos(t)).[/tex]

Now, multiply both sides of the equation by the integrating factor:

[tex]e^{(-cos(t)) \times dy/dt} = (1 - sin(t)) \times e^{(-cos(t))[/tex]

The left-hand side can be rewritten using the chain rule:

[tex]d/dt [e^{(-cos(t))} \times y] = (1 - sin(t)) \times e^{(-cos(t))[/tex]

Integrate both sides with respect to t:

[tex]\int d/dt [e^{(-cos(t))} \times y] dt = \int (1 - sin(t)) \times e^{(-cos(t)) dt[/tex]

[tex]e^{(-cos(t))} \times y = \int (1 - sin(t)) \times e^{(-cos(t)) dt[/tex]

To evaluate the integral on the right-hand side, let u = -cos(t), du = sin(t) dt:

[tex]e^{(-cos(t))} \times y = \int (1 - sin(t)) \times e^{(-cos(t)) dt[/tex]

[tex]= \int (1 - sin(t)) \times e^u du[/tex]

[tex]= \int (e^u - sin(t) \times e^u) du[/tex]

[tex]= e^u - \int sin(t) \times e^u du[/tex]

Now, integrate the second term by parts:

[tex]\int sin(t) \times e^u du = -e^u \times cos(t) + \int e^u \times cos(t) dt[/tex]

Substituting the expression back into the equation:

[tex]e^{(-cos(t))} \times y = e^u - (-e^u \times cos(t) + \int e^u \times cos(t) dt)[/tex]

Simplifying:

[tex]e^{(-cos(t))} \times y = e^{(-cos(t))} + e^{(-cos(t))} \times cos(t) - \int e^{(-cos(t))} \times cos(t) dt[/tex]

To solve the remaining integral, let v = -cos(t), dv = sin(t) dt:

[tex]\int e^{(-cos(t))} \times cos(t) dt = \int e^v \times (-dv)[/tex]

[tex]= -\int e^v dv[/tex]

[tex]= -e^v + C[/tex]

[tex]= -e^{(-cos(t))} + C[/tex]

Substituting back into the equation:

[tex]e^{(-cos(t))} \times y = e^{(-cos(t))} + e^{(-cos(t))} \times cos(t) - (-e^{(-cos(t))} + C)[/tex]

Divide both sides by [tex]e^{(-cos(t))[/tex]:

[tex]y = 1 + cos(t) + 1 + C \times e^{(cos(t))[/tex]

Using the initial condition y(0) = 1, we can substitute the values into the equation:

[tex]1 = 1 + cos(0) + 1 + C \times e^{(cos(0))[/tex]

[tex]1 = 1 + 1 + C \times e^1[/tex]

[tex]C \times e = -1[/tex]

Therefore, the particular solution to the differential equation with the initial condition y(0) = 1 is:

[tex]y = 1 + cos(t) + 1 - e^{(cos(t))[/tex]

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Complete question =

Solve the following differential equation for values of t between 0 and 4, with the initial condition of y= 1 when t = 0,

dy/dt + sin(t) = 1

Answer:

radius of 10.9254843 and height of 10.9254843

Step-by-step explanation:

The equation for the volume of a cylinder is V = 2 pi r h

If V (volume) = 750, find for r and h

(I'm just going to make the radius and height the same thing)

750 = 2 pi r r

375 = pi r^2

119.366207 = r^2

10.9254843 = r

The probability that an individual reaches age 100 is 0.000001.

The theory of cell division process supposes that mistakes occurring in cell division are of Poisson distribution. The given Poisson parameter is 2.5 mistakes per year and an individual dies when 196 mistakes have occurred.

Let X denote the number of mistakes before an individual dies.

(a) The mean lifetime of an individual. A random variable X is said to follow Poisson distribution with mean λ (X ~ Poisson (λ)) if the probability mass function of X is given by: P(X = k) = e^(-λ) (λ^k)/k! Here, rate = 2.5 mistakes per year and an individual dies when 196 mistakes have occurred. Therefore, λ = rate x time = 2.5 mistakes/year × T years = 196 mistakes. T = 196/2.5 = 78.4 years. The mean lifetime of an individual is given by: μ = E(X) = λ = 78.4 years.  

(b) The variance of the lifetime of an individual. The variance of a Poisson distribution is given by: Var(X) = λ. Hence, the variance of the lifetime of an individual is given by: σ² = Var(X) = λ = 78.4 years

(c) .The probability that an individual dies before age 67.2Let Y denote the lifetime of an individual. The number of mistakes before an individual dies is given by X. From the previous results, we know that the mean and variance of X are 196 and 196 respectively. Let y = 67.2 be the age of the individual. We have to find the probability that the individual dies before y. In other words, we need to find P(Y < y). P(Y < y) = P(X < 196/y) = P(X < 196/67.2) = P(X < 2.9137) = 0.9868 approximately

(d) The probability that an individual reaches age 90Let y = 90 be the age of the individual. We have to find the probability that the individual reaches 90 years. In other words, we need to find P(Y ≥ y). P(Y ≥ y) = P(X ≥ 2.5 × 90) = P(X ≥ 225) = 1 - P(X < 225) = 1 - P(X ≤ 224). From Poisson distribution tables, we get:P(X ≤ 224) = 0.9993 approximately. Therefore, P(X ≥ 225) = 1 - P(X ≤ 224) = 1 - 0.9993 = 0.0007 approximately.

(e) The probability that an individual reaches age 100Let y = 100 be the age of the individual. We have to find the probability that the individual reaches 100 years. In other words, we need to find P(Y ≥ y). P(Y ≥ y) = P(X ≥ 2.5 × 100) = P(X ≥ 250) = 1 - P(X < 250) = 1 - P(X ≤ 249)From Poisson distribution tables, we get:P(X ≤ 249) = 0.999999 approximately.

Therefore, P(X ≥ 250) = 1 - P(X ≤ 249) = 1 - 0.999999 = 0.000001 approximately

Therefore, the probability that an individual reaches age 100 is 0.000001.

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Answer:

abd

Step-by-step explanation:

im smart

Answer:

The answer is A B D F

Step-by-step explanation:

I took the test sorry I don't have a better explanation.

Answer:

13.) 237 millimeters

14.) 87.5 feet (87 feet 6 inches)

15.) 28

16.) 121 degrees

Step-by-step explanation:

16.) The "arc length" formula is s = rФ, where Ф represents the central angle in radians (not degrees).

Here r = 18 ft and s = 38 ft, and so:

                                     38 ft

s = rФ becomes Ф = ------------ = 2.111 radians

                                     18 ft

which, in degrees, is:

2.111 rad      180 deg

------------- * --------------- = 121 degrees, to the nearest degree

  1            3.142

Answer:

whats ur question?

Step-by-step explanation:

[tex]4000(1.003)^{(x-1)}[/tex]

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

The aquarium with dimensions 16 in. × 8 in. × 10 in. can hold approximately 30.6 liters of water and approximately 8.09 gallons.

To calculate the volume of the aquarium, we multiply its length, width, and height. Since the dimensions are given in inches, we need to convert the volume to liters and gallons.

First, let's calculate the volume in cubic inches:

Volume = Length × Width × Height = 16 in. × 8 in. × 10 in. = 1280 cubic inches.

To convert cubic inches to liters, we divide the volume by 61.024:

Volume in liters = 1280 in³ / 61.024 = 20.96 liters (rounded to two decimal places).

To convert liters to gallons, we divide the volume by 3.78541:

Volume in gallons = 20.96 liters / 3.78541 = 5.53 gallons (rounded to two decimal places).

Therefore, the aquarium can hold approximately 30.6 liters of water and approximately 8.09 gallons.

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Given piecewise functions are: g(x) = {x² – 5 , 2€ (-[infinity], -7)9x - 17, 9 x € (-7,2](x + 1)(x - 5) , 2 € (2,00)

We are supposed to evaluate g(x) at x = 7. As per the given conditions,

we have the following; g(x) = {x² – 5 , 2€ (-[infinity], -7)9x - 17, 9 x € (-7,2](x + 1)(x - 5) , 2 € (2,00)

Now, g(7) represents the value of function g(x) at x = 7. For finding the value of g(7), we need to look at the different given intervals.

In the interval 2€ (-[infinity], -7), we have the function g(x) = x² – 5, but x = 7 does not belong to this interval.

In the interval 9 x € (-7,2], we have the function g(x) = 9x - 17, but x = 7 does not belong to this interval.

In the interval 2 € (2,00), we have the function g(x) = (x + 1)(x - 5), but x = 7 does not belong to this interval.

As x = 7 does not belong to any of the given intervals, g(7) is not defined.

Hence, the correct option is "Not defined".

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The perimeter of the rectangle given is P = 26x - 62.

The perimeter of a rectangle is the sum of its sides. Mathematically -

Perimeter = [P] = 2(L + B)

Given is a rectangle with its length and breadth.

We can write the perimeter of the rectangle as follows -

[P] = 2(L + B)

L = 5x + 12

B = 8x - 43

Therefore -

P = 2(L + B)

P = 2(5x + 12 + 8x - 43)

P = 2(13x - 31)

P = 26x - 62

Therefore, the perimeter of the rectangle given is P = 26x - 62.

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To find the 95% confidence interval when n=100 and p=0.72, we can use the following formula:

$$\left(\hat{p}-z_{\alpha/2} \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}, \hat{p}+z_{\alpha/2} \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\right)$$

Where, $\hat{p}$ is the point estimate of the population proportion, $n$ is the sample size, $z_{\alpha/2}$ is the critical value of the standard normal distribution at a significance level of $\alpha$, which can be obtained from a table. For a 95% confidence level, $\alpha$ is equal to 0.05/2 = 0.025 on each tail.

The corresponding z-value is 1.96 (approximately).Hence, plugging in the values, we get

$$\begin{aligned}\left(0.72-1.96 \sqrt{\frac{0.72(0.28)}{100}}, 0.72+1.96 \sqrt{\frac{0.72(0.28)}{100}}\right) \\ \left(0.631, 0.809\right)\end{aligned}$$

Therefore, the 95% confidence interval is (0.631, 0.809) rounded to three decimal places.

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Simple random sampling is a statistical method in which every member of the population has an equal chance of being chosen as a subject for the survey. In this case, a student government organization wants to estimate the proportion of students in favor of a mandatory "pass-fail" grading policy for elective courses, and they have a list of names and addresses of the 645 students enrolled in the current quarter from the registrar's office.

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The mean absolute deviation of last week's temperatures is 7.2°F.

Given below is the table of last week's and this week's low temperatures:Last week's temperatures: 29°F, 35°F, 42°F, 46°F, 52°FThis week's temperatures: 27°F, 31°F, 35°F, 38°F, 42°F, 46°F, 50°F

The range of this week's temperatures is found by subtracting the smallest value from the largest value. Therefore, the range of this week's temperatures is 50°F - 27°F = 23°F.

Mean absolute deviation is a measure of how much the data deviates from the mean of the data. To find the mean absolute deviation of last week's temperatures, we first need to find the mean of the data set.Using the formula for mean, we have:

Mean = (29 + 35 + 42 + 46 + 52)/5 = 40.8°F

To find the absolute deviations of each temperature from the mean, we need to subtract each temperature from the mean and take the absolute value.Absolute deviations:

|29 - 40.8| = 11.8|35 - 40.8|

= 5.8|42 - 40.8|

= 1.2|46 - 40.8|

= 5.2|52 - 40.8|

= 11.2

Next, we need to find the mean of these absolute deviations. Using the formula for mean again, we have:Mean absolute deviation = (11.8 + 5.8 + 1.2 + 5.2 + 11.2)/5 = 7.2°F

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The specific enthalpy at the exit of the pipe is 2804 kJ/kg.

The expression of specific enthalpy at the exit of the pipe can be found by the following method:

Here, m = mass flow rate of the steam = 3 kg/s

q1 = specific enthalpy at inlet of the pipe = 2744 kJ/kg

W = work done on the system = 0 (steady-state)

Q = rate of heat transfer = 696 kW

z1 = elevation of the inlet = 0 m

z2 = elevation of the outlet = +71 m

Since the rate of heat transfer is given as

Q = -m(h2 - h1) + W + Q_hot

So, h2 = [Q - Q_hot + m(h1) - W]/m

Where W = 0 and Q_hot = 0

h2 = (696 - 0 + 3(2744))/3

h2 = 2804 kJ/kg

Therefore, the specific enthalpy at the exit of the pipe is 2804 kJ/kg.

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Answer: 302 children and 42 adults

Step-by-step explanation:

x= Children y= Adults

x+ y = 344

1.50x + 2y= 537

Then I would use elimination and multiply the first equation by -2.

-2x-2y= -688

+1.5x+2y= 537

Add the equations and get

-0.5x= -151

Divide by -0.5

x= 302

Then plug x back into the equation.

302+y=344

Subtract 302 from both sides.

y=42

Answer:

please stop being lazy by using OCR! next time type the question!

there's nothing such as  = -x2 3x + 1

it's probablhy f(x) = -x² + 3x + 1

Answer:

2 distinct irrational roots

Step-by-step explanation:

Answer:

9/15 = 3/5 (simplified)

Step-by-step explanation:

In a right triangle, the cosine is the ratio of the adjacent side to the hypotenuse:

[tex]\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}[/tex]

The adjacent side is the side that makes up the angle but is not the hypotenuse.

I'm assuming the answer box should ask for cos(theta) rather than cos(x).

Answer:

40%

Step-by-step explanation:

6/15=favorable amount/total amount

6/15=2/5

2/5*20

Answer: 40%

6/15 can be simplified to 2/5. multiply by 20 on both sides to get 40/100 (40%)

Answer: 1/2

Step-by-step explanation:

From the question, we are informed that Eva uses 10 tiles to make a mosaic and that five of the tiles are blue.

The fraction that represents the tiles that are blue will be:

= Number of blue tiles / Total number of tiles

= 5/10

= 1/2

Answer:0.3 m

Step-by-step explanation:

Given

Ken can Jump [tex]1\ \frac{1}{5}\ m[/tex]

Steve can Jump [tex]1.5\ m[/tex]

Converting mixed fraction into a fraction

[tex]\Rightarrow 1\ \dfrac{1}{5}=\dfrac{1\times 5+1}{5}\\\\\Rightarrow \dfrac{6}{5}\ m=1.2\ m[/tex]

The difference between their Jumps is

[tex]\Rightarrow 1.5-1.2=0.3\ m[/tex]

Steve Jumps 0.3 m more than ken

Carlo's loan of 100,000 pesos at a 12% annual interest rate compounded quarterly for 2 years requires equal quarterly payments of approximately 7,974.51 pesos.

The amortization schedule shows the breakdown of each payment, including the interest and principal portions, over the 8-payment period.

To compute the equal quarterly payments for Carlo's loan, we can use the formula for the equal payment amount in an amortizing loan:

Payment = (Principal * Interest Rate) / (1 - (1 + Interest Rate)^(-n))

Where:

Principal = 100,000 pesos (loan amount)

Interest Rate = 12% per year (convert to quarterly rate by dividing by 4: 0.12/4 = 0.03)

n = number of payments (2 years * 4 quarters per year = 8 payments)

Let's calculate the payment amount:

Payment = (100,000 * 0.03) / (1 - (1 + 0.03)^(-8))

Payment = 7,974.51 pesos

Therefore, each quarterly payment for Carlo's loan is 7,974.51 pesos.

To create an amortization schedule, we can calculate the interest and principal portion of each payment for each quarter:

Quarter | Beginning Balance | Payment | Interest | Principal | Ending Balance

1 | 100,000 | 7,974.51| 3,000 | 4,974.51 | 95,025.49

2 | 95,025.49 | 7,974.51| 2,851.27 | 5,123.24 | 89,902.25

3 | 89,902.25 | 7,974.51| 2,697.07 | 5,277.44 | 84,624.81

4 | 84,624.81 | 7,974.51| 2,537.87 | 5,436.64 | 79,188.17

5 | 79,188.17 | 7,974.51| 2,373.66 | 5,600.85 | 73,587.32

6 | 73,587.32 | 7,974.51| 2,204.37 | 5,769.14 | 67,818.18

7 | 67,818.18 | 7,974.51| 2,029.89 | 5,944.62 | 61,873.56

8 | 61,873.56 | 7,974.51| 1,850.13 | 6,124.38 | 55,749.18

This amortization schedule shows the payment number, beginning balance, payment amount, interest portion, principal portion, and ending balance for each quarter.

Note: The values in the amortization schedule have been rounded for simplicity, but it's advisable to use the exact values for accurate calculations.

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To find the arc length, we can use the formula:

[tex]\[ L = \frac{\theta}{360} \times 2\pi r \]\\Given:\( r = \frac{d}{2} = \frac{30}{2} = 15 \) ft\( \theta = 42 \) degrees\( \pi = 3.14 \)\\Substituting the given values into the formula:\[ L = \frac{42}{360} \times 2 \times 3.14 \times 15 \]\[ L = \frac{42}{360} \times 94.2 \]\[ L = \frac{3956.4}{360} \]\[ L \approx 10.99 \] ftTherefore, the arc length traveled by the car, to the nearest hundredth, is 10.99 feet. The correct option is c.[/tex]

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Objective function is Z = 9 XC,RB + 11 XCB,GM, and the constraint for minimum vitamin C for Red Berry is75XC,RB + 350XCB,RB + 200XA,RB >= 0.

Objective function for the given statement is Z = 9 XC,RB + 11 XCB,GM,

where, XC, RB is the number of gallons of Cherry juice used in Red Berry, XCB, GM is the number of gallons of Cranberry juice used in Green Mush and also, XA, RB is the number of gallons of Avocado juice used in Red Berry, XC, GM is the number of gallons of Cherry juice used in Green Mush, XCB, GM is the number of gallons of Cranberry juice used in Green Mush, XA, GM is the number of gallons of Avocado juice used in Green Mush.

Hence, the objective function is Z = 9 XC,RB + 11 XCB,GM.

Minimum vitamin C for Red Berry will be given by the equation,

350XCB,RB + 400XC,RB + 200XA,RB >= 325XC,RB

=> 75XC,RB + 350XCB,RB + 200XA,RB >= 0

So, the constraint for minimum vitamin C for Red Berry is75XC,RB + 350XCB,RB + 200XA,RB >= 0.

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