In Problems 1 through 16, transform the given differential equation or system into an equivalent system of first-order differential equations.x(3)−2x′′+x′=1+tet.

Answers

Answer 1

The equivalent system of first-order differential equations for the given problem is: 1. dv1/dt = v2 2. dv2/dt = v3 3. dv3/dt = 2v2 - v1 + 1 + t*e ^t

Given differential equation: x''' - 2x'' + x' = 1 + t*e ^t

Step 1: Define new variables.
Let's introduce new variables:
v1 = x'
v2 = v1'
v3 = v2'

Now we have:
v1 = x'
v2 = v1'
v3 = v2'

Step 2: Rewrite the given equation using new variables.
Substitute the new variables into the given differential equation:
v3 - 2v2 + v1 = 1 + t*e ^t

Step 3: Write the equivalent system of first-order differential equations.
Now we have the following equivalent system of first-order differential equations:
dv1/dt = v2
dv2/dt = v3
dv3/dt = 2v2 - v1 + 1 + t*e ^t

So, the equivalent system of first-order differential equations for the given problem is:

1. dv1/dt = v2
2. dv2/dt = v3
3. dv3/dt = 2v2 - v1 + 1 + t*e ^t

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Related Questions

Use the parabola tool to graph the quadratic function f(x)=−1/2x2+7

Answers

Answer:

use desmos cant add pcitures

Step-by-step explanation:

Sweet Glee is an ice cream shop chain that has locations all across the nation. Customers at Sweet Glee have the option of ordering 1, 2 or 3 Scoops of ice cream in their cone. The mean number of scoops ordered is y=2.86, with a standard deviation of o=0.23. Suppose that we will take a random sample of n-7 ice cream cone orders and record the number of scoops for each, Let x represent the sample mean of the number of scoops for the 7 ice cream cone orders. Consider the sampling distribution of the sample meanx Complete the following. Do not round any intermediate computations. Write your answers with two decimal places, rounding if needed. (a) Find (the mean of the sampling distribution of the sample mean). х (b) Find the standard deviation of the sampling distribution of the sample mean). o ?

Answers

(a) The mean of the sampling distribution of the sample mean is equal to the population mean, which is y=2.86. So, х = 2.86.

(b) The standard deviation of the sampling distribution of the sample mean is equal to the population standard deviation divided by the square root of the sample size. So, o = 0.23 / sqrt(7) = 0.087.

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What is the difference in cubic inches between the volume of the large prism and volume of the smaller prism?

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The difference between the large prism and the small prism is 276 inches cube.

How to find the volume of a prism?

The prisms above are rectangular base prisms. Therefore, the difference between the volume of the large prism and volume of the smaller prism can be calculated as follows:

Volume of the larger prisms  = lwh

where

l = lengthw = widthh = height

Therefore,

Volume of the larger prisms  = 6 × 4 × 15

Volume of the larger prisms  = 360 inches³

volume of the smaller prism = 7 × 4 × 3

Volume of the larger prisms  = 28 × 3

Volume of the larger prisms  = 84 inches³

Therefore,

difference of the volume = 360 - 84

difference of the volume = 276 inches³

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Exercise 4. Let n ≥ 2 be an even integer. Determine in how many ways we can color an nxn floor (split into a grid of 1 x 1 tiles) with k colors; we consider two colorings to be the same if we obtain one from the other by rotating the grid.

Answers

The number of ways to color an nxn floor with k colors for an even integer n is:

4 * k^(n^2/4).

To determine the number of ways to color an nxn floor with k colors for an even integer n, and considering two colorings to be the same if obtained by rotating the grid, we need to follow these steps:

1. Identify the even integer n and the number of colors k.
2. Calculate the number of unique configurations considering rotations. For a grid of size nxn, there are 4 unique rotations (0, 90, 180, and 270 degrees).
3. For each unique rotation, calculate the number of possible colorings. Since each tile in the grid can be any of the k colors, the number of colorings for each unique rotation is k^(n^2/4), assuming n is divisible by 4.
4. Add up the colorings for all unique rotations. Since there are 4 unique rotations, the total number of colorings, considering rotations to be the same, is 4 * k^(n^2/4).

So, the number of ways to color an nxn floor with k colors for an even integer n, considering two colorings to be the same if obtained by rotating the grid, is 4 * k^(n^2/4).

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Please give an explanation!

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It’s basically asking what’s the probability of the blue then the white, count the total you have for all the marbles then over the number you have for the blue and white i think.

Which graph is that of the inequality shown below

Answers

Answer:

The correct graph is graph B.

What is the equation of a circle with center (-3,-5) and radius 4?
A. (x-3)2 + (y- 5)² = 16
B. (x+3)2 + (y+ 5)² = 16
C. (x-3)2 + (v-5)2 = 4
O D. (x+3)2 + (y + 5)² = 4
SUB

Answers

The equation of the circle with center (-3, -5) and radius 4 is (x + 3)² + (y + 5)² = 16.

What is the equation of a circle with center (-3,-5) and radius 4?

The standard form equation of a circle with center (h, k) and radius r is:

(x - h)² + (y - k)² = r²

Given that the center of the circle is (-3, -5) and the radius is 4.

Hence, we can substitute these values into the formula to get the equation of the circle:

Plug in h = -3, k = -5 and r = 4

(x - h)² + (y - k)² = r²

(x - (-3))² + (y - (-5))² = 4²

Simplifying and expanding the equation, we get:

(x + 3)² + (y + 5)² = 16

Therefore, the equation of the circle is (x + 3)² + (y + 5)² = 16.

Option B) (x + 3)² + (y + 5)² = 16 is the correct answer.

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Let T be an unbiased estimator of parameter 0. We have that: (a multiple choice question -- please mark all that apply). a. E (T-0)2 = 0 b. E,(T-0) = 0 c. E(T - ET)2 = 0 d. The MSE of T is the same as the variance of T

Answers

If T is an unbiased estimator, then the MSE can be decomposed as follows: MSE(T) = Var(T) + [E(T)-0]^2 = Var(T). Therefore, (d) is true.

(a) E(T-0)^2=Var(T) + [E(T)-0]^2, which is always greater than or equal to 0, but it may not necessarily be 0 unless T is a constant function. Therefore, (a) is false in general.

(b) If E(T-0)=0, then T is an unbiased estimator of 0. This statement is true.

(c) E(T-ET)^2=Var(T) is always greater than or equal to 0, but it may not necessarily be 0 unless T is a constant function. Therefore, (c) is false in general.

(d) The Mean Squared Error (MSE) of T is defined as MSE(T) = E[(T-0)^2]. If T is an unbiased estimator, then the MSE can be decomposed as follows: MSE(T) = Var(T) + [E(T)-0]^2 = Var(T). Therefore, (d) is true.

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I WILL GIVE BRAINLILEST TO WHOEVER GETS IT RIGHT

A 35-year-old person who wants to retire at age 65 starts a yearly retirement contribution in the amount of $5,000. The retirement account is forecasted to average a 6.5% annual rate of return, yielding a total balance of $431,874.32 at retirement age.

If this person had started with the same yearly contribution at age 40, what would be the difference in the account balances?

A spreadsheet was used to calculate the correct answer. Your answer may vary slightly depending on the technology used.

$378,325.90
$359,978.25
$173,435.93
$137,435.93

Answers

Answer:

B

Step-by-step explanation:

Using the same yearly contribution of $5,000 and an average annual rate of return of 6.5%, starting at age 40 instead of 35, the total balance at retirement age of 65 would be $359,978.25.

To calculate this, we can use the future value formula:

FV = PV x (1 + r)^n

where FV is the future value, PV is the present value (initial contribution), r is the interest rate per period, and n is the number of periods.

If we start at age 40 and contribute $5,000 per year for 25 years (until age 65), the present value would be $0 (since we haven't made any contributions yet) and the number of periods would be 25. The interest rate per period would be 6.5% / 1 = 0.065.

Using these values in the future value formula, we get:

FV = $5,000 x ((1 + 0.065)^25 - 1) / 0.065 = $359,978.25

Therefore, the difference in the account balances between starting at age 35 and starting at age 40 would be:

$431,874.32 - $359,978.25 = $71,896.07

So the correct answer is option B: $359,978.25.

Find the value of c on the interval (a, b) such that f'(c) = f(b) − f(a)/b- a

f(x) = 2x^3 - 3x^² - 12x - 4 on interval [5,9]

average rate of change =

Answers

The value of c on the interval (5,9) such that f'(c) = f(b) - f(a) / (b - a) is c = 3, and the average rate of change of f(x) on the interval [5,9] is 139.

First, we can find the average rate of change of f(x) on the interval [a,b] using the formula:

average rate of change = [f(b) - f(a)] / (b - a)

Substituting the given values of a = 5 and b = 9 into the formula, we get:

average rate of change = [f(9) - f(5)] / (9 - 5)

Next, we need to find f(9) and f(5) to calculate the average rate of change. To do this, we first need to find the derivative of f(x) using the power rule:

f'(x) = 6x² - 6x - 12

Now, we can use the Mean Value Theorem to find a value c in the interval (5,9) such that f'(c) equals the average rate of change. According to the Mean Value Theorem, there exists a value c in the interval (5,9) such that:

f'(c) = [f(9) - f(5)] / (9 - 5)

Substituting the derivative of f(x) and the values of f(9) and f(5) into the equation, we get:

6c² - 6c - 12 = [2(9)³ - 3(9)² - 12(9) - 4 - (2(5)³ - 3(5)² - 12(5) - 4)] / (9 - 5)

Simplifying the right-hand side of the equation, we get:

6c² - 6c - 12 = (658 - 204) / 4

6c² - 6c - 12 = 114

6c² - 6c - 126 = 0

Dividing both sides by 6, we get:

c² - c - 21 = 0

Using the quadratic formula, we can solve for c:

c = [1 ± sqrt(1 + 4(21))] / 2

c = [1 ± 5] / 2

The two possible values of c are:

c = 3 or c = -4

However, since the interval is (5,9), c must be between 5 and 9. Therefore, the value of c that satisfies the Mean Value Theorem is c = 3.

Finally, substituting f(5) and f(9) into the formula for the average rate of change, we get:

average rate of change = [f(9) - f(5)] / (9 - 5)

= [(2(9)³ - 3(9)² - 12(9) - 4) - (2(5)³ - 3(5)² - 12(5) - 4)] / (9 - 5)

= [434 - (-104)] / 4

= 139

Therefore, the value of c on the interval (5,9) such that f'(c) = f(b) - f(a) / (b - a) is c = 3, and the average rate of change of f(x) on the interval [5,9] is 139.

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Help me please , I really don't understand this ( Find the major arc, Give an exact answer in terms of pi and be sure to include the correct unit.)

Answers

In the given circle, the length of major arc LNM is 29/3(π)

Calculating the length of an arc

From the question, we are to calculate the length of the major arc in the given diagram

Length of an arc is given by the formula

Length = θ/360° × 2πr

Where θ is the angle subtended by the arc at the center of the circle

r is the radius of the circle

From the given information,

r = 6 cm

θ = 360° - 70°

θ = 290°

Substitute the parameters into the formula

Length = 290/360 × 2×π×6

Length = 29/3(π)

Hence,

Length of arc LNM is 29/3(π)

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Figure A is dilated with scale factor r=3 to create figure A′ .

Answers

Answer:

r=3 to dilation

Step-by-step explanation:

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Prove that for all real numbers r > 0,8 >0 and all vectors a, b, c in a normed vector space V.
a. Br(α) ⊂ Bs(b)→Br(α+2c)⊂Bs(b+2c)
b.Br(α) ⊂ Bs(b)→Br(α+1/2c)⊂Bs(b+1/2c)

Answers

X is in Bs(b+1/2c), which implies Br(α+1/2c)⊂Bs(b+1/2c).

a. We want to show that Br(α+2c)⊂Bs(b+2c) given that Br(α)⊂Bs(b).

Let x be any element in Br(α+2c), then we have ||x-(α+2c)|| < r.

Using the triangle inequality, we get:

||x-(α+2c)|| = ||(x-α)-2c|| ≤ ||x-α||+2||c|| < r+2||c|| = 8 (since r > 0 and ||c|| < 4).

So, ||x-α|| < 8 - 2||c|| < 2.

Thus, x is also in Br(α) ⊂ Bs(b), which implies ||x-b|| < r.

Using the triangle inequality again, we have:

||x-(b+2c)|| = ||(x-b)-2c|| ≤ ||x-b||+2||c|| < r+2||c|| = 8.

Therefore, x is in Bs(b+2c), which implies Br(α+2c)⊂Bs(b+2c).

b. We want to show that Br(α+1/2c)⊂Bs(b+1/2c) given that Br(α)⊂Bs(b).

Let x be any element in Br(α+1/2c), then we have ||x-(α+1/2c)|| < r.

Using the triangle inequality, we get:

||x-(α+1/2c)|| = ||(x-α)-1/2c|| ≤ ||x-α||+1/2||c|| < r+1/2||c|| = 4 (since r > 0 and ||c|| < 8).

So, ||x-α|| < 4 - 1/2||c|| < 3.

Thus, x is also in Br(α) ⊂ Bs(b), which implies ||x-b|| < r.

Using the triangle inequality again, we have:

||x-(b+1/2c)|| = ||(x-b)-1/2c|| ≤ ||x-b||+1/2||c|| < r+1/2||c|| = 4.

Therefore, x is in Bs(b+1/2c), which implies Br(α+1/2c)⊂Bs(b+1/2c).

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employees at an antique store are hired at a wage of $15 per hour, and they get a $0.75 raise each year. write an equation that shows how a worker's hourly wage, y, depends on the number of years he or she has worked at the store,

Answers

To represent the hourly wage of an employee at the antique store, we can use the following equation:
y = 15 + 0.75x
where y represents the worker's hourly wage, and x represents the number of years the employee has worked at the store. In this equation, 15 is the initial hourly wage, and 0.75 is the annual raise.

The equation that shows how a worker's hourly wage, y, depends on the number of years he or she has worked at the store can be written as:

y = 15 + 0.75x

where x represents the number of years the employee has worked at the antique store.

This equation takes into account the starting wage of $15 per hour and the $0.75 raise that the employee receives each year they work at the store.

So, for example, if an employee has worked at the store for 5 years, their hourly wage would be:

y = 15 + 0.75(5) = 18.75

where y represents the worker's hourly wage, and x represents the number of years the employee has worked at the store.

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1. What is the probability of tossing 3 coins of uniform texture at the same time, and two of them happen to be heads up?

Answers

The probability of tossing 3 coins of uniform texture at the same time, and two of them happen to be heads up is [tex]\frac{3}{8}[/tex] or 0.375.

The probability of tossing 3 coins of uniform texture at the same time, and two of them happen to be heads up is as follows:

1. Each coin has 2 possible outcomes: heads (H) or tails (T).
2. Since there are 3 coins, there are [tex]2^3 = 8[/tex] total possible outcomes (HHH, HHT, HTH, THH, HTT, THT, TTH, TTT).
3. We're interested in the outcomes where 2 coins are heads up: HHT, HTH, THH.
4. There are 3 favorable outcomes out of 8 total outcomes.

So, the probability of tossing 3 coins of uniform texture at the same time, and two of them happen to be heads up is 3/8 or 0.375.

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Determine the standard deviation of the random variable, B(400,0.9). O A. 10 B. 360 • CV40 D.2 E. 6

Answers

The standard deviation of the random variable B(400, 0.9) is 6 (option E).

To determine the standard deviation of the random variable B(400, 0.9), we need to use the formula for the standard deviation of a binomial distribution:

Standard deviation (σ) = √(n * p * (1 - p))

Here, n is the number of trials (400) and p is the probability of success (0.9). Now, let's calculate the standard deviation step by step:

1. Calculate the probability of failure (1 - p): 1 - 0.9 = 0.1
2. Multiply n, p, and the probability of failure: 400 * 0.9 * 0.1 = 36
3. Calculate the square root of the result: √36 = 6

So, the standard deviation of the random variable B(400, 0.9) is 6 (option E).

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Which of the following ordered pairs is a solution of 5x + 2y = -3?
a. (2, -4) c. (1, -4)
b. (-4, 2) d. (-4, 1)

Answers

The ordered pair (1, -4) is the solution of equation 5x + 2y = -3.

We can check which of the ordered pairs is a solution of equation 5x + 2y = -3 by substituting the values of x and y in the equation and checking if it is true.

a. (2, -4)

Substituting x = 2 and y = -4 in 5x + 2y = -3, we get:

5(2) + 2(-4) = 10 - 8 = 2

So, (2, -4) is not a solution to the equation.

Similarly

b. (-4, 2)

5(-4) + 2(2) = -20 + 4 = -16

So, (-4, 2) is not a solution to the equation.

c. (1, -4)

5(1) + 2(-4) = 5 - 8 = -3

So, (1, -4) is a solution to the equation.

d. (-4, 1)

5(-4) + 2(1) = -20 + 2 = -18

So, (-4, 1) is not a solution to the equation.

Therefore, the ordered pair (1, -4) is the solution of equation 5x + 2y = -3.

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One apple cost 2x one banana cost x+1 what is the total cost of 2 apples and 5 bananas?

Answers

Nolan bought 2 apples and 10 bananas.

To solve this problem form the system of equations first, then solve them to find the values of the variables.

Nolan bought 2 apples and 10 bananas.

It's given that,

Nolan and his children bought fruits (Apples and bananas) worth $8.

Cost of each apple and bananas are $2 and $0.40 respectively.

Let the number of bananas he bought = y

And the number of apples = x

Therefore, cost of the apples =$2x

And the cost of bananas = $0.40y

Total cost of 'x' apples and 'y' bananas = $(2x + 0.40y)

Equation representing the total cost of fruits will be,

(2x + 0.40y) = 8

10(2x + 0.40y) = 10(8)

20x + 4y = 80

5x + y = 20 --------(1)

If he bought 5 times as many bananas as apples,

y = 5x ------(2)

Substitute the value of y from equation (2) to equation (1),

5x + 5x = 20

10x = 20

x = 2

Substitute the value of 'x' in equation (2)

y = 5(2)

y = 10

Therefore, Nolan bought 2 apples and 10 bananas.

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Full Question ;

Nolan and his children went into a grocery store and he bought $8 worth of apples

and bananas. Each apple costs $2 and each banana costs $0.40. He bought 5 times as

many bananas as apples. By following the steps below, determine the number of

apples, 2, and the number of bananas, y, that Nolan bought.

What is mzQPS?
A. 68
B. 71
C. 84
D. cannot be determined

Answers

The value of the angle m<QPS cannot be determined. Option D

How to determine the value

To determine the value of the angle, we need to take note of the properties of a parallelogram

The opposite sides are parallel and equal.The opposite angles are also equal.The consecutive or adjacent angles are supplementary, that is, they sum up to 180 degrees

From the information given, we have that;

m<R = 6x -14

m<Q = 3x + 8

m< S= 5x + 4

The value of the angle , QPS cannot be determined because the angle is not represented with any variable for calculation

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A cylindrical cooler has a diameter of 30 inches and a height of 24 inches. How many gallons of water can the cooler hold? (1 ft³ ≈ 7. 5 gal) Round your answer to the nearest tenth of a gallon

Answers

Rounding to the nearest tenth of a gallon, we have that the cooler can hold about 74.0 gallons of water.

The volume of a cylinder is given by the formula V = πr^2h, where r is the radius of the base and h is the height.

In this case, the diameter of the cooler is 30 inches, which means the radius is 15 inches (since the radius is half the diameter). The height is 24 inches.

Using the formula for the volume of a cylinder, we have:

V = π[tex]r^2h[/tex]

= π([tex]15^2)(24[/tex])

= 5400π cubic inches

To convert cubic inches to gallons, we need to divide by the conversion factor 231 cubic inches per gallon. Therefore, the volume of the cooler in gallons is:

[tex]V_gal[/tex]= (5400π cubic inches) / (231 cubic inches/gallon) ≈ 74.0 gallons

Rounding to the nearest tenth of a gallon, we have that the cooler can hold about 74.0 gallons of water.

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The power series (r- 5)" 22 has radius of convergence 2 At which of the following values of x can the alternating series test be used with this series to verify convergencer at x? A B 4 с 2 D 0 The alternating series test can be used to show convergence of which of the following alternating series? 14- ) +1-82+ 1 4 1 720 + 1 16 + a + ..., wherea, {} ifnis even in sodd + 1 6 + 5 +1 +...+an +..., where an 3 $ 9 u 13 15 +an + ..., where a, = (-1)". 2+1 I only B ll only С ill only D I and II only E III and III

Answers

Answer:

The alternating series test states that if the terms of an alternating series decrease in absolute value and approach zero, then the series converges.

For the power series (r - 5)^n/22 with radius of convergence 2, the alternating series test can be used at x = 2 and x = -2. This is because the alternating series test requires the terms to decrease in absolute value, and for values of x beyond the radius of convergence, the terms of the series increase in absolute value and do not approach zero.

For the given alternating series:

1/4 - 1/2 + 1/8 - 2/720 + 1/16 - ...

The terms decrease in absolute value and approach zero, so the alternating series test can be used to verify convergence.

1/6 + 5/13 + ... + a_n

Since a_n is odd and greater than 3, the terms do not alternate in sign and the alternating series test cannot be used to verify convergence.

(-1)^n (2n+1)/(n+1)

The terms decrease in absolute value and approach zero, so the alternating series test can be used to verify convergence.

Step-by-step explanation:

The answer is D, I and II only. The alternating series test can be used to verify convergence of an alternating series, which means the signs of the terms alternate.

In the given power series (r-5) ^22, there is no alternating pattern of signs, so the alternating series test cannot be used to verify convergence of this series at any value of x. Therefore, the answer is none of the options provided (N/A).

For the second part of the question, we need to check each series to see if they have an alternating pattern of signs. The first series (1/4^n) has all positive terms, so the alternating series test cannot be used to verify convergence of this series. The second series (-1)^n(1/2^n) has alternating signs, so the alternating series test can be used to verify convergence of this series. The third series (-1)^n(1/(4n+1)) also has alternating signs, so the alternating series test can be used to verify convergence of this series. Therefore, the answer is D, I and II only.

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The mean amount spent by each customer on non-medical mask at Chopper Drug Mart is 28 dollars with a standard deviation of 8 dollars. The population distribution for the amount spent on non-medical mask is positively skewed. For a sample of 36 customers, what is the probability that the sample mean amount spent on non-medical mask is greater than 22 dollars but less than 25 dollars?

Answers

the probability that the sample mean amount spent on non-medical mask is greater than 22 dollars but less than 25 dollars is approximately 0.0668.

We can use the central limit theorem to approximate the sampling distribution of the sample mean. The mean of the sampling distribution of the sample mean is equal to the population mean, which is 28 dollars, and the standard deviation of the sampling distribution of the sample mean is equal to the standard deviation of the population divided by the square root of the sample size, which is 8/sqrt(36) = 4/3 dollars.

Now we need to find the probability that the sample mean is greater than 22 dollars but less than 25 dollars. Let X be the sample mean amount spent on non-medical mask. Then we need to find P(22 < X < 25).

We can standardize X as follows:

Z = (X - μ) / (σ / sqrt(n))

where μ = 28, σ = 8, and n = 36.

Substituting the values, we get:

Z = (X - 28) / (8/√36)

Z = (X - 28) / (4/3)

So we need to find P((22 - 28)/(4/3) < Z < (25 - 28)/(4/3)), which simplifies to P(-4.5 < Z < -1.5).

Using a standard normal table or calculator, we find:

P(Z < -1.5) ≈ 0.0668

P(Z < -4.5) ≈ 0.00003

Therefore, P(-4.5 < Z < -1.5) ≈ 0.0668 - 0.00003 ≈ 0.0668.

So the probability that the sample mean amount spent on non-medical mask is greater than 22 dollars but less than 25 dollars is approximately 0.0668.

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log(x + 2) - log 3 = log (5x + 1)

Answers

Log[(x-2)/3]=log(5x-1)

(x-2)/3=5x-1

(x-2)=3(5x-1)

x-2=15x-3

-2=14x-3

1=14x

x=1/14.

Hope this helps!

The equation of a straight line that is parallel to a straight line. 2y =3x-1​

Answers

The equation of the line that is parallel to 2y = 3x - 1 and passes through the point (4, 2) is: y = (3/2)x - 4

To find the equation of a straight line that is parallel to the line 2y = 3x - 1, we need to remember that parallel lines have the same slope.

First, let's rearrange the given equation into slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept:

2y = 3x - 1

y = (3/2)x - 1/2

So the slope of this line is 3/2.

Now, if we want to find the equation of a line that is parallel to this line, we just need to use the same slope. Let's call the new line y = mx + b, where m is the slope we just found and b is the y-intercept we need to find.

So the equation of the parallel line is:

y = (3/2)x + b

To find the value of b, we need to use a point on the line. Let's say we want the line to go through the point (4, 2):

2 = (3/2)(4) + b

2 = 6 + b

b = -4

So the equation of the line that is parallel to 2y = 3x - 1 and passes through the point (4, 2) is: y = (3/2)x - 4

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16. Express the line 13x - 14y = 70 in slope intercept form

Answers

The line 13x - 14y = 70 expressed in slope-intercept form is y = (13/14)x - 5.

Here are the steps to follow:

Step 1: Start with the given equation, which is in standard form: 13x - 14y = 70.

Step 2: Solve for y to put it in slope-intercept form (y = mx + b, where m is the slope and b is the y-intercept).

First, subtract 13x from both sides of the equation:
-14y = -13x + 70

Next, divide both sides by -14:
y = (13/14)x - 5

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The half-life of radium is 1620 year what fraction of the radium sample will remain after 3240 years

Answers

So, 0.25 or 25% of the radium sample will remain after 3240 years.

The decay chain for radium-226 is as follows: radium-226 has a half-life of 1600 years and produces an alpha particle and radon-222; radon-222 has a half-life of 3.82 days and produces an alpha particle and polonium-218; polonium-218 has a half-life of 3.05 minutes and produces an alpha particle and lead-214; lead-214 has a half-life of 26.8 minutes and produces.

The half-life of radium is 1620 years, which means that after 1620 years, half of the radium sample will decay, and the remaining half will remain. After another 1620 years (3240 years total), the remaining half will decay, and half of that half, or one-fourth of the original sample, will remain.

Therefore, after 3240 years, the fraction of the radium sample that will remain is:

Formula used :[tex]N(t)=2^{-t/1620}[/tex]

[tex]N(t)=2^{-3240/1620}[/tex]

= 1/4

= 0.25

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(7, 1) and (-2, 3)
Slope =

Answers

The slope of the line passing through (7,1) and (-2,3) is -2/9.

We use the following formula to get the slope of a line through two specified points:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

We can calculate the slope of the line passing through the points (7, 1) and (-2, 3) using this formula:

slope = (3 - 1) / (-2 - 7) = 2 / (-9) = -2/9

Therefore, the slope of the line passing through the points (7, 1) and (-2, 3) is -2/9.

The slope of a line, in geometric terms, is the ratio of the vertical change (rise) to the horizontal change (run). If the slope is negative, the line is decreasing as we move from left to right. With a slope of 2 units downward for every 9 units to the right, the line is sloping downward from left to right.

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True or false: A set is considered closed if for any members in the set, the result of an operation is also in the set

Answers

False. A set is considered closed under an operation if the result of that operation on any two elements in the set also belongs to the set.

A set is considered closed if it contains all of its limit points. In other words, if a sequence of points in the set converges to a point that is also in the set, then the set is closed. Another equivalent definition is that the complement of the set.

In mathematics, sets are collections of distinct objects. These objects can be anything, including numbers, letters, or even other sets. The concept of sets is fundamental in mathematics and is used to define many other mathematical structures.

Sets can be denoted in various ways, including listing the elements inside curly braces { }, using set-builder notation, or using set operations to define new sets from existing ones. Some common set operations include union, intersection, difference, and complement.

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Pete’s plumbing was just hired to replace the water pipes in the Johanssons house Pete has two types of pipes. He can use a pipe with a radius of 8pm or a pipe with radius of 4cm

The 4cm pipes are less expensive then the 8cm pipes for Pete to buy so Pete wonders if there are a number of 4cm pipes he could use that would give the same amount of water to the Johanssons house as one 8cm pipe
Circles and ratios water pipes

Answers

It would take 4 pipes with a radius of 4cm to replace one pipe with a radius of 8cm and provide the same amount of water flow.

We have,

The volume of water that can flow through a pipe is proportional to the cross-sectional area of the pipe.

The formula for the area of a circle is:

A = πr²

where A is the area of the circle and r is the radius of the circle.

For a pipe with a radius of 8cm, the cross-sectional area is:

A_8cm = π(8cm)²

     = 64π cm²

For a pipe with a radius of 4cm, the cross-sectional area is:

A_4cm = π(4cm)²

     = 16π cm²

To find out how many 4cm pipes would be needed to replace one 8cm pipe, we can compare the areas of the two pipes:

Number of 4cm pipes

= A_8cm / A_4 cm

= (64π) / (16π)

= 4

                 

Therefore,

It would take 4 pipes with a radius of 4cm to replace one pipe with a radius of 8cm and provide the same amount of water flow.

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Explain why the graph is misleading

For all three points say the reason and explain what specifically is going on in the graph

Answers

The graph is misleading because the y values are not labeled

Explaining why the graph is misleading

The graph represents the given parameter where

The x-axis represent the yearThe y-axis represent the marriage rate

Examining the y-axis of the graph, we can see that

The y-axis is not labeled

This means that

We cannot determine what the y values represent

This is because not labelling  the y-axis do not show the correct representation of the graph

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