Please select a b c or d

To determine which differential equation(s) are linear, we need to examine the form of each equation. A linear differential equation is one that can be written in the form a(x)y" + b(x)y' + c(x)y = g(x), where a(x), b(x), c(x), and g(x) are functions of x.

The differential equation 2xy" - 5xy' + y = sin(3x) is linear. It can be written in the form a(x)y" + b(x)y' + c(x)y = g(x), where a(x) = 2x, b(x) = -5x, c(x) = 1, and g(x) = sin(3x).
The differential equation (v)² + xy = In(x) is not linear. It does not follow the form a(x)y" + b(x)y' + c(x)y = g(x) because it contains a term with (v)², where v represents the derivative of y with respect to x. This term does not have a linear coefficient.
The differential equation y' + sin(y) = e^(3x) is linear. It can be written in the form a(x)y' + b(x)y = g(x), where a(x) = 1, b(x) = sin(y), and g(x) = e^(3x).
The differential equation (x²+1)y" - 3y - 2x³y = -x - 9 is not linear. It does not follow the form a(x)y" + b(x)y' + c(x)y = g(x) because it contains a term with (x²+1)y", where the coefficient is a function of x.
The differential equation y' + xy = y" is linear. It can be written in the form a(x)y' + b(x)y = g(x), where a(x) = 1, b(x) = x, and g(x) = y".

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The system of equations that can be used to find the number of black and white copies and color copies is b + c = 68  , 0.08b + 0.15c = 6.00    .

In the question ,

it is given that

the total amount paid by the customer at the print shop = $6.00

total number of copies that the customer made = 68

the cost for printing 1 black and white copy = $0.08

the cost of printing 1 color copy = $0.15

let the number of black and white copies be "b"

let the number of color copies be "c" .

So ,

b + c = 68  

and

the cost of b black and white copies is = 0.08b

the cost of c color copies is = 0.15c

the total cost = cost of b black and white copies + cost of c color copies

6.00 = 0.08b + 0.15c

0.08b + 0.15c = 6.00

Therefore , The system of equations that can be used to find the number of black and white copies and color copies is b + c = 68  , 0.08b + 0.15c = 6.00   , the correct option is (d) .

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The computation is that the width is 21.5 feet and the height is 12.5.

Let the height = h

Let the width = (3 × h) - 16 = 3h - 16

Therefore, the dimensions will be:

h + 3h - 16 = 34

4h = 34 + 16

4h = 50

Divide

h = 50/4

h = 12.5

Therefore width = 3h - 16 = 3(12.5) - 16

= 37.5 - 16

= 21.5

The width is 21.5 feet and the height is 12.5.

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Answer:

slope: -2

y intercept: 3

Step-by-step explanation:

A Loss of $1.25 was made on each pen.

To calculate the loss made on each pen, we need to determine the cost price of each pen and compare it to the selling price.

Given that 50 pens were worth $250, we can find the cost price per pen by dividing the total value by the number of pens:

Cost price per pen = Total value / Number of pens

                  = $250 / 50

                  = $5

Therefore, the cost price of each pen is $5.

Now, we can calculate the loss made on each pen by finding the difference between the cost price and the selling price:

Loss per pen = Cost price per pen - Selling price per pen

            = $5 - $3.75

            = $1.25

So, a loss of $1.25 was made on each pen.

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Answer:

Pedro: 1,482 hits

Ricky: 1,202 hits

Step-by-step explanation:

p + r = 2,684

p = r + 280

r + 280 + r = 2,684

2r = 2,404

r = 1,202

p = 1,202 + 280 = 1,482

The radius of the base of the cone is approximately 12.65 feet if The cone is formed from 3,200 ft of gravel.

Height of cone =  24 feet

The volume of the cone = \(3,200 ft^3\)

To find the volume of the cone, the formula used here is:

V =π* \(r^2h\)

Here, the values of V and H are known terms. we need to calculate the radius r of the cone.

π = 3.14 constant value

Substituting the values in the above equation, we get:

\(3,200 = (1/3)^2*(24)*\) π

\(r^2\)= 3,200 / (8π)

\(r^2\) = 400 / π

r = 12.65

Therefore, we can conclude that the radius of the base of the cone is  12.65 feet.

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\(\sf\purple{Mutual \:funds}\) collect money from investors, create capital, and offer various investment options.

\(\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘\)

Answer:

8 of 10 free throws

Step-by-step explanation:

10/15 is .6666667 or about 67%

But 8/10 is .8 or 80%

80% > 60%

Volume =  Length * Width * Height

Length = l = 15,5 in = 393,7 cm

Width = w = 11,2 in = 284,48 cm

Height = h = 8 in = 20,32 cm

Volume =  15,5 * 11,2 * 8 = 1388,8 in or 35275.52 cm

Answer: Multiplying both sides of the original equation by 100 gives the same

the solution as follows;

100 × (2.3·p - 10.1) = 100 × (6.5·p - 4 - 0.01·p)

230·p - 1010 = 650·p - 400 - p

Step-by-step explanation:

Answer:

ok

Step-by-step explanation:

The volume of the regular pyramid is 128 unit³.

Option D) 128 unit³ is the correct answer.

This question is incomplete, the missing image is uploaded along this answer below.

The volume of pyramid is expressed as;

V = ( 1/3 ) × l × w × h

Given that;

We substitute our given values into the equation above.

V = ( 1/3 ) × 8 × 8 × 6

V = 128 unit³

The volume of the regular pyramid is 128 unit³.

Option D) 128 unit³ is the correct answer.

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The equation of the line that passes through point (8, -7) and parallel to the line x + 2y = 18 is

A linear function consists of functions where the variables has exponents of 1.

The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

definition of variable

y = output variable

m = slope

x = input variable

c = y intercept

x + 2y = 18

rewriting gives : y = -x/2 + 9

when the line is parallel the slope is equal hence the slope of the line is -1/2.

using the point slope formula for point (8, -7) which is

(y - y') = m(x - x')

(y + 7) = -1/2(x - 8)

y + 7 = -x/2 + 4

y = -x/2 - 3

the equation of the line is y = -x/2 - 3

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When a point on a triangle is dilated, the coordinate of the vertex changes

The coordinate of the vertex after the dilation is (-1.5,4)

The given parameters are:

(x,y) = (-3,8)

k = 0.5

To calculate the coordinate of the vertex after the dilation, we make use of:

(x,y)' = k * (x,y)

So, we have:

(x,y)' = 0.5 * (-3,8)

Evaluate the product

(x,y)' = (-1.5,4)

Hence, the coordinate of the vertex after the dilation is (-1.5,4)

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Answer:

x = 6 (C)

Step-by-step explanation:

x is 6,

it came from formula :

\( \large \boxed{ \sf y - y_1 = m(x - x_1)}\)

we just need to fill the x1 with point (6, 1),

so the answer is :

\( \sf y - 1 = - \frac{1}{3} (x -6)\)

━━━━━━━━━━━━━━━━━

Hope it helps!

The calculate the chi-square statistic using the formula:

χ² = (n - 1) s² / σ²

The correct set of hypotheses to test whether the standard deviation for the age of "gamers" is equal to 6 years can be stated as:

In symbols, the hypotheses can be expressed as:

H0: σ = 6

Ha: σ ≠ 6

Where σ represents the population standard deviation of age for gamers.

To test this hypothesis, we can use a statistical test called the chi-square test for variance.

We would need a sample of ages of gamers and calculate the sample variance, denoted as s².

We can then calculate the chi-square statistic using the formula:

χ² = (n - 1) s² / σ²

where n is the sample size.

Under the null hypothesis, the chi-square statistic follows a chi-square distribution with degrees of freedom equal to n - 1.

We can then calculate the p-value associated with the observed chi-square statistic and reject or fail to reject the null hypothesis based on a chosen significance level.

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Answer:

\(\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}\)

Herefore, the plane was flying at a height of approximately 31680.30 feet or 6.00 miles when it passed over the George Washington Bridge.

a. To determine the height of the plane when it passed over the George Washington Bridge, we need to use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the height of the plane is the hypotenuse, and the distance from the bridge to the landing location is one of the other sides.

First, we need to convert the distance from miles to feet, as the height of the bridge is given in feet:

6 miles = 6 * 5280 feet = 31680 feet

Using the Pythagorean theorem, we have:

Height of plane = sqrt(212^2 + 31680^2) feet

Height of plane = 31680.30 feet (rounded to two decimal places)

To convert this height to miles, we divide by the number of feet in a mile:

Height of plane = 31680.30 / 5280 miles

Height of plane = 6.00 miles (rounded to two decimal places)

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By taking a quotient between the lengths, we can see that Peter can make 7 pieces.

We know that Peter has 17 feet of ribbon, and he wants to cut it in pieces of (2 + 3/7) feet.

To see how many pieces can he get, we just need to take the quotient between the total length and the length of each piece.

We will get:

N = (17 ft)/(2 + 3/7)ft = 17/(2 + 3/7)

The denominator of the quotient can be rewritten as:

2 + 3/7 = 14/7 + 3/7 = 17/7

N = 17/(17/7)  =7

N = 7

So 7 pieces can be made.

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Answer: yes because there's so much that scientists haven't discovered, so that could lead to different creatures like Bigfoot being real.

Answer:

10

Step-by-step explanation: can u tell me if am right

Answer:

2d-5=Q ?

Step-by-step explanation:

Am I supposed to be representing quarters too? I think this should solve it though. Lmk if somethings wrong :)

A) there is 5 blue marbles out of 20 total marbles.

The probability of picking blue would be number of blue/ total marbles = 5/20 which can be reduced to 1/4

The answer is 1/4

B) the more marbles of a color would be a greater chance of picking it.

Green has the highest number of marbles so the answer is green.

Answer:

the rate of change is 16. 2÷32 = 16

4÷32 is 16 etc

Answer:

1X = 16Y every time the X value goes up by one it increase by 16.

Step-by-step explanation:

If you do 32/2 you will get the answer 16 and if you do 4/64 it also says 16.

The difference between (2,32) and (4,64) 64-32 is 32 4-2 is 2 and you also get 32,2 from that equation.

Answer:

I believe the answer is A. 130

Answer:

A 130

Step-by-step explanation:

Answer:

\(\textsf{B.} \quad g(x)=-x^2-2\)

Step-by-step explanation:

Transformations

\(f(x)+a \implies f(x) \: \textsf{translated $a$ units up}.\)

\(f(x)-a \implies f(x) \: \textsf{translated $a$ units down}.\)

\(-f(x) \implies f(x) \: \textsf{reflected in the $x$-axis}.\)

\(f(-x) \implies f(x) \: \textsf{reflected in the $y$-axis}.\)

From inspection of the given graph, we can see that g(x) is function f(x) reflected in the x-axis and translated 2 units down.

Given function f(x):

\(f(x)=x^2\)

Reflected in the x-axis:

\(-f(x) \implies g(x)= -x^2\)

Translated 2 units down:

\(-f(x)-2 \implies g(x)=-x^2-2\)

Therefore:

\(g(x)=-x^2-2\)

Note:  

If the leading coefficient of a quadratic function is positive, the parabola opens upwards.

If the leading coefficient of a quadratic function is negative, the parabola opens downwards.

Therefore, as g(x) opens downwards, the term in x² will be negative.

The closest answer choice to this value is option 1, 33. Therefore, the best estimate for the unicity distance for an affine cipher is 33.

To find the best estimate for the unicity distance for an affine cipher, we can use the following formula:

Unicity Distance  (U) = (keyspace / entropy) × log2(1 / redundancy).

Given the answer choices:
1. 33
2. 35
3. 33
4. 26
5. 17.5

For an affine cipher, the keyspace is 26^2 (since there are 26 possibilities for both 'a' and 'b' in the equation

y = (ax + b) mod 26).

The entropy of English text is roughly 1.5 bits/character, and the redundancy is approximately 0.7.

Using the formula, we have:

U = (26^2 / 1.5) × log2(1 / 0.7)

U ≈ 33.49

Therefore, the best estimate for the unicity distance for an affine cipher is 33.

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In this problem, we are dealing with a random variable related to people's opinions on a new building project. We are given four options for the correct wording of the random variable and need to determine the correct one. Additionally, we are asked to calculate probabilities associated with the number of people who favor the new building project, ranging from exactly 4 to at most 6.

a) The correct wording for the random variable is "rv = the number of people who are in favor of a new building project." This wording accurately represents the random variable as the count of individuals who support the project.

b) To calculate the probability that exactly 4 people favor the new building project, we need to use the binomial probability formula. Assuming the probability of a person favoring the project is p, we can calculate P(X = 4) = (number of ways to choose 4 out of 10) * (p^4) * ((1-p)^(10-4)). The value of p is not given in the problem, so this calculation requires additional information.

c) To find the probability that less than 4 people favor the new building project, we can calculate P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3). Again, the value of p is needed to perform the calculations.

d) The probability that more than 4 people favor the new building project can be calculated as P(X > 4) = 1 - P(X ≤ 4) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)).

e) The probability that exactly 6 people favor the new building project can be calculated as P(X = 6) using the binomial probability formula.

f) To find the probability that at least 6 people favor the new building project, we can calculate P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10).

g) Finally, to determine the probability that at most 6 people favor the new building project, we can calculate P(X ≤ 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6).

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