a certain discrete mathematics class consists of 26 26 students. of these, 15 15 plan to major in mathematics and 15 15 plan to major in computer science. five students are not planning to major in either subject. how many students are planning to major in both subjects? (be prepared to explain your reasoning with some sort of diagram.)

To begin solving this problem, we need to determine the dimensions of the rectangular region that the farmer will fence in. Let's say the length of thr uses, is given by the equation:
e rectangle is L and the width is W. The perimeter of the rectangle, which will be the length of fencing the farme
2L + W = 350

Solving for W, we get:

W = 350 - 2L

Next, we need to divide the rectangular region into three smaller rectangles by placing two parallel fences. Let's say the two fences are placed along the length of the rectangle, dividing it into three sections with widths of x, y, and z. Therefore, we have:

L = x + y + z

Now, we can determine the area of the entire fenced-in region by summing the areas of the three smaller rectangles. The area of a rectangle is given by the equation:

Area = Length x Width

Therefore, the total area of the fenced-in region is:

Area = (xW) + (yW) + (zW)

Substituting W = 350 - 2L and L = x + y + z, we get:

Area = (x(350-2(x+y+z))) + (y(350-2(x+y+z))) + (z(350-2(x+y+z)))

Simplifying this equation, we get:

Area = 350(x+y+z) - 2(x^2 + y^2 + z^2)

To maximize the area, we need to take the derivative of this equation with respect to one of the variables (x, y, or z), set it equal to zero, and solve for the variable. This process is too complicated to do by hand, so we will use a calculator or computer program to find the maximum area.

After finding the maximum area, we can determine the dimensions of the region that give us this maximum area. We do this by using the equations we derived earlier:

W = 350 - 2L

L = x + y + z

With the maximum area and these equations, we can solve for the dimensions of the region that give us the maximum area.

In summary, the farmer should fence in a rectangular region with dimensions that maximize the total area of three smaller rectangles created by placing two parallel fences. The maximum area can be found by taking the derivative of the area equation and setting it equal to zero. The dimensions of the region that give us the maximum area can be found by using the equations we derived earlier.

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Answer:

i belive by rounding you get 1

Step-by-step explanation:

The values of all integration function have been obtained.

Q2.  x²/2 tan²x - x² tan x/2 + x tan x - ln|cosx| + C

Q3.  32 ln|x + 1| + 23/15 ln|x - 2| - 41/8 ln|x + 3| + C.

Q2.

To find the integration of the given function i.e.

∫x tan²xdx,

Using the integration by parts, we use the following formula:

∫u dv = uv - ∫v du

Let us consider u = tan²x and dv = x dx.

So, du = 2 tan x sec²x dx and v = x²/2.

Using these values in the formula we get:

∫x tan²xdx = ∫u dv

                 = uv - ∫v du

                 = x²/2 tan²x - ∫x²/2 * 2 tan x sec²x dx

                 = x²/2 tan²x - x² tan x/2 + ∫x dx     (integration of sec²x is tanx)

                 = x²/2 tan²x - x² tan x/2 + x tan x - ∫tan x dx

                                                                (using integration by substitution)

                 = x²/2 tan²x - x² tan x/2 + x tan x - ln|cosx| + C

So, the integration of the given function using integration by parts is

x²/2 tan²x - x² tan x/2 + x tan x - ln|cosx| + C.

Q3.

To find the integration of the given function i.e.

∫(2x² + 9x - 35)/[(x + 1)(x - 2)(x + 3)] dx,

Using partial fraction, we have to first factorize the denominator.

Let us consider (x + 1)(x - 2)(x + 3).

The factors are (x + 1), (x - 2) and (x + 3).

Hence, we can write the given function as

A/(x + 1) + B/(x - 2) + C/(x + 3),

Where A, B and C are constants.

To find these constants A, B and C, let us consider.

(2x² + 9x - 35) = A(x - 2)(x + 3) + B(x + 1)(x + 3) + C(x + 1)(x - 2).

Putting x = -1, we get

-64 = -2A,

So, A = 32 Putting x = 2, we get

23 = 15B,

So, B = 23/15 Putting x = -3, we get

41 = -8C,

So, C = -41/8

So, we can write the given function as

∫(2x² + 9x - 35)/[(x + 1)(x - 2)(x + 3)] dx = ∫32/(x + 1) dx + ∫23/15(x - 2) dx - ∫41/8/(x + 3) dx

Now, we can integrate these three terms separately using the formula: ∫1/(x + a) dx = ln|x + a| + C

So, we get

= ∫(2x² + 9x - 35)/[(x + 1)(x - 2)(x + 3)] dx

= 32 ln|x + 1|/1 + 23/15 ln|x - 2|/1 - 41/8 ln|x + 3|/1 + C

= 32 ln|x + 1| + 23/15 ln|x - 2| - 41/8 ln|x + 3| + C

So, the integration of the given function using partial fraction is 32 ln|x + 1| + 23/15 ln|x - 2| - 41/8 ln|x + 3| + C.

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The area of the middle rectangle is (d1 * d2) - (A1 + A2). By using the given distances and areas, we can find the area of the middle rectangle.

To find the area of the middle rectangle, we need to use the given information about the two specified distances and the areas of the left and right rectangles. Here are the steps to follow:

Let the two specified distances be d1 and d2, and the areas of the left and right rectangles be A1 and A2, respectively.
The area of the middle rectangle can be found by subtracting the areas of the left and right rectangles from the total area of the three rectangles combined.
The total area of the three rectangles combined is equal to the product of the two specified distances, or d1 * d2.
Therefore, the area of the middle rectangle is (d1 * d2) - (A1 + A2).
Plug in the given values for d1, d2, A1, and A2, and simplify to find the area of the middle rectangle.

So, the area of the middle rectangle is (d1 * d2) - (A1 + A2). By using the given distances and areas, we can find the area of the middle rectangle.

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The general solution of the given homogeneous differential equation is:y = ±x√(Cx² + 2)

The given differential equation is: 2xyy' + (x² - y²) = 0

We have to find the general solution of the given homogeneous differential equation. To solve the above differential equation, we will use the substitution method.

Put y = vx and y' = v + xv'

Differentiating both sides w.r.t x: y' = v + xv' ⇒ v' = (y' - v)/x

Differentiating again w.r.t x: y'' = v' + xv'' + v' ⇒ y'' = (y'' - 2y'v + v² + xv')/x

Substituting these values in the given differential equation:

2x(v)(v + xv') + (x² - v²x²) = 0

2v + 2x²v' + x - v² = 0

2x²v' + 2v/x - v³/x = -1/x

We can write the above differential equation as:

2x²dv/dx + 2v/x = v³/x - 1/x

Separating the variables and integrating both sides:

∫dx/x = ∫[v/(v² - 2)]dv/x

⇒ ln |x| + ln |v² - 2| + C

⇒ ln |x(v² - 2)| = ln |Cx|

⇒ v² - 2 = Cx² (where C is a constant)

⇒ v = ±√(Cx² + 2)

Putting the value of v in y = vx, we get:

y = x√(Cx² + 2) and y = -x√(Cx² + 2)

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Answer: f(2) = -7   , g(3) = -29

Step-by-step explanation: this problem can be solved via substitution

-2(2) - 3 = -4 - 3 = -7

-3(3)^2 - 2 = -3(9) - 2 = -27 - 2 = -29

To solve the given equations, (i) In(t+3) = 4.2 and (ii) In(t + 1) - In(t-1) = 1.504, we can use the properties of natural logarithms and algebraic manipulations. The solutions to the equations are approximately t ≈ 63.686 for equation (i) and t ≈ 1.5715 for equation (ii).

(i) In(t+3) = 4.2
To solve this equation, we can exponentiate both sides using the property of logarithms:
e^(In(t+3)) = e^4.2Simplifying, we have:
t + 3 = e^4.2
Now, we can isolate t by subtracting 3 from both sides:
t = e^4.2 - 3 ≈ 63.686
(ii) In(t + 1) - In(t-1) = 1.504
Using the property of logarithms that ln(a) - ln(b) = ln(a/b), we can rewrite the equation as:
ln((t+1)/(t-1)) = 1.504
To isolate t, we can exponentiate both sides:e^(ln((t+1)/(t-1))) = e^1.504
Simplifying, we have:
(t+1)/(t-1) = e^1.504
Now, we can solve for t by cross-multiplying:
(t+1) = e^1.504 * (t-1)
Expanding and simplifying:
t + 1 = 1.504t - 1.504
Rearranging terms:
0.504t = 2.504
Dividing both sides by 0.504:t ≈ 2.504/0.504 ≈ 4.963
Therefore, the solutions to the equations are t ≈ 63.686 for equation (i) and t ≈ 1.5715 for equation (ii).

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Answer:

2:6 because 2:6 is equivalent to 1:3

Step-by-step explanation:

1x1=1 and 3x2=6

A sequence can be arithmetic, geometric or neither.

The sequence is (c) -19, -9, 1, 11

In this case, the sequence is an arithmetic sequence, and it is represented with the following formula

\(\mathbf{y = 10x - 29}\)

When x = 1, we have:

Substitute 1 for x in \(\mathbf{y = 10x - 29}\)

\(\mathbf{y = 10 \times 1 - 29}\\\)

\(\mathbf{y =- 19}\)

When x = 2, we have:

Substitute 2 for x in \(\mathbf{y = 10x - 29}\)

\(\mathbf{y = 10 \times 2 - 29}\)

\(\mathbf{y = - 9}\)

When x = 3, we have:

Substitute 3 for x in \(\mathbf{y = 10x - 29}\)

\(\mathbf{y = 10 \times 3 - 29}\)

\(\mathbf{y = 1}\)

When x = 4, we have:

Substitute 4 for x in \(\mathbf{y = 10x - 29}\)

\(\mathbf{y = 10 \times 4 - 29}\)

\(\mathbf{y = 11}\)

So, the corresponding y values when x = 1, 2, 3 and 4 are -19, -9, 1 and 11.

Hence, the sequence is (c) -19, -9, 1, 11

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Answer:

? = 120°

Step-by-step explanation:

the central angle is the same as the arc that subtends it , that is

? = 120°

The table is attached below.

What are table entries?

Entities are gathered at tables. A group of properties makes up an entity. Each object may contain up to 252 name-value pairs for its properties.

From the information given, we can make a table to display all the options available for Michael to choose clothing options.

The table is attached as follows:

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There are 12 clothing options for Michael to choose from in his closet. By the fundamental principle of counting, the possible number of options is calculated.

The fundamental principle of counting states that an operation/event can be performed in 'm' ways and a second operation/event can be performed in 'n' ways. Then there are (m × n) ways for the two operations to be performed together.

It is given that,

Michael is having three shirts - yellow, green, and orange; two pairs of shorts: navy, gray and two footwear: tennis shoes and sandals.

So, we can write

the number of shirts = 3

the number of shorts = 2

the number of footwear = 2

Then, according to the fundamental principle of counting, all these are multiplied to get the total number of ways that he can wear them together.

I.e., 3 × 2 × 2 = 12

Therefore, there are 12 combinations for him to choose one among these.

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Answer: 5. 83 1/3*pi, or 261.8 (approx.) 6. 2*pi, or 6.28 (approx.) 7. 42 2/3*pi or 134.04 (approx.) 8. 144*pi or 452.39 (approx.)

Step-by-step explanation:

Volume of a circular cone : pi*r^2*h/3

I applied the formula to find these answers

Answer:

Iam not sure but i think its -14.45$

Step-by-step explanation:

45.55-20-20-20

After withdraw the amount he have - $14.45 in his account.

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

We have to given that;

The balance in Jake's checking account is $45.55.

Here, he wrote three checks for $20.00 each.

Hence, Total amount to withdraw is,

⇒ $20.00 x 3

⇒ $60.00

Hence, Left money in his account = $45.55 - $60.00

                                                     = - $14.45

Thus, After withdraw the amount he have - $14.45 in his account.

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The sequence shows the repetition in order to show the length of the sequence.

A sequence simply means an enumerated collection of objects where repetitions are allowed.

Like a set, the sequence also contains members which are called elements or terms. The number of the elements show the sequence length.

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Answer:

For this one, your answer will be

(x-8) would describe the case here planes grew 8 inches but x inches this weak.

Step-by-step explanation:

hope it helps

have a great day!!

Answer:

the plant was 8 in last week and x inches tall this week

Step-by-step explanation:

it is just fliped

The cost of one knife will be 5.23 which is calculated by using the given information about knives and spoons.

From the given information in the question we can form two equations:

We will consider the variables representing the cost of spoons and knives as k and f respectively.

now we will build the equations to find out the relation between knives and spoons from the given information.

k = s + 3

As the cost of knives is three times more than spoons we add 3 to the cost of spoons

the other information given is about the sum of 9 spoons and 12 knives

which we will write as:

9s + 12k = 82.80

By substituting the first equation in the second equation we will get an equation containing only one variable which is easier to solve

9s + 12(s + 3) = 82.80

9s + 12s + 36 = 82.80

21s = 82.80 - 36

21s = 46.8

s = 46.8 / 21

s = 2.23

now by substituting the value of s in the first equation

k = s + 3

k= 2.23 + 3

k = 5.23

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Answer:

Yes.

Step-by-step explanation: 8/3 is equal to 32/12, but simplified. Hope this helps!

The concentration of the antibiotic will drop below 20.0 micrograms/milliliter at around 11.1 hours after injection.

To find when the concentration drops below a level of 20.0 micrograms/milliliter, we need to solve the equation:

f(t) < 20 for t, where f(t) = t^2 * e^(t-12) and t >= 0.

Set up the inequality
t^2 * e^(t-12) < 20

Solve the inequality
Unfortunately, there's no simple algebraic way to solve this inequality. We'll need to use numerical methods or graphical analysis to approximate the value of t.

One way to approach this is by using a graphing calculator or software to graph the function f(t) = t^2 * e^(t-12) and then finding the value of t where the graph is below the horizontal line y = 20.

Upon analyzing the graph, you'll find that the concentration drops below 20.0 micrograms/milliliter at approximately t ≈ 11.1 hours (keep in mind that the actual value might slightly vary depending on the accuracy of the method used).

So, the concentration of the antibiotic will drop below 20.0 micrograms/milliliter at around 11.1 hours after injection.

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Answer:

j+47=55

Step-by-step explanation:

“the sum of” means adding, so you add j and 47, which is or is equal to 55

j+47=55

Answer:

Approximately = 0.17

Step-by-step explanation:

Answer:

\(\frac{25}{25+4+120 }\)

\(\frac{25}{149 }\)

.17 = 17%

Step-by-step explanation:

Based on their percentages, the total number of students in Ridgewood Junior High School is 170.

The percentage refers to the ratio or relative value of a variable or number compared to another.

Percentages are expressed as the product resulting from the multiplication of a quotient (numerator over denominator) by 100.

The percentage of students who brought their lunch = 20%

The number of students who brought their lunch = 34

Since all students either eat from the school cafeteria or bring their launch, the percentage of students who brought their lunch = 80% (1 - 20%).

34 = 20%

The percentage of students in the school = 100% (20% + 80%)

The number of students in the school = 34/20%

= 170

Thus, using percentage ratios, we can conclude that the total number of students in the school is 170.

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The area of this rectangular figure is equal to 71.3 square centimeters.

In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation (formula):

A = LB

Where:

By substituting the given dimensions into the formula for the area of a rectangle, we have the following;

Area of rectangle = 6.2 cm × 11.5 cm

Area of rectangle = 71.3 square centimeters.

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Complete Question:

Find the area of the rectangular figure shown above.

Answer:

The answer is12 4/11

Step-by-step explanation:

4+7=11 7/11+8/11

= (7+8)/11

= 15/11

= 1 4/11

=11+1 4/11

=12 4/11

Answer:

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Step-by-step explanation:

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Mark sets aside $404 for more supplies.

Mark spent $175 on supplies, so his total cost is $175.

Mark sold 6 pieces of artwork for $70 each, so he earned 6 * $70 = $420 from these pieces.

He sold 15 - 6 = 9 pieces of artwork at $85 each, so he earned 9 * $85 = $765 from these pieces.

His total revenue is $420 + $765 = $1185.

His profit is his revenue minus his cost: $1185 - $175 = $1010.

He plans to set aside 40% of his profit for more supplies, so he will set aside 0.4 * $1010 = $404.

Therefore, Mark sets aside $404 for more supplies.

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Answer:

12. 12 students scored in the 80-89 range

13. 31 students took the maths test

Answer:

-4

It would be -4 because the midpoint of a line is the point thats right in the middle.

Answer:

x=5

Step-by-step explanation:

18x+5+18x-5=180(because they are interior angles)

38x=180

=36x/36=180/36

=5degrees

The number of ways to select 9 players for the starting lineup from a team of 15 players  is 4862 ways.

The number of ways to select 9 players for the starting lineup from a team of 15 players can be calculated using the formula for combinations, which is given by:

C(n,k) = n! / (k! (n-k)!)

Where n is the total number of items, k is the number of items being selected, ! means factorial, and C(n,k) represents the number of combinations of k items from n.

Using this formula, the number of ways to select 9 players from a team of 15 players is:

C(15,9) = 15! / (9! (15-9)!) = 15! / (9! 6!) = 4,862

So, there are 4,862 ways to select 9 players for the starting lineup from a team of 15 players.

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