7283
+3124
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Hello.

sin²x + cos²x = 1

cos²x = 1 - sin²x

secx = 1/cosx

sec²x = tan²x + 1

Use the power rule,

[tex]\displaystyle \int x^n \, dx = \frac{x^{n+1}}{n+1} + C[/tex]

with [tex]n=-8[/tex]. It follows by the fundamental theorem of calculus that

[tex]\displaystyle \int_1^7 \frac{dx}{x^8} = -\frac1{7x^7} \bigg|_{x=1}^{x=7} = -\frac17 \left(\frac1{7^7} - \frac1{1^7}\right) = \boxed{\frac17 - \frac1{7^8}}[/tex]

Answer:

141; 6526; 28d.

Step-by-step explanation:

try this option, all the details are in the attachment.

If each collection consists of at most 3 books on each subject, the number of collection that can be made of 3 English, 4 Economics, and 5 Business Mathematics books are 40.

A combination, as a mathematical technique, determines the number of possible arrangements in a collection of items.

In the combination, the order of the selection does not matter.

The implication is that in combinations, one can select the items in any order, unlike permutations, where the order of selection matters.

English books on shelf = 3

Economics books on shelf = 4

Business Mathematics books on shelf = 5

Collections to be made = 3 books on each subject

The solution can be set up as a combination problem, as follows:

3 C 3 x 4 C 3 x 5 C 3

3! / 3! (3 – 3)! The solution is 1.

4! / 3! (4 – 3)! The solution is 4.

5! / 3! (5 – 3)! The solution is 10.

1 x 4 x 10

= 40

Thus, if each collection consists of at most 3 books on each subject, the number of collections that can be made of 3 English, 4 Economics, and 5 Business Mathematics books is 40.

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The pairs of prime numbers (a,b) between 1 and 10 inclusive such that a^b * b^a+1 is prime are

The expression that is a prime number is given as:

a^b * b^a + 1

The boundary or range of numbers of a and b is not given.

So, we make use of numbers between 1 and 10

i.e. 1 ≤ a ≤ 10 and 1 ≤ b ≤ 10

Using the above range, we have the following program to determine the pairs of prime numbers (a, b).

for a in range(1,11):

   for b in range(1,11):

       num = (a* *b) * (b* *a) + 1

       flg = False

       if num > 1:

           for i in ra nge(2, num):

               if (num % i) == 0:

                   flg = True

                   break

       if not flg:

           print(str(a)+","+str(b))

The output of the above program is:

(1,1), (1,2), (1,4), (1,6), (1,10), (2,1), (2,2), (2,3), (2,4), (3,2), (4,1), (4,2), (4,4) and (4,6)

The above represent all pairs of prime numbers (a,b) such that a^b * b^a+1 is prime

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g(x) is a translation of f(x), we have:

g(x) = f(x) - 3

We have the two functions:

[tex]g(x) = x^2 - 3\\\\f(x) = x^2[/tex]

We can see that g(x) is just a translation of 3 units downwards of f(x), to write g(x) in terms of f(x) we can just replace the first term by f(x):

[tex]g(x) = x^2 - 3 = f(x) - 3[/tex]

So we have:

g(x) = f(x) - 3

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Considering a geometric sequence, the pattern is given as follows:

1, 2, 4, 8, 16, 32, 64.

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

The first term and common ratio are given as follows:

[tex]a_1 = 1, q = 2[/tex].

Hence the remaining terms are:

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For the number line, an open circle will be drawn on the value of 6 and the arrow pointing to the right side.

Given the inequality expression as shown

-2x + 9 < x − 9

Collect the like terms

-2x - x < -9 - 9

-3x < -18

Divide through by -3

x > -18/-3

x > 6

For the number line, an open circle will be drawn on the value of 6 and the arrow pointing to the right side.

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The width and height of the rectangle inscribed in the right triangle have a measure of 3.529 units.

In this problem we must use critical values and algebraic methods to determine to determine the dimensions of the rectangle such that the area is a maximum. The equation of the quadrilateral is formed by definition of the area of a rectangle:

A = w · h    (1)

Where:

And the area of the entire triangle is:

0.5 · (5) · (12) = w · h + 0.5 · w · (12 - h) + 0.5 · (5 - w) · h

30 = w · h + 6 · w - 0.5 · w · h + 2.5 · h - 0.5 · w · h

30 = 6 · w + 2.5 · h

2.5 · h = 30 - 6 · w

h = 12 - 2.4 · w    (2)

The quadrilateral of maximum area is always a square, then we must  solve for w = h:

w = 12 - 2.4 · w

3.4 · w = 12

w = 3.529

Then, the width and height of the rectangle inscribed in the right triangle have a measure of 3.529 units.

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The amount of  earnings per share is $2.77.

a. Earnings per share = price per share / (P/E) ratio

Earnings per share =   ​$46.07 / 16.66

Earnings per share=  $2.77

B. Overpriced or underpriced stock

At P/E ratio = 12

Earnings per share = ​$46.07  / 12

Earnings per share = $3.84

Earning yield = ( Earning per share / market value )× 100

Earning yield =  (3.84 /  ​$46.07   ) × 100

Earning yield  = 8.34%

At P/E ratio = 13

Earnings per share = ​$46.07  / 13

Earnings per share = $3.54

Earning Yield= (3.54 / 46.07 ) × 100

Earning Yield= 7.68%

At P/E ratio = 14

Earnings per share = ​$46.07 / 14

Earnings per share = $ 3.3

Earnings yield= ( 3.3 / 46.07 )×100

Earnings yield= 7.16%

Average of  earning yield given P/E ratio is 12-14

Average of  earning yield= ( 8.34 + 7.68 + 7.16 ) / 3

Average of  earning yield= 7.73%

Earning yield =  ( Earning per share / market value ) × 100

Earning yield= ( 2.77 / 46.07 ) ×100

Earning yield = 6.01%

Hence, Based on the above the stock is underpriced.

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Answer:

22222222222222222222222222+22222222

The solution to the given system of linear equations is x = 1, y = 2. That is (1, 2)

From the question, we are to solve the given system of equations

The given system of equations is

4x + y = 6     -----------(1)

2x - 3y = -4   -----------(2)

From the equation (1)

4x + y = 6

y = 6 - 4x      ----------(3)

Substitute the value of y into equation (2)

2x - 3y = -4

2x -3(6 - 4x) = -4

2x -18 +12x = -4

2x + 12x = -4 + 18

14x = 14

x = 14/14

x = 1

Substitute the value of x into equation (3)

y = 6 - 4x

y = 6 - 4(1)

y = 6 - 4

y = 2

Hence, the solution to the given system of linear equations is x = 1, y = 2. That is (1, 2)

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The value of x is 2 and the length of JK is 4

The given parameters from the circle are:

The lines SR and SQ are the radii of the circle P

This means that lines JK and JL are congruent

So, we have:

JK = KL

Substitute LK = 2x + 4 and JK = 4

4 = 2x + 4

Rewrite the above equation as:

2x + 4 = 8

Subtract 4 from both sides

2x + 4 - 4 = 8 - 4

Evaluate the difference

2x = 4

Divide both sides by 2

2x = 4/2

This gives

x = 2

Substitute x = 2 in LK = 2x + 4

LK = 2*2 + 4

Evaluate the product of 2 and 2

LK = 4 + 4

This gives

LK = 8

The point N divides JK into 2 equal segments

So, we have

JN = JK/2

JN= 8/2

JN = 4

Hence, the value of x is 2 and the length of JK is 4

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Answer: [tex]\sqrt{407}[/tex]

Step-by-step explanation:

In this triangle, we know that [tex]IJ=46, IK=24, JK=36[/tex].

So, using the Law of Cosines in triangle IJK,

[tex]36^2 = 46^2 + 24^2 - 2(46)(24) \cos (\angle JIK)\\\\-1396=-2(46)(24) \cos(\angle JIK)\\\\\cos (\angle JIK)=\frac{349}{552}[/tex]

Using the Law of Cosines in the triangle LIK,

[tex](KL)^2 = 23^2 + 24^2 - 2(23)(24) \cos (\angle JIK)\\\\(KL)^2 = 23^2 + 24^2 - 2(23)(24)\left(\frac{349}{552} \right)\\\\(KL)^2 = 407\\\\KL=\sqrt{407}[/tex]

The points are known to intersect the curve at

We have our equation as: r(t)=ti+(4t-t2)k (4t - t2)k

From  r(t)

We have x to be t, y to be 0 and z=4t-t2

The given paraboloid can be defined to be

z=x^2+y^2

We are to put the values in the equation

4t-t²=t²+0

2t²=4t

Then t wuld be 2 or 0

Hence we have to conclude that ours points of intersection are at (0,0,0) and (2,0,4).

The 0,0,0) and (2,0,4) points is where the intersection of the paraboloid take place.

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The inverse of the demand function is; P = 9 - 0.25Q

The profit-maximizing price and quantity are; $8.5 and 2 units.

The maximum profit is; $1

A) The demand function we are given is;

Q = 36 - 4P

Making P the subject gives the inverse demand function;

P = (36 - Q)/4

P = 9 - Q/4

P = 9 - 0.25Q

B) The profit-maximization point is the point at which MR = MC.

MR refers to the marginal revenue and MC is the marginal cost.

MC can be calculated as the first derivative of the cost function:

C(Q) = 4 + 4Q + Q²

MC = C'(Q) = 2Q + 4

Total Revenue = Price * Quantity

Total Revenue = (9 - 0.25Q) * Q

Total Revenue = 9Q - 0.25Q²

MR is gotten by differentiating Total Revenue to get;

MR = 9 - 0.5Q

Applying the condition MR = MC, we have;

9 - 0.5Q = 4 - 2Q

Solving for Q gives Q = 2

Thus, profit maximizing quantity is 2.

Thus, profit maximizing price will be;

P(2) = 9 - 0.25(2)

P(2) = $8.5

C) Formula for Maximum Profit is;

Profit = Total Revenue - Total Cost

Total Revenue = 8.5 * 2

Total revenue = $17

Total Cost is;

C(2) = 4 + 4(2) + 2²

C(2) = $16

Thus;

Maximum Profit = 17 - 16 = $1

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Answer:

12 inches

Step-by-step explanation:

Perimeter refers to distance around the 2D shape.

A hexagon is a polygon with 6 sides. The formula for the perimeter of a hexagon is P=6s

72=6s

The hexagon is 12 inches long

A hexagon has 6 sides. This means that 72 divided by 6 sides = 12 in.

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—————

Please remember to revise this and make it in your own words if you want! I hope this helps you. -Doodle

—————

The total amount invested was $4000. $2000 was invested at 11% while the remaining $2000 was invested at 10%.

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the total amount of money invested, hence:

(0.5* x * 0.11) + (0.5 * x * 0.1) = 420    

x = 4000

The total amount invested was $4000. $2000 was invested at 11% while the remaining $2000 was invested at 10%.

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To answer the question, we need to convert cups to pints, now here is a way to remember the gallon, quarts, to pints, and to cups

In the Kingdom of Gallons (Write a big G on your paper)

Inside the G write 4 Qs

There were four Queens

Inside the Qs write 2 ps

Each Queen had to princess

In each princess write 2 Cs

And each princess has two Cats

Now we know that there is 2 Cups in each Pints so

since she sold 34 cups of juice in cups then we divide 34 by 2 to get

17 PINTS

Answer:

150 pints

Step-by-step explanation:

I believe you meant "By the end of the day, 3/4th of the quantity was sold."

Recall that 2 cups = 1 pint, so 400 cups = 200 pints, and

3/4 th of that would be 150 pints.

The graph that represents the inequality is:

Number line with an open circle on 1, shading to the right and an open circle on 5, shading to the left.

The inequality is:

|2x - 6| < 4

Which means that the distance of 2x - 6 to the origin is less than 4, hence:

-4 < 2x - 6 < 4.

The solution is:

2x - 6 > -4

2x > 2

x > 1

2x - 6 < 4

2x < 10

x < 5

The solution has open circles at x = 1 and x = 5, as they are not part of the solution, and the shading is in the middle, as the solution is 1 < x < 5, hence the correct option is:

Number line with an open circle on 1, shading to the right and an open circle on 5, shading to the left.

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The conclusion that they would arrive at based on the rejection region would be to reject the null hypothesis.

This is the region that tells us that we are not to accept the null. The conclusion would be to reject the null.

This happens when the rejection region is found to be around the area that is in the critical value.

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The average cost per issue of magazine is $3

The given parameters are:

Cost = $36

Issue = 12

The cost per issue is calculated as:

Average = Cost/issue

This gives

Average = 36/12

Evaluate

Average = 3

Hence, the average cost per issue of magazine is $3

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Answer:

1. 30

Step-by-step explanation:

∠H + ∠T = 180

(2x+60)+(x+30)=180

3x+90=180

3x=90

x=30

Cara has saved 1, 430 pennies. She needs to put the pennies in paper rolls so the bank can count them easily. Each penny roll holds 50 pennies. The number of pennies will be in the last roll is 30.

To find out the number of pennies will be in the last roll.

The branch of mathematics dealing with the properties and manipulation of numbers. a science that deals with the addition, subtraction, multiplication, and division of numbers. Fractions, decimals, percentages, fractions, square root, exponents, and other arithmetic operations are used to achieve mathematical simplifications.

Given that:

Cara has saved 1, 430 pennies.

Each penny roll holds 50 pennies.

1430 divides by 50 = 143/5≈29 roles and in last roll it will be 30 pennies.

So, the number of pennies will be in the last roll is 30.

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The triangle ABC is shifted upwards by 3 units and towards the left by 4 units. After translation again it is rotated 90° counterclockwise. All these transformations are shown in the graph below.

The following are the basic transformation rules:

A triangle ABC is given in the graph with vertices as

A(-1, 2), B(1, 4), and C(4, -1)

The transformation to be applied is A"B"C" = Ro 90°(T(-4,3)(ABC))

Where -

T(-4, 3) represents the translation of 3 units upwards and 4 units towards the left

R0 90° represents the rotation of 90° (counterclockwise) of the translated triangle.

Step 1: applying translation (-4, 3):

The new vertices of the triangle ABC translated by (-4, 3) units are represented by A'B'C'. They are:

A' - (-1 - 4, 2 + 3) = (-5, 5)

B' - (1 - 4, 4 + 3) = (-3, 7)

C' - (4 - 4, -1 + 3) = (0, 2)

These are shown in the graph below.

Step 2: applying rotation 90° (counterclockwise): (x', y') → (-y, x)

Now the new triangle formed after the translation is ΔA'B'C'

So, on applying rotation, the vertices are changed to,

A'(-5, 5) → A"(-5, -5)

B'(-3, 7) → B"(-7, -3)

C'(0, 2) → C"(-2, 0)

These are shown in the graph below.

Therefore, Δ ABC → Δ A'B'C' (by T(-4, 3)) → Δ A"B"C" (by Ro 90°) i.e.,

Δ A"B"C" = Ro 90°(T(-4, 3) ABC).

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The process needs to meet the following criterion:The process must make large amounts of product at a low cost. That is option A.

Ammonia is defined as a gas compound that is made up of nitrogen and oxygen in the ratio of 1:3 respectively.

The industrial and modern method constructed by Engineers for ammonia production is called steam reforming.

The natural resources used for industrial production of ammonia can be gotten from natural gas such as methane.

To make profit, natural products are used which costs less to acquire but will lead to the production of large ammonia quantity.

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Answer:

11

Step-by-step explanation:

try it and see, .........