Solve this recurrence relation together with the initial condition given. an = 2an−1 for n ≥ 1, a0 = 3

The number of pounds of 60% protein and 20% protein supplement used is 700 and 700 pounds respectively.

let

x + y = 1400

0.60x + 0.20y = 1400×0.40

0.60x + 0.20y = 560

From (1)

x + y = 1400

x = 1400 - y

Substitute into (2)

0.60x + 0.20y = 560

0.60(1400 - y) + 0.20y = 560

840 - 0.60y + 0.20y = 560

- 0.60y + 0.20y = 560 - 840

-0.40y = -280

y = -280/-0.40

y = 700 pounds

Recall,

x + y = 1400

x + 700 = 1400

x = 1400 - 700

x = 700 pounds

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Answer + Step-by-step explanation:

2x – y + 1 = 0

We know that the graph of a linear equation is a line.

So ,in order to draw it we need to find two points A and B of the line

Afterward, we join A and B to get the graph.

2x – y + 1 = 0

If x = 0 → y = 1 ⇒ A(0 , 1) lie on the line AB (the graph)

If x = 1 → y = 3 ⇒ B(1 , 3) lie on the line AB

Now ,all we have to do is plotting A and B

on the coordinates plane ,then connecting then with a line.

According to the graph (check the attached image) :

If (h,4) ∈ line AB ⇒ h = 3/2

If (1/2 , k) ∈ line AB ⇒ k = 2

1. The semi inter quartile range is 10

2. The coefficient of quartile deviation is 0.2

1st quartile (Q₁) = (134 + 1) / 4 = 33.75th = 40

3rd quartile (Q₃) = 3 (134 + 1) / 4 = 3 × 33.75 = 101.25th = 60

Semi inter quartile range = (Q₃ - Q₁) / 2

Semi inter quartile range = (60 - 40) / 2

Semi inter quartile range = 10

Coefficient of quartile deviation = (Q₃ - Q₁) / (Q₃ + Q₁)

Coefficient of quartile deviation = (60 - 40) / (60 + 40)

Coefficient of quartile deviation = 0.2

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Answer:

502.4 ft²

Step-by-step explanation:

To find the individual area of the ring, you first need to find the area of the white circle. Then, you need to find the area of the circle and the ring (which can be found by adding the width of the ring to the radius of the circle). Finally, you can find the area of the ring through subtraction.

Area (White Circle)

radius = 1/2 diameter

radius = (1/2) x 36 ft

radius = 18 ft

Area = πr²

Area = π(18 ft)²

Area = π(324 ft²)

Area = 1017.36 ft²

Area (White Circle + Ring)

radius = 1/2 diameter + width of ring

radius = (1/2 x 36 ft) + 4 ft

radius = 22 ft

Area = πr²

Area = π(22 ft)²

Area = π(484 ft²)

Area = 1519.76 ft²

Area (Ring)

Area (Ring) = Area (White Circle + Ring) - Area (White Circle)

Area (Ring) = 1519.76 ft² - 1017.36 ft²

Area (Ring) = 502.4 ft²

The value of the ratio a:b is 2:1

Surds are values of a square roots that cannot be simplified as whole numbers or integers. They are usually called irrational numbers.

Example of some surds are the square root of prime numbers.

Analysis:

a + b[tex]\sqrt{3}[/tex] = [tex]\frac{1}{2 - \sqrt{3} }[/tex]

Rationalizing the right hand side by the conjugate surd which is 2 + [tex]\sqrt{3}[/tex]

[tex]\frac{1}{2 - \sqrt{3} }[/tex]  x [tex]\frac{2 + \sqrt{3} }{2 +\sqrt{3} }[/tex] = [tex]\frac{2 + \sqrt{3} }{4 -2\sqrt{3} +2\sqrt{3} -3}[/tex] = [tex]\frac{2 + \sqrt{3} }{1}[/tex] = 2 + [tex]\sqrt{3}[/tex]

Equating,

a + b[tex]\sqrt{3}[/tex] = 2 + [tex]\sqrt{3}[/tex]

Comparing the variables,

a = 2,   b[tex]\sqrt{3}[/tex] = [tex]\sqrt{3}[/tex], b = 1

The ratio, a: b = 2:1

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Domain of the function is [tex]0\leq b\leq 10[/tex] and range of the function is [tex]0\leq W\leq 120[/tex].

The range of values that we are permitted to enter into our function is known as the domain of a function.

A function's range is the collection of values it can take as input.

Each birdhouse uses 12 square feet of wood. Owen has enough to build 10 birdhouses, so he has 120 square feet of wood.

The function has an input of the number of birdhouses, b, and W as an output of the amount of wood needed. b is domain, and W is the range. The domain is 0 to 10 and range is 0 to 120.

Therefore, the domain of the function is  [tex]0\leq b\leq 10[/tex] and the range of the function is [tex]0\leq W\leq 120[/tex].

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From the information given, the rotated triangle is same as the original triangle. This is because, vertices of the rotation remain at the origin - (0,0).

Notice that the question states:  △A'B'C' is the image of △ABC. Given that the △ without primes is the original and the one with primes depict the rotated triangle,

under a rotation about the origin, (0,0) (0,0) (0, 0), indicating no movement,

△A'B'C' is in the same position with △ABC.

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Answer: D: 60 degrees

Step-by-step explanation:

khan

Given that y varies directly with x in the above table, if the value of x is 5, the value of y is 15.

According to this question, a 2-column table with 5 rows is given.

If y varies directly with x, the mathematical representation is as follows:

y = kx

Since y = 3, when x = 1

3 = k × 1

k = 3

The relationship between x and y is as follows: y = 3x

Therefore, if the value of x is 5, the value of y = 3 × 5 = 15.

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Answer:

The first chose is correct

Step-by-step explanation:

You can see in the first picture that graphed both of the triangles and then I followed the directions.  It is very, very helpful if you have tracing paper.  You can trace the original and then translate it three up.  For the 90 rotation, put a small + on the origin of your tracing paper, then move the tracing paper one one turn on the plus sign.  That would be 90 degrees.

Answer:39084620

Step-by-step explanation:

New questions in Mathematics

19 ft 4 ft l Find l. l = √ [?] ft

flying against the jet stream, a jet travels 3000 in 3 hours. Flying with the jet stream, the same jet travels 5360 miles in 4 hours. What is the rate…e of the jet in still air and what is the rate of the jet stream?

Please help! Express the area of the region bounded by the x-axis, y = 1/2x - 2, and y equals the cubed root of x, using definite integrals.

Solve the equation 7/4x-2=-5x+1

How to Convert 11010112 to base 10?

Answer the following. (a) A certain solution has a hydrogen ion concentration of 0.00000896 moles per liter. Write this number in scientific notation…. (b) A humpback whale can weigh up to ×1.1105 pounds. Write this number in standard notation.

Evaluate the expression if a=2,b=-3,C=-1, and D=4 -2(b^2-5c)

Evaluate the expression if a=2,b=-3,C=-1, and D=4 -2(b^2-5c)

The set of all triples of real numbers with the standard vector addition but with scalar multiplication defined by k(x, y, z) = (k2 x,k2 y,k2 z)

Evaluate each expression if a=2,b=-3,C=-1, and d=4 5+d(3b-2d)

Answer:

e) B. 45°

f) A. 30°

Step-by-step explanation:

e) sec theta = 1/ cos theta

the value of cos theta is 1/√2 at 45°

so , sec 45° = √2 and theta = 45°

f) cot theta = 1/ tan theta

the value of tan theta is 1/ √3 at 30°

so, cot 30° = √3 , theta = 30°

The answers are :

e) B

f) A

For part (e), convert into terms of cosθ.

For part (f), convert into terms of tanθ.

Answer:

A

Step-by-step explanation:

From left to right of the graph, we can observe that the generally the points are going down. This means that the trend line drawn will have a negative slope.

In the slope-intercept form, which is the form the given equations are in, we have y= mx +c, where m is the slope and c is the y-intercept.

We are only interested in the slope in this case, since no actual values are given. Thus, let's focus on the coefficients of x to determine whether the slope is positive or negative.

Option A: Slope= -⅔ (negative)

Option B: Slope= 3 (positive)

Since we have a negative slope, option A would be the best answer.

The attached image shows 2 graphs. The graph in blue shows the shape of a graph with negative slope, while the graph in red has a positive slope.

The remaining amount of the sample after 't' days would be 51. 74g

We have the formula for amount to be;

A = Ao × (1/2)^ t/t^1/2

Where

t1/2 = half -life = 138 days

t = 1

Ao  = 52g

A = Amount after decay

Substitute into formula

A = 52 × (1/2) ^ 1/138

A = 52 ×

[tex] { \frac{1}{2} }^{0.00724} [/tex]

A = 52 × 0. 9950

A= 51. 74 g

Thus, the remaining amount of the sample after 't' days would be 51. 74g

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Answer:

7

Step-by-step explanation:

this is probably a 45-45-90 triangle if its both legs

The average rate of change of credit card is $ 401.79 /year.

Solution

The difference of credit card debt between the year 2006 and 1992 = 8900 - 3275 = $5625

The difference of years between the year 2006 and 1992 = 2006 - 1992 = 14

average rate of change of credit card debt with respect to time = [tex]\frac{difference of credit card debt}{difference of years}[/tex]

average rate = [tex]\frac{5625}{14}[/tex] = $ 401.79 / year

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Answer:

the answer is 22

Step-by-step explanation:

12,15,22,37,49

since 22 is in the middle its the median (make sure you put the #'s from least to greatest)

Answer:

22

Step-by-step explanation:

22, 37, 49, 15, 12

First put the data set from least to greatest.

12, 15, 22, 37, 49

The median is the middle number of the data. In this case, the median is 22.

Hope this helps!

Answer:

Quadrant III

Step-by-step explanation:

Top-right quadrant = QI

Top-left quadrant = QII

Bottom-left quadrant = QIII

Bottom-right quadrant = QIV

The best interpretation of 0.8^a in this exponential equation is that: C. For each mile that the altitude increases, the atmospheric pressure decreases 20%.

An exponential function can be defined as a mathematical function whose values are generated by a constant that is raised to the power of the argument. Mathematically, an exponential function is represented by this formula:

f(x) = aeˣ

Based on the information provided, we can logically deduce that the atmospheric pressure (p) exerted on an airplane flying at an altitude of a miles above sea level is defined by the following exponential function:

p = 14.63 × 0.8^a

Next, we would evaluate as follows;

At a = 0, we have:

p = 14.63 × 0.8^(0)

p = 14.63 psi.

At a = 1, we have:

p = 14.63 × 0.8^(1)

p = 11.704 psi, and this is 20% less than a mile before.

At a = 2, we have:

p = 14.63 × 0.8^(2)

p = 9.3632 psi, and this is 20% less than a mile before.

At a = 2, we have:

p = 14.63 × 0.8^(3)

p = 7.4906 psi, and this is 20% less than a mile before.

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Complete Question:

Atmospheric pressure, measured in pounds per square inch (psi) is the force exerted by Earth's atmosphere over a given area. The atmospheric pressure, p, exerted on an airplane flying at an altitude of a miles above sea level can be approximated by the model shown below. What is the best interpretation of 0.8^a in this equation?

p = 14.63 × 0.8^a

A. If the airplane reaches the outer extent of the Earth's atmosphere, the atmospheric pressure will be 0.8 psi.

B. If the airplane is at sea level, the atmospheric pressure will be 0.8 psi.

C. For each mile that the altitude increases, the atmospheric pressure decreases 20%.

D. For each mile that the altitude increases, the atmospheric pressure increases 20%.

The partial sums are correct are  That is:  (2) and (28/9).

A partial sum would be:

2 + (2/3).

In this case, thus,

Series 1 = 2  - This is correct.

Series 2 = 2 + (2/3) = 8/3 - incorrect

Series 3 = (8/3) + (4/9) = (28/9) Correct

Series 4 = (28/9) + (8/27) = (92/27)

Series 5 = (92/27) + (16/81) = 292/81

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Answer:

9 x 9 = 81

Step-by-step explanation:

area = width x height

Since it's a square, width = height

Answer:30 degress

3 angles in a triangle equal 180-120=60 60÷2=30

Step-by-step explanation:

It is not too many reds, but it is also not a perfectly balanced roulette wheel.

It is given that the red numbers should come up 18 times when the roulette wheel is played 38 times.

Therefore, the ratio of red numbers to the total number of plays is = 18:38

It is also given that a casino tests the wheel with 3800 plays and noticed that the red numbers came up 1890 times.

The ratio is given as 1890:3800.

We have to simplify this.

1890/3800 = 18.9/38

If the roulette wheel was perfect, it should've been 18:38.

Therefore, we can say that the roulette wheel is not perfectly balanced.

Therefore we have found that it is not too many reds, but it is also not a perfectly balanced roulette wheel.

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Solution,

Let P =  ( x, -x + 6) = (x, 6 - x)

We want to solve this

( Distance from P to (0,0) )^2  = (Distance from P to (10, -10) )^2

x^2 + (6 - x)^2  =  [ ( x - 10)^2 + ( 6 - x + 10)^2

x^2 + x^2 - 12x + 36  =   x^2 - 20x + 100  + x^2 - 32x + 256     simplify

-12x + 36  =  -52x + 356

40x =  320

x = 8

And y = -(8) + 6  =  -2

So...P  =  ( 8, -2)

In mathematics, an equation is an equation that expresses two equations by joining them with an equal sign =. Equations in other languages ​​and the word their relatives can have slightly different meanings; for example, in French, an equation is defined as containing one or more variables, but in English, it is an equal sign.

A well-formed expression consisting of two combined equations is an equation, and a variable makes the equation true. The variable for which the equation must be solved is also called the unknown, and the value of the unknown that satisfies the equation is called the solution of the equation. There are two types of equations: identities and constraint equations. The ID applies to all values ​​of the variable. Constraint equations apply only to specific values ​​of variables

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Answer:

a = 2

b = 11

c = 11

d = -2

Step-by-step explanation:

[tex]\sf \left[\begin{array}{cc}a&b\\c&d \end{array}\right] *\left[\begin{array}{ccc} 22&11&7\\ 6&-9&-15 \end{array}\right] =\left[\begin{array}{ccc} 22a+6b&11a-9b&7a-15b\\22c+6d&11c-9d&7c-15d \end{array}\right][/tex]

   [tex]\sf \left[\begin{array}{ccc} 22a+6b&11a-9b&7a-15b\\22c+6d&11c-9d&7c-15d \\ \end{array}\right] =\left[\begin{array}{ccc} 110&-77&-151\\230&139&107 \\ \end{array}\right][/tex]  

On comparing to right side, we get,

 22a + 6b = 110

Divide the entire equation by 2

   11a + 3b = 55  ------------(I)

 11a   - 9b  = -77  -------------(II)

Subtract equation (II) from (I)

       11a + 3b = 55

       11a - 9b = -77

      -      +        +     {Now subtract}

               12b = 132

                 b = 132/12

[tex]\sf \boxed{\bf \ b = 11}[/tex]

Substitute the value of b in eqaution (I)

  11a + 3*11 = 55

  11a + 33   = 55

             11a = 55 - 33

             11a = 22

               a = 22/11

      [tex]\sf \boxed{\bf \ a = 2}[/tex]

           22c + 6d = 230

Divide by 2

           11c + 3d = 115  -----------------(III)

           11c - 9d  = -139 ------------------(IV)

Subtract (IV) from (III)

           11c + 3d  = 115

           11c - 9d  = 139

           -     +         -      

                  12d  =  -24

                      d = -24/12

                     [tex]\sf \boxed{\bf \ d = -2}[/tex]

Plugin d = - 2 in equation (III)

    11c + 3*(-2) = 115

     11c  - 6      = 115

                11c  = 115 + 6

               11c = 121

                  c = 121/11

                 [tex]\sf \boxed{\bf \ c = 11}[/tex]

The expression which can be used to represent the total amount llean earned last week is 75 + 18x

An expression to represent the total amount llean earned last week = Amount earned as a web page designer + (Amount llean earns per hour welding × Number of hours worked as welder)

= 75 + (18 × x)

= 75 + 18x

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Applying the trigonometry ratios, the correct option is: B. none of these are correct.

The trigonometry ratios are SOH CAH TOA, which are used for solving a right triangle.

Use the trigonometry ratio to find out which option is correct.

Cos Z = adj/hyp = 61/CZ, so option A is incorrect.

Sin Z = opp/hyp = 73/CZ,  so option C is incorrect.

Tan Z = opp/adj = 73/61,  so option D is incorrect.

Thus, the answer is: B. none of these are correct.

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The linear equation is 45x+50

Linear equation is the equation having the degree 1

Given that the charge per computer repair service  is $50

The charge per hour of work is $ 45

We need to show the linear equation that  expresses the total amount of money Charlie earns per computer is y

So , Let the number of hours be x

Therefore, the Charlie working hours charge will be 45x

The total amount of money Charlie earns per computer is y

Therefore the linear equation will be

y = 50+45x  

Where y = Total amount of money

x =  number of hours

Hence the linear equation is y = 45x+50

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Jessica purchased a DVD that was on sale for 12% off.

The sales tax in her county is 3%.

Let, y represent the original price of the DVD.

We can simply solve this mathematical problem by using the following mathematical process.

Here, we will form an algebraic expression, according to the given data.

So,

The original price of the DVD = y

Discount on the original price :

y * 12/100

=3y/25

Price after discount :

y - 3y/25

=25y - 3y/25

=22y/25

Sales tax amount :

22y/25 * 3/100

11y/25 * 3/50

=33y/1250

Final price including the sales tax :

22y/25 + 33y/1250

1100y + 33y/1250

1133y/1250

(This will be considered as the final result.)

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Answer:

Please see the answer below.

Step-by-step explanation: