A triangle has 2 angles that measure 60 degrees, what is the measurement of the opposite exterior angle?

a) The expected return for stocks a and b is 13.56% and 20.02% respectively.

b) The standard deviation for stocks a and b are 8.32% and 32.60%.

a) Expected return = Probability of recession × Return during recession + Probability of normal × Return during normal + Probability of boom × Return during boom

Expected return for stock A = 0.21 × 0.04 + 0.61 × 0.12 + 0.18 × 0.30

The expected return for stock A = 0.1356

The expected return for stock A = 13.56%

Expected return for stock B = 0.21 × (-0.41) + 0.61 × 0.31 + 0.18 × 0.54

The expected return for stock B = 0.2002

The expected return for stock B = 20.02%

b) Standard deviation of stock = √{Probability(Recession) × (Rate during recession - expected rate )² + Probability(Normal)(Rate during normal - expected return)² + Probability(Boom) × (Rate in boom - Expected return)²}

Standard deviation of stock A = √[(0.21 × (0.04-0.1356)² + 0.61 × (0.12 - 0.1356)² + 0.18 × (0.30-0.1356)²)]

The standard deviation of stock A = 0.0832

The standard deviation of stock A = 8.32

Standard deviation of stock B = √(0.21 × (-0.41-0.2002)² + 0.61(0.31 - 0.2002)² + 0.18 × (0.54-0.2002)²)]

The standard deviation of stock B = 0.3260

The standard deviation of stock B = 32.60%

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The intervals on which the function f(x) = ax² + bx + c (where "a" doesn't = 0) is increasing and decreasing is x>-b/2a and x<-b/2a

Given that,

We have to find the intervals on which the function f(x) = ax² + bx + c (where "a" doesn't = 0) is increasing and decreasing.

We know that,

Take the function equation,

f(x)=ax² + bx + c

The derivative of the function of x is  

f'(x)=ax+b

So, f(x) is increasing when f'(x) > 0

f(x) is decreasing when f'(x) < 0

Then we can say

f'(x) > 0 , when  b > 0  and a < 0

2ax + b < 0

2ax < - b

x<-b/2a

Now,

f'(x) < 0 , when  b < 0  and a > 0

2ax + b > 0

2ax > - b

x>-b/2a

Therefore, the intervals on which the function f(x) = ax² + bx + c (where "a" doesn't = 0) is increasing and decreasing is x>-b/2a and x<-b/2a.

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Using mathematical operations we can conclude that the rate of lemons being used in a cup of lemonade is 1/4.

Calculating a value using operands and a math operator is referred to as performing a mathematical "operation."

The math operator's symbol has predetermined rules that must be applied to the supplied operands or numbers.

In mathematics, addition, subtraction, multiplication, division, and modular forms are the five basic operations.

So, we know that:

Lemons required to make 16 cups of lemonade: 4 lemons

Then, the rate of lemons being used in lemonade per cup:

4/16

1/4

Therefore, using mathematical operations we can conclude that the rate of lemons being used in a cup of lemonade is 1/4.

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The triangles in the diagram indicates that ΔABD is an isosceles triangle, therefore;∠2 ≅ ∠1

The two-column method can be used to prove that the angle m∠BAC > m∠C as follows;

Statement       [tex]{}[/tex]                         Reasons

1. BC > BA       [tex]{}[/tex]                         1. Given

2. BA ≅ BD      [tex]{}[/tex]                        2. Given

3. ΔABD is an isosceles Δ[tex]{}[/tex]      3. Definition of isosceles triangle

4. ∠1 ≅ ∠2      [tex]{}[/tex]                         4. Base ∠s of isosceles triangle ΔABD

5. ∠1 = ∠2      [tex]{}[/tex]                          5. Definition of congruency

6. ∠1 = ∠3 + ∠C      [tex]{}[/tex]                 6. Exterior angle theorem

7. ∠2 = ∠3 + ∠C      [tex]{}[/tex]                7. Substitution property

8. ∠2 - ∠3 = ∠C [tex]{}[/tex]                     8. Subtraction property

9. ∠2 > ∠C [tex]{}[/tex]                             9. Definition

An isosceles triangle is a triangle that have a pair of congruent sides and one pair of congruent angles.

The reasons in the above two-columns used to prove m∠BAC > m∠C are as follows;

Isosceles triangle ΔABD

The triangle ΔABD that have side AB congruent to side BD is an isosceles triangle by definition of an isosceles triangle.

The base angles of an isosceles triangle that are angles opposite congruent sides in a triangle are also congruent.

Definition of congruency

A geometric figure is congruent to another figure if their measurements are the same.

Exterior angle theorem

The exterior angle of a triangle theorem states that the exterior angle of a triangle is equal to the sum of the two interior opposite angles.

Substitution property

The substitution property of equality states that if a quantity a is equal to another quantity b then a can be substituted by b in expressions and equations without changing their value.

Subtraction property

The subtraction property of equality states that if the same quantity is subtracted from both sides of an equation, then the new amount obtained are also equal

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Answer:

y = [tex]\frac{3}{4}[/tex]x + 2

Step-by-step explanation:

To find the slope we will use the slope formula of y2-y1/x2-x1.

Our two y values are 2 and -1.

Our two x values are 0 and 4.

2 - (-1) = 3

0 - 4 = -4

3/4 = [tex]\frac{3}{4}[/tex]

y = [tex]\frac{3}{4}[/tex]x + 2

The margin of error for the confidence interval (6.5, 6.9) is 0.2 , the correct option is (c) .

In the question ,

it is given that ,

the 95% confidence interval for mean hours slept in the graduate students is (6.5, 6.9) ,

we have to find the margin of error ,

we know that the formula for the margin of error is

= (upper limit of confidence interval - lower limit )/2

From the given interval ,

we see that ,

upper limit of confidence interval = 6.9

lower limit of confidence interval = 6.5

Substituting the above value in margin of error formula ,

we get ,

margin of error = (6.9 - 6.5)/2

= 0.4/2

= 0.2

Therefore , the margin of error is 0.2   .

The given question is incomplete , the complete question is

Suppose that based on a random sample, a 95% confidence interval for the mean hours slept (per day) among graduate students was found to be (6.5, 6.9). What is the margin of error of this confidence interval? responses

(a) 6.7

(b) 0.4

(c) 0.2

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20 minutes is [tex]1/3^{rd}[/tex] of an hour

The relationship between the number of games Carlos buys and the total price is proportional.

A proportional relationship exists between two or more variables if they move in the same direction. If one of the variables increases, the other variable increases.

As the number of games that are bought increases, the total price paid also increases. This means that the relationship is proportional.

The formula that is used to represent proportional relationship is:

T = kg

Where:

T = $36g

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Answer:

  48 = 2⁴ · 3

Step-by-step explanation:

You want the prime factorization of 48.

You recognize that 48 is an even number, so you can divide by 2 and see what's left. You can keep doing that until you get a number divisible by another prime:

  48/2 = 24

  24/2 = 12

  12/2 = 6

  6/2 = 3

3 is prime.

The prime factorization of 48 is ...

  48 = 2⁴ · 3

AS per the permutation concept, the number of ways can Alice win or draw exactly three times is 240

Permutation:

In probability, permutation refers the arrangement of objects in a definite order.

Given,

Alice and Bob are playing a game in which there are several rounds and each round can be a win, a loss, or a draw for Alice.

Here we need to find the number of ways can Alice win or draw exactly three times, if they play 6 rounds.

While we looking into the given question, we know that,

Total number of games = 6

Possible values = 3 ( win, loss, or draw)

Here we need to find the probability of winning 3 times, it can be calculated by using the permutation as,

=> 6! / (6 - 3)!

=> 6! / 3!

=> 120

Similarly, the the probability of draw 3 times, it can be calculated by using the permutation as,

=> 6!/ (6 - 3)!

=> 120

So, the number of ways can Alice win or draw exactly three times is

=> 120 + 120 =  240

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He should order 10 sandwiches of 6 foot long so, as to make sure that everyone will eat 2 pieces.

We need to convert between the units in order to ensure the accuracy and to prevent measurement misinterpretation. For example, we do not measure the pencil's length in kilometres. In this situation, one must convert from kilometres (km) to centimetres (cm) (cm). In most cases, multiplicative conversion factors are used to convert one unit to another of the same quantity. Let's see how to change the length and mass units.

1 Feet = 12 Inches

So, 6 Foot = 72 inches

The Length of sandwich- piece is 4 inch

So, when we convert 6 foot long sandwich into 4 inch,

Then we get number of piece is = 72/4 = 18

From 6 foot long sandwich we get 18 pieces of 4 inch long sub.

Now, Total people who will attend picnic is 40

and each people will eat 2 pieces.

It means total number of piece required = 2 (90) = 180

Mr. eaton required 180 pieces of sandwiches.

Number of sandwiches = 180 / 1.8 = 10

He should order 10 sandwiches of 6 foot long.

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For dimensions of x =10 and y=5 for the base and height that will make the tank weight as little as possible.

Here we are given the information of a square-based, open-top, rectangular steel holding tank, so here the tank is in the shape of a cuboid and we know  the formula  for :

volume = x*y*z, as  here it is a square base, so the volume will be

volume =  x²*y, where x and y are the dimension of the base and height

So for the  given reason,  

=>x²*y =  500

=> y = 500/x²

Again, the surface area formula  will be

S=x²+4xy, substituting the value of  y in this question

=>S=x²+4x(500/x²)

=>S=x²+2000/x

Differentiating the above formula with respect to x, we get

=>2x-2000/x²=0

=>2x³= 2000

=>x³= 1000

=>x =10

so the substituting the x values of x in  the equation y , we get

y = 500/x²

=>y = 5

so the dimensions are x= 10 and y=5

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The range function to add up the series is 15 ,35 ,60 ,90, 125,165,210 ,260

A unit of code with a name is referred to as a function in Python. We utilize functions anytime we need to repeat a process repeatedly without writing the same code.

Given: Series 15, 20, 25, 30,.. 50

Program (Pascal ABC) and Result:

Program:

Var i, Summ : integer;

begin

i : = 15;

Summ : = 15;

While i <= 50 do

begin

WriteIn ( '   ' , Summ)  ;

i : = i + 5 ;

Summ : = Summ + i ;

end ;

end.

Result : 15 ,35 ,60 ,90, 125,165,210 ,260

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The final value of the product = 292

According to the given equation -

= (4a2+3b)x(4a2+36)

multiply the whole equation-

= 16a4+144+12a2b+108

as we can see that the values of a and b are given 1 and 2 respectively,

so putting the values of a and b in the equation we get -

= 16(1)4+144+12(1)2(2)+108

= 292

The product of the following equation will be = 292

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Answer:

whats the question

Answer:

What are you asking?

You need to find what x is equal to for each equation, so you can sub why x is equal to in the place I'd x to eliminate the variable

1. 6x-5y=-4

6x=5y-4

X=5/6y-2/3

2. 4x+2y=28

4x=-2y+28

X=-1/2y+7

Hope this helps!

Answer:

Step-by-step explanation:

.36

The integration by part  is [tex]\frac{x^{3}In x }{3} -\frac{x^{3} }{9} +C[/tex] with indicated choices of u and dv.

The method Integration by Parts is known to be a special method of integration that is often useful. In calculus, definite integrals are referred to as the integral with limits such as upper and lower limits. It is also possible to derive the formula of integration by parts with limits.

Given: ∫ [tex]x^{2} In x dx[/tex] ; [tex]u=In x[/tex] ; [tex]dv=x^{2} dx[/tex]

Consider  [tex]u=In x[/tex] and [tex]dv=x^{2} dx[/tex]

⇒ [tex]u=In x[/tex]             ⇒  [tex]dv=x^{2} dx[/tex]

⇒ [tex]du= \frac{1}{x} dx[/tex]           ⇒ [tex]v=\frac{x^{3} }{3}[/tex]

Now, apply integration by parts to solve the integral

∫ u dv =  uv - ∫ v du

the antiderivative of [tex]x^{n}[/tex][tex]=\frac{x^{n+1} }{n+1}[/tex] and the derivative of In x = [tex]\frac{1}{x}[/tex] .

⇒ ∫ [tex]x^{2} In x dx =[/tex][tex]\frac{x^{3} In x}{3} -\frac{x^{3} }{3} .\frac{1}{x} dx[/tex]

                     = [tex]\frac{x^{3}In x }{3}[/tex] [tex]-\frac{x^{2} }{3} dx[/tex]

                     =  [tex]\frac{x^{3}In x }{3}[/tex] [tex]-\frac{x^{3} }{9} +C[/tex]

Hence, the final integration is   [tex]\frac{x^{3}In x }{3}[/tex] [tex]-\frac{x^{3} }{9} +C[/tex]

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2 notebooks

Step-by-step explanation:

the variables I'm gonna use are t for textbooks and n for notebooks

t = (n•2)+3 (two times the notebooks then add 3)

now we'll plug in the amount of notebooks we have so t=7

7=(n•2)+3

we can subtract 3 from each side that leaves us with

4=n•2

then divide by 2

2=n

Guillermo bought 2 notebooks

The nth term of the pattern is (1+n)/(18+n)

What is a sequence?

succession is the act of doing something after another. successional order: a list of books organized by title. a running or interconnected sequence: a series of sonnets. something that happens after; a following event; a result; or a repercussion. In contrast to a set, the order of the components in a sequence does important, and the same elements may occur more than once at various positions. A series can officially be described as a function from natural numbers.

We are given a sequence

1/18, 2/19, 3/20, 4/21

As we can see the second term is (1+1)/(18+1)

Third term is (1+2)/(18+2)

Hence the n th term of the sequence can be given as (1+n)/(18+n)

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Answer:

XV = 16

Step-by-step explanation:

Triangle VWX is an isosceles triangle. Since the base angles are the same, the sides opposite the angle are also the same. See image. They gave VW so XV is the same as VW.

Answer:

None of the Above?

Step-by-step explanation:

1.) If we put this into words, we would get -5y+7/3y=-5-8/3y-4

2.) By moving all y terms to one side, we get -5y + 7/3y + 8/3y = -5 - 4

3.) By simplifying, you would get -4 2/3y = -9.
4.) If you divide both sides by -4 2/3, you would get that y = -9 * - 3/14 = 27/14

Answer:

20-foot shadow

Step-by-step explanation:

To guarantee that at least on pair o the numbers adds up to 9, you must select at least 3 numbers from the set by combination

1. First, select any two numbers from the set.

2. Now, calculate their sum.

3. If the sum of the two numbers is not equal to 9, select a third number from the set.

4. Determine the three numbers' sum.

5. If the sum of the three numbers is still not equal to 9, select a fourth number from the set and calculate the sum.

6. Repeat this process until the sum of the selected numbers is equal to 9 by combination

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Answer:

I got you!

a ≤ 11

For more info, look at the steps in the attached image!

Step-by-step explanation:

Answer:

a ≥11

Step-by-step explanation:

[tex]21 \geqslant 3a - 21 + 9 \\ 21 \geqslant 3a - 12 \\ 21 + 12 \geqslant 3a - 12 + 12 \\ 33 \geqslant 3a \\ 3a \leqslant 33 \\ a \geqslant 11[/tex]

a) The ratio of tomato plants to lettuce plants:

b) The ratio of lettuce plants to cucumber plants:

Answer:

Using an Equation

Simplify the equation as closely as possible to the form of y = mx + b. Check to see if your equation has exponents. If it has exponents, it is nonlinear. If your equation has no exponents, it is linear.

Answer:

Step-by-step explanation:

To be linear it must have the form  y=mx+b.IN a linear equation the variables are shown in first degree and terms with products of variables are absent .

Answer:

$200

Step-by-step explanation:

so if peter has been depositing 50 each month for 8 months then you would just do 50x8 which equals 400 and 600-400=200

Answer:

35/9

Step-by-step explanation: