Solve the systems of equations
5x - 4y = -10
-4x + 5y = 8
x =
y =

The amount invested in Sock Y is - $126,000 and the Beta of the portfolio is 1.636.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Data provided in the question:

Total amount to be invested = $140000

Stock                          X       Y

Expected return       14%     10%

Beta                          1.42     1.18

Expected return of portfolio = 17.6%

Now,

let the weight invested n stock X be W

therefore,

Weight of Stock Y = 1 - W

thus,

( W × 14% ) + (1 - w) × 10% = 17.6 %

14W + 10% - 10W = 17.6%

4W = 7.6

W = 1.9

Therefore,

weight of Y = 1 - 1.9 = -0.9

Amount investment in Sock Y = Total amount to be invested × Weight

= 140,000 × ( - 0.9 )

= - $126,000 i.e short Y

Beta of portfolio = ∑ (Beta × Weight)

Beta of portfolio= [ 1.42 × 1.9 ] + [ 1.18 × (-0.9) ]

Beta of portfolio= 2.698 - 1.062

Beta of portfolio= 1.636

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4 is the constant of proportionality of given graph.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given,

The graph of the relationships ( dogs,cost) is a line that contains the points(0,0) (3,12) and (6,24).

We need to find the constant of proportionality

The constant of proportionality is the ratio that relates two given values in what is known as a proportional relationship.

To find the constant of proportionality, we have to divide the value of y by x.

12/3=4

24/6=4

Hence, 4 is the constant of proportionality of given graph.

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To decide whether to use the normal or the Student’s t distribution, for an x distribution that is mound-shaped:

Use the normal distribution if the standard deviation is known. Use the Student's t - distribution when the standard deviation is not known.

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution.

It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution is depicted graphically as a bell curve.

For small sample numbers or unidentified variances, population parameters are estimated using a form of probability function called a t-distribution.

Hence t-distribution is suitable when the variance which is standard deviation squared is unknown

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The relation between a and r is 2r

According to the given information

a varies directly with r

a = 8

r = 4

a is directly proportional to r

a ∝ r

a = k r

where k is constant of proportionality

k =  [tex]\frac{a}{r}[/tex]

k = [tex]\frac{8}{4}[/tex]

k = 2

so,

a = k r

putting the value of k in the above equation

we get

a = 2r

The relation between a and r is 2r

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How would you express the area of he rectangle using the Distributive Property?

area = length * width

area using Distributive Property: 3 (x + 5)

The coordinate of the vertices of △A'B'C' are A'(3,6), B'(9,-3), and C'(-12, 6). Since the scale factor is 3.

What is coordinate of a point?

The coordinates are a pair of numbers that, using the horizontal and vertical lines, precisely pinpoint a point's location on a cartesian plane. typically represented by (x, y), the point's x and y values on a graph.

The coordinate of △ABC are A(1,2), B(3,-1) and C(-4,2).

The scale factor is k = 3.

The x-coordinate of A is 1.

The y-coordinate of A is 2.

The x-coordinate of B is 3.

The y-coordinate of B is -1.

The x-coordinate of C is -4.

The y-coordinate of C is 2.

To find the vertices of △A'B'C', multiplying x-coordinate and y-coordinate by 3.

The x-coordinate of A' is 1 × 3 = 3.

The y-coordinate of A' is 2 × 3 = 6.

The x-coordinate of B' is 3 × 3= 9.

The y-coordinate of B' is -1 × 3 = -3.

The x-coordinate of C' is -4 × 3 = -12.

The y-coordinate of C' is 2 × 3 = 6.

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Answer:

2/27 or 0.074 or 7.4%

Step-by-step explanation:

Step 1: Roll a fair 6-sided die 27 times. The following outcomes are obtained. 

roll-

1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27

outcome-

2,2,2,5,6,4,5,3,4,3,2,1,2,1,3,6,6,1,4,3,2,6,3,5,4,2,5

Step 2: Make a table for the frequency of each distinct outcome. 

Outcome-

1,2,3,4,5,6

Frequency:

3,7,5,4,4,4

Step 3:  The probability of rolling a two on the die is obtained using the classical probability formula as follows,

P(X=2)= factorable cases/total cases

from the frequency distribution table,

P(X=2)= 2/27= 0.074=7.4%

Answer:

The vendor sold 212 sodas and 34 hot dogs.

Step-by-step explanation:

Subtract 34 from 246 for the number of sodas sold.

Answer:

24 degree increase

Step-by-step explanation:

If the temperature rises 3 degrees steadily over an eight hour period, the total temperature increase after eight hours would be 3 * 8 = 24 degrees.

Answer:

10

Step-by-step explanation:

Because if you line up the numbers 10 is the least common factor of 110,40,120

Answer: b 10

Step-by-step explanation:

the prime factorization of 110: 2 * 5 * 11

the prime factorization of 40: 2^3 * 5

the prime factorization of 120: 2^3 * 3 * 5

the factor they all share is only 2, and they all share 5 but they dont all share 11 and 3. Multiply 2 * 5 = 10. SO 10 is the GCF (Greatest Common Factor) of 110, 40, and 120.

hope this helps!

By using the concept of compounded interest, it can be calculated that

$9549.02 has to be invested  at 4.3% interest compounded continuously to have $19,000 after 16 years

First option is correct

What is compound interest?

If the interest on a certain principal at a certain rate over a certain period of time increases exponentially rather than linearly, the interest earned is called compound interest.

Let the principal be $p

Rate= 4.3 %

Time = 16 years

[tex]19000 = pe^{\frac{4.3}{100} \times 16}\\19000 = pe^{0.688}\\19000 = p \times 1.989732\\p = \frac{19000}{1.989732}\\[/tex]

p = $9549.02

First option is correct

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Answer:

x = 12/5

Step-by-step explanation:

3 (3x − 1) − 3 (5x − 3) = − (x + 6)

9x − 3 − 15x + 9 = − x − 6

9x − 15x + x = 3 − 9 − 6

− 5x = − 12

5x = 12

x = 12/5

Answer:

[tex]x=\dfrac{12}{5}[/tex]

Step-by-step explanation:

Given equation:

[tex]3(3x-1)-3(5x-3)=-(x+6)[/tex]

Distribute:

[tex]\implies 3 \cdot 3x + 3 \cdot (-1) - 3 \cdot 5x - 3 \cdot (-3)=-x-6[/tex]

[tex]\implies 9x-3-15x+9=-x-6[/tex]

Collect and combine like terms on the left side of the equation:

[tex]\implies 9x-15x+9-3=-x-6[/tex]

[tex]\implies -6x+6=-x-6[/tex]

Add 6x to both sides:

[tex]\implies -6x+6+6x=-x-6+6x[/tex]

[tex]\implies 6=5x-6[/tex]

Add 6 to both sides:

[tex]\implies 6+6=5x-6+6[/tex]

[tex]\implies 12=5x[/tex]

[tex]\implies 5x=12[/tex]

Divide both sides by 5:

[tex]\implies \dfrac{5x}{5}=\dfrac{12}{5}[/tex]

[tex]\implies x=\dfrac{12}{5}[/tex]

Answer: 12 symmetries

Step-by-step explanation:

just draw the lines on the star.

Micro middle sold the least no of different types of consoles.

Matrices represent data in the form of rows and columns together as an array form.

From matrix A we get the data as follows,

A row represents shops and columns represents types of console.

Games Go sold (53 + 21 + 48) = 122 different types of consoles.

Better Buy sold (65 + 34 + 70) = 169 different types of consoles.

Micro middle sold (18 + 11 + 15) = 34 different types of consoles.

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The cost for the sheet is $22.60 and a discount of 30% is given.

It is important to note that a percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

From the information, the brand of sheets is on sale 30% off with a regular price of $18.00 per sheet.

Therefore, the cost for the sheet will be:

= $18 - (30% × $18)

= $18 - $5.40

= $12.60

The cost for the brand of sheet is $22.60.

Note that the information was incomplete and the calculation was based on the information given.

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The dependent variable, y from the given situation is 15

The total number of exercises the individual needs, y = 3x/3

Where,

So,

y = 3x/3

substitute the value of x into the equation

y = 3(15) / 3

open parenthesis

y = 45 /3

y = 15

In conclusion, the value of the dependent variable is 15

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The complete statement will be;

⇒ The product of 7 and 5/8 is 35 / 8 because ​5/8​ is less than 1.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The statement is;

''The product of 7 and 5/8 is Choose... because ​5/8​ is less than 1.''

Now,

Since, The statement is;

''The product of 7 and 5/8 is Choose... because ​5/8​ is less than 1.''

Hence, We get;

⇒ 7 × 5/8 = 35 / 8

Thus, The complete statement will be;

⇒ The product of 7 and 5/8 is 35 / 8 because ​5/8​ is less than 1.

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Comparing the number of same-size bottles drank to the amount of ounces of water consumed. So, option c is correct.

When the ratio of the output to the input stays constant at every given point along the function, the rate of change is said to be constant. A linear function's change will occur at a steady rate.

Comparing the number of same-size bottles drank to the amount of ounces of water consumed.

We say there is a constant rate of change when a quantity varies uniformly in relation to the change of another quantity.

Therefore, there is a constant rate of change if one quantity is directly proportionate to the other.

The number of identical-sized bottles drank is directly proportionate to the number of ounces of water consumed. As a result, the rate of change in water ounces in relation to the quantity of identical-sized bottles is constant. The quantity of the remaining alternatives are not directly proportionate to one another.

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The value of f ( 5 ) in the equation f(x) = 3x² + 2x - 1 is f ( 5 ) = 84

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

f(x) = 3x² + 2x - 1

Now , to calculate the value of f ( 5 ) , substitute the value of x as 5

So , when x = 5 , the equation will be

f(x) = 3x² + 2x - 1

f ( 5 ) = 3 ( 5 )² + 2 ( 5 ) - 1

On simplifying the equation , we get

The value of f ( 5 ) = 3 x 25 + 10 - 1

The value of f ( 5 ) = 75 + 10 - 1

The value of f ( 5 ) = 85 - 1

The value of f ( 5 ) = 84

Therefore , the value of f ( 5 ) is 84

Hence , The value of f ( 5 ) in the equation f(x) = 3x² + 2x - 1 is f ( 5 ) = 84

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The part (a) is not correct i.e. The slope is 3, which indicates that a mouse's weight should increase by about 3 grams for each additional millimeter of tail length.

What is Regression analysis ?

Regression analysis is the process of determining how one or more variables and the outcome variable relate to one another. Risk factors, co-founders, and the outcome variable are all referred to as predictors or independent variables. The result variable is sometimes referred to as the dependent or response variable. Regression analysis displays the dependent variable as "y" and the independent variables as "x".

Given, tail length = (3 × weight) + 20

(a) Here, The slope is 3 which indicates that a mouse's length is the sum of 3 times the weight and 20. So, the statement is not correct.

(b) If weight is 38 gm, then

    tail length = 38 × 3 + 20

                     = 114 + 20 = 134mm.

So, the statement is correct.

(c) We've  tail length = (3 × weight) + 20

we can see that the relationship between the two is positive because when the weight is increased, the tail length also increases.

So, the given statement is correct.

(d) The slope is 3 when the tail length is being measured in millimeters.

Now, If we measure it in centimeter = 3/10 = 0.3 cm

∵ 1 mm = 1/10 cm.

So, the given statement is correct.

(e) when a mouse has weight of 29 grams and tail length of 100 mm.

    When the weight is 29 grams, it should have tail length as :

             tail length = 29 × 3 + 20

                              = 107 mm.

  but, tail length is given as 100 mm.

So, the residual for the mouse is -7 i.e. (100 - 107)

Hence, The given statement is correct.

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Answer: 1

Let's solve your equation step-by-step.

3x+2=5

Step 1: Subtract 2 from both sides.

3x+2−2=5−2

3x=3

Step 2: Divide both sides by 3.

3x/3 = 3/3

(3x divided by 3 cancels the 3 in 3x making it just x)

x=1

Answer:

m= -3

Step-by-step explanation:

5(2m+1)-3m=-16

5(2m)+5(1)-3m= -16

10m+5-3m= -16

7m+5= -16

     -5.   -5

7m= -21

/7.    /7

m= -3

Hopes this helps please mark brainliest

And :-3

process:

5(2m + 1) - 3m = - 16

10m+5-3m=-16

7m=-16-5

m=-21/7

m=-3

The inequality that represent each situations are:

a. 6(n + 3) ≥ 42.

b. 6(n + 3) ≤ 42

c. 6(n + 3) < 42

d. 6(n+3) > 42.

To write the inequality for each of the situations, translate each statement into algebraic expressions and use the appropriate inequality sign where necessary.

Thus, let the unknown number be represented as n.

a. The statement, "at least 42" means not less 42, which is the same as "greater than or equal to 42".

Therefore, the first statement is represented by the inequality, 6(n + 3) ≥ 42.

b. "6 times n and 3 is at most 42" is written as, 6(n + 3) ≤ 42

c. "6 times n and 3 is less than 42" would be translated as: 6(n + 3) < 42

d. "6 times n and 3 is more than 42" would be, 6(n+3) > 42.

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Step-by-step explanation:

6(n+3)>42

this is your answer

arlynn

The value of the function (f⋅g)(3) = 1

The characteristic that every input is associated with exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. It is denoted by the letter f or f(x).  

Here we have

f(x) = − 3x − 2  

g(x) = − x + 2

=> (f · g) = f(g(x))

Now Take x = − x + 2 in f(x)

=> f(g(x)) =  − 3(− x + 2)x − 2  

=  3x − 6 − 2      

=  3x − 8  

From the above calculations,

(f⋅g)(x) =  3x − 8    

Now we need to calculate the value of (f⋅g)(3) as given below

=> (f⋅g)(3) =  3(3) − 8 = 9 − 8 = 1

Therefore,

The value of the function  (f⋅g)(3) = 1

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$1,556.72 is required to deposit in the account each month.

72% of interest is earned.

a)

It is a classic Ordinary Annuity saving plan. The general formula is

FV = P((1+r)^n-1)/r)--------(1)

where  

FV is the future value of the account.  

P is the monthly payment (deposit).

r is the monthly percentage yield presented as a decimal.

n is the number of deposits (= the number of years multiplied by 12, in this case).

From this formula, you get the monthly payment:

P=FV(r/(1+r)^-1)----------(2)

Under the given conditions,

FV = $800,000

r = 0.04/12

n = 25*12.  

So, according to formula (2), the monthly payment is

P=800000(0.04/12(1+0.04/12)^25*12-1)

P=800000(0.003/1.713)

P=$1.556.72

Note that of the projected $800,000 the total you deposit will be only  25*12 times $1.556.72 i.e. about 25*12*1.556.72 = 467016 dollars.                    

The rest is what the account will earn/accumulate over the 25 years.

b)

You will earn:  

(8000000-467016/467016)*100

72% of interest is earned.

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Answer:

-------------------

It is assumed you need to add 5 and square root of 4: