An investment portfolio is shown below.


Investment Amount Invested ROR
Savings Account $2,600 1.7%
Municipal Bond $3,700 3.2%
Preferred Stock $575 12.9%
Common Stock A $1,225 −5.6%


Using technology, calculate the weighted average ROR of the investments. Round to the nearest tenth of a percent.
2.1%
3.1%
5.9%
7.5%

Answer:

19.4

Step-by-step explanation:

The distance between the x coordinates of -4 and 15 would be 19 and the distance between the y coordinates of 2 and 6 would be 4.  We can use these to draw a right triangle.  The legs would be 19 and 4.  We would use the Pythagorean Theorem to find the hypotenuse.

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

[tex]19^{2}[/tex] + [tex]4^{2}[/tex] = [tex]c^{2}[/tex]

361 + 16 = [tex]c^{2}[/tex]

377 =[tex]c^{2}[/tex]

[tex]\sqrt{377}[/tex] = [tex]\sqrt{c^{2} }[/tex]

19.4 ≈ c  That is our answer rounded to the nearest tenth

By substitution, the solution of the system of equations, x + 3y = 7 and 2x - 4y = 24, is (10 , -1).

A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.

There are three methods that can be used to solve system of linear equations.

1. Elimination

2. Substitution

3. Graphing

Using substitution method, given two linear equations in x and y,

x + 3y = 7     (equation 1)

2x - 4y = 24     (equation 2)

Using the first equation, find the value of one variable, lets say x, in terms of the other.

x + 3y = 7     (equation 1)

x = 7 - 3y

Substitute the equation of x to the second equation.

2x - 4y = 24     (equation 2)

2(7 - 3y) - 4y = 24

14 - 6y - 4y = 24

Combining all terms containing the variable y on one side and the constants on the other side of the equality, and solving for y.

14 - 6y - 4y = 24

-6y - 4y = 24 - 14

-10y = 10

y = -1

Substitute the value of y in the equation of x.

x = 7 - 3y

x = 7 - 3(-1)

x = 7 - (-3)

x = 10

Hence, the solution of the given system of equations is (10 , -1).

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The circumference of the circle is approximately 17.6 cm  and the area is approximately 24.6 cm²

The perimeter of a circle or an ellipse in geometry is known as the circumference. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc. The curve length around any closed figure is more often referred to as the perimeter. The term "circumference" can also refer to the circle's actual location, which corresponds to a disk's edge.

The circumference of a circle is calculated by the formula 2πr .

The given coordinates are A(2,3) and B(4,1)

Here A is the center of the circle and B is any point on the circumference.

Now to calculate the radius we will use the distance formula:

therefore radius [tex]AB=\sqrt{(3-1)^2+(2-4)^2}[/tex]

[tex]or,AB=\sqrt{4+4}\\ \\or, AB=2.828[/tex]

[tex]or, AB\approx2.8[/tex]

Now let us calculate the circumference of the circle:

Circumference = 2πr

or, circumference = 2 × π × 2.8 = 17.592

or, circumference ≈ 17.6 cm

Area = π r²

or, Area = π (2.8)²

or, Area = 24.630 cm²

or, Area ≈ 24.6 cm²

The circumference of the circle is approximately 17.6 cm and the area is approximately 24.6 cm².

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The amount that would be saved if 7 bags of grapes were bought on Monday is $2 (option J).

The total cost of items bought on Monday and Wednesday would be added together. This amount would be subtracted from the total cost if the items were all bought on Monday.

The first step is to determine the total cost of the grapes bought on Monday and Wednesday.

Total cost of grapes = cost of grapes bought on Monday + cost of grapes bought on Wednesday

Cost of grapes bought on Monday = number of bags bought x price per bag

3 x $3 = $9

Cost of grapes bought on Wednesday = number of bags bought x price per bag

4 X $2.80 = $11.20

Total cost = $9 + $11.20 = $20.20

Cost or the 7 bags of grapes purchased in 1 trip = number of bags bought x price per bag

7 x $2.60 = 18.20

Amount saved = $20.20 - $18.20 = $2

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The sum of the series of three numbers, which includes the counting number, n, the number before n, and the number after n is 3•n

A series of a sequence of numbers is the sum of the numbers up to a specified term.

The given parameters;

n = A counting number

Counting numbers are the natural numbers which is the set of all positive integers.

Given that n is a counting number, we have that n is a positive whole number.

Which gives;

The whole number before n = n - 1

The whole number after n = n + 1

Which gives;

The sum of n, the whole number before n, and the whole number after n is part of a series and can be written mathematically as follows;

The sum = n + n - 1 + n + 1 = 3•n -1 + 1 = 3•n

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By applying the vertical angles theorem to the two (2) angles, the measures of the labeled angles are equal to 108°.

The vertical angles theorem is also referred to as vertically opposite angles theorem and it states that two (2) opposite vertical angles that are generally formed whenever two (2) lines intersect each other are always congruent i.e equal to each other.

By applying the vertical angles theorem to the two (2) angles, we have:

(x + 81)° = 4x°

x + 81° = 4x°

4x° - x = 81°

3x° = 81°

x° = 81°/3

x° = 27°

Now, we can determine the measures of the labeled angles:

x + 81° = 27° + 81°

x + 81° = 108°

4x° = 4(27)

4x° = 108°

In conclusion, the measures of the labeled angles are equal to 108°.

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Answer:

the answer is 5.

Step-by-step explanation:

used math-way to solve

The value of the expression A will be negative 2.

When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The expression is given below.

A = 5.5 - 2 + (-11.5) - (-6)

Simplify the expression, then the value of the expression A will be

A = 5.5 - 2 - 11.5 + 6

A = 11.5 - 13.5

A = - 2

The value of the expression A will be negative 2.

Your question was incomplete, the question probably was ...

Find the sum of the expression A=5,5-(+2)+(-11,5)-(-6).

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The sample space for the events are given as follows -

Picking up a one ball randomly from six balls -

S [1] = {A, B, C, D, E , F}

Picking up a one ball randomly from balls D to F -

S [2] = {D, E , F}

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur.

Given in the question a bag has six balls labeled A, B, C, D, E , F and one ball is randomly picked.

Sample space is defined as the set of all the outcomes for a given event. In the question given, the event is picking up of a ball randomly. A total number of six balls are there in the bag. Therefore, if a ball is picked up randomly, it could be any of the six. Therefore - the sample space for this event will be -

S [1] = {A, B, C, D, E , F}

Now, for the event of choosing a letter from D to F, we have total three outcomes. So in this case the sample space will be -

S [2] = {D, E , F}

Therefore, the sample space for the events are given as follows -

Picking up a one ball randomly from six balls -

S [1] = {A, B, C, D, E , F}

Picking up a one ball randomly from balls D to F -

S [2] = {D, E , F}

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The solution of the given linear equation in one variable 5(s -12) - 24 = 3(s + 2) is at s = 45.

According to the given question.

We have an equation.

5(s -12) - 24 = 3(s + 2)

Since, we have to solve the above linear equation in one variable.

As we know that, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.

Thereofre, the solution of the linear equation in one variable 5(s -12) - 24 = 3(s + 2) is given by

5(s - 12) -24 = 3(s + 2)

⇒ 5s - 60 - 24 = 3s + 6    ( by distributive rule)

⇒ 5s - 84 = 3s + 6

⇒ 5s - 3s = 84 + 6

⇒ 2s = 90

⇒ s = 90/2

⇒ s = 45

Hence, the solution of the given linear equation in one variable 5(s - 12) -24 = 3(s + 2) is at s = 45.

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Explanation:

You want to identify the step that is occurring on each line of the solution to the equation 2(8u+2) = 3(2u-7).

1. 2(8u+2) = 3(2u-7) . . . . Original Equation

2. 16u +4 = 6u -21 . . . . Apply the distributive property

3. 16u +4 -6u = 6u -21 -6u . . . . subtract 6u from both sides

4. 10u +4 = -21 . . . . collect terms

5. 10u -4 = -21 -4 . . . . subtract 4 from both sides

6. 10u = -25 . . . . collect terms

7. 10u/10 = -25/10 . . . . divide both sides by 10

8. u = -2.5 . . . . simplify

The curl of the vector field is:

[tex]=z e^x \hat{\imath}-\left(y z e^x-7 x y e^z\right) \hat{\jmath}-7 x e^z \hat{k}[/tex]

So,

To find the curve:

[Vector Field] Set up [curl F]:

[tex]Curl F=\left|\begin{array}{ccc}\hat{1} & \hat{\jmath} & \hat{k} \\\frac{\partial}{\partial x} & \frac{\partial}{\partial y} & \frac{\partial}{\partial z} \\7 x y e^z & 0 & y z e^x\end{array}\right|[/tex]

Simplify [3x3 Matrix Determinant] with [curl F]:

[tex]Curl F=\left|\begin{array}{cc}\frac{\partial}{\partial y} & \frac{\partial}{\partial z} \\0 & y z e^x\end{array}\right| \hat{i}-\left|\begin{array}{cc}\frac{\partial}{\partial x} & \frac{\partial}{\partial z} \\7 x y e^z & y z e^x\end{array}\right| \hat{j}+\left|\begin{array}{cc}\frac{\partial}{\partial x} & \frac{\partial}{\partial y} \\7 x y e^z & 0\end{array}\right| \hat{k}[/tex]

Simplify [2x2 Matrix Determinant] with [curl F]:

[tex]Curl F=\left[\frac{\partial}{\partial y} y z e^x-\frac{\partial}{\partial z} 0\right] \hat{\mathrm{i}}-\left[\frac{\partial}{\partial x} y z e^x-\frac{\partial}{\partial z} 7 x y e^z\right] \hat{\mathrm{\jmath}}+\left[\frac{\partial}{\partial x} 0-\frac{\partial}{\partial y} 7 x y e^z\right] \hat{\mathrm{k}}[/tex]

The partial derivatives can be differentiated using the basic differentiation techniques listed above under "Calculus":

[tex]\begin{aligned}&\frac{\partial}{\partial y} y z e^x=z e^x \\&\frac{\partial}{\partial z} 0=0 \\&\frac{\partial}{\partial x} y z e^x=y z e^x \\&\frac{\partial}{\partial z} 7 x y e^z=7 x y e^z \\&\frac{\partial}{\partial x} 0=0 \\&\frac{\partial}{\partial y} 7 x y e^z=7 x e^z\end{aligned}[/tex]

When we substitute our partial derivative values, we get:

[tex]\begin{aligned}Curl F&=\left(z e^x-0\right) \hat{1}-\left(y z e^x-7 x y e^z\right) \hat{\jmath}+\left(0-7 x e^z\right) \hat{k} \\&=z e^x \hat{\imath}-\left(y z e^x-7 x y e^z\right) \hat{\jmath}-7 x e^z \hat{k}\end{aligned}[/tex]

So, we've discovered the curl of the given vector field.

Therefore, the curl of the vector field is:

[tex]=z e^x \hat{\imath}-\left(y z e^x-7 x y e^z\right) \hat{\jmath}-7 x e^z \hat{k}[/tex]

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The correct question is given below:
Consider the following vector field. f(x, y, z) = 7xyezi + yzexk (a) find the curl of the vector field.

The sum of the 9 terms of the given series -5-25-45- . . . . is -765

The given series is:

-5-25-45- . . .

and there are 9 terms.

Notice that the given series is an arithmetic series with:

first term, a(1) = -5

common difference, d = -25 - (-5) = -20

Recall the formula for the nth term of an arithmetic series:

a(n) = a(1) + (n - 1) . d

Substitute a(1) = -5, d = -20, and n = 9 into the formula:

a(9) = -5 + (9 - 1) . (-20)

a(9) = - 5 + (-160)

a(9) = -165

To find the sum of the series, use the sum formula:

S(n) = n/2 [(a(1) + a(n)]

with n = 9.

Hence,

S(9) = 9/2 [-5 + (-165)]

S(9) = -765

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For numbers 5 and 45 the value of the geometric mean of these numbers is

Gm (5, 45) = 15

What is the geometric mean?

  The geometric mean is defined as a type of measure that is calculated as the root of a product between a set of numbers, it can be expressed as follows:

Gm (a, b) = √ab

Then in our case that we have the values 40 and 15, these are equivalent to the variables a and b

a = 5

b = 45

We substitute and solve for the square root

Gm (5, 45) = √5×45

Gm (5, 45) = √225  ;    In this case the square root is direct-

Gm (5, 45) = 15

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Answer:

the answe r is I because it does not mirror the other side

Answer: Evaluate

2(5+6q)

Apply the distributive property

2×5+2×6q

Multiply the terms

10+2×6q

Solution

10+12q

Step-by-step explanation:

hope this helps

Answer:

TWO PAIR OF VERTICAL ANGLES ARE

D,C

A,R

Answer:

Step-by-step explanation:

9989898989

There is a infinite number of real numbers from 1 through 5

The range is given as

1 to 5

The set of numbers is given as

Real numbers

Real numbers are any number that are not complex or imaginary numbers

This type of number covers all types of number that are not complex or imaginary numbers and it has an infinite count

Since the numbers cannot be counted, we can conclude that there is a infinite number of real numbers from 1 through 5

Hence, there is a infinite number of real numbers from 1 through 5

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Step-by-step explanation:

Given,

X = 3/5, Y = 1/3, Z = 2×4/5

the given question is to find out the value of Z+X×Y so the value is stated as

14/5+3/5×1/3

Here, 14/5 will be remains same and you should multiply 3/5×1/3.

Let 14/5 be equation number (1)

The L.C.M for 3/5×1/3 is 15. then,

3/5×15+1/3×15

___________

15

3×3+1×5

= -------------

15

9+5/15 = 14/15.

Let 14/15 be equation number (2)

Combine equation number (1) and (2) then

14/5+14/15

L.C.M.of 14/5 and 14/15 is 15.

14/5×15+14/15×15

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

15

[tex] = \frac{42 + 14}{15} [/tex]

[tex] \frac{56}{15} [/tex]

The value of term a11 is 21k - 43.

The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same value.

The formula of Arithmetic progression is

a(n) = a1 + (n - 1)d

given that the term of arithmetic sequence and common difference,

a1 = k+7 and d = 2k-5.

now find the value of term a11.

a(n) = a1 + (n - 1)d

now, substitute a(n) = a11, a1 = k+7, d = 2k-5.

a11 = k+7 + (11 - 1)(2k-5)

a11 = k + 7 + 10(2k-5)

a11 = k +7+ 20k - 50

a11 = 21k - 43

Hence,The value of term a11 is 21k - 43.

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SSS postulate of congruence, to prove ∠ L N M ≅ ∠ L N P.

What do you mean by congruent?

In triangles MLN and PLN,

MN ≅ PN,

LM ≅ LP

To prove :

Δ MLN ≅ Δ PLN

  Statement                                              Reason

1. LN ≅ LN                                           1. Common segment

2. MN ≅ PN;                                        2. Given

LM ≅ LP

3. Δ MLN ≅ Δ PLN                              3. SSS  postulate of congruence,

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Answer:

17 paintings are displayed

Step-by-step explanation:

Answer:

41. 12, 14

42. 30, 36

43. 0, 1

44. -24, -28

45. 2.5 , 4

46.

47.

48.

49. 63 , 189

Step-by-step explanation:

I don't know answers to 46 , 47 , 48

please make my answer as brainelist

Answer:

Hello,

Step-by-step explanation:

41)

[tex]2,4,6,8,10,...\\\\u_0=2 , u_{n+1}=u_n+2\\\\u_n=2*n+2\\\\[/tex]

42)

[tex]0,6,12,18,24,...\\\\u_0=0 , u_{n+1}=u_n+6\\\\u_n=6*n+0\\\\[/tex]

43)

[tex]-5,-4,-3,-2,-1,...\\\\u_0=-5 , u_{n+1}=u_n+1\\\\u_n=1*n-5=n-5\\\\[/tex]

44)

[tex]-4,-8,-12,-16,-20,...\\\\u_0=-4 , u_{n+1}=u_n-4\\\\u_n=-4*n-4\\\\[/tex]

45)

[tex]-5,-3.5,-2,-0.5,1,...\\\\u_0=-5 , u_{n+1}=u_n+1.5\\\\u_n=1.5*n-5\\\\[/tex]

46)

[tex]-32,-20,-8,4,16,...\\\\u_0=-32 , u_{n+1}=u_n+8\\\\u_n=8*n-32\\\\[/tex]

48)

[tex]0,\dfrac{1}{8},\dfrac{2}{8},\dfrac{3}{8},...\\\\u_0=0 , u_{n+1}=u_n+\dfrac{1}{8}\\\\u_n=\dfrac{1}{8}*n+0\\\\[/tex]

49)

[tex]27,15,3,-9,-21,...\\\\u_0=27 , u_{n+1}=u_n-12\\\\u_n=-12*n+27\\\\[/tex]

47) be carefull this is not a arithmetic sequence but a quadratic.

I show you the general method.

[tex]\begin{array}{c|c|c|c}x&\Delta_1&\Delta_2&\Delta_3\\--&--&--&--\\1&.&.&.\\&&&\\\dfrac{11}{3} &\dfrac{8}{3} &.&.\\&&&\\4 &\dfrac{1}{3}&\dfrac{-7}{3} &.\\&&&\\2 &-2 &\dfrac{-7}{3}&0\\&&&\\--&--&--&--\\\end {array} \\\\Since\ \Delta_3\ is\ null,\ u_n=a*n^2+b*n+c\ has\ for\ degree\ 2.\\[/tex]

[tex]\begin {array} {c|c|c|c|c}n&u_n&equation&\\--&--&-----&\\0&1&=a*0+b*0+c &c=1\\1&\dfrac{11}{3}&=a*1+b*1+c&a+b=\dfrac{8}{3} \\2&4&=a*4+b*2+c&4a+2b=3\\\end {array}\\\\\\\left\{\begin {array} {ccc}4a+2b&=&3\\a+b&=&\dfrac{8}{3}\\\end {array} \right.\\\\\\\left\{\begin {array} {ccc}a&=&\dfrac{-7}{6}\\\\b&=&\dfrac{23}{6}\\\\c&=&1\\\\\end {array} \right.\\\\\\\boxed{u_n=\dfrac{-7}{6}*n^2+\dfrac{23}{6}*n+1} \\[/tex]

[tex]u_n=\dfrac{-7}{6}*n^2+\dfrac{23}{6}*n+1}\\\\u_{n+1}=\dfrac{-7}{6}*(n+1)^2+\dfrac{23}{6}*(n+1)+1}\\\\u_{n+2}=\dfrac{-7}{6}*(n+2)^2+\dfrac{23}{6}*(n+2)+1}\\\\\Delta_1(n)=u_{n+1}-u_{n}=\dfrac{-7}{6}*(2n+1)+\dfrac{23}{6}\\\Delta_1(n+1)=u_{n+2}-u_{n+1}=\dfrac{-7}{6}*(2n+3)+\dfrac{23}{6}\\\\\Delta_2(n)=\Delta_1(n+1)-\Delta_1(n)=\dfrac{-7}{6}*2 \\[/tex]

[tex]\left\{\begin{array}{ccc}u_{n+2}-2u_{n+1}+u_n&=&\dfrac{-7}{3} \\\\u_0&=&1\\\\u_1&=&\dfrac{11}{3} \end {array} \right.[/tex]

The numeric values for the given function are as follows:

a) f(2.7) = 10.

b) f(1.9) = 7.

c) f(-3.6) = -14.4.

To find the numeric value of a function, we replace each instance of the variable by the desired value.

For this problem, the function is defined as follows:

f(x) = int(4x).

The function int(x) has the output as the largest integer that is less or equal to the value of x.

Hence the numeric values are given by:

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Answer:

D, since 7 is less than 10.

The person had been deceased for 12 hours

According to given data,

Temperature of normal person had  98.6 degrees,

and the temperature of the person was 82 degrees

outside temperature  is 55 and

rate of decay is -0.026

The temperature of body drops :

98.6 - 82 = 16.6 degrees

[tex]\frac{16.6}{55}[/tex] ≈ 0.3

[tex]\frac{0.3}{0.026}[/tex]   ≈ 12 hours

therefore, 12 hours had the person been deceased

The rules for exponential decay is f(x) = a b x, where b denotes the decay factor. In the rule of exponential decay function, the decay rate as a decimal. The decay rate represent as a percentage. We change it into a decimal by simply reducing the percent and dividing it by 100.

The amount  reduces by a predetermined percentage at regular periods. The exponential decay formula is used to find  decrease in growth.

f(x) = a (1 – r)x is  form of generic

Where,

a = The initial value

r = decay rate

x = time period

Advantage of the exponential growth and decay graph

The domain is all Real numbers.

The range is all positive real numbers (exclude zero).

Graph has a y-intercept at (0,1). we know that zero power of any number is 1.

we get When b > 1, the graph increases. and 0 < b < 1, the graph decreases.

Has an asymptote (a line that the graph is very close, but never crosses). For  graph the asymptote is the x-axis (y = 0).

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a. The next term in the sequence is 303.75.

b. The sequence is a geometric sequence.

c. The recursive function for the sequence is: aₙ = aₙ₋₁ (1.5) for n≥2.

Given the sequence is : 60,90,135,202.5,....

a. the next term in the sequence is:

Find the common ratio by dividing any term in the sequence by the term that comes before it:

a₂/a₁ = 90/60 = 1.5

a₃/a₂ = 135/90 = 1.5

a₄/a₃ = 202.5/135 = 1.5

The common ratio (r) of the sequence is constant and equals the quotient of two consecutive terms.

r = 1.5

find the sum:

To find the sum of the series, plug the first term: a = 60, the common ratio(r): 1.5 and the number of elements n = 4 into the geometric series sum formula:

Sₙ = a(1₋rⁿ/1₋r)

Sₙ = 60(1 ₋ 1.5⁴/1₋1.5)

Sₙ = 60(1 ₋ 5.0625/1₋1.5)

S₄ = 60(8.125)

S₄ = 478.5

To find the general form of the series, plug the first term:

aₙ = 60×1.5ⁿ⁻¹

use the general form to find the next term:

a₁ = 60

a₂ = a₁rⁿ⁻¹ = 60(1.5)¹ = 90

a₃ = a₁rⁿ⁻¹ = 60(1.5)² = 135

a₄ = a₁rⁿ⁻¹ = 60(1.5)³ = 202.5

a₄ = a₁rⁿ⁻¹ = 60(1.5)⁴ = 303.75

hence the required next term is 303.75

(b) The above sequence is geometric sequence.

(c) recursive function for the sequence : aₙ = aₙ₋₁ (1.5) for n≥2.

Hence we get the required answers.

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