An investment portfolio is shown below.


Investment Amount Invested ROR
Savings Account $3,200 2.1%
Municipal Bond $4,900 4.5%
Preferred Stock $940 10.5%
Common Stock A $1,675 −3.5%


Using technology, calculate the weighted dollar amount of the savings account.
−$58.63
$58.63
−$67.20
$67.20

Answer: h = 8

Using the similar triangle theorem

6 = 3

h = 4

Let me use a diagram to illustrate

From the above figure, you will observed that both 3 and 6 are slantted which make it look similar, and also h and 4 are similar too

Since, they are both similar

6 = 3

h = 4

Therefore, you can introduce cross multiply

Answer:

step two added the 9 to each side :)

\( \{ \: \alpha \: , \: \beta , \: a, \: b \}\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = {2}^{n} \)

where, n denotes to number of elements in set .

Since, given set contains 4 elements .

Thus , 2⁴ {2 raise to power 4} .

\( \sf \longrightarrow \: No. \: of \: \: subsets = {2}^{4} \)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 2 \times 2 \times 2 \times 2\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 4 \times 4\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 16\)

Therefore, Required subsets are 16.

They are , Namely;

\( \sf \longrightarrow \: subsets \: = \phi \: \{ \alpha \} \{ \beta \} \{ a\} \{ b\} \: \{ \alpha \beta \} \{ \alpha a\} \{ \alpha b\} \{ \beta a\} \{ \beta b\} \: .....\)

_____________________________

If n is the number of elements in the set then,

No. of subsets possible for this subset is 2^n that's the (2 raise to the power n).

Let's take another example, {1,2}

Here, n = 2

subsets =2^2 =4

Subsets = ϕ, {1}, {2},{1,2}

Note :- every set is a subset of itself i.e. {1,2} and ϕ is a subset of every set

Answer:

1. True.

3. True

4. True

Step-by-step explanation:

1. The absolute/ modulus of each number is always positive therefore true

2. Take for instance -2, it's opposite will be +2. thus the statement is false

3. True. zero takes no sign hence it's the only number whose opposite is itself.

4. Yes. absolute means it is positive and opposite of negative is positive too

5. absolute value of opposite of 2 is +2, the opposite of absolute value of 2 is -2. thus the statement is false

6. False. zero is neither positive nor negative

Answer:

d) 1/12

Step-by-step explanation:

Answer:

here

Step-by-step explanation:

i played it till 3 am once

Answer:

\((m-n)^{2}-9r\)

Step-by-step explanation:

m²-2mn+n²-9r​

\((m-n)^{2}-9r\)

Answer:

The answer is w=3

Step-by-step explanation:

6w+2=20

6w=18

w=3

Answer:

W = 3

Step-by-step explanation:

6W + 2 = 20

6W + 2-2 = 20-2

6W = 18

6W/6 = 18/6

w = 3

Answer:

6

Step-by-step explanation:

7.5 % × 500 = 37.5

37.5 × 6 = 225

Answer:

6

Step-by-step explanation:

The height of the pile increasing when the pile is 6 ft high is 1.41ft/min (approx.)

Define Volume of cone?

A pyramid having a circular cross section is called a cone. A right cone is a cone with the vertex located above the base's middle. Right circular cone is another name for it. If you know the height and radius of a cone and plug those values into a formula, you can quickly get the volume of a cone. Formula is , V =  1/3 πr²h

We have, dV/dt = 40 ft³/min

h = diameter where, h = 2r

so r = 1/2h

The formula for regular circular cone is,

V =  1/3 πr²h

put the value of r,

V = 1/ 3 * π * (1/2h)² * h

   = 1/12 * π * h³

differentiate it, we get

dV/dt = 3/12 * π * h² * dh/dt

dh/dt = (dV/dt)/(3/12*π*h²)

we have, dV/dt = 40 ft³/min and h = 6

Put these values,

dh/dt = 40 / (3/12 * 22/7 * 6²)               (∵ π = 22/7)

After solving, we get

dh/dt = 1.41 ft/min

Therefore, The height of the pile increasing when the pile is 6 ft high is 1.41ft/min (approx.)

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The measures of the missing angles are:

m∠1 = 123°

m∠2 = 94°

m∠3 = 25°

m∠4 = 25°

m∠5 = 43°

m∠6 = 43°

angles ABD and CBD are similar, so;

m∠1 = 133°

m∠1 + m∠2 + 133° = 360° {sum of angles at a point}

m∠2 = 360° - 266°

m∠2 = 94°

m∠3 = 180° - (22 + 133)°

m∠3 = 180° - 155°

m∠3 = 25°

angles BAD and BCD are similar, so;

m∠4 = 25°

angles m∠5 and m∠6 are base angles of an isosceles so m∠5 = m∠6 and;

m∠5 = (180 - 94)/2

m∠5 = 43°

m∠6 = 43°

Therefore, the measures of the missing angles are: m∠1 = 123°, m∠2 = 94°, m∠3 = 25°, m∠4 = 25°, m∠5 = 43°, and m∠6 = 43°.

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Plan B: Choose 14 of the 28 plants at random. Apply Brand X fertilizer to those 14 plants and Brand Y fertilizer to the remaining 14 plants.

A sample is only a small portion of the population.

Let's imagine you were interested in determining the average income for all Americans in your population.

Instead of knocking on every door in America because of time and money constraints, you decide to ask 1,000 random people. Your sample consists of these a thousand persons.

Given, A gardener wants to determine which of two brands of fertilizer is best for the plants.

And the gardener decides to conduct an experiment using 28 individual plants.

Plan A will be a biased sampling and the experiment would not yield

desired results.

Therefore, The gardener should choose 14 of the 28 plants at random. Apply Brand X fertilizer to those 14 plants and Brand Y fertilizer to the remaining 14 plants.

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Answer:

16pi =2pi r

pi are cancelled

r=16/2

r=8m

area of circle =pi r²

22/7×64

area=201.15m²

Step-by-step explanation:

circumference of circle is 2pie radius

area of circle is pi r²

Answer:

Step-by-step explanation:

Answer:

The Area of the shaded region would be 100 in^2 .

Step-by-step explanation:

Given:

Check the Attachment.

To Find:

The Area of Shaded Region

Solution:

The Triangle and the Rectangle have the same base(b) that is equal to the length(l) of the rectangle.

Note that Height of the triangle is same as breadth of the rectangle.

Now Let's come in the main solving part :-

We know that the formula of Area of the Triangle is ;

\(\boxed{ \rm \: Area \: of \: Triangle= \tt \: 1/2× \rm \: base×height , i.e. \: \tt \: 1/2× \rm\: b×h}\)

Substitute the values where Base= 20 in and Length = 10 in:

\( \tt \: Area \: of \: Triangle=1/2×20 \: \times 10\)

Now Solve it.

\( \tt \: Area \: of \: Triangle= \cfrac{1}{ \cancel2 {}^{1} } \times \cancel{20} {}^{10} \times 10\)

\( \tt \: Area \: of \: T riangle = 10 \times 10\)

\( \tt \: Area \: of \: Triangle=\boxed{\tt 100 \: in {}^{2}} \)

Hence, the area of the shaded region is 100 sq.in or 100 in^2 .

\( \rule{225pt}{2pt}\)

I hope this helps!

Let me know if you have any questions. :)

Answer:

√365 cm

Step-by-step explanation:

We can begin by using the formulas for the area of a rectangle and a square to set up an equation. Let x be the length of the sides of the square that is cut out of each corner of the rectangle.

The area of the original rectangle is 40cm * 89cm = 3560cm^2.

The area of the square that is cut out of each corner is x^2.

The area of the remaining base of the box is 2100cm^2.

So, we have:

3560cm^2 - 4x^2 = 2100cm^2

Solving for x, we get:

x = √(3560cm^2 - 2100cm^2)/4 = √(1460cm^2)/4 =√365cm

So the length of the sides of the square is √365 cm

if i helped you, can you mark my answer as best?

The algebraic expression for Desmond's height is x + 5.

If we let "x" represent Niki's height in inches, then Desmond's height can be represented by "x + 5", since Desmond is 5 inches taller than Niki.

So the algebraic expression for Desmond's height is x + 5.

Algebraic expressions is consist of variables, numbers, and mathematical operations (such as addition, subtraction, multiplication, and division).

They can contain one or more variables and can be evaluated for different values of the variables.

For example, the expression 3x + 5y - 2z is an algebraic expression that contains three variables (x, y, and z) and three coefficients (3, 5, and -2) that are multiplied by those variables. Algebraic expressions are commonly used in algebra to represent mathematical relationships and solve problems.

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Step-by-step explanation:

\(slope \: = \frac{y2 - y1}{x2 - x1} = \frac{3}{4} \)

point 1 ( -7,y)

point 2 (1,13)

\( \frac{13 - y1}{1 - ( - 7)} = \frac{3}{4} \)

\( \frac{13 - y1}{8} = \frac{3}{4} \)

\(13 - y2 = \frac{8 \times 3}{4} = 6\)

\(y2 = 13 - 6 = 7\)

y = 7

Answer:

can't seeit clearly

Step-by-step explanation:

The probability in each case is:

The probabilities provided are the probabilities of each value of X. For example,

Similarly,

When finding probabilities for a range of X values, you need to add up the individual probabilities of all the values in the range. For example, if you are looking for

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Answer:

Step-by-step explanation:

-2x + 2y = -10

2x - 3y = 4

-y = -6

y = 6

2x - 18 = 4

2x = 22

x = 11

(11, 6)

The cost to operate Lee's Tv is 2.88 dollars.

Lee watches TV for 4 hours per day. During that time, the TV consumes 200 watts per hour. Electricity costs (12 cents)/(1 kilowatt-hour).

Therefore, the cost for Lee to operate in 30 days can be calculated as follows:

200 watt = 0.2 kilowatt

Therefore,

1 day = 4 hours

30 days = ?

cross multiply

number of hours = 120 hours.

Therefore, in 30 days he watches television for 120 hours.

Let's find the cost

0.12 dollars  = 12 cent

1 hour  = 0.2 kilowatt

120 hours =

kilowatt use in 30 days = 0.2 × 120 = 24 kilowatts

Therefore,

1 kilowatts = 0.12 dollars

24 kilowatts = ?

cost of Tv for a month of 30 days = 24 × 0.12

cost of Tv for a month of 30 days = 2.88 dollars

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Answer:

8.

Step-by-step explanation:

Constant = Constant

Answer:

The inverse is,

\(f^{-1}(x) = \sqrt[5]{x} - 3\)

Step-by-step explanation:

f(x) = (x+3)^5

Finding the inverse,

\(f(x) = (x+3)^5\\or,\\y = (x+3)^5\)

We replace x with y and vice versa

so,

\(x = (y+3)^5\)

Solving for y,

the the 5th root,

\(\sqrt[5]{x} = y + 3\\y = \sqrt[5]{x} - 3\)

hence the inverse function is,

\(f^{-1}(x) = \sqrt[5]{x} - 3\)

Step-by-step explanation:

f(x)=(x+3)×5

Y=5X+15

now

interxchanging x and y we get,

x=5y+15

5y=x-15

y=x-15/5

therefor f~1(x)=x-15/5

The surface area of the pyramid is A = 265.23 inches²

The total surface area is the summation of the areas of the base and the three other sides. A = B + ( 1/2 ) ( P x h ), where B is the area of the base of the pyramid, P is the perimeter of the base, and h is the slant height of the pyramid

Surface Area of Pyramid = B + ( 1/2 ) ( P x h )

Given data ,

Let the surface area of hexagonal pyramid be represented as A

Surface area of hexagonal pyramid = Area of base + area of lateral surface

Area of the base = 93.5 inches²

Now , the Area of the lateral surface = 3a √ ( h² + ( 3a²/4 ) )

where a = 6 inches

h = 8 inches

Substituting the values in the equation , we get

Area of the lateral surface = ( 3 x 6 ) √ ( 64 + ( 3 x 36 / 4 ) )

On simplifying the equation , we get

Area of the lateral surface = 171.7 inches²

So , Surface area of hexagonal pyramid = Area of base + area of lateral surface

Surface area of hexagonal pyramid A = 93.5 inches² + 171.7 inches²

Surface area of hexagonal pyramid A = 265.23 inches²

Hence , the surface area of hexagonal pyramid is 265.23 inches²

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Answer:

In decimal form 0.4 or 4/10 or 2/5 (simplified). Also, in percentage form 40%.

Step-by-step explanation:

Answer: X\(\geq\)-4

Step-by-step explanation:

4x-5\(\leq\) 6x + 3

-2x \(\leq\) 3 + 5

-2x\(\leq\) 8

X = \(\geq\) - 8/2