3.2 The line drawn from the midpoint of the one side of a triangle, parallel to the second side, ... ACS is a triangle. P is a point on AS and R is a point on AC such that PSRQ is a parallelogram. PQ intersects AC at B such that B is the midpoint of AR. QC is joined. Also, CR-PS, C, -50° and BP- 60 mm. C 2 R 3 2 B/3 2 3.2.1 Calculate the size of A 3.2.2 Determine the length of QP. 2 1 P 2 (5) (3) [9]​

Each step of this theorem is proved below.

Given that,

S is finite,

Now enumerate all of its elements as x₁, x₂,..., x\(_{n}\).

According to the cancellation rule,

This product is independent of the order of the factors.

As a result, we can define the identity element e as this product.

It is simple to demonstrate that e meets the criteria of an identity element.

Now, let's show that every element of S has an inverse.

Let a be any element of S. Consider the set {a, a, a, ...}.

Since S is finite,

There exist positive integers m and n such that

am = an   for some m > n.

By the cancellation law,

We can cancel a power of a from both sides to get a\({(m-n)}\) = e.

This means that a has an inverse, and we can conclude that S is a group.

Consider the set of all positive integers under addition, except 1, as an example of an infinite semigroup in which the cancellation laws hold but which is not a group.

This set clearly meets the cancellation laws, but it does not have an inverse for every element, because the inverse of 2, for example, is not an integer.

As a result, this is not a group.

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Answer:

x is 3

Step-by-step explanation:

You use proportions to figure out x, what you first do is set up the proportion of the big triangle, then the small triangle.

\(\frac{(9+3)}{3}\)= \(\frac{12}{x}\)

By setting up this proportion, you would then cross multiply, and get 12x = 36. This is when you divide by 12 on both sides and get x=3

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See this attachment

\(\boxed{\boxed{\sf{ x=3 }}}\) \(\sf{ }\)

Answer:

Step-by-step explanation:

x - 12 ≤ 3 - 2x

3x ≤ 15

x ≤ 5

To graph this, just draw a VERTICAL line passing through x = 5, then shade the area to the LEFT

Answer: vector equation r = (7+3t)i + (4+2t)j + (5 - 5t)k

parametric equations: x = 7 + 3t; y = 4 + 2t; z = 5 - 5t

Step-by-step explanation: The vector equation is a line of the form:

r = \(r_{0}\) + t.v

where

\(r_{0}\) is the position vector;

v is the vector;

For point (7,4,5):

\(r_{0}\) = 7i + 4j + 5k

Then, the equation is:

r = 7i + 4j + 5k + t(3i + 2j - k)

r = (7 + 3t)i + (4 + 2t)j + (5 - 5t)k

The parametric equations of the line are of the form:

x = \(x_{0}\) + at

y = \(y_{0}\) + bt

z = \(z_{0}\) + ct

So, the parametric equations are:

x = 7 + 3t

y = 4 + 2t

z = 5 - 5t

Answer:

5 • 10^-4 I evaluate this by using scientific notation.

The value of the ratio  (3.5 x 10⁵) : (7x10⁸)  is 0.0005.

An expression is a sentence with at least two numbers or variables having mathematical operation. Maths operations can be addition, subtraction, multiplication, division.

For example, 2x+3

To solve (3.5 x 10⁵) : (7x10⁸), we can simplify the expression by dividing the numerical coefficients and dividing the exponents separately.

Dividing the numerical coefficients 3.5 and 7, we get:

3.5 ÷ 7 = 0.5

Dividing the exponents 5 and 8, we get:

10⁵ ÷ 10⁸ = 10⁵⁻⁸

              = 10⁻³

Therefore, the simplified expression is:

0.5 x 10⁻³

We can further simplify this expression by converting 10⁻³ to a decimal:

10⁻³ = 1/1000 = 0.001

So, the final answer is:

(3.5 x 10⁵) : (7x10⁸) = 0.5 x 10⁻³

                              = 0.5 x 0.001

                              = 0.0005

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Answer:

B

Step-by-step explanation:

On edge

The volume of the solid obtained by rotating the region between the curves x = 2√5y, x = 0, and y = 3 about the y-axis is 36π cubic units.

In calculus, finding the volume of a solid obtained by rotating a region about a line is an important topic. It involves using integration to calculate the volume of the solid.

To find the volume of the solid, we need to use the method of cylindrical shells. This involves taking thin slices of the solid perpendicular to the axis of rotation, finding their volume, and adding them up to get the total volume.

The first step is to sketch the region and the axis of rotation. In this case, the region is bounded by the curves x = 2√5y, x = 0, and y = 3, and the axis of rotation is the y-axis.

Next, we need to express the curves in terms of y. We can rewrite the equation x = 2√5y as y = x²/(20), and since the region is bounded by x = 0 and y = 3, the limits of integration are y = 0 and y = 3.

Now we can set up the integral for the volume using the formula for cylindrical shells:

V = 2π ∫(y)(f(y))dy from a to b,

where f(y) is the distance from the axis of rotation to the curve at a given value of y, and a and b are the limits of integration.

In this case, f(y) is simply the x-coordinate of the curve, which is x = 2√5y. Therefore, we have:

V = 2π ∫(y)(2√5y)dy from 0 to 3

Simplifying and evaluating the integral, we get:

V = 36π

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Let x be the number of square centimeters in 320 square inches

Using proportion,

0.16 square inches = 1 square centimeter

320 square inches = x

cross-multiply

0.16x = 320

Divide both-side by 0.16

x = 2000 square centimeters

Answer:

y > 0

Step-by-step explanation:

\(y = e^{4x}\)

This is an exponential function;

Consider as x → ∞, y → ∞;

If x = 0. y = e⁰ = 1;

As x → -∞, y → 0;

y ranges from 0 to ∞ therefore, i.e. y > 0

Three- month simple moving average (sma) forecast for the average gas prices are $3.08

$3.16 , $3.29 and predict the average retail gasoline price for june 2020 is $3.54.

A simple moving average (SMA) is defined as an arithmetic moving average calculated by adding recent prices and then dividing that figure by the number of time periods in the calculation average. The formula for SMA is:

SMA = (A₁ + A₂ + ------+ Aₙ )/n

where, Aₙ = the price of object at nth period

n = the number of total periods

We have, a average gas prices for different months. Calculate the three-month moving average, add together the first three sets of data, for this example it would be Dec, January, and February. This gives a total of $9.25 , then calculate the average of this total, by dividing this figure by 3 we get 3-month simple moving average. We have to predict the 3-month simple moving average for June 2020. As we seen in above table we calculate the 3-month simple moving average for different months.

The 3-month simple moving average for June 2020 is ( $3.29 + $3.51 + $3.82 )/3 = $3.54

So, required value is $3.54..

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Complete question:

use the gas prices data below to calculate a 3-month simple moving average (sma) forecast for the average gas prices and predict the average retail gasoline price for june 2020. round your answer to two decimal places, if necessary.

Year - month Averge gas price

19-Dec $3.07

20-Jan $3.10

20-Feb $3.08

20-Mar $3.29

20-Apr $3.51

20-May $3.82

20-Jun

The equation will be  \(y=40000+16000*x\)

Solve one of the equations for a particular variable. After that, insert that into the other equation and find the variable there. To find the value for the other variable, enter that value into either equation.

Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true. Two expressions joined by the equals symbol ("=") form an equation.

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using SOH CAH TOA

Tan 85.144 =h/130

h=tan 85.144*130

h=1530.19 fr

To simplify the expression \(\displaystyle\sf 5x-3(-5y+6x)+4y\), we can follow the order of operations, which involves simplifying the expressions within parentheses, applying the distributive property, and combining like terms.

Using \(\displaystyle\sf \) tags for formatting, the expression becomes:

\(\displaystyle\sf 5x-3(-5y+6x)+4y\)

First, we simplify the expression within the parentheses:

\(\displaystyle\sf 5x-3(-5y+6x)+4y\)

\(\displaystyle\sf 5x+15y-18x+4y\)

Next, we can combine the like terms:

\(\displaystyle\sf 5x-18x+15y+4y\)

\(\displaystyle\sf -13x+19y\)

Therefore, the simplified expression is \(\displaystyle\sf -13x+19y\).

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♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

AB= 7.45

Anwer C)

Step-by-step explanation:

Cos (angle) = Nearest side / Huypothenuse

Cos(20)      = 7 / AB

Cos(20) * AB = (7 /AB) * AB

Cos (20) * AB = 7

(Cos(20) *AB) / Cos(20) = 7 / Cos(20)

AB = 7 / cos(20)

AB=    7.45

Answer:

try and solve like this (

2

x

−

1

)

2/1

Step-by-step explanation:

The difference in overall loss or gain between sell at the current day's high price or low price is found tp be the difference in overall gain as $280.10

The third option is correct.

High price value: 115 shares * $105.19 per share = $12,084.85

Low price value: 115 shares * $103.25 per share = $11,858.75

High price value: 30 shares * $145.18 per share = $4,355.40

Low price value: 30 shares * $143.28 per share = $4,298.40

The overall value at high price:

$12,084.85 + $4,355.40

= $16,440.25

The overall value at low price:

$11,858.75 + $4,298.40

= $16,157.15

In conclusion, the difference in overall gain or loss:

$16,440.25 - $16,157.15 = $280.10

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The value of x is given as follows:

x = 1.5.

The measure of each segment is given as follows:

The segment addition postulate is a geometry axiom that states that a line segment, divided into a number of smaller segments, has the length given by the sum of the lengths of the segments.

For this problem, we have that segment WY is divided into two smaller segments, WX and XY.

This means that the equation to find the value of x is presented as follows:

WY = WX + XY

7x - 3 = 9x - 11 + 4x - 1

13x - 12 = 7x - 3

6x = 9

x = 1.5.

Hence the segment lengths are given as follows:

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Answer:

6.2 (Approximated).

Step-by-step explanation:

12x-7 > 67

Add 7 to both sides.

12x > 74

Divide 12 from both sides.

12/12x > 74/12

Final answer

x > 6.2 (approximately)

Answer:

4b + .60a

Step-by-step explanation:

b represents the number of bunches of bananas

a represents the number of apple

Multiply the cost by the number purchased of each item and add them together

4b + .60a

Answer:

\(\huge\boxed{\$ (4 b + 0.60 a)}\)

Step-by-step explanation:

Bananas represented by b

1 banana costs $4 so b bananas will cost $ 4 b

Apples represented  by a

1 apples costs 0.60 $ so a apples will cost $ 0.60 a

Totally, they will cost:

=> $ (4 b + 0.60 a)

The volume of the described solid is V = 16r³/3

Given,

A solid line S should be drawn between z=a and z=b. If S has a cross-sectional area of Px through x and is perpendicular to the x-axis, then A (x)

Volume of S = limₙ→∝ ∑i=₁ⁿ A(xi) Δx = \(\int\limits^b_a {A(x)} \, dx\)

The equation of circle x² + y² = r² where r is the radius of the circle.

Equation of upper semicircle yu= √(r²-x²)  and

Equation of lower semicircle yl = -√(r²-x²)

Area of cross-section A(x) = (yu² - yl²)

Substitute yu and yl values

A(x) = [√(r²-x²) - (-√(r²-x²) )]² = 4(r² -x²)        (1)

The limit for volume v varies from -r to r

Thus Volume v = ₋\(\int\limits^r_r {A(x)} \, dx\)

Substitute A(x) from (1)

V = ₋\(\int\limits^r_r {4(r^{2}-x^{2} ) } \, dx\)

⇒V = 4[r²x - x³/3 ]

⇒V = 4(r³ - r³/3) - 4(-r³ + r³/3) = 4[2 (r³ - r³/3)] = 16r³/3

The volume of the described solid S where the base is a circular disk or radius r and parallel cross sections perpendicular to the base are squares is V = 16r³/3

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The dividend payout ratio is 9%.

The other calculation is not calculated because the required value is not given.

The dividends payout ratio is the ratio between the common stockholder's amount and the net income.

It is important financial analytics because it is used to determine the sustainability of a company's dividend payment analysis.

We have,

Earnings per share.

We need to divide the net income by the number of outstanding shares. We are not given the number of outstanding shares, so we cannot compute the earnings per share.

Price-earnings ratio.

We cannot compute the price-earnings ratio without the stock price.

Dividend payout ratio.

Common stockholders = $320

The net income =$3540

= Dividends to common stockholders / Net income

= $320 / $3540

= 0.09

= 9%

Dividend yield ratio.

= Dividends paid to common stockholders / Stock price.

We are not given the stock price, so we cannot compute the dividend yield ratio.

Book value per share.

= Total stockholders' equity / Number of outstanding shares.

We are not given the number of outstanding shares, so we cannot compute the book value per share.

Thus,

The dividend payout ratio is 9%.

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Answer:

Step-by-step explanation:

Possible outcomes are:

Required probability is one out of the four outcomes:

Answer: k= -.5543

Step-by-step explanation:

Given:

t=1

P(t)=10532

\(P(t)=\frac{22000}{1+1.2e^{-kt} }\)                      >substitute what you know and solve for k

\(10532=\frac{22000}{1+1.2e^{-k(1)} }\)                  >cross multiply

\(10532(1+1.2e^{-k})=22000}\)      >divide both sides by 10532

\(1+1.2e^{-k}= 2.088872\)             >subtract 1 from both sides

\(1.2e^{-k}= 1.088872\)                   >divide both sides by 1.2

\(e^{-k}= 1.74073\)                         >take "ln" of both sides

\(ln (e^{-k})= ln 1.74073\)               >simplify

-k=.55430                             >bring over negative and round

k= -.5543

The x-intercepts represent a zero profit, the maximum value of the graph represents the maximum profit, An approximate average rate of change of the graph from x=3  to x=5 represents the reduction in profit from 3 to 5 and the domain is constrained by x=0.

Part A:

The x-intercepts represent a zero profit.

The maximum value of the graph represents the maximum profit.

The function increases up till the vertex and decreases after it.

This means that the profit increases as it reaches the peak at the vertex.

It decreases after the vertex up till it reaches zero.

On the left of the first zero and on the right of the second zero, the profits are negative.

Part B:

An approximate average rate of change of the graph from x=3  to x=5 represents the reduction in profit from 3 to 5.

Part C:

Simply, the domain is constrained by x=0.

We are obliged at x=6 .

This is because we have to avoid a negative profit.

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Answer:

2/5

Step-by-step explanation:

3/8 x 16/15 = 2/5

Answer:

2/5

Step-by-step explanation:

6/15 x 3/8 = 48/ 120

round it off it equals = 2/5

:)

Answer:

0.58333333333

Efficiency.Compared to solar panels' efficiency range of 18% to 22%, wind turbines typically capture 60% of the energy that flows through them.

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