A certain hospitalization policy pays a cash benefit for up to five days in the hospital. It pays $250 per day for the first three days and $150 per day for the next two. The number of days of hospitalization, X, is a discrete random variable with probability function P(X = k) = t (6 – k) for k = 1, 2, 3, 4, 5. Find Var(X)

Answer:

the answer is 13700m²

Step-by-step explanation:

cut this shape in two parts namely

A and B

from my view it could be cut into 1. two triangles or 2. a triangle and a rectangle

I will pick 2 because it seems much more simpler

let the triangle be A

let the rectangle be B

firstly you have to cut it then separate the shape with name given when dis is done you'll have

for ∆A=length=170-70=100m

but in B the small place is 110m,but the bigger one is 160

so to find height of triangle we say

160m-110m=50m for h of A

so for B we have

length=160m, width of breath=70m

Area of the total shape=area of A + area of B

=1/2(b×h) + (L×B)

=1/2×100×50 + (160×70)

=50m×50m+11200m²

=2500+11200

=13700m²

The area of the given kite to the nearest tenth would be = 135.10mm².

A kite is defined as the type of quadrilateral that has two pairs of sides that are equal in length and which are adjacent to each other.

To calculate the area of the kite given such as ABCD, the formula = ½ × AC × BD.

Given the sides such as:

AP = 6 mm

PB = 6√3 mm

PD = 7mm

But AC = 6mm × 2 = 12mm

BD = 6√3+7 = 13√3mm

Therefore the area = 1/2 × 12× 13√3

= 6×13√3

= 135.10mm²

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The perimeter of the figure is 52 cm

From the question, we have the following parameters that can be used in our computation:

The composite figure

The perimeter of the figure is the sum of the side lengths of the figure

So, we start by calculating the missing lengths as follows

Missing = 12 cm/4

Missing = 3 cm

Using the above as a guide, we have the following:

Perimeter = 12 + 9 + 3 + 3 + 3 + 3 + 3 + 3 + 7 + 9 - 3

Evaluate

Perimeter = 52

Hence, the perimeter is 52 cm

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The simplified expression of (x - 4)/2(x - 3) - (x - 1)/2x is -3/(2x).

The given expression (x - 4)/2(x - 3) - (x - 1)/2x can be simplified to;

(x - 4)/(2x - 6) - (x - 1)/2x

To solve this expression, we need to first find a common denominator for the two fractions.

The least common multiple of the denominators 2x and 2x - 6 is;

2x( x - 3)

So we'll multiply the first fraction by (x - 3)/(x - 3) and the second fraction by (x - 3)/(x - 3) to get a common denominator:

((x - 4)/(2x - 6)) · ((x - 3)/(x - 3)) - ((x - 1)/(2x)) · ((x - 3)/(x - 3))

Now we can combine the numerators over the common denominator:

((x - 4)(x - 3) - (x - 1)(x - 3))/(2x(x - 3))

Expanding the parentheses and combining like terms, we get:

(x² - 7x + 12 - x² + 4x - 3)/(2x(x - 3))

Simplifying the numerator, we get:

(-3x + 9)/(2x(x - 3))

Now we can factor out a -3/2 and simplify:

(-3/2) · (x - 3)/(x(x - 3))

The (x - 3) terms cancel out, leaving us with:

(-3/2) · 1/x

= -3/(2x)

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Answer:

(6, -1)

Step-by-step explanation:

The midpoint formula, (y2+y1)/2 and (x2+x1)/2 will help us find our answer. So (2-4)/2= -1 and (7+5)/2=6, so (6,-1) is the midpoint of segment AB.

x = -1/7.

To solve the absolute value equation or indicate that th |7x-4|+5=5, you should follow the steps given below:Step 1: Write the absolute value equation as two separate equations, one with a positive argument and one with a negative argument. |7x - 4| + 5 = 5, can be written as:7x - 4 + 5 = 5 or 7x - 4 - 5 = -5Step 2: Simplify both equations.7x = 4 or 7x = -1Step 3: Solve for x by dividing both sides by the coefficient of x.7x = 4 → x = 4/7 or7x = -1 → x = -1/7Therefore, the solution of the absolute value equation |7x-4|+5=5 is x = 4/7 and x = -1/7.

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The length of the string which is pulled taut as described in the task content is; 100.2 ft.

As evident in the task content; the kite is flying 85 ft off the ground, and the angle of elevation is; 58°.

It therefore, follows from trigonometric ratios that the ratio which holds true is;

sin (58°) = 85 / l

where l = Length of the string.

Therefore;

Multiply both sides by l;

l sin (58) = 85

Divide both sides by sin (58);

l = 85 / sin (58)

I = 100.2 ft (nearest tenth)

Ultimately, the length of the string as described in the task content is; 100.2 ft.

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Answer:

n = -3 or n = -6

Step-by-step explanation:

Solve for n over the real numbers:

n^2 + 9 n + 18 = 0

Subtract 18 from both sides:

n^2 + 9 n = -18

Add 81/4 to both sides:

n^2 + 9 n + 81/4 = 9/4

Write the left-hand side as a square:

(n + 9/2)^2 = 9/4

Take the square root of both sides:

n + 9/2 = 3/2 or n + 9/2 = -3/2

Subtract 9/2 from both sides:

n = -3 or n + 9/2 = -3/2

Subtract 9/2 from both sides:

Answer: n = -3 or n = -6

There are 132 entertainers who do not have red hair.

What is Percentage?

Percentage is a way of expressing a number or quantity as a fraction of 100. It is represented by the symbol "%". Percentages are commonly used to express the proportion or ratio of one quantity to another.

Percentages are widely used in many fields, including mathematics, science, finance, and economics, among others. They are a convenient way to express a relative quantity or change in quantity, and are easy to compare and interpret.

If 12% of the entertainers have red hair, then 100% - 12% = 88% do not have red hair.

To find out how many entertainers do not have red hair, we can calculate 88% of the total number of entertainers:

88% = 88/100 = 0.88

Number of entertainers without red hair = 0.88 x 150 = 132

Therefore, 132 entertainers do not have red hair.

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Answer:

C)  Both pairs of opposite sides are parallel because mPN = mLM = (1/2) and mPL = mMN = - 2.

Step-by-step explanation:

The corners of a rectangle are all right angles.  The two sets of sides are parallel.  In this example:

 PL ║ MN and

 LM ║ NP

To prove that the corners are all right angles, we could compre the slopes of the two lines that form each corner.  They will be perpendicular if they are 90°.

In this example:

PL ⊥ LM and

MN ⊥ NP

So one approach Sherry may have taken is to compare the slopes of all four lines.  To prove the object is a rectangle she could show that:

1.  The sets of parallel lines have equal slopes, and

2.  The sets of perpendicular lines have slopes that are the negative inverse of each other.  (e.g., if a line has slope 5, a perpendicular line will have slope -(1/5))

To prove these points, Sherry probably used a spreadsheet to calculate each line's slopes.  See the attached spreadsheet for how she may have set up the calculations.  The slopes are the Rise/Run for each line.  Rise is the change in y and x is the change in x between the two points.

Note the green cells.  These are the slopes.  Sherry found that:

a)  PL ║ MN and LM ║ NP,  since PL and MN both have slopes of -2; and  LM and NP both have slopes of -0.5

b)  PL ⊥ LM and MN ⊥ NP, since PL and LM and MN and NP both have slopes that are the negative inverse of each other (-2 and -(1/-2) or 0.5)

Without having checked whether any of the other answer options are viable options, Sherry will likely have seen, and done, enough to have chosen option C as proof that quadrilateral PLMN is a rectangle.

The solution to the equation x² + 2x = 18 is x = 4 ± √19.

Karappan Poochi: Algebra vs The Cockroaches is a math-based game designed to help students learn and practice algebra. The objective of the game is to help Karappan, a character in the game, solve algebraic equations. Players must solve equations by manipulating the variables and constants to reach the correct answer. To reach level six, the player must solve six equations correctly.

The equation for level six is x² + 2x = 18. To solve this equation, the player must first recognize that it is a quadratic equation and can be solved using the quadratic formula. The formula is: x = [-b ± √(b²-4ac)]/2a. For this equation, a = 1, b = 2, and c = -18. Plugging these values in, the player gets: x = [-2 ± √(2²-4(1)(-18))]/2(1). This simplifies to x = [-2 ± √76]/2, which simplifies to x = [8 ± √76]/2. Therefore, the solution to this equation is x = 4 ± √19.

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The difference quotient of the given function is\[\frac{f(x+h) - f(x)}{h} = \frac{-2x - h}{x^2(x+h)^2}\]The given function is\[f(x) = \frac{9}{x^2}\]

Now we have to find the difference quotient of this function, which is given as\[\frac{f(x+h) - f(x)}{h}\]

We are given that \(h ≠ 0\).

So, first let's find \(f(x+h)\).\[f(x+h) = \frac{9}{(x+h)^2}\]

Now we can put both the values of \(f(x+h)\) and \(f(x)\) in the difference quotient.

\[\frac{f(x+h) - f(x)}{h} = \frac{\frac{9}{(x+h)^2} - \frac{9}{x^2}}{h}\]

Let's put the LCM of \((x+h)^2\) and \(x^2\) which is \(x^2(x+h)^2\) in the numerator.

\[\frac{\frac{9x^2 - 9(x+h)^2}{x^2(x+h)^2}}{h}\]

Now, simplify the numerator.

\[\frac{9x^2 - 9(x^2 + 2xh + h^2)}{x^2(x+h)^2h}\]\[\frac{9x^2 - 9x^2 - 18xh - 9h^2}{x^2(x+h)^2h}\]

Now we can cancel out the common factor of 9 from both numerator and denominator.

\[\frac{-2xh - h^2}{x^2(x+h)^2h}\]

Now cancel out h from both numerator and denominator.

\[\frac{-2x - h}{x^2(x+h)^2}\]

So, the difference quotient of the given function is\[\frac{f(x+h) - f(x)}{h} = \frac{-2x - h}{x^2(x+h)^2}\]

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The expected loss for the retailer is $2288.4.

The retailer receives some products from three suppliers: S1, S2, and S3. The probability of successfully delivering the products in time by the suppliers are 0.85 for $1, 0.82 for $2, and 0.91 for S3. The manufacturer orders 500 units of a raw material from $1, 120 units from $2, and 156 units from $3. In case of failure to receive the materials in time, the manufacturer will bear $20 per unit for the product supplied by S1, $30 for the product supplied by S2, and $10 for the product supplied by S3. We have to calculate the expected loss for the retailer.

Let's calculate the expected loss for each supplier separately.Expected loss for supplier S1:Number of units ordered from S1 = 500The probability that the product will not be delivered in time = 1 - 0.85 = 0.15The expected loss per unit = $20Total expected loss for the products supplied by S1 = Expected loss per unit × Number of units ordered from S1 × Probability that the product will not be delivered in time= 20 × 500 × 0.15= $1500Expected loss for supplier S2:Number of units ordered from S2 = 120The probability that the product will not be delivered in time = 1 - 0.82 = 0.18

The expected loss per unit = $30Total expected loss for the products supplied by S2 = Expected loss per unit × Number of units ordered from S2 × Probability that the product will not be delivered in time= 30 × 120 × 0.18= $648 Expected loss for supplier S3:Number of units ordered from S3 = 156The probability that the product will not be delivered in time = 1 - 0.91 = 0.09The expected loss per unit = $10Total expected loss for the products supplied by S3 = Expected loss per unit × Number of units ordered from S3 × Probability that the product will not be delivered in time= 10 × 156 × 0.09= $140.4The total expected loss for the retailer = Expected loss for supplier S1 + Expected loss for supplier S2 + Expected loss for supplier S3= $1500 + $648 + $140.4= $2288.4

Hence, the expected loss for the retailer is $2288.4.

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The social media stock would earn $ more than the conglomerate corporation's stock.

When answering questions on Brainly, it is important to always be factually accurate, professional, and friendly, be concise and not provide extraneous amounts of detail, repeat the question in your answer, provide a step-by-step explanation in your answer, and use the following terms in your answer: geometric, Compare, invested.The value of a conglomerate corporation's stock was $1,145 in 2014.

If $1,000 were invested in this stock, what would its value be in 2017 if the stock had increased 3.5% annually?The solution to the given problem is as follows:Calculate the value of the stock when $1,000 was invested in 2014.Using the geometric mean formula,$\text{Geometric mean} = \sqrt[n]{a_1a_2a_3\cdots a_n}$Here, $n = 3$ since the value is given for the years 2014, 2015, and 2016. $a_1 =$ the value of the stock in 2014, $a_2 =$ the value of the stock in 2015, and $a_3 =$ the value of the stock in 2016.

We have to find $a_1$.Solve for $a_1:$\[a_1 = \frac{\text{Geometric mean}}{\sqrt[n-1]{a_2a_3\cdots a_n}} = \frac{\sqrt[3]{1145}}{\sqrt[2]{1.035^2}} \approx 1042.97\]Therefore, the value of the stock when $1,000$ was invested in 2014 was approximately $1,042.97$.

Calculate the value of the stock in 2017.Using the same formula as before, we have:\[\text{Geometric mean} = \sqrt[3]{1042.97 \cdot 1.035 \cdot 1.035} \approx 1,124.54\]Therefore, the value of the stock in 2017 would be approximately $1,124.54$ dollars.Compare the results obtained from the above two parts to the value of $1,000$ of the social media stock.

The value of $1,000$ of the social media stock after three years with a 7% annual increase is given by:\[\text{Social media stock} = 1000 \cdot (1 + 0.07)^3 \approx 1225.04\]Therefore, we can compare the results obtained from the two previous parts to see which one is greater. It is clear that the social media stock value of $1,000$ is greater than that of the conglomerate corporation's stock. Therefore, the correct answer is:The value of the $1,000 invested in the conglomerate corporation's stock in 2014 was less than that of the value of the $1,000 invested in the social media stock. The social media stock would earn $ more than the conglomerate corporation's stock.

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The total percent of the data falling between 62. 6 and 71. 8 is around 68%

Mean score = 67.2

Standard deviation = 4.6

Standardizing the values of interest by converting them into z-scores by -

z = (x - μ) / σ

where x is the score, μ is the mean, and σ is the standard deviation.

Calculating for the lower bound of 62.6:

z1

= (62.6 - 67.2) / 4.6

= - 4.6/4.6

= -1

Similarly,

Calculating for the upper bound of 71.8:

z2

= (71.8 - 67.2) / 4.6

= 4.6/4.6

= 1

Getting the area under curve between these two z-scores using a table of common normal probability. The normal distribution is symmetric, thus, the area between z1 and z2, can be then subtracted from the area to the left of z2. The Left of z1 is an area of 0.1587 and the left of z2 is an area of 0.8413. Therefore, the area between z1 and z2 is:

= 0.8413 - 0.1587

= 0.6826

Converting this area to a percentage -

0.6826 × 100%

= 68.26%

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The distance between point M and point N is 12 units.

Coordinates are a set of numbers or vaIues that describe the position or Iocation of a point in space. In two-dimensionaI space (aIso known as the Cartesian pIane), coordinates are typicaIIy represented by two vaIues, usuaIIy denoted as (x, y), that describe the horizontaI and verticaI position of a point reIative to a set of axes.

The distance formuIa is a mathematicaI formuIa used to find the distance between two points in a two- or three-dimensionaI space.

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

The distance formuIa is based on the Pythagorean theorem, which states that in a right triangIe, the square of the Iength of the hypotenuse (the side opposite the right angIe) is equaI to the sum of the squares of the Iengths of the other two sides.

In the given question,

We can use the distance formuIa to find the distance between point M and point N:

d = √[(x₂ - x₁)²+ (y₂ - y₁)²]

where (x₁, y₁) are the coordinates of point M and (x₂, y₂) are the coordinates of point N.

PIugging in the given vaIues, we have:

d = √[(-8 - 4)² + (-8 - (-8))²]

d = √[(-12)² + 0²]d = √[144]

d = 12

Therefore, the distance between point M and point N is 12 units.

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The standard deviation of the costs is 37 Dhs

The given mean is 173 and 3% of costs exceed 243. We have to calculate the standard deviation of the cost. Therefore, let's first start by calculating the z-score as follows;z-score formula = `(x - μ) / σ`z-score = `243 - 173 / σ`z-score = `70 / σ`We need to find the standard deviation of the costs. Since the z-score formula includes standard deviation, we can first calculate the z-score and then use it to calculate the standard deviation.Using the z-table, we can find the z-score for 3% = -1.88-1.88 = (243 - 173) / σσ = (243 - 173) / -1.88σ = -70 / -1.88σ = 37.23≈ 37The standard deviation of the costs is 37 Dhs. Hence, the correct option is as follows.Option D is the correct option.

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Check the picture below.

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{9}\\ o=\stackrel{opposite}{8} \end{cases} \\\\\\ c=\sqrt{ 9^2 + 8^2}\implies c=\sqrt{ 81 + 64 } \implies c=\sqrt{ 145 }\implies c\approx 12.04~ft[/tex]

Answer: -3, -2, -1, 0, 1 and 2

Answer:

0, 1, and 2

Step-by-step explanation:

A whole number is any number that does not contain a fraction, decimal, or negative value. For example, 1, 25, and 365 are whole numbers. Whereas the values of -3, 100.01, 365 ¼, and 2006.3 are not.

Answer:

Para saber cuántas galletas puso Mark en cada paquete, podemos dividir el número total de galletas por el número de paquetes:

195 galletas ÷ 13 paquetes = 15 galletas por paquete

Por lo tanto, Mark puso 15 galletas en cada paquete.

¡Espero que esto haya ayudado! Si no es así, lo siento. Si necesitas más ayuda, ¡pregúntame! :]

The volume of the composite figure can be divided into two separate figures: a cylinder and a half-sphere, with the total volume being 108 cubic centimeters.

The composite figure can be divided into two separate figures: a cylinder and a half-sphere.

The formula for the volume of a cylinder is:

Volume of the cylinder = π[tex]r^2[/tex]h, where r is the radius of the cylinder and h is the height of the cylinder.

In this case, the radius of the cylinder is 3 centimeters and the height of the cylinder is 10 centimeters, so the volume of the cylinder is:

Volume of the cylinder = π[tex](3cm)^2(10cm)[/tex] = 90π [tex]cm^3[/tex]

The formula for the volume of a half-sphere is:

Volume of half-sphere = (2/3)π[tex]r^3[/tex], where r is the radius of the half-sphere.

In this case, the radius of the half-sphere is also 3 centimeters, so the volume of the half-sphere is:

Volume of half-sphere = (2/3)π[tex](3cm)^3[/tex] = 18π [tex]cm^3[/tex]

To find the total volume of the composite figure, we add the volume of the cylinder and the volume of the half-sphere:

Total volume = Volume of cylinder + Volume of half-sphere

Total volume = 90π [tex]cm^3[/tex] + 18π [tex]cm^3[/tex]

Total volume = 108π [tex]cm^3[/tex]

Therefore, the exact volume of the composite figure is 108π cubic centimeters.

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The first withdrawal from the account is $200 and another is $150

A mathematical expression made up of variables, coefficients, constants, and operations like addition, subtraction, multiplication, and division is called an algebraic expression. In general, something is considered equal if two of them are the same. Similar to this, analogous expressions in mathematics are those that hold true even when they appear to be different. Yet, both forms provide the same outcome when the values are entered into the formula.

A checking account has a balance of $350

A customer makes two withdrawals

first is $50 more than the other,

let another withdrawal is $x

then first withdrawal is $(50+x)

then,

x+(50+x)=350

2x=300

x=$150

hence first withdrawal is $200

and another is $150

Then he makes a deposit of $75,

So the remaining balance in the account is $75.

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The mean height of camp 1 is 2.5.

A dοt plοt is a type οf graphical display that shοws the distributiοn οf a set οf data values. In a dοt plοt, each data pοint is represented by a dοt that is placed abοve its cοrrespοnding value οn a number line οr axis. The dοts are stacked οn tοp οf each οther tο shοw the frequency οr density οf the data at each value οr range οf values.

Dοt plοts are useful fοr visualizing small tο mοderate-sized data sets and fοr identifying patterns, οutliers, and gaps in the data. They are alsο easy tο cοnstruct and interpret, making them a pοpular tοοl fοr explοratοry data analysis.

Mean height of club fit = (2 + 2 + 3 + 5 + 3 + 3 + 1 + 1)/8

                                      = 2.5

Thus, The mean height of camp 1 is 2.5.

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Complete question:

The area of the given trapezoid would be 176 feet² with the length of the parallel sides of the trapezoid is 13 feet and 31 feet respectively and the height of the trapezoid given is 16 feet.

Given that,

The length of the parallel sides of the trapezoid is 13 feet and 31 feet

The height of the trapezoid given is 16 feet.

We know that area of trapezoid is (a+b)×h/2

Where, (a) and (b) are Length of the parallel sides of trapezoid and h is the height of trapezoid.

Thus, Area = (13+31) × 16/2

 Area = 22×8

  Area = 176 feet²

Hence the area of the given trapezoid would be 176 feet² with the length of the parallel sides of the trapezoid is 13 feet and 31 feet respectively and the height of the trapezoid given is 16 feet.

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Therefore, the apportionment under Hamilton's method is:

State Apportionment

A             18

B             22

C             13

D             30

E             17

What is Hamilton's method?

To use Hamilton's method, we need to calculate each state's priority by dividing its population by the geometric mean of its current seat and the next higher integer seat.

Then, we assign seats based on priority until we reach the total number of seats (in this case, 100).

State Population Standard Quota

A              5.6                      18

B              6.8                      22

C              3.6                      12

D              3.2                      10

E              5.2                      17

To calculate priorities, we first find the geometric mean of the current seat and the next higher integer seat for each state:

State A: sqrt(18*19) ≈ 18.49

State B: sqrt(22*23) ≈ 22.94

State C: sqrt(12*13) ≈ 12.68

State D: sqrt(10*11) ≈ 10.49

State E: sqrt(17*18) ≈ 17.89

Then, we divide each state's population by its corresponding priority:

State A: 5.6/18.49 ≈ 0.303

State B: 6.8/22.94 ≈ 0.296

State C: 3.6/12.68 ≈ 0.284

State D: 3.2/10.49 ≈ 0.305

State E: 5.2/17.89 ≈ 0.291

We then assign seats based on priority, starting with the highest priority and rounding down to the nearest integer:

State D: 30 seats

State A: 18 seats

State E: 17 seats

State B: 22 seats

State C: 13 seats

This adds up to 100 seats, as required.

Therefore, the apportionment under Hamilton's method is:

State Apportionment

A             18

B             22

C             13

D             30

E             17

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The rate of increasing the area of the rectangle is 72cm²/s

We have, The length of a rectangle is increasing at a rate of 5 cm/s and its width is increasing at a rate of 4 cm/s. When the length is 13 cm and the width is 4 cm, we have to find how fast is the area of the rectangle increasing.

The area of a rectangle is given by, A = l × w

Where l is the length and w is the width.

Now we will differentiate the equation with respect to time t.

dA/dt = d/dt (l × w)

dA/dt = l(dw/dt) + w(dl/dt)

We can use this formula to calculate how fast the area of the rectangle increases when the length is 13 cm and the width is 4 cm.

Substituting the given values, l = 13 cm and dl/dt = 5 cm/s w = 4 cm and dw/dt = 4 cm/s

dA/dt = 13(4) + 4(5)

dA/dt = 72 cm²/s

Therefore, the area of the rectangle increasing at a rate of 72 cm²/s.

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After calculations, we find that the company saves a total of $12 x 160 = $1,920 per month by having Alex work instead of a paid employee.

In this scenario, the company has three unpaid interns, including P. Alex, who are working in exchange for college credit. This means that the company does not have to pay these interns any salary or wages.

If the company were to hire a paid employee instead of having an intern like Alex work, they would have to pay that employee $12 per hour for the work that needs to be done. This is the amount that the company would have to spend in wages for each hour worked by the employee.

Now, we know that Alex works for the full 8 hours per day, and for 20 workdays in a month. This means that she works a total of 8 x 20 = 160 hours in a month.

Therefore, the total amount of money the company would have to pay a paid employee for the same amount of work that Alex does would be $12 per hour x 160 hours = $1,920.

Since Alex is working for the company without any payment, the company saves the entire amount of $1,920 per month that they would have had to pay a paid employee to do the same work.

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Therefore , the solution of the given problem of parallelograms comes out to be s intended, overline DE and overline FB are congruent.

In Euclidean mathematics, a simple quadrilateral of two sets of equal distances is referred to as a parallelogram. In a specific kind of quadrilateral known as a parallelogram, both set of opposite sides are straight and equal. There are four types of parallelograms, 3 of which are each mutually exclusive. Rhombuses, parallelograms, squares, but also rectangles are the four distinct shapes.

Here,

We can use the midpoint theorem and the fact that the opposing sides of a parallelogram are parallel and congruent to demonstrate that overline DE is congruent with overline FB.

The midpoint theory tells us that DE EA because we first know that E is the midpoint of overline AB.

The midpoint theory tells us that BF FC because we also know that F is the midpoint of overline DC.

As a result, overline DE and overline BC are parallel, and overline BF and overline AD are parallel.

DE EA and BF FC resulted in:

=> FC = EA Plus DE (Preserving equality by adding identical lengths)

If we replace FC with EA and DE with BF, we get:

=> BF + FC = DE + DE

If we simplify, we get:

=> 2DE = 2BF

When you divide both parts by 2, you get:

=> DE = BF

We have thus demonstrated that, as intended, overline DE and overline FB are congruent.

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Applying the definition of a diameter, we can conclude that m<AOE = 80 degrees. Therefore, m<AOE = 50 is FALSE.

The diameter is the longest chord passing through the center of a circle, while the radius is the distance from the center to any point on the circumference. The diameter forms two semicircles or divides the circle into two halves.

We are given that AD and EC are diameters of the circle O. This means that EOC is a straight angle or semicircle, which is equal to 180 degrees. Therefore:

m<EOC - m<AOB - m<BOC = m<AOE

Substitute:

180 - 50 - 50 = m<AOE

80 = m<AOE

m<AOE = 80°

Therefore, the statement, m<AOE = 50 is FALSE.

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