For each of the following elementary matrices, describe the corresponding elementary row operation and write the inverse.
a. E = 1 0 3
0 1 0
0 0 1
b. E = 0 0 1
0 1 0
1 0 0
c. E = 1 0 0
0 1/2 0
0 0 1
d. E = 1 0 0
-2 1 0
0 0 1
e. E = 0 1 0
1 0 0
0 0 1
f. E = 1 0 0
0 1 0
0 0 5

The probability that no numbers are repeated = [tex]\frac{720}{1000}=0.72[/tex]

The probability that there are no repeated digits in a 3-digit pin number is 0.72.

Formula used:

[tex]P(n,r)=\frac{n!}{(n-r)!}\\ Probability=\frac{Number of favourable outcomes}{Total number of events in the samples pace}[/tex]

There are 10 digits (0,1,2,3,4,5,6,7,8,9) to choose from.

Therefore, the total number of possible 3-digit pin numbers with no repeated digits is

[tex]P(10,3)=\frac{10!}{(10-3)!}\\P(10,3)= \frac{10!}{7!}\\P(10,3)=720[/tex]

The total number of possible 3-digit pin numbers [tex]= 10 * 10 * 10 = 1000[/tex].

Thus, the probability that no numbers are repeated = [tex]\frac{720}{1000}=0.72[/tex]

Therefore, the probability that there are no repeated digits in a 3-digit pin number is 0.72.

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A sampling distribution is normal only if the population is normal. This  statement is false because A sampling distribution is normal only if n≥30.

If the underlying population is normally distributed, the sampling distribution (such as the sample mean distribution, also known as the xbar distribution) is also normally distributed. Even though the population is not normally distributed, the x(bar) distribution is approximately normal if n > 30, due to the central limit theorem. Some textbooks may use values ​​above 30, but after a certain threshold the x(bar) distribution is effectively "normal".

Option B is close, but misses the normal population part. n > 30 is not necessary if we know the population is normal.

A sampling distribution is the probability distribution of a statistic obtained from a large number of samples drawn from a particular population. The sampling distribution for a given population is the frequency distribution of a range of different outcomes that can occur in the population.

In statistics, a population is the entire basin from which a statistical sample is drawn. A population can refer to an entire population of people, objects, events, hospital visits, or measurements. Thus, a population can be said to be a global observation of subjects grouped by common characteristics.

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In the following question, among the various parts to solve on houses - 1. price = β0 + β1sqrft + β2bdrms, 2.  β2, 3. β2 + 140β1, 4. R-squared value is provided in the regression output, 5. 276.878 thousand dollars, 6. 23.122.

1. The regression equation of house price in thousands of dollars to the house size measured in square feet (sqft) and the number of bedrooms in the house (bdrms) can be written as follows: price = β0 + β1sqrft + β2bdrms Here, price refers to the house price in thousands of dollars, sqft refers to the house size measured in square feet and bdrms refers to the number of bedrooms in the house.

2. The estimated increase in price for a house with one more bedroom, holding square footage constant is equal to the coefficient of bdrms in the regression equation, which is β2.

3. The estimated increase in price for a house with an additional bedroom that is 140 square feet in size can be calculated as follows: β2 + 140β1. Comparing this to the answer in question two above, we can see that the price increase is greater when an additional 140 square feet are added to the house rather than an additional bedroom.

4. The percentage of the variation in price explained by square footage and the number of bedrooms can be found using the R-squared value. The R-squared value is a measure of how much of the variation in the dependent variable (house price) is explained by the independent variables (sqft and bdrms). In this case, the R-squared value is provided in the regression output.

5. To find the predicted price for the first house in the sample using the model estimated above, we need to plug in the values of sqft and bdrms for the first house into the regression equation. Here, sqrft = 2,438 and bdrms = 4. Thus, the predicted price for the first house is given by: price = β0 + β1sqrft + β2bdrms = -14.973 + 0.128sqrft + 15.204bdrms = -14.973 + 0.128(2,438) + 15.204(4) = 276.878 thousand dollars.

6. The residual for the first house in the sample can be calculated as follows: Residual = Actual price - Predicted price = 300 - 276.878 = 23.122. The fact that the residual is positive suggests that the buyer overpaid for the house.

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The solution to the inequality f(x) ≤ 0 is the interval [-6, 2]. In other words, the values of x that satisfy the inequality are those that lie between -6 and 2, inclusive.

To solve the inequality f(x) ≤ 0, we need to find the values of x for which the function f(x) is less than or equal to zero.

We start by factoring the quadratic expression f(x) = x^2 + 4x - 12:

f(x) = (x + 6)(x - 2)

Setting this expression to zero, we get:

(x + 6)(x - 2) = 0

This gives us two solutions: x = -6 and x = 2.

Now, we need to determine the sign of f(x) in the intervals between these two solutions. We can use a sign chart to do this:

x f(x)

-∞ +

-6 0

2 0

+∞ +

From the sign chart, we see that f(x) is positive for x < -6 and for x > 2, and it is negative for -6 < x < 2.

To summarize, the solution to the inequality f(x) ≤ 0 for the function f(x) = x^2 + 4x - 12 is the interval [-6, 2].

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The error is the substitution of coordinates. Coordinates are ordered pairs of points that help us locate any point in a 2D plane or 3D space.

Cartesian coordinates, also known as the coordinates of a point in a 2D plane, are two integers, or occasionally a letter and a number, that identifies a specific point's precise location on a grid. This grid is referred to as a coordinate plane.

The distance between two points A(x₁, y₁) and B(x₂, y₂) is given by

[tex]AB = \sqrt{(x_{1} , x_{2})^{2} + (y_{1} - y_{2})^{2} }[/tex]

Observe that the x-coordinate of B is subtracted from the x-coordinate of A. This goes with the y-coordinates.

Therefore, the error is the substitution of coordinates.

The correct computation is

[tex]AB = \sqrt{(6-1)^{2} + [2 - (-4)]^{2} }[/tex]

[tex]= \sqrt{5^{2} + 6^{2} }[/tex]

[tex]= \sqrt{25 + 36} \\[/tex]

[tex]= \sqrt{61}[/tex]

≈ 7.81

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The complete question is as follows:

Describe and correct the error in finding the distance between A(6, 2) and B(1, -4). AB = √[(6 - 2)² + {2 - (-4)}²] = √(4² + 5²) = √(16 + 25) = √41 ≈ 6.4.

In equation A the missing number is 955, In equation B the missing number is 90 and In equation C the missing number is 805.

A) To find the missing number in the equation 872 + ? + 173 = 2000, we need to subtract 872 and 173 from 2000, which gives us:

2000 - 872 - 173 = 955

Therefore, the missing number is 955.

B) To find the missing number in the equation 9180 ÷ ? = 102, we need to divide 9180 by 102, which gives us:

9180 ÷ 102 = 90

Therefore, the missing number is 90.

C) To find the missing number in the equation ? - 99 = 706, we need to add 99 to 706, which gives us:

706 + 99 = 805

Therefore, the missing number is 805.

To obtain the indicated results with the same numbers and operations, we need to use parentheses to change the order of operations.

A) 3 + (5x7) - 2 = 40

B) (3 + 5) × 7 - 2 = 54

C) 3 + (5 × (7-2)) = 28

Equations are used extensively in various fields of science, engineering, economics, and finance, to name a few. It is formed by placing an equal sign between the two expressions. Equations are used to solve problems and find unknown values.

An equation can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The variables in an equation represent unknown values that need to be found, while the constants are known values that are already given. Solving an equation involves manipulating the expressions on both sides of the equal sign using mathematical operations to isolate the variable on one side and constants on the other. The final solution obtained is the value of the variable that satisfies the equation..

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Complete Question: -

Find unknown numbers of these operations

A ) 872 +. + 173 = 2000

B ) 9180:. = 102

C ). -99 = 706

With the same numbers and the same operations we can obtain different results, place the parentheses so that the indicated results are obtained.

A ) 3 + 5 x 7-2 = 40

B ) 3 + 5 × 7-2 = 54

C ) 3 + 5 × 7-2 = 28

IT'S FOR TODAY PLEASE ☹, CAN DO IN A LEAF OR WRITE ASI BUT EXPLAIN WELL!!!!!!HELP IF THEY DON'T KNOW NO RESPOND

Answer:

The point z = 3+4i is plotted as a blue dot, and the two square roots are plotted as a red dot and a green dot. The magnitudes of z and its square roots are shown by the radii of the circles centered at the origin.

Step-by-step explanation:

qrt(z) = +/- sqrt(r) * [cos(theta/2) + i sin(theta/2)]

where r = |z| = magnitude of z and theta = arg(z) = argument of z.

Calculate the magnitude of z:

|r| = sqrt((3)^2 + (4)^2) = 5

And the argument of z:

theta = arctan(4/3) = 0.93 radians

Now, find the two square roots of z:

sqrt(z) = +/- sqrt(5) * [cos(0.93/2) + i sin(0.93/2)]

= +/- 1.58 * [cos(0.47) + i sin(0.47)]

= +/- 1.58 * [0.89 + i*0.46]

Using a calculator, simplify this expression to:

sqrt(z) = +/- 1.41 + i1.41 or +/- 0.2 + i2.8

Answer:

x = 4[tex]\sqrt{2}[/tex]

Step-by-step explanation:

using the cosine ratio in the lower right triangle and the exact value

cos45° = [tex]\frac{1}{\sqrt{2} } }[/tex] , then

cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{4}{x}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex]  ( cross- multiply )

x = 4[tex]\sqrt{2}[/tex]

The roots of the equation 2x² + 10x + 9 = 2x does not exist i.e no real roots

To find the roots of the given quadratic equation 2x² + 10x + 9 = 2x, we can start by rearranging the equation to the standard form of a quadratic equation

2x² + 10x + 9 - 2x = 0

Simplifying the left-hand side, we get:

2x² + 8x + 9 = 0

Now, we can use the quadratic formula to find the roots of the equation:

x = (-b ± √(b² - 4ac)) / 2a

where a = 2, b = 8, and c = 9.

Substituting these values into the formula, we get:

x = (-8 ± √(8² - 4(2)(9))) / 2(2)

Simplifying the expression under the square root, we get:

x = (-8 ± √-8) / 4

The square root of -8 is not a real number

So, the equation has no real root

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D: "[tex]c_{1} = 10[/tex] and [tex]c_{2} = 2[/tex]" are programmer-defined constants for quadratic probing that cannot be used in a quadratic probing equation. Option D is correct answer.

The quadratic probing equation is defined as:

h (k, i) = (h′(k) + [tex]c_{1}[/tex] * i + [tex]c_{2}[/tex] * i^2) mod m,

where h′(k) is the hash value of key

k and m is the size of the hash table.

The constants [tex]c_{1}[/tex] and [tex]c_{2}[/tex] are programmer-defined constants that are used to compute the new hash index when a collision occurs in the hash table.

The given hash function is h(k) = k % 10.

Therefore, the hash value of any key will be between `0` and `9`.Now, let's check which of the given programmer-defined constants for quadratic probing cannot be used in a quadratic probing equation:

Option A: `c1 = 1 and c2 = 0`This option can be used in the quadratic probing equation. It means that linear probing is being used.

Option B: [tex]c_1 = 5[/tex] and [tex]c_2 = 1[/tex] This option can be used in the quadratic probing equation. It means that the new index is being computed as `h(k, i) = (h′(k) + 5i + i^2) mod m`.

Option C: [tex]c_1 = 1[/tex] and [tex]c_2 = 5[/tex] This option can be used in the quadratic probing equation. It means that the new index is being computed as `h(k, i) = (h′(k) + i + 5i^2) mod m`.

Option D: [tex]c_1 = 10[/tex] and [tex]c_2 = 2[/tex] This option cannot be used in the quadratic probing equation. It means that the new index is being computed as `h(k, i) = (h′(k) + 10i + 2i^2) mod m`.

Since [tex]c_{1}[/tex] is greater than or equal to `m`, this equation will always result in a hash index that is greater than or equal to `m`. Therefore, it is not possible to use `[tex]c_{1}[/tex]= 10` in the quadratic probing equation. Hence, the correct option is D.

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The equation of the quadratic function represented by the given table is  y = -x² + 4x - 7.

A quadratic function is a function of the form:\sf(x) = ax^2 + bx + c\swhere a, b, and c are constants and x is the parameter. The graph of a quadratic function is a parabola, which is an Inverted curve. Whether the parabola opens up (if a > 0) or down (if a 0) depends on the sign of the coefficient a.

The width of the parabola is also determined by the coefficient a. The parabola is narrow if |a| is greater than 1. (i.e. it has a small width relative to its height). The parabola is wide if |a| is greater than 1.

The standard form of the quadratic equation is given as:

y = ax² + bx + c

Substitute the value of x and y from the table:

3 = a(2)² + b(2) + c

4a + 2b + c = 3........(1)

For point (4, -1):

-1 = a(4)² + b(4) + c

16a + 4b + c = -1..........(2)

For (6, -13):

-13 = a(6)² + b(6) + c

36a + 6b + c = -13..........(3)

From 1 we have:

c = 3 - 4a - 2b

Substitute the value of c in equation 2 and 3:

16a + 4b + 3 - 4a - 2b = - 1

12a + 2b = - 4........(4)

36a + 6b + 3 - 4a - 2b = -13

32a + 4b = -16.......(5)

Multiply equation 4 with 2 and subtract with equation 5:

32a + 4b = -16

-(24a + 4b = - 8)

a = -1

Substitute the value of a in equation 5:

32(-1) + 4b = -16

-32 + 4b = -16

b = 4

Substitute the value of a and b in equation 1:

16a + 4b + c = -1

16(-1) + 4(4) + c = -1

-16 + 8 + c = -1

-8 + c = -1

c = 7

Using the algebraic techniques we have:

a = -1

b = 4

c = 7

Hence, the equation of the quadratic function represented by the given table is y = -x² + 4x - 7.

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With a [tex]12[/tex]% price rise, the smart mug now costs AED [tex]1003.52[/tex].

The sale price is the price an user pays to purchase a thing or a commodity. It is a cost that is higher than the market cost and also includes a portion of the profit. The cost price refers to the price paid by the seller for the item or service.

Price is the process of figuring out how much a something or service is worth. Price establishes a customer's cost, although it can or cannot be linked to the price a firm pays to manufacture a good or service.

We need to multiply the initial price by [tex]1.12[/tex] which represents a [tex]12[/tex]% increase in decimal form,

New price [tex]=[/tex] Initial price [tex]*[/tex] (1 [tex]+[/tex] Percent increase in decimal form)

New price[tex]= 896 * (1 + 0.12)[/tex]

New price [tex]= 896 * 1.12[/tex]

New price [tex]= 1003.52[/tex]

Therefore, the new price of the smart mug is AED [tex]1003.52[/tex] after a [tex]12[/tex]% increase.

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well, we know the discount is just 30 - 21 = 9, so hmm if we take 30(origin amount) to be the 100%, what's 9 off of it in percentage?

[tex]\begin{array}{ccll} Amount&\%\\ \cline{1-2} 30 & 100\\ 9& x \end{array} \implies \cfrac{30}{9}~~=~~\cfrac{100}{x} \\\\\\ 30x=900\implies x=\cfrac{900}{30}\implies x=30[/tex]

The phone is worth $128 after 2 years, which is option C.

What is exponential decay ?

Exponential decay is a decrease in a quantity over time where the rate of decay is proportional to the current value. In this case, the value of the phone decreases by 3/5 each year after it is released. This means that the value after one year is 2/5 of the original value, and the value after two years is (2/5) times (2/5) of the original value. Exponential decay is a common phenomenon in many areas of science and mathematics, including radioactive decay, population growth and decay, and financial investments.

Calculating the worth of the phone :

The phone is not worth the same amount after 2 years, as it loses 3/5 of its value each year. We need to calculate its worth after 2 years.

Let's use the formula for exponential decay: [tex]A = A_0(1 - r)^t[/tex], where A is the final amount, [tex]A_0[/tex] is the initial amount, r is the decay rate, and t is the time elapsed.

In this case, the initial amount is $800, the decay rate is 3/5, and the time elapsed is 2 years. Substituting these values into the formula, we get:

[tex]A = 800(1 - 3/5)^2[/tex]

[tex]A = 800(2/5)^2[/tex]

[tex]A = 800(4/25)[/tex]

[tex]A = 128[/tex]

Therefore, the phone is worth $128 after 2 years, which is option C.

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In the following question, among the conditions given, the statement is said to be, the exact molarity of the NaOH solution is 0.0960 M.

The question is asking to calculate the exact molarity of the sodium hydroxide from Experiment 1.
KHP stands for potassium hydrogen phthalate, and one mole of sodium hydroxide (NaOH) will neutralize one mole of KHP. To solve the problem, use the mass of KHP and a stoichiometry problem.
First, calculate the number of moles of KHP:
Moles KHP = (Mass KHP (g) / Molar Mass KHP (g/mol))
Then, calculate the moles of NaOH:
Moles NaOH = (Moles KHP * Mole Ratio NaOH/KHP)
Finally, calculate the molarity of NaOH:
Molarity NaOH = (Moles NaOH / Volume NaOH (L))

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In order to expect a return on $400 from across all policies of a similar nature, the insurance firm should charge the policy for about $501.88.

Return[expr] leaves control structures that are present during a function's definition and returns the value expression for the entire function. Even if it comes inside other functions, yield takes effect as quickly as it is evaluated. Functions like Scan can use Return inside of them.

Since p is the chance that the 28-year-old woman survives the year and is given as 0.99962, we can enter this number into the equation for n as follows: n = 400(0.99962)/500,400 n 0.799

In light of this, the insurance provider should impose a premium of: Premium = 400/n

$501.88 is the premium ($Premium = 400/0.799)

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Answer:

235.65

Step-by-step explanation:

The value οf a = 1/2  and b = 19/4 in the equatiοn x² - x + 5 = (x-a)² + b.

The part οf mathematics in which letters and οther general symbοls are used tο represent numbers and quantities in fοrmulae and equatiοn is called algebra.

x² - x + 5 = (x-a)² + b

x² - x + 5 = x² + a² - 2xa + b

-x + 5 = -2xa + a² + b

By matching cοrrespοnding terms,

2a = 1          and        a²+ b = 5

a= 1/2          and        a²+ b = 5

Substituting value οf "a"

(1/2)² + b = 5

1/4 + b = 5

b = 5- 1/4

b = 19/4

Thus, a = 1/2  and b = 19/4.

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The reason we can't use the mean when a data set has one or two values that are much higher than all of the others is that it skews the average, making it not representative of the rest of the data.

The mean is a numerical measure of the central tendency of a data set. It is calculated by dividing the sum of all the values in a data set by the number of data points.

A data set is a collection of observations or measurements that are analyzed to obtain information. It can be represented graphically, in tabular form, or in any other format. The data set may be a sample or the entire population.

If a data set has one or two extremely high or low values, it can significantly impact the mean. These values are known as outliers. The outliers can cause the mean to be higher or lower than the actual middle value of the data.

Hence, in such cases, the median is a better choice for finding the central tendency of the data. The median is the middle value of the data set, and it is less affected by outliers than the mean. The mode, which is the value that occurs most frequently in the data set, is also a measure of central tendency that is less sensitive to outliers than the mean.

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Answer:

3x - (4x - 11) = 3x - 4x + 11 = -x + 11

Step-by-step explanation:

Answer:

$10

Step-by-step explanation:

We Know

Terri pays a monthly cell phone fee of $10. She pays 5 cents for each minute that she talks.

Let C be the total cost, and x be the number of minutes she talks; we have the equation.

C = 0.05x + 10

If Terri does not make any calls, what would her bill be?

C = 0.05(0) + 10

C = $10

So, her bill will be $10

Step-by-step explanation:

The area of a rectangle is 1,872 ft2. The ratio of the length to the width is 9:13. Find the perimeter of the rectangle.

176 ft

You want to make a scale drawing of your bedroom to help arrange your furniture. You decide on a scale of 3 in. = 2 ft. Your bedroom is a 12 ft by 14 ft rectangle. What should the dimensions of your drawing be?

18 in. by 21 in.

If 5/y + 7/x=24 and 12/y + 2/x=24, find the ratio of x to y.

5/7

Simplify the ratio 8ft/12in. Use the conversion 12 in. = 1 ft.

8/1

Analyze the proportion below and complete the instructions that follow.

2x+5/3 = x-5/4

-7

If a+b/2a-b = 5/4 and b/a+9 = 5/9, find the value of b.

30

Analyze the ratio below and complete the instructions that follow.

$30:$6

Simplify the ratio.

5:1

If 14/3 = x/y then 14/x =

3/y

Analyze the diagram below and complete the instructions that follow.

In the diagram, AB:BC is 3:4 and AC = 42. Find BC.

24

Analyze the diagram below and complete the instructions that follow.

If AB:BC is 3:11, solve for x.

9

If a, b, c, and d are four different numbers and the proportion a/b = c/d is true, which of the following is false?

b/a = c/d

Analyze the diagram below and complete the instructions that follow.

Find the ratio of the width to the length of the rectangle, then simplify the ratio. Use the conversion 100 cm = 1 m.

3/4

Simplify the ratio 3 gal./24 qt. Use the conversion 4 qt = 1 gal.

1/2

The area of a rectangle is 4,320 ft2. The ratio of the length to the width is 6:5. Find the length of the rectangle.

72 ft

Analyze the diagram below and complete the instructions that follow.

Given that CB/CA = DE/DF, find BA.

10.5

Analyze the proportion below and complete the instructions that follow.

2/3 = 8/x

3, 8

Analyze the diagram below and complete the instructions that follow.

Are the polygons shown here similar? Justify your answer. The images are not drawn to scale.

Yes, PQR ~TSV with a scale factor of 1:√3

All __________ are similar.

squares

Analyze the diagram below and complete the instructions that follow.

Determine which 2 triangles are similar to each other. The images are not drawn to scale.

GHI ~ JKL

Analyze the diagram below and complete the instructions that follow.

Pentagon PQRST ~ pentagon XYZVW. Find the value of b. The images are not drawn to scale.

3

Analyze the diagram below and complete the instructions that follow.

If ABC ~ XYZ, find XY. The images are not drawn to scale.

24

ABC is a right triangle. The legs of ABC are 9 ft and 12 ft. The shortest side of XYZ is 13.5 ft, and ABC ~ XYZ How long is the hypotenuse of XYZ?

22.5 ft

if the members are in tension or compression. Identify all zero force members: Likewise, we can find the reaction force at A by taking minutes about point A: RA x 8m - 5kN x 8m - 5kN x 8m = 0 RA = 5kN

To begin with, we really want to find the reaction forces at An and G.

We can do this by taking minutes about point G.

We realize that the amount of minutes at any point is zero when the framework is in equilibrium.

Consequently, we can compose: 5kN x 8m - RA x 10m = 0 RA = 4kN

Likewise, we can find the reaction force at A by taking minutes about point A: RA x 8m - 5kN x 8m - 5kN x 8m = 0 RA = 5kN

Since we have two distinct qualities for RA, we can presume that the framework isn't in equilibrium.

This really intends that there should be some outside force following up on the framework.

The two obscure forces are at first thought to be ductile (for example pulling away from the joint). In the event that this underlying supposition is mistaken, the registered upsides of the pivotal forces will be negative, meaning pressure.

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the complete question is:

Question l Find the forces in members HE; FH, FE; and FC of the truss as shown in Figure Q1. State if the members are in tension or compression. Identify all zero force members: (10 marks) 8 m 5 KN 8 m 8 m 5 KN 8 m 10 m Figure Q1.

the exponent of the product of 8.9 x 10¹² and 4.7 x 10⁻² in scientific notation is 11.

Exponential refers to a mathematical function or relationship in which a variable (such as x) is raised to a constant power (such as 2, 3, or e) to produce a result. The term "exponential" can also be used more broadly to describe any situation in which something grows or changes at an increasingly rapid rate over time, often with a compounding effect.

First, we multiply the two numbers:

(8.9 x 10¹²) x (4.7 x 10⁻²) = 41.83 x 10¹⁰

41.83 x 10¹⁰ = 4.183 x 10¹¹

Therefore, the exponent of the product of 8.9 x 10¹²and 4.7 x 10⁻² in scientific notation is 11.

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The answer of  the given question based on the finding the area of the triangle of ABC the answer is the area of triangle ABC is approximately 62.82 square cm.

A triangle is  three-sided polygon with three angles. It is  two-dimensional geometric shape, and one of  basic shapes in geometry. A triangle can be classified based on  length of its sides and  measure of its angles. The sum of the interior angles of  triangle are 180 degrees. Triangles are used in many fields, like mathematics, engineering, architecture, and art.

To find the area of triangle ABC, we can use the formula for the area of a triangle:

Area = (1/2) * base * height

where the base is one side of the triangle and the height is the perpendicular distance from the base to the opposite vertex.

In this case, we know that AB = 11 cm and AC = 17 cm, and angle A is 45 degrees. To find the height of the triangle, we need to use trigonometry.

First, we can find the length of BC using the Law of Cosines:

BC² = AB² + AC² - 2 * AB * AC * cos(A)

BC² = 11² + 17² - 2 * 11 * 17 * cos(45)

BC² = 156 - 265.42

BC² = 109.42

BC = 10.46 cm (rounded to two decimal places)

Now we can use the sine function to find the height of the triangle:

sin(A) = height / BC

height = BC * sin(A)

height = 10.46 * sin(45)

height = 7.39 cm (rounded to two decimal places)

Finally, we can use the area formula to find the area of the triangle:

Area = (1/2) * base * height

Area = (1/2) * 17 * 7.39

Area = 62.82 square cm (rounded to two decimal places)

Therefore, the area of triangle ABC is approximately 62.82 square cm.

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sum area = -3x - 6y + 12 and product area = -36x - 72y.

what is rectangle?

A rectangle is a geometric shape that is defined as a four-sided flat shape with four right angles (90-degree angles) and opposite sides that are parallel and equal in length.

The area of a rectangle is given by the product of its length and width. Assuming that the length of the rectangle is given by -3x - 6y and its width is 12, we can express the area in terms of a sum and a product as follows:

Sum:

Area = length x width

Area = (-3x - 6y) + 12

Area = -3x - 6y + 12

Product:

Area = length x width

Area = (-3x - 6y) x 12

Area = -36x - 72y

Note that the product expression is not equal to the sum expression. This is because we used different assumptions for the length of the rectangle in each case.

Therefore, sum area = -3x - 6y + 12 and product area = -36x - 72y.

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From the given information provided, the value of angle LMP and angle NMP is 77 and 103 degrees respectively.

Since LMN is a straight angle, it measures 180 degrees.

We are given the measures of LMP and NMP, and we are told that LMP + NMP = LMN. Therefore, we can set up an equation:

LMP + NMP = LMN

(-16x + 13) + (-20x + 23) = 180

Simplifying and solving for x, we get:

-36x + 36 = 180

-36x = 144

x = -4

Now that we have found the value of x, we can substitute it back into the expressions for LMP and NMP to find their measures:

LMP = -16x + 13 = -16(-4) + 13 = 77 degrees

NMP = -20x + 23 = -20(-4) + 23 = 103 degrees

Therefore, the measures of LMP and NMP are 77 degrees and 103 degrees, respectively, and the measure of LMN is 180 degrees.

Question - LMN is a straight angle. LMP = -16x + 13 NMP =  -20x + 23 LMP + NMP = LMN What are the measures?

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Answer:

Step-by-step explanation:

To solve this problem, we need to use the formula for compound interest:

A = P*e^(rt)

where A is the final amount, P is the principal (initial investment), e is the base of the natural logarithm (approximately 2.71828), r is the interest rate (expressed as a decimal), and t is the time (in years).

For Sophie's account, we have:

P = $92,000

r = 6 1/8% = 0.06125 (as a decimal)

t = 14 years

A = 92000*e^(0.06125*14)

A = $219,499.70 (rounded to the nearest cent)

For Damian's account, we have:

P = $92,000

r = 6 5/8% = 0.06625/12 = 0.005521 (as a monthly decimal rate)

t = 14*12 = 168 months

A = 92000*(1+0.005521)^168

A = $288,947.46 (rounded to the nearest cent)

Now we can subtract Sophie's final amount from Damian's final amount to find the difference:

Difference = $288,947.46 - $219,499.70

Difference = $69,447.76

Therefore, Damian would have about $69,448 more in his account than Sophie, to the nearest dollar.

An expression for the length of the rectangle in terms of A is [tex]$\boxed{L=x+5}$[/tex]

We are given that the area of a rectangle is [tex]$A=x^2+x-15$[/tex], and we want to find an expression for the length of the rectangle in terms of A.

Recall that the area of a rectangle is given by the formula: [tex]$A=L\cdot W$[/tex], where L is the length and W is the width. We can use this formula to write L in terms of A and W as [tex]$L=\frac{A}{W}$[/tex].

We know that the rectangle has a length and a width, so we need to find an expression for the width W in terms of A. We can rearrange the given formula for A to solve for W:

[tex]&& \text{(substitute }L=x+5\text{)}[/tex]

[tex]W&=\frac{x^2+x-15}{x+5} && \text{(divide both sides by }x+5\text{)}[/tex]

Now that we have an expression for W in terms of A, we can substitute it into our expression for L to get:

[tex]L&=\frac{A}{W}[/tex]

[tex]&=\frac{x^2+x-15}{\frac{x^2+x-15}{x+5}} && \text{(substitute the expression we found for }W\text{)}\&=x+5[/tex]

Therefore, an expression for the length of the rectangle in terms of A is [tex]$\boxed{L=x+5}$[/tex]

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