Determine the values of m and n so that the following system of linear equations have infinite number of solutions:
(2m−1)x+3y−5=0
3x+(n−1)y−2=0

The equation of the line that is parallel to y = 2/5x + 2 and passes through (-5, 6) is y = (2/5)x + 8.

Perpendicular line slopes are the negative reciprocals of one another. In other words, any line that is perpendicular to a line with a slope of m will have a slope of -1/m. If lines are parallel if they have the same slope.

The slope of the given line is 2/5.

We know that, any line perpendicular to it will have a slope that is the negative reciprocal of 2/5, which is -5/2.

Using the point-slope form of a line:

y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.

Substituting the values we know:

y - 6 = (-5/2)(x - (-5))

y - 6 = (-5/2)x - (25/2)

y = (-5/2)x + 17.5

Therefore, the equation of the line perpendicular to y = 2/5x + 2 and passes through (-5, 6) is y = (-5/2)x + 17.5.

The slope of parallel lines are same. Thus, using point slope form:

y - 6 = (2/5)(x - (-5))

y - 6 = (2/5)x + 2

y = (2/5)x + 8

Therefore, the equation of the line that is parallel to y = 2/5x + 2 and passes through (-5, 6) is y = (2/5)x + 8.

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To find theta to the nearest tenth of a degree, we can use a calculator to find the inverse of the given trigonometric function. The inverse of a trigonometric function is denoted by a "-1" superscript.

For the first question, we have cos theta = 0.2442 with theta in QI. To find theta, we can use the inverse cosine function:
theta = cos^-1(0.2442) ≈ 75.7°

For the second question, we have cos theta = -0.7750 with theta in QII. To find theta, we can use the inverse cosine function:
theta = cos^-1(-0.7750) ≈ 139.2°
Since theta is in QII, we can subtract this angle from 180° to find the angle in QII:
theta = 180° - 139.2° ≈ 40.8°

For the third question, we have tan theta = 0.5860 with theta in QIII. To find theta, we can use the inverse tangent function:
theta = tan^-1(0.5860) ≈ 30.4°
Since theta is in QIII, we can add 180° to this angle to find the angle in QIII:
theta = 180° + 30.4° ≈ 210.4°

For the fourth question, we have cos theta = 0.2442 with theta in QI. This is the same as the first question, so the answer is the same:
theta = cos^-1(0.2442) ≈ 75.7°

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Answer:

$7.35

Step-by-step explanation:

no step by step lol heres ur answer

The missing vertex is located at (-14,20).

To find the missing vertex, let's assume that the third vertex is located at (x,20) and the coordinates of the other two vertices are (6,0) and (5,10). Then the coordinates of the two sides of the triangle are:

Side AB: (6,0) to (5,10)

Side AC: (6,0) to (x,20)

Using the formula for the area of a triangle, which is:

Area = 1/2 * base * height

Where the base is one of the sides of the triangle and the height is the perpendicular distance from the third vertex to the base, we can set up an equation to solve for x:

60 = 1/2 * |(6-5)*20 - (x-6)*10|

60 = 1/2 * |200 - 10x + 60|

120 = |260 - 10x|

120 = 10x - 260 or 120 = -(10x - 260)

x = -14 or x = -2

Since x has to be a negative value, the missing vertex is located at (-14,20). Therefore, the three vertices of the triangle are:

A = (6,0)

B = (5,10)

C = (-14,20)

We can verify that the area of the triangle with these vertices is indeed 60 square units using the same formula:

Area = 1/2 * |(6-5)(20-10) - (-14-6)(20-0)|

Area = 1/2 * |10 - (-400)|

Area = 1/2 * 410

Area = 205 square units

Therefore, the missing vertex is located at (-14,20).

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1. (a) The probability that a randomly selected wafer is produced by machine A and not defective is 0.665 or 66.5%.
(b) The probability that a wafer is defective given that it is produced by machine B is 0.06 or 6%.
(c) The probability that a wafer is defective is 0.053 or 5.3%.
(d) The probability that a wafer is 0.947 or 94.7%.

2. (a) The probability that a car requires either a tune-up or a brake job is 0.608 or 60.8%.
(b) The probability that a car requires a tune-up but not a brake job is 0.588 or 58.8%.
(c) The probability that a car requires neither types of repair is 0.392 or 39.2%.
(d) The events "car requires a tune-up" and "car requires a brake job" are independent because the probability of one event occurring does not affect the probability of the other event occurring. They are not mutually exclusive because a car can require both a tune-up and a brake job at the same time.

We can find the probability using this calculation:

The probability that a randomly selected wafer is produced by machine A and not defective is 0.7 x 0.95 = 0.665 or 66.5%.

The probability that a wafer is defective is (0.7 x 0.05) + (0.3 x 0.06) = 0.035 + 0.018 = 0.053 or 5.3%.

The probability that a wafer is not defective is 1 - 0.053 = 0.947 or 94.7%.

The probability that a car requires either a tune-up or a brake job is 0.6 + 0.02 - (0.6 x 0.02) = 0.608 or 60.8%.
(b) The probability that a car requires a tune-up but not a brake job is 0.6 x (1 - 0.02) = 0.588 or 58.8%.
(c) The probability that a car requires neither types of repair is 1 - 0.608 = 0.392 or 39.2%.

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Answer:

3

Step-by-step explanation:

cuz ik

The value of the variable 'x' in the isosceles right-angle triangle will be 2√2 units.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as,

H² = P² + B²

The length of the hypotenuse is 4. And the triangle is an isosceles right triangle.

In the isosceles right triangle, the perpendicular and base of the triangle will be the same. Then the value of the variable 'x' is given as,

4² = x² + x²

2x² = 16

x² = 8

x = 2√2

The value of the variable 'x' in the isosceles right-angle triangle will be 2√2 units.

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The rate of interest per annum when he invested £6,500 and got £6,838 will be 5.2%.

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

The amount after one year is £6838 if he invested £6,500. Then the rate of interest is given as,

£6,838 = £6,500 × (1 + r)¹

1 + r = 1.052

r = 0.052 or 5.2%

The rate of interest per annum when he invested £6,500 and got £6,838 will be 5.2%.

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The solution to this system of equations is: \[ \begin{array}{l} x=40 \\ y=-111 \\ z=-3.5 \end{array} \]

To solve this system of equations using Cramer's Rule, we will begin by finding the determinant of the coefficient matrix, which is an array of the coefficients of the variables in the equations. We will then find the determinants of the matrices that result from replacing each column of the coefficient matrix with the constant terms of the equations. Finally, we will use these determinants to find the values of x, y, and z.

The coefficient matrix is: \[ \begin{array}{ccc} -3 & -4 & -4 \\ 1 & -3 & -3 \\ -1 & 1 & -2 \end{array} \]

The determinant of the coefficient matrix is: \[ \begin{array}{ccc} -3 & -4 & -4 \\ 1 & -3 & -3 \\ -1 & 1 & -2 \end{array} = (-3)(-3)(-2) - (-4)(-3)(-1) - (-4)(1)(1) - (-4)(-3)(-1) - (-4)(-3)(1) - (-4)(1)(-2) = -6 + 4 + 4 + 4 - 12 + 8 = -2 \]

The matrix that results from replacing the first column of the coefficient matrix with the constant terms is: \[ \begin{array}{ccc} -8 & -4 & -4 \\ -19 & -3 & -3 \\ 3 & 1 & -2 \end{array} \]

The determinant of this matrix is: \[ \begin{array}{ccc} -8 & -4 & -4 \\ -19 & -3 & -3 \\ 3 & 1 & -2 \end{array} = (-8)(-3)(-2) - (-4)(-3)(3) - (-4)(-19)(1) - (-4)(-3)(3) - (-4)(-19)(1) - (-4)(-3)(-2) = 48 - 36 - 76 + 36 - 76 + 24 = -80 \]

The matrix that results from replacing the second column of the coefficient matrix with the constant terms is: \[ \begin{array}{ccc} -3 & -8 & -4 \\ 1 & -19 & -3 \\ -1 & 3 & -2 \end{array} \]

The determinant of this matrix is: \[ \begin{array}{ccc} -3 & -8 & -4 \\ 1 & -19 & -3 \\ -1 & 3 & -2 \end{array} = (-3)(-19)(-2) - (-8)(-3)(-1) - (-4)(1)(3) - (-4)(-19)(-1) - (-4)(-3)(1) - (-4)(1)(-2) = 114 + 24 + 12 + 76 - 12 + 8 = 222 \]

The matrix that results from replacing the third column of the coefficient matrix with the constant terms is: \[ \begin{array}{ccc} -3 & -4 & -8 \\ 1 & -3 & -19 \\ -1 & 1 & 3 \end{array} \]

The determinant of this matrix is: \[ \begin{array}{ccc} -3 & -4 & -8 \\ 1 & -3 & -19 \\ -1 & 1 & 3 \end{array} = (-3)(-3)(3) - (-4)(-19)(-1) - (-8)(1)(1) - (-8)(-3)(-1) - (-8)(-19)(1) - (-8)(1)(3) = 27 + 76 + 8 + 24 - 152 + 24 = 7 \]

Using these determinants, we can find the values of x, y, and z: \[ x = \frac{-80}{-2} = 40 \] \[ y = \frac{222}{-2} = -111 \] \[ z = \frac{7}{-2} = -3.5 \]

Therefore, the solution to this system of equations is: \[ \begin{array}{l} x=40 \\ y=-111 \\ z=-3.5 \end{array} \]

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The probability that the next kite Barbara sells will be a diamond is:

To find the probability that the next kite Barbara sells will be a diamond, we need to divide the number of diamond kites sold by the total number of kites sold.

The formula for probability is

= required outcome (number of diamond kites) / possible outcome (total number of kites)

required outcome

The number of diamond kites sold is:

11

possible outcome

The total number of kites sold so far is:

11 + 9 + 6 + 4 = 30

Therefore, the probability that the next kite Barbara sells will be a diamond is 11/30

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The box plot for given minimum, maximum, median, Q1 and Q3  is plotted below.

A box and whisker plot—also called a box plot—displays the five-number summary of a set of data. The five-number summary is the minimum, first quartile, median, third quartile, and maximum. In a box plot, we draw a box from the first quartile to the third quartile.

The given data set is,

14, 13, 13.5, 16, 14, 15.5, 14.5.

Hence, We get;

Order of data is,

⇒ 13, 13.5, 14, 14, 14.5, 15.5, 16.

Here, minimum is 13

Maximum is 16

Median is 14

Lower quartile range(Q1) is 13.5

Upper quartile range(Q3) is 15.5

Therefore, The box plot for given minimum, maximum, median, Q1 and Q3  is plotted below.

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The final factored form of the polynomial is b(a-b) and the category of the remaining polynomial is a binomial.

The first step in factoring out the GCF from the polynomial ab+ay-b^(2)-by is to identify the greatest common factor of all the terms. In this case, the GCF is b. Once we have identified the GCF, we can factor it out from each term by dividing each term by the GCF. This gives us:

ab+ay-b^(2)-by = b(a+y)-b(b+y) = b(a+y-b-y)

Next, we can simplify the remaining polynomial by combining like terms:

b(a+y-b-y) = b(a-b)

Finally, we can identify the category of the remaining polynomial. Since it has two terms and each term has a degree of 1, the remaining polynomial is a binomial.

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The height of the fish tank should be approximately 1.981 feet which is also equivalent to 23.772 inches.

As desired capacity of the fish tank is 100 gallons, and 7.48 gallons of water are equivalent to 1 cubic foot, the desired volume of the fish tank is (100 / 7.48) cubic feet, or approximately 13.369 cubic feet.

The desired volume is stated as a number of cubic feet so the known dimensions of the fish tank must be converted from inches to feet.

length = 54 inches = 4.5 feet

width = 18 inches = 1.5 feet

The formula for the volume V of a rectangular prism with length l, width w, and height h is V = lwh. We will substitute the known dimensions into the formula and solve for h.

V = ℓwh

13.369 ≈ 4.5 × 1.5 × h

13.369 ≈ 6.75h

h ≈ 13.369 / 6.75

h ≈ 1.981

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The ratio of red to blue squares is given by the division of the number of red squares by the number of blue squares.

The ratio between two amounts, a and b, is obtained applying a proportion, as the ratio is the division of the amount a by the amount b.

The amounts for this problem are given as follows:

Hence the ratio is given by the division of the number of red squares by the number of blue squares.

For example, for 10 red and 20 blue squares, the ratio is given as follows:

r = 10:20 = 1:2.

The problem is incomplete, hence the general procedure to obtain the ratio is presented.

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Answer:

We can use the standard normal distribution to solve this problem, by standardizing the salary value of $53,000 using the given mean and standard deviation:

z = (X - μ) / σ

where X is the salary value of $53,000, μ is the mean of $40,756, and σ is the standard deviation of $7500.

z = (53,000 - 40,756) / 7500 = 1.63547

Using a standard normal distribution table or calculator, we can find the proportion of employees who earn at most $53,000 by finding the area to the left of the standardized value of 1.63547:

P(Z ≤ 1.63547) = 0.9514

Therefore, approximately 95.14% of employees in entry-level positions at the company earn at most $53,000.

Harbin was colder than Beijing on that particular day in December because the temperature difference between the two cities was -6ºC.

To figure out which city was colder, we need to compare the difference between the temperatures of the two cities. The temperature difference is the numerical value we get when we subtract one temperature from the other.

In this case, the temperature in Harbin was -8ºC and the temperature in Beijing was -2ºC. To find out which city was colder, we need to calculate the temperature difference between the two cities.

To do this, we subtract the temperature in Beijing from the temperature in Harbin:

-8ºC - -2ºC = -6ºC

So the temperature difference between the two cities is -6ºC. This means that Harbin was colder than Beijing on that day.

We can see that the temperature difference is negative, which tells us that the temperature in Harbin was lower than the temperature in Beijing.

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The answer of the given question based on the graph shows  number of birdhouses Penn and his father can build, if they have enough time to build not more than 10 birdhouses, the correct option is A).

What is Graph?

In mathematics, a graph is a collection of points (called vertices or nodes) and the lines or arcs (called edges) that connect them. Graphs are used to model and analyze a variety of real-world situations, such as social networks, transportation systems, and electrical circuits.

Based on the given graph, the horizontal axis represents the number of birdhouses Penn's father can build and the vertical axis represents the number of birdhouses Penn can build. The graph is bounded by the line x + y = 10, which means that the sum of  number of the birdhouses Penn and his father can build cannot be exceed more than10.

Therefore, the domain of this graph is the set of possible values for the number of birdhouses Penn's father can build, subject to the constraint that the sum of the number of the birdhouses Penn and his father can build cannot be exceed more than 10. This domain is the set of non-negative integers less than or equal to 10, inclusive. In interval notation, this can be written as [0, 10].

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Complete question:-The graph shows the number of birdhouses Penn and his father can build if they have enough time to build no more than 10 birdhouses. What is the domain of this graph?

Answer:

4 to power of 3 in expanded form is 4 x 4 x 4.

HOPE THIS HELPS :)

Y(y) = dF_Y(y)/dy = -y^2

a. Let X be the number of picked points that is smaller than 1/4. Determine the distribution of X.Random variables and distributions Let A be the set of all possible 3-tuples (a1, a2, a3) picked from (0, 1).The number of the picked points that are smaller than 1/4 is random with X: A → {0, 1, 2, 3}X((a1, a2, a3)) = |{i ∈ {1, 2, 3} : ai < 1/4}|This is, X is the number of i's such that ai < 1/4. We would like to compute the distribution of X.Let us count the number of 3-tuples (a1, a2, a3) for which X = 0, 1, 2, or 3. These counts are as follows:X = 0: There is only one tuple for which all ai ≥ 1/4.X = 1: Each of the ai can be either ≥ 1/4 or < 1/4, and there are three ways to choose which one is less than 1/4. Therefore, there are 2^3 · 3 = 24 3-tuples (a1, a2, a3) such that exactly one ai < 1/4.X = 2: Either all ai < 1/4, or two ai's < 1/4 and the other one ≥ 1/4. If all ai < 1/4, then there is one tuple for this. If two ai's < 1/4 and the other one ≥ 1/4, then there are 3 ways to choose which ai is ≥ 1/4, and for each such choice there are 3 · 2 = 6 ways to pick the other two ai's. Thus, there are 1 + 3 · 6 = 19 tuples for which X = 2.X = 3: All ai's < 1/4. There is only one such tuple.Therefore, the probability mass function of X is as follows:P(X = 0) = 1/8P(X = 1) = 3/8P(X = 2) = 19/32P(X = 3) = 1/32b. Let Y be the middle one of the three points. Determine the cdf of Y. (It is a function with domain R!)The range of Y is the interval (0, 1). We can assume that a1 ≤ a2 ≤ a3, since any 3-tuple can be sorted in this way. If Y < y, then the largest of the three points must be less than y. Therefore, we need to find the probability that the largest point is less than y, given that the three points are picked independently at random from (0, 1) and are ordered as a1 ≤ a2 ≤ a3.Let A be the set of all possible 3-tuples (a1, a2, a3) picked from (0, 1), where a1 ≤ a2 ≤ a3. Let B(y) be the set of all 3-tuples (a1, a2, a3) ∈ A such that a3 < y. Then P(Y < y) = P(B(y)).To compute P(B(y)), let us count the number of 3-tuples (a1, a2, a3) ∈ A such that a3 < y. Fix a1 and a2. Then a3 < y if and only if a3 ∈ (0, y), so there are exactly y(1 - y) choices for a3. Therefore,|B(y)| = ∫∫A y(1 - y) da1 da2 = ∫0^1 ∫a1^1 y(1 - y) da2 da1 = ∫0^1 y(1 - y) (1 - a1) da1 = 1/6 - y^3/3Thus,P(Y < y) = P(B(y)) = |B(y)|/|A| = [1/6 - y^3/3]/1 = 1/6 - y^3/3This is the cdf of Y for y ∈ (0, 1). We can extend this function to all of R by setting F_Y(y) = 0 if y ≤ 0 and F_Y(y) = 1 if y ≥ 1.c. Determine the pdf of Y.The cdf of Y isF_Y(y) = 1/6 - y^3/3for y ∈ (0, 1). Therefore, the pdf of Y isf_Y(y) = dF_Y(y)/dy = -y^2for y ∈ (0, 1). Thus, the density is constant, and Y has a uniform distribution on (0, 1).

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The situation in which the quantities combine to make 0 is D.

What is a combination of quantities?

In mathematics, a combination of quantities usually means taking a group of items or values and selecting some of them without regard to their order. A combination is different from a permutation in that order does not matter in a combination, whereas it does matter in a permutation.

For example, if you have three objects labeled A, B, and C, then the possible combinations of two objects are AB, AC, and BC. These combinations are different from the permutations of two objects, which include AB and BA, AC and CA, and BC and CB.

Combinations are often used in probability, statistics, and combinatorics to calculate the number of ways that objects or values can be selected from a set, without regard to their order.

The situation in which the quantities combine to make 0 is:

D. In the morning, the temperature rises 30 degrees. In the evening, it falls by 30 degrees.

In situation D, the temperature rises by 30 degrees in the morning and then falls by 30 degrees in the evening, which means that the overall change in temperature is 0. In situations A, B, and C, the quantities do not combine to make 0. In situation A, the hot air balloon rises a total of 80 feet, which is not 0. In situation B, Kathy has $10 left after giving half to her friend, which is not 0. In situation C, the player earns a total of 8 points, which is not 0.

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The solution to the system of equations is [tex]x = -3/4 $ and $ y = -3^{1/2}.[/tex] The solution has been obtained by using substitution method.

What is substitution method?

The substitution approach is one approach of solving equation problems. To use the substitution method, obtain an expression for one variable in terms of the second variable using one equation. Replace that variable with that expression in the second equation after that.

We are given system of equations as:

y = -2x - 5

y = 2x - 2

Now, by using the substitution method, we get

⇒-2x - 5 = 2x - 2

⇒-4x = 3

⇒x = -3 / 4

On substituting the value of x in y = 2x - 2, we get

⇒y = 2(-3/4) - 2

⇒y = (-3/2) - 2

⇒y = -7/2

Hence, the solution to the system of equations is[tex]x = -3/4 $ and $ y = -3^{1/2}.[/tex]

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The solution to the inequality 5(3y+1)<15 in interval notation is (-∞, 2/3).

To solve the inequality 5(3y+1)<15, we need to isolate the variable y on one side of the inequality. Here are the steps to do so:
1. Start with the given inequality: 5(3y+1)<15
2. Distribute the 5 on the left side: 15y+5<15
3. Subtract 5 from both sides: 15y<10
4. Divide both sides by 15: y<10/15
5. Simplify the fraction: y<2/3

Now, we can write the solution in interval notation. Interval notation uses parentheses or brackets to indicate the range of values that satisfy the inequality. In this case, the solution is all values of y less than 2/3, so we use the notation (-∞, 2/3).

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The complete sentence would be: "For 4x^(2)+6x+2=0, a=4, b=6, and c=2."

To complete the sentence, we need to identify the values of a, b, and c in the given equation. The equation is in the form of ax^(2)+bx+c=0, where a, b, and c are the coefficients of the respective terms.

Therefore, to fill in the blanks in the sentence, we can simply match the coefficients in the given equation with the corresponding letters:

a = 4, because the coefficient of the x^(2) term is 4
b = 6, because the coefficient of the x term is 6
c = 2, because the constant term is 2

So the complete sentence would be: "For 4x^(2)+6x+2=0, a=4, b=6, and c=2."

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Another polynomial with the same factored form of (z-3)(z+5) but different values for z is 2z^(2)+4z-30.

To find another polynomial with the same factored form, we can simply multiply the given factored form by a constant. This will change the values of z, but the factored form will remain the same.

For example, let's multiply the factored form by 2:

2(z-3)(z+5) = 2z^(2)+4z-30

In general form, this polynomial is 2z^(2)+4z-30.

We can see that the factored form is still (z-3)(z+5), but the values of z have changed. In the original polynomial, z^(2)+2z-15, the values of z were 3 and -5. In the new polynomial, 2z^(2)+4z-30, the values of z are 3/2 and -5/2.

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Answer:

We can start by using the slope formula to find the equation of the line:

slope = (change in y) / (change in x)

We know the slope is 4, so we can plug in the coordinates (-10, 15) and (x/2, 7) to solve for x:

4 = (15 - 7) / (-10 - x/2)

Multiplying both sides by (-10 - x/2) gives:

-40 - 2x = 8

Solving for x, we get:

x = -24

Therefore, the missing x-value for the coordinate point is -24.

Step-by-step explanation:

In quadrilateral EFGH, sides FG and EH are congruent because they each have a length of 7.07

The area of quadrilateral EFGH is closest to 30 square units.

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

The quadrilateral EFGH

This quadrilateral is a rectangle

From the figure, we can see that the following side lengths

EF = 3√2 = 4.24

EH = 5√2 = 7.07

So, we have

Area = 3√2 * 5√2

Evaluate

Area = 30

Hence, the area is 30 square units

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The fourth term a₄ of the sequence is -343

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

a₁= -1

aₙ = 7aₙ₋₁

The above definitions imply that we simply multiply 7 to the previous term to get the current term

Using the above as a guide,

so, we have the following representation

a₂ = 7 * -1

a₂ = -7

Also, we have

a₃ = -7 * 7

a₃ = -49

Lastly, we have

a₄ = -49 * 7

Evaluate the equation

a₄ = -343

Hence, the value of a₄ is -343

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The trigonometric value of sin 14° to 4 decimal places is sin 14° = 0.241.

The value of sin 14° to 4 decimal places is 0.2419.

An angle is the measure that determines two straight lines, which when joined together create a point of origin, which is called the vertex of the angle.

The unit of measurement associated with angles is degrees.

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The number of means is 13. Option B

We can use the formula for the nth term of an arithmetic sequence to solve the problem. Let d be the common difference and n be the number of terms between -65 and 125.

Then we have:

a + (n-1)d = 125 (1)

a + nd = -113 (2)

Subtracting equation (2) from equation (1), we get:

(n-1)d + 238 = 0

Solving for d, we get:

d = -238/(n-1)

Using the formula for the twelfth term, we have:

a + 11d = -113

Substituting the expression for d, we get:

a - 11(238/(n-1)) = -113

Multiplying both sides by n-1, we get:

a(n-1) - 11(238) = -113(n-1)

Substituting a = -65 and simplifying, we get:

n = 13

Therefore, the number of means is 13

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