In ARST, RS – TR and mZT = 15°. Find mZS.

The unique solution of the linear system is given by:

x1 = 43/5 + x/2 - x2/10 + x3/10

x2 = 11/5 + x/10 - x2/10 + x3/10

x3 = -2 - 2x/5 + x2/10 + x3/10

For finding the inverse matrix using the adjoint method, follow these steps:

Step 1: Write the given system of equations in matrix form:

 [ 2  -6   3  | -4 ]

 [-1    1     1  |  5 ]

 [ 2   6  -5  |  8 ]

Step 2: Define matrix A as the coefficient matrix:

A = [ 2  -6   3 ]

      [-1    1    1 ]

      [ 2   6 -5 ]

Step 3: Define matrix B as the column vector of constants:

B = [ -4 ]

     [  5 ]

     [  8 ]

Step 4: Calculate the matrix of cofactors, C, and the matrix of minors, M:

C = [ C11  C12  C13 ]

     [ C21 C22 C23 ]

     [ C31 C32 C33 ]

M = [ M11  M12  M13 ]

     [ M21  M22 M23 ]

     [ M31  M32 M33 ]

Step 5: Calculate the determinant of A, denoted as |A|, using the formula:

|A| = 2C11 - 6C12 + 3C13

Step 6: Find the adjugated matrix, adj(A), by transposing the matrix of cofactors, C.

Step 7: Calculate the inverse matrix, A^(-1), using the formula:

A^(-1) = adj(A) / |A|

Step 8: Substitute the corresponding values for Cij and |A| to find A^(-1).

Step 9: Solve the system of equations by multiplying both sides of the matrix equation by A^(-1).

Therefore, the inverse matrix is found, and the unique solution of the linear system is obtained.

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Answer: The answer is y=-2x+5

Answer:

= 4

or

= −5

Step-by-step explanation:

Answer:

\(x=-5\) and \(x=4\)

Step-by-step explanation:

\(x^2+7x-20=6x\)

\(x^2+7x-20-6x=6x-6x\)

\(x^2+x-20=0\)

\((x+5)(x-4)=0\)

\(x=-5\) and \(x=4\)

Answer:

they did the horizontal line test.

Step-by-step explanation:

the vertical line test is to see whether or not a graph is a function. you can draw a vertical line at every x-value to see if there are 2 or more points at that x-value. if there are, then it is not a function. however, this student drew a horizontal line instead. this graph is a function, so the student is incorrect. they did the horizontal line test instead of the vertical line test.

The correct option is (E) more than one of the above, which indicates that all the options are correct.

The laws of nature (as determined by scientists) are constructed from many observations, hypotheses, and experiments, are subject to changes and revisions as new evidence is discovered and are often written in the language of mathematics. The laws of nature refer to the basic set of principles, processes, and facts of nature, as well as the natural relationships between things. These are scientific laws that explain how nature behaves and operates. A hypothesis is a scientific supposition, which means that it has been suggested but has not yet been proven. An observation is a way of collecting data and acquiring knowledge through direct experience. It involves the collection of data, information, and evidence about the natural world through direct and indirect observation. The laws of nature are constructed from many observations, hypotheses, and experiments. They are subject to changes and revisions as new evidence is discovered. The laws of nature are often written in the language of mathematics. Therefore, the correct option is (E) more than one of the above, which indicates that all the options are correct.

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Answer:

735 cm²

Step-by-step explanation:

The figure is a trapezium .The area of the triangle section can be calculated using the Heron's formula.

The other part of the figure will be a square of sides 21 cm by 21 cm

Area of the square section

Area = l²

Area = 21* 21 = 441 cm²

Area of the triangle using Heron's formula

Sides of the triangle are ;

a= 28 cm

c= 35 cm

b = 21 cm -----height of the trapezium

The Heron's formula is given as;

\(A=\sqrt{s( s-a)(s-b )(s-c )}\)

where s is half the perimeter of the triangle

Perimeter of the triangle is given as ;

P= 35 + 28 + 21 =84 cm

s= 84/2 = 42 cm

\(A=\sqrt{42*(42-21 )*(42-35 )*(42-28 )} \\\\A=\sqrt{42*(21 )*(7 )*( 14)} \\\\A=\sqrt{86436} \\\\A=294\\\\\)

Total area = 294 + 441 = 735 cm²

The initial amount of salt in the tank is 60 kg, calculated using the formula M = ρV, where M is the mass of the salt, ρ is the density of the salt, and V is the volume of the tank.

Initially, the tank contains 60 kg of salt and 2000 liters of water. The amount of salt in the tank can be calculated using the formula M=ρV, where M is the mass of the salt, ρ is the density of the salt, and V is the volume of the tank. The density of salt is 2270 kg/m3. Assuming the tank has a constant volume, the mass of the salt in the tank is 60 kg.

The amount of salt in the tank changes due to the addition of pure water and mixing of the solution. The amount of salt in the tank at any given time can be calculated using the formula M=ρV, where M is the mass of the salt, ρ is the density of the salt, and V is the volume of the tank. The rate at which the salt is added to the tank is equal to the rate at which the salt-water solution is drained from the tank.

Therefore, the rate of change of the mass of the salt in the tank is equal to 8 liters/minute of pure water entering the tank minus 4 liters/minute of salt-water solution draining from the tank. Thus, the amount of salt in the tank initially is 60 kg.

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It is True to state that Arcs AB, BC, CD, DE, EF, FA in the circumscribed hexagon are all equal. See the explanation below.

In geometry, a hexagon is a six-sided polygon. A regular hexagon is one in which the lengths of all the sides and the measurements of all the angles are identical. The sides of a regular hexagon are therefore equivalent.

Allow point P to be the hexagon's and circle's center.

The dimension of arc AB is the same as the measure of central angle APB, which are both 360/6 = 60 degrees. This also applies to the other arc measurements. The whole 360-degree circle is divided into six equal parts, each measuring 60 degrees.

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Full Question:

Although the question seems incomplete you may have been referring to this:


A circle P is circumscribed about a regular hexagon ABCDEF

Arcs AB, BC, CD, DE, EF, FA are all equal

Select one:

a. False

b. True

Some information that someone might use to solve problems related to a circle design is the Tangent Arc theorem.

The tangent arc theorem states that if an angle is formed by two secants, one secant, one tangent, or two tangents, and also intersects in a space outside of the circle, then the value obtained will be equal to the difference of the values of the intercepted arcs divided by one and a half.

Also, note that angles outside a circle are those whose vertex or arc is pointed outwards and their sides are either secants or tangents. With this information, it will be possible to solve problems related to tangent lines and arc measures.

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Answer:

\(\frac{dy}{dx}=-2x\csc^2(2x-1)\cos(x\cot(2x-1))+\cot(2x-1)\cos(x\cot(2x-1))\)

Step-by-step explanation:

Differentiate the given expression.

\(y=\sin(x \cot(2x-1))\)

I will be using the following rules of differentiation...

\(\boxed{\left\begin{array}{ccc}\text{\underline{The Chain Rule:}}\\\\\frac{d}{dx}[f(g(x))]=f'(g(x)) \cdot g'(x) \end{array}\right}\\\\ \\\boxed{\left\begin{array}{ccc}\text{\underline{The Product Rule:}}\\\\\frac{d}{dx}[f(x)g(x)]=f(x)g'(x)+f'(x)g(x) \end{array}\right} \\ \\ \\ \boxed{\left\begin{array}{ccc}\text{\underline{Sine Rule:}}\\\\\frac{d}{dx}[\sin(x)]=\cos(x) \end{array}\right}\)

\(\boxed{\left\begin{array}{ccc}\text{\underline{Cotanget Rule:}}\\\\\frac{d}{dx}[\cot(x)]=-\csc^2(x) \end{array}\right} \\ \\ \\ \boxed{\left\begin{array}{ccc}\text{\underline{Power Rule:}}\\\\\frac{d}{dx}[x^n]=nx^{n-1} \end{array}\right}\)

\(\hrulefill\)

\(y=\sin(x \cot(2x-1))\\\\\Longrightarrow \frac{dy}{dx} =\frac{d}{dx}[\sin()] \\\\\Longrightarrow \frac{dy}{dx} =\cos(x \cot(2x-1))\cdot\frac{d}{dx}[x \cot(2x-1)] \\\\\Longrightarrow \frac{dy}{dx} =\cos(x \cot(2x-1))\cdot[x \frac{d}{dx}[\cot(2x-1)]+\frac{d}{dx}[x]\cot(2x-1)] \\\\\Longrightarrow \frac{dy}{dx} =\cos(x \cot(2x-1))\cdot[-x \csc^2(2x-1)\cdot\frac{d}{dx}[2x+1] +\cot(2x-1)] \\\\\Longrightarrow \frac{dy}{dx} =\cos(x \cot(2x-1))\cdot[-2x \csc^2(2x-1)+\cot(2x-1)] \\\\\)

\(\therefore \boxed{\frac{dy}{dx}=-2x\csc^2(2x-1)\cos(x\cot(2x-1))+\cot(2x-1)\cos(x\cot(2x-1)) }\)

Angles Formulas at the center of a circle can be expressed as:

Central angle, θ = (Arc length × 360º)/(2πr) degrees

Sum of Interior angles=180°(n-2)

The angles formulas are used to find the measures of the angles. An angle is formed by two intersecting rays, called the arms of the angle, sharing a common endpoint.

The corner point of the angle is known as the vertex of the angle. The angle is defined as the measure of the turn between the two lines.

There are various types of formulas for finding an angle; some of them are the central angle formula, double-angle formula, etc...

We use the central angle formula to determine the angle of a segment made in a circle.

We use the sum of the interior angles formula to determine the missing angle in a polygon.

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Answer:

\(13.86\)

Step-by-step explanation:

you should see 2 triangles with angle 60 bounded by two equal sides of 4

\(=2(\frac{1}{2} (4)(4)sin 60)\\=13.86\)

Answer:

k=-9

Step-by-step explanation:

\(2k-3(2k-3)=45\\\\2k-3(2k)-3(-3)=45\\\\2k-6k+9=45\\\\(2k-6k)+9=45\\\\(2-6)k+9=45\\\\-4k+9=45\\\\-4k+9-9=45-9\\\\-4k+0=36\\\\-4k=36\\\\\frac{-1}{4}(-4k) =\frac{-1}{4}(36) \\\\k=\frac{-36}{4} \\\\k=\frac{4*9}{4} \\\\k=\frac{9}{1} \\\\k=-9\)

3.15 (plus or minus 0.2 payments) payments of $60,000.00 can Pat expect to receive in retirement .

The number of payments of $60,000.00 can Pat expect to receive in retirement is 3.15 (plus or minus 0.2 payments).

Pat plans to save $8,700 per year in his retirement account for each of the next 12 years.

His first contribution is expected in 1 year.

Pat expects to earn 7.70 percent per year in his retirement account.

Pat will make his last $8,700 contribution to his retirement account in the year of his retirement and he plans to retire in 12 years.

The future value (FV) of an annuity with an end-of-period payment is given byFV = C × [(1 + r)n - 1] / r whereC is the end-of-period payment,r is the interest rate per period,n is the number of periods

To obtain the future value of the annuity, Pat can calculate the future value of his 12 annuity payments at 7.70 percent, one year before he retires. FV = 8,700 × [(1 + 0.077)¹² - 1] / 0.077FV

                                                 = 8,700 × 171.956FV

                                                = $1,493,301.20

He then calculates the present value of the expected withdrawals, starting one year after his retirement. He will withdraw $60,000 per year forever.

At the time of his retirement, he has a single future value that he wants to convert to a single present value.

Present value (PV) = C ÷ rwhereC is the end-of-period payment,r is the interest rate per period

               PV = 60,000 ÷ 0.077PV = $779,220.78

Therefore, the number of payments of $60,000.00 can Pat expect to receive in retirement if he receives annual payments of $60,000.00 in retirement and his first retirement payment is received exactly 1 year after he retires would be $1,493,301.20/$779,220.78, which is 1.91581… or 2 payments plus a remainder of $153,160.64.

To determine how many more payments Pat will receive, we need to find the present value of this remainder.

Present value of the remainder = $153,160.64 / (1.077) = $142,509.28

The sum of the present value of the expected withdrawals and the present value of the remainder is

                       = $779,220.78 + $142,509.28

                          = $921,730.06

To get the number of payments, we divide this amount by $60,000.00.

Present value of the expected withdrawals and the present value of the remainder = $921,730.06

Number of payments = $921,730.06 ÷ $60,000.00 = 15.362168…So,

Pat can expect to receive 15 payments, but only 0.362168… of a payment remains.

The answer is 3.15 (plus or minus 0.2 payments).

Therefore, the correct option is C: 3.15 (plus or minus 0.2 payments).

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Reasoning: Complementary angles always add to 90 degrees.

If angle 2 was x, then x+83 = 90 solves to x = 7

The measure of m∠2 is 7° due to the pair of angles being complementary.

The complementary angles are defined as when pairing of angles addition to 90° then they are called complementary angles. There are two types of supplementary angles.

Adjacent angles: Adjacent angles are the type of supplementary angles. Adjacent angles have a common side and vertex, for example, a corner point. Their points do not overlap in any way. In other terms, adjacent angles are pairs of two angles next to each other.

We have been given that the pair of angles as

m∠1 = 83°  and m∠2 = x

Here, the pairing of angles sums up to 90° then they are called complementary angles.

So x + 83 = 90°

⇒ x = 90° - 83°

⇒ x = 7°

Therefore, the value of m∠2 is 7°.

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It will take approximately 39.532 days for $9500 to earn $800 at an annual interest rate of 8.25%.

To find the number of days it will take for $9500 to earn $800 at an annual interest rate of 8.25%, we need to use the formula for simple interest:

Interest = Principal * Rate * Time

In this case, we are given the interest ($800), the principal ($9500), and the annual interest rate (8.25%). We need to solve for time.

Let's denote the time in years as "t". Since we're looking for the number of days, we'll convert the time to a fraction of a year by dividing by 365 (assuming a standard 365-day year).

$800 = $9500 * 0.0825 * (t / 365)

Simplifying the equation:

800 = 9500 * 0.0825 * (t / 365)

Divide both sides by (9500 * 0.0825):

800 / (9500 * 0.0825) = t / 365

Simplify the left side:

800 / (9500 * 0.0825) ≈ 0.1083

Now, solve for t by multiplying both sides by 365:

0.1083 * 365 ≈ t

t ≈ 39.532

Therefore, it will take approximately 39.532 days for $9500 to earn $800 at an annual interest rate of 8.25%.

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Answer:

20.25?

Step-by-step explanation:

The depth of water at the farthest observation well is 3.11 m. below the ground surface. The drawdown at the first observation well is 1.67 m., and its distance from the test well is 18 m.

Using the Theis equation for confined aquifers, we can calculate the transmissivity (T) of the aquifer: T = (Q/4π) * (S/Δh) * e^(r²S/4Tt) , where Q is the pumping rate, S is the storativity of the aquifer, Δh is the drawdown, r is the distance from the test well, T is the transmissivity, and t is the time.

Substituting the given values, we have:

16.5 m³/hour = (4πT) * (0.00075/1.67) * e^(18² * 0.00075 / (4T * t))

Simplifying the equation and solving for T, we find:

T = 2.16 × 10^4 m²/hourThe depth of water at the farthest observation well is the sum of the initial piezometric level (2.11 m) and the drawdown at the second observation well (0.45 m) : Depth = 2.11 m + 0.45 m = 2.56 m.

The depth of water at the farthest observation well is 3.11 m below the ground surface, and the transmissibility of the impermeable layer is 2.16 × 10^4 cm²/sec.

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Answer: Square and rectangle

Step-by-step explanation:

Answer:

6x=100 that's the algebraic expression

Homogeneity of variance assumption assumes that the two populations have equal variances, so the correct answer is option c, "The two populations have equal variances.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

The homogeneity of variance assumption assumes that the two populations have equal variances. Therefore, the correct answer is option c, "The two populations have equal variances."

This assumption is often made in statistical tests that compare the means of two groups, such as the t-test.

When the variances of the two populations are equal, it allows for more precise estimates of the standard error and can improve the accuracy of the test results.

However, if the variances are not equal, it can lead to biased and unreliable results.

In such cases, alternative methods, such as Welch's t-test or the Brown-Forsythe test, can be used to adjust for unequal variances.

Hence, homogeneity of variance assumption assumes that the two populations have equal variances, so the correct answer is option c, "The two populations have equal variances.

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Answer:

hope this will help you

Step-by-step explanation:

\(b { }^{2} - 81 = 0 \\ b {}^{2} = 81 \\ b = \sqrt{81} \\ b = 9\)

Answer: Heyaa! :D

Your Answer Is... 9

Step-by-step explanation:

Since both terms are perfect squares, factor using the difference of squares formula,

a²−b²=(a + b)(a − b) where a = B and

b = 9.

(B + 9)(B − 9)

The PMF of V can be found by taking the difference of the CDF values:

P_V(v) = F_V(v) - F_V(v-1) = { (1-p)(1-q) for v = 0, pq - (1-p)(1-q) for v = 1 }.

To find the CDF of Z = max{X,Y}, we note that Z = 1 if and only if at least one of X and Y is 1. Since X and Y are independent, we have:

P(Z = 1) = P(X = 1 or Y = 1) = P(X = 1) + P(Y = 1) - P(X = 1 and Y = 1)

= p + q - pq

Similarly, P(Z = 0) = P(X = 0 and Y = 0) = (1-p)(1-q). Therefore, the CDF of Z is given by:

F_Z(z) = P(Z ≤ z) = { 0 for z < 0,

(1-p)(1-q) for 0 ≤ z < 1,

p + q - pq for z ≥ 1 }

The PMF of Z can be found by taking the difference of the CDF values:

P_Z(z) = F_Z(z) - F_Z(z-1) = { (1-p)(1-q) for z = 0,

p + q - pq - (1-p)(1-q) for z = 1 }

Similarly, to find the CDF and PMF of V = min{X,Y}, note that V = 0 if and only if both X and Y are 0. We have:

P(V = 0) = P(X = 0 and Y = 0) = (1-p)(1-q)

Similarly, P(V = 1) = P(X = 1 and Y = 0 or X = 0 and Y = 1) = 2pq - pq = pq.

Therefore, the CDF of V is given by:

F_V(v) = P(V ≤ v) = { 0 for v < 0,

(1-p)(1-q) for 0 ≤ v < 1,

1 - pq for v ≥ 1 }

The PMF of V can be found by taking the difference of the CDF values:

P_V(v) = F_V(v) - F_V(v-1) = { (1-p)(1-q) for v = 0,

pq - (1-p)(1-q) for v = 1 }

The distribution of Z is known as a Bernoulli mixture distribution, while the distribution of V is known as a geometric mixture distribution.

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The quantity of more flour that she needs to add would be = 3/4

A fraction is defined as the representation of the part of a whole data in a form of numerator and denominator.

The quantity of flour Ryan needs for baking = 3¼

The quantity of flour she has already added = 2½

The remaining amount that she needs to add;

= 3¼-2½

= 3/4

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The steps for the geometry sequence with the help of two terms of the sequence, make a system of equation and solve them to find common ratio and first term.

Geometric sequence is the sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.

It can be given as,

\(a_n=a_1r^{n-1}\)

Here, a₁ is the first term of the sequence and r is the common ratio.

The fourth term and sixth term given in for the geometric sequence are 3 and 3/16. For the fourth term,

\(a_4=a_1r^{4-1}\\3=a_1r^3\)             ...1

For the sixth term,

\(a_6=a_1r^{6-1}\\\dfrac{3}{16}=a_1r^5\)           ....2

On solving, we get,  a₁=192 and r=1/4. Thus, the geometric sequence can be given as,

\(a_n=a_1r^{n-1}\\a_n=192\times\dfrac{1}{4}^{n-1}\)

Hence, the steps for the geometry sequence with the help of two terms of the sequence, make a system of equation and solve them to find common ratio and first term.

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The median exceeds the mean by more. The histogram is skewed to the right, which shows that lower values are dragging down the mean.

The median of the histogram on the right is higher than the mean. This is evident from the histogram's form, which is tilted to the right. This shows that the lower values tend to drag the mean down. The median is greater than the mean. The right-handed skewness of the histogram indicates that the mean is being pulled down by lesser values and However, because it is the centre number and is only impacted by the higher and lower values equally, the median is unaffected by the lower values. Because of this, the mean in this histogram is less than the median.

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Answer:

\(f(0) = 6\)

Step-by-step explanation:

Given

See attachment for table

Required

Determine \(f(0)\)

From the table;

\(f(x) = 6\) when \(x =0\)

So:

\(f(0) = 6\)

Answer:

10.25

Step-by-step explanation:

4x+1=42

42-1=41

4x=41/4

x=10.25

Answer:

41/4 or 10.25

Step-by-step explanation:

4x=42‒1

4x=41

4x/4=41/4

x=10.25

i think it is easy &it helps you