From the below table determine the rate of change (which is the same as slope).

x 3 7 11 15 19
y 20 15 10 5 0

Answers:

-5/4

5/4

4/5

-4/5​

The result of the quotient which is to be evaluated as given in the task content is; 4/8.

It follows from the task content that the quotient of the given expression; -12 ÷ (-45) is to be determined.

Since the given expression is; -12 ÷ -45

It follows that we have;

-12 / -45

= 12/45

However, since the greatest common factor of the numerator (12) and the denominator (45) is 3;

The simplest form expression of the fraction is;

4 / 15.

Therefore, the required answer in simplest form is; 4 / 15.

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Answer:

The measure of the central angle whose radii define the arc is \(\mathbf{\frac{4\pi }{5} }\)

Step-by-step explanation:

Radius of circle = 10 cm

Length of arc = \(8\pi\)

We need to find Theta \(\theta\)

The formula used will be: \(S=r \theta\)

S= length of arc, r = radius and \(\theta\) = angle

Putting values and finding \theta

\(S=r \theta\\8\pi =10 \theta\\\theta=\frac{8\pi }{10} \\\theta=\frac{4\pi }{5}\)

So, the measure of the central angle whose radii define the arc is \(\mathbf{\frac{4\pi }{5} }\)

Answer:

A=50 B=40 C=90

Step-by-step explanation:

B is a right angle so its automatically 90 degrees since A=50 and a triangle has to be 180 degrees 90+50= 140, 180-140=40.

Answer: 263.088

Step-by-step explanation:

Multiply the equation

¨What does Multiply mean?¨

To compute a product; to perform a multiplication.

(8.1) x (8.12) x 4

Answer    c

Step-by-step explanation: I did the test i hope this help unlike that girl who just wrote random numbers anyways have a good day

When a point falls outside of control limits in statistical process control, the probability is quite high that the process is experiencing special cause variation.

In statistical process control (SPC), control limits are used to define the range within which a process is expected to operate under normal or common cause variation. Common cause variation refers to the inherent variability of a process that is predictable and expected.

On the other hand, special cause variation, also known as assignable cause variation, refers to factors or events that are not part of the normal process variation. These are typically sporadic, non-random events that have a significant impact on the process, leading to points falling outside of control limits.

When a point falls outside of control limits, it indicates that the process is exhibiting a level of variation that cannot be attributed to common causes alone. Instead, it suggests the presence of specific, identifiable causes that are influencing the process. These causes may include equipment malfunctions, operator errors, material defects, or other significant factors that introduce variability into the process.

Therefore, when a point falls outside of control limits in statistical process control, it is highly likely that the process is experiencing special cause variation, which requires investigation and corrective action to identify and address the underlying factors responsible for the out-of-control situation.

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We can use the formula for inverse variation, which states that the product of the time and the speed is constant:

time × speed = constant

Let's use t to represent the time needed to travel the distance at 54 miles per hour. We know that the time is 10 hours when the speed is 24 miles per hour. So we can set up the equation:

10 × 24 = t × 54

Simplifying, we get:

240 = 54t

Dividing both sides by 54, we get:

t = 240/54

Simplifying this fraction, we get:

t = 40/9

So it will take approximately 4.44 hours, or 4 hours and 26 minutes, to travel the same distance at 54 miles per hour.

1. answer:The mean of X is given set  by:μ = E(X) = ∫ [x (x - 5)/18] dx = 1/18 ∫ [x^2 - 5x] dx = 1/18 [(x^3/3) - (5x^2/2)]_5^11 = 8.

Therefore, the mean of X is 8.The standard deviation of X is given by:

\(σ = sqrt(Var(X)) = sqrt(E(X^2) - [E(X)]^2) = sqrt(∫ [x^2 (x - 5)/18] dx - 8^2) = sqrt(1/18 ∫ [x^3 - 5x^2] dx - 64) = sqrt[1/18 [(x^4/4) - (5x^3/3)]_5^11 - 64] = 1.247\)

Therefore, the standard deviation of X is 1.247.2. The central limit theorem states that if n is sufficiently large, then the sampling distribution of the mean of a random sample of size n will be approximately normal with a mean of μ and a standard deviation of σ/ sqrt(n).Since X is the mean of a random sample of 40 observations having the same distribution, it follows that

\(X ~ N(8, 1.247/ sqrt(40)) or X ~ N(8, 0.197).P(8.2 < X < 9.3) = P[(8.2 - 8)/0.197 < (X - 8)/0.197 < (9.3 - 8)/0.197] = P[1.52 < Z < 15.23],\)

where Z ~ N(0, 1).Using a standard normal table or calculator, we find:

\(P[1.52 < Z < 15.23] = P(Z < 15.23) - P(Z < 1.52) = 1 - 0.9357 = 0.0643\)

Therefore, the approximate value of

P(8.2 < X < 9.3) is 0.0643.3.

:MeanThe mean of X is given by:

μ = E(X) = ∫ [x (x - 5)/18] dx = 1/18 ∫ [x^2 - 5x] dx = 1/18 [(x^3/3) -

(5x^2/2)]_5^11 = (11^3/3 - 5*11^2/2 - 5^3/3 + 5*5^2/2)/18 = (1331/3 - 275/2 -

125/3 + 125/2)/18 = 8

Therefore, the mean of X is 8.Standard deviation

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An example of a +f(pxq) with integer coefficients that factors (poly mod nq), but has no roots is (x^2 + 1)(x^2 + 2). This polynomial satisfies the given conditions and demonstrates that it is possible to have a polynomial with integer coefficients that factors modulo n, but has no roots.

Let's consider the polynomial f(pxq) = (x^2 + 1)(x^2 + 2).
1. This polynomial has integer coefficients as both factors have integer coefficients.
2. Now, let's consider taking the modulo n, where n is any positive integer.
3. Since the modulo operation only affects the coefficients, we will still have a polynomial with integer coefficients after taking the modulo.
4. However, there are no integers x for which f(pxq) = 0 (poly mod n), as the factors x^2 + 1 and x^2 + 2 do not have any integer roots.

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Answer:

Where is the graph?

Step-by-step explanation:

Where is the graph?

m∠E = tan-1(3/4.6)

Explanation

In the circle, the measure of angle ∠RQS is 152 degrees and ∠SQT  is 28 degrees

In the circle QR is a diameter

QT is a tangent at Q

Measure of arc QRS is 304 degrees

We have to find the measure of angle ∠RQS

∠RQS = 1/2  QRS

∠RQS = 1/2(304)

=152 degrees

The measure of angle ∠SQT

∠SQT + 152 =180

∠SQT  = 180 -152

∠SQT  =  28 degrees

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Answer:

From the identity C + I + G + X = Y, where X represents exports, we see that the size of the multiplier depends on the marginal propensities to consume (MPC), which equals the proportion of income spent on consumption out of disposable income (Y - T). MPC = C/ (Y - T). Since we don't know the values of Y and T yet, we can't say what event might affect the multiplier without knowing their effects on T and Y. Answer e is incorrect as it assumes that the change in T only affects the government budget balance, not net tax revenue. Moreover, it also incorrectly assumes that reducing taxes increases disposable income instead of just increasing private sector savings.

The percentage increase in average commute times between these years = 2.25%

In 2010, the average commute time for wake county workers = 23.9 mins

In 2016, the average commute time for wake county workers = 25 mins.

The increase is = 25- 23.9 = 1.1

The average commute time between the two years,

23.9+25 = 48.9 mins

Therefore, the percentage,

= 1.1/48.9×100

= 110/48.9

= 2.249%

= 2.25% to the nearest two decimal places.

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There will be 8 rows of booths at the craft fair.

To determine the number of rows needed for the booths at the craft fair, we divide the total number of booths by the maximum number of booths per row.

Total number of booths = 50

Maximum number of booths per row = 6

Number of rows = Total number of booths / Maximum number of booths per row

Number of rows = 50 / 6

Since we want to put as many booths in each row as possible, any remaining booths after filling complete rows will not be accounted for. Therefore, we use integer division (where the remainder is ignored).

Number of rows = 8 (integer division of 50 by 6)

Therefore, there will be 8 rows of booths at the craft fair.

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Answer:

x=5, y=2 | Equations: 4x+y=22 (or see below) and 12x-5y=50

Step-by-step explanation:

Here's my attempt:

First Equation:

Because triangles ΔSTU and ΔXYZ are congruent, then we can say that:
m∠S = m∠X
m∠T = m∠Y
m∠U = m∠Z

We know that m∠X = 130°, and that m∠X = m∠S, so m∠S = 130°

We also know that the sum of angles in a triangle = 180°

We also know the rest of the angles in ΔSTU: 28° and (4x+y)°

So, we can say that ∠S + ∠T + ∠U = 130+28+4x+y = 180 (we can remove the degree sign)

Now, you can either enter this as it is or simplify it: ❗

130+28+4x+y=180

4x+y+158=180

4x+y=22

Second Equation:

We can do the same thing as for the first equation and get the angles of ΔXYZ:

∠X = 130, ∠Y = 8x-6y, ∠Z = 4x+y

Then, add them and set it to 180:

130+8x-6y+4x+y=180

Simplify:

12x-5y+130=180

12x-5y=50

To solve for x and y:

Now, we have to solve the systems.

Let's start with the first one:

4x+y=22

Isolate y:

y=22-4x (Equation 1)

Then, we plug it into the second equation:

12x-5y=50

12x-5(22-4x)=50

12x-110+20x=50

32x=160

x=5

So we got x, but to find y, we need to plug in x into Equation 1 (where we isolated y

y=22-4x

y=22-4(5)

y=22-20

y=2

We have both our x and y values

That was my attempt, hope it helped!

Answer:

hello your question is incomplete attached below is the missing table

answer = $48700

Step-by-step explanation:

Calculate the total account receivable in each age category

1) not yet due age category

 = $4000 + $4000 + $7000

 = $15000

2) up to 1 year age category

  = $20500 + $7000

  = $27500

3) more than 1 year age category

  = $6200

therefore the total amount of  account receivables =  15000 + 27500 + 6200  = $48700

Answer:

12π meters

Step-by-step explanation:

Area of circle = Pi*r^2 -> 36*Pi = Pi*r^2

So, radius of circle (r) = 6 m

Circumference of circle = 2*Pi*r = 2*Pi*6 = 12Pi m

The two numbers that satisfy the given conditions are 16 and 10.

to find the two numbers with the given properties, we need to consider their highest common factor and lowest common multiple.

given that the highest common factor (hcf) of the two numbers is 8, it means that 8 is the largest number that can divide both numbers evenly.

to determine the lowest common multiple (lcm) of the two numbers, we can use the formula:

lcm = (number 1 * number 2) / hcf

since the hcf is 8, we have:

lcm = (number 1 * number 2) / 8

to satisfy the condition that both numbers are greater than 8, we can start by choosing 16 as one of the numbers. now we can substitute this value into the lcm formula:

lcm = (16 * number 2) / 8

simplifying the equation:

lcm = 2 * number 2

to find the value of number 2, we need it to be a multiple of 2 that is greater than 8. let's choose 10 as number 2:

lcm = 2 * 10 = 20

now we have found the lcm, which is 20. to find the second number, we divide the lcm by the chosen number 2:

number 1 = lcm / number 2 = 20 / 10 = 2

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tis a little of plain differentiation.

we know the radius of the cone is decreasing at 10 mtr/mins, or namely dr/dt = -10, decreasing, meaning is negative.

we know the volume is decreasing at a rate of 1346 mtr/mins or namely dV/dt = -1346, also negative.

so, when h = 9 and V = 307, what is dh/dt in essence.

we'll be needing the "r" value at that instant, so let's get it

\(V=\cfrac{1}{3}\pi r^2 h\implies 307=\cfrac{\pi }{3}r^2(9)\implies \sqrt{\cfrac{307}{3\pi }}=r\)

now let's get the derivative of the volume of the cone

\(V=\cfrac{1}{3}\pi r^2 h\implies \cfrac{dV}{dt}=\cfrac{\pi }{3}\stackrel{product~rule}{ \left[ \underset{chain~rule}{2r\cdot \cfrac{dr}{dt}}\cdot h+r^2\cdot \cfrac{dh}{dt} \right]} \\\\\\ -1346=\cfrac{\pi }{3}\left[2\sqrt{\cfrac{307}{3\pi }}(-10)(9)~~+ ~~ \cfrac{307}{3\pi } \cdot \cfrac{dh}{dt}\right]\)

\(-\cfrac{4038}{\pi }=-\cfrac{180\sqrt{307}}{\sqrt{3\pi }}+\cfrac{307}{3\pi } \cdot \cfrac{dh}{dt}\implies \left[ -\cfrac{4038}{\pi }+\cfrac{180\sqrt{307}}{\sqrt{3\pi }} \right]\cfrac{3\pi }{307}=\cfrac{dh}{dt} \\\\\\ -\cfrac{12114}{307}+\cfrac{180\sqrt{3\pi }}{\sqrt{307}}=\cfrac{dh}{dt}\implies -7.920939735970634 \approx \cfrac{dh}{dt}\)

The two limits when x tends to zero are:

\(\lim_{x \to \ 0^-} f(x) = 1\\\\ \lim_{x \to \ 0^+} f(x) = 0\)

Notice that we have a jump at x = 0.

Then we can take two limits, one going from the negative side (where we will go along the blue line)

And other from the positive side (where we go along the orange line).

We will get:

\(\lim_{x \to \ 0^-} f(x) = 1\\\\ \lim_{x \to \ 0^+} f(x) = 0\)

Notice that the two limits are different, that means that the function is not a continuous function.

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Answer:

f(-3) = 4

Domain: (-infinity, 4), Range: (-infinity, 4]

Step By Step Solution:

Value of f(-3):

Looking at the graph, at x = -3, there is a jump discontinuity, and there appears to be two values that f(-3) can equal.

At x = -3, from the left side, there is a closed circle at y = 4, and from the right side, there is an open circle at y = 3.

A closed circle denotes that the point IS included in the function, while an open circle denotes the point is NOT included in the function and that point is undefined.

Therefore, the value of f(-3) is 4, because (-3, 4) is included in the function.

Domain and range:

The domain represents the set of all x-values that exist for the function.

In this case, we can see that the function continues off the graph on the left side, meaning it continues on to -infinity. We see a jump discontinuity at x = -3, however, because f(-3) is defined, this will not affect the domain. The function continues to the right until x = 4, where there is an open circle.

An open circle denotes undefined, x = 4 is not included in the domain.

Putting everything together, the domain is:

D: (-infinity, 4)

* Note we used a parenthesis after 4. Parenthesis denote that 4 is not included in the answer, whereas a bracket denotes that 4 would be included. Parenthesis are used for infinity and -infinity due to there not being a defined answer for what infinity is, so we would not use a bracket for infinity.

The range represents the set of all y-values that exist for the function.

In this case, we can see on the left side that the function continues downwards, and approaches negative infinity. We can see there is a jump discontinuity when x = -3, and that there is an undefined point at y = 3. We can, however, see that at around x = -4, that y = 3 IS defined there, so this will not affect our range. We can see the highest point is y = 4, which has a closed circle, meaning it is included in the range.

Putting everything together, the range is:

R: (-infinity, 4]

* Note that this time, a bracket IS used. This is because y = 4 IS defined and included in the function's range

Answer: 1 1/8

Step-by-step explanation:

1/4 in half is equivalent to 1/8

The statement "If A is 3 times 3, with columns a_1, a_2, a_3, then det A equals the volume of the parallelepiped determined by a_1, a_2, a_3"  is true as the determinant of a 3x3 matrix equals the volume of the parallelepiped determined by its columns.  The correct option is B).  The second statement "det A^T = (- 1)det A" is false as det A^T = (-1)^(number of row interchanges) det A for any n x n matrix A. So, the correct option is B).

The first statement is true, and the correct answer is: "The statement is true because if A is 3 times 3, with columns a_1, a_2, a_3, then det A equals the volume of the parallelepiped determined by a_1, a_2, a_3. Because det A greater than or equal to 0 for all 3 times 3 matrices A, it follows that |det A| = det A." So, the correct answer is B).

The second statement is also false, and the correct answer is: "The statement is true because a row interchange is needed to turn a matrix into its transpose. A row interchange changes the sign of the determinant." So, the correct ansnwer is B).

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Answer:

three

Step-by-step explanation:

The value of complex number |2 - 3i| will be, 3.605

A complex number is one that has the formula a + bi, where I is the imaginary unit and a and b are real numbers. A and b are the real and imaginary halves of a complex number, respectively.

In order to expand the real number system to include answers to polynomial equations that couldn't be solved with just real numbers, complex numbers were first introduced. Many branches of mathematics and science, such as computer science, physics, and engineering, are based on the idea of a complex number.

The absolute value of a complex number "a + bi" can be calculated as the square root of the sum of the squares of its real and imaginary parts:

|a + bi| = √(a² + b²)

In this case, a = 2 and b = -3, so:

|2 - 3i| = √(2 + (-3)²)

          = √(4 + 9)

          = √(13)

          = approximately 3.6055

So, the value of |2 - 3i| is approximately 3.6055.

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