(b) A square has a perimeter of 12 yd. What is the length of each side?

The fraction of the given equation would be 2/3.

locating the Original number.

The outcome is one less than the original number when a two-digit number with its digits reversed is subtracted from the same number. The number itself can be obtained by adding three times the tens digit and four times the units digit of the original integer.

Suppose that x is the initial or positive number.

(x - 4/7)* 7 = x

7(x) - 7(4/7) = x

7x - 4 = x

7x-x = 4

6x = 4

x = 4/6 = 2/3

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The range of the function is the set of all possible output values, which are {2, 6, 8, 10}. So the correct answer is option C.

In mathematics, a function is a rule that assigns each element of a set (called the domain) to a unique element of another set (called the range). Functions are a fundamental concept in mathematics and are used to describe relationships between variables, as well as to model and solve a wide range of mathematical problems.

A function is typically denoted using a letter such as "f", and is defined by an equation or formula that specifies how the input (or domain) values are transformed into output (or range) values. For example, the function "f(x) = 2x + 1" assigns each input value "x" to an output value equal to twice the input value plus one.

To find the range of the function f(x) = x + 3, we need to apply the function to each value in the given domain and collect the resulting outputs.

When the domain is {-1, 3, 5, 7}, we have:

f(-1) = -1 + 3 = 2

f(3) = 3 + 3 = 6

f(5) = 5 + 3 = 8

f(7) = 7 + 3 = 10

Therefore, the range of the function is the set of all possible output values, which are {2, 6, 8, 10}. So the correct answer is option C.

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Answer:

53.33

Step-by-step explanation:

1/3 of it is 26.66 continuing so it's rounded up

therefore, 80-26.67 is 53.33

The integral of \(x^3/\sqrt(x^2+4)\) using trigonometric substitution is: \(8 * (1/3)tan^2\theta(1 + tan^2\theta)^(3/2) + C\), where θ is determined by x = 2tanθ, and C represents the constant of integration

What is integration?

Integration is a fundamental concept in calculus that involves finding the integral of a function.

To integrate the function \(\int(x^3/\sqrt(x^2+4))\) dx using a trigonometric substitution, we can use the substitution x = 2tanθ. Let's go through the steps:

Substitute x = 2tanθ. This implies \(dx = 2sec^2\theta d\theta.\)

Rewrite the integral in terms of θ:

\(\int((8tan^3\theta)/(\sqrt(4tan^2\theta+4))) * 2sec^2\theta d\theta.\)

Simplify the expression inside the square root:

\(\int((8tan^3\theta)/(2sec\theta)) * 2sec^2\theta d\theta.\\\\\int(8tan^3\theta) * sec\theta d\theta.\)

Simplify further:

\(16\int tan^3\theta sec\theta d\theta.\)

Apply the trigonometric identity: \(sec^2\theta = 1 + tan^2\theta\). Rearranging, we get: \(sec\theta = \sqrt(1 + tan^2\theta).\)

Substitute \(sec\theta = \sqrt(1 + tan^2\theta)\) in the integral:

\(16\int tan^3\theta * \sqrt(1 + tan^2\theta) d\theta.\)

Let u = tanθ, which implies \(du = sec^2\theta d\theta\). We can rewrite the integral in terms of u:

\(16\int u^3 * \sqrt(1 + u^2) du.\)

Now we have a rational power of u. We can use the substitution \(v = 1 + u^2\) to simplify it:

\(v = 1 + u^2\), which implies dv = 2u du.

Rewrite the integral using v:

\(16\int (u^3 * \sqrt v) * (1/2u) dv.\\\\8\int (u^2\sqrt v) dv.\)

Simplify and integrate:

\(8\int (u^2\sqrt v) dv = 8\int(u^2 * v^{(1/2)}) dv = 8\int u^2v^{(1/2)} dv.\)

Integrate \(u^2v^{(1/2)\) with respect to v:

\(8 * (1/3)u^2v^{(3/2)} + C.\)

Replace v with \(1 + u^2\):

\(8 * (1/3)u^2(1 + u^2)^{(3/2)} + C.\)

Substitute u = tanθ back into the expression:

\(8 * (1/3)tan^2\theta(1 + tan^2\theta)^{(3/2)} + C.\)

So, the integral of \(x^3/\sqrt(x^2+4)\) using trigonometric substitution is:

\(8 * (1/3)tan^2\theta(1 + tan^2\theta)^{(3/2)} + C,\)

where θ is determined by x = 2tanθ, and C represents the constant of integration

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Answer:

x = 125°

Step-by-step explanation:

180° - 55° = 125°

125°

If my answer is incorrect, pls correct me!

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Answer:

Tony and his cousin will each have 42 points in 3 turns.

Step-by-step explanation:

10 x 3 = 30

30 + 12 = 42

14 x 3 = 42

The measures of the angles in the completed table of the question can be presented as follows;

Angle AFB \({}\)        \({}\)Angle BFC      Angle DFE   Angle EFA

48          \({}\) \({}\)             42                    48                132

36 \({}\)                       54                    36                144

40\({}\)                        50                    40                140

An angle is a geometric figure formed by the opening (space) at the point where two rays meet.

The specified angle measurement indicates that we get;

Angle AFB and angle BFC are complementary angles

Angle AFB and angle DFE are vertical angles

Vertical angles are congruent

Angle EFA and angle BFD are vertical angles

Angle BFD = Angle BFC + Angle CFD

Therefore;

Angle EFA = Angle BFC + Angle CFD

Angle CFD = 90°

The completed table can be presented as follows;

Angle AFB \({}\)             Angle BFC         Angle DFE              Angle EFA

48 \({}\)                             42                          48                       132

AFB = DFE = 36 \({}\)    BFC=90-36 =54       36                        90 + 54 = 144

90-50 = 40\({}\)      \({}\)      140 - 90 = 50            40                        140

The possible question, obtained from a similar question on the internet can be presented as follows;

The rows in the following table represent a complete set of angle measurement in the attached drawing created with MS Excel

Make use of the drawing and the angle measurements in each row on the table to find the missing (required) angle measurement

Angle AFB \({}\)         Angle BFC             Angle DFE               Angle EFA

48                   \({}\)     42                           48                            132

                                                          36                                

\({}\)                                                                                           140

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Answer:

\( \sf 9,802 \frac{1}{3} \)

Step-by-step explanation:

\( \sf = \frac{588,140}{60} \)

\( \sf = \frac{58,814}{6} \)

\( \sf = 9,802 \frac{2}{6} \)

\( \sf = 9,802 \frac{1}{3} \)

Answer:

Multiplication

Step-by-step explanation:

Multiplication

The system capacity is 2 units per minute, the bottleneck stage is Stage A, and the utilization of Stage 3 is 100%.

A line process has three processing stages with the characteristics given below:

Stage A B C Unit processing time(minutes) 1 2 3 Number of machines 1 1 2 Machine availability 90% 100% 100% Process yield at stage 100% 100% 100%

To determine the system capacity and the bottleneck stage and utilization of Stage 3:

The system capacity is calculated by the product of the processing capacity of each stage:

1 x 1 x 2 = 2 units per minute

The bottleneck stage is the stage with the lowest capacity and it is Stage A. Therefore, Stage A has the lowest capacity and determines the system capacity.The utilization of Stage 3 can be calculated as the processing time per unit divided by the available time per unit:

Process time per unit = 1 + 2 + 3 = 6 minutes per unit

Available time per unit = 90% x 100% x 100% = 0.9 x 1 x 1 = 0.9 minutes per unit

The utilization of Stage 3 is, therefore, (6/0.9) x 100% = 666.67%.

However, utilization cannot be greater than 100%, so the actual utilization of Stage 3 is 100%.

Hence, the system capacity is 2 units per minute, the bottleneck stage is Stage A, and the utilization of Stage 3 is 100%.

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The size of each house of the Texas legislature is as follows:

There are 150 members in the House and 31 members in the Senate.

The Texas legislature consists of two houses: the House of Representatives and the Senate. The size of each house is determined by the number of members serving in it.

In the given choices:

Option 1: There are 181 members in the House and 30 members in the Senate. This option does not match the commonly known structure of the Texas legislature.

Option 2: There are 150 members in the House and 31 members in the Senate. This option matches the commonly known structure of the Texas legislature.

Option 3: There are 150 members in both the House and the Senate. This option implies that both houses have the same number of members, which is not the case in the Texas legislature.

Option 4: There are 150 members in the Senate and 31 members in the House. This option contradicts the typical arrangement of the Texas legislature.

The size of each house of the Texas legislature is as follows:

There are 150 members in the House and 31 members in the Senate.

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Answer:

when a fraction equals 100% it means it has the same numbers for its numerator and denominator such as 4/4 or 18/18

Step-by-step explanation:

When it has the same numbers for its numerator and denominator it will be 100%

If the motion of a point on the drum of a clothes dryer is modeled by the function y=12 sin (4/3π t) +20, the dryer rotates 40 times per minute.

The function y = 12 sin (4/3π t) + 20 models the vertical motion of a point on the drum of a clothes dryer. The amplitude of the function is 12, which represents the maximum displacement of the point from its rest position. The vertical shift of the function is 20, which represents the height of the point from the ground when the drum is at rest.

To determine the number of times the dryer rotates per minute, we need to find the period of the function, which is the time it takes for the function to complete one full cycle. The period of a sinusoidal function is given by the formula:

T = (2π) / b

where b is the coefficient of the t variable in the sine or cosine function.

In this case, b = (4/3)π, so the period of the function is:

T = (2π) / (4/3π) = 3/2 seconds

This means that the point on the drum completes one full cycle of vertical motion every 3/2 seconds. To convert this to rotations per minute, we need to find the number of cycles per minute:

cycles per minute = (60 seconds per minute) / (3/2 seconds per cycle) = 40 cycles per minute

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The distance covered is 5 1/2 miles.

The first step is to determine the speed at which Annie walked. Speed is total distance per time.

Speed = distance / time

1/2 ÷ 1/4

1/2 x 4 = 2 miles / hour

Distance covered = time x speed

= 2 x \(2\frac{3}{4}\)

2 x \(\frac{11}{4}\) = \(\frac{11}{2}\) = 5 \(\frac{1}{2}\) miles

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Answer:

16. real number, rational number, integer

17. real number, rational, integer

18. whole number, real number, integer, rational

19. whole, real, integer, rational

20. irrational

21. rational, real, whole, integer

Step-by-step explanation:

There is no maximum y - value for the given function.

What is maximum?

In mathematical analysis, the maxima and minima of a function, also referred to as extrema, are the highest and lowest values of the function, respectively, either on the whole domain or within a specific range.

The largest amount or value that can be obtained or accomplished. The highest, greatest, or most advanced era of growth. An upper limit permitted (as by a legal authority) or allowable. 3.: The biggest number in a collection.

The given function is,

\(y(x) = sin(6x) - x^2\)          ...(1)

The maximum value occur when

y'(x) = 0

Differentiating equation (1) w.r.t x

\(\frac{d}{dx}(sin(6x)) - \frac{d}{dx}((x^2)=0\\ cos(6x)(6) - 2x = 0\\ 6cos(6x)-2x=0\)

Divide both sides by 2,

\(3cos(6x) - x = 0\)

It is not possible to solve equation further.

Hence, there is no maximum y - value for the given function.

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If the equation (13 + 4i) + n = 0, then the value of n is option (d) -13 - 4i

Additive inverse is a concept in mathematics that refers to the opposite of a given number, such that when the number is added to its additive inverse, the result is zero

To solve for n, we can isolate it by moving (13 + 4i) to the other side of the equation and then taking the additive inverse of both sides.

Starting with: (13 + 4i) + n = 0

Subtracting (13 + 4i) from both sides: n = - (13 + 4i)

Taking the additive inverse of both sides: n = -13 - 4i

Therefore, the correct option is (d) -13 - 4i

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Answer:

C

Step-by-step explanation:

8.5 - 5.6666= 2.83

Answer:

C. 2 5/6

Step-by-step explanation:

8 1/2 - 5 2/3    1. convert mixed numbers into an improper fraction

17/2 - 17/3       2. convert fractions into 2 numbers that can be subtracted

51/6 - 34/6      3. subtract

17/6                 4. convert to mixed number

2 5/6

The crucial value (z) relies on the desired level of confidence and is predicated on a normal distribution when creating a confidence interval for a proportion (p) with a confidence level of 93%.

A 93% confidence level in this instance translates to an alpha level of 0.07 (1 - 0.93 = 0.07) that is split evenly between the two tails. In the usual normal distribution table, we search for the value that falls within the range of 0.07 to find the proper z-value. A 93% confidence level corresponds to a z-value of roughly 1.81. The confidence interval for the proportion p may be calculated using this number and provides a range where the genuine proportion is like to fall.

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(1) The graph shows Sam's payments in blue while that of Carmen is shown in orange color.

(2) The graph shows that the rate of change is negative because it slopes downwards from left to right, which means as the weeks go by, the amount paid decreases. The amount paid is on the y axis while the weeks is on the x axis. As y moves up in the positive direction, x moves towards the left in the negative direction.

(3) I Sam decides to pay in two equal weekly payments, then his payment plan would be $62.5 per week and hence the graph of his payment plan would be steeper than the two currently on the coordinate grid.

Answer:

1

Step-by-step explanation:

Given a figure of a circle:

As shown, the radius of the circle = r = 9 miles

The shown sector bounded by a 60-degree arc

We need to find the area of the shown sector

as we know the area of the circle =

The area of the sector represents 60/360 of the area of the circle

So, the area of the sector =

so, the answer will be the area of the shown sector = 42.4115 square miles

We will write the area in terms of pi and fractions as follow:

So, the answer will be:

Answer:

8

Step-by-step explanation:

Answer:

$27.10

Step-by-step explanation:

$542 x 0.05 = $27.10

The commission he earned last month was amount of $360.

The commission is determined by the product of the commission rate and the total sales.

A salesman receives a 6% commission on all merchandise sold.

He sold $6000 in merchandise last month.

Salesman earns 6% = 6/100 = 0.06

Now, we have to evaluate 6% of $6000

= 0.06 x 6000

Apply the multiplication operation, and we get

= 360$

Thus, the commission he earned last month was the amount of $360.

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The question seems incomplete, the complete question would be as:

A salesman earns 6% commission on all the merchandise that he sells. Last month he sold $6000 worth of merchandise. How much commission (in dollars) did he earn last month?

Answer:

w=4

Step-by-step explanation:

The semicircle has an arc length of 18.84 units.

In this problem we need to determine the arc length of a semicircle, that is, the length of the arc of the half of a circle. This can be computed by circumference formula:

s = π · r

Where:

Please notice that diameter is twice the radius.

If we know that r = 6, then the arc length of the semicircle is:

s = π · 6

s = 6π

s = 6 · 3.14

s = 18.84

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