Determine the number of solutions for the linear equation shown below?
4(3x+8)−9=2(6x−8)−15

The area of the shaded region is 502.4 ft^2

The area of a circle is the space occupied by a circle in a two-dimensional plane. Alternatively, the space taken up inside the boundary/circumference of a circle is called the area of the circle. The formula for the area of a circle is A = πr2, where r is the radius of the circle. The unit of area is the square unit, such as m2, cm2, in2, etc. Area of a circle = πr2 or πd2/4 in square units, where (Pi) π = 22/7 or 3.14. Pi (π) is the ratio of the circumference to the diameter of any circle. It is a special mathematical constant.

It is given that inner diameter is 36 ft and width of the ring is 4 ft

We need to find the area of the shaded region

diameter of outer ring= d1=36+4+4 = 44 ft ,

diameter of inner ring= d2=36 ft,

r1=d1/2= 44/2 = 22 ft , r2=d2/2 = 36/2 = 18 ft

Area of shaded region = Area of Outer circle - Area of inner circle

= π r1^2 - π r2^2

= π ( 22^2 - 18^2 )

= 3.14 * 160

= 502.4 ft^2

Hence the area of the shaded region is 502.4 ft^2

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The area of the shaded region is 502.4 sq. ft.

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The word "area" refers to a free space.

According to the question,

Diameter of inner circle = 36 ft.

Radius of inner circle = 36/2 ft. =18 ft.

As the width of the ring is 4 ft. , the diameter of the outer circle = 36+4+4= 44 ft.

Radius of outer circle = 22 ft.

Area of the shaded region = Area of outer circle - Area of inner circle

                                              = π(22)(22) - π(18)(18)

                                              = π(484 - 324)

                                              = 3.14 * 160

                                              = 502.4 sq. ft.

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There are 720 different ways can a race with 6 runners be completed.

What is a combination?

The process of combining or the condition of combining. a combination of things; an amalgamation of concepts. a grouping of notes: A chord is a grouping of notes. a grouping of people or entities acting together to impede commerce.

Here, we have

The winner can be chosen from all 6 runners, the second person can be chosen from 5 people, the third - from 4, and so on.

So the total number of possible results can be calculated as:

n = 6×5×4×3×2×1= 6!

= 720

Hence, there are 720 different ways can a race with 6 runners be completed.

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Answer:

P(x) = R(x) = -2x^2+63z

As many as possible

Infinite depending on how many people buy it.

$63.00

Best reason would be to make your dog look cool and make the person who sold it happy. Worst reason is that it is extremely expensive for something you don't need.

Step-by-step explanation:

Step-by-step explanation:

Simplify for m by using algebra.

Divide each side by 3:

\( \frac{3m}{3} = \frac{0.95}{3} \)

\( m = \frac{19}{60} \)

Answer:

44.93

Step-by-step explanation:

7.5 x 599 divided by 100 = 44.925 = 44.93

Answer:

Step-by-step explanation:

\(\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}\)

Sam lives 162 miles away from the mountains.

Let's assume that the distance between Sam’s home and the mountains be x miles. Then, let us use the formula for distance which is:Distance = Speed × TimeFor Sam’s journey to the mountain, we know that he took 7 hours, therefore his speed was:S = D / T = x / 7For his return journey, Sam took 5 hours and he traveled 18 mph faster than he did on the way there; therefore, his speed is:S = (x / 5) + 18

Now we know that the distance he traveled to the mountains and back was the same. Therefore:Distance to the mountains = Distance from the mountainsx = (x / 7) × 2 + [(x / 5) + 18] × 2Then we simplify to get rid of the denominators:10x = 2x + 28x + 180Now we solve for x:8x = 180x = 22.5Therefore the distance between Sam's home and the mountains is 22.5 × 7 = 157.5 miles. However, that is only the distance to the mountain. We need to find the total distance of the round trip which is:Total distance = Distance to the mountains + Distance from the mountainsTotal distance = 157.5 + 157.5Total distance = 315 milesTherefore Sam lives 315 / 2 = 157.5 miles away from the mountains.

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Answer: All boundary points of a rational inequality that are found by determining the values for which the denominator is equal to zero should always be represented by plotting an open circle on a number line.

Step-by-step explanation:

Based on the options given in this question, it should be noted that the option that is true is that all boundary points of a rational inequality that are found by determining the values for which the denominator is equal to zero should always be represented by plotting an open circle on a number line.

Therefore, the correct option is A.

Answer:

2 root 10/ 7, or the second option.

Step-by-step explanation:

If a is 3, then b is root 40. (Pythagorean)

root 40= root 4x10, or 2 root 10

Tangent= opposite/hypotenuse

Tangent= 2 root 10/ 7

Answer:

52° and 38°

Step-by-step explanation:

The two angles form a singular right angle.

\((x+33)+(2x)=90\\\\x+33+2x=90\\\\3x + 33 = 90\\\\3x+33-33=90-33\\\\3x=57\\\\\boxed{x=19}\)

The value of 'x' is 19.

\(m$\angle$1 = x + 33\\\\m$\angle$1 = 19 + 33\\\\m$\angle$1 = \boxed{52}\)

The measure of angle 1 is 52 degrees.

\(m\angle2=2x\\\\m\angle2=2(19)\\\\m\angle2=\boxed{38}\)

The measure of angle 2 is 38 degrees.

Hope this helps.

Answer:

B

Step-by-step explanation:

\(tan(R)=\frac{opposite}{adjacent}\)

here, both triangles are similar triangles. So both ratios must be similar.

the side opposite of H is 5. So the side opposite of angle R must also be 5. Similarly, the side adjacent to angle H is 12. So the side adjacent to R must also be 12. Thus we have:

\(tan(H)=tan(r)= \frac{5}{12}\)

So the answer is B. Hope this helps!

Answer: exponential

Step-by-step explanation:

its exponential

count the squares in each one

first is 2 squares

second is 4 squares

third is 8 squares

this is going up exponentially because the first one would be 2^1 the second would be 2^2 and the third would be 2^3

Point estimates themselves do not provide information about their accuracy. The given statement is false.

Point estimates represent a single value that is used to estimate an unknown population parameter. They do not convey any information about the variability or uncertainty associated with the estimate. To assess the accuracy of a point estimate, it is necessary to calculate a measure of uncertainty, such as a confidence interval or a margin of error.

These measures provide information about the range within which the true population parameter is likely to fall. By including a margin of error or confidence interval along with the point estimate, we can gain a sense of the precision and reliability of the estimate.

In summary, point estimates alone do not provide information about their accuracy. Additional measures, such as confidence intervals or margins of error, are needed to assess the accuracy and uncertainty associated with the estimate.

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A unity feedback control system is characterized by an open-loop transfer function G(s)H(s)=k/s(s+10). The system gain k so that the system will have a damping ratio of 0.5 is 4. The corresponding rise time is 2.3s, settling time is 4.4s, and peak overshoot is 0.26.

To determine the system gain k so that the system will have a damping ratio of 0.5, we can use the equation  ζ=1/2ωn. Rearranging the equation yields k=2ωn2. Using the damping ratio of 0.5, this yields k=4.
For this value of k, the rise time, settling time, and peak overshoot can be determined using the following equations:
Rise Time: Tr=4.6/ωn
Settling Time: Ts=4.4/ζωn
Peak Overshoot: Mp=e^(-ζπ/√1-ζ^2)
Given that the damping ratio is 0.5 and the system is subjected to a step input of 1V, we can determine the rise time, settling time, and peak overshoot.
Rise Time: Tr=4.6/ωn=4.6/2=2.3s
Settling Time: Ts=4.4/0.5ωn=4.4/1=4.4s
Peak Overshoot: Mp=e^(-0.5π/√1-0.5^2)=0.26

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Answer:

He is incorrect

Step-by-step explanation:

In 1.967, the hundredth is greater than 5. That means you'd round up! So, the correct answer would be 2.

(I tried my best to explain)

0.0238 is the probability that the student can solve all five problems on the exam.

It is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

Given Data

Total number of questions – 10

Questions selected randomly – 5

The total number of ways in which the teacher can set the questions is given by:

¹⁰C₅ = \(\frac{10!}{5!(10-5)!}\)

¹⁰C₅ = \(\frac{10(9)(8)(7)(6)5!}{5!(5!)}\)

¹⁰C₅ = \(\frac{10(9)(8)(7)(6)}{5!}\)

¹⁰C₅ = \(\frac{30240}{120}\)

¹⁰C₅ = 252

Here the student can solve all the 55 problems if the teacher selects them from the 66 questions that she can solve. The number of ways in which it could happen is given by:

⁶C₅ = 6

The probability of this happening is given by:

Probability = \(\frac{6}{252}\)

Probability = 0.0238

0.0238 is the probability that the student can solve all five problems on the exam.

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Recall the formula for compound interest

Using the formula, rearrange the equation and solve in terms of time t

Substitute the given values and we get

A = $2700, P = $1100, n = 12 (12 months in a year), r = 0.045 (from 4.5%)

Rounding the answer to the nearest tenth, the time it takes is 20 years.

Answer: Part A is (-9, 13) Part B is (9, 13)

Step-by-step explanation:

A+B+C= 40

2C +5=A

B-C=3

A is Amanda, B is Bethany and C is Christina

Answer:

\( \frac{1}{4} \times \frac{1}{8} = \frac{1}{32} \)

Given:

The expression is

\((5-2)^2+2^3\times 4\)

Emily simplified this expression and steps are given.

To find:

The first mistake of Emily.

Solution:

We have,

\((5-2)^2+2^3\times 4\)

Step 1: \((3)^2+2^3\times 4\)

Step 2: \(9+2^3\times 4\)

Step 3: \(9+8\times 4\)

Step 4: \(9+32\)

Step 5: \(41\)

So, she made a mistake in her third step.

Therefore, the correct option is C.

Answer:

27/35 points

Step-by-step explanation:

The probability of getting one double;

P(getting one double) = 5/36

Probability of getting two doubles is;

P(getting two doubles) = 1/36

Probability of getting no doubles is;

P(getting no doubles) = 1/36

For us to find the Number of points that the player should lose for not rolling doubles, we have;

(12/36) + (5(3 - x)/36) - (5x/6) = 0

(12/36) + (15 - 5x)/36 - 5x/6 = 0

Multiply through by 36 to get;

12 + 15 - 5x - 30x = 0

35x = 27

x = 27/35

Bar graphs can be used to display both discrete and continuous data, making them a versatile tool for visualizing a wide range of information.

The graphic presentation of data that displays its categories as rectangles of equal width with their height proportional to the frequency or percentage of the category is called a bar graph.

In a bar graph, the bars represent the categories being compared and are arranged along the horizontal axis, with the height of each bar representing the frequency or percentage of the category being displayed.

Bar graphs are a useful tool for presenting numerical data in a visually appealing way, making it easy for viewers to compare different categories and draw conclusions from the data.

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According to the question we have the solution of the  given differential equation initial value problem is: g(x) = (3/4)x^4 - x + 9/4 .

To solve the given initial value problem, we need to integrate both sides of the differential equation. We have:

g'(x) = 3x(x^2 - 1/3)

Integrating both sides with respect to x, we get:

g(x) = ∫[3x(x^2 - 1/3)] dx

g(x) = ∫[3x^3 - 1] dx

g(x) = (3/4)x^4 - x + C

where C is the constant of integration.

To find the value of C, we use the initial condition g(1) = 2. Substituting x = 1 and g(x) = 2 in the above equation, we get:

2 = (3/4)1^4 - 1 + C

2 = 3/4 - 1 + C

C = 9/4

Therefore, the solution of the given initial value problem is:

g(x) = (3/4)x^4 - x + 9/4

In more than 100 words, we can say that the given initial value problem is a first-order differential equation, which can be solved by integrating both sides of the equation. The resulting function is a family of solutions that contain a constant of integration. To find the specific solution that satisfies the initial condition, we use the given value of g(1) = 2 to determine the constant of integration. The resulting solution is unique and satisfies the given differential equation as well as the initial condition.

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Answer:

I would say it is close to 4, but not 4.

Step-by-step explanation:

So I rounded the distance between the 2 plots with a line, and I got either 3.8 or 3.1

square root of 10 = 3.1

square root of 15 = 3.8

The picture is my graph I used to base it, so I would generally consider how close it is to 4 saying C. Square root of 10.

(I only chose 3.1 because I went up on the graph 3 squares with my line. It did not quite reach. I went 1/10(0.1) of a whole up further, and it resulted in the square root of 10 choice.)

Answer:

Step-by-step explanation:

Dont do it. Just take the detention

Step-by-step explanation:

Here is one way :

  at the x-axis intercepts , the value of 'y' = 0  (obviously)

   0  = x^2 -64

    x^2 = 64

     x = ± 8

Answer:

Henry VII died on 21 April 1509, and the 17-year-old Henry succeeded him as king.