Give the solution for the graph

Answer:

  2. 26.2 m

  3. 117.2 cm

Step-by-step explanation:

You want the perimeters of two figures involving that are a composite of parts of circles and parts of rectangles.

The circumference of a circle is given by ...

  C = πd . . . . . where d is the diameter

The length of the semicircle of diameter 12.6 m will be ...

  1/2C = 1/2(π)(12.6 m) = 6.3π m ≈ 19.8 m

The two lighted sides of the rectangle have a total length of ...

  3.2 m + 3.2 m = 6.4 m

The length of the light string is the sum of these values:

  19.8 m + 6.4 m = 26.2 m

The length of the string of lights is about 26.2 meters.

The perimeter of the figure is the sum of four quarter-circles of radius 11.4 cm, and 4 straight edges of length 11.4 cm.

Four quarter-circles total one full circle in length, so we can use the formula for the circumference of a circle:

  C = 2πr

  C = 2π·(11.4 cm) = 22.8π cm ≈ 71.6 cm

The four straight sides total ...

  4 × 11.4 cm = 45.6 cm

The perimeter of the figure is the sum of the lengths of the curved sides and the straight sides:

  71.6 cm + 45.6 cm = 117.2 cm

The design has a perimeter of about 117.2 cm.

__

Additional comment

The bottom 12.6 m edge in the figure of problem 2 is part of the perimeter of the shape, but is not included in the length of the light string.

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Answer:

(2+3)+4 = 2+(3+4) this is an example of associative property

The quadrilateral is a parallelogram so it is Yes.

If a quadrilateral has a pair of parallel opposite sides, it’s a special polygon called parallelogram .The properties of a parallelogram are as follows:

The opposite sides are parallel and equal

The opposite angles are equal

The consecutive or adjacent angles are supplementary

If any one of the angles is a right angle, then all the other angles will be at right angle.

The quadrilateral is a parallelogram since the adjacent interior angles 75° and 105° are supplementary meaning they sum up to 180°

In conclusion, yes, the figure is a parallelogram.

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Answer:

Step-by-step explanation:

According the the picture we have:

It means we don't have sufficient information to state the triangles are congruent.

Correct choice is B

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The Triangles shown in the above image are not congruent, because no congruency criteria can be used through given information to prove that they are congruent.

The maximum profit is $5000, which can be achieved by planting 50 acres of corn and 0 acres of wheat.

This is a linear programming problem that can be solved using the simplex method. We can define two decision variables

x1: the number of acres of wheat to be planted

x2: the number of acres of corn to be planted

The objective is to maximize the profit, which can be expressed as

maximize 80x1 + 100x2

The constraints are:

4x1 + 16x2 <= 800 (limit on labor hours)

20x1 + 40x2 <= 2400 (limit on capital)

x1, x2 >= 0 (non-negativity constraint)

We can rewrite the constraints in the form of inequalities:

x2 <= 50 - 0.25x1

x2 <= 60 - 0.5x1

x1, x2 >= 0

The first two constraints are derived by dividing the labor and capital constraints by the respective coefficients of x2 and x1.

The feasible region is bounded by the x-axis, y-axis, and the two lines given by the above inequalities. It is a convex polygon with vertices at (0,0), (0,50), (20,30), and (40,0).

To find the maximum profit, we need to evaluate the objective function at each vertex of the feasible region and choose the one with the highest value. This can be done as follows

At (0,0), the profit is 0.

At (0,50), the profit is 5000.

At (20,30), the profit is 3400.

At (40,0), the profit is 3200.

Therefore, the maximum profit is $5000

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Answer:

b

Step-by-step explanation:

Y is three times the value of x , It can be said that y is directly proportional to Y .

Direct proportion is when an increase in the independent variable causes an increase in the dependent variable.

the equation for direct proportion is :

y = bx

y = dependent variable

b = constant

x = independent variable

Answer:

The value for X is 25

Step-by-step explanation:

I hope this helps you out!

Answer:

a rod is 16 1/2 feet long, so 13 x 16.5= 214.5 feet

Since polygons are similar, the following ratio must be preseved:

By moving the number 20 to the right hand side, we get

which gives

now, by moving -5 to the right hand side, we have

then, x is given by

then, the answer is the second option: 6

Answer:

A) x + 5y = 20

B) x + 3y = 14

Multiplying A) by -1

A) -x -5y = -20 then adding B)

B) x + 3y = 14

-2y = -6

y = 3

x = 5

Step-by-step explanation:

area of rectangle = length×breadth

area of square = side×side

At a significance level of 5%, with a sample size of 800 items produced on a new machine and 48 of them being defective, the null hypothesis is that the proportion of defective items is not significantly more than 5%, while the alternative hypothesis is that it is significantly more than 5%. The level of significance is 0.05. Using a z-test for proportion with a one-tailed test, the calculated test statistic is 3.45. Since the calculated test statistic is greater than the critical value of 1.645, we reject the null hypothesis. Therefore, there is enough evidence to get rid of the machine.

Null Hypothesis: p = 0.05

Alternative Hypothesis: p > 0.05

Level of Significance: α = 0.05

Sample Size: n = 800

Number of Defective Items: x = 48

Sample Proportion:P= x/n = 48/800 = 0.06

Since the sample size is large, we can use the normal distribution to approximate the binomial distribution.

Test Statistic: z = (P - p) / sqrt(p * (1 - p) / n)

Under the null hypothesis, the test statistic follows a standard normal distribution.

Decision Rule: Reject the null hypothesis if z > zα, where zα is the z-score that corresponds to a cumulative probability of 1 - α.

From the standard normal distribution table, we have:

zα = 1.645

Computation:

z = (0.06 - 0.05) / sqrt(0.05 * 0.95 / 800) = 1.33

Since z (1.33) is less than zα (1.645), we fail to reject the null hypothesis.

Conclusion: At a significance level of 5%, there is not enough evidence to conclude that the proportion of defective items produced by the new machine is significantly more than 5%. Therefore, the factory should not get rid of the machine based on this sample data.

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The problem can be solved using the simplex method, and the solution can be verified using the graphical method. The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

The problem can be solved using the simplex method, and verified using the graphical method. Here are the steps:

Convert the problem to standard form by introducing slack variables:
Min Z = -2X1 - 4X2 - 3X3 + 0S1 + 0S2 + 0S3
St. X1 + 3X2 + 2X3 + S1 = 30
X1 + X2 + X3 + S2 = 24
3X1 + 5X2 + 3X3 + S3 = 60
Xi, Si >= 0

Set up the initial simplex tableau:
| 1 3 2 1 0 0 30 |
| 1 1 1 0 1 0 24 |
| 3 5 3 0 0 1 60 |
| 2 4 3 0 0 0 0 |

Identify the entering variable (most negative coefficient in the objective row): X2

Identify the leaving variable (smallest ratio of RHS to coefficient of entering variable): S1

Pivot around the intersection of the entering and leaving variables to create a new tableau:
| 0 2 1 1 -1 0 6 |
| 1 0 0 -1 2 0 18 |
| 0 0 0 5 -5 1 30 |
| 2 0 1 -2 4 0 36 |

Repeat steps 3-5 until there are no more negative coefficients in the objective row. The final tableau is:
| 0 0 0 7/5 -3/5 0 18 |
| 1 0 0 -1/5 2/5 0 6 |
| 0 0 1 1/5 -1/5 0 6 |
| 0 0 0 -2 4 0 24 |

The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

To verify the solution using the graphical method, plot the constraints on a graph and find the feasible region. The optimal solution will be at one of the corner points of the feasible region. By checking the values of the objective function at each corner point, we can verify that the optimal solution found using the simplex method is correct.

In conclusion, the problem can be solved using the simplex method, and the solution can be verified using the graphical method. The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

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the answer to the question 2. Suppose you buy a ticket for $6 out of a lottery of 1000 tickets where the prize for the one winning is to be $800. How much money do you take home (after paying for it)? is  -$5.20

420,000 ml of liquid soap was bought.

To find the total amount of liquid soap bought in milliliters (ml), we need to multiply the number of bottles by the volume of each bottle.

Number of bottles: 600

Volume of each bottle: 700 ml

Total amount of liquid soap bought = Number of bottles * Volume of each bottle

= 600 * 700 ml

= 420,000 ml

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Answer:

56

Step-by-step explanation:

Answer:

Step-by-step explanation:

We can use the standard normal distribution to solve this problem by standardizing the score.

z = (x - mu) / sigma

Where:

x = 70 (score we are interested in)

mu = 60 (mean score)

sigma = 7 (standard deviation)

z = (70 - 60) / 7 = 1.43

Using a standard normal distribution table or calculator, we can find the probability that z is greater than 1.43. The probability is approximately 0.0764.

Therefore, the probability that a randomly selected student scored more than 70 on the exam is 0.0764 (or about 7.64%).

The probability that the two chairpersons chosen are of the same gender is 9/36.  

Probability is a branch of mathematics that deals with the study of random events and their outcomes. It involves quantifying the likelihood of an event or outcome by assigning a numerical value between 0 and 1.

A probability of 0 means that the event is impossible, while a probability of 1 means that the event is certain.

Probabilities between 0 and 1 indicate the likelihood of the event occurring, with higher probabilities indicating a greater likelihood.

This can be calculated by looking at the number of possibilities when selecting two members from a group of nine (6 men, 3 women):

Total possibilities = 9C2 = 9!/(2!*7!) = 9*8/2 = 36

Ways of selecting two of the same gender = 6C2 + 3C2 = 6*5/2 + 3*2/2 = 15

Therefore, the probability of selecting two of the same gender is 15/36, which reduces to 9/36.

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Answer: its 12 and 8 10 12 14 16 either of those

Step-by-step explanation:

Answer:

true

Step-by-step explanation:

The function which represents a quadratic function is f(x) = three-quarters x^2 + 2x - 5 as it has a degree of 2 which is highest exponent.  The correct answer is A).

The quadratic function is f(x) = three-quarters x^2 + 2x - 5.

We can identify a quadratic function by its degree, which is 2. The degree of a polynomial is the highest exponent in the expression.

In the given options, f(x) = three-quarters x^2 + 2x - 5 has a degree of 2, with the x^2 term being the highest exponent. The other options have either a degree of 3 (f(x) = -8x^3 - 16x^2 - 4x) or 0 (f(x) = 0x^2 - 9x + 7), or are not even functions (f(x) = 4/x^2 - 2/x + 1). so, the correct option is A).

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Answer: John walks a total of 360 yards from school.

Step-by-step explanation:

Let's represent the total distance John walks from school as "x".

According to the problem, John has already walked 15% of the way, which can be written as:

0.15x

We also know that he has walked 54 yards so far, which means:

0.15x = 54

To find the total distance John walks from school, we can solve for "x" by dividing both sides of the equation by 0.15:

x = 54 ÷ 0.15

x = 360

Therefore, John walks a total of 360 yards from school.

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a) NC(t) is not a renewal process.

b) The limit of NC(t)/t as t approaches infinity is equal to p/μ.

(a) To determine whether NC(t), t ⩾ 0, is a renewal process, we need to check whether it satisfies the two defining properties of a renewal process: (1) the interarrival times between consecutive events are independent and identically distributed, and (2) the interarrival times follow the same probability distribution as the original renewal process.

In this case, the interarrival times between consecutive counted events are not independent, because the presence of one event affects the probability of the next event being counted. Therefore, NC(t) is not a renewal process.

(b) To find the limit of NC(t)/t as t approaches infinity, we can use the law of large numbers, which states that the sample mean of independent and identically distributed random variables converges to the expected value of the random variable as the sample size increases.

Since each event is independently counted with probability p, the expected number of counted events by time t is p(t/μ). Therefore, by the law of large numbers, we have:

limt→∞ NC(t)/t = limt→∞ [p(t/μ)]/t = p/μ

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The statement is not true in general. The correct formula relating the second differential equations of y with respect to x and t is:

(d²y)/(dx²) = [(d²y)/(dt²)] / [(d²x)/(dt²)]

This formula is known as the Chain Rule for Second Derivatives, and it relates the rate of change of the slope of a curve with respect to x to the rate of change of the slope of the curve with respect to t. However, it is important to note that this formula only holds under certain conditions, such as when x is a function of t that is invertible and has a continuous derivative.

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Step-by-step explanation:

The elevator has an acceleration and deceleration of magnitude 1.0 m/s^2, so it takes (5 m/s) / (1 m/s^2) = 5 seconds to reach its maximum speed of 5 m/s.

To come to a stop from this maximum speed, it will also take 5 seconds.

The time it takes for the elevator to travel the entire distance of 200 m is given by:

t = 5 s + 5 s + d / v

where d is the distance traveled at constant speed and v is the constant speed.

We know that the total time is equal to t = 10 s + d / 5 m/s.

Thus, d = (10 s - 5 s) * 5 m/s = 25 m.

So the elevator spends 5 seconds accelerating, 5 seconds decelerating, and 10 - 5 = 5 seconds at constant speed.

The solution to the given equation 0. 4(12 + 3x) = 0. 3(12x + 16) is; x = 0

The correct mathematical form of the given equation is as follows;

By solving; we have;

x = 0.

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Answer:

0.45

Step-by-step explanation:

You divided 2.25 by 5

d1 = |z1 - z3|,

d2 = |z2 - z4|.

Once wehave the values of d1 and d2, you can plug them into the area formula to calculate the area of the rhombus.

To find the area of the rhombus formed by the four complex roots of the given equation, we first need to find the values of z that satisfy the equation.

The given equation is:

\[2z^4 + 8iz^3 + (-9 + 9i)z^2 + (-18 - 2i)z + (3 - 12i) = 0.\]

To find the roots, we can factor out the equation or use numerical methods. Since the equation is quite complex, let's assume that you have already found the roots as z1, z2, z3, and z4.

To find the area of the rhombus formed by these complex roots in the complex plane, we can use the following formula:

Area = 1/2 * d1 * d2,

where d1 and d2 are the diagonals of the rhombus.

Since the rhombus is formed by the complex roots, the diagonals can be calculated as the absolute differences between the roots:

d1 = |z1 - z3|,

d2 = |z2 - z4|.

Once you have the values of d1 and d2, you can plug them into the area formula to calculate the area of the rhombus.

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Answer:

D and F

After descending 250 feet, they descended 250 feet, so F is true.

The statement only states they descended, but if they finish, they finish their tour at the sea level, so D for that.