Chang is building a circular sandbox with a circumference of 31.4 meters. She uses a string tied to a metal stake to trace out a circle in her backyard.

The probability that a randomly selected point within the square falls in the red shaded area is approximately 0.2146 or about 21.46%.

To find the probability that a randomly selected point within the square falls in the red shaded area, we need to compare the area of the red shaded region to the area of the entire square.

Let the side length of the square be 2 units, and let the center of the circle be at the center of the square. Then, the radius of the circle is also 1 unit.

The area of the square is [tex](side length)^2[/tex] = [tex]2^2[/tex] = 4 square units.

The area of the circle is π[tex](radius)^2[/tex] = π[tex](1)^2[/tex] = π square units.

The red shaded area is the difference between the area of the square and the area of the circle, which is 4 - π square units.

Therefore, the probability that a randomly selected point within the square falls in the red shaded area is:

(red shaded area) / (area of the square) = (4 - π) / 4 ≈ 0.2146

So the probability is approximately 0.2146 or about 21.46%.

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Answer:

Either A or c

Step-by-step explanation:

Therefore , the solution of the given problem of function comes out to be the monthly percentage rate of change is roughly 4.56%, to the closest hundredth of a percent.

There will be a range of questions in each subject on the midterm test, including inquiries about both imagined and real locations and also inquiries regarding the design of numerical variables. a schematic illustrating the connections between various components that work together to produce the same outcome.

Here,

The exponential development equation is:

=>[tex]N(t) = N_0 * e^{(rt)}[/tex]

We must first convert the annual growth rate from a percentage to a decimal, which we must then split by 12 to obtain the monthly rate:

Monthly rate at r = 54% is 0.54; r/12 is 0.045.

=>[tex]N(t) = 2600 * e^{(0.045)}[/tex]

=> [tex]N(t) = 2600 * 1.0469^t[/tex]

We can use the following method to determine the monthly percentage rate of change:

=> Monthly Rate of Change equals 100% * (e^(Monthly Rate) - 1)

By substituting the previously calculated monthly rate, we obtain:

=> [tex](e^{(0.045)} - 1)[/tex]* 100% = 4.56% for the monthly rate of change.

In light of this, the monthly percentage rate of change is roughly 4.56%, to the closest hundredth of a percent.

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The surface area of the rectangular prism with a length of 4 units, a width of 3 units, and a height of 5 units is 94 square units.

To find the surface area of a rectangular prism, you need to add up the area of all six faces. The formula for the surface area of a rectangular prism is:

Surface Area = 2lw + 2lh + 2wh

where l, w, and h are the length, width, and height of the rectangular prism.

So, to find the surface area of a rectangular prism, you simply need to plug in the values for l, w, and h into this formula and solve.

For example, if the length of the rectangular prism is 4 units, the width is 3 units, and the height is 5 units, the surface area would be:

Surface Area = 2(4)(3) + 2(4)(5) + 2(3)(5)
Surface Area = 24 + 40 + 30
Surface Area = 94 square units

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Alemu's net income after deducting income tax is 9,470 birrs per month, assuming he lives in Ethiopia and the income tax rates for the current tax year apply.

We must take into account the income tax rates in Alemu's nation for the current tax year in order to determine how much income tax he must pay. We cannot provide an exact response since we are unsure about Alemu's country of residence. The income tax rates in Ethiopia, where the first 6,000 birr of income are tax-free and the remaining amount is subject to progressive taxes, range from 10% to 30%, can be used as an example, though.

Alemu's monthly taxable income, assuming he resides in Ethiopia, would be 4,000 birrs (between 10,000 and 6,000). He must pay the following amount of income tax:

180 birr (10% of the first 1,800 birr)

15% of the following 1,800 birrs is 270 birrs.

80 birrs are 20% of the remaining 400 birrs.

Alemu would therefore pay 530 birrs in total income tax each month.

Alemu's net income would be 9,470 birrs after income tax. This is the sum of cash he would have on hand to cover personal costs, savings, investments, and any other debts. It is crucial to remember that the net income amount may change depending on a number of variables, including deductions for social security, health insurance, or any other needed legal payments.

In conclusion, assuming Alemu lives in Ethiopia and the income tax rates for the current tax year are applicable, Alemu's net income after income tax is 9,470 birrs each month.

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The mean, median, and standard deviation of the given data set are approximately 114.4, 110, and 10.12, respectively.

In statistics, the mean is a measure οf central tendency οf a data set, alsο referred tο as the average. It is calculated by summing up all the values in the data set and then dividing by the tοtal number οf values. The mean represents the typical οr cοmmοn value in the data set.

The mean of the given data set is:

(135 + 115 + 120 + 110 + 110 + 100 + 105 + 110 + 125) / 9 = 114.44 (rounded to the nearest tenth)

To find the median, we first need to arrange the data set in ascending order:

100, 105, 110, 110, 110, 115, 120, 125, 135

Since the data set has an odd number of values, the median is the middle value, which is 110.

To find the standard deviation, we first need to calculate the variance. The variance is the average of the squared differences between each value and the mean. We can use the following formula to calculate the variance:

variance = [(value1 - mean)² + (value2 - mean)² + ... + (value9 - mean)²] / 9

Plugging in the values from the data set and the mean we calculated earlier, we get:

variance = [(135 - 114.44)² + (115 - 114.44)² + ... + (125 - 114.44)²] / 9

Simplifying this expression, we get:

variance = 102.46

The standard deviation is the square root of the variance, which is:

[tex]\sqrt{(102.46)[/tex] = 10.12 (rounded to the nearest tenth)

Therefore, the mean, median, and standard deviation of the given data set are approximately 114.4, 110, and 10.12, respectively.

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ANSWERS:

A. 0.28 ( 28.41% )
B. 89.29%

EXPLANATIONS:

(a) The probability of a randomly chosen U.S. adult investing in both stocks and fixed income instruments is given as 0.25. The probability of a U.S. adult investing in fixed income instruments is 0.88. Using the formula for conditional probability, we have:

P(invests in stocks | invests in fixed income instruments) = P(invests in both stocks and fixed income instruments) / P(invests in fixed income instruments)

= 0.25 / 0.88

= 0.2841 (rounded to the nearest hundredth)

Therefore, the probability that a randomly chosen U.S. adult invests in stocks, given that he or she invests in fixed income instruments is 0.28 (rounded to the nearest hundredth).

To convert A to a percentage, simply multiply it by 100:

A = 0.2841

A as a percentage = 0.2841 x 100% = 28.41% (rounded to two decimal places)

(b) The probability of a randomly chosen U.S. adult investing in both stocks and fixed income instruments is 0.25, and the probability of a U.S. adult investing in stocks is 0.28. Using the formula for joint probability, we have:

P(invests in both stocks and fixed income instruments) = P(invests in stocks) × P(invests in fixed income instruments)

= 0.28 × 0.88

= 0.2464

The probability that a randomly chosen stock investor also invests in fixed income instruments is 0.25 / 0.28 = 0.8929 (rounded to the nearest hundredth), which is equivalent to 89.29%.

How can a telephone survey of 1000 randomly selected US adults provide evidence that more than 1 in 4 US adults believe in ghosts?The survey results provide evidence that more than one in four US adults believe in ghosts. The telephone survey was conducted on a random sample of 1000 US adults. The survey found that 31 percent of US adults believed in ghosts.

To determine whether more than one in four US adults believe in ghosts, the null and alternative hypotheses will be tested.The null hypothesis in this scenario is that less than or equal to 25% of US adults believe in ghosts. The alternative hypothesis is that more than 25% of US adults believe in ghosts.Therefore, the level of significance (α) will be determined.

The α level is typically set to 0.05. This means that the likelihood of making a type I error is 5%. Then, the z-score will be calculated as follows:z = (0.31 - 0.25) / sqrt[(0.25 x 0.75) / 1000]z = 2.83The obtained z-score will be compared to the critical z-value using a z-distribution table. The critical z-value is 1.96. Since the obtained z-score is greater than the critical z-value, the null hypothesis will be rejected. Therefore, there is evidence to suggest that more than one in four US adults believe in ghosts.

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Therefore, the probability of both cubes showing a 4 is 1/36 or approximately 0.028 or 2.8%.

what is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur. Probability can also be expressed as a percentage between 0% and 100%, with 0% indicating impossibility and 100% indicating certainty.

In probability theory, the probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. For example, if you flip a fair coin, there are two possible outcomes: heads or tails. Since each outcome is equally likely, the probability of getting heads is 1/2 or 0.5 or 50%.

Assuming that the number cubes are fair and each face has an equal chance of landing face up, the probability of getting a 4 on any one of the cubes is 1/6, since there are six equally likely outcomes (numbers 1 to 6) and only one of them is a 4.

To find the probability of getting a 4 on both cubes, we need to multiply the probability of getting a 4 on the first cube by the probability of getting a 4 on the second cube, since the outcomes of the two cubes are independent of each other.

So, the probability of getting a 4 on both cubes is:

1/6 x 1/6 = 1/36

Therefore, the probability of both cubes showing a 4 is 1/36 or approximately 0.028 or 2.8%.

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Answer:

Step-by-step explanation:

17f+1i

6f+5f+4f=15f

11i+4i+10i=25i     ---------> 2f+1i

1feet=12inch

Solving the probability and permutations, we get (a) 20,160. (b) Larry, Moe, Curly, and Shemp can be arranged in the four front seats in 24 ways, and the ILB block can be arranged with the remaining students in 720 ways, and (c) 1/280.

(a) The number of possible seating arrangements can be calculated using the formula for permutations of n objects taken r at a time: P(n,r) = n!/(n-r)!. In this case, there are 8 students and 8 desks, so there are 8! possible seating arrangements.

To find the number of days before a seating arrangement is repeated, we need to subtract 1 from this number (since the first day is a unique arrangement) and divide by 2 (since there are two possible ways to arrange the students in any given seating arrangement, by simply rotating the arrangement). So the number of days before a seating arrangement is repeated is (8! - 1)/2 = 20,160.

(b) Larry, Moe, Curly, and Shemp must occupy the four front seats, so we need to choose four of the remaining four desks for the other students to sit at. This can be done in 4!/(4-4)! = 4! = 24 ways.

(c) We can treat the block of three students (ILB) as a single object, and then arrange the five remaining objects (M, O, A, X, and the ILB block) in a row. The ILB block can be arranged in 3! = 6 ways, and the other five objects can be arranged in 5! = 120 ways.

So the total number of potential seating arrangements in which ILB remains together is 6 x 120 = 720.

(d) The probability that Larry, Moe, Curly, and Shemp are sitting in the front seats is the number of possible seating arrangements in which they occupy the four front seats (24, from part b) divided by the total number of possible seating arrangements ([tex]8![/tex], from part a). So the probability is 24/8! = 1/280.

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The equation for the line of best fit is a useful tool in data analysis to describe the relationship between two Variables and make predictions based on that relationship.

The equation for the line of best fit is a mathematical formula that describes the relationship between two variables in a data set. It is used in regression analysis to estimate and predict the value of one variable based on the value of another.

To find the equation for the line of best fit, we use the method of least squares, which minimizes the sum of the squares of the differences between the observed data points and the predicted values from the equation.

The equation takes the form of y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept. The slope represents the rate of change of y with respect to x, and the y-intercept is the value of y when x = 0.

The coefficient of determination, denoted as r, is a measure of how well the line fits the data. It ranges from -1 to 1, where a value of 1 indicates a perfect fit, and a value of 0 indicates no correlation. A negative value indicates an inverse relationship.

In summary, the equation for the line of best fit is a useful tool in data analysis to describe the relationship between two variables and make predictions based on that relationship.

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Answer:

Either plane XYS or plane Q

Step-by-step explanation:

They are the only points lying on the plane in general.

Answer:

534×10³

5340×10²

53400×10

The probability that a person who purchased the game did not see the advertisement is:0.659.

what is  probability?

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain. Probability is used in many areas, including statistics, mathematics, science, finance, and gambling.

In the given question,

To solve this problem, we will use Bayes' theorem, which allows us to update our beliefs about the probability of an event based on new information.

Let A be the event that a person has seen the advertisement, and B be the event that a person has purchased the game. We want to find the probability of A given B, i.e., the probability that a person who has purchased the game has also seen the advertisement.

We know that P(A) = 0.24 (24% of the market has seen the advertisement), P(B|A) = 0.42 (42% of those who see the ad have purchased the game), and P(~A|~B) = 0.93 (93% of those who have not seen the advertisement have not purchased the game).

We can use the complement rule to find P(B|~A), the probability of purchasing the game given that the person has not seen the advertisement:

P(B|~A) = 1 - P(~B|~A) = 1 - 0.93 = 0.07

Now we can use Bayes' theorem:

P(A|B) = P(B|A) * P(A) / P(B)

where P(B) = P(B|A) * P(A) + P(B|~A) * P(~A)

Plugging in the values, we get:

P(B) = 0.42 * 0.24 + 0.07 * (1 - 0.24) = 0.2956

P(A|B) = 0.42 * 0.24 / 0.2956 = 0.3408

Therefore, the probability that a person who purchased the game did not see the advertisement is:

1 - P(A|B) = 1 - 0.3408 = 0.659

Rounded to the nearest thousandth, the answer is 0.659.

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The question you posted is incomplete and does not have a table to complete. Can you please provide the table or the missing information so that I can answer your question properly?

The value of Z is -66.7

What is an inverse function?

An inverse in mathematics is a function that "undoes" another part. In other words, if f(x) produces y, y entered into the inverse of f producing x. An invertible function has an inverse, and the inverse is represented by the symbol f1.

Here, we have

Given: Suppose x varies directly as y, and x varies inversely as z.

Find z when x= 10 and y= −7, if z= 20 when x= 6 and y= 14.

X = K(Y/Z) if x =10, y=-7, Z=20

substituting in the equation 10 = K(-7/20)

solving for K = -28.6

When x = 6, Y = 14, and K(constant) = -28.6

6 = -28.6(14/Z)

solving for Z by cross multiplication, we get

Z = -66.7

Hence, the value of Z is -66.7

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We have: P(brown then yellow) = 2/11 and P(green then green) = 2/132.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

let's calculate the probability of selecting a brown marble followed by a yellow marble without replacement:

P(brown then yellow) = (4/12) * (6/11) = 24/132 = 2/11

We multiply 4/12 (the probability of selecting a brown marble on the first draw) by 6/11 (the probability of selecting a yellow marble on the second draw, after one brown marble has already been removed). Note that we divide by 11 on the second draw, as there are now only 11 marbles left in the bag.

Now let's calculate the probability of selecting two green marbles without replacement:

P(green then green) = (2/12) * (1/11) = 2/132

We multiply 2/12 (the probability of selecting a green marble on the first draw) by 1/11 (the probability of selecting another green marble on the second draw, after one green marble has already been removed). Again, note that we divide by 11 on the second draw, as there are now only 11 marbles left in the bag.

So, we have:

P(brown then yellow) = 2/11

P(green then green) = 2/132

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The child should be given 8.75 mL of the medicine. option B

To determine the correct dosage, we first need to find out how much paracetamol the child needs based on their weight and then convert that amount to the appropriate volume of the medicine.

Calculate the required amount of paracetamol based on the child's weight:

Child's weight: 14 kg

Dosage: 15 mg per 2 kg of body weight

Required_paracetamol = (Child's weight / Dosage per kg) * Dosage

Required_paracetamol = (14 kg / 2 kg) * 15 mg

Required_paracetamol = 7 * 15 mg

Required_paracetamol = 105 mg

The child needs 105 mg of paracetamol.

Convert the required paracetamol amount to the appropriate volume of the medicine:

Medicine concentration: 120 mg of paracetamol per 10 mL

Required_volume = (Required_paracetamol / Medicine concentration) * 10 mL

Required_volume = (105 mg / 120 mg) * 10 mL

Required_volume = 0.875 * 10 mL

Required_volume = 8.75 mL

The child should be given 8.75 mL of the medicine.

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The option B is the correct answer for the above question. The line of symmetry should have been 4 instead -4 is correct.

Line of symmetry - A line of symmetry is a line in mathematics that splits a form or object into two congruent halves, such that if one portion is reflected over the line of symmetry, it will coincide with the other component. A line of symmetry is also known as an axis of symmetry.

Now, we will see to find the line of symmetry for the quadratic equation [tex]f(x) = x^2 - 8x + 15[/tex],

Line of symmetry: [tex]x = \frac{-b}{2a}[/tex]

Vertex: [tex](x,y) = (\frac{-b}{2a}, f(\frac{-b}{2a}))[/tex]

where a, b, and c are the coefficients of the quadratic equation [tex]ax^2 + bx + c.[/tex]

In this case, [tex]a = 1, b = -8, and\ c = 15[/tex], so we can substitute these values into the formulas:

Line of symmetry: [tex]x = \frac{-(-8)}{21} = 4[/tex]

And, From this value of x, we will get the correct value of y.

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Answer: 7

Step-by-step explanation:

If you draw it out, you can visually tell it's 5 units, but you can also tell by looking at the two distinct y values, -2 and 5. The distance between them is 7 units, as you take the absolute value of both of them, then add to get 7.

Answer: I would say 21 feet.

Step-by-step explanation:

Bernard is 12 feet ahead of Austin

So add 12 feet to get to Austin first

Then add the 9 feet that is apart from Austin and Bernard

12+9 = 21

21 feet would be the answer

Hope this helps ! ^^

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Answer:

Area of the rectangle - 144 in^2

Area of the circle - 28,26 in^2

Total shaded area - 115,74 in^2

Step-by-step explanation:

[tex]a(rectangle) = 18 \times 8 = 144 \: {in}^{2} [/tex]

[tex]a(circle) = \pi \times {r}^{2} = {3}^{2} \times \pi = 9\pi = 9 \times 3.14 = 28.26 \: {in}^{2} [/tex]

[tex]a(shaded) = a(rectangle) - a(circle)[/tex]

[tex]a(shaded) = 144 -28.26 = 115.74 \: {in}^{2} [/tex]

[tex]\begin{array}{cccccccccc} &\frac{-1}{4}\left( -\frac{1}{2} \right)&\frac{1}{8}\left( -\frac{1}{2} \right)&\frac{-1}{16}\left( -\frac{1}{2} \right)&\frac{1}{32}\left( -\frac{1}{2} \right)\\ -\cfrac{1}{4}&\cfrac{1}{8}&-\cfrac{1}{16}&\cfrac{1}{32}&-\cfrac{1}{64}... \end{array}\hspace{5em}\stackrel{\textit{common ratio}}{r=-\frac{1}{2}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\qquad \qquad \textit{sum of a finite geometric sequence} \\\\ \displaystyle S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\qquad \begin{cases} n=\textit{last term's}\\ \qquad position\\ a_1=\textit{first term}\\ r=\textit{common ratio}\\[-0.5em] \hrulefill\\ r=-\frac{1}{2}\\ a_1=-\frac{1}{4} \end{cases}\implies \sum_{n=1}^{n=4}~-\frac{1}{4}\left( -\frac{1}{2} \right)^{n-1}[/tex]

Answer:

1.5 m

Step-by-step explanation:

Volume = base * height

12 = 8 * h

12/8 = h

1.5 = h

Answer:

Step-by-step explanation:

Surface area of a cylinder = 2πr(r + h)

radiius = 1/2 diameter so the radius is 1/2 of 2 = 1

Surface are = 2(22/7)(1 )[(1 + 1.25)]

                     44/7 (2.25) = 99/7

This is for ONE muffin - mulitply by 6 to find out how much paper for

6 muffins,

6 × 99/7 = 594/7 = 84 6/7 in²

Answer:

Step-by-step explanation:

You are looking for 1/2 of an unknown number minus 19.  It will equal -13.

                                                                                                  1/2x - 19 = -13

Get x isolated, so add 19 on left to cancel, then add on right)     +19    +19                                                                                                

                                                      And you now are down to   1/2 x      =   6  

Now, let's simplify the fraction (1/2).  Since it is 1 divided by 2, you reverse division with multiplication. Multiply 1/2 by the denominator (2) and you get 1. So, you're down to 1x, or just x.   Then multiply the number on the other side of the equal sign (the 6) by 2 and you get 12.

So x = 12.

Now, let's go back to our original equation and plug in the x and see if it works.

1/2x - 19 = -13

becomes 1/2 (12) - 19 = -13

becomes 6 - 19 = -13

Voila! Our missing number (x) is 12.

The median of the samples can give an idea of the central tendency of the data and can help in making an inference about the population.

In this case, since the percent of students that bike to school varies from 20% to 50% in the samples, the median of the samples can provide an estimate of the median percent of students who bike to school in the population.

By analyzing the median of the samples, it may be possible to make an inference about the central tendency of the population, which could inform decisions about encouraging or improving biking to school.

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--The given question is incomplete, the complete question is given

"  a group of friends wants to know how many students bike to school. Survey Results In the samples, the percent of students that bike to school varies from 20% to 50% 19 20 21 22 14 15 16 17 18 Number of Students that Bike to School How can the median of the samples help you make an inference about the population? "--

The tree's height changes 2.5ft bases per time.

The rate of change function is defined as the rate at which one volume changes relative to another volume. In simple terms, the rate of change is the quantum of change in one item divided by the corresponding quantum of change in another.

We can find the rate of change in the tree's height by calculating the slope of the line that represents the direct function relating the tree's height to the number of times since it was planted.

To do this, we can use the slope formula

Slope = ( change in height)/( change in time)

Let's choose the points

( 1,4.5) and( 4, 12)

Change in height = 12-4.5 = 7.5

Change of time = 4- 1 = 3

Slope = (7.5/ 3) = 2.5

So, the tree's height changes 2.5 bases per time.

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