If a point is chosen inside the regular polygon, what is the probability that the point
chosen is inside the right triangle outlined? Round to the nearest hundredth. Area:
Reg. Polygon=aP/2

Answer: 6

Step-by-step explanation:

If you divide both sides by 63 it isolates the t and leaves you with 6=t.

The first five terms in the recursive sequence are: 2, 3, 6, 18, 108.

First five terms of the recursive sequence defined by a1 = 2, a2 = 3, and an = an-2 * an-1.
1. First term (a1): Given as 2.
2. Second term (a2): Given as 3.
3. Third term (a3): To find a3, use the formula an = an-2 * an-1. In this case, n = 3, so a3 = a1 * a2 = 2 * 3 = 6.
4. Fourth term (a4): Similarly, to find a4, use the formula with n = 4. So a4 = a2 * a3 = 3 * 6 = 18.
5. Fifth term (a5): Finally, to find a5, use the formula with n = 5. So a5 = a3 * a4 = 6 * 18 = 108.
The first five terms in the recursive sequence are: 2, 3, 6, 18, 108.

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(a) The probability of a random high school student having an IQ score between 60 and 75 points is approximately 0.186. (b) About 6.5% of high school students will require special attention based on IQ scores below 55 or above 100 points. (c) The cutoff IQ score to be a member of Mensa International is approximately 105.

To solve these problems, we will use the standard normal distribution, also known as the Z-distribution. We'll need to calculate z-scores and use the z-table or technology to find probabilities.

(a) To find the probability that a high school student chosen at random has an IQ score between 60 and 75 points, inclusive, we need to calculate the area under the normal curve between these two values.

First, we convert the IQ scores to z-scores using the formula:

z = (x - μ) / σ

where x is the value we want to convert, μ is the mean, and σ is the standard deviation.

For 60 points:

z1 = (60 - 80) / 12 = -1.6667

For 75 points:

z2 = (75 - 80) / 12 = -0.4167

Next, we use technology or a z-table to find the probabilities associated with these z-scores:

P(-1.6667 ≤ Z ≤ -0.4167)

Using technology or a z-table, the probability comes out to be approximately 0.186.

Therefore, the probability that a high school student chosen at random has an IQ score between 60 and 75 points, inclusive, is 0.186.

(b) To find the proportion of high school students who will need special attention, we need to calculate the area under the normal curve below 55 points (z ≤ (55 - 80) / 12) and above 100 points (z ≥ (100 - 80) / 12).

P(Z ≤ -2.0833) + P(Z ≥ 1.6667)

Using technology or a z-table, we find the probabilities:

P(Z ≤ -2.0833) ≈ 0.018

P(Z ≥ 1.6667) ≈ 0.047

Adding these probabilities, the proportion of high school students who will need special attention is approximately 0.018 + 0.047 = 0.065.

Therefore, about 6.5% of high school students will need special attention.

(c) To determine the cutoff IQ score to be a member of Mensa International, we need to find the value corresponding to the 98th percentile of the standard normal distribution.

We want to find the IQ score x such that P(Z ≤ z) = 0.98.

Using technology or a z-table, we find the z-score corresponding to a cumulative probability of 0.98 is approximately 2.055.

Now, we solve for x in the z-score formula:

2.055 = (x - 80) / 12

Simplifying and solving for x:

24.66 = x - 80

x = 24.66 + 80

x ≈ 104.66

Therefore, the cutoff IQ score to be a member of Mensa International would be 105 (rounded to the nearest whole number).

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The trigonometric equation is (sinθ+cosθ)²−(sinθ−cosθ)² is equal to 2sin2θ

We can use the identity (a+b)² = a² + 2ab + b² to simplify the left-hand side of the equation:

The trigonometric expression is (sinθ+cosθ)²−(sinθ−cosθ)²

Expand the trigonometric expression by using the identity  (a+b)² = a² + 2ab + b²

(sinθ+cosθ)² will be sin²θ + 2sinθcosθ + cos²θ

(sinθ−cosθ)² is sin²θ - 2sinθcosθ + cos²θ

Now plug in these in the above trigonometric equation

= sin²θ + 2sinθcosθ + cos²θ - (sin²θ - 2sinθcosθ + cos²θ)

= sin²θ + 2sinθcosθ + cos²θ - sin²θ + 2sinθcosθ - cos²θ

= 4sinθcosθ

= 2 × 2sinθcosθ

= 2sin2θ

Hence, the trigonometric equation is (sinθ+cosθ)²−(sinθ−cosθ)² is equal to 2sin2θ

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There are several formulas for finding the area, volume, and perimeter of different shapes. Some examples are: [tex]P = 2(l + w)[/tex], [tex]A = lw[/tex], and [tex]V = lwh[/tex]

Perimeter:

Area:

Volume:

Note: This question is incomplete. Here is the complete question:

What is the formula of perimeter, area and volumen of rectangle, square, and circle

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Ivan has created 9 sculptures.

We know, ratio is a comparison between two quantities or numbers. It expresses how many times one quantity is contained in another or how the two quantities relate to each other.

To find the number of sculptures he has created, we need to divide the number of paintings by the ratio of paintings to sculptures.

Number of paintings: 54

Ratio of paintings to sculptures: 6 paintings : 1 sculpture

Number of sculptures

= Number of paintings / Ratio of paintings to sculptures

= 54 / (6/1)

= 54 / 6

= 9

Therefore, Ivan has created 9 sculptures.

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Answer:

Step-by-step explanation:

Given that vector (g, h) moves a shape g squares right and h squares up, you want the description for the vector (7, 9).

As with a numerical expression, you can substitute the values for the letters in the English description. When (g, h) = (7, 9), it means "g" can be replaced by "7" and "h" can be replaced by "9". The sentence with these replacements is ...

  vector (7, 9) moves a shape 7 squares right and 9 squares up

__

Additional comment

It's not math. It's reading comprehension.

<95141404393>

Answer:

option 2

Step-by-step explanation:

They both travel x miles per week

option 1: SUV (15 + 1)mpg + hybrid (65)mpg = 81combined mpg

option 2: SUV (15)mpg + hybrid (80) mpg = 95 combined mpg

getting 95mpg is better than 81mpg.

so they should choose option 2

If the coach was to pick the player based on the best average, the coach would choose Jessie.

If the coach is picking based on who has been the most consistent, they would pick Sam.

The average for Jessie is :

= ( 150 + 145 + 181 + 235 + 196 + 211 + 204 + 221 + 185 ) / 9

= 192 points

The average for Sam :

= ( 186 + 187 + 192 + 195 + 194 + 157 + 157 + 162 + 200 ) / 9

= 181 points

The coach would pick Jessie based on average.

For consistency, we can use the measure of variability of range. The range for Jessie is:

= 235 - 145

= 90 points

The range for Sam would be:

= 200 - 157

= 43 points

This shows that Sam is more consistent and so would be picked based on consistency.

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The measure of angles ∠1 and ∠2 is 72 and 54.

Option C is the correct answer.

We have,

The total angle of a polygon can be found using the formula:

total angle = (n - 2) x 180 degrees

So,

The given polygon is a pentagon (5 sides).

n = 5

Now,

Total angle.

= (5 -2) x 180

= 3 x 180

= 540

Now,

There are 5 angles that make 540.

So,

1 angle = 540/5 = 108

And,

One angle is split into two where one is ∠2.

So,

∠2 = 108/2

∠2 = 54

Now,

We can see that ∠2 and ∠1 form a triangle.

Where the other angle is equal to ∠2.

So,

∠2 + ∠2 + ∠1 = 180

∠1 = 180 - (54 + 54)

∠1 = 180 - 108

∠1 = 72

Thus,

The measure of angles ∠1 and ∠2 is 72 and 54.

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We need to use the fact that the percentages of all three categories must add up to 100%. Therefore, the percentage of independent voters can be found by subtracting the percentages of democrat and republican voters from 100%.
Percentage of independent voters = 100% - 35% - 40% = 25%
So, 25% of the registered voters are independent.
In conclusion, the percentage of independent voters is 25%. This is because the percentages of democrat, republican, and independent voters must add up to 100%. The percentages of democrat and republican voters are given, so we can find the percentage of independent voters by subtracting those from 100%.
Based on the given information, 35% of registered voters are classified as Democrats, and 40% are classified as Republicans. To find the percentage of registered voters who are independent, we need to subtract the total percentage of Democrats and Republicans from 100%.
100% - (35% + 40%) = 100% - 75% = 25%
Therefore, 25% of the registered voters are classified as independent.

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The graphs of l₁ and l₂ for x from -4 to 6 is attached

From the question, we have the following parameters that can be used in our computation:

y = 1/2x + 3

y = x + 6

The domain is given as

x = -4 to 6

So, we plot the graph of the functions in this domain

See attachment for the graphs

A linear function is represented as

y = mx + c

Where

Gradient = m

So, we have

y = 1/2x + 3 => Gradient = 1/2

y = x + 6  => Gradient = 1

The coordinates of the point when l₁ cuts l₂​ is the point were the lines of both equations intersect

Using the graph plot in (a), the coordinates of the point when l₁ cuts l₂​ does not exist

This is because the lines do not intersect in the given domain

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Answer:

The 95% confidence interval for the population proportion of all persons who do not have any health insurance is (0.148, 0.192).

Here is the calculation:

Sample size = 800

Number of persons who do not have any health insurance = 120

Sample proportion = 120 / 800 = 0.15

Confidence level = 95%

Z-critical value for 95% confidence level = 1.96

Confidence interval = (sample proportion - Z-critical value * standard error of the sample proportion, sample proportion + Z-critical value * standard error of the sample proportion)

Standard error of the sample proportion = sqrt(sample proportion * (1 - sample proportion) / sample size)

Standard error of the sample proportion = sqrt(0.15 * (1 - 0.15) / 800) = 0.0128

Confidence interval = (0.15 - 1.96 * 0.0128, 0.15 + 1.96 * 0.0128)

Confidence interval = (0.148, 0.192)

Step-by-step explanation:

Two years from now, there will be a total of 36 lakh (3.6 million) students using Khan Academy in India.

If 16 lakh students in India are currently using Khan Academy, and the number of users is expected to grow by 50% every year, then the number of users two years from now can be calculated as follows:
- After one year: 16 lakh x 1.5 = 24 lakh
- After two years: 24 lakh x 1.5 = 36 lakh
Therefore, two years from now, it is expected that 36 lakh students in India will be using Khan Academy.
To calculate the number of students using Khan Academy in India two years from now, we'll use the given growth rate of 50% per year.
Currently, there are 16 lakh (1.6 million) students using Khan Academy. After the first year, the number of users will grow by 50%, which is an increase of 8 lakh (0.8 million) students. This will bring the total to 24 lakh (2.4 million) students.
After the second year, the number of users will again grow by 50%. This time, the increase will be 12 lakh (1.2 million) students. So, two years from now, there will be a total of 36 lakh (3.6 million) students using Khan Academy in India.

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Answer:

15 + c ≤ 345

Step-by-step explanation:

Inequality is a mathematical statement that compares two algebraic expressions using the symbols < , > , ≠ ,≤ or ≥.

          'c' is the total cost of all the items sold. The total order should not exceed 345. This 345 includes the total cost and the shipping fee.

     15 + c ≤ 345

The length of the third side is 4.

Given information:

A right-angled triangle is provided in the diagram.

So, as per the diagram,

The hypotenuse leg = √(97)

Opposite leg = 9

Let the length of the adjacent leg, which is the third side be x. By the Pythagorean theorem, we have:

x² + 9² = √(97)²

Simplifying the right side, we get:

x² + 81 = 97

Subtracting 81 from both sides, we get:

x² = 16

Apply square root property, we get,

x = +/- 4

Since the length of a side of a triangle must be positive, the length of the third side is 4.

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The sum of the 4th and 6th square numbers is 52.

The formula for the nth square number is as below

n²

Using this formula we can find the 4th and 6th square numbers

4th square number = 4² = 16

6th square number = 6² = 36

The sum of the 4th and 6th square numbers is solved by addition

16 + 36 = 52

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True.

The expression c(n,r), also known as "n choose r" or the binomial coefficient, represents the number of ways that r elements can be selected from a set of n elements without regard to order. It is commonly used in combinatorics, probability, and statistics. The formula for c(n,r) is c(n,r) = n!/r!(n-r)!, which can be calculated using factorials.

For example, c(5,2) = 10, which represents the number of ways to choose 2 elements from a set of 5 elements (i.e., {1,2}, {1,3}, {1,4}, {1,5}, {2,3}, {2,4}, {2,5}, {3,4}, {3,5}, {4,5}).

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Understanding the truth values and logic behind these statements is important to correctly determine their validity. The questions that are True are B and D, and the questions that are A, C, and E.

a. False. In a conditional statement, if the antecedent (the "if" part) is false, the truth value of the conditional statement depends on the truth value of the consequent (the "then" part). If the consequent is true, the conditional statement is true, but if the consequent is false, the conditional statement is false.

b. True. In a disjunction (logical OR), if at least one of the disjuncts is true, then the entire disjunction is true. It only takes one true statement for the disjunction to be true.

c. False. Similar to statement a, if the consequent of a conditional statement is false, the truth value of the conditional statement depends on the truth value of the antecedent. If the antecedent is true, the conditional statement is true, but if the antecedent is false, the conditional statement is false.

d. True. In a conjunction (logical AND), for the entire conjunction to be true, all conjuncts must be true. If one conjunct is true, it guarantees that the conjunction will be true.

e. False. In a conjunction (logical AND), if at least one conjunct is false, the entire conjunction is false. All conjuncts must be true for the conjunction to be true. If any conjunct is false, the conjunction will be false.

Therefore, it's important to understand the truth values and logic behind these statements to correctly determine their validity.

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The correct answer is Pelicans. they have a larger mean value of about 22.5 inches.To determine which team has the largest overall size hat for their players, we can compare the measures of center for the two teams. The measures of center commonly used are the median and the mean.

To find the median, we arrange the hat sizes in ascending order and find the middle value. For the Pelicans, when we arrange their hat sizes in ascending order, we get:

21 21.5 22 22 22.5 23 23.5 24 24.5

The median is the middle value, which is 22.5 inches

.For the Falcons, when we arrange their hat sizes in ascending order, we get:

20 20.5 21 21.5 22 22.5 23 23.5 24 24.5

The median is also 22.5 inches.

Since both teams have the same median value, we need to compare the mean. To find the mean, we sum up all the hat sizes and divide by the total number of measurements.

For the Pelicans, the sum of their hat sizes is 22 + 21 + 22 + 22 + 23.5 + 22 + 23 + 24 + 21.5 + 24.5 = 225 inches.

Dividing by 10 (the number of measurements) gives a mean value of 22.5 inches.

For the Falcons, the sum of their hat sizes is 20 + 20.5 + 21 + 21.5 + 22 + 22.5 + 23 + 23.5 + 24 + 24.5 = 222 inches.Dividing by 10 (the number of measurements) gives a mean value of 22.2 inches.

Comparing the means, the Pelicans have a larger mean value of about 22.5 inches compared to the Falcons' mean value of about 22.2 inches.

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To draw a table of values for the first 6 natural numbers, draw the rows and columns and input the numbers 1, 2, 3, 4, 5, and 6 against the variables being compared.

A table is a visual representation that is used to compare two or more variables. To draw this sort of table for natural numbers, you need to insert 6 rows to contain all of the numbers.

The number of columns that will e drawn depends on the variable or variables that you are checking. The first 6 natural numbers are numbers 1 to 6.

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The method used to determine the probability of a family having six girls, based on a survey of 1000 families with six children, is the classical method.

The classical method involves calculating probabilities based on the assumption of equally likely outcomes and known sample spaces. In this case, the sample space consists of all possible combinations of genders for six children, and the probability of a family having six girls is calculated as the ratio of the favorable outcome (one specific combination) to the total number of outcomes (all possible combinations).

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Answer:

Sure. Here are the steps on how to construct a confidence interval at a 95% confidence level for the mean amount spent on a child's last birthday gift:

Identify the sample size, n. In this case, n=13.

Identify the sample mean,  

x

ˉ

. In this case, $\bar{x} = $36.

Identify the sample standard deviation, s. In this case, $s = $15.

Identify the t-critical value, t. The t-critical value is the value that cuts off 2.5% of the distribution in each tail, leaving 95% of the distribution in the middle. To find the t-critical value, we need to know the degrees of freedom, df. The degrees of freedom are calculated as df=n−1. In this case, df=13−1=12.

We can find the t-critical value using a t-distribution table. The t-distribution table shows the t-critical values for different degrees of freedom and different confidence levels. For a 95% confidence level and 12 degrees of freedom, the t-critical value is 2.179.

Calculate the confidence interval. The confidence interval is calculated as follows:

$\bar{x} \pm t \cdot \frac{s}{\sqrt{n}}$

In this case, the confidence interval is:

$36 \pm 2.179 \cdot \frac{15}{\sqrt{13}} = (27.28, 44.72)$

Therefore, a 95% confidence interval for the mean amount spent on a child's last birthday gift is $27.28 to $44.72.

Step-by-step explanation:

Step-by-step explanation:

Decimal interset per period (day) = .05/365

# periods = 365 *6 = 2190

FV = 15800 ( 1 + .05/365)^2190  = 21327.33 Euros

We can use the equation for the angle of the bright fringes in a double-slit experiment. The answer is D. 15.1o.

where θ is the angle of the bright fringe, m is the order of the fringe (in this case, m=3), λ is the wavelength of the incident light, and d is the distance between the slits.

Plugging in the given values, we get:

sinθ = (3)(5.04x10^-7m)/(5.82x10^-5m) = 0.260

Taking the inverse sine of both sides, we get:

θ = sin^-1(0.260) = 15.1o

Therefore, the answer is D. 15.1o.

To find the angle of the 3rd order bright fringe, we can use the formula for the double-slit interference pattern:

mλ = d * sinθ

where m is the order number (3 in this case), λ is the wavelength of the incident light (5.04x10^-7 m), d is the distance between the slits (5.82x10^-5 m), and θ is the angle we want to find.

First, rearrange the formula to solve for the angle:

sinθ = (mλ) / d

Now, plug in the given values:

sinθ = (3 * 5.04x10^-7 m) / 5.82x10^-5 m

Calculate the result:

sinθ = 0.02594

Now, find the inverse sine (arcsin) of the result to get the angle:

θ = arcsin(0.02594) ≈ 1.49°

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The value of x in the chord intersection is 16 units.

The intersecting chord theorem  states that the products of the lengths of the line segments on each chord are equal. In other words, If two chords intersect in a circle , then the products of the measures of the segments of the chords are equal.

Therefore, lets find the value of x in the intersecting chords as follows:

15 × x = 24 × 10

15x = 240

divide both sides of the equation by 15

x = 240 / 15

x = 16

Therefore,

x = 16 units

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The subshell designated by each set of quantum numbers is as follows:

a) n=3, l=1 -> 3p subshell

b) n=4, l=2 -> 4d subshell

c) n=2, l=0 -> 2s subshell

d) n=5, l=3 -> 5f subshell

In the electron configuration of an atom, each electron is described by a set of four quantum numbers, which includes the principal quantum number (n), the angular momentum quantum number (l), the magnetic quantum number (m), and the spin quantum number (s). The second quantum number (l) determines the shape of the subshell, which in turn influences the energy level and chemical behavior of the atom. The letter designation for each subshell is based on the value of the angular momentum quantum number (l): s (l=0), p (l=1), d (l=2), f (l=3), and so on. Therefore, for a given set of quantum numbers, we can determine the subshell designation by identifying the value of l.

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The measure of I'J' is 18 units.

We have,

Scale factor= 2

length of IJ = 9

Now, If the segment IJ is dilated by a scale factor of 2, the length of I'J' will be:

I'J' = 2 x IJ

I'J' = 2 x 9

I'J' = 18

Therefore, the measure of I'J' is 18 units.

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Answer: A

Step-by-step explanation: Both distributions are symmetrical, so standard deviation and the mean will be the most useful for comparison because they give more information on the different values in the distribution and their likelihood.

The solution is: 90, 86, 92 and 89 could be Brooke’s sixth quiz score

Here, we have,

step 1

Find the mean

To do this, add all the numbers, then divide by the number of numbers there are.

so

mean = 85.60

step 2

if after taking the sixth quiz, Brooke’s mean score increased

then

the sixth score of Brooke's quiz must be higher than the mean obtained in the first 5 quizzes

case a)

85 < 85.60------> is not a solution

case b)

90 > 85.60------> is a solution

case c)

83< 85.60------> is not a solution

case d)

86 > 85.60------> is a solution

case e)

92 > 85.60------> is a solution

case f)

89 > 85.60------> is a solution

so, we get,

the answers are

90, 86, 92 and 89

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the complete question is

Brooke has scores of 84, 72, 90, 95, and 87 on her first five quizzes. After taking the sixth quiz, Brooke’s mean score increased.

Which could be Brooke’s sixth quiz score? Check all that apply.

85

90

83

86

92

89