the factory will not ship a box of 16 if the average weight of the baseballs in the box exceeds 147 grams. what is the probability that a pack of 16 baseballs would have an average weight of more than 147 grams?

(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 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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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:

pear

Step-by-step explanation:

60/5 = 12

72/8 = 9

so one pear is cheaper than one apple

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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Step-by-step explanation:

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

# periods = 365 *6 = 2190

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

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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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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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

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:

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 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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The height of the new pasta box designed by Kevin is 9 in and the area of the base is 9 in². Kevin’s boss has said that there must be at least 2 in of space between the top of the pasta and the top of the box. Will the pasta fit in the new box with enough space at the top.

Kevin's boss has indicated that there should be at least 2 inches of space between the top of the pasta and the top of the box. This indicates that the maximum capacity of the box will be reduced by this amount.The volume of the pasta box can be calculated as the product of the height and the area of the base. Here's how:Volume of the box = Height × Area of the base Given that the height of the box is 9 inches and the area of the base is 9 square inches.

Thus, the volume of the box is:V = Height × Area of the baseV = 9 × 9V = 81 cubic inchesHowever, the boss has said that at least 2 inches of space must be left between the top of the pasta and the top of the box. This implies that the pasta must occupy a volume that is less than or equal to 81 − 2 = 79 cubic inches.Therefore, the pasta will fit into the new box with enough space at the top since 79 cubic inches are greater than or equal to the volume of pasta in the box.

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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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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:

£200

Step-by-step explanation:

To determine how many pounds Jenny got back, we first need to calculate the exchange rate between pounds (£) and dollars ($).

Jenny initially changed £480 into $744, so £480 = $744.

To find the exchange rate in terms of pounds (£) to dollars ($), divide both quantities by 480:

[tex]\dfrac{480}{480}=\dfrac{744}{480}[/tex]

[tex]\£1=\$1.55[/tex]

Therefore, the exchange rate was £1 = $1.55.  

This means that for every £1 Jenny exchanged, she received $1.55.

To convert the $310 Jenny had left back into pounds (£), divide the dollar amount by 1.55:

[tex]\dfrac{310}{1.55}=200[/tex]

Therefore, if the exchange rate stayed the same, Jenny got back £200.

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:

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 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: 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 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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To answer this question, we need to look at the data from part (a) and only consider the people who named a rainbow color. Out of those people, we can see that 35% preferred red.

To calculate the percentage, we can divide the number of people who preferred red (14) by the total number of people who named a rainbow color (40), and then multiply by 100.
So, (14/40) x 100 = 35%.
Therefore, 35% of the people who named a rainbow color preferred red. It's important to note that this percentage only applies to the subset of people who named a rainbow color, not the entire group of people surveyed.
Overall, it's always important to clarify the specific subset of data you're analyzing when discussing percentages or statistics.

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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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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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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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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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The conclusion that "all employees who attend the sales training program and who attend the technical training program are in department B" does not necessarily follow from the given assumptions.

The assumptions state that all employees in department A attend the sales training and employees in department A attend the technical training. It also mentions that employees who attend both training programs are in department B. However, it does not provide any information about employees who only attend one of the training programs.

Based on the given information, we cannot conclude that all employees who attend both training programs are in department B. There could be employees from department A who attend both programs and employees from department B who only attend one of the programs.

Therefore, the conclusion cannot be determined solely based on the given assumptions. Additional information about the distribution of employees across departments and their training program attendance is needed to draw a conclusive statement about the department affiliation of employees attending both training programs.

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The given integral is: ∫∫R 5/√(2) xy dA, where R is the region in the xy-plane bounded by the curves y = 0, x = √(25 - y^2) and x = 0. The volume of the solid is (5^5/8) cubic units.

Converting to polar coordinates, we have:

x = r cos(θ), y = r sin(θ), and the limits of integration become:

0 ≤ θ ≤ π/2, 0 ≤ r ≤ 5.

Also, the differential of area becomes dA = r dr dθ.

Substituting for x and y, and dA, we have:

∫∫R 5/√(2) xy dA = ∫θ=0π/2 ∫r=0^5 5/√(2) (r cos(θ)) (r sin(θ)) r dr dθ

= 5/√(2) ∫θ=0π/2 ∫r=0^5 r^3 cos(θ) sin(θ) dr dθ

= 5/√(2) ∫θ=0π/2 [sin(θ)/4] ∫r=0^5 r^4 cos(θ) dr dθ

= 5/√(2) ∫θ=0π/2 [sin(θ)/4] [(5^5 cos(θ))/5] dθ

= (5^5/4√(2)) ∫θ=0π/2 sin(θ) cos(θ) dθ

= (5^5/8)

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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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