There are 56 different ways to select three different integers from 1 to 10 such that no two chosen integers are consecutive.
To determine the number of ways to select three different integers from 1 to 10 such that no two chosen integers are consecutive, we can use combinatorics principles.
First, let's consider the total number of ways to choose three integers without any restrictions. This can be calculated using the combination formula:
C(n, r) = n! / (r!(n-r)!)
In this case, we have 10 integers to choose from, and we want to choose 3. Therefore, the total number of ways to choose three integers without any restrictions is:
C(10, 3) = 10! / (3!(10-3)!) = 10! / (3!7!) = 120
Now, let's consider the restricted condition that no two chosen integers can be consecutive. We can approach this by selecting three non-consecutive integers from the available set.
To do this, we can start by choosing any integer, then excluding its two adjacent integers. For example, if we choose 1, we cannot choose 2 or 3. Similarly, if we choose 10, we cannot choose 9 or 8.
Since there are two adjacent integers to exclude for each choice, we have 8 integers remaining to choose from. Therefore, the number of ways to select three non-consecutive integers is:
C(8, 3) = 8! / (3!(8-3)!) = 8! / (3!5!) = 56
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Mr. Jacobs is going to make a histogram of the test scores from the last math test he gave. He plans to first organize the data into a stem-and-leaf plot and then make the histogram from the stem-and-leaf plot. The test scores are listed below.
79, 82, 65, 61, 94, 97, 84, 77, 89, 91, 90, 83, 99, 71, 68, 77, 87, 85
How many bars will his histogram have?
4
6
3
5
The answer could be that Mr. Jacobs's histogram will have 4 bars.
The test scores are listed below;
79, 82, 65, 61, 94, 97, 84, 77, 89, 91, 90, 83, 99, 71, 68, 77, 87 and, 85
We have that the range of the data is from 61 to 99. To create the bars for the histogram, we need to divide this range into intervals.
In that case, the intervals would be:
60-69
70-79
80-89
90-99
thus, the histogram would have 4 bars.
Therefore, Mr. Jacobs's histogram will have 4 bars.
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Answer: that would be 4
Step-by-step explanation: there would be 3 numbers in the 60-69 range, 4 numbers that fall into the 70-79 range, 6 numbers that fall into the 80-89 range, and 5 numbers that fall into the 90-99 range. The interval with more data than any other is the 80-89 range, therefore, making it the mode interval. i hope this helps
What percent of 25.is 12
Answer:
48%
Step-by-step explanation:
Let x equal the percent
25x = 12
25x/25 = 12/25
x =0.48
0.48 = 48%
an rn is preparing to administer 5% dextrose 1000ml iv infusion over 8 hours via an infusion pump. how many ml/hours the rn should set up the infusion pump? round to nearest complete number
Answer:
The RN should set up the infusion pump to deliver 125 mL/hour.
To calculate the infusion rate, we can use the following formula:
Infusion rate = Volume / Time
In this case, the volume is 1000 mL and the time is 8 hours. Plugging these values into the formula, we get the following:
Infusion rate = 1000 mL / 8 hours
Infusion rate = 125 mL/hour
Therefore, the RN should set up the infusion pump to deliver 125 mL/hour.
It is important to note that this is just the calculated rate. The actual rate may vary slightly depending on the type of infusion pump and the settings that are used.
Step-by-step explanation:
Use the following information to answer the question.
The Smiths want to buy a 9 ft. by 12 ft. carpet and center it in a 15 ft. by 20 ft. room.
What is the area of the carpet?
__________sq. ft.
The area of the carpet is 108 sq. ft.
To find the area of the carpet, we first need to multiply the length and width of the carpet. Therefore, 9 ft. x 12 ft. = 108 sq. ft.
The Smiths need to buy a 108 sq. ft. carpet to center it in their 15 ft. by 20 ft. room.
The area of the carpet is 108 sq. ft.
To find the area of the carpet, you need to multiply its length by its width. In this case, the dimensions of the carpet are 9 ft. by 12 ft.
Area = length × width
Area = 9 ft × 12 ft
The area of the 9 ft. by 12 ft. carpet that the Smiths want to buy and center in their 15 ft. by 20 ft. room is 108 sq. ft.
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The equation for a hyperbola is shown
x^2/25 - y^2/49=1
what are the lengths of the transverse and conjugate axes?
We need to look at the coefficients of the x and y terms in the equation. The lengths of the transverse and conjugate axes are 10 and 14, respectively.
The standard form of the equation for a hyperbola with a horizontal transverse axis is (x-h)^2/a^2 - (y-k)^2/b^2 = 1, where (h,k) is the center of the hyperbola. In this case, the equation given is already in standard form with (h,k) = (0,0).
Comparing the given equation to the standard form, we see that a^2 = 25 and b^2 = 49. Therefore, a = 5 and b = 7.
The transverse axis is the longer axis and is parallel to the x-axis, so its length is 2a = 10. The conjugate axis is the shorter axis and is perpendicular to the transverse axis, so its length is 2b = 14.
Therefore, the lengths of the transverse and conjugate axes are 10 and 14, respectively.
The equation of the hyperbola you provided is x^2/25 - y^2/49 = 1. In this equation, we can identify the terms a^2 and b^2:
a^2 = 25
b^2 = 49
To find the lengths of the transverse and conjugate axes, we need to first find the values of a and b:
a = √25 = 5
b = √49 = 7
The length of the transverse axis is 2a, and the length of the conjugate axis is 2b. Therefore:
Length of transverse axis = 2a = 2(5) = 10
Length of conjugate axis = 2b = 2(7) = 14
So, the lengths of the transverse and conjugate axes are 10 and 14, respectively.
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Express each of the following as a rational number 3/7+(-2/9)+7/9
Answer:
=62/63
=[tex]\frac{62}{63}[/tex]
Step-by-step explanation:
Convert everything to a denominator 63
=[tex]=\frac{3*9}{63} +-\frac{2*7}{63} +\frac{7*7}{63}[/tex]
=[tex]\frac{27}{63} +\frac{-14}{63} +\frac{49}{63}\\[/tex]
Add up the numerators
= [tex]\frac{62}{63}[/tex]
If the coach bases her decision on the player who is most consistent, whom should she choose? Justify your answer using measures of variability.
Answer:
Variance is a measure of variability which describes the average degree of spread in the data about the mean.
Step-by-step explanation:
Which graph represents a function?
"
Answer:
the 1rst one.
Step-by-step explanation:
because the other ones represent vertical curves which is impossible.
what is the difference between the mean and median
Answer:
The mean is an average general view of the data while median is the value which divides a distribution into two equal parts showing where 50% of the data lies.
Answer:
Shown below.
Step-by-step explanation:
The mean and median are both ways to describe the center of a set of numbers.
What is the mean and how do you find it?The mean is the average of all the numbers in the set. To find the mean, you add up all the numbers and divide by how many there are.
What is the median and how do you find it?The median is the middle number in a set of numbers when they are arranged in order from smallest to largest. If there are two numbers in the middle, then the answer is simply whatever is between them.
(Ex. if the numbers were 3 and 4, the median will be 3.5.)
So, what's the difference?The biggest difference between the mean and median is that the mean is affected by outliers, which are values that are much larger or smaller than the other values in a set of data. If there are outliers in a data set, the mean will be affected more than the median.
Juan purchased a tool set for $1980 on the installment plan. He made a 10% down payment ans agreed to pay $116 per month
Juan made a 10% down payment of $198 on a $1,980 tool set, leaving a remaining balance of $1,782. He will make 16 monthly payments of $116 to cover the remaining balance.
Juan purchased a tool set for $1,980 using an installment plan.
1. Down payment: Juan made a 10% down payment on the $1,980 tool set. To calculate this, multiply the total cost by the down payment percentage:
$1,980 * 0.10 = $198
2. Remaining balance: Subtract the down payment from the total cost to find the remaining balance:
$1,980 - $198 = $1,782
3. Monthly payments: Juan agreed to pay $116 per month to cover the remaining balance. To determine the number of months needed to pay off the balance, divide the remaining balance by the monthly payment:
$1,782 / $116 ≈ 15.36
Since Juan can't make partial payments, he will need to make 16 monthly payments to fully pay off the balance.
4. In conclusion, Juan made a 10% down payment of $198 on a $1,980 tool set, leaving a remaining balance of $1,782. He will make 16 monthly payments of $116 to cover the remaining balance.
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the total enclosure around a playground at a daycare is to be 800 square feet. one side of the playground is bordered by the school building while the three remaining sides will be enclosed with fencing. find the dimensions that minimize the length of fencing needed
The dimensions that minimize the length of fencing needed are approximately 28.28 feet by 28.28 feet, creating a square-shaped playground.
To minimize the length of fencing needed for the enclosure, we need to find the dimensions that maximize the area of the playground. Since one side of the playground is already bordered by the school building, we can focus on the remaining three sides.
Let's assume the length of the playground parallel to the school building is L, and the width perpendicular to the school building is W. The area of the playground can be expressed as A = L * W.
Given that the total area of the enclosure is 800 square feet, we have the constraint L * W = 800.
To minimize the length of fencing needed, we want to maximize the area A. This occurs when the length and width are as close as possible to each other. In other words, we want to find the dimensions that form a square shape.
In a square, the length and width are equal, so we can solve the constraint equation L * L = 800.
Taking the square root of both sides, we find L = √800 ≈ 28.28 feet.
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a college statistics professor has office hours from 9:00 a.m. to 10:30 a.m. daily. a random sample 20 students waiting has a mean of 22.3 minutes. assuming find the 95.44% confidence interval for the population mean.
The 95.44% confidence interval for the population mean is approximately (19.87 minutes, 24.73 minutes).
To calculate the 95.44% confidence interval for the population mean, we can use the following formula:
Confidence Interval = sample mean ± (critical value) * (standard deviation / sqrt(sample size))
First, let's determine the critical value. Since the confidence level is 95.44%, we need to find the z-score that corresponds to a tail probability of (1 - 0.9544)/2 = 0.0228. Looking up this value in the standard normal distribution table or using a statistical calculator, we find that the z-score is approximately 2.17.
Next, we need to determine the standard deviation of the population. Since we don't have that information, we'll use the sample standard deviation as an estimate. Let's assume the sample standard deviation is 5 minutes.
Now we can calculate the confidence interval:
Confidence Interval = 22.3 ± (2.17) * (5 / sqrt(20))
Calculating the expression inside the parentheses:
= 22.3 ± (2.17) * (5 / sqrt(20))
= 22.3 ± 2.17 * (5 / 4.472)
= 22.3 ± 2.17 * 1.118
Calculating the confidence interval:
Lower Limit = 22.3 - (2.17 * 1.118)
Upper Limit = 22.3 + (2.17 * 1.118)
Lower Limit = 22.3 - 2.42706 ≈ 19.87294
Upper Limit = 22.3 + 2.42706 ≈ 24.72706
Therefore, the 95.44% confidence interval for the population mean is approximately (19.87 minutes, 24.73 minutes).
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Which of the following are proper units of mass in the Metric System? Check
all that apply.
A. liter
B. gram
C. milligram
D. pound
Answer:
Here are the correct answers:
B. gram
C. milligram
If the volume of the the sphere is 20 cubic inches, what are the volumes of the cylinder and the cone?
The volume of the cylinder is 29.78 inches cube.
The volume of the cone is 9.93 inches cube.
How to find the volume of a cylinder and cone?The figure above is a sphere, cylinder and a cone. The volume of the figure can be represented as follows:
volume of a sphere = 4 / 3πr³
where
r = radius20 = 4 / 3 × π × r³
cross multiply
4r³π = 60
r³π = 15
r = ∛15 / π
r = ∛4.78
r = 1.68 inches
volume of a cylinder = πr²h
where
h = height of the cylinderr = radiusvolume of a cone = 1 / 3 πr²h
where
r = radiush = height of the coneTherefore, let's find the volume of the cylinder and cone with the following information.
Hence,
volume of the cylinder = π × (r)² × 2r
volume of the cylinder = 2(1.68)³π
volume of the cylinder = 29.78 inches cube
Therefore,
volume of the cone = 1 / 3 πr²h
volume of the cone = 1 / 3 × 3.14 × r² × 2r
volume of the cone = 1 / 3 × 3.14 × 2(1.68)³
volume of the cone = 29.77744896 / 3
volume of the cone = 9.93 inches cube
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A parabola opening up or down has vertex (0,5)and passes through (-6,4)
The equation of the parabola that opens up or down, with a vertex at (0, 5) and passing through (-6, 4), is y = (-1/36)x^2 + 5
To find the equation of a parabola that opens up or down given the vertex and a point, we can use the standard form of the equation:
y = a(x - h)^2 + k
where (h, k) represents the vertex of the parabola. In this case, the vertex is (0, 5), so we have h = 0 and k = 5.
Now, we can substitute the given point (-6, 4) into the equation to determine the value of a:
4 = a(-6 - 0)^2 + 5
4 = 36a + 5
36a = -1
a = -1/36
Substituting the value of a back into the equation, we have:
y = (-1/36)(x - 0)^2 + 5
y = (-1/36)x^2 + 5
Therefore, the equation of the parabola that opens up or down, with a vertex at (0, 5) and passing through (-6, 4), is y = (-1/36)x^2 + 5.
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Find the last digit of the product when you multiply all the odd numbers from 1 to 2023, inclusive. HELP PLEASE
Answer: 5
Step-by-step explanation:
You could multiply every number but that would take too much time
Instead you have to logic through the problem
Numbers in multiplication follow cyclical sets. i.e. the ones place in the multiples of 3 goes 3,6,9,2,5,8,1,4,7,0,3 forever. (That is why 3 is a "mod 10" number there are 10 possible 1s place values)
The helpful number here is 5
5 is mod 2 because any multiple ends in a 5 or a 0. Given that you are doing all of the odd numbers, five times any odd number will end in a 5, and any odd number ending in 5 times another odd number will also end in 5 so the ones place for all odd numbers multiplied from 1 to 2023 is 5.
When multiplying all the odd numbers from 1 to 2023, inclusive, the last digit of the product will be 5. This is based on the pattern observed in the last digits of the products of odd numbers.
Explanation:In mathematics, specifically in number theory, we often make use of patterns to solve problems. When you're asked to find the last digit of the product when you multiply all the odd numbers from 1 to 2023, inclusive, it is helpful to look for a pattern in the last digits of the products of odd numbers.
Let's start small. The first five odd numbers are 1, 3, 5, 7, and 9. The product of these numbers is 945, and the last digit, or unit digit, is 5. Let's add another odd number to the product, 11. The product becomes 10395, and again, the unit's digit is 5. As you can see, the pattern is that no matter how many odd numbers you multiply together, the unit's digit (or the last digit) of the product is always 5.
Therefore, when you multiply all the odd numbers from 1 to 2023, inclusive, the last digit of the product will be 5.
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Which angle has a measurement of 80°? (1 point)
a
a protractor showing an angle with one side lined up with the base line and one side going right through the fifth tick mark past one hundred five degrees
b
a protractor showing an angle with one side lined up with the base line and one side going right through the tenth tick mark past seventy degrees
c
a protractor showing an angle with one side lined up with the base line and one side going right through the fifth tick mark past one hundred thirty five degrees
d
a protractor showing an angle with one side lined up with the base line and one side going right through the tenth tick mark past one hundred ten degrees
We can see here that the angle has a measurement of 80° is: D. a protractor showing an angle with one side lined up with the base line and one side going right through the tenth tick mark past one hundred ten degrees
What is an angle?A geometric shape known as an angle is created when two rays meet at a location known as the vertex. An angle's measurement, which expresses the amount of rotation required to shift one of the rays to meet the other ray, is frequently expressed in degrees or radians.
Acute angles (less than 90 degrees), right angles (exactly 90 degrees), obtuse angles (more than 90 degrees but less than 180 degrees), straight angles (exactly 180 degrees), reflex angles (greater than 180 degrees but less than 360 degrees), and full angles (exactly 360 degrees) are the several classifications of angles based on their measurement.
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$700 is deposited in an account with 5% interest rate, compounded continuously. What is the balance after 12 years?
Step-by-step explanation:
Continuous compounding formula
FV = PV e^(rt) PV = $ 700 r = .05 t = 12
FV = future value = $ 700 e^(.05 * 12) = $ 1275.48
Find the interval in which y = x squared + 4 is increasing.
Step-by-step explanation:
This is a bowl shaped parabola with axis of symmetry x = 0
From - inf to 0 it is DEcreasing
from 0 to + inf it is INcreasing
PLEASE HELP WILL MARK BRAINLIEST
A researcher determined that the heights of male students in a
particular town are normally distributed with a mean of 63 inches and
a standard deviation of 1.5. Use the graph above to answer the
following questions:
67.5
a. What percentage of these students is taller than 66 inches?
b. If the data are based on 200 students, how many students are
between 60 and 64.5 inches tall? Explain.
Answer:
a) 2.5%
b) 190
Step-by-step explanation:
a) 2.35+0.15=2.5
b) (.34+.34+.135+.135)x200=
.95x200=190
104
103
Simplify.
× 10⁹ = 10[?]
To solve, we'll work left to right.
First, we have division. When we are dividing terms with exponents, given that the base is the same, then we need to subtract the exponents.
10^4 / 10^3 = 10^1
Next, we have multiplication. When we are multiplying terms with exponents, given that the base is the same, then we need to add the exponents.
10^1 x 10^9 = 10^10
Answer: 10^10
Hope this helps!
A car manufacturer can produce 1400 cars in a week how many days will it take to produce 800 cars
Answer:
4 days
Step-by-step explanation:
first, figure out how many cars are produced in a day. since there are 7 days in a week, and 1400 cars are produced in a week, divide 1400 by 7. 1400/7 equals 200. so, if 200 cars produced each day, then:
200x= 800 (x = days)
200x/200 = 800/200
So, 4 days.
a nationwide survey finds that 20% of people like baseball. of those people that like baseball, 50% also like tennis. of the surveyed people that like tennis, what is the minimum percent that could like baseball?
We need to use a bit of math and logic. First, we know that 20 percent of people surveyed like baseball. We also know that 50% of those who like baseball also like tennis. This means that out of the total surveyed population, 10% (50% of 20%) like both baseball and tennis.
Next, we need to find out the minimum percent of people who like tennis that could also like baseball. To do this, we need to consider the fact that there could be some people who like tennis but not baseball, and we want to find the lowest possible percentage of people who like both sports.
Let's say that x% of people surveyed like tennis but not baseball. This means that (100-x)% of people who like tennis also like baseball. We want to find the minimum value of (100-x)% that would still satisfy the conditions given in the problem.
We know that 10% of people surveyed like both baseball and tennis. This means that (100-x)% of people who like tennis but not baseball is equal to 90%.
Using a bit of algebra, we can solve for x:
(100-x)% * 90% = 10%
Simplifying this equation, we get:
(100-x)% = 10%/90%
(100-x)% = 11.11%
Therefore, the minimum percent of surveyed people who like tennis that could also like baseball is 11.11%.
In summary, of the surveyed people that like tennis, the minimum percent that could like baseball is 11.11%. This is found by considering the fact that 50% of people who like baseball also like tennis, and finding the minimum percentage of people who like tennis but not baseball that would still allow for the 10% of people who like both sports.
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Hillsdale Street and Salem Avenue intersect. If Hillsdale Street is 12 meters wide and Salem Avenue is 9 meters wide, what is the distance between two opposite corners of the intersection?
The distance between two opposite corners of the intersection is, 15 meters.
We have to given that;
Hillsdale Street and Salem Avenue intersect.
And, Hillsdale Street is 12 meters wide and Salem Avenue is 9 meters wide,
Since, WE know that;
The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.
Now, Let us assume that, distance between two opposite corners of the intersection is, x
Hence, We can formulate for the given condition,
⇒ Hypotenuse² = Base² + Opposite²
⇒ x² = 12² + 9²
⇒ x² = 144 + 81
⇒ x² = 225
Taking square root on both side,
⇒ x = √225
⇒ x = 15
Therefore, We get;
The distance of two opposite corners of the intersection is,
⇒ 15 meters.
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PLS HELP IF CORRECT BRAINLIEST -3=-11+√2y
Answer:
y= 32
Step-by-step explanation:
Answer:
The answer for y is 32
Step-by-step explanation:
-3=-11+√2y
-3+11=√2y
8=√2y
square both sides
8²=√2y²
64=2y
divide both sides by 2
2y/2=64/2
y=32
Compare the investment below to an investment of the same principal at the same rate compounded annually.
principal: $9,000, annual interest: 9%, interest periods: 12, number of years: 20
After 20 years, the investment compounded periodically will be worth:
(Round to two decimal places as needed.)
more than the investment compounded annually.
After 20 years, the investment compounded periodically will be worth $ 3, 238. 47 more than the investment compounded annually.
How to find the investment value ?First, find the value of the investment when it is compounded periodically, 12 times a year.
The formula is:
= Amount invested x ( 1 + rate ) ^ number of periods
= 9, 000 x ( 1 + 9 % / 12 ) ^ ¹² ˣ ²⁰
= $ 53, 678. 16
If compounded annually, the value would be :
= 9, 000 x ( 1 + 9 % ) ²⁰
= $ 50, 439. 69
The difference is :
= 53, 678. 16 - 50, 439. 69
= $ 3, 238. 47
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PLS HELP IF CORRECT BRAINLIEST -3=-11=√2y
2. Evaluate
45 x ( - 4 + 1 )
Answer:
-135
Step-by-step explanation:
45 x ( -4 + 1 )
BODMAS -> Bracket of Division Multiplication Addition Subtraction
=> 45 x -3
=> -135
Halp me this question
Answer: The third option, 26 plus 22 plus ___ = 52
Step-by-step explanation:
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?
The probability that a pack of 16 baseballs would have an average weight of more than 147 grams, given our assumptions, is approximately 1 - 0.0082 = 0.9918, or 99.18%.
What is probability?
Probability is a way to gauge how likely or unlikely something is to happen. It measures the degree of ambiguity surrounding the result of a single event or a series of related occurrences. Typically, probability is stated as a number between 0 and 1, with 0 denoting an impossibility and 1 denoting a certain or guaranteed event.
To determine the probability that a pack of 16 baseballs would have an average weight of more than 147 grams, we need information about the distribution of baseball weights. Without specific information about the distribution, it is challenging to provide an exact probability.
However, assuming the weights of baseballs follow a normal distribution with a known mean and standard deviation, we can provide a general guideline for calculating the probability using the Central Limit Theorem.
Let's assume the mean weight of a baseball is μ grams, and the standard deviation is σ grams. Since we don't have the exact values, we'll need to make some assumptions. Let's say the mean weight of a baseball is 150 grams, and the standard deviation is 5 grams.
The average weight of the 16 baseballs follows a normal distribution with a mean equal to the population mean (μ) and a standard deviation equal to the population standard deviation divided by the square root of the sample size (σ/[tex]\sqrt[1]{n}[/tex]).
In this case, the mean is 150 grams, and the standard deviation is 5 grams divided by the square root of 16 (since we have 16 baseballs). The square root of 16 is 4.
The standard deviation of the average weight is 5 grams / 4 = 1.25 grams.
Now, we want to calculate the probability that the average weight is more than 147 grams. To do this, we can convert it into a standard normal distribution by subtracting the mean (150 grams) and dividing by the standard deviation (1.25 grams).
The z-score for 147 grams is (147 - 150) / 1.25 = -2.4.
Using a standard normal distribution table or calculator, we can find the probability associated with a z-score of -2.4. Let's assume it is P(Z < -2.4) = 0.0082.
However, since we are interested in the probability that the average weight is more than 147 grams, we need to consider the area to the right of the z-score (-2.4). This is equal to 1 - P(Z < -2.4).
Therefore, the probability that a pack of 16 baseballs would have an average weight of more than 147 grams, given our assumptions, is approximately 1 - 0.0082 = 0.9918, or 99.18%.
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