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In a normal distribution with a mean of 75 and a standard deviation of 5, the approximate value of the median is 75 and approximately 68% of the scores fall between 70 and 75 while 95.45% of the scores lie between two standard deviations below and two standard deviations above the mean.

Standard deviation is a measure of how much variation exists in a set of data. It is used to measure the spread of the data, or how far the data is dispersed from the average. A low standard deviation indicates that data points are close to the average, while a high standard deviation means that the data points are spread out over a wide range of values. Standard deviation is calculated by taking the square root of the variance of the data.

1) The approximate value of the median in a normal distribution with a mean of 75 and a standard deviation of 5 is 75.

2) Approximately 68% of the scores fall between 70 and 75. This can be calculated by using the cumulative probability function for a normal distribution, which is given by: P(x) = 1/2[1 + erf( (x - μ) / (σ*sqrt(2)) ] where μ is the mean, σ is the standard deviation, and erf is the error function. In this case, the cumulative probability of 70 is 0.5 and the cumulative probability of 75 is 0.8413, so the difference of 0.3413 gives the approximate percentage of scores between 70 and 75.

3) Approximately 95.45% of the scores would lie between two standard deviations below and two standard deviations above the mean. This can be calculated by using the cumulative probability function for a normal distribution, which is given by: P(x) = 1/2[1 + erf( (x - μ) / (σ*sqrt(2)) ] where μ is the mean, σ is the standard deviation, and erf is the error function. In this case, the cumulative probability of two standard deviations below the mean is 0.02275 and the cumulative probability of two standard deviations above the mean is 0.97725, so the difference of 0.9545 gives the approximate percentage of scores between two standard deviations below and two standard deviations above the mean.

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Complete questions as follows-
Given a normal distribution with a mean of 75 and a standard deviation of 5, answer the following questions:

1) What is the approximate value of the median?

2) What percentage of scores fall between 70 and 75?

3) What percentage of the scores would lie between two standard deviations below and two standard deviations above the mean?

The 95% confidence interval for the standard deviation of the height of students at UH is (1.918, 5.732), which corresponds to option b.

To construct a 95% confidence interval for the standard deviation of the height of students at UH, we will use the Chi-square distribution. Given the sample standard deviation (s) of 3.2 feet, a sample size (n) of 19 students, and assuming normality for the data, we can find the confidence interval as follows:
1. Determine the degrees of freedom: df = n - 1 = 19 - 1 = 18
2. Identify the Chi-square values for the confidence level (95%): χ²_lower = 7.632, χ²_upper = 32.852 (using a Chi-square table or calculator)
3. Calculate the lower and upper bounds of the confidence interval:
Lower bound = sqrt((n - 1) * s² / χ²_upper) = sqrt(18 * (3.2)² / 32.852) ≈ 1.918
Upper bound = sqrt((n - 1) * s² / χ²_lower) = sqrt(18 * (3.2)² / 7.632) ≈ 5.732

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The 95% confidence interval for the standard deviation of the height of students at UH is approximately (1.918, 5.732), Option B.

Construct a 95% confidence interval for the standard deviation of the height of students at UH, we'll use the given data and the Chi-Square distribution.

Here's a step-by-step explanation:
SRS (simple random sample) of 19 students, which means the degrees of freedom (df) = n - 1 = 19 - 1 = 18.
The sample standard deviation (s) is given as 3.2 feet.
Assume normality for the data.
A 95% confidence interval, we'll use the Chi-Square distribution table to find the critical values.

The two tail probabilities are 0.025 and 0.975, so we'll look up the Chi-Square values for 18 degrees of freedom and these probabilities:
[tex]- X^2_{0.025} = 30.191 (upper limit)[/tex]
[tex]- X^2_{0.975} = 8.231 (lower limit)[/tex]
Calculate the confidence interval for the population standard deviation (σ):
[tex][tex](\sqrt((n - 1) \times s^2 / X^2_{upper}), \sqrt((n - 1) \times s^2 / X^2_{lower}))[/tex][/tex]
Plug in the values:
[tex]- n = 19[/tex]
[tex]- s = 3.2[/tex]
[tex]- df = 18[/tex]
[tex][tex]- X^{2} _{upper} = 30.191[/tex][/tex]
[tex][tex]- X^2_{lower} = 8.231[/tex][/tex]
Calculate the confidence interval:
[tex](√((18 \times 3.2^2) / 30.191), \sqrt((18 \times 3.2^2) / 8.231)) \approx (1.918, 5.732)[/tex]

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Answer:

Step-by-step explanation:

its a rectanlge

Answer: 3 pieces

Step-by-step explanation:First, 6/8 can be converted into fourths by dividing the numerator and the denominator by 2 and we get 3/4. if we want 1/4 slices we divide 3/4 by 1/4 and get 3.

Answer: The least common denominator is 3x(x+10)

The equation will have 2 valid solutions

Step-by-step explanation: sorry if wrong

The amount of money less per hour which Melanie earn than Olivia is equal to $268.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Based on the information provided about Melanie's earnings, we have the following:

y = 22.2x

When x = 40 hours, the y-value is given by;

y = 22.2(40)

y = $888.

Difference in earnings can be calculated as follows;

Difference = $1156 - $888

Difference = $268.

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The probability of selecting such a permutation is very low, only about 0.31%.

The probability of the event when we randomly select a permutation of the 26 lowercase letters of the English alphabet where 'm' immediately precedes 'n', which immediately precedes 'o' can be calculated as follows:

Firstly, we need to determine the total number of permutations of the 26 letters. Since there are 26 letters in the alphabet, there are 26! ways to arrange them.

Next, we need to determine the number of permutations where 'm' immediately precedes 'n', which immediately precedes 'o'. To do this, we can consider 'mno' as a single unit and then there are 24! ways to arrange the 24 units (23 individual letters and 1 unit of 'mno').

However, there are 3! ways to arrange 'mno' within the unit, so we need to multiply by 3!. Therefore, the total number of permutations where 'm' immediately precedes 'n', which immediately precedes 'o' is 24! x 3!.

Thus, the probability of randomly selecting a permutation where 'm' immediately precedes 'n', which immediately precedes 'o' is:

P = (24! x 3!) / 26!

P ≈ 0.0031 or 0.31%

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If the amount of £15837.77 is to be increased by 18.5%, then the resulting amount after the increase is £18764.75.

A percentage is a number or ratio expressed as a fraction of 100. It represents a portion of something relative to the whole, and is commonly used to express changes or comparisons between two values

To increase a number by a percentage, you can use the following formula

New value = Original value + (Percentage increase / 100) × Original value

Using this formula, we can find the new value of £15837.77 after an 18.5% increase

New value = 15837.77 + (18.5 / 100) × 15837.77

= 15837.77 + 2926.98

= 18764.75

Therefore, an 18.5% increase on £15837.77 is £18764.75, rounded to 2 decimal places.

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Using the standard normal distribution, we find that approximately 73.8% of workers receive wages between $4.75 and $5.69 per hour. Using the inverse of the standard normal distribution, we find that the highest 5% of hourly wages are greater than approximately $6.09.

Using a standard normal distribution table or calculator with a mean of 5.25 and a standard deviation of 0.60, we can find that approximately 79.42% of workers receive wages between $4.75 and $5.69 per hour.

Using a standard normal distribution table or calculator, we can find the z-score corresponding to the highest 5% of wages, which is approximately 1.645.

Then, we can solve for x in the equation z = (x - μ) / σ, where z is the z-score, μ is the mean of 5.25, and σ is the standard deviation of 0.60. This gives us x = zσ + μ, which is approximately $6.09 per hour. Therefore, the highest 5% of hourly wages are greater than $6.09 per hour.

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Answer:

189

Step-by-step explanation:

27,006 / 42

= [tex]\frac{27}{6/42}[/tex]

= [tex]\frac{27}{\frac{1}{7} }[/tex]

= 27 x 7

= 189

So, the answer is 189

Answer: 207.338[tex]cm^2[/tex] or 66[tex]\pi[/tex]

Step-by-step explanation:

Lateral Area of a cylinder : 2[tex]\pi[/tex](radius)(height)

Surface Area of a cylinder : Lateral Area + 2 (base area)

LA= 48[tex]\pi[/tex]

= 150.79

SA= 150.79 + (2([tex]\pi[/tex]([tex]3^2[/tex])

= 207.338 [tex]cm^2[/tex]

: )))

The answers are:

a) 2 cakes cost £5

b) 1 cake costs £2.5.

What is an algebraic expression?

An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations. It may also include exponents and/or roots. Algebraic expressions are used to represent quantities and relationships between quantities in mathematical situations, often in the context of problem-solving.

To find the cost of 1 cupcake, we need to subtract the cost of the tea from the total cost of 3 cupcakes:

3 cupcakes + 1 tea = £9

3 cupcakes = £9 - 1 tea = £9 - £1.5 (assuming the cost of 1 tea is the same in both cases) = £7.5

1 cupcake = £7.5 ÷ 3 = £2.5

So 2 cupcakes would cost:

2 cupcakes = 2 × £2.5 = £5

Therefore, the answers are:

a) 2 cakes cost £5

b) 1 cake costs £2.5.

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The probability that the total shown on the two dice after they are rolled is greater than or equal to 8 is 1/9.

The equation of the circle is x² + y² - 4x - 6y - 60 = 0

The equation of a circle is generally given by the formula:

=> (x - a)²+ (y - b)² = r²

Where (a, b) is the center of the circle, and r is its radius. The equation describes all the points (x, y) in the xy-plane that are a fixed distance r from the center point (a, b).

Here we have

A circle with centre O(2, 3) contains the point A(5, 11).  

Since point A(5, 11) is located on the circle with center O(2, 3), use the distance formula to determine whether A is actually on the circle.

The distance between two points (x₁, y₁) and (x₂, y₂) is given by:

=> d = √(x₂ - x₁)² + (y₂ - y₁)²)

Using this formula, the distance between O(2, 3) and A(5, 11) is:

d = √(5 - 2)² + (11 - 3)²)

= √(3² + 8²)

= √(9 + 64)

=√(73)

This distance is the radius of the circle with center O.

Therefore, the equation of the circle is:

(x - 2)² + (y - 3)² = (√(73))²

x² - 4x + 4 + y² - 6y + 9 = 73

x² + y² - 4x - 6y - 60 = 0

Therefore,

The equation of the circle is x² + y² - 4x - 6y - 60 = 0

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Answer:

a 1053

b 250

multiply 650 by 1.62 for part a.

for part b divide by 1.62 since pound is less than dollar

hope this helps :)

Answer:

Step-by-step explanation:

If the solutions are x = -3 and x = -1, then (x - 3) (x - 1) will give us our answer. Using the FOIL method,

(x - 3) (x - 1)

x^2 - x - 3x + 3

x^3 - 4x + 3 = 0

Your answer is 3

Hence correct option or expression are D and F.

its branches of mathematics. The  arithmetic deals with numbers and mathematical procedures. Math think how to add, subtract, multiply, and divide two or more  numbers. Shapes are the main focus  in geometry, which involves creating them with various instruments including a compass, ruler,  and pencil. Another fascinating area of study is algebra, where we use numbers and variables to represent the circumstances we encounter every day.

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth,  and so forth. You will discover  the formulas, guidelines, characteristics, graphs, derivatives, exponential series, and examples of exponential functions in this article.

use,

[tex]\frac{a^{m} }{a^{n} } =a^{m-n}[/tex]

so,

[tex]\frac{b^{-2} }{b^{-6} } =b^{-2+6}\\=b^{4} or \frac{1}{b^{-4} }[/tex]

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Answer:

square, quadrilateral, rhombus, parallelogram, rectangle



Answer:

Quadrilateral, rectangle, parallelogram, rhombus, square

Step-by-step explanation:

It is a quadrilateral bc it has four sides.

It is a rectangle bc it has four right angles.

It is a parallelogram bc it has two pairs of parallel sides.

It is a rhombus bc all four sides are congruent.

It is a square bc it is both a rectangle and a rhombus.

When a researcher uses the Pearson product-moment correlation, two highly correlated variables will appear on a scatter diagram as a tightly clustered group of points that form a linear pattern.

The scatter diagram is a visual representation of the correlation between two variables, where one variable is plotted on the x-axis, and the other variable is plotted on the y-axis. If the two variables have a high positive correlation, then the points on the scatter diagram will form a cluster that slopes upwards to the right.

On the other hand, if the two variables have a high negative correlation, then the points will form a cluster that slopes downwards to the right. The tighter the cluster of points, the higher the correlation between the variables.

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Trigonometric functions are used to model relationships between angles and sides of a right triangle. They are particularly useful in solving problems that involve angles, distances, heights, and lengths that are difficult to measure directly.

For example, consider a problem that involves finding the height of a building. By measuring the length of the shadow cast by the building at a particular time of day, the angle of the sun's rays can be calculated using trigonometry. Once the angle is known, the height of the building can be determined using the tangent function.

In contrast, a non-trigonometric function may not be able to model the relationship between the given quantities in such problems, and may not provide an accurate solution. Therefore, when a problem involves angles or distances that are not directly measurable, trigonometric functions are typically the best tool for setting up and solving the problem.

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Answer:

The y-intercept is at (0, 8).

Answer: (0,8)

Step-by-step explanation: The line only touches the Y-axis Once and its on 8

Answer

Number 14: 7 faces, 15 edges, and 10 vertices.

Number 15: 10 faces, 24 edges, and 16 vertices.

Number 16: 7 faces, 12 edges, and 7 vertices.

:D

Step-by-step explanation:

1) A histogram would be the best graphical representation for the teacher's data on the subject preferences of students. 2) The correct circle graph is option 2. 3) Option 4: Paddleboarding.

The frequency or relative frequency of the data points falling within each interval is depicted by the height of the bars in a histogram, which is a graphical representation of the distribution of continuous data. Histograms are frequently used in data analysis to show how a single variable is distributed and to spot any patterns or trends. Additionally, they can be used to compare the distributions of two or more variables or to spot anomalies or outliers in the data.

1) A histogram would be the best graphical representation for the teacher's data on the subject preferences of students.

2) Given the type of transportation we have he total number of visitors as:

(120+24+45+30+81=300)

Now, for walk we have:

120/300 = 40/100 = 40%

For Bicycle we have:

24/300 = 8%

Thus, the correct circle graph is option 2: circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent

3) For the central angle to be 54 the number of campers needs to correspond to this number. The activity that corresponds to 54 degrees is Paddleboarding.

4) For the number of principals in conference we set up a proportionality with total people as follows:

We know that, 52 principals out of 70 people thus:

52/70 = x/750

Now,

x = (52/70) * 750

x = 557.14

Hence, we can predict that there were about 557 principals in attendance at the conference.

5) Given that, out of 225 students 27 prefer cookies thus,

27/225 = 0.12

That is 12% students like cookies.

Now, for the total number of students we have:

0.12 * 4000 = 480

Thus, option A: The college will have about 480 students who prefer cookies.

6) For the given description of the line plot the median is:

For Bus 47 = 16

For Bus 18 = 13

The faster bus is Bus 47, with a median of 16.

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Answer: To find the average rate of change of the function f(x) over the interval [9, 65], we can use the formula:

average rate of change = (f(b) - f(a)) / (b - a)

where a = 9, b = 65, f(a) = f(9) = 3√8 + 2, and f(b) = f(65) = 3√64 + 2.

Plugging in these values, we get:

average rate of change = (f(65) - f(9)) / (65 - 9)

average rate of change = (3√64 + 2 - 3√8 - 2) / 56

average rate of change = (3(4) + 2 - 3(2) - 2) / 56

average rate of change = (12 - 4) / 56

average rate of change = 8 / 56

average rate of change = 1 / 7

Therefore, the average rate of change of the function f(x) over the interval [9, 65] is 1/7.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer: To find the average rate of change of the function f(x) over the interval [9, 65], we can use the formula:

average rate of change = (f(b) - f(a)) / (b - a)

where a = 9, b = 65, f(a) = f(9) = 3√8 + 2, and f(b) = f(65) = 3√64 + 2.

Plugging in these values, we get:

average rate of change = (f(65) - f(9)) / (65 - 9)

average rate of change = (3√64 + 2 - 3√8 - 2) / 56

average rate of change = (3(4) + 2 - 3(2) - 2) / 56

average rate of change = (12 - 4) / 56

average rate of change = 8 / 56

average rate of change = 1 / 7

Therefore, the average rate of change of the function f(x) over the interval [9, 65] is 1/7.

The number of collections of 50 coins that can be chosen from this pile is: C(125, 25) = 177,100,565,136,000
This is a very large number, which shows that there are many possible collections of 50 coins that can be chosen from the pile.

If the pile contains only 25 quarters but at least 50 of each other kind of coin, then the total number of coins in the pile must be at least 50 + 50 + 50 = 150. Let's assume that there are 150 coins in the pile, including the 25 quarters.
To choose a collection of 50 coins from this pile, we need to exclude the 25 quarters and choose 25 coins from the remaining 125 coins. We can do this in C(125, 25) ways, which is the number of combinations of 25 items chosen from a set of 125 items.
Therefore, the number of collections of 50 coins that can be chosen from this pile is:
C(125, 25) = 177,100,565,136,000

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There are 351 possible collections of 50 coins that can be chosen, considering the given conditions.

To find the number of collections of 50 coins that can be chosen, we will consider the given conditions:
The pile contains only 25 quarters.

There are at least 50 of each other kind of coin (pennies, nickels, and dimes).
Now, let's break this down step by step:
Determine the minimum number of coins from each kind required to make a collection of 50 coins.
- 25 quarters (as it's the maximum available)
- The remaining 25 coins must be a combination of pennies, nickels, and dimes.
Find the different combinations of pennies, nickels, and dimes that can be chosen to make a collection of 50 coins.
- We need 25 more coins, so we can divide them into three groups:
 a) Pennies (P)
 b) Nickels (N)
 c) Dimes (D)
Calculate the combinations for the remaining 25 coins.
- Using the formula for combinations with repetitions: C(n+r-1, r) = C(n-1, r-1)
 Where n is the number of types of coins (3) and r is the number of remaining coins (25)
- C(3+25-1, 25) = C(27, 25) = 27! / (25! * 2!) = 351.

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Answer:52.5

Step-by-step explanation:

Multiply

If we consider a mountain number with its middle digit is larger than any other digit, then there are possible three-digit mountain numbers are equals the 240.

A number is called a 'mountain' if its decimal digits insitiate with 1, i.e. 'base camp', increase continuously to one largest digit, then decrease continuously back to one i.e. back to base camp. We have a number is called a mountain number. Now, there are 100 to 999 total 3-digit numbers. Now, with 2 in the middle, we have = 2 numbers[1 x 2] - 120 = 121

So, we have a total of Total Number = 2 + 6 + 12 + 20 + 30 + 42 + 56 + 72 = 240 "mountain numbers". Hence, the required number , value is 240.

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The GCF of 48 and 60 is 12

To find the greatest common factor (GCF) of 48 and 60, we can start by finding the prime factorization of each number

48 = 2^4 × 3

60 = 2^2 × 3 × 5

Next, we can identify the common factors of both numbers by looking at their prime factorization

The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

The common factors of 48 and 60 are: 1, 2, 3, 4, 6, and 12.

The greatest common factor is the largest number that both 48 and 60 can be divided evenly by. In this case, that number is 12. Therefore, the GCF is 12.

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The given question is incomplete, the complete question is:

Find the GCF of 48 and 60.