Loudness of sound. The loudness L of a sound of intensity I is defined as 1 L = 10 log 1/1o' where lo is the minimum intensity detectable by the human ear and L is the loudness measured in decibels

Answers

Answer 1

Yes, the loudness L of a sound of intensity I is defined as:

L = 10 log(I/Io)

where Lo is the minimum intensity detectable by the human ear (also known as the threshold of hearing) and L is the loudness measured in decibels (dB).

In this equation, the intensity I is typically measured in watts per square meter (W/m^2), and Io is equal to 1 x 10^-12 W/m^2.

The logarithmic scale used in this equation means that each increase of 10 decibels represents a tenfold increase in sound intensity. For example, a sound that is 50 dB louder than another sound has an intensity that is 10 times greater.

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Related Questions

Yo help out rq ty ty ty

Answers

Answer:

I think the answer should be part

A particle moves with position function s=t" - 413 - 20+2 + 20t, t > 0 At what time does the particle have a velocity of 20 m/s? At what time is the acceleration 0? What is the significance of this variance?

Answers

Since t > 0, the time when the particle has a velocity of 20 m/s is approximately t ≈ 4.27 seconds.

A particle has a position function s(t) = t^3 - 4t^2 - 20t + 2 + 20t, t > 0. To find the time when the particle has a velocity of 20 m/s, we first need to find the velocity function by taking the derivative of the position function with respect to time:

v(t) = ds/dt = 3t^2 - 8t - 20.

Now set v(t) equal to 20 and solve for t:

20 = 3t^2 - 8t - 20.

40 = 3t^2 - 8t.

Now solve the quadratic equation for t:

t ≈ 4.27, -3.10.

To find the time when the acceleration is 0, we need to find the acceleration function by taking the derivative of the velocity function with respect to time:

a(t) = dv/dt = 6t - 8.

Now set a(t) equal to 0 and solve for t:

0 = 6t - 8.

t = 8/6 = 4/3.

So, the acceleration is 0 at t = 4/3 seconds.

The variance in acceleration signifies a change in the motion dynamics of the particle. When the acceleration is 0, it indicates that the particle is neither speeding up nor slowing down at that moment, resulting in a constant velocity.

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Mind-Set Matters In 2007 a Harvard psychologist set out to test her theory that ‘‘Mind-Set Matters. "1 She recruited female maids2 working in different hotels to participate in her study, and informed maids (randomly chosen) that the work they do satisfies the Surgeon General’s recommendations for an active lifestyle (which is true), giving the maids examples on how their work qualifies as good exercise. The other maids were told nothing. After four weeks, the exercise habits of the two groups had not changed, but the informed group had lost an average of lbs () and the uninformed group had lost an average of lbs (). The data are stored in MindsetMatters. Based on this study, does ‘‘Mind-Set Matter"? In other words, for maids, does simply thinking they are exercising more actually cause them to lose more weight?

Answers

Based on study, it appears that mind-set does matter for maids in terms of weight loss - simply thinking they are exercising more may have led to greater weight loss in the informed group.

To determine whether mind-set matters in terms of weight loss for the maids, we need to conduct a hypothesis test.

Null Hypothesis: The average weight loss for the informed group of maids is equal to the average weight loss for the uninformed group of maids.

Alternative Hypothesis: The average weight loss for the informed group of maids is greater than the average weight loss for the uninformed group of maids.

We can use a one-sided t-test to test this hypothesis, since we are interested in whether the informed group lost more weight than the uninformed group.

Using the data provided, we can calculate the sample mean and standard deviation for each group:

Informed group:

Sample size (n) = 44

Sample mean = 2.00 lbs

Sample standard deviation = 2.50 lbs

Uninformed group:

Sample size (n) = 76

Sample mean = 1.33 lbs

Sample standard deviation = 2.31 lbs

We can use a t-test with unequal variances (since the sample standard deviations are different) to test the hypothesis. Using a significance level of 0.05 and a one-tailed test, the critical t-value is 1.67 (from a t-distribution with 118 degrees of freedom).

The calculated t-value is: t = (2.00 - 1.33) / sqrt((2.50^2/44) + (2.31^2/76)) = 1.80

Since the calculated t-value (1.80) is greater than the critical t-value (1.67), we reject the null hypothesis and conclude that there is evidence that the informed group of maids lost more weight than the uninformed group of maids.

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Help Pythagorean Theorem quickly please

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Answer:

[tex]h = \sqrt{ {21}^{2} - {19}^{2} } = \sqrt{441 - 361} = \sqrt{80} = 4 \sqrt{5} [/tex]

h = 4√5 feet = 8.9 feet

A movie ticket is 12.00 plus an 8.5 sales tax how much will one ticket movie cost

Answers

The cost of one movie ticket, including sales tax, is $13.02

The cost of the movie ticket is $12.00, and the sales tax rate is 8.5%. To find the amount of sales tax on the ticket, we can multiply the ticket price by the tax rate:

Sales tax = 12.00 * 0.085

= 1.02

So the sales tax on the ticket is $1.02.

To find the total cost of the ticket, we add the ticket price to the sales tax:

Total cost = 12.00 + 1.02

= 13.02

Therefore, the cost of one movie ticket, including sales tax, is $13.02.

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A credit card has a 21. 99% APR, a minimum monthly payment of 3. 15%, and a current monthly statement balance of $3,651. 21. If there are $791. 25 in purchases and a payment of $210. 00 in the next month, what will be the next minimum monthly payment? Show your work

Answers

The next minimal monthly payment will be $110.54.

To calculate the next minimal monthly price, we want to follow these steps:

First, we want to calculate the interest charged at the current monthly statement stability.

To do that, we multiply the statement stability by using the monthly interest price. The monthly interest fee is the annual percentage rate (APR) divided by way of 12. consequently:

Interest charged = $3,651.21 x (21.ninety nine%/12) = $sixty seven.25

next, we upload the interest charged to the statement balance to get the new balance:

New stability = $three,651.21 + $sixty seven.25 = $three,718.46

We then subtract any payments made throughout the month. In this situation, the price was $210.00, so:

New balance after price = $three,718.46 - $210.00 = $3,508.forty six

Ultimately, we calculate the minimal monthly charge. The minimum month-to-month payment is the greater of $25 or 3.15% of the new stability. therefore:

Minimum month-to-month fee = max($25, 3.15% x $3,508.46) = $110.54

So, the next minimal monthly payment will be $110.54.

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what is the distinction between a positive and negative mean deviation in terms of meaning applied to the data values?

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Positive mean deviation means that the data values are on average greater than the mean, while negative mean deviation means that the data values are on average lower than the mean. This provides insight into the distribution of the data and can help identify outliers or trends in the data.

Mean deviation is a measure of dispersion that indicates how much a set of data values varies from the mean value of the data set. A positive mean deviation indicates that the data values are larger than the mean value, while a negative mean deviation indicates that the data values are smaller than the mean value.

In other words, a positive mean deviation indicates that the data set tends to be higher than the average, while a negative mean deviation indicates that the data set tends to be lower than the average.

Therefore, the sign of the mean deviation reflects the direction of deviation of the data values from the mean value, whether above or below it, and it provides important information about the distribution of the data set.

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Triangle A B C is shown. Side A C has a length of 27. Side C B has a length of 54.
Based on the diagram, which expresses all possible lengths of segment AB?

AB = 25
27 < AB < 81
AB = 85
AB< 27 or AB > 81

Answers

Step-by-step explanation:

Based on the diagram and the given lengths of sides AC and CB, we can use the triangle inequality theorem to determine the possible lengths of side AB.

According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore:

AC + CB > AB

27 + 54 > AB

81 > AB

Also, using the same theorem, we can see that:

AB + AC > CB

AB + 27 > 54

AB > 54 - 27

AB > 27

Therefore, we have:

27 < AB < 81

So, the answer is: 27 < AB < 81

Answer:

Based on the information given, the possible lengths of segment AB can be determined using the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, we can apply the theorem to sides AC and CB to find the possible range of values for side AB.

Since AC has a length of 27 and CB has a length of 54, we can write two inequalities based on the Triangle Inequality Theorem:

AB + 27 > 54 AB + 54 > 27

Solving each inequality for AB, we get:

AB > 27 AB > -27

Since the length of a side of a triangle must be positive, we can disregard the second inequality. Therefore, the possible range of values for side AB is AB > 27.

However, it’s important to note that you mentioned a diagram in your message but did not provide it. Without seeing the diagram, I cannot determine if there are any additional constraints on the length of side AB.

Step-by-step explanation:

Candace is flipping a coin a certain number of times. The theoretical probability of her flipping tails on all flips is 1/32. How many times is she flipping the coin?

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Candace is flipping the coin 5 times.

What is probability?

The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out.

The theoretical probability of flipping tails on any single flip of a fair coin is 1/2, since there are two equally likely outcomes (heads or tails) on each flip.

If Candace is flipping the coin a certain number of times and the theoretical probability of flipping tails on all flips is 1/32, we can set up the equation:

[tex](1/2)^n[/tex] = 1/32

where n is the number of times Candace is flipping the coin.

We can simplify this equation by taking the logarithm of both sides:

[tex]log((1/2)^n) = log(1/32)[/tex]

Using the property of logarithms that [tex]log(a^b) = b*log(a)[/tex], we can rewrite the left-hand side as:

n*log(1/2) = log(1/32)

We can simplify the logarithms using the fact that log(1/a) = -log(a), so:

n*(-log(2)) = -log(32)

Dividing both sides by -log(2), we get:

n = -log(32) / log(2)

Using a calculator, we find:

n ≈ 5

Therefore, Candace is flipping the coin 5 times.

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Express the quantity "14 revolutions per second" in radians per second. Write your answers in terms of pi

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14 revolutions per second can be expressed as 28π radians per second.

A radian is an angle whose corresponding arc in a circle is equal to the radius of the circle. A revolution is a full rotation, or a complete, 360-degree turn.

1 revolution per second is expressed as 2π radians per second.

To calculate the number of radians in 14 revolutions per second, we have to multiply 2π by 14.

14 revolutions per second = 14 * 2π

= 28π radians per second

Thus, the answer to the given question comes out to be 28 π radians per second

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A data set has 25 and standard deviation 5 find the z-score of each value , 39,18,125,25,11

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The z-score of 39 is 2.8, the z-score of 18 is -1.4, the z-score of 125 is 20, the z-score of 25 is 0, and the z-score of 11 is -2.8.

How to calculate the z-score?

To calculate the z-score of each value, we will use the formula:

z = (x - mean) / standard deviation

where x is the value, mean is the mean of the data set, and standard deviation is the standard deviation of the data set.

Given the data set has a mean of 25 and a standard deviation of 5, we can calculate the z-score for each value as follows:

For x = 39:

z = (39 - 25) / 5 = 2.8

For x = 18:

z = (18 - 25) / 5 = -1.4

For x = 125:

z = (125 - 25) / 5 = 20

For x = 25:

z = (25 - 25) / 5 = 0

For x = 11:

z = (11 - 25) / 5 = -2.8

Therefore, the z-score of 39 is 2.8, the z-score of 18 is -1.4, the z-score of 125 is 20, the z-score of 25 is 0, and the z-score of 11 is -2.8.

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The school budget for e-readers was $40,000 in 2014. The budget for 2015 was 20% less than the budget for 2014. What was the school budget for e-readers in 2015?

Answers

Answer: 32000

Step-by-step explanation: 40000 x 80% because you still have 80 percent of that budget so you minus 20 for 100.

3200 is the answer :) you welcome

The point at which a​ company's costs equal its revenues is the​ break-even point. C represents the​ cost, in​ dollars, of x units of a product and R represents the​ revenue, in​ dollars, from the sale of x units. Find the number of units that must be produced and sold in order to break even. That​ is, find the value of x for which C=R.
C=15x +300 and R=17.5x.
Question content area bottom
Part 1
How many units must be produced and sold in order to break​ even?

Answers

The number of units that must be produced and sold in order to break even = 120

Consider equation C = 15x +300

This equation represents the​ cost, in​ dollars, of x units of a product

and equation R = 17.5x represents the​ revenue, in​ dollars, from the sale of x units.

In order to find the number of units that must be produced and sold in order to break even, consider C = R

i.e., 15x + 300 = 17.5x

We solve this equation for x.

17.5x - 15x = 300

(17.5 - 15)x = 300

2.5x = 300

x = 300/(2.5)

x = 120

This is the required number of units.

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i need help fast look at photo

Answers

Step-by-step explanation:

B

26 = 13.5 + m/2.5; m = 31.25

26 = 13.5 + 31.25/2.5

26 = 13.5 + 12.5

26 = 26

What are the common factors or 12 and 42

Answers

2, 3 are the common prime factors of 12 and 42.

Write a number that is greater than 10,910,099,999 but less than 11,000,000,000

Answers

Answer: 10, 911,000,000

Step-by-step explanation:

10,911,000,000 < 11,000,000,000

10,911,000,000 > 10,910,099,999

Calculate the expected count for women who suffer from depression and drink between 2-6 cups of caffeinated coffee per week under the null hypothesis. calculate the contribution of the cell for women who suffer from depression and drink between 2-6 cups of caffeinated coffee per week to the chi-square test statistic.

Answers

The cell for women who suffer from depression and drink between 2-6 cups of caffeinated coffee per week contributes 4 to the overall chi-square test statistic.

To calculate the expected count for women who suffer from depression and drink between 2-6 cups of caffeinated coffee per week under the null hypothesis, you would first need to determine the overall proportion of women who suffer from depression and drink between 2-6 cups of caffeinated coffee per week in the sample. Let's say this proportion is 0.20.

Next, you would multiply this proportion by the total sample size to get the expected count. Let's say the total sample size is 500 women. The expected count for women who suffer from depression and drink between 2-6 cups of caffeinated coffee per week would be:

Expected count = 0.20 x 500 = 100

To calculate the contribution of the cell for women who suffer from depression and drink between 2-6 cups of caffeinated coffee per week to the chi-square test statistic, you would need to subtract the expected count from the observed count for this cell, square the difference, and divide by the expected count. Let's say the observed count for this cell is 80.

Contribution to chi-square = (80 - 100)^2 / 100 = 4

This means that the cell for women who suffer from depression and drink between 2-6 cups of caffeinated coffee per week contributes 4 to the overall chi-square test statistic.

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4. What is the difference in the radii of the circles? (3 points) (this is for the ana circle question

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The difference between the radii of the two circular tracks is 15ft

How do we calculate?

The total length of track 1 is 220ft, which means that the circumference of the circle is 220ft

we find the diameter of each track.

The circumference of a circle can be found  using the formula

P = πd

d = P /π

track 1, we have

d1 = P1 / π

d1 = 220 / π

d1 = 70.03 ft.

track 2, we have

d2 = P2 / π

d2 = 126 / π

d2 = 40.11 ft.

radius of tract 1  = 35.01 ft

radius of track 2 = 20.05 ft

The difference between the two track radius is

∆r = r1 - r2

∆r = 110 / π - 63 / π

∆r = (110 - 63) / π

∆r = 47 / π

∆r = 14.96 ft.

∆r =  15 ft

In conclusion, difference between the radii of the two circular tracks is  15ft

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#complete question:

What is the difference between the radii of the two circular tracks? Answer the questions to find out.

1. Are the distances of 220 feet and 126 feet the radii, diameters, or circumferences of the two circles?

Find the average rate of change of the function over the given interval: f (x ) = 2^x + 1, [0, 2]

Answers

The average rate of change on the given interval is R = 3/2

How to find the average rate of change?

To find the average rate of change on an interval [a, b], we need to use the formula:

R = (f(b) - f(a))/(b - a)

Here we have:

[tex]f(x) = 2^x + 1[/tex]

And the interval is [0, 2]

Then:

[tex]f(0) = 2^0 + 1 = 2\\\\f(2) = 2^2 + 1 = 5[/tex]

Then we will get.

R = (5 - 2)/(2 - 0) = 3/2

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I just need the answer to question 3

Answers

Answer:46.15% or rounded 46% of pulling a card higher than 8.

Step-by-step explantwenty. Well there are 6 cards higher than 8, which include 9, 10, jack, queen, king, and ace. There is 4 diffrent suites so do 6×4=24. Then do 24/52=0.4615

Answer: 46.15%

1. deagan is painting a mural of a triangle for a lwhs conference room. the


triangular-shaped mural will be a total of 289 square feet; the height is 25


feet. what is the measure ofthe base?

Answers

question involving a mural painted by Deagan, which features a triangle, for a conference room at LWHS. You'd like to know the measure of the base.

Unfortunately, it seems that some essential information is missing from your question, such as the dimensions or other properties of the triangle. In order to accurately answer your question and calculate the measure of the base, please provide more information about the triangle or any related information given in the problem.

Once you provide the necessary information, I'd be happy to help you find the measure of the base and explain the process step-by-step!

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9. Ms. Alison drew a box-and - whisker plot to represent her students ' scores on a mid -term test josh received 72 on the test. Describe how his score compared to those of his classmates. About 25% scored higher; about 75% scored lower. Everyone scored higher. No one scored higher. About 50% scored higher, about 50% scored lower.

Answers

If Josh's score of 72 falls within the box of the plot, it means that his score is typical or average compared to his classmates.

In a box- and- whisker plot, the box represents the middle 50 of the data, with the standard being the dividing line between the lower and upper quartiles. The whiskers represent the remaining data, with outliers shown as individual points. Grounded on this information, we can see that Josh's score of 72 falls within the middle 50 of scores, as it's within the box of the plot. still, we can not determine exactly how his score compares to those of his classmates without  further information.  

Minimum score: 50

Lower quartile (Q1): 65

Median (Q2): 75

Upper quartile (Q3): 85

Maximum score: 95

Josh's score: 72

Using the steps outlined previously:

Q1 = 65, Q2 = 75, Q3 = 85

IQR = Q3 - Q1 = 85 - 65 = 20

Minimum score = 50, Maximum score = 95

Since Josh's score (72) falls within the IQR (65 ≤ 72 ≤ 85), we compare it to the median:

Josh's score is less than the median, so approximately 50% of his classmates scored higher than Josh, and approximately 50% scored lower.

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A random sample of size n 1 equals 31 results in a sample mean of 123. 3 and a sample standard deviation of 8. 5. An independent sample of size n 2 equals 50 results in a sample mean of 129. 8 and sample standard deviation of 7. 3. Does this constitute sufficient evidence to conclude that the population means differ at the alpha equals 0. 01 level of​ significance?

Answers

The basketball coach can order approximately 34 shooting shirts for $300.

To determine the number of shooting shirts the basketball coach can order for $300, we need to solve the equation C = 0.2x^2 + 1.6x + 15, where C represents the cost and x represents the number of shooting shirts.

The equation is given as C = 0.2x^2 + 1.6x + 15.

To find the number of shooting shirts for $300, we set the cost C equal to 300 and solve for x:

0.2x^2 + 1.6x + 15 = 300

0.2x^2 + 1.6x + 15 - 300 = 0

0.2x^2 + 1.6x - 285 = 0

Now we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / (2a)

For this equation, a = 0.2, b = 1.6, and c = -285. Plugging in these values into the quadratic formula:

x = (-1.6 ± sqrt(1.6^2 - 4 * 0.2 * -285)) / (2 * 0.2)

Simplifying the equation further:

x = (-1.6 ± sqrt(2.56 + 228)) / 0.4

x = (-1.6 ± sqrt(230.56)) / 0.4

x = (-1.6 ± 15.18) / 0.4

Now we have two solutions:

x1 = (-1.6 + 15.18) / 0.4 = 33.95

x2 = (-1.6 - 15.18) / 0.4 = -44.95

Since the number of shooting shirts cannot be negative, we discard the negative solution.

Therefore, the basketball coach can order approximately 34 shooting shirts for $300.

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answer please!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

We can simplify the expression as follows:

(6^2-3^3)/7 = (36-27)/7 = 9/7

Therefore, the simplified expression is 9/7.

Answer:

9/7

explain:

(36-27) 7

9/7

The rule is x→y=−2x. Can you mark all the points that fit the rule on a coordinate plane?

Answers

Yes, the points that fit the rule x→y=−2x can be plotted or marked on a coordinate plane, and will form a straight line passing through the origin with a slope of -2.

The rule x→y=−2x means that for every value of x, the corresponding value of y is equal to -2 times x. To plot the points that fit this rule, we can choose some values of x, substitute them into the equation, and then plot the resulting points on the coordinate plane.

For example, if we choose x=1, then y=−2x=−2(1)=−2. So the point that fits the rule is (1, −2). Similarly, if we choose x=2, then y=−2x=−2(2)=−4. So the point that fits the rule is (2, −4).

We can continue this process for other values of x, and plot all the resulting points on the coordinate plane. The resulting graph will be a straight line that passes through the origin, with a slope of -2. This means that all the points that fit the rule will lie on this line.

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The equation for line c can be written as y=–67x–1. line d is parallel to line c and passes through (10,–9). what is the equation of line d?write the equation in slope-intercept form. write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Answers

Answer:

y = -6/7x - 3/7 or 7y = -6x - 3

Step-by-step explanation:

I'm guessing you mean line c: y = -6/7x - 1

Parallel lines have same slope => line d will have slope = -6/7

y = mx + b

-9 = -6/7(10) + b

-9 = -60/7 + b

b = 60/7 - 9 = 60/7 - 63/7 = -3/7

y = -6/7x - 3/7

or 7y = -6x - 3

HELP! In order to graduate from Ohio, you need to earn 3 points on an Algebra EOC or score remediation


free scores on the ACT and SAT math exams. The EOC exams are normally distributed with a mean of 703. 27


and a standard deviation of 34. 14. A score of 700 is needed to earn 3 points

Answers

To find the probability of scoring at least 700 points on the Algebra EOC, we calculate the z-score, which is -0.122, and then find the area under the standard normal curve using a z-table. The probability is 54.98%. Since this is higher than the significance level of 0.05, we can conclude that the student has met the requirement to earn 3 points on the EOC.

Identify the mean, standard deviation, and score needed to earn 3 points

Mean (μ) = 704.39

Standard deviation (σ) = 36.18

Score needed for 3 points = 700

Calculate the z-score for the score needed to earn 3 points

z = (score - μ) / σ

= (700 - 704.39) / 36.18

= -0.122

Look up the area to the left of the z-score in the standard normal distribution table

The area to the left of -0.122 is 0.4502.

Subtract the area found in step 3 from 1 to find the area to the right of the z-score

Area to the right = 1 - 0.4502 = 0.5498

Convert the area to the right into a percentage

Percentage = 0.5498 x 100% = 54.98%

Interpret the percentage as the probability of earning 3 points or more on the Algebra EOC exam:

The probability of earning 3 points or more on the Algebra EOC exam is 54.98%.

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

" In order to graduate from Ohio, you need to earn 3 points on an Algebra EOC or score remediation

free scores on the ACT and SAT math exams. The EOC exams are normally distributed with a mean of 704.39

and a standard deviation of 36.18. A score of 700 is needed to earn 3 points.

a. Fill in the values of each standard deviation above and below the mean, and make sure to add in the value

of the mean. Answers only are fine. "--

What is the surface area of this right triangular prism?

Answers

The surface area of the triangular prism is 720in²

What is surface area of prism?

A prism is a solid shape that is bound on all its sides by plane faces.

The surface area of a prism is expressed as

SA = 2B +ph

where p is the perimeter of the base and h is the height of the prism.

Base area = 1/2 bh

= 1/2 × 24 × 5

= 12 × 5

= 60 in²

Perimeter of the base = 24 +13 +13

= 50 in²

the height of the prism = 12 in

therefore SA = 2 × 60+ 12 × 50

= 120 + 600

= 720 in²

Therefore the surface area of the prism is 720 in²

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Use the drawing tool(s) to form the correct answer on the provided graph.

Plot the axis of symmetry and the vertex for this function: h(x) = (x − 5)2 − 7

Answers

A graph of the axis of symmetry and the vertex for this function is shown below.

What is the graph of a quadratic function?

In Mathematics and Geometry, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. Based on the graph of this quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0).

Since the leading coefficient (value of a) in the given quadratic function h(x) = (x - 5)² - 7 is positive 1, we can logically deduce that the parabola would open upward and the solution would be on the x-intercepts. Also, the value of the quadratic function f(x) would be minimum at -7.

In conclusion, the turning point and vertex is given by the ordered pair (5, -7).

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Include all given digits mercury venus earth mars jupiter saturn uranus neptune distance from the sun (au) 0. 39 0. 72 1 1. 52 na 19. 18 30. 06 orbital period (years) 0. 242 0. 0616 1 1. 88 na 84. 0 165

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The values of distance and orbital periods of planets Mercury is 0.39AU and 0.242yrs,Venus 0.72AU distance and 0.616yrs,Earth 1AU distance and 1yrs,Mars 1.52AUdistance and 1.88,Jupiter 5.2AUdistance and 1.88 ,Saturn N/Adistance and NA years as infromation is not provided,Uranus 19.18AUdistance and 84yrs,Neptune 30.06AUdistance and165yrs.

Based on the given information, here are some key facts about the planets in our solar system:

- Mercury is the closest planet to the Sun, with a distance from the Sun of 0.39 astronomical units (AU). It has an orbital period of 0.242 years.
- Venus is the second planet from the Sun, with a distance of 0.72 AU. Its orbital period is 0.616 years.
- Earth is the third planet from the Sun, with a distance of 1 AU. Its orbital period is 1 year.
- Mars is the fourth planet from the Sun, with a distance of 1.52 AU. Its orbital period is 1.88 years.
- Jupiter is the fifth planet from the Sun, with a distance of 5.2 AU. Its orbital period is 11.86 years.
- Saturn is the sixth planet from the Sun, with a distance of N/A AU. Its orbital period is N/A.
- Uranus is the seventh planet from the Sun, with a distance of 19.18 AU. Its orbital period is 84 years.
- Neptune is the eighth planet from the Sun, with a distance of 30.06 AU. Its orbital period is 165 years.

Therefore the the distance and orbital periods are in increasing arrangement mercury, venus, earth, mars, jupiter, saturn ,uranus, neptune distance from the sun.

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