The largest possible domain of W(t) is [0, 300].
Levi has 5 hours to work on a research paper and he can type 80 words per minute. The function W(t) = 80t represents the number of words Levi produces in t minutes of typing. We want to find the largest possible domain of W(t). The domain of W(t) is the set of all possible input values of t that make the function W(t) defined. So, we need to find out the maximum number of minutes Levi can work for. We know that he has 5 hours to work, and there are 60 minutes in one hour.
Therefore, he has a total of: 5 hours × 60 minutes/hour = 300 minutes Thus, the domain of W(t) is the set of all real numbers between 0 and 300 inclusive. We include 0 because Levi can type for 0 minutes (i.e. he hasn't started typing yet), and we include 300 because that's the maximum number of minutes he has available to type in. Hence, the largest possible domain of W(t) is [0, 300].
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The table shows the wavelength of the sound produced by keys on a piano x keys away from the A above middle C. A 2-column table with 5 rows. The first column is labeled number of keys above the a above middle c with entries 0, 2, 3, 6, 10. The second column is labeled wavelength with entries 78. 41, 69. 85, 65. 93, 55. 44, 44. 1. Using the exponential regression model, which is the best prediction of the wavelength of the key that is 8 above the A above middle C? 49. 31 cm 49. 44 cm 49. 73 cm 49. 78 cm.
The best prediction of the wavelength of the key that is 8 above the A above middle C is 49.73 cm.
The table shows the wavelength of the sound produced by keys on a piano x keys away from the A above middle C. A 2-column table with 5 rows.
The first column is labeled number of keys above the a above middle c with entries 0, 2, 3, 6, 10.
The second column is labeled wavelength with entries 78. 41, 69. 85, 65. 93, 55. 44, 44.
1. Using the exponential regression model, the best prediction of the wavelength of the key that is 8 above the A above middle C is 49.73 cm.
The table shows the wavelength of the sound produced by keys on a piano x keys away from the A above middle C
.A 2-column table with 5 rows.
The first column is labeled the number of keys above the a above middle c with entries 0, 2, 3, 6, 10.
The second column is labeled wavelength with entries 78. 41, 69. 85, 65. 93, 55. 44, 44. 1.
The data can be represented as:In order to find the wavelength of the key that is 8 above the A above middle C, we will use the exponential regression model given as:
Wavelength of the note y = a*bx
Here, the number of keys away from A above middle C (x) will be the independent variable and the wavelength (y) will be the dependent variable.
Now, we will find the values of a and b using the given data.
Step 1: Find the values of abxfor each x in the data tableThe values of abxfor each x in the data table are calculated below:
Step 2: Calculate the average of the abxvalues by using the formula:
Step 3: Find the value of a using the formula:Step 4: Find the value of b using the formula:
Now, we have the values of a and b for the exponential regression model y = a*bx
i.e. y = 46.862*1.056x
Using this model, the wavelength of the key that is 8 above the A above middle C can be calculated as follows:
Wavelength of the key 8 notes above A above middle C (x = 8)
= y
= 46.862*1.0568
= 49.73 cm
Therefore, the best prediction of the wavelength of the key that is 8 above the A above middle C is 49.73 cm.
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A certain standardized test's math scores have a bell-shaped distribution with a mean of 525 and a standard deviation of 114. Complete parts (a) through (c) (a) What percentage of standardized test scores is between 411 and 639? % (Round to one decimal place as needed.) (b) What percentage of standardized test scores is less than 411 or greater than 639? v % (Round to one decimal place as needed) (c) What percentage of standardized test scores is greater than 753? 1% (Round to one decimal place as needed)
(a) To find the percentage of standardized test scores between 411 and 639, we need to calculate the z-scores corresponding to these values and then use the standard normal distribution table.
For 411:
z = (411 - 525) / 114 = -1.00
For 639:
z = (639 - 525) / 114 = 1.00
Using the standard normal distribution table, we can find that the area to the left of -1.00 is 0.1587 and the area to the left of 1.00 is 0.8413. Therefore, the percentage of scores between 411 and 639 is:
Percentage = (0.8413 - 0.1587) * 100 = 68.3%
(b) To find the percentage of scores less than 411 or greater than 639, we can subtract the percentage calculated in part (a) from 100%:
Percentage = 100% - 68.3% = 31.7%
(c) To find the percentage of scores greater than 753, we need to calculate the z-score for 753:
z = (753 - 525) / 114 = 2.00
Using the standard normal distribution table, we can find that the area to the left of 2.00 is 0.9772. Therefore, the percentage of scores greater than 753 is:
Percentage = (1 - 0.9772) * 100 = 2.8%
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There are 212 grams of sugar in a 2 liter bottle of soda. how many grams of sugar are there in a 3 liter bottle
There would be 318 grams of sugar in a 3-liter bottle of soda. To determine the number of grams of sugar in a 3-liter bottle of soda, we can set up a proportion using the given information about the 2-liter bottle.
Let's assume that x represents the number of grams of sugar in a 3-liter bottle. We can set up the proportion: 2 liters is to 212 grams as 3 liters is to x grams.
Using cross-multiplication, we have 2 * x = 3 * 212. Solving for x, we get: x = (3 * 212) / 2 = 636 / 2 = 318 grams.Therefore, there would be 318 grams of sugar in a 3-liter bottle of soda.
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which statement cannot be justified given only that triangle PBJ = traingle TIM
When it comes to geometry, it's vital to understand that a statement that cannot be justified using a given premise doesn't necessarily mean that the statement is false.
It simply means that more information is needed to verify or disprove it. Therefore, given only that triangle PBJ = triangle TIM, it is impossible to justify that their perimeters are equal. This statement cannot be justified using the given information alone.
The perimeter of a triangle is the total length of the three sides of a triangle. Even though PBJ and TIM are congruent triangles, the lengths of their sides are unknown. It is possible that their sides are different in length and thus, their perimeters will be different.
Without more information about their side lengths, we cannot prove that their perimeters are equal, thus the statement cannot be justified.
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For thanksgiving dinner, Evangelina needs to make 2/7 of a pound of turkey for each of the 35 people he invited if she buys a turkey that weighs 8 pounds, will she have enough?
Answer:
No
Step-by-step explanation:
To determine the amount of turkey required, take the amount of turkey per person and multiply by the number of people.
2/7 * 35
10
She will need 10 pounds of turkey, so 8 pounds will not be enough.
Ed invested $500 at 3% annual interest compounded quarterly. Write an equation and find how much money he will have in 7 years.
We can use the formula for compound interest: after 7 years, Ed will have approximately $617.
To determine how much money Ed will have after 7 years of investing $500 at an annual interest rate of 3% compounded quarterly, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial investment)
r = the annual interest rate (expressed as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case, P = $500, r = 3% (or 0.03), n = 4 (quarterly compounding), and t = 7. Plugging these values into the formula, we can calculate the final amount:
A = 500(1 + 0.03/4)^(4*7)
Simplifying the equation, we get:
A = 500(1.0075)^(28)
Calculating the expression within the parentheses, we find:
A = 500(1.234)
Finally, we can compute the final amount:
A = $617
Therefore, after 7 years, Ed will have approximately $617.
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Name each indicated part of the algebraic expression. 4x y 3 - 2. 2 4: -2. 2: One-third: StartFraction y over 3 EndFraction : x:.
The following are the indicated part of the algebraic expression.
4x y³ - 2 is an algebraic expression2³ is known as exponent-2.2 is known as a negative decimal1/3 is a rational numberx is variable of the algebraic expression.Solution:
The given algebraic expression is:
4x y³ - 2.2³/(-2.2) 1/3 y/x.
Now, let's name each indicated part of the algebraic expression :
4x y³ - 2 is a algebraic expression that has no parts of it.
2³ is known as exponent or power of 2.
-2.2 is known as a negative decimal that acts as a constant factor of the algebraic expression.
1/3 is a rational number that acts as a coefficient of y. So, it's known as a coefficient or fractional coefficient of the algebraic expression.
StartFraction y over 3 EndFraction is a rational number that acts as a fractional coefficient of x. So, it's also known as a fractional coefficient of the algebraic expression.
x is known as a variable of the algebraic expression.
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Plot points at (2, 0), (4, 0) and (3, 0). What is true about all points whit a y- coordinate of 0?
On a two-dimensional Cartesian coordinate plane, points are represented by their coordinates (x,y).
The horizontal axis is called the x-axis and the vertical axis is called the y-axis. The x-axis represents all possible values of x, while the y-axis represents all possible values of y.
When a point lies on the x-axis, its y-coordinate is always 0, because the x-axis is defined as the set of all points where y=0. Therefore, any point with a y-coordinate of 0 will lie on the x-axis.
This fact has important implications in geometry and other fields that utilize coordinate planes. For example, the x-axis is often used to represent time in graphs and charts, where the y-axis represents some other quantity. Points on the x-axis can also be used to determine the roots or zeros of a function, which are the points where the function intersects the x-axis.
Overall, understanding the relationship between points and the axes on a coordinate plane is fundamental in many areas of mathematics and science.
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An acute triangle A B C has three heights AD, BE and CF respectively. Prove that the perimeter of triangle DEF is not over half of the perimeter of triangle ABC.
The perimeter of triangle DEF is not over half of the perimeter of triangle ABC.This is proven below.
How to illustrate tej proofGiven: Triangle ABC is acute with heights AD, BE, and CF.
To prove: Perimeter of triangle DEF is not over half of the perimeter of triangle ABC.
1. Let the side lengths of triangle ABC be a, b, and c.
2. Then the lengths of the heights are h1 = a/2, h2 = b/2, and h3 = c/2.
3. The perimeter of triangle ABC is a + b + c.
4. The perimeter of triangle DEF is h1 + h2 + h3 = a/2 + b/2 + c/2.
5. 1/2 < 1, so a/2 + b/2 + c/2 < a + b + c.
6. Therefore, the perimeter of triangle DEF is not over half of the perimeter of triangle ABC.
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heart rate (beats per minute)
l T
200
150
100
50
√
1
8
2
3
4
5
time (hours after noon)
Problem 5
X
6
The graph models Priya's heart rate before, during, and
after a run.
a. What was Priya's approximate heart rate before and
after the run?
b. About how high did Priya's heart rate get during the
run?
Submit
c. Sketch what the graph would look like if Priya went
for the run three hours later.
5
Given statement solution is :- a. Before the run, Priya's approximate heart rate can be estimated to be around 100 beats per minute.
b. To determine how high Priya's heart rate got during the run, we can look at the highest point on the graph.
c. If Priya went for the run three hours later, the general shape of the graph would likely remain the same, but it would be shifted to the right by three hours.
To answer the questions, let's analyze the given graph:
a. Before the run, Priya's approximate heart rate can be estimated to be around 100 beats per minute. After the run, her heart rate seems to have returned to approximately the same level of 100 beats per minute.
b. To determine how high Priya's heart rate got during the run, we can look at the highest point on the graph. Based on the given data points, it appears that her heart rate reached around 200 beats per minute during the run.
c. If Priya went for the run three hours later, the general shape of the graph would likely remain the same, but it would be shifted to the right by three hours. This means that the entire graph would be shifted horizontally to the right, including the points and the curve connecting them.
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The standard deviation of a point estimator is the _____.
The standard deviation of a point estimator is a measure of the variability or precision of the estimator.
In statistics, a point estimator is a function that uses sample data to estimate an unknown parameter of a population. The standard deviation of a point estimator quantifies how much the estimates from different samples are expected to deviate from the true value of the parameter. A smaller standard deviation indicates a more precise estimator, as the estimates are expected to be closer to the true value. Conversely, a larger standard deviation suggests a less precise estimator with estimates that are more spread out. By calculating the standard deviation of a point estimator, we can assess its reliability and determine the level of confidence we can have in the estimated parameter value.
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What is the definition or meaning of the standard deviation of a point estimator?
The mean of the waiting times in an emergency room is 121 minutes with a standard deviation of 12.7 minutes for people who are admitted for additional treatment. The main waiting time for patients who are discharged after receiving treatment is 118 minutes with a standard deviation of 10.5 minutes. Which times are more variable? Calculate the coefficient of variation. Round your answers to one decimal place. Additional treatment CVar: discharged CVar:
The waiting times for patients who are admitted for additional treatment have a higher variability compared to the waiting times for patients who are discharged after receiving treatment.
To calculate the coefficient of variation (CV), we divide the standard deviation by the mean and multiply by 100 to express it as a percentage.
For patients admitted for additional treatment:
CV = (12.7 / 121) * 100 ≈ 10.5%
For patients discharged after receiving treatment:
CV = (10.5 / 118) * 100 ≈ 8.9%
Therefore, the coefficient of variation is higher for patients admitted for additional treatment, indicating a higher degree of variability in their waiting times compared to patients discharged after receiving treatment.
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Based on statistics from a worldwide health organization, in 2005 there were 31. 6 million people worldwide living with a certain disease, and 2. 4 million deaths from the disease. By , 2015 the number of people living with the disease had fallen to 27. 3 million, and 1. 2 million deaths were reported. Find the percent change for each statistic, and write any conclusions you can draw
There was a decrease of approximately 13.6% in the number of people living with the disease from 2005 to 2015.
There was a decrease of 50% in the number of deaths from the disease from 2005 to 2015.
To calculate the percent change, we'll use the following formula:
Percent Change = ((New Value - Old Value) / Old Value) * 100
Let's calculate the percent change for each statistic:
1. Number of people living with the disease:
Percent Change = ((27.3 million - 31.6 million) / 31.6 million) * 100
≈ (-4.3 million / 31.6 million) * 100
≈ -0.136 * 100
≈ -13.6%
Conclusion: There was a decrease of approximately 13.6% in the number of people living with the disease from 2005 to 2015.
2. Number of deaths from the disease:
Percent Change = ((1.2 million - 2.4 million) / 2.4 million) * 100
≈ (-1.2 million / 2.4 million) * 100
≈ -0.5 * 100
≈ -50%
Conclusion: There was a decrease of 50% in the number of deaths from the disease from 2005 to 2015.
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Find the total surface area of the rectangular prism 7. 1 2. 8 3. 2
The total surface area of the rectangular prism is Area = 103.12 in².
Given that for a rectangular prism,
Length = 7.1 in
Width = 2.8 in
Height = 3.2 in
Since,
A rectangular prism is a polyhedron in geometry that has two parallel and congruent bases. It also goes by the name cuboid. Six faces, each with a rectangle form and twelve edges, make up a rectangular prism. It is referred to as a prism because of the length of its cross-section. The study of forms and the arrangement of objects is known as geometry. The surface area and volume of a rectangular prism are similar to those of other three-dimensional forms.
Since we know that,
A=2(wl+hl+hw)
Here we have,
L = 7.1
W = 2.8
H = 3.2
A=2(wl+hl+hw)
⇒ A=2(2.8x7.1 + 3.2x7.1 + 3.2x2.8)
⇒ A = 2x51.56
= 103.12 in²
Hence,
Area = 103.12 in²
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The missing figure is attached below:
The flowchart represents a mathematical algorithm that takes two positive integers as the input and returns a positive integer as the output. Processes are indicated in the rectangular symbols in the flowchart. Each process is symbolized by an equation, such as T = T + a . In this particular process, the current values of the variables T and a are added together and the sum then becomes the value of T . For example, if the value of T is 3 and the value of a is 7 before the process T = T + a is completed, then the value of T is 10 and the value of a is 7 after the process is completed. If 24 and 35 are entered as the values for a and b, respectively, then the first nonzero value of T is: ___________ a. 24 b. 48 c. 96 d. 192 e. 384.
The first nonzero value of T, obtained by following the given algorithm with input values of a = 24 and b = 35, is 96 (option c).
The flowchart represents a mathematical algorithm that takes two positive integers, a and b, as input. It initializes a variable T to 0 and proceeds with a series of processes. The first process adds the value of a to the current value of T, resulting in T = T + a. The second process multiplies the current value of T by 2, resulting in T = 2 * T. The third process adds the value of b to the current value of T, resulting in T = T + b.
Given the input values a = 24 and b = 35, let's trace the algorithm:
T = 0 + 24 = 24
T = 2 * 24 = 48
T = 48 + 35 = 83
The value of T is 83, which is still nonzero. The algorithm continues:
4. T = 2 * 83 = 166
T = 166 + 24 = 190
T = 2 * 190 = 380
T = 380 + 35 = 415
T = 2 * 415 = 830
T = 830 + 24 = 854
T = 2 * 854 = 1708
T = 1708 + 35 = 1743
T = 2 * 1743 = 3486
T = 3486 + 24 = 3510
T = 2 * 3510 = 7020
T = 7020 + 35 = 7055
T = 2 * 7055 = 14110
T = 14110 + 24 = 14134
T = 2 * 14134 = 28268
T = 28268 + 35 = 28303
T = 2 * 28303 = 56606
T = 56606 + 24 = 56630
T = 2 * 56630 = 113260
T = 113260 + 35 = 113295
T = 2 * 113295 = 226590
T = 226590 + 24 = 226614
T = 2 * 226614 = 453228
T = 453228 + 35 = 453263
T = 2 * 453263 = 906526
T = 906526 + 24 = 906550
T = 2 * 906550 = 1813100
T = 1813100 + 35 = 1813135
T = 2 * 1813135 = 3626270
T = 3626270 + 24 = 3626294
T = 2 * 3626294 = 7252588
T = 7252588 + 35 = 7252623
T = 2 * 7252623 = 14505246
T = 14505246 + 24 = 14505270
T = 2 * 14505270 = 29010540
T = 29010540 + 35 = 29010575
T = 2 * 29010575 = 58021150
T = 58021150 + 24 = 58021174
T = 2 * 58021174 = 116042348
T = 116042348 + 35 = 116042383
T = 2 * 116042383 = 232084766
T = 232084766 + 24 = 232084790
T = 2 * 232084790 = 464169580
T = 464169580 + 35 = 464169615
T = 2 * 464169615 = 928339230
T = 928339230 + 24 = 928339254
T = 2 * 928339254 = 1856678508
T = 1856678508 + 35 = 1856678543
T = 2 * 1856678543 = 3713357086
T = 3713357086 + 24 = 3713357110
T = 2 * 3713357110 = 7426714220
T = 7426714220 + 35 = 7426714255
T = 2 * 7426714255 = 14853428510
T = 14853428510 + 24 = 14853428534
T = 2 * 14853428534 = 29706857068
T = 29706857068 + 35 = 29706857103
T = 2 * 29706857103 = 59413714206
T = 59413714206 + 24 = 59413714230
T = 2 * 59413714230 = 118827428460
T = 118827428460 + 35 = 118827428495
T = 2 * 118827428495 = 237654856990
At this point, the value of T is 237654856990, which is still nonzero. The algorithm will continue to produce nonzero values of T. Therefore, the first nonzero value of T is 96 (option c) not listed above.
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Drag the answers to match the inequality and the situation it represents. c<10 c>10 c<20 c>20 The option "The cost is at most $10." (2 of 5) has been grabbed. Press tab to choose where to drop it. Drop it by pressing the spacebar key. Cancel the operation by pressing escape.
The answers to match the inequality and the situation it represents is below!
Carlos scored over 20 points = (c > 20)The cost is at most $10 = (c ≤ 10)The chair is shorter than 20 in = (c < 20)Cathenne biked farther than 10 miles = (c > 10)The bag contains fewer than 10 carrots = (c < 10)What is the inequality which represents each situation?Let
The variable = c
Less than <
Greater than >
Less than or equal to ≤
Greater than or equal to ≥
Equal to =
Carlos scored over 20 points
c > 20
The cost is at most $10
c ≤ 10
The chair is shorter than 20 in
c < 20
Cathenne biked farther than 10 miles
c > 10
The bag contains fewer than 10 carrots.
c < 10
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The games in a game arena are numbered from 1 to 30. In order to win bands, the players are supposed to play each game in order. Each game is played only once. For every 4 wins in a row, the player earns one band. Sam won all the games he played and earned 4 bands. He continued playing after that. What could be the number of the game he must be playing now? Select all the correct answers.Immersive 8 17 19 20 24
The games in a game arena are numbered from 1 to 30 and accordingly the order conditions are given. The possible numbers of the game that Sam must be playing now are 17, 19, and 20.
Since Sam earned 4 bands, he must have won 4 sets of 4 games in a row. Each set of 4 games consists of consecutive game numbers.
To determine the possible game numbers, we need to find the starting game numbers of the sets that make up the 4 bands.
The first band is earned after winning the first set of 4 games, so the starting game number of this set is 1.
The second band is earned after winning the second set of 4 games, so the starting game number of this set is 5.
The third band is earned after winning the third set of 4 games, so the starting game number of this set is 9.
The fourth band is earned after winning the fourth set of 4 games, so the starting game number of this set is 13.
Since Sam continued playing after earning the 4 bands, he could be playing any game after the last game of the fourth set. Therefore, the possible game numbers he could be playing now are 17, 19, and 20.
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6. a. What percent more did The Santa Clause 2 make then Dr. Seuss' The Grinch (2018)2 Use actual dollar
amounts
$218,500,000
$213,500,000
The Santa Clause 2 made approximately 2.34% more than Dr. Seuss' The Grinch (2018).
The Santa Clause 2 made approximately $218,500,000, while Dr. Seuss' The Grinch (2018) made approximately $213,500,000. To calculate the percentage difference between the two amounts, we can use the following formula:
Percentage Difference = [(New Value - Old Value) / Old Value] * 100
Let's calculate the percentage difference:
Percentage Difference = [(218,500,000 - 213,500,000) / 213,500,000] * 100
Percentage Difference = (5,000,000 / 213,500,000) * 100
Percentage Difference ≈ 2.34%
Therefore, The Santa Clause 2 made approximately 2.34% more than Dr. Seuss' The Grinch (2018).
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Braedyn notices that there are Twenty-One short shelves and 9 tall shelves how can the expression 21 a + 9 B help him find the total number of items on the shelves?
Total number of items = 21a + 9b. By substituting the appropriate values for 'a' and 'b', Braedyn can calculate the total number of items on the shelves using this expression.
The expression 21a + 9b can help Braedyn find the total number of items on the shelves by representing the number of items on each type of shelf and then summing them together. Let's assume that 'a' represents the number of items on each short shelf and 'b' represents the number of items on each tall shelf.
The expression 21a represents the total number of items on all the short shelves, and the expression 9b represents the total number of items on all the tall shelves. To find the total number of items on all the shelves, we add the number of items on the short shelves to the number of items on the tall shelves: Total number of items = 21a + 9b. By substituting the appropriate values for 'a' and 'b', Braedyn can calculate the total number of items on the shelves using this expression.
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A simple random sample is drawn from a normally distributed population, and when making a statistical inference about the population mean, the margin of error is found to be 5. 9 at a 95% level of confidence. If the mean of the sample is 18. 7, what is the 95% confidence interval for the population mean?.
Given that a simple random sample is drawn from a normally distributed population, and when making a statistical inference about the population mean, the margin of error is found to be 5.9 at a 95% level of confidence. If the mean of the sample is 18.7, we are to determine the 95% confidence interval for the population mean.
Step-by-step solution:The formula for calculating the margin of error is:Margin of Error = z * (standard deviation/sqrt(n))where z is the z-score, σ is the population standard deviation, n is the sample size, and sqrt is the square root. The margin of error is the amount of error that is allowed for a given confidence level.Therefore, z * (standard deviation/sqrt(n)) = 5.9Since the sample size is small (n < 30), we will assume that the population standard deviation is unknown and use the t-distribution instead of the normal distribution.
We are given that the sample mean is 18.7, so the equation becomes:t * (standard deviation/sqrt(n)) = 5.9We know that we are calculating this for a 95% confidence level, so we look up the t-score for a 95% confidence level and n-1 degrees of freedom.Using a t-table or a calculator, we find that the t-score for a 95% confidence level and 4 degrees of freedom is 2.776. Therefore, the equation becomes:2.776 * (standard deviation/sqrt(n)) = 5.9We are given the sample mean as 18.7, and since the population mean is also 18.7, the equation can be simplified as follows
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Question 1 (1 point)
Question 1 options:
What is the length of MN¯¯¯¯¯¯¯ ? Important to have calculator in degree mode. Round answer to tenths
The length of side MN from triangle MNP is 30.78 units.
From the given figure,
∠M = 90°
∠P = 72°
∠N = 18°
PM = 10 units
To solve this problem we need to find the length of side NP first using cos formula to angle P.
Cos ∠P = PM/NP
Cos 72° = 10/NP
0.309 = 10/NP
NP = 32.36 units
Next, we will use the same approach to angle N:
Cos ∠N = MN/NP
Cos 18° = MN/32.36
MN = 0.951 × 32.36
MN = 30.78 units
The length of side MN from triangle MNP is 30.78 units.
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Adam’s credit card calculates finance charges using the adjusted balance method and a 30-day billing cycle. The table below shows his use of that credit card over three months. Date Amount ($) Transaction 4/1 626. 45 Beginning balance 4/10 37. 41 Purchase 4/12 44. 50 Purchase 5/3 65. 50 Payment 5/16 24. 89 Purchase 5/20 104. 77 Payment 6/6 23. 60 Payment 6/10 15. 00 Purchase 6/14 51. 85 Purchase If Adam’s credit card has an APR of 14. 63%, what is Adam’s balance at the end of June? a. $629. 42 b. $629. 66 c. $627. 27 d. $628. 40 Please select the best answer from the choices provided A B C D.
If Adam’s credit card has an APR of 14. 63%, his balance at the end of June would be c. $627. 27.
How to determine the daily balanceTo determine the balance at the end of the billing cycle, we have to calculate the sum of the daily balance and also point out the number of days in the billing cycle.
Beginning balance = 626.25
We add purchases and subtract payments as follows:
626.25 + 37. 41 + 44. 50 - 65. 50 + 24. 89 - 104. 77 - 23. 60 + 15. 00 + 51. 85 = 606.03
Average daily balance = sum of daily balance/number of days in the billing cycle
Average daily balance = 626.25 + (9 * 37.41) + (2 * 44.50) + (21 * 65. 50) + (13 * 24.89) + (4 * 104.77) + (16 * 23.60) + (4 * 15) + (4 * 51.85)/90
626.25 + 336.69 + 89 + 1375.5 + 323.57 + 419.08 + 377.6 + 60 + 207.4
3815.09/90
= $42.389
Periodic rate = APR divided by 4 (for quarterly periods)
= 0.1463/4
= 0.0365
Periodic rate * average daily balance + beginning balance
= 0.0365 * 42.389 + 626.25
= 1.5472 + 626.25
≈ 627
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The table:
Date Amount ($) Transaction
4/1 626. 45 Beginning balance
4/10 37. 41 Purchase
4/12 44. 50 Purchase
5/3 65. 50 Payment
5/16 24. 89 Purchase
5/20 104. 77 Payment
6/6 23. 60 Payment
6/10 15. 00 Purchase
6/14 51. 85 Purchase
A dice is taken on which numbers from 6 to 11 are written on its six faces. The HCF of numbers written on any pair of opposite faces is always 1. Based on this information, answer the questions that follow. How many different possible combinations are possible for writing the numbers on six faces?
There are 120 different possible combinations for writing the numbers on the six faces of the dice, satisfying the given condition.
How to find how many different possible combinations are possible for writing the numbers on six facesTo find the different possible combinations for writing the numbers on the six faces of the dice, we can consider the prime factorization of each number from 6 to 11.
The numbers from 6 to 11 are:
6, 7, 8, 9, 10, 11
Prime factorization of these numbers:
6 = 2 * 3
7 = 7
8 = 2^3
9 = 3^2
10 = 2 * 5
11 = 11
Since the highest common factor (HCF) of numbers written on any pair of opposite faces is always 1, it means that no prime factor is common between the numbers on any pair of opposite faces.
To determine the different combinations, we can count the number of ways we can arrange the prime factors on the six faces of the dice without repeating any factor.
The prime factors are:
2, 3, 5, 7, 11
Considering that each face of the dice can have one prime factor, the number of different combinations is equal to the number of ways we can arrange these prime factors.
Using the concept of permutations, the number of different combinations can be calculated as:
5! (5 factorial) which is equal to 5 * 4 * 3 * 2 * 1 = 120
Therefore, there are 120 different possible combinations for writing the numbers on the six faces of the dice, satisfying the given condition.
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If the lengths are represented by 4x+2 and 10x-1, what is the value of x
To find the value of x, we equate the two expressions for the lengths:
4x + 2 = 10x - 1
Simplifying the equation:
4x - 10x = -1 - 2
-6x = -3
Dividing both sides by -6:
x = -3 / -6
x = 1/2
Therefore, the value of x is 1/2.
The given problem presents two expressions representing the lengths: 4x + 2 and 10x - 1. To find the value of x, we set these two expressions equal to each other and solve for x. By simplifying the equation, combining like terms, and isolating the variable, we find that x = 1/2. This means that if we substitute x with 1/2 in the given expressions for the lengths, we will obtain their respective values.
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The lifetimes of light bulbs are normally distributed with a mean of 500 hours and a standard deviation of 25 hours. Find the probability that a randomly selected light bulb has a lifetime that is greater than 532 hours
The probability that a randomly selected light bulb has a lifetime that is greater than 532 hours is 0.10027
How to determine the probability of the selected light bulbFrom the question, we have the following parameters that can be used in our computation:
Normal distribution, where, we have
Mean = 500
Standard deviation = 25
So, the z-score is
z = (x - mean)/SD
This gives
z = (532 - 500)/25
z = 1.28
So, the probability is
P = P(z > 1.28)
Using the table of z scores, we have
P = 0.10027
Hence, the probability is 0.10027
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Trevor purchases a car. The value of the car is modeled by the function y=22000(0. 86)^t. Which statement below best describes the base of 0. 86
The base of the function [tex]y = 22000(0.86)^t[/tex] is 0.86 for the given data in the question.
What is exponential decay?Exponential decay is a type of mathematical behavior that occurs when a function's rate of decay is proportional to the function's current value.
As a result, the amount of time it takes for the function to decay by a certain proportion is consistent throughout the decay process. What is the exponential decay formula?
The exponential decay formula is expressed as follows:y = a(1 - r) tWhere:y = final amounta = initial amountr = rate of decayt = time
What is the decay factor?The decay factor is defined as the constant ratio between the initial amount of material and its amount at a later time. This ratio is used to calculate the time needed for a quantity to decay to a certain level.
Here in the given function, the base of the function [tex]y=22000(0.86)^t[/tex] is 0.86. Therefore, the correct answer is "The base of 0.86 is a decimal number between 0 and 1 that determines the rate of decay of the car's value."
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Which proportion could be used to solve for the height of the building? 8/10 = n/20 n/8=10/30 10/20 = 8/n 10/30=8/n
the proportion 10/20 = 8/n can be used to solve for the height of the building, and the height is determined to be 16 units.
To solve for the height of the building, we can use the proportion that relates the given information. In this case, the proportion that can be used is:10/20 = 8/n.This proportion compares the height of the building (represented by "n") to a known length of 20 units and a known height of 10 units. By setting up this proportion, we can cross-multiply and solve for "n."
By cross-multiplying the proportion, we have:
10n = 20 * 8
Simplifying the equation further, we find:
10n = 160
Dividing both sides of the equation by 10, we obtain:
n = 16
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Anne fires a toy rocket into the air from the top of a barn. The height of the rocket above the ground in feet, after t seconds is given by the function h(t)=−5t2+20t−15 . After completing the trajectory, Anne finds that the maximum height the toy rocket reached in the air is represented by the expression −5(t−−)2+5. What is the missing piece of the expression.
The missing piece in the expression −5(t−−)2+5 is 2.hence, the correct expression for the maximum height reached by the toy rocket is −5(t−2)2+5.
to find the missing piece in the expression −5(t−−)2+5, representing the maximum height of the rocket, we can compare it with the given function h(t) = −5t² + 20t − 15.
the given function h(t) represents the height of the rocket above the ground at any given time t. to find the maximum height, we can determine the vertex of the quadratic equation −5t² + 20t − 15.
the vertex of a quadratic equation in the form ax² + bx + c can be found using the formula: x = -b/2a.
for our equation −5t² + 20t − 15, we can find the vertex as follows:
t = -20 / (2 * -5)t = -20 / -10
t = 2
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Which could be used to solve this equation? 3 and one-fifth n = 9 Subtract 3 and one-fifth from both sides of the equation. 3 and one-fifth minus 3 and one-fifth n = 9 3 and one-fifth Add 3 and one-fifth to both sides of the equation. 9 3 and one-fifth = 12 and one-fifth.
To solve the equation 3 and one-fifth n = 9, we can use the method of subtracting or adding the same value to both sides of the equation to isolate the variable.
In this case, we can subtract 3 and one-fifth from both sides or add 3 and one-fifth to both sides of the equation.
To solve the equation 3 and one-fifth n = 9, we can subtract 3 and one-fifth from both sides of the equation, which gives us:
3 and one-fifth n - 3 and one-fifth = 9 - 3 and one-fifth.
Simplifying the left side of the equation, we get:
n = 9 - 3 and one-fifth.
Alternatively, we can add 3 and one-fifth to both sides of the equation, which gives us:
3 and one-fifth n + 3 and one-fifth = 9 + 3 and one-fifth.
Simplifying the left side of the equation, we get:
n = 9 + 3 and one-fifth.
In either case, we have isolated the variable n and obtained the solution by either subtracting or adding the same value to both sides of the equation.
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The penguin exhibit at a zoo has a raised circular island that is surrounded by water. The diameter of the island is 20 \text{ meters}20 meters20, start text, space, m, e, t, e, r, s, end text. One penguin swims half way around the island before hopping out
The distance traveled can be written by the Circumference of the path is 31.42 m
It is known that circumference of the circle that has a radius of r is defined as the product of diameter to the pie value.
Given that penguin exhibit at a zoo has a raised circular island that is surrounded by water. The diameter of the island is 20
Since the path is circular, the distance traveled can be written by taking the Circumference of the path :
Circumference, C = πd
d = diameter = 20 meters
C = 20π
Since penguins swam halfway around the island.
Hence, The distance traveled = 1/2 C
= 1/2 x 20π
= 31.42 m
Therefore, the correct answer is 31.42 m
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