please help
The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds:
Answers
According to the graph, the balloon ascends between seconds 0 and 2; it remains stable between seconds 2 and 3; drops rapidly between 3 and 4 seconds; it descends slowly between seconds 4 and 6. Additionally, the natural thing is that it does not ascend again because gravity will not allow it to ascend.
How to describe the movement of the pump?To describe the movement of the balloon we must analyze the relationship between the height of the bomb and time. Based on the above, we see that it ascends, holds, descends rapidly, and then slows its rate of descent as described below:
The balloon ascends between seconds 0 and 2.The balloon is stable between 2 and 3 seconds.The balloon descends rapidly between seconds 3 and 4.The balloon slowly descends between seconds 4 and 6.Learn more about balloon in: https://brainly.com/question/18884332
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Related Questions
Kate is x years old. Lethna is 3 times as old as Kate. Mike is 4 years older than Lethna. write down an expression, in terms of x for Mike's age
Answers
Answer: Mike is ( 3x + 4 ) years old
Step-by-step explanation:
K -> x y/o
L -> 3x y/o
M -> (3x + 4) y/o
please help me !!!!!!
Answers
The equation representing total fraction strip is ³/₃ + ¹/₃ = ⁴/₃.
option B.
What is a fraction?
A fraction is a mathematical representation of a part of a whole or a ratio between two numbers. It consists of a numerator, which represents the number of parts being considered, and a denominator, which represents the total number of parts in the whole.
For this case, 1 is divided into, and 1 divide into 3.
To obtain the total fractions, we will add the individual fractions as shown below;
For this first fraction = ¹/₃ + ¹/₃ + ¹/₃
For the second fraction = ¹/₃
Total fraction = 3(¹/₃ + ¹/₃ + ¹/₃) + ¹/₃
Total fraction = ³/₃ + ¹/₃ = ⁴/₃
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Faith is a 95% free throw shooter. At practice, each player shoots 20 free throws. Let x= the number of free throws faith makes out of 20 shots. Calculate and interpret the standard deviation of x
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If at practice, each player shoots 20 free throws, the standard deviation of x is 0.975.
To calculate the standard deviation of x, we need to first determine the variance. The variance is the average of the squared differences of each observation from the mean.
In this case, Faith is a 95% free throw shooter, so she is expected to make 19 out of 20 shots on average. The probability of making a free throw is 0.95, and the probability of missing a free throw is 0.05. Therefore, the mean of x is:
mean(x) = 20 * 0.95 = 19
To calculate the variance, we need to find the expected value of (x - mean(x))^2. Since Faith's free throw shooting is independent, we can use the binomial distribution to find the probability of making x shots out of 20.
The formula for the variance of a binomial distribution is np(1-p), where n is the number of trials and p is the probability of success. Therefore, the variance of x is:
var(x) = 20 * 0.95 * 0.05 = 0.95
Finally, the standard deviation is the square root of the variance:
sd(x) = √(var(x)) = √(0.95) = 0.975
This means that on average, Faith is expected to make 19 out of 20 free throws, but there is a standard deviation of 0.975, which indicates the degree of variability or spread around the mean. In other words, we can expect Faith to make between 18 and 20 free throws in most cases, but there is a small chance that she may make fewer or more than that.
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Urgent Help! 100 points to whoever is willing ^-^
Noise-canceling headphones have microphones to detect the ambient, or background, noise. They interpret those noises as sinusoidal functions. To cancel out that noise, the headphones create their own sinusoidal functions that mimic the incoming noise, but it changes them in one of two ways.
1. The mimic function is the negative of the noise's function.
2. The mimic function is the noise function shifted one-half period.
The headphones then play the noise function together with the mimic function, which cancels the noise.
Instructions
• Find the frequency of any musical note in hertz (Hz).
• Use the frequency to write f(x), the sine function for the note. For example, [tex]A_4[/tex] has a frequency of 440 Hz. In radians, we describe this note as y = sin(440(2πx)) or y − sin(880πx)
• Graph the sine function for the chosen note.
• Use one of the two methods listed above to write g(x), the mimic function that cancels that note's sound. Graph that function.
• Write a third function, h(x), that is the sum of f(x) and g(x). Graph it.
• Use your three graphs to explain why g(x) cancels out f(x).
Answers
f(x) = sin(2πfx)
To cancel out this note, we need to create a mimic function g(x) that is either the negative of f(x) or shifted one-half period. Let's consider the two cases separately:
1. Mimic function is the negative of f(x):
In this case, the mimic function g(x) is simply the negative of f(x):
g(x) = - sin(2πfx)
We can graph f(x) and g(x) together to see how they cancel each other out:
Graph of f(x) and g(x) when g(x) is the negative of f(x):
The blue graph represents f(x), while the red graph represents g(x). As we can see, the two functions are equal in magnitude but opposite in sign. When we add them together, we get:
h(x) = f(x) + g(x) = sin(2πfx) - sin(2πfx) = 0
This means that the sound of the musical note is cancelled out completely.
2. Mimic function is the noise function shifted one-half period:
In this case, the mimic function g(x) is the sine function with the same frequency as f(x), but shifted one-half period:
g(x) = sin(2πfx + π)
We can graph f(x) and g(x) together to see how they cancel each other out:
Graph of f(x) and g(x) when g(x) is the noise function shifted one-half period:
The blue graph represents f(x), while the red graph represents g(x). As we can see, the two functions are equal in magnitude but out of phase by one-half period. When we add them together, we get:
h(x) = f(x) + g(x) = sin(2πfx) + sin(2πfx + π)
Using trigonometric identities, we can simplify this expression to:
h(x) = 2cos(π/2)sin(2πfx + π/2)
h(x) = 2cos(π/2)cos(2πfx) (since sin(2πfx + π/2) = cos(2πfx))
h(x) = 2sin(2πfx)
This means that the sound of the musical note is cancelled out completely.
In summary, the mimic function g(x) cancels out the sound of the musical note by either being the negative of the noise function or being the noise function shifted one-half period. In both cases, the mimic function has the same frequency as the noise function, but is equal in magnitude and opposite in sign or out of phase by one-half period. When we add the noise function and the mimic function together, they cancel each other out and we are left with no sound.
Caleb observed the costumes that people wore to a costume party. The themes of the costumes and the number of people who wore them are shown in the following table.
Costume Theme Superhero Decades Scary TV & Movie Characters Animals Career
Number of People 128 96 72 52 24 28
A circle graph was drawn from the data in the table. What percentage would be on the Decades slice of the circle graph?
24%
26.7%
86.4%
96%
Question 4(Multiple Choice Worth 2 points)
Answers
Answer: 24
Step-by-step explanation:
Find the rate of change of the area of a square with respect to the length z, the diagonal of the square. What is the rate when z = 3? a) dA/dz = z; rate = 6 b) dA/dz = zroot2; rate = 3 root2 c) dA/dz = 2z; rate = 3 d) dA/dz = z; rate = 3 e) dA/dz = 2z; rate = 6
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The rate of change of the area of a square with respect to the length z, the diagonal of the square is dA/dz = 2z; rate = 6. The correct answer is C.
We know that the area A of a square is given by A = s², where s is the length of the sides of the square. Also, we know that the diagonal of the square (z) is related to the sides by the Pythagorean theorem: s² + s² = z² or 2s² = z² or s² = z²/2.
Taking the derivative of both sides of the equation s² = z²/2 with respect to z, we get:
2s ds/dz = 2z/2
s ds/dz = z
Now, since the area A is given by A = s², we can take the derivative of both sides of this equation with respect to z:
dA/dz = d/dz (s²) = 2s ds/dz
Substituting the value of s ds/dz obtained earlier, we get:
dA/dz = 2s (z/s) = 2z
Therefore, the correct option is (c) dA/dz = 2z, and the rate of change of the area of the square with respect to the length z is 2z. When z = 3, the rate of change is 2(3) = 6. So, the answer is (c) dA/dz = 2z; rate = 6.
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Solve the system of equations:
y = 2x – 5
y = x^2 – 5
A. (–1, –7) and (4, 3)
B. (–1, –4) and (3, 4)
C. (0, –5) and (2, –1)
D. (0, 5) and (2, 2)
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Answer:
C. (0, –5) and (2, –1)
use a blank number line to solve. which of the following expressions have a value that is less than 0? select all that apply. Sorry is it says i am in high school i am in 7th grade
a)-5+3
b)6+(-8)
c)5+(-3)
d)-2+5
Answers
The expressions that have values less than 0 are a) and b)
According to the question
Here's how you can use a number line to solve this problem:
Draw a blank number line with a zero in the middle.For each expression, start at zero and move to the right or left depending on the sign of the first number.Then, add or subtract the second number to get the final position on the number line.If the final position is to the left of zero, the expression has a value that is less than 0.For example in expression a) -5 + 3, start at zero and move 5 units to the left (because of the negative sign on 5), and then move 3 units to the right. The final position is at -2, which is to the left of zero. Therefore, expression a) has a value that is less than zero.
Similarly expression b) has a value that is less than zero.
Also expressions c) and d) can be solved in the same way. If the final position is to the right of zero, the expression does not have a value that is less than zero.
In conclusion, expressions a) and b) have a value that is less than zero, while expressions c) and d) do not.
What is a number line?
A number line is a visual representation of real numbers arranged in a straight line used to compare, add, and subtract numbers.
What is meant by expressions?
An expression is a combination of numbers, variables, and mathematical operations used to represent a quantity or a mathematical statement.
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The hanger image below represents a balanced equation.
Write an equation to represent the image
HELP THIS IS DUE TODAY
Answers
Answer:
2 + r = 6
Step-by-step explanation:
2 + r = 6
r = 6 - 2 = 4
6 on the left balanced by 2 plus r on the right
find how many positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, are not divisible by either 5 or 7.
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The number of positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, are not divisible by either 5 or 7 is 4680.
Step by step explanation:
The number of positive integers with exactly four decimal digits between 1000 and 9999 inclusive can be obtained as follows:
Total number of four decimal digits = 9999 − 1000 + 1 = 9000
Numbers that are multiples of 5 are obtained by starting with 1000 and adding 5, 10, 15, 20, ..., 1995, that is, 5k, where k = 1, 2, 3, ..., 399.
Therefore, the number of positive integers with exactly four decimal digits that are multiples of 5 is 399.
Numbers that are multiples of 7 are obtained by starting with 1001 and adding 7, 14, 21, 28, ..., 1428, that is, 7m, where m = 1, 2, 3, ..., 204.
Therefore, the number of positive integers with exactly four decimal digits that are multiples of 7 is 204.
Note that some numbers in the interval [1000, 9999] are divisible by both 5 and 7. Since 5 and 7 are relatively prime, the product of any number of the form 5k by a number of the form 7m is a multiple of 5 × 7 = 35.
The numbers of the form 35n in the interval [1000, 9999] are
1035, 1070, 1105, 1140, ..., 9945, 9980.
We can check that there are 285 numbers of this form.
To find the number of positive integers with exactly four decimal digits that are not divisible by either 5 or 7, we will subtract the number of multiples of 5 and 7 and add the number of multiples of 35.
Therefore, the number of positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, are not divisible by either 5 or 7 is
9000 - 399 - 204 + 285 = 4680.
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the national football league (nfl) records a variety of performance data for individuals and teams. to investigate the importance of passing on the percentage of games won by a team, the following data show the conference (conf), average number of passing yards per attempt (yds/att), the number of interceptions thrown per attempt (int/att), and the percentage of games won (win%) for a random sample of 16 nfl teams for one full season.
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The National Football League (NFL) is an American football league that is based in the United States. The NFL records a variety of performance data for individuals and teams. To investigate the importance of passing on the percentage of games won by a team, the following data show the conference (conf), average number of passing yards per attempt (yds/att), the number of interceptions thrown per attempt (int/att), and the percentage of games won (win%) for a random sample of 16 NFL teams for one full season.The data collected by the NFL shows that passing has a significant impact on the percentage of games won by a team. Teams that have a higher average number of passing yards per attempt tend to win more games than those with a lower average. Additionally, teams that have a lower number of interceptions thrown per attempt also tend to win more games than those with a higher number of interceptions thrown per attempt.The data also shows that the conference a team plays in does not have a significant impact on the percentage of games won by a team. This means that a team's conference is not a good indicator of its performance.The NFL should continue to record data on passing to help teams improve their performance. Coaches can use this data to identify areas for improvement and develop strategies to help their teams win more games.
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Which of the following algorithms sorts data by recursively splitting the array into smaller sub-arrays, until eventually reaching single-element sections, and then joins the sub-arrays back together in sorted order? A Heap Sort B Quick Sort Merge Sort (D Radix Sort
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B) Quick Sort is algorithms sorts data by recursively splitting the array into smaller sub-arrays, until eventually reaching single-element sections, and then joins the sub-arrays back together in sorted order
What is Merge Sort Algorithm?Merge Sort is an effective algorithm for sorting the data items of a list or an array. This algorithm's fundamental idea is to break the unsorted list into many sub-lists until every sub-list contains only one item.
The merging procedure then recombines all of the sublists, resulting in a sorted list. Divide-and-conquer is the name given to this merging process. Merge Sort divides the original list into N sublists, each of which contains one element.
The Merge Sort algorithm is faster than other sorting algorithms when it comes to time complexity. The time complexity of Merge Sort is O (n log n), which is better than Bubble Sort and Insertion Sort.
It is a more efficient sorting algorithm than other algorithms, such as bubble sort, which has a higher time complexity of O (n²).
Therefore, we can say that Merge Sort is the most efficient algorithm to sort an array in ascending or descending order.
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PLSS HELP IVE TRIED EVERYTHING
Answers
Answer:
Step-by-step explanation: To obtain the function g(x) that represents the indicated transformations of the graph of f(x) = 2, which are a translation 1 unit up followed by a horizontal stretch by a factor of 2, we can follow these steps:
To translate f(x) = 2 one unit up, we can add 1 to the function: f(x) + 1.
To horizontally stretch f(x) + 1 by a factor of 2, we can multiply the input (x) by 1/2: f(1/2 x) + 1.
Therefore, the function g(x) that represents the indicated transformations of f(x) is:
g(x) = f(1/2 x) + 1
g(x) = 2(1/2 x) + 1
g(x) = x + 1
What is the slope of the line described by the equation below?
y = -6x +3
O A. -6
() в. -з
O C. 6
OD. 3
SUBMIT
Answers
In this form, M represents the slope of a line, and B represents the line’s y-intercept.
In your equation, y=-6x+3, M is -6 and B is 3. So, your y-intercept is 3 and your slope is -6.
Solve
2n > 20
Pls help really quick
Answers
Answer:
n > 10
Step-by-step explanation:
2n > 20
2n/2 > 20/2
n > 10
stuck on this question need some help
Answers
Answer:
1. The graphs of f(x) and h(x) are both quadratic functions with a minimum point. However, the minimum point of f(x) is located at (6,0), while the minimum point of h(x) is located at (2,3).
2. The graphs of g(x) and h(x) both open upwards and are quadratic functions. However, the vertex of g(x) is located at the origin (0,0), while the vertex of h(x) is located at (2,3).
3. The graph of g(x) is a simple parabola that opens upwards, while the graphs of f(x) and h(x) are more complex parabolas with a minimum point and an upward opening. The graph of f(x) is centered at (6,0), while the graph of h(x) is centered at (2,3).
Emily needs enough fabric for 3½ hats, since she has half done already. If each hat requires1 2/7 feet of fabric how much will she need to make the 3½ hats
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Using simple mathematical operations we know that 4.5 ft of fabric is needed.
What are mathematical operations?A rule that specifies the right procedure to follow while evaluating a mathematical equation is known as the order of operations.
Parentheses, Exponents, Multiplication and Division (from Left to Right), Addition, and Subtraction are the steps that we can remember in that order using PEMDAS (from left to right).
So, to find the fabric needed:
1 2/7 feet of fabric
Then, 3 1/2 hands will need:
= 9/7 * 7/2
= 9/2
= 4.5 ft of cloth
Therefore, using simple mathematical operations we know that 4.5 ft of fabric is needed.
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Correct question:
Emily needs enough fabric for 3 1/2 hat's since she has half a hat done already. if each hat requires 1 2/7 feet of fabric, how much fabric will she need to make the 3 1/2 hat's?
Construct triange ABC, in which AB = 6 cm, angle BAC = 96 degrees and angle ABC = 35 degrees. Measure the length of BC. Give your answer to 1 d. P
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From the construction of the triangle ABC we get that the measure length of BC is approximately 4.22cm
To construct triangle ABC, we can follow these steps:
Draw a line segment AB of length 6 cm.Draw an angle of 96 degrees at point A using a protractor.Draw an angle of 35 degrees at point B using a protractor.The intersection point of the two lines that were drawn in step 2 and 3 will be point C, which is the third vertex of the triangle.To measure the length of BC in triangle ABC, we can use the law of sines.
The law of sines states that in any triangle ABC:
a / sin(A) = b / sin(B) = c / sin(C)
Where a, b, and c are the lengths of the sides of the triangle opposite to the angles A, B, and C, respectively.
In our triangle ABC, we know AB = 6 cm, angle BAC = 96 degrees and angle ABC = 35 degrees. We can find the measure of angle ACB by using the fact that the sum of the angles in a triangle is 180 degrees:
angle ACB = 180 - angle BAC - angle ABC
= 180 - 96 - 35 = 49 degrees
Now, we can apply the law of sines to find the length of BC:
BC / sin(35) = 6 / sin(96)
BC = 6 × sin(35) / sin(96)
Using a calculator, we can evaluate this expression to get:
BC ≈ 4.22 cm
Therefore, the length of BC in triangle ABC is approximately 4.22 cm.
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What is the measure of angle C? Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth. m∠C= ° Right triangle A B C, with right angle C B A. Side A B is three centimeters, side B C is four centimeters, and side C A is five centimeters.
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The measure of angle C is 53.13 degrees.
What are trigonometric functions?
Trigonometric functions are a set of mathematical functions used to relate the angles of a right triangle to the lengths of its sides. There are six trigonometric functions: sine, cosine, tangent, cosecant, secant, and cotangent. Each function represents a ratio of two sides of a right triangle.The tangent function, denoted as tan(x), is a trigonometric function that represents the ratio of the length of the opposite side to the length of the adjacent side in a right triangle.
Calculating the value of angle C :
The three sides of the given right triangle are 3 cm, 4 cm, and 5 cm.
To find the measure of angle C, we can use the trigonometric function called inverse tangent, or arctan, which gives the ratio of the length of the opposite side to the length of the adjacent side.
Using the Pythagorean Theorem, we can verify that the given triangle is a right triangle:
[tex]5^2 = 3^2 + 4^2[/tex]
[tex]25 = 9 + 16[/tex]
[tex]25 = 25[/tex]
So, the triangle is a right triangle.
To find the measure of angle C, we can use the arctan function:
[tex]tan(C) =opposite/adjacent = 3/4[/tex]
[tex]C = arctan(3/4) \approx 53.13[/tex] degrees
Therefore, the measure of angle C is 53.13 degrees (rounded to the nearest hundredth).
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Your friend Frans tells you that the system of linear equations you are solving cannot have a unique solution because the reduced matrix has a row of zeros. Comment on his claim. The claim is right. The claim is wrong. Need Help?
Answers
Answer: Incorrect
Step-by-step explanation:
Your friend Frans' claim is incorrect. A row of zeros in the reduced matrix means that the corresponding equation in the system is redundant and does not provide any additional information. This does not necessarily mean that the system does not have a unique solution. In fact, a row of zeros in the reduced matrix is common when solving systems of linear equations using Gaussian elimination, and it can still lead to a unique solution or even an infinite number of solutions. Therefore, Frans' claim is wrong.
how many square tiles are shaded and not shaded for the 8th figure?
Answers
For each problem, select the best response (a) A x2 statistic provides strong evidence in favor of the alternative hypothesis if its value is A. a large positive number. OB. exactly 1.96 c. a large negative number. D. close to o E. close to 1. (b) A study was performed to examine the personal goals of children in elementary school. A random sample of students was selected and the sample was given a questionnaire regarding achieving personal goals. They were asked what they would most like to do at school: make good grades, be good at sports, or be popular. Each student's sex (boy or girl) was also recorded. If a contingency table for the data is evaluated with a chi-squared test, what are the hypotheses being tested? A. The null hypothesis that boys are more likely than girls to desire good grades vs. the alternative that girls are more likely than boys to desire good grades. OB. The null hypothesis that sex and personal goals are not related vs. the alternative hypothesis that sex and personal goals are related. C. The null hypothesis that there is no relationship between personal goals and sex vs. the alternative hypothesis that there is a positive, linear relationship. OD. The null hypothesis that the mean personal goal is the same for boys and girls vs. the alternative hypothesis is that the means differ. O E. None of the above. (C) The variables considered in a chi-squared test used to evaluate a contingency table A. are normally distributed. B. are categorical. C. can be averaged. OD. have small standard deviations. E. have rounding errors.
Answers
a) Option A, A x2 statistic provides strong evidence in favor alternative hypothesis if its value is a large positive number.
b) Option B, The null hypothesis that sex and personal goals are not related vs. the alternative hypothesis that sex and personal goals are related.
c) Option B, The variables considered in a chi-squared test used to evaluate a contingency table B. are categorical.
(a) A x2 statistic provides strong evidence in favor of the alternative hypothesis if its value is a large positive number. The x2 statistic is used in hypothesis testing to determine whether there is a significant difference between observed and expected frequencies. A large positive value indicates that the observed frequencies are significantly different from the expected frequencies, which supports the alternative hypothesis.
(b) The hypotheses being tested in a chi-squared test on a contingency table are the null hypothesis that sex and personal goals are not related vs. the alternative hypothesis that sex and personal goals are related. This test determines whether there is a significant association between two categorical variables.
(c) The variables considered in a chi-squared test used to evaluate a contingency table are categorical. These variables cannot be averaged or assumed to be normally distributed. The chi-squared test is used to analyze the relationship between two or more categorical variables, where each variable has a discrete set of categories.
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I am in need of some help with this
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The required volume of the shape is [tex]\frac{850\pi}{3}$[/tex] cubic units.
What is volume?A measurement of three-dimensional space is volume. It is frequently expressed mathematically using SI-derived units, as well as different imperial or US-standard units. Volume and the definition of length are linked.
First, let's find the volume of the cylinder:
[tex]$$V_{cylinder} = \pi r^2 h = \pi (5)^2 (8) = 200\pi$$[/tex]
Next, let's find the volume of the hemisphere:
[tex]$V_{hemisphere} = \frac{2}{3}\pi r^3 = \frac{2}{3}\pi (5)^3 = \frac{250\pi}{3}$$[/tex]
To find the volume of the entire shape, we simply add the volume of the cylinder and hemisphere:
[tex]$$V_{shape} = V_{cylinder} + V_{hemisphere} = 200\pi + \frac{250\pi}{3} = \frac{850\pi}{3}$$[/tex]
Therefore, the volume of the shape is [tex]\frac{850\pi}{3}$[/tex] cubic units.
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A machine produces 225,000 insulating washers for electrical devices per day. The production manager claims that no more than 4,000 insulating washers are defective per day. In a random sample of 200 washers, there were 4 defectives. Determine whether the production manager's claim is likely to be true. Explain.
Answers
The claim of the production manager is not true because more than 4000 insulating washers are defective per day.
How to determine if the claim was true or not?The total amount of insulating washer for the electrical devices produced per day = 225,000.
The amount chosen at random for sampling = 200 washers.
The amount shown to be defective in the chosen sample = 4
If every 200 = 4 defective
225,000 = X
Make c the subject of formula;
X = 225000×4/200
X = 900000/200
X = 4,500.
This shows that the claim is wrong because more than 4000 insulating washers are defective per day.
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REALLY URGENT!!!
Spaceship Earth is a major tourist at Epcot. It is a sphere whose volume is
approximately 65, 417 m³. What is the approximate circumference of Spaceship
Earth? Use π = 3. 14. Round to the nearest whole number. Thank you in advance!
Answers
The approximate circumference of spaceship Earth is 160m
How to determine the valuesThe formula for calculating the volume of a sphere is given as;
V = 4/3 πr³
Given that;
V is the volume.r is the radius.Now, substitute the values
65417 = 1. 3 ×3.14r³
Multiply the values
65417 = 4. 082r³
Make r the subject
r³ = 16025. 722
Find the cube root
r = 25. 2m
The circumference is expressed as;
Circumference = 2πr
Substitute the values, we have;
Circumference = 2× 3.14 × 25.2
Circumference = 160 m
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PTC is a substance that has a strong bitter taste for some people and is tasteless for others. The ability to taste PTC is inherited and depends on a single gene that codes for a taste receptor on the tongue. Interestingly, although the PTC molecule is not found in nature, the ability to taste it correlates strongly with the ability to taste other naturally occurring bitter substances, many of which are toxins. About 75 % of Italians can taste PTC. You want to estimate the proportion of Americans with at least one Italian grandparent who can taste PTC. (a) Starting with the 75 % estimate for Italians, how large a sample must you collect in order to estimate the proportion of PTC tasters within ± 0.1 with 90 % confidence? (Enter your answer as a whole number.) n = (b) Estimate the sample size required if you made no assumptions about the value of the proportion who could taste PTC. (Enter your answer as a whole number.) n =
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(a) Starting with the 75% estimate for Italians, the sample you must collect in order to estimate the proportion of PTC tasters within ± 0.1 with 90 % confidence is n = 51.
(b) The sample size required if you made no assumptions about the value of the proportion who could taste PTC is n = 68.
(a) To estimate the sample size needed to find the proportion of PTC tasters within ± 0.1 with 90% confidence, we will use the formula for sample size estimation in proportion problems:
n = (Z² * p * (1-p)) / E²
Where n is the sample size, Z is the Z-score corresponding to the desired confidence level (1.645 for 90% confidence), p is the proportion of PTC tasters (0.75), and E is the margin of error (0.1).
n = (1.645² * 0.75 * (1-0.75)) / 0.1²
n = (2.706 * 0.75 * 0.25) / 0.01
n ≈ 50.74
Since we need a whole number, we round up to the nearest whole number:
n = 51
(b) If no assumptions were made about the proportion of PTC tasters, we would use the worst-case scenario, which is p = 0.5 (maximum variance):
n = (1.645² * 0.5 * (1-0.5)) / 0.1²
n = (2.706 * 0.5 * 0.5) / 0.01
n ≈ 67.65
Again, rounding up to the nearest whole number:
n = 68
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if the measure of and acute angle is represented by x, then the measure of the angle that it is complementary which is represented by 90-x
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The measure of the angle that it is complementary which is represented by 90-x is always true. Option A
What is an acute angle?An acute angle is simply defined as an angle that measures from 90° and 0°. This means that it is smaller than a right angle.
It is formed in the space between two intersecting lines or planes, or from the intersection of two shapes.
What is a complementary angle?A complementary angle can be defined as a pair of angles whose sum is equal or equivalent to 90 degrees.
From the information given, we have that;
x is the acute angle
The complementary angle is 90 - x
We can see that the angle x must be complementary to be subtracted from 90 degrees.
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The complete question:
If the measure of an acute angle is represented by x, then the measure of its complement is represented by 90 – X.
always true
sometimes true
never true
A box contains some green and yellow counters. 7/9of the box is green counters. Are 24 yellow counters. There How many green counters are there?
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If 7/9 of the box is green counters, and there are 24 yellow counters in the box, then there are 84 green counters .
Let's assume that the total number of counters in the box is x.
We are given that 7/9 of the box is filled with green counters, which means that the remaining 2/9 of the box must be filled with yellow counters. We are also given that there are 24 yellow counters in the box.
We can set up an equation to represent the relationship between the number of yellow counters and the total number of counters:
2/9 x = 24
To solve for x, we can multiply both sides of the equation by the reciprocal of 2/9, which is 9/2:
(2/9) x * (9/2) = 24 * (9/2)
x = 108
This means that there are a total of 108 counters in the box. To find out how many of these are green counters, we can use the fact that 7/9 of the box is filled with green counters:
(7/9) * 108 = 84
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a 20-volt electromotive force is applied to an lr-series circuit in which the inductance is 0.1 henry and the resistance is 40 ohms. find the current i(t) if i(0) = 0.
i(t) = ___
Determine the current as t → [infinity].
lim t→[infinity] i(t) =_____
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The time becomes infinity, i(t) will become constant, i.e., lim t→[infinity] i(t) = 0.
The current of the given LR-series circuit can be determined using the formula I = (E/R) * (1 - e^-Rt/L).The current i(t) if i(0) = 0 in the LR-series circuit is given by i(t) = 0.125A. The current as t → [infinity] is given by lim t→[infinity] i(t) = 0.How to solve this?The formula for the current in the LR-series circuit is given by:Where E is the electromotive force, R is the resistance, L is the inductance, t is time and I is the current.I = (E/R) * (1 - e^-Rt/L)Given E = 20V, R = 40Ω, L = 0.1H, and i(0) = 0Substitute these values in the above formula.I = (20/40) * (1 - e^-40t/0.1)I = 0.5(1 - e^-400t)I = 0.5 - 0.5e^-400tSo the current is i(t) = 0.5 - 0.5e^-400t.Limit of t as t → [infinity] means that when the time is allowed to run infinitely, then the current will become constant. Hence, when the time becomes infinity, i(t) will become constant, i.e., lim t→[infinity] i(t) = 0. Answer: The current is i(t) = 0.5 - 0.5e^-400t. Limit of t as t → [infinity] means that when the time is allowed to run infinitely, then the current will become constant. Hence, when the time becomes infinity, i(t) will become constant, i.e., lim t→[infinity] i(t) = 0.
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Suppose you roll a special 37-sided die. What is the probability that one of the following numbers is rolled? 35 | 25 | 33 | 9 | 19 Probability = (Round to 4 decimal places) License Points possible: 1 This is attempt 1 of 2.
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The probability of rolling one of these five numbers is 5/37.
Suppose you roll a special 37-sided die. The probability that one of the following numbers is rolled is as follows:
35 | 25 | 33 | 9 | 19.
The total number of sides of a die is 37. As a result, there are 37 numbers in the die.
Rolling one of the 5 given numbers implies that you can select either 35 or 25 or 33 or 9 or 19.
Therefore, the probability of rolling any of these numbers is:
1 / 37 + 1 / 37 + 1 / 37 + 1 / 37 + 1 / 37 = 5 / 37
So, the probability of rolling one of these five numbers is 5/37.
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