Answers
An equation that models the position of the object at time t is:
s(t) = -2cos(2πt/5).
How to interpret the trigonometric graph?The general form for the equation that will model a wave is:
±a (sin/cos) (2π(x - p)/T)
where:
a is the amplitude
p is the phase shift
T is the period.
The ± will become +ve provided that the graph starts in the positive direction, and the will become -ve provided it starts in the negative direction.
The (sin/cos) will become sine provided the graph starts at 0 before it is being shifted. Then, it becomes cosine provided that the graph starts at the amplitude.
In this case, our graph begins at negative, and the at the amplitude that has no phase shift, the ±ve will become -ve, (sin/cos) will now become cos, and p will become zero. Plugging in the values that were given in the problem, we see that a = 2 and T = 5.
Thus, this equation is: s(t) = -2cos(2πt/5).
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Related Questions
On October 12, 2020, the number of new cases of Covid 19 in Milwaukee was 235. On Oct. 22, 2020, the number of new cases in Milwaukee was 395.
a. Create an exponential model for new cases in terms of days.
b. Based on your model, what would be the number of new cases on Oct. 31, 2020?
c. The actual number of new cases on Oct. 31, 2020, was 1043. How well does this fit your model?
Answers
a. To create an exponential model for new cases in terms of days, we can use the formula: y = a * b ^ x, where y is the number of new cases, x is the number of days since the first observation, and a and b are constants that we need to determine. Using the two data points given, we can set up a system of equations:
235 = a * b ^ 0
395 = a * b ^ 10
Solving for a and b, we get:
a = 235
b = (395/235)^(1/10) = 1.067
Therefore, the exponential model for new cases in Milwaukee is:
y = 235 * 1.067 ^ x
b. To find the number of new cases on Oct. 31, 2020, we need to plug in x = 19 (since Oct. 31 is 19 days after Oct. 12) into the model:
y = 235 * 1.067 ^ 19 = 1018.5
Therefore, based on the exponential model, we would expect around 1019 new cases on Oct. 31, 2020.
c. The actual number of new cases on Oct. 31, 2020, was 1043. This is higher than the predicted value of 1019, but not by a huge margin. Overall, the model seems to fit the data reasonably well, especially considering that there are many factors that can affect the number of new cases in a given area, and that the model is based on only two data points. However, it is worth noting that the exponential model assumes that the growth rate of new cases remains constant over time, which may not be a realistic assumption in the long run.
Pam is visiting a historic town with an old-fashioned water well in the town square. She drops
a pebble into the well from a height of 27 feet above the surface of the water.
To the nearest tenth of a second, how long does it take for the pebble to hit the water?
Hint: Use the formula h = -16t² + 5.
seconds
Answers
The time taken for the pebble to hit the water is 1.41 seconds.
What is the time taken for the pebble to hit the water?The time taken for the pebble to hit the water is calculated by using the equation of the motion as follows;
h = -16t² + 5
where;
h is the height of fall during the motiont is the time of motionwhen the height is 27 ft, the time of motion is calculated as;
-27 = -16t² + 5
16t² = 5 + 27
16t² = 32
t² = 32/16
t² = 2
t = √2
t = 1.41 seconds
Thus, the time of motion is determined by applying the equation of motion as shown above.
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Mario is training for a mile-long swim race. In the first week of training, he swims 3/5 three times, 9/10 two times and 23/25 two times . How many total miles did he swim in the first week of training?
Answers
To find out how many total miles Mario swam in the first week of training, we need to add up the distances he swam each time:
3/5 + 3/5 + 3/5 + 9/10 + 9/10 + 23/25 + 23/25
To add these fractions, we need to find a common denominator. The smallest common multiple of 5, 10, and 25 is 50.
3/5 = 30/50
9/10 = 45/50
23/25 = 46/50
Now we can add the fractions:
30/50 + 30/50 + 30/50 + 45/50 + 45/50 + 46/50 + 46/50
= (30 + 30 + 30 + 45 + 45 + 46 + 46)/50
= 272/50
= 5.44
Therefore, Mario swam a total of 5.44 miles in the first week of training.
Assume that you want to test the claim that the paired sample data come from a population for which the mean difference is µg =0. Compute the value of the t test statistics. Round intermediate
calculations to four decimal places as needed and final answers to three decimal places as needed.
x 9 6 7 5 12
y 6 8 3 6 7
A.t= 2.890
B.t= 1.292
C. t=0.578
D. t=0.415
Answers
Answer: To compute the t-test statistic for the paired sample data, we need to first calculate the sample mean difference and the sample standard deviation of the differences. Then we can use the formula:
t = (sample mean difference - hypothesized mean difference) / (standard error of the mean difference)
where the standard error of the mean difference is calculated as:
standard error = sample standard deviation / sqrt(sample size)
Let's first calculate the sample mean difference:
x 9 6 7 5 12
y 6 8 3 6 7
The differences between each pair of x and y values are:
(9-6), (6-8), (7-3), (5-6), (12-7) = 3, -2, 4, -1, 5
The sample mean difference is the average of these differences:
sample mean difference = (3 - 2 + 4 - 1 + 5) / 5 = 1.8
Next, we need to calculate the sample standard deviation of the differences. To do this, we first calculate the deviations of each difference from the sample mean difference:
(3 - 1.8), (-2 - 1.8), (4 - 1.8), (-1 - 1.8), (5 - 1.8) = 1.2, -3.8, 2.2, -2.8, 3.2
The sample standard deviation of the differences is the square root of the sum of the squared deviations divided by (n-1):
sample standard deviation = sqrt[(1.2^2 + (-3.8)^2 + 2.2^2 + (-2.8)^2 + 3.2^2) / 4] = 3.153
Finally, we can calculate the t-test statistic:
t = (sample mean difference - hypothesized mean difference) / (standard error of the mean difference)
where the hypothesized mean difference is 0, and the standard error of the mean difference is:
standard error = sample standard deviation / sqrt(sample size) = 3.153 / sqrt(5) = 1.410
Substituting the values, we get:
t = (1.8 - 0) / 1.410 = 1.277
Rounding the final answer to three decimal places, we get:
t = 1.277
Therefore, the correct option is B. t = 1.292.
Please if you know the answer put the steps in there thank you.
Answers
Answer:
The market trader should sell each of the remaining 20 packs of muffins for £1.30 to meet his target.
Step-by-step explanation:
To find out how much the market trader needs to sell the remaining 20 packs of muffins, we first need to calculate his total cost and his target revenue.
The cost of the loaves of bread is:
100 loaves x 84p/loaf = £84
The cost of the packs of muffins is:
60 packs x £1.10/pack = £66
Therefore, the total cost for the trader is:
£84 + £66 = £150
To make a 40% profit, the trader needs to make £150 x 40/100 = £60 in profit.
His target revenue is, therefore:
£150 + £60 = £210
The revenue from the loaves of bread is:
100 loaves x £1.20/loaf = £120
The revenue from the 40 packs of muffins sold at £1.60 per pack is:
40 packs x £1.60/pack = £64
So the total revenue from the loaves of bread and the 40 packs of muffins is:
£120 + £64 = £184
This means that the trader needs to make:
£210 - £184 = £26
from the sale of the remaining 20 packs of muffins.
To sell 20 packs of muffins to make £26, he needs to sell each pack for:
£26/20 = £1.30 per pack
Therefore, the market trader should sell each of the remaining 20 packs of muffins for £1.30 to meet his target.
Romero Company has a target capital structure that consists of $3.3 million of debt capital, $3.5 million of preferred stock financing, and $4.3 million of common equity. The corresponding weights of its debt, preferred stock, and common equity financing that should be used to compute its weighted cost of capital (rounded to the nearest wo decimal places) are:
Answers
The weights of the debt, preferred stock, and common equity financing are 28.6%, 30.4%, and 41.0%, respectively.
To calculate the weighted cost of capital (WACC), the proportion of each component of capital structure is needed. The weight of each component of the capital structure is determined by dividing the market value of the component by the total market value of all the components of the capital structure.
In this case, the total market value of the company's capital structure is the sum of the market value of debt, preferred stock, and common equity.
The weights for each component are calculated as follows:
Weight of debt = Market value of debt / Total market value of capital structure
= $3.3 million / ($3.3 million + $3.5 million + $4.3 million)
= 0.286 or 28.6%
Weight of preferred stock = Market value of preferred stock / Total market value of capital structure
= $3.5 million / ($3.3 million + $3.5 million + $4.3 million)
= 0.304 or 30.4%
Weight of common equity = Market value of common equity / Total market value of capital structure
= $4.3 million / ($3.3 million + $3.5 million + $4.3 million)
= 0.410 or 41.0%
These weights can be used to calculate the weighted cost of capital for Romero Company.
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What’s the correct answer to problem 14?
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The distance between the two lines is about 6/√17 units, which is approximately 1.46 units
To find the distance between two parallel lines, we need to find the length of the perpendicular segment that connects them.
Both lines have the same slope (4), so they are parallel and never intersect.
The shortest distance between them will be the perpendicular distance between any point on one line and the other line.
Let's choose a point on the first line, say (0, -1), and find the perpendicular distance from this point to the second line.
We can use the formula for the distance between a point (x₁, y₁) and a line in slope-intercept form y = mx + b:
Distance = |m(x₁) - y₁+ b| /√m² + 1
Plugging in the values for the second line, we get:
Distance = |4(0) - (-1) + 5| / √4² + 1
Distance = 6 / sqrt(17)
Therefore, the distance between the two lines is about 6/√17 units, which is approximately 1.46 units
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Math is hard!!
Point A is shown on the number line below.
What is the location of point A?
Answers
The lines are separating the segment into 20ths. Look at the picture below.
Hope this helps
100 POINTS!
Question:
Answers
Answer: the answer is f
Step-by-step explanation:
Answer:
answer is f
Step-by-step explanation:
what principal will earn $55.99 interest at 9.75% from February 4, 2021, to July 6, 2021?
Answers
A principal of $1,380.89 will earn $55.99 interest at 9.75% from February 4, 2021, to July 6, 2021.
To calculate the interest earned by a principal at a given interest rate over a certain period of time, we use the following formula:
Interest = Principal x Rate x Time
In this case, we need to find the principal, so we can rearrange the formula as follows:
Principal = Interest / (Rate x Time)
First, we need to calculate the time period in years between February 4, 2021, and July 6, 2021.
February 4, 2021 to July 6, 2021 is 152 days or approximately 0.416 years (calculated as (July 6, 2021 - February 4, 2021) / 365).
Principal = 55.99 / (0.0975 x 0.416) = $1,380.89 (rounded to the nearest cent)
Therefore, a principal of $1,380.89 will earn $55.99 interest at 9.75% from February 4, 2021, to July 6, 2021.
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Divide and state the quotient in simplest form.
Answers
The quotient of the two fractions is (x - 5) / (x - 4).
Option D is the correct answer.
We have,
To divide two fractions, we can multiply the first fraction by the reciprocal of the second fraction.
In this case, that means we need to multiply:
(x² - 2x - 15) / (x + 2) x (x + 2) / (x² - x - 12)
Notice that the (x + 2) terms in the numerator and denominator of the first fraction cancel out with the denominator of the second fraction, so we can simplify before multiplying:
(x² - 2x - 15) / 1 x 1 / (x² - x - 12)
Now we can multiply the numerators and the denominators separately:
(x² - 2x - 15) / (x² - x - 12)
To simplify further, we can factor both the numerator and the denominator:
(x - 5)(x + 3) / (x - 4)(x + 3)
Notice that the (x + 3) terms in the numerator and denominator cancel out, leaving:
(x - 5) / (x - 4)
Therefore,
The quotient of the two fractions is (x - 5) / (x - 4).
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What are the domain and range of the function f(x) x^2 +8x+7 over x+1
Answers
Answer: The function given is f(x) = (x^2 + 8x + 7)/(x + 1).
The domain of a function is the set of all possible input values for which the function is defined. In this case, the function f(x) is defined for all real numbers except for x = -1, because division by zero is undefined in mathematics. Therefore, the domain of f(x) is all real numbers except x = -1, or in interval notation: (-∞, -1) ∪ (-1, ∞).
The range of a function is the set of all possible output values that the function can produce. For this rational function, the range depends on the behavior of the function as x approaches positive and negative infinity. As x approaches positive or negative infinity, the function f(x) approaches 0, because the highest power of x in the numerator (x^2) and the highest power of x in the denominator (x) have the same degree, and their coefficients (1 in the numerator and 1 in the denominator) are equal. Therefore, the range of f(x) is all real numbers except 0, or in interval notation: (-∞, 0) ∪ (0, ∞). Note that f(x) never actually equals 0, because the function is defined for all real numbers except x = -1. However, it can arbitrarily approach 0 as x approaches positive or negative infinity. So, 0 is excluded from the range. Therefore, the correct answer is: Range = (-∞, 0) ∪ (0, ∞). Note that the range is expressed in interval notation, which uses parentheses to indicate open intervals (excluding the endpoints) and the union symbol (∪) to indicate the combination of two or more sets. In this case, the range consists of all real numbers except 0, expressed as two separate open intervals. The domain is also expressed in interval notation, with the union symbol (∪) used to indicate the combination of two disjoint sets. In this case, the domain consists of all real numbers except -1, expressed as the union of two separate intervals. So, the final answer is: Domain = (-∞, -1) ∪ (-1, ∞) and Range = (-∞, 0) ∪ (0, ∞). I hope this helps! Let me know if you have any further questions. I am here to help! Keep in mind that if you need to use the function f(x) in a real-world context, you should also consider any additional restrictions or conditions that may apply. It's always important to carefully analyze the properties of a function in the context of the problem you are trying to solve.
Step-by-step explanation:
help struggling pealse if do brainliest!
Answers
Based on the data in the table, if Colin draws a marble 336 times, he predicts a yellow marble will be drawn roughly 63 times, but probably not exactly 63 times.
Based on the data in the table, if Colin draws a marble 216 times, he predicts a white marble will be drawn roughly 2 times that a purple marble will be drawn.
What is the number of times the yellow marble can be drawn?If Colin draws a marble x times, he predicts a yellow marble will be drawn roughly 63 times.
The number of times = 63 / 3/16)
The number of times = 336 times.
If Colin draws a marble 216 times,
Number of times he can draw a white marble = 216 * 1/4
Number of times he can draw a white marble = 54 times
Number of times he can draw a purple marble = 216 * 1/6
Number of times he can draw a purple marble = 36 times
The number of times a white marble can be drawn more than a purple marble = 54/36 or 1.5 times more
The number of times a white marble can be drawn more than a purple marble is approximately two times.
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pls help me on algebra here is screenshot
Answers
Answer:
The answer to the question provided is option 2.
Find the missing information for both parts below.
Answers
The unknown angles in the circle are as follows:
a. m∠AEB = 73°
b. arc angle VW = 155°
How to find arc angles in a circle?a.
If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.
Therefore,
m∠AEB = 1 / 2 (99 + 47)
m∠AEB = 146 / 2
m∠AEB = 73 degrees
b.
If two secants intersect outside a circle , then the measure of an angle formed by the two lines is one half the positive difference of the measures of the intercepted arcs .
Therefore,'
arc angle VW = x
55 = 1 / 2 (x - 45)
55 = 0.5x - 22.5
0.5x = 55 + 22.5
0.5x = 77.5
divide both sides by 0.5
x = 77.5 / 0.5
x = 155 degrees
Therefore,
arc angle VW = 155 degrees
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Factor completely:
[tex] {5x}^{2} + 14x - 3[/tex]
Answers
Answer:
[tex]\Large \boxed{(5x - 1)(x + 3)}[/tex]
Step-by-step explanation:
To factor the expression [tex] {5x}^{2} + 14x - 3 [/tex], we need to find two numbers that multiply to give the coefficient of [tex] {x}^{2} [/tex] (which is 5)
And add up to give the coefficient of x (which is 14).
These two numbers are 5 and 3. We can then rewrite the expression as follows:
[tex]\boxed{{5x}^{2} + 14x - 3 = (5x - 1)(x + 3)}[/tex].
Therefore, the factored form of the expression is [tex](5x - 1)(x + 3)[/tex]
What are the x-intercepts of the function f(x)= 4x^2-36 over x-9?
Answers
Therefore , the solution of the given problem of function comes out to be f(x) = (4x² - 36)/(x - 9) has -3 and 3 as its x-intercepts.
Describe function.On the midterm exam, there will be a variety of inquiries in each subject, including inquiries concerning both hypothetical and actual places as well as inquiries relating the creation of numerical variables. a diagram showing the relationships between different elements that cooperate to generate the same result. A service is composed of numerous distinctive components that cooperate to create distinctive results for each input.
Here,
Setting the y-value (or output) of a function to zero and then solving for the corresponding x-values will allow us to determine the x-intercepts of the function.
The function in this instance is f(x) = (4x² - 36)/(x - 9)
=> 4x² - 36 = 0
To make the equation simpler, we can factor out a 4:
=> 4(x² - 9) = 0
We can factor further based on the difference of squares we now have:
=> 4(x + 3)(x - 3) = 0
We may determine the x-values where the function crosses the x-axis by setting each element to zero:
=> x + 3 = 0 or x - 3 = 0
To find x, solve for:
=> x = -3 or x = 3
The function f(x) = (4x² - 36)/(x - 9) has -3 and 3 as its x-intercepts.
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What number of hours corresponds to making $41
Answers
Which choice is the correct graph of |x|< 3
Answers
The graph that shows the solution set for the given inequality is the one in option B.
Which one is the graph of the given inequality?Here we want to identify the graph of the inequality:
|x| ≤ 3
So, the absolute value of x is smaller or equal to 3, that means that the graph of the solution set is a segment whose endpoints are closed circles at x = -3 and x = 3.
(We use closed circles because these values are also solutions for the inequality).
With that in mind, we can see that the correct option in this case will be graph B.
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Apply the nearest neighbor algorithm to the graph above starting at vertex A. Give your answer as a list of vertices, starting and ending at vertex A. Example: ABCDA
Answers
Starting at vertex A and using the nearest neighbor algorithm, the path is: A-C-B-D-A, with a total distance of 95. This means visiting vertices in the order A, C, B, D, and back to A, and the total distance traveled is 95 units.
The nearest neighbor algorithm is used to find the shortest path between a set of points. Here are the steps to apply the algorithm in this case
Start at vertex A. Look for the closest neighboring vertex to A. In this case, the closest vertex is B, which is 7 units away from A. Move to vertex B and mark it as visited. Look for the closest neighboring vertex to B that has not been visited. In this case, the closest vertex is C, which is 11 units away from B.
Move to vertex C and mark it as visited. Look for the closest neighboring vertex to C that has not been visited. In this case, the closest vertex is D, which is 18 units away from C. Move to vertex D and mark it as visited.
Look for the closest neighboring vertex to D that has not been visited. In this case, the closest vertex is B, which is 15 units away from D. Move to vertex B and mark it as visited.
Look for the closest neighboring vertex to B that has not been visited. In this case, the closest vertex is E, which is 20 units away from B. Move to vertex E and mark it as visited.
Look for the closest neighboring vertex to E that has not been visited. In this case, the closest vertex is A, which is 24 units away from E. Move to vertex A and mark it as visited. All vertices have been visited, so the algorithm is complete.
The list of vertices visited, starting and ending at A, is A, B, C, D, B, E, A and the distance is 95.
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combine like terms 6x^2 - 10x + 21x - 35 = 6x^2 + 11x - 35
Answers
Answer:
Step-by-step explanation:
6x² - 10x + 21x - 35 = 6x² + 11x - 35
6x² - 6x² + 11x - 11x - 35 + 35 = 0
0 = 0
The equation is an identity. Its solution set is {all real numbers}.
all I need to know is the answer to E!!! DUE TOMORROW!!!
Answers
Answer:
Step-by-step explanation:
To estimate the monthly cost of electric, gas, and water utilities as 0.1% of the price of your house, you can multiply the price of your house by 0.001. For example, if the price of your house is $300,000, then the estimated monthly cost of these utilities would be $300,000 * 0.001 = $300.
It’s important to note that this is just an estimate and the actual cost of these utilities can vary depending on factors such as the size of your house, the number of people living in it, and your usage habits.
Which of the following sets of numbers could not represent the three sides of a right
triangle?
11, 60, 61}
{14, 48, 50
{46, 60, 75}
(39,80,89}
Answers
Answer: D
Step-by-step explanation: it equals 181
Can someone help me solve this? I don’t quite understand
Answers
According to the graph, the function that best describes the graph is
[tex]f(x)=|x| = \left\{ \begin{array}{cl}x - 2 \text{ for x \lt -3 } \\8 \text{ for -3 \lt x \lt 5}\\-x + 10 \text{ for x \gt 6}\end{array} \right.[/tex]
(option d).
As we all know that the term function is defined as a rule or relationship that maps each element in one set, called the domain, to exactly one element in another set, called the range.
While we looking into the graph we have identified that there is a straight line that cross the point (0, 8) within the range of -3 to 5.
And then the next line is moves downwards from the range of x whose value is greater than 6.
Final upward slope is moves the range of -3 or less While we looking into these range value we have identified that the the function that refers the graph is (option d).
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Can someone help me please
Answers
The resulting matrix will be in the form :
5 9 -4
0 -14 15
What is a matrix in mathematics ?A matrix is described as a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.
To get a 1 in row 1, column 1, we perform the following elementary row operation:
R2 - 2R1 -> R2
This will subtract 2 times the first row from the second row and give us the result:
5 9 -4
0 -14 15
Matrices are useful for describing systems of linear or differential equations, as well as representing a linear application.
In conclusion, in a matrix function, the input and the output values are matrices.
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I will give brainlyest
Determine if the relationship between x and y is linear or not linear. Explain.
Answers
Answer: To determine if the relationship between x and y is linear, we need to graph the data and look for a straight-line pattern.
If the graph shows a straight-line pattern, then the relationship is linear. If the graph shows a curve or a non-linear pattern, then the relationship is not linear. So it is linear
Step-by-step explanation: can i get brainliest :D
a sample of what size would be needed to estimate a population mean to within 4 units with 95 percent confidence if the population has a standard deviation of 12?
Answers
A sample of at least 139 individuals would need to be taken to estimate the population mean to within 4 units with 95% confidence.
Understanding the Population EstimateTo estimate the sample size needed to estimate the population mean to within 4 units with 95% confidence, we can use the formula:
n = (z * σ / E)²
where:
n = sample size
z = z-score for the desired level of confidence (95% in this case), which can be found using a standard normal distribution table or calculator. For 95% confidence, the z-score is approximately 1.96.
σ = population standard deviation (12 in this case)
E = margin of error (4 in this case)
Plugging in the values, we get:
n = (1.96 * 12 / 4)²
n = 34.5744
Rounding up to the nearest whole number, we get a sample size of 35. Therefore, a sample of at least 35 individuals would need to be taken to estimate the population mean to within 4 units with 95% confidence.
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Carolyn is carpeting her front room.
Work out how much carpet she needs by working out the area.
She will also need skirting boards around the sides of the room. To measure the boards needed, calculate the perimeter.
Area:
Perimeter:
Answers
Carolyn will need 15 square units of carpet to cover her front room. Carolyn will need 16 units of skirting board to go around the sides of her front room.
To find the area of Carolyn's front room, we need to multiply the length by the width. In this case, the dimensions are given as 5 x 3, so the area is:
Area = length x width = 5 x 3 = 15 square units
To find the perimeter of the room, we need to add up the lengths of all four sides. Since the room is rectangular, opposite sides are of equal length. So, we can find the perimeter by adding twice the length and twice the width, which gives:
Perimeter = 2(length + width) = 2(5 + 3) = 16 units
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I need help figuring out this answer
Answers
The proof that angles D and E are congruent is added below
Proving that angles D and E are congruentFrom the question, we have the following parameters that can be used in our computation:
∠CDB and ∠CEB are inscribed in a circle A.
The general rule is that angles that are inscribed in the same arc are congruent.
So, we have the following two column proof
Statements Reasons
∠CDB = ∠CEB Given
Segments BD = CE CPCTC
Segments BE = CD CPCTC
Arcs BE = CD Corresponding arcs
∠D = ∠E Corresponding angles
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The length of a particular animals pregnancies are approximately normally distributed, with a mean of 272 days and a standard deviation of 12 days.
A) what is the proportion of pregnancies that lasts more than 278 days?
B) what is the proportion of pregnancies lasts between 257 and 275 days?
C) what is the probability that a randomly selected pregnancy lasts no more than 266 days?
D) a “very preterm” baby is one whose gestation period is less than 242 days. Are very preterm babies unusual?
Answers
Answer:
To answer these, we can use the standard normal distribution & z-scores. A z-score represents the number of standard deviations a value is from the mean. The formula to calculate a z-score is: z = (x - μ) / σ, where x is the value, μ is the mean and σ is the standard deviation.
A) To find the proportion of pregnancies that last more than 278 days, we first calculate the z-score for 278 days: z = (278 - 272) / 12 = 0.5. Using a standard normal distribution table, we find that the proportion of values above a z-score of 0.5 is approximately 0.3085. So, about 30.85% of pregnancies last more than 278 days.
B) To find the proportion of pregnancies that last between 257 and 275 days, we first calculate the z-scores for both values: z1 = (257 - 272) / 12 = -1.25 and z2 = (275 - 272) / 12 = 0.25. Using a standard normal distribution table, we find that the proportion of values between z-scores of -1.25 and 0.25 is approximately 0.3944. So, about 39.44% of pregnancies last between 257 and 275 days.
C) To find the probability that a randomly selected pregnancy lasts no more than 266 days, we first calculate the z-score for 266 days: z = (266 - 272) / 12 = -0.5. Using a standard normal distribution table, we find that the proportion of values below a z-score of -0.5 is approximately 0.3085. So, there is about a 30.85% chance that a randomly selected pregnancy lasts no more than 266 days.
D) To determine if very preterm babies are unusual, we first calculate the z-score for 242 days: z = (242 - 272) / 12 = -2.5. Using a standard normal distribution table, we find that the proportion of values below a z-score of -2.5 is approximately 0.0062. Since this value is less than 0.05, we can conclude that very preterm babies are unusual.
