Triangle ABC has side lengths of 8.2 cm, 5.6 cm, and 4.49 cm, and angles of approximately 77 degrees, 50.5 degrees, and 52.5 degrees.
We have,
To construct triangle ABC, follow these steps:
- Draw a line segment AB of length 8.2 cm.
- Draw point A, and using a protractor, draw an angle BAC of 77 degrees with AB as its base. Label the intersection of this angle and AB as point C.
- Draw a line segment AC of length 5.6 cm.
- Using a protractor, draw an angle BCA of 103 degrees with AC as its base. Label the intersection of this angle and AB as point B.
- Triangle ABC is now constructed with side lengths AB = 8.2 cm, AC = 5.6 cm, and BC as the unknown side.
To find the length of side BC, we can use the law of cosines:
BC² = AB² + AC² - 2(AB)(AC)cos(BAC)
Substituting in the known values.
BC² = 8.2² + 5.6² - 2(8.2)(5.6)cos(77°)
BC ≈ 4.49 cm
To find the other angles, we can use the law of sines:
sin(BAC) / AC = sin(BCA) / BC
Substituting in the known values.
sin(77°) / 5.6 = sin(103°) / 4.49
sin(BCA) ≈ 0.784
BCA ≈ 50.5°
Finally, we can find angle CAB by subtracting the sum of angles BAC and BCA from 180 degrees:
CAB ≈ 52.5°
Thus,
Triangle ABC has side lengths of 8.2 cm, 5.6 cm, and 4.49 cm, and angles of approximately 77 degrees, 50.5 degrees, and 52.5 degrees.
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from the fictitious study of gender and ear piercing in high school students. what can we conclude? check all that apply group of answer choices the sample provides evidence that is too weak to conclude that gender and ear piercing are dependent in the population of high school students. gender and ear piercing for high school students may be independent. the sample provides strong evidence that gender and ear piercing for high school students are dependent. the differences between observed and expected counts are statistically significant. the differences between observed and expected counts could be attributed to chance variation that occurs in random samples of high school students when gender and ear piercing are independent. conditions are not met for use of the chi-square test of independence. therefore, we cannot draw a conclusion based on this data.
Based on the fictitious study of gender and ear piercing in high school students, we can conclude that the sample provides evidence that is too weak to conclude that gender and ear piercing are dependent in the population of high school students. Gender and ear piercing for high school students may be independent.
The study did not provide strong evidence that gender and ear piercing for high school students are dependent. In addition, the differences between observed and expected counts could be attributed to chance variation that occurs in random samples of high school students when gender and ear piercing are independent.
Therefore, the conditions are not met for use of the chi-square test of independence, and we cannot draw a conclusion based on this data.
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A scientist gathers data by weighing different fruits. The weight of each piece of fruit, in pounds, are as follows. 3/8, 1/4, 1/2, 1/2, 1, 1/8, 1/4, 1/2, 1/4, 1, 3/8, 3/8, 5/8
Create a line plot to represent this data set
A line plot for the weight of each piece of fruit, in pounds is shown in the image attached below.
What is a line plot?In Mathematics and Statistics, a line plot can be defined as a type of graph that is used for the graphical representation of data set above a number line, while using crosses, dots, or any other mathematical symbol.
In this scenario and exercise, we would use an online graphing calculator to graphically represent the weight of each piece of fruit, in pounds on a line plot as shown in the image attached below.
In conclusion, we can reasonably infer and logically deduce that the data set is skewed.
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Write two different quadratic functions whose graphs pass through (4,0) and (1,0)
The quadratic equation of function in the standard form is Y = -1.25 x² + 5x.
Since quadratic equation's x-intercepts are (-5, 0). That indicated that the quadratic equation's two elements are (x + 5) and (x -0).
f(x) = a (x + 5) (x - 0) (x - 0)
= ax+5a
The quadratic equation's graph goes through (4, 0). thus, we must change equation 1 to read x = 4 and f(x) = 0.
0 = a × 4² + (5 × 4)
0 = a × 16 +20
The quadratic equation is known to have the form ax² + bx + c = 0.
f(x) = -1.25 + 5x
Consider y= F(x)
∴ Y = -1.25 x² + 5x.
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if abcd∼efgh, find the value of x
The calculated value of x in the similar shapes given that abcd ∼ efgh is 15
Calculating the value of x in the similar shapesFrom the question, we have the following parameters that can be used in our computation:
abcd ∼ efgh
By the corresponding ratio of similar shapes, we have the following equation
AB/AD = EF/EH
Using the above as a guide, we have the following:
8/14 = (x - 3)/(x + 6)
Cross multiply the equation
This gives
8(x + 6) = 14(x - 3)
When solved for x, we have
x = 15
Hence, the value of x in the shapes is 15
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6 to the power of -4
Answer:
-4,096
Step-by-step explanation:
If you multiply:
4x4x4x4x4x4= 4,096
Then, just make that negative:
-4,069
Hope this helps :3
Interest on $5.255 at 12% for 30 days (use ordinary interest) is: Multiple Choice:
a. $52.55 b. $5,307.55 c. $5.26 d. $5,260.26
The interest on $5.255 at 12% for 30 days using ordinary interest can be calculated using the formula:I = PRT,Where I is the interest, P is the principal amount, R is the rate of interest, and T is the time period.
Here, P = $5.255, R = 12% = 0.12 (as a decimal), and T = 30/365 = 0.08219 (in years, as the time is given in days).
So,
I = 5.255 x 0.12 x 0.08219 = $0.0518
Rounding to two decimal places, the interest on $5.255 at 12% for 30 days using ordinary interest is $5.26. Therefore, the correct answer is option (c).
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HELP ON TIME LIMIT !!!!!Solve the system of equations. Be sure to check your work. Complete the ordered pair to show your answer.
Y=-2
Y=-x+5
Answer:( , )
if you flip a coin 40 times and get heads every time. what is the likelihood of flipping a tails the 41st time
The probability of getting tails on the 41st flip remains the same as any other individual flip: 0.5 or 50%.
When you flip a fair coin, there are two possible outcomes: heads (H) or tails (T). Since it's a fair coin, each outcome has an equal probability of occurring, which is 0.5 or 50%.
Now, let's consider the scenario you mentioned. You have already flipped the coin 40 times, and each time it landed on heads (H). In this case, the probability of getting heads on each of those 40 flips is (0.5)⁴⁰, which is an incredibly small probability because it's unlikely to get heads on 40 consecutive flips of a fair coin.
However, the key point is that each coin flip is an independent event. The outcome of one flip does not affect the outcome of the next flip. So, regardless of the previous 40 flips landing on heads, the probability of getting tails on the 41st flip is still 0.5 or 50%. The coin has no memory of the previous flips and doesn't "know" that it needs to "balance out" the previous heads with a tails.
Therefore, the probability of getting tails on the 41st flip remains the same as any other individual flip: 0.5 or 50%.
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someone pls explain and help :(
Using the tables we can evaluate the given functions to get:
(f + g)(3) = 9(f times g)(-1) = -8f(g(2)) = 8g(f(0)) = 2How to evaluate the given functions?Here we have two tables for the functions f(x) and g(x), first we want to find the sum:
(f + g)(3) = f(3) + g(3)
Using the table we can see that:
f(3) = 8
g(3) = 1
Then:
(f + g)(3) = 8 + 1 = 9
For the second one we have:
(f times g)(-1) = f(-1)×g(-1)
Where:
f(-1)= -2
g(-1) = 4
Then we will get (f times g)(-1) = -2*4 = -8
Now we have the compositions:
f(g(2))
and g(2) = 3, then:
f(g(2)) = f(3) = 8
Finally:
g(f(0))
Where f(0) = 0
Then:
g(f(0)) = g(0) = 2
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Three tenis balls are stored in a cylindrical container with a height of 8. 6 inches and a radius of 1. 39 inches. The circumference of a tennis ball is 8 inches. Find the amount of space within the cylinder not taken up
The space within the cylinder not taken up by the three tennis balls can be found by first determining the volume of the cylinder and the total volume of the three tennis balls.
The volume of the cylinder is given by the formula:
V_cylinder = πr^2h
where r is the radius and h is the height. Substituting the given values, we get:
V_cylinder = π(1.39)^2(8.6) = 50.168 cubic inches
The total volume of the three tennis balls can be found by multiplying the volume of one tennis ball by three. The volume of a tennis ball can be approximated by the formula for the volume of a sphere:
V_ball = (4/3)πr^3
where r is the radius. Since the circumference of a tennis ball is 8 inches, we can solve for the radius using the formula:
C = 2πr
8 = 2πr
r ≈ 1.27 inches
Substituting this value, we get:
V_ball = (4/3)π(1.27)^3 ≈ 8.48 cubic inches
Therefore, the total volume of the three tennis balls is:
V_total = 3V_ball = 25.44 cubic inches
Finally, we can find the amount of space within the cylinder not taken up by the tennis balls by subtracting the total volume of the tennis balls from the volume of the cylinder:
V_not_taken_up = V_cylinder - V_total = 50.168 - 25.44 = 24.728 cubic inches
Therefore, the amount of space within the cylinder not taken up by the tennis balls is approximately 24.728 cubic inches.
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if martins mass is m kilogram , represent his mass after he gains 7 kilogram
If Martin's mass is initially m kilograms, his mass after gaining 7 kilograms would be:
m + 7 kilograms.
In the question, it's given that Martin's initial mass is m kilograms. This means that he weighs m kilograms at some point in time.
If Martin gains 7 kilograms, we need to add 7 to his initial mass to get his new mass. The formula for this is:
Martin's new mass = Martin's initial mass + the mass he gained
Martin's new mass = m + 7
So if Martin's initial mass is m kilograms, his mass after gaining 7 kilograms would be m + 7 kilograms. This means that he would weigh m + 7 kilograms at this point in time.
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ABCD IS A KITE. (4x-2)cm A B AB= (4x-2) cm Jasper says that x could be 0.5 (a) Explain why Jasper cannot be correct.
Answer:
because if you substitute 0.5 for x you get zero as a result
Step-by-step explanation:
ABCD IS A KITE. (4x-2)cm A B AB= (4x-2) cm Jasper says that x could be 0.5 (a) Explain why Jasper cannot be correct.
I answer for what I understand, the question is not clear
because if you substitute 0.5 for x you get zero as a result
(4x - 2) =
4 × 0.5 - 2 =
2 - 2 = 0
How to calculate the Area of a cylinder
Answer:
Surface area of cylinder = 2 π r ² +2 π r h
Step-by-step explanation:
Surface area of cylinder =
area of both circle ends + area of curved surface
= 2 π r ² +2 π r h
can you help me with math
The linear function which represents the total cost is:
c = 11.95 + 48t
How to determine which linear function represents the total cost?The general form of linear function is:
c = mt + b
where m is the cost per ticket
b is the service fee ($11.95)
Total cost of 4 tickets = $203.95
Cost of 4 tickets without service fee = $203.95 - $11.95 = $192
Cost per ticket (m) = $192/4 = 48
Thus, the linear function which represents the total cost will be:
c = 48t + 11.95
c = 11.95 + 48t (When rearranged)
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Given the unit conversion 3 teaspoons = 15 milliliters
(mL), convert 61.4 mL to teaspoons.
Answer:
307.5 milliliters
Step-by-step explanation:
Ratio 3:15, 1:5
61.4 is 1 un 1:5
61.5 x 5= 307.5
307.5 milliliters
diego bought a 3-kilogram bag of carrots from the grocery store. he added 0.8 kilograms of carrots to a pot of vegetable soup. then, he grated 400 grams of carrots for his carrot cake. how many kilograms of carrots does he have left?
Therefore, Diego has 1.8 kilograms of carrots left.
Diego initially had 3 kilograms of carrots. He used 0.8 kilograms for the soup and 0.4 kilograms (400 grams) for the carrot cake.
So the total amount of carrots he used is:
0.8 + 0.4 = 1.2 kilograms
To find out how many kilograms of carrots he has left, we can subtract the amount he used from the initial amount:
3 - 1.2 = 1.8 kilograms
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Find area of pqrs, leave answer in simplest radical form
The required area of the trapezoid PQRS is 144+72√3 square units. Option A is correct.
Area of trapezoid PQRS = [PQ+RS]/2 * QB
We are given PQ=18, QR = 24
The vertical line from Q to line SR is given as,
sin30 = V/24
V = 12
And horizontal measure over SR is given as,
cos30 = H/QR
H = 12√3
The length of QR is given as,
QR = 6 + 12√3
Area of trapezoid PQRS = [PQ+RS]/2 * QB
= [18+6+12√3]/2*12
= 144+72√3
Thus, the required area of the trapezoid PQRS is 144+72√3 square units.
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which of the following is false about the margin of error of a confidence interval? as sample size increases, margin of error increases as well. as confidence level increases, margin of error increases as well. as standard deviation of the sample increases, margin of error increases as well.
The margin of error of a confidence interval is affected by multiple factors, including sample size, confidence level, and standard deviation. Understanding these relationships is essential for making accurate and reliable statistical inferences.
The margin of error of a confidence interval is a measure of the range of values within which the true population parameter is likely to lie. It reflects the amount of sampling error in the estimation process and is influenced by several factors.
Regarding the question, it is false that as sample size increases, the margin of error increases as well. In fact, the opposite is true. As the sample size increases, the margin of error decreases, since larger samples provide more information and reduce the uncertainty in the estimation. This relationship is inversely proportional and can be quantified by the formula: margin of error = z* (standard deviation / sqrt(n)), where z* is the critical value for the desired confidence level, n is the sample size, and standard deviation is the variability of the population.
On the other hand, it is true that as confidence level increases, the margin of error increases as well. This is because a higher confidence level requires a wider interval to capture a larger proportion of the population values, which results in a larger margin of error. For instance, a 99% confidence interval will be wider than a 95% confidence interval for the same sample size and standard deviation.
Finally, it is also true that as standard deviation of the sample increases, the margin of error increases as well. This is because a larger standard deviation implies a greater variability in the population and more uncertainty in the estimation, which requires a wider interval to account for the potential values. Thus, a larger standard deviation leads to a larger margin of error for the same sample size and confidence level.
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URGENT!!!!! Will give brainliest if correct :)
A regression line has a slope of 1.885. If the mean of the x-coordinates of the data points is 3.448, and the mean of the y-coordinates is 12.318, what is the y-value of the y-intercept of the line to three decimal places?
A. -5.819
B. - 19.771
C.19.771
D. 5.819
The equation of a regression line can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept. In this case, the slope m is given as 1.885.
The y-intercept b can be found using the formula b = y_mean - m * x_mean, where x_mean and y_mean are the means of the x-coordinates and y-coordinates of the data points, respectively. Plugging in the given values, we get:
b = 12.318 - 1.885 * 3.448 b ≈ 5.819
So the y-value of the y-intercept of the line to three decimal places is approximately 5.819. The correct answer is D. 5.819.
Explain step by step
Answer:
$40
Step-by-step explanation:
money made = $800 × 5%
= $800 × [tex]\frac{5}{100}[/tex] = $8 × 5 = $40
alison made a three-layer gelatin dessert that was 15 cm long by 10 cm wide. the heights of the layers were 3 cm,2 cm, and 1 cm.a 3-layer prism. the bottom layer has a length of 15, height of 3, and width of 10. the middle layer has a length of 15, height of 2, and width of 10. the top layer has a length of 15, height of 1, and width of 10.what is the total volume?the volume of the bottom layer is 150 cm3.the volume of the middle layer is cm3.the volume of the top layer is cm3.the total volume is 900 cm3.
Answer:
3rd layer: 450
2nd layer: 300
1st layer: 150
Total: 900
Step-by-step explanation:
got it correct!
The total volume of the three-layer gelatin dessert is 900 cm³.
What is Volume?The space occupied within the boundaries of an object in three-dimensional space is known as volume.
To calculate the volume of each layer, we multiply the length, width, and height of each layer.
The volume of the bottom layer:
Volume = length × width × height
Volume = 15 cm × 10 cm×3 cm
Volume = 450 cm³
The volume of the middle layer:
Volume = length×width × height
Volume = 15 cm× 10 cm ×2 cm
Volume = 300 cm³
The volume of the top layer:
Volume = length×width × height
Volume = 15 cm × 10 cm× 1 cm
Volume = 150 cm³
To find the total volume, we add up the volumes of each layer:
Total Volume = 450 cm³ + 300 cm³ + 150 cm³
Total Volume = 900 cm³
Hence, 900 cm³ is the total volume of the three-layer gelatin dessert.
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for the independent-measures t statistic, what is the effect of increasing the difference between sample means?
The increasing the difference between sample means will result in a larger t statistic. This means that the difference between the two sample means is more likely to be statistically significant and less likely to be due to chance.
the t statistic is calculated by taking the difference between the sample means and dividing it by the standard error of the difference. When the difference between sample means increases, the numerator of the t statistic increases, while the denominator (the standard error) remains relatively constant. This leads to a larger t statistic and a smaller p-value, indicating stronger evidence against the null hypothesis.
increasing the difference between sample means has a significant effect on the independent-measures t statistic. It increases the strength of the evidence against the null hypothesis, making it more likely that the difference between the two groups is real and not due to chance.
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Which statement about the the slopes of JL and MP are true
A statement about the the slopes of JL and MP that is true include the following: A. The slope of JL is the same as the slope of MP because △JKL is similar to △MNP.
What are the properties of similar triangles?In Mathematics and Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
Additionally, the lengths of corresponding sides or corresponding side lengths are proportional to the lengths of corresponding altitudes when two (2) triangles are similar and the slopes of side JL and side MP are equal;
Slope of side MP = NP/MN
Slope of side JL = KL/JK
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The function f(x)= -√√x is shown on the graph.
3+
2-
1+
--5-4-3-2-
H
2 3 4 5
Which statement is correct?
O The range of the graph is all real numbers greater
than or equal to 0.
O The domain of the graph is all real numbers greater
than or equal to 0.
O The range and domain of the graph are the same.
O The domain of the graph is all real numbers.
The domain and the range of the given function will be same and all the real numbers.
Given is a function f(x)= -√√x we need to see the range and the domain of the function,
Since the function is a root function, so the range and the domain will be all real numbers and hence equal.
Hence the domain and the range of the given function will be same and all the real numbers.
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The correct statement is: The range and domain of the graph are the same.
The function f(x) = -√-x is a valid function for all real numbers.
When x is negative, -x is positive and √-x is an imaginary number, which is then multiplied by -1 to make the function real.
Therefore, the range of the graph is all real numbers.
Thus, The range and domain of the graph are the same.
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A ferry traveled 1/6 of the distance between two ports 3/7 hour. The ferry travels at a constant rate . At this rate, what fraction of the distance between the two ports can the ferry travel in one hour?
start fraction, 3, divided by, 7, end fraction hour. The ferry travels at a constant rate.
At this rate, what fraction of the distance between the two ports can the ferry travel in one hour?
The ferry can travel 7/18 of the distance between the two ports in one hour.To determine the fraction of the distance between the two ports that the ferry can travel in one hour, we need to find the rate at which the ferry is traveling.
We know that the ferry traveled 1/6 of the distance between the two ports in 3/7 hour. This information allows us to find the rate of the ferry's travel.
The formula to calculate rate is:
Rate = Distance / Time
Let's assume the total distance between the two ports is represented by D. Therefore, the distance traveled by the ferry is 1/6 of D. Similarly, the time taken is 3/7 hour.
Plugging these values into the formula, we get:
Rate = (1/6)D / (3/7) = (1/6)D * (7/3) = (7/18)D
The rate of the ferry's travel is (7/18)D.
To find the fraction of the distance the ferry can travel in one hour, we need to divide the distance traveled in one hour by the total distance:
Fraction = Distance in one hour / Total Distance = Rate / D = (7/18)D / D = 7/18.
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John and Jane are married. The probability that John watches a certain television show is 0.7. The probability that Jane watches the show is 0.1. The probability that John watches the show, given that Jane does, is 0.8.
(a) Find the probability that both John and Jane watch the show.
(b) Find the probability that Jane watches the show, given that John does.
(c) Do John and Jane watch the show independently of each other? Yes or no?
(a) The probability that both John and Jane watch the show is 0.07.
(b) The probability that Jane watches the show, given that John does, is 0.11
(c) No. John and Jane do not watch the show independently of each other.
Probability(a) The probability that both John and Jane watch the show is given by the product of their individual probabilities:
P(John and Jane watch) = P(John watches) x P(Jane watches)
= 0.7 x 0.1
= 0.07.
(b) The probability that Jane watches the show, given that John does, is given by Bayes' theorem:
P(Jane watches | John watches) = P(John watches | Jane watches) x P(Jane watches) / P(John watches)
From the information given, we know that:
P(John watches | Jane watches) = 0.8P(Jane watches) = 0.1.To find P(John watches), we can use the law of total probability:
P(John watches) = P(John watches | Jane watches) * P(Jane watches) + P(John watches | not Jane watches) * P(not Jane watches)
= (0.8 x 0.1) + (0.7 x 0.9)
= 0.71
Therefore,
P(Jane watches | John watches) = 0.8 x 0.1 / 0.71 = 0.1127
(c) John and Jane do not watch the show independently of each other, since the probability that John watches the show changes depending on whether or not Jane watches it. In other words, the events "John watches the show" and "Jane watches the show" are dependent events.
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A right triangle abc is insribed in a circle k(O,r). Find the radius of this circle if m
The radius of given circle would be 18 cm.
Given that a right △ABC is inscribed in circle k(O, r) and m ∠C = 90°, AC = 18 cm, m ∠B = 30°.
We are asked to find the radius of the circle.
Draw a diagram that represent the given scenario. [check the attached diagram]
AB is diameter of circle O and it a hypotenuse of triangle ABC.
We will use sine of the angle to find side AB.
Sin x = AC/AB
Sin 30° = 18 / AB
AB = 36
So, the radius = 18 cm.
Therefore, the radius of given circle would be 18 cm.
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The complete question is =
A right △ABC is inscribed in circle k(O, r). Find the radius of this circle if:
m∠C = 90°, AC = 18 cm, m∠B = 30°.
Use the unit circle to find the value of tan 315˚. Show work
Answer:
Rotate 'r' anticlockwise to form 315° angle with the positive x-axis. The tan of 315 degrees equals the y-coordinate(-0.7071) divided by x-coordinate(0.7071) of the point of intersection (0.7071, -0.7071) of unit circle and r.
Step-by-step explanation:
basicly what I said
the length of a pregnancy from conception to birth is approximately normally dis- tributed with a mean of 272 days and a standard deviation of 9 days. a pregnancy is considered full-term if it lasts between 252 days and 298 days. what percentage of pregnancies are full-term?
The length of a pregnancy from conception to birth follows a normal distribution with a mean (μ) of 272 days and a standard deviation (σ) of 9 days. To find the percentage of pregnancies that are full-term, we need to calculate the probability of a pregnancy lasting between 252 and 298 days.
First, convert the days into z-scores:
z1 = (252 - μ) / σ = (252 - 272) / 9 ≈ -2.22
z2 = (298 - μ) / σ = (298 - 272) / 9 ≈ 2.89
Next, use a standard normal distribution table to find the probabilities corresponding to the z-scores:
P(z1) ≈ 0.0132
P(z2) ≈ 0.9981
To find the percentage of pregnancies that are full-term, subtract the lower probability from the higher probability:
Percentage = (P(z2) - P(z1)) × 100% = (0.9981 - 0.0132) × 100% ≈ 98.49%
Approximately 98.49% of pregnancies are full-term, lasting between 252 and 298 days.
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What are the x-intercepts of the parabola? graph of parabola falling from the left, passing through 3 comma 2 to about 4 and one half comma negative one fourth, and rising to the right, passing through 6 comma 2
a (4.5, 0) and (5, 0)
b (0, 4.5) and (0, 5)
c (0, 5) and (0, 4)
d (5, 0) and (4, 0)
a
(4.5, 0) and (5, 0)
EXPLANATION:The x-intercept of the parabola represents the point where the parabola graph intersects the x-axis. In other words, these are the x values where the y coordinate is 0.
Using the information given, we can observe that the parabola falls from the left, passes through the point (3, 2), reaches the minimum point, then rises to the right and passes through the point (6, 2) .
Since the parabola intersects the x-axis at the x-intercept, we can conclude that the x-intercept is the point where the y-coordinate is 0. In this case, x values of 4.5 and 5 will have a y coordinate of zero. So the x-intercepts of the parabola are (4,5,0) and (5,0).
