The Value of cos B is,
⇒ cos B = 0.64
We have to given that;
Two angles, ∠A and ∠B, are complementary.
And, sin A = 4/7
Now, We can simplify as;
sin A = 4/7
A = sin⁻¹ 4/7
A = 39.8°
Since, Two angles, ∠A and ∠B, are complementary.
Hence, We get;
∠A + ∠B = 90°
39.8° + ∠B = 90°
∠B = 90 - 39.8°
∠B = 50.2°
Thus, Value of cos B is,
⇒ cos B = cos 50.2° = 0.64
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write a formula for the area A of each followi g regions
I need help with 8e and 8f
The formula for the area of the shapes in:
8e). A = a[√(x² + a²)]
8f). A = a² - a[√[(2b)² - a²]]/4
How to derive the formula for the area of the shapesShape in 8e is a triangle and the height is derived using Pythagoras rule as;
triangle height = √(x² + a²)
Area of the triangle = 1/2 × 2a × √(x² + a²)
Area of the triangle = a[√(x² + a²)]
The shape in 8f is observed to be a triangle area cut out from a square area, thus;
Area of the square = a²
The triangle height = √[(b² - (a/2)²]
triangle height = √[(2b)² - a²]
Area of the triangle = 1/2 × a × √[(2b)² - a²]
Area of the triangle = a[√[(2b)² - a²]]/4
Area for the 8f shape = a² - a[√[(2b)² - a²]]/4
Therefore, the formula for the area of the shapes in:
8e). A = a[√(x² + a²)]
8f). A = a² - a[√[(2b)² - a²]]/4
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1.What is the distance between point b and the directrix ?
2.What does this tell you about the distance between p and f ?
Answer: we could be th superheros so we are superheros
Step-by-step explanation:
Answer:
Step-by-step explanation:
SInce the distance between the vertex and the focus is the same as the distance from the vertex to the directrix, the distance from the directrix to the focus is 22‾√.
Since the shortest path from the focus to the directrix goes through the vertex, the distance from the focus to the directrix is the sum of the distance from the focus to the vertex and the distance of the vertex to the directrix, namely 22‾√+22‾√=42‾√
a forester who wants to evaluate the health of maple trees in a large forest randomly selects 10 locations in the forest and creates 20-meter diameter circles with each location as a center (making sure none of the circles overlap). he then evaluates all the maple trees in each circle. which one of the following sampling methods is he using?
The forester is using the systematic sampling method to evaluate the health of maple trees in the large forest. Systematic sampling involves selecting every nth item in a population after randomly selecting a starting point.
In this case, the forester randomly selected 10 locations in the forest and created 20-meter diameter circles with each location as a center. Since the circles do not overlap and are evenly spaced, this indicates that the forester is selecting every 10th circle. The forester then evaluates all the maple trees in each circle.
Systematic sampling is useful when the population is too large to be evaluated in its entirety, but a representative sample is needed. It is also efficient and eliminates bias that can occur when using other sampling methods such as convenience sampling or judgmental sampling. By using systematic sampling, the forester can get an accurate representation of the health of maple trees in the large forest without having to evaluate every single tree.
The forester is using the "cluster sampling" method. In this approach, the population is divided into smaller groups, or clusters, and a random sample of these clusters is selected for evaluation. In this case, the forest is the population, and the 10 locations with 20-meter diameter circles are the selected clusters. The forester then evaluates all maple trees within each chosen cluster to gather data on the health of the trees. This method is useful for studying large populations, as it reduces the time and effort required to collect data by focusing on specific areas rather than the entire population.
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true or false: if this model suffers from heteroskedasticity, then ols estimates of the slope parameters are biased and inconsistent.
True. If a model suffers from heteroskedasticity, it means that the variance of the errors is not constant across all observations, which violates one of the key assumptions of the OLS (Ordinary Least Squares) method.
When the variance of the errors is not constant, the OLS estimates of the slope parameters become biased and inconsistent, which means that the estimated coefficients do not accurately reflect the true relationship between the independent and dependent variables. This can lead to incorrect conclusions and flawed predictions.
Therefore, it is essential to test for heteroskedasticity and take corrective measures such as using weighted least squares or robust standard errors to obtain unbiased and consistent estimates of the regression coefficients.
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What is the product of –3n(–12n)?
–15n.
36n.
–15n2.
36n2
the product of -3n(-12n) is d. 36n2.
Please help this is the final question on my homework and I am lost
Answer:
15.6
Step-by-step explanation:
sin74=15/x
sin74x=15
x=15/sin74
x=15.625
x=15.6 (Nearest tenth)
WHAT IS THE LENGTH OF THE LINE? SOMEONE SMART ANSWER THIS PLS:)
Answer:
D
Step-by-step explanation:
using the bottom left hand corner as the origin
calculate the length d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
the coordinates of the ends of the line are then
(x₁, y₁ ) = (2, 8 ) and (x₂, y₂ ) = (12, 2 )
d = [tex]\sqrt{(12-2)^2+(2-8)^2}[/tex]
= [tex]\sqrt{10)^2+(-6)^2}[/tex]
= [tex]\sqrt{100+36}[/tex]
= [tex]\sqrt{136}[/tex]
in which ways does a nonlinear programming model differ from a linear programming model? multiple select question. nonlinear models have nonproportional relationships between activity levels and the overall measure of performance
A nonlinear programming model differs from a linear programming model in several ways. One key difference is that nonlinear models have nonproportional relationships between activity levels and the overall measure of performance.
Additionally, nonlinear models may have multiple optimal solutions, while linear models typically only have one optimal solution. Nonlinear models may also have discontinuous objective functions or constraints, while linear models have continuous objective functions and constraints.
Nonlinear programming models are used when the relationship between variables is not linear. In a linear programming model, the objective function and constraints are linear, meaning that they have a constant rate of change.
However, in a nonlinear programming model, the objective function and constraints may have nonlinear relationships, which means that they do not have a constant rate of change. This can make it more difficult to optimize the model, as it may have multiple optimal solutions or discontinuous regions. Nonlinear programming models may use techniques such as gradient descent or Newton's method to find the optimal solution, while linear programming models typically use the simplex method. Overall, nonlinear programming models are more complex than linear programming models and require more advanced mathematical techniques to solve.
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The functions f(x) = x2 – 1 and g(x) = –x2 + 4 are shown on the graph.
The graph shows f of x equals x squared minus 1, which is an upward opening parabola with a vertex at 0 comma negative 1 and a point at negative 1 comma 0 and a point at 1 comma 0. The graph also shows g of x, which is a downward opening parabola with a vertex at 0 comma 4 and a point at negative 1 comma 3 and a point at 1 comma 3.
Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the solution set be identified?
y > x2 – 1
y ≤ –x2 + 4
The set of inequalities y ≤ x² - 1 and y > -x² + 4 do not have a solution
How to Interpret Inequality Graphs?From the graph, we have:
f(x) = x² - 1
g(x) = -x² + 4
Next, we change the equations to inequalities as follows:
y ≤ x² - 1
y > -x² + 4
To modify the graph, we then perform the following transformations:
Shift the function g(x) down by 2 units
Reflect across the x-axis
Shift the function g(x) down by 3 units
After the modifications in (a), we have:
y ≤ x² - 3 and y > -x² + 2
Next, we plot the graph of the inequalities
From the graph of the inequalities, the curves of the inequalities have no point of intersection
Hence, the set of inequalities do not have a solution
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Given that x=10, the number 7356 can be expressed as a polynomial 7x cubed + 3x squared + 5x + 6. Write 1892 as a polynomial in terms of x
The number 1892 can be expressed as a polynomial in terms of x as [tex]1x^3 + 8x^2 + 9x + 2.[/tex] By substituting the value of x into each term, we obtain the polynomial expression for the given number.
To express the number 1892 as a polynomial in terms of x, we need to determine the coefficients of each term by considering the place value of each digit.
The given number 1892 has four digits: 1, 8, 9, and 2. Each digit represents a coefficient of a term in the polynomial expression.
Starting from the leftmost digit, we assign the coefficients as follows:
1 is the coefficient of the term with the highest power of x, which is x^3.
8 is the coefficient of the term with the second highest power of x, which is x^2.
9 is the coefficient of the term with the power of x, which is x.
2 is the coefficient of the constant term, which is x^0 or simply 1.
Combining these coefficients with the corresponding powers of x, we obtain the polynomial expression: [tex]1x^3 + 8x^2 + 9x + 2.[/tex]
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HELP ME FAST PLS
A principal of $3300 is invested at 5.25% interest, compounded annually. How much will the investment be worth after 8 years?
Use the calculator provided and round your answer to the nearest dollar.
SHOW YOUR WORK
MAKE YOU THE BRAINLIEST
Answer:
Step-by-step explanation:
formula: p(1+r/n)^nt
p=3300
r= 5.25% = 0.0525
n= 1
t= 8
3300(1+0.0525/1)^8(1)
3300(1.0525)^8
apply exponent to parentheses first, then multiply by 3300. and you get approximately (rounded):
≈49,692
Please someone help me on this
A man has a round clothes rack in his closet. each article of clothing on this rock is distinct.
a. In how many ways can he hang 4 dress shirts and 4 pairs of pants on this rack?
b. In how many ways can he hang 4 dress shirts and 4 pairs of pants on this rack if no shirts are together?
The solution is: the number of total combinations is 24+30=54.
We know that Peg has 4 long-sleeve shirts, 5 short-sleeve shirts, and 6 pairs of pants. We assume that she is going to wear a shirt and a pair of pants.
First, we calculate the number of combinations for a pants and long-sleeve shirts. She have 6 pairs of pants and 4 long-sleeve shirts.
We get: 6 · 4 = 24
Now, we calculate the number of combinations for a pants and short-sleeve shirts. She have 6 pairs of pants and 5 short-sleeve shirts.
We get: 6 · 5 = 30
So the number of total combinations is 24+30=54.
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complete question:
Peg has 4 long-sleeve shirts, 5 short-sleeve shirts, and 6 pairs of pants. (a) How many different ways can Peg dress (assuming she is going to wear a shirt and a pair of pants)
The area of the shaded region is about ___ square yd.
*Remember, don't round until you get to your final answer.
If the image does not come throught for you, look at #24 on the 2.03 Images document.
The area of the shaded region is given as follows:
1323.23 yd².
How to calculate the area of a circle?The area of a circle of radius r is given by the multiplication of π and the radius squared, as follows:
A = πr²
The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle.
The smaller circle has the radius given as follows:
r = 23.1 yd.
Hence the area is given as follows:
A = π x 23.1²
A = 1676.39 yd².
The larger circle has the radius given as follows:
r = 23.1 + 7.8 = 30.9 yd.
Hence the area is given as follows:
A = π x 30.9²
A = 2999.62 yd².
Hence the area of the shaded region is given as follows:
2999.62 - 1676.39 = 1323.23 yd².
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a culinary group surveyed 407 restaurant patrons and found that 129 of them liked chicken the most of any fried rice dish. obtain a point estimate for the proportion of all restaurant patrons who like chicken the most of any fried rice dish. express your answer as a percentage rounded to one decimal place as needed.
Answer:
31,7
Step-by-step explanation:
We divide 129 from 407 and multiply it by 100 to get percentage, then round
ID:
A normal distribution has meanu and standard deviation o. An x-value is randomly selected from the
distribution. Find P(mu - 2sigma <= x <= mu + 3sigma)
Answer:
Step-by-step explanation:
d
How much water can this container hold express your answer in terms of
The container can hold 972π cubic inches of water
Calculating how much water can the container holdFrom the question, we have the following parameters that can be used in our computation:
A spherical container (see attachment)
Diameter = 18 in
The radius of the container is calculated as
r = 18/2
Evaluate
r = 9
The amount of water the container can hold is its volume
This is calculated as
V = 4/3πr³
Substitute the known values in the above equation, so, we have the following representation
V = 4/3π * 9³
Evaluate
V = 972π
Hence, the container can hold 972π of water
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You have a 3 meter length of pipe, you cut off 150cm what length do you have left ?
Answer:
150 cm
Step-by-step explanation:
1 metre = 100 cm
so 3 metres = 300cm
300 - 150 = 150
so we have 150cm left
Find the measure of Arc BED.
(If anyone has answers to the whole test please post them, I'm struggling!!)
The measure of the arc BED is 218°
How to find the measure of the arc?This means that we need to find the angle of the arc BED on the given circle.
We need to remember that the total angle on a circle is 360°.
We can also see that the angle between B and C is 52°, and the angle between C and D is 90° (that is what the little square means).
And the angle between B and D (measured counterclockwise) is the angle we want to find, and it will be equal to 360° minus the two angles above, then we will get:
measure of the arc = 360° - 52° - 90°
measure of the arc = 218°
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please help with these
The coordinates of the image of the quadrilateral by translation are A'(x, y) = (- 4, - 7), B'(x, y) = (- 5, - 2), C'(x, y) = (- 2, - 3) and D'(x, y) = (- 1, - 6).
How to determine the image of a quadrilateral
In this question we need to determine the image of a quadrilateral by a kind of rigid transformation known as translation, whose definition is introduced below:
P'(x, y) = P(x, y) + T(x, y)
Where:
P(x, y) - Original point.T(x, y) - Translation vector.P'(x, y) - Resulting point.First, we determine the coordinates of the vertices of the image of the quadrilateral:
A'(x, y) = (- 2, - 3) + (- 2, - 4)
A'(x, y) = (- 4, - 7)
B'(x, y) = (- 3, 2) + (- 2, - 4)
B'(x, y) = (- 5, - 2)
C'(x, y) = (0, 1) + (- 2, - 4)
C'(x, y) = (- 2, - 3)
D'(x, y) = (1, - 2) + (- 2, - 4)
D'(x, y) = (- 1, - 6)
Second, graph the resulting quadrilateral.
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A company that sells hair-care products wants to estimate the mean difference in satisfaction rating for a product that combines shampoo and conditioner compared with a shampoo and conditioner used separately. A researcher recruits 60 volunteers and pairs them according to age, hair color, and hair type. For each pair, the researcher flips a coin to determine which volunteer will use the shampoo/conditioner combination and which one will use the separate shampoo and conditioner. After using the products for one month, the subjects will be asked to rate their satisfaction with the hair products on a scale of 1–10 (1 = highly dissatisfied and 10 = highly satisfied). The mean difference in satisfaction ratings (Combined – Separate) is calculated. What is the appropriate procedure?
Answer: one-sample t-interval for u diff
Yes, that is correct. A paired t-test could also be used to test whether the mean difference is statistically significant.
The appropriate procedure for estimating the mean difference in satisfaction ratings between the combined shampoo and conditioner and separate shampoo and conditioner is a one-sample t-interval for the population mean difference.
Since the researcher is interested in comparing the means of two related samples (i.e., the same subjects are used for both the combined and separate treatments), a paired t-test could also be used to test whether the mean difference is statistically significant.
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The net below can be folded to form a
square-based pyramid, as shown.
Work out the height of this pyramid.
Give your answer in cm to 2 d.p.
7 cm
6 cm
The required height of the given pyramid is approximately 8.77 cm.
Since the slant height of the pyramid is 9 cm, so a triangle is on one of the triangular faces of the pyramid.
Let h be the height of the pyramid. By the Pythagorean theorem, we know that:
Pythagoras's theorem states that in a right-angled triangle, the square of one side is equal to the sum of the squares of the other two sides.
So, it can be written as follows:
(4/2)² + h² = 9²
4 + h² = 81
h² 81 - 4
h² = 77
h = √(77)
h ≈ 8.77
Therefore, the height of the pyramid is approximately 8.77 cm.
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A bin contains 120 ears of white and yellow corn. There are 78 ears that are yellow. What percent of the ears of corn are white?
Approximately 35% of the ears of corn in the bin are white.
To find the percentage of white ears of corn, we need to determine the number of white ears and then calculate what proportion they make out of the total number of ears in the bin.
Given that there are 78 ears of yellow corn, we can subtract this number from the total number of ears to find the number of white ears:
Total ears - Yellow ears = White ears
120 - 78 = 42
There are 42 white ears of corn in the bin. To calculate the percentage of white ears, we divide the number of white ears by the total number of ears and multiply by 100:
(White ears / Total ears) x 100 = Percentage of white ears
[tex](42 / 120) \times 100 = 35%[/tex]
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Simplify this expression
6x-8y-5x + 3y
Answer:
x - 5y
Step-by-step explanation:
6x - 8y - 5x + 3y
= (6x - 5x) + (-8y + 3y)
= x - 5y
Hope this helps :)
Pls brainliest...
10.
-3 4/5 divided by 6/2
The value of -3 4/5 divided by 6/2 is -8/15.
Algebra is the study of abstract symbols, thus logic is the manipulation of all those ideas. The PEMDAS stands for; Parenthesis, Exponent, Multiplication, Division, Addition, Subtraction.
We are given that;
Numbers= -3 4/5 and 6/2
Now,
We can see that 4 and 6 have a common factor of 2. We will divide both by 2 and get:
26−354=−352×31
Now we can multiply the fractions by multiplying the numerators and the denominators. We get:
26−354=−5×33×2+2×1
Simplifying, we get:
26−354=−8/15
Therefore, by algebra, the answer will be -8/15.
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2. Flip your coin 20 times and record the number of heads you get. Repeat this process 4 more times. Record your results in the table below . trial number 12 3 4 5 number of heads
The correct table is,
trial number Number of heads
1 12
2 11
3 9
4 10
5 8
Given that;
. Flip your coin 20 times and record the number of heads you get.
Now, After flipping the coin we get;
trial number Number of heads
1 12
2 11
3 9
4 10
5 8
Thus, The correct table is shown above.
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PLEASE HELP I DONT UNDERSTAND!!!!!!
The value of P(-1.83 ≤ z ≤ 0.56) for a standard normal distribution is 0.6783, or 68.83%.
To find the value of P(-1.83 <= z <= 0.56) for a standard normal distribution, we need to find the probability associated with each individual value and then subtract the lower probability from the higher probability.
As, P(z <= -1.83) is 0.034, and P(z <= 0.56) is 0.7123.
To find P(-1.83 ≤ z ≤ 0.56), we subtract the lower probability from the higher probability:
P(-1.83 ≤ z ≤ 0.56)
≈ P(z ≤ 0.56) - P(z ≤-1.83)
≈ 0.7123 - 0.034
or, P(-1.83 ≤ z ≤ 0.56) ≈ 0.6783
Therefore, the value of P(-1.83 ≤ z ≤ 0.56) for a standard normal distribution is 0.6783, or 68.83%.
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a null hypothesis is that the average pulse rate of adults is 70. for a sample of 64 adults, the average pulse rate is 71.8. a significance test is done and the p-value is 0.02. what is the most appropriate conclusion?
In conclusion, the most appropriate conclusion is that there is sufficient evidence to suggest that the average pulse rate of adults is greater than 70 beats per minute, based on the sample of 64 adults and the calculated p-value.
Based on the given information, it can be inferred that the null hypothesis is that the average pulse rate of adults is 70 beats per minute. The alternative hypothesis, in this case, would be that the average pulse rate is greater than 70.
A sample of 64 adults is taken, and the average pulse rate is found to be 71.8 beats per minute. This means that the sample mean is slightly higher than the hypothesized value of 70, but it is not clear whether this difference is statistically significant or not.
To test the significance, a significance test is performed, and the p-value is found to be 0.02. This means that there is a 2% chance of observing a sample mean of 71.8 beats per minute or higher, assuming that the null hypothesis is true.
A commonly used threshold for statistical significance is 0.05, which means that if the p-value is less than 0.05, the null hypothesis can be rejected. In this case, the p-value is less than 0.05, which indicates that the observed difference between the sample mean and the hypothesized value of 70 is statistically significant. Therefore, the null hypothesis can be rejected, and the alternative hypothesis can be accepted.
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An open box has a square base and congruent rectangular sides. The total area of the base and the sides is 48cm^2. Determine the dimensions of the box with the maximum value.
The dimensions of the box with the maximum volume are:
Length of the square base (x) = 2 cm
Width of the rectangular side (y) = 5.5 cm
To determine the dimensions of the box with the maximum value, we need to maximize the volume of the box since the surface area is fixed.
Let's assume that the length of one side of the square base is "x," and the width of the rectangular side is "y."
Since the sides are congruent, the other side of the square base will also be "x," and the length of the rectangular side will be "y."
The surface area of the base and sides is given by:
Area = Base Area + 4 × Side Area
The base area is given by:
Base Area = x × x = x²
The side area is given by:
Side Area = x × y
The total area is given as 48 cm², so we have:
x² + 4xy = 48
To find the dimensions that maximize the volume, we need to express the volume in terms of a single variable. The volume of the box is given by:
Volume = Base Area × Height
Since the height is not specified, let's assume it is "h."
Therefore, the volume is:
Volume = x² × h
To solve this problem, we need to express the volume in terms of a single variable using the given information. From the total area equation, we can solve for y:
x² + 4xy = 48
4xy = 48 - x²
y = (48 - x²) / (4x)
Now we can substitute the value of y into the volume equation:
Volume = x²h
Volume = x²(48 - x²) / (4x)
Volume = (12x - x³) / 4
To find the maximum value of the volume, we need to find the critical points by taking the derivative of the volume equation with respect to x:
d(Volume) / dx = (12 - 3x²) / 4
Setting the derivative equal to zero and solving for x:
12 - 3x² = 0
3x² = 12
x² = 4
x = ±2
Since the dimensions of a box cannot be negative, we discard the negative value. Therefore, x = 2.
Now we can substitute x back into the equation for y:
y = (48 - x²) / (4x)
y = (48 - 2²) / (4 × 2)
y = (48 - 4) / 8
y = 44 / 8
y = 5.5
So, the dimensions of the box with the maximum volume are:
Length of the square base (x) = 2 cm
Width of the rectangular side (y) = 5.5 cm
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the statistical abstract of the united states reports that 30% of the country's households are composed of one person. if 20 randomly selected homes are to participate in a nielson survey to determine television ratings, find the probability that fewer than six of these homes are one-person households.
The probability that fewer than six homes are one-person households is approximately 1.0092.
To solve this problem, we can use the binomial probability formula.
The formula for the probability of getting exactly k successes in n independent Bernoulli trials, each with a probability of success p, is:
[tex]P(X = k) = (n C k) \times p^k \times (1 - p)^{(n - k)[/tex]
Where:
P(X = k) is the probability of getting exactly k successes.
n is the number of trials or sample size.
k is the number of successful outcomes.
(n C k) is the number of combinations of n items taken k at a time, also known as "n choose k."
p is the probability of success on each trial.
(1 - p) is the probability of failure on each trial.
^ represents exponentiation.
In this case, the probability of success (p) is 30% or 0.30, since 30% of households are one-person households.
The number of trials (n) is 20, as 20 homes are randomly selected for the survey.
To find the probability that fewer than six of these homes are one-person households, we need to calculate the cumulative probability from 0 to 5. We can do this by summing the individual probabilities for k = 0, 1, 2, 3, 4, and 5.
P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5).
Now let's calculate each term using the binomial probability formula and sum them up:
[tex]P(X = 0) = (20 C 0) \times (0.30)^0 \times (1 - 0.30)^{(20 - 0)}[/tex]
[tex]P(X = 1) = (20 C 1) \times (0.30)^1 \times (1 - 0.30)^{(20 - 1)}[/tex]
[tex]P(X = 2) = (20 C 2) \times (0.30)^2 \times (1 - 0.30)^{(20 - 2)[/tex]
[tex]P(X = 3) = (20 C 3) \times (0.30)^3 \times (1 - 0.30)^{(20 - 3)[/tex]
[tex]P(X = 4) = (20 C 4) \times (0.30)^4 \times (1 - 0.30)^{(20 - 4)}[/tex]
[tex]P(X = 5) = (20 C 5) \times (0.30)^5 \times (1 - 0.30)^(20 - 5)[/tex]
To calculate the binomial coefficients (n C k), we can use the formula:
[tex](n C k) = n! / (k! \times (n - k)!)[/tex]
where "!" denotes the factorial of a number.
Let's calculate each term and sum them up to find the probability using the binomial probability formula:
[tex]P(X = 0) = (20 C 0) \times (0.30)^0 \times (1 - 0.30)^{ (20 - 0)} = 0.0264[/tex]
[tex]P(X = 1) = (20 C 1) \times (0.30)^1 \times (1 - 0.30)^{(20 - 1)} = 0.1305[/tex]
[tex]P(X = 2) = (20 C 2) \times (0.30)^2 \times (1 - 0.30)^{(20 - 2)} = 0.2501[/tex]
[tex]P(X = 3) = (20 C 3) \times (0.30)^3 \times (1 - 0.30)^{(20 - 3)} = 0.2905[/tex]
[tex]P(X = 4) = (20 C 4) \times (0.30)^4 \times (1 - 0.30)^{(20 - 4) } = 0.2088[/tex]
[tex]P(X = 5) = (20 C 5) \times (0.30)^5 \times (1 - 0.30)^{(20 - 5)} = 0.1029[/tex]
Now let's sum up these probabilities.
P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)
= 0.0264 + 0.1305 + 0.2501 + 0.2905 + 0.2088 + 0.1029
= 1.0092.
Therefore, the probability that fewer than six homes are one-person households is approximately 1.0092.
However, probabilities cannot exceed 1, so we can conclude that the probability is 1 (or 100%) that fewer than six homes are one-person households in this sample of 20 homes.
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What is the maximum vertical distance between the line
y=10x+39 and the parabola y=x^2 for -3
The maximum vertical distance between the line y = 10x + 39 and the parabola y = x^2 for -3 ≤ x ≤ 3 is 160 units.
To find the maximum vertical distance between the line y = 10x + 39 and the parabola y = x^2 for -3 ≤ x ≤ 3, we need to determine the points on the parabola that have the maximum vertical distance from the line.
Let's start by finding the points of intersection between the line and the parabola. Setting the equations equal to each other, we have:
10x + 39 = x^2
Rearranging the equation, we get:
x^2 - 10x - 39 = 0
Solving this quadratic equation, we find that x = -3 and x = 13 are the x-coordinates of the points of intersection.
Now, let's calculate the corresponding y-values for these x-coordinates on the parabola:
For x = -3, y = (-3)^2 = 9
For x = 13, y = (13)^2 = 169
Next, we can calculate the y-values for the line at these x-coordinates:
For x = -3, y = 10(-3) + 39 = 9
For x = 13, y = 10(13) + 39 = 169
Since the y-values of the line and the parabola are the same at the points of intersection, the maximum vertical distance occurs at the point (-3, 9) and (13, 169).
The maximum vertical distance between the line and the parabola is the difference in y-coordinates at these points:
169 - 9 = 160
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