In the sample of 500, there are 310 males and 190 females. Out of the total sample, 180 males eat breakfast and 80 females don't eat breakfast.
A 2-way table was created to show the relationship between gender and breakfast eating habits. The table showed that the events "Female" and "Eats Breakfast" are not disjoint and not independent.
a. The percentage of males in the sample is given as 62%. To find the number of males, we multiply the percentage by the total sample size:
Number of males = 62% of 500 = 0.62 * 500 = 310
Therefore, there are 310 males in the sample.
b. The percentage of females in the sample is given as 38%. To find the number of females, we multiply the percentage by the total sample size:
Number of females = 38% of 500 = 0.38 * 500 = 190
Therefore, there are 190 females in the sample.
c. The percentage of males who eat breakfast is given as 58%. To find the number of males who eat breakfast, we multiply the percentage by the total number of males:
Number of males who eat breakfast = 58% of 310 = 0.58 * 310 = 179.8 ≈ 180
Therefore, there are 180 males in the sample who eat breakfast.
d. The percentage of females who don't eat breakfast is given as 42%. To find the number of females who don't eat breakfast, we multiply the percentage by the total number of females:
Number of females who don't eat breakfast = 42% of 190 = 0.42 * 190 = 79.8 ≈ 80
Therefore, there are 80 females in the sample who don't eat breakfast.
e. The probability of selecting a female who doesn't eat breakfast is given by the percentage of females who don't eat breakfast:
P(Female and Doesn't eat breakfast) = 42% = 0.42
f. Using the calculations above, the completed 2-way table is as follows
| Eats Breakfast | Doesn't Eat Breakfast | Total
-----------------------------------------------------------
Male | 180 | 130 | 310
-----------------------------------------------------------
Female | 110 | 80 | 190
-----------------------------------------------------------
Total | 290 | 210 | 500
g. The events "Female" and "Eats Breakfast" are not disjoint because there are females who eat breakfast (110 females).
h. The events "Female" and "Eats Breakfast" are not independent because the probability of a female eating breakfast (110/500) is not equal to the probability of a female multiplied by the probability of eating breakfast ([tex]\frac{190}{500} \times \frac{290}{500}[/tex]). It is equal to 0.1096 or approximately 10.96%.
To know more about the 2-way table refer here :
https://brainly.com/question/29131906#
#SPJ11
Complete question :
500 people were asked this question and the results were recorded in a tree diagram in terms of percent. M= male, F = female, E= eats breakfast, D= doesn't eat breakfast. 62% M 58% E 42% D 40% E 38% F 60% Show complete work on your worksheet! a. How many males are in the sample? b. How many females are in the sample? c. How many males in the sample eat breakfast? d. How many females in the sample don't eat breakfast? e. What is the probability of selecting a female who doesn't eat breakfast? Set up: 2 decimal places: f. Use the calculations above to complete the 2-way table. Doesn't Eats Br. Male Female JUN 3 Total JA f. Use the calculations above to complete the 2-way table. Eats Br. Doesn't Male Female Total g. Are the events Female and Eats Breakfast disjoint? O no, they are not disjoint O yes, they are disjoint Explain: O There are no females who eat breakfast O There are females who eat breakfast. h. Are the events Female and Eats Breakfast independent? O No, they are not independent O Yes, they are independent Justify mathematically. P(F)= P(FE) 1. Find P(Male I Doesn't eat breakfast) 2 decimal places: e. Find P(Female) JUN 3 (G Total 500 . om/assess2/?cid=143220&aid=10197871#/full P(F) = P(FE) = 1. Find P(Male I Doesn't eat breakfast) 2 decimal places: e. Find P(Female) f. Find P(Male or Eats Breakfast) g. Create a Venn Diagram of the information. Male Fats Br O h. Find the probability someone who eats breakfast is male P- 1. Find the probability a female doesn't eat breakfast. P- Submit Question JUN 3 80 F3 * F2 Q F4 F5 (C F6
Garrett found the slope of the values in the table: A 2-column table with 3 rows. Column 1 is labeled Years: x with entries 4, 8, 12. Column 2 is labeled Hourly rate: y with entries 12. 00, 13. 00, 14. 0. 1. Slope = StartFraction 12 minus 8 Over 14. 00 minus 13. 00 EndFraction. 2. Slope = StartFraction 4 Over 1. 00 EndFraction. 3. Slope = 4. Is Garrett’s slope correct? If not, identify his error? Yes. Garrett found the slope correctly. No. He should have put the x values in the denominator and the y values in the numerator. No. He should have gotten a negative answer for slope because the values are decreasing. No. He should have gotten the answer StartFraction 1 Over 25 EndFraction.
Garrett's slope is incorrect. He should have put the x values in the denominator and the y values in the numerator. The correct calculation of the slope for the given table is: Slope = (13.00 - 12.00) / (8 - 4) = 1.00 / 4 = 0.25
To calculate the slope, we need to find the change in the y-values divided by the change in the x-values. In Garrett's case, he incorrectly calculated the slope by subtracting the x-values (years) from each other in the numerator and the y-values (hourly rates) from each other in the denominator.
The correct calculation of the slope for the given table is:
Slope = (13.00 - 12.00) / (8 - 4) = 1.00 / 4 = 0.25
Therefore, Garrett's slope is not correct. He made an error by swapping the x and y values in the calculation. The correct calculation would have the x values (4, 8, 12) in the denominator and the y values (12.00, 13.00, 14.00) in the numerator.
Additionally, Garrett's calculation does not consider the values in the table decreasing. The sign of the slope indicates the direction of the relationship between the variables. In this case, if the values were decreasing, the slope would have a negative sign. However, this information is not provided in the given table.
Learn more about slope here:
https://brainly.com/question/3605446
#SPJ11
Find a vector function, r(t), that represents the curve of intersection of the two surfaces.
The paraboloid
z = 2x^2 + y^2
and the parabolic cylinder
y = 3x^2
The curve of intersection between the paraboloid [tex]z = 2x^2 + y^2[/tex]and the parabolic cylinder y = 3[tex]x^2[/tex] can be represented by the vector function
r(t) = ([tex]t, 3t^2, 2t^2 + 9t^4[/tex]).
To find the curve of intersection between the two surfaces, we need to find the values of x, y, and z that satisfy both equations simultaneously. We can start by substituting the equation of the parabolic cylinder, y = 3[tex]x^2[/tex], into the equation of the paraboloid, [tex]z = 2x^2 + y^2[/tex].
Substituting y = 3[tex]x^2[/tex] into z = [tex]2x^2 + y^2[/tex], we get [tex]z = 2x^2 + (3x^2)^2 = 2x^2 + 9x^4[/tex].
Now, we can express the vector function r(t) as (x(t), y(t), z(t)).
Since [tex]y = 3x^2[/tex], we have y(t) = [tex]3t^2[/tex]. And from [tex]z = 2x^2 + 9x^4[/tex], we have [tex]z(t) = 2t^2 + 9t^4[/tex]
For x(t), we can choose x(t) = t, as it simplifies the equations and represents the parameter t directly. Therefore, the vector function representing the curve of intersection is [tex]r(t) = (t, 3t^2, 2t^2 + 9t^4)[/tex].
This vector function traces out the curve of intersection between the paraboloid and the parabolic cylinder as t varies. Each point on the curve is obtained by plugging in a specific value of t into the vector function.
Learn more curve of intersection here:
https://brainly.com/question/3747311
#SPJ11
Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 2500 grams and a standard deviation of 500 grams, while babies born after a gestation period of 40 weeks have a mean weight of 2900 grams and a standard deviation of 415 grams. If a 32-week gestation period baby weighs 2875 grams and a 41-week gestation period baby weighs 3275 grams, find the corresponding
-scores. Which baby weighs more relative to the gestation period?
By comparing the z-scores we obtain that the 41-week gestation baby weighs more relative to their gestation period compared to the 32-week gestation baby.
To find the z-score for each baby, we can use the formula:
z = (X - μ) / σ
where X is the baby's weight, μ is the mean weight, and σ is the standard deviation.
For the 32-week gestation baby weighing 2875 grams:
z = (2875 - 2500) / 500 = 0.75
For the 41-week gestation baby weighing 3275 grams:
z = (3275 - 2900) / 415 = 0.9
The z-score measures the number of standard deviations a data point is from the mean.
A positive z-score indicates that the data point is above the mean.
Comparing the z-scores, we see that the 41-week gestation baby (z = 0.9) has a higher z-score than the 32-week gestation baby (z = 0.75).
This means that the 41-week gestation baby weighs more relative to their gestation period compared to the 32-week gestation baby.
To know more about z-scores refer here:
https://brainly.com/question/31871890#
#SPJ11
find the volume of the solid bounded by the paraboloids z=−9 2x2 2y2 and z=5−2x2−2y2
We are given two paraboloids as:z = (-9/2)(x^2 + y^2)andz = 5 - 2(x^2 + y^2)The volume of the solid enclosed between the two paraboloids is given byV = ∫∫R[(5 - 2(x^2 + y^2)) - (-9/2)(x^2 + y^2)] d[tex]z = (-9/2)(x^2 + y^2)andz = 5 - 2(x^2 + y^2)[/tex]A
where R is the region in the xy-plane that is bounded by the circular region of radius a centered at the origin.We can rearrange the equation and simplify it as follows:V = ∫∫R (23/2)x^2 + (23/2)y^2 - 5 dAWe will use polar coordinates (r, θ) to evaluate the integral, and the limits of integration for the radius will be 0 and a, and the limits of integration for the angle will be 0 and 2π.
Hence, we can rewrite the integral as:V = ∫[0, 2π] ∫[0, a] (23/2)r^2 - 5r dr dθEvaluating this integral:V = ∫[0, 2π] [23/6 * a^3 - 5/2 * a^2] dθV = 4π [23/6 * a^3 - 5/2[tex]V = ∫[0, 2π] ∫[0, a] (23/2)r^2 - 5r dr dθ Evaluating this integral:V = ∫[0, 2π] [23/6 * a^3 - 5/2 * a^2] dθV = 4π [23/6 * a^3 - 5/2 * a^2]V = (46/3)πa^3 - 10πa^2[/tex] * a^2]V = (46/3)πa^3 - 10πa^2Hence, the volume of the solid enclosed between the two paraboloids is (46/3)πa^3 - 10πa^2.The explanation has a total of 152 words.
To know more about limits visit:
https://brainly.com/question/12211820
#SPJ11
A rectangular prism has a height of h cm. The area of its base is B cm^(2). How much does the volume of the prism increase when the height is increased by 1 cm?
To determine how much the volume of the rectangular prism increases when the height is increased by 1 cm, we need to calculate the difference in volumes between the two configurations.
The volume V of a rectangular prism is given by the formula:
V = B * h
where B represents the area of the base and h represents the height.
When the height is increased by 1 cm, the new height becomes (h + 1) cm. The new volume, V', is given by:
V' = B * (h + 1)
To find the increase in volume, we subtract the original volume V from the new volume V':
Increase in volume = V' - V
Substituting the expressions for V and V', we have:
Increase in volume = (B * (h + 1)) - (B * h)
Simplifying, we get:
Increase in volume = B * h + B - B * h
The term B * h cancels out, leaving us with:
Increase in volume = B
Therefore, the increase in volume when the height is increased by 1 cm is equal to the area of the base B.
To know more about volume visit-
brainly.com/question/16723255
#SPJ11
The joint probability mass function of X and Y, p(x,y), is given by:
p(1,1)=1/9, p(2,1)=1/3, p(3,1)=1/9,
p(1,2)=1/9, p(2,2)=0, p(3,2)=1/18,
p(1,3)=0, p(2,3)=1/6, p(3,3)=1/9
Compute E[X|Y=1], E[X|Y=2], E[X|Y=3]
The marginal probability mass function for X is given by P(X = 1) = 6/18 = 1/3P(X = 2) = 5/18P(X = 3) = 5/18.
First, let us compute the marginal probability mass function for X.
p(1,1) + p(2,1) + p(3,1) = 1/9 + 1/3 + 1/9 = 5/9p(1,2) + p(2,2) + p(3,2) = 1/9 + 0 + 1/18 = 1/6p(1,3) + p(2,3) + p(3,3) = 0 + 1/6 + 1/9 = 5/18
Therefore, the marginal probability mass function for X is given by P(X = 1) = 6/18 = 1/3P(X = 2) = 5/18P(X = 3) = 5/18
We are asked to compute E[X|Y = 1], E[X|Y = 2], and E[X|Y = 3]. We know that E[X|Y] = ∑xp(x|y) / p(y)
Therefore, let us compute the conditional probability mass function for X given Y = 1.
p(1|1) = 1/9 / (5/9) = 1/5p(2|1) = 1/3 / (5/9) = 3/5p(3|1) = 1/9 / (5/9) = 1/5
Therefore, the conditional probability mass function for X given Y = 1 is given by P(X = 1|Y = 1) = 1/5P(X = 2|Y = 1) = 3/5P(X = 3|Y = 1) = 1/5
Therefore, E[X|Y = 1] = 1/5 × 1 + 3/5 × 2 + 1/5 × 3 = 1.8
Next, let us compute the conditional probability mass function for X given Y = 2.
p(1|2) = 1/9 / (1/6) = 2/3p(2|2) = 0 / (1/6) = 0p(3|2) = 1/18 / (1/6) = 1/3
Therefore, the conditional probability mass function for X given Y = 2 is given by P(X = 1|Y = 2) = 2/3P(X = 2|Y = 2) = 0P(X = 3|Y = 2) = 1/3
Therefore, E[X|Y = 2] = 2/3 × 1 + 0 + 1/3 × 3 = 2
Finally, let us compute the conditional probability mass function for X given Y = 3.
p(1|3) = 0 / (5/18) = 0p(2|3) = 1/6 / (5/18) = 6/5p(3|3) = 1/9 / (5/18) = 2/5
Therefore, the conditional probability mass function for X given Y = 3 is given by P(X = 1|Y = 3) = 0P(X = 2|Y = 3) = 6/5P(X = 3|Y = 3) = 2/5
Therefore, E[X|Y = 3] = 0 × 1 + 6/5 × 2 + 2/5 × 3 = 2.4
Therefore,E[X|Y=1] = 1.8,E[X|Y=2] = 2,E[X|Y=3] = 2.4.
To know more about probability visit: https://brainly.com/question/31828911
#SPJ11
Suppose Event is an attribute, and in a dataset it is given as
1_265232_A. What data type is this? Select one answer only
Metric continuous
Categorical ordinal
Categorical metric
Nominal discrete
Nomi
In the dataset, 1_265232_A is given as the attribute for Event. The data type of this attribute can be identified by analyzing the given values.
The first number 1 can be considered as a code that may represent a specific category or level, while 265232 is a numerical identifier. The letter A indicates that the attribute could be classified according to a particular qualitative characteristic, such as quality, color, or size. From this information, it can be determined that the data type of the attribute "Event" is a nominal discrete type. Nominal data is the type of categorical data that does not have any inherent order or ranking to its categories. A nominal variable is typically a categorical variable that is often binary (only two groups, such as sex or yes or no) or Polytomous (more than two categories).
It can be concluded that the data type of the attribute "Event" in the given dataset is nominal discrete, and it is represented by the value 1_265232_A.
To know more about data type visit:
https://brainly.com/question/30615321
#SPJ11
find the points on the cone z 2 = x 2 y 2 z2=x2 y2 that are closest to the point (5, 3, 0).
Given the cone z² = x²y² and the point (5, 3, 0), we have to find the points on the cone that are closest to the given point.The equation of the cone z² = x²y² can be written in the form z² = k²(x² + y²), where k is a constant.
Hence, the cone is symmetric about the z-axis. Let's try to obtain the constant k.z² = x²y² ⇒ z = ±k√(x² + y²)The distance between the point (x, y, z) on the cone and the point (5, 3, 0) is given byD² = (x - 5)² + (y - 3)² + z²Since the points on the cone have to be closest to the point (5, 3, 0), we need to minimize the distance D. Therefore, we need to find the values of x, y, and z on the cone that minimize D².
Let's substitute the expression for z in terms of x and y into the expression for D².D² = (x - 5)² + (y - 3)² + [k²(x² + y²)]The values of x and y that minimize D² are the solutions of the system of equations obtained by setting the partial derivatives of D² with respect to x and y equal to zero.∂D²/∂x = 2(x - 5) + 2k²x = 0 ⇒ (1 + k²)x = 5∂D²/∂y = 2(y - 3) + 2k²y = 0 ⇒ (1 + k²)y = 3Dividing these equations gives us x/y = 5/3. Substituting this ratio into the equation (1 + k²)x = 5 gives usk² = 16/9 ⇒ k = ±4/3Now that we know the constant k, we can find the corresponding value of z.z = ±k√(x² + y²) = ±(4/3)√(x² + y²)
To Know more about derivatives visit:
brainly.com/question/25324584
#SPJ11
find the taylor polynomial t3(x) for the function f centered at the number a. f(x) = ex, a = 1
The Taylor polynomial t3(x) for the function f centered at the number a = 1 and [tex]f(x) = ex is e(x-1)^3 + e(x-1)^2 + e(x-1) + e.[/tex]
The Taylor polynomial for f(x) = e^x centered at a = 1, with degree n = 3 is:
[tex]t_3(x) = f(a) + f'(a)(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \frac{f'''(a)}{3!}(x-a)^3[/tex]
First, we compute the first three derivatives of f(x) = e^x.
[tex]f(x) = e^x\\f'(x) = e^x\\f''(x) = e^x\\f'''(x) = e^x[/tex]
Substituting a = 1 into each of these yields:
[tex]f(1) = e^1\\= e\\f'(1) = e^1 \\= e\\f''(1) = e^1 \\= e\\f'''(1) = e^1 \\= e[/tex]
Therefore,[tex]t_3(x) = e + e(x-1) + \frac{e}{2!}(x-1)^2 + \frac{e}{3!}(x-1)^3= e(1 + (x-1) + \frac{1}{2!}(x-1)^2 + \frac{1}{3!}(x-1)^3)[/tex]
Simplifying, we get:
[tex]t_3(x) = e(x-1)^3 + e(x-1)^2 + e(x-1) + e[/tex]
Therefore, the Taylor polynomial t3(x) for the function f centered at the number a = 1 and [tex]f(x) = ex is e(x-1)^3 + e(x-1)^2 + e(x-1) + e.[/tex]
Know more about Taylor polynomial here:
https://brainly.com/question/30094386
#SPJ11
Use the fundamental identities to completely simplify csc(z) cot(z) + tan(z) (You will need to use several techniques from algebra here such as common denominators, factoring, etc. Make sure you show
The completely simplified form of csc(z) cot(z) + tan(z) is 1 / sin²(z) + sin(z) Using the fundamental identities.
Given,
csc(z) cot(z) + tan(z)
We know that:
cot(z) = cos(z) / sin(z) csc(z)
= 1 / sin(z) tan(z)
= sin(z) / cos(z)
Now, csc(z) cot(z) + tan(z)
= 1 / sin(z) × cos(z) / sin(z) + sin(z) / cos(z)
= cos(z) / sin²(z) + sin(z) / cos(z)
The LCM of sin²(z) and cos(z) is sin²(z)cos(z).
Hence, cos(z) / sin²(z) + sin(z) / cos(z)
= cos²(z) / sin²(z) × cos(z) / cos(z) + sin³(z) / sin²(z) × sin²(z) / cos(z)
= cos²(z) / sin²(z) + sin(z) = 1 / sin²(z) + sin(z)
The completely simplified form of csc(z) cot(z) + tan(z) is 1 / sin²(z) + sin(z).
To know more about identities visit
https://brainly.com/question/32644501
#SPJ11
which function has only one x-intercept at (−6, 0)?f(x) = x(x − 6)f(x) = (x − 6)(x − 6)f(x) = (x 6)(x − 6)f(x) = (x 6)(x 6)
Therefore,the function that has only one x-intercept at (-6, 0) is f(x) = (x + 6)(x - 6).
In this function, when you set f(x) equal to zero, you get:
(x + 6)(x - 6) = 0
For this equation to be satisfied, either (x + 6) must equal zero or (x - 6) must equal zero. However, since we want only one x-intercept, we need exactly one of these factors to be zero.
If (x + 6) = 0, then x = -6, which gives the x-intercept (-6, 0).
If (x - 6) = 0, then x = 6, but this would give us an additional x-intercept at (6, 0), which we do not want.
Therefore, the function f(x) = (x + 6)(x - 6) has only one x-intercept at (-6, 0).
Learn more about equation here:
https://brainly.com/question/29538993
#SPJ11
if the principal is 1,245, the interest rate is 5% and the time is 2 years what is the interest
The interest on a principal of $1,245 at an interest rate of 5% for a period of 2 years is $124.50.
To calculate the interest, we can use the formula:
Interest = Principal × Rate × Time
Given:
Principal (P) = $1,245
Rate (R) = 5% = 0.05 (in decimal form)
Time (T) = 2 years
Plugging these values into the formula, we have:
Interest = $1,245 × 0.05 × 2
Calculating the expression, we get:
Interest = $1245 × 0.1
Interest = $124.50
It's important to note that the interest calculated here is simple interest. Simple interest is calculated based on the initial principal amount without considering any compounding over time. If the interest were compounded, the calculation would be different.
In simple interest, the interest remains constant throughout the period, and it is calculated based on the principal, rate, and time. In this case, the interest is calculated as a percentage of the principal for the given time period.
for more such questions on interest rate
https://brainly.com/question/25793394
#SPJ8
Let X be a continuous random variable taking values between 0 and 2 with probability density function p(x) = 0.5. Find E(X) and Var(X).
Given a continuous random variable X that takes values between 0 and 2 with probability density function p(x) = 0.5, we are to find the expected value E(X) and the variance Var(X).
Expected value E(X)The expected value of a continuous random variable is defined as the integral of the product of the random variable and its probability density function over its range. That is,E(X) = ∫x p(x) dxIn this case, p(x) = 0.5 for 0 ≤ x ≤ 2. Hence,E(X) = ∫x p(x) dx= ∫x(0.5) dx = 0.5(x²/2)|0²= 0.5(2)²/2= 0.5(2)= 1Answer: E(X) = 1Var(X)The variance of a continuous random variable is defined as the expected value of the square of the deviation of the variable from its expected value. That is,Var(X) = E((X - E(X))²)We have already calculated E(X) as 1. Hence,Var(X) = E((X - 1)²)The squared deviation (X - 1)² takes values between 0 and 1 for 0 ≤ X ≤ 2. Hence,Var(X) = ∫(X - 1)² p(x) dx= ∫(X - 1)²(0.5) dx= 0.5 ∫(X² - 2X + 1) dx= 0.5 (X³/3 - X² + X)|0²= 0.5 [(2³/3 - 2² + 2) - (0)] = 0.5 (8/3 - 4 + 2)= 0.5 (2/3)Answer: Var(X) = 1/3
Therefore, E(X) = 1 and Var(X) = 1/3.
Learn more about probability visit:
brainly.com/question/31828911
#SPJ11
This question has two parts. First, answer Part A. Then, answer Part B. Part A BRAKING DISTANCE From the time a driver sees the need to apply the brake to the point at which the car stops completely is known as the total stopping distance. The total stopping distance d can be modeled by the equation d = 0.0515r ^ 2 + 1.1r where is the speed in miles per hourGraph the function. Interpret the key features of the graph in terms of the quantities Select the graph that models this equation.
The quadratic function d = 0.0515r² + 1.1r equations graphed and attached
How to interpret the key features of the graphThe equation plotted is
d = 0.0515r² + 1.1r
The key features includes
a. The graph open upwards: This is so since the quadratic term"r²" of the equation does not have a negative sign
b. The vertex of the quadratic equation is the lowest part of the graph which is (-10.7, 5.9)
c. the intercepts
the x-intercept or the roots are (-21.4, 0) and (0, 0)
the y-intercepts is (0, 0)
d. axis of symmetry
The symmetry is at x = -b/2x = -1.1(2 * 0.0515) = -10.68
Learn more about quadratic function at
https://brainly.com/question/1214333
#SPJ1
Customers arrive at the Wendy's drive-thru at random, at an average rate of 17 per hour. During a given hour, what is the probability that more than 20 customers will arrive at the drive-thru? Oo 0.26
The probability that more than 20 customers will arrive at the drive-thru is 0.025.
Poisson distribution is used to find the probability of a certain number of events occurring in a specified time interval. It is used when the event is rare, and the sample size is large. In Poisson distribution, we have an average arrival rate (λ) and the number of arrivals (x).
The probability of x events occurring during a given time period is :
P(x;λ) = λx e−λ/x!, where e is the Euler's number (e = 2.71828182846) and x! is the factorial of x.
To find the probability that more than 20 customers will arrive at the drive-thru during a given hour, we use the Poisson distribution as follows:
P(x > 20) = 1 - P(x ≤ 20)
P(x ≤ 20) = ∑ (λ^x * e^-λ)/x!, x = 0 to 20
Let's find the probability P(x ≤ 20).
P(x ≤ 20) = ∑ (λ^x * e^-λ)/x!; x = 0 to 20
P(x ≤ 20) = ∑ (17^x * e^-17)/x!; x = 0 to 20
P(x ≤ 20) = 0.975
Therefore, P(x > 20) = 1 - P(x ≤ 20)
P(x > 20) = 1 - 0.975
P(x > 20) = 0.025
This means that the probability that more than 20 customers will arrive at the drive-thru is 0.025.
To learn more about probability visit : https://brainly.com/question/13604758
#SPJ11
If a procedure meets all of the conditions of a binomial distribution except the number of trials is not fixed, then the geometric distribution can be used. The probability of getting the first success on the xth trial is given by P(x) = p(1-p)x-1, where p is the probability of success on any one trial. Subjects are randomly selected for a health survey. The probability that someone is a universal donor (with group O and type Rh negative blood) is 0.14. Find the probability that the first subject to be a universal blood donor is the seventh person selected. C The probability is (Round to four decimal places as needed.) Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. This method is designed to increase the likelihood that each baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5. Assume that the groups consist of 24 couples. Complete parts (a) through (c) below. -C a. Find the mean and the standard deviation for the numbers of girls in groups of 24 births. The value of the mean is μ =. (Type an integer or a decimal. Do not round.) The value of the standard deviation is o= (Round to one decimal place as needed.) b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high. Values of girls or fewer are significantly low. (Round to one decimal place as needed.) Values of girls or greater are significantly high. is effective. (Round to one decimal place as needed.) is not effective. c. Is the result of 22 girls a result that is significantly high? What does it suggest about the effectiveness of the method? ▼ girls. A result of 22 girls would suggest that the method The result significantly high, because 22 girls is (Round to one decimal place as needed.)
When a procedure meets all of the conditions of a binomial distribution except the number of trials is not fixed, the geometric distribution can be used.
Given that subjects are randomly selected for a health survey, the probability that someone is a universal donor (with group O and type Rh negative blood) is 0.14.
We have to find the probability that the first subject to be a universal blood donor is the seventh person selected.Using the formula mentioned above:[tex]P(7) = 0.14(1 - 0.14)6= 0.0878[/tex]
The probability is 0.0878. Option C is correct.
Now, let's solve the next part.Assuming that different groups of couples use a particular method of gender selection and each couple gives birth to one baby.
This method is designed to increase the likelihood that each baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5.
Assuming that the groups consist of 24 couples.
(a)Find the mean and the standard deviation for the numbers of girls in groups of 24 births:
Let X be the number of girls in a group of 24 births.
[tex]X ~ B(24, 0.5)Mean:μ = np= 24 * 0.5= 12[/tex]Standard deviation:[tex]σ = `sqrt(np(1-p))`= `sqrt(24*0.5*0.5)`= `sqrt(6)`≈ 2.449[/tex] (rounded to one decimal place).
To know more about distribution visit:
https://brainly.com/question/29664127
#SPJ11
find the xx coordinate of the point on the parabola y=20x2−12x 13y=20x2−12x 13 where the tangent line to the parabola has slope 1818.
The x-coordinate of the point on the parabola where the tangent line has a slope of 18/18 is 5/8.
We are to find the x-coordinate of the point on the parabola y=20x²−12x/13 where the tangent line to the parabola has a slope of 18/18.
The tangent line to the parabola has a slope of 18/18, so we can find the derivative of the equation y=20x²−12x/13 and set it equal to the given slope.dy/dx = 40x - 12/13
slope = 18/18 = 1
We can set the derivative equal to 1 and solve for x.40x - 12/13 = 1Multiplying both sides of the equation by 13, we have 40x - 12 = 13
Combining like terms, we get
40x = 25Dividing both sides by 40, we obtain x = 25/40 or x = 5/8.
Therefore, the x-coordinate of the point on the parabola where the tangent line has a slope of 18/18 is 5/8.
Know more about the parabola here:
https://brainly.com/question/29635857
#SPJ11
How large a surface area in units of square feet will 1 gallon of paint cover if we apply a coat of paint that is 0. 05 inches thick?
1 gallon of paint will cover approximately 32.14 square feet when applied with a coat that is 0.05 inches thick.
To determine the surface area that 1 gallon of paint will cover, we need to convert the given thickness of 0.05 inches to feet.
Since 1 foot is equal to 12 inches, we have 0.05 inches/12 = 0.004167 feet as the thickness.
The coverage area of paint can be calculated by dividing the volume of paint (in cubic feet) by the thickness (in feet).
Since 1 gallon is equal to 231 cubic inches, and there are [tex]12^3 = 1728[/tex] cubic inches in 1 cubic foot, we have:
1 gallon = 231 cubic inches / 1728 = 0.133681 cubic feet.
Now, to calculate the surface area covered by 1 gallon of paint with a thickness of 0.004167 feet, we divide the volume by the thickness:
Coverage area = 0.133681 cubic feet / 0.004167 feet ≈ 32.14 square feet.
For similar question on surface area.
https://brainly.com/question/27950508
#SPJ8
Use a graphing tool to solve the system. {13x + 6y = −30, x − 2y = −4}. Which ordered pair is the best estimate for the solution to the system?
a. (2, -5).
b. (-1, 2).
c. (4, 3). d. (0, -4).
(B) (-1, 2) ordered pair is the best estimate for the solution to the system.
To solve the system {13x + 6y = −30, x − 2y = −4} using a graphing tool, we need to plot the line for each equation and find the point where they intersect.
This point is the solution to the system.
The intersection point appears to be (-1, 2).
Therefore, the best estimate for the solution to the system is the ordered pair (-1, 2).
Therefore, option b. (-1, 2) is the correct option.
Know more about ordered pair here:
https://brainly.com/question/11139505
#SPJ11
ad←→ is tangent to circle b at point c. the measure of ∠abc is 40º. what is the measure of ∠bac? responses 40º 40º 50º 50º 90º 90º 180º
The value of ∠BAC is 50°. Hence, the correct option is 50º.Given, AD is tangent to circle B at point C. ∠ABC = 40°.We need to find the value of ∠BAC.Therefore, let's solve this problem below:As AD is tangent to circle B at point C, it forms a right angle with the radius of circle B at C.
∴ ∠ACB = 90°Also, ∠ABC is an external angle to triangle ABC. Therefore,∠ABC = ∠ACB + ∠BAC = 90° + ∠BACNow, putting the value of ∠ABC from the given information, we get,40° = 90° + ∠BAC40° - 90° = ∠BAC-50° = ∠BAC
Therefore, the value of ∠BAC is 50°. Hence, the correct option is 50º.
To know more about tangent visit:
https://brainly.com/question/10053881
#SPJ11
1. Which of the following stochastic processes X are adapted to σ (B,0 ≤ s ≤ t): (i) Xt = f Beds, (ii) Xt = maxo
The stochastic process which satisfies the measurability condition adapted to σ (B, 0 ≤ s ≤ t) will only be considered.
Adapted process is a stochastic process that depends on time and which is predictable by the available information in a specified probability space.
An adapted stochastic process X(t) is measurable with respect to the given information up to time t. Here, the following stochastic processes X are adapted to σ (B, 0 ≤ s ≤ t):
(i) Xt = f B(t), if and only if f is σ (Bt; 0 ≤ t ≤ T) measurable.
(ii) Xt = max{0, B(t)}, if and only if the event {X(t) ≤ x} is σ (Bt; 0 ≤ t ≤ T) measurable for every x.
As the maximum function is continuous, it is left continuous and thus adapted to the filtration generated by Brownian motion
The stochastic processes adapted to σ (B, 0 ≤ s ≤ t) are as follows:
(i) Xt = f B(t), if and only if f is σ (Bt; 0 ≤ t ≤ T) measurable.
(ii) Xt = max{0, B(t)}, if and only if the event {X(t) ≤ x} is σ (Bt; 0 ≤ t ≤ T) measurable for every x.
The conclusion is that the stochastic process which satisfies the measurability condition adapted to σ (B, 0 ≤ s ≤ t) will only be considered.
To know more about stochastic process visit:
brainly.com/question/30882590
#SPJ11
HW 3: Problem 15 Previous Problem List Next (1 point) For a x² -curve with 22 degrees of freedom, find the x²-value that has area 0.01 to its right. A. 9.542 B. 40.290 C. 42.796 D. None of the above
That the critical value for a chi-squared distribution with 22 degrees of freedom and an area of 0.99 to its left is approximately 40.290.
To find the x²-value that has an area of 0.01 to its right in a chi-squared distribution with 22 degrees of freedom, we need to find the critical value. The critical value represents the cutoff point beyond which only 0.01 (1%) of the distribution lies.
To solve this problem, we can use a chi-squared table or a statistical calculator to find the critical value. In this case, we are looking for the value with area 0.01 to its right, which corresponds to the area of 0.99 to its left.
After consulting a chi-squared table or using a statistical calculator, we find that the critical value for a chi-squared distribution with 22 degrees of freedom and an area of 0.99 to its left is approximately 40.290.
Therefore, the correct answer is option B: 40.290.
Learn more about critical value here
https://brainly.com/question/28159026
#SPJ11
2) Suppose that 10 cars are selected at random and that the cars are sampled are driven both, with and without additive, producing a paired sample of size 10 given below: Car 1 2 3 4 5 6 7 9 10 8 28.4
The mean difference between the two samples is 4.49. This response is approximately 250 words.
The given data provides a paired sample of 10 cars that have been sampled and driven both with and without an additive. The data is as follows: Car 1 2 3 4 5 6 7 9 10 8 28.4. Based on this data, we need to compute the paired differences and find the mean difference.
Let's start by calculating the paired differences. We can obtain paired differences by subtracting the measurement without an additive from the measurement with an additive. Below is a table of the paired differences:
Car Paired Differences1(28.4 - 21.5) = 6.92(28.8 - 23.2) = 5.63(27.7 - 23.8) = 3.93(29.1 - 25.3) = 3.84(26.4 - 22.2) = 4.25(28.1 - 24.1) = 4.06(27.3 - 22.6) = 4.77(30.3 - 25.7) = 4.68(29.8 - 25.8) = 4.09(25.6 - 22.4) = 3.2
To compute the mean difference, we add all the paired differences and divide by the number of paired differences, which is 10. 6.9 + 5.6 + 3.9 + 3.8 + 4.2 + 4.0 + 4.7 + 4.6 + 4.0 + 3.2 = 44.9So the mean difference is 44.9 / 10 = 4.49. The mean difference is the best estimate of the true mean difference between the two samples if all samples were tested.
To know more about number visit:
https://brainly.com/question/3589540
#SPJ11
Use the properties of logarithms to evaluate each of the following expressions. (a) 2log 3 + log 4 = 0 5 12 Ine = In e (b) 0 - X Ś ?
The answer is - log x.
Here's the solution for the given problem:
Using the properties of logarithms to evaluate each of the following expressions.
2log 3 + log 4
= 0 5 122(log 3) + log 4
= log (3²) + log 4
= log (3² × 4)
= log 36
= log 6²
Now, we have the expression log 6²
Now, we can write the given expression as log 36
Thus, the final answer is log 36
Ine = In e
(b) 0 - X Ś ?
By the rule of logarithm for quotient, we have
log (1/x)
= log 1 - log x
= -log x
We can use the same rule for log (0 - x) and write it as
log (0 - x)
= log 0 - log x
= - log x
Now, we have the expression - log x
Thus, the final answer is - log x
To know more about log visit:
https://brainly.com/question/28225096
#SPJ11
8- Let X and Y be independent RVs, both having zero mean and variance ². Find the crosscorrelation function of the random processes v(t): = X cos wot+ Y sin wot w(t) = Y cos wot - X sin wot (10 marks
The cross-correlation function of the random processes v(t) and w(t) is:
R_vw(tau) = -X^2 sin(wo(t+tau))cos(wot).
The cross-correlation function of the random processes v(t) and w(t) can be found by taking the expected value of their product. Since X and Y are independent random variables with zero mean and variance ², their cross-correlation function simplifies as follows:
R_vw(tau) = E[v(t)w(t+tau)]
= E[(X cos(wot) + Y sin(wot))(Y cos(wo(t+tau)) - X sin(wo(t+tau)))]
= E[XY cos(wot)cos(wo(t+tau)) - XY sin(wot)sin(wo(t+tau)) + Y^2 cos(wo(t+tau))sin(wot) - X^2 sin(wo(t+tau))cos(wot))]
Since X and Y are independent, their expected product E[XY] is zero. Additionally, the expected value of sine and cosine terms over a full period is zero. Therefore, the cross-correlation function simplifies further:
R_vw(tau) = -X^2 sin(wo(t+tau))cos(wot)
Thus, the cross-correlation function is given by:
R_vw(tau) = -X^2 sin(wo(t+tau))cos(wot).
To know more about random processes refer here:
https://brainly.com/question/31601542
#SPJ11
Construct a stem-and-leaf display for the given data table. 10) 12 32 61 18 63 23 42 21 34 29 45 14 55 48 52 35 57 13
Stem-and-leaf display of the given data is shown below: Stem and Leaf
1 | 3, 4, 5, 8
2 | 1, 3, 3
3 | 2, 4, 5, 5, 6
4 | 2, 5, 8
5 | 2, 5, 7
There are two parts of the stem-and-leaf display: the stem, which is the digits in the greatest place value, and the leaf, which is the digits in the lesser place value. The digits in the least place value of each observation are called leaves and are listed alongside the corresponding stem. This gives a clear picture of the distribution of the data.
The stem-and-leaf display for the given data table is as follows: Stem and Leaf
1 | 3, 4, 5, 8
2 | 1, 3, 3
3 | 2, 4, 5, 5, 6
4 | 2, 5, 8
5 | 2, 5, 7
There are two parts of the stem-and-leaf display: the stem, which is the digits in the greatest place value, and the leaf, which is the digits in the lesser place value. The digits in the least place value of each observation are called leaves and are listed alongside the corresponding stem. This gives a clear picture of the distribution of the data. The stem-and-leaf display for the given data table is as follows: Stem and Leaf
1 | 3, 4, 5, 8
2 | 1, 3, 3
3 | 2, 4, 5, 5, 6
4 | 2, 5, 8
5 | 2, 5, 7
The stem and leaf plot is a great way to show how data are distributed. It allows you to see the distribution of data in a more meaningful way than just looking at the raw numbers.
To know more about Leaf visit :-
https://brainly.com/question/14294937
#SPJ11
Question 11 of 12 < > 1 Two sides and an angle are given. Determine whether a triangle (or two) exist, and if so, solve the triangle(s) a-√2.b-√7.p-105 How many triangles exist? Round your answers
1 solution of a triangle exists because all of the angles are less than 180 degrees and the sides and angles have non-negative values.
Therefore, there exists only one triangle.
The given values are:
a = √2, b = √7, and p = 105
The sine law is applied to determine the angle opposite to a. We know that sin(A)/a = sin(B)/b = sin(C)/c
where A, B, and C are the angles of a triangle, and a, b, and c are the opposite sides to A, B, and C, respectively.
Therefore, sin(A)/√2 = sin(B)/√7
We can now get sin(A) and sin(B) by cross-multiplication:
√7 * sin(A) = √2 * sin(B)sin(A) / sin(B) = √(2/7)
Using the sine law, we can now calculate the angle C:
sin(C)/p = sin(B)/b
Therefore, sin(C) = (105 sin(B))/√7
Using the equation sin²(B) + cos²(B) = 1, we can determine
cos(B) and cos(A)cos(B)
= √(1 - sin²(B)) = √(1 - 2/7)
= √(5/7)cos(A) = (b cos(C))/a
= (√7 cos(C))/√2Since sin(A)/√2
= sin(B)/√7sin(A)
= (√2/√7)sin(B)sin(A)
= (√2/√7) [√(1 - cos²(B))]
We can solve the equations above using substitution to find sin(B) and sin(A).
1 solution of a triangle exists because all of the angles are less than 180 degrees and the sides and angles have non-negative values.
Therefore, there exists only one triangle.
To know more about triangle visit:
https://brainly.com/question/2773823
#SPJ11
Solve for measure of angle A.
The measure of angle a is:
a = (140° - 96°) / 2 = 44° / 2 = 22°
Therefore, the answer is 22.
1
If two secant lines intersect outside a circle, the measure of the angle formed by the two lines is one half the positive difference of the measures of the intercepted arcs.
In the given diagram, we can see that the intercepted arcs are 96° and 140°. Therefore, the measure of angle a is:
a = (140° - 96°) / 2 = 44° / 2 = 22°
Therefore, the answer is 22.
Answer: 22
To know more about vectors
https://brainly.com/question/28028700
#SPJ3
Help with this question pls
Answer: 9 s
Step-by-step explanation:
Given:
h(t) = -16t² + 144t
Find:
time when h=0 They want to know when the rocket hits the ground. This happens when h=0
Solution:
0 = -16t² + 144t >Take out Greatest Common Factor
0 = (-16t )(t - 9) >Set each parenthesis = 0
(-16t ) = 0 and (t - 9)=0 >Solve for t
t = 0 and t = 9 >When the rocket launches t=0 and h=0
Also, t=9 when h=0
t=9 s
0.142857 is rational or not
Answer: not rational
Step-by-step explanation:
It's not rational because it has no pattern and probably goes on forever
Irrational means goes on forever without pattern. Ex. [tex]\pi[/tex] or √7