question allistair throws a biased six-sided dice. the probability of getting a 6 with this dice is 0.4. the other numbers are equally probable. if he throws the dice 3 times, what is the probability that he gets 5, 3, and 2 in this order?
The probability that he gets 5, 3, and 2 in this order is 0.92, 0.52, and 0.32 respectively.
The possibility of rolling a 6 with these dice is 0.4, according to the question. The possibility of rolling a 1 through 5 on the dice is also the probability of not obtaining a 6.
a) Chance of receiving 5:
P(6) + Q(6) = 5
Q(6) = 5 - P(6)
Q(6) = 5 - 0.4
Q(6) = 4.6
The probability of obtaining 5 to 5 is 4.6 overall.
The probability of receiving one is,
P(1) + P(2) + P(3) + P(4) + P(5) = 4.6
The first five numbers have an equally likely probability.
P(1) = 4.6 ÷ 5
P(1) = 0.92
b) Probability of getting 3:
P(6) + Q(6) = 3
Q(6) = 3 - P(6)
Q(6) = 3 - 0.4
Q(6) = 2.6
The probability of obtaining 3 to 5 is 2.6 overall.
The probability of receiving one is,
P(1) + P(2) + P(3) + P(4) + P(5) = 2.6
The first five numbers have an equally likely probability.
P(1) = 2.6 ÷ 5
P(1) = 0.52
c) Probability of getting 2:
P(6) + Q(6) = 2
Q(6) = 2 - P(6)
Q(6) = 2 - 0.4
Q(6) = 1.6
The probability of obtaining 2 to 5 is 1.6 overall.
The probability of receiving one is,
P(1) + P(2) + P(3) + P(4) + P(5) = 1.6
The first five numbers have an equally likely probability.
P(1) = 1.6 ÷ 5
P(1) = 0.32
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A SUNY student landed an internship at the Albany Department of Health in vital statistics. They are thrilled! On the second day, they are asked to pull together maternal mortality rates. They are provided with the following data:
There were 209,338 live births in Albany in 2020.
There were 69 pregnancy associated deaths. 41 of those deaths were Black women, 13 were non-Hispanic White, and 15 were Hispanic women.
The student is then asked to create a presentation using the data. What is the maternal mortality rate for Albany women in 2020 per 1000? Round to two decimal places.
The maternal mortality rate for Albany women in 2020 is 0.33 per 1,000.
The maternal mortality rate is a critical indicator of a region's healthcare system and the well-being of women during childbirth. To calculate the maternal mortality rate for Albany women in 2020, we need to determine the number of pregnancy-associated deaths per 1,000 live births.
According to the given data, there were 209,338 live births in Albany in 2020. Out of the 69 pregnancy-associated deaths, 41 were Black women, 13 were non-Hispanic White, and 15 were Hispanic women.
To calculate the maternal mortality rate, we divide the number of pregnancy-associated deaths by the number of live births and multiply the result by 1,000.
Maternal Mortality Rate = (Number of Pregnancy-Associated Deaths / Number of Live Births) * 1,000
Using the given data, the maternal mortality rate for Albany women in 2020 can be calculated as follows:
Maternal Mortality Rate = (69 / 209,338) * 1,000
Calculating this equation gives us a maternal mortality rate of approximately 0.33 deaths per 1,000 live births in Albany in 2020. Rounded to two decimal places, the maternal mortality rate for Albany women in 2020 is 0.33 per 1,000.
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true/false: the this pointer is automatically passed to static member functions of a class.
The given statement "The this pointer is not automatically passed to static member functions of a class." is false as static member functions can be called without creating an object of the class, and the "this" pointer is used to refer to the current instance of the class. Since no instance is required for static member functions, the "this" pointer is not applicable in this case.
In object-oriented programming, a class is a blueprint for creating objects, and member functions are functions defined within a class that can be called on objects of that class.
Static member functions, also known as class methods, are special member functions that are associated with the class itself rather than any specific object or instance of the class. They are declared using the "static" keyword.
Since static member functions do not operate on specific instances of the class, they do not have access to the "this" pointer. The "this" pointer is a hidden pointer that points to the current object instance, allowing non-static member functions to access the data members and other member functions of the object. However, static member functions do not have this pointer because they are not tied to any specific object.
Static member functions can only access static members of the class, which include static variables and other static member functions. They can be called using the class name itself, without creating an instance of the class. This is because they are not associated with any particular object but rather with the class as a whole.
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Understanding the ConceptsIn Exercises 7 and 8, fill in each blank with the appropriate word or phrase.7. To perform a t-test when the sample size is small, the sample must show no evidence of strong and must contain no .
Answer:
7. To perform a t-test when the sample size is small, the sample must show no evidence of strong skewness and must contain no outliers.
Step-by-step explanation:
These are the two conditions required for performing a t test
- Sample Size: A small sample size can reduce the statistical power of a t-test, making it more challenging to detect significant differences between groups. Generally, a larger sample size is desirable to obtain more reliable and representative results.
- Skewness: Skewness refers to the asymmetry of the distribution of data. In a t-test, assuming normality of the data is important for accurate results. If the data exhibits strong skewness, the assumption of normality may be violated. In such cases, alternative non-parametric tests or transformations of the data may be more appropriate.
- Outliers: Outliers are extreme values that significantly differ from the rest of the data. They can have a disproportionate impact on the results of a t-test, particularly when the sample size is small. Outliers can distort the mean and affect the assumptions of normality and homogeneity of variance.
While the presence of skewness or outliers does not prohibit the use of a t-test with a small sample size, it is important to interpret the results with caution and consider alternative approaches if necessary. Robust statistical methods, such as non-parametric tests or bootstrapping, can be useful when dealing with non-normal or outlier-prone data, especially with small sample sizes. Additionally, visual inspection of the data distribution, such as through histograms or box plots, can help identify potential skewness or outliers.
4(2.25w+3.1)-2.75w=44.9
Answer:
w = 5.2
Step-by-step explanation:
4(2.25w + 3.1) - 2.75w = 44.9
9w + 12.4 - 2.75w = 44.9
6.25w + 12.4 = 44.9
6.25w = 32.5
w = 5.2
4(2.25w+3.1)-2.75w=44.9
9w+12.4-2.75w=44.9
9w-2.75w+12.4=44.9
44.9-12.4=32.5
9w-2.75w=32.5
6.3w/6.3=32.5/6.3
=5 10/63
18. If f(x) = arccos(x^2), then f'(x) =
The derivative of f(x) = arccos(x^2) is: f'(x) = -2x / √(1-x^4)
The derivative of f(x) = arccos(x^2), we'll use the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function. In this case, the outer function is arccos(u) and the inner function is u = x^2.
First, let's find the derivative of the outer function, arccos(u). The derivative of arccos(u) is -1/√(1-u^2). Next, we'll find the derivative of the inner function, x^2. The derivative of x^2 is 2x.
Now we'll apply the chain rule. We have:
f'(x) = (derivative of outer function) * (derivative of inner function)
f'(x) = (-1/√(1-u^2)) * (2x)
Since u = x^2, we'll substitute that back into our equation:
f'(x) = (-1/√(1-x^4)) * (2x)
So, the derivative of f(x) = arccos(x^2) is:
f'(x) = -2x / √(1-x^4)
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If Mrs. Maiers buys 24 stickers, is the cost of each sticker more than or less than $0.50? Select all statements that are correct
Answer:
C and E
Step-by-step explanation:
PQ= RQ and PS= RS a=?
The measure of angle a is 15 degrees and this can be determined by using the properties of the isosceles triangle.
What are interior angles?In geometry, interior angles are formed in two ways. One is inside a polygon, and the other is when parallel lines cut by a transversal. Angles are categorized into different types based on their measurements.
Given:
The length of the segment PQ is equal to the length of the segment RQ.The length of the segment PS is equal to the length of the segment RS.The following steps can be used in order to determine the measure of angle a:
Step 1 - According to the given data, it can be concluded that triangle PQR and triangle PSR are isosceles triangles.
Step 2 - Apply the sum of interior angle property on triangle PQR.
\(\angle\text{Q}+\angle\text{P}+\angle\text{R}=180\)
\(\angle\text{Q}+2\angle\text{R}=180\)
\(2\angle\text{R}=180-60\)
\(\angle\text{R}=60^\circ\)
Step 3 - Now, apply the sum of interior angle property on triangle PSR.
\(\angle\text{P}+\angle\text{S}+\angle\text{R}=180\)
\(\angle\text{S}+2\angle\text{R}=180\)
\(2\angle\text{R}=180-90\)
\(\angle\text{R}=45^\circ\)
Step 4 - Now, the measure of angle a is calculated as:
\(\angle\text{a}=60-45\)
\(\angle\text{a}=15\)
The measure of angle a is 15 degrees.
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What number would make this statement true?
1/7 = 7/?
the first step we take to test our multiple regression model is a t-test.a. trueb. false
False. The first step to testing a multiple regression model is to use an F-test to determine if at least one of the predictors is significantly related to the outcome variable.
The statement "the first step we take to test our multiple regression model is a t-test" is false. The first step in testing a multiple regression model is typically to examine the overall significance of the model, which is done using an F-test.
The F-test evaluates whether the model as a whole explains a significant amount of the variance in the dependent variable. Only after we have determined that the model is statistically significant should we proceed to examine the individual predictors using t-tests.
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How do I go about solving this? (Teacher got sick mid-lesson & still wanted us to finish the worksheet but he never went over how to solve this kind of equation) Any kind of help is greatly appreciated.
\(g(a) = 4a-2\\h(a) = 3a\\Find: g(h(8))\)
The composite function g(h(8)) when evaluated is 94.
Evaluating the composite functionsFrom the question, we have the following parameters that can be used in our computation:
g(a) = 4a - 2
h(a) = 3a
To find g(h(8)), we need to first evaluate h(8), and then plug that result into g(a) and simplify.
h(a) is defined as 3a, so h(8) = 3(8) = 24.
Now we can plug in 24 for a in g(a) and simplify:
g(a) = 4a - 2
g(h(8)) = g(24) = 4(24) - 2 = 94
Therefore, g(h(8)) = 94.
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Which of the following statement is correct about secánt and tangent line
to a circle?
A. A secant of a circle contains chord of a circle
B. A secant of a circle always contains diameter of a circle
C. A tangent to a circle contains an interior point of the circle
D A tangent to a circle can pass through the center of the circle
Answer:
option A
Step-by-step explanation:
secant intersects the circle at exactly two points. A chord is the line segment make a chord inside circle
declare two double variables, one named length with a value of 3.5 and the other named width with a value of 1.55.
named width in java with a value of 1.55.
double length = 3.5; double width = 1.55;
Double is a data type in Java that supports storing decimal numbers. It is used to represent values that include a fractional component and is a 64-bit floating-point data type. When exact decimal numbers are required, as in financial or scientific computations, the double data type is frequently utilized. A double's range is roughly ±\(5.0 \times 10^{-324}\) to ±\(1.7 \times 10^{308\) having a 15–17 decimal digit degree of accuracy.
For example:
double myDouble = 3.14; Alternatively, you may define a double variable without first giving it a value and then give it one later on in your code.
3.5 double length, 1.55 double width;
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Jacob has 298 baseball cards. About how many
baseball cards does Jacob have? Round to the
nearest 100.
Answer:
300
Step-by-step explanation:
5 or more raise the score 4 or less let it rest basically 5 or more up 4 or less down
what is the 35th term of : 0.13 , 0.38 , 0.63 , 0.88 , 1.13
Answer:
206
Step-by-step explanation:
I think
Answer: 8.63
Step-by-step explanation:
-5 terms have been given so you need 30 more to reach 35.
-terms are going up by .25
30 * .25 = 7.5
7.5+1.13= 8.63
A residual is the difference between _______.
A residual is the difference between "the measured and predicted values of the quantity of interest".
What is residuals?In regression analysis, a residual would be the difference between an observable and anticipated value.
The formula is;
Residual = Observed value – Predicted value
Some key features regarding the residuals are-
The purpose of linear regression would be to quantify the relationship among one or so more predictor variables one and or more response variables. Linear regression selects the line that best "fits" the data, defined as least squares regression line, to do this. This line generates a prediction for every observation in the dataset, however it is improbable that the regression line's prediction would perfectly match its observed value.The residual is the discrepancy between the predicted and the observed value. The residuals for every observation would represent the vertical distance between both the observation as well as the regression line if we plotted the observed values then overlaid the fitted regression line.To know more about the residual, here
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Can you guys please help me with my problem
Answer:
area of triangle = 1/2 ×base × height
= 1/2×18×6 = 54 unit^2
Answer:
therefore the area = 54cm²
Step-by-step explanation:
Area of a triangle
\( = \frac{1}{2} \times base \times height\)
From the question
base = 18
height =6
therefore the area
\( = \frac{1}{2} \times 18 \times 6 \\ = 1 \times 9 \times 6 \\ = 54 {cm}^{2} \)
How far can you travel at an average speed of 54mph over 3hrs?
Answer:
162 miles
Step-by-step explanation:
54(3) = 162
Answer:
162 miles?
Step-by-step explanation:
Determine whether the lines are parallel, perpendicular, or neither.
a. y = 5x − 2 and y = 10x − 4
b. y = -2x − 6 and 2y + 4x = 12
c. y = 10x − 2 and y + 10x = 0
d. 4y + 3x = -18 and 3y = 4x + 7.
e. 5y = 7x + 2 and y = fx + 12
The given equation of lines for a and e are parallel as their slopes are equal, c is perpendicular as the slopes are negative inverses and b, d are neither parallel nor perpendicular. This can be found using the slope of the given equations of the lines.
To determine whether two lines are parallel, perpendicular, or neither, we can use the following rules:
Two lines are parallel if they have the same slope.
Two lines are perpendicular if the product of their slopes is equal to -1.
Two lines are neither parallel nor perpendicular if they have different slopes and the product of their slopes is not equal to -1.
Let's apply these rules to each of the given lines:
a. y = 5x − 2 and y = 10x − 4
Both lines have a slope of 5, so they are parallel.
b. y = -2x − 6 and 2y + 4x = 12
We can rewrite the second equation as y = -2x + 6. The slopes of these lines are not equal, so they are not parallel. We can also see that the product of the slopes is not equal to -1, so they are not perpendicular. Therefore, these lines are neither parallel nor perpendicular.
c. y = 10x − 2 and y + 10x = 0
We can rewrite the second equation as y = -10x. The slopes of these lines are negative inverses of each other, so they are perpendicular.
d. 4y + 3x = -18 and 3y = 4x + 7.
We can rewrite the first equation as y = -(3/4)x + 4.5. The slopes of these lines are not equal, so they are not parallel. We can also see that the product of the slopes is not equal to -1, so they are not perpendicular. Therefore, these lines are neither parallel nor perpendicular.
e. 5y = 7x + 2 and y = fx + 12
We can rewrite the first equation as y = (7/5)x + (2/5). The slopes of these lines are equal, so they are parallel.
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a) Create an example of a trinomial that has a degree of 4:
Answer:
4x^4 + 16x^3 + 182x^2 + x + 87
Step-by-step explanation:
Solve the equation
-36=4(2x-7)-8x
Answer:
Step-by-step explanation:
Algebra:
Kapil's age is m years. What is his grandfather's age if he is 10 years more than thrice Kapil's age?
The grandfather's age if he is 10 years more than thrice Kapil's age is
3x +10.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Kapil's age is m years.
His Grandfather is 10 years more than thrice Kapil's age.
Thrice Kapil's age = 3x
and, 10 years more than thrice Kapil's age = 3x + 10
Then, the age of Grandfather is
= 3x+ 10
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what is the probability that you will be dealt a poker hand that is a full house(three cards of the same rank a pair in another rank) and includes the ace of hearts?
Thus, the probability of being dealt a full house with an Ace of Hearts is 0.0457% (rounded to 4 decimal places).
To calculate the probability of being dealt a full house with an Ace of Hearts in a standard 52-card deck, we can use the following formula:
=(number of ways to get a full house with an Ace of Hearts) / (total number of 5-card poker hands)
The total number of 5-card poker hands is C(52,5) = 2,598,960.
To count the number of ways to get a full house with an Ace of Hearts, we need to consider the following:
We choose 2 of the remaining 3 Aces from the deck: C(3,2) = 3
We choose 2 of the 12 remaining ranks for the other 2 cards: C(12,2) = 66
For each rank, we need to choose 2 cards from the 4 of that rank: C(4,2) = 6
Therefore, the number of ways to get a full house with an Ace of Hearts is 3 x 66 x 6 = 1,188.
Thus, the probability of being dealt a full house with an Ace of Hearts is:
1,188 / 2,598,960 ≈ 0.000457 = 0.0457% (rounded to 4 decimal places)
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Antonia solves an equation incorrectly. Her work is shown in the table
Original
27 (51x - 1) = -24x + 12
Line 1
-87x +
29
17
-24x +
Line 2
-63x+
29
17
12
17
Line 3
-63x = 1
Line 4
X
1
63
In which line did Antonia make an error based on the previous line?
А
Line 1
B
Line 2
С
Line 3
D
Line 4
Answer:
que no entiendo hablo español
Describe the meaning of the translation (x + 6, y + 10).
All points are moved 6 units right and 10 units up
All points are moved 6 units left and 10 units up
All points are moved 6 units left and 10 units down
All points are moved 6 units right and 10 units down
Answer:
Step-by-step explanation:
The meaning of the translation (x + 6, y + 10) is that all points in a coordinate plane are moved 6 units to the right and 10 units up.
In other words, for any point (x, y) in the original position, after the translation, the new coordinates would be (x + 6, y + 10). This means that the x-coordinate of each point is increased by 6 units, resulting in a shift to the right, and the y-coordinate is increased by 10 units, resulting in a shift upwards.
Given the diagram below, what is the length of segment EF?
A. 4
B. 4.4
C. 5
D. 4.8
The calculated length of the segment EF is (c) 5
How to determine the length of segment EF?from the question, we have the following parameters that can be used in our computation:
The trapezoid
The length of segment EF can be calculated using
EF = 1/2 * Sum of BC and AD
using the above as a guide, we have the following:
EF = 1/2 * (3.3 + 6.7)
Evaluate
EF = 5
Hence, the length of segment EF is (c) 5
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What is the value of x?
Answer:
x=18.75
Step-by-step explanation.
We have to realize that this is a line. A line has 180 degrees.
Therefore we can make the equation;
(6x+30)+2x=180
8x+30=180
8x=150
x=18.75
please mark as branliest
Answer:
x=18.75
Step-by-step explanation:
We can see that these 2 angles are on a straight line, meaning that these 2 angles must add up to 180°.
We can set up an equation:
180=(6x+30)+2x
combine like terms
180=8x+30
subtract 30 from both sides
150=8x
divide both sides by 8
x=18.75
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Joseph typed a 36- word paragraph in 2/3 minute. What is his typing speed in words per minute?
Answer:
It is 54.
Step-by-step explanation:
You divide 36 by 2/3.
The measure of angle D is 47 degrees and the measure of angle C is 57 degrees. What is the
measure of angle A?
47
57
76
104
Answer:
D. 104º
Step-by-step explanation:
So the inside of a triangle is equal to 180º and we already know two of the angles.
D = 47º
C = 57º
47 + 57 = 104
To solve angles A and B, we know that a straight line is 180º and we can figure out the angle of B because now all we have to do is subtract 104 from 180.
180 - 104 = 76, B = 76º
Because we know that a straight line is 180º and we already have the measure of angle B, all we have to do now is subtract 76 from 180.
180 - 76 = 104º
What is the following difference? 2ab * (root(3, 192a * b ^ 2)) - 5(root(3, 81a ^ 4 * b ^ 5))
Answer:
C
Step-by-step explanation:
it was correct for me on edge