a) The probability that the 3 balls chosen were all green is 1/21.
b) The probability that all the balls are chosen is red is 1/252.
What is probability?
Probability is a mathematical concept that measures the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
(a) Given 3 balls were chosen at random without replacement, the probability that they were all green is given by:
P(green) = (number of favorable outcomes) / (number of total outcomes)
The number of favorable outcomes is the number of ways to choose 3 green balls out of 4, which is C(4,3) = 4.
The number of total outcomes is the number of ways to choose 3 balls out of 9, which is C(9,3) = 84.
So, the probability that 3 balls chosen were all green is:
P(green) = C(4,3) / C(9,3) = 4 / 84 = 1/21
(b) The probability that all the balls chosen are red is given by:
P(red) = (number of favorable outcomes) / (number of total outcomes)
The number of favorable outcomes is the number of ways to choose 5 red balls out of 5, which is C(5,5) = 1.
The number of total outcomes is the number of ways to choose 5 balls out of 9, which is C(9,5) = 126.
So, the probability that all the balls chosen are red is:
P(red) = C(5,5) / C(9,5) = 1 / 126 = 1/252
Hence,
a) The probability that the 3 balls chosen were all green is 1/21.
b) The probability that all the balls are chosen is red is 1/252.
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determine whether s is a basis for m2,2. s = 4 0 0 3 , 1 0 4 1 , 0 1 4 1 , 0 2 2 0
The set S is linearly dependent and the matrix A has rank 3.
Sets are groups of well-defined objects or components in mathematics. A set is denoted by a capital letter, and the cardinal number of a set is enclosed in a curly bracket to indicate how many members there are in a finite set.
Set A, for instance, is a collection of all the natural numbers, with the form A = 1, 2, 3, 5, 6, 7, 8, etc.
The maximum number of linearly independent columns (or rows ) of a matrix is called the rank of a matrix. The rank of a matrix cannot exceed the number of its rows or columns.
Thus, The set S is linearly dependent and the matrix A has rank 3.
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Georgia loves to drop water balloons from her third-floor balcony into a dumpster located on the street below. Her brother filmed one balloon falling. He measured the height of the balcony rail. Then he used the video camera's time feature to figure out how far the balloon had traveled from Georgia's hand after each quarter of a second. He listed the times and distances in a table: Time 0.255 Distance 0.3 m 1.2 m 0.55 0.75 s 2.8 m 4.9 m 1.08 1.25 s 7.7 m 11.0 m 1.5 a . graph the distance the water balloon traveled over 1.5 seconds using the data georgia’s brother collected.
The distance the water balloon traveled over 1.5 seconds using the data georgia’s brother collected is attached below.
What is Distance -time Graph?A distance-time graph, also known as a displacement-time graph or position-time graph, is a graphical representation that shows the relationship between the distance traveled by an object and the time it takes to travel that distance.
Using the information gathered by Georgia's brother, we can plot the points on a coordinate plane to graph the distance the water balloon travelled during a period of 1.5 seconds.
The data points provided are as follows:
Time (s) Distance (m)
0.25 0.3
0.5 1.2
0.75 2.8
1.0 4.9
1.25 7.7
1.5 11.0
Plotting these points on a graph with time on the x-axis and distance on the y-axis, we get the graph attached.
The water balloon's route over 1.5 seconds is depicted on a graph. As time increases, the distance traveled by the balloon also increases. The graph shows a curved line, indicating that the distance traveled is not constant but increases at a varying rate.
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voter sentiment: one of the questions rasmussen reports included on a 2018 survey of 2.500 likely voters asked if the country is headed in the right direction. representative data are shown in the file rightdirection. a response of yes indicates that the respondent does think the country is headed in the right direction. a response of no indicates that the respondent does not think the country is headed in the right direction. respondents may also give a response of not sure. a. what is the point estimate of the proportion of the population of likely voters who do think that the country is headed in the right direction? b. at 95% confidence, what is the margin of error? c. what is the 95% confidence interval for the proportion of likely voters who do think that the country is headed in the right direction? d. what is the 95% confidence interval for the proportion of likely voters who do not think that the country is headed in the right direction? e. which of the confidence intervals in parts c and d has the smaller margin of error? why?
Margin of Error is 0.0245, 0.8209 <= p <= 0.8264 and CI in (C) is 0.1291 to 0.1781 and in (d) is 0.8209 to 0.8264.
(a) The point estimate of the proportion of the population of respondents who do think that the country is headed in the right direction is 384 / 2500 = 0.1536.
(b) To find the margin of error for the proportion, we use the formula:
ME = 1.96 * sqrt(p * (1 - p) / n), where p is the point estimate and n is the sample size.
ME = 1.96 * sqrt(0.1536 * (1 - 0.1536) / 2500) = 0.0245
(c) The 95% confidence interval for the proportion of respondents who do think that the country is headed in the right direction is:
0.1536 - 0.0245 <= p <= 0.1536 + 0.0245
0.1291 <= p <= 0.1781
(d) To find the 95% confidence interval for the proportion of respondents who do not think that the country is headed in the right direction, we subtract the proportion from 1:
1 - 0.1536 - 0.0245 <= p <= 1 - 0.1536 + 0.0245
0.8209 <= p <= 0.8264
(e) The confidence interval in part (c) has a smaller margin of error because the sample proportion of respondents who do think that the country is headed in the right direction is closer to 0.5 (the midpoint of the interval) than the sample proportion of respondents who do not think that the country is headed in the right direction.
Confidence interval in part (c): 0.1291 to 0.1781
Confidence interval in part (d): 0.8209 to 0.8264
Therefore, Margin of Error is 0.0245, 0.8209 <= p <= 0.8264 and CI in (C) is 0.1291 to 0.1781 and in (d) is 0.8209 to 0.8264.
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Margin of Error is 0.0245, 0.8209 <= p <= 0.8264 and CI in (C) is 0.1291 to 0.1781 and in (d) is 0.8209 to 0.8264.
(a) The point estimate of the proportion of the population of respondents who do think that the country is headed in the right direction is 384 / 2500 = 0.1536.
(b) To find the margin of error for the proportion, we use the formula:
ME = 1.96 * sqrt(p * (1 - p) / n), where p is the point estimate and n is the sample size.
ME = 1.96 * sqrt(0.1536 * (1 - 0.1536) / 2500) = 0.0245
(c) The 95% confidence interval for the proportion of respondents who do think that the country is headed in the right direction is:
0.1536 - 0.0245 <= p <= 0.1536 + 0.0245
0.1291 <= p <= 0.1781
(d) To find the 95% confidence interval for the proportion of respondents who do not think that the country is headed in the right direction, we subtract the proportion from 1:
1 - 0.1536 - 0.0245 <= p <= 1 - 0.1536 + 0.0245
0.8209 <= p <= 0.8264
(e) The confidence interval in part (c) has a smaller margin of error because the sample proportion of respondents who do think that the country is headed in the right direction is closer to 0.5 (the midpoint of the interval) than the sample proportion of respondents who do not think that the country is headed in the right direction.
Confidence interval in part (c): 0.1291 to 0.1781
Confidence interval in part (d): 0.8209 to 0.8264
Therefore, Margin of Error is 0.0245, 0.8209 <= p <= 0.8264 and CI in (C) is 0.1291 to 0.1781 and in (d) is 0.8209 to 0.8264.
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What is 333333+(5+6)-657-(564-3)
Answer:
332126
Step-by-step explanation:
333333+(5+6)-657-(564-3)=332126
Five items x increased by5gives55
Answer:
x=10
Step-by-step explanation:
5x+5=55
5x=55-5
5x=50
x=10
hth
dried apricots with 3.25 were mixed with dried prunes worth 4.79 to produce a mixture of dried fruit, how much each kind of fruit was used to produce 25 ponds
14.84 pounds of dried apricots were used and 10.16 pounds of dried prunes were used to produce 25 pounds of the dried fruit mixture.
Let's call the weight of dried apricots used in the mixture "x" (in pounds). Then the weight of dried prunes used in the mixture is 25 - x (in pounds).
The cost per pound of dried apricots is 3.25, and the cost per pound of dried prunes is 4.79. So the total cost of the mixture is:
3.25x + 4.79(25 - x) = 3.25x + 119.75 - 4.79x
Expanding both sides:
119.75 = 8.04x
Dividing both sides by 8.04:
x = 14.84 pounds
So 14.84 pounds of dried apricots were used in the mixture, and 25 - 14.84 = 10.16 pounds of dried prunes were used in the mixture.
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14.84 pounds of dried apricots were used and 10.16 pounds of dried prunes were used to produce 25 pounds of the dried fruit mixture.
Let's call the weight of dried apricots used in the mixture "x" (in pounds). Then the weight of dried prunes used in the mixture is 25 - x (in pounds).
The cost per pound of dried apricots is 3.25, and the cost per pound of dried prunes is 4.79. So the total cost of the mixture is:
3.25x + 4.79(25 - x) = 3.25x + 119.75 - 4.79x
Expanding both sides:
119.75 = 8.04x
Dividing both sides by 8.04:
x = 14.84 pounds
So 14.84 pounds of dried apricots were used in the mixture, and 25 - 14.84 = 10.16 pounds of dried prunes were used in the mixture.
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Which of the following would be classified as categoricalâdata?
Choose the correct answer below.
Hair color
Number of suitcases on a plane
Tree height
Amount of rainfall
Categorical data is data that can be divided into different categories. Examples of categorical data include hair color, number of suitcases on a plane, tree height, and amount of rainfall.
Hair color would be classified as categorical data because it can be divided into categories such as black, brown, blonde, and red. Number of suitcases on a plane would also be classified as categorical data because the amount of suitcases can be divided into categories such as 0, 1, 2, 3, etc. Tree height would be classified as categorical data as it can be divided into categories such as small, medium, and large. Amount of rainfall would also be classified as categorical data as it can be divided into categories such as light rainfall, moderate rainfall, and heavy rainfall.
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Real number system using the given theme and its description formulate three conditional statements not written in if then form and convert the three conditional statements into if - then form
Conditional statements using the theme of the real number system:
The product of two positive real numbers is positive.The sum of a positive real number and a negative real number is positive if the magnitude of the negative number is less than the positive number.The quotient of two real numbers is positive if the numerator is positive and the denominator is negative.Conditional statements in if-then form:
If x and y are positive real numbers, then xy is positive.If a is a positive real number and b is a negative real number with |b| < a, then a + b is positive.If x is a positive real number and y is a negative real number, then x/y is positive.Conditional statements are statements in logic and mathematics that assert the truth of a statement based on certain conditions. They are usually written in the form "if P, then Q", where P is a condition and Q is a conclusion that follows from P. Conditional statements are used to make decisions or test certain conditions in programming, mathematics, and everyday life.
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Use algebra to solve these problems Question 1: Work out the sizes of the angles marked with letters. 68⁰ ( 83° 95° 32° d
The sizes of the angles are: a = 112, b = 97, c = 85, d = 148
How to calculate the sizes of the angles marked with lettersTo calculate the sizes of the angles, we substract the given value from 180 (sum of angles on a straight line)
For a = 180 - 68 = 112( sum of angles on a straight line)
b = 180 - 83 = 97( sum of angles on a straight line)
c = 180 - 95 = 85( sum of angles on a straight line)
d = 180 - 32 = 148( sum of angles on a straight line)
Hence, the sizes of the the angles a,b,c,d, are 112,97,85 and 148 respectively
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Ahmad owes $382. 45 on his Visa account. He returns two items costing $25. 10 & $34. 50 for credit. Then he makes purchases of $45 & $98. 17.
A) how much should his payment be if he wants to pay off the balance on the account?
B) Instead of paying off the balance, he makes a payment of $300 and then incurs a finance charge of $24. 66. What is the balance on his account?
By applying the debt concept, it can be concluded that:
A. He should pay $466.02 to pay off the balance on the account.
B. The balance on his account is $190.68
Debt is an obligation that requires one party, the debtor, to pay money or other agreed-upon value to another party, the creditor.
We have the following information:
Ahmad owes $382.45, and because he owes, it means this value is the debt, and we write it:
D = $382.45
Then he returns two items ($25. 10 & $34. 50) so that their values get credited into his accounts.
D = $382.45 - $25.10 - $34.50 = $322.85
Now after this, he makes another two purchases of $45 and $98.17, which increase his debt and makes:
D = $322.85 + $45 + $98.17 = $466.02
Part A: Since the debt or the account balance is $466.02, then he should pay $466.02 to pay off the balance on the account.
Part B: However, instead of paying off the balance, Ahmed makes a payment of $300 and he has to be charged $24.66. It means that his debt is not paid off:
D = $466.02 - $300 + $24.66 = $190.68
So, the balance on his account is $190.68.
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Investigation • Getting to the root
ASAP PLEASE!!!
The exponents of the values are;
1) 343
2) 9
3) 32
4) That the nth root of a and raise to the power of m
What are the laws of exponents?The laws of exponents are a set of rules for performing arithmetic operations with exponential expressions. They include:
Product rule: For any real numbers a, b and positive integers m, n, (am)(bn) = a^m * b^n.
Quotient rule: For any real numbers a, b and positive integers m, n, (a^m)/(a^n) = a^(m-n).
Power rule: For any real number a and positive integers m, n, (a^m)^n = a^(mn).
Zero exponent rule: For any real number a, a^0 = 1.
Negative exponent rule: For any real number a ≠ 0 and positive integer n, (1/a^n) = a^(-n).
Exponent of a power rule: For any real numbers a, b and positive integers m, n, (a^m)^n = (a^n)^m.
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What do you mean by data type?
Answer:
A data type is an attribute associated with a piece of data that tells a computer system how to interpret its value
Step-by-step explanation:
Data types categorize data and specify its nature, amount characteristics, and behavior. It decides how data is handled within a computer system in terms of storage and manipulation.
Data types categorize data and specify its nature, characteristics, and behavior. It is a crucial part of every data structure and computer language. Primitive data types and complex data types are the two basic divisions of data types. Basic types like numbers, characters, booleans, and strings are examples of primitive data types. Arrays, objects, and records are examples of sophisticated data types that are more complex. Data types specify how information is handled and stored by computer systems. Size, precision, and range are a few examples of the unique qualities that each data type possesses. The arithmetic, comparison, and logic operations that can be carried out on the data are also determined by the data types.
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eval calculates an expression and puts the resulting ____ into a new or existing field.
Eval is a function that evaluates an expression and puts the resulting value into a new or existing field.
To calculate the value of an expression using Eval, you must use the correct syntax. The syntax for Eval is Eval(expression, optional_parameter). The expression can take the form of a mathematical equation or a logical expression. For example, if you wanted to calculate the sum of two numbers, you would use the following expression: Eval(A + B). The optional parameter allows you to specify a range of values to evaluate the expression against.
For example, if you wanted to calculate the sum of two numbers within a given range, you would use the following expression: Eval(A + B, range). The range parameter can be used to specify the starting and ending values that the expression should be evaluated against.
Using Eval to calculate an expression is a useful tool for quickly getting the desired value. It is also useful for quickly testing the accuracy of a complex expression before implementing it in your code.
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3/5x - 1/3x = 4 find x
Answer:
x = 15
Step-by-step explanation:
3/5x - 1/3x = 4
9/15x - 5/15x = 4
4/15x = 4
x = 15
a tent has the shape pictured below, where the cross sections are triangles. (the height of each triangle is equal to the base for that triangle.) what is the interior volume of the tent? (all distances are in feet.)
The interior volume of the tent where the cross sections are triangles is given is 120ft³.
There are two cross sectional triangles
The one smaller triangle with the height and base of 2ft
The other bigger triangle has a base and height of 4 ft
And the total length of the Tent is given as 6 ft.
Therefore,
Area of smaller triangle = 2 x 2 = 4m²
Area of bigger triangle = 4 x 4 = 16 ft²
So the Volume of the tent is given by ,
Total length x (Area of smaller triangle + Area of bigger triangle)
= 6 x ( 4 + 16 )
=6 x ( 20 )
= 120 ft ³
A measurement of three-dimensional space is volume. Numerous imperial or US customary units, as well as SI-derived units (such the cubic metre and litre), are frequently used to quantify it numerically (such as the gallon, quart, cubic inch). Volume and length (cubed) have a symbiotic relationship. The capacity of a container is typically regarded to be its volume.
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11). Find the area of the enclosed figure below.
Total area of the enclosed figure is given as 66 sq. units.
What is Area of a figure ?The quantity of unit squares that cover a closed figure's surface is its area. Square units like cm2 and m2 are used to measure area. A shape's area is a two-dimensional measurement.
An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The common ways to depict square units, which are the same as areas, are square inches, square feet, etc.
The space around by a shape's perimeter or boundary is known as its area. Using particular mathematical methods, we may determine the area of shape for various geometric forms.
In the shape there is 2 triangles and 3 rectangle
Area of the bottom triangle = 1/2 * 3*4 = 6 sq. units
Area of the top triangle = 1/2 * 4*2 = 4 sq. units
Area of the bottom rectangle = 8*3 = 24 sq. units
Area of the middle rectangle = 8*3 = 24 sq. units
Area of the top rectangle = 4*2 - 8 sq. units
Total area of the enclosed figure is given as 6+4+ 24+ 24+ 8 = 66 sq. units.
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Write the coordinates of the vertices after a rotation *
270° counterclockwise around the origin. P(-8,3) Q(-8,10) R(-4,2)
The new coordinates for P(-8,3) Q(-8,10) R(-4,2) are (3,-3) (10,-10) and (2,-2) .
What are coordinates ?
Coordinates can be defined as pair of numbers which are used to determine the position of a given point.
Given
to Write the coordinates of the vertices after a rotation 270° counterclockwise around the origin.
Given points are P(-8,3) Q(-8,10) R(-4,2) .
we know that if (x,y) are rotated at an θ, the new coordinates could be ,
x′=xcos(θ)−ysin(θ) y′=xsin(θ)+ycos(θ).
So,
for p (-8,3)
x' = -8*cos270 - 3 * sin270
x' = 0 + 3
x' = 3
y' = -8*cos270 + 3 * sin270
y' = 0 - 3
y' = -3
(x' , y' ) = (3,-3)
similarly,
for q (-8,10)
x' = -8*cos270 - 10 * sin270
x' = 0 + 10
x' = 10
y' = -8*cos270 + 10* sin270
y' = 0 -10
y' = -10
(x' , y' ) = (10,-10)
similarly,
for q (-4,2)
x' = -4*cos270 - 2 * sin270
x' = 0 + 2
x' = 2
y' = -4*cos270 + 2 * sin270
y' = 0 -2
y' = -2
(x' , y' ) = (2,-2)
Therefore, The new coordinates for P(-8,3) Q(-8,10) R(-4,2) are (3,-3) (10,-10) and (2,-2) .
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I need a help on this one asap it can be without step by step just please asap for 25 points.
what is the ratio of number 600g:4kg
Identify the y-intercept. plot that point on the graph
y = 2x - 4
Write the y-intercept as a point, no spaces.
The y-intercept of the line y = 2x - 4 is the point (0, -4), which means that the line crosses the y-axis at a point with a y-coordinate of -4.
What is the slope intercept?
The slope indicates the steepness of a line and the intercept indicates the location where it intersects an axis. The slope and the intercept define the linear relationship between two variables and can be used to estimate an average rate of change.
The equation y = 2x - 4 represents a straight line in a coordinate plane.
In this equation, y is the dependent variable and x is the independent variable.
The slope of the line is 2, meaning that the line rises 2 units vertically for every 1 unit it moves horizontally to the right.
The y-intercept is the point where the line crosses the y-axis, and can be found by setting x equal to zero and solving for y.
In this case, when x = 0, y = 2 * 0 - 4 = -4.
Hence, the y-intercept of the line y = 2x - 4 is the point (0, -4), which means that the line crosses the y-axis at a point with a y-coordinate of -4.
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Hazma’s Logo wants to create a bumper sticker with his design.
Bumper stickers usually have a height of 3 1/2 inches.
What will the width of his sticker be?
The width of the sticker will be 8 3/4 inches.
What is a scale factor?The scale factor defines a variable in a ratio of two different measurements.
Sometimes drawings of large models are represented in a scale factor of a smaller unit.
Given, The given logo has a height of 2 inches and a width of 5 inches.
Bumper stickers usually have a height of 3 1/2 inches which has a
= (7/2)/2 = 7/4 scale factor.
Therefore, The width of the sticker will be,
= 5×(7/4).
= 35/4.
= 8 3/4 iches.
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the sum of squared errors (deviations) is 20 for a sample of 5 scores. what is the variance for this sample?
The variance for this sample of 5 scores with the sum of squared errors (deviations) 20 is 5.
Variance is a measure of the spread of the data around the mean. It can be calculated from the sum of squared deviations (SSE) as follows:
Variance = SSE / (n - 1)
where n is the number of scores in the sample.
In this case, n = 5 and SSE = 20, so the variance is:
Variance = 20 / (5 - 1) = 20 / 4 = 5
So the variance for this sample is "5".
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The image below shows that angles formed by two intersecting lines. What are the correct pairs of vertical angles?
View the image for the answers
By vertical angles theorem, ∠1≅∠3 and ∠2≅∠4. Therefore, option B is the correct answer.
What is vertical angle theorem?Vertical angles theorem or vertically opposite angles theorem states that two opposite vertical angles formed when two lines intersect each other are always equal (congruent) to each other.
From the given figure,
By vertical angles theorem, we have
Angle 1 and angle 3 are congruent.
Angle 2 and angle 4 are congruent
Therefore, option B is the correct answer.
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3/4(12a+8) =27.6
3/4 Multiplied by () + (multiply by 8) = ()
A =?
(Use the distributive property to solve, simplify your answers)
PLEASE HELP THIS IS MY LAST QUESTION!!!!!
3/4(12a+8) =27.6
3/4 Multiplied by () + (multiply by 8) = ()
A = 2.4
How did we get the value?Expanding the expression inside the parenthesis, we have:
3/4 (12a + 8) = 3/4 * 12a + 3/4 * 8 = 9a + 6
Setting this equal to 27.6 and solving for a:
9a + 6 = 27.6
9a = 21.6
a = 2.4
So, the value of a is 2.4
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The following equation follows the commutative property of addition. Find the missing value.
39 + 67 = __ + 39
a, 42
b. 67
c. 39
d. 81
Using commutative property of addition, a + b = b + a, Therefore, 39 + 67 = 67 + 39, Hence the missing number is 67.
What is the commutative property of addition formula?The commutative property formula applies to addition and multiplication. The addition formula states that a+b=b+a, and the multiplication formula states that a×b=b×a.Commutative property of addition: Changing the order of addends does not change the sum. For example, 4 + 2 = 2 + 4 4 + 2 = 2 + 4 4+2=2+44, plus, 2, equals, 2, plus, 4.We learned that the addition property of equality tells us that if we add the same quantity to both sides of an equation, then our equation remains the same. The formula is if a = b, then a + c = b + cThis law simply states that with addition and multiplication of numbers, you can change the order of the numbers in the problem and it will not affect the answerTo learn more about commutative property refers to:
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consider the two functions shown below. assume the blue line represents a(x) and the pink line represents b(x). how do the second derivatives of the two functions with respect to x compare?
The second derivative of a(x) is larger than the second derivative of b(x) for the given x values.
The second derivative of a function with respect to x is the rate of change of the first derivative with respect to x. The second derivative of a function measures the "curvature" of the graph. In the case of the two functions shown, the blue line represents a(x) and the pink line represents b(x). By looking at the graph, we can see that the first derivative of a(x) is steeper than that of b(x). Therefore, the second derivative of a(x) will be larger than the second derivative of b(x). This can be seen by looking at the graph and noting that the blue line has a greater curvature or "bend" than the pink line. In other words, the second derivative of a(x) is larger than the second derivative of b(x) for the given x values.
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According to a recent article the average number of babie born with ignificant hearing lo (deafne) i approximately
two per 1,000 babie in a healthy baby nurery. The number climb to an average of 30 per 1,000 babie in an intenive care
nurery. Suppoe that 1,000 babie from healthy baby nurerie were randomly urveyed. Find the probability that exactly two babie
were born deaf
The probability of exactly two babies being born deaf is approximately 0.037, or 3.7%.
Calculating Deaf Birth ProbabilityThe probability of exactly two babies being born deaf in a sample of 1,000 babies from healthy baby nurseries can be calculated using the binomial distribution.
The binomial distribution formula for finding the probability of exactly "k" successes in "n" trials with a probability of success "p" is:P(X = k) = (n choose k) * (p^k) * ((1-p)^(n-k))
Where "n choose k" is the number of combinations of "n" things taken "k" at a time, and can be calculated as:(n choose k) = n! / (k! * (n-k)!)
For this problem:
n = 1000 (number of babies surveyed)
k = 2 (number of deaf babies)
p = 2/1000 (probability of a baby being deaf in a healthy baby nursery)
Plugging these values into the formula:P(X = 2) = (1000 choose 2) * (2/1000)² * (998/1000)^998
P(X = 2) = 999000 * 4 * (998/1000)⁹⁹⁸
P(X = 2) = approximately 0.037
So the probability of exactly two babies being born deaf in a sample of 1,000 babies from healthy baby nurseries is approximately 0.037, or 3.7%.
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Let u= [-12, 36, 8] and A= [ 5 -2 1 -3 6 1]. Is u in the plane in ℝ3 spanned by the columns of A? Why or why not?
Select the correct choice below and fill in the answer box to complete your choice.
(Type an integer or decimal for each matrix element.)
A.No, the reduced echelon form of the augmented matrix is which is an inconsistent system.
B.Yes, multiplying A by the vector writes u as a linear combination of the columns of A.
Since n•u is not equal to 0, we conclude that the vector u is not in the plane spanned by the columns of A.
Why plane spanned by the columns of A?A vector u is in the plane spanned by the columns of a matrix A if and only if the dot product between u and the normal vector of the plane is equal to 0.
In this case, let A = [5 -2 1; -3 6 1]. To determine if u = [-12, 36, 8] is in the plane spanned by the columns of A, we can calculate the dot product between u and the normal vector of the plane, which can be found by taking the cross product of the two columns of A.
Since the cross product of two columns in A gives the normal vector of the plane spanned by the columns, we have:
According to question:n = (5, -2, 1) × (-3, 6, 1) = (18, -26, -11)
Next, we calculate the dot product of n and u:
n•u = (18, -26, -11) • [-12, 36, 8] = 18 * -12 - 26 * 36 - 11 * 8 = -816 - 936 - 88 = -1840
Since n•u is not equal to 0, we conclude that the vector u is not in the plane spanned by the columns of A. In other words, u is not orthogonal to the normal vector of the plane and therefore, is not in the plane.
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The heights of the bars of a histogram correspond to _______ values.
Answer:
Frequency
Step-by-step explanation:
The heights of the bars of a histogram correspond to Frequency values.
Answer:
frequency values
Step-by-step explanation:
The bars are drawn adjacent to each other.
To find the roots of a polynomial, it is often useful to find the ____ of the polynomial.
Answer:
Factors
Step-by-step explanation:
To find the roots of a polynomial, [factors] help the process of finding them