The textbook search committee can select 3 books out of the 20 in 1140 different ways.
To determine the number of ways the textbook search committee can select 3 books out of the 20 for further consideration, we can use the concept of combinations.
The number of ways to select a group of 3 books from a total of 20 can be calculated using the formula for combinations:
C(n, r) = n! / (r!(n - r)!)
In this case, we have 20 books to choose from, and we want to select a group of 3 books. So, plugging in the values into the combination formula:
C(20, 3) = 20! / (3!(20 - 3)!)
Simplifying this expression gives us:
C(20, 3) = (20 * 19 * 18) / (3 * 2 * 1)
C(20, 3) = 1140
This means that there are 1140 different combinations of 3 books that the committee can choose for further consideration out of the initial set of 20 books.
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Simplify the problem.
Answer:
Option 4: 4¹¹
Step-by-step explanation:
Looking at the problem, I need to work out 4⁴ squared first, which is the same as 4⁸. Then multiply that by 4³ to get 4¹¹. What I did was simply add 3 + (4 * 2), which is 11.
A business student conducts an OLS regression analysis in excel (with usual defaults) with demand for strawberries (in 1000 units) as the dependent and price (in dollars) as an independent variable. The OLS regression line is given by y= 9 − 3x. If the pvalue of the intercept coefficient is 0 and the pvalue of the slope coefficient is 2% & If the standard error of the intercept coefficient is 6 and the standard error of the slope coefficient is 1; the true slope will be ______ to/from the estimated slope and the true intercept will be ________ to/from the estimated intercept.
Group of answer choices
equal, equal
different, equal
equal, different
different, different
The true intercept and slope are both different from the estimated values based on statistical significance.
The p-value of the intercept coefficient and that of the slope coefficients are 0 and 0.02(2%) respectively. This means that they are statistically significant. Thus we can infer that the true intercept and slope is not equal to 0.
The standard error of the intercept coefficient is 6, which means that the true intercept is likely to be within 6 units of the estimated intercept. The standard error of the slope coefficient is 1, which means that the true slope is likely to be within 1 unit of the estimated slope.
Therefore, the true slope and intercept will be different from the estimated slope and intercept.
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find the measure of each interior angle of a regular polygon with the following number of sides 4
Answer:
90°
Step-by-step explanation:
Formula to find EACH interior angle:
[tex]\frac{(n-2) *180}{n}[/tex]
Given:
n (number of sides) = 4
Work:
[tex]\frac{(n-2) *180}{n} \\\\\frac{(4-2) *180}{4} \\\\\frac{(2) *180}{4} \\\\\frac{360}{4} \\\\90[/tex]
HELP PLEASE AND ASAP!! look at screenshot (10 pts)
Answer:
C
Step-by-step explanation:
Add like terms to get
4.5a + 4b + 3.5c
Let In be the number of n-digit quinary (0, 1, 2, 3, 4) sequences with (i) at least one 3 and (ii) the first 3 occurs before the first 0 (possibly no 0's). (Examples of 4-digit legal quinary sequences: 3120, 3000, 4123) (a) Show 91 = 1,92 = 8. = (b) Show a recurrence for an is qn = 39n-1 +5n-1 (91 = 1). = = 5" - 35 (c) A closed form for en is In = (n > 1). Finish the induction proof of this fact 2 (began below) by completing the induction step: 57 - 31 Base case (n = 1): LHS = q1 = 1. RHS 1 2 5k - 3k Induction Hypothesis: Assume true for n=k, i.e., Pk Induction Step: = II 2 N (d) Show how to derive this closed form, i.e., show how one can arrive at this closed form if they only knew the recurrence and the initial values.
Part a:Here, In be the number of n-digit quinary (0, 1, 2, 3, 4) sequences with(i) at least one 3 and (ii) the first 3 occurs before the first 0 (possibly no 0's).Since there is at least one 3 in the n-digit sequence, we start the sequence by selecting one of the 5 digits. There are five ways to do this.The next digits are chosen according to one of the three cases shown below:1) A string of (n-1) digits where no 0's are included in the string.2) A string of (n-1) digits where at least one 0 appears in the string before the first 3.3) A string of (n-1) digits where 3 appears before the first 0 in the string.The first string in case 1 can be formed in 4 different ways because no 0's can appear in the string and there are 4 digits to choose from (0, 1, 2, 4). There are 5 choices for the first digit and thus 5*4 quinary sequences of length n with at least one 3 and no 0's that start with the selected digit.The first string in case 2 can be formed in 5 different ways because the first 3 can appear in any position before the first 0. The remaining digits are chosen in n-2 positions because the first digit is already chosen (which is 3) and n-1 digits are left. There are 4 choices for each of the remaining n-2 positions because no 0's can appear in the string and there are 4 digits to choose from (0, 1, 2, 4). Thus, there are 5*5*4^(n-2) quinary sequences of length n with at least one 3 and at least one 0 that start with the selected digit.The first string in case 3 can be formed in n-1 different ways because the first 3 can appear in any position before the first 0. The remaining digits are chosen in n-2 positions because the first digit is already chosen (which is 3) and n-1 digits are left. There are 4 choices for each of the remaining n-2 positions because no 0's can appear in the string and there are 4 digits to choose from (0, 1, 2, 4). Thus, there are 5*(n-1)*4^(n-2) quinary sequences of length n with at least one 3 and at least one 0 that start with the selected digit.Therefore, the number of n-digit quinary sequences with (i) at least one 3 and (ii) the first 3 occurs before the first 0 (possibly no 0's) is the sum of the number of sequences in each of the three cases above, i.e.In = 5*4^(n-1) + 5*5*4^(n-2) + 5*(n-1)*4^(n-2)Part b:Recurrence: qn = 3q(n-1) + 4^(n-1) + 2. q1 = 1. Let's see if qn = 39(n-1) + 5(n-1) satisfies this recurrence.q1 = 1 = 3(1-1) + 4^(1-1) + 2 = 0 + 1 + 2 = 3(0) + 5(1-1) + 1 = 0 + 0 + 1Thus, q1 = 1 satisfies the recurrence.qn+1 = 3qn + 4^n + 2 = 3(39n-1 + 5n-1) + 4^n + 2= 117(n-1) + 15(n-1) + 4^n + 2= 132(n-1) + 4^n + 3Using this formula, we can see that q2 = 91.Part c:Here, we need to finish the induction proof of this fact 2 that In = (n > 1).Induction Hypothesis: Assume true for n = k, i.e., Pk = Ik = 5*4^(k-1) + 5*5*4^(k-2) + 5*(k-1)*4^(k-2)Induction Step: To show that it is true for n = k+1, we need to show that the formula given above holds. The first digit can be any of the 5 digits (0, 1, 2, 3, 4) and the remaining digits can be selected in one of the three ways discussed in part (a).Case 1: n-1 digits with no 0'sThere are 4 choices for each of the n-1 digits, since 0 cannot be used. Therefore, there are 4^(n-1) such sequences with no 0's.Case 2: n-1 digits with at least one 0 before the first 3The first 3 can be in any of the n-1 positions, and the digits before it must be chosen from the set {0,1,2,4}. The remaining digits can be chosen in any of the 4 choices. Therefore, there are 5*(n-1)*4^(n-2) such sequences.Case 3: n-1 digits with 3 before 0We start by selecting one of the n-1 positions for the 3, then the remaining digits are chosen from the set {0,1,2,4}. There are (n-2) positions left for the remaining digits. There are 4 choices for each position, since 0 cannot be used. Therefore, there are 5*(n-1)*4^(n-2) such sequences.Thus, the total number of n-digit quinary sequences with at least one 3 and with the first 3 before the first 0 isIn = 5*4^(n-1) + 5*5*4^(n-2) + 5*(n-1)*4^(n-2) = qn+1 - qn = 132(n-1) + 4^n + 3 - (39(n-1) + 5(n-1)) = 93(n-1) + 4^n + 3which completes the induction proof.Part d:Since qn = 39n-1 + 5n-1, we haveqn+1 - qn = 132n - 39n - 5n = 88nTherefore, qn+1 = qn + 88nSubstituting qn = 39n-1 + 5n-1, we getqn+1 = qn + 88n = 39n-1 + 5n-1 + 88n = 39n + 5n + 88(n-1)Simplifying, we getqn+1 = 132(n-1) + 4^n + 3Therefore, en = In - In-1 = 93(n-1) + 4^n + 3 - 93(n-2) - 4^(n-1) - 3= 93n - 93(n-1) - 4^(n-1)= 93 - 4^(n-1)Thus, the closed form for en is en = 93 - 4^(n-1).
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Last year the highest temperature in a city was recorded as 23C and the lowest temperature was recorded as -10C how many degree warmer was the highest temperature than the lowest temperature
Answer:
The highest temperature was 33C warmer than the lowest temperature.
Step-by-step explanation:
In order to find how many degrees warmer was the highest temperature, you have to calculate the difference between both temperatures:
23-(-10)
According to the sign rule, you have to change the subtraction sign to addition and then, change the sign on the umber after that and add the numbers, which is:
23+10=33
According to this, the answer is that the highest temperature was 33C warmer than the lowest temperature.
A bag contains 4 blue coins and 7 red coins. A coin is removed at random and placed by three of the other color.
What is the probability that the removed coin is blue?
Answer:
The probability is 7/11
Step-by-step explanation:
This is because there are 7 blue coins that you can grab out of 11 coins in total.
Which of the following indicate that the result from a simple linear regression model could be potentially misleading? a. The error terms follow a normal distribution b. The error terms exhibit homoscedasticity c. Then n th error term (e_n) can be predicted with e_n = 0.91 * e_n - 1 d. The dependent and the independent variable show a linear pattern
The correct answer is: c. The n-th error term (e_n) can be predicted with e_n = 0.91 * e_n - 1.
This statement indicates that there is a correlation or relationship between consecutive error terms, where the n-th error term can be predicted based on the previous error term. In a simple linear regression model, the error terms are assumed to be independent and have no correlation with each other.
However, if there is a correlation between the error terms, it violates the assumption of independence, which can lead to biased and unreliable regression results. Therefore, this condition suggests that the result from the simple linear regression model could be potentially misleading.
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6) You are shooting the puck along the path
seen in the picture of the air hockey table.
Find the mZxº and the mzmº.
Answer:
m = 58°
x = 64°
Step-by-step explanation:
When a puck touches one side of the air hockey table,
All the angles formed are located at a point on a straight line.
Therefore, sum of angles formed is 180°.
m° + m° + 64° = 180°
2m + 64 = 180
2m = 180 - 64
2m = 116
m = 58°
m∠y = m = 58° [Alternate interior angles]
Similarly, on the other side of the table,
58° + y° + x° = 180°
58° + 58° + x° = 180°
x + 116° = 180°
x = 180 - 116
x = 64°
Race) The longest racial grouping of respondents to the 2012 GSS was______, with ______%. The second-largest grouping was _____, with ______%.
The longest racial grouping of respondents to the 2012 GSS was non-Hispanic white, with 78.7%. The second-largest grouping was Black or African American, with 15.6%.
The General Social Survey (GSS) is a nationally representative survey of American adults that has been conducted annually since 1972. The GSS collects data on a wide range of topics, including race and ethnicity. In 2012, the GSS asked respondents to identify their race and ethnicity. The results showed that the largest racial grouping in the United States was non-Hispanic white, followed by Black or African American. in the 2012 GSS or any other related information, it is recommended to refer to the official documentation or reports from the General Social Survey (GSS).
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9-6x+x2 el dos va al cuadrado resuelvan lo porfA
Answer:
6
Step-by-step explanation:
do 9-6 then
50 points
The frequency table below shows the length of selected movies shown in a local
theater over the past six months.
Answer:
Lol its in total of 34
Step-by-step explanation:
Use a scientific calculator to find the Tangent of 180 degrees.
The green house is made completely of glass, except for the door. The entire building is 15 feet tall. The height of the vertical walls is 10 ft. The green house is 20 ft long (on side with door) and 16 feet wide. The triangles that make up the roof are isosceles triangles (both sides are equal and height is measured at the middle of the base). The door is 8 feet wide and 7 feet tall. Answer each of the following questions about your greenhouse.
Hose for watering the plants will be run along the entire outer edge of the floor, and up, around
the door. How much hose will be needed for this task?
A hose will be needed vertical walls to run along the entire outer edge of the floor and up around the door of the greenhouse 88 feet .
To calculate the length of the hose needed to run along the entire outer edge of the floor and up around the door of the greenhouse, we need to consider the perimeter of the floor and the additional distance around the door.
The perimeter of the floor is the sum of the lengths of all four sides of the rectangle. Since the greenhouse is 20 ft long and 16 ft wide, the perimeter of the floor is:
Perimeter of floor = 2(length + width) = 2(20 ft + 16 ft) = 2(36 ft) = 72 ft
In addition to the floor perimeter, to account for the distance around the door. The door is 8 ft wide, so the additional distance around the door is:
Distance around door = 2(width of door) = 2(8 ft) = 16 ft
calculate the total length of the hose needed by adding the perimeter of the floor and the distance around the door:
Total length of hose = Perimeter of floor + Distance around door = 72 ft + 16 ft = 88 ft
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2 8/100 turned into decimal
Answer:
2.08
Step-by-step explanation:
We know 2 is a whole number.
8/100 would be converted to the hundredths place.
0.000
/\
|
This is the hundredths place.
So the decimal is 2.08
---
hope it helps
A school recieved 20 boxes of different stickers.12 boxes contain floral stickers, 14 boxes were with 3-D stickers. There were 6 boxes of sparkly alphabet stickers. How many of 3-D floral stickers were received? Fill in the chart.
Answer:
14
Step-by-step explanation:
Answer:
14
Step-by-step explanation:
Your class is planning a breakfast bake sale and you have been tasked to bake the donuts and bagels. The system below represents the total amount of flour, in pounds, needed to replicate a batch-of-six bagel recipe and a batch-of-twelve donut recipe. You will be replicating the donut recipe d number of times and the bagel recipe b number of times. 3d + 5b = 21 d + b = 5
Answer:
3 bagel recipe and 2 doughnut recipes are needed
Step-by-step explanation:
Given the expression
3d + 5b = 21 .. 1
d + b = 5 .... 2
We can use the expression to look for the amount of doughnut recipe and bagel recipe needed by solving the equations simultaneously
Multiply equation 1 by 1 and 2 by 3 to have;
3d + 5b = 21 .. 3
3d + 3b = 15 .... 4
Subtract 3 from 4
5b - 3b = 21 - 15
2b = 6
b = 6/2
b = 3
Substitute b = 3 into equation 2;
From 2,
d = b = 5
d + 3 = 5
d = 5 - 3
d = 2
Hence 3 bagel recipe and 2 doughnut recipes are needed
If the coordinate of A is (0,-2) and the coordinate of B is (10,-6), then the midpoint of AB is (______).
Answer:
5, -4
Step-by-step explanation:
midpoint = x1 + x2/2 ,y1 + y2/2
= 0 + 10 /2 , -2 + -6/2
= 10/2 , -8/2
midpoint = 5, -4
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
Answer:
The answer is C
Step-by-step explanation:
The mean of math is 84, and the Mean of science is 85.
so, science is clearly one point higher
5x + 2 = x – 10 help
Answer:-3/4
Step-by-step explanation:
5x+2=x-1
5x-x=-1-2
4x=-3
X=-3/4
A student selects three marbles of different color-One is red, the second blue and the third is green. He picks the marbles one at a time without replacement. What is the probability he selects a blue. followed by a red, and then green?
Here's an Overleaf PDF I created with an explanation for your question:
The function h defined by h(t)=(-4.9t + 29.4)(t+2) models the height in meters, of an object t seconds after it is launched. When will the object hit the ground?
Answer:
The time the object will hit the ground is 2 s.
Step-by-step explanation:
Given;
h(t) = (-4.9t + 29.4)(t + 2)
Open the bracket;
h(t) = -4.9t² + 29.4t -9.8t + 58.8
h(t) = -4.9t² + 19.6t + 58.8
When the object hit the ground, the final velocity will be zero;
[tex]v = \frac{dh}{dt} = 0 \\\\\frac{dh}{dt} = -9.8t + 19.6 = 0\\\\9.8t = 19.6\\\\t = \frac{19.6}{9.8} \\\\t = 2 \ s[/tex]
Therefore, the time the object will hit the ground is 2 s.
Let A = {10,20,30}. Find one non-empty relation on set A such that all the given conditions are met and explain why it works: Not Reflexive, Not Transitive, Antisymmetric. (Find one relation on A that satisfies all three at the same time - don't create three different relations).
A non-empty relation on set A which satisfies all the condition is {(10, 20), (20, 30), (30, 10)}.
To find a non-empty relation on set A = {10, 20, 30} that satisfies the given conditions (not reflexive, not transitive, and antisymmetric), we can define the following relation:
R = {(10, 20), (20, 30), (30, 10)}
Explanation:
Not Reflexive: A relation R on set A is reflexive if for every element x in A, (x, x) is in R. In this case, (10, 10), (20, 20), and (30, 30) are not present in the relation R, which makes it not reflexive.
Not Transitive: A relation R on set A is transitive if for every (x, y) and (y, z) in R, (x, z) is also in R. In this case, we have (10, 20) and (20, 30) in R, but (10, 30) is not present. Therefore, the relation R is not transitive.
Antisymmetric: A relation R on set A is antisymmetric if for every (x, y) and (y, x) in R, where x ≠ y, then x and y are not the same element. In this case, we have (10, 20) and (20, 10) in R, but 10 is not equal to 20. Similarly, we have (20, 30) and (30, 20) in R, but 20 is not equal to 30. Therefore, the relation R is antisymmetric.
By defining the relation R as {(10, 20), (20, 30), (30, 10)}, we satisfy all three conditions simultaneously: not reflexive, not transitive, and antisymmetric.
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Find the lateral surface area.
Answer:
Step-by-step explanation:
1. Find the following limits. 2x2 - 8 a) lim * 4x2 + 2 b) lim -0 c) lim 2x +5x+3 2x+3
The limit of the given expression as x approaches infinity is negative infinity. The limit of (4[tex]x^2[/tex] + 2) as x approaches negative infinity is positive infinity. The limit of (2x + 5x + 3) divided by (2x + 3) as x approaches negative infinity is 7/4.
In the first limit, as x approaches infinity, the dominant term in the expression is 2x^2. Since x^2 grows without bound as x becomes larger, the value of 2x^2 will also increase without bound, resulting in a limit of negative infinity.
In the second limit, as x approaches negative infinity, the dominant term in the expression is 4x^2. Similar to the first limit, since x^2 grows without bound as x becomes more negative, the value of 4x^2 will increase without bound, leading to a limit of positive infinity.
In the third limit, as x approaches negative infinity, both the numerator and denominator have the dominant term of 5x. Dividing the numerator and denominator by 5x, we get (2 + 5/x) divided by (2 + 3/x). As x approaches negative infinity, the terms with x in the denominator become negligible, resulting in the limit simplifying to 2/2, which equals 1. Therefore, the limit of (2x + 5x + 3)/(2x + 3) as x approaches negative infinity is 7/4.
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which of the following functions are solutions of the differential equation y′′−9y′ 18y=0? a. y(x)=e6x b. y(x)=e−x c. y(x)=e3x d. y(x)=0 e. y(x)=6x f. y(x)=3x g. y(x)=ex
Only one of the following functions is a solution of the differential equation y′′−9y′+18y=0.
The second-order homogeneous linear differential equation is given as:y'' - 9y' + 18y = 0This differential equation is a linear homogeneous equation. We will have two roots of the characteristic equation: r1 = 3, r2 = 6So, the general solution to the differential equation is given as:y = c1e3x + c2e6xwhere c1 and c2 are arbitrary constants.a. y(x) = e6x is a solution because it is a part of the general solution of the differential equation.y(x) = e−x, y(x) = 0, y(x) = 6x, y(x) = 3x, y(x) = ex are not solutions because they don't satisfy the differential equation. Hence, the correct options are:a. y(x) = e6xTherefore, only one of the following functions is a solution of the differential equation y′′−9y′+18y=0.
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Please tell me if the transformation is a reflection or not!
Answer:
2, 3, & 5 are reflections, the others are rotations.
Susan found the equation of the best fit line for the data shown in the scatterplot. The slope of the line of best fit is
Answer:
Negative
Step-by-step explanation:
From the scatter plot displayed, we could clearly observe the direction of the trend line as it produces a negative slope. For high values of y, the values of x are low and similarly, high values of x have low y values. Therefore, this kind of relationship between the two variables is considered negative.
Write an expression that is equivalent to -4(3x – 7).
-4(3x – 7) =
– D
2 +
?
Josh is starting a round of golf the first hole is 130 yards long he needs advice which club to use for his first shot yes kept careful rack for records and how close is for shots came to the olive from the same distance his records include data from his onto golf clubs a ledge and an eight iron over the past year
Answer:
hello your question is incomplete attached below is the complete question
a) Histogram shows positive skewness and the box plot depicts the fact that the median of the 3-iron club is bigger while the variance of the 5-wood club is more than that of 3-iron club when compared to their distance
b)The Median is a better choice because it is not affected by skewness or outliners
c) Josh should use Club 3 iron. Reason : it has less variance
Step-by-step explanation:
A) Histogram and box plot is attached below
Histogram shows positive skewness and the box plot depicts the fact that the median of the 3-iron club is bigger while the variance of the 5-wood club is more than that of 3-iron club when compared to their distance
B) The Median is a better choice because it is not affected by skewness or outliners
Typical distance when Josh hits with a wedge = 4 , distance when Josh hits with an 8 iron = 10.5
c) Josh should use Club 3 iron. Reason : it has less variance