The student will be out of class for 2n days if the coin comes up tails, where n is the result of the die roll, which the probability will be 25.
An unfortunate student must recover from illness before washing laundry. The following formula is used to calculate the student's illness duration. We roll a fair 6-sided die and toss a fair coin. The student is absent from class for n days if the coin comes up heads, where n is the result of the die roll.
Ex(u) = (1/2)(1/6)*5+(1/2)(1/6)10+(1/2)(1/6)15+(1/2)(1/6)20 + (1/2)(1/6)25+(1/2)(1/6)*30
Probability = 25
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a child is 40 inches tall, which places her at the 90th percentile of all children of similar age. the heights for children of this age form an approximately normal distribution with a mean of 38 inches. based on this information, what is the standard deviation of the heights of all children of this age?
Since the mean height of all children this age is 38 inches, the z-score is 1.282, and the child's height is 40 inches, the standard deviation of all children's heights will be 1561.
What is standard deviation?The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a larger range, a low standard deviation suggests that the values tend to be near to the established mean. The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation indicates that the data are grouped around the mean, whereas a high standard deviation shows that the data are more dispersed.
Here,
The z-score which separates the top 10% of a normally distributed
population is 1.282.
Since z = (x-u)/sigma
1.282 = (40-38)/sigma
sigma = 2/1.282
sigma = 1/0.641 = 1561
The standard deviation of the heights of all children of this age will be 1561 as mean is 38 inch and z-score is 1.282 as well as the height of child is 40 inch.
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The number of
Logan has $0.87 worth of pennies and nickels. He has a total of 31 coins altogether.
Determine the number of pennies and nickels Logan has.
Answer:
17 pennies, 14 nickels
Step-by-step explanation:
let p = pennies and n = nickels
p + n = 31 coins
p = 31 - n
0.01p + 0.05n = $0.87
0.01(31 - n) + 0.05n = 0.87
0.31 - 0.04n = 0.87
0.04n = 0.56
n = 14
p = 31 - 14
p = 17
hope this made sense :)
How do you solve 11=2B+17, what is B
Answer:
b=-3
Step-by-step explanation:
11=2b+17
subtract 11 from both sides
then you get 2b+6=0
so b=-3
Answer: -3
Step-by-step explanation:
Hey! Here's a simple solution -
Step 1 - Subtract 17 from both sides -
11 - 17 = 2B + 17-17
-6 = 2B
Step 2 - Divide both sides by 2
-3 = B
B= -3
Hope this helped you! Peace out!
You have $8.80 in Pennie’s and nickels you have twice as many nickels as pennies write a system of linear equations that model the situation how many coins do you have
Answer:
Step-by-step explanation:
Let p be the number of pennies and n be the number of nickels. As you have $8.80 in total (given that pennies are worth $0.01 and nickels are worth $0.05)
0.01p + 0.05n = 8.80
You also know that there are twice as many nickels than pennies (or alternatively, there are 2 nickels for every penny).
n = 2p
You can substitute this value of n into the first equation
0.01p + 0.05n = 8.80
0.01p + 0.05(2p) = 8.80
0.01p + 0.10p = 8.80 (multiplying out the brackets)
0.11p = 8.80 (collecting the p's)
p = 80
Putting this back into the second equation
n = 2p
n = 2(80) = 160
So there are 160 nickels and 80 pennies.
You can put this back into the first equation to check it.
0.01p + 0.05n = 8.80
0.01(80) + 0.05(160) = 0.80 + 8 =8.80
Stella wants to build up her emergency fund to $10,000. She has $2,000 now and plans on saving $320 every month. To model the situation, she creates this equation, where x represents the number of months and y represents the total amount in her emergency fund:.
The linear equation that represents the total amount in her emergency fund after x number of months be
y = 320x + 2000
Given, Stella wants to build up her emergency fund to $10,000. She has $2,000 now and plans on saving $320 every month.
we have to model the situation in a linear equation,
Let the number of months be, x
and the total amount in her emergency fund be, y
As, she starts with $2000 so the y-intercept will be 2000
also she save $320 every month so the slope be 320
So, the equation be,
y = 320x + 2000
Hence, the linear equation that represents the total amount in her emergency fund after x number of months be
y = 320x + 2000
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let n be a three digit positive integer with all different signs. what can we say about the difference between n and its reverse
By using the expanded form of a number, it can be concluded that
Difference between a three digit positive integer with all digits distinct and its reverse is surely divisible by 1, 3, 9, 11, 33, 99
What is expanded form of a number?
Every number can be written as a sum of the place value of its digit. This is known as expanded form of a number
Let the three digit positive integer be n = abc where a, b and c are distinct positive integers
n can be written as 100a + 10b + c
Its reverse is n' = cba
n' can be written as 100c + 10b + a
Difference between the number and its reverse
= 100a + 10b + c - 100c - 10b -a
= 99a - 99c
= 99(a - c)
= Since a and c are distinct, a - c [tex]\neq[/tex] 0
Difference between a three digit positive integer with all digits distinct and its reverse is surely divisible by 1, 3, 9, 11, 33, 99
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a textbook store sold a combined total of 340 history and sociology textbooks in a week. the number of history textbooks sold was three times the number of sociology textbooks sold. how many textbooks of each type were sold?
Answer:
85 sociology books
255 history books
Step-by-step explanation:
h = history textbooks
s = sociology textbooks
h + s = 340
h = 3s
3s + s = 340
4s = 340
s = 85
h = 3s = 3(85) = 255
Answer:
255 history textbooks
85 sociology textbooks
Step-by-step explanation:
Define the variables:
Let x be the number of history textbooks sold.Let y be the number of sociology textbooks sold.Given information:
Total number of textbooks sold in a week was 340.The number of history textbooks sold was three times the number of sociology textbooks sold.Create a system of equations with the given information and defined variables:
[tex]\begin{cases}x+y=340\\\;\;\;\:\:\:\:x=3y\end{aligned}[/tex]
Substitute the second equation into the first equation and solve for y:
[tex]\implies 3y+y=340[/tex]
[tex]\implies 4y=340[/tex]
[tex]\implies y=340 \div 4[/tex]
[tex]\implies y=85[/tex]
Substitute the found value of y into the second equation and solve x:
[tex]\implies x=3 \times 85[/tex]
[tex]\implies x=255[/tex]
Therefore, the number of each type of textbooks sold were:
255 history textbooks.85 sociology textbooks.Educational Technology, Inc. sells software to provide guided homework problems for a statistics course. They would like to know if students who use the software score better on exams. A sample of students who used the software had the following scores: 86, 78,66,83, 84, 81, 84, 109, 65, and 102. Students who did not use the soft-ware had the following scores:91, 71, 75,76, 87, 79, 73, 76,79, 78, 87, 90, 76, and 72. Assume the population standard deviations are not the same. At the .10 significance level, can we conclude that there is a difference in the mean scores for the two groups of students
a. What are the three assumptions for CASE C?
b. State the null and alternative hypothesis for this problem.
c. State the level of significance for this problem.
d. Which distribution (normal or t) should be used in this problem? Explain why.
e. Create a decision rule for this problem. Include the critical value. (USE TEXTBOOK TABLE.) Make sure it agrees with the excel printout.
f. Calculate the test statistic. (BY HAND). Make sure it agrees with the excel printout.
g. What is your conclusion? EXPLAIN IN DETAIL.
h. Estimate the p-value for this problem. Restate the conclusion. What is the actual p-value from the excel printout?
The assumptions are- Sample of students are independent and samples are simple random samples. Distribution is normal (t distribution). The independent variable measures on interval scale.
What is Statistics?The study and development of techniques for gathering, processing, interpreting, and presenting empirical data are within the purview of statistics, a branch of natural science. Research in stats has application in almost all scientific domains, and software concerns in the many science disciplines inspire the creation of new statistical methods and theories. Statistics is a very multidisciplinary field. Statisticians use a range of mathematical and computational techniques while creating new approaches and researching the concept that supports such methods.
Uncertainty and variation are two cornerstones of the statistical profession. In science, as well as more broadly in life, there are numerous circumstances where the result is unknown. Sometimes the uncertainty is caused by the fact that the result is still up in the air.
How to solve?
ts < tc Do not reject H0
P value > α Do not reject H0
There is insufficient data to determine that the mean scores of the two groups of pupils differ.
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You pend 2/3 hour reading a book daily. How many hour did you pend reading after a week?
The total number of hours spent on reading in a week is 14/3 hours.
Define the term fraction of a number?A fraction is a number that is a component of a whole. By breaking a whole into a number of parts, it is evaluated.The components of a whole or group of items are described by fractions. The numerator is the figure only at top of the line. It details the number of equal portions which have been taken from the total or collection. The denominator is the figure that appears below the line.For the given question-
Number of hours spent of reading = 2/3 hours.
Total number of days in a week = 7.
Total number of hours spent on reading = 2/3 x 7
Total number of hours spent on reading = 14/3
Thus, the total number of hours spent on reading in a week is 14/3 hours.
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question content area top part 1 deborah has two pairs of slacks, six shirts, and five sweaters. from how many combinations can she choose if she chooses a pair of slacks, a shirt, and a sweater each day?
Deborah can choose from a total of 60 combinations.
Here, we are given that Deborah has two pairs of slacks, six shirts, and five sweaters.
She has to choose a pair of slacks, a shirt, and a sweater each day.
She can choose a pair of slacks in 2 ways
Similarly, she can choose a shirt to wear in 6 ways and a sweater in 5 ways.
Since, she wears each one of these items each day, the total number of combinations can be found by multiplying the possibilities for each item as follows-
2 × 6 × 5
= 60
Thus, Deborah can choose from a total of 60 combinations.
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Plsss help!
Geometry A
Brainliest
According to the perpendicular bisector theorem, the statement that is true is: B. BI = BK.
What is the Perpendicular Bisector Theorem?The perpendicular bisector theorem states that if a line segment bisects another line segment perpendicularly, therefore, any point on the perpendicular would be the same distance from the endpoints of each of the line segment that was bisected.
In the diagram above, we are told that line segment AB is a perpendicular bisector of line segment IK. This means that, according to the perpendicular bisector theorem, any point on line segment AB, would be equidistant to the endpoints of line segment IK.
This implies that:
The length of BI is the same as the length of BK. Thus, the correct answer is: B. BI = BK.
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Exhibit 6-3 The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. Refer to Exhibit 6-3. What is the minimum weight of the middle 95% of the players? a. 196 b. 151 c. 249 d. None of the answers is correct.
Option B, The center 95% of players had an average weight of 151 pounds.
Football players' weights have a mean of 200 pounds as well as a standard deviation of 25 pounds, which corresponds to a normal distribution.
So, let x represent a football player's weight.
X ≅ N(200, (25)²)
The minimal weight of the center 95% of the members is
P(X > 95) = P((95 - 200) ÷ 25) < (X - µ) ÷ σ)
P(X > 95) = P(-4.2 < z)
P(X > 95) = - P(z < -4.2)
P(X > 95) = 0.1512
The needed percentage is 0.1512 × 100 = 151.2 percent.
A probability distribution that is equal around the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.
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ABC is congruent to what by what
Answer:
Step-by-step explanation:
Since two angles of △ABC are congruent to two angles of △PQR, the third pair of angles must also be congruent, so ∠C≅∠R, and △ABC≅△PQR by ASA. The corresponding congruent angles are: ∠A≅∠P, ∠B≅∠Q, ∠C≅∠R. The corresponding congruent sides are: AB ≅ PQ, BC ≅ QR, AC ≅ PR.
How is a constant term different than a variable for an expression that represents a real word situation
A constant does not change its value over time. A variable, on the other hand, changes its value dependent on the equation.
What is a tern!?A term is either a number, a variable, or the product of a number and a variable. A coefficient is your term's numerical factor. A constant term is one that only contains a number. In other words, a constant term contains no variables.
Constants are algebraic expression terms that only contain numbers. That is, they are the terms that do not have variables. We call them constants because their value never changes because the term contains no variables that can change its value.
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from a group of 3 freshmen, 4 sophomores, 4 juniors, and 3 seniors, a committee of size four is randomly selected. find the probability that the committee will consists of only sophomores or juniors? round your answer to 2 decimal places.
Probability of randomly selecting four committee members with only sophomores or juniors is equal to 0.77.
As given in the question,
Total number of group members including 3 freshmen, 4 sophomores, 4 juniors, and 3 seniors = 14
Number of members required to form a committee = 4
Condition apply:
Committee consists of only sophomores or juniors
Let 'A' represents the sophomores
'B' represents the juniors
Total number of possible outcomes = ¹⁴C₄
Event A and B are independent of each other.
Favourable outcomes are :
2(⁴C₀⁴C₄ + ⁴C₁⁴C₃) +⁴C₂⁴C₂
Required probability
= 2(⁴C₀⁴C₄ + ⁴C₁⁴C₃) +⁴C₂⁴C₂ / ( ¹⁴C₄)
= [2( 1 + 16) + 36 ] / ( 7 × 13 )
= 70 / 91
=0.77
Therefore, the probability of the committee consists of only sophomores or juniors is equal to 0.77.
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I need help with this please asap
Answer:
estimate - 455
actual sum 376
What is the equation of the line that passes through the point (8,6) and has a slope of 0?.
The equation of line that passes through the point (8,6) and has a slope of 0 is y = 6.
Define the equation of the line?The set of points that make up a line in a coordinates system are represented algebraically by a line's equation. An equation of a line is an algebraic expression that represents the many points that together make up a line with in coordinate axis as a set of variables, x, and y.As the sated question-
The passing point; (x1, y1) = (8,6)
slope m = 0
Thus, equation lo line by slope intercept form is-
y - y1 = m(x - x1)
y - 6 = 0(x - 8)
y = 6
Thus, the equation of the line that passes through the point (8,6) and has a slope of 0 is y = 6.
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Suppose that a One-way ANOVA is being performed to compare the means of 4 populations and that the sample sizes are 14, 16, 19, and 13. Determine the degrees of freedom for the F-statistic. (a) the degree of freedom of the numerator (b) the degree of freedom of the denominator
The degrees of freedom for the F- statistic is:
(a) the degree of freedom of the numerator= 3
(b) the degree of freedom of the denominator= 58
What is Analysis of Variance (ANOVA)?
The statistical analysis tool known as analysis of variance (ANOVA) divides the observed aggregate variability present in a data set into two categories: systematic variables and random components. The random factors have no statistical impact on the presented data set, whereas the systematic factors do.
The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean".
If we assume that we have [tex]p[/tex] groups and on each group from [tex]j=1,...,p[/tex]we have [tex]n_{j}[/tex] individuals on each group we can define the following formulas of variation.
We know, we have this property
[tex]SST=SS_{between} +SS_{within}[/tex]
The degrees for the numerator are [tex]df_{num}=k-1=4-1=3[/tex], where k represents the number of groups (k = 4)
The degrees for the denominator are [tex]df_{den} =N-K=62-4=58[/tex], where N represent the total number of people (N = 14+16+19+13=62)
And the total degrees of freedom are given by:
[tex]df_{tot} =df_{num} +df_{den} =3+58=61[/tex]
Hence, degree of freedom of the numerator is 3 and the degree of freedom of the denominator is 58.
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6. If mLABE = 2n +7 and mZEBF = 4n-13, find mZABE.
Answer: 18°
Step-by-step explanation:
The question doesn’t state where F is in relation to A, B or E, so we have to guess. Here are two guesses.
If ABF is a straight line then ∠ABE+∠EBF=180, so 2n+7+4n-13=180, 6n-6=180.
Divide each side by 6: n-1=30 so n=31 and m∠ABE=2n+7=2×31+7=62+7=69°.
If BF bisects ∠ABE, then ∠ABE=2×∠EBF, so 2n+7=2(4n-13)=8n-26. So 6n=33 and, dividing both sides by 3: 2n=11. Therefore m∠ABE=2n+7=11+7=18°.
Sue wants to leave her grandson a nice inheritance. She has decided to deposit
$350.00 each month into an ordinary annuity that earns 4% compounded monthly.
How much will be in the account after 30 years rounded
The amount that would be in the account in 30 years will be $245,371.
How much will be in the account?An ordinary annuity is when a series of payment is made at the end of the period over a number of years.
The formula that can be used to determine the future value of an ordinary annuity is: monthly deposit x annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r= monthly interest rate = 4/12 = 1/3%n = number of periods = number of years x number of compounding : 30 x 12 = 360$350 x (1.0033)^360 - 1} / 0.0033 = $245,371
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How do I find slope?
The graph of a line is shown on the grid. The
coordinates of both points indicated on the graph of the
line are integers.
What is the rate of change of y with respect to x for
this line?
Answer:
4/5
Step-by-step explanation:
The two points are (5, 7) and (-5, -1). The slope is the difference of y over the difference in x, or [tex](7--1)/(5--5)[/tex]. This simplifies to 8/10, or 4/5.
Question
A local movie theater sells tickets at different prices for an adult and for a child. The price of an adult’s ticket is $10.50 and the price of a child’s ticket is $6.50 . If the theater sells a total of 65 tickets for a total price of $594.50 in an afternoon, how many child tickets did the theater sell?
Answer:22
Step-by-step explanation:
a survey that found that 351 of 547 business travelers use a laptop computer on overnight business trips. based on this survey, what is the sample proportion of business travelers who use a laptop computer on overnight business trips? (round your answer to four decimal places.)
The sample proportion of the business travelers who use a laptop computer on overnight trips is 0.6417.
Given:
a survey that found that 351 of 547 business travelers use a laptop computer on overnight business trips.
we are asked to find the sample proportion based on this survey, who use a laptop computer on overnight business trips = ?
sample proportion:
The sample proportion (p) indicates the percentage of people in a sample who exhibit a particular quality or attribute. Divide the number of individuals (or items) who have the desired attribute by the overall sample size to obtain the sample proportion.
P = X/N
P = 351/547
P = 0.641681
round off to four decimal places.
P = 0.6417
Hence we get the sample proportion as 0.6417
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Assume the birth of a boy or a girl is equally likely. The probability that a single child is born a girl is one-half. What is the probability that the next child born to the same familiy will also be a girl?.
There is a 1/4 probability that the family's next child will be a girl.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.
An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
So, the probability that the next child born will also be a girl:
We know that:
There is a 50% chance that a female will be the only kid born.
That is: 1/2
The likelihood that the family's subsequent kid will be a girl is:
1/2 * 1/2 = 1/4
Therefore, there is a 1/4 probability that the family's next child will be a girl.
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a family begins a car trip at 2:00pm. at 5:00pm, the car has traveled a total of 80 miles. use the mean value theorem to explain why
In one hour, the car covered a distance of 26.66 miles
Given,
The time when the trip begins = 2.00 pm
Distance travelled till 5.00 pm = 80 miles
Here,
Mean value Theorem;-
The Mean Value Theorem says that there exists a point c in the interval (a, b) such that f'(c) equals the function's average rate of change throughout [a, b] if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b).
The Mean Value Theorem is as follows. F is constant over I if f′(x)=0 over a period I. If f′(x)=g′(x) over I for two differentiable functions f and g, then f(x)=g(x)+C for some constant C.
Here,
2 pm to 5 pm = 3 hours
80 miles in 3 hours
That is,
80/3 = 26.66 miles per hour
That is,
The car travelled a distance of 26.66 miles in an hour.
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Hey y’all can y’all help me again
Answer:
Answer
Step-by-step explanation:
10. is (-1,0)
12. is (3,0)
14. is (1,0)
Kelli walks no more than 25 dogs on Mondays. Ms. Lincoln has 5 dogs that Kelli walks. The inequality shown can be used to find x, the number of dogs Kelli can walk on Monday in addition to Ms. Lincoln's dogs. x + 5 25 Which inequality represents all possible values of x?
The inequality x ≤ 20 represents the all possible values of x.
What is inequality?Inequality shows relation between two expression which are not equal to each others.
Given that,
Kelli walks not more than 25 dogs on Mondays,
Also,
Kelli walks 5 dogs that belongs to Ms. Lincoln
The inequality to find the number of dogs Kelli walks on Monday x, in addition to Ms. Lincoln's dogs, can be written as,
x+5 ≤ 25
Subtract 5 from both the sides,
x + 5 - 5 ≤ 25 - 5
x ≤ 20
The required inequality is x ≤ 20.
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5x+4y-2x+3x+3y simplify
The soup pot is 8. 5 inches tall with a radius of 4 inches. What is the volume of the soup pot? answer choices are rounded to the nearest tenth cubic inch.
The volume of the soup pot is 427.04 inches³
The soup pot is 8. 5 inches tall with a radius of 4 inches
We need to find the volume of the soup pot
What is volume?
Volume, is defined as the space that a body occupies. it is the ratio of the mass of object to its density.
Volume of cylinder = 3.14r²h
Where r represents the radius of the cylinder and h represents the height of the cylinder.
Volume of cylinder = 3.14 x 4 x 4 x 8.5
Volume = 427.04 inches³
Thus, the required volume of the soup pot when it is s 8. 5 inches tall with a radius of 4 inches is 427.04 inches³
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Suppose you want to reduce the amount of sugar in your cookie recipe. You decide to subtract ⅛ of cup of sugar from the original amount of ¾ of a cup. How much sugar is now in your recipe? Show your work using two different methods.
The amount of sugar in final recipe will be 5/8
What are fraction?Fractions are used to represent smaller pieces (or parts) of a whole.
Given that, You decide to subtract ⅛ of a cup of sugar from the original amount of ¾ of a cup.
3/4-1/8 = 5/8
Hence, The amount of sugar in final recipe will be 5/8
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