Answer:
Slope = [tex]-\frac{2}{3}[/tex]
Step-by-step explanation:
Slope = [tex]\frac{rise}{run}[/tex]
Slope = [tex]\frac{y2-y1}{x2-x1}[/tex]
Slope = [tex]\frac{4-2}{-3-3}[/tex]
Slope = [tex]-\frac{4}{6}[/tex]
Slope = [tex]-\frac{2}{3}[/tex]
Which equation describes a rational function with x-intercepts at –4 and 2, a vertical asymptote at x = 1 and x = –1, and a horizontal asymptote at y = –3?
Answer:
d on edge
Step-by-step explanation:
-3(x+4)(x-2)/x^2-1`
The equation of the rational function is: [tex]f(x) = \frac{-3(x + 4)(x -2)}{x^2-1}[/tex]
The x-intercepts of the rational function are given as: -4 and 2.
This means that, the zeroes of the function are (x + 4) and (x -2)
Multiply the zeroes of the function
[tex]f(x) = (x + 4)(x -2)[/tex]
The vertical asymptotes of the rational function are given as: 1 and -1.
This means that, the denominator is the product of (x + 1) and (x -1)
So, we have:
[tex]f(x) = \frac{(x + 4)(x -2)}{(x + 1)(x-1)}[/tex]
Express the denominator as the difference of two squares
[tex]f(x) = \frac{(x + 4)(x -2)}{x^2-1}[/tex]
Lastly, the horizontal asymptote is given as y = -3.
So, the actual function is:
[tex]f(x) = y \times \frac{(x + 4)(x -2)}{x^2-1}[/tex]
Substitute -3 for x
[tex]f(x) = -3 \times \frac{(x + 4)(x -2)}{x^2-1}[/tex]
This gives
[tex]f(x) = \frac{-3(x + 4)(x -2)}{x^2-1}[/tex]
Hence, the equation of the rational function is: [tex]f(x) = \frac{-3(x + 4)(x -2)}{x^2-1}[/tex]
Read more about rational functions at:
https://brainly.com/question/1851758
a) A large hotel in Miami has 900 rooms (all rooms are equivalent). During Christmas, the hotel is usually fully booked. However, as it is possible for a customer to cancel their reservation, the hotel overbooks its rooms. 1000 people were given assurance of a room. Let us assume that each customer cancels their reservation with a probability of 0.1. If the total number of customers who still keep their booking is more than 900, the hotel has to unfortunately send some customers to other accommodation. What is the probability that this happens, as per the Central Limit Theorem
Answer:
14.69% probability that this happens
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
1000 people were given assurance of a room.
This means that [tex]n = 1000[/tex]
Let us assume that each customer cancels their reservation with a probability of 0.1.
So 0.9 probability that they still keep their booking, which means that [tex]p = 0.9[/tex]
Probability more than 900 still keeps their booking:
[tex]n = 1000, p = 0.9[/tex]
So
[tex]\mu = 0.9, s = \sqrt{\frac{0.9*0.1}{1000}} = 0.0095[/tex]
901/1000 = 0.91
So this is 1 subtracted by the pvalue of Z when X = 0.91.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{0.91 - 0.9}{0.0095}[/tex]
[tex]Z = 1.05[/tex]
[tex]Z = 1.05[/tex] has a pvalue of 0.8531
1 - 0.8531 = 0.1469
14.69% probability that this happens
Write an expression without exponent that is equivalent to 2 to 3rd power nd 4 to the 3rd power
Answer:
2 to the 3rd power,
2*2*2
4 to the 3rd power,
4*4*4
Step-by-step explanation:
The "3rd power" means how many times the number given to it would be multiplied. Aka, 2 to the 4th power would mean 2 times 2 times 2 times 2, (2 four times).
solve for x
2x/3 + 2 = 16
Answer:
2x/3 + 2= 16
=21
Step-by-step explanation:
Standard form:
2
3
x − 14 = 0
Factorization:
2
3 (x − 21) = 0
Solutions:
x = 42
2
= 21
Let Aequals [Start 2 By 2 Matrix 1st Row 1st Column 3 2nd Column 2 2nd Row 1st Column negative 1 2nd Column 2 EndMatrix ]and Bequals [Start 2 By 2 Matrix 1st Row 1st Column 2 2nd Column 6 2nd Row 1st Column negative 3 2nd Column k EndMatrix ]. What value(s) of k, if any, will make ABequals BA?
Answer:
No value of k will make AB=BA
Step-by-step explanation:
[tex]A=\left(\begin{array}{ccc}3&2\\-1&2\end{array}\right), $ $B=\left(\begin{array}{ccc}2&6\\-3&k\end{array}\right) \\\\\\AB=\left(\begin{array}{ccc}3&2\\-1&2\end{array}\right)\left(\begin{array}{ccc}2&6\\-3&k\end{array}\right)=\left(\begin{array}{ccc}3*2+2*-3&3*6+2*k\\-1*2+2*-3&-1*6+2k\end{array}\right)=\left(\begin{array}{ccc}0&18+2k\\-8&-6+2k\end{array}\right)[/tex]
[tex]BA=\left(\begin{array}{ccc}2&6\\-3&k\end{array}\right)\left(\begin{array}{ccc}3&2\\-1&2\end{array}\right)=\left(\begin{array}{ccc}0&16\\-6&-6+2k\end{array}\right)[/tex]
We can see that [tex]AB \neq BA[/tex]. Therefore, there is no value of k that will make it equal. In general, matrix multiplication is not commutative.
A human resource manager for a large company takes a random sample of 60 employees from the company database. Based on the sample she calculates a 95% confidence interval for the mean time of employment for all employees to be 8.7 to 15.2 years. Which of the following will provide a more informative (i.e., narrower) confidence interval than the 95% confidence interval?
A. Using a 90% confidence level (instead of 95%)
B. Using a 99% confidence level (instead of 95%)
C. Using a sample size of 40 employees (instead of 60)
D. Using a sample size of 90 employees (instead of 60)
Answer:
A. Using a 90% confidence level (instead of 95%)
D. Using a sample size of 90 employees (instead of 60)
Step-by-step explanation:
The margin of error of a confidence interval is given by:
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which z is related to the confidence level, [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
The higher the margin of error, the less precise the confidence interval is.
We have:
A 95% confidence interval, with a sample of 60.
We want to make it more precise:
Two options, decrease z(decrease the confidence level), or increase n(increase the sample size).
So the correct options are:
A. Using a 90% confidence level (instead of 95%)
D. Using a sample size of 90 employees (instead of 60)
Keith Rollag (2007) noticed that coworkers evaluate and treat "new" employees differently from other staff members. He was interested in how long a new employee is considered "new" in an organization. He surveyed four organizations ranging in size from 34 to 89 employees. He found that the "new" employee status was mostly reserved for the 30% of employees in the organization with the lowest tenure.
A) In this study, what was the real range of employees hired by each organization surveyed?
B) What was the cumulative percent of "new" employees with the lowest tenure?
Answer:
a) Real range of employees hired by each organization surveyed = 56
b) The cumulative percent of "new" employees with the lowest tenure = 30%
Step-by-step explanation:
a) Note: To get the real range of employees hired by each organization, you would do a head count from 34 to 89 employees. This means that this can be done mathematically by finding the difference between 34 and 89 and add the 1 to ensure that "34" is included.
Real range of employees hired by each organization surveyed = (89 - 34) + 1
Real range of employees hired by each organization surveyed = 56
b) It is clearly stated in the question that the "new" employee status was mostly reserved for the 30% of employees in the organization with the lowest tenure.
Therefore, the cumulative percent of "new" employees with the lowest tenure = 30%
what is 7/9 x 5 2/5 please!
Answer:
[tex]4\frac{1}{5}[/tex]
Step-by-step explanation:
=>[tex]\frac{7}{9} * 5 \frac{2}{5}[/tex]
=> [tex]\frac{7}{9} * \frac{27}{5}[/tex]
=> [tex]\frac{7*3}{5}[/tex]
=> [tex]\frac{21}{5}[/tex]
=> [tex]4\frac{1}{5}[/tex]
Answer:
[tex]4\frac{1}{5}[/tex]
Step-by-step explanation:
[tex]\frac{7}{9} \times 5 \frac{2}{5}[/tex]
[tex]\frac{7}{9} \times \frac{27}{5}[/tex]
[tex]\frac{7 \times 27}{9 \times 5 }[/tex]
[tex]\frac{189}{45}[/tex]
[tex]\frac{21}{5}[/tex]
[tex]=4\frac{1}{5}[/tex]
In triangle ABC, the measure of angle A is half the measure of angle B, and the measure of angle C is 50° less than the measure of angle B. Find the measure of the smallest angle. (Recall that the sum of the measures of the angles in a triangle is 180°.)
Answer:
42º
Step-by-step explanation:
You can start by setting up the equations that are given in the stem of the problem: a=.5b, c=b-50, a+b+c=180. Then plug in the values of b in relation to the other values into the equation a+b+c=180. This will give you (.5b)+b+(b-50)=180. By expanding this and combining like terms, we will get 2.5b=230. By dividing each side by 2.5, we get b=92. Then, referencing the first equations, a=.5(92)=46, and c=92-50=42. The smallest of all of these is c, 42.
A standardized mathematics test given to 14,000 students had the scores normally distributed. The mean was 850 and the standard deviation was 75. A student scoring below 775 points was deficient in mathematics. About how many students were rated deficient?
x + 7 = 6x - 3
answer plssss
Answer:
x=2
Step-by-step explanation:
x + 7 = 6x - 3
Subtract x from each side
x+7-x = 6x-x
7 = 5x-3
Add 3 to each side
7+3 = 5x-3+3
10 =5x
divide by 5
10/5 = 5x/5
2 =x
Answer:
x= 2
hope it helps!
Step-by-step explanation:
x + 7 = 6x - 3
Bring all the variables to one side
So get 6x to the other side
x+7-6x = -3
-5x +7 = -3
Take 7 to the other side
-5x= -3 -7
-5x = -3 + -7
-5x = -10
x = -10/-5
minus n minus becomes plus
x= 10/5
= 2
Suppose the solutions of a homogeneous system of four linear equations in five unknowns are all multiples of one nonzero solution. Will the system necessarily have have a solution for every possible choice of constants on the right sides of the equations? Explain.
Consider a homogeneous machine of four linear equations in five unknowns are all multiples of 1 non-0 solution. Objective is to give an explanation for the gadget have an answer for each viable preference of constants on the proper facets of the equations.
Yes, it's miles true.
Consider the machine as Ax = 0. in which A is 4x5 matrix.
From given dim Nul A=1. Since, the rank theorem states that
The dimensions of the column space and the row space of a mxn matrix A are equal. This not unusual size, the rank of matrix A, additionally equals the number of pivot positions in A and satisfies the equation
rank A+ dim NulA = n
dim NulA =n- rank A
Rank A = 5 - dim Nul A
Rank A = 4
Thus, the measurement of dim Col A = rank A = five
And since Col A is a subspace of R^4, Col A = R^4.
So, every vector b in R^4 also in Col A, and Ax = b, has an answer for all b. Hence, the structures have an answer for every viable preference of constants on the right aspects of the equations.
Please answer this correctly
Answer:
101-120=4
Step-by-step explanation:
All that you need to do is count how many data points fall into this category. In this case, there are four data points that fall into the category of 101-120 pushups
111111105113Therefore, the answer to the blank is 4. If possible, please mark brainliest.
Answer:
There are 4 numbers between 101 and 120.
Step-by-step explanation:
101-120: 105, 111, 111, 113 (4 numbers)
Janice really likes potatoes. Potatoes cost $1.00 per pound, and she has $6.00 that she could possibly spend on potatoes or other items. Suppose she feels that the first pound of potatoes is worth $1.50, the second pound is worth $1.14, the third pound is worth $1.05, and all subsequent pounds are worth $0.30. how many pounds of potatoes will she purchase?
Answer:
6 pounds
Step-by-step explanation:
Sara is a librarian and works at least 10 hours per week. If Sara would like to work extra shifts, they are added to her
schedule in two-hour increments. Which equation models the number of hours that Sara will work at the library this
week? Assume x is the number of two-hour increments and y is the total number of hours worked.
Answer:
y = 10 + 2x
or
y = 2x + 10
Step-by-step explanation:
She works a fixed 10 hours each week, so we start with
y = 10
Now she adds 2-hour increments. She can have 0, 1, 2, or another number of increments. x represents the number of increments. Since each increment is 2 hours, 2x represents the number of hours added by the increments. Now we add 2x to the fixed number of hours.
y = 10 + 2x
or
y = 2x + 10
Answer:
y = 2x + 10
Step-by-step explanation:
The probability that a house in an urban area will be burglarized is 6%. If 10 houses are randomly selected, what is the probability that none of the houses will be burglarized?
Answer:
[tex](\dfrac{94}{100})^{10} \ or\ \approx 0.54[/tex]
Step-by-step explanation:
Given :
Probability that a house in an urban area will be burglarized,
[tex]p =6\%=\dfrac{6}{100}[/tex]
To find:
Probability that none of the houses randomly selected from 10 houses will be burglarized = ?
[tex]P(r=0) =?[/tex]
Solution:
This question is related to binomial distribution where:
[tex]p =\dfrac{6}{100}[/tex]
[tex]\Rightarrow[/tex] Probability that a house in an urban area will not be burglarized,
[tex]q =1-6\%=94\%=\dfrac{94}{100}[/tex]
Formula is:
[tex]P(r=x)=_nC_xp^xq^{n-x}[/tex]
Where n is the total number of elements in sample space and
x is the number selected from the sample space.
Here, x = 10 and
x = 0
[tex]\therefore P(r=0)=_nC_0p^0q^{10-0}\\\Rightarrow 1 \times (\dfrac{6}{100})^0\times (\dfrac{94}{100})^{10}\\\Rightarrow 1\times (\dfrac{94}{100})^{10}\\\Rightarrow (\dfrac{94}{100})^{10}\\\\\Rightarrow (0.94)^{10}\\\Rightarrow \approx 0.54[/tex]
What is StartAbsoluteValue 9 EndAbsoluteValue? –18 –9 9 18
Answer:
9
Step-by-step explanation:
Answer:
9
Step-by-step explanation:
my chile
Express the following ratio in it’s simplest form
5:20
Answer:
1:4
Step-by-step explanation:
Answer:
1 : 4
Step-by-step explanation:
5:20
Divide each side by 5
5/5 : 20/5
1 : 4
help me please, guys
Answer:
7.7
Step-by-step explanation:
The area of the wall is 4 * 2 = 8.
The radius of each clock is 0.3 / 2 = 0.15.
The area of all 4 circles is 4 * (πr²) = 4 * 3.14 * 0.15² = 0.3.
8 - 0.3 = 7.7
Answer:
6.9
Step-by-step explanation:
Total area of the wall is 4 x 2 = 8
Area for a circle is π x radius^2
Therefore total area of 4 clocks = 4 (π x 0.3^2)
Which is: 1.13...
Now we take away this answer from the area of the wall:
8 - 1.13... = 6.9 (1 d.p)
Find the term independent of x in the expansion of
[tex]( \frac{2}{3} {x}^{2} - \frac{1}{2x})^{9} [/tex]
Step-by-step explanation:
[tex] \frac{19683x {}^{18} }{512} - \frac{59049x {}^{15} }{512} + \frac{19683x {}^{12} }{128 } - \frac{15309x {}^{9} }{?128} + \frac{15309x {}^{6} }{256} - \frac{15309x {}^{9} }{128} + \frac{15309x {}^{6} }{?256} - \frac{5103x {}^{3} }{256} + \frac{567}{128} - \frac{81}{128x {}^{3} } + \frac{27}{512x {}^{6} } - \frac{1}{512x {}^{9} } [/tex] it's long there's some calculations in de side hope its helpful
In a survey, the planning value for the population proportion is p* = 0.26. How large a sample should be taken to provide a 95% confidence interval with a margin of error of 0.05? (Round your answer up to nearest whole number.)
Answer:
n = 296
Sample size n = 296
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
p+/-z√(p(1-p)/n)
x+/-M.E
M.E = z√(p(1-p)/n)
Making n the subject of formula;
n = (p(1-p)/(M.E/z)^2) .....1
Given that;
Proportion p = 0.26
Number of samples n = ?
Confidence interval = 95%
z(at 95% confidence) = 1.96
Substituting the values into equation 1;
n = (0.26(1-0.26))/((0.05/1.96)^2)
n = 295.649536
n = 296
Sample size n = 296
Given that 9 x − 4 y = 20 Find y when x = − 2 Give your answer as an improper fraction in its simplest form.
Answer:
y = [tex]-9 \frac{1}{2}[/tex]
Step-by-step explanation:
9x-4y = 20
Given that x = -2
Putting in the above equation
9(-2) -4y = 20
-18 - 4y = 20
-4y = 20+18
-4y = 38
Dividing both sides by -4
y = [tex]-\frac{38}{4}[/tex]
y = [tex]-\frac{19}{2}[/tex]
y = [tex]-9 \frac{1}{2}[/tex]
Answer:
19/-2
Step-by-step explanation:
the answer is referred in the picture with the working out. hope it was helpful
Any help would be great
Please help me !! ASAP!
Answer:
3√265
Step-by-step explanation:
The distance between the given points is √265. If all the side are the same length on an equilateral triangle, then the perimeter is 3 times as long.
SOMEONE PLEASE HELP ME ASAP PLEASE!!!
Answer:
plane
Step-by-step explanation:
Answer:
D. Plane
Step-by-step explanation:
A plane extends in two dimensions. This figure is a plane. It is not a point, a segment or a ray.
Find the area of a circle with radius, r = 59cm.
Give your answer rounded to 3 SF.
Answer:
3481π or 10935.884
Step-by-step explanation:
Area = πr^2
Area = 3481π or 10935.884
Diego planted a 8 inch tall magical beanstalk. The height of the beanstalk increases by 16% each day.Write a function ff that determines the height of the beanstalk in inches in terms of the number of days tt since Diego planted the beanstalk f(t)=f(1)/f(0)=f(2)/f(1)=f(5.28)/f(4.28)=For any value of x, what is the value of f(x+1)/f(x)?
Answer:
The expression for the height of the plant is: f(x) = 8*(1.16)^x;
The value of f(x+1)/f(x) is 1.16.
Step-by-step explanation:
Since Diego's beanstalk grows at an exponential rate of 16% per day, then the expression that represents the height of the plant, "f", in function of days, "x", can be found as shown below:
Initially the height of the plant was:
[tex]f(0) = 8[/tex]
After the first day however it was:
f(1) = 8*(1 + \frac{16}{100}) = 8*(1.16)
While after the second day:
f(2) = f(1)*(1.16) = 8*(1.16)*(1.16) = 8*(1.16)²
And so on, therefore the expression is:
f(x) = 8*(1.16)^x
The value of f(x + 1)/f(x) is:
[8*(1.16)^(x + 1)]/[8*(1.16)^x]
[8*(1.16)*(1.16)^(x)]/[8*(1.16)^x] = 1.16
A standard deck of cards contains 52 cards. One card is selected from the deck. (a) Compute the probability of randomly selecting a diamond or club. (b) Compute the probability of randomly selecting a diamond or club or heart. (c) Compute the probability of randomly selecting a three or club.
Answer:
Ok, in a deck of 52 cards we have:
13 clubs, 13 diamonds, 13 hearts, and 13 spades.
For this problem, we assume that the probability of selecting a card at random is the same for all the cards, so each card has a probability of 1/52 of being selected.
then the probability of drawing a given outcome, is equal to the number of times that the outcome appears in the deck divided the number of cards.
a) probability of randomly selecting a diamond or club.
in the 52 cards deck, we have 13 diamonds and 13 clubs, so the probability of drawing a diamond or a club is equal to:
P = (13 + 13)/52 = 26/52 = 0.5
b) Compute the probability of randomly selecting a diamond or club or heart.
Same reasoning as before, here we have 13 + 13 + 13 = 39 possible options, so the probability is:
p = 39/52 = 0.75.
c) Compute the probability of randomly selecting a three or club.
we have 13 club cards, and in the deck, each number appears 4 times, so we have 4 cards with a number 3 on them.
But one of those 3's is also a club card, so we already counted it in the 13 club cards, then the number of possible options here is:
13 + 4 - 1 = 13 +3 = 16
then the probability is:
p = 16/52 = 0.31
To solve the questions we must know the concept of Probability.
The probability of randomly selecting a diamond or club is 50%.The probability of randomly selecting a diamond or a club or heart is 75%The probability of randomly selecting a diamond or a club or heart is 30.77%.What is Probability?The probability helps us to know the chances of an event occurring.
[tex]\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
Explanations
(a) Compute the probability of randomly selecting a diamond or club.
Probability( Diamond or club)The number of diamond cards = 13
The number of club cards = 13
The total number of diamond and club cards = 26
[tex]\rm{Probability(Diamond\ or\ club)=\dfrac{Number\ of\ diamond\ or\ club\ cards}{Total\ Number\ of\ cards}[/tex]
[tex]\rm{Probability(Diamond\ or\ club)=\dfrac{26}{52}=\dfrac{1}{2} = 0.5 = 50\%[/tex]
(b) Compute the probability of randomly selecting a diamond or club or heart.
Probability( Diamond or club or heart)The number of diamond cards = 13
The number of club cards = 13
The number of heart cards = 13
The total number of diamond, heart, and club cards = 39
[tex]\rm{Probability(Diamond\ or\ club\ or\ hearts)=\dfrac{Number\ of\ diamond\ or\ club\ or\ hearts\ cards}{Total\ Number\ of\ cards}[/tex]
[tex]\rm{Probability(Diamond\ or\ club\ or\ hearts)=\dfrac{39}{52}=\dfrac{3}{4} = 0.75 = 75\%[/tex]
(c) Compute the probability of randomly selecting a three or club.
Probability( three or club)The number of three cards = 4
The number of club cards = 13
The total number of diamond and club cards = 13+4 - 1 =16
we reduced a card because card three of the club is calculated twice.
[tex]\rm{Probability(three\ or\ club)=\dfrac{Number\ of\ three\ or\ club\ cards}{Total\ Number\ of\ cards}[/tex]
[tex]\rm{Probability(three\ or\ club)=\dfrac{16}{52}=0.3077 = 30.77\%[/tex]
Learn more about Probability:
https://brainly.com/question/743546
Which statement about perfect cubes is true?
Answer:
1. it has different colors
is 614 divisible by both 2 and 6?
Answer:
No
Step-by-step explanation:
It is not divisible by 6, for if you divide by 6, you will get a non natural number,
It is obviously divisible by 2.
So, No.
Answer:
no
Step-by-step explanation:
only by 2
614/2 = 307
614/6 = 102.33