Answer:
5.05 rupees
Step-by-step explanation:
Convert 5 paisa to rupees
100 paisa = 1 rupees
5/100 = 0.05
5 + 0.05 = 5.05 rupees
An industrial psychologist conducted an experiment in which 40 employees that were identified as "chronically tardy" by their managers were divided into two groups of size 20. Group 1 participated in the new "It's Great to be Awake!" program, while Group 2 had their pay docked. The following data represent the number of minutes that employees in Group 1 were late for work after participating in the program.
Does the probability plot suggest that the sample was obtained from a population that is normally distributed? Provide TWO reasons for your classification.
Answer:
The probability plot of this distribution shows that it is approximately normally distributed..
Check explanation for the reasons.
Step-by-step explanation:
The complete question is attached to this solution provided.
From the cumulative probability plot for this question, we can see that the plot is almost linear with no points outside the band (the fat pencil test).
The cumulative probability plot for a normal distribution isn't normally linear. It's usually fairly S shaped. But, when the probability plot satisfies the fat pencil test, we can conclude that the distribution is approximately linear. This is the first proof that this distribution is approximately normal.
Also, the p-value for the plot was obtained to be 0.541.
For this question, we are trying to check the notmality of the distribution, hence, the null hypothesis would be that the distribution is normal and the alternative hypothesis would be that the distribution isn't normal.
The interpretation of p-valies is that
When the p-value is greater than the significance level, we fail to reject the null hypothesis (normal hypothesis) and but if the p-value is less than the significance level, we reject the null hypothesis (normal hypothesis).
For this distribution,
p-value = 0.541
Significance level = 0.05 (Evident from the plot)
Hence,
p-value > significance level
So, we fail to reject the null or normality hypothesis. Hence, we can conclude that this distribution is approximately normal.
Hope this Helps!!!
A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 58 cells. (a) Find the relative growth rate. (Assume t is measured in hours.) k = (b) Find an expression for the number of cells after t hours. P(t) = (c) Find the number of cells after 8 hours. cells (d) Find the rate of growth after 8 hours. (Round your answer to three decimal places.) billion cells per hour (e) When will the population reach 20,000 cells? (Round your answer to two decimal places.) hr
Answer:
a) k=2.08 1/hour
b) The exponential growth model can be written as:
[tex]P(t)=Ce^{kt}[/tex]
c) 977,435,644 cells
d) 2.033 billions cells per hour.
e) 2.81 hours.
Step-by-step explanation:
We have a model of exponential growth.
We know that the population duplicates every 20 minutes (t=0.33).
The initial population is P(t=0)=58.
The exponential growth model can be written as:
[tex]P(t)=Ce^{kt}[/tex]
For t=0, we have:
[tex]P(0)=Ce^0=C=58[/tex]
If we use the duplication time, we have:
[tex]P(t+0.33)=2P(t)\\\\58e^{k(t+0.33)}=2\cdot58e^{kt}\\\\e^{0.33k}=2\\\\0.33k=ln(2)\\\\k=ln(2)/0.33=2.08[/tex]
Then, we have the model as:
[tex]P(t)=58e^{2.08t}[/tex]
The relative growth rate (RGR) is defined, if P is the population and t the time, as:
[tex]RGR=\dfrac{1}{P}\dfrac{dP}{dt}=k[/tex]
In this case, the RGR is k=2.08 1/h.
After 8 hours, we will have:
[tex]P(8)=58e^{2.08\cdot8}=58e^{16.64}=58\cdot 16,852,338= 977,435,644[/tex]
The rate of growth can be calculated as dP/dt and is:
[tex]dP/dt=58[2.08\cdot e^{2.08t}]=120.64e^2.08t=2.08P(t)[/tex]
For t=8, the rate of growth is:
[tex]dP/dt(8)=2.08P(8)=2.08\cdot 977,435,644 = 2,033,066,140[/tex]
(2.033 billions cells per hour).
We can calculate when the population will reach 20,000 cells as:
[tex]P(t)=20,000\\\\58e^{2.08t}=20,000\\\\e^{2.08t}=20,000/58\approx344.827\\\\2.08t=ln(344.827)\approx5.843\\\\t=5.843/2.08\approx2.81[/tex]
Suppose you just purchased a digital music player and have put 12 tracks on it. After listening to them you decide that you like 2 of the songs. With the random feature on your player, each of the 12 songs is played once in random order. Find the probability that among the first two songs played (a) You like both of them. Would this be unusual? (b) You like neither of them. (c) You like exactly one of them. (d) Redo (a)-(c) if a song can be replayed before all 12 songs are played.
Answer:
The answer is below
Step-by-step explanation:
We have the following information:
Number of songs you like = 2
Total number of songs = 12
a) P(you like both of them) = 2/12 x 1/11 = 0.015
This is unusual because the probability of the event is less than 0.05
b) P(you like neither of them) = 10/12 x 9/11 = 0.68
c) P(you like exactly one of them) = 2 x 2/12 x 10/11 = 0.30
d) If a song can be replayed before all 12,
P(you like both of them) = 2/12 x 2/12 =0.027
This is unusual because the probability of the event is less than 0.05
P(you like neither of them) = 9/12 x 9/12 = 0.5625
P(you like exactly one of them) = 2 x 2/12 x 9/12 = 0.25
compute the missing data in the table for the following exponential function f(x)={1/4}
Answer:
1/256
Step-by-step explanation:
The table shows a chain of fractions for f(x), x1 is 1/4, x2 is 1/16 and x3 is 1/64. All you need to do is multiply the denominator by 4 and put 1 over it. 64*4 = 256, adding the 1 as the numerator gives us the answer of 1/256 as x4.
Find the perimeter of the rhombus below, given that a=9 and b=15. Round your answer to one decimal place, if necessary.
Answer: 35.0 units long.
Step-by-step explanation:
You can treat a rhombus as four right triangles, where there is a short side, a long side, and a hypotenuse.
The hypotenuse of a right triangle inside a rhombus will always be on the exterior.
To find the hypotenuse of one of the right triangles, use the Pythagorean theorem:
[tex]a^2 + b^2 = c^2[/tex]
We are given that a = 9 and b = 15, but in order to get the values needed for the theorem, we must divide them by 2 in order to get the sides for the triangles.
9 / 2 = 4.5, 15 / 2 = 7.5
Then, you can substitute your values into the Pythagorean theorem:
[tex]4.5^2 + 7.5^2 = c^2\\\\20.25 + 56.25 = 76.5\\\\c^2 = 76.5\\c = 8.7464[/tex]
Knowing that one of the external sides is 8.7464 units long, you can then multiply that value by 4 to get your perimeter, as there are four identical sides forming the perimeter:
8.7464 * 4 = 34.9856. Rounded: 35.0
Two balls are drawn in succession out of a box containing 2 red and 5 white balls. Find the probability that at least 1 ball was red, given that the first ball was (Upper A )Replaced before the second draw. (Upper B )Not replaced before the second draw.
Answer:
With replacement = 14/49without replacement = 3/7Step-by-step explanation:
Since there are 2 red and 5 white balls in the box, the total number of balls in the bag = 2+5 = 7balls.
Probability that at least 1 ball was red, given that the first ball was replaced before the second can be calculated as shown;
Since at least 1 ball picked at random, was red, this means the selection can either be a red ball first then a white ball or two red balls.
Probability of selecting a red ball first then a white ball with replacement = (2/7*5/7) = 10/49
Probability of selecting two red balls with replacement = 2/7*2/7 = 4/49
The probability that at least 1 ball was red given that the first ball was replaced before the second draw= 10/49+4/49 = 14/49
If the balls were not replaced before the second draw
Probability of selecting a red ball first then a white ball without replacement = (2/7*5/6) = 10/42 = 5/21
Probability of selecting two red balls without replacement = 2/7*2/6 = 4/42 = 2/21
The probability that at least 1 ball was red given that the first ball was not replaced before the second draw = 5/21+4/21 = 9/21 = 3/7
The probability that at least 1 ball was red, given that the first ball was replaced before the second draw is 28.5%; and the probability that at least 1 ball was red, given that the first ball was not replaced before the second draw is 22.5%.
Since two balls are drawn in succession out of a box containing 2 red and 5 white balls, to find the probability that at least 1 ball was red, given that the first ball was A) replaced before the second draw; and B) not replaced before the second draw; the following calculations must be performed:
2 + 5 = X7 = X
(2/7 + 2/7) / 2 = X (0.285 + 0.285) / 2 = X 0.285 = X
(2/7 + 1/6) / 2 = X (0.28 + 0.16) / 2 = X 0.451 / 2 = X 0.225 = X
Therefore, the probability that at least 1 ball was red, given that the first ball was replaced before the second draw is 28.5%; and the probability that at least 1 ball was red, given that the first ball was not replaced before the second draw is 22.5%.
Learn more about probability in https://brainly.com/question/14393430
PLEASE HELP!
Fill in the reason for statement 3 in proof below:
SAS
AA
SSS
Answer:
SAS
Step-by-step explanation:
ΔABD ~ ΔECD is similar through:
S - because ED = CD (Given)
A - same angle ∠D (Statement 2)
S - because AD = BD (Given)
Cheers!
Answer:
SAS
Step-by-step explanation:
You can notice that you have ED/AB = CD/BD You have one common angleAlexandra has $15 to buy drinks for her friends at the baseball game. Soda
costs $2.75 and bottled water costs $2.00. This relationship can be
represented by the inequality 2758+2w $ 15. Three of Alexandra's friends
asked for water. Which inequality represents the number of sodas she can
buy?
A. OS 85 3.27
B. 85 3.27
C. OSSS3
D. 853
Answer:
C
Step-by-step explanation:
write an equation for the costs:
if x is the number of sodas
and y is the number of waters
2.75x + 2y <= 15
(<= is less than or equal to)
if we substitute 3 for y
we get 2.75x + 2(3) <= 15
2.75x + 6 <= 15
2.75x <= 9
9 / 2.75 = 3.2727
however, you cannot buy part of a soda
so, round to 3
you also cannot buy negative sodas
so, the answer is C
The National Safety Council (NSC) estimates that off-the-job accidents cost U.S. businesses almost $200 billion annually in lost productivity (National Safety Council, March 2006). Based on NSC estimates, companies with 50 employees are expected to average three employee off-the-job accidents per year. Answer the following questions for companies with 50 employees.a. What is the probability of no off-the-job accidents during a one-year period (to 4 decimals)?b. What is the probability of at least two off-the-job accidents during a one-year period (to 4 decimals)?c. What is the expected number of off-the-job accidents during six months (to 1 decimal)?d. What is the probability of no off-the-job accidents during the next six months (to 4 decimals)?
Answer:
a. 0.0498 = 4.98% probability of no off-the-job accidents during a one-year period
b. 0.8008 = 80.08% probability of at least two off-the-job accidents during a one-year period.
c. The expected number of off-the-job accidents during six months is 1.5.
d. 0.2231 = 22.31% probability of no off-the-job accidents during the next six months.
Step-by-step explanation:
We have the mean during a period, so we use the Poisson distribution.
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
Companies with 50 employees are expected to average three employee off-the-job accidents per year.
This means that [tex]\mu = 3n[/tex], in which n is the number of years.
a. What is the probability of no off-the-job accidents during a one-year period (to 4 decimals)?
This is [tex]P(X = 0)[/tex] when [tex]\mu = 3*1 = 3[/tex]. So
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0498[/tex]
0.0498 = 4.98% probability of no off-the-job accidents during a one-year period.
b. What is the probability of at least two off-the-job accidents during a one-year period (to 4 decimals)?
Either there are less than two accidents, or there are at least two. The sum of the probabilities of these events is 1. So
[tex]P(X < 2) + P(X \geq 2) = 1[/tex]
We want [tex]P(X \geq 2)[/tex]. Then
[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]
In which
[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]
[tex]P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0498[/tex]
[tex]P(X = 1) = \frac{e^{-3}*3^{1}}{(1)!} = 0.1494[/tex]
[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.0498 + 0.1494 = 0.1992[/tex]
[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.1992 = 0.8008[/tex]
0.8008 = 80.08% probability of at least two off-the-job accidents during a one-year period.
c. What is the expected number of off-the-job accidents during six months (to 1 decimal)?
6 months is half a year, so [tex]n = 0.5[/tex]
[tex]\mu = 3n = 3*0.5 = 1.5[/tex]
The expected number of off-the-job accidents during six months is 1.5.
d. What is the probability of no off-the-job accidents during the next six months (to 4 decimals)?
This is P(X = 0) when [tex]\mu = 1.5[/tex]. So
[tex]P(X = 0) = \frac{e^{-1.5}*1.5^{0}}{(0)!} = 0.2231[/tex]
0.2231 = 22.31% probability of no off-the-job accidents during the next six months.
In a particular year, the mean score on the ACT test was 19.6 and the standard deviation was 5.2. The mean score on the SAT mathematics test was 546 and the standard deviation was 126. The distributions of both scores were approximately bell-shaped. Round the answers to at least two decimal placesFind the z-score for an ACT score of 26. The Z-score for an ACT score of 26 is ______ .
Answer:
0.11
Step-by-step explanation:
Let the random variable score, X = 26; mean, ∪ = 19.6; standard deviation, α = 5.2
By comparing P(0≤ Z ≤ 26)
P(Z ≤ X - ∪/α) = P(Z ≤ 26 - 19.6/5.2)
= P(Z ≤ 1.231)
Using Table: P(0 ≤ Z ≤ 1) = 0.39
P(Z > 1) = (0.5 - 0.39) = 0.11
∴ P(Z > 26) = 0.11
Will anyone help me with geometry ASAP!? Please!? In desperate help!!!
Answer:
14. C 41
15. k = 72
Step-by-step explanation:
14.
For parallel lines, alternate exterior angles must be congruent.
3x - 43 = 80
3x = 123
x = 41
15.
The sum of the measures of the angles of a triangle is 180 deg.
k + 33 + 75 = 180
k + 108 = 180
k = 72
Answer:
1. 32
2. 41
3. 72
Step-by-step explanation:
Brainliest for the correct awnser!!!!! Which of the following is the product of the rational expressions shown below?
Answer:
A.
Step-by-step explanation:
Multiply straight across:
[tex]\frac{2}{x+1}\cdot \frac{5}{3x}=\frac{10}{3x(x+1)}[/tex]
Simplify:
[tex]=\frac{10}{3x^2+3x}[/tex]
This cannot be simplified further.
Answer:
[tex] \boxed{\sf \frac{10}{3 {x}^{2} + 3x}} [/tex]
Step-by-step explanation:
[tex] \sf Expand \: the \: following: \\ \sf \implies \frac{2}{x + 1} \times \frac{5}{3x} \\ \\ \sf \implies \frac{2 \times 5}{3x(x + 1)} \\ \\ \sf 2 \times 5 = 10 : \\ \sf \implies \frac{ \boxed{ \sf 10}}{3x(x + 1)} \\ \\ \sf 3x(x + 1) = (3x)(x) + (3x)(1) : \\ \sf \implies \frac{10}{ \boxed{ \sf (3x)(x) + (3x)(1)}} \\ \\ \sf (3x)(x) = 3 {x}^{2} : \\ \sf \implies \frac{10}{ \boxed{ \sf 3 {x}^{2}} + (3x)(1) } \\ \\ \sf (3x)(1) = 3x : \\ \sf \implies \frac{10}{3 {x}^{2} + 3x} [/tex]
The length of a rectangle is 5M more than twice the width and the area of the rectangle is 63M to find the dimension of the rectangle
Answer:
width = 4.5 m
length = 14 m
Step-by-step explanation:
okay so first you right down that L = 5 + 2w
then as you know that Area = length * width so you replace the length with 5 + 2w
so it's A = (5 +2w) * w = 63
then 2 w^2 + 5w - 63 =0
so we solve for w which equals 4.5 after that you solve for length : 5+ 2*4.5 = 14
Select the correct answer.
If two angles of a triangle have equal measures and the third angle measures 90º, what are the angle measures of the triangle?
ОА.
60°, 60°, 60°
OB.
459,909, 90°
Ос.
30°, 30°, 90°
OD.
45°, 45°, 90°
Answer:
OD. 45,45,90
Step-by-step explanation:
how many types of progression in mathematics?
HELP !!!..... ASAP PLS
Step-by-step explanation:
the average change H = Δy/ Δx
so H = ( f(4) - f(2) )/ (4 -2) = ( 0 -1 ) / 2 = -1/2
A professor would like to test the hypothesis that the average number of minutes that a student needs to complete a statistics exam has a standard deviation that is less than 5.0 minutes. A random sample of 15 students was selected and the sample standard deviation for the time needed to complete the exam was found to be 4.0 minutes. Using α = 0.05, the conclusion for this hypothesis test would be that because the test statistic is
Answer:
[tex]\chi^2 =\frac{15-1}{25} 16 =8.96[/tex]
The degrees of freedom are given by:
[tex] df = n-1 = 15-1=14[/tex]
The p value for this case would be given by:
[tex]p_v =P(\chi^2 <8.96)=0.166[/tex]
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true deviation is not ignificantly lower than 5 minutes
Step-by-step explanation:
Information given
[tex]n=15[/tex] represent the sample size
[tex]\alpha=0.05[/tex] represent the confidence level
[tex]s^2 =16 [/tex] represent the sample variance
[tex]\sigma^2_0 =25[/tex] represent the value that we want to verify
System of hypothesis
We want to test if the true deviation for this case is lesss than 5minutes, so the system of hypothesis would be:
Null Hypothesis: [tex]\sigma^2 \geq 25[/tex]
Alternative hypothesis: [tex]\sigma^2 <25[/tex]
The statistic is given by:
[tex]\chi^2 =\frac{n-1}{\sigma^2_0} s^2[/tex]
And replacing we got:
[tex]\chi^2 =\frac{15-1}{25} 16 =8.96[/tex]
The degrees of freedom are given by:
[tex] df = n-1 = 15-1=14[/tex]
The p value for this case would be given by:
[tex]p_v =P(\chi^2 <8.96)=0.166[/tex]
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true deviation is not ignificantly lower than 5 minutes
Identify the segments that are parallel, if any, if ∠ADH≅∠ECK
Answer:
DF and CG
Step-by-step explanation:
Two or more segments are said to be parallel is the angle between them is [tex]180^{0}[/tex]. While two segments are said to be perpendicular when the angle between them is [tex]90^{0}[/tex].
The given figure is a parallelogram. A parallelogram is a quadrilateral with a pair of parallel opposite sides.
In the given question if ∠ADH ≅ ∠ECK , then the parallel segment would be DF and CG.
Given the following functions, evaluate each of the following
Answer:
[tex](f+g)(5) = 40\\(f-g)(5) = 22\\(f*g)(5) = 279[/tex]
[tex](f/g)(5) = 31/9[/tex]
Step-by-step explanation:
[tex]f(5) = (5)^2+2(5)-4\\f(5) = 25+10-4\\f(5) = 31[/tex]
[tex]g(5) = 5+4\\g(5) = 9[/tex]
[tex](f+g)(5) = 31+9\\(f+g)(5) = 40[/tex]
[tex](f-g)(5) = 31-9\\(f-g)(5) = 22[/tex]
[tex](f*g)(5) = 31*9\\(f*g)(5) = 279\\[/tex]
[tex](f/g)(5) = 31/9[/tex]
At her favorite sneakers store Nyeema saved $48 because of a
sale.
If the sneakers normally cost $120. How much did she save?
Answer:
40%
Step-by-step explanation:
We can find what percent 48 is of 120 by dividing:
48/120 = 0.4 or 40%
So, she saved 40% from the original price.
Which set of numbers can represent the lengths of the sides of a triangle? A. {1,2,3} B. {3,5,7} C. {3,9,14} D. {4,4,8}
The set of numbers that can represent the lengths of the sides of a triangle are 3,5,7. That is option B.
What is a triangle?Triangle is defined as a type of polygon that has three sides in which the sum of both sides is greater than the third side.
That is to say, 3+5 = 8 is greater than the third side which is 7.
Therefore, the set of numbers the would represent a triangle are 3,5,7.
Learn more about triangle here:
https://brainly.com/question/17335144
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how many are 4 x 4 ?
16, think of 4 plus 4 plus 4 plus 4.
which equation represents the graph function?
Answer:
[tex]\displaystyle y=-\frac{1}{3}x+3[/tex]
Step-by-step explanation:
First, notice that since the graph of the function is a line, we have a linear function.
To find the equations for linear functions, we need the slope and the y-intercept. Recall the slope-intercept form:
[tex]y=mx+b[/tex]
Where m is the slope and b is the y-intercept.
We are given the point (0,3) which is the y-intercept. Thus, b = 3.
To find the slope, we can use the slope formula:
[tex]\displaystyle m=\frac{\Delta y}{\Delta x} =\frac{2-3}{3-0}=-1/3[/tex]
Therefore, our equation is:
[tex]\displaystyle y=-\frac{1}{3}x+3[/tex]
In a race, Brian Collins has to cross 10 hurdles. The probability that he clears a hurdle is 2/3. Find P(clears all hurdles).
Answer:
1024/59049
Step-by-step explanation:
P( clear hurdle) = 2/3
There are 10 hurdles
P ( clear all hurdles) = P( clear hurdle) * P( clear hurdle)...... 10 times
= 2/3 * 2/3 *....... 10 times
= (2/3) ^ 10
=1024/59049
Answer:
1024/59049, 1.7%
Step-by-step explanation:
One way to do it would to be simply multiply 2/3 by itself 10 times
2/3 x 2/3 x 2/3 x 2/3 and so on
That would be a really long equation so instead we can use exponents to shorten it. We can simply just do 2^10/3^10
2^10=1024
3^10=59049
1024/59049, 1.7%
15% as a fraction in its lowest terms is:
-3/20
-5/100
-1/15
-3/100
Answer:
3/20
Step-by-step explanation:
15%
15/100
/5 /5
3/20
Fake Question: Should Sekkrit be a moderator? (answer if you can) Real Question: Solve for x. [tex]x^2+3x=-2[/tex]
Answer:
x = -2 , -1
Step-by-step explanation:
Set the equation equal to 0. Add 2 to both sides:
x² + 3x = -2
x² + 3x (+2) = - 2 (+2)
x² + 3x + 2 = 0
Simplify. Find factors of x² and 2 that will give 3x when combined:
x² + 3x + 2 = 0
x 2
x 1
(x + 2)(x + 1) = 0
Set each parenthesis equal to 0. Isolate the variable, x. Note that what you do to one side of the equation, you do to the other.
(x + 2) = 0
x + 2 (-2) = 0 (-2)
x = 0 - 2
x = -2
(x + 1) = 0
x + 1 (-1) = 0 (-1)
x = 0 - 1
x = -1
x = -2 , -1
~
Answer:
x = -2 OR x = -1
Step-by-step explanation:
=> [tex]x^2+3x = -2[/tex]
Adding 2 to both sides
=> [tex]x^2+3x+2 = 0[/tex]
Using mid-term break formula
=> [tex]x^2+x+2x+2 = 0[/tex]
=> x(x+1)+2(x+1) = 0
=> (x+2)(x+1) = 0
Either:
x+2 = 0 OR x+1 = 0
x = -2 OR x = -1
P.S. Ummmm maybe...... Because he usually reports absurd answers! So, Won't it be better that he could directly delete it. And one more thing! He's Online 24/7!!!!!
Which of the following graphs is described by the function given below?
y = 2x^2 + 8x + 3
Answer:
Option A
Step-by-step explanation:
Equation of the given quadratic function is,
y = 2x² + 8x + 3
y = 2(x² + 4x) + 3
= 2(x² + 4x + 4 - 4) + 3
= 2(x + 2)² - 8 + 3
= 2(x + 2)² - 5
By comparing this equation with the equation of a quadratic function in vertex form,
y = a(x - h)² + k
Here (h, k) is the vertex of the parabola
Vertex of the given equation will be (-2, -5) and coefficient 'a' is positive (a > 0)
Therefore, vertex will lie in the 3rd quadrant and the parabola will open upwards.
Option (A). Graph A will be the answer.
Which value of x makes 7+5(x-3)=227+5(x−3)=227, plus, 5, left parenthesis, x, minus, 3, right parenthesis, equals, 22 a true statement? Choose 1 answer:
Answer:
7 + 5(x - 3) = 22
5(x - 3) = 15
x - 3 = 3
x = 6
Answer:
x = 6
Step-by-step explanation:
Step 1: Distribute 5
7 + 5x - 15 = 22
Step 2: Combine like terms
5x - 8 = 22
Step 3: Add 8 to both sides
5x = 30
Step 4: Divide both sides by 5
x = 6
Suppose 150 students are randomly sampled from a population of college students. Among sampled students, the average IQ score is 115 with a standard deviation of 10. What is the 99% confidence interval for the average IQ of college students? Possible Answers: 1) A) E =1.21 B) E = 1.25 C) E =2.52 D) E = 2.11 2) A) 112.48 < μ < 117.52 B) 113.79 < μ < 116.21 C) 112.9 < μ < 117.10 D) 113.75 < μ < 116.3
Answer:
99% confidence interval for the mean of college students
A) 112.48 < μ < 117.52
Step-by-step explanation:
step(i):-
Given sample size 'n' =150
mean of the sample = 115
Standard deviation of the sample = 10
99% confidence interval for the mean of college students are determined by
[tex](x^{-} -t_{0.01} \frac{S}{\sqrt{n} } , x^{-} + t_{0.01} \frac{S}{\sqrt{n} } )[/tex]
Step(ii):-
Degrees of freedom
ν = n-1 = 150-1 =149
t₁₄₉,₀.₀₁ = 2.8494
99% confidence interval for the mean of college students are determined by
[tex](115 -2.8494 \frac{10}{\sqrt{150} } , 115 + 2.8494\frac{10}{\sqrt{150} } )[/tex]
on calculation , we get
(115 - 2.326 , 115 +2.326 )
(112.67 , 117.326)
¿Cuál serie numérica tiene como regla general Xn = 2n +1?
a. 3, 5, 7, 9
b. 2, 4, 5, 8
c. 4, 6, 8,10
d. 2, 3, 4, 5
Answer:
The series of numbers that correspond to the general rule of [tex]X_n=2n+1[/tex] is {3, 5, 7, 9}.
Step-by-step explanation:
We are given with the following series options below;
a. 3, 5, 7, 9
b. 2, 4, 5, 8
c. 4, 6, 8,10
d. 2, 3, 4, 5
And we have to identify what number series has a general rule as [tex]X_n=2n+1[/tex].
For this, we will put the values of n in the above expression and then will see which series is obtained as a result.
So, the given expression is ; [tex]X_n=2n+1[/tex]
If we put n = 1, then;
[tex]X_1=(2\times 1)+1[/tex]
[tex]X_1 = 2+1 = 3[/tex]
If we put n = 2, then;
[tex]X_2=(2\times 2)+1[/tex]
[tex]X_2 = 4+1 = 5[/tex]
If we put n = 3, then;
[tex]X_3=(2\times 3)+1[/tex]
[tex]X_3 = 6+1 = 7[/tex]
If we put n = 4, then;
[tex]X_4=(2\times 4)+1[/tex]
[tex]X_4 = 8+1 = 9[/tex]
Hence, the series of numbers that correspond to the general rule of [tex]X_n=2n+1[/tex] is {3, 5, 7, 9}.