Answer:
Step-by-step explanation:
Let x be the random variable representing the SAT scores for the students at a local high school. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = standard deviation
From the information given,
µ = 1527
σ = 291
the probability to be determined is expressed as P(x > 1207)
P(x > 1207) = 1 - P(x ≤ 1207)
For x < 1208
z = (1207 - 1527)/291 = - 1.1
Looking at the normal distribution table, the probability corresponding to the z score is 0.16
P(x > 1207) = 1 - 0.16 = 0.84
Therefore, the percentage of students from this school earn scores that satisfy the admission requirement is
0.84 × 100 = 84%
14 fewer than 12 times the
number of people in my
family is 46.
Answer:
538
Step-by-step explanation:
12 times 46 is 552 then 552 minus 14 is 538
:D
An article suggests the uniform distribution on the interval (6.5, 19) as a model for depth (cm) of the bioturbation layer in sediment in a certain region.(a) What are the mean and variance of depth
Answer:
The mean of depth is 12.75cm.
The variance of depth is of 13.02 cm².
Step-by-step explanation:
An uniform probability is a case of probability in which each outcome is equally as likely.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The mean of the uniform distribution is:
[tex]M = \frac{a+b}{2}[/tex]
The variance of the uniform distribution is given by:
[tex]V = \frac{(b-a)^{2}}{12}[/tex]
Uniform distribution on the interval (6.5, 19)
This means that: [tex]a = 6.5, b = 19[/tex]
So
Mean:
[tex]M = \frac{6.5+19}{2} = 12.75[/tex]
The mean of depth is 12.75cm.
Variance:
[tex]V = \frac{(19 - 6.5)^{2}}{12} = 13.02[/tex]
The variance of depth is of 13.02 cm².
4. The 92 million Americans of age 50 and over control 50% of all discretionary income. AARP estimates that the average annual expenditure on restaurants and carryout food was $1,873 for individuals in the age group. Suppose this estimate is based on a sample of 80 persons and that the sample standard deviation is $550. a. At 95% confidence, what is the margin of error
Answer:
$120.52
Margin of error M.E = $120.52
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.
x+/-zr/√n
x+/-M.E
Where M.E = margin of error
M.E = zr/√n
Given that;
Mean x = $1,873
Standard deviation r = $550
Number of samples n = 80
Confidence interval = 95%
z(at 95% confidence) = 1.96
Substituting the values we have;
M.E = (1.96 × $550/√80) = 120.5240639872
M.E = $120.52
Margin of error M.E = $120.52
Please answer this correctly
Answer:
There are 5 number of temperature readings.
Step-by-step explanation:
9, 7, 9, 10, 9
5 readings recorded in the range of 6-10°C.
Please answer this correctly
Answer:
Chicken: 36%
Beef: 34%
Black Bean: 30%
Hope this helps!
which of the following describes the zeroes of the graph of f(x)= -x^5+9x^4-18x^3
Answer:
[tex]-x^5+9x^4-18x^3=0\\-x^3(x^2-9x+18)=0\\-x^3(x-3)(x-6)=0\\\\\\\\x=0\\x=3\\x=6[/tex]
Help me solve the equivalent expression (4x+2)-3x+5
Answer:
X+7
Step-by-step explanation:
Remove the parentheses:
4x+2-3x+5
Collect like terms:
4x-3x=x
2+5=7
Solution:
X+7
Hey there!
(4x + 2) - 3x + 5
= 4x + 2 - 3x + 5
COMBINE the LIKE TERMS
= (4x - 3x) + (2 + 5)
= 4x - 3x + 2 + 5
= 1x + 7
= x + 7
Therefore, your answer is: x + 7
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
In a randomly selected sample of 500 Phoenix residents, 445 supported mandatory sick leave for food handlers. Legislators want to be very confident that voters will support this issue before drafting a bill. What is the 99% confidence interval for the percentage of Phoenix residents who support mandatory sick leave for food handlers?
Answer:
The 99% confidence interval for the percentage of Phoenix residents who support mandatory sick leave for food handlers is between 85.40% and 92.60%.
Step-by-step explanation:
Confidence interval for the proportion:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 500, \pi = \frac{445}{500} = 0.89[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.89 - 2.575\sqrt{\frac{0.89*0.11}{500}} = 0.8540[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.89 + 2.575\sqrt{\frac{0.89*0.11}{500}} = 0.9260[/tex]
For the percentage:
Multiply the proportion by 100.
0.8540*100 = 85.40%
0.9260*100 = 92.60%
The 99% confidence interval for the percentage of Phoenix residents who support mandatory sick leave for food handlers is between 85.40% and 92.60%.
John conducted a taste test on a new brand of French fries. He gave each participant 5 of the new brand of fries and 5 of the old brand of fries and asked them to rate which brand they preferred. The participants rated both brands of fries as equally preferable. Based on this, he recommended to the manufacturer to move ahead with producing this new brand. However, the brand did not sell well. People reported feeling nauseous after they had consumed a whole portion.
Which validity is weak in this example?
a. internal validity
b. external validity
c. statistical validity
d. construct validity
Answer:
b. external validity
Step-by-step explanation:
External Validity is the applicability of the results of an experiment to the real world. Most times, there are threats to the validity of an experiment which could result in little or no effect on the general population. For example, if the method of selection reflects a measure of bias, then this could affect the result. Also if the participants are taking different aspects of the same test, it could also affect its validity as they may not be able to make a correct conclusion. If the sample size is not reflective of the entire population, it could also pose a threat to the validity of the experiment.
John's experiment is weak in its external validity because it cannot be generalized to the entire population of customers. He has to identify the threats to the validity of his experiment and correct them. For example, the sample selection may be biased.
Find the midpoint of (9,2) and (-7,-9)
Answer:
(1,-7/2)
Step-by-step explanation:
The midpoint of (9,2)(-7,-9) is (1,-7/2)
Solve (x - 3)2 = 49. Select the values of x.
52
DONE
Answer:
Step-by-step explanation:
[tex](x-3)^2=49[/tex]
<=>
[tex](x-3)^2-49=0\\\\<=> (x-3)^2-7^2=0\\\\<=> (x-3-7)(x-3+7)=0\\<=> (x-10)(x+4)=0\\<=> x -10=0\ or \ x+4=0\\<=> x = 10 \ or\ x = -4[/tex]
solutions are -4 and 10
do not hesitate if you need further explanation
if you like my answer, tag it as the brainliest :-)
A 40-foot ladder leans against a building. If
the base of the ladder is 6 feet from the
base of the building, what is the angle
formed by the ladder and the building?
Answer:
Step-by-step explanation:
draw it out and use trig function to solve for the angle. Keep in mind, after getting trig, need to do inverse
What is the probability that a senior Physics major and then a sophomore Physics major are chosen at random? Express your answer as a fraction or a decimal number rounded to four decimal places
Answer:
The probability that a senior Physics major and then a sophomore Physics major are chosen at random is 0.0095.
Step-by-step explanation:
The complete question is:
There are 103 students in a physics class. The instructor must choose two students at random.
Students in a Physics Class
Academic Year Physics majors Non-Physics majors
Freshmen 17 15
Sophomores 20 14
Juniors 11 17
Seniors 5 4
What is the probability that a senior Physics major and then a sophomore Physics major are chosen at random? Express your answer as a fraction or a decimal number rounded to four decimal places.
Solution:
There are a total of N = 103 students present in a Physics class.
Some of the students are Physics Major and some are not.
The instructor has to select two students at random.
The instructor first selects a senior Physics major and then a sophomore Physics major.
Compute the probability of selecting a senior Physics major student as follows:
[tex]P(\text{Senior Physics Major})=\frac{n(\text{Senior Physics Major}) }{N}[/tex]
[tex]=\frac{5}{103}\\\\=0.04854369\\\\\approx 0.0485[/tex]
Now he two students are selected without replacement.
So, after selecting a senior Physics major student there are 102 students remaining in the class.
Compute the probability of selecting a sophomore Physics major student as follows:
[tex]P(\text{Sophomore Physics Major})=\frac{n(\text{Sophomore Physics Major}) }{N}[/tex]
[tex]=\frac{20}{102}\\\\=0.1960784314\\\\\approx 0.1961[/tex]
Compute the probability that a senior Physics major and then a sophomore Physics major are chosen at random as follows:
[tex]P(\text{Senior}\cap \text{Sophomore})=P(\text{Senior})\times P(\text{Sophomore})[/tex]
[tex]=0.0485\times 0.1961\\\\=0.00951085\\\\\approx 0.0095[/tex]
Thus, the probability that a senior Physics major and then a sophomore Physics major are chosen at random is 0.0095.
If the mean of 5 positive integers is 15, what is the maximum possible difference between the largest and the smallest of these 5 numbers?
Answer:
The maximum possible difference between the largest and the smallest of these 5 numbers is 65( if numbers aren't repeated )
In each of the following situations, data are obtained by conducting a research study. Classify each Experimental or Correlational.
Research Study
1. A researcher is interested in whether listening to different types of music or no music while taking a test affects test scores. Students are randomly assigned to one of three groups: The first group takes a test without listening to an iPod, the second group takes the same test while listening to classical music on an iPod, and the third group takes the test while listening to rock music on an iPod. The researcher compares the test scores across the three groups.
2. A psychologist is interested in gender and cognition. She collects data on a large sample of siblings, recording their gender, birth order, and IQ.
3. A professor of ophthalmology is interested in developmental precursors of vision disorders. He collects data from a sample of teenagers on right-eye vision, left-eye vision, and whether the bedroom light was kept off or on as they slept during the night as babies.
Answer:
1. Experimental
2. Correlational
3. Experimental.
Step-by-step explanation:
1. Experimental.
Researches are interested on finding the effects of music on a test.
2. Correlational
Researchers are interested on finding the correlation of the gender and cognition from different samples
3. Experimental
The Researcher wants to know the effects of bedroom light.
A potter made 4080 diyas in the month of September. If he made the same number of diyas each day, how many diyas did he make in a week?
What is the answer for this one ?
4x+3y=20 2x+y=7
Answer:
x = 1/2 , y = 6
Explanation:
Step 1 - Align the equations and multiply the second row by 2
4x + 3y = 20
2x + y = 7
4x + 3y = 20
4x + 2y = 14
Step 2 - Subtract them both
4x + 3y = 20
4x + 2y = 14
y = 6
So, y = 6
Step 3 - Substitute y into the first equation
4x + 3y = 20
4x + 3(6) = 20
4x + 18 = 20
Step 4 - Subtract 18 from both sides
4x + 18 = 20
4x + 18 - 18 = 20 - 18
4x = 2
Step 5 - Divide both sides by 4
4x = 2
4x / 4 = 2 / 4
x = 2/4
So, x = 1/2
A garden bed contains 8 tomato plants, 4 squash plants and 8 bell pepper plants. What percentage of the plants are tomato plants
Answer:
33.33%
Step-by-step explanation:
Add them together 8 plus 8 plus 8 which is 24 there are 8 tp so its 8/24 which is equal to 1/3 so the percent is
find the equivalent expression using the same bases. (21 x15)9
Answer:
2835
Step-by-step explanation:
(21×15)9=
(315)9=
2835
how many legs totally do five horses, two people,three children and five dogs have
find the vector reciprocal to set. a= i+2j+2k, b= 2i+3j+k, c= i-j-2k
Answer:
I just do a' as a sample. You calculate b' and c'
Step-by-step explanation:
[tex]a'=\frac{b\times c}{a\bullet (b\times c)}, b' = \frac{c\times a}{a\bullet (b\times c)}, c' = \frac{a\times b}{a\bullet (b\times c)}[/tex]
Now, calculate b x c
[tex]\left[\begin{array}{ccc}i&j&k\\2&3&1\\1&-1&-2\end{array}\right] =<-5, 5,-5>[/tex]
[tex]a'=\frac{<-5,5,-5>}{<1, 2, 2>\bullet <-5, 5,-5>}=\frac{<-5, 5, -5>}{-5} =<1,-1,1>[/tex]
5×100+4×10+6×1+2×(110)+8×(11000)
What is the number written in standard form?
Answer: 8.059
Explanation: It's the digit times the column heading.
The first few steps in solving the quadratic equation 9x2 + 49x = 22 − 5x by completing the square are shown. 9x2 + 49x = 22 − 5x 9x2 + 54x = 22 9(x2 + 6x) = 22 Which is the best step to do next to solve the equation by completing the square? 9(x2 + 6x + 3) = 25 9(x2 + 6x + 3) = 49 9(x2 + 6x + 9) = 31 9(x2 + 6x + 9) = 103
Answer:
The Answer is : 9(x2 + 6x + 9) = 103
Step-by-step explanation:
Option D on edge2020 i got a 100 on the quiz
The resulting quadratic equation is [tex](x+3)^2-103/9=0[/tex]
Quadratic equationGiven the quadratic equation [tex]9x^2 + 49x = 22 - 5x[/tex]
Write in standard form:
[tex]9x^2 + 49x = 22 - 5x\\ 9x^2 + 49x + 5x -22= 0\\ 9x^2+54x-22=0[/tex]
Divide through by 9
[tex]x^2+6x-22/9=0\\ [/tex]
complete the square to have:
[tex]x^2+6x-22/9+3^2-3^2=0\\ x^2+6x+3^2-9-22/9 = 0\\ (x+3)^2-103/9=0[/tex]
Hence the resulting quadratic equation is [tex](x+3)^2-103/9=0[/tex]
Learn more on completing the square here: https://brainly.com/question/1596209
In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students from the university was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. This problem is an example of a a. Marascuilo procedure. b. multinomial population. c. z test for proportions. d. test for independence.
Answer:
The correct answer will be Option B (multinomial population).
Step-by-step explanation:
The population is considered as multinomial whether its information is prescriptive or corresponds to the set of discreet non-overlapping groups. The hypothesis again for fitness test besides multinomial distribution is that even though the approximately normal f I seem to be equivalent to the required number e I across each segment.Here, because we have been testing whether the sampling data matches the hypothesized proportions as mentioned, this is indeed a multinomial population issue (because there have been more least two generations).Other given options are not connected to the given situation. So that Option B seems to be the perfect solution.
determine whether these two functions are inverses.
Answer:
Yes,these two functions are the inverse of each other.
Step-by-step explanation:
They way of finding if two functions ([tex]f(x)\,\,and\,\,g(x)[/tex] ) are the inverse of each other is by studying if their composition renders in fact the identity. That is, we see if:
[tex]f(x) \,o \,g(x)=f(g(x))=x[/tex]
in our case:
[tex]f(g(x))=\frac{1}{g(x)+4} -9\\f(g(x))=\frac{1}{(\frac{1}{x+9} -4)+4}-9\\f(g(x))=\frac{1}{\frac{1}{x+9} }-9\\f(g(x))={x+9} -9\\f(g(x))=x[/tex]
The composition does render the identity, therefore, these two functions are indeed the inverse of each other
2. CTfastrak bus waiting times are uniformly distributed from zero to 20 minutes. Find the probability that a randomly selected passenger will wait the following times for a CTfastrak bus. b. Between 5 and 10 minutes. c. Exactly 7.5922 minutes. d. Exactly 5 minutes. e. Between 15 and 25 minutes.
Answer:
b. 0.25
c. 0.05
d. 0.05
e. 0.25
Step-by-step explanation:
if the waiting time x follows a uniformly distribution from zero to 20, the probability that a passenger waits exactly x minutes P(x) can be calculated as:
[tex]P(x)=\frac{1}{b-a}=\frac{1}{20-0} =0.05[/tex]
Where a and b are the limits of the distribution and x is a value between a and b. Additionally the probability that a passenger waits x minutes or less P(X<x) is equal to:
[tex]P(X<x)=\frac{x-a}{b-a}=\frac{x-0}{20-0}=\frac{x}{20}[/tex]
Then, the probability that a randomly selected passenger will wait:
b. Between 5 and 10 minutes.
[tex]P(5<x<10) = P(x<10) - P(x<5)\\P(5<x<10) = \frac{10}{20} -\frac{5}{20}=0.25[/tex]
c. Exactly 7.5922 minutes
[tex]P(7.5922)=0.05[/tex]
d. Exactly 5 minutes
[tex]P(5)=0.05[/tex]
e. Between 15 and 25 minutes, taking into account that 25 is bigger than 20, the probability that a passenger will wait between 15 and 25 minutes is equal to the probability that a passenger will wait between 15 and 20 minutes. So:
[tex]P(15<x<25)=P(15<x<20) \\P(15<x<20)=P(x<20) - P(x<15)\\P(15<x<20) = \frac{20}{20} -\frac{15}{20}=0.25[/tex]
a newborn calf weighs 40 kilograms. Each week its weight increases by 5%. Let W be the weigh in kilograms of the calf after t weeks
Bonnie volunteers to bring bags of candy to her child's class for the Halloween party. She buys a bag containing 240, a bag containing 624, and a bag containing 336 pieces. Age needs to use all the candy to create identical treat bags. How many treat bags can bonnie make so that each one has the same number and variety of candy? How many of each type of candy will be in each bag?
Answer:
Number of bags that Bonnie can make so that each one has the same number of candies = 48
Number of candies from bag I in each of the treat bag = 5
Number of candies from bag II in each of the treat bag = 13
Number of candies from bag III in each of the treat bag = 7
Step-by-step explanation:
Given: One bag (I) has 240 candies, one bag (II) has 624 candies and one bag (III) has 336 candies
To find: Number of bags that Bonnie can make so that each one has the same number of candies and number of each type of candies in each bag
Solution:
[tex]240=2^4\times 3\times 5\\624=2^4\times3\times13\\336=2^4\times3\times7[/tex]
Highest common factor (H.C.F) = [tex]2^4\times3=48[/tex]
So,
Number of bags that bonnie can make so that each one has the same number of candies = 48
Now,
[tex]\frac{240}{48}=5\\ \frac{240}{48}=13\\\frac{240}{48}=7[/tex]
Number of candies from bag I in each of the treat bag = 5
Number of candies from bag II in each of the treat bag = 13
Number of candies from bag III in each of the treat bag = 7
If \\(z_1=3+2i\\) and \\(z_2=4+3i\\) and are complex numbers, find \\(z_1z_2\\)
[tex]z_1z_2=(3+2i)(4+3i)=3\cdot4+2i\cdot4+3\cdot3i+2i\cdot3i[/tex]
[tex]z_1z_2=12+8i+9i+6i^2[/tex]
[tex]i^2=-1[/tex], so
[tex]z_1z_2=12+8i+9i-6=\boxed{6+17i}[/tex]
What is the answer to this question?
Answer:it is b
Step-by-step explanation:
