Answer:
[tex]\frac{7}{120}[/tex] of seed planted in each flower pot.
Step-by-step explanation:
Given:
Total number of marigold seeds packages Trixie have= ¾
Number of seeds Trixie planted in the garden= 1/6
Number of fraction into which Trixie dived the remaining seed =10
To Find:
Fraction of seed planted in each flower pot=?
Solution:
Seed left after planting 1/6 of seeds in the garden = [tex]\frac{3}{4}-\frac{1}{6}[/tex]
=>[tex]\frac{18-4}{24}[/tex]
=>[tex]\frac{14}{24}[/tex]
=>[tex]\frac{7}{12}[/tex]
Now Trixie divides these remaining seeds into 10 parts
=>[tex]\frac{\frac{7}{12} }{10}[/tex]
=>[tex]\frac{7}{12}\times\frac{1}{10}[/tex]
=>[tex]\frac{7}{120}[/tex]
Joe had eight sections of the fence to paint. He painted 2/3 of each section in one hour. How many hours did it take him to paint all the sections of fence?
Answer:
1.5 hours
Step-by-step explanation:
Since Joe painted 2/3 section (2 out of 3 sections) of each section, we can break up the sections into parts of "3".
So 8 sections would have total subsections of 8 * 3 = 24 subsections
He painted 2 subsections of each of the 8 sections, so number of subsections painted would be:
8 * 2 = 16 subsections
There are more 24 - 16 = 8 more subsections to paint
If 1 hour means 16 subsections,
1/16 hour = 1 subjection
Thus,
8 remaining subsections would take:
8 * 1/16 = 8/16 = 1/2 hour
So
Initially 1 hour, then 1/2 hour, so total of 1 + 1/2 = 1.5 hours
So, to paint all sections, he took 1.5 hours
Solve for x: 5/8=x-1/9
A. 37/8
B. 23/4
C. 11/2
D. 53/8
Answer:
53/72
Step-by-step explanation:
5/8 = x - 1/9
+1/9 +1/9
5/8 + 1/9 = x
9(5/8) + 8(1/9)
45/72 + 8/72
x= 53/72
Within the United States, approximately 11.25% of the population is left-handed. Of the males, 12.6% are left-handed, compared to only 9.9% of the females. If a person is selected at random, what is the probability that the selected person is a female, given the person is right-handed?
Answer: Our required probability is 45.05%.
Step-by-step explanation:
Since we have given that
Males Females total
Left handed 6.3 4.95 11.25%
Right handed 43.7 45.05 88.75%
Total 50% 50% 100%
Since 12.6% of 50% are males are left handed = 6.3%
So, 9.9% of 50% are females are left handed = 4.95%
So, Females who are right handed would be
[tex]50\%-4.95\%\\\\=45.05\%[/tex]
Hence, our required probability is 45.05%.
To calculate the probability that the selected person is a female, given the person is right-handed, we need to use conditional probability. The exact probability cannot be calculated without the percentage of females in the population. However, it is known that the probability is less than or equal to 11.25%.
Explanation:To find the probability that the selected person is a female, given that the person is right-handed, we need to use conditional probability. Let's denote the events A and B as follows: A: Selected person is a female, B: Selected person is right-handed.
The probability of event A (P(A)) can be calculated as the product of the probability of event B given event A (P(B|A)) and the probability of event A without any condition (P(A)) divided by the probability of event B (P(B)).
In this case, P(A) refers to the probability of selecting a female, P(B|A) refers to the probability of being right-handed given the person is female, and P(B) refers to the probability of being right-handed.
First, let's calculate the probability of being right-handed (P(B)). Since 90% of people are right-handed, P(B) = 0.9.
Next, let's calculate the probability of being right-handed given the person is female (P(B|A)). Since 9.9% of females are left-handed, the probability of being right-handed is 1 - 0.099 = 0.901.
Finally, let's calculate the probability of selecting a female (P(A)). Since the percentage of females in the population is not provided, we cannot calculate the exact probability. We can only say that it is less than or equal to the total percentage of left-handed people, which is 11.25%.
Therefore, the probability that the selected person is a female, given that the person is right-handed, can be defined as: P(A|B) = (P(B|A) * P(A)) / P(B) = (0.901 * P(A)) / 0.9 = 0.901 * P(A).
Since we don't have the exact value of P(A), we cannot calculate the exact probability. However, we know that it is less than or equal to 11.25%.
Identify the triangle PQR as isosceles (two sides of equal length), equilateral (three sides of equal length), or a scalene triangle (three sides of different lengths). P(negative 4,9), Q(0,8), and R(negative 3,5)
Answer:
Isosceles
Step-by-step explanation:
In order to figure what type of triangle this is out, we need to start by plotting the given points. That will help us visualize the triangle better and see if our conclusions make sense. (See attached picture).
Once we got the triangle, the strategy to follow is to use the distance between two points formula to see what the measurement of each side of the triangle is. This will help us determine if 2, 3 or none of the sides of the tirangle are the same.
The distance formula is the following:
[tex]distance=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
so now we can find the desired distances, let's start with the distance between P and Q:
[tex]|PQ|=\sqrt{(-4-0)^{2}+(9-8)^{2}}[/tex]
which yields:
[tex]|PQ|=\sqrt{17}[/tex]
next, let's find the distance between P and R:
[tex]|PR|=\sqrt{(-4-(-3))^{2}+(9-5)^{2}}[/tex]
which yields:
[tex]|PR|=\sqrt{17}[/tex]
and finally the distance between Q and R:
[tex]|QR|=\sqrt{(0-(-3))^{2}+(8-5)^{2}}[/tex]
which yields:
[tex]|QR|=3\sqrt{2}[/tex]
As you may see from the result, only two of the three sides are the same, |PQ| and |PR|, so this will be an Isosceles triangle.
Suppose you begin a job with an annual salary of $32,900. Each year you are assured of a 5.5% raise. What its the total amount that you can earn in 15 years? A) $34,815 B) $51,751 C) $737,245 D) $1,682,920
Answer: The correct option is C
Step-by-step explanation:
You begin a job with an annual salary of $32,900
Each year you are assured of a 5.5%. If you get the same amount each year, that is a 100% payment. It is neither reducing nor increasing. But with an increase of 5.5% each year, it means you are getting (100+5.5)% each year. This equals 105.5%. So for each year, you get 105.5% of the previous year.
This is a geometric progression. To determine the total amount that you can earn in 15 years, we will find the sum of 15 terms, S15 of the series. The formula for sum of the nth term of a geometric progression is expressed as
Sn = [a(r^n - 1)] / r - 1
Where
Sn = sum of the nth terms of the series
a = the first term(salary of the first year
r = common ratio
n = number of years.
From the question,
a = 32900
n = 15
r = 105.5/100 = 1.055
S15 = [32900(1.055^15 - 1)] / 1.055 - 1
S15 = [32900(2.23247649224 - 1)] / 0.055
S15 = [32900 × 1.23247649224] / 0.055
S15 = $737245
On the square baseball diamond shown below, the distance from first base to second base is 90 feet. How far does the catcher have to throw the ball from home plate to reach second base? Round your answer to the nearest 10th. Show your work
Answer:
127.3 ft
Step-by-step explanation:
The diagonal of a square is √2 times the length of one side. The distance from home plate to second base is ...
(90 ft)√2 ≈ 127.3 ft
The catcher at home has to throw the ball 127.3 ft to reach second base.
help me figure out this problem!!
Answer:
4.47 years
Step-by-step explanation:
Fill in the given value of P and solve for t.
15390 = 19000·0.954^t
15390/19000 = 0.954^t
Taking logarithms ...
log(1539/1900) = t·log(0.954)
t = log(1539/1900)/log(0.954) ≈ 4.47 . . . years
Assume that IQ scores are normally distributed, with a standard deviation of 11 points and a mean of 100 points.
If 85 people are chosen at random, what is the probability that the sample mean of IQ scores will not differ from the population mean by more than 2 points?
Answer: Our required probability is 0.91.
Step-by-step explanation:
Since we have given that
n = 85
mean = 100 points
standard deviation = 11
We need to find the probability that the sample mean will not differ from the population mean by more than 2 points.
so, it becomes,
[tex]P(100-2<\bar{x}<100+2)\\\\=P(98<\bar{x}<102)\\\\=P(\dfrac{98-100}{\dfrac{11}{\sqrt{85}}}<Z<\dfrac{102-100}{\dfrac{11}{\sqrt{85}}})\\\\=P(-1.68<Z<1.68)\\\\=P(z<1.68)-P(z<-1.68)\\\\=0.9535-0.0465\\\\=0.9070\\\\\approx 0.91[/tex]
Hence, our required probability is 0.91.
A very large study showed that aspirin reduced the rate of heart attacks by 44%. A pharmaceutical company thinks they have a drug that will be more effective than aspirin, and plans to do a randomized clinical trial to test the new drug. State the null hypothesis and the alternative hypothesis they should use for completing a hypothesis test.
Answer: [tex]H_0:\mu=0.44\ ,H_a:\mu<0.44[/tex]
Step-by-step explanation:
Since we have given that
A very large study showed that aspirin reduced the rate of heart attacks by 44%.
we claim that they have a drug that will be more effective than aspirin.
so, our hypothesis would be
[tex]H_0:\mu=0.44\\\\H_a:\mu<0.44[/tex]
So, it will be one tail test.
Hence, [tex]H_0:\mu=0.44\\\\H_a:\mu<0.44[/tex]
The null hypothesis (H0) for this clinical trial would state that the new drug is no more effective than aspirin at reducing heart attacks (reduction rate is 44% or less). The alternative hypothesis (Ha) would claim that the new drug is more effective than aspirin (reduction rate greater than 44%).
Explanation:In this context, the null hypothesis (H0) and the alternative hypothesis (Ha) are representations of scenarios that the researchers are trying to investigate through their study. The null hypothesis is typically a statement of no effect or no difference while the alternative hypothesis represents the scenario where there is an effect or difference.
For this case, we could state:
Alternative Hypthesis (Ha): The new drug is more effective at reducing heart attacks than aspirin (i.e., the reduction rate is greater than 44%).
These hypotheses set the stage for the pharmaceutical company to analyze the study's data and determine which hypothesis is most supported by the evidence presented.
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Help please I really need help I need it right now show work please
Answer:
ok with whuth do you need help with
Answer:
The right answer for question 1 is b) -14
Step-by-step explanation:
Since it's a decline, the amount will be negative.
your second question is not clear in the image
3.5 per day for 4 days so multiply 3.5 by 4, which equals: $14
so the overall change is -$14.00
What percent of 71 is 90?
of 71 is 90.
Answer: 126.76056338%
Step-by-step explanation: To answer the question what percent of 71 is 90, we translate the question into an equation.
We have "what percent" which we can represent by the variable X. Next we have "of 71" which means "times 71" and "is 90" means "equals 90."
Now to solve for x, since x is being multiplied by 71, we need to divide by 71 on both sides of the equation.
On the left side of the equation the 71's cancel and we have x. On the right side of the equation we have 90 divided by 71 which is 1.2676056338.
Now, remember that we want to write our answer as a percent. To write 1.2676056338 as a percent, we move the decimal point two places to the right and we get 126.76056338%.
Answer:
78.89%
Step-by-step explanation:
A researcher is wondering whether the smoking habits of young adults (18-25 years of age) in a certain city in the U.S. are different from the proportion of the general population of young adults in the U.S. A recent study stated that the proportion of young adults who reported smoking at least twice a week or more in the last month was 0.16. The researcher collected data from a random sample of 75 adults in the city of interest. State the hypotheses to be tested for this study. Select one: a. H0: p = 0.16; Ha: p < 0.16 b. H0: p = 0.16; Ha: p > 0.16 c. H0: p = 0.16; Ha: p ≠ 0.16 d. H0: p ≠ 0.16; Ha: p < 0.16
Answer: c. H0: p = 0.16; Ha: p ≠ 0.16
Step-by-step explanation:
We know that ,
Null hypothesis is a statement about the population parameter([tex]\mu , p, \sigma....[/tex]) and contains equality (=),≤ or ≥ signs.
Alternative hypothesis is also statement about the population parameter([tex]\mu , p, \sigma....[/tex]) but against null hypothesis and contains signs < , > or ≠.
In the given situation , the parameter is p (population proportion).
A recent study stated that the proportion of young adults who reported smoking at least twice a week or more in the last month was 0.16.
i.e. the point estimate of the population proportion(p) of the young adults who reported smoking at least twice a week or more is 0.16.
Now, the hypotheses to be tested for this study would be :
[tex]H_0: p=0.16\\\\ H_a: p\neq0.16[/tex]
Hence, the correct answer is c. H0: p = 0.16; Ha: p ≠ 0.16
An open-topped glass aquarium with a square base is designed to hold ~62.5~ 62.5 space, 62, point, 5, space cubic feet of water. What is the minimum possible exterior surface area of the aquarium?
Answer:
75 square feet
Step-by-step explanation:
The aquarium is designed to hold 62.5cubic feet
Since the aquarium has a square base, assume the aquaruim is a square prism
Let X be the lenght
Let y be the height
x^2.y = 62.5
y = 62.5x^2
The area of each side of the aquarium is xy. Since there are four sides, the total area of the side= 4xy
The area of the bottom of the aquarium = x^2
Total surface area = 4xy + x^2
Put y = 62.5/x^2 into the total surface area equation
A = 4x(62.5/x^2) + x^2
A= 250/x + x^2
Differentiate A with respect to x
dA/dx = -250(x^-2) + 2x
dA/dx = 0
0 = 2x - 250x^-2
2x = 250x^-2
2x =250/ x^2
2x^3 = 250
x^3 = 250/2
x^3 = 125
x = cbrt (125)
x = 5
Put x= 5 into A = x^2 + 250x^-1
A= 5^2 + 250(5^-1)
A= 25 + 250/5
A = 25 + 50
A = 75 square feet
The surface area of a solid object can be determine by measuring the total area that surface of the object cover.
The minimum possible exterior surface area of the aquarium is [tex]75 \:\rm feet^2[/tex].
Given:
The aquarium designed hold [tex]62.5 \:\rm feet^3[/tex].
Let assume the aquarium is square prism.
Let [tex]x[/tex] is height and [tex]y[/tex] is length.
The aquarium designed hold [tex]62.5 \:\rm feet^3[/tex]. Write the system equation.
[tex]x^2y=62.5\\y=\frac{62.5}{x^2}[/tex]
The area of four side of aquarium is as follows,
[tex]\rm A_1=4xy[/tex]
The bottom area of aquarium is as follows,
[tex]A_2=x^2[/tex]
The total area is as follows,
[tex]A=A_1+A_2\\A=4xy+x^2[/tex]
Put [tex]y=\frac{62.5}{x^2}[/tex] in above expression.
[tex]A=4x(\frac{65.2}{x^2} )+x^2\\A=\frac{250}{x}+x^2[/tex]
Differentiate [tex]A[/tex] with respect to [tex]x[/tex].
[tex]\frac{dA}{dx}=-250(x^{-2})+2x[/tex]
For the minimum possible exterior surface area [tex]\frac{dA}{dx} =0[/tex].
[tex]0=2x-250x^{-2}\\2x=250x^{-2}\\2x^3=250\\x^3=\frac{250}{2}\\x^3=125\\x=5[/tex]
Substitute [tex]x=5[/tex] to find the area.
[tex]A=5^2+250\times 5^{-1}\\A=25+\frac{250}{5}\\A=75\:\rm feet^2[/tex]
Thus, the minimum possible exterior surface area of the aquarium is [tex]75 \:\rm feet^2[/tex].
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Please help me with my homework and explain to me how?
Answer:
350
Step-by-step explanation:
If x is the number of hamburgers and y is the number of cheeseburgers, then:
x + y = 764
y = x + 64
Solve the system of equations with substitution or elimination. Using substitution:
x + x + 64 = 764
2x + 64 = 764
2x = 700
x = 350
350 hamburgers were sold.
Maryam’s wallet contains a combination of $5 and $10 bills. What is the ratio of $5 bills to $10 bills? (1) The ratio of the number of bills to the total dollar value is 1/9. (2) The total dollar value of the bills is $360.
The problem requires finding the ratio of $5 bills to $10 bills given certain conditions. It involves solving two equations and is typically encountered in a high school Mathematics course.
Explanation:The SUBJECT
of Maryam's question involves the field of
Mathematics
, more specifically it belongs to the area of
ratios and proportions
. The problem presents a scenario where she has a combination of $5 and $10 bills in her wallet. Then, given are two conditions - (1) 'The
ratio
of the number of bills to the total dollar value is 1/9.' and (2) 'The total dollar value of the bills is $360.' We are asked to determine the ratio of $5 bills to $10 bills.
Represent $5 bills as 'x' and $10 bills as 'y'. Firstly, considering condition (1), we know that the total number of bills (x + y) divided by the total value (5x + 10y) is 1/9. Secondly, from condition (2), we have that the total dollar value, i.e., 5x + 10y equals $360. By solving these two equations, the values of 'x' and 'y' can be found, and thus, the required ratio will be x:y.
However, the problem requires solving two equations which is a skill typically taught and applied in high school Mathematics courses.
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Find the missing side length
Answer:
The answer to your question is b = 148.5
Step-by-step explanation:
To solve this problem, use trigonometric functions
tan Ф = [tex]\frac{opposite side}{adjacent side}[/tex]
opposite side = b
adjacent side = 60
tan Ф = tan 68° = 2.48
Opposite side = adjacent side x tan Ф
Opposite side = 60 x 2.48
Opposite side = b = 148.5
Answer: 24.24 (24 to the nearest whole number)
Step-by-step explanation:
Following trigonometric rule,
Tan tita = opposite side/ adjacent side
Tan 68° = 60 / b
2.475 = 60 / b
By cross multiplication,
2.475b = 60
Divide both sides by 2.475
2.475b/2.475 =60/2.475
b = 24.24
Hence, adjacent side = 24.24 (24 to the nearest whole number since opposite side is in whole number).
A sporting goods store manager was selling a ski set for a certain price. The manager offered the markdowns shown, making the one-day sale price of the ski set $325. Find the original selling price of the ski set.
Final answer:
To find the original selling price of the ski set, work backward from the sale price by adding the markdowns back to it. Start by assigning a variable to represent the original selling price and use the given markdown amounts to calculate the original price. The original selling price of the ski set is $387.50.
Explanation:
A sporting goods store manager was selling a ski set for a certain price. The manager offered markdowns, making the one-day sale price of the ski set $325. To find the original selling price of the ski set, we will work backwards from the sale price by adding the markdowns back to it.
Step-by-step process:
Let x be the original selling price.
Given markdowns, if the sale price after markdowns is $325, then x - $30 - $20 - $12.50 = $325.
Solving for x, we get x = $387.50.
Nelson grows tomatoes and sells them at a nearby farmers roadside stand. He sells them for $2.50 each. The farmer charges him $15 a day to use the stand. Write a linear function in factored form and general form that represents the amount of money, m, Nelson will make from selling x tomatoes.
Answer:
Step-by-step explanation:
Nelson grows tomatoes and sells them at a nearby farmers roadside stand.
Let x = number of tomatoes sold
Let m = amount of money made for selling x tomatoes.
He sells them for $2.50 each. This means that he sells x tomatoes for 2.5×x = $2.5x
The farmer charges him $15 a day to use the stand. This means that he pays a constant amount of $15 each day.
Amount of money that Nelson will make will be total amount made in selling x tomatoes minus the constant amount being paid for rent. It becomes
m = 2.5x - 15 This is the general form. In the factored form, it will be
m = 2.5(x+6)
Yesterday evening, Emily's journey home took 25% longer than usual, as she was stuck in a traffic jam. By what percentage was her average speed reduced compared to normal
Answer:
20%
Step-by-step explanation:
Time and speed are inversely proportional, so if Emily's time was 5/4 of normal, her speed was 4/5 of normal, or 1/5 = 20% below normal.
Suppose you perform an ANOVA on 18 subjects divided evenly into three groups according to age. Reading speed is measured and averaged for each of the three groups. The reading speed for the Young Group is 10; for the Middle Group, 12; and for the Older Group, 13. Your F-obtained is 9.15. This is a significant F-obtained. Which of the following is the correct way to report this finding? A. The Older Group reads significantly faster than any other group. B. The Young Group reads significantly faster than any other group. C. There is a significant difference between the Older Group and the Middle Group. D. There is a significant difference among the reading speeds somewhere.
Answer:
D. There is a significant difference among the reading speeds somewhere.
Hope this helps!
1. In triangle XYZ, A is the midpoint of XY, B is the midpoint of YZ, and C is the midpoint of XZ. Also, AY = 7, BZ = 8, and XZ = 18. What is the perimeter of triangle ABC? (SHOW WORK)
2. What is y? (SHOW WORK) 2nd picture is the triangle.
Answer:
Part 1) The perimeter of triangle ABC is 24 units
Part 2) [tex]y=97\°[/tex]
Step-by-step explanation:
Part 1)
we know that
The Midpoint Theorem states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side
The perimeter of triangle ABC is equal to
[tex]P=AB+BC+AC[/tex]
Applying the Midpoint Theorem
Find the measure of AB
[tex]AB=\frac{XZ}{2}[/tex]
substitute given value
[tex]AB=\frac{18}{2}=9\ units[/tex]
Find the measure of BC
[tex]BC=\frac{XY}{2}[/tex]
[tex]XY=2AY[/tex]
substitute given value
[tex]XY=2(7)=14\ units[/tex]
[tex]BC=\frac{14}{2}=7\ units[/tex]
Find the measure of AC
[tex]AC=\frac{YZ}{2}[/tex]
[tex]YZ=2BZ[/tex]
substitute given value
[tex]YZ=2(8)=16\ units[/tex]
[tex]AC=\frac{16}{2}=8\ units[/tex]
Find the perimeter of triangle ABC
[tex]P=9+7+8=24\ units[/tex]
Part 2)
step 1
Find the measure of angle z
Remember that the sum of the interior angles in a triangle must be equal to 180 degrees
[tex]55\°+42\°+z=180\°\\97\°+z=180\°\\z=180\°-97\°\\z=83\°[/tex]
step 2
Find the measure of angle y
we know that
[tex]y+z=180\°[/tex] ----> by supplementary angles (form a linear pair)
substitute the value of z
[tex]y+83\°=180\°[/tex]
[tex]y=180\°-83\°=97\°[/tex]
The country A Consumer Price Index is approximated by the following formula, where t represents the number of years after 1990.
a(t)=100e^0.023t
For instance, since A(16) is about 144, the amount of goods that could be purchased for $100 in 1990 cost about $144 in 2006. Use the function to determine the year during which costs will be 90% higher than in 1990.
2012
Step-by-step explanation:
cuz 16 years mande the increase so much the years are making money go worthless faster and faster
Using the given exponential function model for Consumer Price Index (CPI), one can conclude that the costs were approximately 90% higher than 1990 in country A in the year 2018.
Explanation:This question is related to
exponential functions
in Mathematics. The formula given, a(t) = 100e^0.023t, is an exponential function representing the Consumer Price Index (CPI) of country A. In this context, a 90% increase from 1990 corresponds to a cost of $190, as 90% of $100 is $90, and this added onto the initial $100 gives us $190. So, you are looking for the year (t) when a(t) = 190.
This requires simplifying the equation 190 = 100e^0.023t. First, divide by 100 to get 1.9 = e^0.023t. Then take the natural log of each side to get ln(1.9) = 0.023t. Now solve for t by dividing ln(1.9) by 0.023 which gives you approximately 28.71 years. As the question measures years after 1990, add this to 1990 to determine the year costs were 90% higher. This gives us the year 2018 (since we cannot have a fraction of a year) that the goods will cost 90% more than in 1990.
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Jan sold for more than three times the number of magazines Mel sold during the school fundraiser Morgan sold 40 more magazines then melt if Jen and Morgan sold the same number of magazines how many did Mel sell
Answer: eyyyyyy my name is Jan what a coincidence
Step-by-step explanation:
Based on meteorological data for the past century, a local TV weather forecaster estimates that the region’s average winter snowfall is 23'', with a margin of error of {2 inches. Assuming he used a 95% confidence interval, how should view-ers interpret this news? Comment on each of these statements.
a. During 95 of the past 100 winters, the region got between 21" and 25" of snow.
b. There 's a 95% chance the region will get between 21" and 25" of snow this winter.
c. There will be between 21" and 25" of snow on the ground for 95% of the winter days.
d. Residents can be 95% sure that the area's average snowfall is between 21" and 25".
e. Residents can be 95% confident that the average snowfall during the past century was between 21" and 25" per winter.
Answer:
d) Good, the interval is related to the variable of interest and the population mean analyzed.
Step-by-step explanation:
1) Data given
[tex]\bar x = 23[/tex] represent the mean
[tex]ME=2[/tex] represent the margin of error
[tex]confidence=95\%=0.05[/tex]
The confidence interval for the mean is given by the following formula:
[tex]\bar x \pm ME = 23\pm 3=(21,25)[/tex]
Where the margin of error is given by [tex]ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]
Based on the interval obtained we can say that "we have 95% of confidence that the mean winter snowfall would be between 21 and 25"
2) Analyze the possible options
a) Wrong, we are not analyzing the individual winters, the interval is related to the population mean.
b) Wrong, the confidence interval can't be interpreted as a chance that are not related to the population mean of interest.
c) Wrong, the confidence interval is not related to the individual days of winter.
d) Good, the interval is related to the variable of interest and the population mean analyzed.
e) Wrong, the confidence interval is not related to specific events, is related to the population mean.
Viewers should interpret the news by considering the confidence interval and understanding the statements.
The viewers should interpret this news as follows:
a. The statement that during 95 of the past 100 winters, the region got between 21" and 25" of snow is valid.
This is because the average winter snowfall of 23" falls within this range with a margin of error of 2".
b. The statement that there's a 95% chance the region will get between 21" and 25" of snow this winter is not correct.
The confidence interval (21" to 25") represents the range of values in which the true average snowfall is likely to fall, not the probability of the upcoming winter's snowfall falling within that range.
c. The statement that there will be between 21" and 25" of snow on the ground for 95% of the winter days is not supported by the given information.
The confidence interval pertains to the average winter snowfall, not individual daily observations.
d. The statement that residents can be 95% sure that the area's average snowfall is between 21" and 25" is valid.
The confidence interval provides a range of values within which the true average is likely to fall.
e. The statement that residents can be 95% confident that the average snowfall during the past century was between 21" and 25" per winter is valid.
The confidence interval represents the range of likely values for the true average.
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The physical plant at the main campus of a large state university receives daily requests to replace fluorescent light bulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 63 and a standard deviation of 6. Using the 68-95-99.7 rule, what is the approximate percentage of light bulb replacement requests numbering between 63 and 75? _________ % (Round your answer to the nearest tenth of a percent)
Approximately 81.5% of the daily light bulb replacement requests in the state university's physical plant can be expected to number between 63 and 75.
Explanation:The question is asking for the percentage of daily light bulb replacement requests numbering between 63 and 75 at a state university's physical plant. This can be answered using the 68-95-99.7 rule, also known as the Empirical Rule, which applies to a bell-shaped distribution.
Firstly, identify that a request count of 75 is two standard deviations above the mean (63 + 6*2 = 75), because the standard deviation here is 6. According to the Empirical Rule, approximately 95% of the data lies within two standard deviations of the mean.
However, we are only interested until the upper limit of 75 and not the lower limit (63 - 6*2 = 51). Therefore, we consider half of this 95%, which gives us 47.5%. However, don't forget to include the 34% that lies within the first standard deviation (from 63 to 69). Therefore, approximately 81.5% of the light bulb replacement requests should number between 63 and 75.
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the approximate percentage of light bulb replacement requests numbering between 63 and 75 is 47.5%.
Using the Empirical Rule:
Calculate the Z-scores for the given values: Z(63) = (63-63)/6 = 0 and Z(75) = (75-63)/6 = 2.Look up the percentage of data within these Z-scores: Between Z = 0 and Z = 2 is approximately 47.5%.Therefore, the approximate percentage of light bulb replacement requests numbering between 63 and 75 is 47.5%.A barrel contains 10 red balls, 11 blue balls, and 23 green balls. You start taking balls out. How many do you need to remove, at minimum, to ensure you have taken out at least one of each color?
Answer:
The answer is3
Step-by-step explanation:
because there is three colors
Answer:
22.
Step-by-step explanation:
You might take 10 red balls out in the first 10 picks. Now you are left with 11 blue and 23 green and you might take out the 11 blue in 11 picks. The next pick must be green.
So the answer is 10 + 11 + 1 = 22 balls.
Carpetland salespersons average $8,000 per week in sales. Steve Contois, the firm’s vice president, proposes a compensation plan with new selling incentive. Steve hopes that the results of a trial selling period will enable him to conclude that the compensation plan increase the average sales per salesperson.
a. Develop the appropriate null and alternative hypotheses.
b. What is the Type I error in this situation? What are the consequences of making this error?
c. What is the Type II error in this situation? What are the consequences of making this error?
The appropriate null and alternative hypotheses for the situation, the consequences of Type I and Type II errors in this context.
Explanation:a. Null Hypothesis (H0): The compensation plan does not increase the average sales per salesperson. Alternative Hypothesis (H1): The compensation plan does increase the average sales per salesperson.
b. Type I error occurs when the null hypothesis is rejected, but it is actually true. In this situation, it means concluding that the compensation plan increases the average sales per salesperson when it does not. The consequence is that the company may implement the compensation plan and incur unnecessary costs.
c. Type II error occurs when the null hypothesis is accepted, but it is actually false. In this situation, it means concluding that the compensation plan does not increase the average sales per salesperson when it actually does. The consequence is that the company may miss out on the benefits of the compensation plan and fail to motivate its salespeople effectively.
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A box (with no top) is to be constructed from a piece of cardboard of sides A and B by cutting out squares of length h from the corners and folding up the sides. Find the value of h that maximizes the volume of the box if
A = 7 and B = 12
Answer:
h = 1,743
Step-by-step explanation:
Volume of a box is
V(h) = ( A - 2h) * ( B - 2h)* h A = 7 B = 12
We have
V(h) = ( 7 - 2h) * ( 12 - 2h ) * h
V(h) = ( 84 - 14*h - 24*h + 4*h² ) * h
V(h) = ( 84 - 38*h + 4 *h² ) * h ⇒ V(h) = 84h - 38h² + 4h³
Taking derivatives both sides of the equation
V´(h) = 84 - 76h + 12x²
V´(h) = 0 84 - 76h + 12x² = 0 42 - 38h + 6x²
3x² - 19h + 24 = 0
Solving for h h1 = [ ( 19 + √(19)² - 288 ]/ 6 h1 = [ (19 + √73)/6]
h₁ = 4,59 we dismiss this value since 9,18 (4,59*2) > A
h₂ = [ 19 - √73)/6] h₂ = 1,743
h = 1.743 is h value to maximizes V
1. A motorboat leaves a harbor and travels at an average speed of 15 mph toward an island. The average speed on the return trip was 10 mph. How far was the island from the harbor if the total trip took 5 hours
Answer:
30 miles
Step-by-step explanation:
Let d represent the distance to the island. The relation between time, speed, and distance is ...
time = distance/speed
so the total time for the round trip is ...
d/15 +d/10 = 5
Multiplying by 30, we get
2d +3d = 150
d = 150/5 = 30
The island was 30 miles from the harbor.
To solve this problem we use the equation Speed = Distance/Time for both legs of the trip to form an equation and solve for the distance. Through these calculations, we find the distance from the harbor to the island to be 30 miles.
Explanation:This problem can be solved by understanding the relationship of speed, distance, and time, often expressed as Speed = Distance/Time. First, let's define the time it took to go to the island and back. From the problem, we know that the total time was 5 hours but the speeds were different, so the time spent on each leg of the trip was different. We'll define the time it took to get to the island as two hours. Therefore, the return trip took 5-t hours. Solving for Distance To calculate the distance, we use the speed of each leg of the trip multiplied by the time of that leg. So, Distance = 15t = 10(5-t). We can solve this equation for t, finding that t equals to 2 hours. Inserting t back into Distance = 15t gives us a distance of 30mph to the island. This means it is 30 miles from the harbor to the island.
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A jar contains 8 red marbles and y white marbles. If Joan takes 2 random marbles from the jar, is it more likely that she will have 2 red marbles than that she will have one marble of each color?
(1) y ≤ 8
(2) y ≥ 4
Answer:
a) y </= 8 is not sufficient
b) y >/= 4 is sufficient (y is not less than 3.5)
Step-by-step explanation:
Number of Red marbles = 8
Number of white marbles = y
Total number of marbles in the jar = 8+ y
Let Pr(R) be the probability of picking red marbles
Let Pr(W) be the probability picking white marbles
Pr(R) = 8/ (8+y)
Pr(W) = 7/(7+y)
Pr(RR) = Pr(R1) * Pr( R2)
= 8/(8+y) * 7/(7+y)
Pr(RW) = Pr(R1) * Pr(W2) + Pr(W1) * Pr(R2)
= 2[Pr(R1) * Pr(W2)
= 2[8/(8+y) * y/(7+y)]
The probability of having 2 red is greater than one marble of each color.
Pr(RR) > Pr( RW)
8/(8+y) * 7/(7+y) > 2[8/(8+y) * y/(7+y)]
7/(7+y) > 2(y/(7+y)
7/y > 2
7/2 > y
3.5 > y
y < 3.5
Therefore;
a) y </= 8 is not sufficient
b) y >/= 4 is sufficient (y is not less than 3.5)