a. We cannot calculate the probability, because we do not know the shape of the distribution.
b. The mean and standard deviation of the sampling distribution of x are 12 and 0.0566.
c. The shape of the distribution described in part b is symmetrical.
d. The probability that a random sample of 50 cans produces a sample mean amount of 11.9 ounces or less is 0.0386.
We do not know the shape of the distribution, so we cannot calculate the probability that a single randomly selected can contains 11.9 ounces or less. The question given have not told us that the distribution of individual cans was normal, and we cannot assume it is so; therefore, we cannot calculate its probability.
As given information the mean μx = 12.
And standard deviation σx = σ / √n = 0.4 / √50 = 0.566.
The shape of the distribution described in part b is symmetrical, because the two sides of the distribution are a mirror image of each other. Therefore, it is normal distribution.
Since the sample is large n = 50 and 50 > 30, so by CLT (Central Limit Theorem), the distribution of sample means is approximately normal N(12, 0.0566). So, P(x ≤ 11.9) = normalcdf (0, 11.9, 12, 0.0566) = 0.0386.
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It costs $3.50 per hour to rent a bike, plus
a flat fee of $5.50. If Juanita spends a total
of $40.50, for how many hours did she rent the bike?
F. 4 1/2 h
G. 7 h
H. 10 h
J. 12 h
Answer:
H. 10 h
Step-by-step explanation:
40.50-5.5 = 35
35/3.5 = 10 hours
Tony types at a rate of 30 words per minute. how many words does he type in 3 minutes?
Answer:
He can type 90 words in 3 minutes.
Step-by-step explanation:
We know how many words he can type per minute already. So now, to find how many words he can type in 30 minutes, simply multiply 3 by 30.
[tex]3 \times 30=90[/tex]
So 90 is our answer.
A couple quick algebra 1 questions for 50 points!
Only answer if you know the answer, quick shout-out to Subtomex0, tysm for the help!
Answer:
Question 6) Neither (Not an inverse variation)
Question 7) Inverse variation
Question 8) Inverse variation
Step-by-step explanation:
These are the two formulas we need to know prior to solving the question.
Direct variation: c times x
Inverse variation: c times 1/x --> c/x
- Here, c is the constant
6. y = x + 7
This is neither. It is not in the form of a direct, or inverse variation, so it does not belong in any category.
7. 14 = xy
This equation is an inverse variation.
xy = 14
y = 14/x
14 is the constant, and the format is the same as for an inverse variation.
8. x = -8/y
This equation is an inverse variation.
yx = -8
y = -8/x
-8 is the constant, and the format is the same as for an inverse variation.
So we can conclude that questions 7 and 8 is an inverse variations, while question 6 isn't.
General forms
Direct
y=KxInverse
y=k/xso
#6
y=x+7Not inverse and direct also as 7 is present
#7
14=XYy=14/xYes
#8
x=-8/yy=-8/xYes
An oblique cylinder has a radius of 10 units and slant length of 26 units. an oblique cylinder has a radius of 10 units and a slant length of 26 units. what is the volume of the cylinder?
Answer:
The volume of the cylinder is 2,400pi cubic units
Step-by-step explanation:
I hope this helps and have a good day!
Answer these two questions pls
Thank you if your able to answer! :)
Q1) Find the LCM and HCF of the following by using prime factorisation method.
(i) 12,18
(ii) 12,15 and 21
Q2) If LCM (16, y) = 48 and HCF (16, y) = 12
Find y.
[tex]{\large{\textsf{\textbf{\underline{\underline{Question \: 1 :}}}}}}[/tex]
[tex]\diamond\:{\boxed{\tt{\purple{{ part \:(i) :}}}}}[/tex]
❍ Prime factorisation :-
‣ Prime factors of 12 -
[tex]\begin{gathered}\begin{gathered}{\begin{array}{ c|c}2&12 \\\hline 2&6 \\ \hline 3&3\\ \hline &1\end{array}} \end{gathered}\end{gathered}[/tex]
‣ Prime factors of 18 -
[tex]\begin{gathered}\begin{gathered}{\begin{array}{ c|c}2&18 \\\hline 3&9\\\hline 3&3 \\ \hline &1\end{array}} \end{gathered}\end{gathered} [/tex]
Therefore,
[tex]\star \: 12 = {2}^{2} \times {3}^{1}[/tex]
[tex]\star \: 18= {2}^{1} \times {3}^{2}[/tex]
✧ LCM of 12 and 18 = [tex]\sf {2}^{2} \times {3}^{2}[/tex]
[tex]\implies 36[/tex]
✧ HCF of 12 and 18 = [tex]\sf {2}^{1} \times {3}^{1}[/tex]
[tex] \implies 6[/tex]
[tex] \diamond\:{\boxed{\tt{\red{{ part \:(ii) :}}}}}[/tex]
❍ Prime factorisation :-
‣ Prime factors of 12 -
[tex]\begin{gathered}\begin{gathered}{\begin{array}{ c|c}2&12 \\\hline 2&6 \\ \hline 3&3\\ \hline &1\end{array}} \end{gathered}\end{gathered}[/tex]
‣ Prime factors of 15 -
[tex]\begin{gathered}\begin{gathered}{\begin{array}{ c|c}3&15 \\\hline 5&5 \\ \hline &1\end{array}} \end{gathered}\end{gathered}[/tex]
‣ Prime factors of 21 -
[tex]\begin{gathered}\begin{gathered}{\begin{array}{ c|c}3&21 \\\hline 7&7 \\ \hline &1\end{array}} \end{gathered}\end{gathered}[/tex]
Therefore,
[tex]\star \: 12 = {2}^{2} \times {3}^{1}[/tex]
[tex] \star \: 15 = {3}^{1} \times {5}^{1}[/tex]
[tex]\star \: 21 = {3}^{1} \times {7}^{1}[/tex]
✧ LCM of 12, 15 and 21 = [tex]\sf {2}^{2} \times {3}^{1} \times {5}^{1} \times {7}^{1}[/tex]
[tex] \implies 420[/tex]
✧ HCF of 12, 15 and 21 = [tex]\sf {3}^{1} [/tex]
[tex] \implies 3[/tex]
[tex] {\large{\textsf{\textbf{\underline{\underline{Question \: 2 :}}}}}}[/tex]
Using,
LCM × HCF = Product of two given numbers
Putting the values,
[tex]\longrightarrow \sf 48 \times 12 = 16 \times y[/tex]
[tex]\longrightarrow \sf \dfrac{ \cancel{48} _{3} \times 12}{ \cancel{16}{ _1} } = y[/tex]
[tex]\longrightarrow \sf y = 3 \times 12[/tex]
[tex] \longrightarrow {\sf{{{\boxed{\green{\bold {\sf y = 36 }}}}}}}[/tex]
Therefore,
The value of y = 36
[tex]{\large{\textsf{\textbf{\underline{\underline{Important \: points :}}}}}}[/tex]
• A natural number "P" > 1 having only two factor one and "P" itself is called prime number.
• A prime number is never negative.
• H.C.F is the product of smallest power of each common prime factor.
• L.C.M is the product of greatest power of each prime factor.
• HCF is always a factor of LCM.
[tex]\underline{\rule{300pts}{3pt}}[/tex]
anyone know the answer?
Answer:
d. 15√5
Step-by-step explanation:
Perimeter = 3√5 × 5 sides
= 15√5
Answer: B - 15√5
Step-by-step explanation:
As said in the question, the perimeter is the total length of all sides of a figure. The question also says that all sides are the same length, and the length of one side is 3√5 yards.
In that case, all 5 sides have length 3√5 yards, so the perimeter would be this value added 5 times, or this value multiplied by 5:
[tex]P=3\sqrt{5}+3\sqrt{5}+3\sqrt{5}+3\sqrt{5}+3\sqrt{5}=5*3\sqrt{5}[/tex]
[tex]P=15\sqrt{5}[/tex]
Hence, the perimeter of the chicken coop is 15√5 yards.
please help em
A (1,2), B(3,8) and C(7,4) are the corners of a triangle. Draw this triangle on a grid.
The triangle drawn on a grid is in the image attached and the complete procedure for the construction of the triangle is summarized in the explanation.
How to draw a triangle on a Cartesian plane
In this question we are asked to draw a triangle on a Cartesian plane. The procedure is summarized below:
Mark the points of the vertex on the plane with respect to the origin.Connect each pair of points by drawing straight line segments.Lastly, we present the result of this method in the image attached below.
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Divide quotient and remainder (image)
Answer:
Hi, I'm not for sure but I think for sure for the answer is, I haven't done this math in a while btw I like math lol, but I will try my best for this answer:
The quotient: x + 4
The remainder: - 2
Step-by-step explanation:
I hope this helps you and have a lovely day of learning!
What is the sum of the lengths, in centimeters, of the two legs of a 30-60-90 right triangle, if the length of the hypotenuse is $2\sqrt{6}$ centimeters
The sum of the lengths of two legs of the 30°-60°-90° right triangle is 6.69 centimeters. Using the ratio of sides for the 30°-60°-90° triangle, the sum is calculated.
What is the ratio of sides for the 30°-60°-90° triangle?The ratio for the 30°-60°-90° triangle is 1:√3:2 or x:x√3:2x
where x corresponds to the length opposite the 30° angle and x√3 is opposite of the 60° angle and 2x is opposite to the 90° angle.
Calculation:It is given that the triangle is a right triangle with angles 30°-60°-90°
For such a triangle, the ratio of side lengths is x: x[tex]\sqrt{3}[/tex]:2x
we have the length of the hypotenuse is [tex]2\sqrt{6}[/tex]
So, 2x = [tex]2\sqrt{6}[/tex]
⇒ x = [tex]\sqrt{6}[/tex]
So,
the other length of the other leg is x√3 = √6 × √3 = 3 √2
Then, the sum of these two legs = √6 + 3√2 = 6.69 centimeters.
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what does it mean if x=1?
The meaning of the equation x=1 is that the numerical value of variable X is; 1.
What is the meaning of x=1?It follows from the task content that the mathematical meaning of the equation x=1 be explained.
By virtue of the equality sign, it follows that the numerical value of variable x is 1 and hence, 1 can be substituted for variable x in any mathematical expression within the context of discuss.
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GEOMETRY HELP ASAP PLEASE!!)
Chad had a garden that was in the shape of a rectangle Its original width was 3 feet and its original length was 8 feet.
He decided to make a new garden that was 3 feet wider and 2 feet longer than his first garden.
How much larger is the area, in square feet, of his new garden compared to his original garden?
Fill in the blank by entering only a number for your answer.
Answer:
36
Step-by-step explanation:
Chad's original garden is 3 ft x 8 ft.
original area = 3 x 8 = 24 square feet
Chad's super Chadly new garden is 3 feet wider, and 2 feet longer.
new width = 3 + 3 = 6
new length = 8 + 2 = 10
new Area = 6 x 10 = 60 square feet
To find how much larger the new area is, subtract the original area.
60 – 24 = 36 square feet
A red team, blue team and green team were playing a game. The 3 people on the red team each lost 15 points. The 6 people on the blue team each gained 14 points. The 5 people on the green team each lost 11 points.
1. What is the total gain/loss for each team? Write your answer as a integer.
Team red:
Team blue:
Team green:
2. The twist in this game is that you need to multiply your final score by -6. Who won the game and what was their final score? The team with the greatest integer wins.
Team————wins with———-points.
Simplify. Show work.
3² x 5 + 4 =
Answer:
49
Step-by-step explanation:
[tex]3^{2} *5+4[/tex]
= [tex]9*5+4[/tex] Simplify the exponents.
= [tex]45+4[/tex] Multiplication.
= 49 Addition.
Answer:
49
Step-by-step explanation:
1. Whenever there is an exponent, we solve that first. 3^2 is 9.
2. In an equation, multiplication, and division is first, and since there is no division in the equation, we do the multiplication first. 9 x 5 is 45.
3. We finish by adding 4 to 45, which is 49.
A doctor claims that the mean number of hours of sleep that seniors in high school get per night differs from the
mean number of hours of sleep college seniors get per night. to investigate, he selects a random sample of 50
high school seniors from all high schools in his county. he also selects a random sample of 50 seniors from the
colleges in his county. he constructs a 95% confidence interval for the true mean difference in the number of hours
of sleep for seniors in high school and seniors in college. the resulting interval is (0.57, 1.25). based upon the
interval, can the doctor conclude that mean number of hours of sleep that seniors in high school get per night
differs from the mean number of hours of sleen college seniors net ner night?
In light of the provided confidence interval, the following is the best answer on the outcome of the hypothesis test:
Yes, because 0 is not in the confidence interval.
What are the hypotheses tested?At the null hypotheses, it is tested if the difference is equals to zero, that is:[tex]$H_{0}: \mu=0$[/tex]
At the alternative hypotheses, it is tested if it is different, hence:[tex]$H_{1}: \mu \neq 0$[/tex]
The confidence interval is (0.57, 1.25). Since it does not contain 0, there is enough evidence that the difference is different of 0.yes, because 0 is not in the confidence interval
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Assuming a level of significance of 0.01, is there sufficient evidence to show that the manufacturer needs to recalibrate the machines
Answer: Yes, there is
Step-by-step explanation:
A distribution of probabilities for random outcomes of a bivariate or dichotomous random variable is called a Group of answer choices binomial probability distribution distribution of expected values random variable distribution mathematical expectation
A distribution of probabilities for random outcomes of bivariate or dichotomous random variables is called (A) binomial probability distribution.
What is a binomial probability distribution?The binomial distribution with parameters n and p in probability theory and statistics is the discrete probability distribution of the number of successes in a succession of n separate experiments, each asking a yes-no question and each with its own Boolean-valued outcome: success or failure.The binomial distribution is widely used to describe the number of successes in a sample of size n selected from a population of size N with replacement. If the sampling is done without replacement, the draws are not independent, and the resulting distribution is hypergeometric rather than binomial. Binomial probability distribution refers to a distribution of probabilities for random outcomes of bivariate or dichotomous random variables.As the description itself says, binomial probability distribution refers to a distribution of probabilities for random outcomes of bivariate or dichotomous random variables.
Therefore, a distribution of probabilities for random outcomes of bivariate or dichotomous random variables is called (A) binomial probability distribution.
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Complete question:
A distribution of probabilities for random outcomes of bivariate or dichotomous random variables is called a ______.
Group of answer choices
(A) binomial probability distribution
(B) distribution of expected values
(C) random variable distribution
(D) mathematical expectation
The function f(x) = is translated left 5 units and up 3 units to create the function g(x). what is the domain of g(x)? {x | x > –5} {x | x > –3} {x | x > 3} {x | x > 5}
Answer:
{x | x > –5}
{x | x > –3}
{x | x > 3}
{x | x > 5}
Step-by-step explanation:
look at the image for any information and the question thank you
The measure of angle CKB (m ∠CKB) is 144°
Calculating anglesFrom the question, we are to determine the measure of angle CKB (m ∠CKB)
First, we will determine the value of x
From the given information,
m ∠KAE = 3x
m ∠KCD = 2x
In the diagram,
m ∠KCD = m ∠AKE (Alternate angles)
∴ m ∠AKE = 2x
Also,
m ∠KAE + m ∠AKE + m ∠AEK = 180° (Sum of angles in a triangle)
3x + 2x + 90° = 180°
5x = 180° - 90°
5x = 90°
x = 90°/5
x = 18°
But,
m ∠CKB = 180° - m ∠AKE (Sum of angles on a line segment)
m ∠CKB = 180° - 2x
m ∠CKB = 180° - 2(18°)
m ∠CKB = 180° - 36°
m ∠CKB = 144°
Hence, the measure of angle CKB (m ∠CKB) is 144°
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Given the choice between doing an oral and written report ,18 of the 28 students chose to do an oral report find the ratio of written to oral report
Answer:
5:9
Step-by-step explanation:
So since 18 chose to do oral report, that means (28-18) or 10 students decided to do a written report.
To find the written to oral report ration, we need to find for each student that did a written report, how many did an oral report? We can express this as a fraction and simplify to get the simplified ratio. So the the written will be the numerator and the oral will be the denominator: 10/18, to simplify this simply divide both sides by 2, to get 5/9 which gives us the simplified ratio of 5:9 meaning that for every 5 students who decided to do a written report 9 students decided to do an oral report.
pls answer this fast i need the answer
Using a system of equations, the parts are of 14 and 20.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are x and y. The total is of 34, hence:
x + y = 34 -> y = 34 - x.
The ratios are given as follows:
[tex]\frac{4}{7}x = \frac{2}{5}y[/tex]
Then:
[tex]\frac{4}{7}x = \frac{2}{5}(34 - x)[/tex]
20x = 14(34 - x)
34x = 34 x 14
x = 14, y = 34 - 14 = 20.
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LaQuinta is in the French club with 25 other students. Three exchange
students will be attending her school from France. If the French teacher
chooses a student at random to guide each of the visiting students, what is
the probability that LaQuinta will NOT be picked as a guide?
Answer: 23/26
Step-by-step explanation:
Let’s say we have 3 spots, one for each of the three exchange students. It doesn’t matter who goes with who, we’re just going to choose people.
If LaQuinta is NOT one of the people chosen, then there are 25 possible people left to become tour guides. We will need to choose 3 of them, so there are (25 choose 3) = 2,300 ways.
With no restrictions, there are 26 people to choose from and 3 spots to fill. Therefore there are (26 choose 3) = 2,600 ways to fill these 3 spots with no restrictions.
The total probability is 2,300/2,600, which simplifies to 23/26.
If i start my trip driving at x mph for a hours and then go 5 mph slower for the next 2 hours what is the total distance i traveled.
Total distance travelled = (x.a + 2x -10) miles .
How to solve such time related questions?
The key concept for solving such questions is the relationship between speed, distance and time.
The relationship between them is Distance = Speed X Time
The whole trip can be divided into two parts
Part 1 :- Speed = x mph and time = a hours
∴ Distance = x .a miles
Part 2 :- Speed = x -5mph and time = 2 hours
∴ Distance =(x-5).2 = (2x -10)miles
Total distance = (x.a + 2x -10) miles
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Please help me quickly.
Thank you
Answer:
[tex]x = \bf -7[/tex]
Step-by-step explanation:
[tex]\frac{3}{4} (x + 21) = 10\frac{1}{2}[/tex]
• Divide both sides by [tex]\frac{3}{4}[/tex] :
⇒ [tex]x + 21 = 10\frac{1}{2} \space\ \div \frac{3}{4}[/tex]
⇒ [tex]x + 21 = 10\frac{1}{2} \space\ \times \frac{4}{3}[/tex]
⇒ [tex]x + 21 = 14[/tex]
• Subtract 21 from both sides:
⇒ [tex]x = 14 -21[/tex]
⇒ [tex]\boxed {x = \bf -7}[/tex]
Another copy machine also has the ability to reduce image dimensions, but by a different percentage. This graph shows
the results found when copying a design x times. Use the graph to write the equation modeling this relationship.
-10
2 3 4
6 7 8
Enter the correct answer in the box by feplacing the values of a and b.
The correct values for a and b which models this relationship through an exponential function are 8 and 2 respectively.
What is an exponential function?An exponential function can be defined as a mathematical function whose values are generated by a constant that is raised to the power of the argument. Mathematically, an exponential function is represented by this formula:
f(x) = eˣ
How to write an equation modeling this relationship?Based on the information provided, we can logically deduce that the other copy machine can reduce image dimensions by a different percentage and this is defined by the following exponential function:
f(x) = abˣ
From the graph (see attachment), we have;
When x = 0, y = f(x) = 8. Thus, f(0) = 8
f(x) = abˣ
8 = ab⁰
8 = a × 1
a = 8.
Also, from the graph (see attachment), we have;
When x = 1, y = f(x) = 4
f(x) = abˣ
4 = 8b¹
4 = 8 × b
4 = 8b.
b = 8/4
b = 2.
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Erin’s car uses 6 gallons of gas for every 138 miles she drives.which equation could be used to find how many gallons,g, Erin needs to drive 92 miles. Answer choice A : 23=92g B:23=183g C:92=23g D:138=23g
The equation that could be used to find how many gallons Erin would need to drive 92 miles is 92 = 23g (option c)
How many gallons is needed to drive 92 miles?
The first step is to determine the gallons needed to drive 1 mile. To do this, divide the 6 gallons by 138 miles. Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷.
Gallons needed for 1 mile = 6/138
In order to determine the gallons needed for 92 miles, multiply the ratio gotten in the previous step by 92
(6/138) x 92 = 4 gallons
The option that gives 4 gallons is : 92 = 23g
g = 92 / 32 = 4
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.
An ant is standing at the centers of a perfectly circular plate. If the ant crawled in a straight line, he would have to crawl 6 inches to reach the edge of the plate. How many inches would he crawl if he crawled a full circle around the edge of the plate?
The length around the circular edge of the plate is 37.68 inches
How to find the circumference of a circle?The circumference of a circle can be solved as follows:
The ant is standing at the centre of a perfectly circular plate and it walks to the edge of the plate .
The centre of the plate to the edges is 6 inches. Therefore, the radius of the circular plate is 6 inches.
Hence, the distance around the edge of the plate is the circumference of the plate.
Therefore,
circumference of the circular plate = 2πr
circumference of the circular plate = 2 × π × 6
circumference of the circular plate = 12π
circumference of the circular plate = 12 × 3.14
circumference of the circular plate = 37.68 inches
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Suppose the shipping weight of your cheese shop's customized gift baskets is asymmetrically distributed with unknown mean and standard deviation. for a sample of 45 orders, the mean weight is 66 ounces and the standard deviation is 10.2 ounces. what is the upper bound of the 95 percent confidence interval for the gift baskets average shipping weight?
a. note that the correct answer will be evaluated based on the z-values in the summary table in the teaching materials section.
please round your answer to the nearest tenth.
b. note that the correct answer will be evaluated based on the full-precision result you would obtain using excel.
Using the t-distribution, the upper bound of the 95 percent confidence interval for the gift baskets average shipping weight is of 69.06 ounces.
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.For this problem, the parameters are:
[tex]\voerline{x} = 66, t = 2.0154, s = 10.2, n = 45[/tex]
Hence the upper bound of the interval is:
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 66 + 2.0154\frac{10.2}{\sqrt{45}} = 69.06[/tex]
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Which of the following interface validation checks is useful in verifying that the birth data you entered on your job application indicates that you meet the minimum age requirement to serve alcohol
The interface validation that would help to confirm that you meet the minimum age is the range check.
What is the range check?This is the term that is used to refer to the check that is done in such a way that it shows the data that are in a particular range.
This would help to ensure that there is a specified upper and lower boundary for the values to fall into.
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complete questionwhich of the following interface validation checks is useful in verifying that the birth data you entered on your job application indicates that you meet the minimum age requirement to serve alcohol?
Consistency check
Format check
Completeness check
Range check
.- An employee at the local ice cream parlor asks three customers if they like chocolate ice cream. Identify the sample and the population. (circle the letter that is your answer
Sample is the 3 selected customers; And population is all customers
According to the statement
we have given that a shopkeeper asks 3 customers to taste the chocolate icecream.
And we have to identify the sample and population.
So, A definition of sample is that a
A sample is an outcome of a random experiment. When we sample a random variable, we obtain one specific value out of the set of its possible values. That particular value is called a sample.
And a Population is defines as the is a discrete group of people, animals or things that can be identified by at least one common characteristic for the purposes of data collection and analysis.
So, according to definition Sample is the 3 selected customers; And population is all customers.
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standard deviation sign and the mean sign
Answer:
standard deviation sign is σ
mean sign is x , and sometimes it have a hyphen directly above x.
Step-by-step explanation:
Greetings!standard deviationIn statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.
MeanIt is the sum (total) of all the values in a set of data, such as numbers or measurements, divided by the number of values on the list. To find the mean, add up all the values in the set. Then divide the sum by how many values there are.
summationThe symbol ∑ indicates summation and is used as a shorthand notation for the sum of terms that follow a pattern.