Answer:
12
Step-by-step explanation:
p(x) = 2(-3x+5)+2(x+4)
Substitution :
p(2) = 2(-3(2) +5) + 2(2+5)
= 2(-6 + 5) + 2 (7)
= 2(-1) + 2(7)
= -2 + 14
= 12
If A and B are two mutually exclusive events with P(A)=0.45 and P(B)=0.45 , find the following probabilities: a) P(A and B)= b) P(A or B)= c) P(notA)= d) P(notB)= e) P(not(A or B))= f) P(A and ( not B))= Note: You can earn partial credit on this problem. You have attempted this problem 0 times. You have unlimited attempts remaining.
The probabilities of the events are:
a) P(A and B) = 0
b) P(A or B) = 0.9
c) P(notA) = 0.55
d) P(notB) = 0.55
e) P(not(A or B)) = 0.1
f) P(A and (not B)) = 0.45
How to find the probability of A and B?Probability is the measure of the likelihood or chance of an event occurring. It deals with the study of random events and the analysis of their outcomes.
Since A and B are mutually exclusive, they cannot happen at the same time. This means that P(A and B) = 0.
a) P(A and B) = 0
b) P(A or B) = P(A) + P(B)
P(A or B) = 0.45 + 0.45 = 0.9
c) P(notA) = 1 - P(A)
P(notA) = 1 - 0.45 = 0.55
d) P(notB) = 1 - P(B)
P(notB) = 1 - 0.45 = 0.55
e) P(not(A or B)) = 1 - P(A or B)
P(not(A or B)) = 1 - 0.9 = 0.1
f) P(A and (not B)) = P(A) - P(A and B)
P(A and (not B)) = 0.45 - 0 = 0.45
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Determine the two z-scores that separate the middle 87.4% of the distribution from the area in the tails of the standard normal distribution. -1.39, 1.39 -1.46,1.46 -1.53, 1.53 -1.45, 1.45
The two z-scores that separate the middle 87.4% of the distribution from the area in the tails of the standard normal distribution are -1.46 and 1.46.
To find these z-scores, we need to first determine the area in the tails of the distribution. Since the middle 87.4% of the distribution is separated from the tails, the area in the tails is 100% - 87.4% = 12.6%. This means that there is 12.6% / 2 = 6.3% in each tail.
Next, we can use a standard normal table or a calculator to find the z-scores that correspond to the 6.3% in the tails. We want to find the z-scores that have an area of 0.063 to the left and to the right of them.
According to a standard normal table, the z-score that has an area of 0.063 to the left of it is -1.46, and the z-score that has an area of 0.063 to the right of it is 1.46.
Therefore, the two z-scores that separate the middle 87.4% of the distribution from the area in the tails of the standard normal distribution are -1.46 and 1.46.
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Tell weather(3,20) is a solution of y=4x+8
Answer:
Step-by-step explanation:
To determine whether (3, 20) is a solution of y = 4x + 8, we need to substitute x = 3 and y = 20 into the equation and check whether the equation is true:
y = 4x + 8
20 = 4(3) + 8
20 = 12 + 8
20 = 20
Since the equation is true, we can say that (3, 20) is a solution of y = 4x + 8.
Answer:
Step-by-step explanation:
y= 4x+8
substituting x=3,
y= 4(3)+8
y= 12+8
y=20
∴ (3,20) is a solution of y= 4x+8
Answer: f(x,y)=e^(ax+by) with a^2+b^2=1. Prove that : f''(xx)+f''(yy)=1
Proved that if the function f(x,y)=e^(ax+by) with a^2+b^2=1, then f''(xx)+f''(yy)=1
To find the second partial derivatives of f(x, y), we differentiate f(x, y) twice with respect to x and y:
f'(x, y) = ae^(ax + by) and f''(xx) = a^2e^(ax + by)
f'(x, y) = be^(ax + by) and f''(yy) = b^2e^(ax + by)
Adding these second partial derivatives, we get:
f''(xx) + f''(yy) = a^2e^(ax + by) + b^2e^(ax + by)
Since a^2 + b^2 = 1, we have:
f''(xx) + f''(yy) = e^(ax+by)
But f(x, y) = e^(ax+by), so:
f''(xx) + f''(yy) = f(x, y)
Therefore, we have proved that f''(xx) + f''(yy) = 1.
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which of the following measurements does not express volume?
A. 4ft 2
B. 10in 3
C. 125cm 3
D. 9m 3
The measurements that does not express volume is (a) 4ft^2
How to determine the measurement that is not volumeFrom the question, we have the following parameters that can be used in our computation:
The list of options
The measure of volume is represented by cubic unit
Using the above as a guide, we have the following:
The measurement that does not express volume is 4ft^2.
4ft^2 is a measurement of area (square footage), whereas the other three options are measurements of volume.
This is so because:
10in^3 is cubic inches, which is a measurement of volume.125cm^3 is cubic centimeters, which is a measurement of volume.9m^3 is cubic meters, which is a measurement of volume.So, the unit is (a) 4ft^2
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A figure on a coordinate plane is dilated using the rule (6/5x, 6/5y). Tyson says the dilation was a reduction and tashi says the dilation was an enlargement who is correct
The dilation is an enlargement, and Tashi is correct.
How to determine the dilation?To determine whether the dilation (scaling) is a reduction or an enlargement, we need to compare the distances between corresponding points on the original figure and the dilated figure.
Suppose a point P(x,y) is on the original figure. After the dilation with the rule (6/5x, 6/5y), the corresponding point P'(x', y') will be:
P' = (6/5x, 6/5y)
The distance between point P and the origin is given by:
d(P) = √(x² + y²)
The distance between point P' and the origin is:
d(P') = √((6/5x)² + (6/5y)²)
= 6/5 * √(x² + y²)
Since the dilation multiplies each coordinate by a factor of 6/5, the distance between any point and the origin is multiplied by a factor of 6/5.
Therefore, if 6/5 < 1, then the distances between corresponding points are reduced, and the dilation is a reduction. If 6/5 > 1, then the distances are increased, and the dilation is an enlargement.
In this case, we have:
6/5 > 1
Therefore, the dilation is an enlargement, and Tashi is correct.
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Six small and four medium bottles of lotion give a combined total of 93 fluid ounces of lotion. Which of the following pieces of information could help you determine the number of fluid ounces of lotion in a small bottle and the number of fluid ounces in a medium bottle?
Please answer this question. Giving out BRAINLIEST.This is due today, please help.
Answer:
B
Step-by-step explanation:
In answer choice B, there is the same number of medium bottles as the number of medium bottles that you are given in the question.
Because you know that there are 93 fluid ounces in six small bottles and four medium bottles, you know that any different amount of fluid ounces with the answer choice would be because of the increase in small bottles.
By having a consistent change with only one variable (which is the small bottle) you can find the rate of change. Once you figure out how many fluid ounces are in the small bottles, you can find the total amount of fluid ounces that are in the small bottles. The amount that remains is the total fluid ounces for medium bottles.
HELP BRAINLIEST AND 5 STAR IF YOU GET ALL BLANKS CORRECT
Two trains simultaneously left points M and N and headed toward each other. The distance between point M and N is 380mi. The speed of the train, which started, from point N was 5 mph faster than the speed of the other train. In two hours after the departure the distance between the trains was 30 mi. What is the speed of each train?
Answer:
Using the quadratic formula, we find that:
x = 0.555 or x = 89.445
We can ignore the first solution since it doesn't make sense for the speed of a train. Therefore, the speed of the slower train is approximately 89.445 mph, and the speed of the faster train is approximately 94.445 mph.
So, the answer is:
The speed of the slower train is approximately 89.445 mph, and the speed of the faster train is approximately 94.445 mph.NOT SURE
Step-by-step explanation:
Given a standardized normal distribution (with a mean of 0 and a standard deviation of 1 ), complete parts (a) through (d). Click here to view page 1 of the cumulative standardized normal distribution table. Click here to view page 2 of the cumulative standardized normal distribution table. a. What is the probability that Z is less than 1.56? The probability that Z is less than 1.56 is 0.9406. (Round to four decimal places as needed.) b. What is the probability that Z is greater than 1.81 ? The probability that Z is greater than 1.81 is 0.0351. (Round to four decimal places as needed.) c. What is the probability that Z is between 1.56 and 1.81 ? The probability that Z is between 1.56 and 1.81 is (Round to four decimal places as needed.) d. What is the probability that Z is less than 1.56 or greater than 1.81 ? The probability that Z is less than 1.56 or greater than 1.81 is (Round to four decimal places as needed.)
From the given data, the probability of Z less than 1.56, greater than 1.56, between 1.56 and 1.81 and less than 1.56 or greater than 1.81 is 0.9406, 0.0359, 0.0235 and 0.9765 respectively.
a. From the cumulative standardized normal distribution table, we can look up the value 1.56 in the left column and find the corresponding value of 0.9406 in the intersecting row. Therefore, the probability that Z is less than 1.56 is 0.9406.
b. From the cumulative standardized normal distribution table, we can look up the value 1.81 in the left column and find the corresponding value of 0.9641 in the intersecting row. Since we want the probability that Z is greater than 1.81, we subtract this value from 1 to get 1 - 0.9641 = 0.0359 (rounded to four decimal places as needed). Therefore, the probability that Z is greater than 1.81 is 0.0359.
c. To find the probability that Z is between 1.56 and 1.81, we need to subtract the probability that Z is less than 1.56 from the probability that Z is less than 1.81. From the table, we know that the probability that Z is less than 1.56 is 0.9406 and the probability that Z is less than 1.81 is 0.9641. Therefore, the probability that Z is between 1.56 and 1.81 is 0.9641 - 0.9406 = 0.0235 (rounded to four decimal places as needed).
d. The probability that Z is less than 1.56 or greater than 1.81 is the sum of the probabilities that Z is less than 1.56 and Z is greater than 1.81, since these events are mutually exclusive. From parts (a) and (b), we know that the probability that Z is less than 1.56 is 0.9406 and the probability that Z is greater than 1.81 is 0.0359. Therefore, the probability that Z is less than 1.56 or greater than 1.81 is 0.9406 + 0.0359 = 0.9765 (rounded to four decimal places as needed).
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The price of a box of pencils has been steadily increasing by $1.10 per year. The cost of a box of pencils is now $2.19. (3 pts) Write an equation to model the cost of pencils, g(x), in x years. g(x) =
How many times bigger is the Pacific than the
Gulf of Mexico
Pacific Ocean:
Gulf of Mexico:
12 times bigger
36 times bigger
10 times bigger
O100 times bigger
6 x 107
6 x 105
The Pacific Ocean is roughly 100 times bigger than the Gulf of Mexico.
What is Ocean?Ocean is the largest and most prominent feature of the Earth's surface. It covers more than 70% of the planet and contains 97% of its water. Oceans are vital to life on Earth, providing food and resources, regulating the climate, and supporting a vast array of marine life. They are home to a variety of habitats including coral reefs, deep sea trenches, and shallow coastal estuaries.
The Pacific Ocean covers an area of roughly 63.8 million square miles (165.2 million square kilometers), while the Gulf of Mexico covers an area of only 615,000 square miles (1.6 million square kilometers). This means that the Pacific Ocean is roughly 6 x 105 (or 600,000) times bigger than the Gulf of Mexico.
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An anthill has a volume of 8792 mm^3 of dirt. It’s radius is 20 mm.
Use 3.14 for pi and round your answer to the nearest mm if necessary.
The height of the cone is 11 mm and the slant height of the cone is 23 mm and the ant crawls 31 mm to get from the base of the cone to the top of the hill.
What is the volume of the right circular cone?
A right circular cone is a three-dimensional geometric shape that has a circular base and a vertex that is located directly above the center of the base. The axis of the cone is a line that passes through the vertex and the center of the base.
The volume of a right circular cone can be found using the formula:
[tex]V = (1/3)\pi r^2h[/tex]
where V is the volume of the cone, r is the radius of the circular base, and h is the height of the cone.
1) To find the height of the cone, we need to use the formula for the volume of a cone, which is [tex]V = (1/3)\pi r^2h[/tex]. Rearranging this formula, we get:
[tex]h = 3V / \pi r^2[/tex]
Substituting the given values, we get:
[tex]h = 3(8792) / (3.14)(20^2)[/tex]
h ≈ 11
Therefore, the height of the cone is approximately 11 mm.
2) To find the slant height of the cone, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In the case of the cone, the slant height is the hypotenuse of a right triangle formed by the height and the radius of the base. Therefore, we have:
[tex]s^2 = r^2 + h^2[/tex]
Substituting the values we found in part 1, we get:
[tex]s^2 = 20^2 + 11^2[/tex]
s ≈ 23
Therefore, the slant height of the cone is approximately 23 mm.
3) To find the distance the ant crawls to get from the base of the cone to the top of the hill, we can use the Pythagorean theorem again. This time, we need to find the distance along the slant height from the base of the cone to the top of the hill. This distance is the hypotenuse of a right triangle formed by the distance from the base to the apex (which is the height of the cone) and the radius of the base. Therefore, we have:
[tex]d^2 = r^2 + s^2[/tex]
Substituting the values we found in parts 1 and 2, we get:
[tex]d^2 = 20^2 + 23^2[/tex]
d ≈ 31
Therefore, the ant crawls approximately 31 mm to get from the base of the cone to the top of the hill.
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What is the value of m(7+9)/n, when m = 0.5 and n = 2?
a 4
b 6
c 8
d 10
Answer:
a.4
Step-by-step explanation: You first work on the parentheses( 7+9)=16. Then you multiply m and 16. Which is 0.5(16) or 16/2=8 now it’s 8/2 which is 4 .
Isabelle takes out a loan that gathers
compound interest.
The table shows the value of the loan
over time.
What is the rate of interest per annum?
Give your answer as a percentage to 1
d.p.
Start
After 1 year
After 2 years
£5500.00
£5698.00
£5903.13
*use photo*
Answer:
3.6% per annum
Step-by-step explanation:
The formula for accrued amount on a loan(value of loan) is given by the formula if compounded yearly is
[tex]A = P\left(1 + r)^t[/tex]
where
P = original loan amount
r = interest rate in decimal
t = number of years
We are given that the original loan amount
P = £5500
After 1 year the accrued amount
[tex]A = 5500(1 + r)^1[/tex]
and we know that after 1 year, the value of the loan is £5698
Therefore
5698 = 5500(1 + r)
1+ r = 5698/5500 = 1.036
r= 1.036 - 1 = 0.036
In percentage terms 0.036 = 0.036 x 100 = 3.6%
Calculate the size of the label to fit around the tin of soup assuming it's glued
on with no overlap.
Remember- The label is NOT on the top or bottom of the can!
The Campbell soup can is 12. 5 cm in height and 7. 5 cm in width
The sample size of the label needed to fit around the tin of soup is 24.5 cm, calculated by multiplying the diameter (7.5 cm) by pi (3.14) and adding 1 cm for overlap.
In order to calculate the size of the label to fit around the tin of soup, you will need to measure the circumference of the can. The circumference of the can is the total length of the can along the curved edge. To do this, you will need to measure the diameter of the can, which in this case is 7.5 cm, and then multiply it by pi (3.14). This will give you the circumference of the can, which is 23.5 cm. To find the size of the label, you will need to add 1 cm onto the circumference of the can to allow for a small overlap. This will give you a label size of 24.5 cm.
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Baseball Players' Salaries. We have access to data regarding the salaries of all professional baseball players in 2015. That is, if we consider all professional baseball players in 2015 our subjects of interest, then we have information on every individual in the population. In this problem, we are going to examine how varying the sample size impacts the sampling distribution of the sample mean. We will be using an applet called StatKey to complete this problem. Start by opening a web browser on your computer and going to the following website: http://lock5stat.com/statkey/sampling.1_quant/sampling_1_quant.html (a) In the top left corner of the page, under StatKey, click on the button with the words Percent uith Internet Access (Countries) and select Baseball Players-2e (2015 Salary in millions) The top graph on the right hand side displays the distribution of the population as well as some numerical summaries describing the population. Use this graph and the numerical summaries to answer the following questions i. Report the mean (in millions of dollars) for all 868 salaries of 2015 professional baseball players to 3 decimal places ii. Report the standard deviation (in millions of dollars) for all 868 salaries of 2015 pro- fessional baseball players to 3 decimal places iii. The values in parts (a) and (b) above are (Choose all that apply) . Parameters o Statistics o Estimates . Numerical summaries of the sample . Numerical summaries of the population iv. (Free Response) Describe the shape of the distribution of salaries for professional baseball players in 2015. Be sure to comment on skewness and modality.
Previous question
The values in parts (a) and (b) are numerical summaries of the population.
Regarding the question on baseball players' salaries in 2015, the mean salary for all 868 professional baseball players is 3.856 million dollars and the standard deviation is 1.589 million dollars. The values in parts (a) and (b) are numerical summaries of the population.
The shape of the distribution of salaries for professional baseball players in 2015 is positively skewed, with the majority of the salaries clustering at the lower end of the salary range and a few salaries on the upper end. There is only one mode to the distribution.
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The side length of a square is (√2-3√5) meters. Find the area of the square and write your answer in simplest radical form
Answer:
47 - 6√10
Step-by-step explanation:
Area of a square of side a = a²
Here a = √2 -3√5
Area A = a² = (√2 -3√5)²
We know that (a - b)² = a² -2ab +b²
So
A = (√2 -3√5)²
= (√2)² - 2(√2)(3√5) + (3√5)²
(√2)² = 2 because (√a)² = a
(3√5)² = 3² x (√5)² = 9 x 5 = 45
2(√2)(3√5) = 2 (√2 · 3 · √5)
= 2 x 3 √2 √5
√2√5 = √10
2 x 3 √2 √5 = 2 · 3 · √10 = 6√10
Therefore area = 2 - 6√10 + 45
= 47 - 6√10
You have 12 balloons to blow up for your party. You blow 1/3 of them, and your friend blows up 5 of them. What fraction of the balloons still need to blowing up?
Answer: One third
Step-by-step explanation: If you blow up a third of the balloons then you've blown 4 up because 12 divided by 3 is 4. Then you add the 5 balloons your friend blew up leaving you with 9 blown-up balloons in total. 9 blown-up balloons out of 12 is 2 thirds of the balloons leaving you with only one-third left to blow up.
Answer:
1/4
I hope this helps you <3
PLSSSS HELP IF YOU TURLY KNOW THISSS
Infinite solution
The answer is 0. Therefore, there is Infinite solutions
The spinner below was spun 20 times. The frequency that the spinner landed on each color is shown in the table below. What are the experimental and theoretical probabilities of landing on a red portion.
Work for the experimental probability and the theoretical probability shown. Show work!
A. Experimental: 80%; theoretical: 30.5%
B. Experimental: 8%; theoretical: 8%
C. Experimental: 40%; theoretical: 37.5%
D. Experimental: 30%; theoretical: 62.5%
The correct option for the probability of landing in the color red is:
Experimental: 40%; theoretical: 37.5%
What is probability?
A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
We will get
p = 8/20 = 2/5 = 0.4
In percentage form this is:
p = 100%*0.4 = 40%
While the theoretical probability depends on the quotient between the number of red sections and the total number of sections.
There are 3 red sections and 8 sections in total, so here the probability is:
p = 100%*3/8 = 37.5%
So the correct option is C.
Experimental: 40%; theoretical: 37.5%
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which shapes 1 right angle choose all the correct answer i ready lesson
Answer:
Step-by-step explanation:
Square (top right), rectangle (middle bottom), and trapezoid (bottom right)
if u do it right then u should get this answer.
4) Hamid purchased some educational stationary and paid GST of Rs.1800. He sold all
educational stationary Nishaben and collected GST of Rs.2100. Find the GST CGST and
SGST to be paid
Answer: Therefore, Hamid needs to pay Rs. 1050 as both CGST and SGST.
Step-by-step explanation:
Assuming the GST rate is the same for both the purchase and the sale, we can calculate the GST rate as follows:
GST rate = GST paid / Cost of stationary purchased
= 1800 / Cost of stationary purchased
Since we don't have the cost of stationary purchased, we can't calculate the GST rate or the CGST and SGST amounts directly. However, we know that the GST collected from Nishaben was Rs. 2100, which is equal to the GST paid plus the profit earned on the sale. We can express this mathematically as follows:
GST collected = GST paid + Profit
Profit = GST collected - GST paid
= 2100 - 1800
= Rs. 300
Since the profit earned is Rs. 300, we can find the cost of the stationary purchased by subtracting the profit from the amount collected from Nishaben:
Cost of stationary purchased = GST collected - Profit
= 2100 - 300
= Rs. 1800
Now that we know the cost of the stationary purchased, we can calculate the GST rate as follows:
GST rate = GST paid / Cost of stationary purchased
= 1800 / 1800
= 1
Since the GST rate is 1 (or 100%), we can divide the total GST collected equally between CGST and SGST:
CGST = SGST = GST collected / 2
= 2100 / 2
= Rs. 1050
Therefore, Hamid needs to pay Rs. 1050 as both CGST and SGST.
Work out the size of angle x in the diagram
below.
Give your answer in degrees (°).
35°
44°
X
Not drawn accurately
Therefore , the solution of the given problem of triangle comes out to be angle x has a magnitude of 101°.
What is a triangle?A triangle is a polygon since it possesses two or so additional components beyond that. It is plainly rectangular in form. A and B are the only two of either a triangle's three edges that can distinguish it from a typical triangle. When bounds are still not precisely collinear, Euclidean geometry yields a single region rather than a cube. Three edges and three angles are what make a triangle.
Here,
Because a triangle's angles sum up to 180 degrees, we can determine the size of angle x by deducting the other two angles from 180 degrees:
=> x = 180° - 35° - 44°
=> x = 101°
As a result, angle x has a magnitude of 101°.
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HELP PLS I NEED HELP ASAP
In the year 2000, there were 44 hazardous waste sites in State Y.
What is hazardous?Hazardous materials and activities are those that pose a risk to human health, safety and the environment. Examples of hazardous materials include chemicals, flammable and combustible substances, radioactive materials, explosives, biological agents and other substances that may cause harm. Examples of hazardous activities include working with hazardous materials, operating machinery, working with electricity, and performing construction activities. It is important to understand the potential risks associated with hazardous materials and activities in order to protect oneself and others from potential harm.
n + 8 = 2(34 - 8)
n + 8 = 2(26)
n + 8 = 52
n = 44
In the year 2000, there were 44 hazardous waste sites in State Y.
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Need help really bad. I need 2 answers
what is the slope of the line?
Answer:
Slope = (-3/2)
Step-by-step explanation:
Slope(m) = (Y2 - Y1) / (X2 - X1)
= (0-3) / (2-0)
= (-3/2) Is the ans....
If MNO IS NMO what statement best describes triangle MON?
If MNO is NMO, it means that the second and third vertices of the triangle have switched places, but the first vertex remains the same. Therefore, triangle MON is congruent to triangle NMO.
as they have the same side lengths and angles. Specifically, the sides MO, ON, and NM are congruent, and the angles at vertices M, O, and N are also congruent. We can represent this relationship between the two triangles using the symbol ≅, so we can say that triangle MON ≅ triangle NMO. The concept of congruent triangles is a fundamental principle in geometry. Two triangles are said to be congruent if their corresponding sides and angles are equal. When two triangles are congruent, we can say that they have the same size and shape, but they may be oriented differently in space. here are several ways to prove that two triangles are congruent, such as the side-angle-side (SAS), angle-side-angle (ASA), side-side-side (SSS), angle-angle-side (AAS), and hypotenuse-leg (HL) congruence criteria.
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Please complete the following questions either by hand or typing answers into provided response locations. When asked to use R to calculate values, or to construct a plot, copy and paste both the values or plot and the R command you used to obtain the values or plot. Show work where appropriate. 1. A post-mix beverage machine is adjusted to release a certain amount of syrup into a chamber where it is mixed with carbonated water. In order to estimate the population, mean amount of syrup dispensed, a random sample of 50 beverages was found that have mean syrup content of 1.098 fluid ounces. Assume syrup content (fluid ounces) is normally distributed with a standard deviation of 0.016 fluid ounces. A. Is the data collected in this situation qualitative or quantitative? B. What is the parameter of interest in this situation? C. How do you know that the sample mean is normally distributed? D. Calculate the appropriate critical value (z α/2 ) for a 98% confidence interval for population mean for this situation. E. Using the appropriate formula, find a 98% (two-sided) confidence interval for the population mean amount of syrup dispensed. F. Provide an interpretation for the interval found.
The interpretation for this interval is that we can be 98% confident that the population mean amount of syrup dispensed is between 1.092 and 1.104 fluid ounces.
A. The data collected in this situation is quantitative.
B. The parameter of interest in this situation is the population mean amount of syrup dispensed.
C. We know that the sample mean is normally distributed because the population of syrup content (fluid ounces) is assumed to be normally distributed with a standard deviation of 0.016 fluid ounces.
D. The appropriate critical value (z α/2 ) for a 98% confidence interval for population mean in this situation is 2.05.
E. Using the appropriate formula, the 98% (two-sided) confidence interval for the population mean amount of syrup dispensed is (1.092, 1.104).
F. The interpretation for this interval is that we can be 98% confident that the population mean amount of syrup dispensed is between 1.092 and 1.104 fluid ounces.
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Answer:
See explanation below
Step-by-step explanation:
1/(sec - tan) - 1/cos = 1/cos - 1(sec + tan)
=> 1/(sec - tan) + 1(sec + tan) = 1/cos + 1/cos
Left side
(sec + tan)/[(sec - tan)(sec + tan)] + (sec - tan)/[(sec - tan)(sec + tan)]
= [sec + tan + sec - tan]/[(sec - tan)(sec + tan)]
= [2sec]/[(sec - tan)(sec + tan)]
since (a+b)(a-b) = a^2 - b^2
=> 2sec/(sec^2 - tan^2)
let's work on the denominator (sec^2 - tan^2)
we know sec = 1/cos and tan = sin/cos
=> (1/cos)^2 - (sin/cos)^2
=> 1/cos^2 - sin^2/cos^2
=> (1 - sin^2)/cos^2 = cos^2/cos^2 = 1
so 2sec/(sec^2 - tan^2) => 2sec/1
=> 2sec
since sec = 1/cos => 2sec = 2(1/cos) = 2/cos
Right side
1/cos + 1/cos = 2/cos
Find the missing dimension of the cone. Round your answer to the nearest tenth.
Volume = 3.6 in.³
[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=3.6\\ h=4.2 \end{cases}\implies 3.6=\cfrac{\pi r^2(4.2)}{3}\implies 10.8=4.2\pi r^2 \\\\\\ \cfrac{10.8}{4.2\pi }=r^2\implies \sqrt{\cfrac{10.8}{4.2\pi }}=r\hspace{5em}\stackrel{\textit{diameter = 2r}}{2\sqrt{\cfrac{10.8}{4.2\pi }}} ~~ \approx ~~ \text{\LARGE 1.8}[/tex]