Answer:
Check the explanation
Step-by-step explanation:
1
a) A is an Equivalence Relation
Reflexive : x is parallel to itself => x R x
Symmetric : x is parallel to y => y is parallel to x.
Therefore x R y => y R x
Transitive : x is parallel to y and y is parallel to z then x, y, z are parallel to each other.
=> x R y and y R z => x R z
Therefore A is equivalent.
1. b)
x r y if and only if |x-y| less than or equal to 7
Reflexive : |x-x| = 0 <= 7 => x R x Satisfied.
Symmetric : let x R y => |x-y| <= 7
Consider |y-x| = |(-1)*(x-y)| = |x-y| <= 7
=> y R x => Satisfied
Transitive : let x R y and y R x
=> |x-y| <= 7 and |y-z| <= 7
but this doesn't imply x R z
Counter-Example : x = 1, y = 7, z = 10
Therefore this relation is neither Equivalent nor Partial Order Relation.
The relation x r y if and only if x is parallel to y for lines in the plane is an equivalence relation as it is reflexive, symmetric, and transitive. For the set of real numbers with the relation x r y if and only if |x - y| ≤ 7, the relation is neither an equivalence relation nor a partial ordering because it lacks antisymmetry.
Explanation:When determining if a relation is an equivalence relation or a partial ordering, we must assess whether it satisfies specific properties. For a relation to be an equivalence relation, it must be reflexive, symmetric, and transitive. In the case of A = { lines in the plane } and relation r defined by x r y if and only if x is parallel to y, we can say:
Reflexive: Every line is parallel to itself by assumption.Symmetric: If line x is parallel to line y, then line y is also parallel to line x.Transitive: If line x is parallel to line y, and line y is parallel to line z, then line x is parallel to line z.Therefore, this relation is an equivalence relation.
For the set A = R and the relation r defined by x r y if and only if | x − y | ≤ 7, the relation is not a partial ordering because it is not antisymmetric (if x r y and y r x, then x must equal y, which isn't necessarily true for all real numbers within 7 units of each other). However, it is reflexive and symmetric.
Suppose that two balanced dice, a red die, and a green die, are rolled. Let Y denote the value of G - R where G represents the number on the green die and R represents the number on the red die. What are the possible values of the random variable Y?
Answer:
-5,-4,-3,-2,-1,0,1,2,3,4,5
Step-by-step explanation:
The sample space for the two balanced dice, a red die, and a green die is given below in the pair (G,R)
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
For each pair, Y=G-R is presented below:
0 -1 -2 -3 -4 -5
1 (2,2) (2,3) (2,4) (2,5) (2,6)
2 (3,2) (3,3) (3,4) (3,5) (3,6)
3 (4,2) (4,3) (4,4) (4,5) (4,6)
4 (5,2) (5,3) (5,4) (5,5) (5,6)
5 (6,2) (6,3) (6,4) (6,5) (6,6)
The first column and row is representative of the values which will be obtained throughout the table.
Therefore, the possible values of the random variable Y are:
-5,-4,-3,-2,-1,0,1,2,3,4,5
The possible values of Y are its sample space, and the values are 0, -1, -2, -3, -4, -5, 5, 4, 3, 2 and 1
The sample space of the green die is:
[tex]G= \{1,2,3,4,5,6\}[/tex]
The sample space of the red die is:
[tex]R= \{1,2,3,4,5,6\}[/tex]
When the numbers on both dice are combined, we have the following possible outcomes
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6) , (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) , (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) , (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) , (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) , (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
Subtract the second outcomes from the first, to get Y
(0) (-1) (-2) (-3) (-4) (-5) , (-1) (0) (-1) (-2) (-3) (-4) , (2) (1) (0) (-1) (-2) (-3) , (3) (2) (1) (0) (-1) (-2) , (4) (3) (2) (1) (0) (-1) , (5) (4) (3) (2) (1) (0)
List out the unique numbers:
(0) (-1) (-2) (-3) (-4) (-5) (5) (4) (3) (2) (1)
Hence, the possible values of Y are 0, -1, -2, -3, -4, -5, 5, 4, 3, 2 and 1
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An experiment was performed to compare the wear of two different laminated materials. Twelve pieces of material 1 were tested by exposing each piece to a machine measuring wear. Ten pieces of material 2 were similarly tested. In each case, the depth of wear was observed. The samples of material 1 gave an average (coded) wear of 85 units with a sample standard deviation of 4, while the samples of material 2 gave an average of 81 with a sample standard deviation of 5. Can we conclude at the 0.05 level of significance that the abrasive wear of material 1 exceeds that of material 2 by more than two units? Assume the populations to be approximately normal with equal variances pdf
Answer:
At 0.05 level of significance, the abrasive wear of material 1 exceeds that of material 2 by more than 2 units
Step-by-step explanation:
We hypothesize that mean difference between abrasive wear of material 1 and material 2 is greater than 2.
So we write the null hypothesis [tex]H_0 : \mu_1 - \mu_2 >2[/tex],
and the alternative hypothesis [tex]H_1: \mu_1 - \mu_2 \leq 2[/tex].
We will find the T-score as well as the p-value. If the p-value is less than the level of significance, we will reject the null hypothesis, i.e. we will conclude that the abrasive wear of material 1 is less than that of material 2. Otherwise, we will accept the null hypothesis.
Since the variance is unknown and assumed to be equal, we will use the pooled variance
[tex]s_p^2 = \frac{(n_1-1)s_1^2 + (n_2-1)s_2^2}{n_1+n_2-2} = 20.05[/tex],
where [tex]n_1 = 12, n_2 =10, s_1 =4, s_2 = 5[/tex].
The mean of material 1 and material 2 are [tex]\mu_1 =85, \mu_2=81[/tex] respectively and mean difference [tex]d[/tex] is equal to 4. The hypothesize difference [tex]d_0[/tex] is equal to 2.
To find the T-score, we use the following formula
[tex]T = \frac{d - d_0}{\sqrt{\frac{s_p^2}{n_1} + \frac{s_p^2}{n_2} }}[/tex]
Substituting all the values into the T-score formula gives us [tex]T = 1.04[/tex], and the respective p-value is equal to 0.31. This means we have enough statistical evidence not to reject the null hypothesis, and at 5% significance level, the abrasive wear of material 1 exceeds that of material 2 by more than 2 units.
Anne is a tailor and decides to evaluate her business to target potential customers with advertisements. She found that for every 12 women's dresses she alters, she alters 54 men's suits. Write this as a ratio in its simplest form.
Answer:
2/9
Step-by-step explanation:
The ratio is 12/54 which can be simplified by dividing the numerator and denominator by 6 to get 2/9
Write an expression that gives the requested sum.
The sum of the first 20 terms of the geometric sequence with first term 6 and common ratio 3
s20 =
Step-by-step explanation:
To find the sum of first 20 terms,
a = 6, r = 3
By formula, [tex]S_{n} = \frac{a(r^{n}-1) }{r-1}[/tex]
substitute the values in the above formula, the equation becomes,
[tex]S_{20} = \frac{6(3^{20}-1) }{3-1}[/tex]
[tex]S_{20} = \frac{6(3^{20}-1) }{2}[/tex]
[tex]S_{20}[/tex] = [tex]{3(3^{20}-1) }[/tex]
HELP!!!! WILL GIVE BRAINLIEST TO FIRST RIGHT ANSWER!!!
A corporation must appoint a president, chief executive officer (CEO), chief operating officer (COO), and chief financial officer (CFO). It must also appoint a planning committee with five different members. There are 14 qualified candidates, and officers can also serve on the committee.
How many different ways can the officers be appointed?
How many different ways can the committee be appointed?
Answer:
A. 24024
B. 364
Step-by-step explanation:
(a) There are 14*13*12*11 = 24024 ways to select the officers...
(b) Since the officers can also serve on the committee, the sampling
is with replacement, so then there are (14 choose 3) ways to
select the committee members... 364 ways to be exact
Pat needs to determine the height of a tree before cutting it down to be sure that it will not fall on a nearby fence. The angle of elevation of the tree from one position on a flat path from the tree is Upper H equals 60 degrees comma and from a second position Upper L equals 60 feet farther along this path it is Upper B equals 50 degrees . What is the height of the tree?
Answer:
229.23 feet.
Step-by-step explanation:
The pictorial representation of the problem is attached herewith.
Our goal is to determine the height, h of the tree in the right triangle given.
In Triangle BOH
[tex]Tan 60^0=\dfrac{h}{x}\\h=xTan 60^0[/tex]
Similarly, In Triangle BOL
[tex]Tan 50^0=\dfrac{h}{x+60}\\h=(x+60)Tan 50^0[/tex]
Equating the Value of h
[tex]xTan 60^0=(x+60)Tan 50^0\\xTan 60^0=xTan 50^0+60Tan 50^0\\xTan 60^0-xTan 50^0=60Tan 50^0\\x(Tan 60^0-Tan 50^0)=60Tan 50^0\\x=\dfrac{60Tan 50^0}{Tan 60^0-Tan 50^0} ft[/tex]
Since we have found the value of x, we can now determine the height, h of the tree.
[tex]h=\left(\dfrac{60Tan 50^0}{Tan 60^0-Tan 50^0}\right)\cdotTan 60^0\\h=229.23 feet[/tex]
The height of the tree is 229.23 feet.
Please help me 3/4 - minus 5/12
Answer:
1/3
Step-by-step explanation:
For the 1st fraction, since 4 × 3 = 12,
3 /4 = 3 × 3/ 4 × 3 = 9/ 12
Likewise, for the 2nd fraction, since 12 × 1 = 12,
5 /12 = 5 × 1 /12 × 1 = 5 /12
Subtract the two fractions: 9 /12 - 5 /12 = 9 - 5 /12 = 4 /12
So next you simplify the answer how many 4 go in 4 and how many go in 12 the simplified answer is the answer is 1/3
Hope this helps
206, 254, 240, 203, 191, 208, 218, 235, 242, 237, 213, 222, 228, 201, 225, 186 whats the 25th percentile
Answer:
Q1 or the 25th percentile is 204.5
Step-by-step explanation:
Combine all data values in TI-84, excel, or other software and make a box and whisker plot. The Q1 is the first vertical line on the plot
A manufacturer produces piston rings for an automobile engine. It is known that ring diameter is normally distributed with millimeters. A random sample of 15 rings has a mean diameter of . Construct a 99% two-sided confidence interval on the true mean piston diameter and a 95% lower confidence bound on the true mean piston diameter. Round your answers to 3 decimal places. (a) Calculate the 99% two-sided confidence interval on the true mean piston diameter.
Complete Question:
A manufacturer produces piston rings for an automobile engine. It is known that ring diameter is normally distributed with ? = 0.001 millimeters. A random sample of 15 rings has a mean diameter of \bar{X}= 74.106. Construct a 99% two-sided confidence interval on the true mean piston diameter and a 95% lower confidence bound on the true mean piston diameter.
(Round your answers to 3 decimal places.)
(Calculate the 99% two-sided confidence interval on the true mean piston diameter.
Answer:
99% true sided confidence Interval on the true mean Piston diameter = (74.105, 74.107)
Step-by-step explanation:
Check the attached file for the complete solution
Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.) S = {(6, −7, 8, 6), (4, 6, −4, 1)} (a) u = (2, 19, −16, −4) u = −1 s1 + 2 s2 (b) v = 43 2 , 113 4 , −18, 13 2
Answer:
a) Yes, it is a linear combination.
b) Impossible to write as a linear combination.
Step-by-step explanation:
Recall that given vectors u,v,w we say that w is a linear combination of u and v if there exists real numbers a,b such that
[tex]w=au+bv[/tex]
a) [tex] u = (2,19,-16, -4)[/tex]. So, we have the following
[tex] (2,19,-16, -4)=a(6,-7,8,6)+b(4,6,-4,1)[/tex]. Which give us the following equations
[tex]6a+4b = 2[/tex]
[tex]-7a+6b = 19[/tex]
[tex]8a-4b = -16[/tex]
[tex]6a+b =-4[/tex]
Note that if we add the first and the third equation, we get that [tex]14a = -14[/tex] which implies that a=-1. In the first equation, if a=-1, then [tex]4b=2+6[/tex] which implies that b=2. We must check that when (a,b) =(-1,2) the four equations are still valid.
So
[tex]6(-1)+4(2) = -6+8 = 2[/tex]
[tex]-7(-1)+6(2) = 7+12 = 19[/tex]
[tex]8(-1)-4(2) = -8-8 = -16[/tex]
[tex]6(-1)+(2) =-6+2 = -4[/tex]
Since all equations are met, we have written the desired vector u as the linear combination of the initial vectors.
b) Repeating the same analysis, we get
[tex](432 , 1134 , −18, 132)=a(6,-7,8,6)+b(4,6,-4,1)[/tex]
[tex]6a+4b = 432[/tex]
[tex]-7a+6b = 1134[/tex]
[tex]8a-4b = -18[/tex]
[tex]6a+b =132[/tex]
adding the first and third equation we get [tex]14a = 414[/tex] so a = 207/7. Replacing this value will give us that b=891/14.
However,
note that
[tex]-7\frac{207}{7}+6\frac{891}{14} = \frac{1124}{7}\neq 1134[/tex]. Then, it is impossible to write the linear combination.
The question seeks a linear combination of vectors from a given set 'S' that matches specified vectors. Using vector addition and scalar multiplication, it is possible to find a unique combination for each specified vector. If no combination can provide the required vector, 'IMPOSSIBLE' is the answer.
Explanation:In this problem, you're asked to express a given vector as a linear combination of other vectors from the set 'S'. This involves using the properties of vector addition and scalar multiplication to define a unique way to represent each given vector. A linear combination of vectors involves adding or subtracting multiples of these vectors.
For instance, if we have the set S = {(6, -7, 8, 6), (4, 6, -4, 1)}, and we're asked to write the vector u = (2, 19, -16, -4), the correct linear combination would be -1 times the first vector in S plus 2 times the second vector (-1*(6,-7,8,6) + 2*(4,6,-4,1) = (2, 19, -16, -4)). This means vector 'u' would be expressed as u = -1 * S1 + 2 * S2. If no such combination is possible, the answer would be 'IMPOSSIBLE'.
Other important concepts related to this problem include vector addition, scalar multiplication, and the distributive property. Vector addition is both associative and commutative and vector multiplication by a sum of scalars is distributive. The direction and magnitude of vectors are also significant elements to consider while solving such problems.
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Mandy wants to buy a variety of beverages for her birthday party. She wants to make sure she has enough to drink for all her friends, so she decides to buy 10 liters of beverages. If she buys at least one container of each beverage, what combination of beverages can she buy to equal exactly 10 liters? Beverages at the store:
2,000 millilitres of soda, 2.5 liters of apple juice, 1,500 millilitres of fruit punch, 2 liters of lemonade
Answer:
Soda x 2
Apple Juice x 1
Fruit Punch x 1
Lemonade x 1
and
Soda x 1
Apple Juice x 1
Fruit Punch x 1
Lemonade x 2
Step-by-step explanation:
Amounts:
Soda 2L
Apple Juice 2.5L
Fruit Punch 1.5L
Lemonade 2L
S + A + FP + L = 8L
So we need 2 L more. The only way of doing this is by either having 2 lots of soda or 2 lots of lemonade.
The combination of beverages she can purchased;
Soda = 2 container
Apple juice = 1 container
Fruit punch= 1 container
Lemonade = 1 container
Logical reasoning:The quantity of Beverages present at the store ;
Soda = 2000ml = 2L
Apple Juice = 2.5L
Fruit Punch = 1.5L
Lemonade = 2L
We have to buy exactly 10 liters but it should be at least one container of each beverage.
Soda + Apple juice + Fruit Punch + Lemonade = 8L
So we need 2 L more.
The only way of doing this is by either having 2 container of soda or 2 container of lemonade.
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A triangle is drawn on the coordinate plane. It is translated 4 units right and 3 units down. Which rule describes the
translation?
(x, y) - (x + 3, y - 4)
(x,y) → (x + 3, y + 4)
(x, y) - (x +4, Y-3)
(x, y) (x + 4, y + 3)
Answer:
C
Step-by-step explanation:
The correct option is option C , that is the rule which describes the translation is (x, y) → (x + 4, y - 3).
What do you mean by translation ?
The modification of an existing diagram to create a different version of the following diagram is known as translation.
The translated triangle is moved along the x-axis by 4 units, to the right. The numbers get more positive as one moves to the right along the x-axis, hence an additional 4 units should be added to the x-coordinate. So , the coordinate would be x + 4.
Along the y-axis, the triangle is also pushed downward by 3 units. More negative numbers are produced as the axis moves below, hence 3 should be subtracted. So , the coordinate should be y - 3.
Based on the above information, we can conclude that another way to write the given rule by translation is (x, y) → (x + 4, y - 3) .
Therefore , the correct option is option C , that is the rule which describes the translation is (x, y) → (x + 4, y - 3).
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3
4
of a number is 21. What is the number?
Answer:
28
Step-by-step explanation:
3/4x= 21
x= 21(4/3)
x= 28
Check! (optional)
28 x 3/4 = 21
Check correct!!!!!!
Answer:
the number is 28
Step-by-step explanation:
I know this because 21 is 3/4 of a number. 21 divided by 3 is 7, you do this to find what 1/4 of the number is. so then you add 7 to 22 and you get 28!
What is the range of the data below?
—
—
50
60
70
80
90
100
оооо
Answer:
50 all you have to do is subtract the least and the biggest number
Step-by-step explanation:
Making handcrafted pottery usually takes two major steps:wheel throwing and firing. The time of wheel throwing and thetime of firing are normally distributed random variables with meansof 40 min and 60 min and standard deviations of 2 min. and 3 min,respectively.
(a) What is the probability that a piece of pottery will befinished within 95 minutes?
(b) What is the probability that it will take longer than 110minutes?
Answer:
a) [tex]P(R<95)=P(\frac{R-\mu}{\sigma}<\frac{95-\mu}{\sigma})=P(Z<\frac{95-100}{3.606})=P(Z<-1.387)[/tex]
And we can find this probability using the normal standard table or excel and we got:
[tex]P(z<-1.387)=0.0827[/tex]
b) [tex]P(R>110)=P(\frac{R-\mu}{\sigma}>\frac{110-\mu}{\sigma})=P(Z>\frac{110-100}{3.606})=P(Z>2.774)[/tex]
And we can find this probability using the complement rule and the normal standard table or excel and we got:
[tex]P(z>2.774)=1-P(Z<2.774) = 1-0.9972 = 0.0028[/tex]
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Part a
Let X the random variable that represent the time for the step 1 and Y the time for the step 2, we define the random variable R= X+Y for the total time and the distribution for R assuming independence between X and Y is:
[tex]R \sim N(40+60 = 100,\sqrt{2^2 +3^2}= 3.606 s)[/tex]
Where [tex]\mu=65.5[/tex] and [tex]\sigma=2.6[/tex]
We are interested on this probability
[tex]P(R<95)[/tex]
And the best way to solve this problem is using the normal standard distribution and the z score given by:
[tex]z=\frac{R-\mu}{\sigma}[/tex]
If we apply this formula to our probability we got this:
[tex]P(R<95)=P(\frac{R-\mu}{\sigma}<\frac{95-\mu}{\sigma})=P(Z<\frac{95-100}{3.606})=P(Z<-1.387)[/tex]
And we can find this probability using the normal standard table or excel and we got:
[tex]P(z<-1.387)=0.0827[/tex]
Part b
[tex]P(R>110)=P(\frac{R-\mu}{\sigma}>\frac{110-\mu}{\sigma})=P(Z>\frac{110-100}{3.606})=P(Z>2.774)[/tex]
And we can find this probability using the complement rule and the normal standard table or excel and we got:
[tex]P(z>2.774)=1-P(Z<2.774) = 1-0.9972 = 0.0028[/tex]
Given Information:
Mean = μ = 40 + 60 = 100 minutes
Standard deviation = σ = 2² + 3² = 13 minutes
Required Information:
a. P(X < 95) = ?
b. P(X > 110) = ?
Answer:
a. P(X < 95) = 0.0823
b. P(X > 110) = 0 .0028
Explanation:
a)
Let random variable X represents the time in minutes of wheel throwing and firing.
The probability that a piece of pottery will be finished within 95 minutes means,
P(X < 95) = P(Z < (x - μ)/√σ)
P(X < 95) = P(Z < (95 - 100)/√13)
P(X < 95) = P(Z < -1.39)
The z-score corresponding to -1.39 is 0.0823
P(X < 95) = 0.0823
Therefore, there is 8.23% probability that a piece of pottery will be finished within 95 minutes.
b)
P(X > 110) = 1 - P(X < 110)
P(X > 110) = 1 - P(X < (x - μ)/√σ)
P(X > 110) = 1 - P(X < (110 - 100)/√13)
P(X > 110) = 1 - P(X < 2.77)
The z-score corresponding to 2.77 is 0.9972
P(X > 110) = 1 - 0.9972
P(X > 110) = 0 .0028
Therefore, there is 0.28% probability that a piece of pottery will take longer than 110 minutes.
32) In one region, the September energy consumption levels for single-family homes are found to be normally distributed with a mean of 990 kWh and a standard deviation of 198 kWh. For a randomly selected home, find the probability that the September energy consumption level is between 1100 kWh and 1250 kWh.
Answer:
0.1946 is the probability that the September energy consumption level is between 1100 kWh and 1250 kWh.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 990 kWh
Standard Deviation, σ = 198 kWh
We are given that the distribution of energy consumption levels is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
P(September energy consumption level is between 1100 kWh and 1250 kWh)
[tex]P(1100 \leq x \leq 1250)\\\\ = P(\displaystyle\frac{1100 - 990}{198} \leq z \leq \displaystyle\frac{1250 -990}{198}) \\\\= P(0.5556 \leq z \leq 1.3131)\\\\= P(z \leq 1.3131) - P(z < 0.5556)\\\\= 0.9054- 0.7108= 0.1946[/tex]
0.1946 is the probability that the September energy consumption level is between 1100 kWh and 1250 kWh.
Evaluate and simplify the expression when x=1 and y=2. 3(×+2y)-2x+10=?
Answer:
Step-by-step explanation:
Just for some extra closure lol the answer is indeed 23. :)
Follow the steps to finish solving the equation –3x + 18 = 7x.
1. Add 3x to both sides to isolate the variable term.
2. Divide both sides by 10.
18/10
Step-by-step explanation:
Answer:
18/10
Step-by-step explanation:
Just did the question
A cell phone company wants to determine if the use of text messaging is independent of age. The following data has been collected from a random sample of customers. Regularly use text messaging Do not regularly use text messaging Under 21 82 38 21-39 57 34 40 and over 6 83 Based on the data above what is the expected value for the "under 21 and regularly use text messaging" cell? Question 5 options: 58 120 50 82
Answer:
Hi Gabbie,
The answer to your question that was what is the expected value for the "under 21 and regularly use text messaging" cell is 82.
Please rate me good :)
Step-by-step explanation:
The answer is 82 because the table that clearly defines the result was in the question.
Factor the expression completely 8x^2-18 Please help
Answer:
2 (2x - 3) x (2x + 3)
What is the measure of angle DEG on circle O? Please help! Picture included!
I don't know how to do that. Only one angle is given and no relationships between the triangles or any lines are given.
Answer:
The answer is 50.
Step-by-step explanation:
Anyone know how to do this?
Step-by-step explanation:
[tex] {5}^{17} \times {5}^{2} [/tex]
Now adding powers
[tex] {5}^{17 + 2} [/tex]
[tex] {5}^{19} [/tex]
Hope it will help :)
Answer:
5x1^19
Step-by-step explanation:
Basically, the only way to have the 5 be to the power of 1 in this equation is to put it in scientific notation, or in other words, multiply 5 by 1 to the power of 19.
What is the v?
-18 - 3/4v = 3
Step-by-step explanation:
[tex] - 18 - \frac{3}{4v} = 3[/tex]
[tex] - \frac{3}{4v} = 3 + 18[/tex]
[tex] - \frac{3}{4v} = 21[/tex]
Now doing cross multiply
-3 = 21 * 4v
[tex]v = - \frac{3}{21 \times 4} [/tex]
Therefore
[tex]v \: = \frac{1}{28} [/tex]
Hope this helps.
A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 411 gram setting. It is believed that the machine is underfilling the bags. A 26 bag sample had a mean of 406 grams with a variance of 225. Assume the population is normally distributed. A level of significance of 0.02 will be used. Find the P-value of the test statistic. You may write the P-value as a range using interval notation, or as a decimal value rounded to four decimal places.
Answer:
0.0445937
Step-by-step explanation:
-Given that the sample statistic has a mean of 406 grams, standard deviation of sq root(225) and the null statistic is 411 grams.
-Assuming normal distribution, the test statistic is calculated as:
[tex]z=\frac{Sample \ statistic-Null \ statistic}{\sigma/\sqrt{n}}\\\\=\frac{406-411}{\sqrt{225/26}}\\\\=-1.6997[/tex]
-we then find the p-value of the test statistic from the z-tables:
P-value=0.0445937
Explain what "statistical significance" means. Choose the correct explanation below. A. Statistical significance means that the tools used to measure the data introduce error that needs to be accounted for when considering whether or not to reject the null hypothesis. B. Statistical significance means that the sample standard deviation is unusually small, resulting in an unusually large test statistic. C. Statistical significance means that the null hypothesis claims the population proportion is equal to something other than 0.5. D. Statistical significance means that the result observed in a sample is unusual when the null hypothesis is assumed to be true. E. Statistical significance means that the scenario being analyzed will have a meaningful real-world impact.
Answer:
The correct explanation is:
D. Statistical significance means that the result observed in a sample is unusual when the null hypothesis is assumed to be true.
Step-by-step explanation:
The statistical significance gives a threshold to measure if a sample result or observed effect is due only to a sampling or it really reflects a characteristics of the population we are studying.
The level of statistical significance is usually 0.05 or 5%, depending on how strong the evidence needs to be and the consequences of the conclusions of the study, taking into account the Type I and Type II errors.
The statistical significance provides a cutoff point for determining whether a sampling outcome, as well as observable impact, is attributable mostly to screening whether accurately reflects features of the target population under investigation.The threshold of such significance is very often 0.05 as well as 5%, on whatever the documentation has to be because the implications of the study's results, recognize the importance of Type I as well as the Type II mistakes.
Thus the response above i.e., "option D" is appropriate.
Learn more about statistical significance here:
https://brainly.com/question/15873779
You measure 40 watermelons' weights, and find they have a mean weight of 66 ounces. Assume the population standard deviation is 13.3 ounces. Based on this, what is the maximal margin of error associated with a 90% confidence interval for the true population mean watermelon weight.
Answer:
The maximal margin of error associated with a 90% confidence interval for the true population mean watermelon weight is of 3.46 ounces.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.9}{2} = 0.05[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.05 = 0.95[/tex], so [tex]z = 1.645[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
In this problem:
[tex]\sigma = 13.3, n = 40[/tex]
So
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]M = 1.645*\frac{13.3}{\sqrt{40}}[/tex]
[tex]M = 3.46[/tex]
The maximal margin of error associated with a 90% confidence interval for the true population mean watermelon weight is of 3.46 ounces.
Final answer:
The maximal margin of error for a 90% confidence interval for the mean watermelon weight is calculated using the z-score for the confidence level, the known population standard deviation, and the sample size, resulting in 3.463 ounces.
Explanation:
To find the maximal margin of error associated with a 90% confidence interval for the true population mean watermelon weight when the mean weight of the watermelons is 66 ounces, the population standard deviation is 13.3 ounces, and the sample size is 40, we use the formula for the margin of error E = z * (σ / sqrt(n)), where z is the z-score corresponding to the confidence level, σ is the population standard deviation, and n is the sample size.
For a 90% confidence interval, the z-score is approximately 1.645. Plugging in the values, we get:
E = 1.645 * (13.3 / sqrt(40))
= 1.645 * (2.105)
= 3.463 ounces.
The maximal margin of error is therefore 3.463 ounces, which means the interval is 66 ± 3.463 ounces for the true population mean weight of watermelons with 90% confidence.
The radius of a cylinder is 3 cm and the height is 6 cm.
Find the Surface Area. (hint: Use the answer from the previous question.)
Answer
Step-by-step explanation:
A=2πrh+2πr2=2·π·3·6+2·π·32≈169.646
The manager of a fund that provides loans for college students has estimated that the average monthly loan repayment for students borrowing from the fund is $75.00. You are to test this estimate. You take a sample of 20 students and find that the mean monthly payment is $69.46 with a standard deviation of $9.78. Which of the following statements is true about this test?
a. The value of the test statistic is -.57; therefore, the null hypothesis is rejected for mean = 0.02.
b. The value of the test statistic is -2.53; therefore, the null hypothesis is rejected for mean = 0.02.
c. The value of the test statistic is -2.53; therefore, the null hypothesis is rejected for mean = 0.05 but not for mean = 0.02.
d. The value of the test statistic is -.57; therefore, the null hypothesis is rejected for mean = 0.05 but not for mean = 0.02.
Answer:
Step-by-step explanation:
We would set up the hypothesis test.
For the null hypothesis,
µ = 75
For the alternative hypothesis,
µ ≠ 75
Since the number of samples is 20 and no population standard deviation is given, the distribution is a student's t.
Since n = 20,
Degrees of freedom, df = n - 1 = 20 - 1 = 19
t = (x - µ)/(s/√n)
Where
x = sample mean = $69.46
µ = population mean = $75
s = samples standard deviation = $9.78
t = (69.46 - 75)/(9.78/√20) = - 2.53
We would determine the p value using the t test calculator. It becomes
p = 0.01
Since alpha, 0.05 > than the p value, 0.01, then the null hypothesis is rejected.
Therefore,
The value of the test statistic is -2.53; therefore, the null hypothesis is rejected for level of significance = 0.05
the second and third terms in the following fibonacci sequence are X and Y. write down algebraic expressions for the first, fourth and fifth terms
Answer:
(Y-X), X, Y, (X+Y), (X+Y)+Y, ...
Step-by-step explanation:
FIBONACHI SEQUENCE IS A SPECIAL MATHEMATICAL SEQUENCE IN W/C YOU HAVE TO ADD THE LAST AND THE NEXT TERM TO GET THE FOLLOWING TERM, IF SO.. TO GET THE LAST TERM, JUST REDUCE THE 3RD TERM TO YOUR 2ND TERM
TO GET THE 4RTH AMD 5TH TERM, JUST ADD THE FLLOWING CONSECITIVE TERM AS SHOWN IN THE ANSWER
A newspaper published an article about a study in which researchers subjected laboratory gloves to stress. Among 279 vinyl gloves, 60% leaked viruses. Among 279 latex gloves, 14% leaked viruses. See the accompanying display of the technology results. Using a 0.10 significance level, test the claim that vinyl gloves have a greater virus leak rate than latex gloves. Let vinyl gloves be population 1. Identify: null, alternative hypothesis, test statistic, and P-value.
The P-value is (1) the significance level ?, so (2) the null hypothesis. There is (3) evidence to support the claim that vinyl gloves have a greater virus leak rate than latex gloves.
1) greater than / less than 2) reject / fail to reject 3) sufficient / insufficient
(Table at bottom of question)
Technology results:
Pooled proportion: 0.37
Test statistic, z: 11.3049
Critical z: 1.2816
P-value: 0.0000
80% Confidence interval: 0.4163430 < p1 ? p2 < 0.5083882
Answer:
a) H0: Null Hypothesis: P1 = P2
HA: Alternative Hypothesis:P1> P2
The P-value is less than the significance level.
Therefore, Reject the null hypothesis
In conclusion, there is enough evidence to support the claim that vinyl gloves have a greater virus leak rate than latex gloves.
Step-by-step explanation:
(a) From the information given, we can identify the null hypothesis and alternative hypothesis.
H0: Null Hypothesis: P1 = P2
HA: Alternative Hypothesis:P1> P2
(b) n1 which is size of sample 1 = 279
p1 which is proportion of sample 1= 0.60
n2 which is size ofsample 2 = 279
p2 which is proportion of sample 2 = 0.14
P=n1p1+n2p2 / n1+n2
=279 × 0.60+279 × 0.14/279+279
=0.37
Q = 1- P = 0.63
SE= √PQ(1/n1+1/n2)
= √ 0.37 × 0.63(1/279+1/279)=0.0409
So,
Test statistic is:
Z = (p1 - p2) /SE
= (0.60 - 0.14)/0.0409
= 11.3049
(c) The able of Area Under Standard Normal Curve gives the following area =
0.5 approximately.
So,
P-value = 0.5 - 0.5 nearly =0 nearly
(d)From the information derived, the P-value is less than the significance level.
Therefore, Reject the null hypothesis
In conclusion, there is enough evidence to support the claim that vinyl gloves have a greater virus leak rate than latex gloves.