The alternate includes inequality, this is a two-tailed test.
Given:
A sample of 32 observations is selected from a normal population. The sample mean is 66, and the population standard deviation is 5. Conduct the following test of hypothesis using the 0.10 significance level. H0: μ = 68 H1: μ ≠ 68 rev: 10_12_2016_QC_CS-65155 12. value: 1.00 points Required information.
Number of sample observations:
n = 32
Sample mean:
x = 66
Population standard deviation:
σ = 5
Significance level:
α = 0.10
The hypothesis is stated as,
[tex]H_0[/tex] : μ = 68
[tex]H_1[/tex] : μ ≠ 68
Since The alternate includes inequality, this is a two-tailed test.
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How do you prove SAS Theorem?.
If the two corresponding sides and the angle added to these sides of one triangle are the same as the corresponding sides and the included angle of the second triangle,then it is said that the two triangles are congruent.
If AB = XY, angle A = angle X, and angle C = XZ, then triangle ABC is comparable to triangle XYZ mathematically.
All of the sides and angles of one triangle will be equal to those of the other triangle if the SAS congruence theorem holds true for any two triangles.
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Which congruence theorem can be used to prove that ABC is congruent to DCA?.
Side Angle Side(SAS) , theorem can be used to prove that ABC is congruent to DCA.
What is congruency?Congruent refers to something that is "absolutely equal" in terms of size and shape. The shapes hold true regardless of how we rotate, flip, or turn them. Draw two circles with the same radius, for instance, cut them out, and stack them on top of one another. We will see that they will superimpose, or be positioned entirely on top of, one another. This demonstrates the congruence of the two circles. The circles below may be put perfectly over one another and have the same radius, hence they are considered to be congruent. The congruence of figures is represented by the symbol "". Circle A and circle B are congruent, hence we may say the following: A + B = Circle A.According to our question-
The SAS congruency theorem,
two triangles are congruent if any pair of corresponding sides and their included angles are identical in both triangles. In this scenario,
the pair of corresponding sides AB with DC and AD with DA
and their included angles BAD with CDA are equal.
Hence, Side Angle Side(SAS) , theorem can be used to prove that ABC is congruent to DCA.
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if a confidence interval for the difference between a pair of treatment means includes 0, then we reject the null hypothesis that there is no difference in the pair of treatment means. group startstrue or false true, unselected false, unselected group ends
We reject null hypothesis in which there is no difference here between pair of treatment means if the confidence interval for that difference contains zero; this is a "true" statement.
Define the term null hypothesis?A statistical conjecture known as a null hypothesis asserts that certain features of such a population or content process are not different from one another.
Any variation between the selected attributes that you observe in a collection of data is thought to be the result of chance, according to the null hypothesis. Because rejecting the null hypothesis is a firm conclusion, analysts aim for it. Strong evidence for this is needed in the form of just an observed difference that cannot be explained by chance alone. Failure to reject the null hypothesis, which states that outcomes can only be explained by chance, is a weak conclusion since it acknowledges that there may be forces at play that the statistical test is not sensitive enough to detect.Thus, we reject null hypothesis in which there is no difference here between pair of treatment means if the confidence interval for that difference contains zero; this is a "true" statement.
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If the sample size is decreased for any given confidence level, what happens to the confidence interval for the population proportion?.
If the sample size is decreased for any given confidence level, the confidence interval for the population proportion will increase.
What happens to the confidence interval when the confidence level falls?A larger sample size or lower variability results in a more narrow confidence interval with a smaller margin of error. A larger confidence interval with a larger margin of error will result from a smaller sample size or higher variability.
The width of the confidence interval grows as the confidence level grows. As the confidence level falls, so does the width of the confidence interval.
This means that as the sample size is reduced, the width of the confidence interval expands.
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Let u = 2i 3j, v = â€"i, and w = 5i â€" 6j. what is the magnitude of 2(u â€" v w)? 10.0 13.4 17.1 21.6
The magnitude of 2(u-v +w) is 17.1.
The given vectors are u = 2i + 3j, v=-i, and w = 5i – 6j.
We need to find the value of 2(u-v+w).
How to find the magnitude of vector?
The formula to determine the magnitude of a vector (in two-dimensional space) v = (x, y) is: |v| =√(x²+ y²). This formula is derived from the Pythagorean theorem.
Now, 2(2i + 3j-(-i)+5i-6j)
=2(2i+3j+i+5i-6j)
=2(8i-3j)=16i-6j
The magnitude of 16i-6j=√16²+6²=√256+36=√292
Therefore, the magnitude of 2(u-v +w) is √292 which is 17.1.
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Let a,b, and c be three ditinct number uch that (ab)/(a-b)=(bc)/(2b-2c)=(ca)/(3c-3a). Find 8a9b5c
If a, b, and c be three distinct numbers such that (ab)/(a-b)=(bc)/(2b-2c)=(ca)/(3c-3a) then the value of 8a9b5c is 8 [-(b^2)c / (2b^2-bc)] × 9[-2ac^2 / (3c^2 - 5ac)] × 5[3(a^2)b / (4ab - a^2) ]
Let a, b and c be three distinct number
Given that
ab / a-b = bc / 2b - 2c = ca / 3c - 3a
Consider first two term
The equation will be
ab / a-b = bc / 2b - 2c
Cross multiply the terms
ab(2b - 2c) = bc(a - b)
2ab^2 - 2abc = abc - (b^2)c
2ab^2 - abc = -(b^2)c
a(2b^2-bc) = -(b^2)c
a = -(b^2)c / (2b^2-bc)
Similarly
bc / 2b-2c = ca / 3c-3a
bc(3c-3a) = ca(2b-2c)
3bc^2 - 3abc = 2abc - 2ac^2
3bc^2 - 5abc = -2ac^2
b(3c^2 - 5ac) = -2ac^2
b = -2ac^2 / (3c^2 - 5ac)
Then,
ab / a-b = ca / 3c-3aab(3c-3a) = ca(a-b)
3abc - 3(a^2)b = (a^2c) - abc
4abc - 3(a^2)b = (a^2c)
4abc - (a^2)c = 3(a^2)b
c(4ab - a^2) = 3(a^2)b
c = 3(a^2)b / (4ab - a^2)
The value of 8a9b5c = 8 [-(b^2)c / (2b^2-bc)] × 9[-2ac^2 / (3c^2 - 5ac)] × 5[3(a^2)b / (4ab - a^2) ]
Hence, if a, b, and c be three distinct numbers such that (ab)/(a-b)=(bc)/(2b-2c)=(ca)/(3c-3a) then the value of 8a9b5c is 8 [-(b^2)c / (2b^2-bc)] × 9[-2ac^2 / (3c^2 - 5ac)] × 5[3(a^2)b / (4ab - a^2) ]
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2. explain what is meant by (distribution) transparency and give examples of different types of transparency.
The phenomena of hiding distribution characteristics in a system from applications and users is known as distribution transparency. Access transparency, location transparency are some examples.
Define the term (distribution) transparency?Distributed databases have the attribute of distribution transparency, which keeps consumers from knowing the internal workings of the distribution.
The DDBMS designer has the option of replicating table fragments, storing them at several locations, and fragmenting tables.There are numerous distribution methods. Systems that need a wide range of management systems to pinpoint the source of resources, a product, or a service delivery process from the end user.Typically, the distributor, seller, or producer is responsible for maintaining transparency to track the many points at which resources, goods, or services are delivered.Accounting supplied by any intermediary company in the product, service, or resource flow is, of course, the usual approach to determine the degrees of value added through distribution management.Thus, access transparency, location transparency are some examples of the (distribution) transparency.
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solve it.... If you can ???
Answer:
[tex] \frac{ - 112}{15} [/tex]
Step-by-step explanation:
This is my solution and answer hope I'm right
a man wants to construct a rectangular enclosure around his model railroad. only three sides must be enclosed, since his garage wall will form the fourth side. if he uses 24m of fencing, what is the maximum area of the enclosure?
The maximum area of the rectangular enclosure around his model railroad is 72 ft².
Explain the term parabola?Parabola, also known as an open curve or conic section, is formed when a right circular cone and a plane perpendicular to one of the cone's elements cross.For the stated question-
A = L×W
Perimeter P = L + barn + 2W
Barn = 0ft (for no fence)
L + 2W = 24ft
L = 24 - 2W
A = (450 - 2W)×W
A = 24W - 2W²
A = -2W² + 24W
We understand we get a parabola because our equation regarding area in measures of width has the formula ax² + bx + c (since C = 0).
Since the squared term's coefficient is negative (a = -2), we can infer that the parabola's opening is downward.
In the equation y = (x - h)² + k, where k is our greatest area while h is our maximizing number, the vertex will be at point (h, k), which in this case is the width value that provides us our maximum area.
Knowing that h = -b / 2a.
h = -24/ 2(-2) = 6
maximum width = 6 ft
Now,
A = -2(6)² + 24(6)
Maximum area A = 72 ft²
Thus, the maximum area of the rectangular enclosure around his model railroad is 72 ft².
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Please help
In the polynomial expression 12x^2-42x+143, the value of the term of degree ZERO is ____?
Answer:
143
Step-by-step explanation:
You want the value of the term with degree 0 in the polynomial 12x²-42x+143.
DegreesThe degree of each term is the exponent of the variable. A term with no variables has degree 0.
The term with no variables is also called the constant term. The constant in this polynomial is 143.
The value of the term with degree 0 is 143.
__
Additional comment
If there is more than one variable, the degree of the term is the sum of their exponents.
How to dilate a line segment from a point?.
The dilation of a line segment around a point can be accomplished by following a few simple steps as described in the detailed explanation.
The figure of the triangle required to dilate a line around a point is attached.
Here P is the point and AB is the line-segment.
The steps to draw a dilated line is as follows.
Step 1: By drawing a line segment from point P to point A and extending it via point A, we can find the point A'. In order for the distance from P to A' to be twice as great as the distance from P to A, we locate A' on this line. Step 2: The same method is used to find B' and C'.A new line l' that is parallel to line l appears to be formed by the dilations of the points on line l.It appears that the points A', B', and C' are parallel. More points on l can be chosen and dilated around point P to reveal that the dilated points also appear to lie on the line passing through points A', B', and C'.
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What is the mean of 1234567?.
The mean of the 1234567 numbers is 4.
What is mean?
A amount that includes a price intermediate between those of the acute members of some set is known as mean.
Main body:
In this question we have to find the mean of the first 7 numbers. Whole numbers are all non-negative integers which start from 0. Now the mean of the first 7 numbers will be the mean of numbers from 1 to 7, as the count of numbers from 1-7 is 7. Use this concept to reach the answer.
Mean of numbers is equal to the sum of the numbers divided by the count of the numbers that is
Mean = sum of numbers/ total numbers …………………….. (1)
To find the mean of the 1234567 , we will find the sum of numbers from 1 to 7 as 1-7 are the first 7 numbers.
So, the sum of the digits is 1+2+3+4+5+6+7 = 28
total numbers = 7
mean = 28/7 = 4
Hence mean of 1234567 is 4.
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the results of a test that follows a normal distribution have a mean value of 10.0 and a standard deviation of 1. find the probability that a single reading is between 9 and 12
The required probability that a single reading is between 9 and 12 is 0.2493.
What is Z score in probability distribution?While information focuses are alluded to as x in a typical dissemination, they are called z or z-scores in the z-conveyance. A z-score is a standard score that lets you know the number of standard deviations from the mean a singular worth (x) lies: A positive z-score implies that your x-esteem is more noteworthy than the mean.
Its formula is Z = X - x⁻/S
According to question:P(9<x<12)
Z = 12-10/1 = 2 , Z = 8-10/1=-2
Then, P(-2 < Z < 2)
P(z <2) - (z<-2)
0.4773 - 0.228 = 0.2493
P(-2 < Z < 2) = 0.2493.
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a rumor spreads among a population of n people at a rate proportional to the product of the number of people who have heard the rumor and the number of people who have not heard the rumor. if p denotes the number of people who have heard the rumor, which of the following differential equations could be used to model this situation with respect to time t, where k is a positive constant?
The differential equations that could be used to model this situation with respect to time t, where k is a positive constant is db/dt= kp(N-p)
What is a differential equation?A differential equation is a mathematical equation that contains one or more terms and the derivatives of one variable (the dependent variable) with respect to another variable.
A differential equation is an equation that connects one or more unknown functions and their derivatives. In most applications, functions represent physical quantities, derivatives represent their rates of change, and differential equations define a relationship between the two.
This was illustrated regarding the change with respect to the number of people.
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The number of bacteria in a culture is increasing according to the law of exponential growth. After 1 hour there are 100 bacteria, and after 2 hours there are 200 bacteria. How many bacteria will there be after 3 hours?
The number of bacteria that will be there after 3 hours is 6400
What is exponential growth model?
What transpires when you repeatedly multiply by the same amount is described by an exponential growth model. It has a wide range of uses, especially in the economics and life sciences. A population that doubled annually would represent a straightforward exponential growth scenario. For instance, y=A(2)x.
After 1 hour there are 100 bacteria
After 2 hours there are 200 bacteria
Let x be hours and y be the number of bacteria
[tex]y = ab^{x}[/tex]
where, a is initial value and b is growth factor.
After 1 hours, there are 100 bacteria. So, the point is (1,100). Put x=1 and y=100
100 = ab ⇒ (1)
After 2 hours, there are 200 bacteria. So, the point is (2,200). Put x=2 and y=200
200 = ab² ⇒ (2)
Dividing eq (2) and eq(1)
[tex]\frac{200}{100} = \frac{ab^{2} }{ab}[/tex]
b = 2
Putting the value of b in eq 1
100 = 2a
a = 50
When x = 3 what is the y value
y = 50 * [tex]2^{7}[/tex]
= 50*128
= 6400
Therefore, the number of bacteria after 3 hours is 6400.
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A retaurant chef ha 3/4L of trawberry yrup. He ue 1/40L in each deert he i making. How many deert can he make?
A restaurant chef ha 3/4L of strawberry syrup. He uses 1/40L in each desert that he divide for each and every desert. He made 30 deserts.
Given,
Chef has 3/4l strawberry syrup
Each desert uses 1/40l
To determine no of deserts by divide
= total strawberry syrup / syrup for each desert
= ¾ / 1/40
= 30
No of deserts made = 30
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What 2 numbers make 22 but have a range of 5
Range = 12
■ Maximum value = 10.
■ Minimum value = -2
■ Count of numbers within the set = 13
find the general indefinite integral. (use c for the constant of integration.) sec(t)(4 sec(t) 3 tan(t)) dt
The general indefinite integral of the sect (4sect + 5tant) is 4tant + 5sect + c in which c for the constant of integration.
Integration: Integration can be used to find areas, volumes, central points, and many useful things. But it is easiest to start with finding the area between a function and the x-axis.
Given:
∫sect (4sect + 5tant)dt
Multiplying in the bracket by sect. We get,
=> 4∫(sec²t + 5tantsect)dt
=> 4(∫sec²t dt + ∫5tantsectdt)
As we know that:
∫(sec²t) dt = tant, ∫tantsectdt = sect
=> 4tant + 5 sect
Adding constant after integration. We got the value,
=> 4tant + 5 sect + c
The integral of the sect (4sect + 5tant) is 4tant + 5sect + c in which c for the constant of integration.
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A garden measuring 1515 by 2424 feet is to be completely bordered by a fence. Fencing costs $2$2 per foot. What is the total cost to fence the entire garden?$360.00$360.00$78.00$78.00$39.00$39.00$156.00
The entire garden needs to be fence for a total of $156.
Given that,
A fence is required to entirely enclose a garden that is 15 by 24 feet in size. Each foot of fencing costs $2.
To find : The overall cost of fencing the garden?
Dimensions are given by 15 feet and 24 feet
Cost per foot is $2
Total perimeter of garden is given as 2(l+b)
P = 2(l+b)
P= 2(15+24)
P = 78 feet
1 feet = $2
78 feet = 78 * 2 = $156
Therefore, the total cost required to fence the entire garden is $156
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What is a complex fraction 7th grade?.
Complex fractions are fractions with a fractional numerator, denominator, or both.
Given,
We have to state about complex fraction;-
Complex fraction;
When both the denominator and the numerator, or both, contain fractions, the fraction is said to be complicated. A complex fraction with a variable is a complex rational expression. For instance: The complex fraction 4/(1/3) has the denominator as 1/3 and the numerator as 4.
Solving the complex fraction;
In the numerator and denominator, make a single fraction. By multiplying the numerator by the inverse or reciprocal of the denominator, you can use the fractional division rule. If it's required, simplify.
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Find the compound amount due in 8year if 200,000 i inveted at 12% compounded monthly
Compound amount due in 8 year will be 495192.64
What do you mean by simple interest?
Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.
Simple interest is a predetermined proportion of the principle amount borrowed or lent that is paid or received over a set period of time.
Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.
Given principal, P = 2000000
Rate of interest, r = 12%
Time period , n = 8 years
Compound amount = [tex]P(1+\frac{r}{100})^n[/tex]
= [tex]200000(1+\frac{12}{100})^8[/tex]
= [tex]200000(1+0.12)^8[/tex]
= [tex]200000(1.12)^8[/tex]
= 495192.64
Therefore, compound amount due in 8 year will be 495192.64
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Which of the following statements are true for all sets of A,B, and C?
a.(A – C) ∩ (A – B) = A – (B ∪ C)
b.If A ∩ B = ∅, then A ⊂ B
c.∅ X A = ∅
d.(A – B) ∪ (B – C) = A – C
e.∅ ∩ {∅} = ∅
f.B X A = A X B
Aftre solving, the all option is false except option c. Only option c, ∅×A=∅ is correct because cartesian product with non empty set with empty set alsways gives empty set.
In the givn question we have to find which statement is true.
To solve the question we let;
A={1,2,3}; B={2,3,4}; C={2,3}
(a) The first option is (A – C) ∩ (A – B) = A – (B ∪ C)
Now solving the both side by putting the value
({1,2,3} – {2,3}) ∩ ({1,2,3} – {2,3,4}) = {1,2,3} – ({2,3,4} ∪ {2,3})
{1} ∩ {1,4} = {1,2,3} – {2,3,4}
{1} = {1,4} (False)
(b) If A ∩ B = ∅, then A ⊂ B
As we know that if If A ∩ B = ∅, then A=∅ and B=∅. That means both A and B will be empty set. So the option B is false.
(c) ∅ X A = ∅
As we know that cartesian product with non empty set with empty set alsways gives empty set. SO the option C is correct.
(d) (A – B) ∪ (B – C) = A – C
Now solving the both side by putting the value
({1,2,3} – {2,3,4}) ∪ ({2,3,4} – {2,3}) = {1,2,3} – {2,3}
{1,4} ∪ {4} = {1}
{1,4} = {1} (False)
(e) ∅ ∩ {∅} = ∅ (False)
(f) B X A = A X B (False)
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how to get 35 using 1 2 3 4 5 using different operations but the number 1-5 should be in order
Answer:
Polarity of Compound (Ionic/Polar or NonpolarCovalent)
does the 90% confidence interval include the true proportion of youth survey participants who say that they are about the right weight?
Yes , the 90% confidence interval include the true proportion of youth survey participants who say that they are about the right weight.
The confidence interval for a population proportion is calculated by the below formula
p ± z×√(p × (1-p))/n
where p is called as sample proportion
z is called as z-value
and n is sample size
Here, we have sample size(n)=100
and by using the z-table we find that p-value=0.56 and z-value=1.645
90% confidence interval=0.56±(1.645×√[0.56×(1-0.56)]/100)
=>90% confidence interval=0.56± [1.645×√(0.56×0.44)/100]
=>90% confidence interval=0.56±[1.645×(√0.2464/100)]
=>90% confidence interval=0.56±[1.645×(0.049)]
=>90% confidence interval=0.56+0.0816 and 0.56-0.0816
=>90% confidence interval=0.6416 and 0.4784
So,90% confidence intervals covers [0.4784,0.6416] proportion of total population.
Here intervals range is greater than zero, it means 90% confidence interval covers the true proportion.
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(Complete question) is:
does the 90% confidence interval include the true proportion of youth survey participants who say that they are about the right weight? If sample size is 100.
mendel accounted for the observation that traits which had disappeared in the f1 generation reappeared in the f2 generation by proposing that (fill in the blank)
Traits can be dominant or recessive, and the recessive traits were obscured by the dominant ones in the F1 generation.
Given,
In the question:
Mendel accounted for the observation that traits which had disappeared in the f1 generation reappeared in the f2 generation by proposing that___
Now, According to the question:
Fill up the above blank:
Mendel accounted for the observation that traits which had disappeared in the f1 generation reappeared in the f2 generation by proposing that__
Solution:
In the Mendel’s experiment, some traits which were absent in the F1 generation appeared in the second generation cross. By this he concluded, that the traits expressed in the F1 generation were dominant and hence they capped the expression of traits associated with recessive allele. He classified the traits in F2 generation as recessive, because these traits can occur only when they are in pair i.e they form individuals with homozygous recessive genotype.
For instance – If “R” is allele for dominant red color trait and “r” is the allele for recessive white color trait, then the cross between true breeding red flowers and white flowers will produce following offspring
RR * rr
Rr, Rr, Rr, Rr
Thus, in F1 generation all the offspring are heterozygous red
F2 generation-
Rr * Rr
RR, Rr, Rr, rr
The recessive trait of white colored flower reappears in second generation.
Hence, Traits can be dominant or recessive, and the recessive traits were obscured by the dominant ones in the F1 generation.
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Mrs. Brown has been working in a factory for 28 years. She is preparing to retire. Her pension is calculated on the average of her last 3 years' salaries where she earned $38,592, $37,590, and $37,010. Her employer will give her 1. 8% of that average for each year she worked. Calculate her pension.
The pension is equal to $19,016
First, we have to calculate the average of the salaries from the last three years:
avg salary = (38592 + 37590 + 37010)/3
= 113192/3
= 37730.66
Next, calculate the percentage that Mrs. Brown will get, multiplying 1.8% times the amount of years that she worked:
28 x 1.8 = 50.4
Finally, calculate what is 50.4% of the average income equal to:
50.4% of avg salary
50.4 % of 37730.66
(50.4/100) 37730.66
= 19016
Therefore, the pension is equal to $19,016
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the point p p is on the unit circle. if the y-coordinate of p p is 2 7 27, and p p is in quadrant i i ii , then
A unit circle has radius of 1 (r = 1). For any point on the unit circle.
what is a unit circle?In mathematics, the unit circle is the unit radius, i.e. the circle with radius 1. ] Often, especially in trigonometry, the unit circle is the circle of radius 1 centered at the origin (0, 0) of the Cartesian coordinate system in the Euclidean plane. In topology, it is often called S1 because it is a one-dimensional unit n-sphere [2][Note 1].If (x, y) is a point on the perimeter of the unit circle, then |x| and |y| are the leg lengths of a right triangle with hypotenuse length 1. Therefore, by the Pythagorean theorem, x and y satisfyThe unit circle is a circle centered at the origin (0,0) and having a radius of 1 unit. unit circle. Angles are always measured from the positive x-axis (also called the "right horizon"). Angles measured counterclockwise have positive values. Angles measured clockwise have negative values.According to our question-
A unit circle has radius of 1 (r = 1). For any point on the unit circle, we have (by the Pythagorean Theorem):
x2 + y2 = 1
x2 + (-1/4)2 = 1
Hence, A unit circle has radius of 1 (r = 1). For any point on the unit circle
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The original cost of a shirt was £40. It was reduced to £32.80 in a sale.
Calculate the percentage decrease.
Answer:
18% decrease
Step-by-step explanation:
-Subtract the ending value from the starting value.
40.00 - 32.80 = 7.20
-Divide this number by the starting value.
7.20 / 40.00 = 0.18
-Multiply by 100 to find the percentage change
0.18 * 100 = 18% decrease
How do you find the range on a graph?.
The range is the set between all of the possible output values, which always shown on y-axis by identify any given domain and then finding the range of any functions is by taking graphs into consideration.
To discover the area and variety, we without a doubt remedy the equation y = f(x) to decide the values of the unbiased variable x and gain the area. To calculate the variety of the feature, we without a doubt explicit x as x=g(y) after which discover the area of g(y).
Because the area refers back to the set of viable enter values, the area of a graph includes all of the enter values proven at the x-axis. The simplest approach of locating the variety of a feature, say y = f(x), is to explicit x as g(y) and pick out the area set for g(y). This might be the variety for the given feature f(x).
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Work out the size of angle X.
