Answer:
[tex]\frac{da}{dt}=-95.2m/s^2[/tex]
Step-by-step explanation:
From the question we are told that:
Slant height [tex]h=13ft[/tex]
Velocity [tex]v=\frac{dx}{dt}=8[/tex]
Distance [tex]d=12ft[/tex]
Generally the equation for area is mathematically given by
[tex]A=0.5*x*sqrt(169 - x^2)[/tex]
Differentiating
[tex]\frac{da}{dx}=\frac{169-2 x^2}{(2 sqrt(169-x^2))}[/tex]
Multiplying through by dx/dt
[tex]\frac{da}{dx}*\frac{dx}{dt}=\frac{169-2 x^2}{(2 \sqrt{169-x^2})}*\frac{dx}{dt}[/tex]
[tex]\frac{da}{dt}=\frac{169-2x^2}{(2 \sqrt{169-x^2})}*\frac{dx}{dt}[/tex]
[tex]\frac{da}{dt}=\frac{169-(2*12^{2})}{2*\sqrt{(169-12^{2})}}*8[/tex]
[tex]\frac{da}{dt}=-95.2m/s^2[/tex]
A worker in the automobile industry works an average of 43.7 hours per week. Assume the distribution is normal with a standard deviation of 1.6 hours.
(i) What is the probability that a randomly selected automobile worker works less than 40 hours per week?
(ii) If 15 automobile workers are randomly selected, what is the probability that the sample mean of working time is more than 45 hours per week?
Answer:
The solution is:
(1) 0.0104
(2) 0.0008
Step-by-step explanation:
Given:
Mean,
[tex]\mu = 43.7[/tex]
Standard deviation,
[tex]\sigma = 1.6[/tex]
(1)
⇒ [tex]P(X<40) = P(\frac{x-\mu}{\sigma}<\frac{40-43.7}{1.6} )[/tex]
[tex]=P(z< - 2.3125)[/tex]
[tex]=P(z<-2.31)[/tex]
[tex]=0.0104[/tex]
(2)
As we know,
n = 15
⇒ [tex]P(\bar X > 45)= P(\frac{\bar x - \mu}{\frac{\sigma}{\sqrt{n} } } >\frac{45-43.7}{\frac{1.6}{\sqrt{15} } } )[/tex]
[tex]=P(z> 3.15)[/tex]
[tex]=1-P(z<3.15)[/tex]
[tex]=1-0.9992[/tex]
[tex]=0.0008[/tex]
Please help me with this
9514 1404 393
Answer:
1+3x = -89x = -30Step-by-step explanation:
If we let x represent "a number", then "three times a number" is 3x. The usm of that and 1 is ...
1 +3x . . . . . . the sum of 1 and 3 times a number
That is said to be -89, so we have the equation ...
1 +3x = -89
__
To solve this equation, we can subtract 1 from both sides:
3x = -90
Then we can divide by 3 to find x.
(3x)/3 = -90/3
x = -30
Hi! I'd appreciate it if you could help me on this question. The question I need help with is question 42. Thank you If you could help me!!
9514 1404 393
Answer:
19 hours
Step-by-step explanation:
Add up the numbers:
3×3.5 +2×2.0 +4.5 = 19
Jacob trains 19 hours per week.
Help with this please!!!!!!!!!!!!!!
Answer:
A is the correct answer :)
Answer:
A
Step-by-step explanation:
checking if A is correct, if we get x as 76 then it is correct
if 5miles = 8 kilometers
47.5 miles= x
that is
5=8
47.5=x
cross multiply
5x=380
x=380/5
x=76
there fore A is correct
checking if B is correct, if we get x as 86 then it is correct
if 5miles = 8 kilometers
52.5 miles= x
that is
5=8
52.5=x
cross multiply
5x=420
x=420/5
x=84
therefore B is incorrect
checking if C is correct, if we get x as 34 then it is correct
if 5miles = 8 kilometers
22.5 miles=x
that is
5=8
22.5=x
Cross multiply
5x=180
x=180/5
x=36
therefore C is incorrect
checking if D is correct, if we get x as 22 then it is correct
if 5miles = 8 kilometers
12.5miles = x
that is
5=8
12.5=x
5x=100
x=100/5
x= 20
heSellsSeaShells is an ocean boutique offering shells and handmade shell crafts on Sanibel Island in Florida. Find the price SheSellsSeaShells should charge to maximize revenue if p(x)=160−2xp(x)=160−2x, where p(x)p(x) is the price in dollars at which xx shells will be sold per day.
Answer:
it's too much for me im a child u know
How many women must be randomly selected to estimate the mean weight of women in one age group? We want 90% confidence that the sample mean is within 3.7 lbs of the populations mean, and population standard deviation is known to be 28 lbs.
Answer:
155 women must be randomly selected.
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 Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.
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.
The population standard deviation is known to be 28 lbs.
This means that [tex]\sigma = 28[/tex]
We want 90% confidence that the sample mean is within 3.7 lbs of the populations mean. How many women must be sampled?
This is n for which M = 3.7. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]3.7 = 1.645\frac{28}{\sqrt{n}}[/tex]
[tex]3.7\sqrt{n} = 1.645*28[/tex]
[tex]\sqrt{n} = \frac{1.645*28}{3.7}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.645*28}{3.7})^2[/tex]
[tex]n = 154.97[/tex]
Rounding up:
155 women must be randomly selected.
find the surface area of the triangular prism below.
Step-by-step explanation:
At first you need to take its lateral surface area by using the perimeter of base of the triangle and the height of prism.
Then after calculating it you need to find out its total surface area which is asked in the question and that is calculated by adding the area of both triangles of the prism in the lateral surface area.
Then that's your answer.
9514 1404 393
Answer:
544 square units
Step-by-step explanation:
The surface area is the sum of the area of the two triangular bases and the three rectangular faces. The relevant area formulas are ...
A = 1/2bh . . . . area of a triangle with base b and height h
A = LW . . . . . are of a rectangle of length L and width W
__
SA = 2(1/2)(12)(8) + (10 +10 +12)(14)
SA = 96 +448 = 544 . . . square units
What type of equation is 9x-3y=27
Answer:
a first degree equation
The problem solving plan identifies steps to organize your information. Which of the following answer choices are included in the steps to organize your information?
A. Organize the problem and find the question.
B. Solve the problem and change your strategy if necessary.
C. Write the facts, organize your thoughts and define your strategy.
D. Organize the steps and underline the question.
c.write the fact,organize your thoughts and define your strategy.
Answer:
c
Step-by-step explanation:
The increase in length of an aluminum rod is twice the increase in length of an Invar rod with only a third of the temperature increase. Find the ratio of the lengths of the two rods.
Answer:
the ratio of lengths of the two rods, Aluminum to Invar is 11.27
Step-by-step explanation:
coefficient of linear expansion of aluminum, [tex]\alpha _{Al} = 23 \times 10^{-6} /K[/tex]
Coefficient of linear expansion of Invar, [tex]\alpha _{Iv} = 1.2 \times 10^{-6}/K[/tex]
Linear thermal expansion is given as;
[tex]\Delta L = L_0 \times \alpha\times \Delta T\\\\where;\\\\L_0 \ is \ the \ original \ length \ of \ the \ metal\\\\\Delta L \ is \ the \ increase \ in \ length[/tex]
The increase in length of Invar is given as;
[tex]\Delta L_{Iv} = L_0_{Iv} \times \alpha _{Iv}\times \Delta T_{Iv}[/tex]
The increase in length of the Aluminum;
[tex]\Delta L_{ Al} = L_0_{Al} \times \alpha _{Al} \times \Delta T_{Al}\\\\from \ the\ given \ question, \ the \ relationship \ between \ the \ rods \ is \ given \ as\\\\ L_0_{Al} \times \alpha _{Al} \times \frac{1}{3} \Delta T_{Iv}= 2( L_0_{Iv} \times \alpha _{Iv} \times \Delta T_{Iv})\\\\ L_0_{Al} \times \alpha _{Al} \times \Delta T_{Iv}= 6( L_0_{Iv} \times \alpha _{Iv} \times \Delta T_{Iv})\\\\ L_0_{Al} \times \alpha _{Al} \times \Delta T_{Iv} = 6L_0_{Iv} \times 6\alpha _{Iv} \times 6 \Delta T_{Iv}\\\\[/tex]
[tex]\frac{L_0_{Al}}{6L_0_{Iv} } = \frac{6\alpha _{Iv} \ \times \ 6 \Delta T_{Iv}}{\alpha _{Al} \ \times \ \Delta T_{Iv}} \\\\\frac{L_0_{Al}}{6L_0_{Iv} } = \frac{6\alpha _{Iv} \ \times \ 6}{\alpha _{Al} \ } \\\\\frac{L_0_{Al}}{L_0_{Iv} } = 6^3(\frac{\alpha _{Iv} }{\alpha _{Al} } )\\\\\frac{L_0_{Al}}{L_0_{Iv} } = 6^3(\frac{1.2 \times 10^{-6} }{23\times 10^{-6} } )\\\\\frac{L_0_{Al}}{L_0_{Iv} } = 6^3(\frac{1.2}{23} )\\\\\frac{L_0_{Al}}{L_0_{Iv} } = \frac{259.2}{23} \\\\\frac{L_0_{Al}}{L_0_{Iv} } = 11.27[/tex]
Therefore, the ratio of lengths of the two rods, Aluminum to Invar is 11.27
The ratio of the lengths of the two rods which is length of aluminum to length of Invar rod is; 11.27
Formula for linear thermal expansion is;
ΔL = L × α × ΔT
Where;
ΔL is change in original length
L is original length
α is coefficient of linear expansion
ΔT is change in temperature
We are told that increase in length of aluminum rod is twice the increase in length of an Invar rod with only a third of the temperature increase.
Thus;
ΔL = 2ΔL
ΔT for the aluminum rod = ⅓ΔT for the Invar rod.
Thus, we have;
L_al × α_al × ⅓ΔT = 2L_in × 2α_in × 2ΔT
ΔT will cancel out to give;
⅓(L_al × α_al) = 2L_in × 2α_in × 2
Multiply both sides by 3 to get;
(L_al × α_al) = 6L_in × 6α_in × 6
From online tables, the linear coefficient of expansion of aluminum is 23 × 10^(-6) C¯¹
While the coefficient of thermal expansion for Invar rod is 1.2 × 10^(-6) K¯¹
Thus;
L_al × 23 × 10^(-6) = 6L_in × (6 × 1.2 × 10^(-6)) × 6
L_al/L_in = (6 × 6 × 1.2 × 10^(-6) × 6)/(23 × 10^(-6))
L_al/L_in = 11.27
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There are two machines available for cutting corks intended for use in wine bottles. The first produces corks with diameters that are normally distributed with mean 3 cm and standard deviation 0.08 cm. The second machine produces corks with diameters that have a normal distribution with mean 3.04 cm and standard deviation 0.04 cm. Acceptable corks have diameters between 2.9 cm and 3.1 cm.
1. What is the probability that the first machine produces an acceptable cork?
2. What is the probability that the second machine produces an acceptable cork?
3. Which machine is more likely to produce an acceptable cork?
Answer:
Step-by-step explanation:
is y=x^2 a proportional relationship?
is y=2+x a proportional relationship?
is y=2/x a proportional relationship?
is y=2x a proportional relationship?
Answer:
is y=x^2 a proportional relationship?
[tex]{ \sf{yes. \: constant \: of \: proportionality = 1}}[/tex]
is y=2+x a proportional relationship?
[tex]{ \sf{no. \: unless \: y \: is \: proportinal \: to \: (2 + x)}}[/tex]
is y=2/x a proportional relationship?
[tex]{ \sf{yes. \: where \: proportianality \: constant \: is \: 2}}[/tex]
is y=2x a proportional relationship?
[tex]{ \sf{yeah. \: constant \: is \: 2}}[/tex]
The principle
P=6000 A=6810 T=3 years
Answer:
incomplete question
Step-by-step explanation:
that is what is wrong with your question
Answer:
r = 4.3%
Step-by-step explanation:
6810= 6000(x)^3
6810/6000= (x)^3
x = 1.043114431
r = 043114431
Which of the following describes a positive correlation?
As the number of hours spent on homework increases, the tests scores increase.
As the number of apples eaten per year increases, the number of times visiting the doctor every year remains the same.
As the number of times going to bed early increases, the number of times waking up late decreases.
The amount of time a team spent practicing increases, the number of games lost in a season decreases.
THIS IS A MULTIPLE CHOICE QUESTION
Answer:
First Choice: As the number of hours spent on homework increases, the tests scores increase.
Step-by-step explanation:
The definition of a positive correlation is a relationship between two given variables, in which both variables are moving in the same direction. This can mean when one variable increases and the other variable increases, too, or one variable decreases and the other decreases as well.
The first choice is a positive correlation because both variables are changing (increasing) in the same direction. As you spend more time on homework, you're likely to get a higher test score.
The second choice cannot be a positive correlation because only one variable is having some kind of change (increasing). The doctor visits amount remains the same, so we can call this a zero-correlation relationship because the number of apples eaten yearly doesn't affect the amount of doctor visits. An apple a day keeps the doctor a way is just a proverb, not to be taken literally.
The third choice cannot be a positive correlation because the two variables are going different directions. Even though the number of times going to bed early is increasing, the number of times waking up late decreases, which is not moving in the same direction as the other variable.
The fourth choice cannot be a positive correlation because, similarly to the third choice, the two variables are going different directions. One variable is increasing, which is the amount of practice time. Meanwhile, the other variable is decreasing (going in the opposite direction), which is the number of games lost in a season.
sin(180+0).cos(180+0)/cos(180+0).sin(180-0)
(4x^5)^3 what is the equivalent?
[A] 4x^5+3
[B] 4x^5*3
[C] 4^3x^5+3
[D] 4^3x^5*3
Answer:
A
Step-by-step explanation:
They are different exponents but they have the same bas so you add them up.
4x^5+3 = 4x^8
[tex] \pink{ \boxed{\boxed{\begin{array}{cc} \maltese \bf \: \: as \: we \: know \: that \\ \\ \bf\: \: \rightarrow \: {(xy)}^{n} = {x}^{n} . {y}^{n} \\ \\ \bf \rightarrow \: {( {a}^{m} })^{n} = {a}^{m \times n} \\ \\ \bf \: now \\ \: \\ \blue{ {\boxed{\begin{array}{cc} \maltese \bf\: \: \: {(4 {x}^{5} })^{3} \\ \bf = {4}^{3} \times ({x}^{5} )^{3} \\ \bf = {4}^{3} \times {x}^{5 \times 3} \end{array}}}}\end{array}}}}[/tex]
So option D) is the correct answer
I need help please guys thank you
Answer:
Option A, the parent function has been translated up
Option B, the parent function has been compressed
Option C, the parent function has been translated to the right
Five trucks are to be transported on a ship. Each one weighs 3200 kg and comes
with 8 tyres which weigh 125 kg each. what is the total weight
Total No of trucks: 5
Weight of trucks: 3200Kg
Total weight of trucks: 3200×5
= 16000kg
Total no of tyres = 5 ×8
= 40
Weight of each tyre = 125kg
Total weight of tyres = 125 × 40
= 5000Kg
The total weight of trucks and tyres: 16000 + 5000
= 21000Kg
Answered by Gauthmath must click thanks and mark brainliest
I NEED HELP PLEASE ASAP!!
Answer:
Option B, 1
Step-by-step explanation:
tan 45° = 1/1 = 1
Lấy ngẫu nhiên 25 lọ thuốc Vitamin tổng hợp do một máy tự động đóng chai ta thu được s'2 =0,012(l2).Máyđượcgọilàđạtchuẩnnếuđộphântántheoquyđịnhlà2 =0,005(l2). Với mức ý nghĩa 0,05 hãy kiểm định máy đóng chai có đạt chuẩn không? Biết lượng thuốc trong chai là biến ngẫu nhiên có phân phối chuẩn.
Answer:
I really can't read this
Step-by-step explanation:
An object travels along the x-axis so that its position after t seconds is given by x(t) = 2t2 – 5t – 18 for all times t such that t ≥ 0.
Which inequality describes all times t for which the object is traveling toward the right?
the function is given, and it's value is where the object is ("how far to the right").
so as long as it rises (going more right), this will be apply.
in the screenshot I graphed the function. of course t is graphed as x and "along the x-axis" is graphed as y, but the pattern is the same anyways.
for the first 1.25 seconds the object goes to the left, and after that always to the right.
since we look at t to calculate x, t effectively takes the role of the important variable that is normally given to x. the calculation pattern are just the same. so let's find the lowest point of this function by calculating it out.
x(t) = 2t² – 5t – 18
x'(t) = 4t -5
x'(t) = 0
0 = 4t -5
5 = 4t
1.25 = t
plugging it into the second derivative
x''(t) = 4
x''(1.25) = 4
it's positive, so at t=1.25 there is a low point
(of course the second derivative is constant anyways.)
the object is traveling toward the right
the object is traveling toward the rightfor t > 1.25
The object is moving to the right, for t > 1.25, the object is moving in a rightward direction.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
We have:
An object travels along the x-axis so that its position after t seconds is given by:
x(t) = 2t² – 5t – 18
x'(t) = 4t - 5
x'(t) = 0
4t -5 = 0
t = 5/4 = 1.25 seconds
x''(t) = 4
x''(1.25) = 4
x''(1.25) > 0
At t = 1.25 the object travels at a low point.
Thus, the object is moving to the right, for t > 1.25, the object is moving in a rightward direction.
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Can someone please help me with this
9514 1404 393
Answer:
21. D
22. C
Step-by-step explanation:
21. The expansion of the given expression is ...
[tex]\displaystyle -\frac{1}{2}\left(-\frac{3}{2}x+6x+1\right)-3x=\frac{3}{4}x-3x-\frac{1}{2}-3x\\\\=\left(\frac{3}{4}-3-3\right)x-\frac{1}{2}=\boxed{-5\frac{1}{4}x-\frac{1}{2}}[/tex]
__
22. The least likely team to make the championship game is the one with the lowest probability.
3/8 < 1/2 < 2/3 < 4/5
The Bulldogs are least likely to play in the championship game.
A survey asked 25 students about their favorite sport. A frequency table of their responses is below.
Basketball, 4; football, 7; lacrosse, 3; soccer, 8; volleyball, 3.
Which of the following is the correct relative frequency table for the students’ favorite sport?
Answer: The second one
Step-by-step explanation:
response/25=x/100 and then you solve for x
A percentage is a way to describe a part of a whole. The correct table is B.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Given the number of students who play different sports as,
Basketball = 4
Football = 7
Lacrosse = 3
Soccer = 8
Volleyball = 3
Now, the percentage of students for each sport can be written as,
Basketball = 4/25 = 0.16
Football = 7/25 = 0.28
Lacrosse = 3/25 = 0.12
Soccer = 8/25 = 0.32
Volleyball = 3/25 = 0.12
Hence, the correct table is B.
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Complete the statement. A critical value is _____________. Choose the correct answer below. A. A critical value is how far away our sample statistic can be from the true population parameter with a certain level of confidence. B. A critical value is the probability of obtaining a sample statistic like the one obtained from the sample or something more unusual if the null hypothesis is true. C. A critical value is the number of standard errors (or standard deviations) to move from the mean of a sampling distribution to correspond to a specified level of confidence. D. A critical value is the value that best estimates a population parameter.
Answer:
A. A critical value is how far away our sample statistic can be from the true population parameter with a certain level of confidence.
Step-by-step explanation:
Test of a hypothesis:
When we are testing a hypothesis, we have a null hypothesis and an alternative hypothesis, and the conclusion depends on the test statistic, given by:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
The test statistic measures the number of standard errors that we have to move away from the sample mean, and the critical value is how much we can be far from the population parameter with a certain level of confidence, that is, before a certain value we do not reject the null hypothesis, after the value we reject, and this value is the critical value, and thus the correct answer is given by option a.
Diego made the shape on the left and Elena made the shape on the right. Each shape uses 5 circles.
Answer:
a
Step-by-step explanation:
hlo anyone free .... im bo r ed
d
Step-by-step explanation:
Excuse me! Who r u? where r u frm? tell me tht frst.
Answer:
Oop
Step-by-step explanation:
I’m bored
A lawyer commutes daily from his suburban home to his midtown office. The average time for a one-way trip is 24 minutes, with a standard deviation of 3.8 minutes. Assume the distribution of trip times to be normally distributed.
(a) What is the probability that a trip will take at least ½ hour?
(b) If the office opens at 9:00 A.M. and he leaves his house at 8:45 A.M. daily, what percentage of the time is he late for work?
(c) If he leaves the house at 8:35 A.M. and coffee is served at the office from 8:50 A.M. until 9:00 A.M., what is the probability that he misses coffee?
(d) Find the length of time above which we find the slowest 10% of trips.
(e) Find the probability that 2 of the next 3 trips will take at least one half
1/2 hour.
Answer:
Step-by-step explanation:
a) Probability-Above 30 min = 5.72% = .0572
b) Probability-Above 15 min = 99.11% = .9911
c) *Probability-Between 1 - 59.49% = .4051
d) 19.136 minutes z = -1.28
a) The probability that trip will take at least 1/2 hour will be 0.0606.
b) The percentage of time the lawyer is late for work will be 99.18%.
c) The probability that lawyer misses coffee will be 0.3659.
d) The length of time above which we find the slowest 10% of trips will be 0.5438.
e) The probability that exactly 2 out of 3 trips will take at least one half
1/2 hour is 0.0103.
What do you mean by normal distribution ?
A probability distribution known as a "normal distribution" shows that data are more likely to occur when they are close to the mean than when they are far from the mean.
Let assume the time taken for a one way trip be x .
x ⇒ N( μ , σ ²)
x ⇒ N( 24 , 3.8 ²)
a)
The probability that trip will take at least 1/2 hour or 30 minutes will be :
P ( x ≥ 30)
= P [ (x - μ) / σ ≥ (30 - μ) / σ ]
We know that , (x - μ) / σ = z.
= P [ z ≥ (30 - 24) / 3.8)]
= P [ z ≥ 1.578 ]
= 1 - P [ z ≤ 1.578 ]
Now , using the standard normal table :
P ( x ≥ 30)
= 1 - 0.9394
= 0.0606
b)
The percentage of the time the lawyer is late for work will be :
P ( x ≥ 15)
= P [ z ≥ -2.368 ]
= P [ z ≤ 2.368]
= 0.9918
or
99.18%
c)
The probability that lawyer misses coffee :
P ( 15 < x < 25 ) = P ( x < 25 ) - P ( x < 15)
= P [ z < 0.263] - P ( z < -2.368)
or
= 0.3659
d)
The length of time above which we find the slowest 10% of trips :
P( x ≥ X ) ≤ 0.10
= 0.5438
e)
Let's assume that y represents the number of trips that takes at least half hour.
y ⇒ B ( n , p)
y ⇒ B ( 3 , 0.0606)
So , the probability that exactly 2 out of 3 trips will take at least one half
1/2 hour is :
P ( Y = 2 )
= 3C2 × (0.0606)² × ( 1 - 0.0606)
= 0.0103
Therefore , the answers are :
a) The probability that trip will take at least 1/2 hour will be 0.0606.
b) The percentage of time the lawyer is late for work will be 99.18%.
c) The probability that lawyer misses coffee will be 0.3659.
d) The length of time above which we find the slowest 10% of trips will be 0.5438.
e) The probability that exactly 2 out of 3 trips will take at least one half
1/2 hour is 0.0103.
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When the F test is used to test the overall significance of a multiple regression model, if the null hypothesis is rejected, it can be concluded that all of the independent variables x1, x2, . . . , xk are significantly related to the dependent variable y.
A. True
B. False
Answer:
False
Step-by-step explanation:
When the Ftest is used to test the overall significance of a multiple regression model, it evaluates the significance of independent variables to the outcome of the regression model. The null hypothesis of an Ftest when used for multiple regression is that, the independent variables aren't significant in the outcome of the regression model while the alternative Hypothesis claims that the independent variables are significant .
For the overall significance evaluation, once one of the independent variables proves significant, then the overall Ftest is significant, that is it does not require that all individual independent variables are significant. The null only stands when all the independent variables are insignificant.
Therefore, the overall Ftest for significance isn't enough to prove that all individual. Independent variables are significant when the null is rejected.
Given parallelogram ABCD, diagonals AC and BD intersect at point E. AE=2x, BE=y+10, CE=x+2 and DE=4y−8. Find y.
A. 16
B. 6
C. 18
D. 32
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Answer:
B. 6
Step-by-step explanation:
The diagonals of a parallelogram intersect at their midpoints, so ...
DE = BE
4y -8 = y +10
3y = 18 . . . . . . . add 8-y
y = 6 . . . . . . . . divide by 3
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Additional comment
The value of x is found the same way:
2x = x+2 ⇒ x = 2
> There are 14 books on a shelf. 6 of these books are new. The rest of them are used (a) What is the ratio of new books to used books? (b) What is the ratio of used books to all books on the shelf
Answer:
a) 6:8
Because you have 14 books total if you substract 14 - 6= 8, so now you have
14 Books total
6 New Books
8 Used Books.
So, the ratio of new books to used books is 6:8 or if you simplified is 3:4.
b) 8:14
Because you have 8 used books compare to 14 books total. If you simplified your fraction you'll have 4:7
Step-by-step explanation:
