Answer:
Step-by-step explanation:
The method applied in this scenario is called simple random sampling. A sample of 100 customers is chosen from a larger population of customers and each customer has the same chance of being selected for the survey at any given time. Also, the chance of selecting 100 customers from each store is the same during the sampling process. The order of sampling at each store does not follow a certain order, thus, It is different from systematic random sampling.
If a square with a width of 30 feet a length of 72 feet, and the diagonal is 78 feet, would the square have right angles. Yes or No answer please explain
A student carried out an experiment to determine the amount of vitamin C in a tablet sample. He performed 5 trials to produce the following results: 490 mg, 502 mg, 505 mg, 495mg, and 492 mg. The manufacturer claims that the tablet contains 500 mg of vitamin C. Do an appropriate statistical analysis to find out whether the results obtained by the student is consistent with bottle claim.
Answer:
There is not enough evidence to support the claim that the amount of vitamin C in a tablet sample is different from 500 mg.
P-value = 0.166.
Step-by-step explanation:
We start by calculating the mean and standard deviation of the sample:
[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{5}(490+502+505+495+492)\\\\\\M=\dfrac{2484}{5}\\\\\\M=496.8\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{4}((490-496.8)^2+(502-496.8)^2+(505-496.8)^2+(495-496.8)^2+(492-496.8)^2)}\\\\\\s=\sqrt{\dfrac{166.8}{4}}\\\\\\s=\sqrt{41.7}=6.5\\\\\\[/tex]
Then, we can perform the hypothesis t-test for the mean.
The claim is that the amount of vitamin C in a tablet sample is different from 500 mg.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=500\\\\H_a:\mu< 500[/tex]
The significance level is 0.05.
The sample has a size n=5.
The sample mean is M=496.8.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=6.5.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{6.5}{\sqrt{5}}=2.907[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{496.8-500}{2.907}=\dfrac{-3.2}{2.907}=-1.1[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=5-1=4[/tex]
This test is a left-tailed test, with 4 degrees of freedom and t=-1.1, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t<-1.1)=0.166[/tex]
As the P-value (0.166) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the amount of vitamin C in a tablet sample is different from 500 mg.
segment AB is dilated from the origin to create segment A prime B prime at A' (0, 6) and B' (6, 9). What scale factor was segment AB dilated by?
1/2
2
3
4
Answer:
the answer is 3
Step-by-step explanation:
i took the test
5/a - 4/b as a single fraction
Answer:
I'm not completely sure what you mean by a, "single fraction," but I'm pretty sure the answer you are looking for is [tex]\frac{5-4}{a-b}[/tex]
Step-by-step explanation:
Given the following functions f(x) and g(x), solve f[g(6)]. f(x) = 6x + 12 g(x) = x − 8
Answer:
Answer:
Option 2nd is correct.
=0.
Step-by-step explanation:
Given the function:
Solve:
First calculate:
f[g(x)]
Substitute the function g(x)
Replace x with x-8 in the function f(x) we get;
The distributive property says that:
Using distributive property:
⇒
Put x = 6 we get;
Therefore, the value of is 0.
Step-by-step explanation:
Answer:
0
Step-by-step explanation:
f(x) = 6x + 12
g(x) = x − 8
f(g(6))=?
g(6)=6-8= -2
f(-2)= -2*6+12= -12+12=0
f(g(6))= f(-2)=0
Kyra is using rectangular tiles of two types for a floor design. They Tyler each type is shown below:
Answer: b) the tiles are not similar because both SP:SR is 5:4 and MJ:ML is 5:2
Step-by-step explanation:
We are given that the tiles are rectangular which implies that they both have a 90° angle.
In order to prove similarity, We need to show that the lengths and widths are proportional.
P Q R S
J K L M
a) PQ : QR JK : LM
w=4 L=5 w=2 w=2
↓
We need Length (not width)
b) SP : SR MJ : ML
L=5 w=4 L=5 w=2
5 : 4 5 : 2
When comparing length to width they do not have the same ratio so the rectangles are not similar.
c) PQ : QR JK : KL
w=4 L=5 w=2 L=5
4 : 5 2 : 5
When comparing width to length they do not have the same ratio so the rectangles are not similar.
d) SR : ML PQ : JK
w=4 w=2 w=4 w=2
↓ ↓
We need Length (not width)
from what area of the world is the earliest dated inscription with a symbol for zero?
Answer:
india
Step-by-step explanation:
what is the solution to the equation y=2/3x+3 X=-2
Answer: The solution is [tex](-2,\frac{5}{3} )[/tex]
Step-by-step explanation:
it already gives you the solution for x so just plot it into the equation to solve for y.
y= [tex]\frac{2}{3} *\frac{-2}{1}+3[/tex]
y= [tex]\frac{-4}{3}+\frac{3}{1}[/tex]
y= [tex]\frac{5}{3}[/tex]
Answer: -2 5/3
Step-by-step explanation:
y= 2/3*-2/1+3
y= -4+3/1
-2 5/3
An experiment was conducted to record the jumping distances of paper frogs made from construction paper. Based on the sample, the corresponding 95% confidence interval for the mean jumping distance is (8.8104, 11.1248)cm. What is the corresponding 98% confidence interval for the mean jumping distance?
Answer:
[tex] 9.9676 - 2.326*0.5904 =8.594[/tex]
[tex] 9.9676 + 2.326*0.5904 =11.341[/tex]
Step-by-step explanation:
Notation
[tex]\bar X[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
s represent the sample standard deviation
n represent the sample size
Solution to the problem
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
For this case the 9% confidence interval is given by:
[tex] 8.8104 \leq \mu \leq 11.1248[/tex]
We can calculate the mean with the following:
[tex]\bar X = \frac{8.8104 +11.1248}{2}= 9.9676[/tex]
And we can find the margin of error with:
[tex] ME= \frac{11.1248- 8.8104}{2}= 1.1572[/tex]
The margin of error for this case is given by:
[tex] ME = t_{\alpha/2}\frac{s}{\sqrt{n}} = t_{\alpha/2} SE[/tex]
And we can solve for the standard error:
[tex] SE = \frac{ME}{t_{\alpha/2}}[/tex]
The critical value for 95% confidence using the normal standard distribution is approximately 1.96 and replacing we got:
[tex] SE = \frac{1.1572}{1.96}= 0.5904[/tex]
Now for the 98% confidence interval the significance is [tex]\alpha=1-0.98= 0.02[/tex] and [tex]\alpha/2 = 0.01[/tex] the critical value would be 2.326 and then the confidence interval would be:
[tex] 9.9676 - 2.326*0.5904 =8.594[/tex]
[tex] 9.9676 + 2.326*0.5904 =11.341[/tex]
20 points answer thisssss
area =πr²
6.5²xπ=132.73
2.3²xπ=16.62
132.73-16.62= 116.11
116cm^2
i think its this anyway
Answer:
116 cm^2 to 3 s f's.
Step-by-step explanation:
The area of the shaded part = area of the outer circle - area of the inner circle
= π * 6.5^2 - π * 2.3^2
= 132.732 - 16.619
= 116.113 cm^2.
The mean annual tuition and fees for a sample of 15 private colleges was with a standard deviation of . A dotplot shows that it is reasonable to assume that the population is approximately normal. You wish to test whether the mean tuition and fees for private colleges is different from 32,500 a) state the null and alternate hypotheses b) calculate the standard error c) calculate the test statistic d) find the p - value .
Answer:
Step-by-step explanation:
The question is incomplete. The complete question is:
The mean annual tuition and fees for a sample of 15 private colleges was $35,500 with a standard deviation of $6500. A dotplot shows that it is reasonable to assume that the population is approximately normal. You wish to test whether the mean tuition and fees for private colleges is different from $32,500. State the null and alternate hypotheses. A) H0: 4 = 32,500, H:4=35,500 C) H: 4 = 35,500, H7:35,500 B) H: 4 = 32,500, H : 4 # 32,500 D) H0:41 # 32,500, H : 4 = 32,500
Solution
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
H0: µ = 32500
For the alternative hypothesis,
Ha: µ ≠ 32500
This is a two tailed test.
Since the number of samples is small and the population standard deviation is not given, the distribution is a student's t.
Since n = 15,
Degrees of freedom, df = n - 1 = 15 - 1 = 14
t = (x - µ)/(s/√n)
Where
x = sample mean = 35500
µ = population mean = 32500
s = samples standard deviation = 6500
t = (35500 - 32500)/(6500/√15) = 1.79
We would determine the p value using the t test calculator. It becomes
p = 0.095
Assuming alpha = 0.05
Since alpha, 0.05 < than the p value, 0.095, then we would fail to reject the null hypothesis.
Please answer this correctly
Answer:
3/10
Step-by-step explanation:
As director of the employee wellness and productivity program in your company, you are interested in comparing the effects of strength training, aerobic training, and yoga on decreasing rates of injury and absenteeism. The company has 9 divisions with roughly the same number of employees, and you randomly assign 3 divisions to participate in strength training, 3 to aerobic training, and 3 to yoga. Your alternative hypothesis is
Answer:
[tex]\mu_1 \neq \mu_2 \neq \mu_3[/tex]
Where [tex]\mu_1[/tex] is the average effect of strength training
[tex]\mu_2[/tex] is the average effect of aerobic training
[tex]\mu_3[/tex] is the average effect of yoga
Step-by-step explanation:
The aim of this study is to confirm whether the strength training, aerobic training, and yoga have equal effect on the decreasing rates of injury and absenteeism or not. The null hypothesis suggests that these three training have equal effect on the decreasing rates of injury and absenteeism because according to the null hypothesis, there is no statistical difference between observed variables.
The alternative hypothesis on the other hand suggests a statistical difference between the observed variables. In this case, the alternative hypothesis suggests that the observed variables have different effects on the decreasing rates of injury and absenteeism.
My alternative hypothesis as the director of the employee wellness and productivity program is [tex]\mu_1 \neq \mu_2 \neq \mu_3[/tex]
Where [tex]\mu_1[/tex] is the average effect of strength training
[tex]\mu_2[/tex] is the average effect of aerobic training
[tex]\mu_3[/tex] is the average effect of yoga
The alternative hypothesis is, [tex]\mu_1 \neq \mu_2 \neq \mu_ 3[/tex].
Where, [tex]\mu_1[/tex] is the average effect of strength training,
[tex]\mu_2[/tex] is the average effect of aerobic training.
[tex]\mu_3[/tex] is the average effect of yoga.
Given that,
As director of the employee wellness and productivity program in your company,
you are interested in comparing the effects of strength training, aerobic training, and yoga on decreasing rates of injury and absenteeism.
The company has 9 divisions with roughly the same number of employees, and you randomly assign 3 divisions to participate in strength training, 3 to aerobic training, and 3 to yoga.
We have to determine,
Your alternative hypothesis is.
According to the question,
The effects of strength training, aerobic training, and yoga on decreasing rates of injury and absenteeism.
The aim of this study is to confirm whether strength training, aerobic training, and yoga have equal effects on decreasing rates of injury and absenteeism or not.
The null hypothesis suggests that these three pieces of training have an equal effect on the decreasing rates of injury and absenteeism because according to the null hypothesis,
There is no statistical difference between observed variables.
The alternative hypothesis on the other hand suggests a statistical difference between the observed variables.
In this case, the alternative hypothesis suggests that the observed variables have different effects on the decreasing rates of injury and absenteeism.
The company has 9 divisions with roughly the same number of employees, and you randomly assign 3 divisions to participate in strength training, 3 to aerobic training, and 3 to yoga.
Therefore, The alternative hypothesis as the director of the employee wellness and productivity program is,
Where [tex]\mu_1[/tex] is the average effect of strength training,
[tex]\mu_2[/tex] is the average effect of aerobic training.
[tex]\mu_3[/tex] is the average effect of yoga.
To know more about the Hypothesis click the link given below.
https://brainly.com/question/23056080
Each of the following is a confidence interval for μ = true average (i.e., population mean) resonance frequency (Hz) for all tennis rackets of a certain type:(111.6, 112.4) (111.4, 112.6)(a) What is the value of the sample mean resonance frequency?
Answer:
The value of the sample mean resonance frequency is 112Hz
Step-by-step explanation:
A confidence interval has two bounds, a lower bound and an upper bound.
A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.
In this problem, we have that:
Lower bound: 111.6
Upper bound: 112.4
Sample mean: (111.6 + 112.4)/2 = 112Hz
The value of the sample mean resonance frequency is 112Hz
The value of the sample mean resonance frequency is 112 Hz.
What is the value of the sample mean resonance frequency?The value of the sample mean resonance frequency is equivalent to the average of the upper limit and the lower limit.
The sample mean resonance frequency = (lower limit + upper limit) / 2
(111.6 +112.4) / 2
= 224 / 2
= 112 Hz
To learn more about confidence interval, please check: https://brainly.com/question/15905477
Two fair dice are tossed and the number on each die is recorded, e.g. (3,2) indicates the first die had 3 and the second die had a 2. In total, there are 36 (equally likely) outcomes in the sample space. What is the probability the sum of the two dice is 7 or 11? Group of answer choices
Answer:
P(7 or 11) = 0.2222
Step-by-step explanation:
First let's find the cases where we get a sum of 7 and a sum of 11:
The cases where we get a sum of 7 are:
(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)
And the cases where we get a sum of 11 are:
(5,6), (6,5)
So we have a total of 8 cases among the 36 total possible outcomes.
So the probability of the sum of the two dice being 7 or 11 is:
P(7 or 11) = 8 / 36 = 0.2222
Find the equation of the line.
Use exact numbers.
Answer:
y = 2/3x + 4
Step-by-step explanation:
Step 1: Find slope
m = (4-0)/(0+6)
m = 2/3
Step 2: Write in y-int (0, 4)
y = 2/3x + 4
The percentage of households that include at least one frequent gamer is 58%. A gaming magazine is interested in studying this further to see how it impacts their magazine advertisements. For what sample size, n, will the sampling distribution of sample proportions have a standard deviation of 0.02
Answer:
For a sample size of n = 609.
Step-by-step explanation:
Central limit theorem for proportions:
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
We have that p = 0.58.
We have to find n for which s = 0.02. So
[tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
[tex]0.02 = \sqrt{\frac{0.58*0.42}{n}}[/tex]
[tex]0.02\sqrt{n} = \sqrt{0.58*0.42}[/tex]
[tex]\sqrt{n} = \frac{\sqrt{0.58*0.42}}{0.02}[/tex]
[tex](\sqrt{n})^{2} = (\frac{\sqrt{0.58*0.42}}{0.02})^{2}[/tex]
[tex]n = 609[/tex]
For a sample size of n = 609.
A sector of angle 125° is revomed from a thin circular sheet of radius 18cm. it is then folded with straight edges coinciding to form a right circular cone. what are the steps you would use to calculate the base radius, the semi- vertical, and the volume of the cone?
Answer:
Volume of the cone is 1883.7 cm³
Step-by-step explanation:
The circumference of the full circle with radius 18 cm :
360 := 2*π*18 = 36π cm
125 := 125/360 * 36π
The new circumference is maller:
36π - 125/360 * 36π
36π * 0.652(7)
Calculate the new r based on the new circomference:
2*π * r = 36π * 0.652(7)
r = 36π/2π * 0.652(7)
r = 18 * 0.652(7)
r = 11.75 cm
Based on this radius you can calculate the area of the base of the cone.
area base = π*(11.75)²
The Volume V of this cone = 1/3 π r² * h
You can calculate the height h by using Pythagoras theorum.
The sector is the hypothenusa= 18 cm
The h is the height, which is the "unknown"
The r is the new radius = 11.75 cm
s² = r² + h²
h² = s² - r²
h = √(s² - r²)
h = √(18² - 11.75²)
h = 13.6358901432946 cm
h = 13.636 cm
V cone
V = 1/3 π 11.75² * h
V = 1/3 π 11.75² * √(18² - 11.75²)
V = 1/3 π 11.75² * 13.636
V = 1883.7 cm³
Please answer this correctly I want genius expert or ace people to answer this correctly as soon as possible as my work is due today
Answer:
25%
Step-by-step explanation:
The last percentile always contains 25% of the observations.
-3/2 (x-1/3)>1/5-5x
What is the solution for this ^ inequality.
Answer:
[tex]x>\frac{-3}{35}[/tex]I hope this help
Step-by-step explanation:
List the complete list of numbers that make up pi.
Answer:
Sry, i dont know all of the numbers. Hope this helps!
Here are the first:
Step-by-step explanation:
3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609433057270365759591953092186117381932611793105118548074462379962749567351885752724891227938183011949129833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901224953430146549585371050792279689258923542019956112129021960864034418159813629774771309960518707211349999998372978049951059731732816096318595024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303598253490428755468731159562863882353787593751957781857780532171226806613001927876611195909216420198938095257201065485863278865936153381827968230301952035301852968995773622599413891249721775283479131515574857242454150695950829533116861727855889075098381754637464939319255060400927701671139009848824012858361603563707660104710181942955596198946767837449448255379774726847104047534646208046684259069491293313677028989152104752162056966024058038150193511253382430035587640247496473263914199272604269922796782354781636009341721641219924586315030286182974555706749838505494588586926995690927210797509302955321165344987202755960236480665499119881834797753566369807426542527862551818417574672890977772793800081647060016145249192173217214772350141441973568548161361157352552133475741849468438523323907394143334547762416862518983569485562099219222184272550254256887671790494601653466804988627232791786085784383827967976681454100953883786360950680064225125205117392984896084128488626945604241965285022210661186306744278622039194945047123713786960956364371917287467764657573962413890865832645995813390478027590099465764078951269468398352595709825822620522489407726719478268482601476990902640136394437455305068203496252451749399651431429809190659250937221696461515709858387410597885959772975498930161753928468138268683868942774155991855925245953959431049972524680845987273644695848653836736222626099124608051243884390451244136549762780797715691435997700129616089441694868555848406353422072225828488648158456028506016842739452267467678895252138522549954666727823986456596116354886230577456498035593634568174324112515076069479451096596094025228879710893145669136867228748940560101503308617928680920874760917824938589009714909675985261365549781893129784821682998948722658804857564014270477555132379641451523746234364542858444795265867821051141354735739523113427166102135969536231442952484937187110145765403590279934403742007310578539062198387447808478489683321445713868751943506430218453191048481005370614680674919278191197939952061419663428754440643745123718192179998391015919561814675142691239748940907186494231961567945208095146550225231603881930142093762137855956638937787083039069792077346722182562599661501421503068038447734549202605414665925201497442850732518666002132434088190710486331734649651453905796268561005508106658796998163574736384052571459102897064140110971206280439039759515677157700420337869936007230558763176359421873125147120532928191826186125867321579198414848829164470609575270695722091756711672291098169091528017350671274858322287183520935396572512108357915136988209144421006751033467110314126711136990865851639831501970165151168517143765761835155650884909989859982387345528331635507647918535893226185489632132933089857064204675259070915481416549859461637180270981994309924488957571282890592323326097299712084433573265489382
Pls mark Brainliest
what is the length of the line?
Answer:
root 61
Step-by-step explanation:
You can use the distance formula or draw a triangle with sides 5 and 6
Terry has a number cube that is numbered from 1 to 6. She rolls the cube 50 times. Which equation can be used to predict the number of times that she will roll a number that is greater than 4? P (number greater than 4) = StartFraction 1 over 6 EndFraction (50) P (number greater than 4) = StartFraction 2 over 6 EndFraction (50) P (number greater than 4) = StartFraction 3 over 6 EndFraction (50) P (number greater than 4) = StartFraction 4 over 6 EndFraction (50)
Answer:
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
It is known that 4% of children carry a certain virus, but a leading health researcher suspects that the percentage is actually higher. Which of the following provides the most convincing evidence to support the researcher's suspicion?
A. Out of 5,000 randomly chosen children, 210 children carry the virus.
B. Out of 60 randomly chosen children, 3 children carry the virus.
C. Out of 5,000 randomly chosen children, 250 children carry the virus.
D. Out of 20 randomly chosen children, 1 child carries the virus.
Answer:
(C)Out of 5,000 randomly chosen children, 250 children carry the virus.
Step-by-step explanation:
[tex]\text{Option A}: \dfrac{210}{5000}=0.042=4.2\% \\\text{Option B}: \dfrac{3}{60}=0.05=5\% \\\text{Option C}: \dfrac{250}{5000}=0.05=5\% \\\text{Option D}: \dfrac{1}{20}=0.05=5\%[/tex]
The higher the research sample, the more credible the results. In options A and C, the research sample was 5000. However, since the relative frequency of children carrying the virus is 5% in both, we take the result with a higher number of positives.
Option C is the correct option.
The sum of a number and twice the number is 24 what is the number?
Answer:
x = 8
Step-by-step explanation:
Step 1: Write out the expression
x + 2x = 24
Step 2: Combine like terms
3x = 24
Step 3: Isolate x
x = 8
And we have our final answer!
Answer:
X=8
Step-by-step explanation:
Can someone please help me??
Answer : The value of x is 4.1 cm.
Step-by-step explanation :
As we know that the perpendicular dropped from the center divides the chord into two equal parts.
That means,
AB = CB = [tex]\frac{15.6cm}{2}=7.8cm[/tex]
Now we have o calculate the value of x by using Pythagoras theorem.
Using Pythagoras theorem in ΔOBA :
[tex](Hypotenuse)^2=(Perpendicular)^2+(Base)^2[/tex]
[tex](OA)^2=(OB)^2+(BA)^2[/tex]
Now put all the values in the above expression, we get the value of side OB.
[tex](8.8)^2=(x)^2+(7.8)^2[/tex]
[tex]x=\sqrt{(8.8)^2-(7.8)^2}[/tex]
[tex]x=\sqrt{77.44-60.84}[/tex]
[tex]x=\sqrt{16.6}[/tex]
[tex]x=4.074\approx 4.1[/tex]
Therefore, the value of x is 4.1 cm.
Show that every triangle formed by the coordinate axes and a tangent line to y = 1/x ( for x > 0)
always has an area of 2 square units.
Hint: Find the equation of the tangent line at x = a. (It will contain a’s as well as x and y.) Then find the
x-and y-intercepts for that line to find the lengths of sides of the right triangle.
Answer:
Step-by-step explanation:
given a point [tex](x_0,y_0)[/tex] the equation of a line with slope m that passes through the given point is
[tex]y-y_0 = m(x-x_0)[/tex] or equivalently
[tex] y = mx+(y_0-mx_0)[/tex].
Recall that a line of the form [tex]y=mx+b [/tex], the y intercept is b and the x intercept is [tex]\frac{-b}{m}[/tex].
So, in our case, the y intercept is [tex](y_0-mx_0)[/tex] and the x intercept is [tex]\frac{mx_0-y_0}{m}[/tex].
In our case, we know that the line is tangent to the graph of 1/x. So consider a point over the graph [tex](x_0,\frac{1}{x_0})[/tex]. Which means that [tex]y_0=\frac{1}{x_0}[/tex]
The slope of the tangent line is given by the derivative of the function evaluated at [tex]x_0[/tex]. Using the properties of derivatives, we get
[tex]y' = \frac{-1}{x^2}[/tex]. So evaluated at [tex]x_0[/tex] we get [tex] m = \frac{-1}{x_0^2}[/tex]
Replacing the values in our previous findings we get that the y intercept is
[tex](y_0-mx_0) = (\frac{1}{x_0}-(\frac{-1}{x_0^2}x_0)) = \frac{2}{x_0}[/tex]
The x intercept is
[tex] \frac{mx_0-y_0}{m} = \frac{\frac{-1}{x_0^2}x_0-\frac{1}{x_0}}{\frac{-1}{x_0^2}} = 2x_0[/tex]
The triangle in consideration has height [tex]\frac{2}{x_0}[/tex] and base [tex]2x_0[/tex]. So the area is
[tex] \frac{1}{2}\frac{2}{x_0}\cdot 2x_0=2[/tex]
So regardless of the point we take on the graph, the area of the triangle is always 2.
Before a researcher specified the relationship among variables he must have a (an): A: Inventory of variables B: Inventory of propositions C: Arrangement of propositions D: Schematic diagram
Answer:
Option B
Step-by-step explanation:
Before a researcher specifies the relationship among variables he must have an inventory of propositions/constructs which are mostly stated in a declarative form. These are then tested by examining the relationships between measurable variables of this constructs/propositions.
Refer to the following frequency distribution of days absent during a calendar year by employees of a manufacturing company:_______.
Days Absent Number of employees
0 up to 3 60
3 up to 6 31
6 up to 9 14
9 up to 12 6
12 up to 15 2
How many employees were absent fewer than six days?
Answer:
91 employees
Step-by-step explanation:
To find the number of employees absent fewer than six days...add the frequency of those absent for 0 to 3 days and that of 3 to 6 days
The frequency of 0 to 3 days = 60
The frequency of 3 to 6 days = 31
Thus, the numbers of employees absent fewer than 6 days is 60+31 = 91
polygon P'Q'R'S'T' shown on the grid below is an image of polygon PQRST after dilation with a scale factor of 3, keeping the origin as the center of dilation:
Answer: d) SR and S'R' have the ratio 1:3
Step-by-step explanation:
In order for the polygons to be similar, they must have congruent angles and proportional side lengths.
a) ∠Q and ∠Q' have the ratio 1:3
FALSE - The angles must be congruent (not proportional)
b) TS and T'S' have equal lengths
FALSE - We can see that there is a dilation so they cannot be congruent.
c) RT and R'T' have equal lengths
FALSE - We can see that there is a dilation so they cannot be congruent.
d) SR and S'R' have a ratio of 1:3
TRUE! - The sides are proportional so we can use this to prove similarity.
Answer:
D- The lengths of side SR and side S'R' are in the ratio 1:3.
Step-by-step explanation:
I took the test and it was right