Answer:
The number of different computer systems possible is 1440.
Step-by-step explanation:
For each computer, there are 10 options of monitor.
For each monitor, there are 8 printers.
For each printer, there are 2 scanners.
There are 9 computers.
Determine the number of different computer systems possible.
9*10*8*2 = 1440
The number of different computer systems possible is 1440.
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
This table represents a quadratic function with a vertex at (1, 2). What is the
average rate of change for the interval from x = 5 to x = 6?
Answer:
D: 9
Step-by-Step Explanation:
The average rate is synonymous with the slope. Since we want to find the average rate of change from x = 5 to x = 6, we will use the two points (5, 18) and (6, ?). We will need to find ? first.
Since the table represents a quadratic function and we are given the vertex, we can use the vertex form of a quadratic:
[tex]\displaystyle f(x)=a(x-h)^2+k[/tex]
Where (h, k) is the vertex.
The vertex is (1, 2). Hence:
[tex]f(x)=a(x-1)^2+2[/tex]
To determine a, pick a sample point from the table and solve for a. We can use (2, 3). Hence:
[tex](3)=a((2)-1)^2+2[/tex]
Solve for a:
[tex]1=a(1)^2\Rightarrow a=1[/tex]
Hence, our function is:
[tex]f(x)=(x-1)^2+2[/tex]
Evaluate the function when x = 6:
[tex]\displaystyle f(6)=(6-1)^2+2=27[/tex]
So, our two points are (5, 18) and (6, 27).
Again, to find the average rate of change between x= 5 and x = 6, find the slope between their two points. Hence:
[tex]\displaystyle m=\frac{27-18}{6-5}=9[/tex]
Our answer is D.
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
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
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
While conducting a test of modems being manufactured, it is found that 10 modems were faulty out of a random sample of 367 modems. The probability of obtaining this many bad modems (or more), under the assumptions of typical manufacturing flaws would be 0.013. Is this an unusually high number of faulty modems
Answer:
We conclude that this is an unusually high number of faulty modems.
Step-by-step explanation:
We are given that while conducting a test of modems being manufactured, it is found that 10 modems were faulty out of a random sample of 367 modems.
The probability of obtaining this many bad modems (or more), under the assumptions of typical manufacturing flaws would be 0.013.
Let p = population proportion.
So, Null Hypothesis, [tex]H_0[/tex] : p = 0.013 {means that this is an unusually 0.013 proportion of faulty modems}
Alternate Hypothesis, [tex]H_A[/tex] : p > 0.013 {means that this is an unusually high number of faulty modems}
The test statistics that would be used here One-sample z-test for proportions;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion faulty modems= [tex]\frac{10}{367}[/tex] = 0.027
n = sample of modems = 367
So, the test statistics = [tex]\frac{0.027-0.013}{\sqrt{\frac{0.013(1-0.013)}{367} } }[/tex]
= 2.367
The value of z-test statistics is 2.367.
Since, we are not given with the level of significance so we assume it to be 5%. Now at 5% level of significance, the z table gives a critical value of 1.645 for the right-tailed test.
Since our test statistics is more than the critical value of z as 2.367 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that this is an unusually high number of faulty modems.
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.
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
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
−
50
54
−
100
40
+1.65=minus, start fraction, 54, divided by, 50, end fraction, minus, start fraction, 40, divided by, 100, end fraction, plus, 1, point, 65, equals
Answer:
[tex]\frac{-50}{54} - \frac{40}{100} +1.65 = 0.32[/tex]
Step-by-step explanation:
First of all, let us lay out the problem clearly:
[tex]\frac{-50}{54} - \frac{40}{100} +1.65[/tex]
This can be solved using a calculator, by first simplifying the individual fractions first, to decimals, then computing the addition and subtraction.
using your calculator, punch (-50 ÷ 54), your results should be:
-50 ÷ 54 = -0.93
Next, punch ( 40 ÷ 100), you should get 0.4
Now, join the individual results together to get:
- 0.93 - 0.40 + 1.65
Finally, still using the calculator, input the values as shown:
- 0.93 - 0.40 + 1.65 = 0.32
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.
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
Which decimal is closest in value to the fraction below?
1/7
O A. 0.8
O B. .33333
O c. 0.143
Answer:
0.143
Step-by-step explanation:
1/7 means 1 divided by 7. 1 divided by 7 is approximately 0.143.
Hope this helps!
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.
A truck starts off 180 miles directly east from the city of Hartville. It travels due south at a speed of 45 miles per hour. After travelling 49 miles, how fast is the distance between the truck and Hartville changing
Answer:
11.82 mph
Step-by-step explanation:
The angle between the direction of travel and the direction to the city of Hartville is ...
arctan(180/49) ≈ 74.77°
The speed from the direction of Hartville is the the actual speed multiplied by the cosine of this angle:
speed from Hartville = (45 mph)×cos(74.77°) ≈ 11.82 mph
_____
Comment on the solution
There are other approaches you can use to solve this. One is to compute the change in distance over a small period of time, such as 0.02 hours.
0.01 hours before the time of interest, the distance to the city is ...
d1 = √(180² +(49-.01(45))²) ≈ 186.4326 . . . miles
0.01 hours after the time of interest, the distance to the city is ...
d2 = √(180² +(49+.01(45))²) ≈ 186.6690 . . . miles
Then the rate of change of distance is ...
(d2 -d1)/(t2 -t1) = (186.6690 -186.4326)/0.02 = 11.82 . . . mi/h
__
Another is to write the distance equation and differentiate it. (You will find the solution looks very much like the trig solution above.)
d = √(180² +(45t)²)
dd/dt = 45²t/√(180² +(45t)²) . . . . . to be evaluated at t=49/45
rate of change = 45(49/√(180²+49²)) ≈ 11.82 . . . mi/h
Henrique began to solve a system of linear equations using the linear combination method. His work is shown below: 3(4x – 7y = 28) → 12x – 21y = 84 –2(6x – 5y = 31) → –12x + 10y = –62 12x – 21y = 84 + –12x + 10y = –62 –11y = 22 y = –2 Complete the steps used to solve a system of linear equations by substituting the value of y into one of the original equations to find the value of x. What is the solution to the system? ( , )
Answer:
( 3.5 , -2 )
Step-by-step explanation:
Answer:
( 3.5 , -2)
Explanation:
On edge
Find the explicit formula for the arithmetic sequence cn given below. Note that c1=8. 8,17,26,35,44,…
Answer:
[tex]c_n=9\,n-1[/tex]
Step-by-step explanation:
Recall that the general formula for the nth term of an arithmetic sequence is given by:
[tex]c_n=c_1+(n-1)\,d[/tex]
where [tex]c_1[/tex] is the first term of the sequence (in our case 8), and [tex]d[/tex] is the common difference for the sequence (the number that is added to a term in order to get the term that follows. In our case, "9" is the common difference (you can check this by subtraction between any two consecutive terms.
Then, the formula for the nth term of this sequence is
[tex]c_n=8+(n-1)\,9=8+9\,n-9=9\,n-1[/tex]
-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:
What is the present value of a $1,600 payment made in five years when the discount rate is 10 percent?
Answer:
Present value is $993.47
Step-by-step explanation:
PV = present value
Fv = future value = $1,600
Discount (i) = 10%
N = Years = 5
The formula for this is given by:
PV = FV/(1 + i)^N
PV = $1600/(1 + 0.10)^5
PV = $1600/1.1^5
PV = $1600/1.61051
PV = $993.47
An urn contains two blue balls (denoted B1 and B2) and three white balls (denoted W1, W2, and W3). One ball is drawn from the urn, its color recorded, and is replaced. Another ball is then drawn and its color recorded. Let B1W2 denote the outcome that the first ball drawn is B1 and the second ball drawn is W2. Because the first ball is replaced before the second ball is drawn, the outcomes of the experiment are equally likely. List all 25 possible outcomes of the experiment on a sheet of paper. (a) Consider the event that the first ball that is drawn is blue. Count all the outcomes in this event.
Answer:
(a)10 Outcomes
(b)[tex]\dfrac{2}{5}[/tex]
Step-by-step explanation:
An urn contains two blue balls (denoted [tex]B_1 \:and\: B_2[/tex]) and three white balls (denoted [tex]W_1, W_2 \:and\: W_3[/tex]).
In the selection, a ball is picked and replaced.
The possible outcomes of the experiment are:
[tex]B_1B_1,B_1B_2,B_1W_1,B_1W_2,B_1W_3\\B_2B_1,B_2B_2,B_2W_1,B_2W_2,B_2W_3\\W_1B_1,W_1B_2,W_1W_1,W_1W_2,W_1W_3\\W_2B_1,W_2B_2,W_2W_1,W_2W_2,W_2W_3\\W_3B_1,W_3B_2,W_3W_1,W_3W_2,W_3W_3[/tex]
(a)If the first ball drawn is blue. the outcomes are:
[tex]B_1B_1,B_1B_2,B_1W_1,B_1W_2,B_1W_3\\B_2B_1,B_2B_2,B_2W_1,B_2W_2,B_2W_3[/tex]
There are 10 outcomes if the first ball drawn is blue.
Probability that the first ball drawn is blue
[tex]=\dfrac{10}{25}\\ =\dfrac{2}{5}[/tex]
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)
Three years ago Tom was twice as old as Jean. And in two years the sum of their ages will be 28 years. Find their present ages.
Answer:
Jean is 9 years old and Tom is 15 years old.
Step-by-step explanation:
let t = Tom's present age
let j = Jean's age
Three years ago, Tom was twice as old as Jean,
t-3 = 2(j-3)
t - 3 = 2j - 6
t = 2j - 6 + 3
t = 2j - 3
In two years the sum of their ages will be 28 years.
(t+2) + (j+2) = 28
t + j + 4 = 28
t + j = 28 - 4
t + j = 24
For their present ages, replace t with (2j-3) from the 1st statement
2j - 3 + j = 24
2j + j = 24 + 3
3j = 27
j = 27/3
j = 9 yrs is Jean's age
Find Tom's age
t = 2(9) - 3
t = 15 yrs is Tom's age
An equation is formed of two equal expressions. The age of Tom is 15 years and the age of Jean is 9 years.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let the present age of Tom and Jean be represented by x and y, respectively. Therefore, the given statement three years ago Tom was twice as old as Jean in the form of an equation can be written as,
(x-3) = 2(y-3)
Solving the equation for x,
x - 3 = 2y - 6
x = 2y - 3
Also, it is given that in two years the sum of their ages will be 28 years.
(x+2) + (y+2) = 28
(2y - 3 + 2) + (y + 2) = 28
2y -3 + 2 + y + 2 = 28
3y + 1 = 28
3y = 27
y = 9
Substitute the value of y in the equation of x formed above,
x = 2y - 3
x = 2(9) - 3
x = 15
Hence, the age of Tom is 15 years and the age of Jean is 9 years.
Learn more about Equation:
https://brainly.com/question/2263981
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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
Pentagon ABCDE is shown on the coordinate plane below
Answer: c) B' = (6, -3)
Step-by-step explanation:
The simplest way is to rotate the graph.
Rotating the graph 1 time to the left (counterclockwise) = 90°
Rotating the graph 2 times to the left (counterclockwise) = 180°
Rotating the graph 3 times to the left (counterclockwise) = 270°
The longer way is to reflect over the x-axis and over the y-axis, which is the same as a rotation of 180°
Z = (x, y) → Z' = (-x, -y)
the image below shows the graph rotated 2 times = 180°
Answer:
c
Step-by-step explanation:
Please answer this correctly
Answer:
3/10
Step-by-step explanation:
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
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
A quick quiz consists of a multiple-choice question with 6 possible answers followed by a multiple-choice question with 5 possible answers. If both questions are answered with random guesses, find the probability that both responses are correct. Report the answer as a percent rounded to two decimal place accuracy. You need not enter the "%" symbol
Answer:
3.33
Step-by-step explanation:
Independent events:
If two events, A and B, are independent, we have that:
[tex]P(A \cap B) = P(A)*P(B)[/tex]
In this question, we have that:
The question are independent of each other.
Event A: Correct guess on the first question.
Event B: Correct guess on the second question.
A quick quiz consists of a multiple-choice question with 6 possible answers followed by a multiple-choice question with 5 possible answers.
This means that [tex]P(A) = \frac{1}{6}, P(B) = \frac{1}{5}[/tex]
Probability that both responses are correct.
[tex]P(A \cap B) = \frac{1}{6}*\frac{1}{5} = \frac{1}{30} = 0.333[/tex]
The answer is 3.33%. Since it asks without the "%" symbol, 3.33
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.
Verify the identity algebraically. 7 sec(y) cos(y) = 7
Answer:
7 sec(y) cos(y) = 7
Use identity sec(y) = 1/cos(y).
7 * 1/cos(y) * cos(y) = 7
7 * 1 = 7
7 = 7