Important
Given AABC ~ ADE F, determine the following information.
Determine the measure of LB. Show the work that leads to your answer.
Determine the length of EF. Show the work that leads to your answer.
Answers
Answer:
m∠B = 83°
EF = 10
Step-by-step explanation:
Two triangles are similar if their corresponding angles are the same size.
Therefore if ΔABC ~ ΔDEF then:
∠A ≅ ∠D = 24° ∠B ≅ ∠E∠C ≅ ∠F = 73°Interior angles of a triangle sum to 180°:
⇒ m∠A + m∠B + m∠C = 180°
⇒ 24° + m∠B + 73° = 180°
⇒ m∠B + 97° = 180°
⇒ m∠B = 83°
In similar triangles, corresponding sides are always in the same ratio.
Therefore if ΔABC ~ ΔDEF then:
⇒ AB : DE = BC : EF = CA : FD
⇒ 12 : DE = 8 : EF = 16 : 20
Therefore, to find the length of EF:
[tex]\implies \sf 8 : EF = 16 : 20[/tex]
[tex]\implies \sf \dfrac{8}{EF} = \dfrac{16}{20}[/tex]
[tex]\implies \sf 8 \cdot 20= 16 \cdot EF[/tex]
[tex]\implies \sf160= 16 \cdot EF[/tex]
[tex]\implies \sf EF=\dfrac{160}{16}[/tex]
[tex]\implies \sf EF=10[/tex]
Related Questions
Solve for P:
-11 = p - 9
Answers
Answer:
-2Step-by-step explanation:
Add 9 on both sides.
You'll get -2=p
So -2 = p.
-2 is your answer.
Answer:
-2
Step-by-step explanation:
-11 = p - 9
p = -11 + 9
p = -2
Check:
-11 = -2 - 9
Hope that helps!
what is 10/5 + 5????????
Answers
Answer:
7
Step-by-step explanation:
Answer:
mira ami me aparece cien
Step-by-step explanation:
pues creo que no es
This is mathemiatci can you hep
Answers
Answer:
81-x=96-2x
x=15
m <1 = 66
m <2 = 66
Step-by-step explanation:
Because
Make it like this
(81-x)=(96-2x)
And solve for(x)
And x=15
The add 15 to (81-x) =(81-15)=66
And (96-2x) =(96-2(15)=66
At home Moses uses all his free time to play video games, road and skateboard. He spends 75% of his free
te reading. 12.5% of his free time is spent playing video games and he skateboards from 5:15PM to
5:45PM How much free time does Moses get in total?
Answers
I need some help plz!!!
Answers
1 gram = .001 kilogram
2x520= 1040
1040 x .001 = 1.04 kilograms
25 less than 4 times a number is 47. What is the number?
Answers
Answer:
18
Step-by-step explanation:
25 + 47 = 72
72 ÷ 4 = 18
Three fourth of the students and an additional 18
students at the school purchased a spirit shirt during the
last fundraiser. If 336 shirts were ordered, how many
students are there in the school?
Answers
Answer:
424
Step-by-step explanation:
let 's' = number of students
3/4s + 18 = 336
3/4s = 318
3s = 1272
s = 1272/3 = 424
A percentage is another way to write a _________________.
Answers
Answer:
Ratio, Decimal or Fraction
Step-by-step explanation:
Answer:
it's another way to write a fraction:)
El numero tal que su 35% es 7
Answers
no entendo ???????? isto
Molly Invested $50,000 in various stocks and bonds. She earned 15% on the bonds and 18% on the stocks. If Molly's total profit on both types of investment was $8,700, how much of the $50,000 did she invest bonds?
Answers
10000x15%=1500.7200+1500=8700
An urn contains 4 white balls and 6 red balls. A second urn contains 7 white balls and 3 red balls. An urn is selected, and the probability of selecting the first urn is 0.8. A ball is drawn from the selected urn and replaced. Then another ball is drawn and replaced from the same urn. If both balls are white, what are the following probabilities?
a. the probability that the urn selected was the first one
b. the probability that the urn selected was the second one
Answers
Answer:
a) 0.5664 = 56.64% probability that the urn selected was the first one.
b) 0.4336 = 43.36% probability that the urn selected was the second one
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
If both balls are white, what are the following probabilities?
This means that event A is both balls being white.
Probability of both balls being white:
0.8 probability of 4/10 = 0.4 squared(first urn, which each time the ball is drawn will have 4 white balls and 6 red)
1 - 0.8 = 0.2 probability of 7/10 = 0.07 squared(second urn). So
[tex]P(A) = 0.8*(0.4)^2 + 0.2*(0.7)^2 = 0.226[/tex]
a. the probability that the urn selected was the first one
Event B: First urn selected.
The intersection of events A and B is given by both balls being white and selected from the first urn, which has the following probability:
[tex]P(A \cap B) = 0.8*(0.4)^2 = 0.128[/tex]
The desired probability is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.128}{0.226} = 0.5664[/tex]
0.5664 = 56.64% probability that the urn selected was the first one
b. the probability that the urn selected was the second one
The intersection of events A and B is given by both balls being white and selected from the second urn, which has the following probability:
[tex]P(A \cap B) = 0.2*(0.7)^2 = 0.098[/tex]
The desired probability is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.098}{0.226} = 0.4336[/tex]
0.4336 = 43.36% probability that the urn selected was the second one
five more than three times a number is six less than twice the number. find the number
Answers
Answer:
2
Step-by-step explanation:
6x-3=5+2x
-2x on both sides
4x-3=5
+3 on both sides
4x=8
divide 4 on both sides
x=2
-) 2.01 + 8 + 0.593
0,593
200
Answers
Answer:
10.60305932
Step-by-step explanation:
A local radio station conducted a survey about stay-at-home parents by randomly dialing home numbers on weekdays until responses from 500 adults were collected. Twenty-six percent of those who responded said they were stay-at-home parents. In reality, only four percent were actually stay-at-home parents at the time of the survey. Which of the following best explains the difference in the two percentages?
a. The difference is due to voluntary response. Adults are able to volunteer as members of the sample.
b. The difference is due to undercoverage bias. The survey included only adults with telephones.
c. The difference is due to response bias. Adults who are stay-at-home parents are likely to say they are employed outside the home.
d. The difference is due to sampling variability. We should not expect the results of a random sample to match the truth about the population every time.
e. The difference is due to nonresponse bias. Adults who are stay-at-home parents are more likely to be available for the sample than adults who are employed outside the home.
Answers
Answer:
The difference is due to nonresponse bias. Adults who are stay-at-home parents are more likely to be available for the sample than adults who are employed outside the home.
E on multiple choice
Step-by-step explanation:
1 Q1 - Mean
Work out the mean of each set of numbers.
11, 15, 13, 19, 17
[2]
2
56, 78, 63, 61, 74, 72, 81, 74, 75, 67
[2]
4.6, 5.9, 6.1, 2, 3.9, 2.4, 2.6, 1.9, 2.9, 1.3
[2]
o
alc
Jeremy caught 8 fish in a contest.
The mean weight of the fish was 4.35 kg.
He forgot to make his own record of the weight of the last fish,
but the first 7 were: 4.5 kg, 5 kg, 6.8 kg, 2.8 kg, 3.8 kg, 4.4 kg and 4.4 kg.
tal
0
5
What was the weight of the last fish?
kg
[2]
Markeit
Answers
Answer:
3.1 Kg
Step-by-step explanation:
Mean = Sum/Number of data
4.35=Sum/8
Sum= (4.5+5+6.8+2.8+3.8+5.5+4.4+4.4+last fish) = 31.7+last fish
4.35= (31.7+lastfish)/8
Last fish= (4.35×8) - 31.7 = 3.1 Kg
What is 2 7/9 + 8/9 ?
Answers
Answer:
11/6
Step-by-step explanation:
2 7/9 + 8/9
2 7/9 into a mixed fraction which is 25/9
now 25/9 + 8/9 = 33/18 then simplify which is 11/6
The probability that a first year student entering a certain private college needs neither a developmental math course nor a developmental English is 70% while 22% require a developmental math course and 25% require a developmental English course. Find the probability that a first year student requires both a development math course and a developmental English course.
Answers
Answer:
Probability of both English and Maths = 17%
Step-by-step explanation:
Probability of English or Maths
100 -70 = 30%
Probability of English or Maths =
Probability of English + Probability of Maths + Probability of both English and Maths
30 % = 22% + 25 % + Probability of both English and Maths
Probability of both English and Maths = 47% - 30 %
Probability of both English and Maths = 17%
Pls tell me the rest of the angles. Angle 1 is 112.9 degrees.
Answers
Answer:
the rest of the anglesss
Answer:
All together must be 180 but i dont know how to solve that
Show your work on paper. (Include properties) 80 points!!!
Answers
1/4 and 1/2 common denominators
Answers
Answer:
4
Step-by-step explanation:
Answer:
The common denominator of 1/4 and 1/2 is 4.
1/2 = 2/4
The diagram shows two congruent regular pentagons and part of a regular n-sided polygon A. Two sides of each of the regular pentagons and two side of A meet at the pint P. Calculate the value of n.
Answers
Answer:
n=10
Step-by-step explanation:
For a regular polygon with n sides, each interior angle, x, is given by
[tex]x=180\frac{n-2}{n}[/tex]
This can be solved for n
[tex]n=\frac{360}{180-x}[/tex]
For the pentagons
x(5)=180(3/5)=108 degrees.
The angles around P sum to 360, so
2(x(5))+x(A)=360
x(A)=360-2(108)=144.
Substitue in the equation for n.
n=360/(180-144)=10
The number of sides in this polygon is 10.
For any polygon, the sum of interior angles is given as,
[tex]\bold{Sum\ of\ interior\ angles= {(n-2)}\times {180^o}}[/tex]
where,
n = number of sides,
We know that for a pentagon, the number of sides is 5.
thus, substituting the values in the sum of interior angle formula we get,
[tex]{Sum\ of\ interior\ angles= {(n-2)}\times {180^o}}[/tex]
[tex]{Sum\ of\ interior\ angles= {5-2}\times{180^o}}\\= 3 \times {180^o} = 540^o[/tex]
therfore, each angle in a regular pentagon,
[tex]\dfrac{Sum\ of\ interior\ angles}{Number\ of\ Sides} = \dfrac{540^o}{5} = 108^o[/tex],
Let's assume that polygon A is having x number of sides.
At point P, the sum of the angles must be 360°.
The sum of the angles at point P
= interior angle of the first pentagon
+ interior angle of the second pentagon
+ interior angle of the polygon A with x sides
Substituting the values,
360° = 108° + 108° + z
z = 360° - 108° - 108°
z = 144°
Thus, the interior angle of the x sided polygon is z = 144°.
For a regular polygon, all the interior angles are equal,
so, for a polygon with sides x.
the sum of interior angle = measure of interior angle x Number of sides
= [tex]144^o \times x[/tex]
Also, we know
[tex]{Sum\ of\ interior\ angles= {(n-2)}\times {180^o}}[/tex]
Substituting, the values for an x number of side polygon,
[tex]{Sum\ of\ interior\ angles= {(n-2)}\times {180^o}}\\{144^o \times x = {(x-2)}\times {180^o}}\\144x = 180x - 360\\360 = 180x- 144x\\x = \dfrac{360}{36}\\x = 10[/tex]
Hence, the number of sides in this polygon is 10.
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A random sample of 200 adult residents in the U.S reveals that the mean minutes of sleep they received the night prior to the interview was 528 minutes with a standard deviation of 141 minutes. Using a computer, a random sample of 200 observations was taken (with replacement) from these data and an average was computed and recorded. This was repeated 10,000 times and a visualization was made of this sampling distribution. The mean of the sampling distribution was 528 minutes and the standard deviation was 10 minutes. The sampling distribution was symmetric and unimodal. Which of the following is an approximate 95% confidence interval for the mean amount of sleep of all US residents?
a. Lower bound: 528-141, upper bound: 528+141; (387, 669)
b. Lower bound: 528-10, Upper bound: 528+10; (518,538)
c. Lower bound: 528-20141, upper bound: 528 * 2*141; 246,810)
d. lower bound: 528-2-10, upper bound: 528+2*10; (508, 548)
Answers
Answer:
d. lower bound: 528-2-10, upper bound: 528+2*10; (508, 548)
Step-by-step explanation:
The computation of the approximate 95% confidence interval is shown below:
Given that
mean = 528,
standard deviation = 10
[tex]Mean \mp z_{\frac{0.05}{2}}\times standard\ deviation \\\\=528 \mp 2 \times 10\\\\=(508,548)[/tex]
hence, the correct option is d.
The confidence interval gives a range of estimate for the true population mean at a given confidence level. The confidence interval for the mean is lower bound: 528-2-10, upper bound: 528+2*10; (508, 548)
The confidence interval for the mean is obtained using the relation :
μ ± Z*σZ* = 95% critical level = ±1.96μ = sample mean = 528σ = standard deviation = 10 minutesPlugging in the values :
528 ± (1.96 × (10))
Approximating Z* (1.96) = 2.00
Lower boundary = 528 - (2 × 10) = 528 - 20 = 508
Upper boundary = 528 + (2 × 10) = 528 + 20 = 548
Therefore, the confidence interval is lower bound: 528-2-10, upper bound: 528+2*10; (508, 548)
One six-sided die and one sixteen-sided die are rolled. What is the probability of rolling an even number on the six-sided die and rolling a 16 on the other die?
0.031
0.167
0.229
0.063
Answers
Answer:
0.031
Step-by-step explanation:
you have a 1/2 chance of rolling an even number and a 1/16 chance of rolling 16. when you multiply 1/2 by 1/16 you get 1/32 and after converting that to decimal you are left with: 0.031
The probability of rolling an even number on the six-sided die and rolling a 16 on the other die would be 0.031
What is Probability?Probability stands for the branch of mathematics involving numerical descriptions of how likely an event exists to occur, or how likely it stands that a proposition is true. The probability of an event e xists in a number between 0 and 1, where, roughly speaking, 0 demonstrates the impossibility of the event and 1 shows certainty.
chance of rolling an even number= 1/2
chance of rolling 16 =1/16
1/2 * 1/16 = 1/32 = 0.031
The probability of rolling an even number on the six-sided die and rolling a 16 on the other die would be 0.031
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What is the solution to the system of equations below?
y=-1/3x+6
and x = -6
(-6,8)
(-6,4)
(8,-6)
(4, -6)
Answers
Answer:
(-6,8) is the answer using substitution method.
Step-by-step explanation:
y= (-1/3)(-6)+6
y= 2+6
y=8, x=-6
=(-6,8)
Answer:
The solution to this system of equations is [tex](x,y) = (-6, 8)[/tex].
Step-by-step explanation:
Since the number of equations and number of variables is the same, there is only one solution. Let [tex]y = -\frac{1}{3}\cdot x + 6[/tex] and [tex]x = -6[/tex], the solution of this system is found by evaluating the first function, that is:
[tex]y = -\frac{1}{3}\cdot (-6)+6[/tex]
[tex]y = 2+6[/tex]
[tex]y = 8[/tex]
The solution to this system of equations is [tex](x,y) = (-6, 8)[/tex].
Evaluate the limit(-2n^n/4+n
Answers
Answer:
.
Step-by-step explanation:
2x-5y + 11=0 3x-4y=18
Answers
Answer:
x = 134/7
y = 69/7
Step-by-step explanation:
let the x or y have a same coefficient to have a better way to solve it
What is 3+3!!??!!??!!??!!??!!??!!??
Answers
Answer:
6
Step-by-step explanation:
cause 3+3 is 6
thanks for the easy points :3
Answer:
id.kkkkk.. maybe 5.. maybe 6...
:O
please tell fast plzzzzzz
Answers
Answer:
x=90-44=46is your answer
Answer:
46 degrees (complimentary angles add up to 90 degrees)
Step-by-step explanation:
90 - 44 = 46
bro helppppppppppppp
Answers
Answer:
1. 2 and 2 is c
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
Solve the following triangle angles
Answers
Answer:
X=69 degree
?= 50 degree
Step-by-step explanation:
exterior angle prop so 77+X =146
X=146-77
X=69
in sencond triangle
90+40+?=180
?=180-130
?=50