3. Segment GE is an angle bisector of both
angle HEF and angle FGH. Prove triangle HGE is
congruent to triangle FGE.
F
H
G
Answers
ΔHGE and ΔFGE are congruent by the Angle-Side-Angle Congruence Theorem (ASA).
Recall:
A segment that divides an angle into equal parts is known as an angle bisector.Two triangles are congruent by the ASA Congruence Theorem if they share a common side and have two pairs of congruent angles.In the diagram given, Angle bisector, GE, divides ∠HEF into congruent angles, ∠HEG ≅ ∠GEF.
Also divides ∠FGH into congruent angles, ∠HGE ≅ ∠FGE.
Both triangles also share a common side, GE
This implies that: ΔHGE and ΔFGE have:
two pairs of congruent angles - ∠HEG ≅ ∠GEF and ∠HGE ≅ ∠FGE
a shared side - GE
Therefore, ΔHGE and ΔFGE are congruent by the Angle-Side-Angle Congruence Theorem (ASA).
Learn more about ASA Congruence Theorem on:
https://brainly.com/question/82493
Related Questions
(b) If 124n= 232 five, find n.
Answers
Answer:[tex]n=\frac{58}{31}[/tex]
Step-by-step explanation:
[tex]124n=232\\\frac{124n}{124}=\frac{232}{124}\\n=\frac{232}{124}=\frac{58}{31}[/tex]
The value of n is 18.75. To find the value of n, we need to solve the equation: 124n = 232 five
Let's first convert "232 five" into a numerical value:
"232 five" means 2325 (since five is in the units place).
Now, the equation becomes:
124n = 2325
To solve for n, divide both sides of the equation by 124:
n = 2325 / 124
Now, perform the division:
n = 18.75
So, the value of n is 18.75.
To know more about equation:
https://brainly.com/question/10724260
#SPJ2
A local rental car agency has 200 cars. The rental rate for the winter months is 60%. Find the probability that in a given winter month fewer than 140 cars will be rented. Use the normal distribution to approximate the binomial distribution.
Answers
Answer:
[tex]P(Z\leq2.89)=0.9981[/tex]
Step-by-step explanation:
Sample size [tex]n=200[/tex]
Rental Rate [tex]R=60\%[/tex]
Probability =(P<140)
Generally the equation for mean of distribution is mathematically given by
[tex]\mu=nR\\\\\mu=200*0.60\\\\\mu=120[/tex]
Generally the equation for Standard deviation of distribution is mathematically given by
[tex]\sigma=\sqrt{npq}[/tex]
[tex]\sigma=\sqrt{200*0.60*0.40}[/tex]
[tex]\sigma=6.9[/tex]
Therefore
Z-score for x=140 is
[tex]Z=\frac{x-\mu}{\sigma}[/tex]
[tex]Z=\frac{140-120}{6.9}[/tex]
[tex]Z=2.89[/tex]
From table
[tex]P(Z\leq2.89)=0.9981[/tex]
4 pounds of oranges costs $ 12 . What is the unit price per pound?
Answers
Answer:
3 dollars per pound
Step-by-step explanation:
Unit Price = Cost / Pounds of oranges
Unit Price = 12 / 4
Unit Price = 3
The unit price per pound is $3
16. Find the equation of the line that has slope m = 1/2 and passes through (4, 10).
Give your answer in slope-intercept form
Answers
Answer:
Step-by-step explanation:
Recall that the equation of a line is y = mx + b.
Excellent. Let's plug in the values we are given into the general equation for a line. We get 10 = 1/2 * 4 + b.
Simplify to 10 = 2 + b, and we get b = 8.
Our final equation, then, is y = 1/2 x + 8.
Hope this helps!
Find the missing length
Answers
Answer:
x=5.9
i think this the answer
Suppose that we ask n randomly selected people whether they share your birthday. (a) Give an expression in terms of n for the probability that no one shares your birthday (ignore leap years). $$ Correct: Your answer is correct. (b) What is the least number of people we need to select so that the probability is at least 0.8 that at least one person shares your birthday
Answers
Using the binomial distribution, it is found that:
a) The expression is [tex]\left(\frac{364}{365}\right)^{n}[/tex]
b) You need to select at least 587 people.
For each person, there are only two possible outcomes, either they share your birthday, or they do not. The probability of a person sharing your birthday is independent of any other person, hence, the binomial distribution is used to solve this question.
Binomial probability distribution
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.There are 365 days in a non-leap year, hence, the probability of each person sharing your birthday is [tex]p = \frac{1}{365}[/tex]
Item a:
This probability is P(X = 0), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{n,0}.\left(\frac{1}{365}\right)^{0}.\left(\frac{364}{365}\right)^{n} = \left(\frac{364}{365}\right)^{n}[/tex]
Hence, the expression is [tex]\left(\frac{364}{365}\right)^{n}[/tex]
Item b:
The probability that at least one person shares your birthday is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
We want that:
[tex]P(X \geq 1) \geq 0.8[/tex]
Hence:
[tex]1 - P(X = 0) \geq 0.8[/tex]
[tex]P(X = 0) \leq 0.2[/tex]
Hence:
[tex]\left(\frac{364}{365}\right)^{n} \leq 0.2[/tex]
[tex]n\log{\left(\frac{364}{365}\right)} \leq \log{0.2}[/tex]
[tex]n \geq \frac{\log{0.2}}{\log{\left(\frac{364}{365}\right)}}[/tex]
[tex]n \geq 586.6[/tex]
Rounding up: You need to select at least 587 people.
To learn more about the binomial distribution, you can take a look at https://brainly.com/question/24863377
When printing an article of 2400 words, an entrepreneur decides to use two sizes of letters, using the largest one a printed page contains 1200 words. Using the smallest, the page contains 1500 words the article must occupy 17 full pages in the magazine how many pages must be printed using small letters?
Answers
Step-by-step explanation:
x= Number of small pages
y= Number of full pages
1 x + 1 y = 21 .............1
Total words
1200 x + 1500 y = 27000 .............2
Eliminate y
multiply (1)by -1500
Multiply (2) by 1
-1500 x -1500 y = -31500
1200 x + 1500 y = 27000
Add the two equations
-300 x = -4500
/ -300
x = 15
plug value of x in (1)
1 x + 1 y = 21
15 + y = 21
y = 21 -15
y = 6
y = 6
x= 15 Number of small pages
y= 6 Number of full pages
represent - 8,5 - 2 on a number line
Answers
Answer:
I hope this helps
you have to.first draw a number line and mark where the given numbers are
Write the following as an expression: How much water do I need to add to l liters of pure alcohol to obtain a solution of 45% alcohol? The answer is an EXPRESSION, not an actual answer!! WILL MARK BRAINLIST!!!
Answers
Answer:
see below
Step-by-step explanation:
amount of water w
l liter of pure alcohol = 100% alcohol
solution is 45 % percent alcohol
total amount of fluid is w+l
(w+l)( .45) = l*.100
Distribute
.45w + .45 l = 1l
.45 w = 1l - .45l
.45 w = .55l
w = .55l / .45
w =11/9 l
Find the area of the sector round your answer to the nearest 10th
Answers
9514 1404 393
Answer:
398.2 cm²
Step-by-step explanation:
The area of the whole circle is ...
A = πr²
A = π(13 cm)² = 169π cm²
The 270° sector is 3/4 of the whole circle, so its area is ...
sector area = (3/4)(169π cm²) ≈ 398.2 cm²
helpppp asap pleaseee
Answers
Answer:
29/3 is your answer
Step-by-step explanation:
pls mark as brainliest
Area of rectangle or triangle
Answers
Answer:
48 cm²
Step-by-step explanation:
shaded area = area of rectangle - area of triangle
area of rectangle = 7 × 8 = 56 cm²
area of triangle = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
Here b = 7 - 3 = 4 cm and h = 8 - 4 = 4 cm
area of triangle = [tex]\frac{1}{2}[/tex] × 4 × 4 = 2 × 4 = 8 cm²
Then
shaded area = 56 - 8 = 48 cm²
PLEASE ANSWER
The distance from the vertex of the curve to the focus is equal to _____.
Here’s the options
the distance from the vertex to the directrix
the distance from the vertex to the y-axis
the distance from the vertex to the origin
a constant
Answers
Answer:
The distance from the vertex to the directrix.
Step-by-step explanation:
According to this question, we are speaking about a parabola, which has the characteristic that the distance from the vertex to the focus is equal to the least distance from the vertex to the directrix.
Hence, the right answer is: The distance from the vertex to the directrix.
There are 1000 students in a college.Out of 20000 in the whole university in a study of 200 were found to be smokers in the college and 1000 in whole university. Is there any significant difference between the proportion of smokers in college and university
Answers
Answer:
1000 students in college
2000 students in University
200 out of 2000 are smokers
200 out 1000 are smokers
200 : 2000
1 :10
200 : 1000
1 : 5
một công ty kinh doanh 1 loại sản phẩm có
- Đơn giá bán là 20.000 đồng
- Định phs là 150.000 đồng khi mức tiêu thụ nhỏ hơn 30.000 sản phẩm
- Biến phí đơn vị là 10.000 đồng
y/ cầu:
a. Hãy xác định tỷ lệ biến phí và tỷ lệ đảm phí?
b. Hãy xác định điểm hòa vốn?
c. Công ty sẽ lời hoặc lỗ tại mức tiêu thụ là 12.000 sản phẩm? 17.000 sản phẩm?
d. Độ lớn đòn bẩy kinh doanh của cty là bao nhiêu tại mwucs tiêu thục là 12.000 snar phẩm? 17.000 sản phẩm ? Nêu ý nghĩa của các con số đó
e. Nếu giá bán tăng lên 25.000 đ/sp và biến phí tăng lên 17.000 đ/sp thid điểm hòa vốn của cty sẽ như thế nào
Answers
Answer:
ask in English then I can help u
Suppose you are starting your own company selling chocolate covered strawberries. You decide to sell the milk chocolate covered strawberries for a profit of $2.25/box and the white chocolate covered strawberries at $2.50/box. Market tests and available resources, however, have given you the following constraints. The combined production level should not exceed 800 boxes per month. The demand for the white chocolate is no more than half the demand for milk chocolate strawberries. The production level for white chocolate should be less than or equal to 200 boxes.
Using the information in the problem, write the constraints. Let x represent number of milk chocolate boxes produced, and y represent number of white chocolate boxes produced.
Total number of chocolate boxes that can be produced: x+y Answer
≤
Answer
800
Restrictions based on demand of each: y Answer
Answer
200
x
Maximum amount of white chocolate production: y Answer
≤
Answer
200
Minimum amount of milk chocolate production: x Answer
Answer
Minimum amount of white chocolate production: y Answer
Answer
Vertices of the feasible region: (0,0)(400, Answer
)( Answer
, Answer
)( Answer
,0)
Optimization equation: Profit = Answer
x+ Answer
y
Your maximum profit is $ Answer
. You should produce Answer
boxes of milk chocolate and Answer
boxes of white chocolate.
Answers
Answer:
Step-by-step explanation:
I answered this question in question #24285520
Answer:
Step-by-step explanation:
Total number of chocolate boxes that can be produced: x+y Answer
≤
Answer
800
Restrictions based on demand of each: y Answer
≤
Answer
1/2
x
Maximum amount of white chocolate production: y Answer
≤
Answer
200
Minimum amount of milk chocolate production: x Answer
≥
Answer
0
Minimum amount of white chocolate production: y Answer
≥
Answer
0
Vertices of the feasible region: (0,0)(400, Answer
200
)( Answer
600
, Answer
200
)( Answer
800
,0)
Optimization equation: Profit = Answer
2.25
x+ Answer
2.5
y
Your maximum profit is $ Answer
1850
. You should produce Answer
600
boxes of milk chocolate and Answer
200
boxes of white chocolate.
Kofi is 3 years older than Ama.If Ama is now x years old, what is kofi age
Answers
Answer:
x+3
Step-by-step explanation:
Kofi is 3 years older than Ama, so the answer is "x+3".
A pond contains 33 fish. Two are caught, tagged, and released back into the pond. After the tagged fish have had a chance to mingle with the others, eight fish are caught and released, one at a time. Assume that every fish in the pond is equally likely to be caught each time, regardless of which fish have been caught (and released) previously (this is not a realistic assumption for real fish in a real pond). The chance that among the fish caught in the second stage (after the tagging), at least four and at most eight were previously tagged is__________.
Answers
Answer:
0.2424
Step-by-step explanation:
Total number of fish = 33
Total number of tagged fish = 2
Each fish has equal probability of being caught (remember that the focus is on the second stage of fish selection) and that probability is 1/33 = 0.0303
- When the question says at least 4 and at most 8 are tagged fish, it means that 4/8 or 1/2 or half of the fish selected were tagged fish. This gives us the figure to use in computation.
- So first of all, the probability that a fish caught is a tagged fish is (1/33) x 2
which is = 0.0303 x 2 = 0.0606
Now if 8 fish were caught and we want to know the probability that at least half of the eight fish (which is 4 fish) were tagged fish, what do we do?
- Multiply the probability of picking a tagged fish by 4; since each fish is replaced before the next selection.
0.0606 x 4 = 0.2424
Find the measure of the incanted angle to the nearest degree
Answers
Answer:
Sinx = 21/40
x = inverse of sin (21/40)
x= 31.6682
hope u got it
Answer:
31.6 degrees
Step-by-step explanation:
sin-¹(p/h) = 31.6
find the missing segment below brainly
Answers
Let missing side be x
Using basic proportionality theorem
[tex]\\ \sf\longmapsto \dfrac{6}{4}=\dfrac{x}{20-x}[/tex]
[tex]\\ \sf\longmapsto 6(20-x)=4x[/tex]
[tex]\\ \sf\longmapsto 120-6x=4x[/tex]
[tex]\\ \sf\longmapsto 120=6x+4x[/tex]
[tex]\\ \sf\longmapsto 120=10x[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{120}{10}[/tex]
[tex]\\ \sf\longmapsto x=20[/tex]
Use the Unit Circle to find the exact value of the trig function. Cos(45)
1/2
√2/2
√3/-2
1
Answers
In a unit circle a line reaching from origin to the circle's circumference specifies the trigonometric functions.
A point where the line which comes from origin to the circumference intersecting it has coordinates [tex](\cos\theta,\sin\theta)[/tex].
In our case [tex]\theta=45^\circ[/tex] which lifts the line up by 45 degrees and makes it intersect circumference at [tex](\cos45^\circ,\sin45^\circ)[/tex].
In the upper right quadrant the angle between x and y axis is 90 degrees so a line coming in at angle of 45 degrees would split the quadrant in half, that means sine and cosine 45 degrees will be equal.
As you may noticed a point has coordinates cos, sin which means the distance between 0 and y coordinate where the point on a circle is, is called [tex]\cos\theta=\cos45^\circ[/tex].
Because cosine 45 degrees is so simple in interpretation it has a known value of [tex]\cos45^\circ=\sin45^\circ=\frac{\sqrt{2}}{2}[/tex].
Hope this helps :)
PLS HELP
Let f(x) = -2x - 7 and g(x) = -4x + 6. Find (g o f) (-5)
–6
3
–59
26
Answers
Answer:
1st option
Step-by-step explanation:
Evaluate f(- 5) then substitute the value obtained into g(x)
f(- 5) = - 2(- 5) - 7 = 10 - 7 = 3 , then
g(3) = - 4(3) + 6 = - 12 + 6 = - 6
Please help do in an hour
Answers
Answer:
-4
Step-by-step explanation:
a1 = -8
an = an-1 +2
a2 = a1+2 = -8+2 = -6
a3 = a2+2 = -6+2 = -4
Relate what you know about simplifying expressions to what you know about
factoring. For example, before you can factor 12x + 20y + y, you need to simplify it.
Explain why.
Answers
Which number shows four hundredths
.004 .04 .400 4.00
Answers
Answer:
hello the answer is .04/0.04
Answer:
.04 is four hundredths
Step-by-step explanation:
I hope this helps
Which of the following is NOT a requirement for testing a claim about two population standard deviations or variances? A. The populations are independent. B. One of the populations is normally distributed. C. The two samples are simple random samples. D. This test requires that both populations have normal distributions.
Answers
Answer:
B. One of the populations is normally distributed.
Step-by-step explanation:
To test a claim about two population standard deviation or variance, it is imperative that the data meets certain requirements which include :
Randomness : Data must not be biased as such it must be drawn as a random sample from a larger group.
The data must be independent. That is not related to one another, the outcome of one should not rely on the outcome or value of another.
Both groups must be drawn From a population which is normally distributed.
One group being normally distributed by stribuyed while the other isn't a requirement for hypothesis testing in this scenario.
A chocolate chip cookie manufacturing company recorded the number of chocolate chips in a sample of 60 cookies. The mean is 22.36 and the standard deviation is2.97 . Construct a 80% confidence interval estimate of the standard deviation of the numbers of chocolate chips in all such cookies.
Answers
Answer:
2.665 < σ < 3.379
Step-by-step explanation:
Given :
s = 2.97
Sample size, n = 60
α = 80%
χ² Critical value (two - tailed), df = (60-1) = 59
χ² = 45.577 ; χ² = 73.279
The 80% confidence interval for the standard deviation :
s * √(n - 1) / χ² critical
2.97 * √(60 - 1) / 73.279 < σ < 2.97 * √(60 - 1) / 45.577
2.665 < σ < 3.379
t "To Do" list has four items: 1) Organize email folders 2) Create a schedule for next month 3) Help a coworker and 4) Answer a customer inquiry. Which item should you probably do first ? a) Answer a customer inquiry b) Organize email folders c) Help a coworker d) Create a schedule for next month
Answers
Answer:
I think A) Answer a customer inquiry
Step-by-step explanation:
Because customers come first
where are parabolas on your hand?
Answers
parabolas are there on my hand palms and it must be there on your hands too but why are you asking this question?
I NEED HELP PLEASE AND THANK YOU!!! ASAP
Answers
Answer:
71
Step-by-step explanation:
Initial angle lies in 4th quadrant
