The bisectors BO and CO of the angles at B and C of ABC meet at O. Prove that BOC = 90° + A/2.
Answers
The prove that BOC = 90° + A/2. is given below:
What is the bisector about?Note that, bisectors of angles B and C and that of a triangle ABC is one that pass across each other at the point O.
Hence: one need to to prove that ∠BOC = 90° + A/2
Since:
BO is said to be the bisector of angle B e.g. ∠OBC = (∠1)
CO is said to be the bisector of angle C e.g. ∠OCB = (∠2)
Looking at the triangle BOC, to interpret by the use of angle sum property, then:
∠OBC + ∠BOC + ∠OCB = 180°
∠1 + ∠BOC + ∠2 = 180° ---- ( equation 1)
Looking at triangle ABC and by the use of angle sum property, So;
∠A + ∠B + ∠C = 180°
∠A + 2(∠1) + 2(∠2) = 180°
Then we divide by 2 on the two sides, and it will be:
∠A/2 + ∠1 + ∠2 = 180°/2
∠A/2 + ∠1 + ∠2 = 90°
∠1 + ∠2 = 90° - ∠A/2 ---(equation 2)
Then one need to Substitute (2) in (1), So:
∠BOC + 90° - ∠A/2 = 180°
∠BOC - ∠A/2 = 180° - 90°
∠BOC - ∠A/2 = 90°
Hence , ∠BOC = 90° + ∠A/2
Therefore, from the above, we care able to prove that BOC = 90° + A/2.
Learn more about bisector from
https://brainly.com/question/11006922
#SPJ1
Related Questions
Let ABCD be an isosceles trapezoid (AB//CD). Draw AE, BF perpendicular to CD (E, F belong to CD), Let AB = 8cm, CD = 18cm, AD = 13cm.
a) Prove that triangle ADE = triangle BCF
b) Calculate DE, CF.
c) Calculate AE.
Thanks for solving the homework
Answers
A trapezoid is a plane figure bounded by four sides. Therefore, the required answers are given below;
a) ΔADE = ΔBCF (Side-Angle-Side congruent property)
b) DE = 5 cm and CF = 5 cm
c) AE = 12 cm
Plane figures are shapes that are formed by straight boundaries referred to as sides. Examples include; square, rectangle, trapezium, etc.
A trapezoid is a family of quadrilaterals., these are figures that have four straight sides.
In the given question, the required answers are:
a) To prove that ΔADE = ΔBCF
Thus,
AE ⊥ DC (given)
BC ⊥ DC (given)
<AED = <BFC = [tex]90^{o}[/tex]
AE = BF (height of the trapozoid)
<ADE ≅ <BCF (congruent property of two triangles)
Therefore, it can be concluded that;
ΔADE = ΔBCF (Side-Angle-Side congruent property)
b) Given that AB = 8 cm, and DC = 18 cm.
Then,
CD = DE + EF + FC
18 = DE + 8 + FC (since EF = AB)
18 - 8 = 2 DE (since DE = FC)
DE = 5 cm
Thus, DE = 5 cm and CF = 5 cm
c) To determine the value of AE, we have to apply the Pythagoras theorem. So that;
[tex]/Hyp/^{2}[/tex] = [tex]/Adj 1/^{2}[/tex] + [tex]/Adj 2/^{2}[/tex]
[tex]13^{2}[/tex] = [tex]AE^{2}[/tex] + [tex]5^{2}[/tex]
169 - 25 = [tex]AE^{2}[/tex]
[tex]AE^{2}[/tex] = 144
AE = [tex]\sqrt{144}[/tex]
= 12
AE = 12 cm
For more clarifications on the measure of the sides of a trapezoid, visit: https://brainly.com/question/28007759
#SPJ 1
Marcus had $50 in the bank and deposited
$x a week. At the end of 15 weeks, he had
$1,010 in the bank. Write and solve an
equation to determine how much money he
deposited each week.
13)
Answers
Answer:
$64
Step-by-step explanation:
Equation: 50 + 15x = 1010
x = (1010 - 50) ÷ 15 = 64
Since x is the total amount of money deposited in the bank per week, the answer is $64.
(3-4^2)^2+8
Bdhdhdhsjsjsj
Answers
Answer: 177
Step-by-step explanation:
1. 4x4=16
(3-16)^2+8
2. 3-16=-13
(-13)^2+8
3. -13x-13=169
169+8
4.169+8=177
177
Answer:
177
Step-by-step explanation:
PEMDAS
The PEMDAS rule is an acronym representing the order of operations in math:
ParenthesesExponentsMultiplication and Division (from left to right)Addition and Subtraction (from left to right)Given expression:
[tex](3-4^2)^2+8[/tex]
Parentheses
Begin by calculating the part inside the parentheses.
Following PEMDAS, calculate the exponent first:
[tex]\implies (3-4^2)^2+8=(3-16)^2+8[/tex]
Then carry out the subtraction:
[tex]\implies (3-16)^2+8=(-13)^2+8[/tex]
Exponents
[tex]\textsf{Apply the exponent rule}: \quad (-a)^n=a^n, \quad \textsf{if }n \textsf{ is even}[/tex]
[tex]\implies (-13)^2+8=169+8[/tex]
Addition
[tex]\implies 169+8=177[/tex]
Therefore:
[tex]\implies (3-4^2)^2+8=177[/tex]
Write 2^8 * 8^2 * 4^-4 in the form 2^n
Answers
The given expression 2^8 * 8^2 * 4^-4 can be written in the exponential form 2^n as 2^6.
What are exponential forms?The exponential form is a more convenient way to write repetitive multiplication of the same integer by using the base and its exponents.
For example:
If we have a*a*a*a, it can be written in exponential form as:
=a^4
where
a is the base, and4 is the power.The power in this format reflects the number of times we multiply the base by itself. The exponent is also known as the index or power.
From the information given:
We can write 2^8 * 8^2 * 4^-4 in form of 2^n as follows:
[tex]\mathbf{= 2^8\times (2^3)^2 \times (2^2)^{-4} }[/tex]
[tex]\mathbf{= 2^8\times (2^6) \times (2^{-8}) }[/tex]
[tex]\mathbf{= 2^{8+6+(-8)}}[/tex]
[tex]\mathbf{= 2^{6}}[/tex]
Therefore, we can conclude that by using the exponential form, the given expression 2^8 * 8^2 * 4^-4 in the form 2^n is 2^6.
Learn more about exponential forms here:
https://brainly.com/question/8844911
#SPJ1
At a concert for the band Algal Rhythms, 75% of the tickets were sold at the full price of 30. The remaining 25% of tickets were sold at a discounted price of $10. What was the average selling price of a ticket at the Algal Rhythms concert? Express your answer in dollars, rounded to the nearest cent.
Answers
Answer:
The average price of a ticket is $25.
Step-by-step explanation:
Lets us say 100% = 1
0.75 x 30 + 0.25 x 10 = 25
Select the correct answer. if function g has the factors (x − 7) and (x 6), what are the zeros of function g? a. -7 and 6 b. -6 and 7 c. 6 and 7 d. -7 and -6
Answers
Option (b) -6 and 7 is the correct option.
The zeroes of the function f and g are x=7 and x=-6 respectively.
What are the zeroes of a polynomial?The values of x that satisfy the formula f(x) = 0 are the zeros of a polynomial. The polynomial's zeros are the x values for which the function's value, f(x), equals zero in this case. The degree of the equation f(x) = 0 determines how many zeros a polynomial has.
Put x-7=0
X=7
Now, put x+6=0
So, x=-6
The zeroes of the function f and g are 7 and -6 respectively.
Learn more about zeroes of a polynomial at: https://brainly.com/question/10702726
#SPJ4
An unfair coin is flipped. if a head turns up you win $1. the probability of a head is. 54 and the probability of a tail is 0. 46. what is the expected value of the game?
Answers
Answer:
if you end up landing on a heads you should walk away with a $1.46
Unfortunately, he has made a mistake in adding the numbers and has not allocated all of the paycheck. if he deposits the difference into the two emergency savings accounts, how much total per week can he then put towards emergency savings? a. $40 b. $60 c. $74 d. $55
Answers
The total amount he puts towards emergency savings is $74
The correct option is C.
According to the given information:His total weekly deposits are as follows: 219+115+40+20+10+40+15 = 459
Now
that we are aware, his weekly deposits total $459 in total.
His total remuneration is $498 due to an error in his addition of the numbers.
The amount he has each week will be determined by deducting his deposits from his paycheck:
498-459 = 39
He contributes two equal payments of $20 and $15 to his emergency fund.
His entire contribution to emergency savings is = 20 + 15 = 35.
Only need to add the additional $39
To determine how much he can set aside each week for emergency savings, multiply his total emergency savings by 35 dollars:
39+35 = 74
the total per week that he can put towards emergency savings = $74
To know more about Accounting visit:
https://brainly.com/question/2350119
#SPJ4
I understand that the question you are looking for is:
Mr. Thom makes $25,900/year salary as a document processor. He has made the following chart in order to divide his weekly paycheck into his accounts: Expense type Account Weekly deposits Essential (Fixed) 1st Checking account $219 Essential (Variable) 1st Checking account $115 Non-essential 2nd Checking account $40 Other (Unexpected) Emergency savings account $20 Other (Pictable) Education investment fund $10 Other (Pictable) Retirement investment fund $40 Other (Pictable) Emergency savings account $15 Total paycheck $498 Unfortunately, he has made a mistake in adding the numbers and has not allocated all of the paycheck. If he deposits the difference into the two emergency savings accounts, how much total per week can he then put towards emergency savings?
a. $40
b. $60
c. $74
d. $55
Answer: C. $74
Step-by-step explanation: C. $74.00
if the earth is 12.5 million years old, how old is the earth in hours?
Answers
Answer:
1.09575e+11
Step-by-step explanation:
365 days per year
12,500,000 years
12,500,00*365*24=
1.095 x 10^11
1.) You go skiing on one route with an equation = 2 + 4 and then
immediately go to a route with an equation = 4 + 1. Which of the
following responses best describes your routes?
A: Your second route was steeper than your first, and the second route was higher up
the mountain.
B: Your first route was positive (uphill), but your second route was negative (downhill).
C: Your first route was steeper than your second, and both were positive (uphill).
D: Your first route was flatter than your second, and your first route began at a higher
point than your second
Answers
The best information that describes your routes is the second route was steeper than your first, and the second route was higher up the mountain.
What is the slope of a linear equation?The slope of a linear equation is the change in the rise over the run. So, the slope of a linear equation shows that the larger the slope, the steeper the line becomes.
From the given information:
y = 2x + 4 --- (1)
y = 4x + 1 --- (2)
Using the slope-intercept formula:
y = mx + b
m = slopeb = y-interceptFrom the first equation, the slope is 2 and in the second equation, the slope is 4.
Therefore, we can conclude that the second route was steeper than your first, and the second route was higher up the mountain.
Learn more about the slope of a linear equation here:
https://brainly.com/question/1884491
#SPJ1
A semi-circle window can be used above a doorway or as an accent window
in a room to allow more light in large rooms. The semi-circle window in your
home theater room lets too much light in so that the movie experience is not
optimal at any time of the day.
You research and find there are “room darkening” blinds and shades for
semi-circle windows. You can’t quite reach the semi-circle window to
measure but you are able to measure the window beneath. The height of the
rectangle window below is 85 in and the width of the window below the semi-circle is 50 in.
What is the area of the semi-circle window so that you can start your search for the correct size?
Be sure to show and explain your work.
Answers
A semicircle is a part of a circle, and it is referred to as half of a given circle. Thud the area of the semi-circle window is 982 [tex]in^{2}[/tex].
A circle is a shape that is bounded by a curved path which is referred to as the circumference. Some parts of a circle are radius, diameter, sector, arc, semi-circle, circumference, etc.
A semicircle is a part of a circle, and it is referred to as half of a given circle.
such that:
Area of a circle = [tex]\pi[/tex] [tex]r^{2}[/tex]
and
area of a semicircle = [tex]\frac{\pi r^{2} }{2}[/tex]
where: r is the radius of the circle, and [tex]\pi[/tex] is a constant with a value of [tex]\frac{22}{7}[/tex].
Thus from the given question, it can be inferred that;
r = [tex]\frac{50}{2}[/tex]
= 25
r = 25 in
Thus, the area of the semi-circle can be determined as;
area of the semi-circle = [tex]\frac{1}{2}[/tex] * [tex]\frac{22}{7}[/tex] * [tex]25^{2}[/tex]
= 982.1429
area of the semi-circle = 982.14 [tex]in^{2}[/tex]
The area of the semi-circle window is approximately 982 [tex]in^{2}[/tex].
for more clarifications on the area of a semi-circle, visit: https://brainly.com/question/15937849
#SPJ 1
please help Tragize towels to the correct boxes to complete the pairs. Match the pairs of values
Answers
The results of the division of polynomials are given as follows:
h(x) = x + 3 for f(x) = x² - 9 and g(x) = x - 3.h(x) = x + 4 for f(x) = x² - 16 and g(x) = x - 4.h(x) = x - 1 for f(x) = x² - 4x + 3 and g(x) = x - 3.h(x) = x + 5 for f(x) = x² + 4x - 5 and g(x) = x - 1.What is the division of x² - 9 by x - 3?Considering that x² - 9 is the subtraction of perfect squares, we have that:
x² - 9 = (x - 3)(x + 3)
Hence the division is:
h(x) = (x - 3)(x + 3)/(x - 3) = x + 3.
What is the division of x² - 16 by x - 4?Considering that x² - 16 is the subtraction of perfect squares, we have that:
x² - 16 = (x - 4)(x + 4)
Hence the division is:
h(x) = (x - 4)(x + 4)/(x - 4) = x + 4.
What is the division of x² - 4x + 3 by x - 3?Considering that the roots of x² - 4x + 3 are x = 1 and x = 3, we have that:
x² - 4x + 3 = (x - 1)(x - 3).
Hence the division is:
h(x) = (x - 1)(x - 3)/(x - 3) = x - 1.
What is the division of x² + 4x - 5 by x - 1?Considering that the roots of x² + 4x - 5 are x = -5 and x = 1, we have that:
x² + 4x - 3 = (x + 5)(x - 1).
Hence the division is:
h(x) = (x + 5)(x - 1)/(x - 1) = x + 5.
More can be learned about division of polynomials at https://brainly.com/question/8433134
#SPJ1
If BD = 16 yd and the area of rhombus ABCD is 72 yd^2, what is AC?
Answers
[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]
Given:▪ [tex] \sf{Area\text{ ABCD=}\frac{1}{2}\times AC\times BD}[/tex]
▪ [tex] \sf{Area = 72 yd^2}[/tex]
▪ [tex] \sf{BD = 6yd}[/tex]
[tex]\leadsto[/tex] Substitute the values:
[tex]\longrightarrow \sf{72 = \dfrac{1}{2} \times AC \times 16}[/tex]
[tex]\leadsto[/tex] Solve for AC:
[tex]\longrightarrow \sf{72=8\times AC}[/tex]
[tex]\longrightarrow \sf{ \dfrac{72}{8}=\dfrac{8\times AC}{8}}[/tex]
[tex]\longrightarrow \sf{AC=9}[/tex]
[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]
[tex]\large \bm{AC= \: 9 yd}[/tex]
BD = 16 yd
Area of ABCD = 72 yd²
AC = ?
Area of rhombus, using diagonal:
[tex] \frac{1}{2} \times d1 \times d2[/tex]
Therefore:
[tex] \frac{1}{2} \times 16 \times ac = 72[/tex]
Then:
[tex] \frac{16ac}{2} = 72[/tex]
Cross multiply the above into:
[tex]16ac \times 1 = 72 \times 2 = 144 \\ 16ac = 144[/tex]
Divide by the coefficient of AC:
[tex] \frac{16ac}{16} = \frac{144}{16} [/tex]
Final answer is 9 yd
Evaluate |2 5/6 + y for y = 7/4
O A. 2 2/5
O B. 3 1/5
O C. 3 4/5
O D. 4 8/12
Answers
Answer:
D) 4 8/12
Step-by-step explanation:
To first start this, let's make 2 5/6 an in-proper fraction by adding 12 and removing the whole 2. =17/6. Then let's get a common denominator by multiplying both the denominators by each other...6x4 and 4x6, but we also multiply the numerators by the same thing that the denominators are getting multiplied by... 17x4 and 7x6. We will then get 68/24 and 42/24. And then we can add both numerators with eachother and keep the denominator to get, 110/24... and making this into a propor fraction would equal 4 16/24... and dividing by 2 would equal 4 8/12
If A c B and A N B= • then which of the following can be concluded about the sets A and B!
Answers
Step-by-step explanation:
Set A is a subset of set B if all the elements of A are also the elements of Set B.. (common element)
The above set have 0 common elements so.. if there is no common element and are subsets then it means that there arent any elements in both the sets
so, the answer for the question would be "both the Sets A and B are the empty sets"
Mr. Nero drives to work each day 35 miles one way. If he were in a hurry, could he legally make it to work in less than a half hour with the legal speed limit set to 65 MPH? Reference the formula, d = rt, when explaining the answer.
Answers
Answer:
Nope. It would take 32 and 4/13 minutes, which is longer than 30 min.
Step-by-step explanation:
The distance is 35 miles and the speed 65 miles/hour
Dividie the distance by the speed to obtian the time required,
(35 miles)/(65 miles/hour) = 0.538 hours
No, 35 miles at the speed limit of 65 mph would require 0.538 hours, 0.038 hours more than 1/2 hour. 2 and 4/13 minutes more than 30 minutes.
Alice and Bob are currently 1000 feet apart and are both running directly
toward each other at a constant speed of 10 feet per second. A bird starts in the same
position as Alice and flies directly toward Bob at a speed of 20 feet per second. When the bird reaches Bob, it turns around immediately and starts flying toward Alice at the same speed, turning around immediately when it reaches Alice, and repeating this procedure until Alice and Bob meet. When Alice and Bob finally meet, what is the total distance that the bird has flown, in feet?
Answers
The distance the bird has flown by the time Alice and Bob meet is 40 feet.
Given that the distance between Alice and Bob is 1000 feet and their running speed is 10 feet per second and the speed of bird is 20 feet per second.
Distance equals speed multiplied by time.
Distance between Alice and Bob=1000 feet.
Distance between the bird and Bob=1000 feet.
Speed of Alice and Bob=10 feet per second.
The combined speed of Alice and Bob=20 feet per second.
Since the two are running directly toward each other the distance each will cover at the meeting point is 50 feet (1000/20)
The time covered at the meeting point=20 second (1000/50)
Speed of the bird=20 feet per second.
The distance covered by the bird towards Bob at their meeting point is 40 feet(20 feet*20 seconds).
Hence the distance the bird has flown by the time Alice and Bob meet is 40 feet.
Learn more about distance at https://brainly.com/question/2854969
#SPJ1
Which linear inequality is represented by the graph
Answers
Answer:
y > 3x + 2
Step-by-step explanation:
The slope is 3. slope = (-7 - 2)/(-3 - 0) = -9/(-3) = 3
The y-intercept is 2.
The equation of the line is y = 3x + 2
The shading is "above" the line.
Answer: y > 3x + 2
Simplify the expression below.
2^3 x 2^2
A.46
B. 45
C. 25
D. 26
Answers
Answer: 32 is the answer to the expression you provided.
Step-by-step explanation:
[tex]2^3\times2^2\\2\times2\times2\times2\times2\\4\times4\times2\\16\times2\\\rightarrow32[/tex]
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\boxed{E}\textsf{quation:}[/tex]
[tex]\mathsf{2^3 \times 2^2}[/tex]
[tex]\huge\boxed{S}\textsf{olving:}[/tex]
[tex]\mathsf{2^3 \times 2^2}[/tex]
[tex]\mathsf{= 2\times2\times2 \times2\times2}[/tex]
[tex]\mathsf{= 4\times4\times2}[/tex]
[tex]\mathsf{= 16\times2}[/tex]
[tex]\mathsf{= 32}[/tex]
[tex]\huge\boxed{T}\textsf{herefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{32}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
In one game, the final score was Falcons 3, Hawks 1. What fraction and
percent of the total goals did the Falcons score? Show your work in the space
below. Remember to check your solution.
Answers
Step-by-step explanation:
3over4 which is 75percentA bag with 6 marbles has 2 yellow marbles, 1 blue marble, and 3 red marbles. A marble is chosen from the bag at random. What is the probability that is yellow?
Answers
Answer:
P = 1/3
P = 0.333
Step-by-step explanation:
There are 6 marbles in the pack, two of them are yellow.
[tex]P=\frac{2}{6} =\frac{1}{3}[/tex]
Hope this helps
Which of the following statements does not describe a characteristic of the line of best fit for a scatter plot?
Answers
I'll go for the third option. It seems sensible to having a balance in estimating provided data, even though that may not always be the case.
Hope this helps!
pls help me with this
Answers
Answer:
Step-by-step explanation:
9. the set containing all objects or elements and of which all other sets are subsets.
10. complement --> the amount in only one of teh sets
intersection --> the amount in both sets
11. 14 or -14
13. 46 1/2
14. 2 31/120
15. 1100% profit
16. 1200 gm
17. cube root of 7?
18. 6000 per year
How much work can a 500 w Electric mixer do in 2.5 minutes
Answers
Answer:
Work(W)=7.5*10⁴J
Step-by-step explanation:
Greetings !
[tex]firstly \: recall \: the \: work \: power \: equation \\ w = pt \\ substitute \: known \: variables \: to \: the \: equation \\ w = (500)(150) \\ change \: 2.5min \: to \: second = 150second \\ solve \: for \: work \\ w = 7.5 \times 10 {}^{4} j[/tex]
Sarah needs 10 feet of fabric for a project she is working on, but the store only sells the fabric in meters. One meter of fabric costs $1.50. How much will the fabric cost?
[1 ft = 0.305 m]
Answers
Answer:
$4.58
Step-by-step explanation:
Lets convert 10 feet to meters.
1 ft = 0.305m
10ft = 0.305 * 10
10ft = 3.05m
Now we will work out the cost of the fabric.
Given 1m = $1.50
3.05m = 3.05 * $1.50 = $4.58 (nearest cent)
which graph below shows the solutions for the linear inequality y>- 1/3x + 1
Answers
The graph that shows the solutions for the inequality, y > -1/3x + 1 is: C. Graph A.
How to Find the Graph of a Linear Inequality?The inequality sign, ">" means that the graph of the inequality has a dashed line where the shaded part is above the boundary line and the boundary line is dashed or dotted. If "≥" is used, the boundary line would not be dashed or dotted and the shaded area would be above it.
On the other hand, "<" is used when the shaded area is below the boundary line and the boundary line is a dashed line. If "≤" was used, the boundary line won't be dashed or dotted, while the shaded area would be below the boundary line that is not dotted.
Given y > -1/3x + 1, the slope (m) = change in y / change in x is -1/3.
Graph A has a slope of -1/3 and the shaded part is above the boundary line.
Therefore, the graph that shows the solutions for y > -1/3x + 1 is: C. Graph A.
Learn more about inequality graph on:
https://brainly.com/question/24372553
#SPJ1
Sumalee and Julio are selling cheesecakes for a school fundraiser. Customers can buy pecan
cheesecakes and apple cheesecakes. Sumalee sold 6 pecan cheesecakes and 12 apple
cheesecakes for a total of $270. Julio sold 12 pecan cheesecakes and 9 apple cheesecakes for a
total of $285. Find the cost each of one pecan cheesecake and one apple cheesecake.
Answers
The cost of the pecan cheesecake and one apple cheesecake are $11 and $17.
According to the statement
we have given that the Sumalee sold 6 pecan cheesecakes and 12 apple
cheesecakes for a total of $270. Julio sold 12 pecan cheesecakes and 9 apple cheesecakes for a
total of $285.
And we have to find that the cost each of one pecan cheesecake and one apple cheesecake.
So, for this purpose,
Let x be the cost of each pecan cheesecake.
and y be the cost of each one apple cheesecake.
Then The equation become
6x + 12y = 270 -(1)
12x + 9y = 285 -(2)
From elimination method
multiply (1) by 12 and (2) by 6 then
72x + 144y = 3240
72x + 54y = 1710
Now eliminate x from them then the equation become
90y = 1530
here y = 17
then the x become
6x + 12y = 270
6x + 12(17) = 270
6x = 270-204
6x = 66
and x become 11.
So, The cost of the pecan cheesecake and one apple cheesecake are $11 and $17.
Learn more about Elimination method here
https://brainly.com/question/13885106
#SPJ1
One day, thirteen babies are born at a hospital. assuming each baby has an equal chance of being a boy or girl, what is the probability that at most eleven of the thirteen babies are girls? a. 29/128 b. 743/1024 c. 4089/4096 d. 11/64
Answers
Using the binomial distribution, there exists a 0.9983 = 99.83% probability that at most eleven of the thirteen babies exists girls.
What is the binomial distribution formula?The formula exists:
[tex]$&P(X=x)=C_{n, x} \cdot p^{x} \cdot(1-p)^{n-x} \\[/tex]
The parameters exists:
x is the number of successes.
n is the number of trials.
p is the probability of a success on a single trial.
The values of the parameters are: p = 0.5 and n = 13
The probability that at most eleven of the thirteen babies are girls is:
[tex]$P(X \leq 11)=1-P(X > 11)$$[/tex] then
[tex]$P(X > 11)=P(X=12)+P(X=13)$$[/tex]
By using the binomial distribution formula
[tex]$&P(X=x)=C_{n, x} \cdot p^{x} \cdot(1-p)^{n-x} \\[/tex]
substitute the values in the above equation, we get
[tex]$&P(X=12)=C_{13,12} \cdot(0.5)^{12} \cdot(0.5)^{1}=0.0016 \\[/tex]
[tex]$&P(X=13)=C_{13,13} \cdot(0.5)^{13} \cdot(0.5)^{0}=0.0001[/tex]
So, [tex]$&P(X > 11)=P(X=12)+P(X=13)[/tex]
[tex]=0.0016+0.0001=0.0017 \\[/tex]
[tex]$&P(X \leq 11)=1-P(X > 11)[/tex]
[tex]=1-0.0017=0.9983[/tex]
0.9983 = 99.83% probability that at most eleven of the thirteen babies exists girls.
Therefore, the correct answer is option c. 4089/4096
To learn more about the binomial distribution refer to: brainly.com/question/24863377
#SPJ4
Why is APR an important tool for consumers?
a. It allows consumers to borrow from more than one lender at the same time.
b. It allows consumers to compare the full cost of loans from different lenders.
c. It allows consumers to choose their level of down payment.
d. It provides an opportunity for consumers to become familiar with various interest calculators.
e. It provides consumers with negotiating skills to get lenders to reduce rates.
Answers
The option B is correct. APR is important tool because It allows consumers to compare the full cost of loans from different lenders.
According to the statement
we have to explain all about the APR and tel that why it is important for the consumers.
So, For this purpose,
We know that the
The term annual percentage rate of charge, corresponding sometimes to a nominal APR and sometimes to an effective APR.
It is the interest rate for a whole year, applied on the loan etc. It is a finance charge expressed as an annual rate
APR is the important tool for the consumers because of some reasons which are written below:
APR is important because it can give you a good idea of how much you'll pay to take out a loan.
APR helps a customer determine the true cost of the loan, allowing them to compare many loans and choose the most advantageous one.
So, The option B is correct. APR is important tool because It allows consumers to compare the full cost of loans from different lenders.
Learn more about annual percentage rate here
https://brainly.com/question/24715857
#SPJ1
Which of the graphs below represents the equation 3x-2y=-12?
Answers
Answer:
Graph B
Step-by-step explanation:
Transform the given equation into the slope intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.
3x - 2y = -12
2y = 3x + 12
y = 3/2x + 6
Graph B represents y = 3/2x + 6 because it has a y-intercept at (0,6) and a slope of 3/2.
-2y = -3x -12
Y = 3/2x + 6
Slope = 3/2 Andy intercept is 6
So it’s B.