a 12-ft-long ladder is leaning against a wall and makes an 80 degree angle with the ground.how high up the wall does the ladder reach, and how far is the base of the ladder from the base of the wall? round to the nearest inch.,
Answers
Answer:
The ladder reaches 142 inches and the base of ladder is 25 inches far from the base of the wall.
Step-by-step explanation:
Let us draw a diagram for the given situation.
In the attached figure,
AB = the height of wall where the ladder reaches
AC = ladder
BC = distance of base of ladder from the base of the wall
In triangle ABC,
[tex]\sin C=\frac{AB}{AC}\\\\\sin80=\frac{AB}{12}\\\\AB=12\sin80\\\\AB=11.82[/tex]
And
[tex]\cos C=\frac{BC}{AC}\\\\\cos80=\frac{BC}{12}\\\\BC=12\cos80\\\\BC=2.08[/tex]
Now, 1 feet = 12 inches
Hence, 11.82 ft = 141.84 inches
and 2.08 feet = 24.96 inches
Therefore, in the nearest inches, we have
The ladder reaches 142 inches and the base of ladder is 25 inches far from the base of the wall.
Related Questions
What is the sum of the first eight terms of the series?
(−600)+(−300)+(−150)+(−75)+(−37.5)+...
Round the answer to two decimal places.
−1200.50
−1195.31
−1190.63
−1181.25
Answers
A rectangular note card has a perimeter of 18 inches and an area of 20 square inches. What are the dimensions of the note card?
Answers
4 x 5 = 20
5 + 5 + 4 + 4 = 18
hope I helped (:
Can someone check my answers?
1. Simplify the sum or difference.
sqrt 5 + 6 sqrt 5
A) 6 sqrt 5
B) 30
C) 6 sqrt 10
D) 7 sqrt 5
2. Simplify the sum or difference.
4 sqrt 2 - 7 sqrt 2
A) negative sqrt 6
B) -3 sqrt 2
C) -11 sqrt 2
D) 11 sqrt 2
3. Simplify the sum or difference.
3 sqrt 7 - sqrt 63
A) -2 sqrt 7
B) -6 sqrt 7
C) -4 sqrt 3
D) 0
4. Simplify the sum or difference.
-6 sqrt 10 + 5 sqrt 90
A) 9 sqrt 10
B) -9 sqrt 10
C) -39 sqrt 10
D) -10
5. Simplify the product.
sqrt 6 (sqrt 2 + sqrt 3)
A) sqrt 8 + 3
B) sqrt 30
C) 2 sqrt 3 + 3 sqrt 2
D) 4 sqrt 2 + 3
Answers
2. 4sqrt2 - 7sqrt2 = (4-7)sqrt5 = -3sqrt2 (answer is B)
3. 3sqrt7 - sqrt63 = 3sqrt7 - sqrt7 * sqrt9 = 3sqrt7 - 3sqrt7 = 0 (answer is D)
4. -6sqrt10 + 5sqrt90 = -6sqrt10 + 5*(sqrt10 * sqrt9) = -6sqrt10 + 5*(3sqrt10)
= -6sqrt10 + 15sqrt10 = 9sqrt10 (answer is A)
5. sqrt6*(sqrt 2 + sqrt 3) = sqrt12 + sqrt18 = 2sqrt3 + 3sqrt2 (answer is D)
1 - D
2 - B
3 - D
4 - A
5 - C
6 - A
7 - D
8 - B
9 - B
10 - C
i just took the "Operations with Radical Expressions practice" for WA connexus, these answers are 100 percent correct
Use the quadratic formula to solve 9x2 + 6x – 17 = 0.
Answers
Answer:
The person that answered “C” is completely wrong. The answer is D. Mark me brainliest after you get the answer right :)
Step-by-step explanation:
There are many penguins on a hill. 53 penguins waddled off the hill. Now 21 penguins remain on the hill. How many penguins were on the hill to start?
74 penguins
72 penguins
32 penguins
34 penguins
Answers
Answer:
74 Penguins
Step-by-step explanation:
1. 53+21
2. =74
Penguins are my favorite animal. What's yours?
Answer:
There were originally 74 penguins on the hill.
Step 1: Determine the Values we NeedFor starters, we need to define the variable that we will use to solve this equation. I will use x.
We know that our original amount is x, and we need to find it to solve the problem.
The Factsx stands for the original amount of penguins on the hill.53 penguins waddle off of the hill.21 penguins remain after the 53 penguins waddle off of the hill.To find x, we will set up an algebraic equation that allows us to find the value easily.
Step 2: Set up the Algebraic EquationNow, we will need to set up the equation with the facts we have determined.
We know that we need to set our equation equal to x to find our total. To do this, we know that our initial amount is x, and we remove 53 penguins from this total since they waddle off of the hill.
Since we "remove" from the total, this means that we will subtract 53 penguins from x, our initial amount. We are left with the 21 penguins that do not leave the hill, or otherwise, remain on the hill.
[tex]x - 53 = 21[/tex]
Step 3: Rearrange and Solve the EquationFinally, we are ready to solve the equation to find our initial amount of penguins.
To solve this equation, we must combine our like terms.
Because our numbers (constants) do not have any letters (variables) attached to them, we will combine them.
The main goal of an algebraic equation is to get the variable (in this case, x) by itself. To do this, we can perform reverse operations to get the constants together.
You'll notice that 21 does not have a sign associated with it, but 53 does, and it is a subtraction symbol.
The reverse operation of subtraction is addition. Therefore, to combine the two values, we can add both 53 and 21 to each other to find x.
[tex]x = 53 + 21[/tex]
Using any method of choice, add the two values together.
[tex]x = 53 + 21 = 74[/tex]
Then, to simplify, remove the operation and only leave the sum of the operation.
[tex]\boxed{x = 74}[/tex]
Therefore, the initial number of penguins—the number of penguins on the hill to start—is equivalent to 74 penguins.
To learn more about algebraic equations, please visit the following link: https://brainly.com/question/14791317
A recipe calls for 1/4 cup of flour.Carter only a measurement cup that holds 1/8 cup. How can carter measure the flour he needs for his recipe
Answers
⅛ + ⅛ = ¼
Answer:
Carter can measure the flour he needs for his recipe by filling his measurement cup twice.
Step-by-step explanation:
Since Carter has a smaller cup, he would have to fill his cup a number of times until the sum of the number of cups he has fill repeatedly adds up to the recipe requirement.
The number of times Carter would have to measure his cup with flour to get the recipe call may be computed by dividing the recipe call amount with the size of Carter's measurement cup
= 1/4 ÷ 1/8
= 1/4 × 8/1
= 2
Tamara says that raising the number i to any integer power results in either -1 or 1 as the result, since i^2 = -1. Do you agreed or disagree with Tamera? Explain
Answers
Tamara's claim that raising the complex number i to any integer power results in either -1 or 1 is incorrect. The powers of i follow a cyclic pattern which includes i, -1, -i, and 1.
Explanation:I must disagree with Tamara's statement that raising the complex number i to any integer power results in either -1 or 1. The powers of i actually follow a recurring pattern: i^1 = i, i^2 = -1, i^3 = -i, i^4 = 1, and then the pattern repeats.
For i to the power of 1, the result is just i itself.For i to the power of 2 (i^2), the result is indeed -1.For i to the power of 3 (i^3), the result is -i.For i to the power of 4 (i^4), the result is back to positive 1.So, while -1 and 1 are indeed in the sequence of results, they're not the only possibilities. Specifically, -i and i are also possible results of raising i to an integer power.
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A principal of $400 is invested in an account at 6% per year compounded annually. What is the total amount of money in the account after 5 years? A. $526.00 B. $531.37 C. $535.29 D. $520.00
Answers
[tex]e = b \times (1 + \frac{i}{100} ) {}^{n} [/tex]
In this formula:
e represents the outcome
b represents the money at the beginning
i represents the interest rate
n represents the number of years.
Filling in this formula, we get:
[tex]e = 400 \times (1 + \frac{6}{100}) {}^{5} [/tex]
[tex]e = 400 \times 1.06 {}^{5} [/tex]
[tex]e = 535.29[/tex]
Therefore the answer is C. $535.29
The total amount of money in the account after 5 years is $535.29.
To calculate the total amount of money in the account after 5 years, we can use the compound interest formula: [tex]A = P{(1 + r/n)}^{(nt)[/tex], where A is the total amount, P is the principal, r is the annual interest rate, n is the number of times compounded per year, and t is the number of years.
Given that the principal is $400, the annual interest rate is 6%, and the compounding is done annually, we have:
A = 400(1 + 0.06/1)^(1*5) = 400(1.06)^5 = 400 * 1.338225 = $535.29
Therefore, the total amount of money in the account after 5 years is $535.29.
Learn more about Compound interest here:
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helpppppppppppppppppppppppppp
Answers
perimeter = 6 + 3√2 ft
Explanation:
The triangle given is an isosceles right-angled triangle.
This means that two of its legs are equal = 3 ft
Now, we will get the length of the third leg which is the hypotenuse using the Pythagorean theorem as follows:
(third leg)^2 = (3)^2 + (3)^2
(third leg)^2 = 18
third leg = sqrt(18) = 3√2 ft
Finally, we will get the perimeter as follows:
perimeter = 3 + 3 + 3√2
perimeter = 6 + 3√2 ft
Hope this helps :)
7. Given the vertices of ∆ABC are A (2,-5), B (-4,6) and C (3,1), find the vertices following each of the transformations FROM THE ORIGINAL vertices: a. Rx = 3 b. T<3,-6> c. r(90◦, o)
Answers
Rx = 3
in this reflection, the image has been reflected along the x = 3 line. then all the points on the image are reflected along this vertical line. the distance between each point and the vertical line is noted and by that same distance its moved to the opposite side of the vertical line, while the y coordinates stay the same.
A(2,-5)- x coordinate is 2, its 1 unit away from x=3, it should move by 1 unit to the other side of x = 3, then x = 4. y stays as it is.
A' - (4,-5)
B(-4,6) - distance from x = 3, is (-4-+3) is seven units, moves by 7 units to the other side
B' (10,6)
C(3,1) = distance from 3 = 0, therefore the point stays at is,
C' (3,1)
Q2)
next is a translation, in translation the size nor shape changes, each point in the original image moves the same distance in the same direction.
T (3,-6) (x,y) = this means that the x coordinates move by +3 points to the right and y coordinates move downwards by 6 units
A (2,-5) ---> (2+3,-5-6)
A' (5,-11)
B (-4,6) ---> (-4+3,6-6)
B' (-1,0)
C (3,1) ---> (3 + 3, 1-6)
C' (6,-5)
Q3)
r(90°,0)
this is a rotation done in the clockwise direction. then the image takes a rotation to the right direction around the origin.
then the x, y coordinates of the preimage become ;
(x,y) = (y,-x)
A(2,-5) --> A' = (-5,-2)
B(-4,6) ---> B' = (6,4)
C(3,1) ---> C' = (1,-3)
What is the sum of 2 numbers is 100 and their difference is 6?
Answers
x -y = 6
Adding these equations gives
2x = 106
x = 53
y = 53 -6 = 47
The numbers are 47 and 53.
Bc¯¯¯¯¯ is parallel to de¯¯¯¯¯. what is ab? enter your answer in the box.
Answers
The firing of a Revolutionary War cannon is used to open the local Fourth of July festivities. The muzzle of the cannon barrel is 6 feet above ground level. The height of the cannon ball being fired from the Revolutionary War cannon as a function of elapsed time is modeled by the function h(t) = –16t2 + 75t + 6, where h(t) is the height of the cannon ball in feet, and t is the elapsed time since firing in seconds. Determine at approximately what elapsed time(s) the cannon ball will be at a height of 55 feet.
Answers
[tex]-16t^2 + 75t + 6=55\\-16t^2+75t-49=0. \text{ Computing the discriminant:}\\75^2-4(-16)(-49)=2489.\text{ So by quadratic formula we get the sol:}\\\dfrac{-75-\sqrt{2489}}{-32}=3.9\text{ seconds.}[/tex]
The price of a 250 dollar coat increased 7% last year. The coat is now on sale for one half off. What is the sale price?
Answers
7 cakes cost £5.60 , what would be the cost of:
10 cakes
5 cakes
12 cakes
Answers
so 10 cake costs 10×0.8=£8
5cake costs 5×0.8=£4
12 cake costs 12×0.8=£9.6
10 cakes: £0.8×10=£8
5 cakes: £0.8×5=£4
12 cakes: £0.8 ×12=£9.6
Jennifer recorded the temperature of water samples and the time it took 50g of salt to dissolve in the samples. Jennifer's data models a direct variation. Which table contains Jennifer's data?
Answers
80°32
83°33.2
84°33.6
90°36
Answer:
The answer is C.
Step-by-step explanation:
I know that its c because i literatly just tried it and it said corect it was on USA. test prep
what should you do first to simplify the expression (43 + 9) ÷ 76 + 5
Answers
You should always find the value inside the parenthesis first when simplifying an equation.
Tell me if you need help solving the equation!
Hope this helps!
expression (43 + 9) ÷ 76 + 5
43+9 =52 52 ÷ 76 + 5
Find the area of the triangle that has a base of 4.2 mm and a height of 1.5 mm.
Answers
I hope this helps
Brian deposited $4000 into an account with 5.4% interest, compounded monthly. Assuming that no withdrawals are made, how much will he have in the account after 6 years?
Answers
FV=p(1+r/100n)^nt
where:
FV=future value
p=principle
r=rate
n=terms
t=time
thus substituting our values in the formula we get:
FV=4000(1+5.4/1200)^(6×12)
FV=$5,526.57
Answer: $5,526.57
Two cities are 124 miles apart from each other. The cities are 4cm on a map, what is the Scale factor?
Answers
Distance on map = 4 cm
Scale factor = 4 cm : 124 miles
Divide through by 4
Scale factor = 4 cm/4 : 124 miles /4
= 1 cm : 31 miles
The scale factor is 1 cm : 31 miles
Is 11p-7q polynomial
Answers
Specifically, it is a "polynomial EXPRESSION" ; but not a "polynomial equation" ; because it is not an "equation.
There are more than one variables/variable expressions, so it is a polynomial.
a(1)= -2
a(n)=a(n-1)-5
whats the 4th term in the sequence?
Answers
[tex]A_1=-2\\ A_2=A_1-5=-2-5=-7\\ A_3=A_1-2*5=-2-2*5=-12\\ A_4=A_1-3*5=-2-3*5=-17\\ [/tex]
Answer:
The fourth term in the sequence is -17
Step-by-step explanation:
To find the 4th term of the sequence, we will simply follow the steps below;
a(1) = -2
a(n) = a(n-1)-5
We will find the value of the sequence when n = 1, n= 2 n =3 n=4
The first one has been done for us, so we have the first term to be a(1) = -2
The next thing to do, is to find the second term, ie. when n=2
a(n) =a(n-1)-5
a(2) =a(2-1)-5
=a(1) - 5
but a(1) = -2
a(2) =a(1) - 5
=-2-5
=-7
a(2) = -7
next is to find the third term, ie. when n=3
a(n) =a(n-1)-5
a(3) =a(3-1)-5
=a(2) - 5
but a(2) = -7
a(3) =a(2) - 5
=-7-5
=-12
a(3) = -12
next is to find the fourth term, ie. when n=4
a(n) =a(n-1)-5
a(4) =a(4-1)-5
=a(3) - 5
but a(3) = -12
a(4) =a(3) - 5
=-12-5
=-17
a(4) = -17
Therefore, the fourth term in the sequence is -17
What is the measure of AC ? (First Picture)
Enter your answer in the box.
What is the measure of BC ? (Second Picture)
Enter your answer in the box.
Answers
Answer:
Part 1) [tex]arc\ AC=33\°[/tex]
Part 2) [tex]arc\ BC=130\°[/tex]
Step-by-step explanation:
Part 1) What is the measure of AC ?
we know that
The inscribed angle is half that of the arc it comprises.
so
[tex]m<ABC=\frac{1}{2}(arc\ AC)[/tex]
substitute the values and solve for x
[tex]2.5x+4=\frac{1}{2}(7x-2)[/tex]
[tex]5x+8=(7x-2)[/tex]
[tex]7x-5x=8+2[/tex]
[tex]2x=10[/tex]
[tex]x=5\°[/tex]
Find the measure of arc AC
[tex]arc\ AC=7x-2=7(5)-2=33\°[/tex]
Part 2) What is the measure of BC ?
we know that
The inscribed angle is half that of the arc it comprises.
so
[tex]m<BDC=\frac{1}{2}(arc\ BC)[/tex]
substitute the values
[tex]65\°=\frac{1}{2}(arc\ BC)[/tex]
[tex]2*65\°=(arc\ BC)[/tex]
[tex]arc\ BC=130\°[/tex]
Find the missing measure for a right circular cone given the following information. Find L.A. if r = 6 and h = 8 48 60 96
Answers
Final answer:
The Lateral Area (L.A.) of a right circular cone with a base radius of 6 and a height of 8 is 60π square units, calculated by finding the slant height using the Pythagorean theorem and then applying the formula for L.A.
Explanation:
The student is asked to find the Lateral Area (L.A.) of a right circular cone given the base radius (r) is 6 and the height (h) is 8. First, we need to find the slant height of the cone, which can be done using the Pythagorean theorem in a right triangle where one leg is the height of the cone, the other leg is the radius of the base, and the hypotenuse is the slant height (l). The formula is l = [tex]\sqrt{(r^2 + h^2)[/tex]. After calculating l, we use the formula for the Lateral Area: L.A. = π r l.
Calculating the slant height: l = [tex]\sqrt{(6^2 + 8^2)}[/tex] = [tex]\sqrt{(36 + 64)[/tex]= [tex]\sqrt{100[/tex]= 10.
Now, we calculate the Lateral Area: L.A. = π * 6 * 10 = 60π. Hence, the Lateral Area of the cone is 60π square units.
What is the solution of the equation (x – 5)2 + 3(x – 5) + 9 = 0? Use u substitution and the quadratic formula to solve.
Answers
x² - 10x + 25 + 3x - 15 + 9 = 0
x² - 7x - 16 = 0
[tex]x = \frac{7 + \sqrt{(-7)^2-4(1)(-16)} }{2} [/tex] or [tex]x = \frac{7 - \sqrt{(-7)^2-4(1)(-16)} }{2} [/tex]
[tex] x = \frac{7 + 3i \sqrt{3} }{2} [/tex] or [tex] x = \frac{7 - 3i \sqrt{3} }{2} [/tex]
(Answer B)
Answer: [tex]x=\frac{7\pm 3i\sqrt{3}}{2}[/tex]
Explanation:
Since, given quadratic function, [tex](x-5)^2 + 3(x-5) + 9 = 0[/tex] -----(1)
let us consider,[tex]x-5=p[/tex] -----(2)
Put this value in equation (1),
We get, [tex]p^2+3 p+9=0[/tex], which is also a quadratic equation.
Since, quadratic formula for finding the root of quadratic equation of type [tex]ax^2+bx+c=0[/tex] is, [tex]x=\frac{-b\pm\sqrt{b^2-4ac}} {2a}[/tex]
Here, a=1, b=3 and c=9, so, [tex]p=\frac{-3\pm\sqrt{3^2-4\times1 \times9}} {2\times1}[/tex]
Thus, [tex]p=\frac{-3\pm3\sqrt{-3}} {2}[/tex] ⇒ [tex]p=\frac{-3\pm3i\sqrt{3}} {2}[/tex] (because √-1=i)
Now, from equation(2) [tex]x-5=\frac{-3\pm3i\sqrt{3}} {2}[/tex]
⇒[tex]x=\frac{-3\pm3i\sqrt{3}} {2}+5=\frac{7\pm 3i\sqrt{3}}{2}[/tex]
⇒[tex]x=\frac{7\pm 3i\sqrt{3}}{2}[/tex]
find all the zeros for each function.
p(x)=2x^3-3x^2+3x-2
*show work*
Answers
A graph of p(x) shows it has one real zero, at x=1. Dividing that out (and dividing out the scale factor of 2) reveals the remaining factor to be
.. (x -1/4)^2 +15/16
When we set this to zero, we have
.. (x -1/4)^2 +15/16 = 0
.. (x -1/4)^2 = -15/16
.. x -1/4 = i√(15/16)
and the remaining roots are
.. x = 1/4 ±i√(15/16)
.. x = (1 ±i√15)/4
The zeros are x = 1, x = (1 ±i√15)/4.
_____
You could use synthetic or long division to find
.. p(x)/(x -1) = 2x^2 -x +2
and then use any of several methods to determine the zeros of this are
.. x = (1 ±i√15)/4
Miguel is playing a game in which a box contains four chips with numbers written on them. Two of the chips have the number 1, one chip has the number 3, and the other chip has the number 5. Miguel must choose two chips, and if both chips have the same number, he wins $2. If the two chips he chooses have different numbers, he loses $1 (–$1). Let X = the amount of money Miguel will receive or owe. Fill out the missing values in the table. (Hint: The total possible outcomes are six because there are four chips and you are choosing two of them.) Xi 2 –1 P(xi) What is Miguel’s expected value from playing the game? answer= $2 Based on the expected value in the previous step, how much money should Miguel expect to win or lose each time he plays? answer= $2 What value should be assigned to choosing two chips with the number 1 to make the game fair? Explain your answer using a complete sentence and/or an equation. A game at the fair involves a wheel with seven sectors. Two of the sectors are red, two of the sectors are purple, two of the sectors are yellow, and one sector is blue. Landing on the blue sector will give 3 points, landing on a yellow sector will give 1 point, landing on a purple sector will give 0 points, and landing on a red sector will give –1 point. Let X = the points you have after one spin. Fill out the missing values in the table. Xi P(xi) If you take one spin, what is your expected value? What changes could you make to values assigned to outcomes to make the game fair? Prove that the game would be fair using expected values. The point guard of a basketball team has to make a decision about whether or not to shoot a three-point attempt or pass the ball to another player who will shoot a two-point shot. The point guard makes three-point shots 30 percent of the time, while his teammate makes the two-point shot 48 percent of the time. Xi 3 0 P(xi) 0.30 0.70 Xi 2 0 P(xi) 0.48 0.52 What is the expected value for each choice? Should he pass the ball or take the shot himself? Explain. Claire is considering investing in a new business. In the first year, there is a probability of 0.2 that the new business will lose $10,000, a probability of 0.4 that the new business will break even ($0 loss or gain), a probability of 0.3 that the new business will make $5,000 in profits, and a probability of 0.1 that the new business will make $8,000 in profits. Claire should invest in the company if she makes a profit. Should she invest? Explain using expected values. If Claire’s initial investment is $1,200 and the expected value for the new business stays constant, how many years will it take for her to earn back her initial investment?
Answers
2) We can calculate the expected value of the game with the following: E=[tex] \frac{1}{6}*2- \frac{5}{6} *1[/tex]. In general, the formula is [tex]E= \sum{p*V}[/tex] where E is the expected value, p the probability of each event and V the value of each event. This gives a result of E=2/6-5/6=3/6=0.5$ Hence, Miguel loses half a dollar ever y time he plays.
3) We can adjust the value v of the winning event and since we want to have a fair game, the expecation at the end must be 0 (he must neither win or lose on average). Thus, we need to solve the equation for v:
0=[tex] \frac{1}{6}v -\frac{5}{6} =0 [/tex]. Multiplying by 6 both parts, we get v-5=0 or that v=5$. Hence, we must give 5$ if 1-1 happens, not 2.
4) So, we have that the probability that you get a red or purple or yellow sector is 2/7. We have that the probability for the blue sector is only 1/7 since there are 7 vectors and only one is blue. Similarly, the 2nd row of the table needs to be filled with the product of probability and expectations. Hence, for the red sector we have 2/7*(-1)=-2/7, for the yellow sector we have 2/7*1=2/7, for the purple sector it is 2/7*0=0, for the blue sector 1/7*3=3/7. The average payoff is given by adding all these, hence it is 3/7.
5) We can approach the problem just like above and set up an equation the value of one sector as an unknown. But here, we can be smarter and notice that the average outcome is equal to the average outcome of the blue sector. Hence, we can get a fair game if we make the value of the blue sector 0. If this is the case, the sum of the other sectors is 0 too (-2/7+0+2/7) and the expected value is also zero.
6) We want to maximize the points that he is getting. If he shoots three points, he will get 3 points with a probability of 0.30. Hence the average payoff is 0.30*3=0.90. If he passes to his teammate, he will shoot for 2 points, with a success rate of 0.48. Hence, the average payoff is 0.48*2=0.96. We see that he should pass to his player since 0.06 more points are scored on average.
7) Let us use the expections formula we mentioned in 1. Substituting the possibilities and the values for all 4 events (each event is the different profit of the business at the end of the year).
E=0.2*(-10000)+0.4*0+0.3*5000+0.1*8000=-2000+0+1500+800=300$
This is the average payoff of the firm per year.
8) The firm goes even when the total profits equal the investment. Suppose we have that the firm has x years in business. Then x*300=1200 must be satisfied, since the investment is 1200$ and the payoff per year is 300$. We get that x=4. Hence, Claire will get her investment back in 4 years.
Answer:
To check all the events (6), we label the chips. Suppose one chip with 1 is labeled R1 and the other B1 (as if they were red and blue). Now, lets take all combinations; for the first chip, we have 4 choices and for the 2nd chip we have 3 remaining choices. Thus there are 12 combinations. Since we dont care about the order, there are only 6 combinations since for example R1, 3 is the same as 3, R1 for us.
The combinations are: (R1, B1), (R1, 3), (R1, 5), (B1, 3), (B1, 5), (3,5)
We have that in 1 out of the 6 events, Miguel wins 2$ and in five out of the 6 events, he loses one. The expected value of this bet is: 1/6*2+5/6*(-1)=-3/6=-0.5$. In general, the expected value of the bet is the sum of taking the probabilities of the outcome multiplied by the outcome; here, there is a 1/6 probability of getting the same 2 chips and so on. On average, Miguel loses half a dollar every time he plays.
The probability that a bakery has demand for 2 3 4 or 5 birthday cakes on any given day are 0.32, 0.24, 0.25 and 0.19 respectively. construct a probability distribution for this data
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On the horizontal axis, put your 4 different categories of 2, 3, 4, or 5.
On the vertical axis, label it by the percents: 0.10, 0.20, 0.30, 0.40
Then, make a bar at the correct height for each category.
Which ordered pair (a, b) is a solution to the given system?
Answers
(3,1) means that a = 3 and b = 1
Plug in a = 3 and b = 1 into the first equation
2a - 5b = 1
2*3 - 5*1 = 1.... replace 'a' with 3, replace b with 1
6 - 5 = 1
1 = 1
we get a true equation, so we have confirmed the first equation
Do the same for the second equation
3a+5b = 14
3*3+5*1 = 14 .... replace 'a' with 3, replace b with 1
9+5 = 14
14 = 14
we get a true equation, so the second equation has been confirmed
Both equations are true when (a,b) = (3,1). So the answer (3,1) has been confirmed fully
If p is a true statement and q is false then p V q is true
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Answer:
Step-by-step explanation:
True