Answer:
35 cm
Step-by-step explanation:
You can use the Cosine Rule to find the length of a side when two sides and the included angle are given.
a² = b² + c² - 2bc cos A
a² = (36²) + (52²) - 2(36)(52) cos 42°
a² = (1296) + (2704) - (3744)(0.7431448255)
a² = (4000) - (2782)
a² = 1218
a = ✓1218
a = 34.9 cm
5) If the local professional basketball team, the Sneakers, wins today's game, they have a 2/3 chance of winning their next game. If they lose this game, they have a 1/2 chance of winning their next game.
A) Make a Markov Chain for this problem; give the matrix of transition probabilities and draw the transition diagram.
B) If there is a 50-50 chance of the Sneakers winning today's game, what are the chances that they win their next game?
C) If they won today, what are the chances of winning the game after the next?
Answer:
If they win today's game, the probability to win the next game = 2/3
Therefore the probability that they lose the next game when they win today's game = 1-(2/3) =1/3.
If they lose today's game, the probability to win the next game = 1/2
so, the probability to lose is 1/2.
a) [tex]\begin{bmatrix} \frac{2}{3}&\frac{1}{2} & \\\\ \frac{1}{3}&\frac{1}{2} & \end{bmatrix}[/tex]
b) [tex]p=\begin{bmatrix} \frac{1}{2}\\\\ \frac{1}{2} \end{bmatrix}[/tex]
[tex]p^{'} =\begin{bmatrix} \frac{7}{12}\\\\ \frac{5}{12} \end{bmatrix}[/tex]
c) Let them win today's game
[tex]p=\begin{bmatrix} 1\\ 0 \end{bmatrix}\\\\\\p^{'} =\begin{bmatrix} \frac{2}{3}\\\\\frac{1}{3} \end{bmatrix}[/tex]
[tex]p^{''}= \left[\begin{array}{c}\frac{11}{18} \\\\\frac{7}{18} \end{array}\right][/tex]
The chances that they win their next game are 58.33%, while if they won today, the chances of winning the game after the next are 38.88%.
ProbabilitiesGiven that if the local professional basketball team, the Sneakers, wins today's game, they have a 2/3 chance of winning their next game, while if they lose this game, they have a 1/2 chance of winning their next game, to determine, if there is a 50-50 chance of the Sneakers winning today's game, what are the chances that they win their next game, and determine, if they won today, what are the chances of winning the game after the next, you must perform the following calculations:
(2/3 + 1/2) / 2 = X1,666 / 2 = X0.58333 = X((2/3 + 1/2 / 2) x 2/3 = X0.58333 x 0.666 = X0.3888 = XTherefore, the chances that they win their next game are 58.33%, while if they won today, the chances of winning the game after the next are 38.88%.
Learn more about probabilities in https://brainly.com/question/10182808
sin x - cos x - 1/√2 = 0
Find the value of x
Answer:
Step-by-step explanation:
Write the quadratic function in the form g(x) = a (x-h)^2 +k.
Then, give the vertex of its graph.
g(x) = 2x^2 + 8x + 10
9514 1404 393
Answer:
g(x) = 2(x +2)² +2
vertex: (-2, 2)
Step-by-step explanation:
It is often easier to write the vertex form if the leading coefficient is factored from the variable terms:
g(x) = 2(x² +4x) +10
Then the square of half the x-coefficient is added inside parentheses, and an equivalent amount is subtracted outside.
g(x) = 2(x² +4x +4) +10 -2(4)
g(x) = 2(x +2)² +2
Comparing to the vertex form, we see the parameters are ...
a = 2, h = -2, k = 2
The vertex is (h, k) = (-2, 2).
A. If x:y= 3:5, find = 4x + 5 : 6y -3
Answer:
17 : 27
Step-by-step explanation:
x=3
y=5
4(3)+5 : 6(5)-3
= 12+5 : 30-3
= 17 : 27
Write y=2/3x+7 in standard form using intergers
Answer:
a.
Step-by-step explanation:
y = 2/3 x + 7
3 * y = 3 * (2/3 x + 7)
3y = 2x + 21
2x - 3y = -21
-2x + 3y = 21
Answer: a.
is “x = -3” a function
Answer:
No
Step-by-step explanation:
x = -3 is a vertical line at x= -3
Tow points on the line are
(-3,1) and (-3,2)
This means one x value goes to 2 different y values so it is not a function
Answer: No
Step-by-step explanation: The line x = -3 is a vertical or straight up and down line that is parallel to the y-axis. On the vertical line x = -3, when x = -3, y can be 0, 1, 2, -5, or any other number, there are in infinite number of possibilities.
The technical definition of a function is written as "a relation in which each element in the domain is paired with one and only one element in the range."
5x+2y-z=-5
-x+3y+4z=12
x-y-3z=-8
Answer:
4
Step-by-step explanation:
233
What is the solution of the inequality shown below?
-3+a<-7
Answer:
[tex]{ \tt{ - 3 + a < - 7}} \\ { \tt{a < - 4}}[/tex]
Given that fx=2x2-4x+1, then f(-1)is.
Answer:
[tex]f(-1)=7[/tex]
Step-by-step explanation:
I am going to assume your question meant the equation
[tex]f(x)=2x^{2} -4x+1[/tex]
So [tex]f(-1)[/tex] can be found by substituting all the x terms in the equation with -1
[tex]f(-1)=2(-1)^{2} -4(-1)+1[/tex]
And simplifying for our answer
[tex]f(-1)=2(1)+4+1[/tex]
[tex]f(-1) = 2+4+1[/tex]
[tex]f(-1)=7[/tex]
Coordinate plane with quadrilaterals EFGH and E prime F prime G prime H prime at E 0 comma 1, F 1 comma 1, G 2 comma 0, H 0 comma 0, E prime negative 1 comma 2, F prime 1 comma 2, G prime 3 comma 0, and H prime negative 1 comma 0. F and H are connected by a segment, and F prime and H prime are also connected by a segment. Quadrilateral EFGH was dilated by a scale factor of 2 from the center (1, 0) to create E'F'G'H'. Which characteristic of dilations compares segment F'H' to segment FH
Answer:
[tex]|F'H'| = 2 * |FH|[/tex]
Step-by-step explanation:
Given
[tex]E = (0,1)[/tex] [tex]E' = (-1,2)[/tex]
[tex]F = (1,1)[/tex] [tex]F' = (1,2)[/tex]
[tex]G = (2,0)[/tex] [tex]G' =(3,0)[/tex]
[tex]H = (0,0)[/tex] [tex]H' = (-1,0)[/tex]
[tex](x,y) = (1,0)[/tex] -- center
[tex]k = 2[/tex] --- scale factor
See comment for proper format of question
Required
Compare FH to F'H'
From the question, we understand that the scale of dilation from EFGH to E'F'G'H is 2;
Irrespective of the center of dilation, the distance between corresponding segment will maintain the scale of dilation.
i.e.
[tex]|F'H'| = k * |FH|[/tex]
[tex]|F'H'| = 2 * |FH|[/tex]
To prove this;
Calculate distance of segments FH and F'H' using:
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
Given that:
[tex]F = (1,1)[/tex] [tex]F' = (1,2)[/tex]
[tex]H = (0,0)[/tex] [tex]H' = (-1,0)[/tex]
We have:
[tex]FH = \sqrt{(1- 0)^2 + (1- 0)^2}[/tex]
[tex]FH = \sqrt{(1)^2 + (1)^2}[/tex]
[tex]FH = \sqrt{1 + 1}[/tex]
[tex]FH = \sqrt{2}[/tex]
Similarly;
[tex]F'H' = \sqrt{(1 --1)^2 + (2 -0)^2}[/tex]
[tex]F'H' = \sqrt{(2)^2 + (2)^2}[/tex]
Distribute
[tex]F'H' = \sqrt{(2)^2(1 +1)}[/tex]
[tex]F'H' = \sqrt{(2)^2*2}[/tex]
Split
[tex]F'H' = \sqrt{(2)^2} *\sqrt{2}[/tex]
[tex]F'H' = 2 *\sqrt{2}[/tex]
[tex]F'H' = 2\sqrt{2}[/tex]
Recall that:
[tex]|F'H'| = 2 * |FH|[/tex]
So, we have:
[tex]2\sqrt 2 = 2 * \sqrt 2[/tex]
[tex]2\sqrt 2 = 2\sqrt 2[/tex] --- true
Hence, the dilation relationship between FH and F'H' is::
[tex]|F'H'| = 2 * |FH|[/tex]
Answer:NOTT !! A segment in the image has the same length as its corresponding segment in the pre-image.
Step-by-step explanation:
Which of the following pairs of functions are inverses of each other?
O A. f(x) = 2x–9 and g(x) = *7 9
B. f(x)=$+4 and g(x) = 3x-4
C. f(x)=5+*fx and g(x) = 5 - 43
O D. f(x) = 3-6 and g(x) = x26
Answer:
I think its B
Step-by-step explanation:
The pairs of functions which are inverses of each other is A. f(x) = 2x - 9 and g(x) = (x + 9)/2.
What is Inverse Function?Inverse functions are functions which can be reversed in to another function.
Then the function is said to be the inverse of the second function.
If two functions f(x) and g(x) are inverses of each other, then f(g(x) = x and g(f(x)) = x.
A. f(x) = 2x - 9 and g(x) = (x + 9)/2
f(g(x)) = f((x + 9)/2) = 2 [(x + 9)/2] - 9 = x + 9 - 9 = x
g(f(x)) = g(2x - 9) = (2x - 9 + 9) / 2 = 2x / 2 = x
So, the functions are inverses of each other.
B. f(x) = (x/3) + 4 and g(x) = 3x - 4
f(g(x)) = f(3x - 4) = [(3x - 4)/3] + 4 ≠ x
So not inverses of each other.
C. f(x) = 5 + ∛x and g(x) = 5 - x³
f(g(x)) = f(5 - x³) = 5 + ∛(5 - x³) ≠ x
So not inverses of each other.
D. f(x) = (2/x) - 6 and g(x) = (x + 6)/2
f(g(x)) = f((x + 6)/2) = [2 / ((x + 6)/2)] - 6 ≠ x
So not inverses of each other.
Hence the correct option is A.
Learn more about Inverse functions here :
https://brainly.com/question/2541698
#SPJ7
What is the range of possible sizes for side x? Please help!
Answer:
x is smaller than 5.6 and greater than 0
b) What is the 4 times of the sum of 3and9?
Answer:
108
Step-by-step explanation:
sum is a fancy word for add so 3+9=27 and 27*4=108
if the volume of a cube is 2197cm3, find the height of the cube
The product of 86 and the depth of the river
Answer:
Step-by-step explanation:
Are you trying to find a variable expression? the product of 86 means multiplication so 86*n or 86n. Other than that I dont understand the question.
The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000. What percentage of MBA's will have starting salaries of $34,000 to $46,000
Answer:
The correct answer is "76.98%".
Step-by-step explanation:
According to the question,
⇒ [tex]P(34000<x<46000) = P[\frac{34000-40000}{5000} <\frac{x- \mu}{\sigma} <\frac{46000-40000}{5000} ][/tex]
[tex]=P(-1.2<z<1.2)[/tex]
[tex]=P(z<1.2)-P(z<-1.2)[/tex]
[tex]=0.8849-0.1151[/tex]
[tex]=0.7698[/tex]
or,
[tex]=76.98[/tex]%
If u= 70% and o=5%, what % of scores fall within 3 standard deviations from the mean?
Answer:
"85%" is the right answer.
Step-by-step explanation:
Given:
[tex]\mu = 70[/tex] (%)
[tex]\sigma = 5[/tex] (%)
As we know,
The 99.7% observation fall within the 3rd standard deviation, then
⇒ [tex](\mu \pm \sigma ) = (70-(3\times 5)) \ to \ (70+(3\times 5))[/tex]
[tex]=(70-15) \ to \ (70+15)[/tex]
[tex]=55 \ to \ 85[/tex] (%)
Thus the above is the correct solution.
Please help …………………….
9514 1404 393
Answer:
(-3, 3)
Step-by-step explanation:
The blanks are trying to lead you through the process of finding the point of interest.
__
The horizontal distance from T to S is 9 . (or -9, if you prefer)
The ratio you're trying to divide the line into is the ratio that goes in this blank:
Multiply the horizontal distance by 2/3 . (9×2/3 = 6)
Move 6 units left from point T.
The vertical distance from T to S is 6 .
Multiply the vertical distance by 2/3 . (6×2/3 = 4)
Move 4 units up from point T.
__
Point T is (3, -1) so 6 left and 4 up is (3, -1) +(-6, 4) = (3-6, -1+4) = (-3, 3). The point that is 2/3 of the way from T to S is (-3, 3).
The table shows the marginal relative frequencies of surveyed drivers’ plans for their next vehicle.
A 2-way table. A 5-column with 4 rows titled Plan for Next Vehicle. Column 1 has entries Current vehicle, bought new, bought used, leased total. Column 2 is labeled Buy new with entries 0.156, 0.076, 0.02, 0.252. Column 3 is labeled Buy used with entries 0.024, 0.584, 0.008, 0.616. Column 4 is labeled Lease with entries 0.024, 0.036, 0.072, 0.132. Column 5 is labeled Total with entries 0.204, 0.696, 0.1, 1.000.
Which statements appropriately interpret data from the table? Check all that apply.
The majority of drivers, about 62 percent, plan to buy a used vehicle next.
About 25 drivers plan to buy a new vehicle next.
Ten percent of drivers lease their current vehicle.
Only 1.3 percent of drivers plan to lease next.
The least percentage of people will lease their next car.
:Answer:
1.) The majority of drivers, about 62 percent, plan to buy a used vehicle next.
3.) Ten percent of drivers lease their current vehicle.
5.) The least percentage of people will lease their next car.
Correct on EDGE2021
Answer:
A)The majority of drivers, about 62 percent, plan to buy a used vehicle next.
C)Ten percent of drivers lease their current vehicle.
E)The least percentage of people will lease their next car.
Step-by-step explanation:
edge 2023
I need help with this
Serkan teacher regularly buys 75 TL of gasoline in his car every week.
At the end of the 13th week, how much is the total gasoline expenditure made by the serkan teacher?
A)390 B)420 C)900 D)975
Answer:
d
Step-by-step explanation:
75 per week,
after 13 weeks, 75*13 = 975
lisa used 880g of a container of sugar to bake a cake and 1/10 of the creaming sugar to make cookies. She then had 3/7 of the container of sugar left. How much sugar was in the container at first
Answer:
At the beginning, there were 2,678.26 grams of sugar in the container.
Step-by-step explanation:
Since Lisa used 880g of a container of sugar to bake a cake and 1/10 of the creaming sugar to make cookies, and she then had 3/7 of the container of sugar left, to determine how much sugar was in the container at first, the following calculation must be performed:
880 + 1 / 10X = 3 / 7X
880 + 0.1X = 0.4285X
880 = 0.4285X - 0.1X
880 = 0.3285X
880 / 0.3285 = X
2,678.26 = X
Therefore, at the beginning there were 2,678.26 grams of sugar in the container.
Muhammad lives twice as far from the school as Hita. Together, the live a total of 12 km
from the school. How far away drom the school does each of them live?
Answer:
Muhammad lives 8 km away from the school.
Hita lives 4 km away from the school.
Step-by-step explanation:
First of all, find a number that, when you double that number and add both numbers, you will get 12. That number is 4. So double 4 and get 8. Then add both to get 12.
consider the function f(x) = -2x^2 - 7. which of the following functions shifts the graph of f(x) up three units and vertically shrinks it by a factor of 1/2?
a. g(x) = -x^2 - 10
b. g(x) = -x^2 - 4
c. g(x) = x^2 - 4
d. g(x) = -1/2x^2 - 4
Answer: The answer is B.
Step-by-step explanation:
James Madison High School
Find the area of the sector formed by central angle
θ
in a circle of radius
r
if
θ
=
2
;
r
=
6
m
Answer: 0.2pi
Step-by-step explanation:
1. Find the area of the entire circle
2. Set up a proportion that compares the relationship of the Area of sector and the Area of circle to the Arc measure and the circle measure
3. Solve!
Each minute Garret is able to run 124 meters. If he has already run 328 meters, what will his total distance be after 11 minutes?
A. 1,692 meters
B. 2,244 meters
C. 3,674 meters
D. 4,972 meters
Answer:
A.
Step-by-step explanation:
124 * 11 = 1364
1364 + 328 = 1,692
HELP!!!!
Which of the following is the absolute value of 6 − 3i?
A) 3i√3
B) 3√5
C) 3√5i
D) 3√3
Answer:
B
Step-by-step explanation:
We want to find the value of:
[tex]\displaystyle |6-3i|[/tex]
Recall that given a complex number z in the form:
[tex]z=a+bi[/tex]
The absolute value of z will be given by:
[tex]\displaystyle |z| = \sqrt{a^2+b^2}[/tex]
We have the complex number:
[tex]6-3i[/tex]
Thus, a = 6 and b = -3.
Then its absolute value will be:
[tex]|6-3i|=\sqrt{(6)^2+(-3)^2}[/tex]
Evaluate:
[tex]\displaystyle |6-3i|= \sqrt{36+9}=\sqrt{45}=3\sqrt{5}[/tex]
Hence, our answer is B.
two interior angles of a trapezium sum up to 250 degrees If the remaining angles are equal find the value
9514 1404 393
Answer:
each is 55°
Step-by-step explanation:
The sum of angles in a trapezium is 360°, so the sum of the remaining two angles is 360° -250° = 110°. Each of those two equal angles will be ...
110°/2 = 55°
Help me please it will be greatly appreciated!
Answer:
5h + 3p
Step-by-step explanation:
1 hardback weighs 5 pounds, then
h hardbacks weigh 5 × h = 5h
1 paperback weighs 3 pounds, then
p paperbacks weigh 3 × p = 3p
total weight = 5h + 3p
An absolute value function has
A. Curved lines that only increases and decreases.
B. Straight lines that do both increase ,decrease, or stay constant on the same graph
C.Straight line that do both increase and decrease on the same graph
D. Straight lines that only increase or decrease
E. Curved lines that do both increase and decrease on the same graph
