Answer:
[tex]\displaystyle \cos(\alpha+\beta)=\frac{120+8\sqrt{161}}{255}[/tex]
Step-by-step explanation:
We are given the conditions:
[tex]\displaystyle \sin(\alpha)=-\frac{8}{17}\text{ and } \cos(\beta)=-\frac{8}{15}[/tex]
Where α is in QIII and β is in QII and we want to find the exact value of cos(α + β).
The first ratio gives us the opposite side and the hypotenuse with respect to α . Then the adjacent side is (we can ignore negatives):
[tex]a=\sqrt{(17)^2-(8)^2}=15[/tex]
The second ratio gives us the adjacent side and the hypotenuse with respect to β. Then the opposite side is:
[tex]o=\sqrt{(15)^2-(8)^2}=\sqrt{161}[/tex]
Therefore, for α, ignoring negatives, the adjacent side is 15, the opposite side is 8, and the hypotenuse is 17.
And for β, ignoring negatives, the adjacent side is 8, the opposite side is √(161), and the hypotenuse is 15.
We can rewrite our expression as:
[tex]\displaystyle \cos(\alpha+\beta)=\cos(\alpha)\cos(\beta)-\sin(\alpha)\sin(\beta)[/tex]
Since α is in QIII, sin(α), cos(α) < 0, and tan(α) > 0.
And since β is in QII, cos(β), tan(β) < 0, and sin(β) > 0.
Using this information, substitute:
[tex]\displaystyle \cos(\alpha+\beta)=\left(-\frac{15}{17}\right)\left(-\frac{8}{15}\right)-\left(-\frac{8}{17}\right)\left(\frac{\sqrt{161}}{15}\right)[/tex]
Therefore:
[tex]\displaystyle \cos(\alpha+\beta)=\frac{120+8\sqrt{161}}{255}[/tex]
The probability of buying a small car is 1. What does that mean?
It is unlikely.
It is impossible.
It is definite.
It is likely
Answer:
it is unlikely if it is one out of 5
Step-by-step explanation:
answer all of them please
easy math questions for 20 points
PLZ RESPOND AS SOON AS POSSIBLE
What point is located at (-2, -6)
a. F
b. G
c. H
d. K
The answer is for your question is letter k
What is the width of a rectangle with a length of 3/8 ft and and area of
4 square feet?
I need the surface area plz
Answer:
922
Step-by-step explanation:
(5x22)x2=220
(13x5)x2=130
(22x13)x2=572
220+130+572=922
Answer:
Length (l) = 22 ft
Breadth (b) = 13 ft
Height (h) = 5 ft
Surface Area of a cuboid
[tex] = 2(lb + bh + lh)[/tex]
[tex] = 2(22 \times 13 + 13 \times 5 + 5 \times 22) \\ = 2(286 + 65 + 110) \\ = 2(461) \\ = 2 \times 461 \\ = 922 \: ft ^{3} [/tex]
=> Surface area of the cuboid will be 922 ft³.
(8 – 10i) – (-16 + 2i)
Answer:
8-10i - -16+2i= 236
Step-by-step explanation:
I am brainliest
Answer:
-16
Step-by-step explanation:
(8-10i) - (-16+2i)
2i - (-14i)
-16
Arlie is on an airplane that has traveled 420 miles in 3/4 of an hour. At this rate, how far will the airplane travel in the next 1/2 hour?
A trapezoid with a height of 19 meters has a base of 26 meters and another base of 46 meters. What is the area of the trapezoid?
the area of the trapezoid is
A 342m2 B 598m2 C 684 m2D 1,368m2
Answer:684
Step-by-step explanation:
A= 1/2 h (b1+b2)
A= 1/2 19 (46+26)
A= 9.5 (72)
A=684
The Edward James Toy Company uses a Kanban system to make plastic wheels that are a component of several toys. The waiting time for a container of the wheels during production is 0.25 day; average processing time is 0.15 day per container. Each container holds 200 wheels. The company uses 2,000 wheels a day in the production of its products. Use the information in Case 6.1. Using a policy variable of 5%, calculate the number of Kanban containers needed for the wheels.
Answer:
[tex]N_c \approx 5.0[/tex]
Step-by-step explanation:
From the question we are told that:
Waiting time for a container of the wheels during production [tex]T_w=0.25day[/tex]
Average processing time is [tex]T_a=0.15 day per container[/tex]
Wheel per container [tex]N_w=200[/tex]
Total wheel per day [tex]D=2000[/tex]
Policy variable of [tex]X=5%[/tex]
Generally the equation for Total number of container [tex]N_c[/tex] is mathematically given by
[tex]N_c=DT(\frac{1+X}{N_w} )[/tex]
Where
Total time [tex]T=T_w+T_a[/tex]
[tex]T=0.15+0.25[/tex]
Therefore
[tex]N_c=DT(\frac{1+X}{N_w} )[/tex]
[tex]N_c=2000*0.40(\frac{1+0.5}{200} )[/tex]
[tex]N_c=(\frac{840}{200} )[/tex]
[tex]N_c=4.2[/tex]
[tex]N_c \approx 5.0[/tex]
Therefore the number of Kanban containers needed for the wheels is
[tex]N_c \approx 5.0[/tex]
Jelpppsldkdhjdisjsjxjxjzjdjz
Answer:
28716.35 mm³
Step-by-step explanation:
The formula of volume of sphere
[tex] = \frac{4}{3} \pi {r}^{3}[/tex]
The volume of the sphere
[tex] = \frac{4}{3} \times 3.14 \times {(38 \div 2)}^{3} [/tex]
[tex] = \frac{4}{3} \times 3.14 \times {19}^{3} [/tex]
[tex] = \frac{86149.04}{3} [/tex]
[tex] = 28716.34667...[/tex]
= 28716.35 mm³ (rounded to the nearest hundredth)
Dr. Victory is a psychologist studying the effects of high-level classes, bullying, and music classes on the anxiety levels of middle school students. He has previously determined that the effects from class levels, bullying experiences, and music classes are independent. It has been determined that the probability that a student is taking a high-level English class is 0.23, the probability that a student has been bullied is 0.36, and 1/3 of students are in music classes.
(a) What is the probability that a randomly selected student is in a high-level English class and has been bullied?
(b) What is the probability that a randomly selected student is in a music class and has been bullied?
(c) What is the probability that a randomly selected student is in a music class, has been bullied, and is in a high-level English class?
Answer:
a) 0.0828 = 8.28% probability that a randomly selected student is in a high-level English class and has been bullied
b) 0.12 = 12% probability that a randomly selected student is in a music class and has been bullied
c) 0.0276 = 2.76% probability that a randomly selected student is in a music class, has been bullied, and is in a high-level English class
Step-by-step explanation:
Probabilities of independent events happening together:
The probabilities of independent events happening together is the multiplication of the probabilities of each event happening.
In this question:
0.23 probability that a student is taking a high-level English class.
0.36 probability that a student has been bullied.
1/3 = 0.3333 probability that a student is in music class.
(a) What is the probability that a randomly selected student is in a high-level English class and has been bullied?
0.23*0.36 = 0.0828
0.0828 = 8.28% probability that a randomly selected student is in a high-level English class and has been bullied
(b) What is the probability that a randomly selected student is in a music class and has been bullied?
0.36*1/3 = 0.12
0.12 = 12% probability that a randomly selected student is in a music class and has been bullied
(c) What is the probability that a randomly selected student is in a music class, has been bullied, and is in a high-level English class?
0.23*0.36*1/3 = 0.23*0.12 = 0.0276
0.0276 = 2.76% probability that a randomly selected student is in a music class, has been bullied, and is in a high-level English class
Area 15 cm 12 cm 19 cm triangle
Answer:
not clear
Step-by-step explanation:
what is the height and base? need an image
Which histogram correctly displays the information above
Answer: The answer is c
Pls solve the 2nd q fast. Best answer will be marked brainliest
Step-by-step explanation:
[tex] \frac{ - 16}{11} + \frac{ - 3}{9} = \frac{ - 48 - 11}{33} = \frac{ - 59}{33} [/tex]
need help asap i have no clue how to solve this
Answer:
c and
28.57%
Step-by-step explanation:
count how many number fall into each category
50-59 has 1
60-69 has 2
70-79 has 4
80-89 has 4
and 90-99 has 3
So the last histogram fits this data
to find the % of those that are between 70-79, take the total number of items that fit into that category (4) and divide by the total number of items (14)
4/14=.2857 --> turn to a percent .2857*100= 28.57%
Would greatly appreciate the help with both A and B
SOME HELP HERE PLEASE?!!
Solve for x:
x+2 / x+5 = 2/3
A. -11
B. - 3
C. 2
D. 3
E. 4
Thanks!!
Step-by-step explanation:
Your answer is 4. Hope you like my answer.
Answer:
x+2 / x+5 = 2/3
2x + 10 = 3x + 6
•°• x =4
correct option → E
Hope it helped :)
A zoo has 15 toucans and 75 parrots What is the ratio of the number of toucans to the number or parrots in the zoo
Answer:
Since there is 15 toucans and 75 parrots the ratio would be written as
15/75
Step-by-step explanation:
As of 15 to 75. Then write out with a colon between the too! 15:75
Hope this helped and have a wonderful day!! <33
If ax+b=3 and a=0, then x=
Answer: the answer is e
Step-by-step explanation:
If ax + b = 0, is x > 0
(1) a + b > 0
(2) a - b > 0
Please help. I NEED GOOD GRADES
Answer:
The circle should be open and the arrow should go the other way.
Final Question!!!! College Math! I also did half of it!
Answer:
15π/4
9π /4
Step-by-step explanation:
[tex]5 \int\limits^4_1 {f(x)} \, dx[/tex] = 5 ((-π/4)+ π) = 5 (π-π/4) = 5(3π/4) = 15π/4
[tex]5 \int\limits^6_1 {|f(x)|} \, dx[/tex] = 5(π/4 + 2π) = 5(9π /4) = 45π/4
I need help I need the answer
Answer:
(4,4)
Step-by-step explanation:
because it's right in between the school and bank therefore equal distance to both
Answer:
(6,8)
Step-by-step explanation:
the same distance from bank to school (sorry if im wrong)
Find the surface area of the rectangular prism:
Answer: 430 cm²
Step-by-step explanation:
1) Front x Back= 15 x 7 x 2= 210 (We do time 2 because there are two of the same shapes ex. there are two squares that are both 16 ft so just do 16 x 2)
2) Right x Left= 7 x 5 x 2 = 70
3) Top x Bottom= 15 x 5 x2 = 150
4) Add. 150 + 210 + 70 = 430 cm²
Hope that helped! :)
Which of the following represent the numerical expression 2p? (c (Select all that apply.) 1: The product of 2 and p 2: Two more than p 3: Two less than p 4: Two groups of p 5: The quotient of 2 and p 6: Two multiplied by p
Whoever answer this question Get Mark Brainiest
Answer:
(1) The product of 2 and p (6) Two multiplied by p.
Step-by-step explanation:
The given numerical expression is 2p.
Here, 2 is a variable and p is a constant. 2 and p are getting multiplying. The multiplication of two numbers is called their product.
The product of 2 and p is equal to 2p.
Also, product of 2 and p.
Hence, the statement that represents 2p are : (1) The product of 2 and p (6) Two multiplied by p.
Gina will pay $14 for fabric at a crafting store. The tax rate is 8.5%. How much will she pay for her fabric including tax?
Answer:
$15.19
Step-by-step explanation:
8.5% = 0.085
0.085 x 14 = $1.19
1.19+14= $15.19
Help Please!! Struggling with this for a while
Answer:
Area of triangle ABC = 6 square units
Step-by-step explanation:
By applying Pythagoras theorem in right triangle ADC,
AC² = AD² + CD²
3² = (1.8)² + CD²
9 - 3.24 = CD²
CD = √5.76
CD = 2.4 units
By applying mean ratio theorem,
[tex]\frac{AD}{CD}=\frac{CD}{DB}[/tex]
CD² = AD × DB
(2.4)² = 1.8 × DB
DB = [tex]\frac{5.76}{1.8}[/tex]
DB = 3.2 units
AB = AD + DB
AB = 1.8 + 3.2
AB = 5 units
Since, area of a triangle ABC = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(\text{AB})(\text{CD})[/tex]
= [tex]\frac{1}{2}(5)(2.4)[/tex]
= 6 square units
What is the measure of angle A? How do you know this?
HELPPP QUICK ANSWER BOTH PARTS
Answer:
x = 20 degrees
Step-by-step explanation:
We know this because angles next to each other in parallelograms add up to 180 degrees, so if we create an equation, 3x + 120 = 180 meaning that 3x = 60, which means that x = 20 degrees.
please help me how to get the answer for this one
Answer:
i say c sorry if im wrong
Step-by-step explanation:
Graph triangle JKL and its image after a reflection in the line x=2 J(1,-1), K(3,0), L(0,-4)
Answer:
I need more information to help you on this question.
Step-by-step explanation:
The points after image reflection in the line x = 2 will be k'(1, 0), L'(4, -4) and J'(3, -1).
What is a graph?In math, graph science is the theory of geometric structures called graphs that are used to represent pairwise different objects. Vertices—also known as nodes or points—that are joined by edges make form a network in this sense.
Undirected graphs, where edges connect two vertices equally, and focused therapy, where edges connect two vertices unevenly, are distinguished.
As per the given information in the question,
Here mirror (x = 2) is vertical, hence only x-coordinate changes vertical distance from x-axis will not change.
For point k(3, 0)
It is one unit right side or x = 2. So, its image point will be one unit left side that is k'(1, 0).
For point L(0, -4)
It is two unit left side, so L' will be 2 unit right side of x = 2, so the point will be L'(4, -4)
Similarly, point J(1, -1) will become J'(3, -1).
To know more about Graph:
https://brainly.com/question/17267403
#SPJ2
E = (2a + 3b + 2) + (3a + 5b - 1) + (2a - 2b)
Answer:
7a+6b+1
...............
Answer:
7a+6b+1
Step-by-step explanation:
2a+3b+2+3a+5b-1+2a-2b=7a+6b+1
Combine like termsUse this fact:(+)×(+)=+ (-)×(-)=+
(+)×(-)=- (-)×(+)=-