Answer:
1/2
Step-by-step explanation:
The angle 5pi/3 shows up in the 3rd quadrant and is equivalent to the angle 300 degrees. The "reference angle" of 300 degrees is 60 degrees; the reference angle in this case has the same trig function values as does 300 degrees. Thus, the cosine of 5pi/3 is the same as the cosine of 60 degrees, which is 1/2.
Using equivalent angles, it is found that:
[tex]\cos{\left(\frac{5\pi}{3}\right)} = \frac{1}{2}[/tex]
[tex]\frac{5\pi}{3}[/tex] is an angle in the fourth quadrant, as [tex]\frac{2\pi}{3} \leq \frac{5\pi}{3} \leq 2\pi[/tex].
To find the equivalent in the first quadrant to an angle in the fourth quadrant, we subtract [tex]2\pi[/tex] from the angle, then:
[tex]2\pi - \frac{5\pi}{3} = \frac{6\pi}{3} - \frac{5\pi}{3} = \frac{\pi}{3}[/tex]
Just as in the first quadrant, the cosine is positive in the fourth quadrant, thus, applying the equivalent angle:
[tex]\cos{\left(\frac{5\pi}{3}\right)} = \cos{\left(\frac{\pi}{3}\right)} = \frac{1}{2}[/tex]
A similar problem is given at https://brainly.com/question/23843479
-8(4+9x)=7(-2-11x)
please help me solve this i have no clue and this is my math homework
Distributive property
-8*4=-32 -8*9x=-72x
-32-72x=7(-2-11x)
7(-2)=-14 7(-11x)=-77x
-32-72x=-14-77x
Combine Like Terms
-32+14=-18 -77x+72x=-5x
-18=-5x
Divide both sides by -5 and theres your answer
Find the probability that event A will appear at least three times in four independent tests if the probability of occurrence of event A in one test equal to 0.4
This kind of problems are solved using Bernoulli's distribution. Everytime you have a win/lose scenario, and you know the probability [tex] p[/tex] of winning, and you want [tex]k[/tex] successes over [tex]n[/tex] trials, you have the following probability:
[tex]\displaystyle P(k\text{ successes over }n\text{ trials}) = \binom{n}{k}p^k(1-p)^{n-k} [/tex]
You want the probability of having at least three successes, i.e. you are interested in the cases k=3 and k=4. The corresponding probabilities are
[tex]\displaystyle P(3 \text{ successes}) = \binom{4}{3}0.6^3 \cdot 0.4 = 4\cdot 0.216 \cdot 0.4 = 0.3456[/tex]
[tex]\displaystyle P(4 \text{ successes}) = \binom{4}{4}0.6^4 = 0.1296 [/tex]
So, the total probability is [tex] 0.3456+0.1296 = 0.4752[/tex]
it takes an ant farm 3 days to consume half of an Apple at that rate in how many days will the ant farm consume apples?
Answer:
From the comments below we see the missing part of the question is "in how many days will the ant farm consume 3 apples?"
The answer is 18.
Step-by-step explanation:
We will use a proportion to solve this. It takes 3 days to consume 1/2 of an apple; this gives us the ratio
3/0.5
We want to know how many days, x, it will take to consume 3 apples; this gives us the ratio
x/3
Together this gives us the proportion
3/0.5 = x/3
Cross multiply:
3(3) = 0.5(x)
9 = 0.5x
Divide both sides by 0.5:
9/0.5 = 0.5x/0.5
18 = x
The ant farm will take 18 days to consume 3 apples.
Given that,
Ant farm consumes 0.5 apple in 3 Days.We need to find days to consume 3 apples.Let number of days be X.Here we assume 3 apples.According to above information, calculation of data are as follows,
[tex]X = (3 \div 0.5) \times 3\\\\X = 6 \times 3[/tex]
X = 18
So, Total number of days required is 18 days.
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Question 44 Unsaved
Find the measure of an angle between 0° and 360° coterminal with an angle of -271° in standard position.
Question 44 options:
181°
91°
271°
89°
Coterminal angles are angles in standard position (angles with the initial side on the positive x -axis) that have a common terminal side.
Answer: 89°Coterminal angles are angles that have the same terminal sides in standard position.
Anytime we complete a full cycle( a complete revolution) we come back to the same terminal side.
Therefore to find all angles which are coterminal with [tex]-271\degree[/tex] we keep adding or subtracting [tex]360\degree[/tex].
For the given interval, that is, [tex]0\degree[/tex] to [tex]360\degree[/tex],
We add [tex]360\degree[/tex] so that we can obtain an angle coterminal with [tex]-271\degree[/tex] within this interval.
This means that
[tex]-271\degree[/tex] is coterminal with [tex]360\degree + \: -271\degree=89\degree[/tex]
Hence the correct and answer is D
Can u solve for the indicated variable
R= c-s/t. For c
Switch the equation to have c on left side
C-s/t= r
Now multiply t both sides
C-s= r(t)
C-s= rt
Now add s both sides to get your answer
C= s+rt
Tommy has a pet monkey .Every day , his monkey eats 4 apples in the morning.the monkey also eats two bananas for every banana that tommy eats .
Write an equation to describe this situation where x is the number of banana tommy eats and y is the total number of pieces of fruit the monkey eats
What is the least common denominator for the fractions 16 and 34 ?
Answer:
The answer is 4
Step-by-step explanation:
The answer is 4 because if you divide them both by 4 they come out even and they cant be divider by anything less. Therefore the common denominator is 4.
Answer:
12
Step-by-step explanation:
if you said 4 its not answer
if a prescription reads take 2 tablespoons 3 times a day for 10 days how many total tablespoons will the patient take?
Given that m and n are parallel, and p is a transversal that is perpendicular to m, give an explanation for why it must also be perpendicular to n.
We know that if m and n are parallel, then we know that they have the same slope. We can call it x in this case.
Since we know that p is a perpendicular transversal, then we know it is the opposite and reciprocal of m. Therefore, we can label it as -1/x.
Since p = -1/x and n = x, we can tell they are perpendicular.
Parallel lines m and n, with transversal p, imply that if p is perpendicular to m (forming a 90-degree angle), it must also be perpendicular to n because parallel lines have the same inclination. Thus, the angle between n and p also has to be 90 degrees.
Explanation:In the scenario presented, we're dealing with parallel lines m and n, and a transversal, p. The fact that p is perpendicular to m implies that the angle between m and p is 90 degrees. Now, since m and n are parallel, this means they have the same angle of inclination. So, the angle between n and p is also 90 degrees. This essentially means p is perpendicular to n as well.
Parallel lines have the property that they never intersect and are always equidistant. In geometry, when a line crosses two or more other lines, it is called a transversal. And when a line is perpendicular to another, it forms a 90-degree or right angle with the other line.
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An exam has 30 questions. The professor subtracts 8 points for each incorrect answer and adds 7 for each correct answer. If a student ends up receiving 0 points, how many questions were answered correctly?
Wrong answer = x
Correct answer = y
Total questions: x+y = 30
Rewrite for x: x = 30-y
Total points:
-8x + 7y = 0
replace x with 30-y
-8(30-y) + 7y = 0
Simplify:
-240 + 8y + 7y = 0
Combine like terms:
-240 + 15y = 0
Add 240 to each side:
15y = 240
Divide both sides by 15:
y = 240 / 15
y = 16
There were 16 correct answers
30-16 = 14 wrong answers.
use the distributive property to solve the equation 4x/5-x=x/10-9/2
15 i think sorry if its wrong
How many cubic blocks with a side length of 3/8 cm will be required
to find the volume of a cube with a side length of 3/4 cm?
A.
8
B.
10
C.
12
D.
14
E.
16
ANSWER
The correct answer is A.
EXPLANATION
The volume of a cube is given by
[tex]V=l^3[/tex]
First we find the volume of the cube with side length [tex]\frac{3}{4}cm[/tex]
[tex]V_{Cube}=(\frac{3}{4})^3[/tex]
[tex]V_{Cube}=\frac{27}{64} cm^3[/tex]
Next, we find the volume of the cubic block with side length [tex]\frac{3}{8}cm[/tex]
[tex]V_{Block}=(\frac{3}{8})^3[/tex]
[tex]V_{Block}=\frac{27}{512} cm^3[/tex]
We divide the volume of the cube by the volume of the block to get the number of cubic blocks
[tex]Number\: of \: blocks=\frac{\frac{27}{64}} {\frac{27}{512}}[/tex]
[tex]Number\: of \: blocks=\frac{27}{64} \times \frac{512}{27}[/tex]
[tex]Number\: of \: blocks=\frac{1}{1} \times \frac{8}{1}=8[/tex]
Answer:
The correct answer is option A.
8 blocks are needed to fill the box.
Step-by-step explanation:
Given data:
Side length of a block = 3/8 cm
Side length of main block = 3/4 cm
How many blocks are needed to fit in main blocks = ?
Solution:
Volume = length³
Volume of one simple block = (3/8)³ = 27/512 cm³
Volume of one Main block = (3/4)³ = 27/64 cm³
Blocks are needed to fit in main blocks = (27/64) ÷ (27/512) = 8
Answer = 8 blocks
Hence 8 simple small blocks of one side length 3/8 cm will needed to fit in the main block of side length 3/4 cm.
Use the graph below to fill in the blank with the correct number: f(1) = _______ X, Y graph. Plotted points negative 3, 0; negative 2, 2; 0, 1; and 1, negative 2.
Answer:
f(1) = -2
Step-by-step explanation:
Each point is (x, f(x)).
The point (1, f(1)) is given as (1, -2), so f(1) = -2.
Answer:
f(1) = -2
Step-by-step explanation:
Solve for sss.
0.5s+1=7+4.5s
The value of s from the given equation is -1.5.
The given equation is 0.5s+1=7+4.5s.
We solve the given equation for s.
What is an equation?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side). Equations can be solved to find the value of an unknown variable representing an unknown quantity.
Now, the given equation can be solved as follows:
0.5s+1=7+4.5s
⇒0.5s-4.5s=7-1
⇒-4s=6
⇒s=-6/4
⇒s=-1.5
Therefore, the value of s is -1.5.
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Tom is trying to write 3/47 As a decimal. He used long division and divided until he got the quotient 0.638297872, at which point he stopped. Since the decimal doesn’t seem to terminate or repeat, he concluded that 3/47 is not rational. Do you agree or disagree? Why?
Answer:
3/47 is rational because it is a ratio of two integers.
Adding and subtracting like terms
How do I solve w-w*2+-2w*2
Answer:
See two different cases, below:
Step-by-step explanation:
You cannot "solve" w-w*2+-2w*2, because this is not an equation. Rather, you want to simplify w-w*2+-2w*2 by combining like terms. You have w - 2w - 4w, or -5 w.
If, however, you meant "exponentiation" by " * " then you have w^1 - w^2 - 2w^2, which in turn equals w - 3w^2, or, in descending order by powers of w, -3w^2 + W.
Mr. Davies opened a new retail store. During the first week, 360 customers visited the store. During the second week, 300 customers visited the store. What is the percentage change of the number of customers that visited the store in the first week to the number of customers that visited the store in the second week?
the answer is 16.7 because you need to do 60/360
The answer is 16.67%
Explanation:
Number of customers who visited in the first week = 360
Number of customers who visited in the second week = 300
Number of customers decreased in the second week =
[tex]360-300=60[/tex]
So, the percentage change of the number of customers that visited the store in the first week to the number of customers that visited the store in the second week will be = [tex]\frac{60}{360}*100 =16.67[/tex]
20 points- Help me please this is due today
You moved the decimal place, but didn't account for that in your exponent. It should no longer be 10.
The answer is 1.035*10¹¹
What is the LCM for 14,8
Answer,
56
Hope this helps :-)
Hello there!
This question is super easy to me.
You had to find the prime factorization of 14.
7*2=14
Next, you had to find the prime factorization of 8.
2*2*2=8
7*2*2*2=56
Answer⇒⇒⇒56
The least common multiple of 14 and 8 is 56.
Hope this helps!
Thank you for posting your question at here on Brainly.
-Charlie
at an amusement park, 360 visitors rode the roller coaster in 3 hours. write and solve a proportion to find the number of visitors at this rate who will ride the roller coaster in 7 hours
Answer:
840 visitors
Step-by-step explanation:
WILL GIVE 20 POINTS I PROMISE !!!! PLEASE ANSWER FAST
If a piece of ribbon is 4 and 3/4. feet long, how long is it in inches?
A. 48 inches
B. 57 inches
C.60 inches
D. 62 inches
12 inches is equivalent to 1 foot. So 12 times 4 = 48. So, the answer is b because then u know that its a little more than 48.
Hope this helped! Comment if u have questions. :)
2 biscuits cost 80p how much do 12 cost
Well to find how much 12 biscuits cost, you must first find how much each biscuit costs. Therefore, you divide 80p by 2, and get 40p. Then multiply 40p by 12 (the total amount of biscuit). You get the answer, which is 480p.
Show all work to solve the equation below and write your solution on the space provided. 2|x-1|+3=11
Answer: x = 3, -5
Step-by-step explanation:
2 |x + 1| + 3 = 11
-3 -3
2 |x + 1| = 8
÷2 ÷2
| x + 1 | = 4
x + 1 = 4 or x + 1 = -4
-1 -1 -1 -1
x = 3 or x = -5
numbers between 10 and 20 , divisible by 2,3 and 9
By using LCM, the result is-
Number between 10 and 20 divisible by 2, 3 and 9 = 18
What is LCM of two numbers?
LCM means Lowest Common multiple. LCM of two numbers a and b is the lowest numbers which is divisible by both a and b
LCM can be calculated by division method and prime factorization method.
Also there is an important formula relating HCF and LCM
HCF [tex]\times[/tex] LCM = Product of two numbers
Here,
The number which is divisible by 2, 3 and 9 = LCM of 2, 3 and 9.
2 = 2
3 = 3
9 = 3 [tex]\times[/tex] 3
LCM = [tex]2 \times 3 \times 3[/tex] = 18
Next number divisible by 2, 3 and 9 = 18 + 18 = 36
But 36 does not lie between 10 and 20
So number between 10 and 20 divisible by 2, 3 and 9 = 18
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100 POINTS! MUST HAVE CORRECT ANSWER AND EXPLAIN YOUR WORK!
Evaluate the expression:
v ⋅ w
Given the vectors:
r = <5, -5, -2>; v = <2, -8, -8>; w = <-2, 6, -5>
(It's an essay question so please explain throughly.)
Answer:
Step-by-step explanation:
we have to find the dot product here.
From the formula of dot product of vectors,
we know-
if X=<a,b,c> and Y=<d,e,f>
Then dot product of X and Y is-
X.Y=ad+be+cf
Here, we get
v=<2 , -8 , -8>
and w=<-2 , 6 , -5>
So, the dot product is-
v . w=2(-2)+(-8)(6)+(-8)(-5)
=-4-48+40
=-52+40
=-12
So,
v . w= -12
Answer:
-12
Step-by-step explanation:
we have to find the dot product here.
From the formula of dot product of vectors,
we know-
if X=<a,b,c> and Y=<d,e,f>
Then dot product of X and Y is-
X.Y=ad+be+cf
Here, we get
v=<2 , -8 , -8>
and w=<-2 , 6 , -5>
So, the dot product is-
v . w=2(-2)+(-8)(6)+(-8)(-5)
=-4-48+40
=-52+40
=-12
So,
v . w= -12
2x + 2y =6. 5x + 2y =4. Which of the following equations could be the result of multiplication and addiction to eliminate a variable in the system of equations?
A) 19x = 24
B) 19y = 22
C) 11y = 22
2x+2y=6
5x+2y =4
Multiply eq 1 by 5 and equation 2 by -2
10x+10y = 30
-10x - 4y = -8
Now adding we get
6y = 22
Divide by 2
3Y =11
The total height of all three of Thumbelina’s sisters is 60 cm. If the heights of the three sisters are in the ratio 4:3:5, find the height of the shortest sister.
Answer: 15 cm
Step-by-step explanation:
Given : The total height of all three of Thumbelina’s sisters is 60 cm.
The heights of the three sisters are in the ratio 4:3:5 .
Let the heights of the three sisters are 4x , 3x and 5x.
According to the question , we have the following equation :-
[tex]4x+3x+5x=60\\\\\Rightarrow\ 12x=60\\\\\Rightarrow\ x=\dfrac{60}{12}=5[/tex]
Now, the height of the shortest sister will be :-
[tex]3x=3(5)=15\ cm[/tex]
Hence, the height of the shortest sister = 15 cm
The same four friends buy tickets for two shows on consecutive nights. They use a coupon for $5 off each ticket. They pay a total of $416 for 8 tickets. Write and solve an equation to find the original price of the tickets.
Answer:
Original price of the ticket was $57.
Step-by-step explanation:
Four friends buy tickets for two shows.
Let the price of a ticket was $c
Then cost of 4 tickets = $4c
They use a coupon to get the discount = $5 on each ticket
So total discount on 4 tickets = 4×5 = $20
Cost of the tickets after discount = 4c - 20
Cost of the tickets for two consecutive nights = 2(4c - 20)
If they paid total amount = $416 for 8 tickets
Then the equation will be 2(4c - 20) = 416
Now we can solve this equation to get the original price of the ticket.
2(4c - 20) = 416
4c - 20 = 208
4c = 208 + 20
4c = 228
c = [tex]\frac{228}{4}[/tex]
c = $57
Therefore, original price of a ticket was $57.
Answer:
57
Step-by-step explanation:
I did this earlier.
A rope is 66 feet long. It is cut into two pieces such that one piece is half the length of the other. What is the length of the longer piece of rope? 22 feet 26 feet 33 feet 44 feet
33 hope this helps thanks
Answer:
44
Step-by-step explanation:
The answer is 44 because 66-22=44, 44+22=66 44 is twice of 22
Please answer! Will mark as Brainliest if correct.
Pedro, Lena, Harriet, and Yermin each plot a point to approximate the square root of 0.50.
(See picture)
Whose point is the best approximation of the square root of 0.50?
A: Pedro
B: Lena
C: Harriet
D: Yermin
Answer:
D. Yermin
Step-by-step explanation:
\sqrt(0.50) = 0.70710678
When rounded go to 0.7
Answer:It’s D
That’s the answer because I did this test before and got it right