The Pythagorean Identity states that:
(sin x)2 + (cos x)2 = 1
Given cos 6 = 472, find sin .
[?]
sin 0:
O
Simplify the fraction.
Answer:
[tex]sin(\theta) = \frac{\sqrt{17} }{7}[/tex]
Step-by-step explanation:
We know that:
sin(x)^2 + cos(x)^2 = 1
And we know that:
[tex]cos(\theta) = \frac{4\sqrt{2}}{7} }[/tex]
We want to find the value of the sine function evaluated in theta.
If we replace that in the first equation, we get:
[tex]sin(\theta)^2 + cos(\theta)^2 = 1[/tex]
[tex]sin(\theta)^2 + (\frac{4*\sqrt{2} }{7}) ^2 = 1[/tex]
[tex]sin(\theta)^2 + (\frac{4^2*\sqrt{2}^2 }{7^2}) = 1[/tex]
[tex]sin(\theta)^2 + (\frac{16*2 }{49}) = 1[/tex]
Now we can just isolate the sine part of that equation, so we get:
[tex]sin(\theta)^2 = - (\frac{16*2 }{49}) + 1 = \frac{-32}{49} + \frac{49}{49} = \frac{-32 + 49}{49} = \frac{17}{49}[/tex]
[tex]sin(\theta) = \sqrt{\frac{17}{49} } = \frac{\sqrt{17} }{\sqrt{49} } = \frac{\sqrt{17} }{7}[/tex]
(We can't simplify the fraction anymore)
What is the equation of the curve that best fits the data? Round to the nearest hundredths, when appropriate. picture*
Answer:
.....
Step-by-step explanation:
Up and down
A well-conducted opinion poll showed that 48% of voters surveyed favored the reelection of Congressman Porkbarrel. The people who conducted the survey reported that the poll had a margin of error of 3.5%. Which of the following best describes this statement
A. Based on the procedure by which this figure was generated, it is likely that the population proportion is between 44.5% and 51.5%.
B. About 3.5% of the people polled are likely to change their minds about who they will vote foir.
C. Between 44.5% and 51.5% of the voters will vote for Congressman Porkbarrel.
D. About 3.5% ofthe people interviewed refused to answer the question.
E. The probability is .48 that Congressman Porkbarrel will be reelected.
Answer:
A. Based on the procedure by which this figure was generated, it is likely that the population proportion is between 44.5% and 51.5%.
Step-by-step explanation:
Confidence interval:
We build a confidence interval from a sample proportion, to get an estimate of where the population proportion should likely be.
48% of voters surveyed favored the reelection of Congressman Porkbarrel, with a margin of error of 3.5%.
48 - 3.5 = 44.5%.
48 + 3.5 = 51.5%.
Following the concept of a confidence interval, the population proportion is likely to be between 44.5% and 51.5%, and thus, the correct answer is given by option A.
what is the solution set for this inequalty? -8x + 40> -16
Answer:
x < 7
Step-by-step explanation:
-8x + 40> -16
Subtract 40 from each side
-8x + 40-40> -16-40
-8x >-56
Divide each side by -8, remembering to flip the inequality
-8x/-8 < -56/-8
x < 7
Anyone know this answer
Answer:
Step-by-step explanation:
1 is 60 2 i 60 and 3 is 61 ;)
This is a 4th grade level
Ethan puts $1200 into a Certificate of Deposit (CD) account that earns 2.1% interest each year. What will be the interest of the CD account earned after 5 years? Round to the nearest cent (hundredths place).
Answer:
126
Step-by-step explanation:
1200 x .021=25.20 interest per year
25.20x5=126
assumes no compounding
solve the equation
f(x)=13⋅6x for x = 2
Simplify (4a to the fifth power b to the sixth power) to the fourth power
Answer:
(4a^5b^6)^4 = 256a^20b^24
Step-by-step explanation:
does anyone know this?
Answer:80^w2−48
Step-by-step explanation:
Answer:
If You Factor it it will be (w+8) (5w2-3)
Step-by-step explanation:
The area of the rectangle window is4779 cm to the second power if the length of the window is 81 cm what is the width
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Answer:
59 cm
Step-by-step explanation:
The area is the product of length and width. Using the given numbers, we have ...
A = LW
4779 cm² = (81 cm)W
W = (4779 cm²)/(81 cm) = 59 cm
The width of the window is 59 cm.
Find the value of x that makes m || n
Answer:
x = 133
Step-by-step explanation:
x + 14 = 147
x (+ 14 - 14) = 147 - 14
x = 133
Five red marbles and 10 blue marbles. what is the probability that she will not pull out a red marble?
Answer:
5/15 or 1/3
Step-by-step explanation:
Need help answering pls
Answer:
Step-by-step explanation:
angle 2 and angle 3 are complementary angle because their sum is 90 degree as they are perpendicular.
Three coffees and two muffins cost a total of 7 dollars. Two coffees and four muffins cost a total of 8 dollars. What is the individual price for a single coffee and a single muffin?
Answer:
Cost of a coffee = $1.5
Cost of a muffin = $1.25
Step-by-step explanation:
Given:
Cost of 3 coffee and 2 muffins = $7
Cost of 2 coffee and 4 muffins = $8
Find:
Cost of each
Computation:
Assume;
Cost of a coffee = a
Cost of a muffin = b
So,
3a + 2b = 7 .......... Eq1
2a + 4b = 8 .......... Eq2
Eq1 x 2
6a + 4b = 14 ......... Eq3
From Eq3 - Eq2
4a = 6
a = 1.5
Cost of a coffee = $1.5
3a + 2b = 7
3(1.5) + 2b = 7
4.5 + 2b = 7
b = 2.5/2
b = 1.25
Cost of a muffin = $1.25
Which of the following best represents the slope of the line? A. -3 B. - 1 3 C. 1 3 D. 3
What is the value of
(x3 x 7y÷)(10.6+5.4)for x=2 and y=6?
Step-by-step explanation:
Hope you can correct you question
The probability that Bob and Chris go to the movies is 0.35. The probability that Chris goes to the movies is 0.5. What is the probability that Bob goes to the movies given that Chris goes
Answer:
[tex]P(B/C)=0.7[/tex]
Step-by-step explanation:
From the question we are told that:
The probability that Bob and Chris go to the movies [tex]P(BnC)= 0.35.[/tex]
The probability that Chris goes to the movies [tex]P(C)= 0.5[/tex]
Generally the equation for the probability that Bob goes to the movies given that Chris goes P(B/C) is mathematically given by
[tex]P(B/C)=\frac{ P(BnC)}{P(C)}[/tex]
Therefore
[tex]P(B/C)=\frac{0.35)}{0.5}[/tex]
[tex]P(B/C)=0.7[/tex]
Suppose customers arrive at a single-server ice cream parlor times 3, 6, 15, and 17. Further suppose that it takes the server 7, 9, 6, and 8 minutes, respectively, to serve the four customers. When does customer 4 leave the shoppe
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Answer:
time 33
Step-by-step explanation:
The first customer arrives at time 3, and is finished being served at time 3+7 = 10.
The second customer arrives at time 6, so waits until time 10 to be served. The second customer is finished being served at time 10+9 = 19.
The third and fourth customers arrive at times 15 and 17. The third customer waits until time 19 to be served, and is finished being served at time 19+6 = 25.
The fourth customer waits until time 25 to be served, and is finished being served at time 25+8 = 33.
The fourth customer leaves at time 33.
Doug invests in his company's retirement system by depositing $2400 into an account that pays 8% interest compounded quarterly. Approximately how long will Doug need to leave his money in the account for it to have a balance of $25,000? A) 30 years B) 29.6 years C) 29.3 years D) 0.5 year
Your class is selling boxes of flower seeds as a fundraiser. The total profit p depends on the amount x that your class charges for each box of seeds. The equation p= -0.5x2 + 36x - 231 models the profit of the fundraiser. What's the smallest amount, in dollars, that you can charge and make a profit of at least $363?
Answer:
The least amount is $75.50
Step-by-step explanation:
Given
[tex]p \to profit[/tex]
[tex]x \to amount[/tex]
[tex]p = -0.5x^2 + 36x - 231[/tex]
Required
The smallest amount to make at least 363
We have:
[tex]p = -0.5x^2 + 36x - 231[/tex]
Rewrite as:
[tex]-0.5x^2 + 36x - 231=p[/tex]
Substitute 363 for p
[tex]-0.5x^2 + 36x - 231 = 363[/tex]
Collect like terms
[tex]-0.5x^2 + 36x - 231 + 363 = 0[/tex]
[tex]-0.5x^2 + 36x + 132 = 0[/tex]
Using quadratic formula, we have:
[tex]x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]
Where:
[tex]a = -0.5; b= 36; c = 132[/tex]
So, we have:
[tex]x = \frac{-36 \± \sqrt{36^2 - 4*-0.5*132}}{2*-0.5}[/tex]
[tex]x = \frac{-36 \± \sqrt{1560}}{-1}[/tex]
[tex]x = \frac{-36 \± 39.50}{-1}[/tex]
Split
[tex]x = \frac{-36 + 39.50}{-1}; x = \frac{-36 - 39.50}{-1}[/tex]
[tex]x = \frac{3.50}{-1}; x = \frac{-75.50}{-1}[/tex]
[tex]x = 75.50[/tex] and [tex]x = -3.50[/tex]
The amount can't be negative.
So:
[tex]x = 75.50[/tex]
Hence, the least amount is $75.50
Suppose a fair six sided die has been relabeled so that the 6 is replaced with another 5,i.e., the sides read 1,2,3,4,5,5. If the die is rolled five times, what is the probability that we roll five distinct values
Answer:
P(rolling five distinct values) = 1/3888
Step-by-step explanation:
We are told that I the fair sided dice, 6 is replaced with 5.
Thus,the numbers are now;
1,2,3,4,5,5.
This means a total of 6 possible numbers appearing.
Now, in these 6 numbers there are only 5 distinct numbers since 5 occurs twice.
P(1) = 1/6
P(2) = 1/6
P(3) = 1/6
P(4) = 1/6
P(5) = 2/6
Thus,probability of rolling 5 distinct values = 1/6 × 1/6 × 1/6 × 1/6 × 2/6 = 1/3888
Twice a number is 14. What is the number
Answer:
7
Step-by-step explanation:
Divide 14 by 2
find x and y. For one point extra credit each, give the correct name for point P.
Answer:
where is the question?
Step-by-step explanation:
7+2x/3=5
what is x ?
Answer:
x = -3
Step-by-step explanation:
7 + 2x/3 = 5
7*3 + 2x = 5*3 ( we multiply by 3 to remove the denominator )
21 + 2x = 15
2x = 15 - 21
2x = -6
x = -6/2
x = -3
Answer:
X=4
Step-by-step explanation:
Times both side by 3
then you get 7+2x=15
then minus 7 from both sides
2x=8
divide by 2
x=4
Answer for brainlest
Answer:
∠1 = ∠8
Step-by-step explanation:
Because they are ALTERNATE EXTERIOR ANGLE
Answer:
∠1 = ∠8
Step-by-step explanation:
Because alternate exterior angles are equal.
Also there is no angle given so you cant work them out.
simply put:
∠1 = ∠8
∠1 = ∠4
∠3 = ∠2
∠1 = ∠5
∠2 = ∠6
∠2 = ∠7
∠5 = ∠8
∠4 = ∠8
∠7 = ∠6
∠7 = ∠3
Let me know if I missed out on anymore! It was long that's why.
Hope this kind of explained it :)
You fllp a fair coln 7 times in a row. Let X be the number of heads that come up. Which of the following cannot be a
possible value of X?
2
0
7
16
Answer:
16
Step-by-step explanation:
Given
A coin
[tex]n = 7[/tex] --- Number of flips
[tex]x \to heads[/tex]
Required
Which can't be the value of x
From the question, we understand that the coin was flipped 7 times.
This means that, the highest occurrence of head is:
[tex]x = 7[/tex]
And the list is:
[tex]x = 0[/tex]
So, the range of x is:
[tex]x = \{0,1,2,....,7\}[/tex]
In the above range, only (16) is out of range.
Hence:
[tex]x \ne 16[/tex] --- Number of heads can't be 16
what is the area of
Answer:
7 * 9 = 63
63 for when both of the triangles are combined, 31.5 for one triangle.
Rectangle = 18 * 22 = 396
396 + 63
459 cm^2
How do i solve this please help
Answer:
48
Step-by-step explanation:
138-90(right angled triangle)=48
What type of shape is pentagon
Answer:Polygon
Step-by-step explanation:
Given the set of data find the Mean. 4, 5, 6, 12, 12, 12, 14, 16, 22, 23, 28, 28 (round to one decimal place
Answer:
15.2
Step-by-step explanation:
mean=average
to find the mean, add up all of the numbers and divide by the # of numbers that there are
4+5+6+12+12+12+14+16+22+23+28+28=182
182/12=15.2
Answer:
11.3 to 1DP.
Step-by-step explanation:
The mean = sum of the numbers / 12.
= 136/12
= 11.333