The exact value of cos(13π/8) is 1/2 [tex]\sqrt{2-\sqrt{2} }[/tex].
What is trigonometric ratio?Trigonometriic ratios are the ratios of the sides of a right angled triangle. sin , cos, tan, sec, cosec, cot are some of the trigonometric ratios. Sin is the ratio of perpendicular and hypotenuse, cos is the ratio if base and hypotenuse, tan is the ratio of perpendicular and base, secant is the ratio of hypotenuse and base, cosecant is the ratio of hypotenuse and perpendicular, cot is the ratio of base and perpendicular.
How to find value?We have to find the value of cos (13π/8).
We have to use formula which is following:
cos[tex]Θ[/tex]=[tex]\sqrt{1/2(1+cos 2Θ}[/tex]
=[tex]\sqrt{1/2(1+cos(2*13 π/8)}[/tex] (π=[tex]π[/tex])
=[tex]\sqrt{1/2(1+cos(3 π+π/4)}[/tex]
=[tex]\sqrt{1/2(1-cos(π/4)}[/tex]
=[tex]\sqrt{1/2(1-1/\sqrt{2} }[/tex]
=[tex]\sqrt{\sqrt{2}-1/2\sqrt{2} }[/tex]
=1/2[tex]\sqrt{2-\sqrt{2} }[/tex]
Hence the value of cos (13π/8) is [tex]1/2\sqrt{2-\sqrt{2} }[/tex].
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Find the value of x
Answer:
x = 40
Step-by-step explanation:
Two triangles are similar so we can use similarity ratio to find x
x/16 = 35/14 cross multiply expressions
14x = 560 divide both sides by 14
x = 40
Executives from Six Flags, a well-known amusement park chain, had interest in constructing a Six Flags theme park in a location near Ames city limits. Experts believed that approximately 15% of the surrounding population would be interested in becoming season ticket holders. A random sample of 500 residents of Story County was collected (of the approximately 80,000 residents of Story County). Of the 500 people sampled, 124 said that they would be interested in purchasing season tickets to a Six Flags in Ames. The mean of the sampling distribution for the sample proportion when taking samples of size 500 from this population is equal to ___________.
Answer:
The mean of the sampling distribution for the sample proportion when taking samples of size 500 from this population is equal to 0.248.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Of the 500 people sampled, 124 said that they would be interested in purchasing season tickets to a Six Flags in Ames.
This means that [tex]p = \frac{124}{500} = 0.248[/tex]
The mean of the sampling distribution for the sample proportion when taking samples of size 500 from this population is equal to
By the Central Limit Theorem, it is equal to the sample proportion of 0.248.
The in center is the center of the circle of a triangle
1) circumscribed
2) centralized
3) cocentric
4) inscribed
Answer:
inscribed
Step-by-step explanation:
For any given triangle, the circle inside of it is called the Inscribed circle
Somebody else has to comment for me to Mark u as BRAINLIEST!! It won't let me
Answer:
7.5 is the difference
Step-by-step explanation:
basketball mean
(13+22+23+24+36+37+42+43+58+69) ÷10 = 36.7
tennis mean
(14+23+24+38+47+48+57+58+66+67) ÷10 = 44.2
tennis mean - basketball mean
44.2 - 36.7= 7.5
In ΔIJK, the measure of ∠K=90°, KJ = 65, IK = 72, and JI = 97. What is the value of the cosine of ∠J to the nearest hundredth?
Answer:
[tex]\cos(J) = 0.67[/tex]
Step-by-step explanation:
Given
[tex]\angle K = 90^o[/tex]
[tex]KJ = 65[/tex]
[tex]IK = 72[/tex]
[tex]JI = 97[/tex]
Required
[tex]\cos(J)[/tex]
The question is illustrated with the attached image.
From the image, we have:
[tex]\cos(J) = \frac{KJ}{JI}[/tex]
This gives:
[tex]\cos(J) = \frac{65}{97}[/tex]
[tex]\cos(J) = 0.67010309278[/tex]
[tex]\cos(J) = 0.67[/tex] --- approximated
1. Calculate the variance of the set of data to two decimal places.
{ 1,2,4,4,5,6,6}
a. 22
b. 4
c.3.14
d. 1/7
e.2
============================================================
Explanation:
First we need the arithmetic mean
Add up the values to get 1+2+4+4+5+6+6 = 28
Divide this over the number of values (n = 7) to get 28/n = 28/7 = 4
The mean is 4.
Next, we subtract the mean from each data value and square the difference
(1-4)^2 = 9(2-4)^2 = 4(4-4)^2 = 0(4-4)^2 = 0(5-4)^2 = 1(6-4)^2 = 4(6-4)^2 = 4Add up those results: 9+4+0+0+1+4+4 = 22
Lastly, we divide over the number of items (n = 7) to get the population variance: 22/n = 22/7 = 3.14 approximately
----------
Side note:
If you wanted the sample variance, then you divide over n-1 = 7-1 = 6
22/(n-1) = 22/6 = 3.67 is the approximate sample variance
What is the greatest common
factor of the expression?
2x^2y^3+4x^2y^5
Answer:
[tex]2x^2y^3[/tex]
Step-by-step explanation:
The given expression is :
[tex]2x^2y^3+4x^2y^5[/tex]
We need to find the greatest common factor of the expression.
The first term is [tex]2x^2y^3[/tex]
The other term is [tex]4x^2y^5[/tex]
[tex]2x^2y^3[/tex] is common in both terms. So,
[tex]2x^2y^3(1+2y^2)[/tex]
Hence, the greatest common factor of the expression is equal to [tex]2x^2y^3[/tex].
Ann bought 8 bottles of water and 4 sports drinks for $25. Blake bought 2 bottles of water and 9 sports drinks for $32.25. What was the cost of each bottle of water and each sports drink.
it think it is 10 or so but like just read or it and you will get it :)
Is the triangle a right angle? Pythagorean Theorem.
Answer:
yes it is
Step-by-step explanation:
hopefully that helps
195ft i think because 10 x 19.5
because 39 divided by 2 is 19.5
so then 19.5 x 10 = 195ft
In 24.736, which digit is in the thousandths place?
Answer:
6
Step-by-step explanation:
The third digit to the right of decimal point is in the thousandths place. The fourth digit to the right of decimal point is in the ten thousandths place and so on.
In the decimal number 24.736, the digit which is at the thousandth place will be 6.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We know that the number starts from the tenths after the decimal.
....123.456..
The expansion of the number is given as,
... + 100 + 20 + 3 + 0.4 + 0.05 + 0.006 + ......
The expansion is written in form of words. Then
Hundreds + Tens + Ones + Tenths + Hundredths, Thousandths, and so on.
In the decimal number 24.736, the digit which is at the thousandth place will be 6.
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Write the point-slope form of the equation for a line that passes through (-1, 4) with a slope of 2.
The value of xt is
The value of yn is
The point-slope form of the equation is
Answer:
67 f
Step-by-step explanation:
What is the value of f(6) in the function below?
fx) = 2x
Answer:
substitute that (6) in X so f(6) = 2(6) which is = 12
What is one way to determine if two fractions are equivalent?
Answer
Two fractions are equivalent fractions when they represent the same part of a whole. Since equivalent fractions do not always have the same numerator and denominator, one way to determine if two fractions are equivalent is to find a common denominator and rewrite each fraction with that denominator.
write a recursive formula for the following sequence 25,43,61,79,97
F(1)= 25
F(n)= F (n-1) +18
Given:
The sequence is:
25,43,61,79,97
To find:
The recursive formula for the given sequence.
Solution:
We have,
25,43,61,79,97
Here, the first term is 25. Now, the differences between the two consecutive terms are:
[tex]43-25=18[/tex]
[tex]61-43=18[/tex]
[tex]79-61=18[/tex]
[tex]97-79=18[/tex]
The differences between the two consecutive terms is common, i.e., 18. So, the given sequence is an arithmetic sequence.
The recursive formula of an arithmetic sequence is:
[tex]F(n)=F(n-1)+d[/tex]
Where, d is the common difference and F(1) is the first term.
Putting [tex]d=18[/tex], we get
[tex]F(n)=F(n-1)+18[/tex], where [tex]F(1)=25[/tex].
Therefore, the required recursive formula is [tex]F(n)=F(n-1)+18[/tex], where [tex]F(1)=25[/tex].
Marlene is trying to estimate v 42. She uses this table of values:
Square 6.02 6.12 6.22 6.32 6.42 6.52
Value
36.0 37.2 38.4 39.7 41.0 42.3
Square 6.62 6.72 6.82 6.92 7.02
Value
43.6 44.9 46.2 47.6 49.0
What should she do next to find 42 to the nearest hundredth?
A. She should find the squares of numbers between 6.4 and 6.5.
ООО
B. She should find the average of 6.4 and 6.5.
C. She should find the squares of numbers between 6.5 and 6.6.
O D. She should estimate that 42 is 6.50,
Answer:
A
Step-by-step explanation:
Did the quiz
Allison works at a Bank. Her employer offers her a retirement pension plan which will be 1.75% of her average salary for the last five years of employment for every year worked. Allison is planning on retiring after working at the Credit Union for 32 years. Her salaries over the last five years are $70,000; $73,100; $75,200; $77,500; and $79,000. Calculate Allison's annual pension.
9514 1404 393
Answer:
$41,977.60
Step-by-step explanation:
Allison's average salary for the last 5 years is ...
(70 +73.1 +75.2 +77.5 +79)/5 = 74.96 . . . . thousand dollars
Then her annual pension is ...
1.75% × $74,960 × 32 = $41,997.60
Can you help me with this question? 15 points and brainliest if right!
Answer:
3/4
Step-by-step explanation:
because it is a linear function it means it has the same slope in every point
so you have to take 2 points and find the slope
I take points (0,1) and (4,4)
m = (y2-y1) / (x2-x1)
note that it does not matter which points you chose to be second or first
m = (4-1) / (4-0) = 3/4
you can solve it from the graph too 3/4 is y/x it means for every 4 unit right move 3 units up
Question 2 of 20
Which of the following sets represents the range of the diagram below?
Answer:
D. {3, 5, 7}
Step-by-step explanation:
Sets of y-values or outputs of a relation of a function = the range
The outputs/y-values of the relation mapped above are what we have on our right hand, which area {3, 5, 7}
Therefore,
Range = {3, 5, 7}
I need this math problem to be solved ASAP!!! Solve for X.
-8x + 3 ≥ 27 AND −13x + 5 ≥ 57
Choose ONE and ONLY the CORRECT answer.
A: x ≤ −4
B: x ≤ −3
C: −4 ≤ x ≤ −3
D: There are NO solutions.
E: All values of X are solutions.
Answer:
A: x ≤ −4
Step-by-step explanation:
Hi there!
We're given the two inequalities -8x + 3 ≥ 27 and −13x + 5 ≥ 57
we need to find the set of solutions that make the two inequalities true (the intersection)
First, let's solve the two inequalities, starting with -8x + 3 ≥ 27
-8x + 3 ≥ 27
subtract 3 from both sides
-8x≥24
divide both sides by -8 and remember to FLIP the inequality sign, as we're dividing with a negative
x ≤ -3
now for the other inequality:
−13x + 5 ≥ 57
subtract 5 from both sides
-13x ≥ 52
divide both sides by -13 and remember to FLIP the sign
x ≤ -4
please see below for the graph to find the intersection, as well as the final answer
Hope this helps! :)
The function y = sin 2 (x – π∕2) has a period of Question 2 options: A) 4π. B) π. C) 2π. D) π∕2.
Answer:
B) π
Step-by-step explanation:
y = sin 2 (x – π∕2)
y = sin (2x -π)
=> 2x = 2π
x = π
The period of function sin(2x−π) is π, which is correct option(B).
What is the period of the function?The period of the function is defined as the interval between repetitions of any function. A trigonometric function's period is the length of one one completed cycle.
What is the Trigonometric functions?The trigonometric functions defined as the functions which show the relationship between angle and sides of a right-angled triangle.
Given the function as :
y = sin 2 (x – π/2)
y = sin (2x − π)
Use the form asin(bx−c) + d to determine the variables used to find the amplitude, period, phase shift, and vertical shift.
a = 1
b = 2
c = π
d = 0
Determine the period of sin(2x−π).
y = sin (2x -π)
So, the period = c = π
Hence, the period of function sin(2x−π) is π.
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Evaluatef(x) = 2.5x-11 when x = 4
Answer:
-1
Step-by-step explanation:
f(4) = 2.5(4) -11
f(4) = 10 -11
f(4) = -1
A pyramid with a square base, where the side length of the base is 7.2 cm and the height of the pyramid is 10.4 cm. Round your answer to the nearest tenth of a cubic centimeter.
Answer:2647.5
Step-by-step explanation:
What is the pattern?
2x = 3.5
3x = 2.5
4x = 2
5x = ?
6x = 1.6666
7x =
8x =
9x =
10x =
11x =
12x = 1.4166
Answer:
I don't know sorry for your right question ok
What is the domain of the function graphed below?
Answer:
x < 7
Step-by-step explanation:
the domain of a function defines the valid x values for the function.
as we go from left to right through all possible values of x, we see all values incl. x=-1 are creating a valid function result (y) for this function. until we reach x=7.
the empty ball indicates that there is no y value defined here. and for any value x>7 there is no y value defined.
so, x < 7 is the right one.
Answer: A
Step-by-step explanation:
Plz help i need a correct answer
Answer:-244
Step-by-step explanation:
I think you subtract -290 from -46.
Sorry If I am wrong.
========================================================
Explanation:
Imagine reflecting everything so that location A is above location B. Effectively all you're doing is erasing the negative signs.
That would place A at 290 feet and B would be at 46 feet. The difference in elevation is 290-46 = 244 feet
Instead of reflecting, you can turn the page upside down and just ignore the negative signs, and then subtract like normal.
This trick only works if both elevations A and B are below sea level.
--------
Or you could subtract like so:
|A-B| = |-290-(-46)| = |-290+46| = |-244| = 244
The absolute value is used to ensure the result is not negative. A negative difference makes no sense. In this case, "difference" and "distance" mean the same thing more or less.
What is the answer to this equation
Answer:
[tex]x = - \frac{494}{3}[/tex] [tex]= - 164\frac{2}{3}[/tex]
Step-by-step explanation:
[tex]75 + \frac{3}{8} x = 13\frac{1}{4}\\\\75 + \frac{3}{8} x = \frac{53}{4}\\\\\frac{3}{8}x = \frac{53}{ 4} - 75\\\\\frac{3}{8}x = \frac{53-300}{4}\\\\\frac{3}{8}x = - \frac{247}{4}\\\\x = -\frac{247 \times 8}{4 \times 3} \\\\x = -\frac{494}{3}[/tex]
Which score is better in terms of percentages: 12 out of 15 or 23 out of 26?
Answer:
23/26 is a greater percentage, it equals around 88% while 12/15 equals 80%
Step-by-step explanation:
Fractions are hard... Or I'm just to lazy to try and do them.
The height of a triangle is 4 m more than twice the length of the base. The area of the triangle is 35 m^2 . Find the height of the triangle
Answer:
Step-by-step explanation:
Let the Base of the △ be x
Then the Height will be 2 x + 4
Area of △ = 1 2 b h
Where, b = b a s e , h = h e i g h t , A r e a = 35
(in this case)
Substitute the values into the equation → 35 = 1 2 ( 2 x + 4 ) ( x ) → 35 = ( 2 x + 4 ) 2 ( x ) →
35 = ( x + 2 ) ( x ) → 35 = x 2 + 2 x
Subtract 35 both sides
→ 0 = x ^2 + 2 x − 35
Rewrite the equation in the Standard form
x ^2 + 2 x − 35 = 0
Factor the equation
→ ( x + 7 ) ( x − 5 ) = 0
So we have
x = − 7 , 5
numbers So x = 5
They have asked us to find the Height
So, ⇒ H e i g h t = 2 x + 4 = 2
what is the solution
Answer:
c 13 over 12
Step-by-step explanation:
it help I makeit