Answers
Step-by-step explanation:
[tex] \sin( \frac{ \alpha }{2} ) = \sqrt{ \frac{1 - \cos( \alpha ) }{2} } [/tex]
So let find cos
We know that
[tex] \tan {}^{2} (x) + 1 = \sec {}^{2} (x) [/tex]
We know the value of tan
[tex]( \frac{8}{5} ) {}^{2} + 1 = \sec {}^{2} (x) [/tex]
[tex] \frac{64}{25} + 1 = \sec {}^{2} (x) [/tex]
[tex] \frac{89}{25} = \sec {}^{2} (x) [/tex]
[tex] \frac{ \sqrt{89} }{5} = \sec(x) [/tex]
Sec is the reciprocal of cosine so cosine is
[tex] \cos( \alpha ) = \frac{5}{ \sqrt{89} } [/tex]
Which becomes
[tex] \cos( \alpha ) = \frac{5 \sqrt{89} }{89} [/tex]
So since we know cos a, let's find sin
[tex] \sqrt{ \frac{1 - \frac{5 \sqrt{89} }{89} }{2} } [/tex]
[tex] \sqrt{ \frac{89 - 5 \sqrt{89} }{2} } [/tex]
Related Questions
Can any one help with me please
Answers
Answer:
85
Step-by-step explanation:
The vertical line that y is on adds up to 180 so if we take 180 - the number we already know (95) we get 85
why is your answer to part (a) approximately correct even though the population distribution of diameters is clearly not normal? would the same approach be equally valid for a sample of size 2 rather than 25? why or why not?
Answers
In part (a), we used the Central Limit Theorem (CLT) to approximate the sampling distribution of the sample mean. The CLT states that, under certain conditions, the sampling distribution of the sample mean will be approximately normal, regardless of the population distribution.
The conditions for the CLT are:
The sample is randomly drawn from the population.
The sample size is large (usually, n >= 30 is considered large enough).
The samples are independent.
In this case, we assume that the sample was randomly drawn from the population of diameters, and the sample size of 25 is large enough to satisfy the second condition. The samples are assumed to be independent, as we are sampling without replacement from a large population.
Therefore, we can apply the CLT and use the normal distribution to approximate the sampling distribution of the sample mean.
For a sample of size 2, the sample mean will still have a sampling distribution, but the CLT may not be applicable. If the population distribution is highly skewed or has heavy tails, a sample size of 2 may not be sufficient to smooth out the sampling distribution, and it may not be normal.
In this case, a normal approximation may not be appropriate, and other methods, such as bootstrapping or permutation tests, may be more appropriate for inference.
In summary, the normal approximation based on the CLT is valid for large sample sizes, regardless of the population distribution. For small sample sizes, other methods may be more appropriate, and the normal approximation may not be valid if the population distribution is highly skewed or has heavy tails.
Question: The basal diameter of a sea anemone is an indicator of its age. The density curve shown here represents the distribution of diameters in a certain large population of anemones; the population mean diameter is 4.2cm, and the standard deviation is 1.4cm.
Let Y dash represent the mean diameter of 25 anemones randomly chosen from the population.
(a) Find the approximate value of Pr{4 ≤ Ydash ≤ 5}.
(b) Why is your answer to part (a) approximately correct even though the population distribution of diameters is clearly not normal? Would the same approach be equally valid for a sample of size 2 rather than 25?Why or why not?
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uppose that a particular nba player makes of his free throws. assume that late in a basketball game, this player is fouled and is awarded two free throws. a. what is the probability that he will make both free throws? (to 4 decimals) b. what is the probability that he will make at least one free throw? (to 4 decimals)
Answers
Answer:
a. 0.81
b. 0.81
Step-by-step explanation:
Let's assume that the player makes x% of his free throws. Then, the probability that he will make both free throws is (x/100)^2, and he will make at least one free throw is 1 - (1 - x/100)^2.
So if he makes 90% of his free throws, then:
a. The probability that he will make both free throws is (90/100)^2 = 0.81.
b. The probability that he will make at least one free throw is 1 - (1 - 90/100)^2 = 1 - (1 - 0.9)^2 = 1 - 0.19 = 0.81.
The answers to the questions rounded to 4 decimal places are:
a. 0.81
b. 0.81
A Smoothie is mixed with strawberries and bananas in the ratio 7:3. Gill
makes a smoothie using 144g of bananas. How many grams of
Strawberry does she use?
Answers
Answer: et's call the amount of strawberries Gill uses "x" grams. We know that the ratio of strawberries to bananas is 7:3, so we can set up an equation:
x/144 = 7/3
To solve for x, we'll multiply both sides of the equation by 144:
x = 7/3 * 144
x = 7 * 48
x = 336
So Gill uses 336 grams of strawberries in the smoothie.
Step-by-step explanation:
help with question 17
Answers
Answer:
hundredths
Step-by-step explanation:
PLEASE HELP!!! ITS DUE SOON!
Answers
The solutions to the system of linear equation (x, y) are 1 and 4/3 respectively
What is system of linear equationA system of linear equations is a collection of two or more linear equations with the same variables. The goal of solving a system of linear equations is to find the values of the variables that simultaneously satisfy all the equations in the system.
From the question given;
-x + 6y = 7 ...eq(i)
6x - 30y = -34 ...eq(ii)
From eq (i)
x = 6y - 7 ..eq (iii)
Put eq (iii) into eq (ii)
6(6y - 7) - 30y = -34
36y - 42 - 30y = -34
6y - 42 = -34
6y = -34 + 42
6y = 8
y = 4/3
Put y = 4/3 into eq (i)
-x + 6(4/3) = 7
-x + 24 / 3 = 7
x = 24/3 - 7
x = 1
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Question 7 (Mandatory) (1 point)
Which point is on the graph of y = -2x + 1?
Answers
Answer:
y-intercept: (0,-1)
Step-by-step explanation:
please verify
how many such strings are if 2 of the ones are to be next to each other and the third is not next to the other two?
Answers
The number of strings where exactly two of the ones are next to each other, while the third one is not next to the other two, is (n-1) x (n-2).
In combinatorics, one of the fundamental concepts is counting the number of strings or sequences of symbols that satisfy certain conditions.
Let us first consider the case where the two ones that are next to each other are at the beginning of the string. In this case, we can place the third one in any of the remaining positions, which are n-2, where n is the total length of the string. Therefore, the number of such strings is (n-2).
Similarly, if the two ones are at the end of the string, we can place the third one in any of the n-2 remaining positions, and the number of such strings is again (n-2).
Now let us consider the case where the two ones are in the middle of the string. In this case, we can place the two adjacent ones in (n-2) ways, and the third one can be placed in any of the remaining n-3 positions, since it cannot be adjacent to the other two ones. Therefore, the number of such strings is (n-2) x (n-3).
To get the total number of strings that satisfy the given condition, we need to add up the number of strings in each of the three cases:
Total number of strings = (n-2) + (n-2) + (n-2) x (n-3)
Simplifying this expression, we get:
Total number of strings = (n-1) x (n-2)
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Graph the inequality below on the number line. a<3
Answers
The number line for a < 3 is as shown in the figure below and we use an open circle on 3 and all the numbers to the left of 3 in the number line will be the values of a.
What is a number line?
A number line is a representation of a graduated straight line that is used to represent real numbers visually. It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point. The endpoints of this line go on forever.
We can see the values that inequality represents by placing them on a number line. On a number line, inequalities are represented by drawing a straight line and designating the endpoints with either an open or closed circle. An empty circle indicates that the value is not included. A closed circle indicates that the value is included.
Given the inequality a < 3.
This means that the value of a is less than three and does not include three.
Therefore we use an open circle on 3 and all the numbers to the left of 3 in the number line will be the values of a.
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marvin the fly starts at $(0,0).$ each step, marvin moves one unit right or one unit up. he is trying to get to his home at $(4,6)$. however, at $(1,4),$ there is a frog that will eat him if he goes through that point. in how many ways can marvin reach his home?
Answers
There are 50 ways for Marvin to reach his destination without passing through the forbidden point.
To solve this problem, we can use the unitary method. This method involves breaking the problem down into smaller, simpler units to solve it more easily.
In this case, we can break the path from Marvin's starting point to his destination into two smaller paths. The first path is from (0,0) to (1,4), and the second path is from (1,4) to (4,6).
There are five paths from the bottom left corner to the point (1,4) that do not go through the forbidden point.
Once Marvin reaches the point (1,4), he can only go up or to the right to reach his destination. So, we need to count the number of ways to get from (1,4) to (4,6)
We can visualize this by drawing another grid and counting the paths:
In total, there are
=> 5 x 10 = 50
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AB and BC form a right angle at point B. If A= (-3,-1) and B=(4,4), what is the equation of BC
Answers
Answer: AB and BC form a right angle at point B, so BC is perpendicular to AB. To find the equation of BC, we can use the slope-point formula, which is y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line.
The slope of a line perpendicular to AB can be found by finding the negative reciprocal of the slope of AB. To find the slope of AB, we need to find the difference in the y-coordinates and divide it by the difference in the x-coordinates:
m_AB = (y2 - y1) / (x2 - x1)
= (4 - (-1)) / (4 - (-3))
= 5 / 7
The slope of a line perpendicular to AB is the negative reciprocal of m_AB:
m_BC = -1 / m_AB = -1 / (5/7) = -7/5
Now that we have the slope of BC, we can use the slope-point formula to find the equation of BC. We'll use the point B = (4, 4) as (x1, y1):
y - 4 = -7/5 (x - 4)
y = -7/5 x + 4(7/5) + 4
y = -7/5 x + 36/5
So the equation of BC is y = -7/5 x + 36/5.
Step-by-step explanation:
A newspaper randomly chooses 100 names from it's subscriber database and then survey's those subscribers to find if they read the restaurant review is this biased or non biased
Answers
Answer:
Non biased (kind of)
Step-by-step explanation:
It depends on how they randomly chose but if it was truly random it would be non biased as many people will read newspapers for things such as sports or catalogs
Which choice best describes EB
radius
diameter
Line F
Point
Answers
The best describes EB is diameter of circle because it is a chord of circle which passes through the center.
What is a circle?A circle is a two-dimensional object made up of points that are spaced out from a given point (centre) on the plane by a fixed or constant distance (radius). The fixed point is referred to as the circle's origin or centre, and the fixed distance between each point and the origin is referred to as the radius.
The following components make up a circle:
Circumference: Also known as a circle's perimeter, circumference is the distance a circle travels around its circumference.
Radius: The radius is the distance a circle's center is from any point on its edge.
A diameter is a straight line that links two places on the circle's edge and passes through the center.
So that EB is describes as diameter of circle because it is a chord of circle which passes through the center.
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How would you translate a real world verbal expression into an algebraic expression?
Answers
The Translation to algebraic expression is shown below.
What is Expression?A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.Given:
To create a variable expression for a circumstance in the actual world:
Determine which quantity is unknown in the circumstance, then define a variable to represent it.To reflect the circumstance, create an expression utilising the variable. To determine what mathematical procedures to apply, look for essential words.For example, the sum of a and b can be written as
= a+ b
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What number is 30% less than 40?
Answers
Answer: 30% less than 40 is 28
Step-by-step explanation:
Answer:
The answer is 28.
Step-by-step explanation:
I'm bad at proving stuff but that's the answer I promise. (quick tip, you are more likely to get answers if you give more points. :D)
Lisa's average score on 4 tests is 82. What does she need to score on her fifth test to have an average final score of 85?
Answers
Answer:
Lisa would need to score 97 on her 5th test.
Step-by-step explanation:
If Lisa has an average score of 82 on 4 tests, then the total sum of her scores would be 82 multiplied by 4, which is equal to 328.
If she wants an average final score of 85 over 5 tests, then the total sum of her scores needs to be 425 (i.e. 85 multiplied by 5).
To determine what she needs to get on her 5th test we need to subtract 328 from 425.
425 - 328 = 97
Can somebody please look at the picture and help me pleaseeeeeeee
Answers
The equation 2 and 3 would not present linear functions.
What is linear function?
A linear function is one in which the maximum power of the variables is one.
A linear function is a function that has the form f(x) = mx + b, where m and b are constants. In other words, a linear function is a straight line when plotted on a graph.
Out of the given relationships, the following do not represent a linear function:
2) The ant population for a colony that begins with 5 ants and doubles in number every two weeks.
This relationship is not linear because the rate of change (the number of ants per unit time) is not constant. The number of ants increases exponentially, which results in a curve rather than a straight line when plotted on a graph.
3) A history student's grade on a test that begins at 100 but decreases by 4 points for each question answered incorrectly.
This relationship is not linear because the rate of change (the decrease in points per incorrect question) is not constant. The decrease in points results in a curve rather than a straight line when plotted on a graph.
The other two relationships do represent linear functions.
Therefore, The equation 2 and 3 would not present linear functions.
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Tell whether the point lies on the graph of the line 2x+6y=26
A. (-8,7) YES/NO?
B. (-1,4) YES/NO?
C. (2,5) YES/NO?
D. (4,3) YES/NO?
E. (16,1) YES/NO?
Answers
Answer: Yes, No, No, Yes, No
Step-by-step explanation:
I think Graphing is the best way to tackle this. But I prefer algebra:
A) 2(-8) + 6(7) = 26
-16 + 42 = 26
26 = 26
The answer for A is Yes. I wont show work for the others, i think its pretty intuitive, (just substitute the coordinates for x and y, and check if the resulting statement is true)
B. No
C. No
D. Yes
E. No
Write as an algebraic expression: five times the difference between six less than a number
Answers
The algebraic expression is,
⇒ 5 (6 - n)
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ five times the difference between six less than a number.
Now, Let a number = n
Hence, We can formulate;
⇒ 5 (6 - n)
Thus, The value of expression is,
⇒ 5 (6 - n)
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73.
ILLUSTRATION 7
Find a. the length and b. the diameter of the shaft in
Answers
In the illustration given above, the length and the diameter of the shaft would be = 21.8 in and 7/8 in respectively.
How to calculate the total length of the shaft?The total length of the shaft can be calculated through the addition of the various given lengths along the shaft such as follows:
= 5⅛ + 5 + 7⅝ + 4 1/16
First convert all the mixed fraction into single fraction;
= 41/8 + 5/1 + 61/8 + 65/16
= 82+80+122+65/16
= 349/16
= 21.8 in.
The diameter of the shaft can be calculated as follows;
= 7¼ - (3 3/16 + 3 3/16 )
First convert all the mixed fraction into single fraction;
= 29/4 - (51/16 + 51/16)
= 29/4 - 102/16
= 116-102/16
= 14/16
= 7/8 in.
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A water bottle holds 72 ounces of water. How many cups does the water bottle hold? (1 cup = 8 fluid ounces) 4 cups 8 cups 9 cups 64 cups
Answers
Answer:
9 cups
Step-by-step explanation:
1 cup is 8 ounces
72/8 is 9
What is the value of x for each question? Step by step please.
-1/2-4x/5=1/2-2x
7x²+9x²=-6x²-7x
-7x²+6=x²-7x²
Answers
Answer:
-1/2-4x/5=1/2-2x
Starting from the left side, we can simplify:
-1/2 - 4x/5 = 1/2 - 2x
Next, we can isolate x by adding 2x to both sides:
-1/2 - 4x/5 + 2x = 1/2 - 2x + 2x
-1/2 + 2x/5 = 1/2
Adding 1/2 to both sides:
0 + 2x/5 = 1
Finally, solving for x:
2x/5 = 1
Multiplying both sides by 5:
2x = 5
Dividing both sides by 2:
x = 5/2
7x² + 9x² = -6x² - 7x
Combining like terms:
16x² = -6x² - 7x
Adding 6x² to both sides:
22x² = -7x
Dividing both sides by -7:
-22x²/-7 = 7x/-7
-22x²/7 = -7x/7
-22x²/7 = -x
Multiplying both sides by -7:
22x² = x
Dividing both sides by 22:
x² = x/22
Since this equation states that x² equals x divided by 22, it has no real solutions for x.
-7x² + 6 = x² - 7x²
Combining like terms:
-8x² + 6 = 0
Adding 8x² to both sides:
-8x² + 8x² + 6 = 0 + 8x²
6 = 8x²
Dividing both sides by 8:
6/8 = 8x²/8
3/4 = x²
Taking the square root of both sides:
sqrt(3/4) = sqrt(x²)
x = +/- sqrt(3/4)
i need help with this one?
Answers
The best description of the transformation for the image being projected on the retina is A. A dilation with a scale factor between 0 and - 1 and center at the nodal point.
How does the nodal point dilate the retina ?An mage is inverted and reversed as it passes through the lens of the eye, and is then projected upside down and reversed onto the retina. The process of transforming the image is called "rectification."
In mathematical terms, a dilation would have taken place because the object was shrunken by the eyes at the nodal point. When an object shrinks , then the scale factor is between 0 and 1 but because this image is inverted, the scale factor is between 0 and - 1.
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What is the total number of digits used to number 1200 pages?
Answers
Answer:
The correct answer would be 3693
Step-by-step explanation:
9 + 180 + 2,700 + 804
3693
1200 pages were numbered using a total of 3693 digits.
What is total number?The word "total" refers to the addition of numbers or the destruction of something, and a total is a whole or complete sum. In mathematics, adding two or more numbers yields the sum. When you multiply 8 by 8, you get 16.the total of the acquisition's purchase price plus all future expenses that will be spent, including those for installation, consumables, breakdown, maintenance, and disposal. The sum is the outcome or conclusion of adding two or more numbers or phrases. As a result, the sum is a means of assembling objects. In other terms, the process of adding two or more numbers together to create a new result or total is known as the sum.Total digits equal = the digits in the 1 - digit page numbers + the 2 digit page numbers - digit page numbers + 3 digit page numbers - digit page numbers.
Then simplify,
9 + 180 + 2,700 + 804
= 3693
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6x + 24/5x - 35 times 9x - 63/7x + 28 rational expression
Answers
Answer:
Step-by-step explanation:
6(x + 4)/5(x - 7) * 9(x - 7)/7(x + 4) =
Cancel the x + 4 and x - 7
54/35
5x5+67-85=
PLS HURRY
Answers
Answer:
7
Step-by-step explanation:
We start doing the multiplication, and [tex]5 \cdot 5 = 25[/tex]. So we can rewrite it as [tex]25 + 67 - 85.[/tex] Now we work from left to right, where we calculate [tex]25 + 67 = 92[/tex]. Now the final step, [tex]92 - 85 = 7.[/tex] Therefore, the answer is [tex]\boxed{7.}[/tex]
Answer:
sry for being late the answer is 7……I did it in my head and double checked with a calculator. Go ahead and give the other person brainliest they did it first! Hope I helped to!!
Step-by-step explanation:
Can some one help sovle this?
-
Answers
By using the graph of the piecewise function we can see that:
f(0) = 0.
How to find the value of f(0)?Here we have the graph of a piecewise function, and we want to find the function when x = 0.
Remember that on a graph, an open circle means that the value does not belong to the graph, while a closed circle means taht the value belongs to the graph.
Here we can see that the closed circle at x = 0 is on the line at the middle, then we can conclude that f(0) = 0.
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Emma is starting a cupcake business and borrows money from Dixons dynamite deals (DDD) .she agrees to pay back the loan after 10 years by making one payment of 80,000 , interest is compounded and fixed at 14,6% per annum.hpw much did emma borrow from (DDD) ?
Answers
The amount (present value) that Emma borrowed from Dixons Dynamite Deals (DDD) to repay after 10 years with a one-time payment of $80,000 at 14/6% compounded interest per annum is not more than $20,475.94.
Step-by-step explanation:
To find out how much Emma borrowed from Dixons Dynamite Deals (DDD), we can use the formula for the future value of a loan with compound interest:
Future Value (FV) = Principal Amount (P) * (1 + r)^n
Where:
P = Principal amount (the amount borrowed)
r = Interest rate per period (in decimal form)
n = Number of periods
In this case:
Future Value (FV) = $80,000 (the payment Emma will make after 10 years)
Interest rate (r) = 14.6% per annum = 0.146 (in decimal form)
Number of periods (n) = 10 years
Now, let's calculate the principal amount (P):
$80,000 = P * (1 + 0.146)^10
Now, let's solve for P:
P = $80,000 / (1.146)^10
P ≈ $80,000 / 2.97804
P ≈ $26,874.94
So, Emma borrowed approximately $26,874.94 from Dixons Dynamite Deals (DDD) to start her cupcake business.
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A rectangle has a length of ( + ) and a width of ( − ). Determine the expression that represents the area of this rectangle.
Answers
Answer:
Step-by-step explanation:
The expression that represents the area of a rectangle with length (l) and width (w) is given by:
A = l * w
Therefore, the expression that represents the area of a rectangle with a length of ( + ) and a width of ( − ) can be represented as:
A = ( + ) * ( − ) = + × − = + (−) = −.
which expression is equivalent to 5^6
a.125 x 125 b. 6 x 5 c. 35 x 6 x 6 x 6 d. 25 x 5 x 5 x 5
Answers
The expression that is equivalent to 5^6 is A.125 x 125
What are index forms?Index forms are defined as mathematical forms of writing numbers that are too large or small in more convenient forms.
Other terms for index forms are called standard forms or scientific notations.
They are also described as numbers or variables that are raised to an exponent.
From the information given, we have that;
5⁶
This is replicating 5 in 6 places, we have the representation as;
5 × 5 × 5 × 5 × 5 × 5
Hence, the expression is 125 x 125
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