Order (B) 5 × 6 of the matrix can be multiplied by matrix a to create matrix ab.
What is a matrix?A matrix is a rectangular array or table of numbers, symbols, or expressions that are organized in rows and columns to represent a mathematical object or an attribute of such an object in mathematics. For instance, consider a matrix with two rows and three columns.To find the order of matrix:
We must first check the dimension of two matrices, say matrix A by matrix B, before we may multiply them.Multiplication is achievable if the number of columns in the first matrix, A, equals the number of rows in the second matrix.Dimension is assigned to the provided matrix: 6 × 5This means the given matrix contains six rows and five columns.As a result, the second matrix MUST have 5 rows in order for multiplication to be POSSIBLE.The only matrix with 5 rows among the above alternatives is the matrix with dimension (B) 5 × 6.To prove:
In other words, the inner products of the dimensions should be equal.That is; (a × b)(b × a) is possible but (a ×b)(c × b) is impossible.The dimensions of the matrix are given by, row × column.Therefore, order (B) 5 × 6 of the matrix can be multiplied by matrix a to create matrix ab.
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Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer:
[tex]\displaystyle{f(x) = -2(x-3)^2 + 2}[/tex]
Step-by-step explanation:
To find y-intercept of a graph, we have to substitute x = 0 to find it - consider each functions:
First Choice
[tex]\displaystyle{f(x) = 2x(x+14)-64}\\\\\displaystyle{f(0) = 2\cdot 0(0+14)-64}\\\\\displaystyle{f(0) = 0\cdot 14-64}\\\\\displaystyle{f(0) = -64}[/tex]
Second Choice
[tex]\displaystyle{f(x) = (x+4)^2+2x}\\\\\displaystyle{f(0) = (0+4)^2 + 2(0)}\\\\\displaystyle{f(0) = 4^2}\\\\\displaystyle{f(0) = 16}[/tex]
Third Choice
[tex]\displaystyle{f(x) = (x-16)^2 + 4}\\\\\displaystyle{f(0) = (0-16)^2 + 4}\\\\\displaystyle{f(0) = (-16)^2 + 4}\\\\\displaystyle{f(0) = 256 + 4}\\\\\displaystyle{f(0) = 260}[/tex]
Fourth Choice
[tex]\displaystyle{f(x) = -2(x-3)^2 + 2}\\\\\displaystyle{f(0) = -2(0-3)^2 + 2}\\\\\displaystyle{f(0) = -2(-3)^2 + 2}\\\\\displaystyle{f(0) = -2\cdot 9 + 2}\\\\\displaystyle{f(0) = -18+2}\\\\\displaystyle{f(0) = -16}\\[/tex]
Therefore, fourth choice is correct.
5.
A section of a tessellated plane is shown. Which type of symmetry does the tessellated plane have?
The tessellated plane has translational symmetry option (A) translational symmetry is correct.
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
A geometric figure is given:
As we know, from geometric transformation, geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, etc.
Without any further changes, the tessellated plane is moved a few units to the right. If the translated plane is again moved left by the same amount of units, we will once more obtain the original plane. Translational symmetry is present as a result.
Thus, the tessellated plane has translational symmetry option (A) translational symmetry is correct.
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Suppose your parents decide to give you $10,000 to be put in a college trust fund that will be paid in equally quarterly installments over a 5 year period. If you deposit the money into an account paying 1.5% per quarter, how much are the quarterly payments (Assume the account will have a zero balance at the end of period.)
The quarterly annuity payment is $582.46.
What is an ordinary annuity?
An ordinary annuity in case of investment is the one that pays its end-of-the period cash flows rather than at the beginning as it is case of annuity due.
The applicable formula in this case is the present value formula of an ordinary annuity as shown below:
PV=quarterly payment*(1-(1+r)^-N/r
PV=initial investment=$10,000
quarterly payment=unknown(assume it is X)
r=quarterly interest rate=1.5%
N=number of quarterly payments in 5 years=5*4=20(there are 4 quarterly payments in a year)
$10,000=X*(1-(1+1.5%)^-20/1.5%
$10,000=X*(1-(1.015)^-20/0.015
$10,000=X*(1-0.742470418223773)/0.015
$10,000=X*0.257529581776227/0.015
X=$10,000/(0.257529581776227/0.015)
X=quarterly payment=$582.46
Note that the unknown in this case is the annuity payment, the present value can also be the unknown as well.
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Testing: h 0 : p = 0. 74 h0:p=0. 74 h α : p < 0. 74 hα:p<0. 74 your sample consists of 43 subjects, with 33 successes. calculate the test statistic
Test statistic is 0.42.
Given
Testing:
h0 : p = 0.74
h1 : p < 0.74
Successes x = 33
Subject n = 43
A test statistic is a number calculated by a statistical test. It describes how far your observed data is from the null hypothesis of no relationship between variables or no difference among sample groups.
It measures the accuracy of the predicted data distribution relating to the null hypothesis you use when analyzing data samples.
Test statistics z = [tex]\frac{p_{hat} - p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]
Where [tex]p_{hat}[/tex] = Sample proportion = [tex]\frac{x}{n}[/tex]
p = population proportion
n = sample size
z = [tex]\frac{(\frac{33}{43})-0.74 }{\sqrt{\frac{0.74(1-0.74)}{43} } }[/tex]
z = 0.42
Hence,
Test statistics is 0.42..
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A parabola can be represented by the equation y2 = 12x. which equation represents the directrix?
The equation of the directrix is x = -3
What is Parabola?A mirror-symmetrical, roughly U-shaped plane curve known as a parabola. It corresponds to a number of mathematical models that appear to be superficially dissimilar but yet all define the exact same curves. A point and a line are one way to describe a parabola.
According to the given information:Given the general equation of a parabola expressed as
(y-y0)² = 4a(x-x0) ... 1
Equation of the directrix will be expressed as x = x0 - a
From the equation given;
y² = 12x ... 2
Comparing 1 and 2;
x - x0 = x
-x0 = x - x
-x0 = 0
x0 = 0
Similarly;
y-y0 = y
-y0 = y - y
-y0 = 0
y0 = 0
Also;
4a = 12
a = 12/4
a = 3
Substituting x0 =0, y0 = 0 and a = 3 into the equation of the directrix above, we will have;
x = x0 - a
x = 0 - 3
x = -3
Hence,
the equation of the directrix is x = -3
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.
Let’s assume the following statements are true: Historically, 75% of the five-star football recruits in the nation go to universities in the three most competitive athletic conferences. Historically, five-star recruits get full football scholarships 93% of the time, regardless of which conference they go to. If this pattern holds true for this year’s recruiting class, answer the following:
a. Based on these numbers, what is the probability that a randomly selected five-star recruit who chooses one of the best three conferences will be offered a full football scholarship?
b. What are the odds a randomly selected five-star recruit will not select a university from one of the three best conferences? Explain.
c. Explain whether these are independent or dependent events. Are they Inclusive or exclusive? Explain.
The probability that a randomly selected five-star recruit who chooses one of the best three conferences will be offered a full football scholarship is 69.75%.
What is the computation for the above solution?
Note that this is simple probability.
Hence probability of the 75% football starts selected randomly where the chance is 93% =
75% x 93%
= 69.75%
What are the odds a randomly selected five-star recruit will not select a university from one of the three best conferences?The chance that 25% of the five-star recruit will not select a university form one of the three best conferences is explained as follows:
Because only 75% stand the chance of being selected into the three ivy leagues, this means that 25% stand no chance.
Recall that the total population is 100%.
Are these are independent or dependent events. Are they Inclusive or exclusive?From the statement of problem given, it is clear that the events are mutually exclusive. Recall "Historically, five-star recruits get full football scholarships 93% of the time, regardless of which conference they go to.
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which of the tables represent a function??
please help me! asap!
Identify the side lengths of the triangle.
The figure shows an isosceles triangle. One of the congruent sides has a length of 3 x plus 4 units. The other congruent side has a length of x plus 12 units. The third side has a length of 4 x minus 10 units.
The side lengths of the isosceles triangle are:
AO = 16 units
AB = 16 units
OB = 6 units.
What is an Isosceles Triangle?An isosceles triangle is a type of triangles that has two sides that are congruent to each other, and two base angles that are opposite these two sides that are also congruent to each other.
How to Identify the Side lengths of the Triangle?Referring to the isosceles triangle in the image attached below, we have the following:
One of the congruent sides = AO = 3x + 4 units
The other congruent side = AB = x + 12 units
The third side = OB = 4x - 10 units
Applying the definition of an isosceles triangle, we can create an equation as shown below to find x:
AO = AB [congruent sides]
Substitute
3x + 4 = x + 12
3x - x = - 4 + 12
2x = 8
2x/2 = 8/2
x = 4
Find the side lengths of the isosceles triangle by plugging in the value of x:
One of the congruent sides = AO = 3x + 4 = 3(4) + 4 = 16 units
The other congruent side = AB = x + 12 = 4 + 12 = 16 units
The third side = OB = 4x - 10 = 4(4) - 10 = 6 units.
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Geometry: complete this proof (ASAP! It’s urgent)
Answer:
1. <1 ~= <4 (Given)
2. <2 is supplementary to <1; <3 is supplementary to <4 (Because <1 & <2, <3 and <4 form linear pairs, they are supplementary by the linear pair postulate.)
3. <2 ~= <3 (By the definition of supplementary angles, m<1 + m<2 = 180 and m<3 + m<4 = 180. By definition of congruent angles, m<1 = m<4, therefore m<2 = m<3 by substitution property of equality.)
4. AB ~= BC (Converse of Isosceles Triangles Theorem)
5. Triangle ABC is isosceles (Definition of Isosceles Triangles)
(3-4^2)^2+8
Bdhdhdhsjsjsj
Answer: 177
Step-by-step explanation:
1. 4x4=16
(3-16)^2+8
2. 3-16=-13
(-13)^2+8
3. -13x-13=169
169+8
4.169+8=177
177
Answer:
177
Step-by-step explanation:
PEMDAS
The PEMDAS rule is an acronym representing the order of operations in math:
ParenthesesExponentsMultiplication and Division (from left to right)Addition and Subtraction (from left to right)Given expression:
[tex](3-4^2)^2+8[/tex]
Parentheses
Begin by calculating the part inside the parentheses.
Following PEMDAS, calculate the exponent first:
[tex]\implies (3-4^2)^2+8=(3-16)^2+8[/tex]
Then carry out the subtraction:
[tex]\implies (3-16)^2+8=(-13)^2+8[/tex]
Exponents
[tex]\textsf{Apply the exponent rule}: \quad (-a)^n=a^n, \quad \textsf{if }n \textsf{ is even}[/tex]
[tex]\implies (-13)^2+8=169+8[/tex]
Addition
[tex]\implies 169+8=177[/tex]
Therefore:
[tex]\implies (3-4^2)^2+8=177[/tex]
Use the laplace transform to solve the given initial-value problem. y'' + y = f(t), y(0) = 0, y'(0) = 1, where f(t) = 0, 0 ≤ t < 1, ≤ t < 2 0, t ≥ 2
In order to solve this IVP using Laplace transforms, we must first write f(t) in terms of the Heaviside function.
f(t)=0*(u(t)-u(t-Pi))+1*(u(t-Pi)-u(t-2Pi))+0*(u(t-2Pi))
f(t)=u(t-π)-u(t-2π)
So, the rewritten IVP is
y'' +y = u(t-π)-u(t-2π)y(0)=0, y'(0)=1
Taking the Laplace transform of both sides of the equation, we get:
s2L{y}-sy(0)-y'(0)+L{y}=(1/s)*e-πs-(1/s)*e-2πs
s2L{y}-1+L{y}=(1/s)*e-πs-(1/s)*e-2πs
(s2+1)L{y}=1+(1/s)*e-πs-(1/s)*e-2πs
L{y}=1/(s2+1)+(1/s(s2+1))e-πs-(1/s(s2+1))*e-2πs
Now, we must take the inverse transform of both sides to solve for y.
The first inverse transform is easy enough. By definition, it is sin(t).
The second two inverse transforms will be a little tougher, we will have to use partial fraction decomposition to break them down into terms that are easier to compute.
A/s+(Bs+C)/(s^2+1)=1/(s(s^2+1))
A(s^2+1)+(Bs+C)(s)=1
As^2+A+Bs^2+Cs=1
Rewriting this system in matrix form, we get:
1 1 0 A 0
0 0 1 * B = 0
1 0 0 C 1
Using row-reduction we find that A=1, B=-1, and C=0. So, our reduced inverse transforms are:
L-1{(e-πs)(1/s-s/(s2+1))}
and
L-1{(e-2πs)(1/s-s/(s2+1))}
Using the first and second shifting properties, these inverse transforms can be computed as.
L-1{(e-πs)(1/s-s/(s2+1))}=u(t-π)-cos(t-π)u(t-π)
L-1{(e-2πs)(1/s-s/(s2+1))}=u(t-2π)-cos(t-2π)u(t-2π)
Combining all of our inverses transforms, we get the solution the IVP as:
y=sin(t)+u(t-π)-cos(t-π)u(t-π)+u(t-2π)-cos(t-2π)u(t-2π)
In mathematics, the Laplace transform, named after its discoverer Pierre Simon Laplace (/ləˈplɑːs/), transforms a function of real variables (usually in the time domain) into a function of complex variables (in the time domain). is the integral transform that Complex frequency domain, also called S-area or S-plane).
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How do you construct a frequency distribution table using sturge’s approximation
The steps to use to construct a frequency distribution table using sturge’s approximation is as below.
How to construct a frequency distribution table?The steps to construct a frequency distribution table using Sturge's approximation are as follows;
Step 1: Find the range of the data: This is simply finding the difference between the largest and the smallest values.
Step 2; Take a decision on the approximate number of classes in which the given data are to be grouped. The formula for this is;
K = 1 + 3.322logN
where;
K= Number of classes
logN = Logarithm of the total number of observations.
Step 3; Determine the approximate class interval size: This is obtained by dividing the range of data by the number of classes and is denoted by h class interval size
Step 4; Locate the starting point: The lower class limit should take care of the smallest value in the raw data.
Step 5; Identify the remaining class boundaries: When you have gotten the lowest class boundary, then you can add the class interval size to the lower class boundary to get the upper class boundary.
Step 6; Distribute the data into respective classes:
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There are 3 red, 1 blue, and 2 yellow marbles in a bag. Once a marble is selected, it is not replaced. Find P(red and the yellow).
Answer:
5/6
Step-by-step explanation:
we add all the marbles together to get 6
then we seperate the marbles according to the question which would be yellow and red. that would make the probability of getting one of those to 5/6. Hope this helps :)
Jessica's dog weighed 91.5 pounds at the beginning of summer but lost 5.2
pounds by the end of summer. Which number sentence could be used to
determine the dog's weight at the end of the summer?
Answer:
91.5 - 5.2 = 86.3
Step-by-step explanation:
The initial weight was 91.5 pounds.
The dog lost 5.2 pounds which means subtraction.
91.5 pounds subtracted by 5.2 pounds that the dog lost equals 86.3 pounds.
In the expansion of (3a + 4b)8, which of the following are possible variable terms? Explain your reasoning.
a2b3; a7b; ab8; b8; a4b4; a6b2; a3b4; a8
pls help
The terms b⁸, a⁶ · b², a⁴ · b⁴, a⁷ · b and a⁸ are part of the expansion of (3 · a + 4 · b)⁸.
How to find the missing terms of a power polynomials
In this case, we have to expand a power binomial by means of the Pascal's triangle, which offers a useful and quick resource to expand expressions of this kind, now we proceed to present the result of this approach:
(3 · a + 4 · b)⁸ = 6 561 · a⁸ + 69 984 · a⁷ · b + 326 592 · a⁶ · b² + 870 912 · a⁵ · b³ + 1 451 520 · a⁴ · b⁴ + 1 548 288 · a³ · b⁵ + 1 032 192 · a² · b⁶ + 393 216 · a · b⁷ + 65 536 · b⁸
Such combinations of products between variables a and b are also supported by the theorem of the binomial. Finally, the terms b⁸, a⁶ · b², a⁴ · b⁴, a⁷ · b and a⁸ are part of the expansion of (3 · a + 4 · b)⁸.
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Which algebraic expression represents the following: the sum of four times a number and six? (1 point) 4x + 6
Answer:
4x +6
Step-by-step explanation:
No explanation
Straight answer
Last week the value of an investment changed at a rate of -$3.15 each day. After How many days was the total change in value -$12.60?
In four days,the total change in value -$12.60.
According to the statement
we have given that the value of an investment changed at a rate of -$3.15 each day. And we have to find that the after how many days the change in value reaches at the -$12.60.
So, here we use division rule to find the solution.
The given change value is :
-$3.15 each day.
The desired change value is :
-$12.60.
Number of days required = -12.60 / -3.15
Number of days required = 12.60 / 3.15
Number of days required = 4 days.
So, in four days the change in value reaches at the desired value of change.
So, In four days,the total change in value -$12.60.
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What is the domain of the function y = X+ 6 -7?
x>-7
x>-6
x>6
x>7
The domain of the function y = √(x + 6) - 7 is x > -6
How to determine the domain of the function?The equation of the function is given as
y = √(x + 6) - 7
Set the radical greater than 0
x + 6 > 0
Subtract 6 from both sides of the equation
x > -6
Hence, the domain of the function y = √(x + 6) - 7 is x > -6
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The domain of the function in discuss described as; y = √x+6 -7 is; x >= -6.
What is the domain of the function described as in the task content above?According to the task content, it follows that the domain of.the function can be evaluated by means of the characteristics associated with the square root.
The function given is; y = √x+6 -7
Since, the square root of a negative number renders a complex number as it's results, it follows that; x+6 >= 0.
Hence, x >= -6.
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the sum of the digits of a two-digit number is 14. the first digit is 4 less than twice the second digit. what is the number
Answer:
86
Step-by-step explanation:
t = ten's digit u= one's digit
t + u = 14 t = 2u - 4
In the first equation substitute for t 2u - 4 that we find in the second equation above.
t + u = 14
2u - 4 + u = 14 Combine the u's
3u - 4 = 14 Now add 14 to both sides
3u = 18 Divide both sides by 3
u = 6. We found the unit's digit, now we will find the ten's unit by plugging in 6 for u in the first equation above.
t + u = 14
t + 6 = 14 Subtract 6 from both sides
t = 8
So, your answer is 86.
The graph of function f is shown. The graph of an exponential function passes through (minus 10, minus 1), (2, 8) also intercepts the x-axis at minus 2 units and y-axis at 2 units Function g is represented by the table. x -2 -1 0 1 2 g(x) 0 2 8 26 Which statement correctly compares the two functions? A. They have the same x-intercept and the same end behavior as x approaches ∞. B. They have the same x- and y-intercepts. C. They have the same y-intercept and the same end behavior as x approaches ∞. D. They have different x- and y-intercepts but the same end behavior as x approaches ∞.
The correct description that cab made of these graphs is that They have the same x- and y-intercepts.
What is the end behavior of a function?This is the term that is used to describe the behaviors of these functions as they approach infinity.
the y-intercept of a function
This is what is used to tell us the y value when we put x to be = 0
The y-intercept of f(x) is y = -2
The y-intercept of g(x) is y = -2
the x-intercept of a function
It is the value of x when y = 0.
The x-intercept = 2
The x-intercept = 2
Hence statement B is correct. They have the same x- and y-intercepts.
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What is the maximum number of pants per employee that can be washed each week? (2 points)
6. What is the maximum number of chef coats per employee that can be washed
each week? (2 points)
7. What is the maximum total number of items per employee that can be washed in a week? (2 points)
The computation shows that the maximum number of pants per employee that can be washed each week is 6.
How to compute the values?The maximum number of pants per employee that can be washed each week will be:
7 + 4.5x + 12 <= 46
4.5x <= 27
x <= 6
The maximum number is 6.
The maximum number of chef coats per employee that can be washed each week will be:
= 6 + 8
= 14
The maximum total number of items per employee that can be washed in a week will be:
= 6 + 14 = 20
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Which of the following is an even function?
A) f(x) = (x – 1)^2
B) f(x) = 8x
C) f(x) = x^2 – x
D) f(x) = 7
Answer:
D) f(x) = 7Step-by-step explanation:
A function is even when f(-x) = f(x) for all x in the domain of f. We can say that the function is simetrical over x axis.
That's all i know, Hope it helps!
A town is mapped on a coordinate grid. The library is located at point (-3, 9) and the museum is located at
point (8, 2).
Where is the midpoint of the line segment whose endpoints are the library and the museum?
O (-5.5, 5.5)
O (-5.5, 3.5)
O (2.5, 3.5)
O (2.5, 5.5)
Applying the Midpoint Formula, the midpoint of the line segment whose endpoints are the library and the museum is calculated as: D. (2.5, 5.5).
What is the Midpoint Formula?To find the coordinates of the midpoint between two endpoints on a coordinate plane, the midpoint formula that is used is expressed as: M[(x2 + x1)/2, (y2 + y1)/2].
Given the following coordinates:
The library is located at point (-3, 9)
The museum is located at point (8, 2), therefore, let:
(-3, 9) = (x1, y1)
(8, 2) = (x2, y2)
Midpoint = M(x, y)
Substitute the values into M[(x2 + x1)/2, (y2 + y1)/2]:
M(x, y) = [(8 + (-3))/2, (2 + 9)/2]
M(x, y) = (5/2, 11/2)
M(x, y) = (2.5, 5.5)
Thus, the midpoint of the line segment whose endpoints are the library and the museum is calculated as: D. (2.5, 5.5).
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Answer:
Its D (2.5, 5.5) On Edg 2022-23
Step-by-step explanation:
Hope This Helps:))
10x(4-3x) pls someone help???
Answer: [tex]\Large\boxed{-30x^2+40x}[/tex]
Step-by-step explanation:
Given expression
10x (4 - 3x)
Expand the parenthesis by distributive property
= 10x · 4 - 10x · 3x
= (10 × 4)x - (10 × 3) (x × x)
[tex]\Large\boxed{=-30x^2+40x}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Hi :)
We'll use distributive property to solve this
————————[tex]\LARGE\boldsymbol{10x(\hfill\stackrel{\hfill\stackrel{10x}\curvearrowright}4-\hfill\stackrel{\hfill\stackrel{10x}\curvearrowright}{3x)}}}[/tex]
Thus
[tex]\large\boldsymbol{10x\cdot4-3x\cdot10x}[/tex]
Simplify
[tex]\Large\boldsymbol{40x-30x^2}[/tex]
[tex]\tt{Learn~More;Work~Harder}[/tex]
:)
Build Your Math Skills 2C, Round decimals to the nearest hundredth (0.01): 2.364
Answer:2.36
Step-by-step explanation:
pls help with Trigonometric
The value of the given trigonometry function is 2√15/15
Half anglesHalf angles are trigonometric identities used to express sine, cosine and tangent of half angles.
For instance the value of cos theta is expressed as shown below;
cosФ = cos(Ф/2+Ф/2)
cosФ = cos²Ф/2-sin²Ф/2
cosФ = cos²Ф/2-(1-cos²Ф/2)
cosФ = 1 - 2cos²Ф/2
Given the following parameters
cosФ = -7/15
Substitute
cosФ = 1 - 2cos²Ф/2
-7/15 = 1 - 2cos²Ф/2
-2cos²Ф/2 = -7/15 - 1
-2cos²Ф/2 = -8/15
cos²Ф/2 = 4/15
cosФ/2 = 2/√15
Rationalize
2/√15 * √15/√15
2√15/15
Hence the value of the given trigonometry function is 2√15/15
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please answer this I give u thanks and f0ll0w u and mark brainiest
Use of identity for sum of cubes:
x³ + y³ = (x + y)(x² - xy + y²)Change it as:
x³ + y³ = (x + y)(x² + 2xy + y² - 3xy) = (x + y)[(x + y)² - 3xy)]It is easy to notice that:
64a³ = (4a)³ and125b³ = (5b)³.So the sum of cubes for the given expression will be:
64a³ + 125b³ = (4a + 5b)[(4a + 5b)² - 3(4a*5b)] =(4a + 5b)[(4a + 5b)² - 60ab]Now substitute the values and calculate each of these:
(a) 4a + 5b = 5, ab = -1.
(4a + 5b)[(4a + 5b)² - 60ab] = 5[5² - 60(-1)] = 5(25 + 60) = 5(85) = 425(b) 4a + 5b = -2, ab = 1/15.
(4a + 5b)[(4a + 5b)² - 60ab] = -2[(-2)² - 60(1/15)] =-2(4 - 4) = -2(0) = 0(c) 4a + 5b = 1/3, ab = -1/9.
(4a + 5b)[(4a + 5b)² - 60ab] = (1/3)[(1/3)² - 60(-1/9)] =(1/3)(1/9 + 60/9) = (1/3)(61/9) = 61/27 = 2 7/27(d) 4a + 5b = -1, ab = 1.
(4a + 5b)[(4a + 5b)² - 60ab] = -1[(-1)² - 60(1)] = -1(1 - 60) = -1(-59) = 59Determine whether the given correlation coefficient is statistically significant at the specified level of significance and sample size. r=−0. 599, α=0. 01, n=11
Yes, the correlation coefficient is statistically significance
The precise metric used in a correlation analysis to quantify the strength of the linear relationship between two variables is the correlation coefficient. In a correlation report, the r stands for the coefficient.
Given,
Sample size, n = 11
Where ρ is the population correlation.
Then the number of degrees of freedom is, df = n-2 = 11-2 = 9
The corresponding critical correlation value re for a significance level of a 0.01, for a two-tailed test is た= 0.254
Here,
The null hypothesis, = ρ - 0 is rejected
Suppose lr> re 0.254
Because on the sample correlation provided, we know that lrl = 0.599>=0.254.
Here, it is clear that the null hypothesis is rejected.
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Pls help 15. Find the exact area of the shaded region of the circle shown in the diagram.
Answer:
The shaded region is 9.83 cm²Step-by-step explanation:
Refer to attached diagram with added details.
GivenCircle O with:
OA = OB = OD - radiusOC = OD = 2 cmTo findThe area of segment ADB.SolutionSince r = OC + CD, the radius is 4 cm.
Consider right triangles OAC or OBC:
They have one leg of 2 cm and hypotenuse of 4 cm, so the hypotenuse is twice the short leg.Recall the property of 30°x60°x90° triangle:
a : b : c = 1 : √3 : 2, where a- short leg, b- long leg, c- hypotenuse.It means OC: OA = 1 : 2, so angles AOC and BOC are both 60° as adjacent to short legs.
In order to find the shaded area we need to find the area of sector OADB and subtract the area of triangle OAB.
Area of sector:
A = π(θ/360)r², where θ- central angle,A = π*((mAOC + mBOC)/360)*r²,A = π*((60 + 60)/360))(4²) = 16.76 cm².Area of triangle AOB:
A = (1/2)*OC*(AC + BC), AC = BC = OC√3 according to the property of 30x60x90 triangle.A = (1/2)(2*2√3)*2 = 4√3 = 6.93 cm²The shaded area is:
A = 16.76 - 6.93 = 9.83 cm²S=1 - 1/4 + 1/6 - 1/9 + 1/11 - 1/14..........infinity. Find the sum of series.
[tex]1+\frac{1}{6}+\frac{1}{11}+\cdots=\sum^{\infty}_{n=1} \frac{1}{5n-4} \\ \\ \frac{1}{4}+\frac{1}{9}+\cdots=\sum^{\infty}_{n=1} \frac{1}{5n-1} \\ \\ S=\sum^{\infty}_{n=1} \left(\frac{1}{5n-4} -\frac{1}{5n-1} \right) \\ \\ =\frac{\pi}{5} \sqrt{\frac{1}{5} (5+2\sqrt{5})}[/tex]