The expression, written as the sine of an angle is sin (7π/10)
Trigonometry IdentitiesFrom the question, we are to write the given expression as the sine or cosine of an angle.
The given expression is
sin(π/5)cos(π/2) + sin(π/2)cos(π/5)
Let A = π/5
and
B = π/2
Thus, we get
sinA cosB + sinB cosA
From the given information, we have that
sin(A ± B) = sinA cos B ± cosA sinB
∴ sin(A + B) = sinA cos B + cosA sinB
Now,
sinA cosB + sinB cosA = sinA cosB + cosA sin B
∴ sinA cosB + sinB cosA = sin (A + B)
Put A = π/5
and
B = π/2
sinπ/5 cosπ/2 + sinπ/2 cosπ/5 = sin (π/5 + π/2)
sinπ/5 cosπ/2 + sinπ/2 cosπ/5 = sin (7π/10)
Hence, the expression, written as the sine of an angle is sin (7π/10)
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The wheels on a bike have a diameter of twenty six inches. How many full revolutions will the wheels need to make to travel a 100 feet?
The number of revolutions will the wheels need to make to travel 100 feet will be 15.
Given that:
Diameter, d = 26 inches
Let d be the diameter of the circle. The circumference of the circle will be given as,
C = πd units
The number of revolutions will the wheels need to make to travel 100 feet will be given as,
100 = n x 3.14 x (26 / 12)
100 = 6.803 n
n = 14.6986
n ≈ 15 revolution
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find the measure of the angle indicated in bold
PLS HELP
A salesperson at a jewelry store earns 6% commission each week. Last week, jarrod sold $680 worth of jewelry. How much did make in commission? How much did the jewelry store make from sales?
Answer:
1/ $ 4.08
2/ $675.92
Step-by-step explanation:
Take 68 times 0.06% = $4.08
680 - 4.08= 675.92
Answer:
Step-by-step explanation:
40.80 it told me the answer
Select all the statements that describe the distribution of the data
Please see the image below(math)
Answer:
21
Step-by-step explanation:
If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.
AD AH
----- = ---------
AB AH +y
3 9
---- = ------
10 9+y
Using cross products:
3(9+y) = 9*10
27+3y = 90
3y = 90-27
3y =63
y = 63/3
y = 21
Answer:
y = 21
Step-by-step explanation:
According to the Side Splitter Theorem, if a line parallel to one side of a triangle intersects the other two sides, then this line divides those two sides proportionally.
Therefore, according to the Side Splitter Theorem:
\(\boxed{\sf AD : DB = AH : HC}\)
From inspection of the given triangle, the lengths of the line segments are:
AD = 3DB = 7AH = 9HC = yTo find the value of y, substitute the given line segment lengths into the proportion and solve for y:
\(\begin{aligned}\sf AD : DB &=\sf AH : HC\\\\3:7&=9:y\\\\\dfrac{3}{7}&=\dfrac{9}{y}\\\\3 \cdot y&=9 \cdot 7\\\\3y&=63\\\\\dfrac{3y}{3}&=\dfrac{63}{3}\\\\y&=21\end{aligned}\)
Therefore, the value of y is 21.
Consider the following generic C comparison function and its assembly language representation C code: byte compbyte a,byte b)/a in rdi,b in rsi Assembly code cmpb %rsi,%rdi set_inst %a1 ret Your jobs(fill-in blank):now sh given values of a and b g SET instruction and the A.5 points set CI SF OF %al setg 47 23 B.5 points set h SF OF %a setl 23 47 C.5 points ZA SF OF %al set sete 23 23 D.5 points CF ZF SF OF 00%1 set b setne 23 47
The correct answer is D. setne 23 47. Based on the provided information, I understand that you have a comparison function in C code and its corresponding assembly code. You are asked to fill in the blanks by selecting the appropriate instructions based on the given values of a and b and the status flags SF, OF, ZF, and CF. Let's go through the options:
A. setg 47 23: This option is incorrect because setg is used to set a byte to 1 if the Greater flag (ZF=0 and SF=OF) is set, but the given values of a and b are 47 and 23, respectively, so it does not satisfy the condition for setg to be set.
B. setl 23 47: This option is incorrect because setl is used to set a byte to 1 if the Less flag (SF≠OF) is set, but the given values of a and b are 23 and 47, respectively, so it does not satisfy the condition for setl to be set.
C. sete 23 23: This option is incorrect because sete is used to set a byte to 1 if the Zero flag (ZF=1) is set, but the given values of a and b are 23 and 23, respectively, so it does not satisfy the condition for sete to be set.
D. setne 23 47: This option is correct. setne is used to set a byte to 1 if the Zero flag (ZF=0) is not set, which means the values of a and b are not equal. In this case, the given values of a and b are 23 and 47, respectively, so they are not equal, and setne should be used.
Therefore, the correct answer is D. setne 23 47
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The confidence interval for the mean is symmetrical around the population mean.
A confidence interval for the mean is said to be symmetrical around the population mean. Symmetry means that the central tendency measures are equally positioned about the middle of the interval.
When constructing a confidence interval, the interval width on either side of the point estimate is equal (assuming a symmetric distribution). The critical values, the margin of error, and the point estimate are all equidistant from the midpoint of the interval.
This is why a confidence interval for the mean is said to be symmetrical around the population mean. Therefore, a confidence interval for the mean is symmetrical around the population mean as long as the population is normally distributed.
Also, it is worth noting that a confidence interval can only be symmetrical if the sample size is large enough. In the case of a smaller sample size, the distribution of the confidence interval may not be entirely symmetrical and may skew to the left or right. The larger the sample size, the more symmetrical the distribution will be.
A confidence interval is typically expressed in a specific range, such as 95 percent, which means that the population mean is expected to fall within that range 95 percent of the time. In conclusion, the symmetry of a confidence interval around the population mean is important for statistical inference because it ensures that the confidence level is maintained.
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marlena is making her own beaded bracelets. each bracelet will have 10 beads. write a function to describe the number of beads she will use. find a reasonable domain and range for the function if she makes up to 7 bracelets.
Answer:
number of beads to be made x 10
x×10=
Which relation in the below table(s) represents a function?
The relation 2 represents a function.
In order to determine which relation in the below table represents a function, we need to first understand what a function is.A function is a relationship in which each input value corresponds to exactly one output value.
To put it another way, each x-value has one and only one y-value. The most typical method to determine whether a relation is a function is to use the vertical line test.
The vertical line test is a way to determine if a relation is a function graphically. To test if a graph is a function, we draw a vertical line through each x-value on the graph. If a vertical line crosses the graph more than once, it is not a function.
If, on the other hand, the graph passes the vertical line test and no vertical line crosses the graph more than once, it is a function.Now let's look at the table below to determine which relation is a function.
We will first plot the x and y values of each relation on a coordinate system and then apply the vertical line test to each relation.
Relation 1: x | y0 | 10 | 11 | 22 | 23 | 34 | 35 | 4Relation 1 does not represent a function since we can draw a vertical line through x = 3 and the line will cross the graph more than once.
Relation 2: x | y2 | 33 | 34 | 45 | 46 | 57 | 5Relation 2 represents a function since we can draw a vertical line through each x-value on the graph and it will only cross the graph once.
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you wish to determine the average number of orders placed in the west. what excel formula would be best to use.
The following formula to calculate the average number of orders placed in the West:
= AVERAGE(number1, [number2], ...)
To determine the average number of orders placed in the West, you can use the AVERAGE function in Excel.
The syntax for the AVERAGE function is:
= AVERAGE(number1, [number2], ...)
Where number 1, number 2, etc. are the cells or ranges of cells that contain the data that you want to average.
For example, if the data for the number of orders placed in the West is in cells B2:B5, you can use the following formula to calculate the average number of orders placed in the West:
=AVERAGE(B2:B5)
This formula will return the average of the values in cells B2 through B5. If you want to include additional cells or ranges of cells in the calculation, you can simply add them to the formula separated by commas, like this:
=AVERAGE(B2:B5, C2:C5, D2:D5)
This formula will return the average of the values in cells B2 through B5, C2 through C5, and D2 through D5.
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what is the annualized rate of population growth? (write your answer to one decimal places. e.g., 1.5.)
The rate of return (RoR) needed for an population to increase from its starting balance to its ending balance, providing growth were repopulated at the conclusion of each period of the population life span
To determine an population CAGR:
Divide the population worth at the end of the time by the value it had at the start of the period.
The result should be multiplied by one and divided by the number of years.
The outcome is then reduced by one.
To convert the response into a percentage, multiply by 100.
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The absolute value inequality equation |2x – 1| > 3 will have what type of solution set? Question 6 options: A) Intersection B) Union C) All real numbers D) No solution
The absolute value of the inequality |2x -1| >3 will have a union type of solution set.
How do we solve the absolute value of an inequality equation?By using the absolute rule that states:
An inequality equation's absolute value can be solved.
If |u| > a, a > 0, then u < - a or u > awhere the "or" functionality symbolizes the union between the solution sets.
Given that:
|2x - 1| > 3
Applying the absolute rule, we have:
2x - 1 < - 3 or 2x - 1 > 3
2x < -4 or 2x > 4
x < -4/2 or x > 4/2
x< -1 or x > 2
This denotes the union of between the solution sets.
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Electric utility poles in the form of right cylinders are made out of wood that costs $25.37 per cubic foot. Calculate the cost of a utility pole with a diameter of 1.5 ft and a height of 45 ft. Round your answer to the nearest cent.
The cost of the utility pole is approximately $593.96.
What is volume?Volume is a measure of the amount of space occupied by a three-dimensional object. It is usually measured in cubic units such as cubic meters (m³), cubic centimeters (cm³), or cubic feet (ft³). The volume of an object can be found by measuring its length, width, and height and using a formula that relates these dimensions to the amount of space the object occupies. In geometry, the most common shapes for which volume is calculated include cubes, spheres, cylinders, pyramids, and cones.
The volume of a right cylinder is given by the formula V = πr²h, where r is the radius of the base and h is the height.
In this case, the diameter of the utility pole is 1.5 ft, so the radius is 0.75 ft. The height is 45 ft. Therefore, the volume of the utility pole is:
V = π(0.75 ft)²(45 ft) = 23.3826... cubic feet
Rounding to the nearest hundredth, we get:
V ≈ 23.38 cubic feet
The cost of wood per cubic foot is $25.37. Therefore, the cost of the utility pole is:
$25.37/cubic foot × 23.38 cubic feet ≈ $593.96
So the cost of the utility pole is approximately $593.96.
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Which expression is equivalent to 3 4 x + 5 − 7 + 1 2 x 34 x + 5 - 7 + 12x?
A.
5
4
x
−
2
54x-2
B.
4
6
x
−
2
46x-2
C.
1
4
x
+
12
14x+12
D.
4
6
x
+
12
46x+12
Answer:12
Step-by-step explanation:
I did rhos
Find the rate per minute
Answer:
2.67 rounded to the nearest hundredth
Step-by-step explanation:
8/3 = 2.67 est gallons per minute
gallon÷minutes=rate per minute
HELP ASAP WILL GIVE BRAINLIEST, PHOTO
ATTACHED!!!!
Complete the missing parts of the
table for the following function.
y = ( ²1 ) x
X -2 -1 0
12 3
y [?] 7 []
1
1
1
343
Answer:
Mark Me As BrainliestStep-by-step explanation:
as there square of the no. going on so here also it will go on square but at minus.
Can you answer this, as it is greatly appreciated
Answer:
See belowStep-by-step explanation:
Let the amount of pecans is x pounds and cashew is y pounds.
The inequalities according to the question are:
x + y ≥ 36x + 8y ≤ 24The solution of the system is attached as a graph below.
Possible combinations are:
(2, 1) or (1, 2)Answer:
3 pounds of pecans and 0.5 pound of cashews
2.5 pounds of pecans and 1 pound of cashews
Step-by-step explanation:
Given information:
Malik can spend no more than $24 to buy pecans and cashews.Malik wants to buy at least 3 pounds of nuts.Cost of pecans = $6 per poundCost of cashews = $8 per poundDefine the variables:
Let x = number of pounds of pecans Malik can buy
Let y = number of pounds of cashews Malik can buy
Create a system of inequalities from the given information:
6x + 8y ≤ 24x + y ≥ 3Graph the inequalities (see attached)
The possible solutions are any points enclosed by the shaded area where x > 0 and y > 0.
Therefore, two possible combinations are:
3 pounds of pecans and 0.5 pound of cashews2.5 pounds of pecans and 1 pound of cashews
Place the figures in order from least surface area to greatest surface area.
Answer:
hmm im not Shure let me think
Answer:
Figure 2, Figure 1, Figure 3 is the correct way.
Step-by-step explanation:
WILL MARK YOU BRAINLIEST
107 in the verse of 180 the whole turn will evaluate to 73.
Step-by-step explanation:
An office building has three air conditioning units, one for each office. Each unit runs only when employees are
working. The tables below show the number of hours employees worked at each office over a three-month period
and the total air conditioning electric costs for the entire office for each month.
June
July
August
Number of Hours Worked
Unit A
Unit B
184
207
174
198
168
189
Unit C
276
264
242
w
Total Air Conditioning Electric Costs
June
$142.60
July
$135.96
August
$128.30
How much does it cost to run Unit A per hour?
Answer:0.22
Step-by-step explanation:
Answer:$0.22
Step-by-step explanation:
EDGE
HELPPP
12x^5y^4 / 32x^2y^4
Answer:
\( \frac{3x {}^{3} }{8} \)
Step-by-step explanation:
\( \frac{3 {x}^{3} }{8} \)
What is the similarity ratio (scale factor) of the larger triangle to the smaller triangle?
similarity ratio =??
Answer:
5/11Step-by-step explanation:
Corresponding side have same ratio:
55/121 = 5/11 (divide by 11)40/88 = 5/11 (divide by 8)30/66 = 5/11 (divide by 6)The similarity ratio or the scale factor of the larger triangle to the smaller is 5/11
Answer:
5/11
Step-by-step explanation:
Correct answer
f. if a is an m n matrix whose columns do not span rm, then the equation ax d b is inconsistent for some b in rm.
The statement ''f. if a is an m n matrix whose columns do not span rm, then the equation ax d b is inconsistent for some b in rm '' is TRUE.
Let us assume that a is an m x n matrix that doesn't span rm. It means that the columns of a matrix don't contain all the vectors in the m-dimensional vector space that a is associated with. Therefore, it is not possible to find the linear combination of the columns of a that produces some vectors in rm.
We can also say that a matrix is inconsistent when there is no solution possible for the given linear equation. A system of linear equations is inconsistent when it has no solution.To prove the statement f, we need to prove that if a matrix doesn't span rm, then the given equation ax = b is inconsistent for some b in rm.
Here is a proof:
Let's assume that the columns of the matrix a don't span rm. It means that some vector in rm is not in the column space of a matrix.
Let's assume that vector is v.
Now, let's consider the linear equation ax = v. Since v is not in the column space of matrix a, there is no solution to this equation. It means that the equation ax = v is inconsistent.
Hence, we can say that the statement f. if a is an m n matrix whose columns do not span rm, then the equation ax d b is inconsistent for some b in rm is true
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To go on a rollercoaster a persons height, h must be over 140cm. Write this as an inequality
Answer:
h > 140cm
Step-by-step explanation:
The height (h) has to be over 140cm, so we will have the inequality sign opening to h because it's greater than 140cm (see above)
For f(x)=2x 4−4x 2 +9 find the following. (A) f ′ (x) (B) The slope of the graph of f at x=−4 (C) The equation of the tangent line at x=−4 (D) The value(s) of x wherethe tangent line is horizontal (A) f ′ (x)=
The tangent line to the graph of f is horizontal at x = 0, x = 1, and x = -1.
To find the derivatives and the slope of the graph of f at x = -4, we use the following:
(A) To find f'(x), we take the derivative of f(x):
f(x) = 2x^4 - 4x^2 + 9
f'(x) = 8x^3 - 8x
(B) The slope of the graph of f at x=-4 is given by f'(-4).
f'(-4) = 8(-4)^3 - 8(-4) = -1024
Therefore, the slope of the graph of f at x = -4 is -1024.
(C) The equation of the tangent line to the graph of f at x = -4 can be found using the point-slope form:
y - f(-4) = f'(-4)(x - (-4))
y - f(-4) = f'(-4)(x + 4)
Substituting f(-4) = 2(-4)^4 - 4(-4)^2 + 9 = 321 into the above equation, we get:
y - 321 = -1024(x + 4)
Simplifying, we get:
y = -1024x - 4063
Therefore, the equation of the tangent line to the graph of f at x = -4 is y = -1024x - 4063.
(D) The tangent line is horizontal when its slope is zero. Therefore, we set f'(x) = 0 and solve for x:
f'(x) = 8x^3 - 8x = 0
Factorizing, we get:
8x(x^2 - 1) = 0
This gives us three solutions: x = 0, x = 1, and x = -1.
Therefore, the tangent line to the graph of f is horizontal at x = 0, x = 1, and x = -1.
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1. Is g = 2 a solution (the correct
answer) to 3g = 6? PROVE why or why
not.
Answer:
yes this is true
Step-by-step explanation:
this is because 2x3=6 so 2x3g=6g
if the deer population continues to increase by 15% each year, write a function rule that represents the deer population years after 2011.
The function rule that represents the deer population t years after 2011, assuming a 15% annual growth rate, is d(t) = 100 × 1.15^t
Assuming the deer population started at a baseline value of P0 in 2011, we can use the following formula to calculate the population after t years
d(t) = P0 × (1 + r)^t
Where r is the annual growth rate, expressed as a decimal, and t is the number of years since 2011.
Given that the deer population increases by 15% each year, we can express r as
r = 0.15
And since the baseline population in 2011 is not given, we can use P0 as an arbitrary constant value, such as 100
P0 = 100
Therefore, the function rule that represents the deer population t years after 2011 would be
d(t) = 100 × (1 + 0.15)^t
Simplifying the expression
d(t) = 100 × 1.15^t
This function rule gives us the deer population at any time t years after 2011, assuming the population continues to increase by 15% annually.
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The given question is incomplete, the complete question is:
If the deer population continues to increase by 15% each year, write a function rule d that represents the deer population t years after 2011.
consider the function θ : p(z) → p(z) defined as θ(x) = x. is θ injective? is it surjective? bijective? explain
The function θ : p(z) → p(z) defined as θ(x) = x is injective and surjective, therefore bijective.
The function θ(x) = x takes an element x from the set p(z) and returns the same element x. This means that for any input x in p(z), the function simply returns x as the output.
To determine whether θ is injective, we need to check if distinct inputs produce distinct outputs. In this case, since the function θ simply returns the input element x, it is evident that if two different elements are provided as input, they will always produce different outputs. Thus, θ is injective.
To assess the surjectivity of θ, we need to determine if every element in the codomain p(z) has a corresponding preimage in the domain p(z). In this scenario, since the function θ returns the same element x that is provided as input, it covers all elements in p(z). Therefore, for any given element in the codomain, there exists a preimage in the domain. Hence, θ is surjective.
Since the function θ is both injective and surjective, it is bijective. This means that for every input element x, there is a unique output element x, and every element in the codomain p(z) has a corresponding preimage in the domain p(z).
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Is it true that If A is invertible and if r ≠0, then (rA)^−1=rA^−1.
The statement is true. Therefore, we have shown that \((rA)^{(-1)} = A^{(-1)}/r,\)which implies that \((rA)^{(-1)} = r^{(-1)}\times A^{(-1)\). Hence, \((rA)^{(-1) }= rA^{(-1)\), since r is nonzero.
To prove this, we can start with the definition of the inverse of a matrix:
If A is an invertible matrix, then its inverse, denoted as \(A^{(-1),\) is the unique matrix such that \(A\times A^{(-1)} = A^{(-1)} \times A = I\), where I is the identity matrix.
Now, let's consider the matrix rA, where r is a nonzero scalar. We want to find its inverse, denoted as \((rA)^{(-1)\).
We can start by multiplying both sides of the equation \(A\times A^{(-1)} = I\) by r:
\(rA\times A^{(-1)} = rI\)
Next, we can multiply both sides of this equation by A from the left:
\(rA\times A^{(-1)}A = rIA\\rAI = rA = rA(A\times A^{(-1)})\)
Now, we can use the associative property of matrix multiplication to rearrange the right-hand side of this equation:
\(rA\times(AA^(-1)) = (rAA)\times A^{(-1)}\\rA\times I = (rA)\times A^{(-1)}\\rA = (rA)\times A^{(-1)}\)
Finally, we can multiply both sides of this equation by \((rA)^{(-1)\) from the left to obtain:
\((rA)^{(-1)}rA = (rA)^{(-1)}(rA)\times A^{(-1)}\\I = A^{(-1)}\)
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Expand the following :
x (x+2)
Answer:
x^2 + 2x
Step-by-step explanation:
x (x+2)
Distribute the x to each term inside the parentheses
x *x + x*2
x^2 + 2x
Answer:
step 1
use x to multiple the bracket
x(x+2)
x^2+2x