The exact values of sinθ, tanθ, secθ, cscθ, and cotθ are -√8/9, √8/3, -3, -√9/8, and √9/8, respectively.
Given: cosθ = -1/3 and θ is in quadrant III.
This means that sinθ = ± √(1 - (cosθ)2).
We know that cosθ is negative, so sinθ will be negative.
Therefore, sinθ = -√(1 - (-1/3)2 )
sinθ = - √(1 - 1/9)
sinθ = -√8/9
tanθ = sinθ/cosθ
tanθ = (-√8/9)/-1/3
tanθ = √8/3
secθ = 1/cosθ
secθ = 1/-1/3
secθ = -3
cscθ = 1/sinθ
cscθ = 1/-√8/9
cscθ = -√9/8
cotθ = cosθ/sinθ
cotθ = -1/3/-√8/9
cotθ = √9/8
Therefore, the exact values of sinθ, tanθ, secθ, cscθ, and cotθ are -√8/9, √8/3, -3, -√9/8, and √9/8, respectively.
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If h = 7 feet, and r = 2 feet, then what is the volume of the cylinder? (Use = 3.14.)
Answer: 87.964594300514 feet3 or 87.96 feet3
Step-by-step explanation:
πr^2 h
= π×2^2×7
= 28π
= 87.964594300514 feet3
Eight percent of all college graduates hired by companies stay with the same company for more than five years. The probability, rounded to four decimal places, that in a random sample of 14 such college graduates hired recently by companies, exactly 2 will stay with the same company for more than five years is _?_.
P(X=2) &= {14\choose 2}(0.08)^2(0.92)^{12} \
&= \frac{14!}{2!(14-2)!}(0.08)^2(0.92)^{12} \
[tex]\sf\implies\:&=\frac{14\times13}{2\times1}(0.08)^2(0.92)^{12}[/tex]
&= 91(0.08)^2(0.92)^{12} \
&\approx \boxed{0.2166
[tex]\begin{align}\huge\colorbox{black}{\textcolor{yellow}{\boxed{\sf{I\: hope\: this\: helps !}}}}\end{align}[/tex]
[tex]\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}[/tex]
[tex]\textcolor{lime}{\small\textit{If you have any further questions, feel free to ask!}}[/tex]
[tex]\huge{\bigstar{\underline{\boxed{\sf{\color{red}{Sumit\:Roy}}}}}}\\[/tex]
please help me with this question thank you
The difference between the adjustable-rate mortgage (ARM) and the fixed-rate mortgage is $176,494.80.
How to find the difference ?First, find the total amount paid on the adjustable-rate mortgage would be :
= ( 5 years x 12 months x 2, 506.43 payment ) + ( 10 x 12 x 3, 059. 46 ) + ( 5 x 12 x 3, 646.76) + ( 5 x 12 x 3, 630.65 )
= $ 1, 172, 971. 20
Then we can find the total payment for the fixed - rate mortgage :
= Monthly payment x Number of years
= 2, 767. 99 x 30 years x 12 months
= $ 996, 476. 40
The difference is:
= 1, 172, 971.20 - 996, 476. 40
= $ 176,494. 80.
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13pi/6 terminal point
The terminal point of 13π/6 is (-√3/2, 1/2) by using unit circle.
What are the quadrants of a graph?The quadrants of a graph are the four sections that divide the coordinate plane. The quadrants are numbered in a counterclockwise direction starting from the positive x-axis.
1. Quadrant I is located in the upper-right section and contains points with positive x and y-coordinates.
2. Quadrant II is located in the upper-left section and contains points with negative x-coordinates and positive y-coordinates.
3. Quadrant III is located in the lower-left section and contains points with negative x and y-coordinates.
4. Quadrant IV is located in the lower-right section and contains points with positive x-coordinates and negative y-coordinates.
The quadrants are useful for determining the signs of coordinates, angles, and for plotting points on a graph.
To find the terminal point of 13π/6, we can start by recognizing that this angle is greater than 2π, which is one complete revolution around the unit circle.
To bring the angle back within one revolution, we can subtract 2π, which gives us 13π/6 - 2π/1 = 13π/6 - 12π/6 = 1π/6.
The angle 1π/6 is in the standard position between the positive x-axis and the first quadrant. The reference angle is π/6, which is the angle between the terminal side and the x-axis.
Since the angle is in the 2nd quadrant, the x-coordinate will be negative and the y-coordinate will be positive. Using the unit circle, we can find the values of sine and cosine at π/6 and then negate the value of cosine since the angle is in the second quadrant.
cos(π/6) = √3/2
sin(π/6) = 1/2
Therefore, the terminal point of 13π/6 is (-√3/2, 1/2).
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If a coin is flipped five times the probability of getting heads all five times is ______. Mark all that are true.
Answer: 1/2, the same as getting tails 5 times
Step-by-step explanation:
hope this helps
find - 4 - 2 1/2 expression on the number line by drawing an arrow
The resulting arrow should end at -6 1/2. This is because -4 - 2 1/2 is equal to -6 1/2.
In mathematics, an expression is a combination of numbers, variables, and operators that can be evaluated to produce a value. Expressions can be simple or complex and are used to represent mathematical relationships and operations.
How to determine the expression?To find -4 - 2 1/2 expression on the number line by drawing an arrow, we need to start at -4 and then move left by 2 1/2 units.
To do this, we can draw an arrow starting at -4 and then mark off 2 1/2 units to the left. One way to represent 2 1/2 units is to divide the space between -4 and -5 into two equal parts, and then mark off one of those parts.
The resulting arrow should end at -6 1/2. This is because -4 - 2 1/2 is equal to -6 1/2.
Here's an example of what the arrow would look like:
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Work out the largest integer value that x could take if
x+7<13
Answer:
The answer is going to 5
Step-by-step explanation:
I hope this helps you
In the xy-plane, what is the y-intercept of the graph of the equation y=6(x-1/2)(x+3)?
Answer:
The y-intercept of the graph of the equation is -9. This means that the graph crosses the y-axis at the point (0, -9).
Step-by-step explanation:
To solve this question, we need to plug in x = 0 into the given equation and simplify. We get:
y = 6(0 - 1/2)(0 + 3) y = 6(-1/2)(3) y = -9
Therefore, the y-intercept of the graph of the equation is -9. This means that the graph crosses the y-axis at the point (0, -9).
g(x)=2x
h(x)=x^(2)+4
evaluate for g(h(-8))
The value of the function is 136
How to determine the functionIt is important that we note that functions are described as expressions that are used to explain the relationship between two variables.
From the information given, we have that;
g(x)=2x
h(x)=x^(2)+4
To determine the composite function, we would need to substitute the value of h(-8) as x in the function g(x)
Then, we have that;
h(-8) = (-8)^2 + 4
Find the values
h(-8) = 68
Now, substitute the value as x , we have that;
g(h(-8)) = 2(68)
expand the bracket and multiply
g(h(-8)) = 136
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7 centimeters =
millimeters
Answer: 7 centimeters equals 70 millimeters :)
Use a net to find the surface area of the prism.
A. 469 in.2
B. 315 in.2
C. 539 in.2
D. 784 in.2
Answer:
2(1/2)(11)(7) + 11(14) + 14(8) + 14(9) = 469 in.^2
The correct answer is A.
Perimeter=8x-6 find the missing side of triangle
Answer:
Step-by-step explanation:
I'm sorry, but there isn't enough information to solve for the missing side of a triangle with just the perimeter given as 8x-6. We would need at least one more piece of information, such as the lengths of the other sides or angles of the triangle.
5. The population, P, of a city has grown according to the mathematical model P = 50 000(1.15), where t
is the number of years since 2005.
Using a graphing tool or by hand answer the questions below.
a) What was the population of the town in 2005?
I
b) In what year will the population exceed 100 000?
Answer: Therefore, the population will exceed 100,000 in the year 2005 + 10.73 ≈ 2016.
Step-by-step explanation: a) The population of the town in 2005 is given by the formula, where t = 0 since 2005 is the starting year:
P = 50,000(1.15)^0 = 50,000
Therefore, the population of the town in 2005 was 50,000.
b) We need to find the value of t when the population P exceeds 100,000:
100,000 = 50,000(1.15)^t
Divide both sides by 50,000:
2 = 1.15^t
Take the natural logarithm of both sides:
ln 2 = ln (1.15^t)
Apply the power rule of logarithms:
ln 2 = t ln 1.15
Divide both sides by ln 1.15:
t = ln 2 / ln 1.15
Using a calculator, we get:
t ≈ 10.73
Maria has 56 flower seeds. She wants to put an equal amount of seeds into 8 bags How many seeds will go in each bag?
Answer:
7 seeds will go into each bag
Given:
56 flower seeds need to be put into 8 separate bags.
To find out how much go into each bag you will divide the number of seeds by the number of bags
56/8=7
So 7 seeds will go into each of the 8 bags
A pet store has 10 puppies, including 3 poodles, 3 terriers, and 4 retrievers. If Rebecka and Aaron, in that order, each select one puppy at random without replacement, find the probability that Aaron selects a retriever, given that Rebecka selects a poodle.
P(both poodle) = (3/10)(3/10) = 9/100
Answer: The probability of choosing the same puppy is 9/100
Simplify with steps. (Write each expression without using the absolute value symbol)
|x+3| if x>5
The expression without the absolute value symbol is:
|x + 5| = x + 5, if x > 5
|x - 5| = 0, if x = 5
|x - 5| = 5 - x, if x < 5
Since, An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
|(x + 3) | if x > 5
This can be written as,
= |x + 3|
Now,
|x + 5| = x + 5, if x > 5
|x - 5| = 0, if x = 5
|x - 5| = 5 - x, if x < 5
Thus,
The expression without the absolute value symbol is:
|x + 5| = x + 5, if x > 5
|x - 5| = 0, if x = 5
|x - 5| = 5 - x, if x < 5
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what are the answers to these questions_
The general formula for f'(x) would be f' (x) = - 8 sin (x) + C.
The most general formula based on the first would be f(x) = 8 cos ( x ) + Cx + D.
How to find the general formula ?To find the most general formula for f ' ( x ), we need to integrate f'' ( x ) with respect to x:
f'' ( x ) = - 8 cos (x)
f' (x) = ∫ ( -8cos(x)) dx
f ' (x) = - 8 sin(x) + C, where C is an arbitrary constant.
We need to integrate f'( x ) with respect to x to find the most general formula for f ( x ):
f'(x) = - 8 sin(x) + C
f(x) = ∫ ( - 8sin ( x ) + C) dx
f(x) = 8 cos ( x ) + Cx + D, where D is another arbitrary constant.
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Chandra needs to make 3 gallons of punch how many cups of strawberry are needed
The number of cups of frozen strawberries that are needed to make 3 gallons of punch is equal to 48 cups.
How to solveIn this exercise, you're required to determine the number of cups of frozen strawberries that are needed to make 3 gallons of punch.
Thus, we would apply direct proportion.
Note: There are 16 cups of frozen strawberries in a gallon.
By direct proportion:
16 cups = 1 gallon
X cups = 3 gallons
Cross-multiplying, we have:
X = 16 × 3
X = 48 cups of frozen strawberries.
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If angle 3=61, what should angle 1 and angle 2 be?
Answer:
Step-by-step explanation:
so the entire angle sum is 180 degrees then subtract 61 from 180 and divide by 2. hope it helps :)
what are the answers to these questions
Θ(x) = tan⁻¹(5x / (4(x - 13))), and Θ is maximized when the distance the cow must stand from the billboard x₀ = 26.
How to determine angle and distance?To find Θ, use similar triangles. Let the distance from the cow to the top of the billboard be h. Then, using similar triangles:
h / x = 5 / (x - 13)
Solving for h:
h = 5x / (x - 13)
The vertical angle subtended by the billboard at the cow's eye is equal to the angle whose tangent is given by:
tan(Θ) = h / 4
Substituting for h:
tan(Θ) = 5x / (4(x - 13))
To maximize Θ, find the value of x that maximizes tan(Θ). Taking the derivative of tan(Θ) with respect to x and setting it equal to zero:
d/dx (tan(Θ)) = 5(52 - 26x) / (4(x - 13))² = 0
Solving for x:
x₀ = 26
Substituting x₀ into the expression for Θ:
Θ(x₀) = tan⁻¹(5(26) / 4(13)) = tan⁻¹(5/2)
Therefore, Θ(x) = tan⁻¹(5x / (4(x - 13))), and Θ is maximized when x₀ = 26.
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A man drove 14 miles directly east from his home, made a left turn at an intersection, and then traveled 7 miles north to his place of work. If a road was made directly from his home to his place of work, what would its distance be to the nearest tenth of a mile?
CNNBC recently reported that the mean annual cost of auto insurance is 1016 dollars. Assume the standard deviation is 209 dollars. You take a simple random sample of 94 auto insurance policies. Assuming the original population forms a bell-shaped distribution, answer the following and round your answers to three decimals.
Find the probability that a single randomly selected value is more than 979 dollars.
P(X > 979) = ???
Find the probability that a sample of size
is randomly selected with a mean that is more than 979 dollars.
P(M > 979) = ???
1. The probability that P(X > 979) = 0.567
2. The probability that P(M > 979) = 0.956
How do you calculate probability?
To calculate the probability that a single randomly selected value is more than 979 dollars.
979-1016
= -37/209
= -0.177
P(X > -0.177) = 0.5675
Therefore P(X > 979) = 0.568
To calculate that a sample of size is randomly selected with a mean that is more than 979 dollars.
209 / √94 = 21.557
-37/ 21.557 = -1.7164
P(Z > -1.714) = 0.9564
therefore P(M > 979) = 0.956
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a) Close the following accounts. 9
K. Emmanuel
$
2020
$
640
360
2020
800
Feb. 10 Bank Cash
25
200
Feb. 1 15
Sales Sales
J. Amaze
$
$
2020
2020
260 1090
1350
Mar. 12
Returns inwards
Mar4
Sales
18
Bank
Z. Ventour
2020
$
2020
$
May 13
Cash
518
May 10
Purchases
518
FSampath
2020
$
2020
July 14 22
Returns outwards
Bank
$
220
July 3
Purchases Purchases
8
25
Bank
800
1500
830
350
Answer:
I dont know the answer I dont know what it is I just needed points bye
Step-by-step explanation:
Answer this question soon
Answer:
CA - 144
AD - 98
ABD - 49
BC - 134
C - unsure
Step-by-step explanation:
pls solve thank u
100 points for answer
Hence, the darkened sector covers an area of roughly [tex]10.55 km^2[/tex] as circle's radius is 7 km, and the shaded sector's central angle is 154 degrees .
what is radius ?The radii of a circle in geometry is the separation between any two points on the circle's circumference. It is frequently used to describe how far apart two points are. One of a circle's most crucial characteristics is its radius, which is taken into account when calculating a circle's circumference, area, and diameter. The distance around a circle that passes through its centre, or its diameter, is equal to half of its radius. Other shapes like spheres, cylindrical, and cones can also be described using the radius. The radius here means the distance from the shape's centre to any point on its perimeter.
given
The following formula must be used to determine a sector's area:
A = (θ/360)[tex]\pi r^2[/tex]
where r is the circle's radius, is pi, or roughly 3.14, and is the sector's centre angle, expressed in degrees.
The circle's radius is 7 km, and the shaded sector's central angle is 154 degrees, according to the provided figure. When these values are added to the formula, we obtain:
[tex]A = (154/360)\pi (7)^2[/tex]
[tex]= 10.55 km^2[/tex]
Hence, the darkened sector covers an area of roughly [tex]10.55 km^2[/tex] as circle's radius is 7 km, and the shaded sector's central angle is 154 degrees .
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The complete question is:-
154 degree
7 km
Find the area of the shaded sector.
A = __ km2
Carl is buying a shirt that costs $24.00. It is on sale for 50% off. what will the price of the shirt be?
A. 19.00
B. 50.00
C. 12.00
D. 14.00
Please help I’ll give brainly if you explain :)
Answer: C
Step-by-step explanation:
We need to turn 50% into a fraction first to make it easier,
50% is equal to 1/2 because 50/100 is simplified to 1/2.
Now let's multiply!
24 x 1/2 = 24/2 = 12/1 = 12
7. The towns of Washington, Franklin, and Springfield are
connected by straight roads. The towns wish to build an
airport to be shared by all of them.
a. Where should they build the airport if they want it to be the same distance from
each town's center? Describe how to find the precise location.
b. Where should they build the airport if they want it to be the same distance from
each of the roads connecting the towns? Describe how to find the precise
location.
They should build the airport at the
They should build the airport at the
n be found by locating the intersection of at least
which can be found by locating the intersection of a
a circumcenter
medians
Which expression is equivalent to 5/4x +33-2+2
The expression that is equivalent to 5/4x +33-2+2 is 5x + 132/4. Option C
How to determine the valueIt is important to note that algebraic expressions are defined as expressions that consists of factors, variables, constants, coefficients and terms.
These expressions are also made up of arithmetic operations.
These operations are listed as;
AdditionBracketParenthesesMultiplicationDivisionSubtractionFrom the information given, we have that;
5/4x +33-2+2
Add or subtract the values
5/4x + 33
Find the LCM, we have;
5x + 132/4
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Complete question:
Which expression is equivalent to 5/4x +33-2+2
5x + 132
6x + 132/4
5x + 132/4
6x + 132
Solve.
13. A ferry shuttles from Seattle to Vancouver Island and back. Because of
head winds, the return trip is slower than the trip to the island. The
average speed of the, ferry, in miles per hour, is given by the
2d
expression:
What is the average speed of the ferry?
d
+
50 60
The average speed of the ferry is 54.54 miles per hour.
The expression for the average speed is given [tex]\frac{2d}{\frac{d}{50}+\frac{d}{60} }[/tex].
Now, the given expression can be solved as follows
2d÷ (6d/300 + 5d/300)
= 2d÷(11d/300)
= 2d×300/11d
= 600/11
= 54.54 miles per hour
Therefore, the average speed of the ferry is 54.54 miles per hour.
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If the dealership you are buying the car from is offering 6.3% interest on a 5 year loan, what will your monthly payment be? How am I able to solve this when the selling price is $56,937.
Answer:
Step-by-step explanation:
To calculate the monthly payment on a loan, you can use the formula for the monthly payment on an annuity: P = (r * PV) / (1 - (1 + r)^(-n)), where P is the monthly payment, r is the monthly interest rate, PV is the present value of the loan (i.e., the amount borrowed), and n is the total number of monthly payments.
In this case, the amount borrowed is $56,937 and the interest rate is 6.3% per year. To convert this to a monthly interest rate, we divide by 12: r = 0.063 / 12 = 0.00525. The loan term is 5 years, so the total number of monthly payments is n = 5 * 12 = 60.
Substituting these values into our formula for the monthly payment, we get: P = (0.00525 * 56937) / (1 - (1 + 0.00525)^(-60)) ≈ $1102.53. So, the monthly payment on this loan would be approximately $1102.53.
