we have that
sin^2(x)+cos^2(x)=1
we have
cos(x)=0.52
the angle lie in the IV quadrant
substitute
sin^2(x)+0.52^2=1
sin^2(x)=0.7296
sin(x)=(+/-)0.85
but
the angle lie in IV quadrant
so
is negative
sin(x)=-0.85Part 2
cos(x)=-0.54
III quadrant
the sine is negative too
substitute
sin^2(x)+(-0.54)^2=1
sin^2(x)=0.7084
sin(x)=-0.84A certain town has two kinds of youth basketball teams. When is a school team (S) and the other is a rec team (R) . On any given Saturday in December the probability that school team will have the game is 0.8, and the probability that a rec team will have a game is 0.7 and probably that both where the game is 0.65.on any given Saturday in December, what is the probability that either a rec team or a school team has a game?Answer Choices:A. 0.65B. 0.7C. 0.8D. 0.85
Answer:
D. 0.85
Explanation:
We were given the following information:
Probability of S = 0.8
Probability of R = 0.7
Probability of S & R = 0.65
The probability that either a rec team or a school team has a game is given by:
[tex]\begin{gathered} P(S)=0.8 \\ P(R)=0.7 \\ P(S\cap R)=0.65 \\ \text{Since the events are overlaaping, the applicable formula is:} \\ P(S\text{ }or\text{ }R)=P(S)+P(R)-P(S\cap R) \\ P(S\text{ }or\text{ }R)=0.8+0.7-0.65 \\ P(S\text{ }or\text{ }R)=1.5-0.65 \\ P(S\text{ }or\text{ }R)=0.85 \\ \\ \therefore P(S\text{o}r\text{R})=0.85 \end{gathered}[/tex]Therefore, the answer is D
Can u help this problem
Find the equation of the line containing the given points. Write the equation in slope-intercept form. (3,8) and (3,-4)
Answer with explanation: We have to find the equation of the line that passes through the given coordinate points, (3,8) (3,-4) the general equation of the line is as follows:
[tex]\begin{gathered} y(x)=mx+b\rightarrow(1) \\ m=\frac{\Delta y}{\Delta x}\rightarrow\text{ Slope of the equation} \end{gathered}[/tex]The slope of the equation is calculated as follows:
[tex]\begin{gathered} P_1(x_1,y_1)=(3,8) \\ P_2(x_2,y_2)=(3,-4) \\ \therefore\rightarrow \\ m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{-4-8}{3-3}=\infty \\ m=\propto \end{gathered}[/tex]This suggests the equation of the line is simply a vertical line at x = 3, the graph of the equation is as follows:
[tex]x=3\text{ Is the equation of the line}[/tex]Point K is the center of the circle. Which segment is a radius?FGGEFHKEGDKHE
SOLUTION
The radius of a circle is a line segment that runs from the center of the circle to any point of the circumference
Hence from the option provided, only the line |KH| runs from the center to a point of the circumference, hence it is a radius
Therefore the right option is the last one
Can you please help me solve this? It is for HW
Use a rule of three to find the number of won games in a season of 120 games.
If the rate is the same, then, you can write:
[tex]\frac{20}{110}=\frac{x}{120}[/tex]Now, solve for x and simplify:
[tex]\begin{gathered} x=\frac{20}{110}\cdot120 \\ x=21.81 \\ x\approx22 \end{gathered}[/tex]Hence, the Panthers would win 22 games
all you need is on the photo pleaseeeee i really need help
We can find the y-intercept evaluating the function for x = 0, so:
[tex]\begin{gathered} y(x)=-5x^2+20x+60 \\ y(0)=-5(0)^2+20(0)+60=0+0+60 \\ y(0)=60 \end{gathered}[/tex]---------
We can find the zeros evaluating the function for y = 0. So using the factored form:
[tex]\begin{gathered} -5(x-6)(x+2)=0 \\ so\colon \\ x1=6 \\ and \\ x2=-2 \end{gathered}[/tex]-----------------------------------------------
The vertex V(h,k) is given by:
[tex]\begin{gathered} h=\frac{-b}{2a} \\ k=y(h) \end{gathered}[/tex]Or we can find it directly from the vertex form:
[tex]\begin{gathered} y=a(x-h)^2+k \\ so \\ for \\ y=-5(x-2)^2+80 \\ h=2 \\ k=80 \end{gathered}[/tex]So, the vertex is:
[tex](2,80)[/tex]---------
The symmetry axis is located at the same point of the x-coordinate of the vertex, so the axis of symmetry is:
[tex]x=2[/tex]-----------------------
The maximum value is located at the y-coordinate of the vertex (if it is positive) so, the maximum value is:
[tex]y=80[/tex]69). If a restaurant's gross receipts for one day total $39.500, of which $5,600 are expenses that percent of the gross receipts are expenses?
Total receipts = $39,500
Expenses = $5,600
Percentage expenses =
[tex]\frac{5600}{39500}\times100=\frac{5600\times100}{39500}=14.177\approx14.2\text{ \%}[/tex][tex]\text{ \% expenses =}\frac{Actual\text{ expenses}}{\text{Total Receipts}}\times\frac{100}{1}[/tex]Solution: The percentage of expenses is 14.2%
(3,5) and (-1,9) slope finding b and writing equation
Answer:
• Slope, m =-1
,• Equation: y=-x+8
Explanation:
Gien the points: (x1,y1)=(3,5) and (x2,y2)=(-1,9)
Slope
[tex]Slope,m=\frac{y_2-y_1}{x_2-x_1}[/tex]Substitute the points:
[tex]\begin{gathered} m=\frac{9-5}{-1-3} \\ =\frac{4}{-4} \\ m=-1 \end{gathered}[/tex]The slope of the line is -1.
Equation of the Line
We use the point-slope form to find the equation of the line.
Using point (3,5) and slope, m=-1
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-5=-1(x-3) \\ y-5=-x+3 \\ y=-x+3+5 \\ y=-x+8 \end{gathered}[/tex]The equation of the line is y=-x+8.
why does adding and subtracting 2pi or 360 degrees give a coterminal angle?
SOLUTION:
Step 1:
In this question, we are given the following:
Why does adding and subtracting 2pi or 360 degrees give a coterminal angle?
Step 2:
The details of the solution are as follows:
5.Tyler is solving this system of equations:{4p + 2q = 628p -q=59He can think of two ways to eliminate a variable and solve the system:Multiply 4p + 2q = 62 by 2, then subtract 8p - q = 59 from the result.Multiply 8p - q = 59 by 2, then add the result to 4p + 2q = 62.5. Read the information above about how Tyler is solving the problem. Doboth strategies work for solving the system? Explain or show yourreasoning. *
I) 4p + 2q = 62
II) 8p - q = 59
Both strategies will work for solving the system, since, for the first one, he will eliminate the variable p and get the expression 5q = 65, and, for the second one, he will eliminate the variable q and get the expression 20p = 180
Grace and Maria are practicing for a fitness test. Each day, they do as many curl-ups as they can in 1 min. Which measures could best be used to argue that Maria is better at doing curl-ups than Grace is? Mean MAD Min Q1 Median Q3 Max Grace 36 3.25 30 32.5 37 38.5 43 38 4.5 Maria 24 35.5 39 42.5 45
For option A:
MAD and IQR:
MAD means Mean Absolute Deviation:
This is the measure that records the deviation from the average number of curl-ups that both girls can do.
Therefore, if the value of MAD is higher, it just means that the person tends to vary by a larger value, on the number of curl-ups she does.
In this question, Maria has a higher MAD of 4.5 while Grace's MAD is 3.25. This means that Grace's curl-ups tend to be closer to the average number of curl-ups she does over a period of time. While Mar
A window is 3/4 m high and 2/3 of it is covered with frosted glass. What part of a meter is frosted glass?
Since 2/3 of the 3/4 m high window is covered with frosted glass, multiply 2/3 by 3/4 to find what part of a meter is frosted glass:
[tex]\frac{2}{3}\times\frac{3}{4}=\frac{2\times3}{3\times4}=\frac{6}{12}=\frac{1}{2}[/tex]Therefore, 1/2 of a meter is frosted glass.
JetLine Airline provides Michael with the following measurements forcarry-on luggage: 14 in x 9 in x 22 in. Convert the dimensions tocentimeters.
Given that:
Dimensons of luggage = 14 in x 9 in x 22 in
Since 1 inch = 2.54 cm,
[tex]\begin{gathered} 14\text{ in = (14}\cdot2.54)cm \\ =35.56cm \end{gathered}[/tex][tex]\begin{gathered} 9\text{ in=(9}\cdot2.54)cm \\ =22.86cm \end{gathered}[/tex][tex]\begin{gathered} 22\text{ in=(22}\cdot2.54)cm \\ =55.88cm \end{gathered}[/tex]The dimension in centimeters is 35.56 cm x 22.86 cm x 55.88 cm.
Write each equation in standard form10. y + 1 = x + 213. y - 4 = -(x - 1)16. y - 10 = -2(x - 3)
Standard form of a line:
Ax + By = C
where A is a positive integer, B is an integer and C is a constant.
10. y + 1 = x + 2
y + 1 - y = x + 2 - y subtracting y at both sides
1 = x + 2 - y
1 - 2 = x + 2 - y - 2 subtracting 2 at both sides
-1 = x - y
13. y - 4 = -(x - 1)
(y - 4)*(-1) = -(x - 1)*(-1) Multiplying by -1 at both sides
-y + 4 = x - 1
-y + 4 + y = x - 1 + y Adding y at both sides
4 = x - 1 + y
4 + 1 = x - 1 + y + 1 Adding 1 at both sides
5 = x + y
16. y - 10 = -2(x - 3)
(y - 10)/(-2) = -2(x - 3)/(-2) Dividing by -2 at both sides
y/-2 +5 = x - 3
2*(y/-2 +5) = 2*(x - 3) Multiplying by 2 at both sides
-y + 10 = 2x + 6
-y + 10 + y = 2x + 6 + y Adding y at both sides
10 = 2x + 6 + y
10 - 6 = 2x + 6 + y - 6 subtracting 6 at both sides
4 = 2x + y
Caculate question a and b
Answer:
a. 9.4cm
b. 12.0cm
Step-by-step explanation:
a. (HYP)² = (ADJ)² + (OPP)²
= 5² + 8²
= 25 + 64
√(HYP)² = √89cm
HYP = 9.4cm
b. (ADJ)² = (HYP)² - (OPP)²
= 17² - 12²
= 289 - 144
√(ADJ)² = √145cm
ADJ = 12.0cm
Steven and his family are traveling out of town for the weekend. They drove 60 miles during the first two hours of the trip. If there are 5280 feet in a mile, which of the following is equivalent to their rate of speed
The rate of speed is 33 feet/second
The difference between two identical objects that are moving at the same time is the distance they cover is called the rate of speed.
Given that Steven and his family are traveling out of town for the weekend. They drove 60 miles during the first two hours of the trip
We have to find if there are 5280 feet in a mile what is the rate of speed
Distance = 60 miles
Time = 2 hours
The formula for the Rate of speed is given by
Distance travelled / time elapsed = rate of speed
R = d/t
R = 60miles / 2hours
R = 30 miles/hour
Now to determine feet per hour
= 30miles/hour x 5280 feet/mile
= 158400 feet/ hour
To determine feet per second
= 158400feet/hour x 1 hour / 3600sec
= 33 feet/second
Therefore the rate of speed is 33 feet/second
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some similarities and differences of xy plane and the complex plane
The difference between the xy plane and the complex plane is that in the first one we are representing an ordered pair (that is, two numbers) while in the complex plane we are representing only one number (but this number can be decomposed in an real part and an imaginary part).
Now, they are similar in that the construction is the same, that is, they are both made of two perpendicular lines that we call axis, the intersection is called the origin and is represented by the zero in each set.
In circle o, a diameter has endpoints (-5,4) and(3, -6). What is the length of the diameter?Answer choices: a.) sqrt 10b.) 2sqrt 41c.) sqrt 2 d.) 2sqrt 2
Diameter has endpoints (-5,4) and (3, -6).
the endpoints of the diameter = (-5,4) and (3,-6)
The length of diameter can be calculated by sqrt 10,11
Distance between two coordinates (-5,4) and (3,-6).
Distance formula is express as
[tex]\begin{gathered} \text{Distance = }\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^1^{}} \\ \text{Distance}=\sqrt[]{(3-(-5))+(-6+(4))} \\ \text{Diamter = }\sqrt[]{8-(-2)} \\ \text{Diameter = }\sqrt[]{10} \end{gathered}[/tex]Diameter = sqrt 10
Answer: Diameter = sqrt 10
An airplane pilot flies due north from Ft. Myers to Sarasota, a distance of 150 miles. She then turns N50°E and flies to Orlando, a distance of 100 miles How far is it from Ft. Myers to Orlando? Round to the nearest tenths
115 miles
1) Sketching this to better grasp it we have:
2) Since we could draw the route as a triangle, we can use the Law of Cosines to find out the distance between Fort Myers and Orlando:
[tex]\begin{gathered} a^2=b^2+c^2-2bc\cos (\alpha) \\ x^2=(100)^2+150^2-2(100)(150)\cos (50) \\ x^2=32500-2(100)(150)\cos (50) \\ x^2=13216.37 \\ \sqrt[]{x^2}=\sqrt[]{13216.37} \\ x\approx114.96\approx115 \end{gathered}[/tex]Note that we rounded off to the nearest tenth(114.9).
3) Hence, the answer is 115 miles
Which property is shown? 18a X 32b = 325 x 18a a. Associative Property of Multiplication b. Commutative Property of Multiplication c. Distributive Property d. Identity Property
Solution
We have the following equation given:
18a X 32 b = 32 b x 18a
And we can see that the solution is:
b. Commutatitative property of multiplication
since the order of the factors not alter the result
-0- -4 -325Determine the range of the function. If the range is a single value, enter the value. If the range is aninterval, write the interval using interval notation. Example: (2,3) or (-00,5). Enter -oo for negativeInfinity and oo for infinityNOTE: If you do not see an endpoint, assume that the graph continues forever in the samedirectionThe range is:Question Help: MessageinstructorOcType here to search
[-5,-3]
The Range is the set of corresponding outputs for the inputs in the Domain set
So for the function depicted
The Range is
[-5,-3] for these points are included
the US based motorcycle manufacturer says that it expects to build a 145000 motorcycles this year up from 135,000 last year find the percent of increase in production
The number of motor cycles produced last year is 135,000.
The number of motor cycles expected to produce is 145,000.
Therefore, the percentage of increase is,
[tex]\frac{(145000-135000)}{135,000}\times100[/tex]That is,
[tex]\begin{gathered} \frac{10000}{135000}\times100=\frac{10}{135}\times100 \\ =7.4 \end{gathered}[/tex]Therefore, the percentage of increase is 7.4%
Write the equation, (2)x+(3)y=(24) in slope-intercept form
the equation in slope- intercept form:
y = -2x/3 + 8
Explanation:
GIven: (2)x+(3)y=(24)
To write in slope intercept form, we apply the formula for a linear equation:
y = mx + c
where m = slope, c = intercept
2x + 3y = 24
Make y the subject of formula by taking x to the other side of the equation:
3y = -2x + 24
Divide through by 3:
[tex]\begin{gathered} \frac{3y}{3}=\frac{-2x}{3}+\frac{24}{3} \\ y\text{ = }\frac{-2x}{3}+8 \end{gathered}[/tex]when we compare the above equation with the equation of line, they are in alignment.
Hence, the equation in slope- intercept form:
y = -2x/3 + 8
Can 7/20 can be reduced to 3/5
7/20 can't be reduced to 3/5
Circle O shown below has an arc of length 34 inches subtended by an angle of 2.1 radians. Find the length of the radius, x, to the nearest tenth of an inch.
16.2 inches
Explanation
the arc length is given by the formula:
[tex]\begin{gathered} arclength=\theta r \\ where\text{ } \\ r\text{ is the radius } \\ \theta\text{ is the angle in radians} \end{gathered}[/tex]so
Step 1
a)let
[tex]\begin{gathered} r=x\text{ \lparen unknown\rparen} \\ angle=\theta=2.1\text{ rad} \\ arclength\text{ = 34 inches} \end{gathered}[/tex]b) now, replace in the formula and solve for x
[tex]\begin{gathered} arclength=\theta r \\ 34\text{ inches=2.1 rad*x} \\ divide\text{ both sides by 2.1 rad} \\ 16.19\text{ inches =x} \\ rounded \\ x=16.2\text{ inches} \end{gathered}[/tex]
therefore, the answer is
16.2 inches
I hope this helps you
determine wether the point is a solution of the system. (-1,-2) 5x-2y=-1 x-3y=5
Step 1
Given; The system of equation;
[tex]\begin{gathered} 5x-2y=-1--(a) \\ x-3y=5---(b) \\ \text{Required; To know if the point (-1,-2) is a solution to the system} \end{gathered}[/tex]Step 2
Input x=-1 and y=-2 in both equations and find if they will give -1 and 5 respectively.
[tex]\begin{gathered} 5(-1)-2(-2)=-5+4=-1 \\ -1-3(-2)=-1+6=5 \end{gathered}[/tex]Since both equations gave us -1 and 5 respectively when we input x=-1 and y=-2, then we can conclude that the point (-1,-2) is a solution to the system.
I got this wrong can you tell me what I did wrong and show me?
The value of the car after 10 years at the given rate of depreciation will be approximately $5013.02 .
The current value of the car = $18000
Rate of depreciation = 12%
So using the formula for depreciation we get:
Let the final value be A
∴ A = P ( 1 - R/100 )ⁿ
Substituting the values we get :
A = 18000(1-0.12)¹⁰
Solving we get:
A = $ 5013.01756....
A ≈ $ 5013.02
Due to usage, deterioration, or obsolescence, an asset reduces value over time. The unit of measurement for this drop is depreciation.
A reduction in asset value, or depreciation, can be caused by a number of other factors, such as unfavorable market conditions, etc.
Hence the final value of the car after 10 years is approximately
$ 5013.02 .
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if the inequality -8 < x > 10 was placed in interval notation it would be represented by
It would be represented by interval notation (-8,10].
Interval notation:
The collection of real numbers that are located between two numbers is known as an interval in mathematics. The starting and ending numbers will be shown using brackets in the interval notation method. There are two different styles of brackets on it: square and round. The end values are included if the interval is given in square brackets. The end values are not included when an interval is given in round brackets.
Instance: [7, 12] It refers to the range of values between 7 and 12, with 12 included but not 7.
Complete question:
If the inequality -8<x≤10 was placed in interval notation it would be represented by
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given that triangle DEF is a right triangle with acute angles D and F and right angle E, which trigonometric function would be equal to Sin(F).
EXPLANATION
We can represent this situation as shown as follows:
The expression of Sin(F) is equal to Sin F = Opposite/Hypotenuse = DE/DF
[tex]\sin F=\frac{Opposite}{\text{Hypotenuse}}=\frac{DE}{DF}[/tex]The equivalent expression would be:
[tex]Cos\text{ D=}\frac{Adjacent}{\text{Hypotenuse}}=\frac{DE}{DF}[/tex]Susan's Jewelry Shop is having a sale on necklaces. The store is offering a sale pack of 4 necklaces for $48.80. What is the unit price of a necklace in the sale pack?
Carly's ClothinStore is also having a sale on necklaces. The unit price of any necklace at Carly's Clothing Store is the same as the unit price of a necklace at Susan's Jewelry Shop How much would it
cost a customer for 10 necklaces at Carly's Clothing Shop?
Unit Price
The store offers a sales pack of 4 necklaces for $48.80. This means each necklace in this pack has a unit price of:
$48.80 / 4 = $12.20
Now we know the unit price of any necklace at Carly's Clothing Store is the same as the unit price at the competing store. This means each necklace at Carly's Clothing Store has a price of $12.20.
If a customer bought 10 of these necklaces, he would have to pay
10 * $12.20 = $122,00
For 10 necklaces at Carly's Clothing Store, a customer would pay $122