A construction crew is lengthening a road. Let I be the total length of the road (in miles). Let D be the number of days the crew has worked. Suppose that L = 3D + 200 gives L as a function of D. The crew can work for at most 60 days.Identify the correct description of the values in both the domain and range of the function. Then, for each, choose the most appropriate set of values.Onumber of days the crew has worked Olength of the road (in miles)?Onumber of days the crew has worked Olength of the road (in miles)?
Answers
The domain of a function is the set of all values for which the function is defined. In this case, we can see that the function depends of the variable D, which represents the number of days the crew has worked.
Since the crew can work for at most 60 days and the time can not be negative, the domain of the function is the set of all real numbers from 0 to 60.
On the other hand, the range of a function is the set of all values that the function takes. In this case, we can see that the dependent variable is L, which represents the length of the road. Then, we have:
[tex]\begin{gathered} L=3D+200 \\ \text{ If }D=0 \\ L=3(0)+200 \\ L=0+200 \\ L=200 \\ \\ \text{ If }D=60 \\ L=3\left(60\right)+200 \\ L=180+200 \\ L=380 \end{gathered}[/tex]Thus, the range of the given function is the set of all real numbers from 200 to 380.
Answer
Related Questions
Using the net below, find the surface area of the pyramid. Blin 2 in Surface Area . - [?] in.2 Enter
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The Solution:
The correct answer is 16 square in.
Given the net in the picture on the Question section, we are asked to find the surface area of the pyramid that can form using the given net.
The pyramid (or the net) has a total of 5 surfaces, these are:
4 similar triangles, each with a base of 2 inches and a height of 3 inches; and a square of side 2 inches.
So,
The required surface area is the total area of all 5 surfaces.
By formula, the area of a triangle is
[tex]A=\frac{1}{2}bh[/tex]While the area of a square is
[tex]A=l\times l[/tex]So, the required area of the pyramid is
[tex]\text{Area}=4(\frac{1}{2}bh)+(l\times l)[/tex]In this case,
[tex]\begin{gathered} =\text{base}=2\text{ in.} \\ h=\text{height}=3\text{ in.} \\ l=\text{side}=2\text{ in.} \end{gathered}[/tex]Substituting these values in the above formula, we get
[tex]\text{Area}=4(\frac{1}{2}\times2\times3)+(2\times2)=(4\times3)+4=12+4=16in.^2[/tex]Therefore, the correct answer is 16 square in.
Consider functions fg, and h below. 12 + 25 + 3 8 6 2 6 2 6 FB 2 6 8 Х 0 1 2. 3 h(x) -7 -4 -1 2 5
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We have the functions,
[tex]\begin{gathered} f(x)=x^2+2x+3 \\ \text{the rate of change of f(x) over (0,2 ) is } \\ rate-of-change=\frac{f(2)-f(0)}{2-0} \\ f(2)=2^2+2(2)+3=11 \\ f(0)=0^2+0+3=3 \\ so,\text{ average rate of change=}\frac{11-3}{2}=4 \end{gathered}[/tex]We move over to g(x), g(x) is an exponential function;
[tex]\begin{gathered} \text{From the graph,} \\ g(2)=7\text{ and g(0)=4} \\ so\text{ the average rate of change of g(x) over the interval (0,2) is} \\ \frac{g(2)-g(0)}{2-0} \\ =\frac{7-4}{2} \\ =\frac{3}{2}=1.5 \end{gathered}[/tex]We move over to h(x),
[tex]\begin{gathered} \text{From the table, h(0)=-4, h(2)=2} \\ \text{the rate of change of h(x) over the interval (0,2) is;} \\ \frac{2-(-4)}{2-0}=\frac{6}{2}=3 \end{gathered}[/tex]If we rank the rates of change of the function , we see that,
[tex]4>3>1.5[/tex]So, the rates of change from least to greatest is;
g,h,f.
Option B
write the equation of the slope intercept form with the given point and slope or two points. (-7,13) slope = -2
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Slope-intercept form of a line:
y = mx+ b
where m is the slope and b is the y-intercept.
Replacing into the equation with m = -2 and point (-7, 13) we get:
13 = -2(-7)+ b
13 = 14+ b
13 - 14 = b
-1 = b
Then, the equation is:
y = -2x - 1
In the diagram below, AD bisects ZC AB, mZADB = 95º and mZCAD = 34°. Find mZB.
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please send me the picture of your question
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we know that
The sum of the interior angles in any triangle must be equal to 180 degrees
so
In the triangle ADB we have that
mwe have that
m because AD bisects angle CAB
so
msubstitute
34+95+m
mmPlease, Do you understand all the steps so far?Does the explanation satisfy your question and do you understand the answer?
If you don’t need further explanation on this question, we can end the session. A pleasure to attend you, Remember that after our session, the answer is saved in your profile. Thanks and have a great day! Good Bye.
8. What is the radian measure of an angle of 54°
Answers
To get the radian measure of an angle we have to do this conversion:
[tex]54°\times\frac{\pi\text{ rad}}{180°}=0.9425[/tex]The radian measure of an angle of 54° is 0.9425 radians.
8. Pentagon MNOPQ with M(-4,1),N(-2,3). O(0, 3), P(4, 3), and Q(2,-7): rotate 90° counterclockwise, then dilate by a factor of 2/3 120 What are the two arrow rules to show this composition? 12 b. Is the dilation an enlargement or reduction? How do you know? 710 с. What are the vertices of the image after the transformation?
Answers
Given data:
The given coordinates of the pentagon are M(-4,1),N(-2,3). O(0, 3), P(4, 3), and Q(2,-7).
The coordinatte after 90 degrees counterclockwise rotation is,
[tex]\begin{gathered} M(-4,1)\rightarrow M^{\prime}(-1,\text{ -4)} \\ N(-2,\text{ 3)}\rightarrow N^{\prime}(-3,\text{ -2)} \\ O(0,\text{ 3)}\rightarrow O^{\prime}(-3,\text{ 0)} \\ P(4,\text{ 3)}\rightarrow P^{\prime}(-3,\text{ 4)} \\ Q(2,\text{ -7)}\rightarrow Q^{\prime}(7,\text{ 2)} \end{gathered}[/tex]The final coordinates after 2/3 dilation factor is,
[tex]\begin{gathered} M^{\doubleprime}\rightarrow\frac{2}{3}(-1,\text{ -4)} \\ \rightarrow(-\frac{2}{3},\text{ - }\frac{8}{3}) \\ N^{\prime\prime}\rightarrow\frac{2}{3}(-3,\text{ -2)} \\ \rightarrow(-2,\text{ -}\frac{4}{3}) \\ O^{\doubleprime}\rightarrow\frac{2}{3}(-3,\text{ 0)} \\ \rightarrow(-2,\text{ 0)} \\ P^{\doubleprime}\rightarrow\frac{2}{3}(-3,\text{ 4)} \\ \rightarrow(-2,\frac{8}{3})^{} \\ Q^{\doubleprime}\rightarrow\frac{2}{3}(7,\text{ 2)} \\ \rightarrow(\frac{14}{3},\text{ }\frac{4}{3}) \end{gathered}[/tex]Thus, the final coordinates after transformation are M''(-2/3, -8/3), N''(-2, -4/3). O''(-2, 0), P''(-2, 8/3), and Q''(14/3, 4/3).
Two trains leave towns 508 kilometers apart at the same time and travel toward each other. one train travels 16 km/h slower than the other. if they meet in hours, what is the rate of each train?
Answers
Given:
Distance, d = 508 km
Time, t = 2 hours
Let x be the speed of one train.
Let x-16 be the speed of another train.
To find: Speed of the two trains
Explanation:
We know that,
[tex]\text{Speed }\times Time=Dis\tan ce[/tex]Let us frame the equation as follows,
[tex]\begin{gathered} (\text{Speed of the train 1 + Speed of the train }2)\times Time=Dis\tan ce \\ (x+x-16)\times2=508 \\ 2x-16=\frac{508}{2} \\ 2x-16=254 \\ 2x=270 \\ x=135\text{kmph} \end{gathered}[/tex]Final answer:
The speed of the faster train is 135 km/h.
The speed of slower train is 119 km/h
You deposit $4000 in an account earning 8% interest compounded monthly. How much will you have in the account in 15 years?
Answers
Given:
a.) You deposit $4000 in an account earning 8% interest compounded monthly.
Question: How much will you have in the account in 15 years?
We will be using the following formula:
[tex]\text{ A = P(}1\text{ + }\frac{r}{n})^{nt}[/tex]Where,
A=final amount
P=initial principal balance = $ 4,000
r=interest rate = 8% = 8/100 = 0.08
n=number of times interest applied per time period = monthly = 12
t=number of time periods elapsed = 15 years
We get,
[tex]\text{ A = P(}1\text{ + }\frac{r}{n})^{nt}[/tex][tex]\text{ A = (4,000)(}1\text{ + }\frac{0.08}{12})^{(12)(15)}[/tex][tex]\text{ = (4,000)(1 + }0.00667)^{180}=(4,000)(1.00667)^{180}[/tex][tex]\text{ = (4,000)(3.30889307445)}[/tex][tex]\text{ A = 13,235.57229780234 }\approx\text{ \$13,235.57}[/tex]Therefore, in 15 years, you will have $13,235.57 in your account.
3(x-y) when x=4 and y=1
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Solve for x in the equation −2x + 3b > 5
Answers
SOLUTION
We want to solve for x in
[tex]-2x+3b>5[/tex]This becomes
[tex]\begin{gathered} -2x+3b>5 \\ -2x>5-3b \\ \text{divide both sides by -2, and the inequality reverses, we have } \\ \frac{-2x}{-2}<\frac{5-3b}{-2} \\ x<\frac{5-3b}{-2} \end{gathered}[/tex]Hence the answer is
[tex]x<\frac{5-3b}{-2}[/tex]A suit was marked with a 10% discount.
If the discount is $10.00, what was the original price of the suit?
Answers
Answer:
The suit originally cost $100.
Step-by-step explanation:
To find the original price of the suit, you can set up a ratio and solve for the missing variable. In this case, we can set up a ratio as such:
10%/100% = $10.00/x, where x is the original price, and $10.00 is 10% of the original. In fraction form, this looks like [tex]\frac{10}{100} =\frac{10}{x}[/tex]. Here, it is clear that for these two to be equal, x must be equal to 100.
A roast beef sandwich costs $6.75. A customer buys multiple roast beef sandwiches. write an equation that represents the situation. Use x to represent the number of roast beef sandwiches. then determine how many sandwiches tje customer buys. Amount Used for payment =$50Change Received = $16.25The Customer buys. sandwiches ?
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Let x be the number of sandwiches.
Since each sandwich has a cost of $6.75, then for x sandwiches the cost would be:
[tex]\text{6}.75x[/tex]The change received is the difference between the amount used for payment and the cost of the sandwiches.
The difference between the amount used for payment and the cost of the sandwiches can be represented algebraically as:
[tex]50-6.75x[/tex]This number must be equal to the change received. Then:
[tex]50-6.75x=16.25[/tex]Solve for x. To do so, substract 50 from both sides:
[tex]\begin{gathered} \Rightarrow-6.75x=16.25-50 \\ \Rightarrow-6.75x=-33.75 \end{gathered}[/tex]Next, divide both sides by -6.75:
[tex]\begin{gathered} x=\frac{-33.75}{-6.75} \\ \Rightarrow x=5 \end{gathered}[/tex]Therefore, the customer buys 5 sandwiches.
Joe has brownies the length of each brownies is 7 cm and the width is 5 cm is its total area of the pan is 560 cm how many brownies did Joe have
Answers
Start by calculating the area of a single brownie using
[tex]A=L\cdot W[/tex][tex]\begin{gathered} A=7\operatorname{cm}\cdot5\operatorname{cm} \\ A=35\operatorname{cm} \end{gathered}[/tex]To find the amount of brownies Joe can make in his pan, divide the area of the pan into the single brownie area
[tex]\frac{560}{35}=16[/tex]Joe had 16 brownies.
Consider the following function.f(x) = 6x^2 − 4xFind the limit.
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Given:-
[tex]f(x)=6x^2-4x[/tex]To find:-
[tex]\lim _{\Delta x\to0}\frac{f(x+\Delta x)-f(x)}{\Delta x}_{}[/tex]So now we substitute the known values we get,
[tex]\frac{f(x+\Delta x)-f(x)}{\Delta x}_{}=\frac{6(x+\Delta x)^2-6x^2+4x}{\Delta x}[/tex]So by furthur simplification. we get,
[tex]\frac{6(x+\Delta x)^2-6x^2+4x}{\Delta x}=\frac{6x^2+12x\Delta x+(\Delta x)^2-6x^2+4x}{\Delta x}[/tex]So we get is,
[tex]\frac{6x^2+12x\Delta x+(\Delta x)^2-6x^2+4x}{\Delta x}=\frac{12x\Delta x+(\Delta x)^2^{}+4x}{\Delta x}[/tex]So by furthur simplification we get,
[tex]undefined[/tex]17. To measure the amount of space in rectangular prism, we need three dimensional figures as unit of measure. Which is the formula for finding the volume?A. V= 1/3 x B x HB. V= S x S x SC. V= L x W x H18. A rectangular prism has length of 4 cm, width of 3 cm and height of 5 cm. Find the volume.A. 50 cu cmB. 55 cu. cmC. 60 cu. cmD. 45 cu. cm19. A wooden box has 20 cm on each edge. Find its volume.A. 875 cu. cmB. 8 000 cu. cmC. 8 875 cu. cm20. Juana’s sewing box is 3 dm long, 2dm wide, and 4 dm high. What is its volume?A. 12 cu. dmB. 24 cu. dmC. 33 cu. dmD. 34 cu. dm21. Five metal cubes with sides of 5 cm were melted and casted into a bigger cube. Find the volume of the new cube.A. 125 cu.cmB. 405 cu. cmC. 325 cu. cmD. 625 cu. cm
Answers
(17) The First part of the question asked us to find the formula used in determining measure of the amount of space in a rectangular prism which is invariably the volume.
The three dimensions needed to determine the Volume of a rectangular prism are:
Length
width
Height.
To get the volume, we mutiply the three together.
So:
Volume = Length * Width * Height.
V = L * W * H
Therefore, the correct option is C, which is V = L x W x H.
(18) Givne the following dimensios of a rectangular prism as:
Length = 4 cm
Width = 3 cm
Height = 5 cm
We are to find the volume
Recall, the formula for finding volume of the rectangular prism is:
V = L x W x H
V = 4 x 3 x 5
V = 60 cm³
Therefore, the volume of the rectangular prism = 60 cm³
So, the correct option is C, which is 60 cm³.
Find the surface area of the square pyramid. 16 in 5 in
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Answer:
Explanation:
The below formula can be used to find the surface area of a square pyramid;
[tex]SA=A+\frac{1}{2}ps[/tex]where A = area of the base
p = perimeter of the base
s = slant height = 6 in
Since the base of the pyramid is a square, let's go ahead and find the area of the square;
[tex]A=5^2=25in^2[/tex]Let's go and find the perimeter of the square;
[tex]P=4\times5=20in[/tex]Let's substitute the values into our above formula and solve for SA;
[tex]undefined[/tex]Solve the system. 2x + y + 3z = 20 x + 2y - z = -11 3x 2z = -3 Enter your answer as an ordered triple
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The procedure 20 x + 2y - z = -11 3x 2z = -3 denotes an ordered triple with x = 1, z = 3, and y = 2.
What is meant by mathematical equations?A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation. The true power of equations lies in their ability to precisely describe various aspects of the world. (This is why, when one can be found, a solution to an equation can be useful.)Therefore,
let x + 2y + 3z = 14...…(1)
3x + y + 2z = 11.....(2)
2x + 3y + z = 11.....(3)
multiplying (2) by 2 and subtracting (1) from it we get,
=5x + z = 8...…..(4)
again multiplying (2) by 3 and subtracting (3) from it we get,
= 7x + 5z = 22.....(5)
Now multiply (4) by 5 and subtract (5) from it we get 18x = 18
therefore x = 1
substituting the x in (4) we get the value of z as
= 5(1) + z = 8
∴ z = 8 - 5 = 3
and substitute x and z in (1) we get
1 + 2y + 3(3) = 14
2y = 14 - 1 - 9 = 4
∴ y=2
The complete question is:
The solutions of the equations x+2y+3z=14, 3x+y+2z = 11, 2x + 3y + z = 11
A [tex]$\quad \mathrm{x}=\mathrm{O}, \mathrm{y}=2, \mathrm{z}=4$[/tex]
B [tex]$\quad \mathrm{x}=1, \mathrm{y}=\mathrm{O}, \mathrm{z}=4$[/tex]
C [tex]$\mathrm{x}=\mathrm{O}, \mathrm{y}=1, \mathrm{z}=8$[/tex]
D [tex]$x=1, y=2, z=3$[/tex]
To learn more about mathematical equations, refer to:
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A rectangular field has a length that is triple its width and a diagonal of 98 meter find the areaI need help, help me please
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Data:
l = 3w
d = 98
To find the area, lets start drawing the field:
The area of rectangle is
[tex]A=b\cdot h[/tex]In this case
b = w
h= l = 3w
To determine the value of w, we can use the right triangle and the value of the diagonal that is the hypotenuse of the triangle. Then using Pythagoras theorem:
[tex]w^2=d^2-(3w)^2[/tex]We can clear the w from this equation:
[tex]w^2=d^2-9w^2[/tex][tex]w^2+9w^2=98^2[/tex][tex]10w^2=98^2[/tex][tex]w^2=\frac{98^2}{10}[/tex][tex]w=\sqrt[]{\frac{98^2}{10}}=\sqrt[]{960.4}=30.99\approx40[/tex]Now we know the value of w = 40
Then the area of the field is:[tex]A=w\cdot3w[/tex][tex]A=40m\cdot3(40m)=4800m^2[/tex]sina ½ sin ( a + b) + sin(a = b)] OA. cos a OB.. sina OC. sinb D. cos b
Answers
Answer:
A. cos a
Explanation:
The relevant trigonometric formula we have is
[tex]\sin a\cos a=\frac{1}{2}[\sin(a+b)+\sin(a-b)][/tex]Now comparing the above formula with the one given in the question tells us that the missing term in the equation is cos a.
Therefore, choice A is the right answer!
Which equation describes a line of symmetry for square ABCD? x = 0 y = x x = -2 y = -2
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The equation of the line is DB from y = mx + b
From the graph y = 0 when x =0
this means y = x
The graph cuts through the origin, Meaning the y -intercept = 0
answer is: y = x
3) P(A) = 0.65 P(B) = 0.35 P(A and B) = A.0.2275B.0.2c.0.06d.0.315
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For the given probabilities:
[tex]\begin{gathered} p(AandB)=^{}0.65\cdot0.35 \\ p(AandB)=0.2275 \end{gathered}[/tex]Find the standard form of the ellipse with the information below:Foci: (7, 10), (7,2)co vertices: (10,6), (4,6)
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The general form of the equation of an ellipse is given as:
sam was charged $1,050 in interest on a loan with a 2.5% interest rate. What was the original amount of the loan it he took 5 years to pay it back?
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Answer:
$8,400
Explanation:
The interest can be calculated using the following equation:
[tex]I=\text{P}\cdot r\cdot t[/tex]Where P is the original amount of the loan, r is the interest rate, and t is the time that the person tool to pay it back.
So, we can replace I by $1,050, r by 2.5% or 0.025, and t by 5 years. Then:
[tex]1050=P\cdot0.025\cdot5^{}[/tex]Finally, we can solve for P as:
[tex]\begin{gathered} 1050=P\cdot0.125 \\ \frac{1050}{0.125}=\frac{P\cdot0.125}{0.125} \\ 8400=P \end{gathered}[/tex]Therefore, the original amount of the loan was $8,400
)) How many terms are in this expression? 7c+ 3d Submit
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The number of terms is the expression is equal to 2.
7c
3d
In algebra, terms are the values on which the mathematical operations take place in an expression.
A term can be a constant or a variable or both in an expression.
In the expression, 7ca + 3d, 7c and 3d are terms.
amyturner112150 is typing
How Much Paint Would Cover This Pyramid Without The Square Base ?
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To answer this question, we will assume that the pyramid's slant height is 10ft.
We have a square pyramid in which we have:
• The pyramid's base is a square with a side that measures 6ft.
,• The height of the pyramid is equal to 8ft.
,• The slant height is 10ft
Then we need to find the surface area of the pyramid without the square base, and we can see that:
1. We can see that the surface area of the pyramid without the square base is represented by four (4) triangles with equal base (6ft) and equal height (10ft). Then since the area of a triangle is given by:
[tex]A___{triangle}=\frac{bh}{2}[/tex]2. Therefore, we need to find the area of one of the triangles, and then multiply this result by 4 to find the asked area as follows:
[tex]A_{triangle}=\frac{6ft*10ft}{2}=\frac{60ft^2}{2}=30ft^2[/tex]3. Then the total area of the pyramid without the square base is:
[tex]\begin{gathered} A_{4triangles}=4(30ft^2)=120ft^2 \\ \\ A_{4triangles}=120ft^2 \end{gathered}[/tex]Therefore, in summary, the paint would cover 120ft² (square feet) without the square base.
Need to know the answers or how to do them.#1 please
Answers
Looking at angle G, it inscribes the arc FH, which is a diameter of the circle.
Since an inscribed angle measures half the inscribed arc (and arc FH measures 180°), angle G measures 90°.
Now, let's calculate angle F:
[tex]\begin{gathered} F+G+H=180\\ \\ F+90+48=180\\ \\ F+138=180\\ \\ F=180-138\\ \\ F=42° \end{gathered}[/tex]Arc GH is inscribed by the angle F, so we have:
[tex]\begin{gathered} F=\frac{1}{2}GH\\ \\ 42=\frac{1}{2}GH\\ \\ GH=2\cdot42\\ \\ GH=84° \end{gathered}[/tex]So the indicated arc measures 84°.
Parallel lines never meet and will never cross each other.
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True
Parallel lens are never meet and cross each other
Need help with #81, specifically don’t understand how to determine the domain
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ANSWERS
a) Domain: x ∈ (-∞, -1) ∪ (-1, ∞)
b) Domain: x ∈ (-∞, 0) ∪ (0, ∞)
EXPLANATION
These compositions are:
a)
[tex]f\circ g=f(g(x))=\frac{2}{g(x)}=\frac{2}{x+1}[/tex]And
b)
[tex]g\circ f=g(f(x))=f(x)+1=\frac{2}{x}+1[/tex]To find the domain in each function we have to find the values that x cannot take. If there aren't any, then the domain is all real values.
For composition a) note that x is in the denominator as (x+1). As we know, for real numbers the denominator can't be 0, so that's our restriction:
[tex]x+1\ne0[/tex]Solving for x:
[tex]x\ne-1[/tex]The domain for f º g is all real values except x = -1
For composition b) we have x in the denominator too, but it is alone. Therefore, as said before, x cannot be 0.
Can you please help me out with a question
Answers
37.5%
1) Examining the Spinner we can see that the total possibilities are:
90+45+90+135 = 360
2) Since the question is P(green or red) we can write out:
[tex]\begin{gathered} P(g\text{ or r) = }\frac{90}{360}+\frac{45}{360}=\frac{135}{360}=0.375 \\ P(g\text{ or r) = P(g) +P(r) } \end{gathered}[/tex]Note that the event of picking red or picking green can't exist simultaneously so they are mutually exclusive.
The result in percentage will be obtained by multiplying it by 100
3) Hence, the answer is 37.5%
Determine the expected value for the equal segment spinner below: