A target with a diameter of 70 cm has 4 scoring zones formed by concentriccircles. The diameter of the center circle is 10 cm. The width of each ring is 10cm. A dart hits the target at a random point. Find the probability that it will hit apoint in the yellow region.
Answers
The probability is equal to divide the area of the yellow region by the area of the complete circle
so
step 1
Find the area of teh complete circle
r=70/2=35 cm
substitute
[tex]\begin{gathered} A=\pi\cdot35^2 \\ A=1,225\pi\text{ cm2} \end{gathered}[/tex]step 2
Find the area of the yellow region
[tex]\begin{gathered} A=\pi(35^2-25^2) \\ A=600\pi\text{ cm2} \end{gathered}[/tex]step 3
find the probability
P=600pi/1,225pi
P=0.4898
or
P=48.98%
Related Questions
Divide the rational expressions. p2−p−22p2+3p+1÷p2−3p+2p2+5p−6 Enclose numerators and denominators in parentheses. For example, (a−b)/(1+n).
Answers
Given:
[tex]\frac{\frac{p^2-p-2}{2p^2+3p+1}}{\frac{p^2-3p+2}{p^2+5p-6}}[/tex]Simplify in the from of numerators and denominators.
[tex]\frac{p^2-p-2}{2p^2+3p+1}\times\frac{p^2+5p-6}{p^2-3p+2}[/tex]solve the inequality is:
[tex]undefined[/tex]What is the range of the graph for y = |x-2] + 3
Answers
it is easier to see this in the graph
So we can give values to X and look the graph
[tex]\begin{gathered} x=-2\longrightarrow\text{ y=7} \\ x=-1\longrightarrow y=6 \\ x=0\longrightarrow y=5 \\ x=1\longrightarrow y=4 \\ x=2\longrightarrow y=3 \\ x=3\longrightarrow y=4 \end{gathered}[/tex]the graph is something like this
and the range is all the values it can take in Y
From the graph we observe that values less than 3 will not be taken because the function is a absolute value
And it will only take values greater than 3
So the range is:
[tex]\lbrack3,\infty)[/tex]Graph each equation using the intercepts. Re-write in standard form first if necessary.-2x+4y=-8
Answers
-2x+4y = 8
First find the y intercept
Let x =0
-2(0) + 4y = 8
4y = 8
Divide by 4
4y/4 = 8/4
y = 2
The y intercept is 2
(0,2)
Now find the x intercept
y = 0
-2x +4(0) = 8
-2x = 8
Divide by -2
-2x/-2 = 8/-2
x = -4
The x intercept is -4
(-4,0)
We can plot the two points and draw a straight line between them
-4q-(-8q)+10 combine the like terms to create an equivalent expression
Answers
we have
-4q-(-8q)+10
step 1
Remove the parenthesis
-4q+8q+10
step 2
Combine like terms
4q+10
therefore
the answer is
4q+10HELP ME QUICK ASAP PLEASE!!! Name a pair of vertical, adjacnet supplementary angles, a linear pair, 4 colinear points, 3 non-colinear points, 2 different rays.
Answers
Name a pair of vertical, adjacnet supplementary angles, a linear pair, 4 colinear points, 3 non-colinear points, 2 different rays.
Part 1
vertical angles
we have that
m by vertical angles
Part 2
adjacent angles
we have that
mPart 3
supplementary angles (the sum is equal to 180 degrees)
mPart 4
linear pair (the sum of the angle of a linear pair is 180 degrees)
m
Part 5
4 collinear poinrs
D-J-G=N -----> are collinear (the four points lies in the same line)
Part 6
3 non collinear points
J-I-H
Part 7
2 different rays
GN and GH
Please help me with my calculus homework, really appreciate it.
Answers
Solution
For this case we have the following expression:
[tex]\sum ^{10}_{i=1}2i^2+4i-5[/tex]Then we can replace and we have:
[tex]2\cdot\frac{10(10+1)(2\cdot10+1)}{6}+4\cdot\frac{10(10+1)}{2}-5\cdot10=2\cdot385+4\cdot55-50[/tex]Solving we have:
770+ 220 -50= 940
a cyclist rode 3.75 miles in 0.3 hourshiw fast was she going in miles per our
Answers
Distance = 3.75 miles
Time = 0.3 hours
Speed = distance / time
Replacing:
Speed = 3.75/ 0.3 = 12.5 miles/hour
Which polynomial is a binomial?O A. 1 -2x+5x^4 O B. x^2 O C. 2p^3-p O D. 6-2x^3-4x^2+x^5
Answers
A polynomial is said to be binomial if it has 2 terms only.
Here the answer is Option C.
since it has only two terms, that is,
[tex]undefined[/tex]. -6.6 is some number of times as large as 5. What is the number?
Answers
Given that -6.6 is some number of times as large as 5.
Let x be the required number.
Given can be written as follows.
[tex]-6.6=5\times x[/tex][tex]\text{Use 6.6=}\frac{66}{10}\text{.}[/tex][tex]-\frac{66}{10}=5x[/tex]Dividing by 5 into both sides, we get
[tex]-\frac{66}{10\times5}=\frac{5x}{5}[/tex][tex]-\frac{66}{50}=x[/tex]Dividing 66 by 50, we get 1.32.
[tex]x=-1.32[/tex]Hence the required number is -1.32.
Select all of the steps that are possible when solving for X
Answers
We need to solve the following expression:
[tex]5\frac{1}{2}x+\frac{2}{3}x=37[/tex]To find which steps are possible we will solve the equation one step at a time and check which of these steps appear on the options.
The first step is to transform the mixed fraction into a improper fraction, we do that by adding the integer part wih the fraction part.
[tex]\begin{gathered} (5+\frac{1}{2})x+\frac{2}{3}x=37 \\ (\frac{2\cdot5+1}{2})x+\frac{2}{3}x=37 \\ (\frac{10+1}{2})x+\frac{2}{3}x=37 \\ \frac{11}{2}x+\frac{2}{3}x=37 \end{gathered}[/tex]The second step is to find the LCM of the two fractions and add them.
[tex]\begin{gathered} \frac{11\cdot3\cdot x+2\cdot2\cdot x}{6}=37 \\ \frac{33x+4x}{6}=37 \\ \frac{37x}{6}=37 \end{gathered}[/tex]The third step is to multiply both sides by 6.
[tex]\begin{gathered} \frac{37x}{6}\cdot6=37\cdot6 \\ 37x=222 \end{gathered}[/tex]The fourth step is to divide both sides by 37.
[tex]\begin{gathered} \frac{37}{37}x=\frac{222}{37} \\ x=6 \end{gathered}[/tex]The first, second and fourth step appear on the options. Therefore we should marke the option "x=6", the option "37/6 x=37" and the option "11/2 x + 2/3 x= 37".
Find the area of the circle. Use 3.14 for the value of pi and round the answer to nearest tenth
Answers
SOLUTION
Th formula for find the area of a circle is given to be
[tex]A=\pi r^2[/tex]Notice that the radius of the circle is 8 mi
Substitute r=8 into the formula for aea of a circle
[tex]A=\pi\times8^2[/tex]Calculate the area
[tex]\begin{gathered} A=3.14\times64 \\ A=200.96 \end{gathered}[/tex]Therefore the area of the circle is 200.96 square mi
Simplify 2x+10x+12/x^2+3x+2
Answers
we have the expression
[tex]\frac{2x+10x+12}{x^2+3x+2}[/tex]Combine like terms in the numerator
[tex]2x+10x+12=12x+12=12(x+1)[/tex]Simplify the denominator
[tex]x^2+3x+2=(x+2)(x+1)[/tex]substitute in the original expression
[tex]\frac{12(x+1)}{(x+1)(x+2)}=\frac{12}{x+2}[/tex]Jaxon read 12 books in 2 months. What was his rate of reading, in books per month? Give your answer as a whole number or a FRACTION in simplest form.On the double number line below, fill in the given values, then use multiplication or division to find the missing value.
Answers
12 books in two months mean 6 books in a month:
12---2
6--- x
12x=12
x= 1 month
Answer: 1 month.
Place the cards in 3 groups based on the type of polynomial
Answers
A monomial is a one-term polynomial
A binomial is a two-term polynomial
A trinomial is a three-term polynomial
Grouping the expressions given based on type:[tex]\begin{gathered} \text{Monomial: One term: } \\ 16 \\ 4x^2 \end{gathered}[/tex][tex]\begin{gathered} Binomial\colon\text{ Two terms} \\ 6x^2+x \end{gathered}[/tex][tex]\begin{gathered} \text{Trinomial: Thr}ee\text{ terms} \\ 12x^4+4x^3+2x \\ 3a^2+5a-2 \end{gathered}[/tex]Find the inverse function for f(x) = 675 + 2
Answers
Replace f(x) with y .
[tex]y=6x^5\text{ + 2}[/tex][tex]\begin{gathered} \text{make x the subject of the formular } \\ y-2=6x^5 \\ divide\text{ both sides by 6} \\ \frac{y-2}{6}=x^5 \\ \end{gathered}[/tex][tex]\begin{gathered} To\text{ make x stand alone } \\ \sqrt[5]{\frac{y-2}{6}}\text{ = x} \end{gathered}[/tex]Swap x and y
[tex]\sqrt[5]{\frac{x-2}{6}}\text{ = y}[/tex]Therefore,
[tex]f^{-1}(x)\text{ = }\sqrt[5]{\frac{x-2}{6}}[/tex]Suppose that n = 100 and p = 0.5 for a binomial experiment. Find the P(x > 50) A. 0.5398 B. 0.6179 C. 0.4602 D. 0.3821 E. None of these
Answers
we have that
P(x>50)=P(x=51)+P(x=52)+P(x=53)+.....P(x=100)
so
[tex]P(x=51)=\frac{100!}{51!(100-51)!}*0.5^{(51)}*0.5^{(49)}[/tex]P(x=51)=0.0780
If a function f has an inverse and f(-3) = 6. then f '(6) =
Answers
f(-3)=6
so, the points are
x=-3 and y=6
(-3,6)
f'(6)=
if w=f'(6)
f'(6)
x=6
y= by definition of inverse function is -3
f´(-6)=-3
11-1/2×=1A×=-2B×=0.5C×=1D×=20
Answers
11 - 1 / 2x = 1
Firstly, evaluate the numerator
11 - 1/2x = 1
Find the LCM
The LCM is 2x
11 / 1 - 1/2x /2x
22x - 1 /2x = 1
lntroduce cross multiplication
22x - 1 = 1 * 2x
22x - 1 = 2x
Collect the like terms
-1 = 2x - 22x
-1 = -20x
Divide both sides by -20
-1/-20 = -20x/-20
1/20 = x
x = 0.05
The answer is 0.05
(10 points), Joe bought a new car in 2011 for $45,000. In 2015, Joe was offered a fair price of$37,000 for his car, but he turned it downa) Build a linear algebraio model, (ie, a function), that helps Joe find the car's value when itis 7 years oldb) Use your model to give an estimate to the current value of Joe's car?c) Use your model to give an estimate to the value of Joe's car in 2012
Answers
We have two given values:
In 2011 the car costs $45,000
In 2015, the car costs $37,000.
Let's graph this function, the x-axis is going to be the years and the y- axis the cost.
Then, we are going to locate y=45000 at x=2011:
(2011, 45000)
and y=37000 at x=2015:
(2015, 37000).
STEP 2: line graphWe want to find a function for the straight line that connects the points:
STEP 3: line equationWe know that the equation of a line is given by:
y =mx + b
where m and b are numbers: m is the slope (it shows the inclination of the line) and b is the y-intercept.
We want to find m and b to obtain the equation.
m: slope
We have two points (first step):
(x₁, y₁) = (2011, 45000)
(x₂, y₂) = (2015, 37000)
We find the change of each variable from point 1 to point 2:
Δx = x₂ - x₁ = 2015 - 2011
= 4
Δy = y₂ - y₁ = 37000 - 45000
= -8000
We have that the slope is given by the rate between Δy and Δx:
[tex]\begin{gathered} m=\frac{\Delta y}{\Delta x}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ m=-\frac{8000}{4}=-2000 \end{gathered}[/tex]Then m = -2000, so this line equation should look like:
y =mx + b
↓
y = -2000x + b
b: y-intercept
In order to find b we replace x and y in the equation by a value we know they should have.
We have that when it is x=2011, then y=45000. Let's replace:
y = -2000x + b
↓
45000= -2000 · 2011 + b
Let's solve the equation for b:
45000= -2000 · 2011 + b
↓since -2000 · 2011 = -4,022,000
45,000= -4,022,000 + b
↓ taking -4,022,000 to the left
45,000 +4,022,000 =b
4,067,000=b
Then b= 4,067,000, so this line equation should look like:
y = -2000x + b
↓
y = -2000x + 4,067,000
Answer A: a linear model is y = -2000x + 4,067,000STEP 4: estimate to the current value of Joe's carThis is the year 2021. This means that x=2021. Let's replace in the equation and see what happens with y (the price of the car) this year:
y = -2,000x +4,067,000
↓
y = -2,000 ·2021 +4,067,000
Since -2,000 ·2021 = -4,042,000
y = -4,042,000 +4,067,000
y = 25,000
This means that the current value of the car is $25,000
Answer B: the current value of Joe's car is $25,000STEP 5: estimate to the value of Joe's car in 2012In 2012, x=2012. Replacing in the equation:
y = -2,000x +4,067,000
↓
y = -2,000 ·2012 +4,067,000
Since -2,000 ·2012 = -4,024,000
y = -4,024,000 +4,067,000
y = 43,000
Answer C: in 2012 the value of Joe's car was $43,000
what does a sequence of transformation mean?
Answers
A sequence of transformation is when two or more transformations are combined to form a new transformation.
For example, we have a two-step sequence when we rotate 90 degrees counterclockwise and then translate 5 units to the left. Both are transformations that produce an output image, that becames the input of the second transformation, and so on (if the sequence has more steps).
Which inequality represents all values of x for which the quotient below is defined?A.x -1B.x 1C.x < -1D.x > 1
Answers
Given:
[tex]\sqrt{15(}x-1)\div\sqrt{2x^2}[/tex]Required :
To calculate which option is correct
Explanation:
[tex]\begin{gathered} in\text{ the range of real numbers, the even root sign cannot be negative} \\ \\ so\text{ 15\lparen x-1\rparen}\ge0 \\ \\ so\text{ }x\ge1 \\ \\ And\text{ 2x}^2\ge0\text{ is established} \\ \end{gathered}[/tex]Required answer:
Option B
Circle O shown below has an arc of length 29 inches subtended by an angle of 2.6radians. Find the length of the radius, x, to the nearest tenth of an inch.
Answers
Solution
Note: Formula to use
From the question, we have
s = 29 inches
r = ?
theta = 2.6 rad
[tex]\begin{gathered} s=r\theta \\ 29=r(2.6) \\ r=\frac{29}{2.6} \\ r=11.15384615 \\ r=11.2inches \end{gathered}[/tex]Therefore,
[tex]x=11.2inches[/tex]Jerry took a sample of 444 employees in his office and observed how many hours they each worked one day. Here is what he found
Answers
The standard deviation formula is the following:
[tex]\sigma=\sqrt[]{\frac{\sum ^{\infty}_{n\mathop=0}(x_n-\bar{x})^2}{n-1}}[/tex]Since the value of n is 4, the denominator should be 4-1=3. Therefore, the answer is C) The denominator is incorrect.
Fill in the missing reasonA) Definition of Vertical AnglesB) Segment Addition PostulateC) Angle Addition PostulateC) Angle Addition PostulateD) Definition of Congruent
Answers
In this problem, we have that
BE+ED=BD and CE+EA=CA -----> Segment Addition Postulate
therefore
the answer is option B7/8 ÷ 2/8 = ????????
Answers
7/8÷2/8 =
= (7•8)/(8•2) = 56/16
= 56/16= 7/2
Answer is 7/2
find the product-6x^2(x^3+7x^2-4x+3)
Answers
This week I worked 10 hours at the local recreation center coaching soccer.When I picked up my paycheck, it had my pay for the 10 hours this week and $175 pay for thetime I worked last week.If the total paycheck was $325, how much did I get paid per hour (hourly wage)?a) Define your variable. (100b) Write an equation for this situation. (Apes)c) Solve your equation (2008)d) Interpret your solution by using it in acomplete sentence.
Answers
Let
x ------> the hourly rate
we have that
The algebraic expression that represent this situation is
10x+175=325
solve for x
10x=325-175
10x=150
x=15
that means
the hourly rate is $15 per hour
The hourly wage is $15 per one hour of work
a) the variable is x
x is the hourly wage
tb) he equation is
10x+175=325
c) solve the equation
x=15
d) Interpret your solution
the hourly rate is $15 per hour
The hourly wage is $15 per one hour of work
The difference of two rational numbers is an irrational number. Is the statement true or false?
Answers
The difference between the two rational numbers results in a rational number.
A rational number is a number that can be express as a fraction.
Hence the final is FALSE
[tex]\begin{gathered} Forexample2.5\text{ is a rational numner = }\frac{5}{2} \\ 3.1\text{ is a rational number = }\frac{31}{10} \\ Therefore,\text{ = }\frac{31}{10}\text{ - }\frac{5}{2} \\ =\text{ }\frac{31\text{ - 25}}{10} \\ =\text{ }\frac{6}{10} \end{gathered}[/tex]
So, the difference between two rational numbers results in a rational number.
I need some help solving this problem it’s from my ACT prep guide This is trigonometry subject
Answers
From the graph we notice that the period of the function is 2pi, this comes from the fact that the first maximum is at pi/4 and the second at 9pi/4, then the period is:
[tex]\frac{9\pi}{4}-\frac{\pi}{4}=\frac{8\pi}{4}=2\pi[/tex]And hence the period of the function is 2pi.
Also, from the graph we notice that the amplitude is 7 this can be seen as follows: the amplitude is half the distance from the minimum to the maximum, then we have:
[tex]A=\frac{1}{2}(3-(-11))=\frac{1}{2}(14)=7[/tex]The vertical shift of the graph is -4 and the horizontal shift is pi/4 to the right; hence we have that the function is:
[tex]f(x)=7\cos (x-\frac{\pi}{4})-4[/tex]What is the GCF of *9x2 + 12x – 6
Answers
We want to find the greatest common factor of the expression;
[tex]9x^2+12x-6[/tex]Let's expand each of the terms of the expression to find the common factor;
[tex]undefined[/tex]