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enot [183]
3 years ago
10

Suppose that all the points on the circular dartboard shown are equally likely to be hit by a dart. if the radius of the red cir

cle i 2 in. and the radius of the entire dartboard is 6 in, what is the probability of throwing a dart and hitting the white part of the board
Mathematics
2 answers:
Anestetic [448]3 years ago
8 0
This equals the  the area of white part / area of the entire dartboard

area of the entire board = pi * 6^2 = 36pi

area of white part = 36pi  - 2^2*pi  = 32pi

do required probability = 32pi / 36pi  =  0.889   or 88.9 %   (to nearest tenth)


or as a fraction it is 8/9
ch4aika [34]3 years ago
4 0

Answer: 89% is correct!

Step-by-step explanation:

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(2x + 3) - (-8 - 2x)
masha68 [24]

Answer: 4x+11

Step-by-step explanation: Distribute the negative to the -8 and -2x. This will make 2x+3+8+2x. Combine like terms and you will get 4x+11. Hope this helps!

7 0
3 years ago
Log(x-2)+log2=2logy<br>log(x-3y+3)=0​
In-s [12.5K]

Answer:

<h2>x = 4 and y = 2 or x = 10 and y = 4</h2>

Step-by-step explanation:

\left\{\begin{array}{ccc}\log(x-2)+\log2=2\log y&(1)\\\log(x-3y+3)=0&(2)\end{array}\right

===========================\\\text{DOMAIN:}\\\\x-2>0\to x>2\\y>0\\x-3y+3>0\to x-3y>-3\\=====================\\\\\text{We know:}\ \log_ab=c\iff a^c=b,\\\\\text{therefore}\ \log_ab=0\iff a^0=b\to b=1\\\\\text{From this we have}\\\\\log(x-3y+3)=0\iff x-3y+3=1\qquad\text{add}\ 3y\ \text{to both sides}\\\\x+3=3y+1\qquad\text{subtract 3 from both isdes}\\\\\boxed{x=3y-2}\qquad(*)\\\\\text{Substitute it to (1)}

\log(3y-2-2)+\log2=2\log(y)\qquad\text{use}\ \log_ab^n=n\log_ab\\\\\log(3y-4)+\log2=\log(y^2)\qquad\text{subtract}\ \log(y^2)\ \text{from both sides}\\\\\log(3y-4)+\log2-\log(y^2)=0\\\\\text{Use}\ \log_ab+\log_ac=\log_a(bc)\ \text{and}\ \log_ab-\log_ac=\log_a\dfrac{b}{c}\\\\\log\dfrac{(3y-4)(2)}{y^2}=0\qquad\text{use}\ \log_ab=0\Rightarrow b=1\\\\\dfrac{(3y-4)(2)}{y^2}=1\iff y^2=(3y-4)(2)\\\\\text{Use the distributive property}\ a(b+c)=ab+ac

y^2=(3y)(2)+(-4)(2)\\\\y^2=6y-8\qquad\text{subtract}\ 6y\ \text{from both sides}\\\\y^2-6y=-8\qquad\text{add 8 to both sides}\\\\y^2-6y+8=0\\\\y^2-2y-4y+8=0\\\\y(y-2)-4(y-2)=0\\\\(y-2)(y-4)=0\iff y-2=0\ \vee\ y-4=0\\\\\boxed{y=2\ \vee\ y=4}\in D

\text{Put the values of}\ y\ \text{to }\ (*):\\\\\text{for}\ y=2:\\\\x=3(2)-2\\\\x=6-2\\\\\boxed{x=4}\in D\\\\\text{for}\ y=4:\\\\x=3(4)-2\\\\x=12-2\\\\\boxed{x=10}\in D

4 0
3 years ago
FUNCTIONS QUESTION-----IF YOU ARE A GOOD PERSON PLZ SOLVE THIS FOR ME PLZ I WILL FOREVER BE GRATEFUL♥' GRAPH INCLUDED
stira [4]

Answer:

(a) Domain: x > 4

(b) Range: y < -2

Step-by-step explanation:

Domain is the set of x-values that can be inputted into function f(x).

Range is the set of y-values that can be outputted by function f(x).

We see that our x-values span from 4 to infinity. Since it is an open dot, we cannot include it in our domain:

(-4, ∞)

We also see that our y-values span from -2 to negative infinity. Since it is an open dot, we cannot include it in our range:

(-∞, -2)

5 0
3 years ago
Adam got 97, 70, 89, 99, 100, 78, 79, 89, 77, and 72 on his reading test. What is the mean of Adam's reading test?
ipn [44]

Answer: 85

Add up all the numbers: 97+70+89+99+100+78+79+89+77+72=850

Divide 850 by the amount of numbers:

850/10=85

I hope this helps and good luck! :)

5 0
3 years ago
What is the volume of the cylinder below?<br><br> Use 3.14 for pi.
neonofarm [45]

Answer:

about =502.65

Step-by-step explanation:

8 0
2 years ago
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