a spinner is divided into 8 equal sections. 5 sections are red and 3 are green. if the spinner is spun 3 times, what is the probability that it lands on red exactly twice?

Answers

Answer 1

Answer: Your gonna wanna multiple (5/8)(5/8) which is 25/64 or about 39 percent. (I might not be entirely right, sorry. )

Answer 2

Answer:

Answer:

(A) green and grey

Step-by-step explanation:

They both have a 2/8 chance therefore having the same probability

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Find the roots of the equation by completing the square: 3x^2-6x-2=0. Prove your answer by solving by the quadratic formula.

Answers

Calculating delta:
Δ=b²-4ac
a=3
b=-6
c=-2
Δ=36-4*3*(-2)=36+24=60
√Δ=√60
Delta is positive so there are two roots:
x1= $\frac{ -b+ \sqrt[2]{delta} }{2a}$
x1= $(6+ √(delta) )/(2*3)$ = $(3+ √(15) )/(3)$
x2= $(3- √(15) )/(3)$

$3x^2-6x-2=0\n\n(\sqrt3\ x)^2-2\cdot\sqrt3\ x\cdot\sqrt3+(\sqrt3)^2-(\sqrt3)^2-2=0\n\n(\sqrt3\ x-\sqrt3)^2-3-2=0\n\n(\sqrt3\ x-\sqrt3)^2=5\iff\sqrt3\ x-\sqrt3=-\sqrt5\ \vee\ \sqrt3\ x-\sqrt3=\sqrt5\n\n\sqrt3\ x=\sqrt3-\sqrt5\ \vee\ \sqrt3\ x=\sqrt3+\sqrt5\ \ \ \ \ |multiply\ both\ sides\ by\ \sqrt3\n\n3x=3-√(15)\ \vee\ 3x=3+√(15)\ \ \ \ \ \ \ |divide\ both\ sides\ by\ 3\n\nx=(3-√(15))/(3)\ \vee\ x=(3+√(15))/(3)$

$Prove:\n\n3x^2-6x-2=0\na=3;\ b=-6;\ c=-2\n\Delta=b^2-4ac\to\Delta=(-6)^2-4\cdot3\cdot(-2)=36+24=60\n\nx_1=(-b-\sqrt\Delta)/(2a);\ x_2=(-b+\sqrt\Delta)/(2a)\n\n\sqrt\Delta=√(60)=√(4\cdot15)=\sqrt4\cdot√(15)=2√(15)\n\nx_1=(6-2√(15))/(2\cdot3)=(3-√(15))/(3)\ \vee\ x_2=(6+2√(15))/(2\cdot3)=(3+√(15))/(3)$

Paula and Daniel went to the store to by ingredients for 27 cakes. Paula paid for 2/3 of the cakes and Daniel paid 14 dollars for his portion. How much money did Paula and Daniel spend on their portion of the cake in total?

Answers

so Daniel paid for 1 third because paula paid for the other 2/3
he paid 14 dollars so that's 1/3 of the amount
if you times 14 by 3 you get 42
you times the 13 by 3 because Daniel paid 1/3 you have to times it by 3 to get a whole.
so the answer is that they paid 42 dollars all together.

Daniel paid for 1/3 of the total, b/c they had to pay for the total they had to pay for 3/3 1 whole. Paula paid for 2/3 and Daniel paid for the rest which is the 14 if he paid for 1/3 and Paula paid for 2/3 she paid twice as much as he did. 14x2=28 Paula paid 28 dollars out of the total of total 42dollars it cost

PLEASE HELP !!!!!!!!!!!!!!!!!2. Circle P has center P(2, 0) and radius 20. Circle Q has center Q(0, 4) and radius 2.
(a) Describe the rule for translating center Q onto center P.
(b) Determine the scale factor for dilating circle Q so that it has the same radius as circle P.
(c) Are circles P and Q similar? Explain your answer.

Answers

(a) Describe the rule for translating center Q onto center P.
center P(2, 0)
center Q(0, 4)
you would need to add 2 units in x axis, and subtract 4 units on y axis.

(b) Determine the scale factor for dilating circle Q so that it has the same radius as circle P.
P radius 20, Q radius 2, radiusQ*10 = radiusP, so the scale factor is 10

(c) Are circles P and Q similar? Explain your answer.
they are similar because a similarity transformation (translation, dilation) exists between them

For what values of r does the function y = erx satisfy the differential equation y'' + 5y' + 6y = 0?

Answers

Answer:

$\huge\boxed{r=-2,-3}$

Step-by-step explanation:

To solve for the values of $r$ where the differentialequation $y'' + 5y' + 6y = 0$ is satisfied by the function $y=e^(rx)$ , we first need to find the first and second derivatives of $y$ with respect to $x$ , treating $r$ as a constant.

$\left[\frac{}{}y\frac{}{}\right]'=\left[\frac{}{}e^(rx)\frac{}{}\right]'$

↓ applying the chain rule to the right side: $\displaystyle \left[\frac{}{}f(x)^a\frac{}{}\right]' = a \cdot f(x)^((a\, -\, 1)) \cdot f'(x)$ where $f(x) = e^x$ and $a = r$