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Our objective is to add up these probabilities and subtract from 1 to find the probability that we are neither an 8 or an ace.

The probability of getting an ace is 4/52=1/13. The same goes for an 8. So, our probability is 1/13 + 1/13 = 2/13.

The probability of neither an 8 nor an ace is 1-2/13 = 11/13.

Feel free to leave any comments or concerns. -- David

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Sure thing.

4 + m/2=7.
m/2=3.
Cross multiplying, m=6.

You can substitute this value back in to confirm that it is correct.

Feel free to comment with any questions or concerns. -- David

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Let dimes=x.
Let nickles = x+22.

So, 50 = x + x + 22 = 2x + 22
28=2x
14=x
So, you have 14 + 22 or 36 nickels.

Feel free to leave comments with any questions or concerns. -- David

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This is similar to the other question that you submitted a few minutes ago. I solved that one for you. Be sure to check that solution, and then let me know if you can handle this problem or need it solved too.
Thanks,
David

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Here we are dealing with a classic case of pure substitution. Simply take your value for x and substitute it in to find y.

4x-3xy=16; x=-2; 4(-2) -3(-2)y=16
So, -8 +6y =16.
6y=24.
y=4

Feel free to leave comments with any questions or concerns. -- David

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Yes you are correct. Good job!

Feel free to leave comments with any questions or concerns. -- David

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Please clarify this question for me to solve it. It is unclear what is being squared and sqr-rooted.

Thanks,
David

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by foiling, we determine that .... (2 square root 2 + square root 3)(square root 2 + 5 square root 3)= 4 + 10sqr-rt(6) + 1sqr-rt(6) + 15 = 19 + 11 sqr-rt(6)

Feel free to comment with any questions or concerns. -- David

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This question basically says that (x+y+z)/3=80. That means the sum of the three numbers is 240, by cross multiplication. Given that two of the numbers are 74, and 78, and you know that the sum of all three is 240, we can subtract these values from 240 to obtain the value of our third number. So, the value of the third number is 240 - 74 - 78 = 88.

Feel free to comment with any questions or concerns. -- David

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g(x) = (2x+1)/(x-7). The domain is all values of x that make an output (y) possible. All values of X are in the domain, except when the equation is undefined. The rational expression will be undefined when you divide by 0. As such, x-7 is not equal to 0. Therefore, x is not equal to 7.

So your domain is D={x|x is not equal to 7} ... or (- infinity,7) U (7, infinity).

Feel free to leave any comments or concerns. -- David

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To solve this question, use the FOIL process -- First, Outer, Inner, Last.

Your result is -15 + 12 sqr-rt(2) - 5 sqr-rt(2) + 8 = -7 - 7 sqr-rt(2).

Feel free to leave comments or concerns. -- David

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You are right, it is a proportion! This question is purely a ratio problem. Your ratio is (195 bolts)/(20 minutes)=(312 bolts)/(X minutes)

Cross-multiplying and solving for x, you get 32 minutes.

--David

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You are dealing with an arithemetic sequence with d=r, a(sub1)=2, and n=2001.

Your formula for finding the a(subn) term of an arithmetic sequence is
a(subn)=a(sub1) + (n-1)d = 2 + (2001-1)(3) = 6002.

I hope this help! Feel free to leave comments or concerns. -- David

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Including 100, your perfect squares are:

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, which is 10 numbers.

So from 1-100 you have 90 numbers. Add 10 more, and your answer is C) 110.

Feel free to leave comments or concerns.

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Setting the equation into slope-intercept form, you have:

y=-7/4x +33/4

Therefore, your slope (m)= -7/4 and your y-intercept (b)=33/4.

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Standard form for complex expressions is a +/- bi.

Let's simplify. -4-7i/6i + 1/6 = -4 + 1/6 -7i/6i = -23/6 -7/6 (notice how the i's cancel) = -30/6 = -5

Your final answer is -5 + 0i or -5.

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We have five subjects and we are dealing with combinations, not permutations here. We know that if we have five as a subset, there is 1 combination. 5C5. 4 as a subset, leaves us with 5 combinations... 5C4.

Notice how we are working with combinations in the problem. We want sets of 5, 4, 3, 2, 1, and 0 (or empty set).

With combinations, we need only add 5C5 + 5C4 + 5C3 + 5C2 + 5C1 + 5C0.

You can solve a combination based off the definition, which states that nCr= n!/(n-r)!, where ! denotes factorial.

So, 5C5 + 5C4 + 5C3 + 5C2 + 5C1 + 5C0 = 1 + 5 + 10 + 10 + 5 + 1 = 32. Your answer is "B".

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Sure thing. To group, we need to find common factors and split the polynomial into two smaller segments. Our polynomial is: x^3 - 1 - x^2 + x. Let's rearrange it to look like x^3 - x^2 + x - 1. Now, taking our first two terms and factoring out an x^2, we have ... x^2(x-1) + 1(x-1). Notice how we have a common term (x-1), that we can factor out.

Factoring out (x-1), we have our factorized equation... x^3 - 1 - x^2 + x = (x^2+1)(x-1)

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You forgot to provide the midpoint. With the midpoint, you would approach it as such. Endpoints (a,b) and (c,d). Midpoint (e,f)

Midpoint = [(a+b)/2=e,(c+d)/2=f).

You would plug in your given values, cross multiply, subtract, and find the values of the other endpoint.

I hope this helps!

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Width=L-1
Length=L
Area=LW=L(L-1)=6

L^2-L-6=0
(L-3)(L+2)=0

So, L=3 [since -2 is an extraneous solution]
By substitution, Width=L-1=3-1=2

--
David

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A(x)=LW=(2x-1)(x-2)=2x^2-5x+2
A(5)=2(5)^2-5(5)+2=27
--
David

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angle=[180(n-2)]/n.

Typically, your angle will be given. Cross multiplying, you can solve for n.

--
David

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How many different sequences of 4 digits are possible if the first digit must be 3, 4, or 5 and if the
sequence may not end in 000? Repetition of digits is allowed.

Your first digit is 3, 4, or 5.

Assume we have four blanks. Our number is _ _ _ _. The first digit has 3 possibilities. We will multiply possibilities to get our total number of permutations. Since numbers can repeat, our possibilities are 3 x 10 x 10 x 10, or 3,000 total permutations. However, since we can't end in 000, we know that 3,000, 4,000, and 5000 are not possible. Therefore, our answer is 3,000 - 3 or 2,997 permutations.

--
David

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The difference of two numbers is -8 and the product is 20. The smallest number is?

x-y=-8 ; xy=20.

So, x=y - 8. Using substitution, we have:
(y-8)y=20
y^2-8y-20=0
(y-10)(y+2)=0.

Your two numbers are -2 and 10. (Note: It doesn't matter whether x or y is -2 or 10, since you are only looking for the smallest number).

Therefore, your answer is -2.

--
David

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The sum of two complex numbers is 6 and their product is 10. One number is?

a. -3+i
b. -3-i
***c. 3+i***
d. -6+i

We assume that we are dealing with a quadratic equation. The sum of two numbers is -b/a=6. Our product is c/a=10.

A quadratic equation is defined as Ax^2+Bx+C=0.

So, let's simply test our solutions to see which ones hold. We know that imaginary solutions for quadratics come in pairs or conjugates. By testing our answers, we see that C. 3+ i is the only answer to satisfy the solution.
3+i and 3-i. The sum is 6. The product is 10. C. We are done.

--
David

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3 pts) Given U = {21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31}, A = {21, 23, 25, 27, 29}, and
B = {22, 25, 28, 29}. Find A'U B'.
This questions asks for us to find the union (or) for sets A and B NOT, or our composite sets.

A'={22,24,26,28,30, 31}.
B'={21,23,24,26,27,30,31}.

Our Union of the sets is A' U B'= {21,22,23,24,26,27,28,30,31}.

**Notice how we lost both numbers 25 and 29 from set U!

Feel free to comment if you have any questions or concerns. - David

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A stunt diver leaps off a bridge 50m above a river with an initial upward velocity of 10m/s. Her altitude is given by h= (-5t^2+10t+50, where t is in seconds and h is in metres.

a)Construct a table of values to illustrate her height in 1-second intervals
until she hits the water.(2 marks)

We assume that the time function starts at t=0. So, we choose (h,t)= (0,50) (1,55), (2,50) (3,35) (4,10)...

The function reduces to -5(t^2-2t-10) =0, and so you hit the water at time= 1 + sqrt(11) seconds (by solving the quadratic formula).

b)What does a negative value for height represent?(1 mark)

A negative value for height means that you are under water in the river. =)

c)Construct a table showing her velocity during 1-second intervals starting at time 0.(2 marks)

To find the velocity, you need to take the derivative of the height function. so h'(t)=-10t+10. Inserting the time values from above, we have our velocity as (0,10), (1,0), (2,-10), (3,-20), (4,-30), etc... Notice how the velocity becomes negative. This indicates that we are taking a downward trajectory and are accelerating downward from gravity.

d)When does her velocity change from positive to negative?(1 mark)

This is the critical value for the h'(t), which occurs at t=1 or when h'(t)=0.

e)What does this change represent?(1 mark)

That our concavity is changing, we are now accelerating downward, that we have negative velocity, that we have reached our maximum height and are now falling. (When you jump off a bridge you first increase in height ever-so-slightly, before reaching that maximum height and then falling as you dive downward.

f)When does she hit the water?(1 mark)

Review part a) at time= 1 + sqrt(11) seconds.

g)What is her average velocity in the half-second before she hits the river?(1 mark)

Since she hits the water at 1 + sqrt(11) seconds, I assume you are looking for the specific velocity at the half second before, not the average velocity. Therefore, using the time input of 0.5 + sqrt(11) seconds in the h'(t) function, we get her velocity as -10(0.5 + sqrt(11)) + 10 = 5 -10sqrt(11) as her velocity. Notice this is a check for the problem since the velocity is negative, indicating that she is moving downward.

h)Why is her average velocity from t=0 to t=2 equal to 0?(1 mark)

Average velocity is the sum of velocity divided by the time interval. Her velocity at t=2 is -10. Her velocity at 0=10. So average velocity is (-10 + 10)/2=0.

Feel free to comment if you have any more questions or concerns. - David

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simplify: 16t^-224= 16/(t^224)
Thank you.

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35 factors to 5 x 7.
56 factors to 7 x 2 x 2 x 2.
LCD is defined as the greatest set of a prime number from all factors all multiplied together.
In this case, it is 5 x 7 x 2 x 2 x 2 = 280.
The fraction you multiply by 8, the second by 5. Doing so, and adding you get your answer as shown below.

Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result: YOUR ANSWER Here's what you tried: Graphical form: simplifies to Text form: 16/35+11/56 simplifies to 183/280 Cartoon (animation) form: For tutors: simplify_cartoon( 16/35+11/56 ) If you have a website, here's a link to this solution. DETAILED EXPLANATION Look at . Added fractions or integers together It becomes . Result: Universal Simplifier and Solver Done!

I hope this helps. Feel free to leave feedback with comments and concerns. =)

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In the future, please include the carrot (^) bracket for exponents. I will include ones simplified next to classifications. Classifications will be defined as follows:
M= monomial
B=bionmial
T=trinomial
P=polynomial
...
a. P
b. B
c. T
d. M
e. T
f. B -- 2x + 3
g. P
h. M
i. P
j. B -- 4x^2 + x
k. T -- x^4 – 2x^2y^2 + y^4
l. T
m. M -- 10x
n. B
o. M
I hope this helps. Feel free to leave feedback with comments and concerns. =)

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A new candle is 8 inches tall and burns at a rate of 2 inches per hour. what is the equation that would model the height h after t hours?
H=-2t+8, with the boundary on t being [0,4]... unless you want you're candle to burn down your house after four hours? ;P
I hope this helps. Feel free to leave feedback with comments and concerns.