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pshichka [43]
3 years ago
7

Three cards are drawn with replacement from a standard deck. what is the probability that the first card will be a diamond, the

second card will be a black card, and the third card will be a face card
Mathematics
1 answer:
svlad2 [7]3 years ago
6 0
507/17576 or 0.0288 

you take all the probabilities separate then multiply them all together. Then Simplify
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The area of a parallelogram is 131.84 square centimeters and the base is 12.8 centimeters. What is the height of this parallelog
mylen [45]

Answer:

10.3cm

Step-by-step explanation:

h=A

b=131.84

12.8≈10.3cm

8 0
3 years ago
Assuming that the equation defines x and y implicitly as differentiable functions xequals​f(t), yequals​g(t), find the slope of
Doss [256]

Answer:

\dfrac{dx}{dt} = -8,\dfrac{dy}{dt} = 1/8\\

Hence, the slope , \dfrac{dy}{dx} = \dfrac{-1}{64}

Step-by-step explanation:

We need to find the slope, i.e. \dfrac{dy}{dx}.

and all the functions are in terms of t.

So this looks like a job for the 'chain rule', we can write:

\dfrac{dy}{dx} = \dfrac{dy}{dt} .\dfrac{dt}{dx} -Eq(A)

Given the functions

x = f(t)\\y = g(t)\\

and

x^3 +4t^2 = 37 -Eq(B)\\2y^3 - 2t^2 = 110 - Eq(C)

we can differentiate them both w.r.t to t

first we'll derivate Eq(B) to find dx/dt

x^3 +4t^2 = 37\\3x^2\frac{dx}{dt} + 8t = 0\\\dfrac{dx}{dt} = \dfrac{-8t}{3x^2}\\

we can also rearrange Eq(B) to find x in terms of t , x = (37 - 4t^2)^{1/3}. This is done so that \frac{dx}{dt} is only in terms of t.

\dfrac{dx}{dt} = \dfrac{-8t}{3(37 - 4t^2)^{2/3}}\\

we can find the value of this derivative using t = 3, and plug that value in Eq(A).

\dfrac{dx}{dt} = \dfrac{-8t}{3(37 - 4t^2)^{2/3}}\\\dfrac{dx}{dt} = \dfrac{-8(3)}{3(37 - 4(3)^2)^{2/3}}\\\dfrac{dx}{dt} = -8

now let's differentiate Eq(C) to find dy/dt

2y^3 - 2t^2 = 110\\6y^2\frac{dy}{dt} -4t = 0\\\dfrac{dy}{dt} = \dfrac{4t}{6y^2}

rearrange Eq(C), to find y in terms of t, that is y = \left(\dfrac{110 + 2t^2}{2}\right)^{1/3}. This is done so that we can replace y in \frac{dy}{dt} to make only in terms of t

\dfrac{dy}{dt} = \dfrac{4t}{6y^2}\\\dfrac{dy}{dt}=\dfrac{4t}{6\left(\dfrac{110 + 2t^2}{2}\right)^{2/3}}\\

we can find the value of this derivative using t = 3, and plug that value in Eq(A).

\dfrac{dy}{dt} = \dfrac{4(3)}{6\left(\dfrac{110 + 2(3)^2}{2}\right)^{2/3}}\\\dfrac{dy}{dt} = \dfrac{1}{8}

Finally we can plug all of our values in Eq(A)

but remember when plugging in the values that \frac{dy}{dt} is being multiplied with \frac{dt}{dx} and NOT \frac{dx}{dt}, so we have to use the reciprocal!

\dfrac{dy}{dx} = \dfrac{dy}{dt} .\dfrac{dt}{dx}\\\dfrac{dy}{dx} = \dfrac{1}{8}.\dfrac{1}{-8} \\\dfrac{dy}{dx} = \dfrac{-1}{64}

our slope is equal to \dfrac{-1}{64}

7 0
3 years ago
According to a study conducted in one city, 39% of adults in the city have credit card debts of more than $2000. A simple random
Butoxors [25]

Answer:

The sampling distribution of the sample proportion of adults who have credit card debts of more than $2000 is approximately normally distributed with mean \mu = 0.39 and standard deviation s = 0.0488

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

In this question:

p = 0.39, n = 100

Then

s = \sqrt{\frac{0.39*0.61}{100}} = 0.0488

By the Central Limit Theorem:

The sampling distribution of the sample proportion of adults who have credit card debts of more than $2000 is approximately normally distributed with mean \mu = 0.39 and standard deviation s = 0.0488

5 0
3 years ago
2x+y= 5 solve by elimination of addition<br> 3x-y= 5
lys-0071 [83]

Answer:

1; y=3 2; y=3

Step-by-step explanation:

because you have to mines both of the x ones making the 5s 3 leaving y left

4 0
2 years ago
Evaluate -3x 3 - 4x for x = -1. 1 7 -1
7nadin3 [17]
-3x^{3}-4x
=-3(-1)^{3} -4(-1)
=-3*(-1)+4
=3+4
=7
5 0
3 years ago
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