wo cards are selected from a standard deck of 52 playing cards. The first card is not replaced before the second card is selected. Find the probability of selecting a nine and then selecting an eight. The probability of selecting a nine and then selecting an eight is nothing.

Answers

Answer 1

Answer:

Answer:

0.6%

Step-by-step explanation:

We have a standard deck of 52 playing cards, which is made up of 13 cards of each type (hearts, diamonds, spades, clubs)

Therefore there are one nine hearts, one nine diamonds, one nine spades and one nine clubs, that is to say that in total there are 4. Therefore the probability of drawing a nine is:

4/52

In the second card it is the same, an eight, that is, there are 4 eight cards, but there is already one less card in the whole deck, since it is not replaced, therefore the probability is:

4/51

So the final probability would be:

(4/52) * (4/51) = 0.006

Which means that the probability of the event is 0.6%

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Write the standard form of the quadratic function whose graph is a parabola with the given vertex and that passes through the given point. (Let x be the independent variable and y be the dependent variable.)Vertex: (−3, 4); point: (0, 13)

Answers

The standard form of the quadratic function whose graph is a parabola with the given vertex and that passes through the given point is;

y = x² + 6x + 13

We are given;

Vertex coordinate; (-3, 4)

A point on the graph; (0, 13)

The vertex form of a quadratic equation is given by;

y = a(x - h)² + k

Where h, k are the coordinates of the vertex.

a is the letter in general form of quadratic equation which is;

y = ax² + bx + c

Thus, at point (0, 13) at the vertex of (-3, 4), we have;

13 = a(0 - (-3))² + 4

⇒ 13 - 4 = 9a

9a = 9

a = 9/9

a = 1

Since y = a(x - h)² + k is the vertex form, let us put the vertex values for h and k as well as the value of a to get the quadratic equation;

y = 1(x - (-3))² + 4

y = x² + 6x + 9 + 4

y = x² + 6x + 13

Read more at; brainly.com/question/17546421

Answer:

The formula for this quadratic function is x*2 +6x+13

Step-by-step explanation:

If we have the vertex and one point of a parabola it is possible to find the quadratic function by the use of this

y= a (x-h)*2 + K

Quadratic function looks like this

y= ax*2 + bx + c

So let's find the a

y= a (x-h)*2 + K where

y is 13, x is 0, h is -3 and K is 4

13= a (0-(-3))*2 +4

13=9a +4

9=9a

9/9=a

1=a

The quadratic function will be

y= 1(x+3)*2 + 4

Let's get the classic form

(x+3)*2 = (x+3)(x+3)

(x*2+3x+3x+9)

x*2 +6x+13

f(0) = 13

For the characteristic polynomialp(s) =s5+ 2s4+ 24s3+ 48s2−25s−50(a) Use the Routh-Hurwitz Criterion to determine the number of roots ofp(s) in the right-half plane, in the left-half plane, and on thejω-axis.(b) Use Matlab to determine the roots ofp(s), and verify your results in part 2a.

Answers

Answer:

1 root in the right half-plane
1 conjugate pair on the imaginary axis
2 roots in the left half-plane

Step-by-step explanation:

Without using the Routh-Hurwitz criterion at all, you know there is one positive real root. Descartes' rule of signs tells you the number of positive real roots is equal to the number of sign changes in the coefficients (perhaps less a multiple of 2). There is one sign change in + + + + - - , so there is one positive real root.

_____

(a) The Routh array starts as two rows of the polynomial's coefficients, alternate coefficients on each row. For this odd-degree polynomial, the number of coefficients is even, so no zero-padding is necessary at the right end of the second row. That is, we start with ...

$\begin{array}{cccc}s^5&1&24&-25\ns^4&2&48&-50\end{array}$

The next row is formed from combinations of coefficients in the two rows above. The computation is similar to that of a determinant. By matching the numbers to those in the array, you can see the pattern of the computation.

The next row values are ...

$\begin{array}{ccc}s^3&((2)(24)-(1)(48))/(2)&((2)(-25)-(1)(-50))/(2)\end{array}$

Simplifying, we find this row to be ...

$\begin{array}{ccc}s^3&0&0\end{array}$

The zero row is a special case that requires we proceed as follows. The row above (identified with s⁴) represents an "auxiliary polynomial":

$2s^4 +48s^2 -50$

To continue the process, we replace the zero row by the coefficients of the derivative of this auxiliary polynomial. Proceeding as before, the array now becomes ...

$\begin{array}{cccc}s^5&1&24&-25\ns^4&2&48&-50\ns^3&8&96\ns^2&24&-50\ns^1&112(2)/(3)&0\ns^0&-50\end{array}$

The number of sign changes in the first column (1) tells the number of roots in the right half-plane. The auxiliary polynomial will give us the remaining two pairs of roots:

$2s^4+48s^2-50=0\n\n2(s^2+25)(s^2-1)=0\n\ns=\pm 5i,\ s=\pm 1$

So, we have determined there to be ...

1 root in the right half-plane
2 roots on the jω axis
2 roots in the left half-plane

(b) The original polynomial can be factored as ...

p(s) = (s +2)(s² +25)(s +1)(s -1)

p(s) = (s +2)(s +1)(s -5i)(s +5i)(s -1)

This verifies our result from part (a).

_____

Additional comments

Any row can be multiplied by a convenient factor to simplify the arithmetic. Here, it would be convenient to divide the second row by 2 and the third row by 8.

A zero element (not row) in the first column is replaced by "epsilon" (a small positive number) and the rest of the arithmetic is continued as normal. That row is not counted (it is ignored) when counting sign changes in the first column.

Solve the following inequality for k. Write your answer in simplest form.4k + 2(3k + 8) <3k + 10 – 8

Answers

Answer:

k < -2

Step-by-step explanation:

Step 1: Write inequality

4k + 2(3k + 8) < 3k + 10 - 8

Step 2: Solve for k

Distribute: 4k + 6k + 16 < 3k + 10 - 8
Combine like terms: 10k + 16 < 3k + 2
Subtract 3k on both sides: 7k + 16 < 2
Subtract 16 on both sides: 7k < -14
Divide both sides by 7: k < -2

Answer:

10k+16<3k+2

10k-3k+16<2

7k<2-16

k<-2

There were 5,317 previously owned homes sold in a western city in the year 2000. The distribution of the sales prices of these homes was strongly right-skewed, with a mean of $206,274 and a standard deviation of $37,881. If all possible simple random samples of size 100 are drawn from this population and the mean is computed for each of these samples, which of the following describes the sampling distribution of the sample mean? (A) Approximately normal with mean $206,274 and standard deviation $3,788
(B) Approximately normal with mean $206,274 and standard deviation $37,881
(C) Approximately normal with mean $206,274 and standard deviation $520
(D) Strongly right-skewed with mean $206,274 and standard deviation $3,788
(E) Strongly right-skewed with mean $206,274 and standard deviation $37,881

Answers

Approximately normal with mean is $206,274 and standard deviation is $3,788 and this can be determined by applying the central limit theorem.

Given :

There were 5,317 previously owned homes sold in a western city in the year 2000.
The distribution of the sales prices of these homes was strongly right-skewed, with a mean of $206,274 and a standard deviation of $37,881.
Simple random samples of size 100.

According to the central limit theorem the approximately normal mean is $206274.

Now, to determine the approximately normal standard deviation, use the below formula:

$s =(\sigma )/(√(n) )$ ---- (1)

where 's' is the approximately normal standard deviation, 'n' is the sample size, and $\sigma$ is the standard deviation.

Now, put the known values in the equation (1).

$s = (37881)/(√(100) )$

s = 3788.1

$\rm s \approx 3788$

So, the correct option is A).

For more information, refer to the link given below:

brainly.com/question/18403552

Answer:

(A) Approximately normal with mean $206,274 and standard deviation $3,788

Step-by-step explanation:

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 $s = (\sigma)/(√(n))$ .

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

Population:

Right skewed

Mean $206,274

Standard deviation $37,881.

Sample:

By the Central Limit Theorem, approximately normal.

Mean $206,274

Standard deviation $s = (37881)/(√(100)) = 3788.1$

So the correct answer is:

(A) Approximately normal with mean $206,274 and standard deviation $3,788

Which inequality represents the situation: The cost, c is more than $6

Answers

Answer: C > $6

Step-by-step explanation:

C is greater than (but not equal to) $6

C > $6

Two points located on jk are j (-1,-9) and k (5,3). What is the slope of jk?

Answers

Answer:

Slope = 2

Step-by-step explanation:

Slope = $(rise)/(run)$

Slope = $(3+9)/(5+1)$

Slope = $(12)/(6)$

Slope = 2

In the given case, we can conclude that The slope of the line JK is 2.

To find the slope of the line that passes through the points J(-1,-9) and K(5,3), we can use the formula: slope = $(y2 - y1) / (x2 - x1).$

The slope of a line is a measure of how steep the line is. It describes the rate at which the dependent variable (usually denoted as 'y') changes with respect to a change in the independent variable (usually denoted as 'x').

Plugging in the coordinates, we get:

slope = (3 - (-9)) / (5 - (-1)) = 12 / 6 = 2.

Learn more about Slope here:

brainly.com/question/19131126

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