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1 year ago

If you ask three strangers about their birthdays, what is the probability:

1 answer:

8 0

Part A:

The probability that the birthday of three strangers were on Wednesday is given by

$\left( \frac{1}{7} \right)^3= \bold{\frac{1}{343}}$

Part B:

The probability that the birthday of three strangers were on different days of the week is given by

$\left( \frac{1}{7} \right)\left( \frac{1}{6} \right)\left( \frac{1}{5} \right)= \bold{\frac{1}{210}}$

Part C:

The probability that none of the three strangers were born on Saturday is given by

$\left( \frac{6}{7} \right)^3= \bold{\frac{216}{343}}$

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Which inequality represents this situation?

Veseljchak [2.6K]

Answer:

Option D. 1.29x + 1.35y ≤ 12

Step-by-step explanation:

Nick is making a fruit salad.

He buys apples per pound for = $1.29

He buys oranges per pound for = $1.35

He spend no more than $12.00 or we can say less than equal to $12

Let x represent the number of pounds of apples that Nick buys and y represent the number of pounds of oranges.

Cost of x pounds of apples = $1.29x

Cost of y pounds of oranges = $1.35y

Total cost = 1.29x + 1.35y

Total cost should be less than equal to $12.00

Therefore, inequality will be 1.29x + 1.35y ≤ 12

Option D. is the answer.

3 0

1 year ago

Read 2 more answers

tickets to a production of a midsummer night's dream at broward college cost $5 for general admission or $4 with a student ID. I

Elena-2011 [213]

Answer:

76 *5 = 380 $

184 - 76 = 108

108 * 4 = 432

432 + 380 = 812

Step-by-step explanation:

7 0

1 year ago

Solve for x. z = 6 π x y

rusak2 [61]

The answer to the question

3 0

2 years ago

Read 2 more answers

Find the coefficient of variation for each of the two sets of data, then compare the variation. Round results to one decimal pla

svp [43]

Here is the correct computation of the question given.

Find the coefficient of variation for each of the two sets of data, then compare the variation. Round results to one decimal place. Listed below are the systolic blood pressures (in mm Hg) for a sample of men aged 20-29 and for a sample of men aged 60-69.

Men aged 20-29: 117 122 129 118 131 123

Men aged 60-69: 130 153 141 125 164 139

Group of answer choices

Men aged 20-29: 4.8%

Men aged 60-69: 10.6%

There is substantially more variation in blood pressures of the men aged 60-69.

Men aged 20-29: 4.4%

Men aged 60-69: 8.3%

There is substantially more variation in blood pressures of the men aged 60-69.

Men aged 20-29: 4.6%

Men aged 60-69: 10.2 %

There is substantially more variation in blood pressures of the men aged 60-69.

Men aged 20-29: 7.6%

Men aged 60-69: 4.7%

There is more variation in blood pressures of the men aged 20-29.

Answer:

(c)

Men aged 20-29: 4.6%

Men aged 60-69: 10.2 %

There is substantially more variation in blood pressures of the men aged 60-69.

Step-by-step explanation:

From the given question:

The coefficient of variation can be determined by the relation:

$coefficient \ of \ variation = \dfrac{standard \ deviation}{mean}*100$

We will need to determine the coefficient of variation both men age 20 - 29 and men age 60 -69

To start with;

The coefficient of men age 20 -29

Let's first find the mean and standard deviation before we can do that ;

SO .

Mean = $\dfrac{\sum \limits^{n}_{i-1}x_i}{n}$

Mean = $\frac{117+122+129+118+131+123}{6}$

Mean = $\dfrac{740}{6}$

Mean = 123.33

Standard deviation $= \sqrt{\dfrac{\sum (x_i- \bar x)^2}{(n-1)} }$

Standard deviation = $\sqrt{\dfrac{(117-123.33)^2+(122-123.33)^2+...+(123-123.33)^2}{(6-1)} }$

Standard deviation = $\sqrt{\dfrac{161.3334}{5}}$

Standard deviation = $\sqrt{32.2667}$

Standard deviation = 5.68

The $coefficient \ of \ variation = \dfrac{standard \ deviation}{mean}*100$

$coefficient \ of \ variation = \dfrac{5.68}{123.33}*100$

Coefficient of variation = 4.6% for men age 20 -29

For men age 60-69 now;

Mean = $\dfrac{\sum \limits^{n}_{i-1}x_i}{n}$

Mean = $\frac{ 130 + 153 + 141 + 125 + 164 + 139}{6}$

Mean = $\dfrac{852}{6}$

Mean = 142

Standard deviation $= \sqrt{\dfrac{\sum (x_i- \bar x)^2}{(n-1)} }$

Standard deviation = $\sqrt{\dfrac{(130-142)^2+(153-142)^2+...+(139-142)^2}{(6-1)} }$

Standard deviation = $\sqrt{\dfrac{1048}{5}}$

Standard deviation = $\sqrt{209.6}$

Standard deviation = 14.48

The $coefficient \ of \ variation = \dfrac{standard \ deviation}{mean}*100$

$coefficient \ of \ variation = \dfrac{14.48}{142}*100$

Coefficient of variation = 10.2% for men age 60 - 69

Thus; Option C is correct.

Men aged 20-29: 4.6%

Men aged 60-69: 10.2 %

There is substantially more variation in blood pressures of the men aged 60-69.

4 0

1 year ago

Winston pays $8 for a burger, an order of fries, and a soft drink. Tia buys 2 burgers and a soft drink for $10.50. George buys 2

Sonja [21]

Answer:

$A^{-1}=\left[\begin{array}{ccc}2&0&-1\\3&-1&-1\\-4&1&2\end{array}\right]$

X = 4

Step-by-step explanation:

* At first lets revise how to find the inverse of 3 × 3 matrix

- To find the inverse of a 3 x 3 matrix,

# first calculate the determinant of the matrix.

- If the determinant is 0, the matrix has no inverse.

# Second, transpose the matrix by rewriting the first row as the first

column, the middle row as the middle column, and the third row

as the third column.

# Third, Find the determinant of each of the 2 x 2 minor matrices,

- To find the right minor matrix for each term, first highlight the row

and column of the term you begin with. This should include five

terms of the matrix. The remaining four terms make up the

minor matrix.

- Find the determinant of each minor matrix by cross-multiplying

the diagonals and subtracting

# Fourth, create the matrix of cofactors.

- Place the results of the previous step into a new matrix of

co-factors by aligning each minor matrix determinant with the

corresponding position in the original matrix

- When assigning signs, the first element of the first row keeps its

original sign. The second element is reversed. The third element

keeps its original sign. Continue on with the rest of the matrix

- The final result of this step is called the Adj matrix of the original

# The inverse matrix = 1/determinant × Adj matrix

* Now lets find the matrix A from the story problem

∵ x, y, and z represent the cost of a burger, an order of fries, and

a soft drink

- Order of Winston: x + y + z = 8

- Order of Tia: 2x + z = 10.50

- Order of George: x + 2y + 2z = 12

* Lets make the matrix A

# $A=\left[\begin{array}{ccc}1&1&1\\2&0&1\\1&2&2\end{array}\right]$

# Determinant of A = 1(0×2 - 1×2) - 1(2×2 - 1×1) + 1(2×2 - 0×1)

∴ Determinant of A = 1(-2) - 1(3) + 1(4) = -2 - 3 + 4 = -1

* Lets transposed A

# $A^{T}=\left[\begin{array}{ccc}1&2&1\\1&0&2\\1&1&2\end{array}\right]$

* Lets find the minor matrix for each term

- The 1st row

# (0×2 - 2×1) = -2 , (1×2 - 2×1) = 0 , (1×1 - 0×1) = 1

- The 2nd row

# (2×2 - 1×1) = 3 , (1×2 - 1×1) = 1 , (1×1 - 2×1) = -1

- The 3rd row

# (2×2 - 1×0) = 4 , (1×2 - 1×1) = 1 , (1×0 - 2×1) = -2

* Lets Make Adj A

# $AdjA=\left[\begin{array}{ccc}-2&0&1\\3&1&-1\\4&1&-2\end{array}\right] *\left[\begin{array}{ccc}+&-&+\\-&+&-\\+&-&+\end{array}\right]=\left[\begin{array}{ccc}-2&0&1\\-3&1&1\\4&-1&-2\end{array}\right]$

* Lets write inverse of A

# $A^{-1}=\frac{1}{-1}\left[\begin{array}{ccc}-2&0&1\\-3&1&1\\4&-1&-2\end{array}\right]=\left[\begin{array}{ccc}2&0&-1\\3&-1&-1\\-4&1&2\end{array}\right]$

* Now lets find the solution matrix for X

# $A_{x}=\left[\begin{array}{ccc}8&1&1\\10.5&0&1\\12&2&2\end{array}\right]$

∴ Ax = 8(0×2 - 1×2) - 1(10.5×2 - 1×12) + 1(10.5×2 - 0×12)

∴ Ax = -16 - 9 + 21 = -4

* Lets find the value of X

∵ X = Ax/A

∴ X = -4/-1 = 4

5 0

2 years ago