Antonio has a CD-player that holds six CDs. He puts six different
CDs in the player and the CD player randomly plays a song from
any of the CDs. What is the probability that the CD player will
play the first song from the first CD and the first song from the
sixth CD?

Answer: 3:2

Step-by-step explanation:

Answer:

3/2 = 3:2

Step-by-step explanation:

15:10 = 15 /10 = 3/2. { dividing both numerator and denominator by 5}

Answer:

Inequalities are,

y ≥ 4x + 2

y ≥ 2

Step-by-step explanation:

Solid yellow line of the graph attached passes through two points (0, -2) and (1, 2).

Let the equation of this line is,

y = mx + b

Slope of the line = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

                      m = [tex]\frac{2+2}{1-0}[/tex]

                      m = 4

Y-intercept 'b' = -2

Equation of the line will be,

y = 4x - 2

Since shaded area is on the left side of this solid line so the inequality representing this region will be,

y ≥ 4x - 2

Another line is a solid blue line parallel to the x-axis.

Shaded region (blue) above the line will be represented by,

y ≥ 2

Therefore, the common shaded area of these inequalities will be the solution of the given inequalities.

Answer:

Interest= $10000

Step-by-step explanation:

So we are to calculate the interest at 5% annum of $200000.

Ok , we'll use the formula

PRT/100 = interest

Where P = principal

R = rate

T= time

(200000* 5*1)/100 = interest

1000000/100 = interest

10000 = interest

Interest= $10000

Answer:

5 × 10⁶

Step-by-step explanation:

To convert a long number to a scientific notation:

Count the number of zeros in the number

Use the count as the power of 10.

5,000,000 has six zeros

So:

× 10⁶

Now 5 will be left to be added to the notation.

5 × 10⁶

Answer:

5 x 10'6

Step-by-step explanation:

Answer:

zero goats and 120 Ilamas to get profit of $15,120

Step-by-step explanation:

Goats: G

Ilamas: l

Explicit constraints:

2G + 5l ≤ 400

100G+ 80l≤ 13,200

Implicit constraints

G≥0

I≥0

P= 84G+ 126l

See attachment for optimal area

substituting coordinats of optimal region in profit equation to get profit

When G= 132, l=0

P=84(132) + 126(0)

P=11,088

When G=0, l=120

P=84(0)+ 126(120)

P = 15120

When G= 100, l=40

P=84(100)+126(40)

P=13440

Please see attached picture for full solution

Hope it helps

Good luck on your assignment

Answer:

We want to create sentences that are false (this means that the truth value is F

False ---> true: then the statement is false

true-----> false: then the statement is false.

For the first option we have:

"If the GCD of 5 and 12 is 1,____"

the left side is true, so the right side must be false:

"If the GCD of 5 and 12 is 1, then 12 is less than 5"

this means that the truth value is false, because the left side is true and the right side false.

For the second sentence we have:

The sum of 5 and 12 is 7 if and only if _______

The left side is false, so the right side must be true, the only true option is 12 is greater than 5, so the sentence is:

"The sum of 5 and 12 is 7 if and only if 12 is greater than 5."

Answer:

0.965925826

Step-by-step explanation:

Answer:

(pi6 + pi2)/4

Step-by-step explanation:

Answer:

$360

Step-by-step explanation:

If the company charges $30 for $500 in one month.

The interest they will be changing for a year = 30*12 = $360 interest.

It's just simple, multipling the the interest value by 12 to get it's annual interest value.

The inverse of the function g(x)=-2x -3.

A function assigns the value of each element of one set to the other specific element of another set.

Given function:

f(x) = -1/2 x - 3/2

Since the function is inverse, so

g(f(x)) = a(-1x/2 - 3/2) + b

x = -ax/2 - 3x/2 + b

-a/2 = 1

a = -2

and, -3a/2 + b = 0

b= -3

Hence, the inverse of the function g(x)=-2x -3.

Learn more about Function here:

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Answer:

Step-by-step explanation:

5.) here no. of people represent frequencies, so modal group (the group with the highest frequency) is 0.25-0.50.

Estimated Mode = L + (( fm − fm-1) / ( (fm − fm-1) + (fm − fm+1) ) ) × w

where,

L is the lower class boundary of the modal group = 0.25

fm-1 is the frequency of the group before the modal group = 38

fm is the frequency of the modal group = 67

fm+1 is the frequency of the group after the modal group = 50

w is the group width = 0.25

mode= 0.25 + ((67-38)/((67-38)+(67-50)))* 0.25

= 0.25 + (29/ (29+17))*0.25

= 0.25 + 0.63*0.25

= 0.41

6) mean= total(fx) / total(f)

= 166.25/250

= 0.665

7) standard deviation = sqaure root (( total(fx2) - (total(f)* mean2)) / (total(f)-1))

= sqaure root (( 149.906 - 250* 0.6652)/ 249 )

= square root ( (149.906 - 110.556) /249)

= sqaure root (0.158)

= 0.397

8) The median is the middle value, which in our case is the 125 (250/2) , which is in the 0.5 - 0.75 group.

Estimated Median = L + ( ((n/2) − B)/G) × w

where:

L is the lower class boundary of the group containing the median = 0.5

n is the total number of values = 250

B is the cumulative frequency of the groups before the median group = 105

G is the frequency of the median group = 50

w is the group width = 0.25

median = 0.5 + (((250/2)-105)/50)*0.25

= 0.5 + ((125-105)/50)*0.25

= 0.5 + (20/50)*0.25

= 0.6

Answer:

(3)(x+7)(x-1)

Step-by-step explanation:

3x^2+18x-21

Let's start by taking 3 out of the equation.

3(x^2+6x-7)

Now, when we factor, we need to find two numbers that add up to 6 and multiply to -7.

The numbers would be 7 and -1.

So the factored form of this would be:

(3)(x+7)(x-1)

Answer: choice A

Step-by-step explanation:

the transposed matrix would be

5 3

2 -1

so

5*5+2*2=29

3*5+2*-1=13

5*3-2*-1=13

3*3+-1*-1=10

which gives us the answer

29 13

13 10

Answer:

4 oz

Step-by-step explanation:

one cup is 8 oz

1/2 cup is 8/2 oz which is 4 oz

Answer:

4 fluid ounces

Step-by-step explanation:

One cup is 8 oz so we would have to divide 8 by 2 to get 4 because one half of 8 is 4.

Answer:

Confidence interval

[tex]8.98-2.2\frac{1.29}{\sqrt{12}}=8.16[/tex]    

[tex]8.98+2.2\frac{1.29}{\sqrt{12}}=9.80[/tex]  

And the margin of error would be:

[tex] ME=2.2\frac{1.29}{\sqrt{12}}=0.819[/tex]

Step-by-step explanation:

For this case we have the followig dataset:

DATA: 8.2; 9.1; 7.7; 8.6; 6.9; 11.2; 10.1; 9.9; 8.9; 9.2; 7.5; 10.5

We can calculate the mean and the deviation with the following formulas:

[tex]\bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]

[tex]s =\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]

And replacing we got:

[tex] \bar X= 8.98[/tex

[tex]s = 1.29[/tex]

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

The degrees of freedom are given by:

[tex]df=n-1=12-1=11[/tex]

The Confidence level is 0.95 or 95%, the value of significance is [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and the critical value would be [tex]t_{\alpha/2}=2.20[/tex]

Repplacing the info we got:

[tex]8.98-2.2\frac{1.29}{\sqrt{12}}=8.16[/tex]    

[tex]8.98+2.2\frac{1.29}{\sqrt{12}}=9.80[/tex]    And the margin of error would be:

[tex] ME=2.2\frac{1.29}{\sqrt{12}}=0.819[/tex]

The 95% confidence interval is [tex]\mathbf{ (8.17,9.79)}[/tex], and the margin of error is 0.81

The dataset is given as:

[tex]\mathbf{x= 8.2; 9.1; 7.7; 8.6; 6.9; 11.2; 10.1; 9.9; 8.9; 9.2; 7.5; 10.5}[/tex]

Start by calculating the sample mean

This is calculated as:

[tex]\mathbf{\bar x = \frac{\sum x}{n}}[/tex]

[tex]\mathbf{\bar x= \frac{8.2+ 9.1+ 7.7+ 8.6+ 6.9+11.2+ 10.1+ 9.9+ 8.9+ 9.2+ 7.5+ 10.5}{12}}[/tex]

[tex]\mathbf{\bar x= \frac{107.8}{12}}[/tex]

[tex]\mathbf{\bar x= 8.98}[/tex]

Next, calculate the sample standard deviation

This is calculated as:

[tex]\mathbf{\sigma_x = \sqrt{\frac{\sum (x - \bar x)^2}{n-1}}}[/tex]

[tex]\mathbf{\sigma_x= \sqrt{\frac{(8.2 - 8.89)^2 +.......... + (10.5- 8.89)^2}{12 - 1}}}[/tex]

[tex]\mathbf{\sigma_x= 1.29}[/tex]

Calculate the degrees of freedom

[tex]\mathbf{df = n - 1}[/tex]

[tex]\mathbf{df = 12 - 1}[/tex]

[tex]\mathbf{df = 11}[/tex]

Calculate the significance level

[tex]\mathbf{\alpha /2=\frac{1 - 95\%}2 = 0.025}[/tex]

The critical value at [tex]\mathbf{\alpha/2 = 0.025}[/tex]  and df = 11 is:

[tex]\mathbf{t_{\alpha/2} = 2.20}[/tex]

Calculate the margin of error

[tex]\mathbf{E = t_{\alpha/2} \frac{\sigma}{\sqrt n}}[/tex]

So, we have:

[tex]\mathbf{E = 2.20 \times \frac{1.29}{\sqrt{12}}}[/tex]

[tex]\mathbf{E = 0.81}[/tex]

The confidence interval is then calculated as:

[tex]\mathbf{CI =\bar x \pm E}[/tex]

So, we have:

[tex]\mathbf{CI = 8.98 \pm 0.81}}[/tex]

Split

[tex]\mathbf{CI = (8.98 - 0.81,8.98 + 0.81)}[/tex]

[tex]\mathbf{CI = (8.17,9.79)}[/tex]

So, the 95% confidence interval is [tex]\mathbf{ (8.17,9.79)}[/tex], and the margin of error is 0.81

Read more about confidence intervals and margin of errors at:

https://brainly.com/question/19426829

Answer: The constant of proportionality is r = 5.

Step-by-step explanation:

O, we know that x and y are proportional, this means that:

y = r*x

where r is the constant of proportionality.

we also have the table

x    y

7    35

12   60

20   100

Now, we can replace those values in our equation and get, for the first pair:

35 = r*7

r = 35/7 = 5

for the second pair:

60 = r*12

60/12 = 5 = r

So we can conclude that the constant of proportionality is 5.

Answer:

5

Step-by-step explanation:

It was right for me on khan

Step-by-step explanation:

4x+6x-8-12=10

10x-20=10

10x=10+20

10x=30

x=3

Answer:

x=3

Step-by-step explanation:

to find X first find the like terms

like terms: 4x and 6x

like terms: -12 and -8

combine the like the like terms

4x+6x=10x

-12-8=-20

10x-20=10

add 20 on both sides

10x-20+20=10+20

10x=30

divide both sides by 10

10x/10=30/10

x=3

ANSWER CHECK

substitute the variable

4(3) – 8 + 6(3) – 12 = 10

12-8+18-12

4+18-12

22-12 = 10

10=10

Answer:

Step-by-step explanation:

g(6) = 3(6) + 3

      = 18+3

      = 21

Answer: Total time taken by them would be 60 minutes = 1 hour before the tank overflows.

Step-by-step explanation:

Since we have given that

Time taken by an inlet pipe =10 minutes

Time taken by a drain = 12 minutes

So, if both are open together,

Total work done by them would be

[tex]\dfrac{1}{10}-\dfrac{1}{12}\\\\=\dfrac{6-5}{60}\\\\=\dfrac{1}{60}[/tex]

So, total time taken by them would be 60 minutes = 1 hour before the tank overflows.

Answer:

19.9

Step-by-step explanation:

d = sqrt(6^2+19^2) = sqrt( 397) =. 19.9

Answer:

The statements that are true are:

b) n equals 30

c) The number of samples is 8

d) The sample size is 30

f) Each day she collects a total of 240 observations.

Step-by-step explanation:

She takes a sample every hour, so she takes 8 samples during the day.

Each samples consist of 30 individuals (pizzas).

This adds a total of 240 observations during the day.

The statements that are true are:

b) n equals 30

c) The number of samples is 8

d) The sample size is 30

f) Each day she collects a total of 240 observations.

Answer:

Step-by-step explanation:

The record of the statistics and the summary statistics which are the missing files in the question are attached below.

From the given information:

The null hypothesis and the alternative hypothesis can be represented by :

[tex]\mathbf{H_o:}[/tex] There is no difference between the average time  spend by men and women at gym each week

[tex]\mathbf{H_i:}[/tex] The average time  spend by men is greater than the average time spend by women at the gym each week

From the summary statistics in the attached file below:

The p-value = 0.3253

Level of significance = 5% = 0.05

Therefore; it is obvious that the p-value is greater than the level of significance  i.e (0.3253 > 0.05)

Hence; there is no enough evidence to reject the null hypothesis

CONCLUSION: We conclude that the mean number of minutes exercised per week is larger for men than women at the  this gym.

Answer:

0.234

Step-by-step explanation:

Answer:

0.234

To convert from milliliters to liters, divide by 1,000.

234 ÷ 1,000 = 0.234

Step-by-step explanation:

Complete each statement.

? L = 234 mL

234/1000=0.234

There are 1000 milliliters in a liter, therefore dividing the milliliters by 1000 will give you the amount of liters. Liters = 0.234

RESULT

0.234L

Answer:

The coordinate of the wells are

[tex] (-4 -\sqrt[]{\frac{53}{2}}, 70+15\sqrt[]{\frac{53}{2}})[/tex]

[tex] (-4 +\sqrt[]{\frac{53}{2}}, 70-15\sqrt[]{\frac{53}{2}})[/tex]

Step-by-step explanation:

The y coordinate of the stream is given by [tex] y = 4x^2+17x-32[/tex]. Also, the y coordinate of the houses are determined by y=-15x+10. We will assume that the houses are goint to be built on the exact position where we build the wells. We want to build the wells at the exat position in which both functions cross each other, so we have the following equation

[tex] 4x^2+17x-32 = -15x+10[/tex]

or equivalently

[tex]4x^2+32x-42=0[/tex] (by summing 15x and substracting 10 on both sides)

Dividing by 2 on both sides, we get

[tex]2x^2+16x-21=0[/tex]

Recall that given the equation of the form [tex]ax^2+bx+c=0[/tex] the solutions are

[tex] x = \frac{-b \pm \sqrt[]{b^2-4ac}}{2a}[/tex]

Taking a =2, b = 16 and c = -21, we get the solutions

[tex]x_1 = -4 -\sqrt[]{\frac{53}{2}}[/tex]

[tex]x_2 = -4 +\sqrt[]{\frac{53}{2}}[/tex]

If we replace this values in any of the equations, we get

[tex]y_1 = 70+15\sqrt[]{\frac{53}{2}}[/tex]

[tex]y_2 = 70-15\sqrt[]{\frac{53}{2}}[/tex]

Answer:

(2.4, -1)

Step-by-step explanation:

To find the midpoints of two points in the format (x,y), we find the mean for the values of x and y.

In this question:

(3.2, 2.5) and (1.6, -4.5)

Mean for the values of x:

(3.2 + 1.6)/2 = 2.4

Mean for the values of y:

(2.5 - 4.5)/2 = -1

Midpoint:

(2.4, -1)

Answer:

A

Step-by-step explanation:

I'm not sure if it's right though

Answer:

Hence, the system of equation does not have solution.

Step-by-step explanation:

You have the following 2x2 system:

[tex]x-2y=1\ \ \ \ (1)\\\\-4x+8y=-4\ \ \ \ (2)[/tex]

You can obtain the solution to the system by using substitution method.

You solve the first equation for x:

[tex]x=1+2y[/tex]       (3)

Next, you replace (3) in the equation (2), and you solve for y:

[tex]-4(1+2y)+8y=-4\\\\-4-8y+8y=-4\\\\0=0[/tex]

The last result is the trivial solution. This means that the equation (2) is a multiple scale of the first equation. In fact, if you multiply equation (1) by -4, you obtain the equation (2).

Hence, the system of equations does not have solution.

Answer:

Yes, Dayson can completely cover the package with wrapping paper.

Step-by-step explanation:

Given: The rectangular prism is 50 centimeters by 20 centimeters by 18 centimeters.

Area of wrapping paper is 1 square meter.

To find: whether he can completely cover the package with wrapping paper

Solution:

Total surface area of the rectangular prism = 2(lb + bh +hl)

where l denotes length, b denotes breadth and h denotes height

Total surface area of the rectangular prism = [tex]2\left [ (50)(20)+(20)(18)+(18)(50) \right ][/tex]

[tex]=2\left ( 1000+360+900 \right )\\=2(2260)\\=4520\,\,cm^2[/tex]

As [tex]1\,m^2=10000\,cm^2[/tex],

Total surface area of the rectangular prism = [tex]4520\,cm^2=0.4520\,m^2[/tex]

As Dayson has [tex]1\,m^2> 0.4520\,m^2[/tex] of wrapping paper, he can completely cover the package with wrapping paper.

Answer:

$1,944.00

Step-by-step explanation:

Interest= Principal x Rate x Time (years)

Rate: 18%= 0.18

Interest= 5,400 x 0.18 x 2= $1,944