If A and B are independent events with P(A)=0.5 and P(B)=0.1, find P(A AND B).

Question 1

In 2015, [tex]x=5[/tex]. [tex]P(5)=87000(0.9)^5 \approx \boxed{51373}[/tex]

Question 2

[tex]78000(1-0.08)^5 \approx \boxed{51408}[/tex]

Question 3

[tex]51408 > 51373[/tex], so Greene county was more populous.

The fully simplified form of the given expression 16x⁵y⁴ / ( 14x²y² ) following from the laws of indices is; 8x³ y² / 7.

It follows from the task content that the fully simplified form of the given expression 16x⁵y⁴ / ( 14x²y² ) is to be determined.

Since the given expression is; 16x⁵y⁴ / ( 14x²y² ).

As evident in the task content; same base terms are present in the numerator and denominator; we therefore have that;

The expression can be simplified as follows using the laws of indices as follows;

[tex] \frac{16 {x}^{5} {y}^{4} }{14 {x}^{2} {y}^{2} } [/tex]

It follows from the quotient of exponents law of indices; we have that;

[tex] \frac{8}{7} {x}^{5 - 2} {y}^{4 - 2} [/tex]

= 8x³ y² / 7

Therefore, the fully simplified form of the given expression using the laws of indices is; 8x³ y² / 7.

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The required solutions of percentages are below as :

100% of 60 kg = 60 kg, 20% of 60 kg = 12 kg, and 40% of 60 kg = 24 kg.

The percentage is defined as a ratio expressed as a fraction of 100.

The double number line shows that Henrik has a mass of 60kg.

According to the given question, the required solution would be as:

100% of 60 kg

⇒ (100/100) x 60

⇒ 1 x 60

⇒ 60

So, 100% of 60 kg = 60 kg

20% of 60 kg

20%  is expressed as 20/100 in fractional form

⇒ (20/100) x 60

20/100 is expressed as 0.20 in decimal form

⇒ 0.20 x 60

Apply the multiplication operation, and we get

⇒ 12

So, 20% of 60 kg = 12 kg

40% of 60 kg

⇒ (40/100) x 60

⇒ 0.40 x 60

⇒ 24

So, 40% of 60 kg = 24 kg.

Thus, the required solutions are 100% of 60 kg = 60 kg, 20% of 60 kg = 12 kg, and 40% of 60 kg = 24 kg.

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Answer:

Step-by-step explanation:

6t/6 = 2/3/6

6t/6 = t while were left with 2/3 /6

t = 2/3 / 6.

t = 2/3 x 1/6

t = 2/3 x 1/2(3)

t = 1/3 x 1/3

t = 1 / 3 x 3

t=1/9

decimal form: 0.1

Time series forecasts are developed based on time series analysis, which comprises methods for analyzing time series data to extract meaningful statistics and other characteristics of the data.

One of the most often used data science techniques in business, finance, supply chain management, production, and inventory planning is time series forecasting.

A time component is often present in prediction difficulties, necessitating the extrapolation of time series data or time series forecasting. Another crucial field of machine learning (ML) is time series forecasting, which may be viewed as a supervised learning issue.

It can be subjected to ML techniques including regression, neural networks, support vector machines, random forests, and XGBoost. Using models created from historical data to anticipate future observations is known as forecasting.

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Answer:

line | Cartesian equation x + 5 y = 20 | x-intercept = 20 thus: D

Step-by-step explanation:

The graph that shows the proportional relationship between the number of liters of water (y) supplied after some time (x), is shown below.

A proportional relationship can be defined as a relationship between two variables, say x and y, in such a way that the equation, y = kx, models their relationship, where k is the constant of proportionality.

Given that the faucet supplies 12 liters of water after 3 minutes, where:

y = liters of water

x = number of minutes

Constant of proportionality, k = y/x = 12/3 = 4

The equation that describes the relationship would therefore be written by substituting the value of k = 4 into y = kx:

y = 4x

Thus, the graph that shows this proportional relationship is attached below.

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Answer:

please add screenshots of the question and/or illustrations

To obtain a confidence interval for a population mean under the t-interval procedure.

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Answer:

original price is 26 dollars

Step-by-step explanation:

19.50/0.75=26

Answer:

Step-by-step explanation:

10% of 20 is equal to 2. To calculate 10% of a number, we can multiply the number by 10% expressed as a decimal, which is 0.1. For example, 10% of 20 is equal to 20 * 0.1 = 2.

Alternatively, we can calculate 10% of a number by dividing the number by 100 and then multiplying the result by 10. For example, 10% of 20 is equal to (20 / 100) * 10 = 2.

Answer: The common factor is 8

Step-by-step explanation:

Each is a variant of the number 8 and 2 but it called for the greater common factor so 8

Answer:

So there are 32/4= 8 such groups. In each group, every team plays once against every other team

Step-by-step explanation:

The width of the piece of metal will be 21 inches while the length will be 26 inches.

What is a rectangle?

A rectangle is a geometrical figure in which opposite sides are equal.

The angle between any two consecutive sides will be 90 degrees.

Main body:

Area of rectangle = length × width.

Perimeter of rectangle = 2( length + width).

Let's say the width of metal w then the length will be w + 5

Now if we cut 1 inch square from the corner of the metal and then fold then the resultant cuboid will have;

Length = w+5 - 2 -= w + 3

Width = w - 2

Height = 1

So,

Volume = (w+3)(w-2)1

456 = w² - 2w + 3w - 6

w² + w - 462 = 0

By solving this

w = 21 so width will be 21 and length will be 21 + 5 = 26.

Hence "The width of the piece of metal will be 21 inches while the length will be 26 inches".

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Answer:1.7

Step-by-step explanation:

Moment about the pivot must be equal for the seesaw to balance. Initially, the first cat and the bowl are at 2 m from the pivot.

The moment due to cat = 5.3*2 = 10.6 kg.m

The moment due to bowl = 2.5*2 = 5 kg.m

The unbalanced moment = 10.6 - 5 = 5.6 kg.m

Therefore, the 3.7 kg cat should stand at a distance x from the pivot in left to balance the 5.6 kg.m.

That is,

3.7*x = 5.6 => x = 5.6/3.7 = 1.5134 m to the left (on the side of the bowl)

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The expected value of the number of cups of coffee Alex drinks each day is 00.805 cups.

the mean/ average is gotten by dividing the sum of the values in the set by their number.

The concept of mean/average is used in this ques to calculate the expected value of the number of cups of coffee Alex drinks each day.

Mean/ Average=     sum of values

                              number of values

Mean/ Average= 00.200 cups +00.163 cups+ 00.976 cups+ 01.881 cups

                                                                 4

Mean/ Average= 00.805 cups

Hence, The expected value of the number of cups of coffee Alex drinks each day is 00.805 cups.

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Answer:

x = 6

Step-by-step explanation:

the opposite sides of a parallelogram are congruent , then

2x + 3 = 15 ( subtract 3 from both sides )

2x = 12 ( divide both sides by 2 )

x = 6

Answer:

i) 960  ,    ii) 10 cm

Step-by-step explanation:

V of rectangular carton = 80 · 60 · 40 = 192 000

V of a packet of soap = 10 · 5 · 4 = 200

192 000 / 200

1920/2

960

ii)

960 : 1200 = 192 000 : x

x = 192 000 · 1200 / 960

x = 192 000 · 120 / 96

x = 240 000

80 · 60 · x = 240 000

4800 · x = 240 000

x = 240 000/4800

x = 2400/48

x = 200/4

x = 50

50 - 40 = 10

Answer:

i) 960 packets of soap

ii) 10 cm

Step-by-step explanation:

volume of cuboid = l*w*h

volume of carton = 80*60*40 = 192000 cm³

i)

volume of a packet of soap = 10*5*4 = 200 cm³

192000/200 = 960 packets of soaps

ii)

I am assuming the height is 40 cm

volume of carton/volume of a packet of soap = number of soap

x = volume of carton

x/200 = 1200

x = 1200*200 = 240000 cm³

80*60*h = 240000

4800h = 240000

h = 240000/4800 = 50 cm

50cm (desired height) - 40cm (current height) = 10cm

Answer:

A: AB corresponds to FG

Step-by-step explanation:

The question is asking for which statement if not true/false.

Answer choice A is false because when you turn the rectangle, AB does not end up where FG is. Instead, AB ends up where EF is. Also,  the length of AB is 6 units, while the length of FG is 4 units. So, they cannot correspond to each other.

Function f(x)  is 2/9.

f(-2) for f(x) = 2 • 3^x is 2/9.

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If the value of a commodity decreases at a monthly rate of 0.8%, by 9.6 percentage it decreases in a year.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

It is given that, the value of a commodity decreases at a monthly rate of 0.8%,

We have to find by what percentage the rate decreases in a year.

If there are 12 months in a year, the rate decrease in a year obtained as,

=0.8 × 12

=9.6 %

Thus, if the value of a commodity decreases at a monthly rate of 0.8%, by 9.6 percentage it decreases in a year.

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In a year, the value of commodity decreases by 9.6%, at the monthly rate of 8%.

Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

Monthly decrease rate of change in commodity = 0.8 %,

To find the percentage decrease in year,

Use ratio property,

In 1 month, commodity decreases 0.8%

In 12 months commodity decreases = 12 x 0.8 = 9.6 %

The value of commodity will decrease by 9.6% in a year.

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The balance of the bank reconciliation statement  is $3,640

A bank reconciliation is is defined as the process by which the bank account balance in an entity’s books of account is reconciled to the balance reported by the financial institution in the most recent bank statement

The bank Reconciliation statement appears thus

Bank reconciliation statement

                                                                      $                         $

Cash book balance                                   11,670

Add unpresented cheque                          5,120

Over cast (400-40)                                         360

                                                                                             17,150

Cheque not credited                                    5120

Less Uncredited cheque                             4910                  

Notes collected                                            2660

Dishonored  cheque                                       770

Bank charges                                                    50

bank interest                                                    140

                                                                                           13500

Balance as per bank statement                                      3640

In conclusion the balance of the Statement is $3640

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The function has 2 solutions which is x = 2 and x = 8.

What is a quadratic function?

A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two.

Solution:

Given :

a = 2 , vertex = (5, -18)

f(x) = a(x-h)² + K

f(x) = 2(x - 5)² - 18

f(x) = 2(x² -10x + 25) -18

f(x) = 2x² - 20x +50 - 18

f(x) = x² - 10x +16

∴ x² -10x + 16 = 0

x² - 8x - 2x + 16 = 0

x(x-8) -2(x-8) = 0

(x-2) = 0 and (x-8) = 0

∴ x = 2 and x = 8

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The quadratic function has 2 solutions which is x = 2 and x = 8.

A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two. A polynomial of degree two in one or more variables in mathematics is known as a quadratic polynomial. Any polynomial function that is defined by a quadratic polynomial is said to be quadratic.

The terms "quadratic polynomial" and "quadratic function" were almost interchangeable before the 20th century because it was difficult to tell a polynomial from its corresponding polynomial function. This is still true in many elementary courses where "quadratic" is frequently used to refer to both terms.

Solution:

Given :

     a = 2 , vertex = (5, -18)

f(x) = a(x-h)² + K

f(x) = 2(x - 5)² - 18

f(x) = 2(x² -10x + 25) -18

f(x) = 2x² - 20x +50 - 18

f(x) = x² - 10x +16

∴ x² -10x + 16 = 0

x² - 8x - 2x + 16 = 0

x(x-8) -2(x-8) = 0

(x-2) = 0 and (x-8) = 0

∴ x = 2 and x = 8

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The difference in temperature is currently six degrees Celsius. Therefore, the appropriate reaction is six degrees Celsius.

When two independent temperature readings are subtracted, or when calculating the amount of temperature rise or fall, the result is a temperature difference, also referred to as a delta temperature (T).

Simply subtract the smaller amount from the larger one to determine the difference in temperature, in this case 19 degrees Celsius from 25 degrees Celsius. We now have a six-degree Celsius temperature difference as a result. Therefore, six degrees Celsius, is the appropriate response.

Due to the varied amounts of radiation the Earth receives from the Sun at various periods of the year, there are variations in climate all over the world. The equator receives more heat from the Sun than the north and south poles, where the angle of the Sun's beams is lower.

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Step-by-step explanation:

x - 7y = -45

-x +8y = 51

the X's cancel out

-7y + 8y = -45 + 51

y = 6

As described in z-distribution the answers are given below:

a) The 95% confidence interval estimate for the population mean spending by a customer on visiting salon per month is given as follows: (747, 853).

b) The sampling error at 95% confidence level is of: $35.78.

What is a z-distribution ?

The normal distribution with a mean of 0 and a standard deviation of 1 is referred to as the standard normal distribution (also known as the Z distribution) (the green curves in the plots to the right). It is frequently referred to as the bell curve since the probability density graph resembles a bell.

solution:

The bounds of the confidence interval are given as follows:

In which:

is the sample mean.

z is the critical value.

n is the sample size. is the standard deviation for the population.

The parameters for this problem are given as follows:

Hence the lower bound of the interval is of:

800 - 200 x 1.96/square root of 55  = 747.

The upper bound of the interval is of:

800 + 200 x 1.96/square root of 55  = 853.

The sampling error for a sample size of 120 is calculated as follows:

200 x 1.96/square root of 120 = $35.78.

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