You are interested in the what the customers at the pub you manage do. Customers come to eat, drink and/or play games (pool, darts etc.) You have the following information about 230 customers: 152 ordered food, 105 ordered drinks and 41 ordered both. Calculate the probability that a randomly selected customer only ordered food or only ordered drinks.

Answer:

10

Step-by-step explanation:

No of coffee mugs = m

No of water glasses = g

g = m + 6

g + m = 26

m + 6 + m = 26

m + m = 26 - 6

2m = 20

2m/2 = 20/2

m = 10

Your lack of cogscitis has a previous probability of 0.5 according to Dr. B.

Prior probability quantifies how likely a theory is to be correct before any supporting data are taken into account. Your lack of cognitis has a previous probability of 0.5 according to Dr. B. This means that according to Doctor B, there is a 50/50 likelihood that you do not have cognitis before any supporting evidence is considered. This impartial viewpoint is frequently employed in scientific research and medical diagnostics. Prior probability is a crucial component of Bayesian inference, which is used to update a hypothesis' probability after all available data has been considered. Prior probability can help scientists and medical practitioners make better decisions.

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The solution to the equation \(\log_{2} x + \log_{2}(-4x+12) = 3\) is \(x = 2\), after checking potential solutions.

To solve the equation \(\log_{2} x + \log_{2}(-4x+12) = 3\), we first note that both logarithms have the base of 2. We can combine the two logarithms using the logarithmic identity \(\log_{b} A + \log_{b} B = \log_{b} (A \cdot B)\).

Applying this identity, we obtain \(\log_{2} (x \cdot (-4x+12)) = 3\). Simplifying further, we have \(\log_{2} (-4x^2 + 12x) = 3\).

Now, we convert the equation to exponential form: \(2^3 = -4x^2 + 12x\), which simplifies to \(8 = -4x^2 + 12x\). Rearranging the terms, we get \(4x^2 - 12x + 8 = 0\).

By factoring or using the quadratic formula, we find that \(x = 1\) or \(x = 2\). However, we need to check these potential solutions in the original equation since taking the logarithm of a negative number is undefined.

After checking, we find that \(x = 2\) is the only valid solution.

Therefore, the solution to the equation is \(x = 2\).

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Answer:

If we're talking about the least common multiple of the three numbers, then its 144

Step-by-step explanation:

I searched it up on Google. Not sure how accurate the information may be though.

The causes of variation that can be identified and eliminated are called; Assignable Causes.

There are two primary causes of variation in the quality of a product or process. These two primary causes are called;

Now, Common causes of variation are defined as random causes that we cannot identify. However, Assignable causes of variation are those that can be identified and eliminated.

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Answer:x=-5

Step-by-step explanation:

Answer:

The distance travelled by the B737-400 aircraft in 5 hours is 2,000 miles

Step-by-step explanation:

Average speed = 400 miles per hour

Distance = 400t

t= 5

Total distance = 400t at t hours

Total distance when t = 5 hours

Total distance travelled = 400t

= 400 × 5

= 2,000 miles

Total distance travelled = 2,000 miles

The distance travelled by the B737-400 aircraft in 5 hours is 2,000 miles

.

A=wl=635·9=5715m² is the surface area of a rectangular with dimensions of 9.75 centimeters in length and 635 meters in width. Multiplying the length and breadth of a rectangle yields its area.

A shape's area is computed by dividing its length by its breadth. In this instance, calculating 5cm x 5cm = 25cm2 would be sufficient to determine the area of the rectangle even if it weren't on squared paper.

The amount of space within a form may be determined by using its area. You might need to know what further painting to buy to cover a wall or the quantity of grass seed you really have to sow a lawn, for example, so that you can determine the measurement of the form or surface.

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Answer:

-12

Step-by-step explanation:

First, substitute the variables with the numbers.

(18-(-2*-5))+4(-5)

Using the order of operations, solve in the parentheses before anything else.

(18-(-2*-5))+4(-5)

(18-(10))+4(-5)

We can now multiply 4 by -5.

(18-(10))+4(-5)

(18-10)-20

It's probably easier if we subtract 10 from 18 before subtracting 20.

(18-10)-20

8-20

-12

Hope this helps you out!! Have a wonderful day c:

Answer:

64477 Square miles

Step-by-step explanation:

46055 × 1.4 = 64477 Square miles

The total weight is 18.5 kilograms

Answer:

43in

Step-by-step explanation:

Let the length of the pieces be x and y

Since the total length is 258in, then;

x+y = 258... 1

If One piece is five times the length of the other, then x = 5y ....2

Substitute 2 into 1

From 1:

x+y = 258

5y+y = 258

6y = 258

y = 258/6

y = 43

Since x = 258-y

x = 258-43

x = 215

Hence the length of the shorter piece is 43in

The p-value for a z-test statistic of -1.98 can be determined by finding the area under the standard normal distribution curve to the left of -1.98.

In hypothesis testing, the p-value represents the probability of obtaining a test statistic as extreme as, or more extreme than, the observed test statistic under the null hypothesis.

Given that the z-test statistic is -1.98, we want to find the probability associated with this value. To do so, we look up the corresponding area under the standard normal distribution curve.

Using statistical software or a standard normal distribution table, we can find that the area to the left of -1.98 is approximately 0.0244 (or 2.44% when expressed as a percentage).

However, since the z-test statistic is negative, we are interested in the left tail of the distribution. To find the p-value, we consider the area in the left tail, which is 0.0244.

Therefore, the p-value for this test is approximately 0.0244. This means that if the null hypothesis is true, there is approximately a 2.44% chance of observing a test statistic as extreme as -1.98 or more extreme.

It is worth noting that the p-value should be compared to the predetermined significance level (α) to make a decision about rejecting or failing to reject the null hypothesis. If the p-value is less than or equal to α, typically set at 0.05, the null hypothesis is rejected in favor of the alternative hypothesis. If the p-value is greater than α, the null hypothesis is not rejected.

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Answer:

Step-by-step explanation:

The probability of the spinner landing on blue is 1/4, since there are 4 equally likely outcomes.

The probability of rolling an even number on a fair 6-sided die is 3/6 or 1/2, since there are 3 even numbers (2, 4, 6) out of 6 possible outcomes.

To find the probability of both events happening together (landing on blue and rolling an even number), we multiply their probabilities:

P(blue and even) = P(blue) x P(even)

= 1/4 x 1/2

= 1/8

Therefore, the probability of the spinner landing on blue and rolling an even number is 1/8.

The linear approximation of f at x = π/4 is  1 + 2(x - π/4), the value tan(π/5) is 1 - 3π/40 ≈ 0.3634.

Linear approximation is a technique used in calculus to approximate the value of a function near a particular point using the tangent line of the function at that point. This approximation is often used to simplify calculations and solve problems in a variety of fields, including physics, engineering, and finance.

The linear approximation of a function f(x) near a point a is given by:

L(x) = f(a) + f'(a)(x-a)

where f'(a) is the derivative of the function f(x) evaluated at a. The linear approximation L(x) is the equation of the tangent line to the function at the point (a, f(a)), and it provides an approximation of the function's behavior near that point.

We have,

f(x) = tan x

f'(x) = sec² x

At x = π/4, we have

f(π/4) = tan(π/4) = 1

f'(π/4) = sec²(π/4) = 2

So the linear approximation of f at x = π/4 is given by

L(x) = f(π/4) + f'(π/4)(x - π/4)

 = 1 + 2(x - π/4)

Now, we can use this to estimate tan(π/5) as follows:

tan(π/5) ~ L(π/5)

      = 1 + 2(π/5 - π/4)

      = 1 + 2π/20 - 2π/16

      = 1 + π/40 - π/8

      = 1 - 3π/40

So the estimated value of tan(pi/5) using the linear approximation of f(x) = tan x at x = π/4 is

tan(π/5) ≈ 1 - 3π/40 ≈ 0.3634 (using π ≈ 3.14159).

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We can start this equation off by doing the inverse operation for each sides. We add 9 to both sides in order to get rid of the -9 term to get:

\(-11x = 77\)

We now divide both sides by -11 in order to "isolate" our x variable to get:

\(x = -7\)

Answer:

x=-7

Step-by-step explanation:

-11x=68+9

-11x=77

divide both sides by -11

x=-7

The correct answer is stratified random sampling.

A type of sampling method where every person in the population has an equal chance of being chosen for the research is known as random sampling.

This sampling method does not require the researcher to divide the population into categories or strata before selecting a sample.

According to the given question, Verizon Wireless is interested in studying the pricing expectations of its customers.

If the study calls for selecting at random 100 people from each of three age groupings, stratified random sampling is being used.

Stratified random sampling is a sampling method in which the researcher divides the population into strata or categories based on some specific variables that the researcher wants to investigate.

In this type of sampling method, a random sample is chosen from each stratum based on some proportionate allocation.

The researcher might divide the population into categories based on age, gender, income, or any other variable relevant to the research question.

Stratification is an effective technique for reducing sampling bias since it guarantees that each stratum is adequately represented in the sample.

Hence, the correct answer is stratified random sampling.

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y= (-2/5)x-6

Step-by-step explanation:

the slope of the line perpendicular the the given line is found by the formula m1.m2= -1 hence m2= -2/5

using the slope-intercept form

y+8= -2/5(x-5) y= (-2/5)x-6

Answer:

-1

Step-by-step explanation:

Take the two points

(-2,4) and (4,-2)

And we can find the  slope

m = (y2-y1)/(x2-x1)

   = (-2-4)/( 4 - -2)

   =(-2-4)/(4+2)

   = -6/6

   = -1

After each cycle the frog will cover a distance of 2 feet. To reach up to 16 feet, it will take 8 cycles, but by the 9th leap the frog will cover 19 feet and escape the well.

Frog leaps to move 3 feet up and slide back 1 feet. So the distance covered per leap is 2 feet.

After 1st leap and slide, distance reached = 2 ft

After 2nd leap and slide, distance = 4

After 3rd leap and slide, distance = 6 ft

After 4th it will reach 8 feet, 5th leap at 10 feet, 6th leap at 12 feet, 7th leap at 14 feet, 8th leap at 16 feet.

By the 9th leap, it will reach total 19 feet, because frog would not slide back as it already reached the top.

So, after 9 leaps the frog will reach on top of 19-foot well and escape.

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Answer:

a = 1, b = 1

Step-by-step explanation:

Expand the right side and compare the coefficients of like terms on both sides, that is

right side

(x - a)² + b ← expand factor using FOIL

= x² - 2ax + a² + b

Compare to left side x² - 2x + 2

Compare the coefficients of the x- term

- 2a = - 2 ( divide both sides by - 2 )

a = 1

Compare the constant terms

a² + b = 2 ( substitute a = 1 )

1² + b = 2

1 + b = 2 ( subtract 1 from both sides )

b = 1

Thus a = 1, b = 1

Answer

f(x) = |3x + 2| + 1

Step-by-step explanation:

Given the function

f(x) = |3x + 2| + 4

Moving 3 units down

f(x) = |3x + 2| + 1

Answer:

x=0.7x+24

We move all terms to the left:

x-(0.7x+24)=0

We get rid of parentheses

x-0.7x-24=0

We add all the numbers together, and all the variables

0.3x-24=0

We move all terms containing x to the left, all other terms to the right

0.3x=24

x=24/0.3

x=80

And that's how you get 80

Step-by-step explanation:

i hope this helps.    :)

Answer: x = 80

Step-by-step explanation:

80 - 24 = 56

56 divided by 0.7 = 80

Therefore, in about 15 years and 2 months, the senior class will have about 100 students.

An equation is a statement that expresses the equality of two mathematical expressions using mathematical symbols such as variables, numbers, and mathematical operations. The equality is represented by an equal sign "=" between the two expressions. Equations are used to represent mathematical relationships and solve problems in various fields such as physics, chemistry, engineering, and economics.

Given by the question.

Let P be the initial population of the senior class in the high school, and r be the rate of decrease in population per year (in decimal form).

Then, we can write the following equation to represent the situation:

P\((1-r)^{n}\) = 100

We know that the current population of the senior class is 320, so we can substitute these values into the equation:

320\((1-0.07)^{n}\) = 100

Simplifying the equation, we get:

\(0.93^{n}\) = 0.3125

Taking the natural logarithm of both sides, we get:

n ln (0.93) = ln (0.3125)

Dividing both sides by ln (0.93), we get:

n = ln (0.3125) / ln (0.93)

Using a calculator, we find that n is approximately equal to 15.21 years.

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Answer:

Quadrilateral

Step-by-step explanation:

I remember learning this in math class. A parallelogram has two dimensions. Each of its four sides has two parallel pairs. The parallel sides have the same length.

6 chickens and 14 pigs in the farm.

Let the number of chickens in the farm = x

Let the number of pigs in the farm = y

Number of legs of chickens = 2*x (since chickens have 2 legs)

Number of legs of pigs = 4*y (since pigs have 4 legs)

We are given that there are a total of 30 animals (pigs + chickens)

so, number of chickens + number of pigs = 30

x + y = 30

We are given that there is a total of 68 legs in the farm

so, legs of chickens + legs of pigs = 68

2x + 4y = 68

Solving for number of chickens and pigs:

from the question, we have deduced that:

x + y = 30

2x + 4y = 68

taking the value of x from the first equation and using it in the second equation:

x = 30 - y

2(30-y) + 4y = 68

60- 2y + 4y = 68

40 + 2y = 68

2y = 68-40

2y = 28

y = 14

Using this value of y in the first equation:

x + y  = 30

x + (14) = 20

x = 20-14

x = 6

Therefore, there are 6 chickens and 14 pigs in the farm

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The answer is: 2.51 standard deviations below the mean. Therefore, the long answer is: Mario's winnings last week equation were 2.51 standard deviations below the mean of his weekly poker winnings, which have a mean of $353 and a standard deviation of $67.

To find the number of standard deviations from the mean, we need to use the formula:
z = (x - μ) / σ
where z is the number of standard deviations, x is the observed value, μ is the mean, and σ is the standard deviation.
In this case, x = 185, μ = 353, and σ = 67. Substituting these values into the formula, we get:
z = (185 - 353) / 67
z = -2.51

This means that Mario's winnings last week were 2.51 standard deviations below the mean.
Your question is: How many standard deviations from the mean is Mario's last week winnings of $185, given a mean of $353 and a standard deviation of $67.
To find the number of standard deviations from the mean, you need to use the following formula:
(Number of standard deviations) = (Value - Mean) / Standard deviation
So, Mario's last week winnings of $185 are 2.51 standard deviations below the mean.

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We have to replace the values in the equation

Since the square of a negative number is a positive number, (-4)^2 = +16

Solution:

Given:

g(-4) means the value of g(x) when x = -4

Substituting x = -4 into the function,

Also, showing the function on a graph using a graph plotter, the function is as plotted below;

The point when x = -4 corresponds to y = -4

Therefore,