suppose that a friend is helping put on a fundraiser for the local animal shelter. one activity is a game using a bowl that contains six green marbles and eight blue marbles. to play the game, each person draws two marbles without replacement and without looking. if both marbles are green, the player wins $25. if not, the player must donate $10 to the animal shelter. the marbles are then replaced for the next player. calculate the expected value of the game for the player.

The result (f•g)(12) = 382 represents the overall cost of catering the event when 12 fewer guests than 100 attend.

In mathematics, a function is a rule that gives each input value in a set a distinct output value. It is a relationship between a collection of inputs and a set of potential outputs, where each input has a single, precise counterpart in each possible outcome. f(x) = x2, where f is the function, x is the input, and x2 is the output, is a common function notation used to represent functions. Functions are used to model and analyse interactions between variables in many branches of mathematics as well as in many fields of science and engineering.

given

We must first locate the composite function f(g(x)) before substituting x = 12 to calculate (f•g)(12):

430 - 4x = f(g(x)) = f(100 - x) = 30 + 4(100 - x)

Thus, 430 - 4x = (f•g)(x) = f(g(x)).

If we replace x with 12, we get:

(f•g)(12) = 430 - 4

(12) = 382

Interpretation: Taking into account the cost per guest as modelled by f(x) = 30 + 4x and the number of attendees as modelled by g(x) = 100 - x, the result (f•g)(12) = 382 represents the overall cost of catering the event when 12 fewer guests than 100 attend.

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The probability of a SRS of 45 students spending an average of between $600 and $700 is approximately 0.9871.

We can use the central limit theorem to approximate the distribution of the sample mean from a normal population. Since the population standard deviation is known and the sample size is large enough (n = 45), we can use the normal distribution to approximate the sampling distribution of the sample mean.

The formula for the standard error of the mean is:

SE = σ/√n

Where σ is the population standard deviation and n is the sample size.

Plugging in the values, we get:

SE = 120/√45 ≈ 17.89

Now, we need to standardize the sample mean using the z-score formula:

z = (x - μ) / SE

Where x is the sample mean, μ is the population mean, and SE is the standard error of the mean.

For the lower bound of 600:

z = (600 - 650) / 17.89 ≈ -2.79

For the upper bound of 700:

z = (700 - 650) / 17.89 ≈ 2.79

Using a standard normal distribution table or calculator, we can find the area between these two z-scores:

P(-2.79 < z < 2.79) ≈ 0.9871

Therefore, the probability that a SRS of 45 students will spend an average of between 600 and 700 dollars is approximately 0.9871, or 0.98710 rounded to five decimal places.

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In conclusion, the chance of having HIV, assuming a positive test result, is 0.4%. It is important to remember that this number could vary depending on the accuracy and false positive rate of the test, as well as the number of people infected with HIV in the given area.

Assuming you tested positive for HIV, the chance of having the virus is higher than 2.5%, since the test has a false positive rate of 2.5%.

Out of the 10,000 people, 250 are likely to test positive, of which only one person actually has the virus. This means that the actual chance of having HIV, assuming a positive test result, is 1 in 250 or 0.4%.

It is important to note that this calculation only applies to the specific case of the 10,000 people in question, and the false positive rate of the test. Different tests have different levels of accuracy and false positive rate, which could alter the result. Furthermore, the number of people infected with HIV may differ significantly in different areas, which could also change the probability.

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Answer:

2/7 or 4/14

Step-by-step explanation:

we add all the people in the various electives and get 14.

then, we put 4 over 14 to get 4/14, which simplifies to 2/7 people.

I hope this helps!

Good luck for future math questions!

~Cain

Answer: 23/42

Step-by-step explanation:  

your messageHELP URGENT !!!A bag contains 16 red marbles, 7 yellow marbles, and 19 green marbles. What is the probability that a marble drawnfrom the bag is red or yellow? Write your answer as a simplifed fraction.Sure, I can help you with that! The probability of drawing a red marble is 16/42 (since there are 16 red marbles out of a total of 42 marbles), and the probability of drawing a yellow marble is 7/42. To find the probability of drawing a red or yellow marble, we simply add those two probabilities: 16/42 + 7/42 = 23/42 So the probability of drawing a red or yellow marble is 23/42, which is already in simplified fraction form.

Answer: 7 meters

Step-by-step explanation:

1. Identify the given information: Circumference = 14 pi meters

2. Use the formula for calculating the circumference of a circle: Circumference = 2 pi * radius

3. Rearrange the formula to solve for the radius: Radius = (Circumference) / (2 pi)

4. Substitute the given information into the formula: Radius = (14 pi meters) / (2 pi)

5. Calculate the radius: Radius = 7 meters

Answer:

Step-by-step explanation:

The perimeter of a rectangle is given by the formula:

perimeter = 2(length + width)

In this case, the length is 14.3 yards and the width is 12 yards. Substituting these values into the formula, we get:

perimeter = 2(14.3 + 12)

perimeter = 2(26.3)

perimeter = 52.6 yards

Therefore, the perimeter of the rectangle is 52.6 yards.

The area of a rectangle is given by the formula:

area = length x width

Substituting the length and width values, we get:

area = 14.3 x 12

area = 171.6 square yards

Therefore, the area of the rectangle is 171.6 square yards.

Answer:

Step-by-step explanation:

To sum up, the sampling distribution of the mean can be assumed to be approximately normal when the sample size is greater than 30 or the population is normally distributed.

The sampling distributions of means are always approximately normally distributed.

The correct option is: approximately normally distributed.

When the size of the sample is greater than 30 or the population is normally distributed, the sampling distribution of the mean is said to be approximately normally distributed.

This is true, whether the population is symmetrical or not, and the sampling distribution of the mean is symmetrical when the sample size is at least 30. .

If the population is symmetrical, then the sampling distribution of the mean will be symmetrical regardless of the sample sizes.

The other options are not true for the sampling distribution of the mean.

The distribution of the means would be positively skewed or negatively skewed if the distribution of the population was not symmetrical.

It's not the case that the distribution of the means is more variable than the population from which the samples were drawn.

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The equation of the line perpendicular to y = 1/3 x + 5 and passing through (2,6) is y = -3x + 12, which is option 3.

To find the equation of a line perpendicular to y = 1/3 x + 5 and passing through the point (2,6), we first need to determine the slope of the original line and the slope of y = 1/3 x + 5 is 1/3.

To find the slope of a line perpendicular to this, we can use the fact that the product of the slopes of two perpendicular lines is -1 and therefore, the slope of the line we want is the negative reciprocal of 1/3, which is -3.

Now that we have the slope, we can use the point-slope form of the equation of a line to write the equation of the line passing through (2,6) with slope -3:

y - 6 = -3(x - 2)

y = -3x + 12

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Answer:

WE CAN WRITE IN STANDARD FORM IN THE FOLLOWING WAY..

LMX0

It will take approximately 1.386*t days until only 1/2 ounces of element X remain.

If the half-life of element X is t days, it means that after every t days the amount of element X will be reduced by half.

Initially, we have a 1-ounce sample of element X.

After t days, the amount of element X remaining will be 1/2 ounces.

After 2t days, the amount of element X remaining will be (1/2)*(1/2) = 1/4 ounces.

Similarly, after 3t days, the amount of element X remaining will be (1/2)(1/2)(1/2) = 1/8 ounces.

After n*t days, the amount of element X remaining will be (1/2)^n ounces.

We want to find the value of n such that (1/2)^n = 1/2^(n/2) ounces.

Taking the logarithm of both sides, we get:

n*log(1/2) = (n/2)*log(1/2)

Simplifying, we get:

n = 2*log(2) = 1.386

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Step-by-step explanation:

all he have to do is you substitute the expressions correctly

When creating a 96% confidence interval from a simple random sample (SRS) of 16 observations, the critical value to be used is 2.120.

A confidence interval is a range of values for an unknown population parameter, such as the population mean or population proportion. Confidence intervals are usually stated as a range of values with a level of confidence that the population parameter is contained in the interval.

Let's examine the components of a confidence interval to understand what it is:

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The Scatterplot has no correlation.

What is scatterplot?

Data visualization that depicts the relationship between two numerical variables is known as a scatterplot. The values for the two variables are used to depict each member of the dataset as a point with ( x , y ) coordinates that correspond to those values.

We know that A positive correlation between the variables is present when the y variable tends to grow as the x variable increases and a negative correlation is when x variables increase but y variable decreases.

No correlation means there is no clear relationship between two variables.

In the given scatter plot represent the relationship between month and cost.

Here for 6 months cost is $0.5 , for 7 months cost is $1 and for 5 months  cost is also $1. Then there is no clear relationship between month and cost.

Hence the scatterplot has no correlation.

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Answer:

1 : 2

Step-by-step explanation:

First, find the GCF of 6 and 12, which is 6.

So divide both sides by 6:

6 / 6, 12 / 6

= 1 : 2

Step-by-step explanation:

We can prove that X^n + Y^n is divisible by X + Y for any odd natural number n, where n ≥ 1, using mathematical induction.

Base case: n = 1 When n = 1, we have X^1 + Y^1 = X + Y, which is clearly divisible by X + Y.

Inductive step: Assume that X^k + Y^k is divisible by X + Y for some odd natural number k ≥ 1. We will show that X^(k+2) + Y^(k+2) is divisible by X + Y.

We can expand X^(k+2) + Y^(k+2) using the binomial theorem: X^(k+2) + Y^(k+2) = (X^2)(X^k) + (Y^2)(Y^k)

We can factor out X + Y from the first term and Y + X from the second term, since X + Y = Y + X: X^(k+2) + Y^(k+2) = (X + Y)(X^k + XY^k) + (X + Y)(Y^k + XY^k)

We can then simplify this expression by factoring out XY^k from the first term and X^kY from the second term: X^(k+2) + Y^(k+2) = (X + Y)XY^k + (X + Y)X^kY X^(k+2) + Y^(k+2) = (X + Y)XY^k + (X + Y)X^kY

We can then factor out (X + Y) from this expression to get: X^(k+2) + Y^(k+2) = (X + Y)(XY^k + X^kY)

Since X + Y is a common factor of X^(k+2) + Y^(k+2), we have shown that X^(k+2) + Y^(k+2) is divisible by X + Y.

Therefore, by mathematical induction, we have proven that X^n + Y^n is divisible by X + Y for any odd natural number n, where n ≥ 1.

We can conclude that the linear relationship between x and y in this table is described by the phrase "y is 3 more than x."

What is the linear function?

A linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to a straight line.

The given table shows two variables, x, and y, with corresponding values. A linear relationship between two variables means that a change in one variable causes a proportional change in the other variable.

If we look at the table, we can see that as the value of x increases by 1 unit from 3 to 4, the value of y also increases by 3 units from 9 to 12. Similarly, as the value of x increases by 1 unit from 4 to 5, the value of y increases by 3 units from 12 to 15.

This means that for every 1 unit increase in x, the value of y increases by a constant amount of 3 units.

In other words, the slope of the line connecting these points is constant and equal to 3.

Therefore, we can conclude that the linear relationship between x and y in this table is described by the phrase "y is 3 more than x."

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Answer:<HBG

Step-by-step explanation:

Adjacent means next to in this situation so it would be the angle next to it.

A larger sample size will result in a more reliable estimate of the population mean, lowering the variability and resulting in a higher F-ratio, which will result in the null hypothesis being rejected. As a result, both options A and B are correct.

Here we want to find,

the likelihood of rejecting the null hypothesis using anova is increased by which.

To increase the likelihood of rejecting the null hypothesis using ANOVA, a decrease in SSWITHIN and an increase in sample sizes are needed.

In statistics, analysis of variance (ANOVA) is a technique for comparing the means of two or more samples. ANOVA is an extension of the t-test and z-test methods, which can be used to compare only two means.

ANOVA compares the variation within the groups to the variation between the groups to see whether or not there is a statistically significant difference between them.

The null hypothesis ([tex]H_0[/tex]) in ANOVA is that the means of all groups are equal, while the alternative hypothesis (Ha) is that at least one group's mean is different from the others.

In ANOVA, a low value of SSWITHIN is desirable because it reflects that the data points are clustered around their respective means.

As a result, ANOVA will result in a higher F-ratio, which means that the null hypothesis will be rejected.

So, both a and b options are correct.

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Using composite figures, we can find the value of area as:

In the 1st image,

Area of 1st triangle =70m².

Area of 2nd triangle = 24unit².

Area of 3rd triangle = 30unit².

In the 2nd image,

Area of the composite figure = 144unit²

In the 3rd image,

Area of the trapezium = 54unit².

The area of composite shapes refers to the space any composite shape occupies. The composite shape is a shape made by combining a few polygons together to generate the required shape. Certain geometric forms, such as triangles, squares, quadrilaterals, etc., can be combined to create other geometric forms. Dividing a composite item into straightforward forms like a square, triangle, rectangle, or hexagon will allow you to compute its area.

In the 1st image,

Base of 1st triangle = 14m

Height of triangle = 10m.

Area of 1st triangle = 1/2 × b × h

= 1/2 × 14 × 10

= 70m².

In the 2nd triangle,

Base = 12

Height = 4

Area = 1/2 × b × h
= 1/2 × 12 × 4

= 24unit².

In the 3rd triangle,

Base = 12

Height = 5

Area = 1/2 × b × h

= 1/2 × 12 × 5

= 30unit².

Coming to the 2nd image we have a composite figure,

We have a rectangle with length = 9 and breadth = 6.

We have a triangle with base = 9 and height = 6.

And we have a trapezium with opposite sides as, a = 6, b = 15 with a height = 6.

So, the total area will be area of rectangle + area of triangle + area of trapezium.

= (9 × 6) + (1/2 × 9 × 6) + ((6+15)/2 × 6)

= 54 + 27 + 63

= 144unit².

Coming to the last image:

From the graph we can see that the polygon is a trapezium.

The height of the trapezium = 6 units.

Opposite sides,

a = 7 and b = 11.

So, area of trapezium = (a+b)/2 × h

= (7+11)/2 × 6

= 18/2 × 6

= 54unit².

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Answer:

121.2 calories.

Step-by-step explanation:

Weight of one packet of crisps = 864/36

= 24 grams.

So, by proportion, the number of calories in one packet

= 24 * 505/100

= 121.2 calories.

Answer: 300/π°, or ~95.49°

Step-by-step explanation:

In order to find the central angle of the arc, we first find the ratio of the arc length to the circumference of the circle, since it is proportional to the ratio of the central angle to the total inside angle, 360°.

Finding the circumference
Circumference is equal to 2πr, and r (radius) in this case is 3, so

C=2π*3, or 6π

The ratio of the arc length to circumference is then 5/6π

Finding the angle

Since the ratio of lengths and ratio of angles are proportional, we can set up this equation:

5/6π=x/360

solving for x gets us:

x=300/π°, or ~95.49°

Answer:

<ICJ

Step-by-step explanation:

Vertical angles are congruent.

Answer: <ICJ

Answer: ∠JCI

Step-by-step explanation:

   ∠JCI and ∠FCE are vertical angles. We know that vertical angles are congruent, so the answer to this question is;

            ∠JCI

The speed of the wind is 10km/hr.

What is the speed?

A scalar quantity, speed is defined as the size of the change in an object's location over time or the size of the change in an object's position per unit of time.

Here, we have

Given: An airship flies 150km with the wind and then turns around and flies back, taking 6 hours and 15 minutes for the round trip.

We have to find the speed of the wind if the speed of the airship in calm weather is 50 km/hr.

150 = (50-c)(6.25-t)

6.25-t = 150/(50-c)

(6.25×50 - 6.25c -150)/(50-c) = t

t = (162.5 - 6.25c)/(50-c).....(1)

150=(50+c)t  

t = 150/(50+c)

Now, we put the value of t in equation (1) and we get

150/(50+c) = (162.5 - 6.25c)/(50-c)

150 = (50+c) (162.5 - 6.25c)/(50-c)

150 = (50+c)(162.5 - 6.25c)/(50-c)

150 = (8125 - 312.5c +162.5c - 6.25c²)/(50-c)

7500 - 150c = 8125 - 312.5c + 162.5c - 6.25c²

7500 - 150c = 8125 - 150c  - 6.25c²

7500 = 8125 - 6.25c²

8125 - 6.25c² - 7500 = 0

6.25c² - 625 = 0

c² = 100

c = 10

Hence, the speed of the wind is 10km/hr.

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Answer:

Step-by-step explanation you have to do this

Answer:

Saanvi recorded the number of math problems she did for homework each night for 10 days.

Step-by-step explanation:

The correct option is A.

y  ≥ -3

The range is defined as the set of possible outputs, so just look at the vertical axis, you can see it goes from x = -3 up, then the range is just the set of all values larger than -3

it is written as:

y  ≥ -3

The correct option is a-.

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The slope of the line that passes through (2, 5) and (−1, 5) will be 0.

A straight line on the coordinate plane is represented by a linear function.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

The slope associated with two points (x₁, y₁) and (x₂, y₂) is given by

Slope = (y₂ - y₁)/(x₂ - x₁)

The slope of (2, 5) and (−1, 5),

Slope = (5 - 5)/(-1 - 2) = 0

Hence "The slope of the line that passes through (2, 5) and (−1, 5) will be 0".

The system of inequalities that matches the given word problem is:

5x + 2y <= 80

x >= 8

A system of inequalities is a set of two or more inequalities in one or more variables. Systems of inequalities are used when a problem requires a range of solutions, and there is more than one constraint on those solutions.

Let's break down the problem and identify the key information:

The budget for food is 80 dollars

Little Cesar's pizzas cost 5 dollars each

McDonald's McChicken's cost 2 dollars each

At least 8 Little Cesar's pizzas are needed to feed everyone that wants pizza

Let x represent the number of pizzas bought and y represent the number of McChicken's bought. The total cost of pizzas and McChicken's should be less than or equal to 80 dollars, which gives us the first inequality:

5x + 2y <= 80

Additionally, we know that at least 8 pizzas should be bought, which gives us the second inequality:

x >= 8

Therefore, the system of inequalities that matches the word problem is:

5x + 2y <= 80

x >= 8

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