In a lottery game, a player pays $1 and picks six numbers from 1 to 29. This gives 475020 possible ways of choosing six numbers, and just one winning combination. If the player matches all six numbers, they win the jackpot of $50,000, which is $49,999 dollars that they take home after subtracting the $1 ticket cost. Otherwise, they lose $1. What is the expected value of this game?

Answer:

1) The equation has one solution.

2) A value of x that makes the equation true is 7, which when substituted into the equation and simplified makes the equation turn into 10 = 10.

3) A value of x that makes the equation false is 5, which when substituted into the equation and simplified makes the equation turn into 8 = 10.

Step-by-step explanation:

1) Since the equation is a simple problem, and answer question, it only has one solution.

2) The value of x is 7 because 3 + 7 equals 10, making said equation true. Similarly, you could perform 10 - 3, which makes you receive 7 in return. After this, you end up simplifying to 10 = 10, thus also making the equation true.

3) A value of x making the equation false can be many numbers, as long as they’re not 7. I chose 5, which would simplify into 8 (3 + 5 = 8), therefore making the equation false. To further prove this, we realize 8 = 10 makes the equation incorrect.

The area of the base (11.76 cm²) by the height (6.6 cm), resulting in a volume of 77.616 cm³ for the rectangular prism. Volume of a rectangular prism in Part C, we need to multiply the length, width, and height of the prism.

The volume of a rectangular prism is V = l x w x h. In this case, the length is 5.6 cm, the width is 2.1 cm, and the height is 6.6 cm. Therefore, the answer to Part C would be V = 5.6 cm x 2.1 cm x 6.6 cm = 78.624 cm³. When calculating the volume, we need to use the area of the base of the rectangular prism, which is equal to the length multiplied by the width. So, in this case, the area of the base would be 5.6 cm x 2.1 cm = 11.76 cm². Using this value, we can calculate the volume of the rectangular prism as mentioned above.

We need to use the formula V = l x w x h, where the length, width, and height are given. The area of the base, which is equal to the length multiplied by the width, should be used when calculating the volume of the rectangular prism.
To calculate the volume of a rectangular prism, you need to multiply the area of the base by the height. In this case, the base is a rectangle with a length of 5.6 cm and a width of 2.1 cm. Multiply the length by the width. So, 5.6 cm × 2.1 cm = 11.76 cm². This is the value you should use as the area of the base when calculating the answer to Part C.

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Another name for the regression line is the least squares line because it was chosen to make the sum of the squares of the differences between the observed y values ​​and the values ​​predicted by the line as small as possible.

A regression line (LSRL - Least Squares Regression Line) is a straight line that describes how the response variable y changes when the explanatory variable x changes. The line is the mathematical model used to predict the value of y for a given x.

Least squares is a form of mathematical regression analysis used to determine the line of best fit for a data set, providing a visual demonstration of the relationship between data points. Each data point represents the relationship between a known independent variable and an unknown dependent variable.

If the data shows a weak relationship between two variables, the line that best fits this linear relationship is called a least-squares regression line, and it minimizes the vertical distance of the data points from the regression line. The term "least squares" is used because it is the minimum of the sum of squared errors, also known as "variance". In regression analysis, the dependent variable is shown on the vertical y-axis and the independent variable is shown on the horizontal x-axis. These specifications form the equation for the line of best fit, which is determined by the method of least squares.

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Answer: A range of values, created using sample, within which population parameter has a certain probability of occurring.

Reason: E.g. P(a<x>b) = 0.95

confidence interval is A range of values, is created using a sample, within a population parameter that has a certain probability of occurring.

A sampling method's degree of certainty or uncertainty is measured by confidence intervals. In statistics, the probability that a population parameter will fall between a set of values for a certain percentage of the time is referred to as a confidence interval. Confidence intervals that contain either 95% or 99% of expected observations are frequently utilized by analysts. To comprehend the statistical significance of their estimates, inferences, or predictions, statisticians and other analysts employ confidence intervals.

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Answer:

90 students

Step-by-step explanation:

So, if you have 100 students to start and it decreases by 10% then take the 100 and multiply it by .10. You should get 10. Then, subtract 10 from 100 and you end up with 90.

Answer:

hello

2010 = 100 students

2011 = 100 x 0.9 = 90

2012 =  90 x 1.1 =  99  

Step-by-step explanation:

(a) To find the average cost function C, we need to divide the total cost C(x) by the number of units x produced. Therefore, the average cost function is:

C(x) / x = (95x + 180,000) / x

Simplifying this expression, we get:

C(x) / x = 95 + (180,000 / x)

(b) To find the marginal average cost function C', we need to take the derivative of the average cost function C(x) with respect to x. Therefore, we get:

C'(x) = -180,000 / x^2

The marginal average cost function represents the rate of change of the average cost function with respect to the number of units produced. In this case, we see that the marginal average cost function is negative and decreasing as the production level increases. This means that the average cost per unit is decreasing as more units are produced.

(c) When x is very large, the term 180,000 / x in the average cost function becomes very small compared to the term 95x. Therefore, the average cost per unit approaches 95 dollars per unit as the production level becomes very high.

This value is what the average cost per unit approaches if the production level is very high.
(a) To find the average cost function, we need to divide the total cost function C(x) by the number of units produced x.
C(x) = 95x + 180,000

Average cost function, A(x) = C(x) / x
A(x) = (95x + 180,000) / x

(b) To find the marginal average cost function, we will take the derivative of the average cost function A(x) with respect to x.
A'(x) = d(A(x))/dx = d((95x + 180,000) / x)/dx

Using the quotient rule, A'(x) = [(x * 95 - (95x + 180,000) * 1) / x^2]
A'(x) = (-180,000) / x^2

(c) To find the limit of C(x) as x approaches infinity, we can observe the behavior of the average cost function A(x).
lim (x->∞) A(x) = lim (x->∞) ((95x + 180,000) / x)

As x becomes very large, the 180,000 becomes insignificant compared to the 95x term, so the average cost function A(x) approaches:
lim (x->∞) A(x) = 95

As the production level (x) becomes very high, the average cost per unit approaches $95. This means that the company's production becomes more cost-efficient as they produce a larger number of desks.

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Answer:

Step-by-step explanation:

Parallel lines are lines whose slopes are the same

We are given the line \(y = \frac{-1}{2}x + 3\)

so the other line's slope has to be \(\frac{-1}{2}\)

We can use y = mx + b to find the equation of the line

\(y = mx + b\\y = \frac{-1}{2}(x)+b\\1 = \frac{-1}{2}(-3)+b\\1 = \frac{3}{2} + b\\b = \frac{-1}{2}\)

so

\(y = \frac{-1}{2}(x) - \frac{1}{2}\)

The distance the puck traveled from the wall to Pedro is determined as √(ab).

Let's call the distance from Meg to the wall "a" and the distance from Pedro to the wall "b".

Let's also call the distance the puck travels from the wall to Pedro "x".

Since the two triangles are similar, we can set up a proportion:

a / x = x / b

We can cross-multiply to get:

x² = ab

And then take the square root of both sides to get:

x = √(ab)

So the distance the puck traveled from the wall to Pedro is √(ab).

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The three options that are true about the equation of the circle are:

B) The center of the circle lies on the x-axis

A) The radius of the circle is 3 units.

E) The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

The standard equation of a circle is expressed as:

x² + y² + 2gx + 2fy + c = 0

Where:

Center is (-g, -f)

radius = √g²+f²-C

Given a circle whose equation is x² + y² - 2x - 8 = 0

Get the Centre of the circle:

2gx = -2x

2g = -2

g = -1

Similarly, 2fy = 0

f = 0

Centre = (-(-1), 0) = (1, 0)

This shows that the center of the circle lies on the x-axis

r = radius = √g² + f² - C

radius = √1² + 0² - (-8)

radius =√9 = 3 units

The radius of the circle is 3 units.

For the circle x² + y² = 9, the radius is expressed as:

r² = 9

r = 3 units

Hence the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

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a. one sample t procedure for a mean. The appropriate procedure for this scenario would be a one sample t procedure for a mean. This is because we only have sampled information and do not know the population standard deviation.

Therefore, we use the sample standard deviation as an estimate for the population standard deviation and apply the t-distribution to perform the hypothesis test. The t-distribution takes into account the uncertainty in our estimate of the population standard deviation. On the other hand, the one sample z procedure for a mean assumes that we know the population standard deviation, which is not the case here. The one sample z procedure for a proportion is used when we want to test the value of a proportion in a population.

Therefore, option (a) is the correct answer for this scenario.
In this scenario, you want to test the value of the mean in a population using sampled information. Since you have a random sample of 60 with a sample mean and sample standard deviation, the appropriate procedure for your data would be:
This is because you don't know the population standard deviation, and the sample size is relatively small. The t procedure is suitable in such cases, as it takes into account the uncertainty related to estimating the population standard deviation using the sample standard deviation.

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Therefore , the solution of the given problem of expression comes out to be Option E. 16(20−24) is correct and Option F. (20−24)6  is correct.

Mathematical operations like addition, multiplication, and division are needed. They result in the following when combined: An equation, some information, and a mathematical operator Values, parameters, and arithmetic operations like additions, erasures, multiplications, and divisions can all be found in a statement of fact. Different phrases and words can be contrasted and compared.

Here,

Given :

Expression = 6(x+4) =20

=> 6x + 24 = 20

=> 6x = 20-24

=> 6x = -4

=> x = -4/6

=>x = -2/3

Thus ,

Option E. 16(20−24) is correct and Option F. (20−24)6  is correct.

Therefore , the solution of the given problem of expression comes out to be Option E. 16(20−24) is correct and Option F. (20−24)6  is correct.

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Answer: See explanation

Step-by-step explanation:

John said he can find 38×10 by adding a 0 to the end of 38 to get 380. John finds 46.52×10 using the same method and gets 46.520.

For the first one that is, 38 × 10 = 380, John is correct. For the second one, that is, 46.52 × 10 = 46.520. John is incorrect. In this case, the first one is correct because John was multiplying by a whole number.

For the second one involving a decimal, John could have shifted the decimal point one place to the right and not add 0 to the end. Then he will get:

46.52 × 10 = 465.2

Answer:

Step-by-step explanation:

£2.25 X 60 = £135

135 - 125= £10

£10/125 x 100 = 8%

The hypotheses can be written mathematically as follows:

Null Hypothesis (H₀): μmpg_domestic = μmpg_foreign and μprice_domestic = μprice_foreign

Alternative Hypothesis (H₁): μmpg_domestic > μmpg_foreign and μprice_domestic < μprice_foreign

In the null hypothesis, we assume that there is no difference in the mean miles per gallon (mpg) and mean prices between domestic and foreign vehicles. The symbol "μ" represents the population mean.

In the alternative hypothesis, we propose that domestic vehicles have better fuel efficiency (higher mpg) and lower prices compared to foreign vehicles. The ">" sign indicates that the mean mpg of domestic vehicles is greater than the mean mpg of foreign vehicles, and the "<" sign indicates that the mean price of domestic vehicles is lower than the mean price of foreign vehicles.

These mathematical representations of the hypotheses allow for statistical testing to determine whether there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis based on the observed data.

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Explanation: 1 / 2 = 9 / 18 Halfway that and 0 would be 4.5 / 18 Since 3 / 18 is below that, we would round to 0

Answer:

44

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

hope this helps

Answer:

It’s the third option

Step-by-step explanation:

I took the quiz

Answer:

By the time her daughter is 21 years old 300 EUR will have been deposited into the account.

Step-by-step explanation:

Since a woman deposits 100 EUR in her daughter's bank account on her first birthday, and on every subsequent birthday, she deposits 10 EUR more than she deposited the previous year, so on her second birthday, she deposits 110 EUR, and on her third birthday she deposits 120 EUR, to determine, by the time her daughter is 21 years old, how much money has been deposited in her account, the following calculation must be performed:

100 + (20 x 10) = X

100 + 200 = X

300 = X

Therefore, by the time her daughter is 21 years old 300 EUR will have been deposited into the account.

The percentage of his income he saved is 44.4%.

Percentage is a way of expressing a number as a fraction of 100. It is commonly used to represent a proportion or share of a whole, such as a percentage of a total amount, a percentage of a target or goal, a percentage of a population, etc.

In mathematical terms, a percentage can be represented as a decimal or a fraction, and is expressed as a symbol, such as "%".

If Ravindra's monthly income is rupee 90000 and saves rupee 40000 per month, then the percentage can be calculated as:

percentage = (40,000/90,000) x 100% = 44.4%

Hence, she saves 44.4% of his income per month.

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The function composition exists an operation " ∘ " that brings two functions f and g, and has a function h = g ∘ f such that h(x) = g(f(x)).

Let the functions be f(x) = 4x² + 1 and g(x) = x² - 3

The correct answer is (f o g)(x) = 4x⁴ - 96x + 37 and

(g o f)(x) = 16x⁴ + 8x² - 2.

The function composition exists an operation " ∘ " that brings two functions f and g, and has a function h = g ∘ f such that h(x) = g(f(x)). In this operation, the function g exists used for the outcome of applying the function f to x.

Given:

f(x) = 4x² + 1 and g(x) = x² - 3

a) (f o g)(x) = f[g(x)]

f[g(x)] = 4(x² - 3)² + 1

substitute the value of g(x) in the above equation, and we get

    = 4(x⁴ - 24x + 9) + 1

simplifying the above equation

    = 4x⁴ - 96x + 36 + 1

    = 4x⁴ - 96x + 37

(f o g)(x) = 4x⁴ - 96x + 37

b) (g o f)(x) = g[f(x)]

substitute the value of g(x) in the above equation, and we get

g[f(x)] = (4x² + 1)²- 3

      = 16x⁴ + 8x² + 1 - 3

simplifying the above equation

      = 16x⁴ + 8x² - 2

(g o f)(x) = 16x⁴ + 8x² - 2.

Therefore, the correct answer is (f o g)(x) = 4x⁴ - 96x + 37 and

(g o f)(x) = 16x⁴ + 8x² - 2.

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Answer:

$11,611.69

Step-by-step explanation:

Compound Interest Formula

\(\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}\)

where:

Given:

Substitute the given values into the formula and solve for A:

\(\implies \sf A=6000\left(1+\frac{0.045}{1}\right)^{(1 \times 15)}\)

\(\implies \sf A=6000(1.045)^{15}\)

\(\implies \sf A=11611.69466...\)

Therefore, the value of the investment after 15 years will be $11,611.69 to the nearest cent.

Point L is the midpoint

The midpoint is halfway between the two points. In this case, Point F and Point B are 10 units away from each other. The midpoint is the distance between the points (10) divided by 2.

Experimental probability of the arrow of spinner (rotated 80 times) stopping over Section 1 is one fourth or 0.25.

Experimental Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event during the experiment.

Given information-

Total number of sections in a spinner is 3.

Total number of times the trials done is 80.

The three section table given in the problem has the values as,

The experimental probability of the arrow stopping over Section 1 has to be find out.

As the experimental probability of an event is the ratio of number of times it took place to the total trails. Thus the experimental probability of the arrow stopping over Section 1 is,

\(P=\dfrac{20}{80}\\P=\dfrac{1}{4}\\P=0.25\)

Thus experimental probability of the arrow of spinner (rotated 80 times) stopping over Section 1 is one fourth or 0.25.

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Null space is defined as the set of vectors 'x' in Rn that are solutions to the matrix equation A*x = 0. False: The set of all vectors of the form 1 x y where x and y range over all real numbers is a subspace of R3. True: The set of all vectors of the form 0 x y where x and y range over all real numbers is not a subspace of R3.

1) False Null space can consist of zero vector only. A null space is defined as the set of vectors 'x' in R^n that are solutions to the matrix equation A*x = 0.

2) True The number of columns can never be less than the number of rows of the matrix in order for a null space to exist, hence a 4x3 matrix may have the null space of only the zero vector.

3) True The set of all vectors of the form 1 x y where x and y range over all real numbers, is a subspace of R^3. This set contains zero vector because for x=0 and y=0, we get the vector as [0,0,0]. Hence it is a subspace of R^3.

4) False The set of all vectors of the form 0 x y where x and y range over all real numbers, is not a subspace of R^3 as it doesn't contain zero vector. To have a subspace of R^3, it should contain a zero vector.

So, the correct options are:1) False2) True3) True4) False

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The probability of obtaining five tails in a row assuming the coin is​ fair is 1/32.

A person will have to do 5 coin tosses which means,

No. of total observations  = 25

Required outcome → 5 Heads { T , T , T , T , T }

This outcome  can occur only once so required outcome will be 1

Thus, required outcome  =1

Probability (5 Tails) = 1 / 2⁵ = 1 / 32

Hence , the probability of obtaining five tails in a row assuming the coin is​ fair is 1/32.

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