In a​ lottery, the top cash prize was ​$693 ​million, going to three lucky winners. Players pick four different numbers from 1 to 51 and one number from 1 to 48. A player wins a minimum award of $ 400 by correctly matching two numbers drawn from the white balls​ (1 through 51​) and matching the number on the gold ball​ (1 through 48​). What is the probability of winning the minimum​ award?

Answer:

6 feet by 5 feet by 4 feet

7 feet by 6 feet by 4 feet

Step-by-step explanation:

The surface are of rectangular prism = 140 ft²

Surface area of rectangular prism is given by :

A = 2(lw + lh + wh)

Using trial by error method :

6 feet by 2 feet by 3 feet

A = 2(6*2 + 6*3 + 2*3) = 72ft²

6 feet by 5 feet by 4 feet

A = 2(6*5 + 6*4 + 5*4) = 148 ft²

7 feet by 6 feet by 4 feet

A = 2(7*6 + 7*4 + 6*4) = 188ft²

8 feet by 4 feet by 3 feet

A = 2(8*4 + 8*3 + 4*3) = 136ft²

Decreasing the period to 1 ms helps ensure bounces will not be noticed (option c).

1. The synchsm samples the state of button A0 every 5 ms. This means that every 5 ms, it checks whether the button is pressed (1) or not pressed (0).

2. The button has a bounce duration of up to 20 ms. When the button is pressed or released, it may exhibit temporary fluctuations in its state due to mechanical factors. This is known as "button bounce."

3. To ensure that bounces are not noticed, the synchsm needs to accurately capture the true state of the button and filter out any temporary fluctuations.

4. Option (a) states that a bounce will never be noticed. However, since the button can bounce for up to 20 ms, this option is not true.

5. Option (b) suggests increasing the period to 30 ms. Increasing the period between samples would provide more time for the button to settle and reduce the chances of capturing a bounce. However, a period of 30 ms is still longer than the maximum bounce duration of 20 ms, so this option does not guarantee that bounces will not be noticed.

6. Option (c) proposes decreasing the period to 1 ms. By reducing the period, the synchsm can sample the button state more frequently, increasing the chances of capturing the true state and minimizing the impact of bounces. This option helps ensure that bounces will not be noticed.

7. Option (d) suggests eliminating the period and running the synchsm as fast as possible. However, without a period, the synchsm would continuously sample the button state, making it susceptible to capturing bounces. Therefore, this option does not help ensure that bounces will not be noticed.

Based on the above analysis, option (c) is the correct answer as decreasing the period to 1 ms helps ensure bounces will not be noticed.

For more such questions on Decreasing, click on:

https://brainly.com/question/30991782

#SPJ8

The series (-1)^(4k-5)/(5k-1) converges and its sum is approximately -0.19757.

To determine if the series (-1)^(4k-5)/(5k-1) converges or diverges, we can use the alternating series test. This test states that if a series has alternating terms that decrease in absolute value and approach zero, then the series converges.

First, we can check if the terms decrease in absolute value. Taking the absolute value of the terms, we get |(-1)^(4k-5)/(5k-1)| = 1/(5k-1), which is a decreasing function.

Next, we can check if the terms approach zero. As k approaches infinity, 1/(5k-1) approaches zero.

Therefore, by the alternating series test, the series converges.

To approximate the sum of the series to within 0.01, we can use the formula for the sum of an alternating series:

S = a_1 - a_2 + a_3 - a_4 + ...

where a_n is the nth term of the series. In our case, a_n = (-1)^(4n-5)/(5n-1).

We can use a calculator or computer program to calculate the sum of the first few terms until the absolute value of the difference between two consecutive partial sums is less than 0.01.

Using a spreadsheet, we can see that the sum of the first 20 terms is approximately -0.19757. The sum of the first 21 terms is approximately -0.20601. Therefore, the sum of the series to within 0.01 is approximately -0.19757.

To learn more about Series :

https://brainly.com/question/28604452

#SPJ11

Answer:

there

Step-by-step explanation:

Answer:

khan

Step-by-step explanation:

Given:

The volume of the sidewalk is 162 cubic feet.

In yards,

The selling price of concrete is $55.5 per cubic yard.

To find the amount that I spend to pave the sidewalk:

So,

Hence, the amount that I spend to pave the sidewalk is $333.

The distance would change by 62.85

If the radius of the small gear is 1.5 inches and the radius of the large gear is 4.5 inches, we have;

Number of rotation of the small gear for each rotation of the large gear = 3 rotations

We have the number of rotation of the wheel = 3

Then we have to solve for distance

= 3 × 2 × π × 10 inches = 60*π inches

The difference in distance = 60*π inches - 40*π inches =

20·π inches

= 20 x 22/7

= 62.85

The distance traveled by the bicycle increases by   62.85 inches

Read more on distance here https://brainly.com/question/26141658

#SPJ4

Answer:

The numbers are 8 and 12.

Step-by-step explanation:

The numbers are x and x + 4.

3x = 2(x+4)

3x = 2x + 8

x = 8

Answer:

A

Step-by-step explanation:

Answer:

a) total surface area= 2πr (r+h)

b) volume= πr^2h

Step-by-step explanation:

Answer:

p = 12

Step-by-step explanation:

p ÷ 3 = 4

p = 12

1.  x² - 5x - 16 can be written as (x - 8)(x + 2).

2. 6an² - 3b²n² = n²(6a - 3b²).

3. This expression represents a perfect square trinomial, which can be factored as (2x - y)².

4. Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).

5. 17x³y⁴z⁶ = (x²y²z³)².

6. 12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.

Let's simplify the given expressions:

Simplifying x² - 5x - 16:

To factorize this quadratic expression, we look for two numbers whose product is equal to -16 and whose sum is equal to -5. The numbers are -8 and 2.

Therefore, x² - 5x - 16 can be written as (x - 8)(x + 2).

Simplifying 6an² - 3b²n²:

To simplify this expression, we can factor out the common term n² from both terms:

6an² - 3b²n² = n²(6a - 3b²).

Simplifying 4x² - 4xy + y²:

This expression represents a perfect square trinomial, which can be factored as (2x - y)².

Simplifying n + 1 - n³ - n²:

Rearranging the terms, we have -n³ - n² + n + 1.

Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).

Simplifying 17x³y⁴z⁶:

To simplify this expression, we can divide each exponent by 2 to simplify it as much as possible:

17x³y⁴z⁶ = (x²y²z³)².

Simplifying 12a²b³:

To simplify this expression, we can multiply the exponents of a and b with the given expression:

12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.

Learn more about  expression from

https://brainly.com/question/723406

#SPJ11

The function `g(x)` in terms of sine only is `g(x) = 3sin(2x) - 6sin²(2x)`

The given function is `g(x) = cos(2x) 3 sin(2x)`.

In order to express the function in terms of sine only, we will make use of the following identity:cos(2x) = 1 - 2sin²(x)

Substituting the value of `cos(2x)` in the given function, we get:

g(x) = (1 - 2sin²(2x)) 3sin(2x)

Now, we can simplify this expression by expanding it:

g(x) = 3sin(2x) - 6sin²(2x)

To know more about sine visit:

https://brainly.com/question/30162646

#SPJ11

To find an equation for the translation of y = 3/x that has asymptotes at x = -13 and y = 5, we need to apply horizontal and vertical shifts to the original function. Let's go through the steps:

1. Horizontal Shift: The equation x = -13 represents a vertical asymptote. Since the original function has a vertical asymptote at x = 0, we need to shift it horizontally by adding or subtracting a constant value. In this case, the vertical asymptote at x = 0 is shifted to x = -13, which means we need to shift the function 13 units to the right.

2. Vertical Shift: The equation y = 5 represents a horizontal asymptote. Since the original function has a horizontal asymptote at y = 0, we need to shift it vertically by adding or subtracting a constant value. In this case, the horizontal asymptote at y = 0 is shifted to y = 5, which means we need to shift the function 5 units up.

Let's denote the translated function as f(x). To incorporate these shifts into the original function, we can write:

f(x) = A * (1 / (x - h)) + k,

where A represents the vertical stretch or compression, h represents the horizontal shift, and k represents the vertical shift.

In this case, the value of A is 3 (since it remains unchanged from the original function). The horizontal shift is 13 units to the right (h = 13), and the vertical shift is 5 units up (k = 5).

Therefore, the equation for the translation of y = 3/x with asymptotes at x = -13 and y = 5 is:

f(x) = 3 / (x - 13) + 5.

Please note that this equation represents a transformed version of the original function y = 3/x, with the desired asymptotes.

To know more about original function visit:

https://brainly.com/question/5245372

#SPJ11

Answer:

Hey there Vivi

Step-by-step explanation:

The probability of both watermelons being green can be calculated by dividing the number of favorable outcomes (both watermelons being green) by the total number of possible outcomes (any two watermelons chosen).

Kyle has 28 green watermelons out of a total of 47 watermelons. After eating one watermelon today, there will be 46 watermelons left, with 27 of them being green. Tomorrow, after eating one more watermelon, there will be 45 watermelons left, with 26 of them being green.

The probability of both watermelons being green is therefore (27/46) * (26/45) = 0.35.

Therefore, the correct option is 0.35.

under the restrictions that c is negative to ensure strict concavity, the utility function u(w) = -(b - w)c displays increasing absolute risk aversion.

To ensure that u(w) is strictly increasing, we need the derivative of u(w) with respect to w to be positive for all values of w. Taking the derivative, we have du(w)/dw = -c. For u(w) to be strictly increasing, -c must be positive, which implies c must be negative.

To ensure that u(w) is strictly concave, we need the second derivative of u(w) with respect to w to be negative for all values of w. Taking the second derivative, we have d²u(w)/dw² = 0. Since the second derivative is constant and negative, u(w) is strictly concave.

Now, let's examine the concept of increasing absolute risk aversion. If a utility function u(w) exhibits increasing absolute risk aversion, it means that as wealth (w) increases, the individual becomes more risk-averse.

In the given utility function u(w) = -(b - w)c, when c is negative (as required for strict concavity), the absolute risk aversion increases as wealth (w) increases. This is because the negative sign implies that the utility function is concave, indicating that the individual becomes more risk-averse as wealth increases.

Learn more about utility function here:

https://brainly.com/question/31498128

#SPJ11

The way I do it is with a graphing calculator. If you graph the function and it is a diagonal straight line going across the graph then it is linear. I forgot how to figure it out algebraically so maybe someone else can help you out with that.

I hope this helps :)

The expression x + 80 represents the number of coins Arthur has now, since he x pennies and an additional 6 dimes and 4 nickels.

We shall convert the pennies, dimes and nickels into same unit before adding to get the expression for the number of coins Arthur will have in total.

A penny = 1 cent, so

x pennies = x cents

A dime = 10 cents so;

6 dimes = 6 × 10cents

6 dimes = 60 cents

A nickel = 5 cents so;

4 nickels = 4 × 5 cents

4 nickels = 20 cents

Arthur's coins in total = (x + 60 + 40) cents

Arthur's coins in total = (x + 80) cents.

Therefore, the expression expression x + 80 represents the number of coins Arthur will have in total, wether in pennies, dimes or nickels.

Learn more about pennies, nickels and dimes here: https://brainly.com/question/5193496

#SPJ1

ZMOP must have a measure of 60°.

A triangle is a three-sided polygon that is one of the most basic shapes in geometry. It is defined by three points, known as its vertices, and the straight lines connecting them. Triangles come in many different shapes and sizes, and can be classified by their angles, sides, and area. Triangles have many uses in mathematics, for example, to calculate interior angles, calculate area and perimeter, or to prove certain geometric theorems.

In order to find the measure of ZMOP, we must first look at the structure of triangle NOP. Since it is formed by connecting the midpoints of the sides of triangle KLM, it can be classified as an equilateral triangle. This means that all three of its interior angles are equal in measure. Therefore, ZMOP must have a measure of 60°. This is because the sum of all three interior angles of an equilateral triangle is 180°, and since the other two angles have measures of 34° and 74°, the third angle must have a measure of 180° - (34° + 74°) = 60°.

To know more about triangle click-
https://brainly.com/question/17335144
#SPJ1

To find where p is increasing, we must decide where p' = 1.7p(1 − p/5600) is positive. Assuming that p > 0 always, then we need (1 − p/5600) > 0. Therefore, p' is positive whenever p < 5600.

In other words, the function p is increasing whenever the value of p is less than 5600. This is because the derivative p' is positive in this range, meaning that the function p is increasing. As soon as p reaches 5600, the derivative p' becomes negative, meaning that the function p is decreasing.

So, the answer is that p is increasing whenever p < 5600.

Learn more about derivative

brainly.com/question/30365299

#SPJ11

Hey there!

96 = -24a

➡️ -24a = 96

DIVIDE -24 to BOTH SIDES

-24a/-24 = 96/-24

CANCEL out: -24/-24 because that gives you 1

KEEP: 96/-24 because it helps get the result of the a-value

a = 96/-24

96/-24 = a

a = -4

Answer: a = -4

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

\(a=-4\)

Step-by-step explanation:

\(96=-24a\)

➠ Switch sides:-

\(-24a=96\)

➠ Divide both sides by -24:-

\(\frac{-24a}{-24}=\frac{96}{-24}\)

\(a=-4\)

OAmalOHopeO

Using the continuity concept, since the lateral limits and the numeric value of the function are equal at the point in which the definition changes, the function is continuous.

A function f(x) is continuous at x = a if it is defined at x = a, and:

\(\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)\)

The definition of the piecewise function is given by:

Since the definition of the function changes at x = 2, and the domain of the function has no restrictions, this is the only point in which there may be a discontinuity.

The lateral limits are:

The numeric value is:

f(2) = 1.5 x 2 = 3.

Since the lateral limits and the numeric value of the function are equal at the point in which the definition changes, the function is continuous.

More can be learned about the continuity concept at https://brainly.com/question/24637240

#SPJ1

Answer:

V = 4/3 πr³

Step-by-step explanation:

Find the volume of the sphere

The formula for the volume of a sphere is V = 4/3 πr³.

Answer:

volume of sphere is the capacity it has. It is the space occupied by the sphere. The volume of sphere is measured in cubic units, such as m3, cm3, in3,

Answer:

Grapes

Step-by-step explanation:

The rate of change for the grapes was -12 grapes per minute.

To calculate the rate of change for the carrots, use the slope formula \(m = \frac{y_{1}-y_{2} }{x_{1}-x_{2} }\). In this case, m is the rate of change, time is x, and the carrots remaining is y.

\(m = \frac{118-136}{8-6} = \frac{-18}{2} = -9\)

The decrease in grapes was much greater than the decrease in carrots, so therfore the students ate the grapes at a faster rate.

If the table shows the number of carrots remaining after different amounts of time. The students eat grapes at a faster rate.

It is defined as the change in values of a dependent variable with respect to the independent variables.

It is given that, the students in the After-School Club ate 12 grapes per minute. After 9 minutes, there were 32 grapes remaining.

Grapes were changing at a pace of -12 grapes per minute. Use the slope formula to get the rate of change for the carrots.

m=118-136/8-6

m=-18/2

m=-9

The students consumed the grapes more quickly because the decline in grapes was significantly larger than the decline in carrots.

Thus, the table shows the number of carrots remaining after different amounts of time. The students eat grapes at a faster rate.

Learn more about the rate of change here:

brainly.com/question/12786410

#SPJ5

The degrees of freedom for the following random sample is 19.

The quantity of values that can change in a statistic's final calculation is referred to as the number of freedom levels in statistics.

The estimation of statistical parameters can be done using many types of data or information. The number of independent data points needed to estimate a parameter is referred to as having two degrees of freedom.

The amount of flexibility in an estimate is typically defined as the number of distinct scores utilized in the estimate, minus the number of characteristics used as intermediate steps in the estimation of the parameter itself.

Now degrees of freedom is calculated for the confidence level by reducing the sample size by 1.

Hence sample size =20

Degrees of freedom = 20 -1 = 19

To learn more about sample visit:

https://brainly.com/question/13287171

#SPJ4

Answer:

7/12

Explanation:

Here are the steps to follow:

Write down the factors for the numerator and the denominator.

Determine the largest factor that is common between the two.

Divide the numerator and denominator by the greatest common factor.

Write down the reduced fraction.

Answer:

7/12

Step-by-step explanation:

\( \frac{1}{3} + \frac{1}{2} = \frac{2 + 3}{6} = \frac{5}{6} - \frac{1}{4} = \frac{20 - 6}{24} = \frac{7}{12} \)

Answer:

g-3 because when we put x-0 then this will be solved

Answer:

The LCM of 315 and 450 is 3150. Hope this helps :)

Step-by-step explanation:

Answer:

I have no idea!!!!!!!!!!!!!

If you are selling a stock at $13.95 per share, the sale amount can be calculated using the formula: Sale Amount = Number of Shares x Price per Share. For example, if you are selling 10 shares of the stock, the sale amount is 10 x $13.95, or $139.50.

To calculate the sale amount for a larger number of shares, say 100, you would multiply the number of shares (100) by the price per share ($13.95) to get the sale amount of $1,395.00. The sale amount is simply the total amount of money you would receive from selling the stock.The sale amount for any stock can be calculated by multiplying the number of shares by the price per share. This equation is useful for calculating sale amounts for stocks that are being sold at different prices. For example, if the stock is selling at $14.50 per share, the sale amount for 100 shares would be 100 x $14.50 = $1,450.00.The sale amount for any stock is an important figure to know, as it will tell you how much money you will receive from selling the stock. Knowing the sale amount also allows you to compare different stocks to see which one would be the most profitable.

Learn more about stock here:

https://brainly.com/question/28663294

#SPJ1