What is the surface area of the solid?

The probability of drawing at least 7 hearts is 0.0567.

A card is randomly drawn from a deck of cards.

Total number of cards in a deck = 52

The number of times the process is repeated, n = 15

Number of hearts in a deck = 13

The probability of getting a spade is:

p = 13/52 = 1/4

The formula for probability is given as:

P( E ) = favorable cases / total number of cases

The probability of getting no heart is:

q = 1 - p = 1 - 1/4 = 3/4

Using the binomial theorem of probability,

P( X = x ) = \(_{n}C_{r} \times p^{r} \times q^{n-r}\)

So, the probability of drawing at least 7 hearts will be:

P = P( 7 ) + P( 8 ) + .....P( 15 )

Now,

P( 7 ) = 15!/( 15 - 7 )! × (0.25)⁷ × (0.75)⁶ =  0.03932

P(8) = 15!/(15 - 8)! × (0.25)⁸ × (0.75)⁷ = 0.0131

P(9) = 15!/(15 - 9)! × (0.25)⁹ × (0.75)⁶ = 0.003398

P(10) = 15!/(15 - 10)! × (0.25)¹⁰ × (0.75)⁵ = 0.00068

P(11) = 15!/(15 - 11)! × (0.25)¹¹ × (0.75)⁴ = 0.000103

P(12) = 15!/(15 - 12)! × (0.25)¹² × (0.75)³ = 0.000102

P(13) = 15!/(15 - 13)! × (0.25)¹³ × (0.75)² = 8.80099833e-7

P(14) = 15!/(15 - 14)! × (0.25)¹⁴ × (0.75)¹ = 4.19095159e-8

P(15) = 15!/(15 - 15)! × (0.25)¹⁵ × (0.75)⁰ = 9.3132257e-10

So, the probability is:

P = P( 7 ) + P( 8 ) +......P( 15 )

P = 9.3132257e-10 + 4.19095159e-8 + 8.80099833e-7 + 0.000102 + 0.000103 + 0.00068 + 0.003398 +  0.0131 + 0.03932

P = 0.0567

Therefore, the probability of drawing at least 7 hearts is 0.0567

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The coordinate functions of the line parametrized by r(t) = 6t - 1, 9t^2 are x(t) = 2t - (1/3) and y(t) = -10t^2/3 + (10t/3) - (5/9).

To find the coordinate functions of the line parametrized by r(t) = 6t - 1, 9t^2, we need to use the vector form of the line and substitute in the given values of t.

First, let's recall the vector form of the line which is r(t) = a + tb where r(t) is the position vector of a point on the line, a is a point on the line, t is a scalar parameter, and b is the direction vector of the line. In this case, we are given the direction vector as (3,-5) and a point on the line as (2,0). So, the vector form of the line is r(t) = (2,0) + t(3,-5).

Now, we need to find the coordinate functions by replacing t with the given values in the parametrization r(t) = 6t - 1, 9t^2.

For the x-coordinate function, we have:

x(t) = 2 + 3t
x(t) = 2 + 3((6t - 1)/9)
x(t) = 2 + 2t - (1/3)

So, the x-coordinate function is x(t) = 2t - (1/3).

For the y-coordinate function, we have:

y(t) = 0 - 5t
y(t) = 0 - 5((6t - 1)/9)^2
y(t) = 0 - 10t^2/3 + (10t/3) - (5/9)

So, the y-coordinate function is y(t) = -10t^2/3 + (10t/3) - (5/9).

Therefore, the coordinate functions of the line parametrized by r(t) = 6t - 1, 9t^2 are x(t) = 2t - (1/3) and y(t) = -10t^2/3 + (10t/3) - (5/9).

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Answer:

The mean is the average.

Step-by-step explanation:

You add all the numbers up then divide how many numbers in total there are.

Answer:

To calculate the mean, you have to add up all of the numbers. Then you divide the sum by the amount of numbers you added together.

Step-by-step explanation:

Example: 1,2,3,4,5

1+2+3+4+5 = 15

15/5 = 3        (I added 5 numbers together, so I divided by 5)

The train has 12 carriages

Step-by-step explanation:

The total no. of seats =876

No. of seats per carriage =73

It is given that each carriage has equal seats

So,

Let the total no. of carriages be x

According to the given information,

\(73 \times x = 876\)

\(x = 876 \div 73\)

x = 12

Hence the number of carriages is 12

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Answer:

18.18%

Step-by-step explanation:

66 - 54 = $12

% change - 12/66 * 100

simplify - 12/66 --> 2/11

2/11 * 100

200/11

18.18%

Answer:

{-2,-1,0,1,2}

Step-by-step explanation:

When we are talking of the range, we are referring to the possible y-values the relation can take

Hence, a set of y-values will represent the range of the relation

we have this as:

{2, 1 , 0, -1 , -2}

Arranging in order, we have ;

{-2,-1,0,1,2}

Rounding up to the nearest whole number, we need a sample size of 25 to achieve a 95% confidence level with a maximum error of 2 degrees Celsius in estimating the mean temperature.

To calculate the sample size needed to achieve a 95% confidence level with a maximum error of 2 degrees Celsius, we can use the formula:
n = (z * σ / E) ^ 2
Where:
- n is the sample size
- z is the z-score associated with the confidence level (in this case, 1.96 for 95%)
- σ is the standard deviation of the temperature data (if unknown, we can use a conservative estimate of 5 degrees Celsius).
- E is the maximum error we want to allow (in this case, 2 degrees Celsius)
Plugging in the values, we get:
n = (1.96 * 5 / 2) ^ 2
n = 24.01
Rounding up to the nearest whole number, we need a sample size of 25 to achieve a 95% confidence level with a maximum error of 2 degrees Celsius in estimating the mean temperature.

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There are 46 different ways in which a set of 10 coins can have a total value of 59 cents.

To find the number of different ways, we can use a systematic approach. Let's consider the five types of coins: pennies (1 cent), nickels (5 cents), dimes (10 cents), quarters (25 cents), and half-dollars (50 cents).

Since we need a total value of 59 cents, we can start by using as many half-dollars as possible. The maximum number of half-dollars that can be used is one since two half-dollars would already exceed the required total.

Next, we can iterate through the remaining values and combinations of the remaining coins (quarters, dimes, nickels, and pennies) to find all possible ways to reach 59 cents. We can use nested loops to generate all the combinations. By trying different combinations, we find that there are 46 different ways to achieve a total value of 59 cents using 10 coins.

There are 46 different ways in which a set of 10 coins can have a total value of 59 cents. This calculation takes into account all possible combinations of pennies, nickels, dimes, quarters, and half-dollars.

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Answer:

It is -7.

Step-by-step explanation:

Since x = -1, we can replace the x with -1 to get: -3 - 4 which is -7.

Answer: The answer is -7 for #11

Step-by-step explanation:f(x) = 3x - 4

f(x) = 3(-1) - 4 plug in -1 in x

-3-4 subtract both -3 and 4

-7 the answer

Answer:

Step-by-step explanation:

the ordinary form of 2.8 * 10^5 is

= 280000

The value of ∠2KJM for the rhombus is ∠JKM = 23 + (5a/2).

A parallelogram is a particular instance of a rhombus. The opposing sides and angles in a rhombus are parallel and equal. A rhombus also has equal-length sides on each side, and its diagonals meet at right angles to form its shape. The rhombus is sometimes referred to as a diamond or rhombus. Rhombi or rhombuses are the plural forms of rhombus.

Let us suppose the measure of angle = x.

For rhombus all the four angles are congruent, thus,

∠MLN = (9a + 11)°

∠KLM = (-4a + 66)°

∠JLN = x

∠KLJ = x

The sum of the angles of a quadrilateral is 360 degrees, so:

∠JKL + ∠KLM + ∠MLN + ∠NJL = 360

Since JKL and NJL are vertical angles, they are congruent:

∠JKL = ∠NJL = x

Substituting in the given angles, we get:

x + (-4a + 66) + (9a + 11) + x = 360

2x + 5a + 77 = 360

2x = 360 - 5a - 77

2x = 283 - 5a

x = (283 - 5a)/2

Now, ∠JKM = 180 - ∠JKL

∠JKM = 180 - x

∠JKM = 180 - (283 - 5a)/2

Simplifying, we get:

∠JKM = 23 + (5a/2)

Hence, the value of ∠2KJM for the rhombus is ∠JKM = 23 + (5a/2).

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Answer:

$42.00

Step-by-step explanation:

27+15 = 42

(also, Luke Hemmings???)

ok, I didn't know it was percent... 4.05. 15% of 27

The total amount that Luke will pay is $31.05.

From the information given, it was stated that Luke went to a restaurant and his bill was $27.00 and that he wants to leave a 15% tip.

Therefore, the amount that he'll pay to the restaurant will be:

= $27.00 + (15% × $27)

= $27.00 + (0.15 × $27)

= $27.00 + $4.05

= $31.05

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Answer:

3/20

Step-by-step explanation:

Given:

Probability that it is Monday and that a student is absent is 3/100

Probability that a randomly selected day of the school week is monday is 1/5

To Find:

What is the probability that a student is absent given that today is Monday.

Solve:

It may be different if it were on a Wednesday. Because we expect fewer absentees on Wednesday than on Monday/ Friday. In these cases the conditional probability, P(absent/weekday) would differ depending on the day of the week.

3/100 ÷ 1/5 = 3/20

The probability that a student is absent on a Monday is 3/20

[RevyBreeze]

Answer: B) 4

Step-by-step explanation:

Using the formula

Standard deviation = √( (Σ ( x - π)²)/n)

To get the standard deviation, first we workout the Mean which is the simple average of the data set

n = 4

(13 + 17 + 9 + 21) / 4 = 60/4 = 15

Mean(x) = 15

Then (x-π)²

13 - 15 = (-2)² = 4

17 - 15 = (2)² = 4

9 - 15 = (-6)² = 36

21 - 15 = (6)² = 36

Σ ( x - π)² = (4 + 4 + 36 + 36) = 80

Standard deviation = √( (Σ ( x - π)²)/n

= √ (80/4)

=√20

= 4.47

= 4

Answer:1 im pretty sure

Step-by-step explanation:

The relative frequency for the 55 - 60 class is equal to 0.022.

In a frequency distribution table, a class width simply refers to the difference between the maximum) and minimum boundaries of any class in a data set.

This ultimately implies that, all classes must all have the same width in a frequency distribution table.

First of all, we would determine the total frequency as follows:

Total frequency = 8 + 10 + 6 + 7 + 15

Total frequency = 46.

Mathematically, the relative frequency of a class width can be calculated by using this formula:

Relative frequency = class frequency/total frequency

Relative frequency = 1/46

Relative frequency = 0.022

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

By using the concept of Compound interest, Number of payment periods in a 6-year, 8% bond with an effective interest rate of 6%, and paid semiannually = 12

What is Compound interest?

The interest earned on savings that is calculated using both the initial principal and the interest accrued over time is known as compound interest. It is thought that Italy in the 17th century is where the concept of "interest on interest" or compound interest first appeared. It will accelerate the growth of a sum more quickly than simple interest, which is only calculated on the principal sum. Money multiplies more quickly thanks to compounding, and the more compounding periods there are, the higher the compound interest will be.

This problem can be solved by using the concept of compound interest

Number of  payment periods are in a 6-year, 8% bond with an effective interest rate of 6%, and paid semiannually = \(6 \times 2 = 12\)

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Answer: "When we plot a linear function, the graph is always a line. The rate of change, which is constant, determines the slant, or slope of the line. The point at which the input value is zero is the vertical intercept, or y-intercept, of the line."

Step-by-step explanation: Hope it helped! :)

The standard deviation of x when the variable is normally distributed is 19.53125 .

Let X be the random variable.

Here, random variable X is normally distributed with mean 1000.

As 40% area is left of the mean and remaining 40% area is right side of the mean, we can say that the probability that the value of the random variable is lied between 925 and 1000 is 0.4 .

The area under normal curve is evenly distributed with respect to the mean (0).

So, 80% of area around the mean is evenly distributed with mean that mean 40% area is left of the mean and 40% area is right of the mean.

By using one of the above, the value of the standard deviation can be obtained.

As the probability that the value of the random variable X is lies between (1000 , 1025 ) is 0.8 .

From the z-table of P(0<Z<z), it can be fount that in the row 1.2 and column 0.08, value is 0.4.

So, by looking in z-table, it is found that the value of P(0<Z<1.28) is 0.4.

By comparing equation (i) and (ii), we have,

Hence, the value of the standard deviation is 19.53125 .

Given that the 80 % confidence interval around X is given by (975 , 1025). That means there are 80% chances that value of the random variable X lies between (975 , 1025).

So, the probability that the value of the random variable X is lies between (975 , 1025) is 0.8.

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The calculated summation value with the message "Summation: " preceding it. The program assumes that the user will provide valid numerical inputs (integers) when prompted.

Here's a Python program that calculates the sum using a loop based on the user's input values for `i` and `k`. The program handles cases where `i` is larger than `k` and continuously asks for proper values until valid inputs are provided.

```python

while True:

   i = int(input("Enter value for i: "))

   k = int(input("Enter value for k: "))

   if i <= k:

       break

   else:

       print("Error: i cannot be greater than k.")

summation = 0

for x in range(i, k+1):

   summation += 2 * x

print("Summation:", summation)

```

In this program, we use a `while` loop to repeatedly prompt the user for values of `i` and `k`. We convert the inputs to integers using `int()` for numerical comparison. If the condition `i <= k` is satisfied, we break out of the loop; otherwise, an error message is displayed, and the loop continues.

Once we have valid values for `i` and `k`, we initialize the `summation` variable to 0 and use a `for` loop with `range(i, k+1)` to iterate through the values of `x` from `i` to `k` (inclusive). We accumulate the sum by adding `2 * x` to `summation` in each iteration.

Finally, we print the calculated summation value with the message "Summation: " preceding it.

Note: The program assumes that the user will provide valid numerical inputs (integers) when prompted.

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Answer:

in english

Step-by-step explanation:

The number of 250 gram boxes needed for the production would be 1800 boxes and the number 300 gram boxes needed for the production would be 2160 boxes.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have 3600 boxes with a capacity of 1/2 kg are needed to package the daily production.

n(500 gram) boxes needed for production = 3600

n(1 gram) boxes needed for production = 3600/500

n(1/4 kg or 250 gram) boxes needed for the production would be =

(3600/500) x 250 = 1800 boxes

n(300 gram) boxes needed for the production would be =

(3600/500) x 300 = 2160 boxes

Therefore, the number of 250 gram boxes needed for the production would be 1800 boxes and the number 300 gram boxes needed for the production would be 2160 boxes.

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[Refer to the question in english below -

In a chocolate factory, 3600 boxes with a capacity of 1/2 kg are needed to package their daily production. How many boxes with a capacity of 1/4 kg will they need to pack the production of a whole day? And if you want to pack the daily production in boxes with a capacity of 300g?]

The correct options that could be an example of a function with a domain (-∞0,00) and a range (-∞,4) are given below.Option A. V = -(0.25)x - 4 Option B. V = − (0.25)x+4

A function can be defined as a special relation where each input has exactly one output. The set of values that a function takes as input is known as the domain of the function. The set of all output values that are obtained by evaluating a function is known as the range of the function.

From the given options, only option A and option B are the functions that satisfy the condition.Both of the options are linear equations and graph of linear equation is always a straight line. By solving both of the given options, we will get the range as (-∞, 4) and domain as (-∞, 0).Hence, the correct options that could be an example of a function with a domain (-∞0,00) and a range (-∞,4) are option A and option B.

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Answer:

yes

Step-by-step explanation:

Answer:

i think it's true

Step-by-step explanation:

The conical surface is the correct answer as it allows for slopes ranging from 20:1 to 50:1. The FAR Part 77 imaginary surface that has slopes that may range from 20:1 to 50:1 is the conical surface.

The conical surface is a three-dimensional surface defined by a combination of horizontal and inclined planes. It extends upward and outward from the end of the primary surface and has varying slope requirements. The slope of the conical surface represents the ratio of the change in elevation to the horizontal distance. A slope of 20:1 indicates that for every 20 units of horizontal distance, there is a 1-unit increase in elevation.

Similarly, a slope of 50:1 means that for every 50 units of horizontal distance, there is a 1-unit increase in elevation. Therefore, the conical surface is the correct answer as it allows for slopes ranging from 20:1 to 50:1.

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