Suppose that we roll a fair die until a 6 comes up.
a.what is the probability that we roll the die n times

Answer:

Step-by-step explanation:

$6,014.40

Final answer:

The function f(t) can be represented in terms of the unit step function as f(t) = -5u(t) - u(t-1) + 6u(t-7), with each term turning on at specific breakpoints.

Explanation:

To write the function f(t) in terms of the unit step function, you can think of f(t) as a piecewise function that changes values at various breakpoints. The unit step function, denoted as u(t), is defined to be 0 when t < 0 and 1 when t ≥ 0. For the given function f(t), we can write it using the unit step function as follows:

f(t) = -5u(t) -u(t-1) + 6u(t-7)

This representation uses the properties of the unit step function to 'turn on' different function values at specified points. Each term corresponds to a segment of the piecewise function, with the coefficients representing the value of f(t) within each segment.

The new balance after I bought groceries worth of 30.72 dollars is -43.3 dollars.

Sign distributions are of four types they are:- negative distributed to negative results in positive and positive distributed positive results to positive. Negative distributed to positive or vice versa results in negative.

According to the given question on Monday I had -12.58 dollars.

I bought some groceries worth -30.72 dollars which will also be deducted from my bank account.

∴ The final balance I have is ( -12.58 - 30.72) dollars which is,

= -43.3 dollars.

learn more about sign distributions here :

https://brainly.com/question/28608950

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The molar mass of NaCl is 58.44 g / mol. So we can calculate the mass by simply multiplying the number of moles and molar mass. That is:

mass = 1.40 moles * 58.44 g / mol

mass = 81.82 grams

Final answer:

To find the mass in grams of 1.40 moles of sodium chloride, multiply the number of moles by the molar mass of NaCl, which is 58.44 g/mol, resulting in 81.816 grams.

Explanation:

To calculate the mass of 1.40 moles of sodium chloride (NaCl), we will use the molar mass of NaCl as a conversion factor. The molar mass of NaCl is 58.44 grams per mole. Here's how you can do the conversion:

Find the molar mass of NaCl: 22.99 g/mol (Na) + 35.45 g/mol (Cl) = 58.44 g/mol (NaCl).

Multiply the number of moles of NaCl by the molar mass to get the mass in grams: 1.40 moles × 58.44 g/mol = 81.816 grams of NaCl.

So, 1.40 moles of sodium chloride weigh 81.816 grams.

Answer:- Total distance traveled by Suzanne in kilometers=13.2 kilometers.

Explanation:-

Distance traveled by Suzanne in the morning=[tex]3\frac{3}{4}\text{ miles}[/tex]

Distance traveled by Suzanne in the evening=[tex]4\frac{1}{2}\text{ miles}[/tex]

Total distance traveled by Suzanne=[tex][3\frac{3}{4}+4\frac{1}{2}\text{ miles}[/tex]

[tex]=\frac{15}{4}+\frac{9}{2}\text{ miles}[/tex]

[tex]=\frac{15+18}{4}\text{ miles}[/tex]

[tex]=\frac{33}{4}\text{ miles}[/tex]

[tex]=8.25\text{ miles}[/tex]

Total distance traveled by Suzanne in kilometers=[tex]8.25\times1.6\text{ kilometers}=13.2\text{ kilometers}[/tex]

Total distance traveled by Suzanne in kilometers[tex]=13.2\text{ kilometers}[/tex]

Answer:

x = 4 is the answer.

Step-by-step explanation:

List of rides in a month of 30 students have been given in the question.

We have to find the value of x if fraction x/30 shows the ratio of the number of students who ride their bikes more than 10 miles each month to the number of students surveyed.

Therefore x/30 = 4/30

x = 4×30/30 = 4

So x = 4 is the answer.

I believe this problem has 3 questions:

a. Explain why the three conditions are satisfied for X to have the binomial distribution.

b. Identify n and p for the binomial distribution.

c. Find the probability that the family has two girls and two boys.

Answers:

a. First because there are only 2 possible outcomes for each birth: male or female. Hence a binomial distribution. 
Second, because the probability of giving out a girl is constant: 0.49 for each birth. 
Third, the probability of a giving out a girl does not depend on whether or not there is already a boy or a girl in the family. 

b. The n is the total number of children, so n = 4

While the p is the success of being a girls, so P = 0.49

c. We use the binomial probability equation:

P (X) = nCx * p^x * q^(n-x)

P(X=2) = 4!/(2!2!) * 0.49^2 * 0.51^2 = 0.3747

Final answer:

Inheritance of sex chromosomes in babies is determined by the father, leading to a 50:50 chance of a male or female child. The likelihood of a newborn being female is around 0.49.

Explanation:

Sex Inheritance: The sex of a baby is determined by the father, who has a 50 percent chance of passing on a Y chromosome resulting in a male child. If the baby inherits two X chromosomes, it will be female. This 50:50 chance applies to each baby. For a family with four children, let x = the number of girls, the probability of a child being female is approximately 0.49.

Answer:

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Step-by-step explanation:

There are two factors: ( x ) and  (1+y). So option (b) is correct.

To find the factors in the expression ( x(1+y)^z ), we break it down into its components.

1. ( x ) - This is a factor because it's multiplied by the rest of the expression.

2.  (1+y)  - This is also a factor because it's part of the expression being raised to the power of \( z \).

3. ( z ) - The exponent does not affect the number of factors, as it's simply the power to which the expression is raised.

So, there are two factors: ( x ) and  (1+y).

Detailed calculation:

( x ) is multiplied by the entire expression, so it's a factor.

(1+y) is a factor because it's part of the expression.

( z ) is an exponent and doesn't count as a separate factor.

Thus, the answer is (b) 2.

To determine the number of each cable produced, a system of equations is set up with variables representing the cable types and coefficients corresponding to the number of wires used per cable. The system consists of three equations based on the colors of wires and the totals used.

To solve this problem, we can set up a system of equations where the unknowns are the number of each type of cable produced. Let's represent the number of type A cables as x, type B cables as y, and type C cables as z. Considering the number of wires used for each type of cable and the total used, we form the following equations:

To find the number of each cable made, we need to solve this system of equations simultaneously. The coefficients represent the number of each color wire needed for each cable type, and the constants (120, 110, 100) represent the total number of wires used.

Final answer:

Using the principle of Inclusion-Exclusion, and taking the common members in two, three, and four groups into account, we find that there are 3439 unique members across the four groups.

Explanation:

To solve this problem, we need to use the principle of Inclusion-Exclusion. Let's denote the four groups as A, B, C, and D. According to the question, each group has 1000 members (n(A) = n(B) = n(C) = n(D) = 1000).

Any two groups have 100 members in common. That means, for instance, n(A ∩ B) = n(A ∩ C) = n(A ∩ D) = n(B ∩ C) = n(B ∩ D) = n(C ∩ D) = 100.

Any three groups have 10 members in common, which gives us n(A ∩ B ∩ C) = n(A ∩ B ∩ D) = n(A ∩ C ∩ D) = n(B ∩ C ∩ D) = 10.

There is 1 person in all four groups, so n(A ∩ B ∩ C ∩ D) = 1.

The total number of unique members in all groups, denoted as n(A ∩ B ∩ C ∩ D), is given by:

n(A ∩ B ∩ C ∩ D) = n(A) + n(B) + n(C) + n(D) - [sum of the number of common members between every two groups] + [sum of the number of common members between every three groups] - [number of members common to all four groups].

Substituting the values:

n(A ∩ B ∩ C ∩ D) = 4(1000) - [6(100)] + [4(10)] - 1 = 4000 - 600 + 40 - 1 = 3439.

Therefore, there are 3439 unique members across all groups.

First calculate all the deduction

FICA = $10 per hour x 0.0765 = $0.77 per hr

Fed tax = $10 per hr x 0.12 = $1.2 per hr

State tax = $10 per hr x 0.08 = $0.8 per hr

Remaining pay = 10 – 0.77 – 1.2 – 0.8 = $7.23 per hour

Time required = $640 / $7.23 per hr

Time required = 89 hrs

After calculating deductions from the gross wage of $10.00, the net income per hour is $7.235. To buy the new computer for $800, we divide the cost by the net wage, resulting in approximately 110.58 hours. Therefore, the student would need to work about 111 hours to afford it.

To calculate the number of hours needed to work to pay for the new computer, we must first determine the net income per hour after all the deductions. With a gross wage of $10.00 per hour, the deductions would be:

This totals $2.765 in deductions per hour. Subtracting this from the gross wage gives a net income per hour:

$10.00 - $2.765 = $7.235.

To afford the new computer costing $800, we divide the cost of the computer by the net income per hour to find the total number of hours needed:

$800.00 / $7.235 ≈ 110.58 hours.

Since we cannot work a fraction of an hour, we will need to round up to the nearest whole number, which suggests that the student would need to work approximately 111 hours to afford the new computer.

Answer:

Step-by-step explanation:

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