The probability of tossing three coins simultaneously and obtaining two heads and one tail is

Jenna hikes 2 miles in 1 hour, as she covers 1/2 mile in each 1/4 hour and there are four 1/4 hours in a full hour.

Jenna hikes 1/2 mile every 1/4 hour. To determine how far she hikes in 1 hour, we need to calculate the distance she can cover in four such intervals since 1 hour is composed of four 1/4 hours.

So, the calculation would be:
1/2 mile in 1/4 hour

1/2 mile x 4 (since there are 4 quarters in a full hour) = 2 miles

Therefore, Jenna hikes 2 miles in 1 hour.

To determine two numbers where their difference is 16, and their ratio is 5:7, we let the smaller number be 5x and the larger one be 7x, solve for x with the equation 7x - 5x = 16, and find that the numbers are 40 and 56.

To find two numbers with a difference of 16 and a ratio of 5:7, first let's denote the smaller number as 5x and the larger number as 7x. The difference between the two numbers is 16, so we can write the equation 7x - 5x = 16.

Solving for x gives us 2x = 16 or x = 8. Thus, the two numbers we are looking for are 5x = 5 × 8 = 40 and 7x = 7 × 8 = 56.

Check: The difference between 56 and 40 is indeed 16, and the ratio of 40 to 56 simplifies to 5:7, confirming our solution.

Yeah it's B:17.8 I agree with you

Answer:  The required number of cups of frozen mango is 1.125.

Step-by-step explanation:  Given that a smoothie recipe calls for [tex]2\dfrac{1}{4}[/tex] cups of frozen mango and the recipe serves two.

We are to find the number of cups of frozen mango that is needed to serve one.

We will be using the UNITARY method to solve the problem.

We have

The number of cups of frozen mango that needs to serve two is

[tex]2\dfrac{1}{4}=\dfrac{9}{4}=2.25.[/tex]

Therefore, the number of frozen mango that needs to serve one is given by

[tex]\dfrac{2.25}{2}=1.125.[/tex]

Thus, the required number of cups of frozen mango is 1.125.

Final answer:

Sturges' rule suggests using 9 classes or bins for 256 data points.

Explanation:

Sturges' rule is a method for determining the number of classes or bins required for a histogram. According to Sturges' rule, the formula to calculate the number of classes is:

K = 1 + log2(n)

Where K is the number of classes and n is the number of data points. In this case, since you have 256 data points, the number of classes suggested by Sturges' rule would be:

K = 1 + log2(256)

K = 1 + log2(28)

K = 1 + 8

K = 9

Therefore, Sturges' rule would suggest using 9 classes or bins for the histogram.

Answer:

Teachers 4 and Students 100, Teachers 5 and Students 125

Step-by-step explanation:

Going by the chart, by each teacher, the students are increasing by 25. The only ones to follow this pattern is 4:100 and 5:25

To calculate mean and standard deviation for a binomial distribution, use the formulas μ = np and σ = √npq. Ensure both np and nq are greater than five to use the normal approximation.

To find the mean (μ) and standard deviation (σ) for a binomial distribution, you use the formulas μ = np and σ = √npq respectively. Here, 'n' represents the number of trials, 'p' is the probability of success on a single trial, and 'q' is the probability of failure on a single trial, which is calculated as q=1-p.

If you want to determine whether you can use the normal approximation to the binomial, it is essential to ensure that both np and nq are greater than five. This is because the normal approximation is most accurate when the binomial distribution is symmetrical, which typically occurs when both np and nq exceed five.

The volume and the surface area of the rectangular prism will be 66mm and 166mm² respectively.

Length = 11m

Width = 1mm

Height = 6mm

The volume of the rectangular prism will be:

= Length × Width × Height

= 11mm × 1mm × 6mm

= 66mm

The surface area of the rectangular prism will be:

= 2(wl + hl + hw)

= 2(11 + 66 + 6)

= 2(83)

= 166

Therefore, the surface area of the rectangular prism will be 166mm²

In conclusion, the volume and the surface area of the rectangular prism will be 66mm and 166mm² respectively.

Read related link on:

https://brainly.com/question/6842793

The expression that represents the situation is:

                    $ 600+12x

cost of lot is: $ x

This means that 12 times the lot on which it was built is: $ 12x

Also, it is given that:

A house costs $600 more than 12 times the lot on which it was built.

This means that the total cost of the house is:

600 plus the total cost of the lot on which it was built.

i.e.   The expression that represents the total cost of the house is:

                      $ 600+12x

In 2156 ways the selection be made so that at least one of each color is drawn?

The question is asking for the number of ways to select balls from a bowl containing 8 red balls and 9 blue balls if 4 balls are drawn and at least one of each color is drawn.

To solve this, we must consider the different combinations of red and blue balls that meet the requirement.

Calculate the total possible outcomes: 17C4 = 2380

Calculate the outcomes where all balls of one color are drawn: 9C4 + 8C4 = 224

Subtract the outcomes where only one color is drawn from the total: 2380 - 224 = 2156 ways

Answer:

Step-by-step explanation: vertical angel

 1.1      Factoring:  x3-81 

Theory : A difference of two perfect cubes,  a3 - b3 can be factored into
              (a-b) • (a2 +ab +b2)

Proof :  (a-b)•(a2+ab+b2) =
            a3+a2b+ab2-ba2-b2a-b3 =
            a3+(a2b-ba2)+(ab2-b2a)-b3 =
            a3+0+0+b3 =
            a3+b3

Check :  81  is not a cube !! 
Ruling : Binomial can not be factored as the difference of two perfect cubes

 1.2    Find roots (zeroes) of :       F(x) = x3-81
Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q  then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  1  and the Trailing Constant is  -81. 

 The factor(s) are: 

of the Leading Coefficient :  1
 of the Trailing Constant :  1 ,3 ,9 ,27 ,81 

 Let us test ....

Polynomial Roots Calculator found no rational roots

 2.1      Solve  :    x3-81 = 0 

 Add  81  to both sides of the equation : 
                      x3 = 81 
When two things are equal, their cube roots are equal. Taking the cube root of the two sides of the equation we get:  
                      x  =  ∛ 81  

 Can  ∛ 81 be simplified ?

Yes!   The prime factorization of  81   is
   3•3•3•3  
To be able to remove something from under the radical, there have to be  3  instances of it (because we are taking a cube i.e. cube root).

∛ 81   =  ∛ 3•3•3•3   =
                3 • ∛ 3 

The equation has one real solution
This solution is  x = 3 • ∛3 = 4.3267 

Answer:

The initial value is  

✔ 1/3

The simplified base is  

✔ 27

The domain is  

✔ all real numbers

The range is  

✔ y > 0

Step-by-step explanation:

The standard deviation of the original comparison population is 45.

The standard deviation of the original comparison population can be calculated using the formula:

Standard deviation of the sampling distribution = standard error * sqrt(sample size)

Given that the standard error of the sampling distribution is 15 and the sample size is 9, we can substitute these values into the formula:

The standard deviation of the original comparison population can be determined by using the relationship between the standard deviation, standard error, and sample size in a sampling distribution. The formula is:

[tex]\[ \text{Standard deviation of the original comparison population} = \text{Standard error} \times \sqrt{\text{Sample size}} \][/tex]

Given a standard error of 15 and a sample size of 9, substitute these values into the formula:

\[ \text{Standard deviation of the original comparison population} =[tex]15 \times \sqrt{9} = 15 \times 3 = 45 \][/tex]

Therefore, the standard deviation of the original comparison population is 45.

Standard deviation of the original comparison population = 15 * sqrt(9) = 15 * 3 = 45

Therefore, the standard deviation of the original comparison population is 45.