What is the component form of the vector?

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.

In his piggy bank, Dan has 10 nickels, 20 dimes and 5 quarters.

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.

Assume that he had [x] nickels, [y] dimes and [z] quarters. Then we can write -

x = y + 5

x + y + z = 35

x/20 + y/10 + z/4 = 6

Now, the equation → x/20 + y/10 + z/4 = 6, can be written as → (x + 2y + 5z) = 120

We can write, the equations as -

x = y + 5

x + y + z = 35

x + 2y + 5z = 120

Solving the simultaneous equations, we get -

y + 5 + y + z = 35

2y + z = 30         Eq [1]

y + 5 + 2y + 5z = 120

3y + 5z = 115        Eq [2]

Plot Eq[1] and Eq[2] on graph. The point of intersection of both will give the values of y and z.

z = 20

y = 5

We can then find [x] as -

x = y + 5 = 10

x = 10

Therefore, in his piggy bank, Dan has 10 nickels, 20 dimes and 5 quarters.

To solve more questions on equation modelling, visit the link below-

https://brainly.com/question/17965009

#SPJ5

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

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.

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

Answer:

Step-by-step explanation: vertical angel

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.

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.

Yeah it's B:17.8 I agree with you

 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:

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.

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