Questions 1-4 I'm very confused on this

A step that is not performed in the process of solving n² - 12n - 10 = 0 by completing the square is: C. Factor n² - 12n - 10 = 0.

In order to solve the given quadratic equation, we would use the completing the square method as follows;

n² - 12n - 10 = 0

By keeping x terms on the left-hand side of the quadratic equation, we would move the constant term to the right-hand side of the quadratic equation by adding 10 on both sides as follows;

n² - 12n - 10 + 10 = 0 + 10

n² - 12n = 10

In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:

n² - 12n + (12/2)² = 10 + (12/2)²

n² - 12n + 36 = 10 + 36

n² - 12n + 36 = 46

(n - 6)² = 46

By taking the square root of each side, we have:

n - 6 = ±46

n = 6 ±46

Read more on quadratic functions here: brainly.com/question/14201243

#SPJ1

Complete Question:

Which step is NOT performed in the process of solving n² - 12n - 10 = 0 by completing the square?

Add 10 to each side

Add 36 to each side

Factor n² - 12n - 10 = 0

Take the square root of each side

Odds are used to determine the chances of winning an experiment.

The odds of winning two of the three question is: \(\mathbf{0.8634}\)

The given parameter is:

\(\mathbf{Games = 6}\)

The probability of winning "having a ball or strange places" is:

\(\mathbf{p_1 = \frac 12}\)

\(\mathbf{G_1 = 2}\) ---- i.e. 2 games

The probability of winning the other 4 is:

\(\mathbf{p_2 = 90\%}\)

\(\mathbf{G_2 = 4}\) ---- i.e. the other 4

So, the probability of getting a question is:

\(\mathbf{Pr= p_1 \times \frac{G_1}{Games} + p_2 \times \frac{G_2}{Games} }\)

So, we have:

\(\mathbf{Pr= \frac 12 \times \frac{2}{6} + 90\% \times \frac{4}{6} }\)

\(\mathbf{Pr= 0.1667 + 0.6 }\)

\(\mathbf{Pr= 7667 }\)

The odds of winning, is the probability of winning at least two of the three questions.

So, we have:

\(\mathbf{Odds = P(Win\ 3) + P(Win\ 2)}\)

Using binomial theorem, we have:

\(\mathbf{Odds = ^3C_3 \times 0.7667^3 \times (1 - 0.766)^0+ ^3C_2 \times 0.7667^2 \times (1 - 0.766)^1}\)

\(\mathbf{Odds = 1 \times 0.7667^3 \times 1+ 3 \times 0.7667^2 \times 0.234}\)

\(\mathbf{Odds = 0.4507+ 0.4127}\)

\(\mathbf{Odds = 0.8634}\)

Hence, the odds of winning two of the three question is: \(\mathbf{0.8634}\)

Read more about odds and probabilities at:

https://brainly.com/question/7538150

Answer:

length = 4 cm

Width = 5 cm

Step-by-step explanation:

      Area of rectangle = length * width

length = (x - 3) meters

Width = (x - 2) meter

Area = 20 square meters

  (x - 3)*(x - 2) = 20

Use FOIL method.

   x*x + (x)(-2) + (-3)*x + (-3)*(-2) = 20

                         x² -2x  - 3x + 6 =20

         Combine like terms

                        x² - 5x + 6  = 20

Now subtract 20 from both side

                     x² - 5x + 6 - 20 = 0

                           x² - 5x - 14  = 0

Factorize the equation and find the roots

         Sum = -5

   Product = -14

    Factors =  (-7) , 2

When we add (-7) + 2 = -5 and when we multiply (-7)*2 = -14

x² + 2x - 7x - 14 = 0

 x(x + 2) -7(x + 2) = 0

 (x + 2)(x - 7)  = 0

  x - 7 = 0    {Ignore (x + 2 = 0) as measurements wont't be in negative}

x = 7

length = x - 3

          = 7 - 3

   \(\sf \boxed{\bf length = 4 \ cm}\)

width = x - 2

         = 7 - 2

    \(\sf \boxed{\bf width = 5 \ cm }\)

Answer:

6 centimeters

Step-by-step explanation:

There are 6 sides, so each side would have an area of 216/6 = 36.

Then, since each side is a square you know that the length of one side would be \(\sqrt{36} = 6\)

Answer:

\(2x-5=23(19)-56\\x=193\)

-------------------------------

\(4x(2)+2(14)=\frac{102}{2}\\x=\frac{23}{8}\)

Step-by-step explanation:

Answer:

- 1

Step-by-step explanation:

The average rate of change of g(x) in the close interval [ a, b ] is

\(\frac{g(b)-g(a)}{b-a}\)

Here [ a, b ] = [ 3, 6 ] , then

g(b) = g(6) = 6² - 10(6) + 19 = 36 - 60 + 19 = - 5

g(a) = g(3) = 3² - 10(3) + 19 = 9 - 30 + 19 = - 2

average rate of change = \(\frac{-5-(-2)}{6-3}\) = \(\frac{-5+2}{3}\) = \(\frac{-3}{3}\) = - 1

We distribute -3 to 2x and -8, and then we calculate the two multiplications.

We calculate -6x + 4x = -x(6 - 4) = -2x

\( \bf - 3(2x - 8) + 4x = \\ \\ \bf = - 3 \cdot 2x - 3 \cdot ( - 8) + 4x = \\ \\ \bf = - 6x + 24 + 4x = \\ \\ \bf = - 6x + 4x + 24 = \\ \\ \bf = - 2x + 24\)

The answer is B -2x + 24

Hope that helps! Have a nice day! :)

Answer: x=(10-sqrt(128))/14=(5-4sqrt(2))/7=-0.094

Step-by-step explanation:  (7x2 -  10x) -  1  = 0

STEP

2

:

Trying to factor by splitting the middle term

2.1     Factoring  7x2-10x-1

The first term is,  7x2  its coefficient is  7 .

The middle term is,  -10x  its coefficient is  -10 .

The last term, "the constant", is  -1

Step-1 : Multiply the coefficient of the first term by the constant   7 • -1 = -7

Step-2 : Find two factors of  -7  whose sum equals the coefficient of the middle term, which is   -10 .

     -7    +    1    =    -6

     -1    +    7    =    6

Answer:

84 and 35

Step-by-step explanation:

12 - 5 = 7

12(7) = 84

5(7) = 35

Two numbers: 84 and 35

Step-by-step explanation:

Let the two numbers be x and y

Given:

Ratio of two numbers= 12:5

Difference between two numbers= 49

So, we need to find the difference between its ratio in order to get two numbers.

12 - 5 = 7

Thus, simply on multiplying the number so obtained after subtraction we will get:  

12 * (7) = 84

5 * (7) = 35

Also, the difference is given which is 49

so, we can confirm it by finding the difference between the numbers obtained which is 84-35=49

Therefore, the two numbers are 84 and 35.

Learn more:

brainly.com/question/13766258

Hi there,

Recall how each bracelet sells for 6 dollars.

Hence, the expression for selling b bracelets is 6b, where b is the number of bracelets sold for the price of 6 dollars.

Profit is the actual amount of money that is earned after you subtract expenses from the total sales.

For instance, if you make $100 from selling items, and you spent $25 on your supplies, then your profit is \(100-25=75\).

In this case, you need to subtract the $28 spent on supplies from the amount of money that you have made, which is the expression 6b.

Hence, the expression for the profit is: \(6b-28\)

Hope that helps.

The number of different choices for nine questions is 384, when at most one of questions 1 and 2 may be included among the nine.

Given, the exam instructions specify that at most one of questions 1 and 2 may be included among the nine.

We have to find the number of different choices for nine questions.

Now, using the concept of Permutation and Combinations we get

There will be three cases,

Case 1 : we include question 1

Case 2 : we include question 2

Case 3 : we neither include question 1 nor question 2

Case 1 :

question 1 is included, so question 2 can not be included and remaining 7 questions have 2 choices.

Case 2 :  

question 2 is included, so question 1 can not be included and remaining 7 questions have 2 choices.

Case 3 :

neither question 1 nor question 2 is included and also remaining 7 questions have 2 choices.

Total choices = 2^7 + 2^7 + 2^7

So, the number of different choices of nine questions are 384.

Hence, the number of different choices of nine questions are 384, when at most one of questions 1 and 2 may be included among the nine.

Learn more about Permutations and Combinations here https://brainly.com/question/1216161

#SPJ4

Answer:

80

Step-by-step explanation:

1 centimeter is equal to 20 feet so if you have 4 cm, it's will 4*20

Also the other two answers are too small to be possible

The simplest form of the proportion is 2/3

here , it is give that colin picks 3 times as many cola bottles as smarties and twice as many smarties as marshmallows. To simplify this let us suppose colin pic a number of marshmallows then number of smarties he pic will be 2a and also the number of cola bottles will be 6a.

What is proportion ?

A proportion is an equation based on the equality of two ratios.

Therefore, the proportion of the bag of sweets are cola bottles will be :

\(\begin{aligned}\frac{6a}{a+2a+6a}&=\frac{6}{9}\\&=\frac{2}{3}\end{aligned}\)  

Therefore, The simplest form of the proportion is 2/3

check and know more about function here :

https://brainly.com/question/12431044

#SPJ1

Answer:

n=5

Step-by-step explanation:

(1/3)^2 divided by (1/3)^7 = 243

3^5=243

Answer:

n = 5

Step-by-step explanation:

\(\frac{(\frac{1}{3})^{2} }{(\frac{1}{3})^{7} } =(\frac{1}{3} )^{2-7} =(\frac{1}{3})^{-5}\)

\((\frac{1}{3} )^{-5} =\frac{1}{(\frac{1}{3})^{5} } =\frac{1}{\frac{1}{3^{5} } } =3^{5}\)

\(3^{5} =3^{n}\)

\(n=5\)

Hope this helps

Answer:

it's D

Step-by-step explanation:

pls give me da crown

In order to be 96% confident that our sample proportion in Exercise 9.53 will be within 0.02 of the true fraction of the voting population, a large sample size is required.

We are given that the sample proportion must be within 0.02 of the true fraction of the voting population, and we are required to be 96% confident. This can be represented as follows:

p ± 0.02

Where p is the true population proportion. This implies that the margin of error is 0.02. We need to find the sample size, which is usually denoted by n.To find the sample size n, we use the formula:

n = (z/ε)² * p(1 - p)

where z is the critical value, ε is the margin of error, and p is the proportion of the population that is being sampled.In this case, z is the z-score that corresponds to a 96% confidence interval, which can be found using the z-table or a calculator.

The z-score is 1.75068607 (rounded to 1.751).

Also, we are given that the margin of error (ε) is 0.02. Finally, we do not have any information about the true population proportion (p), so we will use 0.5 as a conservative estimate.

Substituting these values into the formula, we have:

n = (1.751/0.02)² * 0.5(1 - 0.5)n = 1764.44 (rounded up to 1765)

Therefore, a sample size of at least 1765 is required to be 96% confident that our sample proportion in Exercise 9.53 will be within 0.02 of the true fraction of the voting population.

To know more about sample size visit:

https://brainly.com/question/30100088

#SPJ11

If the resulting F-statistic is less than the critical value, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the variances are significantly different.

The F-test is a statistical test used to compare the variances of two groups.

In this problem, we will use it to compare the variance of the value added by the manufacturer and the variance of the cost of materials in manufacturing. The F-test is performed by dividing the larger variance by the smaller variance. The resulting F-statistic is then compared to the critical value of an F-distribution with degrees of freedom equal to the sample size minus one for each group.

Before we can perform the F-test, we need to determine which variable will be group 1. Typically, the variable with the smaller mean is designated as group 1. This is because we want to minimize the chance of making a type II error, which is failing to reject the null hypothesis when it is false. If we designated the variable with the larger mean as group 1, we might not detect a significant difference between the groups, even if one exists.

Once we have designated which variable will be group 1, we can perform the F-test. If the resulting F-statistic is greater than the critical value of the F-distribution, we reject the null hypothesis and conclude that the variances are significantly different.

To know more about level of significance here.

https://brainly.com/question/13947717

#SPJ4

Answer:

39

Step-by-step explanation:

To convert an area from inches to centimeters, conversion factor should be 15.24 square centimeters.

To convert an area from inches to centimeters, we use the conversion factor of 2.54 cm per inch.

This means that for every inch, there are 2.54 centimeters. In order to find the area in centimeters, we first need to find the area in inches, and then multiply it by 2.54.

To find the area, we use the formula
=> area = length x width.

Let's say the length of a rectangle is 2 inches and the width is 3 inches. The area of this rectangle would be 6 square inches

=> (2 x 3 = 6).

To convert this area to square centimeters, we multiply the area in inches by 2.54.

So,

=> 6 square inches x 2.54 = 15.24 square centimeters.

To know more about area here.

https://brainly.com/question/14994710

#SPJ4

Answer:

a is greater than -2

Step-by-step explanation:

Solving a comparison like this is the same as solving an equation, except you need to watch out for the signs of numbers.

Given:

-2a - 12 < -8

The first thing we need to do here is to add 12 to both sides:

-2a - 12 + 12 < -8 + 12

-2a < 4

You'll notice we're just increasing both sides, so the relationship stays the same.

Now we divide both sides by -2.  Because the number is negative, it changes whether the result is greater or less.

-2a < 4

-2a ÷ -2 > 4 ÷ -2

a > -2

Giving us our final answer.

We are 99% confident that the true difference in population proportions of people in the eastern half of the country who fly to visit family members for the winter holidays and people in the western half of the country who fly to visit family members for the winter holidays is somewhere between -0.422 and -0.114.

Next, we need to calculate the standard error of the difference in sample proportions. This gives us an idea of how much the sample difference in proportions can be expected to vary from the true population difference in proportions. We use the following formula to calculate the standard error:

√((p₁(1-p₁)/n₁)+(p₂(1-p₂)/n₂))

where p₁ and p₂ are the sample proportions, and n₁ and n₂ are the sample sizes. Plugging in the values we have, we get a standard error of 0.094.

Now that we have the sample proportions and the standard error, we can use a confidence interval formula to calculate the range of values that we can be confident contains the true population difference in proportions. For a 99% confidence interval, the formula is:

(sample proportion 1 - sample proportion 2) +/- (critical value x standard error)

The critical value is obtained from a t-distribution table, with degrees of freedom equal to the smaller of (n1-1) and (n2-1). For a 99% confidence level and 44 degrees of freedom, the critical value is 2.689.

Plugging in the values we have, we get a confidence interval of:

0.438 - 0.75 +/- 2.689 x 0.094

= -0.422 to -0.114

To know more about confidence interval here

https://brainly.com/question/24131141

#SPJ4

The possible 3rd degree binomial with a constant term of 888 is x^3 + 2x^2 + 3x + 888, for the given one degree of freedom.

To find a 3rd degree binomial with a constant term of 888, we can start by writing the general form of a 3rd degree binomial: ax^3 + bx^2 + cx + d.

Since we want the constant term to be 888, we can set d = 888.

Now, we need to choose values for a, b, and c. We have one degree of freedom, so we can choose any values for a, b, and c as long as they satisfy the condition of being a 3rd degree binomial.

For example, let's choose a = 1, b = 2, and c = 3.

Therefore, a possible 3rd degree binomial with a constant term of 888 is x^3 + 2x^2 + 3x + 888.

Know more about the binomial

https://brainly.com/question/15246027

#SPJ11

Answer:

Step-by-step explanation:

1/3(12) - 1/3(9w)

4 - 3w

Answer:

6

Step-by-step explanation:

2(3) = 6

Answer:

6

Step-by-step explanation:

Replace the variable with the given value and evaluate.

\(2a\\\\a=3\\\\2(3)=\\\\\boxed{6}\)

Hope this helps.

Adjust the parameters as needed, such as the step size (h) and the final x-value (xn), and run the code to obtain the solution for y(x).

The resulting plot will show the solution curve.

To solve the given set of differential equations using the Runge-Kutta method in MATLAB, we need to convert the second-order differential equations into a system of first-order differential equations.

Let's define new variables:

y = y(x)

z = dz/dx

Now, we have the following system of first-order differential equations:

dy/dx = z (1)

dz/dx = -k/(2y) (2)

To apply the Runge-Kutta method, we need to discretize the domain of x. Let's assume a step size h for the discretization. We'll start at x = 0 and proceed until x = infinite.

The general formula for the fourth-order Runge-Kutta method is as follows:

k₁ = h f(xn, yn, zn)

k₂ = h f(xn + h/2, yn + k₁/2, zn + l₁/2)

k₃ = h f(xn + h/2, yn + k₂/2, zn + l₂/2)

k₄ = h f(xn + h, yn + k₃, zn + l₃)

yn+1 = yn + (k₁ + 2k₂ + 2k₃ + k₄)/6

zn+1 = zn + (l₁ + 2l₂ + 2l₃ + l₄)/6

where f(x, y, z) represents the right-hand side of equations (1) and (2).

We can now write the MATLAB code to solve the differential equations using the Runge-Kutta method:

function [x, y, z] = rungeKuttaMethod()

   % Parameters

   k = 1;              % Constant k

   h = 0.01;           % Step size

   x0 = 0;             % Initial x

   xn = 10;            % Final x (adjust as needed)

   n = (xn - x0) / h;  % Number of steps

   % Initialize arrays

   x = zeros(1, n+1);

   y = zeros(1, n+1);

   z = zeros(1, n+1);

   % Initial conditions

   x(1) = x0;

   y(1) = 0;

   z(1) = 0;

   % Runge-Kutta method

   for i = 1:n

       k1 = h * f(x(i), y(i), z(i));

       l1 = h * g(x(i), y(i));

       k2 = h * f(x(i) + h/2, y(i) + k1/2, z(i) + l1/2);

       l2 = h * g(x(i) + h/2, y(i) + k1/2);

       k3 = h * f(x(i) + h/2, y(i) + k2/2, z(i) + l2/2);

       l3 = h * g(x(i) + h/2, y(i) + k2/2);

       k4 = h * f(x(i) + h, y(i) + k3, z(i) + l3);

       l4 = h * g(x(i) + h, y(i) + k3);

       y(i+1) = y(i) + (k1 + 2*k2 + 2*k3 + k4) / 6;

       z(i+1) = z(i) + (l1 + 2*l2 + 2*l3 + l4) / 6;

       x(i+1) = x(i) + h;

   end

   % Plotting

   plot(x, y);

   xlabel('x');

   ylabel('y');

   title('Solution y(x)');

end

function dydx = f(x, y, z)

   dydx = z;

end

function dzdx = g(x, y)

   dzdx = -k / (2*y);

end

% Call the function to solve the differential equations

[x, y, z] = rungeKuttaMethod();

Learn more about differential equations click;

https://brainly.com/question/32645495

#SPJ4

Answer:

Matrix is an arrangement of numbers into rows and columns. Make your first introduction with matrices and learn about their dimensions and elements. A matrix is a rectangular arrangement of numbers into rows and columns. For example, matrix A has two rows and three columns.

Step-by-step explanation:

Rows and columns of numbers are arranged in a matrix.

The term "matrix" refers to an assortment of numbers put up in rows and columns to form a rectangular array. The elements, or entries, of the matrix are the integers. A rectangular table of numbers is known as a matrix, or more generally, a table made up of abstract quantities that may be multiplied and added.

In a matrix, the horizontal lines are referred to as rows, and the vertical lines as columns. An m-by-n matrix is one that has m rows and n columns; m and n are referred to as the matrix's dimensions. Always list the number of rows before listing the number of columns when describing a matrix's dimensions.

To know more about matrix :

https://brainly.com/question/29861416

#SPJ4

Answer:

-1/6

Step-by-step explanation:

5-4x=6+2x

Add 4x to each side

5-4x+4x=6+2x+4x

5 = 6+6x

Subtract 6x from each side

5-6 = 6+6x-6

-1 = 6x

Divide by 6

-1/6 = 6x/6

-1/6 =x

Answer:

x = -1/6

Step-by-step explanation:

Answer:

90 pumpkin and 36 green beans

Step-by-step explanation:

Because there is a total of 7 parts (5+2) and I divided 126 by 7 and then put five of the 18ns (the quotient of 126 and 7) for pumpkins (so... multiply 18 by 5) then the other to times 18 is 36. And if you add them together, they equal 126.

Answer:

9 cans

Step-by-step explanation:

126/7=18

18/2=9

so 9 is the answer

(plz mark brainlyist)