If f(x) = 4x12, what is f(2)?

The area of the parallelogram is \(\sqrt{132}\).

A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length, and the opposite angles are equal in measure. Also, the interior angles on the same side of the transversal are supplementary. Sum of all the interior angles equals 360 degrees.

Given that,

vertices k(1, 1, 3), l(1, 3, 5), m(6, 9, 5), and n(6, 7, 3)

Area of Parallelogram = |KL × KN|

KL = (1, 1, 3) - (1, 3, 5) = (0, 2, 2)

KN = (1, 2, 3) - (3, 7, 3) = (2, 5, 0)

Area of the parallelogram = cross product of two vectors, represented by the adjacent sides.

Area of Parallelogram = |(0, 2, 2) × (2, 5, 0)|

                                    = |i(2 × 0 - 5 × 2) - j(0 × 0 - 2 × 2) + k(0 × 5 - 2 × 2)|

                                    = |i(-10) - j(-4) + k(-4)|

                                    = |-10i + 4j - 4k|

                                    = \(\sqrt{(-10)^{2}+(4)^{2}+(-4)^{2} }\)

                                    = \(\sqrt{100+16+16}\)

                                    = \(\sqrt{132}\)

Hence, The area of the parallelogram is \(\sqrt{132}\).

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hexagon = 6 (n)

total angle = 180 (n - 2)

total angle = 180(6-2) =720

4 angles = 4 x 128 = 512

the other two angle = 720 - 512 =208

Answer: G=(3, 4) R=(4, 8) A=(7, 8) M=(6, 4)

Step-by-step explanation:

translation is the movement of a point so 11 units right add 11 to the x value and 2 to the y value then do the opposite for going left and down

Answer:

6.25 gallons

Step-by-step explanation:

If 125 gallon tank in equivalent to 5ft

1 foot is equal to 12inches...

5 ft ×12 =60 inches

So 125 gallon tank= 60 inches

If 60 inches = 125 gallon

3 inches = 125 × 3 / 60

= 375/60

= 6.25 gallons

Answer:

Question 1: ∠3 and ∠7 are corresponding angles.

Question 2: ∠2 and ∠8 are alternate interior angles.

Question 3: ∠4 and ∠6 are alternate exterior angles.

Question 4: ∠2 is congruent to ∠6.

Question 5: ∠8 is not congruent to ∠1.

Question 6: If ∠2 measures 132°, the measure of ∠7 would be 48°.

Answer:

x=㏒3(2189)

Step-by-step explanation:

Answer:

Most precise value of the average weight is 0.56 pounds

Step-by-step explanation:

To get the precise value, we start by getting the average weight

That will be total weight/8

= 4.5 pounds/8 = 0.5625

we are told that the scale records to the nearest hundredth

So we need to express the obtained value in hundredths

That will be 0.56 pounds

Based on the information provided, it is most likely that Professor Anderson's focus on studying how family relationships change over time aligns with the field of developmental psychology.

Based on the given information, Professor Anderson's focus on studying how family relationships change over time and conducting longitudinal surveys with the same group of participants, it is most likely that Professor Anderson is a developmental psychologist. Developmental psychologists study human development and changes that occur across the lifespan, including familial relationships and their dynamics. They are interested in how individuals grow, change, and interact with others over time.

Developmental psychology is a branch of psychology that focuses on studying human development and changes that occur throughout a person's life span. Developmental psychologists are interested in understanding how individuals grow, change, and develop in various aspects such as physical, cognitive, emotional, and social domains.

In the given scenario, Professor Anderson's research interest revolves around tracking and surveying the same group of participants over a period of two decades to investigate the changes in their relationships with their parents and siblings. This longitudinal approach allows for the examination of how these family relationships evolve over time and provides insights into the developmental processes that influence familial dynamics.

By studying the patterns, trajectories, and factors that contribute to changes in family relationships, Professor Anderson can gain a deeper understanding of human development within the context of family dynamics. This knowledge can have implications for various aspects of individuals' lives, including their mental and emotional well-being, interpersonal relationships, and overall development.

Therefore, according to the information given, Professor Anderson's interest in researching how family connections change over time is most likely in line with the discipline of developmental psychology.

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The probability that all four strawberry pieces will be received by the same child 9/10 outcome.

Total piece of candy = 40

Mint flavor = 36

Strawberry = 04

There are 36 + 04 = 40 total outcomes for the chocolate pick.

There are 36 outcomes resulting in you picking a mint candy.

Probability is the number of outcomes you’re testing for divided by the number of total outcomes. So in this case that’s 36/40 or 4/5 . And also,  

04 /40 = 1/10

Therefore, adding both, we get,

4/5 + 1/10 = 9/10

The probability that all four strawberry pieces will be received by the same child is 9/10.

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The factor in the Salk vaccine experiment is the type of injection, which is the independent variable that was manipulated in the experiment to determine its effect on the dependent variable, which is the presence or absence of polio.

The factor in the Salk vaccine experiment is the type of injection, which is either the vaccine or the placebo. This is the independent variable, which is the factor that is being manipulated in the experiment to determine its effect on the dependent variable, which is the presence or absence of polio.

The students were randomly assigned to either the vaccine or placebo injection group, which is an important aspect of the experiment to control for any potential confounding variables. This randomization helps to ensure that any observed differences between the vaccine and placebo groups are due to the type of injection received and not due to any other factors, such as differences in age, gender, or health status.

During the school year, all students were observed for evidence of polio, which is the dependent variable. The purpose of the experiment was to determine whether the vaccine was effective in preventing polio, so the presence or absence of polio is the outcome measure that was used to evaluate the effectiveness of the vaccine.

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Answer: If they're equal sized sections, I would expect it to land on green about 36 times.

Step-by-step explanation:

110/3=36.666667

We have the given equation:

Where:

a=2

b=32

c= 120

Now, we need to find:

b²-4*a *c

Replacing the variables:

(32)²- 4(2)(120)

1024 - 960

= 64

Answer:

x = 43 1/3 degrees

Step-by-step explanation:

sum of interior angles in a triangle = 180 degrees

30 + (3x - 9) + 29 = 180

30 + 29 + (3x - 9) = 180

59 + (3x - 9) = 180

(3x - 9) = 180 - 59

(3x - 9) = 121

3x = 121 + 9

3x = 130

x = 43 1/3

the solution to the equation |x-1|+|x-2|=3 is x = 3.

What is inequality?

Mathematical expressions with inequalities on both sides are known as inequalities. In an inequality, we compare two values as opposed to equations. In between, the equal sign is changed to a less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

|x-1|+|x-2|=3

In this sub-case, we can rewrite the equation as:

-(x-1) + (x-2) = 3

Simplifying, we get:

-2x + 5 = 3

Which gives us x = 1.

However, x < 2 in this sub-case, so x = 1 is not a valid solution.

Sub-case 2.2: x >= 2

In this sub-case, we can rewrite the equation as:

(x-1) + (x-2) = 3

Simplifying, we get:

2x - 3 = 3

Which gives us x = 3.

Therefore, the solution to the equation |x-1|+|x-2|=3 is x = 3.

Since we found that x >= 1, the inequality that represents the solution is:

x >= 1.

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Answer:

its finally sorry it tooke so long

Step-by-step explanation:

Answer:

The answer is finally.

Step-by-step explanation: Both would be a compare and contrast text structure and so would similarly. Since would be a cause and effect text structure so the answer has to be finally. You can also tell because it is using key clues like then, after, and finally.

Answer:

(a) To find a number such that | x 2 2| , , we need to solve the inequality | x 2 2| < «. First, let's solve | x 2 2| < 0.1:

x 2 2 < 0.1

x 2 < 2.1

x < √2.1

Now, let's solve | x 2 2| > -0.1:

x 2 2 > -0.1

x 2 > 1.9

x > √1.9

So, the solution to | x 2 2| < 0.1 is √1.9 < x < √2.1. Any number in this range will satisfy the inequality.

(b) To repeat part (a) with « 5 0.01, we need to solve the inequality | x 2 2| < 0.01. First, let's solve | x 2 2| < 0.01:

x 2 2 < 0.01

x 2 < 2.01

x < √2.01

Now, let's solve | x 2 2| > -0.01:

x 2 2 > -0.01

x 2 > 1.99

x > √1.99

So, the solution to | x 2 2| < 0.01 is √1.99 < x < √2.01. Any number in this range will satisfy the inequality.

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Answer:2/3

Step-by-step explanation:

Slope is 2/3

its a square with 4 sides

Step-by-step explanation:

9 x 4=36 is the answer

hope this helps you

have a nice day:)

Answer:

Andre's

Step-by-step explanation

I think its Andre. I apologize if it is not.

Step-by-step explanation:

If they are similar, then 10 is to 3      as  x is to 15

10/3 = x/15    multiply both sides by 15

 50 mm = x

t\The answer is 0.016. Since the p-value is less than 0.05 (level of significance), we reject the null hypothesis and accept the alternative hypothesis.

In a test of hypotheses of the form h0: p = 0.69 versus ha: p ≠ 0.69 a sample of size 1,250 produced the test statistic z = −2.417.

We are to find the p-value (observed significance) of the test.

Here, the test statistic is z = −2.417.The formula to calculate the p-value (observed significance) of the test is:

p-value = 2P(Z > |z|),

\Where Z is the standard normal distribution, and z is the test statistic.

For the two-tailed test, the test statistic is beyond both tails of the distribution.

So, P(Z < −2.417) = 0.0078 (from z table).

Therefore, p-value = 2P(Z > |z|) = 2(0.0078) = 0.0156.

Hence, the answer is 0.016.Since the p-value is less than 0.05 (level of significance), we reject the null hypothesis and accept the alternative hypothesis.

The evidence suggests that the population proportion is not equal to 0.69.

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Answer:

8

Step-by-step explanation:

Answer:

77.00

Step-by-step explanation:

the price is going by 1.50 a year so it would be 77.00 in 2020

Answer:

x – 4.9 = 0.3 and x – 4.9 = –0.3

Answer:

d

Step-by-step explanation:

Answer:

Step-by-step explanation:

Proportional relationship formula is:

a) Use point (1, 3.5) to find k:

b) Unit rate is:

c) Point (8, 28) indicates:

d) x = 20, y =?

Answer:

Step-by-step explanation:

Since one side of the square is 16 cm, the diameter of the circle is also 16 cm. Which means that the radius is 8. the area of a circle is pi times radius square. so it is pi times 8 squared, which is 64pi

The closest option to the calculated net present value is d. $(15,542).

To calculate the net present value (NPV) of the project, we need to discount the annual cash flows to their present value and subtract the initial investment.

Using the formula for the present value of a cash flow:

PV = CF / (1 + r)^n

Where PV is the present value, CF is the cash flow, r is the discount rate, and n is the number of years.

For the given data:

Initial investment = $380,000

Annual cash flow = $133,000 per year

Expected life of the project = 4 years

Discount rate = 13%

Calculating the present value of the annual cash flows:

PV = $133,000 / (1 + 0.13)^1 + $133,000 / (1 + 0.13)^2 + $133,000 / (1 + 0.13)^3 + $133,000 / (1 + 0.13)^4

PV ≈ $133,000 / 1.13 + $133,000 / 1.28 + $133,000 / 1.45 + $133,000 / 1.64

PV ≈ $117,699 + $104,687 + $91,724 + $81,098

PV ≈ $395,208

Finally, calculating the net present value:

NPV = PV - Initial investment

NPV ≈ $395,208 - $380,000

NPV ≈ $15,208

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The system 21+12 +2.13 2 11 - 309+ 3.13 -3 (2:11 +19-33 -1 :

(a) Finding the reduced row echelon form of the augmented matrix: This is the augmented matrix for the given system of linear equations. First, we will perform some basic row operations in order to convert this matrix to its row echelon form. Now, we want to get rid of the entry in the second row and first column. In order to do that, we will subtract the twice the first row from the second row. The second row is already in the correct form. Now, we will subtract 2 times the second row from the first row. This step is not necessary, but it helps simplify the computation for the next step. Next, we will subtract 33 times the second row from the third row.

Now, we want to get rid of the entry in the third row and second column. In order to do that, we will subtract -13 times the second row from the third row. The third row is already in the correct form (leading entry equal to 1).Finally, we will subtract 19 times the third row from the first row. The matrix is now in row echelon form. In order to convert it to reduced row echelon form, we need to get rid of the entry in the first row and second column. We will subtract 5 times the first row from the second row in order to do that. The matrix is now in reduced row echelon form.

(b) Solving the system of equations using the reduced row echelon form: This is the same matrix as before, but we only consider the coefficients and the constants. We can see that the last column is equal to the right-hand side of the equations. Therefore, the third equation is 0 = -16, which is impossible to satisfy. This means that the system of equations is inconsistent. Therefore, there is no solution to the original system of equations.

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    To consider the system MATRIX

How to solve Matrix for this system

(a) Find the reduced row echelon form of the augmented matrix for this system.

The augmented matrix for this system is:

 [2, 1, 2, 16]

 [2, -3, 3, -3]

 [2, 1, -3, -1]

]

We can reduce this matrix to row echelon form as follows:

Swap row 1 and row 2.

[2, -3, 3, -3]

[2, 1, 2, 16]

[2, 1, -3, -1]

Add row 1 to row 2.

[2, -3, 3, -3]

[0, -2, 5, 13]

[2, 1, -3, -1]

Subtract row 1 from row 3.

[2, -3, 3, -3]

[0, -2, 5, 13]

[0, 4, -6, 2]

Swap row 2 and row 3.

[2, -3, 3, -3]

[0, 4, -6, 2]

[0, -2, 5, 13]

Add 1/2 * row 2 to row 3.

[2, -3, 3, -3]

[0, 4, -6, 2]

[0, 0, 1, 15]

Divide row 3 by 1.

[2, -3, 3, -3]

[0, 4, -6, 2]

[0, 0, 1, 15]

Add 6*row 3 to row 2.

[2, -3, 3, -3]

[0, 4, 0, 92]

[0, 0, 1, 15]

Subtract 3*row 3 from row 1.

[2, -3, 0, -48]

[0, 4, 0, 92]

[0, 0, 1, 15]

]

Divide row 2 by 4.

[

[2, -3, 0, -48]

[0, 1, 0, 23]

[0, 0, 1, 15]

Add 3*row 2 to row 1.

[2, 0, 0, 36]

[0, 1, 0, 23]

[0, 0, 1, 15]

Now, we have reduced the matrix to row echelon form. The last column of the matrix represents the values of x, y, and z, respectively, in the solution to the system of equations.

Therefore, the solution to the system of equations is x = 36, y = 23, and z = 15.

(b) Solve the original system of equations.

The solution to the original system of equations is x = 36, y = 23, and z = 15.

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