Write the equation of the line in slope intercept from that: Has a slope of m= −2 and goes through (1, 2). please help

"Nathan rolls a number cube and records the result of each roll in the table" is a true statement. Probability can be used to make predictions or decisions in a variety of situations, such as in gambling, finance, and science. In these situations, probabilities can be calculated based on statistical data or by using mathematical models.

"He spun a 4 five times." is not a valid statement, as it is not clear what "he" or "a 4" refers to.

A valid probability distribution is a set of possible outcomes of a random event, along with the corresponding probabilities of those outcomes occurring. For example, if we roll a number cube, the possible outcomes are 1, 2, 3, 4, 5, and 6, and the probability of each outcome occurring is 1/6.

Learn more about probability, here https://brainly.com/question/11234923

#SPJ4

Answer:

300

Step-by-step explanation:

Divide 12 and 4.

12/4 = 3

Each piece is 3 meters long.

To convert meters to centimeters you have to multiply 3 by 100.

100 x 3 = 300.

The doubling time of a bank account balance is the amount of time it takes for the balance to double. In this case, the doubling time is 10 years, which means that the balance will double every 10 years.

Let's say the initial balance in the bank account is B. After 10 years, the balance will have doubled to 2B. After another 10 years (i.e., 20 years from the initial balance), the balance will have doubled again to 4B. Finally, after another 10 years (i.e., 30 years from the initial balance), the balance will have doubled one more time to 8B.

Therefore, after 30 years, the balance in the bank account will have grown by a factor of 8B/B, which simplifies to just 8. This means that the balance in the bank account will be 8 times the initial balance after 30 years.

To summarize, the balance in the bank account will double every 10 years due to the given doubling time. After 30 years, it will have doubled three times, resulting in a growth factor of 2 x 2 x 2 = 8, which means the balance will be 8 times the initial balance.

To learn more about balance click:

https://brainly.com/question/24914390

#SPJ1

The  average density of the planet is approximately 5.6g/cm³

The formula for density is expressed as;

D = m/v

Such that;

From the information given, we have that;

Volume = 1.02×10⁹ km³

Mass = 5.683 × 10²¹ kg

Convert the parameters

Volume = 1.02×10²⁴cm³

Mass = 5.683 × 10²⁴g

Substitute the values, we have;

Density = 5.683 × 10²⁴g/1.02×10²⁴cm³

Density = 5.6g/cm³

Learn about density at: https://brainly.com/question/1354972

#SPJ1

Answer:

The correct answer is: 3, 4, 5, 6.

Step-by-step explanation:

The correct answer is: 3, 4, 5, 6.

To check, we can substitute each number into the inequality:

When x = 3: 9 - 2(3) ≥ 3, which simplifies to 3 ≥ 3 (true)

When x = 4: 9 - 2(4) ≥ 3, which simplifies to 1 ≥ 3 (false)

When x = 5: 9 - 2(5) ≥ 3, which simplifies to -1 ≥ 3 (false)

When x = 6: 9 - 2(6) ≥ 3, which simplifies to -3 ≥ 3 (false)

Therefore, only the numbers in the set {3, 4, 5, 6} satisfy the inequality.

The amount  that he invested in Fund B if the total profit from the two funds together was $2200 is $8,800.

Let x represent the amount invested in Fund B

Let 3x represent the  amount  invested in Fund A

Hence,

.07x + .05(3x) = 2200

.07x + .15x = 2200

.25x = 2200

Divide both side by .25x

x = 2200/.25

x = $8,800  (invested in Fund B)

Fund A:

3x = 3(8,800)

3x = $26,400 (Invested in Fund A)

Therefore $8800 was invested in Fund B.

Learn more about amount invested here:https://brainly.com/question/25545513

#SPJ1

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

Read more about tangent lines at

https://brainly.com/question/21595470

#SPJ1

the area of the region of points satisfying the inequalities x ≤ 0, y ≤ 0, and y ≥ |x + 4| − 5 is 12.5 square units.

Answer:

80

Step-by-step explanation:

15 percent of 80 is 12

and 12 is 60 percent of 80!

hope this helps :)

The requried, Multiplies(with switching factors.) area given below,

a.

693 x 83 = 57489

83 x 693 = 57489

The answer is 57489.

b.

910 x 45 = 40950

45 x 910 = 40950

The answer is 40950.

c.

38 x 84 = 3192

84 x 38 = 3192

The answer is 3192.

d.

409 x 89 = 36401

89 x 409 = 36401

The answer is 36401.

Learn more about multiply here:

https://brainly.com/question/30875464

#SPJ1

Based on the maximum taxable amount for social security in 2009, and the social security tax rate, the social security tax that Larry paid was $7,347.

The total amount paid by Larry as Social security tax can be found as;

= Maximum amount allowable for social security tax x Social security tax rate

The social security tax rate was 6.2% not 62.2%.

The social security tax was therefore:

= 118,500 x 6.2%

= $7,347

Find out more on social security taxes at https://brainly.com/question/13255138

#SPJ1

Answer:

It is 16

Step-by-step explanation:

Because 64÷4=16 80÷5=16 96÷6=16

So to find the constant of portionality you divide the second number by the first number.

Answer:its 16

Step-by-step explanation:

Answer:

5/51 or 9.8

Step-by-step explanation:

Since she does not put the marble back it's dependent.

1/3 chances the first marble is red and 5/17 the second is too.

Multiply and you get 5/51 odds, or approximately 9.8% chance

Answer:

1/9.

Step-by-step explanation:

Prob(First marble is red) = 6/18 = 1/3

Prob(Second marble is red) = 1/3

Required probability = 1/3 * 1/3 = 1/9.

Answer:

120

Step-by-step explanation:

Answer:

Formula for area:

\(area = \frac{1}{2} \times( base) \times (height) \\ \\ { \boxed{A = \frac{1}{2}(b)(h) }}\)

according to triangle given;

base, b » 30 ft

height, h » 40 ft

substitute the variables for the equation:

\(A = \frac{1}{2} \times (30) \times (40) \\ \\ A = 30 \times 20 \\ \\ { \boxed{ \boxed{area \: \: A = 600 \: {ft}^{2} }}}\)

The number of times the students on your floor order pizza in a week, population.

A population is a complete set of individuals or objects that share common characteristics. It is an entire group of people, animals, plants, or objects that can be studied. A population can also be a group of people living in a certain geographical area.

A sample is a subset of a population. It is a smaller group of individuals or objects drawn from the population that are used to make inferences about the population as a whole.

A sample is used in statistical analysis to estimate population characteristics, such as mean, median, and variance. The accuracy of the estimates depends on the size and representativeness of the sample.

To learn more about a population or a sample link is here

brainly.com/question/9295991

#SPJ4

The complete question is:

Determine whether the statement describes a population or a sample. The number of times the students on your floor order pizza in a week, ___.

Answer:

13

Step-by-step explanation:

To find g f(2) , evaluate f(2) and substitute the value obtained into g(x)

f(2) = 2(2) + 1 = 4 + 1 = 5 , then

g(5) = 3(5) - 2 = 15 - 2 = 13

Answer:

= y + x - 4 = 0

Step-by-step explanation:

a slope or -1

The point = (0,4).

the equation =

\( \frac{y - y1}{x - x1} = m\)

y - 4 = -1

x - 0

note: Perform close multiplication

remember every whole number is over 1

y - 4 = - ( x - 0)

y - 4 = - x + 0

y + x - 4 = 0.

Answer:

n=1

Step-by-step explanation:

-2(6 - 3n) + 27n = -3(n - 8)

-12+6n+27n=-3n+24

-12+33n=-3n+24

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

33n=-3n+36

+3     +3

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

36n=36

----    ----

 n=1

=======================================================

Explanation:

a)

The domain is the set of allowed x inputs. The graph spans forever to the left and to the right, meaning the set of all real numbers is the domain. We can write that as an inequality like this \(-\infty < x < \infty\) which becomes the interval notation \((-\infty, \infty)\)

The range is the set of possible y outputs of a function. The highest y can go is y = 4 shown by the mountain peak on the left side at (-2,4). The range as an inequality is \(-\infty < y \le 4\) which becomes the interval notation \((-\infty, 4]\)

The use of a square bracket means we include the endpoint 4.

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

b)

The x intercepts are the locations where the function curve crosses the x axis. That would be at the locations (-4,0) and (4,0).

The y intercept is where the graph crosses the y axis and it is at (0,1)

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

c)

A decreasing function slopes downhill when moving to the right.

For this f(x) function, such a thing occurs on the interval -2 < x < 0 and on the interval 3 < x < infinity.

Those translate over to the interval notation of \((-2,0)\) and \((3, \infty)\) respectively. Use the union symbol to glue the intervals together getting the final result of \((-2,0) \cup (3,\infty)\)

That notation says "x is in the interval -2 < x < 0, or it is in the interval 3 < x < infinity".

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

d)

I'm not sure how to do this without knowing what the function is (eg: something like f(x) = -x^4+5x). The graph alone isn't enough to accurately pinpoint the locations of concave down vs concave up.

We'll have to eyeball it. The portion on the interval -infinity < x < -1 appears to be concave down. Then we have -1 < x < 1.5 or so appear to be concave up. Then finally 1.5 < x < infinity seems to be concave down.

The -1 < x < 1.5 then translates to the interval notation \((-1, 1.5)\) which is not to be mixed up with ordered pair notation. Unfortunately the two notations look identical sometimes.

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

e)

The graph is on or below the x axis for the intervals of:

Those lead directly to the interval notation \((-\infty, -4] \cup [4, \infty)\)

I'm using square brackets to include the endpoints -4 and 4. Like with part c, the union symbol U represents the word "or" pretty much. Either we're in one interval or the other, but not both.

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

f)

The critical points are where the graph changes direction. These represent vertex points, which are either the highest or lowest of a given neighborhood.

The graph shows we have three such points:

The first and last points are local maxes, and the middle point mentioned is a local min.

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

g)

We have f(x) not being odd because the graph does not go through the origin. All odd functions must go through the origin. This is possibly the quickest way to rule out f(x) being odd.

Another way is to show that f(-x) = -f(x) is false for any counter-example.

For instance, if x = 2 then f(-x) = f(-2) = 4 while -f(x) = -f(2) = some value between 1 and 2. So it's hopefully fairly clear that f(-2) = -f(2) is false which means f(-x) = -f(x) is false in general.

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

h)

f(-2) = 4 according to the graph, due to the point (-2,4)

From here we can say

f(f(-2)) = f(4) = 0

The volume of the given cylinder in terms of pi as required to be determined in the task content is; 5000 pi.

It follows from the task content that the volume of the cylinder which is as represented is to be determined.

Since the volume of a cylinder is;

V = 2πr²h

where r = 10 and h = 25.

V = 2π × 10² × 25.

V = 5000π.

Ultimately, the volume of the given cylinder as required to be determined is; V = 5000 pi.

Read more on volume of a cylinder;

https://brainly.com/question/9554871

#SPJ1

================================================

Work Shown for problem 1

P(pink, then violet) = P(pink)*P(violet given 1st was pink)

= (4/14)*(2/13)

= 8/182

= 4/91

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

Work Shown for problem 2

P(gray, then gray)

= P(gray)*P(gray given 1st was gray)

= (3/14)*(2/13)

= 6/182

= 3/91

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

Work Shown for problem 3

P(not yellow, not yellow)

= P(not yellow)*P(not yellow given 1st was not yellow)

= (9/14)*(8/13)

= 72/182

= 36/91

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

Work Shown for problem 4

P(yellow, not yellow)

= P(yellow)*P(not yellow given 1st was yellow)

= (5/14)*(9/13)

= 45/182

Answer:

Try looking at each angle and add the sides

Step-by-step explanation:

Answer:

(-4, -7)

Step-by-step explanation:

reflection over the y-axis means the x-value becomes the opposite (+ → - or - → +)

(4, -7) → (-4, -7)

Answer:

(-4, -7)

Step-by-step explanation:

Answer:  The total interest is 656.25.

Step-by-step explanation:

T = 3yrs

P = 3500

R = 6.25%

I = PTR/100

 = 3500*3*6.25/100

 = 65625/100

= 656.25

Answer:

it is 42

Step-by-step explanation:

12 ×9/64

when it simplify u get

42

Answer:

it is 42 when you simplify you get 42

Answer:

See below

Step-by-step explanation:

Starting with 42, there would be two branches of 2 and 21 connected to 42. Since 2 is prime, there are no more branches. Since 21 is composite, then two more branches are drawn of 3 and 7 connected to 21. Since 3 and 7 are prime, there are no more branches.

Therefore, the prime factorization of 42 is 2*3*7, and its factors would be 1,2,3,6,7,14,21,42.

Answer:

-9  1/4

Step-by-step explanation:

Answer:

- 9 and 1/4

Step-by-step explanation:

I converted fractions to decimals.

-5 and 3/4 = -5.75

3 and 1/2 = 3.5

-5.75 - 3.5 = -9.25

-9.25 = -9 and 1/4

The equation of the line that passes through the point P(1/3,4) and has no slope is y = 4.

According to the question,

We have the following information:

Point through which line is passing = (1/3,4)

Slope of the line = 0

We know that the following formula is used to find the equation of the line passing through a point:

y-y' = m(x-x')

We have x' = 1/3 and y' = 4.

y-4 = 0(x-1/3)

y-4 = 0

Adding 4 on both sides of the equation:

y = 4

Hence, the equation of the line that passes through the point P(1/3,4) and has no slope is y = 4.

To know more about equation of the line here

https://brainly.com/question/21511618

#SPJ1

The expression (sinx + cosx)^2 + (sinx - cosx)^2 simplifies to

To simplify the expression (sinx + cosx)^2 + (sinx - cosx)^2 using trigonometric identities, we can expand and simplify the expression.

Expanding the squared terms

(sin^2x + 2sinxcosx + cos^2x) + (sin^2x - 2sinxcosx + cos^2x)

Using the trigonometric identity sin^2x + cos^2x = 1, we can simplify further:

(1 + 2sinxcosx + 1) + (1 - 2sinxcosx + 1)

Simplifying the expression, we have:

2 + 2sinxcosx + 2

Combining like terms, we get:

4 + 2sinxcosx

Learn more about identities at

https://brainly.com/question/7331447

#SPJ1