Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. (Assume that n begins with 1.)
{2, 6, 10, 14, 18, . . . }

The constants 0.693 is the natural log of 2 and the constant 2.303 is the multiplicative factor of converting log of a number to the natural log of that same number.

It follows from the task content that the calculation involves the use of the half-life of radioactive materials formula.

Hence, the constant 0.693 is the real number value of ln(2). Additionally, the constant 2.303 as used by convention is used to convert log value of a number x to its natural log value. Hence,. it follows that the relation which holds true is; ln(x) = 2.303 × log(x).

Read more on natural log;

https://brainly.com/question/305900

#SPJ1

The observation about the student's grade with the z score illustrated is that it's a half standard deviation above the mean of the total test score.

It should be noted that the z score is a numerical measurement which describes the relationship of a value to the mean value of the group.

In this case, the observation about the student's grade with the z score illustrated is that it's a half standard deviation above the mean of the total test score.

This is illustrated as the z score is 0.5.

Learn more z score on:

brainly.com/question/25638875

#SPJ1

The non-extraneous solutions are -6 and -5.

By checking these solution values in the original equation.

[tex](x+6)^{1/2}-5=x+1\\(x+6)^{1/2}=x+6\\((x+6)^{1/2})^2=(x+6)^2\\x+6=x^2+12x+36\\0=x^2+11x+30\\(-11+(11^2-4(1)(30))^{1/2})/2\\(-11+((1)^{1/2})/2\\(-11+1)/2=-5\\(-11-1)/2=-6\\((-6)+6)^{1/2}-5=(-6)+1\\(0^{1/2})-5=-5[/tex]

Thus, -6 is non-extraneous.

[tex]((-5)+6)^{1/2}-5=(-5)+1\\(1^{1/2})-5=-4\\1-5=-4\\-4=-4[/tex]

Thus, -5 is non-extraneous.

Learn more about non-extraneous solutions;

https://brainly.com/question/7536891

#SPJ1

Answer: A. DC||AB

Step-by-step explanation:

Line DC is parallel to AB so the correct answer is option B.

If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.

In the given image we can see that the two angles ABC and HCB are congruent to each other. So the line DC is parallel to AB.

Therefore Line DC is parallel to AB so the correct answer is option B.

To know more about similarities follow

https://brainly.com/question/24184322

#SPJ1

The solution to the system of equations is x = 0.5, y = 0

The system of equations is given as:

y = 2x-1

4x + y=2

Substitute y = 2x-1  in 4x + y=2

4x + 2x-1  =2

Evaluate the like terms

6x = 3

Divide by 6

x = 0.5

Substitute x = 0.5 in y = 2x-1

y = 2 * 0.5 - 1

Evaluate

y = 0

Hence, the solution to the system of equations is x = 0.5, y = 0

Read more about system of equations at:

https://brainly.com/question/13729904

#SPJ1

it's B why they need me to write something long the answer is ez B

Step-by-step explanation:

it f common sense

Answer:

Step-by-step explanation:

$18. 50÷25=0. 74$

The simplified expression of axaxbxb is a^2b^2

The expression is given as;

axaxbxb

Rewrite properly as:

a * a * b * b

Evaluate the product

a^2b^2

Hence, the simplified expression of axaxbxb is a^2b^2

Read more about expressions at:

https://brainly.com/question/723406

#SPJ1

Based on the calculations, Tart & Sweet's total profit from April to June is equal to -2 dollars.

A bar chart can be defined as a type of chart that is used for the graphical representation of a data set, especially by using rectangular bars or vertical columns.

In order to determine Tart & Sweet's total profit, we would simply add the amount of money (in dollars) generated from April to June as follows:

Total profit = -8 + 2 + 4

Total profit = -$2.

Read more on bar chart here: https://brainly.com/question/24741444

#SPJ1

Answer:

0.23

Step-by-step explanation:

5y+14=27y+9

14-9=27y-5y

5=22y

dividing through by 22

y=0.23

Step-by-step explanation:

the area of s circle is

pi×r²

r being the radius.

so, in our case

pi×17.8² = pi×316.84 = 995.3822164... ≈ 995 m²

Round this however your teacher instructs.

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

Work Shown:

mu = 830 = mean

sigma = 96.7 = standard deviation

x = 915 = given raw score we want to convert

z = (x - mu)/sigma

z = (915 - 830)/(96.7)

z = (85)/(96.7)

z = 0.8790072 approximately

[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]

Step-by-step explanation:

As the given figure is a rectangle, therefore the opposite sides should be equal. So -

3x + y = 12 – y...(eqn (i) )

and

y – x = x – 1...(eqn (ii) )

Solving eqn (ii) we get -

→ y – x = x – 1

→ y = x + x – 1

→ y = 2x – 1...eqn(iii)

Solving eqn (i) we get -

→ 3x + y = 12 – y

→ 3x = 12 – y – y

→ 3x = 12 – 2y

Substituting the value of eqn (iii)

→ 3x = 12 – 2(2x– 1)

→ 3x = 12 – 4x + 2

→ 3x + 4x = 14

→ 7x = 14

→ x = 14/7

→ x = 2

Answer:

x = 2; y = 3

Step-by-step explanation:

Since the quadrilateral has 4 right angles, it is a rectangle.

In a rectangle, opposite sides are congruent.

3x + y = 12 - y

x - 1 = y - x

We have a system of two equation is 2 variables.

Let's simplify both equations.

3x + 2y = 12

2x - y = 1

Rewrite the first equation. Multiply both sides of the second equation by 2. Add the equations.

      3x + 2y = 12

(+)   4x - 2y = 2

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

      7x        = 14

Divide both sides by 2.

x = 2

Substitute 2 for x in the second original equation and solve for y.

x - 1 = y - x

2 - 1 = y - 2

1 = y - 2

y = 3

Answer: x = 2; y = 3

Answer:

See attached

Step-by-step explanation:

The graph of a proportional linear relationship is a line that passes through the origin (0, 0).

From inspection of the given tables, the linear equations for each table of points is:

The only equation for which y = 0 when x = 0 is y = x/2  →  Table 2.

Given points from Table 2:

To graph the line, plot the given points and draw a line through them (see attached).

Answer:

4 quarts of milk

Step-by-step explanation:

4 quarts = 1 gallon

so, melissa needs to buy 4 quarts

Evaluating the given algebra fraction (x - 1)²/(1 - x)² at x = 0 gives; 1

We want to evaluate the algebra fraction;

(x - 1)²/(1 - x)² at x = 0.

Now, let us first break down the expression to get;

[(x - 1) * (x - 1)]/[(1 - x) * (1 - x)]

At x = 0, we have;

[(0 - 1) * (0 - 1)]/[(1 - 0) * (1 - 0)]

⇒ (-1 * -1)/(1 * 1)

⇒ 1

Read more about Algebra Fractions at; https://brainly.com/question/24705296

#SPJ1

Point F is on line a, so it does represent Josiah's distance at a certain time. Also, point F is below line b, so it represents a distance that is less than Chana's distance. This is a distance-time graph problem.

Recall that Josiah had a head start of 10 meters and he skates at 2 meters per second.

Since Y is the function that represents the distance in meters from the finished line, by observation, it is clear to see that all the factors that are related to his race are adequately represented in:

y = 10 + 2x

Where 10 is the head start in meters

2 is the rate at which he skates per second; and

x is the unknown amount of time in seconds.

Given that the point F sits over 25 seconds,

that is F(y) = 10 + 2 * 25

= 60 meters.

Hence, Point F is on line a, so it does represent Josiah's distance at exactly 25 seconds.

Learn more about distance-time graphs at:
https://brainly.com/question/4931057
#SPJ1

A constant function is exactly that - constant - meaning it exhibits no change whatsoever with respect to any change in its input. If [tex]f(x) = 1[/tex], then it doesn't matter what value of [tex]x[/tex] I give you, the value of [tex]f(x)[/tex] will always be nothing other than 1.

That the derivative of such a function is zero follows immediately from the definition of the derivative. If [tex]c\in\Bbb R[/tex] and [tex]f(x) = c[/tex], then

[tex]f'(x) = \displaystyle \lim_{h\to0}\frac{f(x+h)-f(x)}h = \lim_{h\to0} \frac{1 - 1}h = \lim_{h\to0}\frac0h = 0[/tex]

[tex]\huge\boxed{4x}[/tex]

Start by simplifying the power.

[tex](5x)^3=5^3x^3=125x^3[/tex]

[tex]\dfrac{500x^4}{125x^3}[/tex]

Cancel out the common factor of [tex]125[/tex].

[tex]\dfrac{4x^4}{x^3}[/tex]

Finally, cancel out the common factor of [tex]x^3[/tex].

[tex]\boxed{4x}[/tex]

Step-by-step explanation:

[tex]f(x) = 3 {x}^{2} + 2x + 4[/tex]

[tex] \: [/tex]

[tex]f(2) = 3. {2}^{2} + 2.2 + 4[/tex]

[tex]f(2) = 3.4 + 4 + 4[/tex]

[tex]f(2) = 12 + 8[/tex]

[tex]f(2) = 20 \\ [/tex]

[tex] \: [/tex]

[tex]f(a + h) = 3 {(a + h)}^{2} + 2.(a + h) + 4[/tex]

[tex]f(a + h) = 3( {a}^{2} + 2ah + {h}^{2} ) + 2a + 2h[/tex]

[tex]f(a + h) = 3 {a}^{2} + 6ah + 3 {h}^{2} + 2a + 2h + 4[/tex]

[tex]f(a + h) = 3 {a}^{2} + 3 {h}^{2} + 6ah + 2a + 2h + 4[/tex]

By applying the concept of composition between two functions and utilizing the information given in the two tables, we find the following results: f ° g (0) = - 2, f ° g (x) = 1.

Compositions are binary operators between two functions: f - Former function, g - Latter function.

f ° g (x)

Where the input of the former function is the output of the latter function. By a brief observation, we find the following relationships in accordance with the two tables:

Case I

f(x):

0 → 1

g(x):

1 → - 2

Case II

f(x):

1 → 0

g(x):

0 → 1

By applying the concept of composition between two functions and utilizing the information given in the two tables, we find the following results: f ° g (0) = - 2, f ° g (x) = 1.

To learn more on composition of functions: https://brainly.com/question/20379727

#SPJ1

The answer to the question that is modeled here is one sixth plus four sixths.

We have the following fractions

1/6 and 5/6

We are to find the fraction which when added to 1/6 would give us 5/6. Hence we have

1/6 + 4/6 = 5/6

Hence the correct answer to the question here is option a.

PLS HELP 1HOUR LEFT Select the expression that is modeled on the number line. A number line from zero to one partitioned into sixths. There are four hops beginning at one sixth and ending at five sixths one sixth plus five sixths

one sixth plus four sixths

five sixths minus one sixth

five sixths minus four sixths

Read more on number line here:

https://brainly.com/question/4727909

#SPJ1

From the statements and reasons given below as regards the Isosceles Triangle, we have been able to prove that; ∆BAM ≅ ∆CAN

Isosceles Triangle means that two sides of the triangle are equal and also 2 angles are equal.

Now, we are told that triangle ABC is an Isosceles and as such, AB and AC are congruent.

We are given that BM and NC are congruent. Now, due to the fact that Triangle AMN is an isosceles triangle, it means that the sides AM and AN are congruent to each other.

Thus, from the proofs above and from the definition of the isosceles Triangle, we can say that triangles BAM and CAN are congruent.

Read more about Isosceles Triangle at; https://brainly.com/question/1475130

#SPJ1

Answer & Step-by-step explanation:

To prove ∆BAM ≅ ∆CAN:

1. Given that ∆ABC is an isosceles triangle with base BC, and BM = CN, we know that AB = AC.

2. Using the Side-Angle-Side (SAS) congruence criterion, we can show that ∆ABM and ∆ACN are congruent.

3. Therefore, corresponding angles ∠BAM and ∠CAN are congruent.

4. Similarly, ∠BMA and ∠CNA are congruent.

5. By showing that corresponding angles in ∆ABM and ∆ACN are congruent, we can conclude that ∆BAM ≅ ∆CAN.

To prove ∆AMN is an isosceles triangle:

1. From the given information, we know that BM = CN.

2. By proving ∆BAM ≅ ∆CAN, we have shown that ∠BAM ≅ ∠CAN.

3. Since ∠BAM and ∠CAN are congruent, we can conclude that ∠BAN ≅ ∠CAM using the Transitive Property of Congruence.

4. By establishing that ∠BAN ≅ ∠CAM, we can conclude that ∆AMN is an isosceles triangle because it has two congruent angles.

The expression that represents a complex number is the one in the second option.

[tex]\frac{2}{3} + \sqrt{-\frac{27}{28} }= \frac{2}{3} + \sqrt{\frac{27}{28} } i\\[/tex]

Remember that the complex number i is given by:

[tex]i = \sqrt{-1}[/tex]

So we have complex numbers when we have negative arguments inside of square roots.

In this particular case, the only option with a negative argument on a square root is on the second option:

[tex]\frac{2}{3} + \sqrt{-\frac{27}{28} } \\\\\frac{2}{3} + \sqrt{-1} *\sqrt{\frac{27}{28} } \\\\\frac{2}{3} + \sqrt{\frac{27}{28} } i\\[/tex]

We conclude that the correct option is the second one.

If you want to learn more about complex numbers:

https://brainly.com/question/10662770

#SPJ1

Answer:

(2)/(3)+\sqrt(-(27)/(28))

Step-by-step explanation:

Plato/Edmentum

Answer:

Step-by-step explanation:

F = [tex]\frac{mv^2}{r}[/tex]

mv² = Fr

m = [tex]\frac{Fr}{v^2}[/tex]

Answer:

5, 7

Step-by-step explanation:

The mode of the numbers is 5, which means that 5 should be the most common card (highest frequency). Therefore the cards should have at least one more 5 among them.

Considering that 5 is one of the hidden cards and x is the other,

• Using the equation for the mean:

[tex]mean = \frac{sum \space\ \space\ of \space\ \space\ numbers}{number \space\ \space\ of \space\ \space\ numbers}[/tex]

[tex]6 = \frac{4+5+ 9 + 5 + x}{5}[/tex]

⇒ [tex]30=23 + x[/tex]

⇒ [tex]x = 7[/tex]

This means 5 and 7 are the hidden cards.