2,10,50,... find the sum of the first 6 terms. r=

a¹ (1,-rn)
(1-r)

A.8,215
B.14,610
C.7,812
D.6,694​

The prompt on fractions is given as follows:

1 ) (1/2) ÷ 4 = 1/8
2) ( 1/5) ÷ 2 = 1/10

3) (1/3) ÷ 5 = 1/15

4) (1/4) ÷ 4 = 1/16
5) The solution to the puzzle for (1/2) ÷ 3 is given below.

The calculations are given as follows;

1 )

= (1/2) x (1/4) [dividing by a number is the same as multiplying by its reciprocal]

= 1/8

2) (1/5) ÷ 2

= (1/5) x (1/2)

= 1/10

3)

(1/3) ÷ 5

= (1/3) x (1/5)

= 1/15

4) (1/4) ÷ 4

= (1/4) x (1/4)

= 1/16

5) Mary had 1/2 of a pie that she wanted to share with 3 of her friends. She decided to divide it equally among them. Each friend got 1/6 of the pie. To check, Mary multiplied 1/6 by 3 and got 1/2. This shows that (1/2)/3 equals 1/6, since dividing by 3 is the same as multiplying by its reciprocal, 1/3.


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Answer:

C

Step-by-step explanation:

The red graph is obtained by shifting the graph of f(x) = 4 - x² upwards by some amount. We can see that the highest point on the red graph occurs at x = 0, where the value is 4.

To shift the graph of f(x) upwards by 3 units, we can add 3 to the entire function:

f(x) + 3 = 4 - x² + 3

= 7 - x²

So the equation of the red graph is:

g(x) = 7 - x²

Therefore, the correct answer is option C: g(x) = 7 - x².

The "x is small" approximation only works when the initial concentration of the reactant is relatively large and the equilibrium constant is small.

What does the "x is small" approximation mean? The x is small approximation does not mean that x is zero. If that were the case, the reactant and product concentrations wouldn't change from their initial values. The x is small approximation just means that when x is added or subtracted to another number, it doesn't change that number by very much. When does the "x is small" approximation work? The "x is small" approximation only works when the initial concentration of the reactant is relatively large and the equilibrium constant is small. What is the <5% rule? The x is small approximation must satisfy the <5% rule, whereby the x approximation divided by the number it was subtracted from is less than 5% (or 0.05). What is the method of successive approximation? The method of successive approximation is solving for x as if it were small, and then substituting the value obtained back into the equation (where x was initially neglected) to solve for x again. This can be repeated until the calculated value of x stops changing with each iteration, an indication that we have arrived at an acceptable value for x.

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According to the question, it’s given that the sum of two numbers is 42.

On substituting the values -

[tex]\:\:\:\:\:\:\:\star \small \underline{ \boxed{ \sf{ x+\bigg(x-12\bigg) = 42}}}\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf { x + x -12 = 42}\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf {2x -12 =42}\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf {2x = 42+12}\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf {2x = 54}\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf {x = \dfrac{54}{2}}\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \boxed{ \tt{ \pmb{ \pink{x = 27}}}}\\[/tex]

Henceforth,the larger number is 27 and the smaller number is (x-12)=(27-12)=15.

[tex]\:\:\:\:\:\:\longrightarrow\underline{\rm{\sf Larger \: Number =\pink{ \underline{27}}}}[/tex]

[tex]\:\:\:\:\:\:\longrightarrow\underline{\rm{\sf Smaller \: Number =\pink{ \underline{15}}}}[/tex]

Answer:

radius=PC

diameter=AB

chord=AC

central angle=angleAPC

tangent=AD

Answer:

A circle has 360 degrees, so 5/6 of the circle can be found by multiplying 360 by 5/6:

5/6 of 360 = (5/6) × 360 = 300

Therefore, the angle measures of 5/6 of the circle is 300 degrees.

Answer:

The mean increases by 1.4

The correct solutions for the given equation is given by table in option 3.

A straight line is produced when a linear equation, which is a two-variable equation, is graphed. The intersection of corresponding values which satisfy the equation results in the line.

The variables x and y are most frequently used in linear equations, hence the associated values can be shown as (x,y) on the coordinate plane, pairs. A collection of two maybe more linear equations is known as a system of linear equations.

The given equation is-

y = x - 6

Put the value of 'x' from the options and check for 'y', if its correct.

The option are the solution of the equation.

option 1:

y = x - 6

x = --5

y = -5 - 6 = -11  (incorrect)

option 2:

y = x - 6

Put x = -8

y = -8 - 6 = -14 (incorrect)

option 3:

y = x - 6

Put x = -7

y = -7 - 6 = -13 (correct)

Thus, the correct solutions for the given linear equation is given by table in option 3.

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Dan had 50% fewer stickers than Jeff. After Jeff gave 20 of his stickers to Dan, Dan had 40% fewer stickers than Jeff. Dan had 320 stickers first.

Dan had 50% fewer stickers than Jeff.

After Jeff gave 20 of his stickers to Dan, Dan had 40% fewer stickers than Jeff (had after he gave away 20 of his stickers).

How many stickers did Dan have at first?

The total number of stickers that Jeff had is denoted by J, and the total number of stickers that Dan had is denoted by D.

In order to solve the question, let us first represent the given data mathematically:

J = 1.5D; D+20 = 0.6(J-20)

We have 2 equations and 2 unknowns, J and D.

We can solve these equations using simultaneous linear equations.

Substitute the first equation in the second equation:

D+20=0.6(J-20)

⇒ D+20=0.6J-12

⇒ D=0.6J-32

Now substitute the value of D in the first equation:

J=1.5D

⇒ J=1.5(0.6J-32)

⇒ J=0.9J-48.

Therefore, J=480

The total number of stickers that Jeff had initially was 480.

Now, to calculate the total number of stickers that Dan had, we can use the equation

J=1.5D:J=1.5D

⇒ 480=1.5D

⇒ D=320

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Answer:

Changes in light and dark.

Step-by-step explanation:

I also do K12 loll

Changes in light or dark is the environmental stimulus which is detected by flatworm's eyespots.

A sum total of all the living and non-living elements and their effects that influence human life.

Flatworm's eyespots detect changes in light or dark in the environment. They are not capable of detecting distinct shapes or a wide variety of colors.

The eyespots are simple sensory structures that are used to detect the presence or absence of light and dark, and to detect changes in light intensity.

They are primarily used to help the flatworm locate and respond to light, which can be important for activities such as finding food or avoiding predators.

Hence, changes in light or dark is the environmental stimulus which is detected by flatworm's eyespots.

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Answer: Should be standard form.

Step-by-step explanation: Just cause the others don't really make sense and the equation looks basic.

Answer:

To convert a decimal to an equivalent fraction, we need to first determine the place value of the decimal. For example, a decimal that ends in the tenths place (such as 0.4) has a denominator of 10. A decimal that ends in the hundredths place (such as 0.25) has a denominator of 100.

Once we have determined the denominator, we can convert the decimal to a fraction by placing the digits of the decimal in the numerator and the denominator. For example, 0.4 can be converted to the fraction 4/10. We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which in this case is 2. So 4/10 simplifies to 2/5.

In general, to convert a decimal to a fraction, we can follow these steps:

1. Determine the denominator based on the place value of the decimal.

2. Place the digits of the decimal in the numerator and the denominator.

3. Simplify the fraction by dividing both the numerator and denominator by their greatest common factor.

It's important to note that sometimes decimals can be rounded, so the resulting fraction may not be exact. In such cases, we can use approximations or continue to simplify the fraction until we reach a desired level of accuracy.

The estimated enrollment of a high school in 2022 is approximately 2775 students.

To calculate the estimated enrollment in 2022, we need to use the formula for compound interest:

A =[tex]P(1 + r)^t[/tex]

where:

A = final amount (enrollment in 2022)

P = initial amount (enrollment in 2012)

r = annual interest rate (increase rate)

t = number of years (10)

We know that P = 1350 and r = 0.09 (9%). We can plug these values into the formula:

A = [tex]1350(1 + 0.09)^{10[/tex]

A = [tex]1350(1.09)^{10[/tex]

A = 2774.92

Therefore, the estimated enrollment in 2022 is approximately 2775 students.

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The relative frequency of the event "spin a 2" is given as follows:

0.2.

To calculate the relative frequency of an event, you need to divide the number of times the event occurs by the total number of events in the data-set.

Hence the formula to calculate the relative frequency is presented as follows:

Relative frequency = (Number of times the event occurs) / (Total number of events)

From the table, the parameters for the event "spin a 2" are given as follows:

Hence the relative frequency is given as follows:

10/50 = 0.2.

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The factors that affect the width of a confidence interval are a. population variation, c. sample size, and d. confidence level

Confidence interval refers to a statistical measure that attempts to estimate the range of values that could plausibly contain the true value of a population parameter. A confidence interval, in other words, is a statistical range that tells us how sure we are that a statistical estimate we're interested in lies between two values.

There are several factors that can affect the width of a confidence interval. Here are some of them:

The Question was Incomplete, Find the full content below :

what factors of the following affect the width of a confidence interval?

a. population variation

b. none of them

c. sample size

d. confidence level

e. sample mean

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The width of the rectangle is 5 meters.

To find the width of the rectangle, let's use the formula for the area of a rectangle, which is:

Area = length x width

We know that the area of the rectangle is 65 square meters. We also know that the length of the rectangle is 8 meters more than the width. Let's call the width "w". Then, the length can be expressed as:

length = w + 8

Substituting this expression for length into the formula for the area, we get:

65 = (w + 8) x w

Simplifying and solving for w, we get:

w² + 8w - 65 = 0

Using the quadratic formula, we get:

w = (-8 ± √(8² + 4(1)(65))) / (2(1))

w = (-8 ± √(324)) / 2

w = (-8 ± 18) / 2

We take the positive value for w since the width cannot be negative:

w = (-8 + 18) / 2

w = 5

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As the given abc is a right triangle with points a(2, 5), b(2, 0), and c(x, 0). The area of 'abc' is 25 square units. and the equation of AC is x = 5√5.

The equation of ac has to be found. Since triangle ABC is right-angled, it can be shown that

                  AC² = AB² + BC²

    Finding the lengths of AB and BC before using the Pythagorean theorem to find AC.

    Using the distance formula,

                     AB =√(5²+0²)

                           = √25

                          = 5,

           And BC = √(x²+0²)

                         = √x²

                          = x.

  Area of a right triangle = ½(base × height)

          Here base = AB and height = BC,

              So,  ½ × 5 × x = 25

                            ⇒ 5x = 50

                              ⇒ x = 10

       Now, to find AC, use the Pythagorean Theorem.

                      AC² = AB² + BC²

                             = 5² + 10²

                             = 25 + 100

                             = 125AC

                             = √125

                             = 5√5

     Thus, the equation of AC is x = 5√5. Answer: x = 5√5.

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For each of the businesses below:

Business A: Loss (Income £100 - Expenditure £200 = -£100)

Business B: Loss (Income £49.85 - Expenditure £71.24 = -£21.39)

Business C: Profit (Income £21,357 - Expenditure £7,028 = £14,329)

Percent is a term used to describe a fraction or ratio as a portion of 100. It is commonly denoted by the symbol %, which means "per hundred." For example, the percentage 50% means 50 out of 100 or 0.5 as a fraction. Percentages are often used to express change, growth, or comparison between different quantities. Percentages are commonly used in many fields, including finance, science, and statistics, to express values in a more convenient and easily interpretable way.

Here,

Business A:

Income = £100

Expenditure = £200

Profit/Loss = Income - Expenditure = £100 - £200 = -£100

Since the result is negative, the business made a loss.

Business B:

Income = £49.85

Expenditure = £71.24

Profit/Loss = Income - Expenditure = £49.85 - £71.24 = -£21.39

Since the result is negative, the business made a loss.

Business C:

Income = £21,357

Expenditure = £7,028

Profit/Loss = Income - Expenditure = £21,357 - £7,028 = £14,329

Since the result is positive, the business made a profit.

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Answer:

$12.50

Step-by-step explanation:

62% would be left,so

[tex]\frac{62}{100}[/tex] × $20

=$12.50

Therefore, the inequality that can be used to determine p, the maximum number of people who can go to the amusement park, is p ≤ 30.

In mathematics, inequalities are statements that compare two values or expressions and indicate whether they are equal, greater than, or less than each other. An inequality is typically represented by a symbol, such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).

Given by the question.

Let's assume that the maximum number of people that can go to the amusement park is p. The cost of parking is $8.75, and the cost of admission for each person is $15.50.

Then, the total cost for p people can be calculated as:

Total cost = (Cost of parking) + (Cost of admission per person x number of people)

Total cost = $8.75 + $15.50p

The group has no more than $480 to spend, so we can set up an inequality:

Total cost ≤ $480

$8.75 + $15.50p ≤ $480

Subtracting $8.75 from both sides:

$15.50p ≤ $471.25

Dividing both sides by $15.50:

p ≤ 30.35

Since the number of people cannot be a decimal, we round down to the nearest whole number: p ≤ 30.

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Answer:

“change” or “the change”

Step-by-step explanation:

An equation of a line that is parallel to this line is y = -x + 3.

An equation of a line that is perpendicular to this line is y = x + 3.

An equation of a line that is neither parallel nor perpendicular to this line is y = 3x + 3.

Based on the information provided about this line, an equation that models it is given by:

4x + 4y = 4.

4y = -4x + 4

y = -x + 1

In Geometry, two (2) lines are parallel under the following conditions:

m₁ = m₂ ⇒ -1 = -1

Slope (m) = -1

Therefore, the required equation is y = -x + 3

In Mathematics, a condition that must be met for two lines to be perpendicular is given by:

m₁ × m₂ = -1

-1 × m₂ = -1

m₂ = 1

Slope, m₂ = 1

Therefore, the required equation is y = x + 3

By using a line with a different slope other than 1 and -1 would produce a line that is neither parallel nor perpendicular to the given line.

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Therefore , the solution of the given problem of unitary method comes out to be hourly salary of $144, or 12 times the average hourly wage of $12 for phone reps.

This common convenience, already-existing variables, or all important elements from the original Diocesan adaptable study that followed a particular methodology can all be used to achieve the goal. Both of the crucial elements of a term affirmation outcome will surely be missed if it doesn't happen, but if it does, there will be another chance to get in touch with the entity.

Here,

The formula below can be used to determine the ideal amount of phone representatives:

=>  MR = MC

Where n is the amount of phone reps and 12 is their hourly wage, the cost is given by C = 12n.

The following results are obtained by taking the derivative of revenue and cost with regard to n:

=> MR=dR/dn = k

=>  dC/dn = 12 for MC.

When we set MR equal to MC, we obtain:

=> k = 12

Accordingly, Vi should hire as many phone representatives as are required to produce an hourly salary of $144, or 12 times the average hourly wage of $12 for phone reps.

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Answer:

Step-by-step explanation:

2560

The measure of angle ACD is approximately 109.5 degrees.

What are parallel lines ?

Parallel lines can be defined in which the lines which are equidistant to each other and they never intersect.

To solve for m<ACD, we can use the fact that the sum of the angles in a triangle is 180 degrees.

We can start by finding the measure of angle ACD, which is opposite to the known side length of 10 units. Using the Law of Cosines, we have:

cos(ACD) = (AD * AD + CD * CD - 100) / (2 * AD * CD)

We know that AD = 8 units and CD = 6 units, so plugging in these values, we get:

cos(ACD) = (64 + 36 - 100) / (2 * 8 * 6) = -1/3

Since -1/3 is negative, we know that angle ACD is obtuse, meaning it measures between 90 and 180 degrees. Therefore, we can take the inverse cosine of -1/3 to find its measure:

cos(ACD) = (-1/3) ≈ 109.5 degrees

Therefore, the measure of angle ACD is approximately 109.5 degrees.

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Answer:

z ≥ 9

Step-by-step explanation:

z ≥ 9

(The number z is greater than or equal to 9)

...

The balance after 6 years when the interest is compounded monthly is $7289.60

To find the balance after 6 years when the interest is compounded monthly, we can use the formula:

A = P(1 + r/n)^(nt)

where:

In this case, P = $5000, r = 6.3% = 0.063 (annual interest rate as a decimal), n = 12 (since interest is compounded monthly), and t = 6.

Plugging in these values, we get:

A = $5000(1 + 0.063/12)^(12*6)

Evaluate

A = $7289.60

Therefore, the balance after 6 years when the interest is compounded monthly is $7289.60

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Answer:

58.8 gallons

Step-by-step explanation:

Answer:

x = 17/4, or 4.25

The x-intercept is (4.25, 0)

Step-by-step explanation:

We can get the intercepts by isolating x and y.

4x - 3y = 17

Subtract 4x from both sides.

-3y = -4x + 17

Divide both sides by -3.

y = 4/3x - 17/3

Input 0 for x.

y = -17/3

The y-intercept is (0, -17/3)

4x - 3y = 17

Add 3y to both sides.

4x = 3y + 17

Divide both sides by 4.

x = 3/4y + 17/4

Input 0 for y.