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There are 7 seats in the first row of a theater, 9 seats in the second row, and 11 seats in the third row. This pattern continues for each row in the theater. Write a rule for an, the number of seats in the nth row.

p + 5p-2p + 4p = -40 ​

Solving for p:

6p - 2p + 4p = -40

4p + 4p = -40

8p = -40

p = -40/8

p = -5

Answer:

p = -5

Answer:

16.5 m/s

Step-by-step explanation:

Answer:

a. \(\tt \frac{1}{9}\)

b. \(\frac{1}{16}\)

c. 4

Step-by-step explanation:

\(\tt a. \:3^{-2}\)

We can use the negative exponent rule, which states that \(\boxed{\tt a^{-n} = \frac{1}{a^n}}\) So, we have:

\(\tt 3^{-2} = \frac{1}{3^2} = \frac{1}{9}\)

\(\hrulefill\)

\(\tt b.\: -2^{-4}\)

We can use the rule that \(\boxed{\tt -a^{-n} = (-1)^n \cdot a^n}.\) So, we have:

\(\tt -2^{-4} = (-1)^4 \cdot 2^{-4} = 1 \cdot \frac{1}{2^4} = \frac{1}{16}\)

\(\hrulefill\)

\(\tt c. \:(\frac{1}{2})^{-2}\)

We can use the negative exponent rule, which states that \(\boxed{\tt a^{-n} = \frac{1}{a^n}}\). So, we have:

\(\tt (\frac{1}{2})^{-2} = \frac{1}{(\frac{1}{2})^2} = \frac{1}{\frac{1}{4}} = 4\)

Answer:

Step-by-step explanation:

(a) 3^-2 = 1/9

(b) (-2)^-4 = 1/(-2)^4 = 1/16

(c) (1/2)^-2 = 1/(1/2)^2=1 / 1/4 = 4

The Probability that the randomly chosen coin is gold, given that it is small, is 4/5 or 0.8 when expressed as a decimal.

To find the probability that the randomly chosen coin is gold, given that it is small, we need to determine the number of small gold coins and the total number of small coins.

From the given information, Marco has 12 small gold coins and 3 small silver coins, making a total of 12 + 3 = 15 small coins.

The probability that the coin is gold, given that it is small, can be calculated as the ratio of the number of small gold coins to the total number of small coins:

P(Gold|Small) = Number of Small Gold Coins / Total Number of Small Coins

P(Gold|Small) = 12 / 15

Simplifying the fraction, we have:

P(Gold|Small) = 4 / 5

Therefore, the probability that the randomly chosen coin is gold, given that it is small, is 4/5 or 0.8 when expressed as a decimal.

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Answer:

1661.06 cm²

Step-by-step explanation:

From the question given above, the following data were obtained:

Radius (r) = 11.5 cm

Size of synthetic leather needed =?

To know how many square centimetres of synthetic leather needed to cover the ball, we shall determine the area of the ball. This can be obtained as follow:

Radius (r) = 11.5 cm

Pi (π) = 3.14

Area of ball =?

The shape of a ball is spherical in nature. Thus, we shall apply the formula for calculating the area of a sphere. This is illustrated below:

A = 4πr²

A = 4 × 3.14 × 11.5²

A = 4× 3.14 × 132.25

A = 1661.06 cm²

Thus, 1661.06 cm² of synthetic leather needed to cover the ball.

Answer: Your not alone!

The length of the zip wire is approximately 25.42 meters.

To calculate the length of the zip wire, we can use trigonometry and the given information about the angle and the distance between the two posts.

Given:

Distance between the two posts: 25m

Angle of the zip wire to the horizontal: 10°

We can use the trigonometric function cosine (cos) to find the length of the zip wire. Cosine relates the adjacent side to the hypotenuse of a right triangle.

In this case, the adjacent side is the distance between the two posts (25m) and the hypotenuse is the length of the zip wire that we want to calculate.

Using the cosine function:

cos(angle) = adjacent/hypotenuse

cos(10°) = 25m/hypotenuse

To find the hypotenuse (length of the zip wire), we can rearrange the equation:

hypotenuse = 25m / cos(10°)

Using a calculator or trigonometric tables, we can find the value of cos(10°) to be approximately 0.9848.

Therefore, the length of the zip wire is:

hypotenuse = 25m / 0.9848 ≈ 25.42m

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Answer:

Step-by-step explanation:

Multiples of 5 5 , 10 , 15 , 20 , 25 , 30 , 35 , 40 , 45 , 50 , 55 , 60

Multiples of 6 6, 12, 18 , 24 , 30, 36 , 42 , 48, 54, 60

Common Multiples of 5 and 6 30 and 60

Answer:

Step-by-step explanation:

\(\dfrac{5*2}{6*2}= \dfrac{10}{12}\\\\ \dfrac{5*3}{6*3}= \dfrac{15}{18}\\\\\\ \dfrac{5*4}{6*4}= \dfrac{20}{24}\)

Hello!

4^16

note that 16 = 4²

thus (16)^8 = (4²)^8 = 4^(2 × 8) = 4^16.

Answer:

22,400

Step-by-step explanation:

80,000 x .28

With a monthly repayment of $809.49, the total interest on the car loan will be $5,569.67.

We assume that there are monthly repayments and compounding interest on the car loan.

With periodic repayments and compounding interest, the total interest paid on the car loan will be as shown by the car loan calculator.

Car loan = $43,000

Down payment = $0

Fixed Annual Percentage Rate (APR) = 4.9%

Loan term = 5 years

Car Loan Calculator with monthly Repayment:

Payment = $809.49/month

Interest Paid =$5,569.67

Total Paid = $48,569.67

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Answer:

can we get a picture

Step-by-step explanation:

Answer:

5-gallon = 20 quarts

4 quarts is a gallon 4 x 5 = 20 quarts

The radius and the center of the circle are 4 units and (1,2), respectively

The center of the circle is on

y = 2x and x = 1

Substitute x = 1 in y = 2x

y = 2 * 1

Evaluate

y = 2

This means that the center is

Center = (1, 2)

Also, we have the point of tangency to be:

(x, y) = (1, 6)

This point and the center have the same x-coordinate.

So, the distance between this point and the center is

d = 6 - 2

d = 4

This represents the radius

Hence, the radius and the center of the circle are 4 units and (1,2), respectively

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The required probability is 0.970 (approx.) or 97/100 (in fraction).

Given that 69% of people in a large population have been vaccinated. We are required to determine the probability of at least one person being vaccinated if three people are randomly selected. Let's solve it using the complement rule.

The complement rule states that the probability of an event occurring is equal to 1 minus the probability of that event not occurring. That is, if A is an event, then P(A) = 1 - P(A').

We can solve the given problem using the complement rule as follows: Let P(A) be the probability of at least one person being vaccinated.

Then, the probability of no one being vaccinated is P(A') = (100 - 69) = 31%.

To find the probability of at least one person being vaccinated, we can subtract the probability of none of them being vaccinated from 1. That is, P(A) = 1 - P(A') = 1 - 0.31 × 0.31 × 0.31 = 1 - 0.029791 = 0.97021.

Hence, the probability of at least one person being vaccinated if three people are randomly selected is 0.97021 (rounded to 3 decimal places).

Therefore, the required probability is 0.970 (approx.) or 97/100 (in fraction).

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Answer:

The average speed for the four laps is 9 km/h.

Step-by-step explanation:

The average speed of the four laps can be calculated as follows:

\( \overline{v_{T}} = \frac{\overline{v_{1}} + \overline{v_{2}} + \overline{v_{3}} + \overline{v_{4}}}{4} \)

Where:

\(\overline{v_{1}}\): is the average speed for the first lap

\(\overline{v_{2}}\): is the average speed for the second lap

\(\overline{v_{3}}\): is the average speed for the third lap

\(\overline{v_{4}}\): is the average speed for the fourth lap

Hence, the average speed for the four laps is:  

\( \overline{v_{T}} = \frac{12 km/h + 10 km/h + 8 km/h + 6 km/h}{4} \)

\( \overline{v_{T}} = 9 km/h \)                                      

Therefore, the average speed for the four laps is 9 km/h.

I hope it helps you!

After answering the presented question, we may conclude that  the solution of the expressions are as follows.

In mathematics, you can multiply, divide, add, or subtract. An expression is constructed as follows: Number, expression, and mathematical operator A mathematical expression (such as addition, subtraction, multiplication, or division) is made up of numbers, variables, and functions. It is possible to contrast expressions and phrases. An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For example, the phrase 4m + 5 has the terms 4m and 5, as well as the provided expression's variable m, all separated by the arithmetic sign +.

the solution of the expressions are as follows -

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For the given median, there are 50 students who scored greater than 72.

What is median?

The median is a measure of central tendency in a set of numerical data. It is the value that separates the higher half of the data from the lower half when the data is arranged in order from least to greatest or greatest to least.

We are given that 99 6th graders took a test and the median score was 72. We want to find out how many students scored greater than 72.

Let the scores be denoted by S1, S2, ..., S99. We can sort these scores in order from least to greatest:

S1 ≤ S2 ≤ ... ≤ S99

Since the median score is 72, exactly half of the scores are above 72 and half are below 72. Thus, the 50th score in the sorted list is 72.

Since there are 99 scores in total, we can approximate the number of students who scored above 72 by dividing the total number of students by 2:

\($\frac{99}{2} = 49.5$$\)

This means that approximately 49.5 students scored above 72.

Since 0.5 rounds up to 1, we round 49.5 up to 50. Therefore, approximately 50 students scored greater than 72.

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The expected total dollar net operating Income for next year = $70,000

1) The contribution format income statement for the game last year, and the degree of operating leverage is computed below:

Contribution format income statement for the game last year Sales (15,000 × $20) = $300,000

Variable expenses (15,000 × $6) = $90,000

Contribution margin = $210,000

Fixed expenses = $182,000Net operating income = $28,000

Degree of operating leverage = Contribution margin / Net operating income= $210,000 / $28,000= 7.5 2)

The expected percentage increase in net operating income for next year:

The expected sales in next year = 18,000

games selling price per game = $20

Therefore, Total sales revenue = 18,000 × $20 = $360,000

Variable expenses = 18,000 × $6 = $108,000

Fixed expenses = $182,000

Expected net operating income = Total sales revenue – Variable expenses – Fixed expenses

= $360,000 – $108,000 – $182,000= $70,000

The expected percentage increase in net operating income = (Expected net operating income - Last year's net operating income) / Last year's net operating income*100= ($70,000 - $28,000) / $28,000*100= 150%

The expected total dollar net operating income for next year = $70,000

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Answer:

CAB is 37 degrees

Step-by-step explanation:

90 + 53 = 143

180 - 143 = 37

Answer:

c

Step-by-step explanation:

14-11=3

12-9=3

10-7=3

8-5=3

Answer:

A

Step-by-step explanation:

It isn’t proportional because when you graph the coordinates, it doesn’t pass the origin, so it isn’t equivalent. Therefore, making the answer A.

The number of different ways that the three positions can be filled is 504 ways.

From the information, there are 9 candidates for three positions at a restaraunt. Based on the data, one position is for a cook, the second position is for a food server and the third position is for a cashier.

Therefore, the number of ways will be:

= 9P3

= 9! / (9 - 3)!

= 9! / 6!

= 9 × 8 × 7

= 504

The number of ways is 504 ways.

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The distance in miles between the two electric scooters travelling in opposite direction is 2 miles.

An equation is a formula that proves the equality of two mathematical expressions in algebra and is the most commonly used formula. For example, in the expression 3x + 5 = 14 the two terms 3x + 5 and 14 are separated by the "equals" symbol.

What is distance?

The length or width in between two objects, points, lines, etc. Distance is the condition or fact that something or someone is physically apart.

Given 4x - 4 = 2x,

so 2x = 4

x = 2

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Answer:

The y-intercept of the equation is zero. It is possible that the line on the graph is horizontal.

Step-by-step explanation:

Answer:

The y-intercept of the equation is zero.

It is possible that the ine on the graph is horizontal

Step-by-step explanation:

The only thing we know for sure is that the function goes through the point (0,0).  The line y = 0 passes through (0,0), so it is possible that the line on the graph is horizontal.  Since x = 0 where y = 0, the y-intercept is also 0.  However, we have no way of knowing for sure what the slope of the equation is.

The value of df, when x = π/4 and dx = 1/24, is (-5π - 5√2)/(96√2).

To find the derivative of the function f(x) = -5cos(x) + xtan(x), we'll use the sum and product rules of differentiation. Let's start by finding df/dx.

Apply the product rule:

Let u(x) = -5cos(x) and v(x) = xtan(x).

Then, the product rule states that (uv)' = u'v + uv'.

Derivative of u(x):

u'(x) = d/dx[-5cos(x)] = -5 * d/dx[cos(x)] = 5sin(x) [Using the chain rule]

Derivative of v(x):

v'(x) = d/dx[xtan(x)] = x * d/dx[tan(x)] + tan(x) * d/dx[x] [Using the product rule]

= x * sec^2(x) + tan(x) [Using the derivative of tan(x) = sec^2(x)]

Applying the product rule:

(uv)' = (5sin(x))(xtan(x)) + (-5cos(x))(x * sec^2(x) + tan(x))

= 5xsin(x)tan(x) - 5xcos(x)sec^2(x) - 5cos(x)tan(x)

Simplify the expression:

df/dx = 5xsin(x)tan(x) - 5xcos(x)sec^2(x) - 5cos(x)tan(x)

Now, we need to evaluate df/dx at x = π/4 and dx = 1/24.

Substitute x = π/4 into the derivative expression:

df/dx = 5(π/4)sin(π/4)tan(π/4) - 5(π/4)cos(π/4)sec^2(π/4) - 5cos(π/4)tan(π/4)

Simplify the trigonometric values:

sin(π/4) = cos(π/4) = 1/√2

tan(π/4) = 1

sec(π/4) = √2

Substituting these values:

df/dx = 5(π/4)(1/√2)(1)(1) - 5(π/4)(1/√2)(√2)^2 - 5(1/√2)(1)

Simplifying further:

df/dx = 5(π/4)(1/√2) - 5(π/4)(1/√2)(2) - 5(1/√2)

= (5π/4√2) - (10π/4√2) - (5/√2)

= (5π - 10π - 5√2)/(4√2)

= (-5π - 5√2)/(4√2)

= (-5π - 5√2)/(4√2)

Now, to evaluate df/dx when dx = 1/24, we'll multiply the derivative by the given value:

df = (-5π - 5√2)/(4√2) * (1/24)

= (-5π - 5√2)/(96√2)

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The number of miles planned on Saturday is 19 milea

This means the sequence where the difference between one term and the next term is a constant.

In this case, the following information are illustrated:

Sunday: 1 miles

Monday: 4 miles

Tuesday: 7 miles

Wednesday : 10 miles

Thursday: 13 miles

Friday: 16 miles

As we can see there's a difference of three between them. This can be seen as:

= 4 miles - 1 mile

= 3 miles

Therefore, the number planned on Saturday will be:

= Friday + 3 miles

= 16 miles + 3 miles

= 19 miles

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The length of HI when  EF = 49.5, HG = 30, and EH = 24 and is parallel to EF is 27.5 unit.

Two triangles are comparable if the measurements of their corresponding sides are proportionate. The same is true if the lengths of two sides in one triangle are proportional to the lengths of the corresponding sides in another triangle and the included angles are congruent.

Given:

In Triangle GHI and GEF

<G= <G

<GHI = <GEF {Corresponding Angle}

<GIH = <GFE {Corresponding Angle}

So, by AA Similarity Criteria Triangle GHI and GEF are similar.

Then, GH / GE = HI/ EF

30/ 54 = HI/ 49.5

HI = 27.5

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The value of the expression 18 + 4(28) will be 130.

When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The expression is given below.

⇒ 18 + 4(28)

Simplify the expression, then the value of the expression will be

⇒ 18 + 4 x (28)

⇒ 18 + 4 x 28

⇒ 18 + 112

⇒ 130

Thus, the value of the expression 18 + 4(28) will be 130.

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