Write an explicit rule for the sequence -20, -13.-6, 1,8

The probability that a randomly selected customer who is on plan B uses the phone most often to text is; 13/23

We are given that;

The data by payment plans are;

Plan A: 27 texts, 21 Internet

Plan B: 13 texts, 10 Internet

Now, the probability is defined as the ratio of the sum of all observations and the total number of observations.

The total number of observations for plan B is; 13 +10 = 23

The number of customers that are on payment plan B = 23 customers are on payment plan B.

The number of customers that are on plan B text is; 13

Thus, the probability that a randomly selected customer who is on plan B uses the phone most often to text is;

Probability = 13/23

The probability that a randomly selected customer who is on plan B uses the phone most often to text is 13/23.

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The equation for the proportion, p, of consumers who shop with coupons is: p = C/N where C is the number of consumers who use coupons and N is the total number of consumers asked.

An equation is a mathematical statement that indicates the equality of two expressions. It consists of two expressions separated by an equal sign (=). The expression on the left side of the equal sign is equivalent to the expression on the right side. Equations can have one or more variables, which are usually represented by letters such as x, y, or z. The goal in solving an equation is to determine the value(s) of the variable(s) that make the equation true. This involves manipulating the expressions on both sides of the equal sign using algebraic operations such as addition, subtraction, multiplication, and division, to isolate the variable on one side of the equation. Equations are used in many areas of mathematics and science to represent relationships between variables and to solve problems. They are also used in various fields such as engineering, physics, and economics to model real-world situations and make predictions based on mathematical analysis.

Here,

This equation represents the ratio of the number of consumers who use coupons to the total number of consumers. It is commonly used in statistics and market research to measure the prevalence of a certain behavior or preference among a population. By calculating the proportion of consumers who use coupons, businesses can make informed decisions about their pricing strategies, promotions, and advertising campaigns.

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Answer:

The answer is below

Step-by-step explanation:

The empirical rules states that for a normal distribution, 68% of the data falls within one standard deviation from the mean, 95% falls within two standard deviation from the mean and 99.7% falls within three standard deviations from the mean.

Given that:

mean (μ) = 71 inches, standard deviation (σ) = 4.3 inches

One standard deviation = μ ± σ = 71 ± 4.3 = (66.7, 75.3)

Two standard deviation = μ ± 2σ = 71 ± 2*4.3 = (62.4, 79.6)

Three standard deviation = μ ± 3σ = 71 ± 3*4.3 = (58.1, 83.9)

The graph is attached

By proportion formula and Pythagorean theorem, the length of line segment AB is equal to 8 units.

Herein we find a geometric system formed by two similar right triangles, then we can determine the length of side BD by following proportion formula:

BD / AD = CD / BD

BD² = AD · CD

BD = √(AD · CD)

And the length of the line segment AB can be determined by Pythagorean theorem:

AB = √(BD² + AD²)

If we know that AD = 4 and CD = 12, then the length of the line segment AB is:

BD = √(4 · 12)

BD = √48

BD = 4√3

AB = √[(4√3)² + 4²]

AB = 8

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Answer:

3x+6

Step-by-step explanation:

(x+2)3

3(x)+3(2)

3x+6

The contractor should lower the ramp by approximately 4.62° to meet safety regulations.

We have,

To determine the angle created by the bottom of the ramp and the ground, we can use the trigonometric function of sine.

In the given triangle, the height is 6 ft and the base is 16 ft.

The angle we want to find is opposite the height (let's call it θ).

The sine of an angle is defined as the ratio of the opposite side to the hypotenuse.

sin(θ) = opposite/hypotenuse

sin(θ) = 6/16

sin(θ) = 0.375

To find the angle θ, we can take the inverse sine (also known as arcsine) of 0.375:

θ = arcsin(0.375)

θ ≈ 22.62°

To meet safety regulations, the angle should be no more than 18°. Therefore, the contractor needs to lower the ramp by:

22.62° - 18° ≈ 4.62°

Thus,

The contractor should lower the ramp by approximately 4.62° to meet safety regulations.

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The sum of measure of exterior angles of a regular polygon is always 360 degree.

Determine the measure of a exterior angle for a regular nonagon.

Determine the measure of exterior angle for a regular pentagon.

The angle RST is equal to sum of exterior angle of nonagon and exterior angle of pentagon. So,

Thus measure of angle RST is 112 degree.

We are given the equation of circle (x - 7)² + (y - 3)² = 64² , but let's recall the standard equation of circle i.e (x - h)² + (y - k)² = r², where (h, k) is the centre of the circle and r being the radius ;

So, consider the equation of circle ;

\({:\implies \quad \sf (x-7)^{2}+(y-4)^{2}=(64)^{2}}\)

On comparing this equation with the standard equation of Circle, we will get, centre and radius as follows

how many 2/3 are in 9/8?

or another way to put it will be

how many times does 2/3 go into 9/8?

well, is simply a division.

\(\cfrac{9}{8}\div \cfrac{2}{3}\implies \cfrac{9}{8}\cdot \cfrac{3}{2}\)

Answer:

i think the fourth one is equvilent ratio

Step-by-step explanation:

The calculated area of the composite figure is 85 cm².

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

The composite figure (see attachment)

Where, we have

Rectangle:

Area = length × width.

Therefore, the area of the rectangle is 10 cm × 6 cm = 60 cm².

Triangle:

Area = (1/2) × base × height.

Therefore, the area of the triangle is (1/2) × 5 cm × 10 cm = 25 cm².

To find the total area of the composite figure, we add the areas of the rectangle and the triangle:

Total Area = Area of Rectangle + Area of Triangle

= 60 cm² + 25 cm²

= 85 cm².

Therefore, the area of the composite figure is 85 cm².

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The solution to the system of equations is (3, 2)

Give the system of equation below

y = -x + 5

y=x-1

Equate both expression

-x+5 =x - 1

Equate

-x - x = -1 - 5

-2x = -6

x = 3

Since y = x - 1

y = 3 - 1

y = 2

Hence the solution to the system of equations is (3, 2)

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The linear speed of the bicycle is 20891.59 inches / min

The bike moving in 19.78 mph

As per the given data:

A bicycle with 20-in.-diameter wheels

Determine the speed that needs to be determined either angular or linear. Determine the given speed and radius.

Determining the linear speed is the task at hand. The indicated angular speed is 190 rpm.

To find the linear speed when the angular speed and the radius of the circular object are given, k revolutions per minute \($ =\frac{k \text { revolutions }}{1 \text { minute }} \times \frac{2 \pi}{1 \text { revolution }} \\\)

\($=\frac{2 \pi k}{\text { minute }}\)

For every cycle of the 7-inch sprocket, the 4-inch goes around

\($\frac{7}{4}$\) = 1.75 times.

Therefore 190 × 1.75+ π × 20 = 20891.59 inches / min

Therefore the linear speed of the bicycle is 20891.59 inches / min

Now, determine how fast the bike is moving in mph.

\($\frac{20891.59}{12} \times \frac{60}{5280}$\)

= 19.78 mph

Bike moving in 19.78 mph.

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A bicycle with 20-in.-diameter wheels has its gears set so that the chain has a 7-in. radius on the front sprocket and 4-in. radius on the rear sprocket. the cyclist pedals at 190 rpm.

Find the linear speed of the bicycle (correct to at least two decimal places) in/min

How fast is the bike moving in mph (to two decimal places)?

Answer:

decrease

Step-by-step explanation:

The impact on Carns Company's income from eliminating the Small Tools Division would be a decrease of $1,209,000.

To determine the impact on Carns Company's income from eliminating the Small Tools Division, we need to consider the avoidable costs associated with the division.

The avoidable costs include all of the variable costs of the division and a portion of the fixed costs that are specifically related to the Small Tools Division. In this case, the variable costs of the division are $1,295,000, and $119,000 of the fixed costs are avoidable.

To calculate the impact on income, we subtract the avoidable costs from the loss reported by the division:

Impact on income = Loss - Avoidable costs

Impact on income = $205,000 - ($1,295,000 + $119,000)

Impact on income = $205,000 - $1,414,000

Impact on income = -$1,209,000

The negative sign indicates a decrease in income.

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The number of times the spinner lands on a shaded section are 8 times.

What is the probability?

Probability is the branch of mathematics concerned with numerical descriptions of the likelihood of an event occurring or of a proposition being true.

We have,

2 Shaded sections are on a spinner,

8 unshaded sections are on a spinner,

10 total sections are on a spinner,

Therefore,

The probability of the spinner to land on a shaded section:

P = 2 ÷ 10 = 1 ÷ 5

consider x, the number of times the spinner lands on a shaded section.

If the spinner were spun 40 times:

so,   \(\frac{x}{40} = \frac{1}{5}\)

By cross multiplying we get,

5x = 40

x = 8

Hence, the number of times the spinner lands on a shaded section are 8 times.

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Answer:

f(1)= 3×1 + 2 = 5

....

.....

....

f(5)= 3×5 + 2 = 17

Answer:

f(5) = 17

Step-by-step explanation:

Given: f(x) = 3x + 2

We are asked to find the value of the function when the value of x is 5

Substitute 5 as the value of x in the function:

⇒ f(x) = 3x + 2

⇒ f(5) = 3(5) + 2 [multiply]

⇒ f(5) = 15 + 2 [add]

⇒ f(5) = 17

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Answer:

go look at my first question

Step-by-step explanation:

The value of common ration r is 4.

Given that,

a₁ = 9

a₅ = 2304

We know that,

A geometric sequence  is a sequence in which each term (except from the first term) is multiplied by a fixed amount to obtain the following term.

The following term in the geometric sequence must be obtained by multiplying it by a set term (referred to as the common ratio), and the previous term in the sequence can be obtained by dividing it by the same common ratio.

Since we know that nth term of GP is,

\(a_{n}\) = a₁ \(r^{n-1}\)

Therefore,

a₅ = a₁ \(r^{4}\)  = 2304

⇒  9 x \(r^{4}\)  = 2304

⇒        \(r^{4}\)  = 256

⇒           r = 4

Hence, r = 4

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(A) The data provided is modeling a geometric sequence, (B) the recursive formula is T(5) = T(4) * 2., and (C) the explicit formula T(n) = T(1) * r^(n-1).

What is the explicit formula?

The explicit formula for an arithmetic sequence is an = a + (n - 1)d, and any term of the sequence can be computed, without knowing the other terms of the sequence. In general, the explicit formula is the nth term of arithmetic, geometric, or harmonic sequence.

A. The data provided is modeling a geometric sequence.

This is because the common ratio between consecutive terms is a constant value, specifically in this case is the ratio between consecutive terms is multiplied by 2.

B. To find the time Aurora will complete station 5 using a recursive formula,

we can use the formula T(n) = T(n-1) * r,

where T(n) is the time at the nth station, T(n-1) is the time at the (n-1)th station, and r is the common ratio.

In this case T(5) = T(4) * 2

and T(4) = 24 (from the data provided)

Therefore, T(5) = 24 * 2 = 48 minutes

C. To find the time Aurora will complete the 9th station using an explicit formula,

we can use the formula T(n) = T(1) * r^(n-1)

In this case, T(9) = T(1) * 2^(9-1)

and T(1) = 3 (from the data provided)

Therefore, T(9) = 3 * 2^8 = 3 * 256 = 768 minutes

The explicit formula assumes that the first term of the sequence is T(1) and the common ratio of the consecutive term is r.

Hence, (A) The data provided is modeling a geometric sequence, (B) the recursive formula is T(5) = T(4) * 2., and (C) the explicit formula T(n) = T(1) * r^(n-1).

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The graph that shows the following system of equations and its solution is graph number C

A graph is the graphical representation of equations on a graph sheet

The given equations are

-4x-3y=4

4x-y=-4 Solving the equations

In equation 1

When x = 0

-3y = 4

y=-4/3                  (0, -4/3)

When y = 0

-4x = 4

x= -1            (-1, 0)

In equation 2 when x = 0

-y = -y = 4             (0, 4)

When y = 0

4x=-4 x=-1              (-1, 0)

When these coordinates are used to plot the graph, graph number is is obtained.

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Answer:

Step-by-step explanation:

Let total mass be x

(3/4)*x=15

on solving

x=20

now,

mass of 2/5 of piece of metal is-

=> (2/5)*20

=> 8

Ans- 8kg

A Ferris wheel with a diameter of 10 m and makes one complete revolution every 80 seconds. Assuming that at time t = 0, the Ferris Wheel is at its lowest height above the ground of 2 m, the cosine equation of the graph drawn is, y = 5 cos [( π/40)(x - (π/2))] + 3.  Here, amplitude of the graph is 5, value of k is  π/40, d is π/2 and c is 3.

Developing the Equation of a Cosine Graph

The given information constitutes the following,

Diameter = 10 m

⇒ Radius, r = 5 m

Time, t = 80 s

Height above the ground, h = 2 m

Thus, we can infer that,

Amplitude, A = 5 m

Period, T = 80 s

Minimum height = 2 m

The cosine function is given as,

a cos [k(x − d)] + c

Here, A is amplitude

B is cycles from 0 to 2π and thus period = 2π/k

d is horizontal shift

c is vertical shift (displacement)

Now, 2π/k = 80

⇒ k = 2π/80 = π/40

The value of c is given as,

c = Amplitude - Minimum height

c = 5 - 2

c = 3

For a shift to the left by π/2 gives, we have,

d = π/2

Thus, the desired equation of the drawn cosine graph is,

y = 5 cos [( π/40)(x - (π/2))] + 3

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Answer:

Part A: 9.75x > 195

Part B: x > 20

Step-by-step explanation:

Let's say Mark works for x hours. For each hour he works, 9.75 dollars are added to Mark's salary. Therefore, for 1 hour, he gets $9.75, for 2 hours, he gets $9.75 + $9.75 = $9.75 * 2 = $19.50, and for x hours, he gets $9.75 * x as his salary.

We want his salary to be more than $195, so we have $9.75 * x (his salary) > $195, which can be written as 9.75x > 195

divide both sides by 9.75 to solve for x

x > 20

Hi there!

\(\large\boxed{UV = 13}\)

Since U and V are midpoints of the legs, then UV is the average of both WX and ZY.

Therefore:

(ZY + WX)/2 = UV

Substitute in the given expressions:

[(6x + 5) + (x + 7)]/2 = 8x - 3

Simplify by combining like terms:

(7x + 12)/2 = 8x - 3

Multiply both sides by 2:

7x + 12 = 16x - 6

Subtract 7x from both sides and add 6 to both sides:

18 = 9x

Divide both sides by 9:

18/9 = x

x = 2.

Plug in this value of x into the equation for UV:

8(2) - 3 = 16 - 3 = 13.

According to the internet it states, The median of a triangle is a line segment joining the vertex of the triangle to the mid-point of its opposite side.

It bisects the opposite side, dividing it into two equal parts.

The median of a triangle further divides the triangle into two triangles having the same area

Answer: 2/3 , -1

Step-by-step explanation: