Identify the first term and common difference, then write
a recursive rule for each of the sequences below:
a) 1, -4,-9, -14, ....
b) 11, 23, 35, 47, ....

Jane sold approximately 7.8 cups of lemonade. Since she cannot sell a fractional number of cups of lemonade, we can round up to 8 cups.

Let x be the number of cups of lemonade Jane sold.

The total earnings she made from selling x cups of lemonade is:

Total earnings = price per cup * number of cups sold

Total earnings = $0.25 * x

The total cost of making x cups of lemonade is:

Total cost = cost per cup * number of cups sold

Total cost = $1.50 * x

Jane's profit is equal to her total earnings minus her total cost:

Profit = Total earnings - Total cost

Profit = $0.25x - $1.50x

Profit = -$1.25x

We know that Jane's earnings were $9.75, so we can set up the equation:

$9.75 = -$1.25x

To solve for x, we can divide both sides by -$1.25:

-$9.75 / -$1.25 = x

x = 7.8

Jane sold approximately 7.8 cups of lemonade. Since she cannot sell a fractional number of cups of lemonade, we can round up to 8 cups.

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Answer:

Step-by-step explanation:

5th term is 6 and the 7th term is 48, we know the nth term for a GP is  arn−1

 so let's substitute the given information in that formula for the nth term

ar3=6

  ar6=48

ar6ar3=486

The  a

and  a

cancelout hence we remain with  r3=8

 take a cube root on both sides and we end up having  r=2

Substitute the value of r in any given equation to get the value of a

ar3=6

a(2)3=6

8a=6

a=34

The formula for the nth term of this GP is given by  34(2n−1)

And when you substitute the value of n in the above formula of nth term you will get the following values; 3/4, 3/2, 3, 6…

The expressions are simplified to give;

7. 4n³(3n² + 4)

8. -3x(3x² - 4)

9. 5(k² - 8k + 2)

10. -10(6 + 6n² + 5n³)

11. 3(6n³ - 4n - 7)

12. 9(7n³ + 9n + 2)

Algebraic expressions are defined as mathematical expressions that are composed of variables, coefficients, terms, factors and constants.

These algebraic expressions are also made up of arithmetic operations, such as;

To factorize the expressions, we have;

12n⁵ + 16n³

Find the common term

4n³(3n² + 4)

-9x³ - 12x

find the common term

-3x(3x² - 4)

5k² - 40k + 10

find the common terms

5(k² - 8k + 2)

-60 + 60n² + 50n³

find the common term

-10(6 + 6n² + 5n³)

18n³ -12n - 21

find the common term

3(6n³ - 4n - 7)

63n³ + 81n + 18

Find the common term

9(7n³ + 9n + 2)

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The linear equatiοn that best represents the depth οf the bοne in feet is x-4.

A linear equatiοn is an algebraic equatiοn that represents a straight line οn a graph. It cοnsists οf variables raised tο the first pοwer, cοnstants, and cοefficients, and can be written in the fοrm y = mx + b, where m is the slοpe οf the line and b is the y-intercept.

Linear equatiοns can be used tο mοdel a wide range οf real-wοrld situatiοns, including the relatiοnship between twο variables that are directly prοpοrtiοnal tο each οther. They are fundamental tο the study οf algebra and are widely used in many fields, including physics, engineering, and ecοnοmics.

Nοw,

The equatiοn that represents the depth οf the bοne in feet is:

depth =x-4  (As Jamal's dοg buried a bοne 4 feet belοw the grοund)

where x is the distance in feet frοm the surface οf the grοund.

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Complete Question :

After the calculations, we know that the probability of "no blue" is (D) 75/100.

Science uses a figure called the probability of occurrence to quantify how likely an event is to occur.

It is written as a number between 0 and 1, or between 0% and 100%, when represented as a percentage.

The possibility of an event occurring increases as it gets higher.

The study of events that fit into a probability distribution is known as statistics.

So, we must determine the likelihood of drawing two white marbles in order to determine the probability of "no blue."

A white marble is 5/7 likely to be drawn in one draw.

The likelihood of getting two white marbles is therefore:

(5/7) * (5/7) = 25/49

Then, the probability of no blue will be:

25/49 = 25/100 = 25%

Which is 75/100.

Therefore, after the calculations, we know that the probability of "no blue" is (D) 75/100.

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Correct question:

An experiment is conducted with a bag of marbles containing 5 white and 2 blue marbles. The results of marble being drawn twice and replaced 100 times are shown in the table.

Outcome Frequency

White, White 27

White, Blue 22

Blue, Blue 18

Blue, White 33

Find P(no blue).

a. 25 over 100

b. 27 over 100

c 33 over 100

d. 75 over 100

its 21/100

Step-by-step explanation:

i did the test sorry if im too late

The rate of return on the account was 11.429% over the course of 15 years.

Interest rate is the percentage charged by a lender to a borrower for the use of money. It is the cost of borrowing money, expressed as a percentage of the amount borrowed. Interest rates are typically determined by the prevailing market conditions, the type of loan product being offered, the borrower's credit score, and the lender's risk tolerance. The higher the interest rate, the more expensive the loan will be for the borrower.

The rate at which the account earned interest can be calculated using the following formula:

Rate = (Interest Earned/Principal) * (1/Number of Years)

In this case, the rate is:

Rate = (2000/3500) * (1/15)

Rate = 0.11429 or 11.429%

This means that the account earned 11.429% in interest over the course of 15 years. This rate of return is relatively modest, as interest rates are often much higher than this. In fact, the current average rate of return for a 15-year CD is around 1.75%.

The reason why the rate of return is so low is likely due to the fact that the account was earning interest at a fixed rate. Fixed rate accounts typically offer lower interest rates than variable rate accounts, since the bank or financial institution is making a guarantee that the rate will not change. This makes them less risky for the investor, but also less profitable.

In conclusion, the rate of return on the account was 11.429% over the course of 15 years.

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this is "Repeated measures ANOVA, which is a statistical test used to analyze data from experiments in which the same participants are measured multiple times under different conditions.

A repeated measures ANOVA is a statistical test used to analyze data from experiments in which the same participants are measured multiple times under different conditions. This design is sometimes referred to as a "within-subjects design" because each participant is measured within the same group.

Here are the steps for conducting a repeated measures ANOVA:

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The probability that at most 70 switches fail during the first year is low, at around 1.3%.

The problem involves the use of the exponential distribution to model the lifetime of a certain type of electrical switch. Specifically, we are given that the average life of these switches is beta = 3.

The exponential distribution is often used to model the time between occurrences of a certain event, such as the failure of a component. In this case, we can use it to model the time between failures of the electrical switches.

To answer the question, we need to find the probability that at most 70 switches fail during the first year. Let X be the number of switches that fail during the first year. We know that X follows a Poisson distribution with parameter lambda = (1/3)*300 = 100.

This is because the expected number of failures per year for each switch is 1/3 (since the average life is 3 years), and there are 300 switches installed.

Therefore, we can use the Poisson distribution to calculate the probability that at most 70 switches fail during the first year:

P(X <= 70) = e^(-100) * (100^0/0!) + e^(-100) * (100^1/1!) + ... + e^(-100) * (100^70/70!)

This can be calculated using a calculator or software such as Excel. The answer is approximately 0.013, or 1.3%. This suggests that the switches are fairly reliable, and that it is unlikely that a large number of them will fail in a short period of time.

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Answer:

40 ft

Step-by-step explanation:

the starting point is like the origin on the coordinate grid.

let's say forward for your friends is the positive y direction, and right for your friend is positive x direction.

the end point coordinates of your friend are then

(15, 20)

forward for you (facing in the other direction) is the the negative y direction. and going right for you is then actually going in the negative x direction.

your end point is therefore

(-9, -12)

the distance between both points is then per Pythagoras (and the derived distance formula) :

distance² = (x1 - x2)² + (y1 - y2)² =

= (15 - -9)² + (20 - -12)² = 24² + 32² =

= 576 + 1024 = 1600

distance = 40 ft

The probability of drawing a face card followed by condition of drawing non face card is equal to 18% ( approximately).

In a standard deck of cards,

There are 12 face cards 4 jacks, 4 queens, and 4 kings

And 40 non-face cards 10 numbered cards each for the 4 suits.

The probability of drawing a face card on the first draw is

=  12/52

= 3/13.

Assuming a face card was drawn on the first draw,

There are now 51 cards remaining in the deck.

Of which 40 are non-face cards.

Probability of drawing a non-face card on the second draw is

= 40/51.

Probability of both events happening drawing a face card followed by a non-face card

= Multiply the probabilities of the individual events

= (3/13) x (40/51)

= 120/663

=  0.181approximately  

= 18% (rounded to the nearest whole number).

Therefore,  the probability of drawing a face card followed by drawing a non-face card in a standard deck of cards is approximately 18%.

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If some students checked 6 bags of Doritos marked with a "net-weight" of 28.3 grams, then these data satisfies all the three assumptions for inference (random condition, independent condition and normal condition.

To determine whether weight of bag satisfy the assumptions for inference, we need to consider the assumptions of statistical inference.

The assumptions are :

(i) Random Sampling: The data should be collected from a random sample, where each bag of Doritos has an equal chance of being selected.

This assumption is satisfied, because we assume that the "6-bags" are randomly selected.

(ii) Independence: The data points should be independent of each other, meaning that the weight of one bag of Doritos should not depend on the weight of another bag.

This assumption is satisfied as, bags were weighed separately and their weights were recorded without any influence from other bags.

(iii) Normality: The distribution of the data should be approximately normal.

This assumption is also satisfied , because histogram shows that there are "No-Outliers" and normal "quantile-plot" is linear.

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The tax on the belt buckle is $1.56

What is Rate?

In general terms, a rate is a measure of the relationship between two quantities that are measured in different units. A rate expresses how much of one thing there is per unit of another thing. For example, miles per hour is a rate that expresses how many miles are traveled in one hour.

To calculate the tax on the belt buckle, we need to multiply the price of the belt buckle by the sales tax rate:

Tax = Price x Tax rate

In this case, the price of the belt buckle is $25 and the sales tax rate is 6.25%. To convert the tax rate from a percentage to a decimal, we need to divide it by 100:

Tax rate = 6.25% ÷ 100 = 0.0625

Now we can calculate the tax on the belt buckle:

Tax = Price x Tax rate

= $25 x 0.0625

= $1.56

Therefore, the tax on the belt buckle is $1.56. The total cost of the belt buckle including tax would be $25 + $1.56 = $26.56.

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Rotating EF 90° clockwise would produce the same image as rotating CD

270° counterclockwise

There are different ways of transformations such as:

Rotation

Dilation

Translation

Reflection

Now, the coordinates are given as:

EF = E(4, -5) and F(3, -2)

Now, rotation by 90° clockwise would produce:

E'(-5, -4) and F(-2, -3)

This is a rotation rule of (x, y) → (y, -x)

Thus, if CD has the coordinates C(-4, 5) and D(-3, 2), then the rotation by 270° counterclockwise would produce:

C'(5, 4) and D(2, 3)

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Answer: 1. 48.356 2. 75.3982236862

Step-by-step explanation:

Radias*2 pi

The answer is B, because a function has each input value paired to no more than 1 output value. Since 1, 0, and 5 are already in the sets of ordered pairs given, none of those can be the x value.

The value of the given trigonometric ratio: Cos A = 4/5,  tan C = 4/3 for the given right angle triangle ABC.

A collection of mathematical functions that relate the angles and sides of a right triangle are known as the trigonometric functions.

Cosine (cos): The ratio of the length of the adjacent side to the length of the hypotenuse is known as the cosine of an angle in a right triangle.

⇒ Cos(θ) = adjacent/hypotenuse

⇒ Cos A = AB/AC

⇒ Cos A = 32/40

⇒ Cos A = 4/5

Similarly;

Tan tangent: The ratio of the length of the side opposite to the length of the side adjacent to is what is referred to as the tangent of an angle in a right triangle.

⇒ tan(θ) = opposite/adjacent

⇒ tan C = AB/BC

⇒ tan C = 32/24

⇒ tan C = 4/3

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To graph the points, plot each point on a coordinate plane with the x-coordinate on the horizontal axis and the y-coordinate on the vertical axis. See the attached graph.

To find the slope of each segment, use the formula:

slope = (change in y) / (change in x)

FG: slope = (2 - (-2)) / (-2 - (-4)) = 1

GH: slope = (3 - 2) / (4 - (-2)) = 1/2

HJ: slope = (-1 - 3) / (2 - 4) = -2

JF: slope = (-1 - (-2)) / (2 - (-4)) = 1/2

The sides FG and JF have the same slope of 1/2. The sides GH and HJ have opposite reciprocal slopes of 1/2 and -2, respectively.

None of the sides have the same length.

To find the perimeter of the polygon, add up the lengths of the sides:

FG: distance = √((2 - (-2))^2 + (-2 - (-4))^2) = 4.47

GH: distance = √((3 - 2)^2 + (4 - (-2))^2) = 6.08

HJ: distance = √((-1 - 3)^2 + (2 - 4)^2) = 4.47

JF: distance = √((-1 - (-2))^2 + (2 - (-4))^2) = 6.08

Perimeter = FG + GH + HJ + JF = 4.47 + 6.08 + 4.47 + 6.08 = 21.10

Therefore, the perimeter of the polygon is 21.10 units.

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Answer:

To find the volume of a rectangular prism, we need to multiply its length, width, and height.

The given dimensions are:

Length = 9 yd

Width = Pyd (it's unclear what this means, so let's assume it's a typo and the intended value is 3 yd or 4 yd)

Height = 4 yd

Assuming the width is 3 yd, the volume of the rectangular prism is:

Volume = Length x Width x Height

Volume = 9 yd x 3 yd x 4 yd

Volume = 108 cubic yards

Assuming the width is 4 yd, the volume of the rectangular prism is

Volume = Length x Width x Height

Volume = 9 yd x 4 yd x 4 yd

Volume = 144 cubic yards

Therefore, the volume of the rectangular prism is either 108 cubic yards or 144 cubic yards, depending on the intended value of the width.

Answer:

use desmos graphing calculator it helps alot

Step-by-step explanation:

x^{2}-x-6=0 has two zeros/solutions

x^{2}-x-6=0 has 1 zero/solution

x^{2}-x-6=0 has no zero/solution

The best interpretation of the results would depend on the specific statistical analysis used and the results obtained.

The results indicated a statistically significant difference between the mean anticipated study times for men and women, the interpretation would be that men and women have different average anticipated study times for the introduction to statistics course.

Conversely, if there was no statistically significant difference, the interpretation would be that there is no evidence to suggest that men and women have different average anticipated study times for the course.

As the Minitab results are not provided in the question, I cannot interpret them.

Provide a general interpretation of the statistical analysis based on the information given.

The instructor was interested in seeing if there was a difference in the average amount of time that men and women anticipated studying for an introduction to statistics course in the summer.

To test this hypothesis, a group of men and women were randomly selected from the University of Florida.

The statistical analysis may have involved using a t-test or a similar method to compare the mean anticipated study times between men and women.

The results of this analysis would provide information on whether there is a statistically significant difference between the mean anticipated study times for men and women.

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A student willing to participate in a debate competition is required to fill out a registration form.

Form filling in two types of data i.e.,

Quantitative data is data that can be counted or measured in numerical values. The two main types of quantitative data are discrete data and continuous data. Height in feet, age in years, and weight in pounds are examples of quantitative data. Qualitative data is descriptive data that is not expressed numerically.

Categorical data is a collection of information that is divided into groups. i.e., if an organization or agency is trying to get a biodata of its employees, the resulting data is referred to as categorical.

a. What is your date of birth?

Quantitative.

b. Have you participated in any debate competition previously?

Categorical.

c. If yes, how many debate competitions have you participated so far?

Quantitative.

d. Have you won any of the competitions?

Categorical.

e. If yes, how many have you won?

Quantitative.

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The given question is incomplete, complete question is:

A student willing to participate in a debate competition required to fill a registration form. State

whether each of the following information about the participant provides categorical or quantitative

data.

a. What is your date of birth?

b. Have you participated in any debate competition previously?

c. If yes, how many debate competitions have you participated so far?

d. Have you won any of the competitions?

e. If yes, how many have you won?

Please write answer in two parts. A. Main answer (correctly paraphrased, addressing all aspect of the question) B. Explanation (Step-by-step explanation)

Among these expressions, (4+1)x(12-6) has a total value of 30.

To determine which expression has a total value of 30, let's evaluate each expression one by one:

4+1x12-6

Following the order of operations (PEMDAS/BODMAS), we first do the multiplication:

4 + (1x12) - 6 = 4 + 12 - 6

Now, we do the addition and subtraction from left to right:

16 - 6 = 10

(4+1x12-6)

This expression has the same operations as the first one, so its total value is also 10.

(4+1)x(12-6)

First, we evaluate the expressions within the parentheses:

(5)x(6)

Now, we do the multiplication:

5 x 6 = 30

(4+1)x12-6

First, we evaluate the expression within the parentheses:

(5)x12 - 6

Now, we do the multiplication:

60 - 6

Finally, we do the subtraction:

54
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All the possible angle measures are given as follows:

25º and 35º.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

On the first quadrant, we have that:

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A circle is a closed curve with all points equidistant from a fixed point called the center, characterized by a radius and diameter.

A circle is a two-dimensional geometric shape consisting of all points in a plane that are equidistant from a fixed point called the center. In other words, a circle is a closed curve that forms a perfect, continuous loop, where every point on the curve is the same distance from the center.

The distance between the center of the circle and any point on the curve is called the radius, which is denoted by the letter 'r'. The diameter of a circle is the distance across the circle passing through the center and is twice the length of the radius.

Circles have many important properties and are fundamental to many areas of mathematics, science, and engineering. They are often used in geometry to model real-world phenomena and are used in a wide range of applications, from constructing wheels to designing satellites.

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I have solved the question in general, as the given question is incomplete.

The complete question is:

What is circle?

The approximate p-value is 5.1250%.

P-value is the probability of obtaining a test statistic as or more extreme than what was actually observed, given that the null hypothesis is true.

Two-sided significance test, with a significance level of 2%. you then randomly sample 420 items from the production line, and find that 22 of the items are defective.

The approximate p-value for this two-sided significance test, with a significance level of 2%, is 5.1250%.

This is the probability of observing 22 or more defective items given that the true rate is 3.2%.

This was calculated using a binomial test, which takes into account the sample size and the expected rate of defects.

This p-value indicates whether or not the observed rate of defects is significantly different from the expected rate.

In this case, the p-value is the probability of observing 22 or more defective items given that the true rate is 3.2%.

This can be calculated using a binomial test.

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7.071 is the length, in inches, of each side of the square.

What is meant by "square"?

The term "square" refers to a regular quadrilateral having four equal-length sides and angles. Angles in the square are at right angles or are separated by 90 degrees. The diagonals of the square are also equal and meet at a 90-degree angle.

                             Having equal length sides and right angles on all four, a square is a quadrilateral. Due to the fact that a square's sides are all the same length, it may be distinguished from other types of rectangles. Every square consequently becomes a rectangle since it is a quadrilateral with right angles at all four of its angles.

If the side od=f a square is s, the diagonal is  s√2

  This comes from Pythagoras as diagonal is

   √s² + s²  = √2s² = s√2

 as such s√2 = 10

           s = 10/√2

        = 10 * √2/√2  * √2

         = 5√2

    5 * 1.4142  = 7.071

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Answer: False

Step-by-step explanation:

1/7 x 1/7 = 1/49 x 1/7 = 1/343

Answer:

1. 92

2. Jason is 21

Bruce is 35

sorry but I will have to focus more on the remaining questions. Hope this helps.

Answer:

6.75 ounces of Skittles

Step-by-step explanation:

If there are 4.5 bags of Skittles left and each bag weighs 1.5 ounces, then the total amount of Skittles in ounces can be found by multiplying the number of bags by the weight per bag:

4.5 bags x 1.5 ounces/bag = 6.75 ounces

Therefore, there are 6.75 ounces of Skittles at the candy shop.

6.75 ounces

Step-by-step explanation:

1.5 x 4.5 = 6.75 ounces

Answer:

50 inches

Step-by-step explanation:

Using the Pythagorean theorem, we can find the length of the diagonal of the TV:

diagonal^2 = height^2 + width^2

diagonal^2 = 30^2 + 40^2

diagonal^2 = 900 + 1600

diagonal^2 = 2500

Taking the square root of both sides, we get:

diagonal = sqrt(2500)

diagonal = 50

Therefore, the length of the diagonal of the TV is 50 inches.