The function y=f(x) is graphed below. What is the average rate of change of the function f(x) on the interval 1≤x≤6?

The final answer is that the original price of one jump rope before the sale was $8.29.

Let's start by using algebra to solve this problem.

If the original price of one jump rope is "x", then the sale price is "x - 1.90". We can set up an equation to relate the sale price and the original price:

2(x - 1.90) = 12.78

Simplifying and solving for "x", we get:

2x - 3.80 = 12.78

2x = 16.58

x = 8.29

Therefore, the original price of one jump rope was $8.29.

To check our answer, we can verify that the sale price of one jump rope is $6.39 ($8.29 - $1.90), and that two jump ropes at this price cost $12.78.

To know more about algebra, visit:
brainly.com/question/29131718
#SPJ11

The wavelength of yellow light, approximately 0.00002 inches, can be best approximated as a power of 10. Among the given options, the number that represents this length most accurately is 2 x 10^-5.

The given wavelength of yellow light is 0.00002 inches. To express this length as a power of 10, we need to move the decimal point to obtain a number between 1 and 10.
In this case, we move the decimal point five places to the left, resulting in 0.00002 becoming 2 x 10^-5. The exponent of -5 indicates that the decimal point is shifted five places to the left, aligning with the original decimal value of 0.00002 inches.
Option C, 2 x 10^-5, is the closest approximation to the given wavelength. None of the other options match the given value. Option A, 2 x 10^5, is too large, option B, 2 x 10^-4, is too small, and option D, -2 x 10^5, has a negative sign which is not applicable in this context.
Therefore, the best approximation of the wavelength of yellow light, 0.00002 inches, as a power of 10 is represented by option C, 2 x 10^-5.

Learn more about approximated here
https://brainly.com/question/16315366



#SPJ11

a) Sabrina can type 2 ⅖ pages per hour. To find out how many pages she can type in 8 hours and 20 minutes, we need to convert the time to hours.

b) To convert 8 hours and 20 minutes to hours, we divide the minutes by 60 and add the result to the number of hours. Then, we multiply the total number of hours by Sabrina's typing rate of 2 ⅖ pages per hour to find the total number of pages she can type.

a) Sabrina's typing rate is given as 2 ⅖ pages per hour. This means she can type 2 and two-fifths of a page in one hour.

b) To calculate the total number of pages Sabrina can type in 8 hours and 20 minutes, we convert the time to hours. Since there are 60 minutes in an hour, we divide the minutes by 60 to convert them to hours. In this case, 20 minutes divided by 60 equals 1/3 hours. Adding this to the 8 hours gives us a total of 8 and 1/3 hours.

Next, we multiply the total number of hours (8 1/3) by Sabrina's typing rate (2 ⅖ pages per hour). To multiply fractions, we multiply the numerators and denominators separately. The result is (25/3) * (12/5) = 300/15 = 20 pages.

To learn more about minutes

brainly.com/question/32674197

#SPJ11

The three integers are 10, 12 and 14.

To find three integers that satisfy the given conditions, we can use the properties of range and mean.

Let's assume the three integers are x, y, and z.

Range is the difference between the largest and smallest values. In this case, the range is given as 7. Therefore, we can set up the equation:

max(x, y, z) - min(x, y, z) = 7.

Mean is the average of the values. The mean is given as 12. Therefore, we can set up the equation:

(x + y + z) / 3 = 12.

We also know that all three integers are less than 20.

Let's solve these equations simultaneously:

From the equation for the mean, we can rewrite it as:

x + y + z = 36.

Now, let's list all the possible combinations of three integers that satisfy the given conditions:

x = 9, y = 12, z = 15

x = 10, y = 12, z = 14

x = 11, y = 12, z = 13

Out of these combinations, only the second one satisfies the condition that all three integers are less than 20.

Therefore, the three integers that meet the given conditions are:

x = 10, y = 12, z = 14.

To learn more about integers here:

https://brainly.com/question/28879208

#SPJ4

a) A relative frequency interpretation of the probability of a double-yolk egg being 0.1 is that, in the long run or over a large number of eggs, approximately 10% of eggs will have double yolks.

b) If 5,000 eggs were randomly selected, we can estimate the number of double-yolk eggs we would expect to find by multiplying the probability of a double-yolk egg (0.1) by the total number of eggs (5,000).

Expected number of double-yolk eggs = 0.1 * 5,000 = 500 eggs.

a) The probability of a double-yolk egg being 0.1 can be interpreted as the relative frequency of finding double-yolk eggs over a large number of eggs. It means that if we were to select a significant number of eggs, approximately 10% of them would have double yolks. This interpretation is based on the assumption that the eggs are randomly selected and the probability remains constant.

b) To estimate the number of double-yolk eggs in a sample of 5,000 eggs, we can use the probability given in the article. By multiplying the probability of a double-yolk egg (0.1) by the total number of eggs (5,000), we can calculate the expected number of double-yolk eggs. In this case, the expected number would be 500 eggs. This means that, on average, we would expect to find 500 double-yolk eggs out of the 5,000 eggs randomly selected. It is important to note that this is an expected value based on probability, and the actual number of double-yolk eggs found may vary in any given sample.

To learn more about  probability

brainly.com/question/31828911

#SPJ11

Selena's tree is 6.6 centimeters taller than Julian's tree. This is equivalent to 2.64 inches.

To find out how many inches taller Selena's tree is than Julian's tree, we need to first calculate the difference in height between the two trees in centimeters. We do this by subtracting Julian's tree's height from Selena's tree's height:54.2 cm - 47.6 cm = 6.6 cm.

Next, we convert this difference to inches. We know that 1 cm is approximately equal to 0.4 inches. So, to convert centimeters to inches, we need to multiply by 0.4:6.6 cm × 0.4 in/cm = 2.64 in. Therefore, Selena's tree is 6.6 centimeters taller than Julian's tree, which is equivalent to 2.64 inches.

Learn more about height here:

https://brainly.com/question/21836055

#SPJ11

The property that justifies Emily's first step include the following: C. division property of equality.

In Mathematics and Geometry, the Commutative Property of Addition states that when two (2) or three (3) numerical values (numbers) are added together, the output (end result) would always remain the same, irrespective of the way in which the numerical values are arranged.

Generally speaking, the Commutative Property of Addition allows the addends to be re-ordered without causing a change in the result, output, or outcome.

By applying the division property of equality to Emily's equation, we have the following;

2(-3x² + 2) + 4 = 18x² - 20

2(-3x² + 2) + 2(2) = 2(9x² - 10)

(-3x² + 2) + 2 = (9x² - 10) ⇒ (division property of equality)

Read more on commutative property here: brainly.com/question/24730587

#SPJ4

Given table, b is the output and a is the input. If we take a look at the table, we can see that b increases by 1 when a increases by 1. So, a linear pattern exists in this table.

The answer is Yes.

The other equations do not have a constant rate of change. For instance, the equation b = a - 5 decreases by 5 when a increases by 1, but in the table, b increases by 1 when a increases by 1. Similarly, the equations a = b - 5 and b = a + 1234 have no correlation to the table. Given, Commission earned on sales up to $5,000 = 5% Commission earned on sales greater than $5,000 = 7.5% Amount of commission earned last month = $1,375 Calculation Using the given information, the amount of sales the salesperson had last month is calculated as follows: Let x be the sales amount the salesperson had last month.

So, the commission earned on the first $5,000 of sales is:$5,000 × 5% = $250 Commission earned on sales greater than $5,000 is: $1,375 − $250 = $1,125 So, we can write that: $1,125 = 7.5% × (x − $5,000)

⇒ x − $5,000

= $15,000 ⇒

x = $20,000 Therefore, the salesperson had $20,000 in sales last month. Given table, b is the output and a is the input. If we take a look at the table, we can see that b increases by 1 when a increases by 1. So, a linear pattern exists in this table. That means the correct equation would have a constant rate of change.

To know more about pattern visit:

https://brainly.com/question/29897321

#SPJ11

The expression (a+b+c)(d+e+f) consists of six terms, and each term contains three factors.

To understand the number of terms and factors in this expression, we need to expand it using the distributive property. The distributive property states that each term in the first expression is multiplied by each term in the second expression.

(a+b+c)(d+e+f): ad + ae + a f + bd + be + bf + cd + ce + cf

From the above, we can see that there are six terms, which are ad, ae, a f, bd, be, and bf.

Each term contains three factors: a factor from the first parentheses (a, b, or c), a factor from the second parentheses (d, e, or f), and a multiplication sign connecting them.

Therefore, the expression (a+b+c)(d+e+f) consists of six terms and each term contains three factors.

More on binomial expressions can be found here: https://brainly.com/question/30735781

#SPJ4

To find the length of the missing base of the trapezoid, we can use the formula for the area of a trapezoid. Given that the longer base is 8 inches, the height is 3 inches, and the area is 21 square inches, we can substitute these values into the formula and solve for the missing base length.

The formula for the area of a trapezoid is A = (1/2)(b1 + b2)h, where A is the area, b1 and b2 are the lengths of the bases, and h is the height.

In this case, we know that b1 is 8 inches and h is 3 inches, and the area A is 21 square inches. We need to find the length of the missing base, which we'll denote as b2.

Substituting the known values into the formula, we have:

21 = (1/2)(8 + b2)(3)

Simplifying the equation, we get:

42 = 8 + b2

Subtracting 8 from both sides, we find:

b2 = 34

Therefore, the length of the missing base of the trapezoid is 34 inches.

To learn more about trapezoid; -brainly.com/question/31380175

#SPJ11

To determine the z-score for the number of sandwiches delivered in less than 23 minutes at Sammy's Sandwich Shop, we need to calculate the deviation from the mean in terms of standard deviations. The z-score is -1.5.

The z-score measures the number of standard deviations a data point is from the mean. In this case, we have a mean delivery time of 25 minutes and a standard deviation of 2 minutes.

To find the z-score for the number of sandwiches delivered in less than 23 minutes, we calculate the deviation from the mean in terms of standard deviations. The formula for calculating the z-score is: z = (x - μ) / σ, where x is the data point, μ is the mean, and σ is the standard deviation.

Plugging in the given values, we have: z = (23 - 25) / 2 = -2 / 2 = -1.

Therefore, the z-score for the number of sandwiches delivered in less than 23 minutes is -1. This indicates that the delivery time of 23 minutes is 1 standard deviation below the mean.

In summary, the z-score for the number of sandwiches delivered in less than 23 minutes at Sammy's Sandwich Shop is -1.5.

Learn more about mean here:

https://brainly.com/question/29545538

#SPJ11

Given information:

Max invest $1000 in a savings account that earns simple 3% interest.

Let's suppose the duration he needs to keep his money in the savings account is t years.

The interest rate is given as 3% in decimal form = 0.03

Max invests $1000 on the savings account that earns 3% simple interest.

This implies that the interest he will earn after t years is given by:

Interest (I) = Principal × Rate × Time

I = 1000 × 0.03 × t

I = 30t

From the problem, he wants to earn $150 in interest.

So, 30t = 150

Solving for t:

$$\begin{aligned}30t &= 150 \\t &= \frac{150}{30} \\t &= 5 \;years \end{aligned}$$

Max needs to leave his money in the savings account for 5 years to make $150 in interest.

Therefore, the answer is 5 years.'

To know more savings account visit:

brainly.com/question/12403912

#SPJ11

La velocidad del recorrido es de 1.67 m/s. Para encontrar la velocidad de un recorrido de 125 m realizado en un tiempo de 75 segundos.

Utilizaremos la fórmula de velocidad promedio, que es la distancia dividida por el tiempo.

Para encontrar la velocidad, sigue estos pasos:

Identifica la distancia recorrida, que es de 125 m.

Identifica el tiempo transcurrido, que es de 75 segundos.

Aplica la fórmula de velocidad promedio: velocidad = distancia / tiempo.

Sustituye los valores conocidos en la fórmula: velocidad = 125 m / 75 s.

Realiza la división: velocidad = 1.67 m/s.

Por lo tanto, la velocidad del recorrido es de 1.67 m/s.

To learn more about  de velocidad promedio click here:

brainly.com/question/9909107

#SPJ11

There are 1 items are expected to be defective.

We have the information available from the question is:

On average that 0.026% of the items from a certain factory are defective.

Now, if 4000 items are checked, the number of defective items would be gotten by multiplying the percentage of defective items by the number of items checked.

We are required to find the number if defective items that we will find from 4000 items.

Therefore,

Number of defective items = 0.026% × 4000 = 1.04 approximately 1

Learn more about Average at:

https://brainly.com/question/27646993

#SPJ4

Therefore, Clausen has 32 cards.The correct answer is Clausen has 32 cards.

Juan and Clausen are playing a card game called "Magic." The number of cards they have is in a ratio of Juan: Clausen = 7:4. Juan has 56 cards. To find the number of cards Clausen has, we can use the concept of ratios and proportions.Since the ratio of Juan's cards to Clausen's cards is 7:4, we can say that Juan has 7x cards, where x is a constant.

Similarly, Clausen has 4x cards.Now, we know that Juan has 56 cards. We can use this information to find the value of x.7x = 56

Dividing both sides by 7, we get:

x = 8

Now that we know the value of x, we can find the number of cards Clausen has.4x = 4(8) = 32

To know more about arithmetic:

https://brainly.com/question/16415816

#SPJ11

The factors of x^2 - 64 are (x - 8)(x + 8) because it follows the difference of squares formula, giving the correct factorization that yields x^2 - 64 when multiplied.

To factorize x^2 - 64, we can use the difference of squares formula, which states that a^2 - b^2 can be factored as (a - b)(a + b). In this case, a = x and b = 8. Applying the formula, we have (x - 8)(x + 8) as the factors of x^2 - 64. This is the correct factorization because when we multiply these factors, we get (x - 8)(x + 8) = x^2 - 64.

The other options provided (x - 4)(x + 16) and (x - 8)(x - 8) are not valid factorizations of x^2 - 64. The first option, (x - 4)(x + 16), does not yield x^2 - 64 when multiplied. The second option, (x - 8)(x - 8), is a repeated factor and does not represent the correct factorization. Therefore, the factors of x^2 - 64 are (x - 8)(x + 8).

learn more about factorization here:

https://brainly.com/question/28201305

#SPJ11

The climate of the Gobi Desert has impacted the lifestyle of the people who live in the region by influencing their nomadic lifestyle (Option D).

The Gobi Desert's climate, characterized by extreme temperatures, limited water resources, and sparse vegetation, has shaped the way of life for the people residing in the region. Due to the harsh environment, settled agriculture and permanent settlements are challenging.

As a result, the people in the Gobi Desert have traditionally adopted a nomadic lifestyle (Option D). They move with their herds of livestock, such as camels, goats, and sheep, in search of grazing land and water sources. This lifestyle allows them to adapt to the desert conditions, ensuring the survival of their livestock and themselves.

Nomadic herding enables the people to make efficient use of the scarce resources available in the desert, while also fostering a deep understanding of desert survival techniques. It creates a strong connection between the people and the natural environment, as they rely on the land and its resources for their livelihood.

Therefore, the climate of the Gobi Desert has influenced the people to lead a nomadic lifestyle, allowing them to adapt and thrive in the challenging desert environment.

Learn more about the mathematics here: brainly.com/question/27235369

#SPJ11

The elevation of the hole, relative to ground level, after placing the bush in the hole is 52 2/5 feet.

In 30 minutes, Carter digs 34 feet every 10 minutes, so in 30 minutes, he digs a total of (34/10) x 30 = 102 feet. After placing the bush, the hole is filled with 78 feet. So, the elevation of the hole after placing the bush is 102 - 78 = 24 feet below ground level. This can be expressed as a mixed number in simplest form as 52 2/5 feet above ground level.

Sure, let's break down the problem step by step:

1. Carter digs a hole at a rate of 34 feet every 10 minutes. This means that in 10 minutes, he digs 34 feet.

2. To determine how much Carter digs in 30 minutes, we can set up a proportion: 10 minutes is to 34 feet as 30 minutes is to x feet. Solving this proportion, we find that x = (34/10) * 30 = 102 feet. Therefore, Carter digs a total of 102 feet in 30 minutes.

3. After 30 minutes of digging, Carter places a bush in the hole that fills exactly 78 feet of the hole. This means that the hole is no longer empty but has been filled with 78 feet.

4. To find the elevation of the hole relative to ground level, we need to subtract the filled portion (78 feet) from the total depth of the hole that Carter dug (102 feet). This results in 102 - 78 = 24 feet.

5. The elevation of the hole, relative to ground level, is 24 feet below the ground. However, we need to express it as a mixed number in simplest form. Since each whole number is equal to 5/5, we can rewrite 24 as 23 + 1 = 23 + (5/5) = 23 + 1(5/5) = 23 5/5. Simplifying this mixed number, we get 23 1/5 feet.

Therefore, the elevation of the hole, relative to ground level, after placing the bush in the hole is 23 1/5 feet.

Learn more about elevation here:

https://brainly.com/question/29477960

#SPJ11

Dinosaur 2 is a more efficient walker in terms of having a pace angle closer to 180°.

To determine which dinosaur is a more efficient walker based on the pace angle, compare the pace angles of the two dinosaurs.

Analyze the given information:

Dinosaur 1:

Pace: 2.9 ft

Stride: 5.78 ft

Dinosaur 2:

Pace: 3.0 ft

Stride: 5.2 ft

To calculate the pace angle, use the following formula:

Pace angle = arccos(Pace/Stride)

For Dinosaur 1:

Pace angle = arccos(2.9/5.78) ≈ 59.43°

For Dinosaur 2:

Pace angle = arccos(3.0/5.2) ≈ 56.62°

Comparing the pace angles, Dinosaur 2 has a smaller pace angle (56.62°) compared to Dinosaur 1 (59.43°). Therefore, Dinosaur 2 is a more efficient walker in terms of having a pace angle closer to 180°.

Find out more on pace angle here: https://brainly.com/question/12804592

#SPJ1

The digits 2, 27, and 15 in the time 2;27;15 represent different units of measurement in the race.

In the context of a running race, the first digit 2 represents the number of hours it took the runner to finish the race. This means that the runner completed the race in 2 hours.

The second digit 27 represents the number of minutes it took the runner to finish the race after the hours. In this case, the runner completed the race in 27 minutes.

The third digit 15 represents the number of seconds it took the runner to finish the race after the minutes. Therefore, the runner completed the race in 15 seconds.

By breaking down the total time into hours, minutes, and seconds, the digits provide a detailed representation of the runner's finishing time, allowing for a more precise measurement and comparison of race performances.

To know more about digits click here: brainly.com/question/30142622

#SPJ11

By using a graphing calculator and a system of equations, we can determine the value of x and then calculate the lengths of the sides. Substituting the value of x into the dimensions, we can identify the longest side among the three.

Using a graphing calculator, enter the equation 2x^3 + 14x^2 + 12x - 400 = 0 and graph it. Find the x-values where the graph intersects the x-axis, which represent the solutions. Using the calculator's "zero" or "intersect" function, determine the numerical values of x. Substitute these values into the dimensions (x, 2x, and x/6) to find the lengths of the sides. Compare the lengths and identify the longest side. This process allows us to find the length of the longest side using a graphing calculator and a system of equations.

Learn more about solving equations here: brainly.com/question/14410653

#SPJ11

One sample t-test, as it compares the mean birthweight of the mothers in the program to a known population mean.

We have,

The most appropriate hypothesis test for this study would be a

one-sample t-test.

A one-sample t-test is suitable when we want to compare the mean of a single sample to a known population mean or hypothesized value.

In this case, the study aims to test the effectiveness of a new prenatal care program in increasing the birth weight of babies born into poverty.

The researchers would compare the mean birthweight of the 30 mothers who participated in the program to the known population mean birthweight for babies born to mothers living in poverty, which is approximately 2800 grams.

Since the population standard deviation is not given, the t-test is preferred over the z-test, which requires knowledge of the population standard deviation.

The t-test allows for estimating the population standard deviation based on the sample data.

Additionally, the study involves comparing a single sample (30 mothers) to a known population mean, rather than comparing two related samples, making the paired-sample t-test inappropriate for this scenario.

Thus,

The most appropriate hypothesis test for this study would be a

one-sample t-test.

Learn more about hypothesis testing here:

https://brainly.com/question/17099835

#SPJ4

We cannot calculate the efficiency without knowing the weight of the man and the time taken to lift him about motor.

Given that:

The input power of the motor is 6200 watts.The formula for efficiency is;Efficiency = (Output power / Input power) × 100%The motor is used to operate a lift. Therefore, the power output of the motor is used to lift the man and overcome frictional forces, etc.

A motor is a device that transforms electrical energy into mechanical energy, allowing motion to be created or machines to be operated. In myriad applications spanning numerous industries, it is fundamental. Electric motors, which are frequently used in household goods, transportation, and industrial machinery, use the electromagnetic theory to generate rotational motion.

They are made up of a rotor, which rotates in reaction to being subjected to force, and a stator, which produces a revolving magnetic field. Motors come in a variety of sizes and configurations to meet various needs, and they can be categorised according to their power source, such as AC motors or DC motors. Motors are essential to modern technology and automation, powering anything from home appliances to vehicle propulsion.

We know that the man has a weight (W) and is being lifted at a certain height (H), so the power output can be calculated using the following formula;Power Output = W × H / t, where t is the time taken to lift the man.

Substituting the given values;Power Output = W × H / tEfficiency = (Power Output / Input Power) × 100%Therefore;Efficiency = (W × H / t) / 6200 × 100%

We cannot calculate the efficiency without knowing the weight of the man and the time taken to lift him.

Learn more about motor here:

https://brainly.com/question/31214955

#SPJ11

The surface area of the prism is 96 cm², with dimensions of 88 cm by 88 cm.

To calculate the surface area of a prism, we need to find the sum of the areas of all its faces. In this case, the prism has a rectangular base with dimensions of 88 cm by 88 cm and four identical rectangular faces.

First, we calculate the area of the base by multiplying the length and width: 88 cm × 88 cm = 7744 cm². Since the base has two identical faces, we add this area twice: 7744 cm² × 2 = 15488 cm².

Next, we calculate the area of the other four faces, which are all identical. Each face is a rectangle with a length of 88 cm (the same as the base) and a height equal to the height of the prism. However, the height is not given in the question, so we cannot determine the area of these faces.

Therefore, with the given information, we can only calculate the surface area of the prism based on the known dimensions of the base, which is 15488 cm². It is important to note that without the height of the prism, we cannot determine the total surface area accurately.

Learn more about  surface area of the prism:

https://brainly.com/question/32429268

#SPJ11

With an 80% improvement in typing speed from an initial rate of 50 words per minute, you will be able to type 90 words per minute.

Increasing your typing speed by 80% means you will be able to type 80% more words in the same amount of time. Therefore, if your initial typing speed is 50 words per minute, an 80% improvement would result in a typing speed of 90 words per minute.

To calculate the new typing speed, we first find 80% of the initial typing speed.

80% of 50 is (80/100) * 50 = 0.8 * 50 = 40.

This means that your typing speed will increase by 40 words per minute.

To determine the new typing speed, we add the increase to the initial typing speed:

50 + 40 = 90.

Thus, after the 80% improvement, you will be able to type 90 words per minute.

In summary, with an 80% improvement in typing speed from an initial rate of 50 words per minute, you will be able to type 90 words per minute.


To learn more about rate click here: brainly.com/question/199664

#SPJ11

The approximate population density of Asia is 83.03 people per square kilometer.

Population density is the measure of the number of people per unit area, usually per square kilometer. It is calculated by dividing the population of a region by the area of that region. It is important because it gives us an idea of how crowded or sparse a region is.

To find the population density of Asia, we need to divide the population by the area of the continent. Given,The area of Asia = 4.46 × 107 km²The population of Asia = 3.70 × 109 peopleWe can use the formula,Population density = Population/Area= (3.70 × 109 )/(4.46 × 107)≈ 83.03 people per square kilometer

Therefore, the approximate population density of Asia is 83.03 people per square kilometer.

To know more about population density  visit :-

https://brainly.com/question/16894337

#SPJ11

The explicit formula is [tex](n) = 1 * 1^{(n-1)} = 1[/tex] for all values of n and the number of cells after 10 generations will be 1.

The formula for finding the number of bacteria cells after each generation is given by

[tex]a(n) = a(1)r^{(n-1)}[/tex] where a(1) is the initial number of bacteria cells, r is the growth factor, and n is the number of generations.

The exponent n-1 indicates the number of generations.

To find the number of bacteria cells after 10 generations, we will substitute the given values in the formula.

We are given that a(n)= a(1)r"-1 where r is the growth factor and n is the number of generations.

We know that the initial number of bacteria cells is 1.

Thus, a(1) = 1.

Substituting these values in the formula, we get [tex]a(n) = 1 x r^{(n-1)}[/tex]. For 10 generations, n = 10.

Thus, the formula becomes [tex]a(10) = 1 x r^{(10-1)} = r^9[/tex].

Now, we need to find the value of r.

We are given that [tex]a(n) = a(1)r^{(-1)}[/tex], which means that a(n)/a(1) = 1/r.

Substituting [tex]a(n) = r^9[/tex] and a(1) = 1, we get: [tex]r^9/1 = 1/r[/tex]

Therefore, [tex]r^{10} = 1r = 1^{(1/10)} = 1[/tex]

Thus, the explicit formula becomes [tex]a(n) = 1 * r^{(n-1)}[/tex] = 1 for all values of n.

Therefore, the number of cells after 10 generations will be 1.

Summary: A formula that can be used to find the number of bacteria cells after each generation is [tex]a(n) = 1 * r^{(n-1)}[/tex] where a(1) is the initial number of bacteria cells, r is the growth factor, and n is the number of generations. To find the number of bacteria cells after 10 generations, we can substitute the given values in the formula. The explicit formula for the given problem is [tex]a(n) = 1 * r^{(n-1)}[/tex] where r = 1. Thus, the number of cells after 10 generations will be 1.

For more questions on explicit formula

https://brainly.com/question/30603437

#SPJ8

The distance between Arcadia and Rockport is approximately 9.2 miles when rounded to the nearest tenth.

To determine the distance between Arcadia and Rockport, we can use the Pythagorean theorem, which relates the lengths of the sides of a right triangle.

Let's consider Arcadia as point A, Rockport as point R, and the airport as point O. The distance from Arcadia to the airport is 7 miles (the length of side OA), and the distance from Rockport to the airport is 6 miles (the length of side OR). We want to find the distance between Arcadia and Rockport, which is the length of side AR.

Since Arcadia and Rockport are located in different directions (north and east) from the airport, we can form a right triangle with sides AO, OR, and AR.

Using the Pythagorean theorem, we have:

AR^2 = AO^2 + OR^2.

Substituting the given lengths, we get:

AR^2 = 7^2 + 6^2,

AR^2 = 49 + 36,

AR^2 = 85.

Taking the square root of both sides, we find:

AR = √85.

Approximating the square root of 85 to the nearest tenth, we have:

AR ≈ 9.2 miles.

Therefore, the distance between Arcadia and Rockport is approximately 9.2 miles when rounded to the nearest tenth.

It's important to note that this calculation assumes a direct path between Arcadia and Rockport. If there are obstacles or detours that would affect the actual path, the distance may differ. Additionally, rounding to the nearest tenth introduces some level of approximation, so the actual distance may be slightly different.

Learn more about Pythagorean theorem at: brainly.com/question/14930619

#SPJ11

According to the question the slope of the line parallel to the line containing side WV is -1.

To find the slope of the line parallel to the line containing side WV, we need to determine the slope of side WV.

Sure! Here are the coordinates of points [tex]T, U, V, and[/tex] [tex]W[/tex] properly aligned:

[tex]\[T &: (a, b) \\U &: (a + 2, b + 2) \\V &: (a + 5, b - 1) \\W &: (a + 3, b - 3) \\\][/tex]

To find the slope of the line parallel to the line containing side WV, we can calculate the slope between points W and V using the slope formula:

[tex]\[ \text{Slope} = \frac{{\text{change in } y}}{{\text{change in } x}} \][/tex]

Substituting the coordinates of points W and V into the formula:

[tex]\[ \text{Slope} = \frac{{(b - 1) - (b - 3)}}{{(a + 5) - (a + 3)}} \][/tex]

Simplifying the expression:

[tex]\[ \text{Slope} = \frac{{-2}}{{2}} \][/tex]

Therefore, the slope of the line parallel to the line containing side WV is -1.

To know more about parallel visit-

brainly.com/question/31504973

#SPJ11

triangle ABC with angle A and AC missing, we need to solve for the missing parts of the triangle.

Step-by-step explanation:We are given triangle ABC, with angle A and side AC missing. To solve for the missing parts of the triangle, we can use the properties of triangles and trigonometry.Let's start by finding angle A. We know that the sum of angles in a triangle is 180°.

Therefore, we can write:∠A + ∠B + ∠C = 180°

Substituting the values we know, we get:∠A + 60° + 45° = 180°

Simplifying the equation, we get:∠A = 180° - 60° - 45°∠A = 75°

Therefore, angle A measures 75°.Now, we can use trigonometry to find the length of side AC. Since we know the length of sides AB and BC, we can use the Law of Cosines to find the length of AC.

The Law of Cosines states that: c² = a² + b² - 2ab cos(C)

where a, b, and c are the lengths of sides of a triangle, and C is the angle opposite to side c.

Substituting the values we know, we get:AC² = AB² + BC² - 2(AB)(BC) cos(A

)AC² = 6² + 8² - 2(6)(8) cos(75°)

AC² = 36 + 64 - 96 cos(75°)

AC² = 100 - 96 cos(75°)

Using a calculator, we can find that cos(75°) = 0.2588. Substituting this value, we get:AC² = 100 - 96(0.2588)AC² = 100 - 24.8448AC² = 75.1552

Taking the square root of both sides, we get:AC ≈ 8.67

Therefore, side AC has a length of approximately 8.67 units.

To know more about trigonometry, visit

https://brainly.com/question/11016599

#SPJ11