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9


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Skylar travels 50 meters N and then goes 30 meters West before coming


straight back south 20 meters. What distance did she travel?


12

The problem states that there are 125 Grade 8 learners and that they jog and cycle in the ratio of 3:2. So we will take the total ratio of joggers and cyclers as 3 + 2 = 5.

In order to find out how many learners participate in each sport, we must first find the ratio of joggers to cyclers. We can do that by setting up a proportion:3/5 = joggers/1252/5 = cyclers/125Now we can solve for joggers and cyclers by cross multiplying:3/5 * 125 = joggers75 = joggers2/5 * 125 = cyclers50 = cyclersSo, there are 75 Grade 8 learners who jog and 50 Grade 8 learners who cycle. More than 250 learners will be participating in the activity.

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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.

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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.

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Factor completely 4x2 25x 6 is (4x + 3)(x + 2)(x + 1). The factors of 6 are (1)(6) or (2)(3).Let's find out which of these pairs will sum up to give 25x.

To factor completely 4x2 25x 6, we first find the factors of the quadratic equation and then group them together. We can start by the factoring of the quadratic term and the constant term separately, and then use the distributive law of multiplication to simplify the result.

Given expression: 4x2 25x 6The factors of 4x2 are (2x)(2x) or (4x)(x).

The factors of 6 are (1)(6) or (2)(3).Let's find out which of these pairs will sum up to give 25x.

The possible ways are:(2x)(3) and (4x)(1) with the product 6x and 4x, respectively.

(2x)(1) and (4x)(6) with the product 2x and 24x, respectively.

We can notice that (2x)(3) and (4x)(1) can give us 2x + 24x = 25x.

So, we can rewrite the given expression as:(4x + 3)(x + 2)(x + 1)

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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.

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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.

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The rational subgroup concept is a subset of data where variation is due to common causes only. This type of subgroup is used in control chart analysis to make sure that variation in the process is predictable and does not include any special causes of variation.

Control charts are graphical representations of process data over time. They help in detecting the changes or variations in the process and identify the root cause of the variation. Control charts are used to analyze process performance and identify areas where improvement is needed. The rational subgroup concept plays an essential role in the control chart analysis as it helps in selecting the appropriate data to plot on the control chart.To use control charts, a subgroup of data must be selected. The rational subgroup concept ensures that the data in the subgroup is due to common causes only and does not include any special causes of variation. By selecting a rational subgroup, the control chart shows the natural variation in the process and helps in identifying any trends or patterns that require attention.

Control charts are graphical representations of process data over time. They help in detecting the changes or variations in the process and identify the root cause of the variation. Control charts are used to analyze process performance and identify areas where improvement is needed.The rational subgroup concept plays an essential role in the control chart analysis as it helps in selecting the appropriate data to plot on the control chart. By selecting a rational subgroup, the control chart shows the natural variation in the process and helps in identifying any trends or patterns that require attention. The rational subgroup concept ensures that the data in the subgroup is due to common causes only and does not include any special causes of variation. This ensures that the control chart is an accurate representation of the process performance and helps in identifying areas where improvement is needed.Overall, the rational subgroup concept is a critical part of the control chart analysis. It ensures that the control chart accurately reflects the process performance and helps in identifying areas where improvement is needed. By selecting a rational subgroup, the control chart shows the natural variation in the process and helps in identifying any trends or patterns that require attention.

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The sampling distribution of the sample minimum, in this case, consists of the values 2, 4, 6, 30, and 32, each occurring three times, and represents the range of possible minimum ages when randomly selecting two family members.



The sampling distribution of the sample minimum represents the distribution of all possible sample minimum values that can be obtained by randomly selecting two family members from the given family. To determine this distribution, we need to consider all possible combinations of two family members and calculate the minimum age within each combination.

In this case, we have five family members with ages 2, 4, 6, 30, and 32. To calculate the sample minimum, we consider all possible combinations of two family members: (2, 4), (2, 6), (2, 30), (2, 32), (4, 6), (4, 30), (4, 32), (6, 30), (6, 32), (30, 32). Within each combination, we determine the minimum age.The resulting sample minimums are: 2, 2, 2, 2, 4, 4, 4, 6, 6, 30.

The sampling distribution of the sample minimum is the distribution of these values. In this case, it is a discrete distribution with ten possible outcomes: 2, 4, 6, 30, each occurring three times, and 32 occurring once. This distribution describes the range of possible sample minimums that can be obtained by randomly selecting two family members from the given family.

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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.

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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)

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Tori and her two friends listened to music for a total of 2 hours and 2/5 of an hour (or 2.4 hours) in all.

Tori and her two friends each listened to music for 4/5 of an hour.

To find out how long they listened to music in total, we need to multiply the duration by the number of people.

Since Tori and her two friends listened to music for the same amount of time, we can simply multiply the duration by 3 (to account for Tori and her two friends).

Duration per person: 4/5 hour

Total duration: (4/5) [tex]\times[/tex] 3 = 12/5 hour

To simplify the fraction, we can express 12/5 as a mixed number.

Since 5 goes into 12 evenly twice, with a remainder of 2, the total duration can be written as 2 2/5 hours.

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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.

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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.

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The line tangent to the graph of f at x and to the graph of g at x is given by yx.

To find the line tangent to the curves at x, we can determine the slopes of the curves at that point. The slope of the tangent line to the graph of f at x is equal to the derivative of f evaluated at x. Similarly, the slope of the tangent line to the graph of g at x is given by the derivative of g evaluated at x. Since both tangent lines have the same slope, the derivatives of f and g must be equal at x. By finding the common derivative, we can obtain the slope of the tangent line, and by using the point-slope form, we can determine the equation of the line.

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Consider two functions, f(x) and g(x), with graphs in a coordinate plane. Suppose there exists a point (x, f(x)) on the graph of f, where the tangent line to f at that point is represented by the equation y = x. Additionally, suppose the same tangent line, y = x, is also the tangent line to the graph of g at the point (x, g(x)). Find the equation of the tangent line to each of the following curves at the given x-values.

Deepak paid a total of Rs. 33,000 to settle the account after borrowing Rs. 25,000 to buy a laptop at an 8% per annum simple interest rate for 4 years. The additional Rs. 8,000 accounts for the interest charged over the 4-year period.

Deepak borrowed Rs. 25,000 to purchase a laptop, with a simple interest rate of 8% per annum. After 4 years, he settled the account. The total amount he paid can be calculated using the simple interest formula, which is Principal × Rate × Time. In this case, the principal amount is Rs. 25,000, the interest rate is 8% per annum, and the time is 4 years. The simple interest for one year can be calculated as Rs. 25,000 × (8/100) = Rs. 2,000. Therefore, the interest for 4 years would be Rs. 2,000 × 4 = Rs. 8,000. Adding the interest to the principal amount, Deepak paid a total of Rs. 25,000 + Rs. 8,000 = Rs. 33,000 to settle the account after 4 years.

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The expression that represents the amount of money Madeline would have saved in w weeks is S(w) = 65 + 5w.

After 5 weeks of saving, Madeline would have a total of $90.

Madeline already has $65 and can save an additional $5 per week. Therefore, after 5 weeks, she would have saved 5 * $5 = $25.

Adding the initial amount of $65 to the savings of $25, Madeline would have a total of $65 + $25 = $90 after 5 weeks.

Expression representing the amount of money Madeline would have saved in w weeks:

Let's represent the amount of money Madeline has saved in w weeks as "S(w)".

Given that Madeline saves an additional $5 per week, we can express the savings as:

S(w) = 65 + 5w

Therefore, the expression that represents the amount of money Madeline would have saved in w weeks is S(w) = 65 + 5w.

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The fraction of trick-or-treaters dressed as either ghosts or witches is 9/10.

To find the fraction of trick-or-treaters dressed as either ghosts or witches, we need to add the fractions representing the proportion of ghosts and witches.

Given that 1/2 of the trick-or-treaters were dressed as ghosts and 2/5 were dressed as witches, we can add these fractions together:

1/2 + 2/5

To add these fractions, we need a common denominator. The least common multiple of 2 and 5 is 10.

Converting the fractions to have a common denominator of 10:

(1/2) * (5/5) + (2/5) * (2/2)

5/10 + 4/10

Now, we can add the fractions:

5/10 + 4/10 = 9/10

Therefore, the fraction of trick-or-treaters dressed as either ghosts or witches is 9/10.

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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.

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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).

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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.

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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.


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The equation that best models the data in the scatter plot is option D: y = x - 1.

In the given scatter plot, the data points appear to form a straight line that slopes upwards from left to right. The equation y = x - 1 represents a linear function with a slope of 1 and a y-intercept of -1. This means that for every unit increase in x, y increases by the same amount (1), and when x is 0, y is -1.

Option A, y = -x + 1, has a negative slope and would result in a line that slopes downwards from left to right, which does not match the data in the scatter plot.

Option B, y = -x - 1, also has a negative slope and a different y-intercept, which does not align with the data in the scatter plot.

Option C, y = x + 1, has a positive slope but a different y-intercept, which does not accurately represent the data points in the scatter plot.

Therefore, option D, y = x - 1, is the equation that best models the data in the scatter plot, based on the observed trend and the characteristics of the given options.

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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.

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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.

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To determine the expression that represents the volume of the prism, we need to consider the dimensions given for the prism.

Unfortunately, the dimensions of the prism are not explicitly provided in the question, so it is difficult to determine the correct expression with certainty. However, I will explain how to calculate the volume of a prism based on the given expressions.

In general, the volume of a rectangular prism can be calculated by multiplying the length, width, and height of the prism. The volume formula for a rectangular prism is V = length × width × height.

Let's analyze the given expressions one by one:

10 × 4 units³: This expression represents the product of two values, which could potentially represent the length and width of the prism. However, since we are looking for the volume, we need to multiply the length, width, and height together, not just two of the dimensions.

7 × 7 units³: This expression represents the product of two identical values, which could potentially represent the length and width of the prism. However, again, we need to multiply all three dimensions together to calculate the volume.

3 × 11 units³: This expression represents the product of two values, which could potentially represent the length and width of the prism. However, we still need the height dimension to calculate the volume.

21 × 4 units³: This expression represents the product of two values, which could potentially represent the length and width of the prism. Again, we are missing the height dimension.

Based on the information provided, none of the given expressions represent the volume of the prism accurately, as they only include two out of the three necessary dimensions. Without the complete dimensions of the prism, we cannot determine the correct expression for the volume.

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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.'

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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.

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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.

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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.

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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

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