The region bounded by the given curves is rotated about the specified axis. Compute the volume Vof the resulting solid by any method.x=(y−9)2,x=16;about the line y=5

Using the properties of rational exponents, the value of y is 7/3.

Solve the equation using the properties of rational exponents. We are given the equation: (x^(4/3))^2 / x^(1/3) = x^y, and we need to find the value of y.

Step 1: Apply the power rule of exponents to (x^(4/3))^2.
The power rule states that (a^m)^n = a^(m*n).

So, in our case, (x^(4/3))^2 = x^((4/3)*2) = x^(8/3).

Step 2: Rewrite the equation with the result from step 1.
Now, our equation is x^(8/3) / x^(1/3) = x^y.

Step 3: Apply the quotient rule of exponents.
The quotient rule states that a^m / a^n = a^(m-n).

In our case, x^(8/3) / x^(1/3) = x^((8/3) - (1/3)) = x^(7/3).

Step 4: Compare the resulting expression to x^y.
Now our equation is x^(7/3) = x^y.

Since the bases (x) are the same, we can conclude that the exponents must be equal. Therefore, y = 7/3.

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Answer:

38

Step-by-step explanation:

The answer to this question is  the test statistic is a. option a. 100.75.

To arrive at this answer, we need to use the chi-square distribution to test the null hypothesis that the population variance (σ2) is equal to 20. The test statistic for this hypothesis test is given by:

χ2 = (n - 1) * s²  / σ2

where n is the sample size, s is the sample standard deviation, and σ is the population standard deviation (which is assumed to be equal to the hypothesized value of 20).

Substituting the given values, we get:

χ2 = (41 - 1) * 5² / 20
χ2 = 40 * 25 / 20
χ2 = 50

Therefore, the test statistic is 50.

However, to determine the p-value (i.e. the probability of obtaining a test statistic as extreme or more extreme than the observed one, assuming the null hypothesis is true), we need to consult a chi-square distribution table with (n - 1) degrees of freedom. For this problem, the degrees of freedom is 40 (i.e. 41 - 1).

Using the chi-square distribution table, we find that the p-value for a test statistic of 50 with 40 degrees of freedom is less than 0.001. This means that the probability of obtaining a sample with a variance as extreme or more extreme than 20 (assuming the null hypothesis is true) is less than 0.001.

Therefore, we can reject the null hypothesis at a significance level of 0.001 or lower. This leads us to the conclusion that the population variance is unlikely to be 20, based on the given sample of 41 observations with a sample standard deviation of 5.

finding the p-value using a chi-square distribution table, and making a conclusion based on the significance level. The main answer is option a. 100.75, which corresponds to the test statistic calculated using the formula χ2 = (n - 1) * s²  / σ2.

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The formula for the least squares curve y = ax2 that best fits the data set d is:
y = (Σ2(xi^2)(yi) / Σ2(xi^4)) x^2
where Σ2 denotes the sum of squares over all data points in the data set d.

To derive the formula for "a" for the least squares curve y = ax2 that best fits the data set d, we need to follow these steps:
Step 1: Write down the equation for the least squares curve y = ax2 that we want to fit to the data set d.
Step 2: Write down the formula for the sum of squares of residuals, which is the sum of the squares of the differences between the observed values in the data set d and the predicted values from the least squares curve y = ax2.
Step 3: Differentiate the sum of squares of residuals formula with respect to "a" and set it equal to zero, in order to find the value of "a" that minimizes the sum of squares of residuals.
Step 4: Solve for "a" to get the formula for the least squares curve y = ax2 that best fits the data set d.
Therefore, the formula for the least squares curve y = ax2 that best fits the data set d is:
y = (Σ2(xi^2)(yi) / Σ2(xi^4)) x^2
where Σ2 denotes the sum of squares over all data points in the data set d.

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The marble took 4 seconds to roll from one end of the room to the other end.

To find the time it took for the marble to roll from one end of the room to the other, we can use the formula:

Time = Distance / Speed

Given that the distance between the two ends of the room is 1.92 m and the speed of the marble is 48 cm/s, we need to convert the distance to centimeters to match the unit of speed.

1.92 m = 192 cm

Now we can calculate the time:

Time = 192 cm / 48 cm/s

Time = 4 seconds

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Answer: The volume of the solid obtained by rotating the region between the curve y = 3x − x^2 and the x-axis, about the y-axis, is 27π/5.

Step-by-step explanation:

To obtain the volume of the solid obtained by rotating the region between the curve y = 3x − x^2 and the x-axis, about the y-axis, we use the formula:

V = ∫a^b π y^2 dx

where a and b are the x-coordinates of the points of intersection of the curve with the x-axis.

To obtain these points, we set y = 0:

3x − x^2 = 0x(3 − x) = 0x = 0, x = 3

Thus, the limits of integration are a = 0 and b = 3. Now we express y in terms of x:

y = 3x − x^2

We substitute this expression for y in the formula for V:

V = ∫0^3 π (3x − x^2)^2 dx

Expanding the square, we get:

V = ∫0^3 π (9x^2 − 6x^3 + x^4) dx

Integrating, we obtain:

V = π [3x^3 − 3/2 x^4 + 1/5 x^5]0^3V = π [27/5]

Therefore, the volume of the solid obtained by rotating the region between the curve y = 3x − x^2 and the x-axis, about the y-axis, is 27π/5

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The sum of 8 + 2 ¹ / ₂ would be c. 10 ¹ / ₂.

To calculate the sum of mixed fractions and whole numbers, you can convert the mixed fraction into an improper fraction by adding the numerator to the product of the denominator and the whole number. Then determine a common denominator for both the whole number and the improper fraction.

Finally, simplify the resulting fraction by dividing its numerator and denominator by their greatest common factor.

This means that the sum of 8 and 2 ¹ / ₂ would therefore be :

= 8 + 2

= 10

Then involve the fraction :

= 10 + 1 / 2

= 10 ¹ / ₂

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The sum of the measurements we have is 1.2. The missing measurement is 0.1 centimeters.

To find the missing measurement, we need to first calculate the sum of all the measurements. We can do this by adding up all the measurements:

0.1 + 0.2 + 0.1 + 0.2 + 0.3 + 0.1 + 0.2 = 1.2

Now, we know that the mean of the measurements is 1 centimeter, and we have a total of 7 measurements. To find the missing measurement, we need to figure out what the sum of all the measurements would have been if we had included the missing measurement. We can do this by multiplying the mean by the total number of measurements:

1 x 8 = 8

We know that the sum of the measurements we have is 1.2. So, to find the missing measurement, we can subtract the sum of the measurements we have from the total sum of all the measurements:

8 - 1.2 = 6.8

Now we need to divide this result by the number of missing measurements (which is 1) to get the value of the missing measurement:

6.8 ÷ 1 = 6.8

Therefore, the missing measurement is 0.1 centimeters.

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The probability of picking a card that is blue or has an odd number is approximately 0.7333 or 73.33%.

There are 11 cards that are either blue or have an odd number in the deck of cards. These are:

Blue cards numbered 1, 2, and 3

Red cards numbered 1, 3, and 5

Green cards numbered 1, 3, and 5

There are a total of 15 cards in the deck, so the probability of picking a card that is blue or has an odd number is:

P(blue or odd) = number of blue or odd cards / total number of cards

               = 11 / 15

               = 0.7333 (rounded to 4 decimal places)

Therefore, the probability of picking a card that is blue or has an odd number is approximately 0.7333 or 73.33%.

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The graph 1 represents the subtraction of given vectors.

Hence option (a) is correct.

The given vectors are

vector c = < 5, 2 , -4>

vector d = < 6, -3, -2>

To show the graphical representation of subtraction of vectors

We add the vectors after changing the direction vector which would be subtracted.

Now ,

vector c - vector d = < 5, 2 , -4> - < 6, -3, -2>

                               = < 5-6, 2+3, -4+2 >  

                               = < -1, 5, -2 >

Thus,

vector c - vector d = < -1, 5, -2 >

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a multiple regression model, the error term `e’ is assumed to be a random variable with a mean of is A) zero. This means that in a multiple regression model, the errors are assumed to have a mean of zero. This assumption is necessary to ensure that the model is unbiased and accurate in predicting the outcome variable.

this assumption is that the error term represents the unexplained variation in the outcome variable that is not accounted for by the predictor variables. If the error term had a mean value other than zero, this would indicate that there is a systematic bias or error in the model, which would affect the accuracy of the predictions.

the assumption of a zero mean error term is a critical aspect of multiple regression modeling and helps to ensure that the model is reliable and valid for predicting the outcome variable.

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The original endpoints of the segment are the ones in option A:

C (4, 1) D (2, 4)

If we have a point (x, y), and we dilate it with a scale factor k centered at the origin, the new coordinates will be (k*x, k*y)

Here te scale factor is 2, then if:

C = (x, y), we have that:

(2x, 2y) = (8, 2)

Then:

C = (8/2, 2/2) = (4, 1)

And for the other point we have:

(2x, 2y) = (4, 8), then:

D = (4/2, 8/2) = (2, 4)

Thus, the correct option is the first one.

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The statement that best describes how to determine whether

f(x) = x² - x + 8 is an even function is "Determine whether (-x)² - (-x) + 8 is equivalent to x² - x + 8."

Option

We have,

To determine whether f(x) = x² - x + 8 is an even function, we need to check whether the function satisfies the property of even functions, which is f(-x) = f(x) for all values of x in the domain of the function.

We can test this property by plugging in -x for x in the given function and simplifying it to see if we get the same function back.

Testing each option:

Option 1:

-x² - (-x) + 8 = x² - x + 8

This option does not satisfy the property of even functions, so it cannot be the correct answer.

Option 2:

(-x)² - (-x) + 8 = x² + x + 8

This option also does not satisfy the property of even functions, so it cannot be the correct answer.

Option 3:

-x² - (-x) + 8 = -(x² - x + 8)

This option satisfies the property of even functions since both sides are equal after multiplying the right-hand side by -1.

However, this option describes whether the function is odd, not even.

Option 4:

(-x)² - (-x) + 8 = x² - x + 8

This option satisfies the property of even functions since both sides are equal. This is the correct answer.

Therefore,

The statement that best describes how to determine whether

f(x) = x² - x + 8 is an even function is "Determine whether (-x)² - (-x) + 8 is equivalent to x² - x + 8."

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TRUNCATED to one decimal place, it's 50.2

ROUNDED to one decimal place, it's 50.3

The round-off of 50.272 to 1 decimal place using rules of rounding

numbers are 50.3.

Rounding off numbers means making a number simpler by adjusting it to its nearest place according to certain rules.

Rounding a number to one decimal place means keeping only the first digit after the decimal point and neglecting the rest. In this case, the digit in the second decimal place is 7, which is greater than or equal to 5. As per the rounding rules, if the digit is greater than 5, the preceding digit is increased by 1.

So, 50.272 becomes 50.3 when rounded to one decimal place.

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Part A:

The population declined the fastest over the time interval [20,30], which has the greatest negative average rate of change (-138.11).

Part B:

The population declined the slowest over the time interval [60,70], which has the smallest negative average rate of change (-35.14).

We have,

To calculate the average rate of change of the population, we need to find the change in population over the given time interval and divide it by the length of the time interval.

The formula for an average rate of change over an interval [a, b].

average rate of change = (f(b) - f(a)) / (b - a)

where f(x) is the population function.

Using this formula, we can calculate the average rate of change over the given intervals as follows:

[0,10]:

f(10) = -1.2^(0.710) + 10,000 = 7,686.53

f(0) = -1.2^(0.70) + 10,000 = 8,800

average rate of change = (7,686.53 - 8,800) / (10 - 0) = -111.45

[20,30]:

f(30) = -1.2^(0.730) + 10,000 = 2,376.47

f(20) = -1.2^(0.720) + 10,000 = 3,759.54

average rate of change = (2,376.47 - 3,759.54) / (30 - 20) = -138.11

[40,50]:

f(50) = -1.2^(0.750) + 10,000 = 742.39

f(40) = -1.2^(0.740) + 10,000 = 1,690.88

average rate of change = (742.39 - 1,690.88) / (50 - 40) = -94.55

[60,70]:

f(70) = -1.2^(0.770) + 10,000 = 231.51

f(60) = -1.2^(0.760) + 10,000 = 581.92

average rate of change = (231.51 - 581.92) / (70 - 60) = -35.14

Thus,

Part A:

The population declined the fastest over the time interval [20,30], which has the greatest negative average rate of change (-138.11).

Part B:

The population declined the slowest over the time interval [60,70], which has the smallest negative average rate of change (-35.14).

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The volume of the composite solid which is the combined volume of the rectangular prism is 272 cm³

To determine the volume of the composite solid, we have to find the volume of two different rectangular prism.

volume of rectangular prism = length * width * height

for the first prism;

volume of rectangular prism = 8 * 4 * 5

volume of rectangular prism = 160cm³

For the second prism

volume of rectangular prism = 14 * 8 * 1

volume of rectangular prism = 112 cm³

The volume of the composite solid = volume of first rectangular prism  + volume of second rectangular prism

volume of composite solid = (160 + 112) cm³

volume of composite solid = 272cm³

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The function f(x) is not a straight line and therefore cannot be represented by a linear function like g(x).

The function g(x)=2x-3 is a linear function with a slope of 2 and a y-intercept of -3. It is not directly related to the function f(x) represented by the graph.

The graph of f(x) shows a non-linear function with a maximum value at x=2 and a minimum value at x=6. The function f(x) is not a straight line and therefore cannot be represented by a linear function like g(x).

While the functions f(x) and g(x) may have different shapes and characteristics, they can still be compared and analyzed in various ways. For example, one could find the x- and y-intercepts of both functions, determine their rates of change or slopes, or find their zeros or critical points. However, it's important to note that the relationship between two functions depends on the specific context and the questions being asked.

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What is the relationship between the two functions f(x) and g(x) based on the graph shown? A graph is shown for a function f(x) . The equation g(x)=2x-3 represents a second function.

The quadrilateral with no pair of parallel sides is trapezium

Given data ,

A = a quadrilateral with no pair of parallel sides

This type of quadrilateral is called a trapezium. In some countries, a trapezium is defined as having exactly one pair of parallel sides, while in other countries, a trapezium is defined as having at least one pair of parallel sides.

In any case, a quadrilateral with no pair of parallel sides is not considered a trapezium. Instead, it is known as a general quadrilateral.

There are three types of trapezoids , and those are given below:

a) Isosceles Trapezoid

b) Scalene Trapezoid

c) Right Trapezoid

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Answer:

[tex]a_n=1.04\cdot a_{n-1}\ \ ,\ \ a_1=35,000[/tex]

Step-by-step explanation:

The salary is dependent upon the number of years you have worked.

Your salary increases by 1.04 times every year.

So, your salary over the years can be expressed as a Geometric Progression

35000, 35000*(1.04)², 35000*(1.04)³, ...

=> Common Ratio (r) = 1.04

∴ [tex]a_n=1.04\cdot a_{n-1}\ \ ,\ \ a_1=35,000[/tex]

The probability of two sixes when the dice is rolled twice is 9/25

Given that;

probability of getting 6,

P(6) = 3/5

Since both dice can be rolled independently

Therefore,

So to find probability of getting two 6 when two dices are rolled twice

We directly multiply it

= (3/5) x (3/5)

=  9/25

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Five pairs of size 8 shoes, lined up end to end, will cover 483 1/3 inches.

Since one size 8 shoe measures 9 2/3 inches, a pair of size 8 shoes will measure 19 1/3 inches (9 2/3 x 2). To determine how many inches five pairs of size 8 shoes will cover, we can multiply the length of one pair (19 1/3 inches) by 5.

19 1/3 x 5 = 96 2/3

Therefore, five pairs of size 8 shoes, lined up end to end, will cover 96 2/3 inches.

However, since the measurement for one size 8 shoe was given as a mixed number, we need to convert the final answer to a mixed number as well.

96 2/3 can be expressed as 95 5/6, which is the final answer. Therefore, five pairs of size 8 shoes, lined up end to end, will cover 483 1/3 inches (95 5/6 x 5).

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The 50th percentile is a commonly used statistic in data analysis. It represents the value below which 50% of the data falls.

In other words, it divides the data into two equal parts. There are two other statistics that have the same value as the 50th percentile, namely the second quartile and the median. The second quartile is the middle value of the data when it is arranged in ascending or descending order.

It is also known as the 50th percentile or the median. The first quartile is the value below which 25% of the data falls, and the third quartile is the value below which 75% of the data falls.

The mean is another commonly used statistic in data analysis. It is the sum of all the values in the data divided by the total number of values. Unlike the median, the mean is affected by extreme values or outliers in the data. This means that if there are outliers in the data, the mean may not be a good measure of central tendency.

The mode is the value that occurs most frequently in the data. It is another measure of central tendency that can be used in addition to the median and mean.

In summary, the 50th percentile is equivalent to the second quartile and the median. These statistics are all measures of central tendency that help to describe the distribution of data. The choice that best answers the question is option A: Second quartile; median.

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Step-by-step explanation:

A higher confidence interval means less power which in turns means a smaller rejection religion.So our confidence interval would become wider.

It will take 8 hours for 4 painters to paint a building

Using direct variation  formula

t = k * n

where

t is the time it takes to paint the building,

n is the number of painters and

k is the constant of proportionality.

For the problem we have that

it takes 7 painters 14 hours to paint the building

solving for k

14 = k * 7

k = 2

time for 4 painters

t = 2 * 4

t = 8

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The opposite side is 12x. Since angle β terminates in Quadrant I, both the adjacent and opposite sides are positive. cosβ = 5/13, sinβ = 12/13, and tanβ = sinβ/cosβ = 12/5

The sine of an angle is equal to the length of the opposite side divided by the length of the hypotenuse, and the cosine of an angle is equal to the length of the adjacent side divided by the length of the hypotenuse. Using this information, we can find the lengths of the sides of two right triangles that have angles α and β.

For angle α, since sinα = 3/5 and the sine of an angle is the opposite side divided by the hypotenuse, we can let the opposite side be 3x and the hypotenuse be 5x for some positive value of x. Then, using the Pythagorean theorem, we can find the length of the adjacent side:

cosα = √(1 - sin^2α) = √(1 - 9/25) = 4/5

Therefore, the adjacent side is 4x. Since angle α terminates in Quadrant II, the adjacent side is negative. So, we have:

cosα = -4/5, sinα = 3/5, and tanα = sinα/cosα = -(3/4)

For angle β, since cosβ = 5/13 and the cosine of an angle is the adjacent side divided by the hypotenuse, we can let the adjacent side be 5x and the hypotenuse be 13x for some positive value of x. Then, using the Pythagorean theorem, we can find the length of the opposite side:

sinβ = √(1 - cos^2β) = √(1 - 25/169) = 12/13

Therefore, the opposite side is 12x. Since angle β terminates in Quadrant I, both the adjacent and opposite sides are positive. So, we have:

cosβ = 5/13, sinβ = 12/13, and tanβ = sinβ/cosβ = 12/5

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The critical numbers of g(θ) on the interval 0 ≤ θ < 2π are:  θ = π/3, 2π/3, 4π/3, 5π/3, 7π/3, 8π/3, 10π/3, and 11π/3.

To find the critical numbers of g(θ) = 4θ - tan(θ) on the interval 0 ≤ θ < 2π, we need to find the values of θ where the derivative of g(θ) is equal to 0 or undefined.

First, we find the derivative of g(θ) using the chain rule and quotient rule:

g'(θ) = 4 - sec²(θ)

To find where g'(θ) is equal to 0, we set the derivative equal to 0 and solve for θ:

4 - sec²(θ) = 0

sec²(θ) = 4

Taking the square root of both sides, we get:

sec(θ) = ±2

Since sec(θ) = 1/cos(θ), we can rewrite this as:

cos(θ) = ±1/2

We know that on the interval 0 ≤ θ < 2π, the cosine function is positive in the first and fourth quadrants and negative in the second and third quadrants.

Therefore, we need to find the values of θ in the first and fourth quadrants where cos(θ) = 1/2, and the values of θ in the second and third quadrants where cos(θ) = -1/2.

For cos(θ) = 1/2, we have:

θ = π/3 or 5π/3 in the first quadrant
θ = 7π/3 or 11π/3 in the fourth quadrant

For cos(θ) = -1/2, we have:

θ = 2π/3 or 4π/3 in the second quadrant
θ = 8π/3 or 10π/3 in the third quadrant

Therefore, the critical numbers of g(θ) on the interval 0 ≤ θ < 2π are:

θ = π/3, 2π/3, 4π/3, 5π/3, 7π/3, 8π/3, 10π/3, and 11π/3.

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If the marginal cost differs across the two groups, then a monopoly can price discriminate among groups of buyers. This is because the monopoly can charge a higher price to the group with a relatively lower elasticity of demand, which will generate more revenue and profits for the monopoly.

A monopoly can price discriminate among groups of buyers. A monopoly can price discriminate among groups of buyers if demand elasticity differs across the two groups. This means that the monopoly can charge different prices based on the varying price sensitivities of different consumer groups.

                                     However, if the average total cost differs across the two groups, then price discrimination may not be possible because the monopoly cannot charge a higher price without incurring higher costs. Therefore, the correct answer is C) marginal.

The options A (average total cost differs), B (marginal cost differs), and C (marginal) do not complete the sentence accurately.

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To evaluate which of a set of curves fits the data best, you can use the option "c. R2", also known as the coefficient of determination.

R2 is a statistical measure that helps determine the proportion of variance in the dependent variable explained by the independent variable(s) in the regression model. It ranges from 0 to 1, with higher values indicating a better fit of the curve to the data.

To evaluate which of a set of curves fits the data best, we can use the R2 (coefficient of determination) metric. R2 is a statistical measure that represents the proportion of the variance in the dependent variable that is explained by the independent variable(s) in a regression model.

                                         A higher R2 value indicates a better fit of the curve to the data. APE (absolute percentage error), MAPE (mean absolute percentage error), and NPV (net present value) are not appropriate metrics for evaluating the fit of a curve to data. APE and MAPE are typically used to measure forecasting accuracy, while NPV is a financial metric used to determine the present value of future cash flows.

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Aliaa is skating down a ramp with skateboard wheels that have a diameter of 60mm.

The diameter of Aliaa's skateboard wheels is given as 60mm. The diameter is the distance across the wheel through its center. It is important to note that the diameter is not the same as the radius, which is the distance from the center of the wheel to its outer edge. To calculate the radius of the wheel, we divide the diameter by 2. So, the radius of Aliaa's skateboard wheels is 30mm (60mm/2).

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The probability that Anna and Ben both pick a red sweet is 1/5.

We know that the probability of Anna picking a red sweet from bag A is 2/5.

Therefore, the probability of her picking a yellow sweet from bag A is 1 - 2/5 = 3/5.

We also know that the probability of Anna and Ben both picking a yellow sweet from their respective bags is 1/10.

Therefore, the probability of Anna picking a yellow sweet from bag A is 3/5, and the probability of Ben picking a yellow sweet from bag B is 1/2, since we know nothing about the composition of bag B.

The probability of Anna and Ben both picking a yellow sweet can be expressed as:

(3/5) × (1/2) = 3/10

We can use this information to set up an equation involving the probabilities of Anna and Ben both picking a red sweet:

(2/5)×P(Ben picks red sweet from bag B) = P(Anna and Ben both pick red sweets)

We know that the sum of the probabilities of all possible outcomes must be 1.

Therefore, we can express the probability of Ben picking a red sweet from bag B as:

P(Ben picks red sweet from bag B) = 1 - P(Ben picks yellow sweet from bag B)

= 1 - 1/2

= 1/2

Substituting this value into our equation, we get:

(2/5) × (1/2) = P(Anna and Ben both pick red sweets)

1/5 = P(Anna and Ben both pick red sweets)

Therefore, the probability that Anna and Ben both pick a red sweet is 1/5.

To learn more on probability click:

https://brainly.com/question/11234923

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