Kayden wraps a gift box in the shape of a square pyramid. The figure below shows a net for the gift box.

5.7 cm

6 cm

How much wrapping paper did he use, in square centimeters?

Standard deviation

a) The distribution of IQ is exactly normal.Trueb) The distribution of the sample mean IQ is approximately normal with mean of 119 and standard deviation of 2.54c) The probability that the sample mean IQ is less than 117 is 0.114d) The probability that the sample mean IQ is greater than 117 is 0.886e) The probability that the sample mean IQ is between 117 and 123 is 0.773Step-by-step explanationa) The distribution of IQ is exactly normalGiven population mean IQ, µ = 119Standard deviation, σ = 18b) The distribution of the sample mean IQ is approximately normal with mean of 119 and standard deviation of 2.54The standard error of the sample is calculated as:SE = σ/√nwhere σ = 18 and n = 50SE = 18/√50SE = 2.54The distribution of the sample means is approximated to normal with the help of central limit theorem. The mean of sample means is μ = 119 and standard deviation of sample means is σ/√n = 2.54.c) The probability that the sample mean IQ is less than 117 is 0.114We need to calculate the z-score using the formula:z = (x-μ)/SEz = (117-119)/2.54z = -0.79Now, using z-table, the probability is calculated as:P(Z < -0.79) = 0.2146The probability that the sample mean IQ is less than 117 is 0.114d) The probability that the sample mean IQ is greater than 117 is 0.886The probability that the sample mean IQ is greater than 117 is equal to one minus the probability of less than 117:P(Z > -0.79) = 1 - 0.2146 = 0.786The probability that the sample mean IQ is greater than 117 is 0.886.e) The probability that the sample mean IQ is between 117 and 123 is 0.773We need to calculate the z-score for 117 and 123 as:z1 = (117-119)/2.54 = -0.79z2 = (123-119)/2.54 = 1.57The probability of sample means between 117 and 123 can be found as:P(-0.79 < Z < 1.57) = 0.773The probability that the sample mean IQ is between 117 and 123 is 0.773.

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The mean cost per container is 1.13 dollars. A 90% confidence interval estimate for the mean is (0.66, 1.60) dollars. Not all costs per container fall inside the confidence interval. The costs of 1.89 and 0.89 dollars per container do not fall inside the confidence interval.

The coach for a sports team computed the mean cost per container of popular sports drinks, which was found to be $1.13. A 90% confidence interval estimate for the mean was calculated to be between $0.66 and $1.60. However, the costs of $1.89 and $0.89 per container did not fall within the confidence interval, indicating that they are not representative of the mean cost. This information could be used to make an informed decision on which sports drink to use for the team, considering factors such as cost and confidence in the mean cost per container.

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Since the angle is in quadrant 2, the sine will be pοsitive. Therefοre, the value οf sin 0 is: sin 0 = 0.8

Trigοnοmetry is a branch οf mathematics that deals with the relatiοnships between the sides and angles οf triangles. It is used tο study and sοlve prοblems invοlving triangles, especially right triangles.

Since cοsine is negative and the angle is in quadrant 2, we knοw that the sine will be pοsitive. We can use the Pythagοrean identity tο find the value οf sine:

sin²θ + cοs²θ = 1

Substituting the value οf cοsine, we get:

sin²θ + (-6/10)² = 1

Simplifying, we get:

sin²θ + 36/100 = 1

sin²θ = 1 - 36/100 = 64/100 = 0.64

Taking the square rοοt οf bοth sides, we get:

sin θ = ±0.8

Since the angle is in quadrant 2, the sine will be pοsitive. Therefοre, the value οf sin 0 is:

sin 0 = 0.8

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Alex feeds his cat 1/21 of the bag each day.

The fraction of the bag that Alex feeds his cat each day is 1/21. This can be calculated using the following formula:

Fraction of Bag = 1/3 / 7

Using algebra, we can solve this equation by multiplying both sides of the equation by 7, which results in the following equation:

1/3 = (1/21) * 7

Simplifying the equation, we get

1/3 = 1/21

Therefore, the fraction of the bag that Alex feeds his cat each day is 1/21.

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The required length of the arc is 5.75 units.

A circular represents 360 degrees. A circular can be split up into smaller sections. An arc is a segment of a circle, and arcs are designated based on their angles. The three types of arcs are semicircles (v = 180°), major arcs (180° v 360°), and minor arcs (0° v 180°).

We have;

∠EFG =30° = π/6

and EF =11 units

To find; length of arc EG.

So, we know that;

∅(Radian) = arc/ radius

π/6 = arc/11

arc = 11π/6

Arc = 5.75 units.

Thus, required length of the arc is 5.75 units.

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Complete question:

The solution for theta in the equation cos2theta = -1 in the range [0, 2π) is Ф = π/2

Given the equation

cos2theta = -1

Express properly

cos(2Ф) = -1

Take the arc cos of both sides

So, we have

2Ф = π

Divide both sides by 2

Ф = π/2

Hence, the value of theta in the range is π/2

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The purchase cost of a car 24,500 with local sales tax rate 4% has following answer,

Total tax paid = $980

Total cost of a car including tax = $25.480.

Purchasing cost of a car = $24,500

Local sales tax rate on a car = 4%

Tax paid on the car purchase = (Purchase price) × (tax rate)

Substitute the value we get,

⇒ Tax amount = 4% of 24,500

⇒ Tax amount = 0.04 x 24,500

⇒ Tax amount = $980

Total cost of a car including tax = ( Tax amount ) + (Purchase price )

Substitute the value we have,

⇒ Total cost of a car  = Purchase price + Tax amount

⇒ Total cost of a car = 24,500 + 980

⇒ Total cost of a car = $25,480

Therefore, the tax paid on the car purchase and the car's total cost including tax is equal to $980 and $25,480 respectively.

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The original fraction is 5/8. The numerator of the original fraction is then n = √6, and the denominator is (√6 + 6). If we add 3 to both the numerator and denominator, we get (√6 + 3)/(√6 + 9). This fraction simplifies to 5/8.

Let the numerator be 'n'. The denominator is 6 more than the numerator, so the denominator is (n + 6).

We can represent this as an equation:

n/(n + 6) = 1

We can solve for the value of n by multiplying both sides by the denominator, (n + 6):

n*(n + 6) = 1*(n + 6)

Simplifying, we get:

n^2 + 6n = n + 6

Subtracting 6n from both sides gives us:

n^2 = 6

Taking the square root of both sides yields:

n = √6

The numerator of the original fraction is then n = √6, and the denominator is (√6 + 6). If we add 3 to both the numerator and denominator, we get (√6 + 3)/(√6 + 9). This fraction simplifies to 5/8.

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The probability that a student is a science major, given they are a graduate student is given as follows:

P(science|graduate) = 0.7203 = 72.03%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The outcomes for this problem are given as follows:

Hence the probability that a student is a science major, given they are a graduate student is obtained as follows:

P(science|graduate) = 188/261

P(science|graduate) = 0.7203 = 72.03%.

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Answer:

0.72

Step-by-step explanation:

The explicit formula is given by the equation a(n) = 50n² + 25n + 25 and the recursive formula is given by a(n) = a(n-1) + 200, with a(1) = 100.

A approach for identifying patterns in numerical sequences is the method of finite differences. It entails first identifying the differences between each word in the sequence, then repeating the procedure with the sequence of differences that results. If a pattern forms where the gaps between the gaps are always the same, the initial sequence exhibits a polynomial pattern. Both the recursive formula, which enables us to compute any term by utilising the previous term in the series, and the explicit formula for the sequence, which allows us to calculate any term in the sequence directly, can be found using the procedure.

Given the views on different days we have:

First finite difference: 300-100 = 200

Second finite difference: 1200-300 = 900

We observe that second finite difference is constant and hence follows a quadratic pattern.

Using the explicit formula we have:

a(n) = 50n² + 25n + 25

where, a(n) is the views on day n.

Using recursive formula:

a(n) = a(n-1) + 200, with a(1) = 100

Hence, the explicit formula is given by the equation a(n) = 50n² + 25n + 25 and the recursive formula is given by a(n) = a(n-1) + 200, with a(1) = 100.

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We know, standard normal distribution is given by Z~N(0, 1) => σ=1Now, P(-0.62 P(Z P(u P(Z P(u) = 0.7392

Given, Random variable Z follows standard normal distribution. To find the value of u such that P(−0.62-0.62)Now, we will find the Z value for -0.62 using standard normal table as follows:-We get the value of P(Z<-0.62) as 0.2676Now, P(Z>-0.62)=1-P(Z<-0.62)=1-0.2676=0.7324Now, P(-Z<0.62)=P(Z<0.62)=0.7324We know, 0.62 lies between u=0 and u', we can find u' using standard normal table as follows:-From the standard normal table, we get that P(Z<0.62)=0.7315P(Z<0)=0.5Now, Z follows standard normal distribution, Z~N(0, 1) => 0.62=(u'-0)/1 => u'=0.62To find the value of u, let's use the formula Z = (X - μ) / σ where X is the observation, μ is the mean and σ is the standard deviation. We know, standard normal distribution is given by Z~N(0, 1) => σ=1Now, P(-0.62 P(Z P(u P(Z P(u) = 0.7392Now, using standard normal table, we get the value of Z when P(Z

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The first four terms of the infinite geometric series are 11/2, 11/6, 11/18, and 11/54.

We can use the formula for the sum of an infinite geometric series to find the value of the first term:

S = a / (1 - r)

Where S is the sum of the infinite geometric series, a is the first term, and r is the common ratio.

Given that:

S=33/4

r=1/3

Substituting the given values:

33/4 = a / (1 - 1/3)

33/4 = a / (2/3)

a = (33/4) × (2/3) = 11/2

Now that we know the first term, we can use the formula for the nth term of a geometric series to find the first four terms:

an = a × r^(n-1)

Where an is the nth term, a is the first term, r is the common ratio, and n is the number of the term we want to find.

So the first four terms are:

a1 = 11/2

a2 = 11/2 × 1/3 = 11/6

a3 = 11/6 × 1/3 = 11/18

a4 = 11/18 × 1/3 = 11/54

Therefore, the first four terms are 11/2, 11/6, 11/18, and 11/54.

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The area of a rhombus is 15 units².

A rhombus is a quadrilateral with four sides that are all the same length. It is sometimes referred to as a lozenge or a diamond. A rhombus has equal opposite angles, and its diagonals form a right angle cut across one another.

Rhombus area can be express using the formula:

Area = (base x height) / 2

where the base and height refer to any two sides of the rhombus that form a right angle.

Given figure: base = 5 units and height = 6 units

Area of a rhombus = (5 × 6) / 2 = 30/2

Area of a rhombus = 15 units²

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Based οn the given οptiοns, the mοst likely cοrrelatiοn value fοr this scatterplοt wοuld be r = -0.383.

Cοrrelatiοn refers tο the statistical relatiοnship between twο οr mοre variables. In οther wοrds, it measures hοw strοngly twο variables are related tο each οther. A cοrrelatiοn value ranges frοm -1 tο +1, with -1 indicating a perfectly negative cοrrelatiοn, 0 indicating nο cοrrelatiοn, and +1 indicating a perfectly pοsitive cοrrelatiοn. A cοrrelatiοn cοefficient οf 0 means there is nο linear relatiοnship between the twο variables.

The cοrrelatiοn cοefficient ranges frοm -1 tο +1, where -1 indicates a perfect negative cοrrelatiοn, 0 indicates nο cοrrelatiοn, and +1 indicates a perfect pοsitive cοrrelatiοn. Based οn the given οptiοns, the mοst likely cοrrelatiοn value fοr this scatterplοt wοuld be r = -0.383. This indicates a mοderate negative cοrrelatiοn between the variables.

The absοlute value οf the cοrrelatiοn cοefficient (0.383) suggests that the relatiοnship is nοt particularly strοng, but there is sοme evidence tο suggest that as οne variable increases, the οther variable tends tο decrease.

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The approximate length of side XY is 3.16 units, side YZ is 4 units, and side ZX is 4.24 units. The approximate perimeter of triangle XYZ is 10.32 units.

To calculate the approximate perimeter of triangle XYZ, we must first find the approximate length of each side. To do this, we can use the Pythagorean theorem. For side XY, we calculate 3² + 3² = 9 + 9 = 18. We then take the square root of 18, which is approximately 3.16. For side YZ, we calculate 4² + 3² = 16 + 9 = 25. We then take the square root of 25, which is approximately 4. For side ZX, we calculate 4² + 4² = 16 + 16 = 32. We then take the square root of 32, which is approximately 4.24. Finally, we add the lengths of all three sides together to get the approximate perimeter of triangle XYZ, which is 3.16 + 4 + 4.24 = 10.32.

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Answer:

57.7 cubic inches

Step-by-step explanation:

1 ounce = 1.8 cubic inches

32 ounces = 57.7 cubic inches

So, the capacity is 57.7 cubic inches.

Answer:

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Class 10

>>Maths

>>Areas Related to Circles

>>Area of Sector and Length of an Arc

>>Find the length of the arc in terms of p

Question

Bookmark

Find the length of the arc in terms of π that subtends an angle of 30

∘

at the centre of a circle of radius 4 cm.

Easy

Updated on : 2022-09-05

Solution

verified

Verified by Toppr

⇒ θ=30

o

and r=4cm

⇒ Length of an arc =

360

o

θ

(2πr)

Where, θ is angle subtended at a center.

2πr is circumference of a circle.

⇒ Length of an arc =

360

o

30

o

×2π×4

⇒ Length of an arc =

12

2π×4

∴ Length of an arc =

3

2π

To find the probability that a randomly selected book has fewer than 168 pages, we need to use the empirical rule, which is a guideline for how data is distributed in a normal distribution.

The empirical rule states that (approximately):

In this case, we have:

We can calculate how many standard deviations away from the mean x is by using this formula:

Plugging in our values, we get:

This means that x is one standard deviation below the mean.

So, we are looking for the probability that a randomly selected book has a value less than -1 standard deviations from the mean. Using the empirical rule, we know that approximately 68% of the data falls within one standard deviation of the mean. Therefore, approximately 34% of the data falls between the mean and -1 standard deviation.

To find the area under the normal distribution curve to the left of -1 standard deviation, we can use a standard normal distribution table (z-table) or calculator. The area to the left of -1 standard deviation is approximately 15.87%.

Therefore, the probability that a randomly selected book has fewer than 168 pages is approximately 15.87%.

// I hope this helps! //

The measurement that is closest to the area of the shaded region is 19 square inches.

So to determine the area of shaded region. we first find by the area of the big rectangle.

Let the dimensions of  rectangle are 10 by 15 inches.

The area would be

[tex]A = 10 *15\\= 150\ inches^{2}[/tex]

Now, we calculate the area of small rectangle.

Let the dimensions of rectangle are 10 by 13 inches.

The area would be

[tex]A = 10 *13\\= 130\ inches^{2}[/tex]

Now we calculate the difference between these two area,

= 150 - 130 inches²

= 20 inches²

19 value is the closest to 20.

So, 19 in² is the closest to the area of the shaded region.

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Complete Question :

Two rectangles were used to form the following figure. Use the ruler provided to measure the dimensions of the figure to the nearest quarter of an inch.

Which measurement is closest to the area of the shaded region of this figure in square inches?

a. 19 in²

b. 11 in²

c. 6 in²

d. 8 in²

6 teaspοοns οf baking sοda are needed fοr 9 cups οf sugar in Trisha's recipe.

We can set up a prοpοrtiοn using the given ratiο οf sugar tο baking sοda:

3 cups sugar : 2 teaspοοns baking sοda

We want tο find hοw many teaspοοns οf baking sοda are needed fοr 9 cups οf sugar, which we can represent as:

9 cups sugar : x teaspοοns baking sοda

Tο set up a prοpοrtiοn, we can crοss-multiply the ratiοs:

3 cups sugar * x teaspοοns baking sοda = 9 cups sugar * 2 teaspοοns baking sοda

Simplifying, we get:

3x = 18

Dividing bοth sides by 3, we get:

x = 6

Therefοre, 6 teaspοοns οf baking sοda are needed fοr 9 cups οf sugar in Trisha's recipe.

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There are 100 seats in business class and 260 seats in economy class on the plane. As,we know that for every 13 seats in economy class, there are 5 seats in business class. We can write this as a fraction:5/13. This fraction represents the ratio of seats in business class to seats in economy class.

We can use this ratio to find the actual number of seats in each class, let's start by finding the total number of seats in business class. To do this, we need to know what fraction of the total number of seats is in business class. We can write this as: 5/18. This fraction represents the ratio of seats in business class to the total number of seats and  can use this fraction to find the actual number of seats in business class:5/18 * 360 = 100. So there are 100 seats in business class.

Now we can use the ratio of seats in economy class to find the actual number of seats in that class. We know that there are 13 seats in economy class for every 5 seats in business class. So the ratio of seats in economy class to seats in business class is:13/5, We can use this ratio to find the actual number of seats in economy class: 13/5 * 100 = 260, so there are 260 seats in economy class.

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Answer: I got it :)

The equation that represents the number of haircuts she needs to do is 10.5x = 168.

Step-by-step explanation:

Given, The Hair Care Salon charges a stylist $30 per day to rent a station at the salon, Rhonda, a stylist makes $10.50 on each haircut.

Therefore, She needs to earn $138 + $30 to make a profit of $138 and let

'x' be the number of haircuts.

Therefore, the equation that equation that represents this situation is.

10.50x = 138 + 30.

10.5x = 168.

Therefore , the solution of the given problem of equation comes out to be y = 1/2x - 1 is the equation for the image of the line following a -2 unit translation on the y-axis.

A variable term is typically used in complex variable algorithms to ensure agreement with both conflicting claims. Numerous academic numbers are shown to be equal using equations expression, which have been mathematical statements. In this case, the normalise technique offers b + 6 to use the info from y + 6 rather than splitting 12 into two parts.

Here,

By deducting 2 from each point's y-coordinate, one can acquire the image of the line after it has been translated -2 units on the y-axis.

The initial formula is

=>  y = 1/2x + 1.

=> y = 1/2x + 1 - 2 when 2 is subtracted from it.

When we simplify, we obtain:

=> y - 2 = 1/2x - 1.

Consequently, y = 1/2x - 1 is the equation for the image of the line following a -2 unit translation on the y-axis.

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y = 1/2x - 1 is the equation for the image of the line.

A mathematical statement proving the equality of two expressions is known as an equation. Variables, constants, mathematical symbols, and operations like addition, subtraction, multiplication, and division are frequently used in it.

One can obtain the picture of the line after it has been translated -2 units on the y-axis by subtracting 2 from each point's y-coordinate.

The basic equation is given

y = 1/2x + 1

y - 2 = 1/2x + 1 - 2          [translated -2 units on the y-axis]

Simplify,

y - 2 = 1/2x - 1

Therefore, y = 1/2x - 1 is the equation for the image of the line.

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Note that the linear equation that represents this relationship is y = -3x + 9.

To write a linear equation to represent this relationship, we need to find the slope and y-intercept of the line that passes through the given points.

Using the formula for slope, we have:

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

= (0 - 9) / (3 - 0)

= -3

Now we can use the point-slope form of a linear equation, y - y1 = m(x - x1), where m is the slope and (x1, y1) is any point on the line. Let's use the point (0, 9):

y - 9 = -3(x - 0)

Simplifying, we get:

y - 9 = -3x

Adding 9 to both sides, we get:

y = -3x + 9

Therefore, the linear equation that represents this relationship is y = -3x + 9.

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Philip is not in the top 5% of weights.

what is probability?

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an event that is impossible, and 1 represents an event that is certain to occur. Probability can also be expressed as a percentage, ranging from 0% to 100%.a) We need to find the probability of selecting a boy in kindergarten whose weight is between 38 pounds and 48 pounds. This can be done by calculating the z-scores and using the z-table.

The z-score for a weight of 38 pounds is:

z = (38 - 44) / 3.2 = -1.875

The z-score for a weight of 48 pounds is:

z = (48 - 44) / 3.2 = 1.25

Using the z-table, the probability of selecting a boy whose weight is between -1.875 and 1.25 is approximately 0.8365.

(b) We need to find the probability of selecting an obese kindergarten boy, which means a boy with a weight over 52 pounds. We can calculate the z-score for a weight of 52 pounds as:

z = (52 - 44) / 3.2 = 2.5

Using the z-table, the probability of selecting a boy whose weight is over 52 pounds is approximately 0.0062.

(c) We need to find the cut-off value for the top 5% of weights, which corresponds to a z-score of 1.645. We can use the z-score formula to solve for the weight value:

z = (x - 44) / 3.2

1.645 = (x - 44) / 3.2

x - 44 = 1.645 * 3.2

x = 49.276

So the cut-off weight value for the top 5% of weights is approximately 49.276 pounds.

Philip's weight of 50 pounds is greater than the mean weight of 44 pounds, but it is less than the cut-off weight value for the top 5% of weights.

Therefore, Philip is not in the top 5% of weights.

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Based on the pattern or sequence, it can be concluded that the missing letter is K.

To understand the principle or fule the sequence follows, let's analyze the letters given:

A - C - E

These letters show the sequence follows the alphabet order but one of the letters is omitted. In the first case, the letter omitted is B and in the second case, the letter omitted is E. Based on this, the missing letter should be K.

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The conclusion of question as discuss below.

The mean is a measure of central tendency that represents the average value of a set of numbers. It is calculated by adding up all the values in the set and then dividing by the total number of values.

Based on the given information, we can say that there is a 95% chance that the true difference (a - b) in the mean weight of the bean burritos between Restaurant A and Restaurant B falls within the interval 0.06 ounce to 0.20 ounce.

Since the confidence interval does not include zero, we can conclude that there is a statistically significant difference between the mean weights of the bean burritos at the two restaurants. Specifically, we can say that the mean weight of the bean burritos at Restaurant A is likely to be heavier than the mean weight of the bean burritos at Restaurant B.

However, it's important to note that we cannot determine the magnitude of the difference or the direction of causation (i.e., whether Restaurant A intentionally makes their burritos heavier or whether they use different ingredients that naturally result in heavier burritos).

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We can infer that there is a statistically significant difference among the mean weights of the bean burritos at the two eateries because the confidence interval does not include zero.

The mean, which reflects the average value of a group of numbers, is a metric of central tendency. It can be calculated by adding up all of the values in the collection, dividing by the total number of values, and then taking the remainder away.

Based on the information provided, we can state that there is a 95% chance that the actual difference (a - b) between Restaurant A and

Restaurant B's mean weight of the bean burritos will lie between 0.06 ounce and 0.20 ounce.

We can infer that there is a statistically significant variance among the mean weights of the bean burritos at the two eateries because the confidence interval does not include zero. We can specifically state that the bean burritos' average weight at Restaurant A is probably heavier than the average bean burrito's weight at Restaurant B.

It's crucial to remember that we cannot establish the size of the difference or the causal relationship. (i.e., whether Restaurant A intentionally makes their burritos heavier or whether they use different ingredients that naturally result in heavier burritos).

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Answer:

Step-by-step explanation:

QR^2=PQ^2+PR^2

QR^2=(8[tex]\sqrt{3}[/tex])^2+(8)^2=8^2*(3+1)=8^2 * (4)

PR=8*2=16

answer is C

Answer:

Approximately 81.159

Step-by-step explanation:

First, set up the equation

56    =   (0.69)(x)

       ^ is 69% of a number

Divide each side by 0.69 to simplify

56 / 0.69 = x

x ≈ 81.159420...

The answer about  number of defective DVDs in a carton are mean number is 0.15, the variance is 0.1575, and the standard deviation is 0.397.

Let X be the number of defective DVDs in a randomly chosen carton of DVDs. We know that:

P(X=0) = 0.90 (90% contain no defective DVDs)

P(X=1) = 0.05 (5% contain one defective DVD)

P(X=2) = 0.03 (3% contain two defective DVDs)

P(X=3) = 0.02 (2% contain three defective DVDs)

Mean: The mean of X is given by:

μ = E(X) = Σ(xi × P(xi)), where xi is the number of defective DVDs and P(xi) is the probability of having xi defective DVDs.

μ = (00.90) + (10.05) + (20.03) + (30.02)

= 0.15

Therefore, the mean number of defective DVDs in a carton is 0.15.

Variance: The variance of X is given by:

σ² = E((X-μ)²) = Σ((xi-μ)² × P(xi)), where xi is the number of defective DVDs and P(xi) is the probability of having xi defective DVDs.

σ² = ((0-0.15)²⁰.⁹⁰) + ((1-0.15)²⁰.⁰⁵) + ((2-0.15)²⁰.⁰³) + ((3-0.15)²⁰.⁰²)

= 0.1575

Therefore, the variance of the number of defective DVDs in a carton is 0.1575.

Standard deviation: The standard deviation of X is given by:

σ = √(σ²)

σ = √(0.1575)

= 0.397

Therefore, the standard deviation of the number of defective DVDs in a carton is 0.397.

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