Question 5 of 25
The standard deviations of four data sets are shown in the table below. Which
of the data sets is the most spread out?
Data set
Standard deviation
Data set A
5.21
Data set B
4.88
Data setc
0.00
Data set D
3.39
O A. Data set B
B. Data set
C. Data set A
D. Data set D

The sampling distributions are used for statistical tets.

Hence,The sampling distributions are used for statistical tets.

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Answer:

8π

Step-by-step explanation:

2 * π * r * 0.5

16π * 0.5

8π

Answer:

4 pi

Step-by-step explanation:

Step-by-step explanation:

1. Review a given problem : \(1+4(3x-10)-12x\)

2.distributive property:  \(4\left(3x-10\right) = 12x-40\)

\(=1+12x-40-12x\)

3. Simplify:  \(1+12x-40-12x\)

\(-39 +12x-12x\)

\(=-39\)

The height and radius of the cone that will use the smallest amount of paper are h ≈ 2.45 cm and r ≈ 1.22 cm, respectively.

The minimum paper will be used when the surface area of the cone is minimized. Let the height and radius of the cone be h and r, respectively. Then, using the formula for the volume of a cone, we have:

V = (1/3)πr^2h = 33 cm^3

Solving for h, we get:

h = 99/(πr^2)

Next, we need to express the surface area of the cone in terms of r. The surface area is given by:

A = πr√(r^2 + h^2)

Substituting the expression for h obtained above, we have:

A = πr√(r^2 + (99/πr^2)^2)

To find the value of r that minimizes A, we take the derivative of A with respect to r and set it equal to zero:

dA/dr = π(2r√(r^2 + (99/πr^2)^2) + (r^2 + (99/πr^2)^2)^(-1/2)(2r(99/πr^3)))

Setting dA/dr = 0 and solving for r, we get:

r = (33/(2π))^(1/4) ≈ 1.22 cm

Substituting this value of r back into the equation for h, we obtain:

h ≈ 2.45 cm

Therefore, the height and radius of the cone that will use the smallest amount of paper are h ≈ 2.45 cm and r ≈ 1.22 cm, respectively.

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Answer:

Please see the attachment, none of the graphs you showed was correct.

Step-by-step explanation:

Hope it helps :)

Answer:

4545

Step-by-step explanation:

1. Factor the following integer:

20657025

The last digit of 20657025 is 5, which means it is divisible by 5

20657025 = 5×4131405:

20657025 = 5×4131405

The last digit of 4131405 is 5, which means it is divisible by 5

4131405 = 5×826281:

20657025 = 5×5×826281

The sum of the digits of 826281 is 8 + 2 + 6 + 2 + 8 + 1 = 27, which is divisible by 9. This means 826281 is too

826281 = 9×91809:

20657025 = 5×5×9×91809

9 = 3^2:

20657025 = 5×5×3^2×91809

The sum of the digits of 91809 is 9 + 1 + 8 + 0 + 9 = 27, which is divisible by 9. This means 91809 is too

91809 = 9×10201:

20657025 = 5×5×3^2×9×10201

9 = 3^2:

20657025 = 5×5×3^2×3^2×10201

Because 10201 is odd, only test odd numbers for divisibility

10201 is not divisible by 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97 or 99

10201 = 101×101 which means 10201 is divisible by 101:

20657025 = 5×5×3^2×3^2×101×101

3 is prime:

20657025 = 5×5×3^2×3^2×101×101

5 is prime:

20657025 = 5×5×3^2×3^2×101×101

Because 101 is odd, only test odd numbers for divisibility

101 is not divisible by 3, 5, 7 or 9

Since 101 is not divisible by any integer up to 10, it is prime:

20657025 = 5×5×3^2×3^2×101×101

There are 4 copies of 3, 2 copies of 5 and 2 copies of 101 in the product:

Answer: 20657025 = 3^4×5^2×101^2

----------------------------------------

2. Simplify the following:

sqrt(3^4×5^2×101^2)

| | 1 | 0 | 1

× | | 1 | 0 | 1

| | 1 | 0 | 1

| 0 | 0 | 0 | 0

1 | 0 | 1 | 0 | 0

1 | 0 | 2 | 0 | 1:

sqrt(3^4×5^2×10201)

5^2 = 25:

sqrt(3^4×25×10201)

3^4 = (3^2)^2:

sqrt((3^2)^2 25×10201)

3^2 = 9:

sqrt(9^2×25×10201)

9^2 = 81:

sqrt(81×25×10201)

81×25 = 2025:

sqrt(2025×10201)

2025×10201 = 20657025:

sqrt(20657025)

sqrt(20657025) = sqrt(81×255025) = sqrt(3^4×505^2):

sqrt(3^4 505^2)

sqrt(3^4 505^2) = sqrt(3^4) sqrt(505^2) = 3^(4/2)×505^(2/2) = 9×505:

9×505

9×505 = 4545:

Answer: 4545

Without specific data on the number of students who prefer each option, we cannot calculate the probability.

To determine the probability that a student prefers the zoo or the water park, we need to know the total number of students and the number of students who prefer each option. Without this information, it is not possible to calculate the probability accurately.

To calculate the probability, we would need to divide the number of students who prefer the zoo or the water park by the total number of students. For example, if there are 50 students in total and 30 prefer the zoo and 20 prefer the water park, the probability would be:

P(prefer zoo or water park) = (30 + 20) / 50 = 50 / 50 = 1

However, without specific data on the number of students who prefer each option, we cannot calculate the probability.

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Sue Smith can calculate confidence limits for sampling error by using a confidence interval. a confidence interval is a range of values that is likely to contain the true population parameter.

The confidence interval is calculated from the sample data and the confidence level. The confidence level is the probability that the true population parameter is within the confidence interval.

For example, if Sue Smith wants to calculate a 95% confidence interval for the mean age of homemakers in the midwestern United States,

she would need to collect a sample of homemakers and calculate the sample mean. She would then use the sample mean and the confidence level to calculate the confidence interval.

The confidence interval would be a range of values that is likely to contain the true mean age of homemakers in the midwestern United States. For example, the confidence interval might be 35 to 45 years old.

This means that there is a 95% probability that the true mean age of homemakers in the midwestern United States is between 35 and 45 years old.

Sue Smith can use the confidence interval to calculate the sampling error. The sampling error is the difference between the sample mean and the true population mean.

The sampling error can be calculated by subtracting the sample mean from the confidence interval. For example, if the confidence interval is 35 to 45 years old and the sample mean is 40 years old, the sampling error is 5 years.

The sampling error is important because it tells Sue Smith how accurate her estimate of the true population mean is. The smaller the sampling error, the more accurate the estimate.

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Answer:

12 to 27! :D

Step-by-step explanation:

In the case of a plane mirror, the height of the image formed is equal to the height of the object. Therefore, the image produced by the mirror will have the same height as the 12-inch object. Hence, the height of the image produced by the mirror is 12 inches.

When light rays reflect off a plane mirror, the image formed appears to be behind the mirror and is a virtual image. The image distance and the object distance are equal in magnitude but opposite in direction. However, the size and orientation of the image are the same as that of the object. In this scenario, the object has a height of 12 inches, and it is placed 30 inches in front of the mirror. When a ray of light from the object strikes the mirror at a 45-degree angle, it reflects off the mirror following the law of reflection. According to the properties of reflection in a plane mirror, the image formed will be located behind the mirror, at the same distance as the object, and the size of the image will be the same as that of the object. Therefore, the height of the image will also be 12 inches. So, the image produced by the mirror will have a height of 12 inches, the same as the object's height.

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a. There would be 2,023,203 5-card hands have at least one club.

b. There would be 1,329,168  5-card hands have at least two cards with the same rank

(a) To find the number of 5-card hands with at least one club, we can find the total number of 5-card hands and subtract the number of 5-card hands with no clubs.

Total number of 5-card hands = C(52,5) = 2,598,960

Number of 5-card hands with no clubs = C(39,5) = 575,757

So, the number of 5-card hands with at least one club = 2,598,960 - 575,757 = 2,023,203.

Therefore, there are 2,023,203 5-card hands with at least one club.

(b) To find the number of 5-card hands with at least two cards with the same rank, we can use the principle of inclusion-exclusion.

Number of 5-card hands with at least one pair = C(13,1) × C(4,2) × C(12,3) × C(4,1)³

Number of 5-card hands with at least two pairs = C(13,2) × (C(4,2))² × C(11,1) × 4

Number of 5-card hands with at least three of a kind = C(13,1) × C(4,3) × C(12,2) × (C(4,1))²

Number of 5-card hands with at least one four of a kind = C(13,1) × C(4,4) × C(12,1) × C(4,1)

So, the total number of 5-card hands with at least two cards with the same rank = Number of 5-card hands with at least one pair + Number of 5-card hands with at least two pairs + Number of 5-card hands with at least three of a kind + Number of 5-card hands with at least one four of a kind

= (13 × 6 × 220 × 256) + (78 × 6 × 11 × 4) + (13 × 4 × 66 × 256) + (13 × 1 × 12 × 4)

= 1,098,240 + 13,728 + 216,576 + 624

= 1,329,168.

Therefore, there are 1,329,168 5-card hands with at least two cards with the same rank.

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Answer:

y=-3x-4

for the line that passes through the points

Comparing 7/10 and 1/3 by first comparing both to 1/2,

Hence, the first mistake was in Step 1

If the columns of matrix B are linearly dependent, then the columns of AB are also linearly dependent.

Suppose the columns of matrix B are linearly dependent, which means there exist constants c₁, c₂, ..., cₙ (not all zero) such that c₁b₁ + c₂b₂ + ... + cₙbₙ = 0, where b₁, b₂, ..., bₙ are the columns of B.

Now, let's consider the product AB. Suppose A is an m × n matrix.

The jth column of AB is given by the product AB(:, j) = A(b₁j) + A(b₂j) + ... + A(bₙj), where b₁j, b₂j, ..., bₙj are the jth columns of B.

Substituting the linear dependence relation for the columns of B into the expression for AB(:, j), we get:

AB(:, j) = A(c₁b₁ + c₂b₂ + ... + cₙbₙ)

         = c₁A(b₁) + c₂A(b₂) + ... + cₙA(bₙ)

Since matrix multiplication distributes over column vectors, we have:

AB(:, j) = c₁A(b₁) + c₂A(b₂) + ... + cₙA(bₙ)

This shows that the jth column of AB can be expressed as a linear combination of the columns of A, multiplied by the corresponding coefficients c₁, c₂, ..., cₙ. Therefore, if the columns of B are linearly dependent, the columns of AB are also linearly dependent.

In conclusion, if the columns of matrix B are linearly dependent, then so are the columns of the product AB.

Complete Question:

Show that if the columns of B are linearly dependent, then so are the columns of AB.

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Answer:

The answer to the question provided is possibly 2.

Step-by-step explanation:

\( \: \: \: \: \: \: \: \: \: \: \: \: 3y + 77 = 2y + 79 \\ \frac{ - 2y \: \: \: \: \: \: = - 2y}{1y + 77 = 79} \\ \frac{ \: \: \: \: \: \: \: \: - 77 = - 77}{ \frac{1y}{1} = \frac{2}{1} } \\ \\ y = 2\)

The fraction of vehicles on the road are trucks is 3/7

Let's assume there are a total of x vehicles on the road.

According to the first statement, 3/7 of those vehicles are trucks followed by a car. This means that (3/7)x trucks are on the road and are followed by a car.

According to the second statement, 3/9 of the vehicles are cars followed by a truck. This means that (3/9)x cars are on the road and are followed by a truck.

We know that the total number of vehicles on the road is x. So we can write

(3/7)x + (3/9)x = x

Simplifying this equation

(27/63)x + (21/63)x = x

(48/63)x = x

We can then solve for x

x = 63

So there are 63 vehicles on the road.

To find out what fraction of vehicles on the road are trucks, we need to determine what fraction of those 63 vehicles are trucks.

According to the first statement, 3/7 of the vehicles are trucks followed by a car.

So the fraction of vehicles that are trucks is 3/7

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73. ∫sin³(x)cos(x) dx = (sin⁴(x))/4 + C

75. ∫tan³(2x)sec²(2x) dx = (tan⁴(2x))/8 + C

77. ∫tan(2)sec²(1) dx = tan(2) + C

79. ∫sin³(x) dx = (-3/4)cos(x) + (1/12)cos(3x) + CC



 73. To evaluate the integral ∫sin³(x)cos(x) dx, we can use the substitution u = sin(x), which gives du = cos(x) dx. Substituting these values, the integral becomes ∫u³ du. Integrating u³ gives u⁴/4 + C, where C is the constant of integration. Substituting back, the final solution is (sin⁴(x))/4 + C.

75. For the integral ∫tan³(2x)sec²(2x) dx, we can use the substitution u = tan(2x), which gives du = 2sec²(2x) dx. Substituting these values, the integral becomes (1/2)∫u³ du. Integrating u³ gives u⁴/4 + C, where C is the constant of integration. Substituting back, the final solution is (tan⁴(2x))/8 + C.

77. The integral ∫tan(2)sec²(1) dx can be evaluated without substitution as it does not contain any variables. Using the property ∫sec²(x) dx = tan(x) + C, where C is the constant of integration, the solution is tan(2) + C.

79. To evaluate ∫sin³(x) dx, we can use the identity sin³(x) = (3/4)sin(x) - (1/4)sin(3x). The integral becomes ∫[(3/4)sin(x) - (1/4)sin(3x)] dx. Integrating term by term, we have (3/4)∫sin(x) dx - (1/4)∫sin(3x) dx. Using the property ∫sin(x) dx = -cos(x) + C and ∫sin(3x) dx = -(1/3)cos(3x) + C, where C is the constant of integration, we obtain the final solution as (-3/4)cos(x) + (1/12)cos(3x) + C.

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The division of 2.079 by 0.693 is approximately equal to 2.996.

To divide 2.079 by 0.693, we follow these steps:

Write down the division problem: 2.079 ÷ 0.693.

Perform the division operation: Divide 2.079 by 0.693.

- Start by dividing the whole numbers: 2 ÷ 0 = 0.

- Bring down the decimal point and write 0. in the quotient.

- Now, divide the decimal parts: 0.079 ÷ 0.693.

- To simplify the division, multiply both the dividend and divisor by 1000 to eliminate the decimal points: 0.079 × 1000 ÷ 0.693 × 1000.

- This gives us 79 ÷ 693.

- Divide 79 by 693: 79 ÷ 693 = 0.114.

Combine the whole number and decimal part: 0 + 0.114 = 0.114.

Round the answer to the correct number of significant figures, which is three in this case. Since the digit following the third significant figure (4) is less than 5, we keep the third significant figure unchanged.

Therefore, the final answer is approximately 0.114.

Thus, 2.079 ÷ 0.693 is approximately equal to 2.996 when rounded to three significant figures.

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Triangles AED and ABC are congruent to one another according to SSS congruency.

Given,

The side BC is equal to side DE.

The side AC is equal to side AD.

∠BAC = ∠DAE

We have to find that whether  triangle ABC congruent to triangle AED;

Here,

The side AB = 7 units.

The side AE = 7 units.

Therefore,

The side AB is equal to side AE.

The sum of all the angle of a triangle is 180°.

Consider the triangle ABC and triangle AED.

AB = AE

AC = AD

BC = DE

So, the triangle ABC is congruent to triangle AED by SSS congruency.

That is,

The triangle AED and triangle ABC are congruent by to each other by SSS congruency.

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The image for the question is attached below.

Answer:

The answer is 15.9 centimeters. If you work backward with the formula 2pir = circumphrence, you get diameter *pi = 50. To find diameter, you divide 50 by pi and the answer is 15.9 centimeters.

Step-by-step explanation:

The diameter to the nearest tenth of a centimeter is mathematically given as

31.8cm, option D

Question Parameters:

Circle Q has a circumference of approximately 50 centimeters.

Generally, the equation for the circumference   is mathematically given as

C=2\pir

Therefore

r=C/ \pi

r=50/3.14

r=15.9cm

Therefore,

d=2r

d=2*15.9

d=31.847

In conclusion, the diameter to the nearest tenth of a centimeter. is

31.8cm

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Answer:

See below

Step-by-step explanation:

Question 1:

For polynomial:

\( x^2 + 11x + 24\)

add upto 11 x

multiply to 24

Question 2:

For polynomial:

\( x^2 - 12x + 20\)

add upto - 12 x

multiply to 20

Answer: 90

Step-by-step explanation:

91 - 1  = 90

Answer: 90

Step-by-step explanation:

The direction of vector B is 80 degrees counterclockwise from the positive x-axis. The magnitude of vector A + B is approximately 9.2 m, and its direction is approximately -61 degrees counterclockwise from the positive x-axis.

To find the magnitude of vector A + B, we need to add the components of A and B separately.

Let's assume vector A is given by (A_x, A_y). Adding A and B, we have (A_x + B_x, A_y + B_y). Given that A = (-3.2 m) x^ + (2.7 m) y^, and B = (-1.1 m) x^ + (5.3 m) y^, we can add their components: (-3.2 m - 1.1 m, 2.7 m + 5.3 m) = (-4.3 m, 8 m).

The magnitude of the vector A + B can be calculated using the Pythagorean theorem: magnitude = sqrt((-4.3 m)^2 + (8 m)^2) ≈ 9.2 m.

To find the direction of the vector A + B, we can use the inverse tangent function. The direction is given by the angle between the positive x-axis and the vector A + B. Using the components of A + B, we find the angle: angle = arctan((8 m) / (-4.3 m)) ≈ -61 degrees counterclockwise from the positive x-axis.

Therefore, the direction of vector A + B, expressed using two significant figures, is approximately -61 degrees.

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1.   4x − 2y = 10 and 2x − y = 5

Lines are coincident.

2.  y = 2x − 3 and −2x + y = −5

Lines are parallel.

3.  2x − 5y = 14  and 3x + 4y = 10

Lines are intersecting.

It is a system of an equation in which the highest power of the variable is always 1. A one-dimension figure that has no width. It is a combination of infinite points side by side.

1.   4x − 2y = 10 and 2x − y = 5

2.  y = 2x − 3 and −2x + y = −5

3.  2x − 5y = 14  and 3x + 4y = 10

\(\rm \dfrac{a_1}{a_2} \neq \dfrac{b_1}{b_2} \ \ \ \ \ \ \ \ \ \ \ Lines\ are\ intersecting\\\\\rm \dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} \neq \dfrac{c_1}{c_2}\ \ \ \ Lines \ are\ parallel\\\\\rm \dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} = \dfrac{c_1}{c_2} \ \ \ \ Lines\ are\ coincident\)

1.   4x − 2y = 10 and 2x − y = 5

Lines are coincident.

2.  y = 2x − 3 and −2x + y = −5

Lines are parallel.

3.  2x − 5y = 14  and 3x + 4y = 10

Lines are intersecting.

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The completed table is:

Term Number    1       2    3    4   5     6

Term Value       6     10   14   18  22   26

In order to determine the term values, the rate of increase in the number of videos that Violet has at the end of each week has to be determined.

Rate of increase in the number of videos can be determined by dividing the change in the number of videos per week by the change in the number of weeks.

Rate of increase = change in the number of videos / change in the number of weeks

(10 - 6) / (2 - 1)

4 / 1 = 4 videos per week

Number of videos in week 5 = 18 + 4 = 22

Number of videos in week 6 = 22 + 4 = 26

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Answer:

-1/2

Step-by-step explanation:

Answer:

Compared to the graph of y = x, the graph of y = -2x is steeper.

Compared to the graph of y = x, the graph of y = -2x intersects the y-axis at the same point.

Compared to the graph of y = x, the graph of y = x + ⅔ is equally steep.

Compared to the graph of y = x, the graph of y = x + ⅔ intersects the y-axis at a higher point.

hiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiStep-by-step explanation:

The energy transferred to the water in 5 minutes is 2700 Joules.

To calculate the energy transferred to the water, we can use the formula:

Energy = Power x Time

where Power = Potential Difference x Current

Given potential difference = 12V and current = 750mA, we can calculate the power as:

Power = 12V x 750mA = 9W

Now, the time taken to heat the water is given as 5 minutes. We need to convert this into seconds to use the SI unit of power, which is watts. So,

Time = 5 minutes = 300 seconds

Putting the values in the formula for energy, we get:

Energy = Power x Time
Energy = 9W x 300s
Energy = 2700 Joules

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