In the data set below, what is the interquartile range?

12 44 45 45 46 56 57 67 83 94

The rectangular prism has a greater volume than the cylinder.

Here, we have,

Volume of shapes:

The rectangular prism has a greater volume than the cylinder. This is because the rectangular prism fully occupies the space within its boundaries, while the cylinder has empty space above and below it.

The cylinder's rounded shape leaves gaps between its curved surface and the boundaries of the rectangular prism.

Therefore, the rectangular prism can hold more volume than the cylinder as it utilizes the entire space within its shape efficiently.

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The total number of outcomes is given as follows:

12.

The Fundamental Counting Theorem states that if there are m ways for one experiment and n ways for another experiment, then there are m x n ways in which the two experiments can happen simultaneously.

This can be extended to more than two trials, where the number of ways in which all the trials can happen simultaneously is the product of the number of outcomes of each individual experiment, according to the equation presented as follows:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

In the context of this problem, we have that the parameters are given as follows:

Hence the total number of outcomes is given as follows:

3 x 4 = 12.

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Answer:

138,488

Step-by-step explanation:

To find the population of the city in 19 years, we can use the formula for compound interest:

Population = Initial Population × (1 + Growth Rate)^Number of Years

Given that the initial population is 100,000 and the growth rate is 2% per year, we can plug in these values into the formula:

Population = 100,000 × (1 + 0.02)^19

Calculating this expression:

Population = 100,000 × (1.02)^19 ≈ 138,488.12

Rounding this to the nearest whole number, the population of the city in 19 years would be approximately 138,488.

Therefore, the population of the city in 19 years, rounding to the nearest whole number, is 138,488.

From the students diagnostic exam, the 43rd Percentile, 3rd Quartile and 8 Decile are 84.5, 138.5 and 140 respectively.

We first need to sort the scores in ascending order:

34, 36, 66, 74, 76, 78, 84, 85, 99, 103, 121, 123, 123, 125, 130, 133, 137, 140, 145, 156

P43 represents the 43rd percentile, which is the score below which 43% of the scores fall. To find P43, we need to calculate the index of the score that corresponds to the 43rd percentile:

P43 = (43/100) * (n + 1)

P43 = (43/100) * (20 + 1)

P43 = 8.44

Since P43 is not an integer, we can take the average of the scores at the indices 8 and 9 (since the index starts from 1):

P43 = (84 + 85) / 2

P43 = 84.5

Therefore, P43 is 84.5.

The third quartile, Q3, represents the score below which 75% of the scores fall. To find Q3, we calculate the index of the score that corresponds to the 75th percentile:

Q3 = (75/100) * (n + 1)

Q3 = (75/100) * (20 + 1)

Q3 = 15.75

Since Q3 is not an integer, we can take the average of the scores at the indices 15 and 16:

Q3 = (137 + 140) / 2

Q3 = 138.5

Therefore, Q3 is 138.5.

D8 represents the score below which 80% of the scores fall. To find D8, we calculate the index of the score that corresponds to the 80th percentile:

D8 = (80/100) * (n + 1)

D8 = (80/100) * (20 + 1)

D8 = 16.8

Since D8 is not an integer, we can round up to the nearest whole number and consider the score at the 17th index:

D8 = 140

Therefore, D8 is 140.

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The most its volume can be is approximately 0.286 cm³

The least the volume of the tablet can be is approximately 0.4 cm³.

The density of calcium chloride solution depends on its concentration. Let's assume a saturated solution, which has a density of about 1.4 g/cm³ (this value could be slightly different depending on temperature and exact concentration).

Given:

mass (m) = 0.4 grams

density (ρ) = 1.4 grams/cm³

We can rearrange the density formula to solve for volume:

ρ = m/V --> V = m/ρ

So, substituting in our values:

V = 0.4 g / 1.4 g/cm³

= 0.286 cm³

The tablet must have a volume less than or equal to 0.286 cm³ to float in the calcium chloride solution. Therefore, the most its volume can be is approximately 0.286 cm³.

b. Since the tablet sinks in water and alcohol, its density is greater than these liquids. Assuming the alcohol is ethanol, the density of ethanol is about 0.789 g/cm³, and the density of water is 1 g/cm³. As the tablet sinks in both, its density must be higher than 1 g/cm³.

Using the same volume formula and considering the density of water:

V = m/ρ

= 0.4 g / 1 g/cm³

= 0.4 cm³

Therefore, the least the volume of the tablet can be is approximately 0.4 cm³.

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The area of APT by the given data is 0.65 m^2.

We are given that;

PV = VR 35° 5 cm

Now,

The formula to calculate the area of APOR is to draw RT so that RT bisects ∠PRQ and point T is on PQ. This will create two congruent triangles, PRT and QRT, by the ASA criterion. Then, the area of APOR can be found by subtracting the area of QRT from the area of APT.

The length of the bottom base of APT is 2(1.5) = 3 m and the length of the top base of APT is 2(1.5 - 0.4) = 2.2 m.

You are also given that each step is 0.25 m higher than the previous one. This means that the height of APT is 0.25 m.

Using these values, you can plug them into the formula for the area of a trapezoid:

A = 0.5(a + b)h A = 0.5(3 + 2.2)(0.25) A = 0.5(5.2)(0.25) A = 0.65 m^2

Therefore, by the area answer will be 0.65 m^2.

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The statement that will help Melody determine the amount of water needed to fill the tank is D . Find the volume by using the formula V = lwh

The amount of water that Melody needs to be able to fill up the tank would be the volume of the tank .

To find the volume of a rectangular prism, the formula is:

V  = L × W × H

Which is length x width x height. This is the exact formula shown in option D so this is the correct option .

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Options include:
A Find the surface area by using the formula SA = 2hw + 2lh + 2wh

B Find the surface area by using the formula SA = pi * r ^ 2 * h

C. Find the volume by using the formula V = 2lw + 2lh + 2wh

D Find the volume by using the formula V = lwh

The total cost of rents is $180.

In the given table,

The cost of skis per day  = $48

The cost of pole per day = $12

Now since given that,

Alveres rents for 3 days

Therefore,

The cost of skis for 3 days  = $48 x 3

                                             =  $144

The cost of pole for 3 days = $12 x 3

                                             = $36

To find the total cost of rental,

Adding the cost of 3 days of skis and cost of 3 days of poles,

Hence,

Total cost of rents = $144 + $36

                               = $180

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The volume of the cylinder is 9071.65 cubic centimeters.

We have to find the volume of the cylinder with a height of 25 cm.

The base has a diameter of 21.5 cm.

Radius of cylinder = 21.5/2

=10.75 cm

The formula for Volume =πr²h

Where r is the radius and height is 25 cm.

Plug in the values of radius and height in to the volume formula.

=3.14×10.75²×25

=9071.65 cubic centimeters.

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The index in the radical is,

⇒ 7

We have to given that,

The expression is,

⇒ [tex]\sqrt[7]{3^{4} }[/tex]

Since, We know that,

The index of a radical indicates the degree of the root, such as the square root has index 2 or the cube root has index 3.

Here, the radical symbol has a small 7 in the corner, which implies that the index is 7.

Therefore, the expression  [tex]\sqrt[7]{3^{4} }[/tex] represents the seventh root of 34.

Thus, The index in the radical is,

⇒ 7

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Answer:

Step-by-step explanation:

The following can be determined about the slopes and y-intercepts of the system of equations: A. The slopes are different, and the y-intercepts are different.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + b

Where:

Based on the information provided above, we have the following system of equations in standard form:

4x + 2y = −2

x − 3y = 24

By rewriting system of equations in slope-intercept form, we have:

y = -2x - 1  ⇒ m = -2, b = -1

y = x/3 - 8  ⇒ m = 1/3, b = -8

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The x-coordinates of the points where the curve intercepts the x-axis are:

x₁ = 2 + (1/2)√26

x₂ = 2 - (1/2)√26

To find the x-coordinates of the points where the curve intercepts the x-axis, we need to set y equal to zero and solve for x.

In other words, we need to find the values of x that make the equation y = 2x² - 8x - 5 equal to zero.

Setting y to zero, we have:

0 = 2x² - 8x - 5

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, we'll use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

For our equation, a = 2, b = -8, and c = -5. Substituting these values into the quadratic formula, we get:

x = (-(-8) ± √((-8)² - 4 × 2 × (-5))) / (2 × 2)

= (8 ± √(64 + 40)) / 4

= (8 ± √104) / 4

Simplifying further:

x = (8 ± 2√26) / 4 = 2 ± (1/2)√26

Therefore, the two x-coordinates where the curve intercepts the x-axis are:

x₁ = 2 + (1/2)√26

x₂ = 2 - (1/2)√26

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h can be written as the composition of:

f(x) = x⁴ and  g(x) = 8x - 6

We know that the function h is written as:

h(x) = (8x - 6)⁴

And we want to write h(x) as a composition of other two functions, such that:

h(x) = f(g(x))

Then we can define f(x) as a quartic power, f(x) = x⁴, and g(x) as the argument g(x) = 8x - 6, then we will get:

f(g(x))  = g(x)⁴ = (8x - 6)

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Answer:

  a) x ≈ -0.5958

  b) x ≈ 1.1403

  c) no solutions

Step-by-step explanation:

You want to solve various exponential equations:

The first of these can be solve using logarithms to transform it to a linear equation. The other two can be solve by the substitution z=3^x. They each then become ordinary quadratic equations in z.

Taking logs, we have ...

  (3x -2)log(9) = (7x -1)log(5)

  x(3log(9) -7log(5)) = -log(5) +2log(9)

  x = log(81/5)/log(729/78125) ≈ -1.2095/-2.0301

  x ≈ -0.5958

Using the substitution described above, this is ...

  2z² -5z = 7

  z² -(5/2)z = 7/2 . . . . . divide by 2

  z² -(5/2)z +25/16 = (7/2) +(25/16) . . . . . . complete the square

  (z -5/4)² = 81/16

  z = 5/4 +9/4 . . . . . . z cannot be negative

  x = log(3.5)/log(3)

  x ≈ 1.1403

  z +1 +56/z = 0 . . . . . using z = 3^x

  z² +z +56 = 0 . . . . . multiply by z

Descartes' rule of signs tells you this has no positive real solutions for z, so the original equation has no solutions. (The graph in the third attachment has no x-intercepts.)

__

Additional comment

In general, equations consisting of a combination of polynomial and exponential expressions (as in (b) and (c)) cannot be solved algebraically. If the exponential expressions are related in a way that allows substitution (as here), then there may be algebraic methods that will work.

We like to write the equations in the form f(x) = 0, so a graphing calculator's display of the function zeros is a display of solutions to the equation. This is what we have done in the first three attachments.

Using the log expressions we developed, you can find the values of x to as many decimal places as your calculator provides. More significant digits are shown in the fourth attachment.

<95141404393>

Answer: x=26 degrees. These angles are complementary angles, meaning they add up to 90 degrees. if you do 90-64, you get 26 degrees.

Answer:

  (b)  3 units

Step-by-step explanation:

You want to know the length of OB' when OB = 3/4 and ∆ABC is dilated about point O by a factor of 4.

The dilation factor multiplies every length.

If OB is 3/4, then OB' is 4(3/4) = 3.

The length of OB' is 3 units.

<95141404393>

The point (x, y) = (- 1, 2) (Point A) is the solution to the system of linear equations.

In this problem we find the representation of two linear equations set on Cartesian plane, the system consists in two equations with two variables. We are asked to find the solution to the system of linear equations. Graphically speaking, the solution to the system of linear equations is represented by a point of intersection.

Then, by direct inspection, we find that the solution to the system of linear equations is (x, y) = (- 1, 2). (Point A)

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The measurement of each numbered angle are,

⇒ ∠10 = 115°

⇒ ∠ 11 = 65 degree

⇒ ∠12 = 115°

We have to given that,

Two intersecting lines are shown in figure.

Since, We know that,

Opposite angle of intersecting lines are vertically opposite angle and both are equal.

Hence, We get;

⇒ ∠ 11 = 65 degree

And, By definition of linear pair angle,

⇒ ∠11 + ∠10 = 180°

⇒ 65° + ∠10 = 180°

⇒ ∠10 = 180° - 65°

⇒ ∠10 = 115°

And, ∠11 + ∠12 = 180°

⇒ 65° + ∠12 = 180°

⇒ ∠12 = 180° - 65°

⇒ ∠12 = 115°

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The side that has been marked as x by the Pythagorean theorem is found to be 8.

The Pythagorean theorem allows us to find the length of one side of a right triangle if we know the lengths of the other two sides. It also helps in determining whether a triangle is a right triangle by checking if the given side lengths satisfy the theorem.

We know that;

x^2 = (√89)^2 - 5^2

x^2 = 89 - 25

x = 8

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The rectangular prism has a greater volume than the Cylinder.

Since the rectangular prism has a greater volume than the cylinder because the rectangular prism fully occupies the space within its boundaries, while the cylinder has empty space above and below it.

The cylinder is rounded shape leaves gaps between its curved surface and the boundaries of the rectangular prism.

Therefore, the rectangular prism could hold more volume than the cylinder as it utilizes the entire space within its shape efficiently.

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Answer:

C.   AB=10.56, BC=7.68

Step-by-step explanation:

AB) 8.8x7.32÷6.1=10.56

BC) 6.4x7.32÷6.1=7.68

The components of the vector with magnitude 8 and a direction angle of 210° are

(-4√3, -4)

To find the components of a vector with magnitude 8 and a direction angle of 210°, we can use the following formulas

x-component = magnitude * cos(angle)

y-component = magnitude * sin(angle)

given that:

magnitude = 8

angle = 210°

convert the angle from degrees to radians:

angle in radians = angle * π / 180

= 210° * π / 180

= 7π/6 radians

calculate the components:

x-component = magnitude * cos(angle in radians)

= 8 * cos(7π/6)

= 8 * (-√3/2)

= -4√3

y-component = magnitude * sin(angle in radians)

= 8 * sin(7π/6)

= 8 * (-1/2)

= -4

Therefore, the components of the vector with magnitude 8 and a direction angle of 210° are (-4√3, -4).

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The volume of cone is 175 m³

Firstly,

Volume of Pyramid.

The volume (V) of a pyramid is  

V = ⅓Ah

Data:

V = 175m³

Calculation:

175 = ⅓× A× h

Ah = 175*3

Ah = 525m³

Secondly,

The volume (V) of a cone is

V = ⅓Ah

Data:

Ah = 525 m³

Calculation:

V = ⅓ A× h

V = 175 m³

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The equivalent to √-25 is 5i.

A complex number is a number of the form a + bi, where a and b are real numbers, and i is an imaginary number.

Where i² = -1 or i =√(-1)

A complex number can be visually represented as a pair of numbers (a, b) forming a vector on a diagram called an Argand diagram, representing the complex plane.

Thus, we can find the equivalent to √-25 as follow:

√-25 = √(-1 * 25)

         = √(-1)* √(25)

        = i * 5

        = 5i

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Answer:

40 degrees

Step-by-step explanation:

66-26 = 40 degrees

Answer:40 degrees

Step-by-step explanation:

You know that the whole angle is 66 degrees and there is another angle with 26 degrees. Subtract 26 from 66 and you get your answer

Answer:

Hi

please mark brainliest ❣️

Thanks

Step-by-step explanation:

10 + x / 3 = 12

Cross multiply

10 + x = 12× 3

10 + x = 36

Collect like terms

x= 36 - 10

x = 26

The term that can be added to the list so that the greatest common factor of the three terms  12h3 36h3, 12h6, is 48h5

A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, 12, 20, and 24 all share two characteristics.

The term that  can fit in to the list so the GCF is 12h3 would be 48h5, this is so because 48 is first divisible by 12  without any  fraction, and we can remove upon dividing 3 h's from this term as it contains a total of 5 h's.

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The inequalities represent the constraints on the variables and ensure that the farmer stays within the given limitations.

P ≥ 0

C ≥ 0

Variables:

Let's define the following variables:

P = Number of acres of potatoes planted

C = Number of acres of corn planted

Objective function:

The objective is to maximize the profit, which can be represented by the following objective function:

Profit = 150P + 50C

Constraints:

The farmer has a field of 70 acres, so the total number of acres planted cannot exceed 70:

P + C ≤ 70

The cost of seed cannot exceed the budget of $3000:

20P + 60C ≤ 3000

The number of acres of potatoes and corn cannot be negative:

P ≥ 0

C ≥ 0

These inequalities represent the constraints on the variables and ensure that the farmer stays within the given limitations.

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