a data analyst is using a function in a spreadsheet. when they input the function, they follow a predetermined structure that includes all required information for the function and its proper placement. what aspect of a function does this describe?

Therefore , the solution of the given problem of area comes out to be  the pizza only occupies 0.24 square inches of the box's bottom.

The object's overall size can be determined by figuring out how much room would be required to completely enclose the object's exterior. When selecting an analogous item with a tubular form, the environment is taken into account. Anything's total dimensions are determined by its surface area. The amount of water that a cuboid can hold depends on the number of sides that link its four trapezoidal shapes.

Here,

Assume that the square box's side length is "s" inches.

The pizza's size is specified as 254.47 in2. The area of the pizza would be equal to the area of the square box because it fits tightly inside of it.

=> s² = 254.47

=> s = √(254.47)

=> s = 15.95 inches

If you round to two decimal places, the area of the square box minus the area of the pizza is equal to (15.95)2 - 254.47, or 0.24 in2.

Therefore, the pizza only occupies 0.24 square inches of the box's bottom.

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Six semicircles lie in the interior of a regular hexagon with a side length of 2 so that the diameters of the semicircles coincide with the sides of the hexagon. The zone of the shaded locale is around 10.3923 square units.

 We will approach this problem by first finding the region of the hexagon and after that subtracting the zones of the six semicircles from it. The zone of a customary hexagon with side length 2 can be found utilizing the equation:

Region of hexagon = (3√3/2) x side[tex]^{2}[/tex]

Substituting the given esteem of side length, we get:

Area of hexagon = (3√3/2) x 2[tex]^{2}[/tex] = 6√3

The range of a crescent is half the region of the comparing circle. So, the zone of each crescent is:

Range of semicircle = 1/2 x π x radius[tex]^{2}[/tex] = 1/2 x π x 1^[tex]^{2}[/tex]= π/2

There are six semicircles, so the whole range of the semicircles is:

Add up to the zone of semicircles = 6 x π/2 = 3π At long last, able to find the zone of the shaded locale by subtracting the region of the semicircles from the range of the hexagon:

Zone of shaded locale = Range of hexagon - Add up to a range of semicircles

= 6√3 - 3π

≈ 10.3923 thus, the zone of the shaded locale is around 10.3923 square units. 

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The length of the hypotenuse of a 45-45-90 triangle is √2x units.

To find the hypotenuse of a 45-45-90 triangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse).

Let's denote the length of each leg of the triangle as "x". Since the triangle is isosceles, both legs are of equal length. Therefore, we can write:

Leg 1 = Leg 2 = x

To find the length of the hypotenuse (which we'll call "h"), we can use the Pythagorean theorem as follows:

x² + x² = h²

Simplifying this equation, we get:

2x² = h²

To solve for h, we need to take the square root of both sides of the equation:

√(2x²) = √(h²)

√2 * x = h

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The density of the milk is 1031.25 kg/m³.

Density refers to the mass of a unit volume of a material substance.

Density (ρ) = mass (m) / volume (V)

Given:

Volume (V) = 320cm³ = 0.00032m³

Mass (m) = 330g = 0.33kg

The Density (ρ) of the milk wll be:

= 0.33kg / 0.00032m³

= 1031.25 kg/m³

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12) There were about 557 principals in attendance. 13) Option A: The college will have about 480 students who prefer cookies. 14) Option C: bar graph, title favorite sport and the x axis labeled sport and the y axis.

The relationship between two quantities that are measured on the same scale and in the same units is known as a percentage. The relative size or magnitude of one thing in comparison to another is represented by proportions, which are frequently stated as ratios, fractions, or percentages. For instance, if there are 8 girls and 12 boys in a class, the girl-to-boy ratio is 8:12, or 2:3, which indicates that there are 3 guys for every 2 girls. Statistics, geometry, and physics are just a few of the mathematical and scientific disciplines that use proportions. Proportions are frequently used in statistics to describe the distribution of a population or a sample.

12) For the number of principals in conference we set up a proportionality with total people as follows:

We know that, 52 principals out of 70 people thus:

52/70 = x/750

Now,

x = (52/70) * 750

x = 557.14

Hence, we can predict that there were about 557 principals in attendance at the conference.

13) Given that, out of 225 students 27 prefer cookies thus,

27/225 = 0.12

That is 12% students like cookies.

Now, for the total number of students we have:

0.12 * 4000 = 480

Thus, option A: The college will have about 480 students who prefer cookies.

14) For the collected data the best representation is option C: bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44.

15) For the given description of the line plot the median is:

For Bus 47 = 16

For Bus 18 = 13

The faster bus is Bus 47, with a median of 16.

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Answer:

Step-by-step explanation:

36

Answer:

D.

Step-by-step explanation:

By looking at them I feel like D. is the best option

To measure a length of 10 meters without any measuring devices from 100 meters rope is fold the rope ten times and 10th fold of 100 m rope is equals to 10 m.

Total Length of rope = 100 meters

We need to measure a length of 10 meters without using any measuring devices. The ways that we can use to measure the required length includes only fold or manipulate the rope, but you cannot cut or mark it. Now, we use the division arithmetic operation to measure the length. The factors of 100 is written as 100 = 2×2× 5×5 = 10× 10

If we divide 100 by 10 then results 10 as quotient and 0 as remainder. So, the rope with length 100 meters is divided into 10 parts of 10 meters length of rope. But we cannot cut the rope, so folds the rope ten times ( i.e, first half -half then again half into half-half). Therefore, the last fold is measure of length 10 meters.

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Answer:

Step-by-step explanation:

1 )

a) quotient of powers as dividing two powers with the same base, we subtract the exponents.

b) product of powers when you are multiplying two terms with the same base, you add their exponents

c) property of negative exponents. According to the rules of exponents, a negative exponent can be rewritten as the reciprocal of the base raised to the positive exponent.

2)

Yes, when raising a fraction to a power with parentheses, the same principles apply as when raising a fraction to a power without parentheses. When evaluating expressions with fractions and exponents, the order of operations, including parentheses, is followed. To re-write the expressions (1/3)^2 is = (1/9) and (1/3)^-2 is equal to 9 9*(1/9) is 1 which is the rule of the product of powers. then the same applies to the second expression

3)

[tex](-2.3^{2})^{6}[/tex]  power to a power rule

[tex](\frac{1}{4}) ^{3}[/tex] power of a quotient

[tex]6^{4}[/tex] power to a power rule

[tex]7^{-1}[/tex] product of powers

ps: please grade me appropriately if you need more help with problems I am glad to help and these stars mean a lot to me. make sure you study your exponent laws and all the best!

Hence,The equation that models the height of the roller coaster is  [tex]x^{2} +y^{2}=900[/tex]. and solution of y =[tex]\sqrt{(900-x^{2})}[/tex].

A roller coaster, or roller coaster, is a type of amusement ride that employs a form of elevated railroad track designed with tight turns, steep slopes, and sometimes inversions. Passengers ride along the track in open cars, and the rides are often found in amusement parks and theme parks around the world.

We have given that ,

the Center the circle at the origin and assume the highest point on this leg of the roller coaster is 30 feet above the ground.

we know that equation of circle ,

[tex]x^{2} +y^{2}=r^{2}[/tex]

Where r is the radius

From given we can say that the radius =30

since the radius is 30 ft

[tex]x^{2} +y^{2}=30^{2}\\x^{2} +y^{2}=900[/tex]

so, the equation that models the height of the roller coaster. [tex]x^{2} +y^{2}=900[/tex].

We have to find the equation that can be represent the height of the roller coaster so find the value of y

[tex]x^{2} +y^{2}=r^{2}[/tex]

⇒[tex]y^{2}=r^{2}-x^{2}[/tex]

⇒[tex]y^{2}=30^{2}-x^{2}[/tex]

⇒[tex]y^{2}=900-x^{2}[/tex]

⇒y =±[tex]\sqrt{(900-x^{2})}[/tex]

⇒y =[tex]\sqrt{(900-x^{2})}[/tex]   ∵according to question choose positive sign only

Therefore the models the height of the roller coaster y =[tex]\sqrt{(900-x^{2})}[/tex].

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The number of feet per second that the remote control car travels is: 5 ft/s

The formula to find the speed from distance and time is:

Speed = Distance/time

Now, we are given:

Time: t = 3/40 seconds

Distance = 3/8 ft

Thus:

Speed = (3/8)/(3/40)

Speed = (3/8) * (40/3)

Speed = 5 ft/s

Thus, that is the speed that the remote control car travels

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There are 36 ways to arrange the letters d, i, g, i, t so that the two i's are not next to each other.

To find the number of ways the letters d, i, g, i, t can be arranged so that the two i's are not next to each other, follow these steps:
Consider the four non-i letters: d, g, t.

There are 3! (3 factorial) ways to arrange these letters, which is equal to 3 x 2 x 1 = 6 ways.

Since we want to prevent the two i's from being next to each other, we can think of placing them in the "gaps" between the non-i letters.

There are 4 possible gaps for the i's to be placed: (i) d (i) g (i) t (i).
Since there are two i's, we need to choose 2 of the 4 gaps to place them in.

This can be done in 4C2 ways (combination), which is equal to 4! / (2! x (4-2)!) = 6 ways.
Multiply the number of ways to arrange the non-i letters (step 1) with the number of ways to place the i's (step 3): 6 x 6 = 36.

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There are 72 ways to arrange the letters d, i, g, i, t so that the two i's are not next to each other.

To arrange the letters d, g, i, t, and i so that the two i's are not next to each other, follow these steps:

Step 1: Treat the two i's as one entity for now (denoted as [i]). So, we have 4 entities: d, g, t, and [i].
Step 2: Arrange these 4 entities (d, g, t, and [i]) in any order. There are 4! (4 factorial) ways to do this, which is 4 x 3 x 2 x 1 = 24 ways.
Step 3: Now, we need to separate the two i's. There are 3 spaces between the other letters (d, g, and t) where we can place the second i.
For example: if the arrangement is d-[i]-g-t, the second i can be placed in any of the three spaces indicated by the dashes.
Step 4: For each of the 24 arrangements from Step 2, there are 3 possible ways to place the second i. So, the total number of arrangements is 24 x 3 = 72 ways.

Thus, there are 72 ways to arrange the letters d, i, g, i, t so that the two i's are not next to each other.

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The 6 steps for inferential statistics to test researchers question can be:

It is the branch of statistics that is concerned with obtaining information about a population from a sample of that population. It is used to make inferences, that is, draw conclusions and make predictions about the population based on the information obtained from the sample.

These assertions are based on hypothesis tests, confidence intervals and statistical models.

Therefore, the goal of inferential statistics is to make accurate and reliable statements about the population using limited sample information.

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The mean score of the given three scores is approximately 26.6, which is not the mean score for all ninth graders in the city.

To find the mean score for all ninth graders in the city, we need more information than just three scores. Without additional data, we cannot accurately determine the mean score for all ninth graders in the city.

However, we can calculate the mean of the given scores to verify that it is not 79.7 as claimed by the PR manager:

Mean = (77 + 91 + 71) / 3 = 79.7/3 = 79.7 ÷ 3 ≈ 79.7/3 ≈ 26.6

So the mean score of the given three scores is approximately 26.6, which is not the mean score for all ninth graders in the city.

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The volume of cone as per given figure is 314cm³.

The following mathematical operation must be carried out in order to determine a cone's volume: V = Π(h/3)r². The surface area of the circular portion of a cone is simply πr2. The lateral face wrapping around this base is calculated as πrl, or if you aren't given the slant height, you can use the formula πr√(r2+h2).

To calculate the volume of a cone, we apply the following formula:

, where V = volume

h = height

r = radius

π = pi

(h = height of cone, r= radius of cone)

Given:

Height of cone = 12 cm

Radius of cone = 5 cm

Volume of cone, V =  3.14 * (12/3 )* 5* 5

= 3.14 * 20 * 5

= 3.14 * 100

= 314 cm³

Therefore, The volume of cone as per given figure is 314cm³.

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The length of ST obtained using Pythagorean Theorem is about 13.2 units

Pythagorean Theorem states that the square of the length of the hypotenuse side of a right triangle is the sum of the square of the other two legs of the triangle.

The length of the segment [tex]\overline{PR}[/tex] = 18

[tex]\overline{RS}[/tex] = [tex]\overline{SP}[/tex] = 16 (Radial length of the same circle)

Triangle ΔSRP is an isosceles triangle, therefore, ∠SRP ≅ ∠SPR

[tex]\overline{ST}[/tex] ≅ [tex]\overline{ST}[/tex] (Reflexive property of congruence)

Triangles ΔRST and ΔPST are congruent by the Hypotenuse Leg, HL rule of congruent triangles

Therefore; RT ≅ PT

RT + PT = 18

RT + RT = 18

2 × RT = 18

RT = 18/2 = 9

RT = 9

Therefore, ST, can be obtained using Pythagoras Theorem as follows;

ST = √(16² - 9²) = 5·√7 ≈ 13.2

The length of the side ST is about 13.2 units long

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Answer: The answer to

sinΘ = 7/7√2

cosΘ = 7/7√2

tanΘ = 7/7

cosecΘ = 7√2/7

secΘ = 7√2/7

cotΘ = 7/7

Step-by-step explanation:

The given triangle consists of three sides namely, hypotenuse, opposite and adjacent.

The value of the hypotenuse is 7√2 and the value of the adjacent is 7.

We will calculate the value of the adjacent.

By Pythagoras' theorem,  (hypotenuse)^2=(opposite)^2+(adjacent)^2

Putting the given values, (7√2)^2=(opposite)^2+(7)^2

                                         (opposite)^2=(7√2)^2-(7)^2

                                         (opposite)^2=98-49

                                         (opposite)^2=49

Therefore, the value of the opposite is 7.

Now, we can put the following values in the trigonometric table.

sinΘ = opposite/hypotenuse = 7/7√2

cosΘ = adjacent/hypotenuse = 7/7√2

tanΘ =  opposite/adjacent = 7/7

cosecΘ = hypotenuse/opposite = 7√2/7

secΘ = hypotenuse/adjacent = 7√2/7

cotΘ = adjacent/opposite = 7/7

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The equation of the parabola in vertex form is y = (1/4)x² - 6.

To write the equation of the parabola in vertex form, we use the formula:

y = a(x-h)² + k

Where (h,k) is the vertex and "a" is a constant that determines the shape of the parabola.

Given that;

The vertex is (0,-6)

Hence:

h = 0 and k = -6.

We can substitute these values into the formula to get:

y = a(x-h)² + k

y = a(x - 0)² - 6

y = ax² - 6

Now we need to find the value of "a". We are also given that the parabola passes through the point (-6,3).

x = -6 and y = 3

We can substitute this point into the equation to get:

y = a(x - h)² + k

3 = a( - 6)² - 6

3 = 36a - 6

9 = 36a

a = 1/4

Now we know the value of "a", we can substitute it back into the equation we derived earlier:

y = ax² - 6

y = (1/4)x² - 6

Therefore, the equation in vertex form is y = y = (1/4)x² - 6.

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The small two above the radical symbol indicates that the square root of a mathematical number or expression is being taken, which means that the number under the radical must be squared to obtain the original number

Therefore,the correct answer is True.

An expression is a mathematical phrase that combines numbers, variables, and operations to create a value. It can include arithmetic, algebraic, or trigonometric operations and may contain parentheses, exponents, or radicals.

The square root of a number is a value that, when multiplied by itself, gives the original number. It is denoted by the symbol √ and is a type of radical.

According to the given information:

The correct answer is True.

The radical symbol, which looks like a division bar with a dot on top, is used to denote a root operation in mathematics. The index or degree of the root indicates the number of times the root must be multiplied by itself to obtain the number under the radical. In the case of the square root, the index is 2, which means that the number under the radical must be squared to obtain the original number.

Therefore, when the radical symbol has a small two above it, it is indicating that the square root of the number or expression below the radical is being calculated. The result of the square root operation is always a positive number, since the negative sign is indicated separately outside the radical symbol.

For example, the square root of 25 is written as √25 = 5, since 5 squared is equal to 25. Similarly, the square root of 4 is written as √4 = 2, since 2 squared is equal to 4.

In summary, the small two above the radical symbol indicates that the square root of a mathematical number or expression is being taken, which means that the number under the radical must be squared to obtain the original number.

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The radian measure of the central angle which intercepts the arc is 6.2 radians.

We can use the formula relating the arc length to the angle and radius of the circle:

arc length = radius x central angle in radians

Plugging in the given values, we get:

148.8 = 24 x central angle in radians

Solving for the central angle, we have:

central angle in radians = 148.8/24

central angle in radians = 6.2 radians

Therefore, the radian measure of the central angle which intercepts the arc is 6.2 radians.

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The mass of water vapor (g) / mass of dry air (kg) is the humidity measure of  the mixing ratio

The mixing ratio is defined as the mass of water vapor in grams divided by the mass of dry air in kilograms in a mixture of air and water vapor. It is a useful parameter for meteorologists and atmospheric scientists to describe the amount of water vapor in the atmosphere, particularly in the upper atmosphere where the relative humidity may be very low.

Relative humidity is the ratio of the partial pressure of water vapor in the air to the equilibrium vapor pressure at a given temperature and pressure, expressed as a percentage. Vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases at a given temperature in a closed system. Absolute humidity is the mass of water vapor per unit volume of moist air.

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Answer:

Both 2B and 2A are not similar.

Step-by-step explanation:

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

Let me be helpful!

Let's start with 2B. It is easier to understand the subject that way.

->for a triangle to be similar, it's angles and sides must be the same.

-2B's triangle shows that line TW got scaled by x2.2 (22/10)

-Line ZW got scaled by 1.18

-2b are not similar.

Now on it 2A!

- line JK got scaled by 0.75

- Line JL got scaled by 0.5

-they are not similar

Let me know if I am incorrect!

-A friendly 8th grader :)

Thus, the value of x for the given output of the function f(x) = 1 is found as: x = -1.

A function is a mathematical construct that receives an input, processes it according to a rule, and then outputs the outcome.

Given that:

Put f(x) = 1 in the given function to find x.

f (x) = - 5x - 4

1 = - 5x - 4

Isolating the x

-5x = 1 + 4

-5x = 5

x = 5/ -5

x = -1

Thus, the value of x for the given output of the function f(x) = 1 is found as: x = -1.

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation: Multiplication first 7x1 = 7, Take 7 and divide it by 10 which gives you 0.7, Do the same but for the other 2 questions,

(9x1/100 = 0.09)

(9x1/1000 = 0.009)

(7x1/10 = 0.7)

Now take the answers and add them up

0.09 + 0.009 + 0.7 = 0.799

Answer: 0.799