Which of the following statements is true about the greatest integer function? A. The function is defined as the greatest integer greater than or equal to x. B. The greatest integer function is classified as a piecewise function. C. The range of the greatest integer function is the set of natural numbers. D. The domain of the greatest integer function is all whole numbers. 2. What's the common difference of the sequence –5, –2, 1, 4, 7, . . . ?

Answer:

 11 13/15

Step-by-step explanation:

-3 2/3+b = 8 1/5

Add 3 2/3 to each side

-3 2/3 + 3 2/3+b = 8 1/5+ 3 2/3

b = 8 1/5 + 3 2/3

We need to get a common denominator of 15

8 1/5 = 8 3/15

3 2/3 = 3 10/15

           ----------------

             11 13/15

Answer:

8 cm

Step-by-step explanation:

The circumference (C) of a circle is

C = π d  ← d is the diameter

Here C = 8π, hence

πd = 8π ( divide both sides by π )

d = [tex]\frac{8\pi }{\pi }[/tex] = 8 cm

A circle is a curve sketched out by a point moving in a plane. The diameter of the circle whose circumference is 8π cm is 8cm.

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

The circumference of a circle is given by πD, where D is the diameter. Now, the circumference can be written as,

Circumference of the circle = πD

8π cm = πD cm

D = 8 cm

Hence, the diameter of the circle whose circumference is 8π cm is 8cm.

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Answer:

Option C (Median: 347 and Mode: 347 and 348)

Step-by-step explanation:

Median is the middle point of the data and mode is the most repeated observation is the data. The first step involved in calculating the median it to list the observations in the ascending order. This gives:

335, 336, 337, 338, 339, 340, 347, 347, 348, 348, 356, 357, 358, 359

The second step is to identify the middle number (in case the observations are in odd numbers) or numbers (in case the observations are in even numbers) after the ascending order step has been done. It can be observed that the middle numbers in this data set are 347 and 347. Since there are two numbers, so their average will be the median of this data set. Therefore, the median is 347. It can be seen that maximum repetitions are 2 times for 347 and 348. So the mode is 347 and 348.

Therefore, Option C is the correct answer!!!

The correct option is c: Median: 347, Mode: 347 AND 348. This is determined by sorting the numbers and finding that 347 is the median and both 347 and 348 are the modes.

This question involves identifying measures of central tendency, specifically the median and the mode, from a list of numbers.

To determine the correct answer, we proceed step-by-step to calculate the median and mode from the provided sequence: 359, 357, 348, 347, 337, 347, 340, 335, 338, 348, 339, 356, 336, 358.

Step 1: Sorting the List
The sorted list is: 335, 336, 337, 338, 339, 340, 347, 347, 348, 348, 356, 357, 358, 359

Step 2: Finding the Median
The median is the middle value of a sorted list. For a list of 14 numbers, it is the average of the 7th and 8th values:
Median = (347 + 347) / 2 = 347

Step 3: Finding the Mode
The mode is the number that appears most frequently. Here, 347 and 348 each appear twice.
Mode = 347 and 348

Based on these calculations, the correct option is Option c: Median: 347, Mode: 347 AND 348.

              The value is:

                      -4

We are asked to find the value of the ceiling function: [tex]\left \lceil -4.6 \right \rceil[/tex]

As we know that the ceiling function always occupy the higher value in integers.

i.e. the ceiling function act as follows:

it takes value 0 when   -1< x≤0

                       1 when  0 < x ≤ 1

                       2 when  1 < x ≤2

and so on.

As we know that:

            -4.6 lie between -5 and -4.

            Hence, we have:

            [tex]\left \lceil -4.6 \right \rceil=-4[/tex]

Answer:  -4

Step-by-step explanation:

The ceiling function (also known as the least integer function) is written as

[tex]f(x) = [x][/tex]

It gives the smallest integer greater than or equal to x .

For example : [5.6]=6

or [-1.9]= -1   [∵- 1 > -1.9 ]

To find : The value of [-4.6]

Clearly ,  [-4.6] is written in ceiling function notation.

Then,  [-4.6]  = smallest integer greater than or equal to -4.6

= -4              [∵ -4>-4.6]

Hence, the value of [-4.6] = -4

The shape of the resulting two-dimensional cross section is a . A right rectangular pyramid.

The trapezoid is a quadrilateral with one pair of opposite sides that are parallel. These are sometimes classified as having at most one pair of opposite sides parallel, and sometimes as containing one pair of different sides parallel.

This trapezoid limits the goaltender's ability to play the puck by giving them a small amount of space behind the goal line.

It was trapezoidal when we slice the pyramid, we obtain two shapes: a triangle and a trapezoid.

Trapezoidal is the appropriate two-dimensional shape.

a triangle

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The resulting two-dimensional cross section of a right rectangular pyramid sliced through its vertex and perpendicular to its base is a triangle.

The shape of the resulting two-dimensional cross section is a triangle.

When a right rectangular pyramid is sliced through its vertex and perpendicular to its base, the resulting cross section will be a triangle. This is because the cut passes through the top vertex of the pyramid and intersects all the edges of the base, forming a triangle shape.

For example, if the base of the pyramid is a rectangle, the resulting cross section will be an isosceles triangle with its top vertex at the center of the rectangle's longer side.

Answer:

Step-by-step explanation:

start with 35 and add 1 repeatedly.

y=x+1 for ex, y= 35+ 1 and so on

Answer:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the

10

. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

The answer is 9x10 to the positive 16 power

The sum of the given equation in the scientific notation should be [tex]9 \times 10^{16}[/tex]

Here we Move the decimal due to this there is one non-zero digit to the left of the decimal point. In the case when the decimal is being moved to the right, so the exponent will be negative and vice versa.

So,

[tex]= (2 \times 10^{16}) + (7 \times 10^{16}) = 9 \times 10^{16}[/tex]

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Answer:

(4, 7)

Step-by-step explanation:

The midpoint formula is (((x1 + x2)/2), ((y1+y2)/2)))

x1 +x2 = 1 +7 = 8

8/2 = 4

y1 + y2 = 10 + 4 = 14

14/2 = 7

(4, 7) is the midpoint

Answer:

M = (4, 7)

Step-by-step explanation:

Using the midpoint formula

M = [[tex]\frac{1}{2}[/tex](x₁ + x₂ ), [tex]\frac{1}{2}[/tex](y₁ + y₂ ) ]

with (x₁, y₁ ) = P(1, 10) and (x₂, y₂ ) = Q(7, 4)

M = [ [tex]\frac{1}{2}[/tex](1 + 7), [tex]\frac{1}{2}[/tex](10 + 4) ] = (4, 7)

Answer:

$4.60

Step-by-step explanation:

To find the amount of tax, multiply the number of gallons by the tax per gallon.

20*.23 = $4.60

Answer:

249/10 = x, or x = 24.9

Step-by-step explanation:

25 1/2 × 5 –3 = 5 x  should be written as  25 1/2 × 5 –3 = 5x

The goal here is to solve for x (you should state this specifically).

Start by multiplying 25  1/2 by 5, since we must multiply before addition or subtraction:

One way of doing this multiplication is to multiply 25 by 5 and then 1/2 by 5 and then summing up the results:

25×5 = 125, and 1/2 × 5 = 5/2, so the end result is:

125  + 5/2, or 125 + 2  1/2, or  127 1/2.

Next, subtract 3 from this result:

127  1/2 - 3 = 124  1/2

Then 124  1/2 = 5x.  Solve for x.  Converting 124  1/2 into an improper fraction:

249/2 = 5x.  Dividing both sides by 5, we get:

249/10 = x, or x = 24.9

x = total number of candies

[tex]\bf \stackrel{\textit{my brother}}{\cfrac{1}{5}x}+\stackrel{\textit{my friend}}{\cfrac{1}{4}x}+11~~=~~\stackrel{\textit{total}}{x} \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{20}}{20\left( \cfrac{x}{5}+\cfrac{x}{4}+11 \right)=20(x)}\implies 4x+5x+220=20x\implies 9x+220=20x \\\\\\ 220=11x\implies \cfrac{220}{11}=x\implies 20=x~\hspace{10em}\stackrel{\textit{to my brother}}{\cfrac{20}{5}\implies 4}[/tex]

Answer: Last Option

[tex]x=2,\ y=-5[/tex]

Step-by-step explanation:

Cramer's rule says that given a system of equations of two variables x and y then:

[tex]x =\frac{Det(A_X)}{Det(A)}[/tex]

[tex]y =\frac{Det(A_Y)}{Det(A)}[/tex]

For this problem we know that:

[tex]Det(A) = |A|=\left|\begin{array}{ccc}4&-6\\8&-2\\\end{array}\right|[/tex]

Solving we have:

[tex]|A|= 4*(-2) -(-6)*8\\\\|A|=40[/tex]

[tex]Det(A_X) = |A_X|=\left|\begin{array}{ccc}38&-6\\26&-2\\\end{array}\right|[/tex]

Solving we have:

[tex]|A_X|=38*(-2) - (-6)*26\\\\|A_X|=80[/tex]

[tex]Det(A_Y) = |A_Y|=\left|\begin{array}{ccc}4&38\\8&26\\\end{array}\right|[/tex]

Solving we have:

[tex]|A_Y|=4*(26) - (38)*8\\\\|A_Y|=-200[/tex]

Finally

[tex]x =\frac{|A_X|}{|A|} = \frac{80}{40}\\\\x=2[/tex]

[tex]y =\frac{|A_Y|}{|A|} = \frac{-200}{40}\\\\y=-5[/tex]

Answer:

Step-by-step explanation:

This is a course specific question. What I think is a postulate may not be listed in your lesson. A postulate is a statement that is assumed to be true. There has not been an exception found in over 2000 years. A postulate does not require proof: its truth is accepted.

Example: Two points on the same plane have exactly 1 line that can go through them.

Theorem: using the postulates to begin with, a theorem is a statement that can (and should) be proved.

Example: Two lines that are on the same plane, if they intersect at all, intersect only once.

a^2 + b^2 = c^2

This well known theorem can be proved well over 100 ways.

In geometry, a postulate is an accepted statement without proof that serves as a fundamental assumption, while a theorem is a proven statement based on previously established postulates, theorems, and definitions.

An example of a postulate is the "Parallel Postulate," and an example of a theorem is the "Pythagorean Theorem."

To find the difference between a postulate and a theorem

Now,

A postulate is a statement that is accepted without proof and serves as a fundamental assumption. It provides the basis for building geometric reasoning.

An example of a postulate is the "Parallel Postulate," which states that if a line intersects two other lines forming congruent alternate interior angles, then the two lines are parallel.

On the other hand, a theorem is a statement that has been proven based on previously established postulates, theorems, and definitions.

An example of a theorem is the "Pythagorean Theorem," which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

So, while postulates are accepted as true without proof, theorems are derived from logical deductions and require proof.

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Answer:

(n+4)(n+5)

Step-by-step explanation:

Answer:

(n + 4)(n + 5)

Step-by-step explanation:

to factor n² + 9n + 20, we need to find 2 numbers that when multiplied together equal 20 and when added together equal 9

these two numbers are 4 and 5 so the factorization looks like this:

(n + 4)(n + 5) < you can FOIL this out to check if the solution is correct, and you would get: n² + 9n + 20

Answer:

22 feet²

Step-by-step explanation:

We are given:

height of tree h = 45 inches

Circumference= πd × inches

But d = 22.2inches

Therefore area will be

Area = 22.2π × 45 inches²

Area = 3137 inches²

Let's convert from inches² to feet², we have:

1 foot = 12 inches.

Therefore,

1 square foot = 1foot × 1foot = 12inches×12inches

= 3137inches² / 144 inches²

= 22feet²

Note: I attached missing data which states that diameter at year 13 is 22.2inches

To calculate the square footage of the tree wrap needed, we multiply the circumference of the tree trunk by the desired height. Assuming the tree trunk is cylindrical, we use the formula for the circumference of a circle: C = 2πr. Then, we convert the height to feet and calculate the square footage.

To calculate the square footage of the tree wrap needed, we need to find the circumference of the tree trunk and multiply it by the desired height. Assuming the tree trunk is cylindrical, we can use the formula for the circumference of a circle: C = 2πr. We can then multiply the circumference by the desired height to get the square footage. Since we know the height is 45 inches, we need to convert it to feet by dividing by 12. Let's say the circumference of the tree trunk is 10 feet. The square footage of the tree wrap needed would be C * H = (2πr) * H = (2π * 5) * 3.75 = 47.12 square feet (rounded to the nearest square foot).

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Answer:

Step-by-step explanation:

We have four congruent triangles with base b = 16cm and height h = 12cm.

The formula of an area of a triangle:

[tex]A=\dfrac{bh}{2}[/tex]

Substitute:

[tex]A=\dfrac{(16)(12)}{2}=(8)(12)=96\ cm^2[/tex]

The latearal area:

[tex]L.A.=4A\to L.A.=4(96)=384\ cm^2[/tex]

For the surface area we need the area of a base.

The base is a square with side a = 16cm.

The area of the base:

[tex]B=16^2=256\ cm^2[/tex]

The surface area:

[tex]S.A.=L.A.+B\to S.A.=384+256=640\ cm^2[/tex]

Using the Empirical Rule, it is found that the percent best represents the probability that any student scored between 61 and 93 on the test is of:

B. 95%.

It states that, for a normally distributed random variable:

In this problem, the mean is of 77 while the standard deviation is of 8, hence scores between 61 and 93 are exactly 2 standard deviations from the mean, hence 95% of the students scored in this range, and option B is correct.

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Answer:

76 mL

Step-by-step explanation:

40*19/10

40*19= 760 / 10 = 76mL

the correct answer is A. 316.7 mL.

The question involves calculating the fluid volume that a 19 kg dog would receive if fluids were administered at a rate of 40 mL/kg/day. Here is the step-by-step calculation:

Therefore, the correct answer is A. 316.7 mL.

Answer:

focus point of  satellite is (-125,-3)

Step-by-step explanation:

The question is on finding the focus point of a parabola

Given y²+6y-3x+3=0

Rewrite the equation

y²+6y=3x-3

Complete square on both sides

y²+6y+9=3x-3+9

Factorize

(y+3)²= 3x+6---------------------------------------(a)

(y+3)²= 3(x+2)

Compare  equation (a) to standard equations for parabola

(y+3)²= 3(x+2)

(y-b) ²= 2p(x-a),,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,(b)

2p=3------------divide both sides by 2

p=3/2

Vertex (a,b)=( -2,-3)........from equation (b)

Focus point is given by  (a+p/2 , b)...........................(c)

Substitute values in equation c above;

(-2+3/4 , -3) = (-5/4 ,-3) =(-1.25, -3)

Answer:

For the graph, 111 is the: y-intercept

In the situation, it represents the hiker's: starting distance

11 is the: slope

It represents the hiker's: speed

Hope this helped C:

The question pertains to the physics of a hiker ascending and descending a mountain, considering potential energy changes and work done by the hiker. The scenario's analysis includes calculations of potential energy at various altitudes relative to sea level, given the hiker's mass.

The scenario involves a hiker ascending and descending a mountain, which can be analyzed from a physics perspective, particularly focusing on potential energy, work, and energy conservation. The hiker's journey begins at 200 m above sea level, progresses to an overnight hut at 800 m, descends to another hut at 500 m, and finally returns to the starting point. The mass of the hiker is given as 70 kg.

When the hiker ascends to a height of 800 m, she gains potential energy, which can be calculated using the formula Potential Energy (PE) = mass (m) × gravity (g) × height (h). Therefore, the increase in potential energy when reaching the first hut is:

PE = 70 kg × 9.8 m/s2 × (800 m - 200 m)

Similarly, when descending to the second hut, the hiker loses some potential energy. Finally, upon returning to the starting point, the hiker's potential energy returns to its initial value, assuming the starting point is the reference level of potential energy.

The exercise involved in hiking up and down the mountain also involves work done against the force of gravity and could be discussed in terms of energy expended by the hiker.

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Answer:

Step-by-step explanation:

You subtract 310 from 25 and get 285 then you multiply 285 x 21 and I believe that should solve this equation.

To find the value of 'y' when 'x' equals 21 in this equation, we substitute 21 for 'x', perform the multiplication 25*21 first, and then subtract this result from 310, yielding a 'y' value of -215.

This question pertains to the mathematical equation y=310-25x. To find the value of 'y' when 'x' equals 21, we simply substitute 21 for 'x' in the equation. So, y = 310 - 25*(21). Multiplication happens first (due to the order of operations), yielding 525. When you subtract this from 310 (310-525), you get -215. Therefore, the value of 'y' when 'x' is 21 in this equation is -215.

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I believe it would be C

Answer:

C. measurement of one angle and length of one side.

Step-by-step explanation:

A rhombus is a parallelogram with four sides of equal length and two different pairs of angles. Hence, the measurement of one angle and length of one side is need to construct a rhombus. The right answer is C.

Answer:

option A

The base is e^-1

Step-by-step explanation:

Given in the question a function, f(x) = (1/e)[tex]^{x}[/tex]

This function can also be write as.

f(x) =[tex](e^{-1})^{x}[/tex]

by using Negative Exponent Rule

[tex]x^{-n}=\frac{1}{x^{n}}[/tex]

This says that negative exponents in the numerator get moved to the denominator and become positive exponents.

C= equilateral triangle

To find this answer we need to know what a cube is. A cube is a prism whose sides all have the same length. It's something like the three dimensional version of a square. In the figure below, we have labeled each length of the cube as [tex]x[/tex]. Also, the vertex we taken is in blue color, so we need to find each side length of the triangle. Since the cross section passes through the midpoints of three edges that intersect at the same vertices of the cube, then:

[tex]L_{1}=\sqrt{(\frac{x}{2})^2+(\frac{x}{2})^2} \\ \\ L_{1}=\sqrt{\frac{x^2}{4}+\frac{x^2}{4}} \\ \\ L_{1}=\sqrt{\frac{2x^2}{4}} \\ \\ L_{1}=\sqrt{\frac{x^2}{2}} \\ \\ L_{1}=\frac{x}{\sqrt{2}} \\ \\ L_{1}=\frac{x}{\sqrt{2}}\frac{\sqrt{2}}{\sqrt{2}} \\ \\ L_{1}=\frac{\sqrt{2}x}{2}[/tex]

Since this is a cube, then it is true that:

[tex]L_{1}=L_{2}=L_{3}=\frac{\sqrt{2}x}{2}[/tex]

Since the side lengths have the same value, this is an equilateral triangle.

Answer:

[tex]\large\boxed{x>-25}[/tex]

Step-by-step explanation:

[tex]-\dfrac{3}{10}x-7<\dfrac{1}{2}\qquad\text{multiply both sides by 10}\\\\10\!\!\!\!\!\diagup^1\cdot\left(-\dfrac{3}{10\!\!\!\!\!\diagup_1}x\right)-(10)(7)<10\!\!\!\!\!\diagup^5\cdot\dfrac{1}{2\!\!\!\!\diagup_1}\\\\-3x-70<5\qquad\text{add 70 to both sides}\\\\-3x<75\qquad\text{change the signs}\\\\3x>-75\qquad\text{divide both sides by 3}\\\\x>-25[/tex]

Answer:

A

Step-by-step explanation:

That the answer Plss follow me thanks

The equivalent expressions for the perimeter of a square whose side length is represented by the expression n -1.5 are A and F, specifically: n + n + n + n - 1.5 - 1.5 - 1.5 - 1.5 and 4(n - 1.5)

The length of a side of a square is given by the expression n - 1.5. The perimeter of a square is calculated by adding up all its four sides. Hence, in this case, the perimeter would be (n - 1.5) + (n - 1.5) + (n - 1.5) + (n - 1.5). Perform the addition to get 4n - 6, simplifying to 4(n - 1.5). From the provided options, the equivalent expressions for the perimeter of the square are A and F, that is, n + n + n + n - 1.5 - 1.5 - 1.5 - 1.5 and 4(n - 1.5).

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The whole circle is 360 degrees. So cut the circle in half and BDC=180

To find the measure of arc BDC, use the triangulation measurements and the angular displacements ZBOC and ZDOC. Apply geometric principles and the law of sines, then relate the arc's angle to the circle's circumference to approximate the arc measure.

To find the measure of arc BDC, we must consider the geometrical properties of circles and triangles mentioned in the provided information. Since the arc length for a small part of the circle can be approximated as equal to the straight-line segment, we can use this approximation along with the given relationships to solve for the arc BDC measurement.

First, establish a second control point (B) in a triangulation network and measure the interior angles at points A, B, and C. The 'law of sines' can be used to determine lengths of the sides of the triangles formed. Once you have the lengths AC and BC, you can measure CD and BD to fix point D in a coordinate system.

This geometric consideration allows us to construct right triangles and use the Pythagorean theorem to find missing lengths. To calculate the measure of arc BDC, we can add the displacement angles (ZBOC and ZDOC) which can be found by using the angular displacement values between 2 and 2.5 seconds, and between 2.5 and 3 seconds. Using these angles and the lengths of segments BC, CD, and BD, we can apply the principle that in a circle, the ratio of the arc's length to the circumference is equal to the ratio of the angle to 360 degrees.

Answer:

I think it is a but it is hard to see

Step-by-step explanation:

Answer:

the first option

Step-by-step explanation:

Given the triangle is right, then use Pythagoras' theorem

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

The hypotenuse is 5, hence

5² = 4² + b² OR 4² + b² = 5²

Answer:

8[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Rationalise the denominator by multiplying both the numerator and denominator by the radical on the denominator, that is

[tex]\frac{32}{\sqrt{8} }[/tex]

= [tex]\frac{32\sqrt{8} }{8 }[/tex] → ([tex]\sqrt{8}[/tex])² = 8

= [tex]\frac{32\sqrt{4(2)} }{8}[/tex]

= 4× 2[tex]\sqrt{2}[/tex]

= 8[tex]\sqrt{2}[/tex]

Answer: The greatest distance, in feet is the first one 3ft.

Answer: 3 feet

Step-by-step explanation:

Given: The blueprints for a police station show that one of the lamp posts has a motion detector on it, and that the equation describes the boundary within which motion can be sensed. :

[tex](x+14)^2+(y-6)^2=9[/tex] → which is a equation of a CIRCLE.

When we compare it to the standard form of equation of circle i.e. [tex](x-(-14))^2+(y-6)^2=3^2[/tex] , we get the radius of the circle = 3

Consider the lamp post as the center of the area covered by the detector.

Then the greatest distance a person could be from the lamp and be detected = Radius of the circular area

=3 feet.