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Przykład 5.

a) The plot cross the horizontal line [tex]y=2[/tex] when the time is [tex]t=5,5[/tex], so it took 5,5 s to cover the first 2 m.

b) If [tex]f(x)[/tex] denotes the distance from the starting position of the object, then its average speed over the entire 6-s period is

[tex]v_{\rm ave} = \dfrac{3\,\mathrm m - 0\,\mathrm m}{6\,\mathrm s - 0 \,\mathrm s} = \dfrac36 \dfrac{\rm m}{\rm s} = \boxed{0,5 \dfrac{\rm m}{\rm s}}[/tex]

c) In the last 3 seconds, the object covers a distance of

[tex]3\,\mathrm m - 1\,\mathrm m = \boxed{2\,\mathrm m}[/tex]

d) False. The average speed over the first 3-s period is

[tex]v_{\rm ave[0,3]} = \dfrac{1\,\mathrm m - 0\,\mathrm m}{3\,\mathrm s - 0\,\mathrm s} = \dfrac13 \dfrac{\rm m}{\rm s} \approx 0,33 \dfrac{\rm m}{\rm s}[/tex]

while over the second 3-s period, it is

[tex]v_{\rm ave[3,6]} = \dfrac{3\,\mathrm m - 1\,\mathrm m}{6\,\mathrm s - 3\,\mathrm s} = \dfrac23 \dfrac{\rm m}{\rm s} \approx 0,66\dfrac{\rm m}{\rm s} \neq 0,33\dfrac{\rm m}{\rm s}[/tex]

Przykład 2.

In total there are

8 + 24 + 28 + 16 + 4 = 80

graded assignments. Compute the percentages of students whose scores fall into the given categories:

• 0-8 : 8/80 = 1/10 = 10/100 = 10%

• 9-16 : 24/80 = 3/10 = 30/100 = 30%

• 17-24 : 28/80 = 7/20 = 35/100 = 35%

• 25-32 : 16/80 = 1/5 = 20/100 = 20%

• 33-40 : 4/80 = 1/20 = 5/100 = 5%

See the attached pie chart.

Zadanie 3.

From the plot, it appears that Mateusz

• took 6 min to reach the bus stop

• waited for 2 min

• took 5 min to return home

• took 1 min to grab his notebook

• took 5 min to return to the bus stop

• waited for 3 min

• and after the bus arrives, moves further away over the next 4 min

This means the total time Mateusz needed to (1) return home to get the notebook, (2) find the notebook, and (3) return to the bus stop is

5 min + 1 min + 5 min = 11 min

Zadanie 4.

True. Mateusz walks the distance between his house and the bus stop within the first 6 min, which is 2/5 of 1 km = 0,4 km = 400 m.

True. The bus arrives after 22 min, and its average speed is equal to Mateusz's average speed over the next 4 min. At 22 min, he is 0,4 km from home, and at 26 min, he is 4 km away from home, so the average speed is

[tex]v_{\rm ave} = \dfrac{4\,\mathrm{km} - 0,4\,\mathrm{km}}{26\,\mathrm{min} - 22\,\mathrm{min}} = \dfrac9{10} \dfrac{\rm km}{\rm min} = 0,9\dfrac{\rm km}{\rm min}[/tex]

Convert the speed to km/h.

[tex]\dfrac9{10} \dfrac{\rm km}{\rm min} \times \dfrac{60\,\rm min}{1\,\rm h} = 54 \dfrac{\rm km}{\rm h}[/tex]

Answer:

1.) 9

2.) 15

3.) 7

Step-by-step explanation:

1.) There are no repeat letters, so the cardinality is the number of letters, here 9

2.) There's half the numbers from 1 to 30 in the set, so 30/2 = 15

3.) There are 7 distinct days of the week, so the answer is 7

Answer:

the second piece of rope

Step-by-step explanation:

2.63 ≥ 2.5

2.085≤2.5

The correct way of writing the equation of the line that passes through the points are y = -3x - 5.

Two expressions are combined by the equal sign to form a mathematical statement known as an equation. For instance, a formula might be 3x - 5 = 16. After solving this equation, we learn that the value of the variable x is 7.

The slope-intercept form, point-slope form, and standard form are the three primary types of equations. These equations provide sufficient details about the line to make graphing them simple.

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Answer:

The answer is %11.42 I think

Step-by-step explanation:

30+10=40

40/350= 0.1142

0.1142x100= %11.42

First divide the total of people who didn't complete the race by the total of racers which is 350 total racers.

Then u multiply ur answer by 100 to get ur percentage which is 11.42.

The value of Sin 496.4° is 0.6896.

Trigonometry functions:

Trigonometry is a type of mathematics that deals with the specific function of angles and their application.

There are six functions of an angle used in trigonometry sine(sin), cosine(cos), tangent(tan), cotangent(cot), secant(sec) and cosecant(cosec). All these functions are based on the measurement of the triangle.

Given,

Sin 496.4°

Here we need to find the value of it.

While using the sine table,

The value of 496.4° = 0.6896

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(A) Undefined terms are Point and Line.

(B)  Each point has at least two separate lines.

(C)  "P" does not lay on "m," hence the statement is contradictory.

A set of axioms from which one or more theorems may be logically deduced is known as an axiomatic system in mathematics and logic. A theory is a coherent, mostly self-contained body of knowledge that typically includes an axiomatic framework and all of the theorems that are deduced from it.

(A) Undefined terms are :

A location is a point. It is empty, meaning it has no width, length, or depth. A dot indicates a point.

A line is described as a collection of points that stretches in both directions indefinitely.

(B) Each point now has at least two separate lines.

A line 's' that is not incident on point 'P' must exist according to axiom 4 if we use point 'P' as our starting point.

Axiom 2 states that if a line exists, it must have the two points "R" and "S" on it.

(C) Since "P" does not lie on "m." P thus differs from 'e' and 's'

Points that stand out. They are different because they would be referred to as "m" if both lines "n" and I passed via "r" and "s."

However, "P" does not lay on "m," hence the statement is contradictory.

So it is proved

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The speed and the course of the aircraft  is 27465 km/h.

A machine or vehicle can fly by obtaining support from the air, and this is how an airplane works. It uses either static lift, dynamic lift provided by an airfoil, or, in certain rare situations, the downward thrust from jet engines to counteract the pull of gravity.

From the figure, let us use cosine formula to calculate the resultant displacement.

B^2 = C^2 + A^2 - 2(A)(C) cosØ

Where C = 580km

A = 360 km

Ø = 153 degree

Substitute all the parameters into the formula

B^2 = 580^2 + 360^2 - 2(360)(580)cos153

B^2 = 466000 - ( - 372084.32 )

B^2 = 466000 + 372084.32

B^2 = 838084.32

Square root both sides

B = 915.5 km

You are told to use a scale of 1 cm to 50 km.

Therefore, B = 915.5/50 = 18.3 cm

The time given are: 09:23 and 09:25.

The time difference = 25 - 23 = 2 minute

Convert minutes to hours

2 minute = 2/60 = 1/30 hours

Speed = distance/time

Speed = 915.5 ÷ 1/30

Speed = 915.5 × 30

Speed = 27465 km/h

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Answer:

27

Step-by-step explanation:

just subtract 153 from 180

The distance on the map is 3/4 inch

Given data

scale of the map = 1 inch : 2 miles

measurement from garage to the entrance of the skatepark = 3,520 feet

1 mile = 5,280 feet

The required measurement to convert to map measurement = 3520 feet

we solve for number of miles in 3520 feet knowing that 1 mile = 5,280 feet.  we solve this by:

5280 / 3520= 3 / 2 miles

so if scale of the map is 1 inch : 2 miles

x : 3 / 2 miles

we cross multiply to find x as

x = 3/2 / 2

x = 3/4

The distance on the map is 3/4 inch

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Answer:

25.12 cm

Step-by-step explanation:

The circumference of a circle can also be understood as the perimeter of the circle.

Circumference of circle= 2πr= πd

r refers to radius while d refers to diameter

Given that r= 4,

circumference of circle

= 2(π)(4)

= 8π

≈ 8(3.14)

= 25.12 cm

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Step-by-step explanation:

the diagonals in a square are intersecting each other at 90°.

that means that G1 + G2 = 90

and because of the symmetry of a kite, it also means that G1 = G2.

combined this tells us

G1 = G2 = 90/2 = 45°.

also due to its symmetry one of the rules of a kite is that its diagonals are also intersecting each other at 90°.

so,

E1 = E2 = 90°.

the sum of all angles in a triangle is always 180°.

so,

180 = F1 + G1 + (D2 + D3) = F1 + 45 + 110

F1 = 180 - 45 - 110 = 180 - 155 = 25°

again, due to the symmetry of the kite

F1 = F2 = 25°.

also

C2 + C3 = D2 + D3 = 110°

due to the properties of a square (e.g. the angle in every corner is 90°, the diagonals are splitting each corner angle in half) we know that

D1 = D2 = 45°.

and again, therefore

C1 = C2 = D1 = D2 = 45°

and so

(1)

due to the law of the angles of a line intersecting parallel lines are equal for every parallel line, we see that

the line BD intersects the lines AD and GEF equally at 45°. therefore, GEF || AD.

(2)

as we know that F1 = F2 = 25°,

F1 + F2 = 2×25 = 50°

(3)

the angles in the triangle GDE are

E1 = 90°

D2 = 45°

G1 = 45°

the angles of GE and DE with their baseline GD are equal, that means this is an isoceles triangle, meaning the legs have an identical length, and therefore

DE = GE.

(4)

as GDE is a right-angled triangle we can use Pythagoras :

GD² = GE² + DE² = 2×DE² = 2×GE²

GD = 3×sqrt(2)

GD² = 9×2 = 18

18 = 2×DE² = 2×GE²

DE² = GE² = 18/2 = 9

DE = GE = 3

By consideration of congruence and collinearity, the value of x behind the geometric system formed by two collinear linear segments is equal to 3 / 8.

Two line segments are congruent when the line segments have the same length, then the following condition has to be fulfilled:

AB = BC      (1)

Where AB and BC are the lengths of the line segments AB and BC.

If we know that AB = 4 · x + 1 and BC = 20 · x - 5, then we solve the equation for x is:

4 · x + 1 = 20 · x - 5

6 = 16 · x

16 · x = 6

x = 6 / 16

x = 3 / 8

Then, the value of x behind the geometric system formed by two collinear linear segments is equal to 3 / 8.

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The number of meters of fence he would need is 45.72 meters

The given parameters are

Length of backyard = 150 ft

As a general rule, we have the following conversion equation

1 foot = 0.3048 meters

So, we have

Length of backyard = 150 * 0.3048 meters

Evaluate the product

So, we have

Length of backyard = 45.72 meters

Hence, the number of meters of fence he would need is 45.72 meters

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The value of the composite functions, (h ° f)(1) = 0.5.

Given the function, (h ° f)(1), this means h(f(1)) as a composition of functions.

Using the table given for the function, f(x), f(1) = -1.

This means that, to find (h ° f)(1) = h(f(1)), we would find the value of h(x) in the table where x = -1.

Thus, from the table for h(x), when x = -1, h(-1) = 0.5.

Therefore, the value of the composite functions, (h ° f)(1) = 0.5.

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The value of full positive integer k such that  [tex]O(n^k)[/tex] is the most restrictive polynomial-time upper bound of f(n) are as follows : (A) 9 (B) no integer exists (C)5/3(not an integer) (D)no integer exists (E) [tex]3e^{99}[/tex]

Using the Lower and Upper Bound Theory, it is possible to identify the algorithm with the lowest level of complexity. Let's quickly review what Lower and Upper bounds are before we can understand the theory.

A)[tex]2^{lg(3n+4n+5)}+lg {\spaceh} n \inO(n^k)[/tex]

or, [tex]O(2^{lgn^9}+lgn)\inO(n^k)[/tex]    since   [tex]3n^9+4n+5=O(n^9)[/tex]  

or, [tex]O(2^{lgn^9})\in O(n^k)[/tex] as [tex]2^m+lg m=O(2^m)[/tex]

Applying lg 2 on both sides we get:

[tex]lg_22^{lgn^9}=lg_2n^k[/tex]

solving we get:

k=9 × lg2 × lg n

At n=1/2

k=9

Hence the minimum integer for K is 9.

B) [tex]7lgn+13lg^5n\in O(n^k)[/tex]

Solving for k we get:

k=lgₙ(lg⁵n)

C) [tex]\sqrt[3]{7n^5+2n^3-4}\in O(n^k)[/tex]

Solving by exponent rule we get:

[tex]O(n^{5/3})\in O(n^k)[/tex]

k=5/3

D)[tex]13lg2^{3^n\inO(n^k)}[/tex]

or, [tex]k=lg_n(lg2^{3^n})[/tex]

E)[tex]7^{20!+1} \inO(n^k)[/tex]

As we don't have any term of n on the Left Hand Side, therefore no most restrictive polynomial-time upper bound exist for [tex]O(n^k)[/tex]

[tex]k=e^{99}[/tex]

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Answer:

See explanation

Step-by-step explanation:

3x/(-8)=-21/4

-3x/8=-21*8/4

-3x*8/8=-21*8/4    ==> multiply 8 on both sides to get rid of denominator

-3x=-21*2

-3x=-42

3x=42   ==> Multiply by -1 on both sides to get positive values on both sides

x=14

Answer:

6+3+11/4[tex]\neq[/tex]5

Step-by-step explanation:

Answer:

The answer to the question is 0

Answer:

62%

Step-by-step explanation:

31/50 can be multiplied by 2 to get 62/100. 62/100 is equal to 62%. to get percents, attempt to get the demoninator (bottom number in fraction) to be 100, then the top number is the percent (because its basically saying 62 out of 100 pieces, which is 62 percent)

The translation of the graph that has the domain [−3, 6] is:

B. g(x) = |x + 3|.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

In this problem, the parent function is given by:

f(x) = |x|.

The domain changed by [−6, 3] to [-3,6], meaning that 3 units was added to each bound of the domain, hence x -> x + 3 and:

g(x) = |x + 3|.

Which means that option B is correct.

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The total number of Cubes that can be packed in the Rectangular Prism will be 84 Cubes

In the picture mentioned below, We have a Rectangular prism with the dimensions Length = [tex]3\frac{1}{2}[/tex] in, Breadth = 2 in, Height =  [tex]1\frac{1}{2}[/tex] in

Also, It is given that cubes of Dimension [tex]\frac{1}{2}[/tex] inches are to be packed in the Rectangular Prism.

Firstly, We need to find the volume of Both the Prism & the Cube.

Since, The it is a Rectangular Prism, Volume of cuboid = ( l*b*h )

Volume of Prism, V1 = l*b*h => l =[tex]3\frac{1}{2}[/tex], b = 2, h = [tex]1\frac{1}{2}[/tex]

                        => V1 = [tex]3\frac{1}{2} * 2 * 1\frac{1}{2}[/tex]    => V1 = 10.5 [tex]in^{3}[/tex]

Volume of Cube, V2 = l * l * l => l = [tex]\frac{1}{2}[/tex]

                       => V2 = [tex]\frac{1}{2} * \frac{1}{2} * \frac{1}{2}[/tex]       => V2 = 0.125 [tex]in^{3}[/tex]

To find out the number of cubes that can fit inside the prism we need to divide the volume of the prism by the volume of cube => V1/V2

                       =>  N =  [tex]\frac{V1}{V2}[/tex]  =>  [tex]\frac{10.5}{0.125}[/tex]

                       =>  N = 84 Cubes.

Hence, the Total number of cubes that can fit inside the Prism will be 84.

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The transformation was not done is Shifted right 5 units and vertically compressed by a factor of 2.

 function g(x) = - f(x)

 function g(x) = f(-x)

 by h units, then the new function g(x) = f(x - h)

 by h units, then the new function g(x) = f(x + h)

 by k units, then the new function g(x) = f(x) + k

 by k units, then the new function g(x) = f(x) – k

A vertical stretching is the stretching of the graph away from

 the x-axis

 the x-axis.

 stretched by multiplying each of its y-coordinates by k.

 by multiplying each of its y-coordinates by k.

 followed by a reflection across the x-axis.  

So, we can write,

f(x) = x

g(x) = -1/(x+5)+7

 and reflected over the x-axis

Therefore,

The transformation was not done is Shifted right 5 units and vertically compressed by a factor of 2.

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Answer: 7/39

Step-by-step explanation:

Find the GCD (or HCF) of numerator and denominator GCD of 7 and 39 is 1

Divide both the numerator and denominator by the GCD 7 ÷ 1 39 ÷ 1

Reduced fraction: 7 39 Therefore, 7/39 simplified to lowest terms is 7/39.

Answer:

  P = (2, 7)

Step-by-step explanation:

You want to find coordinates of P on segment AB such that P is 3/4 is of the way from A to B.

For some fraction q of the distance from A to B, the point P that lies at that fraction of the distance is given by ...

  P = A +q(B -A) = (1 -q)A +qB

For q = 3/4, the location of P is ...

  P = (1 -3/4)A + 3/4B = (A +3B)/4

Using the given point coordinates, we have ...

  P = ((-4, -2) +3(4, 10))/4 = (-4 +12, -2 +30)/4 = (8, 28)/4

  P = (2, 7)

The interval representing the expression "82 less than a is at least −82." is given by ( -82, 82).

We are given an expression that:

82 is less than a which is at least - 82.

This expression can also be written as:

- 82 < a and a > 82

where a is any variable that can take any value according to the expression.

This can also be written as:

- 82 < a < 82

In interval form, it will be written as:

( -82, 82)

"()" brackets are used as -82 and 82 are not included in the interval.

Therefore, we get that, the interval representing the expression "82 less than a is at least −82." is given by ( -82, 82).

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Answer:

[tex]y=\dfrac{7}{3}\left(\dfrac{1}{3}\right)^x[/tex]

Step-by-step explanation:

Given table:

[tex]\begin{array}{|c|c|}\cline{1-2} \phantom{\dfrac{1}{1}} x & y \\\cline{1-2} \phantom{\dfrac{1}{1}} -1 & 7 \\\cline{1-2} \phantom{\dfrac{1}{1}} 0 & \frac{7}{3}\\\cline{1-2} \phantom{\dfrac{1}{1}} 1 & \frac{7}{9}\\\cline{1-2} \phantom{\dfrac{1}{1}} 2 & \frac{7}{27}\\\cline{1-2} \phantom{\dfrac{1}{1}} 3 & \frac{7}{81}\\\cline{1-2}\end{array}[/tex]

Work out the first differences between the y-values:

[tex]7 \underset{-\frac{14}{3}}{\longrightarrow} \dfrac{7}{3} \underset{-\frac{14}{9}}{\longrightarrow} \dfrac{7}{9} \underset{-\frac{14}{27}}{\longrightarrow} \dfrac{7}{27} \underset{-\frac{14}{81}}{\longrightarrow} \dfrac{7}{81}[/tex]

As the first differences are not the same, it is not a linear function.

Work out the second differences:

[tex]-\dfrac{14}{3} \underset{+\frac{28}{9}}{\longrightarrow} -\dfrac{14}{9} \underset{+\frac{28}{27}}{\longrightarrow} -\dfrac{14}{27} \underset{+\frac{28}{81}}{\longrightarrow} -\dfrac{14}{81}[/tex]

As the second differences are not the same, it is not a quadratic function.

Work out if the second differences have a common ratio:

[tex]\implies \sf \dfrac{28}{27} \div \dfrac{28}{9}=\dfrac{1}{3}[/tex]

[tex]\implies \sf \dfrac{28}{81} \div \dfrac{28}{27}=\dfrac{1}{3}[/tex]

As the second differences have a common ratio of ¹/₃, the function is exponential with base ¹/₃.

General form of an exponential function:

[tex]y=a(b)^x[/tex]

where:

The y-intercept is the value of y when x = 0.

From inspection of the table, the y-intercept is ⁷/₃.

Therefore:

  [tex]a = \dfrac{7}{3}[/tex]

  [tex]b = \dfrac{1}{3}[/tex]

Substitute the found values of a and b into the formula to create an exponential function that models the given data:

[tex]\implies y=\dfrac{7}{3}\left(\dfrac{1}{3}\right)^x[/tex]

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Answer: y - 2 = 2(x + 7)

Step-by-step explanation:

        Point-slope form is written as y - [tex]y_{1}[/tex] = m(x - [tex]x_{1}[/tex]) where m is the slope and ( [tex]x_{1}[/tex], [tex]y_{1}[/tex]) are points on the line.

y - [tex]y_{1}[/tex] = m(x - [tex]x_{1}[/tex])

y - 2 = 2(x + 7)