The post office will only accept packages for which the length plus the "girth" (distance around) is no more than 108 inches. Thus, we must have L+2(x+y)<=108.
What is the greatest acceptable length for a package that has a square base measuring 9 inches by 9 inches?

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:

the second piece of rope

Step-by-step explanation:

2.63 ≥ 2.5

2.085≤2.5

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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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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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:

  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)

Answer:

                  Equation: Y'=33.67+0.54*X'

Step-by-step explanation:

Given that

General regression line equation is:

Y'=a+b*X'

Therefore, the slope of the regression line is equal to the linear correlation coefficient times the difference between the standard deviations of y' and x'.

[tex]b = r\times\frac{S_y}{S_x}[/tex]

[tex]b = 0.5\times\frac{2.7}{2.5}[/tex]

b = 0.54

The mean of the lowered by the slope and mean of x is the intercept with axis y.

[tex]a = y'-b\times x'[/tex]

[tex]a = 68.5-0.54\times 64.5[/tex]

[tex]a = 33.67[/tex]

Now, putting the values of a and b in regression equation

So, we get

                  Y'=a+b*X'

Equation: Y'=33.67+0.54*X'

Answer:

                  Equation: Y'=33.67+0.54*X'

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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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By finding square numbers, we will get:

8 < √80 < 9

And we can assume that √80 is closer to 9 than to 8, so a good estimation can be 8.95

We want to approximate √80, now we need to find two consecutive square numbers such that one is smaller and the other is larger than 80.

We know that:

9*9 = 81

8*8 = 64

Then:

√81 = 9

√64 = 8

So we can see that:

√64 < √80 < √81

Then:

8 < √80 < 9

And we can assume that √80 is closer to 9 than to 8, so a good estimation can be 8.95

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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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The final answer is -9, -30.75, -13

What is Quotient?

The number resulting from the division of one number by another.

In the given statement is:

What is the quotient for 81/-9

If we divide 81 by -9

The Quotient will be -9

And, come to the next :

-123 divide by -4

The quotient will be -30.75

And, 65 divided by (-5)

The Quotient will be -13

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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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The algebraic expression from the given statement is (a+b)/ab.

Given the statement is the quotient of the sum of a and b and the product of a and b.

In mathematics, an expression is defined as a set of numbers, variables, and operations that are formed according to context-dependent rules.

In the given statement the sum of a and b means a+b.

And the product of a and b means ab.

Now, as it is given in the statement that the quotient of the sum of a and b and the product of a and b can be written as

(a+b)/ab.

Hence, the algebraic expression from the given statement "the quotient of the sum of a and b and the product of a and b" is (a+b)/ab.

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Answer:

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

Step-by-step explanation:

Answer:

The answer to the question is 0

Answer:

x=11

Step-by-step explanation:

let number =x

(8+3x)=41

group like terms

3x=41-8

3x=33

divide both side by the coefficient of x

3x/3=33/3

x=11

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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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.

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:

27

Step-by-step explanation:

just subtract 153 from 180

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

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:

x = 22.5

2x = 45

5x = 112.5

Step-by-step explanation:

The sum of all internal angles in a triangle is 180 degrees. This can be expressed as the following:

x + 5x + 2x = 180

Combine the like terms:

8x = 180

Divide both sides by 8 to find the value of x:

x = 180/8

Simplify:

x = 22.5

Multiply by 2 to get 2x:

2x = 22.5 * 2

2x = 45

Multiply by 5 to get 5x:

5x  = 22.5 * 5

5x = 112.5

Verify the answer is correct by taking all the obtained values and ensuring they sum to 180:

22.5 + 45 + 112.5 = 180

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: 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)

Answer:

10 x 12 x 9 cm^2

= 1080 cm^2

Answer:

105

Step-by-step explanation:

a = 1/2(bh) + 1/2(bh)

a = 1/2(12)(10) + 1/2 (9)(10)

a= 1/2 (120) + 1/2(90)

a = 60 + 45

a = 105

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)

Answer:

C. two-thirds raised to the fourteenth

Step-by-step explanation:

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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Applying the definition of bisection, PR = RQ = 28.5 cm.

When a line segment bisects another line segment, it divides the line into two equal segments. This means the two resultant line segments formed have the same length.

The image below shows the bisection of segment PQ by segment ST at point R, which forms two equal segments, PR and RQ.

This means that the length of segments PR and RQ will be equal to each other.

Given that, PQ = 57 centimeters, therefore:

PR = RQ = 1/2(PQ)

PR = RQ = 1/2(57)

PR = RQ = 28.5 cm

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