is 8.2 and 5.15 proportional

The value of the limit of the function given when the value of x tends to zero is 0

The limit of a function is a fundamental concept in calculus and analysis concerning the behavior of that function near a particular inputs.

Given the function limit below;

lim x→0 [1 − cos(2x) /x]

Substitute the value of x into the expression to have;

f(0) = 1-cos2(0)/0
f(0) = 1-1/0

f(0) = 0/0 (ind)

Apply the L'hospital rule to have:

lim x→0 [ − (-2sin2x)) /1]

Substitute the value of x into the result

f(0) = 2sin2(0)/1

f(0) = 2(0)

f(0) = 0

Hence the value of the limit of the function given when the value of x tends to zero is 0

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The mean = 28.55, while the standard deviation is 13.16

1. The histogram is an attachment

We have the following numbers

24 30 4 42 40 26 23 36 12 45 29 21 34 16 47 28 32 54 19 9

The sum of these numbers is given as

571

The total numbers = 20

The mean = 571/20

= 28.55

=  (24 - 28.55)2 + ... + (9 - 28.55)/20 - 1

=  3292.95/19

=  173.31315789474

s =  √173.31315789474

=  13.164845532506

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The number section A, section B and section C seats sold are 26500, 14200 and 12300 respectively.

The stadium has 53,000 seats.

Seats sell for $25 in Section A, $20 in Section B, and $15 in Section C.

The number of seats in Section A equals the total number of seats in Sections B and C.

Therefore,

a =  b + c

a + b + c = 53000

b + c + b + c = 53000

2b + 2c = 53,000

25a + 20b + 15c = 1131000

25(b + c) + 20b + 15c  = 1131000

25b + 25c + 20b + 15c = 1131000

45b + 40c = 1131000

Hence,

2b + 2c = 53000

45b + 40c = 1131000

40b + 40c  = 1060000

45b + 40c = 1131000

-5b = - 71000

b = - 71000 / -5

b = 14,200

Therefore,

2(14,200) + 2c = 53000

2c = 53000 - 28400

2c = 24600

c = 24600 / 2

c = 12300

Hence,

a =  b + c

a = 14200 + 12300

a = 26500

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Given that, Nathan shares out 12 sweets, if he gives Yasmin 1 sweet for 3 sweets he buys, Nathan will get 9 sweets.

Given that, Nathan shares out 12 sweets, he gives Yasmin 1 sweet for 3 sweets he buys.

Let the sweet be represented by x

For each x sweet for Yasmin, Nathan gets 3x sweets

Hence

x + 3x = 12

We solve for x

4x = 12

x = 12/4

x = 3

Hence;

Yasmin gets x sweet = 3

Nathan gets 3x sweets = 3 × 3 = 9

Given that, Nathan shares out 12 sweets, if he gives Yasmin 1 sweet for 3 sweets he buys, Nathan will get 9 sweets.

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The inverse proportional relationship that models this variation is given as follows:

[tex]y = \frac{10,000}{x}[/tex]

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

An inverse proportional relationship is given as follows:

[tex]y = \frac{k}{x}[/tex]

In this problem, we have an inverse relation in which y(2) = 5000, hence the constant k is found as follows:

[tex]y = \frac{k}{x}[/tex]

[tex]5000 = \frac{k}{2}[/tex]

k = 10,000

Hence the relation is:

[tex]y = \frac{10,000}{x}[/tex]

As stated in the problem, when x = 5, y = 2,000, which we can verify replacing in the relation.

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The missing side in the given triangle is x = √193 km

The Pythagoras theorem is expressed as;

x^2 = a^2 + b^2

where

x is the longest side

Substitute the given side

x^2 = 12^2 + 7^2

x^2 = 144 + 49

x = √193 km

Hence the missing side in the given triangle is x = √193 km

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From the information given about the square pyramid, the maximum base length of the building is 67.42 cm.

We are given the following  details  are:

Base = b

Slant height (l) = 5b

The lateral surface area is calculated using:

L = 2bl

So, we have:

L = 2 * b * 5b

Evaluate the product

L = 10b²

The total surface area is calculated using:

T = L + b²

So, we have:

T = 10b² + b²

Evaluate the sum

T = 11b²

Recall that the maximum surface area is 50,000 square feet

So, we have:

11b² = 50000

Divide both sides by 11

b² = 50000/11

Taking the square root of both sides, we have

b = 67.42

Hence, the maximum base length of the building is 67.42 cm

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The probability that the diameter of the electric cable that is normally distributed will exceed 0.92 inch is 0.841

Probabilities are used to determine the chances, likelihood, possibilities of an event or collection of events

The given parameters are:

Mean = 0.9

Standard deviation = 0.2

Calculate the z-score at x = 0.92 using

[tex]z = \frac{x - \mu}{\sigma}[/tex]

This gives

z = (0.92 - 0.9)/0.02

Evaluate the numerator; subtract 0.9 from 0.92

z = 0.02/0.02

Divide 0.02 by 0.02. This gives

z = 1

The probability is then represented as:

P(x > 0.92) = P(z > 1)

Next, we look up the value of the z table of probabilities

From the z table of probabilities, we have:

P(x > 0.92) = 0.841

Hence, the probability that the diameter of the electric cable that is normally distributed will exceed 0.92 inch is 0.841

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Answer:

The value of tan M = 15/8

Step-by-step explanation:

[tex]tan \: m \: = \frac{p}{b} \\ tan \: m \: = \frac{15}{8} [/tex]

The solution to the given inequality expression is expressed as x ≥ 6

Given the inequality expression shown below;

5x-9/7≥3

Cross multiply

(5x -9)≥7(3)

Expand

5x-9≥21

Add 9 to both sides

5x ≥ 21 + 9

5x ≥ 30

x ≥6

The solution to the given inequality expression is expressed as x ≥ 6

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Based on the graph which depicts the United States domestic market for  corn at different prices, we can logically deduce the following information:

Assuming France is the only other corn-producing nations at a domestic price of $4, we can reasonably infer that the United States will export corn while France will import it.

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Answer:

hey its me again so the answer is 11.

I'm sure because I did this.

The number of marriage licenses were issued in 2003 is 21586.

According to the statement

we have to find the number of marriage licenses were issued in 2003

and the given equation is y=3.405x^2-17674x+21533000

And in this equation x represent the time

And Y represent the number of marriage certificate issued.

So, in given equation

y=3.405x^2-17674x+21533000

we fill the value of X and find the value of Y means tne number of marriage license is issued in 2003

We know that X = 3 from 2000 to 2003

Then put X=3 in the given equation.

Then

This is the equation (1) represent the change

y=3.405(3)^2-17674(3)+21533000 -(1)

y = 30.645+53022+21533000

y = 21586052.645

On nearest hundred the value becomes 21586.

So, The number of marriage licenses were issued in 2003 is 21586.

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DISCLAIMER: The question was incomplete. please find the full content below.

QUESTION:

According to the model, how many marriage licenses were issued in 2003? Round your answer to the nearest hundred.

The number of marriage licenses issued by Clark county Nevada, the county where Las Vegas is located, has been decreasing since the year 2000. This can be modeled by y=3.405x^2-17674x+21533000 where x is the year and y is the number of marriage licenses issued.

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Answer: A. 137,000

Step-by-step explanation: I did the quiz.

Answer: equation: y=-4x+1

slope: -4

y intercept:1

area = 25.5 cm²

Step-by-step explanation:

i have shown in the image you have to rotate it to see how i worked the area out

i am very sorry i cant work the perimeter out since i have no idea what the length of the two sides of the triangle are . if you need help on understanding how i worked out the area please let me know .

hopefully i was able to help you in half of the question i am sorry for not helping on the perimeter :)

Answer:

Step-by-step explanation:

Perimeter=25

The exact values of sec θ, tan θ and sin θ are 6.4/4, 5/4 and 5/ 6.4 respectively.

From the figure, we have the values of the sides to be;

Let's use Pythagorean theorem to find the hypotenuse(x)

Hypotebuse square = opposite side square + adjacent side square

Substitute the values deduced from the figures given

x² = 5² + 4²

x² = 25 + 16

x² = 41

x = [tex]\sqrt{41}[/tex]

x = 6. 4

sin θ = opposite/hypotenuse

Substitute the values

sin θ = 5/ 6. 4

tan θ = opposite/ adjacent

Substitute the values

tan θ = 5/ 4

sec θ = hypotenuse/ adjacent

substitute the values

sec θ = 6. 4/ 4

Thus, the exact values of sec θ, tan θ and sin θ are 6.4/4, 5/4 and 5/ 6.4 respectively.

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Answer:

(4,-5)

Step-by-step explanation:

The composition of transformation that maps ABCD to EHGF is reflect over the y-axis, then translate (x - 1, y + 1)

Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.

Translation is the movement of a point either up, left, right or down in the coordinate plane.

The composition of transformation that maps ABCD to EHGF is reflect over the y-axis, then translate (x - 1, y + 1)

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Answer:

[tex] \sf{b. \frac{x}{2} <3}[/tex]

step by step explanation:

We will try one by one.

A. x + 5 < 3

Step 1. Subtitution Value of x

= 4 + 5 < 3

Step 2. Add by 4 with 5

= 9 < 5

A is wrong because 9 is bigger then 5

B. x/2 < 3

= 4/2 < 3

= 2 < 3

is true because 2 is smaller than 3

C. 9x > 36

9(4) > 36

36 > 36

is wrong, should 36 = 36

D. 18 < 8

is wrong because 18 is bigger than 8

A) The Period is 30 seconds

D) The amplitude is 25 m

A) Since the Ferris wheel makes 2 rotations every minute, then we can say that the period is;

T = 1/2 = 0.5 minutes = 30 seconds

B) Let t be time in seconds and let h be height and as such, we have the formula; h = 25 - 25 cos ((2π/30)t)

Thus, the table is attached showing input values of t and their corresponding h values.

C) The graph of the table above is as attached below.

D) The amplitude is;

Amplitude = (Maximum Point - Minimum Point)/2

Amplitude = (50 - 0)/2

Amplitude = 25

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Answer:

the difference between them is zero cause on first year simple interest and compound interest are equal

Fractions are mathematical expressions that relate two numbers as a quotient. Thus the answer to this question is:  [tex]\frac{3d + b}{d}[/tex]

Fractions are expressions in a form of a quotient that relates one number to another number. The two numbers can be classified as either the numerator or the denominator. The number above the division line is the numerator, while that below the line is the denominator. Some types of fractions are proper fractions, improper fractions, and mixed fractions.

A given fraction can undergo basic arithmetic operations when two or more are involved. Also, a fraction can be added to one another, or subtracted from a whole number.

The given expression in the question involves the addition of a whole number (3), to a fraction (b/d).

Given: 3 + b/d

The LCM is d, thus;

3 + b/d = [tex]\frac{3d + b}{d}[/tex]

Therefore, the required answer is: [tex]\frac{3d + b}{d}[/tex]

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The factor of the polynomial expression 4x^3 – 12x^2 + 4x by using GCF method is  4x(x^2 - 3x + 1).

The factors of a given number are those numbers that are divisible by the given number without a remainder.

By using the GCF method in an algebraic, i.e. the factors of the algebraic equation will be dependent on the greatest common factor.

From the given information, we are to factorize the following expression by using the GCF method as follows.

1.

4x^3 – 12x^2 + 4x

Here; the common expression in all the three variables is 4x. So, we have:

= 4x(x^2 - 3x + 1)

Option A is correct

2.

9x^4 + 4x^3 - 27x^2 + 12x

The common expression here is (x); So,

= x(9x^3 +4x^2 - 27x + 12)

Option B is correct

3.

x^2 - 3x + 4

This polynomial expression cannot be factored.

Option F is correct.

4.

17x^5 + 51x^2 - 34

= 17(x^5 + 3x^2 - 2)

Option D is correct.

The factorization of a quadratic equation (polynomial expression) in the form (ax^2 + bx + c) by grouping results into two factors that if multiplied together result back into the original equation.

Given that:

5.

x^2 – 2x + 1

Factors are two numbers that if the multiplied result in (ac) and if added it gives us (b)

By grouping, the polynomial expression is:

= (x - 1)(x - 1)

Option A is correct

6.

x^2 + 2x - 15

= (x + 5) (x - 3)

Option C is correct

7.

x^2 – 3x – 18

=(x + 3)(x - 6)

Option B is correct

8.

8x^2 + 47x + 28

= This polynomial expression cannot be factored in as it contains rational numbers.

Option A is correct.

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Answer:

$160

Step-by-step explanation:

115% = $184

100% = X

let X be the original salary

(X is unknown)

115% = $184

100% = X

cross mutiply

115 x X = 100 x 184

115X = 18400

X = 18400 divided by 115

X = $160

therefore,Mr Black's original salary before increased by 15% was $160

hope am helpful.

Answer:

y=-2x+12

Step-by-step explanation:

First, subtract 1/2 from each side

1/4y = -1/2x + 3 --> multiply each side by 4

y = -2x + 12 is your final answer

Answer: 208

Step-by-step explanation:

[tex]\frac{p}{-1+17} =13[/tex]

[tex]\frac{p}{16} =13[/tex]

[tex](16)\frac{p}{16} =13(16)[/tex]

[tex]p=13*16[/tex]

[tex]p=208[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{p}{-1}+17=13 \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{Apply \ the \ properties \ of \ fractions: \frac{a}{-b}=-\frac{a}{b}. } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{=-\frac{P}{1} } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{Apply\:the\:rule \:\frac{a}{1}=a} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{Subtract \ 17 \ from \ both \ sides. } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{Simplify } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{Divide\:both\:sides\:by\:-1} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{Simplify } \end{gathered}$}[/tex]

The sum accumulated by 31st December 2018 is Rs 4,163,060.00

What is future value?

Future value is the accumulated amount that investments would yield in future period when the amounts invested are added with the total interest earned.

Note in this case that Rs500,000  would be invested subsequently for 4 years( 2015-2018 , January 1st of each year)

We can determine the future value of each investment using the future value formula shown below:

FV=PV*(1+r)^N

PV=amount invested

r=interest=10%

N=number of years that an amount is invested(for instance, the amount invested on 1st January 2014 will earn interest in 2014,2015,2016, 2017 and 2018 i.e. for 4 years)

Total FV=1,000,000*(1+10%)^5+500,000*(1+10%)^4+500,000*(1+10%)^3+500,000*(1+10%)^2+500,000*(1+10%)^1

Total FV=Rs 4,163,060.00

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The formula for the squirrel population is P(t) = 400 e^0.5t and the doubling time of the population is 17. 68 years

The growth constant k can be defined as the frequency or also known as the number of times per unit time of growing by a factor

it is also called the logarithmic return, compounded return, or the force of interest.

Note that the general formula for growth rate is given as;

[tex]P(t) = P0 e^k^t[/tex]

Where,

Po =  Initial value = 400 squirrels

r = Rate of growth

k = constant of proportionality = 0. 5 per year

t = time = 1 year

The function P(t) is given as;

P(t) = 400 e^0.5t

Note that the formula for doubling time is given as;

[tex]TD = t \frac{In 2}{In 1 + r/ 100}[/tex]

r = 4

t = 1

substitute into the formula

[tex]TD = 1 \frac{0. 693}{0. 0392}[/tex]

Doubling time  = 1 × 17. 68

Doubling time = 17. 68 years

Thus, the formula for the squirrel population is P(t) = 400 e^0.5t and the doubling time of the population is 17. 68 years

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Answer: c, y ≤ -3x+6

Step-by-step explanation:

for example we could use a point on the graph such as (-2, 0)

now we would insert the numbers into the inequality:

y ≤ -3x+6

= 0 ≤ -3(-2) +6

= 0 ≤ 6+6

= 0 ≤ 12

which is true! therefore it is y ≤ -3x+6

Answer:

[tex]\bf m = - 1[/tex]

Step-by-step explanation:

[tex]\bf m= −(4+m)+2[/tex]

First of all, let's Rearrange the given terms :-

[tex]\bf m = - ( m +4) + 2[/tex]

Now, let's distribute:-

[tex]\bf m = - m - 4 + 2[/tex]

Add numbers -4 + 2 = -2

[tex]\bf m = - m - 2[/tex]

Add m to both sides, and combine like terms :-

[tex]\bf 2m = - 2[/tex]

Divide both sides by 2 :-

[tex]\bf m = - 1[/tex]