the length of the rectangle is 12 cm more than the width of the perimeter is 68cm find the length and width of this rectangle

Answer:

1

Step-by-step explanation:

the answer is 1.21576655000000000.

the unit of this no. is 1.

Answer:

13/9

Step-by-step explanation:

The mixed fraction is,

→ 1 4/9

Converting into improper fraction,

→ 1 4/9

→ ((9 × 1) + 4)/9

→ (9 + 4)/9

→ 13/9

Hence, the fraction is 13/9.

The required conversion of mixed number 1 4/9 to an improper fraction is 13/9.

A fraction is defined as a numerical representation of a part of a whole that represents a rational number.

A mixed number is made up of a whole number and a fractional portion. An improper fraction is one in which the numerator (upper number) exceeds the denominator (bottom number). Without modifying the value of the figure, you may convert between mixed numbers and improper fractions.

As per the question, we have to convert 1 4/9 to an improper fraction

Multiply the denominator by the whole number

⇒ 9 × 1 = 9

Add the answer from Step 1 to the numerator

⇒ 9 + 4 = 13

Write the answer from Step 2 over the denominator

13/9

Thus, we can write 1 4/9 to an improper fraction as 13/9.

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Answer:

Step 1: Write your hypotheses and plan your research design

Step 2: Collect data from a sample

Step 3: Summarize your data with descriptive statistics

Step 4: Test hypotheses or make estimates with inferential statistics

Step 5: Interpret your results

Step-by-step explanation:

Answer:

(-2,0)

Step-by-step explanation:

the x-intercept is when the y = 0 and you have to make one of them has to equal to 0 ;  (4,0) or (-2,0) and the only one is (-2,0).

Answer:

(-2, 0)

Step-by-step explanation:

As shown in this picture

The value of distance between two points on graph is,

⇒ d = √32 units

We have to given that;

The coordinates of two points are,

⇒ (9, - 4) and (5, -8)

We know that;

The distance between two points (x₁ , y₁) and (x₂, y₂) is,

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

Hence, The value of distance between two points on graph is,

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

⇒ d = √ (5 - 9)² + (- 8 - (-4))²

⇒ d = √ 16 + 16

⇒ d = √32

Thus, The value of distance between two points on graph is,

⇒ d = √32 units

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Question 24 :

P594.65 : 35 days

P594.65/7 : 35/7 days

P84.95 : 5 days

⇒ A. P84.95

Question 25 :

88.75 + 85.5 + 90.5 + 87.25 / 4

352/4

88

⇒ B. 88

Question 26 :

I = P × r × t

I = 580.00 × 0.065 × 1

I = P37.70

⇒ B. P37.70

Answer:

\(y=(x+8)(x+10)=x^2 + 18x + 80\)

\(\frac{dy}{dx} = 2x + 18\)

\(y=0\) when \(x=-8\) and \(x=-10\)

so the tangent slopes are \(\frac{dy}{dx} = 2\) and -2 at those x.

The lines are y = 2x + b and y = -2x + c.

We need to find b and c.

The first line must go through (-8,0) and the second one through (-10,0).

For the first line: 0 = 2*(-8) + b and b = 16.

For the second line: 0 = -2*(-10) + c and c = -20.

Step-by-step explanation:

I have  bunch of videos on calculus on my "Sciency Sergei" you tube channel. You are welcome to stop by :).

Solving the inequality given algebraically, the solution of the inequality for the value of m is:

m < -4 OR m > 3

Given the following inequality,

\(\frac{m - 2}{3} < -2 \\\)

or

4m + 3 > 15

Let's solve algebraically for the value of m in both inequality statements given.

\(\frac{m - 2}{3} < -2 \\\)

\(\frac{m - 2}{3} \times 3 < -2 \times 3\\\\m - 2 < -6\)

\(m - 2 + 2 < -6 + 2\\\\m < -4\)

Or

4m + 3 > 15

4m + 3 - 3 > 15 - 3

4m > 12

\(\frac{4m}{4} > \frac{12}{4} \\\\\)

m > 3

Therefore, solving the inequality given algebraically, the solution of the inequality for the value of m is:

m < -4 OR m > 3

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Answer:

1. ∆CBD:      ∠B = 70°; ∠BCD = 20°; ∠ BDC = 90°

2. ∆CDA: ∠ACD = 70°;      ∠A = 20°; ∠ ADC = 90°

Step-by-step explanation:

1. ∆DBC

In ∆ABC

 ∠A + ∠B + ∠C = 180°

20° + ∠B + 90 ° = 180°

         ∠B + 110 ° = 180°

      ∠DBC = ∠B =  70°

In ∆CBD

                      ∠BDC =  90°

∠B + ∠BCD + ∠CBD = 180°

  70° + ∠BCD + 90 ° = 180°

           ∠BCD + 160° = 180°

                        BCD =   20°

2. ∆CAD

∠A + ∠ACD + ∠ADC = 180°

   20° + ∠ACD + 90° = 180°

            ∠ACD + 110° = 180°

                      ∠ACD =   70°

The types of variation and their constants are;

1) Direct variation with constant of variation as -1/4

2) Direct variation with constant of variation as ³/₂

A variation is defined as a relation that exists between a set of values of one variable and then a set of values of other variables.

In variation, if the variables change proportionately that is they either increase together or decrease together, then they are said to vary directly.

1) We are given the equation;

4y = -x

Now, y is the output while x is the input and so we make y the subject to get; y = -¹/₄x

Now, writing the relationship between y and x as a variation, we will have; y ∝ x

For this to be equal, there has to be a constant of proportionality which means; y = kx

Comparing with our equation tells us that;

This is a direct variation with constant of variation as -1/4

2) We are given the equation;

3x = 2y - 7

Rearranging gives;

2y = 3x + 7

y = ³/₂x + 7

Now, the greater the value of x, the greater the value of y and as such this is also a direct variation with the constant of variation being 3/2.

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Using the binomial distribution, it is found that there is a 0.38 = 38% theoretical probability that all 6 bulbs will last for 4 months.

The formula is:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

In this problem, we have that:

The probability that all 6 bulbs will last for 4 months is P(X = 6), hence:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 6) = C_{6,6}.(0.85)^{6}.(0.15)^{0} \approx 0.38\)

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The following statements are true:

A:The car makes a complete revolution in 10 seconds

B:The maximum height of the Ferris wheel is 65 feet

A full rotation or turning around a focal point is referred to as a revolution. Revolution is the act of rotating around a fixed point or axis . Examples of this include the rotation of a planet around its star or a wheel around its axle.

A. The car makes a complete revolution in 10 seconds:

This can be deduced from the fact that the height of the Ferris wheel car returns to 35 feet after 10 seconds, which means that it has completed one full revolution.

B. The maximum height of the Ferris wheel is 65 feet:

This can be seen from the table, where the height of the Ferris wheel car reaches 65 feet at 2.5 seconds and 12.5 seconds.

C. If the car is loaded at 0 seconds, then the people are loaded at the lowest point of the Ferris wheel: This can be seen from the table, where the height of the Ferris wheel car is 35 feet at 0 seconds.

It is not possible to determine the radius of the Ferris wheel based on the given information alone.

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Answer:

The correct answer is true.

Step-by-step explanation:

To differentiate the function f(x) = 1/x^3, we can use the power rule of differentiation. Here's the step-by-step process:

Write the function: f(x) = 1/x^3.

Apply the power rule: For a function of the form f(x) = x^n, the derivative is given by f'(x) = nx^(n-1).

Differentiate the function: In our case, n = -3, so the derivative is:

f'(x) = -3 * x^(-3-1) = -3 * x^(-4) = -3/x^4.

Therefore, the derivative of the function f(x) = 1/x^3 is f'(x) = -3/x^4.

Answer:

10.70 a CD without tax (11.90 with tax)

Step-by-step explanation:

Answer:

the slope is undefined

Step-by-step explanation:

since x=33 is a vertical line the slope is undefined.

Answer:

The maximum value of f(x) occurs at:

\(\displaystyle x = \frac{2a}{a+b}\)

And is given by:

\(\displaystyle f_{\text{max}}(x) = \left(\frac{2a}{a+b}\right)^a\left(\frac{2b}{a+b}\right)^b\)

Step-by-step explanation:

Answer:

Step-by-step explanation:

We are given the function:

\(\displaystyle f(x) = x^a (2-x)^b \text{ where } a, b >0\)

And we want to find the maximum value of f(x) on the interval [0, 2].

First, let's evaluate the endpoints of the interval:

\(\displaystyle f(0) = (0)^a(2-(0))^b = 0\)

And:

\(\displaystyle f(2) = (2)^a(2-(2))^b = 0\)

Recall that extrema occurs at a function's critical points. The critical points of a function at the points where its derivative is either zero or undefined. Thus, find the derivative of the function:

\(\displaystyle f'(x) = \frac{d}{dx} \left[ x^a\left(2-x\right)^b\right]\)

By the Product Rule:

\(\displaystyle \begin{aligned} f'(x) &= \frac{d}{dx}\left[x^a\right] (2-x)^b + x^a\frac{d}{dx}\left[(2-x)^b\right]\\ \\ &=\left(ax^{a-1}\right)\left(2-x\right)^b + x^a\left(b(2-x)^{b-1}\cdot -1\right) \\ \\ &= x^a\left(2-x\right)^b \left[\frac{a}{x} - \frac{b}{2-x}\right] \end{aligned}\)

Set the derivative equal to zero and solve for x:

\(\displaystyle 0= x^a\left(2-x\right)^b \left[\frac{a}{x} - \frac{b}{2-x}\right]\)

By the Zero Product Property:

\(\displaystyle x^a (2-x)^b = 0\text{ or } \frac{a}{x} - \frac{b}{2-x} = 0\)

The solutions to the first equation are x = 0 and x = 2.

First, for the second equation, note that it is undefined when x = 0 and x = 2.

To solve for x, we can multiply both sides by the denominators.

\(\displaystyle\left( \frac{a}{x} - \frac{b}{2-x} \right)\left((x(2-x)\right) = 0(x(2-x))\)

Simplify:

\(\displaystyle a(2-x) - b(x) = 0\)

And solve for x:

\(\displaystyle \begin{aligned} 2a-ax-bx &= 0 \\ 2a &= ax+bx \\ 2a&= x(a+b) \\ \frac{2a}{a+b} &= x \end{aligned}\)

So, our critical points are:

\(\displaystyle x = 0 , 2 , \text{ and } \frac{2a}{a+b}\)

We already know that f(0) = f(2) = 0.

For the third point, we can see that:

\(\displaystyle f\left(\frac{2a}{a+b}\right) = \left(\frac{2a}{a+b}\right)^a\left(2- \frac{2a}{a+b}\right)^b\)

This can be simplified to:

\(\displaystyle f\left(\frac{2a}{a+b}\right) = \left(\frac{2a}{a+b}\right)^a\left(\frac{2b}{a+b}\right)^b\)

Since a and b > 0, both factors must be positive. Thus, f(2a / (a + b)) > 0. So, this must be the maximum value.

To confirm that this is indeed a maximum, we can select values to test. Let a = 2 and b = 3. Then:

\(\displaystyle f'(x) = x^2(2-x)^3\left(\frac{2}{x} - \frac{3}{2-x}\right)\)

The critical point will be at:

\(\displaystyle x= \frac{2(2)}{(2)+(3)} = \frac{4}{5}=0.8\)

Testing x = 0.5 and x = 1 yields that:

\(\displaystyle f'(0.5) >0\text{ and } f'(1) <0\)

Since the derivative is positive and then negative, we can conclude that the point is indeed a maximum.

Therefore, the maximum value of f(x) occurs at:

\(\displaystyle x = \frac{2a}{a+b}\)

And is given by:

\(\displaystyle f_{\text{max}}(x) = \left(\frac{2a}{a+b}\right)^a\left(\frac{2b}{a+b}\right)^b\)

The top left graph represents the weight of the radioactive isotope over time.

An exponential function has the definition presented according to the equation as follows:

\(y = ab^x\)

In which the parameters are given as follows:

The parameter values for the function in this problem are given as follows:

a = 96, b = 0.5.

Hence the function is given as follows:

\(y = 96(0.5)^x\)

Two points on the graph of the function are given as follows:

(1,48) and (2, 24).

Hence the top left graph represents the weight of the radioactive isotope over time.

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Answer:

Graph W

Step-by-step explanation:

The given information describes a radioactive decay process, where the weight of the isotope decreases by half at regular intervals. This type of decay is characteristic of exponential decay.

Based on the description, the graph that represents the weight of the radioactive isotope over time would be a decreasing exponential curve, where the y-axis represents the weight of the isotope (in grams), and the x-axis represents time (in hours).

The initial weight of the isotope is 96 grams, and after each subsequent hour, the weight becomes half of what it was in the previous hour. Therefore, the correct graph would start at 96 grams (the initial weight when x = 0) and then decrease by half every hour. It would be a curve that gets closer and closer to zero but never quite reaches it.

Initial weight: 96 grams

After 1 hour: 96 / 2 = 48 grams

After 2 hours: 48 / 2 = 24 grams

After 3 hours: 24 / 2 = 12 grams

After 4 hours: 12 / 2 = 6 grams

After 5 hours: 6 / 2 = 3 grams

So, the points on the graph would be:

Therefore, the graph that represents the weight of the radioactive isotope over time is Graph W.

Answer:

The answer is the D : 729

Step-by-step explanation:

The area of a cube is wide x length x height

9x9x9 = 729

Answer:

729

Step-by-step explanation:

The first cellphone service provider to be established in South Africa was Vodacom. Vodacom was launched on April 1, 1994, and it became the country's first cellular network operator.

The company was a joint venture between Telkom, the national telecommunications company of South Africa, and Vodafone, a global telecommunications giant.

Vodacom introduced the GSM network to South Africa, providing mobile voice and data services to customers across the country. Its launch marked a significant milestone in the telecommunications industry in South Africa, as it brought mobile communication to the masses and revolutionized the way people connect and communicate.

Since its inception, Vodacom has played a pivotal role in the development of the telecommunications sector in South Africa. It has continually expanded its network coverage, introduced innovative services, and played an active role in bridging the digital divide in the country.

Today, Vodacom remains one of the leading mobile network operators in South Africa, providing a wide range of mobile services to millions of customers.

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The probable question may be:

Which cellphone service provider was the first to be established in south africa

Answer:

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The distance is 710000 km and the first spaceship has travelled 110000 km in the first hour.

The remainder of the distance is reducing by:

Time to travel before they meet:

Add the first hour to this to get total travel time of 4 hours.

The proportional relationship that gives the cost of x tickets is:

\(y = 18x\)

\(y = kx\)

Two tickets to an ice skating performance costs $36, hence, when \(x = 2, y = 36\), then:

\(y = kx\)

\(36 = 2k\)

\(k = \frac{36}{2}\)

\(k = 18\)

Hence, the relationship is described by:

\(y = 18x\)

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Answer:

Find the amount for $250 compounded yearly at a rate of 25% for a period of x years.

Explanation:

Given the function f(x) defined as follows:

We can rewrite f(x) as:

If we compare this with the compound interest formula:

We can see that:

• Principal, P=250

• Interest Rate =0.25 = 25%

A word problem for the function will be:

Find the amount for $250 compounded yearly at a rate of 25% for a period of x years.

Answer:

20°

Step-by-step explanation:

\( \because \: l = \frac{ \theta}{360 \degree} \times c \\ \\ \therefore \: \frac{1}{3} = \frac{ \theta}{360 \degree} \times 6 \\ \\ \therefore \: \theta = \frac{360 \degree}{3 \times 6} \\ \\ \therefore \: \theta = \frac{360 \degree}{18} \\ \\ \therefore \: \huge \red{ \boxed{ \theta = 20 \degree}} \\ \)

Answer:no

Step-by-step explanation:

the (x) fators out more than once