The length of a rectangle is three times the width. The perimeter of the rectangle is 72 cm. Find the dimensions of the rectangle.

Answer: x and y = 3

Step-by-step explanation:

Answer:

Each shirt costed 9 dollars.

Step-by-step explanation:

35+10=45 (initial price)

45/5=9 dollars per shirt

The best-fitting regression model for the scatter plot is exponential curve , Option C is the right answer.

The missing graph is attached with the answer.

An exponential graph is given by y = aˣ , the graph for an exponential growth is also attached with the answer,

From the graph given in the question it can be concluded that it is not linear , not quadratic and it is not true that it doesn't have a pattern , It is an exponential growth graph, Therefore Option C is the right answer.

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Answer:

3Meter Per Second Square

Step-by-step explanation:

Accelaration=Vf-vi/t

A=21-6/5

A=3

The statement 'In order to calculate MACRS depreciation, the business needs to know the asset's original cost, the depreciation period, and which depreciation method (i.e. 200% declining balance) is used.' is false. because, the asset was used for both personal and business purposes, the business must calculate the percentage of business use in order to determine the correct depreciation deduction.

While the asset's original cost, depreciation period, and depreciation method are all necessary inputs for calculating MACRS depreciation, there are other pieces of information that are also required.

For example, the business must determine the applicable MACRS recovery period and the property's placed-in-service date, as well as any applicable conventions for calculating the depreciation.

Additionally, if the asset was used for both personal and business purposes, the business must calculate the percentage of business use in order to determine the correct depreciation deduction.

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800 people in the cinema are eating popcorn by probability.

What does math probability mean?

Total people in cinema = 200

probability of choosing a person eating popcorn is = 0.25

people in the cinema are eating popcorn = 200/0.25

people in the cinema are eating popcorn     = 800

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Answer:

1306.24 cm².

Step-by-step explanation:

From the diagram given above, we obtained the following information:

Radius (r) = 13 cm

Pi (π) = 3.14

Slant height (l) = 19 cm

Surface Area (SA) =.?

The surface area of the cone can be obtained as follow:

SA = πr² + πrl

SA = πr ( r + l)

SA = 3.14 × 13 ( 13 + 19)

SA = 40.82 (32)

SA= 1306.24 cm²

Therefore, the surface area of the cone is 1306.24 cm².

Answer:

(2, –3) is a solution to the system of linear equations.

Step-by-step explanation:

Given: Equations:

3x - y = 9 --------(1),

4x + y = 5 --------(2),

Add Equation (1) + Equation (2),

3x + 4x = 9 + 5

7x = 14  ( Combine like terms )

x = 2   ( Divide both sides by 7 ),

From equation 1:

3(2) - y = 9

6 - y = 9

-y = 9 - 6    ( Subtraction 6 on both sides )

-y = 3

y = - 3     ( Multiplying -1 on both sides )

Answer:

true

Step-by-step explanation:

if you rewrite \(sec\left(\frac{\pi }{2}\:-x\right)\) with trigonometric identities:

\(sec\left(\frac{\pi }{2}\:-x\right)\)    \(=\frac{1}{\sin \left(x\right)}\)

\(\frac{1}{\sin \left(x\right)}\)  \(=\csc \left(x\right)\)

so, yes,  \(sec\left(\frac{\pi }{2}\:-x\right)\)  \(=\csc \left(x\right)\)

hope this helps!!

The speed of the object is 12121 m per week.

What does it mean to do speed?

The object is moving at a speed of 2 centimeters every 7 seconds.

We need to find the speed in m per week.

2 cm = 0.02 m

1 week = 604800 s

7 s =  \(1.65 * 10^{-6} week\)

Speed = distance/time

So,

\(v = \frac{0.02 m}{1.65 * 10^{-6 } week}\)

\(v = 12121.21 m/ week\)

or v = 12121 m/ week

So, the speed of the object is 12121 m per week.

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The  total distance it flies, rounded to the nearest mile is: d. 1,692 miles .

First distance= 550 miles (given)

Second distance=483 miles (given)

Now let find the third distance

Let x represent the third distance

Hence:

x/sin79 = 550/sin55

x= 659.1

Now let calculate the total distance

Total distance=550+483+659.1

Total distance= 1692.1

Total distance= 1692 miles (rounded)

Therefore the correct option is d.

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If Elizabeth throws a coin vertically into the air. At its highest point, it is 3.1 meters above the ground. Then 0.05 sec is the velocity of the coin at its highest point.

Velocity defines the direction of the movement of the body or the object.

Given that Elizabeth throws a coin vertically into the air. At its highest point, it is 3.1 meters above the ground. We need to find the velocity.

The formula for velocity = Change in distance/Change in time

The distance in the given problem is 3.1 meters.

Velocity=3.1/60

=0.051m/s

Therefore the coin's velocity when it is at its highest point is 0.051 m/s.

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By solving the original equation numerically, you can find the values of \(\(x_1\)\), \(\(f(x_1)\)\), \(\(f'(x_1)\)\), and \(\(f''(x_1)\)\) at one of the solutions.

A statement that affirms the equivalence of two expressions joined by the equals symbol "=" is known as an equation. For illustration, 2x - 5 = 13. 2x - 5 and 13 are expressions in this case. These two expressions are joined together by the sign "=".

To analyze the given equation \(\(x^3 + (1 - 4\epsilon)x = \sqrt{1 + 4\epsilon}\)\), we can follow the steps below:

(a) Curve Sketching:

To determine the number of real-valued solutions, we can observe the behavior of the equation by plotting its graph.

1. Set the equation equal to zero:

\(\(x^3 + (1 - 4\epsilon)x - \sqrt{1 + 4\epsilon} = 0\)\)

2. Consider the limiting cases:

 - When \(\(\epsilon = 0\)\), the equation becomes \(\(x^3 + x - 1 = 0\)\).

 - When \(\(\epsilon\)\) is sufficiently small, we can approximate \(\(\sqrt{1 + 4\epsilon} \approx 1 + 2\epsilon\)\) and rewrite the equation as \(\(x^3 + (1 - 4\epsilon)x - (1 + 2\epsilon) = 0\)\).

3. Sketch the graphs of these equations:

  - When \(\(\epsilon = 0\)\), we have a cubic polynomial equation \(\(x^3 + x - 1 = 0\)\).

  - For small \(\(\epsilon\)\), the graph of \(\(x^3 + (1 - 4\epsilon)x - (1 + 2\epsilon) = 0\)\) will be similar to the cubic polynomial with slightly different parameters due to the presence of \(\(\epsilon\)\).

  By examining the graph of the cubic polynomial equation \(\(x^3 + x - 1 = 0\)\), we can observe that it intersects the x-axis at two points. Therefore, for small \(\(\epsilon\)\), the equation \(\(x^3 + (1 - 4\epsilon)x - \sqrt{1 + 4\epsilon} = 0\)\) will also have two real-valued solutions.

(b) Two-Term Asymptotic Expansion for Small \(\(\epsilon\)\):

To find a two-term asymptotic expansion for small \(\(\epsilon\)\), we'll assume that \(\epsilon\)\) is small and perform a Taylor series expansion.

Let's denote the two solutions of the equation as \(\(x_1\)\) and \(\(x_2\)\).

1. Express the equation as a function:

\(\(f(x) = x^3 + (1 - 4\epsilon)x - \sqrt{1 + 4\epsilon}\)\)

2. Expand the function using a Taylor series about \(\(x = x_1\)\) (first solution):

\(\(f(x) = f(x_1) + f'(x_1)(x - x_1) + \frac{1}{2}f''(x_1)(x - x_1)^2 + \mathcal{O}((x - x_1)^3)\)\)

3. Set \(\(f(x) = 0\)\) and solve for \(\(x - x_1\)\):

\(\(0 = f(x_1) + f'(x_1)(x - x_1) + \frac{1}{2}f''(x_1)(x - x_1)^2 + \mathcal{O}((x - x_1)^3)\)\)

4. Neglect higher-order terms and rearrange the equation:

\(\(f'(x_1)(x - x_1) + \frac{1}{2}f''(x_1)(x - x_1)^2 \approx -f(x_1)\)\)

5. Divide both sides by \(\(x - x_1\)\) (assuming \(\(x \neq x_1\)\)):

\(\(f'(x_1) + \frac{1}{2}f''(x_1)(x - x_1) \approx -\frac{f(x_1)}{x - x_1}\)\)

6. Set \(\(x = x_2\)\) (second solution) and substitute the values of \(\(f(x_1)\)\) and \(\(f'(x_1)\)\):

\(\(f'(x_1) + \frac{1}{2}f''(x_1)(x_2 - x_1) \approx -\frac{f(x_1)}{x_2 - x_1}\)\)

7. Solve for \(\(x_2 - x_1\)\):

\(\((x_2 - x_1) \approx -\frac{2f(x_1)}{f'(x_1) + \frac{1}{2}f''(x_1)(x_2 - x_1)}\)\)

This equation provides an approximation for \(\(x_2 - x_1\)\) in terms of \(\(x_1\)\), \(\(f(x_1)\)\), \(\(f'(x_1)\)\), and \(\(f''(x_1)\)\). By solving the original equation numerically, you can find the values of \(\(x_1\)\), \(\(f(x_1)\)\), \(\(f'(x_1)\)\), and \(\(f''(x_1)\)\) at one of the solutions. Substitute those values into the above equation to calculate the two-term asymptotic expansion for small \(\(\epsilon\)\).

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Answer:

2430kg

Step-by-step explanation:

3 tonnes is 3000kg so 3 tonnes 335kg is 3335kg. Take 3335 - 905 you get 2430

Answer:

144 :)

Step-by-step explanation:

Answer:

144

Step-by-step explanation:

12x12=144

Answer:

Equation to determine number of albums sold: 12a +200 = 644

Step-by-step explanation:

Given that:

Base rate earned by Floyd = $200

Amount for per album sold = $12

Let,

a be the number of albums sold by Floyd

Amount earned last month = $644

According to given statement;

Total earned = 12a + 200

12a +200 = 644

Hence,

Equation to determine number of albums sold: 12a +200 = 644

Answer:

-2

(0, 1)

Step-by-step explanation:

Giveb the function :

F(x) = 3^x + 1 – 2

To obtain the asymptote, take the limit of f(x) as x as tends to ∞

3^(∞+1) - 2 = 0 - 2

Hence,

y = 0 - 2.

y = - 2

The y intercept, this is the value of y when x = 0

Hence, put x = 0

F(0) = 3^(0 + 1) – 2

f(0) = 3^1 - 2

f(0) = 3 - 2

f(0) = 1

Y - intercept = (0, 1)

Answer: The answer is 49.32

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

The Values of (a+b)ab are undefined.

Given that, a = 3an and db = -2We need to find the values of (a+b)

Now, we have a = 3an... equation (1)Also, we have db = -2... equation (2)From equation (1), we get: n = 1/3... equation (3)Putting equation (3) in equation (1), we get: a = a/3a = 3... equation (4)Now, putting equation (4) in equation (1), we get: a = 3an... 3 = 3(1/3)n = 1

From equation (2), we have: db = -2=> d = -2/b... equation (5)Multiplying equation (1) and equation (2), we get: a*db = 3an * -2=> ab = -6n... equation (6)Putting values of n and a in equation (6), we get: ab = -6*1=> ab = -6... equation (7)Now, we need to find the value of (a+b).For this, we add equations (1) and (5),

we get a + d = 3an - 2/b=> a + (-2/b) = 3a(1) - 2/b=> a - 3a + 2/b = -2/b=> -2a + 2/b = -2/b=> -2a = 0=> a = 0From equation (1), we have a = 3an=> 0 = 3(1/3)n=> n = 0

Therefore, from equation (5), we have:d = -2/b=> 0 = -2/b=> b = ∞Now, we know that (a+b)ab = (0+∞)(0*∞) = undefined

Therefore, the values of (a+b)ab are undefined.

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Answer:

63

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

A because it requires experimental and control groups

In this problem, we have a continuous exponential growth model

so

the equation is of the form

where

a is the initial value ------> a=2,100

y is the number of bacteria

x ----> number of hours

so

For x=2.5 hours, y=2,249 bacteria

substitute

solve for k

apply ln both sides

k=0.0274

convert to percentage

Answer:

hjyfgtuygtfvfvhjkoijuhgytfrdetrft

Step-by-step explanation:

dcfgvhbjnkiouytrfdr

Answer:

-2.94

Step-by-step explanation:

I got the answer correct on edge

the approximate percentage of daily phone  calls is 0.

Mean= 58

Standard deviation= 4

x= 54 and 62.

Now, solving to find the percentage of daily phone calls numbering between 54 and 62.

\(let x_{1} =54 and x_{2}=62\)

first calculating the z-score for daily 54 phone calls.

Formula used:

\(z-score = x-mean/standard deviation\)

\(z- score=54-58/4\)

\(z-score=-4/4\)

z-score= -1

∴ z-score for daily 54 phone call is -1.

Next, calculating the z-score for daily 62 phone calls.

z-score= 62-58/4

z-score= 4/4

z-score= 1

∴ z-score for daily 62 phone call is 1.

We can observe that there is change in z-score for 54 phone call and 62 phone call.

Lets use the normal distribution table to find the percentage of daily phone calls numbering between 54 and 62.

⇒ Percentage of daily phone calls numbering between 54and 62=

\((z-scorex_{1})-(z-scorex_{2} )\)

⇒ Percentage of daily phone calls numbering between 54 and 62=

(z-score1) - (z-score-1)

Using normal distribution table

⇒ Percentage of daily phone calls numbering between 54 and 62=

0.34134-0.34134 = 0

Hence, 0 is the percentage of daily phone calls numbering between 54 and 62.

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On solving the provided question, we can say that the probability it is back or female is  55/6 and P( 1 or 6) = 12/7

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

1 gray female, 2 gray males, 2 black male and 2 black males

picked one random kitten

the probability it is back or female is \(^7C_4 + ^6C_3\) = 7!/4!*3! + 6!/3!*3!

= 7*6*5/6+6*5*4/6 = 55/6

A jar contain 7 balls numbered from 1 to seven. You randomly pick a ball. It is numbered 1or 6.

P( 1 or 6) = 12/7

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Answer:

15

Step-by-step explanation:

let total num of boys be X.

then,2/5 of X = 8

2 ×x = 40

X = 20

Now, let the total num of students be y,then we get,

4/7 of y = 20

4 × y = 140

y = 35

similarly, total num of girls = total num of students - total num of boys

= 35 - 20

= 15 ans

Answer:

$180 USD

Step-by-step explanation:

Since currency is constantly changing I will round the answer. 1 pound is equal to $1.20 US currency. Hope it helped!

Solution:

The equation of a line in slope-intercept form is expressed as

Given that

By substituting these values into the above equation, we have

Hence, the equation of the line is