Graph this compound inequality: x <-8 or x ≥ 3

Answer:18 days

Step-by-step explanation:

Here's a short table of heights:

 day 0: height = 1

 day 1: height = 1 + (1/2)(1) = 3/2

 day 2: height = (3/2) + (1/3)(3/2) = 3/2 + 1/2 = 2

The pattern of heights is ...

 (day, height) = (0, 1), (1, 1.5), (2, 2)

The plant is growing 1/2 its original height each day, so we can write the equation ...

 h = 1 + d/2

We want to find the number of days (d) that result in a height of 10 (ten times the original height).

 10 = 1 + d/2

 9 = d/2 . . . . subtract 1

 18 = d . . . . . multiply by 2

It took 18 days for the plant to grow to 10 times its original height.

Answer:

it would take 9 weeks for both of the plants to equally meet the same height which is 33 inches

Step-by-step explanation:

Can i please get branelist

The answer to the equation (5+12i) + (7-5i) is found to be 12-7i.

The provided equation is a simple algebraic relation between two complex numbers.

The given complex numbers are 5+12i and 7-5i.

We have to add these two complex numbers.

We will add the real part of the complex number to the real part and complex part of one complex number to the complex part of the complex number.

Sum of number = (5+12i) + (7-5i)

Sum of number = 12-7i

The sum of the two complex numbers is also complex number that has a real part has 12 and the imaginary or the complex part as -7.

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On average, a customer spends approximately 1.16 minutes waiting time on hold before they can start speaking to a representative.

To find the average waiting time for a customer on hold before they can start speaking to a representative, we need to consider both the arrival rate of calls and the average service time of the staff members.

Given:

9 staff members taking calls.

On average, one call arrives every 5 minutes (standard deviation of 5 minutes).

Each staff member spends on average 18 minutes with each customer (with a standard deviation of 27 minutes).

To calculate the average waiting time, we need to use queuing theory, specifically the M/M/c queuing model. In this model:

"M" stands for Markovian or memoryless arrival and service times.

"c" represents the number of servers.

In our case, we have an M/M/9 queuing model since we have 9 staff members.

The average waiting time for a customer on hold is given by the following formula:

Waiting time = (1 / (c * (μ - λ))) * (ρ / (1 - ρ))

Where:

c = number of servers (staff members) = 9

μ = average service rate (1 / average service time)

λ = average arrival rate (1 / average interarrival time)

ρ = λ / (c * μ)

First, let's calculate the average arrival rate (λ):

λ = 1 / (average interarrival time) = 1 / 5 minutes = 0.2 calls per minute

Next, calculate the average service rate (μ):

μ = 1 / (average service time) = 1 / 18 minutes = 0.0556 customers per minute

Now, calculate ρ:

ρ = λ / (c * μ) = 0.2 / (9 * 0.0556) ≈ 0.407

Finally, calculate the waiting time:

Waiting time = (1 / (c * (μ - λ))) * (ρ / (1 - ρ))

= (1 / (9 * (0.0556 - 0.2))) * (0.407 / (1 - 0.407))

≈ 1.16 minutes

Therefore, on average, a customer spends approximately 1.16 minutes waiting on hold before they can start speaking to a representative.

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Answer:

see explanation

Step-by-step explanation:

(a)

calculate the lengths using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = J (- 3, - 7 ) and (x₂, y₂ ) = K (3, - 8 )

JK = \(\sqrt{(3-(-3))^2+(-8-(-7))^2}\)

    = \(\sqrt{(3+3)^2+(-8+7)^2}\)

    = \(\sqrt{6^2+(-1)^2}\)

    = \(\sqrt{36+1}\)

    = \(\sqrt{37}\)

repeat with (x₁, y₁ ) = M (8, 3 ) and (x₂, y₂ ) = N (7, - 3 )

MN = \(\sqrt{(7-8)^2+(-3-3)^2}\)

      = \(\sqrt{(-1)^2+(-6)^2}\)

     = \(\sqrt{1+36}\)

     = \(\sqrt{37}\)

repeat with (x₁, y₁ ) = P (- 8, 1 ) and (x₂, y₂ ) = Q (- 2, 2 )

PQ = \(\sqrt{-2-(-8))^2+(2-1)^2}\)

      = \(\sqrt{(-2+8)^2+1^2}\)

      = \(\sqrt{6^2+1}\)

      = \(\sqrt{36+1}\)

      = \(\sqrt{37}\)

(b)

JK ≅ MN ← true

JK ≅ PQ ← true

MN ≅ PQ ← true

The length of this rectangular room is equal to 9 meters.

The breadth of this rectangular room is equal to 5 meters.

In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:

A = xy

Where:

If length would become 3 meters less and breadth would become 1 meter more, we have the following expressions;

y = x - 3

x = y + 1

45 = xy

When the rectangle turns to a square, all of the side lengths become equal;

y + 1 = x - 3

x = y + 4

From the area of a rectangle formula, we have:

45 = (y + 4)y

45 = y² + 4y

y² + 4y - 45 = 0

y² + 9y - 5y - 45 = 0

y(y + 9) - 5(y + 9) = 0

y = 5 or -9 meters.

For the length, we have:

x = y + 4

x = 5 + 4

x = 9 meters.

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The probability of rolling a total of 7 on the two dice is 8/63

Probability:

In Mathematics, Probability is a branch that deals with the occurrence of possible outcomes in a random event or experiment. It is also defined as the ratio of the number of favorable outcomes and the total number of outcomes.

The probability of an event is denoted by P(E). And the probability of all the events in the sample space will equal to 1.  

Probability P(E) = No of favorable outcomes /Total No of outcomes  

Here we have,

The probabilities of rolling 1, 2, 3, 4, 5, and 6, on each die, are in the ratio 1: 2: 3: 4: 5: 6  

Let x, 2x, 3x, 4x, 5x, and 6x are the probabilities of rolling 1, 2, 3, 4, 5, and 6, on each die [ since they are in ratio 1: 2: 3: 4: 5: 6 ]  

As we know the total events in a probability = 1

=> x + 2x + 3x + 4x + 5x + 6x = 1  

=> 21 x = 1

=> x = 1/21  

From the above calculations,

The probabilities of rolling 1, 2, 3, 4, 5, and 6 are  \(\frac{1}{21} , \frac{2}{21}, \frac{3}{21}, \frac{4}{21}, \frac{5}{21}, \frac{6}{21}\) respectively.  

The possible combinations of two dies that can give a total of 7 are

(1, 6) (2, 5) (3, 4) (4, 3) (5, 2) (6, 1)

Therefore, the probability of rolling a total of 7 on the two dice

=  the sum of the probabilities of rolling each combination

=  \(\frac{1}{21} . \frac{6}{21} + \frac{2}{21} .\frac{5}{21} + \frac{3}{21} . \frac{4}{21} + \frac{4}{21} . \frac{3}{21} + \frac{5}{21} .\frac{2}{21} + \frac{6}{21} .\frac{1}{21}\)  

=  \(\frac{6}{441} + \frac{10}{441} + \frac{12}{441} + \frac{12}{441} + \frac{10}{441} + \frac{6}{441}\)  

=  \(\frac{56}{441}\)

=  \(\frac{8}{63}\)

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The complete question is

For a particular peculiar pair of dice, the probabilities of rolling 1, 2, 3, 4, 5, and 6, on each die are in the ratio 1:2:3:4:5:6. What is the probability of rolling a total of 7 on the two dice

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Slope of given line is ~

\( \boxed{2}\)

\( \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}\)

Let's find the slope of given line using coordinates of points (2 , 2) and (5 , 8) ~

To identify the curve given the polar equation r = 5 cos(theta) and theta = pi/3, we need to convert the polar equation into a Cartesian equation. This will allow us to express the curve in terms of x and y coordinates.

Convert polar equation to Cartesian equation: To convert the polar equation r = 5 cos(theta) into a Cartesian equation, we can use the relationships x = r cos(theta) and y = r sin(theta).

Substitute the given value of theta: Since theta = pi/3 is specified, we substitute this value into the equations from step 1.

x = 5 cos(pi/3) = 5 * (1/2) = 2.5

y = 5 sin(pi/3) = 5 * (√3/2) = 5√3/2 ≈ 4.33

Write the Cartesian equation: The Cartesian equation for the given polar equation is (x, y) = (2.5, 4.33).

Therefore, the curve identified by the given polar equation r = 5 cos(theta) and theta = pi/3 can be expressed in Cartesian coordinates as the point (2.5, 4.33).

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Answer:

11n

Step-by-step explanation:

8n + 3= 11n

11n-4=7n

+4n=11n

Answer:

1.Subtract the numbers:

8n+3-4+ 4n

8n-1+ 4n

2.Combine like terms

8n-1+4n

12n-1

solution

12n-1

Step-by-step explanation:

I hope this can help you!!

Answer:

Therefore m angle 2 is 86°.

Step-by-step explanation:

Given:

m∠ 1 = 17x + 1

m∠ 2 = 20x - 14

To Find:

m∠ 2   =?

Solution:Vertical Angles:  

The angles opposite each other when two lines cross. They are always equal.

∴ m∠ 1 = m∠ 2  

Substituting the given values we get

Now for m∠ 2  

Therefore m angle 2 is 86°.

Answer:  \(6\sqrt{5}\)  miles

This is the same as writing 6*sqrt(5) miles

==========================================================

Work Shown:

P = park

C = city hall

Point P is at the location (10,11)

Point C is at the location (7,5)

Apply the distance formula to find the length of segment PC

\(d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(10-7)^2 + (11-5)^2}\\\\d = \sqrt{(3)^2 + (6)^2}\\\\d = \sqrt{9 + 36}\\\\d = \sqrt{45}\\\\d = \sqrt{9*5}\\\\d = \sqrt{9}*\sqrt{5}\\\\d = 3\sqrt{5}\\\\d \approx 6.7082039\\\\\)

The exact distance between the park (P) and city hall (C) is \(3\sqrt{5}\) miles.

This doubles to \(2*3\sqrt{5} = 6\sqrt{5}\) miles because the runners go from P to C, then back to P again. In other words, they run along segment PC twice. This is assuming there is a straight line road connecting the two locations.

Extra info:

\(6\sqrt{5} \approx 13.41641\) so the runner travels a total distance of roughly 13.4 miles.

Answer:

8%

Step-by-step explanation:

Answer:

x= 1.79

Step-by-step explanation:

x-0.63=1.16 add 0.63 to both sides

x= 1.79

Answer:

x =1.79

Step-by-step explanation:

x -0.63 = 1.16

Add .63 to each side

x -0.63+.63 = 1.16+.63

x =1.79

Answer:

1/2 OR 0.5

Step-by-step explanation:

(*￣3￣)╭

Answer:

1/2

Step-by-step explanation:

The crude oil is likely to be paraffinic. Paraffinic crude oils are characterized by having a high API°, low Watson characterization factor, and low refractive index. They also tend to have a high surface tension.

Specific gravity at 60 °F: 0.88

API° at 60 °F: 28

Watson characterization factor: 1.014

Refractive index: 1.44

Surface tension: 20 dyne/cm

Paraffinic, naphthenic, or aromatic: Paraffinic

Specific gravity at 60 °F the specific gravity of a liquid is its density relative to the density of water. The specific gravity of crude oil is typically between 0.8 and 1.0. A specific gravity of 0.88 means that the crude oil is 88% as dense as water.

API° at 60 °F: The API°, or American Petroleum Institute gravity, is a measure of the lightness or darkness of crude oil. A higher API° indicates a lighter crude oil. A crude oil with an API° of 28 is considered to be a medium-heavy crude oil.

Watson characterization factor the Watson characterization factor is a measure of the aromaticity of crude oil. A higher Watson characterization factor indicates a more aromatic crude oil. A crude oil with a Watson characterization factor of 1.014 is considered to be a paraffinic crude oil.

Refractive index the refractive index of a liquid is a measure of how much light is bent when it passes through the liquid. The refractive index of crude oil is typically between 1.4 and 1.5. A refractive index of 1.44 indicates that the crude oil is slightly more refractive than water.

Surface tension the surface tension of a liquid is a measure of the force that acts at the surface of the liquid, tending to minimize the surface area. The surface tension of crude oil is typically between 20 and 30 dyne/cm. A surface tension of 20 dyne/cm indicates that the crude oil has a relatively high surface tension.

Based on the estimated values, the crude oil is likely to be paraffinic. Paraffinic crude oils are characterized by having a high API°, low Watson characterization factor, and low refractive index. They also tend to have a high surface tension.

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The term civil disobedience suggest that make someone else to decide what is right or what is wrong.

As in the concept of Civil Disobedience, the author called Thoreau's basic premise is that a higher law than civil law demands the obedience of the individual. And it will also states that Human law and government are subordinate. According to the given cases where the two are at odds with one another, then the individual must follow his conscience and, and if is necessary, then it disregard human law.

And it will also states that a refusal to obey an order from a civil authority or public nonviolent violation of a legal prohibition. And then It can be an individual or corporate act. By those undertaking civil disobedience seek to understand and act on a higher law.

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the ladder leaning against the wall has slope 3

A student must earn 13 points in the three races to be guaranteed of earning more points than any other student.

A student can obtain information in two possible ways

If someone gets one of these combinations, someone else could get the other, so we are not guaranteed to get the most points with this combination that is  5+5+1or 5+3+3= 11

Guaranteed earning more points than any other student can only be obtained in one way.: 5+5+3=13 In this case, the highest possible score for another person is  =5+3+3=11, So having 13 points ensures that you have more points than anyone else.

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Answer:

250 in^3

Step-by-step explanation:

V=BH

v=10(25)

v=250 in^3

The equation of g(x) is given as follows:

\(g(x) = -\sqrt{x - 6} + 6\)

A translation happens when either a figure or a function are moved horizontally or vertically.

The four translation rules for functions are given as follows:

The first move was reflecting the parent function f(x) over the x-axis, hence:

g(x) = -f(x)

\(g(x) = -\sqrt{x}\)

Then the translations are given as follows:

Hence the function g(x) is defined as follows:

\(g(x) = -\sqrt{x - 6} + 6\)

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Answer:

12.9 cm

Explanation:

Volume of rectangular box = Length × Width × Height

Given following:

Solve for volume:

\((6x+5)/(x+7)\\\) can be represented as in the form quotient \(+( remainder )/( divisor )\) as \(6 + 47/(x+7)\) using division.

The methods below show how to use synthetic division to write (6x+5)/(x+7) in the form quotient +(remainder)/(divisor):

So, (6x+5)/(x+7) is the divisor x+7 divided by the quotient 6 plus the remainder 47. Hence, we can write:

(6x+5)/(x+7) = 6 + 47/(x+7)

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Answer:

Width = 21.75 m

Length = 21.75 m

Step-by-step explanation:

The last two digits of your student number are 37.

Therefore, the length of fencing we will work with is 37 + 50 = 87 m.

The perimeter of a rectangle is twice the sum of its width (w) and length (l). Therefore, if the total length of fencing is 87 m, the equation for the perimeter of the rectangular fence is:

\(\textsf{Perimeter}=2(w+l)=87\)

Rearrange the equation to isolate length (l):

\(\begin{aligned}2(w+l)&=87\\\\w+l&=\dfrac{87}{2}\\\\l&=\dfrac{87}{2}-w\end{aligned}\)

The area of a rectangle is the product of its width (w) and length (l):

\(\textsf{Area}=wl\)

Substitute the expression for length into the area formula to create an equation for area with respect to width only:

\(\begin{aligned}\textsf{Area}&=wl\\\\&=w\left(\dfrac{87}{2}-w\right)\\\\&=\dfrac{87}{2}w-w^2\end{aligned}\)

To find the width that will maximize the area, differentiate the equation for area with respect to w, set it zero, and solve for w:

\(\dfrac{\text{d}A}{\text{d}w}=1 \cdot \dfrac{87}{2}w^{1-1}-2 \cdot w^{2-1}\)

\(\dfrac{\text{d}A}{\text{d}w}=\dfrac{87}{2}w^{0}-2w^{1}\)

\(\dfrac{\text{d}A}{\text{d}w}=\dfrac{87}{2}(1)-2w\)

\(\dfrac{\text{d}A}{\text{d}w}=\dfrac{87}{2}-2w\)

Set dA/dw to zero and solve for w:

\(\begin{aligned}\dfrac{87}{2}-2w&=0\\\\2w&=\dfrac{87}{2}\\\\w&=\dfrac{87}{4}\\\\w&=21.75\;\sf m\end{aligned}\)

Therefore, the width that maximizes the area of a rectangle with a perimeter of 87 m is 21.75 m.

To find the length, substitute the found value of w into the expression for length (l):

\(\begin{aligned}l&=\dfrac{87}{2}-\dfrac{87}{4}\\\\l&=\dfrac{87}{4}\\\\l&=21.75\; \sf m\end{aligned}\)

Therefore, the length that maximizes the area of a rectangle with a perimeter of 87 m is 21.75 m.

In conclusion, the dimensions of the rectangle with a perimeter of 87 m than maximize the area are:

This proves that among all rectangles with a fixed perimeter, the square has the maximum area.

Answer:

Mm I didn't get the picture

21

Anonymous has the correct months, but the average is (21 + 23 + 22 + 24 + 15)/5 =

21 eggs

Answer:

7

Step-by-step explanation:

To find the weight of the soup in each tin, we need to subtract the weight of the empty tin from the total weight of the box. The soup in each tin weighs 3980 grams.

The weight of the box of 12 tins of condensed soup is 4.02 kg, which is equal to 4020 grams.

The weight of the empty tin is 40 grams.

To find the weight of the soup in each tin, we subtract the weight of the empty tin from the total weight of the box:

Weight of soup in each tin = Total weight of box - Weight of empty tin

= 4020 grams - 40 grams

= 3980 grams

Therefore, the soup in each tin weighs 3980 grams.

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Answer:

64 in²

Step-by-step explanation:

I did not ever do a problem like this, however this is the beauty of math, you can easily reverse engineer it.

Remember,

A = \(\pi r^2\)

And if we have 4 circles that means the area of one circle is 1/4th the total

So,

\(A=\frac{\pi r^2}{4}\)

Assuming that 16 is the radius squared times 4 lets ignore that squared for now because when going backwards we would get rid of the squared last as that was the first step.

\(A=\frac{16\pi }{4}=\frac{4\pi }{1}=4\pi\)

Now lets get it back to  by square rooting the 4

\(A=\sqrt4\pi =2\pi\)

The radius of one small circle is 2. Therefore; the diameter would be 4 for each. This in mind we know that two small circles diameters make up the radius of the larger circle we will multiply it by two again.

This gives us a final radius of the bigger circle of 8

Therefore, the area of the bigger circle is 8² which simplifies to 64

And a final answer of

64\(\pi\) in²

Hope this helps :)

Answer:

potato paste recipe for the same recipe as it has made

Step-by-step explanation:

French fry