A plumber has 150m of pipes.The plumber uses 20% fitting a central heating system,and then 25% of what is left to fit a bathroom. How much pipe does the plumber use to fit the bathroom?

\(~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ (4)^{\frac{-4}{2}} \implies (4)^{-2}\implies 4^{-2}\implies \cfrac{1}{4^2}\implies \cfrac{1}{16}\)

Answer:

The equation is already answered

The exponential function is given by f(x) = 2ˣ and the  value of f(6) is 64

An equation is an expression that shows the relationship  between two or more numbers and variables.

An exponential funtion is in the form y = abˣ

At point (0, 1):

1 = ab⁰

a = 1

At point (2, 4):

4 = 1(b)²

b = 2

Hence:

f(x) = 2ˣ

Hence f(6):

f(6) = 2⁶ = 64

The exponential function is given by f(x) = 2ˣ and the  value of f(6) is 64

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Answer:  38.46

Step-by-step explanation:

             ↓

   38.456 It means round by 0.05, so when you round you look at the place value after the specified digit.

Answer:

y= 2x + 4

Step-by-step explanation:

Answer:

(-2, 21) and (2, -11)  let me know if anything didn't make sense

Step-by-step explanation:

Try and put the symbols in, so for x to the third power write x^3  just makes it all much easier.

The turning point is when a graph changes from increasing to decreasing, or the other way around.  What this means is that its slope is changing from positive to negative, or the other way around.  

The derivative allows you to find the slope at any point of a graph.  If you are unfamiliar witht his concept let me know and I can go more into it.  

Since the derrivative tells you the slope, if you find a spot where it equals 0 then you know before that point it was positive or negative, and then after that point it was the opposite.  In other words it changes, so it's exactly what we are looking for.  Also if a derrivative is ever non existant, like in the square root function the numbers under the square root cannot be negative, so any x value that makes them negative doesn't exist, this means you would want to check these point too because they can be turning points as well.

There are certain special cases where a derivative does not coss 0, and if that happens then the original function does not have a turning point.  So keep that in mind.

The derivative is 3x^2 - 12.  So we want to find when this equals 0.   We also know it always exists so only need to worry about the 0s. Hopefully you are familiar with quadratics having two zeroes, if not let me know.

3x^2 - 12 = 0

3x^2 = 12

x^2 = 4

x = 2 and-2

So these are the turning points.  You should double check though and choose an x value below -2, then between -2 and 2, then larger than 2 and make sure the signs swap.

These are the x values of the turning points.  Solve f(x) at these points to find the y values.  so f(-2) = (-2)^3 - 12(-2) + 5 = 21 and f(2) = -11  so now we know the turning points are (-2, 21) and (2, -11)

The coordinates of the turning points of f(x) are (-2, 21) and (2, -11).

An equation containing derivatives of a variable with respect to some other variable quantity is called differential equations. The derivatives might be of any order, some terms might contain product of derivatives and the variable itself, or with derivatives themselves.

The turning point is when a graph changes from increasing to decreasing, or the other way around that means, its slope is changing from positive to negative.

Given that the derivative of f(x) = x³ – 12x + 5 is 3x² - 12.

Since the derrivative tells the slope, if you find a spot where it equals 0 then before that point it was positive or negative, and then after that point it was the opposite.

The derivative is 3x² - 12.

3x² - 12 = 0

3x²  = 12

x²  = 4

Thus, x = 2 and-2

So, these are the turning points.  

Now Solve f(x) at these points to find the y values.  

so f(x) = x³ – 12x + 5

f(-2) = (-2)³ - 12(-2) + 5 = 21

f(2) = -11  

Hence, the coordinates of the turning points of f(x) are (-2, 21) and (2, -11).

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Answer:

D

Step-by-step explanation:

Number of clients who do not play either the piano or the guitar is 22

To find the number of clients who do not play either instrument, we need to subtract the number of clients who play either the piano or the guitar or both from the total number of clients.

Let A be the set of clients who play the piano, and B be the set of clients who play the guitar. Then, we can use the formula A union B

|A ∪ B| = |A| + |B| - |A ∩ B|

where |A ∪ B| is the number of clients who play either the piano or the guitar or both, |A| is the number of clients who play the piano, |B| is the number of clients who play the guitar, and |A ∩ B| is the number of clients who play both instruments

Substituting the given values, we get

|A ∪ B| = 46 + 58 - 17

|A ∪ B| = 87

Therefore, the number of clients who do not play either instrument is:

109 - 87 = 22

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The expected correlation between the supply of a commodity (x) and the price of a commodity (y) depends on the nature of the commodity and market dynamics. However, in general, we would expect a **negative correlation** between the supply of a commodity and its price. Correct option is C.

The law of supply states that as the supply of a commodity increases, assuming demand remains constant, the price tends to decrease. This is because an increase in supply leads to a higher quantity of the commodity available in the market, potentially causing an excess supply or surplus. In such situations, suppliers may lower prices to attract buyers and reduce their inventory.

Conversely, when the supply of a commodity decreases, assuming demand remains constant, the price tends to increase. A decrease in supply results in a lower quantity available in the market, potentially leading to a scarcity or shortage. In such scenarios, suppliers may increase prices to maximize their profits due to the limited availability of the commodity.

It's important to note that real-world markets can be influenced by various factors, including changes in demand, production costs, technological advancements, government policies, and market competition, which can complicate the relationship between supply and price. Nonetheless, the general expectation is that a decrease in supply tends to lead to an increase in price, and an increase in supply tends to lead to a decrease in price, indicating a negative correlation.

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Simple Random ford wants to administer a satisfaction survey to its current customers. using their customer​ database, the company randomly selects customers and asks them about their level of satisfaction with the company.

What is an example of a basic random sample?

Is a straightforward random sample representative?

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Answer:

Y= -1/3 |x+3| +5

Step-by-step explanation:

An absolute value will always make a V line.

In your particular problem it wants you to reflect it over the x axis, and to do this you simply need to place a negative.

A negative in the beginning of the problem is only there to say whether you flip your line or not, and this means you don't have to worry about it any more.

What it looks like so far: Y= -

Next it wants you to compress the line vertically by 1/3

A number that causes your line to compress is always less than one

A number that stretches your line would be 1 or more

This number is always placed right next to the left of the parenthesis or absolute value.

What it looks like so far: Y= - 1/3

Now we want the line to move left 3 units.

We are now inside of the absolute value because this is where we move the line left or right. This can get a little confusing, but once you get it then you don't forget it.

Inside the line.. a -# moves right and a +# moves left.

This number should be placed inside the absolute value and to the right of the x.

What it should look like: Y= - 1/3 |x + 3|

Now they want us to move the line up by 5 points.

To the outer right side of the absolute value is where we move things up or down.

To move a number up you need to place a + sign with however many places it wants you to move to the right of the sign, but to move the line down you need to place a - sign with however many places it wants you to move to the right of the sign.

To move this up you simply need to place a +5 to the outer right side of the absolute value.

What you should end up with: Y= - 1/3 |x+3| +5

Answer:

81%

Step-by-step explanation:

First, let's set up 3 equations:

w*0.6 = x

x*1.5=y

y*0.9=z

Now, we can substitute x in the second equation for w*0.6:

w*0.6*1.5 = y

Lastly, we can substitute y in the last equation for w*0.6*1.5:

w*0.6*1.5*0.9=z

w*0.81=z

Therefore, z is 81 percent of w.

Step-by-step explanation:

<_________-9_________>

this way

<less than

>greater than

your welcome gimme points

Answer:

90

Step-by-step explanation:

I got it off of goggle-

Answer: C

Step-by-step explanation:

The best statistic to use to describe each variable will depend on the specific characteristics of the data distribution and the research question of interest. However, in general:

LOS (length of stay): The most appropriate statistic to use to describe LOS would be the median, as it is less affected by outliers and skewed distributions than the mean. The median represents the central value of the distribution, i.e., the value that separates the top 50% from the bottom 50% of observations. This is useful in understanding the typical or average length of stay, without being overly influenced by unusually long or short stays that may be present in the data.

Charge: The most appropriate statistic to use to describe charges would be the mean, as it is a measure of central tendency that reflects the total amount charged divided by the total number of cases. The mean is sensitive to outliers and extreme values, so if the distribution is heavily skewed or contains extreme values, the median may be a more appropriate measure.

Admission source: The most appropriate statistic to use to describe admission source would be the mode, as it is a categorical variable that represents the most common source of admission. The mode provides insight into the most frequent route of admission for patients, which can be useful in identifying patterns and trends in patient flow.

Gender: The most appropriate statistic to use to describe gender would be the frequency or count of males and females in the dataset, as it is a binary categorical variable. The frequency provides insight into the distribution of males and females in the sample, which can be useful in identifying gender-related disparities or trends in healthcare utilization.

Discharge status: The most appropriate statistic to use to describe discharge status would be the frequency or count of each category of discharge status, such as home, skilled nursing facility, hospice, etc. This provides insight into the distribution of patients' discharge destinations, which can be useful in understanding the healthcare needs and outcomes of different patient populations.

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The p-value for a right-tailed test is 0.0096.so the melodic kortholt company should consider changing its current health plan.the standard error for the proportion (SE = sqrt(0.64*(1-0.64)/25) = 0.144).

1. Calculate the proportion of employees dissatisfied (16/25 = 0.64).

2. Calculate the standard error for the proportion (SE = sqrt(0.64*(1-0.64)/25) = 0.144).

3. Calculate the z-score for the test (z = (0.64 - 0.5)/SE = 1.39).

4. Calculate the p-value (p-value = 1 - cdf(z) = 0.0096).

The p-value is an indication of how likely it is that the proportion of employees dissatisfied is significantly different from the expected proportion (in this case, half). The p-value of 0.0096 means that there is only a 0.96% chance that the observed proportion of employees dissatisfied is due to chance alone, and so the melodic kortholt company should consider changing its current health plan.

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The area of the window is 8\(m^{2}\).

An object's area is how much space it takes up in two dimensions. It is the measurement of the number of unit squares that completely cover the surface of a closed figure.

The word "area" refers to a free space. The length and width of a form are used to compute its area.

Any shape's area can be calculated by counting how many unit squares will fit inside of it.

According to the question,

Length of window=2m

Width of window=4m

Area of window=Length*Width

                          =2*4

                          =8\(m^{2}\)

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Answer:

yes

The statement 'C' explains the difference between a plane and a ray.

i.e. A plane does not have a formal definition, and a ray is described through undefined terms.

Step-by-step explanation:

A plane does not have a formal definition, and a ray is described through undefined terms. The statement is true because

A plane is basically an undefined term as it could be named using three non-straight points - also called noncollinear points. A plane is basically a flat two-dimensional object having no thickness.

In Geometry, we have a variety of undefined terms, including point, line and plane. All other terms in Mathematics (Geometry) could be defined from the mentioned three undefined terms.

Therefore, the statement 'C' explains the difference between a plane and a ray.

i.e. A plane does not have a formal definition, and a ray is described through undefined terms.

Keywords: plane, point, line, ray

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Cindy and tom, working together, can rake the yard in 8 hours. Working alone, Tom takes twice as long as Cindy, it takes Cindy to rake the yard 2 hours

To find the time it takes Cindy to rake the yard alone, let's use the following steps:Let x be the time taken by Cindy to rake the yard alone . Then the time taken by Tom to rake the yard alone will be 2xIt is given that Cindy and Tom can rake the yard in 8 hours when they work together.

Using the formula for working together, we get:\(\[\frac{1}{x} + \frac{1}{2x} = \frac{1}{8}\]\) Multiplying the equation by the least common multiple of the denominators, we get:\(\[16 + 8 = 2x\]\) Simplifying, we get:\(\[2x = 24\]\)Dividing both sides by 2, we get:\(\[x = 12\]\)Therefore, it takes Cindy 12 hours to rake the yard alone.

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Answer:

1. Axis of Symmetry: x=-4, Vertex: (-4, -6)

2. Axis of Symmetry: x=2, Vertex: (2, 8)

Step-by-step explanation:

Based on the workers performance of consistently meeting orders for 100, 200, 275, and 325 widgets within the workday, it is likely that they will successfully complete the order for 350 widgets on Friday. However, fulfilling orders for 400 or 450 widgets may present a challenge and require additional resources or extended work hours.

Based on the information, it seems that the workers have been consistently meeting their production targets within the allocated time. They have successfully completed orders for 100, 200, 275, and 325 widgets within the workday.

Based on their previous performance, it is likely that the workers will continue to work diligently and efficiently to meet the order for 350 widgets on Friday.

However, meeting an order for 400 or 450 widgets may pose a challenge as it exceeds the previous order quantities.

The workers may need to work extra hours, increase their pace, or employ additional resources to complete these larger orders within the same time frame. It is important to consider the capacity and capabilities of the workers and the factory to determine if such larger orders can be fulfilled successfully.

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The required quadratic regression is y = 0.27x² - 2.44x + 7.49

Given,

The data; {(1, 5), (3, 4), (4, 1), (5, 2), (7,4)}

The quadratic regression;

y = ax² + bx + c

To get the quadratic regression we have to simplify;

a ∑ xi⁴ + b  ∑ xi³ + c  ∑ xi² =  ∑ xi² yi

a  ∑ xi³ + b  ∑ xi² + c  ∑ xi =  ∑ xi yi

a  ∑ xi² + b  ∑ xi + c ni =  ∑ yi

Now,

3364 × a + 560 × b + 100 × c = 303

560 × a + 100 × b + 20 × c = 59

100 × a + 20 × b + 5 × c = 16

By solving the above system of equations we get;

a = 0.27 , b = - 2.44 , c = 7.49

Then,

The required quadratic regression is;

y = 0.27x² - 2.44x + 7.49

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Answer:

the difference is 127.23 ....

The equation that represents the number of time a cricket chirp (y) given the temperature (x) in degree Fahrenheit is y = 0.23 x + 40

Steps to translate a word problem into an equation or a function:

- Assign the unknowns to variables

- Identify which one is independent variables, which one is dependent variables. The independent variable will become the input while the dependent variable will become the output.

In the given problem, there are two variables:

- temperature in the air (in Fahrenheit)

- number of time a cricket chirp

From the problem, we can conclude that the number of time a cricket chirp depends on the temperature of the air. Hence,

independent variable =  temperature in the air (in Fahrenheit)

dependent variable = number of time a cricket chirp

Let:

y =  number of time a cricket chirp

x =  temperature in the air (in Fahrenheit)

It is said: The number of chirp per minute is equal to 0. 23 times the temperature of the air, in degree Fahrenheit, plus forty.

We can translate it into an equation:

y = 0.23 x + 40

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The initial cash outlay for the project, considering the cost of the new network system and the tax benefit from donating the old mainframe, is -$479,109.32.



To calculate the initial cash outlay for the project, we need to consider the cost of the new network system, the tax benefit from donating the old mainframe, and any changes in working capital.The cost of the new network system, including installation, is $495,009.00. This amount will be considered as a cash outflow at year 0.

The remaining book value of the old mainframe is $42,964.00. Since it will be donated to a charity, Kimco can claim a tax benefit for this donation. The tax benefit is equal to the remaining book value multiplied by the tax rate, which is $42,964.00 * 0.37 = $15,899.68. This tax benefit will reduce the initial cash outlay.There is no information provided about any changes in working capital, so we can assume there are no additional cash flows related to working capital.

Therefore, the initial cash outlay for the project is the cost of the new network system minus the tax benefit from donating the old mainframe: $495,009.00 - $15,899.68 = $479,109.32.So the initial cash outlay for the project is -$479,109.32.

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Answer:

f(1)=8

Step-by-step explanation:

f(1)= 7(1-1)+8

f(1)= 7(0) +8

f(1)= 0+8

f(1)= 8

Answer:

(1  , 9/2)

Step-by-step explanation:

(x1 + x2/2  ,  y1 + y2/2)

(-2 + 4/2    ,  6 + 3/2)

(2/2   , 9/2)

(1,9/2)