Inequality for x when x is greater than 3 and less than or equal to 9

Solving a system of equations we will see that the width is 40 feet.

We know that the floor has a rectangular shape, and the length is 20 feet longer than the width, so we can write the relation:

L = 20ft + W

Also, we know that a scale model of the floor has a length of 15 inches and a width of 10 inches, the same scale factor k is applied  to the two of these, then we can write:

15 in = k*L

10in = k*W

So we have a system of equations:

L = 20ft + W

15 in = k*L

10in = k*W

Taking the quotient between the second and third equations we will get:

15in/10in = (k*L)/(k*W)

15/10 = L/W

1.5*W = L

Now we have two equations:

L = 20ft + W

1.5*W = L

We can substitute the second equation into the first one, so we will get:

1.5*W = 20ft+  W

1.5*W - W = 20ft

0.5*W  =20ft

W = 20ft/0.5

W = 40ft

The width is 40 feet.

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The slope of a line indicates how steep it is calculated mathematically as "rise overrun". It calculates the rate where the variable y changes when the relevant variable changes, and the further calculation can be defined as follows:

Given Points:

\((-4,-2) , (-2,-10)\)

To find:

slope (m)=?

Solution:

\((-4,-2),(-2,-10)\\x_{1} =-4\\y_{1} =-2\\x_{2}= -2\\y_{2}=-10\\\)

Using formula:

\(slope(m)=\frac{y_{2-} y_{1} }{x_{2-} x_{1} } \\=\frac{-10-(-2)}{-2-(-4)} \\\\=\frac{-10+2}{-2+4}\\=\frac{-8}{2} \\=-4\)

Therefore,  the slope is "- 4".

Answer:

There are a total of 25 marbles in the bag.

The probability of choosing a red marble first is 8/25 since there are 8 red marbles out of 25 marbles in the bag.

Since a marble is not replaced after the first selection, there are now 24 marbles in the bag. There are still 3 blue marbles in the bag.

The probability of choosing a blue marble second, after a red marble has already been selected, is 3/24 or 1/8 since there are 3 blue marbles left out of 24 marbles in the bag.

To find the probability of both events occurring together, we multiply their individual probabilities:

8/25 x 1/8 = 1/25

Therefore, the probability that a red marble is chosen first, followed by a blue marble, is 1/25.

Answer:

Step-by-step explanation Let a =3 and b=3 we are given this information.

6a^3-1/9b^4

Substitute values for a=3 and b=3

=6(3)^3-1/9(3)^4

=6 x27-1/9 x 81

=162-9

153

reminder 3^3=27=3 x 3 x 3

reminder 3^4=81=3 x 3 x 3 x 3

A study based on a population sample that includes 2000 respondents would be the most reliable out of the given options.

In statistical analysis, the reliability of a study depends on the representativeness and size of the sample.

A larger sample size generally provides more reliable results as it reduces the sampling error and increases the precision of the estimates.

Given that the population contains 20,000 people, we need to consider which number of respondents would yield the most reliable study.

Option A: 200 respondents

This represents only 1% of the population.

While it is better than having just 2 respondents, it may not be sufficient to accurately capture the characteristics of the entire population.

Option B: 20 respondents

This represents only 0.1% of the population.

With such a small sample size, the study would likely suffer from a high sampling error and may not provide reliable results.

Option C: 2000 respondents

This represents 10% of the population.

While it is a larger sample size compared to the previous options, it still only captures a fraction of the population.

The study may provide reasonably reliable results, but there is room for potential sampling error.

Option D: 2 respondents

This represents an extremely small sample size, accounting for only 0.01% of the population.

With such a small sample, the study would be highly susceptible to sampling bias and would likely yield unreliable results.

Based on the options provided, option C with 2000 respondents would be the most reliable study.

Although it does not include the entire population, a sample size of 2000 respondents provides a larger representation of the population and reduces the potential for sampling error.

However, it's important to note that the reliability of a study depends not only on sample size but also on the sampling method, data collection techniques, and other factors that ensure representativeness.

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Answer:

y= -x²-4x+2

Step-by-step explanation:

write in vertex form

a(x-h)²+k

in our case h = -2 and k= 6

y=a(x+2)²+6

now we just need to solve for a. we know that when x= 1 y = -3. plug these values in and solve for a

-3= a(1+2)²+6

-9=9a

a= -1

thus the formula is -(x+2)²+6

generally, teachers want things in standard form, so expand the exponent and simplify.

-(x²+4x+4)+6

y= -x²-4x+2

Answer:

\(y = -x^2 - 4x + 2\)

Step-by-step explanation:

The equation of a parabola in vertex form is:

\(y = a(x - h)^2 + k\)

where (h, k) is the vertex of the parabola.

In this case, the vertex is (-2, 6), so h = -2 and k = 6.

We also know that the parabola passes through the point (1, -3).

Plugging these values into the equation, we get:

\(-3 = a(1 - (-2))^2 + 6\)

\(-3 = a(3)^2 + 6\)

-9 = 9a

a = -1

Substituting a = -1 into the equation for a parabola in vertex form, we get the equation of the parabola:

\(y = -1(x + 2)^2 + 6\)

This equation can also be written as:

\(y = -x^2 - 4x -4+6\\y=x^2-4x+2\)

The signature of the Principal Investigator on the final proposal does not imply responsibility for the availability of funding or the financial aspects of the project.

The complete question should be What does the signature of the Principal Investigator on the final proposal NOT imply responsibility for?

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The value of the constant c which would make the function continuous for all values of r is c = \(\frac{5}{3}\).

We are given that f(x) = \(\left \{ {{x-c,x < 5} \atop {4x+2c,x > 5}} \right.\)

since we are given that the function f is continuous at x = 5, then we can Lim f (x) = Lim f (x) = f (5) .......(1)

x---->5⁻       x---->5⁺

now then that we have equate f(5) we can proceed as given below

Lim f (x) = Lim (x² = c) = 5² = c = 25-c

x---->5⁻       x---->5⁺

and from the above solution we can get,

Lim f (x) = Lim (4x + 2c) = 4.5 + 2c

x---->5⁻       x---->5⁺

then we can solve for =20 + 2c

then we get f(5) when we solve for 20 + 2c

now from .....(1) we can put the values for the following, we get

then we get, 25 - c = 20 + 2c

when we solve for c we get, 3c = 5

therefore we know that, c = \(\frac{5}{3}\)

therefore we get the solution for the function as the value of the constant c which would make the function continuous for all values of r is c = \(\frac{5}{3}\).

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Answer:

the only one that i know is skill that is D Something you have already developed

Step-by-step explanation:

According to the quotient rule of differentiation, if \(y(x) = u(x)/v(x),\) then its derivative is given by

\(\dfrac{dy}{dx} = \dfrac{v\dfrac{du}{dx} - u\dfrac{dv}{dx}}{v^2}\:\:\:\:\:\:\:\:\:(1)\)

We can see that

\(u(x) = \ln (4x^2 + 1)\)

\(\dfrac{du}{dx} = \dfrac{8x}{4x^2 + 1}\)

\(v(x) = 2x - 3\)

\(\dfrac{dv}{dx} = 2\)

Plugging the above expressions into Eqn(1), we find that the derivative is

\(\dfrac{dy}{dx} = \dfrac{\dfrac{8x(2x - 3)}{(4x^2 + 1)} - 2\ln (4x^2 + 1)}{(2x - 3)^2}\)

\(\:\:\:\:\:\:\:= \dfrac{8x}{(4x^2 + 1)(2x - 3)} - \dfrac{2\ln (4x^2 + 1)}{(2x - 3)^2}\)

Answer:

|4| = 4

|-4| = 4

Step-by-step explanation:

Answer:

its 4

Step-by-step explanation:

absolute value of 4 is 4 you get rid of any signs co efficients etc.

Answer:

x2/3

Step-by-step explanation:

Just add 1/6 four times because of  the root.

Approximately 37.5% of the data are greater than 28, 33.3% of the data are less than 23, 91.7% of the data are greater than 17.5, and 62.5% of the data are between 17.5 and 28.

To answer the questions, we can analyze the given data set.

First, let's count the number of data points that satisfy each condition:

Greater than 28:

There are 9 data points greater than 28 (29, 29, 29, 30, 29, 29, 28, 28, 28).

Less than 23:

There are 8 data points less than 23 (20, 18, 15, 17, 17, 15, 17, 19).

Greater than 17.5:

There are 22 data points greater than 17.5.

Between 17.5 and 28:

There are 15 data points between 17.5 and 28.

Now, let's calculate the approximate percentage for each condition:

Percent greater than 28:

The total number of data points is 24. Approximately, 9 out of 24 data points are greater than 28.

Percentage =\((9 / 24) \times 100 = 37.5\)%.

Percent less than 23:

Approximately, 8 out of 24 data points are less than 23.

Percentage = \((8 / 24) \times 100 = 33.3\)%.

Percent greater than 17.5:

Approximately, 22 out of 24 data points are greater than 17.5.

Percentage = \((22 / 24) \times 100 = 91.7\)%.

Percent between 17.5 and 28:

Approximately, 15 out of 24 data points are between 17.5 and 28.

Percentage = \((15 / 24) \times 100 = 62.5\)%.

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Answer:

31120 ounce

Step-by-step explanation:

Answer:31120

Step-by-step explanation:Use google

We can see that the correct equation that can depict the problem is 3(d+17.20) = 782.07. Option D

We have to look at the problem that we have here. In the case of the question that we have been asked, we can see that for the problem that has been given here, it is clear that; Allison went on a business trip and stayed at a hotel for three nights. She paid a total of $782.07 for the room and to park her car.

If it is known that Each night, the hotel charged d dollars and $17.20 for parking. We can say that let the amount that is charged for the lodging be d and we have the equation as; 3(d+17.20) = 782.07.

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Answer: $3648

Step-by-step explanation:

Firstly, we have to calculate the interest which will be:

= Principal × Rate × Time

= $1600 × 8% × 16

= $1600 × 0.08 × 16

= $2048

Therefore, the amount in the account after 16 years will be:

= Principal + Interest.

= $1600 + $2048

= $3648

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

Explanation:

Refer to the figure below.

The cone has a circle at the base which has a diameter of 8 cm. This cuts in half to 4 cm, and that's the radius. This forms the horizontal leg of the right triangle highlighted in red.

The vertical leg of the triangle is the height of the cone (9 cm).

---------

Use the pythagorean theorem to find the hypotenuse of the triangle, which is exactly the slant height.

a^2 + b^2 = c^2

4^2 + 9^2 = c^2

16 + 81 = c^2

97 = c^2

c^2 = 97

c = sqrt(97)

c = 9.84886

When rounding to one decimal place, we get 9.8 cm which is the final answer.

Answer:

Y less than

Step-by-step explanation:

Answer: 5/7 of the kids chose New York or L.A.

Step-by-step explanation:

All you need to do in this problem is add the fraction of people that chose New York and the fraction of people that chose L.A:

4/7 + 1/7 = 5/7

In the given triangle the sum of the interior angles of triangle ACB is equal to 180 degrees, therefore, we have the following relationship:

Replacing the values we get:

Solving the operations:

Now we solve for angle BCA by substracting 138 to both sides:

Now, since segments CD and CE are equal, this means that triangle CDE is an isosceles triangle, therefore, its base angles are the same, and we have the following relationship:

Replacing the known values:

Now we solve for angle DEC by subtracting 42 to both sides:

Now we divide both sides by 2:

Now, angles DEC and DEB are supplementary, therefore, their sum adds up to 180, therefore, we have:

Replacing the known angle:

Subtracting 69 to both sides:

Therefore, angle DEB measures 111 degrees.

Answer:

Step-by-step explanation:

Approximately 3.2 million shelter animals are adopted each year (1.6 million dogs and 1.6 million cats). About 710,000 animals who enter shelters as strays are returned to their owners. Of those, 620,000 are dogs and only 90,000 are cats.

2 feet: 3 inches

1 feet: 3/2 inches

4*5 feet: 3x4*5/2

=6.75 Inchea

Answer:

Step-by-step explanation:

12nl-4=8 start by adding 4 to both sides.

12nl=12/l Divide both sides by l.

12n=12 then divide both sides by 12.

n=1/l

Answer: 1.4

Step-by-step explanation: Just divide.

16.80 divided by 12, is 1.4(0). And if you multiply 1.4 by 12 you get 16.8(0)

Answer:

7,37,77,80 Is ur c.f and ur lengths r 48.5-53.5, 53.5-58.5, 58.5-63.5, 63.5-68.5

Answer:

Step-by-step explanation:

a) Total weight comprises of the weight of jar plus weight of Jolly Ranchers

b) When the candy jar is full, it weighs 1224 grams. How many Jolly Ranchers can the jar hold?  

Given w = 1224, then to find j we solve the equation:

The jar can hold 129 Jolly Ranchers

Answer:

144 - 36×3.142 = 30.888

30.888 ÷4 = 7.722