5 times a number, subtracted from six, is triple the number

Answer: It is called "rounding"

Step-by-step explanation: Well you can't really explain this one.

Answer:

Rounding

Step-by-step explanation:

Rounding means to give an approximation of a decimal number. The number may be irrational. Rational numbers have a terminating decimal expansion. When rounding off a number first consider to how many decimals you want to round off the number. Then check the next decimal number if it is 5 or more than 5 then increase the preceding decimal number by 1.

Let us take and example

√2 = 1.41.........

Round to the nearest tenths

√2 = 1.4

Round 1.65 to the nearest tenths

1.7

The directional derivative of [tex]\(f(x, y, z) = z^3 - x^2y\) at \((-5, 5, 2)\)[/tex] in the direction of [tex]\(\mathbf{v} = \langle -3, 2, -4 \rangle\) is \(-248\).[/tex]

To find the directional derivative of [tex]\( f(x, y, z) = z^3 - x^2y \)[/tex] at the point [tex]\((x_0, y_0, z_0) = (-5, 5, 2)\)[/tex] in the direction of the vector[tex]\( \mathbf{v} = \langle -3, 2, -4 \rangle \),[/tex] we'll use the formula for the directional derivative:

[tex]\[ D_{\mathbf{v}} f = \nabla f \cdot \mathbf{v} \][/tex]

where [tex]\( \nabla f \)[/tex] is the gradient of  f  and [tex]\( \cdot \)[/tex] denotes the dot product.

First, let's find the gradient of  f :

[tex]\[ \nabla f = \left\langle \frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}, \frac{\partial f}{\partial z} \right\rangle \][/tex]

Taking partial derivatives:

[tex]\[ \frac{\partial f}{\partial x} = -2xy \][/tex]

[tex]\[ \frac{\partial f}{\partial y} = -x^2 \][/tex]

[tex]\[ \frac{\partial f}{\partial z} = 3z^2 \][/tex]

Substituting the given point [tex]\((x_0, y_0, z_0) = (-5, 5, 2)\)[/tex] into these partial derivatives:

[tex]\[ \frac{\partial f}{\partial x} = -2(-5)(5) = 50 \][/tex]

[tex]\[ \frac{\partial f}{\partial y} = -(-5)^2 = -25 \][/tex]

[tex]\[ \frac{\partial f}{\partial z} = 3(2)^2 = 12 \][/tex]

So,[tex]\( \nabla f = \langle 50, -25, 12 \rangle \).[/tex]

Now, let's find the directional derivative using the dot product:

[tex]\[ D_{\mathbf{v}} f = \langle 50, -25, 12 \rangle \cdot \langle -3, 2, -4 \rangle \][/tex]

[tex]\[ D_{\mathbf{v}} f = (50)(-3) + (-25)(2) + (12)(-4) \][/tex]

[tex]\[ D_{\mathbf{v}} f = -150 - 50 - 48 \][/tex]

[tex]\[ D_{\mathbf{v}} f = -248 \][/tex]

Therefore, the directional derivative of  f  at the point (-5, 5, 2) in the direction of the vector[tex]\( \mathbf{v} = \langle -3, 2, -4 \rangle \) is \( -248 \).[/tex]

The Correct question is:

Find the directional derivative of f(x,y,z)=z^3−x^2y,f(x,y,z)=z3−x2y at the point (−5,5,2),(−5,5,2) in the direction of the vector v=⟨−3,2,−4⟩,v=⟨−3,2,−4⟩.

Answer:

Probability of observed is less that probability of theoretical of getting an even  number.

Step-by-step explanation:

Given : A student decides to run a simulation of rolling an even number with a single die.

Outcomes - 1 5 3 2 3 6 5 6 3 3 4 4 1 3 6 5 3 2 2 6

To find : Use the simulate results from 20 attempts to estimate the probability, then compare your estimation with the theoretical probability?

Solution :

First we make the frequency distribution table,

X    Frequency

1         2  

2         3

3         6

4         2

5         3

6         4

Total - 20

Now, The observed probability of getting an even number.

Favorable outcomes of number appeared even = 3+2+4=9

Total  number of outcome = 20

Probability of getting even number is [tex]P=\frac{9}{20}=0.45[/tex]

Then, Theoretical probability of getting an even number.

Favorable outcome = 3

Total  number of outcome = 6

Probability of getting even number is [tex]P=\frac{3}{6}=\frac{1}{2}=0.5[/tex]

As 0.45<0.5 , Observed < Theoretical

We simulate that probability of observed is less that probability of theoretical of getting an even  number.

The estimated probability is 0.45 while theoretical probability is 0.5

Estimated probability :

The estimated probability can be computed thus ;

Now we have ;

The theoretical probability can be computed thus ;

Hence, theoretical probability= 3/6 = 0.5

Hence, the theoretical probability is greater than the estimated probability.

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The Answer would be 4. 4(x+20)

The corresponding point for the function f(x) - 4 is (2, -1)

A function in mathematics set up a relationship between the dependent variable and independent variable. on changing the value of the independent variable the value of the dependent variable also changes.

given that (2,3) is on the graph of f(x)

So, for x = 2, f(x) = f(2) = 3

Now, define another function g(x) such that

g(x)   =   f(x)  -  4

g(2)   =   f(2)  -  4

g(2)   =   3  -  4  =  -1

Hence, corresponding point for the function f(x) - 4 is (2, -1)

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Answer:

[tex]\frac{Gallons}{Feet^{2} }[/tex]

Step-by-step explanation:

We have been told that Luiza runs a lawn-mowing business she decides to measure the rate at which the volume of fuel she uses increases with the area of the lawn and we are asked to determine an appropriate unit for Luiza's purpose.

Since we can represent rate of units as [tex]\frac{Dependent Variable}{Independent Variable}[/tex]

We can see that in this case dependent variable is amount of fuel used in lawn-mowing and area of lawn is independent variable.

We know that we can represent volume of fuel as gallons and area of lawn as square feet.  

Therefore, appropriate unit for Luiza's purpose is [tex]\frac{Gallons}{Feet^{2} }[/tex].

Answer:

L/KM^2

Step-by-step explanation:

The point-slope form of a line:

[tex]y-y_0=m(x-x_0)[/tex]

We have

[tex]m=-\dfrac{1}{4}\\\\(-2,\ 9)\to x_0=-2,\ y_0=9[/tex]

Substitute

[tex]y-9=-\dfrac{1}{4}(x-(-2))\\\\y-9=-\dfrac{1}{4}(x+2)[/tex]

Answer

192 ft²

Explanation

The rooms measures 12 feet by 8 feet. So it is a rectangle.

The area of a rectangle = length × width

                                       = 12 × 8

                                       = 96 ft²

The area of one room is 96 ft². There are 2 similar rooms.

The area of the 2 rooms = 96 × 2

                                        = 192 ft²

It's answer B since when you plug in -7 into x, the value then becomes absolute value of 2(-7) - 1, which is absolute value of -15, which becomes 15, and plugging 8 into x gives us absolute value of 2(8) - 1, which is absolute value of 15, which is just 15. That divided by 3 makes 5, so that solution is true when plugging those numbers in for x

Answer:

the first one (the one with more lines which is the centimeter (cm) one)

Step-by-step explanation:

Precision is when you know the exact measurement like 4.756

Accuracy is when your kind of close to the precise measurement like 4.75

Precision means exact and accuracy means close enough.

Remark

It is a direct variation.

y = k x

You can solve for k .

y  = 208

x = 4

k= ??

y = k * x

208 = k * 4   Divide by 4

208 / 4 = k

k = 52

So the equation becomes

y = 52 x

The area of the field is obtained by multiplying length by width resulting 75,000 square meters. Converting this to square kilometers by dividing by 1,000,000 gives the area in square kilometers as 0.075 km².

To calculate the area of the rectangular field, we multiply the length by the width. Given that the length is 300 meters and the width is 250 meters, the area in square meters would be 300 meters * 250 meters = 75,000 square meters.

Keep in mind that 1 square kilometer (km²) is equivalent to 1,000,000 square meters (m²). So, to convert the area from square meters to square kilometers, we divide the area in square meters by 1,000,000. Therefore, the area of the field in square kilometers is 75,000 m² / 1,000,000 = 0.075 km².

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[tex]\left[\begin{array}{ccc}150&160&180\end{array}\right]\\\\Answer:\ B)\ \left[\begin{array}{ccc}4&0&0\\0&4&0\\0&0&4\end{array}\right][/tex]

[tex]Check:\\\\\left[\begin{array}{ccc}150&160&180\end{array}\right] \cdot\left[\begin{array}{ccc}4&0&0\\0&4&0\\0&0&4\end{array}\right][/tex]

[tex]=\left[\begin{array}{ccc}(150)(4)+(160)(0)+(180)(0)&(150)(0)+(160)(4)+(180)(0)&(150)(0)+(160)(0)+(180)(4)\end{array}\right][/tex]

[tex]=\left[\begin{array}{ccc}600&640&720\end{array}\right][/tex]

Cost of four of each of the tickets:

[tex]Chicago:4\cdot\$150=\$600\\\\Boston:4\cdot\$160=\$640\\\\Dallas:4\cdot\$180=\$720[/tex]

CORRECT :)

The ratio is 4:5

because 8 divided by 2 is 4

and 10 divided by 2 is 5

so the answer as said before is 4:5

I hope this helps :)

Answer:

Step-by-step explanation:

4 inches

We are required to find all the possible length of lakeisha’s sunroom

The possible length of the rectangle are length greater than 40 which are 54 feet and 60 feet

perimeter of a rectangle = 2(length + width)

perimeter > 108 feet

Width of the sunroom = 14 feet

The inequality:

2(x + 14) > 108

2x + 28 > 108

2x > 108 - 28

2x > 80

divide both sides by 2

x > 80 / 2

x > 40 feet

Therefore, the possible length of the rectangle are length greater than 40 which are 54 feet and 60 feet

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[tex]2^{5^{8}}[/tex]

that is a number with more than 100,000 digits

Using each of those numbers as digits of a number then it is 852

However, if we raise each number to a power then 2^(5^8) where

5^8 = 390,625  So, 2^390,625 can be estimated by

multiplying the log of 2 (0.30102999566) by 390,625 which equals

117,589.842054688   So, 117,589 is our exponent and then we need to look up the anti-log of .842054688 which equals  6.9511184318 and our number is  6.9511184318 x 10^117,589

DON'T read my comments.  I can't delete them.

The correct answer would be

C. All Real Numbers

That is C. my fellow brainy hope you get an A+

Answer: 18 hundreds

Step-by-step explanation:

 9 x   200

= 9 x 2 x 100

=    18   x 100

=       1800  

aka: 18 hundreds

To find an equivalent form of the equation 2x-y=12, isolate y by moving 2x to the other side and changing the sign of each term.

To find an equivalent form of the equation 2x-y=12, we want to isolate y. To do this, we need to get y alone on one side of the equation. Let's start by moving the 2x term to the other side by adding 2x to both sides of the equation, giving us -y=12+2x. Next, we can multiply every term in the equation by -1 to change the sign of each term, resulting in y=-12-2x.

So the equivalent form of the equation 2x-y=12 is y=-12-2x, which is option D.

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Answer:

B) Circle

Step-by-step explanation:

What we will do is to define all the term, then we will now pick the correct option

Angle :  An angle can simply be define as a point where two straight line meets.

Arc : An arc is a curved line which formed a circle or  part of the circumference of a circle

Circle : A circle is an arc that goes round a central points. A circle subtends a full angle of 360°

Line Segment: A line segment is the shortest distance between two points, or simply put a line that connects to points or joins two points together.

From the above definitions, we can deduct that an arc that subtends a full angle of 360 degree is called a circle.

One pound of berries each. 8 divided by 8 is 1 Hope this helps!