Are my answers correct? Precalculus!!

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

To solve the problem, we set up a system of two equations to represent the given conditions. By solving this system, we found that 1200 children and 2000 adults went to the movies.

We can solve the problem using a system of linear equations. Let's denote the number of children as C and the number of adults as A. From the question, we know two things:

By solving this system, we can find the number of children and adults. Using the elimination method, multiply the first equation by 5 and subtract it from the second equation, we get 4A = 8000, so A = 2000. Substituting A = 2000 into the first equation gives us C = 1200, which means 1200 children went to the movies.

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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: 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

Let rental rate be denoted by 'y' and years be denoted by 'x'

coordinates become: (2003,551) (2013,730)

Rental rate in  = $551(y1)

Rental rate in =$730(y2).

So, change in rate = [tex]730-551=179[/tex]

Years given are 2003(x1) and 2013(x2) so, change is [tex]2013-2003=10[/tex]

Here, to find the rate we use the slope formula:

[tex]\frac{y2-y1}{x2-x1}[/tex]

Now putting the values of coordinates in the formula we get:

[tex]\frac{730-551}{2013-2003}[/tex]

= [tex]\frac{179}{10}[/tex]

= 17.9

So, the rate of change for rent is $17.9

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

You must multiply the numerators and denominations of each fraction

Hope this helped. If there is anything else l can help with, just let me know!

To multiply two fractions, multiply the numerator by the numerator and the denominator by the denominator.

A fraction can be defined as a numerical quantity that isn't a whole number.

Hence, a fraction is simply a part of a whole number.

Generally, a fraction comprises two (2) main parts and these include:

Mathematically, a fraction is represented as:

[tex]Fraction \;A = \frac{1}{2} \\\\Fraction \;B = \frac{2}{3}[/tex]

In order to multiply the two fraction, we would multiply the numerator by the numerator and the denominator by the denominator:

[tex]Fraction \;A \times Fraction \;B = \frac{1}{2} \times \frac{2}{3} \\\\Fraction \;A \times Fraction \;B = \frac{1\times 2}{2 \times 3} \\\\Fraction \;A \times Fraction \;B = \frac{2}{6} \\\\Fraction \;A \times Fraction \;B = \frac{1}{3}[/tex]

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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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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]

The correct answer would be

C. All Real Numbers

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

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⟩.

[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.

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.

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.

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

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:

if the blue radius below is perpendicular to the green chord and the segment AB is 6.5 units long what is the length of the chord? the correct answer is:

13 units

Answer:

If the radius is perpendicular to a chord, the length of the chord is 13 units (option A).

Step-by-step explanation:

AB=6.5 units

When a radius is perpendicular to a chord divides it into to equal parts, then:

AB=BC=6.5 units

Chord: AC=AB+BC

Chord: AC=6.5 units+6.5 units

Chord: AC=13 units

Graph the inequality by finding the boundary line, then shading the appropriate area.

C.

The linear inequality shown on the graph is x − y ≤ 2. Correct option is c.

A linear inequality represents a region on the coordinate plane. The inequality may be of the form "y ≤ mx + b," "y ≥ mx + b," "y < mx + b," or "y > mx + b," where m is the slope and b is the y-intercept of the line.

To identify the correct linear inequality from the graph, look for the shaded region (if any) and the direction of the shading. The shading indicates the solution region of the inequality. If the shaded region is above the line, it represents "y > mx + b" or "y ≥ mx + b" depending on whether the line is solid or dashed, respectively. If the shaded region is below the line, it represents "y < mx + b" or "y ≤ mx + b" depending on whether the line is solid or dashed, respectively.

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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 :)

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

If you have 1,000,000 $ and you spend 9,899 what does that =

1,000,000 - 9,899 = 990,101

Answer: $990,101

The given problems on subtraction is solved as follows:

a. 1.8 - 0.9 = 0.9

b. 41.84 - 0.8 = 41.04

c. 341.84 - 21.92 = 319.92

d. 5.182 - 0.09 = 5.092

e. 741 - 3.91 = 737.09

The detailed explanation is as follows:

a. 1.8 - 0.9 = 0.9

Explanation: When you subtract 0.9 from 1.8, you get 0.9. This is a straightforward subtraction of two decimal numbers.

b. 41.84 - 0.8 = 41.04

Explanation: When you subtract 0.8 from 41.84, you get 41.04. Again, this is a simple subtraction of decimals.

c. 341.84 - 21.92 = 319.92

Explanation: Subtracting 21.92 from 341.84 results in 319.92. This is a standard decimal subtraction.

d. 5.182 - 0.09 = 5.092

Explanation: Subtracting 0.09 from 5.182 gives you 5.092. Decimal subtraction works the same way as whole number subtraction.

e. 741 - 3.91 = 737.09

Explanation: When you subtract 3.91 from 741, you get 737.09. This involves carrying over from the hundredth's place to the tenth's place.

In all these calculations, it's essential to align the decimal points and perform the subtraction as you would with whole numbers, taking care to carry over as needed when subtracting decimal places.

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Answer:

D. 4r + 3(10 – r) = 37

Explanation:

Let r be the roller coaster ride.  Since it costs 4 tickets, this gives us the expression 4r.

We know that there were 10 rides total; this leaves Michael 10-r for the number of times he rode the boat ride.

Each boat ride costs 3 tickets; this gives us the expression

3(10-r)

Together, this gives us

4r+3(10-r) = 37

Answer:

A ride on the roller coaster costs 4 tickets while the boat ride only costs 3 tickets. Michael went on the two rides a total of 10 times and spent a total of 37 tickets.

A table titled Ride Tickets, showing Times on the Ride, Tickets per Ride, and Total Tickets. The first row shows Roller Coaster, with r, 4 and 4 r. The second row shows Boat Ride, with 10 minus r, 3, and 3 left parenthesis 10 minus r right-parenthesis. The third row shows, Total, with 10, blank, and 37.

Which equation is true?

r(10 – r) = 10

r + (10 – r) = 4 + 3

4r[3(10 – r)] = 37 this is your answer

4r + 3(10 – r) = 37

Step-by-step explanation:

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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