I need help with this question

Answer:

The 14-ounce bottle is the better deal

Step-by-step explanation:

I know this beause inorder to figure out which one is better you have to make them the same price and then see which bottle has more ounces. So I made each price 1$ so there is 1.58-ounces per dollar in the 5-ounce bottle and 1.17 -ounces per dollar in the 14-ounce bottle.

Answer:

6090

Step-by-step explanation:

Given h(x), find h(4x) as shown below

Answer:

32

Step-by-step explanation:

Since there are 20 total pieces of gum, we divide 20 by 5 to figure out how many groups of 8 pieces of candy there are (For every 8, 5 are gum). This gives us 4 groups of 8. Because for every 8 pieces, 5 are gum, we subtract 5 from 8 and get three. Multiply 3 by 4 (the number of groups), and we get 12 other pieces of candy. Add to 20, and we get 32. To check, divide 32 by the number of groups (4) and we get 8, which is how many pieces of candy are in each group.

The intersection of the given sets is represented as A ∩ B = {2, 4, 6, 8}.

Option (D) is correct.

What is the intersection of two sets?

The intersection of two sets, A and B, is the set of elements that are common to both sets. It is often represented by A ∩ B.

In this case, Set A = {2, 4, 6, 8} and set B = {1, 2, 3, 4, 5, 6, 7, 8}. The set that represents A ∩ B is {2, 4, 6, 8} because these are the elements that are common to both sets A and B.

So the correct answer is {2, 4, 6, 8}

Hence, the intersection of the given sets is represented as A ∩ B = {2, 4, 6, 8}.

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In this manner, the number of wolves changes by around 8 percentage 8% each year based on the given work.

To determine the percentage change within the number of wolves each year, we ought to look at the development rate of the work w(x) = 14 * 1.08^x.

The development rate in this case is given by the example of 1.08, which speaks to the figure by which the number of wolves increments each year. In this work, the coefficient 1.08 speaks to a development rate of 8% per year.

To calculate the percentage change, we subtract 1 from the growth rate and increase by 100 to change over it to a rate:

Percentage change = (1.08 - 1) * 100 = 0.08 * 100 = 8%.

In this manner, the number of wolves changes by around 8 percentage 8% each year based on the given work.

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Answer:

\(x= \dfrac{\pi}{3}, \;\;x=\dfrac{5 \pi}{3}\)

Step-by-step explanation:

Given trigonometric equation:

\(2 \tan\left(\dfrac{x}{2}\right)- \csc x=0\)

To solve the equation for x in the given interval [0, 2π), first rewrite the equation in terms of sin x and cos x using the following trigonometric identities:

\(\boxed{\begin{minipage}{4cm}\underline{Trigonometric identities}\\\\$\tan \left(\dfrac{\theta}{2}\right)=\dfrac{1-\cos \theta}{\sin \theta}$\\\\\\$\csc \theta = \dfrac{1}{\sin \theta}$\\ \end{minipage}}\)

Therefore:

              \(2 \tan\left(\dfrac{x}{2}\right)- \csc x=0\)

\(\implies 2 \left(\dfrac{1-\cos x}{\sin x}\right)- \dfrac{1}{\sin x}=0\)

  \(\implies \dfrac{2(1-\cos x)}{\sin x}- \dfrac{1}{\sin x}=0\)

\(\textsf{Apply the fraction rule:\;\;$\dfrac{a}{c}-\dfrac{b}{c}=\dfrac{a-b}{c}$}\)

\(\dfrac{2(1-\cos x)-1}{\sin x}=0\)

Simplify the numerator:

\(\dfrac{1-2\cos x}{\sin x}=0\)

Multiply both sides of the equation by sin x:

\(1-2 \cos x=0\)

Add 2 cos x to both sides of the equation:

\(1=2\cos x\)

Divide both sides of the equation by 2:

\(\cos x=\dfrac{1}{2}\)

Now solve for x.

From inspection of the attached unit circle, we can see that the values of x for which cos x = 1/2 are π/3 and 5π/3. As the cosine function is a periodic function with a period of 2π:

\(x=\dfrac{\pi}{3} +2n\pi,\; x=\dfrac{5\pi}{3} +2n\pi \qquad \textsf{(where $n$ is an integer)}\)

Therefore, the values of x in the given interval [0, 2π), are:

\(\boxed{x= \dfrac{\pi}{3}, \;\;x=\dfrac{5 \pi}{3}}\)

To solve the exercise you can use a rule of three, like this

Therefore,

Your image attached has not  sufficient criteria for Brainly users to answer. We will assume for now that you are asking what the line is equal to. This question will be deleted eventually due to Brainly ToS most likely

We note that this line is not linear, or squared. This means it might be cubical.

If it is cubical the line must be a variant of

f(x)=\(x^{3}\).
However f(x)=\(x^{3}\) points the opposite direction so we must make it negative.

We also noticed we had to stretch it, so we had to add a fraction.

Your answer is f(x)=\(-\frac{1}{8} x^{3}\)

Answer:

Relative minimum: \(\left(-\frac{5}{2}, -\frac{33}{4}\right)\), Relative maximum: \(DNE\)

Step-by-step explanation:

First, we obtain the First and Second Derivatives of the polynomic function:

First Derivative

\(f'(x) = 2\cdot x + 5\) (1)

Second Derivative

\(f''(x) = 2\) (2)

Now, we proceed with the First Derivative Test on (1):

\(2\cdot x + 5 = 0\)

\(x = -\frac{5}{2}\)

The critical point is \(-\frac{5}{2}\).

As the second derivative is a constant function, we know that critical point leads to a minimum by Second Derivative Test, since \(f\left(-\frac{5}{2}\right) > 0\).

Lastly, we find the remaining component associated with the critical point by direct evaluation of the function:

\(f\left(-\frac{5}{2} \right) = \left(-\frac{5}{2} \right)^{2} + 5\cdot \left(-\frac{5}{2} \right) - 2\)

\(f\left(-\frac{5}{2} \right) = -\frac{33}{4}\)

There are relative maxima.

Answer:

A. March

Step-by-step explanation:

You can tell by subtracting the tallest bar in the month from the shorter one, and seeing which number is bigger out of all of them.

Hope this helped :)

Answer:

A. March

Step-by-step explanation:

March:

10 - 2 = 8

April:

14 - 10 = 4

May:

18 - 16 = 2

June:

16 - 16 = 0

From this data, we can see that March has the largest difference in the amount of money between year 1 and year 2.

Answer:

$16

Step-by-step explanation:

if 5=20 then 20÷5=4 and 4x4=16

Answer:

16

Step-by-step explanation:

$20/5notebooks=$4 each

4$*4notebooks=16$

Step-by-step explanation:

the center of the circle is the midpoint of the diameter.

and the radius is the distance of the midpoint to either endpoint (or simply half of the distance between the diameter endpoints).

the midpoint between points A and B

(xm, ym) = ((xa + xb)/2, (ya + yb)/2)

in our case the midpoint (center of the circle) is

((-6 + 2)/2, (10 + 3)/2) = (-4/2, 13/2) = (-2, 6.5)

about the radius

diameter² = (-6 - 2)² + (10 - 3)² = (-8)² + 7² = 64 + 49 =

= 113

diameter = sqrt(113) = 10.63014581...

radius = diameter / 2 = 5.315072906... ≈ 5.315

We have shown that dⁿ⁺¹ / d xⁿ⁺¹ (xⁿ ln x) = n!/x using Leibniz's theorem.

What is the Leibniz's theorem?

Leibniz's theorem, also known as the product rule for derivatives, is a rule for finding the nth derivative of a product of two functions. It states that if u(x) and v(x) are functions of x, then the nth derivative of their product

To apply Leibniz's theorem, we need to express the function in terms of a product of two functions: u and v.

Let u = xⁿ and v = ln(x)

Then, du/dx = n*xⁿ⁻¹ and dv/dx = 1/x

Using the formula,

d/dx(xⁿ ln(x)) = u(dv/dx) + v(du/dx)

= xⁿ * (1/x) + ln(x) * n * xⁿ⁻¹

= xⁿ⁻¹ + n*xⁿ⁻¹ ln(x)

To find the nth derivative, we differentiate n times using the product rule.

First, we need to find the first few derivatives:

f(x) = xⁿ⁻¹ + n*xⁿ⁻¹ ln(x)

\(f'(x) = nx^{(n-2)} + (n-1)*x^{(n-2)} ln(x)\)

\(f''(x) = n(n-2)x^{(n-3)} + 2(n-1)x^{(n-3)} ln(x) - (n-1)x^{(n-3)}/(x^2)\)

\(f'''(x) = n(n-2)(n-3)x^{(n-4)} + 3(n-1)(n-2)x^{(n-4)} ln(x) - 3(n-1)x^{(n-4)}/(x^2) - 2(n-1)x^{(n-4)} ln(x)/(x^2)\)

and so on...

The pattern becomes apparent and the nth derivative can be expressed as:

\(f^{(n)}(x) = n!/(x^{(n+1)})\)

So,

dⁿ⁺¹ / d xⁿ⁺¹ (xⁿ ln x) = \(f^{(n)}(x) = n!/(x^{(n+1)})\)

Hence, we have shown that dⁿ⁺¹ / d xⁿ⁺¹ (xⁿ ln x) = n!/x using Leibniz's theorem.

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Answer:

Step-by-step explanation:

To solve the problem, we start by labeling 1/3 of 3/8 like this:

N1/D1 of N2/D2

Then we use this fraction of a fraction formula to solve the problem:

(N1 x N2) / (D1 x D2)

When we enter 1/3 of 3/8 into the formula, we get:

(1 x 3) / (3 x 8) = 3/24

Therefore, the answer to 1/3 of 3/8 in its lowest form is:

1/3 of 3/8 = 1/8

The numbers 4 and - 4 have an absolute value equal to 4.

In this question we need to find all the numbers such that absolute value is equal to 4. This can be found by using the definition of absolute value:

Absolute values are functions that contains only the magnitudes of the numbers, that is, their distances with respect to zero. Then, if the absolute value is 4, then, the number may be 4 or - 4.  

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The absolute value is 4, then, the number may be 4 or - 4.  

Absolute value describes the distance from zero that a number is on the number line, without considering direction

To find all the numbers such that absolute value is equal to 4.

By definition of absolute value we have

|x| = x for x ≥ 0.

|x| = - x for x < 0.

Absolute values contains magnitude which does not have direction.

|4|=4 for 4≥ 0.

|4| = -4 for x < 0.

Then, if the absolute value is 4, then, the number may be 4 or - 4.  

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Given equation to us is , \((m-3)r^2+9r-2=0\) .

The given equation is a quadratic equation and it has two real solutions if it's discriminant is greater than or equal to 0 .

For a quadratic equation in standard form of

\(ax ^{2} + bx + c = 0\)

the discriminant is given by b² - 4ac .

On comparing wrt to Standard form, we have ;

Now we have,

\(\longrightarrow b^2-4ac \geq 0\\\\\longrightarrow 9^2-4(m-3)(-2)\geq 0\\\\\longrightarrow 81 +8(m-3)\geq 0 \\\\\longrightarrow 81 +8m-24\geq 0 \\\\\longrightarrow 8m \geq 24-81 \\\\\longrightarrow 8m \geq -57 \\\\\longrightarrow \underline{\underline{ m \geq \dfrac{-57}{8}}}\)

Therefore for all values greater than or equal to -57/8 the equation will have a real solution .

And we are done!

The equation (m-3)r² + 9r -2 = 0 will have two real solution for the value of m, greater than or equal to -57/8.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

The standard form of equation of power two is ax²+bx+c =0 .

The given equation,

(m-3)r² + 9r -2 = 0

Compare the given equation with standard equation ax²+bx+c =0,

The value of a=m-3, b=9 and c=-2

An equation has two real solutions if a discriminant of the equation is greater than or equal to zero.

⇒D ≥ 0

⇒b²-4ac ≥ 0

Substitute the value of a, b and c,

⇒9² - 4×(m-3)(-2) ≥ 0

⇒81 +8m - 24 ≥ 0

⇒8m ≥ -57

⇒ m ≥ -57/8

For the values of m greater than or equal to -57/8, the equation have two real solutions.

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Answer:

Step-by-step explanation:

The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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Answer:

C.

Step-by-step explanation:

In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

A.

9 + 9 = 18

18 < 22

No triangle

B.

7 + 3 = 10

10 = 10

No triangle

C.

5 + 6 = 11 and 11 > 9  good

5 + 9 = 14 and 14 > 6  good

9 + 6 = 15 and 15 > 5  good

There is a triangle.

Answer: C.

According to the information we can infer that the period of the graph is 8.

To determine the period of the graph we have to consider that the period of a grah is the distance between rigdes. So, in this case we have to count what is the difference between each rigde.

In this case, the distance between rigdes is 8 units because the first is located in the line 1 an the second is located in the line 9. So we can conclude that the period of the graph is 8.

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Answer:

1 - 31 + 191 does not represent the distance of the 2 given points.

The distance between the 2 points is 12

Step-by-step explanation:

Remember distance formula: \(d = \sqrt{(x2-x1)^2 + (y2-y1)^2}\)

When we plug in our values into the distance formula into a calc,

d = \(\sqrt{(9-(-3))^2 + (-5-(-5))^2}\)

We get d = 12. This does not equal 1 - 31 + 191 (which equals 161).

Answer:

Sample Response: The points are on a horizontal line, parallel to the x-axis. The absolute value of −3 represents the distance from (−3, −5) to the y-axis, and the absolute value of 9 represents the distance from the y-axis to (9, −5).

Step-by-step explanation:

Answer: The negative sign in front of 7/8 indicates that the fraction is negative. To find an equivalent fraction, we can keep the same value but change the sign. Therefore, an equivalent fraction that is positive would be (-(7/8)) = (-7)/8.

Step-by-step explanation:

Answer: 64in cubed

Step-by-step explanation:

4x4x4

Answer:

64

Step-by-step explanation:

Volume of a cube-shaped box = a*a*a

4*4*4=64

Note that the coordinates of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4). (Option B)

To rotate a point 90 degrees  clockwise about a given point,we can follow these steps -

Translate the coordinates   of the given point so that the center of rotation is at the origin.   In this case,we subtract the coordinates   of the center (0,1) from the coordinates of point A (5,4) to get (-5, 3).

Perform the rotation by swapping the x and y coordinates and changing the sign of the   new x coordinate. In this case,we  swap the x and y coordinates of (-5, 3)   to  get (3, -5).

Translate the coordinates back to their original position   by adding the coordinates of the center (0,1)  to the result from step 2. In   this case, we add (0,1) to (3, -5) to get (3, -4).

Therefore, the coordinates   of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4).

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Rewrite the innermost expressions with negative exponents:

\(\displaystyle \left[\left(\frac{a^6}{5b^{-1}}\right)^2 \cdot \left(\frac{b}{9a^{-11}}\right)^{-1}\right]^{-3}\)

\(\displaystyle \implies \left[\left(\frac{a^6b^1}{5}\right)^2 \cdot \left(\frac{ba^{11}}{9}\right)^{-1}\right]^{-3}\)

\(\displaystyle \implies \left[\left(\frac{a^6b^1}{5}\right)^2 \cdot \left(\frac9{ba^{11}}\right)^1\right]^{-3}\)

Simplify the product:

\(\displaystyle \implies \left[\left(\frac{a^6b}{5}\right)^2 \cdot \frac9{ba^{11}}\right]^{-3}\)

\(\displaystyle \implies \left[\frac{\left(a^6b\right)^2}{5^2} \cdot \frac9{ba^{11}}\right]^{-3}\)

\(\displaystyle \implies \left[\frac{\left(a^6\right)^2b^2}{25} \cdot \frac9{ba^{11}}\right]^{-3}\)

\(\displaystyle \implies \left[\frac{a^{12}b^2}{25} \cdot \frac9{ba^{11}}\right]^{-3}\)

\(\displaystyle \implies \left[\frac{9ab}{25}\right]^{-3}\)

Rewrite the last negative exponent:

\(\implies \boxed{\left(\frac{25}{9ab}\right)^3}\)