Amelia can buy a 12-pack of juice for $3.36. Write a proportion relating the cost to the number of bottles and answer how much would Amelia have to pay for a 18-pack of juice if the ratios are proportional

Answer:

I was told about this question by brainly in my email...

Step-by-step explanation:

To find the exact value of each of the six trigonometric functions of angle θ, we need to determine the values of the sine, cosine, tangent, cosecant, secant, and cotangent.

Given that a point on the terminal side of angle θ in standard position is (-24, 18), we can use the coordinates of this point to find the values of the trigonometric functions.

First, let's find the length of the hypotenuse by using the Pythagorean theorem. The hypotenuse is the distance from the origin (0, 0) to the point (-24, 18):

Hypotenuse = √((-24)^2 + 18^2) = √(576 + 324) = √900 = 30

Now, let's determine the values of the trigonometric functions:

1. Sine (sinθ) = opposite/hypotenuse = 18/30 = 3/5

2. Cosine (cosθ) = adjacent/hypotenuse = -24/30 = -4/5

3. Tangent (tanθ) = opposite/adjacent = 18/-24 = -3/4

4. Cosecant (cscθ) = 1/sinθ = 1/(3/5) = 5/3

5. Secant (secθ) = 1/cosθ = 1/(-4/5) = -5/4

6. Cotangent (cotθ) = 1/tanθ = 1/(-3/4) = -4/3

Therefore, the exact values of the six trigonometric functions of angle θ are as follows:

sinθ = 3/5
cosθ = -4/5
tanθ = -3/4
cscθ = 5/3
secθ = -5/4
cotθ = -4/3

These values provide information about the relationship between the angles and the sides of a right triangle formed by the given coordinates.

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The cost to download a single song is $0.35. This can be determined by rearranging the equation c = 0.35s, as c/s = 0.35.

Equation is a mathematical statement that shows the relationship between two or more entities (such as variables or numbers) in an equal sign. Equations are used to solve mathematical problems and can also be used to express relationships between physical, chemical and other types of phenomena. In mathematics, an equation is a statement that asserts the equality of two expressions. In other words, an equation is a statement that two expressions are equal.

This means that for every song downloaded, the cost is $0.35. Therefore, the cost to download a single song is $0.35.

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Take the differences, it will give 35

Add 35 to 315

35 + 315 =350

The initial value is 350 euros

Answer:

Step-by-step explanation:

Hi ,  Butteryfly   :P

given  m= -2

Point P1( -1, -4)    in the form (x1,y1)

use the point-slope formula, below, and plug in our knows.

y - y1 = m(x -x1)

y-(-4) = -2(x-(-1)

note the careful detail of the negatives

y+4 = -2(x+1)

y+4 = -2x -2

y = -2x -2 -4

y = -2x -6

now use Desmos or your favorite free on-line graphing tool.  i'm litterally copy and pasting our line equation into Desmos for the graph attached.

Answer:

\(2p^2\)

Step-by-step explanation:

Step 1: Apply the exponentiation property:

\((8p^6)^\frac{1}{3} = 8^\frac{1}{3} * (p^6)^\frac{1}{3}\)

Step 2: Simplify the cube root of 8:

The cube root of 8 is 2:

\(8^\frac{1}{3} =2\)

Step 3: Simplify the cube root of \((p^6)\):

The cube root of \((p^6)\) is \(p^\frac{6}{3} =p^2\)

Step 4: Combine the simplified terms:

\(2 * p^2\)

So, the simplified expression is \(2p^2\).

According to given information, the point Z(8,3) lies on the circle centered at P(0,0).

Given, the circle is centered at P(0,0) and the point W(-6,√37) is on the circle.

To find where the point Z(8,3) lies, we can use the distance formula.

If the distance between Z and P is equal to the radius of the circle, then Z lies on the circle.

That is, if we get the distance between Z and P, and it's equal to the radius, then the point Z will lie on the circle with center P.

Let's find the radius of the circle.

The point W(-6,√37) is on the circle. So, we can use this point to find the radius of the circle.

Radius = PW=√((-6 - 0)² + (√37 - 0)²) = √(36 + 37) = √73

Now we can find the distance between Z and P and check if it's equal to the radius.

If it is, Z lies on the circle.

DP=√((8 - 0)² + (3 - 0)²) = √(64 + 9) = √73

Since DP = radius of the circle, point Z lies on the circle with center P.

Therefore, the point Z(8,3) lies on the circle centered at P(0,0).

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Given:

The vertices of a triangle are D(1,5), O(7,-1) and G(3,-1).

To find:

The perpendicular bisector of line segment DO.

Solution:

Midpoint formula:

\(Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)\)

The midpoint of DO is:

\(Midpoint=\left(\dfrac{1+7}{2},\dfrac{5+(-1)}{2}\right)\)

\(Midpoint=\left(\dfrac{8}{2},\dfrac{4}{2}\right)\)

\(Midpoint=\left(4,2\right)\)

Therefore, the midpoint of DO is (4,2).

Slope formula:

\(m=\dfrac{y_2-y_1}{x_2-x_1}\)

Slope of DO is:

\(m=\dfrac{-1-5}{7-1}\)

\(m=\dfrac{-6}{6}\)

\(m=-1\)

Therefore, the slope of DO is -1.

We know that the product of slopes of two perpendicular line is -1.

\(m_1\times m_2=-1\)

\(m_1\times (-1)=-1\)

\(m_1=1\)

The slope of perpendicular bisector is 1 and it passes through the point (4,2). So, the equation of the perpendicular bisector of DO is:

\(y-y_1=m(x-x_1)\)

\(y-2=1(x-4)\)

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

\(y=x-2\)

Therefore, the equation of the perpendicular bisector of DO is \(y=x-2\).

Answer:

well, took me some time but I did answer all of em

Answer:

5. The Answer is 45.

6. 75

7. 110

8. 30

9. 12

10. 4

11. 5

12. 9

13. 60

14. 60

Step-by-step explanation:

When you solve it out, you know that vertical angles are congruent. So the top angle is 42. Then you need to find out the angle adjacent to the 87. This is a supplementary angle. Supplementary angles add up to 180. So, 180 - 87 = x. This comes out to 93. Then you just need to find ?. All angles in a triangle add up to 180. So 180 - 93 -42 = 45. ? = 45

For this one we know that the angles in a triangle add up to 180. So, 180 - 35 - 70 = 75. Vertical angles are congruent so ? is also equal to 75.

For this one, we know supplementary angles add up to 180. We use this for every angle. 180 - 145 = 35. 180 - 105 = 75. Angles in a triangle add up to 180 so, 180 - 75 - 35 = 70. We know the other angle in the triangle, we now need to find the angle that is supplementary. We know they add up to 180 so, 180 - 70 = 110. ? = 110

We know 2 of the angles, 90 and 60. We can solve for the third angle. 180 - 90 - 60 = 30. Vertical angles are congruent so ? also equals 30.

We now 2 angles. 60 and 70. We can find the third angle. 180 - 60 -70 = 50. We now need to solve for x. We can subtract 14 from 50 then divide it by 3. We get 12. X is = 12.

We know 2 angles. 65 and 90. This means the third angle is 25. We need to solve for x so 25 - 1 = 24. Then divide that by 6. We get 4. X = 4.

We know 2 angles. 70 and 70. This means the third angle is 40. We can divide that by 8 to find x. X = 5.

We know 2 angles. 70 and 90. This means the third angle is 20. We can subtract 2 to get 18. Then divide by 2. We get 9. X = 9.

We first need to find the last angle in the first triangle. 180 - 85 - 50. The third angle is 45. We now know 2 angles in the second triangle. We can now solve for ?. 180 - 75 - 45. ? = 60

We first need to find the last angle in the first triangle. 180 - 70 - 70. 40 is the last angle. We now have 180 - 40 - 80. It comes out to 60. ? = 60.

a) In an Excel Data Model, the foreign key column is typically chosen in the lookup table.

b) A PivotTable in Excel is called a "PivotTable" because it allows you to pivot or reorganize your data dynamically.

a) The lookup table is a table that contains the primary key values from the master table and the corresponding foreign key values that are used to establish relationships between the tables. This table is commonly used to create relationships between different tables in the data model.

b) A PivotTable is called a PivotTable because it allows you to pivot or rotate the data in order to view it from different perspectives. The term "pivot" refers to the action of changing the arrangement or structure of the data.

While a PivotTable offers filtering capabilities and can be connected to data in different sheets or sources, the fundamental aspect that distinguishes it is its ability to pivot or rotate the data to provide flexible analysis and visualization options.

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Answer:

A. the degree is 4         11x^4-4x^2-12

B. The degree is 5        2x^5-3x^4+3x^3+7x+14

Step-by-step explanation:

The degree is always the highest or greatest exponent in the polynomial. To rearrange the polynomial put it in descending order from highest exponent to lowest exponent with x as an exponent of 1

1) the coordinate pairs that are solutions to the system are:
i) The three coordinate pairs that are solutions to the system are:

ii) three coordinate pairs that are not solutions to the system are:

iii) See the attached graph.

To find coordinate pairs that satisfy both inequalities, we can select values for x and y that satisfy each inequality individually and simultaneously.

Let's choose three coordinate pairs that satisfy the system:

Coordinate Pair 1: (x = 0, y = 0)

Substituting the values into the inequalities:

3(0) - 5(0) ≤ 0 ⇒  0 ≤ 0 (True)

(0) - (0) > -1 ⇒ 0 > - 1 ( True)

Cordinate  Pair 2: (x = 2, y = 1 )

Substituting the values into the inequalities

3(2) - 5(1) ≤ 0 ⇒ 6 - 5 ≤ 0 => 1 ≤ 0 (False)

(2) - (1) > -  1 ⇒ 1 > - 1 ( True)

Coordinate Pair 3    (x  = -1, y = -2)

Substituting the values into the inequalities

3(-1) - 5(-2) ≤ 0 ⇒ -3 + 10 ≤ 0 => 7 ≤ 0 (False)

(-1) - (-2) > -1 ⇒ 1 > -1 (True)

ii) To get the coordinate pairs that DO NOT  satisfy the system, we can choose values for x and y that violate either one   or both of the inequalities.

Coordinate Pair 1: (x = 1, y = 2)

Substituting the values into the inequalities:

3(1) - 5(2) ≤ 0 ⇒ 3 - 10 ≤ 0 => -7 ≤ 0 (True)

(1) - (  2) >  -1 ⇒ - 1 > - 1 (False)

Coordinate Pair 2: (x = -2, y = -1)

Substituting the values into the inequalities:

3(-2) - 5(-1) ≤ 0 ⇒ -6 + 5 ≤ 0 => -1 ≤ 0 (True)

(-2) - (-1) > -1 ⇒ -1 > -1 (False)

so, i) The three coordinate pairs that are solutions to the system are:

ii) three coordinate pairs that are not solutions to the system are:

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Answer:

It should be 60 degrees

Step-by-step explanation:

Given the word phrase ( 16 more than m )

More than mean addition, so we will use the sign (+)

so, the expression will be:

The statements given are mostly true, except for the statements that V_4 is parallel to V_3 and that V_3 is greater than V_1.

The magnitude of a vector can be different in different coordinate systems. True

It is possible to add a scalar to a vector. True

A 2D vector can have a magnitude equal to zero even when one of its components it nonzero. True

The direction of a vector can be different in different coordinate systems. True

A 2D vector can have a component equal to zero even when its magnitude is nonzero. True

The components of a vector can be different in different coordinate systems. True

It is possible to multiply a vector by a scalar. True

If V_3 = V_1 + V_2, then V_4 = 3V_1 + 3V_2 is parallel to V_3. False

If V_3 = V_1 + V_2, then V_3 - V_2 is parallel to V_1. True

If V_3 = V_1 + V_2, then V_3 = V_1 + V_2. True

If V_3 = V_1 + V_2, then V_3 > V_1. False

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Answer:

2

Step-by-step explanation:

Use the vertex form equation first since you are given the vertex (-1,-2) where you have (h,k) so h = -1 and k = -2

y =  \(a (x - -1)^{2}\) + (-2) so if you simplify we get y =  a(x+1)^2 -2

Since we are also given a point we can solve for a so x = 2 and y = 16

16 = a(2+1)^2 - 2

16 = a(3)^2 - 2

18 = 9a

a = 2

Answer: 6,192 paperclips, 3,826 paperclips

Step-by-step explanation:

a) To find the sum of all the children's paperclips, you must find each of them.

First, to start off, create some equations that represent this information:

k = j * \(\frac{6}{7}\)

m = 3k

m = j + 2552

Then, for starts you can use the equation m = 3k and plug in for the variables

m = 3k

(j+2552) = 3(j * 6/7)

j + 2552 = 3j + 2.57

2549.43 = 2j

j = 1274.715

j = 1274 (round down because you can't have a fraction of a paper clip)

Next, use j to solve the other equations

m = j + 2552

m = 1274 + 2552

m = 3826

k = j * 6/7

k = 1274 * 6/7

k = 1092

sum = k + j  + m

sum = 1092 + 1274 + 3826

sum = 6,192 paperclips

b) We already know m, which is 3826.

3,826 paperclips

The length of the shadow casted by the building is 31.06 meters. The solution has been obtained by using trigonometry.

What is trigonometry?

Trigonometry is a discipline of mathematics that deals with the study of sides, angles, and relationships in triangles.

We are given that at a certain time of day, the angle of elevation of the sun is 44 degrees. The height of the building is given as 30 meters.

Using trigonometry,

We know that tan theta = opposite side/ adjacent side

So,

⇒tan 44° = 30/x

⇒0.9657 = 30/x

⇒x = 31.06

Hence, the length of the shadow casted by the building is 31.06 meters.

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The histogram is attached.

Given that, we need to draw a histogram,

Data :-

1-3        3, 2, 3     Frequency = 3

4-6       4, 6, 5     Frequency = 3

7-9       7, 8, 8, 7  Frequency = 4

10-12    10, 10       Frequency = 2

Hence, you can draw the histogram according to the table.

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Answer(s):

\(\displaystyle y = 4cos\:(2x - \frac{\pi}{2}) - 1 \\ y = 4sin\:2x - 1\)

Explanation:

\(\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow -1 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\frac{\pi}{4}} \hookrightarrow \frac{\frac{\pi}{2}}{2} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 4\)

OR

\(\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow -1 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 4\)

You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the sine graph, if you plan on writing your equation as a function of cosine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of \(\displaystyle y = 4cos\:2x - 1,\) in which you need to replase "sine" with "cosine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the sine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the cosine graph [photograph on the right] is shifted \(\displaystyle \frac{\pi}{4}\:unit\) to the left, which means that in order to match the sine graph [photograph on the left], we need to shift the graph FORWARD \(\displaystyle \frac{\pi}{4}\:unit,\) which means the C-term will be positive, and perfourming your calculations, you will arrive at \(\displaystyle \boxed{\frac{\pi}{4}} = \frac{\frac{\pi}{2}}{2}.\) So, the cosine graph of the sine graph, accourding to the horisontal shift, is \(\displaystyle y = 2cos\:(2x - \frac{\pi}{2}) - 1.\) Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph hits \(\displaystyle [-\frac{\pi}{4}, -5],\) from there to \(\displaystyle [\frac{3}{4}\pi, -5],\) they are obviously \(\displaystyle \pi\:units\) apart, telling you that the period of the graph is \(\displaystyle \pi.\) Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at \(\displaystyle y = -1,\) in which each crest is extended four units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

Consider a homogeneous linear system with a 4 by 9 coefficient matrix. The coefficient matrix has rank at most equal to 4 and at least 5 free variable columns.

This is because the rank of a matrix cannot exceed the number of rows or columns it has. In this case, the matrix has 4 rows, so the rank cannot exceed 4.

Additionally, the number of free variable columns can be found by subtracting the rank of the matrix from the number of columns. In this case, there are 9 columns, so subtracting the maximum rank of 4 gives us 5 free variable columns.

Therefore, The coefficient matrix has rank at most equal to 4 and at least 5 free variable columns.

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Answer:

m = - \(\frac{2}{3}\) , c = - \(\frac{1}{3}\)

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

2x + 3y + 1 = 0 ( subtract 2x + 1 from both sides )

3y = - 2x - 1 ( divide terms by 3 )

y = - \(\frac{2}{3}\) x - \(\frac{1}{3}\) ← in slope- intercept form

with m = - \(\frac{2}{3}\) and c = - \(\frac{1}{3}\)

Answer:

Below in bold.

Step-by-step explanation:

y = x^2 - 8x + 6

Convert to vertex form.

We complete the square:-

y = (x - 4)^2 - 16 + 6

y = (x - 4)^2 - 10.

So, the vertex is at (4, -10).

Answer:

(1.2, –4.7)

Step-by-step explanation:

Since in the question it is mentioned that on the plane of coordinate, a line is made from point A (7,-2) to point B(-8,-9)

Also, the ratio of A to B is 5:8

Based on this, the x and y coordinates at point C is

\(= [\frac{5\times (-8) + 8\times 7}{5 + 8} , \frac{5\times (-9) + 8\times -2}{5 + 8}]\\\\= [\frac{16}{3}, \frac{-61}{13}]\)

= (1.2, –4.7)

Hence, the x and y coordinates of point C is (1.2, –4.7)

Therefore the last option is correct

Answer:

D

Step-by-step explanation:

The overall sample for the survey consists of 50 freshmen, 40 sophomores, 35 juniors, and 30 seniors, totaling 155 students.

To create an overall sample for the survey, the administrators selected a certain number of students from each class level. They randomly sampled 50 freshmen, 40 sophomores, 35 juniors, and 30 seniors. By combining these individual samples from each class, the administrators obtained an overall sample size of 50 + 40 + 35 + 30 = 155 students. This overall sample represents a portion of the student population from each class level and allows for a representation of students from different academic years in the survey.

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The researcher needs to compute an estimated standard error for the mean difference score to calculate a t statistic.

This is done by calculating the standard deviation of the difference scores and dividing it by the square root of the sample size. The standard error measures the variability in the sample mean difference scores.

To compute a t statistic, the researcher also needs to calculate a pooled variance. This is done by combining the variances of the two groups being compared. The pooled variance takes into account the sample sizes and the variances of each group.

To compute a t statistic, the researcher needs to compute an estimated standard error for the mean difference score and a pooled variance. These calculations are necessary to determine the significance of the difference between the two groups.

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The amount of the remittance from ABC is $1,960.

The given information states that merchandise is sold for $2,000 with terms of 2/10, n/30 to ABC. The terms 2/10, n/30 imply a 2% discount if payment is made within 10 days, with the full amount due within 30 days.

Since ABC sends a remittance on Dec. 26, it means the payment is made after the discount period but within the credit period. Therefore, ABC is not eligible for the discount of 2%.

To calculate the amount of the remittance, we simply subtract the discount from the total amount. In this case, the discount is $2,000 * 2% = $40. Thus, the remittance amount is $2,000 - $40 = $1,960.

In conclusion, the amount of the remittance from ABC is $1,960, as they did not qualify for the early payment discount.

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ANSWER

EXPLANATION

We want to identify the option that is completely factored.

For an expression to be completely factored, it means that there are no more common terms between the terms in the expression.

That means it can not be factored any further.

Therefore, the only correct option is:

The balance in the fund at the end of 23 years, with monthly deposits of $1,150 and a 3.25% annual interest rate, is approximately $449,069.51. The amount of interest earned over the period is approximately $420,630.49.

a. The balance in the fund at the end of the 23-year period, considering a monthly deposit of $1,150 and an annual interest rate of 3.25% compounded annually, is approximately $449,069.51.

To calculate the balance, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where A is the accumulated balance, P is the monthly deposit, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

In this case, we have monthly deposits, so we need to convert the annual interest rate to a monthly rate:

Monthly interest rate = (1 + 0.0325)^(1/12) - 1 = 0.002683

Using this monthly interest rate, we can calculate the accumulated balance over the 23-year period:

A = 1150 * [(1 + 0.002683)^(12*23) - 1] / 0.002683 = $449,069.51

Therefore, the balance in the fund at the end of the 23-year period is approximately $449,069.51.

b. The amount of interest earned over the 23-year period can be calculated by subtracting the total deposits from the accumulated balance:

Interest earned = (Monthly deposit * Number of months * Number of years) - Accumulated balance

Interest earned = (1150 * 12 * 23) - 449069.51 = $420,630.49

Therefore, the amount of interest earned over the 23-year period is approximately $420,630.49.

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