A beverage company advertises that they have increased their bottle size to 14.4 ounces, which is 20% more than the original size. What is the original size of the bottle

Answer:

Slope: 1/2.5

Y-intercept: -1

Step-by-step explanation:

Answer:

x = 30.6 ft

A = 58.1°

Step-by-step explanation:

\(\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}\)

As the triangle is a right triangle, use Pythagoras Theorem to find length x.

\(\implies x^2+19^2=36^2\)

\(\implies x^2+361=1296\)

\(\implies x^2=935\)

\(\implies x=\sqrt{935}\)

\(\implies x=30.6\; \sf ft \;\; (3\;s.f.)\)

\(\boxed{\begin{minipage}{9 cm}\underline{Cos trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

From inspection of the given right triangle:

Substitute the values into the formula and solve for A:

\(\implies \sf \cos A=\dfrac{19.0}{36.0}\)

\(\implies \sf A= \cos^{-1}\left(\dfrac{19}{36}\right)\)

\(\implies \sf A=58.1^{\circ}\;\;(3\;s.f.)\)

New York had the larger population with 1.9 x 10⁷ people. The correct option is B.

To compare the populations of the states, we need to convert all the populations to the same unit of measurement. In this case, all the populations are given in terms of millions (10⁶).

We can see that New York's population is 1.9 x 10⁷, which means 19 million people. Georgia's population is given as 9.6 x 10⁶, which is 9.6 million people. Comparing these two values, it is evident that New York has a larger population than Georgia.

Check the populations of the other states:

Alaska: 7.1 x 10⁵ = 0.71 million people

Wyoming: 5.6 x 10⁵ = 0.56 million people

Idaho: 1.5 x 10⁶ = 1.5 million people

New York's population of 19 million is much larger than any of the other states listed, making it the state with the largest population among the options provided. The correct option is B.

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Complete question:

Based on the 2010 census, the population of Georgia was 9.6 x 10^6 people. Which state had a larger population? A. Alaska: 7.1 x 10^5 B. New York: 1.9 x 10^7 C. Wyoming: 5.6 x 10^5 D. Idaho: 1.5 x 10^6

If a person has a slow reaction time that puts them in the top 10% of responses, it means that their reaction time is slower than 90% of the population.

The value that separates the top 10% of responses from the bottom 90% is determined by the distribution of reaction times in the population.

Assuming a normal distribution of reaction times, the value that separates the top 10% of responses from the bottom 90% is the 90th percentile. This means that 90% of the population has a reaction time below this value, while the top 10% have a reaction time equal to or above it.

The specific value that separates the top 10% from the bottom 90% can vary depending on the population being studied and the task being performed. However, in general, a value around 1.5 standard deviations above the mean reaction time would be a reasonable estimate for the 90th percentile.

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Answer:

(–8, 1), (8, –8)

Step-by-step explanation:

Answer:

(-8, 1), (8, -8) has a negative slope

Step-by-step explanation:

1). y2 - y1 / x2 - x1

7 - 9 / 5 - 6

= 2

2). y2 - y1 / x2 - x1

6 - (-2) / 3 - (-9)

= 2/3

3). y2 - y1 / x2 - x1

-8 - 1 / 8 - (-8)

-9/16

4). y2 - y1 / x2 - x1

-9 - (-8) / -1 - 2

= 1/3

Answer:

(1,5)

Step-by-step explanation:

x = 1

y = 8

If you move down 3 units, it means the y would be lower. This is because y is the vertical value in a pair of coordinates.

8-3 = 5

Answer:

(1, 5)

Step-by-step explanation:

A coordinate defined as point (x, y) is called Cartesian Coordinate. The x-coordinate represents right-left direction while the y-coordinate represents up-down direction.

Its transformation depends on how would you move the coordinate point. An example is if you start with (x, y) point and move to right 3 units, our new position will be at (x + 3, y).

Properties

Suppose we have point (x, y), if we move to right “a” units then the new point will be (x + a, y)

If we move (x, y) to left “a” units, our new point will be (x - a, y)

If we shift (x, y) up “a units”, you’ll get (x, y + a)

If we shift (x, y) down “a units”, we’ll have (x, y - a)

Suppose you start at (1, 8) and you move down 3 units, you can apply the transformation property to find your new position.

Since you move down, this means you are dealing with y-coordinate only so you’ll apply property of (x, y - a)

You’ll have (1, 8 - 3) which equals to (1, 5).

Hence, you’ll end at (1, 5).

No, the relation is not a function. Because at x = 0, the value of y will be 2 and 1 which is not possible.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

We know that if the number of dependent values is more than one for a given independent value. Then the relation is not a function.

But if the number of dependent values is more than one for a different given independent value. Then the relation is a function.

At x = 0, the value of y will be 2 and 1 which is not possible.

Thus, No, the relation is not a function.

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Answer:

Square root of 29.

Step-by-step explanation:

Distance = sqrt(2^2 + (-5)^2)

= sqrt 29.

The perimeter of the triangle is 170 inches.

To solve for the perimeter, we first need to find the length of the perpendicular height. We can do this using the sine function:

sin(35°) = 46/x

x = 46/sin(35°) = 65 inches

Now that we know the length of the perpendicular height, we can find the length of the base of the triangle using the cosine function:

cos(35°) = 65/x

x = 65/cos(35°) = 75 inches

The perimeter of the triangle is the sum of the lengths of the three sides, so the perimeter is:

P = 65 + 75 + 30

= 170 inches

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Answer:   True

Step-by-step explanation:

The term inside the parentheses after the summation sign is

       x-sub-i    minus    x-bar

x-bar is the mean average of all the individual n observations. In statistics, it is usually just called the 'mean' for short.

x-sub-i stands for each individual observation: x-sub-1, x-sub-2, and so on

So that means (x-sub-i   -   x-bar) means the difference we get if we do the subtraction, using x-sub-i as the first term in the subtraction.

For an illustration of this, suppose we have a sequence of 5 observations. Since there are 5 observations, n = 5.

x-sub-1  = 4

x-sub-2 = 7

x-sub-3 = 3

x-sub-4 = 11

x-sub-5 = 5

We obtain the mean by adding all the observations and then dividing by the number of observations, n.

The sum 4+7+3+11+5 = 30 and 30/5 = 6.

So the mean, x-bar, = 6.

Now let's look at all the differences between each observation and x-bar.

In the same order as the observations, we get

4 - 6  = -2

7 - 6  =  1

3 - 6 = -3

11 - 6 = 5

5 - 6  = -1

If we add up all the differences, just like we are doing in the summation homework problem, we have (-2)+1+(-3)+5+(-1) = 0.

It also works if you make x-bar the first term in the subtraction. Either way will work, as long as you are consistent about it from one subtraction to the next.

This is always the case with a mean average, so the summation is assured to be zero.

I hope this helps.

Answer:

Approximately 1.05 × 10⁹ pounds of food are consumed by African elephants in one day.

Step-by-step explanation:

Answer:

Step-by-step explanation:

its 7 or 6\

The maximum profit if the profits per acre are $75 for corn and $40 for soybeans is $371,255.83. Therefore, the correct option is c.

To find the maximum profit from planting corn and soybeans, we can use linear programming. Let's first define the variables and write the constraints.

Let x be the number of acres of corn and y be the number of acres of soybeans.

1. Total acre constraint: x + y ≤ 6,000

2. Fertilizer/herbicide constraint: 9x + 3y ≤ 40,501

3. Labor constraint: 0.75x + y ≤ 5,250

The objective function to maximize is the profit function: P(x,y) = 75x + 40y

Now, we will use the Solver to find the maximum profit:

Step 1: Set up a spreadsheet with the constraints and the objective function.

Step 2: Go to the Data tab and click on Solver. If Solver is not available, you may need to add it in Excel Options.

Step 3: Set the objective function by selecting the cell with the profit function.

Step 4: Choose "Max" for the objective.

Step 5: Add the constraints by selecting the corresponding cells.

Step 6: Click on "Solve" and the Solver will find the optimal values for x and y.

After using Solver, we find that the optimal values are x = 4,363.89 (corn) and y = 1,636.11 (soybeans), which yields a maximum profit of $371,255.83. Therefore, the correct answer is c: $371,255.83

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The nature of the solution to the system of linear equations is a unique solution.

To determine the nature of the solution to each system of linear equations, we need to examine the slopes of the two equations.

For the first equation, y = (-1/4)x + 1, the slope is -1/4.

For the second equation, y = (2/3)x + 4, the slope is 2/3.

Now let's analyze the nature of the solutions:

1. If the slopes of the two equations are different, the system has a unique solution. This means the lines represented by the equations intersect at a single point.

2. If the slopes of the two equations are the same and the y-intercepts are different, the system has no solution. This means the lines represented by the equations are parallel and do not intersect.

3. If the slopes of the two equations are the same and the y-intercepts are the same, the system has infinitely many solutions. This means the lines represented by the equations are identical and overlap.

In this case, the slope of the first equation (-1/4) is different from the slope of the second equation (2/3). Therefore, the system has a unique solution, and the lines represented by the equations intersect at a single point.

The nature of the solution to the system of linear equations is a unique solution.

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The points will  meet x when it is folded are C or E

A point is a location of an object by taking reference of origin, In general case we consider it at (0,0), At the origin value of both the coordinate position is considered as Zero, In simple words point indicates how much it is above or below from the coordinate axes.

Vertical distance from the x axis is known as y coordinate and horizontal distance from the y axis is known as x coordinate.

Given that,

A green colored Net,

After folding x point will  meet the points = ?

When we start folding,

First step,

Side ABCD and DEFG will be folded,

C and E will meet with each other

Second Step,

Side ABCD and AGHI will be folded,

B and I will meet with each other

Third step,

Side DEFG and AGHI will be folded,

F and H will meet each other

Fourth step,

Upper portion AHI will cover the upper portion BCF of the box

X will at position of C or E

Hence, the X will meet C or E

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Answer:

i dont know sry....i ned points..

Given: The image shown in the question

To Determine: 3 collinearpoints

Solution

Collinear points are the points that lie on the same straight line or in a single line. If two or more than two points lie on a line close to or far from each other, then they are said to be collinear

d. Therefore Points D, G, and F are collinear

Coplanar points are three or more points which lie in the same plane. Recall that a plane is a flat surface which extends without end in all directions.

e. Therefore, the points A, D, G, and F are coplanar points

If two planes intersect each other, the intersection will always be a line

f. Thereffore, the intersection of plane ABC and plane ABE is the line AB

g. The intersection of planes BCH and DEF.

From the image, there is no intersection between the planes BCH and DEF

h. The intersection of line AD and line DF is point D

According to the information, it can be inferred that the answer is No, because informing the students that there will be a $10 increase... (option B).

This question is not valid because it specifies information that would surely change the answer of the respondent.

The information that the question reveals is that there is going to be a raise, this will cause a refusal in people to accept that raise just to see a live band.

According to the above, the question is invalid because it reveals information that will modify the answer of those who respond.

Note: This question is incomplete because the options are missing. Here are the options:

A. No, because questions about musical preferences are always invalid because you cannot measure people's opinions on subjective manners like music and other creative arts.

B. No, because informing the students that there will be a $10 increase in the cost of a prom ticket may make them more likely to say that they would not like a live band to perform.

C. No, because students should be given a sample of the band's music to allow them to offer a more informed opinion.

D. No, because a random sample of all seniors in the country should have been taken to determine if a live band should perform at this high school's senior prom.

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Answer:

Step-by-step explanation:

Alternate interior angles are congruent if the two parallel lines are intersected by the transversal.

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, vertically opposite angles etc.

The parallel lines in the diagram has two red arrows on it.

The transversal line is the one that cut the other two parallel lines.

The angles formed are 9x + 5 and 10x - 5.

Therefore, if the two parallel lines are intersected by the transversal then alternate interior  angles are congruent.

Hence,

9x + 5 = 10x - 5

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Answer:

(2x-1)(2x+3)

Step-by-step explanation:

4x^2 + 4x - 3

4x^2 + 6x - 2x - 3

2x(2x + 3) - 1(2x + 3)

(2x - 1) (2x + 3)

Answer:

Circumference = (3.14)(15) = 47.1 in

Step-by-step explanation:

The expression equivalent to x - 3y + 4 is x + 4 - 3y

From the question, we have the following parameters that can be used in our computation:

x - 3y + 4

Next, we change the positions of the terms of the expression

So, we have the following representation

x - 3y + 4 = x + 4 - 3y

This means that x + 4 - 3y is equivalent to x - 3y + 4

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Complete question

Write expression equivalent to x - 3y + 4

Answer:

box plot becauase wire width is numerical :)

Step-by-step explanation:

Marvin has to take 29 trips to the school to make in all to walk a total of 40 kilometers with the help of algebraic equation.

Marvin has already walked 11 kilometers this week, so he needs to walk an additional 29 kilometers (40 - 11) to reach his goal.

If he plans to walk 1 kilometer during each trip to school, we can use algebra to solve for the number of trips he needs to make:

Let's call the number of trips Marvin needs to make "x".

Then, the total distance he walks during these trips is 1 kilometer times "x".

So we can set up the following equation to solve for x:

1x + 11 = 40

Subtracting 11 from both sides:

1x = 29

Dividing both sides by 1:

x = 29

Therefore, Marvin needs to make 29 trips to school to walk a total of 40 kilometers.

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Hence, a cylinder with height h and base area \(\pi r^{2}\) may be proven to have the same volume as a triangular prism.

Two parallel circular bases joined by a curving surface form the three-dimensional geometric object known as a cylinder. Due of its parallel and congruent bases, it is a sort of prism.

When someone uses the word "cylinder,” they often mean a right circular cylinder with circles for bases and an axis that is perpendicular to the bases' planes.

A cylinder's volume may be calculated using the formula V = \(r^{2}\)h, where r denotes the perimeter of the base and h the height of the cylinder. L = 2rh, where r is the radius of a base and h is the height of the cylinder, is the formula for a cylinder's lateral surface area.

Cavalieri's principle states that if two solid objects have the same height and every cross-section taken perpendicular to a common axis has the same area, then the two objects have the same volume.

Let's consider the given triangular prism with base area  \(\pi\)\(r^2\) and height h. If we take a cross-section perpendicular to the base at a height y, we get a circle with radius r multiplied by a triangle with base 2r and height y. The area of this cross-section is:

\(A(y) = \pi r^2 + (2r)(y) / 2\)

Simplifying, we get:

\(A(y) = \pi r^2 + ry\)

Now, let's consider a cylinder with base area pi r² and height h. If we take a cross-section perpendicular to the height at a height y, we get a circle with radius r multiplied by a rectangle with base 2r and height h. The area of this cross-section is:

\(A'(y) = \pi r^ + (2r)(h) = \pi r^2 + 2rh\)

By Cavalieri's principle, the triangular prism and the cylinder have the same volume if A(y) = A'(y) for all y from 0 to h. Let's check:

\(\pi r^² + ry = \pi r^² + 2rh\)

\(ry = 2rh\)

\(y = 2r\)

So, we see that the areas are equal for all y between 0 and h, except at \(y = 2r.\) However, this is just a single point and has no effect on the volume,

Therefore,  the cylinder with base area \(\pi\)\(r²\) and height h has the same volume as the triangular prism, with base area \(\pi\)r² and height h.

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The distance between Phoenix and Helena is estimated to be around 900 miles.

Given that the location of Phoenix, Arizona, is 112°W longitude, 33.4°N latitude, and the location of Helena, Montana, is 112°W longitude, 46.6°N latitude, the mean radius of the earth is 3960 miles. To estimate the distance between Phoenix and Helena, we need to use the Haversine formula.

We can use the Haversine formula to calculate the distance between two coordinates using the Earth's radius and the difference between the two latitudes and longitudes. Haversine Formula:  d = 2r sin^(-1) (sqrt (sin² ((lat_2-lat_1)/2)+cos(lat_1)cos(lat_2)sin² ((long_2-long_1)/2)))where d is the distance, r is the radius of the Earth, lat_1 is latitude 1, lat_2 is latitude 2, long_1 is longitude 1, and long_2 is longitude 2.

Since Phoenix and Helena have the same longitude, the difference in longitudes will be zero. Therefore, we can use the formula:d = 2r sin^(-1) (sqrt (sin² ((46.6-33.4)/2)+cos(33.4)cos(46.6)sin² (0/2))))On solving this, we get,d ≈ 900 miles. Therefore, the distance between Phoenix and Helena is estimated to be around 900 miles.

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The ordered pairs of Nicole and Ian's sequence pattern are:(5,1),(17,3),(53,5),(161,10),(485,20).

Given that Nicole uses the  rule multiply by 3 then add 2 starting with it and Ian uses the rule add 1/2 then multiply by 2 starting from 0,

We ar rquired to find the ordered pairs of Nicole's and Ian's rules.

We are told that Nicole's pattern is multiply by 3 then add 2 starting with 1.

Thus Nicole's pattern is :5,17,53,161,485.

Ian's pattern is add 1/2 then multiply by 2 and starting with 0.Thus the  numbers are :1,3,5,10,20.

If we combine the numbers of both the person'rule then we will get the ordered pairs which can be written as under:

The ordered pairs are (5,1),(17,3),(53,5),(161,10),(485,20).

Hence the ordered pairs are (5,1),(17,3),(53,5),(161,10),(485,20).

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200 is the mean absolute deviation. Therefore, choice three (200) is the right one.

The absolute difference between the predicted and actual values must be determined, added together, and divided by the total number of periods.

Forecasted values are as follows: 1,500 and 1,400

Values in actuality: 1,200 and 1,500

Absolute differences:

|1,500 - 1,200| = 300

|1,400 - 1,500| = 100

Now, we calculate the MAD:

MAD = (300 + 100) / 2 = 400 / 2 = 200

Therefore, 200 is the mean absolute deviation. Therefore, choice three (200) is the right one.

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Answer:

Real numbers have two categories: rational and irrational. If a square root is not a perfect square, then it is considered an irrational number. These numbers cannot be written as a fraction because the decimal does not end.

Step-by-step explanation:

So as to say that irrational numbers can't be a squared root because of there decimals.