which is more 7,000 milliliters or 7 liters?

The inequality can be solved to get 2 > x, and the graph on the number line can be seen in the image at the end.

Here we have an inequality and we want to sole it, to do so, we just need to isolate the variable in the inequality.

Here we have:

10 > 5x

To isolate the variable we can divide both sides of the inequality by 5, then we will get:

10/5 > 5x/5

2 > x

So x is the set of all values smaller than 2.

That is the inequality solved, to graph this, drawn an open circle at x = 2 and a line that goes to the left. The graph is the one you can see in the image below.

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Answer:

26° 180 -81 - 73 = 26

Step-by-step explanation:

Answer:

26

Step-by-step explanation:

triangle= 180

81 + 73 = 154

180 - 154= 26

Answer:

B.  There is no maximum value.

C.  There is no maximum value of z.

Step-by-step explanation:

To solve this linear programming problem using graphical methods, start by graphing the feasible region determined by the given constraints:

We can graph each of these inequalities by first plotting the corresponding boundary line, and then shading in the appropriate region.

Rearrange the first three inequalities to isolate y:

[tex]\boxed{\begin{aligned}2x - 3y & \leq 12\\2x - 12 & \leq 3y \\3y &\geq 2x - 12\\y& \geq \dfrac{2}{3}x-4\end{aligned}}[/tex]  [tex]\boxed{\begin{aligned}x + y & \geq 3\\y & \geq -x+3\\ \phantom{w}\\\phantom{\dfrac12}\end{aligned}}[/tex]  [tex]\boxed{\begin{aligned}3x + 4y & \geq 24\\4y & \geq -3x + 24\\y & \geq -\dfrac{3}{4}x + 6\\\phantom{w}\end{aligned}}[/tex]

Graph the inequalities.

The feasible region is the region that is shaded by all of the inequalities.

Please see the attached graph.

A bounded feasible region may be enclosed in a circle and will have both a maximum value and a minimum value for the objective function.

If a feasible region is unbounded, and the coefficients on the objective function are all positive, then an unbounded feasible region will have a minimum but no maximum, since there is no limit on how big it can get.

Therefore, as the feasible region for the given constraints is unbounded, and the coefficients of the objective function z = 3x + 4y are all positive, there is no maximum value.

Answer:

Step-by-step explanation:

modal weight:  the weight that appear most often

4.5 kg  appears 3 times

6-sided polygon:  even though it is an irregular polygon, the interior angles still add up to (6 - 2)180 = 720

therefore, angle f = 720 - 576 = 144      (the sum of a+b+c+d+e is very blurry in the image, it looks like 576--please double check that!)

modal score:  read this right off the graph.  The score with the highest frequency is the modal score:  14   (meaning, 9 contestants got this score)

Answer:

85 degrees.

Step-by-step explanation:

These are parallelograms, meaning the opposite sides are parallel. Since they are parallel, that the line EA becomes a transversal and a bisector for the angle CEK. That means the angle 8 and 3 are equivalent and 7 and 4 are equivalent. This is due to Same Side Interior Angles. These are two halves of the big angle. If the halves are equal, so are the angles. Therefore, CEK = CAK.

If Point A is located at (4, 3). Point A is reflected.  the final location of A after both transformations is (-4, -7).

To reflect point A across the line y = -2, we need to find the point that is the same distance from the line but on the other side. The line y = -2 is a horizontal line that is 5 units above the point A (since the y-coordinate of A is 3). Therefore, the reflected point will be 5 units below the line, which gives us:

A' = (4, -7)

To rotate point A' 90 degrees clockwise about the origin, we can use the following rotation matrix:

| 0 1 |

| -1 0 |

Multiplying this matrix by the coordinates of A', we get:

| 0 1 | | 4 | | -7 |

| -1 0 | * | -7 | = | -4 |

So the final location of A after both transformations is (-4, -7).

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Answer:

linear

Step-by-step explanation:

this is a linear function!

linear functions follow y = mx+b, where m is the slope and b is the y-intercept

let's write our y = mx+b equation

for each value that x increases, y increases by DOUBLE that amount. slope is y/x, so since y increases by 2 and x increases by 1, the slope is 2/1 which is 2.

the y-intercept is where the line passes the x axis, or when x is 0. in this table, it gives you your y-intercept, which is -6

your equation is y=2x+(-6); which simplified to y=2x-6

if you plug in the y and x values, you'll get the same thing. i hope this helped!

The z-score that corresponds to a cumulative area of 0.3897 is 0.25.

A Z-score is a statistical measurement that indicates how many standard deviations a data point is from the mean of a distribution.

It is calculated by subtracting the mean of the distribution from the data point and then dividing the result by the standard deviation of the distribution.

Here we have

The cumulative area is 0.3897

Using the standard normal table, we can find the z-score that corresponds to a cumulative area of 0.3897 as follows:

1. Locate the entry in the body of the table that is closest to 0.3897. In this case, the closest entry is 0.3897 in the body of the table.

2. Identify the corresponding row and column headers for this entry. The row header is 0.0 and the column header is 0.08.

3. The z-score that corresponds to the area of 0.3897 is the value at the intersection of the row and column headers. In this case, the value is 0.25.

Therefore,

The z-score that corresponds to a cumulative area of 0.3897 is 0.25.

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The constant of proportionality of this table  is: k = 1/7.

The ratio between two quantities that are directly proportional is the constant of proportionality.

When y and x are two values that are direct proportion to one another, the proportionality constant k is defined as k=y/x.

Thus, using the x and its respective y values.

As the values are in direct proportion.

The constant of proportionality is:

k = 1/7

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The wire can be divided into five equal parts, where one portion is one-fifth of the total length and the other four parts are four-fifths of the total length. the measure of the longer part of the wire after cutting is 2 meters.

If the wire was cut in a ratio of 1:4, then the total length of the wire can be divided into 5 parts, where one part is 1/5 of the total length, and four parts are 4/5 of the total length. Let's call the length of one part "x".

So, the total length of the wire is:

 [tex]5x = 2.5[/tex] meters

To find the length of the longer part of the wire, we need to find how many parts are in the longer portion. Since the wire was cut in a 1:4 ratio, the longer portion has four parts.

Therefore, the length of the longer part of the wire is:

[tex]4x = 4/5 \times 2.5 meters = 2 meters[/tex]

Therefore, the measure of the longer part of the wire after cutting is 2 meters.

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Therefore, knowing the slant height is important in calculating the lateral area of the pyramid, which is one component of the total surface area.

by the question.

Option 2 is the correct response. Knowing the slant height is helpful because it represents the height of the rectangle that makes up each lateral face of the pyramid. The lateral faces are made up of triangles and rectangles, and the slant height is used to find the height of these rectangles.

Knowing the slant height helps because it represents the height of the rectangle that makes up each lateral face. So, the slant height helps you to find the area of each lateral face. The formula for the lateral area of a pyramid involves the slant height, the perimeter of the base, and the apothem (the distance from the center of the base to the midpoint of a side). Once you know the lateral area, you can add it to the area of the base to find the total surface area of the pyramid.

The slant height of a pyramid is the height of each triangular lateral face, which is an essential component in calculating the lateral surface area of a pyramid. Knowing the slant height is used in the formula for finding the lateral area of a pyramid, which is the sum of the areas of all the triangular lateral faces. Additionally, the base area of the pyramid is also needed to find the total surface area of the pyramid. So, knowing the slant h

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Answer: it depends; if exam day, no

Step-by-step explanation:

Therefore, cos(K) = √(17)/9, sin(L) = 8/9, and cos(K) and sin(L) together are (√(17)/9, 8/9) are trigonometric ratios as fractions in simplest terms.

It is possible to calculate trigonometric ratios for various orientations. However, we memories the trigonometric ratios of a few particular angles, such as 0°, 30°, 45°, 60°, and 90°, to make computations easier. The numbers of the ratios at these angles can be found in the trigonometric ratios table.

The Pythagorean formula can be applied to the illustration to determine the length of the third side:

c²= a²+ b²

c²= 8² + √(17)²

c²= 64 + 17

c² = 81

c = 9

We can now calculate the trigonometry ratios of angles K and L:

cos(K) = adjacent/hypotenuse = √(17)/9

sin(L) = opposite/hypotenuse = 8/9

Using the same hypotenuse number of 9, we can calculate both cos(K) and sin(L) as follows:

cos(K) = adjacent/hypotenuse = √(17)/9

sin(L) = opposite/hypotenuse = 8/9

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let's bear in mind that on the III Quadrant, sine and cosine are both negative, whilst on the IV Quadrant, sine is negative and cosine is positive, that said

[tex]\cos(\alpha )=\cfrac{\stackrel{adjacent}{3}}{\underset{hypotenuse}{5}}\hspace{5em}\textit{let's find the \underline{opposite side}} \\\\\\ \begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{5}\\ a=\stackrel{adjacent}{3}\\ o=opposite \end{cases} \\\\\\ o=\pm \sqrt{ 5^2 - 3^2} \implies o=\pm \sqrt{ 16 }\implies o=\pm 4\implies \stackrel{IV~Quadrant }{o=-4} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\tan(\beta )=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{3}}\implies \tan(\beta )=\cfrac{\stackrel{opposite}{-4}}{\underset{adjacent}{-3}} \\\\[-0.35em] ~\dotfill\\\\ \tan(\alpha + \beta) = \cfrac{\tan(\alpha)+ \tan(\beta)}{1- \tan(\alpha)\tan(\beta)} \\\\\\ \tan(\alpha + \beta)\implies \cfrac{ ~~\frac{-4}{3}~~ + ~~\frac{-4}{-3} ~~ }{1-\left( \frac{-4}{3} \right)\left( \frac{-4}{-3} \right)}\implies \cfrac{0}{1-\left( \frac{-4}{3} \right)\left( \frac{-4}{-3} \right)}\implies \text{\LARGE 0}[/tex]

(a) The relative rate of growth of the bacterium population is 15% per unit time; (b) the initial population of the culture is 90 bacteria; (c) the culture will contain approximately 239 bacteria at time t=5.

(a) The relative rate of growth of the bacterium population can be calculated by taking the derivative of the function n(t) with respect to t and then dividing it by the value of n(t) at that point, which gives:

relative rate of growth = (dn/dt) / n(t)

= (0.15 * 90[tex]e^0.15t[/tex]) / (90[tex]e^0.15t[/tex])

= 0.15

Therefore, the relative rate of growth is 15%.

(b) The initial population of the culture at t=0 is given by plugging in t=0 in the function n(t):

n(0) = 90[tex]e^0.15[/tex]*0

= 90

Therefore, the initial population of the culture is 90.

(c) The number of bacteria in the culture at time t=5 can be found by plugging in t=5 in the function n(t):

n(5) = 90[tex]e^0.15[/tex]*5

= 385.97 (rounded to two decimal places)

Therefore, the culture will contain approximately 385.97 bacteria at time t=5.

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in a symmetric distribution, the value that could be the median of the distribution must be equal to the mean.

In probability and statistics, the mean and median are two measures of central tendency that are commonly used to describe a data set. The mean, also known as the arithmetic mean or average, is calculated by summing up all the values in the data set and dividing by the total number of values. The median, on the other hand, is the middle value of a data set when the values are arranged in order from lowest to highest.

For a symmetric distribution, the mean and median are the same, because the data values on one side of the mean balance out the values on the other side. In other words, if the distribution is symmetric, then the data values are evenly distributed around the mean.

In this case, if the mean of a symmetric distribution is 130, then the median must also be 130. This is because the median is the middle value of the data set, and in a symmetric distribution, the middle value is the same as the mean.

To illustrate this, consider a simple example of a symmetric distribution with the following values: 125, 130, 135, 140. The mean of this distribution is (125 + 130 + 135 + 140) / 4 = 132.5. However, the median is the middle value of the data set, which is 130. Since the distribution is symmetric, the middle value is the same as the mean.

Therefore, in a symmetric distribution, the value that could be the median of the distribution must be equal to the mean.
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Complete question:- If the mean of a symmetrical distribution is 130, which of these values could be the median of the distribution?

Answer: yes, no, yes, no

Step-by-step explanation:

The ranking from greatest to least goes on Nick, Olivia, Grace, and Brandon.

So in this, we have to rank the person who got most of the candy bars first and that is Nick.

After Nick Olivia has 94 candy bars so she is second in order.

Then on the third Grace had 75 candy bars.

And at the least Brandon is there with 53 candy bars.

Nick sold 100 candy bars

Olivia sold 94 candy bars

Grace sold 75 candy bars

Brandon sold 53 candy bars

Therefore, the ranking from greatest to least is Nick, Olivia, Grace, and Brandon.

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Answer:

1039.23 square inches

Step-by-step explanation:

                      a = 20 inches

    [tex]\sf \boxed{\text{\bf Area of regular hexagon = $\dfrac{3\sqrt{3}}{2}a^2$}}[/tex]

                                                   [tex]= \dfrac{3\sqrt{3}}{2}*20*20\\\\= 3\sqrt{3}*200\\\\= 1039.23 \ inches^2[/tex]

Answer:

Step-by-step explanation:

Let x be the measure of the first angle.

According to the problem, we know that:

The sum of the angles of the triangle is 180: x + y + z = 180

The sum of the second and third angles is five times the measure of the first angle: y + z = 5x

The third angle is 16 more than the second: z = y + 16

We can substitute the third equation into the second equation to get:

y + (y + 16) = 5x

Simplifying this equation, we get:

2y + 16 = 5x

We can rearrange this equation to get:

y = (5/2)x - 8

Now we can substitute this equation and the equation z = y + 16 into the first equation to get:

x + (5/2)x - 8 + (5/2)x + 8 = 180

Simplifying this equation, we get:

6x = 360

Dividing both sides by 6, we get:

x = 60

Now we can use this value of x to find y and z:

y = (5/2)x - 8 = (5/2)(60) - 8 = 58

z = y + 16 = 58 + 16 = 74

Therefore, the measures of the three angles are x = 60, y = 58, and z = 74.

Problems:

Solve for x: 2x - 5 > 9x + 2

Solve for x: 3x + 2 < 7x - 5

Solve for x: 4x + 3 < 2x - 1

Solve for x: -2x - 4 > -8x + 3

Solve for x: 5x + 1 < 2x + 7

Answers:

x < -0.7

x > 1.75

x < -1

x < 0.875

x < 1.2

Answer:  

Example 1

Solve 3x − 5 ≤ 3 − x.

Solution

We start by adding both sides of the inequality by 5

3x – 5 + 5 ≤ 3 + 5 − x

3x ≤ 8 – x

Then add both sides by x.

3x + x ≤ 8 – x + x

4x ≤ 8

Finally, divide both sides of the inequality by 4 to get;

x ≤ 2

Example 2

Calculate the range of values of y, which satisfies the inequality: y − 4 < 2y + 5.

Solution

Add both sides of the inequality by 4.

y – 4 + 4 < 2y + 5 + 4

y < 2y + 9

Subtract both sides by 2y.

y – 2y < 2y – 2y + 9

Y < 9 Multiply both sides of the inequality by −1 and change the inequality symbol’s direction. y > − 9

Solving linear inequalities with subtraction

Let’s see a few examples below to understand this concept.

Example 3

Solve x + 8 > 5.

Solution

Isolate the variable x by subtracting 8 from both sides of the inequality.

x + 8 – 8 > 5 – 8 => x > −3

Therefore, x > −3.

Example 4

Solve 5x + 10 > 3x + 24.

Solution

Subtract 10 from both sides of the inequality.

5x + 10 – 10 > 3x + 24 – 10

5x > 3x + 14.

Now we subtract both sides of the inequality by 3x.

5x – 3x > 3x – 3x + 14

2x > 14

x > 7

Solving linear inequalities with multiplication

Let’s see a few examples below to understand this concept.

Example 5

Solve x/4 > 5

Solution:

Multiply both sides of an inequality by the denominator of the fraction

4(x/4) > 5 x 4

x > 20

Step-by-step explanation:

Hope this helps :3

Using the product rule of logarithms, we can condense the expression as follows:

log(x/3 * y/3 * z/3)

= log((xyz) / 27)

So, the condensed form of the given expression is log((xyz) / 27).

The angles and lines that match the angles and lines in the diagram consisting of two lines and their common transversal to the correct description  are;

Alternate Interior Angles; 2. ∠4 and ∠8

Consecutive Exterior  Angles; 5. ∠1 and ∠6

Alternate Exterior Angles; 3. ∠1 and ∠5

Transversal; line l

Consecutive Interior Angles; 4. ∠3 and ∠4

Corresponding Angles; 1. ∠1 and ∠7

A transversal is a line that intersects two or more other lines.

The description of the relationship between the angles in the question are;

Alternate Interior Angles

Alternate interior angles are a pair of angles formed when a transversal intersects two lines. They are located between the two lines on opposite side of the transversal.

Consecutive Exterior Angles

Consecutive Exterior Angles are a pair of angles formed when a transversal intersects two lines. They are located outside the two lines on the same side of the transversal

Alternate Exterior Angles

Alternate exterior angles are a pair of angles formed when a transversal intersects two lines. They are located outside the two lines on the opposite sides of the transversal.

Consecutive Interior Angles

Consecutive Interior Angles, also known as Same-Side Interior Angles are a pair of angles formed when a transversal intersects two parallel lines. They are located between the two parallel lines on the same side of the transversal.

Corresponding Angles

Corresponding angles are a pair of angles formed when a transversal intersects two lines. They are located on the same relative positions with respect to the transversal and the two lines.

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The area of the region in which the burro can graze will be 833 pi square feet.

Each interior vertex angle of a regular hexagon is (n - 2)·180°/n  =  (6 - 2)·180°o/6  =  120°

I'll break up the area into three sections.

There is one major section, going 150' along one side in a circular arc to 150' along the adjacent side.

Since the interior angle is 120°, the exterior angle will be 240°.

The area of this section will be:  (240°/360°)·pi·radius2  =  (2/3)·pi·1502  =  15,000 pi

Then, on each end, around the corner of the barn, the goat can go in a circular arc with radius = 50'.

This angle will be 60°, or one-sixth or a circle.

The area of each section will be (1/6)·pi·502  =  416 2/3 pi

Total area:  15,000 pi + 416 2/3 pi + 416 2/3 pi  =  833 1/3 pi square feet.

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Answer:

260

Step-by-step explanation:

First you find the area of the triangle

1/2×base×height

1/2×20×10

=100

Then you find the area of the rectangle

A=l×b

=20×8

=160

Then you add the area of the triangle with the area of the rectangle

160+100=260

Randomly selected trip: 24.5% chance > $3000. Sample mean of 30 trips: very small chance > $3000.

Utilizing z-score recipe:

z = (x - μ)/σ

where x is the worth we're keen on, μ is the mean, and σ is the standard deviation.For the primary inquiry:

z = (3000 - 2708)/405 = 0.69

Utilizing a standard typical circulation table or number cruncher, we can track down that the likelihood of getting a z-score more prominent than 0.69 is around 0.245. Consequently, the likelihood that the expense for a haphazardly chosen trip is more than 3000 is around 0.245 or 24.5%.

For the subsequent inquiry:

The example size (n) = 30, and the standard deviation (σ) = 405/sqrt(30) = 74.02 (approx.)

z = (3000 - 2708)/74.02 = 3.94

Utilizing a standard typical dissemination table or number cruncher, we can track down that the likelihood of getting a z-score more prominent than 3.94 is tiny, near 0. Consequently, the likelihood that the mean expense of an example of 30 abroad excursions is more noteworthy than 3000 is tiny.

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The probability that the mean is greater than 3000 is 24.5%

A probability is a number that reflects the chance or likelihood that a particular event will occur.

Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

Given that, the average overseas trip cost 2708 per visitor, assuming a normal distribution with a standard deviation of 405 what is the probability that the cost for a randomly selected trip is more than 3000

z-score:

z = (x - μ)/σ

where μ is the mean, and σ is the standard deviation.

So,

z = (3000 - 2708)/405 = 0.69

Z-score 0.69 = 0.245.

Thus, the likelihood that the expense of the chosen trip is more than 3000 is around 0.245 or 24.5%.

The sample size (n) = 30, and the standard deviation (σ) = 405/√(30) = 74.02 (approx.)

z = (3000 - 2708)/74.02 = 3.94

z-score 3.94 = 0.

Thus, the likelihood that the mean expense of an example of 30 abroad excursions is more noteworthy than 3000 is tiny.

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The range of the function is the set of all real numbers greater than or equal to -2, because the lowest possible value of the function is -2, which occurs at x = 2.

What is a piecewise function ?

A piecewise function is a function that is defined by different equations on different parts of its domain. The graph of a piecewise function consists of several distinct parts, each corresponding to a different equation.

The graph shown is an example of a piecewise function. The function is defined using different equations on different intervals of the domain.

On the interval from negative infinity to negative 2, the function is defined by the equation y = 2. This means that the value of the function is always 2 on this interval, regardless of the value of x.

On the interval from negative 2 to 2, the function is defined by the equation y = -x. This means that the value of the function is equal to the negative of x on this interval.

On the interval from 2 to positive infinity, the function is defined by the equation y = 2. This means that the value of the function is always 2 on this interval, regardless of the value of x.

At the point x = -2, the function experiences a discontinuity, because the two equations that define it have different values at this point. The function is not differentiable at this point, because it does not have a well-defined tangent line.

The domain of the function is the set of all real numbers, because there are no restrictions on the values of x that are allowed.

Therefore, The range of the function is the set of all real numbers greater than or equal to -2, because the lowest possible value of the function is -2, which occurs at x = 2.

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