Hello guys. If you could help me with this one question you shall get 80 whole points!

After solving the given inequality question, we will get  x < -9.

A mathematical sign for comparing two values or expressions is an inequality symbol. Inequality symbols include: (less than), > (greater than), (less than or equal to), and (greater than or equal to). Inequalities can be used to represent connections between two or more variables, for as 5 10 indicating that 5 is less than 10. Inequalities can also be used to define mathematical equations or to describe connections between variables. The equation x + 2 7 can, for example, be used to represent the relationship between x and 7, or to communicate that the value of x must be less than 5 for the equation to be true.

In the given question,

2/3x + 2y < -1/3x + 1

⇒ 2/3x + 2y - (-1/3x + 1) < 0

⇒ 5/3x + 3 < 0

⇒ 5/3x < -3

⇒ x < -9

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In part (a), we used the Central Limit Theorem (CLT) to approximate the sampling distribution of the sample mean. The CLT states that, under certain conditions, the sampling distribution of the sample mean will be approximately normal, regardless of the population distribution.

The conditions for the CLT are:

The sample is randomly drawn from the population.

The sample size is large (usually, n >= 30 is considered large enough).

The samples are independent.

In this case, we assume that the sample was randomly drawn from the population of diameters, and the sample size of 25 is large enough to satisfy the second condition. The samples are assumed to be independent, as we are sampling without replacement from a large population.

Therefore, we can apply the CLT and use the normal distribution to approximate the sampling distribution of the sample mean.

For a sample of size 2, the sample mean will still have a sampling distribution, but the CLT may not be applicable. If the population distribution is highly skewed or has heavy tails, a sample size of 2 may not be sufficient to smooth out the sampling distribution, and it may not be normal.

In this case, a normal approximation may not be appropriate, and other methods, such as bootstrapping or permutation tests, may be more appropriate for inference.

In summary, the normal approximation based on the CLT is valid for large sample sizes, regardless of the population distribution. For small sample sizes, other methods may be more appropriate, and the normal approximation may not be valid if the population distribution is highly skewed or has heavy tails.

Question: The basal diameter of a sea anemone is an indicator of its age. The density curve shown here represents the distribution of diameters in a certain large population of anemones; the population mean diameter is 4.2cm, and the standard deviation is 1.4cm.

Let Y dash represent the mean diameter of 25 anemones randomly chosen from the population.

(a) Find the approximate value of Pr{4 ≤ Ydash ≤ 5}.

(b) Why is your answer to part (a) approximately correct even though the population distribution of diameters is clearly not normal? Would the same approach be equally valid for a sample of size 2 rather than 25?Why or why not?

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Answer:

( [tex]-\frac{1}{3}[/tex] , [tex]-\frac{41}{21}[/tex] )

Step-by-step explanation:

Answer:

Step-by-step explanation:

14 doughnuts in total

Let's call the time it takes to install all the chairs from start to finish "t". The workers install 840 chairs per day, so in "t" days they will have installed 840 * t chairs.

At the end of 5 days, they still have 240 chairs to install, so they have installed 840 * 5 chairs so far. We can use this information to write an equation:

840 * t - 840 * 5 = 240

Expanding and simplifying the equation gives us:

840t - 4200 = 240

Adding 4200 to both sides gives us:

840t = 4440

Finally, dividing both sides by 840 gives us:

t = 5.2857142857...

So it takes approximately 5.29 days to install all the chairs from start to finish.

A heavy rope, 30 ft long, weighs 0.7 lb/ft and hangs over the edge of a building 80 ft high, the work done in pulling the rope to the top of the building is 1785 ft-lb.

To calculate the work done in pulling the rope to the top of the building, we need to use the formula:

W = F x d

where W is the work done, F is the force applied, and d is the distance over which the force is applied.

In this problem, we can calculate the force required to pull the rope as the product of its weight per unit length (0.7 lb/ft) and the length of the rope (30 ft). Thus, the force required is:

F = 0.7 lb/ft x 30 ft = 21 lb

To calculate the distance over which the force is applied, we need to calculate the total length of the rope that needs to be lifted. This can be found using the Pythagorean theorem, as follows:

l = √(30^2 + 80^2) = 85 ft

So the distance over which the force is applied is 85 ft.

Now we can substitute the values for F and d into the formula for work to get:

W = F x d = 21 lb x 85 ft = 1785 ft-lb

This calculation shows how the formula for work can be used to calculate the energy required to lift an object against gravity over a given distance.

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Answer:

The correct answer would be 3693

Step-by-step explanation:

9 + 180 + 2,700 + 804

3693

1200 pages were numbered using a total of 3693 digits.

Total digits equal =  the digits in the 1 - digit page numbers + the 2 digit page numbers - digit page numbers  + 3 digit page numbers - digit page numbers.

Then simplify,

9 + 180 + 2,700 + 804

= 3693

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Answer:

Step-by-step explanation:

87.5% = 87.5/100 = 875/1000= 7/8

The equation 2 and 3 would not present linear functions.

What is linear function?

A linear function is one in which the maximum power of the variables is one.

A linear function is a function that has the form f(x) = mx + b, where m and b are constants. In other words, a linear function is a straight line when plotted on a graph.

Out of the given relationships, the following do not represent a linear function:

2) The ant population for a colony that begins with 5 ants and doubles in number every two weeks.

This relationship is not linear because the rate of change (the number of ants per unit time) is not constant. The number of ants increases exponentially, which results in a curve rather than a straight line when plotted on a graph.

3) A history student's grade on a test that begins at 100 but decreases by 4 points for each question answered incorrectly.

This relationship is not linear because the rate of change (the decrease in points per incorrect question) is not constant. The decrease in points results in a curve rather than a straight line when plotted on a graph.

The other two relationships do represent linear functions.

Therefore, The equation 2 and 3 would not present linear functions.

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A two-tailed test is a hypothesis test in which the rejection region is option (B) in both tails of the sampling distribution

The hypothesis test is defined as the statistic approach checking the results of a research study support a particular theory when we apply that result to population

A two-tailed test is a hypothesis test that defined in which the critical area of the distribution is two sided, so the sample will be greater than or less than a certain range of values

Therefore, the rejection region of a two-tailed test is a hypothesis test is in both tails of the sampling distribution.

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The number of strings where exactly two of the ones are next to each other, while the third one is not next to the other two, is (n-1) x (n-2).

In combinatorics, one of the fundamental concepts is counting the number of strings or sequences of symbols that satisfy certain conditions.

Let us first consider the case where the two ones that are next to each other are at the beginning of the string. In this case, we can place the third one in any of the remaining positions, which are n-2, where n is the total length of the string. Therefore, the number of such strings is (n-2).

Similarly, if the two ones are at the end of the string, we can place the third one in any of the n-2 remaining positions, and the number of such strings is again (n-2).

Now let us consider the case where the two ones are in the middle of the string. In this case, we can place the two adjacent ones in (n-2) ways, and the third one can be placed in any of the remaining n-3 positions, since it cannot be adjacent to the other two ones. Therefore, the number of such strings is (n-2) x (n-3).

To get the total number of strings that satisfy the given condition, we need to add up the number of strings in each of the three cases:

Total number of strings = (n-2) + (n-2) + (n-2) x (n-3)

Simplifying this expression, we get:

Total number of strings = (n-1) x (n-2)

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Answer:

-1/2-4x/5=1/2-2x

Starting from the left side, we can simplify:

-1/2 - 4x/5 = 1/2 - 2x

Next, we can isolate x by adding 2x to both sides:

-1/2 - 4x/5 + 2x = 1/2 - 2x + 2x

-1/2 + 2x/5 = 1/2

Adding 1/2 to both sides:

0 + 2x/5 = 1

Finally, solving for x:

2x/5 = 1

Multiplying both sides by 5:

2x = 5

Dividing both sides by 2:

x = 5/2

7x² + 9x² = -6x² - 7x

Combining like terms:

16x² = -6x² - 7x

Adding 6x² to both sides:

22x² = -7x

Dividing both sides by -7:

-22x²/-7 = 7x/-7

-22x²/7 = -7x/7

-22x²/7 = -x

Multiplying both sides by -7:

22x² = x

Dividing both sides by 22:

x² = x/22

Since this equation states that x² equals x divided by 22, it has no real solutions for x.

-7x² + 6 = x² - 7x²

Combining like terms:

-8x² + 6 = 0

Adding 8x² to both sides:

-8x² + 8x² + 6 = 0 + 8x²

6 = 8x²

Dividing both sides by 8:

6/8 = 8x²/8

3/4 = x²

Taking the square root of both sides:

sqrt(3/4) = sqrt(x²)

x = +/- sqrt(3/4)

Answer:

Step-by-step explanation:

6(x + 4)/5(x - 7) * 9(x - 7)/7(x + 4) =

Cancel the x + 4 and x - 7

54/35

The best describes EB is diameter of circle because it is a chord of circle which passes through the center.

A circle is a two-dimensional object made up of points that are spaced out from a given point (centre) on the plane by a fixed or constant distance (radius). The fixed point is referred to as the circle's origin or centre, and the fixed distance between each point and the origin is referred to as the radius.

The following components make up a circle:

Circumference: Also known as a circle's perimeter, circumference is the distance a circle travels around its circumference.

Radius: The radius is the distance a circle's center is from any point on its edge.

A diameter is a straight line that links two places on the circle's edge and passes through the center.

So that EB is describes as diameter of circle because it is a chord of circle which passes through the center.

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A histogram would be the most appropriate graphical display to present data by grouping the results into groups of 25 cm.

A histogram is a graphical representation of data that shows the distribution of a set of continuous data by dividing the data into bins (or intervals) and showing the frequency of observations within each bin. The histogram provides a visual representation of the distribution of data, showing the shape, central tendency, and spread of the data.

In this case, the farmer has measured the height of every tree in a large orchard in centimeters and wants to present the data in groups of 25 cm. To create a histogram for this data, the first step would be to divide the data into bins, or intervals, of 25 cm.

Once the bins are created, the next step is to count the number of observations (tree heights) that fall within each bin. This information can be represented as a bar graph, where the height of each bar represents the frequency of observations within the corresponding bin.

By presenting the data in this way, the farmer can easily see the distribution of tree heights in the orchard. The shape of the histogram can indicate whether the data is symmetrical, skewed, multimodal, or uniform.

The central tendency of the data can be determined by looking at the peak of the histogram, which represents the most frequent range of tree heights. The spread of the data can be determined by looking at the width of the histogram and the range of tree heights represented.

In conclusion, a histogram is the most appropriate graphical display to present the results of the tree heights in groups of 25 cm because it provides a visual representation of the distribution of the data and allows the farmer to see the shape, central tendency, and spread of the tree heights in the orchard.

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The function g(x) can be written as -

g(x) = f(x - 1)

Graph translation is a process of moving the graph over the dimensional plane either vertically, horizontally or both.

A translation can take place either horizontally or vertically as -

Given are the graphs of exponential functions f(x) and g(x).

We can write the exponential function g(x) as -

g(x) = f(x - 1)

Therefore, the exponential function g(x) can be written as -

g(x) = f(x - 1).

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Create a proportion using the given information to determine how long it will take for Cheryl's phone battery to totally drain. Total time divided by the remaining charge's percentage equals the remaining time (total charge)

Enter these values because Cheryl is aware that the battery will continue to operate for 1.5 hours at a 55% charge. 1.5 / 0.55 = (total time) / 1 = (total time) / (total charge) (amount of time left) / (remaining percentage of the charge)

When we calculate the total amount of time, we get:

Time: 2.727 hours (1.5 / 0.55 × 1) * 1

To determine how long the battery will survive after fully charged, we may simply reverse the rate of discharge:

Total time / Total charge / (time left) / 1 = Total time / 100 (time left) = Total time / 100 (time left) (percent charge remaining)

The battery's lifespan after being completely charged is as follows:

(Total time) / 100 divided by the remaining time gives us 2.727 / 100 or 0.02727 hours.

As a result, after 1.64 minutes, or 0.02727 hours, Cheryl's phone battery will be fully charged.

Therefore,  It takes 2.727 hours for Cheryl's phone battery to totally drain at a constant rate.

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Answer:

Therefore, the correct answer is (a) 24.52 cm^2.

Step-by-step explanation:

To find the area of the figure, we need to find the area of the two triangles and the trapezoid and add them together.

The top triangle has a base of 5 cm and a height of 2.7 cm, so its area can be found by multiplying the base by the height and dividing by 2: (5 * 2.7) / 2 = 13.5 cm^2.

The bottom triangle has a base of 3 cm and a height of 2.7 cm, so its area can be found by multiplying the base by the height and dividing by 2: (3 * 2.7) / 2 = 4.05 cm^2.

The trapezoid has a base of 5 cm, a top length of 6.8 cm, and a height of 3.4 cm, so its area can be found using the formula for the area of a trapezoid: ((5 + 6.8) / 2) * 3.4 = 20.06 cm^2.

The total area of the figure is the sum of the areas of the three shapes: 13.5 + 4.05 + 20.06 = 37.61 cm^2.

Therefore, the correct answer is (a) 24.52 cm^2.

Since angle S is 65°, angle Y will also be 65°

Similar shapes are shapes that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

Since quadrilateral QRST is similar to quadrilateral WXYZ, then angle Q = angle W , angle R = angle X and angle S = angle Y and angle T = angle Z.

Since angle S is 65° from the diagram shown, angle will be measured as 65°.

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2 , 3, 5 all are that prime of 30

5×6

Answer: Yes, No, No, Yes, No

Step-by-step explanation:

I think Graphing is the best way to tackle this. But I prefer algebra:

A) 2(-8) + 6(7) = 26

-16 + 42 = 26

26 = 26

The answer for A is Yes. I wont show work for the others, i think its pretty intuitive, (just substitute the coordinates for x and y, and check if the resulting statement is true)

B. No

C. No

D. Yes

E. No

The expression when completed is 0.9 [<] 0.95

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

9 10 19 20​

Rewrite the expression properly

So, we have the following representation

9/10 [ ] 19/20​

Next, we evaluate the expressions

This gives

0.9 [ ] 0.95

0.9 is less than 0.95

So, we have

0.9 [<] 0.95

The above represents the complete statement

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Answer:

85

Step-by-step explanation:

The vertical line that y is on adds up to 180 so if we take 180 - the number we already know (95) we get 85

The number line for a < 3 is as shown in the figure below and we use an open circle on 3 and all the numbers to the left of 3 in the number line will be the values of a.

What is a number line?

A number line is a representation of a graduated straight line that is used to represent real numbers visually. It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point. The endpoints of this line go on forever.

We can see the values that inequality represents by placing them on a number line. On a number line, inequalities are represented by drawing a straight line and designating the endpoints with either an open or closed circle. An empty circle indicates that the value is not included. A closed circle indicates that the value is included.

Given the inequality a < 3.

This means that the value of a is less than three and does not include three.

Therefore we use an open circle on 3 and all the numbers to the left of 3 in the number line will be the values of a.

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The work done in pulling the rope up 10 ft is 864 ft-lbs, calculated by multiplying the rope's weight (72 lbs) by the distance (10 ft) it was lifted.

Work done = Weight x Distance

Work done = 72 lbs x 10 ft

Work done = 720 ft-lbs

Additional work done for weight of rope = Weight of rope x Distance

Additional work done for weight of rope = 90 x 10

Additional work done for weight of rope = 900 ft-lbs

Total work done in pulling the rope up 10 ft = 720 ft-lbs + 900 ft-lbs

Total work done in pulling the rope up 10 ft = 864 ft-lbs

The work done in pulling the rope up 10 ft is calculated by multiplying the weight of the rope (72 lbs) by the distance (10 ft) it was lifted. This gives us a result of 720 ft-lbs. However, since the rope is 90 ft long, we must also take into account the additional weight of the rope beyond the 10 ft that was lifted. So, we multiply the weight of the rope (90 lbs) by the distance (10 ft) to get an additional work done of 900 ft-lbs. Adding the two results together gives us 864 ft-lbs of work done in pulling the rope up 10 ft. This shows that the heavier a rope is, the more work must be done to lift it.

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The third side is between 7 and 17 inches long.

This theorem states that for any triangle, the sum of the lengths of the first two sides will always be greater than the length of the third side.

A triangle's two sides have lengths of 5 and 12 inches.

According to the triangle Inequality (theorem), any triangle's two sides must add up to more than its third side.

The length of the third side will be,

5 + 12 = 17 inches

It is to be noted that the difference between the two sides cannot be less on the third side.

The third side must be greater than,

12 – 5 = 7 inches.

As a result, the third side's length ranges from 7 to 17 inches.

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