6th Grade Mathematics Inequalities

Answer:

5 bags will cost $47.09

Step-by-step explanation:

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The numbers that are less than 3/7 are 1/8 and 3/10, while the numbers that are greater than 3/7 are 1/2 and 2/3. The decimal 0.102, which is equivalent to 51/500 as a fraction, is also less than 3/7.

To determine which of the given numbers are less than 3/7, we can convert them to fractions and compare them to 3/7.

12.5% is equivalent to 0.125 as a decimal or 1/8 as a fraction. To compare 1/8 and 3/7, we can convert them to a common denominator. The least common multiple of 8 and 7 is 56, so we can rewrite 1/8 as 7/56 and 3/7 as 24/56. Therefore, 1/8 is less than 3/7.

0.3 is equivalent to 3/10 as a fraction. To compare 3/10 and 3/7, we can also convert them to a common denominator. The least common multiple of 10 and 7 is 70, so we can rewrite 3/10 as 21/70 and 3/7 as 30/70. Therefore, 3/10 is less than 3/7.

50% is equivalent to 0.5 as a decimal or 1/2 as a fraction. To compare 1/2 and 3/7, we can convert 3/7 to a fraction with a denominator of 2. Multiplying the numerator and denominator of 3/7 by 2 gives us 6/14. Therefore, 1/2 is greater than 3/7.

2/3 is already a fraction, and we can compare it directly to 3/7. Multiplying the numerator and denominator of 3/7 by 3 gives us 9/21, and we can see that 2/3 is greater than 3/7.

0.102 is a decimal that is less than 1, but it can also be written as a fraction. To do so, we can place the decimal over 1 followed by the appropriate number of zeros. This gives us 102/1000, which can be simplified to 51/500. To compare 51/500 and 3/7, we can convert them to a common denominator. The least common multiple of 500 and 7 is 3500, so we can rewrite 51/500 as 357/3500 and 3/7 as 1500/3500. Therefore, 51/500 is less than 3/7.

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Answer:

x = 5

Step-by-step explanation:

A zero is another word for an x-intercept, which is where the function crosses the x-axis on a graph. One way to find the x-intercept is by graphing the equation. I did so, and I found that the x-intercept of this function is x=5. I'll attach a photo of the function below.

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Answer:

5.

Step-by-step explanation:

I graphed it on my calculator, and the x intercept of this function is x=5.

Answer: 400 miles

Step-by-step explanation: every hour, his distance decreases by 50 miles. After 4 hours, his distance is 200 miles, so 50 miles times 4 hours = 200 miles+the original 200 miles =400 miles.

Answer: \(26,400\ ft\)

Step-by-step explanation:

Given

Each side of the pentagon measures \(1760\ ft\)

A complete trip is equivalent to the perimeter of the perimeter

\(\Rightarrow \text{Perimeter of the Pentagon P=}5\times 1760\\\Rightarrow P=8800\ ft\)

For Three rounds, he completed a distance of  

\(\Rightarrow P=3\times 8800\\\Rightarrow P=26,400\ ft\)

For dimensions of x =10 and y=5 for the base and height that will make the tank weight as little as possible.

Here we are given the information of a square-based, open-top, rectangular steel holding tank, so here the tank is in the shape of a cuboid and we know  the formula  for :

volume = x*y*z, as  here it is a square base, so the volume will be

volume =  x²*y, where x and y are the dimension of the base and height

So for the  given reason,  

=>x²*y =  500

=> y = 500/x²

Again, the surface area formula  will be

S=x²+4xy, substituting the value of  y in this question

=>S=x²+4x(500/x²)

=>S=x²+2000/x

Differentiating the above formula with respect to x, we get

=>2x-2000/x²=0

=>2x³= 2000

=>x³= 1000

=>x =10

so the substituting the x values of x in  the equation y , we get

y = 500/x²

=>y = 5

so the dimensions are x= 10 and y=5

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By evaluating areas, we calculate that the amount of fencing the gardener needs to purchase is \(8\frac{1}{3}\)

The gardener currently has already fence = \(4\frac{2}{3}\)

Length of one side =\(3\frac{1}{4}\)

Since the square garden has four equal-length sides because it is square, we must multiply the length of one side by four to determine the total length of the fence required:

\(4*(3\frac{1}{4}) = 4*(3+\frac{1}{4} ) = 4*3 + 4*\frac{1}{4} = 12 + 1 = 13\)

13 sq. feet is the total area of the garden.

The gardener already fence \(4\frac{2}{3}\). As a result, we can calculate the remaining amount needed by subtracting the amount needed from the amount the gardener already has. So let's do that:

\(=13 - 4\frac{2}{3} \\=13 - \frac{14}{3}\\ =\frac{39-14}{3} \\=\frac{25}{3} \\=8.33\)

Hence, the amount of fencing the gardener needs to purchase is \(8\frac{1}{3}\)

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Answer:

Step-by-step explanation:

It would be D I think...

The estimated δf for f(x) = 112 * x^2 when a = 2 and δx = -1/2 is approximately -224.

To estimate δf using linear approximation, we will use the formula: δf ≈ f'(a) * δx
Here, f(x) = 112 * x^2, a = 2, and δx = -1/2. First, we need to find the derivative of f(x) with respect to x: f'(x) = d(112 * x^2) / dx = 224 * x

Now, we will find the derivative at the point a: f'(a) = f'(2) = 224 * 2 = 448
Finally, we'll use the linear approximation formula to estimate δf: δf ≈ f'(a) * δx = 448 * (-1/2) = -224

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Answer:

-25

Step-by-step explanation:

The results of the significance test suggest that there is no statistically significant change in the average consumption of sweet snacks among healthy weight children aged 12 to 19 years.

The previous study reported an average consumption of 369.4 kcal/d, with a standard deviation of 10.2 kcal/d. The current study reported an average consumption of 375.2 kcal/d, with a standard deviation of 10.2 kcal/d.

To perform a significance test, we can use the z-score formula:

z = (observed value - mean) / standard deviation

In this case, the observed value is 375.2 kcal/d, the mean is 369.4 kcal/d, and the standard deviation is 10.2 kcal/d. This gives us a z-score of 0.56.

The p-value for a z-score of 0.56 is 0.5696. This means that there is a 56.96% chance of getting a z-score of 0.56 or greater if the null hypothesis is true.

Since the p-value is greater than the significance level of 0.05, we cannot reject the null hypothesis. This means that there is not enough evidence to conclude that there has been a statistically significant change in the average consumption of sweet snacks.

In other words, the results of the current study are consistent with the results of the previous study. There is no evidence to suggest that the average consumption of sweet snacks has changed in the past four years.

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Here, we have two pairs of similar triangles.

Let's find the values of x and y.

• Sol,vin,g for x:

Given:

Length of longer base = 9

Length of shorter base = 5

Length of smaller leg = 8

Let's solve for x.

Since the triangles are similar, the corresponding sides will be in proportion.

To solve for x, apply the proportionality equation:

Cross multiply and solve for x:

• Solving for y:

Given:

Length of longer base = 3

Length of longer leg = 6

Length of smaller leg = 4

Length of total base = y

To solve for y, we have the equation:

Cross multiply and solve for y:

ANSWER:

• x = 12

• y = 5

The number of ways to choose 5 people from a total of 15 people is given by 15C5. This can be calculated as follows:15C5 = (15!)/((15-5)! * 5!) = (15 * 14 * 13 * 12 * 11)/(5 * 4 * 3 * 2 * 1) = 3003Therefore, there are 3003 ways to select a committee of 5 people from the group of 15 people. The probability of selecting any given committee is 1/3003.

There are a total of 15 people in the group. A committee of size 5 is to be chosen from a group of 7 men and 8 women randomly. Therefore, the sample space for this situation is 15C5 ways to choose 5 people from a total of 15 people. 15C5 = 3003 ways. That means there are 3003 ways to select 5 people from the group of 15 people. The probability of selecting any given committee is 1/3003. That means the probability of selecting any one committee out of 3003 committees is 1/3003.To compute the probability of selecting any given committee, we first need to determine how many possible committees can be formed from the group of 15 people. The number of ways to choose 5 people from a total of 15 people is given by 15C5. This can be calculated as follows:15C5 = (15!)/((15-5)! * 5!) = (15 * 14 * 13 * 12 * 11)/(5 * 4 * 3 * 2 * 1) = 3003Therefore, there are 3003 ways to select a committee of 5 people from the group of 15 people. The probability of selecting any given committee is 1/3003.

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If the experiment uses a sample of university students, it would likely not have a  a. external validity.

External validity refers to the extent to which the findings from a study can be generalized to a larger population or real-world settings.

If an experiment uses a sample of graduate college students to study how consumers choose life insurance policies,

It is likely that the findings may not accurately represent the broader population of consumers.

Graduate college students may have different characteristics, preferences,

And decision-making processes compared to the general population when it comes to life insurance policies.

Laboratory validity (b), internal validity (c), and extraneous validity (d) are not relevant to the issue of representativeness of the sample.

Laboratory validity refers to the extent to which the experimental conditions accurately represent real-world situations.

Internal validity refers to the extent to which the experiment allows for causal inferences within the study itself.

Extraneous validity is not a recognized term in experimental design.

Therefore, the correct answer for an experiment uses a sample of university students is a. external validity.

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The above question is incomplete, the complete question is:

an experiment is designed to test how consumers go about choosing life insurance policies. if this experiment uses a sample of graduate college students, it would likely not have an experiment is designed to test how consumers go about choosing life insurance policies. if this experiment uses a sample of graduate college students, it would likely not have a. external validity b. laboratory validity c. internal validity d. extraneous validity e. it would have all of these

Answer:

divide all terms by same numeral

Step-by-step explanation:

4x-6y+16

2x-3y+8

Answer:

The answer is C.   16(0.5x-0.75y+2)

Step-by-step explanation:

I just got it correct on e d g e n u i t y!!!!!!!!!!!!!!!!!

Also the math the do it is this. Take the first answer for example. because of the parentheses you are going to take the number out side of the parentheses and multiply it by the numbers that are in the parentheses. So lets apply this.  

1st Example... 16(0.5x-4y+32)  

16 * 0.5x (When using a calculator just put in 16*0.5) The answer is 8 add on the x so it is 8x. 16*4y= 64y 16*32= 512. Then when you add symbols in you turn out with an answer for 1 that should look like this... 8x-64y+512 That is not equivalent to 8x-12y+32. So this is not the correct answer. (Because it isn't equivalent)

2nd Example... You can narrow down the search and make it easier if you do this... There is still a 32 in it and multiplying 32 and 16 will always equal 512 so you know it is not the second answer.

3rd Example... The third example Is correct because 1 all the other answers aren't lol. and 2 because the math steps are correct I will show you.  16(0.5x-0.75y+2)   16*0.5x=8x   16*0.75y=12y (looking pretty good!!) 16*2= 32!!

So in an equation it looks like this... 8x-12y+32 Thus leading us to the answer that the third option(Option C. ) Is correct!!

4th Example... This can not be correct because you are looking for an answer with 12y and 4y*16 will always equal 64y so it cannot be this answer.

KEY= * is the times symbol!!

Also if you want to right great answers like this put in an extra little bit of effort to learn the material and you will be golden in no time at all!!!

Have a great day!!!!

Also can I have a five star a thank you and a Brainliest it would really make my day! UwU

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The data analyst should a)investigate the outlier to determine if it can lead to any important observations and b)use a filter to highlight the outlier, as it is more important than the rest of the data.

When analyzing data, it is important to look at outliers as they can provide valuable information. Outliers can point to an unexpected correlation or reveal a hidden trend that could be missed if they were removed. By investigating the outlier, a data analyst can look for any important observations the outlier might reveal.

Additionally, using a filter to highlight the outlier allows the analyst to focus on the outlier and compare it to the other data points. This can help the analyst to understand how the outlier differs from the rest of the data and draw any relevant conclusions.

Removing the outlier should be avoided as it can lead to data bias and remove important information from the analysis.

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Answer:

The probability is \(P(|p-\^{p}| >  0.03)  =   0.0040\)

Step-by-step explanation:

From the question we are told that

   The population proportion is \(p =  0.07\)

   The mean of the sampling distribution is   \(\mu_p =  0.07\)

   The sample size is n = 600

Generally the standard deviation is mathematically represented as

     \(\sigma_p  =  \sqrt{\frac{p (1 -p)}{n} }\)

=>    \(\sigma_p  =  \sqrt{\frac{0.07(1 -0.07)}{600} }\)    

=>    \(\sigma_p  =  0.010416 \)    

Generally the probability that the proportion of airborne viruses in a sample of 600 viruses would differ from the population proportion by greater than 3% is mathematically represented as

      \(P(|p-\^{p}| >  0.03) =  1 - P(|p -\^{p}| \le 0.03)\)

=>   \(P(|p-\^{p}| >  0.03)  =  1 -  P(-0.03 \le p -\^{p} \le 0.03 )\)

Now  add p  to  both side of the inequality

=>   \(P(|p-\^{p}| >  0.03)  =  1 -  P( 0.07-0.03  \le \^{p} \le 0.03+ 0.07 )\)

=>   \(P(|p-\^{p}| >  0.03)  =  1 -  P(0.04 \le \^{p} \le 0.10 )\)

Now  converting the probabilities to their respective standardized score

=> \(P(|p-\^{p}| >  0.03)  =  1 -  P(\frac{0.04 - 0.07}{0.010416}  \le Z \le \frac{0.10 -0.07}{0.010416}  )\)

=> \(P(|p-\^{p}| >  0.03)  =  1 -  P(-2.88  \le Z \le 2.88 )\)

=>   \(P(|p-\^{p}| >  0.03)  =   1 - [P(Z \le 2.88) - P(Z \le -2.88)]\)

From the z-table  

       \(P(Z \le 2.88)  =  0.9980\)

and

       \(P(Z \le -2.88)  = 0.0020\)

So

     \(P(|p-\^{p}| >  0.03)  =   1 - [0.9980 - 0.0020]\)

=>   \(P(|p-\^{p}| >  0.03)  =   0.0040\)

Answer:

Step-by-step explanation:

I typed the wrong answer and I cant delete so dont do it at all

In the given right triangle, one leg has a length of 6 cm and the other leg has a length of 8 cm. Since it is a right triangle, you can use the Pythagorean theorem to find the length of the hypotenuse: a² + b² = c². In this case, a = 6 and b = 8.

6² + 8² = 36 + 64 = 100. Taking the square root of both sides, we get c = 10 cm. So, the hypotenuse of the triangle is 10 cm.

Now, let's denote the length of one side of the square as s. Since the square has a vertex on each of the two legs of the triangle and one side on the hypotenuse, we can form two similar right triangles within the triangle. The ratio of their sides will be the same.

For the smaller right triangle formed, the length of the leg along the 6 cm side is s, and the length of the leg along the 8 cm side is (8 - s). The ratio of the sides in this triangle to the original triangle is s/6 = (8 - s)/8.

Cross-multiplying, we get:

8s = 6(8 - s)
8s = 48 - 6s
14s = 48
s = 48/14

Simplifying the fraction, we get:

s = 24/7 cm

So, the length of one side of the square is 24/7 cm.

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The value of the expression tan(-5π/6) can be determined using trigonometric properties and  identities.

First, let's consider the unit circle. The angle -5π/6 is measured in the clockwise direction from the positive x-axis. In this position, the reference angle is π/6, which is the positive angle formed with the x-axis.

The tangent function (tan) is defined as the ratio of the sine (sin) of an angle to the cosine (cos) of the angle. Using the reference angle π/6, we can determine the value of tan(π/6) as the ratio of sin(π/6) to cos(π/6). sin(π/6) equals 1/2, and cos(π/6) equals √3/2. Therefore, tan(π/6) is (1/2) divided by (√3/2), which simplifies to 1/√3 or √3/3. Since tan is an odd function, tan(-5π/6) is equal to the negative of tan(5π/6). Therefore, tan(-5π/6) has the same value as -√3/3.

In conclusion, the value of tan(-5π/6) is -√3/3, which means that the tangent of the angle -5π/6 is negative and equal to the ratio of -√3 to 3.

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Answer and Step-by-step explanation:

These triangles are similar by AA.

This is because the point that connects the triangles together have the same angle value. We also see that they both have 90 degrees as an angle, making it similar by AA~.

The other angle that shows the 38 in it is 52, so it is definitely proven by AA~.

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The maximum profit is achieved when approximately 312.5 units of lab equipment are sold.

The revenue function R(x) represents the amount of money the company earns from selling x units of lab equipment. It is given by the equation:

R(x) = -0.32x^2 + 270x

The costs function C(x) represents the expenses incurred by the company for producing and selling x units of lab equipment. It is given by the equation:

C(x) = 70x + 52

To determine the company's profit, we subtract the costs from the revenue:

Profit = Revenue - Costs

P(x) = R(x) - C(x)

Substituting the given revenue and costs functions:

P(x) = (\(-0.32x^2 + 270x)\) - (70x + 52)

Simplifying the equation:

P(x) = -0.32x^2 + 270x - 70x - 52

P(x) = -\(0.32x^2\)+ 200x - 52

The profit function P(x) represents the amount of money the company makes from selling x units of lab equipment after deducting the costs. It is a quadratic function with a negative coefficient for the x^2 term, indicating a downward-opening parabola. The vertex of the parabola represents the maximum profit the company can achieve.

To find the maximum profit and the corresponding number of units sold, we can use the vertex formula:

x = -b / (2a)

For the profit function P(x) = -\(0.32x^2 + 200x\)- 52, a = -0.32 and b = 200.

x = -200 / (2 * -0.32)

x = 312.5

Therefore, the maximum profit is achieved when approximately 312.5 units of lab equipment are sold.

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Answer:

Angle MJK = 64°

Step-by-step explanation:

In ∆MJL & ∆LJK,

JL= JL ...(common side)

Angle JML = Angle JKL ....( each 90°)

MJ = JK ....( Both measures 7)

Hence, by SAS criteria, ∆ MJL = ∆ LJk

.°. by C.P.C.T , ∠MJL = ∠LJK = 32°

Also,

∠MJK = ∠MJL+∠LJK

∠MJK = 32°+32°

The cost of goods sold for the period is $748,400.By accurately calculating the cost of goods sold, businesses can make informed decisions regarding pricing, inventory management, and overall financial performance.

To calculate the cost of goods sold (COGS), we add up the values provided in the data:

COGS = $246,800 + $242,800 + $258,800

= $748,400

The cost of goods sold for the period, based on the given data, is $748,400. The COGS represents the direct costs incurred by a company to produce the goods sold during a specific period. It includes the cost of raw materials, direct labor, and other direct production expenses.

Accurately calculating the COGS is crucial for financial analysis and decision-making. By subtracting the COGS from the total sales revenue, we obtain the gross profit, which is a key indicator of a company's profitability. The COGS also helps determine the company's gross margin, which indicates the percentage of revenue that remains after accounting for the cost of producing goods.

For effective inventory management, it is important for businesses to monitor and control their COGS. It allows them to assess the efficiency of their production processes, identify cost-saving opportunities, and evaluate pricing strategies. Additionally, tracking the COGS helps businesses determine the profitability of specific product lines or services.

The COGS provides valuable insights into a company's operational efficiency and profitability.

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Step-by-step explanation:

180 degrees is (-a, -b) and 360 is (a, b). 360 degrees doesn't change since it is a full rotation or a full circle. Also this is for a counterclockwise rotation. If you want to do a clockwise rotation follow these formulas: 90 = (b, -a); 180 = (-a, -b); 270 = (-b, a); 360 = (a, b)

Answer:

Condition:

If a series converges, then the terms of the series approach 0.

Converse:

If the terms of a series approach 0, then the series converges.