HELP ASAP ! Write a function rule for the table.

A. ƒ(x) = 3x

B. ƒ(x) = x + 3

C. ƒ(x) = –3 – x

D. ƒ(x) = x – 3

As per the properties of parallel lines and interior alternate angles postulate, we can prove that:

⇒ m ∠5+ m ∠2+ m ∠6 = 180°

Given that;

Line y || z

i.e. y is parallel to z.

To Prove:

⇒ m ∠5+ m ∠2+ m ∠6 = 180°

Since, It is given that the lines y and z are parallel to each other.

m∠5, m∠1 are interior alternate angles because lines y and z are parallel and one line AC cuts them.

So, m∠5 = m∠1  ..... (1)

Similarly,

m∠6, m∠3  are interior alternate angles because lines y and z are parallel and one line AB cuts them.

So, m∠6 = m∠3  ...... (2)

Now, we know that the line y is a straight line and A is one point on it.

Sum of all the angles on one side of a line on a point is always equal to 180 degree .

i.e. ⇒ m ∠1+ m ∠2+ m ∠3 = 180°

Using equations (1) and (2):

We can see that:

⇒ m ∠5+ m ∠2+ m ∠6 = 180°

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The most appropriate statistical test to determine if there is a difference in history of fracture in the past 5 years between 60-year-old men with normal bone density, those with osteopenia, and those with osteoporosis is the chi-square test for independence.

       The chi-square test for independence is used to determine whether there is a relationship between two categorical variables. In this case, the two variables are bone density (normal, osteopenia, osteoporosis) and history of fracture in the past 5 years (at least once or none). The test determines if there is a significant association between these two variables, and if so, how strong the association is. The null hypothesis is that there is no association between the two variables, while the alternative hypothesis is that there is a significant association. The test calculates a chi-square statistic and a p-value, which is compared to a significance level to determine if the null hypothesis should be rejected.

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The most appropriate statistical test to determine if there is a difference in history of fracture in the past 5 years between 60-year-old men with normal bone density, those with osteopenia, and those with osteoporosis is the chi-square test for independence.

      The chi-square test for independence is used to determine whether there is a relationship between two categorical variables. In this case, the two variables are bone density (normal, osteopenia, osteoporosis) and history of fracture in the past 5 years (at least once or none). The test determines if there is a significant association between these two variables, and if so, how strong the association is. The null hypothesis is that there is no association between the two variables, while the alternative hypothesis is that there is a significant association. The test calculates a chi-square statistic and a p-value, which is compared to a significance level to determine if the null hypothesis should be rejected.

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Census data comparing earnings by gender and race can be used to provide evidence of discrimination or lack thereof.

However, it is important to interpret this data cautiously as there may be factors beyond discrimination that contribute to observed differentials. Culture and individual choice are two such factors. For example, certain cultural norms may dictate that women and minorities pursue lower-paying careers, or that they prioritize family responsibilities over career advancement. Similarly, individual choices such as level of education, experience, and negotiation skills can also contribute to differences in earnings.
While caution must be exercised when interpreting census data, there is still evidence to suggest that discrimination does exist. For instance, studies have shown that even when controlling for factors such as education and experience, women and minorities still earn less than their white male counterparts. This suggests that there are systemic barriers preventing these groups from achieving equal pay. Moreover, the fact that certain industries and occupations are dominated by men and have wider pay gaps also suggests discrimination.
However, it is also important to acknowledge that these issues are politically sensitive and can be difficult to address. Some may argue that affirmative action policies aimed at promoting diversity and equal pay are discriminatory against white men. Others may argue that there are no barriers to equal pay, and that individuals should be responsible for their own career choices. Ultimately, the interpretation of census data should be based on a nuanced understanding of all these factors.

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The speed is 3.6 meters per second.

Given that Laura ran 1 km in 4 minutes and 37 seconds.

We know that, 1 km =1000 meters

1 minute =60 seconds

So, 4 minutes and 37 seconds

We know that one minute is equal to sixty seconds

So let us convert four minutes to seconds by multiplying four with sixty seconds

= 4×60 +37

When four is multiplied with sixty we get two hundred forty

= 240+37

= 277 seconds

4 minutes and 37 seconds is equal to two hundred seventy seven seconds.

Now, the formula for speed is distance by time

Speed = Distance/Time

Distance =1000 and time is 277

= 1000/277

= 3.6 meters per second

Therefore, the speed is 3.6 meters per second.

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Laura ran 1 km in 4 minutes and 37 seconds. What was her speed in metres per second (m/s)? If your answer is a decimal, give it to 1 d.p.​

Answer: 8

Step-by-step explanation:

9+10+6+7=32

32/4=8

The solution to the given differential equation is:ln|1/√(1 - y^2) + y/√(1 - y^2)| = x + C where C is the constant of integration.

To solve the differential equation dy/dx = x/(1 - y^2) by separation of variables, we can rewrite it as:

(1 - y^2) dy = x dx

Now we can separate the variables by bringing all the y-related terms to one side and x-related terms to the other side:

(1 - y^2) dy = x dx

1/(1 - y^2) dy = x dx

Integrating both sides with respect to their respective variables, we get:

∫1/(1 - y^2) dy = ∫x dx

To integrate the left side, we can use partial fraction decomposition or trigonometric substitution. Let's use the latter approach:

Using the substitution y = sin(theta), we have dy = cos(theta) d(theta) and (1 - y^2) = (1 - sin^2(theta)) = cos^2(theta). The integral becomes:

∫1/cos^2(theta) * cos(theta) d(theta) = ∫sec(theta) d(theta) = ln|sec(theta) + tan(theta)| + C

Now, we need to substitute back y = sin(theta):

ln|sec(theta) + tan(theta)| + C = ln|sec(arcsin(y)) + tan(arcsin(y))| + C = ln|1/√(1 - y^2) + y/√(1 - y^2)| + C

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Answer:

reflect the parent function over the y-axis, and translate it 3 unit to the left

[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=158055.04\\ h=78 \end{cases}\implies 158055.04=\cfrac{\pi r^2(78)}{3} \\\\\\ (3)158055.04=78\pi r^2\implies \cfrac{(3)158055.04}{78\pi }=r^2 \\\\\\ \sqrt{\cfrac{(3)158055.04}{78\pi }}=r\implies \sqrt{\cfrac{(3)158055.04}{78(3.14) }}=r\implies 44=r[/tex]

The correct choice for the transformation of the function f (x) = (x + 3)² from the parent function f (x) = x² is,

⇒ Horizontal translation.

Since, A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

Here, Parent function is,

⇒ f (x) = x²

And, After translation the function is,

⇒ f (x) = (x + 3)²

Now, We can draw the graph of both function.

Hence, By graph we get;

The correct choice for the transformation of the function f (x) = (x + 3)² from the parent function f (x) = x² is,

⇒ Horizontal translation.

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The repeating decimal 11.454545... can be expressed as the ratio of two integers: 1134/99.Simplifying the fraction, if possible, we find that:1134/99 = 114/11Hence, the repeating decimal 11.454545... can be written as the ratio 114/11.

To express the repeating decimal 11.454545... as a ratio of two integers, we can use algebraic manipulation to convert it into a fraction.

Let's denote the repeating decimal as x:

x = 11.454545...

Multiplying x by 100, we get:

100x = 1145.454545...

Subtracting the original equation from the multiplied equation, we have:

100x - x = 1145.454545... - 11.454545...

Simplifying both sides:

99x = 1134

Dividing both sides by 99:

x = 1134/99.

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It rained approximately 4.47 inches on Tuesday.

The meaning of SUBTRACT is to take away by or as if by deducting. How to use subtract in a sentence.

On Monday, it rained 4(1/2) inches.

On Tuesday, it rained 0.03 inches less than on Monday.

To find out how much it rained on Tuesday, we need to subtract 0.03 inches from the rainfall on Monday.

4(1/2) inches - 0.03 inches = 4.5 inches - 0.03 inches = 4.47 inches

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They would spend approximately 13.33 hours driving if they plan to cover a total distance of 800 miles at an average speed of 60mph.

To answer this question, we need to use the formula: time = distance/speed. In this case, the distance is 800 miles and the average speed is 60mph. Therefore, the time spent driving can be calculated as:
Time = 800 miles / 60 mph
Simplifying this equation, we get:
Time = 13.33 hours
So, the total time that they would spend driving is 13.33 hours. It's important to note that this is the average time it would take them if they maintained a constant speed of 60mph throughout their journey. However, if they encountered traffic, roadworks, or took any breaks during their trip, the actual time spent driving would be longer than this.
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Answer:

Use the radioactive decay formula: A = Ao*2^(-t/h), where

A = 722*2^(-17/71)

find 2^(-17/71) with a calc

A = 722*.847076

A = 611.59 kg after 17 hrs

Step-by-step explanation:

Answer:

The formula for the amount of radioactive material remaining after a certain time can be expressed as:

N(t) = N₀ * (1/2)^(t/h)

Where:

N(t) is the amount of radioactive material remaining after time t

N₀ is the initial amount of radioactive material

h is the half-life of the material

Substituting the given values, we have:

N(14) = 439 * (1/2)^(14/76)

N(14) = 386.377 kg

Therefore, the amount of radioactive material remaining after 14 hours is 386.377 kg. The answer is option (d).

Step-by-step explanation:

The number line will begin at point 8 and point in the negative direction, with the circle darkened.

Inequalities are expression not separated by an equal sign. Given the inequality expression below:

2x-5≤11

Add 5 to both sides

2x-5 + 5≤11 + 5

2x≤16

Divide both sides by 2

2x/2 ≤16/2

x≤8

The number line will start from the point 8 pointing towards the negative direction and the circle shaded.

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Answer:

A

Step-by-step explanation:

Hope this helps

The distance between points A and B will be 6.71 units.

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

The graph (see attachment)

Where we have

A = (0, 0)

B = (6, 3)

This means that the point A is on the origin and point B will be (6, 3).

Then the distance between points A and B will be

D² = (6 - 0)² + (3 - 0)²

D² = 6² + 3²

D² = 36 + 9

D² = 45

D = √45 units

Evaluate

D = 6.71 units

Hence, the distance between points A and B will be 6.71 units.

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The solutions to the equation √(2x² - 7) - x = 3 are x = -2 and x = 8 and x = -2 is an extraneous solution

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

√2x²-7-x=3

Express properly

So, we have

√(2x² - 7) - x = 3

Add x to both sides of the equation

This gives

√(2x² - 7) = x + 3

Take the square roots of both sides

So, we have

2x² - 7 = x² + 6x + 9

So, we have

x²  - 6x - 16 = 0

When solved for x, we have

x = -2 and x = 8

Hence, the solutions to the equation are x = -2 and x = 8 and x = -2 is an extraneous solution

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Answer:

scienific

Step-by-step explanation:

To find the general solution of the second-order differential equation 5y'' + y' = 0, we can use the method of separation of variables.

Let's assume y = e^(mx), where m is a constant.

Taking the first and second derivatives of y with respect to x, we have:

y' = me^(mx)

y'' = m^2e^(mx)

Substituting these expressions into the differential equation, we get:

5(m^2e^(mx)) + (me^(mx)) = 0

Now, we can factor out e^(mx):

e^(mx) * (5m^2 + m) = 0

For this equation to hold true, either e^(mx) = 0 or 5m^2 + m = 0.

Since e^(mx) is never zero for any real value of x, we focus on the second equation:

5m^2 + m = 0

We can factor out m:

m(5m + 1) = 0

Setting each factor equal to zero, we have two possible solutions:

m = 0 or 5m + 1 = 0, which gives m = -1/5.

Therefore, the general solution of the given second-order differential equation is:

y(x) = C1e^(0x) + C2*e^((-1/5)*x)

Simplifying this expression, we have:

y(x) = C1 + C2*e^(-x/5)

Here, C1 and C2 are arbitrary constants that can be determined based on initial conditions or additional information about the problem.

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The measure of each of the angles are calculated as:

m<1 = 63 degrees.; m<2 = 49 degrees; m<3 = 87 degrees; m<4 = 44 degrees.

The measure of each angle can be calculated as explained below:

m<2 = 49 degrees [based on the vertical angles].

m<1 = 180 - m<2 - 68 [based on the triangle sum theorem]

Plug in the values:

m<1 = 180 - 49 - 68

m<1 = 63 degrees.

m<3 = 180 - 93 [linear pair theorem]

m<3 = 87 degrees.

m<4 = 180 - m<3 - 49 [based on the triangle sum theorem]

Substitute:

m<4 = 180 - 87 - 49

m<4 = 44 degrees.

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Answer:

do it yourself what do you do while teacher is teaching

Hello

4/2 + 7/2 - 3/2

= 11/2 - 3/2

= 8/2

= 4

Knowing whether the mean is more than or less than the median can give us information about the skewness of a distribution because the mean and median represent different aspects of the distribution's central tendency.

In a positively skewed distribution, the tail of the distribution extends towards higher values, meaning there are some extreme high values that pull the mean towards the right. In this case, the mean is greater than the median because it is influenced by those high values, shifting the central tendency towards the right.

On the other hand, in a negatively skewed distribution, the tail of the distribution extends towards lower values, indicating the presence of extreme low values that pull the mean towards the left. As a result, the mean is lower than the median because the central tendency is shifted towards the left by those low values.

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The normal distribution is often used to model real-world phenomena, and one of its important properties is that about two-thirds of observations fall within one standard deviation of the mean. This makes it useful for analyzing data sets with a large number of observations, such as in Variation 2 or egg roulette.

Many natural phenomena do not follow a perfectly normal distribution, but certain aspects of these phenomena may be modeled using a normal distribution with some degree of accuracy. For example, the distribution of hemoglobin levels in a population may not be perfectly normal, but it may be close enough to a normal distribution for practical purposes.

The central limit theorem states that as the sample size increases, the distribution of the sample means approaches a normal distribution, regardless of the distribution of the original population. The sample size required to see this effect depends on the shape of the original distribution, but generally, a sample size of 30 or more is often considered sufficient to see a normal distribution emerge.

The results of many studies may involve adding up a large number of random events, but it is important to note that this does not necessarily mean that the results are normally distributed. However, the central limit theorem suggests that the distribution of the means of many independent random variables will approach a normal distribution, which can be useful in statistical analysis.

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a. It will take 392 minutes for just 1 machine to produce same batch.

b. it will take 49 minutes for 8 machines to produce same batch.

a) To get minutes its take for just 1 machine, we will use the following formula:

Time = (Number of machines * Original time) / New number of machines

Time = (7 * 56) / 1

Time = 392 / 1

Time = 392 minutes

b. To get minutes its take for just 8 machine, we will use the following formula:

Time = (Number of machines * Original time) / New number of machines

Time = (7 * 56) / 8

Time = 392 / 8

Time = 49 minutes.

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Answer:

[tex]\large \sf \longrightarrow \: {3}^{5} [/tex]

[tex]\large \sf \longrightarrow \: 3 \times 3 \times 3 \times 3 \times 3[/tex]

[tex] \large\sf \longrightarrow \: 9 \times 9 \times 3[/tex]

[tex] \large\sf \longrightarrow \: 9 \times 27[/tex]

[tex] \large\sf \longrightarrow \: 243[/tex]

______________________________________________________

Answer:

Step-by-step explanation:

3⁵

Here,

[tex]\large\sf{3 }^{5 }[/tex]

[tex]\large\sf{=3 \times 3 \times 3 \times 3 \times 3 }[/tex]

[tex]\large\bf{= 243}[/tex]

The equivalent expressions of 3(2/3p+3-1/3p-5) is 2p - 6.

By simplifying 3(2/3p+3-1/3p-5), we first have to combine the constants in the parentheses:

2/3p + 3 - 1/3p - 5 = (2/3p - 1/3p) + (3 - 5) = (1/3p) - 2

Substituting this expression back into the original equation, we get:

3(2/3p+3-1/3p-5) = 3[(1/3p) - 2 + 3 - 5]

Simplifying inside the brackets, we have:

3[(1/3p) - 2 + 3 - 5] = 3[(1/3p) - 2 - 2]

Multiplying by 3, we get:

3[(1/3p) - 2 - 2] = (1/p) - 6

Therefore, the equivalent expression of 3(2/3p+3-1/3p-5) is (1/p) - 6.

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We need to first determine how many total spins there were. Nolan spun the spinner 12 times. We also know that the spinner has 5 equal parts and there are 5 possible toys to win. Therefore, the probability of the spinner landing on bat is 4/12 or 1/3. This means that out of all the spins, one-third of them landed on bat.
Next, we need to determine how many times the spinner landed on bat. Looking at the data, we can see that the spinner landed on bat 4 times.
It's important to note that this probability is based on the 12 trial spins that Nolan conducted before the guests arrived. The actual probability of winning a specific toy during the festival may differ due to the randomness of each spin.
Based on the data you provided, we can determine the probability of the spinner landing on "bat." Out of the 12 spins Nolan tried, the spinner landed on "bat" 4 times. To calculate the probability, we simply divide the number of successful outcomes (landing on "bat") by the total number of trials (12 spins):
Probability of landing on "bat" = (Number of times "bat" occurred) / (Total number of spins)
Probability of landing on "bat" = 4/12
By simplifying the fraction, we get:
Probability of landing on "bat" = 1/3
So, the probability of the spinner landing on "bat" is 1/3 or approximately 33.33%.

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To determine how many sections of pipe the plumber needs to buy, we need to calculate the total length of pipe required and divide it by the length of each section available for purchase. In this case, the plumber needs eight sections, each 3'2" long, and the pipe is sold in 10' sections. The answer will indicate the number of sections the plumber must buy.

  The length of each section of pipe needed is 3'2", which can be converted to 3.17 feet. To find the total length of pipe required, we multiply the length of each section by the number of sections needed:

Total length of pipe = 3.17 feet/section × 8 sections = 25.36 feet

Since the pipe is sold in 10' sections, we need to determine how many 10' sections are needed to cover a length of 25.36 feet. Dividing the total length by the length of each section, we get:

Number of sections needed = 25.36 feet ÷ 10 feet/section = 2.54 sections

Since we can't purchase a fraction of a section, the plumber needs to buy 3 sections of pipe (as 2.54 is closer to 3 than 2).

Therefore, the answer is option C - 3.

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To determine how many sections of pipe the plumber needs to buy, we need to calculate the total length of pipe required and divide it by the length of each section available for purchase. In this case, the plumber needs eight sections, each 3'2" long, and the pipe is sold in 10' sections. The answer will indicate the number of sections the plumber must buy.

    The length of each section of pipe needed is 3'2", which can be converted to 3.17 feet. To find the total length of pipe required, we multiply the length of each section by the number of sections needed:

Total length of pipe = 3.17 feet/section × 8 sections = 25.36 feet

Since the pipe is sold in 10' sections, we need to determine how many 10' sections are needed to cover a length of 25.36 feet. Dividing the total length by the length of each section, we get:

Number of sections needed = 25.36 feet ÷ 10 feet/section = 2.54 sections

Since we can't purchase a fraction of a section, the plumber needs to buy 3 sections of pipe (as 2.54 is closer to 3 than 2).

Therefore, the answer is option C - 3.

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