Please help me, been struggling for a hot minute. Questions are in the image down below, 50 points.

Answer:

neither.

Step-by-step explanation:

perpendicular would have to be -1/2x instead of 1/2x and parallel would have to be 2x.

a) The probability that X lies between 2 and 3.5 is 0.2.

b) The probability that Y lies between 18 and 22 is 0.1196.

a) Since X is a uniform continuous random variable on the interval (0, 5), the probability density function (pdf) of X is given by:

f(x) = 1/(b-a) = 1/(5-0) = 1/5 for 0 < x < 5

To find P(2 < x < 3.5), we integrate the pdf f(x) over the interval (2, 3.5):

P(2 < x < 3.5) = ∫[tex]2.5^{3.5[/tex] f(x) dx = ∫[tex]2.5^{3.5[/tex] (1/5) dx = (1/5) * [x][tex]2.5^{3.5[/tex] = (1/5) * (3.5 - 2.5) = 0.2

Therefore, the probability that X lies between 2 and 3.5 is 0.2.

b) If Y has an exponential distribution with mean 20, then the pdf of Y is given by:

f(y) = (1/20) * exp(-y/20) for y > 0

To find P(18 < Y < 22), we integrate the pdf f(y) over the interval (18, 22):

P(18 < Y < 22) = ∫[tex]18^{22[/tex] f(y) dy = ∫[tex]18^{22[/tex] [(1/20) * exp(-y/20)] dy

Using integration by substitution, let u = -y/20, then du = -dy/20:

= ∫[tex](-9/20)^{(-11/20)} exp(u)[/tex] du

= [tex]exp(u)^{(-11/20)[/tex]

= [exp(-11/20) - exp(-9/20)]

= 0.1196

Therefore, the probability that Y lies between 18 and 22 is 0.1196.

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In this case, as the number of hours spent on television increases, the GPA decreases. This relationship is called a negative correlation.

The plot of data that demonstrates the relationship between the number of hours a person watches television and their GPA is an essential tool to understand the correlation between these two factors.

From the plot, we can see that as the number of hours of television increases, the GPA goes down. This relationship suggests that the more time a person spends watching television, the lower their academic performance tends to be.

It is crucial to note that this relationship is not a direct causation. The plot of data does not prove that watching television causes a decrease in GPA.

It merely shows that there is a correlation between these two factors. There may be other underlying factors that contribute to the lower GPA of people who watch more television, such as lack of study time or poor time management skills.

Therefore, it is essential to use caution when interpreting the plot of data and not make any hasty conclusions about the relationship between the number of hours a person watches television and their academic performance.

Still, the data provides valuable insights that can help individuals make informed decisions about how they manage their time and prioritize their activities .A plot of data illustrates the relationship between the number of hours a person watches television and their GPA.

In this case, as the number of hours spent on television increases, the GPA decreases. This relationship is called a negative correlation.

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The curl of F is not equal to the zero vector, the given vector field is not conservative. Therefore, there is no function f such that F = ∇f. The answer is DNE (Does Not Exist).

The given vector field F(x, y, z) = 6xy i + (3x^2 + 10yz) j + 5y^2 k is conservative and find a function f such that F = ∇f, if possible.

A vector field F is conservative if its curl (∇ x F) is equal to the zero vector. The curl of F can be found using the determinant of the following matrix:

| i     j      k  |
| ∂/∂x  ∂/∂y  ∂/∂z |
| 6xy   3x^2+10yz  5y^2 |

Calculating the curl, we get:

∇ x F = (0 - 10y) i - (0 - 6x) j + (0 - 0) k = -10y i - 6x j

Since the curl of F is not equal to the zero vector, the given vector field is not conservative. Therefore, there is no function f such that F = ∇f. The answer is DNE (Does Not Exist).

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The sum of squares of sample means about the grand mean (SSM) is a measure of how much variation there is among

Step 1 of 8: The sum of squares of experimental error (SSE) is the variation of the individual measurements about their respective means. It can be calculated by adding up the squared differences between each observation and its group mean. ¹²

SSE = ∑ni=0 (yi - f(xi))^2

where yi is the ith value of the variable to be predicted, f(xi) is the predicted value (group mean), and xi is the ith value of the explanatory variable (treatment).

To calculate SSE by hand, you need to know the values of yi and f(xi) for each observation. You can find f(xi) by taking the average of yi for each treatment group. Then, you can subtract f(xi) from yi and square the result for each observation. Finally, you can add up all the squared differences to get SSE.

SSE = (99.0 - 98.87)^2 + (98.6 - 98.87)^2 + ... + (99.1 - 98.87)^2

SSE = 6.92 (rounded to two decimal places)

Step 2 of 8: The degrees of freedom among treatments (DFT) is the number of independent comparisons that can be made between the treatment means. It can be calculated by subtracting one from the number of treatments. ³

DFT = k - 1

where k is the number of treatments.

To calculate DFT by hand, you need to know how many treatments there are in the data set. In this case, there are four treatments: A1, B2, C3, and D4. Therefore,

DFT = 4 - 1

DFT = 3

Step 3 of 8: The mean square among treatments (MST) is the average variation between the treatment means and the grand mean. It can be calculated by dividing the sum of squares among treatments (SST) by the degrees of freedom among treatments (DFT). ⁴

MST = SST / DFT

where SST is the sum of squares among treatments and DFT is the degrees of freedom among treatments.

To calculate MST by hand, you need to know the values of SST and DFT. You can find SST by subtracting SSE from SSTotal, where SSTotal is the total sum of squares corrected for the mean.

SSTotal = ∑ni=0 (yi - ybar)^2

where yi is the ith value of the variable to be predicted and ybar is the grand mean.

SSTotal = (99.0 - 98.87)^2 + (98.6 - 98.87)^2 + ... + (99.1 - 98.87)^2

SSTotal = 13.84

SST = SSTotal - SSE

SST = 13.84 - 6.92

SST = 6.92

MST = SST / DFT

MST = 6.92 / 3

MST = 2.31 (rounded to two decimal places)

Step 4 of 8: The F-value is a ratio that compares the variation between the treatment means to the variation within the treatment groups. It can be calculated by dividing MST by MSE, where MSE is the mean square error or mean square within groups.

F = MST / MSE

where MST is the mean square among treatments and MSE is the mean square error.

To calculate F by hand, you need to know the values of MST and MSE. You can find MSE by dividing SSE by DFE, where DFE is the degrees of freedom within groups or error degrees of freedom.

DFE = n - k

where n is the total number of observations and k is the number of treatments.

DFE = 18 - 4

DFE = 14

MSE = SSE / DFE

MSE = 6.92 / 14

MSE = 0.49

F = MST / MSE

F = 2.31 / 0.49

F = 4.71 (rounded to two decimal places)

Step 5 of 8: The sum of squares of sample means about

the grand mean (SSM) is a measure of how much variation there is among

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the complete question is:

Consider The Following Table: Among Treatments 5144.72 .  Error ? 10 728.54 Total   17 Step 1 Of 8:

Consider the following table:

SS DF MS F

Among Treatments 5144.72      

Error ? 10 728.54

Total   17  

Step 1 of 8: Calculate the sum of squares of experimental error. Please round your answer to two decimal places.

Step 2 of 8: Calculate the degrees of freedom among treatments.

Step 3 of 8: Calculate the mean square among treatments. Please round your answer to two decimal places.

Step 4 of 8: Calculate the F-value. Please round your answer to two decimal places.

Step 5 of 8: What is the sum of squares of sample means about the grand mean? Please round your answer to two decimal places.

Step 6 of 8: What is the variation of the individual measurements about their respective means? Please round your answer to two decimal places

Step 7 of 8: What is the critical value of F at the 0.1 level? Please round your answer to four decimal places, if necessary.

Step 8 of 8: Is F significant at 0.1 ?

A graphical tool used to help determine whether a process is in control or out of control is known as a Control Chart.

Control charts are essential in quality control and statistical process control (SPC). They allow you to monitor process performance and variability over time, enabling you to identify trends, shifts, or deviations from the established process baseline.

Control charts typically consist of a centerline, representing the process mean, and upper and lower control limits, which indicate the acceptable range of variation. Data points are plotted on the chart, and if they fall within the control limits, the process is considered to be in control. If data points fall outside the control limits or display non-random patterns, the process is considered out of control, signaling potential issues that need to be investigated and addressed.

In summary, control charts are a valuable graphical tool that assists in determining the stability of a process, facilitating continuous improvement efforts and ensuring product quality. They provide a visual representation of process variation and help identify when corrective actions are needed to bring a process back into control.

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This is an example of a biased research sample. By only surveying students at a wealthy private college, the researcher may not accurately capture the budgeting behavior of college students as a whole.

The sample is limited and not representative of the entire population of college students. To ensure more accurate and unbiased results, the researcher should consider surveying a diverse range of college students from different socioeconomic backgrounds and institutions. In this scenario, a researcher wants to study budgeting behavior among college students but only surveys students at a wealthy private college with a tuition of $65,000 per year. This is an example of a biased research sample. The sample is not representative of the broader population of college students, as it only includes students from a specific socio-economic background attending a wealthy private college.

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The y is a constant function, since its derivative is 0, Therefore, y(64) = 1

To solve this problem, we need to use implicit differentiation. First, we differentiate both sides of the equation VI + Vy = 9 with respect to x (since y is a function of x) using the chain rule:

d/dx(VI) + d/dx(Vy) = d/dx(9)

Since VI is a constant, its derivative is 0, and we can simplify to:

V d/dx(y) = 0

Now we can solve for d/dx(y):

d/dx(y) = 0/V = 0

This tells us that y is a constant function, since its derivative is 0. Therefore, y(64) = 1 is the only possible value for y(64), since it is given in the problem.

So, to answer the question, y(64) = 1.

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it is important to carefully analyze survey data and look for patterns and similarities in order to determine which samples are the most representative of a larger population, in this case, the student body.

In order to determine which pair of samples is the most representative of student preference for a new school mascot, we need to analyze the data that was collected by the student representatives who surveyed their classmates.

Looking at the table provided, we can see that there were four different options for a school mascot: an eagle, a lion, a wolf, and a bear. The number of students who preferred each option is listed in the table, along with the total number of students who were surveyed.

To determine which pair of samples is the most representative, we should look for samples that are similar in size and show similar preferences for a particular mascot. For example, if Sample A had 100 students surveyed and 80 of them preferred the lion, while Sample B had 50 students surveyed and 40 of them preferred the lion, these two samples could be considered representative of student preference for the lion as a mascot.

Based on this analysis, it seems that Sample C and Sample D are the most representative of student preference. Both samples have a similar number of students surveyed, and both show a preference for the eagle as a mascot. While there is some variation in the numbers between the two samples, this could be due to chance or other factors and does not necessarily indicate that one sample is more or less representative than the other.

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If the rank of a matrix A is less than the number of columns (n) and the system is consistent, an infinite number of solutions exist because there are more variables than equations. The dependent variables can take on any value.

1. Rank(A): The rank of a matrix A refers to the maximum number of linearly independent rows or columns it possesses.

2. n: In this context, n represents the number of variables in a given system of linear equations.

3. Consistent System: A system of linear equations is consistent if it has at least one solution.

Now, let's put these terms together to explain the statement:

If the rank of a matrix A is less than n (the number of variables), it means that the system of linear equations has fewer linearly independent equations than variables. In such a case, there will be at least one free variable, which can take an infinite number of values.

Since the system is consistent, there is at least one solution, and due to the free variable, each of these infinitely many values will result in a different answer. Consequently, when the rank of a matrix A is less than n and the system is consistent, an infinite number of solutions exist.

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a. The number of bricks required for the top step is 795.

b. The total number of bricks required for all the steps is 2250.

(a) To find the number of bricks required for the top step, we need to use the information that each successive step requires two less bricks than the prior step.

So, we can start by finding the total number of bricks required for all the steps and then subtracting the number of bricks required for the bottom 29 steps.

The total number of bricks required for all the steps can be found using the formula for the sum of an arithmetic sequence:

S = n/2 * (a1 + an)

where S is the sum, n is the number of terms, a1 is the first term, and an is the nth term.

In this case, we have:

n = 30 (since there are 30 steps)

a1 = 100 (since the bottom step requires 100 bricks)

d = -2 (since each successive step requires 2 less bricks than the prior step)

an = a1 + (n-1)d = 100 + (30-1)(-2) = 40.

Plugging these values into the formula, we get:

S = 30/2 * (100 + 40) = 2250

So, the total number of bricks required for all the steps is 2250.

To find the number of bricks required for the top step, we subtract the number of bricks required for the bottom 29 steps from the total number of bricks required for all the steps:

number of bricks required for top step = total number of bricks - number of bricks for bottom 29 steps

= 2250 - [100 + 98 + 96 + ... + 6 + 4 + 2]

= 2250 - 1455

= 795

Therefore, the number of bricks required for the top step is 795.

(b) To find the total number of bricks required to build the staircase, we simply add up the number of bricks required for each step. We can use the formula for the sum of an arithmetic series again to simplify the calculation:

S = n/2 * (a1 + an)

where S is the sum, n is the number of terms, a1 is the first term, and an is the nth term.

In this case, we have:

n = 30 (since there are 30 steps)

a1 = 100 (since the bottom step requires 100 bricks)

d = -2 (since each successive step requires 2 less bricks than the prior step)

an = a1 + (n-1)d = 100 + (30-1)(-2) = 40

Plugging these values into the formula, we get:

S = 30/2 * (100 + 40) = 2250

Therefore, the total number of bricks required to build the staircase is 2250.

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The problem involves finding the probability that a randomly selected monitor from TSI electronics will have a lifespan of more than 18,000 hours given that the lifespan follows a normal distribution with a mean of 17,000 hours and a standard deviation of 1000 hours.

This requires calculating the area under the normal curve to the right of 18,000. The answer is expected to be a probability value rounded to four decimal places.

To solve this problem, we use the z-score formula, which involves calculating the number of standard deviations a value is from the mean. Once we have the z-score, we can look up the corresponding area under the standard normal distribution table or use a calculator to find the probability. In this case, we need to find the z-score corresponding to 18,000 given the mean and standard deviation of the distribution.

After finding the z-score, we can use the standard normal distribution table or calculator to find the probability that a randomly selected monitor will have a lifespan of more than 18,000 hours. This probability represents the area under the normal curve to the right of 18,000 and is a measure of the likelihood of a monitor having a lifespan greater than 18,000 hours.

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Option D). " The product rule" must be used to find the number of ways to form a committee consisting of one representative from each of the 50 states in the United States.

The product rule is a counting principle used in mathematics to determine the total number of possible outcomes for two independent events. If two events E1 and E2 can occur in m and n ways, respectively, the product rule states that the total number of outcomes for both events is given by mn.

Example: If a student has 4 different shirts and 3 different pants to choose from, how many different outfits can they make,

Solution: There are 4 choices for the shirt and 3 choices for the pants. By the product rule, the total number of outfits is given by 4 x 3 = 12.

Therefore, the product rule must be used to find the number of ways to form a committee consisting of one representative from each of the 50 states in the United States.

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The set of all integer solutions for the inequality -1 ≤ x - √5 < 4 is {-1, 0, 1, 2, 3, 4}.

The inequality:

-1 ≤ x - √5 < 4

To isolate x by adding √5 to each side:

-1 + √5 ≤ x < 4 + √5

The inequality is now expressed in terms of x with lower and upper bounds.

To find the set of all integer solutions for this inequality, we need to identify all integer values of x that fall within this range.

The integer values between -1 + √5 and 4 + √5 are:

-1 + √5 ≈ 0.236 and 4 + √5 ≈ 5.236

The integers between these two values are 0, 1, 2, 3, 4, and 5.

The inequality is inclusive of the lower bound (-1 ≤ x - √5), we need to include the integer value that satisfies this condition.

Thus, the set of integer solutions for the inequality is:

{-1, 0, 1, 2, 3, 4}

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The simplified form of expression is [tex]14x^3y^{-5}(49x^5y^2)^{-\frac{1}{2}}=\frac{2x^{\frac{1}{2}}}{y^6}[/tex]

The correct answer is an option (B)

We know that the rule of exponents.

[tex](ab)^m=a^mb^m[/tex]

[tex](a^m)^n=a^{m\times n}[/tex]

Consider an expression.

[tex]14x^3y^{-5}(49x^5y^2)^{-\frac{1}{2}}[/tex]

We need to simplify this expression.

[tex]14x^3y^{-5}(49x^5y^2)^{-\frac{1}{2}}[/tex]

We know that rule of exponent that [tex]a^{-m}=\frac{1}{a^m}[/tex]

Using this rule we can write [tex](49x^5y^2)^{-\frac{1}{2}}[/tex] as [tex]\frac{1}{(49x^5y^2)^{\frac{1}{2}}}[/tex]

so, our expression becomes,

[tex]14x^3y^{-5}(49x^5y^2)^{-\frac{1}{2}}\\\\=\frac{14x^3y^{-5}}{(49x^5y^2)^{\frac{1}{2}}}[/tex]

We know that any number to the 1/2 means the square root of that number.

[tex](49x^5y^2)^{\frac{1}{2}}=\sqrt{(49x^5y^2)}}[/tex]

so, our expression becomes,

[tex]=\frac{14x^3y^{-5}}{\sqrt{(49x^5y^2)} } \\\\=\frac{14x^3y^{-5}}{7x^2\sqrt{x} ~ y}[/tex]                                 ...............(simplify)

[tex]=\frac{14~x~ x^{-\frac{1}{2} }}{7~y~ y^5}[/tex]

We know that the exponent rule while multiplying the two numbers if the base of exponents is same then we add the powers.

i.e., [tex]a^m\times a^n=a^{m+n}[/tex]

So, our expression becomes,

[tex]=\frac{2x^{(1-\frac{1}{2})}}{y^6}[/tex]                    

[tex]=\frac{2x^{\frac{1}{2}}}{y^6}[/tex]

This is the simplified form of expression [tex]14x^3y^{-5}(49x^5y^2)^{-\frac{1}{2}}[/tex]

Therefore, the correct answer is an option (B)

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The correct choice is:

D. The larger the sample size, the smaller the standard deviation of X, because the denominator of the standard deviation of x contains the square root of the sample size.

To explain this answer, let's consider the formula for the standard deviation of the sample means, which is:

The standard deviation of sample means = σ/√n

Here, σ is the population standard deviation, and n is the sample size. As you can see, the standard deviation of the sample means is inversely proportional to the square root of the sample size. This means that as the sample size (n) increases, the standard deviation of the sample means will decrease. Therefore, a larger sample size will lead to a smaller standard deviation of all possible sample means, as it will provide a more precise estimate of the population mean.

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Based on the past data indicating that 30% of the general population holds the belief that life exists elsewhere within 4% of the real answer, we can use statistical analysis to determine the level of confidence we can have in this statement.

With a 95% confidence level, we can say that there is a high likelihood that this belief is true within a margin of error of 4%. In other words, we can be 95% confident that the true percentage of people who believe that life exists elsewhere within 4% of the real answer falls somewhere between 26% and 34%.

Based on the information provided, it seems that 30% of the general population believes that life exists elsewhere in the universe. There is a 95% confidence level that the true percentage of people holding this belief is within 4% of the given 30% estimate. This means that the actual percentage of people with this belief likely falls between 26% and 34%.

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The integral converges, the series also converges by the integral test. Therefore, ∑ infinity _n=4 (14ne^(-n^2)) converges.

For the first series, we can use the integral test. We need to find a function f(x) that is continuous, positive, and decreasing such that f(n) = ((n^2)/((n^3 +6)^9/2)) for all positive integers n. Then, we can use the integral test to determine whether the series converges or diverges by evaluating the integral of f(x) from 20 to infinity.

Let f(x) = (x^2)/((x^3 + 6)^9/2). Then, we can take the derivative of f(x) and find that f'(x) = ((x^3 - 18)/(x^3 + 6)^(11/2)) which is negative for all x > 0. This means that f(x) is decreasing for all x > 0. Additionally, f(x) is positive for all x > 0 since the numerator and denominator are both positive. Therefore, we can use the integral test.

We evaluate the integral of f(x) from 20 to infinity by using a substitution. Let u = x^3 + 6. Then, du/dx = 3x^2 and dx = du/(3x^2). Substituting, we get:

∫((x^2)/((x^3 + 6)^9/2))dx = (1/3)∫u^(-9/2)du
= (-2/15)u^(-7/2) from 20^3 + 6 to infinity
= (2/15)(20^3 + 6)^(-7/2)

Since the integral converges, the series also converges by the integral test. Therefore, ∑ infinity _n=20 ((n^2)/((n^3 +6)^9/2))) converges.

For the second series, we can also use the integral test. We need to find a function f(x) that is continuous, positive, and decreasing such that f(n) = 14ne^(-n^2) for all positive integers n. Then, we can use the integral test to determine whether the series converges or diverges by evaluating the integral of f(x) from 4 to infinity.

Let f(x) = 14xe^(-x^2). Then, we can take the derivative of f(x) and find that f'(x) = (14 - 28x^2)e^(-x^2) which is negative for x > 1/sqrt(2) and positive for 0 < x < 1/sqrt(2). This means that f(x) is decreasing for x > 1/sqrt(2) and increasing for 0 < x < 1/sqrt(2). Additionally, f(x) is positive for all x > 0 since e^(-x^2) is always positive. Therefore, we can use the integral test.

We evaluate the integral of f(x) from 4 to infinity by using a substitution. Let u = x^2. Then, du/dx = 2x and dx = du/(2x). Substituting, we get:

∫(14xe^(-x^2))dx = 7∫e^(-u)du
= -7e^(-u) from 4^2 to infinity
= 7e^(-16)

Since the integral converges, the series also converges by the integral test. Therefore, ∑ infinity _n=4 (14ne^(-n^2)) converges.

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Answer:

Table D

Step-by-step explanation:

To determine which table shows a negative slope, we need to identify which table has points that, when plotted on a graph, decrease from left to right.

Let's start by plotting the points in Table A on a graph:

y

|

|    o

|       o

|          o

|             o

|___________________________

          x

As we can see, the points in Table A form a line that increases from left to right. So Table A does not have a negative slope.

Next, let's plot the points in Table B:

y

|

|     o

|         o

|             o

|                 o

|___________________________

          x

The points in Table B form a line that increases from left to right as well. So Table B does not have a negative slope.

Now, let's plot the points in Table C:

y

|

|    o

|         o

|              o

|                     o

|___________________________

          x

The points in Table C form a line that increases from left to right, so Table C does not have a negative slope either.

Finally, let's plot the points in Table D:

y

|

|               o

|          o

|       o

|    o

|___________________________

          x

The points in Table D form a line that decreases from left to right, so Table D has a negative slope.

Therefore, the correct answer is D.

The equation that model the relationship on the graph in slope-intercept form can be presented as follows;

y = (7/3)x + (-2/3)

The slope-intercept form of a linear equation is an equation of the form; y = m·x + c

Where;

m = The slope of the graph of the equation

c = The y-intercept

The first difference are;

-3 - (-10) = 7

4 - (-3) = 7

11 - 4 = 7

The data on the table represent the data for a linear equation, since the difference between the successive x-values are the same and equivalent to 3

The slope of the graph of the equation is therefore;

(11 - 4)/(5 - 3) = 7/3

The equation of that represents the data is therefore;

y - 11 = (7/3)·(x - 5) = (7/3)·x - 35/3 = (7/3)·x - 11 2/3

y = (7/3)·x - 11 2/3 + 11 = (7/3)·x - 2/3

The equation is therefore;

y = (7/3)·x - 2/3

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The function for the force f needed to balance a weight when the force is applied c centimetres away from the fulcrum is: f = 17.5/c. 8.75 newtons of force is needed to balance the weight if it is applied 2 cm from the fulcrum.

a. The relationship between the force needed to balance weight and the distance from the fulcrum at which force is applied can be expressed as follows:
f = k/d
where f is the force needed to balance the weight, d is the distance from the fulcrum at which force is applied, and k is a constant of proportionality.
To find the value of k, we can use the given information:
3.5 = k/5
k = 17.5
Therefore, the function for the force f needed to balance weight when the force is applied c centimetres away from the fulcrum is:
f = 17.5/c

b. If the force is applied 2 cm away from the fulcrum, we can use the function we found in part (a) to calculate the force needed to balance the weight:
f = 17.5/2
f = 8.75 newtons
Therefore, 8.75 newtons of force is needed to balance the weight if it is applied 2 cm from the fulcrum.

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To find the dimensions of the poster with the smallest area, we need to use the given information to set up an equation for the total area of the poster. So, the dimensions of the poster with the smallest area are 64 cm by 128 cm.

Let's start by representing the width of the printed material as "w" and the height as "h".
Since the top and bottom margins are each 12 cm, we can subtract 24 cm from the total height to get the height of the printed material:
h - 24 = height of printed material
Similarly, since the side margins are each 8 cm, we can subtract 16 cm from the total width to get the width of the printed material:
w - 16 = width of printed material
The total area of the poster is the product of the width and height:
Total area = w x h
We are given that the area of printed material is fixed at 1,536 cm2, so we can write:
1,536 = (w - 16) x (h - 24)
Now we can use this equation to express one of the variables in terms of the other, and then substitute into the equation for total area.
Solving for "h" in the second equation, we get:
h = 1,536 / (w - 16) + 24
Substituting this expression for "h" into the equation for total area, we get:
Total area = w x (1,536 / (w - 16) + 24)
Expanding and simplifying this expression, we get:
Total area = 1,536 + 24w - 1,536(16 / (w - 16))
To find the dimensions that minimize the area, we need to find the value of "w" that makes this expression as small as possible.
Taking the derivative of the expression with respect to "w" and setting it equal to zero, we get:
24 + 1,536(16 / (w - 16)2) = 0
Solving for "w", we get:
w = 64
Now we can use this value to find the corresponding height:
h = 1,536 / (64 - 16) + 24 = 128
Therefore, the dimensions of the poster with the smallest area are 64 cm by 128 cm.

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Answer:

28

Step-by-step explanation:

circle = 360 degrees, the sector is 90 degrees, so it's a 1/4 of the circle. to find area of the whole circle multiply 7 sq inches by 4 ->

area of the circle = 7*4 = 28 sq inch

Answer:

the eight answer is E hope it helped can you help me with my question

The cheetah can travel 74.6 miles in 1 hour at its top speed.

To determine how far a cheetah can travel in 1 hour, we need to use the information provided and make some calculations.

First, we know that the cheetah can travel at its top speed for 1.5 hours, covering a distance of 111.9 miles. This means that we can calculate the cheetah's average speed during this time as follows:

Average speed = Distance covered / Time taken

Plugging in the values, we get:-

Average speed = 111.9 miles / 1.5 hours = 74.6 miles/hour

This means that the cheetah can run at an average speed of 74.6 miles per hour.

Now, to determine how far the cheetah can travel in 1 hour, we can use the formula:

Distance = Speed x Time

Plugging in the values, we get:-

Distance = 74.6 miles/hour x 1 hour = 74.6 miles

Therefore, the cheetah can travel 74.6 miles in 1 hour at its top speed.

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So, the correct answer is: A) y = 10 (This is NOT a solution to the given differential equation.)

The given differential equation is y" + 4y = 0, which can be rewritten as y" = -4y. To check which of the given functions is not a solution to this equation, we can simply substitute them into the equation and see if it holds true.a) y = 10 .

y" = 0 (second derivative of a constant is always zero)
Substituting into the equation:  y" + 4y = 0 + 4(10) = 40 ≠ 0 ,
Therefore, y = 10 is not a solution to the differential equation.
b) y = 4e^-2x
y" = 16e^-2x

Substituting into the equation: y" + 4y = 16e^-2x + 4(4e^-2x) = 32e^-2x ≠ 0, Therefore, y = 4e^-2x is not a solution to the differential equation. c) y = 3sin(2x), y" = -12sin(2x)

Substituting into the equation: y" + 4y = -12sin(2x) + 4(3sin(2x)) = 0, Therefore, y = 3sin(2x) is a solution to the differential equation.(d) y = 2cos(2x) + 4, y" = -8cos(2x).

Substituting into the equation:y" + 4y = -8cos(2x) + 4(2cos(2x) + 4) = 0, Therefore, y = 2cos(2x) + 4 is a solution to the differential equation. In conclusion, the function that is not a solution to the differential equation y" + 4y = 0 is y = 10 (option A).

Comparing this general solution to the given options, we can see that options C) and D) fit the general form. Options A) and B) do not fit the general solution form.

However, since A) is a constant function, its second derivative is y'' = 0, which means y'' + 4y = 4 * 10 = 40, not satisfying the differential equation. So, the correct answer is: A) y = 10 (This is NOT a solution to the given differential equation.)

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The eight number is 45

Let x represent the unknown number

The mean is 47

The seven numbers are

50,27,45,72,67,32 and 38

The eight number can be calculated as follows

50 + 27 + 45 + 72 + 67 + 32 + 38 + x/8= 47

cross multiply both sides

331 + x/8= 47

331 + x= 47× 8

331 + x= 376

x= 376-331

x= 45

Hence the eight number is 45

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