If y ∝ \(\frac{1}{x}\) and y = 4 when x = 2.5, find :


(a) y when x = 20

(b) x when y = 5

Answer:

B) Variable Expense

Step-by-step explanation:

trust me

yes youre right its b trust him

The correlation analysis indicates a moderate positive relationship between Column X and Column Y.

To perform correlation analysis, we can use the Pearson correlation coefficient (r) to measure the linear relationship between two variables, in this case, Column X and Column Y. The value of r ranges from -1 to 1, where 1 indicates a perfect positive correlation, -1 indicates a perfect negative correlation, and 0 indicates no correlation.

Here are the steps to calculate the correlation coefficient:

Calculate the mean (average) of Column X and Column Y.

Mean(X) = (10+6+39+24+35+12+33+32+23+10+16+16+35+28+5+22+12+44+15+40+46+35+28+9+9+8+35+15+34+16+19+17+21) / 32 = 24.4375

Mean(Y) = (37+10+18+12+11+34+26+9+42+24+40+1+39+24+42+7+17+17+27+47+35+14+38+18+17+22+12+30+18+43+24+45+24) / 32 = 24.8125

Calculate the deviation of each value from the mean for both Column X and Column Y.

Deviation(X) = (10-24.4375, 6-24.4375, 39-24.4375, 24-24.4375, ...)

Deviation(Y) = (37-24.8125, 10-24.8125, 18-24.8125, 12-24.8125, ...)

Calculate the product of the deviations for each pair of values.

Product(X, Y) = (Deviation(X1) * Deviation(Y1), Deviation(X2) * Deviation(Y2), ...)

Calculate the sum of the product of deviations.

Sum(Product(X, Y)) = (Product(X1, Y1) + Product(X2, Y2) + ...)

Calculate the standard deviation of Column X and Column Y.

StandardDeviation(X) = √[(Σ(Deviation(X))^2) / (n-1)]

StandardDeviation(Y) = √[(Σ(Deviation(Y))^2) / (n-1)]

Calculate the correlation coefficient (r).

r = (Sum(Product(X, Y))) / [(StandardDeviation(X) * StandardDeviation(Y))]

By performing these calculations, we find that the correlation coefficient (r) is approximately 0.413. Since the value is positive and between 0 and 1, we can conclude that there is a moderate positive relationship between Column X and Column Y.

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Answer:C

Step-by-step explanation:

Answer:

First of all, let us have a look at the formula for Total Surface Area of triangular prism:

TSA = B + p\times hTSA=B+p×h

Where B is the area of base

p is the perimeter of base and

h is the height of prism.

here base is a right angled triangle (because 3, 4, 5 is a triplet) Base and Height will be 3 , 4 cm or 4, 3 cm and 5 will be hypotenuse.

So formula for B:

\begin{gathered}B = \dfrac{1}{2}\times Base \times Height\\B = \dfrac{1}{2}\times 3\times 4 = 6 cm^2\end{gathered}

B=

2

1

×Base×Height

B=

2

1

×3×4=6cm

2

So, TSA = 6 + (3+4+5) \times× 10 = 6 + 120 = 126 cm^2cm

2

So, total surface area of given prism is 126cm^2cm

2

.

Answer:

Step-by-step explanation:

The first 5 multiples of 37 are 37, 74, 111, 148, 185. The sum of the first 5 multiples of 37 is 555 and the average of the first 5 multiples of 37 is 111. Multiples of 37: 37, 74, 111, 148, 185, 222, 259, 296, 333, 370 and so on.

Answer:

Proved below!

Step-by-step explanation:

Start by multiplying both sides by 2 (as said in the question):

\(\implies 4c + 10a = 388\)

\(\implies 2(4c + 10a) = 2(388)\)

\(\implies 8c + 20a = 776\)

Substitute the solution(s) in the equation:

\(\implies 8(52) + 20(18) = 776\)                                                                   (c = 52; a = 18)

\(\implies 416 + 360 = 776\)

\(\implies \bold{776 = 776 \ \ \ (Proved)}\)

Answer:

Let c = number of children's tickets sold

Let a = number of adults tickets sold

Given:

⇒ 4c + 10a = 388

Multiply both sides of the equation by 2:

⇒ 2(4c + 10a) = 2 × 388

⇒ 8c + 20a = 776

If c = 52 and a = 18, substitute these values into the equation and solve:

⇒ 8(52) + 20(18)

⇒ 416 + 260

⇒ 776

As 776 = 776, this proves that c = 52 and a = 18 is a solution to this equation.

The probability that Z is less than 1.09 can be found by looking up the value of 1.09 in the cumulative standardized normal distribution table. From the table, we can find that the corresponding probability is 0.8621.

To find the probability that Z is less than -0.22 or greater than the mean, we need to find the probability of Z being less than -0.22 and the probability of Z being greater than the mean, and then add them together. From the table, we can find that the probability of Z being less than -0.22 is 0.5871, and the probability of Z being greater than the mean is 0.5. Adding these probabilities, we get 0.5871 + 0.5 = 1.0871.

To find the probability that Z is less than -0.22 or greater than 1.09, we need to find the probability of Z being less than -0.22 and the probability of Z being greater than 1.09, and then add them together. From the table, we can find that the probability of Z being less than -0.22 is 0.5871, and the probability of Z being greater than 1.09 is 1 - 0.8621 = 0.1379. Adding these probabilities, we get 0.5871 + 0.1379 = 0.725.

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Answer:

Here is your answer!

Sorry I'm late but hopefully I can help others when looking for answers.

Step-by-step explanation:

Brainlist? :)

The  values of x will f(x) > 0 for x < 0, and f(x) < 0 for -6 < x < 0 and x > -6.

To determine the values of x for which f(x) > 0, we need to find the intervals where the function is positive. Let's analyze the function f(x) = x*-x³-6x².

First, let's factor out an x from the expression to simplify it: f(x) = x(-x² - 6x).

Now, we can observe that if x = 0, the entire expression becomes 0, so f(x) = 0.

Next, we analyze the signs of the factors:

1. For x < 0, both x and (-x² - 6x) are negative, resulting in a positive product. Hence, f(x) > 0 in this range.

2. For -6 < x < 0, x is negative, but (-x² - 6x) is positive, resulting in a negative product. Therefore, f(x) < 0 in this range.

3. For x > -6, both x and (-x² - 6x) are positive, resulting in a negative product. Thus, f(x) < 0 in this range.  

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The true statement about effect size is: The effect size is the extent to which the null or statistical hypothesis is false. Effect size is a measure used in research studies to quantify the magnitude of the difference between groups or the strength of an association between variables.

It helps determine the practical significance of the research findings, as opposed to the statistical significance.
When the effect size is small, detecting it is not necessarily easier, and a larger sample size may be required to achieve adequate statistical power. A larger effect size, on the other hand, might be easier to detect and might require a smaller sample size.
There is not just one type of effect size measure used in research studies. There are various measures of effect size, such as Cohen's d, Pearson's correlation coefficient (r), and odds ratio (OR), among others. Each type of effect size is suitable for different research designs and data types.

Choosing the appropriate effect size measure depends on the research question, the design of the study, and the type of data being analyzed.

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Answer:

100 x 25 x 4 = 10000\(m^{3}\)

Step-by-step explanation:

1.The staff at the clinic will be busy for 12 x 0.625 = 7.5 hours in a 12-hour time period.

2. The expected waiting time is 0.444 minutes.

3. A person is expected to spend 10 minutes in the clinic.

4.The two chairs in the waiting area should be enough to meet the 75% target.

1. To estimate the number of hours that the staff at the clinic are busy in a 12-hour time period, we need to calculate the average utilization of the server. The service rate is the reciprocal of the average service time, so u = 1/8 = 0.125 customers per minute. The arrival rate is given as 5 customers per hour, so λ = 5/60 = 0.0833 customers per minute. The utilization of the server is P(1), which can be calculated using the formula P(1) = (1-λ/u). Therefore, P(1) = 0.625, indicating that the server is busy 62.5% of the time.

2. To estimate the time a person coming to the clinic is expected to wait to get served after he/she arrives, we need to calculate the average waiting time in queue. The formula for the mean waiting time in queue is Ta = λ (u²+1)/(2u(1-u)), which equals to Ta = (0.0833 x (0.125²+1))/(2 x 0.125 x (1-0.125)) = 0.444 minutes.

3. To estimate the time a person is expected to spend in the clinic (including waiting and being served) after he/she arrives, we need to calculate the mean time in the system. The formula for mean time in the system is Ts = 1/(u-λ), which equals to Ts = 1/(0.125-0.0833) = 10 minutes.

4. To estimate if the two chairs in the waiting area are enough to meet the 75% target, we need to calculate the probability of having two or fewer people in the system, including the one being served and those waiting. P(0) = (1-λ/u) = 0.625, and P(1) = λ/u x P(0) = 0.208. Hence, the probability of having two or fewer people in the system is P(0) + P(1) + P(2) = 0.739. This means that 73.9% of the time, there will be two or fewer people in the system, which exceeds the target of 75%.

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Answer:

y=-1.5x+0.5 or y+1.5x-0.5=0

a) The point estimate for the population mean weight can be calculated as the sample mean, which is the sum of all the weights divided by the number of boxes in the sample:

(3 + 2.3 + 2.5 + 2.3 + 2.8 + 2.7 + 2.3 + 2.7 + 2.8 + 2.3 + 2.2 + 3.2 + 2002.6) / 13 ≈ 154.673 pounds

So the point estimate for the population mean weight is approximately 154.673 pounds.

b) To construct a confidence interval for the population mean weight, we must know the population standard deviation or the sample standard deviation, as well as the sample size. In this case, we are given the sample size but not the population standard deviation or the sample standard deviation. Therefore, we need to assume that the population standard deviation is unknown and use the t-distribution to construct the confidence interval.

c) To construct a 98% confidence interval for the population mean weight, we first need to calculate the standard error of the mean:

SE = s / sqrt(n)

where s is the sample standard deviation and n is the sample size. Since we do not have the sample standard deviation, we can use the formula for the unbiased estimator of the population standard deviation:

s = sqrt(Σ(xi - x)^2 / (n - 1))

where xi is the weight of the i-th box, x is the sample mean, and n is the sample size. Plugging in the values, we get:

s = sqrt((Σ(xi - x)^2) / (n - 1)) = sqrt(163077.0357 / 12) ≈ 152.064

So the standard error of the mean is:

SE = 152.064 / sqrt(13) ≈ 42.013

Using a t-distribution with 12 degrees of freedom (n - 1), and a confidence level of 98%, the critical value is:

t* = 2.681

The 98% confidence interval for the population mean weight is:

(154.673 - 2.681 * 42.013 / sqrt(13), 154.673 + 2.681 * 42.013 / sqrt(13))

which simplifies to:

(108.987, 200.359)

Rounding to 3 decimal places, the 98% confidence interval is (108.987, 200.359).

d) Being "98% confident in this problem" means that if we were to repeat this experiment many times and construct 98% confidence intervals for the population mean weight based on each sample, we would expect 98% of those intervals to contain the true population mean weight. In other words, we are very likely to capture the true population mean weight within the calculated confidence interval.

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The required critical value of the confidence interval is Tc = 2.947

Given data ,

Let the confidence interval value be = 0.99

Now , the sample size is n = 17

And , we have,

For a confidence level of c = 0.99 and a sample size of n = 17

(which is relatively small), we will use a two-tailed t-distribution.

we know that,

df = Sample Size - 1

So, we need to check the critical value column under confidence level 0.99 and across the row showing df = 16.

From the t-table this value comes out to be 2.921

Using a t-distribution table or statistical software, we get,

the critical value tₓ for a confidence level of 0.99 and a sample size of 17 is approximately 2.921.

Hence , the critical value tₓ for a confidence level c = 0.99 and sample size n = 17 is approximately 2.921

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Answer:

\(f(x+2)=2x^2+8x+13\)

\(f(x) + f(2)= 2x^2+18\)

Step-by-step explanation:

Given function:

\(f(x)=2x^2+5\)

To find f(x + 2), substitute (x + 2) in place of x in the function:

\(\begin{aligned}\implies f(x+2) & = 2(x+2)^2+5\\& = 2(x+2)(x+2)+5\\& = 2(x^2+4x+4)+5\\& = 2x^2+8x+8+5\\& = 2x^2+8x+13\end{aligned}\)

To find f(x) + f(2), substitute x = 2 into the function and add this to the original function:

\(\begin{aligned}\implies f(x) + f(2) & = [2x^2+5]+[2(2)^2+5]\\& = 2x^2+5+2(4)+5\\& = 2x^2+5+8+5\\& = 2x^2+18\end{aligned}\)

The polar representation of the point (2, 30°) is given by options 3. (2, π/6) and 5, (-2, 7π/6). In polar representation, a point is represented by its distance from the origin (r) and the angle it makes with the positive x-axis (θ).

The given point (2, 30°) has a distance of 2 units from the origin and makes an angle of 30° with the positive x-axis.

Option 3, (2, π/6), represents the same point in radians. The angle π/6 is equivalent to 30°, so it matches the given polar representation.

Option 5, (-2, 7π/6), represents the point (-2, -330°) in radians. The angle 7π/6 is equivalent to -330°, so it also matches the given polar representation.

Options 1, 2, and 4 do not match the given polar representation. Option 1, (-2, -30°), has the correct distance but the angle is negative. Option 2, (-2, 330°), has the correct angle but the distance is negative. Option 4, (2, -330°), has the correct distance but the angle is negative.

Therefore, options 3 and 5 are the polar representations that match the given point (2, 30°).

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Answer:

-12

Step-by-step explanation:

Step1: Add 3 to both sides of the equation

2x -3 = 5x +6

    +3         +3 = 9

Step2: subtract 5x from both sides of the equation

2x = 5x +9

-5    -5

Step3: divide both sides of the equation by the same term

-3x(/ -3) = 9(/-3)    

Step4: multiply -3 with 2

-3x2= -6

Step4: subtract -6 with 3

-6 - 3= -9

Step5: add the -9 to -3

-9 + -3 = -12

ANSWER: -12

\(\qquad \textit{perfect square trinomial} \\\\ (a\pm b)^2\implies a^2\pm \stackrel{\stackrel{\text{\small 2}\cdot \sqrt{\textit{\small a}^2}\cdot \sqrt{\textit{\small b}^2}}{\downarrow }}{2ab} + b^2 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ x^2 \pm \stackrel{\stackrel{2\sqrt{x^2}\sqrt{c^2}}{\downarrow }}{6x} +c^2~\hspace{10em}6x=2\sqrt{x^2}\sqrt{c^2}\implies 6x=2xc \\\\\\ \cfrac{6x}{2x}=c\implies 3=c\implies 9=c^2~\hfill \boxed{(x\pm 3)^2}\)

c=9 makes the given expression a perfect square trinomial.

The given expression is:

\(x^{2} +6x+c\)

We can rewrite it as:

\(x^{2} +2*x*3 + c\).....(1)

The expansion of \((a+b)^2\) is \(a^{2} +2ab+b^{2}\)

Comparing (1) with \(a^{2} +2ab+b^{2}\)

We get

a=x

b=3

c=b²

So, c=3² =9.

So, c=9 makes the given expression a perfect square trinomial.

Hence,  c=9 makes the given expression a perfect square trinomial.

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Questions :

(a) Determine the total length of the circular portions in terms of

pi. Show the work that leads to your answer.

(b) Determine the total length of wire needed, both circular and

square portions, to the nearest tenth of an inch.

G

(c) Determine the total weight of the ornament to the nearest

gram.

Answer:

12π

53.68 in

96.624g

Step-by-step explanation:

The total length of the circular portion :

Perimeter of circle = Circumference of the circle = 2πr ; r = radius = 2

Size of each circle is 3/4

Number of circles = 4

Number of complete circles :

4 × 3/4 = 3 complete circles

Perimeter of circle:

Number of circles * (2πr)

3 * 2 * π * 2 = 12π

Total wore needed :

Circular + Square

Perimeter of square = 4s

s=side length = 4

Total square 4 * 4 = 16

Perimeter of Square + perimeter of circle

16 + 12π = 16 + (12 * 3.14) = 53.68 in

Total weight of ornament :

1.8 g * perimeter

1.8 * 53.68 = 96.624g

Answer:

There can be infinetly many numbers including negative and positive number which add up to 31.

Example

31 -1 1

31 -2 2……

But if your question ask for sum of 3 positive integers which give 31, then you can compile following code in C++.

Answer:

The answer would be the third one, 3(x -2)=18

Answer: D

Step-by-step explanation:

Answer:

\(6x^{2}+10x-12\)

Step-by-step explanation:

Calculating the factorials, we find that the person can make 2,380 different selections of 4 bags of chips out of the 17 varieties.

To find out how many different selections of chips the person can make, we need to use the combination formula. The formula for combinations is:

nCr = n! / r!(n-r)!

Where n is the total number of options (in this case, 17 varieties of chips) and r is the number of choices we want to make (in this case, 4 bags of chips).

So, plugging in the values we have:

17C4 = 17! / 4!(17-4)!
17C4 = 17! / 4!13!
17C4 = (17x16x15x14)/(4x3x2x1)
17C4 = 2380

Therefore, the person can make 2,380 different selections of chips.

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The main difference between the reciprocal and inverse of a function is their definition and properties. The reciprocal of a function f(x) is defined as 1/f(x), while the inverse of a function f(x) is a function f^(-1)(x) such that \(f(f^(-1)(x))=x and f^(-1)(f(x))=x\) for all x in their respective domains.

The domains of sine, cosine, and tangent functions need to be restricted to define their inverse functions because they are not one-to-one functions. In order to have an inverse, a function must be both one-to-one (each output has only one input) and onto (each output value is mapped by at least one input value).

For example:
- sine: restricted domain to [-π/2, π/2] to define its inverse, arcsin (sin^(-1))
- cosine: restricted domain to [0, π] to define its inverse, arccos (cos^(-1))
- tangent: restricted domain to (-π/2, π/2) to define its inverse, arctan (tan^(-1))

These restrictions ensure that the functions become one-to-one and onto, making it possible to define their inverses uniquely.

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Answer:

a couple different obes

Step-by-step explanation:

there are five

Answer:

0

3

6

9

12

Step-by-step explanation:

since it says y= you just have to plug in the x into y=2/4x

Answer:

0,3,6,9,12

Step-by-step explanation:

y=3/4x

divide 3/4=.75

substitute x value and multiply by .75

4*.75=3

8*.75=6

12*.75=9

16*.75=12

hope this helps :)

Answer:

Hi,

The first one is the second one, the one on the top right. This is because you add two branches every step.

I'm not so sure about the second question. sorry ! hope it helps tho

(D) "effective in . . administered"

Anything that is "effective" results in the desired outcome. "Administered" refers to being given out. The phrase would read "The new vaccine is effective in preventing certain forms of pneumonia and should, therefore, be more widely administered in order to avoid outbreaks of the disease." if these terms were added to the text.

The use of the word "therefore" suggests that, in light of the first portion of the phrase's assertion, the second part of the statement should logically follow. The claim that an effective vaccination ought to be distributed extensively makes sense.

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