Guesstimate how much total time do Americans spend driving in one year? Express the answer in hours, years and lifetimes.

How would one go about guestimating a problem like this.

Answer:

The required function is [tex]p\left(x\right)=1.325-0.675x+0.375x^2[/tex].

Step-by-step explanation:

The given data points are (0, 1), (1, 2), (2, 1/2) and (3, 3).

Let the quadratic function is defined as

[tex]p(x)=a_0+a_1x+a_2x^2[/tex]              .... (1)

Using graphing calculator, we get

[tex]a_0=1.325[/tex]

[tex]a_1=-0.675[/tex]

[tex]a_2=0.375[/tex]

Substitute [tex]a_0=1.325[/tex], [tex]a_1=-0.675[/tex] and [tex]a_2=0.375[/tex] in function (1), to find the quadratic function.

[tex]p\left(x\right)=1.325-0.675x+0.375x^2[/tex]

Therefore the required function is [tex]p\left(x\right)=1.325-0.675x+0.375x^2[/tex].

The graph of data points and quadratic function is shown below.

Answer:

233 days.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

[tex]\mu = 200, \sigma = 10[/tex]

To be 99% sure that we will not be late in completing the project, we should request a completion time of ...

This is the value of X when Z has a pvalue of 0.99. So X when Z = 2.325.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]2.325 = \frac{X - 200}{10}[/tex]

[tex]X - 200 = 10*2.325[/tex]

[tex]X = 232.5[/tex]

So the correct answer is 233 days.

Answer:

It's actually C

Step-by-step explanation:

don't forget about the probability of 0 too

you have to add the two probability formulas

The probability of observing, at most, one patient who will be cured of breast Cancer will be P = (20 / q²⁰) + 20 / (0.20 x 0.80¹⁹). Then the correct option is C.

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

A new drug on the market is known to cure 20% of patients with breast cancer.

p = 0.20

q = 1 – 0.20

q = 0.80

If a group of 20 patients is randomly selected.

The probability of observing, at most, one patient who will be cured of breast Cancer will be

P = (20 / q²⁰) + 20 / (0.20 x 0.80¹⁹)

Then the correct option is C.

More about the probability link is given below.

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Answer:

The cutoff score should be 75.8 marks

Step-by-step explanation:

The cut-off should be set as the value corresponding to an area 15% in the normal distribution diagram.

Using the standard distribution tables we have value of standard normal deviate (Z) corresponding to area of 15% = -1.04

Thus we have

[tex]-1.04=\frac{X-\bar{X}}{\sigma }\\\\X=-1.04\times 5.5+81\\X=75.8[/tex]

Answer:

12 minutes

Step-by-step explanation:

First we figure out how much of a car each person can wash in 1 minute.

Shea can wash the car by herself in 20 minutes

Therefore, she can wash a car in 1 minute = [tex]\frac{1}{20}[/tex]

Tucker can wash a car in 30 minutes.

Tucker can wash the car in 1 minute = [tex]\frac{1}{30}[/tex]

Thus, in one minute together they wash a car

[tex]\frac{1}{20}[/tex] + [tex]\frac{1}{30}[/tex] = [tex]\frac{50}{600}[/tex] = [tex]\frac{1}{12}[/tex]

In one minute together they can wash  = [tex]\frac{1}{12}[/tex] of a car

Time needed to wash entire car together = 12 minutes.

It takes them 12 minutes to wash the car.

Final answer:

Shea and Tucker can wash their father's car in 12 minutes if they work together.

Explanation:

To find out how long it takes Shea and Tucker to wash the car together, we can use the concept of work rates.

Shea can wash the car by herself in 20 minutes, so her work rate is 1/20 of the car per minute.

Tucker can wash the car by himself in 30 minutes, so his work rate is 1/30 of the car per minute.

When two people work together, their work rates are additive. So, if Shea and Tucker work together, their combined work rate is 1/20 + 1/30 = 1/12 of the car per minute.

Since the work rate is the reciprocal of the time taken, the time it takes them to wash the car together is 12 minutes. Therefore, it takes Shea and Tucker 12 minutes to wash their father's car if they work together.

To construct a 95% confidence interval with a margin of error of 0.052, a sample size of 300 is needed.

To determine the sample size needed for the 95% confidence interval with a margin of error of 0.052, we can use the formula:

n = (Z^2 * p * (1 - p)) / (E^2)

where n is the sample size, Z is the Z-score corresponding to the desired confidence level (in this case, 1.96), p is the estimated proportion (0.33), and E is the margin of error (0.052).

Substituting the given values into the formula:

n = (1.96^2 * 0.33 * (1 - 0.33)) / (0.052^2)

Simplifying the equation:

n = 299.5554

Rounding up to the nearest whole number, the sample size needed is 300.

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To construct a 95% confidence interval for the proportion of adults who believe economic conditions are getting better with a margin of error of 0.052, the required sample size is approximately 577 participants.

To calculate the sample size needed to construct a 95% confidence interval for the proportion of adults who believe that economic conditions are getting better, with a Gallup poll estimate of 0.33 and a desired margin of error of 0.052, the formula for determining the sample size (n) is:

n = (Z^2*p*(1-p))/E^2,

where Z is the Z-score corresponding to the 95% confidence level, p is the estimated proportion (0.33) and E is the margin of error (0.052). The Z-score for a 95% confidence level is 1.96. Plugging in the values gives:

n = (1.96^2*0.33*(1-0.33))/(0.052^2),

Solving this, we find the sample size required:

n= 576.7.

Since we cannot have a fraction of a person, we round up to the next whole number. Therefore, the sample size needed is 577 participants.

To find x, find the difference between the outer angle and middle angle, then divide by two.

X = (210 - 72) / 2

x = 138 / 2

x = 69

The answer is D.

Answer

subtract 210 with 72 and then divide that by 2 and you get 138. so x=138.

Answer:

  a) at 16%: $10,936.47

  b) at 8%: $124,177.02

Step-by-step explanation:

At annual rate of return "r", the multiplier of Sarah's initial investment will be ...

  k = (1+r)^34

For r = 0.16, k ≈ 155.433166, and Sarah's investment needs to be ...

  $1.7·10^6/k ≈ $10,936.47

__

For r= 0.08, k ≈ 13.6901336, and Sarah's investment needs to be ...

  $1.7·10^6/k ≈ $124,177.02

Answer: i dont now

Step-by-step explanation:

u have to add them togther i guess

Divide both sides by [tex]x^2-1[/tex] to get a linear ODE,

[tex]\dfrac{\mathrm dy}{\mathrm dx}+\dfrac2{x^2-1}y=\dfrac{x+1}{x-1}[/tex]

In order for this operation to be valid in the first place, we require that [tex]x\neq\pm1[/tex] (since that would make [tex]\dfrac1{x^2-1}[/tex] undefined, which we don't want to happen). Then we are forcing any solution to the ODE to exist on any of the three intervals, [tex](-\infty,-1)[/tex], [tex](-1, 1)[/tex], or [tex](1,\infty)[/tex], and either the first or third of these can be chosen as the largest interval.

In case you also need to solve the ODE: Multiply both sides by [tex]\dfrac{1-x}{1+x}[/tex], so that

[tex]\dfrac{1-x}{1+x}\dfrac{\mathrm dy}{\mathrm dx}-\dfrac2{(1+x)^2}y=-1[/tex]

Then the left side can be condensed as the derivative of a product, since

[tex]\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac{1-x}{1+x}\right]=-\dfrac2{(1+x)^2}[/tex]

and we have

[tex]\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac{1-x}{1+x}y\right]=-1[/tex]

Integrate both sides:

[tex]\displaystyle\int\frac{\mathrm d}{\mathrm dx}\left[\frac{1-x}{1+x}y\right]\,\mathrm dx=-\int\mathrm dx[/tex]

[tex]\dfrac{1-x}{1+x}y=-x+C[/tex]

[tex]\implies\boxed{y=\dfrac{(-x+C)(1+x)}{1-x}}[/tex]

The largest interval over which the general solution is defined for the given differential equation is [-1, ∞).

Here's how:

Answer: There is 162 ml of first brand and 108 ml of second brand.

Step-by-step explanation:

Since we have given that

Percentage of vinegar that the first brand contains = 7%

Percentage of vinegar that the second brand contains = 12%

Percentage of vinegar in mixture = 9%

Total amount of dressing = 270 ml

We will use "Mixture and Allegation":

First brand                  Second brand

     7%                                12%

                       9%

--------------------------------------------------------

12%-9%             :                9%-7%

 3%                   :                    2%

So, ratio of first brand to second brand in a mixture is 3:2.

So, Amount of first brand she should use is given by

[tex]\dfrac{3}{5}\times 270\\\\=162\ ml[/tex]

Amount of second brand she should use is given by

[tex]\dfrac{2}{5}\times 270\\\\=108\ ml[/tex]

Hence, there is 162 ml of first brand and 108 ml of second brand.

Answer:

[tex]a_{n}=\frac{1}{2n}[/tex] [Where a ≥ 1 ]

Step-by-step explanation:

The pattern of the given sequence is {[tex]\frac{1}{2},\frac{1}{4},\frac{1}{6},\frac{1}{8},\frac{1}{10},......[/tex]

We have to find a formula for the general term [tex]a_{n}[/tex] of the given sequence.

We can rewrite the terms of the sequence as

[tex]\frac{1}{2}=\frac{1}{(2)(1)}[/tex]

[tex]\frac{1}{4}=\frac{1}{(2)(2)}[/tex]

[tex]\frac{1}{6}=\frac{1}{(2)(3)}[/tex]

[tex]\frac{1}{8}=\frac{1}{(2)(4)}[/tex]

[tex]\frac{1}{10}=\frac{1}{(2)(5)}[/tex]

Now we can write the term [tex]a_{n}[/tex] as

[tex]a_{n}=\frac{1}{2n}[/tex]

Where n = 1, 2, 3, 4, 5......

Answer:

[tex]\large\boxed{B=A+2I}[/tex]

Step-by-step explanation:

It's possible if dimensions of a matrix A and matrix B are n × n

[tex]AB=A^2+2A\qquad\text{multiply both sides on the left by}\ A^{-1}\\\\A^{-1}AB=A^{-1}A^2+A^{-1}(2A)\qquad\text{we know}\ A^{-1}A=I\\\\IB=A^{-1}A\cdot A+2A^{-1}A\\\\IB=IA+2I\qquad\text{we know}\ IA=A\\\\B=A+2I[/tex]

Matrices is an array of numbers, usually 2 dimensional, but can be single dimensional too.

A matrix B such that [tex]AB = A^2 + 2A[/tex] is given as

[tex]B = A + 2I = \left[\begin{array}{cc}4&0\\0&4\end{array}\right][/tex]

(Assuming A is left invertible and  [tex]A = \left[\begin{array}{cc}2&0\\0&2\end{array}\right][/tex])

Suppose that there is an equation

[tex]AB = AC[/tex]

We cannot always say that [tex]B = C[/tex]

If we assume that A is left invertible, then only we can surely say that we have got [tex]B = C[/tex]

Similarly, for [tex]BA = CA[/tex] to imply  [tex]B = C[/tex], we need A to be right invertible.

Assuming that we have A as a left invertible matrix, say

[tex]A = \left[\begin{array}{cc}2&0\\0&2\end{array}\right][/tex]

and [tex]L_A[/tex] be its left inverse, then [tex]L_A A = I[/tex] ([tex]I[/tex] is identity matrix)

Then,

[tex]AB = A^2 + 2A\\A(B) = A(A + 2I_2)\\\\\Multiplying L_{A}\text{ on left side of both terms,}\\\\L_{A} AB = L_{A}A(A + 2I_2)\\B = A + 2I_2\\\\B = \left[\begin{array}{cc}2&0\\0&2\end{array}\right] + \left[\begin{array}{cc}2&0\\0&2\end{array}\right] = \left[\begin{array}{cc}4&0\\0&4\end{array}\right] = 4I_2\\\\B = 4I_2[/tex]

Thus, i

A matrix B such that [tex]AB = A^2 + 2A[/tex] is given as

[tex]B = \left[\begin{array}{cc}4&0\\0&4\end{array}\right][/tex]

(Assuming A is left invertible and  [tex]A = \left[\begin{array}{cc}2&0\\0&2\end{array}\right][/tex])

Learn more about invertible matrices here:

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Answer:

7/32

Step-by-step explanation:

There are 16 numbers.

The median is 92.5 ( find the middle two values and divide by 2).

Minumum is 81

Maximum is 109

First quartile is 88.25 (Find median of the lower half of numbers).

Third quartile is 97.75 (Find median of the upper half of numbers.)

The interquartile range is 9.5 ( Difference between the first and third quartile).

Plotting that data in a box plot, the correct one looks like #1

Find the median.

92 and 93 are both middle numbers so add and divide by two.

92 + 93 = 185

185 / 2 = 92.5

Minimum (smallest number): 81

Maximum (largest number): 109

Find the median of the lower values behind the median.

88.25

Find the mean of the higher values ahead of the median.

97.75

Subtract to find the interquartile range.

97.75 - 88.25 = 9.5

The only option with these characteristics is Option A.

Best of Luck!

For this case we have the following functions:

[tex]F (x) = 3x ^ 2 +1\\G (x) = 2x-3\\H (x) = x[/tex]

We have to:

[tex]G (x) * - 1[/tex] is given by:

[tex](2x-3) * - 1 = -2x +3[/tex]

Thus, the correct option is the option is A.

On the other hand,

[tex]F (x) +G (x) = 3x ^ 2 +1 +(2x - 3) = 3x ^ 2+ 1+ 2x-3 = 3x ^ 2 +2x-2[/tex]

Thus, the correct option is the option is A.

We also have:

[tex]F (-2) = 3 (-2) ^ 2+ 1 = 3 (4)+ 1 = 12+ 1 = 13[/tex]

Thus, the correct option is the option is B.

Last we have:

[tex]F (3)+G (4) -2H (5) = (3 (3) ^ 2+ 1)+ (2 (4) -3) -2 (5) = (3 (9)+ 1) - (8-3) 10 = 28+ 5-10 = 33[/tex]

Thus, the correct option is the option is C.

ANswer:

Option A, A, B, C

Answer:

G-1(x)= -2x+3

F(x)+G(x)=3x^2+2x-2

F(-2)=13

F(3)+G(4)-2H(5)=33

A,A,B,C are the answers to the equations

Answer:

$5.80 Option B.

Step-by-step explanation:

It is given that a 20% tip on a meal that costs $29.17.

The cost of the meal = $29.17

Tip on a meal = 20%

Therefore, 20% of $29.17

= [tex]\frac{20}{100}[/tex] × 29.17

= 0.20 × 29.17

= 5.834

= $5.80

The correct estimate would be $5.80 Option B.

Answer: 0.0222

Step-by-step explanation:

Given : The distribution of trout weights is normally distributed with

Mean : [tex]\mu=402.7\text{ grams}[/tex]

Standard deviation : [tex]\sigma=8.8\text{ grams}[/tex]

Sample size : [tex]n=40[/tex]

The formula to calculate the z-score is given by :-

[tex]z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

Let x be the weight of randomly selected trout.

Then for x = 405.5  , we have

[tex]z=\dfrac{405.5 -402.7}{\dfrac{8.8}{\sqrt{40}}}\approx2.01[/tex]

The p-value : [tex]P(405.5<x)=P(2.01<z)[/tex]

[tex]1-P(2.01)=1-0.9777844=0.0222156\approx0.0222[/tex]

Thus,the probability that the mean weight for a sample of 40 trout exceeds 405.5 grams= 0.0222.

The probability that the mean weight for a sample of 40 trout exceeds 405.5 grams is  0.0222.

The distribution of trout weights is normally distributed with

We have given that

Mean=402.7 grams

Standard deviation =8.8  grams  

Sample size (n)=40

We have to calculate

The probability that the mean weight for a sample of 40 trout exceeds 405.5 grams

Te formula of Z score is given by,

[tex]z=\frac{x-\mu }{\frac{\sigma }{\sqrt{n}}}[/tex]

n= the ample size

x=mean

sigma=standard deviation

So by using the formula we have,

Let x is  the weight of randomly selected trout.

Then for x = 405.5  

[tex]z=\frac{405.5-\402.7}{\frac{\8.8 }{\sqrt{40}}}\\\\\z=2.01[/tex]

we have

The p-value :(405.5<x)

(1-2.01)=1-0.97778

           =0.02221

           =0.0222

Therefore,the probability that the mean weight for a sample of 40 trout exceeds 405.5 grams= 0.0222.

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We have to show that

[tex]\frac{\partial ^{2}u}{\partial t^{2}}=a^{2}\frac{\partial ^{2}u}{\partial x^{2}}[/tex]

for [tex]\frac{\partial ^{2}u}{\partial t^{2}}[/tex] we have

[tex]\frac{\partial ^{2}u}{\partial t^{2}}=a^{2}\frac{\partial ^{2}u}{\partial x^{2}}[/tex]

[tex]\frac{\partial ^{2}u}{\partial t^{2}}=\frac{\partial ^{2}[f(x-at)+g(x+at)]}{\partial t^{2}}[/tex]

[tex]=\frac{\partial }{\partial t}[\frac{\partial[f(x-at)+g(x+at)] }{\partial t}][/tex]

[tex]\frac{\partial }{\partial t}[-a\cdot f'(x-at)+a\cdot g'(x+at)][/tex]

[tex]=a^{2}f''(x-at)+a^{2}g''(x+at)[/tex]

[tex]=a^{2}[f''(x-at)+g''(x+at)].............(i)[/tex]

similarly,

[tex]\frac{\partial ^{2}u}{\partial x^{2}}=\frac{\partial ^{2}[f(x-at)+g(x+at)]}{\partial x^{2}}[/tex]

[tex]=\frac{\partial }{\partial x}[\frac{\partial[f(x-at)+g(x+at)] }{\partial x}][/tex]

[tex]=\frac{\partial }{\partial x}[f'(x-at)+g'(x+at)][/tex]

[tex]=f''(x-at)+g''(x+at).......(ii)[/tex]  

Comparing i and ii we get  

[tex]a^{2}\frac{\partial ^{2}u}{\partial x^{2}}=\frac{\partial ^{2}u}{\partial t^{2}}[/tex]

Hence proved

Answer:

The only bijection is f(x)=2x+1.

I took r to be a constant.

Step-by-step explanation:

Bijections are both onto and one-to-one.

Onto means every element of the codomain gets hit.  Here the codomain is the set of real numbers.  So you want every y to get hit.

One-to-one means you don't want any y to get hit more than once.

f(x)=2x+1 is a linear function.  It is diagonal line so every element of the codomain will get hit and hit only once so this function is onto and one-to-one.

f(x)=x^2+1 is a quadratic function.  It is parabola so not every element of our codomain will get not get hit and of those that do get hit they get hit more than once.  So this is neither onto or one-to-one.

f(x)=r^3 is a constant function.  It is a horizontal line so not every y will get hit so it isn't onto.  The same y is being hit multiple times so it isn't one-to-one.

f(x)=(x^2+1)/(r^2+2) is a quadratic. It is a parabola. Quadratic functions are not onto or one-to-one.

Answer:

Step-by-step explanation:

The Inverse of the matrix doesn't exist because the determinant is equal to 0.

Answer:

The inverse of given matrix is not exist, since determinant is 0.

Step-by-step explanation:

The inverse of a square matrix [tex]A[/tex] is [tex]A^{-1}[/tex] such that

[tex]A A^{-1}=I[/tex] where I is the identity matrix.

Consider, [tex]A = \left[\begin{array}{ccc}3&3&-1\\-12&-12&4\\2&6&0\end{array}\right][/tex]

[tex]\mathrm{Matrix\:can\:only\:be\:inverted\:if\:it\:is\:non-singular,\:that\:is:}[/tex]

[tex]\det \begin{pmatrix}3&3&-1\\ -12&-12&4\\ 2&6&0\end{pmatrix}\ne 0[/tex]

[tex]\det \begin{pmatrix}3&3&-1\\ -12&-12&4\\ 2&6&0\end{pmatrix}[/tex]

[tex]\mathrm{Find\:the\:matrix\:determinant\:according\:to\:formula}:\quad \:[/tex]

[tex]\det \begin{pmatrix}a&b&c\\ d&e&f\\ g&h&i\end{pmatrix}=a\cdot \det \begin{pmatrix}e&f\\ h&i\end{pmatrix}-b\cdot \det \begin{pmatrix}d&f\\ g&i\end{pmatrix}+c\cdot \det \begin{pmatrix}d&e\\ g&h\end{pmatrix}[/tex]

[tex]=3\cdot \det \begin{pmatrix}-12&4\\ 6&0\end{pmatrix}-3\cdot \det \begin{pmatrix}-12&4\\ 2&0\end{pmatrix}-1\cdot \det \begin{pmatrix}-12&-12\\ 2&6\end{pmatrix}[/tex]

[tex]=3\left(-24\right)-3\left(-8\right)-1\cdot \left(-48\right)[/tex]

[tex]3\left(-24\right)-3\left(-8\right)-1\cdot \left(-48\right)=0[/tex]

Therefore, the inverse of given matrix is not exist, since determinant is 0.

Final answer:

The test statistic for the proportion of yellow pea pods being 25% is calculated using the sample proportion, hypothesized proportion, and sample size. Using the given data, the test statistic (Z-score) comes out to approximately -1.412.

Explanation:

To find the value of the test statistic for the claim that the proportion of peas with yellow pods is equal to 0.25 (25%), we use the sample statistics provided from the experiment. You mentioned that there were 590 peas in total, with 139 having yellow pods. First, we check if the conditions for the binomial distribution are met, which in this case they are as we are dealing with two outcomes (yellow pods and not yellow pods), a fixed number of trials (590 peas), and each pea is independent of the others.

The test statistic for a proportion is calculated using the formula:

Z = (p' - p) / (sqrt(p(1 - p) / n))

Where:

Now, we calculate the test statistic:

Z = (0.2356 - 0.25) / (sqrt(0.25 × (1 - 0.25) / 590))

Z ≈ -1.412

This Z-score tells us how many standard deviations the observed sample proportion (0.2356) is from the hypothesized proportion (0.25).

[tex]1.\rightarrow \frac{dy}{dx}-y=e^x y^2\\\\\rightarrow \frac{1}{y^2}\frac{dy}{dx}-\frac{1}{y}=e^x\\\\ \text{put},\frac{-1}{y}=z\\\\ \frac{dy}{y^2} =d z\\\\ \frac{dy}{dx} \times \frac{1}{y^2}=\frac{dz}{dx}\\\\\frac{dz}{dx} +z=e^x\\\\ \text{Integrating factor}=e^{\int {1} \, dx}\\\\=e^x \\\\ \text{Multiplying both sides by }e^x\\\\e^x(\frac{dz}{dx} +z)=e^{2x}\\\\ \text{Integrating both sides}\\\\z e^x=\frac{e^{2x}}{2}+C\\\\ \frac{-e^x}{y}=\frac{e^{2x}}{2}+C[/tex]

-----------------------------------------------------------------------------------------------------------------

[tex]\rightarrow \frac{dy}{dx}=x+\frac{y}{x}-y\\\\\rightarrow \frac{dy}{dx}-x=\frac{y}{x}-y\\\\\rightarrow \frac{dy}{dx}+y(1-\frac{1}{x})=x\\\\\text{Integrating factor}=e^{\int{1-\frac{1}{x}}\,dx}\\\\=e^{x-\log x}\\\\ \text{Multiplying both sides by} e^{x-\log x}\\\\e^{x-\log x}\times[\frac{dy}{dx}+y(1-\frac{1}{x})]=x \times e^{x-\log x}\\\\y\times e^{x-\log x} =\int x \times e^{x-\log x} \, dx}\\\\y\times e^{x-\log x}=\int x \times \frac{e^x}{e^{\log x}}\,dx\\\\y\times e^{x-\log x}=\int x \times \frac{e^x}{x} \, dx\\\\y\times e^{x-\log x}=e^x+K[/tex]

Answer:

flow rate of to infuse the 1000 mL over 5 hours is 33.33 gtt/min

Step-by-step explanation:

Given data

volume = 1000 mL

time =  5 hours

drop factor = 10 gtt/min

to find out

flow rate of to infuse the 1000 mL over 5 hours

Solution

we know flow rate formula  i.e.

flow rate =  ( volume × drop factor )  / time   .................1

here time will be in min so time =  5 hours = 5  × 60 = 300 min

put volume, drop factor and time value in equation 1 and we get flow rate

flow rate =  ( volume × drop factor )  / time

flow rate =  ( 1000 × 10 )  / 300

flow rate = 33.33 gtt/min

flow rate of to infuse the 1000 mL over 5 hours is 33.33 gtt/min

Answer:

if x= -1 then its is NOT in the domain of h.

Step-by-step explanation:

Domain is the set of values for which the function is defined.

we are given the function

[tex]h(x) =\frac{x+1}{x^2 + 2x + 1}[/tex]

Solving the denominator by factorization

[tex]h(x) =\frac{x+1}{x^2 + x+x + 1}\\h(x) =\frac{x+1}{x(x+1)+1(x + 1)}\\h(x) =\frac{x+1}{(x+1)(x+1)}\\h(x) =\frac{1}{(x+1)}[/tex]

So, if x = -1 then its is NOT in the domain of h.

Answer:

a > 12

Step-by-step explanation:

Isolate the variable a. Treat the > sign like the = sign. What you do to one side, you do to the other. Add 1 to both sides:

a - 1 (+1) > 11 (+1)

a > 11 + 1

a > 12

a > 12 is your answer.

~

Answer:

[tex]\huge \boxed{a>12}[/tex]

Step-by-step explanation:

Add by 1 from both sides.

[tex]\displaystyle a-1+1>11+1[/tex]

Simplify, to find the answer.

[tex]\displaystyle 11+1=12[/tex]

[tex]\displaystyle a>12[/tex], which is our answer.

Answer: 0.3439

Step-by-step explanation:

Total number of digits : 10

The number of digits except zero =9

The probability of selecting non-zero number :-

[tex]\dfrac{9}{10}=0.9[/tex]

Then, the probability that one such phone number , the last four digits do not include any zero:-

[tex]\text{P(no zero )}=(0.9)^4[/tex]

Then , the probability that for one such phone​ number, the last four digits include at least one 0:-

[tex]\text{P(at-least one zero )}=1-(0.9)^4=0.3439[/tex]

Hence, the probability that for one such phone​ number, the last four digits include at least one 0 is 0.3439 .

To find the probability of at least one 0 in a four-digit number, one can use the complement of the probability of no 0s occurring in any of the digits. The probability of at least one 0 is approximately 34.39%.

The student is inquiring about the probability of a certain event, specifically related to randomly generating telephone numbers. To find the probability that at least one digit is a 0 in a randomly generated four-digit number, we can use the complementary probability approach. The probability of not getting a 0 in one digit is 9/10 since there are 9 other possible digits (1-9). Hence, the probability of not getting a 0 in any of the four digits is (9/10)^4. Subtracting this from 1 will give the probability of having at least one 0 in the four-digit sequence:

Probability of at least one 0 = 1 - (Probability of no 0 in any digit)

Probability of at least one 0 = 1 - (9/10)^4

After calculating, we have:

Probability of at least one 0 = 1 - 0.6561 = 0.3439

Therefore, the probability of having at least one 0 in a randomly chosen telephone number with four digits is approximately 34.39%.

Answer: They meet after 1 hour 42 minutes.

Step-by-step explanation:

Since we have given that

Dana leaves Las Vegas for LA at 2 p.m. driving at 55 mph.

Let the time taken by Dana be 't'.

Distance traveled by Dana would be 55t.

At 4 p.m. Lance leaves LA for Las Vegas driving at 45 mph along the same route.

It means after 2 hours Lance leave for LA.

So, time taken by Lance be 't-2'.

Distance traveled by Lance would be 45(t-2)

Total distance  = 260 miles

According to question, it becomes,

[tex]55t+45(t-2)=260\\\\55t+45t-90=260\\\\100t=260-90\\\\100t=170\\\\t=1.7\ hours=1\dfrac{7}{10}=1\ hour\ and\ \dfrac{7\times 60}{10}\ minutes=1\ hour\ 42\ minutes[/tex]

Hence, they meet after 1 hour 42 minutes.

Answer:

Mean = 7.38

SD = 0.148

b. 95%

Step-by-step explanation:

Given data is:

7.1 7.5 7.6 7.4 7.3 7.3 7.3 7.5

Mean:

Mean = Sum/No. of values

= (7.1+7.5+7.6+7.4+7.3+7.3+7.3+7.5)/8

=59/8

=7.38

Standard Deviation:

x                  x-x'           (x-x')^2

7.1               -0.28           0.0784

7.5              0.12            0.0144

7.6              0.22           0.0484

7.4              0.02           0.0004

7.3             -0.08           0.0064

7.3             -0.08            0.0064

7.3              -0.08            0.0064

7.5              0.12              0.0144

                      Total :     0.1752

Variance = Sum of squares/No of items

= 0.1752/8 = 0.0219

SD =√0.0219 = 0.148

b. What percentage of the data is within 2 standard deviations of the​ mean?

95% of data is within two standard deviations of mean in a standard normal distribution ..

The mean of the pH test results is 7.375, and the standard deviation is approximately 0.086.

To find the mean and standard deviation of the pH test results, we can use the following formulas:

Mean: Add up all the pH values and divide by the total number of samples (in this case, 8). So, (7.1 + 7.5 + 7.6 + 7.4 + 7.3 + 7.3 + 7.3 + 7.5) / 8 = 7.375.

Standard Deviation: Calculate the difference between each pH value and the mean, square each difference, calculate the mean of those squared differences, and then take the square root. Let's break it down into steps: Subtract the mean from each pH value: (7.1 - 7.375), (7.5 - 7.375), (7.6 - 7.375), (7.4 - 7.375), (7.3 - 7.375), (7.3 - 7.375), (7.3 - 7.375), (7.5 - 7.375). Square each difference: (0.0425)^2, (0.125)^2, (0.225)^2, (0.025)^2, (-0.075)^2, (-0.075)^2, (-0.075)^2, (0.125)^2. Calculate the mean of the squared differences: (0.0018 + 0.0156 + 0.0506 + 0.000625 + 0.005625 + 0.005625 + 0.005625 + 0.0156) / 8 = 0.0074. Take the square root of the mean: √0.0074 ≈ 0.086.

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Answer:

The probability is 0.2356.

Step-by-step explanation:

Let X is the event of using the smartphone in meetings or classes,

Given,

The probability of using the smartphone in meetings or classes, p = 51 % = 0.51,

So, the probability of not using smartphone in meetings or classes, q = 1 - p = 1 - 0.51 = 0.49,

Thus, the probability that fewer than 5 of them use their smartphones in meetings or classes.

P(X<5) = P(X=0) + P(X=1) + P(X=2) + P(X=3)+P(X=4)

Since, binomial distribution formula is,

[tex]P(x) = ^nC_r p^x q^{n-x}[/tex]

Where, [tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]

Here, n = 11,

Hence,  the probability that fewer than 5 of them use their smartphones in meetings or classes

[tex]=^{11}C_0 (0.5)^0 0.49^{11}+^{11}C_1 (0.5)^1 0.49^{10}+^{11}C_2 (0.5)^2 0.49^{9}+^{11}C_3 (0.5)^3 0.49^{8}+^{11}C_4 (0.5)^4 0.49^{7} [/tex]

[tex]=(0.5)^0 0.49^{11}+11(0.5)0.49^{10} + 55(0.5)^2 0.49^{9}+165 (0.5)^3 0.49^{8} +330(0.5)^4 0.49^{7} [/tex]

[tex]=0.235596671797[/tex]

[tex]\approx 0.2356[/tex]