In the slideshow Simplifying Radicals, under media in Chapter 9, one specific condition to satisfy is to use the quotient rule.

A. True
B. False

Answer:

4×10⁶

Step-by-step explanation:

Concept to know is that when you divide two numbers with the same base, you subtract their exponent.

So this problem could be split into 2 parts. The non power-of-ten numbers, and the power of tens numbers.

I divided 9.2/2.3 and got 4.

I then divided 10⁸/10² and got 10⁸⁻² = 10⁶.

Put it together and you get 4×10⁶

Number of times the value of 2.3×10² from 9.2×10⁸ is 4×10⁶.

Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as 1.56×10⁷.

The given numbers are 9.2×10⁸ and 2.3×10².

Now, number of times =9.2×10⁸/2.3×10²

= 4×[tex]10^{8-2}[/tex]

= 4×10⁶

Therefore, number of times the value of 2.3×10² from 9.2×10⁸ is 4×10⁶.

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Answer:

[tex]ME= \frac{Width}{2}=\frac{0.078}{2}=0.039[/tex]

[tex]\hat p =0.688+0.039=0.727[/tex]

[tex]\hat p =0.766-0.039=0.727[/tex]

Step-by-step explanation:

Assuming that the confidence interval is (0.688; 0.766)

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The population proportion have the following distribution  

[tex]p \sim N(p,\sqrt{\frac{p(1-p)}{n}})[/tex]  

The confidence interval would be given by this formula  

[tex]\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]  

For the 95% confidence interval the value of [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2=0.025[/tex], with that value we can find the quantile required for the interval in the normal standard distribution.  

[tex]z_{\alpha/2}=1.96[/tex]  

Use the confidence interval to find the point estimate and margin of error for the proportion

The margin of error is given by :

[tex]Me=z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

And for our case we can find the width of the confidence interval like this:

Width =0.766-0.688=0.078

And the estimation for the margin of error would be given by:

[tex]ME= \frac{Width}{2}=\frac{0.078}{2}=0.039[/tex]

Now we can find th point of estimate adding the margin of error to the lower limit of the interval or subtracting the margin of error to the upper limit, like this:

[tex]\hat p =0.688+0.039=0.727[/tex]

[tex]\hat p =0.766-0.039=0.727[/tex]

The point estimate is the midpoint of the confidence interval, calculated using the equation: (a + b) / 2. The margin of error is the amount by which the point estimate could differ from the actual proportion, calculated as the absolute difference between the point estimate and either limit of the confidence interval.

The question doesn't provide a specific confidence interval. Hence, let's take it in a general form as (a, b). Here, a and b are the lower and upper limits of the 95% confidence interval for the proportion of customers interested in a breakfast menu.

As per the properties of confidence intervals, the point estimate is the midpoint of the interval. It is calculated as the sum of the lower and upper limits divided by 2.

To calculate this: Point estimate = (a + b) / 2

On the other hand, the margin of error is the distance from this point estimate to either of the confidence interval limits (upper or lower). It can be calculated as the difference between the point estimate and the lower limit (or the upper limit).

To calculate this: Margin of Error = |Point estimate - a| = |Point estimate - b|

If you have specifics for 'a' and 'b', you can substitute those values into the point estimate and margin of error equations to get those values precise to three decimal places.

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The solution is a three-step process. First, solve the characteristic equation and determine the homogeneous solution. Second, use the method of undetermined coefficients to find the particular solution. Finally, the general solution to the nonhomogeneous differential equation equals the sum of the homogeneous solution and the particular solution.

To solve this, we'll need to go through three stages: solving the homogeneous equation, finding the particular solution, and finally combining these to form the general solution.

Step 1: The associated homogeneous equation is y'' + 4y' + 5y = 0. The general solution to this homogeneous equation can be obtained by solving the characteristic quadratic equation r^2 + 4r + 5 = 0. You will find that the roots are complex, and the general solution for the homogeneous differential equation would be in the form yh = c1*e^(-2x)cos(x)+c2*e^(-2x)sin(x).

Step 2: The particular solution of the nonhomogeneous differential equation can be obtained using the method of undetermined coefficients or the method of variation of parameters. For this case, we will use the method of undetermined coefficients. You will eventually find after performing these methods that the particular solution yp is of the form yp = Ax + Be^(?x), where A and B are constants which can be calculated.

Step 3: Finally, the general solution to the nonhomogeneous differential equation we are trying to solve is simply the sum of the general solution from Step 1 (the homogeneous solution) and the particular solution from Step 2. This would yield a solution y = c1*e^(-2x)cos(x) + c2*e^(-2x)sin(x) + Ax + Be^(?x).

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The solution to the homogeneous differential equation is yh=c1e^-2x cos(x) + c2e^-2x sin(x). The particular solution, yp, can be obtained using the method of undetermined coefficients for the nonhomogeneous part, -10x+e^(-x). The final solution y is the sum of yh and yp.

The nonhomogeneous differential equation you have provided is in the form of y″+4y′+5y=-10x+e^(-x).

To find the particular solution (yp), we first need to find the homogeneous solution. The characteristic equation of the associated homogeneous differential equation is r^2+4r+5=0. Solving this quadratic equation, we obtain complex roots as r = -2±i. Hence, the homogeneous solution (yh) is expressed as yh= c1e^-2x cos(x) + c2e^-2x sin(x)

Next, to find yp for f(x)= -10x+e^(-x), we use the method of undetermined coefficients. However, due to the limitation of the platform, it would be too complicated to carry out this procedure here.

Eventually, the final solution of the original nonhomogeneous differential equation will be obtained by adding yh and yp, i.e., y= yh+yp.

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Compute the volume of [tex]Q[/tex]:

[tex]\displaystyle\iiint_Q\mathrm dV=\int_0^2\int_0^{2-x}\int_0^{2-x-y}\mathrm dz\,\mathrm dy\,\mathrm dx=\frac43[/tex]

Integrate [tex]f(x,y,z)=x+y+z[/tex] over [tex]Q[/tex]:

[tex]\displaystyle\iiint_Qf(x,y,z)\,\mathrm dV=\int_0^2\int_0^{2-x}\int_0^{2-x-y}(x+y+z)\,\mathrm dz\,\mathrm dy\,\mathrm dx=2[/tex]

So the average value of [tex]f[/tex] over [tex]Q[/tex] is 2/(4/3) = 3/2.

To solve this mathematical problem, we need to understand the Average Value of a Continuous function.

The average value of a continuous function is derived by taking the integral of the function over the interval. This is then divided using the length of that interval.

To determine the average value of the function  f(x, y, z), over the  solid region named Q,

we can say:

[tex]\int\int\int _{Q}[/tex]  dV = [tex]\int_{0}^{2} \int_{0}^{2-x} \int_{0}^{2-x-y}[/tex]  dzdydx = 4/3

Integrating the above, we have

[tex]\int\int\int _{Q}[/tex] [tex]f(x,y,z)[/tex] dV = [tex]\int_{0}^{2} \int_{0}^{2-x} \int_{0}^{2-x-y}[/tex]   (x+ y + z) dzdydx  = 2

Therefore, the average value of the function f over the Solid region Q becomes:

2/ (4/3) = 1.5 or 3/2

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Answer:

n=1041  or higher

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The population proportion have the following distribution

[tex]p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})[/tex]

2) Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by [tex]\alpha=1-0.99=0.01[/tex] and [tex]\alpha/2 =0.005[/tex]. And the critical value would be given by:

[tex]z_{\alpha/2}=-2.58, z_{1-\alpha/2}=2.58[/tex]

The margin of error for the proportion interval is given by this formula:  

[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]    (a)  

And on this case we have that [tex]ME =\pm 0.04[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex]   (b)  

Since we don't have a prior estimation for th proportion of interest, we can use this value as an estimation [tex]\hat p =0.5[/tex] And replacing into equation (b) the values from part a we got:

[tex]n=\frac{0.5(1-0.5)}{(\frac{0.04}{2.58})^2}=1040.06[/tex]  

And rounded up we have that n=1041  or higher.

Answer:

d. 126; 70

Step-by-step explanation:

given that Ron  finds 9 books at a bookstore that he would like to buy, but he can afford only 5 of them.

Out of 9 books he has to select 5 of them

Here selection of books can be done in any order.  Hence order does not matter

No of ways he selects 5 books out of 9 books = 9C5

= 126

Part II

One book is a must

Hence he has options only 4 books from the remaining 8.

No of ways when one book is compulsory = selecting 3 books from 8 books

= 8C4

= 70

Option d is right.

The Triangle Angle Sum Theorem states that the sum of interior angles in any triangle is always 180 degrees. Represented by the equation x + y + z = 180°, it allows for solving missing angles in a triangle using x = 180° - y - z or similar expressions.

Understanding the Triangle Angle Sum Theorem:

In any triangle, regardless of its shape or size, the sum of the interior angles always equals 180 degrees. This is known as the Triangle Angle Sum Theorem.

This theorem is a fundamental property of triangles and has numerous applications in geometry and other mathematical fields.

Representing the Angle Sum with an Equation:

Let's use variables to represent the angle measures of a triangle:

Angle 1 = x

Angle 2 = y

Angle 3 = z

According to the Triangle Angle Sum Theorem, the equation becomes:

x + y + z = 180°

Solving for Missing Angles:

This equation can be used to solve for any missing angle if we know the values of the other two angles.

For example, if we know the measures of angles y and z, we can find x using:

x = 180° - y - z

Similarly, we can find y or z if we know x and the other angle.

Example:

Consider a triangle with angles x = 50°, y = 70°, and z unknown.

Using the equation:

z = 180° - x - y = 180° - 50° - 70° = 60°

The equation that represents the sum of the angle measures of the triangle is 2y + x = 198.

The value of x is 86 and the value of y is 56.

A)

The sum of the interior angles of a triangle adds up to 180 degrees.

Hence, the equation that represents the sum of the angle measures of the given triangle is:

( y - 18 ) + y + x = 180

Simplifying; we get:

y + y + x = 180 + 18

2y + x = 198

B)

To solve for the values of x and y, we solve the system of equations:

2y + x = 198

3x - 5y = -22

Solve for x in equation 1:

2y + x = 198

x = -2y + 198

Plug x = -2y + 198 into equation 2 and solve for y:

3( -2y + 198 ) - 5y = -22

-6y + 594 - 5y = -22

-11y + 594 = -22

11y = 594 + 22

11y = 616

y = 616/11

y = 56

Now, plug y = 56 into equation 3 and solve for x:

x = -2y + 198

x = -2( 56 ) + 198

x = -112 + 198

x = 86

Therefore, the x = 86 and y = 56.

The missing image is uploaded below:

Work is provided in the image attached.

The probability is approximately 0.0833, indicating an 8.33% chance that the mean falls between 119 and 122 mm Hg.

To determine the probability that the mean systolic blood pressure of 23 randomly selected women aged 18-24 falls between 119 and 122 mm Hg, we utilize the Central Limit Theorem and z-scores.

First, we calculate the standard error of the mean (SEM) using the population standard deviation and the sample size. With a mean of 114.8 mm Hg and a standard deviation of 13.1 mm Hg, the SEM is approximately 2.7316 mm Hg.

Then, we standardize the values of 119 and 122 mm Hg into z-scores. For 119 mm Hg, the z-score is approximately 0.3206, and for 122 mm Hg, it's approximately 0.5496.

Using a standard normal distribution table or calculator, we find the area under the curve between these z-scores, representing the probability. Subtracting the cumulative probability of the lower z-score from the higher z-score gives us approximately 0.0833. This indicates that there's an 8.33% chance that the mean systolic blood pressure of the 23 randomly selected women aged 18-24 falls between 119 and 122 mm Hg. Thus, within the specified range, there's a moderate probability of occurrence based on the given parameters of the population distribution.

Answer:

1,non linear and separable

Step-by-step explanation:

given is a differential equation as

[tex]\frac{dy}{dx} =y(y-2)e^x[/tex]

Here we have derivative highest is first derivative

I) Order = 1 (since first derivative is used)

2) It is not linear since the variable y has power 2.

3) To check whether separable or not

[tex]\frac{dy}{dx} =y(y-2)e^x[/tex]

we can take all y variables to left side and x to right side

Hence separable

Answer:

Flux across S = 72π

Step-by-step explanation:

First we need to calculate the divergence of the vector field:

Div F = [tex]\frac{dFx}{dx} + \frac{dfy}{dy} + \frac{dFz}{dz}[/tex]

Where

Fx = 8y^2 - 3x

Fy = -9x+4y

Fz = -2y^3 +z

Then

Div F = -3 +4 + 1  = 2

And how the vector field’s divergence is a constant, we can calculate the flux across of the surface how:

Flux across S = Div F * Volume of Sphere

Fluz acroos S = 2(4/3)π[tex]r^{3}[/tex]

                 r : Sphere’s radio

Flux across S = (2)(4/3)π[tex]3^{3}[/tex]

                       = 72π

To compute the net outward flux of the field across the sphere, first calculate the divergence of the field and then apply the Divergence Theorem. The flux equals the integral of the divergence over the volume of the sphere.

The first step of this problem is to compute the divergence of the vector field F. The divergence is the scalar quantity obtained by performing a dot product of the del operator with the field. For the given field F = <8y² - 3x, -9x + 4y, -2y³+ z>, the divergence is thus Div(F) = ∇.F = d(8y² - 3x)/dx + d(-9x + 4y)/dy + d(-2y³ + z)/dz.

For the sphere S where x² + y² + z² = 9, the radius r is √9 = 3. According to the Divergence Theorem, the flux across the boundary of the volume enclosed by S equals the triple integral of the divergence over the volume. So, the outward flux = ∫∫∫(Div(F).dV), where the triple integral is taken over the volume of the sphere.

Carry out the calculations to find the exact value of the outward flux.

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Answer: the principal is approximately 23377

Step-by-step explanation:

Let the Initial amount deposited into the account be $x This means that the principal is P = $x

It was compounded quarterly. This means that it was compounded four times in a year. So

n = 4

The rate at which the principal was compounded is 3.575%. So

r = 3.575/100 = 0.03575

It would be compounded for 30 years So

t = 30

The formula for compound interest is

A = P(1+r/n)^nt

A = total amount in the account at the end of t years.

A is given as $68,000

Therefore

68000= x (1+0.03575/4)^4×30

68000= x (1+0.0089375)^120

68000= x (1.0089375)^120

68000 = 2.90878547719x

x = 68000/2.90878547719

x = 23377.4545

Answer:

The answer is B.

Step-by-step explanation:

23,377.

Answer:

Null hypothesis:[tex]p_{1} = p_{2}[/tex]  

Alternative hypothesis:[tex]p_{1} \neq p_{2}[/tex]

[tex]z=\frac{0.41-0.43}{\sqrt{0.42(1-0.42)(\frac{1}{1300}+\frac{1}{1300})}}=-1.033[/tex]    

[tex]p_v =2*P(Z<-1.033)=0.302[/tex]  

So the p value is a very high value and using any significance level for example [tex]\alpha=0.05, 0,1,0.15[/tex] always [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the the proportion 1 is not significantly different from the proportion 2.  

Step-by-step explanation:

1) Data given and notation  

n = 1300 sample size selected

[tex]p_{1}=0.41[/tex] represent the proportion of adults approve of President1.

[tex]p_{2}=0.42[/tex] represent the proportion of adults approve of President2.

z would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the value for the test (variable of interest)  

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to check if the proportion 1 is different from proportion 2  , the system of hypothesis would be:  

Null hypothesis:[tex]p_{1} = p_{2}[/tex]  

Alternative hypothesis:[tex]p_{1} \neq p_{2}[/tex]  

We need to apply a z test to compare proportions, and the statistic is given by:  

[tex]z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}[/tex]   (1)  

Where [tex]\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{0.41+0.43}{2}=0.42[/tex]  

3) Calculate the statistic  

Replacing in formula (1) the values obtained we got this:  

[tex]z=\frac{0.41-0.43}{\sqrt{0.42(1-0.42)(\frac{1}{1300}+\frac{1}{1300})}}=-1.033[/tex]    

4) Statistical decision

For this case we don't have a significance level provided [tex]\alpha[/tex], but we can calculate the p value for this test.    

Since is a two sided test the p value would be:  

[tex]p_v =2*P(Z<-1.033)=0.302[/tex]  

So the p value is a very high value and using any significance level for example [tex]\alpha=0.05, 0,1,0.15[/tex] always [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the the proportion 1 is not significantly different from the proportion 2.  

Answer:

d) 35

Step-by-step explanation:

Consider the venn diagram attached below

Given

n(U) = 200

n(A) = 165

n(B) = 95

n(A ∩ B ) = 80

n([tex]A^{c}[/tex] ∪ B) =?

Using

n(A  ∪ B) = n(A) + n(b) - n(A ∩)B

For [tex]A^{c}[/tex]

[tex]n(A^{c}\cup B) = n(A^{C})+ n(B)-n(A^{c}\cap B)---(1)\\n(A^{c})=U-A\\n(A^{c})=n(U)-n(A)\\A^{c}\cap B=B\\n(A^{c}\cap B) =n(B)\\[/tex]

Then (1) becomes

[tex]n(A^{c}\cup B) = n(U)-n(A)+ n(B)-n(B)\\n(A^{c}\cup B)=200-165+95-95\\n(A^{c}\cup B)=35[/tex]

Answer:

The smallest integer is 9 and there are 19 terms in the sequence.

Step-by-step explanation:

Arithmetic Sequence

The general term of an arithmetic sequence is

[tex]\displaystyle a_n=a_1+(n-1)r\ ........[eq\ 1][/tex]

And the sum of all n terms is

[tex]\displaystyle s_n=\frac{a_1+a_n}{2}n...... [eq\ 2][/tex]

The sequence of the question complies with

[tex]\displaystyle s_n=342[/tex]

[tex]\displaystyle a_n=3a_1[/tex]

Using the last condition in eq 1 and knowing that r=1 (consecutive numbers)

[tex]\displaystyle a_n=a_1+n-1=3a_1[/tex]

Rearranging

[tex]\displaystyle 2a_1=n-1[/tex]

Using eq 2

[tex]\displaystyle \frac{a_1+a_n}{2}n=342[/tex]

Replacing the first condition

[tex]\displaystyle \frac{a_1+3a_1}{2}n=342[/tex]

Simplifying

[tex]\displaystyle 2a_1\ n=342[/tex]

Since  

[tex]\displaystyle 2a_1=n-1[/tex]

We have

[tex]\displaystyle n(n-1)=342[/tex]

Factoring

[tex]\displaystyle n(n-1)=(19)(18)[/tex]

We find the number of terms

[tex]\displaystyle n=19[/tex]

The first term is

[tex]\displaystyle a_1=\ \frac{342}{38}=9[/tex]

Final answer:

The smallest integer is 6, and the sequence contains 19 terms.

Explanation:

To solve the problem about a sequence of consecutive integers where the sum is 342 and the largest integer is three times the smallest integer, we will use the formula for the sum of an arithmetic sequence and set up a system of equations. The sum of an arithmetic sequence is given by: S = ½ n(first integer + last integer), where S is the sum of the sequence, n is the number of terms, the first integer is a, and the last integer is l. We are given S = 342 and l = 3a.

Let's set up the system of equations:

By substituting l = 3a into the first equation, we get:

Hence, n and a must be factors of 684 (since 342 = 2 × 171 = 4 × 342). Through trial and error or using a system of linear equations, we can find the appropriate values of n and a that will satisfy both the sum and the relationship between the smallest and largest integers.

Ultimately, we find that the smallest integer in the sequence is 6, and the sequence contains 19 terms.

Answer: B. 0.036

Step-by-step explanation:

Formula for standard error :

[tex]SE=\sqrt{\dfrac{p(1-p)}{n}}[/tex]

, where p = Population proportion and n= sample size.

Let p be the population proportion of the people who favor new taxes.

As per given , we have

n= 170

[tex]p=\dfrac{55}{170}\approx0.324[/tex]

Substitute these values in the formula, we get

[tex]SE=\sqrt{\dfrac{0.324(1-0.324)}{170}}\\\\=\sqrt{0.00129}\\\\=0.0359165699921\approx0.036[/tex]

Hence, the standard error of the estimate is 0.036.

∴ The correct answer is OPTION B. 0.036

Answer:

a. The rock's velocity is [tex]v(t)=36-1.6t \:{(m/s)}[/tex]  and the acceleration is [tex]a(t)=-1.6  \:{(m/s^2)}[/tex]

b. It takes 22.5 seconds to reach the highest point.

c. The rock goes up to 405 m.

d. It reach half its maximum height when time is 6.59 s or 38.41 s.

e. The rock is aloft for 45 seconds.

Step-by-step explanation:

a.

The rock's velocity is the derivative of the height function [tex]s(t) = 36t - 0.8 t^2[/tex]

[tex]v(t)=\frac{d}{dt}(36t - 0.8 t^2) \\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\v(t)=\frac{d}{dt}\left(36t\right)-\frac{d}{dt}\left(0.8t^2\right)\\\\v(t)=36-1.6t[/tex]

The rock's acceleration is the derivative of the velocity function [tex]v(t)=36-1.6t[/tex]

[tex]a(t)=\frac{d}{dt}(36-1.6t)\\\\a(t)=-1.6[/tex]

b. The rock will reach its highest point when the velocity becomes zero.

[tex]v(t)=36-1.6t=0\\36\cdot \:10-1.6t\cdot \:10=0\cdot \:10\\360-16t=0\\360-16t-360=0-360\\-16t=-360\\t=\frac{45}{2}=22.5[/tex]

It takes 22.5 seconds to reach the highest point.

c. The rock reach its highest point when t = 22.5 s

Thus

[tex]s(22.5) = 36(22.5) - 0.8 (22.5)^2\\s(22.5) =405[/tex]

So the rock goes up to 405 m.

d. The maximum height is 405 m. So the half of its maximum height = [tex] \frac{405}{2} =202.5 \:m[/tex]

To find the time it reach half its maximum height, we need to solve

[tex]36t - 0.8 t^2=202.5\\36t\cdot \:10-0.8t^2\cdot \:10=202.5\cdot \:10\\360t-8t^2=2025\\360t-8t^2-2025=2025-2025\\-8t^2+360t-2025=0[/tex]

For a quadratic equation of the form [tex]ax^2+bx+c=0[/tex] the solutions are

[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]\mathrm{For\:}\quad a=-8,\:b=360,\:c=-2025:\\\\t=\frac{-360+\sqrt{360^2-4\left(-8\right)\left(-2025\right)}}{2\left(-8\right)}=\frac{45\left(2-\sqrt{2}\right)}{4}\approx 6.59\\\\t=\frac{-360-\sqrt{360^2-4\left(-8\right)\left(-2025\right)}}{2\left(-8\right)}=\frac{45\left(2+\sqrt{2}\right)}{4}\approx 38.41[/tex]

It reach half its maximum height when time is 6.59 s or 38.41 s.

e. It is aloft until s(t) = 0 again

[tex]36t - 0.8 t^2=0\\\\\mathrm{Factor\:}36t-0.8t^2\rightarrow -t\left(0.8t-36\right)\\\\\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}\\\\t=0,\:t=45[/tex]

The rock is aloft for 45 seconds.

Final answer:

The question explores kinematic principles by calculating the velocity, acceleration, time to reach the highest point, maximum height, time to reach half the maximum height, and total duration aloft for a rock thrown vertically on the moon, giving us the values as follows upon solving.

v(t) = (36 - 1.6t) m/s

a(t) = -1.6 m/s²

t_highest = 22.5 seconds

h_max = 405 meters

t_half ≈ 11.6 seconds

t_total = 45 seconds

Explanation:

The question involves calculating velocity, acceleration, and the dynamics of a rock thrown vertically on the moon, illustrating concepts from kinematic equations in physics.

a. Velocity and acceleration at time t

The velocity of the rock at time t is given by the derivative of the position function s = 36t - 0.8t², which is v(t) = 36 - 1.6t Acceleration, being the derivative of velocity, is constant at -1.6 m/s², due to moon's gravity.

b. Time to reach the highest point

At the highest point, the velocity is 0. Setting v(t) = 0, we find t = 22.5 seconds.

c. Height at the highest point

Plugging t = 22.5 into the position function, we find the maximum height is 405 meters.

d. Time to reach half the maximum height

Setting s = 202.5 meters in the original equation and solving for t, we find two values, but the relevant one is approximately 11.6 seconds.

e. Total duration aloft

To find when the rock returns to the surface, set s = 0 in the original equation and solve for t, giving a total duration of 45 seconds.

Answer:

Option D -[tex]\frac{7}{8}\times 8\frac{1}{10}\approx 1\times 8[/tex]

Step-by-step explanation:

To find : Which expression is the best estimate of the product of [tex]\frac{7}{8}[/tex] and [tex]8\frac{1}{10}[/tex]?

Solution :

We estimate the number individually,

[tex]\frac{7}{8}=0.875[/tex]

Estimate the number we get 0.875≈1.

[tex]8\frac{1}{10}=\frac{81}{10}[/tex]

[tex]8\frac{1}{10}=8.1[/tex]

Estimate the number we get 8.1≈8.

The product of [tex]\frac{7}{8}[/tex] and [tex]8\frac{1}{10}[/tex] is

[tex]\frac{7}{8}\times 8\frac{1}{10}\approx 1\times 8[/tex]

Therefore, option D is correct.

Answer:

Option B) In control as this one data point is not more than three standard deviations from the mean

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 104 rotations per minute

Standard Deviation, σ = 8.2 rotations per

We are given that the distribution of process is a bell shaped distribution that is a normal distribution.

Formula:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

For x = 118

[tex]z = \displaystyle\frac{118-104}{8.2} = 1.7073[/tex]

Thus, we could say that this data point lies within three standard deviations from the mean as:

[tex]\mu - 3\sigma < x < \mu + 3\sigma\\104-3(8.2) < x < 104 + 3(8.2)\\79.4 < 118 < 128.6[/tex]

Thus, it could be said

Option B) In control as this one data point is not more than three standard deviations from the mean

The process would be considered out of control as the randomly selected minute has more than two standard deviations away from the mean.

To determine whether the process is in control or out of control, we can use the Empirical Rule. The Empirical Rule states that approximately 68 percent of the data is within one standard deviation of the mean, approximately 95 percent of the data is within two standard deviations of the mean, and more than 99 percent of the data is within three standard deviations of the mean. In this case, since the randomly selected minute has 118 rotations per minute, which is more than two standard deviations away from the mean (104 rotations per minute), the process would be considered out of control.

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Your Answer Should Be

3m+6=24

Answer:

Step-by-step explanation:

Let x represent the number of trips to the airport and

Let y represent the number of trips from the airport.

A taxi driver had 44 fares to and from the airport last Monday. This means that

x + y = 44

The price for a ride to the airport is $7, and the price for a ride from the airport is $6. The driver collected a total of $289 for the day. This means that

7x + 6y = 289 - - - - - - - - - - - 1

Substituting x = 44 - y into equation 1, it becomes

7(44 - y) + 6y = 289

308 - 7y + 6y = 289

- 7y + 6y = 289 - 308

-y = - 19

y = 19

x = 44 - y

x = 44 - 19

x = 25

Answer:

b. severs the corpus callosum between hemispheres.

Step-by-step explanation:

The split-brain surgery is used to alleviate epileptic seizures. It involves the severing of the corpus callosum, that is the bond between both hemispheres of the brain.

So the correct answer is:

b. severs the corpus callosum between hemispheres.

Answer:

Step-by-step explanation:

Answer: No, the Volume is x^3 - 3x^2 - 10x

Step-by-step explanation:

Since the volume of the cubic storage unit is x^3

Therefore,

Length = x

Width = x

Height = x

For the new storage unit

Length = x + 2

Width = x

Height = x - 5

Volume = ( x + 2)(x)(x -5)

V = x (x^2 -3x - 10)

V = x^3 - 3x^2 - 10x

Therefore, the volume of the new storage unit is x^3 - 3x^2 - 10x

Answer:the customer is incorrect

Step-by-step explanation:

In a cube, all 4 sides are equal. The volume of a cube that has x as the length of each side would be x^3

If the customer thinks that f the volume of the cube is x^3, it means that each side is x. Then the other storage unit offered to the customer is 2 feet longer,5 feet shorter than the first unit. Its dimensions would be (x+ 2) feet, (x - 5) feet and x feet

The volume of the other storage unit should be

x[(x + 2)(x - 5)] = x(x^2 - 5x + 2x + 10)

= x(x^2 - 3x + 10)

= x^3 - 3x^2 + 10x

Answer:

We have a strong negative relationship between the variables.

Step-by-step explanation:

Given two random variables X and Y, it is possible to calculate the covariance as Cov(X, Y) = E(XY)-E(X)E(Y). We have E(X)=5, E(Y)=6 and E(XY)=21. Therefore Cov(X,Y)=21-(5)(6)=21-30=-9. On the other hand, we know that the correlation of X and Y is the number defined by [tex]Cov(X,Y)/\sqrt{Var(X)}\sqrt{Var(Y)}[/tex] and because in this particular case we have V(X)=9 and V(Y)=10, we have [tex]-9/\sqrt{9}\sqrt{10}[/tex] = -0.9487. Therefore, we have a strong negative relationship between the variables.

Final answer:

The X and Y variables have a strong negative relationship.

Explanation:

The X and Y variables have a strong negative relationship. This can be determined by analyzing the correlation coefficient, which indicates the strength and direction of the relationship between two variables.

In this case, since the correlation coefficient is significantly different from zero (positive or negative), we can conclude that there is a significant linear relationship between X and Y. The fact that the correlation coefficient is negative indicates that as X increases, Y tends to decrease, and vice versa.

Therefore, the correct answer is strong negative relationship.

Answer:

$173493.8

Step-by-step explanation:

Data provided in the question:

LSRL for the data is ? = 3.8785x + 18.3538

Here,

x is area in 100 square feet

and

price in thousands of dollar

Thus,

For the given area 4000 square foot

x = 4000 ÷ 100 = 40                  [Area in 100 square feet]

Therefore,

Using the given equation

Price  = 3.8785(40) + 18.3538

or

Price = 173.4938 in thousands of dollar

or

Price = 173.4938 × $1000

Price = $173493.8

Answer:

(A) oo, ou, uo, uu

(B) 1/4

(C) 1/2

Step-by-step explanation:

(A) When using o for overweight and u for underweight, there are four possible weight outcomes which are; oo, ou, uo, uu

                   The sample space would be: oo, ou, uo, uu

This implies there are 4 possible outcomes.

(B) From the sample space, the event, getting two underweight weight children occurs only once, uu. The probability of getting two underweight children = 1/4

(C)  From the sample space, the event, getting one overweight child and one underweight child occurs twice, ou, uo.

    The probability of getting one overweight child and one underweight child = 2/4 = 1/2

The integral of [tex]z[/tex] over [tex]S[/tex] is equal to the sum of the integrals of [tex]z[/tex] over [tex]S_1,S_2,S_3[/tex].

Parameterize the surface by

[tex]\vec r(u,v)=(9\cos u,9\sin u,v)[/tex]

with [tex]0\le u\le2\pi[/tex] and [tex]0\le v\le9+9\cos u[/tex]. Take the normal vector to [tex]S_1[/tex] to be

[tex]\dfrac{\partial\vec r}{\partial u}\times\dfrac{\partial\vec r}{\partial v}=(9\cos u,9\sin u,0)[/tex]

Then the integral of [tex]z[/tex] over [tex]S_1[/tex] is

[tex]\displaystyle\iint_{S_1}z\,\mathrm dS=\int_0^{2\pi}\int_0^{9+9\cos u}v\|(9\cos u,9\sin u,0)\|\,\mathrm du\,\mathrm dv=\frac{2187\pi}2[/tex]

Parameterize [tex]S_2[/tex] by

[tex]\vec s(u,v)=(u\cos v,u\sin v,0)[/tex]

with [tex]0\le u\le9[/tex] and [tex]0\le v\le2\pi[/tex]. Since [tex]z=0[/tex], the integral over [tex]S_2[/tex] is also 0.

Parameterize [tex]S_3[/tex] by

[tex]\vec t(u,v)=(u\cos v,u\sin v,9+u\cos v)[/tex]

with [tex]0\le u\le9[/tex] and [tex]0\le v\le2\pi[/tex]. The normal to [tex]S_3[/tex] is

[tex]\dfrac{\partial\vec t}{\partial u}\times\dfrac{\partial\vec t}{\partial v}=(-u,0,u)[/tex]

so that the integral over [tex]S_3[/tex] is

[tex]\displaystyle\iint_{S_3}z\,\mathrm dS=\int_0^{2\pi}\int_0^9(9+u\cos v)\|(-u,0,u)\|\,\mathrm du\,\mathrm dv=729\sqrt2\,\pi[/tex]

Putting the results together, the integral of [tex]z[/tex] over [tex]S[/tex] is

[tex]\iint_Sz\,\mathrm dS=\boxed{\left(\frac{2187}2+729\sqrt2\right)\pi}[/tex]

The procedure to evaluate this integral begins by evaluating integrals over the three distinct parts of the surface: the side, bottom, and top. Both the side and bottom integrals are zero and the integral over the top can be evaluated using polar coordinates, however, without specified boundaries for the upper bound, we cannot determine the exact result.

The task is to evaluate a surface integral over a surface S, which consists of a cylinder, a disk on the bottom, and a plane on the top. The surface integral of a scalar function z over a surface S is computed by taking the antiderivative of the function with respect to both dimensions defining the area. Since S consists of three parts, S1 (the side), S2 (the bottom), and S3 (the top), we must perform this process for each part and sum the results.

The key steps in the procedure are:

Summing the results of our calculations on S1, S2, and S3 would yield the final answer. Unfortunately, without the boundaries for the upper bound for the integration, we cannot provide the exact result.

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The test and evaluation (T&E) product that is required will be

It should be noted that a Test and Evaluation Master Plan is used as the planning and management tool for the test activities.

On the other hand, Milestone B is assumed as the official start of a program. It's a MDA led review at the final phase of the Technology Maturation and Risk Reduction.

Learn more about milestone B on:

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Among the options provided, the correct answer is B. Operational Assessment, as it is a required T&E product at Milestone B.

In the Department of Defense Acquisition Process, Milestone B represents a significant point in the acquisition lifecycle where programs are reviewed and approved for entry into the Engineering and Manufacturing Development (EMD) phase.

At Milestone B, the primary focus is on ensuring that the program is mature enough to proceed into EMD with an acceptable level of risk and that adequate planning has taken place.

Among the options provided:

A. Waiver of Military Equipment Program Description: This document is typically not required at Milestone B. It may be relevant in other phases but not a direct requirement at this milestone.

B. Operational Assessment: Operational Assessment (OA) is a crucial T&E product at Milestone B. It assesses the operational effectiveness and suitability of the system under realistic operational conditions, helping to determine whether the system is suitable for further development and production.

C. Identification of LRIP Quantities: The identification of Low-Rate Initial Production (LRIP) quantities is also an important consideration at Milestone B. Decisions about LRIP quantities are critical for moving forward with limited production to further test and refine the system.

D. No T&E products are required at MS B: This statement is not accurate. Milestone B does require specific T&E products, such as the Operational Assessment and considerations related to LRIP quantities, as mentioned above.

For more such questions on Operational Assessment

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Answer:

F = 7476 N

Step-by-step explanation:

given,

diameter of hemispherical plate = 6 ft

height of submergence = 1 ft

the weight density of water =  62.5 lb/ft³

Assuming that hemispherical plate is residing on x and y axis.

bottom of plate is on x-axis and left side of the plate touches y-axis

now, plate is defined by the upper half of the circle

(x - 3)² + (y-0)² = 3²

  y² = 9 - (x - 3)²

  y = √(9 - (x - 3)²)

hydro static pressure on one  side of plate.

[tex]F = \int \rho g x w(x)dx[/tex]

[tex]F = \int_0^3 62.5\times 9.8 x \times \sqrt{9-(x-3)^2}dx[/tex]

[tex]F = 612.5 \int_0^3 x \times \sqrt{9-(x-3)^2}dx[/tex]

on solving the above equation

[tex]F = 612.5(27\dfrac{\pi}{4}-9)[/tex]

F = 7476 N