The probability a guest at a downtown hotel arrived via taxi is 0.42. The probability a guest arriving at a downtown hotel requested parking for a car is 0.29. Assume a guest arriving by taxi is mutually exclusive of a guest requesting parking for a car. What is the probability of a guest arriving by taxi and requesting parking for a car?

Formula for monthly payment is:

A = P x (r(1+r)^t)/((1+r)^t-1) where P is the amount financed, r is the interest rate divided by 12 and t is the amount of time for the loan in months.

P = 33714 x 0.85 = 28656.90

A = 28656.90 x (0.07/12 (1+0.07/12)^48) / (1 +0.07/12)^48 - 1)

A = $686.23

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:

Step-by-step explanation:

Given

There are 52 cards in total

there are total of 13 pairs of same cards with each pair containing 4 cards

Probability of getting a pair or three of kind card=1-Probability of all three cards being different

Probability of selecting all three different cards can be find out by selecting a card from first 13 pairs and remaining 2 cards from remaining 12 pairs i.e.

[tex]=\frac{52\times 48\times 44}{52\times 51\times 50}[/tex]

for first card there are 52 options after choosing first card one pair is destroyed as we have to select different card .

For second card we have to select from remaining 12 pairs i.e. 48 cards and so on for third card.

Required Probability is [tex]=1-\frac{52\times 48\times 44}{52\times 51\times 50}[/tex]

[tex]=\frac{22776}{132600}[/tex]

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

Learn more about the average value of a continuous function at:

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Answer:

a discrete random variable

Step-by-step explanation:

You can only have a natural number of clients entering the store.

For example, 0 clients, 1 client, 2 clients, 100 clients, ...

You cannot have a decimal value, for example, 0.5 clients.

So the correct answer is:

a discrete random variable

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.

Step-by-step explanation:

∑ (4ⁿ⁺¹ / 5ⁿ)

Rewrite 4ⁿ⁺¹ as 4 (4ⁿ).

∑ 4 (4ⁿ / 5ⁿ)

∑ 4 (4/5)ⁿ

This is a geometric series.  The sum of an infinite geometric series is:

S = a / (1 −r)

where a is the first term and r is the common ratio.

Here, the first term is 16/5 (because n starts at 1), and the common ratio is 4/5.

S = 16/5 / (1−4/5)

S = 16/5 / (1/5)

S = 16

Answer:

Radius of convergence of power series is [tex] \lim_{n \to \infty}\frac{a_{n}}{a_{n+1}}=\frac{1}{108}[/tex]

Step-by-step explanation:

Given that:

n!! = 1⋅3⋅5⋅⋅⋅⋅(n−2)⋅n        n is odd

n!! = 2⋅4⋅6⋅⋅⋅⋅(n−2)⋅n       n is even

(-1)!! = 0!! = 1

We have to find the radius of convergence of power series:

[tex]\sum_{n=1}^{\infty}[\frac{8^{n}n!(3n+3)!(2n)!!}{2^{n}[(n+9)!]^{3}(4n+3)!!}](8x+6)^{n}\\\\\sum_{n=1}^{\infty}[\frac{8^{n}n!(3n+3)!(2n)!!}{2^{n}[(n+9)!]^{3}(4n+3)!!}]2^{n}(4x+3)^{n}\\\\\sum_{n=1}^{\infty}[\frac{8^{n}n!(3n+3)!(2n)!!}{[(n+9)!]^{3}(4n+3)!!}](x+\frac{3}{4})^{n}\\[/tex]

Power series centered at x = a is:

[tex]\sum_{n=1}^{\infty}c_{n}(x-a)^{n}[/tex]

[tex]\sum_{n=1}^{\infty}[\frac{8^{n}n!(3n+3)!(2n)!!}{2^{n}[(n+9)!]^{3}(4n+3)!!}](8x+6)^{n}\\\\\sum_{n=1}^{\infty}[\frac{8^{n}n!(3n+3)!(2n)!!}{2^{n}[(n+9)!]^{3}(4n+3)!!}]2^{n}(4x+3)^{n}\\\\\sum_{n=1}^{\infty}[\frac{8^{n}4^{n}n!(3n+3)!(2n)!!}{[(n+9)!]^{3}(4n+3)!!}](x+\frac{3}{4})^{n}\\[/tex]

[tex]a_{n}=[\frac{8^{n}4^{n}n!(3n+3)!(2n)!!}{[(n+9)!]^{3}(4n+3)!!}]\\\\a_{n+1}=[\frac{8^{n+1}4^{n+1}n!(3(n+1)+3)!(2(n+1))!!}{[(n+1+9)!]^{3}(4(n+1)+3)!!}]\\\\a_{n+1}=[\frac{8^{n+1}4^{n+1}(n+1)!(3n+6)!(2n+2)!!}{[(n+10)!]^{3}(4n+7)!!}][/tex]

Applying the ratio test:

[tex]\frac{a_{n}}{a_{n+1}}=\frac{[\frac{32^{n}n!(3n+3)!(2n)!!}{[(n+9)!]^{3}(4n+3)!!}]}{[\frac{32^{n+1}(n+1)!(3n+6)!(2n+2)!!}{[(n+10)!]^{3}(4n+7)!!}]}[/tex]

[tex]\frac{a_{n}}{a_{n+1}}=\frac{(n+10)^{3}(4n+7)(4n+5)}{32(n+1)(3n+4)(3n+5)(3n+6)+(2n+2)}[/tex]

Applying n → ∞

[tex]\lim_{n \to \infty}\frac{a_{n}}{a_{n+1}}= \lim_{n \to \infty}\frac{(n+10)^{3}(4n+7)(4n+5)}{32(n+1)(3n+4)(3n+5)(3n+6)+(2n+2)}[/tex]

The numerator as well denominator of [tex]\frac{a_{n}}{a_{n+1}}[/tex] are polynomials of fifth degree with leading coefficients:

[tex](1^{3})(4)(4)=16\\(32)(1)(3)(3)(3)(2)=1728\\ \lim_{n \to \infty}\frac{a_{n}}{a_{n+1}}=\frac{16}{1728}=\frac{1}{108}[/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:

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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Answer:

[tex]z=\frac{120-200}{\frac{25}{\sqrt{30}}}=-17.527[/tex]  

[tex]p_v =P(Z<-17.527) \approx 0[/tex]  

If we compare the p value and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v<<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis.  

We can say that at 5% of significance the mean average waiting time is significantly less than 200 seconds per call.

Step-by-step explanation:

Data given and notation  

[tex]\bar X=120[/tex] represent the sample mean  

[tex]\sigma=25[/tex] represent the population standard deviation  

[tex]n=30[/tex] sample size  

[tex]\mu_o =200[/tex] represent the value that we want to test  

[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.  

z would represent the statistic (variable of interest)  

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

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the population mean is less than 200, the system of hypothesis are :  

Null hypothesis:[tex]\mu \geq 200[/tex]  

Alternative hypothesis:[tex]\mu < 200[/tex]  

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:  

[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)  

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic  

We can replace in formula (1) the info given like this:  

[tex]z=\frac{120-200}{\frac{25}{\sqrt{30}}}=-17.527[/tex]  

P-value  

Since is a one-side left tailed test the p value would given by:  

[tex]p_v =P(Z<-17.527) \approx 0[/tex]  

Conclusion  

If we compare the p value and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v<<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis.  

We can say that at 5% of significance the mean average waiting time is significantly less than 200 seconds per call.

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:

(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 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:

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:

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: 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: 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:

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

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.

In hypothesis testing, it is critical to state the null and alternative hypotheses, choose an appropriate significance level, and conclude in the context of the problem. Decisions must reflect the probabilistic nature of the tests, with careful consideration of Type I and Type II errors.

In hypothesis testing, the following statements are indeed true:

You must state null and alternative hypotheses in the context of the problem.

You must state a significance level so you can decide if a given P-value provides evidence to reject the null hypothesis.

You must state a conclusion in the context of the problem.

When conducting a hypothesis test, one must also be mindful not to claim that a hypothesis is definitively proven true or false due to the probabilistic nature of hypothesis testing. Instead, you can infer whether there is sufficient evidence to support the alternative hypothesis if the null hypothesis is rejected. However, remember that making a decision at a certain significance level involves a trade-off between Type I and Type II errors.

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:

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:

a) (y-16)/y = -7*e∧(-0.016946*t)

b) y = 6.34

c) t = 129.66 years in 2055

Step-by-step explanation:

a) dy/dt = ky*(16-y)

Solving the differential equation we have

dy / (y*(y-16)) = -k dt

∫ dy / (y*(y-16)) = ∫ -k dt

(-1/16)*Ln (y) + (1/16)*Ln (y-16) = -k*t + C

(1/16) Ln ((y-16)/y) = -k*t + C

Ln ((y-16)/y) = -16*k*t + C  

(y-16)/y = C*e∧(-16*k*t)

If  t = 0  and y = 2

(2-16)/2 = C*e∧(0)  

C = -7   then we have

(y-16)/y = -7*e∧(-16*k*t)

In 1975 we have t = 1975 - 1925= 50 years   and  y = 4

(4-16)/4 = -7*e∧(-16*k*50)

k= - Ln (3/7) / 800 = 0.001059

Finally, the differential equation will be

(y-16)/y = -7*e∧(-16*0.001059*t)

(y-16)/y = -7*e∧(-0.016946*t)

b)  In 2015 we have t = 2015 – 1925 = 90 years

(y-16)/y = -7*e∧(-0.016946*90)

Solving the equation we get

y = 6.34

c) If  y = 9

(9-16)/9 = -7*e∧(-0.016946*t)

t = 129.66 years  in 2055

The solution for (a)[tex]a) (y-16)/y = -7*e^{(-0.016946*t)}[/tex]b) y = 6.34 and (c) the value of t is  129.66 years  in 2055

We have given that,

[tex]a) dy/dt = ky*(16-y)[/tex]

By using variable separable form we have,

A variable separable differential equation is any differential equation in which variables can be separated

Therefore by solving the differential equation we have

[tex]dy / (y*(y-16)) = -k dt[/tex]

integrating both side with respect to t

[tex]\int dy / (y*(y-16)) = \int -k dt[/tex]

Solve the integration of the above

[tex](-1/16)*ln (y) + (1/16)*ln (y-16) = -k*t + C[/tex]

[tex](1/16) ln ((y-16)/y) = -k*t + C[/tex]

[tex]ln ((y-16)/y) = -16*k*t + C[/tex]

[tex](y-16)/y = C*e^{(-16*k*t)}[/tex]

If  t = 0  and y = 2

[tex](2-16)/2 = C*e^{0}[/tex]

C = -7   then we have

[tex](y-16)/y = -7*e^{(-16*k*t)}[/tex]

In 1975 we have t = 1975 - 1925= 50 years   and  y = 4

[tex](4-16)/4 = -7*e^{(-16*k*50)[/tex]

[tex]k= - Ln (3/7) / 800 = 0.001059[/tex]

Finally, the differential equation will be

[tex](y-16)/y = -7*e^{(-16*0.001059*t)}[/tex]

[tex](y-16)/y = -7*e^{(-0.016946*t)}[/tex]

b)  In 2015 we have t = 2015 – 1925 = 90 years

[tex](y-16)/y = -7*e^{(-0.016946*90)}[/tex]

Solving the equation we get

y = 6.34

c) If  y = 9

[tex](9-16)/9 = -7*e^{(-0.016946*t)}[/tex]

Therefore we get the value of t is  129.66 years  in 2055

To learn more about the differential equation visit:

https://brainly.com/question/1164377

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.

Answer:

after 15%, discount = $5,015

after 10%, discount = $5,310

after 4%, discount=  $5,664

Step-by-step explanation:

1.discount of  15 % of the price listed

so 15 % of $5,900 will be=    15/100      x 5900  =    885 $

 so after discounting the price =$5,900 - $885    = $5,015

2. discount of  10 % of the price listed

so 10 % of $5,900 will be=    10/100      x 5900  =    590 $

 so after discounting the price =$5,900 - $590    = $5,310

3. discount of  4 % of the price listed

so 4 % of $5,900 will be=    4/100      x 5900  =    236 $

 so after discounting the price =$5,900 - $236  = $5,664

Answer:

12 feet

Step-by-step explanation:

Draw a diagram (see picture below). The tree and its shadow is one triangle, the man and its shadow is another triangle. We assume both are right triangles because people and trees stand vertical.

Create a proportion to solve. Put the missing value in a numerator.

Tree height / Tree shadow = Man height / Man shadow

[tex]\frac{x}{8} =\frac{6}{4}[/tex]

Solve using cross multiplication. Multiply x by 4. Multiply 6 by 8.

4x = 48    Divide both sides by 4 to isolate x.

x = 12       Height of tree

The tree is 12 feet tall.

Answer:

186

Step-by-step explanation:

The sample mean, x, is the central value in the confidence interval, that is, the average between the upper and lower bounds of the interval.

In this case, the Lower bound is 184.00 and the upper bound is 188.00. Therefore, the sample mean is given by:

[tex]x = \frac{184+188}{2}\\x=186.00[/tex]

The mean length, in seconds, of the sampled songs is 186.00.

The sample mean is 186.

The sample mean, denoted as [tex]\( x \)[/tex], can be found by taking the midpoint of the confidence interval. In this case, the confidence interval is (184.00, 188.00). To find [tex]\( x \)[/tex], we take the average of the lower and upper bounds of the interval. Thus,

[tex]\[ x = \frac{184.00 + 188.00}{2} = \frac{372.00}{2} = 186.00 \][/tex]

Therefore, the sample mean [tex]\( x \)[/tex] is 186.00 seconds. This means that, on average, the length of songs in the online database, based on the given sample, is 186.00 seconds.

Work is provided in the image attached.