Solve this please :)

Answer:

C. 288π cm^3

Step-by-step explanation:

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Based on the speed that light travels and the distance around the Earth along the Equator, the number of times the space ship would travel in 1 second is 0.133 times

The number of times that the space ship would travel around Earth around the Equator, going at the speed of light is:

= Distance around the Earth along the Equator / Speed of light

Solving for the number of times around the Earth for the space ship gives:

= 2.48×10⁴  / 1.86×10⁵

= 24,800 / 186,000

= 0.133 times

In conclusion, going at the speed of light, the space ship would go around the Earth, along the equator, 0.133 times.

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When population variances are unknown but assumed to be equal, the formula for a confidence interval for the difference in population means might include a pooled estimate of the common variance. This statement is true.

When the population variances are unknown but assumed to be equal, a pooled estimate of the common variance can be used in the formula for a confidence interval for the difference in population means. The pooled estimate of the common variance is calculated by combining the sample variances from two independent samples, taking into account the degrees of freedom for each sample.

The formula for a confidence interval for the difference in population means when population variances are unknown but assumed equal is:

\($\large (\bar{X}_1 - \bar{X}2) \pm t{\alpha/2, s_p} \sqrt{\frac{1}{n_1} + \frac{1}{n_2}}$\)

where \($\large \bar{X}_1$\) and \($\large \bar{X}_2$\) are the sample means for two independent samples, \(n_1\), and \(n_2\) are the sample sizes for the two samples, s_p is the pooled estimate of the common variance, \($\large t_{\alpha/2}$\) is the t-value corresponding to the desired level of confidence, and sqrt is the square root.

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An inverse-square central force field is  \(mx^{''} = -\frac{kx}{r^3}\\ \\mx^{''} = -\frac{ky}{r^3}\\\).

From Newton's second law of motion,

mass × acceleration = Force acting on the mass

Resolving the force F along x and y directions and applying Newton's second law of motion,

Using,

\(r = \sqrt{x^2+y^2}\)

​

Therefore,

\(m\frac{d^2x}{dt^2} =-|F|cos \theta\)

\(mx^{''} = -\frac{k}{x^2+y^2} \frac{x}{\sqrt{x^2+y^2} } \\\\mx^{''} = - \frac{kx}{(x^2+y^2)^\frac{3}{2} }\\ \\mx^{''} = - \frac{kx}{r^3}\)

Where \(r = \sqrt{x^2+y^2}\)

​ and cos⁡θ = \(\frac{x}{\sqrt{x^2+y^2} }\)

Similarly using,

\(r = \sqrt{x^2+y^2}\)

we get,

 \(m\frac{d^2y}{dt^2} = -|F|sin\theta\)

\(mx^{''} = -\frac{k}{x^2+y^2} \frac{x}{\sqrt{x^2+y^2} } \\\\mx^{''} = - \frac{kx}{(x^2+y^2)^\frac{3}{2} }\\ \\mx^{''} = - \frac{kx}{r^3}\)

Where \(r = \sqrt{x^2+y^2}\)

​ and sinθ = \(\frac{y}{\sqrt{x^2+y^2} }\)

Therefore we showed that holds

\(mx^{''} = -\frac{kx}{r^3}\\ \\mx^{''} = -\frac{ky}{r^3}\\\)

Hence the answer is an inverse-square central force field is  \(mx^{''} = -\frac{kx}{r^3}\\ \\mx^{''} = -\frac{ky}{r^3}\\\).

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Answer:

The length of the park is 175 feet

Step-by-step explanation:

Let us solve the question

∵ The perimeter of a rectangular park is 500 feet

∵ The formula of the perimeter of the rectangle is P = 2(L + W)

∵ L is the length and W is the width

→ Equate the rule of the perimeter by 500

∴ 2(L + W) = 500

→ Divide both sides by 2

∴ L + W = 250 ⇒ (1)

∵ The length of the park is 100 feet longer than the width

→ That means L is W plus 100

∴ L = W + 100 ⇒ (2)

→ Substitute L in (1) by (2)

∵ W + 100 + W = 250

→ Add the like terms

∵ (W + W) + 100 = 250

∴ 2W + 100 = 250

→ Subtract 100 from both sides

∵ 2W + 100 - 100 = 250 - 100

∴ 2W = 150

→ Divide both sides by 2

∴ W = 75

→ Substitute the value of W in (2) to find L

∵ L = 75 + 100 = 175

∴ The length of the park is 175 feet

Before performing a significance test about a population mean or proportion, the following conditions must be verified:

Sample Size: The sample size should be sufficiently large to allow the application of the normal distribution. A minimum sample size of 30 is required to meet this requirement.

Normality: The sample should be approximately normally distributed. When the sample size is greater than or equal to 30, the central limit theorem ensures normality. For sample sizes of less than 30, the data should be examined for normality. If the distribution is skewed or has outliers, nonparametric tests should be considered.

Independence: The observations in the sample should be independent of one another. This means that the response from one observation does not depend on the response from another observation.

Equal Variance: The variance of the population should be approximately equal to the variance of the sample. If the variances are unequal, a modified t-test should be used instead of the traditional t-test.

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On average, a customer spends approximately 1.16 minutes waiting time on hold before they can start speaking to a representative.

To find the average waiting time for a customer on hold before they can start speaking to a representative, we need to consider both the arrival rate of calls and the average service time of the staff members.

Given:

9 staff members taking calls.

On average, one call arrives every 5 minutes (standard deviation of 5 minutes).

Each staff member spends on average 18 minutes with each customer (with a standard deviation of 27 minutes).

To calculate the average waiting time, we need to use queuing theory, specifically the M/M/c queuing model. In this model:

"M" stands for Markovian or memoryless arrival and service times.

"c" represents the number of servers.

In our case, we have an M/M/9 queuing model since we have 9 staff members.

The average waiting time for a customer on hold is given by the following formula:

Waiting time = (1 / (c * (μ - λ))) * (ρ / (1 - ρ))

Where:

c = number of servers (staff members) = 9

μ = average service rate (1 / average service time)

λ = average arrival rate (1 / average interarrival time)

ρ = λ / (c * μ)

First, let's calculate the average arrival rate (λ):

λ = 1 / (average interarrival time) = 1 / 5 minutes = 0.2 calls per minute

Next, calculate the average service rate (μ):

μ = 1 / (average service time) = 1 / 18 minutes = 0.0556 customers per minute

Now, calculate ρ:

ρ = λ / (c * μ) = 0.2 / (9 * 0.0556) ≈ 0.407

Finally, calculate the waiting time:

Waiting time = (1 / (c * (μ - λ))) * (ρ / (1 - ρ))

= (1 / (9 * (0.0556 - 0.2))) * (0.407 / (1 - 0.407))

≈ 1.16 minutes

Therefore, on average, a customer spends approximately 1.16 minutes waiting on hold before they can start speaking to a representative.

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The presence of maximum and minimum on the quadratic functions in this problem are given as follows:

The standard definition of a quadratic function is given as follows:

y = ax² + bx + c.

The coefficient a determines if the quadratic function has a maximum or a minimum, as follows:

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Answer: the circumference is the perimeter of a circle or ellipse. That is, the circumference would be the arc length of the circle, as if it were opened up and straightened out to a line segment. More generally, the perimeter is the curve length around any closed figure.

C

C is the answer. It is the only one that gives y when you input x.

Answer:

Your answer is C :)

Y = 3^x + 2.

You just substitute this into any of the functions. If you need more clarification I can help :)

Answer:

Step-by-step explanation:

So negitive have the - besides it and + mean its negative .

Answer:

-29

-6

.5

105

Step-by-step explanation:

Given parameters:

Number of chairs  = 3

Number of tables = 4

Cost of 3 chairs and 4 tables = Rs 7540

Price of 1 table = Rs220

Unknown:

Price of 1 table  = ?

Solution:

Let the cost of 1 table = t

 So,

        3(220) + 4(t) = 7540

         660 + 4t = 7540

         4t = 7540 - 660

          4t = 6880

            t = Rs. 1720

The cost of 1 table is Rs. 1720

Answer:

an infinite number of solutions

Step-by-step explanation:

−3x −17 = −17 −3x

left side = right side  TRUE because -3x-17 is the same as -17-3x

we can rearrange  the the equation

−3x −17 +17 = −17 +17−3x, add 17 on both sides of the equations

            -3x = -3x, divide both sides by (-3)

               x = x

Since this equation is always true ( for any number ) we have an infinite number of solutions (since there are is an infinity of numbers.)

Answer:

− x + 16y

Step-by-step explanation:

2x + 5y − 3x + 11y

= 2x + 5y + − 3x + 11y

Combine Like Terms:

= 2x + 5y + − 3x + 11y

= (2x + − 3x) + (5y + 11y)

= − x + 16y

Answer:

the volume of the cube will be 44 cm³ or D (nearest whole number)

Step-by-step explanation:

A cube has equal size of edges. Since it has a face diagonal of 5cm then using Pythagoras theorem s²+ s²= 5², where s is the side of the cube.

Therefore, 2s²=25

                   s²= 12.5

                    s = √12.5 = 3.536 cm

The volume of a cube is s³ (s×s×s) = 3.536³= 44.212 cm³,

Answer:

Slope-intercept form: y = 9/4x - 53/4

Point-slope form: y + 2 = 9/4(x - 5)

Answer:

if the x and y coordinates that mean that number is the solution to whatever the question is.

Step-by-step explanation:

Population density of the wolves is 0.156 wolves per square mile.

The term "population density" refers to the measurement of population per unit land area.

To get population density of wolves in Yellowstone park, we divide the estimated number of wolves by the park's area which give us:

= 540 / 3,471

= 0.15557476231

= 0.1557 wolves per square mile.

By rounding to the thousandth, the population density of wolves in Yellowstone park is 0.156 wolves per square mile.

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The boundaries between the various plot sections of electric field will be two vertical lines.

In this work, the distance from a point charge must be calculated under three different circumstances: (1) when the distance is less than the radius of the point charge; (2) when the distance is greater than the radius of the outer sphere; and (3) when the distance is between the radii of two concentric charged spheres.

Numerous calculations that connect the charge distribution and distance to the electric field are used to determine the electric field at each site. The absolute value of the electric field is then displayed as a function of distance using the numerous formulas that were employed, and the different places where the electric field varies are identified.

The boundaries between the various plot sections will be two vertical lines.

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Answer:

A central angle, such as angle of circle Z, is an angle whose vertex is and whose sides are radii of the circle.

Answer:

do you have a pic of the circle

Step-by-step explanation:

Answer:

s = 6√3

Step-by-step explanation:

We can recognize that the triangle in the image is a special 30 - 60 - 90 triangle. In a 30 - 60 - 90 triangle, the leg opposite the 60 degree angle, s,  is √3 times the leg opposite the 30 degree angle, in this case 6m. We can write an equation to model the situation:

s = 6 * √3

s = 6√3

Answer:

  −13.8654599313 and 0.8654599313

Step-by-step explanation:

The two numbers of interest will be the solutions to ...

  xy = -12

  x +y = -13

Substituting for y, this becomes the quadratic ...

  x(-13 -x) = -12

  x^2 +13x = 12 . . . . . multiply by -1

  x^2 +13x +6.5^2 = 12 +6.5^2 . . . . . complete the square

  (x +6.5)^2 = 54.25

  x = -6.5 ± √54.25 . . . . . . take the square root, subtract 6.5

  x ≈ -13.865499313 or 0.8654599313

The value of y is the other of these two numbers. So, the two numbers of interest are {-13.865499313, 0.8654599313}.

Answer:

42 yards

Step-by-step explanation

There are 4 sides to a rectangle. 2 lengths, and 2 widths. That means that you multiply both values by 2 and then add them together, so 40 + 2. A more basic way to think of it is 20+20+1+1. Therefore, the perimeter is 41 yards.

If the faculty went on a weight watchers diet plan and now weight an average of 185 pounds in 2021.  The faculty's average weight loss per year : 185 pounds and 155 pounds.

First step is to find the difference between the initial weight and the final weight

Difference = Initial weight - Final weight

Difference = 215 pounds - 185 pounds

Difference = 30 pounds

Now let find the lost per year

2018

Lost per year = 215 pounds - 30 pounds

Lost per year = 185 pounds

2021

Lost per year = 185 pounds - 30 pounds

Lost per year = 155 pounds

Therefore the loss is 185 and 155 pounds.

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Answer:

697 marbles

Step-by-step explanation:

We know:

Briley- 374 marbles

Joey- 374*4

Carson- (374*4)-799

Solve:

374*4= 1496 (This is how many Joey has)

1496-799= 697 (This is how many Carson has)

Hope this helps!

The length of the third side of this isosceles triangle is 2 units.

We have,

If two sides of an isosceles triangle are equal, then the third side must also be equal in length.

So,

If two sides of the triangle are 2 and 2, the length of the third side must also be 2.

Thus,

The length of the third side of this isosceles triangle is 2 units.

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The arithmetic sequence given is 100, 96, 92, 88, ... In order to find an expression for the nth term in the sequence, we need to determine the common difference. Since each term is decreasing by 4, the common difference is -4.

(a) To express the nth term in the form an + b, we substitute the first term (a1 = 100) and the common difference (d = -4) into the formula. The expression becomes: an = 100 - 4(n-1).

(b) To find the twentieth term, we substitute n = 20 into the expression: a20 = 100 - 4(20-1) = 100 - 4(19) = 100 - 76 = 24.

(c) To find the sum of the positive terms, we first need to determine the number of positive terms. The sequence consists of positive terms up to the 25th term (a25 = 100 - 4(25-1) = 100 - 4(24) = 4). The sum of the positive terms can be calculated using the formula for the sum of an arithmetic series: Sn = (n/2)(a1 + an). Substituting the values, we have: S25 = (25/2)(100 + 4) = 6250.

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Answer:

  z ≈ -0.92

Step-by-step explanation:

Put the numbers in place of the corresponding variables and do the arithmetic.

  \(z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{pq}{n}}}=\dfrac{\dfrac{495}{1708}-0.30}{\sqrt{\dfrac{0.30(1-0.30)}{1708}}}=\dfrac{495-0.30(1708)}{\sqrt{1708(0.30)(0.70)}}=\dfrac{-17.4}{\sqrt{358.68}}\\\\\boxed{z\approx -0.92}\)

Answer:

A) 33+3i

Step-by-step explanation:

Use the FOIL method: (a+b)(c+d)=ac+ad+bc+bd(a+b)(c+d)=ac+ad+bc+bd.

15−15i+18i+18

combine like terms

(15+18)+(−15i+18i)

simplify

33+3i