given the distance from the center of the earth to the center of the moon is, r em, 384 million meters and the moon revolves around the earth in 27.3 days, tm, what is the mass of the earth? g

The price we have to pay for the disc after 10% discount is 1467 dollars.

Percentage is the value per hundredth.

According to the given question we bought a disc which costs 1630 dollars there's a 10% discount we have to find how much i have to pay.

10% of 1630 dollars will be

= (10/100) × 1630 dollars.

= 16300/100 dollars.

= 163 dollars.

So, the price we have to pay for the disc after 10% discount is

= (Total amount - Discount amount)

= ( 1630 - 163 ) dollars.

= 1467 dollars.

learn more about percentage here :

https://brainly.com/question/24159063

#SPJ4

The approximate probability of exactly two people in a group of seven having a birthday on April 15 is (C) \(7.4 x 10^-^6\)

To calculate the probability of exactly two people in a group of seven having a birthday on April 15, we can use the binomial distribution formula:

\(P(X = k) = C(n, k) * p^k * (1 - p)^(^n^-^k^)\)

Where:

So, plugging in the values, we get:

\(P(X = 2) = C(7, 2) * (1/365)^2 * (1 - 1/365)^(7 - 2)\)

\(= 21 * (1/365)^2 * (364/365)^5\)

\(= 2.38 x 10^-5\)

The probability of exactly two people in a group of seven having a birthday on April 15 can be calculated using the binomial distribution formula.

The formula takes into account the number of trials, the probability of success in a single trial, and the number of successes desired.

In this case, we want to find the probability that exactly two people in a group of seven have a birthday on April 15, assuming that all days of the year are equally likely for a birthday.

Plugging in the values into the formula gives us an approximate probability of \(7.4 x 10^-^6\), which is the answer (C).

Learn more about Approximate probability

brainly.com/question/15696262

#SPJ11

To price the derivative using the two-period binomial model, we need to calculate the expected payoff of the derivative using the risk-neutral probabilities.

The possible outcomes for the two-period binomial model are H and T,  there are four possible states of the world: HH, HT, TH, and TT.

To calculate the expected payoff we need to calculate the probability of each state occurring. The probability of HH occurring is pp=0.60.6=0.36, the probability of HT and TH occurring is pq+qp=0.60.4+0.40.6=0.48, and the probability of TT occurring is qq=0.40.4=0.16.

Next, we can calculate the expected payoff in HH and TT states, the derivative pays off 1, and in the HT and TH states, the derivative pays off 0. The expected payoff of the derivative in the HH and TT states is 10.36=0.36, and the expected payoff in the HT and TH states is 00.48=0.

We need to discount the expected payoffs back to time 0 using the risk-neutral probabilities.

The probability of that state occurring multiplied by the discount factor, which is 1/(1+r), where r is the risk-free interest rate.

Since this is a risk-neutral model, the risk-free interest rate is equal to 1. Therefore, the risk-neutral probability of each state occurring is

HH: 0.36/(1+1) = 0.18

HT/TH: 0.48/(1+1) = 0.24

TT: 0.16/(1+1) = 0.08

Finally, we can calculate the price of the derivative

Price = 0.181 + 0.240 + 0.240 + 0.081 = 0.26

Therefore, the price of the derivative is 0.26.

For similar question on two-period binomial model

https://brainly.com/question/9362207

#SPJ11

On solving the given problem by help of mathematical operations, we got - After Ray poured 0.47L, he was left with 2.201L.

The term "operation" in mathematics refers to the process of calculating a value using operands and a math operator. For the given operands or numbers, the math operator's symbol has predetermined rules that must be followed.

In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Total amount of tea Ray has - 2.671L

Amount of tea Ray poured - 0.47

Therefore,

amount he was left with was  = 2.671- 0.47 = 2.201L

To know more about mathematical operations visit:
https://brainly.com/question/8959976

#SPJ9

formula 50 + 10 + x = 180

To find the surface area of the figure, we need to consider the individual surfaces and add them together.

First, let's identify the surfaces of the figure:

The lateral surface area of the larger prism (excluding the base)

The two bases of the larger prism

The lateral surface area of the smaller prism (excluding the base)

The two bases of the smaller prism

The lateral surface area of a prism is given by the formula: perimeter of the base multiplied by the height.

The bases of the prisms are rectangles, so their areas can be calculated by multiplying the length by the width.

To find the missing prism's surface area, we need to consider that it is a smaller prism nested inside the larger prism. The lateral surface area and bases of the missing prism should also be included.

Once we have calculated the individual surface areas, we add them together to find the total surface area of the figure.

Without specific measurements or dimensions of the figure, it is not possible to provide a numerical answer. Please provide the necessary measurements or dimensions to calculate the surface area.

Learn more about surface here

https://brainly.com/question/16519513

#SPJ11

The area of the triangle is 4.5 square unit.

We have, y= 4x/ (1 + x³)

Now, differentiating the above equation wrt to x we get

y' = 4(1 + x³)- 4x . 3x² / (1+ x³)²

y'= -8x³ + 4/ (1+x³)²

When x = 1 then y' = -4/4 = -1

so, y -2 = -1 (x-1)

y= -x+ 3

Here the x intercept is (3, 0) and y intercept is (0, 3).

so, Area of Triangle is

= 1/2 x 3 x 3

= 9/2

= 4.5 square unit

Learn more about intercept here:

https://brainly.com/question/14180189

#SPJ1

The uncertainty in the best estimate for the length of the side of the block is approximately 0.0447 mm.

To determine the uncertainty in the best estimate for the length of the block side, we can consider the range of values obtained from the measurements. Since the uncertainty represents the possible deviation from the true value, the range of measurements can be used to estimate the uncertainty in the best estimate

To find the standard deviation represents the average amount of variation or spread among the measurements , we use the formula σ = Δb / √n, where σ is the standard deviation, Δb is the uncertainty in each measurement, and n is the number of measurements.

In this case, Δb = 0.1 mm and n = 5. Plugging these values into the formula, we get σ = 0.1 / √5 ≈ 0.0447 mm.

learn more about standard deviation here:

https://brainly.com/question/29115611

#SPJ11

Answer:

EBC is 55 degrees :)

Step-by-step explanation:

Since ABD and EBC are congruent, it means that they share the same amount of degrees, and 150 - 40 is 110, which divided by two is 55, so both ABD and EBC are 55 degrees.

Answer:

B and D

Step-by-step explanation:

A translation of a triangle is moving it up down or side to-side on the axis, not changing the shape flipping it or the orientation,so the translations of a would be B and D!

Hoped this helped, have a good one!

Answer:

B, D

Step-by-step explanation:

Using the principle of pigeonhole , we conclude that 621 is minimum needed number. So, if there is 620 people then given fact is not true .

The generalized pigeonhole principle:

• Assume N objects are placed into k boxes.

• So, there is at least one box containing at least [N/k ] Objects

We know that one month consists 31 days . Let us consider 31 pigeonholes each corresponding to a day of month i.e., 1 to 31 .

If we place 621 people ( pigeon) into the hole corresponding to the day of month they are born then they must be a hole with [ 621/ 31] = 21 pigeon that is 21 people born on same day of month from a group of 621 people. This results is coming from the extended pigeonhole principle.

If we consider a group 620 people then [ 620/31] = 20 people must be born in same day of month. But according to question atleast 21 people born on same day of month. So, same fact is not true for a group of 620 people.

To learn more about pigeonhole principle, visit:

https://brainly.com/question/24491336

#SPJ4

Answer:

Step-by-step explanation:

Simply it is 2/5.

This is because overall 5/5 is the amount of people at the tennis club.

3/5 of the people in the tennis club are women meaning:

5/5 - 3/5 = 2/5

So 2/5 of the people in the tennis club are men.

4(a-3)

Distribute the 4 by multiply it by each term inside the parentheses

Answer: 4a-12

4 > |x+1| + 2

======================================================

Explanation:

Choice A can be ruled out because the result of any absolute value is never negative.

This means |x+1| cannot be smaller than -3.

In other words:  -3 > |x+1| has no solutions

Similarly, choice B also leads to "no solutions" because we subtract 2 from both sides to get -1 > |x+2|. Therefore, we rule out choice B as well.

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

Choice C can be solved through these steps

2 < |x+3| - 2

2+2 < |x+3|

4 < |x+3|

|x+3| > 4

x+3 > 4 or x+3 < -4

x > 4-3 or x < -4-3

x > 1 or x < -7

x < -1 or x > 1

The graph of this will have open holes at -7 and 1. Then you shade to the left of -7 and to the right of 1. This does not match the graph given to us.

We'll rule out choice C.

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

Choice D can be solved through these steps

4 > |x+1| + 2

4-2 > |x+1|

2 > |x+1|

|x+1| < 2

-2 < x+1 < 2

-2-1 < x < 2-1

-3 < x < 1

The graph will have open holes at -3 and 1, with shading in between. This matches perfectly with the given graph.

This is why choice D is the answer.

Answer:

should be acute

Step-by-step explanation:

hypotenuse is smaller than both sides combined

A sample size of 17 is required to construct a 90% confidence interval for a population proportion with an error of 0.2.

To determine the sample size required to construct a 90% confidence interval for a population proportion with an error of 0.2 (or 20%), we need to use the formula for sample size calculation in proportion estimation.

The formula for sample size in proportion estimation is:

n = (Z² * p * q) / E²

Where:

n = required sample size

Z = Z-score corresponding to the desired confidence level (90% confidence level corresponds to a Z-score of approximately 1.645)

p = estimated or assumed population proportion (since there is no knowledge about the population proportion, we can assume a conservative value of 0.5 to get the maximum sample size)

q = 1 - p (complement of p)

E = desired margin of error (0.2 or 20% in this case)

Substituting the values into the formula:

n = (1.645² * 0.5 * (1 - 0.5)) / 0.2²

n = (2.705 * 0.5 * 0.5) / 0.04

n = 0.67625 / 0.04

n ≈ 16.90625

Since the sample size must be a whole number, we round up the result to the nearest whole number:

n = 17

Therefore, a sample size of 17 is required to construct a 90% confidence interval for a population proportion with an error of 0.2.

It's important to note that this calculation assumes maximum variability in the population proportion (p = 0.5) to ensure a conservative estimate. If there is any information or prior knowledge available about the population proportion, it should be used to refine the sample size calculation.

for more such question on interval visit

https://brainly.com/question/30460486

#SPJ8

The first 3 terms of the sequence are 21, 24 and 29

From the question, we have the following parameters that can be used in our computation:

n² + 20

This means that

f(n) = n² + 20

The first 3 terms of the sequence is when n = 1, 2 and 3

So, we have

f(1) = 1² + 20 = 21

f(2) = 2² + 20 = 24

f(3) = 3² + 20 = 29

Hence, the first 3 terms of the sequence are 21, 24 and 29

Read more about sequence at

https://brainly.com/question/30499691

#SPJ1

Answer:

5x + y = 8

Step-by-step explanation:

Given the equations:

x+3y=10 ____ (1)

2x−y=−1 ____ (2)

Multiply (2) by 2

2(2x - y = - 1) = 4x - 2y = - 2

4x - 2y = - 2 - - - (3)

Add (1) and (3)

4x - 2y = - 2

x + 3y = 10

___________

5x + y = 8

_________

Answer:

5x + 3y = 6

Step-by-step explanation:

The equilibrium point for the supply and demand equations p² + 4q = 253 and 183p² + 6q = 0 is (q, p) = (3, 10).

To find the equilibrium point, we need to solve the system of equations formed by the supply and demand equations. By substituting the value of q = 3 into the first equation, we get p² + 4(3) = 253, which simplifies to p² + 12 = 253.

Solving this equation gives us p = 10. Substituting the values of q = 3 and p = 10 into the second equation, we get 183(10)² + 6(3) = 0, which simplifies to 18300 + 18 = 0.

Since this equation holds true, we have found the equilibrium point to be (q, p) = (3, 10), where the equilibrium quantity is q = 3 and the equilibrium price is p = 10.

Learn more about Equation click here :brainly.com/question/13763238

#SPJ11

Answer:

\(y =\frac{4}{5}x-6\)

Step-by-step explanation:

Hi there!

Linear equations are typically organized in slope-intercept form: \(y =mx+b\) where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)

1) Determine the slope (m)

\(m=\frac{y_2-y_1}{x_2-x_1}\) where two given points are \((x_1,y_1)\) and \((x_2,y_2)\)

Plug in the given points (5,-2) and (15, 6)

\(=\frac{6-(-2)}{15-5}\\=\frac{6+2}{15-5}\\=\frac{8}{10}\\=\frac{4}{5}\)

Therefore, the slope of the line is \(\frac{4}{5}\). Plug this into \(y =mx+b\):

\(y =\frac{4}{5}x+b\)

2) Determine the y-intercept (b)

\(y =\frac{4}{5}x+b\)

Plug in one of the given points and solve for b

\(6=\frac{4}{5}(15)+b\\6=12+b\)

Subtract 12 from both sides of the equation to isolate b

\(6-12=12+b-12\\-6=b\)

Therefore, the y-intercept of the line is -6. Plug this back into \(y =\frac{4}{5}x+b\):

\(y =\frac{4}{5}x-6\)

I hope this helps!

Answer:

R___S____T

RT = RS+ ST

5.2 = RS + 3.4

RS = 5.2 - 3.4

RS = 1.8

I hope I helped you^_^

Answer:

35

Step-by-step explanation:

Answer:

the answer is 35.

Step-by-step explanation:

Answer:

A) x=23

B) angle 1 = 73, angles 4, 5, and 8 are congruent

C) angle 2 = 107, angles 3, 7, and 6 are congruent

Step-by-step explanation:

When we calculate probabilities involving one event AND another event occurring, we multiply their probabilities.

According to me , independent is the word which is associated with multiplication when computing probabilities . Because when the events are independent then we multiply the probabilities .

According to the multiplication rule of probability, the probability of occurrence of both the events A and B is equal to the product of the probability of B occurring and the conditional probability that event A occurring given that event B occurs.

The probability of the union of two events is equal to the sum of individual probabilities. The union of two set contains all the elements of previous sets. The union is denoted by ∪. The equation for the students earnings will be expressed as P(A∪B). The occurrence of event A changes the probability of B then the events are dependent. If the probability of two events happening together is zero then the events are mutually exclusive.

Therefore,

When we calculate probabilities involving one event AND another event occurring, we multiply their probabilities.

To learn more about Probability visit :

brainly.com/question/13490624

#SPJ4

Answer:

8

Step-by-step explanation:

2 : 1/4

2 x 4/1

2 x 4

8

Yes, if all the edge weights in graph G are nonnegative, the minimum spanning tree (MST) T' of the graph G' formed by multiplying each edge weight by 2 will be the same as the MST T for G.

When all edge weights in G are nonnegative, multiplying each edge weight by 2 in G' does not change the relative order of the weights. Therefore, any spanning tree of G that minimizes the total weight will also minimize the total weight in G'. This is because doubling all the edge weights in G' simply scales the weights uniformly without changing the relative differences between them.

To prove this formally, let's consider two MST algorithms: Prim's algorithm and Kruskal's algorithm.

Prim's Algorithm:

Start with an arbitrary vertex v in G.

Add the edge with the minimum weight incident to v to the MST.

Repeat the previous step, adding the edge with the minimum weight that connects to the existing MST until all vertices are included.

When applying Prim's algorithm to G and G', the selection of edges and the resulting MST will be the same because the weights of the edges are doubled uniformly in G'. The order of selection remains unchanged, ensuring that the same edges are added to both MSTs.

Kruskal's Algorithm:

- Sort the edges of G in non-decreasing order of their weights.

- Starting with an empty MST, consider each edge in the sorted order. If adding the edge does not form a cycle, include it in the MST.

Kruskal's algorithm also yields the same MST T for G and G' when all edge weights are nonnegative. The sorting order is based on the weights, and doubling the weights in G' maintains the same relative order. Hence, the same edges will be selected in both cases.

Therefore, in both Prim's and Kruskal's algorithms, the MST T' of G' will be the same as the MST T for G when all edge weights in G are nonnegative.

Learn more about edge weights

brainly.com/question/32082486

#SPJ11

The measure of the angle z of triangle ∆ABD in the same segment with angle C of triangle ∆ABC is equal to 51°

When two angles are in the same segment, they have the same measure. This means that if you know the measure of one angle in a particular segment, you can determine the measure of any other angle in that segment.

angle z = angle C

angle C = 180° - (55 + 34 + 40)° {sum of interior angles of triangle ABC

angle C = 180° - 129°

angle C = 51°

also;

angle z = 51°

Therefore, the measure of the angle z of triangle ∆ABD in the same segment with angle C of triangle ∆ABC is equal to 51°

Read more about angle here:https://brainly.com/question/24423151

#SPJ1

The mean is 58.319 m/h and the standard deviation is 11.665 m/h of the vehicle speed if 5% of all vehicles travel less than 39.13 m/h and 10% travel more than 73.25 m/h.

The mean and standard deviation of the vehicle speed can be calculated by using the formula for z-score.

The z-score of measure X can be given as;

Z = X - μ / σ

In this case, 39.13 m/h is the 5th percentile; therefore when X = 39.13, Z has a p-value of 0.05, hence Z = -1.645

Z = X - μ / σ

-1.645 = (39.13 - μ) / σ

39.13 - μ = -1.645σ

μ = 39.13 + 1.645σ

Additionally, 73.25 m/h is the 90th percentile (100 - 10 = 90), therefore when X = 73.25, Z has a p-value of 0.9, hence Z = 1.28

1.28 = (73.25 - μ) / σ

73.25 - μ = 1.28σ

μ = 73.25 - 1.28σ

We can find the standard deviation by equalling both equations as follows;

39.13 + 1.645σ = 73.25 - 1.28σ

1.645σ + 1.28σ = 73.25 - 39.13

2.925σ = 34.12

σ = 34.12/2.925 = 11.665 m/h

Now the mean can be calculated as follows;

μ = 73.25 - 1.28σ

μ = 73.25 - 1.28(11.665)

μ = 58.319 m/h

To learn more about standard deviation; click here:

https://brainly.com/question/28225633

#SPJ4