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Answer:

610.75

Step-by-step explanation:

48.86 divided by 0.08

Answer:

6x + 5y - 5z = -17

Step-by-step explanation:

Find the midpoint between P and Q.

Midpoint = (-1 + 5)/2, (-3 + 2)/2, (5 + 0)/2) = 2, -1/2, 2.5)

Find the vector pointing from P to Q.

Vector PQ = (5 - (-1), 2 - (-3), 0 - 5) = 6, 5, -5)

The normal vector of the plane is perpendicular to the vector pointing from P to Q.

Normal Vector = (6, 5, -5)

The equation of the plane can be written in the form of ax + by + cz + d = 0, where (a, b, c) is the normal vector and d is the distance between the plane and the origin.

(6x + 5y - 5z + d) = 0

We know that the point (2, -1/2, 2.5) lies on the plane

(6 * 2 + 5 * (-1/2) - 5 * 2.5 + d) = 0

-17/2 + d = 0

d = 17/2

(6x + 5y - 5z + 17/2) = 0

12x + 10y - 10z + 17 = 0

6x + 5y - 5z = -17

This is the equation of the plane consisting of all points that are equidistant from P=(-1, -3, 5) and Q=(5, 2, 0), and having 6 as the coefficient of z.

Answer:190000

Step-by-step explanation: To find the half of a number, You divide the number by 2, so it will be 380000/2 =190000

The general solution to the given differential equations are as follows:

17. y = C₁e^(-2x) + C₂e^x + (5/9)e^(3x)

18. y = C₁e^(-5x) + C₂e^(2x) + (7/9)e^(2x)

19. y = C₁sin(4x) + C₂cos(4x) + (1/4)sin(x)

20. y = C₁e^x + C₂xe^x + 3e^x

21. y = C₁e^(-x) + C₂e^(2x) + x(x-2)/3

22. y = C₁e^x + C₂e^(-x) + (3/7)e^(2x) - (17/21)e^(3x)

23. y = C₁e^(-x) + C₂e^(3x) + e^(-x) - 2sin(x)

24. y = C₁e^(-3x) + C₂e^(-x) + (5x+4)/18

25. y = C₁e^(-x) + C₂e^x + 6e^x

26. y = C₁e^(-2x) + C₂xe^(-2x) + (5/6)x^2 - (5/6)x - (5/9)e^(-2x)

27. y = C₁cos(2x) + C₂sin(2x) - 2sin(2x) + 2cos(2x)

28. y = C₁e^(-x) + C₂e^(2x) + (5/6)e^(2x)

29. y = C₁e^(-x)cos(x) + C₂e^(-x)sin(x) + (1/2)sin(2x)

30. y = C₁e^(-x) + C₂e^x + (1/2)x^2 + (5/3)x + 1

31. y = C₁e^x + C₂e^(-x) + 2e^(-x) - (9/10)e^(-x)

32. y = C₁e^(-x) + C₂e^(-2x) + 2e^(-x) + 3e^(2x)

Differential equations using the annihilator technique, we will find the complementary function and particular solution.

The annihilator for a term of the form (D-a)^n, where D represents the differential operator and a is a constant, is (D-a)^n.

For each given differential equation, we will find the complementary function by applying the appropriate annihilator to the equation. Then, we will find the particular solution using the method of undetermined coefficients or variation of parameters, depending on the form of the non-homogeneous term.

Finally, we will combine the complementary function and particular solution to obtain the general solution by adding the two solutions.

Derivation of each trial solution and the subsequent calculation of the general solution for each differential equation is a complex and lengthy process. Due to the character limit, it is not feasible to provide the detailed derivation here. However, the summary section provides the general solutions for each equation.

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Explanation:

Let's calculate the time taken to drive at 100 km/hr

distance = rate*time

time = distance/rate

time = 160/100

time = 1.6 hours exactly

Do the same for when she drove at 90 km/hr

time = distance/rate

time = 160/90

time = 1.7778 hours approximately

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

Next, subtract the time values

1.7778 - 1.6 = 0.1778

The difference in time values is about 0.1778 hours.

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

The last step is to multiply by 60 to convert from hours to minutes.

0.1778*60 = 10.668

This then rounds to 11 minutes

Answer:  The answer is D (4). The expression cannot be factored.

Answer:

no because she would get the same total if she added it before or after

Step-by-step explanation:

Answer:

The age of brothers are 4 years and 2 years respectively.

Step-by-step explanation:

We are given that the ages of two brothers have a ratio of 2 to 1. When 4 years have passed, the ratio of their ages will be 8 to 6.

Let the age of the first brother be 'x years' and the age of the second brother be 'y years'.

So, according to the question;

                                      \(\frac{x}{y} =\frac{2}{1}\)  

                                      \(x=2y\)  -------------- [equation 1]

                                       \(\frac{x+4}{y+4}=\frac{8}{6}\)

                               \(6({x+4})=8}(y+4)\)

                               \(6x+24=8y+32\)

                               \(6(2y)+24=8y+32\)

                               \(12y-8y=32-24\)

                                    \(4y=8\)

                                     \(y=\frac{8}{4}\) = 2 years

Putting the value of y in equation 1 we get;

                                     x = 2y

                                      x = \(2 \times 2\) = 4 years

Hence, the age of brothers are 4 years and 2 years respectively.

Answer:

part a: The slope of the function represents the rate of change of the balance in the bank account per day. To find the slope, we can use the formula: slope = (change in y)/(change in x).

Using the values from the table, we have: slope = (720-600)/(3-0) = 120/3 = 40. Therefore, the slope of the function g(x) is 40.

part b: Using the point-slope form of the equation of a line, we can write: g(x) - 600 = 40(x-0). Simplifying, we get: g(x) = 40x + 600. This is the slope-intercept form of the equation, where the y-intercept is 600 and the slope is 40.

To write in standard form, we can rearrange the equation as: -40x + g(x) = 600.

part c: Using function notation, we can write the equation as: g(x) = 40x + 600.

part d: To find the balance in the bank account after 7 days, we can use the equation we found in part c and substitute x = 7: g(7) = 40(7) + 600 = 880. Therefore, the balance in the bank account after 7 days is $880.

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Answer:

1400 cm/ 2.54 cm per inch = 551 inches. Step-by-step explanation: There are 39.3701 inches in 1 meter, so all you have to do is multiply. :) 551 inches.Step-by-step explanation:

Answer:

Step-by-step explanation:

The probability P(Z>1.28) represents the area under the standard normal distribution curve to the right of the z-score 1.28.

Using a standard normal distribution table or a calculator, we find that the area to the right of 1.28 is approximately 0.1003.

Therefore, the answer is closest to option (b) 0.10. there is a 10% chance of obtaining a value above 1.28 in a standard normal distribution.

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The one mean z test can be used for a sample of moderate size (between 15 and 30) when the population standard deviation is known and the population distribution is approximately normal or the sample size is sufficiently large (n ≥ 30).

When to use the one mean z-test for a sample of moderate size (between 15 and 30).
The one mean z-test is used to compare the sample mean to a known population mean when the population standard deviation is known.

we can use this test for a sample of moderate size (between 15 and 30) under the following conditions:
The population is normally distributed, or the sample size is large enough (usually greater than 30) for the Central Limit Theorem to apply.

However, since your sample size is between 15 and 30, it is crucial that the population is normally distributed.
The population standard deviation is known.

This is essential for calculating the z-score.
The sample is random and independent, meaning each observation in the sample is unrelated to the others.
If these conditions are met, we can use the one mean z-test for a sample of moderate size (between 15 and 30) to test hypotheses about the population mean.

The test will allow you to determine if there is a significant difference between the sample mean and the known population mean.

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Answer:

I think the answer is rotation

Step-by-step explanation:

because it's the only possible answer as refraction is quite similar to reflection but the question says an entirely different spot.

Answer:

A bus (contracted from omnibus,[1] with variants multibus, motorbus, autobus, etc.) is a road vehicledesigned to carry many passengers. Buses can have a capacity as high as 300 passengers.[2] The most common type is the single-deck rigid bus, with larger loads carried by double-decker and articulated buses, and smaller loads carried by midibuses and minibuses while coaches are used for longer-distance services. Many types of buses, such as city transit buses and inter-city coaches, charge a fare. Other types, such as elementary or secondary school buses or shuttle buses within a post-secondary education campus do not charge a fare. In many jurisdictions, bus drivers require a special licence above and beyond a regular driving licence.

In order to simplify and verify trig identities, one needs to use the rules of trigonometry and algebra to manipulate the equation until it is in a simplified form.

The most common trig identities to remember include the Pythagorean identity, reciprocal identities, quotient identities, and sum and difference identities. When simplifying an equation, it is important to remember to include the negative sign when necessary and to factor out any common factors.

After simplifying, it is important to verify the equation. This can be done by plugging in known values for the variables and verifying that the equation is true. By utilizing the rules of trigonometry and algebra, one can simplify and verify trig identities. This process is essential for working with trigonometric functions.

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The investment of each brother is $21,000, $14,000, and $14,000 if they are in the ratio 3 : 2 : 2 and they all are investing a total of $49,000.

As the brother invest in the ratio of 3 : 2 : 2 then,

Let the investment of the first brother be 3x

the investment of the second brother be 2x

the investment of the third brother be 2x

Total investment = 3x + 2x + 2x

= 7x

Thus, the fraction of investment of the first brother = \(\frac{3x}{7x}\)

The fraction of the investment of the second brother = \(\frac{2x}{7x}\)

The fraction of the investment of the third brother = \(\frac{2x}{7x}\)

Hence, the investment of the first brother = \(\frac{3x}{7x}\) * 49000 = $21,000

The investment of the second brother = \(\frac{2x}{7x}\) * 49000 = $14,000

The investment of the third brother = \(\frac{2x}{7x}\) * 49000 = $14,000

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Answer: there is so picture

Step-by-step explanation: it should give you the option when you ask the question it’s the little paper clip

No, ordering a soft drink is not independent of ordering a pizza

An independent event is one that is unrelated to the likelihood of another event occurring (or not happening). In other words, the occurrence has no bearing on the likelihood that a subsequent event will also occur.

P (square pizza is ordered) = 50% or 0.5

P (Soft drink is ordered) = 72% or 0.72

P ( squared pizza and soft drink are ordered) = 36 % or 0.36

Computing independency:

Ordering pizza and ordering a soft drink will be independent if:

P (squared pizza) + P (soft drink) = 1

0.5 + 0.72 ≠1

1.22≠1

Therefore, ordering pizza and ordering a soft drink is not independent

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Answer:

1 7/18

Step-by-step explanation:

2 7/9= 25/9

25/9 divided by 2 is 25/18

Answer:

1 7/8

Step-by-step explanation:

2 7/9 simplified as 25/9 divided by 2 is 25/18 which is 1 7/8 if you simplify it. I hope my answer helps!

Answer:

26 R 1

Step-by-step explanation:

Etruscsn small mammals on earth the Bumblebee bat

Answer:

Step-by-step explanation:

y is the value obtained from 4 and 12

y^2  =  4 * 12            Combine

y^2 = 48                   Square root both sides.

√y^2 = √48

y = √(3 * 4 * 4)

y = 4√3

Use the Pythagorean Theorem to obtain x

x^2 = y^2 + 4^2

x^2 = 48 + 16

x^2 = 64                    Take the square root of both sides

√x^2 = √64

x = 8

Answer

Answer:

the second and 3rd one

Step-by-step explanation:

Answer:

60^2-10/5 = 3600-2 = 3598

Step-by-step explanation:

The number of managers are in this survey = 96

Let us assume that A represents the set of managers with BS degree and B represents the set of managers with masters degree.

46 managers have a masters degree.

⇒ n(A) = 46

60 managers have a B.S. degree

⇒ n(B) = 60

20 have both a masters and bs degree.

⇒ n(A ∩ B) = 20

10 managers have neither degree

⇒ n(A ∪ B)c = 10

We know that the set formula,

n(P U Q) = n(P) + (n(Q) – n (P ⋂ Q)

So,  n(A ∪ B) = n(A) + n(B) – n (A ⋂ B)

n(A ∪ B) = 46 + 60 - 20

n(A ∪ B) = 86

Let n(S) be the be the total managers are in this survey.

n(S) = n(A ∪ B) + n(A ∪ B)c

n(S) = 86 + 10

n(S) = 96

Therefore, there are 96 managers in this survey.

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(a) shows that every pair of opposite sides in the hexagon a′b′c′d′e′f′ are parallel and equal in length. On the other hand, (b) demonstrates that the triangles a′c′e′ and b′d′f′ have equal areas.

(a) To show that every pair of opposite sides in hexagon a'b'c'd'e'f' are parallel and equal in length, we can use the fact that the centroids of triangles divide the medians into segments of equal length.

Let's consider a'b' and d'e'. The centroid of triangle fab, a', divides the median fb into two segments, a'f and a'b', such that a'f = 2/3 * fb. Similarly, the centroid of triangle def, e', divides the median de into two segments, e'd and e'f', such that e'd = 2/3 * de.

Since fb = de (opposite sides of hexagon abcdef), we have a'f = e'd. Now, we can consider the triangles a'f'd' and e'df'. By the properties of triangles, we know that if two sides of a triangle are equal, and the included angles are equal, then the triangles are congruent.

In this case, a'f' = e'd' (as shown above) and angle a'f'd' = angle e'df' (corresponding angles). Therefore, triangle a'f'd' is congruent to triangle e'df'.

By congruence, the corresponding sides a'd' and e'f' are equal in length.

By similar reasoning, we can show that b'c' and e'f', as well as c'd' and f'a', are parallel and equal in length.

(b) To show that triangles a'c'e' and b'd'f' have equal areas, we can use the fact that the area of a triangle is one-half the product of its base and height.

In triangle a'c'e', the base is c'e' and the height is the perpendicular distance from a' to c'e'. Similarly, in triangle b'd'f', the base is d'f' and the height is the perpendicular distance from b' to d'f'.

Since opposite sides in hexagon a'b'c'd'e'f' are parallel (as shown in part (a)), the perpendicular distance from a' to c'e' is equal to the perpendicular distance from b' to d'f'.

Therefore, the heights of triangles a'c'e' and b'd'f' are equal. Additionally, the bases c'e' and d'f' are equal (as shown in part (a)).

Using the area formula, area = 1/2 * base * height, we can see that the areas of triangles a'c'e' and b'd'f' are equal.

Hence, we have shown that triangles a'c'e' and b'd'f' have equal areas.

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