Sal bought three CDs for 1598 each a computer cable for 3995 and a case for his MP3 player for 2499 sales tax is 7% to the nearest cent what is the total cost of his purchases




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The probability of drawing the slips '1', '2', '3', and '4' in that order is 1/126 or approximately 0.0079.

The probability that the drawn slips are '1', '2', '3', and '4', in that order, can be calculated by considering the number of favorable outcomes and the total number of possible outcomes.

There are 9 slips in the box, so the total number of possible outcomes is 9 choose 4, which is denoted as C(9,4) or 9!/(4!(9-4)!), which simplifies to 126.

Since we want the slips to be drawn in a specific order, the number of favorable outcomes is 1, because there is only 1 way to arrange the slips in the order '1', '2', '3', and '4'.

Therefore, the probability is 1/126, which simplifies to approximately 0.0079 or 0.79%.

divide

42/96 = 0.4375

0.4375*100 = 43.75 percent

 round the answer as needed.

A vector can be defined as an element of a vector space, which represents an object that has both magnitude and direction.

Assuming that; [tex]\left \{ {{x=rcos \theta} \atop {y=rsin \theta}} \right.[/tex]

For the channel:

The vector representing the flow from North to South is given by:

[tex]15 cos (\frac{3\pi}{2} ), \; 15 sin (\frac{3\pi}{2} )\\\\15(0),\; 15(-1)[/tex]

Vector = 0, -15

For the sailboat:

The vector representing the sailboat is given by:

[tex]40 cos (30 ), \; 40 sin (30)\\\\30(\frac{\sqrt{3} }{2} ),\; 30(\frac{1 }{2} )\\\\15\sqrt{3} ,\;15[/tex]

Vector = [tex]15\sqrt{3} ,\;15[/tex]

For the strong wind:

The vector representing the strong wind blowing towards northwest is given by:

[tex]30 cos (\frac{3\pi}{4} ), \; 30 sin (\frac{3\pi}{4} )\\\\30(\frac{-\sqrt{2} }{2} ),\; 30(\frac{\sqrt{2} }{2} )\\\\-15\sqrt{2},\;15\sqrt{2}[/tex]

Vector = [tex]-15\sqrt{2},\;15\sqrt{2}[/tex]

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To solve this problem, let us first calculate the probability of designing one shoe out of all the combinations.

Probability of designing one shoe = (probability of choosing 1 color for the base) * (probability of choosing 1 color for the accent) * (probability of choosing 1 font for the embroidery)

We know that probability is:

Probability = number of chosen event / number of total events

Therefore:

Probability of designing one shoe = (1 / 4) * (1 / 6) * (1 / 2)

Probability of designing one shoe = 1 / 48

This means that either Ray or Lilli has this probability of designing a specific shoe. Since we are asked for the probability that they will both design this specific shoe, so we multiply:

Probability they will design the same shoe = (1 / 48) * (1 / 48)

Probability they will design the same shoe = 1 / 2304 = 4.34 * 10^-4

The probability is around 0.043% that they will design the same shoe.

Answer:

1 acre foot = 43560 ft³

Step-by-step explanation:

1 square mile = 640 acres.

5280 feet = 1 mile

5280 x 5280 ft² = 640 acres.

1 acre = 43560 ft².

1 acre foot = 43560 x 1 ft³ = 43560 ft³

1 acre foot = 43560 ft³

The amount of cobalt-60 will decrease with each half-life, which is 5.26 years. After 5 half-lives (26.3 years), the 200g sample will reduce to 6.25g.

The subject of the question is the half-life of a radioactive substance, in this case, cobalt-60. Half-life is the time required for half the atoms in a sample to decay. Given that the half-life of cobalt-60 is 5.26 years, and we are interested in a period of 26.3 years, we first classify this period into 'half-life' units, which equals 26.3 / 5.26  = 5 half-lives.

With each half-life, the quantity of cobalt-60 is cut in half. We start with a 200g sample and after 5 half-lives, the amount of cobalt-60 would decrease as follows:

Therefore, after 26.3 years, only 6.25g of the original 200g sample of cobalt-60 will remain.

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515x + 285y = 11,080

x + y = 30

The probability of getting either a sum of 5 or at least one 5 in the roll of a pair of dice will be 5/12.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

The total number of probability is given as,

Total event = 6 x 6

Total event = 36

The samples are given as,

(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)

(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)

Then the probability of getting either a sum of 5 or at least one 5 in the roll of a pair of dice will be given as,

P = (4/36) + (11/36)

P = 15/36

P = 5/12

The probability of getting either a sum of 5 or at least one 5 in the roll of a pair of dice will be 5/12.

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Final answer:

To show that z = (xy)/(x+y) given that 3^x = 4^y = 12^z, logarithms and the properties of exponents are used to simplify and solve for z.

Explanation:

The problem given is to show that if 3^x = 4^y = 12^z, then z = (xy)/(x+y). To solve this, we can use logarithms or equate the expressions to a common variable. Since 12 = 3 × 4, it means that 12^z = (3^z)(4^z).

Remember that the original equations given were 3^x = 12^z and 4^y = 12^z.

Substituting z into these equations we have 3^x = 3^z × 4^z and 4^y = 3^z × 4^z.

Taking logarithms, we find

[tex]log(3^x) = log(3^z) + log(4^z) and log(4^y) = log(3^z) + log(4^z).[/tex]

Applying the power rule of logarithms, the equations simplify to

[tex]x log(3) = z log(3) + z log(4)[/tex]and  [tex]y log(4) = z log(3) + z log(4).[/tex]

Dividing these equations by log(3) and log(4) respectively gives

[tex]x = z + z(log(4)/log(3))[/tex] and [tex]y = z + z(log(3)/log(4)).[/tex]

Adding these equations, we get

[tex]x + y = 2z + z[(log(4)/log(3)) + (log(3)/log(4))],[/tex]

which simplifies to x + y = 2z because [tex](log(4)/log(3)) + (log(3)/log(4)) = 1.[/tex]Finally, solving for z gives z = (xy)/(x+y) as desired.

The time taken to reach the maximum height = 3 s

Quadratic function is a function that has the term x²

The quadratic function forms a parabolic curve

The general formula is

where a, b, and c are real numbers and a ≠ 0.

The parabolic curve can be opened up or down determined from the value of a. If a is positive, the parabolic curve opens up and has a minimum value. If a is negative, the parabolic curve opens down and has a maximum value

So the maximum is if a <0 and the minimum if a> 0.

After t seconds, a ball height h (in feet) is given by the function h (t) = 96t-16t²

The maximum value of the function is obtained if the first derivative of the function h (t) = 0

96-32t = 0

96 = 32t

t = 3 s

The maximum height

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Final answer:

The ball reaches its maximum height after 3 seconds. This is determined by finding when the derivative of the height function h(t) = 96t - 16t² equals zero and solving for t.

Explanation:

To determine the time at which the ball reaches its maximum height, we need to analyze the function h(t) = 96t - 16t². Here, h(t) represents the height of the ball after t seconds. The ball achieves its maximum height when the derivative of the height function with respect to time is zero (i.e., when its upward velocity is zero).

To find this, we can take the derivative of h(t) and set it equal to zero to find the critical points:

h'(t) = d/dt (96t - 16t²) = 96 - 32t.

Setting the derivative equal to zero:

96 - 32t = 0

32t = 96

t = 96/32 = 3 seconds.

Therefore, the ball reaches its maximum height after 3 seconds.

Answer:

five ordered pairs are (-2,1) (-1,3) (0,5) (1, 7) (2, 9)

y intercept is (0,5)

x intercept is (-2.5, 0)

Step-by-step explanation:

y=2x+5

To get 5 ordered pairs , plug in some random number for x and find out y

x           y= 2x+5

-2            2(-2) + 5= 1

-1             2(-1) + 5= 3

0             2(0) + 5= 5

1             2(1) + 5= 7

2             2(2) + 5= 9

five ordered pairs are (-2,1) (-1,3) (0,5) (1, 7) (2, 9)

When x=0 , the value of y = 5

So y intercept is (0,5)

To find x intercept we plug in 0 for y

y=2x+5

0 = 2x +5

subtract 5 from both sides

-5 = 2x

divide by 2 on both sides

x= -5/2

so x intercept is (-2.5, 0)

Answer:

18 boxes of wrenches and 22 boxes of hammers.

Step-by-step explanation:

The rarest form of dichromatism is tritanopia. This condition affects the perception of blue and yellow colors and is less common than protanopia and deuteranopia which affect red and green perception respectively.

The rarest form of dichromatism is tritanopia. The term dichromatism refers to an abnormality in color vision where an individual can only perceive two of the three primary colors. This question is related to the broader topic of color vision deficiencies, a study within biology. Among the options listed, protanopia and deuteranopia tend to be the most common color vision deficiencies, both affecting the perception of red and green respectively. Tritanopia is a condition that impacts the ability to perceive blue and yellow and is the least common form, while 'Fruitopia' is not related to this topic as it's a brand of fruit drinks.

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Due to the lack of numerical details, a precise ratio of men to all members at the swim club cannot be determined. The ratio would be based on the exact number of men verses total members. Ratios offer a method to compare quantities.

Unfortunately, without more information, it's impossible to definitively say what the precise ratio of men to all members at the swim club is. To determine the correct ratio, we would need to know the total number of members at the club, and the number of those members who are men. A ratio is a way to compare quantities or numbers, and in this case, the quantity of men compared to the quantity of all members.

For example, if there were 20 members total in the club, and 10 of those members were men, the ratio would be 1:2 (choice C), because for every one man, there are two total members. However, if there were 4 members and 3 of them were men, then the ratio would be 3:4 (choice B). Without the specific numbers, we cannot determine the correct answer from choices A, B, C, or D.

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This is a binomial probability problem where we calculate the probability of fewer than 9 successful surgeries out of 10, given a success rate of 75% for each surgery. The probabilities of 0 to 8 successful surgeries are calculated and summed up.

The question asks for the probability that fewer than 9 out of 10 surgeries are successful, given that each surgery has a 75% chance of being successful. This is a binomial probability problem since each surgery can result in either success (75%) or failure (25%), and we are dealing with a fixed number of independent trials (10 surgeries).

To solve this, we first calculate the probability of exactly 8 successes, exactly 7 successes, and so on down to 0 successes, then sum these probabilities. The binomial probability formula is P(x) = (nCx) * (p^x) * ((1-p)^(n-x)), where n is the number of trials, x is the number of successes, p is the probability of success, and nCx is the combination of n items taken x at a time.

However, calculating each probability individually and summing them can be tedious, and tools or calculators designed for binomial distributions are often used to compute this more efficiently. For a result of fewer than 9 successes, we would add the probabilities of getting 8, 7, ..., down to 0 successful surgeries.

The standard form of the equation for the line passing through (-5, -1) and (10, -7) is y = x - 17.

The standard form of the equation for the line passing through the points (-5, -1) and (10, -7) can be found using the point-slope form given, which is y + 7 = (x - 10).

First, let's convert this equation into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

Subtracting 7 from both sides of the equation, we get y = x - 17.

This is the standard form of the equation for the line passing through (-5, -1) and (10, -7).

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Answer:

The missing coordinate is 5

Step-by-step explanation:

The probability of having at most three defects in a four-hour period is approximately 0.8572.

The Poisson probability distribution is used to model the number of events that occur in a fixed interval of time or space, given the average rate at which the events occur. In this problem, the rate of errors is given as one error every two hours. We need to find the probability of having at most three defects in a four-hour period.

To solve this problem, we can use the Poisson probability formula, which is:

P(x; λ) = (e^(-λ) * λ^x) / x!

where P(x; λ) is the probability of having exactly x events occur in the given interval, λ is the average rate of events, e is the base of the natural logarithm, and x! is the factorial of x.

First, we need to calculate the average rate of events in a four-hour period. Since the rate is given as one error every two hours, we can calculate the rate for a four-hour period as follows:

Average rate = (4 hours) / (2 hours/error) = 2 errors

Now, we can plug this average rate (λ = 2) into the Poisson probability formula for x = 0, 1, 2, and 3 to find the probabilities of having at most three defects:

P(0; 2) = [tex](e^{(-2)} * 2^0)[/tex] / 0! ≈ 0.1353

P(1; 2) = ([tex]e^{(-2)} * 2^1[/tex]) / 1! ≈ 0.2707

P(2; 2) = [tex](e^{(-2)} * 2^2)[/tex] / 2! ≈ 0.2707

P(3; 2) = [tex](e^{(-2)} * 2^3)[/tex] / 3! ≈ 0.1805

To find the probability of at most three defects, we sum up these individual probabilities:

P(at most 3 defects) = P(0; 2) + P(1; 2) + P(2; 2) + P(3; 2) ≈ 0.8572

So, the probability of having at most three defects in a four-hour period is approximately 0.8572.

Answer:

3181 yards.

Step-by-step explanation:

All the given information can be used to draw a simple diagram. The diagram shows a triangle which is formed by the ships. There are two angles given and one side is given. Therefore, the sine rule must be used to solve the question. The sine rule can be written as:

sin V / v = sin G / g.

It can be observed that the angle V is unknown, however, it can be calculated very easily. Simply use the law of triangle in which all the 3 angles sum up to 180 degrees. So V = 180 degrees - 44 degrees - 36 degrees = 100 degrees. So plugging in v = 4510 yards, V = 100 degrees, G = 44 degrees, and g = x yards into the sine rule gives:

sin 100 / 4510 = sin 44 / x.

Cross multiplying gives:

x*sin 100 = 4510*sin 44

Making x the subject gives:

x = (4510*sin 44)/sin 100.

x = 3181 yards (to the nearest yard).

Therefore, Norman and Voyager are 3181 yards apart from each other!!!

The required distance between the Norman and the Voyager is 3181 yards.

Given that,
A ship at sea, the Gladstone, spots two other ships, the Norman and the Voyager, and measures the angle between them to be 44°. The distance between the Gladstone and the Norman is 4510 yards. The Norman measures an angle of 36° between the Gladstone and the Voyager. To the nearest yard, what is the distance between the Norman and the Voyager is to be determined.

These are the equation which contains trigonometric operators such as sin, cos.. etc.. In algebraic operation.

Here,
The measure of the angle between Gladstone and the norman,
= 180 - 44 + 36
= 100°

sin(100) / 4510 = sin(44) / x.

x = 3181.12

x ≈ 3181 yards

Thus, the required distance between the Norman and the Voyager is 3181 yards.

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