a bookshelf holds 55 sports magazines and 55 architecture magazines. when 33 magazines are taken from the shelf at random, without replacement, what is the probability that all 33 are architecture magazines?

The system can be written as a vector equation as [5, 1, -3] [x1, x2, x3]^T = [8, 0]^T and as a matrix equation as AX = B, where A = [5 1 -3; 0 2 4], X = [x1; x2; x3], and B = [8; 0].

To write the given system as a vector equation, we group the variables and the constants into vectors and write the equations in a matrix form. Thus, the system can be written as [5x1 + x2 - 3x3; 2x2 + 4x3] = [8; 0], which is a vector equation.

To write the system as a matrix equation, we can write the coefficients of the variables in a matrix A, the variables in a vector X, and the constants in a vector B. Thus, the system can be written as AX = B, where A = [5 1 -3; 0 2 4], X = [x1; x2; x3], and B = [8; 0].

We can then solve for X by finding the inverse of A and multiplying both sides of the equation by it.

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Answer:

approximately 43 - 44 minutes exact

Answer:

It would take you 2917 hours.

Step-by-step explanation:

Do 777,777,777 divided by 266,560.

I hope this helped at all.

To determine the probability that the coin landed heads given that a red ball was selected, we can use Bayes' theorem. The probability that the coin landed heads is approximately 0.55.

According to Bayes' theorem, we can calculate this probability using the formula:

P(H|R) = (P(H) * P(R|H)) / P(R

P(R|H) is the probability of selecting a red ball given that the coin landed heads. In this case, a red ball can be chosen from urn A, which has 14 red balls out of 25 total balls. Therefore, P(R|H) = 14/25.

P(R) is the probability of selecting a red ball, which can be calculated by considering both possibilities: selecting from urn A and selecting from urn B. The overall probability can be calculated as (P(R|H) * P(H)) + (P(R|T) * P(T)), where P(T) is the probability of the coin landing tails (0.5). In this case, P(R) = (14/25 * 0.5) + (5/11 * 0.5) ≈ 0.416.

Plugging the values into the formula:

P(H|R) = (0.5 * (14/25)) / 0.416 ≈ 0.55.

Therefore, the probability that the coin landed heads given that a red ball was selected is approximately 0.55.

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Answer:

-2, -1

Step-by-step explanation:

The height of the cylinder is 3 inches if the cylinder has a volume of 12π cubic inches and a diameter of 4 inches.

In geometry, it is defined as the three-dimensional shape having two circular shapes at a distance called the height of the cylinder.

We know the volume of the cylinder is given by:

\(\rm V = \pi r^2 h\)

We have:

Volume of the cylinder = 12π cubic inches

Dimeter of the cylinder = 4 inches

Radius of the cylinder = 2 inches

Here no other information is given in the question, Let suppose it is required to find the height of the cylinder

12π = π(2)²h

12  = 4h

h = 3 inches

Thus, the height of the cylinder is 3 inches if the cylinder has a volume of 12π cubic inches and a diameter of 4 inches.

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For the transformation at -78 °C, appropriate reagents include lithium aluminum hydride (LiAlH4) and diethyl ether.

At -78 °C, certain chemical reactions require the use of specific reagents to achieve the desired transformation. One commonly used reagent is lithium aluminum hydride (LiAlH4), which acts as a strong reducing agent. It is capable of reducing various functional groups, such as carbonyl compounds, to their corresponding alcohols.

Diethyl ether is typically employed as a solvent to facilitate the reaction and ensure efficient mixing of the reactants. Researchers often utilize this low temperature for reactions involving sensitive or reactive intermediates, as it helps control the reaction and prevent unwanted side reactions.

The use of LiAlH4 and diethyl ether provides a reliable combination for achieving the desired transformation at this temperature, enabling chemists to manipulate and modify compounds in a controlled manner.

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We have been given the coordinate plane showing the points (1, 3); (2, 0.6); and (3, 0.12). We need to find the sequence that is modeled by the graph below. Let us analyze the given points of the graph. It can be noticed that the y-values decrease as x increases.

So, it appears that the given graph represents an exponential function with a common ratio that is less than one. Since we have to find the sequence, we need to determine the general term of this sequence.Let a_n be the nth term of the sequence.The general formula for an exponential function is a_n = a_1 r^(n-1), where a_1 is the first term of the sequence and r is the common ratio.We can find a_1 from the given points of the graph.

We see that when x = 1, y = 3. So, a_1 = 3.To find r, we can find the ratio between any two successive terms of the sequence.Let's take the ratio between the second and first term of the sequence.The second term has coordinates (2, 0.6) and the first term has coordinates (1, 3).So, r = 0.6/3 = 0.2.Substituting the value of a_1 and r in the general formula, we get a_n = 3 x (0.2)^(n-1).Therefore, the sequence that is modeled by the given graph is an = 0.3(5)n − 1.I hope this helps.

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Answer:

2/3

Step-by-step explanation:

32/48= 16*2/16*3= 2/3

Answer:

the trains will be 48 miles apart at 4 mph

Step-by-step explanation:

hope this helps :D brainliest?

To calculate the probability that less than 1/3 of the tosses are heads, we find the cumulative probability.  The probability that less than 1/3 of the tosses are heads when the coin is tossed 60 times is 3.34%.

Using the binomial probability formula, the probability of getting exactly k heads in n tosses is given by P(X = k) = (n C k) * \(p^k\) * \(q^{n-k}\), where (n C k) is the binomial coefficient, p is the probability of heads, and q is the probability of tails.

In this case, p = 0.5 and q = 1 - p = 0.5. We want to calculate the cumulative probability P(X < 1/3 * 60) = P(X < 20) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 19).

Using a calculator or statistical software, we can compute the cumulative probability:

P(X < 20) ≈ 0.0334

Therefore, the probability that less than 1/3 of the tosses are heads when the coin is tossed 60 times is approximately 0.0334, or 3.34%.

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Answer:

The correct answer would be C

Step-by-step explanation:

I hope this helps, if it doesn't then just message me and ill be more than happy to help :)

The ratio of the original heights of the two candles which are lighted at the same time is 3:4.

A ratio is a quantitative relationship between two or more quantities or values, expressing how many times one quantity is contained in or is equal to another quantity.

Let the original height of the first candle as h1 and the original height of the second candle as h2.

we have,

- In six hours, the first candle is extinguished.

- The second candle burns down in 8 hours.

- After 3 hours, both candles are equally high.

From this, we can deduce that after 3 hours, both candles have burned down to the same fraction of their original heights.

For the first candle:

Remaining height of the first candle = h1/2

For the second candle:

Remaining height of the second candle = (3/8) h2

Since both candles are equally high after 3 hours, we can set up the following equation:

h1/2 = (3/8) h2

h1/h2 = (3/8) 2

h1/h2 = 3/4

Therefore, the ratio of the original heights is 3:4.

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Answer:

science type of food group : fibre

Based on the data points given, the type of function shown is a Quadratic function.

A quadratic function is one where the values of x and y form data points that lead to a parabola being formed.

This parabola forms when the values of the data points start away from 0 and then reach zero and rise again. This is what happens with these points so the function must be a quadratic function.

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Answer:

5. Slope: 2

Y-intercept: 3

6. Slope: 1/2

Y-intercept:  5

Step-by-step explanation:

Answer: C.\(\left \{ {{a1=-2} \atop {an=a(n-1)+3}} \right.\)

because it is the arithmetic progression with d = 3

=> a(n) = a1 + (n - 1).3

so, have: a1 = -2

               an = a(n-1) + 3

Step-by-step explanation:

Answer:

1000 km^3

Step-by-step explanation:

1 km=1000m

1 cubic kilometer is equivalent to 1,000,000,000 cubic meters, due to cubing the conversion factor of 1,000 (meters per kilometer).

1 cubic kilometer is equivalent to 1,000,000,000 (one billion) cubic meters. When converting units, you need to remember the relationships between those units. In this case, 1 kilometer is equivalent to 1000 meters. Therefore, to convert from cubic kilometers to cubic meters, you need to cube the conversion factor (1000 meters/kilometer). Hence, 1 cubic kilometer = 1,000^3 cubic meters = 1,000,000,000 cubic meters.

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The given polynomials are discussed and grouped into each given category as given below.

What is a polynomial?

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

We can now look into each polynomial.

a) x³ + 125

   125 is a cube of 5 and also  x³  is the power of x.

So this is a perfect cube.

b) 8p³ - 27

    8p³ is a perfect cube of 2p and 27 is a perfect cube of 3.

So it is a perfect cube.

c) 12x³-9

    This is neither a cube nor a square.

d) a²-100

   100 is a perfect square and so is a².

So this is a difference of perfect squares.

e) 4m² + 25

4m² is a square of 2m and 25 is a square of 5.

But the operator is +

So this is neither a cube nor a difference of a perfect square.

f) 16x²-9

16x² is a square of 4x and 9 is a square of 3.

Also, the operator is -

So this is a difference of perfect squares.

Therefore the above polynomials are discussed and grouped into each given category accordingly.

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Answer:

I think 1575000 but not sure sorry if i'm wrong

The probability that abby, barry, and sylvia win the 1st, 2nd, 3rd prizes resprctively, in a drawing of 200 people in contest that no one win the prize is equals to 0.0000001269.

Total number of people present= 200

so, total possible outcomes= 200

We have to determine the probability that abby, barry, and sylvia win the 1st, 2nd, 3rd prizes resprctively.

The number of favourable outcomes for winning first prize = 1

So, probability that abby win the first prize = \(\frac{1}{200} \)

The number of favourable outcomes for winning second prize = 1

So, probability that barry win the second prize = \(\frac{1}{199} \)

The number of favourable outcomes for winning third prize = 1

So, probability that sylvia win the third prize = \(\frac{1}{198} \)

Now, total probability that no one can win more than one prize = \(\frac{1}{200} × \frac{1}{199} × \frac{1}{198} \)

= 0.0000001269

Hence, required probability value is 0.0000001269.

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Complete question :

what is the probability that abby, barry, and sylvia win the 1st, 2nd, 3rd prizes resprctively, in a drawing of 200 people enter the contest no one can win more than one prize.

Four variables that are most important to control in an experiment about the rate at which bread turns moldy are:

So, the variables that are most important in an experiment about the rate at which bread turns moldy are:

Therefore, four variables that are most important to control in an experiment about the rate at which bread turns moldy are:

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The correct question is given below:
Choose the four variables that are most important to control in an experiment about the rate at which bread turns moldy.

a. humidity

b. B time of day

c. age of bread

d. type of bread

e. shape of bread

f. height of observer

g. type of shelf surface

h. type of storage container

Answer:

Step-by-step explanation:

\((2x + 9) + (6x + 6)\)

\((2x + 6x) + (9 + 6)\)

\(8x + 15\)

Answer:

72 degrees

Step-by-step explanation:

A pentagon has five lines of symmetry. For rotation symmetry, the order of any regular polygon is the number of sides. The angle of rotation would be 360 degrees divided by that order. Therefore, the answer is 72 degrees.

Answer:

3/4 of the ribbon is needed to make a bow

Step-by-step explanation:

12 ÷ 4 = 3

so out of that foot of ribbon you use 3/4 of it for the bow

Answer: it’s all about the angle and length of it

Step-by-step explanation:

1st get sumthing that’s as long as that

2st do u see the point and what it’s touching use that follow alone with it

3

Answer:

they warned me and deleted my answer  for no reason i think its because i sent a link to a calculator

Step-by-step explanation:

but the answer is the last one yes

Answer:

1) V≈923.62824

2) V= 28.27433

Answer:

1. 923.16 or 294 Pi

2. 3052.08 or 972 Pi

Step-by-step explanation:

Formula for volume of a cone = Pi r^2 h/3

If diameter is 14, radius is 7

Pi 7^2 18/3

Pi 49 6

Pi 294

923.16

Formula for volume of a sphere = 4/3 pi r^3

If diameter is 18, radius is 9

4/3 pi 9^3

4/3 pi 729

972 pi

3052.08

Given :-

To find :-

Solution :-

Let :-

According to the statement :-

Simplify :-

Answer:

• let the number be x:

\( \hookrightarrow \: { \boxed{ \rm{ \: \frac{x}{3} + 2 = 6 }}} \\ \\ { \rm{x + (2 \times 3) = (6 \times 3)}} \\ \\ { \rm{x + 6 = 18}} \\ \\ { \underline{ \underline{ \rm{ \: \: x = 12 \: \: }}}}\)

The Fahrenheit temperature of the cup of water, after 4.5 minutes, is given as follows:

155ºF.

The temperature function is defined as follows:

\(T(t) = T_a + (T_0 - T_a)e^{-kt}\)

Considering the surrounding and initial temperature, we have that the function is given as follows:

\(T(t) = 69 + 135e^{-kt}\)

The temperature after 1.5 minutes is of 185ºF, hence the coefficient k is obtained as follows:

\(185 = 69 + 135e^{-1.5k}\)

\(e^{-1.5k} = \frac{116}{135}\)

\(k = -\frac{\ln{\left(\frac{116}{135}\right)}}{1.5}\)

k = 0.1011.

Hence:

\(T(t) = 69 + 135e^{-0.1011t}\)

Hence the temperature after 4.5 minutes is given as follows:

\(T(4.5) = 69 + 135e^{-0.1011 \times 4.5}\)

T(4.5) = 155ºF.

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