Suppose there are four boxes which look the same on the outside but each of them has a different number of black and white balls inside. The number of balls varies according to the following chart Box # of Black # of White 1 0 2 2 2 1 3 1 3 4 4 1 In our experiment, a box is first picked at random and then a ball is withdrawn, its color thus noted. 1) What is the probability of choosing a black ball out of: a) Box 1? b) Box 2? c) Box 3? d) Box 4?

The expected value for a student to spend on lunch each day from the survey of 50 students is $5.18.

The expected value for a student to spend on lunch each day is derived from the survey of 50 students. This value is calculated by taking the total number of dollars spent by all of the surveyed students and dividing it by the total number of students surveyed. In this particular survey, the total number of dollars spent was $247, and the total number of students surveyed was 50. Dividing $247 by 50 gives us a value of $4.94. This value is then rounded up to the nearest cent to give us the expected value of $5.18. This expected value is the average amount of money that a student can expect to spend on lunch each day from the survey. It is important to note that this value is an estimate, as individual student spending habits may vary greatly.

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To determine which interval has the most confidence in capturing the population mean, we need to look at the confidence level associated with each interval. A confidence interval is a range of values that we believe contains the true population parameter.

If we have three intervals with different confidence levels, the interval with the highest confidence level would be the one with the most confidence in capturing the population mean. For example, if Interval A has a confidence level of 90%, Interval B has a confidence level of 95%, and Interval C has a confidence level of 99%, then Interval C would have the most confidence in capturing the population mean.

It's important to note that the level of confidence we choose affects the width of the interval. The higher the confidence level, the wider the interval will be. Therefore, we need to balance the desire for a high level of confidence with the need for a narrow interval.

In summary, the interval with the highest confidence level is the one with the most confidence in capturing the population mean. Confidence intervals are a powerful tool in statistics that allows us to estimate population parameters from a sample with a known degree of uncertainty.

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\(\boxed{275.67+3(16.32)+24.39+27.40x \leq 560}\\\\27.40x +349.02 \leq 560\\\\27.40x \leq 210.98\\\\x \leq 7.7\)

Rounding down yields \(\boxed{x \leq 7}\).

Answer:

Step-by-step explanation:

560

Answer:

Step-by-step explanation:

3.25 hours

Answer:

(D)3.6 cm esa es amigo buen dia

Answer:

x = 9

Step-by-step explanation:

Similar Triangles

We are given a shape where two similar triangles are given. The similarity theorem states that the side lengths of the triangles must be proportional in the same scale factor.

The total length of the left side is 72+9 = 81 cm

The smaller length of the left side is 9 cm

The proportion is 81/9 = 9. This is the scale factor.

The total length of the right side is 3x - 20 + 56 = 3x + 36

The smaller length of the right side is 3x-20

The proportion must be equal to 9:

\(\displaystyle \frac{3x+36}{3x-20}=9\)

Multiplying by 3x-20:

3x+36=9(3x-20)

Operating

3x+36=27x-180

Rearranging:

24x = 216

Dividing by 24:

x = 9

the Greatest Common Divisor is 252 and it can be expressed as the linear combination -2 * 6,066 + 3 * 2,286.

The greatest common divisor (GCD) is the biggest positive integer that divides two or more integers without leaving a remainder. It's also referred to as the greatest common factor (GCF) or the highest common factor (HCF). The Euclidean procedure, which continually divides the greater of the two integers by the smaller until a remainder of zero is obtained, is one way to calculate the GCD. The GCD is a crucial idea in mathematics, notably in number theory, and it has several applications in other disciplines, such as computer science and encryption. Finding the greatest common divisor of the coefficients of a linear equation in two variables is another popular geometry task.

How to solve?

The Greatest Common Divisor of 6,066 and 2,286 can be expressed as 252 = 6,066 * (-2) + 2,286 * 3. So, the GCD is 252 and it can be expressed as the linear combination -2 * 6,066 + 3 * 2,286.

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A standard normal distribution is a normal distribution with a mean of zero and a standard deviation of one. Option A is the correct answer.

The standard normal distribution, often known as the z-distribution, is a special sort of ordinary distribution with a mean of zero and a standard deviation of one. Option A is the correct answer.

Any normal distribution can be standardized through transforming its values into z scores. The Z scores indicate how many standard deviations a certain result is from the mean. All normal distributions are unimodal, symmetrically distributed, and have a bell-shaped curve. One such distribution is the common normal distribution. On the other hand, a normal distribution's mean and standard deviation can be any value. In the typical normal distribution, the mean and standard deviation remain constant.

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A standard normal distribution is a normal distribution with a mean of zero and a standard deviation of one.

A standard normal distribution, also known as the Z-distribution, is a specific type of normal distribution. It has a mean of zero and a standard deviation of one. The Z-distribution is often used in statistics to standardize data and calculate probabilities.

The standard normal distribution is represented by a bell-shaped curve that is symmetric around the mean of zero. The area under the curve represents the probability of a random variable falling within a certain range.

The Z-score, which measures the number of standard deviations a data point is from the mean, is commonly used in hypothesis testing and confidence interval calculations.

The standard normal distribution is widely used in various fields, including finance, psychology, and quality control.

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Answer:

64 cups

Step-by-step explanation:

If 1 gallon is equal to 16 cups then 4 gallons will be 16×4= 64

Hope that helps you!

The perimeter of the rectangle, when the area is maximized, is approximately 24.63 units. Therefore, correct option is a.

To maximize the area of the rectangle inscribed in the parabola \(y^2 = 16x\), we need to find the dimensions of the rectangle. Since the side of the rectangle is along the latus rectum of the parabola, we know that the length of the rectangle is equal to the latus rectum.

The latus rectum of the parabola \(y^2 = 16x\) is given by the formula 4a, where "a" is the distance from the focus to the vertex of the parabola. In this case, the focus is located at (4a, 0).

To find "a," we can equate the equation of the parabola to the general equation of a parabola in vertex form: \(y^2 = 4a(x - h)\), where (h, k) is the vertex of the parabola.

Comparing the two equations, we get:

4a = 16

a = 4

Therefore, the latus rectum of the parabola is 4a = 4 * 4 = 16 units.

Since the length of the rectangle is equal to the latus rectum, we have length = 16 units.

Now, to find the width of the rectangle, we need to determine the corresponding y-coordinate on the parabola for the given x-coordinate of the latus rectum. The x-coordinate of the latus rectum is half the length, which is 16/2 = 8 units.

Substituting x = 8 into the equation of the parabola, we get:

\(y^2 = 16(8)\\y^2 = 128\\y = \sqrt{128} = 11.31\)

Therefore, the width of the rectangle is approximately 11.31 units.

The perimeter of the rectangle is given by the formula:

Perimeter = 2(length + width)

Plugging in the values, we have:

Perimeter = 2(16 + 11.31)

Perimeter ≈ 2(27.31)

Perimeter ≈ 54.62

Rounding the perimeter to two decimal places, we get approximately 54.62 units, which is equivalent to 24.63 units.

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The expected number of rolls until all faces have appeared in some order in six consecutive rolls is 1 / [1 - (5/6)^6].

To find the probability that all faces have appeared in some order in six consecutive rolls of a 6-sided die, we can use the principle of inclusion-exclusion.

Let's calculate the probability of the complement event first, which is the probability that at least one face is missing from the sequence in six consecutive rolls.

In the first roll, there are 6 possibilities for the face that appears. In the second roll, there are 5 possibilities remaining, and so on. Therefore, the probability of missing a face in one roll is (5/6).

Since we want to find the probability of missing a face in six consecutive rolls, we multiply the probabilities together: (5/6)^6.

Now, to find the probability of all faces appearing in some order in six consecutive rolls, we can subtract the probability of the complement event from 1.

Probability = 1 - (5/6)^6.

For the expected number of rolls until such a sequence appears, we can use the concept of geometric distribution. The expected number of rolls for a geometric distribution is equal to 1 divided by the probability of success.

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The correct answer is answer choice- A.

Step-by-step explanation:

Answer:

Option A

Step-by-step explanation:

See the attached worksheet. The use of a filled or unfilled circle on a number indicates whether that actual number is included (solid circle) or not included (empty circle)  A solid bar between two points telss us these points are all included.  

 -3<x<3 does not have an equality ("=") for ether +3 nor -3.  The the line between those points would be solid (all points are allowed).  Either 3 would be an empty circle.  

Option A seems to have these features.

The expression for the perimeter of the triangle is 4v + 8s + 5

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

The figure

The perimeter of the figure is the sum of the side lengths

Using the above as a guide, we have the following:

Perimeter = 6v + s + 5s - 2v + 2s + 5

When the expression is evaluated, we have

Perimeter = 4v + 8s + 5

Hence, the perimeter of the figure is 4v + 8s + 5

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Answer:

The formula for the volume of a sphere is 4⁄3πr³. For a cylinder, the formula is πr²h. A cone is ⅓ the volume of a cylinder, or 1⁄3πr²h.

Answer:

Step-by-step explanation:

d = 180 - 131 = 49

e = 180 - (90 + 49) =

     180 - 139 =

     41

Hope that helps!

Answer:

d: 49

e:41

Step-by-step explanation:

180-131=d which is 49

90+49=139

180-139= e which is 41

Answer:

Therefore , the solution of the given problem of circle comes out to be  ratio of the areas of the smaller and bigger circles is r1: r2.

When observed from this fresh vantage point and a certain distance distant, each airplane part forms a circle. (center). Surfaces and undulating zones that are different from one another make up its structure. Moreover, it revolves equally within the centre in every direction. Every extreme extent is equidistant from the "centre" in any type of circular or constrained double sphere.

Here,

The general connection between the areas of two circles can be established.

The equation A = r2, where r is the circular's radius, determines the area of a circle.

The areas of two circles whose diameters are r1 and r2, r1 being smaller than r2, are as follows:

=> A1 = πr1²

=> A2 = πr2²

We can divide A1 by A2 to get the ratio of the smaller circle's area to the bigger circle's area:

=> A1 / A2 = (πr1²) / (πr2²)

=> r1² / r2²

The ratio of the areas of the smaller and bigger circles is therefore r1: r2. Note that this has been completely reduced.

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In functions, value of x = 45 and y = 45

What is function in math?

6)  x = 15

 y = 49

3x = 3 * 15 = 45

y - 4 = 49 - 4 = 45

7)  3x + 23 = 4x

    4x - 3x = 23

     x = 23

    y =  4 * 23 =   92°

8) y + 12 = 5x °

  3x + 50  =

According to the question

     y + 12 = 3x  + 50

      5x   = 3x + 50

      2x = 50

        x = 25

y + 12 = 5x °

y = 5 * 25 - 12

y = 125 - 12 =   113

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Continental mountain ranges are formed when two tectonic plates collide and push against each other. This process is known as orogeny, and it results in the uplift of the Earth’s crust and the formation of mountains.

The energy of the colliding plates is so great that it causes the crustal rock to become deformed and folded. This process can be seen in mountain ranges such as the Himalayas and the Rocky Mountains. Orogeny can also cause earthquakes, volcanoes, and other seismic activity. Orogeny typically takes place over a very long period of time, sometimes millions of years. Plate tectonics are thought to be responsible for the formation of the Earth’s major mountain ranges. The collision of two or more plates creates an enormous amount of energy, which is released in the form of uplift, earthquakes, and volcanoes. This energy has the potential to drastically change the landscape, forming vast mountain ranges and rugged terrain.

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Answer: A.

Step-by-step explanation:

Answer:

w = x - 2yz

w + 2yz = x

2yz = x - w

y = (x - w)/2z

Answer:

There is an error in the question.

All angles in an equilateral triange are 60º

Answer:

Price of copy = $5

Step-by-step explanation:

Situation:

Tommy purchases five copies and five pencils. He gives $130 to the shopkeeper.

If the price of a pencil is $13, find the price of a copy.

Assume

Number of copy = 5

Number of pencil = 5

Price of copy = x

Price of Pencil = $13

So,

5(x) + (5)(13) = 130

6(x) + 65 = 130

x = 5

So,

Price of copy = $5

Answer:

Angle CBA

Step-by-step explanation:

It would be CBA because Angle 1 is between those 3 points. Angle 1 is where B is so B would have to go in the middle.

Hope this helps :)

The end of the plank is sliding along the ground at a rate of approximately -0.08 m/s when it is 1.4 meters from the wall of the building. The negative sign indicates that the end of the plank is sliding in the opposite direction.

To find how fast the end of the plank is sliding along the ground, we can use related rates. Let's consider the position of the end of the plank as it moves along the ground.

Let x be the distance between the end of the plank and the wall of the building, and y be the distance between the end of the plank and the ground. We are given that dx/dt = 0.26 m/s, the rate at which the worker pulls the rope.

We can use the Pythagorean theorem to relate x and y:

x² + y² = 5²

Differentiating both sides of the equation with respect to time, we get:

2x(dx/dt) + 2y(dy/dt) = 0

At the given moment when x = 1.4 m, we can substitute this value into the equation above and solve for dy/dt, which represents the rate at which the end of the plank is sliding along the ground.

2(1.4)(0.26) + 2y(dy/dt) = 0

2(0.364) + 2y(dy/dt) = 0

0.728 + 2y(dy/dt) = 0

2y(dy/dt) = -0.728

dy/dt = -0.728 / (2y)

To find y, we can use the Pythagorean theorem:

x² + y² = 5²

(1.4)² + y² = 5²

1.96 + y² = 25

y² = 23.04

y = √23.04 ≈ 4.8 m

Substituting y = 4.8 m into the equation for dy/dt, we have:

dy/dt = -0.728 / (2 * 4.8) ≈ -0.0757 m/s

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Answer:

0.21428571428

Step-by-step explanation:

hope it helps

Answer:

W x 3 = 64

Step-by-step explanation:
Let x be the dog's weight when he was 6 months old. Since the dog's weight is 3 times as heavy now, we can say: w = 3x But we also know that the current weight of the dog is 64 pounds, so we can substitute w = 64: 64 = 3x Dividing both sides by 3, we get: x = 21.33 Therefore, the equation to find the dog's weight when he was 6 months old is: x = 21.33

Answer:

x=−5+3–√2

x=−5−3–√2

Step-by-step explanation: