Cube A and cuboid B have the same volume. Calculate the missing length on cuboid B. Do not include units.

Xavier's average speed is 1 kilometer per minute.

To calculate Xavier's average speed, we need to determine the total time it took him to reach Terminal B and the distance traveled.

Given that Henry had completed 3/4 of the journey when Xavier reached Terminal B, it means Xavier took 1/4 of the total time for the journey. Since Xavier reached Terminal B 30 minutes earlier than Henry, we can infer that Xavier took 30 minutes for his part of the journey.

Since Henry was 30 km away from Terminal B when Xavier reached it, we can assume that Xavier traveled the remaining 30 km to reach Terminal B.

Therefore, Xavier's average speed can be calculated as the distance divided by the time:

Average Speed = Distance / Time = 30 km / 30 minutes = 1 km/minute.

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Answer:

See below!

Step-by-step explanation:

1) 720cm - m

2) 983 mm - m

3) 130.5kL - L

4) 0.03 g - mg

5) 997 g - kg

6) 9.1 l - ml

7)3.75 c - ml

8) 41.8 in - cm

9) 156.25 lb - kg

10) 9.5 gal - l

11) 680.4 g - lb

12) 4.725 m - ft

Hope this helps, have a lovely day! :)

Answer:

x = 13.3125

Step-by-step explanation:

Since it is a square, divide the area (225) by 4: 56.25

Now solve for x

56.25 - 3 = 53.25

53.25 / 4 = 13.3125

Please check if this is the method you need, and if I solved for the right thing!

Answer:

a) + x direction, b) +2yd

Step-by-step explanation:

a) According to the Cartesian plane, an eastward translation implies a movement in the +x direction.

b) + 2yd

The expected waiting time is 1.2 minute

According the statement

We know that the kingman formula is

\({ E(W) = \left ( \frac{p}{1-p} \right )\cdot \left ( \frac{ C_{a}^{2}+ C_{s}^{2} }{2} \right ) \cdot \mu_{s} }\)

According to statement the mean value μs is 6 min.

Here the value of P is 6/36 = 1/6

And the value of ca and cs is 1

Substitute the values in formula then

\({ E(W) = \left ( \frac{0.17}{1-0.17} \right )\cdot \left ( \frac{ 1^{2}+ 1^{2} }{2} \right ) \cdot \m6} }\)

\({ E(W) = \left ( \frac{0.17}{0.83} \right )\cdot \left ( 1 ) \cdot \m6} }\)

\({ E(W) = \left ( 0.20} \right )\cdot \left ( 1 ) \cdot \m6} }\)

\({ E(W) = 1.22\)

So, the expected waiting time is 1.2 minute

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Answer:

(b)

\(V_2 = \frac{\pi}{4} [ \frac{(2r)^2h}{3}]\) or \(V_2 = \frac{1}{3}\pi r^2h\)

Step-by-step explanation:

Given

\(Ratio = \frac{\pi}{4}\)

See attachment for complete question

Required

Determine the volume of the cone

The volume of a square pyramid is:

\(V = \frac{a^2h}{3}\)

Where

a = base dimension

From the attachment, the base dimension of the square pyramid is 2r.

So:

\(a = 2r\)

The volume becomes;

\(V = \frac{(2r)^2h}{3}\)

To calculate the volume of the cone, we simply multiply the given ratio and the volume of the prism.

So, we have:

\(V_2 = Ratio * V\)

\(V_2 = \frac{\pi}{4} [ \frac{(2r)^2h}{3}]\)

\(V_2 = \frac{\pi}{4} * \frac{(2r)^2h}{3}\)

Open bracket;

\(V_2 = \frac{\pi}{4} * \frac{4r^2h}{3}\)

Cancel out 4

\(V_2 = \pi * \frac{r^2h}{3}\)

The above can be written as:

\(V_2 = \frac{1}{3} * \pi r^2h\)

\(V_2 = \frac{1}{3}\pi r^2h\)

So, we have:

\(V_2 = \frac{\pi}{4} [ \frac{(2r)^2h}{3}]\)

or

\(V_2 = \frac{1}{3}\pi r^2h\)

Answer:

Yes, the total cost of Lacey lesson is a split function of hours scheduled

Step-by-step explanation:

The amount Lacey pays for each hour of golf = $15

The amount Lacey pays for equipment rental = $10

The amount Lacy pays for equipment rental for a 3 hours long lesson = $5

Therefore, we have

Let C represent the total cost of Lacey lesson and let t represent the number of hours, we have;

C = $10 + t × $15 for 0 ≤ t ≤ 3

C = $5 + t × $15 for t > 3

Therefore, the total cost of Lacey lesson is a split function of hours scheduled

Answer: The answer is 30x-2y

Step-by-step explanation: Subtract 4x from 34x to get 30x. Then the rest just falls down and you are left with 30x-2y. Also can you please give me a brainliest. I really need one.

If an interval estimate is said to be constructed at the 90 confidence level, the confidence coefficient would be 0.9.

Confidence level:

Confidence level means the proportion or frequency of acceptable confidence intervals that contain the true value of the unknown parameter.

For example,

A 0% confidence level means you have no faith at all that if you repeated the survey that you would get the same results.

Confidence Coefficient:

Confidence coefficient states the confidence level stated as a proportion, rather than as a percentage.

For example, if you had a confidence level of 99%, the confidence coefficient would be .99.

Given,

Here we know that the confidence level is 90%, now we have to find the confidence coefficient of it.

Based on the definition,

The confidence coefficient for 90% confidence level is 0.9.

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A plot that will present the information that will highlight how many trees are in a range of heights, such as 60–64, 65–69, etc. : histogram

In this question, we have been given the tree heights recorded on a school campus.

A science teacher wants to choose a data display that will highlight how many trees are in a range of heights, such as 60–64, 65–69, etc.

We need to find a correct plot that will present the information in this way.

We know that in bar charts, each bar represents one value(category). And  in a histogram, each bar will represent a continuous data

Therefore, a plot that will present the information that will highlight how many trees are in a range of heights, such as 60–64, 65–69, etc. : histogram

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Answer:

Step-by-step explanation:

A plot that will display information highlighting the number of trees in a range of heights, such as 60-64, 65-69, and so on: histogram

We were provided the tree heights reported on a school grounds in this question. A science instructor needs to select a data presentation that will show how many trees are in a given height range, such as 60-64, 65-69, and so on. We must find a suitable plot to portray the data in this manner. We know that each bar on a bar chart represents one value (category). And each bar in a histogram represents continuous data.

Answer:

An example is the following:  \(\sqrt{45}\)

Step-by-step explanation:

Simplify the radical: \(\sqrt{45}\)

1.We must write the radicand as a product, and then we must use the product property for simplicity.

The roof of \(\sqrt{45\) is equal =\(\sqrt{9 x 5}\)

2.We must use the property of the product: \(\sqrt {a} x \sqrt{b}\)

\(\sqrt{9x 5}\)=\(\sqrt{9} x\sqrt{5}\)

\(3\sqrt{5}\)

The lengths of the sides of the triangle with vertices A(0, 0, 4), B(2, 6, 7), and C(6, 4, -8) are AB = 7, BC = sqrt(245), and CA = 14. The triangle is neither a right triangle nor an isosceles triangle.

We can use the distance formula to find the lengths of the sides of the triangle

The distance between points A and B

d_AB = sqrt((2-0)^2 + (6-0)^2 + (7-4)^2) = sqrt(4 + 36 + 9) = sqrt(49) = 7

The distance between points B and C

d_BC = sqrt((6-2)^2 + (4-6)^2 + (-8-7)^2) = sqrt(16 + 4 + 225) = sqrt(245)

The distance between points C and A

d_CA = sqrt((0-6)^2 + (0-4)^2 + (4+8)^2) = sqrt(36 + 16 + 144) = sqrt(196) = 14

Therefore, the lengths of the sides of the triangle are AB = 7, BC = sqrt(245), and CA = 14

To determine whether the triangle is a right triangle, we can check if any of the three angles are 90 degrees. One way to do this is to compute the dot product of each pair of vectors formed by the three points and check if any of them are equal to zero (which would mean the vectors are perpendicular, and hence the corresponding sides are perpendicular). If any of the sides are perpendicular, then the triangle is a right triangle.

The dot product of vectors AB and BC

AB . BC = (2-0)(6-2) + (6-0)(4-6) + (7-4)×(-8-7) = 8 + (-12) + (-33) = -37

The dot product is not equal to zero, so AB and BC are not perpendicular.

The dot product of vectors BC and CA:

BC . CA = (6-2)(-6) + (4-6)(-4) + (-8-7)*4 = -24 - 4 - 44 = -72

The dot product is not equal to zero, so BC and CA are not perpendicular.

The dot product of vectors CA and AB

CA . AB = (0-6)×2 + (0-4)×6 + (4+8)×7 = -12 + (-24) + 84 = 48

The dot product is not equal to zero, so CA and AB are not perpendicular.

Therefore, none of the sides are perpendicular, and the triangle is not a right triangle.

To determine whether the triangle is an isosceles triangle, we can check if any two sides have the same length. We have already found the lengths of the sides to be AB = 7, BC = sqrt(245), and CA = 14. None of the sides have the same length, so the triangle is not an isosceles triangle.

Therefore, the triangle with vertices A(0, 0, 4), B(2, 6, 7), and C(6, 4, -8) is neither a right triangle nor an isosceles triangle.

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Answer:

Graph A

Step-by-step explanation:

A = y = 1.5   x =  -2\<x,< 3  

B = y = 0.2   x =  -2<x < 2

C = y = -1.2  x =  -2< x\< 3

D = y =  1.2   x = - 2< x < 2

The range of people who like both coffee and tea is between 75% and 75%, with the total number of people who like both being 75%.

If 70% of people like coffee, and 80% of people like tea, the minimum number of people who like both coffee and tea is the smaller percentage, which is 70%. The maximum number of people who like both coffee and tea is the smaller of the two percentages, which is 80%.

Therefore, the range of people who like both coffee and tea is 70% to 80%.

To calculate the actual range, you must first calculate the difference between the two percentages:80% - 70% = 10%

Then divide that difference by 2 and subtract and add it to the smaller number:

10% ÷ 2 = 5%

Lower bound: 70% + 5% = 75%

Upper bound: 80% - 5% = 75%

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(a) For t ≤ 0, F(t) = 0, and for t > a, F(t) = 1.

(b) \(F (or) t < = 0, R(t) = 1, and f(or) t > a, R(t) = 0.\)

(c)The hazard rate h(t) for a uniform distribution is a decreasing function.

(d) \(t_median = (0 + a) / 2 = a / 2\)

(e)\(p(T > 1/2a + 1/4a | T > 1/2a) = length of interval (1/2a + 1/4a, a] / length of interval (1/2a, a] = (a - (1/2a + 1/4a)) / (a - 1/2a) = (3/4).\)

(f)The uniform distribution does not exhibit the memoryless property because the remaining time to failure is dependent on the time already passed.

What is Probability?

Probability is a branch of mathematics that deals with the study of uncertainty and the likelihood of events occurring. It provides a quantitative measure of the likelihood or chance of an event happening. Probability is used to analyze and predict outcomes in various fields, including statistics, physics, economics, and engineering.

In probability theory, an event is defined as a specific outcome or set of outcomes of an experiment or random process. The probability of an event is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain or guaranteed event. Intermediate probabilities indicate varying degrees of likelihood.

(a) To find the cumulative distribution function (CDF) F(t), we need to determine the probability that the time to failure T is less than or equal to a given value t.

Since T follows a uniform distribution over (0, a], the probability density function (PDF) f(t) is constant within this interval:

f(t) = 1/a, for 0 < t ≤ a

To find the CDF, we integrate the PDF from 0 to t:

\(F(t) = \int[0 to t] f(x) dx\)

For 0 < t ≤ a, the integral evaluates to:

\(F(t) = \int[0.. t] (1/a) dx = (t/a), for 0 < t < = a\)

For t ≤ 0, F(t) = 0, and for t > a, F(t) = 1.

(b) The reliability function R(t) represents the probability that the time to failure T is greater than a given value t. It can be calculated as the complement of the CDF:

R(t) = 1 - F(t)

For 0 < t ≤ a, we have:

\(R(t) = 1 - (t/a)\)

\(F (or) t < = 0, R(t) = 1, and f(or) t > a, R(t) = 0.\)

(c) The hazard rate h(t) represents the instantaneous rate of failure at time t. It can be calculated as the ratio of the PDF to the reliability function:

\(h(t) = f(t) / R(t)\)

For a uniform distribution, the PDF is constant, so:

\(h(t) = (1/a) / (1 - (t/a)) = 1 / (a - t)\)

The hazard rate h(t) for a uniform distribution is a decreasing function.

(d) The mean time to failure (MTTF) represents the average time until failure occurs. For a uniform distribution, the MTTF can be calculated as the average of the lower and upper bounds:

\(MTTF = (0 + a) / 2 = a / 2\)

The median time to failure (t_median) is the value of t such that the probability of failure is 0.5. For a uniform distribution, the median time is simply the midpoint between the lower and upper bounds:

\(t_median = (0 + a) / 2 = a / 2\)

(e) To find the conditional probability\(p(T > 1/2a + 1/4a | T > 1/2a)\), we need to calculate the probability that T is greater than 1/2a + 1/4a, given that it is already known to be greater than 1/2a.

Since T follows a uniform distribution, the conditional probability is determined by the relative lengths of the intervals. The interval (1/2a + 1/4a, a] represents the remaining possible values of T when T > 1/2a. The interval (1/2a, a] represents the possible values of T when T > 1/2a + 1/4a.

Therefore, \(p(T > 1/2a + 1/4a | T > 1/2a) = length of interval (1/2a + 1/4a, a] / length of interval (1/2a, a] = (a - (1/2a + 1/4a)) / (a - 1/2a) = (3/4).\)

(f) The uniform distribution does not have the memoryless property. The memoryless property states that the conditional probability of an event occurring in the future does not depend on how much time has already passed.

In the case of a uniform distribution, knowing that T > t does affect the probability of T > t + Δ for any positive value Δ. The uniform distribution does not exhibit the memoryless property because the remaining time to failure is dependent on the time already passed.

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The required rate of return (or minimum acceptable rate of return) is 20 percent. If the net cash flows are $15,000 per year for ten years, the total cash flow is $150,000. The project's cost is $47,500. We can now apply the net present value formula to determine whether or not the project is feasible.

Net Present Value (NPV) = Cash flow / (1 + r)^n - Cost Where, r is the discount rate, n is the number of years, and Cost is the initial outlay.

Net Present Value = 150000 / (1 + 0.20)^10 - 47500

Net Present Value = $67,482.22

Since the NPV is positive, the project is feasible. When calculating net present value, it's important to remember that a positive NPV implies that the project is expected to generate a return that exceeds the cost of capital, whereas a negative NPV indicates that the project is expected to generate a return that is less than the cost of capital, and as a result, it should be avoided.

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Answer:

B. -h

Step-by-step explanation:

Additive inverses are two numbers that add to 0.

h + (-h) = 0

-h is the additive inverse of h since h and -h add to 0.

Answer: B. -h

Answer:

-h

Step-by-step explanation:

The additive inverse of a number simply means that same number, but with an opposite sign. For example:

Additive inverse of 9 = -9

Additive inverse of -2 = 2

Additive inverse of -(-6) = -6

Additive inverse of -(+4) = 4

Answer:

32.9811320755

Step-by-step explanation:

Written out it is 32.9811320755 but the way i thing that your test or question will take is is 32.98

a. For an angle that measure of 110 degrees, the angle in radians is 1.92 radians. b. Formula that expresses the radian angle measure of an angle is radian_angle = (d degrees) * (π radians / 180 degrees).

a. To convert an angle of 110 degrees to radians, we can use the following conversion factor:

1 radian = 180 degrees / π radians.

So, to find the measure of the 110-degree angle in radians, we can use this formula:

radians = (110 degrees) * (π radians / 180 degrees)

radians = (110 * π) / 180

radians ≈ 1.92 radians

The angle with a measure of 110 degrees is approximately 1.92 radians.

b. To write a formula that expresses the radian angle measure of an angle in terms of the degree measure (d), we can use the conversion factor mentioned above:

radian_angle = (d degrees) * (π radians / 180 degrees)

This formula allows you to convert any angle from degrees to radians by simply replacing d with the degree measure of the angle.

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Answer:

Step-by-step explanation:

yyes

The probability distribution of Y will have the same shape as the probability distribution of X, The center of the probability distribution of Y will be $73,000 and variability of the probability distribution of Y will be  $18,000.

The probability distribution of Y will have the same shape as the probability distribution of X, since the distribution of Y is simply a shifted version of the distribution of X. Since the distribution of X is skewed to the right, the distribution of Y will also be skewed to the right.

The center of the probability distribution of Y will be $73,000, which is the mean of X plus the bonus amount of $5,000.

The variability of the probability distribution of Y will be the same as the variability of the probability distribution of X, since the bonus amount is the same for all employees and does not affect the variability of the salaries. Therefore, the standard deviation of the probability distribution of Y will be $18,000, the same as the standard deviation of the probability distribution of X.

Thus, The probability distribution of Y will have the same shape as the probability distribution of X, The center of the probability distribution of Y will be $73,000 and variability of the probability distribution of Y will be  $18,000.

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The solution of the equation x^ay! + 5xy + (4 + x)y = 0, where x > 0, can be represented as a power series of the form y = ΣCnx^n, where C0 = 1 and Cn = 0 for n = 1, 2, 3, ...

To find the solution of the equation x^ay! + 5xy + (4 + x)y = 0, we can represent the solution as a power series expansion of the form y = ΣCnx^n, where Cn is the coefficient of x^n and n ranges from 0 to infinity. Plugging the power series into the equation, we get:

x^a*(ΣCnx^nn!) + 5x*(ΣCnx^n) + (4 + x)(ΣCn*x^n) = 0

We can then collect the terms with the same powers of x:

ΣCnx^(n+a)n! + Σ5Cnx^(n+1) + Σ(4 + x)Cnx^n = 0

For the equation to hold true for all powers of x, each term with the same power of x must be zero. Therefore, we can determine the coefficients Cn for each power of x. For n = 0, the term ΣCnx^a0! simplifies to C0x^a0! = C0*x^a. Since the equation must hold for all x > 0, the coefficient C0 must be non-zero. Therefore, C0 = 1. For n = 1, the term Σ5Cnx^2 simplifies to 5C1x^2 = 0. Therefore, C1 = 0. Similarly, for n = 2, 3, 4, ... , the terms involving Cn will also be zero, as they are multiplied by powers of x. Hence, the solution of the equation x^ay! + 5xy + (4 + x)y = 0 can be represented as y = C0x^a = x^a, where a is a positive real number, and the coefficients Cn are zero for n = 1, 2, 3, ....

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Assuming 100% efficiency, the current in the secondary coil will be the same as the current in the primary coil.

The current in the secondary coil is dependent on the voltage ratio of the primary and secondary coils. If the voltage ratio of the coils is the same as the turns ratio, then the current in the secondary coil will be identical to that in the primary coil. Therefore, assuming 100% efficiency, the current in the secondary coil will be the same as the current in the primary coil.

The current in the secondary coil is determined by the voltage ratio of the primary and secondary coils. The voltage ratio is equal to the turns ratio, which is the ratio of the number of turns in the secondary coil to the number of turns in the primary coil. In an ideal transformer with 100% efficiency, the power output in the secondary coil will be equal to the power input in the primary coil. Since power is equal to voltage multiplied by current, and the voltage ratio is equal to the turns ratio, the current in the secondary coil will be the same as the current in the primary coil.

Therefore, assuming 100% efficiency, the current in the secondary coil will be the same as the current in the primary coil.

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Mark was 105 miles from home when he stopped for lunch.

Let's denote the distance from Mark's home to the restaurant as "x" miles. We can set up two equations based on the given information.

1. Two hours after leaving the restaurant, Mark has traveled 110 miles. This can be expressed as:

Distance traveled in 2 hours = 110 miles

Since Mark drove at a constant speed, we can write the equation:

Speed * Time = Distance

Speed * 2 = 110

2. Four hours after leaving the restaurant, Mark has traveled 210 miles. This can be expressed as:

Distance traveled in 4 hours = 210 miles

Using the same equation:

Speed * 4 = 210

Now we have a system of two equations:

1) Speed * 2 = 110

2) Speed * 4 = 210

We can solve this system to find the value of the speed and, consequently, the distance from home to the restaurant.

Dividing equation 2) by 2, we get:

Speed = 210 / 4

Speed = 52.5 miles per hour

Now, we can substitute this speed value into equation 1) to find the distance:

52.5 * 2 = 110

Distance = 105 miles

Therefore, Mark was 105 miles from home when he stopped for lunch.

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The price of the cycle is 2800 and the price of the scooter is 2800+ 4200=7000

Let the price of the cycle be x

Then the price of the scooter will become X + 4200

As the price of a scooter and the price of a cycle are in the ratio of 5:2

So, it can be written as

 x+4200: x:: 5:2

which implies

x= 2a and x+4200= 5a

a= x/2 and x+4200/5

equating both the equations, we get

x/2=(x+4200)/5

in order to solve this linear equation, we need to move 2 from the left-hand side to the right-hand side which would result in the change of sign from division to multiplication and we need to move 5 from the right-hand side to the left-hand side which would result in the change of sign from division to multiplication

5x=2x+8400

3x= 8400

X= 8400/3

X= 2800

So, the price of the cycle is 2800 and the price of the scooter is 2800+ 4200=7000

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The given problem is asking for a test to see if the sample mean is significantly different from 85 at the 0.05 level. To solve the problem, we can use the following formula:$$t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}$$where$\bar{x}$ = sample mean$\mu$ = population mean$s$ = sample standard deviation$n

$ = sample sizeTo calculate the t-value, we need to calculate the sample mean and the sample standard deviation. The sample mean is calculated as follows:$$\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$$where $x_i$ is the score of the $i$th student and $n$ is the sample size.

Using the given data, we get:$$\bar

{x} = \frac{78+89+67+85+90+83+81+79}{8}

= 81.125$$The sample standard deviation is calculated as follows:$$

s = \sqrt{\frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{n-1}}$$Using the given data, we get:$$

s = \sqrt{\frac{(78-81.125)^2+(89-81.125)^2+(67-81.125)^2+(85-81.125)^2+(90-81.125)^2+(83-81.125)^2+(81-81.125)^2+(79-81.125)^2}{8-1}}

= 7.791$$Now we can calculate the t-value as follows:$$

t = \frac{\bar{x} - \mu}{\frac{s}

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Answer:

9/26

Step-by-step explanation:

Word : CONFIDENCE

Consonants in word : C, N, F, D, N, C = 6

Total alphabets = 10

Probability =required outcome /Total possible outcomes

Probability (consonants) = 6 /10 = 3/5

Number of red catds in deck = 26

Number of aces in a card deck = 4

Total number of cards = 52

P(red) or P(ace)

(4/52) + (26/52) = (4 + 26) / 52 = 30 / 52 = 15 / 26

P(getting a consonant, then a red card or ace)

(3 /5) * (15/26) = (3 * 15) / (26 *5) = 45/130 = 9/26