Cindy and Richard leave their dorm in Charleston
at the same time. Cindy rides her bicycle north at a
speed of 18 miles per hour. Richard rides his bicycle
south at a speed of 14 miles per hour. How long will it
take them to be 96 miles apart?

Step-by-step explanation:

To find the Highest Common Factor (H.C.F.) of 567 and 255 using Euclid's division lemma, we can follow these steps:

Step 1: Apply Euclid's division lemma:

Divide the larger number, 567, by the smaller number, 255, and find the remainder.

567 ÷ 255 = 2 remainder 57

Step 2: Apply Euclid's division lemma again:

Now, divide the previous divisor, 255, by the remainder, 57, and find the new remainder.

255 ÷ 57 = 4 remainder 27

Step 3: Repeat the process:

Next, divide the previous divisor, 57, by the remainder, 27, and find the new remainder.

57 ÷ 27 = 2 remainder 3

Step 4: Continue until we obtain a remainder of 0:

Now, divide the previous divisor, 27, by the remainder, 3, and find the new remainder.

27 ÷ 3 = 9 remainder 0

Since we have obtained a remainder of 0, the process ends here.

Step 5: The H.C.F. is the last non-zero remainder:

The H.C.F. of 567 and 255 is the last non-zero remainder obtained in the previous step, which is 3.

Therefore, the H.C.F. of 567 and 255 is 3.

Answer:

102.9

Step-by-step explanation:

Area of a triangle is A=(1/2)(h)(b) where h is the height and b is the base.

7.35 is the height and 28 is the base

A=(1/2)(7.35)(28)

A=102.9

Answer:

x = 7.55

Step-by-step explanation:

a = x

b = 8

c = 11

a² + b² = c²

x² + 8² = 11²

x² + 64 = 121

x² = 121 - 64

x² = 57

\(\sqrt{x^2} =\sqrt{57}\)

x = 7.5498

Rounded to hundredths:

7.55

Answer:

3 men at 7 hours per day complete flooring of 84 m in 2 days. how many men can floor 256 m in 4 days working 8 hours brainly

Step-by-step explanation:

3 men at 7 hours per day complete flooring of 84 m in 2 days. how many men can floor 256 m in 4 days working 8 hours brainly

Answer:

<BAC=60°

Step-by-step explanation:

THIS IS THE ANSWER

The least expensive computer after the 20% discount would be $400.

To calculate the price of the least expensive computer after the 20% discount, we need to find 20% of the original price and subtract it from the original price.

Let's assume the original price of the least expensive computer is x. The discount of 20% can be calculated as 0.20 * x. To find the discounted price, we subtract the discount from the original price: x - 0.20 * x = 0.80 * x.

Since we know that the cost of the least expensive computer ranges from $500 to $1000, we can substitute x with $500 and calculate the discounted price: 0.80 * $500 = $400. Therefore, the least expensive computer after the 20% discount would be $400.

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Answer:

D

Step-by-step explanation:

Hope this helps

The value of ΔH°(2000 K) - ΔH°(0 K) for H(g) is the enthalpy change of formation of H(g) at 2000 K minus the enthalpy change of formation of H(g) at 0 K.

The enthalpy change of formation (ΔH°f) is the heat energy released or absorbed when one mole of a substance is formed from its elements in their standard states. To calculate ΔH°(2000 K) for H(g), we need to find the enthalpy change of formation of H(g) at 2000 K.

At 2000 K, H(g) is in a gaseous state. To determine its enthalpy change of formation, we compare it to the elements in their standard states. The standard state of hydrogen is H₂(g) at 298 K and 1 atm. Thus, we need to consider the energy required to convert H₂(g) at 298 K and 1 atm to H(g) at 2000 K.

The enthalpy change of formation at a specific temperature can be calculated using the equation:

ΔH°(T₂) = ΔH°(T₁) + ∫Cp(T)dT

Where ΔH°(T₂) is the enthalpy change of formation at temperature T₂, ΔH°(T₁) is the enthalpy change of formation at temperature T₁ (in this case, 298 K), Cp(T) is the heat capacity of the substance as a function of temperature, and the integral is taken over the temperature range from T₁ to T₂.

To obtain an accurate calculation, we would need the specific heat capacity data for H(g) over the temperature range from 298 K to 2000 K. Unfortunately, without this data, we cannot provide a precise value for ΔH°(2000 K) for H(g).

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Step-by-step explanation:

yes they are because they have the same variables which are X& Y

Answer:

5yx-7xy

they are like terms, it's all multiplication just a different arrangement

5xy-7xy=-2xy

Step-by-step explanation:

hope this is helpful

This question is solved using translation concepts, and doing this, it is found that the equation of the new graph is:

\(y = |x - 3|\)

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

When a function f(x) is translated a units to the left, we get f(x - a).

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

In this question:

The original function is \(y = |x|\)

Point (1,1) is moved to (4,1), that is, 3 is added to the x-coordinate, meaning that the function was shifted 3 units to the left.

Thus, the new equation is:

\(y = g(x) = f(x - 3) = |x - 3|\)

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Answer:

\(m = \frac{2k}{v^{2} } \)

Step-by-step explanation:

\(k = \frac{1}{2} mv ^{2} \)

\(v ^{2} m = 2k\)

\(m = \frac{2k}{v ^{2} } \)

The larger the \(r^{2}\) and the smaller the s ( standard error).

          \(s = \sqrt{\frac{1-r^{2} }{n-2} }\)

          Where, \((1-r^{2} )\) is the non determination factor, and (n−2)      represents the degrees of freedom.

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Answer:

Student has made an error

Step-by-step explanation:

If two figures are said to be congruent, this implies that area of both is same and both as exactly same or copy or each other.

But from the graph, it can be stated that height of figure JKLM is 4 units whereas that of other is 6 unit.

Hence explained !

Answer:

y = 5x - 14

Step-by-step explanation:

*Parallel lines have the same slopes*

Rewrite your equation to slope-intercept form: y = mx + b

y = mx + b

y - 5x = 10 <== add 5x to both sides

   + 5x   + 5x

y = 5x + 10

The slope of the line that is parallel to this line is 5.

We need to find the y-intercept (b) for the parallel line using (2, -4):

y = 5x + b <== substitue 2 for x and -4 for y

-4 = 5(2) + b

-4 = 10 + b <== subtract 10 from both sides to isolate b

-10  -10

-14 = b

y = 5x + b changes to y = 5x - 14

Hope this helps!

Slope:-

Parallel lines have equal slope

Equation in point slope form

72 three course meals we can order.

Question states that;

A restaurant offers a special menu with three salad options, six meal options, and eight dessert options.

Counting Principle:

The counting rule is another name for the Fundamental Counting Principle. It's a way to figure out how many possible outcomes there are in a probability word problem. Probability is the likelihood that an event will occur. An event's probability is always a number between 0 and 1. The probability of all events added together equals one.

We need to find how many three course meals we can order;

Total number of ways,

P(A) = 3 * 6 * 8

P(A) = 72

72 three course meals we can order.

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The given statement " there exists an integer b such that for all integers n > b, n^3 - 8 is prime." is proved by contradiction.

Consider the sequence of integers a_n = n^3 - 8 for n = 1, 2, 3, .... By assumption, for every integer b, there exists an integer m > b such that a_m is not prime. Let p be a prime factor of a_m. Then, p is a prime factor of a_n for all n that are multiples of m.

Consider the sequence of integers a_{km} for k = 1, 2, 3, .... By the above reasoning, each term in this sequence has a prime factor p. However, as k becomes larger, a_{km} becomes arbitrarily large, and thus the prime factor p must eventually be smaller than a_{km}. This means that there exists an integer n such that a_n has a prime factor p that is smaller than a_n itself.

But this is a contradiction, since a_n cannot have a prime factor smaller than itself. Therefore, our assumption that there does not exist an integer b such that for all integers n > b, n^3 - 8 is prime must be false. Hence, there exists an integer b such that for all integers n > b, n^3 - 8 is prime.

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Answer:

2=n

Step-by-step explanation:

-6=n-4n

1. n-4n is -3

2. new equation (-6=-3n)

3. Divide: -6 and -3 =2 to get the n by itself

4. final answer 2=n

The reason for throwing a die 108 times can vary depending on the context and the purpose of the experiment.

The binomial distribution to model the probability of a success (rolling a 6) in n independent trials (rolls of the die). The formula for the probability of k successes in n trials is:

P(k) = (n choose k) p^k (1-p)^(n-k)

where "n choose k" is the binomial coefficient, p is the probability of success in a single trial (1/6 for rolling a 6), and (1-p) is the probability of failure.

To estimate the probability of rolling a 6 with a fair die, we could throw the die a large number of times and count the number of times we get a 6.

If we throw the die n times, the expected number of 6s is np, and the variance is np(1-p). As the number of trials increases, the distribution of the number of 6s we observe will approach a normal distribution with mean np and variance np(1-p).

To have a reasonably accurate estimate of the probability of rolling a 6, we would need to throw the die enough times to ensure that the sample mean (i.e., the number of 6s we observe) is close enough to the true mean (i.e., the expected number of 6s).

This requires a sufficient sample size, which depends on the level of accuracy we desire and the variability of the data.

For example, if we want to estimate the probability of rolling a 6 with a margin of error of 0.01 with 95% confidence (i.e., we are 95% confident that the true probability lies within the interval defined by the estimate ± the margin of error), we can use the formula:

n = (z^2 p(1-p)) / (ME^2)

where z is the z-score corresponding to the desired confidence level (1.96 for 95% confidence), ME is the margin of error (0.01), and p is the estimated probability of rolling a 6.

If we don't have an estimate of p, we can use 0.5 as a conservative estimate of the variance.

For a fair die, p = 1/6, so plugging in the numbers, we get:

n = (1.96^2 * 1/6 * 5/6) / 0.01^2 ≈ 108

This means that we would need to throw the die at least 108 times to estimate the probability of rolling a 6 with a margin of error of 0.01 and 95% confidence.

This choice of frequency is based on statistical considerations and the desired level of accuracy and confidence. Other frequencies could be chosen based on different criteria or assumptions.

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Answer:

(5,-1), (5,-4), (-2,-3) and (0,-1)

Step-by-step explanation:

You use the formula for 180 rotation about the origin (x,y)➡️(-x,-y)

(-5,1)➡️(5,-1)

(-5,4)➡️(5,-4)

(2,3)➡️(-2,-3)

(0,1)➡️(0,-1)

Answer:

x=2.488966,−2.488966

Step-by-step explanation:

The system capacity is 2 units per minute, the bottleneck stage is Stage A, and the utilization of Stage 3 is 100%.

A line process has three processing stages with the characteristics given below:

Stage A B C Unit processing time(minutes) 1 2 3 Number of machines 1 1 2 Machine availability 90% 100% 100% Process yield at stage 100% 100% 100%

To determine the system capacity and the bottleneck stage and utilization of Stage 3:

The system capacity is calculated by the product of the processing capacity of each stage:

1 x 1 x 2 = 2 units per minute

The bottleneck stage is the stage with the lowest capacity and it is Stage A. Therefore, Stage A has the lowest capacity and determines the system capacity.The utilization of Stage 3 can be calculated as the processing time per unit divided by the available time per unit:

Process time per unit = 1 + 2 + 3 = 6 minutes per unit

Available time per unit = 90% x 100% x 100% = 0.9 x 1 x 1 = 0.9 minutes per unit

The utilization of Stage 3 is, therefore, (6/0.9) x 100% = 666.67%.

However, utilization cannot be greater than 100%, so the actual utilization of Stage 3 is 100%.

Hence, the system capacity is 2 units per minute, the bottleneck stage is Stage A, and the utilization of Stage 3 is 100%.

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$3420 will be charged to Mrs. Casen for the carpet and installation.

Due to that,

Mrs. Casen plans to install three to five rolls of carpet in her new home. Each half carpet roll costs $450 when the cost of installation is added.

Supposedly, the price will be

$500 - one-half carpet roll

? - 3 4/5 carpet rolls

Changing 3 4/5 into the proper fraction

3 4/5 -----> 19/5,

Now that I think about it,

$500 - one-half carpet roll

? - 19.5" carpet roll

Through cross-multiplication

19/5 * 450 = 1/2 * ?

1710=1/2* ?

3420 = ?

As a result, Mrs. Casen will have to pay $3420 to put carpet in her new home.

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Answer:

(1,4.5)

Step-by-step explanation:

the midpoint of -2 and 4 is 1

the midpoint of 0 and 9 is 4.5

Answer:

(1, 4.5)

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Okay so the shape has an area of 60 square inches. The formula for the area of a triangle is A = b*h where A = area, b = base, and h = height

So we are given the value for A (60)

We are given the value for height (10)

So we just need to find the value of the base

So let's set this up as an equation. Input the given values into the area for triangle formula

A = B*h

60 = B * 10

So we need to solve for B. To do that we need to get B alone on one side of the = sign. B is being multiplied by 10 so do the opposite and divide both sides by 10

60 divided by 10 = 6

10 divided by 10 = 1 (don't actually put a 1 down, just drop it)

So we are left with

6 = B

So the base is 6 square inches. To test, put it in the equation:

A = B*h

60 = 6*10

60 = 60

Answer:

2

Step-by-step explanation:

Answer:

0.51 or 51%.

Step-by-step explanation:

If there were 100 students in the school, then  38 have a dog 24 a cat and 11 have both.

So there are 38 - 11 = 27 who only have a dog and 24-11 = 13 who only have a cat.

So total number having a pet = 27+11+13

= 51 students.

So Prob(You will choose a student with a pet) = 51%.

Drawing a Venn diagram would help to answer this and make it  clearer.

Answer: answer above me is correct

The Correct  option A: summarizing data.



- Summarizing data involves finding ways to represent the data in a concise and meaningful manner.
- Computing the average number of dollars college students have on their credit card balances is an example of summarizing data because it provides a single value that summarizes the data for this group.
- Generalizing data involves making conclusions or predictions about a larger population based on data collected from a smaller sample. Computing the average credit card balance for college students does not necessarily generalize to other populations, so it is not an example of generalizing data.
- Comparing data involves looking at differences or similarities between two or more sets of data. Computing the average credit card balance for college students does not involve comparing different sets of data, so it is not an example of comparing data.
- Relating data involves examining the relationship between two or more variables. Computing the average credit card balance for college students does not examine the relationship between credit card balances and other variables, so it is not an example of relating data.

Therefore, The correct option is A , computing the average number of dollars college students have on their credit card balances exemplifies summarizing data.

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Answer:

y = 2x + 5

Step-by-step explanation:

First, find the slope using rise over run, (y2 - y1) / (x2 - x1)

With this information, we can create 2 points: (2, 9) and (5, 15)

Plug in the points:

(15 - 9) / (5 - 2)

6 / 3

= 2

Plug in the slope and a point into y = mx + b, and solve for b:

y = mx + b

15 = 2(5) + b

15 = 10 + b

5 = b

Plug in the slope and b into the equation:

y = 2x + 5 is the equation of the line

where is the line or the picture

The given system of equations to have a Unique solution, the value of k must be any real number except 1 (k ≠ 1).

The value of k for which the given system of equations has a unique solution, we can use the concept of determinants. The system of equations is as follows:

kx + 2y = 3   -- (1)

3x + 6y = 10  -- (2)

To have a unique solution, the determinant of the coefficients of x and y must not be zero.

The determinant of the coefficient matrix for the system is:

D = | k   2 |

       | 3   6 |

By calculating the determinant, we have:

D = (k * 6) - (2 * 3)

D = 6k - 6

For the system to have a unique solution, the determinant D must not equal zero.

6k - 6 ≠ 0

Simplifying the inequality:

6k ≠ 6

Dividing both sides by 6:

k ≠ 1

Therefore, for the given system of equations to have a unique solution, the value of k must be any real number except 1 (k ≠ 1).

In other words, if k is not equal to 1, the system of equations will have a unique solution. If k is equal to 1, the system will either have infinitely many solutions or no solution.

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