a 2-person relay is 1-16 mile long. if each person runs the same length, how far will each person run

Therefore , the solution of the given problem of expressions comes out to  5.6, -5, -5.8 .

Instead of producing estimates at random, it is better to utilize movable numerals variables, which can be rising, falling, or blocking. They could only help one another by sharing materials, information, or solutions to issues. A declaration of truth may contain arguments, elements, and annotations to mathematical operations like additional disapproval, manufacturing, and mixture.

Here,

Sort these figures from greatest to least in sequence.

=> -5.8, -5, 5.6

So,

=>5.6, -5, -5.8

Therefore , the solution of the given problem of expressions comes out to
5.6, -5, -5.8 .

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Therefore, the global maximum value of the function on the region B is 12, and the global minimum value is 4.

To find the global maximum and minimum values of the function f(x, y) = x² + y² + x²y + 4y² + x²y + 4 on the region B = {(x, y) ∈ R² | −1 ≤ x ≤ 1, -1 ≤ y ≤ 1}, we need to evaluate the function at its critical points within the given region and compare the function values.

1. Critical Points:

To find the critical points, we need to find the points where the gradient of the function is zero or undefined.

The gradient of f(x, y) is given by:

∇f(x, y) = (df/dx, df/dy) = (2x + 2xy + 2x, 2y + x² + 8y + x²).

Setting the partial derivatives equal to zero, we get:

2x + 2xy + 2x = 0          (Equation 1)

2y + x² + 8y + x² = 0      (Equation 2)

Simplifying Equation 1, we have:

2x(1 + y + 1) = 0

x(1 + y + 1) = 0

x(2 + y) = 0

So, either x = 0 or y = -2.

If x = 0, substituting this into Equation 2, we get:

2y + 0 + 8y + 0 = 0

10y = 0

y = 0

Thus, we have one critical point: (0, 0).

2. Evaluate Function at Critical Points and Boundary:

Next, we evaluate the function f(x, y) at the critical point and the boundary points of the region B.

(i) Critical point:

f(0, 0) = (0)² + (0)² + (0)²(0) + 4(0)² + (0)²(0) + 4

       = 0 + 0 + 0 + 0 + 0 + 4

       = 4

(ii) Boundary points:

- At (1, 1):

f(1, 1) = (1)² + (1)² + (1)²(1) + 4(1)² + (1)²(1) + 4

       = 1 + 1 + 1 + 4 + 1 + 4

       = 12

- At (1, -1):

f(1, -1) = (1)² + (-1)² + (1)²(-1) + 4(-1)² + (1)²(-1) + 4

         = 1 + 1 - 1 + 4 + (-1) + 4

         = 8

- At (-1, 1):

f(-1, 1) = (-1)² + (1)² + (-1)²(1) + 4(1)² + (-1)²(1) + 4

         = 1 + 1 - 1 + 4 + (-1) + 4

         = 8

- At (-1, -1):

f(-1, -1) = (-1)² + (-1)² + (-1)²(-1) + 4(-1)² + (-1)²(-1) + 4

          = 1 + 1 + 1 + 4 + 1 + 4

          = 12

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Answer:

I'm pretty sure it is A

Step-by-step explanation:

Answer:

please see the attached I put the answer

Step-by-step explanation:

you answer were correct but you change the sign one of them will be positive.

Answer:

70

Step-by-step explanation:

Hello there! Let's work this through:

Firstly, we might want to simply 2 1/2 into 5/2, for simplification.

So, we now have 4 * 7 * 5/2

Simplifying we have \(\frac{4*7*5}{2}\)

We see that we can easily simplify 4/2 into 2 * 7 * 5

Further simplifying we get 10*7

Last bit and we get our answer of 70

From here we get 2

Answer:

I think its A

Step-by-step explanation:

The probability that tails appears on the next toss is 0.5

Given,

In the question:

If I toss a fair coin five times and the outcomes are TTTTT,

To find the probability that tails appears on the next toss is.

Now, According to the question:

The possible ordered outcomes are listed as elements in a sample space, which is commonly indicated using set notation.

A sequence of five fair coin flips has a sample space that contains all potential outcomes. \(2^3\) {H, T}  is the sample of a fair coin toss. {HHHHH, HHHHT, HHHTH, HHTHH, HTHHH,...…TTTTT} .

The probability of a tails result on the next flip is always equal to 0.5 It makes no difference if previous outcomes were {TTTTT} , {HHHHH}  or {THTHT} In each of these and all other circumstances, the probability of the next being tails is still 0.5

Hence,  the probability that tails appears on the next toss is 0.5

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Answer:

The minimum number of different rooms for accommodating 390 classes if there are 10 different time periods is 39

Step-by-step explanation:

Number of time periods = 10

Number of Classes = 390

Now, if we have a single room, then we can accommodate 10 classes

if we have 2 rooms, we can accommodate (10)(2) = 20 classes

and so on

so we have the relation,

(number of rooms)(number of time periods) = (number of classes that can be accommodated)

We need to find the number of rooms for 390 classes, given that number of time periods is 10, so we get,

(number of rooms)(10) = 390

number of rooms = 390/10

number of rooms =39

The length of the deep end is 12 feet of the swimming pool.

Given: Area of the swimming pool is 210 square feet

Width of the pool = 10 feet

The length of the shallow end is 9 feet and the length of the deep end is d.

To find the value of d.

Let's solve the problem.    

The area of the swimming pool is 210

The width is 10

The deep end length is d

The shallow end length is 9

The total length of the swimming pool = The length of the deep end + The length of the shallow end

=> d + 9

Therefore, the total length of the swimming pool is d + 9

The surface of the swimming pool is rectangular, so

The area of rectangle = width × length

Therefore,

area of swimming pool = width of the pool × length of the swimming pool

=> 210 = 10 × (9 + d)

or 10 × (9 + d) = 210

Dividing both sides by 10:

10 × (9 + d) / 10 = 210 / 10

9 + d = 21

Subtracting 9 on both sides:

9 + d - 9 = 21 - 9

d = 12

Therefore the length of the deep end is 12 feet

Hence the length of the deep end is 12 feet of the swimming pool.

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The length of the deep end of the swimming pool is 12 feet.

We are given that:

The Area of the swimming pool = 210 square feet

width of the swimming pool = 10 feet

Length of shallow end = 9 feet

Let the length of the deep end be d.

Total length of the swimming pool = length of deep end + length of shallow end =  d + 9

Area of swimming pool = width × length

Substituting the values, we get that:

210 = 10 × (9 + d)

9 + d = 21

d = 12

Therefore the length of the deep end of the swimming pool is 12 feet.

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Answer:

N+1

Step-by-step explanation:

It begins with = 2

then n+1=3

then n+2=4 and so on it is n+1

Answer:

24

Step-by-step explanation:

Answer

24!

Step-by-step explanation:

Person above me is correct :)

Answer and explanation:

Take the area formula:

A = L * W

Then manipulate it to fit the context of which unknown you are finding:

Problem 1

\(\dfrac{36 = 4 * W}{4}\)

\(9 = W\)

So, the length of side c is 9 mm.

Problem 2

\(\dfrac{21 = W * 21}{21}\)

\(1 = W\)

So, the length of side a is 1 m.

Problem 3

\(\dfrac{49 = 7 * W}{7}\)

\(7=W\)

So, the length of side t is 7 cm.

EXPLANATION

We are told that the payoff for the raffle is one million dollars and we know that each ticket has the following chances of being a winner:

1:125,000

The probability is given by the following relationship:

We need to use the expected means formula and substitute the x variable for the given payoff for the lottery ticket.

Replacing terms:

Simplifying:

The expected payoff is 8 dollars. If

The 95% confidence interval for the true population mean, based on a sample with a sample size (n) of 225, a sample mean (X) of 8.5, and a sample standard deviation (σ) of 45, is (2.62, 14.38).

To calculate the confidence interval, we can use the formula:

Confidence interval = X ± Z * (σ/√n)

where X is the sample mean, Z is the critical value for the desired level of confidence (in this case, 95%), σ is the sample standard deviation, and n is the sample size.

The critical value Z can be obtained from a standard normal distribution table or calculated using statistical software. For a 95% confidence level, the Z-value is approximately 1.96.

Plugging in the values into the formula, we get:

Confidence interval = 8.5 ± 1.96 * (45/√225)

                  = 8.5 ± 1.96 * (45/15)

                  = 8.5 ± 1.96 * 3

Calculating the upper and lower bounds of the confidence interval:

Upper bound = 8.5 + 1.96 * 3

           = 8.5 + 5.88

           = 14.38

Lower bound = 8.5 - 1.96 * 3

           = 8.5 - 5.88

           = 2.62

Therefore, the 95% confidence interval for the true population mean is (2.62, 14.38).

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Answer:

D) she can divide 7 by 2

Step-by-step explanation:

As, Division is not same as multiplication, so not the a option

And b doesn't have the right values

C is also wrong bc it have multiplication

So D is right

Answer:

Therefore, the book value of the equipment at the end of year four (including year four) is $2,880.

Step-by-step explanation:

To calculate the book value of the equipment at the end of year four using the MACRS method with GDS recovery period of five years, we can use the following steps in Excel:

1. Open a new Excel spreadsheet and create the following headers in row 1: Year, Cost, Depreciation Rate, Annual Depreciation, Cumulative Depreciation, and Book Value.

2. Fill in the Year column with the years 1 through 6 (since the truck has a life of six years).

3. Enter the cost of the truck, $12,000, in cell B2.

4. Use the following formula in cell C2 to calculate the depreciation rate for each year:

=MACRS.VDB(B2, 5, 5, 1, C1)

This formula uses the MACRS.VDB function to calculate the depreciation rate for each year based on the cost of the truck (B2), the GDS recovery period of five years, the useful life of six years, the salvage value of $2,000, and the year (C1).

5. Copy the formula in cell C2 and paste it into cells C3 through C7 to calculate the depreciation rate for each year.

6. Use the following formula in cell D2 to calculate the annual depreciation for each year:

=B2*C2

This formula multiplies the cost of the truck (B2) by the depreciation rate for each year (C2) to get the annual depreciation.

7. Copy the formula in cell D2 and paste it into cells D3 through D7 to calculate the annual depreciation for each year.

8. Use the following formula in cell E2 to calculate the cumulative depreciation for each year:

=SUM(D$2:D2)

This formula adds up the annual depreciation for each year from D2 to the current row to get the cumulative depreciation.

9. Copy the formula in cell E2 and paste it into cells E3 through E7 to calculate the cumulative depreciation for each year.

10. Use the following formula in cell F2 to calculate the book value of the equipment for each year:

=B2-E2

This formula subtracts the cumulative depreciation for each year (E2) from the cost of the truck (B2) to get the book value.

11. Copy the formula in cell F2 and paste it into cells F3 through F7 to calculate the book value for each year.

12. The book value of the equipment at the end of year four (including year four) is the value in cell F5, which should be $2,880.

Answer:

960

Step-by-step explanation:

We can calculate the value of x using Euclidean theorem

x^2 = 576 × 1600

x = 960

Answer:

30

Step-by-step explanation:

65+75= 140

180-140 = 40

Transversal Angle so Angles are corresponding

40+110=150

180-150=30

Answer 30 degrees

Answer:

Step-by-step explanation:

In ΔABE

∠A + ∠B + ∠AEB = 180 {Angle sum property of triangle}

65 + 75 + ∠AEB = 180

          140 + ∠AEB = 180

                    ∠AEB = 180 - 140 = 40

∠CED = ∠AEB    {Vertically opposite angles}

∠CED = 40

ΔDCE,

∠D + ∠C + ∠CED = 180

x + 110 + 40 = 180

x = 180 - 150

x = 30°

The smallest number that has 1, 2, 3, 4, 5 as factors is 60. This number is called the LCM (Least Common Multiple) of the given numbers.

The smallest number that has 1, 2, 3, 4, 5 as factors is 60. This number is called the LCM (Least Common Multiple) of the given numbers.The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both of these numbers. We can find the LCM of more than two numbers by following the below procedure:Firstly, find the LCM of two numbers.

This will be the smallest number that is a multiple of both these numbers. Then, find the LCM of this number and the third number. This will be the smallest number that is a multiple of all the three numbers. Repeat the same process for other numbers until we have found the LCM of all the given numbers.

Here, the given numbers are 1, 2, 3, 4, and 5.LCM of 1 and 2 is 2.LCM of 2 and 3 is 6.LCM of 6 and 4 is 12.LCM of 12 and 5 is 60.

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After figuring out the given issue, we discovered that the original square's area and the dilated square's area differ by 32 square centimeters.

Square Area = Side x Side. Hence, Side2 square units are equivalent to the area of the square. and four side units make up a square's perimeter.

The formula for calculating the area of a initial square with sides that are 2 centimeters long is:

A = s²

A = 2²

A = 4 square centimeters

The revised side length of this square after dilation by a scale factor of 3 is:

s' = 3s

s' = 3(2)

s' = 6 centimeters

Calculations for the dilated square's area are as follows:

A' = s'²

A' = 6²

A' = 36 square centimeters

The area of a dilated square differs from the size of the original square by:

A' - A = 36 - 4

A' - A = 32 square centimeters

As a result, the original square's area and the dilated square's area differ by 32 square centimeters.

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Answer:

C

Hope This Helps Friend!

Answer:

1. How to Solve using Algebra

Make both equations into "y =" format.

Set them equal to each other.

Simplify into "= 0" format (like a standard Quadratic Equation)

Solve the Quadratic Equation!

Use the linear equation to calculate matching "y" values, so we get (x,y) points as answers.

Algebraic method is more easy to do

2. linear functions have constant first differences. quadratic functions have constant second differences. exponential functions have a constant ratio.

When a distribution is shown as a symmetrical bell-shaped curve then the mean, median, and mode are equal i.e., option (a) is correct.

A symmetrical bell-shaped curve, also known as a normal distribution or Gaussian distribution, is characterized by its symmetry around the mean.

In this type of distribution, the mean, median, and mode all coincide at the center of the curve.

This means that the central tendency measures, such as the mean (average), median (middle value), and mode (most frequent value), are all equal.

Option (a) states that the mean, median, and mode are equal, which aligns with the properties of a symmetrical bell-shaped curve. This equality occurs because the data is evenly distributed on both sides of the mean, resulting in a balanced distribution.

Options (b) and (d) suggest that the mean is either less than or greater than the median and mode, which does not hold true for a symmetrical distribution.

In a symmetrical distribution, the mean is located at the center of the data, and the median and mode share the same value as the mean.

Option (c) mentions moderate uniformity, but a symmetrical bell-shaped curve does not specifically indicate uniformity. Uniformity refers to a distribution where all data points have equal probability, resulting in a flat line.

In contrast, a symmetrical bell-shaped curve indicates a normal distribution with the majority of data concentrated around the mean, gradually decreasing towards the tails.

Therefore, based on the given options, option (a) is the correct conclusion when the distribution is shown as a symmetrical bell-shaped curve.

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Answer:

D)

Step-by-step explanation:

You have to show the picture of what your talking about. Please do so if you want someone to answer your question.

Given that y varies directly with x in the above table, if the value of x is 5, the value of y is 15.

According to this question, a 2-column table with 5 rows is given.

If y varies directly with x, the mathematical representation is as follows:

y = kx

Since y = 3, when x = 1

3 = k × 1

k = 3

The relationship between x and y is as follows: y = 3x

Therefore, if the value of x is 5, the value of y = 3 × 5 = 15.

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Answer:

yes, after 7 weeks they will have the same amount of money. 46 dollars.

Step-by-step explanation:

First start of by writing an expression to represent this problem

11 + 5x = 60 - 2x

combine like terms. and find value of x.

subtract 11 from the 60

5x = 49 - 2x

move the 2x over to the other side. So + 2x

7x = 49

divide 7 from 49

49/7

x = 7

x=7 amount of weeks they will have the same amount of money

Answer:

-44.35

Step-by-step explanation:

1/4 = 0.25 (as 0.25 * 4 = 1)

-25 1/4 = -25.25

-25.25 - 19.1 = -44.35

The value is -44.35.

The process of replacing a mathematical expression with one that is equivalent, simpler, and typically shorter. Examples of simplification include simplifying algebraic expressions in computer algebra, simplifying Boolean expressions in logic optimization, and simplifying fractions by using conjunction elimination in logic inference to produce a formula that is simpler but typically not equivalent to the original.

Given \(-25\frac{1}{4}\) - 19.1

\(-25\frac{1}{4}\) can be written as -(25 + 1/4)

1/4 multiply and divide by 25

we get 25/100

to convert fraction into decimal make the base multiple of 10 and put decimal ahead the no. of digits

20/100 = 0.25

equation is -25.25 - 19.1 = -44.35

Hence the value is -44.35.

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Jordan would take 22 hours to drive 1,188 miles at the same speed he drove 378 miles in 7 hours.

We can use the formula:

time = distance / speed

where speed is constant, to find the time it would take Jordan to drive 1,188 miles.

The speed at which Jordan drove can be calculated as:

speed = distance / time

where distance is 378 miles and time is 7 hours.

speed = 378 / 7 = 54 miles per hour

Now, we can use the speed to find the time it would take to drive 1,188 miles:

time = distance / speed = 1,188 / 54 = 22 hours

Therefore, if Jordan can maintain the same pace, it would take him 22 hours to drive 1,188 miles.

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we know that 76% of the specialty soaps are made with fresh herbs, and we also know that there are a total of 350 specialty soap bars, so how many are made with fresh herbs?  well, just 76% of those 350

\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{76\% of 350}}{\left( \cfrac{76}{100} \right)350}\implies 266\)