Does 7 feet by 10 feet by 8 feet make a right triangle?

Therefore, it will take approximately 1415.7 weeks for all of the chemical to evaporate.

To calculate the volume of a cone, we can use the formula:

\(Volume = (1/3) * π * r^2 * h\)

Given that the height (h) of the cone is 240 inches and the radius (r) is 150 inches, we can substitute these values into the formula:

\(Volume = (1/3) * 3.14 * 150^2 * 240\)

Simplifying the equation:

Volume = 3.14 * 22500 * 240

Volume ≈ 16988400 cubic inches

Now, we know that the liquid chemical evaporates at a rate of 12,000 cubic inches per week. To find out how many weeks it will take for all the chemical to evaporate, we can divide the total volume of the chemical by the evaporation rate:

Number of weeks = Volume / Evaporation rate

Number of weeks = 16988400 / 12000

Number of weeks ≈ 1415.7 weeks

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5/98 is the probability he will choose one green marble and then one red marble.

Definition of probability

Three Types of Probability-

P(green) = ⇒ 5/14

P(red) = ⇒ 2/14

P(green and red) = ⇒ 5/98

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The statement "Which statement about the average rate of change from 3 seconds to 7 seconds is correct?" requires us to determine the correct average rate of change over the given interval for both the baseball and golf ball.

To find the average rate of change, we need to calculate the slope of the line connecting the two points on the position-time graph for each ball. We can use the formula:

average rate of change = change in position / change in time

For the baseball, the change in position is 14 meters (36m - 22m) and the change in time is 4 seconds (7s - 3s). Therefore, the average rate of change is:

average rate of change for baseball = 14m / 4s = 3.5 m/s

For the golf ball, the change in position is 18 meters (28m - 10m) and the change in time is 4 seconds (7s - 3s). Therefore, the average rate of change is:

average rate of change for golf ball = 18m / 4s = 4.5 m/s

Thus, the correct statement is "The golf ball has a greater average rate of change over the interval, 4.5 meters per second."

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Answer:

You need to solve X first, then answer __x - 10 so example x=7 so 74 - 10 is 64. SO that would be 64 degrees.

None of the wind gusts (17, 22, 8, 13, 19, 36, and 14) fall below -0.5 or above 35.5, there are no outliers in this data set. Therefore, the correct answer is D) none.

To identify any outliers in the data set, we can use a common method called the 1.5 interquartile range (IQR) rule.

The IQR is a measure of statistical dispersion and represents the range between the first quartile (Q1) and the third quartile (Q3) of a dataset. According to the 1.5 IQR rule, any value below Q1 - 1.5 × IQR or above Q3 + 1.5 × IQR can be considered an outlier.

To determine if there are any outliers in the given data set of wind gusts (17, 22, 8, 13, 19, 36, and 14), let's follow these steps:

Sort the data set in ascending order: 8, 13, 14, 17, 19, 22, 36.

Calculate the first quartile (Q1) and the third quartile (Q3).

Q1: The median of the lower half of the data set (8, 13, 14) is 13.

Q3: The median of the upper half of the data set (19, 22, 36) is 22.

Calculate the interquartile range (IQR).

IQR = Q3 - Q1 = 22 - 13 = 9.

Step 4: Identify any outliers using the 1.5 IQR rule.

Values below Q1 - 1.5 × IQR = 13 - 1.5 × 9 = 13 - 13.5 = -0.5.

Values above Q3 + 1.5 × IQR = 22 + 1.5 × 9 = 22 + 13.5 = 35.5.

Since none of the wind gusts (17, 22, 8, 13, 19, 36, and 14) fall below -0.5 or above 35.5, there are no outliers in this data set.

Therefore, the correct answer is D) none.

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Answer:

y=3/10;X=-7/10

Step-by-step explanation:

put y=x+1 into where you find y.

solve for X which is -7/10

and put -7/10 into the second equation and solve for y. which is also =3/10

R script that performs the tasks you mentioned:

```R

# Task (a)

x <- 3

y <- 4

# Task (b)

ln_result <- log(x + y)

# Task (c)

log_result <- log10(x * y²)

# Task (d)

sqrt_result <- 2 * sqrt(3) * x + sqrt(4) * y

# Task (e)

exp_result <-\(10^{x - y\) + exp(x * y)

# Printing the results

cat("ln(x + y) =", ln_result, "\n")

cat("log10(\(xy^2\)) =", log_result, "\n")

cat("2√3x + √4y =", sqrt_result, "\n")

cat("\(10^{x - y\) + exp(xy) =", exp_result, "\n")

```

When you run this script, it will assign the values 3 to `x` and 4 to `y`. Then it will calculate the results for each task and print them to the console.

Note that I've used the `log()` function for natural logarithm, `log10()` for base 10 logarithm, and `sqrt()` for square root. The caret `^` operator is used for exponentiation.

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To perform a rotation of axes to eliminate the xy-term, use x² and y² for the rotated coordinates.

Given equation:

6x² - 4√3xy + 2y² + 4x + 4√3y = 0

Before we eliminate the xy-term, let's determine the angle of rotation using the following formula:

tan2θ = 2B / (A - C)

Where A = 6, B = -4√3 / 2 = -2√3 and C = 2tan2θ = 2(-2√3) / (6 - 2)

tan2θ = -2√3 / 2tan2θ = -√3θ = -30° (negative angle means clockwise rotation)

Thus, the equation is to be transformed with a rotation of 30°, which is equivalent to introducing a new coordinate system with axes given by:

x = x'cosθ - y'sinθy = x'sinθ + y'cosθ

Substitute the given equation to the new coordinate system:

x = x'cos(-30°) - y'sin(-30°)y

= x'sin(-30°) + y'cos(-30°)x

= x'cos30° + y'sin30°y

= -x'sin30° + y'cos30°x

= (x'√3 + y') / 2y = (-x' + y'√3) / 2

Rewrite the given equation in terms of x' and y':

6[(x'√3 + y') / 2]² - 4√3[(x'√3 + y') / 2](-x' + y'√3) / 2 + 2[(-x' + y'√3) / 2]² + 4[(x'√3 + y') / 2] + 4√3[(-x' + y'√3) / 2] = 0

Simplify the equation:

3x'² + 5y'² - 4√3x' - 4y' = 0

This equation has eliminated the xy-term using a rotation of 30°. The rotation of axes is a technique used in geometry to change a coordinate system's orientation. This process allows us to eliminate the xy-term in a given equation.

To determine the angle of rotation, we use the formula tan2θ = 2B / (A - C), where A, B, and C are the coefficients of x², xy, and y², respectively. Once we know the angle of rotation, we can substitute the given equation into the new coordinate system, where the axes are given by x = x'cosθ - y'sinθ and y = x'sinθ + y'cosθ.

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Shortest distance from the point (2, 0, -3) to the plane x + y + z = 1 is √3 units.

To find the shortest distance between a point and a plane, we can use the formula:

distance = |ax + by + cz + d| / √(a² + b² + c²)

where a, b, and c are the coefficients of the plane's equation, d is the constant term, and (x, y, z) is the coordinates of the point.

In this case, the plane is x + y + z = 1, so a = 1, b = 1, c = 1, and d = -1. The point is (2, 0, -3), so x = 2, y = 0, and z = -3. Plugging in these values, we get:

distance = |1(2) + 1(0) + 1(-3) - 1| / √(1² + 1² + 1²)

= 3 / √3

= √3

Therefore, the shortest distance from the point (2, 0, -3) to the plane x + y + z = 1 is √3 units.

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If X has the hypergeometric distribution, the minimum value that X can take is option (e) 0

The hypergeometric distribution models the probability of getting a certain number of successes in a fixed-size sample drawn without replacement from a finite population containing a known number of successes and failures.

The minimum value that X can take depends on the specific parameters of the distribution.

If the population size is N, the number of successes in the population is K, and the sample size is n, then the minimum value that X can take is max(0, n - (N - K)).

This is because the sample can contain at most n items, and if all of them are failures (i.e., none of them are successes), then X would be 0. On the other hand, if there are fewer than n failures in the population, then the sample can contain at most n - (N - K) successes. If n - (N - K) is negative, then there are more successes than failures in the population, and X can take any value between 0 and n, inclusive.

Therefore, the correct option is (e) 0

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We can conclude that the function f(x) = ln(1 + x) on the interval (-1, +[infinity]0) has no absolute maximum or minimum.

In order to prove that the function f(x) = ln(1+x) on the interval (-1, +[infinity]0) has no absolute maximum or absolute minimum, we must examine the behavior of this function on the boundary points and its behavior at the endpoints of the interval.

To analyze the behavior of this function at the boundary points of the interval, we must analyze the limits of this function. Since ln(1+x) is a continuous function, its limit as x approaches -1 from the right side is equal to its value at x = -1, which is ln(0) = -∞. Similarly, the limit of this function as x approaches +[infinity]0 is equal to +∞. Thus, since both limits exist and are unbounded, the function does not have an absolute maximum or minimum at the boundary points of the interval.

Next, we must analyze the endpoint behavior of the function. For the endpoint at x = -1, the function is ln(0) = -∞, so it clearly has no absolute maximum or minimum here. For the endpoint +[infinity]0, the function is +∞ and therefore has no absolute maximum or minimum here either. Therefore, the function has no absolute maximum or minimum at either endpoint of the interval.

Therefore, we can conclude that the function f(x) = ln(1 + x) on the interval (-1, +[infinity]0) has no absolute maximum or minimum.

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Answer: 60

Step-by-step explanation:

From the question, we are informed that pencils come in packages of 10 while erasers come in package of 12 .

We are further told that Phillip wants to purchase the smallest number of pencils and erasers so that he will have exactly 1 eraser per pencil, this simply means that we have to calculate the lowest common multiple for 10 and 12.

Multiples of 10 = 10, 20, 30, 40, 50, 60,

Multiples of 12 = 12, 24, 36, 48, 60, 72

Therefore, the packages of pencils and erasers that Phillip should buy will be 60

The required average speed of the given train is 42 km/hour.

Speed is what it means. the speed at which an object's location changes in any direction.

The distance traveled in relation to the time it took to travel that distance is how speed is defined.

As speed simply has a direction and no magnitude, it is a scalar quantity.

So, we have:

63/x + 72/6+x = 3

63(x+6)+72x/x(x+6) = 3

63x + 378 + 72x/x²+6x = 3

378 + 135x = 3x² = 18x

3x² - 117x - 378 = 0

x² - 39x - 126 = 0

x² - 42x + 3x - 126 = 0

x(x-42)+3(x-42) = 0

(x+3)(x-42) = 0

x = 42, -3

As speed cannot be zero, the first average speed is 42 km per hour.

Therefore, the required average speed of the given train is 42 km/hour.

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Correct question:

A train travels at a certain average speed for a distance 63 km and then travels a distance of 72 km at an average speed of 6 km/hr more than the original speed. If it takes 3 hours to complete total journey, what is its original average speed?

Answer:

10+(-8)

Step-by-step explanation:

Answer:

The original width was 94.71 cm

Step-by-step explanation:

Given:

new smaller area = 1.2m^2

Decrease in length of the rectangular sheet = 34.5cm

Therefore:

1. the final width of the sheet is given as

2X^2 = 1.2 m^2

X^2 - 0.6 m^2

X^2 = 10000 * 0.6 cm

X = 77.46 cm (this is the width)

2. The length of the sheet

= 2 * 77.46

= 154.92 cm.

3. Initial length of the sheet

= 154.92 + 34.5

= 189.42 cm.

4. Initial width of the sheet ( original ).

= 189.42 / 2

= 94.71 cm.

5. Initial area of the sheet

= 94.71 * 189.92

= 17939.9 cm^2

New area of the sheet

= 79.46 * 154.92

= 12000.1 cm^2

Difference between the initial and new area

= 17939.9 - 12000.1

= 5939.86 cm^2

Percentage of area decrease

= 5939.86 ' 17939.9

= 33.1%

The statement that is true on the soccer game, given the shots made and taken is D. He made a third of the shots he took.

The proportion of the shots made by Warren is :

= Number of shots made / Total number of shots taken

= 3 / 9

= ( 3 / 3 ) / ( 9 / 3 )

= 1 / 3

This shows that out of every shot taken, Warren has a 1 / 3 probability of being able to make it based on the three shots he made and the nine shots he took.

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Options for this question include:

Answer:

x 2 − y = 2 ,  2 x − y = − 1

x + y = 3  ,  2 x − 8 y = 19

x + 2 y = 4  ,  x − y = − 3

Step-by-step explanation:

HOPE IT HELPS

Given data;

The given length of one leg is a=6 cm.

The given hypotenuse is c=10 cm.

The expression for the pythagoras theorem is,

Substitute the given values in the above expr

There are 77,910 ways to distribute the seven distinct apples and six distinct pears to three distinct people such that each person has at least one pear.

We can use the principle of inclusion-exclusion to solve this problem. Let A be the set of all possible ways to distribute the apples and pears without any restrictions, and let B, C, and D be the sets of ways to distribute the apples and pears such that person 1, person 2, and person 3, respectively, does not receive a pear.

We can compute |A|, the total number of ways to distribute the apples and pears, as follows:

|A| = (7 + 6) choose 3 = 78 choose 3 = 82,251

To compute |B|, we can first choose 6 pears to give to persons 2 and 3 (since person 1 cannot receive a pear). This can be done in (6 choose 2) = 15 ways. Then, we can distribute the remaining 7 apples and 1 pear to the three people in any way, which can be done in (8 choose 1) * (6 choose 2) = 84 ways. Therefore, |B| = 15 * 84 = 1,260.

Similarly, |C| = |B| and |D| = |B|, since the problem is symmetric with respect to the three people.

To compute |B intersection C|, we can choose 6 pears to give to person 3 (since persons 1 and 2 cannot receive a pear). This can be done in (6 choose 1) = 6 ways. Then, we can distribute the remaining 7 apples and 2 pears to persons 1 and 2 in any way, which can be done in (9 choose 2) = 36 ways. Therefore, |B intersection C| = 6 * 36 = 216.

Similarly, |B intersection D| = |C intersection D| = |B intersection C|, since the problem is symmetric with respect to the three people.

To compute |B intersection C intersection D|, we can simply distribute the 7 apples and 3 pears among the three people in any way, which can be done in (13 choose 3) = 286 ways.

Therefore, by the principle of inclusion-exclusion, the number of ways to distribute the apples and pears such that each person has at least one pear is:

|A intersection complement(B union C union D)| = |A| - |B union C union D| = |A| - (|B| + |C| + |D| - |B intersection C| - |B intersection D| - |C intersection D| + |B intersection C intersection D|) = 82,251 - (3 * 1,260 - 3 * 216 + 286) = 77,910.

Therefore, there are 77,910 ways to distribute the seven distinct apples and six distinct pears to three distinct people such that each person has at least one pear.

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The information that is not needed to determine the total bill after tax is is the tax was 7%.

The total bill is $11.

The total bill paid is the sum of the cost of the meal, tax and the tip paid. The tip and tax would increase in the total amount that is paid by the customers.

Tax is a compulsory amount that is levied by the government on certain goods and services.

Percentage is the fraction of an amount expressed as a number out of hundred. To convert a number from percentage to a number, divide the percentage by 100.

Tax paid = 10% x total bill

$1.10 = 0.1 x b

1.10 = 0.1b

b = 1.10 / 0.1

b = $11

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a. The information that is needed to solve the problem is D. All of this information is needed to solve the problem.

b. The total bill is $117.

It should be noted that an expression shows the relationship between the numbers or the variables

The total bill will be:

Tip = $1.10

Tax = 7%

Tip = 10% of cost:

$10 = 10% × c

0.1c = $10

c = $10/0.1 = $100

Cost = $100

The total bill. = Cost + Tip + Tax

= $100 + $10 + (7% × $100)

= $100 + $10 + $7

= $117

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Answer:

(0,4)

Step-by-step explanation:

read the graph from left to right. As you move right from -4,-16, y increases as x increases. then once you hit zero there is no increase or decrease. Then from zero to 4 the y value is decreasing as x increases.

Answer:

$0.3

Step-by-step explanation:

8.90x2=17.8

1.75x2=3.5

17.8+3.5=21.3

21.90-21.3=0.6

0.6/2=0.3

The sample standard deviation is approximately 5.61 and sample variance is approximately 31.46.

To compute the range of a sample,

we subtract the minimum value from the maximum value.

Range = Maximum value - Minimum value

For the given sample,

the minimum value is 15 and the maximum value is 34.

Range = 34 - 15 = 19

The range of the sample is 19.

To compute the interquartile range (IQR) of a sample, we need to find the difference between the third quartile (Q3) and the first quartile (Q1).

IQR = Q3 - Q1

To calculate the quartiles,

we first need to arrange the data in ascending order:

15, 20, 20, 24, 25, 27, 30, 34

The sample size is 8,

so the median (Q2) will be the average of the fourth and fifth values:

Q2 = (24 + 25) / 2 = 24.5

To find Q1, we take the median of the lower half of the data:

Q1 = (20 + 20) / 2 = 20

To find Q3, we take the median of the upper half of the data:

Q3 = (27 + 30) / 2 = 28.5

Now we can calculate the interquartile range:

IQR = 28.5 - 20 = 8.5

The interquartile range of the sample is 8.5.

To compute the sample variance, we use the formula:

Variance = Σ\([(x - X)^2]\) / (n - 1)

where Σ represents the sum of, x is each data value, X is the mean, and n is the sample size.

First, let's calculate the mean (X):

X = (24 + 20 + 25 + 15 + 30 + 34 + 27 + 20) / 8 = 24.625

Now we can calculate the sample variance:

Variance = \([(24 - 24.625)^2 + (20 - 24.625)^2 + (25 - 24.625)^2 + (15 - 24.625)^2 + (30 - 24.625)^2 + (34 - 24.625)^2 + (27 - 24.625)^2 + (20 - 24.625)^2]\) / (8 - 1)

Variance = 31.46

To compute the sample standard deviation,

we take the square root of the sample variance:

Standard deviation = √(Variance) = \(\sqrt{(31.46}\)) ≈ 5.61

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Compared with the graph of the parent function, an equation which shows only a vertical compression by a scale factor of 1/3 and a shift downward of 4 units is: A. y = 1/3∛x - 4.

In Geometry, a scale factor can be defined as the ratio of two corresponding side lengths or diameter in two similar geometric objects (shapes) such as equilateral triangles, square, quadrilaterals, polygons, etc., which can be used to either vertically or horizontally enlarge or reduce (compress) a function representing their size.

Generally speaking, the transformation rule for the dilation of a geometric object (square) based on a specific scale factor is given by this mathematical expression:

(x, y)      →    (SFx, SFy)  = (1/3x, 1/3y)

Where:

In this scenario, the only equation that is vertically compressed by a scale factor of 1/3 and translated (shifted) downward by 4 units is given by:

y = 1/3∛x - 4.

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Answer:

The first part is A

and second part is D

Step-by-step explanation:

100% on edge 2023

Answer:

Step-by-step explanation: 3x-5+13+6= 3x+1+13= 3x+14(simplified) If you graph this the y intercept is 14  the growth is 3. I don't think it can be solved. 3x is not compatible when solving for are of a triangle unless you are trying to solve for x and you already have the area. Yes this is insolvable

please give brainliest

Answer:

To shift the graph of the function f(x) = cos(x) downward by 2.5 units, you can subtract 2.5 from the function. The equation of the middle for the shifted function would be:

f(x) = cos(x) - 2.5

Answer:

y=-2.5

Step-by-step explanation:

f(x) =0 -2.5

y=-2.5

Hope this helped buddy

peace ️



SteSteAnswerAnswer:

x = 3/4 and -2

Step-by-step explanation:

If x²+ 5/4x = 3/2, x²+ 5/4x - 3/2 = 0

Multiply by 4 to get 4x²+ 5x - 6 = 0

Factor it to get (4x - 3)(x + 2) = 0

anything times 0 = 0, so x = 3/4 and -2

Answer:

V≈134.0

Step-by-step explanation:

divide 8 by 2 to get the radius .

V=πr2h /3

V=πr2 h /3=π·42·8 /3≈ 134.0

Answer:

12.656

Step-by-step explanation:

1) BODMAS = 23.98-(1.49*7.6)

2) 1.49*7.6 = 11.324

3) 23.98-11.324 = 12.656

Hope this helps, have a great day! :)

Answer:

12.656

Step-by-step explanation:

You have to subtract the first two numbers(23.98-1.49).The answer you will get you will then multiply it buy the last number(7.6)

The number of pheasants in 2012 was 1832. The number of pheasants in 2016 was 422. The minimum viable density is 100 pheasants per hectare.

So, we need to find out the year in which the population will fall below 100 pheasants per hectare.

First, we need to find out the rate of decline per year which can be calculated as follows: Rate of decline per year = (1832 - 422) / (2016 - 2012)= 1410 / 4= 352.5 per yearNow, let the number of pheasants per hectare be y after t years from 2012.

Then, y = 1832 - 352.5t (as we know the rate of decline per year)We need to find the year in which the population will fall below 100 pheasants per hectare. So, we need to solve the equation:1832 - 352.5t = 100⇒ 352.5t = 1732⇒ t = 1732 / 352.5⇒ t = 4.91 Therefore, the population will fall below the minimum viable density of 100 pheasants per hectare after 4.91 years from 2012, which is around 2017 or 2018.

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