Prove that in , (0.5,1] is a relatively open set of [0,1], although it is not itself an open set.

Answer:

x = 4

Step-by-step explanation:

The 2 indicated angles are alternate and congruent, that is

26x - 4 = 24x + 4 ( subtract 24x from both sides )

2x - 4 = 4 ( add 4 to both sides )

2x = 8 ( divide both sides by 2 )

x = 4

The wheels of the tricycle are turning approximately 7.68 revolutions per second.

To convert the speed from feet per hour to revolutions per second, we need to know the circumference of the wheels. The circumference of a circle with radius 5 inches is 2 * pi * 5 = 10 * pi inches. To convert the speed from feet per hour to inches per second, we multiply by 12, since there are 12 inches in 1 foot. So, the speed in inches per second is 20 * 12 = 240 inches per second. The number of revolutions per second is then equal to the speed divided by the circumference:

240 inches per second / (10 * pi inches) = 240 / (10 * pi) revolutions per second

Rounding to the nearest hundredth:

240 / (10 * pi) ≈ 24 / (pi) ≈ 7.68 revolutions per second

So, the wheels are turning approximately 7.68 revolutions per second.

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Answer:

-5 x

Step-by-step explanation:

Simplify the following:

-6 x + x

Combine like terms in -6 x + x.

x - 6 x = -5 x:

Answer:  -5 x

Answer:

R = 18.5

Step-by-step explanation:

Answer: 18.5

Step-by-step explanation: Divide 74 by 4

Answer:

1. Equation: x/-9=-16

solution: x=144

2. Equation:15*x=-75

solution: x=-5

3.Equation:0.75n=36

solution: n=48

Step-by-step explanation:

As range doesn't reveal anything about the distributive property of the data, it is the least helpful measure of variability because it is the most generic.

1. Sort the data either ascendingly or descendingly.

2. Determine how many items are in the data set.

3. The median is the number in the middle of the list if the number of items is odd.

4. The median is the average of the two middle numbers in the list if the number of items is even.

To figure out the range:

1. Sort the data either ascendingly or descendingly.

2. To determine the range, deduct the smallest number from the largest.

As range does not reveal anything about the distribution of the data, it is the least useful measure of variability because it is the most generic. Range does not indicate where the values fall within the range; rather, it measures the difference between the highest and lowest values in a data collection.

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Solution:

We know that:

Since the sprinkler sprays water 4 feet in all directions, the radius will be 4 ft.

This means that:

Now, let's solve for the area.

Answer:1.345299 = -1/3

Step-by-step explanation:

Answer:

6/7

Step-by-step explanation:

The constant rate of change is also know as the slope of the expression

Given

24x-28y=14

Write in standard form y = mx+c

m is the slope

24x-28y=14

-28y = -24x + 14

y = -24x/-28 + 14/-28

y = 6/7 x - 1/2

Compare

mx = 6/7 x

m = 6/7

Hence the  constant rate of change is 6/7

The function f(x) = arcsin(\(x^2\)- 2x) is increasing for x > 1. To determine where the function f(x) = arcsin(\(x^2\) - 2x) is increasing, we need to find the intervals where its derivative, f'(x), is positive.

First, find the derivative of the inner function, g(x) = \(x^2\) - 2x:
g'(x) = 2x - 2
Now, find the derivative of the outer function, h(u) = arcsin(u), where u = g(x):
h'(u) = 1/√(1 - \(u^2\))
Using the chain rule, the derivative of f(x) is the product of the derivatives of the inner and outer functions:
f'(x) = h'(g(x)) * g'(x) = (1/√(1 - \((x^2 - 2x)^2)\)) * (2x - 2)
To find where f(x) is increasing, we need to determine where f'(x) > 0. Since the denominator of the fraction is always positive, we only need to focus on the numerator:
2x - 2 > 0
Solving for x, we get:
x > 1

The complete question is:-

Determine where f(x) = arcsin (\(x^{2}\) − 2x) is increasing.

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True, an iterative algorithm will usually run faster than an equivalent recursive algorithm. This is because iterative algorithms use loops to repeat a set of instructions, whereas recursive algorithms call themselves repeatedly until they reach a base case.

An iterative algorithm will usually run faster than an equivalent recursive algorithm. This is because recursive algorithms often involve function calls, which have overhead costs such as saving and restoring the call stack. In contrast, iterative algorithms use loops and do not require the same overhead, making them more efficient in terms of both time and memory usage.

However, it's important to note that some problems may be more elegantly or intuitively solved using recursion, even if it's less efficient. The repeated function calls in a recursive algorithm can lead to slower performance and higher memory usage compared to the more direct approach of an iterative algorithm.

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√(12) is a finite value less than 1, the limit is less than 1. Therefore, by the root test, the series ∑ (-3n/n+1) 4n converges.

In conclusion, the series is convergent.

To determine whether the series ∑ (-3n/n+1) 4n from n=1 to infinity converges or diverges, we can use the root test.

The root test states that for a series ∑ aₙ, if the limit of the absolute value of the nth root of the terms, lim(n→∞) √(|aₙ|), is less than 1, the series converges. If it is greater than 1, the series diverges. If it is exactly equal to 1, the test is inconclusive.

Let's apply the root test to the given series:

lim(n→∞) √(|(-3n/n+1) 4n|)

First, let's simplify the expression inside the root:

|(-3n/n+1) 4n| = |-3n/(n+1)| * |4n|

Since the absolute value of -3n/(n+1) is the same as 3n/(n+1), we can rewrite the expression as:

= (3n/(n+1)) * (4n)

Taking the nth root:

lim(n→∞) √((3n/(n+1)) * (4n))

Now, simplify further:

= lim(n→∞) (√(3n/(n+1))) * (√(4n))

= lim(n→∞) (√(3n) / √(n+1)) * (√(4n))

= lim(n→∞) √(12n² / (n+1))

= √(12)

Since √(12) is a finite value less than 1, the limit is less than 1. Therefore, by the root test, the series ∑ (-3n/n+1) 4n converges.

In conclusion, the series is convergent.

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Answer:

what is this man huh oooo

Given curves: x = 2y and x = y² - 4y

We can find the points of intersection of the curves as follows: 2y = y² - 4yy² - 6y = 0y(y - 6) = 0

Thus, the two points of intersection are y = 0 and y = 6 We can now set up the integral for finding the area:

\(Area = ∫(x₂ to x₁) [f₁(y) - f₂(y)]dy\) where, x₂ is the x-coordinate of the point of intersection of x = 2y and x = y² - 4y when y = 6 and x₁ is the x-coordinate of the point of intersection when y = 0

We can express x = 2y in terms of y as x = f₁(y) = 2y

Also, x = y² - 4y can be written as x = f₂(y) = y(y - 4)

When y = 0, x = f₂(0) = 0 and when y = 6, x = f₂(6) = 12

Thus, the area of the region enclosed by the given curves is:

Area = ∫(0 to 6) [f₁(y) - f₂(y)]dy= ∫(0 to 6) (2y - y² + 4y)dy= ∫(0 to 6) (6y - y²)dy= [3y² - (1/3)y³] from 0 to 6= 3(6)² - (1/3)(6)³= 108 square units

Therefore, the area of the region enclosed by the given curves is 108 square units.

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Answer:

4

Step-by-step explanation:

3 1/2= 3.5

5 rounds up, so it'll be 4

Answer:

4 hope this helps

Interquartile Range for the given graph is 24.

What is Interquartile Range?

A particularly helpful measurement is the IQR. Because it restricts the range to the middle 50% of the numbers, it is useful because it is less influenced by extreme values.

Main body:

How do you find the interquartile range and range on a box-and-whisker plot?

The distance between the third and first quartiles is known as the interquartile range or IQR.

In the box and whisker plot given,

Upper Quartile, Q₃ is 80

Lower Quartile, Q₁ is 66

Interquartile Range = Q₃ - Q₁

                                = 80-66

                                = 24

Hence , Interquartile Range for the given graph is 24.

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Answer:

hope it helps you........

Step-by-step explanation:

The midpoint formula is

\( (\frac{x1 + x2}{2} ) \: and \: ( \frac{y1 + y2}{2} )\)

Where (x1,y1) is one pair of the points and (x2,y2) is the other pair of points.

The points are

(-5,-4)

(-3,3) So the midpoint is

\(( \frac{( - 5 + ( - 3)}{2} )\: and \:( \frac{ - 4 + 3}{2} )\)

Which gives us

\( - 4 \: and \: - 0.5\)

So the midpoint is

(-4,-0.5)

Answer:

the best answer is option d

Step-by-step explanation:

4/5 x -10 = -40/5 = -8

t x t = t^2

-8t^2

Answer:

\( \sf \: d) \: - 8 {t}^{2} \)

Step-by-step explanation:

Given expression,

\( \sf \rightarrow \: \frac{4}{5}t \: ( - 10t )\)

Let's simplify the expression,

\( \sf \rightarrow \: \frac{4}{5} t \: ( - 10t) \: \)

\( \sf \rightarrow \: ( \frac{4}{5} \times - 10)( {t} \times t)\)

\( \sf \rightarrow \: ( \frac{ - 40}{ \: 5} )( {t}^{2} )\)

\( \sf \rightarrow \: - 8{t}^{2} \)

Hence, the option (d) is correct.

Answer:

4 gallons have 16 quarts and 64 cups

5 gallons have 20 quarts and 40 pints

Step-by-step explanation:

Hope ghis helps!!

Answer:

4 gal = 16 quarts

5 gal = 20 quarts

5 gal =  40 pints

4 gal =  64 cups

Step-by-step explanation:

i got the gal to quarrts by multiplying the gallon value by 4 ( 4x4 = 16 5x4= 20) so multiply the volume for that.

now for gal to pints you multiply the volume value by 8 (5x8=40)

for cups multiply by 16

The approximate percentage of men with heights between 155 cm and 197 cm is 100 %.

The empirical rule, also known as the 68-95-99.7 rule, is a statistical guideline used to estimate the percentage of data that falls within a certain number of standard deviations from the mean in a normal distribution.

To use the empirical rule, we need to determine the number of standard deviations that correspond to the given heights. First, we calculate the z-scores for the lower and upper bounds of the height range:

Lower bound: z = (155 - 176) / 7 = -3
Upper bound: z = (197 - 176) / 7 = 3

Now, we can apply the empirical rule. According to the rule:

- Approximately 68% of the data falls within 1 standard deviation of the mean.

- Approximately 95% of the data falls within 2 standard deviations of the mean.

- Approximately 99.7% of the data falls within 3 standard deviations of the mean.

Since the range between -3 and 3 standard deviations covers the entire distribution, we can conclude that approximately 100% of the data falls within this range.

Therefore, the approximate percentage of men with heights between 155 cm and 197 cm is 100%.

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Answer:

b

Step-by-step explanation:

Answer:

B. 439.

Step-by-step explanation:

7 * (6 + 2)^2 - 3^2

= 7 * 8^2 - 9

= 7 * 64 - 9

= 448 - 9

= 439.

Hope this helps!

Answer:

3.6

Step-by-step explanation:

Answer:

slope m = - 8

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

y + 3 = - 8(x - 4) ← is in point- slope form

with slope m = - 8

The slope is :

Solution:

Given: \(\bf{y+3=-8(x-4)}\)

To determine the slope, it's important to know the form of the equation first.

There are 3 forms that you should be familiar with.

The three forms of equations of a straight line are:

This equation matches point slope perfectly.

The question becomes, how do you work with point slope to find slope?

In point slope, m is the slope and (x₁, y₁) is a point on the line.

Similarly, the slope of \(\bf{y+3=-8(x-4)}\) is -8.

Answer: 2\(\sqrt{2}\)

Step-by-step explanation: First plug in the value, which is \(\sqrt{8}\)

Then divided to 2\(\sqrt{2}\)

Answer:

The answer to this question can be defined as follows:

Step-by-step explanation:

In the motion of an object to the various points without altering its size or shape when its translation takes place in geometry, and all other container throughput shift their vertices or alter their shape.

The scale of the figure doesn't alter the transitions, and  Its statistics remain consistent if the scale and shape of its figure are not modified. In this figure, each point is shifted 2/3 away from the y-axis.

Answer:

The 2nd one. (A translation of 4 units up...)

Step-by-step explanation:

I had a better answer last time in answered this, but a rude user named katie deleted it. (She always does that)