For each of the following subsets of R2 , with it's usual metric,say whether it is connected or not if not give a disconnection.

1.1{(x,y) E R2 : xy>0}

1.2 {(x,y) E R2 : 1
1.3{(x,sinx)E R2 : x E (-pi,2pi]}

1.4{ (x,y) E R2 : |x|>2}

Answer:

\({ \boxed{ \bf{c}}} \: \: \frac{3.8}{4} = s\)

Step-by-step explanation:

\({ \tt{4 \: pies \: = \: 3.8 \: ounces}} \\ { \tt{1 \: pie \: = \: ( \frac{1}{4} \times 3.8) \: ounces}} \\ { \tt{ = 0.95 \: ounces}}\)

\({ \underline{ \sf{ \blue{christ \: † \: alone}}}}\)

198714 to the nearest ten thousand:

The digit in the ten thousands place is:

Which place is used to decide which way to round the ten thousands place:

The second place from the left

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

302895 to the nearest thousand:

7142 to the nearest ten:

24793 to the nearest hundred:

It should be noted that AC is perpendicular to BD.

Given A (0,4), B(1,2) and C(4,6)

AB (Slope of AB) = 2-4/1 = -2

BC (slope of BC) = (6-2/4-1) = 4/4

MAC (Slope of AC) = 6-4 /4 - 0= 1/2

AB × AC = -1

In this case, it should be noted that the are perpendicular as the slopes are -1 and -1/2 whch indicate the negative reciprocals.

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The height of the building is 313 m while the friend is 192 m above me.

The angle of elevation is the angle between the horizontal plane and the line of sight or upward direction to an object or point of interest. It is typically measured in degrees, minutes, and seconds.

The angle of elevation is commonly used in trigonometry, surveying, and navigation to determine the height or distance of an object.

Let the distance from the ground frond to the 86th floor be x

We would now have that;

Tan 82 = 121 + x/44

44Tan 82 = 121 + x

313 = 121 + x

x = 313 - 121

x = 192 meters

Total height of the building = 192 m + 121 m = 313 m

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Answer:9200

Step-by-step explanation: .09 * 2000 = 180 * 40 = 7200 + 2000 = 9200

Balance amount in Jermaine account after 40 years is equals to $9200.

" Simple interest is the process of calculating amount of interest  given on the principal amount at the rate of interest over period of time."

Formula used

S.I. = = (P × R × T) / 100

S.I.= Simple Interest

P = Principal amount

R = Rate of interest

T = Time

Total amount = P + S.I.

According to the question,

Given

P = $2000

R = 9%

T = 40 years

Substitute the given values in the formula we have,

Simple Interest = (2000 × 9 × 40) / 100

                         = $7200

Total balance amount after 40 years = $2000 + $ 7200

                                                              = $9200

Hence, balance amount after 40 years is equals to $9200.

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Answer:

the difference is the + and the -

sorry if it's wrong

Answer:

To find a formula for the nth term of the given sequence, we can analyze the pattern and identify the relationship between the terms.

If we observe the numerator of each term, we can see that it follows the pattern 7, 10, 13, 16, 19, ... This is an arithmetic sequence with a common difference of 3.

If we examine the denominator of each term, we can see that it follows the pattern 1, 2, 6, 24, 120, ... This is not a common arithmetic sequence, but it can be described as a factorial sequence.

The nth term of a factorial sequence can be represented as n!, where n! denotes the factorial of n.

Combining these patterns, we can express the nth term of the given sequence as:

an = (3n + 4)/(n!)

Therefore, the formula for the nth term of the sequence is (3n + 4)/(n!).

Step-by-step explanation:

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The time at which the system fails, denoted by X, is the minimum of the lifetimes of the five components.

In this system, each component has a lifetime that follows an exponential distribution with a parameter λ = 0.01. The exponential distribution is commonly used to model the time until an event occurs in a system with a constant failure rate.

The probability that a component lasts at least t hours is given by P(Ai) = e^(-λt), where Ai is the event that the ith component lasts at least t hours.

Since the components fail independently of one another, the probability that all five components last at least t hours is the product of their individual probabilities: P(A1 ∩ A2 ∩ A3 ∩ A4 ∩ A5) = e^(-λt)^5 = e^(-5λt).

Now, let X be the time at which the system fails, which is the minimum of the lifetimes of the five components. Since X is the minimum, we can write X = min(T1, T2, T3, T4, T5), where Ti represents the lifetime of the ith component.

The probability distribution of X can be obtained by considering the complement event. The complement of X > t is that all five components last at least t hours, which is P(X > t) = P(A1 ∩ A2 ∩ A3 ∩ A4 ∩ A5) = e^(-5λt).

Therefore, the time at which the system fails, X, follows an exponential distribution with a parameter of 5λ = 0.05. This means that the system has a constant failure rate of 0.05 and the probability density function (pdf) of X is given by f(x) = 0.05 * e^(-0.05x).

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Answer:

The amount invested in the 5% account is $4,250

Step-by-step explanation:

Let the amount invested in the first be $x and the amount invested in the second be $y

Total of both is $11,000

Thus, we have

x + y = 11,000 •••••••••(i)

For the first account, the interest earned will be;

5/100 * x = 5x/100 = 0.05x

For the second account , the interest earned will be;

8/100 * x = 0.08x

Adding both gives the total amount of interest

That will be ;

0.05x + 0.08y = 752.50 •••••(ii)

From equation i above;

y = 11,000 - x

Substitute this into ii

0.05x + 0.08(11,000-x) = 752.5

0.05x + 880 - 0.08x = 752.5

0.08x-0.05x = 880-752.5

0.03x = 127.5

x = 127.5/0.03

x = $4,250

The measure of one interior angle of the decagon is 144 degrees

From the question, we have the following parameters that can be used in our computation:

The decagon

The sum of interior angles of a polygon is calculated as

Sum = 180 * (n - 2)

Where

n = number of sides

In a decagon, we have

n = 10

This means that

Sum = 180 * (10 - 2)

When evaluated, we have

Sum = 1440

The measure of one interior angle of the decagon is then calculated as

One interior angle = 1440/10

Evaluate

One interior angle = 144

Hence, the measure of one interior angle of the decagon is 144 degrees

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Answer:

12

Step-by-step explanation:

Because < this means less than. So therefore 5 is less than 12

Answer: I think x=22.

Step-by-step explanation:

If you look at half of the circle you can see a line in it right? This line measures to 180 degrees. This is a right triangle. Usually triangles have a little box in the corner to tell you that is it indeed a right triangle. I don't know why this one doesn't. anyways, if you add 90+68, you get 158. Now you need to get to 180 by simply adding 22. Thats why i think the answer is 22. Sorry if im wrong.

The probability that z lies between -2.41 and 0 is approximately 0.9911.

To find the probability that a standard normal variable, z, falls within a specific range, we can use the standard normal distribution table or a statistical calculator.

In this case, we want to find the probability that z lies between -2.41 and 0. By referencing the standard normal distribution table or using a calculator, we can determine the area under the curve corresponding to this range. The resulting value represents the probability of z falling within that range.

Approximately 0.9911 is the probability that z lies between -2.41 and 0 when rounded to four decimal places. This means that there is a high likelihood (approximately 99.11%) that a randomly chosen value of z from a standard normal distribution falls within this range.

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The number formed by the digits 16, 06, and 68 is 160668, which is determined by concatenating them in the given order.

To determine the number formed by the given digits, we concatenate them in the given order. Starting with the first digit, we have 16. The next digit is 06, and finally, we have 68. By combining these three digits in order, we get the number 160668.

When concatenating the digits, the position of each digit is crucial. The placement of the digits determines the resulting number. In this case, the digits are arranged as 16, 06, and 68, and when they are concatenated, we obtain the number 160668. It's important to note that the leading zero in the digit 06 does not affect the value of the resulting number. When combining the digits, the leading zero is preserved as part of the number.

Therefore, the number formed by the digits 16, 06, and 68 is 160668.

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To find the average rate of change of f(x) on the interval [-2, -2h], we need to first find f(-2) and f(-2h) and then use the formula for average rate of change, which is (f(-2h) - f(-2))/(-2h - (-2)).This is the expression for the average rate of change of f(x) on the interval [-2, -2 + h].

Let's start by finding f(-2) and f(-2h):
f(-2) = (-2)^2 + 5(-2) = 4 - 10 = -6
f(-2h) = (-2h)^2 + 5(-2h) = 4h^2 - 10h

Now we can plug these values into the formula for average rate of change:
(f(-2h) - f(-2))/(-2h - (-2)) = [(4h^2 - 10h) - (-6)]/(-2h + 2) = (4h^2 - 10h + 6)/(2 - 2h)

So the expression for the average rate of change of f(x) on the interval [-2, -2h] is (4h^2 - 10h + 6)/(2 - 2h).

Now, we'll substitute these values into the formula:

Average Rate of Change = ((-2 + h)^2 - 5(-2 + h) - ((-2)^2 - 5(-2))) / h

Simplify the expression:

Average Rate of Change = (4 - 4h + h^2 + 10 - 5h - 4 + 10) / h

Combine like terms:

Average Rate of Change = (h^2 - 9h + 20) / h

This is the expression for the average rate of change of f(x) on the interval [-2, -2 + h].

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Answer:

A = 120 cm²

Step-by-step explanation:

The 4 part of the ratio relates to the height of triangle A , then

16 ÷ 4 = 4 cm ← value of 1 part of the ratio, then

5 parts = 5 × 4 cm = 20 cm

The area (A) of triangle B is calculated as

A = \(\frac{1}{2}\) bh ( b is the base and h the height )

Here b = 12 and h = 20 , then

A = \(\frac{1}{2}\) × 12 × 20 = 6 × 20 = 120 cm²

The height of the triangle is 20 and the area of the triangle B is 120 cm^2

Area of the triangle:

The area of the triangle can be calculated as

Area = \(\frac{1}{2}*base*height\)

Here we have given that

The base of the triangle A = The base of the triangle B = 12 cm

The ratio of the height of triangle A to triangle B is = 4/5

And the height of the triangle A is = 16 cm

If x is the height of the triangle B then

\(\frac{16}{x}=\frac{4}{5}\)

4x = 80

x = 20

Therefore the height of the triangle B is 20 cm

Now substitute these values in the above formula we have

Area of triangle B = 1/2 x 12 x 20

Area of triangle B = 120 cm^2

Hence the final answer is 120 cm^2

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The rose gold bracelets sold by Chantel's fine jewelry store are considered price elastic, as an increase in price resulted in an apparent increase in demand and sales.

Based on the information provided, Chantel raised the price of her rose gold bracelets by $75 to cover unexpected expenses. Surprisingly, she observed an increase in sales at the higher price point. This suggests that the rose gold bracelets are price elastic.

Price elasticity of demand refers to the responsiveness of the quantity demanded to changes in price. When a product is price elastic, an increase in price leads to a proportionately larger decrease in quantity demanded, resulting in a decrease in total revenue. Conversely, a decrease in price would lead to a proportionately larger increase in quantity demanded and total revenue.

This suggests that the demand for these bracelets is relatively elastic, meaning that customers are responsive to changes in price and perceive the higher price as an indicator of increased value, exclusivity, or quality.

Several factors may contribute to this phenomenon. The rose gold bracelets may have unique design elements or craftsmanship that customers are willing to pay a higher price for.

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The media challenge faced in the scenario is increasing audience fragmentation.

The cost price is abbreviated as C.P.  The price at which an article is sold is known as its selling price. The selling price is abbreviated as S.P.It is a price above the cost price and includes a percentage of profit also.

The media challenge described in the scenario is increasing audience fragmentation. Audience fragmentation occurs when there are numerous media options available, and consumers have different preferences and behaviors regarding media consumption. This makes it challenging for media planners and buyers to identify the most effective media outlets to reach their target audience. In the case of Ford, their media planners and buyers had put a lot of effort into selecting the best media outlets, but still had to pull their campaign due to the challenges posed by audience fragmentation. Therefore, the media challenge faced in the scenario is increasing audience fragmentation.

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Answer:  x > -8

Step-by-step explanation:

3x - 17 < 4x -  9   subtract 3x from both sides, and add 9 to both sides

-3x + 9 < -3x + 9

0  - 8   <  x  +  0      Rewrite and reverse the sign to simplify

     x > -8

Answer:

4

Step-by-step explanation:

To solve for x in the equation:

√(2x - 7) = 1

We can start by isolating the square root by squaring both sides of the equation:

(√(2x - 7))^2 = 1^2

2x - 7 = 1

Next, we can isolate the variable by adding 7 to both sides of the equation:

2x = 8

Finally, we can solve for x by dividing both sides by 2:

x = 4

Therefore, the solution to the equation √(2x - 7) = 1 is x = 4.

Answer:

-1/3

Step-by-step explanation:

None of the answers are correct the slope is -1/3

The slope in a slope-intercept equation is always followed by x.

In the equation provided ( y=-1/3x+1/4) the number followed by x is -1/3 so the slope is -1/3.

If you are looking for the y=intercept it is 1/4, but the slope is -1/3.

Option (a) is correct. The value of sinθ will be \(-\frac{5\sqrt{41} }{41}\)

We are given the value of the cosθ  = \(\frac{4\sqrt{41} }{41}\) where, θ is in the IV Quadrant.

We know that cosine is the ratio of the adjacent side to the hypotenuse.  Also, we have
hypotenuse = h = 41, And Adjacent Side = b = \(4\sqrt{41}\)
So, for the value of the opposite side, we need to use the Pythagorean theorem which is stated as:\((Hypotenuse)^{2} = (opposite side)^{2} + (adjacentside)^{2}\)
\(h^{2} = a^{2} + b^{2}\)

\(a^{2} = h^{2} - b^{2}\)

a = \(\sqrt{41^{2} -(4\sqrt{41})^{2} }\) =  \(\sqrt{1681 - 656 }\) = \(\sqrt{1025}\) = \(5\sqrt{41}\)

The opposite side is  \(5\sqrt{41}\) , as sine is negative (-) in the IV quadrant so the value will be   \(-5\sqrt{41}\).

So we know that Sine is the ratio of the Opposite side to the hypotenuse, which can be written as:

sineθ = \(\frac{Opposite}{Hypotenuse}\)

sineθ =  \(-\frac{5\sqrt{41} }{41}\)

So, option (a) will be the right option.

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Your Question is incomplete, but most probably your full question was

Consider this equation. cosθ  = \(\frac{4\sqrt{41} }{41}\) if θ is an angle in quadrant IV, what is the value of sinθ?
(a)       \(-\frac{5\sqrt{41} }{41}\)

(b)   \(\frac{5\sqrt{41} }{41}\)

(c) \(-\frac{5}{4}\)

(d) \(\frac{5}{4}\)

Answer: c

Step-by-step explanation:

Answer: 21120 feet.

Step-by-step explanation: We start with the fraction 1/180, found by putting 20 seconds over one hour. Then, we need to get the amount of miles the speed of sound travels in 20 seconds. We can use the fraction above as a ratio to get it. 720/1 x 1/180 = 4 miles. Then, we'll just do 4 times 5280, which is 21120.

The distance travelled by sound in 20 seconds is 21120 feet.

In unit time the distance covered by any object is called speed.

In mathematical term, Speed is express as S=D/T,

where S=speed, D=distance, T= time.

Given that,

The speed of sound = 720 miles per hour.

According to given condition,

1 hour = 720 miles

Since, 1 hour = 60 minutes

60 minutes = 720 miles

1 minute = 12 miles.

1 minute = 60 seconds

60 second = 12 miles

1 second = 12 / 60  = 1/5 miles

20 second = 20 / 5 = 4 miles

According to given condition,

1 mile = 5280 feet

Therefore,

20 second = 5280 x 4 = 21120 feet

The distance travelled in 20 seconds is 21120 feet.

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Using translation concepts, the series of transformations that shows that pentagon A is congruent to pentagon B is:

B. Rotate pentagon A 90° clockwise about the point (1, 1), reflect it over the x-axis, and translate it 3 units to the left.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

In this problem, we have that the Pentagons have different orientations, meaning that it was rotated, eliminating options A and D.

For the vertices to reach the position they reached in Pentagon B, there had to be a shift left, and before the shift left, the Pentagon must have been entirely at the fourth quadrant, meaning that it was reflected about the point (1,1), and option B is correct.

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A = 72.134554140127 in²

Rounded to the nearest tenth: A = 72.1 in²

30.1 = 2πr
> divide by 2 on both sides

15.05 = πr
> divide by π (3.14) on both sides

4.7929936305732... = r
> Radius = 4.7929936305732...

A = π(4.7929936305732...)²
> Substitute your radius for r

A = π(4.7929936305732...)²
> use PEMDAS or BEDMAS. Do exponents before multiplying π (3.14)

A = π(22.472787942715)

> Multiply your new number by π (3.14)

A = 72.134554140127 in²

> Round to the nearest tenth as the circumference is rounded to the nearest tenth

A = 72.1 in²

3/4 is equivalent to 75%.

To find the percentage of a fraction, you simply just divide the numerator by the denominator. 3/4=0.75, which is 75%.

Answer:

75%....3/4 expressed as a percentage is just multiplying 3/4 and 100

Answer:

Step-by-step explanation:

Answer:

answer:3x

Step-by-step explanation:

4x15=60

60-17=43

4x10=40

43-40=3x