−8x 4y>3 6x−7y<−5 is (2,3) a solution of the system?

To test the effect of living environment on cholesterol levels using samples from rural and urban areas, the best statistical test to utilize would be the two-sample t-test.

The two-sample t-test is appropriate in this case because it compares the means of two independent groups (rural and urban residents) to determine if there is a significant difference between their cholesterol levels.

This test will help researchers determine if living environment has an impact on cholesterol levels.

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(1,2,4)

Range describes the y-values of a graph.

Range

Range is the y-values that a graph covers. Remember that the y-values are found on the vertical axis. If the graph is not continuous, then the values between the points are not included in the range. Similar to the range, the domain of a graph is the x-values that a graph covers. If there is a coordinate point with a y-value, then that y-value should be included in the range.

Finding Range

In order to find the range, we need to find all the unique y-values of the graph. Additionally, the range is given in numerical order. This means starting from the least value and going up to the greatest. The lowest y-value is 1, then 2, and finally 4. Even though there are two points where y = 2, we are only looking for unique values. This means that the range is (1,2,4).

Answer:

15 feet

Step-by-step explanation:

Subtract 10 feet from the height of the ladder

Answer:

30/50

Step-by-step explanation:

here are the pictures  HOPE I HELP :)

Answer:

Simplify the expression.

−16x

Step-by-step explanation:

The percent error of the measurement, to the nearest tenth of a percent, is 5.6.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

John measured a line to be 1.7 inches long.

The actual length of the line is 1.8 inches.

The amount of error = 1.8 - 1.7

The amount of error = 0.1

Let 1 - n be the required percentage of error.

Then applying the percentage formula,

1.8 x n /100 = 1.7

Applying cross multiplication,

we get,

1.8n = 170

n = 170/1.8

n = 94.4

So, 1 - n = 100 - 94.4 = 5.6

Therefore, the percentage is 5.6.

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To find P(B) given P(A) = 0.4, P(B|A) = 0.3, and P(A U B) = 0.6, we can use the formula for conditional probability.

The calculation involves using the formula P(A U B) = P(A) + P(B) - P(A ∩ B), where P(A U B) represents the probability of the union of events A and B, and P(A ∩ B) represents the probability of the intersection of events A and B.

First, we know that P(A U B) = 0.6 and P(A) = 0.4. Rearranging the formula, we get P(A ∩ B) = P(A) + P(B) - P(A U B).

Substituting the given values, we have 0.6 = 0.4 + P(B) - P(A ∩ B).

Simplifying the equation, we can isolate P(B) by subtracting 0.4 from both sides: P(B) = 0.6 - 0.4 + P(A ∩ B).

Therefore, the probability of event B, denoted as P(B), depends on the value of P(A ∩ B) and cannot be determined with the given information.

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Increasing marginal productivity infers that extra units of capital and labor contribute more to yield, driving productive asset allotment. ∝ and ß < 1 expect reducing returns, adjusting with reality.

To appear that the generation work has to expand the marginal productivity of capital (in case ∝ > 1) and labor (on the off chance that ß > 1), we ought to take fractional subsidiaries with regard to each input calculation. For capital (K), the fractional subsidiary of the generation work is:

\(\dfrac{dy}{dK }= \alpha AK^{(\alpha-1)}L^\beta\)

Since ∝ > 1, (∝ - 1) is positive, which implies that the fractional subordinate \(\dfrac{dy}{dK}\) is positive. This shows that an increment in capital input (K) leads to an increment in yield (y), appearing to expand the marginal efficiency of capital.

Additionally, for labor (L), the fractional subordinate of the generation work is:

\(\dfrac{dy}{dL} = \beta AK^{\alpha}L^{(\beta-1)}\)

Since \(\mathbf{\beta > 1, (\beta-1)}\) it is positive, which implies that the halfway subordinate \(\dfrac{dy}{dL}\) is positive. This demonstrates that an increment in labor input (L) leads to an increment in yield (y), appearing to increase the marginal productivity

The economic importance of increasing marginal productivity is that extra units of capital and labor contribute more to yield as their amounts increment.  This suggests that the more capital and labor a firm employments, the higher the rate of increment in yield. This relationship is vital for deciding the ideal assignment of assets and maximizing generation effectiveness.

In most generation capacities, it is accepted that ∝ and ß are less than 1. This presumption adjusts with experimental perceptions and financial hypotheses.

In case ∝ or ß were more prominent than 1, it would suggest that the marginal efficiency of the respective factor increments without bound as the calculated input increments.

In any case, there are decreasing returns to scale, which suggests that as calculated inputs increment, the Marginal efficiency tends to diminish. Therefore, accepting ∝ and ß are less than 1 permits for more reasonable modeling of generation forms and adjusts with the concept of diminishing marginal returns.

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Answer:

2

Step-by-step explanation:

y=mx+b, where m=the slope. 2=m, so 2 is the slope.

Answer:

The slope of this is 2

Step-by-step explanation:

all u have to do is find the coefficant of x or what number is right next to x and in this problem it is 2

Answer:

I think the answer is D. (2,6,8) because if the ones on the right are y - coordinates in the Function then it should be correct. If not sorry

(Range is y - coordinate)

(Domain is x - coordinate)

Answer:The slope-intercept form is y=mx+b y = m x + b , where m m is the slope and b b is the y-intercept. Add 10 10 to both sides of the equation. Using the slope-intercept form, the y-intercept is 10 .

Step-by-step explanation:

By proving both directions, we have shown that for all k ∈ N, 5 | Fₖ if and only if 5 | k.

To prove that every fourth Fibonacci number is a multiple of 3 (i.e., for all k ∈ N, 3 | F₄ₖ), we can use mathematical induction.

Base case: We start by checking the statement for the base case, k = 1. The first Fibonacci number, F₁, is 1, which is not a multiple of 3.

Hence, the statement holds true for k = 1.

Inductive step: Now, assume the statement is true for some arbitrary positive integer m, i.e., assume 3 | F₄ₘ.

We need to show that the statement is also true for m + 1, i.e., we need to prove that 3 | F₄ₘ₊₁.

Using the definition of the Fibonacci sequence, we have:

F₄ₘ₊₁ = F₄ₘ₋₁ + F₄ₘ₋₂

Now, let's consider F₄ₘ₋₁ and F₄ₘ₋₂ separately:

F₄ₘ₋₁ ≡ F₄ₘ - F₄ₘ₋₁ (mod 3)  [Using the induction hypothesis]

       ≡ -F₄ₘ₋₁ (mod 3)

F₄ₘ₋₂ ≡ F₄ₘ - F₄ₘ₋₁ - F₄ₘ₋₂ (mod 3)  [Using the induction hypothesis]

       ≡ -F₄ₘ₋₁ - F₄ₘ₋₂ (mod 3)

Now, substituting these values back into the equation for F₄ₘ₊₁, we get:

F₄ₘ₊₁ ≡ -F₄ₘ₋₁ + (-F₄ₘ₋₁ - F₄ₘ₋₂) (mod 3)

F₄ₘ₊₁ ≡ -2F₄ₘ₋₁ - F₄ₘ₋₂ (mod 3)

Now, since we assumed that 3 | F₄ₘ, we know that F₄ₘ is a multiple of 3. Hence, -2F₄ₘ₋₁ and -F₄ₘ₋₂ are also multiples of 3. Therefore, their sum, F₄ₘ₊₁, is also a multiple of 3.

By the principle of mathematical induction, we have shown that for all k ∈ N, 3 | F₄ₖ.

To prove that for all k ∈ N, 5 | Fₖ if and only if 5 | k, we can use a similar approach.

First, let's prove the forward direction: 5 | Fₖ ⇒ 5 | k.

Base case: We start by checking the statement for the base cases. For k = 1, F₁ = 1, and it is not divisible by 5. Hence, the statement holds true for the base case.

Inductive step: Now, assume the statement is true for some arbitrary positive integer m, i.e., assume 5 | Fₘ. We need to show that the statement is also true for m + 1, i.e., we need to prove that 5 | Fₘ₊₁ ⇒ 5 | (m + 1).

Using the definition of the Fibonacci sequence, we have:

Fₘ₊₁ = Fₘ + Fₘ₋₁

Now, let's assume that

5 | Fₘ₊₁. This implies that Fₘ₊₁ is divisible by 5. Since Fₘ = Fₘ₊₁ - Fₘ₋₁, and we assumed that 5 | Fₘ, it means that Fₘ is also divisible by 5.

Now, using the induction hypothesis that 5 | Fₘ, we have:

Fₘ ≡ 0 (mod 5)

Since Fₘ₊₁ = Fₘ + Fₘ₋₁, we can rewrite this as:

Fₘ₊₁ ≡ 0 + Fₘ₋₁ (mod 5)

Now, using the induction hypothesis that 5 | Fₘ₋₁, we have:

Fₘ₊₁ ≡ 0 + 0 (mod 5)

Fₘ₊₁ ≡ 0 (mod 5)

Therefore, we have shown that if 5 | Fₘ, then 5 | Fₘ₊₁, which completes the forward direction of the proof.

To prove the reverse direction: 5 | k ⇒ 5 | Fₖ, we can use a similar approach.

Assume that 5 | k. This means that k is divisible by 5. We can express k as k = 5n for some integer n.

Now, let's consider the Fibonacci number Fₖ:

Fₖ = Fₖ₋₁ + Fₖ₋₂

Using the induction hypothesis that 5 | Fₖ₋₁ and 5 | Fₖ₋₂, we have:

Fₖ ≡ 0 + 0 (mod 5)

Fₖ ≡ 0 (mod 5)

Therefore, we have shown that if 5 | k, then 5 | Fₖ, which completes the reverse direction of the proof.

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In order to find the area of the region between the graphs of f(x)=11 - 8x and g(x)=2x² over the interval [0,2], we need to integrate the difference between the two functions from 0 to 2.

This can be represented as follows:∫[0,2] (11 - 8x - 2x²) dxWe can use the power rule of integration and the constant multiple rule to simplify this expression:∫[0,2] (11 - 8x - 2x²) dx = ∫[0,2] 11 dx - ∫[0,2] 8x dx - ∫[0,2] 2x² dx= 11x |[0,2] - 4x² |[0,2] - (2/3) x³ |[0,2]Evaluating this expression at the limits of integration, we get:11(2) - 11(0) - 4(2²) + 4(0²) - (2/3)(2³) + (2/3)(0³) = 22 - 16/3 = 50/3Therefore, the area of the region between the two graphs over the interval [0,2] is 50/3 square units.

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Answer:

Because they are both negative that means they are on the left side so -0.4 is closer to the 0 so less.

Answer:

B

Step-by-step explanation:

Categorical data is also known as qualitative variable. It is a data that can take up one or a limited set of values. e.g race, sex,  occupation.

To verify that the conclusion of Clairaut's theorem holds for f at the point (0,π/2), we need to check that the partial derivatives of f with respect to x and y are continuous at (0,π/2) and that they are equal at this point. Since e^(π/2) is not equal to π/2, the conclusion of Clairaut's theorem does not hold for f at the point (0,π/2).

First, let's find the partial derivative of f with respect to x:
∂f/∂x = yexy sin(y)
Now, let's find the partial derivative of f with respect to y:
∂f/∂y = exy cos(y) + exy sin(y)
At the point (0,π/2), we have:
∂f/∂x = π/2
∂f/∂y = e^(π/2)
Both partial derivatives exist and are continuous at (0,π/2).
To check that they are equal at this point, we can simply plug in the values:
∂f/∂y evaluated at (0,π/2) = e^(π/2)
∂f/∂x evaluated at (0,π/2) = π/2
Since e^(π/2) is not equal to π/2, the conclusion of Clairaut's theorem does not hold for f at the point (0,π/2).
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The equation of the parabola with a focus at (-2,-5) and a directrix of x = 6

x = -1/24(y + 5)² + 4

When the directrix is given in x the parabola is a horizontal parabola

The line x = 6 is the directrix, With the focus given as F (-2,-5).

Using the factored form of the equation

x = a(y - k)² + h

The vertex has same y-coordinate as the focus for a vertical parabola

the x-coordinate of the vertex is midpoint of -2 and 6 is the vertex and this is = 4

v(h, k) = v(4, -5)

F (-2, -5) = F (h + p, k) and a =  1/4p

h + p = -2 and from vertex h = 4, hence p = -6

a = 1/4p = 1/4*-6 = -1/24

substituting gives

x = -1/24(y + 5)² + 4

complete question

A parabola has focus F(-2, -5) and directrix x = 6. Find the standard equation of the parabola

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Answer: 54, if 1 book cost $6 and 1 boots cost's $8

5x6= 30

3x8=24

30+24=54

But if the whole 5 books only cost's $6 and the 3 boots cost's $8

answer is: $14

Answer:

need to see what its talking about

Step-by-step explanation:

Answer:

help answer pls... this the picture

First off, no sides have the same length as the others, so it cannot be an equilateral or an isoceles triangle, as it would required at least 2 sides to have the same length.

So, we're left with scalene triangle options.

There is an angle that is an obtuse angle (as it is more than 90 degrees and less than 180 degrees), so this is a scalene obtuse triangle.

Answer:

Look to explanation

Step-by-step explanation:

The question says the original mosaic  is surrounded by a 3 inch by 5 inch frame.  The length has 5 squares & the width has 3 squares, so that means each square is an inch long.

1.  Perimeter is adding up how long all the sides are.  So for the original you add 3 + 5 + 3 + 5 = 16 inches

2.  Area is length x width, so we multiply 3 x 5 = 15 inches squared

3.  Since each square is an inch, to find the length we add up all the squares & we get 10.  Then we do the same for the width & get 6.  To figure perimeter, we add up all the sides  10 + 6 + 10 + 6 = 32 inches

4.  Area is length x width, so 10 x 6 = 60 inches squared

5.  For the original we needed 16 inches of steel.  For the larger one, we needed 32 inches.  32 inches is 2x bigger than 16.

6.  For the original we had an area of 15 inches squared.  For the larger one we had 60 inches squared.  60 is 4x bigger than 15.

We have the average deviation of set of data 4.6, 4.5, 4.8, 4.4, 4.7 is

σ = 0.12

We have to find average deviation of the time period of pendulum in five different trials (4.6s, 4.5s, 4.8s, 4.4s, 4.7s)

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers. It is one of the measures of the central tendency.

Average Deviation of set of observations is calculated by computing the mean and then the specific distance between each observation and that mean.

Total number of observations, N = 5

Sum of observations = 4.6 + 4.5 + 4.8 + 4.4 + 4.7 = 23

\(Mean, x = \frac{Sum of observations}{Total no of observations } = \frac{23}{5}\)

Mean = 4.6

\(Average Deviation = \frac{|4.6-4.6| + |4.5-4.6| + |4.8-4.6| + |4.4-4.6| + |4.7-4.6|}{5}\)

\(= \frac{0 + 0.1 + 0.2 + 0.2 + 0.1}{5}\)

\(= \frac{0.6}{5}\)

= 0.12

The Average Deviation for  the observation of time period of pendulum is 0.12.

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The average deviation of 4.6, 4.5, 4.8, 4.4, and 4.7 is σ = 0.12

In five different trials, we must calculate the average deviation of the pendulum's time period (4.6s, 4.5s, 4.8s, 4.4s, 4.7s).

N = 5 is the total number of observations.

4.6 + 4.5 + 4.8 + 4.4 + 4.7 = 23 is the total number of observations.

Mean = 23/5 = 4.6

Average deviation is equal to (4.6-4.6+4.5-4.6+4.8-4.6+4.4-4.6+4.7-4.6)/5.

= 0.6/5

= 0.12

The Average Deviation for  the observation of time period of pendulum is 0.12.

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The domain and range of y = 5^x is all real numbers.

The domain of y = 5^x is all real numbers, x. There are no restrictions on the input value for x, so any real number can be used as the exponent.

The range of y = 5^x is all positive real numbers, y. This is because the base of the exponential function, 5, is positive and the exponent, x, can be any real number. As the exponent increases, the value of the function will also increase and the function will approach positive infinity. Similarly, as the exponent decreases, the value of the function will also decrease and approach zero. Therefore, the range of y = 5^x is all positive real numbers, y.

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Answer:

38.66 meters.

Step-by-step explanation:

Let's denote the height of the building as 'h' (to be determined). Given that the tower is 30m high, we can use trigonometry to solve for the height of the building.

From the information provided, we can form a right triangle with the height of the tower as one side, the height of the building as another side, and the distance between the tower and the building as the hypotenuse.

Considering the angle of depression of 30 degrees, we have the following equation:

tan(30°) = h / d

Where 'd' is the distance between the tower and the building. We don't have the exact value of 'd,' but we can use the second angle of depression to find the relationship between 'd' and the height of the tower.

Using the angle of depression of 45 degrees, we have:

tan(45°) = 30 / d

We can rearrange this equation to solve for 'd':

d = 30 / tan(45°)

Now we can substitute this value of 'd' into the first equation:

tan(30°) = h / (30 / tan(45°))

To find the value of 'h,' we can solve this equation:

h = (30 / tan(45°)) * tan(30°)

Using a calculator, we can calculate the value of 'h' to be approximately 38.66 meters.

Therefore, the height of the building is approximately 38.66 meters.

Answer:

$9

Step-by-step explanation:

Answer:

15/3 x 2

Step-by-step explanation:

I hope this helps

The total cost of each utility eliminating 450 tons of pollution is $180,000.

To calculate the total cost for each utility to eliminate 450 tons of pollution, we need to multiply the cost per ton of pollution elimination by the number of tons each utility needs to eliminate.

For People's Electric, the cost of eliminating one ton of pollution is $400. So, to eliminate 450 tons, the total cost would be 450 tons * $400/ton = $180,000.

For Municipal Energy, the cost of eliminating one ton of pollution is $350. Again, to eliminate 450 tons, the total cost would be 450 tons * $350/ton = $157,500.

Therefore, the total cost for each utility to eliminate 450 tons of pollution is $180,000 for People's Electric and $157,500 for Municipal Energy.

The cost calculation is based on the given information that each utility is provided with 450 pollution permits by the government. These permits allow them to legally produce a ton of pollution. By setting a limit on the number of permits, the government aims to reduce pollution by half. The utilities have the option to trade permits with each other.

In this scenario, People's Electric has a higher cost of eliminating pollution per ton compared to Municipal Energy ($400 vs. $350). It means that People's Electric would find it more expensive to reduce pollution through internal measures like investing in cleaner technology or implementing environmental initiatives. On the other hand, Municipal Energy has a lower cost, indicating that they have relatively more cost-effective methods for pollution reduction.

Given these costs, it is more beneficial for People's Electric to purchase permits from Municipal Energy rather than eliminating the pollution themselves. By purchasing permits, People's Electric can meet the pollution reduction target at a lower cost. Conversely, Municipal Energy can generate additional revenue by selling their permits.

This permit trading mechanism allows for cost efficiency in achieving the government's pollution reduction goal. The total cost for each utility is determined by multiplying the cost per ton of pollution elimination with the number of tons they need to eliminate.

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Here the parameters, p =0.489 and n=15, and the probability of winning more than 8 times is  0.17946

while you playing an arcade game, there are two possible outcomes: win or lose, which is related to the binomial distribution, such as :

P= \(C_{n,k}\) \(p^{n}\) \(q^{n-k}\)

where C is the  combination, p is the probability of success and the q is the complement of the p (q=1-p) .Here we are given that the probability of winning an arcade game is 0.489 and  the probability of losing is 0.511.  So p=  0.489, since the number of the trial are 15, we need to  find the probability for more  than 8 times, which means

P(X>8)= P(X=9)+P(X=10)+P(X=11)+P(X=12)+P(X=13)+P(X=14)+P(X=15)              P(X>8)=P(X>=8)- P(X=8)  

           = 0.34328- 0.16382  

            =0.17946

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