does the equation describe a linear relationship between two variables 10x-2=y

The population was 6.98 million in 1900. The population of New York decreased with respect to time.

What is an exponential function?

An exponential function is a mathematical function with the formula f (x) = axe, where "x" is a variable and "a" is a constant that is called the function's base and must be greater than zero. The transcendental number e, which is approximately equal to 2.71828, is the most commonly used exponential function base.

The population of New York state can be modeled by

\(P(t)=\frac{19.71}{1+61.22e^{-0.03513t}}\)

P is the population and t is the number of years since 1800.

The difference between the year 1900 to 1800 is 100.

Putting t = 100 in the given model:

\(P(t)=\frac{19.71}{1+61.22e^{-0.03513\times 100}}\)

\(P(t)=\frac{19.71}{1+61.22e^{-3.513}}\)

P(t) = 19.71/2.8248

P(t) = 6.9774

P(t) = 6.977 (rounded to the nearest thousands)

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Answer

1. Cardiovascular endurance

2. Muscular strength

3. Muscular endurance

4. Flexibility

5. Body composition

Step-by-step explanation:

Answer:

\(\large\boxed{\textsf{Option B. Right Scalene Triangle.}}\)

Step-by-step explanation:

\(\textsf{For this problem, we are asked which triangle has no equal sides and a right angle.}\)

\(\textsf{Let's review the types of triangles, according to the options.}\)

\(\large\underline{\textsf{What is an Isosceles Triangle?}}\)

\(\textsf{An Isoceles Triangle is a triangle that has \underline{2 congruent sides}.}\)

\(\textsf{Option A is incorrect.}\)

\(\large\underline{\textsf{What is a Right Scalene Triangle?}}\)

\(\textsf{An Isoceles Triangle is a triangle that has \underline{no congruent sides} and has \underline{1 right angle}.}\)

\(\boxed{\textsf{Option B is correct.}}\)

\(\large\underline{\textsf{What is a Right Isosceles Triangle?}}\)

\(\textsf{A Right Isoceles Triangle is a triangle that has \underline{2 congruent sides}. and 1 right angle}\)

\(\textsf{Option C is incorrect.}\)

\(\large\underline{\textsf{What is a Right Triangle?}}\)

\(\textsf{A Right Triangle is a triangle that has \underline{1 right angle}.}\)

\(\textsf{We're not sure how many equal sides this triangle has as it can be none, or 2.}\)

\(\textsf{Option D is incorrect.}\)

To approximate the signed volume of the solid S above the rectangular region R and under the function z=f(x,y), we divide R into four squares and evaluate the function at sample points, multiplying the height by the area of each square and summing them up.

To approximate the signed volume of the solid S that lies above the rectangular region R=[0,2) x (0,2) and under the graph of the function z=f(x,y)=3x^2-y, we divide R into four squares with m=n=2.

The sample points for each square are:

(0,1)

(1,1)

(0,2)

(1,2)

For each square, we evaluate the function f(x,y) at the corresponding sample point to obtain the height of the solid at that point. Then, we multiply the height by the area of the square to get the approximate volume of the solid over that square.

Finally, we sum up the volumes of the four squares to get the overall approximation of the signed volume of the solid S.

Note: The specific values for the height and area of each square need to be calculated using the given function and the dimensions of the squares.

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Given, the height \($h=6$, the base $b_1=9$ and $b_2=12$.\)

The area of the trapezoid is given by the formula,

\(\[A = \frac{1}{2}h(b_1+b_2)\]\)

Substitute the given values,  

\(\[A = \frac{1}{2} \times 6 \times (9+12)\]\\\)

Simplifying the above expression,

\(\[A = 45 \text{ square feet}\]\)

Therefore, the area of the trapezoid is $45$ square feet.

The perimeter of a two-dimensional geometric shape is the entire length of the boundary or outer edge. It is the sum of the lengths of all the shape's sides or edges.

The perimeter of a square, for example, is calculated by adding the lengths of all four sides of the square.

Similarly, to find the perimeter of a rectangle, sum the lengths of two adjacent sides and then double the result because there are two pairs of adjacent sides.

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First, let's calculate the z-score for the value 2.025 liters using the formula:

z = (x - μ) / σ

Where:

x = the value we want to calculate the probability for (2.025 liters)

μ = the mean of the process (2.050 liters)

σ = the standard deviation of the process (0.020 liters)

Plugging in the values:

z = (2.025 - 2.050) / 0.020

Simplifying:

z= -0.025 / 0.020

z = -1.25

Now, we can look up the probability corresponding to a z-score of -1.25 in the standard normal distribution table or use a calculator.

Using a standard normal distribution table, the probability is approximately 0.1056. This means that the probability of randomly selecting an output from the process that is less than 2.025 liters is approximately 0.1056 or 10.56%.

Alternatively, you can use a calculator or statistical software to find the probability directly by looking up the cumulative distribution function (CDF) of the standard normal distribution at -1.25. The result will also be approximately 0.1056 or 10.56%.

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Answer: spiral

Step-by-step explanation:

The shape that our galaxy have is : Spiral, because "Spiral-Structure" provides the Milky-Way its name. option (b) is correct.

Our galaxy, the Milky-Way, is classified as a spiral galaxy. Spiral-Galaxies are characterized by their distinct spiral arms that radiate from a central bulge. These arms contain stars, gas, dust, and other celestial objects.

The Milky-Way's spiral arms are home to a significant portion of its stars and are formed due to the gravitational interactions between different parts of the galaxy. This spiral structure gives the Milky-Way its name and appearance when observed from certain angles.

Spiral galaxies are one of the most common types of galaxies in the universe, and they play a crucial role in our understanding of cosmic structures.

Therefore, the correct option is (b).

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The given question is incomplete, the complete question is

Which shape does our galaxy have?

(a) circular

(b) spiral

(c) irregular

(d) elliptical.

Answer:

A. \(3<\sqrt{15} <4\)

Step-by-step explanation:

First we need to know what \(\sqrt{15}\) equals.

It equals around 3.87, which is more than 3 and less than 4.

Answer: It might be "A" i dont know.

The justification for the third step of the proof as given in the task content is; Reflexive property of ~; SSS.

The justification for the fourth step of the proof as required is; Symmetric Property of ~; SSS.

Recall that the; Reflexive Property as used in mathematical operations is such that: x = x. Therefore, the length of line segment ST and the length of line segment TS are equal and the segments are congruent.

Also, it follows from the task content that ∆RST ~ ∆UTS which means that both triangles are congruent by the Symmetric Property of SSS.

Ultimately, the justification for steps 3 and 4 are therefore, Reflexive Property of mathematical operations and the Symmetric property of SSS respectively.

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Answer:

55

Step-by-step explanation:

11 x 5 = total combinations

11 x 5 = 55

Answer:

HTML Formatting basically refers to the enhancing of text in order to increase the visual appeal. HTML provides a range of formatting tags that can be used to make the text attractive to the users. There are many options available that can be used for formatting, just like any other text editor.

Step-by-step explanation:

Answer:

17.39%.

Step-by-step explanation:

As a percentage (rounded to two decimal places):

A decrease of 17.39%.

Answer:

so I'm guessing you're solving for x

because angle 2 is the vertical angle to angle 3 so this means that they are congruent

4x-26=3x+4

4x-3x=4+26

x=30

==============================================================

Explanation:

Let's say your first selection was red. If you have really good luck, you'll pick 7 more red and the answer would be 8. However, we need to consider the opposite side of the spectrum. We need to consider the worst possible scenario and having the worst luck ever. In this scenario, we don't match colors until the very last possible moment. If you pick red first, then you cannot pick red again until you've picked blue, yellow and black/white.

There are a few ways to consider the worst case scenario. One way is to form a table as shown below. See the attached image. Each row represents the colors "red, blue, yellow, black/white" in that exact order. This could be one way to select the items. For this row, we haven't selected a repeat color. Red is selected first. Each row repeats itself, although the black/white gets exhausted after 4 rows.

By the 7th row, we have 7 red, 7 blue and 7 yellow. We don't need a full 8th row to reach our goal. We can stop once we reach the highlighted cell I marked in the table. That cell represents picking the 8th red. You could replace that highlighted cell with "blue" or "yellow" and still achieve the goal because you'd get 8 of that color. I'm just picking on red since it's the first one listed.

If you count out the items, you should count out 33 total. Ignore the stuff after the highlighted cell in row 8.

We have a 7 by 3 rectangle that has 7*3 = 21 items. Then the highlighted cell bumps the count up to 21+1 = 22. Finally, the four black/white items are counted as well to get to 22+4 = 26 as the final answer

We need to make 26 selections to guarantee that we selected 8 of the same color. Again, this is because we're considering a scenario in which we get the worst luck ever and don't make any color matches until the last possible moment.

Answer:

15 feet

Step-by-step explanation:

since its 2 inches to 1 foot, just divide the 30 inches by 2 to get 15 feet

Answer:

8

Step-by-step explanation:

The triangle is isosceles so the answer is either 3 or 8.

You might think there are 2 answers. There are not. The base is 3 inches and the two equal sides are 8 inches a piece.

If you say that there are 2 sides of 3 inches each, they add up to 6. They can't. Six is much smaller than 8 and so two sides of 3 don't even cover up the 8, let alone make a triangle.

Answer:

\(x = -8\)

Step-by-step explanation:

We can solve for x by isolating it on one side of the equation.

If we're given the equation \(3x + 5 - x = x-3\), we can simplify it down.

First let's combine like terms on the left side.

\(2x + 5 = x-3\)

Now subtract x from both sides:

\(x + 5 = -3\)

Subtract 5 from both sides:

\(x = -8\)

Hope this helped!

Answer:

-8

Step-by-step explanation:

Simplify to 2x + 5 = X - 3

Subtract and you end up with x = -3 - 5

Answer:

40%

Step-by-step explanation:

In order to turn a fraction into a decimal or percentage, you need to make the denominator 100. In this case you just need to multiply the numerator and denominator by 20:

2/5 --> 2*20/5*20 --> 40/100

So, it is 40%. Though if you want to turn ANY fraction (specifically fractions with hard to multiply denominators) into a percentage, just follow this rule:

(100n/d)%

The 2/5 is equivalent to 40%.

To calculate what percent is equivalent to 2/5, we can use the formula:

Percent = (Part / Whole) * 100

In this case, the part is 2 and the whole is 5.

Percent = (2 / 5) * 100

Now, perform the division:

Percent = 0.4 * 100

To find the percentage, multiply 0.4 by 100:

Percent = 40%

Therefore, 2/5 is equivalent to 40%. To understand this better, consider that 2 out of 5 parts is 40% of the whole. The percentage represents the proportion of the part (2) in relation to the whole (5) expressed as a fraction of 100. In this scenario, 2/5 is equivalent to 40%, indicating that 40% of the whole is represented by the fraction 2/5.

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The x-intercept of the given linear function is 0 and the graph of the linear ufnction is shown.

So, plot the linear function:

(Refer to the graph attached below)

Therefore, the x-intercept of the given linear function is 0 and the graph of the linear ufnction is shown.

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The Law of Large Numbers is a fundamental concept in probability theory and statistics stating the number of trials of a random event increases, the average of the outcomes approaches the expected value of the event. It's better to use 500 trials.

In other words, as we repeat an experiment a large number of times, the proportion of times that a certain outcome occurs will converge to its probability of occurrence. This is an important concept in statistical inference, as it helps to ensure that the results of a sample are representative of the population from which it was drawn.

Now, if you were using the relative frequency of an event to estimate the probability of the event, it would be better to use 500 trials rather than 100 trials. The reason is that the larger the number of trials, the more accurate the estimate of the probability is likely to be.

Using a larger sample size reduces the impact of random variation and provides a more precise estimate of the true probability. The Law of Large Numbers tells us that as the sample size increases, the relative frequency of the event should converge to the true probability, so a larger sample size will generally give a more reliable estimate

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The coefficient of determination (R²) for the given data is approximately 0.920. This value indicates that approximately 92% of the variability in the dependent variable can be explained by the independent variable using the least squares regression line.

Calculate R² using the given information. R², also known as the coefficient of determination, measures the proportion of variability in the dependent variable that can be explained by the independent variable using the least squares regression line.

calculate R²:

1. You have been provided with the total sum of squares (SST) which is 2640.8, and the sum of squares of regression (SSR) which is 2429.8.

2. To calculate R², you need to divide SSR by SST:
  R² = SSR / SST

3. Now, substitute the given values:
  R² = 2429.8 / 2640.8

4. Perform the division:
  R² ≈ 0.920

5. Finally, round R² to three decimal places:
  R² ≈ 0.920

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Buying from Value World would cost Binita £0.72 less (in pounds) than buying from Letters2go.

To compare the costs of envelopes from both shops, we need to calculate the price per envelope.

At Letters2go, the price per envelope is:

3.29 pounds / 25 envelopes = 0.1316 pounds per envelope

At Value World, the price per envelope is:

(1.95 pounds * 2 packs) / (10 envelopes * 2 packs + 1 free pack) = 0.1300 pounds per envelope

So the price per envelope at Value World is slightly less than the price per envelope at Letters2go.

To buy 450 envelopes, Binita would need to purchase:

18 packs of 25 envelopes at Letters2go (18 x 25 = 450 envelopes)

45 packs of 10 envelopes at Value World (45 x 10 = 450 envelopes)

At Letters2go, the cost of 18 packs of 25 envelopes would be:

18 packs x £3.29 per pack = £59.22

At Value World, the cost of 45 packs of 10 envelopes (with 15 packs being free) would be:

30 packs x £1.95 per pack = £58.50

Therefore, buying from Value World would cost Binita £59.22 - £58.50 = £0.72 less than buying from Letters2go.

Correct Question :

Binita is going to buy 450 envelopes.

Here is some information about the cost of envelopes in two shops,

Letters2go : Pack of 25 envelopes for £3.29

Value World : Pack of 10 envelopes for £1.95, Buy 2 packs get 1 pack free

How much less, in pounds (£), will it cost Binita to buy the envelopes from Value World.

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Answer:

R(-2,0)

S(0,-4)

T(-4,-3)

Step-by-step explanation:

So first you gotta subtract 2 from each x value and 1 from each y value. After you do that, you get:

R(0,2)

S(-4,0)

T(-3,4)

then i put it all onto a graph, and rotated it 90* counterclockwise, from the origin, which puts it in quadrant 3, with the final coordinates above.

(hope this helps <3 )

Here is the five-number summary, range and interquartile range:

Minimum: 9

Lower quartile:   11

Median: 24

Upper quartile:  34

Maximum: 45

Interquartile range: 23

The minimum number is the smallest number in the data. The  minimum number is 9. The maximum number is the biggest number in the dataset. The maximum number is 45.

The first quartile, third quartile and the interquartile range are used to measure dispersion.

The first quartile : 1/4(n + 1)

1/4 x (12) = 3rd term = 11

The third quartile : 3/4 x (n + 1)

3/4 x (12) = 9th term = 34

Interquartile range = third quartile - first quartile

34 - 11 = 23

Median can be described as the number that is at the center of the dataset when the number is arranged in either ascending or descending order.

Median = 25

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\(625=5^{7x-3}\implies 5^4=5^{7x-3}\implies 4=7x-3 \\\\\\ 7=7x\implies \cfrac{7}{7}=x\implies 1=x\)

Answer: C) I think?

Step-by-step explanation:

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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