Round off 8 146,628 to the 2 decimal place

The constant is [tex]$y_0$[/tex] and the function is [tex]$y(t) = 4e^{-2t} + 2t - 9$[/tex].

The unique solution to the given initial value problem can be expressed as:

[tex]\begin{align}y(t) = 4e^{-2t} + 2t - 9 + y_0\end{align}[/tex][tex]\begin{align}y(t) = 4e^{-2t} + 2t - 9 + y_0\end{align}[/tex][tex]y(t) = 4e^{-2t} + 2t - 9 + y_0\end{align}[/tex]

where the constant is [tex]$y_0$[/tex] and the function is [tex]$y(t) = 4e^{-2t} + 2t - 9$[/tex].

To calculate the constant and the function, we solve the differential equation [tex]$y' = g(t)$[/tex] with the initial condition [tex]$y(0) = y_0$[/tex]. We start by differentiating both sides of the equation and rearranging to get the differential equation:

[tex]y' = g(t) \implies \frac{dy}{dt} = 4e^{-2t} + 2\end{align}[/tex]

Integrating both sides and using the initial condition gives us:

[tex]\int \frac{dy}{dt} dt &= \int (4e^{-2t} + 2)dt \\y &= 4e^{-2t} + 2t + c \\y(0) &= 4e^{-2(0)} + 2(0) + c \\y_0 &= 4 + c \\y(t) &= 4e^{-2t} + 2t - 9 + y_0\end{align}[/tex]

Therefore, the constant is [tex]$y_0$[/tex] and the function is [tex]$y(t) = 4e^{-2t} + 2t - 9$[/tex].

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When reviewing the rates for the reaction at a constant temperature CH4(g) +202 CO2(g) + 2 H2O(g): the magnitude is the same, but the sign is opposite.

Correct option: D

A chemical reaction's forward motion. It is frequently defined in terms of either the concentration of a reactant which is consumed in a period of time or the concentration of a product that is generated in a unit of time (amount per unit volume).

Methane concentration drops during the reaction, hence the rate of the reaction is equal to the rate at which methane is vanishing. It will have a negative value since methane concentration is falling during the process.

However, the rate of reaction is positive.

Therefore, while having opposing signs, the rates of reaction and methane's disappearance will be of equal size.

Hence option D is the correct answer.

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Adding and subtracting fractions with unlike denominators involves finding a common denominator, which is the least common multiple of the denominators of the fractions.

Once you have found the common denominator, you can convert each fraction so that it has the same denominator, and then you can add or subtract the numerators to find the final answer.

Here's an example word problem:

A baker has 3/4 of a bag of flour and 1/2 of another bag of flour. How much flour does the baker have in total?

To solve this problem, we need to find a common denominator for 3/4 and 1/2. The least common multiple of 4 and 2 is 4, so we can use 4 as the common denominator. We then convert each fraction so that it has a denominator of 4:

3/4 = (3 x 4) / (4 x 1) = 12/4

1/2 = (1 x 2) / (2 x 1) = 2/4

Now that both fractions have the same denominator, we can add their numerators to find the total:

12/4 + 2/4 = 14/4 = 3 1/2

So, the baker has 3 1/2 bags of flour in total.

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Answer:

9.75

Step-by-step explanation:

7+2.75 =9.75

Based on exponential growth, city with a population of 700,000 growing at an annual rate of 7% will be 2,898,394 in 21 years.

Exponential growth refers to an increase where a constant proportional amount is added to the initial value.

Exponential growth function can be modeled as follows:

f(x)=a(1+r)ˣ

Where:

f(x) = exponential growth function

a = initial amount

r = growth rate

{x} = number of time intervals

The current population of the city, a = 700,000

The annual growth rate, r = 7% = 0.07

The number of time intervals, x = 21 years

The population in 21 years = 700,000 x (1 + 0.07)²¹

= 700,000 x (1.07)²¹

= 700,000 x 4.14056237

= 2,898,394

Thus, using an exponential growth rate, the population of the city will grow to 2,898,394 after 21 years.

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Derivative of arcsin x is 1/√1-x²

The derivative of arcsin x is denoted by d/dx(arcsin x) (or) d/dx(sin-1x) (or) (arcsin x)' (or) (sin-1x)'. Its value is 1/√1 - x². We will prove it in two methods in the upcoming sections. The two methods are:

Using the chain rule

Using the first principles

Derivative of arcsin x Formula

The derivative of the arcsin function is,

d/dx(arcsin x) = 1/√1 - x² (OR)

d/dx(sin^-1x) = 1/√1 - x²

Derivative of Arcsin

d/dx(arcsinx) (or) d/dx(sin^-1x)

=1/√1-x²

arcsinx=1/√1-x²

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These functions have restricted domains: f(x) is defined only for x >= 3 and g(x) is defined only for x < 3.

A function is a mathematical concept that assigns exactly one output (or "output value") to each input (or "input value"). It provides a way to describe the relationship between inputs and outputs and can be thought of as a machine that takes inputs and produces outputs. Functions can be represented using equations or graphs.

In mathematical terms, a function can be formally defined as a set of ordered pairs (x,y), where x is the input (independent variable) and y is the output (dependent variable). The output value for a given input value is unique, and a single input value cannot correspond to multiple output values.

Functions are widely used in mathematics, science, and engineering to model real-world phenomena and to describe mathematical relationships. There are many types of functions, including linear functions, polynomial functions, exponential functions, logarithmic functions, and trigonometric functions, among others.

The equation y = 2|x - 3| + 5 can be rewritten as two separate linear functions, f(x) and g(x), as follows:

f(x) = 2(x - 3) + 5, for x >= 3

g(x) = -2(x - 3) + 5, for x < 3

So, for x >= 3, y is given by the linear function f(x) = 2(x - 3) + 5, and for x < 3, y is given by the linear function g(x) = -2(x - 3) + 5.

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all solutions r made there...pls like, follow for more answers

Since R is inversely proportional to A, the numerical value of A when R equal 9 is 2.

Proportional relationships are relationships between two variables where their ratios are equivalent.

Inversely proportional relation is expressed as;

R ∝ 1/A

then, R = k/A

Where k is the proportionality constant.

Given that;

First, we determine the proportionality constant.

R = k/A

12 = k/1.5

k = 18

Now, the value of A when R = 9 will be;

R = k/A

A = k/R

A = 18 / 9

A = 2

Therefore, the value of A is 2.

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The probability that the first child selected will be a girl is 0.5 or 50%.

The probability of a child being a boy or a girl is equal, as long as the parents are healthy and have no genetic conditions that affect the gender of the child. In general, the chance of having a boy or a girl is about 50-50.

However, it is important to understand that each individual birth is a random event and that the probability of having a boy or a girl is calculated over a large number of births.

This means that even though the overall probability of having a boy or a girl is equal, it is possible to have a run of several boys or several girls in a row.

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Answer:

B

Step-by-step explanation:

There's really no work to show, but... you see those two little blue lines under the 127? Now you see the ones under the P? That means that the those two angles are the same

Given the class width of 6 and the minimum value of 12, the maximum value in the first class would be 12 + 6 - 1 = 17. The maximum value in the 6th and last class would be 17 + (6 x 5) = 42. Hence, the largest possible value in the data set is '42'.

A frequency table is used to organize and represent the distribution of a set of data. In this case, the data set has 6 classes and a class width of 6. This means that the range of values in each class is 6 units. The minimum value in the data set is 12, so the first class starts at 12 and ends at 12 + 6 - 1 = 17. This is because the class width is 6, so the end value of the first class would be the starting value plus the class width minus 1.

For the last class, the end value would be 17 + (6 x 5) = 42. This is because the end value of the first class is 17 and each subsequent class increases by 6 units. The largest possible value in the data set would be the end value of the last class, which is 42. This means that any value greater than 42 would not be part of the data set and would not be included in the frequency table.

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This refers to the summation of the area including the base(s) and the curved parts of an object. It is the total area occupied by the surface of the object.

Solving for answers we have:

D =  6 inches (diameter of a cone's circular base )

s = 8 inches (the slant height of the cone)

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The frequency function in Excel can be used to determine the frequency of student absences based on the criteria in a specified range.

To simultaneously insert the FREQUENCY function in cells I12:I14, you can use the following steps:

Select the range I12:I14

Type the following formula in the formula bar: "=FREQUENCY(data_range,bin_range)"

Replace "data_range" with the range of values containing the student absences

Replace "bin_range" with the range of values containing the criteria (H12:H14)

Press enter to insert the formula in all of the selected cells

To calculate the results as percentages, divide the function by the number of records in the data and multiply by 100. You can do this by modifying the formula as follows:

=FREQUENCY(data_range,bin_range)/COUNT(data_range)*100

Replace "data_range" and "bin_range" with the appropriate cell references.

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5/4  is fraction and  1.25 is decimal of the number 125.

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To find the volume of the solid using the slicing method, we need to find the area of each cross-sectional square and then multiply it by the length (or height) of the solid.

Let's call the height of the solid h and the side length of each square cross-section s. The radius of the base of the solid is 15, so the diameter of the base is 2 * 15 = 30. Half of the diameter is the chord of the semicircular base, and it's also equal to the side length of the square cross-section.

So, s = 30 / 2 = 15

Since the cross sections are squares, the height of the solid (h) is equal to the side length of the square (s).

Now we can find the area of each cross-sectional square:

A = s^2 = 15^2 = 225

Finally, to find the volume of the solid, we need to multiply the area of each cross-sectional square by the height of the solid:

V = A * h = 225 * 15 = 3375

So, the volume of the solid is 3375 cubic units.

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Let's call the height of the solid h and the side length of each square cross-section s. The radius of the base of the solid is 15, so the diameter of the base is 2 * 15 = 30. Half of the diameter is the chord of the semicircular base, and it's also equal to the side length of the square cross-section.

Now we can find the area of each cross-sectional square:

A = s^2 = 15^2 = 225

V = A * h = 225 * 15 = 3375

The y values are also equal at x=-2. Thus, f(-2) = g(-2) is true. D is the right answer, thus.

Quantity and their permutations, relationships and associated tissues, shapes and their locales, and locations in which they are found are all components of the mathematics classroom. The relationship among a group of inputs, each of which has a productivity commission, is referred to by the term "function." A function is a relationship involving inputs and outputs where each input produces a single, unique result. Every function has an area and a codomain, often known like a scope. F is typically used to describe functions (x). An x is the input. Based on the following criteria, there are four primary categories of functions that are available: on functions, yet another functions, many-to-one functions, within functions, and on functions.

given

In the given graph, the two lines intersects at x = -2

And intersection point is that point , where the y values of the two graphs are equal .

That is  f(x) = g(x)

The y values are also equal at x=-2. Thus, f(-2) = g(-2) is true. D is the right answer, thus.

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Caesars should use variables such as weather, season, holidays, local events, and occupancy rate to predict check-ins.

1. Weather: The weather conditions on a given day can impact the number of check-ins, as people may be less likely to travel or spend time outdoors in inclement weather.

2. Season: The time of year can also play a role in the number of check-ins, as some seasons may be busier than others due to holidays or peak travel times.

3. Holidays: Holidays can have a significant impact on the number of check-ins, as people may travel more during these times for vacation or to visit family.

4. Local events: Any local events taking place near the Caesars property, such as concerts or sporting events, could also impact the number of check-ins.

5. Occupancy rate: The occupancy rate of the Caesars property on previous days can also provide insight into the expected number of check-ins for a given day, as it can indicate trends or patterns in customer behavior.

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The correct statement is:

Given a p-value of 0.02 and a significance level of 3%, you should reject the null hypothesis.

Given,

Four statements regarding p value and null hypothesis.

Now,

Depends on if the p-value is less or more than the significance level:

Hence the correct statement for this problem is given by:

Given a p-value of 0.02 and a significance level of 3%, you should reject the null hypothesis.

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Answer:

a) 2

b)4

c) 8

To find the solution to a fractional power, you root the number with the denominator and the amount of times you times the number by itself is the numerator e.g. 16^3/4 is 8.

Hope this helps  

Answer:

a.) 2

b.) 4

c.) 8

Step-by-step explanation:

When an exponent is a fraction, you use the denominator as an exponent, then use the denominator as the root.

a.) [tex]8^{\frac{1}{3}}=\sqrt[3]{8^{1}}[/tex]

[tex]8=2*2*2[/tex]

[tex]\sqrt[3]{8}=2[/tex]

b.) [tex]8^{\frac{2}{3}}=\sqrt[3]{8^{2}}[/tex]

[tex]64=4*4*4[/tex]

 [tex]\sqrt[3]{64}=4[/tex]

c.) [tex]16^{\frac{3}{4}}=\sqrt[4]{16^{3}}[/tex]

[tex]4096=8*8*8*8[/tex]

[tex]\sqrt[4]{4096}=8[/tex]

The most consistent player is Player A, with a standard deviation of 1.4.

To compare the variability of the two players' data, we can use either the interquartile range (IQR) or the standard deviation.

The interquartile range (IQR) is a measure of the spread of the data that takes into account the values of the first quartile (Q1), the median, and the third quartile (Q3). It is calculated as the difference between Q3 and Q1. A smaller IQR indicates that the data is more tightly clustered and, therefore, more consistent.

The standard deviation is a measure of the average spread of the data from the mean. A smaller standard deviation indicates that the data is more tightly clustered around the mean and, therefore, more consistent.

In this case, we can calculate the IQR and standard deviation for each player's data. After sorting the data and finding the quartiles, we get the following:

Player A:

Q1: 1.5

Median: 2

Q3: 3

IQR: 1.5

Standard deviation: 1.4

Player B:

Q1: 2

Median: 4

Q3: 5

IQR: 3.5

Standard deviation: 2.9

From the calculations, we can see that Player A has a smaller IQR (1.5) and a smaller standard deviation (1.4) compared to Player B (IQR = 3.5, Standard deviation = 2.9). This means that Player A's data is more tightly clustered around the median, indicating that he is more consistent in his performance.

Therefore, the correct answer is (C).

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--The given question is incomplete; the complete question is

"The table shows the number of goals made by two hockey players during the season's games.

Player A                  Player B

2, 3, 1, 3, 2, 2, 1, 3, 6  1, 4, 5, 1, 2, 4, 5, 5, 11

Which measure of variability is best for the data, and which player is more consistent?

A) Player A is the most consistent, with an IQR of 1.5.

B) Player B is the most consistent, with an IQR of 3.5.

C) Player A is the most consistent, with a standard deviation of 1.4.

D) Player B is the most consistent, with a standard deviation of 2.9."--

Answer:

one so that is the ansa mi

The factor for the Expression 7[tex]z^4[/tex]-5 + 10y³ + 20 is (y³ + 2)

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

7[tex]z^4[/tex]-5 + 10y³ + 20

Factorizing the expression

7[tex]z^4[/tex]-5 +10(y³ + 2)

So, the factor in the expression is (y³ + 2).

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The table you mentioned shows that the area of the bottom of the box, f(x), is equal to x2 when one side of the box is x feet long.

This can be written as f(x) = x2. You can also use this equation to calculate the area of the bottom of any rectangular box if you know the length of one of its sides. For example, if one side of the box is 4 feet then the area of the bottom of the box is f(4) = 42 = 16 square feet.

The bottom of the box refers to the bottom surface of a rectangular box. It is the surface that is parallel to the surface on which the box is resting. The area of the bottom of a box can be calculated by multiplying the length of one side of the box by the width of the other side. The bottom of the box can be used to hold items, and can also provide a stable platform for stacking items.

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Answer:

3/4

Step-by-step explanation:

[tex] \sqrt{ \frac{9 }{16?} \ } [/tex]

[tex] \sqrt{9 } [/tex]

=3

[tex] = 3[/tex]

[tex] \sqrt{16} [/tex]

[tex] = 4[/tex]

ans=3/4

7x+2y=1 is the formula used to represent linear equations in two variables.

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Answer: - 1/3

Step-by-step explanation:

To solve this algebraic expression, you will need to evaluate the equation like this:

13(9x + 3) = 3x + 1

117x + 39 =  3x + 1

117x + 39 - 39 =  3x + 1 - 39

117x = 3x - 38

117x - 3x = 3x - 38 - 3x

114x = -38

 x =  - 1/3

Therefore, the solution to this equation is -1/3. Hope this helps!

Answer:

y = -6

Step-by-step explanation:

We know the formula for slope is:

m = ( y2-y1)/(x2-x1)

We are given the two points using a variable and the slope.

-8 = (2-y)/(3-4)

-8 = (2-y)/(-1)

Multiply each side by -1.

8 = 2-y

Subtract 2 from each side.

8-2 = 2-y-2

6 = -y

Multiply by -1.

-6 =y

Answer:

y = -6

Step-by-step explanation:

The formula to find the slope is:

[tex]m = \frac{y_1 - y_2}{x_1-x_2}[/tex]

Given that,

( 4, y ) ⇒ ( x₁ , y₁ )

( 3, 2 ) ⇒ ( x₂ , y₂ )

m ( slope ) = -8

Accordingly, we have to find the value of y₁.

Let us find it now by making y₁ the subject.

[tex]\sf m = \frac{y_1 - y_2}{x_1-x_2} \\\\-8 = \frac{y_1 - 2}{4-3}\\\\-8 = \frac{y_1 - 2}{1}\\\\Multiply\:\:Both\:\:sides\:\:by\:\:1.\\\\-8=y_1-2\\\\Add \:\:2\:\:to\:\:both\:\:sides.\\\\-8+2=y_1\\\\-6=y_1=y[/tex]

One possible equation to model the population of foxes, P, as a function of time, t, in years, based on the information provided, is:

This equation uses a sinusoidal function with a period of 2.2 years (the time between minimum and maximum values) and an amplitude of 400 (the difference between minimum and maximum values).

The phase shift of 2.9 years is also incorporated, so that the minimum value of 200 foxes occurs at t = 2.9 years. The vertical shift of 500 was added to ensure that the maximum value of 800 foxes is achieved.

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