Evaluate -2/5 - 4/5 + (-9/10)

Answer:

The slope is 2 and the y-intercept is three

Step-by-step explanation:

So y-intercept is the point in which the line crosses the y axis.

And the slope is rise/run or rise over run so it goes over one and up two meaning it will be 2/1 and the slope is two.

The correct scientific notation for the number 0.00050210 is 5.0210 x 10^(-4).

Here's a step-by-step explanation:

1. To convert a decimal number to scientific notation, we need to move the decimal point until we have a number between 1 and 10. In this case, we need to move the decimal point 4 places to the right to get 5.0210.

2. Next, we determine the power of 10 by counting the number of places we moved the decimal point. In this case, since we moved it 4 places to the right, the power of 10 is -4.

3. Finally, we write the number in the form of "a x 10^n", where "a" is the number between 1 and 10 (5.0210 in this case), and "n" is the power of 10 (-4 in this case).

So, the correct scientific notation for 0.00050210 is 5.0210 x 10^(-4).

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Question- The correct scientific notation for the number 0.00050210 is: a. 5.0210 x 10° b. 5.021 x 10 c. 5.021 x 10 d. 5.0210 x 10 e. None of the choices listed are correct.

The scientific notation for 0.00050210 is 5.0210 x 10^-4. It was calculated by moving the decimal point 4 places to the right, resulting in 5.0210, and then multiplying by 10 to the power of -4.

The given number is 0.00050210. We're trying to express it in scientific notation which is a shorthand way to write numbers that are either very large or very small by representing them as the product of a number (between 1 and 10) and a power of ten.

First, let's consider the number 0.00050210. We shift the decimal point 4 places to the right until we have a number that is between 1 and 10. So, we get 5.0210. Then, we multiply by 10 to the power of minus the number of places we moved the decimal (in this case, -4) to write the scientific notation.

So, the scientific notation of 0.00050210 is 5.0210 x 10^-4.

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Answer:

c=√a²b²

Step-by-step explanation:

Answer:

B (2.72, 1)

Step-by-step explanation:

The equation is y = 2.72x is in slope intercept form y = mx + b

since there is no b (y-intercept), b = 0

So you could rewrite the equation y = 2.72x + 0

You're first point is b which is 0 on the y axis.

From the 0 you are going to do the slope, which is m.

The slope is 2.72. Since it is positive you will go up 2.72 and right 1.

The inverse of the table and the function given are (5-x)/2 and y = -9x/2 respectively.

The standard linear equation is represented as y = mx + b

where:

m is the slope

b is the intercept

Using the coordinate points (0, 5) and (1, 3) from the table;

Slope = 3-5/10
Slope =-2

The y-intercept is 5

The equation of the table will be y = -2x + 5

Find the inverse

y = -2x + 5

x = -2y + 5

2y = 5 - x

y = (5-x)/2

f^-1(x) = (5-x)/2

For the function

f(x) = -2/9 x

x = -2/9 y

9x = -2y

y = -9x/2

Hence the inverse of the table and the function given are (5-x)/2 and y = -9x/2 respectively.

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Given two calculations are different.

What is a square of a number?

The square of any number can be calculated by multiplying the number by itself twice.

Let 'a' be any number then the square of this number 'a' will be

                        a² = a × a

Now  - 3² = - (3) × (3)

               = -9  ----------(I)

and (-3)² = (-3) × (-3)

              = 9 ----------(II)

By observing (I) and (II) we can say that in the second case just because of the scope of brackets the square of -3 would result in 9.

But in the first case square of 3 would give 9 and because of the minus sign, it gave -9.

Hence, These two calculations are different.

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Answer:

17/ 30 ???

Step-by-step explanation:

.....................

Answer:

17/30

Step-by-step explanation:

2          1                   =            17

5          6                  =            30

Answer:

37

Step-by-step explanation:

10z - 3 = 10(4) - 3

=40-3

=37

Answer:

37

Step-by-step explanation:

10*4-3 (z=4)

40-3

37

Hope it helps you

Answer:

Jwvqucagabanakabakqbaoanq??

ywuquqkqkakak

Answer:

a. y-intercept:(0,  -6), x-intercepts: (3, 0) and (-2, 0). vertex: (0.5, -6.25)

b. y-intercept: (0, 6), x-intercepts(3, 0) and (-2, 0). vertex: (0.5, 6.25)

Step-by-step explanation:

a:

 So finding the y-intercept is really easy and is simply when x=0. If you plug in 0 as x it makes \(y=(0)^2-0-6\) which simplifies to -6, which is the y-intercept. As for the x-intercepts you can calculate that by using the quadratic equation \(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\). In this case a=1, b=-1, c=-6. So plugging those values in you get \(x=\frac{-(-1)\pm\sqrt{(-1)^2-4(1)(-6)}}{2(1)}\), which simplifies to \(x=\frac{1\pm5}{2}\). This gives you the x-intercepts 6/2 and -4/2 which are 3 and -2. The vertex can be calculated by manipulating the equation so it's in the form of \(y=(x-h)^2+k\) where (h, k) is the vertex of the parabola. This is done by moving c to the other side and then completing the square and the isolating y. So the first step will be

Move c to the other side

\(y+6=x^2-x\)

Complete the square by adding (b/2)^2

\(y+6+0.25 = x^2-x+0.25\)

Rewrite as square binomial

\(y+6.25 = (x-0.5)^2\)

Isolate y

\(y=(x-0.50)^2-6.25\)

(h, k) = 0.50, -6.25 which is the vertex

b: To identify the y-intercept you plug in 0 as x which will only leave c which in this case is 6 which is the y-intercept. (0, 6). To identify the x-intercepts you can simplify plug in the values a, b, c into the quadratic equation which was stated in the previous answer. In this case a, b, c = -1, 1, 6. Plugging these values in gives the equation \(y=\frac{-(1)\pm\sqrt{1^2-4(-1)(6)}}{2(-1)}\). which simplifies to \(x=\frac{-1\pm5}{-2}\) which gives the values -2 and 3. To find the vertex it's the same process as before

Factor out -1

\(y=-(x^2-x-6)\)

Add 6 to both sides (on the left side add -6 since -1 was factored out).

\(y-6=-(x^2-x)\)

Complete the square by adding (b/2)^2 to both sides (add -(b/2)^2 to left side since -1 was factored out)

\(y-6-0.25 = -(x^2-x+0.25)\)

Rewrite as square binomial

\(y-6.25=-(x-0.5)^2\)

Add 6.25 to both sides

\(y=(x-0.50)^2+6.25\)

(h, k) = (0.50, 6.25)

When you graph the parabolas you'll notice there just flipped relative to the x-axis. This can be deduced by simply looking at the two equations, since the two equations have the same absolute value coefficients, the signs are just different, and more specifically they're all opposite. If you took the first equation and multiplied the entire right side by -1 you would get the same equation. And since that equation really represents the value of y (since it's equal to y) you're reflecting it across the x-axis.

Answer:

a) y-intercept (0,  -6); x-intercepts (3, 0) and (-2, 0); vertex (0.5, -6.25)

b) y-intercept (0, 6); x-intercepts (3, 0) and (-2, 0); vertex (0.5, 6.25)

Step-by-step explanation:

The length of median A is 11.7.

The point of intersection of a triangle's medians is its centroid (the lines joining each vertex with the midpoint of the opposite side).

If the triangle has its vertices as   (x_1, y_1), (x_2, y_2) , \: (x_3, y_3), then the coordinates of the centroid of that triangle is given by:

\((x,y) = \left( \dfrac{x_1 + x_2 + x_3}{3} + \dfrac{y_1 + y_2 + y_3}{3} \right)\)

Given;

The sides of triangle

a = 4, b = 5 and c = 6

The median of triangle =½√(2b2+2c2-a2).

=(2*5*5+2*6*6-4*4)

=(50+72-16)

=\(\sqrt{138}\)

=11.7

Therefore, the median of triangle will be 11.7

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Answer:

your mom

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The formula to calculate the new value after an increase is to multiply the original value by the percentage of the increase.

The formula to calculate the new value after an increase is to multiply the original value by the percent of the increase. For example, if the original value is $100 and the increase is 10%, the new value would be $100 x 1.10 = $110. This formula can be applied to any original value and any percentage increase. It is useful for calculating the new value after applying a percentage increase, such as when calculating a pay raise or the cost of goods after a price increase. The formula can also be applied to calculate the new value after a percentage decrease, by multiplying the original value by 1 minus the percentage of the decrease.

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The complete question is

the formula for calculating the value after an increase by multiplying the original value by the percent for a new value is: value after increase  by multiplying the original value by the percent for a new value?

Treatment Group:

$\mu = 22, \sigma = 2.30$

Placebo Group:

$\mu = 22, \sigma= 0.77$

The radius of each cylinder is approximately 3.49 cm and the length of the plastic strip is approximately 65.84 cm.

Cylinder is a basic 3 dimensional solid with a curved surface. A cylinder can be identified as a prism with circular base.

The cross-section of a cylinder gives a circle whose area can be represented by πr² where r is the radius of the base of the cylinder.

Here the plastic wire encloses the area of cross-section of three cylinders.

Therefore area of cross-section of one cylinder=115÷3=(115/3) cm ²

Since area of cross-section of a cylinder=πr²

Therefore πr²=(115/3)

or, r=3.4931...

or, r≈3.49 cm

Hence the radius of each cylinder is approximately 3.49 cm

Now the plastic strip covers 3 cylinders .

Circumference of each cross-section of cylinder is given by =2πr

Total length of 3  cylinders = 2πr×3 = 6πr cm

Therefore total length= 64.843...cm ≈ 65.84 cm

Therefore the length of the plastic strip is approximately 65.84 cm

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The asymptotic notation relationship between the functions \(f(n) = n^3 (8 + 2 cos 2n)\) and \(g(n) = n^2 + 2n^3 + 3n\) is f(n) ∈ Θ(g(n)). Therefore, the growth rates of f(n) and g(n) are primarily determined by the cubic terms, and they grow at the same rate within a constant factor.

To determine the asymptotic notation relationship between the functions \(f(n) = n^3 (8 + 2 cos 2n)\) and \(g(n) = n^2 + 2n^3 + 3n\), we need to compare their growth rates as n approaches infinity.

Θ (Theta) Notation: f(n) ∈ Θ(g(n)) means that f(n) grows at the same rate as g(n) within a constant factor. In other words, there exists positive constants c1 and c2 such that c1 * g(n) ≤ f(n) ≤ c2 * g(n) for sufficiently large n.

o (Little-o) Notation: f(n) ∈ o(g(n)) means that f(n) grows strictly slower than g(n). In other words, for any positive constant c, there exists a positive constant n0 such that f(n) < c * g(n) for all n > n0.

ω (Omega) Notation: f(n) ∈ ω(g(n)) means that f(n) grows strictly faster than g(n). In other words, for any positive constant c, there exists a positive constant n0 such that f(n) > c * g(n) for all n > n0.

Now let's analyze the given functions:

\(f(n) = n^3 (8 + 2 cos 2n)\\g(n) = n^2 + 2n^3 + 3n\)

Since both functions have the same dominant term, we can say that f(n) ∈ Θ(g(n)) because they grow at the same rate within a constant factor. The other notations, o and ω, are not applicable here because neither function grows strictly faster nor slower than the other.

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Figure R'S'T'U' is the image of Figure RSTU after a translation of 2 units left and 2 units down, and a reflection across the y-axis.

Examples of transformations are given as follows:

The rule applied for the translation is given as follows:

(x,y) -> (x - 2, y - 2).

Hence:

The rule applied for the reflection is of:

(x, y) -> (-x, y).

Hence the figure was reflected over the y-axis.

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\(\huge\text{Hey there!}\)

\(\mathsf{x^3 + 2x = 40}\)

\(\large\text{Subtract 40 to both sides:}\)

\(\mathsf{x^3 + 2x - 40 = 40 - 40}\)

\(\large\text{Simplify it:}\)

\(\mathsf{x^3 + 2x - 40 = 40 - 40}\)

\(\mathsf{x^3 + 2x - 40= 0}\)

\(\large\text{If you're familiar with the cubic formula use that to solve this portion:}\)

\(\large\textsf{If you're unfamiliar with the cubic formula we will study that another}\\\large\textsf{time whenever you're ready to understand it }\heartsuit\)

\(\mathsf{x = 3.22524}\)

\(\mathsf{x \approx 3}\)

\(\huge\text{Therefore, your answer should be: \boxed{\mathsf{3.22524}}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

Answer: ∠A=45° & ∠B=45°

Step-by-step explanation:

In triangle ABC, all angles are less than 180° but their sum is 180°

For the trigonometric statements  

sin(A)=cos(B)

sin(B)=cos(A)

These are true when these angles that are A and B are equal and on these angles the sin and cos value must be same.

Hence, both angles are of 45°

Using compound interest, it is found that:

a) Pietro will have $1,719.49 in his account after 5 years.

b) The interest rate is of 8.19%.

The amount of money earned, in compound interest, after t years, is given by:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

In which:

Item a:

Then:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

\(A(5) = 1500\left(1 + \frac{0.0275}{2}\right)^{2(5)}\)

\(A(5) = 1719.49\)

Pietro will have $1,719.49 in his account after 5 years.

Item b:

Then:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

\(1.5(1500) = 1500\left(1 + \frac{r}{4}\right)^{20}\)

\(1.5 = (1 + \frac{r}{4}\right)^{20}\)

\(\sqrt[20]^{(1 + \frac{r}{4}\right)^{20}} = \sqrt[20]{1.5}\)

\(1 + 0.25r = 1.02048015365\)

\(0.25r = 0.02048015365\)

\(r = \frac{0.02048015365}{0.25}\)

\(r = 0.0819\)

The interest rate is of 8.19%.

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Answer:

It should be -5, 5 to the power of -1, 0.5, 5 to the power of 0 in least to greatest form.

Step-by-step explanation:

Among the three options provided, the cross-sectional data set is the demographic data. Correct option is B).

Cross-sectional data refers to a type of data that captures information about different individuals, entities, or units at a specific point in time. It provides a snapshot of a population or sample at a particular moment, allowing for comparisons and analysis of various characteristics or variables. In the case of demographic data, it typically includes information about individuals' age, gender, education level, income, and other demographic attributes. This data set does not capture changes or trends over time but rather provides a snapshot of the population's characteristics at a specific time.

On the other hand, the BCAD data and links could refer to data related to building codes, regulations, and their corresponding references, while code cases may refer to specific instances or examples of code violations or compliance. These data sets may be specific to certain incidents or cases and do not necessarily capture information about a population or sample at a particular point in time, making them less likely to be considered cross-sectional data.

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Answer:

Step-by-step explanation:

sean

Triangular prism is an example of a solid from which a triangular, hexagonal, and trapezoidal cross-section can be formed.

A triangular prism is a polyhedron that is made up of triangular bases and three rectangular sides. It is a three-dimensional shape that has three side faces and two base faces, connected to each other through the edges to the vertex.

Some properties of a triangular prism:

Thus, triangular prism is an example of a solid from which a triangular, hexagonal, and trapezoidal cross-section can be formed.

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The code sorts the skill array in ascending order.

It then creates a HashMap to store the number of occurrences of each skill level. The left and right pointers are initialized to point to the first and last elements of the skill array. The result variable is used to store the sum of the effectiveness of all teams that can be created. The code then iterates through the skill array using the left and right pointers. If both pointers point to skills that have more than one occurrence, then two of each skill are used to create the team, and effectiveness is added to the result.

If only one pointer points to a skill with more than one occurrence, then one instance of that skill is paired with one instance of the other skill to form a team. Otherwise, if both pointers point to skills that have only one occurrence, then one instance of each skill is used to create the team. In any case, when a team is created, the HashMap is updated accordingly.

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We have proven that no two events a and b can be independent unless either a or b is the whole sample space or the empty set below.

A sample space can be defined as the set of all possible outcomes of any experiment.

We are already aware that the outcomes of this die are going to be (1,2,3,..p). If we have a pair of proper events A, B which are independent, this would mean that = A∩B={∅}  (i)

This is a contradiction. So, now we suppose that = A∩B=C, for some proper event C (ii)

Using the values of (i) and (ii), we get -

= |C|p=P(A∩B)=P(A)P(B)=|A||B|p2.

= p|C|=|A||B|.

From this, we understand that neither A nor B are going to be full spaces and hence, no two events a and b are independent and 0<|A|<p and 0<|B|<p. Since |C| is also going to be less than 0 and p is prime, p divides either |A| or |B|.  if p was not prime (say, p=4), then you would only need the factors of p to divide either |A|,|B|, so, it becomes necessary for p to be a prime number. Hence, proved.

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Answer:

Step-by-step explanation:

The average rate of change of a function over an interval is equal to the total change in the function's output divided by the total change in the input over the interval. In other words, it is the slope of the secant line that connects the two points on the function defined by the interval.

If the function is represented by y = f(x), the average rate of change of the function over the interval [-4, -3] can be calculated as:

Δy / Δx = (f(-3) - f(-4)) / (-3 - (-4))

So, to calculate the average rate of change, you would need to know the values of the function f(x) at x = -3 and x = -4. If you provide the equation for the function f(x), I can help you find the average rate of change.

The new differential equation modeling the population of the island P is P′=3(M−P)−7.  

Given,  the population of Cook island is modeled by a logistic equation

P′=k(M−P) with growth rate k=3 and carrying capacity M=6000 with time t in years.

Starting in the year 2000, 7 citizens of Cook island have left every year to become mathematicians, never to return.To determine the new differential equation modeling the population of the island P, we need to modify the logistic equation as follows:

For every year since 2000, the population has decreased by 7.

Therefore, the equation that models the decrease in population is -7, and it has to be subtracted from the original equation.

Therefore, we obtain the new differential equation as P′=3(M−P)−7.

The above equation models the rate of change of population for Cook island.

Thus, the new differential equation modeling the population of the island P is P′=3(M−P)−7.

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Question 1a

To calculate the book value at the end of the first year using straight-line depreciation, we need to determine the annual depreciation expense first. The straight-line method assumes that the asset depreciates by an equal amount each year over its useful life. Therefore, we can use the following formula to calculate the annual depreciation:

Annual Depreciation = (Cost - Salvage Value) / Useful Life

Substituting the given values, we get:

Annual Depreciation = ($200,000 - $20,000) / 10 years = $18,000 per year

This means that the tractor will depreciate by $18,000 each year for the next 10 years.

To determine the book value at the end of the first year, we need to subtract the depreciation expense for the year from the original cost of the tractor. Since one year has passed, the depreciation expense for the first year will be:

Depreciation Expense for Year 1 = $18,000

Therefore, the book value of the tractor at the end of the first year will be:

Book Value = Cost - Depreciation Expense for Year 1

= $200,000 - $18,000

= $182,000

So the book value of the tractor at the end of the first year, December 31, 2022, using straight-line depreciation is $182,000. so the answer is D

Question 1(b)

To determine the farmer's noncurrent liabilities, we need to use the information provided to calculate the total liabilities and then subtract the current liabilities from it. Here's the step-by-step solution:

Calculate the total current liabilities using the current ratio:

Current Ratio = Current Assets / Current Liabilities

2 = $80,000 / Current Liabilities

Current Liabilities = $80,000 / 2

Current Liabilities = $40,000

Calculate the total liabilities using the debt/equity ratio:

Debt/Equity Ratio = Total Liabilities / Owner Equity

1.0 = Total Liabilities / $100,000

Total Liabilities = $100,000 * 1.0

Total Liabilities = $100,000

Subtract the current liabilities from the total liabilities to get the noncurrent liabilities:

Noncurrent Liabilities = Total Liabilities - Current Liabilities

Noncurrent Liabilities = $100,000 - $40,000

Noncurrent Liabilities = $60,000

Therefore, the farmer's noncurrent liabilities are $60,000. so the answer is B.