Find MN to the nearest tenth?

A. 11.34
B. 16.1
C. 39.6
D. 23.8

Answer:

The answer you're looking for is 1470.

Step-by-step explanation:

The method I used was PEMDAS

Since there was no parenthesis, I simplified the exponents.

2.130 x 10³ - 6.6 x 10² = ?
2.130 x 1000 - 6.6 x 100 = ?

After that, I multiplied all terms next to each other.

2.130 x 1000 - 6.6 x 100 = ?
2130 - 660 = ?

The final step I did was to subtract the two final terms and ended up with 1470 as my final answer.

1470 = ?

I hope this was helpful!

Using Marked recapature formula for estimation on population size we get,

the estimate for total population size is 1200.

Marked recaputure Method :

first step is to capture and mark a sample of individuals. The assumption behind mark-recapture methods is that the proportion of marked individuals recaptured in the second sample represents the proportion of marked individuals in the population as a whole. In algebraic terms,

R/S = M/N

where R --> second time marked

S---> size of sample second time

N --> estimate population size

M ---> Marked in start point

We have given that ,

Total marked turtles by researchers (M) = 800

Second time total sample size (S) = 300

second time marked turtles(R) = 200

we have to find out estimate for total population size .

For this , Mark -Recapture method is very efficient to calculate estimate for total population size.

putting all known values in above formula we get, R/S = N/M

=> 200/300 = 800/N

=> 800× 300 = N× 200

=> N × 200 = 240000

=> N = 240000/200

=> N = 1200

so, the estimate for total population size is 1200.

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Answer:

32+30+x=180

Step-by-step explanation:

Answer:

Equation would be

X= 32°+30°+x

Step-by-step explanation:

X= 180°

Hope this helped...

Answer:

$36,075

Step-by-step explanation:

Cheryl's annual rent as a function of her annual sales is:

\(R = 1,400*2*12+(x-100,000)*0.055\)

Where x are her annual sales, if x > $100,000. This function considers her fixed rent of $2 per square foot for 12 months, and her sales dependent rent.

Since she made $145,000 last year, her annual rent is:

\(R = 1,400*2*12+(145,000-100,000)*0.055\\R=\$36,075\)

Her annual rent is $36,075.

Answer:

Step-by-step explanation:

Term Definition

Linear regression line The line that goes through a set of points either exactly or approximately.

Difference The result of a subtraction operation is called a difference.

Answer:

0.6 + 15b + 4 = 25.6

15b +4 = 25

15b = 25 - 4

15b = 21

b = 21/15

b = 7/5

hope it helps

Answer:

Exact Form:

b=7/5

We can clearly see that the area must be more than \($\frac{8 \pi}{3}$\), and the only such answer is \(3 \pi\).

Part of what Spot can reach is \($\frac{240}{360}=\frac{2}{3}$\) of a circle with radius 2, which gives him \($\frac{8 \pi}{3}$\). He can also reach two\($\frac{60}{360}$\)parts of a unit circle, which combines to give \($\frac{\pi}{3}$\). The total area is then \($3 \pi$\).

A circle is a two-dimensional closed shape in which the set of all points in the plane is equidistant from a particular point known as the "centre."

A Sphere is a three-dimensional object, whereas a Circle is a two-dimensional figure. All points in a circle are the same distance from its center along a plane, whereas all points in a sphere are equidistant from the center along any of the axes.

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Answer:

Step-by-step explanation:

Only a straight line can be formed at the intersection of a plane with another plane. The faces of a cube are planes, so a 2-dimensional (planar) cross section of a cube cannot be a curve. It cannot be an ellipse or circle.

The intersection of a plane with a cube can be a polygon with 3, 4, 5, or 6 sides. That is, the 2-D cross section of a cube can be ...

  triangle, rectangle, square, pentagon, hexagon

__

The attachment shows some possibilities.

Answer:

a) The sinusoidal equation is;

The function is h = -24·cos[π(t )] + 24

The sketch of one full revolution is attached

b) The height of the nail at 0.8 seconds is 43.42 cm

Step-by-step explanation:

The sinusoidal equation that models the nails height can be given as follows;

y = A·cos[B(x - C)]+D

A = The amplitude = Half maximum height =  48/2 = 24 cm

The period = 2·π/B = Time to complete one oscillation = 2 seconds

∴ B = 2·π/2 = π

x = t  = Time

C = The horizontal shift

D = the vertical shift = 24 cm

y = The height of the nail = h

We have;

h = -24·cos[π(t - C)] + 24

At t = 0, h = 0, therefore, we have;

0 = -24·cos[π(0 - C)] + 24

24·cos[π(0 - C)] = 24

∴ cos[π(0 - C)] = 24/24 = 1

π(0 - C) = 0

C = 0

The function is h = -24·cos[π(t )] + 24

b) The height of the nail at 0.8 seconds is given as follows;

h = -24×cos[π(0.8)] + 24 =

h = 19.42 + 24 = 43.42 cm.

The integral, ∫ [ (9ˣ - eˣ )/3ˣ ] dx evaluate value is 3ˣ/ ln(3) - eˣ/3ˣ(1 - ln 3). So, the correct answer is option (c).

Integration is defined as the process of finding the area of the region under the curve. This is done by drawing as many small rectangles covering up the area and summing up all their areas. If d/dx(F(x) = f(x), then ∫ f(x) dx = F(x) + C, where C is integration constant and indefinite integrals. We have an integral, say , I = ∫ [ (9ˣ - eˣ )/3ˣ ] dx

and we have to determine its value.

I = ∫ [ (9ˣ - eˣ )/3ˣ ] dx

=> I = ∫ [ (9ˣ/3ˣ - eˣ/3ˣ ] dx

=> I = ∫ [ (3²ˣ/3ˣ - eˣ/3ˣ ] dx

=> I = ∫ [ (3²ˣ/3ˣ - eˣ/3ˣ ] dx

=> I = ∫ [ (3ˣ - eˣ/3ˣ ] dx

=> I = ∫ 3ˣ dx - ∫ eˣ3⁻ˣ dx

=> I = 3ˣ/ ln(3) - eˣ/3ˣ(1 - ln 3) + C

( since, ∫aˣ dx = aˣ/ln a)

where C --> integration constant

So, the required value is 3ˣ/ln(3)-eˣ/3ˣ(1 - ln 3).

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Complete question:

Find integral ∫ [ (9ˣ - eˣ )/3ˣ ] dx .

a) 3ˣ - eˣ/(1 - ln 3) + C

b) 9ˣ/2ln3 - eˣ/(3ˣ ln 3) + C

c) 3ˣ/ln3 - eˣ/3ˣ(1 - ln 3) + C

d) 3ˣ/ln3 - eˣ/3ˣ + C

The quotient include the following: D. \(\frac{x(2x-3)}{7}\)

In Mathematics and Geometry, a quotient is a mathematical expression that is simply used to represent the division of a number (numerator) by another number (denominator).

Based on the information provided above, we can logically deduce the following mathematical expression;

\(\frac{2x-3}{x} \div \frac{7}{x^2}\)

By rearranging the mathematical expression using the multiplication operation, we have:

\(\frac{2x-3}{x} \times \frac{x^{2} }{7}\\\\2x-3 \times \frac{x }{7}\\\\\frac{x(2x-3)}{7}\)

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A plane cannot be named by any three points in the plane because there are infinitely many planes that can pass through those points. By specifying only three points, we do not have enough information to uniquely identify a single plane.

To uniquely define a plane, we need to use three noncollinear points. Noncollinear points are points that do not lie on the same line. By choosing three noncollinear points, we can determine a unique plane that passes through those points. The combination of these three points creates a plane that is different from any other plane passing through any other set of three noncollinear points.

In summary, naming a plane requires three noncollinear points because this combination uniquely identifies a plane, whereas three points alone are not sufficient for this purpose.

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From the given statement:

The hypotenuse of a right triangle = 25 Units

The measure of one leg of the right triangle = 20 Units

From Pythagoras Theorem

Therefore:

The area of a two-dimensional cross-section depends on the shape it represents, such as a square, rectangle, triangle, circle, or any other polygon. Each shape has its own formula for calculating its area.

In order to determine the area of the cross-section, we need additional information such as the shape of the cross-section, its dimensions, or any other relevant details. Without this information, it is not possible to calculate the area. Please provide more details or a specific shape or scenario so that an accurate answer can be generated. Once the shape is specified, the appropriate formula can be applied to calculate the area.

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The minimum volume of the box is 48 feet³.

The volume of the empty space that needs to be filled with packing peanuts to protect the model is 32 feet³.

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume.

Given:

Pyramid base= 4 cm, height= 4 cm

So, Volume of pyramid

= a²h/3

= 16 x 3 /3

= 16 feet³

and, Volume of Cuboidal box

= lbh

= 4 x 4 x 3

= 16 x 3

= 48 feet³

So, Volume of empty space in box

= 48- 16

= 32 feet³

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For n ≥ 459, Algorithm A is better than Algorithm B when B uses n√n operations.

To determine the value of n₀ for which Algorithm A is better than Algorithm B when B uses n√n operations, we need to find the point at which the number of operations for Algorithm A is less than the number of operations for Algorithm B.

Algorithm A: 10n log n operations

Algorithm B: n√n operations

Let's set up the inequality and solve for n₀:

10n log n < n√n

Dividing both sides by n gives:

10 log n < √n

Squaring both sides to eliminate the square root gives:

100 (log n)² < n

To solve this inequality, we can use trial and error or graph the functions to find the intersection point. After calculating, we find that n₀ is approximately 459. Therefore, For n ≥ 459, Algorithm A is better than Algorithm B when B uses n√n operations.

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R-1.3: For \($n \geq 14$\), Algorithm A is better than Algorithm B when B uses \($n^2$\) operations.

R-1.4: Algorithm A is always better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

R-1.3:

Algorithm A: \($10n \log n$\) operations

Algorithm B: \($n^2$\) operations

We want to determine the value of \($n_0$\) such that Algorithm A is better than Algorithm B for \($n \geq n_0$\).

We need to compare the growth rates:

\($10n \log n < n^2$\)

\($10 \log n < n$\)

\($\log n < \frac{n}{10}$\)

To solve this inequality, we can plot the graphs of \($y = \log n$\) and \($y = \frac{n}{10}$\) and find the point of intersection.

By observing the graphs, we can see that the two functions intersect at \($n \approx 14$\). Therefore, for \($n \geq 14$\), Algorithm A is better than Algorithm B.

R-1.4:

Algorithm A: \($10n \log n$\) operations

Algorithm B: \($n\sqrt{n}$\) operations

We want to determine the value of \($n_0$\) such that Algorithm A is better than Algorithm B for \($n \geq n_0$\).

We need to compare the growth rates:

\($10n \log n < n\sqrt{n}$\)

\($10 \log n < \sqrt{n}$\)

\($(10 \log n)^2 < n$\)

\($100 \log^2 n < n$\)

To solve this inequality, we can use numerical methods or make an approximation. By observing the inequality, we can see that the left-hand side \($(100 \log^2 n)$\) grows much slower than the right-hand side \($(n)$\) for large values of \($n$\).

Therefore, we can approximate that:

\($100 \log^2 n < n$\)

For large values of \($n$\), the left-hand side is negligible compared to the right-hand side. Hence, for \($n \geq 1$\), Algorithm A is better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

So, for R-1.4, the value of \($n_0$\) is 1, meaning Algorithm A is always better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

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Step-by-step explanation:

\(\text{Denote The sum of all the integers from 1 to 100 inclusive that are NOT multiples of 7 as } S.\)

\(\text{Denote The sum of all the integers from 1 to 100 inclusive that are multiples of 7 as } P.\)

\(\text{Denote The sum of all the integers from 1 to 100 inclusive as } Q.\)

Then

\(\begin{align}S&=Q-P\\&=\frac{100(100+1)}{2}-(7+2\cdot7+\ldots+14\cdot7)\\&=\frac{100(100+1)}{2}-7\cdot\frac{14(14+1)}{2}\\&=4315\end{align}\)

A statistic is a a) sample characteristic, so the correct option is a) a sample characteristic.

A statistic is a numerical value calculated from a sample of data that is used to describe or make inferences about a larger population from which the sample was drawn. It is different from a parameter, which is a numerical value that describes a characteristic of a population.

Statistics are used in various fields, including science, business, economics, social sciences, and government. They can help researchers to summarize and analyze data, test hypotheses, and make predictions about future events or outcomes.

It is important to note that statistics are subject to variability due to sampling error, which can be reduced by increasing the sample size. Additionally, the distribution of statistics depends on the underlying distribution of the population from which the sample was drawn, and it may not always be normally distributed.

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In a simple linear regression analysis, the correlation coefficient (r) and the slope (m) Always have the same sign.

What is linear regression?

Predictive analysis and modelling frequently use linear regression. It can be used, for instance, to measure the proportional effects of diet, age, and gender (the predictor variables) on height (the outcome variable).

A correlation coefficient is a metric that expresses a correlation, or a statistical relationship between two variables, in numerical terms.

Two columns of a given data set of observations, also known as a sample, or two parts of a multivariate random variable with a known distribution may serve as the variables.

Hence, in a simple linear regression analysis, the correlation coefficient (r) and the slope (m) Always have the same sign.

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The survey that illustrates an example of quantitative data is: - The time, in minutes, it took students to finish their exams.

Quantitative data is numerical data that can be measured or counted. In this case, the time taken to finish exams is a numerical value, making it a quantitative variable.

Certainly! Quantitative data refers to information that can be measured or expressed as numbers. It provides a numerical description or measurement of a particular characteristic or variable. It allows for mathematical operations such as addition, subtraction, multiplication, and division.

In the given options, the survey asking about the time it took students to finish their exams is an example of quantitative data. This is because time can be measured in minutes, which are numerical values. Each student's exam time can be represented by a specific number, such as 30 minutes, 45 minutes, and so on.

On the other hand, options like the eye color of students, characteristics of different types of birds, and weights of different books are not inherently numerical and do not provide measurable quantities. While they can be categorized or described qualitatively, they do not represent quantitative data.

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The translation of X represented by the translation rule T < -7, -8 > (X) is 7 units to the left and 8 units down. (Answer: D)

The translation rule T < -7, -8 > (X) describes how to translate or move a point X in a coordinate plane. The numbers in the translation rule represent the amount of horizontal and vertical displacement for the point.

In this case, the translation rule T < -7, -8 > (X) indicates that the point X should be moved 7 units to the left and 8 units down. This means that the x-coordinate of the point will decrease by 7 units, moving it to the left on the x-axis. Similarly, the y-coordinate of the point will decrease by 8 units, moving it downward along the y-axis.

By applying this translation rule to the point X, we can visualize the new position of the point after the translation. The detailed answer is that the point X will be shifted 7 units to the left and 8 units down from its original position.

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The center of gravity of the combination of the two circles is at (x, y) = (0, 4/5).

The center of gravity, or the center of mass, of a two-dimensional object can be found by taking the weighted average of the x-coordinates and y-coordinates of the individual masses making up the object.

In this case, the two circles can be treated as point masses, with the mass of each circle being proportional to its area. The area of a circle with radius r is given by pi * r^2.

So, for circle c1 with radius 2, its mass is given by:

m1 = pi * 2^2 = 4 * pi

And for circle c2 with radius 1, its mass is given by:

m2 = pi * 1^2 = pi

The x-coordinate of the center of gravity is given by the weighted average of the x-coordinates of the two masses:

x = (m1 * 0 + m2 * 0) / (m1 + m2) = 0

Similarly, the y-coordinate of the center of gravity is given by the weighted average of the y-coordinates of the two masses:

y = (m1 * 0 + m2 * 4) / (m1 + m2) = 4 * (m2 / (m1 + m2)) = 4 * (pi / (4 * pi + pi)) = 4 * (pi / 5 * pi) = 4/5

So, the center of gravity of the combination of the two circles is at (x, y) = (0, 4/5).

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The greatest rate of change can be seen in a straight line plotted using the coordinates of the tabular data in part [B].

The slope of a straight line is the measure of the tangent of the angle that the line makes with the + x axis. The intercept of a straight line is -

y = mx + c

from this we can write slope [m] as -

mx = y - c

m = (y - c)/x

If y - intercept [c] is zero, then -

m = y/x

Given is a equation, tabular data and a graph representing a straight line

Slope of a line also tells us about the rate of change of [y] value with respect to the [x] value.

[A]

For the equation -

D = 55t

The slope will be [m] = 55.

[B]

For the tabular data, take two coordinates -

(1, 475) and (2, 535)

The slope of the line can be calculated using the formula -

m = (y₂ - y₁)/(x₂ - x₁)

The slope will be -

[m] = (535 - 475)/(2 - 1)

[m] = 60

[C]

For the graph we have a straight line that passes through the coordinates as follows -

(0, 100)

(1, 150)    

The slope of the line can be calculated using the formula -

m = (y₂ - y₁)/(x₂ - x₁)

m = (150 - 100)/(1 - 0)

[m] = 50

The slope of the line is maximum for the tabular data [B].

Therefore, the greatest rate of change can be seen in a straight line plotted using the coordinates of the tabular data in part [B].

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To find the area to the left of z = -a, we can use the properties of the standard normal distribution and symmetry.

The standard normal distribution is a symmetric distribution with a mean of 0 and a standard deviation of 1. The area to the right of z = a is given as 0.3, which means the area to the left of z = a is 1 - 0.3 = 0.7.

Since the standard normal distribution is symmetric, the area to the left of -a is the same as the area to the right of a. Therefore, the area to the left of z = -a is also 0.7.

This symmetry property of the standard normal distribution allows us to find probabilities and areas without using tables or technology. By utilizing the properties of symmetry and the known areas, we can determine probabilities and areas associated with different z-values. In this case, the area to the left of z = -a is simply the same as the area to the right of z = a, which is 0.7.

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Answer:

A system of equations are two or more equations that has to be valid at the same time. It means that the variables of one equation can be substitute in the other equation.

For example we have y=5x−8 and we can substitute this value of y in the other equation

4x+3y=33

4x+3(5x−8)=33 we can solve now for x

4x+15x−24=33

19x=33+24

19x=57

x=5719=3.

y can be obtained from the first equation

y=5x−8

y=5⋅3−8=15−8=7

Then x=3 and y=7.

Step-by-step explanation:

Answer:

x = 3

y = 7

Step-by-step explanation:

y = 5x - 8  ---------------(I)

4x + 3y = 33 ------------(II)

Substitute y = 5x - 8 in equation (II)

4x + 3 (5x - 8) = 33  

4x + 3*5x - 8*3 = 33

4x + 15x - 24 = 33           {Combine like terms}

      19x  - 24 = 33            {Add 24 to both sides}

            19x = 33 + 24

           19x = 57           {Divide both sides by 19}

             x = 57/19

x = 3

Substitute x = 3 in equation (I)

y = 5*3 - 8

y = 15 - 8

y = 7

Answer:

d = -3

Step-by-step explanation:

-3 -9 = -12

-12/6

= -2

By using the properties of real numbers the given expression can be written as  -8y.

What is solving an expression?

Another word for "solving a math problem" is "simplifying an expression." When you simplify an expression, your goal is essentially to make it as simple as you can. There shouldn't be any additional multiplying, dividing, adding, or subtracting to be done at the conclusion.

Given:

The given expression is, \(\frac{4}{3}(-6y)\)

According to the distributive property of real numbers, if a, b, c are three real numbers the,

a(bc) = (ab)c

Using the associative property of multiplication, the given expression can be written as,

\(\frac{4}{3}(-6y) = (\frac{4}{3}*(-6))*y \\\frac{4}{3}(-6y) = (\frac{-24}{3} )*y\\\frac{4}{3}(-6y) = -8y\)

Hence, by using the properties of real numbers the given expression can be written as  -8y.

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Answer:

\(\frac{6}{7}\)

y = \(\frac{6}{7}\) x

Step-by-step explanation:

Leave your answer as a fraction and do not change it into a decimal.

Your y is changing by 6 as your x is changing by 7

Answer:

the lcd for both is 60 5/12 is 25/60 and 1/5 is 12/60

Step-by-step explanation:

Hello and Good Morning/Afternoon:

Let's take this problem step-by-step:

What does this problem want us to solve:

   \(\hookrightarrow \text{Find least common denominator of 5/12 and 1/5}\)

Essentially:

 \(\hookrightarrow \text{Find the least common multiple or LCM of 5 and 12}\)

The LCM of 5 and 12:

 \(\hookrightarrow \text{is 60}\)

Answer: 60 is the least common denominator of 5 and 12

Terms used:

Hope that helps!

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