Given a positive integer n, display all the equivalence re- lations on the set of the m smallest positive integers

The required probability for the given event is given as 0.5.

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lie in the close interval of 0 and 1 [0,1].

Given that,

The probability of a door being locked is 70% = 0.7

Total number of keys is 10.

The number of keys being carried is 2.

Thus, there can be two cases for getting through the door.

Case 1: The door is locked.

The probability to open the door by 1 key is 1/10.

Then, the probability to open the door by 2 keys is 2/10 = 1/5.

Case 2: The door is open.

In this case no keys are needed which means the chance of getting through is the probability of door not being locked which is given as,

1 - 0.7 = 0.3.

Now, the overall probability should consider both the cases as,

P(getting through the door) = P(Door is closed and keys open it)

+ P(The door is open)

= 0.3 + 1/5

= 0.3 + 0.2

= 0.5.

Hence, the probability to get through the door without returning for more keys is 0.5.

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The key features of this exponential function include the following:

y-intercept of f: (0, 10).

y-intercept of g: (0, 5).

Domain of both f and g: All real numbers or (-∞, ∞).

Range of both f and g = (0, ∞) or {y|y ≥ 0}.

End behavior of both f and g: as x → -∞, y → 0 and x → ∞, y → ∞

In Mathematics and Geometry, an exponential function is typically represented by the following mathematical equation:

\(f(x) = a(b)^x\)

Where:

Based on the given exponential function f, we can logically deduce that the y-intercept is represented by a, which is equal to 10 while the y-intercept of g is equal to 5.

In conclusion, there is a horizontal asymptote at y = 0 because it is a line which the graph of a given function approaches, but never touches or crosses.

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Answer:

The answer is C because 40% of 1450 is 580.

Replacing stoplights with roundabouts does not significantly reduce the rate of accidents at intersections based on the given data.

Based on the statistical analysis, replacing stoplights with roundabouts does not significantly reduce the rate of accidents at intersections.

To test this hypothesis, we will use a paired t-test, which compares the means of two sets of paired data. The null hypothesis is that there is no significant difference between the mean accident rates before and after installing roundabouts, while the alternative hypothesis is that the mean accident rate after installing roundabouts is significantly lower than before.

Here are the steps to conduct the paired t-test:

Using the given data, the differences between the accident rates before and after installing roundabouts are:

-0.6, 0.2, 0.6, -0.1, 0

The mean of the differences is 0.02, and the standard deviation is 0.43. There are 5 paired observations, so the degrees of freedom are 4.

Using the formula, we get:

t = 0.02 / (0.43 / √(5)) = 0.14

The critical t-value at a 0.05 level of significance and 4 degrees of freedom is 2.776 from a t-distribution table.

Since the calculated t-value (0.14) is less than the critical t-value (2.776), we fail to reject the null hypothesis. Therefore, we can conclude that replacing stoplights with roundabouts does not significantly reduce the rate of accidents at intersections based on the given data.

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the volume in the first octant bounded by\(y^2=4−x\) and y=2z is pi/36 sqrt(3).

(1) To find the volume in the first octant bounded by the surfaces \(y^2 = 4 - x\) and y = 2z, we can set up a triple integral in cylindrical coordinates.

First, we need to determine the bounds for our variables. Since we are working in the first octant, we know that 0 <= z, 0 <= theta <= pi/2, and 0 <= r.

Next, we need to find the equation for the upper and lower bounds of z in terms of r and theta. We can start with the equation \(y^2 = 4 - x\) and substitute y = 2z to get:

\((2z)^2 = 4 - x\)

\(4z^2 = 4 - x\)

\(x = 4 - 4z^2\)

We can then use this equation along with the equation z = y/2 to get the bounds for z:

\(0 < = z < = (4 - x)^(1/2)/2 = (4 - 4z^2)^(1/2)/2\)

Squaring both sides, we get:

\(0 < = z^2 < = (1 - z^2)/2\)

\(0 < = 2z^2 < = 1 - z^2\)

\(z^2 < = 1/3\)

So the bounds for z are:

\(0 < = z < = (1/3)^(1/2)\)

Finally, we can set up the triple integral in cylindrical coordinates:

V = ∫∫∫ r dz dtheta dr

with bounds:

0 <= r

0 <= theta <= pi/2

\(0 < = z < = (1/3)^(1/2)\)

and integrand:

r

So the volume in the first octant bounded by y^2=4−x and y=2z is:

V = ∫∫∫ r dz dtheta dr

= ∫ from 0 to\((1/3)^(1/2) ∫ from 0 to pi/2 ∫ from 0 to r r dz dtheta dr\)

= ∫ from 0 to\((1/3)^(1/2) ∫ from 0 to pi/2 r^2/2 dtheta dr\)

= ∫ from 0 to\((1/3)^(1/2) r^2 pi/4 dr\)

\(= pi/12 (1/3)^(3/2)\)

= pi/36 sqrt(3)

Therefore, the volume in the first octant bounded by\(y^2=4−x\) and y=2z is pi/36 sqrt(3).

(2) To find the volume bounded by z = x^2 + y^2 and z = 4, we can use a triple integral in cylindrical coordinates.

First, we need to determine the bounds for our variables. Since we are working in the region where z is bounded by \(z = x^2 + y^2\) and z = 4, we know that 0 <= z <= 4.

Next, we can rewrite the equation \(z = x^2 + y^2\) in cylindrical coordinates as \(z = r^2.\)

So the bounds for r and theta are:

0 <= r <= 2

0 <= theta <= 2pi

And the bounds for z are:

\(r^2 < = z < = 4\)

Finally, we can set up the triple integral in cylindrical coordinates:

V = ∫∫∫ r dz dtheta dr

with bounds:

0 <= r <= 2

0 <= theta <= 2pi

\(r^2 < = z < = 4\)

and integrand: 1

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Answer:

39001

Step-by-step explanation:

Answer:

the answer is 7

Answer:

7

Step-by-step explanation:

Answer:

It is C, because to find volume you must use the formula l×w×h, or length times the width times the height. (cm^3)

Answer:

C

Step-by-step explanation:

Unlike area that's cm² because it's like A= L*W

Volume is cm³ because it's like A= L*W*H

Vertical lines do not have positive slopes or negative slopes. They have undefined slopes.

Now, According to the question :

What is Vertical line?

A vertical line is a line, parallel to y-axis and goes straight, up and down, in a coordinate plane. Whereas the horizontal line is parallel to x-axis and goes straight, left and right.

Is a vertical line positive or negative?

The slope of a line can be positive, negative, zero, or undefined. A horizontal line has slope zero since it does not rise vertically (i.e. y1 − y2 = 0), while a vertical line has undefined slope since it does not run horizontally (i.e. x1 − x2 = 0).

Hence, Vertical lines do not have positive slopes or negative slopes. They have undefined slopes.

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Answer: The answer is 144 grams of zinc

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

A(x) = x^2 + 5x

A(x) = x^2 + 5x = 14

x^2 + 5x - 14 = 0

(x + 7)(x - 2) = 0

x + 7 = 0  or  x - 2 = 7

x = -7 or x = 2

x is the height of a rectangle.

The only viable solution is x = 2 because the height of a rectangle cannot be a negative number such as -7.

The only viable solution for the height is x= 2, because height cannot be a negative value.

A rectangle is a quadrilateral with four right angles.

Area is the quantity that expresses the extent of a region on the plane or on a curved surface.

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is \(ax^{2} +bx+c=0\)

Given,

Area of the rectangle = \(x^{2} +5x\) = 14

Then,

\(x^{2} +5x-14=0\\(x+7)(x-2)=0\)

Therefore x = -7 and 2

But the Height cannot be negative therefore x = 2

Hence, only viable solution for the height is x= 2, because height cannot be a negative value.

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Answer:

Step-by-step explanation:

Nothing to choose from??/

But 2x^2+3x=-5 is

- 3± i√31 / 4

Answer:

\(\frac{-3+-i\sqrt{31} }{4}\)

ye

The inequality that represents the situation is 8.50x < 35 and the pounds of shrimp Luna can buy is 4.

Inequality is a statement that two or more mathematical expressions are unequal.

Inequalities are represented as greater than (>), less than (<), greater than or equal to (≥), less than or equal to (≤), and not equal to (≠).

The cost price of shrimp per pound = $8.50

The total spending budget = $35

Let the number of pounds of shrimp Luna can buy = x

8.50x < 35

x = 4

Thus, the total amount Luna can spend on shrimp is $34 (4 x $8.50), which is less than $35.

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a) To maximize its net savings, the company should use the new machine for 7 years.  b) The net savings during the first year of use of the machine are $405 (rounded off to the nearest dollar).  c) The net savings over the period determined in part a are $1,833.33 (rounded off to the nearest cent).

Step-by-step explanation: a) To determine for how many years should the company use the new machine to maximize its net savings, we need to find the value of x that maximizes the difference between the savings and the costs.To do this, we need to first calculate the net savings, N(x), which is given by:S'(x) - C'(x) = 175 - x² - (x² + 11x) = -2x² - 11x + 175To find the maximum value of N(x), we need to find the critical values, which are the values of x that make N'(x) = 0:N'(x) = -4x - 11 = 0 ⇒ x = -11/4The critical value x = -11/4 is not a valid solution because x represents the number of years of operation of the machine, which cannot be negative. (i.e., not use it at all).However, this answer does not make sense because the company would not introduce a new machine that it does not intend to use. Therefore, we need to examine the concavity of N(x) to see if there is a local maximum in the feasible interval.

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Answer:

45 for complement

90 for supplement

Step-by-step explanation:

If one of the longer sides of the Isosceles triangle is 6.3 centimeters, the length of the base is 3.1 centimeters.

Let's solve the problem step by step:

1. Identify the given information:

  - The triangle is isosceles, meaning it has two equal sides.

  - The two equal sides, labeled "a," are longer than the base, labeled "b."

  - The perimeter of the triangle is 15.7 centimeters.

  - One of the longer sides is 6.3 centimeters.

2. Set up the equation based on the given information:

  Since the triangle is isosceles, the sum of the lengths of the two equal sides is twice the length of the base. Therefore, we can write the equation:

  2a + b = 15.7

3. Substitute the known value into the equation:

  One of the longer sides is given as 6.3 centimeters, so we can substitute it into the equation:

  2(6.3) + b = 15.7

4. Simplify and solve the equation:

  12.6 + b = 15.7

  Subtract 12.6 from both sides:

  b = 15.7 - 12.6

  b = 3.1

5. Interpret the result:

  The length of the base, labeled "b," is found to be 3.1 centimeters.

Therefore, if one of the longer sides of the isosceles triangle is 6.3 centimeters, the length of the base is 3.1 centimeters.

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2

\(\\ \sf\longmapsto 5.5\times 10^3\)

\(\\ \sf\longmapsto 55\times 10^4\)

We know

Hence number of significant figures is 2

9514 1404 393

Answer:

  2

Step-by-step explanation:

When a number is written in scientific notation, all of the digits of the mantissa are considered significant. The mantissa is 5.5, which has 2 digits.

There are 2 significant digits in the number.

Answer: \(n\geq17\)

Step-by-step explanation:

Let n= Number of packs John needs.

Tiles in 1 pack = 6

Tiles in n pack = 6n

If he needs at least 100 tiles.

then

6n ≥ 100

\(\Rightarrow\ n\geq100\\\\\Rightarrow\ n\geq\dfrac{100}{6}\\\\\Rightarrow\ n\geq\dfrac{50}{3}\\\\\Rightarrow\ n\geq16.67\\\\\Rightarrow\ n\geq 17\)

The required inequality: \(n\geq17\)

Let the breadth of the lawn be X

therefore, Length=2X

By condition,

=≥2(L+B)=128

=>4X + 2X = 128

=>6X=128

=>X=21.333

Length=42.666m

Breadth=21.333m

Answer:

b?

Step-by-step explanation:

Answer:

31

Step-by-step explanation:

16(3)-3(-1)+5(-4)

48+3-20

51-21

31

the explicit rule of the nth term of the arithmetic

sequence is A. aₙ = 6n-8

                    B. aₙ = 6n-26

                     C. aₙ= 6n-26

                     D. aₙ =6n-14

the sequence of numbers having constant differences between two successive numbers.

the explicit formula is used for determining any term of an arithmetic sequences directly in where only the first term and differences between two consecutive terms are needed to know.

Given, -20,-14,-8,-2,...are the terms. an explicit rule for the nth term of the arithmetic sequence is given by the formula, aₙ=a₁+(n-1) d

where, a₁ is the first term, aₙ is the nth term, d is the difference between two terms, n is the number of terms.

as per question a₁= -20, d= 6

now A. aₙ = -20+6(n+2)

           aₙ = 6n-8

B. aₙ= -20+6(n-1)

 aₙ = 6n-26

C. aₙ =-20+6(n-1)

   aₙ = 6n-26

D. aₙ= -20+6(n+1)

  aₙ = 6n-14

the above are the explicit rules for the arithmetic sequence.

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The correct formula for the revenue generated by the item is Revenue = 200p - 5p^2.

The revenue generated by the item can be calculated by multiplying the price (p) by the unit sales (200 - 5p). Therefore, the correct formula for the revenue generated by the item is:

Revenue = Price x Unit Sales
Revenue = p(200 - 5p)
Revenue = 200p - 5p^2

The revenue generated by the item is a quadratic function of the price (p). To find the maximum revenue, we need to differentiate the function with respect to p and set it equal to zero:

dRevenue/dp = 200 - 10p = 0
10p = 200
p = 20

Therefore, the maximum revenue is generated when the price of the item is $20. Substituting p = 20 in the revenue formula, we get:

Revenue = 200(20) - 5(20^2) = $2000

Hence, the correct formula for the revenue generated by the item is Revenue = 200p - 5p^2, and the maximum revenue is achieved when the price of the item is $20, generating a revenue of $2000.

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The answer of the given question based on the the number of students using the cafeteria's healthy lunch line can be found by solving the inequality 1/5s - 51 < 20, the correct answer is (1) 142 , (1) or more.

An equation is  mathematical statement that shows  equality of two expressions, typically separated by  equal sign. Equations are used to express relationships between variables and to solve problems in various fields of mathematics, science, and engineering. In essence, an equation is representation of  real-world scenario or problem in mathematical terms.

The variables in equation can take on different values, and  equation remains true regardless of the values chosen for  variables. Solving  equation means finding  values of the variables that make  equation true.

Equations can be linear, quadratic, polynomial, exponential, logarithmic, or trigonometric, among other types. They are fundamental tool in mathematics and have numerous applications in fields like physics, engineering, economics, and finance.

There are 155 students or more students that use this lunch line.

The correct answer is 1. or more.

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Answer:

Step-by-step explanation:

The expression for calculating the point that divides the coordinate of two endpoints A(x, y) and B (x₁, y₁) in the ratio a:b with point C(X, Y) on the line is as shown below;

\(B\)\((X, Y) =\) \((\dfrac{ax_1+bx}{b+a}, \dfrac{ay_1+by}{b+a})\)

Given B(X, Y) = (4, 1), C(x₁, y₁) = (12,5) and AB:BC = a:b = 3/4

From the given coordinates, X = 4, Y = 1, x₁ = 12 y₁ = 5, a = 3 and b =4

From the coordinates above;

\(X = \dfrac{ax_1+bx}{b+a}\)

\(4 = \dfrac{3(12)+4x}{4+3}\\\\4 = \dfrac{36+4x}{7}\\\\\\4*7 = 36+4x\\28 = 36+4x\\28-36 = 4x\\-8 = 4x\\x = -8/4\\x= -2\)

Similarly to get y;

\(1 = \dfrac{3(5)+4y}{4+3}\\\\1 = \dfrac{15+4y}{7}\\\\\\1*7 = 15+4y\\7 = 15+4y\\7-15 = 4y\\-8 = 4y\\y= -8/4\\y= -2\)

Hence the value of x is -2 and y is -2.

Answer:

a+b+c =13

Step-by-step explanation:

\(\left\begin{array}{ccccccc}aX^2&+&bX&+&c&=&0\\ \downarrow&&\downarrow&&\downarrow&&\downarrow\\9.X^2&-&2.X &+& 6 &=& 0\end{array}\right \implies \left\{\begin{array}{ccccccc}a=9\\b=-2\\c=6\end{array}\right\)

\(\implies a+b+c = 9+(-2)+6\\=9-2+6\\=7+6\\=13\\\\\therefore a+b+c =13\)

Answer:

0.4615

Step-by-step explanation:

1/780 x 360 = 0.4615

Answer:

3/4°

Step-by-step explanation:

84+72+108+60+156= 480 people

480*x= 360°

x= 360°/480= 3/4°

The percentage of the players on the tennis team belongs to 8th graders  from the given ratio is equal to 62.5%.

Ratio of the players of 7th graders to 8th graders on the tennis team = 3 : 5

Let the number of 7th graders on the tennis team be represented by 3x.

And let the number of 8th graders on the tennis team be represented by 5x.

Then,

The total number of players on the tennis team is 3x + 5x = 8x.

Percentage of players who are 8th graders,

= (the number of 8th graders (5x))/(the total number of players (8x)) × 100

Substitute the values we have,

⇒Percentage of players who are 8th graders = (5x / 8x) x 100%

⇒Percentage of players who are 8th graders = 62.5%

Therefore, percentage of the players on the tennis team are 8th graders is equal to 62.5%.

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There are 9240 ways to select a committee to develop a discrete math course if the committee is to consist of three faculty from the math department and four from the computer science department.

It is given that there are 9 faculty members in the math department and 11 in the computer science department.

\(C^{9} _{3} * C^{11} _{4}\)

\(= \frac{9!}{(9-3)!3!} * \frac{11!}{(11-4)!4!}\\= 28 * 330\\= 9240\)

Therefore, there are 9240 ways to select the committee.

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