The distribution of the amount of money spent by students on textbooks in a semester is
approximately normal in shape with a mean of 399 and a standard deviation of 34.
According to the standard deviation rule, approximately 99.7% of the students spent between $ ___ and $ ___ on textbooks in a semester.

A. No accidents occur in one week. Probability = 0.0113

B. 10 or more accidents occur in a week. Probability = 0.0018

C. One accident occurs today. Probability =0.2122

A. No accidents occur in one week.

Probability = e^(-4.7)

= e^(-4.7)

= 0.0113

B. 10 or more accidents occur in a week.

Probability = 1 - e^(-4.7)(1 + 4.7 + (4.7^2)/2 + (4.7^3)/6 + (4.7^4)/24 + (4.7^5)/120)

= 1 - e^(-4.7)(1 + 4.7 + 22.09 + 100.521 + 470.4724 + 2,054.085)

= 1 - e^(-4.7)(3,648.78)

= 1 - 0.0050

= 0.0018

C. One accident occurs today.

Probability = 4.7e^(-4.7)

= 4.7e^(-4.7)

= 0.2122

The probability of no accidents occurring in one week is 0.0113, the probability of 10 or more accidents occurring in one week is 0.0018, and the probability of one accident occurring today is 0.2122. These probabilities are calculated using the Poisson distribution with a mean of 4.7 accidents per week.

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We use the concepts of continuity and differentiability to prove that a continuous function of order 3 is continuous of order 1 after being differentiated twice.

Let us assume the function x³ as the function of order 3. We know that its 1st derivative will be 3x² and its 2nd derivative will be, 6x. Now, let's check both of their continuities at any point "a" on the function. By putting a limit x tending to a to the function

= lim (x³) = a³

  x→a

and putting a directly to the equation i.e, f(a) = a³ therefore, x³ is a continuous function at a. Similarly, by putting a limit x tending to a to the function

= lim (6x) = 6a

  x→a

and putting a directly to the equation i.e, f(a) = 6(a) therefore, 6x is also a continuous function at a. Hence we can say that the continuous function of order 3 is continuous of order 1 after being differentiated twice.

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Decisions at this level are typically strategic in nature and involve long-term planning and goal setting. These decisions may involve large amount investments of resources and have a significant impact on the organization's future.

Decisions at this level are typically strategic in nature and involve long-term planning and goal setting. These decisions may involve large investments of resources and have a significant impact on the organization's future. Examples of decisions at this level include setting the overall strategy, developing new products and services, entering new markets, and deciding on organizational structure. Due to the nature of these decisions, they require extensive data analysis and research. It is important for decision makers at this level to have knowledge about the industry, the marketplace, and the competitive environment in order to make informed decisions. Additionally, since these decisions have a long-term impact, it is important to consider the potential risks and opportunities associated with them. Furthermore, the decisions made at this level must align with the overall mission and vision of the organization. As such, these decisions must be made with careful consideration, as they can have far-reaching implications for the entire organization.

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[tex]\it AC=2\cdot EC=2\cdot6=12[/tex]

Answer: The slope is 2.

Step-by-step explanation:

We can use this formula to help us solve:

                  [tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

Given:

      [tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

Substitute values and simplify to solve:

      [tex]\displaystyle \frac{6--6}{2--4}=\frac{6+6}{2+4}=\frac{12}{6} =2[/tex]

Answer:

The slope is 2

Step-by-step explanation:

The formula for slope is y2-y1/x2-x1

So just fill out the points and do the calculations.

There are 9,999 positive integers less than 100,000 that contain at least one "1" in their decimal representation.

There are 9,999 positive integers less than 100,000 that contain at least one "1" in their decimal representation. This can be determined by counting the number of possible combinations of digits that can be formed with the numbers 0-9. Since there are five digits in a number less than 100,000, the total number of combinations is 10^5 (10 to the power of 5). Of these combinations, 1/10th will contain at least one "1" as there are 10 possible ways to include a "1" in the five-digit number. Thus, 10^5/10 = 9,999. This means that there are 9,999 positive integers less than 100,000 that contain at least one "1" in their decimal representation.

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The coefficient of static friction is a dimensionless value that represents the ratio of the maximum static friction force to the normal force. It is used to determine the maximum angle at which an object can be inclined on a surface without slipping. The coefficient of static friction between the right bar and the surface at point A is not given in the information provided.

To determine the largest angles at which the right bar can be inclined without slipping on the surface at point A, one would need to know the coefficient of static friction between the bar and the surface, as well as the weight of the bar and the normal force acting on it. The coefficient of static friction multiplied by the normal force must be greater than or equal to the weight of the bar in order for it to remain in static equilibrium.

It is also worth mentioning that the coefficient of static friction varies depending on the materials of the two surfaces in contact and the normal force acting on it. The coefficient of static friction can be measured experimentally and is usually provided in the material properties of the surfaces.

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Answer:

Step-by-step explanation:

You want to know the volume of a cylindrical container 6 inches in diameter and 4.5 inches high, and you want to know how many times larger this volume is than if the diameter were 4 inches.

The volume of a cylinder is given by the formula ...

  V = πr²h

where r is half the diameter, and h is the height.

The volume of your large popcorn container is ...

  V = 3.14·(3 in)²·(4.5 in) = 127.17 in³

The volume of the large container is 127.17 in³.

For a given height, the volume ratio is the square of the ratio of diameters. That ratio is given as 3/2, so the volume ratio is ...

  (3/2)² = 9/4 = 2.25

The large container is 2.25 times the volume of the small container.

According to the report, 80% of those who purchased new cars received loans, compared to 60% of those who purchased older cars.

The population size estimate is calculated by dividing the total number of people getting a service or the total number of unique items delivered (M) by the percentage of people reporting receiving the service or item in a representative survey (P).

Given a car dealership wants to conduct a survey of 100 people who bought ​a new or used car at the dealership in the last three months. ​

number of people          new car       old car     received Loan       No loan

   2,000                             yes                No           1600                    400

      500                            No                  Yes           300                    200

Percentages of people who received Loans bought new cars:

Percentage = 2000-400 / 2000

Percentage = 1600/2000

Percentage = 80%

Percentages of people who received Loans bought used cars:

Percentage = 300 * 100 / 500

Percentage = 3/5 * 100

Percentage = 60%

Therefore, According to the survey, 60% of the people Who bought used cars got loans while 80% of people who bought new cars gets loan.

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The quadratic equation whose roots are -1 and 6 and the leading coefficient is 4 is written in the form

The roots of a quadratic equation is the value of x when y is zero hence we have the equation

x = -1 and x = 6

(x + 1)(x - 6)

with the  leading coefficient of 4

4(x + 1)(x - 6)

expanding will result to

= 4(x² - 6x + x - 6)

= 4(x² - 5x - 6)

= 4x² - 20x - 25

The quadratic equation is 4x² - 20x - 25

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Answer: -2 i think

Step-by-step explanation:

(5-4)-3*(5-4)

1-3*1

1-3=-2

Answer:

The value is 0

The simplified expression is

3• (5 - 4) -3 (5 - 4)

Step-by-step explanation:

The triangle formed is an isosceles triangle since two sides of the triangle are equal .

The point on the shoreline is the point of tangency between the shoreline and the circle centered at the boat with a radius equal to the distance between the boat and the shoreline. The angle from the boat to that point is equal to the angle of the central angle of the circle whose radius is equal to the distance between the boat and the shoreline.

Let the radius of the circle be r and the angle from the boat to the point on the shoreline be θ. Then the formula for the distance between the boat and the shoreline is:

r = θ × (2π/360)

To calculate the distance traveled by the boat, we need to use the formula for the circumference of a circle:

C = 2πr

Substituting the above formula for r into the formula for the circumference of a circle, we get:

C = 2π(θ × (2π/360))

Therefore, the distance traveled by the boat is:

C = (2π)2 × θ/360

The triangle formed is an isosceles triangle since two sides of the triangle are equal (the radius of the circle and the distance between the boat and the shoreline).

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[tex]6m - 2( - 3m + 8)\\ Multiplying :\ each \\ term \\ - 18m + 48m + 6m - 16 \\ - 18m + 54m - 16 \\ 36m - 16 \\ 2(18m - 8)[/tex]

Lebesgue outer measure in this instance is a complete extension of Lebesgue measure that meets all other criteria.

The translation invariant is the Lebesgue measure, and the length of the interval I is the same for that measure when it is on the interval I. The Lebesgue measure of E, for instance, is given by  λ(E) = l if E is any collection of real numbers (E).

As with a single point or a countable number of points, every set that is a finite collection of points has a Lebesgue measure of zero. The measure of finite and countable unions of disjoint sets has the property of being equal to the total of the measures.

An interval's length is its Lebesgue value. The formal foundation for probability theory is measure theory.

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Answer:

14.115

Step-by-step explanation:

Recall Trapezoidal Rule

[tex]\displaystyle \int\limits^b_a {f(x)} \, dx=\frac{1}{2}\biggr(\frac{b-a}{n}\biggr)\biggr[f(x_0)+2\bigr(f(x_1)+f(x_2)+\text{... }+f(x_{n-1})\bigr)+f(x_n)\biggr][/tex]

Make necessary substitutions and evaluate

[tex]\displaystyle \int\limits^5_1 {\sqrt{x^2+3}} \, dx=\frac{1}{2}\biggr(\frac{5-1}{4}\biggr)\biggr[2+2\bigr(\sqrt{7}+\sqrt{12}+\sqrt{19}\bigr)+\sqrt{28}\biggr]\approx14.115[/tex]

Note that the actual value of the integral is [tex]\displaystyle \int\limits^5_1 {\sqrt{x^2+3}} \, dx\approx14.078[/tex], so we can see how accurate the Trapezoidal rule is with just a few equal partions.

Answer: 125

Step-by-step explanation: product of 5 and 75 = 5*75 = 375 divided by 3 which is 375/3 = 125.

The angle for each animal is;

Horse - 40 degrees

Goats - 120 degrees

Sheep - 20 degrees

Cows - 180 degrees

We can see that we want to plot the data that we have on the circle graph and each of the values is going to occupy a given part of the sector and would subtend an angle. We are to obtain the angle that is subtended by each value.

We have;

Total number of farm animals = 4 + 12 + 2 + 18 = 36 animals

Angle for horses = 4/36 * 360 = 40 degrees

Angle for goats = 12/36 * 360 = 120 degrees

Angle for sheep = 2/36 * 360 = 20 degrees

Angle for cows = 18/36 * 360 = 180 degrees

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Missing parts

Ted’s farm has 4 horses, 12 goats, 2 sheep, and 18 cows. Find the angle measure of the sector of a circle graph that represents each animal. Enter the correct answers in the boxes.

Answer:

D or 12.8

Step-by-step explanation:

Distance (d) = √(-2 - 8)2 + (9 - 1)2

= √(-10)2 + (8)2

= √164

= 2√41

= 12.806248474866

Answer:

Hello

Hi 2√41 approximately equals to 12.8, good luck and please see the file below for the answer.

It is D.

We cannot the time period of 25 min using two ropes that when lit burn in one hour. Hence, option C is the correct answer.

This problem is an example of a mathematical puzzle. In order to measure a time period of 30 min, all we need to do is burn one rope from both ends. Since it takes 60 minutes for the rope to burn when lit from one end, it will take half that time i.e., 30 min to burn when lit from both ends.

We can also measure a time period of 35 min if we burn one rope from both ends and the other a bit differently. If we burn a rope from both ends, it will take 30 mins. As for the extra 5 mins, we can take the other rope and first burn it from both ends and then burn it from the middle again. That makes 2 separate ropes and thus the burning time is 15 min. We can then again burn one of these from the middle and wait until one of them completely burns out. This will give us a time period of 35 minutes.

As for 50 minutes, we can use the same method as above for burning one rope completely from both ends and the other from the ends and the middle. We can't really burn the ropes in a way that will give us the time period of 25 min so option C is the correct answer.

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Answer for the "different" question: The distance between -4.5 and 3.5 is 8.

Answer for the "same" questions:

O Add -4.5 and 3.5: -4.5 + 3.5 = -1

O What is -4.5 increased by 3.5: -4.5 + 3.5 = -1

Find the sum of -4.5 and 3.5: -4.5 + 3.5 = -1

Answer: What is the distance between -4.5 and 3.5?

Step-by-step explanation:

         The distance between -4.5 and 3.5 and will be different than all the others because the distance it's asking for the distance between the absolute values, not adding them together.

          Find "both" answers.

➜ Answer for the "different" question:

           What is the distance between -4.5 and 3.5? = 4.5 + 3.5 = 8

➜ Answer for the "same" questions:

           Add -4.5 and 3.5 = -4.5 + 3.5 = -1

Answer: To find the inverse of a function, we first need to make sure that the function is one-to-one, meaning that no two different input values map to the same output value.

If the function B is one-to-one, we can find the inverse by switching the x and y values, and then solving for y.

y = B^-1(x)

We can then use algebraic manipulation to solve for y.

For example, if B(x) = 2x + 1, we can find the inverse by switching x and y:

x = 2y + 1

Solving for y:

y = (x - 1)/2

So the inverse function of B(x) = 2x + 1 is B^-1(x) = (x - 1)/2

Please note that if the function B is not one-to-one, it will not have an inverse.

Step-by-step explanation:

Using multiplication, In Alfred's store, there are 75 bags of potato chips.

The fundamental concept of repeatedly adding the same number is represented by the process of multiplication.

The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

When we need to merge groups of similar sizes, we employ it. For instance, if there are 5 baskets, each containing 4 apples, we can use multiplication to get the total number of apples, which is 5 x 4 = 20 apples.

In Cecilia's store, there are five times fewer bags of potato chips than there are in Alfred's. This indicates that Alfred's has five times as many bags as Cecilia's does. We must multiply to determine how many bags there are in Alfred's store:

15 x 5 = 75

In Alfred's store, there are 75 bags of potato chips.

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The graph of the quadratic function, y = -x² + 8·x - 15, created with MS Excel is attached.

The  roots are; (3, 0) and (5, 0)

The location of the vertex of a parabola is; (4, 1)

A parabola is a curve formed uy the path of an object that moves such that the distance of the object from a fixed point is the same as the distance of the point from a fixed line.

The specified function is f(x) = -x² + 8·x - 15

The equation is a quadratic equation, and the shape of the graph of the function is a parabola.

The points that can be used to graph tjhe function, obtained using MS Excel are;

x  [tex]{}[/tex]    f(x)

2  [tex]{}[/tex]    -3

3  [tex]{}[/tex]    0

4  [tex]{}[/tex]    1

5  [tex]{}[/tex]    0

6  [tex]{}[/tex]    -3

The roots are the x-intercept of the graph, which are the points the graph intersects the x-axis, which are the points where, y = 0.

The roots obtained from the values in the above table are; (3, 0), and (5, 0)

The vertex point is the highest point on the graph. The heighest point or vertex is the point where the y-value is maximum

From the table and the attached graph, the vertex is the point (4, 1)

The vertex of the parabola, obtained using the graph is (4, 1)

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cos⁻¹  ( 7/23) is the measure of the largest angle.

What is known as a triangle?

The three vertices of a triangle make it a three-sided polygon. The angles of the triangle are formed by the connection of the three sides end to end at a single point.

                            The triangle's three angles add up to a total of 180 degrees.

  The lengths are given as a = 725 feet, b = 650 feet, and c = 575 feet.

Since, we know the fact that angle opposite to largest side is greatest. Hence, the largest angle would be opposite to side a.

Now, use the law of cosine

          cosA = b² + c² - a²/2bc

On substituting the values, we get

      cosA = (650)² + ( 575 )² - ( 725)²/2*650*575

                = 422500 + 330625 - 525625/747500

                 =  227500/747500

                 =  7/23

           A =   cos⁻¹  ( 7/23)

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Using the associative property of multiplication the missing value of (x × 8) × 2 =  4 × (2 × 8) is 4.

The associative property of multiplication tells us how we group factors that does not alter the result of the multiplication. Therefore, the associative property of multiplication can be represented as follows:

a x (b x c) = (a x b) x c

where

Therefore, let's use the associative property of multiplication to solve the following.

(x × 8) × 2 =  4 × (2 × 8)

Hence, using the rule, of associative property of multiplication, a x (b x c) = (a x b) x c, the missing variable is 4.

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The number of groups of one third in 9 is 27

The problem requires the use of division

To determine the number of groups of 1/3 in 9, we can divide 9 by 1/3:

= 9 / (1/3)

= 9 * 3

= 27

Therefore, there are 27 groups of 1/3 in 9.

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When Kayla was instructed to rewrite the polynomial expression x2 + 6x + 9, she wrote [tex]x^2+2 x-3+3^2=(x+3)^2[/tex].

Factor [tex]$ x^2+6 x+9: \quad(x+3)^2$[/tex]

[tex]$$x^2+6 x+9$$[/tex]

Rephrase in the manner of [tex]$a^2+2 a b+b^2$[/tex] :

[tex]$9=3^2$[/tex]

[tex]$6 x=2 x \cdot 3$\\$=x^2+2 x \cdot 3+3^2$[/tex]

Using the Perfect Square Formula : [tex]$\quad a^2+2 a b+b^2=(a+b)^2$[/tex]

[tex]$$\begin{aligned}& x^2+2 x-3+3^2=(x+3)^2 \\& =(x+3)^2\end{aligned}$$[/tex]

An expression that solely uses the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables is said to be a polynomial. Variables, which are sometimes known as indeterminates, and coefficients make up a polynomial. x2 4x + 7 is an illustration of a polynomial of one uncertain x.

An expression with a single or a number of terms is referred to as a polynomial. The words "polynomial" and "nomial," which are two distinct phrases, are the origins of the term. Nominal is another word for many, while poly is another word for many. An algebraic expression with two or more algebraic terms is referred to as a polynomial.

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Answer:

Bigger number: 20

Smaller number: 13

Step-by-step explanation:

Let smaller number = x

Bigger number. = x + 7

From the question; 2x + 3(x + 7) = 86

2x + 3x + 21 = 86

5x + 21 = 86

5x = 86 - 21

5x = 65

x = 13

Therefore the smaller number is 13, and the bigger number is 13 + 7 = 20