Traveling with the wind, a plane takes 2 1/2 hours to fly a distance of 1500 miles. The return trip of 1500 miles against the same wind speed, takes 3 hours. Find the speed of the plane with no wind and the speed of the wind.

Answer:

Option A) is correct.

Step-by-step explanation:

We need to use normalcdf command to find the probability that the variable would fall into a certain interval that we would supply.

As

and

And we have to determine the percent of students have scored more than 75 points.

So,

Mean = μ = 60

Standard Deviation = σ = 5

As we have to determine the percent of students have scored more than 75 points.

Hence,

normalcdf(75,100,60,5) = .0013

Converting on percentage → .0013 × 100 = 0.1

Therefore, option A) is correct as 0.1 percent of students have scored more than 75 points.

Keywords: distribution, mean, median

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Answer:

Step-by-step explanation:

The square sheet has an area of 100 square meters.

Hence, the width of the sheet is [tex]\sqrt{100} = 10[/tex] meters.

The scale factor is needs to be in such a way, so that the film's wide will be match perfectly with the square sheet. Hence, 35x millimeters = 10 meters = 10000 millimeters .

[tex]x = \frac{10000}{35} = 285.7143[/tex].

Answer: 2,970

Step-by-step explanation:

The number of ways to arrange n things such that a things are identical , b things are identical , and so on is  [tex]\dfrac{n!}{a!\cdot b!\cdot ....}[/tex] .

As per given , we have

Number of Geometry books = 2

Number of Algebra books = 8

Number of Pre-Calculus books =2

Total books = 2+8+2=12

Then, the number of ways to arrange them : [tex]\dfrac{12!}{2!\cdot 8!\cdot 2!}[/tex]

[tex]=\dfrac{12\times11\times10\times9\times8!}{2\times8!\times2}=2970[/tex]

Hence, the total number of ways to arrange 2 Geometry books, 8 Algebra books and 2 Pre-Calculus books is 2,970.

To find the number of arrangements of different books on a shelf, we use the concept of permutations of multiset in combinatorics. For 12 books (2 Geometry, 8 Algebra, 2 Pre-Calculus), the number of arrangements is the factorial of the total (12!) divided by the product of factorials for each group of identical items (2!, 8!, 2!).

The question is asking how many ways you can arrange identical books of different subjects on a shelf. Here, we need to use the concept of permutations of multiset, often used in combinatorics. For 12 books in which 2 are Geometry, 8 are Algebra and 2 are pre-Calculus, the number of permutations is given by 12! / (2! * 8! * 2!). This formula is derived from the general principle of permutations of multisets where you divide the factorial of the total number of items by the product of factorials for each group of identical items.

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Answer:

The exact value of cotФ  is  [tex]\frac{\sqrt{7}}{3}[/tex]  

Step-by-step explanation:

Given as:

The value of cosec Ф = [tex]\frac{-4}{3}[/tex]

Let the value of  cotФ = x

Now, According to question

∵  sinФ = [tex]\frac{1}{cosec\Theta }[/tex]                       .....1

Put the value of cosec Ф = [tex]\frac{-4}{3}[/tex] in eq 1

i.e  sinФ = [tex]\frac{1}{\frac{-4}{3} }[/tex]

Or,  sinФ = [tex]\frac{-3}{4}[/tex]

Again

∵ cosФ = [tex]\sqrt{1-sin^{2}\Theta }[/tex]

So,  cosФ = [tex]\sqrt{1-(\frac{-3}{4})^{2}}[/tex]

Or, cosФ = [tex]\sqrt{1-(\frac{9}{16})}[/tex]

Or,  cosФ = [tex]\sqrt{\frac{16 - 9}{16})}[/tex]

∴  cosФ = [tex]\frac{\sqrt{7}}{4}[/tex]

Again

we know that cotФ = [tex]\frac{cos\Theta }{sin\Theta }[/tex]

So,  cotФ  = [tex]\frac{\frac{\sqrt{7}}{4}}{\frac{-3}{4}}[/tex]

Or,  cotФ  = [tex]\frac{-\sqrt{7}}{3}[/tex]

As according to question sinФ lies in third quadrant

So,  cotФ  =  [tex]\frac{\sqrt{7}}{3}[/tex]

Hence, The exact value of cotФ  is  [tex]\frac{\sqrt{7}}{3}[/tex]   . Answer

You can use any of the available methods for solving system of linear equations like method of elimination or method of substitution etc.

There are no solutions to the given system of equations.

For that , we will try solving it first using the method of substitution in which we express one variable in other variable's form and then you can substitute this value in other equation to get linear equation in one variable.

If there comes a = a situation for any a, then there are infinite solutions.

If there comes wrong equality, say for example, 3=2, then there are no solutions, else there is one unique solution to the given system of equations.

The given system of equations is

[tex]2x - 6y = 5\\x - 3y = -12[/tex]

Using second equation to get x in terms of y

[tex]x - 3y - 12\\x = 3y - 12[/tex]

Substituting this expression for x in place of x in first equation,

[tex]2x - 6y = 5\\2( 3y - 12) - 6y = 5\\6y - 24 - 6y = 5\\-24 = 5[/tex]

The last statement we got is incorrect.

That conclusion above shows that the given system of equation has no solution.

We could've detected it from the fact that

[tex]2x - 6y = 5\\\text{dividing both sides by 2}\\x - 3y = 2.5[/tex]

Converting both equations to slope intercept form, we get:

[tex]x - 3y = 0.5\\\\y = \dfrac{1}{3}x - \dfrac{1}{6}[/tex]

and

[tex]x - 3y = -12\\\\y = \dfrac{1}{3}x + 4[/tex]

We see that both lines have same slope but different y intercept, which tells that both lines are parallel but not coincident, thus, not intersecting and thus, no common point(common points are solutions).

The graph of this system of linear equation is given below where lines represented by both linear equations are plotted.

Thus,

There are no solutions to the given system of equations.

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Final answer:

To solve the system of equations using substitution, rearrange one of the equations to solve for a variable and substitute that expression into the other equation. In this case, the system of equations is inconsistent and has no solutions.

Explanation:

To solve the system of equations using substitution, we rearrange one of the equations to solve for a variable, then substitute that expression into the other equation. Let's solve the system of equations:

Equation 1: 2x - 6y = 5

Equation 2: x - 3y = -12

Therefore, the system of equations is inconsistent, and there are no solutions.

Answer:

  20 1/6 ft

Step-by-step explanation:

The perimeter is the sum of the lengths of the sides:

  2×(5 1/3 ft) + 2×(4 3/4 ft) = 10 2/3 ft + 8 6/4 ft

  = 10 2/3 ft + 9 2/4 ft . . . . change 6/4 ft to 1 1/2 ft

  = 10 8/12 ft + 9 6/12 ft = 19 14/12 ft  . . . . . use common denominator of 1/12 ft

  = 20 2/12 ft . . . . . . change 14/12 ft to 1 2/12 ft; next reduce that fraction

  = 20 1/6 ft . . . . perimeter of Caleb's bathroom

Answer: x = 5

Step-by-step explanation: This is an isosceles triangle, which means two sides are equal in length and two angles are equal in measurement.

Line BA = Line BC

Similarly, Angle A = Angle C

Angle A plus Angle C equals 146°

Also the sum of the interior angles of a triangle is 180°

Therefore, 146 + (6x + 4) = 180

Subtract 146 from both sides of the equation

6x + 4 = 34

Subtract 4 from both sides of the equation

6x = 30

Divide both sides of the equation by 6

x = 5

Answer:

.

Step-by-step explanation:

Answer:

Because order matters when performing subtraction or division.

Step-by-step explanation:

Consider the provided information.

We need to determine why there no commutative property for subtraction or division.

Commutative property states that although the numbers in an expression are interchanged, there is no change in result.

Let us understand with the help of an example

For addition: The commutative rule is a + b = b + a.

An example in numbers would be 5 + 2 = 2 + 5

Both give 7 as result.

For Subtraction:  4 – 2 = 2, but 2 – 4 = –2

So, in the case of subtraction, moving the numbers around produces a different answer.

For division: 4 ÷ 2 = 2,  2 ÷ 4 = [tex]\frac{1}{2}[/tex]

So, in the case of division, moving the numbers around produces a different answer.

Hence, order matters when performing subtraction or division.

Answer: Using Pythagoras Rule the ladder touches 13.75ft ~ 14ft up the wall.

Step-by-step explanation: Using the Pythagoras Rule the Hypothenus is the leaning hieght of the ladder 15ft

And the base is 6ft. Now let's find the height of the wall h¹

h¹ = √{15² - 6²}

h¹ =√{225 - 36}

h¹ = √189

= 13.74ft

Answer:

100

189

83

Step-by-step explanation:

Firstly, we can see that there are three aircrafts. Let the number of aircrafts in the second aircraft be x.

Then the first has 89 more seats meaning it has a total seats of x + 89

The third has 17 fewer seats meaning x - 17

Now we are expected to find the number of seats on each of the aircraft officials.

We add all and then sum to the total 372.

This means

x + x + 89 + x - 17 = 372

3x + 72 = 372

3x = 300

x = 300/3 = 100

The aircrafts thus have 100 seats, 189 and 83 seats in no particular order

Answer:

Step-by-step explanation:

The Standard Deviation Rule states that for a normal distribution, nearly all of the data will fall within three standard deviations of the mean . The empirical rule is further illustrated below

68% of data falls within the first standard deviation from the mean.

95% fall within two standard deviations.

99.7% fall within three standard deviations.

The distribution of the IQ (Intelligence Quotient) is approximately normal in shape with a mean of 100 and a standard deviation of 15.

Therefore, the range of IQ scores that many (68%) people have is between

100 - 15 and 100 + 15

It becomes

85 to 115

The range of  IQ scores for 68% of the people varies from 85  to 115

Given that the distribution of IQ (Intelligence Quotient) is approximately normal in shape

[tex]\rm Mean\; IQ =\mu = 100 \\Standard\; deviation = \sigma = 15[/tex]

According to the empirical relation for normal curve 68% of the data lies in the range

[tex]\rm \mu + \sigma\; to \; \mu - \sigma[/tex]

So the  lower limit of the range of  the normal distribution of IQ score  = 100 -15 = 85

The upper limit of the range of the normal distribution of IQ score  = 100 + 15 = 115

So we can conclude that the range of  IQ scores for 68% of the people varies from 85  to 115

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Answer:

Step-by-step explanation:

11)

√(343 x^4)=√(7×7×7×x^4)=7√7 x^2

Answer: 7√ 7x^2

7 √ 7= 18.52x^2

Step-by-step explanation:

√ 343x^4 = √ 7×49x^4

=7 √ 7x^4×1/2

=7 √ 7x^2

Answer:

Option 3) area space occupied by any sample of matter              

Step-by-step explanation:

We define volume of an object as:

Option 3) area space occupied by any sample of matter

It is not a unit for measuring distance.

It cannot be defined as amount of matter in an object force per unit

Answer:

2 hours working on problems, 2 hours reading

Step-by-step explanation:

The question is incomplete. Here is the complete question:

Ben is a hard-working college senior. One Thursday, he decides to work nonstop until he has answered 150 practice problems for his math course. He starts work at 8:00 AM and uses a table to keep track of his progress throughout the day. He notices that as he gets tired, it takes him longer to solve each problem.

Time          |   Total Problems Answered

8:00 AM   |   0

9:00 AM   |   60

10:00 AM |   105

11:00 AM  |   135

Noon   |   150

The marginal, or additional, gain from Ben's first hour of work, from 8:00 AM to 9:00 AM, is 60 problems.

The marginal gain from Ben's third hour of work, from 10:00 AM to 11:00 AM, is 30 problems.

Later, the teaching assistant in Ben's math course gives him some advice. Based on past experience, the teaching assistant says, "working on 40 problems raises a student's exam score by about the same amount as reading the textbook for 1 hour". For simplicity, assume students always cover the same number of pages during each hour they spend reading.

Given this information, in order to use his 4 hours of study time to get the best exam score possible, how many hours should he have spent working on problems, and how many should he have spent reading?

The marginal or additional gain in the above question is calculated by obtaining the difference in problems solved between two selected time frames . For example, the marginal or additional gain from Ben's 11 AM to Noon work is :

Additional gain from 11 AM to Noon = 150 - 135 = 15 problems

Ben should therefore make his decision at the margin. Each hour, he should select the option that will improve his exam grade by the largest amount. If he can do more than 40 problems in an hour, working on problems will help raise his grade more for that hour than reading would.The marginal gain from the first hour is 60 problems. The marginal gain from the second hour is 45 problems. He will stop there, because he will get only 30 problems done if he spends the third hour working on problems. Therefore, he should stop working on problems and spend his remaining 2 hours reading instead.

Answer:

see explanation

Step-by-step explanation:

(1)

Given

[tex]\frac{n}{5}[/tex] = - 0.3

Since n is divided by 5 then use the inverse operation, multiplication.

Multiply both sides by 5 to clear the fraction

n = 5 × - 0.3 = - 1.5

(2)

Given

- 2n = 4 [tex]\frac{1}{3}[/tex] ← change to an improper fraction

- 2n = [tex]\frac{13}{3}[/tex]

Since n is multiplied by - 2 then use the inverse operation, division.

Divide both sides by - 2

n = [tex]\frac{13}{-6}[/tex] = - [tex]\frac{13}{6}[/tex]

Answer:

The signal will not be picked up if he drives from the first city to the second city as far as he drives along a straight line.

Step-by-step explanation:

The attachment to the answer clearly explains why no signal will be picked up

Answer:

The answer is 38.5 miles

Step-by-step explanation:

From the attached diagram

AC represents the distance needed to be traveled before picking the signal.

Using Pythagoras'rule to solve for AC from triangle ACO

(AO)^2 = (AC)^2 + (CO)^2

(60)^2 = (AC)^ + (46)^2

(AC) = ✓[(60)^2 - (46)^2]

AC = 38.5 miles

Answer:the first place seller receives $56

The second place seller receives $28

The third place seller receives $20

Step-by-step explanation:

Let x represent the amount that the first place seller would receive.

Let y represent the amount that the second place seller would receive.

Let z represent the amount that the third place seller would receive.

The second place winner will receive 8 more dollars than the third place winner. This means that

z = y - 8

The first place seller will receive twice as much as the second place seller. It means that

x = 2y

The profit portion they will share is $ 104. It means that

x + y + z = 104 - - - - - - - - - - - 1

Substituting z = y - 8 and x = 2y into equation 1, it becomes

2y + y + y - 8 = 104

4y = 104 +8 = 112

y = 112/4 = 28

x = 2x = 2 × 28

x = 56

z = y - 8 = 28 - 8

z = 20

Answer: each salesperson sold 89 cars last year.

Step-by-step explanation:

The total number of sales people at the dealership shop is 13.

Last year they each sold the same number of cars. The total number of cars that they sold together last year was 1157. Therefore, the number of cars that each salesperson sold would be

Total number of cars sold/ number of salespersons

It becomes

1157/13 = 89

Answer:

The answer to your question is 40.60°

Step-by-step explanation:

Data

Right triangle

Opposite side = 6

Adjacent side = 7

Process

1.- To find angle A, use trigonometric functions.

The trigonometric function that relates the opposite side and the adjacent side is tangent

           tanA = [tex]\frac{Opposite side}{Adjacent side}[/tex]

2.- Substitution

           tan A = [tex]\frac{6}{7}[/tex]

3.- Find tan⁻¹A

        tan⁻¹ A = A = 40.60°

Answer:

1. Given

2. Alternate interior angle theorem

3. Alternate interior angle theorem

4. Reflexive property of congruence

5. ASA

Step-by-step explanation:

1. JK || LM, JL || KM

This is the information given in the problem statement.

2. ∠JKL ≅ ∠MLK

∠JKL and ∠MLK are alternate interior angles.  Since JK and LM are parallel, the alternate interior angles are congruent.

3. ∠JLK ≅ ∠MKK

∠JLK and ∠MKL are alternate interior angles.  Since JL and KM are parallel, the alternate interior angles are congruent.

4. KL ≅ LK

According to reflexive property, a segment is always congruent to itself.

5. ΔJKL ≅ ΔMLK

We have two triangles with two pairs of congruent angles, and a pair of congruent sides between those angles.  Therefore, the triangles are congruent by ASA.

Answer:

The amount invested at 6% is $12,857.14

The amount invested at 13% is $17,142.86

Step-by-step explanation:

Let

x ----> the amount invested at 6%

30,000-x -----> the amount invested at 13%

we know that

The interest earned by the amount invested at 6% plus the interest earned by the amount at 13% must be equal to the interest earned by the total amount of $30,000 at 10%

Remember that

[tex]6\%=6\100=0.06[/tex]

[tex]13\%=13\100=0.13[/tex]

[tex]10\%=10\100=0.10[/tex]

so

The linear equation that represent this situation is

[tex]0.06x+(30,000-x)0.13=0.10(30,000)[/tex]

solve for x

[tex]0.06x+3,900-0.13x=3,000\\0.13x-0.06x=3,900-3,000\\0.07x=900\\x=\$12,857.14$[/tex]

[tex]x-\$30,000=\$17,142.86[/tex]

therefore

The amount invested at 6% is $12,857.14

The amount invested at 13% is $17,142.86

Answer:

Segments with positive slope, negative slope, zero slope and undefined slope are indicated in the attach.

Step-by-step explanation:

When you represent or consider a segment in a coordinate axis system, the slope of the segment is the variation in "x" axis in relation to variation in "y" axis, it means the quotient Δx/Δy. If we select two different pairs of points (x1, y1) (x2, y2) ⇒slope =  Δx/Δy ⇒ slope = (x2 - x1)/(y2 - y1).

There four main options:

- If  Δx/Δy > 0 ⇒ Positive slope (In this case: Δx >0 and Δy> 0 or Δx˂ 0 and Δy ˂  0).

- If Δx/Δy ˂  0 ⇒Negative slope (this happens when Δx > 0 and Δy˂0 or

Δx˂0 and Δy>0)

- If Δx/Δy = 0 ⇒ zero slope (This happens when Δx =0).

-If Δx/Δy =∅ ⇒ undefined slope (only when Δy = 0).

Given this explanation and considering the word MATH in a coordinated system, we clasiffied the segments as you can see in the attach. Segments denoted by: 1 have positive slopes, 2 negative slopes, 3 zero slope and 4 unddefined slope.

Answer:

number  ,proportion

Step-by-step explanation:

Data is a collection of facts, such as numbers, words, measurements, observations. Data is organised in graphs or charts for analysis and conclusions.

A frequency distribution lists the number of occurrences of each category of data.

A relative frequency distribution lists  the proportion of occurrences of each category of data.

A frequency distribution lists the number of occurrences, and a relative frequency distribution lists the proportion of occurrences of each category of data. Frequency tables compile occurrences, while relative frequencies are calculated as a ratio of the frequency to the total number of observations. Histograms and bar graphs visually represent these distributions.

A frequency distribution lists the number of occurrences of each category of​ data, while a relative frequency distribution lists the proportion of occurrences of each category of data. When we compile a frequency table, the data are organized so that we know how many times a particular value or category occurs. For example, a frequency distribution can inform us that 15 students spend five hours or more studying for an exam.

Conversely, a relative frequency distribution provides us with a ratio or fraction that represents how often a value appears relative to the entire set of data. To calculate relative frequency, one would divide each frequency by the total number of observations. If 20 students were surveyed, and 5 studied for more than five hours, the relative frequency would be 5/20 or 0.25 (which can also be expressed as 25%).

Graphical representations such as histograms and bar graphs are valuable for visualizing both frequency and relative frequency. A histogram is suitable for displaying the distribution of interval or ratio variables, particularly with a large number of cases. Bar graphs are more commonly used for nominal or ordinal data, which usually involves fewer categories.

Answer:

Each tank would have 27 gold fish in it.

Step-by-step explanation:

Given:

Number of fish tanks = 8

Number of gold fish = 216

We need to find the number of goldfish in each tank.

Solution:

Now we know that;

Number of gold fish must be equal in each tank.

To find the number of gold fish in each tank we will divide Number of gold fish by Number of fish tanks.

framing in equation form we get;

number of gold fish in each fish tank = [tex]\frac{216}{8} = 27 \ fish[/tex]

Hence Each tank would have 27 gold fish in it.

Answer:

18.3 pounds of water must evaporate to make it 8% solution

Step-by-step explanation:

Brine is a solution containing water & salt

Weight of brine solution = 50 pounds

amount of salts = 5% of 50 pounds = (5 ÷ 100) × 50 = 2.5 pounds.

Amount of water = 50 - 2.5 = 47.5 pounds

The new solution is to be made 8%, which indicates that 2.5 pounds of salt is going to be equivalent to 8% of the new salt and some amount of water has to be evaporated for the amount of salt to increase

Using direct relation expression

8% of the solution equivalent to 2.5 pounds of salt

100% will be equivalent to X pounds of solution

Upon cross multiplication,  

X = (100 × 2.5) ÷ (8) = 31.25 pounds of solution

There amount of water that must evaporate is difference between weight of initial solution & final solution

Amount of water to be evaporated = 50 - 31.25 = 18.25 pounds ∞ 18.3 lbs

The inequality required is t < 55.

Given:

To qualify for the championship, a runner must complete the race in less than 55 minutes.

In this question, we are dealing with the time taken by runners to complete a race. Let's use 't' to represent the time in minutes of a runner who qualifies for the championship. The condition for qualification is that the runner must complete the race in less than 55 minutes.

So, the inequality that represents this situation is: t < 55.

Any runner who completes the race in less than 55 minutes will qualify for the championship.

Answer:

Step-by-step explanation:

The total cost function based on the number of games sold can be written as C(x) = $6200 + $0.90x. This equation depicts that for every game produced and sold, the total cost increases by $0.90 from a base cost of $6200.

In this particular scenario, fixed costs are constant and turnover does not affect them, hence, a fixed cost of $6200. Variable costs, on the other hand, depend on the quantity produced, which in this case, is $0.90 per unit.

Therefore, as the production output - denoted as 'x' - increases, variable costs also increase, forming a direct relationship. According to the given information, the cost function, denoted as 'C', which represents the total cost, will be the sum of both fixed and variable costs.

So, the total cost function based on the number of games sold, can be written algebraically as: C(x) = $6200 + $0.90x.

This equation implies that for each game produced and sold, the total cost increases by $0.90, with a starting cost of $6200, the fixed costs.

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Final answer:

Ms. Vargas wants to sell 2/3 of her 4/5 acre of land. By multiplying the fractions, we find that she intends to sell 8/15 of an acre to her neighbor.

Explanation:

Ms. Vargas owns 4/5 of an acre of land and wants to sell 2/3 of her land. To find out what fraction of an acre Ms. Vargas wants to sell, we need to multiply these two fractions together.

Here is the step-by-step calculation:

Multiply the numerators (top numbers) of the fractions: 4 × 2 = 8.

Multiply the denominators (bottom numbers) of the fractions: 5 × 3 = 15.

Combine the products to get the fraction of the land she wants to sell: 8/15 of an acre.

Therefore, Ms. Vargas wants to sell 8/15 of an acre of her land to her neighbor.