two airplanes leave chicago at the same time and fly in opposite directions. if one travels at 430 miles per hour and the other at 570 miles per hour, how long will it take for them to be 2000 miles apart?

The functions are classified as follows:

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

Hence the conditions needed for a function to be a linear function are given as follows:

The functions are given as follows:

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The value of x and y for the parallelogram PQRS is 2 and 5 respectively.

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.

A parallelepiped is a three-dimensional shape with parallelogram-shaped faces.

The qualities of a parallelogram are shared by the shapes of a square and a rectangle.

PT=​y, TR=2x+​1, QT=45y, TS=7x+11

The diagonals of a parallelogram bisect each other:

So, PT = TR and QT = TS

Thus, the system of equation is:

y = 2x+1  

5y = 7x+11

Multiply the first equation by 5:

5y = 10x+5  

Set the two equations as equal:

10x + 5 = 7x + 11

Subtract 7x from each side.

10x + 5 -7x = 7x + 11 -7x

3x + 5 = 11

Subtract 5 from both sides:

3x + 5 - 5 = 11 - 5

3x = 6

x = 2

Now solve for y:

y = 2x+1

y =2(2)+1

y =5

Hence, the value of x and y for the parallelogram PQRS is 2 and 5 respectively.

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As per the above given question the reflection of m∠O=112°.

A process of introspection or self-examination is reflection. It entails reflecting critically on one's thoughts, feelings, and experiences in order to comprehend oneself better. Self-awareness and insight can be developed through reflection, which can result in personal development and change.

In a larger sense, reflection also refers to the bouncing back of light, sound, or other waves from a surface and is employed in many disciplines, including arithmetic, computer science, and optics. The capacity of a computer program to review and alter its own structure and behavior at runtime is known as reflection in computer programming.

According to question:

Here are given m∠G=61 m∠f=7

From angle sum property of triangle, we get in ΔGFA

m∠G+m∠F+m∠O=180°

⇒61+7+m∠O=180

⇒68+m∠O=180

Therefore m∠O=180-68=112

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The plane is 361.99 miles from its starting point on a bearing of 147.72 degrees from due north.

To calculate the distance travelled by plane, we can use the formula:

distance = speed x time

First, let's calculate the distance travelled from point A to B:

distance = 110 mph x 1.6 hours = 176 miles

Next, let's calculate the distance travelled from point B to C:

distance = 110 mph x 2.9 hours = 319 miles

To calculate the total distance from the starting point, we need to find the hypotenuse of the triangle formed by points A, B, and C. To do this, we need to utilise the Pythagorean theorem:

c² = a² + b²

Where c is the distance between the two points and a and b are the distances travelled in each direction. In this case, a is the distance from A to B (176 miles), and b is the distance from B to C (319 miles).

c² = 176² + 319²

c = √(176² + 319²)

c = √(31,521 + 100,761)

c = √(132,282)

c = 361.99 miles (rounded to three decimal places)

So, the plane is 361.99 miles from its starting point.

To find the bearing of the plane from its original location, we need to use the arctangent formula:

θ = arctan(b/a)

Where θ is the bearing, and a and b are the distances travelled in each direction. In this case, a is the distance from A to B (176 miles) and b is the distance from B to C (319 miles).

θ = arctan(319/176)

θ = 57.72 degrees (rounded to three decimal places)

This means the plane is 57.72 degrees from due north. To find the actual bearing from due north, we need to add 90 degrees since the plane is travelling in the northeasterly direction:

Bearing = 90 + 57.72 = 147.72 degrees (rounded to three decimal places)

In conclusion, the plane is 361.99 miles from its starting point on a bearing of 147.72 degrees from due north.

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The gross pay is $496.68.

To calculate the gross pay, you need to calculate the total pay for the regular hours worked and the overtime hours worked separately, and then add them together.

Total pay for regular hours: 51 hours x $7.35/hour = $375.35

Overtime hours worked: 11 hours

Overtime rate of pay: 1.5 times the regular rate of pay, or $7.35 x 1.5 = $11.03

Total pay for overtime hours: 11 hours x $11.03/hour = $121.33

Gross pay: $375.35 + $121.33 = $496.68

So the gross pay is $496.68.

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Amount of pretzel each person receives is 17/16 lb.

Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.

Here, a is called the numerator and b is called the denominator.

Total weight of the bag of pretzels = 34 ounce

Elisa shares this among her two sisters equally.

Share of pretzels each sister gets = 34 / 2 = 17 ounces

We need this amount in pounds.

We know that,

16 ounce = 1 lb.

17 ounces = 17/16 lb.

Hence the amount of pretzels each get is  17/16 lb.

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Answer:

c below

Step-by-step explanation:

you: 25 +$3 /week * x weeks

sis: 40 + 2/week * x weeks

they have to equal to each other

so 25 + 3x = 40 +2x

move x around & simplify

so x = 15

total 25+3*15 = 25+45 = 70

Answer:

[tex]0 < \text{x} \le 4[/tex]

If x is an integer, then x is any value in the set {1,2,3,4}

======================================================

Work Shown:

x = length of each side

6x = perimeter of the regular hexagon

The perimeter must be greater than 0.

Also, the perimeter must be less than or equal to 24. This is because of the phrasing "perimeter is at most 24 inches".

In other words, the perimeter is between 0 and 24, excluding 0 and including 24.

[tex]0 < \text{ perimeter } \le 24\\\\0 < 6\text{x} \le 24\\\\0/6 < 6\text{x}/6 \le 24/6\\\\0 < \text{x} \le 4\\\\[/tex]

If x is an integer, then x can be any value in the set {1,2,3,4}

Examples:

The slope of the line represented by the given data is; 1

The slope of a line is defined as the rate of change of y divided by the rate of change of x.

Thus, the formula to find the slope between two coordinates is;

m = (y2 - y1)/(x2 - x1)

Taking the last two coordinates gives us;

m = (16 - 13)/(7 - 3)

m = 3/3

m = 1

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Answer:

x = 50

Step-by-step explanation:

50 + 2x = 150

2x = 100

x = 50

Step-by-step explanation:

A,No, there isn't a more efficient way to solve this system.

B.Yes, a more efficient way is to multiply the first equation by 4, add to eliminate y, then solve for x.

C.Yes, a more efficient way is to multiply the first equation by −4, add to eliminate y, then solve for x.

D.Yes, a more efficient way is to multiply the first equation by −4, add to eliminate x, then solve for y.

The Answer is 1440 There are two possibilities for the person who demands to be either first or last: they can be first in line, or they can be last in line.

The problem is asking for the number of ways 7 engineering students can line up for presentations at a hiring fair, where one person demands to be either the first or last in line.

If they are first in line, then there are 6 students left to line up. The number of ways to line up 6 students is 6!, which is 720.

If they are last in line, then there are also 6 students left to line up, and the number of ways to line up 6 students is 6! or 720.

So, the total number of ways to line up the 7 students is 720 + 720 = 1440.

Therefore, the answer to the question is 1440.

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Answer:

Decimal0.395062

Step-by-step explanation:

16

(18)(1)

2

32/81

Answer:

The value of (16/81)^1/2 is  4/9.

Step-by-step explanation:

What is the expression?

An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

= the square root of 16/81

=4/9.

The value of (16/81)^1/2 is  4/9.

Answer: yes

Step-by-step explanation:

false :) thats ur answer

The value for x is 30 cm.

equivalent triangles

According to  the following equation is valid:

x/75 = 12/30

30x = 900 is obtained by dividing by 12 * 75.

Divide both sides of 30x/30 to get 900/30x = 30.

As a result, the value of x is 30 cm.

Two rectangles are said to be comparable if the ratio of one triangle's two sides to the two sides of that other triangle is the same, and the angles that the two sides of both triangles inscribe are equal. This means that if A = X and Acceptor = AC/XZ, then ABC XYZ.

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I understand the question looking for is :

What is the value of x?

X= 4.8 cm

X= 30 cm

X= 93 cm

X= 187.5 cm

The value for x is 30 cm.

equivalent triangles

x/75 = 12/30

30x = 900 is obtained by dividing by 12 * 75.Divide both sides of 30x/30 to get 900/30x = 30.

As a result, the value of x is 30 cm.

What are some similar triangles?

Two rectangles are said to be comparable if the ratio of one triangle's two sides to the two sides of that other triangle is the same, and the angles that the two sides of both triangles inscribe are equal. This means that if A = X and Acceptor = AC/XZ, then ABC XYZ.

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I understand the question looking for is :

What is the value of x?

X= 4.8 cm

X= 30 cm

X= 93 cm

X= 187.5 cm

given information are :- test mean () = 25.5 populace sd () = 5.3 example size (n) = 360 a).z critical value for 95% confidence level,

both followed tests be:- the 95% confidence interval for the mean load of every one of the one-year-old child young men in the US.

To get a 95% confidence interval, we should incorporate the focal 90% of the probability of the normal distribution. On the off chance that we incorporate the focal 90%, we leave out a sum of α = 10% in the two tails, or 5% in each tail, of the normal distribution.

To catch the focal 95%, we should go out 1.645 "standard deviations" on one or the other side of the determined example mean. The value 1.645 is the z-score from a standard normal probability distribution that puts an area of 0.90 in the middle, an area of 0.05 in the extreme left tail, and an area of 0.05 in the extreme right tail.

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The complete question is:

According to the National Health Statistics Reports, a sample of 360 one-year-old baby boys in the United States had a mean weight of 25.5 pounds. Assume the population standard deviation is σ = 5.3 pounds.

a. Construct a 95% confidence interval for the mean weight of all one-year-old baby boys in the United States

b. Should this confidence interval be used to estimate the mean weight of all one-year old babies in the United States? Explain.

c. Based on the confidence interval constructed in part (a), is it likely that the mean weight of all one-year-old boys is less than 28 pounds?

The value of n that makes the equation true is 0.

In Mathematics, an exponent is sometimes referred to as power and it can be defined as a mathematical operation that is used in conjunction with an algebraic expression to raise a quantity to the power of another and it is generally written as;

bⁿ

Where:

the variables b and n represent numerical values or an algebraic expression.

By applying the property of exponents based on the law of indices for powers and division, we have the following:

Expression = 85^n/85^6 = 85^{-6}.

Expression = 85^{n - 6} = 85^{-6}

Since the powers both have a common base, we have:

n - 6 = -6

n = 6 - 6

n = 0.

Check:

85^0/85^6 = 85^{-6}

1/85^6 = 85^{-6}

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Answer:

196.1 cm^2

Step-by-step explanation:

The area of a circle is given by Area = πr^2

R is (15.8 cm)/2 = 7.9 cm

Area = (3.14)*(7.0cm)^2

Area = 196.1 cm^2

Answer:

The formula to calculate the area of a circle is given by: A = π * r^2, where r is the radius of the circle.

Given the diameter of 15.8 cm, we can calculate the radius by dividing the diameter by 2: r = 15.8 cm / 2 = 7.9 cm

Plugging the value of the radius into the formula: A = π * 7.9^2 = 3.14 * 62.41 = 196.0794 cm^2

Rounding the answer to the nearest hundredth, the area of the circle with a diameter of 15.8 cm is approximately 196.08 cm^2.

If x > y and a > b, the option that must be true is D. x + a > y + b.

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

If two inequalities have inequality symbols facing the same direction, we can add the inequalities

For example: 4 < 7 and 1 < 10

So, we can add them to get: 4 + 1 < 7 + 10

Since x > y and a > b have inequality symbols facing the same direction, we can add the inequalities to get: x + a > y + b

The correct option is D.

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If x > y and a > b, which of the following must be true?

A. x > a

B. y > b

C. x + b > y + a

D. x + a > y + b

E. a + b > x + y

There are 107 different methods to disembark.

When you mention "no two folks exit on the same floor," I suppose you mean that each of the seven people exits the elevator on a different floor.

The first person can exit the elevator on any of the building's 10 levels, followed by the second person on any of the other 9 floors, and so on.

The total number of ways in which the 7 people can exit the elevator from different floors is 10P7 ways.

The first person, as well as the second, third, and other people, can exit from any of the ten floors, thus we take this into consideration when calculating the overall number of exits. Therefore, there are 107 different methods to disembark.

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Answer:

1 year

Step-by-step explanation:

the equation to find simple interest

A = P (1 + rt)

so plug in yore numbers

400=300(1+0.4*t)

400=300+120t

120=120t

1=t

The circumference of the circle in terms of π is 8π yards.

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications.

Perimeter refers to the total outside length of an object,

here, we have,

the diameter of the circle = 8yrd

the circumference of the circle in terms of π

=π  * 8

= π8 yrd.

Hence, The circumference of the circle in terms of π is 8π yards.

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The graph presents information gathered through a survey or questionnaire, and the information is presented as a percentage to show the proportion of participants who answered in a particular way.

Percentage is a mathematical concept that represents a proportion of a whole as a fraction of 100. It is used to express how much of a whole something is and is commonly used in statistics and data analysis.

The bar graph shows three different percentages: 1.59%, 17.46%, and 25.4%. To verify these percentages, we need to know the total number of participants who answered the question and the number of participants who answered in a particular way.

If 100 participants answered the question, then 1.59% would represent 1.59 participants, 17.46% would represent 17.46 participants, and 25.4% would represent 25.4 participants.

It is important to consider whether the percentages reported in this graph are likely to be representative of all people.

This will depend on a number of factors, including the sample size, the method used to select participants, and the representativeness of the sample in relation to the population as a whole.

If the sample size is small, or if the participants were selected in a biased way, then the percentages may not be representative of all people.

If, however, the sample size is large and the participants were selected randomly, then the percentages may be representative of the population as a whole.

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The required value of the cos(θ) for the interval 0 < θ < π/2 is given as 0.857.

These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.

The value of cos(θ) can be found using the Pythagorean identity:

cos²(θ) + sin²(θ) = 1

Substituting the given value of sin(θ) = 0.515, we have:

cos²(θ) + 0.515² = 1

cos²(θ) = 1 - 0.515²

cos(θ) = √(1 - 0.515²)
        = √(1 - 0.265)
        = √(0.735) ≈ 0.857

So, cos(θ) = 0.857.

Thus, the required value of the cos(θ) for the interval 0 < θ < π/2 is given as 0.857.

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The volume of the solid given by rotating the region bounded by the curves y = x^2, x = 5, and y = 0 about the x-axis is 625π.

When the region bounded above by the graph of f, below by the x-axis, and on the sides by x = a and x = b is rotated about the x-axis, the volume V of the generated solid is given by V = ∫ab π [f(x)]^2 dx. We can also find solids by revolving curves about the y-axis.

Whereas the basic formula for the area of a rectangular shape is length * width, the basic formula for volume is length * width * height. How we refer to the different dimensions does not change the calculation. We may, for example, use depth instead of height.

In this case, the bounds of integration are from 0 to 5. The radius function is going to be:

r (x) = x^2

Now, substitute the value into the formula for the disk method:

V = π * ∫ba * [r(x)]^2 * dx

So, in this case it will be:

V = π * ∫5 0 * [x^2]^2 * dx

= π * ∫5 0 * x^4 * dx

= π * x^5 / 5 ∣ 5 0

= π * ((x^5 / 5) – (0 / 5))

= 625π

Hence, the volume of the solid is 625π.

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The division problem that the area model represents is; 0 remainder 32

We are given that the accurate division;

3600/45 = 80

We are also given that the accurate division as;

315/45 = 7

Now, we want to find 32/45 which would lead to a remainder. Thus, we have;

45 cannot go into 32 at all and as such, we will have the result as 0 remainder 32

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