how many different triangles can be constructed with angles that measure 120, 40, and 60

Answer:

The slope of a parallel line are equal,and the slope of perpendicular line are opposite reciprocals

The probability that exactly 15 out of 20 adults use their smartphones in meetings or classes is approximately 0.0667, rounded to four decimal places as requested.

This is a binomial distribution problem where:

n = 20 (number of trials)

p = 0.57 (probability of success)

We want to find the probability that exactly 15 out of 20 adults use their smartphones in meetings or classes.

Using the binomial probability formula:

[tex]P(X = k) = (n choose k) * p^k * (1-p)^(n-k)[/tex]

where (n choose k) = n!/(k!(n-k)!)

[tex]P(X = 15) = (20 choose 15) * 0.57^15 * (1-0.57)^(20-15)[/tex]

[tex]P(X = 15) = (15504) * 0.57^15 * 0.43^5[/tex]

[tex]P(X = 15) ≈ 0.0667[/tex]

Therefore, the probability that exactly 15 out of 20 adults use their smartphones in meetings or classes is approximately 0.0667, rounded to four decimal places as requested.

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Assume that when adults with smartphones are randomly​selected, 57​% use them in meetings or classes. If 20 adult smartphone users are randomly​ selected, find the probability that exactly 15 of them use their smartphones in meetings or classes. The probability is _____? ​(Round to four decimal places as​ needed.)

Answer:

Step-by-step explanation:

7

We can solve it by using a fractional part of a component of your body known as brain... which you might not have considering you asked such an high end mathematical question... This can be solved using the concept of Addition...

Answer:

V = [tex]40in^{3}[/tex]

Step-by-step explanation:

V = [tex]\frac{lwh}{3}[/tex]= [tex]\frac{5*4*6}{3}[/tex]= [tex]40in^{3}[/tex]

Answer:

The probability that the damaged thing came from B is .04/,19 = .2105 or 21.05% of the damaged goods come from company B.

Step-by-step explanation:

2030 military time is equivalent to 8:30 PM in standard 12-hour time notation.

2030 is a military time notation for 8:30 PM in standard 12-hour time notation.

In military time, the 24-hour clock is used, where the first two digits indicate the hour and the last two digits indicate the minutes. The hour digits range from 00 to 23, and the minute digits range from 00 to 59.

To convert 2030 military time to standard 12-hour time notation, you can use the following steps:

Check if the hour digits are greater than 12. If the hour digits are 13 or higher, subtract 12 from the hour digits to get the equivalent hour in standard time notation.

Add "PM" after the hour and minute digits to indicate that it is in the evening.

Using these steps, we can convert 2030 military time to 8:30 PM in standard time notation:

Since the hour digits 20 are greater than 12, we subtract 12 from 20 to get 8.

Add "PM" after 8:30 to indicate that it is in the evening.

Therefore, 2030 is 8.30 PM

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The matrix equation [4 5 40 - 9 - 5 27 1 - 7 32] can be written as a vector equation Ax = <40 27 32>

A matrix is a rectangular array of numbers, often denoted as Ax, where A is the matrix itself and x is the vector of numbers that make up the columns of the matrix.

In this problem, we are given the matrix equation 4 5 40 - 9 - 5 27 1 - 7 32 and asked to use the definition of Ax to write it as a vector equation.

To do this, we need to identify which numbers are in the matrix A and which numbers are in the vector x.

The numbers 4, 5, -9, -5, 1, and -7 represent the matrix A, while the numbers 40, 27, and 32 represent the vector x.

Therefore, the matrix equation can be written as Ax = 40 27 32.

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The magnitude of -v is [tex]\sqrt{(89)}[/tex]

In physics and mathematics, magnitude refers to the size or quantity of a physical or mathematical property. It can be represented by a scalar value or a vector with a scalar magnitude.

In the case of scalar magnitude, it represents a property's absolute value, which is always positive. For example, the magnitude of a force, velocity, or acceleration represents its absolute value without any direction.

In contrast, vector magnitude represents the length or size of a vector, including both its magnitude and direction. It can be calculated using the Pythagorean theorem, where the magnitude of a vector V with components (Vx, Vy, Vz) is:

[tex]|V| = sqrt(Vx^2 + Vy^2 + Vz^2)[/tex]

The magnitude of a vector is always positive and can be used to determine the distance between two points in space.

Overall, magnitude is an essential concept in many fields, including physics, mathematics, engineering, and computer science, and it plays a crucial role in understanding various physical and mathematical phenomena.

The magnitude of a vector is its length, which is calculated using the Pythagorean theorem. For a vector v = (a, b), the magnitude is given by:

[tex]|v| = sqrt(a^2 + b^2)[/tex]

The negative of a vector simply reverses its direction, but not its magnitude. Therefore, the magnitude of -v is the same as the magnitude of v.

Using this information, we can calculate the magnitude of -v as follows:

[tex]|-v| = |-( -5, 8)| = |(5, -8)|\\\|-v|\ = \sqrt{(5^2 + (-8)^2)} = \sqrt{(25 + 64) }= \sqrt{(89)}Therefore, the magnitude of -v is \sqrt{(89)}[/tex]

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The value after converting the length 178 cm  to inches , is 178 cm is equivalent to 70 inches .

The Centimeters (cm) and inches are both the units of measurement that  are used to measure length .

They both belong to different systems of measurement. Centimeters are used in the International System of Units (SI), whereas  inches are used in the Imperial and US Customary systems.

We know that 1 centimeter is = 0.3937 inches .

that means that conversion factor is 0.3937 ,

So , we can write ; 178 cm = 178 × 0.3937 inches ;

⇒ 178 cm = 70.0786 inches ≈ 70 inches .

Therefore , 178 cm is approximately equal to 70 inches .

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The diameter of the circle is 30 units, and the equation is:

(x + 3)^2 + (y - 3)^2 = 15^2

We know that the diameter of the circle is defined by the points (12, 3) and (-18,3)

Notice that the y-value is the same one in both points, then the diameter is the difference between the x-values:

d = 12 - (-18) = 30

The diameter is 30 units.

Then the radius, half the diameter, is 15 units.

To write the circle equation we need to find the center.

Because of the points (12, 3) and (-18,3) we know that the y-value of the center must be y = 3.

And the x-value is the midpoint between x = -18 and x = 12, that is:

x = (-18 + 12)/2 = -6/2 = -3

The center is at (-3, 3)

Remember that the equation for a circle of center (a, b) and radius R is:

(x - a)^2 + (y - b)^2 = R^2

Here the center is (-3, 3) and the radius is 15, so the equation is:

(x + 3)^2 + (y - 3)^2 = 15^2

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The height of the object is at least 1300 feet after 9 seconds. The solution has been obtained by solving the algebraic equation.

What is algebraic equation?

A mathematical expression is said to be "algebraic" if it includes variables, constants, and algebraic operations (addition, subtraction, etc.). The expression has to satisfy the algebraic equation and have the equals sign in it.

We are given an equation as h = - 16t² + 32t + 2308

Since, we need to find the times at which the height of the object at least 1300 feet so, we will substitute h = 1300 in the equation.

From this, we get

⇒1300 = - 16t² + 32t + 2308

⇒0 = - 16t² + 32t + 1008

⇒0 = -t² + 2t + 63                       (On dividing both sides by 16)

⇒t² - 2t - 63 = 0

⇒t² - 9t + 7t - 63 = 0

⇒t(t - 9) + 7(t - 9) = 0

⇒(t - 9) (t + 7) = 0

⇒t = 9 , -7

Hence, the height of the object is at least 1300 feet after 9 seconds.

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The volume of the empty portion of Container B is approximately 47.1 cubic feet, to the nearest tenth of a cubic foot.

The formula V = r2h, where r is the cylinder's radius and h is its height, can be used to determine a cylinder's volume.

Water in Container A has a volume of:

V A is equal to (3 ft)2(5 ft) 141.37 ft3.

This amount of water will be moved to Container B, which has a 15-foot height and a 2-foot radius. Container B contains a total of:

V B = (1.5 x 2 x 15) x 188.5 ft 3

The volume of the empty space in Container B after the water has been pumped from Container A to Container B can be estimated by deducting the volume of the water from the overall volume of Container B:

47.1 ft3 = V empty = V B - V A

As a result, to the nearest tenth of a cubic foot, the volume of Container B's empty space is roughly 47.1 cubic feet.

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The conversion from mililitres to litre will be done using the relation between the two, where 1 liter has 1000 mililitres.

Firstly know the abbreviations. In this question, ml represents mililitres. Now, The mentioned problem is from unit conversion. As we know the relation, that one litre contains 1000 milliliters of any fluid. So, this is the method of conversion from mililitres to litre.

We can understand given conversion through example. Let us say Zainab has a bottle of 2000 mililitres. Now how many litres of liquid can this bottle contain?

1000 mililitres is present in 1 liter

So, 2000 mililitres will contain = 2000/1000

Performing division

2,000 mililitres will contain 2 litre liquid.

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The coordinates of Room 1314 are given as follows:

(2, 13).

We are going to label the rooms are follows:

Then the coordinates of Room 1314 are obtained applying the proportions in the context of the problem.

Room 1314 is located five-sevenths of the distance from Room 1305 to Room 1324, hence the equation is given as follows:

Z - X = 5/7(Y - X).

Then the x-coordinate is obtained as follows:

x + 8 = 5/7(6 + 8)

x = 10 - 8

x = 2.

The y-coordinate is obtained as follows:

y + 2 = 5/7(19 + 2)

y + 2 = 15

y = 13.

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This value is approximate. The more accurate answer is roughly 266.66667 square feet but even this value is approximate as well.

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

Explanation:

The scale of 1:40 means 1 inch on paper corresponds to 40 inches in real life. This type of notation is typically found on maps in the bottom corner.

What we'll do is multiply by 40 to go from the measurement on paper to the measurement in real life.

In short,

From here we multiply the length and width to get the area.

area = length*width

= 20*13.333

= 266.66 which rounds to about 267 square feet.

Feel free to round to some other level of precision. I'm rounding to the nearest square foot because that's the typical precision when it comes to listing sizes of houses and apartments.

Answer:

It will take about 13.5 years for the money to grow to $5,500
That would be about 13 years and 6 months

Step-by-step explanation:

The formula for accrued amount(principal + interest) is given by:
[tex]A = P\left(1 + \dfrac{r}{n}\right)^{nt}\quad(1)\\[/tex]

where
P = Principal amount
r = R/100 where R is the annual interest rate as a percentage
n= number of times compounded per year
t = number of years

Given

A = $5,600
P = $3,500
R = 3.35% ==> r = 3.35/100 = 0.0335
n = 12 (since there are 12 months in a year)

We have to find out t

Plugging known values into equation (1)

[tex]5500 = 3500\left(1+ \dfrac{0.0335}{12}\right)^{12t}\\\\5500 = 3500 \left(1+ 0.002791\right)^{12t}\\\\5500 = 3500 (1.002791)^{12t}[/tex]

Switch sides so unknown appears on the left side:
[tex]3500 (1.002791)^{12t} = 5500[/tex]

Divide by 3500 both sides:
[tex](1.002791)^{12t} = \dfrac{5500 }{3500}\\\\(1.002791)^{12t} = 1.5714\\\\[/tex]

Take logs on both sides:
[tex]\ln \left(1.002791^{12t}\right)=\ln \left(1.5714\right)\\\\[/tex]

We have
[tex]\ln \left(1.002791^{12t}\right) = 12t\ln \left(1.002791\right)\\\\[/tex]

Therefore we get
[tex]12t\ln \left(1.002791\right)=\ln \left(1.5714\right)\\\\t\ln \left(1.002791\right)=\ln \left(1.5714\right)\\\\\\[/tex]

Dividing both sides by [tex]12\ln \left(1.002791\right)[/tex] this works out to
[tex]t=\dfrac{\ln \left(1.5714\right)}{12\ln \left(1.002791\right)}[/tex]

[tex]t = 13.51359\; years[/tex]

Rounding to one decimal place
[tex]t = 13.51\; years\\[/tex]

This would be roughly 13 years and 6 months

Answer:

I would assume that 100 would be 100 minutes in the air, if -100 represents 100 minutes before take-off.

Step-by-step explanation:

Percent difference is a measure of the relative difference between two values, expressed as a percentage.

It is determined as follows:

% difference = |(Value 1 - Value 2) / (Average of Values 1 and 2)| x 100%

where:

Assume that the value of a quantity in 2019 is 100 and that the same amount in 2020 is 120. The percentage difference between these two values is determined as follows:

Percent difference = |(100 - 120) / ((100 + 120) / 2)| x 100%

= |(-20) / (220 / 2)| x 100%

= 9.09%

This signifies that the quantity's value increased by 9.09% between 2019 and 2020. If the percentage difference is negative, it signifies that the quantity's value has fallen by that proportion.

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According to the Centers for Disease Control and Prevention (CDC) growth charts, the average height for a 14-year-old guy in the United States is about 5 feet, 5 inches (165 cm). Some 14-year-old guys may be taller or shorter than the average.

Height is a measure of the distance between the base of an object and its highest point. Human height is commonly described as the vertical distance between the bottom of the feet and the top of the head. Height is generally measured in centimetres or feet and inches. Height is an important physical feature that can be influenced by both inherited and environmental factors such as nutrition and physical activity.

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Answer:

when the input t is -7, the output k is -89.

Using the equation k = 10t - 19 and substituting t = -7, we have:

k = 10(-7) - 19

k = -70 - 19

k = -89

Therefore, when the input t is -7, the output k is -89.

The chances of Renata being ready to complete kindergarten tasks when she enters school are about 1/2. The solution has been obtained by using the concept of probability.

What is probability?

To calculate the chance of an event, use the mathematical notion of probability. It only enables us to estimate the likelihood that an event will take place. On a scale of 0 to 1, where 0 represents impossible and 1 represents a certain event.

We are given that Renata is a 5-year-old girl from a poor family in the united states, who is about to enter kindergarten.

The chances of Renata being ready to complete kindergarten tasks when she enters school are about 1/2 because it is not necessary that she will be able to do all the tasks. She might be able to do and she might not be able to do.

So, there are equal chances of both.

Hence, chances of Renata being ready to complete kindergarten tasks are 1/2.

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Part A) Solve for x because it has a coefficient of 1 in both equations.

Part B)  The solution is,

⇒ (x, y) = (57/8, 16/3)

Part C) The slope is,

⇒ m = 128/171

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The system of equation are,

⇒ x + y = 10

⇒ 2y = x + 6

Now, We can solve the equation as,

⇒ x + y = 10

⇒ 2y - x = 6

Add both equation,

⇒ 3y = 16

⇒ y = 16/3

⇒ x + y = 10

⇒ x + 16/13 = 10

⇒ x = 10 - 16/13

⇒ x = 57/8

Hence, The solution is,

⇒ (x, y) = (57/8, 16/3)

Thus, The slope is,

⇒ m = (16/3) / (57/8)

       = 16×8 / 3×57

       = 128/171

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A volume of 2 liters is needed to obtain a 92 % solution.

In this problem we need to determine the volume of pure acid to be added with a volume of four liters of 88 % acid solution to get a 92 % solution. This can be done by definition of weighted average:

(88 / 100) · (4 L) + (100 / 100) · V = (92 / 100) · (4 L + V)

Where V is the volume needed of the pure acid, in liters.

3.52 L + V = 3.68 L + 0.92 · V

0.08 · V = 0.16 L

V = 2 L

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Not necessarily. It is true that if a function F is differentiable at a point A, then F must be continuous at A. This is one of the basic properties of differentiable functions.

However, the converse is not necessarily true. A function can be continuous at a point A without being differentiable at A. In fact, there are many examples of such functions, such as the absolute value function f(x) = |x| at x = 0, which is continuous but not differentiable at x = 0.

To see why a function can be continuous at a point A without being differentiable at A, let's consider the definition of continuity and differentiability.

A function F is continuous at a point A if and only if:

F(A) is defined.

The limit of F(x) as x approaches A exists.

The limit of F(x) as x approaches A is equal to F(A).

Therefore, we can conclude that if a function F is continuous at a point A, we cannot infer that F is differentiable at A.

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Is it true if F is continuous at A then F is differentiable at A?

Counter example:

3 - 7 = -4

5 - 8 = -3

8 -9 = -1

Conclusion: the difference between two positive numbers can also be a negative number.

What is meant by negative numbers?

Given are given a set of difference of positive numbers.

7 - 3 = 4

8 - 5 = 3

9 - 8 = 1

The conclusion for this difference is given as the difference between two positive numbers is always positive.

We are asked to give a counter example.

Now a counterexample means an example that makes the given conclusion invalid.

So the counterexample of given example would be to prove the difference between positive numbers can also be a negative number.

For example,

3 - 7 = -4

5 - 8 = -3

8 -9 = -1

Therefore using the same numbers but subtracting the larger numbers from smaller number, we proved that the difference between positive numbers can also be a negative number.

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On converting 168 lbs to Kilogram , we get that 168 lbs is equivalent to  76.188 Kg .

The conversion factors can be used to convert between pounds and kilograms. For example ;

To convert 1 pound to kilograms: We multiply the number of pounds by 0.4535  .

We have to convert 168 pounds to kilograms ;

So , we multiply the given weight in pounds with 0.4535 .

On multiplying ,

We get ;

⇒ 168 pounds = 168 × 0.4535 Kg ;

⇒ 168 pounds = 76.188 Kg .

Therefore , 168 lbs is approximately equal to 76.188 Kg .

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