A rocket flies 10 km vertically, then 20 km at an angle of 15° to the vertical and finally 60 km at an angle of 26° to the vertical. Calculate the vertical height of the rocket at the end of the third stage.​

The set of natural numbers {1,2,3,4,...} and the set of positive even numbers {2, 4, 6, 8, . . .} are different because natural numbers include all positive integers, while even numbers only include those that are divisible by 2 with no remainder.

Two important sets of numbers are natural numbers and even numbers. The set of natural numbers consists of numbers that are not negative, beginning with 1 and continuing indefinitely with 2, 3, 4, and so on.

The set of even numbers, on the other hand, consists of numbers that are divisible by 2, beginning with 2, 4, 6, and so on.

Positive integers refer to natural numbers. Any integer greater than zero is a positive integer.

Zero is not a positive integer. Hence, the set of natural numbers consists of {1,2,3,4,…}

On the other hand, the set of even numbers consists of {2, 4, 6, 8, . . .}.

Therefore, {1,2,3,4,…} and {2, 4, 6, 8, . . .} are two different sets of numbers where one set is composed of positive integers (natural numbers) and the other is composed of positive even numbers.

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Answer:

$22.84

Step-by-step explanation:

21.25 + (0.075)(21.25)= 21.25+1.59

= 22.84

Answer:

Last Option: y=2x-2

Answer:

Step-by-step explanation:

Answer:1 1/12

Step-by-step explanation: 3/4+1/3=13/12=1 1/12

True.

If adding two positive integers results in a negative number, it means that an overflow has occurred. The overflow flag is set when the result of an operation is too large to be represented with the given number of bits.
If bx and dx both contain positive integers and adding them produces a negative result, the overflow flag will be set. This is because when two positive integers are added, the result should also be a positive integer. If the result is negative, it means there was an overflow during the addition process, and the overflow flag will be set to indicate this issue.

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The cylindrical coordinates of (−7, 7, 7) are (√98, -π/4, 7). cylindrical coordinate (−7, 7 3 , 1) is  (14, -π/3, 1).

We must switch from rectangular to cylindrical coordinates in the provided problem. (let r ≥ 0 and 0 ≤ θ ≤ 2π.)

A)(−7, 7, 7)

Given rectangular coordinates(x, y, z) =(−7, 7, 7)

The cylindrical coordinates are (r, θ, z)

As a result, we determine each value of r and θ  separately.

r = √x²+y²

r = √(-7)²+(7)²

r = √49+49

r = √98

θ = tan⁻¹ (y/x)

θ =tan⁻¹  (7/-7)

θ =tan⁻¹  (-1)

θ = -π/4

So cylindrical coordinate = (r, θ, z) = (√98, -π/4, 7)

B) (-7,7√3,1)

Given rectangular coordinates(x, y, z) = (-1,1,1)

The cylindrical coordinates are (r, θ, z)

As a result, we determine each value of r and θ  separately.

r = √x²+y²

r = √(-7)²(7√3)²

r = √49+147

r = √196

r = 14

θ = (y/x)

θ = (7√3/-7)

θ = (-√3)

θ = -π/3

So cylindrical coordinate = (r, θ, z) = (14, -π/3, 1)

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Answer:

Number 1

Step-by-step explanation:

The only one that makes sense

The percent increase in the cost of the uniform from last year to this year is 25%.

To find the percent increase in the cost of the uniform from last year to this year, we need to calculate the difference between the two prices, divide it by the original price, and then multiply by 100 to express the result as a percentage.

The difference between this year's price and last year's price is:

$65 - $52 = $13

The original price (last year's price) is $52.

So the percent increase in the cost of the uniform is:

percent increase = (difference / original price) x 100

percent increase = ($13 / $52) x 100

percent increase = 0.25 x 100

percent increase = 25%

Therefore, the percent increase in the cost of the uniform from last year to this year is 25%.

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Answer:

1.4

Step-by-step explanation:

-2.6---------------1.3

0.5 is between

-2.1 is between

1.4 is not between

-1.8 is between

All of the aforementioned are factors that influence whether an infant will show stranger wariness except: A. the infant's ability to regulate emotion.

In Psychology, stranger wariness is sometimes referred to as stranger anxiety or stranger fear and it can be defined as any form of distress and apprehension that is typically experienced by infants (young children or babies) when they are around or within the proximity of individuals who are strange (unfamiliar) to them.

This ultimately implies that, stranger wariness simply refers to a form of distress and apprehension which an infant (young child or baby) experiences when exposed to strangers.

In this context, we can reasonably infer and logically deduce that the ability of an infant (young child or baby) to regulate emotion is not a factor that would influence whether an infant shows stranger wariness.

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Complete Question:

All of these are factors that influence whether an infant will show stranger wariness EXCEPT ______.

A. the infant's ability to regulate emotion

B. the overall temperament of the infant

C. the past experience of the infant

D. the situation in which the infant meets the stranger

Answer: \(\dfrac{3}{8}\)

Step-by-step explanation:

Given

Julio traveled \(\frac{3}{8}\) of distance to his aunt's house on Saturday

they have traveled \(\frac{3}{5}\) of the remaining distance on Sunday

suppose the total distance is \(x\)

Distance traveled on Saturday

\(\dfrac{3x}{8}\)

Remaining distance is

\(x-\dfrac{3x}{8}=\dfrac{5x}{8}\)

Distance traveled on Sunday

\(\Rightarrow \dfrac{3}{5}\times \dfrac{5x}{8}=\dfrac{3x}{8}\)

The fraction of distance traveled on Sunday is

\(\Rightarrow \dfrac{\frac{3x}{8}}{x}=\dfrac{3}{8}\)

The graph of y=3x^4-16x^3+24x^2+48 is concave down for x values greater than or equal to 0.

The graph of y=3x^4-16x^3+24x^2+48 is an example of a polynomial function. To determine the concavity of a polynomial function, we must first identify the intervals where the function is increasing and decreasing. In this case, the function is increasing for all x values greater than or equal to 0.

Next, we must find the second derivative and determine the intervals where the second derivative is negative. If the second derivative is negative, then the graph is concave down. For this polynomial, the second derivative is y'' = -48x + 48, which is negative for all x values greater than or equal to 0. This means that the graph of y=3x^4-16x^3+24x^2+48 is concave down for all x values greater than or equal to 0.

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Answer:

60 minutes

Step-by-step explanation:

Latitude and longitude are measuring lines used for locating places on the surface of the Earth. They are angular measurements, expressed as degrees of a circle. A full circle contains 360°. Each degree can be divided into 60 minutes, and each minute is divided into 60 seconds.

One degree of latitude is equal to approximately 60 nautical miles or 69 statute miles. Since a minute of latitude is one-sixtieth of a degree, it follows that one degree of latitude is equal to 60 minutes.

This means that there are 60 nautical miles or 69 statute miles between two points that differ by one minute of latitude.

The minute of latitude is a widely used unit for measuring distances on Earth, particularly in navigation and aviation. It allows for precise calculations and is crucial for determining positions accurately. Understanding the relationship between degrees of latitude and minutes helps in determining distances, estimating travel times, and ensuring accurate navigation across the globe.

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Answer:

IF its a pretest the grade doesnt count im pretty sure.

Answer:

1. 15% of 48= 7.2

2. 25% of 80= 20

3. 135% of 70= 94.5

4. 7/10 of 100= 0.7

5. Solution for 36 is what percent of 50:

36: 50*100 =

(36*100): 50 =

3600: 50 = 72

6. Solution for 4 is what percent of 20:

4: 20*100 =

(4*100): 20 =

400: 20 = 20

7 30 is 50% of what number

50% is half of 100 so all you do is times the number by 2 which is 30 to get 60

8. 2 is 25 percent of what number?

again 25% you need to do 4 times 25 to get 100 so you do 12 x 4 and you get 48

9 its 800 so 75 again is 3 x 25 so you divide 600 by 3 and you get 200 so then to get 100 percent you do 4 x 200 and you get 800 so the awnser is 800

Step-by-step explanation:

Answer:

78

Step-by-step explanation:

because I know everything

Once we have categorized an object, our memory of the object increasingly resembles the category is B) prototype. This means that when we categorize an object, our memory of it begins to resemble the prototype or typical example of that category. For example, if we categorize a bird as a robin, our memory of the bird will increasingly resemble the characteristics of a typical robin.

This happens because our brain uses prototypes as a shortcut to process information and make sense of the world around us. We use prototypes to quickly identify objects and make assumptions about their characteristics based on their category.

our memory of an object after categorization is influenced by the prototype of the category. This helps us to quickly process and make sense of information, but it can also lead to errors and biases in our thinking.


A prototype is a mental image or best example of a category. When we categorize an object, our memory of the object increasingly resembles the prototype because we tend to recall the most representative or typical example of the category.

Once we categorize an object, our memory of the object becomes more like the prototype, which is the best example of the category. This is because we tend to remember the most representative or typical examples of a category.

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Answer:$ 1341.99

Step-by-step explanation: Hope its helps

the options are: Injective but not surjective but not injective Bijective None of the above options (a) is correct: Injective but not surjective.

a) i. $f_1(x) = 8x^2 + 8$ is a function from real numbers to real numbers and is quadratic in nature.ii.

$f_2(z) = 8z^2 + 8$ is a function from complex numbers to complex numbers and is quadratic in nature.

iii. $f_3(n) = 8n^2 + 8$ is a function from natural numbers to natural numbers and is quadratic in nature.iv. $f_4(x + yi) = (2 + 3x) + i(1 - 2y)$ is a function from complex numbers to complex numbers, and is linear in nature

.b) To find the inverse function of $f_4$,

we need to solve for $x + yi$ in the equation $f_4(x + yi) = (2 + 3x) + i(1 - 2y)$ as follows

:$(2 + 3x) + i(1 - 2y) = x' + yi'$(

where $x' + yi'$ is the inverse function of $f_4(x + yi)$

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In this scenario, the outcome of each flip of the coin can be modeled as a Bernoulli random variable Y, where Y takes the value 1 (heads) with a probability of 0.7 and the value 0 (tails) with a probability of 0.3.

A Bernoulli random variable is a discrete random variable that can take only two possible outcomes, typically labeled as success (1) and failure (0), with a fixed probability associated with success. In this case, the outcome of each flip of the coin can be represented by the Bernoulli random variable Y, where Y = 1 represents the event of getting heads and Y = 0 represents the event of getting tails.

Given that the probability of landing on heads is 0.7, we can assign the following probabilities to the outcomes:

P(Y = 1) = 0.7 (probability of getting heads)

P(Y = 0) = 0.3 (probability of getting tails)

Thus, for each individual flip of the coin, we can use the Bernoulli random variable Y to model the outcome, where Y takes the value 1 (heads) with a probability of 0.7 and the value 0 (tails) with a probability of 0.3.

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Answer:

142 506

Step-by-step explanation:

here the order does not matter

Then

we the number of sets is equal to the number of combinations.

Using the formula :

the number of sets is 30C5

\(C{}^{5}_{30}=\frac{30!}{5!\left( 30-5\right) !}\)

      \(=142506\)

There are 142506 ways in which 5 students can be selected out of 30 students.

The selection of 5 students out of 30 students can be achieved with the use of combination since the order of selection is not required to be put into consideration.

By using the formula:

\(\mathbf{^nC_r = \dfrac{n!}{r!(n-r)!}}\)

where;

\(\mathbf{^nC_r = \dfrac{30!}{5!(30-5)!}}\)

\(\mathbf{^nC_r = \dfrac{30!}{5!(25)!}}\)

\(\mathbf{^nC_r = 142506}\)

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Answer:

(0,1)

Step-by-step explanation:

The line meets the y-axis at the point (0,1)

Answer:

The U.S. won 101 medals.

Step-by-step explanation:

101

Hope it helped and have a great day!

b=0

To find the constant b so that the function g(x)=⎧⎩⎨⎪⎪⎪⎪2x bx−5x 16x2−16 is continuous at x=0, we must make sure that the limit g(x)limx→0 is equal to g(0). To do this, we will set up an equation that sets the limit of g(x) as x approaches 0 equal to g(0) and solve for b.

We start with the equation g(0)limx→0−g(x)limx→0 g(x)= -1.

The limit of g(x) as x approaches 0 is the same as the value of g(0), so we can replace g(0)limx→0 with g(0) and g(x)limx→0 with g(0). This leaves us with the equation g(0)−g(0) g(x)= -1.

Since g(0) is on both sides of the equation, we can cancel out the g(0) and the equation simplifies to g(x)= -1.

We can now plug in the equation for g(x) to solve for b:
⎧⎩⎨⎪⎪⎪⎪2x bx−5x 16x2−16 = -1
⎧⎩⎨⎪⎪⎪⎪2x bx−5x 16x2−16 + 1 = 0
2x bx−5x 16x2−16 + 1 = 0
bx−5x 16x2−15 = 0
bx(x−5 16x+15) = 0
bx = 0, x−5 16x+15 = 0
b = 0, x=4

Therefore, b=0 is the constant we are looking for.

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Answer:

ur black lol

Step-by-step explanation:

being black is racist

To prove the first absorption law from table 1, we need to show that for any sets a and b, the union of a and the intersection of a and b is equal to a.

We can start by using the definition of union and intersection:

a ∪ (a ∩ b) = {x : x ∈ a or x ∈ (a ∩ b)}

and

a = {x : x ∈ a}

To prove that these two sets are equal, we need to show that they contain the same elements.

First, let's consider the elements in a ∪ (a ∩ b).

If x ∈ a, then x ∈ a ∪ (a ∩ b) since it satisfies the condition x ∈ a.

If x ∈ (a ∩ b), then x ∈ a ∪ (a ∩ b) since it satisfies the condition x ∈ (a ∩ b), which means that x ∈ a and x ∈ b. But since x ∈ a, we can conclude that x ∈ a ∪ (a ∩ b) as well.

Therefore, every element that belongs to a or (a ∩ b) also belongs to a ∪ (a ∩ b).

Now, let's consider the elements in a.

If x ∈ a, then x ∈ a since it satisfies the condition x ∈ a.

If x ∉ a, then x cannot belong to the intersection of a and b, since by definition, a ∩ b only contains elements that belong to both a and b. Therefore, x cannot belong to a ∪ (a ∩ b) either, since it doesn't satisfy any of the conditions.

Therefore, every element that belongs to a also belongs to a ∪ (a ∩ b).

Since we have shown that every element in a ∪ (a ∩ b) also belongs to a, and every element in a belongs to a ∪ (a ∩ b), we can conclude that a ∪ (a ∩ b) = a.

Thus, we have proven the first absorption law from table 1 for any sets a and b.

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Answer:

£4500

Step-by-step explanation:

12500 ×9/100

=1125

4 years =1125×4

=£4500

To find the arc length, we use the formula L = rθ, where r is the radius of the circle, θ is the central angle of the arc in radians, and L is the arc length.

Arc length refers to the distance covered along the curved portion of a circle or any other curved shape. It is an important concept in geometry and trigonometry and is used to measure the size of circular arcs, the size of angles, and in many other mathematical applications.

To find the arc length, we need to use the formula for the circumference of a circle and the central angle of the arc.

The circumference of a circle is given by the formula 2πr, where r is the radius of the circle.

The central angle of the arc is given in radians and is defined as the angle between two radii that meet at the endpoints of the arc.

To find the arc length, we use the formula

=> L = rθ,

where L is the arc length, r is the radius of the circle, and θ is the central angle of the arc in radians.

To convert the central angle from degrees to radians, we use the formula θ = (π/180) x degrees, where degrees are the central angle in degrees.

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The value of the expression "true && !false" can be determined by evaluating each part separately and then combining the results.

1. The "!" symbol represents the logical NOT operator, which negates the value of the following expression. In this case, "false" is negated to "true".

2. The "&&" symbol represents the logical AND operator, which returns true only if both operands are true. Since the first operand is "true" and the second operand is "true" (as a result of the negation), the overall expression evaluates to "true".

Therefore, the value of the expression "true && !false" is "true".

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There are four levels of measurements in statistics, namely nominal, ordinal, interval, ratio. These levels are important when it comes to analyzing data, since it helps us determine the technique that we can use to support or refute our study.

In the nominal level, we can categorize data but they cannot be ranked. An example would be hair color. In an ordinal data, the data can be both categorize and ranked, but doing mathematical calculation may not make sense. Also, the intervals between rankings doesn't necessarily dictate how close or far apart the data are.

A good example is level of education. In an interval level, the data can be categorized, ranked, and measured but they do not have a true zero. An example could be a range of values that does not include zero. Lastly, in the Ratio level the data can be categorized, rank, and measured, and it has a true zero.

So ratio level is most appropriate for ages of children. Note that ages can be categorized, rank, and measured .Moreover, an age equal to zero means that there is no age or the absence of age.  

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