HD Find the time of flight, range, and maximum height of the following two-dimensional trajectory, assuming no forces other than gravity. The initial position is (0,0) and the initial velocity Initial speed vo-100 m/s, launch angle = 60° The object is in the air for seconds (Type an integer or decimal rounded to two decimal places as needed.) The range of the object ismeters (Type an integer or decimal rounded to two decimal places as needed.) The object reaches a maximum height of meters. (Type an integer or decimal rounded to two decimal places as needed)

Answer:

Step-by-step explanation:

Average rate of change is the slope in same interval:

In 1998, Journeys sold 15 million pairs of Vans.

In 2008, Journeys sold 45 million pairs of Vans.

The average rate of change in show sales for the store.

Final year : 2008

Initial year : 1998

Final sale : 45 million

Initial sale : 15 million

Average sales = Final sale - Initial sale / Final year - Initial year

Average sales = 45 million - 15 million / 2008 - 1998

Average sales = 30 million / 10 years

Average sales = 3 million / 1 year

The average rate of change in show sales for the store is 3 million per year.

If x is an int and y is a float then only option that is not legal is D) x = (int) y.

Option A is legal because an int can be assigned to a float without any issues. The float will simply contain the same value as the int, but with a decimal point (e.g. 5 will become 5.0). Option B is not recommended because it involves converting a float to an int. The decimal point will be dropped, so information will be lost. However, it is still legal to do so. Option C is legal because it explicitly converts the int to a float, which can then be assigned to y. Option D is not legal because it involves converting a float to an int. This can lead to unexpected behavior, such as truncating the decimal point or rounding the value. It is generally safer to avoid such conversions. Option E is not correct because option D is not legal, as explained above.

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The value of x for which (f - g)(x) = 0 is x = 12.

To find the value of x for which (f - g)(x) = 0, we need to subtract g(x) from f(x) and set the resulting expression equal to zero. Let's perform the subtraction:

(f - g)(x) = f(x) - g(x)

= (16x - 30) - (14x - 6)

= 16x - 30 - 14x + 6

= 2x - 24

Now, we can set the expression equal to zero and solve for x:

2x - 24 = 0

Adding 24 to both sides:

2x = 24

Dividing both sides by 2:

x = 12

Therefore, the value of x for which (f - g)(x) = 0 is x = 12.

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the answer is in the pic

Using conditional probability, it is found that there is a 0.83 = 83% almost 0.8403  probability that this student does spend more than $25 a week on gas, given that he/she does commute to school each day.

Probability: -

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%).

Conditional Probability :

Using conditional probability, it is found that there is a 0.83 = 83% = P( A∩ B) / P(A)

In which

In this problem:

Event A: Commute to school each day.

Event B: Spends more than $25 a week.

80% indicated that they commute to school each day. of those that commute to school each day, hence , P(A) = 0.8

Of those, 83% spend more than $25 a week on gasoline, hence .

                     P(B|A) = 0.83

Thus, 0.83 = 83% probability that this student does spend more than $25 a week on gas, given that he/she does commute to school each day.

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Answer:A, 52

Step-by-step explantion:

We can conclude that it is extremely unlikely to obtain a sample mean greater than 904.8 minutes if the design engineer's claim about the population variance and mean is true.

We can use the Central Limit Theorem to approximate the distribution of the sample means.

Under the given assumptions, the mean of the sampling distribution of the sample means is equal to the population mean, which is 886886 minutes, and the standard deviation of the sampling distribution of the sample means is equal to the population standard deviation divided by the square root of the sample size, which is\(\sqrt{84648464/145145} = 41.77\) minutes.

Therefore, we can standardize the sample mean using the formula:

\(z = (\bar{x} - \mu) / (\sigma / \sqrt{n } )\)

where \(\bar{x}\)  is the sample mean, \(\mu\)  is the population mean, sigma is the population standard deviation, and n is the sample size.

Plugging in the values we get:

z = (904.8 - 886886) / (41.77) = -21115.47

The probability of getting a sample mean greater than 904.8 minutes can be calculated as the area under the standard normal curve to the right of z = -21115.47.

This probability is essentially zero, since the standard normal distribution is symmetric and nearly all of its area is to the left of -6.

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Answer:

i think its A i may be wrong

The answers are :

a) The derivative of this function at the point (3,256) is -96.

b) The speed at which the supply bundle is falling is negative.

What is derivative ?

Derivative is the slope of the graph of function or the slope of the tangent line at a point.

A function is given which is h(t) = 400 - 16t².

Here , h(t) gives the height of the supply bundle in feet , t seconds after it is dropped from a height of 400 feet.

a)

We have to find out the derivative of the given function at a point (3,256).

h'(t) = \(\frac{d}{dt}\) (400 - 16t²)

h'(t) = 0 - 2 × 16 × t

h'(t) = -32 t

This function at (3,256) so , value of t is 3.

h'(t) = -32 × 3

h'(t) = -96

b)

Speed = -32 t

So , the speed at which the supply bundle is falling is negative. With increase in value of t it will keep decreasing.

Therefore , the answers are :

a) The derivative of this function at the point (3,256) is -96.

b) The speed at which the supply bundle is falling is negative.

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We can show that if (A) is the matrix of an orthogonal projection of (\mathbb{R}^n) onto a subspace (W), then (A) is diagonalizable as follows:

Since (A) is the matrix of an orthogonal projection, it satisfies the following properties:

(A^{2} = A), since projecting twice onto a subspace is equivalent to projecting once.

(A^{T} = A), since (A) is an orthogonal projection.

Let (V) denote the subspace onto which we are projecting, and let (U) denote its orthogonal complement. Since the projection is orthogonal, we have (A_{ij} = 0) for all (i \in V) and (j \in U), and (A_{ij} = 1) for all (i \in V) and (j \in V). Therefore, the matrix (A) has the block form:

[\begin{pmatrix} I & 0 \ 0 & 0 \end{pmatrix}]

where (I) is the identity matrix on the subspace (V), and (0) is the zero matrix on the orthogonal complement (U).

Now, consider the characteristic polynomial of (A):

[\det(\lambda I - A) = \det\begin{pmatrix} \lambda I - I & 0 \ 0 & \lambda I \end{pmatrix} = \det((\lambda - 1)^{\dim(V)} \lambda^{\dim(U)}) = (\lambda - 1)^{\dim(V)} \lambda^{\dim(U)}]

Since the eigenvalues of (A) are either (0) or (1), this shows that (A) is diagonalizable, with eigenvalues (0) (with multiplicity (\dim(U))) and (1) (with multiplicity (\dim(V))). Therefore, we can find a diagonal matrix (D) and an invertible matrix (P) such that (A = PDP^{-1}), which shows that (A) is diagonalizable.

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Answer:

\(\mathrm{Range\:of\:}x^2:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\ge \:0\:\\ \:\mathrm{Interval\:Notation:}&\:[0,\:\infty \:)\end{bmatrix}\)

The graph is also attached below.

Step-by-step explanation:

Given the function

\(y=x^2\)

\(\mathrm{For\:a\:parabola}\:ax^2+bx+c\:\mathrm{with\:Vertex}\:\left(x_v,\:y_v\right)\)

\(\mathrm{If}\:a<0\:\mathrm{the\:range\:is}\:f\left(x\right)\le \:y_v\)

\(\mathrm{If}\:a>0\:\mathrm{the\:range\:is}\:f\left(x\right)\ge \:y_v\)

\(a=1,\:\mathrm{Vertex}\:\left(x_v,\:y_v\right)=\left(0,\:0\right)\)

\(f\left(x\right)\ge \:0\)

Thus,

\(\mathrm{Range\:of\:}x^2:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\ge \:0\:\\ \:\mathrm{Interval\:Notation:}&\:[0,\:\infty \:)\end{bmatrix}\)

The graph is also attached below.

The product of the two given binomials can be expressed as the trinomial 2561104x³ + 684636x² + 87719x + 736, which is in its simplest form.

In this case, we will multiply the first two binomials (12x+1)(21x+1) and then multiply the second two binomials (65x+32)(56x+23). We will then multiply the two resulting expressions to get the final trinomial.

To multiply (12x+1)(21x+1), we can use the distributive property of multiplication, which states that a(b+c) = ab + ac. Therefore, we have:

(12x+1)(21x+1) = 12x(21x) + 12x(1) + 1(21x) + 1(1) = 252x² + 12x + 21x + 1 = 252x² + 33x + 1

Similarly, to multiply (65x+32)(56x+23), we have:

(65x+32)(56x+23) = 65x(56x) + 65x(23) + 32(56x) + 32(23) = 3640x² + 1495x + 1792x + 736 = 3640x² + 3287x + 736

Now, to find the product of the two expressions, we can multiply them using the distributive property again:

(252x² + 33x + 1)(3640x² + 3287x + 736) = 252x²(3640x²) + 252x²(3287x) + 252x²(736)

   • 33x(3640x²) + 33x(3287x) + 33x(736)

   • 1(3640x²) + 1(3287x) + 1(736)

Simplifying this expression by combining like terms, we get:

= 917280x⁴ + 1573824x³ + 684636x² + 87719x + 736

This final expression has four terms, but it can be simplified further to a trinomial by combining the first two terms using the associative property of addition. We have:

917280x⁴ + 1573824x³ + 684636x² + 87719x + 736 = (917280x⁴ + 1573824x³) + (684636x² + 87719x + 736) = 2561104x³ + 684636x² + 87719x + 736

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Complete Question:

Express the product of(12x+1)(21​x+1) and(65x+32)(56​x+23​) as a trinomial in simplest form

Answer:

y-axis and x-axis

Step-by-step explanation:

Answer:

4 months because 2 months is 5 paintings times 2 =10 paintings 10 months

The repairs have indeed changed the nature of the output of the machine, with an overall improvement in the quality of the parts produced.

To determine if the repairs have changed the nature of the output of the machine, we can compare the percentages of excellent, good, and unacceptable parts before and after the repairs.

Before repairs:
- 80% excellent
- 16% good
- 4% unacceptable

After repairs, we can calculate the percentages based on the sample of 200 parts:
- 157 excellent parts: (157/200) * 100 = 78.5% excellent
- 42 good parts: (42/200) * 100 = 21% good
- 1 unacceptable part: (1/200) * 100 = 0.5% unacceptable

Comparing these percentages, we can see that the output has changed after the repairs:
- Excellent parts decreased from 80% to 78.5%
- Good parts increased from 16% to 21%
- Unacceptable parts decreased from 4% to 0.5%

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Answer:

I prefer 5% of your income should be saved each month

Answer:

b. you must decide what you can afford

Step-by-step explanation:

i just took the quiz and that's the correct answer

Answer:

E

Step-by-step explanation:

NO

The opportunity cost of consuming one more unit of good x in terms of how much good y must be given up is 1/2 unit of good y.

The opportunity cost of consuming one more unit of good x in terms of how much good y must be given up can be calculated using the Marginal Rate of Substitution (MRS). MRS is calculated as the ratio of the change in the amount of good x to the change in the amount of good y, as the consumer moves from one point on the indifference curve to another. Mathematically, MRS is expressed as:

MRS = Δx/Δy

For example, if a consumer moves from consuming 2 units of good x and 4 units of good y, to consuming 3 units of good x and 6 units of good y, then the MRS would be calculated as:

MRS = (3 - 2) / (6 - 4) = 1 / 2

Therefore, the opportunity cost of consuming one more unit of good x in terms of how much good y must be given up is 1/2 unit of good y.

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The Pythagorean Theorem, often known as Pythagoras Theorem, is a crucial concept in mathematics that describes how the sides of a right-angled triangle relate to one another. Pythagorean triples are another name for the sides of the right triangle. Here, examples help to demonstrate the formula and proof of this theorem.

In essence, the Pythagorean theorem is used to determine a triangle's angle and length of an unknown side. This theorem allows us to obtain the hypotenuse, perpendicular, and base formulae.

In order to determine sin a without using the Pythagorean theorem, we will need to have the value of the opposite side and angle. Sin (a) = opposite / hypotenuseHere, the hypotenuse is not given, so we will need to have the value of the opposite side and angle (a) in order to determine sin a without using the Pythagorean theorem.

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Value of r is different for every series

let

a , b , c , d ..... be geometric series then

r = b/a or d/c and so on

where r is common ratio

Answer:

1

Step-by-step explanation:

To find the median number of musical instruments played, we first need to arrange the data in ascending order:

0, 0, 0, 0, 1, 1, 2, 2, 3, 3, 3

Next, we count the total number of responses, which is 15. Since 15 is an odd number, the median will be the average of the middle value.

The middle value is 1

Hence, the median number of musical instruments played is 1.

Answer:

38+12=50

Step-by-step explanation:

3 plus 1 is 4. 8 plus 2 is 10. Put the 1 on the 4 add it and its 5 so now its 50.

Answer:

y=-4x-2

Step-by-step explanation:

With the equation provided, you can plug in the 3 or -4 into the x-value, and will get the corresponding y-value.

Hope this helps!

TLDR: Your answer is D. 260 square feet.

To find the area of a triangle, you must use the formula "1/2 B ⋅ H."

In this problem, your values are the following:

B = 20

H = 26

Now, you just plug these values in and solve.

1/2 (20) ⋅ 26  >  10 ⋅ 26 = 260 ft

well, the volume of that triangular prism will just be the area of the triangle times the length.

now, what's the area of that triangular face?  well, let's say it has a base of "b" and a height of 3, whilst the prism has a length of 6, Check the picture below.

\(\stackrel{\textit{triangle's area}}{\cfrac{1}{2}(b)(3)}\stackrel{\textit{prism's length}}{(6)}~~ = ~~4\frac{1}{2}\implies 9b=\cfrac{9}{2}\implies b=\cfrac{9}{18}\implies b=\cfrac{1}{2}\)

Answer:

Area of table cloth =  49/9 m² or 5.44 m²

Step-by-step explanation:

Given:

Side of table cloth  = \(2\frac{1}{3}m\) = 7/3 m

Shape of cloth is square

Find:

Area of table cloth

Computation:

Area of square = side²

So,

Area of table cloth = side²

Area of table cloth = (7/3)²

Area of table cloth =  49/9 m² or 5.44 m²

Solving an algebra problem exemplifies Objective because there is generally one right answer to such a problem.

How is the objective determined?

Objective refers to a fact that is not influenced by personal opinions or feelings and is quantifiable.

In the case of solving an algebra problem, the solution is based on a set of pre-established rules and formulas that result in a single correct answer that is quantifiable and objective.

A variable is any symbol that can represent any number. It can be used in place of a specific number and can take on a range of values. In algebra, equations and formulas are used to manipulate these variables to find their values.

The use of objective rules and formulas is what makes solving algebra problems objective.

Therefore, it can be concluded that solving an algebra problem exemplifies Objective because there is generally one right answer to such a problem.

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The number 5 can be either a geometric sequence or a arthimetic sequence

A geometric sequence is a series in which each term is found by multiplying the preceding term by the same value. Its general term is. aₙ= a₁rⁿ⁻¹.

The r represents the common ratio, and a is the initial term. r is found by taking any term in the sequence and dividing it by its preceding term.

The example of a geometric sequence with 5 as initial term is

5, 10, 20, 40.....

In an arithmetic sequence, the difference between consecutive terms is always the same.

aₙ = a + (n - 1)d

The example of a arithmetric sequence with 5 as initial term is

5, 7, 9, 11 .....

Therefore, The number 5 can be either a geometric sequence or a arthimetic sequence.

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Answer:

the  amount that paid by lily is £49.8

Step-by-step explanation:

The computation of the amount that paid by lily is shown below:

= Total amount × (1 - saving percentage)

= £60 × (1 - 0.17)

= £60 × 0.83

= £49.8

Hence, the  amount that paid by lily is £49.8

We simply applied the above formula and same would be relevant

Step-by-step explanation:

First find the total weight of the male students

5/3 = x / 870     cross multiply

4350 = 3x

x = total boys' weight = 1450 kg

    if the mean is GREATER THAN 80 then    

               1450 / n > 80     where n is the number of boys

                   1450/80 > n

                              n< 18.125         max number would be 18 boys

Answer:

x = 57

Step-by-step explanation:

180 degrees in a triangle

67 + 56 = 57

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

Explanation:

The three angles of any triangle always add to 180

x+67+56 = 180

x+123 = 180

x+123-123 = 180-123 .... subtract 123 from both sides

x = 57

The missing angle is 57 degrees

-------------

Check:

x+67+56 = 57+67+56 = 180

Answer is confirmed.