A ball is launched directly in the air at a speed of 60 feet per second from a platform located 20 feet in the air. The motion of the
ball can be modeled using the function
where t is time in seconds and is the height of the ball. What is the maximum height of the ball?

Ellie's pre-pregnancy BMI is 38. Thus, her weight-gain goal should be 11-20 pounds for the entire pregnancy.

Having a BMI of 30 or higher during pregnancy can increase the risk of complications for you and your baby. Working with your health care provider can help you manage your risks and promote a healthy pregnancy.

If before pregnancy, you were…                      You should gain…

Underweight BMI less than 18.5                      50-62 pounds*

Normal Weight BMI 18.5-24.9                      37-54 pounds

Overweight BMI 25.0-29.9                              31-50 pounds

Obese BMI greater than or equal to 30.0      25-42 pounds

Body Mass Index (BMI) is calculated by dividing a person's height in feet by their weight in kilos or pounds (meters). The BMI of healthy pregnant women should be between 18.5-24.9.

Preconception, the time before and between pregnancies, is another name for the pre-pregnancy phase.

Therefore,

Ellie's pre-pregnancy BMI is 38. Thus, her weight-gain goal should be 11-20 pounds for the entire pregnancy.

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Any n-dimensional vector should be able to be represented in space.

The highest degree of terms is written first when writing a polynomial in its standard form, then the next highest degree, and so on.

If there are multiple variables in a single term, add the exponents of each term together and choose the largest sum or highest power of the variable to determine the polynomial's degree.

It should be possible to represent any n-dimensional vector in space. It can only express polynomials of degree n if it only has terms of degree n.

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A rectangle's greatest area is 32 square units.

Given:

A parabola's equation is y = 12 - x2, which is an even function

As a result, its rectangular shape is also even at the origin.

We are aware that the area of a rectangle is equal to its length times its width.

Here,

width = y, length = 2x

A = 2x, where (12 -  [tex]x^{2}[/tex])

⇒ A = 24x - 2[tex]x^{3}[/tex]

Consider the A derivative with regard to x.

⇒ A' = 24 - 6 [tex]x^{2}[/tex]

When A' = 0, the area is the largest.

⇒ 24 - 6x2 = 0

⇒ [tex]x^{2}[/tex] = 4

⇒ x = 2

Replace x with its value in y = 12 -  [tex]x^{2}[/tex].

⇒ y = 12 - 4

⇒ y = 8

Area = 2(2)(8) = 32

Hence, a rectangle's greatest area is 32 square units.

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Answer:

I think its (-4,2)

Step-by-step explanation:

Events A and B dependent as the occurrence of one event affect the chances of the occurrence of the other event.

Probability is a branch of mathematics in which the chances of experiments occurring are calculated. It is by means of a probability, for example, that we can know from the chance of getting heads or tails in the launch of a coin to the chance of error in research.

To understand this branch, it is extremely important to know its most basic definitions, such as the formula for calculating probabilities in equiprobable sample spaces, probability of the union of two events, probability of the complementary event, etc.

Two events are independent if the occurrence of one event does not affect the chances of the occurrence of the other event. The mathematical formulation of the independence of events A and B is the probability of the occurrence of both A and B being equal to the product of the probabilities of A and B (i.e., P(A and B).

Since we have given that

A be the event that Callista drives faster than the speed limit.

P(A)=0.34

B be the event that she gets to a wedding on time.

P(B)=0.45

The probability that she gets to the wedding on time given that she drives faster than the speed limit is 0.85 i.e.

P(A|B)=0.85

but for A and B to be independent ,

P(A).P(B)= P(A and B)

0.34×0.45=0.153

but,

[tex]P(A|B) = \frac{P(AnB)}{P(B)}[/tex]

P(AnB) = 0.85 x 0.45

P(AnB) = 0.3825

So, P(A∩B) does not satisfy the condition.

Hence, A and B are not independent events.

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the evaluation of the expression 2x−yz is 69.2.

What is polynomials?

Using variables and coefficients, polynomials are algebraic expressions. The term "indeterminates" is sometimes used to describe variables. For polynomial expressions, addition, subtraction, multiplication, and positive integer exponents are all arithmetic operations that are possible, however division by variables is not one of them. The polynomial x2+x-12 is an illustration of one with one variable. Three terms—x2, x, and -12—are included in this case.

the expression 2x−yz , where x=34 , y=−0.2 , and z = 6.

So putting the value of x,y and z.

2(34)- (-0.2*6) = 68+1.2

=69.2

Hence the evaluation of the expression is 69.2.

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The exact values of the inverse trigonometric functions are introduced below:

a) π / 6 or 11π / 6.

b) 0 or 2π.

c) 2π / 3 or 4π / 3.

In this problem we must determine the exact values of three inverse trigonometric functions, all of them from inverse cosine function. This can be found only easily for certain cases. For the case of the inverse cosine in [0, 2π], there are the following values:

cos⁻¹ 0 = π / 2 or 3π / 2

cos⁻¹ 1 = 0 or 2π

cos⁻¹ (- 1) = π

cos⁻¹ (√3 / 2) = π / 6 or 11π / 6

cos⁻¹ (- √3 / 2) = 5π / 6 or 7π / 6

cos⁻¹ (1 / 2) = π / 3 or 5π / 3

cos⁻¹ (- 1 / 2) = 2π / 3 or 4π / 3

Then, by direct inspection we get the following results:

a) cos⁻¹ (√3 / 2) = π / 6 or 11π / 6

b) cos⁻¹ 1 = 0 or 2π

c) cos⁻¹ (- 1 / 2) =  2π / 3 or 4π / 3

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The market price in this economy equals to $9.

Basically, a market price is the amount of money for what an asset can be sold in a market. In other word, it is the cost of the products determined with respect to the point where the demand meets supply.

The value of marginal product of labor (VMPL) is equal to the marginal product of labor (MPL) multiplied by the market price (P).

In this case, to find market price, we will divide the the value of the marginal product of labor by the marginal product of labor:

= 90/10

= $9

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Only duo mode players who play on any platform .

The correct answer will be Option D.

Given, Popular online video game .

As they have taken the random sample from the population of duo mode players from any of the three platform, in this regard, 558 points will be the legitimate estimate of the mean from that population only as this sample is a part of that population.

In general, we can say 558 points is the point estimate of the mean of the population that play duo mode in any platform.

Hence option D is correct .

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Mr. Powel, who is our geometry teacher, told us we have a geometry test next week.

A nonrestrictive element is an element of a sentence that is not necessary for understanding the basic meaning of the sentence, but instead provides additional information. Nonrestrictive elements are usually set off with commas, while restrictive elements are not. For example, “My brother, who is an engineer, works in Chicago” is a sentence with a nonrestrictive element. The nonrestrictive element (“who is an engineer”) provides additional information about the brother, but does not provide any information about which brother is being referred to. The restrictive element “My brother who works in Chicago” does provide information about which brother is being referred to.

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The total amount Emily spent each month for 20 days will be $142.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

In this situation, Emily spends $4.85 on a latte and $2.25 on a scone. The total amount spent for 20 days will be:

= (4.85 + 2.25) × 20

= 7.1 × 20.

= 142

The amount is $142.

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The volume of the tube is increasing at the rate of 0.6 cubic millimeters per second.

The formula V = r2h, where r is the radius and h is the height, describes the volume of a cylinder.

The tube's volume is V = (2 mm)2 (20 mm), which equals 125.66 mm3.

Dr/dt = -0.1 mm/s and dh/dt = 3 mm/s are the formulas used to calculate the rate of change of the radius and height, respectively.

Using the chain rule, the rate of change of the volume is given by

dV/dt = π·2·[(2 mm)·(-0.1 mm/s) + (20 mm)·(3 mm/s)] = 0.6 mm3/s.

Therefore, the volume of the tube is increasing at the rate of 0.6 cubic millimeters per second.

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A LCM is smallest number among all common multiples of the given numbers. LCM of 24 is 2³ × 3

The least common multiple is also known as LCM (or) the lowest common multiple in math. The least common multiple of two or more numbers is the smallest number among all common multiples of the given numbers

There are 3 methods to find the least common multiple of two numbers.

According to the question,

(a) LCM of 24 : 2³ × 3

(b) LCM of 2 , 6 , 12  : 2 × 2 × 3

(c) To find the LCM of two number use the prime factorization of each number and then the product of the highest powers of the common prime factors will be the LCM of those numbers.

(d) Least common factor of 12 : 2 × 2 × 3

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The range of time it could take a Monarch to reach Mexico based on the variation in travel speeds is 25 - 100 days

From the given information, Monarch butterflies travel between 25-100 miles per day during their 2,500-mile journey to Mexico in winter.

Based on the information, the shortest number of days taken will be:

= 2500 / 100

= 25 days

The longest number of days used will be:

= 2500 / 25

= 100 days.

The time range will be 25 - 100 days

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Answer:

Step-by-step explanation:

Solving for X in Other Triangles In any triangle, the sum of the squares of the two shorter sides is equal to the square of the length of the longest side. This is known as the Pythagorean theorem.

Answer:

5

Step-by-step explanation:

First, work out parenthesis 5*5/5(1)

Then, Multiply/divide from left to right 25/5(1) -> 5(1) = 5

The simplest form of  the exponent number of 3^(5/2) is √243.

What is exponential form of a number?

To express numbers that are either too large or too tiny, use exponential notation, which raises the number to the power of the appropriate exponent. The exponent's power might either take the positive or negative form.

For instance, we may express the exponential form of 5 × 5 × 5 × 5 as 5⁴, where 5 is the base and 4 is the power. The power here indicates how many times we are multiplying the base by itself.

Given number is 3^(5/2)

The base of the given number is 3 and exponent 5/2.

Apply the formula a^(m/2) = √a^m in the given number:

3^(5/2) = √3⁵

Putting 3⁵ = 243

3^(5/2) = √243.

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Answer:

After tax = Bill * (1 + rate)

25.30 = x * (1 + 0.08)

25.30 = x * 1.08

25.30 = 1.08x                 (divide 1.08 both side)

x = 23.43

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Step-by-step explanation:

Answer:

  y = 9x² +9x +2

Step-by-step explanation:

You want a quadratic equation with roots -1/3 and -2/3.

When p is a root of a polynomial, x-p is a factor. That means your quadratic will have factors (x -(-1/3)) and (x -(-2/3)). If we want integer coefficients, we can multiply each of these by 3:

  y = (3x+1)(3x+2)

  y = 9x² +9x +2 . . . . . . the result of multiplying it out

Division C’s highest acceptable transfer price if it were to buy 4,000 units from Division B should be $58.

The transfer price is the price that Division B should charge Division C for the internal supply of goods or services.

Ordinarily, the transfer price equals the outlay cost (production cost) plus the opportunity cost (profit from selling outside).

The highest acceptable transfer price that Division C should reflect the market price at which Division C could acquire the parts from outside.

Division B:

Outside market selling price per unit = $60

Variable cost per unit = $44

Fixed cost per unit = $8

Capacity in units = 20,000 units

Units sold outside by Division B = 15,000 units

Excess units = 5,000 units (20,000 - 15,000)

Units required by Division C = 4,000 units

Outside supplier's price per unit = $58

Thus, the highest acceptable transfer price should be $58 and not $60.

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The absolute value of |-32| is 32; absolute value of |27| is 27; absolute value of |-12| is 12; absolute value of -|14| is -14.

The Absolute value |x| of a real number x is the non-negative value of x without regard to its sign.

|x| = x ; |-x| = x

Therefore absolute value of

|-32| = 32

|27| = 27

|-12| = 12

- |14| = - 14

Absolute value describes the distance from zero that a number is on the number line , without considering direction. The absolute value of a number is never negative. Sometimes a sign is attributed to a numeric value to signify the direction, in addition to the value.

The absolute value of a number is defined as its magnitude irrespective of the sign of the number.

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Answer: the answer is your mom

Step-by-step explanation:

Answer:

Step-by-step explanation: 720 ways overall , First and Last set = 24 ways, Probability of First and Last happening =130

The similarities between matrix factorization and content-based filtering and/or collaborative filtering are given below.

What is matrix factorization and collaborative filtering?

A group of cooperative filtering algorithms used in recommender systems is called matrix factorization. The user-item interaction matrix is broken down into the product of two rectangular matrices with lower dimensions by matrix factorization algorithms.

Collaborative filtering makes recommendations by simultaneously comparing similarities between users and items, addressing some of the drawbacks of content-based filtering.

collaborative filtering: user-based for example, CF calculates users' similarities in the item space. Then taking similar users's interest to do a recommendation for the target user. CF is one case of neighborhood methods.

matrix factorization amounts to mapping features of user and item via linear combination to latent factor space respectively.

Then calculating the similarity via inner-product of latent user factor and latent item factor.

CF covers local information of target user for the sake of neighborhood methods, while MF covers global information.

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The statement that is true about Denzel's experiment is that D. The outcomes do not appear to be equally likely, so a uniform probability model is not a good model to represent probabilities in Denzel's experiment.

Uniform models are only useful for equally likely probabilities, so they are ineffective here. In statistics, a uniform distribution is a type of probability distribution in which every possible outcome has an equal chance of occurring. Because each variable has an equal chance of being the outcome, the probability is constant.

All events have an equal chance of occurring in a uniform probability mode. Rolling any one side of a six-sided fair die, for example, has the same probability: one out of six. In this situation, when Denzel randomly selects a single card, writes down the number, and then places it back in the bag, the probability are different.

Therefore, the correct option is D.

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Part 1: The point of maxima is 21.212

Part 2: x = 21.212 is approximately equal to the year 2022

Part 3: The percentage at that time is 16.37%

Part 4: The rate of change of the percentage at that time is 0.294

Part 1:

p(x) = −0.00022x^3 + 0.014x^2 − 0.0033x + 12.236

where x is the number of years since 2000, data from 0<=x<=50

Differentiating the function with respect to x and equating it to 0

p'(x) = -0.00066x^2 + 0.028x - 0.0033

We will find the critical points of p'(x)

p''(x) = dp'(x)/dx  = -0.00132x + 0.028

Critical points of p'(x) lies at x where p''(x) = 0

Thus, -0.00132x + 0.028 = 0

x = 0.028/0.00132 = 21.212

Now, p'''(x) = -0.00132<0

x = 21.212 is a point of maxima of p'(x)

Therefore, the maximum possible values of x could lie at x = 21.212 as well as the extreme points of the domain p'(x), i.e. at x = 0 and 50

p'(0) = -0.00066(0)^2 + 0.028(0) - 0.0033 = -0.0033

p'(21.212) = -0.00066(21.212)^2 + 0.028(21.212) - 0.0033 = 0.2936

p'(50) = -0.00066(50)^2 + 0.028(50) - 0.0033 = -0.2533

Hence p'(x) attains maxima at x = 21.212

Therefore, p(x) increases most rapidly at x = 21.212

Part 2:

From the given condition in the question, x = 0 corresponds to the year 2000

Thus x = 21.212 is approximately equal to year 2022

Part 3:

The percentage at that time:

p(x) = −0.00022x^3 + 0.014x^2 − 0.0033x + 12.236

p(21.212) = -0.00022(21.212)^3 + 0.014(21.212)^2 - 0.0033(21.212) + 12.236

= 16.365

= 16.37%

Part 4:

Rate of change of the percentage at that time

p(x) = −0.00022x^3 + 0.014x^2 − 0.0033x + 12.236

p'(21.212) = -0.00066(21.212)^3 + 0.028(21.212) - 0.0033

= 0.2936

=0.294

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Answer:

0

Step-by-step explanation:

Answer:

82 degrees

Step-by-step explanation:

due to the resemblance of 90 degrees

The volume of the gas at 6.4 × 10⁴ Pascals is 7.44×10⁻⁷m³.  The pressure of the gas is  5.47× 10⁶ Pascals

At a constant temperature, the volume of a gas is inversely proportional to its pressure. We can write:

V α 1/P

V = T/P   (where T is the constant of proportionality)

T = PV

SInce T₁ = T₂

Also, P₁V₁ = P₂V₂

We have pressure of 2.8 x 10⁶ Pascals and a volume of 1.7 x 10⁻⁸ m³

a) What will the volume of the gas be when its pressure is 6.4 × 10⁴ Pascals?

P₁V₁ = P₂V₂

2.8 × 10⁶ × 1.7×10⁻⁸ = 6.4 × 10⁴ × V₂

V₂ = (2.8 × 10⁶ × 1.7×10⁻⁸)/ (6.4 × 10⁴)

V₂ = 7.44×10⁻⁷m³

b) Work out the pressure of the gas when its volume is 8.7 x 10⁻⁹ m³

P₁V₁ = P₂V₂

2.8 × 10⁶ × 1.7×10⁻⁸  = 8.7 ×10⁻⁹ × P₂

P₂ = (2.8 × 10⁶ × 1.7×10⁻⁸)/ (8.7 ×10⁻⁹)

P₂ =  5.47× 10⁶ Pascals

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Answer:

[tex]x = 1 , y = 3[/tex]

Step-by-step explanation:

Note that each equation is equal to y. Set the equations equal to each other:

[tex]y = x + 2\\y = 3x\\\\x + 2 = y = 3x\\x + 2 = 3x[/tex]

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Subtract x from both sides of the equation:

[tex]x + 2 = 3x\\x (-x) + 2 = 3x (-x)\\2 = 3x - x\\2 = 2x[/tex]

Next, divide 2 from both sides of the equation:

[tex]2x = 2\\\frac{2x}{2} = \frac{2}{2} \\x = \frac{2}{2} = 1\\x = 1[/tex]

Next, plug in 1 for x in one of the given equations:

[tex]y = x + 2\\\\x = 1 \\[/tex](given).

[tex]y = (1) + 2\\y = 3[/tex]

[tex]x = 1 , y = 3[/tex] is your answer.

~

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Layla should by not more than 4 outfits in order not to exceed her budget

The inequality expression is n  ≤ 4

price of a new bicycles = $418.55

2 bicycle reflectors = $19.39

a pair of bike gloves = $27.23

new biking outfits = $38.86 each

Nora's total money to spend at a bicycle store = $38.86

Layla's spending will never exceed the total spending at the bike shop, so it will be less than or equal to the total of other items

We write the expression as;

$640 ≤ $418.55 + 2 * $19.39 + $27.23 + n * $38.86

where n represents the number of the new biking outfits

$640 - ( $418.55+ 2 * $19.39 + $27.23 ) ≤. + n * $38.86

( $640 - ( $418.55 + 2 * $19.39 + $27.23 ) ) /  $38.86≥ n

( $640 - $484.56 ) /  $38.86 ≥ n

( $155.44) /  $38.86  ≥ n

4  ≥ n

Layla should by not more than 4 outfits in order not to exceed her budget

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