A toy rocket is launched vertically upward from a 12 foot platform with an
initial velocity of 128 feet per second. Its height h, at time t seconds after
launch is given by the equation h(t) = -16t^2 + 128t +12 . How long will it
take the rocket to reach the ground?

Answer:

100:60:80

Step-by-step explanation:

240÷12=20

20×5=100

20×3=60

20×4=80

Answer:

100: 60: 80

Step-by-step explanation:

5/(5+3+4) *240= 100

3/(5+3+4)* 240= 60

4/(5+3+4)* 240= 80

Using the Binomial probability distribution,

the probability that sheer guesswork will yield exactly 18 correct answers is ²⁷C₁₈(0.2)¹⁸(0.8)⁹

We have given that,

total number of multiple choice questions= 27

each question has number of possible answer

= 5

but only one is correct .

we have to find out the probability that sheer guesswork will yield 18 correct answer.

P(C) = probability of answering any question correctly = (1 / 5) = 0.2

P(W) = probability of answering any question wrongly = (4/ 5) = 0.8

Using the Binomial probability distribution,

P(X= x) = ⁿCₓ(p)ˣ(q)⁽ⁿ⁻ˣ⁾

Probability of answering exactly 18 questions correctly = P(X=18) = ²⁷C₁₈(0.2)²⁸(0.8)⁹

Hence, the probability value is ²⁷C₁₈(0.2)²⁸(0.8)⁹

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Answer:

46.5

Step-by-step explanation:

The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

Given a function:

f(t)=e5t+4t+7ln(t2+3c)+te-1+5e6

where c is a constant.

The solution to the question is shown below.

Step 1: We have given a function:

f(t)=e5t+4t+7ln(t2+3c)+te-1+5e6

We have to find the number of words we have to write to express this function in words.

Step 2: Solution

f(t) = et5+4t + ln(t²+3c)⁷ +te-1+5e⁶

Where,

et5+4t = exponential function

ln(t²+3c)⁷ = natural logarithmic function

te-1 = linear function

e⁶ = exponential function

Therefore, f(t) can be expressed in words as:

The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

Step 3: Conclusion

Hence, the function f(t) can be expressed in words with:The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

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Suppose we want to compute x≡ab(mod pq) for primes p and q, utilizing the Chinese Remainder Theorem and Fermat's Little Theorem. True statements are:

According to the Chinese remainder theorem, if one knows the remainders of the Euclidean division of an integer n by multiple numbers, one may uniquely calculate the remainder of the division of n by the product of these integers, provided that the divisors are pairwise coprime (no two divisors share a common factor other than 1).

Fermat's little theorem is identical to the assertion that ap 1 1 is an integer multiple of p if an is not divisible by p, that is, if an is coprime to p. If a = 2 and p = 7, for example, 26 = 64, then 64 1 = 63 = 7 9 is therefore a multiple of 7.

x≡ab(mod pq)

Thus, (x1 - x2) divided by m1

Since, m1, m2,........mk are relatively prime

This follows system of congruence in CRT at most one solution.

Fermat's Little Theorem allows us to conclude that a^p−1 ≡1(modp) for any integer a and any prime p,

assume 0≤a≤p-1. This is result of modular arithmetic. So, results hols trivially.

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If each of the 100 people is asked to give one preference ballot for one of the five beverage choices, then the winner of the election will be the beverage with the most votes.

We have,

To determine the winner, we need to count the number of ballots for each choice and compare them.

For example, if we count 30 ballots for Coke, 20 for Diet Coke, 15 for Truly, 10 for Wine, and 25 for Beer, then the winner would be Beer, with 25 votes.

If there is a tie between two or more choices, we would need to have a run-off election or some other method to determine the winner.

Thus,

If each of the 100 people is asked to give one preference ballot for one of the five beverage choices, then the winner of the election will be the beverage with the most votes.

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Answer: x-6, x+3, x-3

Step-by-step explanation;

Split the equation into two.

x2(x-6)-9(x-6)

(x-6) is seen as one of the tiles. Now work on x2-9

x2-9 is a difference of squares meaning the last two are (x+3) and (x-3).

The ideal utilization would be $150but he can choose to borrow $1050

A credit card is a type of credit facility, provided by banks that allow customers to borrow funds within a pre-approved credit limit. It enables customers to make purchase transactions on goods and services.

Given here: Bob's credit limit is $3500 and he has a balance of $2200

Therefore available credit is equal to $3500-$2200=$1300

Thus if he spends more than $1300 then he goes over his limit.

But ideal utilization ratio is 30% and therefore 30%×3500=$1050

Thus ideal credit usage would be = 3500-1050

                                                        =2450

Then $2450-$2200=150

Hence, The ideal utilization would be $150but he can choose to borrow $1050

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Answer:

- 1

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

\(\frac{f(b)-f(a)}{b-a}\)

Here [ a, b ] = [ - 6, 6 ]

From the graph

f(b) = f(6) = - 2

f(a) = f(- 6) = 10 , thus

average rate of change = \(\frac{-2-10}{6-(-6)}\) = \(\frac{-12}{12}\) = - 1

step by step explanation:

I don't know

sorry really wanna help

Answer:

y=1/4x-2

Step-by-step explanation:

formula

y=mx+b

Answer:

25+0.35x

Step-by-step explanation:

The function which can be used to find the total cost in dollars of renting a van for a day and driving x miles is total cost = 25 + 0.35x.

The total cost of renting a moving van can be calculated using the following function:

Total Cost = Daily Rental Cost + (Miles Driven × Cost per Mile)

The daily rental cost is $25 and the cost per mile driven is $0.35.

So, the function to find the total cost in dollars of renting a van for a day and driving x miles would be:

Total cost(x) = 25 + 0.35x

Where, "x" represents the number of miles driven.

Plugging in the value of "x" will give you the total cost for renting the van for a day and driving that number of miles.

Hence,  total cost = 25 + 0.35x is the function which can be used to find the total cost in dollars of renting a van for a day and driving x miles.

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Answer:

(C) x=50

Step-by-step explanation:

\(\frac{3}{5 }x -7=23\)

\(\frac{3x}{5} -7=23\)

\(\frac{3x}{5} -7+7=23+7\)

\(\frac{3x}{5}=30\)

\(3x=30* 5\)

\(3x=150\)

\(x=50\)

Answer:

(C) X = 50

Step-by-step explanation:

(3/5)*x-7 = 23 // - 23

(3/5)*x-23-7 = 0

3/5*x-30 = 0 // + 30

3/5*x = 30 // : 3/5

x = 30/3/5

x = 50  (Sorry if it's wrong)

The Answer is "X=2" awodkawopdawdawd

Answer:

X=2

Step-by-step explanation:

The statement one interesting feature of the natural numbers is that while each individual natural number is finite, the set of natural numbers is infinite is true.

The natural numbers, denoted by the set N = {1, 2, 3, 4, 5, ...}, represent a countable and infinite set. This means that for every natural number we can think of, there is always a larger natural number.

No matter how high we go, there is always another natural number that can be generated by adding 1 to the previous highest number.

To understand why the set of natural numbers is infinite, we can use a simple proof by contradiction. Suppose we assume that the set of natural numbers is finite, and there exists a highest natural number, say n.

However, by adding 1 to n, we can generate a new number, n + 1, which contradicts the assumption that n is the highest natural number. Therefore, the set of natural numbers cannot be finite.

This infinite nature of the set of natural numbers has profound implications in various mathematical and theoretical contexts. It forms the basis for concepts such as infinity, recursion, and mathematical induction.

The infinite set of natural numbers provides a foundation for the study of numbers, patterns, and mathematical structures, serving as a cornerstone of mathematics and its applications in various fields.

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Answer: The volume of the cylinder is greater than the volume of the prism.

Step-by-step explanation:

The Volume of a cylinder is given as:

= πr²h

Therefore, the volume of a cylinder with a radius of 12 units and a height of 15 units will be:

= πr²h

= 3.14 × 12² × 15

= 6782.4

The volume of a rectangular prism with dimensions 12 units x 12 units x 15 units will be:

= Length × Width × Height

= 12 × 12 × 15

= 2160

Based on the calculation, the volume of the cylinder is greater than the volume of the prism.

To solve for x, we just need to compute the inverse of A (if it exists) and multiply it by b. If A is invertible, then this method will give us the unique solution to the linear system Ax=b.

To solve a linear system of the form Ax=b using inverse matrices, we can first find the inverse of matrix A (if it exists) and then multiply both sides of the equation by \(A^-1\), giving us:

\(A^-1Ax = A^-1b\)

Since\(A^-1A\) is the identity matrix I, we can simplify the left-hand side to just x:

\(x = A^-1b\)

However, it's worth noting that computing the inverse of a matrix can be computationally expensive, particularly for large matrices.

So, while using inverse matrices can be a useful technique for solving small systems, it may not be the most efficient approach for larger systems. In those cases, other techniques such as Gaussian elimination or LU decomposition may be more appropriate.

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Answer:

36 38 40 42

and

38 40 42 44.

Step-by-step explanation:

160 / 4 = 40  so the numbers are close to 40.

38 + 40 + 42 + 44 = 164

36 + 38 + 40 + 42 = 156.

Hello!

Answer:

22-3= 19

Step-by-step explanation:

Hope this helps!

\(Given\: equation\: ➠ \:{c}^{2}\:+\:5c\:-\:8 \)

\( Value\: of\: c \:=\: 4 \)

Evaluating c = 4 in equation .

\(⟶\:{c}^{2}\:+\:5c\:-\:8 \)

\(⟶\:{4}^{2}\:+\:5(4)\:-\:8 \)

\(⟶\:16\:+\:20\:-\:8 \)

\(⟶\:36\:-\:8\)

\(⟶\:28\)

Answer:

if c=4

then c2+5c-8

4*3+5*4-8

12+20-8

32-8

24.

Answer: y=0.05x-23540

Step-by-step explanation: We turn 5% into a decimal which is 0.05 and we add x to it so we can pick how many years. Then we subtract 23540 because he has used that money to buy the car.

Answer:

(3x + 4y)(x + 2y)

Step-by-step explanation:

3x^2+ 10xy + 8y^2

All signs are positive, so we'll only look at positive factors of 3 and 8.

3 factors into 3 and 1.

8 factors into 4 and 2, and it also factors into 8 and 1.

I like to try closer factors in value, so I'll start with 4 and 2 for 8.

Try:

(3x + 2y)(x + 4y) = 3x^2 + 12xy + 2xy + 8y^2 = 3x^2 + 14xy + 8y^2

The middle term does not work. Switch 2y and 4y and try again.

Try:

(3x + 4y)(x + 2y) = 3x^2 + 6xy + 4xy + 8y^2 = 3x^2 + 10xy + 8y^2

It works.

Answer: (3x + 4y)(x + 2y)

Answer:

I would use equation d

Step-by-step explanation:

because need to find out X which is the second section so you would do 60 subtract 35 which gives 25 so X would be 25 .

I hope this helped . if you need any more help pls ask :)

pls give brainliest if you like my answer :)

Answer:

Part A: (C) 16 square inches

Part B: (C) 36 square inches

A repeating decimal is something like 0.2727272727....  

It never end and keeps repeating forever.

Your number is not this.

A non-repeating decimal (also implying that it's non-terminating) is something that goes on forever without a repeating pattern.  

π  = 3.141592653589793... is a regular example.

Your number also isn't this, because your number stops after 4 decimal places.

Decimals that stop like that are called "terminating".

To solve this problem, we need to find the antiderivative of f'(x) = 9x^1/2 + 10x^3/2. However, this function cannot be integrated directly using basic integration techniques. Instead, we need to rewrite f(x) as a sum of terms with fractional exponents, which can be integrated using the power rule. To do this, we can use the property that (a+b)^n = sum of (n choose k) * a^(n-k) * b^k, where (n choose k) represents the binomial coefficient. In this case, we have f(x) = V(9 + 10x) = (9(1 + 10x/9))^1/2 = 3(1 + 10x/9)^1/2. Using the binomial theorem, we can expand this expression as f(x) = 3(1 + 1/9(10x))^1/2 = 3(1/9(10x))^1/2 * sum of (1/2 choose k) * (1/9(10x))^k.

Next, we can integrate each term using the power rule, which states that the antiderivative of x^n is (1/(n+1))x^(n+1) + C, where C is the equation of integration. Applying the power rule, we get f(x) = 3(1/9(10x))^1/2 * sum of (1/2 choose k) * (1/(k+1))(1/9(10x))^(k+1) + C.To find the constant of integration C, we use the fact that f(1) = 14. Substituting x = 1 into the expression for f(x), we get f(1) = 3(1/9(10))^1/2 * sum of (1/2 choose k) * (1/(k+1))(1/9(10))^(k+1) + C = 3/3 + C = 1 + C. Therefore, C = 14 - 1 = 13.In summary, the antiderivative of f'(x) = 9x^1/2 + 10x^3/2 is f(x) = 3(1/9(10x))^1/2 * sum of (1/2 choose k) * (1/(k+1))(1/9(10x))^(k+1) + 13. The constant of integration C is found by using the condition that f(1) = 14, which gives C = 13.

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If volleyball team purchased 15 jackets, 12 pairs of sweatpants for $348 and basketball team purchases 8 jackets , 8 pairs of sweatpants for $200, the the system of equations that represent the situation is (b)  \(15x+12y = 348\) and \(8x+8y = 200\) .

let the number of jackets purchased be = x ;

let the number of pairs of sweatshirts purchased be = y ;

the volley ball team purchased 15 jackets and 12 pairs of sweatpants for $348 ,

that means the equation that represents the situation is :

\(15x+12y = 348\) .

Also given that , the basketball team purchased 8 jackets and 8 pairs of sweatpants for $200 ,

that means the equation that represents the situation is :

\(8x+8y = 200\) .

Therefore , the system of equations are \(15x+12y = 348\) and \(8x+8y = 200\) .

The given question is incomplete , the complete question is

A sports apparel supplier offers teams the option of purchasing extra apparel for players. A volleyball team purchases 15 jackets and 12 pairs of sweatpants for $348. A basketball team purchases 8 jackets and 8 pairs of sweatpants for $200. Let x represent the price of a jacket and let y represent the price of a pair of sweatpants. Which system of equations can be used to find the price of each item ?

(a) 8x + 8y = 200  ;  12x + 15y = 348   ;

(b) 8x + 8y = 200  ; 15x + 12y = 348 ;  

(c) 8x + 8y = 348  ;  12x + 15y = 200 ;  

(d) 8x + 8y = 348 ;  15x + 12y = 200 .

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A: (a) A = [0 1; -1 0]. This matrix has only real entries and when we square it, we get A² = [-1 0; 0 -1], which is equal to -I.

(b) B = [0 1; 0 0]. This matrix is not 0, but when we square it, we get B² = [0 0; 0 0], which is equal to 0.

(c) C = [0 1; -1 0] and D = [1 0; 0 -1]. When we multiply these two matrices, we get CD = [-1 0; 0 1] and DC = [0 -1; 1 0], which are opposite matrices.

(d) E = [1 1; 1 1] and F = [-1 1; 1 -1]. When we multiply these two matrices, we get EF = [0 0; 0 0], which is equal to 0, although no entries of E or F are zero.

Here is explanation -

(a) A = [[0, -1], [1, 0]] is a 2x2 matrix with real entries that satisfies A^2 = -I. To see this, we can simply calculate the square of the matrix A:

A^2 = [[0, -1], [1, 0]] * [[0, -1], [1, 0]]

= [[00 + -11, 0*-1 + -10], [10 + 01, 1-1 + 0*0]]

= [[-1, 0], [0, -1]]

As we can see, A^2 = -I, where I is the 2x2 identity matrix.

(b) B = [[0, 1], [0, 0]] is a 2x2 matrix with real entries that satisfies B^2 = 0, although B ≠ 0. To see this, we can calculate the square of the matrix B:

B^2 = [[0, 1], [0, 0]] * [[0, 1], [0, 0]]

= [[00 + 10, 01 + 10], [00 + 00, 01 + 00]]

= [[0, 0], [0, 0]]

As we can see, B^2 = 0, although B ≠ 0.

(c) C = [[0, 1], [-1, 0]] and D = [[0, -1], [1, 0]] are 2x2 matrices with real entries that satisfy CD = -DC. To see this, we can calculate the product of matrices C and D:

CD = [[0, 1], [-1, 0]] * [[0, -1], [1, 0]]

= [[00 + 10, 0*-1 + 11], [-10 + 01, -1-1 + 0*0]]

= [[0, 1], [1, 1]]

DC = [[0, -1], [1, 0]] * [[0, 1], [-1, 0]]

= [[00 - 11, 01 + -10], [10 - 0-1, 11 + 00]]

= [[-1, 0], [1, 1]]

As we can see, CD ≠ -DC, so C and D do not satisfy the condition CD = -DC, not allowing the case CD = 0.

(d) E = [[1, 1], [0, 1]] and F = [[1, 0], [1, 1]] are 2x2 matrices with real entries that satisfy EF = 0, although no entries of E or F are zero. To see this, we can calculate the product of matrices E and F:

EF = [[1, 1], [0, 1]] * [[1, 0], [1, 1]]

= [[11 + 10, 11 + 11], [01 + 10, 01 + 11]]

= [[1, 2], [0, 1]]

As we can see, EF = 0, although no entries of E or F are zero.

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Answer:

2nd one

Step-by-step explanation:

(90 x 5) - 3 = 447