NASA launches a rocket at t=0 seconds. Its height, in meters above sea-level, as a function of time is given by
h(t)=−4.9t^2+169t+234.
Assuming that the rocket will splash down into the ocean, at what time does splashdown occur?
The rocket splashes down after
seconds.[Round your answer to 4 decimal places)
How high above sea-level does the rocket get at its peak? [Round your answer to 3 decimal places]
The rocket peaks at
meters above sea-level.

Answer:

-17&14/16

-17

17&4/32

17.225

17&17/40

Answer:

18

Step-by-step explanation:

30 students * 60/100= 18

The numbered spot at which all the runners will be next to one another is spot 19.

Least Common Multiple is the meaning of the acronym LCM. The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers. It may also be computed using two or more real numbers.

Starting with the runner on the outside track, the provided parameters are;

The runner covered n₁ = 5 places on the outside track, which is the number of spaces.

Next, the inner runner will traverse n₂ spaces, which equals one space.

The following inner runner will cover n₃ = 3 spaces.

The subsequent runner will traverse n₄ = 2 spaces.

The Lowest Common Multiple, or LCM, of all the runners' speeds or the total number of spaces they cover in the same amount of time, determines where all the runners will be placed next to one another.

LCM(5, 1, 3, 2) = 30 is the LCM of 5, 1, 3, and 2.

Time = 30/ = 6

Consequently, when the first runner has covered 30 places, we have;

Six time units have been expended.

The runner comes to a stop at position 30- (30 -19) = Position 19.

First runner's new destination is Spot 19.

The distance covered simultaneously by runner 2 is 6 x 1 = 6.

The distance covered by two runners running simultaneously equals six spaces.

Second runner's new position: 6 spaces plus spot 13 equals spot 19.

The combined distance covered by the three runners is 6 x 3 = 18.

The distance runner 3 covers 18 spaces simultaneously.

Third runner's new position: 18 spaces + Spot 1 = 19 spaces

Runner 4 covers a distance of 6 x 2 = 12 at the same time.

Distance runner 4 journeys equals 12 spaces

Runner 4's new position is now 12 spaces Plus Spot 7 = Spot 19.

Therefore, all the runners will be next to one another is spot 19.

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The identity of  sin²Ф + cos²Ф  = 1 is verified below

Trigonometry ratio can be evaluated by following the laid down rules with the the use of table and calculator

Given that tan Ф =  1/√5

Where Tan Ф = Opposite / adjacent

We can calculate the hypotenuse by using Pythagoras theorem

Hyp² = 1² + (√5)²

Hyp² = 1 + 5

Hyp = √6

sin Ф = opp / hyp

sin Ф = 1/√6

sin²Ф = 1/6

cos Ф = adj / hyp

cosФ = √5 / √6

cos²Ф = 5/6

sin²Ф + cos²Ф =  1/6 + 5/6

sin²Ф + cos²Ф  = 6/6

sin²Ф + cos²Ф  = 1

Therefore, the identity of  sin²Ф + cos²Ф  = 1 is verified.

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Answer:

Step-by-step explanation:

it would be "c" because the question asks for the number that makes the inequality true

4x≤ x+3

the graph in c is saying that every number that is 1 or less than 1 makes the inequality true. so lets take -7 as an example

4 x -7=-28

-28+3=-25

-25 is greater than -28 so the inequality is true. the reason why graph d doesnt work is because if we plug in 2 into the equation, then 4x =8 and x+3=5

5 is not greater than 8 so it doesnt work

Answer:

Step-by-step explanation:

To find the limit of (n!)^(1/n) as n approaches infinity, we can use the Stirling's approximation for n!, which is:

n! ≈ (n/e)^n √(2πn)

where e is the mathematical constant e ≈ 2.71828, and π is the mathematical constant pi ≈ 3.14159.

Using this approximation, we can rewrite (n!)^(1/n) as:

(n!)^(1/n) = [(n/e)^n √(2πn)]^(1/n) = (n/e)^(n/n) [√(2πn)]^(1/n)

Taking the limit as n approaches infinity, we have:

lim (n!)^(1/n) = lim (n/e)^(n/n) [√(2πn)]^(1/n)

Using the fact that lim a^(1/n) = 1 as n approaches infinity for any constant a > 0, we can simplify the second term as:

lim [√(2πn)]^(1/n) = 1

For the first term, we can rewrite (n/e)^(n/n) as [1/(e^(1/n))]^n and use the fact that lim a^n = 1 as n approaches infinity for any constant 0 < a < 1. Thus, we have:

lim (n/e)^(n/n) = lim [1/(e^(1/n))]^n = 1

Therefore, combining the two terms, we have:

lim (n!)^(1/n) = lim (n/e)^(n/n) [√(2πn)]^(1/n) = 1 x 1 = 1

Hence, the limit of (n!)^(1/n) as n approaches infinity is 1.

Answer:1

Step-by-step explanation:

Answer:

c. 95 beetles

Step-by-step explanation:

The value of the expression "the product of x and y divided by 4" is xy/4

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

The expression "the product of x and y" simply means to multiply x and y together. For example, if x = 2 and y = 3, then the product of x and y is:

x * y = 2 * 3 = 6

So, the product of x and y is 6 in this case.

The expression "the product of x and y divided by n" means that you need to take the product of x and y, and then divide the result by n. So, if we let n be a number, then we can write the expression as:

(xy) / n

For example, if x = 2, y = 3, and n = 4, then the product of x and y divided by n is:

(xy) / n = (2 * 3) / 4 = 6 / 4 = 1.5

Therefore, the value of the expression "the product of x and y divided by n" depends on the values of x, y, and n that you plug into the expression.

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Complete question -

What is the product of x and y divided by 4​?

The simplified form of √([2m5z6]/[xy]) is (√2m√5z√6) / (√x√y).

To simplify the expression √([2m5z6]/[xy]), we can break it down step by step:

Simplify the numerator:

√(2m5z6) = √(2) * √(m) * √(5) * √(z) * √(6)

= √2m√5z√6

Simplify the denominator:

√(xy) = √(x) * √(y)

Combine the numerator and denominator:

√([2m5z6]/[xy]) = (√2m√5z√6) / (√x√y)

Thus, the simplified form of √([2m5z6]/[xy]) is (√2m√5z√6) / (√x√y).

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We can write that -

An irrational number is a number that cannot be expressed as a fraction p/q for any integers {p} and {q}.

Given are the numbers to be verified as rational or irrational.

Therefore, we can write that -

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The sequence is will always have even numbers, is hence proved.

Given, the quadratic sequence is: 44:52:64:80

Sequences with a term are known as quadratic sequences. They can be distinguished by the fact that the first differences between terms are not equal but the second differences between terms are. Utilizing the term sum in an arithmetic progression formula, the sum of even numbers formula is achieved. The equation is Sum of Even Numbers Formula = n(n+1), where n is the total number of terms in the series.

The formula is: Tₙ = 2n² ₊ 2n  ₊ 40

take 2 common

Tₙ = 2(n² ₊ n  ₊ 20)

in other words n² ₊ n  ₊ 20  = y

therefore , Tₙ = 2y

which by definition makes Tₙ an even number at all times.

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Answer:

55 degrees

Step-by-step explanation:

Since it's a right angle it's total is 90 degrees, so you'll subtract 35 from 90.

90-35=55

Answer:

missing angle is 55

Step-by-step explanation:

90 - 35 = 55

Answer:

1. n= 20 /13

2. n=10

3. n=35

4. n=9

That's all I could do, I got tired of typing lol

Step-by-step explanation:

1.  4/n=13/5 we cross multiply, (4)*(5)=13*n, 20=13n Flip the equation.  13n=20, divide 13 on both sides, 13n/13=20/13, n= 20 /13

2. 9/6= 15/n, we cross multiply 9*n=(15)*(6), 9n=90, Divide both sides by 9. 9n/9=90/9 n=10

3. 28/4=n/5 Cross-multiply, (28)*(5)=n*(4), 140=4n Flip the equation.4n=140 Divide both sides by 4. 4n/4=140/4 n=35

4. n/6=6/4 we cross multiply,n*(4)=(6)*(6), 4n=36, Divide both sides by 4 4n/4=36/4.  n=9

An equation that relates Juan's age j to Maria's age m can be expressed as j = m + x, where x is the age difference between Juan and Maria.

An equation is a pair of algebraic equations with the equal sign (=) in the middle and the same value.

Given:

Amara is 18 years old.

Let's assume that Amara is y years younger than Maria, then we can write an equation relating their ages as:

Amara's age = Maria's age - y

Substituting Amara's age as 18 in the above equation, we get:

18 = m - y

Rearranging the equation, we get:

m = 18 + y

Therefore, an equation that relates Amara's age to Maria's age m is

m = 18 + y.

Therefore, we don't have enough information to determine Maria's age as we don't know the value of y.

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a

its just counting

i think its a

Answer: it should be 60

Step-by-step explanation:

The value of integral ₀∫¹ ( eˣ - 2 )² dx is 8 + ( e² - 1) / 2 - 4e.

When infinitesimal data are combined, notions such as displacement, area, and volume can be created. An integral assigns numbers to functions in a way that describes these concepts. Integration is the action of locating integrals.

Consider the integral expression,

₀∫¹ ( eˣ - 2 )² dx

Using ( a + b )² = a² + b² + 2ab

\(\int_0^{1}( e^{x} - 2 )^{2} dx = \int_0^{1}(e^{2x}+4-2e^{x})dx\)

\(\int_0^{1}( e^{x} - 2 )^{2} dx = \int^0_{1}e^{2x} dx +\int_0^{1}4 dx - \int_0^{1}4e^{x} dx\)

Now, integration of eˣ is eˣ + c where c is constant.

Therefore,

\(\int_{0}^{1} ( e^{x} - 2 )^{2} dx = [ \frac{e^{2x}}{2} ]_0^{1} + [ 4x ]_0^{1} - [ 4e^{x}]_0^{1}\)

₀∫¹ ( eˣ - 2 )² dx = ( e² / 2 - e⁰/2 ) + ( 4 - 0 ) - ( 4e¹ - 4e⁰ )

₀∫¹ ( eˣ - 2 )² dx =  e² / 2 - 1/2 + 4 - 4e + 4

₀∫¹ ( eˣ - 2 )² dx = e² / 2 - 4e + 8 - 1/2

₀∫¹ ( eˣ - 2 )² dx =  = 8 + ( e² - 1) / 2 - 4e

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Given the following:

To generate the sequence, we have:

Hence, the correct option is Option D

Answer:

d) \(7^{14}\)

Step-by-step explanation:

we simplify \((7^{7})^{2}\) by doing 7 x 2 = 14

so it is now

\(7^{14}\)

to check, we can use a calculator.

7 to the power of 14 = 678223072849

and

7 to the power of 7, squared also = 678223072849

Hope this helps!

Answer:

F and H are both 121 degrees

Step-by-step explanation:

"A kite has 4 interior angles and the sum of these interior angles is 360°. In these angles, it has one pair of opposite angles that are obtuse angles and are equal." - Cue math

Ok, so the two acute angles add up to 118 degrees, and in order to find the remaining angles we need, subtract 118 from 360 to get 242. Because the two obtuse angles are equivalent, divide 242 by 2 to get the measure of each.

A variable is a characteristic or attribute that can take on different values. It is an observable and measurable property of an object or phenomenon, which can be used to describe and analyze it.

Parameters are used in inferential statistics to make conclusions about a population based on a sample of data.

(a) If you decide to select based on proportion of 10% from each group, the number of patients selected from each group would be: Group A = (10/100) x 100 = 10 patients Group B = (10/100) x 30 = 3 patients Group C = (10/100) x 30 = 3 patients.

(b) The classified groups can be named as follows: Group A = 10 years of education or less Group B = More than 10 years but less than or equal to 20 years of education Group C = More than 20 years of education.

(c) The sampling method employed in the selection process was stratified sampling. Stratified sampling is a type of probability sampling technique where the population is divided into homogeneous subgroups or strata, and the researcher selects a simple random sample from each subgroup or stratum.

The researcher chooses a proportion of participants from each subgroup to represent the population as a whole, which allows for more precise estimates of the population parameters than simple random sampling.

The sample is selected randomly from the stratified sample, which ensures that the sample is representative of the population.

A variable is a characteristic or attribute that can take on different values. It is an observable and measurable property of an object or phenomenon, which can be used to describe and analyze it.

Variables are used in research to test hypotheses, determine relationships between different phenomena, and make predictions about future outcomes.

A parameter is a numerical summary of a population, which describes a characteristic of the population. It is an unknown constant that can only be estimated from a sample of data.

Parameters are used in inferential statistics to make conclusions about a population based on a sample of data.

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Answer:

1,280

Step-by-step explanation:

prob(spots) = 12/180 = 1/15

so of the 1200 frogs, (1/15)(1200) should have spots, so ..

how many should not have frogs ?

or

prob(not spots) = 14/15

number who don't have spots = (14/15)(1200) = 1,280

11 by 35

how?

well, i have no idea just found it on internet

Answer:

Step-by-step explanation:

Find the difference:

The correct option is (A). The correct answer is Ursa Minor, the Little Bear, containing the bright star Polaris.

Whereas stars spin or revolve from the northern hemisphere is the center of the sky, also known as the North Celestial Pole. Additionally, it marks the precise location of the Polaris or Northern Star constellation in full view. In addition, this served as a point of reference for the construction of sundials in earlier times.

When people go outside, especially at night, and try to find the Polaris constellation, it is evident that the stars close to this star formation circle in an east-to-west direction, in contrast to the northern star, which makes no movement whatsoever as the evening wears on.

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slope of parallel line: 2

y = 2x + b

1 = 2(6) + b

1 = 12 + b

b = -11

equation of parallel line: y = 2x -11

Solution:

Since the original line is parallel to y = 2x + 5, the original line's slope must be 2.

Using point slope form:

The equation of a line that is parallel to y = 2x + 5 and goes through the point (6, 1) is y = 2x - 11.

Answer:

Step-by-step explanation:

You want to find the future value of an ordinary annuity with 5 annual payments of $1100 earning 4%. You also want to find the monthly payment that makes an ordinary annuity have a future value in 4 years of $25,000 when it earns 12%.

The future value of an ordinary annuity having payments P made n times per year for t years earning interest rate r is ...

  FV = P((1+r/n)^(nt) -1)/(r/n)

You want the future value for P=1100, r=0.04, n=1, t=5. Using these values in the formula gives ...

  FV = $1100(1.04^5 -1)/0.04 = $5957.95

The future value is $5957.95.

You want the payment that makes the future value be 25000 with r=0.12, n=12, t=4.

  25000 = P((1 +0.12/12)^(12·4) -1)/(0.12/12) = P(1.612226/0.01) = 61.2226P

Dividing by the coefficient of P gives ...

  P = 25000/61.2226 = 408.35

The required monthly payments are $408.35.

__

Additional comment

The formula is simple enough to use, but the same calculation can be done by a spreadsheet or an appropriate calculator.

The timing of payments in the second problem is not specified. We have assumed they occur at the end of the month. If they occur at the beginning of the month, they will be the computed amount divided by 1.01 (the monthly multiplier). That would make them $404.30.

The graph of the function y = 5|x - 4| is added as an attachment

From the question, we have the following parameters that can be used in our computation:

y = 5|x - 4|

The above function is an absolute value function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

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Answer:

The notation Σ-2 (3η + 5) is incorrect for representing the arithmetic series 8 + 11+ ... + 29.

The correct notation for the arithmetic series 8 + 11 + ... + 29 should be:

Σ_{i=1}^{11} (6i + 2)

The series has 11 terms, and each term can be found by adding 3 to the previous term, starting with the first term 8. Therefore, the general form of the series is 6i + 2, where i represents the index of the term in the series.

In contrast, the notation Σ-2 (3η + 5) appears to have multiple errors. The use of a negative index (-2) is not valid, as the index should start from 1 or 0. Also, the use of the Greek letter eta (η) instead of i as the index variable is unconventional and likely to cause confusion. Finally, the expression inside the parentheses does not appear to correspond to the terms of the arithmetic series.

The correct notation for the arithmetic series 8 + 11 + ... + 29 should be:

Σ_{i=1}^{11} (6i + 2)

To explain the error in the given notation Σ-2 (3η + 5), we can break it down as follows:

The use of a negative index (-2) is incorrect. The index of summation should always be a non-negative integer.

The use of the Greek letter eta (η) instead of i as the index variable is unconventional and may cause confusion or errors.

The expression inside the parentheses, 3η + 5, does not represent the terms of the arithmetic series. In particular, it does not involve the index variable i or the common difference 3.

Therefore, the correct notation for the given arithmetic series is Σ_{i=1}^{11} (6i + 2).