A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 72 feet per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=-16 t²+72 t+7. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at ? second(s) after launch.
(Simplify your answer.)
The maximum height reached by the object is ? feet.
(Simplify your answer.)

After simplification,  the factor of the expression [tex]x^{-1/2}+x^{-3/2}+x^{-5/2}[/tex] is [tex]\frac{x^2+x+1}{x^{5/2}}[/tex].

In the given question,

We have to factor the expression [tex]x^{-1/2}+x^{-3/2}+x^{-5/2}[/tex].

The given expression is [tex]x^{-1/2}+x^{-3/2}+x^{-5/2}[/tex].

The given all term having negative power. So make the term in positive we can write it as

[tex]x^{-1/2}+x^{-3/2}+x^{-5/2}=\frac{1}{x^{1/2}}+\frac{1}{x^{3/2}}+\frac{1}{x^{5/2}}[/tex]

Taking 1/[tex]x^{1/2}[/tex] from the left side

[tex]x^{-1/2}+x^{-3/2}+x^{-5/2}=\frac{1}{x^{1/2}}(1+\frac{1}{x}+\frac{1}{x^2})[/tex]

Now solving the bracket by multiply and divide [tex]x^2[/tex] in each term.

[tex]x^{-1/2}+x^{-3/2}+x^{-5/2}=\frac{1}{x^{1/2}}(1\times\frac{x^2}{x^2}+\frac{1}{x}\times\frac{x^2}{x^2}+\frac{1}{x^2}\times\frac{x^2}{x^2})[/tex]

[tex]x^{-1/2}+x^{-3/2}+x^{-5/2}=\frac{1}{x^{1/2}}(\frac{x^2}{x^2}+\frac{x}{x^2}+\frac{1}{x^2})[/tex]

Simplifying the bracket

[tex]x^{-1/2}+x^{-3/2}+x^{-5/2}=\frac{1}{x^{1/2}}(\frac{x^2+x+1}{x^2})[/tex]

[tex]x^{-1/2}+x^{-3/2}+x^{-5/2}=\frac{x^2+x+1}{x^{5/2}}[/tex]

Hence, the factor of the expression [tex]x^{-1/2}+x^{-3/2}+x^{-5/2}[/tex] is [tex]\frac{x^2+x+1}{x^{5/2}}[/tex].

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The value of 6 is equal to 3.

Given that:

If 1=3, 2=3, 3=5, 4=4, 5=4.

So, we have to find the value of 6.

To calculate the value of 6 we have to think logically.

Looking at this question logically,

1 is written as ONE, so it contains three alphabets.

2 is written TWO, so it contains three alphabets.

3 is written as THREE, so there are 5 alphabets.

4 is written as FOUR, so it contains four alphabets.

5 is written as FIVE, so it contains four alphabets.

6 is written as SIX, so it contains three alphabets.

So, in this way, 6 can be written as 3.

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The numbers which are divisible by 3 are 6, 6, 6, and 9.

What is the divisibility of 3?

The rule of three states that a number is completely divisible by three if the sum of its digits is divisible by three.

Consider the number 308: To determine whether 308 is divisible by three, add the digits together (i.e. 3+0+8= 11). Check to see if the total is divisible by three.

From the given numbers the numbers which are divisible by 3 are:

                         6, 6, 6, and 9.

Hence, The numbers which are divisible by 3 are 6, 6, 6, and 9.

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Find the negative reciprocal of the original line and use point slope formula y-y1=m(x-x1)  to find the perpendicular line.

y= -x+3

a. The function m = 200 - 50v is interpreted as

m = amount left

200 = amount available for buying video games

50 = cost per video game

v = number of video games

b. The domain of the function is 0 < v ≤ 4

the domain is discrete

c. explanation of the graph is below

In the graph, the input values is the number of video games, v while the output value is amount, m(in dollars) left for buying games.

The domain is controlled by the input values. considering the amount set out for games which is 200 we solve for v at zero amount

0 = 200 - 50v

50v = 500

v = 4

The maximum number of video games the amount can buy is 4. For the minimum we can not buy 0 video game but the graph can show amount available before buying the game.

The domain starts from 0, with 0 not inclusive to 4 with 4 included

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The rate of change in the volume of water will be -6 L/min in the fish tank. which is the correct answer would be an option (A).

The given graph shows the linear relationship between the volume of water in the fish tank in liters and the time in minutes the tank has been draining.

To determine the rate of change in the volume of water in the fish tank

The rate of change in the volume of water is equal to the slope of the given linear function.

As per the given graph, we take two points (0, 60) and (10,0)

The slope of the linear function = (0 - 60) / (10 - 0)

The slope of the linear function = -60/10

The slope of the linear function = -6

Therefore, the rate of change in the volume of water will be -6 L/min in the fish tank.

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The question seems to be incomplete the correct question has been attached below.

Product of the given expression (3 x 10⁹) and (2 x 10⁹) in the scientific notation is given by 6 x 10¹⁸.

As given in the question,

Given expression is equal to :

(3 x 10⁹) and (2 x 10⁹)

Apply law of indices of multiplication to get the product of the given expression

mᵃ × mᵇ = mᵃ⁺ᵇ

Product of the given expression (3 x 10⁹) and (2 x 10⁹) in the scientific notation is equal to

(3 x 10⁹) and (2 x 10⁹)

= ( 3 × 2 ) × ( 10⁹ × 10⁹ )

= 6 × 10⁹ ⁺ ⁹

= 6 × 10¹⁸

Therefore, product of the given expression (3 x 10⁹) and (2 x 10⁹) in the scientific notation is given by 6 x 10¹⁸.

The complete question is:

Find the product of (3 x 10⁹) and (2 x 10⁹). Write the final answer in scientific notation.

6 x 10⁸¹

6 x 100¹⁸

6 x 10¹⁸

6 x 10⁹

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Answer:

1. [tex]\frac{6}{11}[/tex] × [tex]\frac{1}{4}[/tex] = [tex]\frac{3}{22}[/tex]

2. [tex]4\frac{1}{3}[/tex] × [tex]\frac{9}{14}[/tex] = [tex]\frac{13}{3}[/tex] × [tex]\frac{9}{14}[/tex]

               = [tex]\frac{39}{14}[/tex]

               = [tex]2\frac{11}{14}[/tex]

3. [tex]3\frac{3}{6}[/tex] × [tex]\frac{2}{3}[/tex] = [tex]\frac{21}{6}[/tex] × [tex]\frac{2}{3}[/tex]

             = [tex]\frac{7}{3}[/tex]

             = [tex]2\frac{1}{3}[/tex]

4. [tex]\frac{6}{15}[/tex] ÷ [tex]\frac{2}{5}[/tex] = [tex]\frac{6}{15}[/tex] × [tex]\frac{5}{2}[/tex]

            = 1

5. [tex]1\frac{4}{5}[/tex] ÷ [tex]\frac{3}{25}[/tex] = [tex]\frac{9}{5}[/tex] × [tex]\frac{25}{3}[/tex]

               = [tex]\frac{45}{3}[/tex]

               = 15

Answer:

y = -3/8 x - 4

Step-by-step explanation:

y-(-7) = -3/8 (x-8)

y+7 = -3/8x + 3

y = -3/8 x +3 - 7

y = -3/8 x -4

The annual interest rate needed to accumulate $ 21.02 in simple interest from a $400.00 principal over 0.416667 years (5 months) is 12.612%.

The amount that the lender charges the borrower above and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also earns additional income in terms of the recipient, known as interest, taking into account the time value of money.

Here,

Simple interest paid=421.02-400

=$21.02

For ease of calculation, convert 5 months to 12 months per year, which equals 0.416667 years.

In order to convert r's decimal value to a percentage, we must solve our equation:

r = 21.02 / (40080.416667) = 0.1261199

R = 0.1261199 * 100 = 12.612%/year

For a $400.00 principal to earn $ 21.02 in simple interest over 0.416667 years (5 months), an annual interest rate of 12.612% is required.

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Answer:

y=-6

Step-by-step explanation:

2.3y - 4.2 = -18

       +4.2     +4.2

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

2.3y = -13.8

divide by 2.3 on both sides

y = -6

The value of y for the given equation, 2.3y - 4.2 = -18 will be 6.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, the equation is 2.3y - 4.2 = -18.

We have to simplify the equation in order to find the value of y as,

2.3y - 4.2 = -18.

Rearrange the equation as

2.3y= -18+4.2

2.3y= -13.8

y= -13.8/2.3

y= 6

Thus, the value of y for the given equation, 2.3y - 4.2 = -18 will be 6.

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Answer: sin(E) = 0.6

Step-by-step explanation:

10² = DF² + 8² ( Pythagoras theorem)

100 = DF² + 64

DF² = 36

DF = 6

sin(E) = opposite side/ Hypotenuse

          = DF/EF

          = 6/10 = 3/5 = 0.6

The roller coaster has a deceleration of 3 meters per second.

In this problem we need to calculate the magnitude of the deceleration experimented by the roller coster, which is under uniform accelerated motion. This can be easily found by means of the following formula:

a = (v' - v) / t

Where:

If we know that v = 20 m / s, v' = 2 m / s and t = 6 s, then the magnitude of the deceleration of the roller coster is:

a = [(2 m / s) - (20 m / s)] / 6 s

a = - 18 m / s / 6 s

a = - 3 m / s²

The magnitude of deceleration is 3 meters per square second.

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Answer:

b

Step-by-step explanation:

Number of ounces in a juice box is an example of quantitative.

What is Quantity?

A property called quantity or amount can take the form of a plurality or magnitude, which shows both discontinuity and continuity. Comparing quantities can be done by using phrases like "greater," "less," or "equal," as well as by assigning a numerical value that is a multiple of the unit of measurement.

Let the number of ounces in a juice box means, there are  number of ounces in a box.

The term "number of" is referred as quantity.

Therefore, the number of ounces in a juice box is an example of quantitative.

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210 is the smallest number with exactly four different prime factors.

Prime factors:

In math, the  natural number, other than 1, whose only factors are 1 and itself. And the first few prime numbers are actually 2, 3, 5, 7, 11, and so on.

Given,

The smallest number with exactly three different prime factors is 30.

The prime factors of 30 are 2, 3 and 5.

Here we need to find the smallest number with exactly four different prime factors.

While we looking into the given question we have identified that the first three smallest prime factors are,

=> 2, 3 and 5

Now, we have to identify the fourth prime factor,

According to the definition of the prime factors, we have identified that the fourth prime factor is 7.

So, the number is calculated as,

=> 2 x 3 x 5 x 7

=> 210.

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Answer: 56.70 g

Step-by-step explanation:

Answer: 54, if there are 9 pages with 6 photos each, then you would do 6 x 9 = 54.

Answer:

54 pictures

Step-by-step explanation:

9 pages, 6 pictures in each page, 9*6=54

Answer:

u need a chart image

Step-by-step explanation:

The volume of a conic wrap would be 209.44 cubic inches.

What is the volume of the cone?

The volume of a cone defines the cone's space or capacity. Cones are three-dimensional geometric shapes with a circular base that tapers from a flat base to a point known as the apex or vertex. A cone is made up of a series of line segments, half-lines, or lines that connect a common point, the apex, to all the points on a base in a plane that does not contain the apex.

      Volume of the cone = 1/3 ×πr²h

Given data:

Height of the conic wrap(h) = 8 inches.

Diameter of the conic wrap = 10 inches.

So radius(r) = 10/2 = 5 inches.

Now by using the formula for finding out the volume of the conic wrap, we get

            V = 1/3 × πr²h

               = 1/3 × 3.14 × (5)² × 8

            V = 209.44 cubic inches.

Hence, the volume of a conic wrap would be 209.44 cubic inches.

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a) The ratio system that models this situation which has an equation.

0.20 m + 1 (5 m) = 0.60 x (5)

0.80 m + 0 (5 m) = 0.40 x (5)

b) The system solution is:

m = 2.5 lb

p = 5-m = 2.5 lb

This is a mixing issue.

Mixture A of 20% peanuts + 80% almonds

Let's call the 100% peanut mixture B and the mixture C of 60% peanuts + 40% almonds

Adding mixture A and mixture B together gives mixture C, so we know that the pounds of mixture A and mixture B is 5 lb.

Let m be the amount in pounds of the 20% peanut and 80% almond mixture or mixture A

When 5-m = p is the amount of mixture B in pounds.

The system of equations that models this situation is, therefore:

0.20 m + 1 (5 m) = 0.60 x (5) ...... (1)

0.80 m + 0 (5 m) = 0.40 x (5) ...... (2)

Solving any of the above equations we find the value of m = 2.5 lb

Amount of mixture A in pounds = 2.5 lb

Amount of mixture B in pounds = 5-2.5 = 2.5 lb

The system solution is:

m = 2.5

p = 2.5

So, we can make 5 lbs of mixture C (60% peanuts + 40% almonds) from 2.5 lbs of mixture A (20% peanuts + 80% almonds) and 2.5 lbs of mixture B (100% peanuts).

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The length of ladder is 11.5 m.

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Main body:

Let the length of ladder = y

And distance of bottom of ladder from the wall = X

According to the given,

Length of ladder y =

√(7² + x²)

Since, the bottom of the ladder is moved 1 meter farther away from the wall, so

Length of ladder y = √(5² +(x+1)²)

as in both equation y is equated

√(7² + x²) = √(5² +(x+1)²)

square root will get cancel on both sides

(7² + x²) = (5² +(x+1)²)

49 + x² = 25 + x² +1+2x

cancelling x² on both sides

49 = 26 +2x

2x = 23

x =11.5 meters

Hence the length of ladder is 11.5 m

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The total amount after merging their account will be $34.34.The sum of $75 + $156.56 will make $231.56.

A summation, also abbreviated as a sum, is the outcome of adding two or more numbers or quantities. Here are always an integer number of terms in a summation. There could be only two terms, but there could be one hundred, a thousand, or a million. There are summations with an infinite set of parameters.

As per the given,

Mohan has 2 current accounts, the first has a balance of $101.46.

The second has -$21.21.

Total amount of Mohan = 101.46 - 21.21 = $80.25

Eve's balance = -$45.91

Combined balance = $80.25 - $45.91 = $80.25

As per the given,

Eve has a savings account with $231.56 in it. She wants to buy a new coat for $75.00. She calculates that she will have $156.56

$231.56 = $156.56 - $75

$231.56 + $75 = $156.56

Hence "The total amount after merging their account will be $34.34.The sum of $75 + $156.56 will make $231.56".

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Answer:

D

Step-by-step explanation:

x³ + 3x² ← factor out x² from each term

= x²(x + 3)

Answer:

Step-by-step explanation:

The value of addition for the equation (f + g) (-2) is 15 and the value of subtraction for the equation (f + g) (-2) is 39.

A function is a relationship that assigns exactly one output value to each input value. Like numbers and polynomials, functions can be added, subtracted, multiplied, and divided to create new functions. Here are the rules for performing these operations on functions.

Let f(x) and g(x) be two functions:

Addition:

We can add two functions:

(f + g)(x) = f(x) + g (x) ...... (1)

Given that:

f(x) = 5x^2 + 7

g(x) = 3x - 6

Putting the value of f(x) and g(x) in equation (1).

(f + g)(x) = 5x^2 + 7 + 3x - 6

(f + g)(x) = 5x^2 + 3x + 1 .......(2)

We have to evaluate the value of (f + g) (-2). Therefore, put the value of x = -2 in equation (2). We get,

(f + g) (-2) = 5 (-2)^2 + 3 x -2 + 1

(f + g) (-2) = 20 - 6 +1

(f + g) (-2) = 15

Hence, for the addition of the equation (f + g) (-2) the value is equal to 15.

Subtraction:

We can add two functions:

(f - g)(x) = f(x) - g (x) ...... (3)

Given that:

f(x) = 5x^2 + 7

g(x) = 3x - 6

Putting the value of f(x) and g(x) in equation (3).

(f - g)(x) = 5x^2 + 7 - (3x - 6)

(f - g)(x) = 5x^2 + 7 - 3x + 6

(f - g)(x) = 5x^2 - 3x + 13 ....... (4)

We have to evaluate the value of (f - g) (-2). Therefore, put the value of x = -2 in equation (4). We get,

(f - g)(-2) = 5(-2)^2 - 3(-2) + 13

(f - g)(-2) = 5 x 4 + 6 + 13

(f - g)(-2) = 20 + 6 + 13

(f - g)(-2) = 39

Hence, for the subtraction of the equation (f - g) (-2) the value is equal to 39.

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Answer:

1 1/4

Step-by-step explanation:

2 divided by 2 is 1.

1/2 or 0.5 divided by 2 is 0.25. this is equal to 1/4.

Answer: 1 [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

First of all, we need to multiply 2 [tex]\frac{1}{2}[/tex] by 1/2.

But to do that, we need to turn 2 [tex]\frac{1}{2}[/tex]  into an improper fraction.

First of all, we need to multiply the whole number by the denominator, which is 2 x 2, to get 4.

Now, we need to add the numerator to our product, which is 4 + 1.

This gives us the improper fraction of 5/2.

Now, we need to multiply 5/2 by 1/2.

To do this, we need to multiply across.

5 x 1 = 5

2 x 2 = 4

This gives us 5/4.

Now, we turn it into a mixed number.

5/4 is 1 [tex]\frac{1}{4}[/tex].

This gives us our final answer of 1 [tex]\frac{1}{4}[/tex]

Answer:

B

Step-by-step explanation:

because im smart :) give me brainliest or else

Answer:

f(x)=5(x^2)

Step-by-step explanation:

The actual number of respondents who rated themselves as above average drivers is 852 and we can conclude that the proportion respondents who rated themselves as above average drivers is greater than 0.5007.

Given that, 84% of the sample of 1014 adults rated themselves as above average drivers.

In statistics, a simple random sample is a subset of individuals chosen from a larger set in which a subset of individuals are chosen randomly, all with the same probability. It is a process of selecting a sample in a random way.

Now,

84% of 1014

= 0.84×1014

= 851.76

≈ 852

Thus, the actual number of respondents who rated themselves as above average drivers is 852.

At the null hypothesis, we test if the proportion is 4/5 =0.8, that is

[tex]H_0:p=0.8[/tex]

At the alternative hypothesis, we test if the proportion is greater than 80%, that is:

[tex]H_0:p\ge0.8[/tex]

The test statistic is given by

[tex]z=\frac{\bar{p}-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]

In which:

[tex]$\bar{p}$[/tex] is the sample proportion.

p is the proportion tested.

n is the size of the sample.

In this problem, the parameters are [tex]$\bar{p}$[/tex]=0.84, p=0.8 and n=1014

Thus, the value of the test statistic is

[tex]z=\frac{0.84-0.8}{\sqrt{\frac{0.8(1-0.8)}{1014} } }[/tex]

= 0.04/0.0125

z=3.2

0.4993

So, 1-0.4993=0.5007

Therefore, the actual number of respondents who rated themselves as above average drivers is 852 and we can conclude that the proportion respondents who rated themselves as above average drivers is greater than 0.5007.

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