what is 8 1/2 / 11 as a mixed number or fraction

1. The velocity at time t , v(t) = (18t² + 3 ) m/s

2. The velocity at time t = 3 seconds = 165 m/s

3. The acceleration at time t, a(t) =( 36t )m/s²

4. The acceleration at time t = 3 seconds = 108 m/s²

The quantity that tells us how fast an object is moving anywhere along its path is the instantaneous velocity.

Instantaneous acceleration is defined as the ratio of change in velocity during a given time interval such that the time interval goes to zero.

1. s(t) = 6t³ + 3t +9

to find the velocity at time t, we differentiate s(t)

= 18t² + 3

2. at t = 3s

= 18(3)² +3

= 165 m/s²

3. v(t) = 18t² + 3

to get the acceleration at time t, we differentiate v(t)

= 36t

4. when t = 3

a = 36 × 3

= 108 m/s²

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Answer:

Step-by-step explanation:

Among the roles in the digital media production team, the creative director is in charge of overseeing the creative element.

The Volume of the box is 3.75in³

The volume of the box is dependent on the volume of the cube in it.

To obtain the volume of a cube, we use the relation, V = s³

s = side of the cube

Volume = 0.5³ = 0.125 in³

Number of cubes in box = 30

Volume of each cube × Number of cubes

0.125 × 30 = 3.75 in³

Hence, the volume of the box is 3.75in³

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Answer:

The point estimate for the population proportion of people who performed volunteer work in the past year is 0.396.

Step-by-step explanation:

Point estimate of a proportion:

Proportion is the number of desired outcomes divided by the number of total outcomes.

518 out of 1309 people performed volunteer work:

This means that:

\(p = \frac{518}{1309} = 0.396\)

The point estimate for the population proportion of people who performed volunteer work in the past year is 0.396.

Answer:

The probability that atleast one ticket labeled 2-6 is drawn is 0.94

Numbered ticket = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Number of draws = 4

Required picks = {2, 3, 4, 5, 6}

Recall :

Probability = required outcome / Total possible outcomes

Probability of choosing a required ticket :

5/10 = 1/2

Therefore, the probability that none of the required tickets is chosen :

(1/2 × 1/2 × 1/2 × 1/2) = 1/16

The probability that atleasr one ticket labeled 2-6 is drawn is :

1 - P(none is chosen) = 1 - 1/16 = 15/16 = 0.9375

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\(\\ \sf\longmapsto 2:3=1:n\)

\(\\ \sf\longmapsto \dfrac{2}{3}=\dfrac{1}{n}\)

\(\\ \sf\longmapsto 2n=3\)

\(\\ \sf\longmapsto n=\dfrac{3}{2}\)

__________

2/3 = 1/n

2n = 3(1)

2n = 3

n = 3/2

n = 1½

Based on mathematical operations, the lowest amount that Annabel can pay for pencils is $15.20

The lowest amount that Annabel can pay for pencils can be determined using the mathematical operations of multiplication and division.

Multiplication and division are two of the four basic mathematical operations, including addition and subtraction.

If Annabel chooses to purchase the first pencil at 30p each, she would pay £22.80 (£0.30 x 76).

If Annabel chooses to purchase the second pencil class of a pack of 10 pencils for £2, she would pay £15.20 [£2 x (76 ÷ 10)].

Pencils for sale

30p each

Pack of 10 pencils for £2

Thus, if Annabel wants to buy the pencils, she can either pay £15.20 or £22.80, but using mathematical operations, the lowest amount she can pay is £15.20.

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Answer:

yes

Step-by-step explanation:

12+3=5x-3+3

15=5x

15=5(3)

15=15

The area of the Region bounded by y = √x, y = 2-x², and y = -√2x is $\frac{32}{15}$.

To find the area of the region bounded by y = √x, y = 2-x², and y = -√2x, we need to graph the equations and determine the points of intersection. Then we can integrate to find the area.

Firstly, we'll graph the equations and find the points of intersection:

y = √xy = 2-x²y = -√2xGraph of y = √x, y = 2-x², and y = -√2xWe need to solve for the points of intersection, so we'll set the equations equal to each other and solve for x:√x = 2-x²√x + x² - 2 = 0Let's substitute u = x² + 1:√x + u - 3 = 0√x = 3 - u

(Note: Since we squared both sides, we have to check if the solution is valid.)u = -2x²u + x² + 1 = 0 (substituting back in for u

)Factoring gives us:u = (1, -2)We can then solve for x and y:x = ±1, y = 1y = 2 - 1 = 1, x = 0y = -√2x = -√2, x = 2y = 0, x = 0Graph of y = √x, y = 2-x², and y = -√2x with points of intersection to find the area, we need to integrate.

The area is bounded by the x-values -1 to 2, so we'll integrate with respect to x:$$\int_{-1}^0 (2 - x^2) - \sqrt{x} \ dx + \int_0^1 \sqrt{x} - \sqrt{2x} \ dx$$

We can then simplify and integrate:$$\left[\frac{2x^3}{3} - \frac{2x^{5/2}}{5/2} + \frac{4}{3}x^{3/2}\right]_{-1}^0 + \left[\frac{2x^{3/2}}{3} - \frac{4x^{3/2}}{3}\right]_0^1$$$$= \frac{4}{3} + \frac{4}{3} - \frac{4}{15} + \frac{4}{3} - \frac{4}{3}$$$$= \frac{32}{15}$$

Therefore, the area of the region bounded by y = √x, y = 2-x², and y = -√2x is $\frac{32}{15}$.

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For a game, Bob has a total of 60 adventure cards. The distribution of cards, c, to players, p, is shown in the table. c = 60 ÷ p

Probability defines the possibility of occurrence of an event. Probability is the unit of measurement for an event's likelihood. It represents the proportion of positive results to all results. For instance: Receiving the numbers 3 and 5 while rolling the dice, as well as getting both an even and an odd number.

The equation would read: c = 60 / 2, which implies c = 30 if p=2. The equation would read 12 = 60 / p, p = 5, 20 = 60 / 3, etc. If c = 12, the equation would read... 12 = 60 / p, and p = 5, and so on, 20 = 60 / 3, and 15 = 60 / 4.

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Answer:

Step-by-step explanation:

This number line says that  we can take all values of x that are less than or equal to 2. That is, the solution is

                                  \(x\leq 2\)

NOTE: if the circle at 2 were not filled in then that would mean x<2 (2 would not be an accepted value of x)

The values 8, 15 and 17 is a Pythagorean triple and therefore a right angle triangle.

A Pythagorean triple is a set of three positive integers, a, b, and c, such that a^2 + b^2 = c^2, which represents the sides of a right-angled triangle, where c is the hypotenuse.

In this problem, we can we can check if the values are for a right angle triangle.

Assuming this is a right angle triangle which obeys Pythagoras theorem, the longest side will be the hypothenuse.

c² = a² + b²

17² = 15² + 8²

289 = 225 + 64

289 = 289

From the calculation above, the values of is a Pythagorean triple.

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Answer:

-1.3n+1.5

-6.4n+9.8

-0.36n-4

Step-by-step explanation:

Answer:

i think its

x^2 + (y + 2)^2 = 21.

Step-by-step explanation:

The formula cosec (A + B) = sinA cosB - cosA sinB ÷ (sinA + sinB)(sinA - sinB) can be proven using the trigonometric identities.

Starting with the definition of cosecant:

cosec (A + B) = 1/sin (A + B)

Using the sum-to-product identity:

sin (A + B) = sinA cosB + cosA sinB

Substituting this expression into the definition of cosecant:

cosec (A + B) = 1 / (sinA cosB + cosA sinB)

Using the difference-to-product identity:

sinA - sinB = 2sin((A - B)/2)cos((A + B)/2)

Dividing both numerator and denominator by 2sin((A - B)/2)cos((A + B)/2), we get:

cosec (A + B) = (sinA cosB - cosA sinB) ÷ (sinA + sinB)(sinA - sinB)

Therefore, the formula cosec (A + B) = sinA cosB - cosA sinB ÷ (sinA + sinB)(sinA - sinB) has been proven.

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The four rectangles can be painted with 7 different paints in 840 ways.

A permutation is an arrangement of objects in a definite order. The members or elements of sets are arranged here in a sequence or linear order. For example, the permutation of set A={1,6} is 2, such as {1,6}, {6,1}, there are no other ways to arrange the elements of set A.

The formula for permutattion is;

\(P_r_n = \frac{n!}{(n-r)!} \\\)

where r = 4

n = 7

Substituting the values for n and r

\(P = \frac{7!}{(7-4)!}\)

\(P = \frac{7!}{3!}\)

P = 840 ways.

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Let:

(x1,y1) = Initial point

(x2,y2) = End point

mp= midpoint = ((x1+x2)/2,(y1+y2)/2)

We know the midpoint and the endpoint, therefore:

(x1+x2)/2=14

(x1+13)/2 = 14

Solving for x1:

Multiply both sides by 2:

x1 + 13 = 28

Subtract 13 from both sides:

x1 = 15

And

(y1 + y2)/2 = 3

(y1 + (-6))/2 = 3

Solving for y1:

Multiply both sides by 2:

y1 - 6 = 6

Add 6 to both sides:

y1 = 12

Therefore the initial point is:

(x1,y1) = Initial point = (15, 12)

The transformation of f(x) to p(x) is that (a) the graph is reflected and shifted down

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

The functions f(x) and g(x)

In the function equations, we can see that

f(x) = x²

p(x) = -f(x) - 3

So, we have

Vertical Difference = 0 - 3

Evaluate

Vertical Difference = - 3

This means that the transformation of f(x) to p(x) is that f(x) is reflected and shifted down 3 units to p(x).

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Answer:

x = 14

Step-by-step explanation:

To solve this problem, we must remember that the addition of two angles that create a straight line should have a sum of 180 degrees.

From this information, we can create the following equation.

(7x - 1) + (6x - 1) = 180

Eliminating the parentheses and grouping like terms gives us:

(7x + 6x) + (-1 + -1) = 180

Simplifying inside the parentheses on the left side produces:

13x - 2 = 180

Next, we should add 2 to both sides to isolate the variable term:

13x = 182

Finally, we should divide by 13 to get the x by itself on the left side of the equation:

13x/13 = 182/13

x = 14

Therefore, the answer to your question is x = 14.

Hope this helps!

Answer:

x = 14

Hope it helps u

plz mark it as brainlist

Answer:

Aircraft A: 403 seats

Aircraft B: 298 seats

Step-by-step explanation:

Let's x represent the seats in Aircraft B

We have the equations:

Aircraft A: (x + 105)

Aircraft B: x

We Know

Their total number of seats is 701; find the number of seats for each aircraft.

We Take

x + (x + 105) = 701

2x + 105 = 701

2x = 596

x = 298 seats

So, there are 298 seats in Aircraft B

Aircraft A has how many seats?

We Take

701 - 298 = 403 seats

So, there are 403 seats in Aircraft A

Final Answers:

Aircraft A: 403 seats

Aircraft B: 298 seats

Answer:

0 hundreds

0 tens

7 ones

.

4 tenths

0 hundredths

8 thousandths

Standard form=7.408

Step-by-step explanation:

Lets first solve (7x1)+(4x1/10)+(8x1/1000)

7+0.4+0.008

Simplify:

7.408

Answer:25

Step-by-step explanation:

so use fractoin to anwer

Answer:

15x+50

Step-by-step explanation:

multiply both numbers that are inside the parentheses by the number ouside of it. So 5×3=15, but the 3 also had an x atratched to it, hence 15x and 5×10=50, so combine them and you have your answer of 15x+50.

The expanded form of the expression is 10 + 9 + 0.3 + 0.00 + 0.005

He runs the 100 meters dash in 19.305 seconds.

Therefore, the seconds he runs the race can be represented in expanded form as follows:

Expanded form is a way to write a number by adding the value of its digits.

We can use a place value chart to think of the value of a number's digits.

Therefore,

19.305 in expanded form is as follows:

19.305 = 10 + 9 + 0.3 + 0.00 + 0.005

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Answer:

5.4 lbs

Step-by-step explanation:

5.94 / 1.10 = 5.4

hope this helps! <3

The number of baseballs which Wei Jing would have left if he arranged them in groups of 8 as required is; 1.

According to the task content;

Since the number of baseballs available is between; 70 and 150 and

When he arranges them in groups of 10, he has 3 left over.

The possible numbers are; (70 + 3), (80 + 3), (90 + 3), (100 + 3), (110 + 3), (120 + 3), (130 + 3), (140 + 3).

Therefore, the possible numbers according to the first condition are; 73, 83, 93, 103, 113, 123, 133, 143.

Also, When he arranges them in groups of 9, he has 5 left over, the possible numbers are; ( 72 + 5 ), ( 81 + 5 ), ( 90 + 5 ), ( 99 + 5 ), ( 108 + 5 ), ( 117 + 5 ), ( 126 + 5 ), ( 135 + 5 ), ( 144 + 5 ).

Therefore, the possible numbers according to the second condition are; 77, 86, 95, 104, 113, 122, 131, 140, 149.

On this note, by comparison; Only 113 is common to the both sets of numbers.

Hence, the number in discuss is; 113.

Ultimately, if the arrangement is in groups of 8; it follows that the remainder would be; 1 since; 113 / 8 = 14 ⅛.

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\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill &\$\stackrel{12000~~ + ~~1200}{13200}\\ P=\textit{original amount deposited}\dotfill &\$12000\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &1.8 \end{cases}\)

\(13200=12000\left(1+\frac{~\frac{r}{100}~}{1}\right)^{1\cdot 1.8}\implies \cfrac{13200}{12000}=\left( 1+\cfrac{r}{100} \right)^{1.8} \\\\\\ \cfrac{11}{10}=\left(\cfrac{100 + r}{100} \right)^{1.8}\implies \cfrac{11}{10}=\left(\cfrac{100 + r}{100} \right)^{\frac{9}{5}} \\\\\\ \left( \cfrac{11}{10} \right)^{\frac{5}{9}}=\left[ \left(\cfrac{100 + r}{100} \right)^{\frac{9}{5}} \right]^{\frac{5}{9}}\implies \left( \cfrac{11}{10} \right)^{\frac{5}{9}}=\cfrac{100+r}{100}\)

\(\sqrt[9]{\left( \cfrac{11}{10} \right)^5}=\cfrac{100+r}{100}\implies 100\sqrt[9]{\left( \cfrac{11}{10} \right)^5}=100+r \\\\\\ 100\sqrt[9]{\left( \cfrac{11}{10} \right)^5}-100 = r\implies 5.44\approx r\)

Answer:

Step-by-step explanation:

f(x)=2(2x+3)(x−3)
hope this helps