The height above ground of a cannon is a function of the time since it was shot.
Question: When time equals 0, why is the height of the cannon ball not equal to 0? Describe the domain of this function. Describe the range.

The equation of the future value function if x represents the number of weeks is [tex]= P((1+r/x)^{nt} - 1)/(r/x)[/tex].

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.

Given:

Robbie depositing= $100

Interest=2.4%

Time=3 years.

According to given question we have

P = periodic payment = $100 / week

r = interest rate = 2.4%, compounded weekly

t = 3 years

x = 52 weeks (# of times interest is compounded per year)

To write a equation we have

B = Future Value

[tex]= P((1+r/x)^{nt} - 1)/(r/x)[/tex]

Therefore, the equation of the future value function if x represents the number of weeks is [tex]= P((1+r/x)^{nt} - 1)/(r/x)[/tex].

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Car A consumes 11.9 gallons.

Car B consumes 13 gallons

Car A consumes 16.3 gallons

Car B consumes 11.6 gallons

In order to determine the required values, the mathematical operation that would be used is division. Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷.

Gallons that would be consumed when driving  300 mi of city driving plus 100 mi of highway driving:

For Car A = (300 / 36) + (100 / 28) = 11.9 gallons

For Car B: (300 / 29) + (100 / 37) = 13 gallons

Gallons that would be consumed when driving  100 mi of city driving plus 300 mi of highway driving:

For Car A = (100 / 36) + (300 / 28) = 16.3 gallons

For Car B: (100 / 29) + (300 / 37) = 11.6 gallons

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Answer:

12-4i

Step-by-step explanation:

i means √-1

(3 - i)(3 + 1) =

3*3=9

3*1=3

-i*3= -3i

-i*1 = -i

9+3-3i-i=

12-4i <--- answer

(3 - i)(3 + i) =

3*3=9

3*i=3i

-i*3= -3i

-i*i = -(√-1)*(√-1) = -(-1) = 1

9+3i-3i+1 =

10 <--- answer

Answer:

Hello,

Step-by-step explanation:

Let's say 2x the smaller number,2x+2 the greater.

2x*(2x+2)=12+(2x)²

2x²+4x=12+4x²

4x=12

x=3

The smaller numbre is 2x=6 and the greater is 8

6*8=48 =12+6²

An all-terrain vehicle can travel the fastest.

Speed can be define as the time rate by which an object is moving or running along a path. A speed is the quantity which describes the moving rate of any object. We can define the speed with respect to distance and time . Or we can say speed is distance per unit of time . It is calculate in term of kilometers per hour.

Mathematically, we can write:

[tex]Speed = \frac{Distance}{Time}[/tex]

where, distance is measured in km

           and Time is measured in hours

In the question, the distance for three different types of vehicles are given and we have to find fastest vehicle for which we need to find the speed.

For  self-balancing scooter

Time = 1 hour

Distance = 12 miles

Therefore, Speed = 12 miles/h

For all-terrain vehicle

Time = 1 hour

Distance = 12 . 6 = 72 miles

Therefore, speed = 72 miles/h

For a go-kart

Time = 1 hour

Distance = 67 miles

Therefore, speed = 67 miles/h

Hence it is cleared that An all-terrain vehicle can travel the fastest.

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The price of the adult's ticket is $20 and the price of a child's ticket is $14.

Let adults = a

Let children = c

The appropriate equation will be:

3a + 4c = 116

2a + 3c = 82

Multiply equation I by 2

Multiply equation ii by 3

6a + 8c = 232

6a + 9c = 246

Subtract

c = 14

Price for children = 14

Since 2a + 3c = 82

2a + 3(14) = 82

2a + 42 = 82

2a = 82 - 42

2a = 40.

a = 40/2

a = 20

Therefore, the price of the adult's ticket is $20 and the price of a child's ticket is $14.

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Answer:

3311

Step-by-step explanation:

The steps are as follows

1. Divide 456 by 5. This gives a quotient of 91 with a remainder of 1. This remainder becomes the least significant digit of the new base number. This would be the right most digit. So the number is _ _ _ 1

2. Take the quotient, 91, divide by 5 again. This gives a quotient of 18 with a remainder of 1. Put this remainder to the immediate left of the previous value. So we have the number as _ _ 1 1

3. Take the previous quotient, 18, divide by 5 again. 18/5 gives quotient of 3 with a remainder of 3. Put this to the immediate left of the previous number giving the number as _ 3 1 1

4. Repeat the division of the new quotient by 5. 3/5 gives a quotient of 0 with remainder of 3 so we stop

Number = 3 3 1 1

Best done by writing a program or using a calculator

Step-by-step explanation:

3.5(12)=42

3.5(55)=192.5

192.5

-42

150.5 more miles

Answer:

G(0) = 3

Step-by-step explanation:

g(0) means what is the value of g(x) when x = 0

substitute x = 0 into g(x)

g(0) = 2(0) + 3 = 0 + 3 = 3

The range of the data is 5.

Ensure that the score column entries are listed in ascending numerical order. The entries in our example are listed in numerical order.

According to the definition, range is determined for continuous frequency distribution as the difference between the upper limit of the maximum interval and lower limit of the minimum interval of the grouped data.

1. Find the score column entry with the lowest value (with a Frequency greater than 0).

here we have 1 as the lowest entry. The lowest test score is 1.

2. Find the highest entry in the Score column (with a Frequency greater than 0).

here, we have 6 as the highest entry  The highest test score is 6.

Subtract the lowest number (1) from the highest number (6).

6 - 1 = 5

The range of the test scores is 5.

Hence we get the range of the given data as 5.

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The capacity of the full tank is 16 hectolitre. percentage problem.

A gasoline tank contains 9.6 hectolitres (hL) when it is 60% full. when the tank is 100% full that is the capacity of the tank.

so, the capacity of the full tank is 9.6x(100/60) = 16 hL.

this a percentage problem. In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%". A percentage is a dimensionless number; it has no unit of measurement.

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Answer:

Angle B equals 139

Step-by-step explanation:

6x -6 = 90 is the simplified equation. Solving the equation would make x = 31. Then, plugging in x would make Angle A 41 and Angle B 139

The value of the z-score is calculated as 0.259.

The standard normal distribution is the variable of a normal distribution to mean 0 and variance 1. The normal distribution follows a bell curve. The z-table aids in determining the area beneath the curve.

Now, as per the given question;

The formula for the z-score is;

z = (x - μ)/σ

x = sample size

σ = standard deviation

μ =  mean of the sample

For the given values in the question;

x = 31.1

σ = 7.7

μ = 30.9

Substitute the given values in the formula to fine z-score;

z-score = (31.1 - 30.9)/7.7

z-score = 0.259

Therefore, the value of the z-score is computed as 0.259.

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The area of the parallelogram is 475.2 square units.

A parallelogram is a polygon with four sides whose each pair of opposite sides are equal and parallel.

The properties of parallelogram are:

Given base b of the parallelogram a 36 units and height h of the parallelogram as 13.2 units.

Therefore we know from the properties of the parallelogram that area is given by the product of base and height.

∴area = b × h

or, area = 36 × 13.2

or, area = 475.2 square units

Hence the area of the parallelogram is 475.2 square units .

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Answer:

15.479

Step-by-step explanation:

This is a geometric series with common ratio of 6/5
Any term is 6/5 times the previous term

The general formula for the nth term of a geometric series given the common ration r and the first term a₁ is

[tex]a_n = a_1\cdot r^{n-1}[/tex]

Here r = 6/5 and n = 10

So the 10th term is
[tex]a_{10} = 3\cdot(\dfrac{6}{5})^9[/tex]

= 3 x (6⁹/5⁹) = 3 x (10077696/1953125) = 30233088/1953125 = 15.479

Answer: 0.100

Step-by-step explanation: In the table, it shows that the number of people who have a Bachelor's Degree AND are aged 50 or over is 1958. The total amount of residents in the town are 19623. 1958/19623 gives us the probability. In decimal, the answer is 0.09978086938, which rounds to 0.100

Answer:

The correct answer would be,

= 10m^3 + 8m^2 - 10m - 0.8

Step-by-step explanation:

First you subtract the m^3 terms :

> 7m^3 + 3m^3

> 10m^3

Then you subtract m^2 , in this case we only have 1 m^2 :

> 8m^2

Then you subtract the m terms :

> -m - 9m

> -10m

The lastly you subtract the last terms :

> 2.8 - 3.6

> -0.8

= 10m^3 + 8m^2 -10m -0.8

(Make sure to distribute the negative before you solve it.) Just a point!!

Answer:

10m³+8m²-10m-0.8

Step-by-step explanation:

(7m³ +8m²-m+2.8)-(-3m³ +9m+3.6)

Use the sign to open the bracket we have;

7m³ +8m²-m+2.8+3m³-9m-3.6

bring like terms together

7m³+3m³+8m²-9m-m-3.6+2.8

Simplifying we have;

10m³+8m²-10m-0.8

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Answer:

1.5 teaspoons for each dozen

Step-by-step explanation:

A recipe calls for 4.5 teaspoons of sugar for 3 dozen cookies explain the process to find how much is needed for each dozen?

Divide 4.5 teaspoons by 3:

4.5/3 = 1.5 teaspoons for each dozen

since 4.5 teaspoons of sugar will make 3 dozen, we divide 4.5 by 3 to find for each dozen.

Answer:

x + y ≤ 7

(if that doesn't work, 0 ≤ x + y ≤ 7)

Rew wants to buy 7 items or less, so the number of dubbles and totts combined can't be bigger than 7, and is therefore less than or equal to 7.

Answer:

6

Step-by-step explanation:

In 3 cups you have 6 half cups with the remainder being 1/4 of a cup.

Answer:

If we're talking whole batches then I'm pretty sure you can make six batches

Answer:

Mark has 18 and Don has 73

Step-by-step explanation:

Let M = Mark and let D = Don

D = 4M + 1

D + M = 91

Substitute and solve for M

4M +1 + M = 91

5M = 90

M = 18

Therefore D = 4(18) + 1 = 73

Answer:

(22v and 10w)

Step-by-step explanation:

A rectangle is a 4 sided figure. Perimeter is the distance around the rectangle.  The total distance would be

(5v -2w) + (5v - 2w) + (6v+7w) + (6v + 7w)  Add all the like terms together

5v + 5v + 6v + 6v - 2w - 2w + 7w + 7w

The v's add up to 22 and the w's add up to 10

Answer:

  5%

Step-by-step explanation:

You want the interest rate that makes the difference between compound and simple interest on ₹8000 for two years be ₹20.

The formula for the value of an account earning simple interest is ...

  A = P(1 +rt) . . . . P earning interest rate r for t years

The formula for the value of an account earning compound interest is ...

  A = P(1 +r)^t . . . . P earning interest rate r for t years

We want the difference in these amounts over 2 years to be ₹20.

  8000(1 +r)^2 -8000(1 +2r) = 20

  1 +2r +r^2 -(1 +2r) = 20/8000 . . . . . divide by 8000, expand the square

  r^2 = 1/400 . . . . . . simplify

  r = 1/20 = 5% . . . . . take the square root

The rate of interest is 5% per year.

Answer: 1 1/4 batches of muffins

Step-by-step explanation:

Answer:

5.

Step-by-step explanation:

32-20-12.

Answer:

(a) --> f(x) = -(x - 4)²

(b) --> f(x) = x² + 3

(c) --> f(x) = (x - 2)²

(d) --> 6. f(x) = 3 - x²

Parent function of all the graphs is y = x²

(a)

The graph makes a sad face meaning the coefficient will be negative.

Comparing to the parent function y = x², the graph has been translated 4 units to the right.

Equation: f(x) = -(x - 4)²

(b)

The graph makes a happy face meaning the coefficient will be positive.

Comparing to the parent function y = x², the graph has been translated 3 units up.

Equation: f(x) = x² + 3

(c)

The graph makes a happy face with translation 2 units to the right.

Equation: f(x) = (x - 2)²

(d)

The graph makes a sad face with translation 3 units up across y axis.

Equation: f(x) = -x² + 3

f(x + a)  :  translation a units left in the x axis.

f(x - a) : translation a units right in the x axis.

f(x) + b :  translation b units up in the y axis.

f(x) - b : translation b units down in the y axis.

The figure will be a sphere with center T and radius 8 1/2 inches, that is, option D.

A circle is a closed curve constituting of the set of all points in a plane that are equidistant from a given point. This point is the center of the circle and the distance is the radius of the circle.

A circle is a 2-dimensional figure, and the two dimensional does not contain the set of all points in the 3-dimensional plane.

A sphere is a round geometrical object and is the set of all points that are equidistant from a given point, in the three-dimensional space.

Here, we are given that there is a point T and we need to describe the collection of all points in the same plane that are 8.5 inches from point T.

Going by the definitions given above, we can infer that it is a sphere with center T and radius 8.5 inches. If we take it to be a circle then it will not include the points in the 3D plane, hence, sphere.

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Your question was incomplete, check for the full content below-

Which describes the collection of all points in the same plane that are 8 1/2 inches from point T?

A.) Circle T with radius 8 1/2 inches

B.) circle T with diameter 8 1/2 inches

C.) circle T with radius 17 inches

D.) a sphere with center T and radius 8 1/2 inches