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.
Answers
The height of the cannonball not equal to 0 when time equals 0 because initial height of the cannonball is above the ground
When time equals 0, why is the height of the cannonball not equal to 0?From the graph, we have the y-intercept to be
y-intercept = (0, y), where y > 0
This means that the graph starts above the origin
This in other words mean that the initial height of the cannonball is above the ground (e.g. it could be on a building)
Hence, the height of the cannonball not equal to 0 when time equals 0 because initial height of the cannonball is above the ground
Describe the domain and the range of this functionIn this case, the domain is from t = 0 till the ball lands on the floor, while the range is from the initial height of the cannonball till the maximum height
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Related Questions
Robbie opens an account at a local bank by depositing $100. The account pays 2.4% interest, compounded weekly. He deposits $100 every week for 3 years.
b. Write the future value function if x represents the number of weeks.
c. Use a graphing calculator to graph the future value function.
d. Using the graph, what is the approximate balance after 2 years?
Answers
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].
What is equation?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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Given g(x)=2x+3g(x)=2x+3, find g(0)
Answers
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
Car A is rated at 36 mi/gal (miles per gallon) for city driving and 28mi/gal for highway driving. Car B is rated at 29 mi/gal city and 37 mi/gal highway. How many gallons of gas would each vehicle consume for the following amounts of driving?
(a) 300 mi of city driving plus 100 mi of highway driving
(b) 100 mi of city driving plus 300 mi of highway driving
Question content area bottom
Part 1
(a) Car A consumes
enter your response here gallons; Car B consumes
enter your response here gallons.
(Do not round until the final answer. Then round to the nearest tenth as needed.)
(b) Car A consumes
enter your response here gallons; Car B consumes
enter your response here gallons.
(Do not round until the final answer. Then round to the nearest tenth as needed.)
Answers
Car A consumes 11.9 gallons.
Car B consumes 13 gallons
Car A consumes 16.3 gallons
Car B consumes 11.6 gallons
How many gallons would be used?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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A recipe calls for ½ cup of
flour. Kenneth has 3 and 1/4
cups of flour. How many
batches of the recipe can
he make?
Answers
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
the difference between compound interest and simple interest on the same sum of rupees 8000 for 2 year is rupees 20 find the rate of interest ?
Answers
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.
Interest formulasThe 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
ApplicationWe 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.
A recipe calls for 4.5 teaspoons of Suger for 3 dozen cookies explain the process to find how much is needed for each dozen
Answers
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.
The table lists the eight human blood types.
It also shows how blood types determine who a person can donate blood to and receive blood from.
Blood type
A+
B+
AB+
AB-
A-
B-
0+
0-
Can donate to
A+, AB+
B+, AB+
AB+
AB+, AB-
A+, A-, AB+, AB-
B+, B-, AB+, AB-
(a) X = 1
(b) x = 0
A+, B+, AB+, 0+
All blood types
Can receive from
A+, A-, 0+, 0-
B+, B-, 0+, 0-
All blood types
A-, B-, AB-, 0-
A-, O-
B-, 0-
0+, 0-
0-
Let U be the set of all eight human blood types.
U=(A-, B-, AB+, AB-, A-, B-, 0-,0-)
Let X be the set of blood types that type AB- cannot receive blood from.
Let I be the set of blood types that type B+ can donate blood to.
Find the sets below. Write each answer in roster form or as 2.
CE
D
AB-
0.0 Ø
8+
AB+
Answers
NO LINKS!! Please help me with these problems. Part 4a
Answers
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
Translation rules: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 first three terms of a sequence are given. Round to the nearest thousandth (if necessary).
3,18/5, 108/25...
Find the 10th term
Answers
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
Order the list of numbers written in Scientific Notation from small to large.
4.5 x 10^4
1.9 x 10^7
7.6 x 10^-9
9.3 x 10^-15
5.7 x 10^13
Answers
2. 7.6 x 10^-9
3. 4.5 x 10^4
4. 1.9 x 10^7
5. 5.7 x 10^13
The greater the exponent the larger the number, no matter the coefficients.
Consider a set of data in which the sample mean is 30.9 and the sample standard deviation is 7.7. Calculate the z-score given that x = 31.1. Round your answer to
two decimal places.
Answers
The value of the z-score is calculated as 0.259.
What is descried as normal distribution?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.
The normal distribution is also known as the Gaussian distribution, after just a German mathematician.The t-distribution is another distribution that may be described as having a bell shape. It differs as from normal distribution in that the tails are thicker. It is commonly employed in the analysis of small sample size datasets.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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I need an answer please
Answers
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
Which describes the collection of all points in the same plane that are 81/2 inches from point T
Answers
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
below
(3 - i)(3 + 1) =
Answers
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
A gasoline tank contains 9.6 hectolitres (hL) when it is 60% full. What is the capacity of the tank (in hL)?
Answers
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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the tiles (right angled triangles) are arranged around a parallelogram-shaped tile. Calculate the area of the parallelogram. b= 36 h= 13.2
Answers
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:
Both pairs of opposite side are equal and parallel .Both diagonals are equal.Each diagonal divides the parallelogram into 2 congruent triangles.Squares , rectangles and rhombus are parallelograms.The area of a parallelogram is given by the product of base and height of the parallelogram.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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First try was incorrect
Rew decided to purchase some dubbles (x) and totts (y). Altogether,
he planned to buy at most 7 items.
Write an inequality, in standard form, to model this relationship.
Answers
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.
Pe un stadion se găsește un grup de sportiv cuprins între 50 și 100 care se pot grupa în coloane de câte 12 18:24 tarif fiecare dată rămân șase sportiv care nu pot forma o coloană completă care este numărul minim de sportiv? Va rog sa ma ajutati repede!!!!
Answers
The width of a rectangle measures (5v - 2w) centimeters, and its length measures (6v+7w) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle? (10w +22v) (-2+14w + 22v) (22v + 10 )( 11v +5 )
Help asaP!!!
Answers
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
Maths help 10 points awarded and brainiest for correct answer
Answers
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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Jen Butler has been pricing Speed-Pass train fares for a group trip to New York.
Three adults and four children must pay $116
Two adults and three children must pay $82
Find the price of the adult's ticket and the price of a child's ticket.
Answers
The price of the adult's ticket is $20 and the price of a child's ticket is $14.
How to calculate the valuesLet 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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32 - (4 x s) = 12
What does the s stand for?
PLEASEEE HELPPPP
ASAP 20 POINTS!!!!!
Answers
Answer:
5.
Step-by-step explanation:
32-20-12.
At a berry farm, Clayton picks 1 1/4
cups of blackberries and twice as many raspberries. He takes the berries home and uses them to make mixed-berry muffins. If Clayton needs 3/4
of a cup of mixed berries for each batch of muffins, how many batches can he make?
Write your answer as a whole number, fraction, or mixed number. Simplify any fractions.
Answers
Answer: 1 1/4 batches of muffins
Step-by-step explanation:
multiply 1 1/4 (5/4) by 2 and get 5/2 (2 1/2)next add 5/2 (10/4) and 5/4 and get 15/4divide 15/4 by 3 and get 5/4simplify that out into 1 1/4no the projvet iS 348
3=20
14. Model Real Life A self-balancing scooter travels 12 miles
per hour. An all-terrain vehicle can travel 6 times as
fast as the scooter. A go-kart can travel 67 miles
per hour. Which vehicle can travel the fastest?
Answers
An all-terrain vehicle can travel the fastest.
What is Speed ?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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How do you solve this??
Answers
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
The product of two consecutive even number is 12 more than the square of the smaller number. Find the smaller number
Answers
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
Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 1 more than 4 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 91 ?
Answers
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
55 mph
BIKE
12 mph
How many more hours can the bus travel than the bike in a 3.5 hour period?
Answers
Step-by-step explanation:
3.5(12)=42
3.5(55)=192.5
192.5
-42
150.5 more miles
convert each of the following base-ten numberals in the indicated bases
456 in base 5
Answers
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
(7m³ +8m²-m+2.8)-(-3m³ +9m+3.6)
Answers
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
hope it helps...
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