Answer:
a) 64 feetb) 1 secStep-by-step explanation:
Given the height in feet represented by the equation H = -16t²+32t+48, at maximum height, the velocity of the water balloon is zero.
Velocity = dH/dt = 0
dH/dt = -32t+32 = 0
-32t+32 = 0
-32t = -32
t = -32/-32
t = 1sec
Substituting t = 1sec into the modeled equation of the height
H = -16t²+32t+48
H = -16(1)²+32(1)+48
H = -16+80
H = 64 feet
The maximum height of the water balloon is 64 feet
b) In order to know how long it takes to reach its maximum height, we will substitute H = 64 feet into the equation of the height.
64 = -16t²+32t+48
-16t²+32t = 16
16t²-32t+16 = 0
t²-2t+1 = 0
t²-t-t+1 = 0
t(t-1)-1(t-1) = 0
(t-1)² = 0
t-1 = 0
t = 1sec
It took the water balloon 1 sec to reach its maximum height.
Determine the mean of the following set of numbers: 40, 61, 95, 79, 9, 50, 80, 63, 109, 42
Round to the nearest tenth place. The mean is
Step-by-step explanation:
work is shown and pictured
Looking at the histogram, where would the median fall?
Answer:
The median would be found in the middle of the histogram
Step-by-step explanation:
It looks like 70-79, would fall in being the median because it is in the middle and it has the most results. In this case, I think it 70-79.
Hope this helps.
Answer:
70-79
Step-by-step explanation:
I took the test :)
when rewriting in the form y=a(x-h)+k, by completing the square, the relation y=-x*2+6x+12 becomes:
Answer:
Step-by-step explanation:
you can complete the square or use a calculator online that does it for you.
the equation is in the for y = a(x-h)^2 + k
it should be y = (x + 3)^2 + 3
Answer:
The correct answer is [tex]y = - (x - 3)^{2} +21[/tex].
Step-by-step explanation:
To solve this equation (y = [tex]-x^{2} +6x + 12[/tex]), we want to first complete the square. To do this, we want to add a -9 to the expression in order to achieve [tex]y = -x^{2} +6x - 9 + 12[/tex].
Then, you want to add the -9 to the other side of the equation to get [tex]y - 9 = -x^{2} + 6x - 9 + 12[/tex].
Then, we factor out the negative sign from the right side of the equation. This is a negative 1 that can therefore make the polynomial easier to factor. This leaves us with [tex]y - 9 = -(x^{2} -6x+9) + 12[/tex].
Now, we use an identity in algebra that is difference of two squares identity. This says that [tex]a^{2} -2ab +b^{2} =(a-b)^{2}[/tex].
So, we will then factor the trinomial -[tex]x^{2} -6x+9[/tex] to get [tex]-(x-3)^{2}[/tex]. Our new and updated equation is [tex]y-9 = -(x-3)^{2} +12[/tex].
Now, we move the constant of -9 to the right side of the equation. This just means we are going to add this to 12. This gives us [tex]y = -(x-3)^{2} +21[/tex].
This is our final equation.
Probability Race game
Read the whole thing. Question 2 will be posted separately to make the question simple.
Question 1:
Why should you not play this game with Roland? Use probability to prove that
the game is unfair and Roland is likely to win. SHOW ALL YOUR WORK!
Answer:
see below
Step-by-step explanation:
There are 36 possible outcomes when rolling 2 die
P( number) = number of times the sum appears / total outcomes
p(1) =0/36
P(2) = 1/36
p(3) = 2/36
p(4) = 3/36
p(5) = 4/36
p(6) = 5/36
p(7) = 6/36
p(8) = 5/36
p(9) = 4/36
p(10) = 3/36
p(11) = 2/36
p(12) = 1/36
Since he picked first he has the greatest odds so he is most likely to win
The probability of getting a number divisible by 3 is 3/10 using a game spinner.
The denominator of that probability is:
Answer:
B
Step-by-step explanation:
the denominator should be the total amount of outcomes.
Factor out the GCF from the following polynomials.
1) 45m^5-25m^4-20m^2-35m=? 2) 35x^2-15x^3+5x^4=? 3) 6ab^6-14a^2b^4+2a^5b^3=?
Answer:
Step-by-step explanation:
i hope
the the answer is 2ab3(a4+3b3−7ab)
hope it helps.
sorry if it wrong
-Delilah
21. A quantity of food would last a
family of 5 for 21 days. How long
would the same quantity last a
family of 7 if thev all eat at the same
rate?
Answer:
15 days
Step-by-step explanation:
5 x 21 = 105
105/7 = 15
Answer:
15 days
Step-by-step explanation:
As the number of people in that family increases the time taken reduces, so the time is in inverse proportion to the number of people in that family.
Let the number of days taken by a family of 7 to finish a quantity of food be x.
⇒ [tex]\frac{x}{21}[/tex] = [tex]\frac{1}{\frac{7}{5} }[/tex]
⇒ [tex]\frac{x}{21}[/tex] = [tex]\frac{5}{7}[/tex]
⇒ x = [tex]\frac{21 * 5}{7}[/tex]
x = 15
∴ It would take a family of 7 15 days to finish a quantity of food.
Hope this helps!!!
Please help! Correct answer only!
For a fundraiser, there is a raffle with 100 tickets. One ticket will win a $150 prize, and the rest will win nothing. If you have a ticket, what is the expected payoff?
$ ___
Answer:
Expected Payoff ⇒ $ 1.50 ; Type in 1.50
Step-by-step explanation:
Considering that 1 out of the 100 tickets will have a probability of winning a 150 dollar prize, take a proportionality into account;
[tex]100 - Number of Tickets,\\1 - Number of Tickets You Can Enter,\\\\1 / 100 - Probability of Winning,\\$ 150 - Money Won,\\\\Proportionality - 1 / 100 = x / 150, where x - " Expected Payoff "\\\\1 / 100 = x / 150,\\100 * x = 150,\\\\Conclusion ; x = 1.5 dollars[/tex]
Thus, Solution ; Expected Payoff ⇒ $ 1.50
HELP!!!! Identify the volume of the composite figure rounded to the nearest tenth.
Answer:
4618.1 ft³
Step-by-step explanation:
Volume of the cone:
[tex]V_{cone} = \frac13 \pi r^2 h[/tex]
[tex]V_{cone} = \frac13 \cdot \pi \cdot 49 \cdot 12 = 196\pi[/tex]
Volume of the cilinder:
[tex]V_{cilinder} = \pi r^2 h[/tex]
[tex]V_{cilinder} = \pi \cdot 49 \cdot 22 = 1078\pi[/tex]
Total volume is 2*Vcone + Vcilinder = 1470π ≈ 4618.1 ft³
The equation a=180(n-2)/n represent the angle measures,a in a regular n-sided polygon. When the equation is Solved for n,n is equal to a fraction with a denominator of a-180. What is the numerator of the fraction.
Answer:
The
numerator is 360
Step-by-step explanation:
What we need to do here is make n the subject of the formula;
a = 180(n-2)/n
an = 180n-360
180n - an = 360
n(180-a) = 360
n = 360/(180-a)
Express the ratio 700g to 1.75kg in its lowest terms.
Give your answer in the form m:n where m and n are integers
Answer:
2 : 5
Step-by-step explanation:
700 g : 1.75 kg
Since ratio should be between same units, so we'll convert either g into kg or kg into g. For convenience, kg will be converted to g
700 g : 1.75 kg × 1000
700 g : 1750 g
÷ 50 ÷50
14 : 35
÷7 ÷7
2 : 5
PLZ ANSWER THIS ASAP
Answer:
C. Hollow cone frustum
Step-by-step explanation:
Revolved it in my head, because the line isn't touching the triangle it will be hollow, because the triangle has a slope the shape will taper.
no solution for 6x-3x+4-2x
Answer:
4+x
Step-by-step explanation:
you combine your like terms so you take 6x-3x and you end up with 3x than you take that 3x and subtract the 2x from it so you are left with just x so that would be 4+x
Write in standard form an equation for the line with slope 1/3 through
the point (2,-2).
Answer:
x - 3y = 8.
Step-by-step explanation:
Use the point-slope form of the equation of a line:
y - y1 = m(x - x1) where m = the slope and (x1, y1) is a point on the line.
So substituting the given values:
y - (-2) = 1/3(x - 2)
y + 2 = 1/3x - 2/3 Multiply through by 3:
3y + 6 = x - 2
x - 3y = 6 + 2
x - 3y = 8 <---- Standard Form.
Calculate the measures of variability for the data set. The range is
I really need help with this I don't understand it.
Answer:
(10x + 37) and (15x+7) are vertical angles which are always equal
10x + 37 = 15x +7
5x = 30
x = 6
The angle (15x +7) equals 97 and the other angle (10x + 37) also equals 97 degrees. All 4 of the angles add up to 360 degrees.
Therefore, 360 = 2z + 97 + 97
2z = 166
z = 83
Step-by-step explanation:
I’ll mark you brainliest!!!!! Which point is a solution to the inequality represented by this graph?
Answer:
A is a solution because it is in the shaded area.
Step-by-step explanation:
What is the angle relationship shown below?
A)Corresponding
B)Same side interior
C)Alternate interior
D)Alternate exterior
E)Vertical
Answer:
The relationship between the angles is alternate exterior angles.
Step-by-step explanation:
Exterior means outside.
Alternate means every other or in this case across form each other.
These angles represent alternate exterior angles because they are on the outside of the transversal and they are alternating each other.
Help me ASAP
Estimate the measure of ∠DBC.
Answer:
135°
Step-by-step explanation:
Considering it's estimation, there isn't too much of an explanation, but here you go anyways.
A straight angle is equal to 180°. DBE is a straight angle.
DBC and CBE added together appear to be 180° (supplementary).
We are trying to find DBC. An obtuse angle has to be over 90°, which in this case DBC clearly is over 90°. From that you can conclude it isn't any of the first 3, so it's D. 135°
hope this helps and give brainliest if I am epic blah blah blah ;)
Lin’s family has completed 70% of a trip. They have traveled 35 miles. How far is the trip?
Answer:
The trip is 45 and 1/2 miles long
Step-by-step explanation:
Write an integer that represents this scenario:
18-point gain
Answer:
+18
Step-by-step explanation:
A gain is a positive number
+18
Answer:
+18
Step-by-step explanation:
Neg = Drop
Pos = Gain
Gain so +
+18
What’s the square root of 500
Answer:
22.360679775
Step-by-step explanation:
i used a calulator on the web
Answer:
±10 sqrt(5)
Step-by-step explanation:
sqrt(500)
We know that sqrt(ab) = sqrt(a) sqrt(b)
sqrt(100*5)
sqrt(100) sqrt(5)
±10 * sqrt(5)
En una granja se observa que por 12 patos hay 5 gallinas, por tres gallinas hay 8 pavos ;por 10 pavos hay 9 cerdos. ¿A cuantos patos equivalen 7 cerdos?
Answer:
7 ducks equals 7 pigs.
Step-by-step explanation:
English Translation
On a farm it is observed that for 12 ducks there are 5 chickens, for three chickens there are 8 turkeys, for 10 turkeys there are 9 pigs. How many ducks equals 7 pigs?
Solution
For 12 ducks, there are 5 chickens
12 ducks = 5 chickens
For 3 chickens, there are 8 turkeys
3 chickens = 8 turkeys
For 10 turkeys, there are 9 pigs
10 turkeys = 9 pigs
We first need to create a direct relationship between ducks and pigs to know how many ducks are equivalent to 7 pigs.
9 pigs = 10 turkeys
8 turkeys = 3 chickens
10 turkeys = (10×3/8) chickens = 3.75 chickens
Hence, 9 pigs = 10 turkeys = 3.75 chickens
9 pigs = 3.75 chickens.
12 ducks = 5 chickens
5 chickens = 12 ducks
3.75 chickens = (3.75×12/5) ducks = 9 ducks.
9 pigs = 3.75 chickens = 9 ducks
9 pigs = 9 ducks.
Hence, 7 pigs = 7 ducks too.
Hope this Helps!!!
what does the symbol mean on the image?
Answer:
Step-by-step explanation:
a) U -----> union
Union of two sets is the set of all distinct elements that are in A or B
A U B = {8 , 14 , 17 , 16, 9 , 15}
∩ ----------> intersection
Intersection of two sets is the set of all distinct elements that are in both A and B
A ∩ B = {14,17}
b) A' = {9 , 15 , 16 , 10 , 11 , 12 , 13}
P(A') = 7/10
Fatima has 72 oranges. Four oranges are needed to make a glass of freshly squeezed orange juice. How many glasses of orange juice can she make?
Answer:
Step-by-step explanation:
18
Complete the equation of the line through (–6,5) and (-3, -3).
Use exact numbers.
Answer:
-3, -3
Step-by-step explanation:
what is the answer to 18−(2x+1) = ???
Answer & Step-by-step explanation:
18 - (2x + 1)
Distribute the negative sign (-) to 2x + 1.
18 - 2x - 1
Put -2x in the beginning of the expression and combine like terms.
-2x + 17
So, the answer to 18 - (2x + 1) is -2x + 17.
Which datum is most unlikely to occur? A. a 7 foot tall person if the mean is 6 feet and the standard deviation is 3 inches B. a 13 foot tall moose if the mean is 12 feet and the standard deviation is 4 inches C. a 17 foot tall filbert tree if if the mean is 20 feet and the standard deviation is 6 inches D. a 20 foot tall giraffe if the mean is 23 feet and the
Answer: idk man
Step-by-step explanation: rg
Answer:iidk
Step-by-step explanation:
I will mark you brainliest! How much money did Nikki orginally invest?
Answer:D
Step-by-step explanation:
Is number one congruent? If it is how?
Answer:
Yes, Triangles in (1) are congruent
Step-by-step explanation:
Two conditions must be satisfied before two triangles can be deemed or declared as being congruent.
1.) They must posses similar shape
2.) They must posses similar size ( that is the corresponding sides and angles of both triangles must be the same)
Triangles in (1) meet both criterias by possessing similar shape with the size and length of the corresponding angles also being the same.
Therefore, the two triangles are congruent.