The maximum height of the firework is 64 feet.
Explanation:The equation y = -16x^2 + 32x + 48 represents the height, in feet, of a firework x seconds after it is launched. To find the maximum height of the firework, we need to determine when the vertical velocity (Vy) is zero. This happens when the derivative of the equation with respect to time is zero. So, we differentiate the equation, set it equal to zero, and solve for x. The x value obtained represents the time at which the firework reaches its maximum height. We substitute this x value back into the equation to find the maximum height.
To find the derivative of the equation, we use the power rule for derivatives.
y' = -32x + 32
Setting y' equal to zero and solving for x:
-32x + 32 = 0
-32x = -32
x = 1
Substituting x = 1 into the original equation:
y = -16(1)^2 + 32(1) + 48 = 64
Therefore, the maximum height of the firework is 64 feet.
Paula is going to choose the size, color, phrase, and picture for a birthday card for her friend. There are
2
22 sizes,
4
44 colors,
7
77 phrases, and
4
44 pictures for her to choose from. (The printing company charges a fee to add extra design elements, so she will choose only one of each.)
How many different card designs are possible?
Answer:
224 card combinations
Step-by-step explanation:
The total number of card designs can be found by multiplying the number of options available for each design element.
Total number of cards= 2x4x7x4=?
224 cards altogether
If this trapezoid is moved through the translation (x+3,y-2), what will be the coordinates of c
Answer:
C'(1, 2 )
Step-by-step explanation:
The translation (x + 3, y - 2 ) means add 3 to the original x- coordinate and subtract 2 from the original y- coordinate, thus
C(- 2, 4 ) → C'(- 2 + 3, 4 - 2 ) → C'(1, 2 )
Answer:
C = ( 1 , 2 )
Step-by-step explanation:
original : C = ( -2 , 4 )
formula : ( x+3 , y-2 )
( -2 + 3 ) , ( 4 - 2 )
C = ( 1 , 2 )
ill answer the other 3 as well :)
original : A = ( -6 , 2 )
formula : ( x+3 , y-2 )
( -6 + 3 ) , ( 2 - 2 )
A = ( -3 , 0 )
___________________
original : B = ( -5 , 4 )
formula : ( x+3 , y-2 )
( -5 + 3 ) , ( 4 - 2 )
B = ( -2 , 2 )
___________________
original : D = ( 1 , 2 )
formula : ( x+3 , y-2 )
( 1 + 3 ) , ( 2 - 2 )
D = ( 4 , 0 )
yw :)
A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly. He started at 90 kilograms and gained weight at a constant rate of 8 lbs. a week.
a. Write a function to represent this situation. Use x and y as your variables.
b. What would his weight be after 8 weeks?
a) The function that represent this situation is y = 90 + 8x.
b) His weight be after 8 weeks is 154 lbs.
Step-by-step explanation:
It is given that,
He started at 90 kilograms.And gained weight at a constant rate of 8 lbs a week.a) Write a function to represent this situation. Use x and y as your variables.
Let 'x' be the number of weeks he gained weight.Let 'y' be the total weight.Hence the equation can be framed as,
Total weight = starting weight + weight gained in x weeks.
We know that, each week he gains 8 lbs. Therefore, for 8 weeks he gained 8x lbs of weight.
⇒ y = 90 + 8x.
∴ The function that represent this situation is y = 90 + 8x.
b) What would his weight be after 8 weeks?
To find his week after 8 weeks, substitute x=8 in the function y = 90 + 8x.
⇒ 90 + 8(8)
⇒ 90 + 64
⇒ 154 lbs.
∴ His weight be after 8 weeks is 154 lbs.
On a map the scale is shown as 0.5 inches equaling 15 miles. If two towns
are 2.25 inches apart on the map, what is the distance in miles between
the towns?
Answer:
The distance in miles between the towns is 67.5.
Step-by-step explanation:
Given:
On a map the scale is shown as 0.5 inches equaling 15 miles.
If the distance are 2.25 inches apart on the map between the towns .
Now, to find the distance in miles between the towns.
The distance on the map between the towns = 2.25 inches.
Let the actual distance between the two towns be [tex]x.[/tex]
The scale of the map is 0.5 inches equaling 15 miles.
If, 0.5 is equivalent to 15 miles.
Thus, 2.25 is equivalent to [tex]x.[/tex]
Now, to solve using by cross multiplication method:
[tex]\frac{0.5}{15} =\frac{2.25}{x}[/tex]
By cross multiplying we get:
[tex]0.5x=33.75[/tex]
Dividing both sides by 0.5 we get:
[tex]x=67.5\ miles.[/tex]
The actual distance between the two towns = 67.5 miles.
Therefore, the distance in miles between the towns is 67.5.
How do I solve this equation
Answer: 14
Step-by-step explanation:
the question is just asking you to replace the x and y with the corresponding numbers.
x = 4
y = -3
Since x is 4 squared it would be 16.
-4 times -3 equals positive 12.
That would make the equation
(16 + 12) divided by 2
16 + 12 = 28 divide that by 2 and you’ll get 14.
Answer: 14
Step-by-step explanation:
First plug 4 in for x.
4^2 is equal to 16 because 4 x 4 is 16.
Next, plug in -3 for y.
-4 x -3
4 times 3 is 12 and they are both negative, therefore it turns out as a positive 12.
Then add the numbers on the top of your equation.
16+12=28.
Finally divide the sum by 2.
28 divided by 2= 14
Your answer is 14.
Hope this helps!
A person read that the average number of hours an adult sleeps on Friday night to Saturday morning was 7.2 hours. The
researcher feels that college students do not sleep 7.2 hours on average. The researcher randomly selected 15 students and
found that on average they slept 8.3 hours. The standard deviation of the sample is 1.2 hours. If you wanted to test this claim,
what type of statistical test would you do and why?
Calculate the value of z and its probability, since with this we can know how likely it is that this will happen.
We have that the mean (m) is equal to 8.3, the standard deviation (sd) 1.2 and the sample size (n) = 15
They ask us for P (x =7.2)
For this, the first thing is to calculate z, which is given by the following equation:
z = (x - m) / (sd / (n ^ 1/2))
We have all these values, replacing we have:
z = (7.2 - 8.3) / (1.2 / (15 ^ (1/2))
z = -3.55
With the normal distribution table (attached), we have that at that value the approximate probability is:
P (z = -3.55) = 0.0001
The probability is 0.01 %
This affirms that the students do not sleep what the study says because the probability of this happening according to the survey is almost nil.
I NEEP HELP ON THIS NOWWWWWW
i need the vertex, axis of symmetry, as well as if it is a vertical strech, shrink, and by a factor of how much for the graph in the picture above.
PLEASE HELP QUICK
Answer:
vertex and AOS is 0, and i think the stretch is 1
Step-by-step explanation:
Answer: vertex (0,0)
Vertical stretch
Axis of symmetry X=0
Step-by-step explanation:
With which information can you construct more than one triangle?
Answer:
The measurements of all the right angles and the lengths of the two sides and the measurement of the included angle.
Step-by-step explanation:
the measurements of two angles
the measurements of two angles and the length of the included side
the lengths of two sides and the measurement of the included angle
A cereal company is putting 1 of 4 prizes in each box of cereal. The prizes are evenly distributed so the probability of winning any given prize is always 1 / 4. Lily wonders how many boxes she should expect to buy to get all 4 prizes. She carried out 20 trials of a simulation and her results are shown below. Each dot represents how many boxes it took to get all 4 prizes in that trial.
Answer: The answer is 0.3
Step-by-step explanation:
Lily should expect to buy 1.5 boxes to get all four prizes.
Explanation:This question belongs to the field of probability in Mathematics. The problem is asking how many boxes Lily should expect to buy in order to get all four prizes. This is a geometric problem because each box has a probability of 1/4 of containing a prize, and each trial is independent with the same probability of success. To solve this problem, we can use the concept of expected value.
The expected value is the average number of boxes Lily needs to buy to get all four prizes. The expected value can be calculated by multiplying the probability of each outcome by the number of boxes it takes to achieve that outcome, and then summing up these products:
Expected value = (1/4) * 1 + (1/4) * 2 + (1/4) * 3 + (1/4) * 4 = 1.5
Therefore, Lily should expect to buy approximately 1.5 boxes to get all four prizes.
Learn more about geometric problem here:https://brainly.com/question/32540853
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Odette has two investments that she purchased at the same time. Investment 1 cost $10,000 and earns 4% interest each year. Investment 2 cost $8000 and earns 6% interest each year.
Write exponential growth functions
that could be used to find v1(t) and v2(t), _________________________________
the values of the investments after t years.
Find the value of each investment after 5 years.
Explain why the difference between their values, ____________________________ which was initially $2000, is now less
Answer: The functions are v1(t)=10000*(1.04)^5 and v2(t)=8000(1.06)^5
v1(5)=12166$
v2(5)=10705 $
Step-by-step explanation:
Given:
Investment cost for 1st=10,000$ ,at 4%rate.
Investment cost for 2nd=8000$ ,at 6% rate.
To Find:
Exponential growth functions ,
that could be used to find v1(t) and v2(t),
the value of each investment after 5 years
And difference between their values.
Solution:
Consider for 1st investment function be v1(t) and for 2nd be v2(t)
and t be time period
Exponential growth is given by, as time function,
v(t)=initial cost*(1+rate)^time period.
for 1st investment its cost is 10000$ at 4 % rate.
[tex]v1(t)=10000(1+0.04)^t[/tex]
[tex]v1(t)=10000(1.04)^t[/tex]
for 2nd investment its cost is 8000$ at 6% rate.
[tex]v2(t)=8000(1+0.06)^t[/tex]
[tex]v2(t)=8000(1.06)^t[/tex]
For t=5 calculating for both investment,
[tex]v1(5)=10000(1.04)^5[/tex]
[tex]=10000*1.2166[/tex]
v1(5)=12166 $
For 2nd investment,
[tex]v2(5)=8000(1.06)^5[/tex]
[tex]=8000*1.3382[/tex]
v2(t)=10705.8 $
Now after 5 years the difference is =v1(t)-v2(t)
Which is about 1460 $ only.
This because of the both functions depends upon time,initial investment and rate of interest .
Here time period being same.But the rate of interest are different and initial values are different.
Please help! Please let me know if you need a better picture.
Answer:
(x, -y)
Step-by-step explanation:
Look at the coordinates of the point C before the transformation (-2, 2)
look at the coordinates of the point C after the transformation, (-2,-2)
What is the difference between these two points?
Well the x is the same, the y is just the negative version of itself!
Answer:i need a better pic
Step-by-step explanation:
Travis's purchasing an $225000 home with a 30 year mortgage at 5.15% because he is not making a down payment PMI in the amount of $84.50 a month is required for the 1st 2 years of the loan based on this information what is the total cost of his loan
Answer:
The total cost of the loan = $444,208.80¢
Step-by-step explanation:
Please kindly check the attached files for details
Answer: $444,309.60
Step-by-step explanation:
Find the area of the shape shown below
Answer:
A = (1/2)(3)(7 + 3) = 5(3) = 15
15 goes into the box.
1. The sides of a triangle measure 6 inches, 10 inches, and 13 inches. What type of triangle is it?
A. right
B. scalene
C. isosceles
D. equilateral
Answer:
Step-by-step explanation:
The base and height of a triangle with base 12 in and the height 6 in are both tripled
Answer:
Base=36
Height=18
Step-by-step explanation:
To work this out you would first multiply 12 by 3, which gives you 36. Then you would multiply 6 by 3, which gives you 18.
1) Multiply 12 by 3.
[tex]12*3=36[/tex]
2) Multiply 6 by 3.
[tex]6*3=18[/tex]
3) Base=36
Height=18
[tex]\large\bf{\underline{\underline{\mathfrak{Question}:}}}[/tex]
The base and height of a triangle with base 12 in and the height 6 in are both tripled.
[tex]\large\bf{\underline{\underline{\mathfrak{Solution}:}}}[/tex]
It is given that,
[tex]:{\Longrightarrow{\small{\rm{The\:base\:of\:a\:triangle\:=\:12}}}}[/tex]
[tex]:{\Longrightarrow{\small{\rm{The\:height\:of\:a\:triangle\:=\:6}}}}[/tex]
And if both base and height get tripled then the base and height would be:
[tex]:{\Longrightarrow{\small{\rm{The\:base\:of\:a\:triangle\:=\:3×12}}}}[/tex]
[tex]{\therefore{\small{\rm{The\:new\:base\:of\:a\:triangle\:=\:36}}}}[/tex]
And,
[tex]:{\Longrightarrow{\small{\rm{The\:height\:of\:a\:triangle\:=\:3×6}}}}[/tex]
[tex]{\therefore{\small{\rm{The\:new\:height\:of\:a\:triangle\:=\:18}}}}[/tex]
*
25 points
Captionless Image
A
B
C
D
Answer:
c
Step-by-step explanation:
The correct option is Option B: is an A.P., because d = 10
What is an Arithmetic Progression?An arithmetic progression, also known as an arithmetic sequence, is a sequence of numbers in which the difference between consecutive terms is constant. This constant difference is called the common difference and is denoted by 'd'.
The given sequence is:
-5, 5, 15, 25, ....
In every Arithmetic Progression (A.P.)
The common difference d
d= 2nd term - 1st term = 3rd term - 2nd term
d = 5-(-5) = 15 - 5
d = 10
Hence the common difference is 10,
Therefore the sequence is an A.P., because d = 10
Learn more about arithmetic progression on https://brainly.com/question/30364336
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The correct question
The sequence: -5, 5, 15, 25, ...
A. is not an A. P.
B. is an A.P., because d = 10
C. is an A.P because d = 5
D is an A. P., because d = -10
Multiply the binomial. To write x2 use "^". X^2
(3x + 2) (x– 4)
Answer:
3x^2-10x-8
Step-by-step explanation:
I need some help :,)
a sheet of acrylic has a mass of 95.2g. Acrylic has a density of 1.19g/cm³ What is the volume of the sheet of acrylic
Answer:
80 cm³
Step-by-step explanation:
Density = mass/volume
1.19 = 95.2/volume
Volume = 95.2/1.19
= 80
Answer:
80 cm cubed
Step-by-step explanation:
The density of a substance is denoted by d = m/V, where d is the density, m is the mass, and V is the volume.
Here, we know that the mass m = 95.2 grams and the density d = 1.19 g/cm cubed. So, plug these values into the formula:
1.19 = 95.2/V
Divide both sides by 1.19 and multiply both sides by V:
V = 95.2/1.19 = 80 cm cubed
Thus, the volume is 80 cm cubed.
Hope this helps!
If a is a rational number and b is an irrational number, then the sum a + b is
Answer:
Sum a + b is irrational
Step-by-step explanation:
Any irrational number plus a rational number is always irrational.
A grocer is making 26 pounds of a batch of
mixed nuts containing cashews and peanuts. The
peanuts cost $2.95 per pound, and the cashews
cost $9.95 per pound. How many pounds of each
item are in the mix if the total value of the mixed
nuts is $132.70?
Answer:
rdgvvsssddas
Step-by-step explanation:
42423412
A round mirror has a radius of 5.3 inches. What is the area of the mirror in square inches, rounded to the nearest tenth?
Answer:
88.2 squared
Step-by-step explanation:
The formula to find the area of a circle is a = pi * r ^2
Let's replace the values that we know.
a = 3.14 x 5.3 ^2
First, we should do 5.3 ^2, which is 28.09.
a = 3.14 x 28.09
Now we are able to do 3.14 x 28.09 which is 88.2026
But that isn't it! We need to round to the nearest tenth, which is this digit:
88.2026
Since next to the 2 there is a 0, you take out all the numbers after that 2. Which leaves you with:
88.2
Final answer:
The area of the round mirror with a radius of 5.3 inches, when calculated using the formula A = πr^2 and rounded to the nearest tenth, is 88.2 square inches.
Explanation:To find the area of the round mirror with a radius of 5.3 inches, we will use the formula for the area of a circle, which is A = πr^2, where A is the area, π is approximately 3.14, and r is the radius of the circle.
Given that the radius of the mirror is 5.3 inches, we can substitute this value into the formula to find the area:
A = π(5.3)^2 ≈ 88.2 square inches.
Let's plug in the radius:
A = π * (5.3 inches)^2A = 88.2026 square inchesWhen rounded to the nearest tenth, the area of the mirror is 88.2 square inches.
An equation is shown below 12 -9 + c=12 .What value of c makes the equation true?
A 0
B 3
C 9
D 12
Answer:9
Step-by-step explanation:
12-9=3 12-3=9 3+9=12
So C=9
Hey there!
[tex]\large\boxed{c=9}[/tex]
12 - 9 + c = 12
Combine like terms.
3 + c = 12
Subtract 3 from each side of the equation.
3 - 3 + c = 12 - 3
c = 9
Check:
12 - 9 + c = 12
12 - 9 + 9 = 12
3 + 9 = 12
12 = 12
Hope this helps!
Determine perimeter
Answer:
20cm
Step-by-step explanation:
7.2 + 7.2 + 2.8 + 2.8 = 20
Each side of the rectangle is equal to the side opposite from it. That means you have 2 sides of 7.2 cm and 2 sides of 2.8 cm.
To find perimeter, you add all the sides. So that's 7.2 + 7.2 + 2.8 + 2.8, which is 20 cm altogether.
PLEASE HELP QUICK I WILL MARK BRAINLIEST!
Which value for Y in the table would be least likely to indicate an association between the variables?
Find AC and round to the nearest hundredth
Answer:
2.18
Step-by-step explanation:
tan 70°=x/6
by cross multiplication
xtan70°=6
divide both sides by tan70°
x=6/tan70°
x=6/2.7475
x=2.18
Which algebraic expression has like terms?
o 9n - 2n+3-4n
O 7n2+3n-3-6172
O 7n2 +4n-37 – 512
O 67° -4n4+67-512
Answer:
The third choice
What is the y-intercept of =1+6x
Answer:
(0,1)
Step-by-step explanation:
Simon can spend no more than $50 on gifts for his family. Let srepresent the
amount he can spend. Choose the symbol that correctly completes the inequality
need help will give brainist
Answer:
1: -2.33 or -7/3
2: - 2.16 or -13/6
3: 3.49 x 10^4
4: 4.28*10-7
5: 0.81 or 9/11
6. 3
7: 8
8: 9 or up
9: 5 or up
10: 0-36
I hope any of this helps.... :D