The set of parametric equations representing the skater's jump is:
x = 52t
y = 5 + 16t²
We have,
Let's denote the time as t.
Horizontal motion:
The skateboarder's horizontal velocity remains constant throughout the jump, so the horizontal position (x) can be represented as:
x = vt
where v is the horizontal velocity, which in this case is 52 ft/s.
Vertical motion:
The vertical position (y) can be determined using the equations of motion under constant acceleration.
The skateboarder experiences acceleration due to gravity (g) acting downward.
The initial vertical position is 5 ft, and the initial vertical velocity is
0 ft/s.
Using the equation of motion:
[tex]y = y_0 + vy_0t + 0.5gt^2[/tex]
Substituting the given values:
y = 5 + 0t + 0.5(32)t²
y = 5 + 16t²
Thus,
The set of parametric equations representing the skater's jump is:
x = 52t
y = 5 + 16t²
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A teacher would like to estimate the mean number of steps students take during the school day. To do so, she selects a random sample of 50 students and gives each one a pedometer at the beginning of the school day. They wear the pedometers all day and then return them to her at the end of the school day. From this, she computes the 98% confidence interval for the true mean number of steps students take during the school day to be 8,500 to 10,200. If the teacher had used a 90% confidence interval rather than a 98% confidence interval, what would happen to the width of the interval
Answer:
The answer is "It would decrease, but not necessarily by 8%".
Step-by-step explanation:
They know that width of the confidence level is proportional to a confidence level. As just a result, reducing the confidence level decreases the width of a normal distribution, but not with the amount of variance in the confidence level. As just a result, when a person teaches a 90% standard deviation rather than a 98 percent normal distribution, the width of the duration narrows.
pleas help a lot of points
Answer:
54 ft
Step-by-step explanation:
Add all the side lengths ; 18+18+18 = 54.
Find the volume of each cylinder. Which cylinder has the greater volume? Use 3.14 for π and round your answers to the nearest hundredth.
Two cylinders. The circumference of the base of cylinder A is 3 meters and the height of the cylinder is 5 meters. The circumference of the base of cylinder B is 5 meters and the height of the cylinder is 3 meters.
Answer:
cylinder A is 141.3 meters
cylinder b is 245.5 meters
Step-by-step explanation:
Cylinder a: 3x3x5x3.14
cylinder B : 5x5x3x3.14
Marcus is choosing 4 books to read from a list of 15 books. If order matters, how many ways can he choose to read the books?
4
32,760
23,760
60
Answer:
32,760
Step-by-step explanation:
Given :
Since the order matters, we use the permutation relation :
Recall :
nPr = n! ÷ (n - r)!
n = 15 ; r = 4
15P4 = 15! ÷ (15 - 4)!
15P4 = 15! ÷ 11!
15P4 = (15 * 14 * 13 * 12)
15P4 = 32,760
2
2. This system of equations has : y = -2x
y = -2x + 1
A. One Solution
B. Infinitely Many Solutions
C. No Solutions
Answer:
C. no solutions
Step-by-step explanation:
Both equations have a slope of -2, but have different y-intercepts. Therefore, the graphs of the equations are parallel, but don't coincide, nor do they intersect. So, there are no solutions
Need help finding the length of AC
Answer:
I would have to say that the length of AC is 22.5
Please help !!!!!!
Clare is deriving the quadratic formula by solving ax^2+bx+c=0 by completing the square.
She arrived at this equation:
(2ax+b)^2=b^2-4ac
Briefly describe what she needs to do to finish solving for I and then show the steps.
Answer:
Clare starts with:
a*x^2 + b*x + c = 0
And she gets to:
(2*a*x + b)^2 = b^2 - 4*a*c
Now we want to show the final steps to solve the equation (isolating x)
First, we apply the square root to both sides:
[tex]\sqrt{(2*a*x + b)^2} = \sqrt{(b^2 - 4*a*c)}[/tex]
Because the square root has two solutions, (one negative and one positive), we will write:
[tex]2*a*x + b = \pm \sqrt{b^2 - 4*a*c}[/tex]
Now we subtract b in both sides:
[tex](2*a*x + b) - b = \pm \sqrt{b^2 -4*a*c} - b[/tex]
[tex]2*a*x = \pm \sqrt{b^2 -4*a*c} - b[/tex]
Now let's divide by 2*a in both sides:
[tex]2*a*x/(2*a) = \frac{\pm \sqrt{b^2 -4*a*c} - b}{2*a}[/tex]
[tex]x = \frac{\pm \sqrt{b^2 -4*a*c} - b}{2*a}[/tex]
Please help.
Determine which lines are parallel and which are perpendicular. Explain your reasoning.
Answer:
Parallel: a and b, p and q, p and r, q and r
PErpendicular: p&a, p&b, q&a, q&b, r&a, r&b
Step-by-step explanation:
Parallel lines have the same slope so both of the lines would be going in the same direction and will never cross each other.
Perpendicular lines cross at a 90 degree angle.
Technically you do not know if q&a and q&b are perpendicular because you do not know if there is a 90 degree angle
Answer:
Parallel lines are equally spaced out in the same direction so it would be p,q, and r, Purpendicular Lines intersect at a 90 degee angle so it would be q and a, q and b, r and b, and r, and so on
Step-by-step explanation:
1.99 divided by 3 to the nearest cent.
Answer:
nearest tenth?
Step-by-step explanation:
your answer would be .663
Simplify to the tenth would be make it .7
Distance = Speed & Time
If I increase speed, but hold time constant what happens to
distance? What is this relationship called?
Complete the square 6v^2-12v-18=0 showing work
choose all of the points that are solutions to y<3x+2:
A. (0,0)
B. (0,2)
C. (1,4)
D. (1,7)
E. (2,6)
F. (2,8)
Answer:
ACEStep-by-step explanation:
✓ A. (0, 0) [y < 3x + 2 → 0 < 2]
× B. (0, 2) [y < 3x + 2 → 2 < 2]
✓ C. (1, 4) [y < 3x + 2 → 4 < 5]
× D. (1, 7) [y < 3x + 2 → 7 < 5]
✓ E. (2, 6) [y < 3x + 2 → 6 < 8]
× F. (2, 8) [y < 3x + 2 → 8 < 8]
What is the value of x?
Answer:
3
Step-by-step explanation:
u just gotta find the area
Answer:
28
Step-by-step explanation:
18 is 4.5 times a number.
The value of x is equal to 4, that is 4.5 times 18 is 4
Given that the expression:
18 is equal to 4.5 times a number.
Assume that the number be x.
To find the number that is 4.5 times 18, we can set up the following equation:
4.5 × x = 18
Now, to find the value of x, divide both sides of the equation by 4.5:
4.5 × x / 4.5 = 18 / 4.5
x = 18 / 4.5
x = 4
So, the number that is 4.5 times 18 is 4.
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Find the value of z.
A. 55
B. 90
C. 238
D. 122
Answer:
Not sure
Step-by-step explanation:
Still not sure
You are playing a game using this spinner. You get one spin on each turn. Provide a probability model.
Answer:
THE ANNOYING ORANGE THE ANOYING ORANGE THE ANNOYING ORANGE THE ANNOYING ORANGE!!!!!!!
Step-by-step explanation:
Answer:
1:4 is the ratio
Step-by-step explanation:
2:8 simplified is 1:4
not sure if this is exactly the right answer but I hope it helps
Are these two lines parallel?
y = 3x – 2
X 0 1 2 3
y3 6 9 12
Yes
No .
Answer:
Yes
Step-by-step explanation:
The cost for a pool membership for a family at a community pool is $350 plus $125 per month. A family paid a total of $1,350. How many
months did the family use the pool?
a-11
b-14
c-8
d-12
Answer:
The family used the pool for 8 months
Step-by-step explanation:
We know that the family paid a total amount of $1,350 dollars. We also know that they had to pay $350 dollars for joining the community pool. Lastly, they paid a monthly fee of $125 dollars. The value "x" represents months.
With that being said, here's our equation.
350 + 125x = 1,350
Subtract 350 from both sides and you should get this:
125x=1,000
Finally, divide 125 from both sides to get the x value.
x=8
:)
the cost of fun for kids magazine for x number of months is shown below
The cost (C) of another magazine, Family Fun, for x number of months is
given by C-1.99x.
The cost of another magazine, Kidz Comics, is $1.85 for each month. The
annual subscription includes a delivery charge of $10, while the annual
subscription for Fun for kids and Family Fun has no such extra charge
Which annual subscription costs the most?
Answer:
Kidz comic costs the most
Step-by-step explanation:
Given
Family Fun
[tex]C(x) = 1.99x[/tex]
Kidz Comics
[tex]m = 1.85[/tex] --- monthly rate
[tex]b = 10[/tex] --- delivery charge
Required
Which is more expensive
A linear function is represented as:
[tex]f(x) = mx + b[/tex]
Where
[tex]m = rate[/tex]
[tex]b = y\ intercept[/tex] --- i.e. the base charge
So, for Kidz comic; We have:
[tex]f(x) = mx + b[/tex]
[tex]C(x) = 1.85x + 10[/tex]
To calculate the annual cost, we set x = 12; i.e. 12 months.
So, we have:
[tex]C(x) = 1.99x[/tex] ---- Family Fun
[tex]C(12) = 1.99 * 12[/tex]
[tex]C(12) = 23.88[/tex]
[tex]C(x) = 1.85x + 10[/tex] --- Kidz comic
[tex]C(12) = 1.85*12 + 10[/tex]
[tex]C(12) = 22.2 + 10[/tex]
[tex]C(12) = 32.2[/tex]
By comparison
[tex]32.2 > 23.88[/tex]
Hence, Kidz comic is more expensive
PLSSSS HELP ME !!!! Need ASAP Which pair of figures shows a dilation with a scale factor
of 1 1/2centered at the origin?
Answer:
Figures ABC and DEF
Step-by-step explanation:
Why is there a hole in your screen?
Answer:
The answer is QRS and TRU !!
Step-by-step explanation:
Suppose a man has a mass of 76kg and a density of 0.92g/cm3.
A) Calculate his volume.
b) Calculate the mass of air that he displaces, using the density of air from Table 5.2. The density of air is 1.29kg/m3
c) Calculate the buoyant force on him due to the air he displaces and compare this to his weight in newtons.
Answer:
A) 0.08260 cubic meter
B) 106.554 grams
C) 1.044 Newton
Step-by-step explanation:
A) Volume = mass/density
Substituting the given values, we get -
Volume = [tex]\frac{76000}{0.92} =82608.69[/tex] cubic centimeter
[tex]= 0.08260[/tex] cubic meter
B) Mass = volume * density
Mass of air =
[tex]= 0.08260 * 1.29 \\= 0.106554\\[/tex]Kilogram
[tex]106.554[/tex] grams
C) Buoyant force = density * acceleration due to gravity * Volume
Buoyant force due to air =
[tex]0.08260 * 9.8 * 1.29 \\1.044[/tex]Kg-m/s or Newton
If SW ⊥ RT, m< RSU = 5x+17, and m<VST = 9x-11, find m<WSV.
Answer:
uhhhh.....wut?
Step-by-step explanation:
The measure of the angle WSV is 38 degrees.
What is the complementry angles?Complementary Angles Two angles are Complementary when they add up to 90 degrees.
The value of x is;
[tex]\rm 5x+17=9x-11\\\\ 5x-9x=-11-17\\\\-4x=-28\\\\x =\dfrac{-28}{-4}\\\\x=7[/tex]
The angle VST is equlas to;
[tex]\angle \rm VST=9x-11=9(7)-11=63-11=52 \ degrees[/tex]
The angle VST and angle WSV are the complementary angles;
[tex]\angle \rm WSV+\angle VST=90\\\\\angle \rm WSV+52=90\\\\ \angle \rm WSV=90-52\\\\\angle \rm WSV=38[/tex]
Hence, the measure of the angle WSV is 38 degrees.
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3a-2b=14. 3a+2b=28
..
Answer:
a = 7
b = 3 1/2
Step-by-step explanation:
if you add the equations together then the 'b' will zero out
6a = 42
a = 7
substitute 7 for 'a' to solve for 'b'
3(7) - 2b = 14
21 - 2b = 14
-2b = -7
b = 7/2 or 3 1/2
Pls help I’ll give brainliest if you show ur work
Answer:
DB = 20 cm
Step-by-step explanation:
Given:
║AB = 12 cm (represented by 'a' leg)
║AD = 16 cm (represented by 'b' leg)
║DB = x cm (hypotenuse represented by 'c' leg)
These formulas are used to solve for a missing side length:
║a = [tex]\sqrt{(c^2 - b^2)}[/tex]
║b = [tex]\sqrt{(c^2 - a^2)}[/tex]
║c = [tex]\sqrt{(a^2 + b^2)}[/tex]
Because we are solving for side length c, we will be using the third formula.
║c = [tex]\sqrt{(a^2 + b^2)}[/tex]
║c = [tex]\sqrt{(12^2 + 16^2)}[/tex]
║c = [tex]\sqrt{(144 + 256)}[/tex]
║c = [tex]\sqrt{400}[/tex]
║c = 20
Therefore, the value for side length DB should be:
║DB = 20 cm
Daniel placed $2,500 in a one-year time deposit (CD) with a 2.7% annual interest rate. Approximately how much interest will Daniel earn at maturity?
Ok. So I need help with this problem that wants me to find the side length of a rectangle. The area of it is 3 sq. ft, and the top of it is 1/7 ft. I need to find the other side of it. Thank you!
is anyone have the answer to 9,576,984.9874 x 98.84
Answer:
946589196.155
Step-by-step explanation:
Hope that helps
need help ace plsssz
Answer:
150 multiply the 2 numbers
hope this helps
have a good day :)
Step-by-step explanation:
What is m
A: 19°
B: 68°
C: 112°
Answer:
m<N=68
Step-by-step explanation:
opposite angles of the parallelogram are equal(or congruent):
4x+36=6x-2
6x-4x=36+2
2x=38
x=38/2=19
the sum of the angles of the parallelogram =360
4x+36=4(19)+36=112 angle P
6x-2=6(19)-2=112 angle M
let Q= N=x
2x+112+112=360
2x=360-224
2x=136
x=136/2=68