Answer:
The projectile will hit the ground after 38.8 seconds.
Step-by-step explanation:
You know that the height s (t) in feet of the projectile after t seconds is given by the function
s(t) = - 16t² + 600t + 800.
To know the time at which the projectile will hit the ground, you must replace s(t) by height 0:
0=- 16t² + 600t + 800
This is a quadratic function of the form ax2 + bx + c, where a= -16, b=600 and c=800.
To solve a quadratic function, you must apply the expression:
[tex]x1,x2=\frac{-b+-\sqrt{b^{2}-4*a*c } }{2*a}[/tex]
In this case:
[tex]x1,x2=\frac{-600+-\sqrt{600^{2}-4*(-16)*800 } }{2*(-16)}[/tex]
Solving:
[tex]x1,x2=\frac{-600+-\sqrt{360000+51200 } }{-32}[/tex]
[tex]x1,x2=\frac{-600+-\sqrt{411200 } }{-32}[/tex]
[tex]x1,x2=\frac{-600+-641.25 }{-32}[/tex]
So:
[tex]x1=\frac{-600+641.25 }{-32}[/tex]
[tex]x1=\frac{41.25 }{-32}[/tex]
x1= -1.289 seconds
and
[tex]x2=\frac{-600-641.25 }{-32}[/tex]
[tex]x2=\frac{-1241.25 }{-32}[/tex]
x2= 38.789 ≅ 38.8 seconds
Time cannot be negative. So, the projectile will hit the ground after 38.8 seconds.
Cyber Monday Shopping A survey of U.S. adults found that of people said that they would get no work done on Cyber Monday since they would spend all day shopping online. Find the confidence interval of the true proportion. Round intermediate answers to at least five decimal places. Round your final answers to at least three decimal places.
Complete question :
Cyber Monday Shopping A survey of 1000 U.S. adults found that 33% of people said that they would get no work done on Cyber Monday since they would spend all day shopping online. Find the 95% confidence interval of the true proportion.
Answer:
(0.301 ; 0.359)
Step-by-step explanation:
Sample size, n = 1000
Phat = 0.33
(1 - phat) = 1 - 0.33 = 0.67
Zcritical at 95% = 1.96
Confidence interval :
Phat ± margin of error
Margin of Error = Zcritical * sqrt[(phat(1 - phat)) /n]
Margin of Error = 1.96 * sqrt[(0.33 * 0.67) / 1000]
Margin of Error = 1.96 * 0.0148694
Margin of Error = 0.0291440
Lower boundary = (0.33 - 0.0291440) = 0.300856
Upper boundary = (0.33 + 0.0291440) = 0.359144
(0.301 ; 0.359)
Suppose you want to factor the expression x2 + 2xn+n?. Given that n>0, what are the factors? Explain.
Select the correct answer below and, if necessary, fill in the answer box to complete your choice.
O A. The value of n can be any positive integer resulting in the same factor
O B. The value of n can be any positive integer resulting in the distinct factors
(Use a comma to separate answers as needed.)
O C. The value of n can be any prime integer resulting in the same factor
O
D. The value of n can be any prime integer resulting in the distinct factors
(Use a comma to separate answers as needed.)
O E. The expression cannot be factored for the given values of n.
Answer:
A. The value of n can be any positive integer resulting in the same factor
Step-by-step explanation:
Given
[tex]x^2 + 2xn + n^2[/tex] --- the right expression
[tex]n > 0[/tex]
Required
Possible values of n
[tex]x^2 + 2xn + n^2[/tex]
Expand
[tex]x^2 + 2xn + n^2 = x^2 + xn+xn + n^2[/tex]
Factorize
[tex]x^2 + 2xn + n^2 = x(x + n)+n(x + n)[/tex]
Factor out [tex]x + n[/tex]
[tex]x^2 + 2xn + n^2 = (x + n)(x + n)[/tex]
From the expression above, we can see that the result has the same factor. This means that options (b), (d) and (e) are not possible
[tex]x^2 + 2xn + n^2 = (x + n)^2[/tex]
The above also shows that n can take any positive value.
Hence: (a) is correct
A system of equations is shown below.
8x - 2y = -4
4x - y = -2
Answer:
Step-by-step explanation:
Solve this system using elimination by addition and subtraction:
Multiplying the second equation by -2 yields the modified system
8x - 2y = -4
-8x + 2y = +4
Adding these together, we get 0 + 0 = 0 (This is always true.)
There are an infinite number of solutions.
In the third quarter of 2001, the median sale price for a single-family
home in Putnam County, New York, was $259,970. A year earlier, the
price was $242,555. What was the percent increase?
Answer:
The % increase is 7.179 but see the remark I made below. What I have given and what it could be is a rounding error. Less than 2 dollars error is not much when you are calculating something for someone just to show them how to do it.
Step-by-step explanation:
242,555 * x/100 = 259,970 Multiply by 100
242,555 * x = 259970 * 100
242,555 * x = 25997000 Divide by 242555
x = 24997000/242444
x = 107.179
That's the total increase.
What you want is 7.179%
If you take 7.179% of 242,555 and add it onto 242555 you should get 259,970
7.1797/100 * 242555 = 17413.02
17413.02 + 242555 = 259968.02
Why isn't it exact. I'm out just about 2 whole dollars. The reason is that the % isn't exact. It's only out to 3 decimal places which apparently is not enough. You can go over my numbers if you want more exactness us use something that is rounded to 7.180 if you like.
Consider the functions below. f(x)=|x+2| AND g(x)=x+8
Which of the following is the solution to f(x)=g(x) ?
A. (-5,3)
B. (-3,1)
C. (-2,-8)
D. (0,8)
What’s the answer for NLK?
Answer:
180 degrees
Step-by-step explanation:
because NJK adds up to 180 degrees and a circle is 360 degrees. Hope this helped :)
PLEASE HELP! Whoever solves it first gets Brainliest!
Answer:
There mistake was on step three because 5 x 5 is 25 and the answer he got was 80.
Step-by-step explanation:
Solve the system of equations using elimination
10x−3y−81=0
−5x−7y−19=0
x = ?
y = ?
Answer: i took a screen shot not sure if that is what you need but i hope it helps
Step-by-step explanation:
If right pleas make brainly
Question 7: Find the value of x.
Help
Answer:
x+50°=180°{alternate enterior angle}
x=180-50
x=130°
hope it helps ....
Base your answer on Betty is thinking of two consecutive integers whose sum is 41.
What is the value of the larger integer?
Answer:
let the numbers be, x and x+1 ( as it is consecutive number the next number will have 1 more than the number )
sum = 41
so, x + ( x + 1 ) = 41
x + x + 1 = 41
2x + 1 = 41
2x = 41 -1 = 40
2x = 40
x = 40/2 = 20
x = 20
x + 1 = 20 + 1 = 21
so the consecutive numbers whose sum is 40 are, 20 and 21
hope this answer helps you.....
please mark as brainliest... thank you!
Please help I beg like right now and explain peae
Answer and Step-by-step explanation:
When we take a look at the graph, we can see that at around 1 gallon, which would be halfway between 0 and 2, the line is underneath $5.
That means we can eliminate any number that is or above $5.
That leaves us with answer choices A and C.
Let's go to a point that is easily readable. Point (4, 15) is readable, and we can use this to find the price per gallon.
Divide 15 by 4. We get 3.75 as the result.
This means that the answer choice is:
C. The cost of gas is $3.75 per gallon.
#teamtrees #PAW (Plant And Water)
David has a monthly after-tax income of $ 1430.15 1430.15 . He will be using the companies health insurance plan which costs $ 63 63 a monthand the retirement option which takes 7 7 % of his after tax income. Calculate David's Monthly Take-Home pay.
Answer:
$ 1267.
Step-by-step explanation:
Given :
David's monthly income after tax = $ 1430.15
His health insurance cost him in a month = $ 63
Percent deducted from his income after tax for his retirement option is = 7%
Therefore money left after retirement option deduction is :
$ 1430.15 - 7% of $ 1430.15
= 1430.15 - 100.11
= $ 1330.04
= $ 1330 (aprrox)
Money deducted from this amount for his health insurance plan
= $ 1330 - $ 63
= $ 1267
Therefore, David's monthly take home pay is $ 1267.
Help would be gradually appreciated
Answer:
area is 60.75 m^2
Step-by-step explanation:
A group of students was asked about the number of e-mails they each sent that day. The results are: 0,0,0,0,1,2,2,3,5,5, 8, 9, 10, 10, 10 Which histogram correctly shows the data set?
Answer:
Step-by-step explanation: I don’t know I’m sorry
Answer:
is the photo
Because I had that question
Find the area of the blue shaded region.
10 m
8 m
18 m
20 m
A 144 m2
B 200 m2
C 56 m2
D 344 m2
Answer:
56
Step-by-step explanation:
area of whole figure=
l×b
=20×10
=200
also,area of small fig.
=l×b
=18×8
=144
thus area of shaded part =a of whole- a of small
=200-144
=56
Can you guys help me solve this
PLEASE HELP!!!!!!!!!!!
Solve each equation:
a. x+3+3x=x+15
b. 3x+5=-3x+5x+10
c. n+n+3n=15
Answer:
A. X=4
B. X=5
C. N=3
Step-by-step explanation: Hope this help :D
12 1/2 - (-4 1/2) = ?
Answer:
17
Step-by-step explanation:
12 1/2-(-4 1/2)
12 1/2+ 4 1/2
17
What is an equation of the line that passes through the points (0,0) and (5,2)
Answer:
y = 2/5x
Step-by-step explanation:
slope = 2-0/5-0 = 2/5
y - 2 = 2/5(x - 5)
y = 2/5x
2. 64 oz = ? lb
A. 2 lb
B. 4 lb
C. 8 lb
D. 128 lb
Answer: b) 4lb
Step-by-step explanation:
Answer:Your answer is B
Step-by-step explanation:
64 oz is= to 4 lb
Help, please!! I really need a correct answer, please don't answer to get points. :(
Answer:
Multiyply all 3 numbers to get your answer.
Step-by-step explanation:
4.5*2*2
Answer: 1st one is 18
second one is 44
Step-by-step explanation:
2*2*4.5=18
A=2(wl+hl+hw)=2·(2·4.5+2·4.5+2·2)=44
Solve the following quadratic equation for all values of xx in simplest form.
5(x^2-4)+10=10
Mrs. Young passed out 7 pipe cleaners to each of the 32 students in her class. When she was finished passing them out, she had 26 pipe cleaners left over. How many pipe cleaners did she start with?
Answer:
250
Step-by-step explanation:
32(7) + 26 = 224 + 26
For the school play, tickets cost $9.50 for adults and $3 for kids under 12. What
would be the total cost for 8 adult tickets and 21 kids tickets? What would be the total
cost for a adult tickets and k kids tickets?
Answer:
250 $3 tickets and 100 $2 tickets were sold
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
Answer:
so how many units are they away from each other
Step-by-step explanation:1,
1.1-2.0 how many units are they away from each other
u could drag the number from the top to the chart below
good luck!
A toy store’s percentage of markup is 25%. A modeltrain costs the store $120. Find themarkup.
a.$120 b. $30c. $90 d. $150
(pls help)
Please answer correctly
Answer:
answer correctly definition.
Step-by-step explanation:
When something is correct, it is right or accurate. The correct answer to a problem is the right answer, so if you answered to a problem right, you answered it correctly.
what is the question for this?
let me know so i can help!
Answer? please i really need help
On Tuesday Jack bought four boxes. On Wednesday half of all the boxes that he had were destroyed. Write an expression for how many boxes Jack has now.
this was the question it got deleted I just need 1,2,5
Answer:
1. The volume of the cylinder is 263 [tex]cm^{3}[/tex].
2. The volume of the cylinder is 12 [tex]m^{3}[/tex].
3. The volume of the cylinder is 3165.1 [tex]cm^{3}[/tex].
4. The radius of the cylinder is 3.6 cm.
5a. Area of the base is 50.2 [tex]cm^{2}[/tex].
5b. The curved surface area of the pencil holder is 351.7 [tex]cm^{2}[/tex].
5c. The surface are of the pencil holder is 452.2 [tex]cm^{2}[/tex].
Step-by-step explanation:
1. The given shape is a cylinder, so that;
volume of a cylinder = [tex]\pi[/tex][tex]r^{2}[/tex]h
= 3.14 x [tex](3.8)^{2}[/tex] x 5.8
= 262.98128
The volume of the cylinder is 263 [tex]cm^{3}[/tex].
2. This is also a cylinder, but with a given diameter.
radius = [tex]\frac{diameter}{2}[/tex]
= [tex]\frac{1.2}{2}[/tex] = 0.6 m
volume of a cylinder = [tex]\pi[/tex][tex]r^{2}[/tex]h
= 3.14 x [tex](0.6)^{2}[/tex] x 10.6
= 11.98224
The volume of the cylinder is 12 [tex]m^{3}[/tex].
3. volume of a cylinder = [tex]\pi[/tex][tex]r^{2}[/tex]h
= 3.14 x [tex]6^{2}[/tex] x 28
= 3165.12
The volume of the cylinder is 3165.1 [tex]cm^{3}[/tex].
4. volume of a cylinder = [tex]\pi[/tex][tex]r^{2}[/tex]h
239 = 3.14 x [tex]r^{2}[/tex] x 6
239 = 18.84 [tex]r^{2}[/tex]
[tex]r^{2}[/tex] = [tex]\frac{239}{18.84}[/tex]
= 12.6858
r = [tex]\sqrt{12.6858}[/tex]
= 3.5617
The radius of the cylinder is 3.6 cm.
5. Area of the base = [tex]\pi[/tex][tex]r^{2}[/tex]
radius = [tex]\frac{diameter}{2}[/tex]
= [tex]\frac{8}{2}[/tex] = 4 cm
Area of the base = 3.14 x [tex]4^{2}[/tex]
= 50.24
Area of the base is 50.2 [tex]cm^{2}[/tex].
5b. Area of the curved surface of the pencil holder = 2[tex]\pi[/tex]rh
= 2 x 3.14 x 4 x 14
= 351.68
The curved surface area of the pencil holder is 351.7 [tex]cm^{2}[/tex].
5c. Surface area of the pencil holder = 2[tex]\pi[/tex]rh + 2[tex]\pi[/tex][tex]r^{2}[/tex]
= 2[tex]\pi[/tex]r(h + r)
= 2 x 3.14 x 4 (14 + 4)
= 452.16
The surface are of the pencil holder is 452.2 [tex]cm^{2}[/tex].