Complete question is;
The polynomial -16t² + v_o(t) + s_o represents the height (in feet) of an object, where v_o is the initial vertical
velocity (in feet per second), s_o is the initial height of the object (in feet), and t is the time in seconds. Write a polynomial that represents the height of the object that has an initial velocity of 25 ft/s and initial height of 4ft. Then find the height of the object after 1 second.
Answer:
A) Polynomial is h(t) = -16t² + 25t+ 4
B) h(1) = 13 ft
Step-by-step explanation:
A) We are given;
h = -16t² + v_o(t) + s_o
Where;
v_o = the initial vertical velocity
s_o = the initial height of the object
t = the time
We are given;
v_o = 25 ft/s
s_o = 4 ft
Thus, polynomial that represents the height is;
h(t) = -16t² + 25t+ 4
B) after a time of 1 second, height is;
h(1) = -16(1²) + 25(1) + 4
h(1) = -16 + 25 + 4
h(1) = 13 ft
HELP ASAPPPPP! I WILL GIVE BRAINLEST
The two numbers have 1 as a common factor and nothing else. Hence 1 is the HCF. This proves that the HCF of any two consecutive numbers is always a one.
Two integers are relatively prime (or coprime) if there is no integer greater than one that divides them both (that is, their greatest common divisor is one). For example, 12 and 13 are relatively prime, but 12 and 14 are not.
Which is larger 64 inches or 5 feet
Answer:
64 inches
Step-by-step explanation:
There are 12 inches in a foot
12 x 5 is 60
64 is greater then 60
C=2πr
Diameter is 10
You can get 6 tickets for $39 at the local movie theater. How much is each ticket?
Answer:
$6.50
Step-by-step explanation:
39 / 6 = 6.5
Answer:
$6.50
Step-by-step explanation:
Hi,
To get the cost per ticket, all you have to do is divide 39 by 6. When you do that you get, 6.5 which means each ticket costs $6.50.
I hope that helps :)
Order the angle measures from least to greatest
help please
Answer:
m<B, m<C, m<A
Step-by-step explanation:
The length of sides and angle measures correspond. This means the angle opposite to the longest side is the largest, etc. The shortest side is AC, which is the opposite of <B, making it the smallest. Then, the same logic can be applied to <C which is the middle, and <A which is the largest. Therefore, from least to greatest the angles are m<B, m<C, m<A.
Find x to the nearest tenth
Answer:
x=30.6
Step-by-step explanation:
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!1111 I REALLY NEED HELP I A, BEGGIN YOU GUYS!!!!!!!!!!!!!!!!!!!!!!!!!!! ILL GIVE BRAINLIEST AND EXTRA POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
4y - 2(5 - y + 4) = 4y - 2(9 - y)
= 4y + 9*(-2) - y *(-2)
= 4y - 18 + 2y {Combine like terms 4y and 2y}
= 6y - 18
6y - 18 = 6*y - 6*3
= 6(y - 3)
6y- 18 = 2 *3y - 2*9
= 2(3y -9)
2(3y - 9) and 6(y- 3 ) are equivalent to 4y - 2(5- y +4)
Others are not equivalent
The first bus stop on a bus route is 4 miles from school. How many yards is the first bus stop from school?
Answer:
7040 yards
Step-by-step explanation:
1 mile = 1760 yards
1 x 4 miles = 1760 x 4 yards
4 miles = 7040 yards
SOMEONE PLSS HELP ME, THIS IS DUE TODAY (I WILL GIVE BRAINLIEST)
A) less than -5
B) less than or equal to -5
C) greater than -5
D) greater than or equal to -5
Answer:
A
Step-by-step explanation:
Answer:
A) less than -5
Step-by-step explanation:
If it is lesser than -5, that means the line will be going to the left. This also means that the circle will be an open circle, not shaded.
Pls I neeed help very hard
Answer:
96 ft
Step-by-step explanation:
Well add the given numbers up and calculate unkown sides using given measurments
What number is 15 less than 63?
Answer:
48
Step-by-step explanation:
Answer:
48
Step-by-step explanation:
A beach umbrella has a circumference of 8.8 feet what is the radius of an umbrella?
Answer:
radius = 1.4
Step-by-step explanation:
The formula for circumference is as follows:
[tex]C = d\pi[/tex]
or
[tex]C = 2r\pi[/tex]
However, these formulas are the same, because the diameter is equal to the radius times 2. I prefer to use the first (it gives you less values to work with).
Anyhow, We would substitute like this:
[tex]8.8 = d\pi[/tex]
We know that pi, is going to be equal to: 3.14159
So we work from there...
[tex]8.8=d(3.14159)\\2.8011=d[/tex]
Diameter divided by 2 would be the radius, and thats:
1.4006
or 1.4
Solve for x. -4.5 = -0.5(x – 7.1)
Answer:
16.1
Step-by-step explanation:
Answer:
I believe the answer is x = 16.1
Step-by-step explanation:
Quinn correctly answered 72 questions on a test, getting a score of 80%. How many questions were on the test?
Answer:
90
Step-by-step explanation:
What is the square root of 460
Answer:
21.4476105895
Step-by-step explanation:
Using a calculator [tex]\sqrt{460\\}[/tex]
Answer:
approximately 21.448 or 2 times the square root of 115
Step-by-step explanation:
PLEASEEEEEE HELPPPPPPPPPP MEEEEEEEEEEEEEEEE
Answer:
120.2 or in other words, the answer is the last option, D
what are irrational numbers
Answer:
hi
Step-by-step explanation:
Irrational numbers are numbers that cannot be expressed as the ratio of two whole numbers.
7,653 to nearest hundreds
Jonathan took 33 pictures on the class trip and 67
pictures on field day. He gave 12 pictures to his friends.
He wants to put the remaining photos in a photo album.
Each page in the album can hold 6 pictures. How many
pages is he going to need so that all the remaining
pictures fit in the album?
Answer:
JONATHAN WILL NEED 14 PAGES.
Explanation:
33 + 67 = 100
100 - 12 = 88
88 ÷ 6 = 14.6666667
14.6666667 ⇒ 14
(Round 14.6666667 down to 14 because Johnathan does not have .6666667 of a page.)
Can someone help me with this please ?
I really need help plsss!!!
Answer:
(a)
[tex]f(x) = \left \{ {{5x;\ 0<x\le 5} \atop {5x-5; x > 5}} \right.[/tex]
(b) Rate = 5
(c) Rate = 5
Step-by-step explanation:
Given
The attached graph
Solving (a): The piece-wise function
For the first line
Calculate the slope of the first line
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where
[tex](x_1,y_1) = (0,0)[/tex]
[tex](x_2,y_2) = (5,25)[/tex]
So, the slope is:
[tex]m = \frac{25 - 0}{5 - 0}[/tex]
[tex]m = \frac{25}{5}[/tex]
[tex]m = 5[/tex]
The equation is then calculated as:
[tex]y = m(x - x_1) + y_1[/tex]
Where: [tex]m = 5[/tex] and [tex](x_1,y_1) = (0,0)[/tex]
[tex]y = 5(x - 0) + 0[/tex]
[tex]y = 5(x) + 0[/tex]
[tex]y = 5x[/tex]
So, the function of the first line is:
[tex]f(x) = 5x;\ 0 < x \le 5[/tex]
For the second line
Calculate the slope of the second line
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where
[tex](x_1,y_1) = (5,20)[/tex]
[tex](x_2,y_2) = (9,40)[/tex]
So, the slope is:
[tex]m = \frac{40 - 20}{9 - 5}[/tex]
[tex]m = \frac{20}{4}[/tex]
[tex]m = 5[/tex]
The equation is then calculated as:
[tex]y = m(x - x_1) + y_1[/tex]
Where: [tex]m = 5[/tex] and [tex](x_1,y_1) = (5,20)[/tex]
[tex]y = 5(x - 5) + 20[/tex]
[tex]y = 5x - 25 + 20[/tex]
[tex]y = 5x -5[/tex]
So, the function of the second line is:
[tex]f(x) = 5x -5;\ x>5[/tex]
Hence, the piece-wise function is:
[tex]f(x) = \left \{ {{5x;\ 0<x\le 5} \atop {5x-5; x > 5}} \right.[/tex]
Solving (b): The rate at which customers that buy up to 5lb buy.
[tex]x = 5[/tex]
This question implies that, we determine the rate at which this customer buys.
For [tex]x = 5[/tex]
[tex]f(x) = 5x;\ 0 < x \le 5[/tex]
The slope of the above function is 5.
So, this customer buys at the rate of $5 per lb
Solving (b): The rate at which customers that buy more than 5lb buy the extra pounds above 5lb.
For [tex]x > 5[/tex]
[tex]f(x) = 5x -5;\ x>5[/tex]
Assume x = 6
[tex]f(6) = 5 * 6 - 5[/tex]
[tex]f(6) = 30 - 5[/tex]
[tex]f(6) = 25[/tex]
Express as 20 + 5
[tex]f(6) = 20 + 5 * 1[/tex]
Assume x = 7
[tex]f(7) = 5 * 7 - 5[/tex]
[tex]f(7) = 35 - 5[/tex]
[tex]f(7) = 30[/tex]
[tex]f(7) = 20 + 10[/tex]
Express 10 as 5 * 2
[tex]f(7) = 20 + 5 * 2[/tex]
So, we have:
[tex]f(6) = 20 + 5 * 1[/tex]
[tex]f(7) = 20 + 5 * 2[/tex]
This can be generalized as:
[tex]f(x) = 20 + 5(x - 5)[/tex]
For the above functions;
20 represents the amount they buy the first 5
5 represents the rate at which they buy extra pounds above 5
Hence, they buy the extra pounds at the rate of $5 per pound
5(a-b), if a= -4, b =-2
Answer:
-10
Step-by-step explanation:
a= -4
b = -2
5(a-b)
5( -4 - (-2))
5( -4 + 2)
5(-2)
-10
NEED HELP ASAP PLEASE HELP I NEED HELP! :/
Answer:
130 square feet
Step-by-step explanation:
Can someone help me with these two questions
PLEASE HELP ME!! A: Given that the triangles are similar, find the length of side KL
The life in hours of a biomedical device under development in the laboratory is known to be approximately normally distributed. A random sample of 15 devices is selected and found to have an average life of 5625.1 hours and a sample standard deviation of 226.1 hours.
(a) Test the hypothesis that the true mean life of a biomedical device is greater than 5500 using the P-value approach.
(b) Construct a 95% lower confidence bound on the mean.
(c) Use the confidence bound found in part (b) to test the hypothesis
Answer:
Kindly check explanation
Step-by-step explanation:
H0 : μ = 5500
H1 : μ > 5500
The test statistic assume normal distribution :
Test statistic :
(Xbar - μ) ÷ s/sqrt(n)
(5625.1 - 5500) ÷ 226.1/sqrt(15) = 2.1429 = 2.143
Pvalue from test statistic :
The Pvalue obtained using the calculator at df = 15 - 1 = 14 is 0.025083
α = 0.05
Since ;
Pvalue < α
0.025083 < 0.05 ; Reject H0
The confidence interval :
Xbar ± Tcritical * s/sqrt(n)
Tcritical at 95% = 1.761 ;
margin of error = 1.761 * 226.1/sqrt(15) = 102.805
Lower boundary : (5625.1 - 102.805) = 5522.295
(5522.295 ; ∞)
The hypothesized mean does not occur within the constructed confidence boundary. HENCE, there is significant eveidbce to support the claim that the true mean life of a biomedical device is greater than 5500
What is the value of x in centimeters?
Answer:
2.5 cm
Step-by-step explanation:
Since the triangles are similar, we can use ratios to solve
AC BC
-------- = ---------
FH GH
12 15
-------- = ---------
18 x
Using cross products
12x = 15*18
Divide each side by 12
12x/12 = 15*18/12
x = 2.5
The average home in the U.S. is expected to cost $240,000. A random sample of 65 homes sold this month showed an average price of $232,000. Assume that you have access to this data. We are interested in determining if the cost of the average home has decreased this month. If the test statistic is -1.79, what is the p-value
Solution :
It is given that we have a null and an alternative hypothesis. The hypothesis are :
[tex]$H_0: \mu = 240,000$[/tex]
[tex]$H_a : \mu < 240,000$[/tex]
We have to find if the cost of average home has decreased or not in this month.
So it is given that the test statics is -1.79, so the p value associated with the test statics is less than ( α ) 0.01
Therefore, we can conclude that the cost of the average house is less than $ 240,000.
What is one strength that Percy shows in chapter 3
What is one weakness that Percy shows in chapter 3
please answer both questions above correctly please im giving brainliest to the fastest and correct answer
Answer:
Percy’s strengths is his loyalty to his friend. When he was in danger, he could have escaped and saved his own life. But he showed loyalty by choosing to stay and fight to help his friend. He says, “… there was Grover, needing my help.” Percy’s only weakness in this section is becoming frozen by his fear. When his mother tells him to run, he can’t. The text says, “But I just stood there, frozen in fear, as the monster charged her.”
Step-by-step explanation:
which of the following piecewise graphs is not a function
Answer:
The first graph is not a function because it has two values at x = 3. Definition of a function is that it is a relation that assigns exactly one value for each value on its domain