The function (1) describes the height, in feet, of an object at time, in seconds, when it is launched upward from the ground at an initial speed of 112 feet per second.
a. Find the domain.
b. What does the domain mean in this context?
Answers
Answer:
see below
Step-by-step explanation:
The domain is the values that the input takes
The values go from 0 to 7
0≤x≤7
This is the time from the initial launch until the object hits the ground
Related Questions
A box contains a yellow ball, an orange ball, a green ball, and a blue ball. Billy randomly selects 4 balls from the box (with replacement). What is the expected value for the number of distinct colored balls Billy will select?
Answers
Answer:
[tex]Expected = 0.09375[/tex]
Step-by-step explanation:
Given
[tex]Balls = 4[/tex]
[tex]n = 4[/tex] --- selection
Required
The expected distinct colored balls
The probability of selecting one of the 4 balls is:
[tex]P = \frac{1}{4}[/tex]
The probability of selecting different balls in each selection is:
[tex]Pr = (\frac{1}{4})^n[/tex]
Substitute 4 for n
[tex]Pr = (\frac{1}{4})^4[/tex]
[tex]Pr = \frac{1}{256}[/tex]
The number of arrangement of the 4 balls is:
[tex]Arrangement = 4![/tex]
So, we have:
[tex]Arrangement = 4*3*2*1[/tex]
[tex]Arrangement = 24[/tex]
The expected number of distinct color is:
[tex]Expected = Arrangement * Pr[/tex]
[tex]Expected = 24 * \frac{1}{256}[/tex]
[tex]Expected = \frac{3}{32}[/tex]
[tex]Expected = 0.09375[/tex]
A person walks away from a pulley pulling a rope slung over it. The rope is being held at a height 10 feet below the pulley. Suppose that the weight at the opposite end of the rope is rising at 4 feet per second. At what rate is the person walking when s/he is 20 feet from being directly under the pulley
Answers
The image of this question is missing and so i have attached it.
Answer:
dd/dt = 4.47 ft/s
Step-by-step explanation:
From the image attached, let's denote the following;
d = horizontal distance beneath pulley
h = height of pulley
l = diagonal from the pulley to the head of the person
v = velocity of rope rising
Using pythagoras theorem;
l² = d² + h²
Differentiating with respect to time and considering h = c^(te) gives;
2l(dl/dt) = 2d(dd/dt)
We are given;
d = 20 ft
h = 10 ft
v = 4 ft/s
We know that velocity in this case is change in diagonal distance with time. Thus;
v = dl/dt = 4 ft/s
From earlier, we saw that;
2l(dl/dt) = 2d(dd/dt)
Thus, reducing it gives
(dl/dt)(l/d) = dd/dt
Now, l² = d² + h²
l = √(d² + h²)
Also, v = dl/dt = 4
Thus;
4(√(d² + h²))/d = dd/dt
4(√(20² + 10²))/20 = dd/dt
dd/dt = 4.47 ft/s
Guys please help me solve this I’m struggling
Answers
Answer:
[tex]Max\ z = 1[/tex]
[tex]Min\ z = -9[/tex]
Step-by-step explanation:
Given
[tex]z = 4x + 5y[/tex]
[tex]x \ge -1[/tex]
[tex]y \le 2x +3[/tex]
[tex]y \le -1[/tex]
Required
The maximum and minimum of z
To do this, we make use of the graphical method
See attachment for graphs of
[tex]x \ge -1[/tex]
[tex]y \le 2x +3[/tex]
[tex]y \le -1[/tex]
The corner points of the function are:
[tex](x,y) = (-1,1)[/tex]
[tex](x,y) = (-1,0)[/tex]
[tex](x,y) = (-1,-1)[/tex]
We have:
[tex]z = 4x + 5y[/tex]
Calculate z with the above values
[tex]z = 4(-1) + 5(1) = 1[/tex]
[tex]z = 4(-1) + 5(0) = -4[/tex]
[tex]z = 4(-1) + 5(-1) = -9[/tex]
So, we have:
[tex]Max\ z = 1[/tex]
[tex]Min\ z = -9[/tex]
Please help i do not understand this question!
Answers
Answer:
Distributive property
Step-by-step explanation:
The rule being shown here is the distributive property, because the first binomial is taken apart and separately multiplied with the other binomial.
A chef mix his salt and pepper. If he put 2/3 cup of salt and 1/2 cup of pepper in his shaker, what is the ratio of salt to pepper ?
Answers
Answer:
4 to 3
Step-by-step explanation:
The ratio of salt to pepper is
2/3 to 1/2
Multiply both fractions by 6
6 * 2/3 to 6 * 1/2
4 to 3
20) solve:
[tex] {8}^{2} + 2 = [/tex]
21) solve:
[tex]4(2x + 5y = [/tex]
22) simplify the expression
[tex]4( {2}^{2} + 30) - 4 = [/tex]
Answers
Ques21. 8x+20y
Ques22. 132
You order CDs for $14.25 each and the website charges $4.50 for each shipment.
The expression $14.25p + $4.50 represents the cost of p CDs. Find the total cost for
ordering 4 CDs.
Answers
Answer:
$61.50
Step-by-step explanation:
14.25(4) + 4.50
= 57.00 + 4.50
= 61.50
help me please !! find the domain and range of the function represented by the graph. determine wether the domain is discrete or continuous.
Answers
Answer:
Domain is the whole R and the range is R+. The domain is continuous
Match the answers……………..
Answers
9 in 8956 = 900
9 in 95675 = 90000
9 = 9 in 124569
9 in 68795 = 90
90000 = 9 in 2549652.........
hope it helps...
Independent Practice
Find the first, fourth, and eighth terms of the sequence.
an=0.5 · 3n−1a subscript n baseline equals 0.5 times 3 superscript n minus 1 baseline
A.
0.667; 4.5; 364.5
B.
3; 0.375; 0.0234375
C.
0.5; 13.5; 1093.5
D.
0.5; 121.5; 280.5
Answers
Answer:
C.
0.5; 13.5; 1093.5
Step-by-step explanation:
#What is the value of the discriminant for the quadratic equation –3 = –x2 + 2x?
Discriminant = b2 – 4ac
–8
4
8
16
Answers
Answer:
16
Step-by-step explanation:
the quadratic equation –3 = –x2 + 2x can be changed into :
x²-2x-3= 0
a=1, b= -2 , and c = -3
so, the discriminant = (-2)²-4(1)(-3)
= 4 + 12 = 16
A plank 6m long leans against a vertical wall so that the foot of the plank is 4m away from the wall. A lizard climbs 2m up the plank. Calculate the horizontal distance between the lizard and the wall.
Answers
Answer: [tex]\dfrac{8}{3}\ m[/tex]
Step-by-step explanation:
Given
Length of the plank is [tex]6\ m[/tex]
Foot of the flank is [tex]4\ m[/tex] away from the wall
Lizard climbs 2 m up the wall
from the figure, the two triangles are similar
[tex]\therefore \dfrac{2}{6}=\dfrac{x}{4}\\\\\Rightarrow x=4\times \dfrac{2}{6}\\\\\Rightarrow x=\dfrac{4}{3}\ m[/tex]
So, the distance from the wall is
[tex]\Rightarrow 4-x\\\\\Rightarrow 4-\dfrac{4}{3}\\\\\Rightarrow \dfrac{8}{3}\ m[/tex]
The 12th term of the arithmetic sequence is 10.5. The 18th term of this sequence is 13.5. Find the common difference and the first term.
Answers
let the n'th term be called x, and the value of the term y,
then there is a function y=a*x + b
that will give us all term we want.
this formula is also used for straight lines.
we just need a and b. we already got two data points. we can just plug the known x/y pairs into the formula
10.5 = a*12 + b
13.5 = a*18 + b
now lets manipulate these lines.
multiply the first line by 3 and the second line by 2
31.5 = a*36 + 3b
27 = a*36 + 2b
subtract the second line from the first line
4.5 = b
yey, we now know b, let's plus b into either line from above, I'll go with the first one, looks easier.
10.5 = a*12 + 4.5
6 = a*12
0.5 = a
now y=a*x + b can be filled with a and b
y = 0.5 * x + 4.5
for x=1 (the first term) it's f(1)=5
each step is 0.5, hence the common difference.
2and way:(13.5-10.5)/(18-12)
= 3 / 6
= 0.5
we got the comment difference by looking at the full difference over 6 steps and divined by these 6 steps.
from step 12 to step one it's 11 steps down
10.5 - 0.5*11
= 10.5 - 5.5
= 5
okay I admit... 2and way to do it might be faster and more intuitive... :DValue of the boat after 3 years?
Answers
after each year it's 83% of it's value from last year (100%-17%=83%)
the function in 19000 * (0.83) ^x
3 will be filled in for x
19000 * (0.83) ^3= 10863.953
$10863.95
Answer:
$10,863.95
Step-by-step explanation:
y = 19,000[tex](.83)^{t}[/tex]
y = 19,000[tex](.83)^{3}[/tex]
y =$10,863.95
if f(x) = 2x²+2x-1, g(x) = x²+5x+2 f(x)=g(x), find the value of x
Answers
Answer:
Possible Answers: –5. –21. 7. –1
Answer:
just put the values and simpilyfy it untill you get the value of X
hence, the value of X is either 3 or, -1
working alone, aliyah can dig a 10ft by 10 ft hole is 6 hours. one day her friend eugene helped her and it only took 3.75 hours. how long would it take eugene to do it alone? disclaimer: the answer is 11.95 hours, but i keep getting 10. please use the 1/x+1/y=1/z strategy
Answers
Answer:
I think the answer is 10 hours
the 11.95 seems wrong
Step-by-step explanation:
[tex]\frac{1}{6} + \frac{1}{y} = \frac{1}{3.75}[/tex]
multiply by 22.5 y
3.75 y + 22.5 = 6y
y = 10
Help anyone can help me do the question,I will mark brainlest.
Answers
Answer:
a) 30
b)600pi
Step-by-step explanation:
For the first questions, since the arc is 240°, the area of the sector and circumference will be 240/360 or 2/3 of the total of the circles'. Therefore 125.6 x 3/2 is the circumference, which is 188.4. When we divide this by 6.28, we get 30
Now, since the area is pi r^2 where we know that r=30, we get 900pi as the area of the whole thing, however since the sector is 2/3 of the whole circle, 2/3 x 900pi = 600pi
Pls help me ! L need help here
Answers
Answer:
H. 40 inches
Step-by-step explanation:
On Wednesday, he is 40 inches taller. ... That would make 5 days of growth, for 100 inches. But this is only 3 days therefore he would grow 40 inches taller
Write down at least five number pairs to solve the equation vw = 50
Answers
Answer:
1, 50
2, 25
5, 10
10, 5
25, 2
Answer:
Step-by-step explanation:
V W
1 x 50 = 50
1.5 x 33 1/3 = 50
2 x 25 = 50
2.5 x 20 = 50
3 x 16 2/3 = 50
3.5 x 14 2/7 = 50
4 x 12 1/2 = 50
4.5 x 11 1/9 = 50
5 x 10 = 50
5.5 x 9 = 50
6 x 8 1/3 = 50
6.5 x 7 2/3 = 50
7 x 7 1/7 = 50
7.5 x 6 2/3 = 50
8 x 6 1/4 = 50
8.5 x 5 8/9 = 50
9 x 5 5/9 = 50
9.5 x 5 1/4 = 50
10 x 5 = 50
10.5 x 4 3/4 = 50
11 x 4 5/9 = 50
11.5 x 4 1/3 = 50
12 x 4 1/6 = 50
12.5 x 4 = 50
13 x 3 6/7 = 50
13.5 x 3 5/7 = 50
14 x 3 4/7 = 50
Use the Diagram to find BC.
Answers
Answer:
Step-by-step explanation: you have to ask your parents for help
The bar graph shows the median income for families in the United States from 1993 through 2000.
Which two consecutive years saw the largest increase in median income?
A. 1994–1995
B. 1997–1998
C. 1998–1999
D. 1999–2000
Answers
The two consecutive years in which there is the largest increase in the median income is option B i.e. 1997-1998.
Given that
In 1994-1995, the median income is 37,500 and 38,500.In 1997-1998, the median income is 39,700 and 41,000.In 1998-1999, the median income is 41,000 and 42,200.In 1999-2000, the median income is 42,500 and its less.So after analysis, we can conclude that The two consecutive years in which there is the largest increase in the median income is option B i.e. 1997-1998.
Learn more about the bar graph here: brainly.com/question/14894834
Find a 2-digit number smaller than 50, the sum of whose digits does not change after being multiplied by a number greater than 1
Answers
The only 2-digit number that is lesser than 50 and the sum of its digits remain unaffected despite being multiplied by a number < 1 would be '18.'
To prove, we will look at some situations:
If we add up the two digits of 18. We get,
[tex]1 + 8 = 9[/tex]
And we multiply 18 by 2 which is greater than 1. We get,
[tex]18[/tex] × [tex]2 = 36[/tex]
The sum remains the same i.e. [tex]3 + 6 = 9[/tex]
Similarly,
If 18 is multiplied to 3(greater than 1), the sum of the two digits comprising the number still remains the same;
[tex]18[/tex] × [tex]3 = 54[/tex]
where (5 + 4 = 9)
Once more,
Even if 18 is multiplied to 4 or 5(greater than 1), the sum of its digits will still be 9.
[tex]18[/tex] × [tex]4 = 72[/tex]
[tex](7 + 2 = 9)[/tex]
[tex]18[/tex] × [tex]5 = 90[/tex]
[tex](9 + 0 = 9)[/tex]
Thus, 18 is the answer.
Learn more about 'numbers' here: brainly.com/question/1624562
What is (0,6] n (6,8]?
Answers
Answer:
(6) the letter n : intersection which means the number you will find at the first bracket and has the same number at the other bracket
indentify the explicit function for the sequence in the table
Answers
Answer:
Option B
a(n) = 8 + (n-1) • 6
Answered by GAUTHMATH
A game involves correctly choosing the 5 correct numbers from 1 through 18 that are randomly drawn. What is the probability that a person wins the game, if they enter a) once? b) 7 times with a different choice each time?
Answers
Answer:
[tex]=\frac{1}{8568}\ = .00011\\\ =\frac{7}{8568} = .00081[/tex]
Step-by-step explanation:
[tex]5/18\cdot \:4/17\cdot \:3/16\cdot \:2/15\cdot \:1/14=\frac{1}{8568}[/tex]
What is the volume?
9 ft
4 ft
2 ft
HELPPPP
Answers
Answer:
72?
Step-by-step explanation:
V=whl=4 x 2 x9=72
72 cubic feet
Step-by-step explanation:
*this formula doesn’t work for all shapes*
Volume = length x width x height
Volume = 4 x 2 x 9
Volume = 72 cubic feet
3 different problems.
solve b - 4 = 3.
solve -32 = 8w
solve n
— = -4
7
Answers
Answer:
see below
Step-by-step explanation:
b - 4 = 3
Add 4 to each side
b - 4+4 = 3+4
b = 7
-32 = 8w
Divide by 8
-32/8 = 8w/8
-4 = w
n/7 = -4
Multiply by 7 to each side
n/7 *7 = -4*7
n = -28
1. b = 7
2. w = -4
3. n = -28
Step-by-step explanation:
1. b - 4 = 3
Tip: Whenever there’s a number being subtracted or added, it’s best to make that number a 0
Step 1. Add 4 to both sides
b - 4 = 3
b + 4 = +4
b = 7
—————————————
2. -32 = 8w
Step 1. Isolate the variable
(by dividing both sides by 8)
w = -32/8
w = -4
—————————————
3. n/7 = -4
Step 1. Multiply 7 x -4
n = -28
Rhombus LMNO is shown with its diagonals.
Rhombus L M N O is shown. Diagonals are drawn from point L to point N and from point M to point O and intersect at point P. All sides are congruent.
Angle MNO measures 112°. What is the measure of angle LMN?
Answers
Answer:
hope this help
Step-by-step explanation:
Answer:
90
51
10
Step-by-step explanation:
given m||n, find the value of x
Answers
Answer:
x = 155º
Step-by-step explanation:
y = 25° {Vertically opposite angles}
x + y = 180 {Co-interior angles are supplementary}
x + 25 = 180
Subtract 25 from both sides
x = 180 - 25
x = 155°
In the PQRS triangle PQ=QR, QR side extended to S Show that PQ+RS=QS. -S Q R
pls explain too
Answers
Answer:
Step-by-step explanation:
from the picture:
QP = QR
and
QR = RS
so
PQ + RS = QS
