Jennifer serves the volleyball to Marsha with an upward velocity of 10.5 ft/s. The ball is 5 feet above the ground when she strikes it. How long does Marsha have to
react, before the volleyball hits the ground? Round your answer to two decimal
Answer:
0.98 seconds
Step-by-step explanation:
We assume the height of the volleyball is described by the equation for ballistic motion. We want to find the time it takes for the height to become zero.
__
motion equationThe general form of the equation of height for ballistic motion is ...
[tex]h(t)=-16t^2+v_0t+h_0\qquad\text{$v_0$ and $h_0$ are the initial velocity and height}[/tex]
The coefficient 16 in the equation is an approximation of 1/2g, where g is the acceleration due to gravity in ft/s². This means the units of time and distance are expected to be seconds and feet.
For the problem at hand, the initial velocity and height are 10.5 ft/s and 5 ft. Then the height equation is ...
h(t) = -16t² +10.5t +5
__
reaction timeMarsha has until the ball hits the ground to react to the serve. To find out how long that is, we need to solve the height equation for t when h=0. This is most easily done using the quadratic formula with ...
a = -16b = 10.5c = 5The solution is ...
[tex]t=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}= \dfrac{-10.5\pm\sqrt{10.5^2-4(-16)(5)}}{2(-16)}\\\\=\dfrac{10.5\pm\sqrt{430.25}}{32}=\dfrac{21\pm\sqrt{1721}}{64}[/tex]
The positive solution is ...
t ≈ 0.976327 ≈ 0.98
Marsha has about 0.98 seconds to react before the volleyball hits the ground.
_____
Additional comment
After about 0.33 seconds, Marsha knows she doesn't need to react at all. The serve will not clear the net. Its maximum height is about 6' 8 5/8". A women's volleyball net is 7' 4 1/8" high. Jennifer's serve velocity must be at least 12.3 ft/s for the ball to go over the net. With that upward velocity, Marsha has about 1.06 seconds to react.
How many liters each of a 24% iodine solution in a 40% iodine solution must be used to produce a total make sure of 100 L of 28% iodine solution
By weighted average, we need 75 liters of 24 % iodine solution and 25 liters of 40 % iodine solution to obtain 100 liters of 28 % iodine solution.
How to determine the volume associated with a given concentrationPhysically speaking, concentration is equal to the amount of solute divided by the volume of solution. We have two solutions with same solute and different concentration and can find the right proportion between the 24 % solution and the 40 % solution by concept of weighted average:
x · 24 + (1 - x) · 40 = 28
40 - 16 · x = 28
16 · x = 40 - 28
16 · x = 12
x = 3/4
By weighted average, we need 75 liters of 24 % iodine solution and 25 liters of 40 % iodine solution to obtain 100 liters of 28 % iodine solution.
To learn more on weighted average: https://brainly.com/question/18554478
#SPJ1
Please pick one of the options.
9880 different possibilities are there in Sally's new combination option second 9880 is correct.
What is permutation and combination?A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.
We have:
Total unique numbers consists in a Sally locker = 3
From the digits 0 to 39
Total numbers = 40
Apply combination formula:
= C(40, 3)
= 40!/(3!37!)
= 9880
Thus, 9880 different possibilities are there in Sally's new combination option second 9880 is correct.
Learn more about permutation and combination here:
https://brainly.com/question/2295036
#SPJ1
hey can someone help me on this"in your own words describe when you should use area and when you should use volume in calculating the amount of space an object occupies.
Answer:
Normally,in calculating the amount of space an object occupies...the volume method is require due to 3 dimensional rule,vice versa an area
A box has candies in it: are taffy, are peppermint, and are caramel. (Each candy falls into only one of these categories.) Brian wants to select two candies to eat for dessert. The first candy will be selected at random, and then the second candy will be selected at random from the remaining candies. What is the probability that the first candy selected is taffy and the second candy is caramel?
Do not round your intermediate computations. Round your final answer to three decimal places.
Probability that the first candy selected is taffy and the second candy is caramel is 0.144.
The data missing in the question is
A box has 18 candies in it: 3 are peppermint, 4 are caramel, and 11 are taffy.
What is Probability ?Probability can be defined as the study of likelihood of an event to happen.
It has a range of 0 to 1.
Probability is the ratio of the expected outcomes / total coutcome.
Total outcomes = 18
The probability that the first candy is taffy is 11/18
Now as there is no replacement , the total outcomes can be 17
The probability that the second candy is caramel is 4/17
Probability that the first candy selected is taffy and the second candy is caramel = (11/18)(4/17)
= 0.144
Therefore the Probability is 0.144
To know more about Probability
https://brainly.com/question/11234923
#SPJ1
15 ( y - 4 ) - 2 (y - 9 ) + 5 (y + 6) = 0
Answer:
y = 2/3
Step-by-step explanation:
Assuming you are looking for "y":
15 * ( y - 4 ) - 2 * (y - 9 ) + 5 * (y + 6) = 0
15y - 60 - 2y + 18 + 5y + 30 = 0
15y - 2y + 5y -60 + 18 + 30 = 0
18y = 60 - 18 - 30
18y = 12
y = 12/18
y = 2/3
mohjjbn bn hjbjn hjbnm
1. Solve the quadratic function by graphing. x²-3x - 18 - 0
Answer:
that's easy all you have to do is find out what is the value of x then divided by 2 once you divide by 2 subtract 3x 18 and 0
Which represents the solution(s) of this system of equations?
(4, 4)
(–4, –12)
(4, 4) and (–4, 12)
(–4, 4) and (4, 12)
The solution to the given system of equation is (4, 4)
Factorizing quadratic functionsFrom the solved steps, the final quadratic functions is given as;
x^2 - 8x + 16 = 0
Factorize to have;
x^2 - 4x - 4x + 16 = 0
x(x-4)-4(x-4) = 0
(x-4)(x-4) = 0
x = 4 and 4
Hence the solution to the given system of equation is (4, 4)
Learn more on system of equation here: https://brainly.com/question/847634
#SPJ1
a. The velocity, v, of an object is moving in a medium at time t is given by
t = √ 30² +50+2 du. Evaluate t.
+
The value of "t" in the given expression for the velocity of the object moving in the medium is t = u³ + 2.5u² + 2u.
Velocity of the object moving in the medium
The velocity of the object moving in the medium is given as;
t = ∫(3u² + 5u + 2)du
the value of t is obtained by integrating the function as follows;
t = (3u³)/3 + (5u²)/2 + 2u
t = u³ + 2.5u² + 2u
Thus, the value of "t" in the given expression for the velocity of the object moving in the medium is t = u³ + 2.5u² + 2u.
Learn more about velocity here: https://brainly.com/question/4931057
#SPJ1
Adult tickets to a basketball game cost $5. Student tickets cost $1. A total of $3,128 was collected on the sale of 1,336 tickets. How many of each type of ticket were sold?
Answer:
Adults = 448
Students = 888
Step-by-step explanation:
Write equations with info given
A = Adult tickets
S = Student tickets
5A+1S=3,128
A+S=1336
Subtract equations from each other
4A=1792
Solve for A
A=448
Plug A into second equitation
448+S=1336
Solve for S
S=888
find the slope of the lined graph
Answer:
1
Step-by-step explanation:
The points go rise:1 up:1 so the slope is 1.
Answer:
hey!! we can taIk here
Step-by-step explanation:
tn=2(n-1)
Given the formula for the nth term, state the first 5 terms of each sequence.
Answer:
0, 2, 4, 6, 8
Step-by-step explanation:
substitute 1 for n in first term, 2 for n in second term, 3 for n in third term, 4 for n in fourth term, 5 for n in fifth term
2 (1) -2 = 0 first term
2 (2)-2 = 2 second
2 (3)-2 = 4 third
2 (4)-2 =6 fourth
2 (5)-2 =8 fifth
If you help me you get a lot of points
Answer:
Step-by-step explanation:
#a
pattern 0 will include 4 reds in square
Because it's independent of pattern no
#b
Figure 1 has 4+4=8
Figure 2=4+8+2=14
Figure 3=4+12+3=19
The pattern n rule is
n²+3n+4So for 13th n
13²+3(13)+4169+39+4212squares#c
attached
y=x²+3x+4#d
Already given in c
Suppose a nuclear power plant disaster occurs. How could GDP be a "false beacon" in this case?
If there was a nuclear plant disaster, then GDP would be a false beacon because it would account for government spending but not for the pollution caused.
Why would GDP be a false beacon?Two of the components of GDP are government spending and private investment.
If there is a nuclear plant disaster, either the government will spend a lot to clean it up, or a private company will depending on if the plant is public or private.
GDP would therefore increase.
This would be a false beacon however, because this increase would not take into account the nuclear pollution that would have occurred that would negatively impact future production.
Find out more on the problems with GDP at https://brainly.com/question/13701371.
#SPJ1
Write the standard number.
3.6 * 10^-6
Answer:
The answer is 0.0000036.
Step-by-step explanation:
Move the decimal place 6 spaces to the left. I hope this helps! :)
Evaluate the expression.
Follow the steps below for the following set of data. In your final answer include all of your calculations and all work in steps 1, 2, and 3.
8, 3, 5, 5, 4, 7
Find the median, lower quartile, and upper quartile of the set of data.
Use the median, lower quartile, upper quartile, lowest value, and highest value of the set to construct a box-and-whisker plot on your own sheet of paper.
Use the box-and-whisker plot to find the range and the interquartile range of the set of data.
The answers to the question are
Median = 5Lower quartile = 4Upper quartile = 7What is the median?The median of the data set is gotten by arranging the values in order
3, 4, 5, 5, 7, 8
The median can be gotten by
5 + 5 / 2
= 10/2
Median = 5
What is the lower quartile?This is the value under which 25 percent of the data are found in the group of data. The lower quartile is 4.
What is the upper quartile?This is the point from which 75 percent of the data is found when it is in ascending order. The upper quartile is 7.
What is the lowest valueThe lowest value in the data set is 3
What is the highest valueThe highest value in the data set is 8
Read more on median here:
https://brainly.com/question/26151333
#SPJ1
Calculate the discriminant to determine the number of real roots of the equation.
y = x2 + 3x + 9
one real root
no real roots
three real roots
two real roots
find D which is the discriminant and with D < 0.
therefore the equation has an imaginary root and not a real root.
HELPP PLEASE!!!
Harry is 5 years older than his sister, and the product of their
ages is 84.
Let h represent Harry's age, then h- 5 represents his
sister's age, and h (h-5) = 84 models the situation.
The equation can also be written as h² - 5h = 84.
Rewrite the equation so that it is in the form polynomial = 0.
Enter the polynomial, in standard form, in the box.
= 0
Answer:
See below
Step-by-step explanation:
h^2 - 5h = 84
h^2 - 5h - 84 = 0
Find the area of a regular polygon with 5 sides that has a side length of 6 inches and an apothem of 9 inches.
Area = [?]in2
Answer:
see the attachment photo!
Answer: The correct answer is 135 in².
Step-by-step explanation: An area of a polygon is this:
Area = (number of sides × length of one side × apothem)/2
(5 x 6 x 9) / 2 = 135
A group of kids just finished trick-or-treating. The number of pieces of candy collected by each of the 5 kids is listed below.
31,33,36,41,34
Find the standard deviation of the data set. Round your answer to the nearest hundredth.
A bowl contains 28 black, 21 red, 23 blue, and 10 green balls
A ball is drawn at random. P (blue).
Answer:
P (blue) = 23 / 82
Step-by-step explanation:
There are 23 blue out of 82 (28 + 21 + 23 + 10 = 82) balls
or,
23 / 82
So, the probability of a blue ball being chosen is 23/82
(or a 28% chance [rounded])
A gardener has 75 clients, 45% of whom are businesses. Find the number of business clients.
Answer:
33,75 clients(huh?)
Step-by-step explanation:
75 / 100 = 0,75(1% of all clients)
0,75 * 45 = 33,75(number of business clients)
I need help ASAP PLEASE > How does the graph of f(x) = (x + 7)3 − 8 compare to the parent function g(x) = x3? (Please explain with your on words)
Answer:
The graph has been moved 7 units to the left and 8 units down.
Step-by-step explanation:
When numbers are added directly to the "x" value, the graph shifts to the left. If negative numbers are added directly to the "x" value, the grap shifts to the right. Therefore, if there is a +7 directly altering the "x" value, the function shifts 7 units to the left.
When a number is added to the overall function, it shifts upwards. If this number is negative, the entire function shifts downwards. Therefore, if there is a -8 outside altering the function, then it has been shifted 8 units down.
Solve the following radical equation.
√2x-3 =2
Answer:
First, we have to add 3 to both sides.
[tex]\sqrt{2x} - 3 + 3 = 2 + 3[/tex]
Then we simplify the equation,
[tex]\sqrt{2x} = 5[/tex]
Divide both sides of the equation by [tex]\sqrt{2}[/tex]
[tex]\frac{\sqrt{2x} }{\sqrt{2}} = \frac{5}{\sqrt{2}}[/tex]
Finally, simplify.
[tex]x = \frac{5\sqrt{2}}{2}[/tex]
Therefore, our answer is [tex]x = \frac{5\sqrt{2}}{2}[/tex]
3.5
Step-by-step explanation:
square means 1/2.so,1/2(2x-3)=(2)^2
then square cancel by square. 2x-3=4
2x=4+3, 2x=7then divided by 2.
x=3,5
S 2. Let f(x) = x - k√x
a. Find a value of k such that the function has a critical point at x = 25.
b. Is the above critical point a local maximum, local minimum or neither? Show calculus to support your answer.
a. A critical point at x = 25 would mean f'(25) = 0 or doesn't exist. We have derivative
[tex]f(x) = x - k \sqrt x \implies f'(x) = 1 - \dfrac k{2\sqrt x}[/tex]
so that
[tex]f'(25) = 1 - \dfrac k{2\sqrt{25}} = 1 - \dfrac k{10} = 0 \implies \boxed{k=10}[/tex]
b. Taking the second derivative, we get
[tex]f''(x) = \dfrac k{4 x^{3/2}} = \dfrac5{2 x^{3/2}}[/tex]
At x = 25, the second derivative has a positive sign,
[tex]f''(25) = \dfrac 5{2 \times 25^{3/2}} = \dfrac 5{2\times5^3} = \dfrac1{50} > 0[/tex]
which means f(x) is concave upward around x = 25, so this critical point is a local minimum.
At her sisters birthday party Cheyenne thought it would be funny to drink lemonade from a party hat if the radius is 4.8 cm and the height of a hat is 12 cm how many cubic centimeters of lemonade can Cheyenne pour into the hat
92.16 pi cm^3.
Step-by-step explanation:
Shape of a party hat : conical
Volume of a cone = (1/3)(pi)(r^2)(h)
(pi(1/3)(23.04)(12))cm^3
Therefore, approximately
92.16 pi cm^3.
A family plan for a cell phone has a monthly base price of $75 plus $10.99 for each additional family member added beyond the primary account holder. The linear function to model the monthly cost C(x) (in $) of a family for x additional family members added is C(x)=
The linear equation that models the cost for having x additional family members added is:
c(x) = $75 + $10.99*x
How to get the linear equation?
Here we know that the plan has a fixed price of $75 plus $10.99 for each family member added beyond the primary account holder.
Then if there are x family members added, the cost will be:
$75 + $10.99*x
Then the linear equation that models the cost for having x additional family members added is:
c(x) = $75 + $10.99*x
If you want to learn more about linear equations:
https://brainly.com/question/1884491
#SPJ1
x² + 10x + 3 = -21?!?!!?!?!!!?
Answer:
-6,-4
Step-by-step explanation:
if you have to evaluate its 4
and there is 2 solutions