Using the z-distribution, it is found that since the p-value of the test is less than 0.05, we reject the null hypothesis and find that there is enough evidence to conclude that the true proportion of all life insurance claims made to this company that are settled within 30 days is less than 85%.
What are the hypothesis tested?At the null hypothesis, it is tested if there is not enough evidence that the proportion is below 85%, that is:
[tex]H_0: p \geq 0.85[/tex]
At the alternative hypothesis, it is tested if there is enough evidence that the proportion is below 85%, that is:
[tex]H_0: p < 0.85[/tex]
What is the test statistic?The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.For this problem, the parameters are:
[tex]p = 0.85, n = 250, \overline{p} = \frac{203}{250} = 0.812[/tex]
Hence the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.812 - 0.85}{\sqrt{\frac{0.85(0.15)}{250}}}[/tex]
z = -1.68
What is the p-value and the conclusionUsing a z-distribution calculator, with a left-tailed test, as we are testing if the proportion is less than a value, and z = -1.68, the p-value is of 0.0465.
Since the p-value of the test is less than 0.05, we reject the null hypothesis and find that there is enough evidence to conclude that the true proportion of all life insurance claims made to this company that are settled within 30 days is less than 85%.
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Name a line that does not appear to intersect plane L.
Answer:
BE
Step-by-step explanation:
A line and a plane will not intersect if they are parallel. A line is named by naming any two points on it, in any order.
LineThe line containing points B, E, F appears to be parallel to plane L. As such, it will remain at the same distance from plane L throughout its infinite length. The line can be named by 2 points in any of 6 different ways.
Line BE is parallel to plane L.
__
Additional comment
Other names for the same line include ...
BF, EF, EB, FB, FE.
Jake goes to the grocery store and buys 3 apples, 2 cans of soup, and 1 box of cereal. The apples cost $0.89 each; the soup costs $2.98 per can; and the box of cereal costs $4.99. Write an equation that represents the total cost c of Jake’s purchases.
The equation that represents the total cost, c, of the purchases made by Jake is: c = 3(0.89) + 2(2.98) + 4.99.
How to Write the Equation of Total Cost?To write the equation that represents the total cost of a given scenario like the one given, you can use variables to represent each component that makes up the total cost in the given situation.
Thus, let:
a = apple = 3a
s = can of soup = 2s
b = box of cereal = b
c = total cost
We know that unit price of each items are:
Apple = $0.89
Can of soup = $2.98
Box of cereal = $4.99
Equation would be:
c = 3a + 2s + b
Plug in the values
c = 3(0.89) + 2(2.98) + 4.99
Therefore, the equation that represents the total cost, c, of the purchases made by Jake is: c = 3(0.89) + 2(2.98) + 4.99.
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Cody earned 600 from delivering groceries last year. He deposited this money in an account that pays an interest rate of 2% compounded annually. What will be his balance after 20 years. pls answer asap
The balance that Cody earned after 20 years is 891.57. Using the compound interest formula, the required value is calculated.
How to calculate the compound interest?The compound interest is calculated by
[tex]A = P(1 + \frac{r}{n} )^n^t[/tex]
Where,
A - Total amount (Future value)
P - Principal amount (Initial value)
r - The rate of interest
n - Number of times compounded per 't'
t - Total number of years the money is invested
Calculation:It is given that,
P = 600
r = 2% = 0.02
t = 20 years
n = 1 (since the amount is compounded annually)
Then,
[tex]A=600(1+\frac{0.02}{1})^1^*^2^0[/tex]
= 600 (1 + 0.02)²⁰
= 600 (1.02)²⁰
= 891.57
Therefore, the balance after 20 years is 891.57.
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A 25-year old woman burns 200−20t cal/hr while walking on her treadmill. Her caloric intake from drinking Gatorade is 110t calories during the t th hour. What is her net decrease in calories after walking for 5 hours?
The net decrease in calories after walking for 5 hours is 50 calorie.
According to the statement
we have given that the
A 25-year old woman burns 200−20t cal/hr and Her caloric intake from drinking Gatorade is 110t calories during the t hour.
And we have to find the net decrease in calories after walking for 5 hours.
So, For this purpose,
We know that the
calories burns in one hour = 200−20t
calories burns in 5 hours = 5(200−20t)
calories burns in 5 hours = 1000 - 100t
Now,
Calorie intake in t hours = 110t
And
net decrease in calories after walking for 5 hours = 100t - 1000 + 110t
put t is 5 then
net decrease in calories after walking for 5 hours = 210(5) - 1000
net decrease is 50 cal.
So, The net decrease in calories after walking for 5 hours is 50 calorie.
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List the domain and range in interval notation for the following graphs listed?
The domain and range of the given graphs are as follows,
(b) Domain: x ∈ (-∞, ∞), Range: y ∈ (-∞, ∞)
(c) Domain: x ∈ [-2, ∞), Range: y ∈ [1, ∞)
Determining the Domain and Range from a Graph
The domain of a graph is made up of all the input values displayed on the x-axis since the term "domain" refers to the set of potential input values. The various output values are represented on the y-axis as the range.
Thus, in graph (b),
Since the values of the given curve extends infinitely (denoted by arrowhead of the curve) on positive as well as negative sides for both the axes, x and y, its domain and range both are (-∞, ∞).
Similarly, in graph (c),
The minimum value on x-axis or abscissa is -2 and maximum is infinity. Hence, its domain is [-2, ∞). The minimum ordinate value or y-coordinate is 1 and maximum is infinity. Thus, its range is [1, ∞).
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You are on the Arithmetic Reasoning section.
Q: If 12 men are needed to run 4 machines. How many men are needed to
run 20?
A. 24
B. 48
C. 60
D. 80
Answer:that will be c 60
Step-by-step explanation: Because 12/4 but than the machines turn to 20 so 4x5 equals 20 so you got to do it to both sides
12x5=60 so its 60 men to run 20 machines
The table gives a partial set of values of a polynomial h(x), which has a leading coefficient of 1. x –2 0 1 2 3 h(x) 0 –12 0 8 0 If every x-intercept of h(x) is shown in the table and has a multiplicity of one, what is the equation of the polynomial function?
Using the Factor Theorem, the equation of h(x) is given as follows:
h(x) = -2(x³ - 2x² - 5x + 6)
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
Looking at the table, considering the values of x when h(x) = 0, the roots of h(x) are given as follows:
[tex]x_1 = -2, x_2 = 1, x_3 = 3[/tex]
Then the rule is:
h(x) = a(x + 2)(x - 1)(x - 3)
h(x) = a(x² + x - 2)(x - 3)
h(x) = a(x³ - 2x² - 5x + 6)
The h-intercept is of -12, as when x = 0, h = -12, hence this is used to find a as follows:
6a = -12
a = -12/6
a = -2.
Hence the function is given by:
h(x) = -2(x³ - 2x² - 5x + 6)
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IM IN A HURRY PLEASE HELP ME QUESTION IS DOWN BELOW WORTH 15 POINTS each
A circle is a shape formed by a curved side. Therefore, the required answers are:
1. An example of an inscribed angle is: <SQT or <QST or <QTS
2. An example of a minor arc is: arc QT or RS or QR
3. An example of a semicircle is: QRS or QTS
4. <QPR = [tex]\frac{264600}{44r}[/tex] degrees
An angle is said to be formed whenever two or more straight lines intersect or meet. But an inscribed angle is an angle formed within a given circle.
A circle is a shape formed by a curved side. Some of its parts are semicircle, radius, diameter, chord, sector, segment, etc.
Thus the following can be deduced from the given question:
1. An example of an inscribed angle is: <SQT or <QST or <QTS
2. An example of a minor arc is: arc QT or RS or QR
3. An example of a semicircle is: QRS or QTS
4. <QPR.
length of an arc = [tex]\frac{x}{360}[/tex] 2[tex]\pi[/tex]r
where r is the radius of the circle
105 = [tex]\frac{x}{360}[/tex] x 2 x [tex]\frac{22}{7}[/tex] x r
= [tex]\frac{44xr}{2520}[/tex]
44 xr = 105 x 2520
44xr = 264600
x = [tex]\frac{264600}{44r}[/tex]
Therefore the measure of angle QPR in terms of r is [tex]\frac{264600}{44r}[/tex] degrees.
5. The length of arc QTR can be determined by;
Arc QTR = [tex]\frac{x}{360}[/tex] 2[tex]\pi[/tex]r
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Calculate the volume of a sphere that has a radius of 4 meters
Answer:
268.08
Step-by-step explanation:
use the formula 4/3πr^3Answer:
803.84 m³
Step-by-step explanation:
The formula to find the volume of a sphere is:
V = 4 π r³
Given that,
radius ⇒ 4m
Let us find the volume now.
V = 4 π r³
V = 4 π × ( 4 )³
V = 4 π × 64
V = 4 π × 64
V = 12.56 × 64
V = 803.84 m³
The tree diagram represents an
experiment consisting of two trials.
5
5
VV
P(A and D)= [?]
Based on the given parameters in the question, the value of the probability of A and D is 0.30
How to determine the probability?The given parameters from the tree diagram are:
Probability of event A: P(A) = 0.5Probability of event D: P(D) = 0.6The probability P(A and D) is calculated using the following probability formula
P(A and D) = P(A) × P(D)
Substitute the known values in the above equation
P(A and D) = 0.5 × 0.6
Evaluate the product of 0.5 and 0.6
P(A and D) = 0.30
Hence, the value of the probability of A and D is 0.30 based on the given parameters in the question
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(sin alpha +cos alpha )2
Step-by-step explanation:
sin alpha^2 + 2sin alpha* cos alpha + cos alpha^2
sin alpha^2 + cos alpha^2 +2sin alpha* cos alpha
1+ 2sin alpha* cos alpha
1+sin2 alpha
(x^2-y^2)dx+2xydy=0
so this is a problem of a differential equation I've been trying so hard to match with the given answer but failed every time I tried. So, is there anyone who can really can help me out to catch the mistakes that I'm making?
* The last line of my workout is just a dump guess.
The pictures are my workouts also the answer to this question is attached. Please read my solutions by this order : pic-1, pic-3 & pic-2, if necessary.
[tex](x^2 - y^2) \, dx + 2xy \, dy = 0[/tex]
Multiply both sides by [tex]\frac1{x^2}[/tex].
[tex]\left(1 - \dfrac{y^2}{x^2}\right) \, dx + \dfrac{2y}x \, dy = 0[/tex]
Substitute [tex]y=vx[/tex], so [tex]v=\frac yx[/tex] and [tex]dy=x\,dv+v\,dx[/tex].
[tex](1-v^2) \, dx + 2v (x\,dv + v\,dx) = 0[/tex]
[tex](1 + v^2) \, dx + 2xv \, dv = 0[/tex]
Separate the variables.
[tex]2xv\,dv = -(1 + v^2) \, dx[/tex]
[tex]\dfrac{v}{1+v^2}\,dv = -\dfrac{dx}{2x}[/tex]
Integrate both sides
[tex]\displaystyle \int \frac{v}{1+v^2}\,dv = -\frac12 \int \frac{dx}x[/tex]
On the left side, substitute [tex]w=1+v^2[/tex] and [tex]dw=2v\,dv[/tex].
[tex]\displaystyle \frac12 \int \frac{dw}w = -\frac12 \int\frac{dx}x[/tex]
[tex]\displaystyle \ln|w| = -\ln|x| + C[/tex]
Solve for [tex]w[/tex], then [tex]v[/tex], then [tex]y[/tex].
[tex]e^{\ln|w|} = e^{-\ln|x| + C}[/tex]
[tex]w = e^C e^{\ln|x^{-1}|}[/tex]
[tex]w = Cx^{-1}[/tex]
[tex]1 + v^2 = Cx^{-1}[/tex]
[tex]1 + \dfrac{y^2}{x^2} = Cx^{-1}[/tex]
[tex]\implies \boxed{x^2 + y^2 = Cx}[/tex]
Your mistake is in the first image, between third and second lines from the bottom. (It may not be the only one, it's the first one that matters.)
You incorrectly combine the fractions on the left side.
[tex]\dfrac1{-2v} -\dfrac v{-2} = \dfrac1{-2v} - \dfrac{v^2}{-2v} = \dfrac{1-v^2}{-2v} = \dfrac{v^2-1}{2v}[/tex]
Choose the correct graph of the given system of equations. y + 2x = −1 3y − x = 4 graph of two lines that intersect at the point negative 1, 1, with text on graph that reads One Solution negative 1, 1 graph of two lines that intersect at the point 1, 1, with text on graph that reads One Solution 1, 1 graph of two parallel lines with positive slopes with text on the graph that reads No Solution graph of two lines on top of each other with text on graph that reads Infinitely Many Solutions Question 4(Mul
The system of equations has one solution (-1, 1)
Graph of system of linear equationsFrom the question, we are to graph the given system of equations.
The given system of equation is
y + 2x = −1
3y − x = 4
The graph of the given system of equations is shown below.
From the graph, we can observe that the solution to the given system of equation is given by two lines that intersect at the point (-1, 1).
Hence, the system of equations has one solution (-1, 1)
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I think the answer is A. The first one
Jocelyn has a ladder that is 15 ft long. She wants to lean the ladder against a vertical wall so that the top of the ladder is 13.5 ft above the ground. For safety reasons, she wants the angle the ladder makes with the ground to be less than 75°. Will the ladder be safe at this height? Show your work and equation to support your answer
By using trigonometric relations, we will see that the angle that the ladder makes with the ground is 64.2°, so we conclude that the ladder is safe.
Will the ladder be safe at this height?Notice that the ladder makes a right triangle with the wall.
Such that the hypotenuse (the ladder itself) measures 15 ft, and one of the catheti (distance between the ground and top of the ladder) measures 13.5ft
If we considerate the angle that the ladder makes with the ground, the known cathetus is the opposite cathetus.
Then we can use the relation:
sin(x) = (opposite cathetus)/(hypotenuse)
Then:
sin(x) = (13.5ft)/(15ft)
If we use the inverse sine function on both sides, we get:
Asin(sin(x)) = Asin( 13.5ft/15ft)
x = Asin(13.5/15) = 64.2°
So the angle is less than 75°, which means that in fact, the ladder is safe.
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On Wednesday, the temperature changes -3
∘
each hour for 10 hours. If the temperature was 12
∘
to begin with on Wednesday, what was the temperature after the 10 hours.
Answer:
-24 would be the temperature
Answer:
-24 BECAUSE I did all the math.
A glass vase weighs 0.17 lb. How much does a similarly shaped vase of the same glass weigh if each dimension is 6 times as large?
Answer:
7,647.4?
Step-by-step explanation:
The Mogul Runners ski club planned a trip to Park City. Of the total number of club members, 11 signed up to go. If this is 25% of the club, how many members does the ski club have?
The ski club has 44 members in all
What is population?
Population refers to the total number of items or individuals that form a group.
In this case, the population means the total number of all members in the Mogul Runners ski club.
What is sample?
Sample means a fraction of the total population, in other words, the 25% of the members, whose number is 11, that signed up to go for the planned trip.
We can convert 25% to 100% by equation 25% to 11 members that signed up to go for the planned trip.
25% of club members=11 members
divide both sides by 25%
25%/25% of club members=11/25% members
club members=44 members
The ski club has 44 members altogether as computed above.
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Ama and her son Brandon's average age is currently 36 years. When Brandon was born, Ama was 34 years old. How old is Brandon now?
If Ama and her son Brandon's average age is currently 36 years. then
Brandon's age is 38 years.
What is Equation?Two or more expressions with an equal sign is called as Equation.
Let the Brandon age be x
Ama was 34 years old
Ama and her son Brandon's average age is currently 36 years
(34 + x)/2= 36
Use cross multiplication
34 + x = 72
x=72-34
x = 38
So Brandon's average age is 38.
Hence Brandon is 38 years old.
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How many significant figures are in this number? 2.583 x 10^12
Answer:
2583000000000
Step-by-step explanation:
[tex]2.583*10^{12} = 2583000000000[/tex]
5x-3>17 or -2x+2>8 inequality
The solution of the inequality is as follows;
x > 4 or x < -3
How to solve inequality?The inequality can be solve as follows:
5x - 3 > 17 or -2x + 2 > 8
Let's solve the first inequality,
5x - 3 > 17
add 3 to both sides of the inequality
5x - 3 + 3 > 17 + 3
5x > 20
divide both sides by 5
5x / 5 > 20 / 5
x > 4
-2x + 2 > 8
subtract 2 from both sides
-2x + 2 - 2 > 8 - 2
-2x > 6
divide both sides by -2
-2x / -2 > 6 / -2
x < -3
Therefore, x > 4 or x < -3
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Assume the graph is derivative f(x). Answer for f(x)
The intervals which the original function f(x) concave down are (-5, -2) and (3, 5)
How to determine the intervals which the original function f(x) concave down?The information that completes the question are added as an attachment
The question requires that we determine the intervals which the original function f(x) concave down
From the attached graph, we have the following turning points
(-2, -4) and (3, 2)
From the domain of the graph, the curve starts at (-5, 0), turns at (-2, -4), also turns at (3, 2) and then stops at (5, 0)
So, we have:
(-5, 0), (-2, -4), (3, 2) and (5, 0)
Remove the y coordinates
x = -5, -2, 3 and 5
Express as intervals
(-5, -2) and (3, 5)
Hence, the intervals which the original function f(x) concave down are (-5, -2) and (3, 5)
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Janet plans to save $22.50 each week until she has enough to buy a $180 bicycle. After how many weeks will she have enough money for a bicycle.
Answer:
Step-by-step explanation:
8weeeks bc 22.50*8=180
If my goal was to be above 85% I my final number was 80 what was my percentage for the month?
Using it's concept, your percentage for the month was of 94.12%.
What is a percentage?The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:
P = a/b x 100%
In this problem, your goal was of 85, with a grade of 80, hence the percentage is:
P = 80/85 x 100% = 94.12%.
Hence, your percentage for the month was of 94.12%.
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What is the mean absolute deviation of this? 1 is 2 sundaes.
Using it's concept, the mean absolute deviation of the data-set is of 2 sundaes.
What is the mean absolute deviation of a data-set?The mean of a data-set is given by the sum of all observations divided by the number of observations.The mean absolute deviation of a data-set is the sum of the absolute value of the difference between each observation and the mean, divided by the number of observations.The mean absolute deviation represents the average by which the values differ from the mean.The mean for this problem is:
(4 + 6 + 2 + 4)/4 = 4
Hence the MAD is:
(|4-4| + |6-4| + |2-4| + |4-4|)/4 = 1
Since each unit represents 2 sundaes, the mean absolute deviation is of 2 sundaes.
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Which expression represents the
number of reams of paper the company
produced during the second year?
The expression that represents the number of reams of paper produced in the second year is 4.704 x [tex]10^{10}[/tex] (option d)
What is the expression that represents the reams produced in the second year.The quantity of paper produced in the first year is written in scientific notation. Scientific notation is used to compress larger numbers into smaller numbers.
In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10.
For example, The number 5 x 10³ is equivalent to 500
Paper produced in the second year = paper produced in the first year x 5.6
(8.4 x [tex]10^{9}[/tex] ) x 5.6 = 47.04 x [tex]10^{9}[/tex]
4.704 x [tex]10^{9 + 1}[/tex]
= 4.704 x [tex]10^{10}[/tex]
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△ABC has vertices A(-2, 0), B(0,8), and C(4,2). Find the coordinates of the point of congruency of the altitudes (H)
Based on the calculations, the coordinates of the point of congruency of the altitudes (H) are (-160/11, 40/11).
What is a triangle?A triangle can be defined as a two-dimensional geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.
What is a slope?A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.
How to determine a slope?Mathematically, the slope of a straight line can be calculated by using this formula;
[tex]Slope, m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope, m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Assuming the following parameters for triangle ABC:
Let AM be the altitudes on BC.Let BN be the altitudes on CA.Let CL be the altitudes on AB.For the slope of BC, we have:
Slope of BC = (2 - 8)/(4 - 0)
Slope of BC = -6/4
Slope of BC = -3/2.
For the slope of CA, we have:
Slope of CA = (2 - 0)/(4 - (-2))
Slope of CA = 2/6
Slope of CA = 1/3.
For the slope of AB, we have:
Slope of AB = (8 - 0)/(0 - (-2))
Slope of AB = 8/2
Slope of AB = 4.
Note: The point of concurrency of three altitudes in a triangle is referred to as orthocenter.
Since side AB is perpendicular to side QC, we have:
m₁ × m₂ = -1
Slope of AB × Slope of QC = -1
Slope of QC = (k - 4)/(h - 2)
4 × (k - 4)/(h - 2) = -1
(4k - 16)/(h - 2) = -1
4k - 16 = -h + 2
4k + h = 18 .......equation 1.
Similarly, we have the following:
Slope of BC × Slope of AH = -1
-3/2 × (k)/(h + 2) = -1
3k/(2h + 4) = 1
3k = 2h + 4
3k - 2h = 4 .......equation 2.
Solving eqn. 1 and eqn. 2 simultaneously, we have:
8k + 2h = 36
3k - 2h = 4
11k = 40
k = 40/11.
For the value of h, we have:
h = -4k
h = -4 × (40/11)
h = -160/11
Therefore, the coordinates of the point of congruency of the altitudes (H) are (-160/11, 40/11).
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When a lilac bush is planted, it is 24 inches tall. Each month, it grows 6 inches taller. How tall will It get over time?
Dependent variable: ______
Independent variable: ______
Equation: ______
Answer:
Dependent variable: time(months) or [tex]t[/tex]
Independent variable: 6
Step-by-step explanation:
[tex]h=24+6t[/tex]
(h=height)
7x-3y=-7 slope of line perpendicular
Answer: -3/7
Step-by-step explanation:
The first step is to find the slope of the line
y = mx + c where m is the slope of the line
Rearrange the equation and we get
3y = 7x + 7
y = 7x/3 + 7/3
So the slope of the line 7x - 3y = -7 is 7/3
There is another rule that states: The product of the slopes of two lines perpendicular to each other is -1
So, the slope of the line perpendicular to 7x - 3y = -7 is -1/(7/3) = -3/7
95 m
b =
b
57 m
What is the length of the missing leg? If necessary, round to the nearest tenth.
meters
If the length of hypotenuse is 95 m ,perpendicular is 57 m then the length of missing leg is 76m.
Given that the length of hypotenuse is 95 m ,the length of perpendicular is 57 m.
We are required to find the length of base or missing leg.
The given triangle is a right angled triangle. We can easily find out the length of the base of the triangle by using pythagoras theorem.
Pythagoras theorem says that the square of hypotenuse of a right angled triangle is equal to the sum of squares of the base and perpendicular of that triangle.
[tex]H^{2} =P^{2} +B^{2}[/tex]
We have to find the base of the triangle.
B=[tex]\sqrt{H^{2} -P^{2} }[/tex]
=[tex]\sqrt{(95)^{2} -(57)^{2} }[/tex]
=[tex]\sqrt{9025-3249}[/tex]
=[tex]\sqrt{5776}[/tex]
=76 m.
Hence if the length of hypotenuse is 95 m ,perpendicular is 57 m then the length of missing leg is 76m.
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A cannonball is shot straight upward with a velocity of 80 ft/sec. Its height after t seconds is given by f (t) = 80t - 16 t to the second power. Round your answers to 1 decimal place if necessary.
How high will the cannon ball go?
How many seconds will it take to reach this maximum height?
Check the picture below, so the ball's path is pretty much like so, and it reaches its hightest at its vertex, so
[tex]~~~~~~\textit{initial velocity in feet} \\\\ h(t) = -16t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&80\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&0\\ \qquad \textit{of the object}\\ h=\textit{object's height}&h\\ \qquad \textit{at "t" seconds} \end{cases} \\\\\\ f(t)=80t-16t^2\implies f(t)=-16t^2+80t+0 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-16}x^2\stackrel{\stackrel{b}{\downarrow }}{+80}x\stackrel{\stackrel{c}{\downarrow }}{+0} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]
[tex]\left(-\cfrac{ 80}{2(-16)}~~~~ ,~~~~ 0-\cfrac{ (80)^2}{4(-16)}\right) \implies \left( - \cfrac{ 80 }{ -32 }~~,~~0 - \cfrac{ 6400 }{ -64 } \right) \\\\\\ \left( \cfrac{5}{2}~~,~~100 \right)\implies \underset{~\hfill feet ~~ }{\stackrel{seconds\qquad }{\left( 2\frac{1}{2}~~,~~100 \right)}}[/tex]