a) The ball reaches a maximum height of 182.25 feet.
b) The ball has a travel time of 6 seconds.
How to find the main features of a free fall case by analyzing quadratic equations
In this case we find a kind of uniform accelerated motion known as free fall, in which a particle is accelerated uniformly by gravity and any effect of other forces are neglected. The height of the ball in terms of time is described by a quadratic equation, whose definition is shown below:
h(t) = h' + v' · t + 0.5 · g · t²
Where:
h' - Initial height, in feet.v' - Initial velocity, in feet per second.t - Time, in seconds.g - Gravitational acceleration, in feet per square second.First, write the complete the equation of the height of the ball:
h(t) = - 16 · t² + 84 · t + 72
a) Second, clear the expression on one side and use the discriminant of the quadratic formula:
- 16 · t² + 84 · t + [72 - h(t)] = 0
84² - 4 · (- 16) · [72 - h(t)] = 0
7056 + 64 · [72 - h(t)] = 0
7056 + 4608 - 64 · h(t) = 0
11664 - 64 · h(t) = 0
h(t) = 729 / 4 ft
h(t) = 182.25 ft
The maximum height of the ball is 182.25 feet.
b) Third, use the quadratic formula to determine the roots of the quadratic equation:
t = - 84 / [2 · (- 16)] ± [1 / [2 · (- 16)]] · √[84² - 4 · (- 16) · 72]
t = 2.625 ± (1 / 32) · 108
t₁ = 6 s and t₂ = -0.75 s
The travel time of the ball is 6 seconds.
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In the exponential decay function ƒ(x) = a • bx, the b is between 0 and 1.
True
False
False, In the exponential decay function ƒ(x) = a • bx, the b is between 0 and 1.
What is exponential decay function?
In mathematics, the term "exponential decay" refers to the process of a constant percentage rate decline in a value over time.
It can be written as y=a(1-b)x, where y represents the final amount, a represents the initial amount, b represents the decay factor, and x is the amount of time that has passed.
How do you calculate an exponential function?
The equation f(x) = ax, in which the input variable x appears as an exponent, describes an exponential function. Both the exponential function and the value of x are dependent on the exponential curve.
The exponential function, which has the form, is a significant mathematical function. f(x) = ax.
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IL GIVE BRAINLIEST Question 1 of 10
Which is an expression?
A. 3 + 2 = 5
OB. 2+1>0
OC. 1+4= 2 + 3
OD. 4+6
Answer:
D
Step-by-step explanation:
A and C are equations. B is an inequality.
An expression does not have an inequality or equal sign.
Hence, D is the answer.
A shipment of 50 inexpensive digital watches, including 7 that are defective, is sent to a department store. The receiving department selects 10 at random for testing and rejects the whole shipment if 1 or more in the sample are found defective. What is the probability that the shipment will be rejected?
0.8926 is the probability that the shipment will be rejected.
What does the math term "probability" mean?
Probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out.
Statistics describes the examination of events subject to probability.
The probability that a digital watch is defective p = 10/50 = 0.2
n = 10
Using the binomial probability formula
P(x) = ⁿCₓ pˣ ( 1 - p)ⁿ⁻ˣ
Let x be the random variable that represents the number of defective watches.
The probability that the shipment will be rejected
P(x ≥ 1 ) = 1 - P(0)
= 1 - ¹⁰C₀ ( 0.2)⁰ ( 0.8)¹⁰
= 1 - ( 0.8)¹⁰
= 0.8926258176 ≈ 0.8926
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A
Choose the correct symbol to
compare these numbers.
-42 [?] -19
=
B
C
V
Answer:
<
Step-by-step explanation:
On a number line, -42 is to the left of -19.
When you compare two numbers on a number line, the number to the left is smaller.
-42 is less than -19
-42 < -19
can someone help me? I can't get rid of this test and it won't let me do it, I really don't know what to do and my grades will start to go down because I can't do it. (sorry if none of this makes sense)
Answer:
Step-by-step explanation:
There is no question to help with? Maybe ask your teacher or computer guy.
Can someone help with that?
Answer:
Step-by-step explanation:
i think it's black people x chicken = happy
Cost of a sled = $99.50, markup = 95%
Answer:
take wholesale cost and multiply it by 95%, then add to the original value
another way, just multiply by 1.95
Retail cost: 1.95*($99.50) = $194.03
Step-by-step explanation:
Answer:
Below
Step-by-step explanation:
So the sales price of the sled is 100% + 95 % = 195 % of the cost
= 1.95 * cost = 1.95 * 99.50 = 194.03 dollars
What is the solution to the system of linear equations?
(–4.5, 4.25)
(–1.7, –2.8)
(0, –7)
(3, 0.5)
Answer:
−903.65625
Step-by-step explanation:
((((−4.5)(4.25))(−1.7−2.8))(0−7))((3)(0.5))
=((−19.125(−1.7−2.8))(0−7))((3)(0.5))
=(((−19.125)(−4.5))(0−7))((3)(0.5))
=86.0625(0−7)(3)(0.5)
=(86.0625)(−7)(3)(0.5)
=−602.4375(3)(0.5)
=(−602.4375)(1.5)
=−903.65625
Solve for x. √x+3 = 6 A.3 B.9 C.33 D.36
Answer:
C. 33
Step-by-step explanation:
Given:
[tex]\sqrt{x+3}=6[/tex]
Solution:
(square both sides)
[tex]x+3=6^{2}[/tex]
[tex]x+3=36[/tex]
[tex]x=36-3[/tex]
[tex]x=33[/tex]
Answer is 33
option C
A gasoline tank holds 3 3/4
gallons. If 1/3 of the tank has been used,
then how many gallons have been used?
Answer:
3/5
Step-by-step explanation:
Reduce fraction to lowest terms
1 is the greatest common divisor of 41 and 12. The result can't be further reduced.
Step 2 of 2: Simplify, sub-step b: Convert improper fraction to mixed number.
Convert improper fraction to mixed number
41 over 12
41
12
= 3 and 5 over 123
5
12
41 ÷ 12 = 3 remainder 5
Answer: [tex]\frac{5}{4}[/tex]
Step-by-step explanation:
Create two groups of cards with the SAME SUM using as many cards as possible using the numbers 1 2 3 4 5 6 7 8 9
Group 1: 1, 2, 3, 4, 5
Group 2: 6, 7, 8, 9
In this case, the sum of the numbers in Group 1 is 1 + 2 + 3 + 4 + 5 = 15, and the sum of the numbers in Group 2 is 6 + 7 + 8 + 9 = 30. The sum of the numbers in both groups is 15 + 30 = 45, which is the same.
Alternatively, we could create the following two groups:
Group 1: 1, 2, 3, 4
Group 2: 5, 6, 7, 8, 9
In this case, the sum of the numbers in Group 1 is 1 + 2 + 3 + 4 = 10, and the sum of the numbers in Group 2 is 5 + 6 + 7 + 8 + 9 = 35. The sum of the numbers in both groups is 10 + 35 = 45, which is the same.
There are many other ways to create two groups of cards with the same sum using as many cards as possible. The key is to use all of the numbe
Answer:
group 1: 1,2,3,4,5
Group 2: 6,7,8,9
Step-by-step explanation:
my brain
Use the following probabilities to answer the question. It may be helpful to sketch a Venn diagram.
P(A) = 0.37, P(B) = 0.43 and P(AandB) = 0.20.
P(B | not A) =
=
The probability of B | not A i.e. P(B | not A) is 0.3651
How to find P(B | not A)?Probability is defined as the likelihood of a desired event happening.
Given that: P(A) = 0.37, P(B) = 0.43 and P(AandB) = 0.20.
We want to find P(B | not A)
Remember: P(A | B) = P(A n B) / P(B)
Thus, P(B | not A) = P(B and not A) / P(not A)
P(not A) = 1 - P(A) = 1 - 0.37 = 0.63
P(B and not A) = P(B) - P(A and B) = 0.43 - 0.20 = 0.23
Hence,
P(B | not A) = P(B and not A) / P(not A) = 0.23 / 0.63 = 0.3651
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At an art store, 1/4 of
the supplies are for
painting and 13% of the
supplies are for
drawing. What percent
of the supplies are not
for painting or
drawing?
Solve the triangle using the Law of Sines. (Assume b and c = 20, and ∠C = 63°. Round the length to two decimal places.)
Answer:
a = 16.51
angle A = 54
angle B = 63
Step-by-step explanation:
Recall the law of sines:
sinA/a = sinB/b = sinC/c
We know c is 20, and angle C is 63. Since b is also 20, angle B must also be 20. We know have two of the 3 angles, summing to 126, and we can find the last angle from that. 180-126=54, so angle A must be 54.
To solve for a, we need to know the ratio of the other two terms. Sin(63) is around 0.99, and 0.99/20 is 0.049. So we have 0.049=sin(54)/a. To solve for a, we divide by sin(54) and take the reciprocal of both sides, giving a = (sin54)/0.049, which is about 16.51, which is the length of the side a.
please help i will give brainliest
Explanation:
We want to prove by contradiction that corresponding angles 1 and 5 made by a transversal crossing non-parallel lines are not congruent.
To prove by contradiction, we make an assumption that results in a demonstrably false conclusion. This allows us to conclude the assumption is false.
ProofAssume angles 1 and 5 are congruent.
Then lines m and n are parallel by the converse of the corresponding angles theorem.
Lines m and n are not parallel, hence our assumption must be false.
Angles 1 and 5 are not congruent.
Which rule explains why these triangles are congruent?
Karl earns $11.20/hr. How much will he be paid this week?
Answer:11.20*168=$1 881.6
Step-by-step explanation:
Find equivalent decimal number of (1100111)²and (16742)³
Answer:
[tex]1100111_2 = 103_{10}\\\\16742_3 = 7650_{10}[/tex]
Step-by-step explanation:
[tex]\textsf{I just used the programmer's version of the built-in calculator that comes with Windows}[/tex]
Give the degree of the polynomial
Answer:
10
Step-by-step explanation:
Given polynomial:
[tex]3x^2y^3+8x^3y^7[/tex]
The degree of a polynomial is the largest exponent in the function.
When a polynomial has more than one variable, add the exponents of each variable in each term.
3x²y³ has a degree of 5, since both exponents add up to 5.
8x³y⁷ has a degree of 10, since both exponents add up to 10.
So the polynomial has a degree of 10.
Question
The product of two consecutive odd integers is 99. Find the integers. Answer only with the positive integers. For example, if
the integers are 8, 10 and -8, -10, then answer 8, 10.
Provide your answer below:
n=
n =
Answer: n= 9 and n=11
Step-by-step explanation:
Assume that x is the lesser of the two numbers. The second figure must be x+2.
Since x*(x+2) = 99, we know that
x^2 + 2x - 99 = 0
We obtain x = 11 and 9 by searching for the roots of this equation.
This can also be resolved in the following ways:
We are aware that the two numbers (x and x +2) are consecutive odd numbers. Since x * (x + 2) = x2 + 2x, the value of x must be near to the square root of 99.
The squares 81 and 100 are the ones closest to the number 99. Additionally, we know that x * (x+2) is bigger than x2 (by a factor of 2x), therefore x must equal 9 and x+2 must equal 11.
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What is 417 divided by 3 and what is the remainder
Answer:
139
Step-by-step explanation:
The number 417 divided by 3 gives the quotient of 139 and leaves the remainder of 0.
Given a division problem.
Here, the dividend is 417.
The divisor is 3.
It is required to find the quotient and the remainder of this division problem.
It can be done using the normal division method.
The first term of the dividend is 4.
4 = (3 × 1) + 1
So, the first digit of the quotient is 1.
The remainder, 1, goes to the other digit of the dividend and it becomes 11.
11 = (3 × 3) + 2
The second digit of the quotient is 3.
The remainder 2 goes to the last digit and it becomes 27.
27 = (3 × 9) + 0
The third digit of the quotient is 9.
The remainder is 0.
Hence, the quotient is 139 and the remainder is 0.
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1
Rebecca has 3 boxes of shells
with 30 shells in each box.
Which equation can be used
to find the total number of
shells in Rebecca's boxes?
A3 x 3 + 0 =
B3+3 x 10 =
3x3 + 10 =
3 x 3 x 10
Answer:
Step-by-step explanation: the answer is 90
the answer is 3 x 3 x 10 because she has 3 boxes and 30 shells in each box. 30 divided by 3 is 10 therefore you would multiply 3 by 3 to get 9 then multiply 9 times 10 to get 90.
FIRST ANSWER WILL GET 100 PTS!
Eight soccer players order 14 pizzas to share equally among themselves.
How much pizza will each player receive?
Select each correct answer.
Responses
8 1/4 pizza
1 4/8 pizzas
1 4/8 pizzas
1 6/8 pizzas
Answer:
8 1/4
Step-by-step explanation:
Sould be your anwser.
5. The population of deer in a park is growing over the years. The table below gives the population found in a
survey by local wildlife officials.
Year
2000
2003
2006
2009
Deer Population
168
216
264
312
(a) Find the average rate that the deer population is changing over each time interval below:
From 2000 to 2003
From 2003 to 2006
From 2006 to 2009
(b) Why does this calculation indicate a linear (c) Ift stands for the number of years since 2000,
relationship?
write an equation for the deer population, p, as a
function of 1.
(d) What does your model predict the deer (e) How many years will it take for the deer
population to be in the year 2014?
population to reach 500? Round to the nearest
year.
a) The average rate of change is 16.
b) The Calculation is linear because the average rate of change is same.
c) p= 16t + 168
d) The population in 2014 is 8168.
What is Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
a) The average rate of change
From 2000 to 2003 = (216- 168)/ 3
= 16
From 2003 to 2006 = (264- 216) / 3
= 16
From 2006 to 2009 = (312- 264)/ 3
= 16
b) The Calculation is linear because the average rate of change is same.
c) From the year 2000, the intercept is 168.
So, p= 16t + 168
e) The population in 2014
p = 16(500)+ 168
= 8168.
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Solve for x:-12x-14=34
Answer: x=4
Step-by-step explanation:
first you add both side by 14 to get 12x=48 then you divide both sides by 12 to get 4 so x=4
5 1/2 + 3/4 Give your answer in its simplest form.
Answer:
5 1/2 + 3/4
11/2 + 3/4
22+3/4
25/4
=6 1/4
Find the difference, and explain how you did it. Explain both the number part and the sign
4-(-6)
Answer:
10
Step-by-step explanation:
The 2 subtracting signs become addition, which is 4 + 6
At a local sandwich shop, 55% of customers preferred white bread over whole wheat bread. Of those who chose whole wheat bread, 61% preferred ham for the protein, and 41% of those who chose white bread preferred turkey.
What percentage of customers chose whole wheat bread with turkey? Round your answer to the nearest whole percentage.
18%
28%
39%
41%
Answer:
≈ 18%
Step-by-step explanation:
% of customers preferring whole wheat bread = 100 - 55 = 45%
% of choosers of whole wheat bread who prefer turkey = 100 - 61 = 39%
Multiply: 0.45×0.39 = .1755
Answer:
18%
Step-by-step explanation:
i took the test :)
Use the graph of the function to find its domain and range. Write the domain and range in interval notation.
Domain : {-4, 3} and Range : {-1, 4}
What is Domain and Range ?
A relation's domain and range are established, and they consist of all ordered pairs' x and y coordinate sets, respectively.
Domain = the set of all x-coordinates Range = the set of all y-coordinatesHere, observe the line through x-axis
you'll see the it range from -4 to 3 on x-axis.
Therefore, Domain is {-4, 3}
Now, observe the line through y-axis
you'll see the it range from -1 to 4 on y-axis.
Therefore, Range is {-4, 3}
Hence, Domain : {-4, 3} and Range : {-1, 4}
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please help want! easy thank you so much!!
7. Serena estimates that she can paint 40 square feet of wall space every half-hour. Can Serena paint at least 180 square feet of wall space in 2.5 hours? Why or why not?
A. Yes, 180(2.5)= 450, and 450 > 180
B. Yes, 80(2.5) = 200, and 200 > 180
C. No, 40(2.5) = 100, and 100 < 180
D. No, 80(0.5)= 40, and 40 < 180
B. Yes, 80(2.5) = 200, and 200 > 180
Step-by-step explanation:1. Addition:If Serena can paint 40 square feet in 30 minutes, then:
40 + 40 = 80 sq. ft.
30 + 30 = 1 hour
80 + 40 = 120 sq. ft.
60 + 30 = 1.5 hours
120 + 40 = 160 sq. ft.
90 + 30 = 2 hours
160 + 40 = 200 sq. ft.
120 + 30 = 2.5 hours
So, what I just did was adding the 30 minutes and the 40 square feet at the same time until I got to 2.5 hours, and seeing if I also got to 180 square feet. Which I did. I actually got to 200 sq. ft. That means our answer is B. Yes, 80(2.5) = 200, and 200 > 180
Solution:
B. Yes, 80(2.5) = 200, and 200 > 180
I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!