Examples of Quadratic Equation. A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared. The standard form is ax² + bx + c = 0 with a, b, and c being constants, or numerical coefficients, and x is an unknown variable.
Final answer:
A real-life example of a quadratic model is a ball's trajectory when thrown upwards, described by the quadratic equation h(t) = -4.9t^2 + v0t + h0, with -4.9 representing the acceleration due to gravity.
Explanation:
A common example of a quadratic model in real life is the path of a projectile. For instance, when you throw a ball, its trajectory can be described by a quadratic equation. Let's say a person throws a ball upwards with an initial velocity, and we want to model the ball's height above the ground over time.
The quadratic equation for the ball's height h at time t can be written as: h(t) = -4.9t2 + v0t + h0, where -4.9 is the acceleration due to gravity (in meters per second squared), v0 is the initial velocity (in meters per second), and h0 is the initial height (in meters).
For example, if the initial velocity is 14.3 m/s and the ball is thrown from the ground (initial height is 0), the equation becomes h(t) = -4.9t2 + 14.3t. To find when the ball hits the ground, we solve for t when h(t) = 0 using the quadratic formula.
Hey guys I need help simplifying this radical expression please. ASAP please.
Answer:
go on symbolab type the equation in and it gives u anwsers and work
Step-by-step explanation:
=\frac{4}{\left(x+2\right)\left(x+4\right)}
Lacy draws a diamond from a standard deck of 52 cards. Without replacing the first card, she then proceeds to draw a second card and gets a spade.
Are these events independent?
Input Yes or No:
Determine the probability of drawing a diamond and then a spade without replacement.
Write your answer in decimal form, rounded to four decimal places as needed.
Answer =
Linda draws a diamond from a standard deck of 52 cards. She returns the diamond to the deck, then draws a second card. Her second card is a spade.
Are these events independent?
Input Yes or No:
Determine the probability of drawing a diamond and then a spade with replacement.
Write your answer in decimal form, rounded to four decimal places as needed.
Answer =
Answer:
a) i) No
ii) Probability of drawing a diamond and then spade without replacement is 0.0637.
b) i) Yes
ii) Probability of drawing a diamond and then spade with replacement is 0.0625
Step-by-step explanation:
Part a) Without replacement:
i) Are these events independent?
No, because the both events are dependent. because a card taken out of the deck is not replaced back before taking out the other card so the chances of event occur change.
ii) Determine the probability of drawing a diamond and then a spade without replacement.
Probability of drawing a diamond and then spade = (Probability of drawing a diamond) * (Probability of drawing a spade)
Probability of drawing a diamond :
Total cards in deck = 52
Diamonds = 13
Probability of drawing a diamond = 13/52
Probability of drawing a spade:
Total cards in deck after taking diamond = 52 -1 =51
Spades = 13
Probability of drawing a spade = 13/51
Probability of drawing a diamond and then spade = 13/52 * 13/51
= 169/2652
=0.0637
So, Probability of drawing a diamond and then spade without replacement is 0.0637
Part b) With replacements
i) Are these events independent?
Input Yes or No:
Yes, these events are independent because a card taken out of the deck is replaced back before taking out the other card so the chances of event occur doesn't change.
ii) Determine the probability of drawing a diamond and then a spade with replacement.
Probability of drawing a diamond and then spade = (Probability of drawing a diamond) * (Probability of drawing a spade)
Probability of drawing a diamond :
Total cards in deck = 52
Diamonds = 13
Probability of drawing a diamond = 13/52
Probability of drawing a spade:
Total cards in deck after replacing diamond = 52
Spades = 13
Probability of drawing a spade = 13/52
Probability of drawing a diamond and then spade = 13/52 * 13/52
= 169/2704
=0.0625
So, Probability of drawing a diamond and then spade with replacement is 0.0625
The first two events are not independent, with a probability P = 0.0637
The second pair of events is independent, and the probability is P = 0.0625
How to get the probabilities?
First, all the cards on the deck have the same probability of being randomly drawn, which will be p = 1/52.
A) Now, if Lacy first draws a diamond card, now the number of cards in the deck are less (now there are 51 cards on the deck). So the probability of drawing now a spade is larger than before. Then the first two events are not independent.
The probability of drawing a diamond card at first is:
P = 13/52 (because there are 13 diamonds and a total of 52 cards).
The probability of drawing a spade after is:
Q = (13/51)
The joint probability is the product of the individual probabilities, this will give:p = P*Q = (13/52)*(13/51) = 0.0637
B) Now we replace the first card, then the events are now independent, as the probability of drawing a spade after the first draw is not changed (because the total number of cards will be 52).
The probability of drawing a diamond is:
P = 13/52
Now we replace the diamond card drawn.
The probability of drawing a spade will be:
Q = 13/52
The joint probability is:
p = P*Q = (13/52)^2 = 0.0625
If you want to learn more about probability, you can read:
https://brainly.com/question/251701
Help me don’t respond if you aren’t 100% sure please please
it is 8/15 because if you count all the groups it is 15 and if you count all the numbers 1 it is 8 which is 8/15
The value of the expression -
+ x(100 - 15x) when x = 5 is
Answer:
Step-by-step explanation:
Warning:
. You just wrote - and +, adding them both would result in a 0; (positive + negative = 0). If you haven't checked twice before asking, it is your problem. I'm going to solve for:
x(100-15x) when x = 5.
Answer:
Step By Step Explanation:
You'll need to substitute (that word is hard, it means replace though) the x, and get a proper equation (because they already gave you the x).
Look at how ugly and hard this is: x(100-15x) When x = 5.
Now it's better when replacing the x: 5(100-15×5)
Put it in a calculator if you wanted to avoid step by step work, but I'll show you how to do it step by step if you wanted.
5(100-15×5)
(5)×(100)+(5)(-75)
500-375
=125.
So, write this for your answer:
x(100-15x) = 125 Because 5(100-15×5)=125. And x = 5.
What is the probability of on-time arrival in class given that the subject is biology? A. 90.1% B. 88.5% C. 84.7% D. 82.4% E. insufficient data
Answer:
Answer is D 82.4%
Step-by-step explanation:
Got it right on the test :)
The probability of on-time arrival in class given that the subject is biology is 82.4%
What is probability?It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
From the definition, the probability is the ratio of total favourable outcome to total outcome.
From the data table, the probability of on-time arrival in class given that the subject is biology:
= 82.4%
Thus, the probability of on-time arrival in class given that the subject is biology is 82.4%
Learn more about the probability here:
brainly.com/question/11234923
#SPJ2
what is 1449.09/81 I need help asap
Answer:
if its division then: 17.89
Step-by-step explanation:
The result of the division 1449.09 divided by 81 equals approximately 17.89 .
To find the result of 1449.09 divided by 81, we simply divide the numerator by the denominator.
The division can be calculated as follows :
1449.09 ÷ 81 = 17.892654321.
Rounded to two decimal places , the result is approximately 17.89.
The result of the division 1449.09 divided by 81 equals approximately 17.89. This means that 1449.09 can be divided evenly by 81 a total of 17 times with a remainder of 0.
The quotient, 17.89, represents the value obtained when equally distributing 1449.09 among 81 parts.
Learn more about division here
http://brainly.com/question/231633
#SPJ2
Michael practiced batting and kept track of his hits. He missed 2 balls but hit 8 balls that were pitched to him. How many balls can Michael predict to hit if he is pitched 20 balls?
Answer: He can predict 16 balls
Step-by-step explanation:
Answer:
16 balls; c
Step-by-step explanation:
Antonia is standing 2.8 miles away from Mt. Drash. She has to tilt her head upwards 68° in order to look straight at the peak of the mountain. She wants to figure out how high the mountain is.
Please Help!
Answer:
5.3 miles
Step-by-step explanation:
tan(62) = x / 2.8 where x = the height of the mountain
tan(62) * 2.8 = x = 5.3 miles
Using the law of tangents.
Tan(angle) = Opposite Leg / adjacent leg
Tan(68) = x / 2.8 miles
x = 2.8 x tan(68)
x = 6.93
The mountain is about 6.9 miles high.
the table below shows all possibilities of the outcome of rolling two 6-sided number cubes what is the possibility of rolling a sum of 8
Answer:
Final answer is [tex]\frac{5}{36}[/tex].
Step-by-step explanation:
Given that two 6-sided number cubes are rolled. Now we need to find about what is the possibility of rolling a sum of 8.
From the sample space, you can see that there are total 36 possible outcomes.
out of those outcomes, there are only 5 outcomes that has sum = 8
which are {(2,6), (3,5), (4,4), (5,3), (6,2)}.
Hence probability of rolling a sum of 8 [tex]=\frac{5}{36}[/tex].
Hence final answer is [tex]\frac{5}{36}[/tex].
1) Write the recursive rule for the sequence.
40 , 30 , 20 , 10 , 0 , -10, ,-20
2) Write the explicit rule for the sequence. -1, 14, 29, 44, 59
3)If the probability of an event is P(A) = 2/25 and the probability of the next event is P(B) = 5/6, what is the P(A and B) ?
4)The average weight of the animals in a petting zoo is 40 pounds. The weights of 10 animals in the zoo selected randomly are 35, 46, 59, 18, 44, 23, 61, 45, 40, 38.
The population mean is 40 pounds. What is the sample mean to the nearest pound?
Question 4 options:
43
42
39
41
Question 5 (5 points)
For which intervals is the function positive?
Question 5 options:
(−∞, 4)
(−∞, −6) (−2,4 )
( ∞ , 6) (∞, 4)
(−4, 4)
Question 6 (5 points)
What is the average rate of change from year 30 to year 60?
Question 6 options:
-.44
- .04
4.4
4
Question 7 (5 points)
A rectangular quilt has a long side of 8 feet. A ribbon runs diagonally through the center of the quilt. The angle formed by the ribbon and the shorter side is 50 degrees. What is the perimeter of the quilt? Round to the nearest foot.
Question 7 options:
31 feet
29 feet
32 feet
16 feet
Question 8 (5 points)
Which scenario would most likely be normally distributed?
Question 8 options:
Number of fingers each person has in a restaurant.
Length of a movies at the theater.
Number of crayons in a box.
Age of children at a park.
Answer:
Step-by-step explanation:
i) Recursive rule is
[tex]a_{n+1} =a_n-10[/tex]
2) Explicit rule for the sequence is
this is arithmetic sequence with a = -1 and d = 15
Hence
[tex]a_n=-1+15(n-1)\\a_n=15n-16[/tex]
3) [tex]P(A and B) = \frac{2}{25} (\frac{5}{6} )\\=\frac{1}{15}[/tex]
4) Sample men = total/no of entries
=[tex]\frac{409}{10} =40.9[/tex]
=41
can someone help with this
Answer:
∠4 = 50°
Step-by-step explanation:
∠1 + ∠5 = 100°, but ∠1 = ∠5 ( corresponding angles ), hence
∠1 = ∠5 = 50°
∠4 = ∠1 = 50° ( vertical angles )
Which of the following numbers is located between points Q and R on the number line?
your answer is b) 3.88
How can this be solved?
Answer:
by multiplying all numbers seperatly by each other and adding those
Step-by-step explanation:
solve the system of equations
-2×+9y=11
-5×+2y=-34
×=____
y=____
someone help please!
X will equal 8 and y would equal 3
The solution to the system of equations -2x + 9y = 11 and -5x + 2y = -34 is found using the elimination method. The solution is x = 8 and y = 3.
Explanation:The system of equations provided appears to be:
-2x + 9y = 11 -5x + 2y = -34
To solve this system, we can use the method of substitution or elimination. In this case, we'll use the elimination method. First, we want to manipulate the equations so that when we add them together, one of the variables gets eliminated.
Let's multiply the first equation by 5 and the second equation by 2:
(-2x + 9y) * 5 => -10x + 45y = 55 (-5x + 2y) * 2 => -10x + 4y = -68
Now, we subtract the second equation from the first:
-10x + 45y - (-10x + 4y) = 55 - (-68)
Which simplifies to:
41y = 123
Divide both sides by 41 to find the value of y:
y = 123 / 41 = 3
Now, substitute y = 3 into one of the original equations to solve for x. We'll use the first equation:
-2x + 9(3) = 11
-2x + 27 = 11
-2x = 11 - 27
-2x = -16
Divide both sides by -2:
x = -16 / -2 = 8
The solutions to the system of equations are x = 8 and y = 3.
Based on the sample results, about what proportion of the population has a favorite social network?
HURRYYYYYY XD
Social Network | Proportion
-------------------------------------------
Site A: | P= 0.24
Site B: | P= 0.30
Site C: | P= 0.26
No Favorite: | P= 0.20
Options--
A-about 0.54
B-about 0.80
C-about 0.20
D-about 0.24
Answer:
the real answer is about 0.80
Step-by-step explanation:
so it is asking you about what proportion of the population has a favorite social network, and you see that there is a category that is a no favorite and site A B and C are the sites that are favorites. You add 0.24 + 0.30 + 0.26 and you get 0.80. And that is how you get 0.80
Product or quotient
3.92·0.6
0.78·0.13
5.004×1.2
6.3÷0.7
2.25÷1.5
8.1÷0.003
Answer:
2 44⁄125 [2,352] → Product
507⁄5000 [0,1014] → Product
6 3⁄625 [6,0048] → Product
9 → Quotient
1½ [1,5] → Quotient
2700 → Quotient
Step-by-step explanation:
Treat the decimals as whole numbers by moving the decimal marks all the way to the end of each decimal first, evaluate, then move the decimal mark back to the left the number of times as you started on for both decimals in total.
I hope this helps you out, and as always, I am joyous to assist anyone at any time.
The length of a rectangular park is 20 feet longer than the width of the park. If the lenght of the park is 36 feet, what is the width of the park?
Below is a labeled rectangle:
length = w + 20
we know length is 36 so we plug that in:
36 = w + 20
We need to isolate w and to do that we must subtract 20 from both sides:
(36 - 20) = w + (20 - 20)
16 = w + 0
w = 16
width is 16 feet
Hope this helped!
The focus point of the parabola?
The focus point of the parabola is (2,-2).
ANSWER
[tex](2,- 1)[/tex]
EXPLANATION
The given parabola is
[tex]y = \frac{1}{4} {x}^{2} - x - 1[/tex]
We need to write this parabola in the vertex form by completing the square,
[tex]y = \frac{1}{4} ( {x}^{2} - 4x) - 1[/tex]
[tex]y = \frac{1}{4} ( {x}^{2} - 4x + 4) - \frac{1}{4} \times 4 - 1[/tex]
[tex]y = \frac{1}{4} (x - 2 )^{2} - 2[/tex]
[tex] {(x - 2)}^{2} = 4(y + 2)[/tex]
The vertex is
(2,-2)
The focal length is
[tex]p = 1[/tex]
The focus is
[tex](2,-2 + 1)[/tex]
[tex](2,- 1)[/tex]
Find the sum of the first 25 terms of a geometric sequence where the first term is 177,147 and the common ratio is -1/3
Answer:
132860 to nearest whole number.
Step-by-step explanation:
Sum of n terms = a1 .(r^n - 1) / (r - 1).
S25 = 177,147 ((-1/3)^25 - 1) / (-1/3 - 1)
= 177,147 * -1 / -4/3
= 132860.
The given task involves finding the sum of the first 25 terms of a geometric sequence with a specific first term and common ratio. This is done using the sum formula for a finite geometric sequence, with the terms alternating in sign due to a negative common ratio.
Explanation:The subject question deals with the concept of a geometric sequence, specifically finding the sum of the first 25 terms. A key formula to solve this question is the sum of a finite geometric sequence: Sₙ = a₁(1 - rⁿ)/(1 - r), where a1 is the first term, r is the common ratio, and n is the number of terms.
In this case, a₁ is 177,147, r is -1/3 and n is 25. Substituting these values into the formula, the sum, S25 = 177,147 × (1 - (-1/3)25) / (1 - -1/3).
By solving this equation, we get the sum of the first 25 terms of the given geometric sequence. Note that due to the negative common ratio, the terms alternate in sign in this particular geometric sequence.
Learn more about Geometric Sequence here:https://brainly.com/question/34721734
#SPJ3
Find the eighth term of the
geometric sequence, given the
first term and common ratio.
a1=6 and r=-1/3
PLEASE HELP
Answer:
see explanation
Step-by-step explanation:
The n th term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio, hence
[tex]a_{8}[/tex] = 6 × [tex](-1/3)^{7}[/tex] = 6 × - [tex]\frac{1}{3^{7} }[/tex] = 6 × - [tex]\frac{1}{2187}[/tex] = - [tex]\frac{2}{729}[/tex]
If triangle ABC is an equilateral triangle and BD = 36 inches, find the value of x
Answer:
The value of x is [tex]24\sqrt{3}\ in[/tex]
Step-by-step explanation:
we know that
An equilateral triangle has three equal sides and three equal internal angles (each internal angle measure 60 degrees)
In this problem
see the attached figure to better understand the problem
In the right triangle ABD
[tex]sin(60\°)=BD/AB[/tex]
Solve for AB
[tex]AB=BD/sin(60\°)[/tex]
we have
[tex]BD=36\ in[/tex]
[tex]sin(60\°)=\frac{\sqrt{3}}{2}[/tex]
substitute
[tex]AB=36/(\frac{\sqrt{3}}{2})=24\sqrt{3}\ in[/tex]
Using the sine ratio, the value of x in the equilateral triangle is: 24√3 inches.
What is the Sine Ratio?The sine ratio used to solve a right triangle is given as, sin ∅ = opposite side/hypotenuse.
Given the following:
∅ = 60 degrees; sin 60 = √3/2Opposite length = 36 inchesHypotenuse length = xApply the sine ratio:
sin 60 = 36/x
√3/2 = 36/x
x = 36/√3/2
x = (36 × 2)/√3
x = 72/√3
Rationalize
x = (72)(√3) / (√3)(√3)
x = 72√3 / 3
x = 24√3
Learn more about the sine ratio on:
https://brainly.com/question/2920412
#SPJ5
Classify the triangle shown below. Check all that apply.
Answer:
It's actually right and scalene
Step-by-step explanation:
Since there is a ninety degree angle, it isn't obtuse or acute because the angle is a right angle. And since all the side lengths are different, it must be scalene in comparison to isoceles or equilateral.
The given triangle is Right angled triangle and Scalene triangle i.e. option A and E.
What is triangle ?Triangle is a two dimensional shape having three side and sum of all angles is equals to .
We have,
A triangle with,
Angles of 90°, 53°, 37° and
Sides 3, 4, 5.
So,
We know that,
When a triangle have any angle equals to 90° then it is a Right angled triangle.
Now,
When a triangle have any three sides unequal and all three angles are of different measures, then it is Scalene triangle.
So,
From the above mentioned statements we can say that triangle is Right angled and Scalene triangle.
Hence, we can say that the given triangle is Right angled triangle, Scalene triangle.
To know more about triangle click here
https://brainly.com/question/2773823
#SPJ2
kent can paint a certain room in 6 hours, but Kendra needs 4 hours to paint the same room. How long does it take them to paint the room if they work together?
About 2 and a half hours
Which statement is true about the given information?
BD = 1/2BC
BC = 1/2 BE
OBD CE
BC - BD
- Since lines BC, CD, and DE are all congruent, then we know that every time a line reaches either a point or an orange line, we can consider that to have a value of 1, for instance. BD and CE, in this case, both have a value of 6, and therefore the correct answer is BD=CE.
The option third BD ≅ CE is correct because BD and CE are equal in length, so they are congruent.
What is the congruent geometry?Congruent geometry are those that are exactly the same size and shape. Congruent is represented by the symbol ≅
We have a line segment shown in the figure:
From the figure:
BD = 2BC
BE = 3BC
BC ≅ BD (as the BC and BD are unequal in length, so they cannot be congruent)
BD ≅ CE (as the BD and CE are equal in length, so they are congruent)
Thus, the option third BD ≅ CE is correct because BD and CE are equal in length, so they are congruent.
Learn more about the congruent geometry here:
brainly.com/question/12413243
#SPJ2
Please help and with steps. I suck at these and really don’t understand them
Answer:
see explanation
Step-by-step explanation:
The n th term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 10 and d = - 3, hence
[tex]a_{n}[/tex] = 10 - 3(n - 1) = 10 - 3n + 3 = - 3n + 13, so
[tex]a_{n}[/tex] = - 3n + 13 ← n th term formula
Collin surveyed 12 teachers At his school to determine how much each person budgets for lunch. He recorded his results in the table.
(Answers are listed in photo)
Answer:
mean =median, so the data is symmetrical
Step-by-step explanation:
Given
Data set= {10,5,8,10,12,6,8,10,15,6,12,18}
Mean= Sum of data points/number of data points
= (10+5+8+10+12+6+8+10+15+6+12+18)/12
=10
Median= mid value
={5,6,6,8,8,10,10,10,12,12,15,18}
Middle values are 10 and 10
Median = 10+10/2
= 20/2
= 10
Mean= median so there will be no skewness and the distribution is equal !
A line segment begins at the point (-4,-9) and ends at the point (21, 31.625).
What are the coordinates of the point that partitions this line segment into two line segments whose lengths are in the ration of 2:3?
Answer:
(6 , 7.25)
Step-by-step explanation:
Given in the question coordinates (-4,-9) and (21,31.625)
x1 = -4
y1 = -9
x2 = 21
y2 = 31.625
Ratio
a : b
2 : 3
Formula to use
x = x1 + [tex]\frac{a}{a+b}[/tex](x2-x1)
y = y1 + [tex]\frac{a}{a+b}[/tex](y2 -y1)
Plug values on the formula
x = -4 + [tex]\frac{2}{2+3}(21+4)[/tex]
x = 6
y = -9 + [tex]\frac{2}{2+3}(31.625+9)[/tex]
y = 7.25
Co-ordinates of the point which divide the line into 2:3 is
(6 , 7.25)
Final answer:
To divide a line segment with endpoints (-4, -9) and (21, 31.625) in a 2:3 ratio, we use the section formula to find the partition point, which is (21, 7.25).
Explanation:
The student is asking how to find the point that divides a line segment in a particular ratio, which is a common problem in coordinate geometry. Given the end points of the line segment at (-4,-9) and (21, 31.625) and the ratio of 2:3, we can use the section formula to find the required point.
Here's how we do it step by step:
To partition the segment in the ratio of 2:3, multiply the coordinates of the first point by 3, and the coordinates of the second point by 2.Add the results from step 1 to obtain the sum for each coordinate.Finally, divide these sums by the sum of the ratios, which is 2+3=5.Applying the formula, the coordinates of the point (x, y) are:
x = (-4×3 + 21×2)/5 = (63 + 42)/5 = 105/5 = 21
and
y = (-9×3 + 31.625×2)/5 = (-27 + 63.25)/5 = 36.25/5 = 7.25
Therefore, the coordinates of the partitioning point are (21, 7.25).
Apply the distributive property to simplify the expression.
−9(−2x − 3)
A) 18x + 27
B) 18x − 27
C) −18x + 27
D) −18x − 27
we called it the rainbow method :)
The answer is A.
-9 • -2x = 18x
-9 • -3 = 27
Therefore, it is 18x+27
PROBLEM 1 An instant lottery game gives you probability 0.10 of winning on
any one play. Plays are independent of each other. You play 4 times. Let X
represent the number of times you win.
o What is the probability that you don't win at all?
Answer:
X=60% Chance
Step-by-step explanation:
This is because if you take 1 whole (100%), imagine it is at the value of 1, 4x.10=.40. 1-.40=.60 which is equal to 60%
A line passes through the points (1,2) and (3,1) what is the slope of the line
Answer:
-1/2
Step-by-step explanation:
The slope of a line is given by
m = (y2-y1)/(x2-x1)
= (1-2)/(3-1)
= -1/2
The slope is -1/2
Answer:
The slope is -1/2.
Step-by-step explanation:
Slope formula:
[tex]\displaystyle \frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\displaystyle \frac{1-2}{3-1}=\frac{2}{-1}=-\frac{1}{2}[/tex]
[tex]\Large\textnormal{Therefore, the slope is -1/2.}[/tex]