Pekka tosses a ball out of a window that is 40 feet in the air. Its initial velocity is 15
feet per second. The path of the ball is represented by
h = -16t2 + 15t + 40
How long does it take for the ball to hit the ground (in seconds) rounded to the
nearest hundredth?
Answers
Answer:
2.12 seconds
Step-by-step explanation:
Given
\(h(t) = -16t^2 + 15t + 40\)
Required
Determine how long the ball hits the ground
When the ball hits the ground means that \(h(t) = 0\)
So, we have that:
\(h(t) = -16t^2 + 15t + 40\) becomes
\(0 = -16t^2 + 15t + 40\)
Reorder
\(-16t^2 + 15t + 40 = 0\)
Multiply through by -1
\(16t^2 - 15t - 40 = 0\)
Solve using quadratic:
\(t = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}\)
Where
\(a = 16\) \(b = -15\) \(c = -40\)
So, we have:
\(t = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}\) becomes
\(t = \frac{-(-15)\±\sqrt{(-15)^2 - 4*16*-40}}{2*16}\)
\(t = \frac{15\±\sqrt{(-15)^2 - 4*16*-40}}{2*16}\)
\(t = \frac{15\±\sqrt{225 +2560}}{32}\)
\(t = \frac{15\±\sqrt{2785}}{32}\)
\(t = \frac{15\±52.77}{32}\)
Split:
\(t = \frac{15+52.77}{32}\) or \(t = \frac{15-52.77}{32}\)
\(t = \frac{67.77}{32}\) or \(t = \frac{-37.77}{32}\)
\(t = 2.12\) or \(t = -1.18\)
But time can't be negative
So:
\(t = 2.12\)
Hence, time to hit the ground is 2.12 seconds
Related Questions
Solve for x 3.8+4.5x-1.4=8.25
Answers
Answer:
1.3 should be right
Step-by-step explanation:
X = 1.3
What is the circumference of a circle whose radius is 20 feet? Leave answer in terms of it. ) A) 107 feet B) 20 feet 407 feet D) 1007 feet
Answers
Determine the equation of the parabola with vertex (1, -3) and directrix x = = -1.
Answers
\((x - 1)^2\) = 4|x + 1|(y + 3) This is the equation of the parabola with the given vertex (1, -3) and directrix x = -1.
To determine the equation of the parabola with the given vertex and directrix, we can use the standard form of the equation for a parabola
with a vertical axis of symmetry:
\((x - h)^2\) = 4p(y - k)
where (h, k) represents the vertex coordinates, and p is the distance between the vertex and the directrix.
In this case, the vertex is (1, -3), so h = 1 and k = -3. The directrix is x = -1, which means the distance between the vertex and the directrix is 1 unit.
Substituting the values into the standard form equation, we have:
\((x - 1)^2\)= 4p(y + 3)
To find the value of p, we can use the distance formula between a point (x, y) on the parabola and the directrix x = -1:
p = |x - (-1)|
Since the distance is 1 unit, we have:
p = |x + 1|
Now we can substitute this value back into the equation:
\((x - 1)^2\) = 4|x + 1|(y + 3)
This is the equation of the parabola with the given vertex (1, -3) and directrix x = -1.
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You bought one of Rocky Mountain Manufacturing Co. ’s 8 percent coupon bonds one year ago for $1,052. 80. These bonds make annual payments and mature nine years from now. Suppose that you decide to sell your bonds today, when the required return on the bonds is 7. 5 percent. If the inflation rate was 4 percent over the past year, what would be your total real return on the investment? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e. G. , 32. 16. )
Answers
The bond's present value is $1,127.06 with a required return of 7.5%. Adjusting for 4% inflation, the real invested amount was $1,010.69, resulting in a total real return of 11.51%.
The first step is to calculate the coupon payment. The bond has an 8 percent coupon rate and a face value of $1,000, so the annual coupon payment is 0.08 x $1,000 = $80.
Since the bond was purchased one year ago, the number of coupon payments remaining is 9 - 1 = 8.
Using the present value formula, we can find the value of the bond today:
PV = (coupon payment / required return) x [1 - 1 / (1 + required return)^n] + face value / (1 + required return)^n
where PV is the present value of the bond, n is the number of years remaining until maturity, and the required return is 7.5 percent.
Plugging in the values, we get:
PV = ($80 / 0.075) x [1 - 1 / (1 + 0.075)^8] + $1,000 / (1 + 0.075)^8 = $1,127.06
To calculate the real return on investment, we need to adjust for inflation. Since the inflation rate was 4 percent over the past year, the purchasing power of $1,052.80 has decreased by 4 percent, or $42.11. Therefore, the real amount invested was $1,052.80 - $42.11 = $1,010.69.
The total real return on investment is the difference between the present value of the bond and the real amount invested, expressed as a percentage of the real amount invested:
Total real return = (PV - real amount invested) / real amount invested x 100%
Plugging in the values, we get:
Total real return = ($1,127.06 - $1,010.69) / $1,010.69 x 100% = 11.51%
Therefore, the total real return on investment is 11.51 percent.
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The width of a rectangle is 2 cm less than the length. The
perimeter is greater than 28 inches. Describe the dimensions
of the rectangle.
Length=?
Width=?
Answers
Answer:
2+2+28+28=60 is the answer of the perimeter
Step-by-step explanation:
Inequalities help us to compare two unequal expressions. The length of the rectangle can be 19 cm, while its width will be 17 cm.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.
It is mostly denoted by the symbol <, >, ≤, and ≥.
Let the length of the rectangle be represented by x centimeters. Given the width of a rectangle is 2 cm less than the length. Therefore, the width of the rectangle is (x-2) centimeters.
Since the perimeter of the rectangle should be greater than 28 inches, therefore,
Perimeter of the rectangle > 28 inches × 2.54 = 71.12 centimeters
Now, given the perimeter is greater than 28 inches. Therefore,
2[x+(x-2)] > 71.12
x + (x-2) > 35.56
x + x - 2 > 35.56
2x - 2 > 35.56
2x > 37.56
x > 18.78
x = 19
Thus, the length of the rectangle can be 19 cm, while its width will be 17 cms.
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Normalmente, el concepto griego "logos" se entiende como la máxima expresión de la cultura racionalista occidental, fundada por las primeras escuelas de filosofía clásica. De hecho, el nombre de las disciplinas científicas provienen de él: biología, filología, psicología, tecnología, etc. No obstante, el concepto "logos" no tiene un significado tan abstracto, puesto que involucra tanto el pensamiento como la acción, tanto lo interno como lo externo, tanto la idea mental como el decir la palabra. Tema:_________________________________________________________ Idea Principal: ___________________________________________________
Answers
Concept: "Logos" has had a significant impact on Western thought. Importance: its recognition of the interplay between rational thought and empirical observation Acknowledgement: role of language and discourse in shaping our understanding of the world.
Topic: The concept of "Logos" in Greek philosophy and its significance in modern scientific fields.
The concept of "Logos" is central to Greek philosophy and has been interpreted in various ways throughout history. In its most basic sense, "Logos" refers to rational thought, speech, and language. It is often associated with the divine or the cosmic principle that governs the universe, as well as human reasoning and discourse.
The significance of "Logos" can be seen in its influence on modern scientific fields, including biology, psychology, and technology, among others. The term "biology," for example, comes from the Greek words "bios" (life) and "logos" (word or reason), reflecting the idea that the study of life requires both empirical observation and rational analysis.
Similarly, the field of psychology, which deals with the workings of the human mind and behavior, derives its name from the Greek word "psyche," meaning "soul," and "logos," meaning "reason." This reflects the idea that the study of the mind and behavior requires both empirical research and theoretical analysis.
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Translation: The Greek word "logos" is typically interpreted as the pinnacle of Western rationalist civilization, having been established by the first schools of classical philosophy. In reality, he is responsible for the names of many scientific fields, including biology, philology, psychology, technology, and others. Since it requires both mind and action, internal and external, the mental notion and pronouncing the word, the concept of "logos" does not have such an abstract meaning. Topic:____________________________________________________ Principal Concept:
Dath on the weights (fb) of the contents of cans of det soda vecsus the contents of cans of the repiar version of the soda is summasized to the eigh. Assume that the hwo samples are independoct simple
Answers
The data on the weights (in fluid ounces) of the contents of cans of regular soda versus the contents of cans of the diet soda are summarized to eight. It is assumed that the two samples are independent and simple.
The given information is not clear and contains typographical errors, making it difficult to provide a specific explanation or analysis. The terms "dath," "fb," "det soda," "vecsus," and "repiar" are not recognizable or properly defined, which hinders a meaningful interpretation of the data.
To provide a thorough analysis, it is important to have accurate and well-defined data variables, clear research objectives, and an understanding of the study design. Without this information, it is not possible to generate a meaningful response or draw any conclusions from the given statement.
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Does the graph represent a linear expression?
Yes or No
Please answer fast!
Answers
What is 2x+8y in distributive property
Answers
g researchers are concerned about the rising prevalence of caesarian section undergone by pregnant women across the country. suppose that national statistics assume that only 32.7% of women undergo the risky procedure due to medical complications. in a sample of 16 expecting mothers, 7 reported undergoing a caesarian. a) can researchers continue their investigation assuming an approximation to the normal distribution is possible? b) calculate the probability of observing the results seen in the sample conducted by the researchers.
Answers
a) Yes, researchers can assume an approximation to the normal distribution.
b) The probability of observing 7 cases of caesarian in a sample of 16 is calculated using the binomial distribution.
To determine if researchers can assume an approximation to the normal distribution, we need to check if the sample size is sufficiently large. The sample size in this case is 16, and the probability of undergoing a caesarian is
7/16 = 0.4375.
We check the conditions np ≥ 10 and n(1-p) ≥ 10. For np, we have 16 * 0.4375 = 7, which is greater than 10. For n(1-p), we have
16 * (1 - 0.4375) = 9,
which is also greater than 10.
Since both np and n(1-p) are greater than 10, researchers can assume an approximation to the normal distribution for their investigation.
To calculate the probability of observing 7 cases of caesarian in a sample of 16, we use the binomial distribution. The probability is calculated as P(X = 7) = C(16, 7) * (0.327)⁷ * (1 - 0.327)⁽¹⁶⁻⁷⁾.
Evaluating this expression gives us the probability of observing the specific results seen in the sample.
Therefore, researchers can assume an approximation to the normal distribution, and the probability of observing the specific results in the sample can be calculated using the binomial distribution.
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does anybody understand
Answers
Answer:
A=6(9n^2+26n+36)
Step-by-step explanation:
A=6s^2
s=3n+6
A=6(3n+6)^2
A=6(3n+6)(3n+6)
A=6(9n^2+18n+18n+36)
A=6(9n^2+26n+36)
I hope this helps; please award brainliest!
The point at which two lunes intersect.
Answers
The point at which two lines intersect is referred to as point of intersection.
What is a point of intersection?In Mathematics and Geometry, a point of intersection simply refers to the location on a graph where two (2) lines intersect or cross each other, which is primarily represented as an ordered pair containing the point that corresponds to the x-coordinate (x-axis) and y-coordinate (y-axis) on a cartesian coordinate.
In order to graph the solution to a system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;
x² + y² = 100 ......equation 1.
3x - y = 30 ......equation 2.
Based on the graph shown, the solution to this system of equations is the point of intersection of the lines given by the ordered pairs (10, 0) and (8, -6).
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Complete Question:
What is the point at which two lines intersect?
PLSSS HELPP
2. Graph the piecewise function.
Answers
The graph for the given piecewise function is as provided in image.
What is piecewise function?
A piecewise function is a function f(x) which has different definitions in different intervals of x. The graph of a piecewise function has different pieces corresponding to each of its definitions. The absolute value function is a very good example of a piecewise function. Let us see why is it called so. We know that an absolute value function is f(x) = |x| and it is defined as:
f(x)=(x if x≥0 ,
-x if x><0)
We should read this piecewise function as
f(x) is equal to x when x is greater than or equal to 0 and
f(x) is equal to -x when x is lesser than 0.
Given piecewise function
f(x)=(3x-5 if x<=-1
-2x+3 if -1<x<4
2 if x>=4)
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For what value of the constant c is the function f continuous on (−[infinity], [infinity])?f(x) = cx^2 + 4x if x < 5x^3 − cx if x ≥ 5
Answers
The value of constant c for the given function is 3.5 .
The function says the when
x<5 f(x) = cx² + 4x
x>=5 f(x) = x³ - cx
Since the function is continuous from (-∞ , ∞) implies that the limits from both sides that is left hand limit (L.H.L) and right hand limit(R.H.L) must be equal .
\(lim_{x \rightarrow 5^{-}}\) = \(lim_{x \rightarrow 5^{+}}\\\)
Now , solving Left Hand Limit
\(lim_{x \rightarrow 5^{-}}\) f(x) = \(\lim_{h \rightarrow 0}\\\) f(5-h)
= \(\lim_{h \rightarrow 0}\\\\\) [c(5-h)² + 4(5-h)]
= c(5)² + 20
= 25c + 20
Now , solving Right Hand Limit
\(lim_{x \rightarrow 5^{+}}\) f(x) = \(\lim_{h \rightarrow 0}\\\) f(5+h)
= \(\lim_{h \rightarrow 0}\\\) [(5+h)³ - c(5+h)]
= (5)³ - 5c
= 125 - 5c
Now equate both LHL and RHL
25c + 20 = 125 - 5c
30c = 105
c = 105/30 =3.5
So , The value of constant c for the given function is 3.5 .
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the critical difference between statistical and nonstatistical sampling is: question 4 options: the required use of judgment in nonstatistical sampling.
Answers
statistics is the calculation or manipulation of data or any other things where the operation of addition division multiplication substraction will be held but not any other logic related to non tangible
non statistical sampling is where calculation or any other means of addition substraction is not done but the judgement is done on the basis of examiners mind but not on the basis of any calculation .
we can use statistic in every day life also in every field because if we do any calculation then it is a part of mathematical statistic
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In an election, 1200 total votes were cast for the 3 candidates. The second-place candidate received 155 fewer votes than the winner and 200 votes more than the third-place candidate. How many votes did the winner receive
Answers
The winner received 570 votes.
Let the winner candidate be c1
Let the second-place candidate be c2
Let the third-place candidate be c3
\(c2=c1-155\\\).........equation 1
\(c2=c3+200\\\)
\(c3=c2-200 \\\)
\(c3=c1-155-200\\\).........by equation 1
\(c3=c1-355\)........equation 2
Now we know,
\(c1+c2+c3=1200\)
\(c1+(c1-155)+(c1-355)=1200\) .....by equations 1 and 2
\(3c1-510=1200\)
\(3c1=1200+510\\3c1=170\\c1=570\)
Hence, The winner received 570 votes.
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Jessica is buying chicken wings and hamburger meat for a party. One bag of chicken wings costs $6. Hamburger meat costs $3 per pound. She must spend no more than $30. She also knows that she needs to buy at least 5 pounds of hamburger meat. Which system of inequalities can be used to determine the number of bags of chicken wings, x, and the number of pounds of hamburger meat, y, that Jessica should buy?(1 point)
Answers
Answer:
6x + 3y ≤ 30
y ≥ 5
Step-by-step explanation:
Let
x = number of bags of chicken wings
y = number of pounds of hamburger meat
Cost of one bag of chicken wings = $6
Cost of one pound of Hamburger meat = $3
She must spend no more than $30.
The inequality
6x + 3y ≤ 30
She also knows that she needs to buy at least 5 pounds of hamburger meat.
y ≥ 5
what is the sum of 3 2/3 - 1 4/5
Answers
Answer: 3 7/
Step-by-step explanation: Change 3 2/3 and 1 4/5 from mixed fraction to improper fraction, giving 11/2 (3×3=9, then 9+2=11) and 9/5 (1×5=5, then 5+4=9)1.
With 11/2 and 9/5, the LCM(Lowest Common Multiple) is 10. So 10÷2=5, then 5×11=55. Likewise, 10÷5=2, then 2×9=18.
55-18=37. Therefore the answer is 37/10. Change that back to mixed fraction and it gives you 3 7/10
La probabilidad de que el estudiante A apruebe un examen de MM-100 es 0.6, la probabilidad de que apruebe un estudiante B es 0.4 y la probabilidad de que ambos estudiantes aprueben es 0.3. ¿Cual es la probabilidad de que apruebe el estudiante B dado que el estudiante A aprueba.?
Answers
Answer:
0.5 = 50% probabilidad de que apruebe el estudiante B dado que el estudiante A aprueba.
Step-by-step explanation:
La probabilidad condicional :
\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)
En el cual:
P(B|A) es la probabilidad de que ocurra el evento B, dado que A sucedió.
\(P(A \cap B)\) es la probabilidad de que ocurran tanto A como B.
P(A) es la probabilidad de que ocurra A.
En esta pregunta :
Evento A: Estudiante A aprueba.
Evento B: Estudiante B aprueba.
La probabilidad de que el estudiante A apruebe un examen de MM-100 es 0.6
Entonces \(P(A) = 0.6\)
La probabilidad de que ambos estudiantes aprueben es 0.3
Entonces \(P(A \cap B) = 0.3\)
¿Cual es la probabilidad de que apruebe el estudiante B dado que el estudiante A aprueba.?
\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.3}{0.6} = 0.5\)
0.5 = 50% probabilidad de que apruebe el estudiante B dado que el estudiante A aprueba.
Please answer- what is the length of BW? ANSWER DIRECTLY NO LINK ( will give brainlist to whoever answers)
Answers
Answer:
148.49
Step-by-step explanation:
105 x √2 = 148.49
have a great day
help help please? i need it
Answers
Answer:
C, $12
Step-by-step explanation:
Every hour worked the employee earns $12. This is a fixed rate and the answer is shown in the 1st slot of the table -- 1 hour = $12
Answer:
12 dollars per hour
Step-by-step explanation:
For each hour worked, we make 12 dollars as show in the first column, 1 hour is 12 dollars
We can check using the last colum
48 dollars / 4 hours = 12 dollars per hour
Andrés va a colocar piso
a su cuarto, si el cuarto mide
3. 7m de ancho por 4. 5m de
largo y cada caja de piso
alcanza para 1. 54m2. ¿Cuántas
cajas de piso va a necesitar?
Answers
The number of floor boxes required to covered the entire room as per given area is equal to 11.
Length of the room = 3.7m
Width of the room = 4.5m
Area of each box = 1.54 square meters
To calculate the number of floor boxes needed,
Determine the total area of the room and then divide it by the area of each floor box.
The area of the room is ,
Area of the room = length × width
Plugging in the values we get,
⇒ Area of the room = 3.7m × 4.5m
⇒ Area of the room = 16.65m²
Now, calculate the number of floor boxes needed.
Number of floor boxes = Area of the room / Area of each floor box
Plugging in the values we have,
⇒Number of floor boxes = 16.65m² / 1.54m²
⇒Number of floor boxes ≈ 10.81
Since you cannot have a fraction of a floor box, we round up to the nearest whole number.
Therefore, Andres will need 11 floor boxes to cover the room.
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Las dos cifras de un número suman 11 . Si las cifras se invierten de orden se invierten de orden , se obtiene otro número que excede en 27 unidades al anterior¿De q número se trata ?
Answers
Answer:
El número es el 47
Step-by-step explanation: Con los dígitos de los siguientes números se obtiene que su suma es 11
47 4 + 7 = 11
38 3 + 8 = 11
29 2 + 9 = 11
Si se cambia el orden de los dígitos:
47 se convierte en 74 74 - 47 = 27
38 " " 83 83 - 38 = 45
29 " " 92 92 - 29 = 63
Entonces el número solicitado es el 47
Please help I’ll give brainliest
Answers
(2a-7) (2a-7)
ANSWER QUICK. PERSON WILL BE MARKED BRAINLY
Answers
Answer:
(2a-7)(2a-7) can be expanded using the FOIL method (First, Outer, Inner, Last):
Step-by-step explanation:
First: (2a)(2a) = 4a^2
Outer: (2a)(-7) = -14a
Inner: (-7)(2a) = -14a
Last: (-7)(-7) = 49
Combining these terms, we have:
(2a-7)(2a-7) = 4a^2 - 14a - 14a + 49
Simplifying further:
= 4a^2 - 28a + 49
Answer:
4a² - 28a + 49
Step-by-step explanation:
Either use FOIL or (a + b)² = a² + 2ab + b²
Using FOIL:
(2a - 7)(2a - 7) = 4a² - 14a - 14a + 49 = 4a² - 28a + 49
Using (a + b)² = a² + 2ab + b²:
(2a - 7)(2a - 7) = (2a - 7)² = 4a² - 28a + 49
plzzz helpppppppppp meeeeeeeeeee
Answers
Answer:
254.47 m or B
Step-by-step explanation:
First you find the area of the circle and then you subtract it from the area of the square to get your answer.
Hope it helps c:
Answer: Choice A) about 69.53 m^2
==========================================================
Work Shown:
A = area of the square
A = side*side
A = 18*18
A = 324 square meters
---------
B = area of the circle
B = pi*r^2
B = pi*9^2 ..... note that the radius is half the diameter
B = 81pi
B = 254.469004940773
B = 254.4690 square meters
I used the calculator's stored version of pi to compute that approximate value.
---------
C = area of shaded region
C = A - B
C = 324 - 254.4690
C = 69.531
C = 69.53 square meters
So that points us to choice A as the final answer.
---------
Side note: The shaded region is about C/A = (69.531)/(324) = 0.2146 = 21.46% of the square's area. So this is the approximate chances of landing in the shaded area if you randomly threw a dart.
if you were 2 years old in 2011 how old would you be in 2020?
Answers
Answer:
11 years
Step-by-step explanation:
2 years that you were in 2011
2020-2011= 9
2+9=11
also meaning they were born in 2009
2020-2009 also equals 11
this prolly doesnt make sense but hope it helps :) <3
Answer:
11 years old?
Step-by-step explanation:
Solve for x ( 5 x − 1 = 2 ) Give your answer as a fraction in its simplest form.
Answers
Answer: x is 3/5
Step-by-step explanation: your welcome
help pls
The base of a fountain is in the shape of a quadrilateral, as shown.
Find the measure of each interior angle of the fountain.
Answers
Answer:
∠ A = 96° , ∠ B = 112° , ∠ C = 64° , ∠ D = 88°
Step-by-step explanation:
the sum of the interior angles of a quadrilateral is 360°
sum the angles and equate to 360
14n + 8n + 11n + 12n = 360
45n = 360 ( divide both sides by 45 )
n = 8
Then
∠ A = 12n = 12 × 8 = 96°
∠ B = 14n = 14 × 8 = 112°
∠ C = 8n = 8 × 8 = 64°
∠ D = 11n = 11 × 8 = 88°
In a class of 25 students, 15 of them have a cat, 16 of them have a dog and 3 of them have neither.
Find probability that a student chosen at random has a cat or a dog.
Answers
The probability that a student chosen at random has a cat or a dog is; P(cat or dog) = 22/25.
What is probability?
Probability is that the branch of arithmetic regarding numerical descriptions of however probably an incident is to occur, or however probably it's that a proposition is true. The likelihood of an incident could be a range between 0 and 1.
Main body:
According to the question, the total number of students is; 25.
15 of them have a cat
16 of them have a dog
while, 3 of them have neither
where, x = number if students who own a cat and a dog.
Consequently, the total number of students who own a cat, a dog, both or neither is as follows;
15-x + x + 16-x + 3 = 25.
-x = 25 - 34
In essence, x = 9
the number of students who own a cat and a dog is 9.
Therefore, probability that a student chosen at random has a cat and a dog is therefore;
P(cat and dog) = 9/25.
Therefore probability that a student chosen at random has a cat or a dog is 22/25.
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