Answer:
3.0 seconds
Step-by-step explanation:
i took the test.
The time it takes the rock to reach 50 feet on its way down is 13.2 seconds and option B is the correct answer.
We have,
We are given the equation for the height of the rock as it travels upward and then downward:
h = -1672 + 63.2t - 4.9t²
We want to find the time it takes for the rock to reach a height of 50 feet on its way down.
This means we need to solve for t when h = 50:
50 = -1672 + 63.2t - 4.9t²
Rearrange the equation to isolate the quadratic term:
4.9t² - 63.2t + (1672 + 50) = 0
4.9t² - 63.2t + 1722 = 0
For an equation of the form "ax² + bx + c = 0", the solutions for "x" are given by:
x = (-b ± √(b² - 4ac)) / 2a
In your equation, the coefficients are:
a = 4.9
b = -63.2
c = 1722
Plugging these values into the quadratic formula:
t = (-(-63.2) ± √((-63.2)² - 4 * 4.9 * 1722)) / (2 * 4.9)
Now, let's calculate the discriminant (the value inside the square root):
Discriminant = (-63.2)² - 4 * 4.9 * 1722 ≈ 39884.96 - 33529.6 ≈ 6355.36
Since the discriminant is positive, there are two distinct real solutions for "t".
Now, plug the discriminant back into the quadratic formula and solve for "t":
t = (63.2 ± √6355.36) / 9.8
Now, calculate the square root of the discriminant:
√6355.36 ≈ 79.58
Now, plug in the values for "t":
t₁ = (63.2 + 79.58) / 9.8 ≈ 13.02
t₂ = (63.2 - 79.58) / 9.8 ≈ -1.69
So, the solutions for the equation 4.9t² - 63.2t + 1722 = 0 are approximately:
t₁ ≈ 14.61
t₂ ≈ -1.69 (rejected)
Thus,
The time it takes the rock to reach 50 feet on its way down is B. 13.2 seconds.
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Which shape has the least lines of symmetry?
Answer:
A
Step-by-step explanation:
B, C, D are all symmetrical
Answer:
a
Step-by-step explanation:
since B, C, D are all symmetrical it should be a
Seamus draws a triangle with angles of measures 40°, 60°, and 80°. Edwina draws a triangle with these same three angle measures. Which statement must be true?
A Edwina's triangle is the same size as Seamus's triangle.
B Edwina's triangle is the same shape as Seamus's triangle.
C The perimeter of Seamus's triangle is greater than the perimeter of Edwina's triangle.
D The area of Edwina's triangle is less than the area of Seamus's triangle.
Answer:
It may be D or A hopeit helps
Step-by-step explanation:
find the difference quotient of the rational function, r(t) = -3/t+6
Answer:
r(t)= -3/t+6
r(t)= -3/6t=6
Answer: the answer is D
Step-by-step explanation:
Just did the assignment rn
The probability distribution for a
random variable x is given in the table.
-5
3
-2
0
2
3
Probability
117
.13
.33
-16
11
-10
Find the probability that x<-3
Answer:
[tex]P(x \le -3) =0.30[/tex]
Step-by-step explanation:
Given
The attached probability distribution of x
Required
Find [tex]P(x \le -3)[/tex]
To do this, we consider all values of x less than or equal to-3.
So, we have:
[tex]P(x \le -3) =P(x=-5) + P(x = -3)[/tex]
From the table:
[tex]P(x=-5) = 0.17[/tex]
[tex]P(x = -3) = 0.13[/tex]
So, the equation becomes
[tex]P(x \le -3) =P(x=-5) + P(x = -3)[/tex]
[tex]P(x \le -3) =0.17 + 0.13[/tex]
[tex]P(x \le -3) =0.30[/tex]
student will randomly select a tile from a bag containing one red one yellow one blue and one green tile and then roll a cube with faces numbered 1 through 6 what is the probability that a student draws a red or yellow towel in rolls a number between 1 and 3 enter your answer as a percentage to the nearest percent
I NEeD My BRiAnLiEsT PeRsOn
Answer:
25%Step-by-step explanation:
There are 4 colors, probability of red or yellow:
P(red or yellow) = 2*1/4 = 1/2And a cube faces 1 to 3:
P(1 to 3) = 3*1/6 = 1/2Probability of the two events above:
1/2*1/2 = 1/4 = 25%Solve the system of equations. 2 x − 6 y = 5 x + y = 2 no solution ( 17 8 , − 1 8 )
Answer:
it seems you have made a typo
Step-by-step explanation:
A rectangle has a length of 17 less than 6 times it's width. If the area of the rectangle is 7585 square feet find the length of the rectangle
9514 1404 393
Answer:
205 ft
Step-by-step explanation:
Let w represent the width of the rectangle. Then the length is (6w-17) and the area is ...
A = LW
7585 = (6w-17)(w)
6w² -17w -7585 = 0
Perhaps most straightforward is using the quadratic formula to solve this.
For ax² +bx +c = 0, the solution is x = (-b±√(b²-4ac))/(2a). For the above quadratic, the solution is ...
[tex]x=\dfrac{-(-17)\pm\sqrt{(-17)^2-4\cdot6\cdot(-7585)}}{2\cdot6}=\dfrac{17\pm\sqrt{182329}}{12}\\\\x=\dfrac{17\pm427}{12}=\{-34\frac{1}{6},37\}[/tex]
The width is 37 feet, so the length is ...
6(37) -17 = 205 . . . feet
The length of the rectangle is 205 feet.
Write an inequality for the sentence below and then solve and check it. The sum of w and nine is less than 18
Answer:
w < 9
Step-by-step explanation:
w + 9 < 18
To solve this inequality, we MUST get the w by itself
Subtraction Property of Equality w + 9 - 9 < 18 - 9
Answer w < 9
As the teams fundraiser,Agnes and Betty both sold candy bars at the end of the fundraiser Agnes determined that she sold 8 more candy bars than Betty sold if Agnes and Betty sold a total of 348 candy bars how many did Betty sell the
Answer:
356
Step-by-step explanation:
HELPPPP!!!!! What is the value of y?
B
60
А
5
с
Enter your answer, as an exact value, in the box.
y =
Answer:
y = 8.66
Step-by-step explanation:
tan 60° = y/5
1.7321= y/5
y = 8.66
Which graph represents the parametric equations x = 3t and y = One-halft3 – 1, where –2 ≤ t ≤ 3?
Answer:
D
Step-by-step explanation:
EDG 2021
Answer:
D is the answer
Step-by-step explanation:
WILL MARK BRAINLIEST!!! PLEASE ANSWER!!! WRONG ANSWERS JUST FOR POINTS WILL BE REPORTED!!!!!!!!!!!!!!
Answer:
where's the question???
Step-by-step explanation:
Step-by-step explanation:
Volume of cylinder=πr²h
A shark swims at a constant rate of
25
miles per hour. If
h
represents the number of hours, and
m
represents the total number of miles the shark swims, which equation correctly represents the relationship?
Help pls help plsssssss
Answer:
bro its 10
Step-by-step explanation:
5 kilometers in 30mins and if he stayed at the same rate for an hour he would have ran 10 kilometers cause 5 x 2 = 10
find the missing side lengths
Answer:
Step-by-step explanation:
first use tan Ф = opp /adj to find x tan(30) = √3 / 3
then use sin Ф = opp / hyp to find y sin(30) = 1/2
tan(30) = (√3) / 3 = x / 48
x = (48√3) / 3
x = 16√3
sin(30) = 1/2 = x / y
y = x / (1/2)
y = 2x x = 16√3
y = 2[16√3]
y = 32√3
check using a² + b² = c²
x² + 48² = y²
(16√3)² + 48² = (32√3)²
256 · 3 + 2304 = 1024 · 3
768 + 2304 = 3072
3072 = 3072
The average winter snowfall for Syracuse, New York, for December, January, February is 27.5 inches per month. If Syracuse receives 24 inches of snow in December and 32 inches in Januar how much snow is required in February to exceed the 3 month average?
Answer: More than 26.5 inches
Step-by-step explanation:
Solve this equation :
[tex]\frac{32+24+x}{3} \geq 27.5[/tex]
x>26.5
Wayne Gretsky scored a Poisson mean six number of points per game. sixty percent of these were goals and forty percent were assists (each is worth one point). Suppose he is paid a bonus of 3K for a goal and 1K for an assist. (a) Find the mean and standard deviation for the total revenue he earns per game. (b) What is the probability that he has four goals and two assists in one game
Answer:
a) The mean for the total revenue he earns per game is of 13.2K while the standard deviation is of 3.63K.
b) 0.05 = 5% probability that he has four goals and two assists in one game
Step-by-step explanation:
In hockey, a point is counted for each goal or assist of the player.
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval. The standard deviation is the square root of the mean.
(a) Find the mean and standard deviation for the total revenue he earns per game.
60% of six are goals, which means that 60% of the time he earned 3K.
40% of six are goals, which means that 40% of the time he earned 1K.
The mean is:
[tex]\mu = 6*0.6*3 + 6*0.4*1 = 13.2[/tex]
The standard deviation is:
[tex]\sigma = \sqrt{\mu} = \sqrt{13.2} = 3.63[/tex]
The mean for the total revenue he earns per game is of 13.2K while the standard deviation is of 3.63K.
(b) What is the probability that he has four goals and two assists in one game
Goals and assists are independent of each other, which means that we find the probability P(A) of scoring four goals, the probability P(B) of getting two assists, and multiply them.
Probability of four goals:
60% of 6 are goals, which means that:
[tex]\mu = 6*0.6 = 3.6[/tex]
The probability of scoring four goals is:
[tex]P(A) = P(X = 4) = \frac{e^{-3.6}*(3.6)^{4}}{(4)!} = 0.19122[/tex]
Probability of two assists:
40% of 2 are assists, which means that:
[tex]\mu = 6*0.4 = 2.4[/tex]
The probability of getting two assists is:
[tex]P(B) = P(X = 2) = \frac{e^{-2.4}*(2.4)^{2}}{(2)!} = 0.26127[/tex]
Probability of four goals and two assists:
[tex]P(A \cap B) = P(A)*P(B) = 0.19122*0.26127 = 0.05[/tex]
0.05 = 5% probability that he has four goals and two assists in one game
What is the surface area of the composite figure shown?
Answer:
531 m²
Step-by-step explanation:
9x9x5=405 (5 sides that are 9x9, including the bottom)
1/2x9x7x4=126 (4 triangles on top)
405+126=531
Flip-flop sets are on sale at buy
one, get one half-off. Maria and
Jackie each decide to get a pair.
The flip-flops are priced at $24.00.
If they decide to split the total
evenly, then how much will each
pay?
7,485 divived by 6 equals
1247.5
Hope this helps :T
A water storage tank is cone shaped. The radius of the tank is 20 feet and the height of the tank is 35 feet.
Study the figure below...
20 feet...
35 feet...
Which measurement represents the volume of the water storage tank
What figure can be made using the net shown?
a triangular prism
a rectangular prism
a triangular pyramid
a rectangular pyramid
Answer:
A rectangular pyramid
Answer:
rectangular pyramid
Step-by-step explanation:
just took the test
The figure can be made using the net shown is a rectangular pyramid.
What is Difference between Pyramid and Prism?A three-dimensional shape is a pyramid. A pyramid's flat triangular faces unite at a common point known as the apex and have a polygonal base.
A prism is a polyhedron in geometry made up of an n-sided polygon basis, a second base that is a rigidly translated copy of the first base, and n additional faces that must all be parallelograms and connect the corresponding sides of the two bases.
Pyramids and prisms are both three-dimensional solids with flat faces and bases.
Yet, a pyramid only has one base, whereas a prism has two bases that are identical.
Here, the base is rectangular then the figure shows A rectangular pyramid.
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Cory has $24 more than twice as much as Stan. Together they have $150. How much money dose each have ?
Answer:
99 and 51
Step-by-step explanation:
worth 25 help and show work :)
Answers:
x = 7*sqrt(3)
y = 7
===========================================================
Explanation:
We have a 30-60-90 triangle here since the missing acute angle is 90-60 = 30 degrees. Or you could note how 30+60+90 = 180.
The side length y is the shorter leg as it's opposite the smallest angle. It's equal to half of the hypotenuse. So y = 14/2 = 7.
The longer leg x is equal to y*sqrt(3). We multiply the shorter leg by sqrt(3) to get the longer leg. This means
x = y*sqrt(3) = 7*sqrt(3)
----------
You could also use the pythagorean theorem if you knew that y = 7 and you had the hypotenuse value as well. You could solve like so
a^2 + b^2 = c^2
7^2 + b^2 = 14^2
b^2 = 14^2 - 7^2
b^2 = 147
b = sqrt(147)
b = sqrt(49*3)
b = sqrt(49)*sqrt(3)
b = 7*sqrt(3)
Which matches up with the value of x we found earlier.
PLEASE !!! HELP QUICKLY !!!
Some credit cards offer a low introductory APR for a set period of time. After the introductory period is over, the APR is increased to a new rate. According to the sample credit card disclosure agreement, after a period of ,_______ the APR will increase to ______.
Blank 1 options (one month, six months, one year)
Blank 2 options (8.99%, 10.99%, 12.99%, 14.99%, 28.99%)
Answer:
1 Year & 14.99%
Step-by-step explanation:
During the holiday season,
9,456 people visit the mall
every day. How many
people visit the mall in 7
Solve the equation 23+n=29 using the inverse operation.
Answer:
n=6
Step-by-step explanation:
i used math-way :P
Is Michael correct? Will choose brainly
What is the measure of RST? S O A. 158° 07 O B. 790 G. 689 R D. 2020 158°
Create a table and a graph from the equation y=4x