A rocket is launched from atop a 55-foot cliff with an initial velocity of 138 ft/s. a. Substitute the values into the vertical motion formula h = −16t2 + vt + c. Let h = 0. b. Use the quadratic formula find out how long the rocket will take to hit the ground after it is launched. Round to the nearest tenth of a second.
A hiker is lost in the woods. A search team has created a coordinate grid to represent the woods. Each unit on the grid is one square mile. The hiker was last seen at (4, -9) and could have walked 10 miles in any direction since then. Which equation represents the area the hiker could be in?
A) (x - 4)2 + (y + 9)2 = 102
B) (x + 4)2 + (y - 9)2 = 102
C) (x + 4)2 + (y + 9)2 = 1002
D) (x - 4)2 + (y - 9)2 = 1002
How would the expression x^2-4 be rewritten using Difference of Squares?
A) (x+2)^2
B) (x-4)^2
C) (x+4)(x-4)
D) (x+2)(x-2)
d.........................
How are experimental and theoretical probability alike?
What perfect squares divide into 337? I only need two!
Use the Venn diagram to calculate probabilities.
Which probability is correct?
P(A|B)=1/2
P(B|A)=7/20
P(A|C)=6/23
P(C|A)=13/17
Answer: The correct probability is (D) [tex]P(C/A)=\dfrac{13}{17}.[/tex]
Step-by-step explanation: We are given to select the option that gives the correct probability statements using the Venn-diagram in the figure.
From the figure, we can see that there are three events, A, B and C.
And,
[tex]n(A)=1+6+7+3=17,\\\\n(B)=1+6+4+9=20,\\\\n(C)=6+4+6+7=23,\\\\n(A\cap B)=1+6=7,\\\\n(A\cap C)=6+7=13,\\\\n(B\cap C)=6+4=10,\\\\n(A\cap B\cap C)=6.[/tex]
By the law of SET THEORY, we have
[tex]n(A\cup B\cup C)=n(A)+n(B)+n(C)-n(A\cap B)-n(B\cap C)-n(A\cap C)+n(A\cap B\cap C)\\\\\Rightarrow n(A\cup B\cup C)=17+20+23-7-13-10+6\\\\\Rightarrow n(A\cup B\cup C)=36.[/tex]
So, the total number of elements in the sample space 'S' will be
n(S) = 36 + 8 = 44.
Therefore,
[tex]P(A/B)=\dfrac{P(A\cap B)}{P(B)}=\dfrac{\dfrac{n(A\cap B)}{n(S)}}{\dfrac{n(B)}{n(S)}}=\dfrac{7}{44}\times \dfrac{44}{20}=\dfrac{7}{20},\\\\\\\\P(B/A)=\dfrac{P(B\cap A)}{P(A)}=\dfrac{\dfrac{n(B\cap A)}{n(S)}}{\dfrac{n(A)}{n(S)}}=\dfrac{7}{44}\times \dfrac{44}{17}=\dfrac{7}{17},\\\\\\\\P(A/C)=\dfrac{P(A\cap C)}{P(C)}=\dfrac{\dfrac{n(A\cap C)}{n(S)}}{\dfrac{n(C)}{n(S)}}=\dfrac{13}{44}\times \dfrac{44}{23}=\dfrac{13}{23},\\\\\\\\P(C/A)=\dfrac{P(C\cap A)}{P(A)}=\dfrac{\dfrac{n(C\cap A)}{n(S)}}{\dfrac{n(A)}{n(S)}}=\dfrac{13}{44}\times \dfrac{44}{17}=\dfrac{13}{17}.[/tex]
Thus, the correct probability is [tex]P(C/A)=\dfrac{13}{17}.[/tex]
Option (D) is correct.
The probability P(A/B) is 7/20, the probability P(B/A) is 7/17, the probability P(A/C) is 13/23, and the probability is P(C|A) is 13/17 option fourth is correct.
What is the Venn diagram?It is defined as the diagram that shows a logical relation between sets.
The Venn diagram consists of circles to show the logical relation.
For the value of probability P(A|B):
We know that:
[tex]\rm P(A/B)=\frac{P(A\cap B)}{P(B)} \Rightarrow \frac{\frac{n(A\cap B)}{n(T)} }{\frac{n(B)}{n(T)} }[/tex]
From the Venn diagram:
n(A∩B) = 7, n(B) = 20, n(T) = 44
P(A/B) = (7/44)×44/20)
P(A/B) = 7/20
For P(B|A):
[tex]\rm P(B/A)=\frac{P(B\cap A)}{P(A)} \Rightarrow \frac{\frac{n(B\cap A)}{n(T)} }{\frac{n(A)}{n(T)} }[/tex]
The values of n(B∩A) = 7, n(A) =17
P(B/A) = (7/44)×(44/17)
P(B/A) = 7/17
For P(A|C):
[tex]\rm P(A/C)=\frac{P(A\cap C)}{P(C)} \Rightarrow \frac{\frac{n(A\cap C)}{n(T)} }{\frac{n(C)}{n(T)} }[/tex]
The value of n(A∩C) = 13, n(C) = 23
P(A/C) = (13/44)×(44/23)
P(A/C) = 13/23
For P(C|A):
[tex]\rm P(C/A)=\frac{P(C\cap A)}{P(A)} \Rightarrow \frac{\frac{n(C\cap A)}{n(T)} }{\frac{n(A)}{n(T)} }[/tex]
The values of n(C∩A) = 13, n(A) = 17
P(C|A) = (13/44)×(44/17)
P(C|A) =13/17
Thus, the probability P(A/B) is 7/20, the probability P(B/A) is 7/17, the probability P(A/C) is 13/23, and the probability is P(C|A) is 13/17 option fourth is correct.
Learn more about the Venn diagram here:
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HELP PLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
[tex]\sqrt{a}=b\iff b^2=a\\\\a\geq0\ \wedge\ b\geq0\\\\\text{therefore your answer is}\\\\\text{(A) The equation has no solutions.}[/tex]
Plot the data for the functions f(x) and g(x) on a grid
The new number, 550, is 200 more than the original number. What is the approximate percent change?a The percent change is 33%. b The percent change is 55%. c The percent change is 150%. d The percent change is 175%
The approximate percent change is:
55%
Step-by-step explanation:It is given that:
The new number, 550, is 200 more than the original number.
Let the original number be: x
That means:
550=200+x
x=550-200
x=350
Now, the percent change is calculated as:
[(New number-Original number)/original number]×100
= [tex]\dfrac{550-350}{350}\times 100\\\\=\dfrac{200}{350}\times 100\\\\=57.14\%[/tex]
which is approximately equal to :
55%
a doctor is using a treadmill to assess the strength of a patients heart. he sets the 48 inch long treadmill at an incline of 10 degrees. how high is the treadmill raised
In this exercise we have to use the knowledge of sine to be able to calculate the triangle values, in this way we can say that:
[tex]h= 8.3[/tex]
So from the values initially given we can describe that the calculation for this triangle will be:
[tex]x / 48 = sin(10)\\ x = 48* .1736\\ x = 8.3335\\ sin 10^0 = h/48\\ h = 48 sin 10^0\\ h = 8.3 inches[/tex]
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Water flowing at the rate of 15km/hr through a pipe of diameter 14cm into a cuboidal pond which is 50m long and 44m wide. In which time will the level of water in the pond rise 21cm?
If a fair coin is tossed 5 times what is the probability of getting 3 heads in a row
1 question pleasee i need this asap!! thank you :D
f √6 is the geometric mean between 6 and another number, then the number is
HELLO!!! ^-^
The answer is 1.
If √6 is the geometric mean between 6 and another number, then the number is 1.
(I had the same question and got it right using this answer so yeah) ^-^
Have an amazing day!!! ^-^
Historical Fact:
Back in the older days, the word awful was a word used to praise someone! That is because aw in awful comes from the origin awe which is used when someone is in awe of you!!! For example: You are AWESOME!!!
Just a short answer please help :( the top
Which of the following best describes the solutions to the inequality shown below?
4c + 5 < 4c + 3
A. All real numbers
B. c < 1/2
C. c > 1/4
D. No solution
Marie decides to work all summer rather than going on vacation. She will be able to earn money and learn new skills but will not be able to spend much time with her friends. What is the opportunity cost in this scenario?
The opportunity cost in this scenario is the value of the best alternative that Marie gives up by choosing to work all summer rather than going on vacation.
Explanation:The opportunity cost in this scenario is the value of the best alternative that Marie gives up by choosing to work all summer rather than going on vacation. In this case, the opportunity cost could be the time she could have spent with her friends. By deciding to work, Marie forgoes the opportunity to socialize and spend quality time with her friends.
Opportunity cost is an important concept in economics that highlights the trade-offs we face when making choices. It helps us understand the value of the options we give up when we choose one alternative over another. In Marie's case, the opportunity cost of earning money and learning new skills is the limited time she can spend with her friends.
Two number cubes are rolled. What is the probability that the sum of the numbers rolled is either 3 or 9?
A.1/6
B.1/13
C.1/18
D.1/162
[tex] |\Omega|=6^2=36\\
|A|=\underbrace{2}_{\text{the sum is 3}}+\underbrace{4}_{\text{the sum is 9}}=6\\\\
P(A)=\dfrac{6}{36}=\dfrac{1}{6}\approx17\% [/tex]
PLEASE HELP ME QUICKLY!!
Find the slope intercept form for the equation of the line which passes through the point ( -2,15 )and has a slope of -1
The answer is:
y = -x + 13
Work/explanation:
First, we will write the equation in the form of [tex]\sf{y-y_1=m(x-x_1)}[/tex], which is point slope.
Plug in the data
[tex]\large\begin{gathered}\sf{y-15=-1(x-(-2)}\\\sf{y-15=-1(x+2)}\\\sf{y-15=-1x-2}\\\sf{y-15=-x-2}\\\sf{y=-x-2+15}\\\sf{y=-x+13}\end{gathered}[/tex]
Hence, the slope intercept is y = -x + 13.
The center of a circle is at (−2, −7) and its radius is 6.
What is the equation of the circle?
(x−2)2+(y−7)2=36
(x−2)2+(y−7)2=3
(x+2)2+(y+7)2=3
(x+2)2+(y+7)2=36
The equation of a circle is (x+4)2+(y−5)2=121.
What is the center and radius of the circle?
center: (4, −5); radius: 11
center: (−4, 5); radius: 121
center: (−4, 5); radius: 11
center: (−4, −5); radius: 121
Answer:
1. option D is correct; [tex](x+2)^2+(y+7)^2=36[/tex]
2. option C is correct; center: (-4, 5) and radius = 11 unit
Step-by-step explanation:
The general equation of the circle is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex] .....[1]
where,
(h, k) is the center of the circle and r is the radius of the circle.
1.
As per the statement:
The center of a circle is at (−2, −7) and its radius is 6.
⇒(h, k) = (-2, -7) and r = 6 units
Substitute these in [1] we have;
[tex](x-(-2))^2+(y-(-7))^2=6^2[/tex]
⇒[tex](x+2)^2+(y+7)^2=36[/tex]
Therefore, the equation of circle is, [tex](x+2)^2+(y+7)^2=36[/tex]
2.
As per the statement:
The equation of a circle is:
[tex](x+4)^2+(y-5)^2 = 121[/tex]
We can write this as:
[tex](x-(-4))^2+(y-5)^2 = 11^2[/tex]
On comparing with equation [1] we have;
(h, k) = (-4, 5) and r = 11 units
Therefore, the center and radius of the circle is,
center: (-4, 5) and radius = 11 unit
Multiply. −5m(−2m6+4m4+m−9) Express the answer in standard form. Enter your answer in the box.
show or describe two different ways to complete the comparison using < , > ,or =: 0.26 () 0.4
An apple farm yields an average of 31 bushels of apples per tree when 17 trees are planted on an acre of ground. each time 1 more tree is planted per acre, the yield decreases by 1 bushel (bu) per tree as a result of crowding. how many trees should be planted on an acre in order to get the highest yield?
To maximize the apple yield from an acre, the optimal number of apple trees to plant is 24 trees.
Explanation:In this problem, we need to maximize the yield of apples from an acre of an apple farm. The yield of apples from an acre is given by the product of the number of trees and the number of bushels per tree. The number of bushels of apples per tree decreases by 1 bushel every time an additional tree is added due to crowding. In mathematical terms, this can be expressed as the equation Y = N * (31 - (N - 17)), where Y is the total yield, and N is the number of trees per acre.
To find the maximum yield, we differentiate this equation with respect to N and set the derivative equal to zero. This gives us N = 24. Therefore, the optimal number of trees to plant per acre in order to maximize apple yield is 24 trees.
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To maximize the yield of apples per acre, plant 24 trees. This balances the number of trees and the yield per tree due to crowding.
To find the number of trees that should be planted per acre to get the highest yield, we need to model the yield per acre as a function of the number of trees planted and then find the maximum value of this function.
1. Define the variables:
- Let ( n ) be the number of trees planted per acre.
- The yield per tree decreases by 1 bushel for each additional tree planted, starting from 31 bushels per tree when there are 17 trees planted.
2. Model the yield per tree:
- If ( n = 17 ), the yield per tree is 31 bushels.
- For each additional tree, the yield decreases by 1 bushel, so the yield per tree can be expressed as ( 31 - (n - 17) ).
Simplifying this, we get:
Yield per tree = 31 - n + 17 = 48 - n
3. Model the total yield per acre:
- The total yield ( Y ) per acre is the number of trees ( n ) times the yield per tree.
Y = n × (48 - n)
4. Formulate the quadratic function:
Y = 48n - [tex]n^2[/tex]
5. Find the maximum yield:
- This is a quadratic function of the form [tex]\( Y = -n^2 + 48n \)[/tex], which is a downward-opening parabola. The maximum value of \( Y \) occurs at the vertex of the parabola.
- The vertex of a quadratic function [tex]\( ax^2 + bx + c \)[/tex] occurs at [tex]\( x = -\frac{b}{2a} \)[/tex] . In our case, ( a = -1 ) and ( b = 48 ).
[tex]\[ n = -\frac{48}{2(-1)} = \frac{48}{2} = 24 \][/tex]
So, to get the highest yield, 24 trees should be planted per acre.
The birdwatching club has 27 members, 18 girls and 9 boys. What is the ratio of the girls to boys in the birdwatching club?
32 deanna bought a shirt that was on sale for 40% off the original price. she also used a coupon that gave her an additional 20% off the sale price of the shirt. the original price of the shirt was $54. what is the new price of the shirt before tax?
PLEASE HELP ASAP!!!1
TIME SENSITIVE
The range of [tex]y= \frac{4}{5} sinx[/tex] for [tex] \pi \leq x \leq \frac{3 \pi }{2} [/tex] is _____.
In the graph below, find the coordinate of the image point, P(3, 0). O is the origin and O,90 is a rotation of 90 degrees about the origin. Rx and Ry are reflections around the x- and y-axes.
Rx O,90: (3,0)
(0, 3)
(-3, 0)
(0, -3)
Answer:
Thus, (3,0) Rx O,90° changes to (0,-3)
Step-by-step explanation:
O is the origin and O,90 is a rotation of 90 degrees about the origin. Rx and Ry are reflections around the x- and y-axes.Given: Rx O,90: (3,0)
To determine:
Point P (3,0) rotation about origin (0,0) of 90°
and then Reflection about x-axis.
Rotation of P(x,y) about origin of 90°
P(x,y) changes to P'(y,x)
Therefore, P(3,0) changes to P'(0,3)
Now we take reflection about x-axis
R(x,y) changes to R'(x,-y)
Therefore, P'(0,3) changes to P''(0,-3)
Please see the attachment for both rule.
Thus, (3,0) Rx O,90° changes to (0,-3)
Jessica is designing a large, circular garden for a neighborhood park. A part of the garden will be occupied by a fountain. If the diameter of the garden is 82 meters and the measure of the angle formed by the fountain is 126°, what will be the approximate length of the garden cover by the fountain?