Answer:
235.5
Step-by-step explanation:
Substitute the values into the equation [tex]V=\pi r^2 \frac{h}{3}[/tex], which is the formula for finding the volume of a cone.
[tex]V=(3.14)(5^2)\frac{(9)}{3}[/tex]
Simplify.
[tex]V=(3.14)(25)(3)[/tex]
Simplify again.
[tex]V=(78.5)(3)[/tex]
Simplify for the last time.
[tex]V=235.5[/tex]
Note, using 3.14 will give you 235.5, but if you use the [tex]\pi[/tex] button on a scientific calculator, your answer will be 235.62. Given the constraints of the problem, your best bet will be 235.5.
Determine whether the following individual events are independent or dependent. Then find the probability of the combined event.
Randomly drawing and immediately eating two red pieces of candy in a row from a bag that contains red pieces of candy out of pieces of candy total.
Answer:
Dependent event
[tex]P(Red = 2) = \frac{5}{588}[/tex]
Step-by-step explanation:
Given
[tex]Total = 49[/tex]
[tex]Red = 5[/tex]
Solving (a): Are the events dependent?
Yes, they are.
When the first red candy is selected and eaten, the total number of candies reduced to 48 and the number of red candies also reduced to 4.
So, the probability of selecting a 2nd candy is dependent on the first candy selected.
Solving (b): P(Red = 2)
This is calculated as:
[tex]P(Red = 2) = P(Red) * P(Red | Red)[/tex]
The first selection has the following probability:
[tex]P(Red) = \frac{Red}{Total}[/tex]
[tex]P(Red) = \frac{5}{49}[/tex]
The second selection has the following probability:
[tex]P(Red|Red) = \frac{Red - 1}{Total - 1}[/tex]
[tex]P(Red|Red) = \frac{5 - 1}{49 - 1}[/tex]
[tex]P(Red|Red) = \frac{4}{48}[/tex]
So, we have:
[tex]P(Red = 2) = P(Red) * P(Red | Red)[/tex]
[tex]P(Red = 2) = \frac{5}{49} * \frac{4}{48}[/tex]
Reduce fraction
[tex]P(Red = 2) = \frac{5}{49} * \frac{1}{12}[/tex]
Multiply
[tex]P(Red = 2) = \frac{5}{588}[/tex]
What is the five-number summary for this data set? 22, 29, 33, 38, 44, 47, 51, 56, 64, 69 Assume the numbers in each answer choice are listed in this order: min, Q1, median, Q3, max.
A. 22, 33, 45.5, 56, 69
B. 22, 38, 45.5, 51, 69
C. 22, 38, 41, 51, 69
D. 22, 33, 41, 56, 69
Answer: A: 22, 33, 45.5, 56, 59
Step-by-step explanation:
The minimum is the lowest number in the data, in this case, it was 22.
Q1 is the median of the lower quartile range, anything below the median of the overall data.
Median, the middle number in the overall data. You first need to put them from lowest to highest (numerical order). After that, I find it a lot easier to cross one from each side until I'm either left with one or two. If I'm left with one, then that is my median for the overall data set. If I'm left with two, then I simply need to add both the numbers together and divide it by 2. Typically if it is a whole number, and the numbers are 1 number value away from each other, it is usually just 0.5 more of the lower value of the two. (For example, the two numbers I come down to is 10 and 11. The median would be 10.5).
Q3 is the exact same principle as Q1 just on the upper quartile range. Just repeat what you did in Q1 but for the numbers above the overall median of the data set.
Maximum is the highest number in the data set, in this case, it was 69.
Hope this helps!
Near the beginning of Lesson 5.3, a strategy for factoring trinomials of the form x^2+ bx+c was
developed by exploring the product of the binomials (x+p) and (x+q).
Explain how the development of this factoring strategy is an example of working backwards
to solve a problem.
Answer:
Step-by-step explanation:
there are function that "invert" each other..
subtraction inverts addition...
3+2 = 5 ... 5-2 = 3
division inverts multiplication
5*2 = 10 ... 10/2 = 5
Using that concept, "factoring" is basically the inverse of multiplication
3x^2 + 9x can be factored to 3x(x+3)
if you multiply that out it reverts back to the original equation
so x^2 + 5x + 6 factors to (x+3)(x+2)
if you multiply that out (foil it)
you get x^2 + 5x + 6
The length AB of a rectangle ABCD is 8cm and its diagonal BD and measures 10 cm Find its breadth BC
helppp outt plss....
============================================================
Explanation:
For any cyclic quadrilateral (aka inscribed quadrilateral), the opposite angles are always supplementary.
One pair of such angles is A and C
A+C = 180
x+y = 180 is one equation to form
The other pair of supplementary angles is B and D
B+D = 180
y-45+2x+15 = 180
2x+y-30 = 180
2x+y = 180+30
2x+y = 210 is the other equation to form
--------------
So the system of equations we have is
[tex]\begin{cases}x+y = 180\\2x+y = 210\end{cases}[/tex]
Both equations involve 'y', with the same coefficient, so we can subtract straight down to eliminate this variable.
The x terms subtract to x-2x = -xThe y terms subtract to y-y = 0y = 0, so the y terms go awayThe right hand sides subtract to 180-210 = -30We end up with -x = -30 which solves to x = 30
--------------
Once we know x, we can determine y by plugging it into any equation involving x,y and solving for y
Let's say we picked on the first equation
x+y = 180
30+y = 180
y = 180-30
y = 150
Or we could pick on the second equation
2x+y = 210
2(30) + y = 210
60+y = 210
y = 210-60
y = 150
Only one equation is needed. However, doing both like this shows that we get the same y value, and it helps confirm the answers.
A company produces 2 types of computers; desktops and laptops
Answer:
?
Step-by-step explanation:
The critical value of F for an upper tail test at a 0.05 significance level when there is a sample size of 21 for the sample with the smaller variance and there is a sample size of 9 for the sample with the larger sample variance is _____. a. 2.94 b. 2.45 c. 2.10 d. 2.37
Answer:
2.45
Step-by-step explanation:
Given that :
α = 0.05
Larger sample variance= numerator, sample size = 9
Smaller sample variance = denominator, sample size = 21
Hence,
DFnumerator = n - 1 = 9 - 1 = 8
DFdenominator = n - 1 = 21 - 1 = 20
Critical value for upper tail test using the F distribution table at α = 0.05 ; DFnumerator on horizontal ; Df denominator as vertical ;
F critical = 2.447
F critical = 2.45
Convert 2 1/3 into improper fraction: *
7/3
O 7/6
O 6/3
O 3/6
Answer:
7/3 is the answer
Step-by-step explanation:
A math class has a total of 31 students. The number of females is seven less than the number of meals. How many miles and how many females are in the class?
Answer:
Male-19&Female-13
Step-by-step explanation:
See the image for solution
Hope it helps
Have a great day
the quotient of (x^4 - 3x^2 + 4x - 3) and a polynomial is (x^2 + x - 3) what is the polynormial
Answer:
Hello,
polynomial is x²-x+1
Step-by-step explanation:
if a=b*c+r then a=c*b+r
Using a long division, see the picture.
72
60
48
36
Number of Computers
The graph shows a proportional relationship between
the number of computers produced at a factory per
day in three days, 36 computers are produced, 48
computers are produced in 4 days, and 60 computers
are produced in 5 days.
Find the unit rate of computers per day using the
graph.
Unit rate
computers per day
I
24
12
3 4 5 6 7 8 9 10 11 12
Number of Days
Intro
Done
Graph is attached below ;
Answer:
Unit rate = 12 computers per day
Step-by-step explanation:
To obtain the unit rate of computers sold per day using the graph, we need to obtain the slope of the graph, which is the change in y per change in x
That is ; the gradient ;
Slope = change in y / change in x
Slope = (y2 - y1) / (x2 - x1)
y2 = 60 ; y1 = 36 ; x2 = 5 ; x1 = 3
Slope = (60 - 36) / (5 - 3) = 24 / 2 = 12
Slope = 12
Unit rate = 12 computers per day
(WILL GIVE YOU 30 POINTS!!!)
The graph shows the functions f(x), p(x), and g(x):
Graph of function g of x is y is equal to 3 multiplied by 1.2 to the power of x. The straight line f of x joins ordered pairs minus 3, minus 3 and 4, 4 and is extended on both sides. The straight line p of x joins the ordered pairs minus 6, 1 and minus 3, minus 3 and is extended on both sides.
Part A: What is the solution to the pair of equations represented by p(x) and f(x)? (3 points)
Part B: Write any two solutions for f(x). (3 points)
Part C: What is the solution to the equation p(x) = g(x)? Justify your answer. (4 points)
Answer:
(a) No solution
(b)
[tex](x_1,y_1) =(-3,-3)\\(x_2,y_2) =(4,4)[/tex]
(c) [tex](-6,1)[/tex]
Step-by-step explanation:
Given
See attachment for graph
Solving (a): Solution to p(x) and f(x)
Curve p(x) and line f(x) do not intersect.
So, there is no solution to the pair of p(x) and f(x)
Solving (b): Two solutions to f(x)
This means that we select any two point on straight line f(x)
From the line of f(x), we have:
[tex](x_1,y_1) =(-3,-3)\\(x_2,y_2) =(4,4)[/tex]
Solving (c): Solution to p(x) = g(x)
Here, we write out the point of intersection of p(x) and g(x)
From the graph, the point of intersection is: [tex](-6,1)[/tex]
Arrange the following rational numbers in descending order. 5/8 ,-11/15 , 17/(-24) ,7/12
Solve for x . 7 - (2 x + 11) + 3(3 - x ) = 20
A.7/5
B.-3
C.-4
Answer:
the answer to the question is a:-3
In a scatter plot, each ____. Group of answer choices individual is represented by a single point group mean is represented by a single point individual is represented by two data points group mean is represented by two data points
Answer:
Individual is represented by a single point
Step-by-step explanation:
Find the area bounded by the curves x = 2y2 and x = 1 - y. Your work must include an integral in one variable.
Please help!!
Answer:
Hello,
in order to simplify, i have taken the inverses functions
Step-by-step explanation:
[tex]\int\limits^\frac{1}{2} _{-1} {(-2x^2-x+1)} \, dx \\\\=[\frac{-2x^3}{3} -\frac{x^2}{2} +x]^\frac{1}{2} _{-1}\\\\\\=\dfrac{-2-3+12}{24} -\dfrac{-5}{6} \\\\\boxed{=\dfrac{9}{8} =1.25}\\[/tex]
find the values of x and y for the following matrix equations
Answer:
Step-by-step explanation:
Sets L and M are defined as follows.
L={-1,1,4,5,7,8)
M={1,2,7)
Answer each part below. Write your answer in roster form or as Ø.
(a) Find the union of L and M.
(b) Find the intersection of L and M
Answer:
the union of l and m is minus 1,1,2,4,5,7,8.....and the intersection of l and m is 1.......
Country Financial, a financial services company, uses surveys of adults age 18 and older to determine whether personal financial fitness is changing over time. A recent sample of 1000 adults showed 410 indicating that their financial security was more than fair. Just a year prior, a sample of 900 adults showed 315 indicating that their financial security was more than fair. Conduct the hypothesis test and compute the p-value. Round your answer to four decimal places. What is the 95% confidence interval estimate of the difference between the two population proportions? Round your answers to four decimal places.
Answer:
hey, how you're day going
Step-by-step explanation:
.................
What is 3 times 10^9
Answer:
3 times 10 ^ 9
Step-by-step explanation:
3 × 10 ^ 9 = 3000000000
If £15=$20 and $5=390 find the number of pounds that can be exchanged
200
Mark as braianlist
15 multiple by 5 equal 75 -390 equal 315 -15equal 200
what vulnerable does the 4 represents in the number 487.009
Answer:
400 :D
Step-by-step explanation:
What is the surface area of a cylinder that has a radius of 7 m and a height of 18 m?
879.65 m2
1099.56 m2
615.75 m2
395.84 m2
1099.56m² is the surface area of a cylinder that has a radius of 7 m and a height of 18 m.
What is the GCF of the expression 7xyz - 21xyz + 49yz + 14yz2?
Answer:
7yz
Step-by-step explanation:
You can take 7yz common from all the terms in the given expression
Answered by GAUTHMATH
Solve for x
X-8 = -10
A) X = 2
B) X = -2
C) X = 18
D) X = -18
Answer:
x=–2
Step-by-step explanation:
x-8=-10
x=-10-8
x=–2
Answer:
-8= -10
, = -10+8
, = -2
.......... is a factor of every even number.
Answer:
2 is the factor of every even number hope this help you
Find the length of DM
Answer:
67
Step-by-step explanation:
DM=JM-JD=84-17=67
Answer:
Step-by-step explanation:
Find the missing side round your answer to the nearest tenth
Answer: 15
Step-by-step explanation:
Factorise: 25x^2 - 1/49
Answer:
[tex] (5x + \frac{1}{7} )(5x - \frac{1}{7} )[/tex]Step-by-step explanation:
Given,
[tex] {25x}^{2} - \frac{1}{49} [/tex]
[tex] = {(5x)}^{2} - {( \frac{1}{7}) }^{2} [/tex]
Since,
[tex] {x}^{2} - {y}^{2} = (x + y)(x - y)[/tex]
Then,
[tex] = (5x + \frac{1}{7} )(5x - \frac{1}{7} )(ans)[/tex]
4. Write 3x(x + 4)(x - 1) in standard form.
3x3 + 9x2 - 12x
3x3
- 12x + 9x2
3x3 + 9x2 - 12x + 1
1 - 12x + 9x2 + 3x3
Answer:
i thank the ans id 450
Step-by-step explanation:
