Answers
16. The first attachment shows a table of the given values and the function evaluated at those points.
Maximum: 11 at (4, -3)Minimum: -8 at (-4, 0)___
17. The cost function for this problem is an expression of the total cost as a function of number of days open:
c(x, y) = 40x + 50y
The system of inequalities expresses the constraints on delivery of glass and aluminum in terms of the number of days open:
140x + 100y ≥ 154060x + 180y ≥ 1440To minimize costs, Center 1 should be open 6 15/16 days; Center 2 should be open 5 11/16 days. The cost function is minimized when it goes through the vertex of the feasible region that puts it closest to the origin.
___
18. (a) Jane can use the revenue function ...
r(x, y) = 120x +70y
(b) The constraints on hours and numbers of visits are ...
x + (1/2)y ≤ 8 . . . . . . hours in the dayy ≤ 7 . . . . . . . . . . . . . constraint on follow-up visits(c) For the given vertices, Jane's best choice is (4, 7), which will produce $970 in revenue for the office.
As is sometimes the case, the integer vertex closest to the corner of the feasible region is not the one that maximizes revenue. Jane's best choice is not on the problem's list. It is (5, 6), which will produce $1020 in revenue.
See the second attachment for the graph related to the problem.
_____
Apology
The graphs are out of order because my first attempt at 17 had an error. The corrected graph was added as the last attachment.
_____
Steps
In all of these linear programming problems, the "objective function" is the function of the problem variables that you want to maximize or minimize. In order to write it, you need to understand what the problem variables are and how they relate to the objective. In each of these problems, you are told what x and y stand for and their relation to the objective.
When considering the constraints, you must consider how the problem variables relate to any limits imposed. As in problem 17, sometimes the limits are minima (must deliver at least ...). In problem 18, the limits are maxima (8 hours in a day; no more than 7 follow-ups).
So, first read and understand the problem statement and the relationships it is telling you. Then, do what the problem asks you to do. Sometimes that will involve finding a solution; sometimes not.
Often, you can use logic to help you understand whether your solution is reasonable. In the doctor problem (18), the doctor makes more money per hour doing follow-ups, so would probably want to maximize those (4, 7). However, doing that leaves a half-hour with zero revenue. That last hour is better spent seeing a new patient ($120) than seeing only one follow-up patient ($70).
Related Questions
PLEASE HELP!!!!!! 20 POINTS!!! (BOTH QUESTIONS) VERY EASY!!!!!
Answers
The second one is d I’m pretty sure
Answer:
#23, A
#24, D
Hope this helped!!
~A̷l̷i̷s̷h̷e̷a̷♡
A restaurant offers a lunch special for $15 plus a $3 tip for the server. Write an expression that represents the total cost for the special in 2 different ways.
Answers
Answer:
s= 15x+3x and s=18x
Step-by-step explanation:
Answer:
The total cost for the special would be $15.45
Step-by-step explanation:
One equation would be 15 x 1.03 = 15.45
Second equation would be (15 x .03) + 15 = $15.45
The function f(x) is shown in this graph. The function g(x)=-2x-6. Compare the slopes
Answers
Since f(x) = -3x + 2, the slope of f(x) is greater than the slope of g(x).
Hence, the answer is (D).
The slope of f(x) is greater than the slope of g(x) because the slope of f(x) is 1 option (D) is correct.
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have:
g(x) = -2x - 6
f(x) is shown in the graph
The slope of g(x), m = -2
From the graph:
(0, 2) and (-1, 1)
M = (1-2)/(-1) = 1
Thus, the slope of f(x) is greater than the slope of g(x) because the slope of f(x) is 1 option (D) is correct.
Learn more about the slope here:
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A plumber charges a rate of $65 per hour for his time but gives a discount of $7 per hour to senior citizens. Write an expression which represents a senior citizen’s total cost for the plumber in 2 different ways.
Answers
Answer:
t = 58x or t + 7x = 65x
The expression that represents a senior citizen's total cost for the plumber in 2 different ways can be written as: Method 1: Total Cost = $65 - $7 per hour. Method 2: Total Cost = $65 - ($7 per hour x Number of hours)
Explanation:The expression that represents a senior citizen's total cost for the plumber in 2 different ways can be written as:
Method 1: Total Cost = $65 - $7 per hourMethod 2: Total Cost = $65 - ($7 per hour x Number of hours)Method 1 calculates the total cost by applying the discount of $7 per hour directly to the base rate of $65. Method 2 calculates the total cost by multiplying the discount per hour ($7) by the number of hours and subtracting it from the base rate of $65.
Learn more about Plumber here:https://brainly.com/question/3200361
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Evaluate the exponential expression: (2x)2−3y2=___, if x = 5 and y = 3.
-125
-73
125
73
Answers
Answer:
73
Step-by-step explanation:
Put the values of the variables where the variables are, then do the arithmetic.
(2·5)^2 -3·3^2 = 10^2 -3·9 = 100 -27 = 73
___
Or, you can let a calculator or spreadsheet evaluate the function for you.
Find the area of the Figure.
would love some help, please, and thank you
Answers
Answer:
430
Step-by-step explanation:
All you have to do is add up all the sides So 80+80+250+20=430 And there you have it!
The school yearbook committee surveyed the student body for an article about colleges in which they are pursuing enrollment. The table below shows the number of students in each grade level who are pursuing one or more college.
If there are 170 students in 12th grade, what percentage of the twelfth grade students have more than one college in mind? Round your answer to the nearest percent.
Answers
Out of 170 students in 12th grade, 27+23 = 50 students have more than 1 college in mind.
So 50/170, or 29% is your answer.
Answer:
29%
Step-by-step explanation:
A rectangle’s width is one-fourth of its length. Its area is 9 square units. The equation l(1/4l) = 9 can be used to find l, the length of the rectangle.
Answers
I see no actual question, but I'm assuming that you want to find the dimensions of the rectangle.
In general, the area of a rectangle with width [tex]w[/tex] and length[tex]l[/tex] is
[tex] A = wl [/tex]
In this case, we know that the width is one-fourth of its length, which means [tex] w = \frac{1}{4}l[/tex]
If we plug this expression for w in the formula for the area, we get
[tex] A = wl = \dfrac{1}{4}l\cdot l = \dfrac{1}{4}l^2 [/tex]
We also know that the area is 9 squared units, so we have
[tex] 9 = \dfrac{1}{4}l^2 [/tex]
If we multiply both sides by 4, we get
[tex] l^2 = 36 [/tex]
Consider the square root of both sides (we only accept the positive solution, since a negative length would make no sense:
[tex] l = \sqrt{36} = 6 [/tex]
So, the length is 6, and the width is one-fourth of 6, i.e.
[tex]\dfrac{1}{4} \cdot 6 = \dfrac{6}{4} = \dfrac{3}{2} = 1.5[/tex]
Answer:
1.5
Step-by-step explanation:
What is the answer for #7?
Answers
Answer:
radius: 1.84 inheight: 3.68 inStep-by-step explanation:
After you've worked a couple of "optimum cylinder" problems, you find that the cylinder with the least surface area for a given volume has a height that is equal to its diameter. So, the volume equation becomes ...
V = πr²·h = 2πr³ = 39 in³
Then the radius is ...
r = ∛(39/(2π)) in ≈ 1.83779 in ≈ 1.84 in
h = 2r = 3.67557 in ≈ 3.68 in
_____
The total surface area of a cylinder is ...
S = 2πr² + 2πrh
For a given volume, V, this becomes ...
S = 2π(r² +r·(V/(πr²))) = 2πr² +2V/r
The derivative of this with respect to r is ...
S' = 4πr -2V/r²
Setting this to zero and multiplying by r²/2 gives ...
0 = 2πr³ -V
r = ∛(V/(2π)) . . . . . . . . looks a lot like the expression above for r
__
If we substitute the equation for V into the equation just above this last one, we have ...
0 = 2πr³ - πr²·h
Dividing by πr² gives ...
0 = 2r - h
h = 2r . . . . . generic solution for cylinder optimization problems
solve
y^2 + 3y = -1
-PlushDNA
Answers
Answer:
[tex]y=-\frac{3+\sqrt{5}}{2}[/tex] AND [tex]y=-\frac{3-\sqrt{5}}{2}[/tex]
Step-by-step explanation:
Given: [tex]y^2+3y=-1[/tex]
To solve for [tex]y[/tex], we need to get everything on one side of the equal sign and set it to zero. We can do this by adding 1 to both sides. We then get:
[tex]y^2+3y+1=0[/tex]
We can solve for [tex]y[/tex] by using the quadratic formula:
[tex]y=\frac{-b+\sqrt{(b)^2-4(a)(c)}}{2a}[/tex] AND [tex]y=\frac{-b-\sqrt{(b)^2-4(a)(c)}}{2a}[/tex]
Let's identify our values:
[tex]a: 1\\b: 3\\c: 1[/tex]
Plug in the values and simplify.
[tex]y=\frac{-3+\sqrt{(3)^2-4(1)(1)}}{2(1)}\\y=\frac{-3+\sqrt{5}}{2}\\-------------------------\\y=\frac{-3-\sqrt{(3)^2-4(1)(1)}}{2(1)}\\\\y=\frac{-3-\sqrt{5}}{2}\\[/tex]
Your final answers are:
[tex]y=-\frac{3+\sqrt{5}}{2}[/tex] AND [tex]y=-\frac{3-\sqrt{5}}{2}[/tex]
HELP
Nevin started a geometric sequence. The first four terms of his sequence are show below.
162,54,18,6, . . .
3.) What is the sixth therm of Nevin sequence? Show or explain how you got the answer.
4.) Write an expression that represents the ᵗʰ term of Nevin sequence.
Answers
Answer:
3) 2/3
4) an = 162·(1/3)^(n-1)
Step-by-step explanation:
3) A geometric sequence has a common ratio between adjacent terms. Here, that ratio is ...
r = 54/162 = 18/54 = 6/18 = 1/3
Then the next two terms can be found by multiplying by the common ratio:
6 · 1/3 = 2
2 · 1/3 = 2/3 . . . . . the sixth term
____
4) The generic expression for the n-th term of a geometric sequence with first term a1 and common ratio r is ...
an = a1·r^(n-1)
We can put in the numbers for a1 and r, and we have ...
an = 162·(1/3)^(n-1)
Hi if someone could explain the right answer that would be great i’m totally lost!!
Answers
Answer:
A. lim [x ⇒ -∞] g(x) = -5 . . . . . . written in text form, not typeset
Step-by-step explanation:
A horizontal asymptote is a line that the function approaches but never reaches. It represents the limiting value that the function can have. (The function can come as close to that value as you like for some value of x, but can never actually reach that value.)
Here, you're told the asymptote for negative x values is -5. That means g(x) gets closer and closer to -5 for values of x that are more and more negative. That is, as x approaches infinity, g(x) approaches -5. We say -5 is the limit of g(x) as x approaches negative infinity.
___
The attached graph shows a function that has characteristics like those of g(x).
___
This question is about vocabulary: what is the meaning of "asymptote" and "limit", and how do you read a description of a limit written using math language.
HELP BRAINIEST AND LOTS OF POINTS Two twins, Mason and Jason, play a game in which they have a pile of 99 marbles. They can take anywhere from 1 to 10 marbles each turn. Whoever takes the last marble loses. Mason starts. Both play optimally. Who wins, and how many turns will Mason and Jason take combined? NEED NOW
Answers
Answer:
Mason wins after 18 total moves
Step-by-step explanation:
Mason's optimal strategy is to keep the total number of marbles at 11n+1, so he will take 10 marbles to start. For each move Jason makes, Mason will take a number of marbles that makes the sum from the two turns be 11.
After each of Mason's 9 turns, the number of remaining marbles will be ...
89, 78, 67, 56, 45, 34, 23, 12, 1
It doesn't matter how many marbles Jason takes. He will lose on his 9th turn.
Mason's best strategy is to stay the overall variety of marbles at 11n+1, thus he can take ten marbles to begin. for every move Jason makes, Mason can take variety of marbles that creates the add from the 2 turns be eleven.
After every of Mason's nine turns, the amount of remaining marbles are
89, 78, 67, 56, 45, 34, 23, 12, 1
It doesn't matter what number marbles Jason takes. He can lose on his ninth flip.
mason will win after 18 moves
A party rental company has chairs and tables for rent. The total cost to rent 3
chairs and 8 tables is $55. The total cost to rent 5 chairs and 2 tables is $18. What is the cost to rent each chair and each table
Answers
Answer:
chair: $1.00table: $6.50Step-by-step explanation:
When you have a non-trivial number of sets of equations to solve, it can be useful to let a machine solve them for you. Here, suitable equations for chair cost (c) and table cost (t) can be written as ...
3c+8t = 555c+2t = 18___
I find a graphing calculator easy to use for solving such equations.
___
A spreadsheet programmed with Cramer's Rule can do it, too. The second attachment shows the spreadsheet formulas used to solve the standard-form linear equations of the kind that can be written for this problem. The third attachment shows the solution(s).
Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a radius of 13 feet and a height of 13 feet. Container B has a radius of 9 feet and a height of 14 feet. Container A is full of water and the water is pumped into Container B until Conainter B is completely full.
To the nearest tenth, what is the percent of Container A that is full after the pumping is complete?
Answers
The percent that Container A is full after pumping its water into Container B until it is full is that Container A is 49.1% full after pumping water to Container B.
The problem asks us to determine what percent of Container A is full after Container B is full when water is transferred from Container A to Container B. We start by calculating the volume of both cylinders. The volume of a cylinder is given by the formula V = π r² h where V is volume, r is radius, and h is height.
Container A has a radius of 13 feet and a height of 13 feet, so:
π r² h ≈ 6985.3 cubic feet
Container B has a radius of 9 feet and a height of 14 feet, so:
π r² h≈ 3553.0 cubic feet
After filling Container B completely, the volume of water left in Container A is the original volume of Container A minus the volume of Container B. Therefore, the remaining volume in Container A is (6985.3 - 3553.0) cubic feet ≈ 3432.3 cubic feet.
To find the percentage full, we divide this remaining volume by the total volume of Container A and multiply by 100:
Percentage = (3432.3 / 6985.3) * 100 ≈ 49.1%.
After the pumping is complete, Container A is 48.4% full.
Calculate the volume of each container
The volume of a cylinder is given by the formula:
[tex]\[V = \pi r^2 h\][/tex]
Volume of Container A
- Radius [tex]\( r_A = 13 \)[/tex]feet
- Height [tex]\( h_A = 13 \)[/tex] feet
[tex]\[V_A = \pi (13)^2 (13) = \pi (169)(13) = 2197\pi \text{ cubic feet}\][/tex]
Volume of Container B
- Radius [tex]\( r_B = 9 \)[/tex]feet
- Height [tex]\( h_B = 14 \)[/tex] feet
[tex]\[V_B = \pi (9)^2 (14) = \pi (81)(14) = 1134\pi \text{ cubic feet}\][/tex]
Calculate the remaining volume of water in Container A
Since Container A is initially full and the water is pumped into Container B until Container B is full, the remaining volume of water in Container A is:
[tex]\[V_{\text{remaining}} = V_A - V_B = 2197\pi - 1134\pi = (2197 - 1134)\pi = 1063\pi \text{ cubic feet}\][/tex]
Calculate the percent of Container A that is still full
The percent of Container A that is full is given by:
[tex]\[\text{Percent full} = \left( \frac{V_{\text{remaining}}}{V_A} \right) \times 100\%\][/tex]
Substituting the volumes we calculated:
[tex]\[\text{Percent full} = \left( \frac{1063\pi}{2197\pi} \right) \times 100\% = \left( \frac{1063}{2197} \right) \times 100\%\][/tex]
Simplifying the fraction:
[tex]\[\text{Percent full} = 0.484 \times 100\% = 48.4\%\][/tex]
Which is the rate of change for the interval between 3 and 6 on the x-axis?
–3
–2
2
3
Answers
Answer:
The correct answer is 2.
Step-by-step explanation:
To find this, first identify the ordered pairs at those two points. They would be (3, -2) and (6, 4). Then use the slope formula with those two points to find the rate of change.
m(slope) = (y2 - y1)/(x2 - x1)
m = (4 - - 2)/(6 - 3)
m = 6/3
m = 2
Answer:
2
Step-by-step explanation:
Rate of change on the given interval a to b is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
a=3 and b=6
f(a) and f(b) are the y values on the graph at x=3 and x=6
f(3)= -3 and f(6) is 4
Now plug in the values in the formula
[tex]rate of change =\frac{4-(-2)}{6-3} =\frac{6}{3} =2[/tex]
answer is 2
What is B help pleaseeee
Answers
Answer:
59.0°
Step-by-step explanation:
Many triangle solvers are available for your phone, tablet, or browser. The attachments show the input and output of one of them.
___
You can use the law of cosines to compute the result yourself.
b^2 = a^2 + c^2 - 2ac·cos(B)
cos(B) = (a^2 +c^2 -b^2)/(2ac) = (22^2 +18^2 -20^2)/(2·22·18) = 408/792
B = arccos(408/792) ≈ 58.9924° ≈ 59.0°
HELP ME ASAP!!!! Will somebody please explain to me how to do this. I can't pass Freshman year without getting this done.
Answers
Answer:
cot(x) = 3
Step-by-step explanation:
The cotangent is the reciprocal of the tangent.
cot(x) = 1/tan(x) = 1/(1/3) = 3
_____
It is helpful to memorize the relationships between the trig functions: SOH CAH TOA is a mnemonic that relates triangle sides to trig function values. The remaining relationships you need to know are ...
secant = 1/cosine . . . . . . so cosine = 1/secant
cosecant = 1/sine . . . . . so sine = 1/cosecant
cotangent = 1/tangent . . . . . so tangent = 1/cotangent
It is also helpful to realize that ...
tan = sin/cos
sin² + cos² = 1 . . . the "Pythagorean" relationship between sine and cosine
sec² = 1 + tan²
csc² = 1 + cot²
What is this quadratic function in standard form? y=(x+7) (x−5) Enter your answer in the box.
Answers
Answer:
y = x^2 +2x -35
Step-by-step explanation:
Multiply the binomials. The distributive property is helpful.
y = x(x -5) +7(x -5) . . . . the terms of the first binomial multiplied by the second
= x^2 -5x +7x -35 . . . . eliminate parenthses
y = x^2 +2x -35 . . . . . . collect terms
Solve algebraically
y=x^2 + 2x
y=3x+20
Answers
Answer:
x = 5 and y = 35
OR
x = -4 and y = 8.
Step-by-step explanation:
Equate the right-hand side of the two equations:
x² + 2 x = y = 3 x + 20.
x² + 2 x - 3 x - 20 = 0.
x² - x - 20 = 0.
Quadratic discriminant
Δ = b² - 4 a · c
= (-1)² - 4 × 1 × (-20)
= 81.
There are two roots:
x₁ = (-b + [tex]\sqrt{\Delta}[/tex]) / (2 a)
= (- (-1) + [tex]\sqrt{81}[/tex]) / (2 × 1)
= (1 + 9) / 2
= 10 / 2
= 5
and
x₂ = (-b - [tex]\sqrt{\Delta}[/tex]) / (2 a)
= (1 - 9) / 2
= -4.
Find the value of y in both case.
y₁ = 3 × 5 + 20 = 35.
y₂ = 3 × (-4) + 20 = 8.
The solution to the system of equations is [tex]\( x = 5 \)[/tex] with [tex]\( y = 35 \)[/tex] and [tex]\( x = -4 \)[/tex] with [tex]\( y = 8 \)[/tex].
To solve these equations algebraically, we'll set them equal to each other since they both represent [tex]\( y \)[/tex].
Given equations:
[tex]\[ y = x^2 + 2x \][/tex]
[tex]\[ y = 3x + 20 \][/tex]
Setting them equal to each other:
[tex]\[ x^2 + 2x = 3x + 20 \][/tex]
Now, let's rearrange this equation to solve for \( x \):
[tex]\[ x^2 + 2x = 3x + 20 \[/tex]
[tex]x^2 + 2x - 3x - 20 = 0 \[/tex]
[tex]x^2 - x - 20 = 0[/tex]
This is a quadratic equation in the form [tex]\( ax^2 + bx + c = 0 \)[/tex]. We need to factorize or use the quadratic formula to solve for [tex]\( x \)[/tex]. Factoring might work here:
[tex]x^2 - x - 20 = 0[/tex]
[tex](x - 5)(x + 4) = 0[/tex]
Setting each factor equal to zero:
[tex]\[ x - 5 = 0 \] or \( x + 4 = 0 \)[/tex]
Solving for [tex]\( x \)[/tex] in each case:
[tex]\[ x = 5 \] or \( x = -4 \)[/tex]
Now that we have found the potential values of [tex]\( x \)[/tex], let's find the corresponding [tex]\( y \)[/tex] values using either of the original equations. Let's use [tex]\( y = x^2 + 2x \)[/tex]:
For [tex]\( x = 5 \)[/tex]:
[tex]y = 5^2 + 2(5)[/tex]
[tex]y = 25 + 10[/tex]
[tex]y = 35[/tex]
For [tex]\( x = -4 \)[/tex]:
[tex]y = (-4)^2 + 2(-4)[/tex]
[tex]y = 16 - 8[/tex]
[tex]y = 8[/tex]
Therefore, the solution to the system of equations is [tex]\( x = 5 \)[/tex] with [tex]\( y = 35 \)[/tex] and [tex]\( x = -4 \)[/tex] with [tex]\( y = 8 \)[/tex].
Three people share half a pizza evenly. What fractional part of the original pizza does each one get?
Answers
Answer:
The fractional part of the original pizza is [tex]\frac{1}{6}[/tex]
Step-by-step explanation:
Let
x-----> the original pizza (complete pizza)
we know that
Half a pizza represent ------> [tex]\frac{x}{2}[/tex]
Divide half a pizza by three people
[tex](\frac{x}{2})/3=\frac{x}{6}[/tex]
therefore
The fractional part of the original pizza is [tex]\frac{1}{6}[/tex]
Find the quotient 3/4 divided by 1/3 =
Answers
Answer:
1/4
Step-by-step explanation:
3 x 1 = 3
4 x 3 = 12
3/12 simplified is 1/4
The quotient of the numbers 3/4 and 1/3 will be 9/4.
What is division?Division means the separation of something into different parts, sharing of something among different people, places, etc.
Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.
The numbers are given below.
3/4 and 1/3
The quotient of the numbers 3/4 and 1/3 is given by the number 3/4 divided by 1/3. Then we have
⇒ (3/4) / (1/3)
Simplify the expression, then we have
⇒ (3/4) x (3/1)
⇒ 9 / 4
The quotient of the numbers 3/4 and 1/3 will be 9/4.
More about the division link is given below.
https://brainly.com/question/369266
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How do I answer this question on khan academy.
Answers
If [tex]b[/tex] is Ben's age and [tex]i[/tex] is Ishaan's age, then
present day: [tex]b=4i[/tex]6 years ago: [tex]b-6=6(i-6)[/tex]Rewrite the second equation as
[tex]b-6=6(i-6)\implies b-6=6i-36\implies b+30=6i[/tex]
Substitute [tex]b=4i[/tex] into this equation to solve for [tex]i[/tex]:
[tex]b+30=6i\implies4i+30=6i\implies30=2i\implies i=15[/tex]
Then
[tex]b=4i\implies b=4\cdot15=60[/tex]
So Ben is 60 years old now.
All rectangles are parallelogram. Are all parallelogram rectangles? Explain
Answers
Answer:
No
Step-by-step explanation:
A parallelogram may have a right angle (making it a rectangle), but may not.
Need help multiplying -300 to N+M&M=10 for equation (1)
Answers
Answer:
3.5 pounds of nuts; 6.5 pounds of M&Ms
Step-by-step explanation:
Let m represent the number of pounds of M&Ms to use. Then 10-m is the number of pounds of nuts, and the cost of the mix is ...
6·m + 3·(10-m) = 4.95·10 . . . . . cost = cost per pound times pounds
3m +30 = 49.5 . . . . . . simplify
3m = 19.5 . . . . . . . . . . . subtract 30
m = 6.5 . . . . . . . . . . . . . divide by 3
Then 10-m = 10-6.5 = 3.5.
The manager should use 3.5 pounds of nuts and 6.5 pounds of M&Ms in the mix.
9 out of 10 people at a game are rooting for the home team. What is the probability that exactly 6 of 8 people sitting together are rooting for the home team?
Answers
A random supporter roots the home team with probability 0.9, and the away team with probability 0.1.
Choosing 6 out of 8 supporters who root for the home team has probability
[tex]\displaystyle\binom{8}{6}\cdot 0.9^6\cdot 0.1^2 = 28\cdot0.531441\cdot 0.01=0.14[/tex]
Practice zscore question help??
The height of a sunflower is normally distributed with a mean of 14.2 feet and a standard deviation of 2.15
what is the probability of picking a sunflower that has a height greater than 16.4 feet?
Please show all work (how you found z score and final answer)
Answers
The [tex]z[/tex]-score for a height of 16.4 feet is
[tex]z=\dfrac{16.4-14.2}{2.15}\approx1.023[/tex]
So
[tex]P(\text{height}>16.4\,\mathrm{ft})=P(Z>1.023)=1-F_Z(1.023)\approx0.153[/tex]
where [tex]F_Z(z)=P(Z\le z)[/tex] is the cumulative distribution function for the standard normal distribution.
What is the first step when dividing 3x^2+3x+1 by x-2 using long division?
Answers
Answer:
You need to find the number of times x goes into 3x^2 which is 3x, so you write 3x as the beginning of the quotient to start the division.
Answer:
3x^2 / x.
Step-by-step explanation:
The first step is to divide 3x^2 by the first term of x - 2 ( that is x).
You have $2000 to deposit for 7 years and two account options. The first earns you simple interest at a rate of 4% and the second earns you compound interest (compounded annually) at a rate of 2%. Which account earns you more money?
First account (simple interest)
Second account (compound interest)
They earn you the same
Not enough information to say
Answers
Answer:
First account (simple interest)
Step-by-step explanation:
The amount of interest earned by the first account is ...
I = Prt = $2000·0.04·7 = $2000·0.28 = $560
The amount in the second account at the end of 7 year is ...
FV = P·(1+r)^t = $2000·1.02^7 = $2297.37
so you have earned $297.37 in interest on the second account.
$560 is more than $297, so the First Account (simple interest) earns more money.
Could someone plz help with number 4 ? Thanks
Answers
Answer:
255π (cm³).
Step-by-step explanation:
1. the initial formula for the required volume is V=V1-V2, where V1=π(r1)²h, V2=π(r2)²h;
h=20m=2000cm, r1=0.5*d1, r2=0.5*d2;
d1=1cm., d2=0.7 cm.
2. the final formula of the required volume is
[tex]V=\frac{ \pi*h}{4} (d_1^2-d_2^2);[/tex]
3. if to substitute the values of d1, d2 and h, then
[tex]V=\frac{ \pi*2000}{4} (1-0.49)=500 \pi*0.51=255 \pi \ (cm^3).[/tex]