Answer:
it's 2$ per guest
he needs 2$ for any guest
Mad Scientist Max wants to make 3 liters of 15% solution of hydrochloric acid by mixing some 10% acid solution with some 27% acid solution. How much of the 10% solution should he use for his diabolical recipe? Round answer to 3 decimal places.
Answer:
Dont you you jusy divide?
Step-by-step explanation:
What is the slope of the line that passes throug the points (5,-1) and (-3,3)?
Answer:
negative slope.............
Answer:
c
Step-by-step explanation:
The linear and quadratic ape nature of these critical points. respectively
P
1
(x)=f
′
(a)(x−a)+f(a)
P
2
(x)=
2
1
f
′′
(a)(x−a)
2
+f
′
(a)(x−a)+f(a)
(a) (8pt) Find the linear and the quadratic approximations of f(x)=e
4x
cos3x at x=0 (b) (5pt) Sketch the graph of the linear and quadratic approximation of f(x) found in part (a). The sketch must be in the same axis and it must be neatly labelled.
(a) The linear approximation is P1(x) = 4x + 1. (b) the quadratic approximation is P2(x) = (7/2)x² + 4x + 1.
Linear approximation, also known as tangent line approximation, is a method used to estimate the value of a function near a specific point by using the equation of the tangent line at that point. It is based on the concept that a tangent line to a curve at a certain point can closely approximate the behavior of the curve in the vicinity of that point.
The linear approximation can be derived using the first-order Taylor series expansion. Given a function f(x) and a point (a, f(a)), the linear approximation can be written as:
L(x) = f(a) + f'(a)(x - a)
In this equation, L(x) represents the linear approximation of f(x) near the point (a, f(a)). f(a) is the value of the function at the point a, and f'(a) is the derivative of the function evaluated at a.
To find the linear and quadratic approximations of f(x) = \(e^{(4x)\) * cos(3x) at x = 0, we need to evaluate the function and its derivatives at x = 0.
a) Linear Approximation:
The linear approximation P1(x) is given by:
P1(x) = f'(a)(x - a) + f(a)
First, let's find f'(x) and f(x):
f(x) = \(e^{(4x)\) * cos(3x)
f'(x) = \((4e^{(4x)\) * cos(3x)) - \((3e^{(4x)\) * sin(3x))
Now, evaluate the function and its derivative at x = 0:
f(0) = \(e^{(4 * 0)\) * cos(3 * 0) = 1 * 1 = 1
f'(0) = (\(4e^{(4 * 0)\) * cos(3 * 0)) - (\(3e^{(4 * 0)\) * sin(3 * 0)) = 4 * 1 - 3 * 0 = 4
Substituting these values into the linear approximation formula:
P1(x) = f'(0)(x - 0) + f(0)
P1(x) = 4x + 1
b) Quadratic Approximation:
The quadratic approximation P2(x) is given by:
P2(x) = (1/2)f''(a)\((x - a)^2\) + f'(a)(x - a) + f(a)
To find f''(x), we differentiate f'(x):
f''(x) = (\(16e^{(4x)\)* cos(3x)) - (\(12e^{(4x)\) * sin(3x)) - (\(9e^{(4x)\)* cos(3x)) - (\(12e^{(4x)\) * sin(3x))
Now, evaluate the function and its derivatives at x = 0:
f''(0) = (\(16e^{(4 * 0)\)* cos(3 * 0)) - (\(12e^{(4 * 0)\) * sin(3 * 0)) - (\(9e^{(4 * 0)\) * cos(3 * 0)) - (\(12e^{(4 * 0)\) * sin(3 * 0)) = 16 - 0 - 9 - 0 = 7
Substituting these values into the quadratic approximation formula:
P2(x) = (1/2)(7)(x - 0)² + 4(x - 0) + 1
P2(x) = (7/2)x² + 4x + 1
c) Sketching the Graph:
To sketch the graph of the linear and quadratic approximations, plot the points for various values of x on the same axis. Label the axes neatly.
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Find the average value of the function f(x) = (x + 2) on the interval [0, 3].
The average value of the function f(x) = (x + 2) on the interval [0, 3] is 7/2.
Calculate the definite integral of the function over the interval [a, b], then divide it by the interval's length (b - a), in order to determine the average value of a function f(x) over the interval.
Given that the interval is [0, 3] and the function f(x) = (x + 2), we have:
= (1/3) × [1/2 x² + 2x] evaluated from x=0 to x=3
= (1/3) × [(1/2 × 3² + 2×3) - (1/20² + 20)]
= (1/3) × [(9/2 + 6) - 0]
= (1/3) × (21/2)
= 7/2
Therefore, the average value of the function f(x) = (x + 2) on the interval [0, 3] is 7/2.
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Use polar coordinates to find the volume of the given solid.
Below the paraboloid z = 18 − 2x² − 2y² and above the xy-plane
V = π [(3(\(\sqrt{18/2}\))³/1) - (2(\(\sqrt{18/2}\))⁵/15)] - π [0]
Simplifying this expression will give us the final volume of the solid.
, we need to evaluate the triple integral:
V = ∫₀²π ∫₀ᵣ ∫(18 - 2r²) r dz dr dθ
Integrating with respect to z first, we have:
V = ∫₀²π ∫₀ᵣ (18 - 2r²) r dr dθ
Integrating the volume with respect to r, we get:
V = ∫₀²π [(9r² - 2/3r⁴)]ᵣ₀ dθ
Simplifying the expression inside the brackets and evaluating the integral, we have:
V = ∫₀²π (9r² - 2/3r⁴) dθ
V = π [(9/3)r³ - (2/15)r⁵]ᵣ₀
V = π [(3r³/1) - (2r⁵/15)]ᵣ₀
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if the sum of two number is 37 and the greater number exceeds the smaller by 5, find the numbers.
Answer:
21 and 16
Step-by-step explanation:
x= big number
x`-5 = small number
x + x-5 = 37
2x-5 =37
2x= 42
x = 21
21-5 = 16
21+16 = 37
When m>n what is the horizontal asymptote?
O y=0
O y=a/b
O none
Answer:
a, y = 0
Step-by-step explanation:
when n<m or m>n, the horizontal asymptote is y=0
i have 17 coins. N of them are nickels and the rest are dimes. write an expression in two different ways for the amount of money that i have. (Hint: one is the other simplified)
Answer:
(N)0.05 + (17-N)0.1 = M; M = amount of money I have.
Or 1.7-0.05N = M.
Step-by-step explanation:
What is centroid and circumcentre?
The centroid and circumcenter of triangles are both geometric notions.
The distinction between a circumcenter and a centroid
Centroid:is a place where the triangle's medians coincide is known as the centroid. A triangle's median is a line segment that runs from one of the triangle's vertices to the middle of the other side. The centroid, which is sometimes designated as "G," is situated at the junction of all three medians. It is regarded as the triangle's center of mass or equilibrium point. Each median is split into two segments by the centroid, with the larger segment being closer to the vertex and the ratio of the segments' lengths being 2:1.
The centroid's characteristics
The centroid is situated two-thirds of the way between each vertex and the opposing side's middle.
It is located within the triangle.
The centroid is a triangle's uniformly thick and dense center of gravity.
The triangle is divided into three equal-sized triangles by the centroid.
A circumcenter's is perpendicular to a triangle's side and runs through that side's midpoint is called a perpendicular bisector. The unique circle that traverses all three of the triangle's vertices is called the circumcircle, and its center is known as the circumcenter. It is frequently indicated as "O"
The circumcenter's characteristics are:
Depending on the type of triangle, the circumcenter may be within, outside, or on the triangle.
The circumcenter is located inside the triangle if the triangle is sharp.
The circumcenter is outside the triangle if the triangle is acute.
The midpoint of the hypotenuse is where the circumcenter is found in a triangle with a right angle.
The triangle's three vertices are all equally far from the circumcenter.
The circumcenter is the point where the perpendicular bisectors, which are equally spaced from the triangle's respective sides, intersect.
Both the centroid and circumcenter are significant triangle locations with unique geometric characteristics.
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What shows the relationship between bivariate data graphed as ordered pairs on a coordinate plane?
a.
line of best fit
b.
bivariate data
c.
scatter plots
OPTION C : scatter plots
A baker has 2 1/4 cups of blueberries to make three batches of muffins. How many cups of blueberries should the baker put into each batch?
Answer:
0.75
Step-by-step explanation:
To answer this question you need to divide 2 1/4 by 3. To make it easier turn 2 1/4 to 2.25 because .25 = 1/4.
Find the percent of increase or decrease. Round to the nearest tenth of a percent where necessary.
32 to 40.
Answer:
Step-by-step explanation:
bro i dont know sory
Answer:
The number increased by 25%.
Step-by-step explanation:
If you divide 32 into 40 (40 / 32), it will get you 1.25.
Subtract 1 from 1.25 (1.25 - 1.00) and you'll get 0.25.
0.25 is a 25% increase
If the length of a rectangle is
expressed by 22 + 41-8 and the
width is 3x What is the area of the
rectangle?
I think that the length's area is 6075
Two cards are drawn without replacement from a standard deck of 5252 playing cards. What is the probability of choosing a black card for the second card drawn, if the first card, drawn without replacement, was a diamond
The probability of choosing a black card for the second card drawn, if the first card, drawn without replacement, was a diamond is 26/51.
We are given that two cards are drawn without replacement from a standard deck of 5252 playing cards. We need to find the probability of choosing a black card for the second card drawn, if the first card, drawn without replacement, was a diamond.
So, let us first find the probability of drawing a diamond card from a deck of 52 cards:4/52 = 1/13 (There are 4 diamond cards in a deck of 52 cards)
Now, if we draw a diamond card in the first draw, there will be 51 cards left in the deck of which 26 are black. Therefore, the probability of drawing a black card after drawing a diamond card is:26/51
Therefore, the probability of choosing a black card for the second card drawn, if the first card, drawn without replacement, was a diamond is 26/51.
Summary:Two cards are drawn without replacement from a standard deck of 52 playing cards. The probability of choosing a black card for the second card drawn, if the first card, drawn without replacement, was a diamond is 26/51.
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The following table shows how the average constituency changes for two regional governing boards, joshua and salinas, when a new representative is added to each board.
joshua's
average
constituency salinas's
average
constituency
joshua receives
new board
member 1232 1520
salinas receives
new board
member 1448 1333
(a) determine the relative unfairness of an apportionment that gives a new board member to joshua rather than to salinas. round to the nearest thousandth.
(b) determine the relative unfairness of an apportionment that gives a new board member to salinas rather than to joshua. round to the nearest thousandth.
(c) using the apportionment principle, determine which regional governing board should receive the new board member.
joshua
salinas
The relative unfairness of an apportionment that gives a new board member to joshua rather than to salinas will be
How to calculate the values?The relative unfairness of an apportionment that gives a new board member to joshua rather than to salinas will be:
= (1520 - 1232)/1232
= 288/1232
= 0.234
The relative unfairness of an apportionment that gives a new board member to salinas rather than to Joshua will be:
= (1448 - 1333)/1333
= 115/1333
= 0.086
The regional governing board that should receive the new board member is Salinas.
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what aspect of this data may make the traditional (parametric) test for a sample mean un-advisable?
The traditional (parametric) test for a sample mean assumes that the data is normally distributed. If the data is not normally distributed, then this test may not be appropriate. Additionally, the parametric test assumes that the sample size is sufficiently large (usually greater than 30) in order for the Central Limit Theorem to apply.
If the sample size is too small, then this test may not be reliable. Furthermore, if there are outliers or extreme values in the data, then the parametric test may not accurately reflect the true underlying population. In such cases, non-parametric tests may be more appropriate, as they do not rely on assumptions about the distribution of the data. It is important to carefully consider the nature of the data before choosing a statistical test to ensure accurate and reliable results.
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Please help!! :)
what is the value of X to the nearest 10th?
A: 8.6
B: 5.1
C: 1.3
D: 13.3
Bottles of water come in three sizes.
Small bottle: A 200 ml bottle costs 25p;
Medium bottle: A 750 ml bottle costs 84p;
Large bottle: A 1 litre bottle costs £1.08.
Calculate the cost of 3 litres for each bottle.
Give your answer in pence to the nearest penny.
Write the bottle that is the better value in the comments.
Small:
Р
Medium:
P
Large:
Р
Answer:
Step-by-step explanation:
Can someone explain how to do this:
If you put 10 in to the function f(x) = 2x, what would be the output?
--
Im so lost-
Answer:
It would be 2 (10)
Step-by-step explanation:
If you replace x with 10 then you have a multiplacation problem and the output of the answer is 20
Andrew is standing at point b looking up at an airplane in the sky. The angel of elevation is 55 degrees. What is the distance from Andrew to the plane.
In a case whereby Andrew is standing at point b looking up at an airplane in the sky. The angel of elevation is 55 degrees the distance from Andrew to the plane is \(13.0758 ft\)
How can the distance be calculated?Based on the figure using trigonometry, we can use the
cosx = adjacent/ hypotenuse
where the adjacent 7.5 ft
hypotenuse = the distance from Andrew to the plane
\(cos 55 = \frac{7.5}{hypotenus}\)
cos 55°= 0.5735764.
\(0.5735764 = \frac{7.5}{hypothenus}\)
\(hypotenuse = \frac{7.5}{0.5735764} =13.0758 ft\)
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You have 12 balloons to blow up for your party. You blow 1/3 of them, and your friend blows up 5 of them. What fraction of the balloons still need to blowing up?
Answer: One third
Step-by-step explanation: If you blow up a third of the balloons then you've blown 4 up because 12 divided by 3 is 4. Then you add the 5 balloons your friend blew up leaving you with 9 blown-up balloons in total. 9 blown-up balloons out of 12 is 2 thirds of the balloons leaving you with only one-third left to blow up.
Answer:
1/4
I hope this helps you <3
A caterer charges a flat fee of $345 in addition
to $45 per person to serve food at a family
reunion.
Write an equation to represent the total cost of
hiring the caterer and the number of people
attending the family reunion?
Answer: y = 45x + 345
Step-by-step explanation:
So y is the total cost of hiring the caterer and the number of people attending the family reunion.x represents how many people attend. It is $45 per person, so it would be 45 times the number of people attending, or 45x.345 is the extra amount that is added on and must be paid.So...the equation is y = 45x + 345.Hope this helps!!! :)
the mean score of 888 players in a basketball game was 14.514.514, point, 5 points. if the highest individual score is removed, the mean score of the remaining 777 players becomes 121212 points. what was the highest score?
The highest score is 32 points.
Given,
Mean score of 8 players =14.5
After removing highest score then,
Mean score of 7 players =12
let
the sum of all score be 'x'
highest score be 'y'
At first,
\(Mean=\frac{sum\ of\ all\ scores}{total\ number\ of\ scores}\\\\14.5=\frac{x}{8}\\\\x=116\)
after removing the highest score, mean will be
\(Mean=\frac{sum\ of\ all\ scores-highest\ score}{number\ of\ scores}\\\\12=\frac{x-y}{7}\\\\x-y=84\)
substituting 'x'
\(116-y=84\\\\116-84=y\\\\y=32\)
Thus, the highest score is 32 points.
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Select ALL of the data sets for which you would use the mean to describe the center of the data
Answer:ALLL
Step-by-step explanation:A:::::LLL
What is 3 y + 5 x = negative 15 written in slope-intercept form?
Answer:
The answer would be y=-5/3x-5!
Step-by-step explanation:
You want to make the equation to y=mx+b, so you have to make y by its self. Subtract 5x from both sides and you'll get 3y=-5x-15. Now divide 3 by both sides and you'll get y=-5/3x-5 which would be the answer!
Answer:
y=(-5/3)x-5
Step-by-step explanation:
so the slope intersect form is y=mx+b
3y+5x=-15
subtract 5x from both sides
3y= -5x-15
divide both sides by 3
y= (-5/3)x - 5
What is 5 1/2+(−3/4) =
Answer:
4 and 3/4
(Decimal: 4.75)
Hope this helps!
Please give brainliest
have a nice day
Josh has a triangular garden with sides represented with 15g²- 6g + 8.The other sides are -17g² - 22g - 13 and the third side represented by 6g² - 6g + 3. What is the perimeter of her garden?
The perimeter of her garden is 4g² -34g - 2 cm.
How to calculate the perimeter?It is important to note that the perimeter of a triangle is the addition of all its side. This will be illustrated thus:
In this case, Josh has a triangular garden with sides represented with 15g²- 6g + 8. The other sides are -17g² - 22g - 13 and the third side represented by 6g² - 6g + 3.
The perimeter will be:
= 15g²- 6g + 8 -17g² - 22g - 13 + 6g² - 6g + 3.
= 4g² -34g - 2
The perimeter is (4g² -34g - 2)cm.
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Help me pleasee !!!!
Answer:
here (edit I made a mistake)
Step-by-step explanation:
9) \(y=\frac{3}{5} x +5\)
10) y = x - 3
11) \(y=-\frac{3}{5} x - 3\)
12) \(y=\frac{5}{4} x + 2\)
these are the slop int forms, my bad...
sorry
Answer:
9) -3/5x + y = 5
10) -x + y = -3
11) 3/5x + y = -3
12) -5/4x + y = 2
Step-by-step explanation:
HELP I’m confused!
Does DA = DC? Explain
Answer:
pls add me as a friend pls
Step-by-step explanation:
The diagram below shows ano exterior wall of a house. The wall has a door opening that measures 3 feet by 7 feet and two windows opening that each measure 6 feet by 4 feet the wall,but not the openings will be covered with siding material that cost $1.50mper square foot. Find the total cost of the siding material.
The total cost of the siding material is given as follows:
B. $292.50.
How to obtain the cost of material?To obtain the cost of material, the first step is obtaining the area that will be covered, which is given as follows:
The rectangular area of 8 feet by 24 feet will be covered, with these following exceptions:
Two windows measuring 6 feet by 4 feet.One door measuring 3 feet by 7 feet.The triangular area with base 24 feet and height 6 feet will also be covered.
Then the total area to be covered is given as follows:
Area = 8 x 24 - (2 x 6 x 4) - (3 x 7) + 0.5 x 24 x 6
Area = 195 ft².
The total cost is of $1.5 per ft², hence it is calculated as follows:
Total cost = 195 x 1.5 = $292.50.
Meaning that option B is correct.
Missing InformationThe problem is given by the image shown at the end of the answer.
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