So from a table, we want to find an equation that models the mass as a function of time, we will get the equation:
M(t) = 0.02*t^2 - 2.42*t + 99.57
And with that equation, we will find that the mass after 11 seconds is 75 grams.
From the table we have the points:
(2, 94.8)
(5, 87.9)
(8, 81.3)
And we know that this follows a quadratic model, then we have:
M(t) = a*t^2 + b*t + c
Notice that from the known points, we have 3 equations:
94.8 = a*2^2 + b*2 + c
87.9 = a*5^2 + b*5 + c
81.3 = a*8^2 + b*8 + c
So we have a system of equations, we can simplify the equations to get:
94.8 = a*4 + b*2 + c
87.9 = a*25 + b*5 + c
81.3 = a*64 + b*8 + c
To solve this, we start by isolating one of the variables in one of the equations, let's isolate c in the first one.
c = 94.8 - a*4 - b*2
now we replace this in the other two equations to get:
87.9 = a*25 + b*5 + (94.8 - a*4 - b*2)
81.3 = a*64 + b*8 + ( 94.8 - a*4 - b*2)
Now we simplify these two equations to get:
-6.9 = a*21 + b*3
-13.5 = a*60 + b*6
Now we do the same thing, I will isolate b in the first equation:
b = (-6.9 - a*21)/3 = -2.3 - a*7
Now we replace this in the other equation:
-13.5 = a*60 + (-2.3 - a*7)*6
Now we can just solve this for a:
-13.5 = a*(60 - 7*6) - 2.3*6
0.3 = a*18
0.3/18 = a = 0.016
Wich can be rounded to:
a = 0.02
Then the value of b is:
b = -2.3 - a*7 = -2.3 - 0.016*7 = -2.42
And the value of c is:
c = 94.8 - a*4 - b*2 = 94.8 - 0.016*4 - (-2.42)*2 = 99.57
So the equation is:
M(t) = 0.02*t^2 - 2.42*t + 99.57
Now we can evaluate this in t = 11s to get:
M(11) = 0.02*11^2 - 2.42*11 + 99.57 = 75.37
Wich can be rounded to 75 grams.
If you want to learn more, you can read:
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Is (2, 2) a solution to this system of inequalities? 2x + 3y ≤ 10 x + 4y < 10
Answer:
No
Step-by-step explanation:
Plug the coordinates into the given inequality
2(2) + 3(2) ≤ 10(2) + 4(2) < 10
4 + 6 ≤ 20 + 8 < 10
10 ≤ 28 < 10
(2,2) is not a solution to this system of inequalities since 28 cannot be less than 10.
Which graph represents the following piecewise defined function? f(x)= x,x<-2\\ -2,-2<= x<1\\ x-3,x>=1
Answer:
The answer is -2/2x=1
Step-by-step explanation:
Its the second graph on edge
Which of these angle pairs are congruent because they are corresponding
angles?
A. 2 and 4
B. 2 and 3
C. 2 and 5
D. 2 and 6
SUBMIT
Answer: it’s 2 and 6
Step-by-step explanation:
how many litres of water can the cylinder hold if the volume is 1385.4cm
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Answer:
1.3854 liters
Step-by-step explanation:
1000 cm³ = 1 liter
1385.4 cm³ = 1.3854 liters
Hello help help please help help
Answer:
[tex]8x + 6 > 38 \\ 8x > 38 - 6 \\ 8x > 32 \\ x > \frac{32}{8} \\ \color{yellow} \boxed{x > 4}[/tex]
20 points again please help
Answer:
60°
G
mweheheh I just think
The number of coupons x used by a customer in a grocery store is a random variable with the probability density function f(x) = 4x + 3 27 , [0, 3] Find the expected number of coupons a customer will use.
Applying the integral formula, it is found that the expected number of coupons a customer will use is of 1.83.
The probability density function is given by:
[tex]f(x) = \frac{4x + 3}{27}, [0,3][/tex]
The integral formula for the expected value is:
[tex]E(x) = \int_0^3 xf(x) dx[/tex]
Hence, applying the formula for f(x) given in this problem, the expected number of coupons a customer will use is:
[tex]E(x) = \int_0^3 \frac{4x^2}{27} + \frac{x}{9} dx[/tex]
[tex]E(x) = \frac{4x^3}{81} + \frac{x^2}{18}|_{x = 0}^{x = 3}[/tex]
[tex]E(x) = 1.83[/tex]
The expected number of coupons a customer will use is of 1.83.
A similar problem, which also involves the calculation of the expected value via integral, is given at https://brainly.com/question/14263236
1.6 ACSF L5 SC Number: Simple and Compound Interest
Sandra plans to retire and can receive a lump sum of $26,376 from her pension provider.
2
She decides to invest of the lump sum for 8 years and use the rest for travelling.
3
Her bank account pays 4.99% compound interest per annum.
How much interest will Sandra receive from this investment after 8 years?
Round your answer to the nearest thousand dollars.
$
Answer:
$12,000
Step-by-step explanation:
[tex]p(({1 + i})^{n} - 1)[/tex]
[tex]26376( ({1 +.0499 })^{8} - 1) \\ = 12000[/tex]
Rewrite the equation y=|x+3|-1 as two linear functions f and g with restricted domains
You can write it as:
f(x) = - x - 4
{x | x ≤ -3, x ∈ R}
f(x) = x + 2
{x | x ≥ -3, x ∈ R}
After buying supplies ruby had $32 left over she spent $4 on notebooks $18 on a backpack and $30 on a new calculator how much money did ruby start with write an equattion to show your work
Answer:
$84
Ruby started with $84 before purchasing the school supplies.
Step-by-step explanation:
$32 + $4 + $18 + $30 = $84
Ill give brainliest
find the coefficient of x² of (2-2x+x²)⁵
Answer:
400.
Step-by-step explanation:
(2-2x+x²)⁵
= x^10 - 10 x^9 + 50 x^8 - 160 x^7 + 360 x^6 - 592 x^5 + 720 x^4 - 640 x^3 + 400 x^2 - 160 x + 32
5x+3x=16
find X
Thanks
Answer:
5 + 3 = 1 6
8 = 1 6
8 = 1 6
8 /8 = 1 6 /8
= 2
100 POINTS HELP ASAP NOW!!!!!!
Find the value of x in each case.
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Answer:
x = 22.5°
Step-by-step explanation:
The interior angle at E is (180 -4x), the supplement of the exterior angle there, 4x. The sum of angles 2x and (180-4x) will be equal to 6x, because alternate interior angles at transversal BE are congruent:
2x +(180 -4x) = 6x
180 = 8x . . . . . . . add 2x and simplify
22.5 = x . . . . . . . divide by 8
The value of x is 22.5°.
Please help quick will give brainly points
Answer: They are not inverse.
Step-by-step explanation:
4 boys weighed themselves in different pairs and alone. The weights of the pairs were 110kg, 112 kg, 113kg, 118kg, 121 kg, and the weight of one pair was lost. The total weight of the 4 boys was 230kg. What was the lost weight?
Answer:
116
Step-by-step explanation:
you can use variables
a+b=110
a+c=112
a+d=113
b+c=118
b+d=121
add up the weights and you get 574 kg (you need to find c+d)
3a+3b+2c+2d=574
a+b+c+d = 230 as given then you multiply by 3 so you can cancel out 3a and 3b and subtract 690-574 because we multiplied by 3
you are left with c+d=116
answer quick for brainiest
Answer:
a=120, b=75, c=60, d=105
There were 20 questions on the last quiz in Mrs. Lorenzo's class. A student answered 17 questions correctly. Write the ratio of correct answers to total questions as a decimal
Answer:
The answer would be 1.17.
Step-by-step explanation:
What is the slope of the line that contains the points (5,-1) and (3,-5)? The solution is
Answer:
slope = 2
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (5, - 1 ) and (x₂, y₂ ) = (3, - 5 )
m = [tex]\frac{-5-(-1)}{3-5}[/tex] = [tex]\frac{-5+1}{-2}[/tex] = [tex]\frac{-4}{-2}[/tex] = 2
An antique has a price tag of $275. The sales tax rate for the county is 8.2%. How much sales tax will be due?
Answer:
$22.55
Step-by-step explanation:
To find the tax due divide 8.2% by 100 to convert it into a decimal which equals to .082 . Next multiply 275 by .082 which gives you $22.55.
To make fuel for the main engines of a space shuttle, 102,619.377 kilograms of liquid hydrogen and 616,496.4409 kilograms of liquid oxygen are mixed together in the external tank. How much fuel is
stored in the external tank?
There are kilograms of fuel stored in the external tank.
Answer:
There are 719,115.8179 KG of fuel stored in the external tank
Step-by-step explanation:
102619.377 + 616496.4409 = 719,115.8179
If an item that originally cost $20 is increased to $27, what is the percentage of increase in the item?
Answer:
135%
Step-by-step explanation:
Answer:
35% increase
Step-by-step explanation:
27-20=7
7/20=0.35
How many times larger is
9 x 104 than 4.5 x 102 ?
Answer:
477
Step-by-step explanation:
9*104=936
4.5*102=459
936-459=477
What is numerical value of 35 - 4(5 - 9) + 7?
a. -58
b. -42
c. 42
d. 58
Pls helppp
Answer:
refer to the picture attached for steps
Step-by-step explanation:
hope it helps
d option
Answer:
58
Step-by-step explanation:
35 - 4 (5 - 9) + 7
Opening Brackets
= 35 - [4 x (-4) ] +7
= 35 + 16 + 7
= 58(9 + 31 + 5)[(7 x 5) x 4]
Answer:
The answer to your question is (7.5.4
if f(x)=2x^2-5 and g(x)=5x+7 g(x)=
Answer in the picture.
A function assigns the values. The value of f(g(x)) is 50x² + 140x + 93.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given the value of f(x)=2x²-5 and g(x)=5x+7, therefore, the value of f(g(x)) can be written as,
f(g(x)) = 2(5x+7)²-5
f(g(x)) = 2(25x²+49+70x)-5
f(g(x)) = 50x² + 98 + 140x - 5
f(g(x)) = 50x² + 140x + 93
Hence, the value of f(g(x)) is 50x² + 140x + 93.
Learn more about Function:
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Write the ratio in simplest form. 10 seconds to 5 min
Answer:
10:5
Step-by-step explanation:
The simplest form of the ratio 10 seconds to 5 min will be;
⇒ 1 : 30
What is mean by Ratio?
A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.
Where, x and y are individual amount of two quantities.
And, Total quantity gives after combine as x + y.
Given that;
The ratio is,
⇒ 10 seconds to 5 minutes.
Now,
Since, The ratio of two numbers has always same units.
So, We change 5 minutes into seconds as;
Since, 1 minutes = 60 seconds
Hence, 5 minutes = 5 x 60 seconds
= 300 seconds
Thus, The ratio becomes,
⇒ 10 seconds to 300 seconds
⇒ 10 : 300
⇒ 10 / 300
⇒ 1 / 30
⇒ 1 : 30
Thus, The simplest form of the ratio 10 seconds to 5 min will be;
⇒ 1 : 30
Learn more about the ratio visit:
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The temperature of a substance in an experiment changes by −8.7°F from 10 a.m. to 1 p.m. At 5 p.m., the temperature is 33.5°F. It is 23 of what the temperature was at 1 p.m.
What was the temperature at 10 a.m. of the substance?
Enter your answer as a decimal in the box.
Please answer completely
Answer:
58.95
Step-by-step explanation:
I took the quiz using K-12, and this is what I got!
Sorry If I am late to answer!
What is the answer for 14.05 x 7
Answer:
98.35
there that is the answer
you found a recipe which calls for 1/2 pound of chicken per person, if 4 pounds of chicken costs $8, what is the cost per person for the recipe you are using?
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Answer:
$1 per person
Step-by-step explanation:
The per-person cost (x) can be found from the proportion ...
x/(0.5 lb) = $8/(4 lb)
Multiplying by 0.5 gives ...
x = (0.5 lb) × ($8 /(4 lb)) = $1 . . . . . . units of lb cancel
The cost per person will be $1.
Tell whether the ordered pair (−5, −4) is a solution of the system
Step-by-step explanation:
3x - y = -11
(-15) + 4 is 11 hence RHS = LHS
