Using an exponential function, the expected mass of the sample in the year 2001 would be of 16 mg.
What is the exponential function for the amount of a substance?The function is:
[tex]A(t) = A(0)e^{-kt}[/tex].
In which:
A(0) is the initial amount.k is the decay rate.The information given is as follows:
A(0) = 440, A(8) = 40.
Hence:
[tex]A(t) = A(0)e^{-kt}[/tex].
[tex]40 = 440e^{-8k}[/tex].
[tex]e^{-8k} = 0.09090909[/tex]
[tex]\ln{e^{-8k}} = \ln{0.09090909}[/tex]
[tex]-8k = \ln{0.09090909}[/tex]
[tex]k = -\frac{\ln{0.09090909}{8}[/tex]
k = 0.29973691
Then the function is:
[tex]A(t) = 440e^{-0.29973691t}[/tex]
2001 is 11 years after 1990, hence the amount is:
[tex]A(11) = 440e^{-0.29973691 \times 11} = 16[/tex]
More can be learned about exponential functions at https://brainly.com/question/25537936
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estimate 5/8 - 1/10 explain
Answer:
21/40.
Step-by-step explanation:
Find the LCD (Least Common Denominator) of the fractions. The LCD of 5/8 and 1/10 is 40.
Convert both fractions into denominators of 40.
So then we have: 25/40 - 4/40 which is equal to: 21/40.
21/40 is the estimated value of the expression 5/8 -1/10
What is Number system?A number system is defined as a system of writing to express numbers.
The given expression is 5/8 -1/10
The terms in the expression are in the form of fractions, A fraction represents a part of a whole.
To find the value of expression firstly find the LCM of 8 and 10
40 is the LCM
5(5)-1(4)/40
25-4/40
The value of 25 minus 4 is twenty one.
21/40 is the value of the expression 5/8 -1/10
Hence, 21/40 is the estimated value of the expression 5/8 -1/10
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four times a number increased by 8 is 54?
Answer:
4x+8=54 this is the correct answer
Guys I need help !! X=2 evaluate 5x-2
Answer:
Step-by-step explanation:
Evaluate means to see what value the equation has given x is 2
substitute x for 2 (write instead of x, write 2)
5x-2 will be 5*2-2 , calculate 5*2-2= 10-2 = 8
To keep in shape, Vincent exercises at a track near his home. He requires 40 minutes to do 4 laps running and 7 laps walking. In contrast, he requires 18 minutes to do 2 laps running and 3 laps walking. Assuming he maintains a consistent pace while running and while walking, how long does Vincent take to complete a lap at each pace?
Answer:
He completes a lap running in 3 minutes, and walking in 4 minutes.
Step-by-step explanation:
This question can be solved by a system of equations.
I am going to say that:
x is the time needed to complete a lap running.
y is the time needed to complete a lap walking.
He requires 40 minutes to do 4 laps running and 7 laps walking.
This means that:
[tex]4x + 7y = 40[/tex]
[tex]4x = 40 - 7y[/tex]
He requires 18 minutes to do 2 laps running and 3 laps walking.
This means that
[tex]2x + 3y = 18[/tex]
Multipluing everything by 2
[tex]4x + 6y = 36[/tex]
Since [tex]4x = 40 - 7y[/tex]
[tex]40 - 7y + 6y = 36[/tex]
[tex]y = 4[/tex]
And
[tex]4x = 40 - 7y[/tex]
[tex]4x = 40 - 7*4[/tex]
[tex]4x = 12[/tex]
[tex]x = \frac{12}{4}[/tex]
[tex]x = 3[/tex]
He completes a lap running in 3 minutes, and walking in 4 minutes.
Why is it important that you put the polynomial in standard form (largest power
to smallest-power)? *
Answer: Polynomials like to be written in standard form. This means they contain no like terms and the exponents are in descending order (largest to smallest).
Step-by-step explanation:
Select the correct answer.
What is the complete factorization of x2 + 2x - 63?
A. (x+ 21)(x-3)
B.
(x-9)(x+7)
C.
(x + 9)(x-7)
D.
(x-21)(x + 3)
Reset
Answer:
the answer of this question is
c
47. Health care costs per capita Rising health care costs
are a growing concern for everyone in the United
States. Using U.S. Centers for Medicare and
Medicaid Services data from 2006 and projected to
2021, U.S. per capita health care costs can be modeled
by
y = 20.61x? - 116.4x + 7406
where x is the number of years past 2000. Use this
equation to find, to the nearest dollar, the average rate
of change of U.S. per capita health care costs from 2010
to 2015 and from 2015 to 2020.
PLEASE HELP!!! WILL GIVE BRAINLIEST!!!
Instructions
Search your home for a rectangular prism. Some examples are a cereal box, a CD case, or a coffee table. Measure your prism using appropriate units, such as inches, centimeters, or feet.
Complete the following. Show all work for calculations.
List the dimensions of your box. Be sure to include the units (in, cm, ft, etc.).
Length: 6 inches
Width: 2 and a half inches
Height: 12 inches (1 foot)
Describe the shape of the cross section when the box is cut parallel to the base.
What is the surface area of the box?
What is the surface area of the box if it is scaled up by a factor of 10?
What is the volume of the box?
What is the volume of the box if it is scaled down by a factor of 1/10?
Answer:
I chose a box of cereal-------> rectangular prism
see the attached figure
Part 1)List the dimensions of your box. Be sure to include the units (in, cm, ft, etc.).
Length: 20 cm
Width: 8 cm
Height: 32 cm
Part 2).
Describe the shape of the cross-section when the box is cut parallel to the base
the shape of the cross-section would be a rectangle of dimensions
20 cm x 8 cm
Part 3)
What is the surface area of the box?
surface area=2*area of the base+perimeter of the base*height
area of the base=20*8=160 cm²
perimeter of the base=2*[20+8]-----> 56 cm
height=32 cm
surface area=2*160+56*32------> 2,112 cm²
the answer part 3) is
2,112 cm²
Part 4)
What is the surface area of the box if it is scaled up by a factor of 10?
we know that
surface area of the larger box=[scale factor]²*surface area original box
scale factor=10
surface area original box=2,112 cm²
so
surface area of the larger box=10²*2,112-----> 211,200 cm²
the answer part 4) is
211,200 cm²
Part 5)
What is the volume of the box?
volume of the box=L*W*H-----> 20*8*32------> 5,120 cm³
the answer Part 5) is
5,120 cm³
Part 6)
What is the volume of the box if it is scaled down by a factor of 1/10
we know that
volume of the smaller box=[scale factor]³*volume original box
scale factor=1/10
volume original box=5,120 cm³
so
volume of the smaller box=[1/10]³*5,120-----> 5.12 cm³
the answer part 6) is
5.12 cm³
Step-by-step explanation:
Answer:
541/2 square
Step-by-step explanation:
we know that
the volume of the smaller box=[scale factor]³*volume original box
scale factor=1/10
volume original box=5,120 cm³
so
volume of the smaller box=[1/10]³*5,120-----> 5.12 cm³
the answer part 6) is 541/2 square
7+9 x (3+8) Order of operations. Please explain.
Answer:
Not sure if that is "9x" or "9 times" but I will do both. I have attached a picture of me solving and explaining the steps. Hope this helps, thank you !!
origanal price $60 sale price $45
Answer:
di ko po alam ehh
Step-by-step explanation:
sorry po
Answer:
Step-by-step explanation:
What is the question?
Price reduced by $15
Percentage reduction = 15/60 = 0.25 = 25%
Solve for x in the following equation.
X/5=25
X=?
Answer:
125
Step-by-step explanation:
25 × 5 = 125
x/5 = 25 × 5 = 125
x = 125
If a sprinkler waters 1/20 of a lawn in 1/5 of an hour how much time will it take to water the entire lawn?
• 3/20 hour
• 1/4 hour
• 4 hours
• 5 hours
Answer:
4 hours
Step-by-step explanation:
if the force acting on a body of mass 4kg accelerates it at a constant rate of 4m/s. what would be the acceleration of the mass is doubled?
Answer:
4kg=4m/s
8kg=?
3m/s
Step-by-step explanation:
12kgm/s/4kg
если x=6 то y=
если y=-4 то x=
Step-by-step explanation:
ssshzvecucsussddyz wksoav
Answer:
X=6 To y=-6
y=-4 TO X = 4
꧁꧁꧁꧁꧂꧂꧂꧂
꧂꧂꧂꧂꧂
12 more than the square of a number is the same as 7 times the number.
Answer: Sorry I don't know
Step-by-step explanation:
Write out the form of the partial fraction decomposition of the function (as in this example). Do not determine the numerical values of the coefficients. (a) x − 20 x2 + x − 20 Incorrect: Your answer is incorrect. (b) x2 x2 + x + 20 Incorrect: Your answer is incorrect.
Answer:
[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{5}{9(x-4)}+\frac{4}{(x+5)}[/tex]
Step-by-step explanation:
Given
[tex]\frac{x - 20}{ x^2 + x - 20}[/tex]
Required
Decompose into partial fraction
Start by factorizing the denominator:
[tex]x^2 + x - 20 =x^2 + 5x -4x- 20[/tex]
[tex]x^2 + x - 20 =x(x + 5)-4(x+5)[/tex]
[tex]x^2 + x - 20 =(x-4)(x+5)[/tex]
So, we have:
[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{A}{x-4}+\frac{B}{x+5}[/tex]
Take LCM
[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{A(x+5)+B(x-4)}{(x-4)(x+5)}[/tex]
Cancel out the denominator
[tex]x - 20 = A(x+5)+B(x-4)}[/tex]
Open brackets
[tex]x - 20 = Ax+5A+Bx-4B[/tex]
Collect Like Terms
[tex]x - 20 = Ax+Bx+5A-4B[/tex]
[tex]x - 20 = (A+B)x+5A-4B[/tex]
By comparison;
[tex](A +B)x = x[/tex] ==>[tex]A + B = 1[/tex]
[tex]5A - 4B = 1[/tex]
Make A the subject in [tex]A + B = 1[/tex]
[tex]A = 1 - B[/tex]
Substitute 1 - B for A in [tex]5A - 4B = 1[/tex]
[tex]5(1-B) -4B = 1[/tex]
[tex]5-5B -4B = 1[/tex]
[tex]5-9B = 1[/tex]
Collect Like Terms
[tex]-9B = 1 - 5[/tex]
[tex]-9B = - 4[/tex]
[tex]B = \frac{4}{9}[/tex]
[tex]A = 1 - B[/tex]
[tex]A = 1 - \frac{4}{9}[/tex]
[tex]A = \frac{9-4}{9}[/tex]
[tex]A = \frac{5}{9}[/tex]
So:
[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{A}{x-4}+\frac{B}{x+5}[/tex]
[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{5}{9(x-4)}+\frac{4}{(x+5)}[/tex]
A computer laboratory manager was in charge of purchasing new battery packs for her lab of laptop computers. She narrowed her choices to two models that were available for her machines. Since the models cost about the same, she was interested in determining whether there was a difference in the average time the battery packs would function before needing to be recharged. She took two independent samples and computed the following summary information: Battery Pack Model 1 Battery Pack Model 2Sample Size 9 9Sample Mean 5 hours 5.5 hoursStandard Deviation 1.5 hours 1.3 hoursUsing the null and alternate hypothesis:H0:mu1-mu2=0 vs. Ha: mu1-mu2 not equal 0Calculate the test statistic for this test.
Answer:
-0.756
Step-by-step explanation:
N1 = 9
N2 = 9
Sd1 = 1.5 hours
Sd2 = 1.3 hours
X1 = 5 hours
X2 = 5.5 hours
Hypothesis
H0: mu1 - mu2 = 0
H1 : mu1 - mu2 not equal to 0
Test statistic
t = (x1 - x2)/SE
SE is the standard error, which is unknown
SE = √sd1²/n1 + sd2²/n2
= √1.5²/9 + 1.3²/9
= √0.25+0.1878
= √0.4378
= 0.66166
t statistics = (5-5.5)/0.66166
= -0.5/0.66166
= -0.756
The 2010 U.S. Census asked every household to report information on each person living there. Suppose for a sample of 30 households selected, the number of persons living in each was reported as follows. 2 3 1 2 6 4 2 1 5 3 2 3 1 2 2 1 3 1 2 2 4 2 1 2 9 3 2 1 1 3 Compute the mean, median, mode, range, lower and upper quartiles, and interquartile range for these data. (Round the mean to 2 decimal places.) Mean
Answer:
[tex]\bar x =2.53[/tex] -- Mean
[tex]Median= 2[/tex]
[tex]Mode = 2[/tex]
[tex]Range = 8[/tex]
[tex]Q_1 = 1[/tex]
[tex]Q_3 = 3[/tex]
[tex]IQR = 2[/tex]
Step-by-step explanation:
Given
n = 30
Data: 2 3 1 2 6 4 2 1 5 3 2 3 1 2 2 1 3 1 2 2 4 2 1 2 9 3 2 1 1 3
Solving (a): The mean
This is calculated as:
[tex]\bar x =\frac{\sum x}{n}[/tex]
[tex]\bar x =\frac{2 +3 +1 +2 +6 +4 +2 +1 +5 +3 +2 +3+ 1+ 2 +2 +1 +3 +1 +2 +2 +4 +2 +1 +2 +9 +3 +2 +1 +1 +3}{30}[/tex]
[tex]\bar x =\frac{76}{30}[/tex]
[tex]\bar x =2.53[/tex]
Solving (b): The median
First arrange the given data
Arranged: 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 4 4 5 6 9
[tex]Median =\frac{1}{2}(n+1)[/tex]
[tex]Median =\frac{1}{2}(30+1)[/tex]
[tex]Median =\frac{1}{2}(31)[/tex]
[tex]Median = 15.5th[/tex]
This implies that the median is the average of the 15th and 16th item
[tex]Median = \frac{2+2}{2}[/tex]
[tex]Median = \frac{4}{2}[/tex]
[tex]Median= 2[/tex]
Solving (c): The mode
From the given data; 2 has the highest frequency of 11.
So,
[tex]Mode = 2[/tex]
Solving (d): The Range
[tex]Range = Highest\ Data - Lowest\ Data[/tex]
The highest is 9 and the lowest is 1,
So:
[tex]Range = 9 - 1[/tex]
[tex]Range = 8[/tex]
Solving (e): Lower (Q1) and Upper (Q3) quartile.
Q1 is calculated as:
[tex]Q_1 = \frac{1}{4}(n+1)th[/tex]
[tex]Q_1 = \frac{1}{4}(30+1)th[/tex]
[tex]Q_1 = \frac{1}{4}(31)th[/tex]
[tex]Q_1 = 7.75th[/tex]
[tex]Q_1 = 8th\ item[/tex]
[tex]Q_1 = 1[/tex] -- from the arranged data
Q3 is calculated as:
[tex]Q_3 = \frac{3}{4}(n+1)th[/tex]
[tex]Q_3 = \frac{3}{4}(30+1)th[/tex]
[tex]Q_3 = \frac{3}{4}(31)th[/tex]
[tex]Q_3 = 23.25th[/tex]
[tex]Q_3 = 23rd\ item[/tex]
[tex]Q_3 = 3[/tex] -- from the arranged data
Solving (f): The interquartile range (IQR)
[tex]IQR = Q_3 - Q_1[/tex]
[tex]IQR = 3-1[/tex]
[tex]IQR = 2[/tex]
Mr. Hernandez dilates the triangle shown below by a scale factor of 2 with the origin
as the center to obtain AA'B'C'.
Answer: only student 2
Evaluate
ifr=9 and s = 2.
S
Answer:
(4 × 9) / 2 = 36/2 = 18 gitu yaaa
Answer:
18
Step-by-step explanation:
plug in r and s
4(9)/2
36/2
18
Find set A' n B'
U= {1, 2, 3, 4, 5, 6, 7}
A= {4, 5, 6, 7}
B = {3, 4, 7}
Answer:
its 1 and 2
Step-by-step explanation:
first find A' which is(1,2,3) since these are in the universal set but not in A.
similary B' which is (1,2,5,6)
and since (1,2) are both in A' and B' set A'nB'=(1,2)
Answer:
Step-by-step explanation:
U={1,2,3,4,5,6,7}
A={4,5,6,7}
B={3,4,7}
A'={1,2,3}
B'={1,2,5,6}
A'∩B'={1,2}
PLS Help While on a strenuous hike, Tara recorded her distance from the peak of the mountain at two different time intervals. The table shows the two pieces of data she collected.
Answer:
Step-by-step explanation:
Equation of a line representing the relation between distance from the peak of the mountain and time is,
h = mt + b
Here, m = Slope of the line
b = y-intercept
Since, slope of the line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
From the table attached,
Slope of the line passing through (2, 2600) and (5, 950) will be,
m = [tex]\frac{2600-950}{2-5}[/tex]
= -550
Therefore, equation of the line will be,
h = -550t + b
Since, point (2, 2600) lies on this line,
2600 = -550(2) + b
b = 2600 + 1100
b = 3700
So, equation of the line will be,
h = -550t + 3700
Input - output values for this line,
t 2 4 6
h 2600 1500 400
Now we can plot these points and get the graph of the line.
✨6 Grade Math✨ Pls help
Answer:
37Step-by-step explanation:
89 - 4²×4 + 12 = 89 - 16×4 + 12 = 89 - 64 + 12 = 25 + 12 = 37Answer:
[tex]89 - 4 {}^{2} \times 4 + 12 = 89 \\ - 16 \times 4 + 12 \\ \\ = 89 - 64 + 12 \\ \\ = 25 + 12 \\ \\ = 37[/tex]
89-4^2×4+12=89-16×4+12
= 89-64+12
= 25+12
= 37
what is 3333 x 33 x 23 - 908
Answer:
2528839
Step-by-step explanation:
your welcome
This year 0.3 of the x students at Mega Middle School are in 7th grade. There are 294 students in 7th grade.
Answer:
is that even a question ?
Step-by-step explanation:
3/10x=294
x=294*10/3
x=980 students
if you found my answer helpful please mark as brainliest.
Pls help due in 10 minutes
Answer:
Boy I'm really boutta get to yo pickle chin ahh boy, egg head like collard greens head a//ss boy, oh hell nah boy yo dirt ahh boy stank ahh boy afro head ahh, lip gloss chin ahh boy ugly ahh boi
Step-by-step explanation:
Aawdadakdaw da awdwa dadeefdcdcs
7x= -42
What is the solution to this equation?
Answer:
X= -6
Step-by-step explanation:
7x = -42
(÷7) (÷7)
X = -6
Evaluate (–6)^2 – 7^2.
A) 85
B) 169
C) –85
D) –13
Need Trig Help plz Picture attached
To test the effectiveness of a drug proposed to relieve symptoms of depression, psychiatrists recruited volunteers for clinical tests. All of the volunteers were diagnosed with symptoms of depression. The psychiatrists provided the drug to first group and a sugar pill to the second group. In the description of the above situation, determine the control group.
Answer:
The control group is the group that takes the sugar pill
Step-by-step explanation:
In drug testing, to determine the efficacy of a drug, different groups of experimental subjects are recruited, one group is given the drug to be tested (treatment group) while another group is given a placebo.
A placebo is a fake version of the drug to be tested that does not have any therapeutic effect on the test subjects that receive it. In this case, the control group receives the placebo which is the sugar pill. They serve as the baseline of measurement when the outcome of the effect of the drug testing is done. The groups that received the actual drugs are compared against the groups that received the hoax treatment, and any change occuring in the test subjects become the changes occuring as a result of the test drug used, when the observations on the control group has been ruled out.