The value of f(16)=903.99, if f(x) is an exponential function where f(2)=3 and f(10.5)=96
What is meant by exponential function?The exponential function is a mathematical function that is represented by f(x)=exp or ex. Unless otherwise specified, the term refers to a positive-valued function of a real variable, though it can be extended to complex numbers or generalized to other mathematical objects such as matrices or Lie algebras. Although the exponential function was derived from the concept of exponentiation (repeated multiplication), modern definitions (there are several equivalent characterizations) allow it to be rigorously extended to all real arguments, including irrational numbers. Because of its prevalence in pure and applied mathematics, mathematician Walter Rudin called the exponential function the most important function in mathematics.
For exponential function,
f(x)= abˣ ; b>0, a, b ∈R
Given, f(2)=3
f(10.5)=96
Therefore, f(2)=ab²
3=ab²
a=3/b²
f(10.5)=a[tex]b^{10.5}[/tex]
96=a[tex]b^{10.5}[/tex]
a=96/[tex]b^{10.5}[/tex]
By equating a values then,
3/b²=96/[tex]b^{10.5}[/tex]
3[tex]b^{10.5}[/tex]=96b²
32=[tex]b^{10.5}[/tex]b⁻²
[tex]b^{8.5}[/tex]=32
b=[tex](32)^{1/8.5}[/tex]
Therefore, b=1.5034
a=3/b²
a=3/(1.5034)²
a=1.3273
f(16)=ab¹⁶
f(16)=(1.3273)(1.5034)¹⁶
f(16)=903.99
Therefore, the value of f(16)=903.99
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A 3/8-pound piece of cheese contains 4 servings. How much cheese is in 1 serving?
Answer:
3/32-pound cheese in 1 serving
Step-by-step explanation:
(3/8)/4=3/32 or 0.09375 lbs
4. The first three terms of an infinite geometric sequence are m – 1,6, m + 8.
(a)write down two expressions for r.
(b) the find two possible values of m.
(c) Hence, find two possible values of (r)
In the given geometric sequence
a) The expression of the common ratio r = -6 and (m+8)/2
b) The possible value of m = -28
c) The possible value of r = -6
The geometric sequence is
-1 , 6, m+8
The the common ratio = second term / first term
= 6 / -1
= -6
The common ratio = third term / second term
= (m+8)/6
The two expressions of common ratio is -6 and (m+8)/6
Part b
The third term = second term × common ratio
= 6 × -6
= -36
Then,
m +8 = -36
m = -36 + 8
m = -28
The possible value of m = -28
Part c
The possible value of r = -6
Hence, in the given geometric sequence
a) The expression of the common ratio r = -6 and (m+8)/2
b) The possible value of m = -28
c) The possible value of r = -6
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What are the domain and range of the function on the
graph?
The domain includes all integers, and the range is y 2
0.
The domain includes all integers, and the range is y >
0.
The domain includes all real numbers, and the range
is y ≥ 0.
The domain includes all real numbers, and the range
is y > 0.
The domain includes all real numbers, and the range is y > 0
What are domain and range?
A function's domain and range are its constituent parts. A function's range is its potential output, whereas its domain is the set of all possible input values. Range, Domain, and Function. A is the domain and B is the co-domain if a function f: A B exists that maps every element of A to an element in B. 'b', where (a,b) R, provides the representation of an element 'a' under a relation R. The set of images is the function's range. In general, a function's domain and range are denoted as follows: Range(f) = f(x): x domain(f) and domain(f) = f(x): x R
Domain: The domain is the set of all possible x-values.
Range: The range of a function is the complete set of all possible resulting values of the dependent variable y.
We can see from the graph, x values include all real numbers and range ( y values greater than 0 because the graph line does not intersect at 0.
we know that
The domain of the function of the graph is the interval (-∞,∞)
That means the domain is all real numbers.
The range of the function of the graph is the interval is (0,∞)
That means the domain is all real numbers greater than zero.
So, Option d is correct.
Therefore,
The domain includes all real numbers, and the range is y > 0.
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show that, if the wait() and signal() semaphore operations are not executed atomically, then mutual exclusion may be violated.
If the wait() and signal() semaphore operations are not executed atomically, then mutual exclusion may be violated as a wait operation atomically decrements the value associated with a semaphore.
Semaphores refers to integer variables utilized to solve the critical section problem by using two atomic operations, wait and signal that are used for process synchronization. The wait operation decreases the value of its argument S, if it is positive and if S is negative zero or negative, then no operation occurs. The signal operation increases the value of its argument S. Operation wait() and signal() must be completely atomic or else it violates the mutual exclusion. Mutual exclusion refers to the property of process synchronization which asserts that “no two processes can exist in the critical section at any given point of time”.
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Which graph represents f(x)=5⋅3x?
Answer:
the first one, the top left corner
Step-by-step explanation:
y- int = 5
no x int
A parabola can be drawn given a focus of (-4,-3) and a directrix of y = 1. Write the equation of the parabola in any form?
Answer:
Step-by-step explanation:
To plot
(
−
4
,
−
3
)
, start at the origin
(
0
,
0
)
and move left
4
units and down
3
units.
(
−
4
,
−
3
)
Ayúdame de método de eliminación 3x3
5× - 3y - z =1
× + 4y - 6z = -1
2× + 3y + 4z =9
The solution to the system of equations, using elimination, is given as follows:
x = 0.0135, y = -0.2767, z = -0.1024.
How to obtain the solution to the system of equations?The solution to the system of equations is obtained using the elimination method, as the variables are written as functions of each other and then solved.
The system in this problem is composed by the equations presented as follows:
5x - 3y - z = 1.x + 4y - 6z = -1.2x + 3y + 4z = 9.From the first equation, the variable z is written as function of variables x and y, as follows:
z = 5x - 3y - 1.
Replacing in the second equation, we have that:
x + 4y - 6(5x - 3y - 1) = -1
-29x + 22y = -7.
Replacing in the third equation, we have that:
2x + 3y + 4(5x - 3y - 1) = -1
22x - 9y = 3.
Hence the system is now:
-29x + 22y = -7.22x - 9y = 3.Multiplying the first equation by 9 and the second by 22, we have that:
-261x + 198y = -63.484x - 198y = 66.Adding the equations, the solution for x is obtained as follows:
223x = 3
x = 3/223
x = 0.0135.
Then the solution for y is obtained as follows:
-261(0.0315) + 198y = -63
y = (-63 + 261(0.0315))/198
y = -0.2767.
The solution for z is:
z = 5(0.0135) - 3(-0.2767) - 1 = -0.1024,
TranslationThe problem asks to solve the system of equations using the elimination method.
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A waitress sold 19 ribeye steak dinners and 12 grilled salmon dinners, totaling $581.52 on a particular day. Another
day she sold 24 ribeye steak dinners and 6 grilled salmon dinners, totaling $581.59. How much did each type of
dinner cost?
The each type of dinner cost is ribeye steak dinner cost is $20.05 and grilled salmon dinner cost is $16.74 by using the equation.
Given that,
On one particular day, a waitress served 12 grilled salmon dinners and 19 ribeye steak dinners for a total of $581.52. She made $581.59 on another day by selling 24 ribeye steak dinners and 6 grilled salmon entrees.
We have to find what was the price of each kind of dinner.
So,
We take R as a ribeye steak dinner and S as grilled salmon dinners.
We get,
19R+12S=$581.52 ---> equation(1).
24R+6S=$581.59 ----> equation(2).
Now Take the equation (2)
24R+6S=$581.59
6S=$581.59-24R
Multiply 2 on both sides of equation.
12S=$1163.18-48R
Now take the equation(1)
19R+12S=$581.52
Take the 12S as 12S=$1163.18-48R
19R+$1163.18-48R=$581.52
-29R=$581.52-$1163.18
-29R=-581.66
29R=581.66
R=581.66/29
R= $20.05
Now substitute R in 12S=$1163.18-48R
We get,
12S=$1163.18-48($20.05)
12S=$1163.18-962.4
12S=200.78
S=200.78/12
S=$16.74
Therefore, The each type of dinner cost is ribeye steak dinner cost is $20.05 and grilled salmon dinner cost is $16.74 by using the equation.
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Identify a reasonable domain and range.
Tickets that cost $125 dollars each
Well the domain is the number of tickets and the range is the cost for those tickets.
So x = 1 when y = 125 (1 ticket is 125 dollars). Here is a reasonable domain and range comparision:
x = 1 , y = 125
x = 2, y = 250
x = 3, y = 375
x = 4, y = 500
ect...
The lower limit of the domain is 0 because you cannot have less than 0 tickets.
I hope this helps!
g(x) is a vertical shift of f(x) , as shown in the graph. How do the two equations relate to each other?
Answer:
A
Step-by-step explanation:
g(x) = f(x) + 3
an unbiased coin is tossed 20 times. 6. find the probability that the coin lands heads exactly 11 times. a. 0.1602 b. 0.5731 c. 0.2941 d. 0.1527 e. 0.6374 7. find the probability that the coin lands tails at most 17 times. a. 0.0002 b. 0.8748 c. 0.7812 d. 0.0176 e. 0.9998 8. find the probability that the coin lands heads at most 3 times. a. 0.0004 b. 0.9963 c. 0.9556 d. 0.8751 e. 0.0013
Probability that the coin lands heads exactly 11 times is 0.1602 so Option a is correct.
Given:
an unbiased coin is tossed 20 times.
The probability that the coin lands heads exactly 11 times:
P = n(E)/n(S)
n(S) = 2^tosses
= 2^20
= 1048576
n(E) = C(20,11)
= 20!/11!(20-11)!
= 20!/11!*9!
= 167960
Probability P = 167960/1048576
= 0.16017 ≈ 0.1602
Therefore Probability that the coin lands heads exactly 11 times is 0.1602 so Option a is correct.
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a particle moves in a vertical plane along the closed path seen in (figure 1) starting at aa and eventually returning to its starting point. figure1 of 1 part a is the work done by gravity positive, negative, or zero? explain.
In the given situation, the work done by gravity is zero as any work done during a downward part of the motion as undone during the upward parts.
Work refers to the measurement of energy transfer that happens when an object is moved over a distance by an external force which is applied in the direction of the displacement. Hence, the work done is given by the multiplication of force and displacement in the direction of force i.e., W = F x d. As in the given case, the displacement d = 0 as the particle returns to the same point. The work done by gravity would measure the displacement along the y-axis and as the total displacement is zero, hence, work done will be zero.
Note: The question is missing the figure which is attached.
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What is the equation for the constant of proportionality that
matches the table?
y = 9x
y=18x
y = Ox
y = x
Answer:
y=9x
Step-by-step explanation:
For these x's and y's, we can notice that y is always equal to 9 times the value of x. 0 equals 9 * 0, 9 equals 9 * 1, 18 equals 9 * 2, 27 equals 9 * 3, and 36 equals 9 * 4.
We have just shown that y equals 9 times x, which is just y=9*x, or y=9x.
3- (pogil) a friend claims that flipping a coin 100 times and finding that it comes up heads only 45% of the time shows that the coin is biased. how should you reply?
with 100 flips, the outcome is very likely to be 45 heads or even less.
just because you have a 50% chance of getting heads, does not necessarily mean that you will get heads at exactly 50%.
100 coin flips will not always produce a 50-50 outcome of heads or tails. This is due to the fact that random events, while predictable in the long run, are not 100% predictable in small cases. For example, if we flipped a fair coin a quadrillion times, the variability in the outcomes caused by the coin's randomness would amount to a fractional value so small that calculators might even round the percentage of heads to 50%. However, with 100 flips, the outcome is very likely to be 45 heads or even less.
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What type of angles are < 3 and < 6
Answer:
Obtuse Angles
Step-by-step explanation:
Both < 3 and < 6 are visibly over 90° and less than 180°, so both are obtuse.
can someone please help me?
Answer:
b i think
Step-by-step explanation:
becuase 45f in total and for every hour it decreses 2f the anwser would be b but i may be wrong
(b) The amount of pure acid in 40 oz of 15% acid solution is
(Type an integer or a decimal.)
OZ.
Using the percentage, the amount of pure acid in 40 oz of 15% acid solution is 6 OZ.
In the given question,
The amount of pure acid in 40 oz of 15% acid solution is in OZ.
As we know that percentage is represent as a ratio of 100. So we solve it by converting the percentage.
So
=40×15%
So the simplified form is
=40×15/100
Simplifying
=6
Hence, the amount of pure acid in 40 oz of 15% acid solution is 6 OZ.
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The average cost to a 50-year-old male for a $100,000 term life policy is $14. 34 per month. The same policy would cost a 70-year-old male $79. 79 per month. How much more will the 70-year-old pay for a 20-year term?.
70-year-olds pay an extra $15708 for a 20-year term.
Given;
The average cost to a 50-year-old male for a $100,000 term life policy is $14. 34 per month. The same policy would cost a 70-year-old male $79. 79 per month.
A 70-year-average old's monthly expense (MAC) is $79.79
A 50-year-average old's monthly expense (MAC) is $14.34
MAC → Monthly Average Cost
To get how much more will the 70-year-old pay for a 20-year term;
We will multiply the monthly value by the yearly and solve the given data,
The extra amount paid = (MAC of 70 years old * 12 - MAC of 50 years old * 12) * 20 years term.
= ($79.79 * 12 - $14.34 * 12) * 20
= ($957.48 - $172.08) * 20
= $15708
Hence, the excess amount 70-year-old pay for a 20-year term is $15708.
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in a survey, 24 people were asked how much they spent on their child's last birthday gift. the results were roughly bell-shaped with a mean of $35 and standard deviation of $15. construct a confidence interval at a 90% confidence level.
The confidence interval at a 90% is 29.533 ≤ μ ≤ 40.467
Given that
mean = 35
standard deviation = 15
We compute the confidence interval as follows:
μ =¯ˣ± ME
Where:
μ = is the population mean,¯x = 35 is the sample mean and,ME = is the margin of error.To calculate the margin of error, we will use the t-distribution since the sample is very small n<30. Thus, our margin of error will be calculated as:
ME = t ×[tex]\frac{s}{\sqrt{n} }[/tex]
Where:
t = is the t-score at the 90% confidence level
degree of freedom df = 24 -1 =23
s = 15 is the standard deviation and,
n =24 is the sample size.
From the t-distribution tables, we will read the values of t at a critical value [tex]\alpha[/tex] = 0.10, and the degree of freedom is 23. This will give t= 1.714.
Thus, the margin of error is:
ME = 1.714 ×[tex]\frac{15}{\sqrt{23} }[/tex]
ME = 1.714 ×3.19
ME = 5.467
the confidence interval for the population mean is equal to:
μ = 35 ± 5.467
29.533 ≤ μ ≤ 40.467
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suppose the true proportion of voters in the county who support a restaurant tax is 0.55. consider the sampling distribution for the proportion of supporters with sample size n
The mean of this distribution is 0.55
The standard error of this distribution is 0.0384
We have the following:
p=0.55
sample size, n=168
Mean of distribution:
Mean=true proportion of voters who support a restaurant
Mean=p=0.55
Hence, the mean of distribution is 0.55
Standard error of the distribution:
[tex]=\sqrt{\frac{p(1-p)}{n} }[/tex]
[tex]=\sqrt{\frac{0.55(1-0.55)}{168} }[/tex]
=0.0384
Hence, the standard error is 0.0384
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The questions was incomplete, the complete question is given below:
Suppose the true proportion of voters in the county who support a restaurant tax is 0.55. Consider the sampling distribution for the proportion of supporters with sample size n = 168.
What is the mean of this distribution?
What is the standard error of this distribution?
help please..............................
Answer:
With what?
Step-by-step explanation:
Answer:
Step-by-step explanation:
d
an anonymous survey of college students was taken to determine behaviors regarding alcohol, cigarettes, and illegal drugs. the results were as follows:837 drank alcohol regularly, 639 smoked cigarettes, 176 used illegal drugs, 388 drank alcohol regularly and smoked cigarettes, 100 drank alcohol regularly and used illegal drugs, 105 smoked cigarettes and used illegal drugs, 83 engaged in all three behaviors, and 358 engaged in none of these behaviors. a) how many students were surveyed? of those surveyed, b) how many drank alcohol or smoked cigarettes ? c) how many drank alcohol only? d) how many drank alcohol and smoked cigarettes , but did not use illegal drugs ? e) how many smoked cigarettes or used illegal drugs , but did not drink alcohol ? f) how many engaged in exactly two of these behaviors? g) how many engaged in at least one of these behaviors?
a) Total surveyed students=1500
b) Drank alcohol or smoked cigarettes=1088.
c) Drank alcohol only=432
What is Venn Diagram?
A Venn diagram employs circles or other shapes that overlap to show the logical connections between two or more groups of objects. They frequently serve to visually group objects while highlighting how they differ and how they are similar.
Given, Alcohol drank → 857
Smoked cigarettes → 639
Illegal drugs used → 176
Drank alcohol regularly and smoked cigarettes → 388
Drank alcohol regularly and used illegal drugs →100
Smoked cigarettes and used illegal drugs → 105
Engaged in all three behaviors → 83
Engaged for none of these → 358
Notation used, Alcohol (A), Drugs (D), Cigarettes (C)
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Choose the graph of Y=1/2|x|+3
Find the zeros of the function. Enter the solutions from least to greatest.
f(x) = (x+8)² - 1
lesser x =
greater x =
The zeroes of the polynomial is -7,-9 and the lesser x = -9, greater x = -7.
What is zeroes of polynomial?
We already know that a polynomial is an algebraic term with one or many terms. Zeroes of Polynomial are the real values of the variable for which the value of the polynomial becomes zero. So, real numbers, ‘m’ and ‘n’ are zeroes of polynomial p (x), if p (m) = 0 and p (n) = 0.
Given
f(x) = (x+8)² - 1
=x^2+64+16x-1
=x^2+16x+63
=x^2+7x+9x+63
=x(x+7)+9(x+7)
=(x+7)(x+9)
therefore, x=-7,-9
The lesser x = -9,
the greater x = -7.
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The population of a specific species of nocturnal mammal is decreasing at a rate of 3.5%/year. The graph models the number of mammals x years after they were originally counted.
Identify and interpret the key features of the exponential function modeled in terms of this situation.
Select each correct answer.
Question 1 options:
The y-intercept represents the number of mammals when they were originally counted.
The line y = 0 is an asymptote of the graph.
The y-intercept.is 75.
The y-intercept is 120.
The asymptote indicates that the number of mammals counted when the study began was 120.
The asymptote indicates that as years pass, the number of mammals will approach 0.
The line x = 0 is an asymptote of the graph.
The key features of the graph of the exponential function are given as follows:
The y-intercept represents the number of mammals when they were originally counted.The y-intercept is 120.The line y = 0 is an asymptote of the graph.The asymptote indicates that as years pass, the number of mammals will approach 0.What are the key features of the graph?The y-intercept of a function gives the value of the function when it crosses the y-axis, that is, when x = 0, hence it is the initial number of mammals, which is of 120.
As x goes to infinity, the number of mammals will never be of zero but it will get very close to zero, hence the line y = 0 is the horizontal asymptote of the graph.
Missing InformationThe graph is shown by the image given at the end of the answer.
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What is the first step to find the volume of the solid?
Answer: c
Step-by-step explanation:
Lance threw a die six times. His median score was 3.5. His first five throws were 1,5,3,5,1. What was his sixth throw?
Answer: Sixth throw is 6
Step-by-step explanation: Let sixth throw be 'x'
1+5+3+5+1+x/6=3.5
15+x=3.5*6
15+x=21
x=6
Answer:3
Step-by-step explanation: literally just subtract 2 each time its not hard
Which graph represents the function
f(x)=√x+3-4
Answer:
I believe it is the last option but I'm not completely sure because the pic is blurry. But if the beginning of the graph is at (-3, -4) then the last option is definitely correct.
Step-by-step explanation:
Remember h controls horizontal movement k controls vertical movements.
always remember to take the opposite of h.
;)
pls explain how to do this
The x value for each of the equation.
1)The x is 10 when the equation is 8=x-2
2)If x+2=-2, then the value of x is -4.
3)If 2=x+8, then the value of x is -6.
4)The x is -10 when the equation is x+8=-2
Given that,
The given equation are
1) 8=x-2
2) x+2=-2
3) 2=x+8
4)x+8=-2
We have to find the x value for each of the equation.
Take the equations,
1) 8=x-2
Adding 2 on both sides
8+2=x-2+2
10=x
The x is 10 when the equation is 8=x-2
2) x+2=-2
Adding 2 on both sides
x+2+2=-2+2
x+4=0
Adding -4 on both side
x+4-4=0-4
x=-4
If x+2=-2, then the value of x is -4.
3) 2=x+8
Subtracting 8 on both sides
2-8=x+8-8
-6=x
x=-6
If 2=x+8, then the value of x is -6.
4)x+8=-2
Adding -8 on both sides
x+8-8=-2-8
x=-10
The x is -10 when the equation is x+8=-2
Therefore, the x value for each of the equation.
1)The x is 10 when the equation is 8=x-2
2)If x+2=-2, then the value of x is -4.
3)If 2=x+8, then the value of x is -6.
4)The x is -10 when the equation is x+8=-2
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If transcription progresses at the rate of 40 nucleotides per second, how long it would take to transcribe a sequence that is 3. 6 x 104 bases long?.
20 to 25 minutes Transcription occurs at a rate of 40 nucleotides per second.
Given,
In the question:
If transcription progresses at the rate of 40 nucleotides per second.
To find the how long it would take to transcribe a sequence that is 3. 6 x 104 bases long?
Why is a nucleotide necessary?
Nucleotides have a variety of roles in animal physiology, including those of energy storage, transporters of activated metabolites for biosynthesis, structural moieties of coenzymes, and metabolic regulators.
Give an example of nucleotides and describe them.
A nucleotide is the fundamental part of nucleic acids (RNA and DNA). A nucleotide is made up of a nitrogen-containing base, a phosphate group, and a sugar molecule (either ribose in RNA or deoxyribose in DNA). The nucleotides used in DNA are adenine (A), cytosine (C), guanine (G), and thymine (T).
Hence, 20 to 25 minutes Transcription occurs at a rate of 40 nucleotides per second.
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