Given the logarithmic equations, it can be deduced that m is 100 times greater than p, assuming n>0 which is not zero to avoid division by zero and it is positive as logarithm is undefined for negative numbers.
Explanation:The question asks to find the relationship between p and m given two log equations. Using the rule of logarithms The logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers (also known as the quotient rule), we can work out the relationship.
Given that log p/n = 6, it can be rearranged in exponential form: p = 106*n. And log m/n = 8 can be rewritten as m = 108*n.
Therefore, the relationship between p and m is that m is 100 times p, assuming n>0.
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The population of a local species of beetle can be found using an infinite geometric series a1=960 and the common ratio is .25 write the sum in sigma notation and calculate the sum of possible that will be the upper limit of this population
Sigma 960 (1/4)^i-1 ; the sum is 1280
Signa 960 (1/4)^-1 the sun is divergent
Sigma 960 (1/4)^i sum is 1280
Sigma (1/4)^i sum is divergent
I=1 for them all
The answer is:
Sigma 960 (1/4)^i-1 ; the sum is 1280
Step-by-step explanation:We are given the first term of the geometric sequence as:
[tex]a_1=960[/tex]
Also, the common ratio of the terms in geometric sequence is: [tex]\dfrac{1}{4}[/tex]
We know that if the series is a geometric series than the sum of the terms is given by:
[tex]a+ar+ar^2+.....\\\\=a(1+r+r^2+....)\\\\=\sum ar^{n-1}[/tex]
where a is the first term of the series and r is the common difference.
Here a=960
and r=1/4
Hence,
The sum of the series is:
[tex]=\sum 960(\dfrac{1}{4})^{i-1}[/tex]
Now we know that the sum of the infinite geometric series is given by:
[tex]S=\dfrac{a}{1-r}[/tex]
where S is the sum of the series.
Hence, here the sum of the series is calculated by:
[tex]S=\dfrac{960}{1-\dfrac{1}{4}}\\\\\\S=\dfrac{960}{\dfrac{3}{4}}\\\\\\S=\dfrac{960\times 4}{3}\\\\\\S=1280[/tex]
Hence, the sum is: 1280
True or false some drugs like Tylenol or available over-the-counter because they are safe in any dose
Which of the following is the sum of the polynomials 5x2 - 4x + 1 and -3x2 + x - 3 ?
2x2 + 3x + 2
8x2 - 5x - 2
2x2 - 3x - 2
-8x2 - 3x - 2
Jayla has a USB stick that transfers data at 2.4 x 10^9 bytes per second. Her modem transfers data at 1.2 x 10^7 bytes per second. Which statement is true?
A.There is no way to compare the transfer rates.
B.The transfer rate of the USB is 2 times the transfer rate of the Modem.
C.The transfer rate of the USB stick is 200 times the trasnfer rate of the modem
D.The transfer rate of the USB stick is 2,000 times the transfer rate of the modem
Answer: C.The transfer rate of the USB stick is 200 times the transfer rate of the modem .
A Web music store offers two versions of a popular song. The size of the standard version is 2.8 megabytes (MB). The size of the high-quality version is 4.9 MB. Yesterday, there were 1070 downloads of the song, for a total download size of 3521 MB. How many downloads of the high-quality version were there?
x= standard
y = high quality
x +y = 1070
y=1070-x
2.8x + 4.9y =3521
2.8x +4.9(1070-x) = 3521
2.8x+5243-4.9x =3521
-2.1x=-1722
x=-1722/-2.1 = 820
820*2.8 =2296
1070-820 =250
250*4.9 = 1225
1225+2296 = 3521
there were 250 high quality downloads
When flipping a coin three times, what is the probability of landing on heads all three times?
(08.02)The coordinate grid shows the plot of four equations.
Which set of equations has (−1, 5) as its solution?
A and B
B and D
A and C
B and C
A ramp 28 ft long rises to a platform. the bottom of the platform is 15 ft from the foot of the ramp. find x , the angle of elevation of the ramp
Max is in a control tower at a small airport. He is located 50 feet above the ground when he spots a small plane on the runway at an angle of depression of 27. What is the distance of the plane from the base of the tower? Round to the nearest foot. A. 25 feet B. 110 feet C. 56 feet D. 98 feet
The distance of the plane from the base of the tower is:
Option: D
D. 98 feet
Step-by-step explanation:Let x denotes the distance of the plane from the base of the tower.
Now, in the right angled triangle we will need to use trignometric identity corresponding to 63°.
Based on the figure we have:
[tex]\tan 63=\dfrac{x}{50}\\\\\\x=50\times \tan 63[/tex]
[tex]x=50\times 1.9626\\\\\\x=98.13\ feet[/tex]
which to the nearest feet is:
98 feet
Find the length of arc VZX in circle C
Length of arc VZX is 27.92 units.
What is arc?
The arc is a portion of the circumference of a circle.
Given,
Radius of circle = 8 units
∠VCX = 160°
Let length of arc VZX = x
x = area of circle×(360°- ∠VCX)/360°
x = 2π×8×(360-160)/360
x = 2π×8×(200)/360
x = 400π/45
x = 80π/9
x = 27.92 units
Hence, length of arc VZX is 27.92 units.
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A function f satisfies g(7) = 13 and g(1) = 6. a function f satisfies h(13) = 2 and h(6) = 7. what is the value of g(h(6))
What is the equation of a line that goes through the point
(0,
5
6
)
(0,56)
and has a slope of 1?
Select one:
a.
y=x+
5
6
y=x+56
b.
5
6
y=x
56y=x
c.
y=−x+
5
6
y=−x+56
d.
y=
5
6
x+1
y=56x+1
What is the expected number of heads for Danielle's experiment? (Enter your answer as a decimal)
I’ve answered this before so here’s the complete given for
this problem.
Danielle conducts an experiment by tossing a fair
coin three times. She records the number of heads out of the three trials. The
probabilities are given in the table below (X = number of heads out of three
trials).
Given:
x 0 1 2 3
P(x)1/8 3/8 3/8 1/8
n = 3; p = 0.5; q = 0.5; P(x = 0) =
nCx p^x
x N(x) P(x) ΣP(x) 1- ΣP(x) x * P(x)
--- ----- --------- --------- ---------
---------
0 1 0.125 0.125 0.875 0
1 3 0.375 0.5 0.5 0.375
2 3 0.375 0.875 0.125 0.75
3 1 0.125 1 0 0.375
0+.375+.75+.375 = 1.5
So, in this problem, the expected number of heads for Danielle's experiment is 1.5.
Using the Rational Root Theorem, what are all the rational roots of the polynomial f(x) = 20x4 + x3 + 8x2 + x – 12?
Answer: The all possible rational roots are [tex]x=\pm1,\pm2,\pm3,\pm4,\pm6,\pm12,\pm\frac{1}{2},\pm\frac{3}{2},\pm\frac{1}{4},\pm\frac{3}{4},\pm\frac{1}{10},\pm\frac{1}{5},\pm\frac{3}{5}\pm\frac{3}{10},\pm\frac{2}{5},\pm\frac{6}{5},\pm\frac{1}{20},\pm\frac{3}{20},\pm\frac{4}{5},\pm\frac{12}{5}[/tex].
Explanation:
The given polynomial is,
[tex]f(x)=20x^4+x^3+8x^2+x-12[/tex]
The Rational Root Theorem states that the all possible roots of a polynomial are in the form of a rational number,
[tex]x=\frac{p}{q}[/tex]
Where p is a factor of constant term and q is the factor of coefficient of leading term.
In the given polynomial the constant is -12 and the leading coefficient is 20.
All possible factor of -12 are [tex]\pm1,\pm2,\pm3,\pm4,\pm6,\pm12[/tex].
All possible factor of 20 are [tex]\pm1,\pm2,\pm4,\pm5,\pm10,\pm20[/tex].
So, the all possible rational roots of the given polynomial are,
[tex]x=\pm1,\pm2,\pm3,\pm4,\pm6,\pm12,\pm\frac{1}{2},\pm\frac{3}{2},\pm\frac{1}{4},\pm\frac{3}{4},\pm\frac{1}{10},\pm\frac{1}{5},\pm\frac{3}{5}\pm\frac{3}{10},\pm\frac{2}{5},\pm\frac{6}{5},\pm\frac{1}{20},\pm\frac{3}{20},\pm\frac{4}{5},\pm\frac{12}{5}[/tex]
Answer:
A.) -4/5 and 3/4
Step-by-step explanation:
The value of m in the following system of equations is:
m-2n=8
n=m-2
A) m= -4
B) m= -6
C) m= 2
D) None of the choices are correct
The correct option is A. [tex]m=-4[/tex]. By substituting the second equation into the first one in the system of equations, the value of m is -4.
The value of m in the system of equations can be found by substitution or elimination. Starting with the given equations:
[tex]m - 2n = 8 (1)[/tex]
[tex]n = m - 2 (2)[/tex]
Using the second equation (2) to substitute for n in the first equation (1):
[tex]m - 2(m - 2) = 8[/tex]
[tex]m - 2m + 4 = 8[/tex]
[tex]-m + 4 = 8[/tex]
[tex]-m = 8 - 4[/tex]
[tex]-m = 4[/tex]
[tex]m = -4[/tex]
This means that the value of m is -4, which corresponds to option A.
Help please. I need the answer fast.
What is the slope of a line that is perpendicular to the line x=-3?
A(-3
B(0
C(1/3
D(underfined
The slope of a line perpendicular to x = -3 is 0. Option B is correct answer.
What is the slopes of perpendicular lines?Perpendicular line slopes are the negative reciprocals of one another. In other words, if one line has a slope of m, a line perpendicular to it has a slope of -1/m. The definition of perpendicular lines, which states that the angles created by the lines are 90 degrees, may be used to demonstrate this relationship. The product of the slopes of perpendicular lines must be -1 in order to meet the requirement that the tangent of a 90 degree angle be specified.
Given the line x = -3.
Any line perpendicular to this line will have slopes of negative reciprocals of each other.
The slope of a horizontal line is 0, since the line does not change in the y-direction.
Hence, the slope of a line perpendicular to x = -3 is 0.
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QUESTION 18 I want to build a right triangular garden on the side of my house. Find the sides of the triangle if the hypotenuse is 6 feet and the two sides are equal in length.
Mr. Rr the Rreliable Rrobot has been programmed to whistle every $18$ seconds and do a jumping jack every $42$ seconds, starting from the moment he is turned on. (For example, he does his first jumping jack $42$ seconds after he is turned on.)
How many times during the first $15$ minutes after activation will Mr. Rr whistle and do a jumping jack at the same instant?
Answer:
7 times during the first 15 minutes
Step-by-step explanation:
Remember that
[tex]1\ min=60\ sec[/tex]
so
[tex]15\ min=15(60)=900\ sec[/tex]
Decompose the numbers 18 and 42 in prime factors
we know that
[tex]18=(2)(3^2)[/tex]
[tex]42=(2)(3)(7)[/tex]
Find the least common multiple (LCM)
The LCM is
[tex](2)(3^2)(7)=126\ sec[/tex]
we need to find all multiples of 126 that are less than or equal 900.
[tex]126*1=126\ sec\\126*2=252\ sec\\126*3=378\ sec\\126*4=504\ sec\\126*5=630\ sec\\126*6=756\ sec\\126*7=882\ sec[/tex]
therefore
7 times during the first 15 minutes
Does Verona have enough information to determine the areas of both triangles?
What is the probability of drawing two yellow marbles if the first one is NOT placed back into the bag before the second draw? Their is 10 marbles total, 2 yellow, 3 pink, and 5 blue
Final answer:
The probability of drawing two yellow marbles in succession without replacement from a bag of 10 marbles, where 2 are yellow, is 1/45.
Explanation:
The student is asking about the probability of drawing two yellow marbles successively without replacement from a bag containing a total of 10 marbles with different colors. To solve this problem, we use conditional probability. The probability of drawing the first yellow marble is 2 out of 10 since there are 2 yellow marbles among 10 total marbles. This can be written as P(Y1) = 2/10 or 1/5. After the first yellow marble is drawn, there is only 1 yellow left among 9 total marbles, so the probability of drawing a second yellow marble is P(Y2|Y1) = 1/9.
The two events are dependent since the outcome of the first draw affects the second draw. Therefore, to find the overall probability of both events happening, we multiply their probabilities: P(Y1 and Y2) = P(Y1) × P(Y2|Y1) = (1/5) × (1/9) = 1/45. So, the probability of drawing two yellow marbles successively without replacement is 1/45.
Look at the triangle. What is the value of sin x°?
If there are 190 contestants in a competition, how many ways can the first, second, and their place winner be chosen
Assume that you randomly select 6 cards from a deck of 52. what is the probability that all of the cards selected are hearts?
Drag the tiles to the correct boxes to complete the pairs. Match the numerical expressions to their simplified forms.
Drag the tiles to the correct boxes to complete the pairs. Match the numerical expressions to their simplified forms
Tiles:
A).
(P^5) ^1/4
---------------
(P^-3 Q^-4)
B).
(P^2Q^7) ^1/2
----------
(Q^4)
C).
(P^6Q^3/2)^1/3
D).
(PQ^3)^1/2
--------------
(PQ)^-1/2
Pairs:
1.)
P^2Q^1/2
2.)
PQ^2
3.)
P^2Q
4.)
PQ^3/2
A person purchased a leather jacket that was marked down by 40%. if the sale price of the jacket was $101.79, what was its original price?
5/3(6x+3)<2x-7 what is the solution for the iniquality
Scientific notation definition math is fun
Answer:
Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power, as 1385.62 written as [tex]1.3862*10^{4}[/tex].
Step-by-step explanation:
Let $AB = 6$, $BC = 8$, and $AC = 10$. What is the area of the circumcircle of $\triangle ABC$ minus the area of the incircle of $\triangle ABC$?
Which of the relationship below are function
A functions B and D are valid functions because they meet the criteria of each x value having only one corresponding y value.
Function B: You mentioned that B is a function because each x value has only one corresponding y value. In mathematical terms, a function is defined as a relation between a set of inputs (x values) and a set of outputs (y values), where each input (x) maps to exactly one output (y). So, if B satisfies this definition, it is indeed a function.
Function D: Similar to B, if D also adheres to the definition of a function, where each x value corresponds to only one y value, then it is a function as well.
Function A: You mentioned that for A, the x value of 1 has 2 y values. In mathematical terms, a function cannot have one input (x) mapping to multiple outputs (y). If this is the case for A, it does not meet the definition of a function.
Function C: You mentioned that for C, the x value of 7 has 2 y values, 10 and 3. Again, if one input (x) is associated with multiple outputs (y) in C, it does not qualify as a function.
In summary, functions B and D are valid functions because they meet the criteria of each x value having only one corresponding y value. Functions A and C do not meet this criterion and are not functions in the mathematical sense.
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