The logarithmic form of 8 = (1/2)⁻³ is given by log₍₁/₂₎(8) = -3.
The logarithm is exponentiation's opposite function in mathematics. This means that the logarithm of a fixed number, base b, represents the exponent to which that fixed number must be raised in order to create a particular number x.. The logarithm counts the number of times the same factor appears during repeated multiplication in the simplest scenario.
The given exponential form of the equation is 8 = (1/2)⁻³
To transform this exponential form into logarithmic form, we are requested.
Consider the given exponential form: 8 = (1/2)⁻³
Taking logarithm on both sides with the base as (1/2), we get,⇒ log₍₁/₂₎(8) = log₍₁/₂₎(1/2)⁻³
Now using the logarithmic rule logₐ(aⁿ) = n × logₐ(a) in the RHS of the above equation, we get
⇒ log₍₁/₂₎(8) = (-3) × log₍₁/₂₎(1/2)
⇒ log₍₁/₂₎(8) = (-3) × 1
(Since logₐ(a) = 1, for a > 0)
⇒ log₍₁/₂₎(8) = -3
Therefore, the logarithmic form of 8 = (1/2)⁻³ is given by log₍₁/₂₎(8) = -3.
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Find any points of discontinuity for each rational function. y=x+5 / x²+9 x+20
points of discontinuity for each rational function. y=x+5 / x²+9 x+20 is x = -4
Given,
y=x+5 / x²+9 x+20
It can be expressed in the form of -
⇒ y = (x+5) / (x+5) (x+4)
⇒ y = 1 / (x+4)
The function will be undefined if the denominator will be 0
⇒ x+4 = 0
⇒ x = -4
So, we can conclude that the given function will be having points of discontinuity as x = -4
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What is the difference in the approximate number of wins between the first place team and the last place team?
A. 50
B. 45
C. 40
D. 35
Answer:
65-72
Step-by-step explanation:
Identify the number types that describe 7 squared
The square root value of 7 is 2.645.
Irrational number
All real numbers that are not rational are considered irrational numbers. In other words, it is impossible to describe an irrational number as the ratio of two integers.
Any square root number that cannot be represented as a fraction [tex]\frac{P}{Q}[/tex] for any integer p and q is said to be irrational.
A real number that cannot be expressed as a straight forward fraction is referred to as an irrational number. It cannot be described using a ratio. When p and q are integers and q is not equal to 0, N is not equal to [tex]\frac{P}{Q}[/tex] if N is irrational.
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Find the compound interest and the amount after twelve seconds if the interest is compounded
every three seconds.
Principal 20,000
Rate of interest = 800% per minute
=
Total amount =
Compound interest =
well, we know the rate is compounding at 800% per minute.
the elapsed time will be 12 seconds, and since a minute has 60 seconds, that'd be 12/60 minutes.
the compounding period is 3 seconds, and since a minute has 60 seconds, that means is compounds 60/3 times, or namely 20 times.
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$20000\\ r=rate\to 800\%\to \frac{800}{100}\dotfill &8\\ n= \begin{array}{llll} \textit{times it compounds per minute}\\ \textit{twenty times} \end{array}\dotfill &20\\ t=minutes\to \frac{12}{60}\dotfill &\frac{1}{5} \end{cases}[/tex]
[tex]A=20000\left(1+\frac{8}{20}\right)^{20\cdot \frac{1}{5}} \implies A =20000(1.4)^4\implies A=76832[/tex]
Albert invested money into the stock market, and the table represents his earnings. What type of function could be used to model his bank account as a function of time? Justify your answer.
Week Balance ($)
1 1,400.00
2 1,470.00
3 1,543.50
4 1,620.68
This is a linear function because there is a common difference in the balance between the weeks.
This is a linear function because there is a common ratio in the balance between the weeks.
This is an exponential function because there is a common difference in the balance between the weeks.
This is an exponential function because there is a common ratio in the balance between the weeks.
The correct option regarding the bank amount as a function of time is:
This is an exponential function because there is a common ratio in the balance between the weeks.
When a linear function should be used and when an exponential function should be used?A linear function should be used when there is a common difference between the amounts.An exponential function should be used when there is a common ratio between the amounts.For this problem, the differences are given as follows:
1620.68 - 1543.5 = $77.18.1543.5 - 1470 = $73.5.1470 - 1400 = $70.The ratios are given as follows:
1620.68/1543.5 = 1.05.1543.5/1470 = 1.05.1470/1400 = 1.05.Due to the same ratios, an exponential function should be used, and the correct option is given by:
This is an exponential function because there is a common ratio in the balance between the weeks.
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Answer:c
Step-by-step explanation:
The price of Stock A at 9 A.M. was $15.03. Since then, the price has been increasing at the rate of $0.05 each hour. At noon the price of Stock B was $15.53. It begins to decrease at the rate of $
0.14 each hour. If the two rates continue, in how many hours will the prices of the two stocks be the same?
After 1.842 hours the price of Stock A and Stock B will be the same using a set of linear equations.
A grouping of one or more linear equations containing the same variables is known as a system of linear equations.
For Stock A :
The initial price = $15.03
The rate of increase = $0.05
For Stock B :
The rate of decrease = $15.53
The rate of decrease per hour = $0.13
Then the price of stock A at noon will be:
$ 15.03 + $ (0.05 × 3) = $ 15.03 + $ 0.15 = $15.18
The period of time during which the stock price will remain constant:
15.18 + 0.05t = 15.53 - 0.14t
Simplifying the terms we get,
0.05t + 0.14t = 15.53 - 15.18
0.19t = 0.35
t = (0.35 ÷ 0.19) hours
t = 1.842 hours
Therefore, the stocks will be of equal price after 1.842 hours.
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Amy inputs 1÷17 in her calculator. The calculator displays 0.0588235294. Is the quotient a rational or an irrational number? Explain.
Answers with explanation please and thank you:))
The quotient of 1 ÷ 17 is a rational number.
In this question, Amy inputs 1÷17 in her calculator.
The calculator displays 0.0588235294
We need to check whether the quotient is a rational or an irrational number.
The quotient of 1 ÷ 17 is a rational number.
1 ÷ 17 can be written as 1/17, which is a rational number.
The quotient of 1 ÷ 17 is a decimal: the quotient a rational or an irrational number.
Therefore, the quotient of 1 ÷ 17 is a rational number.
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Model with mathematics. Graph the fraction -1 2/5 on the number line.
The fraction -1 2/5 is modeled on the number line by: graph A.
What is a fraction?A fraction can be defined as a numerical quantity which isn't expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.
What is a number line?A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.
In this scenario, we can reasonably infer and logically deduce that the fraction -1 2/5 is modeled on the number line by graph A because each interval increases by 2/5 or 0.4.
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Write each equation in logarithmic form.
10⁴=10,000
The equation of 10⁴=10,000 in logarithm form will be log₁₀ (10000) = 4.
Given that
10^4 = 10000 - - - - - -( 1 )
We have [tex]a^{y}[/tex] = x - - - - - ( 2 )
Comparing ( 1 ) and ( 2 ) we get
a = 10, y = 4, x = 10000
The logarithmic form is written as logₐ (x) = y .It is rearrangement of the exponential form [tex]a^{y}[/tex] = x.
By logarithmic definition
y = logₐ (x)
so we got 4 = log₁₀ (10000)
Therefore, the equation of 10⁴=10,000 in logarithm form will be log₁₀ (10000) = 4.
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10)110
help me please
Answer:
If it is a division problem, then it is 11.
If it is a multiplication problem then it is 1100.
But it looks like division, so probably 11.
Answer:
011
Step-by-step explanation:
0 1 1
--------------------------------
1 /
0 1 1 0
− 0
1 1
− 1 0
1 0
− 1 0
0
PLEASE HELP!!! PLEASE HELP RIGHT NOW ASAP!!!!!
Kevin has a pitcher that holds 2.75 quarts of juice. How many 1.4 quart cups can he fill up with one pitcher of juice?
2x(4+1)+(3x+5)+(2x+1)
suppose you want to line pennies up, diameter to diameter, until the total length is 1 kilometer. assume the width of 1 penny is 2 cm. how many pennies will you need? how accurate is this estimation?
Answer: 50,000 pennies
Step-by-step explanation: there are 100,000 centimeters in a kilometer, since a penny is 2 centimeters in length, divide 100,000 by 2 t get 50,000
Nathan is planning to ride his bike for 24 minutes if he rides at a rate of 5 miles per hour how far will he travel
The distance that Nathan can ride his bike is 2 miles.
What is the distance Nathan can ride?The rate is the total distance per time. Rate is determined by dividing the total distance travelled by the total time travelled.
Rate = total distance / total time.
Distance = rate x time
The rate is in miles per hour while the time given is in minutes. Thus, minutes has to be changed to hour. To do this, divide 24 minutes by 60.
60 minutes = 1 hour
24/ 60 = 2/5
Distance = 2/5 x 5= 2 miles
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Complete the identities.
csc θ =1/?
Answer:
? = sin θ
Step-by-step explanation:
csc θ =1/?
csc θ =1/sin θ
4r-4s+4t = -4
4r+s-2t= 5
-3r-3s-4t=-16
Answer:
1) R = 1 S = 3 T = 1
2) R = 1 S = 3 T = 1
3) R = 1 S = 3 T = 1
Step-by-step explanation:
Surprisingly each of the situations end up with 1, 3, 1. I double checked with a calculator and they all end up being true. Hope this helps. Have a great night. :)
Find the difference.
(9ab+7a-7) (4ab-5)
The difference is 5ab + 7a + 13
What is Arithmetic Operation?An arithmetic operation is specified by combining operands with one arithmetic operator. Arithmetic operations can also be specified by the ADD, SUBTRACT, DIVIDE, and MULTIPLY
given:
(9ab+7a-7) (4ab-5)
So, the difference is
(9ab+7a-7) - (4ab-5)
=9ab + 7a - 7 -4ab + 20
=9ab - 4ab +7a -7 +20
=5ab + 7a + 13
Hence, the difference is 5ab + 7a + 13.
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Lisa has a button collection and decided to measure her 12 favorite buttons to the nearest 1/8 inch. Her results are shown in the line plot below.
(look at photo attached)
If she took one of her smallest buttons, one of her largest buttons, and one of her most common-sized buttons and laid them side-by-side, what would be their combined length?
Answer:
2 3/4
Step-by-step explanation:
the Smallest is 1/2
the biggest is 1 1/2
the most common is 3/4
Adding them all up will give you 2 3/4 or 11/4
Answer:
2[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
the smallest button is [tex]\frac{1}{2}[/tex]
the most common button is [tex]\frac{3}{4}[/tex]
the largest button is 1 [tex]\frac{1}{2}[/tex]
add these buttons together
[tex]\frac{1}{2} + \frac{3}{4} + 1 \frac{1}{2} =[/tex]
find the LCD of the denominators
factors of 2: 2, 4, 6, 8, 10
factors of 4: 4, 8, 12, 16, 20
find the factor that is the same in the two rows
factors of 2: 2, 4, 6, 8, 10
factors of 4: 4, 8, 12, 16, 20
2*2 = 4
[tex]\frac{1}{2}[/tex]· 2 = [tex]\frac{2}{4}[/tex]
[tex]\frac{2}{4} + \frac{3}{4} + 1 \frac{2}{4} =[/tex]
1[tex]\frac{7}{4}[/tex]
[tex]\frac{7}{4} = 1 \frac{3}{4}[/tex] + 1
2[tex]\frac{3}{4}[/tex]
ײ + 5× - 11 + 3ײ - 11 × + 2
hello guys please solve and give a solution tthankyou
Step-by-step explanation:
start by collecting like terms
4x² - 6x -9
use quadratic equation, a=4, b= 6 and 9 = c.
x = 5,78 or x = -4,28
17 + x = 15
pls help
Answer:
x = -2
Step-by-step explanation:
The equation is,
→ 17 + x = 15
Now the value of x will be,
→ 17 + x = 15
→ x = 15 - 17
→ [ x = -2 ]
Hence, the value of x is -2.
Step-by-step explanation:
17+x=15
17+x-17=15-17
x=-2
Questions on the picture below or above
Answer:
hundred
million
hundredth
5800
2
460000
0.07
Step-by-step explanation:
Christmas tree lights are used not only for christmas trees, but sometimes to decorate college dorm rooms. Suppose that a string has 20 light bulbs. These lights are all wired in series, so that if one light bulb fails, the whole string fails. The probability that any one light fails is 0. 2. Each of the individual lights are independent of each other. What is the probability that the string will not fail?.
If a string has 20 light bulbs and these lights are all wired in series, so that if one light bulb fails, the whole string fails and the probability that any one light fails is 0.2 and each of the individual lights are independent of each other, then the probability that the string will not fail is 0.0115.
Probability in mathematics deals with the likelihood of an event to take place.
The probability that the string will not fail refers to when all 20 bulbs will not fail. As given in the conditions, each of the individual lights are independent of the other. Therefore;
the probability that any one of the lights will not fail is:
1 - probability that any one light fails = 1 - 0.2 = 0.8
And we need all 20 to be complete. The unity of events is a product of probabilities. Therefore the probability that the string will not fail is:
P = 0.8^20
P = 0.0115
Hence 0.0115 is the probability that the string will not fail.
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What is the value of the expression 8 + (9 -1) \div÷ 4?
Answer:10
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
8 + (9- 1) ÷ 4
Use PEMDAS to determine order of operations in a mathematical expression
The order of operations is
P = parentheses
E = exponent
M = multiplication
D == division
A = addition
S = subtraction
Note that multiplication and division have the same priority and we go from left to right that case. Because it does not affect the answer.
So 12 ÷ 4 x 6 = 12 x 6 ÷ 4
Same for addition and subtraction - same priority
Using PEMDAS
(9 - 1) is executed first giving 8
The expression becomes 8 + 8 ÷ 4
Next division is performed so 8 ÷ 4 is executed giving 2 as the answer
Finally 8 + 2 is executed giving 10
I need help figuring out what 7x + 5 divided by x is
Answer:
The way you described this question was a bit confusing- but here is what I can provide based off of what you said.
Step-by-step explanation:
7x+5/x
Please provide a picture next time
Write an equation for the parabola in vertex form whose vertex is at (2, 3) and passes through (0, 2).
The equation of the parabola in discuss such that the parabola has a vertex at (2, 3) and passes through (0, 2) is; y = (-1/4) (x - 2)² + 3.
What is the equation of.the parabola in discuss whose vertex is at (2, 3) and passes through (0, 2)?It follows from the task content that the equation of the parabola whose vertex is at (2, 3) and passes through (0, 2) is to be determined.
Since, the vertex form equation of a parabola is;
y = a (x-h)² + k
where the vertex is; (h, k) which is (2, 3) in this scenario.
Therefore, we have;
y = a (x - 2)² + 3
Ultimately, to find the value of a; substitute; x = 0 and y = 2 from the point (0,2) into the equation;
2 = a (0-2)² +3
-1 = 4a
a = -1/4.
Ultimately, the equation of the parabola as required in the task content is;
y = (-1/4) (x - 2)² + 3
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Please help me please help me please please
Answer:
Step-by-step explanation:
180-degree rotation
I explained previously, but I will explain again.
A 180-degree rotation is just a switch of signs on the numbers
Explanation:
Replica U=(2, 1) Original U=(-2, -1)
At a constant temperature, the atmospheric pressure p in pascals is given by the formula p=101.3 e⁻⁰.⁰⁰¹h , where h is the altitude in meters. What is p at an altitude of 500 m ?
At an altitude of 500 meters, the atmospheric pressure (p) will be 61.46 pascals.
The exponential constant, denoted by the symbol e, is an essential mathematical constant. Its value is approximately equal to 2.718. This value occurs very frequently in mathematics when it is used to model physical and economic phenomena.
Here, we are given an exponential function- p = 101.3[tex]e^{-0.001h}[/tex]
where p = atmospheric pressure in pascals
h = altitude in meters.
If the altitude is 500m
h = 500
Then,
p = 101.3 [tex]e^{-0.001 * 500}[/tex]p
= 101.3 [tex]e^{-0.5}[/tex]p
= 101.3/ [tex]e^{-0.5}[/tex]p
= 101.3/ 1.648p
= 61.46
Thus, at an altitude of 500 meters, the atmospheric pressure (p) will be 61.46 pascals.
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The average temperature in the mountains is 65° in April. The average temperature in that same spot is −5° in December. Determine how much warmer this location is in April than in December, and determine which temperature is the farthest away from 0°.
Answer:
65 + |-5| = 70, 65 is the farthest away from 0
Step-by-step explanation:
Please help
Which of the following lines is perpendicular to y = 1/4x -3. Select all that apply.
A. Y=4x+9
B. 8x-2y=3
C. 4x-y=-2
D. Y=-4x+6
E. Y=4x
The slope of a line is y=mx+c, where m is the slope. The lines is perpendicular to y = 1/4x -3 is Y=-4x+6.
What is slope intercept form?
The slope of a line is y=mx+c, where m is the slope.
The given line is y = 1/4x -3.
slope m1=1/4.
slope of second line=-(1/m)
=-(1/1/4)
=-4
point slope intercept form is y-y1=m(x-x1)
Equation of the perpendicular line passing through point (0,6) is
y-6=-4(x)
y=-4x+6
Therefore the line perpendicular to y = 1/4x -3 is Y=-4x+6.
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Martha spent of her pocket money on
magazines.
She then spent
of what she had left on a
present.
After that, she had £3 left.
How much pocket money did she have to start
with?
Give your answer in pounds (£).
Answer:
Step-by-step explanation:
Martha spent 1/6 of her pocket money on magazines.