The value of logarithmic expression (2logbx/3 + 3logby / 4) - 5logbz is logbx/3^2(by / 4)^3/logbz^5.
By considering the given logarithmic expression
(2logbx/3 + 3logby / 4) - 5logbz
logb(x/3)^2 +log(by / 4)^3-log(bz)^5
logb(x/3)^2(by / 4)^3-logbz^5
logbx/3^2(by / 4)^3/logbz^5
The logarithm is exponentiation's opposite function in mathematics. This means that the exponent to which a fixed number, base b, must be raised in order to produce a given number x, is represented by the logarithm of that number.
Based on the logarithm base, the logarithmic functions are broadly divided into two types. There are common and natural logarithms. Common logarithms are based on the number 10, while natural logarithms are based on the base "e." The power to which a number must be raised in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents).
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Make y the subject of this equation:
ty = a + k
Answer:
y = [tex]\frac{a+k}{t}[/tex]
Step-by-step explanation:
ty = a + k ( isolate y by dividing both sides by t )
y = [tex]\frac{a+k}{t}[/tex]
Answer:
[tex]\sf y =\dfrac{a+k}{t}[/tex]
Step-by-step explanation:
To make 'y' as the subject, isolate y by dividing both sides by t
ty = a + k
Divide both sides by t,
[tex]\sf \dfrac{ty}{t}=\dfrac{a+k}{t}\\\\[/tex]
[tex]\sf y = \dfrac{a +k}{t}[/tex]
In 2010, the population of a city was 228,000. From 2010 to 2015, the population grew by 7.7%. From 2015 to 2020, it fell by 4.2%. To the nearest 100 people, what was the population in 2020?
The population in the city in 2020 to the nearest 100 is 235242.65.
The population of the city was 228,000 in the year 2010.
From 2010 to 2015, the population grew by 7.7%.
The population decreases by 4.2 % from 2015 o 2020.
Initially, the population of the city is 228,000.
From 2010 to 2015,
The city's population increased by 7.7%.
7.7% of 228,000 = ( 7.7 / 100) × 228,000 = 17556
The population of the city from 2010 to 2015 = 228,000 + 17556 = 245556
From 2015 to 2020,
Now, the city's population decreases by 4.2%.
4.2% of 245556 = ( 4.2 /100) × 245556 = 10313.352.
Therefore,
The population of the city in the year 2020 = 245556 - 10313.352 = 235242.648
Therefore, the population in the year 2020 to the nearest 100 is 235242.65.
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Answer:
235200
Step-by-step explanation:
Prior to an election, 6,504 people vote in the advance polls for a riding. On election day, thepolling stations for that riding record an average of 407 voters per hour. How long were thepolls open on election day, if a total of 10,167 people voted in that riding?
**USE LET STATEMENTS, AND THEREFORE STATEMENTS**
The number of hours the polls open on the election day was 9 hours
From the question, we are to determine how long the polls opened on the election day
From the given information,
6,504 people vote in the advance polls for a riding prior to the election
and
A total of 10,167 people voted in that riding
Thus,
The number of people that voted on the election day = 10167 - 6504
Number of people that voted on the election day = 3663
Also, from the given information
The polling stations for the riding record an average of 407 voters per hour
Then,
Number of hours the polls open on election day = Number of people that voted on the election day ÷ Average number of voters per hour
Number of hours the polls open on election day = 3663 ÷ 407
Number of hours the polls open on election day = 9 hours
Hence, the number of hours the polls open on the election day was 9 hours
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Divide the following and then check by multiplying.
9043 +18
What is the value of the expression below when z = 5?
8z - 9
Answer: 31
Step-by-step explanation:
1. Replace z by 5, meaning that 8*5
2. Then, subtract 40 by 9 (8*5 = 40, 40-9 = 31)
Write each expression as a single natural logarithm. ln 18-ln 10
Expression as a single natural logarithm of equation ln 18-ln 10 is = 0.5877866649.
What is natural logarithm?ln 18-ln 10
= [tex]ln (18/10)[/tex]
= ln 1.8
= 0.5877866649
The inverse of an exponential function, the natural log is the logarithm to the base of the number e. Natural logarithms are unique varieties of logarithms that are employed in the treatment of time and growth-related issues.
The distinction between log and ln is that log is expressed in terms of base 10, while ln is expressed in terms of base e. As an illustration, log of base 2 is denoted by log2 and log of base e by loge = ln (natural log).
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Given that a function, g, has a domain of -1 ≤ x ≤ 4 and a range of 0 ≤ g(x) ≤ 18 and that g(-1) = 2 and g(2) = 8, select the statement that could be true for g.
we can state that Option D may be accurate and true.
Assuming that the function, g, it has a domain of -1 ≤ x ≤ 4 and a range of 0 ≤ g(x) ≤ 18 and that g(-1) = 2 and g(2) = 8
Then the following properties must hold
1. The value(s) of x must be between -1 and 4
2. The values of g(x) must be between 0 and 18.
3. g(-1)=2
4. g(2)=9
We consider the options and state why they are true or otherwise.
A: g(5)=12
The value of x=5. This contradicts property 1 stated above. Therefore, it is not true.
B: g(1) = -2
The value of g(x)=-2. This contradicts property 2 stated above. Therefore, it is not true.
C: g(2) = 4
The value of g(2)=4. However by property 4 stated above, g(2)=9. Therefore, it is not true.
D: g(3) = 18
Given that its domain is between -1 and 4 and its range is between 0 and 18, this claim is reasonable.
Therefore, we can say that Option D can be true.
This question is incomplete
The provided options are:
Options
(A) g(5) = 12
(B) g(1) = -2
(C) g(2) = 4
(D) g(3) = 18
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The equation y=(-16t-4)(t-2) represents the height in feet of a beach ball thrown by a child Find the zeros of the functionWhat do the zeros tell us in this situation? From what height is the beach ball thrown ?
Answer:
See below
Step-by-step explanation:
To find zeroes:
0 = (-16t-4)(t-2)
so -16t-4 = 0 t = -1/4
or t-2 = 0 t = 2
when the ball is thrown, t= 0
put t= 0 in the equation to find the initial height
y = ( -16t -4)(t-2)
= ( -16(0)-4)(0-2) = (-4)(-2) = 8 ft
Can y’all pls give me the answers
Answer:
A:0.11 B:I can't a diagram in here
Simplify 3.42 + (−5.6). 39.8 9.02 −2.18 −3.98
Answer: c 2.18
Step-by-step explanation:
pray to god that its right
Simplify each radical expression. Use absolute value symbols when needed. 5√-64 x¹⁴ y²⁰
The rationalize of all denominators is [tex]40x^{14} y^{20} i[/tex]
We rationalize the denominator to make certain that it will become less complicated to carry out any calculation at the rational number. while we rationalize the denominator in a fraction, then we are eliminating any radical expressions inclusive of rectangular roots and dice roots from the denominator.
The distinction is that denial flat out says there may be no trouble whilst clarification is smarter, it justifies thoughts and behaviors on some different grounds in the try to convince Self and others that these minds and behaviors are not maladaptive, that they may be definitely adaptive.
The rationalize is a disavowal defense mechanism that permits an individual to address emotional conflicts, or inner or external stressors, via devising reassuring or self-serving however incorrect factors for his or her personal or others' mind, actions, or feelings, which cowl up different reasons (Perry 1990).
[tex]5 \sqrt{-64 x^{14} y^{20} }[/tex]
[tex]\sqrt{-64} = i8[/tex]
[tex]5i8x^{14} y^{20}[/tex]
[tex]40ix^{14} y^{20}[/tex]
[tex]40x^{14} iy^{20}[/tex]
= [tex]40x^{14} y^{20} i[/tex]
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After simplifying the radical expression 5 √(-64) x¹⁴ y²⁰, the result is 40 x¹⁴ y²⁰ i.
We are given the radical expression as:
5 √(-64) x¹⁴ y²⁰
We need to simplify the radical expression and find the value of the expression.
Now, we will first simplify the term √(-64)
We know that:
√(-64) = √( - 1 × 8 × 8 )
= 8 √ -1
Using the properties of complex numbers, we get that:
√ - 1 = i
= 8 i
Putting it in the expression, we get that:
= 5 ( 8 i ) x¹⁴ y²⁰
= 40 x¹⁴ y²⁰ i
Therefore, we get that, after simplifying the radical expression 5 √(-64) x¹⁴ y²⁰, the result is 40 x¹⁴ y²⁰ i.
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Kallie thinks that each double
problem will have an even sum.
Do you agree or not?
Since Kallie thinks that each double problem will have an even sum. in my response, it is Yes, I do not agree with her.
Why do i not agree with her?The reason why i agree with her is that the odds that is double will also give you an odd double and get an even double.
What happens when you double an odd number?An odd number is known to be one that be looked at as an even number and this is one that happens if one added to it .
For example 5 is 4+1.
Therefore, if you add two odd numbers together, there is the probability that a person may get an even number.
For example is 3 + 5 = 8
Therefore, Since Kallie thinks that each double problem will have an even sum. in my response, it is Yes, I do not agree with her.
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14 less than the quotient of 11 and a number
Answer:
(11/x) - 14
Step-by-step explanation:
(11/x) - 14 or 11 - 14x/x
if the point P(-4/5,y) lies on the unit circle and P is in the third quadrant, what does y equal
The value of y on the unit circle is y =-3/5
What is a circle?A circle is defined as the locus of a point such that it is equidistant from a fixed point.
The equation of a circle with center at the origin is given by x² + y² = r² where r = radius of circle
What is a unit?A unit circle is a circle with radius, r = 1.
So, the equation of a unit circle is x² + y² = 1
How to find the value of y on the unit circle?Given that the point P(-4/5, y) lies on the unit circle, and P is int he third quadrant, making y subject of the formula in the equation for unit circle, we have
y = ±√(1 - x²)
Substituting x = -4/5 into the equation, we have
y = ±√(1 - x²)
y = ±√(1 - (-4/5)²)
y = ±√(1 - 16/25)
y = ±√[(25 - 16)/25]
y = ±√[9/25]
y = ±3/5
Now, given that P is in the third quadrant, it implies that y is negative. so, y = -3/5
So, the value of y on the unit circle is y =-3/5
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Help its A Math Question Please Help I am givng you 35 points for this question and a brainly crown if another person answers the question aswell thanks !
[tex]sum \: of \: interior \: angles = (9 - 2)180 = 1260 \\ one \: angle \: in \: th e\: nonagon = \frac{1260}{9} = 140 \\ x + nop = 180 \: (supplementary \: angles) \\ x + 140 = 180 \\ x = 180 - 140 \\ x = 40[/tex]
Alma is choosing a new smartphone and cellular service plan. let p be the phones price in dollars, m be the cost of the selected plan in dollar per month, and c be alma's total cost in dollars after time t, measured in months of service. write an equation that expresses c in terms of p, m, and t. then solve your equation for t.
The equation which expresses c in terms of p, m and t as in the task content is; c = mt + p and the solution of the equation for t is; t = (c -p)/m.
What is the equation of the situation such that c is expresses in terms of p, m and t?It follows from the fact that the rate of change, m is constant in the situation described. Hence, the equation is a linear equation.
On this note, the required equation which represents total cost, c in terms of p, m and t can be written as;
C = mt + p.
Hence, to solve the equation above for t;
Subtract p from both sides so that;
c - p = mt
Divide both sides by m;
(c - p)/m = t.
Ultimately, The equation which expresses c in terms of p, m and t as in the task content is;
c = mt + p
and the solution of the equation for t is;
t = (c -p)/m.
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Please help I need this
Answer:
11 inches
Step-by-step explanation:
The sides of the teacher's model are 110 inches
Henry's model should be 10 times shorter.
110 ÷ 10 = 11
For the coordinates A(5,8) and M(9,14), A is an endpoint of AB and M is the midpoint. Find the coordinates of endpoint B.
Answer:
(13, 20)
Step-by-step explanation:
L. (4, 7); y = 3x + 6
y = 3x -5 is the equation of the line parallel to the line and going through the point (4,7). The format is slope intercept.
Slope intercept is what?A method of formulating a line's equation that makes it simple to identify the slope and y-intercept is known as the slope-intercept form. The point where the line crosses the y-axis is known as the y-intercept, and the slope refers to how steep the line is.
Using the information provided,
y= 3x – 5
First, we must keep in mind that parallel lines have an equal slope.
In essence,
m1 = m2 if line 1 and 2 are parallel.
Y = mx + c is the slope-intercept form of the equation; y = 3x + 6, which already has this form.
incline of the m1 = 3.
Consequently, m1 = 3 = m2.
The slope of the parallel line, m2 = 3 and the line passes through the point (4,7).
Therefore;
3 = (y - 7)/(x-4)
By cross product;
3x - 12 = y - 7
y = 3x - 5
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what is the outlier for the nmbers 2 4 6 8 10 and 12
The outliers of the given data set are 2 and 12.
The given data set is 2, 4, 6, 8, 10 and 12.
What is the outlier of numbers?Outliers are extreme values that stand out greatly from the overall pattern of values in a dataset or graph
A value that "lies outside" (is much smaller or larger than) most of the other values in a set of data. For example in the scores 25,29,3,32,85,33,27,28 both 3 and 85 are "outliers".
In the given data set 2, 4, 6, 8, 10 and 12.
2 is the lowest observation and 12 is the highest observation.
So, 2 and 12 are two extreme values and these two are outliers.
Therefore, the outliers of the given data set are 2 and 12.
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Use the following setup and given equation to find your solution:
1st integer = x
2nd integer = x+2
3rd integer = x+4
Equation: x+(x+2)+(x+4)=267
Solve the equation above. What is the largest integer?
The largest integer in the set of number is 91
How to use the given equation to determine the largest integer?The given parameters are
1st integer = x2nd integer = x+23rd integer = x+4Equation: x+(x+2)+(x+4)=267So, we have
x+(x+2)+(x+4)=267
Open the brackets
x + x + 2 + x + 4 = 267
Evaluate the like terms
3x = 261
Divide both sides by 3
x = 87
Substitute x = 87 in 3rd integer = x+4
3rd integer = 87 + 4
Evaluate
3rd integer = 91
Hence, the largest integer is 91
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simplify the following
Answer:B
Step-by-step explanation:
Hey, so I need to find the y-intercept, the slope, and the equation for it. Help please
Answer:
f= 1.3s - 8.7
Step-by-step explanation:
Slope is M
M = 1.3 feet per second
y=mx+ b your b= 8.7ft
your equation is
f= 1.3s - 8.7
Need some assistance with this question
The equation is y = 30x +3000
$ 10500 is the rent for 250 guests.
What is slope intercept form?The slope intercept form in math is one of the forms used to calculate the equation of a straight line, given the slope of the line and intercept it forms with the y-axis. The slope intercept form is given as, y = mx + b.
Given:
(100, 4350) and (155, 6000)
So, slope = 6000- 4350 / 155-100
slope = 1650/55
slope= 30
So, the equation is
y-6000 = 30( x- 100)
y - 6000 = 30x - 3000
y = 30x +3000
Now,
and, for 250 guests the rent would be
y= 30 * 250 + 3000
y = 7500+3000
y= $ 10500
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Convert 168 pounds to kilograms. Use 1 kg = 2.2 lb.
Round your answer to the nearest tenth.
(……) kg
Answer:
about 76.36 kgis the answer
Step-by-step explanation:
168 divided by 2.2 is 76.36.
Which three relations are functions? Select all correct answers
Answer: what am i supposed to choose from?
Step-by-step explanation:
What is the answer to -10+7 and how do you solve it
Answer:
-3
Step-by-step explanation:
[tex](-a) + (+b) = -c\\= -10 + 7\\= -3[/tex]
Rory records the percentage of battery life remaining on his phone throughout a day. The battery life decreases as Rory uses the phone, but will increase or stay at 100% while charging. The graph represents the percentage of battery life remaining after a certain number of hours.
A graph titled Phone Battery Life. The horizontal axis shows Elapsed Time (hours) numbered 2 to 20, and the horizontal axis shows Battery Life (%) numbered 10 to 120. A line begins at 100% in 0 hours, to 20% in 8 hours, to 100% from 10 to 12 hours, to 60% in 16 hours, to 100% from 17 to 20 hours.
At which times could Rory's phone have been plugged into the charger? Select three options.
6 hours
9 hours
11 hours
14 hours
19 hour
Answer:
9, 11, and 19
Step-by-step explanation:
9, 11, and 19 are the only plausible answers because there were only 2 periods where the phone was at 100% (other than when the graph started) and these are the only hours that fell within those periods..
Family Dinner Combinations A family special at
a neighborhood restaurant offers dinner for four for
$39.99. There are 3 appetizers available, 4 entrees, and
3 desserts from which to choose. The special includes
one of each. Represent the possible dinner combinations
with a tree diagram.
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The number of dinner combinations that will be represented in the Tree Diagram is 36.
What is a Tree Diagram?A tree diagram is a new management planning tool that depicts the hierarchy of tasks and subtasks needed to complete and objective. The tree diagram starts with one item that branches into two or more, each of which branch into two or more, and so on. The finished diagram bears a resemblance to a tree, with a trunk and multiple branches.It is used to break down broad categories into finer and finer levels of detail. Developing the tree diagram helps you move your thinking step by step from generalities to specifics.
Given that a neighborhood restaurant offers dinner for four for
$39.99 which includes
Three types of appetizers =(a1,a2,a3)
Four types of entrees = (e1,e2,e3,e4)
3 types of desserts = (d1,d2,d3)
Therefore, we can conclude the Number of combinations = 3*4*3=36
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What’s the unit rate for four pounds of bananas for $2.36
Answer:
$0.59/pound
Step-by-step explanation:
Since there are four pounds you divide $2.36 by 4 to get the unit rate.