find the value of n.
8 × 2^3n = 2^12
6th grade math help me
Answers
8=2^3
2^3*2^3n=2^12
2^3+3n=2^12
3+3n=12
3n=12-3
3n=9
n=9/3
n=3
find the value of n.
8 × 2^3n = 2^12
Answer :-n = 3
Solution :-[tex]\sf\ given \:: \: 8 \times 2 ^{3n} [/tex]
[tex]\sf\rightarrow 8 \times 2 ^{3n} \: = {2}^{12} [/tex]
[tex]\sf\rightarrow {2}^{3n} = {2}^{12} \: \: (8 = {2}^{3} )[/tex]
[tex] \sf\rightarrow {2}^{3n + 3} = {2}^{12} \: \: \: ( {a}^{m} \times {a}^{n} = {a}^{m + n} )[/tex]
Equating powers since bases are same.
[tex]\sf\rightarrow 3n \: + 3 = 12[/tex]
[tex]\sf\rightarrow 3n \: + 3 - 3 = 12 - 3[/tex]
[tex]\sf\rightarrow 3n = 9[/tex]
Divide both sides by 3.
[tex]\sf\rightarrow n = 3[/tex]
Thus the value of n is 3 .
Related Questions
Calculating Binomial Probabilities - Suppose you work for an airline and you are taking reservations for a flight on an aircraft that has 152 seats. You know, based on historical flights trends, that if you sell a single ticket there is a 91% chance that the person with the ticket will actually show up for the flight. You decide to try to make a little extra money by overbooking your flight and you sell 160 tickets hoping that not more than 152 people will actually show up for the flight (note: this is a common business practice! Click here to watch a video that explains why)
Explain how this scenario meets the four requirements in the definition of a Binomial Distribution.
Identify what n and p are in this example
Use technology (StatCrunch, Statdisk, or Excel) to calculate the probability that if you sell 160 tickets for your flight, more passengers will show up than there are seats available (again, the plane has 152 seats total). Post an image of your technology output using the Insert/Edit Image feature in Blackboard (no attachments!)
Based on this probability, do you think it is a wise business practice to oversell your flight in this manner? Explain.
Answers
The probability that if you sell 160 tickets for your flight, more passengers will show up than there are seats available is 0.02
How the scenario meet the requirements?The scenario meets the following requirements
The value of n is fixed i.e. 160The outcome has two possible values i.e. seats available or notThe chance that a person shows up is the same for each outcome i.e. p = 91%Each observation is independent.Identify n and pThe given parameters are:
n = 160
p = 0.91 i.e. 91%
x = 152
How to determine the probability?The distribution is a binomial distribution, and it is calculated using:
[tex]P(x) = ^nC_x * p^x * (1 - p)^{n -x}[/tex]
The probability is represented as:
P(x > 152) = P(153) + ..... P(160)
Using a technology tool, we have:
P(x ≤ 152) = 0.02
Conclusion on the calculationProbability values less than 0.25 are unlikely probabilities.
Because the probability value 0.02 is less than 0.25, then we can conclude that it is a wise business practice to oversell your flight in this manner.
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To walk to school, Pablo first walks 1/2 kilometer to Tanya's house.
Then Pablo and Tanya walk 3/5 kilometer to school. How far
does Pablo walk to school?
Answers
Answer:
1 1/10
Step-by-step explanation:
1/2 + 3/5
1/2 = 5/10
3/5 = 6/10
6/10 + 5/10 =
1 1/10
please help!!!!!!!!!!
Answers
Answer:
8.4852814
Step-by-step explanation:
x^2=11^2-7^2
x^2=121-49
x^2=72
x=8.4852814
Can Someone please help me with my math
Answers
Answer: option 2 which is 1.825*10^-7
Step-by-step explanation:
can someone tell me what letter or variable it is after the = sign, is it an K or R?
Answers
Identify all points and line segments in the picture below
Answers
Answer:
should be the first one
Step-by-step explanation:
any point connected
Answer:
The answer is:
line segment D
Step-by-step explanation:
Points: A, B, C, D Line segments: Bar (AB), Bar (AC), Bar (BD)
PLEASE HELP
The volume of a right rectangular prism can be found by using the product 6(4)(18). Which expression could also be used to determine the volume of this prism?
6 + 4 + 18
2(6 + 4 + 18)
32(18)
4(6)(18)
Answers
Answer:
The last one is 4(6)(18).
Please give Brainliest
Answer:
4(6)(18)
Step-by-step explanation:
the last option is your right answer
Please help me in my math problem! Need within 10 minutes!
Answers
The length of the short and long diagonals of the parallelogram to 3 decimal places are 5.244 units and 14.370 units respectively.
What are parallelogram?
Parallelograms are quadrilateral. They have opposite sides equal to each other. Opposite sides are also parallel. The opposite angles are equal to each other.
Therefore, the angles are as follows;
34°34°146°146°Hence,
length of small diagonal = √9²+ 6² - 2(9)(6) cos 34
length of small diagonal = √81 + 36 - 108(0.82903757255)
length of small diagonal = √117 - 89.5360578359
length of small diagonal = √27.5
length of small diagonal = 5.24404424085
length of small diagonal = 5.244 units
5.244² + d² = 2(9² + 6²)
27.499536 + d² = 2(81+36)
d² = 234 - 27.499536
d²= 206.5
d = √206.5
d = 14.3701078632
d = 14.370 units
length of the longer diagonal = 14.370 units
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A student graphs the functions f(x) = | x+3 | and g(x) = x2-2x+3 on the coordinate plane shown.
Which are the solutions of f(x) =g(x)?
A. -3 and 1
B. -1 and 1
C. 0 and 3
D. 3 and 6
Answers
The solutions are the intersection point of both graphs
The left side graph is y=|x+3|The right side top graph is x²-2x+3(Parabola)So there mUST be two solutions
The intersections are
(0,3)(3,6)The x values are solution
They are 0,3Option C
Answer:
C. 0 and 3
Step-by-step explanation:
The solutions of f(x) = g(x) are the values of the x-coordinates of the points where the two graphed functions intersect.
From inspection of the graph, the points of intersection are:
(0, 3)(3, 6)Therefore, the solutions are 0 and 3 (since they are the x-values).
Proof
[tex]\implies f(x) = g(x)[/tex]
[tex]\implies |x + 3| = x^2-2x+3[/tex]
We only need to take the positive form of |x+3| since we can see from the graph that g(x) intersects f(x) when |x+3| is positive:
[tex]\implies x + 3 = x^2-2x+3[/tex]
[tex]\implies x^2-3x=0[/tex]
[tex]\implies x(x-3)=0[/tex]
[tex]\implies x=0, 3[/tex]
Thus confirming that the solutions are when x = 0 and 3
IN THE FIGURE BELOW LINES P AND Q ARE PARALLEL. WHAT DO YOU NOTICE
IREADY 50 POINTS!!!
Answers
Answer:
-> Supplementary
-> Add up to 180°
Explanation:
A straight line has a measurement of 180°. Supplementary angles are angles that, when added together, equal 180°.
Since angles 5 and 6 make up a straight line, we know they will add up to 180°.
Evaluate the given expressions.
1. 6^4
2. 3^5
3. 4^3
4. 5^5
Answers
Answer:
1. 1296
2. 243
3. 64
4. 3125
Simplify the expression. Write your answer as a power.
6¹⁰/6⁴
The simplified expression is
Answers
Answer:
The answer is 6^6
Step-by-step explanation:
When you divide exponents, you actually substract the exponent from the equation
Answer:
[tex]6^4[/tex]
Step-by-step explanation:
Recall the exponent quotient rule [tex]\displaystyle \frac{x^a}{x^b}=x^{a-b}[/tex]
This means that [tex]\displaystyle \frac{6^{10}}{6^4}=6^{10-6}=6^4[/tex]
What is the slope of the line shown below?
Answers
1/6
Step-by-step explanation:
Answer:
B. 6
Step-by-step explanation:
(y1 - y2) ÷ (x1 - x2)
(6 - 3) ÷ (12 - (-6))
3 ÷ 18 = 6
hope this helps
have a good day
I need help with this question
Answers
Answer:A
Step-by-step explanation: because there is an association with the child’s hight and age so the answer is A ( plus I have did this before and got it wrong and the actual Answer was A when I picked B
Answer: A
Step-by-step explanation:
Option 1: use the applet to construct circles for problems 1 & 2 or 3 & 4.
take a screenshot and insert them into your student companion.
1. circle a, with a diameter of
6 cm.
2. circle c, with a radius that is
equal to circle a's diameter.
3. circle b, with a radius of 5
cm.
4. circle d, with a diameter
that is equal to circle b's
radius.
Answers
Answer:
9
Step-by-step explanation:
Option 1: use the applet to construct circles for problems 1 & 2 or 3 & 4.
take a screenshot and insert them into your student companion.
1. circle a, with a diameter of
6 cm.
2. circle c, with a radius that is
equal to circle a's diameter.
3. circle b, with a radius of 5
cm.
4. circle d, with a diameter
that is equal to circle b's
radius.
Select the correct answer.
Which outcome is an advantage of the SMBO approach?
OA. It takes into consideration the point of view of management.
OB. The customer is the focus of this approach.
OC. It provides motivation to salespeople.
OD. It narrows sales to specific items.
SOE.
It allows for the adoption of multiple and changing sales objectives.
Answers
An advantage of the SMBO approach it allows for the adoption of multiple and changing sales objectives.
What is SMBO?SMBO is for Sales Management by Objective and is a selling technique or approach that focuses on achieving a specific set of goals. The entire quantity of products sold is known as the sales volume. It can also be expressed in monitory terms.
An advantage of the SMBO approach it allows for the adoption of multiple and changing sales objectives.
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The first two numbers in a sequence h are h(1)=2 and h(2)=6
If h is an arithmetic sequence, write a definition for the nth term of h explain or show your reasoning.
Answers
An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference. The nth term of the arithmetic series can be defined as hₙ = 4n - 2.
What is an arithmetic sequence?An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.
If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:
a, a + d, a + 2d, ... , a + (n+1)d, ...
The nth term of an arithmetic sequence is given by the formula,
aₙ = a₁ + (n-1)d
Since the first term of the arithmetic sequence is 2, while the difference is 4. Therefore, the definition for the nth term of arithmetic sequence,h can be written as,
hₙ = 2 + (n-1)4
hₙ = 2 + 4n -4
hₙ = 4n - 2
Hence, the nth term of the arithmetic series can be defined as hₙ = 4n - 2.
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Given g(x) = x2-8x-20, which statement is true?
A. The zeros are -10 and 2, because the factors of g are (x+10) and (x-2)
B. The zeros are 10 and 2, because the factors of g are (x-10) and (x-2)
C. The zeros are 10 and -2, because the factors of g are (x-10) and (x+2)
D. The zeros are -10 and -2, because the factors of g are (x+10) and (x+2)
Answers
Answer:C
Step-by-step explanation:
The statement which is true is C. The zeros are 10 and -2, because the factors of g are (x-10) and (x+2).
What are Quadratic Functions?Quadratic functions are polynomial functions consisting of variables and exponents and the degree of the variable is 2.
The general form of a quadratic function is f(x) = ax² + b x + c.
Given is a function,
g(x) = x² - 8x - 20
We have to factorize the expression in order to find the zeroes.
Using factorization method, we can say that, the given function can be factorized (x + p) (x + q) as there exists two numbers p and q such that pq = -20 and p + q = -8
Two such numbers are -10 and 2.
So,
g(x) = x² - 8x - 20
g(x) = (x - 10) (x + 2)
So the zeroes are x = 10 and x = -2.
Hence the zeroes are 10 and -2.
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In the figure below, lines p and q are parallel. What do you notice?
the options are alternate exterior,
alternate interior,
vertical, corresponding
and supplemantary.
Answers
What I notice about the lines p and q that are parallel is that they are both supplementary angles. Lines p and q are parallel because alternate exterior angles are congruent Lines l and m are parallel because same side interior angles are supplementary Lines l and m are parallel because alternate interior angles are supplementary
his table gives the dimensions for a scale drawing of a house. Every 2 inches on the scale drawing represents 1.5 feet of the original house. Use proportional reasoning to complete the table with the original lengths. A 2-column table with 4 rows. Column 1 is labeled Scale model (inches) with entries 2, 8, 12, 16. Column 2 is labeled Original length (feet) with entries 1.5, a, b, 12. a = b =
Answers
The value of the a and b will be 6 and 9 feet. Every 2 inches on the scale drawing represents 1.5 feet of the original house.
What is unit conversion?The process of converting the unit form is known as the unit conversion. For example, in the SI unit system, mass is in kg. While in CGS, it is represented in grams.
The given conversion is ;
[tex]\rm 2 \ inch = 1.5 \ feet \\\\ 1 inch = \frac{1.5}{2} \ feet[/tex]
For 8, 12 inches, the values in feet is;
[tex]\rm 8 \times \frac{1.5}{2} = 6 \ feet[/tex]
[tex]\rm 12 \times \frac{1.5}{2} = 9 \ feet[/tex]
Hence, the value of the a and b will be 6 and 9 feet.
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The value a= 6 and b=9.
What is unit conversion?
The process of converting the unit form is known as the unit conversion.
For example, in the SI unit system, distance is in meter while in CGS, it is represented in cm.
Given that:
2 inch = 1.5 feet
1 inch = [tex]\frac{1.5}{2}[/tex]
then, 8 inches =[tex]\frac{1.5}{2} *8[/tex]
= 1.5*4
= 6 feet
again, 12 inches= [tex]\frac{1.5}{2} *12[/tex]
= 1.5*6
= 9 feet
and, 16 inches =[tex]\frac{1.5}{2} *16[/tex]
= 1.5*8
= 12 feet
The value of a & b is 6 and 9 respectively.
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what is 18/6 redused?
Answers
Answer: 3
Step-by-step explanation:
3/1 or 3
hope it helps...!!!
Hey, could someone help me with this? If you could that would be great!
It's a 3 part question, this is the first part.
The quadratic function is f(x) = x^2 - 7.
I would like help on the third question...
Answers
Answer:
The correct answer should be C.
Step-by-step explanation:
A. is equal to x² -5.291503x +7
B. is equal to x² +5.291503x +7
C. is equal to x²2 -7
C. is the only one with a negative 7 since (-)(+)= -
NEED HELP PLEASE ANSWER ASAP!
Answers
Answer:
(2) Graph 2
Step-by-step explanation:
Question 40
| 2x + 3 | > 7It means the absolute value has to be greater than 7At x = -5 and x = 2, the absolute value is 7So, the numbers between them won't be includedThe points have an open dotx < -5 and x > 2(2) Graph 2Solve the inequality -4x +1 > 13
Answers
Answer:
The inequality is x is less than negative 3.
Answer:
x < -3
Step-by-step explanation:
. subtract 1 from both sides.
. subtract the numbers
. divide both sides by the same factor and flip the relation
because the factor is negative
. cancel the terms that are both in the numerator and the denominator
. divide the numbers
.then you get youre solution
-9<2x+1<5
A. -5
B. -4
C. 4>x>-3
D. 5>x>-2
Answers
Answer:
B
Step-by-step explanation:
1.
- 9 < 2x + 1
- 10 < 2x
X > - 5
2.
2x + 1 < 5
2x < 4
X < 2
Estimate the instantaneous rate of change in the percent of households that used the internet
for electronic banking in the year 2000.
Answers
The instantaneous rate of change in the percent of households that used the internet for electronic banking in the year 2000 is; 6.8%
How to find the instantaneous rate of change?Formula for instantaneous rate of change is;
f'(x) = (f(b) - f(a))/(b - a)
From the table showing the the percent of households that used the internet for electronic banking in the year 2000, we can find the instantaneous rate of change as;
f'(2000) = (f(2001) - f(1999)]/(2001 - 1999)
f'(2000) = (21.6 - 8)/(2001 - 1999)
f'(2000) = 13.6/2
f'(2000) = 6.8
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If the coordinates of point Q are (−12,√32), then what is the value of tan(m) ?
Answers
Vector components are expressed in the form (x, y). The measure of tan m given the coordinate Q is -√32/12
Direction of a vectorVector components are expressed in the form (x, y). Given the coordinates of point Q are (−12,√32), the measure of the angle is expressed as;
m = arctan(y/x)
m = arctan (-√32/12)
Take the tan of both sides
tan m = tan arctan(-√32/12)
tan m = -√32/12
Hence the measure of tan m given the coordinate Q is -√32/12
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How do you solve pythagorean theorem??
Full Explanation
Will Mark Brainlist
Answers
Pythagoras theorem is a formula that helps us determine the missing side of a triangle, with the measure of two sides, given.
The Pythagoras theorem formula is expressed as:
[tex](\small\text{Hypotenuse})^{2} = (\small\text{side}_{1} )^{2} + (\small\text{side}_{2} )^{2}[/tex]
Now, let us take an example to understand the concept better.
Example:A triangle with longest side given as 15 centimeters. The base of the triangle has a length of 9 centimeters. What is the measure of the height?
Solution:We are given the following:
Longest side (hypotenuse of the triangle) = 15 cm Base of the triangle (Not the longest side) = 9 cmWhen we plug the hypotenuse and the base, in the formula, we get;
⇒ 15² = 9² + (side₂)²Subtract 9² on both sides of the equation to isolate (side₂)².
⇒ 15² = 9² + (side₂)²⇒ 15² - 9² = 9² + (side₂)² - 9²We can use the rule [a² - b² = (a - b)(a + b)] to simplify the L.H.S
⇒ (15 - 9)(15 + 9) = (side₂)²⇒ (6)(24) = (side₂)²⇒ 144 = (side₂)²Now, take square root on both sides of the equation to determine the measure of the missing side (height of triangle).
⇒ √144 = √(side₂)²⇒ 12 = side₂Therefore, the measure of the height is 12 centimeters.
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Taking successive discounts of 15% off and then 25% off is the same as taking a one time discount of 40%. true or false
Answers
Answer:
False
Step-by-step explanation
Let's take the example starting number as 100
15% off of 100 gives us 85.
25% off of 85 is 63.45
40% off of 100 would be 60.
How many times does 26 go into 1,793?
Answers
Answer:
68.96Step-by-step explanation:
"How many times does 26 go into 1793?" is the same as asking "How much is 1793 divided by 26?" Thus, the answer can be calculated as follows:
1793/26 = 68.96 ( you can round up to 69)
Answer:
69 times
Step-by-step explanation:
to get the number of times, divide 1,793 by 26
1793/26 = 68.96153846
= 69 times (approximately)