The interval does not include the null hypothesis value, then the results are significant.
When calculating a confidence interval for the difference between two means or proportions, the significance level must be considered to determine whether the results suggest a significant difference.What is a confidence interval?A confidence interval (CI) is an interval estimate that quantifies the uncertainty associated with the unknown population parameter. Confidence intervals are used to express how confident we are about the accuracy of an estimated population parameter.The significance level is the level at which the results of a statistical test are considered statistically significant. The significance level is frequently represented as alpha, and its value is usually set to 0.05 (5%) in most statistical analyses. This implies that there is a 5% chance that the statistical test findings will indicate a significant difference when, in fact, there is no such difference. The significance level is the probability of rejecting a true null hypothesis.Therefore, in order to determine whether or not the results of a confidence interval for the difference between two means or proportions indicate a significant difference, we must compare the interval with the significance level (alpha) that was established before the test. If the interval contains the null hypothesis value (usually 0), then the results are not significant. If the interval does not include the null hypothesis value, then the results are significant.
Learn more about Hypothesis
brainly.com/question/20165896
#SPJ11
Please help it is due tomorrow
Answer: 30
Step-by-step explanation: So what you do is,
1) Add the 25 to the 8
2) Find the sum
3) Subtract 3 from the sum
4) Done!
I hope this helps!
Best,
Abigail H
8th Grade
let x1 and x2 be two independent random variables both with mean 10 and variance 5. let y 2x1 x2 3 2. find the mean and the variance of y.
As a result, y has a mean of 203 and a variance of 85 as let x1 and x2 be two independent random variables both with mean 10 and variance 5.
what is variable ?A variable is a symbol or letter that is used to indicate a variable quantity in mathematics. The context or issue under consideration can alter the value of a variable. In order to express relationships between quantities, variables are frequently utilized in equations, formulae, and functions. For instance, x and y are variables in the equation y = mx + b, which depicts the linear relationship between x and y. Variables in statistics can reflect various traits or features of a population or sample, such as age, body mass index, or income.
given
To get the mean and variance of y, we can apply the characteristics of expected value and variance:
We can start by determining the expected value of y:
E[y] = 2E[x1] = E[2x1x2 + 3x1 + 2]
By the linearity of expectation, E[x2] + 3E[x1] + 2 is 2(10)(10) + 3(10) + 2 = 203.
Next, we may determine y's variance:
Var(y) = Var(3x1 + 2 + 2 + 3x1 ) = 4
Var(x1)
Var(x2) + 9
Var(x1) + Var(constant) = 4(5)(5) + 9(5) + 0 = 85 since x1 and x2 are independent.
As a result, y has a mean of 203 and a variance of 85 as let x1 and x2 be two independent random variables both with mean 10 and variance 5.
To know more about variable visit :-
https://brainly.com/question/2466865
#SPJ1
What is 252 divided by 9
Answer:
28 is the ans of 252÷9here we go
252 divided by 9 equals 28.
To divide 252 by 9, you can use long division, which involves dividing the number in steps until there is no remainder left.
Here's the step-by-step process:
Write down the dividend (252) and the divisor (9), and set up the long division format:
9 | 252
Look at the leftmost digit of the dividend (2) and see if it's divisible by the divisor (9). Since 2 is less than 9, we bring down the next digit (5) to the right of 2, making it 25.
9 | 252
2
Divide the new number (25) by the divisor (9). The result is 2, which is the first digit of the quotient. Multiply this result by the divisor (2 x 9 = 18) and write it below the 25, then subtract it from 25:
9 | 252
25
18
--
7
Bring down the next digit (2) from the dividend to the right of the remainder (7), making it 72. Now, divide 72 by 9, which gives you 8. Multiply this result by the divisor (8 x 9 = 72) and write it below the 72, then subtract it from 72:
9 | 252
25
18
--
72
72
---
0
There is no remainder left, and the dividend has been completely divided. The quotient is the result of the division, which is 28.
Therefore, 252 divided by 9 equals 28.
Learn more about long division click;
https://brainly.com/question/28824872
#SPJ6
What is the y-intercept of the line
with the equation y = - 4x - 12
Answer:
-12 is the y intercept while your slope is -4
Step-by-step explanation:
please help with question 6
Answer:
a = -13b = 6f(x) = (2x -1)(x -2)(x +3)Step-by-step explanation:
Given f(x) = 2x³ +x² +ax +b has a factor (x -2) and a remainder of 18 when divided by (x -1), you want to know a, b, and the factored form of f(x).
RemainderIf (x -2) is a factor, then the value of f(2) is zero:
f(2) = 2·2³ +2² +2a +b = 0
2a +b = -20 . . . . . . . subtract 20
If the remainder from division by (x +1) is 18, then f(-1) is 18:
f(-1) = 2·(-1)³ +(-1)² +a·(-1) +b = 18
-a +b = 19 . . . . . . . . . . add 1
Solve for a, bSubtracting the second equation from the first gives ...
(2a +b) -(-a +b) = (-20) -(19)
3a = -39
a = -13
b = 19 +a = 6
The values of 'a' and 'b' are -13 and 6, respectively.
Factored formWe can find the quadratic factor using synthetic division, given one root is x=2. The tableau for that is ...
[tex]\begin{array}{c|cccc}2&2&1&-13&6\\&&4&10&-6\\\cline{1-5}&2&5&-3&0\end{array}[/tex]
The remainder is 0, as expected, and the quadratic factor of f(x) is 2x² +5x -3. Now, we know f(x) = (x -2)(2x² +5x -3).
To factor the quadratic, we need to find factors of (2)(-3) = -6 that have a sum of 5. Those would be 6 and -1. This lets us factor the quadratic as ...
2x² +5x -3 = (2x +6)(2x -1)/2 = (x +3)(2x -1)
The factored form of f(x) is ...
f(x) = (2x -1)(x -2)(x +3)
What is the scale factor of the following pair of similar polygons ?
The scale factor of the following pair of similar polygons after the dilation is 0.7
Calculating the scale factor of the similar polygonsGiven
The pair of similar polygons
From the pair of similar polygons, we have the following corresponding side lengths
Pre-image of the polygon = 30
Image of the polygon = 21
The scale factor of the similar polygons is then calculated as
Scale factor = 21/30
Evaluate the quotient
Scale factor = 0.7
Hence, the scale factor is 0.7
Read more about scale factor at
https://brainly.com/question/17031580
#SPJ1
Solve the inequality 12≥ 73x + 2
10/73 is the value of x in inequality.
What does the word "inequality" mean?
In mathematics, inequalities describe the connection between two values that are not equal. Equal does not imply inequality. The "not equal symbol ()" is typically used to indicate that two values are not equal.
However different inequalities are used to compare the values to determine if they are less than or higher than. The term "inequality" refers to a relationship between two expressions or values that is not equal to one another. Inequality originates from an imbalance, thus.
the inequality 12≥ 73x + 2
= 12 - 2 ≥ 73x
= 10 ≥ 73x
= 10/73 ≥ x
Learn more about inequality
brainly.com/question/30231190
#SPJ1
solve for x and graph the solution on the number line below
We can graph this solution on the number line by placing a point at 7.6.
What is graph ?Graphs are visual representations of data or information. They are used to show relationships between different pieces of data and display numerical data in a more meaningful way. Graphs are made up of individual elements called nodes which are connected by edges. Nodes represent individual data points or pieces of information. Edges represent the relationship between two nodes and can represent either a physical or a logical link. Graphs can be used to represent many different types of data or information, such as social networks, transportation networks, and even biological relationships. Graphs are a powerful tool for understanding complex data sets, making them an essential tool for data analysis.
80∠ 10x + 4 = 20
80 10x + 4 = 20
80 - 4 = 10x
76 = 10x
7.6 = x
To learn more about graph
https://brainly.com/question/19040584
#SPJ1
We can graph this solution on the number line by placing a point at 7.6.
What is graph ?Graphs are visual representations of data or information. They are used to show relationships between different pieces of data and display numerical data in a more meaningful way. Graphs are made up of individual elements called nodes which are connected by edges. Nodes represent individual data points or pieces of information. Edges represent the relationship between two nodes and can represent either a physical or a logical link. Graphs can be used to represent many different types of data or information, such as social networks, transportation networks, and even biological relationships. Graphs are a powerful tool for understanding complex data sets, making them an essential tool for data analysis.
80∠ 10x + 4 = 20
80 10x + 4 = 20
80 - 4 = 10x
76 = 10x
7.6 = x
To learn more about graph
brainly.com/question/19040584
#SPJ1
HELPPPP HURRY PLSS………………..
Answer:
C is your answer
Step-by-step explanation:
in my opinion, i think it would be the mode.
The speed s (in miles per hour) of a car can be given by s = √(30fg), where fis the
coefficient of friction and d is the stopping distance (in feet). The table shows the
coefficient of friction for different surfaces. You are driving 35 miles per hour on an
icy road when a deer jumps in front of your car. How far away must you begin to
brake to avoid hitting the deer? Round your answer to the nearest whole integer. NO
UNITS NEEDED
Answer:
Step-by-step explanation:
lknk
pihpin
87647fpom';
oiy69877t7gbkjb
Answer:
s= 6
Step-by-step explanation:
The speed s (in miles per hour) of a car can be given by s = √(30fg), where fis the
coefficient of friction and d is the stopping distance (in feet). The table shows the
coefficient of friction for different surfaces. You are driving 35 miles per hour on an
icy road when a deer jumps in front of your car. How far away must you begin to
brake to avoid hitting the deer? Round your answer to the nearest whole integer. NO
UNITS NEEDED
A wire first bent into the shape of a rectangle with width 5cm and lenth 11 cm.then the wire is unbent and reshaped into a square what is the length kf a side of the square
The length of a side of the square is 8 cm.
What do you mean by perimeter of a rectangle and square?
When a wire is bent into the shape of a rectangle, its length becomes the perimeter of the rectangle. Similarly, when the wire is reshaped into a square, its length becomes the perimeter of the square.
The perimeter of a rectangle is given by the formula [tex]P=2(l+w)[/tex] , where [tex]l[/tex] is the length and [tex]w[/tex] is the width.
The perimeter of a square is given by the formula [tex]P=4s[/tex] , where [tex]s[/tex] is the length of a side.
Calculating the length of a side of the square:
The length of the rectangle is 11 cm and the width is 5 cm.
Therefore, the perimeter of the rectangle is [tex]P=2(11+5)=32[/tex] cm.
Since the wire is reshaped into a square, the perimeter of the square is also 32 cm.
Using the formula [tex]P=4s[/tex], we can solve for the length of a side of the square:
[tex]32 = 4s[/tex]
[tex]s = 32/4[/tex]
[tex]s = 8[/tex]
Therefore, the length of a side of the square is 8 cm.
To know more about square visit :
brainly.com/question/28776767
#SPJ1
Arrange the steps to find an inverse of a modulo m for each of the following pairs of relatively prime integers using the Euclidean algorithm in the order. a = 2, m=17 Rank the options below. The ged in terms of 2 and 17 is written as 1 = 17-8.2. By using the Euclidean algorithm, 17 = 8.2 +1. The coefficient of 2 is same as 9 modulo 17. 9 is an inverse of 2 modulo 17. The Bézout coefficients of 17 and 2 are 1 and 8, respectively. a = 34, m= 89 Rank the options below. The steps to find ged(34,89) = 1 using the Euclidean algorithm is as follows. 89 = 2.34 + 21 34 = 21 + 13 21 = 13 + 8 13 = 8 + 5 8 = 5 + 3 5 = 3 + 2 3 = 2+1 Let 34s + 890= 1, where sis the inverse of 34 modulo 89. $=-34, so an inverse of 34 modulo 89 is -34, which can also be written as 55. The ged in terms of 34 and 89 is written as 1 = 3 - 2 = 3-(5-3) = 2.3-5 = 2. (8-5)- 5 = 2.8-3.5 = 2.8-3. (13-8)= 5.8-3.13 = 5. (21-13)-3.13 = 5.21-8. 13 = 5.21-8. (34-21) = 1321-8.34 = 13. (89-2.34) - 8.34 = 13.89-34. 34 a = 200, m= 1001 Rank the options below. By using the Euclidean algorithm, 1001 = 5.200 +1. Let 200s + 1001t= 1, where sis an inverse of 200 modulo 1001. The ged in terms of 1001 and 200 is written as 1 = 1001 - 5.200. s=-5, so an inverse of 200 modulo 1001 is -5.
We have that, using Euclid's algorithm, we find the inverse of 200 modules 1001 is -5 (or 1001+5).
How do we find the inverse of a modulus?To find the inverse of a module m using Euclid's algorithm, the steps are as follows:
1. Calculate the greatest common divisor (GCD) of a and m using the Euclidean algorithm.
2. Let a = GCD * s + m*t, where s is the inverse of a module m.
3. The GCD in terms of a and my is written as 1 = m-s*a.
4. Find s = -a, so the inverse of a module m is -a (or m+s).
For example, a = 2, m=17, so GCD = 1 = 17-8*2 and the inverse of 2 modulo 17 is -8 (or 17+8). Similarly, for a = 34, m= 89, the GCD = 1 = 89-34*2 and the inverse of 34 modulo 89 is -34 (or 89+34). Finally, for a = 200, m= 1001, the GCD = 1 = 1001-5*200 and the inverse of 200 modulo 1001 is -5 (or 1001+5).
See more information about Euclid's algorithm at: https://brainly.com/question/24836675
#SPJ11
11. How much time will it take for ₹5000
5618 at 6% per annum
annually?
to become
compounded
Answer:
2.31 Years
Step-by-step explanation:
To calculate the time it will take for ₹5000 to grow to ₹5618 with a 6% annual interest rate when compounded annually, we can use the following formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (₹5618)
P = the principal amount (₹5000)
r = the annual interest rate (6% or 0.06)
n = the number of times the interest is compounded per year (1, since it's compounded annually)
t = the time period in years
Plugging in the values, we get:
5618 = 5000(1 + 0.06/1)^(1t)
Simplifying:
1.1236 = 1.06^t
Taking the natural logarithm of both sides:
ln(1.1236) = ln(1.06^t)
Using the power rule of logarithms:
ln(1.1236) = t ln(1.06)
Solving for t:
t = ln(1.1236) / ln(1.06)
t ≈ 2.31 years
Therefore, it will take approximately 2.31 years for ₹5000 to grow to ₹5618 at a 6% annual interest rate when compounded annually.
The average mass of six people is 58kg. The lightest person has a body mass of 43kg. What is the average mass of the other 5 people.
Answer: 61 kg
Step-by-step explanation:
To find the average mass of the other 5 people, we need to subtract the mass of the lightest person from the total mass of all six people and then divide by 5 (since we're looking for the average of the other 5 people). Here are the steps:
Find the total mass of all six people:
To find the total mass of all six people, we can multiply the average mass by 6:
Total mass of all six people = 58 kg/person x 6 people = 348 kg
Subtract the mass of the lightest person:
We need to subtract the mass of the lightest person (43 kg) from the total mass of all six people:
Total mass of the other 5 people = Total mass of all six people - Mass of the lightest person
Total mass of the other 5 people = 348 kg - 43 kg = 305 kg
Find the average mass of the other 5 people:
Finally, we divide the total mass of the other 5 people by 5 to find the average mass:
Average mass of the other 5 people = Total mass of the other 5 people / 5
Average mass of the other 5 people = 305 kg / 5 = 61 kg
Therefore, the average mass of the other 5 people is 61 kg.
why does a square root have a plus or minus sign attached to it.
Answer:
To indicate that we want both the positive and the negative square root of a radicand
Answer:
Because a negative number times a negative number has a positive answer
Step-by-step explanation:
Find the circumference of a circle with diameter, d = 1.26m.
Give your answer rounded to 2 DP
Answer: b
Step-by-step explanation: just took it on edge.
James has 27 metres of red wire and 12 metres
of black wire. He needs to cut both wires into
smaller pieces so that all of the smaller pieces are
the same length and there is no wire left over. The
length of each piece must be a whole number of
metres.
What is the longest he can make each smaller
piece of wire? Give your answer in metres (m).
Answer:
3m
Step-by-step explanation:
red wire = 27
black wire= 12
so, we take HCF (highest common factor)
which would be 3 so all the wires would be cut into 3m long.
I hope it helps.
Answer:2m
Step-by-step explanation:
as the factors of 12 are:1, 2, 3, 4, 6 and 12
and the factors of 26 are:1, 2, 13 and 26
so if you are talking meters 2 would be the longest
i hope you get this right x
4)) FH and IK are parallel lines. J K F G E Which angles are alternate exterior angles?
Answer: I couldn't honestly help with that I would if I could
Step-by-step explanation:
a teacher monitored the number of people texting during class each day and calculated the corresponding probability distribution. what type of probability distribution did the teacher use?
The given probability distribution "a teacher monitored the number of people texting during class each day and calculated the corresponding probability distribution." is a type of discrete probability distribution.
What is the Probability distribution?The probability distribution is used to describe the probability of each outcome in a series of possible outcomes. It is a mathematical representation of the outcomes of an experiment.
The teacher likely used a discrete probability distribution to calculate the probability of a certain number of people texting during class each day.
A discrete probability distribution is used to analyze data where the outcome is counted in whole numbers, such as the number of people texting in a given class period.
Learn more about Probability distribution here:
https://brainly.com/question/14210034
#SPJ11
if a traingle with all sides of equal legnth has a perimeter of 15x 27 , what is an expression for the legnth of one of the sides
If a triangle with all sides of equal length has a perimeter of 15x + 27, the expression for the length of one of the sides is (5x + 9).
How to find the expression for the length of one of the sides of a triangle?The perimeter of a triangle is the sum of the lengths of all three sides. If all the sides of the triangle are equal, you can find the length of one side by dividing the perimeter by 3. Here, the perimeter is given as 15x + 27. Therefore, the length of one side will be (15x + 27) / 3 = 5x + 9. Hence, an expression for the length of one of the sides is (5x + 9).
Learn more about expression here: https://brainly.com/question/1859113.
#SPJ11
Mark wants to buy a new pair of sneakers that cost 215. His aunt gave him 100 for the sneakers. Market also lnow sthat he can esrn 16 for each hour that he works at his aunts store how many full hours must mark work to buy the sneakers
Mark needs a total amount of 215 to buy sneakers and we know that his aunt gave him 100 for the same, he also know that he can earn 16 for each hour that he works at his aunt's store, therefore he needs to work 8 hours.
Mark needs a total amount of 215 to buy sneakers and we know that his aunt gave him 100 for the same,
therefore, we can say that 215 - 100 = 115
therefore, Mark now needs only 115 for him to buy sneakers and now we need to find how many full hours do Mark need to work to buy sneakers:
therefore, we need to divide 115 by 16 to find out the hours he needs to work at his aunt's store:
115/16 = 7.2
we get 7.2 which also means 7 hours 20 mins but we need to find full hours Mark needs to work, that will be:
8 hours.
Therefore, we know that Mark needs to work 8 full hours for him to buy sneakers.
To learn more about division, click here:
brainly.com/question/21416852
#SPJ4
Un número tiene 8 divisores. Además, cada uno de la mitad y la tercera parte de él tienen cuatro divisores. Si la suma de todos los divisores del número es 216, obtén tal número
The number we are looking for is N = 2 × 2^3 × 3^2 = 72.
Let's first recall some properties of the number of divisors of an integer. If we factorize an integer n as a product of prime powers, say
n = p_1^a_1 × p_2^a_2 × ... × p_k^a_k
then the number of divisors of n is given by
d(n) = (a_1 + 1) × (a_2 + 1) × ... × (a_k + 1).
Using this fact, we can deduce some information about the number we are looking for. Let's call it N. We know that N has 8 divisors, so it must be of the form
N = p_1^2 × p_2^2, or N = p_1^7,
where p_1 and p_2 are distinct prime numbers.
Now, we are told that each of N/2 and N/3 has four divisors. We can use the same fact about the number of divisors to conclude that
N/2 = q_1^3 × q_2, or N/2 = q_1^1 × q_2^3,
and
N/3 = r_1^3 × r_2, or N/3 = r_1^1 × r_2^3,
where q_1, q_2, r_1, and r_2 are distinct prime numbers.
To simplify the notation, let's introduce the variables a, b, c, d, e, and f, defined by
p_1 = q_1^a × q_2^b,
p_2 = r_1^c × r_2^d,
N/2 = q_1^e × q_2^f,
N/3 = r_1^g × r_2^h.
Using the information we have so far, we can write down equations for a, b, c, d, e, f, g, and h in terms of unknown exponents:
a + 1 × (b + 1) = e + 1 × (f + 1) = 4,
c + 1 × (d + 1) = g + 1 × (h + 1) = 4,
2a × 2b = ef,
2c × 2d = gh.
We can solve this system of equations by trial and error. For example, we can start by trying all possible values of a and b such that 2a × 2b = 4. This gives us two possibilities: a = 0, b = 2, or a = 1, b = 1. Using the first possibility, we get e = 3, f = 1, which leads to N/2 = q_1^3 × q_2, and hence N = 2 × q_1^3 × q_2^2. Substituting this into the equation for the sum of divisors, we get
(1 + q_1 + q_1^2 + q_1^3) × (1 + q_2 + q_2^2) = 216.
We can solve this equation by trial and error as well, or by observing that 216 = 2^3 × 3^3, and hence the two factors on the left-hand side must be equal to 2^3 and 3^3, respectively. This gives us the unique solution q_1 = 2 and q_2 = 3, and hence N = 2 × 2^3 × 3^2 = 72.
Learn more about divisor here
brainly.com/question/17879555
#SPJ4
Use the unique factorization theorem to write the following integers in standard factored form. (a) 756 2^2.3^3.7. (b) 819 3^2.7.11 (c) 9,075 3^2.5^2.7
The factorizations of these integers above represent their factorizations into their respective prime numbers.
(a) 756 = 2^2.3^3.7, (b) 819 = 3^2.7.11, (c) 9,075 = 3^2.5^2.7The unique factorization theorem refers to an essential theorem in standard algebraic theory that characterizes the unique factorization properties of integers. Standard factored form, on the other hand, refers to an expression in which an integer is factored into its standard, irreducible components.In view of this, the three provided integers, 756, 819, and 9,075 can be factored as follows:756 = 2^2.3^3.7 (in standard factored form)819 = 3^2.7.11 (in standard factored form)9,075 = 3^2.5^2.7 (in standard factored form)Note that the factorizations of these integers above represent their factorizations into their respective prime numbers.
Learn more about Factorizations
brainly.com/question/14067703
#SPJ11
16. In Δ ABC and Δ PQR, , AB = PR, BC = RQ and AC = PQ. Δ ABC is congruent to a) Δ RPQ b) Δ QRP c) Δ PQR d) Δ PRQ
In Δ ABC and Δ PQR, if AB = PR, BC = RQ and AC = PQ, then Δ ABC is congruent to Δ PRQ, which means option D is the right answer.
The congruency theorem is used to determine the relation between two similar looking figures in two dimensional space. The word congruent itself means being in harmony. There are different rules which are used to determine the congruency between the triangles.
These rules are given as follows:
All three pairs of corresponding sides are equal = SSS CongruencyTwo pairs of corresponding sides and the corresponding angles between them are equal = SAS congruencyTwo pairs of corresponding angles and the corresponding sides between them are equal = ASA CongruencyIn the given question, it is given that sides AB = PR, BC = RQ and AC = PQ, this implies that the congruency can be setup using SSS rule, which if followed will suggest that Δ ABC will be congruent to Δ PRQ.
Learn more about congruency at:
brainly.com/question/29789999
#SPJ4
Q4 NEED HELP PLEASE HELP
Answer:
D. The electrician charges $23 per hour.
Step-by-step explanation:
C(h)= 23h+30 is in the form y=mx +b
$30 is the initial fee (b)
$23 is the amount charged per hour (h)
Solve 2log 12 (-8x)=6
The solution to the logarithmic equation [tex]2log12(-8x) = 6[/tex] is [tex]x = -9/32[/tex] .
What are logarithmic properties ?
Logarithmic properties are the rules that govern the behavior of logarithmic functions. These properties are important in simplifying logarithmic expressions and solving logarithmic equations. Some of the commonly used logarithmic properties include:
Product property: [tex]logb(xy) = logb(x) + logb(y)[/tex]
This property allows us to simplify the logarithm of a product of two numbers into the sum of logarithms of the individual numbers.
Quotient property: [tex]logb(x/y) = logb(x) - logb(y)[/tex]
This property allows us to simplify the logarithm of a quotient of two numbers into the difference of logarithms of the individual numbers.
Power property:[tex]logb(x^y) = ylogb(x)[/tex]
This property allows us to simplify the logarithm of a power of a number by bringing the exponent outside of the logarithm and multiplying it with the logarithm of the base.
Change of base formula: [tex]logb(x) = logc(x) / logc(b)[/tex]
This property allows us to change the base of a logarithm by dividing the logarithm of the number by the logarithm of the base in a different base.
Solving the given logarithmic equation :
The equation can be solved by using logarithmic properties and basic algebraic manipulation.
We can begin by using the property that states [tex]loga(b^n) = nloga(b)[/tex] for any base a and any positive real number b. Applying this property, we can rewrite the left side of the equation as:
[tex]log12((-8x)^2) = log12(64x^2)[/tex]
Next, we can use the property that states [tex]loga(b) = c[/tex] is equivalent to [tex]a^c = b[/tex]. Applying this property, we can rewrite the equation as:
[tex]12^{2log12(64x^2)} = 12^6[/tex]
Simplifying the left side, we get:
[tex]64x^2 = 12^6 / 12^2[/tex]
[tex]64x^2 = 144[/tex]
Dividing both sides by 64, we get:
[tex]x^2 = 144/64[/tex]
[tex]x^2 = 9/4[/tex]
Taking the square root of both sides, we get:
[tex]x=\pm 3/2[/tex]
However, we need to check the solutions for extraneous roots since the original equation has a logarithm with a negative argument. We can see that the solution x = 3/2 is extraneous since it results in a negative argument for the logarithm. Therefore, the only valid solution is x = -9/32.
To know more about logarithmic equation visit :
brainly.com/question/30085872
#SPJ1
Find The surface area of the composite figure
Answer: It should be 470 cm^2
Step-by-step explanation:
2.3. Ntando can either walk to school at 5 km/h or ride his bicycle at 15 km/h. If he rides his bicycle, it takes him 10 minutes to get to school. 2.3.1. How long will it take him if he walks to school?
Answer:
30 minutes
Step-by-step explanation:
Use ratios. This is an inverse function, as speeding up makes the time traveling go down. So, when dividing the speed by 3 (done so 15 can get to 5), we multiply the time traveled by 3.
10 minutes * 3 = 30 minutes
Find the value of x.
22
39
X
The value of x in the right triangle when calculated is approximately 13.8 units
Calculating the value of x in the triangleGiven the right-angled triangle
The side length x can be calculated using the following sine ratio
So, we have
sin(39) = x/22
To find x, we can use the fact that sin(39 degrees) = x/22 and solve for x.
First, we can use a calculator to find the value of sin(39 degrees), which is approximately 0.6293.
Then, we can set up the equation:
0.6293 = x/22
To solve for x, we can multiply both sides by 22:
0.6293 * 22 = x
13.8446 = x
Rewrite as
x = 13.8446
Approximate the value of x
x = 13.8
Therefore, x is approximately 13.8 in the triangle
Read about right triangle at
https://brainly.com/question/2437195
#SPJ1
what is 2 1/2 + x = 3 1/2. Please answer it quick
Answer:
x=1
Step-by-step explanation:
2.5+x=3.5
3.5-2.5=x
1=x
x=1
