The expression "log[a * b.c]" can be rewritten as 2 * log a + log b + log c.
How did we arrive at the expression?The expression "log[a*b.c]" can be rewritten using the properties of logarithms as follows:
Use the logarithmic property log(a * b) = log a + log b:
log[a * b.c] = log (a * b) + log c
Apply logarithmic property log(a^n) = n * log a:
log[a * b.c] = log (a^2 * b) + log c = 2 * log a + log b + log c
So, the expression "log[a * b.c]" can be rewritten as 2 * log a + log b + log c.
Therefore, the correct answer is as given above. It could then be concluded that the rewritten expression will then be 2 * log a + log b + log c.
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Simplify imporper fractions as mixed number 14 1/4 -10 3/7 =
The value of the expression [tex]14\frac{1}{4} -10\frac{3}{7}[/tex] is 107/28.
What is Fraction?A fraction represents a part of a whole.
The given expression is [tex]14\frac{1}{4} -10\frac{3}{7}[/tex]
A proper fraction is a fraction that has no whole number part and its numerator is smaller than its denominator.
An improper fraction is a fraction that has a larger numerator than denominator and it represents a number greater than one.
[tex]14\frac{1}{4}[/tex] to improper fraction is 57/4
[tex]10\frac{3}{7}[/tex] to improper fraction is 73/7
Now 57/4-73/7 we have to solve
LCM of 4 and 7 is 28
399-292/28
107/28
Hence, 107/28 is the value of the expression [tex]14\frac{1}{4} -10\frac{3}{7}[/tex]
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Provide evidence of how you manage your staff to manage complain
One way to manage your staff to manage complaints would be to establish clear procedures for handling complaints and regularly train staff on these procedures.
How to manage staff complaints ?Establishing clear procedures for handling complaints and training staff helps to ensure that all complaints are handled consistently and effectively, reducing the potential for misunderstandings or conflicts to arise.
Additionally, creating an open-door policy for staff to voice their concerns and providing regular opportunities for feedback can help to identify and address issues before they escalate into complaints. Regular communication and coaching can also help to build strong working relationships and foster a positive workplace culture, reducing the likelihood of complaints in the first place.
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The sum of one and six times a number is 151. What is the number?
This is a word problem and the value of the unknown number is equal to 25
Word problems in mathematicsWord problems are mathematical problems which involves the use of ordinary words, instead of mathematical symbols.
Let us represent the unknown number with the letter x so that we derive the equation;
1 + 6x = 151
we subtract 1 from both sides of the equation
1 - 1 + 6x = 151 - 1
6x = 150
divide through by the coefficient of x which is 6
6x/6 = 150/6
x = 25
Therefore, the value of the unknown number for the word problem is equal to 25
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If the scale factor of figure A to figure B is 3:8 find x
If the x-values are equal for two points, then the two points are on a ____ line
If a line has two points with the same x-value, then the two points are on a vertical line.
What type of line we have here?So we know that we have some kind of a linear equation, such that in two points on the line we have the same x-value.
Then we can write these two points like (x₁, y₁) and (x₁, y₂). If the x-value is the same one, then we have a line of the form:
x = x₁
Which is a vertical line, then that is the correct answer.
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In 2015, there were about 22 million teenagers (aged 13–17) in the United States. They each sent an average of 800 text messages per month. About how many text messages did all of the teenagers in the United States send each month? Express your answer using scientific notation.
The number of text messages all of the teenagers in the United States send each month is 17600 million.
What are integers?In mathematics, an integer is a grouping comprising both positive and negative numbers. Integers are similar to whole numbers in that they do not include the fractional portion. Integers are thus numbers that can be positive, negative, or zero but not fractions. All mathematical operations, including addition, subtraction, multiplication, and division, can be carried out on integers.
Given that,
Number of teenagers = 22 million
Text sent on average = 800
Total messages sent = (22)(800) = 17600 million
Hence, the number of text messages all of the teenagers in the United States send each month is 17600 million.
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Can someone pls help me?
What is the initial value of the function?
The initial value of the function is 1.
What is a function?
A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two varying quantities.
A relationship in which one input value exactly equals one output value is known as a function. A function's initial value is a crucial component. A starting value or starting point is exactly what it sounds like: It is an initial value.
The line intersects the y-axis at (0,1).
The initial value of the function is 1.
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j is the midpoint of HI and GH. complete the proof that GHJ ≅ GIJ
4. Reflexive property
5. SSS
The 8 red markers in a box account for 4% of all markers in the box. How many markers are in the box?.
Answer: 32
Step-by-step explanation: divide 8 into 4/100
Kcf
Keep change flip
Keep the 4/100 change the division sign to multiplication then flip the 8 to 8/1 then just multiply across.
A certain model car has a keypad with 5 numbers on the door. To open the door, 5 numbers must be entered in the correct order and no number can be used more than once. What is the probability that someone could guess the correct code?
Answer:
Step-by-step explanation:
The probability that someone could guess the correct code for the car model with a keypad of 5 numbers is 1 in 120,000, or approximately 0.0000083.
To calculate this, we need to determine the total number of possible combinations of 5 numbers (without repetition) from a set of 5 numbers. This can be calculated as 5!/(5-5)! = 5! = 5x4x3x2x1 = 120.
So, the probability of guessing the correct code is 1/120 or 0.0000083. This means that the chances of guessing the correct code are very low and the car's security system is fairly secure.
What is the solution to the equation?
2(x + 7) 2/3 = 8
Answer: x = -1
Step-by-step explanation:
simplify 2(x + 7) 2 / 3 = 8 to 4x + 28 = 24 and then solve it from there
please help with explanation
The answer to the question on the value of x in a triangle is x = 60 degrees.
What is the value of x ?The fact that all the angles are labeled as x means that this is an equilateral triangle which is a triangle where all the angles are equal.
Should this be the case, the value of x would be:
= Sum of interior angles of triangles / Number of sides in triangle
Sum of interior angles of triangles = 180 degrees
Number of sides = 3 sides
The value of x is:
= 180 / 3
= 60 degrees
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Look at the inequality below.
−6 ≥ 13 + 5×
Which of these values of x makes the inequality true?
A -3.9
B -1.2
C -7/15
D 3/13
Answer:
a -3.9
Step-by-step explanation:
Subtract 13 from both sides which makes it -19 > 5x. then divide by 5 on both sides
If a seed is planted, it has a 95% chance of growing into a healthy plant.
If 7 seeds are planted, what is the probability that exactly 4 don't grow? Round answer to 4 decimal places.
The probability that exactly 4 out of 7 seeds planted do not grow is 0.0007 (approximately), given that each seed has a 95% chance of growing into a healthy plant.
Calculating the probability of a specific outcome using the binomial distribution formula.The probability that a seed doesn't grow is 1 - 0.95 = 0.05.
To calculate the probability that exactly 4 seeds don't grow out of 7, we need to use the binomial distribution formula, which is:
P(X=k) = C(n, k) * [tex]p^k[/tex] * [tex](1-p)^{(n-k)}[/tex]
where:
X is the random variable representing the number of seeds that don't grow.
k is the specific number of seeds that don't grow (in this case, k=4)
n is the total number of seeds planted (n = 7)
p is the probability that a seed doesn't grow (p=0.05)
C(n,k) is the number of ways to choose k items out of n, also known as the binomial coefficient.
Plugging in the values, we get:
P(X=4) = C(7,4) * 0.05⁴ * 0.95³
= 35 * 0.00000625 * 0.857375
= 0.0006522
Rounding to four decimal places, the probability that exactly 4 seeds don't grow is 0.0007 (approximately).
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a triangle has ___ , ___ and ____ .
Use an appropriate modification of the law of cosines to find the angle in degrees. assign the result to q4.
A triangle has three sides, three angles, and three vertices (also known as corners).
What is a Triangle?A triangle is a geometric shape that consists of three line segments that connect three non-collinear points.
Each of these line segments is called a side of the triangle. The three points where these sides meet are called the vertices (singular: vertex) of the triangle.
The triangle also has three interior angles formed by its sides. These angles are located inside the triangle, and their sum is always equal to 180 degrees.
In summary, a triangle is defined by its three sides, three angles, and three vertices.
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Name one pair of congruent sides. A. Segments PR and SV B. Segments QR and ST C. Segments RP and TS D. Segments PQ and VS
Answer:
Step-by-step explanation:Base on the diagram, and the following question, the following are the answers to your question.
#1 Congruent Angle
#2 Congruent Sides
#3 Side Angle Side
I hope you are satisfied with my answer and feel free to ask for more if you have question and further clarification
HELP ASAP!!! WILL MARK BRAINIEST
The value of the network density is 0.9
How to determine network density?
Since the potential connections (PC) formula is n(n-1)/2 and number of nodes is 5 (i.e. n = 5). We have:
PC = n(n-1)/2
PC = 5(5-1)/2
PC = (5*4)/2
PC = 20/2
PC = 10
Actual connection (AC) = 9
Network Density = AC/PC
Network Density = 9/10
Network Density = 0.9
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Find the magnitude and vector
-22.2m
12.6m
The magnitude of the vector is 25.5 metres.
How to find magnitude of a vector?The magnitude of a vector is the length of the vector. Therefore, the magnitude of a vector can be found using Pythagoras's theorem as follows:
Hence,
c² = a² + b²
where
c = hypotenusea and b are the other legsTherefore,
| N | = √22.2² + 12.6²
| N | = √492.84 + 158.76
| N | = √651.6
| N | = 25.5264568634
| N | = 25.5 metres
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A. SSS
B. Neither
C. SAS
#
Copyright © 2003-2023 International Academy of Science. All Rights Reserved.
These triangles
are congruent by
the triangle
congruence
postulate [? ].
The congruence theorem that justifies the congruence of the two triangles is given as follows:
A. SSS.
What is the SSS congruence theorem?
The Side-Side-Side (SSS) congruence theorem states that three sides of a triangle are equivalent to the corresponding three sides of the another triangle, then the two triangles are said to be congruent by SSS rule.
In this problem, we have that:
The | and || sides are equivalent.The bisection belongs to both triangles.Hence the triangles are congruent by the SSS postulate and the correct option is given by option A.
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O REAL NUMBERS
Signed fraction multiplication: Basic
Multiply.
(-9) (-7/3)
Write your answer in simplest form.
Answer:
21
Step-by-step explanation:
(-9)([tex]-\frac{7}{3}[/tex]) = 63/3 = 21
To build a new skate park, a community board must have at least 50% of the voters agree to the build. At a recent voters meeting, 125 voters were asked if they would vote for the new skate park and 72 responded yes. Should the community board go ahead and start planning the park?
No, they should not plan for the skate park because the sample had about 42.4% people vote no.
No, they should not plan for the skate park because the sample had about 57.6% people vote no.
Yes, they should plan for the skate park because the sample had about 42.4% people vote yes.
Yes, they should plan for the skate park because the sample had about 57.6% people vote yes.
The solution is Option D.
The skate park should be build as the percentage of votes was 57.6 %
What is Percentage?A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %
The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.
Percentage change is the difference between the measured value and the true value , as a percentage of the true value
Percentage change =( (| Measured Value - True Value |) / True Value ) x 100
Given data ,
Let the percentage of votes be represented as A
Now , the skate park will be built if the percentage of votes is greater than 50 %
Now , the total number of voters = 125 voters
The number of voters who responded to building the park = 72 voters
Substituting the values in the equation , we get
A = ( number of voters who responded to building the park / total number of voters ) x 100
On simplifying the equation , we get
A = ( 72 / 125 ) x 100
A = 0.576 x 100
A = 57.6 %
And , A > 50 %
Therefore , they should plan for the skate park because the sample had about 57.6% people vote yes
Hence , the percentage of votes is 57.6 %
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Is 2/3 equal or bigger than 1/2
Answer: 1/2 is
Step-by-step explanation:
Stats Determine the y-intercept and slope from the equation: y = 5.8 +2.5x
The slope is 2.5
The y-intercept is 5.8.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
y = 5.8 + 2.5x
This is in the form of y = mx + c
So,
m = 2.5
And,
The y-intercept is when x = 0.
So,
y = 5.8 + 2.5x
Substitute x = 0,
y = 5.8
Thus,
Slope is 2.5
The y-intercept is 5.8.
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In a fair out of 5 people 2 are men and 2 are women and the remaining are children there are 2500 people at the fair. what percentage of people are adult?
Answer:
Step-by-step explanation:
4 out of the 5 people are adults (since 2 women and 2 men) therefore 80% of people are adults.
Answer:
80%
Step-by-step explanation:
Its either too easy or too hard. 2+2=4 obviously, and 4/5=8/10. 8/10, 0.80, or 80% is the answer. If I got this right I don't know how lol.
Find an equation of the circle that satisfies the given conditions. (Use the variables x and y.)
Center (−3, 2); passes through (−6, −6)
An equation of the circle that satisfies the given condition is (x+3))^2 + (y - 2)^2 = 73
Finding an equation of a circleThe formula for finding the equation of a circle is expressed as:
(x-a)^2 + (y - b)^2 = r^2
Determine the value of r^2 using the distance between two points
r^2 = (-6-2)^2 + (-6+3)^2
r^2 = 64 + 9
r^2 = 73
Given the centre (a, b) as (-3, 2), the equatio of the circle will be;
(x-(-3))^2 + (y - 2)^2 = 73
(x+3))^2 + (y - 2)^2 = 73
Hence the equation of the circle is (x+3))^2 + (y - 2)^2 = 73
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A middle school took all of its 6th grade students on a field trip to see a play at a theater that has 1700 seats. The students left 1037 seats vacant. What percentage of the seats in the theater were filled by the 6th graders on the trip?
Answer: 39%
Step-by-step explanation:
using calculator
1 seat = 0.058%
1700 - 1037 = 663 seats are taken.
0.058% x 663 seats = 39%
Of the 125 persons applying for a certain job at data processing center,79 had previous work experience and 62 had college degree, while 38 has both work experience and college degree.
i)How many applicants did not have college degree
ii)how many applicants did not have experience
iii) how many applicants had college degree but no experience
iv)how many applicants had either college degree or experience but not both
1. the number ( of people without college degree ) = 125 - (24 +38)= 63
2. number of people without experience ) = 125- ( 41+38) = 46
3. number ( of applicants with college degree but no experience) = 24
4. n( of applicants with either college degree or experience) = 24+41 + 38 = 103
What is set?A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.
number of people that have previous work experience only) = 79-38 = 41
number ( of persons that have college degree only) = 62- 38 = 24
1. the n( of people without college degree ) = 125 - (24 +38)= 63
2. n( of people without experience ) = 125- ( 41+38) = 46
3. n( of applicants with college degree but no experience) = 24
4. n( of applicants with either college degree or experience) = 24+41 + 38 = 103
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What fraction of an inch is 1 millimeter? Show reasoning
The fraction of an inch in 1 millimeter is given by 1mm = 0.03937008 inches.
How to convert inch to millimeter?One inch is equivalent to 25.4 millimeters internationally.
Expressing this relationship as a formula is as follows.
1 inch = 25.4mm
This official, standardized measurement has been used in international records since 1959.
Both inches and millimeters are units of measurement. Inches belong to the British system of units, and millimeters belong to the metric system of units.
Inches are used in the United States, but it is often necessary to convert this unit of measurement to a metric unit of measurement, such as "millimeters." for scientific purposes. Conversely, there are 0.0393700787402 inches in millimeters.
Thus , the fraction of an inch in 1 millimeter is given by 1mm = 0.03937008 inches.
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A family of 5 went to a matinee movie on a Saturday afternoon. The movie tickets for the matinee were a special
price for each person. The family spent a combined $25 at the concession stand on drinks and popcorn. Altogether,
the family spent $57.50 at the movies.
a. Draw a tape diagram to represent the situation above. Then write an equation.
b. How does the tape diagram help you understand how much the special price was?
The tape diagram helped to understand by that we can subtract the combined $25 at the concession stand from the total and divide it by 5.
What is a tape diagram?A tape diagram is a rectangular visual model resembling a piece of tape, that is used to assist with the calculation of ratios and addition, subtraction, and commonly multiplication. It is also known as a divided bar model, fraction strip, length model or strip diagram.
Given that, a family of 5 went to a matinee movie on a Saturday afternoon. The movie tickets for the matinee were a special price for each person. The family spent a combined $25 at the concession stand on drinks and popcorn. Altogether, the family spent $57.50 at the movies.
By using the tape diagram we get an equation,
5x+25 = 57.50
5x = 32.5
x = 6.5
Therefore, the special price for each person was $6.5
The figure is attached
Hence, the tape diagram helped to understand by that we can subtract the combined $25 at the concession stand from the total and divide it by 5.
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show that the following function are continuos and discontinuos
A.(f×)={×+1 ,for×less than or equai to 2
{ 2×–1 ,for 1<×<2
{×–1 ×<1
f(x) is discontinuous.
Since LHS ≠ RHS ≠ f(x).
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) = x + 1, for x ≤ 2
f(x) = 2x - 1, for 1 < x < 2
f(x) = x - 1, for x < 1
Now,
A x = 1
LHS of f(x) = [tex]\lim_{x\to1^-}[/tex] f((h - 1)) = [tex]\lim_{h \to 0}[/tex] (h - 1 - 1) = 0 -2 = -2
RHS of f(x) = [tex]\lim_{x\to1^+}[/tex] f(h + 1) = [tex]\lim_{h \to 0}[/tex] (2(h + 1) - 1) = 2h + 2 - 1 = 0 + 1
f(1) = x + 1 = 1 + 1 = 2
We see that,
LHS ≠ RHS ≠ f(x)
So,
f(x) is not continuous, it is discontinuous.
Thus,
f(x) is discontinuous.
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The complete question.
Show that the following functions are continuous or discontinuous at x = 1.
f(x) = x + 1, for x ≤ 2
f(x) = 2x - 1, for 1 < x < 2
f(x) = x - 1, for x < 1
