Answer:
[tex]2ab^{(-6)}[/tex]
Step-by-step explanation:
Multiply exponents/group exponents
[tex]2ab^{(-2)} \times b^{(-4)}\\2ab^{-2 + -4}\\2ab^{-6}[/tex]
When a distribution is skewed, the _______ is used to measure the center and the _______ is used to measure variation.
When a distribution is skewed, the median is used to measure the center and the interquartile range is used to measure variation.
The fundamental characteristics of mean for skewed data distribution:
A skewed distribution's mean will always lag behind the distribution's tail.The median is bigger than the mean when the data set is skewed to the right, which causes the mean to be located toward the right of the distribution.Additionally, if the data set has a leftward skew, the mean will be less than the median and will be located nearer the left of the distribution.Therefore, a skewed data set's center cannot be found using the mean.
In a skewed data collection, the median always stays quite near to the center. The best way to measure the center is hence to use the median.
Additionally, the mean and median of a normal distribution are equal, and both are used to locate the middle of the data set.
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Marsha pays $30 each month for a car wash membership. Which of the following represents the total amount subtracted from her account after 8 months of having the membership?
|−30| − 8 = $22
−8|30| = −$240
8|−30| = $240
|−30| − |8| = $22
The total amount subtracted from her account after 8 months of having the membership is given by −8|30| = −$240
What is the number operation symbol of the amount subtracted from her account?
The amount subtracted from Marsha's account per month would be negative since it reduces the account balance after the car wash membership fee has been paid, in other words, the total amount subtracted for 8 months is determined as the negative $30 per month multiplied by 8 months
total amount subtracted for 8 months=-30*8
total amount subtracted for 8 months=-$240
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Answer:
I think it is b
Step-by-step explanation:
Here are the first 7 terms of a quadratic sequence.
(a) Find an expression, in terms of n, for the nth term of this sequence.
6 11 18 27 38 51
Solve each equation. log₂(x²+2 x)=3
The value of x for a given logarithmic expression is 2 or -4.
What is a logarithmic function?
Logarithmic function is the inverse of an exponential function. It is denoted by using the word, log. For example log 10 = 1.
Solving the given equation: log ₂ ( x² + 2x ) = 3
Applying given properties of logarithmic and exponential function;
log a + log b = log (ab)
4 log x = log x⁴
e^(log x) = 1
Now, the equation becomes,
log ( x² + 2x ) / log 2 = 3
log ( x² + 2x ) = 3 × log 2
log ( x² + 2x ) = log 2³
log ( x² + 2x ) = log 8
Applying exponent both the sides, we get,
e^[log ( x² + 2x )] = e^[log 8]
x² + 2x = 8
x² + 2x - 8 = 0
(x + 4)(x - 2) = 0
x = 2 or -4
Hence, the value of x for a given logarithmic expression is 2 or -4.
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4. The simple interest on a savings account is directly proportional to the amount of the investment.
A savings account with $6,000 earns $75.00 after 1 year. Find a mathematical model that gives the
interest Nafter 1 year in terms of the amount invested P, then calculate the simple interest after
saving an amount of $10,500.
If f ( x ) = 3 x + 2 and g ( x ) = x 2 − x , find the value. f ( x ) + 1
This is a translation of one unit up of f(x), and we will get:
f(x) + 1 = 3x + 3
How to find the value of f(x) + 1?
Here we need to learn to rewrite functions:
Here we know that:
f(x) = 3x + 2
And
g(x) = x^2 - x
(we will not use g(x) in this problem)
So, f(x) +1 can be rewritten by just replacing f(x) by the equation above, so we can redefine:
h(x) = f(x) + 1
Now we replace the function f of x to get:
h(x) = 3x + 2 + 1 = 3x + 3
In this way, we conclude that:
f(x) + 1 = 3x + 3
This is a translation of one unit up of f(x).
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The formula for finding the volume of a cube is V = s³, where
s is the length of one side. What is the volume, in cubic units, of
a cube with side length 3 units? Round to the nearest
hundredth when necessary.
The volume of the cube is determined as 27 unit³.
What is defined as the volume of the cube?A cube's volume is the total number of cubic units it occupies in three dimensions. A cube is a three-dimensional shape with six faces, twelve edges, and eight vertices. As a result, the volume of a cube is defined as the space enclosed by it's own six faces.We can calculate the volume of such a square box simply by measuring the length of one of its sides. The volume of a square box is equal to a cube of the length of its side.The volume is calculated using the formula V = s³, in which "s" is the length of a square box's side.
The cube's side length is 3 units.
The volume of a cube = 3³ unit³.
= 3×3×3
= 27
Thus, the volume of the cube is estimated as 27 unit³.
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I just need the mathematical statement asap like rn
The number 8 is a solution to the equation 3m + 7 = 31
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the equation:
3m + 7 = 31
Subtracting 7 from both sides of the equation:
3m + 7 - 7 = 31 - 7
3m = 24
Dividing both sides of the equation by 3:
3m/3 = 24/3
m = 8
The number 8 is a solution to the equation 3m + 7 = 31
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the quotient of a number x and five is half the difference of the number and four write an equation that represents the statement
Answer:
x/5 - 4
Step-by-step explanation:
A committee of four is to be selected from a group of sixteen people. How many different committees are possible, given the following conditions?
(a) There is no distinction between the responsibilities of the members
(b) One person is the chair, and the rest are general members.
(c) One person is the chair, one person is the secretary, one person is responsible for refreshments, and one person cleans up after meetings.
permutations and combinations, the various ways in which objects from a set may be selected, generally without replacement, to form subsets. This selection of subsets is called a permutation when the order of selection is a factor, a combination when order is not a factor.
The factorial function (symbol: !) just means to multiply a series of descending natural numbers.
a) The number of four people committees that can be selected from a group of 16 people is:
no. of committees are possible = 16!/ 4!
(16x15x14x13)/(1x2x3x4)=1820
b)Given that
One person is the chair, and the rest are general members
n! / (n − r)!
where n is the number of things to choose from,
Pick a chairman:: 16 ways
Pick 3 others:: 15C3 = 455 ways
Ans: 16×455 = 7200
c)
Each committee has a chair, a secretary, a refreshment person and a cleanup person.
The number of combinations of assignments within each committee is: 4x3x2x1=24.
The total number of committees with each committee member’s responsibility is: 1820x24=43680.
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Determine whether each function is an example of exponential growth or decay. Then, find the y -intercept. y=0.5(1/4) x
4x you had 0.5x are the y -intercept.
How can you tell whether an exponential function is growing or deteriorating?
As the exponential's base is greater than 1, which occurs when those numbers increase, we are seeing exponential growth. When the exponential's base is between 1 and 0, and those numbers decrease, we have exponential decay.You can obviously plot it but if you can also conside that in your function you have 4x
; this tells you that as
x increases (gets bigger) certainly
4x will increase as well (you can consider
4²= 16 and 4³ = 64
). It is true that you have to multiply by
0.5
but nevertheless the entire function will grow anyway!
Graphically:
graph{0.5*(4^x) [-14.24, 14.24, -7.12, 7.12]}
If you want, try to think at the case where instead of having
4x you had 0.5x .
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Make g the subject of the formula w = 7 - Vg
Answer:Isolate the g
w = 7 - √g
Do the opposite of PEMDAS, first subtract 7 from both sides
w (-7) = -√g + 7 (-7)
w - 7 = -√g
multiply -1 (as -√g is the same as -1√g) to both sides
-1(w - 7) = √g
-1w + 7 = √g
to get rid of the square root, you must square both sides
Note: -1w is the same as -w
Note: you are squaring all the terms on the other side, not just one.
(-w + 7)² = (√g)²
g = (-w + 7)²
g = (-w + 7)(-w + 7) (note, this can be the answer your teacher wants, or g = (-w + 7)² )
Use the FOIL method (First, Outside, Inside, Last)
(-w)(-w) = w²
(-w)(7) = -7w
(7)(-w) = -7w
(7)(7) = 49
g = w² - 7w - 7w + 49
simplify (combine all like terms)
g =w² - 7w - 7w + 49
g = w² - 14w + 49
g = w² - 14w + 49 is your answer
hope this helps
Step-by-step explanation:
a candidate was to subtract 15 from a certain number but mistakenly added 25 and his answer was 145 calculate the percentage error correct to 1 decimal places
The percentage error of the candidate is 38.1%.
What is the percentage?A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" is also used, and the percent sign, "%," is frequently used to indicate it. A percentage is a number without dimensions and without a standard measurement.So, the percentage error:
Let x be the specified number.What he ought to have received is x-15.What he actually obtained is given as x+25, which equals 145.Now,
x+25 = 145x = 120He ought to have received x-15 = 120-15 = 105.
Percentage error = [(what he actually got - what he should have gotten)/what he should have gotten] × 100Percentage error = [(145 - 105)/105] × 100 = 38.1%Therefore, the percentage error of the candidate is 38.1%.
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What is logbase 3√81
Answer:
log3(sqrt(81)) = 2
Step-by-step explanation:
Solve for y. −140=18+20y−8
The solution for the variable y according to the one-variable equation given in the task content is; y = -7.5.
What is the solution for the variable y according to the given equation in the task content?It follows from the task content that the equation which is given in the task content and from which the variable y is to be determined is;
−140 = 18 + 20y − 8.
Hence, the equation can be solved as follows;
−140=18+20y−8
Evaluate each side of the equation;
-140 = 10 + 20y
Subtract 10 from both sides;
-150 = 20y
Divide through by 20; we have;
-7.5 = y.
Ultimately, the solution for the variable y as required in the task content is; y = -7.5.
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Find the inverse of each function. Is the inverse a function?
f(x)=x²-1
In mathematics, an inverse function is one that "reverses" another function. The inverse function of F(x) = x² - 1 is ±√(x + 1).
What is the inverse function of F(x) =x²-1?The inverse function of a function f in mathematics exists a function that reverses the operation of f. If the inverse of f exists, it is shown by the f⁻¹. The inverse of f exists if and only if f is bijective.
An inverse in mathematics is a function that "undoes" another function. In other words, if f(x) produces y, then y entered into the inverse of f produces x. An invertible function is one that has an inverse, and the inverse is represented by the symbol f ⁻¹.
Let the function be f(x) = x² - 1
y = x² − 1
x = y² − 1
simplifying the above equation, we get
y² = x + 1
y = ± √(x + 1)
Because there are two possible values of y for each value of x, there is no inverse function.
The inverse function of F(x) = x² - 1 is ±√(x + 1).
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Which is the logarithmic form of the exponential equation 2³=8 ?
(A) logB 2=3
(B) log₈ 3=2
(C) log₃ 8=2
(D) log₂ 8=3
The logarithmic form of the exponential equation 2³=8 is (D) log₂ 8=3 .
In mathematics, the inverse function of an exponent is a logarithm. This means that the logarithm of a fixed number, such as a, at base b, is used to represent the exponent to which the fixed number must be raised in order to create the number x.
The general properties of logarithm for a fixed base are:
logₐa=1logₐx+logₐy=logₐxylogₐx-logₐy=logₐ(x/y)logₐxⁿ=n logₐxlogₓy=(logₐy)/(logₐx)The given exponential equation is 2³=8.
To convert the above equation to logarithmic form we have to take logarithm to the base 2 on both sides of the equation.
Taking log₂ on both sides of the equation we get:
log₂(2³)=log₂(8)
Now we know from the properties of logarithms
logₐxⁿ=n logₐx
therefore:
3×log₂(2)=log₂8
Now logₐa=1, so
3×1=log₂8
or, log₂ 8 = 3
Therefore the required logarithmic equation is log₂ 8 = 3.
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In order for the parallelogram to be a rhombus, x = [?]. 32 (9x +31)°
In order for the parallelogram to be a rhombus, Then the value of x is equal to 3°.
Rhombus : A rhombus is a diamond-shaped quadrilateral that has all four sides equal. We can see rhombus-shaped figures in our day-to-day lives. Some of the real-life examples of a rhombus are shown in the below-given figure: a diamond, a kite, an earring, etc.
Since Diagonals bisect at 90°
(9x +31)° = 180° - 90° - 32°
To solve the product or quotient,
9x = 180° - 90° - 32° - 31°
We can add or subtract the values,
9x = 58° - 31°
We can divide the products,
x = (58° - 31°)/9
x = 27°/9
x = 3°
Therefore,
The value of x must be 3° in order for the parallelogram to be a rhombus.
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Least to greatest x-1, V26, 24/5
V 26
1
<
24
5
Step-by-step explanation:
The mean height of the corn plants of variety A is 43.8 inches. Interpret the value of the mean in the situation.
Type your response in the space below.
The mean or the average height of all the corn plants is 43.8 inches.
There are various mean types in mathematics, especially in statistics.
Each mean is used to summarize a specific set of data, usually to clarify the overall magnitude and sign of the data set.The mean may be mistaken for the median, mode, or midpoint when using descriptive statistics because any of these could be referred to as a "average" (more formally, a measure of central tendency).The arithmetic mean of a set of observations is the sum of all the individual values; however, for skewed distributions, the mean could not be the same as the median or the mode.The average of the frequency distribution is given by the mean of the data set .
Hence the statement here indicates that the average height of all the plants combined is 43.8 inches
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Quincy was stuck inside for an hour during a storm. He spent 20 minutes reading, 18 minutes
eating lunch, 12 minutes watching television, and 10 minutes drawing.
Match the following ratios to what they describe.
Description
The ratio of time inside to time eating lunch
The ratio of time eating lunch to time watching television
The ratio of time reading to time drawing
Ratio
2:1
10:3
3:2
The ratio of time inside to time eating lunch Ratio: 3:2
The ratio of time eating lunch to time watching television Ratio: 10:3
The ratio of time reading to time drawing Ratio: 3:2
What is the ratio?
A ratio is a mathematical comparison between two numbers that indicates how many times one value is contained within the other.
Description: The ratio of time inside to time eating lunch
Ratio: 3:2
Description: The ratio of time eating lunch to time watching television
Ratio: 10:3
Description: The ratio of time reading to time drawing
Ratio: 3:2
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Answer:
the ratio of time inside to time eating lunch 10: 3
the ratio of time eating lunch to time watching television 3:2
the ratio of time reading to time drawing 2:1
Step-by-step explanation:
I got it wrong following the other person this is what Khan academy says is correct.
Which function correctly describes the zeros given?
0,−1,2
A) F(x)= x(x+1)(x-2)
B) F(x)= x(x-1)(x+2)
C) F(x)= (x+1)(x-2)
D) None of these
Using the factored form of a polynomial for the given zeros, we can see that option A is the correct one, the function is:
F(x) = x*(x + 1)*(x - 2)
Which function correctly describes the zeros given?For a polynomial with the zeros:
x₁, x₂, x₃, ..., xₙ
The polynomial can be written as:
y = (x - x₁)*(x - x₂)*...*(x - xₙ)
In this case, the zeros are:
0, -1, and 2
Then we can write the polynomial as:
y = (x - 0)*(x + 1)*(x - 2)
If we simplify this, we get:y = x*(x + 1)*(x - 2)Which is the one we can see in option A, so we conclude that option A is the correct one.F(x) = x*(x + 1)*(x - 2)
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Evaluate the following.
||-2|-|3-12||
Answer:
7
Step-by-step explanation:
You want the value of the expression ||-2|-|3-12||.
EvaluationInner groups are evaluated first:
||-2|-|3-12|| = |2 -|-9||
= |2 -9|
= |-7| = 7
The value of the expression is 7.
__
Additional comment
The absolute value function changes negative signs to positive:
|-2| = 2
It has no effect on positive signs.
|2| = 2
Elissa can do a job in 5 hours. Elissa and Lori working together
can do the same job in 2 hours. How long would it take Lori to
do the job alone?
Evaluate the following expression
Find 2x - 3y - z if x = -2, y = 3, and z = -2
Answer:
-11
Step-by-step explanation:
2x - 3y - z
2(-2) - 3(3) - (-2)
-4 -9 +2
-13+2
-11
Answer:
-11
Step-by-step explanation:
What we are solving for: 2x - 3y - z
x = -2
y = 3
z = -2
We can just plug in the variables.
[tex](2*-2) - (3*3) - (-2)[/tex]
[tex]-4-9+2[/tex]
Therefore, the answer is -11.
Hope this helped!!
please help, no troll answers. will give brainliest to correct answers. option answers are
54
46
44
90
Answer:
46
Step-by-step explanation:
A right angle is always equal to 90.
You are given the angle 44 so all you need to do is 90-44 which gives you 46
Hope this helps! Have a great day :)
Answer:
<2 = 46 degrees
Step-by-step explanation:
The angle measuring 44 degrees and <2 are complementary, therefore, they add up to 90 degrees.
Let [tex]x[/tex] be <2
[tex]44 + x = 90 \text{ // Subtract 44 on both sides}\\44 + x - 44 = 90 - 44\\\to x = 46[/tex]
14-3m=4m
what is the value of m?
Answer:
2
Step-by-step explanation:
Which of these numbers lies between 4 and 4.5 on a number line? A √13 B √17 C √22 D √28
Therefore √17 will lie between 4 and 4.5 on the number line .
In basic mathematics, real numbers are shown as a graphic of a graduated straight line called a number line. Every point on a number line is considered to correspond to a real number, and every real number is assumed to correspond to a point.
According to one standard, positive numbers always fall on the right side of zero, whereas negative numbers always fall on the left. The line also contains arrowheads at both ends, signifying that it continues in both the positive and negative directions indefinitely.
Let us find the decimal values of the given numbers.
13 lies between 9 and 16 , therefore √13 lies between 3 and 4 on the number line .
17 lies between 16 and 25 , therefore √17 lies between 4 and 5 on the number line .
22 lies between 16 and 25 , therefore √22 lies between 4 and 5 on the number line .
28 lies between 25 and 36 , therefore √28 lies between 5 and 6 on the number line.
Therefore √17 will lie between 4 and 4.5 on the number line as 4.5² = 20.25.
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m∠WYX = (2x − 7)° and m∠WYZ = (3x + 2)°. If ∠WYX and ∠WYZ are complementary,
what is the measure of each angle?
A) m∠WYX = 67°; m∠WYZ = 113°
B) m∠WYX = 27°; m∠WYZ = 63°
C) m∠WYX = 31°; m∠WYZ = 59°
D) m∠WYX = 63°; m∠WYZ = 117°
The values of m∠WYX and m∠WYZ are 31° and 59° respectively. Option C
What are complementary angles?Complementary angles are defined as angles that sum up to 90 degrees.
Example:
If x and y are complementary angles, then;
x + y = 90°
From the information given, we have the angles;
m∠WYX = (2x − 7)° m∠WYZ = (3x + 2)since they are complementary, then;
2x - 7 + 3x + 2 = 90
collect like terms
2x + 3x = 90 + 5
Add like terms
5x = 95
Make 'x' the subject of formula
x = 95/5
x = 19
But;
m∠WYX = (2x − 7) = ( 2(19) - 7) = 38 - 7 = 31°
m∠WYZ = (3x + 2)° = (3(19) + 2) = 57 + 2 = 59°
Thus, the values of m∠WYX and m∠WYZ are 31° and 59° respectively. Option C
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Divide. Rationalize all denominators. √3x⁵ / 8 x²
The value of the expression [tex]\frac{\sqrt{3} x^{5}}{8x^{2}}[/tex] after rationalizing the denominator is [tex]\frac{\sqrt{3}(x^{3})}{8}[/tex]..
A finite collection of symbols that is well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.
Rationalizing the denominator is the process of shifting a root, such as a cube root or a square root, from the fraction's denominator to its numerator (numerator).
Any number of equal parts is represented by a fraction, which also represents a portion of a whole.
The numerator is the part of a fraction that comes before the vinculum.
The denominator of a fraction is the phrase that comes before the vinculum.
Consider the expression,
[tex]\frac{\sqrt{3} x^{5}}{8x^{2}}[/tex]
Now, let [tex]y=\frac{\sqrt{3} x^{5}}{8x^{2}}[/tex]
[tex]y=\frac{\sqrt{3} x^{2}(x^{3})}{8x^{2}}[/tex]
Using the exponent rule [tex]\frac{x^a}{x^b}=x^{a-b}[/tex]
[tex]y=\frac{\sqrt{3}(x^{3})}{8}[/tex]
The value of the expression when rationalized [tex]\frac{\sqrt{3} x^{5}}{8x^{2}}[/tex] is [tex]\frac{\sqrt{3}(x^{3})}{8}[/tex].
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