Answers
Solving the given equation we get value of x as -3/2 i.e option (a) is correct option.
What are exponents and its properties?
A number's exponent indicates how many times the number has been multiplied by itself. Example: Since 2 is multiplied by itself 4 times, 2×2×2×2 can be expressed as [tex]2^{4}[/tex]. Here, 4 is referred to as the "exponent" or "power," while 2 is referred to as the "base."
Generally speaking, [tex]x^{n}[/tex] denotes that x has been multiplied by itself n times.
Raise a power to a power
[tex](x^{a}) ^{b}=x^{ab}[/tex]
This is called the power of a power property
Negative exponents are the reciprocals of the positive exponents.
[tex]x^{-a}=\frac{1}{x^a}[/tex]
The same properties of exponents apply for both positive and negative exponents.
[tex](1/25)^x = 125\\ 25^{-x} = 125\\(5^2)^{-x} = 5^3\\5^{-2x} = 5^3\\\implies -2x = 3\\\implies x = -3/2[/tex]
i.e.
Option (a) is correct.
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Related Questions
3
6
1
2
8
7
Press "Deal" to receive your cards.
Drag cards from your hand to the red and blue areas.
GOAL: Create two groups of cards with the SAME SUM
using as many cards as possible.
Submit
Answers
Answer:
I'm sorry I don't know
Step-by-step explanation:
........
A figure on a coordinate plane is dilated. Point a A(3,9) is dilated to A(1,3). Royce says the dilation can be represented by (1/3x, 1/3y) Ruby says the dilation can be represented by (3x, 3y). Who is correct?
Answers
Royce statement is the correct statement that is dilation can be represented by (1/3x, 1/3y).
What is a coordinate plane?
Two number lines combine to generate the two-dimensional surface known as the coordinate plane. The x-axis is a single horizontal number line. The y-axis is the name of the vertical number line that is the other number line. The origin is where the two axes come together. The coordinate plane can be used to graph points, lines, and other things.
Scale Factor is defined as the ratio of the size of the new image to the size of the old image.
The x-coordinate of old point is 3.
The y-coordinate of old point is 9.
The x-coordinate of new point is 1.
The y-coordinate of new point is 3.
The dilation is (x-coordinate of old point)/ (x-coordinate of new point) = 1/3.
The dilation is (y-coordinate of old point)/ (y-coordinate of new point) = 3/9 = 1/3.
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There is a “buy two, get one free” sale on energy bars that regularly cost $1.25 each. How much do four bars cost?
Answers
Answer:
5
Step-by-step explanation:
1.24 × 4 = 5
or it can be 1.24 ÷2 =0.265
Find each of these values. a) (19² mod 41) mod 9 b) (32³ mod 13)² mod 11 c) (7³ mod 23)² mod 31 d) (21² mod 15)³ mod 22
Answers
The remainder will be 33, 9, 7, and 14 for options a, b, c, and d respectively.
The Remainder is the extra part of a number that restricts the number to be divided completely.
a)
(19² mod 41) mod 9
Let us determine 361 mod 41
a=361 = 328+33= 8*41+33 =8d+33
The remainder is the constant in the final expression: 361 mod 41=33
33 mod 9 = 6 (since a=33= 27+6=3*9+6=3d+6)
b)
(32³ mod 13)² mod 11
Let us determine 32 mod 13
a=32=26+6=2*13+6+2d+6
The remainder is the constant in the final expression: 32 mod 13=6
[tex](6^{3} mod13)^{2} mod 11\\(216mod13)^{2} mod 11[/tex]
Let us determine 216 mod 13
a= 216= 208+8=16*13+8 = 16d+8
The remainder is the constant in the final expression: 216 mod 13=8
[tex]8^{2} mod 11\\64 mod 11[/tex] = 9 (since, 64= 55+9= 11*5+6= 11d+6)
c)
(7³ mod 23)² mod 31
[tex](343mod23)^{2} mod 31\\[/tex]
Let us determine 343 mod 23
a=343=322+21=14*23+21=14d+21
The remainder is the constant in the final expression: 343 mod 23= 21
[tex]21^{2} mod 31 = 441 mod 31=7[/tex] (since a = 441=434+7=14*31+7=14d+7)
d)
(21² mod 15)³ mod 22
[tex](441mod15)^{3} mod 22[/tex]
Let us determine 441 mod 15
a=441 = 435+6= 29*15+6= 29d+6
The remainder is the constant in the final expression: 441 mod 15= 6
[tex]6^{2} mod 22=36mod22= 14[/tex] (since a = 36= 22+14= 1*22+14= d+14)
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Is a origin on a graph proportional relationship?
Answers
Answer: Yes
Step-by-step explanation:
Most of the time, if a graph passes through the origin it is a proportional relationship!
The average daily balance is the mean of the balance in an account at the end of each day in a month. The following table gives the dates and amounts of the transactions in Elliott's account in June.
Answers
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{\$1583.9 per day}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{The table with the information}[/tex]
Find: [tex]\textsf{The average daily balance of Elliott's account for the month of June}[/tex]
Solution: In order to get the average daily balance, we need to use a formula where we have a weighted balance for each day. For example, out of the 30 days in June, 9 of the days there was $1223 in the account, for 5 days there was $1223 + $615 in the account, for 7 days there was $1223 + $615 - $63 in the account, and for the last 9 days there was $1223 + $615 - $63 - $120 in the account. This all happened over 30 days and to translate this to an equation it will look something like the following.
Convert to equation and simplify
[tex]\frac{(1223\ *\ 9)\ +\ (1223\ +\ 615)\ *\ 5\ +\ (1223\ +\ 615\ -\ 63)\ *\ 7\ +\ (1223\ +\ 615\ -\ 63\ -\ 120)\ *\ 9}{30\ days}[/tex][tex]\frac{(11007)\ +\ (9190)\ +\ (12425)\ +\ (14895)}{30\ days}[/tex][tex]\frac{(47517)}{30\ days}[/tex][tex]\textsf{1583.9 per day}[/tex]Therefore, the final answer would be that the average daily balance of Elliott's account for the month of June would be $1583.9 per day.
THREE HOLIDAY ASSIGNMENT -mati 1. A husband earns sh 2450 more than his wife. If the wife earns sh 9470. Find their total earnings.
Answers
Answer:
husband = wife earn + 2450
wife = 9 470
Husband earnings:
9 470 + 2 450 = sh 11 920
husband + wife
11 920 + 9 470 = sh 21 390
Therefore their total earnings is sh 21 390Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-a data set is summarized in the frequency table below. using the table, determine the number of values greater than or equal to 7.
Answers
Using the frequency table, the number of values greater than or equal to 7 is 36.
What is a frequency table?Frequency refers to the number of times an event or a value occurs.
A frequency table is a table that lists objects and shows the number of times the items occur.
The distribution of observations based on a variable's possible values is displayed in a frequency table.
Frequency tables are helpful to determine which alternatives appear more or less often in the dataset.
This is useful for better understanding each variable and determining whether or not variables need to be recorded.
So, values greater than or equal to 7:
Refer to the frequency table attached below.
The value of 7 is 3.
Sum of all values that is equal to 3 or greater than 3 as follows:
3+4+6+3+3+4+5+4+4
36
Therefore, using the frequency table, the number of values greater than or equal to 7 is 36.
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each person at a pizza party received four slices of pizza how many attended the party if 48 slices were given out
Answers
Answer: 12 attendee
Step-by-step explanation:
Take 48 divided by 4 = 12 attendee
So there are 12 atteded
Answer: 12
Step-by-step explanation:
12 x 4 = 48
what is the area of florida rounded to the nearest tenth?
what is the area of south carolina rounded to the nearest ten?
what is the area of georgia rounded to the nearest square mile?
Answers
ur not the smartest person
65,760,000
while virtually all time series exhibit _______ a random component, not all time series exhibit other components.
Answers
In contrast to the fact that almost all time series contain a random component, certain time series do not.
A TIME SERIES IS WHAT?
A time series is a group of observations of clearly defined data points produced over time via repeated measurements. A time series would include, for instance, calculating the amount of retail sales for each month of the year. This is due to the well defined and regular measurement of sales income at uniformly spaced intervals. Time series data are not those that are irregularly or once collected.
Three parts can be separated out of a time series observation: the trend (long-term direction), the seasonal (systematic, calendar-related motions), and the irregular (unsystematic, short term fluctuations).
In mathematics, a time series is a collection of data points that have been indexed chronologically.
A time series is typically a sequence that was recorded at a number of evenly spaced points in time.
It is therefore a set of discrete-time data.
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An art class is making a mural for the
school that has a triangle drawn in the middle. The length of
the bottom of the triangle is x. Another side is 1 more than three
times the length of the bottom of the triangle. The last side is 2 more
than the bottom of the triangle. Write an expression for the
perimeter of the triangle. Then combine like terms.
Answers
The expression representing the perimeter of the triangle is (5x+3)
What is an expression?An expression in maths is a sentence with a minimum of two numbers or variables and at least one maths operation.
Given that, The length of the bottom of the triangle is x. Another side is 1 more than three times the length of the bottom of the triangle. The last side is 2 more than the bottom of the triangle.
Let the bottom length of the triangle be x, then, according to question, other two sides will be, (3x+1) and (x+2)
Perimeter = sum of all the side
Perimeter = x+x+2+3x+1
= 5x+3
Hence, The expression for the perimeter of the triangle is (5x+3)
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The value of x is the equation X + 5 = 12 is
Answers
Answer:
x+5=12
or,x=12-5
or,x=7
Please help!!! Mathematics uhhhh.
Answers
If the bookstore sells 15 pencils, the ratios of pens to pencil written as fraction is 2 / 3.
How to solve for variables in proportional graph?Proportional relationships are relationships between two variables where their ratios are equivalent.
A proportional relationship is one in which two quantities vary directly with each other.
Therefore, proportional relationship can be represented as follows:
y ∝x
y = kx
where
k = constant of proportionalityx = number of pencilsy = number of pensTherefore,
4 = 6k
k = 4 / 6
k = 2 / 3
Therefore, let's find the number of pen sold when the bookstore sells 15 pencils.
y = 15 × 2 / 3
y = 30 / 3
y = 10
Therefore, if the bookstore sell 15 pencils the ratio of pen to pencil is 10 / 15 = 2 / 3
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solving systems by substation
x-4y=15
3x-12y=12
Answers
Answer:
There is no solution
Step-by-step explanation:
x - 4y = 15
3x -12y = 12
Times the first equation by -3
-3x +12y = -45
3x - 12y = 12
0 = -33
This is untrue; 0 is not equal to -33
So, there is no solution for this system.
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If f(x)= x³ + 7x²-x and g(x)=x²-3, what is the degree of g(f(x))?
•2
•3
•6
•8
Answers
g(x) = x^2 - 3
f(x) = x^3+7x^2-x
Start with the g(x) function. Replace every x with f(x)
g(x) = x^2 - 3
g(f(x)) = ( f(x) )^2 - 3
Then replace the f(x) on the right side with x^3+7x^2-x
g(f(x)) = (x^3+7x^2-x)^2 - 3
The highest term inside the parenthesis is x^3. Squaring this leads to (x^3)^2 = x^(3*2) = x^6
So the highest exponent found in g(f(x)) is 6, meaning the degree of is 6
Shawn is typing a paper for class. He can type 1 2/7 pages in 1/3 of an hour. How many pages can Shawn type in one hour? A. B. C. D.
Answers
Shawn can type [tex]1\frac{6}{21}[/tex] pages in an one hour.
What is typing speed?
How many words a person can correctly type in one minute. He types at a 60 wpm rate.
Given:
Shawn is typing a paper for class. He can type 1 2/7 pages in 1/3 of an hour.
We have to find how many paged he can type in one hour.
First to convert improper fraction 1 2/7 into a fraction.
⇒ [tex]1\frac{2}{7} = \frac{7*1+2}{7} = \frac{9}{7}[/tex]
So, Shawn can type 9/7 pages in 1/3 of an hours.
i hour = 3/3
So, Shawn can type
9/7 x 3/3 = 27/21 = [tex]1\frac{6}{21}[/tex] pages in one hour.
Hence, Shawn can type [tex]1\frac{6}{21}[/tex] pages in an one hour.
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Which expression is equivalent to (m^-2n^-3)^-4
Answers
By using some exponent properties, we will find the equivalent expression:
(m⁻²*n⁻³)⁻⁴ = m⁸*n¹²
How to find an equivalent expression?Here are some exponent properties that we need to use:
(aⁿ)ˣ = aⁿ*ˣ
(a⁻ⁿ) = (1/a)ⁿ
Here we have the expression:
(m⁻²*n⁻³)⁻⁴
The exponents can be distributed under multiplication, then:
(m⁻²)⁻⁴*(n⁻³)⁻⁴
Now we can use the first property so we get:
(m⁻²)⁻⁴*(n⁻³)⁻⁴ = m⁽⁻²*⁻⁴⁾*n⁽⁻³*⁻⁴⁾
m⁽⁻²*⁻⁴⁾*n⁽⁻³*⁻⁴⁾ = m⁸*n¹²
That is the equivalent expression.
(m⁻²*n⁻³)⁻⁴ = m⁸*n¹²
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a medical researcher surveyed a large group
Answers
The probability that the person selected will be someone whose response is never and who is a woman is 0.0636 = 6.36%.
A probability of an occurrence in the context of a problem is calculated by dividing the desired outcomes in the problem by the entire number of outcomes in the problem.
In the context of this problem, these outcomes are given as follows:
Desired outcomes: people whose response is never and who are women.
Total outcomes: all participants.
Hence, as all participants represent the desired outcomes, the probability that the person selected will be someone whose response is never and who is a woman is the relative frequency of people who are women and who respond never, which is: 0.0636 = 6.36%.
Missing question:
(Refer to the image for the complete question)
One person surveyed will be selected at random:
What is the probability that the person selected will be someone whose response is never and who is a woman?
What is the probability that the person selected will be someone whose response is never 0r who is a woman?
What is the probability that the person selected will be someone whose response is never given and that the person is a woman?
For the people surveyed are the events of being a person whose response is never and being woman independent?
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A store is offering a 30% discount on all jeans. If the regular price of a pair of jeans is $49. 99, what is the sale price of the jeans? responses.
Answers
When a store is offering a 30% discount on all jeans. If the regular price of a pair of jeans is $49.99, then the sale price of the jeans after discount will be $34.99 per pair.
The computation of the discounted price or the actual sales price of the jeans after applying the given discount can be calculated using the generalized formula, and putting the values of the provided information, as below,
Sale Price = Regular Price – Discount Rate
Sale Price = 49.99 – 30%
Sale Price = 49.99–14.97
Sale Price = $34.99
Therefore, the actual sales price of the pair of jeans will be $34.99.
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The set C ={x:x<=-3}
Illustrate the set C' using number line.
Answers
The number line of the set C ={x : x ≤ -3} is attached
How to illustration the solution to the inequality?From the question, we have the following parameters that can be used in our computation:
Set C ={x:x<=-3}
Rewrite properly
So, we have
Set C ={x : x ≤ -3}
Remove the curly braces from the set notation
So, we have the following representation
x ≤ -3
There are no multiples and factors to divide or multiply
Also, there are no terms to subtract or add
This means that the inequality to represent on the number line is x ≤ -3
See attachment for the number line
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In the given figure, write the relation between AB and CD as well as AB and AE.
Answers
Answer:
A point and C point are correspondingC and D point are parallel linesI'm not really sure about this one but I think A and E point are also parallel as there is a straight lineHope this Helps!!!
elizabeth's family went to nyc for their vacation. at the gift shop on liberty island, valerie bought three t-shirts and four keychains for $134, and jennifer bought four t-shirts and five key chains for $175. find the price of each item.
Answers
Using the elimination method, the price of one t-shirt is $30 and one key-chain is $11.
In the given question, Elizabeth's family went to NYC for their vacation.
At the gift shop on Liberty Island, Valerie bought three t-shirts and four key chains for $134, and Jennifer bought four t-shirts and five key chains for $175.
We have to find the price of each item.
Let the price of one t-shirt = $x
Let the price of one Key chain = $y
According to question
Price of three t-shirts and four key chains = $134
So the equation is
3x + 4y = $134……………….(1)
Also,
Price of four-shirts and five Key chains = $175
So the equation is
4x+5y = $175……………………..(2)
Now solving the equation using the elimination method.
Multiply Equation (1) by 5 and Equation (2) by 4, we get
15x+20y = 670....................(3)
16x+20y = 700......................(4)
Subtract equation 4 and 3, we get
x = 30
Now put the value of x in equation 1,
3*30 + 4y = $134
90+4y=$134
Subtract 90 on both side, we get;
4y = 44
Divide by 4 on both side, we get;
y = 11
Hence, the price of one t-shirt is $30 and one key-chain is $11.
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Solve this and I give you brain crown and points please quickly
Answers
Answer:
one solution
Step-by-step explanation:
because it has diffrent slopes
identify the surface whose equation is given. rho = sin(θ) sin(φ)
Answers
Step-by-step explanation:
Given;The equation of the surface is, ρ = sin(θ) sin(φ)The spherical and Cartesian coordinates are related by the equations,
x = ρ sin(φ) cos(θ)
y = ρ sin(φ) sin(θ)
z = ρ cos(φ)
Here, x, y and z represent the coordinates of the center of the sphere on x, y and z axes respectively.
Now, multiply the given surface equation by ρ.
ρ² = ρsin(θ) sin(φ)
We have, ρ² = x² + y² + z².
Substitute this value in above equation and also replace the RHS by y coordinate.
x² + y² + z² = y
Now, simplify the above equation.
x² + y² - y + z² = 0
x² + y² - 2y½ + (1/2)² + z² = (1/2)²
x² + (y - 1/2)² + z² = (1/2)² ...(1)
The general form of equation of sphere is,
(x - a)² + (y - b)² + (z - c)² = r²
Here, a, b, c are the coordinates of the center of the sphere on x, y, z axes respectively and r is the radius of the sphere.
Compare equation (1) with the general form of equation of sphere. Therefore we get,
a = 0b = 1/2c = 0r = 1/2Therefore, the radius of the sphere is 1/2 and center of sphere is at (0, 1/2, 0).
Thus, The given equation represents - a sphere of radius 1/2 centers at (0, 1/2, 0).
determine if the following statements are true or false, and explain your reasoning. (a) describe the strength of the relationship in the data, and whether or not fitting a linear model would be reasonable: weak relationship moderate, linear model is reasonable strong, linear model is reasonable strong, but linear model is not reasonable moderate, but linear model is not reasonable (b) describe the strength of the relationship in the data, and whether or not fitting a linear model would be reasonable: strong, linear model is reasonable moderate, but linear model is not reasonable moderate, linear model is reasonable strong, but linear model is not reasonable weak relationship (c) describe the strength of the relationship in the data, and whether or not fitting a linear model would be reasonable: moderate, linear model is reasonable strong, but linear model is not reasonable strong, linear model is reasonable moderate, but linear model is not reasonable weak relationship (d) describe the strength of the relationship in the data, and whether or not fitting a linear model would be reasonable:
Answers
Part-A: linear model is not reasonable which is strong
Part-B : Strong, but linear model is not reasonable
Part-C : Strong, linear model is reasonable
Part-D : moderate, linear model is not reasonable
Given that,
We have to find explain the strength of the relationship in the data and whether or not it would be appropriate to fit a linear model.
We know that,
There are 4 options that are:
weak relationship
moderate, linear model is reasonable
strong, linear model is reasonable
strong, but linear model is not reasonable
moderate, but linear model is not reasonable
Therefore,
Part-A: linear model is not reasonable which is strong
Part-B : Strong, but linear model is not reasonable
Part-C : Strong, linear model is reasonable
Part-D : moderate, linear model is not reasonable
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What is 25+(−15)−(−10)?
Answers
When two numbers have the same sign, the result will be the number with the larger absolute value. 25 + (-15) - (-10) = 30
To calculate 25 + (-15) - (-10), we must first look at the order of operations. We start with the parentheses, so we need to calculate -15 and -10 first. When two numbers have the same sign, the result will be the number with the larger absolute value. In this case, -15 and -10 both have negative signs, so the result will be -15.
Next, we move on to the addition and subtraction signs. We add 25 and -15 to get 10. Then we subtract -10 from 10, and the result is 30. So, 25 + (-15) - (-10) = 30.
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if 80% of the drivers in the community are in the low-risk category this year (10% in medium- risk and 10% in high-risk), what is the probability that a driver chosen at random from the community will be in the low-risk category for the next year? the year after next?
Answers
The probability that a driver chosen at random from the community will be in the low-risk category for the next year is 0.8
Probability:
In math, the ratio of the times an event is likely to occur divided by the total possible events is known as probability.
Given,
Here we need to find if 80% of the drivers in the community are in the low-risk category this year, then the probability that a driver chosen at random from the community will be in the low-risk category for the next year.
Here we know that, 80% of the drivers in the community are in the low-risk category this year.
Then as per the definition of probability, the the community will be in the low-risk category for the next year is calculated as,
=> 80/100
=> 0.8
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there
Write an equivalent expression for 6a + a + 8b + b.
A
Answers
Answer:
7a + 9b
Step-by-step explanation:
"a" is basically a shorter way of writing "1a;" and this is the same way for any singular variable. Examples would variables like "a," "b," "c," and so on. So the real equation would be 6a + 1a + 8b + 1b. If 2 numbers have the same variable then you can add them together. You solve it like this:
6a + 1a = 7a
8b + 1b = 9b
The equivalent of 6a +a + 8b + b is 7a + 9b.
The monthly income of a man is Rs. 53000. He deposits 20% of his yearly income in the Civil investment Fund and 10% in Charity. If Rs.300000 is his yearly income exempted and 1% social security charge and 15% tax is imposed yearly, how much tax should he pay?
Answers
Answer:
Monthly income of a Man is ₹53000
Total salary earned in an year = 53000 × 12
= 636000
20% in civil investment fund.
So, 636000 × 20 ÷ 100 = 127200.
10% in charity.
So, 636000 × 10 ÷ 100
= 63600.
1% is social security tax on first 300000 = 3000.
300000 × 15 ÷ 100 = 45000.
Total tax he should pay = Amount remained is 390840
Step-by-step explanation:
