Answers
Answer:
\(\begin{aligned}&\phantom{=.} \dfrac{1}{8}x \cdot \dfrac{-4}{5}x\\\\&=\dfrac{1}{2} \cdot \dfrac{\boxed{-1}}{5} \cdot x \cdot \boxed{x}\\\\& = \dfrac{\boxed{-1}}{\boxed{10}} \;x\;^\boxed{2}\end{aligned}\)
Step-by-step explanation:
According to the Commutative Property Law of Multiplication, changing the order or position of the numbers does not change the end result.
Therefore, collect like terms by moving the fractions to the left and the variables to the right.
As the denominator of the first fraction has been divided by 4, the numerator of the second fraction should also be divided by 4.
Therefore:
\(=\dfrac{1}{2} \cdot \dfrac{\boxed{-1}}{5} \cdot x \cdot \boxed{x}\\\)
\(\textsf{Apply\;the\;fraction\;rule} \quad \dfrac{a}{c}\cdot \dfrac{b}{d}=\dfrac{ab}{cd}.\)
\(\textsf{Apply\;the\;exponent\;rule}\quad \:aa=a^2.\)
Therefore:
\(=\dfrac{\boxed{-1}}{\boxed{10}} \;x\;\boxed{^2}\)
Related Questions
A gas occupies 4.23 l at 2.25 atm. What is the volume at 3.46 atm?
a. 1.84 l
b. 2.75 l
c. 6.50 l
d. 32.9 l
e. 0.364 l
Answers
A gas occupies 4.23 l at 2.25 atm. 2.75 L is the volume at 3.46 atm. This can be solved using the concept of Boyle's law.
What is Boyle's law?Boyle's law gives the relationship between pressure and volume of gas.
It states that at constant temperature pressure in inversely proportional to volume.
PV = k
where P - pressure V - volume and k - constant
P₁V₁ = P₂V₂
Given that,
initial pressure (P₁) = 2.25 atm
final pressure (P₂) = 3.46 atm
initial volume (V₁) = 4.23 L
final volume (V₂) = ?
where parameters for the first instance are on the left side and parameters for the second instance are on the right side of the equation
substituting the values in the equation
2.25 atm x 4.23 L = 3.46 atm x V
V = 2.75 L
Thus, the final volume is 2.75 L
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What is one minus three z less than or equal to seven
Answers
Answer:
-2
Step-by-step explanation:
1 - 3z ≤ 7
First you subtract 1 from both side, then you should get an answer of 6. After that divided by -3 on both side and you should ended up with a answer of z ≤ -2.
Hope this help!
Due in 2 minutes, please help me!
1+2+3+4+5+...+112
Answers
Step-by-step explanation:
we can idnetify that it is arithmetic due to it being a linear sequnce. Therefore we find Tn and equate it to the last term to find the number of terms. We then use that to find the sum of the series using the following formula where n is the number of terms, a is the first term and L represents your last term.
Create ABC by drawing AC. AC represents the foreman’s line of sight to the top of the landfill. What is m
Answers
Where the above is given, the required angle m∠BAC = 45°.
In triangle ABC. AC represents the foreman’s line of sight to the top of the landfill. Landfill height is BC
What is triangle?The triangle is geometric shape which includes 3 sides and sum of interior angle should not grater than 180°
According to conditions angle b = 90°
The sum of angles of a triangle= 180°
That is a + b + c = 180
Therefore, c = a
a = (180 - b)/2
= (180 - 90) / 2
= 90 / 2
= 45°
Hence, the required angle m∠BAC = 45°
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Full Question:
Although part of your question is missing, you might be referring to this full question:
Question 1 Create Triangle ABC by drawing AC. Segment AC represents the foreman’s line of sight to the top of the landfill. What is Angle m BAC?
Help, please! If possible explain it like your talking to a little kid :) Thank you♡
Answers
Answer:
GCF: y³z³
Step-by-step explanation:
The greatest common factor is the a term that you can take out of all the terms given to you. This term, when multiplied to each of the individual numbers in the set, will return you to the original amount.
In this case, note that they all share the variables y and z, and that each of them have at least 3 y's and 3 z's. For you to factor, you will divide these from all the terms.
\(\frac{x^{3}y^{5}z^{5} , y^{3}z^{5} , xy^{3}z^{3} }{y^{3}z^{3}} = x^{3}y^{2}z^{2} , z^{2} , x\)
y³z³(x³y²z² , z² , x)
~
Solve for x
Help me
Answers
Answer: 18.5 equals x.
You set the equation to 90 since it's a square.
Step by step explanation:
Researchers conducted an experiment to test the effects of alcohol. Errors were recorded in a test of visual and motor skills for a treatment group of 22 people who drank ethanol and another group of 22 people given a placebo. The errors for the treatment group have a standard deviation of 2.30, and the errors for the placebo group have a standard deviation of 0.77. Assume that the two populations are normally distributed. Use a 0.05 significance level to test the claim that both groups have the same amount of variation among the errors.
Answers
Treatment Group:
$\mu = 22, \sigma = 2.30$
Placebo Group:
$\mu = 22, \sigma= 0.77$
what rational number is halfway between 1/5 and 1/3?
Answers
Answer:
¼I'm pretty sure, if I'm wrong lmk.
Answer:
4/15 or 7/30
Step-by-step explanation:
lmk if thats right or wrong
The radius of a circle is 2 miles. What is the circle's area?
Answers
Answer:
4π square miles.
Step-by-step explanation:
The area of a circle is given by the formula A = πr², where A is the area and r is the radius.
Substituting r = 2 miles, we get:
A = π(2 miles)² = 4π square miles
Answer: 12.5664 Mi^2
Step-by-step explanation:
Circle area = π * r² = π * 4 [inch²] ≈ 12.566 [in²]
π ≈ 3.14159265 ≈ 3.14
d = r * 2 = 2 [inch] * 2 = 4 [inch]
Read the numbers and decide what the next number should be. 1 1.25 7 7.50 2 2.25 8
Answers
Aaron had $22 to spend on 4 beakers for his science class. After buying them, Aaron had $2 left. How much did each of the beakers cost?
Answers
Answer:4
Step-by-step explanation:22-4=18-4=14-4=10-4=6=2
A company can make 12 printing presses for $78,600. It can make 19 printing presses for $82,380. Find the linear equation that models the cost to produce x printing presses. Use slope-intercept form
Answers
Answer:
\(C(x) = 540x + 72120\)
Step-by-step explanation:
Given
Cost = $78,600 when Printing Press = 12
Cost = $82,380 when Printing Press = 19
Required
Determine the linear equation
From the given parameters; Cost is a function of Printing Press
Represent Cost by C and Printing press by x;
This implies that C = f(x)
The given parameters can then be modeled as; \((x, C)\)
\((x_1, C_1) = (12,78600)\)
\((x_2, C_2) = (19,82380)\)
The first step is to calculate the slope, m;
\(m = \frac{C_1 - C_2}{x_1 - x_2}\)
\(m = \frac{78600 - 82380}{12 - 19}\)
\(m = \frac{-3780}{-7}\)
\(m = 540\)
The linear equation can then be calculated using slope formula
\(m = \frac{C- C_2}{x - x_2}\)
Substitute 540 for m and \((x_2, C_2) = (19,82380)\)
\(540 = \frac{C- 82380}{x - 19}\)
Multiply both sides by x - 19
\(540 * (x-19)= \frac{C- 82380}{x - 19} * (x-19)\)
\(540 * (x-19)= C- 82380\)
Open bracket
\(540x - 10260 = C - 82380\)
Add 82380 to both sides
\(540x - 10260 + 82380= C - 82380 + 82380\)
\(540x - 10260 + 82380= C\)
\(540x + 72120= C\)
\(C = 540x + 72120\)
Hence;
\(C(x) = 540x + 72120\)
which one is smallest 0.28,1/4,15%,0.65,32%,1/3
Answers
Answer:
15%
Step-by-step explanation:
Is the perimeter of an equilateral triangle proportional to the side length of the triangle?Explain your reasoning.
Answers
Answer:
Yes
Step-by-step explanation:
I think so because it's the same on both sides.
I don't know man. I'm not the best at math :)
Wendy traveled 12 miles to school in 20 minutes. What was her speed in
miles per hour?
Answers
Answer:
36 mph.
Step-by-step explanation:
Speed is a rate. It can be represented as the distance traveled/the time spent traveling.
\(s=d/t\)
In this problem, we know the distance and the time. All that needs to be done is some conversion and then plugging in.
In the problem, we know that Wendy travels 12 miles in 20 minutes. But to get her speed in miles per hour, we need to convert 20 minutes into hours.
To do this, let's set up a quick proportion. Let's call the number of hours in 20 minutes x.
I\(\frac{20minutes}{xhours}=\frac{60 minutes}{1 hour}\)
If there are 60 minutes in an hour, then there are 20 minutes in 1/3 of an hour.
Now we can plug 1/3 hours in.
\(s=\frac{12}{1/3}\)
This is the same as saying
\(s=12*3\)
\(s=36\)
Without computing, tell whether each product or quotient is positive or negative. EXPLAIN WHY.
(5)(-1)(4)
Answers
Answer:
negative because any positive number multiplied by a negative number will be negative, the only way to make it positive is to multiply a negative number by another negative number.
Step-by-step explanation:
8, 5, 6, 16, 22, 13, 24, 2
Median -
Q1 -
Q3 -
IQR -
______________
63, 45, 21, 14, 7, 3, 1
Median -
Q1 -
Q3 -
IQR -
Answers
Answer:
Median #1: 10.5
Q1 #1: 5.5
Q3 #1: 19
IQR #1: 13.5
Median #2: 14
Q1 #2: 3
Q3 #2: 45
IQR #2: 42
Step-by-step explanation:
Question 1:
First order the data so that they are in order from least to greatest:
2, 5, 6, 8, 13, 16, 22, 24
Now, find the median by crossing out one value on the left and one value on the right until you get to the center value.
2, 5, 6, 8, 13, 16, 22, 24
/2/, /5/, /6/, /8/, /13/, /16/, /22/, /24/
In this case, there were four values crossed off of each side, so you'll need to find the average of the final two crossed out values: 8 and 13.
(8+13)/2 = 10.5
To find the first quartile, find the median of all values below the median.
2, 5, 6, 8
/2/, /5/, /6/, /8/
The median of these values is the average of the center two, so
(5+6)/2 = 5.5
The third quartile is the median of all values above the median.
13, 16, 22, 24
/13/, /16/, /22/, /24/
The median of those values is the average of the center two as well, so
(16 + 22)/2 = 19
The IQR can be found by subtracting Q1 from Q3. (IQR = Q3 - Q1)
Q3 - Q1
19 - 5.5
IQR = 13.5
Question 2:
Arrange the values from least to greatest and cross them out until you find the middle falue, like in problem one.
1, 3, 7, 14, 21, 45, 63
/1/, /3/, /7/, 14, /21/, /45/, /63/
The center value is 14, so the median is 14.
The first quartile can be found by finding the median of all values below the median.
1, 3, 7
/1/, 3, /7/
The first quartile is 3.
The third quartile can be found by finding the median of all values above the median.
21, 45, 63
/21/, 45, /63/
The third quartile is 45.
The interquartile range can be found using the equation from above.
Q3 - Q1
45 - 3
The interquartile range is 42.
Q2
2. The function 1+21 - e - - 5x sin(27) is annihilated by (a) D'(D-2)(D2 - 4) (b) D'(D-2)'(D2 + 4) (c) D(D-2)(D2+4)* (d) D (D-2)(D2 - 4)2 (e) D'(D-2)(D2+4)
Answers
The correct option is (c) D(D - 2)(D^2 + 4). To determine which operator annihilates the function 1 + 2x - e^(-5x) sin(27x), we can analyze the differential operator options given.
Let's denote the differential operator as D. The given function involves exponentials and trigonometric functions, so we need to find an operator that nullifies both types of functions.
First, we observe that the function contains terms with exponentials of the form e^(kx) and trigonometric functions sin(mx).
To nullify the exponential term e^(kx), we need the operator D - k.
To nullify the trigonometric term sin(mx), we need the operator D^2 + m^2.
Therefore, the differential operator that annihilates both the exponential and trigonometric terms is (D - 0)(D^2 + (27)^2).
Simplifying this expression, we have:
(D)(D^2 + 729).
So, the correct option is (c) D(D - 2)(D^2 + 4).
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Select the correct solution for 5x = 50
Answers
Hi there!
This is the way to solve this one-step equation:
5x=50
We divide both sides by 5 to isolate x:
x=10
Therefore, x=10. Hope it helps.
~GracefulGirlie
Good luck on your assignment.
a
Piper is going to use a computer at an internet cafe. The cafe charges $0.60 for every
minute using a computer on top of an initial charge of $6. Make a table of values and
then write an equation for C, in terms of t, representing the total cost of using a
computer for t minutes at the internet cafe.
Number of Minutes Total Cost to Use Computer
0
1
2
3
Answers
$6.60 because 6.00 + 0.60 = 6.60
what was the difference in the average amounts raised by incumbents and challengers in 2020 house races?
Answers
The difference in fundraising between incumbents and challengers highlights the significant advantages of incumbency in American politics and the challenges that challengers face in trying to unseat an incumbent candidate.
In the 2020 House races, there was a significant difference in the average amounts raised by incumbents and challengers. According to data from the Center for Responsive Politics, the average amount raised by incumbents was $2.9 million, while the average amount raised by challengers was $676,000.
This discrepancy can largely be attributed to the advantages of incumbency. Incumbent candidates already have established networks of donors and supporters, name recognition, and a record of legislative accomplishments that they can leverage to raise funds. Additionally, incumbents are often able to attract larger donations from political action committees (PACs) and other interest groups who are more likely to support the candidate who already holds the office.
Challengers, on the other hand, often struggle to gain traction in fundraising due to their lack of name recognition and the fact that they are not yet seen as viable candidates. They also face more difficulty in attracting larger donations from PACs and interest groups, as these organizations tend to favor incumbents who are seen as more likely to win.
Overall, the difference in fundraising between incumbents and challengers highlights the significant advantages of incumbency in American politics and the challenges that challengers face in trying to unseat an incumbent candidate.
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is the following a probability model? what do we call the outcome "red"?
Answers
The following a probability model? what do we call the outcome No, the provided information is not sufficient to determine if it is a probability model. The outcome "red" is typically referred to as an event.
A probability model is a mathematical representation of a random experiment, where the sample space is defined, and probabilities are assigned to all possible outcomes. To determine if the given information is a probability model, we would need to know the complete list of possible outcomes, their corresponding probabilities, and ensure that the probabilities meet the necessary conditions (sum up to 1 and are non-negative).
Based on the limited information provided, we cannot determine if it is a probability model. The outcome "red" is called an event in the context of probability.
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Which expression is equivalent to (14x)⁰y-⁷z?
Answers
The expression which is equivalent to (14x)⁰y-⁷z as required in the task content is; z / y⁷.
Laws of indicesIt follows from the task content that the expression which is equivalent to the given expression (14x)⁰y-⁷z is to be determined.
Recall from the laws of indices that a⁰ = 1 where a represents any mathematical entity.
Therefore, the resulting expression is;
1 • y -⁷ • z
= z • 1 / y⁷
= z / y⁷.
Ultimately, the resulting expression which is equivalent is; z / y⁷.
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2 If x and y vary directly and y=32 when x=18, then which of the following equations correctly represents
the algebraic relationship between x and y?
(A)y=16/9x
(B)y=x+14
(C) x+y=50
(D)y=9/16x
Answers
The equation would be y = 16/9x which represents the algebraic relationship between x and y which is the correct answer would be an option (A).
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Given that x and y vary directly and y = 32 when x = 18
Direct variation equation can be written as:
y = kx where "k" is a constant.
Substitute the values of y = 32 and x = 18 in the direct variation equation and solve for k:
⇒ 32 = k(18)
⇒ k = 32/18
⇒ k = 16/9
The direct variation equation :
⇒ y = 16/9x
Therefore, the equation would be y = 16/9x which represents the algebraic relationship between x and y.
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the captain gave 1/3 of the coins to his first mate. From the remaining coins, he gave 1/2 to his second mate. How many coins did he leave himself
Answers
So, the captain was left with 33 coins after giving away 1/3 of the coins to his first mate and 1/2 of the remaining coins to his second mate.
To solve this problem, we need to use fractions. Let's start by assuming that the captain had 100 coins.
If he gave 1/3 of the coins to his first mate, he would have given away 1/3 x 100 = 33.33 (we round this to 33) coins.
This means he would be left with 100 minus 33, or 67 coins.
Next,he gave half of the remaining coins (67) to his second mate. That would be 1/2 x 67 = 33.5 (we round this to 34) coins.
Therefore, he would be left with 67 minus 34, or 33 coins.
So, the captain was left with 33 coins after giving away 1/3 of the coins to his first mate and 1/2 of the remaining coins to his second mate.
In summary, is that the captain was left with 33 coins.
The captain initially had a total of C coins. He gave 1/3 of the coins to his first mate, which equals (1/3) C coins. The remaining coins are 2/3C.
From the remaining coins, the captain gave 1/2 of them to his second mate, which equals (1/2)(2/3)C = 1/3C coins.
Now, the captain is left with the remaining coins, which are the initial amount minus the coins given to both mates:
C - (1/3)C - (1/3)C = C - (2/3)C = (1/3)C
So, the captain is left with (1/3) C coins.
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Help I need this urgently please help!
Answers
Using translation concepts, the transformation is defined by:
J. A translation of triangle XYZ to the right.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the orientation of the triangle remains the same, hence it is a translation of the triangle to the right.
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a ship keaves port and proceeds west 30 miles. it then changes course to 020 until it is due north of its origin. how far north of its origin is it
Answers
The ship is north of its origin by 30 miles.
A ship leaves port and proceeds west 30 miles. It then changes course to 020 until it is due north of its origin. The ship is how far north of its origin?The ship is north of its origin by 30 miles.Origin refers to the point from where the ship started its journey or voyage.
When a ship leaves port and proceeds west 30 miles, it moves from the original point to a different point that is 30 miles away from its origin. After proceeding west 30 miles, it changes course to 020 until it is due north of its origin. This means that it moves in the north direction until it is directly north of its origin.
This implies that the new point is on the north-south line passing through the origin.As a result, the distance between the new point and the origin is equal to the distance between the new point and the north-south line passing through the origin, which is 30 miles. Hence, the ship is north of its origin by 30 miles.
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Evaluate the function please help
Answers
Answer:
Well, this is not an answer but, i would like do know your grade. ( & WHO'S idea was it to add LETTERS to MATH!?)
True or False: Mutual funds can include a wide variety of industries and sectors of the economy.
Answers
Answer:
that's The truth
Step-by-step explanation:
that's more like a trade
Which expression is equivalent to (12 + 5) – (14 ÷ 7)²
A] 5 + 15 ÷ (3 + 2)²
B] 2 × (9 × 5 + 3²) + 4
C] 7 + 10 × 5 + 10
D] 5 • 6 + 1 – (10 + 8)
Answers
Answer:
bro its d
Step-by-step explanation:
the math
5 • 6 + 1 = 31
31 - (10+8 or 18) = 13 and
(12 + 5) – (14÷ 7)² = 13
17 – 2 = 13