Answer:
Yes,
Step-by-step explananation
The quotient of two rational numbers is always rational, and the reason for this lies in the fact that the product of two integers is always an rational number.
The Quotient of two Rational Numbers is a Rational Number if and only if Numerator and Denominator are Multiples.
From Algebra, we know that a Rational Number is a Real Number of the form:
[tex]x = \frac{a}{b}[/tex], [tex]a, b\in \mathbb{N}[/tex], [tex]x \in \mathbb{R}[/tex] (1)
Where:
[tex]a[/tex] - Numerator.[tex]b[/tex] - Denominator.[tex]x[/tex] - Quotient.The Quotient can be an Integer or not. In the first case, all Quotients have their equivalent Rational Numbers.
Now, if we divide a Rational Number by another Rational Number, then we have the following expression:
[tex]x' = \frac{x_{1}}{x_{2}}[/tex]
If [tex]x'[/tex] is a Rational Number, then it must also an Integer and if [tex]x'[/tex] is an Integer, then [tex]x_{1}[/tex] and [tex]x_{2}[/tex] must be Multiples of each other.
The Quotient of two Rational Numbers is a Rational Number if and only if Numerator and Denominator are Multiples.
Please see this question related to Rational Numbers: https://brainly.com/question/24398433
Simply this question and get marked branlist
Answer:
72/n^5r
Step-by-step explanation:
Answer:
Below
Step-by-step explanation:
13)
● 2d^3 × c^6 × 8d^5 × c^2
Isolate the similar terms
● (2×8)× (d^3 × d^5)×(c^6×c^2)
● 16 × d^(3+5) × c^(6+2)
● 16 × d^8 × c^8
● 16 × (dc)^8
● 16(dc)^8
■■■■■■■■■■■■■■■■■■■■■■■■■■
● 8n×r^(-4) ×9×n^(-6)×r^3
Isolate the similar terms
● (8×9)× (r^(-4)×r^3) × (n×n^(-6))
● 72 × r^(-4+3) × n^(1-6)
● 72 × r^-1 × n^(-5)
● 72 ×(1/r) × (1/n^5)
● 72/(r×n^5)
What two rational expressions sum to [tex]\frac{4x+2}{x^{2}-9+8 }[/tex] Enter your answer by filling in the boxes. Enter your answer so that each rational expression is in simplified form.
Answer:
[tex]\frac{4x+2}{x^2 - 9x + 8} = \frac{4x}{(x-8)(x-1)} + \frac{2}{(x-8)(x-1)}[/tex]
Step-by-step explanation:
Given
[tex]\frac{4x+2}{x^{2}-9+8 } = \frac{A}{()(x-1)} + \frac{B}{()(x-8)}[/tex]
Required
Fill in the gaps
Going by the given parameters, we have that
[tex]\frac{4x+2}{x^{2}-9+8 } = \frac{A}{()(x-1)} + \frac{B}{()(x-8)}[/tex]
[tex]x^2 - 9x + 8[/tex], when factorized is [tex](x-1)(x-8)[/tex]
Hence; the expression becomes
[tex]\frac{4x+2}{(x-1)(x-8)} = \frac{A}{(x-8)(x-1)} + \frac{B}{(x-1)(x-8)}[/tex]
Combine Fractions
[tex]\frac{4x+2}{(x-1)(x-8)} = \frac{A + B}{(x-8)(x-1)}[/tex]
Simplify the denominators
[tex]4x + 2 = A + B[/tex]
By direct comparison
[tex]A = 4x[/tex]
[tex]B = 2[/tex]
Hence, the complete expression is
[tex]\frac{4x+2}{x^2 - 9x + 8} = \frac{4x}{(x-8)(x-1)} + \frac{2}{(x-8)(x-1)}[/tex]
Answer:4x+2/x2−9x+8 = −6/7(x−1) + 34/7(x−8)
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Astrid is in charge of building a new fleet of ships. Each ship requires 40 tons of w
sailors. She receives a delivery of 4 tons of wood each day. The deliveries can con
afterwards the weather is too bad to allow them. Overall, she wants to build enou
least 2100 sailors.
How much wood does Astrid need to accommodate 2100 sailors?
tons
Show Calculator
This question is incomplete.
Complete Question
Astrid is in charge of building a new fleet of ships. Each ship requires 40 tons of wood, and accommodates 300 sailors. She receives a delivery of 4 tons of wood each day. The deliveries can continue for 100 days at most, afterwards the weather is too bad to allow them. Overall, she wants to build enough ships to accommodate at least 2100 sailors. How much wood does Astrid need to accommodate 2100 sailors?
Answer:
280 tons of wood.
Step-by-step explanation:
From the above question:
To make 1 ship = we require 40 tons of wood.
1 ship = can accommodate 300 sailors.
Step 1
If :
300 sailors = 1 ship
2100 sailors = y ships
Cross Multiply
300 × y ships = 1 ship × 2100 sailors
y ships = 2100 / 300
y ships = 7
Hence, 2100 sailors can occupy 7 ships.
Step 2
We are told in the question that:
Astrid wants to build enough ships to accommodate at least 2100 sailors. How much wood does Astrid need to accommodate 2100 sailors?
If:
1 ship = 40 tons of wood
Since 7 ships can accommodate 2100 sailors,
7 ships =
7 × 40 tons of wood = 280 tons of wood.
Therefore , Astrid needs 280 tons of wood to accommodate 2100 sailors.
he sum of two nonnegative numbers is 300. What is the maximum value of the product of these two numbers?
Answer:
[tex]\boxed{22,500}[/tex]
Step-by-step explanation:
Hey there!
Well, half of 300 is 150, and 150•150 = 22500
So 150 and 150 are it's highest numbers.
Hope this helps :)
what is PI numbers?
Answer:
These are the first 100 digits of pi: 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 7067
Step-by-step explanation:
Pi goes on continuously forever, so this is a reduced version, by including the first 100 digits.
What is the solution to this system of linear equations?
y-x = 6
y + x = -10
(-2,-8)
(-8.-2)
(6.-10)
(-10.6)
Answer:
The correct answer is A
Step-by-step explanation:
Answer:
(-8, -2)
Step-by-step explanation:
y-x = 6
y + x = -10
Add the two equations together to eliminate x
y-x = 6
y + x = -10
--------------------
2y = -4
Divide by 2
2y/2 = -4/2
y = -2
Now find x
y+x = -10
-2+x = -10
x = -8
An oblique cylinder is shown.
An oblique cylinder is shown. It has a radius of 5, a height of 12, and a slant length of 13.
Which represents the volume of the cylinder, in cubic units?
120π
130π
300π
325π
Answer:
The volume in terms of Pi is 300πStep-by-step explanation:
This problem is on the mensuration of solid shapes, an oblique cylinder.
the expression for the volume of an oblique cylinder is given as
[tex]volume= \pi r^2h[/tex]
Given data
radius r= 5
height h= 12, and
slant length of 13.
Substituting the given data into the expression we can solve for the volume below
[tex]volume= \pi* 5^2*12\\\ volume= \pi*25*12\\\ volume= \pi*300\\\ volume= 300\pi[/tex]
Answer:
300
Step-by-step explanation:
Sarah has $30,000 in her bank account today. Her grand-father has opened this account for her 15 years ago when she was born. Calculate the money that was deposited in the account 15 years ago if money has earned 3.5% p.a. compounded monthly through all these years.
Answer:
Deposit value(P) = $17,760 (Approx)
Step-by-step explanation:
Given:
Future value (F) = $30,000
Number of Year (n) = 15 year = 15 × 12 = 180 month
rate of interest (r) = 3.5% = 0.035 / 12 = 0.0029167
Find:
Deposit value(P)
Computation:
[tex]A = P(1+r)^n\\\\ 30000 = P(1+0.0029167)^{180} \\\\ 30000 = P(1.68917) \\\\ P = 17760.2018[/tex]
Deposit value(P) = $17,760 (Approx)
Evan’s dog weighs 15 3/8 pounds. What is this weight written as a decimal? A. 15.125 Ib B. 15.375 Ib C. 15.385 Ib D. 15.625 Ib Please include ALL work!
Answer:
ok as we know 15 is a whole number by itself and 3/8 is the decimal part
so we know it is 15. something
that something is 3/8 to find decimal you do 3/8
3/8 is = .375
so 15.375 is the answer
hope it helps
brainliest give me pls
Test scores in a Test were normally distributed with a mean of 75 and a standard deviation of 10. Carl scored 90 in the Test . What is the z-score of Carl’s test score?
Answer:
Z-score = 1.5
Step-by-step explanation:
Z-score = (x-mean)/standard deviation
= (90-75)/10
= 1.5
If a dog has 2,000,000 toys and he gives 900,000 away. Then gets 2,000 more, also looses 2,000,000. He's sad but then also got 5,000,000,000 more and gives 1,672,293 out. How much does he have now? And how much he gave away. And how much he got.
Answer:
See below.
Step-by-step explanation:
He does not have enough to loose 2,000,000 at that point, so this whole problem is nonsense.
Find the value of 18÷9•3
Answer:
6
Step-by-step explanation:
18 : 9 · 3 = 2 · 3 = 6
Find an equation in slope-intercept form of the line that has slope –9 and passes through point A(-9,-1)
Answer:
y = -9x - 82
Step-by-step explanation:
Line with slope m=-9 passing through A(x1, y1) =A(-9,-1)
y-y1 = m(x-x1)
Substitute values
y-(-1) = -9(x-(-9)
y+1 = -9x -81
y = -9x - 82
. Simplify the sum. (2u3 + 6u2 + 2) + (7u3 – 7u + 4)
Answer:
9u^3 + 6u^2 - 7u + 6
Step-by-step explanation:
plsss i need help pls is urgent it is trigonometric ratio to find the length side in right angle plsss i will mark u as brainliest
Answer:
which side are you looking for, SOHCAHTOA
OPPOSITE
tan50.34=x÷180
x=180×1.2062(tan50.34)
x=2117.116
Records indicate that x years after 2008, the average property tax on a three bedroom home in a certain community was T(x) =20x^2+40x+600 dollars.
Required:
a. At what rate was the property tax increasing with respect to time in 2008?
b. By how much did the tax change between the years 2008 and 2012?
Answer:
a) 40 dollars
b) 480 dollars
Step-by-step explanation:
Given the average property tax on a three bedroom home in a certain community modelled by the equation T(x) =20x²+40x+600, the rate at which the property tax is increasing with respect to time in 2008 can be derived by solving for the function T'(x) at x=0
T'(x) = 2(20)x¹ + 40x° + 0
T'(x) = 40x+40
At x = 0,
T'(0) = 40(0)+40
T'(0) = 40
Hence the property tax was increasing at a rate of 40dollars with respect to the initial year (2008).
b) There are 4 years between 2008 and 2012. To know how much that the tax change between the years 2008 and 2012, we will find T(4) - T(0)
Given T(x) =20x²+40x+600
T(4) =20(4)²+40(4)+600
T(4) = 320+160+600
T(4) = 1080 dollars
Also T(0) =20(0)²+40(0)+600
T(0) = 0+0+600
T(0)= 600 dollars
T(4) - T(0) = 1080 - 600
T(4) - T(0) = 480 dollars
Hence, the tax has changed by $480 between 2008 and 2012
Timothy invested $2,000 in an account earning 3.5% annual interest that is compounded continuously. How long will it take the investment to grow to $3,500?
Answer: 16 years
Step-by-step explanation:
The exponential function for continuous growth is given by :-
[tex]P=Ae^{rt}[/tex]
, where A = initial amount, r= rate of growth and t = time.
As per given , we have
A= $2,000, =r 3.5%=0.035 and P= $3500
put these vales in equation , we get
[tex]3500=2000e^{0.035t}\\\\\Rightarrow\ \dfrac{3500}{2000}=e^{0.035t}\\\\\Rightarrow\ 1.75=e^{0.035t}[/tex]
Taking log on both sides , we get
[tex]\ln 1.75=0.035t\\\\\Rightarrow\ t=\dfrac{\ln1.75}{0.035}=\dfrac{0.560}{0.035}=16[/tex]
Hence, it will take 16 years to grow to $3,500.
Monique makes $11 per hour delivering pizzas. Monique works Monday
through Friday, and on average she earns $20 a day in tips. If Monique
made no less than $450 for one week, find an inequality for the number
of hours she worked
Answer:
x > 39 hours
Step-by-step explanation:
Let x be the number of hours she worked.
11x - is how much she would get paid for working for x hours
11x + 20 > 450
11x > 430
x > 39 hours
Hope that helped!!! k
A waiter earns $11.00 an hour and approximately 10% of what he serves in a shift. If he works a 6 hour shift and takes $425 in orders, his total earnings for the six hours would be:
Answer:
108.50
Step-by-step explanation:
First find the wages
11* 6 = 66 dollars
Then figure the commission
10% of 425
.10 * 425
42.5
Add the two amounts together
42.5+66
108.50
Solve x/5 - 1/2 = x/6 (make sure to type the number only)
X/5 -1/2 = x/6
Find the least common denominator of the 3 denominators:5,2,6
The limited is 30
Multiply all 3 fractions by 30:
6x -15 = 5x
Subtract 6x from both sides:
-15 = -x
Multiply both sides by -1:
X = 15
How to graph the line y=4/3x
Answer:
make a table of values
Step-by-step explanation:
then plot using those values
The required graph has been attached which represents the line y = 4/3x
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
We have been given the equation of a line below as:
y = 4/3x
Rewrite in slope-intercept form.
y = (4/3)x
Use the slope-intercept form to discover the slope and y-intercept.
Here the slope is 4/3 and y-intercept = (0, 0)
Any line can be graphed using two points. Select two x values, and plug them into the equation to find the corresponding y values.
When substitute the value of x = 0, then the value of y = 0, and When substitute the value of x = 3, then the value of y = -4,
Hence, the graph represents the line y = 4/3x
Therefore, the required graph of the line y=4/3x will be shown in the as attached file.
Learn more about the graphs here:
brainly.com/question/16608196
#SPJ2
Please help with this
Answer:
A
Step-by-step explanation:
● first one:
The diagonals of a rhombus are perpendicular to each others wich means that they form four right angles.
STP is one of them so this statement is true.
● second one:
If ST and PT were equal this would be a square not a rhombus.
● third one:
If SPQ was a right angle, this woukd be a square.
● fourth one:
Again if the diagonals SQ and PR were equal, this would be a square.
Lena is comparing offers from two banks on checking accounts that include debit cards. Bank A charges $20 monthly fee for a checking account and debit card, with unlimited transactions. Bank B charged a $5 monthly fee for a checking account and debit card, plus
$ 0.50 for each transaction.
Suppose Lena makes 35 transactions in a given month.
How much would she pay at each bank for the given month?
Bank A
Bank B
For the given month, which bank is cheaper and by how much?
Bank A. is cheaper than Bank B by $
or
Bank B is cheaper than Bank A by $
Answer:
Bank A spending= $20
Bank B spending= $22.5
Bank A is cheaper with $2.5
Step-by-step explanation:
Bank A charges $20 monthly fee for a checking account and debit card, with unlimited transactions.
Sheade 35 transactions.
Total charges from bank A
= $20 monthly
Bank B charged a $5 monthly fee for a checking account and debit card, plus
$ 0.50 for each transaction.
She made 35 transactions.
Total charges on bank B= $5 + (0.5)35
Total charges on bank B= $5+17.5
Total charges on bank B= $22.5
a) which function has the graph with the greatest y intercept?
b) which functions have graphs with slopes less than -3
c) which functions graph is the least steep?
Answer:
a =4,b=2, c=3
Step-by-step explanation:
Suppose that the director of manufacturing at a clothing factory needs to determine whether a new machine is producing a particular type of cloth according to the manufacturer’s specifications, which indicate that the cloth should have a mean breaking strength of 70 pounds and a standard deviation of 3.5 pounds. A sample of 49 pieces reveals a sample mean of 69.1 pounds.
(a) State the null and alternative hypotheses.
(b) Is there evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength? (Use a 0.05 level of significance.)
(c) Compute the p-value and interpret its meaning.
(d) What will your answer be in (b) if the standard deviation is 1.75 pounds?
(e) What will your answer be in (b) if the sample mean is 69 pounds?
Answer:
a.H0 : u1= u2 against Ha : u1≠ u2 This is a two sided test
b) There isn't enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.
c) the p- value is 0.0359*2= 0.0718. It is greater than the value of ∝ so there isn't enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.
d) There is enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.
e) There isn't enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.
Step-by-step explanation:
Formulate the null and alternative hypotheses as
a) H0 : u1= u2 against Ha : u1≠ u2 This is a two sided test
Here ∝= 0.005
For alpha by 2 for a two tailed test Z∝/2 = ± 1.96
Standard deviation = s= 3.5 pounds
n= 49
The test statistic used here is
Z = x- x`/ s/√n
Z= 69.1- 70 / 3.5 / √49
Z= -1.80
Since the calculated value of Z= -1.80 falls in the critical region we reject the null hypothesis.
b) There isn't enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.
c) the p- value is 0.0359*2= 0.0718. It is greater than the value of ∝ so there isn't enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.
d) If standard deviation is 1.75 pounds
The test statistic used here is
Z = x- x`/ s/√n
Z= 69.1- 70 / 1.75 / √49
Z= -3.6
This value does not fall in the critical region.
d) There is enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.
e) If the sample mean is 69 pounds
Z = x- x`/ s/√n
Z= 69.1- 69 / 3.5 / √49
Z= 0.2
This value falls in the critical region
e) There isn't enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.
Select the correct answer from each drop-down menu.
The function f is given by the table of values as shown below.
x 1 2 3 4 5
f(x) 13 19 37 91 253
Use the given table to complete the statements.
The parent function of the function represented in the table is
.
If function f was translated down 4 units, the
-values would be
.
A point in the table for the transformed function would be
.
Answer:
3^x9, 15, 33, 87, 249(4, 87) for exampleStep-by-step explanation:
a) First differences of the f(x) values in the table are ...
19 -13 = 6, 37 -19 = 18, 91 -37 = 54, 253 -91 = 162
The second differences are not constant:
18 -6 = 12, 54 -18 = 36, 162 -54 = 108
But, we notice that both the first and second differences have a common ratio. This is characteristic of an exponential function. The common ratio is 18/6 = 3, so the parent function is 3^x.
__
b) Translating a function down 4 units subtracts 4 from each y-value. The values of f(x) in the table would be ...
9, 15, 33, 87, 249
__
c) The x-values of the function stay the same for a vertical translation, so the points in the table of the transformed function are ...
(x, f(x)) = (1, 9), (2, 15), (3, 33), (4, 87), (5, 249)
Answer: I think this is it:
The parent function of the function represented in the table is exponential. If function f was translated down 4 units, the f(x)-values would be decreased by 4. A point in the table for the transformed function would be (4,87)
Step-by-step explanation: I got it right on Edmentum!
The sum of the product of a number x and 14, and 13
Answer:
ax+182
Step-by-step explanation:
a*x+14*13
ax+182
There are 4 roads leading from Bluffton to Hardeeville, 10 roads leading from Hardeeville to Savannah, and 5 roads leading from Savannah to Macon. How many ways are there to get from Bluffton to Macon
Answer: 200 ways
Step-by-step explanation:
From the given information:
Total number of roads leading from Bluffton to Hardeeville = 4
Total number of roads leading from Hardeeville to Savannah = 10
Total number of roads leading from Savannah to Macon = 5
We need to find the total number of ways to get from Bluffton to Macon.
Total number of ways to get from Bluffton to Macon = 4 * 10 * 5
= 200
Therefore, there are 200 required number of ways to get from Bluffton to Macon.
Last Sunday, the average temperature was 8\%8%8, percent higher than the average temperature two Sundays ago. The average temperature two Sundays ago was TTT degrees Celsius. Which of the following expressions could represent the average temperature last Sunday?
Work Shown:
T = average Celsius temperature two Sundays ago
8% = 8/100 = 0.08
8% of T = 0.08T
L = average Celsius temperature last sunday
L = 8% higher than T
L = T + (8% of T)
L = T + 0.08T
L = 1.00T + 0.08T
L = (1.00 + 0.08)T
L = 1.08T
The 1.08 refers to the idea that L is 108% of T
Answer:
b and d
Step-by-step explanation:
khan
Randy is walking home from school. According to the diagram above, what is his total distance from school to home? Show your work and include units. If he had a jet pack, would you use distance or displacement? Why?
Answer:
if he needs to walk, we can see that between the street and his house he must walk 4 times a distance of 0.5km, so this is a total of 4¨*0.5km = 2km.
Now he has a jet-pack, he can ignore the buildings and just travel in the shorter path, so we can draw a triangle rectangle, in such a way that the hypotenuse of this triangle is the distance between the home and the school.
One of the cathetus is the vertical distance, in this case, is 1km, and the other one is the horizontal distance, also 1km.
So the actual distance is given by the Pythagorean's theorem:
A^2 + B^2 = H^2
Where A and B are the cathetus, and H is the hypotenuse, then:
H^2 = 1km^2 + 1km^2
H = (√2)km = 1.41km.
Now, in the case that he has a jet-pack, he can actually go to the school using this hypotenuse line as his path, so in this case the distance and the displacement would be the same.
Distance: "how much ground an object has covered"
Displacement: "Difference between the final position and the initial position"
When he walks, the distance is 2km, but the displacement is 1.41km
When he uses the jet-pack, both the distance and the displacement are 1.41km
Answer and Step-by-step explanation:
The first thing is we can see in the image, when he walks, that between the house and his school he has to walk four times a distance of 0.5 km. The result of this is a total of 4¨*0.5 km = 2 km. The second thing is that he must walk 2 kilometers. On the other hand, if he has a jetpack, he can simply take the shorter path by ignoring all the buildings. This idea is where we can draw a triangular rectangle on the map in a way so that the hypotenuse of the triangle is the distance between the school and the home. As for the Catheti, it is a vertical distance which in this case is two blocks of 0.5 km. The result is that these catheti have a length of 2*0.5 km = 1 km. The other is the distance of the horizontal line, which is 1 km. The absolute distance of this path is given by Pythagorean's theorem, which is A^2 + B^2 = H^2. Here, A and B are the cathetus, and H is the hypotenuse, then, H^2 = 1 km^2 + 1 km^2. As well, H = (√2)km = 1.41 km. Currently, in the situation where he has a jetpack, he can literally fly to the school utilizing this hypotenuse line for the path he would need to follow. For this specific situation, the displacement, and the distance would be the exact same. The reason for this is that the definitions of displacement and distance are displacement is the difference between the final position and the initial position and distance is how much area an item has covered. Also, when he walks, the distance is 2 km and the displacement is 1.41 km. Also, when he utilizes the jet pack, the distance is equal to the displacement. Both of these are 1.41 km.
