can whole numbers be rational numbers
Answers
From the inside, whatever that layer is, it can be any of the layers outside of it.
All whole numbers can be a rational number, but not all rational numbers be a whole number.
Kind of like all squares can be rectangles, but not all rectangles can be a square.
The whole number has all the attributes of a rational number, but not all rational numbers have all of the attributes of a whole number.
Related Questions
Manuel stores his favorite CDs in a box like the one shown
Answers
a carpenter uses 65 shelves to make 13 bookcases. she uses the same number of shelves for each bookcase. are 32 shelves enough to build 6 more shelves?
Answers
65 ÷ 13 = 5
Now we know, it takes 5 shelves to build a single bookcase. The next step would be to find out how many shelves it would take to build 6 more bookcases. To find the answer, you would multiply the number of shelves it takes to build 1 bookcase by the number of bookcases that need to be built.
5 x 6 = 30
So, yes, 32 shelves would be more than enough to build 6 more bookcases.
I hope this helps!
In the 30-60-90 triangle below side s has a length of ___ and the hypotenuse has a length of
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so, h^2 = s^2 + 1
However, if we have two sides of the same length, we should have a isosceles triangle, meaning that two of the angles are the same. However, this is not the case here.
the only possible answer is , s = sqrt(3) and h = 2
In a 30-60-90 triangle, the side opposite the 30-degree angle (s) has a length of "s," and the hypotenuse has a length of "2s."
The side opposite the 60-degree angle is "s√3."
We have,
In a 30-60-90 triangle, the sides are in a specific ratio:
x, x√3, and 2x,
where x is the length of the shortest side (opposite the 30-degree angle).
Step 1:
Identify the shortest side (opposite the 30-degree angle).
Let's assume the length of the shortest side (opposite the 30-degree angle) is "s."
Step 2:
Find the other side lengths.
The side opposite the 60-degree angle is s√3.
The hypotenuse is twice the length of the shortest side, so it is 2s.
Thus,
In a 30-60-90 triangle, the side opposite the 30-degree angle (s) has a length of "s," and the hypotenuse has a length of "2s."
The side opposite the 60-degree angle is "s√3."
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A survey of 2,000 doctors showed that an average of 3 out of 5 doctors use brand X aspirin. How many doctors use brand X aspirin? (Hint: Solve for X
Answers
X/2,000 = 3/5
Multiply: 2,000*3= 6,000
Divide: 6,000/5
Answer: 1,200 doctors use brand x
If the food is good or if I eat too much, I'll exercise. How do you write this compound statement in symbols.
Answers
Y=the food is yummy
O=overeat
E=exercise
Note:
∪ = or
-> if ... then
(Y∪O)->E
Franks quarter grades are 82.5, 94.7, and 87.9 what grade rounded to the nearest percent will frank need to recieve at least a an 89 % final course grade A.92% B.90% C.91% D.89% please show work
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Frank would have to get a 92% on his final course grade in order to get above an 89%.
A student is taking a test. He has 37 questions left. If the test has 78 questions
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a. Let x represent the number of questions finished.
b. The equation is x + 37 = 78 , and solving yields x = 41 .
c. The student finished 41 questions.
a. Define a variable for the unknown value. Let x represent the number of questions the student has finished.
b. Write and solve the equation. The total number of questions is the sum of the questions finished and the questions left: x + 37 = 78 . Now solve for x :
x = 78 - 37 = 41
So, the student has finished 41 questions.
c. Answer the question with the correct units. The student has finished 41 questions out of the total 78. Therefore, the student has [tex]\( \frac{41}{78} \)[/tex] of the test complete. To express this as a percentage, multiply by 100:
[tex]\[ \frac{41}{78} \times 100 \approx 52.56\% \][/tex]
The student has finished approximately 52.56% of the test.
Que. A student is taking a test. He has 37 questions left. If the test has 78 questions, how many questions has he finished? a. Define a variable for the unknown value. Let ...........represent............
b. Write and solve the equation.
c. Answer the question with the correct units........
3m-5m-12=7m-88-5
plz show all work
Answers
-2m - 12 = 7m - 88 - 5
-2m - 12 = 7m - 93
-12 = 7m - 93 + 2m
-12 = 9m - 93
-12 + 93 = 9m
81 = 9m
9 = m
hope that helps, God bless!
Jackie's watch loses two minutes every hour. Adam's watch gains one minute every hour. They both set their watches at the radio at 6:00 am, then start their journey to the airport. When they arrive (at the same time) their watches are twelve minutes apart. What is the real time they arrive at the airport?
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Let the number of hour ellapsed at the time they are twelve minutes apart be x, then
2x + x = 12
⇒ 3x = 12
⇒ x = 12 / 3 = 4
Thus, after 4 hours Jackie's watch has lost 8 minutes and Adam's watch has gained 4 minutes.
Therefore, the real time at the time they arrive at the airport is 10:00 am.
What is 27 multiplied by 36 worked out?
Answers
4
36
27
x___
252
72
_____
972
You are 5 feet tall and cast an 8-foot shadow. A lamppost nearby casts a shadow that is 20 feet. Which equation can you use to solve for the height (h) of the lamppost?
A. 5/8 = h/20
B. 8/5= h/20
C. 5/9 = h/20
D. 5/20 = h/8
Answers
Answer:
A. 5/8 = h/20
Step-by-step explanation:
Topic: Triangle Similarity
As you can see in the image you can paint the problem that way, it means that each side of the triangle is a multiplier from the other one same side, so you can build a relation as follows:
[tex]\frac{5}{h} = \frac{8}{20} \\[/tex]
you can re arrange the equality as
[tex]\frac{5}{8} = \frac{h}{20}[/tex]
as you can ssee you just reached the option A. 5/8 = h/20
subtract the fractions and simplify the answer 7 8/9-5 3/5
Answers
To subtract 3/5 from 8/9, you'd need to find the lowest common denominator (LCD) of 3/5 and 8/9, convert both fractions to have this LCD, and then subtract.
The LCD is (5)(9)=45. Then 8/9 and 3/5 become 40/45 and 27/45.
Subtracting 27/45 from 40/45 results in the fraction 13/45.
Then the full solution is 2 13/45.
You could also do this problem by converting 7 8/9 and 5 3/5 into improper fractions:
71/9 - 28/5. Again, the LCD is 45. Can you rewrite both fractions with 45 as the common denominator and then perform the subtraction?
To subtract the fractions 7 8/9 and 5 3/5, first convert them into improper fractions. Then, adjust them to the common denominator (45 in this case) and subtract to get the answer of 2 13/45.
Explanation:To begin, we need to convert these mixed fractions (7 8/9 and 5 3/5) into improper fractions. 7 8/9 equals 71/9 (since 7*9 + 8 = 71) and 5 3/5 equals 28/5 (since 5*5 + 3 = 28). Now, we can subtract these fractions by finding a common denominator or a number that 9 and 5 mutually divide into. This number is 45. Therefore, we adjust these fractions to have the denominator of 45, getting 355/45 and 252/45. The subtraction of these adjusted fractions equals 103/45. That can be simplified into 2 13/45.
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Suppose w=xy+yz, where x=e2t, y=2+sin(4t), and z=2+cos(7t).
a. use the chain rule to find dwdt as a function of x, y, z, and t. do not rewrite x, y, and z in terms of t, and do not rewrite e2t as x.
Answers
i.e
dx/dt = 2e^2t
dy/dt= 4cos 4t
dZ/dt = -7sin 7t
now
from
W=xy+yz
dw/dx = y ( by partial differentiation)
dw/dy= x+z
dw/dz= y
now Dw/dt = ⅓{ (dx/dt×dw/dx) + (dy/dt×dw/dy)+(dz/dt×dw/dz)
dw/dt = ⅓{ (2e^2t×y) + (4cos4t×(x+z) + (-7sin7t×y)}
= ⅓{ 2ye^2t + 4(x+z)Cos4t - 7ySin7t}
pheww
that should help...
Final answer:
To find dwdt using the chain rule, differentiate w=xy+yz, where x=e^2t, y=2+sin(4t), and z=2+cos(7t), as functions of t, apply partial derivatives and multiply by dx/dt, dy/dt, and dz/dt.
Explanation:
The student asked how to use the chain rule to find dwdt as a function of x, y, z, and t, without rewriting x, y, and z in terms of t, and keeping e2t as x. Given w=xy+yz, where x=e2t, y=2+sin(4t), and z=2+cos(7t), we apply the chain rule to differentiate w for t, remembering that x, y, and z are all functions of t. To find debt, we derive each component individually and sum their contributions. The calculation involves taking partial derivatives of w to x, y, z, multiplied by their respective derivatives to t (dx/dt, dy/dt, dz/dt).
The last wednesday in a certain month is on the 26th day of that month. What day of the week is the first day of that month?
Answers
Subtract the first day of the month from the date of the last Wednesday and divide by 7 to find the remainder. Count backwards from Wednesday to determine the day of the week for the first day of the month, which is Saturday in this case.
Explanation:The subject of this question pertains to dates and the calendar, which fall under the domain of Mathematics. To answer the question, we need to calculate how many days have passed from the 26th (the last Wednesday) to the 1st day of the same month. A week has seven days so we use the principles of modular arithmetic, a branch of number theory. The 26th day is a Wednesday, and for every seven days we go back, it will still be Wednesday. Thus, the difference from 26 to 1 is 25. Dividing 25 by 7, we get a quotient of 3 and a remainder of 4. This tells us that four days before the last Wednesday, which was the 26th, would be the first day of the month. Going backwards from Wednesday, we count Tuesday (1), Monday (2), Sunday (3), and Saturday (4). Therefore, the first day of that month falls on a Saturday.
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An investment firm recommends that a client invest in bonds rated AAA, A, and B. The average yield on AAA bonds is 4%, on A bonds 6%, and on B bonds 11%. The client wants to invest twice as much in AAA bonds as in B bonds. How much should be invested in each type of bond under the following conditions?
A. The total investment is $26,000, and the investor wants an annual return of $1,620 on the three investments.
B. The values in part A are changed to $38,000 and $2,360, respectively
A. The client should invest $(?) in AAA bonds, $(?)in A bonds, and $(?)in B bonds.
Answers
1) Variables:
X: amount invested in AAA bonds
Y: amount invested in A bonds
Z: amount invested in B bonds.
2) Return:
4%* X + 6% * Y + 11% * Z = 1620
3) Investment:
X + Y + Z = 26,000
4) Ratio between AAA and B bonds.
X = 2*Z
5) Solution of the system of equations:
Replace X with 2Z in the two first equations:
2Z * 4% + Y * 6% + Z * 11% = 1620
=> 0.08Z + 0.06Y + 0.11Z = 1620
=> 0.19Z + 0.06Y = 1620
2Z + Y + Z = 26,000
=> 3Z + Y = 26,000 => Y = 26,000 - 3Z
Replace Y with 26,000 - 3Z
0.19Z + 0.06(26,000 - 3Z) = 1620
0.19Z + 1560 - 0.18Z = 1620
0.01Z = 1620 - 1560
0.01Z = 60
Z = 60 / 0.01 = 6000
=> X = 2*6000 = 12,000
=> Y = 26,000 - 12,000 - 6,000 = 8,000
Answer: 12,000 in bonds AAA, 8,000 in bonds A, and 6000 in bonds B.
Part B.
2) Return:
0.04X + 0.06 Y + 0.11Z = 2360
3) Investment:
X + Y + Z = 38,000
4) Ratio between AAA and B bonds.
X = 2Z
5) Solution of the system of equations:
Replace X with 2Z in the two first equations:
=> 0.08Z + 0.06Y + 0.11Z = 2360
=> 0.19Z + 0.06Y = 2360
2Z + Y + Z = 38,000
=> 3Z + Y = 38,000 => Y = 38,000 - 3Z
Replace Y with 38,000 - 3Z
0.19Z + 0.06(38,000 - 3Z) = 2360
0.19Z + 2280 - 0.18Z = 2360
0.01Z = 2360 - 2280
0.01Z = 80
Z = 80 / 0.01 = 8000
=> X = 2*8000 = 16,000
=> Y = 38,000 - 16,000 - 8000 = 14,000
Answer: 16,000 in AAA bonds, 14,000 in A bonds, and 8,000 in B bonds.
80 miles per hour is how many feet per minute?
Answers
[tex]\bf \cfrac{80~\underline{mile}}{\underline{hr}}\cdot \cfrac{5280~feet}{\underline{mile}}\cdot \cfrac{\underline{hr}}{60~min}\implies \cfrac{80\cdot 5280~feet}{60~min}\implies \cfrac{422400~feet}{60~min} \\\\\\ 7040\frac{feet}{min}[/tex]
What must the distance be between charges of +2.35 and −1.96 for the attractive force between them to be the same as that between charges of +4.06 and −2.11 separated by a distance of 2.26 pm?
Answers
The distance between charges of +2.35 and −1.96, should be approximately 1.566 picometers (pm).
Coulomb's law states that the force (F) between two point charges is given by:
F =[tex]\dfrac{(k \times q1 \times q2)}{r^2}[/tex]
Where:
The electrostatic force between the charges is F
k is Coulomb's constant, approximately equal to 8.99 × 10^9 N m²/C².
The magnitudes of the two charges are [tex]q_1[/tex] and [tex]q_2[/tex].
The distance between the charges is r.
Given that the charges are +2.35 and −1.96, we'll call the distance between them x (in pm). Similarly, for charges +4.06 and −2.11, the distance is given as 2.26 pm.
Setting up the equation:
For the first pair of charges (q1 = +2.35 C and q2 = −1.96 C):
F1 =[tex]\dfrac{(k \times |2.35 \times (-1.96)|)}{x^2}[/tex]
For the second pair of charges (q1 = +4.06 C and q2 = −2.11 C):
F2 =[tex]\dfrac{(k \times |4.06 \times (-2.11)|)}{(2.26)^2}[/tex]
Since the forces are said to be equal, we have:
F1 = F2
The solution of the expression for x is given by:
[tex]\dfrac{(k \times |2.35 \times (-1.96)|}{x^2}[/tex] =[tex]\dfrac{(k \times |4.06 \times (-2.11)|)}{(2.26)^2}[/tex]
|[tex]\dfrac{(2.35 \times (-1.96)}{x^2}[/tex]| =[tex]\dfrac{|4.06 \times (-2.11)|}{ (2.26)^2}[/tex]
[tex]{(2.35 \times 1.96)} {x^2}[/tex] = [tex]\dfrac{(4.06 \times 2.11)} { (2.26)^2}[/tex]
[tex]x^2[/tex] =[tex]\dfrac{(2.35 \times 1.96 \times (2.26)^2} {(4.06 \times 2.11)}[/tex]
[tex]x^2[/tex] = 2.450206485
x ≈ [tex]\sqrt{2.450206485[/tex]
x ≈ 1.566 pm
Therefore, the distance between charges of +2.35 and −1.96, should be approximately 1.566 picometers (pm).
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To find the distance between charges of +2.35 and -1.96 for the attractive force to be the same, use Coulomb's Law to calculate the force between charges of +4.06 and -2.11 separated by a distance of 2.26 pm. Then solve for the distance using the same formula and the calculated force value.
Explanation:To find the distance between charges of +2.35 and -1.96 for the attractive force to be the same as between charges of +4.06 and -2.11, we can use Coulomb's Law. The formula for calculating the force between two charges is F = k * (|q1 * q2| / (d^2)) where k is the proportionality constant and d is the distance between the charges.
First, we calculate the force between charges of +4.06 and -2.11. Let q1 = +4.06, q2 = -2.11, and d = 2.26 pm. Plugging these values into the formula, we get:
F = (1/47e) * (|4.06 * -2.11| / (2.26^2))
Next, we can find the distance between charges of +2.35 and -1.96 such that the attractive force is the same. Let q1 = +2.35, q2 = -1.96, and F = the value we calculated earlier. Rearranging the formula to solve for d, we get:
d = sqrt((|q1 * q2| / (F * k)))
Lenox ironed 1/4 of the shirts over the weekend. She plans to split the remainder of the work equally over the next 5 evenings.
Answers
3/20, or 0.15 of the shirts each evening
1 - 1/4 = 3/4
(3/4) / 5 = (3/4) / (5/1) = (3/4) x (1/5) = 3/20 = 0.15
The probability that Jinelle’s bus is on time is 2/3 , and the probability that Mr. Corney is driving the bus is 4/5. What is the probability that on any given day Jinelle’s bus is on time and Mr. Corney is the driver?
Answers
The probability that on any given day Jinelle’s bus is on time and Mr. Corney is the driver is (8/15).
What is probability?Probability is the chance of happening an event or incident.
Given, the probability that Jinelle’s bus is on time is 2/3.
The probability that Mr. Corney is driving the bus is 4/5.
Therefore, the probability that on any given day Jinelle’s bus is on time and Mr. Corney is the driver is:
= (2/3) × (4/5)
= (8/15)
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A book has a front and a back and 400 pages. The front and back cover are each 0.9mm thick measured to 1 decimal place. Each page is 0.13 mm thick measured to 2 decimal places. Calculate the minimum thickness of the book.
Answers
Answer:
The answer is actually 5.17 centimeters
Step-by-step explanation:
The question is asking you to calculate the minimum thickness so you have to find the lowest bounds.
The covers are 0.9 mm to 1 d.p so the minimum thickness is 0.85 because that is the lowest bound.
The pages are 0.13 mm to 2 d.p so the minimum thickness is 0.125 as that is the lowest bound.
0.85 x 2 = 1.7 and 0.125 x 400 = 50
50 + 1.7 = 51.7 which is the minimum length.
Final answer:
The minimum thickness of a book with 400 pages, each 0.13mm thick, and two covers, each 0.9mm thick, is calculated to be 53.8mm.
Explanation:
The minimum thickness of a book can be calculated by summing the thickness of the covers and all the pages. We are given that each cover is 0.9mm thick and each page is 0.13mm thick. To find the minimum thickness of the book, we multiply the thickness of each page by the total number of pages and then add the thicknesses of the front and back covers.
To calculate:
Thickness of all pages: 400 pages × 0.13 mm/page = 52 mm
Thickness of both covers: 2 covers × 0.9 mm/cover = 1.8 mm
Total minimum thickness: 52 mm + 1.8 mm = 53.8 mm
The minimum thickness of the book is therefore 53.8 mm.
find the missing value in the ratio table .
Answers
5 x 3 = 15, therefore, 3 x 3 = 9
because you multiplied 3 for 5, you will be doing the same for 3, which means 3 x 3
hope this helps
3/5 = 9/15 = 12/20...so ur missing number is 9
What is the greatest perfect square that is a factor of 396? Explain
Answers
Factors of 396 are: 1,2,3,4,6,9,11,12,18,22,33,36,44,66,99,132,198,396
Now we check which is the greatest perfect square in these.
396, 198, 132, 99, 66,44 are not perfect square,
so 36 is the largest perfect square from the factors of 396, 6 x 6 = 6² = 36
6× 532 expanded form
Answers
Find the x-intercept of the graph of the equation: x + 6y = 7
Answers
x + 6(0) = 7
x + 0 = 7
x = 7
so x intercept is (7,0)
What is the value of k? 0.5k+6=4k-8
Answers
6+8=4k-.5k
14=3.5k
So K=4
1 and 2/5(-3/5) in simplest form
Answers
Please help with homework (it's not 40 or 60) also please say how to work out if you can
Answers
How many 5-digit numbers (including leading 0s) are there with no digit appearing exactly two times?
Answers
30240 are 5-digit numbers (including leading 0s) are there with no digit appearing exactly two times
What is Number system?A number system is defined as a system of writing to express numbers.
By means of Permutation we solve this
The term permutation refers to a mathematical calculation of the number of ways a particular set can be arranged.
The formula for permutation is [tex]^{n}P_{r} =\frac{n!}{(n-r)!}[/tex]
n is total number of objects
r is number of objects selected
We need to find 5-digit numbers (including leading 0s) are there with no digit appearing exactly two times
¹⁰P₅=10!/(10-5)!
=10!/5!
=10×9×8×7×6×5!/5!
=30240
Hence, 30240 are 5-digit numbers (including leading 0s) are there with no digit appearing exactly two times
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How do I solve 9a-7=110
Answers
Please add 7 to both sides of the eqn, obtaining 9a = 117.
Solve for a by dividing both sides by 9: a = 117/9 = 13 (answer)
[tex]9a=110+7 [/tex]
[tex]9a=117 [/tex]
[tex]a= \dfrac{117}{9} [/tex]
[tex]a=13[/tex]
There are five shelves of video games in a video store. There are six video games on each shel. how many video games are there on the shelves?
Answers
Answer:
I think its 30 as well
Step-by-step explanation: