Answers
Related Questions
Simplify the expression 3 1/3/3 1/3. Explain how the expression and its simplified form show that the set of irrational numbers is not closed under division
Answers
From the context, I assume it to mean
(3^(1/3)) / (3^(1/3)) = 1
Since 3^(1/3) is the cube-root of 3, and is thus irrational.
However, the quotient is exactly 1, which is a rational number.
The example is therefore a counter-example for the statement that "set of irrational numbers is closed under division", or stated differently,
"the set of irrational numbers is not closed under division"
I have 5 digits. My 4s are worth 4 [10,000s] and 4 * 10. One of my 3s is worth 3,000. The other is worth 1/10 as much. My other digit is a 2. What number am I?
Answers
4(10,000) + 4(10) + 3,000 + 3,000(1/10) + 2 = 43,342
Thus, the 5-digit number is 43,342.
The sample variance is 18.7. what is the sample standard deviation? answer to two decimal places.
Answers
What is the value of x?
6 + 8x
-------------- = 5x
2
A) -2
B) -1
C) 1/3
D) 3
Answers
Rational numbers are _____ natural numbers.
always
sometimes
never
Answers
There are 60 minutes in 1 hour. What fraction of an hour is 4 minutes? Write your answer in lowest terms.
Answers
Divide the numerator and denominator by 4
1/15
Final answer: 1/15
The fraction of an hour is 4 minutes in lowest terms is 1/15.
What fraction of an hour is 4 minutes in lowest terms?To find the fraction of an hour that 4 minutes represents, we need to compare the number of minutes to the total number of minutes in an hour, which is 60.
We can set up a fraction where the numerator represents the number of minutes we want to find the fraction for (4 minutes) and the denominator represents the total number of minutes in an hour (60 minutes).
So, the fraction can be written as 4/60.
To simplify the fraction to its lowest terms, we can divide both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 4 and 60 is 4.
Dividing both the numerator and denominator by 4, we get:
4/60 = (4 ÷ 4) / (60 ÷ 4) = 1/15.
Therefore, 4 minutes in lowest terms is equal to 1/15th of an hour.
Read more about lowest terms here: https://brainly.com/question/28635285
#SPJ2
Which of the following is a true equation?
1) 10 + 3 + 1 = 13 + 6
2) 4 - 3 = 7
3) 4 + 3 - 3 = 7 - 3
4) 4 + 3 = 7 + 3
Answers
4 = 4
answer
3) 4 + 3 - 3 = 7 - 3
domain of the function
Answers
y exist : x+6 ≥ 0
x ≥ -6
You want to replace the countertops in a kitchen. One counter measures 24 inches by 6 feet. The other is 30 inches by 4 feet. If the new countertop costs $42.00 per square foot, what will be the cost of the new top?
Answers
2 ft x 6 ft=12 square feet
2.5 ft x 4 ft=10 square feet
Total square feet of the counter is 22 square feet.
To find the total cost, just multiply the area by the cost per square foot.
$42 x 22=$924
Answer:
The cost of the new top $924.
Step-by-step explanation:
You want to replace the counter-tops in a kitchen.
The dimensions of the first counter is 24 inches by 6 feet.
i.e [tex]24 \text{ inch} \times 6 \text{ feet}[/tex]
or [tex]2\text{ feet} \times 6 \text{ feet}[/tex]
As 1 feet =12 inches
Hence the area of the counter is [tex]2\times 6=12\text{ feet}^2[/tex]
The dimensions of the second counter is 30 inches by 4 feet.
i.e [tex]30 \text{ inch} \times 4 \text{ feet}[/tex]
or [tex]2.5\text{ feet} \times 4 \text{ feet}[/tex]
Hence the area of the counter is [tex]2.5\times 4=10\text{ feet}^2[/tex]
Hence, the total area will be [tex]12+10=22 \text{ feet}^2[/tex]
The unit cost of the counter-top is [tex]\$42.00\text{ feet}^2[/tex]
So the net cost will be,
[tex]=42\times 22=\$924[/tex]
Which of the following equations is of a parabola with a vertex at (0, 3)?
y = (x - 3) 2
y = (x + 3) 2
y = x 2 - 3
y = x 2 + 3
Answers
Answer:
Option D.
Step-by-step explanation:
We have to find the equation of the parabola which has vertex at ( 0,3 )
If we write the equation of a parabola in the vertex from then we will write
y = ( x - h )² + (k)²
In this equation ( h, k) will be the vertex.
(a) y = (x-3)² + 0
so ( 3,0) will be the vertex
(b) y = ( x+3)² + 0
or y = [x - (-3)]² + 0
then ( -3,0) will be the vertex
(c) y = (x² - 3)
y = ( x-0 )² + (-3)
then ( 0, -3) is the vertex.
(d) y = x² + 3
y = ( x-0 )² + 3
Then ( 0, 3 ) will be the vertex of this parabola.
Option D. is the answer.
The following formula relates three quantities force mass and acccelerations
F=ma
Answers
Find the range of the graphed function?
Answers
B is true
B is the correct answer
Express each repeating decimal as a fraction.
1.
1.8[4]
2.
2.1[26]
Answers
1.8444444....=1.8+1/10*0.44444....
=1.8+1/10*4/9
=1.8+4/90
=162/90+4/90
=166/90
=83/45
2.126262626...=2.1+1/10*0.262626...
=2.1+1/10*26/99
=2.1+26/990
=2079/990+26/990
=2105/990
=421/198
Answer:
1.8444444....=1.8+1/10*0.44444....
=1.8+1/10*4/9
=1.8+4/90
=162/90+4/90
=166/90
=83/45
2.126262626...=2.1+1/10*0.262626...
=2.1+1/10*26/99
=2.1+26/990
=2079/990+26/990
=2105/990
=421/198
Tyquan uses the greatest common factor and the distributive property to rewrite this sum: 75 + 60 What expression does Tyquan write? 3(25 + 20) 5(15 + 12) 25(3 + 60) 15(5 + 4)
Answers
75/15 = 5
60/15 = 4
so ur expression is : 15(5 + 4) <==
Jacks has 18 marbles,he loses 6 of them.
What fraction of the marbles does he lose?
Answers
1/3
Hope this helps!
Distributive property of 68/4
Answers
The trick here is to rewrite 68 as 4(17).
write 4 hundred-thousand, 13 thousand, 11 hundreds, 4 ones in standard form
Answers
The standard form of the expression 4 hundred-thousand, 13 thousand, 11 hundreds, 4 ones is [tex]4.14104 \times10^5[/tex]
In order to write 4 hundred-thousand, 13 thousand, 11 hundreds, 4 ones in standard form, let us write each of the expressions in figures
4 hundred-thousand = 400,000
13 thousand = 13,000
11 hundreds = 11 x 100
11 hundreds = 1100
4 ones = 4 x 1
4 ones = 4
The next step is to sum up all the figures together
400000 + 13000 + 1100 + 4 = 414,104
Convert 414104 to standard form
[tex]414104 = 4.14104 \times10^5[/tex]
Therefore, the standard form of the expression 4 hundred-thousand, 13 thousand, 11 hundreds, 4 ones is [tex]4.14104 \times10^5[/tex]
Learn more here: https://brainly.com/question/19169731
which
of the following is the least?
A.0.105
B.0.501
c.o.015
D.0.15
Answers
what is (9x^4-x^2y^2-5y^4)-(3x^4+2x^2y^2-7y^4)
Answers
9x⁴ - x²y² - 5y⁴ - 3x⁴ - 2x²y² + 7y⁴
6x⁴ - 3x²y² + 2y⁴
How many pairs of whole numbers have a sum of 99
Answers
Between two tenths of a mile will the second relay exchange occur? Explain.
Answers
2/10
There is one tenth in a mile. I have the same question. But I am just guessing.
Use the function below to find f(4).
Answers
f(4) = 1/3 * 4^4
f(4) = 1/3 * 256
f(4) = 256/3 <===
Answer: The correct option is (C) [tex]\dfrac{256}{3}.[/tex]
Step-by-step explanation: The given function is
[tex]f(x)=\dfrac{1}{3}\times 4^x.[/tex]
We are to find the value of f(4).
To find the value of f(4), we need to substitute the value of x as 4 in the given definition of function f(x).
Substituting x = 4 in f(x), we have
[tex]f(4)=\dfrac{1}{3}\times 4^4=\dfrac{1}{3}\times 256=\dfrac{256}{3}.[/tex]
Therefore, the value of f(4) is [tex]\dfrac{256}{3}.[/tex]
Option (C) is correct.
Find the equation in standard form of the line with slope
[tex] \frac{7}{2} [/tex] that passes through the point (5,7)
Please explain as well
Answers
There are six different sixth roots of 64. That is, there are six complex numbers that solve x^6=64
Please help
Answers
1)
When we know that:
[tex]\sqrt[n]{z}=\sqrt[n]{|z|}\Big(\cos\frac{\phi+2k\pi}{n}+i\sin\frac{\phi+2k\pi}{n}\Big)\qquad\text{for}\quad k=0,1,\ldots,n-1[/tex]
when [tex]z=|z|(\cos\phi+i\sin\phi)[/tex]
then:
[tex]x^6=64\quad|\sqrt[6]{(\ldots)}\\\\x=\sqrt[6]{64}[/tex]
For [tex]x=64[/tex] we have:
[tex]64=|64|(\cos0+i\sin0)\quad\Rightarrow\quad \phi=0[/tex]
and:
[tex]\sqrt[6]{64}=\sqrt[6]{64}\Big(\cos\frac{0+2k\pi}{6}+i\sin\frac{0+2k\pi}{6}\Big)\qquad\text{for}\quad k=0,1,\ldots,5\\\\\\ \sqrt[6]{64}=2\Big(\cos\frac{k\pi}{3}+i\sin\frac{k\pi}{3}\Big)\qquad\text{for}\quad k=0,1,\ldots,5 [/tex]
k = 0
[tex]2\Big(\cos\frac{0}{3}+i\sin\frac{0}{3}\Big)=2(1+0i)=2\cdot1=\boxed{2}[/tex]
k = 1
[tex]2\Big(\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\Big)=2\Big(\frac{1}{2}+i\frac{\sqrt{3}}{2}\Big)=\boxed{1+i\sqrt{3}}[/tex]
k = 2
[tex]2\Big(\cos\frac{2\pi}{3}+i\sin\frac{2\pi}{3}\Big)=2\Big(-\frac{1}{2}+i\frac{\sqrt{3}}{2}\Big)=\boxed{-1+i\sqrt{3}}[/tex]
k = 3
[tex]2\Big(\cos\frac{3\pi}{3}+i\sin\frac{3\pi}{3}\Big)=2\Big(\cos\pi+i\sin\pi\Big)=2(-1+0i)=\boxed{-2}[/tex]
k = 4
[tex]2\Big(\cos\frac{4\pi}{3}+i\sin\frac{4\pi}{3}\Big)=2\Big(-\frac{1}{2}-i\frac{\sqrt{3}}{2}\Big)=\boxed{-1-i\sqrt{3}}[/tex]
k = 5
[tex]2\Big(\cos\frac{5\pi}{3}+i\sin\frac{5\pi}{3}\Big)=2\Big(\frac{1}{2}-i\frac{\sqrt{3}}{2}\Big)=\boxed{1-i\sqrt{3}}[/tex]
So the answer is:
[tex]x=\{2,\,1+i\sqrt{3},\,-1+i\sqrt{3},\,-2,\,-1-i\sqrt{3},\,1-i\sqrt{3}\}[/tex]
2)
We don't know method (1). If so, we could use following identities:
[tex](1)\quad a^2-b^2=(a+b)(a-b)\\\\(2)\quad a^3-b^3=(a-b)(a^2+ab+b^2)\\\\(3)\quad a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]
There will be:
[tex]x^6=64\\\\x^6-64=0\\\\(x^3)^2-8^2=0 \qquad\text{from (1)}\\\\(x^3+8)(x^3-8)=0\\\\(x^3+2^3)(x^3-2^3)=0\qquad\text{from (2) and (3)}\\\\ (x+2)(x^2-2x+4)(x-2)(x^2+2x+4)=0\qquad(\star)[/tex]
Now, we complete the square for:
[tex]x^2-2x+4=x^2-2x+1+3=(x^2-2x+1)+3=(x-1)^2+3=\\\\=(x-1)^2+(\sqrt{3})^2=(x-1)^2-(-1)(\sqrt{3})^2=(x-1)^2-i^2(\sqrt{3})^2=\\\\=(x-1)^2-(i\sqrt{3})^2=\text{from (1)}=\boxed{(x-1-i\sqrt{3})(x-1+i\sqrt{3})}[/tex]
and for:
[tex]x^2+2x+4=x^2-2x+1+3=(x^2+2x+1)+3=(x+1)^2+3=\\\\=(x+1)^2+(\sqrt{3})^2=(x+1)^2-(-1)(\sqrt{3})^2=(x+1)^2-i^2(\sqrt{3})^2=\\\\=(x+1)^2-(i\sqrt{3})^2=\text{from (1)}=\boxed{(x+1-i\sqrt{3})(x+1+i\sqrt{3})}[/tex]
When we return to [tex](\star)[/tex]:
[tex](x+2)(x^2-2x+4)(x-2)(x^2+2x+4)=0\\\\(x+2)(x-1-i\sqrt{3})(x-1+i\sqrt{3})(x-2)(x+1-i\sqrt{3})(x+1+i\sqrt{3})=\\=0[/tex]
And we have answer:
[tex]x=\{-2,\,1+i\sqrt{3},\,1-i\sqrt{3},\,2,\,-1+i\sqrt{3},\,-1-i\sqrt{3}\} [/tex]
To find the six sixth roots of 64, you can use polar form and De Moivre's Theorem to calculate the complex numbers. The roots are 2, 1+i√3, -1+i√3, -2, -1-i√3, and 1-i√3.
[tex]X^6 = 64[/tex]
The sixth roots of 64 are complex numbers and can be found by writing 64 in polar form and applying De Moivre's Theorem. Let's find the six roots:
First root: 2(cos(0) + i sin(0)) = 2
Second root: 2(cos(π/3) + i sin(π/3)) = 2(1/2 + i√3/2) = 1 + i√3
Third root: 2(cos(2π/3) + i sin(2π/3)) = 2(-1/2 + i√3/2) = -1 + i√3
Fourth root: -2
Fifth root: -2(cos(-π/3) + i sin(-π/3)) = -2(1/2 - i√3/2) = -1 - i√3
Sixth root: -2(cos(-2π/3) + i sin(-2π/3)) = -2(-1/2 - i√3/2) = 1 - i√3
Express the area of each square below as a monomial
14g5h9
Answers
So, the resulting expression is found using the properties of the power.
=> (14)^2 (g^5)^2 (h^9)^2 = 196 g^10 h^18.
Answer: 196 g^10 h^18
Solve For L: A = L ⋅ W ⋅ H
L=aw/h
L=wh/a
L=a/wh
L=w/ha
Answers
A=L*WH
[tex] \frac{A}{WH} [/tex]=L
So you answer would be: C
The tensile strength of paper is modeled by a normal distribution with a mean of 35 pounds per square inch and a standard deviation of 2 pounds per square inch. what is the probability that the strength of a sample is less than 38 lb/in2? round your answer to 4 decimal places.
Answers
mean=35 psi
std dev=2 psi
distribution normal
For probability that X<38,
calculate
Z score = (X-mean)/std dev
=(38-35)/2=1.5
P(X<38)
=P(Z<1.5)
=0.9331928 from tables.
So probability that the strength of a random sample <38 pis = 0.9332
one positive integer is 5 less than another. the product of the two integers is 36. what are the integers?
Answers
x(x-5)=36
x^2-5x-36=0
solving the equation we get
x=9 and x= -4
now find out the integers
1st number = x
2nd number = x-5
x*(x-5) = 36
x^2-5x =36
x^2 -5x-36 = 0
factor the polynomial:
(x-9) (x+4)
9-9 = 0, -4 +4 = 0
so x = 9 or -4
the question states a positive number
so x = 9
the 2 numbers are 9 and 4
What is 8.038×108 in standard form?
80,308,000
80,380,000
83,800,000
803,800,000
Answers
Answer:
803,800,000
Step-by-step explanation:
8.038×10^8 in standard form
To get standard form we multiply the decimal number by 10^8
10^8 is 100000000
Now we multiply
8.038×100000000
Move the decimal number 3 places to the right and add 5 more zeros
803800000
So the standard form of the given expression is
803,800,000
pls I help I need answers and work shown
Answers
0.30 as a fraction is 30/100 = 3/10
0.30 as a percent = 0.30 * 100 = 30%
answer is D. 3/10 and 30%
.30 is .3
do .30 divided by 1 and you get 3/10
Percentage= move the decimal 2 places to the right and you get 30%
So your answer is D.