Perfect squares are the squares of integers
There are 990 integers between 50000 and 60000 that are squares of integers
There are 1000 perfect squares, and 100 perfect cubes between 1 and 1000000
This is because:
[tex]\mathbf{100000 = 1000^2 = 100^3}[/tex]
Rewrite as:
[tex]\mathbf{100000 = x^2 = y^3}[/tex]
Where x lies between 1 and 1000, and y lies between 1 and 100.
If y^3 is a perfect square, then y is a perfect square
List out the perfect squares from 1 to 1000
[tex]\mathbf{y = 1, 4, 9, 16, 25, 36, 49, 64, 81, 100}[/tex]
Take the cube of these numbers
[tex]\mathbf{y^3 = 1^3, 4^3, 9^3, 16^3, 25^3, 36^3, 49^3, 64^3, 81^3, 100^3}[/tex]
[tex]\mathbf{y^3 = 1, 64, 729, 4096, 15625, 46656, 117649, 262144, 531441, 1000000}[/tex]
So, the count of numbers that are perfect squares and perfect cubes between 1 and 1000000 is 10.
The count of integers between 50000 and 60000 that are squares of integers is:
[tex]\mathbf{n = x -10}[/tex]
Substitute 1000 for x
[tex]\mathbf{n = 1000 -10}[/tex]
[tex]\mathbf{n = 990}[/tex]
Hence, there are 990 integers between 50000 and 60000 that are squares of integers
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Please help me ASAP please I need help
Answer:
147°
Step-by-step explanation:
Solving for x
To make a straight line the angles have to have a sum of 190. So 180°-33° would equal 147°
Answer:
x = 147°
Step-by-step explanation:
A line is 180°
180 - 33 = 147
There are 12 girls and 8 boys in Ms. Crabapple's class. If 25% of the girls and 25% of the boys are going on a field trip to a nuclear power plant, what percent of the entire class is going on the field trip?
Answer:
25%
Step-by-step explanation:
25% of 12 is 3
25% of 8 is 2
5 people out of 20 people
5/20 = 25%
25% percent of the entire class is going on the field trip
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
There are 12 girls and 8 boys in Ms. Crabapple's class.
The total number of students
12+8=20
25% of the girls and 25% of the boys are going on a field trip to a nuclear power plant,
25% of the girls =0.25×12=3
25% of the boys =0.25×8=2
So the total number of students went to field trip
3+2=5
So out of 20 student, 5 students went to the field trip.
Which means 25% of the entire class is going on the field trip
Hence, 25% percent of the entire class is going on the field trip
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what number is its own opposite?
Answer:
0Step-by-step explanation:
what number is its own oppositie?
The number 0 is the only number that is its own opposite.
Hi! Can someone help me with this lab? It's 67% of my grade and I totally forgot to study for it.. It's only 4 questions but they count a lot!
Answer:
C. Transitive property of ≅Step-by-step explanation:
The statement #5 and #7 give an outcome of the statement #8:
ΔABG ~ ΔACF and ΔACF ~ ΔDCB ⇒ ΔABG ~ ΔDCBThis is called transitive property of congruence:
If one triangle is similar with another two, then the the other two triangles are similar to each otherCorrect choice is C
Answer:
C. Transitive property of congruence
Step-by-step explanation:
Transitive property of congruence means, if one pair of lines or angles or triangles are congruent to a third line or angle or triangle, then the first line or angle or triangle is congruent to the third line or angle or triangle.
Exit
Lin wants to bike of a mile. She has already biked of a mile. How much farther does she have to bike?
Simplify your answer.
what should be added to -1 to get 5/7
Pls answer thiss
Answer:
The answer is 12/7.
Step-by-step explanation:
To get the answer, simply subtract -1 to 5/7
[tex]\frac{5}{7} - (-1)\\[/tex]
Find the least common denominator.
[tex]\frac{5}{7} - (-1) = \frac{5}{7} - \frac{(-7)}{7}[/tex]
= 12/7
To check, add -1 to 12/7.
[tex]\frac{12}{7} + (-1)[/tex]
Find the least common denominator.
[tex]\frac{12}{7} + (-1) = \frac{12}{7} + \frac{(-7)}{7}[/tex]
= 5/7
right answer only plz and thank u
Answer:
[tex](x-1)^2(x+3)[/tex]
Step-by-step explanation:
For factorization the given expression you can use the Ruffini's rule.
First find the divisors of the independent term (these are the possible rational roots), in the given polynomial the independent term is [tex]3[/tex].
[tex]3 = \{\pm1,\pm3\}[/tex]
Now replace each number in the polynomial
[tex]P(1) = 1^3 + 1^2 - 5(1) + 3 = 0[/tex]
If the result is equal to 0 that's meaning that is a possible root of the polynomial. Then for know if is a root you have to divide the polynomial by [tex](x - \text{possible root})[/tex].
[tex](x^3 + x^2 -5x+3 )/ (x-1)[/tex]
In the first row are the coefficients of the given polynomial.
In the second row are the product between the coefficients and the independent term of the [tex]x-1[/tex].
The third row are the coefficients of the quotient polynomial (except the last that is the remainder).
[tex]\qquad 1\qquad 1\qquad-5\qquad \quad3\\1\qquad\qquad1\qquad \quad 2\qquad-3\\-------------\\ 0 \ \ \quad1 \qquad 2 \qquad -3 \qquad \quad 0[/tex]
Because the last term is the remainder and it's 0 you can factorizate [tex](x-1)[/tex] and the quotient polynomial is equal to
[tex]x^2 + 2x -3[/tex]
So our current expression is [tex](x-1)(x^2 + 2x -3)[/tex], however you can factorizate the quotient polynomial in:
[tex]x^2 +sx +rx +rs = x^2 + 3x -x + 3(-1) = (x + 3)(x -1)[/tex]
So the last expression is:
[tex](x-1)(x+3)(x-1) = (x-1)^2(x+3)[/tex]
pls help me i will mark as brilliant
Answer:
6
Step-by-step explanation:
[tex]45 \: min = 0.75 \: hour[/tex]
[tex]0.75 * 8 = 6 \: hours[/tex]
Please help
Solve.
(5√5)^−2x+1 = 1/5 ⋅ 125^x−3
Enter your answer in the box. Enter any fraction as a simplified fraction.
Step-by-step explanation: (5√5)−2x+1=
1
5
(125x)−3
0.008x+1=
1
5
(125x)−3
Step 1: Flip the equation.
1
5
(125x)−3=0.008x+1
Step 2: Add 3 to both sides.
1
5
(125x)−3+3=0.008x+1+3
1
5
(125x)=0.008x+4
Step 3: Divide both sides by 1/5.
1
5
(125x)
1
5
=
0.008x+4
1
5
125x=0.04x+20
The value of x is 46.
What are Exponents and power?Exponents and powers can be used to represent extremely big or extremely small numbers in a more straightforward fashion.
The number of times a number is multiplied by itself is defined by the exponent. The power is an expression that displays the same number or factor being multiplied repeatedly.
Given:
[tex](5\sqrt{5} )^{-2x+1 }= 1/5 * 125^{x-3}[/tex]
ow, using exponents and powers
[tex](5\sqrt{5} )^{-2x+1 }= 1/5 * 125^{x-3}[/tex]
[tex](5\sqrt{5} )^{-2x+1 }= 1/5 * 5 ^{3(x-3)\\[/tex]
[tex](5\sqrt{5} )^{-2x+1 }= 5^{3x - 9 - 1}[/tex]
[tex](5\sqrt{5} )^{-2x+1 }= 5^{3x -10}[/tex]
[tex]5^{3/2(-2x+ 1)}= 5^{3x - 10}[/tex]
[tex]5^{-x+ 3/2}= 5^{3x -10}[/tex]
Now, Comparing
-x+ 3/2 = 3x- 10
-x - 3x = -10 - 3/2
-4x = -23/2
x= 46
Hence, the value of x is 46.
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0.98x0.23 what is 0.98 times 0.23?
Answer:
0.2254
Step-by-step explanation:
multiply using long multuplication
These signs give information about two different towns.
Study these signs carefully. Then, answer the questions and complete the statements
about them below.
Use the drop-down menus to complete each statement.
Answer:
In which town does the total number have meaning?
Answer: Town B
For Town A, it does not, cannot, does not.
For Town B, does, can, does.
Please take a look at the picture.
Answer:
[tex]1 \frac{1}{12} [/tex]Step-by-step explanation:
Question:To find the value of b.Equation:[tex]b - \frac{7}{4} = - \frac{2}{3} [/tex]Solution :[tex] = > b - \frac{7}{4} = - \frac{2}{3} [/tex]
[tex] = > b = - \frac{2}{3} + \frac{7}{4} [/tex]
As when -7/4 goes on the other side becomes +7/4[tex] = > b = \frac{ - 8 + 21}{12} [/tex]
Simplification[tex] = > b = \frac{13}{12} \: or \: 1 \frac{1}{12} [/tex]
(Ans)right answers only plz and thank you
Answer:
letter A
Step-by-step explanation:
3x=0
x=0
x-2=0
x=2
2x+7=0
2x=-7
x=-7/2
Solve the equation for x:
x2 = 196
Answer: x= 1/196
Step-by-step explanation:
Graph the number on the number line.
Answer:
Step-by-step explanation:
can u take good picture
What is the answer =2^3(10-7)/3*7?
Answer:
the ansewer is 56
Step-by-step explanation:
by appling bodmas rule which means if such type of operation apper in one question we work it step by step first bracket then division next multiplication then addition finaly substruction 2^3(10-7)/3*7(10-7)=32^3(3)/3*73/3=12^3*1*72^3=88*1*7=8*7=56Use the Chain Rule to express the second derivative of f∘g in terms of the first and second derivatives of f and g.
The second derivative of the composition between two functions is described by the following expression:
[tex]\frac{d^{2}}{dx^{2}} (f\,\circ\,g\,(x)) = \frac{d^{2}f}{dg^{2}}\cdot \frac{dg}{dx} + \frac{df}{dg} \cdot \frac{d^{2}g}{dx^{2}}[/tex]
Mathematically speaking, a composition between two functions is defined by the following operation:
[tex]f\,\circ\,g\,(x) =f(g(x))[/tex] (1)
By Chain Rule we get the first and second derivatives of the composition:
First derivative
[tex]\frac{d}{dx} (f\,\circ\,g\,(x)) = \frac{df}{dg}\cdot \frac{dg}{dx}[/tex] (2)
Second derivative
[tex]\frac{d^{2}}{dx^{2}} (f\,\circ\,g\,(x)) = \frac{d^{2}f}{dg^{2}}\cdot \frac{dg}{dx} + \frac{df}{dg} \cdot \frac{d^{2}g}{dx^{2}}[/tex] (3)
The second derivative of the composition between two functions is described by the following expression:
[tex]\frac{d^{2}}{dx^{2}} (f\,\circ\,g\,(x)) = \frac{d^{2}f}{dg^{2}}\cdot \frac{dg}{dx} + \frac{df}{dg} \cdot \frac{d^{2}g}{dx^{2}}[/tex]
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Answer:
x = 10
Step-by-step explanation:
the unmarked angle in the triangle is the supplement to 6x - 7
180 - (6x - 7)
180 - 6x + 7
187 - 6x
The sum of the angles in a triangle is 180
therefor
(2x + 7) + 26 + (187 - 6x) = 180
Combine like terms
-4x + 220 = 180
Subtract 220 from both sides
-4x = -40
divide both sides by -4
x = 10
Please help me ASAP
Step-by-step explanation:
a= 3×(-2)+3=-6+3=3
b=3×(-1)+3=-3+3=0
c=3×1+3=3+3=6
d=2×3+3=6+3=9
-------------------------
a=3, b=0, c=6, d=9
Good work!
Katie is 1.83 m tall. George is 9 cm shorter than Katie. How tall is George?
Give your answer in cm
Answer:
174 cm
Step-by-step explanation:
1.83 m to cm is 183.
So, 183 cm - 9 cm = 174cm
Hope you understand ^^
Answer:
174 cm
Step-by-step explanation:
1 meter is equal to 100 centimeter so 1.83m times 100 is equal to 183cm. so 183 cm-9cm=174 cm
How much money was invested at 5% annual simple interest for 4 years to earn $2870?
Answer:
Principal (amount invested) = $14,350
Step-by-step explanation:
Given the simple interest amount of $2,870 earned in 4 years at 5% interest rate:
In order to find the principal amount that was invested, we could use the simple interest formula and isolate the variable, P, algebraically.
I = P × r × t
where:
I = interest earned = $2,870
P = principal amount invested = ?
r = interest rate = 5% or 0.05
t = time = 4
Divide both sides by (r × t ) to isolate P :
[tex]\displaystyle\mathsf{\frac{I}{(r\:\times\:t)}\:=\:\frac{P\:\times\:r\:\times\:t}{(r\:\times\:t)}}[/tex]
[tex]\displaystyle\mathsf{P\:=\frac{I}{(r\:\times\:t)}}[/tex]
Substitute the given values into the formula for P:
[tex]\displaystyle\mathsf{P\:=\frac{I}{(r\:\times\:t)}\:=\:\frac{2870}{0.05\:\times\:4}}[/tex]
[tex]\displaystyle\mathsf{P\:=\frac{2870}{0.20}=14,350}[/tex]
Therefore, the principal amount invested is $14,350.
What is the value of x?
14(6x−2)=x−2
A)-3
B)2
C)-7
D)-9
14(6x-2)=x-2
84x-28=x-2
84x-x= 28-2
83x = 26
x = 26/83
there are no corect answer below
ok done. Thank to me :>
7.
V= lwh for w
What’s the explanation
Answer:
w=[tex]\frac{V}{lh}[/tex]
Step-by-step explanation:
just divide lh from both sides
Anyone able to help with this?
[tex]W = 23.7°[/tex]
Step-by-step explanation:
The formula given is the statement of Snell's law of refraction. We are given the following:
[tex]I_a = 1.0003[/tex]
[tex]I_w = 1.3[/tex]
[tex]A = 31.5°[/tex]
So we need to find the angle of refraction W. Starting with Snell's law,
[tex]\dfrac{I_w}{I_a} = \dfrac{\sin A}{\sin W} \Rightarrow \sin W = \left(\dfrac{I_a}{I_w}\right)\sin A[/tex]
Plugging in the given values, we get
[tex]\sin W = \left(\dfrac{1.0003}{1.3}\right)\sin{31.5°} = 0.402[/tex]
Solving for the angle W, we then get
[tex]W = \sin^{-1}(0.402) = 23.7°[/tex]
can anyone solve this step by step for me
Answer:
0.5 ㏑ | 1-2x | +c
Step-by-step explanation:
Formula: ∫ 1/ax+b dx = 1/a ln Iax+bI +c
Ramon Escalante purchases a digital camera for $399.99 in Omaha Nebraska, where the sales tax rate is 5.75 percent
A. what is the sales tax?
B. what is the total purchase price?
Answer:
[tex] \: [/tex]
A. The sales tax will be $ 22.999425
so, the sales tax » $ 23
5.75 % of $ 399.99
B. The Total Purchase will be →
$ ( 399.99 + 22.999425 ) $ 422.989425or
$(23 + 399.99) $ 422.99HELP ME PLEASE !!!!!!!!
What is 20% of $1575.00
step:
20% = 20/100
of = ×
20/100 × $1575.00
answer : $315
Step:
20% = 20/100
of = ×
20/100 × $1575.00
Answer : $315
A single card is drawn at random from a standard 52 card deck. Work out the following probabilities in their simplest form: P(4)= P(not 4)=
Answer:
Step-by-step explanation:
Total Number of possible outcomes = 52
Getting a jack from a deck of 52 cards for a certain event (A) = 4
The Probability (A) = 4/ 52
= 1 / 13 = 0.07
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you have to estimate I need help please