=========================================================
Explanation:
Let x = 0.370370370...
The "370" block repeats forever, due to the horizontal bar up top.
Multiply both sides by 1000 so that the decimal point moves three spots to the right.
x = 0.370370370...
1000x = 1000*0.370370370...
1000x = 370.370370370...
Then notice both x and 1000x involve the *exact* same decimal string of "370" repeating forever. This perfect match lets us cancel the decimal portions out when we subtract, and allows us to isolate x to get some fraction of integers.
1000x - x = 370.370370370... - 0.370370370...
999x = 370
x = 370/999
You can use your calculator to confirm that 370/999 = 0.370370370...
----------------
In fact, you can use your calculator to determine the following:
A) 37/100 = 0.37
B) 370/999 = 0.370370370...
C) 37/99 = 0.373737...
D) 37/9 = 4.1111111....
This allows us to see fairly quickly that choice B is the final answer and that we can rule out the others.
----------------
Side note: your calculator may round the last digit by mistake.
Suppose that two lines, AB and CD, are intersected by a transversal.
Which of the following reasons alone could be used to show that the lines are parallel?
Answer: A, B
Step-by-step explanation:
A and B are unique to parallel lines, C and D are not.
Find an equation equivalent to 2x 3y = 6 in polar coordinates.
Type the correct answer, PLS HELP ASAP, I AM GIVING BRAINLIEST FOR THE CORRECT ANSWER!!!!
Answer:
x = 3
Step-by-step explanation:
3^3 = 4(3) + 15 = 27
AB||CD . Find the value of x.
A. 25
B. 45
C. 15
D. 10
Answer:
The value of x is 10.
3x+15=5x-5
3x=5x-5-15
3x=5x-20
3x-5x=(-20)
(-2x)=(-20)
x=10
Can someone please explain this to me very detailed I don’t understand it. Please
Answer:
a140 b10
Step-by-step explanation:
a x(all the pupil)×25%=35
x=140
b. 16:y=40:25
y=16×25/40=20
the cost of 3 7/9m cloth is rs 212 4/5.find the cost of
7 2/3m cloth.
Answer:
[tex]\sf Rs. \ 431\dfrac{73}{85} \quad or \quad Rs. \ 431.86[/tex]
Find the unit rate:
[tex]\rightarrow \sf 3\dfrac{7}{9} m = Rs. \ 212\dfrac{4}{5}[/tex]
[tex]\rightarrow \sf 1 m = Rs. \ \dfrac{212\dfrac{4}{5}}{3\dfrac{7}{9} }[/tex]
[tex]\rightarrow \sf 1 m = Rs. \ \dfrac{4788}{85} \quad or \quad Rs. \ 56\dfrac{28}{85}[/tex]
Then find the cost of 7 2/3m cloth:
[tex]\rightarrow \sf 7\dfrac{2}{3} \ m = Rs. \ \dfrac{4788}{85} \ * \ 7\dfrac{2}{3}[/tex]
[tex]\rightarrow \sf 7\dfrac{2}{3} \ m = Rs. \ \dfrac{36708}{85}[/tex]
[tex]\rightarrow \sf 7 \dfrac{2}{3} \ m = Rs. \ 431\dfrac{73}{85} \quad or \quad Rs. \ 431.86[/tex]
6) three fourth of cars in a showroom are land rover , one half of land rover are black. what fraction of land rover are black?
Answer:
3/8
Step-by-step explanation:
(3/4)/2=3/8
What is the exact area of a circle having diameter 3 in.?
Answer:
7.065 in^2
Step-by-step explanation:
Answer:
7.06858...in²
if we are using 3.14
7.065in²
Step-by-step explanation:
3 / 2 = 1.5
A = πr²
A = π(1.5²)
A = π(2.25)
A = 7.068in²
(if we are using 3.14 for pi)
A = πr²
A = 3.14(1.5²)
A = 3.14(2.25)
A = 7.065in²
due to a leakage 30% of the water was lost from a water tank if only 340 litres of the water is left in the tank now find out the total capacity of the water tank
Answer:
1133.3 liters of water after leakage.
Step-by-step explanation:
x*.30=340
x=340/.30
x=1133.33
Use long division to find the quotient 1234 and 19. What is the remainder?
18
6
13
9
Answer:
18
Step-by-step explanation:
science 19 does not fit into 12, you would do 123/19 and the closes would be 19*6 which would get you 114 then you do 123-114 which is 9 then you bring down the 4 then it would be come 94 then you do 19*4 which would be 76 then you subtract 94 by 76 which would get you 18 and with nothing left you bring down, the remainder would be 18
2. Write each of the following in set builder form. A = [5, 10, 15,20]
Answer:
A={x:x is a multiple of five }
bag contains eight red marbles and
seven blue marbles. You randomly pick a
marble and then pick a second marble
without returning the marbles to the bag.
The first marble is red and the second
marble is blue.
The probability of getting first marble is red and the second
marble is blue is 4/15.
What is probability?
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes.
Given that:
Number of red marbles= 8
Number of blue marbles= 7
Total Number of marbles= 8+7 = 15 marbles.
P(red Marble) =[tex]\frac{8}{15}[/tex]
No replacement, now the total marbles = 14
P( blue marbles) = 7/14
Now, P( first marble is red and the second marble is blue.)
= 8/15*7/14
= 4/15
Hence, the probability of getting first marble is red and the second
marble is blue is 4/15.
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Which 3-D object is a polyhedron?
A. sphere
B. cube
C. cone
Answer:
The answer is A.
Step-by-step explanation:
A polyhedron is a three-dimensional solid made up of polygons. It has flat faces, straight edges, and vertices. For example, a cube, prism, or pyramid are polyhedrons.
Lea and adam are selling cheesecakes for a school fundraiser. customers can by new york cheesecakes and chocolate marble cheesecakes. lea sold 14 new york cheesecakes and 11 chocolate marble cheesecakes for a total of $293. adam sold 7 new york cheesecakes and 2 chocolate marble cheesecakes for a total of $80. what was the cost for one chocolate marble cheesecake?
Answer: $19
Step-by-step explanation:
We will set up equations to solve and pull the information we need from the given passage. Let x be new york cheesecakes and y be chocolate marble.
Lea sold 14 new york and 11 chocolate marble. She made $293 total.
14x + 11y = 293
Adam sold 7 new york and 2 chocolate marble for $80 total.
7x + 2y = 80
Now I will graph the two equations. The y-coordinate in the point of intersection is the solution is the answer to your question.
(6, 19)
$19
The cost for one chocolate marble cheesecake is $19.
Consider the diagram.
2 triangles are connected at their hypotenuse to form a rectangle. The rectangle has a length of 7 meters and width of 6 meters.
Mia plans to build a fence to divide her rectangular garden into two triangular areas. Use the diagram to find the length of fence she will need to divide the garden. Round up to the nearest hundredth.
Mia will need a fence that is
meters long.
The length of fence she will need to divide the garden is 9.22 m.
What is a Rectangle?A Rectangle is a quadrilateral having four sides and four right angles in which both sides are parallel and opposite to each other.
Pythagoras TheoremThe Pythagorean Theorem states that the sum of the squared sides of a right triangle equals the length of the hypotenuse squared.
Let us consider the length of the fence be 'x'
Using Pythagoras Theorem,
x² = 6² + 7²
[tex]x^{2} =36+49\\x^{2} = 85[/tex]
x = 9.22 m
So, the length of fence is 9.22 m.
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Answer:
9.22
Step-by-step explanation:
edge
Grace is an hourly employee
Answer:
full question Grace is an hourly employee, and the line that models her total pay in dollars
as it relates to the number of hours she has worked has a slope of 45 and a y
intercept of 35. Which statement is true?
A. Grace's wage is $35 an hour, and it appears that she received a
signing bonus of $45.
B. Grace's wage is $35 an hour, but it appears that she received no
signing bonus.
C. Grace's wage is $45 an hour, and it appears that she received a
signing bonus of $35.
D. Grace's wage is $45 an hour, but it appears that she received no
signing bonus.
Step-by-step explanation:
if x is the amount of hours worked, 45 is the slope and the y intercept is 35.
A linear equation has the form of y = ax + b, where a is the slope and b is the y-intercept, then the equation that we have is:
y = 45*x + 35
this means that she wins $45 per hour, and has a plane amount of $35, indiferent of the amount of hours worked.
Then the correct answer is
C) Grace's wage is $45 an hour, and it appears that she received a signing bonus of $35.
Answer:
wow........mmm.................
plspls help i will give u brainliest!!!! answer questions correctly please.
17-(-5)=
(-12)+(-6)=
8(-5)=
-72 divided by (-9)=
1/9+3/8
-2 1/2+(-5 3/4)
3 2/3-1 5/6
-4/5-2/3
-3 1/4 x 2 2/3
-5/9 x -2/9
1 7/8 divided by 3
-1/3 divided by 7/8
you will get brainliest please give right answers i need a good grade in this!!
i only have 11 points im sorry
but you will get the best rating and brainliest
What is the mode of the following numbers?
6, 4, 1, 9, 3, 8, 3, 5, 10
Explanation:
The mode is the most frequent number. It is the number that shows up the most.
Sorting the values gets us {1, 3, 3, 4, 5, 6, 8, 9, 10} in which we can see that "3" shows up twice, which is the most compared to any other value. Therefore the mode is 3.
Prove the following tan^2 A/(tan A -1 )+ cot A/(1 - tan A)=1 +sec A cosec A
In Image, Question is No.4 (vi)
See below for the proof of the trigonometry identity [tex]\frac{\tan^2(A)}{\tan(A) - 1} + \frac{\cot(A)}{1 - \tan(A)} =1 + \sec(A)\csc(A)[/tex]
How to prove the trigonometry identity?The trigonometry equation is given as:
[tex]\frac{\tan^2(A)}{\tan(A) - 1} + \frac{\cot(A)}{1 - \tan(A)} =1 + \sec(A)\csc(A)[/tex]
Rewrite the equation as:
[tex]\frac{\tan^2(A) }{\tan(A) - 1} - \frac{\cot(A)}{ \tan(A) - 1} =1 + \sec(A)\csc(A)[/tex]
Take LCM
[tex]\frac{\tan^2(A) - \cot(A)}{ \tan(A) - 1} =1 + \sec(A)\csc(A)[/tex]
Express cot(A) as 1/tan(A)
[tex]\frac{\tan^2(A) - \frac{1}{\tan(A)}}{ \tan(A) - 1} =1 + \sec(A)\csc(A)[/tex]
Take LCM
[tex]\frac{\tan^3(A) - 1}{\tan(A)(\tan(A) - 1)} =1 + \sec(A)\csc(A)[/tex]
Apply the difference of two cubes on the numerator
[tex]\frac{(\tan(A) - 1)(\tan^2(A) + \tan(A) + 1)}{\tan(A)(\tan(A) - 1)} =1 + \sec(A)\csc(A)[/tex]
Cancel out the common factors
[tex]\frac{\tan^2(A) + \tan(A) + 1}{\tan(A)} =1 + \sec(A)\csc(A)[/tex]
Rewrite as:
[tex]\frac{\tan(A) + \tan^2(A) + 1}{\tan(A)} =1 + \sec(A)\csc(A)[/tex]
Split the fraction
[tex]1 + \frac{\tan^2(A) + 1}{\tan(A)} =1 + \sec(A)\csc(A)[/tex]
Express [tex]\tan^2(A) + 1[/tex] as [tex]\sec^2(A)[/tex]
[tex]1 + \frac{sec^2(A)}{\tan(A)} =1 + \sec(A)\csc(A)[/tex]
Divide [tex]\sec^2(A)[/tex] by [tex]\tan(A)[/tex]
[tex]1 + \frac{1}{\sin(A)\cos(A)} = 1 + \sec(A)\csc(A)[/tex]
Take the inverse of sin and cosine
[tex]1 + \sec(A)\csc(A) = 1 + \sec(A)\csc(A)[/tex]
Both sides of the equation are the same.
Hence, the trigonometry identity [tex]\frac{\tan^2(A)}{\tan(A) - 1} + \frac{\cot(A)}{1 - \tan(A)} =1 + \sec(A)\csc(A)[/tex] has been proved
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solve the equation b/4+2=-1.
b=
Answer:
[tex] \frac{b}{4} + 2 = - 1[/tex]
[tex] \frac{b}{4} = - 1 - 2[/tex]
[tex] \frac{b}{4 } = - 3[/tex]
[tex]b = - 3 \times 4[/tex]
[tex]b = - 12[/tex]
hope this helps you!!
The answer is -12
What is the solution to a linear equation?The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.
Given here: The equation b/4 +2 = -1
b=-12
Hence, The answer is -12
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(PLEASE HELP) What are the values of a and b that make this equation have solutions of {3, -2}? (x + a)(x + b) = 0
Answer:
x = -a or x = -b
Step-by-step explanation :
What is the volume of a sphere with a diameter of 8.6 m, rounded to the nearest
tenth of a cubic meter?
Please help me with these questions. Thank you.
Answer:
36 x⁸y⁶
√2/2
Step-by-step explanation:
Factor 1296 into its prime factors
1296 = 24 • 34
To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent.
Factors which will be extracted are :
1296 = 24 • 34
No factors remain inside the root !!
To complete this part of the simplification we take the squre root of the factors which are to be extracted. We do this by dividing their exponents by 2 :
36 = 22 • 32
At the end of this step the partly simplified SQRT looks like this:
36 √(x¹⁶y¹²)
STEP2:Simplify the Variable part of the SQRT
Rules for simplifing variables which may be raised to a power:
(1) variables with no exponent stay inside the radical
(2) variables raised to power 1 or (-1) stay inside the radical
(3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:
√(x⁸)=x⁴
√(x^-6)=x^-3
Applying these rules to our case we find out that
SQRT(x¹⁶y¹²) = x⁸y⁶
Combine both simplifications
sqrt (1296x¹⁶y¹²) = 36 x⁸y⁶
Simplified Root : 36 x⁸y⁶
number 2)
3√2/3√4=
=3√2/3×2
=3√2/6
=3√2/6 ×3/3
=1√2/2
=√2/2
If sin = 2/5, what is csc ? (Answer must be in fraction form)
Answer:
csc x = [tex]\frac{5}{2}[/tex]
Step-by-step explanation:
using the identity
csc x = [tex]\frac{1}{sinx}[/tex]
then
csc x = [tex]\frac{1}{\frac{2}{5} }[/tex] = [tex]\frac{5}{2}[/tex]
(a) A farmer has x apple trees which produce 25 kg of apples per tree. Write an expression,b
in terms of x, for the total mass of apples produced.
(b) He uses 800 ml of fertiliser for each tree. The fertiliser is sold in 5-litre containers.
Write down an expression, in terms of x, for the number of containers of fertiliser
required, given that there is no left-over.
(c) Each container costs $90. If the total cost of the fertiliser is $648,
(i) form an equation in x.
(ii) Solve this equation to find the number of apple trees
Answer:
the number of apple trees = 45
Step-by-step explanation:
a) the total mass of apples produced = 25x
b) the number of containers of fertilizer required :
[tex]=\frac{0.8x}{5} \\= 0.16x[/tex]
c)
(i) the equation :
648 = 90 × (0.16x)
⇔ 648 = 14.4x
(ii) solving :
648 = 14.4x
⇔ x = 648 ÷ 14.4
= 45
6=3n/5
thats the equation and i need to find out what n is
Answer:
n=10
Step-by-step explanation:
6=3n/5
multiply both sides by 5
30=3n
divide both sides 3
10=n
A company charges 5% shipping fee. What are the shipping charges for an item that costs $1,200? Need help ASAP please.
Answer:
shippng charge = 60 dollars
Step-by-step explanation:
5% is .05 in decimal form
.05 x 1200 = 60 dollars
what is this? please help
Answer:
50
Step-by-step explanation:
to find the mean you have to add all the number up together. then divide that number by how many numbers it is in all:
48+50+5+60+37+50=300
divide 300 by 6= 50
Answer: it is the first choice which is 50 .
Step-by-step explanation: to find the mean it means you have to find the average total so you will have to add them together and divide by 6 as they are 6 numbers . When you add them the answer is 300 , divide by 6 the answer is 50 .
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HOPE IT HELPS YOU .PLEASE GIVE BRAINLIEST . THANKS .
The amount of time a certain brand of light bulb lasts is normally distributed with a
mean of 800 hours and a standard deviation of 50 hours. what is the probability that
a randomly chosen light bulb will last between 780 hours and 810 hours, to the
nearest thousandth?
Answer:
23.47 % ( or .2347)
Step-by-step explanation:
780 is 20/50 = .4 for z score - .4
810 is 10/50 = .2 z-score = .2
Use z-score table .5793 - .3446 = .2347 23.47%
Which of the three following graphs display the same data? i. a bar graph titled county voter turnout (thousands) has year on the x-axis and number on the y-axis. 1992, 99; 1996, 107; 2000, 103; 2004, 97; 2008, 98. ii. a line graph titled county voter turnout (thousands) has year on the x-axis and number on the y-axis. 1992, 99; 1996, 107; 2000, 103; 2004, 97; 2008, 98. iii. a circle graph titled county voter turnout (thousands). cuyahoga county, 99; maricopa county, 107; fort bend county, 103; susquehanna county, 97; clark county, 98. a. i and ii b. i and iii c. ii and iii d. i, ii, and iii
The graphs that display the same data are a. I and II
What is Data Representation?This refers to the different ways in which a set of data are displayed in a certain place such as a bar graph, frequency table, line graph, etc.
Hence, we can see that from the evaluation of the data, there is the use of the same data in I and II as the bar and line graphs contain the same country voter turnout.
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Answer:
a
Step-by-step explanation: