Solution :
Repeating or recurring decimals :
Repeating or recurring decimals are those decimal expansions that do not terminate or end after a specific number of digits. Such numbers have an infinite number of digits after the decimal point. And there is a repetitive pattern in those digits.
Decimal numbers can be converted to fractions by dividing the number with a power of 10 which is equal to the number of decimal places. For example, 1.5 = 15/10 = 3/2. But with repeating decimals, it is impossible to count the number of decimal places as it is infinite. So, there are some specific steps to be followed to convert repeating decimals to fractions.
The repeating decimal to fraction steps of conversion are given below:
Step 1: Identify the repeating digits in the given decimal number.
Step 2: Equate the decimal number with x or any other variable.
Step 3: Place the repeating digits to the left of the decimal point by multiplying the equation obtained in step 2 by a power of 10 equal to the number of repeating digits. This way you will get another equation.
Step 4: Subtract the equation obtained in step 2 from the equation obtained in step 3.
Step 5: Simplify to get the answer.
Let us take an example to understand the conversion of repeating decimals to fractions in a better way. Convert 0.77777... to a fraction.
Step 1: We can observe that 7 is repetitive in the given decimal number.
Step 2: Let x = 0.7777...
Step 3: There is only 1 repetitive digit, so multiply this equation by 10. We get, 10x = 7.7777...
Step 4: Subtract x = 0.7777... from 10x = 7.7777... We will get 9x = 7.
Step 5: x = 7/9. Therefore, 0.7777... = 7/9.
Hence,
you multiply 10 by the repeating decimal to make a fraction
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What is the number of combinations on a lock. (for a 40-number lock, no successive repeating numbers)
(permutations or combinations).
Find the smallest value of k if 360k is a perfect square
Answer:
k = 1
Step-by-step explanation:
since 360 = 60² , a perfect square , then
360 × 1 ← is a perfect square
that is 360k with k = 1 is a perfect square
Which is true?
5/4 > 5/6
3/3 > 4/3
3/3 < 3/6
Answer:
5/4 > 5/6
Step-by-step explanation:
PLEASE HELP 4/z>3; z=2
answer and steps to get it in the picture
10x-15=15x+50 ise x kaçtır?
Help me ASP SHOW UR WORK THANK YOU!!
The value of x is 4 , 12 , - 1 resp. in eq 1 , 2 and 3 .
Finding values of unknown variable x .
Following are linear equations in one variable .
On solving them we get ,
1 ) 2 ( 3 x - 5 ) = - 4 x + 30
6 x - 10 = - 4 x + 30
10 x =40
x = 4
2 ) 5 x - 6 - 3 x = 18
2 x = 18 + 6
2 x = 24
x = 12
3 ) - 11 - 5 x = 6 ( 5 x + 4 )
- 11 - 5 x = 30 x + 24
- 35 x = 35
x = - 1
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Round 1803.2684 to the nearest thousandth
Answer:
1,803.268
Step-by-step explanation:
so thousandths place is three number after the decimal just see the fourth number after the decimal and if it 5 or greater round the (in this case) 8 but since the fourth number was 4 it stays the same but only three numbers
2(x-1)+5(x-9) Show your work please!
Step-by-step explanation:
2(x-1) + 5(x-9)
2x - 2 + 5x - 45
2x + 5x - 2 - 45
7x - 47
Answer:
2x -2 + 5x -45 7x -47
Step-by-step explanation:
2*x = 2x
2*-1 = -2
5*x =5x
5*-9 = -45
[tex] \boxed{\begin{gathered} \rm Let \: \psi_1 : [0, \infty ) \to \mathbb{R} , \psi_2 : [0, \infty ) \to \mathbb{R},f :[0, \infty )\to \mathbb{R} \: and \: g :[0, \infty) \to \mathbb{R} \: be \\ \rm functions \: such \: that \: f(0) = g(0) = 0, \\\\ \rm \psi_{1}(x) = {e}^{ - x} + x, \: \: x \geq0, \\ \rm \psi_{2}(x) = {x}^{2} - 2x - 2 {e}^{ - x} + 2, \: \: x > 0, \\ \rm f(x) = \int_{ - x}^{x} ( |t| - {t}^{2} ) {e}^{ - {t}^{2} } \: dt, \: \: x > 0 \\\\ \rm g(x) = \int_0^{ {x}^{2} } \sqrt{t} \: {e}^{ - t} \: dt, \: \: x > 0 \end{gathered}}[/tex]
Which of the following is True?
[tex] \rm (A) \: \rm \: f ( \sqrt{ \ln 3 } )+ g( \sqrt{ \ln3} ) = \dfrac{1}{3} [/tex]
(B) For every x>1, there exists an α ∈ (1,x) such that ψ₁(x)=1+ax
(C) For every x>0, there exists a β ∈ (0,x) such that ψ₂(x)=2x(ψ₁(β)-1)
(D) f is an increasing function on the interval [tex] \bigg [0 , \dfrac{3}{2} \bigg][/tex]
(A) is false. By symmetry,
[tex]\displaystyle f(x) = \int_{-x}^x (|t|_t^2) e^{-t^2} \, dt = 2 \int_0^x (t-t^2) e^{-t^2} \, dt[/tex]
where [tex]|t|=t[/tex] since [tex]x>0[/tex]. Substitute [tex]s=t^2[/tex] to get the equivalent integral,
[tex]\displaystyle f(x) = \int_0^{x^2} (1 - \sqrt s) e^{-s} \, ds[/tex]
Then
[tex]\displaystyle f(x) + g(x) = \int_0^{x^2} e^{-s} \, ds[/tex]
[tex]\displaystyle f(\sqrt{\ln(3)}) + g(\sqrt{\ln(3)}) = \int_0^{\ln(3)} e^{-s} \, ds = \frac23 \neq \frac13[/tex]
(B) is false. Note that [tex]1+\alpha x[/tex] is linear so its derivative is the constant [tex]\alpha[/tex] at every point. We then have
[tex]{\psi_1}'(\alpha) = -e^{-\alpha}+1 = \alpha \implies 1-\alpha = e^{-\alpha}[/tex]
But this has no solutions, since the left side is negative for [tex]\alpha>1[/tex] and the right side is positive for all [tex]\alpha[/tex].
(C) is true. By the same reasoning as in (B), the line [tex]2x(\psi_1(\beta)-1)[/tex] has constant derivative, [tex]2\psi_1(\beta)-2 = 2e^{-\beta+2\beta-2[/tex]. Then
[tex]{\psi_2}'(\beta) = 2\beta-2+2e^{-\beta} = 2e^{-\beta}+2\beta-2[/tex]
holds for all values of [tex]\beta[/tex].
(D) is false. We use the first derivative test. By the fundamental theorem of calculus,
[tex]\displaystyle f(x) = 2 \int_0^x (t-t^2)e^{-t^2}\,dt \implies f'(x) = 2(x-x^2)e^{-x^2}[/tex]
Solve for the critical points.
[tex]f'(x) = 0 \implies x-x^2 = 0 \implies x = 0 \text{ or } x = 1[/tex]
[tex]e^{-x^2}>0[/tex] for all [tex]x[/tex], so the sign of [tex]f'[/tex] depends on the sign of [tex]x-x^2[/tex]. It's easy to see [tex]f'>0[/tex] for [tex]x\in(0,1)[/tex] and [tex]f'<0[/tex] for [tex]x\in\left(0,\frac32\right)[/tex]
Determine if the following relations represent a function
1. {(-1, -2), (0, -2), (1, -2), (2, -2)}
2. {(1, 0), (1,1), (1, 2), (1, -2)}
1) Yes, because each value of x maps onto only one value of y.
2) No, because the x-value of 1 maps onto 4 different y values.
Answer:
yes, a function.no, not a function.Step-by-step explanation:
You want to know if the given sets of ordered pairs represent a function.
FunctionA function is a relation that maps an input value to a single output value. On a graph, this means no two points are vertically aligned. For a table or set of ordered pairs, it means no input (x) value is repeated.
1.The input (x) values are {-1, 0, 1, 2} with no repeats. This relation is a function.
2.The input values are {1, 1, 1, 1} with repeats. This relation is not a function.
Alonso's family rented a car when they flew to
Orlando for a 4-day vacation. They paid $39
per day and $0.09 for each mile driven. How
much did it cost to rent the car for 4 days and
drive 350 miles, not including tax?
Answer:
$187.5
Step-by-step explanation:
39 (4) + 0.09 (350)
156 + 31.5
$187.5
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Answer:
$187.5
Step-by-step explanation:
You need to multiply the daily cost by the days. In this case, 39*4 = 156. Then, we can get the cost for the miles driven, being 0.09*350 = 31.5.
We can now add the two numbers together:
156 + 31.5 = $187.5
If f(x) = 2ax + b/x-1, lim x→0 f(x) = -3, lim x→∞ f(x)=4, prove that: f(2)= 11.
If
[tex]f(x) = \dfrac{2ax+b}{x-1}[/tex]
Note that
[tex]f(2) = \dfrac{4a+b}{2-1} = 4a+b[/tex]
From the given information we have
[tex]\displaystyle \lim_{x\to0} f(x) = \lim_{x\to0} \frac{2ax+b}{x-1} = \frac{0+b}{0-1} = -b = -3 \\\\ ~~~~ \implies b=3[/tex]
and
[tex]\displaystyle \lim_{x\to\infty} f(x) = \lim_{x\to\infty} \frac{2ax+b}{x-1} = \lim_{x\to\infty} \frac{2a+\frac bx}{1-\frac1x} = \frac{2a+0}{1-0} = 2a = 4 \\\\ ~~~~ \implies a=2[/tex]
It follows that
[tex]f(2) = 4\cdot2+3 = 11[/tex]
as required.
A thermometer in Grand Forks, North Dakota, reads -4.5 °F in January.
The temperature on the same day in February has the same absolute value
as the temperature in January but is not the same temperature. What is
the temperature in February?
According to this the temperature in February = 4.5°F.
What do you mean by absolute value:The absolute value (or modulus) of a real number x is its non-negative value regardless of its sign. For example, 5 has an absolute value of 5, and 5 has an absolute value of 5. A number's absolute value can be conceived of as its proximity from zero along the real number line.
Briefing:The temperature on the same day in February has the same absolute vale as the temperature in the January, but is not the same temperature according to this the temperature in February = 4.5°F.
According to the data:The absolute value is the same but not the same temperature:
|-4.5| = 4.5
So,
Its 4.5°F
According to this the temperature in February = 4.5°F.
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Under her cell phone plan, Morgan pays a flat cost of $54 per month and $5 per gigabyte, or part of a gigabyte. (For example, if she used 2.3 gigabytes, she would have to pay for 3 whole gigabytes.) She wants to keep her bill under $70 per month. What is the maximum whole number of gigabytes of data she can use while staying within her budget?
Answer: She can use 4 gigabyte while remaining in her budget.
Step-by-step explanation:
You would first subtract 54 from 70 which leaves you with 16,
Then you would divide 16 by 4 to find how many gigabytes she could use which gives you 4
So she can use 4 gigabyte while remaining in her budget.
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Answer: Answer is 3
Step-by-step explanation:
let the maximum number of gigabytes of data is x
total budget is $70
then, flat cost is $54 and $5per gigabyte
we get:
54 +5 × x= 70
5x =70 - 54
x = [tex]\frac{16}{5}[/tex] = 3.2 ≈ 3
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(3, 4, 5, ...} is finite or infinite
The given set is (3, 4, 5, ...} is infinite set.
A set with an infinite number of elements is one that cannot be numbered. A set that has no last element is said to be endless. A set that can be put into a one-to-one correspondence with a suitable subset of itself is said to be infinite. No issue with the in-class assignment.
The stars in the clear night sky, water droplets, and the billions of cells in the human body are just a few examples of endless sets of objects that surround us. A set of natural numbers, however, serves as the best illustration of an infinite set in mathematics. There is no limit to the amount of natural numbers.
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What is the slope of a line parallel to the line whose equation is 2x - 5y = 30. Fully simplify your answer.
Answer: [tex]\boxed{y=\frac{2}{5} x-7}\ as\ an\ example[/tex]
Step-by-step explanation:
Find the slope-intercept form:
[tex]2x-5y=30\\\\-5y=-2x+30\\\\y=\frac{-2x+30}{-5} \\\\y=\frac{2}{5} x-6[/tex]
Therefore the slope is 2/5
An example of a line parallel to this line is
[tex]y=\frac{2}{5} x-7[/tex]
Convert the following temperatures from Fahrenheit to Celsius or vice versa.
C= F-32/1.8
F = 1.8C+32
a. 50°F
b. 75°C
c. -40°C
Answer:
10°C
Step-by-step explanation:
c = [tex]\frac{F - 32}{1.8}[/tex] Plug in 50 for F and solve for C
c = [tex]\frac{50-32}{1.8}[/tex]
C = [tex]\frac{18}{1.8}[/tex] Divide
c = 10
Which measurement is closet to the lateral surface area in square centimeters of the cylinder?
H = 7.6
B = 5.8
Answers
A. 164.9 cm (2)
B. 277.0 cm (2)
C. 138.5 cm (2)
D. 191.3 cm (2)
The value closest to the lateral area of the cylinder is 138. 5cm^2. Option C
How to determine the valueThe formula for determining the lateral area of a cylinder is expressed as;
Lateral area = 2 πrh
Where;
r is the radiush is the height of the cylinderNote that radius is half the diameter;
radius, r = 5. 8/ 2 = 2. 9 cm
Substitute into the formula
Lateral area = 2 ( 3. 142 × 2. 9 × 7. 6)
Lateral area = 2 ( 69. 249)
Lateral area = 138. 49 cm^2
Thus, the value closest to the lateral area of the cylinder is 138. 5cm^2. Option C
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What is 5+3 72 times
Answer: 576
Step-by-step explanation:
5+3 = 8
8*72=576
Answer:576
Step-by-step explanation: just add and multiply
5000 nails in five boxes. the first and second boxes have 2700 nails all together. the second and the third boxes have 2000 nails all together. the third and fourth boxes have 1800 nails all together. the fourth and the fifth boxes have 1700 nails all together. how many nails are in each box
The number of nails in each box is: 1300, 1400, 600, 1200, and 500
Given 5000 nails in five boxes.
Let X denote the universal set.
Then n(X) = 5000.
Let A denote the first box,
B denote the second box,
C denote the third box,
D denote the fourth box, and
E denotes the fifth box.
The first and second boxes have 2700 nails altogether.
⇒n(A ∪ B) = 2700
The second and third boxes have 2000 nails altogether.
⇒n(B ∪ C) = 2000
The third and fourth boxes have 1800 nails altogether.
⇒n(C ∪ D) = 1800
The fourth and fifth boxes have 1700 nails altogether.
⇒n(D ∪ E) = 1700
We need to find out how many nails are there in each box.
That is to find out: n(A), n(B), n(C), n(D), and n(E).
Note that all these five sets are disjoint. This means that the intersection is empty.
n(A ∪ B ∪ C ∪ D) = n(A ∪ B) + n(C ∪ D) = 2700 + 1800 = 4500
n(E) = n(X) - n(A ∪ B ∪ C ∪ D) = 5000 - 4500 = 500
n(D) = n(D ∪ E) - n(E) = 1700 - 500 = 1200
n(C) = n(C ∪ D) - n(D) = 1800 - 1200 = 600
n(B) = n(B U C) - n(C) = 2000 - 600 = 1400
n(A) = n(A U B) - n(B) = 2700 - 1400 = 1300
Therefore, the number of nails in each box is 1300, 1400, 600, 1200, and 500.
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A high school student decides to apply four of six famous colleges. I’m how many possible ways can the four colleges be selected
If a high school student decides to apply four of six famous colleges, then the four colleges can be selected in as many as 15 different combinations.
As per question statement, a high school student decides to apply four of six famous colleges.
We are required to calculate the number of combinations in which the four colleges can be selected.
To solve this question, we need to know the formula of Combination which goes as [tex](nCr)=\frac{n!}{r!(n-r)!}[/tex]
, i.e., we are to select a set or "r" from a set of "n".
Here, we have to select a combination of 4 from a set of 6.
Therefore applying (nCr) formula with (n = 6) and (r = 4), we get,
[tex](6C4)=\frac{6!}{4!(6-4)!} =\frac{6!}{4!2!}=\frac{4!*5*6}{4!*2}=\frac{5*6}{2}=(5*3)=15[/tex].
Combinations: In mathematics, a combination is a method of selecting items from a particular set, where the order of selection does not matter, i.e., if we have a set of three P, Q and R, then in how many ways we can select two numbers from each set, can be easily defined by combination.To learn more about combinations, click on the link below.
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2 and 3 50 points and Brainlyest
AAnswer:
AB (-1, 4) = 34^ and B = (3,-1) 249*32 = 20
Step-by-step explanation:
Answer:
[tex]AB=\sqrt{53}\:\sf units[/tex]
[tex]EF=\sqrt{349}\:\sf units[/tex]
Step-by-step explanation:
Distance between two points
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\textsf{where }(x_1,y_1) \textsf{ and }(x_2,y_2)\:\textsf{are the two points}.[/tex]
Given:
A = (-4, 1)B = (3, -1)Substitute the given points into the distance formula and solve for AB:
[tex]\begin{aligned}\implies AB & =\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\& =\sqrt{(3-(-4))^2+(-1-1)^2}\\& =\sqrt{(7)^2+(-2)^2}\\& =\sqrt{49+4}\\& = \sqrt{53}\end{aligned}[/tex]
Given:
E = (-7, -2)F = (11, 3)Substitute the given points into the distance formula and solve for EF:
[tex]\begin{aligned}\implies EF & =\sqrt{(x_F-x_E)^2+(y_F-y_E)^2}\\& =\sqrt{(11-(-7))^2+(3-(-2))^2}\\& =\sqrt{18^2+5^2}\\& =\sqrt{324+25}\\& =\sqrt{349}\end{aligned}[/tex]
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The sum of two numbers is -316. One number is 94 less than the other. Find the numbers
The perimeter of the pentagon below is 63 units. Find the length of side AB.
Write your answer without variables.
Answer:
15
Step-by-step explanation:
The sides add to 63, so:
[tex]11+3x+11+x+2+2x+3=63 \\ \\ 6x+27=63 \\ \\ 6x=36 \\ \\ x=6 \\ \\ \implies AB=2(6)+3=15[/tex]
An automobile purchased for $28,000 is worth $2500 after 5 years. Assuming that the car's value depreciated steadily from year to year, what was it worth at the end of the third year?
The value 3 years after it was purchased is
Answer:
$3285.47
Step-by-step explanation:
We know the value decreased by a factor of 2500/28000 after 5 years.
This means the value decreased by a factor of (2500/28000)⅕ per year.
Therefore, after 3 years, the value is
[tex]28000(2500/28000)^{3/5} \approx 3285.47[/tex]
need help on 11-17 pls. Thank u
Helppp!
h(x)=x^2-6
Evaluate h(-3)
Answer:
3
Step-by-step explanation:
input -3 into h(x)=x^2-6
h(-3)=-3^2-6=9-6=3
Find the measure of angle X.
Answer:
x = 23 degrees
Because if you look at diagram x is vertical to angle FBC, and angle FEC and angle EBA are alternate interior angles so they are equal to each other, and AC is a straight line which means it equals to 180 degrees.
[tex]4x+65+x = 180[/tex]
x = 23 degrees
Please answer fast..............................................
Answer:
[tex]V=lwh\\\frac{V}{lw} = \frac{lwh}{lw} \\\frac{V}{lw} = h[/tex]
could someone please help answer this.
Answer:
C.) Equally as distant.
