The representation of 1 / 8 in decimal form will be 0.125 and it is a rational number as it is a terminating decimal.
We are given a fraction:
1 / 8.
We have to represent it as a decimal and tell that it is a rational number.
To write it as a decimal, First we will make the denominator a multiple of 10:
1 / 8 × 125 / 125 = 125 / 1000.
Now writing it in the decimal form, we get that:
= 0.125.
Now, we can see that it is a non repeating terminating number.
So, we can say that it is a rational number.
Therefore, the representation of 1 / 8 in decimal form will be 0.125 and it is a rational number as it is a terminating decimal.
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Identify a pattern in each list of numbers. Then use this pattern to find the next number.
5, 12, 33, 96, 285, ___
=====================================================
Explanation:
The given sequence is 5, 12, 33, 96, 285, ...
The jump from 5 to 12 is +7The jump from 12 to 33 is +21The jump from 33 to 96 is +63The jump from 96 to 285 is +189The sequence of increases is: 7, 21, 63, 189
Then notice,
The jump from 7 to 21 is "times 3"The jump from 21 to 63 is also "times 3"The jump from 63 to 189 is also "times 3".Assuming this pattern keeps up, the next increment will be 189*3 = 567
We add this increment to the last term of the original sequence
285+567 = 852
The sequence is now 5, 12, 33, 96, 285, 852, ...
Make x the subject of this formula: c = 7x - hx
Answer:
x = c / (7 - h)
Step-by-step explanation:
c = 7x - hx
c = x(7 - h)
x = c / (7 - h)
What is the meaning of selling price?
Answer:
noun. Britannica Dictionary definition of SELLING PRICE. [singular] : the price for which something actually sells. They asked $200,000 for the house, but the eventual selling price was $175,000.
5 divisible my 3 and 9
Answer:
5 is not divisible by 3 and 9 .
Estimate actual problem by rounding all the way and do actual division: LU 1-1(2), LU 1-3(2)
Actual. Estimate
695)8,950
The actual problem will be 9000 % 700, with the remainder 600 and quotient 12.
Since we are with the actual problem, which is 8,950 % 695, here the dividend is 8950 and the divisor is 695, the actual division we come up with the 12 as quotient and remainder 620. Now making the expression simple using the round-off rule, here in the dividend 8950, the last two digits are 50, so we can round off it to 9000 and in the divisor 695, the last digit is 5, so we add 1 in the preceding number converting it to 700, after the actual division of the estimated expression, the quotient we come up with is 12, and the remainder is 600.
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If anyone can help me to solve this!!
Answer:
[tex]\begin{array}{|l|l|c|c|c|}\cline{1-5} \textbf{Equation} & \textbf{Standard Form} & \textbf{a} & \textbf{b} & \textbf{c}\\\cline{1-5} \text{1.}\:\:x^2+x=20 & x^2+x-20=0 & 1 & 1 & -20\\\cline{1-5} \text{2.}\:\:4x^2-2x=28 \phantom{)))}& 4x^2-2x-28=0 \phantom{)))}& 4 & -2 & -28\\\cline{1-5} \text{3.}\:\:5x^2=225 & 5x^2-225=0 & 5 & 0 & -225\\\cline{1-5} \text{4.}\:\:x^2-x=36 & x^2-x-36=0 & 1 & -1 & -36\\\cline{1-5} \text{5.}\:\:3x^2-4=7x & 3x^2-7x-4=0 & 3 & -7 & -4 \\\cline{1-5}\end{array}[/tex]
Step-by-step explanation:
Standard form of a quadratic equation:
[tex]\boxed{ax^2+bx+c=0}[/tex]
Question 1
Given:
[tex]x^2+x=20[/tex]
Rearrange to standard form by subtracting 20 from both sides:
[tex]\implies x^2+x -20=20-20[/tex]
[tex]\implies x^2+x -20=0[/tex]
Therefore:
a = 1b = 1c = -20Question 2
Given:
[tex]4x^2-2x=28[/tex]
Rearrange to standard form by subtracting 28 from both sides:
[tex]\implies 4x^2-2x-28=28-28[/tex]
[tex]\implies 4x^2-2x-28=0[/tex]
Therefore:
a = 4b = -2c = -28Question 3
Given:
[tex]5x^2=225[/tex]
Rearrange to standard form by subtracting 225 from both sides:
[tex]\implies 5x^2-225=225-225[/tex]
[tex]\implies 5x^2-225=0[/tex]
Therefore:
a = 5b = 0c = -225Question 4
Given:
[tex]x^2-x=36[/tex]
Rearrange to standard form by subtracting 36 from both sides:
[tex]\implies x^2-x-36=36-36[/tex]
[tex]\implies x^2-x-36=0[/tex]
Therefore:
a = 1b = -1c = -36Question 5
Given:
[tex]3x^2-4=7x[/tex]
Rearrange to standard form by subtracting 7x from both sides:
[tex]\implies 3x^2-4-7x=7x-7x[/tex]
[tex]\implies 3x^2-4-7x=0[/tex]
[tex]\implies 3x^2-7x-4=0[/tex]
Therefore:
a = 3b = -7c = -4Which mixed number is equivalent to the improper fraction?
37
3
O A. 12
OB. 3/1/2
O C. 10
3
OD. 12/
Answer:
Mixed fractions is equivalent to improper fraction both A and C
A. 12 1/3
C. 10 7/3
A piece of rope 20 feet long is cut from a longer piece that is at least 32 feet long. The remainder is cut into four pieces of equal length. Describe the length of each of the four pieces.
Answer:
3
Step-by-step explanation:
32 - 20 = 12
12/4 = 3
This assumes that by remainder they mean they twelve feet left over and not the twenty feet removed. This is likely what it means.
Solve for x.
8x - 2 = 3x + 5x
Answer:
x=-8
Step-by-step explanation:
8x-2=3x+5x
1. Combine Like Terms
3x+5x=8x
Now your equation looks like this:
8x-2=8x
+8x +8x
2. Move Variables to one side
Now this is your equation:
-2=16x
3. Divide to isolate "x"
16/-2
x=-8
Let me know if this helped! :)
What inequality is shown by a number line that shows 12 to the right of −2?
The inequality shown by a number line which describes that 12 is to the right of -2 is; 12 > -2.
What inequality is shown by the number line that shows that 12 is to the right of 2?It follows from the task content that the inequality which represents the number line as described in the task content is to be determined
On this note, it follows that since, numbers are arranged from left to right in increasing order on the number line, then;
Since 12 is to the right of -2, the inequality which represents the situation is; 12 > -2.
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Round the decimal to the given place value.
124.123474
hundred-thousandth
Answer: 124.12347
Step-by-step explanation:
A textbook store sold a combined total of 414 physics and psychology textbooks in a week. The number of physics textbooks sold was 68
more than the number of psychology textbooks sold. How many textbooks of each type were sold?
If Thomas has 92 donuts and the box requires 3 donuts each box, once each donut is put in the boxes how many donuts would be left over?
Answer:
2
Step-by-step explanation:
Take 92 and divide by 3
3*30 = 90
92-90 = 2
There are 2 donuts left over
f (a) = 3a + 2, When
f(a) = 11
Answer:
3
Step-by-step explanation:
Think of "f(a)" like "y" in this context. You can set that equal to 11 and solve for a:
f(a) = 3a + 2
11 = 3a + 2
9 = 3a
3 = a
Anais bought 5/2 yards of ribbon. She had 1 feet 6 inches of ribbon left after trimming some curtains. How many inches of ribbon did Anais use to trim the curtains?
Answer: The number of ribbons used to trim the Curtains are 72 inches.
Step-by-step explanation:
Let us convert all numbers into inches.
Then, 1 yard= 36 inches
Given data, 5/2yards
So, 5/2 yards means.,
5/2= 2.5 yards
We can write: 2.5yards=2.5x36inches
=90inches
We convert feet into inches
1feet=12inches
We consider 1feet=12inches
In this question she had 1feet 6 inches of ribbons left.
Then 1x12=12inches
More 6 inches: 12+6=18inches
Now subtract 18 inches from 90 inches to get the inches used to trim curtains
Then, 90inches-18inches=72 inches
Thus, the number of ribbons used to trim the Curtains are 72 inches.
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the numbers being multiplied in a product are called
Answer:factors
Step-by-step explanation:
Find the value of x.
(4x12)°
(7x-28)
The value of x in the angles is 20
How to determine the value of x?The angles are given as
4x - 12 and 7x - 28
These angles are same side interior angles
So, we have
4x - 12 + 7x - 28 = 180
Collect the like terms
So, we have
4x + 7x - 12 - 28 = 180
Evaluate the like terms
So, we have
11x = 220
Divide both sides by 11
x= 20
Hence, the value of x in the angles is 20
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The governor of state A earns $54,900 more than the governor of state B. If the total of their salaries is $310,850, find the salaries of each.
need to find a and b
Answer:
$127975, $182875
Step-by-step explanation:
Let the salary in state A be x. Then, the salary in state B is x+54900.
[tex]x+x+54900=310850 \\ \\ 2x=255950 \\ \\ x=127975 \\ \\ x+54900=182875[/tex]
Evaluate the expression when m= -4
m2 +6m +9
Answer:
41
Step-by-step explanation:
because if m=-4 that means (-4)2+6(-4)+9=41
determine whether the graph is a fraction
Answer:
no, in a function x can not repeat so points (2,-1) and (2,-2) makes it wrong bc 2 is your x
Choose all degrees of rotation that will carry the regular pentagon onto itself.
A. 72°
B. 90°
C. 108°
D. 144°
E. 216°
Answer:
A. 72°
D. 144°
E. 216°
Step-by-step explanation:
I just answered this.
in short : we rotate each vertex on a circle arc. the center of that circle being P.
so, at the end of every 1/5 of the circle arc there is a vertex of the polygon.
therefore, with every 1/5 of a full circle rotation we move the pentagon visually onto itself.
that is starting at
360/5 = 72°
and then every additional 72°
144°
216°
288°
360°
so, A, D and E are correct
Laura is completing a 15-week exercise program where she increases the amount of time she works out by the same amount. She exercised 20 minutes per day the third week, 50 minutes per day the ninth week, and 60 minutes per day the eleventh week.
What is the function that represents the sequence?
The logical function that represents the amount of workout Laura does in each week along with her simultaneous increase in workout can be given by Arithmetic Progression.
It is represented as An = A + (n-1)d. Here, A represents the first term, or the amount of workout done in first week, d represents common difference or the difference in workout done in next week to its previous week, n represents the number of terms or the number of weeks for which data is to be calculated and An represents the workout done in nth week.
Arithmetic progression refers to the sequence of numbers such that each succeeding number increases with respect to previous number by fixed/ constant value. Thus, there exists constant amount of difference between each consecutive pair of number.
Since, Laura's workout pattern varies such that the amount of workout she does in one week increases by same amount in next week, so we get an arithmetic progression of her workout pattern.
Hence, her workout pattern can be traced as A, A+d, A+2d, A+3A, ..., An.
Thus, An = A + [(n-1)*d]
A3 = A +[(3-1)*d] = A + [2d] = 20 ...(1)
A9 = A +[(9-1)*d] = A + [8d] = 50 ...(2)
A11 = A +[(11-1)*d] = A + [10d] = 60 ...(3)
Solving equation (1) and (2), we get d = 5 and A = 10.
Thus, we conclude by saying that the function of her exercise routine is given by arithmetic progression and the amount of workout that she increases each week is given by 'd' that is 5 minutes.
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Stretched 1 cm beyond its natural length, a rubber band exerts a restoring force of magnitude 2 newtons. Assuming that Hooke's Law applies, answer the following questions:
(a) How far will a force of 3 newtons stretch the rubber band?
(b) How much work does it take to stretch the rubber band this far?
A) The distance that a force of 3 newtons would stretch the rubber band is; 0.015 m
B) The amount of work it takes to stretch the rubber band this far is; 0.0225 J
How to solve Hooke's Law?
From Hookes's law, as long as the elastic limit is not exceeded the extension is directly proportional to the force applied.
F = Ke
Where;
F = force
K = force constant
e = extension
Thus, for a restoring force of magnitude 2 newtons ;
2 N = K(1 × 10⁻²) m
K = 2 N /(1 × 10⁻²) m
K = 200 N/m
a) For a force of 3 newtons, we have;
3N = 200 N/m × a
Where a is the extension in meters
a = 3N/200 N/m
a = 0.015 m
b) The formula to find the work done is;
P.E = ¹/₂Ke²
P.E = ¹/₂ * 200 * 0.015²
P.E = 0.0225 J
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A group of 2129 students were surveyed about the courses they were taking at their college with the following results:
921 students said they were taking History.
987 students said they were taking Dance.
1012 students said they were taking Psychology.
474 students said they were taking Dance and History.
466 students said they were taking Psychology and History.
457 students said they were taking Dance and Psychology.
235 students said they were taking all three courses.
a) How many students took Dance or didn't take Psychology?
b) How many students took Dance & Psychology or took Psychology & History?
c) How many students took Dance, Psychology, or History?
d) How many students took Dance or History, but not Psychology?
e) How many students took none of the courses?
f) How many students took Psychology and History, but not Dance?
Using the Venn sets, the amounts are given as follows:
a) 1358 students.
b) 688 students.
c) 1758 students.
d) 746 students.
e) 371 students.
f) 771 students.
What are the Venn Sets?For this problem, we consider the following sets:
Set A: students taking History.Set B: students taking Dance.Set C: Students taking Psychology.235 students said they were taking all three courses, hence:
(A ∩ B ∩ C) = 235.
457 students said they were taking Dance and Psychology, hence:
(B ∩ C) + (A ∩ B ∩ C) = 457
(B ∩ C) = 222.
466 students said they were taking Psychology and History, hence:
(A ∩ C) + (A ∩ B ∩ C) = 466
(A ∩ C) = 231.
474 students said they were taking Dance and History, hence:
(A ∩ B) + (A ∩ B ∩ C) = 474
(A ∩ B) = 239.
1012 students said they were taking Psychology, hence:
C + (A ∩ C) + (B ∩ C) + (A ∩ B ∩ C) = 1012
C + 231 + 222 + 235 = 1012
C + 688 = 1012
C = 324.
987 students said they were taking Dance, hence:
B + (A ∩ B) + (B ∩ C) + (A ∩ B ∩ C) = 987
B + 239 + 222 + 235 = 987
B + 696 = 987
B = 291.
921 students said they were taking History, hence:
A + (A ∩ B) + (A ∩ C) + (A ∩ B ∩ C) = 921
A + 239 + 231 + 235 = 921
A + 705 = 921
A = 216.
The number of students who took no courses is given as follows:
None + A + B + C + (A ∩ B) + (A ∩ C) + (B ∩ C) + (A ∩ B ∩ C) = 2129
None + 216 + 291 + 324 + 239 + 231 + 222 + 235 = 2129
None + 1758 = 2129
None = 2129 - 1758
None = 371.
For item a, the amount is:
Dance + None = 987 + 371 = 1358 students.
For item b, the amount is:
(B ∩ C) + (A ∩ B ∩ C) + (A ∩ C) = 457 + 231 = 688 students.
For item c, the amount is the total subtracted by none, hence:
2129 - 371 = 1758 students.
For item d, the amount is:
A + B + (A ∩ B) = 216 + 291 + 239 = 746 students.
For item e, the amount is of 371, as we found previously.
For item f, the amount is:
A + C + (A ∩ C) = 216 + 324 + 231 = 771 students.
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In an election of a municipality two candidates A and B stood for the post of Mayor and 25000 people were in the voter list. Voters were supposed to cast the vote for a single candidate. 12000 people cast vote for A, 10000 people cast for B and 1000 people cast vote even for both. Show these informations in a Venn-diagram. How many people didn't cast vote ? Find it. How many votes were valid ? Find it.
Venn diagram{image attached},2000 people didn't cast their vote and 1000 votes are not valid in the election
Given that In a municipal election, two candidates, A and B, ran for the position of Mayor, and 25000 people voted. Voters were supposed to vote for only one candidate. A received 12000 votes, B received 10,000 votes, and 1000 cast votes for A and B both.
Number of votes for A=12,000
Number of votes for B=10,000
1000 cast votes to Both A and B, these votes are not valid because each one is supposed to vote only for one.
Therefore, the number of votes not valid is 1000
Total people cast vote= sum of votes for every party
Total people cast vote=12,000+10,000+1000
Total people casted vote=23,000
Therefore, Venn diagram{image attached},2000 people didn't cast their vote and 1000 votes are not valid in the election
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whst will be the multiplicative inverse of
3/5 - 4/27 + 5/18
Answer:


Find the multiplicative inverse of the following
(i) -13 (ii) -13/19 (iii) 1/5 (iv) -5/8 × -3/7 (v) -1 × -2/5
(vi) -1
Solution:
The reciprocal of a given rational number is known as its multiplicative inverse. The product of a rational number and its multiplicative inverse is 1.
(i) The Multiplicative inverse of -13 is -1/13
∵ -13 × (-1/13) = 1
(ii) The Multiplicative inverse of -13/19 is -19/13
∵ -13/19 × (-19/13) = 1
(iii) The Multiplicative inverse of 1/5 is 5
∵ 1/5 × 5 = 1
(iv) The Multiplicative inverse of -5/8 × -3/7 is 56/15
∵ -5/8 × (-3/7) = 15/56 and 15/56 × 56/15 = 1
(v) The Multiplicative inverse of -1 × -2/5 is 5/2
∵ -1 × (-2/5) = 2/5 and 2/5 × 5/2 = 1
(vi) The Multiplicative inverse of -1 is -1
∵ -1 × (-1) = 1
Evaluate
3(x+4)(x+1)
(x+2)(x-2)
for x = 4.
Answer:
1440
Step-by-step explanation:
3(4+4)(4+1)(4+2)(4-2)
3*8*5*6*2
1440
A student is given this proof.
Given: AOM DON
Prove: CON~ BOM
ZAOM ZDON
given
ZBOM DON
vertical angles
theorem
ZAOM ZBOM
transitive
property of
congruence
ZAOM ZCON
vertical angles
theorem
ZCON BOM
transitive
property of
congruence
The student says that the proof shows that AOM BOM because they
are vertical angles.
Which statement best corrects the student's interpretation?
From the steps below, it has been proved that by transitive property of congruence, we can say that; ∠CON ≅ ∠BOM
How to prove congruent angles?
We are given;
∠AOM ≅ ∠DON
To prove that;
∠CON ≅ ∠BOM
Now, from the image attached, we can say that;
∠BOM ≅ ∠DON because of vertical angles theorem
Similarly, we can say that ∠AOM ≅ ∠BOM due to transitive property of congruence.
Also, we can say that from vertical angles theorem, ∠AOM ≅ ∠CON
Finally, since ∠AOM ≅ ∠BOM, then by transitive property of congruence, we can say that;∠CON ≅ ∠BOM
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asha saves coins in a jar. The table shows how the amount of money was in the jar at the end of every three-month period. A line of best fit for this
ata is B= 0.45m + 1.93.
Month, m
Balance, B
($)
3
6
9
3.24 4.63 5.97 7.26
12
Which value is the best estimate of the amount of money in the jar at the end of the first month?
A $0.45
OB. $1.08
OC. $1.93
OD. $2.3
If A line of best fit for the data is B= 0.45m + 1.93. The value that is the best estimate of the amount of money in the jar at the end of the first month is: D. $2.38.
Best estimate of the amount of moneyGiven:
B= 0.45m + 1.93.
Where:
m= 1 month (First month)
Hence:
B= 0.45(1) + 1.93
B= 0.45+ 1.93
B=$2.38
Therefore if A line of best fit for the data is B= 0.45m + 1.93. The value that is the best estimate of the amount of money in the jar at the end of the first month is: D. $2.38.
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Real number root for V-49
Step-by-step explanation:
there is no real number solution for the square root of a negative number.
a sqare root multiplied by itself had to deliver exactly the number inside the square root.
so for sqrt(-49), what can be the answer ?
which number multiplied by itself gives -49 ?
it any negative number at that.
because
a × a = a²
and
-a × -a = a² but definitely not -a².
we get a negative number only, when we multiply a positive number with a negative number or vice versa.
the only solution is complex or imaginary (based on the imaginary number i):
i² = -1
i = sqrt(-1)
so, sqrt(-49) = sqrt(49 × -1) = 7×sqrt(-1) = 7i
but again, no real solution.