The original number from the given decimal number is 0.02.
Define the term reciprocal of the number?A multiplicative inverse of such a number is referred to as the reciprocal. In other words, 1 divided by a number is the definition of the reciprocal. Any given number multiplied by its reciprocal would always yield the value 1. By swapping the values of a numerator and denominator, one can find exact reciprocal of a fraction.For the given question;
Moving a decimal point 4 places towards the right corresponds to multiplying the given integer by 10,000 if it is x.
This results in:
10000x = 4.(1/x)
Simplifying.
x² = 4/10000
x > 0.
Taking square root of the number.
x = 2/100
x = 0.02
Thus, the original number from the given decimal number is 0.02.
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Mr. fitzpatrick is taking his math class to see a pearl jam concert because they have worked so hard this week in class. he purchases 22 tickets for a total of $265. tickets cost $10 for students and $15 for adults. some students must pay adult prices because they are over 18 years of age. what are the number of student tickets purchased and the number of adult tickets purchased
Mr. Fitzpatrick bought 9 adult tickets and 13 children's tickets.
It is given that Mr. Fitzpatrick bought 22 tickets
The tickets collectively cost him $265
The student tickets cost $10 while adult tickets cost $15
Let the no. of adult tickets sold be x
Let the no. of children's tickets sold be y
Therefore we get the equations
x + y = 22 [1]
15x + 10y = 265 [2]
or, 5x + 10x + 10y = 265
or, 5x + 10(x + y) = 265
from equation [1] we get
5x + 220 = 265
or, 5x = 265 - 220
or, 5x = 45
or, x = 9
Therefore,
y = 22 - 9
= 13
Therefore he bought 9 adult tickets and 13 children tickets.
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Rich is attending a 4-year college. As a freshman, he was approved for a 10-year, federal unsubsidized student loan in the amount of $7,900 at 4.29%. He knows he
has the option of beginning repayment of the loan in 4.5 years. He also knows that during this non-payment time, interest will accrue at 4.29%.
If Rich decides to make no payments during the 4.5 years, the interest will be capitalized at the end of that period.
a. What will the new principal be when he begins making loan payments?
b. How much interest will he pay over the life of the loan?
a) The new principal (principal + capitalized interest) when Rich begins making loan payments will be $9,425.10.
b) The total interest that Rich will pay over the life of the loan is $4,914.20.
How is interest on student loans determined?The interest on student loans is based on simple interest.
The only interest capitalized is the interest during the non-payment period if the student does not pay the interest.
Some students elect to pay the interest during the non-payment period to reduce the capitalized interest and principal during the payment period.
Capitalization refers to the addition of interest to the principal amount.
Period of student loan = 10 years
The amount of the federal unsubsidized student loan = $7,900
Interest rate = 4.29%
Capitalized interest during the non-payment time = $1,525.10 ($7,900 x 4.29% x 4.5)
New principal when Rich begins making loan payments = $9,425.10 ($7,900 + $1,525.10)
Total interest for loan = $4,914.20 ($7,900 x 4.29% x 14.5)
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Ibram got a job selling bags of peanuts at the local fairground. He is paid a fixed amount of $340 per week plus $0.84 per item sold. This is represented by the equation P = 0.84 + 340 where P is the amount he is paid for the week and n is the number of bags of peanuts he sold. How much will Ibram be paid if he sells 380 bags of peanuts? If Ibram sells 380 bags of peanuts, he will earn S How many bags of peanuts did Ibram sell if he earned $1,087.60? for the week. If Ibram has earned $1,087.60, he sold bags of peanuts.
Answer:
Assuming the bags sold were for 1 week period.
1. $659.20 for 1 week and 380 bags of peanuts
2. 890 bags
Step-by-step explanation:
The equation is missing the variable, n (the number of bags sold). I'll take the liberty to add it after the $0.84/bag term, where it belongs:
P = 0.84n + 340
The 340 is $340/week. n must be in units of "bags/week."
1. How much will Ibram be paid if he sells 380 bags of peanuts?
P = $0.84n + $340
n = 380 bags (we will assume in 1 week).
P = $0.84n + $340
P = $0.84(380) + $340
P = $659.20
2. How many bags of peanuts did Ibram sell if he earned $1,087.60?
P = $0.84n + $340
P = $1087.60
$1087.60 = $0.84n + $340
$1087.60 - $340 = $0.84n
$0.84n = $1087.60 - $340
$0.84n = $747.60
n = 890 bags ( ! - I'm impressed)
6. Find the distance between each pair of points. Then order each line segment from longest to shortest.
a. A(−6, 1), B(−1, 6)
c. E(2,7), F(4, -2)
e. J(−4, −2), K(1, −5)
b
C(-5, 8), D(5,8)
d. G(7,3), H(7,−1)
f. L(3, -8), M(7, −5)
Using the distance formula, the order of each line segment from longest to shortest is b→c→a→e→f→d.
What is the distance Formula?The formula for the distance(d) , between two points whose coordinates are (x₁ ,y₁) and (x₂, y₂) is:Distance Formula: d = √[(x₂ - x₁)² - (y₂ - y₁)²]
Now, calculate the distance using the distance formula as follows:
(A) The distance between A and B is:
d = √(-1-(-6))²+(1-6)²)d = √5² + 5²d = √50(B) The distance between C and D is:
d = √[(5 -(-5))²+ (8-(8))²]d = √10² + 0d = 10(C) The distance between E and F is:
d = √[(4-2)²+ ((-2)-7)²]d = √2² + 9²d = √85(D) The distance between G and H is 2.
(E) The distance between J and K is:
d = √ [(1-(-4))² + (-5-(-2))²]d = √5² + 3²d = √34(F) The distance between L and M is:
d = √[(7-3)²= (-5-(-8))²]d = √4² + 3²d = 5Hence, the distance using the distance formula is:
(A) The distance between A and B is √50.(B) The distance between C and D is 10.(C) The distance between E and F is √85.(D) The distance between G and H is 2.(E) The distance between J and K is √34.(F) The distance between L and M is 5.Therefore, using the distance formula, the order of each line segment from longest to shortest is b→c→a→e→f→d.
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Direct or Inverse variation
3y=x
{(2,6),(3,9),(5,15)}
{(1,16),(2,8),(4,4)}
The answers are as follows -
Relation 3y=x represents direct variation.Relation {(2,6),(3,9),(5,15)} represents direct variation.Relation - {(1,16),(2,8),(4,4)} reflects inverse relation.What is the general equation of a Straight line?
The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
y = mx also represents direct proportionality. We can write [m] as -
m = y/x
OR
y₁/x₁ = y₂/x₂
Given are the following relations -
3y = x
{(2,6),(3,9),(5,15)}
{(1,16),(2,8),(4,4)}
We can write -
x = 3y
as
y = (1/3)x
m = 1/3
Relation 3y=x represents direct variation.
For the relation - {(2,6),(3,9),(5,15)}, we can write -
We can write it as -
y = 3x
Relation {(2,6),(3,9),(5,15)} represents direct variation.
For the relation - {(1,16),(2,8),(4,4)} , as [x] increases, [y] decreases, so it is a inverse relation.
Therefore -
Relation 3y=x represents direct variation.Relation {(2,6),(3,9),(5,15)} represents direct variation.Relation - {(1,16),(2,8),(4,4)} reflects inverse relation.To solve more questions on proportional relationship, visit the link below-
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a stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 3.3 ft/s. how rapidly is the area enclosed by the ripple increasing at the end of 6.4 seconds?
In 139.4 [tex]\pi[/tex] [tex]ft^2[/tex]sec rapidly is area of enclosed by the ripple increasing at the end of 6.4 seconds.
What is area of circle?
For measuring the area occupied by a circular field or plot, use the area of a circle formula. The area formula will allow us to determine how much fabric is required to completely cover a circular table, for example. We can determine the boundary length, or the circle's circumference, using the area formula.
Here area of circle
=> A= π[tex]r^2[/tex]--------> 1
Differentiating 1 with respect to to time then
=> [tex]\frac{dA}{dt}= 2\pi r\frac{dr}{dt}[/tex]
If the radius is increasing at a constant rate 3.3ft/sec then after 6.4 seconds, radius is
=> 6.4*3.3=21.12 ft.
We know [tex]\frac{dr}{dt}= \frac{3.3ft}{sec}[/tex] and so ,
=> [tex]\frac{dA}{dt}[/tex] = 2*[tex]\pi[/tex]*21.12*3.3=139.4 [tex]\pi[/tex] [tex]ft^2[/tex]sec.
Hence In 139.4 [tex]\pi[/tex] [tex]ft^2[/tex]sec rapidly is area of enclosed by the ripple increasing at the end of 6.4 seconds.
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A horse that weighs 1 1/4 tons carries a 110-pound person, a 15-ounce water bottle, and a 16 1/2-pound basket. What is the total weight of the horse, riders, and items?
Answer:
143.75
Step-by-step explanation:
11/4+110+15+16 1/2=143.75
Murphy and Nikita can fill their swimming pool with one hose in 10 hours. If they use another hose to help fill the pool, the pool
can be filled in 4 hours. How long would it take the other hose to fill the pool working alone? Round to the nearest tenth.
Answer:
Step-by-step explanation:
so you just have to round where it came from
simplify each expression x = 2x + 48
(please its for today
a school is organizing a weekend trip to a nature preserve. for each student, there is a $60 charge, which covers food and lodging. there is also a $40 charge per student for the bus. the school must also pay a $30 cleaning fee for the bus. if the total cost of the weekend is $4,030, how many students will be going on the trip?
Using the concept of linear equation in one variable, it is concluded that the total number of students who will go on the trip are 40.
What is a linear equation in one variable?An equation that contains only one variable and has its degree one is called a linear equation in one variable. The general form of linear equation in one variable is ax + b = 0, where a and b are real numbers and a ≠ 0.
Given that food and lodging charge per student = $ 60
Charge per student for bus = $ 40
And the amount paid for the cleaning fee for the bus = $ 30
Let the total number of students who are going on the trip = x
Now, the Total charge for food and lodging = $60x
The total charge for bus fare = $ 40x
Given that total cost paid = $ 4030
Hence, $60x + $40x + $30 = $4030
$100X = $4030 - $30
$100X = $4000
x = 40
Hence, the total number of students who will go on a trip is 40.
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just confused,, brainliest?
Answer:
14
Step-by-step explanation:
Calculate the distance around a triangle whose sides are :
The distance around the triangle is equivalent to 13x/12.
What is triangle?
A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -
∠x + ∠y + ∠z = 180°
The sum of two sides of a triangle is greater then the third side. Mathematically -
a + b > c
There are different types of triangles such as -
equilateral triangle , scalene triangle , isosceles triangle etc.
Given are the sides of triangle as x/2, x/3, x/4
The distance around the triangle is equivalent to perimeter of triangle. We can write perimeter as -
P = x/2 + x/3 + x/4
P = (6x + 4x + 3x)/12
P = 13x/12
Therefore, the distance around the triangle is equivalent to 13x/12.
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AWNSER PLSS !How can a negative number be written in scientific notation?
Simplify these pls I’ll brainlist.
1) 3b (b+4) - 4 (b-5)
2) 12(3y + 6)
Final answer: 3[tex]b^{2}[/tex] + 8b + 2
12(3y + 6) = 12 x 3(y + 2) // Factor out 12 = 36(y + 2) // Simplify the multiplication Final answer: 36(y + 2)
What is equation?An equation is a statement that two mathematical expressions are equal. It consists of two expressions separated by an equal sign (=), where one expression is on the left side and the other expression is on the right side of the equal sign. An equation represents a balance or equivalence between the two expressions, and it can be solved for the unknown variable(s) by applying mathematical operations to both sides of the equation.
Given by the question.
3b (b+4) - 4 (b-5)
= 3[tex]b^{2}[/tex] + 12b - 4b + 20 // Distribute the terms.
= 3[tex]b^{2}[/tex] + 8b + 20 // Simplify the like terms.
Final answer: 3[tex]b^{2}[/tex]+ 8b + 20
12(3y + 6)
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the graph of a lnear function passes through the point (-2, -7). When the input increses by 3 the value of the function increses by 8. what is the equation that models the function
The equation that models the function is y = 8/3(x) - 5/3.
Given:
The graph of a linear function passes through the point (-2, -7).
When the input increases by 3 the value of the function increases by 8.
(x,y) = (x+3,y+8)
(-2,-7) = (-2+3,-7+8)
= (1,1)
slope between (1,1) and (-2,-7) is m = -7-1/-2-1
= -8/-3
m = 8/3.
substitute m in y = mx + c
y = 8/3(x)+c
substitute (-2,-7)
-7 = 8/3(-2) + c
-7*3 = -16 + 3c
-21+16 = 3c
-5 = 3c
c = -5/3
y = 8/3(x) - 5/3.
Therefore the equation that models the function is y = 8/3(x) - 5/3.
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PLEASE ANSWER
What are the coordinates of the point that is one half the distance between A(−1, −2) and B(6, 12)?
( , )
line that passes through the point (8,−3) and has a slope of 1/4
The equation of line having a slope of 1/4 which passes through point (8,-3) is y = (1/4)x - 5.
What is the equation of line with the given point and slope?The equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given the data in the question;
Point (8, -3 )
x = 8y = -3Slope m = 1/4Determine the y-intercept 'b'.
Substitute the point and slope into the equation of line formula and solve for b.
y = mx + b
-3 = (1/4)(8) + b
-3 = 8/4 + b
-3 = 2 + b
b = -3 - 2
b = -5
Now, substitute slope and y-intercept into y = mx + b to determine the equation of the line.
y = mx + b
y = (1/4)x + (-5)
y = (1/4)x - 5
Therefore, the equation of the line is y = (1/4)x - 5.
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the width of bolts of fabric is normally distributed with mean 951 mm (millimeters) and standard deviation 10 mm. (a) what is the probability that a randomly chosen bolt has a width between 942 and 959 mm? (round your answer to four decimal places.) (b)
The probability that a randomly chosen bolt has a width between 942 and 959 mm is 0.647.
Define probability.The area of mathematics known as probability explores potential outcomes of events as well as their relative probabilities and distributions. A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities. Information about the possibility that something will happen is provided by probability. For instance, meteorologists use weather patterns to forecast the likelihood of rain. Probability theory is utilized in epidemiology to comprehend the connection between exposures and the risk of health outcomes.
Given,
The width of bolts of fabric is normally distributed with mean 951 mm (millimeters) and standard deviation 10 mm.
Z = X - 951/10 ≈ N(0.1)
P(942 ≤ X ≤ 959)
P(942 - 951/10 ≤ X - 951/10 ≤ 959- 951/10)
P( -0.9 ≤ Z ≤ 0.8)
P(Z ≤ 0.8) - P(Z ≤ -0.9)
∅(0.8) - (1 - ∅(0.9))
∅(0.8) + ∅(0.9) - 1
0.788 + 0.859 - 1
0.647
The probability that a randomly chosen bolt has a width between 942 and 959 mm is 0.647.
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An engineering technician makes $25 an hour for the first 40 hours she works
during a week and $32 an hour for each hour over 40 hours. Which piecewise
equation models her total weekly pay y in dollars as it relates to the number
of hours x that she has worked during the week?
O A. y=
O C. y =
(25x
132(x-40)+1000
OB. y=-
OD. y=
[25x
132x+1000
(25x
(32(x-40)
(25x
132x
0≤x≤ 40
x> 40
0≤x≤ 40
x> 40
0≤x≤ 40
x> 40
0≤x≤ 40
X> 40
SUBMIT
The Piecewise Function be
25x when x < 40
y =
1000+32(x-40) when x > 40
Given, an engineering technician makes $25 an hour for the first 40 hours she works.
and $32 an hour for each hour over 40 hours.
Let the number of hours be x and her total weekly pay in dollars be, y
then the piecewise function,
25x when x < 40
y =
1000+32(x-40) when x > 40
Hence, the piecewise function be
25x when x < 40
y =
1000+32(x-40) when x > 40
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Miguel took his son to college in boulder, colorado, 300mi from their hometown. on his way home, he was slowed by a snowstorm so that his speed was 10mph less than when he was driving to boulder. his total driving time was 11hr. how fast did miguel drive on each leg of the trip?
Miguel drove at a speed of 60 mph in the first part of the trip and at a speed of 50 mph in the second part of the trip.
Let the speed while dropping his son to college be x mph
Therefore speed while returning is (x - 10) mph
The distance is 300 mi
Speed = Distance/Tie
or, Time = Distance/Speed
Hence the time taken during the first part of the journey = 300/x hrs
and,
Time taken for the next part of the journey
= 300/(x - 10) hrs
It is given that the total time taken was 11 hrs
Hence we get
300/x + 300/(x - 10) = 11
or, (300x - 3000 + 300x) / x(x - 10) = 11
or, (600x - 3000) / (x² - 10x) = 11
or, 600x - 3000 = 11x² - 110x
or, 11x² -710x + 3000 = 0
Applying the shreedharacharya rule gives us
x = (710 ± √(710² -132000)/22)
x = 50/11 or x = 60
If x = 50/11 then x - 10 will be negative.
hence x = 60
Therefore Miguel drove at a speed of 60 mph in first half and 50 mph in second half.
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What type of angles are labeled and what is the value of m? Show your work.
Answer:
see explanation
Step-by-step explanation:
m + 20 and 100 are vertically opposite angles and are congruent , then
m + 20 = 100 ( subtract 20 from both sides )
m = 80
The angles are vertically opposite angles and value of m is 80°
What is vertically opposite angles?Vertically opposite angles are angles that are opposite one another at a specific vertex and are created by two straight intersecting lines.
Given two angles which are Vertically opposite to each others,
We know Vertically opposite angles are equal to each other, so,
m + 20° = 100°
m = 100° - 20°
m = 80°
Hence, the value of m is 80°
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Martina purchased a prepaid phone card for 45.50$ calls cost 10 cents a minute using this card. The credit, C (in dollars) , left on the card after it is used for x minutes of calls is given by the following function
Answer:
Credit (C) = $45.50 - 0.10x
Step-by-step explanation:
Since you are wanting the credit (C) that is the y variable.
The prepaid phone card starts off with a balance of $45.50.
Every minute a call is made $0.10 is deducted (subtracted) from the card.
The unknown number or 'x' represents the number of minutes the calls lasted.
Figure E is dilated from point D, the center of dilation
The figure that is a dilation of figure E is the figure F
What is dilation?Dilation involves enlarging or reducing the side length of a shape to create another shape by a constant scale factor, where the scale factor does not equal one.
How to determine the dilated figure?The graph represents the given parameter
From the figure, we have the original shape to be figure E
The center point of figure E is the origin
This means that a line drawn from the origin that passes through point E must pass through the same point on the shape
From the figure, the line passes through the same point on figure E and F
Hence, figure F is a dilation of figure
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if f represents the number of lots of fliptop pens to produce and t represents the number of lots of tiptop pens to produce, the linear programming model for this problem is:
The linear programming model for this problem is Max 1000F + 1000T
Given that,
If the quantity of flip top pens to be produced is f and the quantity of tiptop pens to be produced is t, then
Number of lots of Flip top pens to produce = F
Number of lots of Tip top pens to produce = T
Therefore, The linear programming formulation is given by:
Max 1000F + 1000T
s.t.
Plastic: 3F + 4T <= 39
Ink Assembly: 5F + 4T <= 45
Molding time: 5F + 2T <= 37
F, P >= 0
Hence, the linear programming model for this problem is Max 1000F + 1000P
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Which function matches the table? Number of Days Rented 1 2 3 4 Rental Cost ($) 12 17 22 27 A. f(x) = 5x B. f(x) = 5 + 5x C. f(x) = 7 + 5x D. f(x) = 12 + 5x
Then the equation that represents the total rent will be y = 5x + 7. Then the correct option is C.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The table is given below.
Number of Days Rented Rental Cost ($)
1 12
2 17
3 22
4 27
At x = 1, the value of y is 12.
12 = m + c ...1
At x = 2, the value of y is 17.
17 = 2m + c ...2
Subtraction equation 1 from equation 1, then we have
2m - m = 17 - 12
m = 5
Then the value of 'c' is given as,
17 = 2 x 5 + c
17 = 10 + c
c = 7
Then the equation that represents the total rent will be y = 5x + 7. Then the correct option is C.
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How can you write the equation of the
line?
(: before the lady in the video shows
you :)
y 5x = 3
y = 3x - 5
y = -5x + 3
y + 3 = -5x
Write a letter to your friend wishing him success
Answer:
Hello _____,
You are a pig, a fatty, a dunce, and a monkey. Also, you smell like a diseased pustule on the butt of a wildebeest.
Cordially,
_____
Step-by-step explanation:
Use remainder theorem for x^3+8x^2+11x-20 by (x+4)
Answer:
x^3 + 64 + 11x - 20bxy - 80by
(if I am wrong, apologies)
Answer:
x^2+4x-5
Step-by-step explanation:
x^3+8x^2+11x-20/x+4=x^2+4x-5
Given the relation {(3,4),(-2,1),(0,6),
(5,-3)), what is the domain of the
relation?
Answer:
Domain: {-2, 0, 3, 5}
Step-by-step explanation:
The domain is the list of possible inputs
-13-7=
+
?
Write as addition.
Answer:
As addition: -13+(-7)=-20