A student imagined one number. 2 is written to the right side of the number and 14 is added to the obtained number. 3 is written to the right side of the obtained number and 52 is added to the newly obtained number. The result of dividing the final number by 60 is the quotient that is for 6 greater than the initial number and the remainder is a two-digit number with both digits the same as the initial number. Find the initial number
Answers
The initial number is approximately 7.33.
Let's call the initial number "x".
According to the problem, the first step is to write 2 to the right of the number: this gives us the number 10x + 2.
-The next step is to add 14 to this number, which gives us:
10x + 2 + 14 = 10x + 16
-Then we write 3 to the right of this number, giving:
100x + 16 + 3 = 100x + 19
-And finally, we add 52 to this number:
100x + 19 + 52 = 100x + 71
Dividing this final number by 60 gives a quotient that is 6 greater than the initial number and a remainder that is a two-digit number with both digits the same as the initial number.
-So we have the equation:
(100x + 71) ÷ 60 = x + 6 + 0.01x
-We want to solve for x, so we first multiply both sides by 60:
100x + 71 = 60(x + 6 + 0.01x)
-Simplifying the right-hand side:
100x + 71 = 60x + 360 + 0.6x
Combining like terms:
39.4x =289
Dividing both sides by 39.4:
x =7.33
Therefore, the initial number is approximately 7.33.
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Related Questions
Suppose each license plate in a certain state has three digits followed by three letters. The digits 4 and 5 are not used. So, there are 26 letters and 8 digits that are used. Assume that the letters and digits can be repeated. How many license plates can be generated using this format?
Answers
The required, there are 8998912 possible license plates that can be generated using this format.
Here, we have,
There are 8 digits that can be used for each of the three digits on the license plate, with two digits (4 and 5) that cannot be used.
Therefore, there are 8 choices for each of the three digits,
giving us 8 x 8 x 8 = 512 possible combinations for the digits.
Similarly, there are 26 letters that can be used for each of the three letters on the license plate.
Therefore, there are 26 choices for each of the three letters, giving us 26 x 26 x 26 = 17576 possible combinations for the letters.
Total number of license plates = number of choices for the digits x number of choices for the letters
= 512 x 17576
= 8998912
Therefore, there are 8998912 possible license plates that can be generated using this format.
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Mrs. Piazza invested $8000 in a certificate of deposit that pays 3% simple interest for 4 years. How much will be in Mrs. Piazza's account at the end of 4 years?
Answers
Answer:
$8960
Step-by-step explanation:
Given
principal = $8000
rate= 3%= 0.03
time = 4 years
Required
the final amount, we assume that this is a simple interest investment.
Step two:
\(A= P(1+rt)\\\\A=8000(1+0.03*4)\\\\A=8000(1+0.12)\\\\A=8000*(1.12)\\\\A=8960\)
The final amount in the account is $8960
What are the domain and range of the real-valued function f(x)=2/(x+5)?
Answers
Answer:
Domain is all real numbers, x ≠ -5
Range is all real numbers, y ≠ 0
Step-by-step explanation:
(-infinity, -5)U(-5, infinity)
Range: all real numbers except y=0
(-infinity, 0)U(0, infinity)
A mailing supply company produces yellow mailing envelopes. The envelopes come in
a variety of sizes, but the length is always 4 centimeters more than double the width.
Write an equation to find the dimensions of an envelope that has a perimeter of 26
centimeters.
Answers
Answer:
Step-by-step explanation:
L=2W+4
P=2(L+W), using L from above makes this
P=2(2W+4+W)
P=2(3W+4)
P=6W+8
6W=P-8
W=(P-8)/6, since we are told P=26
W=(26-8)/6
W=18/6
W=3 cm, and since L=2W+4
L=2(3)+4
L=6+4
L=10 cm
So the dimensions of the envelope with a perimeter of 26cm is 3cm by 10cm
5) x + y / 3 = 5 (x)
Answers
Answer:heloooooooo
Step-by-step explanation:
PLEASE HELPI GIVE 20 POINTS
Answers
Answer:
D) 4 7/12
Step-by-step explanation:
55 divided by 12 is
4 remainder 7/12
so
4 7/12 which is D
The distance , d, a train travels in miles depends on the hours, h. The equation shows this relationship, d=120h. How many miles does the train travel in one hour ?
Answers
Answer:
120h
Step-by-step explanation:
because one miles is equal to one hour so 120 hours is equivalent to 120 miles
Evaluate the integral. (Use C for the constant of integration.)
∫2 tan3(x) sec(x) dx
Answers
To evaluate the integral ∫2 tan^3(x) sec(x) dx, we can use the substitution method and trigonometric identities. By making suitable substitutions and applying trigonometric identities, we can simplify the integral and find its antiderivative.
Let's start by making the substitution u = tan(x). This substitution helps simplify the expression involving tangent and secant functions.
Differentiating both sides with respect to x, we get du/dx = sec^2(x).
Rearranging the equation, we have dx = du/sec^2(x).
Now, let's substitute the values in the integral:
∫2 tan^3(x) sec(x) dx = ∫2 u^3 du/sec^2(x)
= ∫2 u^3 du/(1 + tan^2(x))
Using the identity 1 + tan^2(x) = sec^2(x), we can simplify further:
∫2 u^3 du/(1 + tan^2(x)) = ∫2 u^3 du/sec^2(x)
= ∫2 u^3 du/((1 + u^2)/1)
= ∫2 u^3 du/(1 + u^2)
Integrating with respect to u, we have:
= (1/4) u^4 + C
= (1/4) tan^4(x) + C
Therefore, the antiderivative of 2 tan^3(x) sec(x) dx is (1/4) tan^4(x) + C, where C is the constant of integration.
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Last month it rained 16 out of 30 days. Which ratio is equivalent to the number of days it did NOT rain last month?
A.32:60
B.8:15
C.7:15
D.6:3
Answers
c, 7:15
Hope this helps! May I please have brainliest? :D
Answer:
C.7:15
Step-by-step explanation:
•<Have a nice day
•Hope this helps•
The microsphere nanoscope is a powerful tool that allows humans to see structures 9 × 10–9 meter in diameter.
How is this number expressed in standard form?
Answers
The standard form of the microsphere nanoscope that allows humans to see structure is a diameter of 9 * 10⁻⁹ meter.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.
A standard form is a form of writing an equation, number, or an expression in a form using certain rules.
The standard form of the microsphere nanoscope that allows humans to see structure is a diameter of 9 * 10⁻⁹ meter.
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There are _____________ natural numbers between n2 and (n+1)2
Answers
Answer:
there is only 1 natural number between n2 and (n+1)2
Step-by-step explanation:
expand/open brackets of (n+1)2
(2×n)+(2×1) = 2n+2 can also be written as n2+2
the questions asks for the numbers between so the number between is n2+ 1. we should not count the n2 and n2+2
this is the "closure" property of natural numbers
Answer:
1
Step-by-step explanation:
convert 7.25 kL to mL
Answers
So that would be 7250 ok
What is the value of -2 to the power of 4
Answers
We can find the value if we write the complete expression:
\((-2)^4=(-2)\cdot(-2)\cdot(-2)\cdot(-2)\)Considering only two factors at a time, and knowing that - * - = +, we have:
\((-2)\cdot(-2)\cdot(-2)\cdot(-2)=4\cdot4=16\)Therefore, (-2)^4 = 16
Answer:
-16!!
-2x-2x-2x-2= -16.
Find the coordinates of the image of G(−3,9) after the translation (x,y)→(x+10,y−7) .
(13, 2)
(13, 16)
(7, 16)
(7, 2)
Answers
Answer:
D. (7,2)
Step-by-step explanation:
-3 +10 is 7
9-7 is 2.
kinda just put them together, you get (7, 2)
I hope this helps!
pls ❤ and mark brainliest pls!
The image of (-3, 9) is (7,2).
Mathematically speaking, a translation is defined by the following operation:
\(P'(x, y) = P(x,y) + T(x,y)\) (1)
Where:
\(P(x,y)\) - Original point.\(T(x,y)\) - Translation vector.\(P'(x,y)\) - Resulting point.If we know that \(P(x,y) = (-3, 9)\) and \(T(x,y) = (10, -7)\), then the resulting point is:
\(P'(x,y) = (-3, 9) + (10, -7)\)
\(P'(x,y) = (7, 2)\)
Hence, the image of (-3, 9) is (7,2).
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If f(x) = 9^x , them prove that : f(m+n+p) = f(m) × f(n) × f(p) .
Answers
Answer:
f(m+n+p) = 9^(m+n+p)
while f(m) × f(n) × f(p) = 9^m+9^n+9^p = 9^(m+n+p)
so the second property explains why it's a + instead of ×
you need to paint office 143. if one gallon of paint covers 50 sf, how many gallons of pant will you need?
Answers
To determine the number of gallons of paint needed to cover office 143, we need to know the square footage of the office.
Once we have that information, we can divide the square footage by the coverage rate per gallon to calculate the required amount of paint.
Let's assume the square footage of office 143 is 800 square feet.
Number of gallons needed = Square footage / Coverage rate per gallon
Number of gallons needed = 800 square feet / 50 square feet per gallon
Number of gallons needed = 16 gallons
Therefore, you would need approximately 16 gallons of paint to cover office 143, assuming each gallon covers 50 square feet.
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The slope of the line which connect
points G(-3, -2) and H(x, 11) is
undefined. What is the value of x?
Answers
Answer:
-3
Step-by-step explanation:
A vertical line has undefined slope. These two points will be stacked one directly above (below) the other. The x will be the same in both points.
So the unknown in H(x,11) is -3
H (-3, 11)
Answer:
Below
Step-by-step explanation:
Vertical lines have slope = 'undefined'
so the 'x' values in the two points have to be the same (vertical line)
x = -3
As a side note: Horizontal lines have a slope = 0
Juan invests $7500 at 6% interest in one year. How much money will he have if the interest were compounded A. yearly B. Daily C. why are the amounts in answers a and b different
Answers
Answer:
A) 7,950$, B) 7,963.73$, C) Since daily interest means that 6%/365 of 7500 will be added and compounded every day for the given amount of time(in this case, one year), while annual interest means that 6% of 7500 will be added and compounded yearly for the given amount of time(I'm this case, one year).
Step-by-step explanation:
Given the compound interest formula, A = P(1+r/n)^nt, where A = total amount(final amount), P = principle or amount of money deposited(starting amount), r = annual interest rate(percent interest in respect to t ; decimal = %/100), and n = conversion rate(number of times compounded per t; how much is it compounded)
t = time(time in respect to years ; how long it is compounded).
For A) A = 7500( 1 + 6%/365 ) ^ 365 = 7500(1 + 0.06/365) ^365 = 7500(1 + 0.00016438356..)^365= 7500(≈1.0001644^365) = 7500(100.01644%^365) = 7500(≈106.183%) = 7963.725 ≈ 7963.73$
For B) A = 7500( 1 + 6% ) ^ 1 = 7500(1 + 0.06) = 7500(1.06) = 7500(106%) = 7950$
C) this is because compounding something with a higher frequency leads to a different percentage (as n approaches infinity with time proportional to the annual rate, the ratio between the principle and total amount are proportional to e)
quadrlateral abcd has coordinates A(3,-5) B (5, -2) C (10, -4) D (8,-7) quadrilateral abcd is a (4 points)
Answers
Answer:
a square
Step-by-step explanation:
What is the distance between A(7, 4) and B(2, −8)?
Answers
Answer:
The distance would 13 square units
Step-by-step explanation:
Well follow the formula
=√(2−1)^2+(2−1)^2
Plug in everything and solve, remeber to follow order of operations
Write the slope-intercept form of the equation of each line.3) 6x - 8y = 404) -10 + 3x = -5y
Answers
Given data:
The expression for the equation of the line is 6x-8y=40.
The given equation can be written as,
6x-8y=40
8y=6x-40
y=6x/8-40/8
=3x/4-5
Thus, the slope intercept form is y=3x/4-5.
Can someone help me on this question I kinda forgot how to find slope lol
Answers
Answer:
D
Step-by-step explanation:
Can someone help me with this
Answers
Answer:
Options A, C, and F
Step-by-step explanation:
Jennifer opened a savings account a year ago. Her savings account earned $12 in interest and now has a balance of $1012. What was her initial investment (principal)?
Answers
Answer:
I think its $1000
Step-by-step explanation:
if she earned $12 the 1012-12=1000
Answer:
I really don't know much but this is what I know
If she has $12 dollars in interest and a year later she has $1012 making it so she earned EXACTLY $1,000 in the time being.
Please help! See the image.
Answers
3(4 - 2/3x > 2 - x)
12 - 2x > 6 - 3x
+ 3x + 3x
12 + x > 6
-12 -12
x > -6
Put an open circle on -6 (like this o), and the line is going RIGHT.
I attached what it should look like.
Hope that helps!
15% off of $60, then subtracting 10% from that cost, is equal to
Answers
Answer:
8.1 i think
Step-by-step explanation:
What is the missing statement and the missing reason in step 5? A 2-column table with 7 rows. Column 1 is labeled statements with the entries measure of angle A D E = 60 degrees and measure of angle C D F = (3 x + 15) degrees, angle A D E and angle C D F are vertical angles, angle A D E is-congruent-to angle C D F, measure of angle A D E = measure of angle C D F, question mark, 45 = 3 x, and, 15 = x. Column 2 is labeled reasons with the entries given, definition of vertical angles, vertical angles congruent, definition of congruency, question mark, subtractive property, division property. Statement: 60 = 3x + 15; Reason: substitution Statement: x = 15; Reason: subtraction property of equality Statement: 60 = 3x + 15; Reason: transitive property Statement: x = 15; Reason: subtraction and division properties of equality
Answers
Answer:
Statement: 60 = 3x + 15; Reason: substitution
(aka A)
Step-by-step explanation:
The missing statement and the missing reason in step 5 is;
Statement: 60 = 3x + 15; Reason: substitution
Here,
We have to find the missing statement and missing reason.
What is Substitution method?
Substitution method is algebraic method to solve the linear equations .
Now,
Column 1 and column 2 are labeled here as;
Angle A D E = 60 degrees ( entries given)
Angle C D F = (3 x + 15) degrees
Angle A D E and Angle C D F are vertical angles. (definition of vertical angles)
Angle A D E is-congruent-to Angle C D F. ( definition of congruency)
Measure of angle A D E = Measure of angle C D F.
⇒ 60 = 3x + 15 ( substitution )
⇒ 45 = 3 x ( subtractive property )
⇒ 15 = x ( division property )
Hence, The missing statement and the missing reason in step 5 is;
Statement: 60 = 3x + 15; Reason: substitution
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what is the area? Please help me.
Answers
Answer:
106 square meters.
Step-by-step explanation:
First find the whole orange rectangular figure and then remove a part of it. The original orange figure appears to be 10 x 12 = 120 m. Next we would need to find the amount that is removed. To find this we need to find the length and width of the thing. The length is 7 and the width looks to be 10 - 4 - 4 = 2. 7 x 2 = 14. Subtract 14 from 120 to get 106 square meters.
Answer: 106 m^2
Step-by-step explanation:
For her birthday party, Kelly invited her friends to a nearby roller-skating rink. The area of the rectangular rink is 1,530 ft2, and the length is 51 ft. What is the width of the rink?
Answers
Answer:
30ft
Step-by-step explanation:
1530ft2 divided by 51ft.
2. The height (cm) of a plant during a period can be described with a function where time is 24 hours after planting. y=3+34x
How tall is the plant after 4 days?
What does the value y=3 mean?
Answers
Here given ,
y = 3 + 34x
We have to find height of plant after 4 days,
so, x = 4,
by substituting x,
y = 3 + 34 x 4
= 3 + 136
= 139 cm
here y = 3 means,
The corresponding function when the value of y =3 .
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