Answer: The value of x is [tex]\frac{50}{3}[/tex]
Step-by-step explanation:
Let the original price of gasoline be y
Since we have given that
Price of gasoline rose by 20% during January fell by 20% during February rose by 25% in March and fell by x% in April.
So, According to question,
In January, Price became
[tex]\frac{100+20}{100}\times y=\frac{120}{100}\times y=\frac{6}{5}\times y=\frac{6y}{5}[/tex]
Similarly, In February, Price became
[tex]\frac{100-20}{100}\times \frac{6y}{5}=\frac{80}{100}\times \frac{6y}{5}=\frac{4}{5}\times \frac{6y}{5}=\frac{4}{5}\times \frac{6y}{5}=\frac{24y}{25}[/tex]
Similarly, in March, Price became,
[tex]\frac{100+25}{100}\times \frac{4\times 6y}{25}=\frac{125}{100}\times \frac{6\times 4y}{25}=\frac{5}{4}\times \frac{24y}{25}=\frac{5}{4}\times \frac{24y}{25}=\frac{6y}{5}[/tex]
similarly, in April , Price became,
[tex]\frac{100-x}{100}\times \frac{6y}{5}[/tex]
so, we have given that the price of gasoline at the end of April was the same as it had been at the beginning of January.
So, it becomes,
[tex]\frac{6y}{5}\times \frac{100-x}{100}=y\\\\6(100-x)=500\\\\600-6x=500\\\\600-500=6x\\\\100=6x\\\\x=\frac{100}{6}=\frac{50}{3}[/tex]
Hence, the value of x is [tex]\frac{50}{3}[/tex]
Answer:
x= 16 2/3
Step-by-step explanation:
Price will be p
The price in January increases by 20%, it will be 6p/5. The price in February decreased by 20%, it becomes 24p/25. The price in March rose by 25%, it will be 6y/5.
April: 6y/5 times 100-x/100 = p 6(100-x)=500 100=6x x= 16 2/3
Diego has 49 square inch tiles. He wants to use to make a square mosaic. How long can each side of the mosaic be?
Answer:
side of the mosaic = 7 inches
Step-by-step explanation:
Diego has 49 square inch tiles. He wants to use to make a square mosaic.
Area of the tile = 49 square inches
We know , area of the square = s^2
where 's' is the side of the square
[tex]Area = s^2[/tex]
Plug in 49 for area and solve for 's'
[tex]49 = s^2[/tex]
Take square root on both sides
s= 7
side of the square = 7 inches
Diego can make a square mosaic where each side is 7 inches using his 49 square-inch tiles. This is found by calculating the square root of the total area.
Explanation:The subject of this question is Mathematics, specifically dealing with square roots and area calculations. Diego has 49 square inch tiles and wants to make a square mosaic. Since a square has equal sides, the length of each side of the mosaic will be the square root of the total area. The total area of the tiles is 49 square inches. The square root of 49 is 7. Therefore, each side of Diego's mosaic will be 7 inches in length. This conclusion is reached by understanding how the area of a square works. The area of a square can be calculated by multiplying the length of one side by the length of another side. When we know the total area, we can find the length of one side by taking the square root.
Learn more about Square Roots here:https://brainly.com/question/3120622
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How many degrees are each angle of a regular 7 sided shape?
Answer:
Step-by-step explanation:
Here is a diagram of a seven sided regular polygon. You use this diagram to find out how many degrees total are in the interior of a the heptagon. There are 5 such triangles which means that since each triangle has 180o the total amount of the interior angles must be 5 * 180 = 900
Since there are 7 interior angles, the answer to how large each one of them is is found by
900/7 = 129.57 which is slightly off because it is a rounded error.
In general, the size of the angles in a regular polygon
180(n - 2 ) / n
Where n is the number of degrees in each interior angle. For example for an 8 sided figure you would get
180(8 - 2) / 8 = 180 * 6/8 = 133 degrees.
A leprechaun places a magic penny under a girl's pillow. The next night there are 2 magic pennies under her pillow. Each night the number of magic pennies doubles. How much money will the girl have after 22 nights?
Answer:
tn = 2097152 penniestn = 20971.52 dollars.Step-by-step explanation:
A surprisingly large amount of money.
The question is "Does the amount of money just double or do the previous amounts add to the present amount?"
I think it just doubles. Not only that, but she can't spend any of it until night 22 is reached.
tn = a*2^(n - 1)a = 1 She starts with 1 penny.n = 22tn = 1*2^(22 - 1)tn = 1*2^21tn = 2097152 penniestn = 20971.52 dollars.I need some help with math
Answer:
PT, VP
Step-by-step explanation:
if p is the center and T V and W are on the circle
the radius goes from the center of the circle to the edge of the circle
then PW PT and PW are radii of the circle
What is the slope of the line
Answer:
The slope is 7/4.
What is the probability that someone in the survey considered reading books or surf the internet as the best entertainment?
Answer:
31/100
Step-by-step explanation:
From the given table
Reading books percentage is 22
so Probability (reading books) = [tex]\frac{22}{100}[/tex]
Surf the internet percentage is 9
Probability (surf the internet) =[tex]\frac{9}{100}[/tex]
the probability (reading books or surf the internet)= P(reading books) + P(surf the internet)
probability (reading or surf)= [tex]\frac{22}{100} +\frac{9}{100}[/tex]
= [tex]\frac{31}{100} [/tex]
Answer:
Answer is [tex]\frac{31}{100}[/tex]
Step-by-step explanation:
values given in table
Reading books percentage is 22
hence we can write probability as
Probability (reading books) = [tex]\frac{22}{100}[/tex]
percentage of surfing internet is= 9
Probability of surfing internet is =[tex]\frac{09}{100}[/tex]
the probability (reading books or surf the internet)= P(reading books) + P(surf the internet)
probability (reading or surf)= [tex]\frac{22}{100}[/tex]+[tex]\frac{09}{100}[/tex]
=[tex]\frac{31}{100}[/tex]
PLEASE HELP!!
Given: line segment AB is 10 inches long.
Find the length of A'B' if AB is dilated to form A'B' with a scale factor of 2.
A) 1/2 inches
B) 5 inches
C)10 inches
D)20 inches
Answer:
D or 20
Step-by-step explanation:
If the scale factor is 2 then you take the original number, 10, and multiply it by 2.
10*2=20
Answer:
Option D). 20 inches
Step-by-step explanation:
Length of AB which is of length = 10 inches.
If the length of AB is dilated to form A'B' with a scale factor of 2, then we have to find the length of A'B'
Since we know the formula of dilation as
New dimension = Scale factor × Old dimension
So A'B' = Scale factor × AB
A'B' = 2× 10 = 20 Inches
Option D). 20 inches is the solution.
Can someone please explain how to solve this step by step with answer? Thank you.
a)
well, she put 4000, and she earned in interest 960, so her accumulated amount is just their sum, 4960.
b)
now, it doesn't say, so we're assuming is simple interest, as opposed to compound interest.
[tex]\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill&960\\ P=\textit{original amount deposited}\dotfill & \$4000\\ r=rate\to r\%\to \frac{r}{100}\dotfill\\ t=years\dotfill &3 \end{cases} \\\\\\ 960=(4000)(r)(3)\implies \cfrac{960}{(4000)(3)}=r\implies 0.08=r \\\\\\ \stackrel{\textit{converting to percentage}}{r=0.08\cdot 100}\implies r=\stackrel{\%}{8}[/tex]
c)
let's make the rate 1% greater then, and check
[tex]\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill\\ P=\textit{original amount deposited}\dotfill & \$4000\\ r=rate\to \stackrel{8+1}{9\%}\to \frac{9}{100}\dotfill&0.09\\ t=years\dotfill &3 \end{cases} \\\\\\ I=(4000)(0.09)(3)\implies I=1080 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{at 9\%}}{1080}-\stackrel{\textit{at 8\%}}{960}\implies \stackrel{\textit{that much more}}{120}[/tex]
The sum of two numbers is 80. The larger number is four more than three times the smaller number. Find both numbers.
Let the smaller number = X
Then the larger number is 3x+4 ( four more than 3 times the smaller number)
The sum of both numbers = 80
so you have X + 3X+4 = 80
Simplify the left side:
4x+4 = 80
Subtract 4 from each side:
4x = 76
Divide both sides by 4:
X = 76/4
X = 19
The smallest number is 19
The largest number is 80 - 19 = 61 ( check: 3*19 = 57+4 = 61)
The two numbers are 19 and 61
List the following numbers in order from least to greatest. 2.31,2.13,0.123,3.12
Answer:
Step-by-step explanation:
0.123
2.13
2.31
3.12
That is least to greatest. I hope I answered your ?. Can you help me?
Answer:
0.123, 2.13, 2.31, 3.12
Step-by-step explanation:
look at first number and put those in order.
with both numbers that start with 2, look at the next number and put the lowest one first
Given: ABCD is a rectangle. If AC = 10, then BD = 5 8 10
Answer:
[tex]BD=10[/tex]
Step-by-step explanation:
We are given rectangle ABCD
Firstly, we will draw a rectangle
we can see that
AC and BD are diagonals of rectangle
and we know that
Diagonals of any rectangle are always equal
so,
[tex]AC=BD[/tex]
we are given
AC=10
we can plug it
and we get
[tex]10=BD[/tex]
so,
[tex]BD=10[/tex]
What true about centimeters and kilometers
Answer:
Centimeters and kilometers are used to measure length
Step-by-step explanation:
Centimeters and kilometers are related to each other.
We can represents centimeters in kilometers and kilometers in centimeters
Short form
The short form of kilometers = km
The short form of centimeters = cm
1 km = 100000 cm
1 cm = 1/100000 km
We can also represent both in terms of meters
1 m = = 100 cm
1000 m = 1 km
Find 1/8 of 12. Express your answer in simplest form.
1 1/2
2/3
1/96
12/8
Question
Find 1/8 of 12. Express your answer in simplest form.
1 1/2
2/3
1/96
12/8
Answer:
1 1/2Step-by-step explanation:
12 : 8 = 1.5 (1 1/2)
To find 1/8 of 12, multiply 12 by 1/8 and simplify the fraction to its simplest form, which is 3/2.
Explanation:To find 1/8 of 12, we can multiply 12 by 1/8. Multiplying fractions is done by multiplying the numerators together and multiplying the denominators together. In this case, 12 multiplied by 1 equals 12, and 8 multiplied by 1 equals 8, so the answer is 12/8.
However, 12/8 is not in simplest form because the numerator and denominator have a common factor of 4. To simplify the fraction, we divide both the numerator and denominator by 4. 12 divided by 4 is 3, and 8 divided by 4 is 2. So, the simplest form of 12/8 is 3/2.
Learn more about Multiplying Fractions here:https://brainly.com/question/660389
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One minus the product of four and a number x
Answer:
[tex]1-4x[/tex]
Step-by-step explanation:
A product of two numbers is the result we get from multiplying them together. The product of 4 and x would then be [tex]4\times x[/tex], which we can rewrite as [tex]4x[/tex]. We're then told by the statement "one minus the product..." that we'll be taking this [tex]4x[/tex] away from 1, giving us the answer [tex]1-4x[/tex].
Answer:
The numerical expression would be 1-4x
Step-by-step explanation:
[One] - [minus] [the product of]
4 and x is the product of 4 and 4.x
10 Points! No wrong answers pls
The answer is 12
i hope this helps
Answer:
the answer is 12 units squared
Step-by-step explanation:
count the boxes and add the halves together.
Hope this helps :)
7x−5=4y−6 x determine the intercepts of the line
Answer:
see explanation
Step-by-step explanation:
to find the intercepts, that is where the line crosses the x and y axes
• let x = 0, in the equation for the y-intercept
• let y = 0, in the equation for x-intercept
x = 0
⇒ - 5 = 4y ( divide both sides by 4 )
y = - [tex]\frac{5}{4}[/tex] ← y- intercept
y = 0
7x - 5 = - 6x ( add 6x to both sides )
13x - 5 = 0 ( add 5 to both sides )
13x = 5 ( divide both sides by 13 )
x = [tex]\frac{5}{13}[/tex] ← x- intercept
Evaluate the expression when x = 4. 3x + 2 A. 36 B. 24 C. 18 D. 14
Put the value of x = 4 to the expression 3x + 2.
(3)(4) + 2
first multiplication and next addition
= 12 + 2 = 14
Answer: D. 14wat is 78×748 plz help i cant be on mah phone someone answer quick plz
Answer:
the answer is 58344
Step-by-step explanation:
word form of 16.0215
Answer: sixteen and two-hundred fifteen ten thousandths
You'd have to correspond the numbers to words and associate the period with and
Answer: Sixteen and two hundred fifteen ten-thousandths
We read off "16" as normal. Nothing too special about it.
The same goes for the 0215 which is really just 215, even though this part is after the decimal point. However, because it is after the decimal point, we tack on a "ten thousandths" to indicate it's a fractional non-whole portion
Note: if you change the 0 to something like a 3, then we would have 3215 which is less than ten-thousand. This might help you remember that four decimal spots out is the ten-thousandth place value.
another note: the "and" mentioned in the answer is a key word that indicates "decimal point". Only use it for decimal points. Do not use it for a number like "215". In other words, don't say "two hundred and fifteen" because that might seem like you are trying to say 2.15 or something along those lines.
Given the equation: y−6=1/2(x+2) in point slope form, rewrite the equation into standard form. Show your work for full credit.
Answer:
x - 2y = - 14
Step-by-step explanation:
the equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
given y - 6 = [tex]\frac{1}{2}[/tex](x + 2)
multiply all terms by 2 to eliminate the fraction
2y - 12 = x + 2 ( subtract 2 from both sides )
2y - 14 = x ( subtract 2y from both sides )
- 14 = x - 2y, hence
x - 2y = - 14 ← in standard form
A guide wire for a palm tree makes a 32°angle with the ground and is staked 6 feet from the base of the tree. What is the length, to the nearest tenth of a foot, of the guide wire from the ground to the palm tree? A. 7.1, B. 8.5, C. 9.6, D. 11.3
Answer:
b) 8.5 feet
Step-by-step explanation:
Answer:
Answer is 9.6
Step-by-step explanation:
From the illustration above. See attachment for interpretation of this illustration.
To find the part label a in the attachment which is the length of the foot of the guide wire from the ground to the palm tree, we apply the sine rule, which says
a/sineA = b/sineB
In this case
a = ? , A = 58° , b = 6ft, B = 32°
So
a/sine58 = 6/sine32
a/0.848 = 6/0.5299
a = 6*0.848/0.5299
a = 5.088/0.5299
a = 9.601 ~ 9.6
1.74÷(−0.06)?
PLEASE HELP ME
1.74/-0.06 is -29.
You can use your calculator next time. Its easier than using points.
angle rst = 2x+8, angle tsw= 3x+14, angle rsw= 7x-2. find tsw. apparently x= 12, but idk the steps to get it bc whatever i do, i get 6x=8... please help
Answer:
angle(TSW) is 18
Step-by-step explanation:
we are given angles
angle(RST)=2x+8
angle(TSW)=3x+14
angle(RSW)=7x-2
Firstly, we will draw diagram
so, we get
angle(TSW)=angle(RST)+angle(RSW)
so, we can plug values
[tex]3x+14=2x+8+7x-2[/tex]
now, we can solve for x
[tex]9x-3x=14-6[/tex]
[tex]6x=8[/tex]
now, we can solve for x
[tex]x=\frac{4}{3}[/tex]
now, we can find angle (TSW)
angle(TSW) is
[tex]=3\times \frac{4}{3} +14[/tex]
[tex]=4 +14[/tex]
[tex]=18[/tex]
So, angle(TSW) is 18
To solve for x, we set up an equation based on the sum of angles forming a straight line. Solving the equation, we find x=12. Substituting x into the equation for angle tsw, we find that angle tsw measures 50 degrees.
To find the value of x for the angles rst, tsw, and rsw, you need to understand that they are all connected by their location on a straight line or a point. If angles rst and tsw are adjacent angles that form a straight line, their measures would add up to 180° because a straight line measures 180°. The same is true for the angle rsw if it is the full angle at that point or the sum of angles rst and tsw.
The equations are given as:
angle rst = 2x + 8angle tsw = 3x + 14angle rsw = 7x - 2Since angle rsw is the full angle, you can write the equation:
7x - 2 = (2x + 8) + (3x + 14)
Now, solve for x:
7x - 2 = 2x + 8 + 3x + 14
7x - 2 = 5x + 22
7x - 5x = 22 + 2
2x = 24
x = 24 / 2
x = 12
Now that we have the value of x, we can find angle tsw by substituting x into its equation:
angle tsw = 3x + 14
angle tsw = 3(12) + 14
angle tsw = 36 + 14
angle tsw = 50°
2x + 5y = 17 and 6x - 5y = -9 what is the solution of the system use elimination
x = 8.5 + 2.5y answer one can’t figure out answer two. Sorry
Answer:
{x = 1 , y = 3
Step-by-step explanation:
Solve the following system: using elimination:
{2 x + 5 y = 17 | (equation 1)
{6 x - 5 y = -9 | (equation 2)
Swap equation 1 with equation 2:
{6 x - 5 y = -9 | (equation 1)
{2 x + 5 y = 17 | (equation 2)
Subtract 1/3 × (equation 1) from equation 2:
{6 x - 5 y = -9 | (equation 1)
{0 x+(20 y)/3 = 20 | (equation 2)
Multiply equation 2 by 3/20:
{6 x - 5 y = -9 | (equation 1)
{0 x+y = 3 | (equation 2)
Add 5 × (equation 2) to equation 1:
{6 x+0 y = 6 | (equation 1)
{0 x+y = 3 | (equation 2)
Divide equation 1 by 6:
{x+0 y = 1 | (equation 1)
{0 x+y = 3 | (equation 2)
Collect results:
Answer: {x = 1 , y = 3
There are 732 students trying out for baseball teams there will be exactly 15 players on each team how many students will not make a baseball team
I need help its due tomorrow
Answer:
12) -60/1 =60
14) 110
16)45
18) 7
32) -18
Step-by-step explanation:
What Multiplies to get 540, but adds to get -16?
Polynomial help! Show your work! There is no multiple choice. I know how to solve the problem just can’t figure this one step
A committee of three students is to be formed from six juniors and five seniors. If three names are drawn at random, what is the probability that they are all juniors or all seniors?
turn 20/12 into a mixed number
Answer:
1 2/3
Step-by-step explanation:
well first reduce it which would be 5/3 since the greatest common denominator would be 4. Then put 3 in the 5 which goes only once and 2 is left over. Keep the threeas the denominator instead of the numerator.
Use the given graph to determine the limit, if it exists.
Find lim f(x) x\to 3
A. -1
B. 7
C. -3
D. Does not exist
Answer:
Correct choice is D
Step-by-step explanation:
The graph of the function shows that the function is not continuous at point x=3.
When moving to the point x=3 from the left side, you can see that y approaches to -1. When moving to the point x=3 from the right side, then y approaches to -3 and at x=3, y=7. This gives you that the limit doesn't exist.