Answer:
[tex]\large\boxed{\dfrac{8}{9}n-\dfrac{4}{3}}[/tex]
Step-by-step explanation:
[tex]\dfrac{4}{9}(2n-3)\qquad\text{use the distributive property}\\\\=\left(\dfrac{4}{9}\right)(2n)+\left(\dfrac{4}{9}\right)(-3)=\dfrac{8}{9}n-\dfrac{4}{3}[/tex]
Equivalent expression are the equation which have the same identical solution for the variable but the way of representation is different. The given expression in the problem is equivalent to the,
[tex]f(n)=\dfrac{8}{9}n -1\dfrac{1}{3}[/tex]
Thus the option 4 is the correct option.
Given Information-The given expression [tex]f(n)[/tex] is,
[tex]f(n)=\dfrac{4}{9} (2n-3)[/tex]
Equivalent expression-Equivalent expression are the equation which have the same identical solution for the variable but the way of representation is different.
Open the bracket of above equation by multiplying the fraction with the numbers inside the bracket.
[tex]f(n)=\dfrac{4\times 2n}{9} -\dfrac{4\times 3}{9}[/tex]
[tex]f(n)=\dfrac{8n}{9} -\dfrac{12}{9}[/tex]
[tex]f(n)=\dfrac{8n}{9} -\dfrac{4}{3}[/tex]
Fraction 4/c can be written as the mixed number. Thus,
[tex]f(n)=\dfrac{8}{9}n -1\dfrac{1}{3}[/tex]
Hence the given expression in the problem is equivalent to the,
[tex]f(n)=\dfrac{8}{9}n -1\dfrac{1}{3}[/tex]
Thus the option 4 is the correct option.
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............................................................h............................................................help............................................................
Answer:
D (136 -2a) + (3a+39) = 180
Step-by-step explanation:
Since XQR = 180
<XQM + < MQR = XQR
136 -2a + (3a+39) = 180
A tree company charges a delivery fee for each tree purchased in addition to the cost of the tree. The delivery fee decreases as the number of trees purchased increases. The table below represents the total cost of x trees purchased, including delivery fees.
Which best describes why the function is nonlinear?
The rate of change between 1 and 2 trees is different than the rate of change between 2 and 3 trees.
The rate of change between 1 and 2 trees is different than the rate of change between 1 and 3 trees.
The rate of change between 2 and 3 trees is different than the rate of change between 3 and 4 trees.
The rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.
The correct option is d) The rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.
Step-by-step explanation:
Given :
Number of tree purchased Total Cost ($)
1 60
2 120
3 180
4 240
5 290
Solution :
For a linear function rate of change is constant.
Now, between 2 and 3 trees rate of change is given by
[tex]=\dfrac{180-120}{3-2}=60[/tex]
Now, between 3 and 5 trees rate of change is given by
[tex]=\dfrac{290-180}{5-3}=55[/tex]
It is clearly seen that the rate of change is not constant. Therefore, the function is non-linear.
Therefore, the correct option is d) The rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.
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Step-by-step explanation:
Given information:
Number of tree purchased and total cost:
No. Cost($)
1 60
2 120
3 180
4 240
5 290
The rate of change between 2 and 3 is given by
[tex]=\frac{180-120}{3-2}=60[/tex]
Now, between 3 and 5 the change is given by:
[tex]=\frac{290-180}{5-3} =55[/tex]
From the above information one can conclude that the change is not constant and hence the function is not linear.
Hence, The correct option is: The rate of change between 2 and 3 is different than the rate of change between 3 and 5 trees.
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The playlist consists of 21 songs by The Working Mamas, 12 songs by Chef Mo Cheese, 36 songs by the Snippers, 54 by Lucy and The Jungle Cats, and 27 by Nuestra Paradise. If her playlist randomly shuffles through each song, what is the probability of The Working Mamas being played? Write the answer as a percent.
Answer:
14%
Step-by-step explanation:
Answer:
The answer is 14%
Step-by-step explanation:
Two sides of a triangle have lengths 10 and 18. Which inequalities describe the values that possible lengths for the third side?
Answer:
[tex]8\ units < x < 28\ units[/tex]
Step-by-step explanation:
we know that
The Triangle Inequality Theorem, states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side
Let
x---->the possible lengths for the third side
Applying the triangle inequality theorem
Analyze two cases
case 1)
[tex]10+18 > x[/tex]
[tex]28 > x[/tex]
Rewrite
[tex]x < 28\ units[/tex]
case 2)
[tex]10+x > 18[/tex]
[tex]x > 18-10[/tex]
[tex]x > 8\ units[/tex]
therefore
The inequalities that describe the values that possible lengths for the third side are
[tex]x > 8\ units[/tex]
[tex]x < 28\ units[/tex]
The compound inequality is
[tex]8\ units < x < 28\ units[/tex]
The possible lengths for the third side of a triangle with sides of lengths 10 and 18 can be found using the triangle inequality theorem. These lengths are denoted by 'x', and must satisfy the inequalities: 8 < x < 28. This rule applies to all triangles, not just right-angled ones.
Explanation:The question relates to the rules governing triangle side lengths. Specifically, the question draws from the triangle inequality theorem, which states that the length of any side of a triangle must be less than the sum of the lengths of the other two sides, but more than the absolute difference of those lengths. Hence, for a triangle with sides of lengths 10 and 18, the possible lengths of the third side (denoted 'x') must satisfy the inequalities: 8 < x < 28.
These inequalities come from the principle that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side: 10 + 18 > x and 18 - 10 < x. Otherwise, the lengths would not meet to form a closed three-sided figure.
It's also worth noting that these rules hold true for any triangle, not just right triangles. Hence, this problem doesn't involve the Pythagorean theorem, which specifically relates the sides of a right-angled triangle.
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A small plane travels north at 240 mph. A jet leaves the same airport 30 minutes later and follows the other plane at 360 mph. How long does it take the jet to take over the other small plane? what distance are they from the airport?
SHOW ALL YOUR EQUATIONS.
Two cars start at the same point and travel in the same direction on the same road. one travels 50 kmph and the other 45kmph. After how many hours will they be 20km apart?
SHOW ALL YOUR EQUATIONS, USE ALGEBRAIC EQUATIONS.
Thank you!
1.
Solution here,
let the both planes covers same distance x while over taking.
For the small plane, let time be t.
speed= 240 mph
now,
distance covered by it,
x=240t--------(1)
For jet plane,let the time be t'.
speed=36mph
since it is flewed after 30 mins, it can be written as,
t'=t-30 min=t-0.5 hr
now distance covered by it,
c=360t'=360(t-0.5)=360t-180----------(2)
equating (1) and (2)
240t=360t-180
or, -120t=-180
or, t=1.5 hr
therefore two planes wiil meet after 1.5 hrs.
putting the value of t in (1)
x=240×1.5=360 m
therefore they travel through 360 m from the airport whlie over taking.
2.
For the first car,
speed=50 Kmph
let it covers x distance at time t
so,diatance x=50t--------(1)
For the second car,
speed=45 Kmph
according to the question, in time t, it will covers the distance (x-20)Km
so, distance(x-20)=45t
or, x=45t+20---------(2)
equating (1) and (2),
50t=45t+20
or, 5t=20
or, t=4 hrs.
therefore cars will be apart of 20 km after 4 hrs.
The jet will overtake the small plane in 1 hour, and they will be 360 miles from the airport. Two cars traveling at 50 kmph and 45 kmph will be 20 km apart after 4 hours.
Explanation:To solve for the time it takes for the jet to overtake the small plane, we can use the relative speed between the two planes.
First, we calculate the distance the small plane has traveled in the 30 minutes (0.5 hours) head start:
Distance = speed × time = 240 mph × 0.5 hours = 120 milesNext, we set up the equation to find the time (t) it takes for the jet to catch up:
120 miles + 240t = 360tSolving for t:
120 miles = 360t - 240t120 miles = 120tt = 1 hourThe jet will catch up to the small plane in 1 hour.
To find the distance from the airport when they meet:
Distance = speed of jet × time = 360 mph × 1 hour = 360 milesFor the two cars traveling at different speeds, let's use algebra to determine when they will be 20km apart:
Let t be the time in hours when they are 20 km apart.50t - 45t = 20 km5t = 20 kmt = 4 hoursThe two cars will be 20 km apart after 4 hours.
3. The results of the primary election are shown. (a) Order the popularity of the choices from greatest to least. (b) It was estimated that 280 people were going to vote. If this was true, how many people would have voted for Goron? Show your work. (c) 40 people voted for “Other.” Was the estimate of total voters from Part (b) accurate? Explain.
The answers for the given questions are:
(a) Order of popularity: Goron, Zora, Hylian,Gerudo, Other.
(b) Number of people voting for Goron: 89
(c) The estimate was not accurate.
(a) The popularity of the choices from greatest to least is:
1. Goron
2. Zora
3. Hylian
4. Gerudo
5. Other
(b) To find out how many people would have voted for Goron if 280 people voted in total, we first need to determine the proportion of votes Goron received in the primary election.
Total votes cast in the primary election = Sum of votes for all choices
= Goron + Zora + Hylian + Gerudo + Other
= 100 + 75 + 60 + 40 + 40
= 315 votes
Proportion of votes for Goron = (Votes for Goron / Total votes cast) * 100%
= (100 / 315) * 100%
≈ 31.75%
Now, to find out how many people would have voted for Goron out of the estimated 280 people:
Number of people voting for Goron = (Proportion of votes for Goron / 100%) * Estimated total voters
= (31.75 / 100) * 280
≈ 89 people
(c) The estimate of total voters from Part (b) was not accurate. The estimate was based on the assumption that all choices would receive votes in the same proportion as they did in the primary election. However, in reality, the number of votes for "Other" was higher than expected, indicating that the actual total number of voters might be higher than the estimated 280. Therefore, the estimate was not accurate.
Complete question:
The results of the primary election are shown. (a) Order the popularity of the choices from greatest to least. (b) It was estimated that 280 people were going to vote. If this was true, how many people would have voted for Goron? Show your work. (c) 40 people voted for “Other.” Was the estimate of total voters from Part (b) accurate? Explain.
What is the measure of
60°
50°
65°
70°
Answer:
∠G = 50°
Step-by-step explanation:
The measure of the angle between the 2 tangents is
[tex]\frac{1}{2}[/tex] ( major arc - minor arc )
minor arc HF = 130° and major arc HF = 360° - 130° = 230°
Hence
∠G = 0.5(230° - 130°) = 0.5 × 100° = 50°
A ball is thrown from first base to second base and then from second base to home plate. How many feet has the ball been thrown?
A. 90 √2
B. 90 + 90 √2
C. 180 √2
D. 270 √2
Answer:
B. 90 + 90 √2
Step-by-step explanation:
From first base to the second base, it will travel 90 feet.
From the second base to the home plate, it will travel a longer distance. How much? Well, if you look at the layout of the field, you'll see that if you draw a line from second base to the home plate, you'll form two rectangular triangles, one with the 1st base, another one with the 3rd base.
The line from the 2nd base to home plate is the hypotenuse, which we can easily find by:
h²=90² + 90²
h = √(2 * 90²)
h = 90 √2
So, from second base to home plate, the ball has traveled 90 √2
Overall: 90 + 90 √2
A beach ball has a diameter of 18 inches. What is the approximate volume rounded to the nearest whole number of the ball
The formula for volume of a sphere is V = 4/3 x PI x r^3
r is 1/2 the diameter = 9 inches.
Volume = 4/3 x 3.14 x 9^3 = 3,052 cubic inches.
Answer:
3052 cubic inches
Step-by-step explanation:
George sold 18, 22, 26, 12, 25, 20, and 19 cars per month over the past seven months. He followed the steps below to
determine the number of cars he needs to sell in the next month to have a mean number of sales per month of 24
Step 1: Find the total cars needed to have a mean of 24: 24 x 7 = 168
Step 2. Find the total cars sold: 18+22+26+ 12+25+20+ 19 = 142
Step 3: Subtract the total cars sold from the total cars needed: 168 - 142 = 26
Step 4: State the answer: George needs to sell 26 cars next month.
Where did George make his first mistake?
Answer:
George made the first mistake by multiplying by 7 instead of 8
Step-by-step explanation:
The total cars needed to have a mean of 24:
24 x 8 = 192
Total cars sold during the seven months:
18 + 22 + 26 + 12 + 25 + 20 + 19 = 142
Subtract the total cars sold from the total cars needed:
192 - 142 = 50
George needs to sell 50 cars in the eight month in order to have an average of 24 cars sold per month.
Answer:
Step 1
Step-by-step explanation:
on edg
7(2e−1)−3=6+6e
solve for e
Answer:
2
Step-by-step explanation:
7 ( 2 e - 1 ) - 3 = 6 + 6 e
Expand brackets
14 e - 7 - 3 = 6 + 6 e
Simplify
14 e - 10 = 6 + 6 e
Minus 6 e from both sides
8 e - 10 = 6
Add 10 on both sides
8 e = 16
Divide by 8 from both sides
e = 2
The value of e from the given expression is e = 2.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Given expression is;
7 ( 2 e - 1 ) - 3 = 6 + 6 e
Expand brackets;
14 e - 7 - 3 = 6 + 6 e
Simplify;
14 e - 10 = 6 + 6 e
Minus 6 e from both sides;
8 e - 10 = 6
Add 10 on both sides;
8 e = 16
Divide by 8 from both sides;
e = 2
Hence, the value of e from the given expression is e = 2.
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The mean height of plants is 18 inches. The height of seven plants are 12 inches, 13 inches, 15 inches, 15 inches, 17 inches, 23 inches, and 24 inches. Find the height of the eighth plant.
Answer:
25 inches
Step-by-step explanation:
i first started with 18×8=144 then i did 144-119 and got 25.
Which of the following are exterior angles? Check all that apply.
The correct answers are: C. Angle 4 F. Angle 6 In mathematics, exterior angles are formed outside between any side of a shape and a line extended from the next side.
The correct answer is option C and F.
In a triangle, the sum of the measures of the interior angles is always 180 degrees. Since angles 5, 3, and 1 are interior angles, their sum is 180 degrees.
The sum of the measures of the exterior angles of a triangle is always 360 degrees. Therefore, the sum of exterior angles 4, 6, and 2 is also 360 degrees.
Now, to determine the individual measures of the exterior angles, we know that the sum of the measures of the linear pairs (an exterior angle and its adjacent interior angle) is 180 degrees.
Therefore, angle 4 is an exterior angle since it forms a linear pair with angle 1.
Similarly, angle 6 is an exterior angle since it forms a linear pair with angle 3.
Angle 2 is not an exterior angle since it does not form a linear pair with any other angle in the given triangle.
So, the correct answers are:
C. Angle 4
F. Angle 6
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What is the answer to this Jayla multiplies 8.0 by 40 and says the product is 8.0000 is Jayla correct?
Answer:
No she is wrong
Step-by-step explanation:
The correct answer is 320
Answer:
No, Jayla just added 4 zeros after the decimal.
Identify the inverse variation and graph in which y = 0.75 when x = 4.
Answer:
[tex]y=3/x[/tex] or [tex]yx=3[/tex]
The graph in the attached figure
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]
so
in this problem we have
y=0.75 when x=4
Find the value of k
[tex]y*x=k[/tex]
[tex]k=0.75*4=3[/tex]
The equation is equal to
[tex]y=3/x[/tex]
using a graphing tool
see the attached figure
Answer:
Y=3/x is the correct answer
radius of cylinder = 5 cm
radius of cone = 4 cm
A cylinder has a height of 16 cm and a radius of 5 cm A cone has a height of 12 cm and a radius of 4 cm. If the cone is placed inside the cylinder as
shown what is the volume of the air space surrounding the cone inside the cylinder (Use 3.14 as an approximation of pi)
A
B.
452 16 cm
340.54 cm
C
1055 04 cm
D.
1456 96 cm
Signo
Answer:
C 1055 04 cm
Step-by-step explanation:
We don't need to see the figure, since we know for sure the cone fits into the cylinder (smaller diameter and height).
So, we first need to calculate the volume of the cylinder, which is given by the formula:
VT = π * r² * h
VT = 3.14 * 5² * 16 = 3.14 * 400 = 1,256 cubic cm
Then we calculate the volume of the cone, which is given by:
VC = (π * r² * h)/3
VC = (3.14 * 4² * 12)/3 = (3.14 * 192)/3 = 200.96 cu cm
Then we calculate the void space left inside the cylinder by subtracting the volume of the cone from the volume of the cylinder:
NV = VT - VC = 1,256 - 200.96 = 1,055.04 cu cm
Answer:
C)1055.04cm^3
Step-by-step explanation:
(picture explains)
Consider the dot plot which shows the distribution of data collected on the number of pets at home. Which statement BEST describes the center of the data collected?
A) The mean is greater than the middle value of the range.
B) The median is greater than the middle value of the range.
C) The mean is closer to the middle value of the range than the median.
D) The median is closer to the middle value of the range than the mean.
Answer:
c
Step-by-step explanation:
Mean=7/3
median=2
mode=2
rnge=4
2 1/3 is closer to 3 than 2
Answer:
its C :3Step-by-step explanation:
The dot plot below shows the drawing scores of some students:
A number line is shown from 1 to 5 in increments of 1. The horizontal axis label is Score. There is 1 dot above 1, 2 dots above 2, 3 dots above 3, 2 dots above 4, and 1 dot above 5. The title of the line plot is Dance Scores.
Which statement best describes the shape of the data?
It is symmetric and has a peak at 3.
It is symmetric and has a peak at 5.
It is not symmetric and has a peak at 3.
It is not symmetric and has a peak at 5.
Answer:
It is symmetric and has a peak at 3.
Step-by-step explanation:
Symmetric dot plots are shown to be equivalent on both sides. Any symmetric dot plot can be folded in half and each side will be identical. The peak of a dot plot is where the most dots are located.
Answer:
It is symmetric and has a peak at 3.
Step-by-step explanation:
pls rate thx
a fair die is tossed four times. Find the probability of obtaining each of the following. 5 on all four tosses
Answer:
[tex]\dfrac{1}{1296}[/tex]
Step-by-step explanation:
When a fair die is tossed once, there are 6 possible outcomes: 1, 2, 3, 4, 5, 6.
The probability of rolling 5 is [tex]\dfrac{1}{6}.[/tex]
When a fair die is tossed four times, the probability of rolling 5 all four times is
[tex]\dfrac{1}{6}\cdot \dfrac{1}{6}\cdot \dfrac{1}{6}\cdot \dfrac{1}{6}=\dfrac{1}{6^4}= \dfrac{1}{1296}[/tex]
y=5x Identify the dependent and independent variables.
Independent is x. Dependent is y
Answer:
Independent : x
Dependent: y
Step-by-step explanation:
y= 5x
The independent variable is the variable we change
Independent : x
The dependent variable depends on the value of the other variable
Dependent: y
work out the hcf of 600 and 128
The answer is 8
You work out all the factors for both 600 and 128 and they are :
600 -1,600,2,300,3,200,4,150,5,120,6,100,8,75,10,60,12,50,15,40,20,30,24 and 25
128-1,128,2,64,4,32,8 and 16
And you see what is the highest common factor which is 8
Which of the following is the solution to 3/x + 2/(x+1) = 3/5x?
-11/6
-6/11
11/6
6/11
Answer:
3/x + 2/(x+1) = 3/5x
[3 · 5(x + 1) + 2 · 5x] / 5x(x + 1) = 3(x + 1) / 5x(x + 1)
3 · 5(x + 1) + 2 · 5x = 3(x + 1)
15x + 15 + 10x = 3x + 3
15x + 10x - 3x = -15 + 3
22x = -12
x = -12/22 = -6/11
If f(x) =6x-4, what is f(x) when x=8
Answer:f(x) = 8x + -4
Multiply f * x
fx = 8x + -4
Reorder the terms:
fx = -4 + 8x
Solving
fx = -4 + 8x
Solving for variable 'f'.
Move all terms containing f to the left, all other terms to the right.
Divide each side by 'x'.
f = -4x-1 + 8
Simplifying
f = -4x-1 + 8
Reorder the terms:
f = 8 + -4x-1
Step-by-step explanation:
Answer:
44
Step-by-step explanation:
when you plug x into the equation, you get
6(8)-4, which simplifies to 48-4. After this, you get 44.
How many terms are in the expression shown below? 5u 3 v + 3u 2 v 2 + 4uv + 5
Answer:
There are four terms of the expression [tex]5u^3v+3u^2v^2+4uv+5[/tex].
Step-by-step explanation:
The given expression is [tex]5u^3v+3u^2v^2+4uv+5[/tex].
The first term of this expression is [tex]5u^3v[/tex].
The second term of this expression is [tex]3u^2v^2[/tex].
The third term of the expression is [tex]4uv[/tex].
The fourth term of the expression is [tex]5[/tex].
Therefore, there are four terms in the given expression.
Answer:
4 terms
Step-by-step explanation:
The diameter of a circular tablecloth is 72 inches. Find the area and circumference. Use 3.14 as an approximation for pi.
Please show work
Answer:
Part 1) The area is [tex]A=4,069.44\ in^{2}[/tex]
Part 2) The circumference is [tex]C=226.08\ in[/tex]
Step-by-step explanation:
step 1
Find the area
we know that
The area of a circle (circular tablecloth) is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=72/2=36\ in[/tex] ------> the radius is half the diameter
[tex]\pi =3.14[/tex]
substitute
[tex]A=(3.14)(36)^{2}[/tex]
[tex]A=4,069.44\ in^{2}[/tex]
step 2
Find the circumference
we know that
The circumference of a circle (circular tablecloth) is equal to
[tex]C=\pi D[/tex]
we have
[tex]D=72\ in[/tex]
[tex]\pi =3.14[/tex]
substitute
[tex]C=(3.14)(72)[/tex]
[tex]C=226.08\ in[/tex]
Please answer 19,20,21
19) 38.75 miles
62*.625(aka 5/8) =38.75
20) x = -4 / x = +4
X^2 + 1 = 17 >subtract 1 from both sides.>X^2 = 16. both -4 and +4 squared equal +16.
21)
With 6 pints for 1.92, each pint is worth .32
With 4 pints for 1.26, each pint is worth .315
The smaller bottle has a smaller pint to cost ratio allowing for same item but at a smaller cost. If the 4 pints are bought, one saves a total of .02.
Find the mean, median, and mode of the data.
The mean is the sum of the elements, divided by the number of the elements:
[tex]\text{mean} = \dfrac{21+32+16+27+22+19+10}{7} = 21[/tex]
The median is the element in the middle of the dataset, once you sort it:
[tex] 10,\ 16,\ 19,\ 21,\ 22,\ 27,\ 32[/tex]
So, the middle element is 21
Finally, the mode is the element that appears more often in the dataset. Since every number appears only once in the dataset, there is no mode.
Answer:
Mean: 10 + 16 + 19 + 21 + 22 + 27 + 32 = 147/7 = 21
Median: 21
Mode: there are no mode in the following data set.
Tons of points
what is the common difference in the following arithmetic sequence 2/3 1/6 -1/3 -5/6 \
Answer:
The common difference is -1/2
Step-by-step explanation:
we know that
In an Arithmetic Sequence the difference between one term and the next is a constant and is called the common difference
we have
a1=2/3
a2=1/6
a3=-1/3
a4=-5/6
so
a2-a1=1/6-2/3=-1/2
a3-a2=-1/3-1/6=-1/2
a4-a3=-5/6-(-1/3)=-5/6+1/3=-1/2
therefore
The common difference is -1/2
three years ago, hari was 5 years older than anushka .if he is now twice as old as she is ,find their present ages
hari was 7 then which would mean that Anushka was 2. now he is ten and she is five
because you add three more years to each to get present ages
Answer: The present age of Hari is 10 years and that of Anushka is 5 years.
Step-by-step explanation: Given that three years ago, Hari was 5 years older than Anushka and he is now twice as old as she is.
We are to find their present ages.
Let x years and y years represents the present ages of Hari and Anushka respectively.
Then, according to the given information, we have
[tex](x-3)-5=y-3\\\\\Rightarrow x-8=y-3\\\\\Rightarrow x=y+5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
and
[tex]x=2\times y\\\\\Rightarrow y+5=2y\\\\\Rightarrow 2y-y=5\\\\\Rightarrow y=5.[/tex]
From equation (i), we get
[tex]x=5+5=10.[/tex]
Thus, the present age of Hari is 10 years and that of Anushka is 5 years.
In the formula I=P·r·t, what does P stand for? a. Percent: the interest rate expressed as a percentage b. Principal: the amount of money you initially invested c. Period: how often the interest is calculated d. Payout: how much money you end up with
Answer:
B) Principal: the amount of money you initially invested
Step-by-step explanation:
The given formula I=P·r·t is of Interest
In this formula
I is simple interest
r is the interest rate
t is the amount of time
P is the principle amount invested on which interest is calculated
hence of the given options, option b is correct i.e.
Principal: the amount of money you initially invested !
Answer: Option 'b' is correct.
Step-by-step explanation:
Since we have given that
[tex]I=\dfrac{P\times R\times T}{100}[/tex]
Here, I stands for Simple interest
R stands for rate of interest
T stands for time period
P stands for the principal amount i.e. the amount of money you initially invested.
Hence, Option 'b' is correct.