According to the total interest gained, the sum deposited by Madan Bahadur was Rs 4,000.
What is the formula for total interest?For the principal [tex]P[/tex] and the rate of interest [tex]r\%[/tex] per annum, the total interest after [tex]t[/tex] years is given by the formula: [tex]I=\dfrac{Prt}{100}[/tex].
Given that after 5 years Madan Bahadur got a net interest of Rs 1900 after charging 5% of the total interest as income tax where the rate of interest was 10% p.a.
Suppose the sum deposited was [tex]P[/tex] and the total interest was [tex]I[/tex].
So, the net interest would be [tex]I_n=I-I\times \frac{5}{100}=\frac{19I}{20}[/tex].
Now, given that the net interest [tex]I_n=1900[/tex]. So, we must have [tex]\frac{19I}{20}=1900\\\Longrightarrow I=\frac{1900\times 20}{19}\\\therefore I=2000[/tex] (1)
Thus, the total interest after 5 years is Rs 2,000.
Also, using the above formula for the total interest, the total interest of the sum [tex]P[/tex] at the rate [tex]r=10\%[/tex] p.a. after [tex]t=5[/tex] years would be [tex]I=\frac{Prt}{100}=\frac{P\times 10\times 5}{100}=\frac{P}{2}[/tex].
So, we must have from (1),
[tex]\frac{P}{2}=2000\\\Longrightarrow P=2000\times 2\\\therefore P=4000[/tex]
Therefore, according to the total interest gained, the sum deposited by Madan Bahadur was Rs 4,000.
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trị tuyệt đối(x+1) = 3*x
u need first to understand the thing
Michael has $15 and wants to buy a combination of school lunches to feed at least three classmates. A sandwich costs $2, and hot lunch costs $3.
This system of inequalities models the scenario:
2x + 3y ≤ 15
x + y ≥ 3
Part A: Describe the graph of the system of inequalities, including shading and the types of lines graphed. Provide a description of the solution set. (4 points)
Part B: Is the point (5, 1) included in the solution area for the system? Justify your answer mathematically. (3 points)
Part C: Choose a point in the solution set and interpret what it means in terms of the real-world context. (3 points)
The description of this graph tells us that the equation 2x + 3y ≤ 15 was shaded to the bottom while x + y ≥ 3 was shaded to the top as shown in the diagram.
How to create and explain the grapha. The first equation of the graph when it was drawn was shaded to the bottom, while the upper part of the shading has is that of the equation x + y ≥ 3.
b. (5,1) are the solutions for the equation 2x+3y<15. This is given that when x and y are substituted we would still have less than 15.
C The point in the graph would be 2,3. At this point, Michael would be able to buy 2 sandwiches and 3 hot lunches. This is still within his budget for 3 students.
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Answer:
Step-by-step explanation:
2,3 is the anwser
Hodaya is drawing a map of the trails in the canyon near her house. she knows that the distance from the first creek crossing to the second creek crossing is 1.8 miles. if every 3 inches on the map represents 0.75 of a mile, how far apart will the two creek crossings be on the map, to the nearest tenth of an inch? 2.3 4.1 5.4 7.2
The correct answer is 7.2 inch.
What is meant by distance?The length of the path joining two points determines their distance from one another.The entire journey that an object has taken can be used to define distance. An illustration. If an automobile drives 5 km east, then turns and drives 8 km further north, the total distance driven by the car is 13 km.'Distance' can be a verb or a noun, as was said above. He set himself apart from the remarks made by several of his coworkers. Thirty miles separate Peterborough from the nearest point. He had pledged to complete this duty but fell short of his commitment.The length of the line segment connecting any two points is referred to as their distance. In coordinate geometry, the distance between two points can be computed by measuring the length of the line segment connecting the two points.The nearest tenth of a 7inch.
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A piece of PVC material weighs 0.063 pounds per cubic inch. What's the weight of a 36-inch piece of PVC pipe with an outside diameter of 0.82 inches and an inside diameter of 0.75 inches?
The weight of a 36-inch piece of PVC pipe is 0.20 pounds
How to determine the weight of a 36-inch piece of PVC pipe?The given parameters about the 36-inch piece of PVC pipe are
Height, h = 36 inches
Outside diameter, D = 0.82 inches
Inside diameter, d= 0.75 inches
The volume of the PVC pipe is then calculated as:
V = πh(D/2)^2 - πh(d/2)^2
Substitute the known parameters in the above equation
V = 3.14 * 36 * (0.82/2)^2 - 3.14 * 36 * (0.75/2)^2
Evaluate the quotients
V = 3.14 * 36 * 0.41^2 - 3.14 * 36 * 0.375^2
Evaluate the exponents
V = 3.14 * 36 * 0.1681 - 3.14 * 36 * 0.140625
Evaluate the products
V = 19.002024 - 15.89625
Evaluate the difference
V = 3.105774 cubic inches
From the question, we have:
Weight = 0.063 pounds per cubic inch
So, the total weight is
Total weight = 3.105774 cubic inches * 0.063 pounds per cubic inch
Evaluate the product
Total weight = 0.195663762 pounds
Approximate
Total weight = 0.20 pounds
Hence, the weight of a 36-inch piece of PVC pipe is 0.20 pounds
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What are the solutions of the equation x4 6x2 5 = 0? use u substitution to solve.
The value of the x from the given equation is a +i and -i and +5i and -5i.
According to the statement
we have given that the equation [tex]x^4 + 6x^2 +5 =0[/tex]
and we have to find the value of x by the u substitution.
So,
The given equation is
[tex]x^4 + 6x^2 +5 =0[/tex]
Put [tex]x^2 = u[/tex]
By substitution method
Then the equation become
[tex]u^2 +6u +5 = 0[/tex]
And solve the equation then
[tex]u^2+ u +5u +5 = 0[/tex]
Then
u(u +1) + 5(u +1) = 0
(u+5) (u +1) = 0
Then
the value of u is -1 and -5 then
The value of x is
[tex]x = \sqrt{u}[/tex]
x = √-5 And √-1
Then the value of x is +i and -i and +5i and -5i.
So, The value of the x from the given equation is a +i and -i and +5i and -5i.
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In the accompanying diagram, three vertices of parallelogram ORST are O(0,0), R(b,d), and T (a,0). What are the coordinates of S
Based on the coordinates of the vertices of the parallelogram ORST, the coordinates of S can be found to be (a + b, d).
What are the coordinates of point S?As this is a parallelogram, the horizontal distance between O and R would be the same as the horizontal distance between S and T.
The horizontal distance between O and R is represented by "b".
The horizontal distance between T and S would therefore be:
= a + b
The fact that R and S are on the same plane would mean that the y-value of S is the same as that of R which is d.
The coordinates of S is:
( a + b, d).
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5. If a, s are the zeroes of 2 -8x +λ ,such that a – s = 2, then λ=
The value of λ = 8s + 6
What are the zeroes of a function?The zeroes of a function f(x) are the values of x at which f(x) = 0.
How to find λ?Given that a, s are the zeroes of 2 - 8x + λ ,such that a - s = 2.
Since we require λ,
So, let f(x) = 2 - 8x + λ.
At x = a, f(x) = 0.
So, substituting the value of x = a into f(x), we have
f(a) = 2 - 8a + λ
Since f(a) = 0, we have
2 - 8a + λ = 0
2 + λ = 8a (1)
Also, x = s, f(x) = 0.
So, substituting the value of x = s into f(x), we have
f(s) = 2 - 8s + λ
Since f(s) = 0,we have
2 - 8s + λ = 0
2 + λ = 8s (2)
Since a - s = 2
Making a subject of the formula, we have
⇒ a = s + 2
So, substituting the value of a into equation (1), we have
2 + λ = 8a (1)
2 + λ = 8(s + 2) (1)
2 + λ = 8s + 16
- 14 + λ = 8s (3)
Adding equation (2) and (3), we have
-14 + λ = 8s (3)
+
2 + λ = 8s (2)
-12 + 2λ = 16s
2λ = 16s + 12
Dividing through by 2, we have
2λ/2 = (16s + 12)/2
λ = 4(4s + 3)/2
λ = 2(4s + 3)
λ = 8s + 6
So, the value of λ = 8s + 6
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Legs: The two ________ sides of a right triangle; the sides that meet at ___ degrees.
Evaluate :11/3 + -3/7 + -4/9
Answer:
3.67+(-0.43)+(-0.44)
3.67-0.43-0.44
3.24-0.44
2.8 Ans
A quarterback throws an incomplete pass. the height of the football at time t is modeled by the equation h(t) = –16t2 40t 7. rounded to the nearest tenth, the solutions to the equation when h(t) = 0 feet are –0.2 s and 2.7 s. which solution can be eliminated and why? the solution –0.2 s can be eliminated because time cannot be a negative value. the solution –0.2 s can be eliminated because the pass was not thrown backward. the solution 2.7 s can be eliminated because the pass was thrown backward. the solution 2.7 s can be eliminated because a ball cannot be in the air for that long due to gravity.
The solution that can be eliminated is (a) the solution –0.2 s can be eliminated because time cannot be a negative value.
How to determine the solution that can be eliminated?The equation is given as:
h(t)) = -16t^2 + 40t + 7
From the question
When h(t) = 0, the values of t are
t = -0.2 and t = 2.7
The t in the function h(t) represents time
As a general rule, time cannot be negative.
This means that the solution t = -0.2 can be eliminated
Hence, the solution that can be eliminated is (a) the solution –0.2 s can be eliminated because time cannot be a negative value.
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pleaseeee hurrryyyyyyyy
Answer:I THINK IT IS 1,-3
Step-by-step explanation:
If a polynomial function, f(x), with rational coefficients has roots 3 and startroot 7 endroot, what must also be a root of f(x)?
The conjugate which is 3 - √7 is also a root of f(x).
What is the root of a polynomial function?The root of a polynomial function f(x) is the value of x for which f(x) = 0.
Now if a polynomial function has a root x = a + √b then the conjugate of x which is x' = a - √b is also a root of the function, f(x).
What must also be a root of f(x)?
Given that the polynomial function, f(x), with rational coefficients has roots
3 + √7, then by the above, the conjugate which is 3 - √7 is also a root of f(x).
So, 3 - √7 is also a root of f(x).
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The equation 2x2 − 12x 1 = 0 is being rewritten in vertex form. fill in the missing step. given 2x2 − 12x 1 = 0 step 1 2(x2 − 6x ___) 1 ___ = 0 step 2 2(x2 − 6x 9) 1 − 18 = 0 step 3 ✔ 2(x − 3)2 17 = 0 2(x − 3)2 − 17 = 0 2(x 3)2 − 17 = 0 2(x − 6)2 − 17 = 0
Given: [tex]2x^2 - 12x + 1 = 0[/tex]
Step 1: [tex]2(x^2- 6x + 3^2) + 1 - 2(3^2) = 0[/tex]
Step 2: [tex]2(x^2 - 6x + 9) + 1 - 18 = 0[/tex]
Second answer: [tex]2(x - 3)^2 - 17 = 0[/tex]
Explanation in detail:
The quadratic equation a[tex]x^{2} + bx + c = 0[/tex]'s vertex form is
where a[tex](x - h)^{2} + k[/tex] equals zero
A is the [tex]x^{2}[/tex] coefficient, and h is the vertex's x-coordinate on the equation's graph.
The vertex of the equation's graph, k, has the y-coordinate.
The completing square can be used to determine the vertex form.
[tex]2x^{2} - 12x + 1 = 0[/tex] is the equation.
Put[tex]2x^{2} -12x[/tex] in a bracket and subtract 2 from them as a common component to utilize the completing square.
∵ [tex]2(x^{2} - 6x) + 1 = 0[/tex]
To determine the product of the first and second terms in the binomial, divide the second term by two.
∵ [tex]6x / 2 = 3x[/tex]
∵[tex]3x = 3 * x[/tex]
∴ The binomial's first and second terms are x and 3, respectively.
The phrase in the bracket's middle is (-)
∴ Middle of the binomial's sign is (-)
∴ The binary value is [tex](x - 3)^2[/tex]
Square 3 is nine.
To keep the equation from altering, you must deduct the same number from the bracket after adding 9 there.
∴ [tex]2(x^2 - 6x + 9 - 9) + 1 = 0[/tex]
- Remove the brace and multiply -9 by 2.
∵ [tex]2 *-9 = -18[/tex]
∴ [tex]2(x^2- 6x + 9) + 1 - 18 = 0[/tex]
- Construct a square binomial from [tex](x^{2} - 6x + 9)[/tex]
∵ [tex]x^2 - 6x + 9 = (x - 3)^2[/tex]
∴ [tex]2(x - 3)^2 + 1 - 18 = 0[/tex]
Include related terms.
∴[tex]2(x - 3)^2 - 17 = 0[/tex]
∴ The equation's vertex form is[tex]2(x - 3)^2 - 17 = 0.[/tex]
Given that: [tex]2x^2 - 12x + 1 = 0[/tex]
Step 1: [tex]2(x^2- 6x + 3^2) + 1 - 2(3^2) = 0[/tex]
Step 2: [tex]2(x^2 - 6x + 9) + 1 - 18 = 0[/tex]
Step 3: [tex]2(x - 3)^2 - 17 = 0[/tex]
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For what value of x does 4^x=(1/8)^x+5
A) -15
B)-3
C)3
D) 15
the value of x is -3. Option B
How to determine the valueWE have the expression to be;
4^x=(1/8)^x+5
With the knowledge of indices, we have that;
2 = 2 ^1
4 = 2^2
8 = 2^3
16 = 2^4
32 = 2^5
So from this given information,
we can express the expression as;
4^x = 2^2x
1/8^x = 2^-3x
Substitute into the formula
2^2x = 2^-3x - 15
Cancel out the like terms
2x = -3x - 15
collect like terms
2x + 3x = - 15
x = -15/ 5
x = -3
Thus, the value of x is -3. Option B
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Jonathan uploaded some original songs and also some pictures. alissa uploaded four times as many songs, but only uploaded twice as many pictures. jonathan uploaded 11 items while alissa uploaded 24. how many songs did jonathan upload? (1 point) 1 4 6 10
X is the number of songs and Y the number of pics
our 2 equations will be - X+y=11 & 4x+2y=24
consider x=11-y
Lets replace x in 2:
=4(11-y) +2y=24
=44-4y+2y=24
=44-24= 4y-2y
=20= 2y
=Y=20/2
=Y=10
Lets replace y in 1
=X+10=11
=X=11-10
=X=1
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Dave is helping his grandmother make trail mix. His grandmother asks him to add 1/5 cup of fruit for every 1/3 cup of nuts.
Answer:
dave needs 3/5
Step-by-step explanation:
Step-by-step explanation:
what is the question ?
what problem needs to be solved ?
is it to find the ratio between fruit and nuts ?
then remember, a ratio is a fraction.
so, the ratio fruit : nuts is
1/5 / 1/3 = 1×3 / 5×1 = 3/5 or 3 : 5
or is it about any fraction problems and we need to bring them to the same denominator to add our compare them ?
to compare the 1/5 cup of fruit with the 1/3 cup of nuts, the smallest common multiple of 5 and 3 is 15. so we need to bring all to .../15.
how to make 15 out of 5 ? by multiplying 5 by 3. and we need to do this on the top of the fraction as well to keep the original value of the fraction.
1/5 = 1/5 × 3/3 = 3/15.
and with the same line of thinking :
1/3 = 1/3 × 5/5 = 5/15.
so, when mixing 1/5 cup of fruit with 1/3 cup of nuts, we get 3/15 + 5/15 = 8/15 cup of trail mix.
here you can clearly see the ratio again : 3/15 : 5/15 = 3:5
the first solution to get only full cups of trail mix is
3 cups of fruit and 5 cups of nuts = 8 cups of trail mix.
anything less will always end up with parts of cups (since 3/5 can't be simplified anymore).
Which of the following is an example of the associative property of multiplication?
07-(3+5)=21+35
7-(3-5)=(7-3)-5
7-(3-5)=7-(5-3)
Answer:
think its number 2 7-(3-5)=(7-3)-5
Step-by-step explanation:
pls help asap screenshot also posted- Which expression is equivalent to the given expression? 180‾‾‾‾√⋅230‾‾
The expression √180 * 2√30 is equivalent to the expression 60√6
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
The square root is a factor of a number that, when multiplied by itself, gives the original number.
Given the expression √180 * 2√30
Collecting like terms give:
= 2√(180 * 30)
Simplifying:
= 60√6
The expression √180 * 2√30 is equivalent to the expression 60√6
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find PQ if possible
Answer:
11 units.
Step-by-step explanation:
can someone help me with the graph I don't get it thanks
Answer: Refer to the histogram diagram below
The frequency table is in another attachment, and may be optional.
======================================================
Explanation:
The first task is to sort the values from smallest to largest. Luckily the data set is already sorted for us.
The smallest number is 22. This is the min. Since we're doing intervals of 10 percent, this means the first bin spans from 20% to 29%, assuming we're only involving whole number percentages. Then the next bin is from 30% to 39%, and so on, until reaching the last bin of 90% to 99%
The bin labels are shown along the bottom of the histogram.
-----------
The height of each bar represents how many students are in that specific bin. The first bar is 1 unit tall because there's only one student in the 20% to 29% range (that 22% mentioned earlier).
The next bar is 2 units tall because of the scores of 30% and 37%. They are in the range from 30% to 39%
The next bar is 4 units tall because of the scores 45,46,46,49.
This process is done with the other values to get the histogram you see below.
The frequency table is shown in a separate attachment, but your teacher may only want the histogram part. I would ask him/her for clarification.
The third column of the frequency table is optional to show where all the scores fit (and to help confirm the frequencies). This will help confirm the answer. Most histograms commonly only show the first two columns.
------------
While it's a good thing to know how to do this by hand, it's recommend to use software to generate the histograms when it comes to real world applications. Eg: making a presentation to the boss.
The program I used was LibreOffice which is free and effectively identical to excel. There are other options you could pick from.
Side note: There are no gaps between the bars when it comes to histograms. In contrast, a bar chart will have gaps.
pls solve if u can <3 much appreciated
Step-by-step explanation:
that is only possible, if we don't need to use a 2 and a 5 (but especially the 2) to create the 1 in the middle (log(10) = log(2×5) or log (5×2) = 1).
in other words, if the 1 in the middle is just a given, and does not use any of our digits for is creation, then a solution is possible.
first of all, the upper left corner has to be log(0⁰). we cannot use the digit 0 for anything else. and 0^n (except for n = 0) is not a valid argument for a logarithm.
log(0⁰) = 0 log(2×1) = 0.3... log(9/4) = 0.35...
log(1×2) = 0.3... 1 log(3×6) = 1.26...
log(7/3) = 0.37... log(4×5) = 1.3... log(6⁹) = 7.0...
but as soon as we need to build the center 1 by log(10), which takes then away one of the 2s (as the only way to build 10 by multiplication is 2×5 or 5×2), there is no possible solution.
Answer:
Please see attachment.
Step-by-step explanation:
There are many possible solutions to this problem.
A few things to note:
[tex]\log_a1=0[/tex]The log of a number smaller than its base is less than 1.The log of a number larger than its base is more than 1.[tex]\log_a0\:\:\textsf{is und\;\!efined}[/tex]There are 8 red boxes and 8 blue boxes, so we do not have to use every digit from 0 to 9.
Place zero in the blue box in the top left of the grid, since any number raised to zero is 1 and [tex]\log_a1=0[/tex]. Leave the red box blank for the moment, and fill it with any number not used at the end.
The value of the product of the red and blue boxes in the top-middle and left-middle of the grid should be less than 10. It is advisable to place the lowest numbers in these boxes, i.e. 1 and 2.
The value of the product of the red and blue boxes in the bottom-middle and right-middle of the grid should be more than 10.
It is advisable to place some of the highest numbers in the bottom right corner of the grid, as this is the box with the greatest value.
Please see the attached image for one possible way of filling the grid. The actual values of the logarithms (to 3 decimal places) have been placed in the bottom right corners of each box of the grid for verification.
Calculate the perimeter of 5y + 9 (3y+15) cm (7y+3)cm
Answer:
Step-by-step explanation:
assuming that the figure is a triangle with sides (5y + 9) and (3y + 15) and (7y + 3) we find the perimeter by adding everything
5y + 9 + 3y + 15 + 7y + 3 =
15y + 27
or
3(5y+9)
next time put all the data and figures, we are doing you a pleasure, at least put ALL the data.
The graph of y=√x is reflected in the x-axis and then translated
down 3 units. What is an equation that produces this transformation?
A. -√x-3
B. y= -3-(√x)
C. y= 3- (√x)
D. y= -(√x-3)
how do you know if two line segments are perpendicular
Answer:
Step-by-step explanation:
Measure the angle between the lines
It should be 90 degrees,
Find the value of x
a. 13 b. 14/5 c. 5 d. 8
Using the chord theorem, option C is the best solution since x = 5.
The four line segments that are created by two intersecting chords inside of a circle are explained by the chord theorem, sometimes referred to as the intersecting chords theorem, a statement in fundamental geometry. The products of the line segment lengths on each chord are equal, according to this assertion.
The value of x must be determined in order to answer the question.
We may determine the following using the chord property:
8*x = 4*10,
or, 8x = 40,
or, x = 40/8,
or x = 5.
Given that x = 5, option C is the best option according to the chord theorem.
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Solve:
8(3 + a) = 64
A =
Answer: 8
Step-by-step explanation:
PEMDAS
4|a| + 8 -a, if a = -2
PLEASE HELP!!!!!!!!!!!!!! I'm stuck on this!!
4|a| + 8 - a, if a = -2
What we're doing here is plugging in the given value of a for every instance of a in the expression.
4|-2| + 8 - (-2)
---The absolute value of a number is its distance from 0. -2 is 2 units away from 0, so the absolute value of -2 is 2. And, remember two negatives make a positive!
4(2) + 8 + 2
8 + 8 + 2
16 + 2
18
Hope this helps!
what is 1016/86.89 include all your steps
Answer:
11.692945103
Step-by-step explanation:
take out a calculator divide 1016 by 86.89
3. Choose the two correct transformations for:
Ay
T
R'
RSTU to R'S'T'U'.
S'
A Rotation 180°clockwise
B Reflection across y = x
OC Reflection across y = -x
OD Rotation 180°counterclockwise
The following formula relates three quantities: Force (F), mass (m), and acceleration (a). F = ma
F = ma is [tex]a=\frac{F}{m}[/tex]
Why is the formula F=ma?The equation for Newton's Second Law of Motion is F = ma. Force is equal to the rate of change of momentum, according to the definition of Newton's Second Law of Motion. Force is defined as mass times acceleration for a constant mass.The following formula relates three quantities: Force (F), mass (m), and acceleration (a). F = ma
F = ma
F= force
m= mass
a= acceleration
[tex]F = ma[/tex]
Divide both sides by the mass
[tex]a=\frac{F}{m}[/tex]
F = ma is [tex]a=\frac{F}{m}[/tex]
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