Sammy lend altogether Rs 10,000 to James and Sophie for 2 years. James agrees to pay simple interest at 12% p.a and Sophie agrees to pay compound interest at the rate of 9% p.a. If Sophie paid Rs 596.70 more than James as the interest , find how much did he lend to each.

* Show your workings!

Help! Random/ Irrelevant answers will be reported!~​

We can use the sine ratio to solve this problem and the value of x would be 8.604.

What are trigonometric ratios?

Trigonometric ratios are ratios of the side lengths of a right triangle with respect to its acute angles.

Sine (sin) ratio: The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.

In the given figure, we have given the hypotenuse of the triangle, and  an angle is given which is opposite to 35 degree, so we can use the sine ratio to find the value of x

sin35°= x/15

To solve for x, we can use the following steps:

Multiply both sides of the equation by 15 to isolate x:

sin 35° = x/15

15 * sin 35° = x

Use a calculator to approximate sin 35°:

sin 35° ≈ 0.5736

Substitute the approximation into the equation and solve for x:

x = 15 * 0.5736

x ≈ 8.604

Therefore, x is approximately equal to 8.604.

Hence, we can use the sine ratio to solve this problem and the value of x would be 8.604.

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The statement "System analysts define an object's attributes during the systems design process" is true because  defining object attributes is an essential part of the systems design process to ensure that the system meets the desired functional requirements.

In systems design, objects are used to represent real-world entities that are relevant to the system being developed. These objects have attributes that describe their characteristics or properties, which are used to identify and manipulate them within the system. System analysts define these attributes during the systems design process to ensure that the system meets the desired functional requirements.

For example, in a library system, a book object may have attributes such as title, author, publisher, and ISBN. Defining these attributes helps ensure that the system can properly manage and retrieve books as needed. Object-oriented design is a popular approach to systems design that relies heavily on defining objects and their attributes.

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The volume of the solid is π (243/5), which corresponds to option 1.

The correct answer is (d) 1 and 3.

To find the volume of the solid formed by rotating the region bounded by the graph of y=x^2, x=3, y=0 around the y-axis, we can use the formula:

V = ∫[a,b] π (f(x))^2 dx

where a and b are the limits of integration (in this case, 0 and 3), and f(x) is the function defining the curve being rotated (in this case, f(x) = x^2).

Using this formula, we get:

V = ∫[0,3] π (x^2)^2 dx

= ∫[0,3] π x^4 dx

= π [x^5/5] from 0 to 3

= π [(3^5/5) - (0^5/5)]

= π (243/5)

So the volume of the solid is π (243/5), which corresponds to option 1.

Option 2 is incorrect because the integral given in that option corresponds to the volume of the solid formed by rotating the region bounded by the graph of y=3-x, x=0, y=0 around the y-axis, not the region defined in the question.

Option 3 is also incorrect because the integral given in that option corresponds to the volume of the solid formed by rotating the region bounded by the graph of y=x^2, x=0, y=9 around the x-axis, not the y-axis as required in the question.

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The first appointment for both doctors starts at 8:30am.

Next appointment that they start at same time.

For the same time same time take LCM of 20 and 35.

20= 2x2x5

35= 5×7

hcm (20,35) = 2X2X5X7 = 140

They will take appointment after 140 minutes. 1.e. 2 hours 20 minute.

so, next appoitment will be 10:50a.m.

The next time that they have an appointment start at the same time is at  10:50 a.m.

We are given that the first appointment for both doctors starts at 8:30am while the Next appointment also started at same time but Doctor Jones starts his every 20 minutes while Doctor Warholm starts his every 35 minutes.

For the same time, take LCM of 20 and 35.

20 = 2 * 2 * 5

35 = 5 * 7

HCM (20, 35) = 2 * 2 * 5 * 7

HCM (20, 35) = 140

Hence, it will take the appointment after 140 minutes which equals to 2 hours 20 minute.

Now, from 8.30 am, the addition of the 2 hours 20 minute gives us 10:50 a.m which is the next time that they have an appointment start at the same time.

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Answer:

1 trillion times larger

Step-by-step explanation:

One kilogram (kg) is equal to 1,000,000,000,000 (1 trillion) nanograms (ng).

Therefore, one kilogram is 1 trillion times larger than one nanogram.

The value represents the climber's change in elevation during the first minute of the training session is  1/5.

Given,

During the second minute of a two-minute training session, a rock climber completed a 12-meter ascent up the wall. The climber returned to the identical location she had been in at the beginning of the two-minute session.

Let x be the distance climbed by the climber is x m

During the first minutes(60 seconds): distance climbed =\(\frac{x}{60}\)

In the 2nd minute, they climbed 12 m higher than in the 1st minute.

Now, the distance climbed by the climbed in the Second minute = \(\frac{x+12}{60}\)

Now, the change in the elevation during the first minute of the training session= \(\frac{x+12}{60}-\frac{x}{60} = \frac{12}{60}=\frac{2}{10}=\frac{1}{5}\)

Hence, the value represents the climber's change in elevation during the first minute of the training session is \(\frac{1}{5}\)

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the answer of this is 19.5 pounds

Explanation

We are given a triangle

and then asked to determine the value of x

To do so, we know that the total angles in a triangle are 180 degrees

Thus

The value of x is 41 degrees

Answer:

Step-by-step explanation:

We may first get rid of the fractions by multiplying both sides of the equation by the least common multiple (LCM) of the denominators, which is 18. This will allow us to rewrite the equation 8 - 2/3x = 5/6 without using fractions or decimals. Thus, we get:

18(8) - 18(2/3)x = 18(5/6)

144 - 12x = 15

The left side of the equation can be made simpler by multiplying -12 by 3 to get -36x:

144 - 36x = 15

Finally, by taking 144 off of both sides and then dividing by -36, we can find x:

-36x = -129

x = 129/36

As a result, the solution is x = 129/36 and the equation 8 - 2/3x = 5/6 is identical to the equation 144 - 36x = 15.

Answer: 4x = 43

Step-by-step explanation:

Work towards isolating the x with an end result of whole numbers

Start by making the coefficient 2/3 into an equivalent fraction of 4/6 to have a common denominator with 5/6.

8-4/6x = 5/6

Subtract 8 to move it to the other side of the equation to keep it less complicated

-4/6x = 5/6-8

Find the sum of the right side of the equation, 5/6-8, and turn it into an improper fraction.

-4/6 x= -43/6

Now, we can multiply everything by 6 to get rid of the denominators, and then divide it by -1 to make both sides positive.

-4x=-43 ---> 4x=43

There was probably a simpler way to do this but I hope it helps !!

The value x = - 2 is not part of the domain of the function f(x) = √(x + 1).

Radical functions are functions that involves root operators. We see here a radical function of the form f(x) = √(x + a), whose domain is x ∈ [- a, + ∞), that is, x ≥ - a. If we know that f(x) = √(x + 1), then a = 1 and the domain of the function is x ∈ [- 1, + ∞), that is, x ≥ - 1.

Hence, the value x = - 2 is not part of the domain of the function f(x) = √(x + 1).

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The rate of change for the equation y - x = 10 is 1.

To find the rate of change for the equation y - x = 10, we need to determine how y changes with respect to x.

We can rewrite the equation as y = x + 10 by adding x to both sides.

Now, we can observe that the coefficient of x is 1. This means that for every unit increase in x, y will increase by 1. Therefore, the rate of change for this equation is 1.

In other words, as x increases by 1 unit, y will increase by 1 unit as well.

As a result, 1 represents the rate of change for the equation y - x = 10.

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The required measure of the angle ∠spq of a rhombus is 110°.

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

Here,
For rhombus,
m∠spr=(2x + 15)°
m∠qpr=(3x−5)°

And,
m∠spr = m∠qpr
2x + 15 = 3x - 5
x = 20

Now,
∠spq = m∠spr + m∠qpr
        = 2x + 15 + 3x - 5

        = 5x + 10
        = 5(20) + 10
        = 110°

Thus, the required measure of the angle ∠spq of a rhombus is 110°.

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To assess the correctness of the curved arrow notation in each case, specific examples or instances of the notation are needed. Without such examples, it is challenging to provide a meaningful analysis or explanation of whether the curved arrow notation is correct or incorrect.

Curved arrow notation is commonly used in organic chemistry to represent electron movement in chemical reactions and mechanisms. It indicates the flow of electrons, such as the movement of lone pairs, bonding electrons, or the formation/breakage of bonds. The notation is essential for understanding reaction mechanisms and the distribution of electron density in molecules.

To determine the correctness of curved arrow notation, one needs to evaluate whether it accurately represents the movement of electrons according to the established rules and principles of organic chemistry. This involves considering factors such as electron pair repulsion, formal charges, bond breaking/forming, and resonance structures.

Without specific examples or instances of the curved arrow notation in question, it is not possible to provide a comprehensive analysis or explanation. If you can provide specific examples or questions regarding the curved arrow notation, I would be glad to assist you further.

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Answer:

Yes.

Step-by-step explanation:

One term .

The remaining zero of polynomial is (5 + i).

And, the linear factorization of the polynomial are;

(x - 2) (x - (5-i)) (x - (5 + i)).

What is Zeros of polynomial?

Zeroes of a polynomial are the points where the polynomial becomes zero.

Given that;

Zeroes of the polynomial are 2, 5 - i

Now, If one zero of polynomial is complex then another zero of the polynomial is its conjugate.

So, One root of polynomial = 5 - i

Then, The third zero of the polynomial = 5 + i

Thus, The polynomial are find as;

(x - 2) (x - (5-i)) (x - (5 + i)) = 0

So, The remaining zero of polynomial is (5 + i).

And, the linear factorization of the polynomial are;

(x - 2) (x - (5-i)) (x - (5 + i)).

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Answer:

it should be D. subtraction

Answer:

c

Step-by-step explanation:

we have that

the area of the shaded region is equal to the area of rectangle minus the area of the circle

step 1

Find the area of the circle

A=pi(r^2)

we have

r=4 units

substitute

A=pi(4^2)

A=16pi unit2

step 2

Find the area of rectangle

A=b*h

we have

h=2(4)=8 units

b=9+4=13 units

substitute

A=13(8)

A=104 unit2

therefore

the area of the shaded region is

The upper bound of an algorithm with best case runtime t(n) = 3n + 16 and worst case runtime t(n) = 4n² + 10n + 5 can be determined by analyzing the growth rate of these functions.

In this case, the highest order term, which dominates the overall runtime, is 4n² in the worst case scenario. Therefore, the upper bound of the algorithm's worst case runtime is O(n²).

In the worst case scenario, the algorithm's runtime can be approximated by the function t(n) = 4n² + 10n + 5. As n grows larger, the contribution of the higher order terms becomes more significant.

The leading term, 4n², represents the dominant factor in the runtime.

The coefficients of the lower order terms, 10n and 5, become less significant as n increases. Consequently, the overall growth rate of the algorithm can be approximated as O(n²), indicating that the upper bound of the worst case runtime is quadratic.

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Answer:

17

18.4

Step-by-step explanation:

c² = a² + b²

EB² = 15² + 8²

EB = 17 cm

c² = a² + b²

HB² = HE² + EB²

HB² = 7² + 17²

HB² = 338

HB = 18.4 cm

According to the statement the equation of the line through (-3,4) that is parallel to the given line is y = -2x - 2.

A parallel line is a line that remains the same distance apart from a given line and does not intersect it. The slope of the given line is -2 because y=-2x+2 is in the slope-intercept form, y=mx+b, where m is the slope of the line and b is the y-intercept.Now, to find the equation of a line through (-3,4) that is parallel to the given line, we need to use the point-slope form of a line: y - y₁ = m(x - x₁)where (x₁, y₁) is the given point and m is the slope of the line we want to find.

Since the line we want to find is parallel to the given line, it has the same slope as the given line. So, m = -2. Also, x₁ = -3 and y₁ = 4 (these are the coordinates of the given point).Substitute these values into the point-slope form: y - 4 = -2(x - (-3))Simplify: y - 4 = -2(x + 3) y - 4 = -2x - 6y = -2x - 6 + 4y = -2x - 2. The equation of the line through (-3,4) that is parallel to the given line is y = -2x - 2.

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9514 1404 393

Answer:

  7%

Step-by-step explanation:

Let x represent the percentage of water in the mix. The amount of water in the mix is ...

  5%·120 +10%·80 = x·(120 +80)

  14/200 = x = 7% . . . . . . . . . . . . . . simplify, divide by 200

The percentage of water in the mixture is 7%.

The probability that she selects the route of three specific capitals is 97290/1.

The probability that she selects the route of three specific capitals can be calculated by taking the total number of possible routes and dividing it by the total number of routes that involve the three specific capitals. To calculate the total number of possible routes, multiply the number of states (47) by the number of routes that could be selected from each state (2). This gives 94 total possible routes.

47 x 46 x 45 ways = 97290 ways

= 1/97290

Now, calculate the number of routes that involve the three specific capitals. Since the president is selecting three states, the total number of routes will be 3. Therefore, the probability that she selects the route of three specific capitals is 3/94, which can be simplified to 97290/1.

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The correct answer is

(a) manipulating two or more independent variables. 

A factorial plan could be a sort of test plan utilized in investigating to examine the impacts of two or more free factors on a subordinate variable.

In a factorial plan, analysts control each free variable over different levels to watch the one-of-a-kind impacts of each free variable and how they connected with each other to impact the subordinate variable.

For case, in a ponder examining the impacts of two autonomous factors (e.g., temperature and mugginess) on a subordinate variable (e.g., plant development), analysts may control the temperature at three distinctive levels (moo, medium, and tall) and mugginess at two diverse levels (moo and tall) to watch how these components influence plant development individually and in combination. 

Therefore, the correct answer is (a) manipulating two or more independent variables. 

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There are 252 distinct ways to dispatch the taxis to the three airports.

We need to find the number of distinct ways in which we can dispatch the taxis to the three airports, given that two taxis go to airport A, six go to airport B, and one goes to airport C.

First, we choose two taxis out of nine to send to airport A. This can be done in C(9, 2) = 36 ways.

Next, we choose six taxis out of the remaining seven to send to airport B. This can be done in C(7, 6) = 7 ways.

Finally, the last taxi is sent to airport C.

Therefore, the total number of distinct ways to dispatch the taxis is:

C(9, 2) x C(7, 6) = 36 x 7 = 252

There are 252 distinct ways to dispatch the taxis to the three airports.

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We can infer that those assertions do not provide us with adequate details on the hundredths in the decimal system.

The decimal numeral system is widely used to express both integer and non-integer numbers.

The Hindu-Arabic number system has been expanded to include non-integer values.

The way of representing numbers in the decimal system is known as decimal notation.

(1) Since 2 is the eleventh digit of 100z, we may begin writing 100z.

10z = 100(a.bcd)

The decimal point is moved two places to the right by multiplying by 100, giving us the value of:

10z = 100abc.d

Then we shall have d = 2 if the tenths of 100z equal 2.

We have so far: z = a.bc2

(2) Since 1000z's units digit is 2, we may begin writing 1000z.

1000z = 1000a.bc2

We need to move the decimal point three places to the right so that we have order to multiply by 1000:

1000z = abc2

As a result, we can now confirm that the unit digit is actually 2.

However, the number is as follows: z = a.bc2

Therefore, we can infer that those assertions do not provide us with adequate details on the hundredths in the decimal system.

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Answer:

Step-by-step explanation:

lim x -> +oo    -2x³ - 13x² + 8x + 52

x³ (-2 -13/x + 8/x² + 52/x³)

+oo³ (-2 - 13/+oo + 8/+oo² + 52/oo³)

+oo(-2 + 0 + 0 + 0)

-oo

lim x -> -oo    -2x³ - 13x² + 8x + 52

x³ (-2 -13/x + 8/x² + 52/x³)

-oo³ (-2 - 13/-oo + 8/-oo² + 52/-oo³)

-oo(-2 + 0 + 0 + 0)

+oo

Answer:

25%

Step-by-step explanation:

Answer:d 16 hours

Step-by-step explanation:you count how many hours it took to get back

Answer:



Step-by-step explanation: