Rajesh gave ½ of his provident fund to his wife, ¼ to his son and the remainder was to be divided equally between his two brothers so that each brother got Rs 10000. What was the amount of provident fund ?​

Answer:

5

Step-by-step explanation:

a^2 + b^2 = c^2

12^2 + b^2 = 13^2

144 + b^2 = 169

169 - 144 = 25

sqrt of 25 = 5

Answer:

look on the yt theres alot of helpful things on there and ive had to do this simliar things and stuff so thats why yt viedo of this should help you

Step-by-step explanation: try a yt viedo to help on this math i wish you luck

Let 'h' represent the number of hours that Charles will work. Since he wants to work for at least six hours, then we have the following inequality:

but he also must work fewer than 16 hours this week, then the next inequality is:

then, combining the inequalities, we have:

Selecting all students with last names beginning with the letter M would not produce a random sample of a school population of 1000 students. Hence the answer is no.

A random sample is obtained by selecting individuals from a population in a way that ensures every member of the population has an equal chance of being included in the sample.

By choosing only students with last names beginning with the letter M, you are introducing a bias and not providing an equal chance for all students to be selected.

To obtain a random sample of 1000 students from a school population, you would need to use a random selection method that ensures each student has an equal probability of being chosen.

This could be achieved through techniques such as random number generators, random sampling software, or random sampling techniques like stratified or cluster sampling.

Selecting all students with last names beginning with the letter M would not meet the requirements of a random sample, as it would not provide an equal chance for all students in the population to be included.

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Answer:

3x-x+2=4

Step-by-step explanation:A=9000(1.02125)^.25

A=9000*1.00527

A=9047.44

The equation of the line passing through two points (-5, 2) and (0, 7) is represented by x - y + 7 = 0.

It is given that there are two points (-5, 2) and (0, 7) and we need t determine the equation of the line passing though these points. Fist we need to determine the slope of the line. The slope can be determined by the formula (y₂ - y₁)/(x₂ -x₁). Here, x₁ = -5, x₂ = 0, y₁ = 2 and y₂ = 7.

Now, slope of line is given by m = (7 - 2)/(0 + 5)

m = 5/5 = 1

Now, equation of the line having the slope equal to m is given by

(y - y₁) = m (x - x₁)

=> (y - 2) = 1 × (x + 5)

=> y = x + 5 + 2

=> y = x + 7

=> x - y +7 = 0

Thus, the equation of the line passing through two points (-5, 2) and (0, 7) is represented by x - y + 7 = 0.

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Answer:

7x^2+x+3

Step-by-step explanation:

collect the like terms:

3x^2-2x+1+4x^2+3x+2

7x^2-2x+1+3x+2

7x^2+x+1+2

solution:

7x^2+x+3

Answer:

sample response: Since both points have the same x-coordinate, the line would be vertical. A vertical line has no slope because the run of the graph, which is the denominator, is zero and therefore an undefined fraction.

Step-by-step explanation:

Answer:

324

Step-by-step explanation:

Answer:

324

Step-by-step explanation:

√16*9²

4*81

324

Plz mark as brainliest

The following time Joey's age is greater than Zoe's, his two numbers add up to 11 years.

Consider Chloe to be c years old and Joey to be c+1 years old. After n years, Chloe and Zoe will be n + c and n + 1 respectively.

Based on the given conditions,

(n + c) ÷ (n + 1) = 1 + [(c - 1) ÷ (n + 1)]

n is an integer for 9 non-negative integers.

C – 1 hence has 9 positive divisors.

Either \(p^{8}\) or \(p^{2} q^{2}\) is the prime factorization of c-1 < 100

Since c - 1 < 100, is

c - 1 = \(2^{2} *3^{2}\)

c - 1 = 36,

c = 36 + 1

We can calculate the coefficient,

c = 37

We can infer that Joey is 38 years old as of right now.

Assume that after k years, Joey's age is multiplied by Zoe's age, making Joey and Zoe k + 38 and k + 1 years old, respectively.

So,

We can write,

(k + 38) ÷ (k + 1) = 1 + [(38 - 1) ÷ (k + 1)]

K is an integer for some positive integers.

Since 37 can be divided by k + 1,

k = 36 is the only viable option.

Using the assumption that Joey will be k + 38 = 74 years old, the result is 7 + 4 = 11.

Therefore,

11 years is the sum of Joey's two digits the next time his age is a multiple of Zoe's age.

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Answer: i don’t know

Step-by-step explanation:

Answer: 40

Step-by-step explanation:

Answer:

40 basketballs in 5 hours

Step-by-step explanation:

If in 1/2 hour she makes 4, multiply it by 2 to know how much she can make in a wholw hour. So she can make 8

Multiply how much she can make every hour by the amount of hours.

8 x 5 = 40

The value of f[g(x)] is - 64x³ - 336x² - 588x - 340 and the value of g[f(x)] is -4x³ + 19

The functions are as follows; f(x) = -x³ +3 and g(x) = 4x+7

The value of f[g(x)] is obtained by replacing every x in f(x) with the value of g(x) as given below

f[g(x)] = f(4x + 7) = - (4x + 7)³ + 3

When we expand (4x + 7)³, it gives us 64x³ + 336x² + 588x + 343

Then

f[g(x)] = - 64x³ - 336x² - 588x - 340

Similarly, g[f(x)] is obtained by replacing every x in g(x) with the value of f(x) as shown below;

g[f(x)] = g(-x³ + 3) = 4(-x³ + 3) + 7g

[f(x)] = -4x³ + 19

Therefore,

f[g(x)] = - 64x³ - 336x² - 588x - 340

g[f(x)] = -4x³ + 19

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Answer:

18%

Step-by-step explanation:

65 + x = 76.70

x = 11.70

11.70/65 = 0.18 or 18%

Answer:

Explanation:

The logarithm

can be written as the product of 2 and the logarithm of x to base 3.

This is written as:

Answer:

Exponential decay

Step-by-step explanation:

The general form of an exponential function is

\(P=P_{0}a^t\), where P0 is the initial value, a is the base, and t is the exponent.

In your example, P0 is 1 and a is 4/5.

A function is experiencing exponential growth when a > 1.

A function is experiencing exponential decay when 0 < a < 1.

4/5 lies between 0 and 1, so the function is experiencing exponential decay.

Answer:

\(Red = \frac{10}{37}\)

Step-by-step explanation:

Given

\(Red:Yellow = 2 : 3\)

\(Yellow: Blue = 5 : 4\)

Required

Determine the fraction of Red

First, we need to link the given ratios.

Since yellow is present in both ratios, we start by making the ratio of yellow equal in both ratios

Multiply this ratio by 5

\(Red:Yellow = 2 : 3\)

This becomes

\(Red:Yellow = 10 :15\)

Similarly, multiply this ratio by 3

\(Yellow: Blue = 5 : 4\)

This becomes

\(Yellow:Blue =15:12\)

At this point, we have:

\(Red:Yellow = 10 :15\) and \(Yellow:Blue =15:12\)

Combine

\(Red:Yellow:Blue = 10:15:12\)

The fraction is then calculated as:

\(Red = \frac{Red}{Red +Yellow + Blue}\)

This gives

\(Red = \frac{10}{10+15+12}\)

\(Red = \frac{10}{37}\)

Answer:

131

Step-by-step explanation:

The n th term of an arithmetic sequence is

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₁₂ = 38 and a₈₅ = 257 , then

a₁ +11d = 38 → (1)

a₁ + 84d = 257 → (2)

Subtract (1) from (2) term by term

73d = 219 ( divide both sides by 73 )

d = 3

Substitute d = 3 into (1)

a₁ + 11(3) = 38

a₁ + 33 = 38 ( subtract 33 from both sides )

a₁ = 5

Thus

5 + 3(n - 1) = 395 ( subtract 5 from both sides )

3(n - 1) = 390 ( divide both sides by 3 )

n - 1 = 130 ( add 1 to both sides )

n = 131

Thus there are 131 terms in the sequence

Answer:

Hi there!

I might be able to help you!

It is NOT a function.

Determining whether a relation is a function on a graph is relatively easy by using the vertical line test. If a vertical line crosses the relation on the graph only once in all locations, the relation is a function. However, if a vertical line crosses the relation more than once, the relation is not a function. X = y2 would be a sideways parabola and therefore not a function. Good test for function: Vertical Line test. If a vertical line passes through two points on the graph of a relation, it is not a function. A relation which is not a function. The x-intercept of a function is calculated by substituting the value of f(x) as zero. Similarly, the y-intercept of a function is calculated by substituting the value of x as zero. The slope of a linear function is calculated by rearranging the equation to its general form, f(x) = mx + c; where m is the slope.

A relation that is not a function

As we can see duplication in X-values with different y-values, then this relation is not a function.

A relation that is a function

As every value of X is different and is associated with only one value of y, this relation is a function.

Step-by-step explanation:

It's up there!

God bless you!

Answer:

The equation will change by an increase in the angular frequency of motion by a factor of 2 to become  d(s) = 7·sin(720s)

Step-by-step explanation:

The given oscillatory motion equation of the swinging pocket watch is d(s) = 7sin(360s)

The general equation of simple harmonic motion is x = A·sin(ω₁t + ∅)

Comparing, we have;

x = d(s)

A = 7

ω₁t = 360

∅ = 0

The period of oscillation = The time to complete a cycle =  2·π/ω₁

Therefore;

ω₁ = 2·π/T₁

When the cycle or the watch swing rate is doubled, the time taken to compete one cycle is halved and the new period, T₂ = T₁/2

ω₂ = 2·π/T₂  = 2·π/(T₁/2) = 4·π/T₁ = 2ω₁

The equation becomes;

x = A·sin(ω₂t) =  A·sin(2ω₁t) which gives;

d(s) = 7·sin(2 × 360s) = 7·sin(720s)

The equation will change by the doubling of the angular frequency of the motion

On solving the provided question, significant difference between the four testing conditions is α = 0.10

An alternative hypothesis is one in which the researchers predict a difference (or an effect) between two or more variables, indicating that the observed pattern of the data is not the result of chance.

Null hypothesis:  : μ1 ≥ μ2, There is no significant difference in history test scores between students with different academic major

Alternative Hypothesis: Ha : μ1 < μ2. Exam outcomes in history are substantially more varied among students with different academic specialties.

Determine the significance level. α = 0.10

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Answer:

Asymptotic discontinuities at \(x = (-2)\) and \(x = 4\).

Step-by-step explanation:

A linear function has an asymptotic discontinuity at \(x = a\) if \((x - a)\) is a factor of the denominator after simplification.

The numerator of this function, \((x - 1)\), is linear in \(x\).

The denominator of this function, \((x^{2} - 2\, x - 8)\), is quadratic in \(x\). Using the quadratic formula or otherwise, factor the denominator into binominals:

\(\begin{aligned}y &= \frac{(x - 1)}{x^{2} - 2\, x - 8} \\ &= \frac{(x - 1)}{(x - 4)\, (x + 2)}\end{aligned}\).

Simplify the function by liminating binomials that are in both the numerator and the denominator.

Notice that in the simplified expression, binomial factors of the denominator are \((x - 4)\) and \((x + 2)\) (which is equivalent to \((x - (-2))\).) Therefore, the points of discontinuity of this function would be \(x = 4\) and \(x = (-2)\).

The probability that Jack arrives at least two minutes before Jill is 0.313 or 31.3%. The probability that the first person arrives by 12:05 p.m. and the last person arrives after 12:10 p.m. is 0.556 or 55.6%.

Let X be the arrival time of Jack, and Y be the arrival time of Jill, both in minutes after noon. Then X and Y are independent and uniformly distributed random variables on the interval [0, 15]. We want to find P(X < Y - 2).

The probability can be found by integrating the joint density function of X and Y over the region where X < Y - 2

P(X < Y - 2) = ∫∫[x < y - 2] f(x,y) dxdy

= ∫[0,13]∫[x+2,15] 1/225 dxdy

= (1/225) ∫[0,13] (15-x-2) dx

= (1/225) [13(13/2) - 13 - (2/2)(13/2)(13/15)]

= 0.313

Therefore, the probability that Jack arrives at least two minutes before Jill is 0.313, or approximately 31.3%.

Let Z be the arrival time of the first person, and W be the arrival time of the last person. Then Z and W are independent and uniformly distributed random variables on the interval [0, 15]. We want to find P(Z < 5 and W > 10).

The probability can be found by using the complement rule

P(Z < 5 and W > 10) = 1 - P(Z ≥ 5 or W ≤ 10)

To find P(Z ≥ 5), we integrate the density function over the interval [5, 15]

P(Z ≥ 5) = ∫[5,15] 1/15 dx = 2/3

To find P(W ≤ 10), we integrate the density function over the interval [0, 10]

P(W ≤ 10) = ∫[0,10] 1/15 dx = 2/3

Since Z and W are independent, we can multiply their probabilities to find the probability that both events occur

P(Z ≥ 5 or W ≤ 10) = P(Z ≥ 5) × P(W ≤ 10) = (2/3)² = 4/9

Therefore, P(Z < 5 and W > 10) = 1 - P(Z ≥ 5 or W ≤ 10) = 1 - 4/9 = 5/9, or approximately 0.556.

Therefore, the probability that the first of the 10 persons to arrive does so by 12:05 p.m., and the last person arrives after 12:10 p.m. is 0.556, or approximately 55.6%.

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The length of one edge of the tabletop is 4.89 feet.

We know that square is a shape that has all the side equal. Based on this using the formula to find the length of edge of the tabletop.

The area of square table is given by the formula -

Area of square table = side²

We will keep the value of area of square table to find the value of side which will be length of edge

24 = side²

Side = ✓24

Taking square root for the value on right side of the equation

Side = 4.89

Hence, the length of one edge of the tabletop is 4.89 feet.

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This is pseudo-trig.  It has a trig function but it's irrelevant.

Let y = cos X

y + 1/y = 40

Squaring,

y² + 2(y)(1/y) + 1/y² = 1600

y² + 2 + 1/y² = 1600

y² + 1/y² = 1598

cos² X + 1/cos²X = 1598

Answer: 1598

Answer:

○ \(\displaystyle \pi\)

Step-by-step explanation:

\(\displaystyle \boxed{y = 3sin\:(2x + \frac{\pi}{2})} \\ y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{\pi}{4}} \hookrightarrow \frac{-\frac{\pi}{2}}{2} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 3\)

OR

\(\displaystyle \boxed{y = 3cos\:2x} \\ y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 3\)

You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of \(\displaystyle y = 3sin\:2x,\)in which you need to replase "cosine" with "sine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the sine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted \(\displaystyle \frac{\pi}{4}\:unit\)to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACKWARD \(\displaystyle \frac{\pi}{4}\:unit,\)which means the C-term will be negative, and by perfourming your calculations, you will arrive at \(\displaystyle \boxed{-\frac{\pi}{4}} = \frac{-\frac{\pi}{2}}{2}.\)So, the sine graph of the cosine graph, accourding to the horisontal shift, is \(\displaystyle y = 3sin\:(2x + \frac{\pi}{2}).\)Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph WILL hit \(\displaystyle [-1\frac{3}{4}\pi, 0],\)from there to \(\displaystyle [-\frac{3}{4}\pi, 0],\)they are obviously \(\displaystyle \pi\:units\)apart, telling you that the period of the graph is \(\displaystyle \pi.\)Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at \(\displaystyle y = 0,\)in which each crest is extended three units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

Answer:

\(\pi\)

Step-by-step explanation:

The trigonometric function shown on the graph is a continuous function, and so its period is the length of one wave of the function (i.e. the horizontal distance between a peak and the next peak, or a trough and the next trough).

From inspection of the graph, the horizontal distance between one peak and the next of the given function is \(\pi\).  

Therefore, the period of this trigonometric function is \(\pi\)

Answer:

B. y=1/3x+4

Step-by-step explanation:

Hi there!

We are given the line PQ and we want to find the line that is perpendicular to it

Perpendicular lines have slopes that are negative and reciprocal. When they are multiplied together, the result is -1

So first, let's find the slope of the line PQ

The point P is given as (-8, 7) and the point Q is given as (-4, -5)

The formula for the slope calculated from two points is \(\frac{y_2-y_1}{x_2-x_1}\) where (\(x_{1}\) \(y_1\)) and (\(x_2\), \(y_2\)) are points

We have the needed information for the slope, but let's label the values of the points to avoid any confusion

x1=-8

y1=7

x2=-4

y2=-5

Now substitute into the formula (m is the slope, and remember: the formula contains SUBTRACTION):

m=\(\frac{(-5-7)}{(-4--8)}\)

simplify

m=\(\frac{-5-7}{-4+8}\)

add

m=-12/4

divide

m=-3

So the slope of the line PQ is -3

As said above, perpendicular lines have slopes that have a product of -1

So to find the slope of the line perpendicular to PQ, use this formula:

-3m=-1

divide both sides by -3

m=1/3

The only line that has a slope of 1/3 is B (y=1/3x+4), so B is the answer.

Hope this helps!

The height of the pyramid is 16 feet.

What is Pythagoras Theorem?

Pythagoras' theorem is a fundamental principle in geometry that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

We can use the Pythagorean theorem to find the height of the pyramid.

The slant height of the pyramid is the hypotenuse of a right triangle whose legs are the height of the pyramid and half the length of the base of the pyramid. Since the base is a square, half the length of the base is 12 feet.

Using the Pythagorean theorem:

height² + 12² = 20²

height² = 20² - 12²

height² = 256

height = 16 feet

Therefore, the height of the pyramid is 16 feet.

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a) The circle crosses the y-axis at the points (0, 6) and (0, -2). b) the radius of the circle is 5. c) (i) The length of CP is √34. (ii) The length of PQ is 10.

(a) To find the y-coordinates of the points where the circle crosses the y-axis, we substitute x = 0 into the equation of the circle:

0² + y² + 6(0) - 4y = 12

y² - 4y = 12

y² - 4y - 12 = 0

To solve this quadratic equation, we can factor it:

(y - 6)(y + 2) = 0

Setting each factor to zero, we find two possible values for y:

y - 6 = 0 => y = 6

y + 2 = 0 => y = -2

Therefore, the circle crosses the y-axis at the points (0, 6) and (0, -2).

(b) To find the radius of the circle, we can complete the square to rewrite the equation of the circle in standard form:

x² + y² + 6x - 4y = 12

(x² + 6x) + (y² - 4y) = 12

(x² + 6x + 9) + (y² - 4y + 4) = 12 + 9 + 4

(x + 3)² + (y - 2)² = 25

Comparing this equation with the standard form of a circle, (x - h)² + (y - k)² = r², we can see that the center of the circle is at (-3, 2) and the radius is √25 = 5.

Therefore, the radius of the circle is 5.

(c) (i) To find the length of CP, we can use the distance formula between two points. The coordinates of C are (-3, 2), and the coordinates of P are (2, 5).

The distance formula is given by:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Substituting the coordinates into the formula, we have:

CP = √((2 - (-3))² + (5 - 2)²)

= √(5² + 3²)

= √(25 + 9)

= √34

Therefore, the length of CP is √34.

(ii) To find the length of PQ, we can use the fact that PQ is a tangent to the circle. The radius of the circle is 5, and the line segment CP is perpendicular to PQ.

Since CP is perpendicular to PQ, CP is the radius of the circle. Therefore, CP = 5.

Therefore, the length of PQ is equal to 2 times the length of CP:

PQ = 2 * CP

= 2 * 5

= 10

Therefore, the length of PQ is 10.

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Answer:

Hope this helps it is in the file below.