A began business with Rs.4200 and joined B with capital Rs.7200. When did B join if the profits at the end of the year are equally divided? a. 4 months b. 5 months c. 6 months d. 7 months​

Answer:

\(m=\frac{1}{4}\)

Step-by-step explanation:

Given

\(y+2=\frac{1}{4}(x-3)\)

Required

Find the slope

\(y+2=\frac{1}{4}(x-3)\)

Subtract 2 from both sides

\(y+2-2=\frac{1}{4}(x-3) - 2\)

\(y=\frac{1}{4}(x-3) - 2\)

Open bracket

\(y=\frac{1}{4}x-\frac{1}{4}*3 - 2\)

\(y=\frac{1}{4}x-\frac{3}{4} - 2\)

Take LCM

\(y=\frac{1}{4}x+\frac{-3 - 8}{4}\)

\(y=\frac{1}{4}x+\frac{-11}{4}\)

\(y=\frac{1}{4}x-\frac{11}{4}\)

An equation has the form:

\(y = mx + b\)

Where

\(m = slope\)

By comparing: \(y = mx + b\) and \(y=\frac{1}{4}x-\frac{11}{4}\)

\(m=\frac{1}{4}\)

So, the slope is 1/4

Answer:

e-5=2f

take '-5' to the other side where '2f' is

e=2f+5

Answer:

The sample size is  \(n = 384 \)  

Step-by-step explanation:

From the question we are told that

     The margin of error is \(E = 0.05\)

Here we will assume that the sample proportion is  \(\^ p = 0.5\)

 From the question we are told the confidence level is  95% , hence the level of significance is    

      \(\alpha = (100 - 95 ) \%\)

=>   \(\alpha = 0.05\)

Generally from the normal distribution table the critical value  of  \(\frac{\alpha }{2}\) is  

   \(Z_{\frac{\alpha }{2} } =  1.96\)

Generally the sample size is mathematically represented as  

    \(n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p ) \)

=> \(n = [\frac{1.96 }{0.05} ]^2 * 0.5 (1 - 0.5  ) \)        

=> \(n = 384 \)    

Answer: 0.754

Step-by-step explanation:

Given that, it is twice as likely to come up heads as tails in a coin ;

Let tail = T ; head = H

Total possible outcomes in the coin toss = 3

Number of heads = 2

Number of tails = 1

Probability = required outcome / Total possible outcomes

Then

P(T) = 1 / 3

P(H) = 2/3

What is the most likely outcome of a series of 2000 coin tosses using this biased coin?

Most likely outcome :

P = 2/3 = 0.667 ; n = 3

Using binomial distribution formula:

nCr * p^r * (1-p)^(n-r)

P=0 :

3C0 * 0.667^0 * (1 - 0.667)^(3-0) = 0.037

P=1 :

3C1 * 0.667^1 * (1 - 0.667)^(3-1) = 0.2218 = 0.222

P= 2 :

3C2 * 0.667^2 * (1 - 0.667)^(3-2)

= 0.444

b. What is the relative probability of getting 1300 heads versus 1350 heads in a series of 2000 coin tosses using this coin?

Answer:

35

Step-by-step explanation:

\(\angle FGH \cong \angle FDE\) and \(\angle FHG \cong \angle FED\) by the corresponding angles theorem.

Therefore, \(\triangle FDE \sim \triangle FGH\) by AA similarity.

Corresponding sides of similar triangles are proportional, so \(\frac{FD}{20}=\frac{49}{28} \implies FD=35\).

EXPLANATION

Given the expression 12(3y+x).

Let's solve it:

Applying the distributive property:

12*3y + 12*x

Multiplying like terms:

36y + 12x

The answer is 36y + 12x

(i)To make 8 pancakes 250 ml milk is needed. So, to make 4 pancakes=

(250/8)×4=120 ml is needed!

(ii)To make 8 pancakes 5g butter is needed and to make 12 pancakes=

(5/8)×12=7.5 g butter is needed!

The values of independent random variables (a)E(Y), (b)V(Y), (c) E(2Y), and (d) V(2Y) using covariance are 36, 1296, 72, and 5184 respectively.

We can use the following properties of expected value and variance:

E(aX) = aE(X) for any constant a

V(aX) = a² V(X) for any constant a

E(X + Y) = E(X) + E(Y) for any random variables X and Y (assuming they have finite expected values)

V(X + Y) = V(X) + V(Y) + 2Cov(X, Y), where Cov(X, Y) is the covariance between X and Y.

(a) E(Y) = E(6X1 - 6X2) = 6E(X1) - 6E(X2) (by linearity of expectation)

= 6(9) - 6(3) = 36

Therefore, E(Y) = 36.

(b) V(Y) = V(6X1 - 6X2) = 36V(X1) + 36V(X2) - 72Cov(X1,X2) (by the variance formula)

To find the covariance between X1 and X2, we note that they are independent, so Cov(X1, X2) = 0.

Substituting the values of the variances, we get:

V(Y) = 36(6²) + 36(4²) - 72(0) = 1296

Therefore, V(Y) = 1296.

(c) E(2Y) = 2E(Y) (by linearity of expectation)

= 2(36) = 72

Therefore, E(2Y) = 72.

(d) V(2Y) = 4V(Y) (by the variance formula)

= 4(1296) = 5184

Therefore, V(2Y) = 5184.

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ANSWER

5 miles

EXPLANATION

Let's draw the two possible paths Bob can take. One is walking 3 miles south and 4 miles west, and the other is walking in a straight line from where he is to the park,

If Bob takes the red path, the total distance he will travel is 7 miles. If he takes the blue path, the total distance he will travel can be found with the Pythagorean Theorem,

Solve for c taking the square root of both sides,

Replace a and b, and solve,

Hence, the distance Bob will walk if he takes the blue path is 5 miles, which is the shortest path.

The histogram given in the following question is approximately symmetric.

Skewness is a measure of the distribution's symmetry. The skewness of the normal distribution is zero.

If the skewness is positive, we have a right skewed histogram. If the skewness is negative, the histogram is said to be left skewed.

Skewness is a degree of asymmetry in a probability distribution.

The majority of the data values occur on the left side of the right skewed distribution, with diminishing data on the right side.

The mean is on the right side of the curve, the mode is towards the peak, and the median is in the middle. Three is not the same number.

The majority of data values appear on the right side of the left skewed distribution. The mean is on the left side of the curve, the mode is towards the peak, and the median is in the middle. Three is not the same number. It is the inverse of a right-skewed distribution.

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In abstract algebra, a subset of a group is considered a subgroup if it satisfies certain conditions. One of these conditions is closure under the group operation (i.e., multiplication).

Abstract algebra is a branch of mathematics that studies algebraic structures, which are sets with operations (such as addition, multiplication, or other binary operations) defined on them that satisfy certain axioms or properties. Algebraic structures can be extremely diverse and abstract, ranging from familiar structures such as the integers, rational numbers, and real numbers, to more complex structures such as groups, rings, fields, and modules.

If we take any two elements from the subset and multiply them together, the result must also be in the subset. However, a subset that is closed under multiplication is not necessarily a subgroup.

To see why this is the case, consider the set {1, -1} under multiplication. This set is closed under multiplication, since 1 * 1 = 1 and (-1) * (-1) = 1, which are both in the set. However, this set is not a subgroup of the group of real numbers under multiplication, because it does not contain an identity element (i.e., an element that behaves like a "neutral" element under multiplication). In this case, the identity element is 1, which is in the larger group but not in the subset {1, -1}. Therefore, {1, -1} is not a subgroup, even though it is closed under multiplication.

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Answer:

1-2x

Step-by-step explanation:

\((7+2x)-(4x+6)=7+2x-4x-6=1-2x\)

Huda's error in evaluating (3) squared incorrectly led to the incorrect final result.

The correct answer should be -20, not 34.

Huda's error was that she evaluated (3) squared incorrectly.

Instead of calculating 3 squared as 9, she mistakenly considered it as 3. This error led to incorrect subsequent calculations and the final result of 34, which is not the correct answer.

To evaluate the expression correctly, let's go through the steps:

Negative 3 (8 minus 5) squared minus (negative 7) \(= -3(3)^2 - (-7)\)

First, we simplify the expression within the parentheses:

\(-3(3)^2 - (-7) = -3(9) - (-7)\)

Next, we evaluate the exponent:

-3(9) - (-7) = -3(9) + 7

Now, we perform the multiplication and addition/subtraction:

-3(9) + 7 = -27 + 7 = -20

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Answer:

For s students, at least 6s liters of water will be needed. So, for 30 students, at least 6*30 = 180 liters of water will be needed.

Step-by-step explanation:

This question is solved by proportions, using rule of three.

I am going to say that:

s is the number of students.

l is the number of liters of water needed for s students.

I have found that with five students in the class at least 30 litres of water is needed.

This means that:

\(\frac{s}{l} = \frac{5}{30}\)

\(5l = 30s\)

\(l = \frac{30s}{5}\)

\(l = 6s\)

This means that for s students, at least 6s liters of water will be needed. So, for 30 students, at least 6*30 = 180 liters of water will be needed.

Answer:

x = 82, y = 8

Step-by-step explanation:

1. What does complementary mean? - The angles must add up to 90 degrees.

2. Form your equation: x + y = 90°

3. Let's say x is the larger angle and y is the smaller angle. So, form another equation: x = 74 + y

4. Put the two equations next to each other:

x + y = 90

x = 74 + y

5. We know what x is equal to, so plug it in!

74 + y + y = 90

74 + 2y = 90

-74           -74

2y = 16

y = 8

6. Now we know y = 8! So let's plug it back in!

x + 8 = 90

  -8      -8

x = 82

Using the rules of significant figures the expression 47.5-6.12 can be simplified as 41.38.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The number 6.12 has two digits after the decimal while the number 47.5 has only one digit after the decimal therefore, as per the law of significant figures, to deduct 6.12 from 47.5, we need to put one zero at the end of 47.5.

Also, there are two digits in 47.50 before the decimal while 6.12 has only one, therefore, As per the law of significant figures, one zero will be added before 6.12. Thus, the deduction now can be done as,

    4  7  .  5  0

-   0  6  .  1  2

   4   1  .  3  8

Hence, Using the rules of significant figures the expression 47.5-6.12 can be simplified as 41.38.

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Answer: More than 26.5 inches

Step-by-step explanation:

Solve this equation :

\(\frac{32+24+x}{3} \geq 27.5\)

x>26.5

Answer: Unfactorable

Step-by-step explanation:

5v^2-30v+70

5(v^2-6v+14)

You can't factor v^2-6v+14 with rational numbers

Answer:

40/49

Step-by-step explanation:

probability that a point chosen at random in the given figure will be inside the larger circle and outside the smaller circle = ( area larger circle - area of smaller circle / area of larger circle )

area of a circle = πr² where r = radius

area of smaller circle :

radius = 6

==> plug in 6 for r

A = π(6)²

==> evaluate exponent

A = 36π

Area of larger circle :

Radius = 14

==> plug in 14 for r

A = π(14)²

==> evaluate exponent

A = 196π

We have probability = area larger circle - area of smaller circle / area of larger circle

area of larger circle = 196π

area of smaller circle = 36π

probability = (196π - 36π)/196π

==> subtract 36 from 196

probability = 160π/196π

==> simplify fraction and cancel out π

probability = 40/49

Answer:

54 (also include units squared as the picture isn't clear)

Step-by-step explanation:

3×3=9 (area of square =l×b)

9×6= 54cm² (since a cube has 6 faces)

Answer:

the answer is 123,343,435.4421

The given information does not provide any clear indication for determining the position that should be taken on 3/01 and 3/02. Without additional information, it is not possible to make a decision. The table only displays the closing prices of the July GBP Futures Contract on different days, and it is unclear what trading strategy or what scenario is being considered. Additional information about the goals and objectives, the market conditions, and other relevant factors would be necessary to make a decision about trading positions.

The equation for the graph above is y = 5sin(2x/3).

In Mathematics and Geometry, a sine wave is sometimes referred to as a sinusoidal wave, or sinusoid and it can be defined as a fundamental waveform that is typically used for the representation of periodic oscillations, in which the amplitude of displacement at each interval is directly proportional to the sine of the displacement's phase angle.

Mathematically, a sine wave can be represented or modelled by this mathematical equation:

y = asin(bx)

Where:

Based on the graph of this sine wave, we have:

Amplitude, a = 5.

Periodicity, b = 2π/period = 2π/(3π) = 2/3

Therefore, the required sine wave function is given by;

y = asin(bx)

y = 5sin(2x/3)

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Answer:

the slope is 1/2

Step-by-step explanation:

We can just use the formula to get the slope

y1-y2 / x1-x2

Fit in both points to get:

3-5 / -2-2

Then, simple algebra gets us:

-2/-4

Simplifying the fraction gives us : 1/2 as the slope

Answer:

14/5 cm3 ??

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given function: f(x)=|3x-6|

To find: Vertex of the function

When we solve the given equation, 3x-6, by equating it to 0, we get

3x=6

x=2 ......(1)

Now, we will use the obtained value of x to find the value of y

To find the vertex at x=2, we will have to find the value of the y coordinate

let's assume the equation to be: 3x-6+y ......(2)

Let's solve equation (2) by equating it to 0

3x-6+y=0

Substituting equation (1), we get

3(2)-6+y=0

6-6+y=0

y=0

Therefore, we get the value of x as 2 and y as 0.

Therefore the vertex of f(x)=|3x-6| is (2,0).

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12x ≥ 420

is solution, simple