if my sugar is 1rupee per 20 gram.What is the weight of sugar if it's MRP is 120 rupees?​

Answer:

-2/4 or -1/2

Step-by-step explanation:

y1-y2                   -1-1=-2                

_____                 6-2=4

x1-x2

Answer:

slope= -4

Step-by-step explanation:

1-(-1)=2

(-2) - 6 = -8

-8/2= -4

Answer:

B(6, 5), C(1, -7)

Step-by-step explanation:

A(2, 5)

From A to B, there is translation x, (4, 0).

Add 4 to A's x-coordinate, and add 0 to A's y-coordinate.

B(2 + 4, 5 + 0) = B(6, 5)

From C to B there is the translation y, (5, 12).

Since we are going from B to C, we undo translation y.

The translation from B to C is (-5, -12).

C(6 - 5, 5 - 12) = C(1, -7)

A)

Explanation

Step 1

Let x represents the number of board games

Let y represent the number of remote controlled cars

i)

a)Board games weigh 3 pounds

b) remote-controlled cars weigh 1.5 pounds

The box can hold no more than 24 pounds( in other words it must be equal or less thant 24),so

ii) in each box, the amount of remote control cars must be at least 4 times the amount of board games( in other words, the number of remote control cars must be equal or greater than 4 times the amount of board games, so,

hence

so,

A)

Step 2

graph the inequalities

a) set the sign = to convert the inequality in a funcion, isolate for y

b) fnd 2 coordinates of the line

C) draw the line

i)

draw a line(continuosus) that passes trougth P1 and P2

ii)

draw a line(continuosus) that passes trougth P3 and P4

I hope this helps you

Answer:

divide 31 by 49 and multiply the result by 100

(31÷49 ) × 100

Line with slope\($\mathrm{m}=\frac{3}{2}$\) and passing through \($(13,-8): \quad y=\frac{3}{2} x-\frac{55}{2}$\).

What is Line?

A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature. Since lines can exist in two, three, or higher dimensional environments, they are one-dimensional things. The term "line" may also be used to describe a line segment in daily life that contains two locations that serve as its endpoints.

Compute the line equation\($\mathbf{y}=\mathbf{m x}+\mathbf{b}$\) for slope \($m=\frac{3}{2}$\) and passing through (13,-8)

Compute the y intercept:\($\quad b=-\frac{55}{2}$\)

Construct the line equation y=m x+b where \(m=\frac{3}{2}$ and $b=-\frac{55}{2}$\)

\(y=\frac{3}{2} x-\frac{55}{2}$$\)

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Answer: f=6x-7/x

Step-by-step explanation:

Applying the triangle proportionality theorem, the value of x is: 6.

According to the triangle proportionality theorem, the following proportions that shows the relative lengths of he segments is given as:

17/5 = 10x - 9/2x + 3

Cross multiply:

17(2x + 3) = 5(10x - 9)

34x + 51 = 50x - 45 (distribution property)

34x - 50x = -51 - 45

-16x = -96

x = 6

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The radius of the semicircle protractor is approximately 4.693 cm.

Given,Perimeter of a semicircle protractor = 14.8 cm.

To find:The radius of a semicircle protractor.Solution:We know that the perimeter of a semicircle protractor is the sum of the straight edge of a protractor and half of the circumference of the circle whose radius is the radius of the protractor.

Circumference of a circle = 2πrWhere, r is the radius of the circle.If the radius of the semicircle protractor is r, then Perimeter of a semicircle protractor = r + πr [∵ half of the circumference of a circle =\((1/2) × 2πr = πr]14.8 = r + πr14.8 = r(1 + π) r = 14.8 / (1 + π)r ≈ 4.693\) cm.

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Answer:

-3,2

Step-by-step explanation:

Answer:

The answer is 1.

Step-by-step explanation:

Given the expression:

\(|z-6|-|z-5|,\ if\ z<5\)

To find:

The expression without absolute value.

Solution:

First of all, let us learn about the absolute value function:

\(y = f(x) = |x| =\left \{ {{x\ if\ x>0} \atop {-x\ if\ x<0}} \right.\)

i.e. value is x if x is positive

value is -x if x is negative

Here the given expression contains two absolute value functions:

\(|z-6|\) and \(|z-5|\)

Using the definition of absolute value function as per above definition.

\(|z-5| =\left \{ {{(z-5)\ if\ z>5} \atop {-(z-5)\ if\ z<5}} \right.\)

\(|z-6| =\left \{ {{(z-6)\ if\ z>6} \atop {-(z-6)\ if\ z<6}} \right.\)

Now, it is given that z < 5 that means z will also be lesser than 6 i.e. z < 6

So, given expression \(|z-6|-|z-5|,\ if\ z<5\) will be equivalent to :

\(-(z-6) - (-(z-5))\\\Rightarrow -z+6 +z-5 = \bold{1}\)

So, the expression is equivalent to 1.

I WILL FIRST GROUP THE LIKE TERMS AND SIMPLIFY THEM BEFORE FACTORISING

IT IS VITAL TO SIMPLIFY LIKE TERMS BEFORE FACTORISING.

\(12 {x}^{2} - 3x + 20 - 5 \\ = 12 {x}^{2} - 3x + 15\)

THE GCF IN THE EXPRESSION IS 3 MEANING WE WILL DIVIDE EACH AND EVERY TERM IN THE P

EXPRESSION BY 3

\( = 3(4 {x}^{2} - x + 5)\)

HOPE THIS HELPS.

Answer:

-3/10

Step-by-step explanation:

The graph of the system of the inequalities is attached.

To graph the inequalities y < -x - 4 and y ≥ (3/5)x + 4, we can start by graphing the corresponding equations and then shade the appropriate regions based on the inequality signs.

Let's begin with the equation y = -x - 4:

Choose a range of x-values to plot.

For simplicity, let's use x-values from -10 to 10.

Substitute different x-values into the equation to find corresponding y-values.

For example:

When x = -10, y = -(-10) - 4 = 10 - 4 = 6.

When x = 0, y = -(0) - 4 = -4.

When x = 10, y = -(10) - 4 = -10 - 4 = -14.

Plot these points on the coordinate plane and draw a straight line passing through them.

This line represents the equation y = -x - 4.

Next, let's graph the equation y = (3/5)x + 4:

Again, choose a range of x-values to plot. Let's use the same range of -10 to 10.

Substitute different x-values into the equation to find corresponding y-values. For example:

When x = -10, y = (3/5)(-10) + 4 = -6 + 4 = -2.

When x = 0, y = (3/5)(0) + 4 = 0 + 4 = 4.

When x = 10, y = (3/5)(10) + 4 = 6 + 4 = 10.

Plot these points on the coordinate plane and draw a straight line passing through them.

This line represents the equation y = (3/5)x + 4.

Now, let's shade the regions based on the inequalities:

For y < -x - 4, we need to shade the region below the line y = -x - 4.

For y ≥ (3/5)x + 4, we need to shade the region above or on the line y = (3/5)x + 4.

Hence, the region where the shaded regions overlap represents the solution to both inequalities.

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Answer:

To write a system of equations for this problem, we need to define two variables:

Let x be the number of hours the worker worked.

Let y be the number of shirts the worker made.

We can use the given information to write two equations:

The first equation relates the total expenses to the labor and material costs:

144 = 28x + 2y

The second equation relates the number of shirts to the number of hours and the average rate:

y = 4x

This is the system of equations we need to solve:

{144=28x+2yy=4x​

Simplify and solve for x:

144 = 28x + 8x

144 = 36x

x = 4

Now we can plug x = 4 into either equation to find y:

y = 4(4)

y = 16

So the worker worked for 4 hours and made 16 shirts.

The Total length of two sides based on the information will be 7x²+2x+1

The Length of the third side will be 4 x³-10x²-7.

Total length of two sides= Side 1 + Side 2

= 8x² − 5x − 2+ 7x − x²+ 3

= 8x²-x²-5x+7x-2+3

= 7x²+2x+1

Length of the third side = Perimeter - Total length of two sides

Length of the third side=4x³ − 3x² + 2x − 6-(7x²+2x+1)

= 4x³ − 3x² + 2x − 6-7x²-2x-1

= 4 x³-10x²-7

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The distance covered by the bicycle at a speed of 19 miles per hour is 418 feet

The rate of change in an object's position with regard to a scalar quantity of reference and time is what is meant by speed, according to its definition. Although it may appear difficult, speed is essentially speeding in a particular direction. Due to the fact that it is a scalar quantity, speed must be defined in terms of both magnitude (speed) and direction. It has a meter per second SI unit (ms-1). A body is considered to be accelerating if there is a change in the magnitude or the direction of its speed.

we know that 1 mile is 5280 feets

so, the speed of 19 miles per hour will be 100320 feet in 3600 seconds

we know

distance = speed × time

distance = 100320/ 3600 ×15

distance = 418 feet

hence the distance covered is 418 feet.

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Answer:

To fill in the table of values for the equation y = 2x + 1, we can choose different values of x and substitute them into the equation to find the corresponding values of y. For example:

x y

0 1

1 3

2 5

3 7

4 9

To get the value of y, we substitute each value of x into the equation and simplify:

When x = 0:

y = 2(0) + 1 = 1

When x = 1:

y = 2(1) + 1 = 3

When x = 2:

y = 2(2) + 1 = 5

When x = 3:

y = 2(3) + 1 = 7

When x = 4:

y = 2(4) + 1 = 9

Therefore, the table of values for the equation y = 2x + 1 is:

x y

0 1

1 3

2 5

3 7

4 9

Juliet will earn the same amount of money whether she chooses a monthly salary of ​$1900 from the company or a base salary of ​$1800 plus a ​5% commission on furniture sales if her sales amount to $2000.

To find the amount of sales for which the two salary choices are equal, we set the equation for the base salary plus commission equal to the equation for the flat monthly salary. The equation can be written as:

1800 + 0.05x = 1900

where x is the amount of furniture sales in dollars.

Simplifying and solving for x, we get:

0.05x = 100

x = 2000

If she sells less than $2000 of furniture, she will earn more with the flat monthly salary of $1900. If she sells more than $2000 of furniture, she will earn more with the base salary plus commission. This calculation provides an important decision-making tool for Juliet, as she can tailor her salary choice based on her expected sales for the month.

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The answer of the given question based on finding the length of EF from the triangle is, the length of EF is approximately 1.2. The answer is (d).

The Law of Sines is a trigonometric rule that relates the angles and sides of a triangle. Specifically, it states that for any triangle ABC, the ratio of the length of a side of the triangle to the sine of the angle opposite that side is equal to the same ratio for any other side and its opposite angle:

a/sin(A) = b/sin(B) = c/sin(C) ,where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the opposite angles, respectively. This law is useful in solving problems involving triangles, such as finding the length of a side or the measure of an angle when given certain other information about the triangle.

To find the length of EF, we can use the Law of Sines,

Let x be the length of EF. Then we have:

sin(75°)/3 = sin(50°)/x

Solving for x, we get:

x = 3*sin(50°)/sin(75°) ≈ 1.2

Therefore, the length of EF is approximately 1.2. The answer is (d).

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Answer:

The probability that a given user is transmitting is 0.1 = 10%.

The probability that at any given time, exactly n users are transmitting simultaneously is \(P(X = n) = C_{120,n}.(0.1)^{n}.(0.9)^{120-n}\).

0.0048 = 0.48% probability that there are 21 or more users transmitting simultaneously.

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

\(E(X) = np\)

The standard deviation of the binomial distribution is:

\(\sqrt{V(X)} = \sqrt{np(1-p)}\)

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that \(\mu = E(X)\), \(\sigma = \sqrt{V(X)}\).

Each user transmits only 10 percent of the time.

This means that \(p = 0.1\)

Find the probability that a given user is transmitting.

The probability that a given user is transmitting is 0.1 = 10%.

Suppose there are 120 users.

This means that \(n = 120\)

Find the probability that at any given time, exactly n users are transmitting simultaneously.

This is \(P(X = n)\).

This n is different from the n of total number of users(120 in this case) from the standard binomial formula. This is the number of successes, which is the equivalent of x. So

\(P(X = n) = C_{120,n}.(0.1)^{n}.(0.9)^{120-n}\)

The probability that at any given time, exactly n users are transmitting simultaneously is \(P(X = n) = C_{120,n}.(0.1)^{n}.(0.9)^{120-n}\)

Find the probability that there are 21 or more users transmitting simultaneously.

Now we use the binomial approximation to the normal. We have that:

\(\mu = E(X) = np = 120*0.1 = 12\)

\(\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{120*0.1*0.9} = 3.2863\)

Using continuity correction, this probability is \(P(X \geq 21 - 0.5) = P(X \geq 20.5)\), which is 1 subtracted by the pvalue of Z when X = 20.5. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{20.5 - 12}{3.2863}\)

\(Z = 2.59\)

\(Z = 2.59\) has a pvalue of 0.9952

1 - 0.9952 = 0.0048

0.0048 = 0.48% probability that there are 21 or more users transmitting simultaneously.

The three solutions of the inequalities are x < 0 , x <  0.8 , x< -2

Inequalities are defined as mathematical expressions in which both sides are not made equal to each other.

Given the inequalities;

Let's solve for the value of x

x - 0.8 < 0

Make 'x' the subject

x < 0 + 0. 8

x < 0. 8

-5x < 10

Make 'x' the subject by dividing both sides by - 5

-5x/ 5 < 10/ -5

x < -2

Thus, the three solutions of the inequalities are x < 0 , x <  0.8 , x< -2

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Answer:

64π^2  cubic inches

Step-by-step explanation:

The question is not complete, the shapes are not given

Diameter of base= 16π

Radius of base= 8π

Height of cylinder = 8 inches

Let us find the volume of the cylinder

V= πr^2h

V= π* (8π)* 8

V= 64π^2  cubic inches

Hence the volume of the cylinder is 64π^2  cubic inches

Answer:

Trapezoid

Step-by-step explanation:

It has two opposite parallel lines and the other two are not parallel

Answer:

the sum of 17+36 =53

Step-by-step explanation:

cause, when we add 17+36 ,we should first add the numbers in the ones place ( 7+6=13).second add the numbers in the tens place(1+3=4).So lastly add every thing and you will have the sum.(13+40=53)

Answer:

total pencil = 5 orange pencils + 8 yellow pencils + 4 green pencils

= 17 pencils

P (g n y) = 4/17 + 8/17

= 0.706

Step-by-step explanation:

1. first find the total number of pencils

2. since there is a replacement the demoinator remains the same

3. find the probability of each green and yellow

4. add the two probability

Answer:

74

Step-by-step explanation:

Answer: 32 + 1 and 5 x 2