Given that m= -2 and n=¾, find the value Of
i)m²(n-1)
ii) n²-3/m​

Answer:

The distance between park and museum is 12km.

Step-by-step explanation:

Given that the map shows 1cm represents 3km. In this question, the distance between park and museum is 4cm so in order to find the real-life distance, you have to multiply by 4 :

[tex]1cm = 3km[/tex]

[tex]4cm = 3km \times 4[/tex]

[tex]4cm = 12km[/tex]

Hence, the real-life distance between the park and the museum is [tex]12km[/tex].

What is the simplification?

Simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

Here given that,

Here is a map of a town.The map shows a centimetre ruler [tex]1[/tex] cm represents [tex]3[/tex] km.

In a map it is mentioned that [tex]1[/tex]cm which represents the [tex]3[/tex] km. So, the distance between park and museum is

[tex]1+3=4[/tex]cm

So for the real-life distance, we multiply by [tex]4[/tex]

then,

[tex]1cm=3km\\\\4cm=3(4)km\\\\4cm=12km[/tex]

Hence, the real-life distance between the park and the museum is [tex]12km[/tex].

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Answer:

C. x=(p−ny)/m

Step-by-step explanation:

mx + ny = p

Subtract ny from each side

mx + ny -ny= p -ny

mx = p-ny

Divide each side by m

mx/m = (p-ny)/m

x=(p−ny)/m

Answer:

it is a horizontal stretch by 2.

Step-by-step explanation:

AB=3-1=2

A'B'=6-2=4

[tex]\frac{A'B'}{AB} =\frac{4}{2} =2\\A'B'=2(AB)[/tex]

Answer:

1.332 × 10-3

Step-by-step explanation:

you move the decimal point to the right until there's only one digit on the left side of it. the exponent is 3 because that's the number of places you moved the decimal point, and it's negative because you moved it to the right. if you move the decimal to the left it is positive, to the right is negative :)

Answer:

[tex]t_7 =\frac{5}{729} [/tex]

Step-by-step explanation:

We are given that:

First term (a) = 5

common ratio (r) =[tex]\frac{1}{3}[/tex]

The nth term of a geometric sequence is given as:

[tex]t_n =ar^{n-1} \\\therefore t_7 =5\times \bigg(\frac{1}{3}\bigg) ^{7-1} \\\therefore t_7 =5\times \bigg(\frac{1}{3}\bigg) ^{6} \\\therefore t_7 =5\times \bigg(\frac{1}{3}\bigg) ^{6} \\\therefore t_7 =5\times \frac{1}{729}\\\\\huge\red{\boxed{\therefore t_7 =\frac{5}{729} }}[/tex]

Answer:

[tex] = 2.3 \times {10}^{7} \\ [/tex]

Step-by-step explanation:

[tex]23000000 \\ = 2.3 \times {10}^{7} [/tex]

hope this helps

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good luck! have a nice day!

Answer:

A, C

Step-by-step explanation:

10x+ 4y = -2

5x -2y = 2

We can multiply the first equation by 1/2

5x+2y = -1

And then add the equations to eliminate y

5x+2y = -1

5x -2y = 2

--------------------

10x +0y = 1

Adding the equations will not eliminate any variables

15x +2y =0

Multiply the bottom equation by 2 and then subtract

10x -4y = 4

10x+ 4y = -2

-10x +4y = -4

------------------

0x +8y = -6  will eliminate x

Answer:

Answer A, C

Step-by-step explanation:

When multiplying the bottom equation by two, you get 10x-4y=4

After subtracting 10x-4y=4 and the top equation you will be able to eliminate the variable x.

You can also also get the same result and eliminate a variable with answer A.

Answer:

1

Step-by-step explanation:

For this problem, the negative sign on the 38 stays.  You can remove the parentheses and addition sign and subtract 38 from 12.

12 + (-38) + 27

12 - 38 + 27

-26 + 27

1

If the problem was (12 - (-38), than the negatives would cancel out and form (12 + 38).

Using BODAMAS rule, the equation 12 + -(38) - 27 the simplified answer is 1.

The full form of BODAMAS is" bracket, orders, divisions, multiplication, addition, subtraction. Any calculation follows the order of BODAMAS rule".

According to the question,

12 + (-38) + 27

= 12 - 38 + 27           [Removing the Parentheses]

= 26.

Hence, Using BODAMAS rule, the equation 12 + -(38) - 27 the simplified answer is 1.

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Answer:

Option D

Step-by-step explanation:

Out of all given options, Option D (the parallelogram) will tessellate the easiest.

Option B's shape (the Trapezoid) is also possible. However, it would take a little more work for it to tessellate. The trapezoid provided would not tessellate alone.

Option A and Option C's shape wouldn't tessellate because it would leave a gap.  To add, Option C's shape is nearly impossible to tessellate.

Answer: B, C, D

step by step explaniation

i think the answer might be 2948m^3

Answer:

Step-by-step explanation:

(3 + 1)/(-2 - 4) = 4/-6 = -2/3

y + 1 = -2/3(x -4)

y + 1 = -2/3x + 8/3

y + 3/3 = -2/3x + 8/3

y = -2/3x + 5/3

2x + 3y - 5 = 0 is the standard form

The required equation of the line that passes through (4, -1) and (-2, 3) is 2x+3y-5 = 0

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, A line is passing through points (4, -1) and (-2, 3)

We know that, the equation of a line passing through two points is given by, (y-y₁) = (y₂-y₁)/(x₂-x₁)(x-x₁)

y+1 = (3+1)/(-2-4)(x-4)

y+1 = -2/3(x-4)

3y+3 = -2x+8

2x+3y-5 = 0

Hence, The required equation of the line that passes through (4, -1) and (-2, 3) is 2x+3y-5 = 0

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Answer:

(–4, 1)  

Step-by-step explanation:

1. Calculate the slope of AB

m₁ = (y₂ - y₁)/(x₂ - x₁) = (-4 - 4)/(0 -(-2))= -8/2 = -4

2. Calculate the slope of the perpendicular line

m₂ = -m₁ = ¼

3. Calculate its y-intercept

Point Z, (0,2), is the y-intercept.

4. Write the equation for the line

Insert the values of m and b

y = ¼x + 2

5. Check the points

(a) (-4,1)

1 = ¼(-4)+ 2

1 = -1 + 2

1 = 1

TRUE

(b) (1,-2)

-2 = ¼(1) + 2

-2 = ¼ + 2

-2 = 2¼

FALSE

(c) (2,0)

0 = ¼(2) + 2

0 = ½ + 2

0 = 2½

FALSE

(d)  

4 = ¼(4) + 2

4 = 1 + 2

4 = 3

FALSE

Only (-4,1) is on the perpendicular line.

The diagram shows the line going through AB in red and the perpendicular line in purple.

Answer:

-4,1

Step-by-step explanation:

Answer:

v = -1

Step-by-step explanation:

First, you will need to solve it step-by-step:

(4v − 9)(1 + v) = 0

Next, you need to simplify both sides of the equation:

4v(2) − 5v − 9 = 0

Now, factor the left side of equation:

(4v − 9)(v + 1) = 0

The last thing you need to do is to set all of the factors to equal to zero:

4v − 9 = 0 or v + 1 = 0

So, that means that you answer:

v=9/4 or in your case, v = −1

Answer:

2/3

Step-by-step explanation:

2/9+4/9

The denominator is the same, so we add

6/9

Divide the top and bottom by 3

2/3

6/9simplified = 2/3 or ≅ 0.6666667

Answer:

The angle is 53.13 degrees

Step-by-step explanation:

In this question, we are to calculate the angle to which a ladder is to be set to get to a window.

Now, looking at this, we can picture a triangle where the length of the ladder represents the the hypotenuse while the angle we are considering makes the height of the room from the floor.

Please check attachment for picture of triangle

Since we are considering the hypotenuse and the opposite, the mathematical term we would be using is the sine.

Sine of an angle = length of opposite/length of hypotenuse

Sine angle = 8/10

since angle = 8/10

angle = arc sin 0.8

angle = 53.13 degrees

Answer:

x = 15/11

Step-by-step explanation:

(segment piece) x (segment piece) =  (segment piece) x (segment piece)

(x+3) *x = 2x*(6x-6)

Divide each side by x

x+3 = 2(6x-6)

Distribute

x+3 = 12x-12

Subtract x from each side

x+3-x = 12x-x-12

3  = 11x-12

Add 12 to each side

3+12 = 11x-12+12

15 = 11x

Divide each side by 11

15/11 =x

Answer:

15/11

Step-by-step explanation:

(x + 3) *x = 2x * (6x - 6)

x^2 + 3x = 12x^2 - 12x

x^2 - 12x^2 = - 12x - 3x

- 11x^2 = - 15x

11 x * x = 15 * x

Like terms cancel out

11x = 15

= 15/11

Hope this helps!

Answer:

[tex]17[/tex]

Step-by-step explanation:

[tex]\sqrt{285}[/tex]

[tex]=16.8819430161[/tex]

9514 1404 393

Answer:

  43/120 ≈ 0.3583

Step-by-step explanation:

Adding up the folks who use two facilities counts the folks who use all three 3 times. So, the number who use two or more facilities is ...

  21 +16 +24 -2(9) = 43 . . . . people who use 2 or more facilities

The probability that a person chosen randomly from the 120 at the sports center uses at least 2 facilities is ...

 43/120 ≈ 0.3583

_____

The given numbers add up as follows:

  Gym only: 42

  Pool only: 18

  Track only: 14

  Gym and Pool only: 12

  Gym and Track only: 15

  Pool and Track only: 7

  Gym and Pool and Track: 9

  No facilities: 3

Answer:9 packets

Step-by-step explanation:

You simply divide 144 by 16: )

Answer:

9 packages

Step-by-step explanation:

Take 144 ounces and divide by 16 ounces per package

144/16 = 9

You will get 9 packages

Answer:

40

Step-by-step explanation:

The number of gift baskets Nikki can make varies directly with the amount of time she spends making the baskets .

Let n be the number of baskets and let t be the mount of time it takes to make the basket. This means that:

n α t

=> n = kt

where k = constant of proportionality

She can make 4 baskets in every 1/2 hour.

This means that:

4 = k * 1/2

=> k = 4 * 2 = 8 baskets per hour

The time is now 5 hours (t = 5). Therefore:

n = 8 * 5 = 40 baskets

She can make 40 baskets in 5 hours.

Answer:

Step-by-step explanation:

x+2/3=2

multiply by 3

3x+2=6

3x=6-2

3x=4

x=4/3

if it is (x+2)/3=2

multiply by 3

x+2=6

x=6-2=4

Answer:

[tex]x=\frac{4}{3}[/tex]

Step-by-step explanation:

[tex]x+\frac{2}{3}=2[/tex]

to find the value of x we subtract 2/3 on both sides

[tex]x+\frac{2}{3}-\frac{2}{3}=2-\frac{2}{3}[/tex]

taking LCM AS 3

[tex]x=\frac{2*3}{1*3}-\frac{2}{3}[/tex]

[tex]x=\frac{6}{3}-\frac{2}{3}[/tex]

[tex]x=\frac{4}{3}[/tex]

[tex]i hope this will help you:)[/tex]

Answer:

A =101.956 cm^2

Step-by-step explanation:

The area of the parallelogram is given by

A = bh

A = 14.2 * 7.18

A =101.956 cm^2

Answer:

101.956

Step-by-step explanation:

Area equals bh

7.18(14.2)

Answer:

101[tex]cm^{2}[/tex]

Answer:

$675

Step-by-step explanation:

If it is 24% less than the regular price then it is 76% of the original price

$675 multiplied by 0.76 is $513

Answer:

30° and 110°

55° and 85°

70° and 70°

Step-by-step explanation:

Given that:

[tex]\angle B = 90^\circ[/tex]

To find the possible values for the other two angles [tex]\angle A\ and\ \angle C[/tex].

Property of a triangle is that the sum of all three angles is always equal to [tex]180^\circ[/tex].

OR

[tex]\angle A +\angle B +\angle C = 180^\circ\\\Rightarrow \angle A + 40^\circ + \angle C = 180^\circ\\\Rightarrow \angle A + \angle C = 180^\circ - 40^\circ\\\Rightarrow \angle A + \angle C = 140^\circ[/tex]

So, the sum of [tex]\angle A\ and\ \angle C[/tex] should be [tex]140^\circ[/tex]. We can select our answers according to this condition.

Option 1: 20° and 30°: the sum is [tex]50^\circ \neq 140^\circ[/tex] hence, not correct.

Option 2: 30° and 110°: the sum is [tex]140^\circ[/tex] hence, correct.

Option 3: 55° and 85°: the sum is [tex]140^\circ[/tex] hence, correct.

Option 4: 60° and 90°: the sum is [tex]150^\circ \neq 140^\circ[/tex] hence, not correct.

Option 5: 70° and 70°: the sum is [tex]140^\circ[/tex] hence, correct.

Hence, the possible answers can be:

30° and 110°

55° and 85°

70° and 70°

Answer:

30º and 110º

55º and 85º

70º and 70º

Step-by-step explanation:

got it right on edge. !

Answer:

31.25

Step-by-step explanation:

Answer:

31.25 is right.

Step-by-step explanation:

Answer:

V = 6.26 (2.5)

Step-by-step explanation:

The volume of a cube is given by

V = s^3 where s is the side length

V = (2.5)^3

V = 6.26 (2.5)

Answer: The correct answer is C

Answer:

Step-by-step explanation:

The geometric mean has a set up it must follow in order to "work". If you look at #3, x is a side of the smaller triangle that has a base of 3, but it's also a side of the large triangle that has a base of 3 + 8 which is 11.  That means that x is your geometric mean. Setting up the geometric mean will look like this:

[tex]\frac{3}{x}=\frac{x}{11}[/tex]

where x is the geometric means and the 3 and the 11 (the positions they are in) are the geometric extremes.

Now we cross multiply to solve for x:

[tex]x^2=33[/tex] and

[tex]x=\sqrt{33}[/tex]

That's the length of x in #3.

For #4, x is the side of the small triangle with the base of 7 and it's also the side of the large triangle with the base of 7 + 13 which 20. That means that x is the geometric mean. Setting up like above:

[tex]\frac{7}{x}=\frac{x}{20}[/tex] and

[tex]x^2=140[/tex] so

[tex]x=\sqrt{140}[/tex]

Complete Question:

A chemical supply company currently has in stock 100 lb of a certain chemical, which it sells to customers in 5-lb batches. Let X = the number of batches ordered by a randomly chosen customer, and suppose that X has the pmf shown in the table below. Compute E(X) and V(X).

Then compute the expected number of pounds left after the next customer’s order is shipped and the variance of the number of pounds left.

NOTE: The pmf is shown in the file attached

Answer:

Expected number of batches, E(X) = 2.0 batches

Variance of batches, V(X) = 0.8 batches²

Expected number of pounds left, E(Y) = 90 lb

Variance of pounds left, V(Y) = 20 lb²

Step-by-step explanation:

The company has 100 batches and it sells to customers in 5 lb batches. The number of pounds left after each customer is filled will be modeled by the mathematical formula: Y = 100 - 5X

The expected value of X, E(X) can be calculated using the formula:

[tex]E(X) = \sum x p(x)[/tex]

E(X) = (1*0.3) + (2*0.5) + (3*0.1) + (4*0.1)

E(X) = 0.3 + 1 + 0.3 + 0.4

E(X) = 2.0

Expected number of batches, E(X) = 2.0 batches

The variance of X, V(X) can be calculated using the formula:

[tex]V(X) = E(X^2) - [E(X)]^2\\ E(X^2) = \sum x^2 p(x)\\ E(X^2) = (1^2 *0.3) + (2^2 * 0.5) + (3^2 * 0.1) + (4^2 * 0.1)\\ E(X^2) = 0.3 + 2 + 0.9 + 1.6\\ E(X^2) = 4.8\\V(X) = 4.8 - 2^2\\V(X) = 0.8[/tex]

Variance of batches, V(X) = 0.8 batches²

Y = 100 - 5X

E(Y) = E(100 - 5X)

E(Y) = 100 - 5E(X)

E(Y) = 100 - 5(2)

E(Y) = 90 lb

Expected number of pounds left, E(Y) = 90 lb

Variance of the number of pounds left:

V(Y) = V(100 - 5X)

V(Y) = V(100) + V(-5X)

V(100) = 0

V(Y) = (-5)² V(X)

V(Y) = 25 * 0.8

V(Y) = 20

Variance of pounds left, V(Y) = 20 lb²

The question is incomplete. Here is the complete question.

A chemical supply company currently has in stock 100 lb of a certain chemical, which it sells to customers in 5-lb batches. Let X 5 the number of batches ordered by a randomly chosen customer, and suppose that X has the following pmf.

 x      1         2        3       4

P(x)  0.3     0.5     0.1     0.1

Compute E(X) and V(X). Then compute the expected number of pounds left after the next customer’s order is shipped and the variance of the number of pounds left.

Answer: E(X) = 2

V(X) = 0.8

Expected number of pounds left = 90

Variance of the number of pounds left = 20

Step-by-step explanation: Since this is a probability distribution, to determine E(X), which is a measure of central tendency:

E(X) = ∑[x*P(x)]

E(X) = 1*0.3+2*0.5+3*0.1+4*0.1

E(X) = 2

V(X) is the variance for this type of distribution and is calculated as:

V(X) = ∑{[x - E(x)]²*P(x)} = (1-2)²*0.3+(2-2)²*0.5+(3-2)²*0.1+(4-2)²*0.1

V(X) = 0.8

The number of pounds left after the next costumer's order is shipped is given by the equation: Y = 100 - 5X

The expected number is equal to E(Y), which is this case is:

E(Y) = E(100 - 5X)

One property of E(X) is that if a and b are constants:

E(aX+b) = aE(X) + b

Taking that a = - 5 and b = 100:

E(100 - 5X) =  (-5).2 + 100

E(Y) = 90

The variance of the number of pounds left is given by:

V(Y) = V(100 - 5X)

For variance, the property is: if a and b are constants:

V(aX+b) = a²V(X)

V(100 - 5X) = (-5)²*0.8

V(Y) = 20