A machine costing N$200 000 has effective life of 7 years and its scrap value is N$30000. What amount should
the company deposit annually into a sinking fund earning 5% per annum so that it can replace the machine
after its useful life? Assume that a new machine will cost N$300 000 after 7 years.

Answer:

x = -1

Step-by-step explanation:

6+4 = 10

14-10 = 4

2x + 6 = 4

2x (-2) = -2

-2 + 6 = 4

The intersection of sets M and F contains the elements "c" and "d".

To find the intersection of sets M and F, we need to identify the elements that are common to both sets.

M = {a, b, c, d}

F = {c, d, e, f}

The intersection of M

and F is denoted by M ∩ F, which represents the set containing elements that are present in both M and F.

Looking at the elements in M and F, we can see that the common elements between the two sets are "c" and "d".

Therefore, the intersection of M and F can be expressed as:

M ∩ F = {c, d}

So, the intersection of sets M and F contains the elements "c" and "d".

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Answer:

True

Step-by-step explanation:

The easiest way to understand this problem is to first breakdown the notation. In words, the problem is stating 9 is NOT an element of the set containing the elements 4, 1, 8, and 7. Since 4\(\neq\)9, 1\(\neq\)9, 8\(\neq\)9, and 7\(\neq\)9 then 9 is not an element of this set and the statement is true.

Answer:

Step-by-step explanation:

front side: 6x3 = 18

back : 6x3 = 18

right:6x2 = 12

left:6x2 = 12

top: 3x2 =6

bottom: 3x2 =6

18 + 18 + 12 + 12 + 6 + 6

= 72

Answer:

Step-by-step explanation: true

Answer:

Step-by-step explanation:

x^2 + 6x + 8 = 0

(x + 4)(x + 2) = 0

x + 4 = 0

x = -4

x + 2 = 0

x = -2

The solution of quadratic equation by factoring is -4.

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

We are given that;

x^2+8=-6x

Now,

To solve the quadratic by factoring, we need to first write it in the standard form: x2+6x+8=0

Then we need to find two numbers that multiply to 8 and add to 6. These are 2 and 4. So we can write the quadratic as: (x+2)(x+4)=0

To find the solutions, we need to set each factor equal to zero and solve for x: x+2=0⟹x=−2

x+4=0⟹x=−4

So the solutions are x=−2

and x=−4

Therefore, by quadratic equations the answer will be -4.

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Answer:

1. B.

2. C.

Step-by-step explanation:

1. It only has one cell so it needs to rely on other organisms in order for it to survive

2. Chloroplasts are only found in plants you can remember it by "Chloroplants"

Answer:

x= 1 and y= 3

Step-by-step explanation:

2*1+3*3=12.

Answer:

(X'U'Y) + (XUY')

Step-by-step explanation:

Starting with [Xn(X'nY)]', we can use De Morgan's laws to simplify the expression:

[Xn(X'nY)]' = (Xn)' + (X'nY)'

Recall that Xn represents the logical operator "and", while X' represents "not X". Using these definitions, we can expand the expression:

(Xn)' + (X'nY)' = (X'U'Y) + (XUY')

where U represents the logical operator "or".

Therefore, [Xn(X'nY)]' simplifies to (X'U'Y) + (XUY').

Answer:

Step-by-step explanation:

Answer:

The product of the slopes of  and the line perpendicular to  through C is -1 in all cases. So, I can conclude that any two perpendicular lines have slopes that are negative reciprocals of each other.

Step-by-step explanation:

its correct

As a result, either 684 or 685 passes were sold for $6 each.

An element of a whole is a portion. The number is represented mathematically as a fraction, where the numerator and denominator are split. Both are numbers in a straightforward fraction. A fraction appears in the accumulator or base of a complicated fraction. The numerator of a perfect proportion is smaller than the denominator.

Let's start by dividing the total amount collected by the price of each ticket:

$4108 ÷ $6 = 684.666...

Since we can't sell a fraction of a ticket, we need to round this number to the nearest whole number.

If we round down, we would sell 684 tickets at $6 each, and the total collected would be:

684 × $6 = $4104

This is $4 less than the total collected, so we know we need to sell at least one more ticket.

If we round up, we would sell 685 tickets at $6 each, and the total collected would be:

685 × $6 = $4110

This is $2 more than the total collected, so we know we can't sell more than 685 tickets.

Therefore, the number of tickets sold at $6 each is either 684 or 685.

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Answer:

104.8cm³(1 decimal place)

Step-by-step explanation:

Volume of a cone is given by the formula

V=1/3πr²h

we are given a radius of 5 and a height of 4 so we will just substitute for the values and we will give our pie as 22/7

V=1/3× 22/7×5²×4

V=1/3 × 22/7 ×25 ×4

V=2200/21

V=104.76190476

V=104.8cm³(1decimal place)

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Step 1: Given a rectangle has a perimeter of 68 ft.

Formula

Step 2: Find the perimeter when scaled by a factor 1.5

Then the perimeter of the resulting rectangle

Hence the perimeter of the resulting rectangle is 102ft​

Answer:

Step-by-step explanation:

3.6*

It is very easy to find the perimeter of a square when its area is given in the question. For that, you only ned to know one fomula. That formula is: Area = side^2

For this particular question, the given value for the area of the square is 36 sq.cm. So, we can solve for the side(s) by substituting the given value in the above mentioned formula.

We get

36 = s^2

Now, we need to get the square root of both sides, which gives us

s = √36 s = 6 cm

Since all the sides of a square are equal in length, the side length is 6 cm. Now to determine the perimeter, we must multiply the side length by 4 (because there are 4 equal sides in a square). That gives us Perimeter = 4 x side length Perimeter = 4 x 6 cm.

Therefore, the perimeter of the square is 24 cm.

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Answer:

21/32

Step-by-step explanation:

0.65625 = \(\frac{65625}{100000}\) = \(\frac{13125}{20000}\) = \(\frac{2625}{4000}\) = \(\frac{525}{800}\) = \(\frac{105}{160}\) = \(\frac{21}{32}\)

When the number, 0.65625 is converted to a fraction, the result would be 21/32.

To convert a decimal to a fraction, you first need to determine the place value of the decimal. In this case, 0.65625 ends in the fifth decimal place, so it's in the hundred-thousands place.

However, this fraction can be simplified. Both 65625 and 100000 are divisible by 25. Dividing both the numerator and the denominator by 25 gives us:

= 2625/400

= 105/160

We can simplify this one more time by dividing both the numerator and the denominator by 5, resulting in:

= 21/32

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From the given picture, we can note that the interior angles of both triangles measure the same, that is,

This implies that the triangles are similar each other. Then, first answer is:

Similar: YES

Then, the similarity statement is:

Finally, if the left triangle is the original and the other triangle is the reduced one, the scale factor is

Then, the scale factor is:

The estimated sum of 7 83/84 is 8 to the nearest whole number.

Mixed fractions are fraction that has a whole number attached to an improper fraction. A mixed fraction can be added by first adding the real whole numbers together, then adding their improper fraction counterparts with it.

Also, we can add two mixed fractions together by first converting all the mixed fractions to improper fractions before adding them together.

Using the first process:

= 4 5/12 + 3 8/14

The whole number are 4 and 3, adding those two together, we have:

= 7 (5/12 + 8/14)

The L.C.M of 12 and 14 is 84.

= 7( (7×5)+ (6*8) )  /84

= 7 (35+ 48/84)

= 7 (83/84)

To decimal, we get 7.988. Therefore, the estimated sum of 7 83/84 is 8 to the nearest whole number.

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Answer:

142

Step-by-step explanation:

180-10-28 = 142

hope this helps

Answer:

∡3=142°

Step-by-step explanation:

∠3 and 38° are supplementary angles, which means their sum must equal 180°, therefore, we make an equation and solve for ∡3:

∠3+38°=180°

∡3=142°

So ∡3=142°

Answer:

the standard error of data set is 2.628

Step-by-step explanation:

Given the data in the question;

set;

x = 9, 13, 21, 30, 31, 31, 34, 25, 28, 20

To get the standard of Error for this data set, we use the formual

S.E = s / √n

First we determine the mean average;

Mean x' = ∑x / n =  ( 9 + 13 + 21 + 30 + 31 + 31 + 34 + 25 + 28 + 20 ) / 10

x' = 242 / 10

Mean x' = 24.2

Next we find the standard deviation s:

x             (x-x')²

9           231.04

13          125.44

21          10.24

30         33.64

31         46.24

31         46.24

34        96.04

25        0.64

28        14.44

20        17.64

Total ∑(x-x')² = 621.6

so Variance = ∑(x-x')² / (n-1) = 621.6 / ( 10 - 1 )  = 621.6 / 9

Variance = 69.0667

Standard deviation S = √Variance

Standard deviation S = √69.0667

Standard deviation S = 8.3106

So we substitute into our formula to get the standard of error;

S.E = 8.3106 / √10

S.E = 2.628

Therefore, the standard error of data set is 2.628

Answer:

2.63

Step-by-step explanation:

The perimeter of the figure with side length of 5 units is 50 units

From the question, we have the following parameters that can be used in our computation:

Shape = rectangle

Smaller shapes = squares

Side lengths = 5 units

The perimeter of the figure is calculated as

Perimeter  = Number of visible sides * Side length of the square shape

In this case, we have

Number of visible sides = 10

Substitute the known values in the above equation, so, we have the following representation

Perimeter  = 10 * 5

Evaluate the products

Perimeter  = 50 units

Hence, the perimeter is 50 units

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Answer:

\(f(x)=2^x\)

Step-by-step explanation:

Exponential function:

\(f(x)=a(b^x)+c\)

Step 1. Find a, y-intercept

Step 2. Find b, slope

Step 3. Find c, horizontal asymptote

a = 1

m = (y₂ - y₁)/(x₂ - x₁)

m = (3 - 1)/(1 - 0) = 2/1

b = 2

c = 0

\(f(x)=1(2^x)+0\\f(x)=2^x\)

Answer:

\(t=22\)

Step-by-step explanation:

First, note that the entire thing is a square. This is because since two of the opposite angles are right angles, the remaining two must also be right angles.

In a square, all four sides are equivalent.  

Therefore, the sides PS an RS are equal to each other. Thus:

\(PS=RS\\t+22=2t\\22=t\\t=22\)

Answer:

B. $104.95

Step-by-step explanation:

$160.45-$55.50=$104.95

Answer:

Step-by-step explanation:

The milepost number of the rest area is 7 miles away from milepost 58, so it can be represented by the equation:

m = 58 + 7

This equation states that the milepost number of the rest area is equal to 58 plus 7, or 65. Therefore, the rest area can be located at milepost 65.

Answer:

12/35 of the road

Step-by-step explanation:

To find 2/5 of 6/7 you simply multiple and simplify if possible.

2/5 * 6/7 = (2*6)/(5*7) = 12/35

Answer:

300 glass beads

Step-by-step explanation:

There are 30 beads in each box so you multiply 30 by 10.

\(10*30=300\)

Jake measured a hotel and made a scale drawing, the length of the room in the drawing is 24 inches.

If the scale of the drawing is 8 inches : 7 feet, this means that for every 8 inches in the drawing, there are 7 feet in real life.

To find out length of the room is in the drawing, we need to set up a proportion:

8 inches / 7 feet = x inches / 21 feet

where x is the length of the room in the drawing.

We can cross-multiply and solve for x:

8 inches × 21 feet = 7 feet × x inches

168 inches = 7 feet × x inches

Dividing both sides by 7, we get:

24 inches = x

Therefore, the length of the room in the drawing is 24 inches.

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Answer:

86.60254

Step-by-step explanation:

30-60-90 triangle, which means that the base is 10. 1/2(10)(10 rt 3). Simplify answer as needed :)

Answer:

3/2

Step-by-step explanation:

Simplify the following:

((4 + 1/5)×5)/14

((4 + 1/5)×5)/14 = ((4 + 1/5)×5)/14:

((4 + 1/5)×5)/14

Put 4 + 1/5 over the common denominator 5. 4 + 1/5 = (5×4)/5 + 1/5:

(((5×4)/5 + 1/5) 5)/14

5×4 = 20:

((20/5 + 1/5)×5)/14

20/5 + 1/5 = (20 + 1)/5:

(((20 + 1)/5)×5)/14

20 + 1 = 21:

(21/5×5)/14

21/5×5 = (21×5)/5:

((21×5)/5)/14

((21×5)/5)/14 = (21×5)/(5×14):

(21×5)/(5×14)

(21×5)/(5×14) = 5/5×21/14 = 21/14:

21/14

The gcd of 21 and 14 is 7, so 21/14 = (7×3)/(7×2) = 7/7×3/2 = 3/2:

Answer:  3/2