QUESTION 1
1.1 Given the arithmetic series: - 7 - 3+1 ........... + 173
1.1.2 Calculate the sum of the series.
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Answer:

5 is their common denominator

Step-by-step explanation:

A common denominator is when both denominators are the same.

Answer:

5 is the common denominator of 3/5 and 2/5

Answer:

g(8) = 3(8)-2

g(8) = 24-2

g(8)= 22

Step-by-step explanation:

Answer:

242 ft²

Step-by-step explanation:

The shape can be decomposed to give us a trapezium and a rectangle

Area of the shape = area of the trapezium + area of the rectangle

✔️Area of the trapezium = ½(a + b)h

a = 14 ft

b = 20 ft

h = 13 - 7 = 6 ft

Area = ½(14 + 20)*6

Area of trapezium = 102 ft²

✔️Area of rectangle = L*W

L = 20 ft

W = 7 ft

Area = 20*7 = 140 ft²

✔️Area of the shape = 102 + 140 = 242 ft²

Answer:

The rearrenged formula is [tex]C = \frac{5(F - 32)}{9}[/tex]

Step-by-step explanation:

Celsius to Fahrenheit:

To realize the conversion of the temperature in degrees Celsius to degrees Fahrenheit, we use the following equation:

[tex]F = \frac{9C}{5} + 32[/tex]

Rearrange the formula to highlight the measure in degrees Celsius.

We want to find C in function of F. So

[tex]F = \frac{9C}{5} + 32[/tex]

[tex]\frac{9C}{5} = F - 32[/tex]

[tex]C = \frac{5(F - 32)}{9}[/tex]

Answer:

zero

Step-by-step explanation:

the slope does not change in y at all.

Answer: The second and the last answer are correct

Step-by-step explanation:

0.8 repeting

Step-by-step explanation: 1/6 times 64 divded by 12.

Answer:

He bought 5

Step-by-step explanation:

Answer:

So, I think you're talking about 180-118, which is 62

Step-by-step explanation:

180-118=62

Answer:

way too hard

Step-by-step explanation:

Answer:

Some 224 people were in favor of the expansion.

Step-by-step explanation:

Given that, according to the recent poll, 22 1/4% of the people polled said that they approved of the city plan to expand the library, if 1004 people was polled, to determine how many were in favor of the expansion should be done the following calculation:

1/4 = 0.25

100 = 1004

22.25 = X

1004 x 22.25 / 100 = X

223.39 = X

Thus, some 224 people were in favor of the expansion.

Answer:

We know that the original price of the bike was $8,000.

After one year, the price of the bike decays a 12%, then the new price of the bike is:

P(1) = $8,000*( 1 - 12%/100%) = $8,000*(1 - 0.12)

After another year, the price again decays a 12%, the new price will be:

P(2) = $8,000*(1 - 0.12)*(1 - 12%/100%) = $8,000*(1 - 0.12)*(1 - 0.12) = $8,000*(1 - 0.12)^2

We already can see the pattern here, after t years, the price of the bike will be:

P(t) = $8,000*(1 - 0.12)^t

With this equation, we can find the price of the bike after 5 years, where we only need to replace t by 5

We will get:

P(5) = $8,000*(1 - 0.12)^5 = $4,221.9

The price of the bike after 5 years is  $4,221.9.

Now we want two equations to represent this, so we need another.

This is kinda trivial, because there is only one equation that represents this, so we only can rewrite our equation in another form.

We could say that the price of the bike after t years is:

P(t) = $8,000*(0.88)^t

or something like:

P(t) = $7040*(0.88)^(t - 1)

Where i multiplied the initial value by 0.88, and then reduced the exponent by one.

Answer:

it is 2,800 miles from ny to la

Step-by-step explanation:

Answer:

i tthat hink it is a plane

Answer:

PLANE

Step-by-step explanation:

No 4 can be factored from each term of the trinomial. Therefore, option C is the correct answer.

The factorization method uses basic factorization formula to reduce any algebraic or quadratic equation into its simpler form, where the equations are represented as the product of factors instead of expanding the brackets. The factors of any equation can be an integer, a variable, or an algebraic expression itself.

The given polynomial is x(4x²+8x+12).

Here, in the trinomial 4x²+8x+12, 4 is common factor in each term.

So, group and factor out the greatest common factor (GCF), then combine.

That is, 4(x²+2x+3)

Now, x(4x²+8x+12)= 4x(x²+2x+3)

Therefore, option C is the correct answer.

To learn more about the factorization visit:

https://brainly.com/question/26923098

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Consider the function f(x) = x ³. Since 2³ = 8 is a perfect cube that is pretty close to x = 1.999, take the linear approximation to f(x) at x = 2. It is

f(x) ≈ L(x) = f (2) + f ' (2) (x - 2)

Compute the derivative:

f(x) = x ³   →   f ' (x) = 3x ²   →   f ' (2) = 12

Then

L(x) = 8 + 12 (x - 2) = 12x - 16

Now approximate 1.999³ :

f (1.999) ≈ L (1.999) = 12•1.999 - 16 = 7.988

(Compare this to the actual value, 7.98801.)

Answer:

104 in total

6.5k+12a=18.5ka

Step-by-step explanation:

Answer:

B. 2⁵ + 7²

Step-by-step explanation:

2 to the fifth power is: 2⁵

7 squared (7 to the second power) is: 7²

Answer:

55.5 percent of the way!!!!!!

Answer:

Time of murder = 10:39 am

Step-by-step explanation:

Let the equation of exponential function representing the final temperature of the body after time 't' is,

f(t) = [tex]a(e)^{nt}[/tex]

Here, a = Initial temperature

n = Constant for the change in temperature

t = Duration

At 11:30 am temperature of the body was 91.8°F.

91.8 = [tex]98.6(e)^{nt}[/tex] --------(1)

Time to reach the body to the morgue = 12:30 pm

Duration to reach = 12:30 p.m. - 11:30 a.m.

                              = 1 hour

Therefore, equation will be,

84.4 = [tex]91.8(e)^{n\times 1}[/tex]

eⁿ = [tex]\frac{84.4}{91.8}[/tex]

ln(eⁿ) = ln(0.9194)

n = -0.08403

From equation (1),

91.8 = [tex]98.6(e)^{-0.08403t}[/tex]

[tex](e)^{0.08403t}=\frac{98.6}{91.8}[/tex]

[tex]ln[(e)^{0.08403t}]=ln[\frac{98.6}{91.8}][/tex]

0.08403t = 0.07146

t = 0.85 hours

t ≈ 51 minutes

Therefore, murder was done 51 minutes before the detectives arrival.

Time of murder = 11:30 - 00:51

                          = 10:90 - 00:51

                          = 10:39 am

Answer:

1 1/2 cups you multiply 1/8 ×12

Answer: 0.13

Step-by-step explanation:

Answer:

Surface area = 80 cm²

Step-by-step explanation:

Surface Area of rectangular prism = 2(LW + LH + WH)

L = 4 cm

W = 4 cm

H = 3 cm

Plug in the values

Surface Area = 2(4*4 + 4*3 + 4*3) = 2(16 + 12 + 12)

Surface Area = 2(40) = 80 cm²

Answer:

65

Step-by-step explanation:

x=52+y

x=5y

y=x/5

x=52+(x/5)

x-(x/5)=52

(5x-x)/5=52

4x=52×5

4x=260

x=260/4

x=65

Bunga is 65 yrs old

Metali is 13 yrs old

Answer:

X = 30 degrees, z = 80 degrees and y = 70 degrees