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3 years ago

Which is equivalent to the expression below? |-3| O 13 -1-31 O 3

Mathematics

2 answers:

Genrish500 [490]3 years ago

7 0

Answer is 3 because absolute value is always positive

hichkok12 [17]3 years ago

4 0

It’s 3, absolute value makes everything positive

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Work out the surface area of this cylinder.<br><br> 12 cm radius<br> 35 cm height

zaharov [31]

Answer:

The surface area of this cylinder is 3545 $\frac{1}{7}$ cm²

Step-by-step explanation:

The formula of the surface area of the cylinder is

Surface area = later area + 2 base area, where

Lateral area = perimeter of the base × height of the cylinder

Let us use the rules above to solve the question

∵ The base of the cylinder is a circle

∵ The perimeter of the circle = 2 π r

∵ The radius of the cylinder is 12 cm

∴ r = 12

∴ The perimeter of the base = 2 (12) (π)

∴ The perimeter of the base = 24π cm

∵ The height of the cylinder is 35 cm

∴ h = 35 cm

→ By using the rule of the lateral area above

∵ The lateral area = 24π × 35

∵ π = $\frac{22}{7}$

∴ The lateral area = 24 × $\frac{22}{7}$ × 35

∴ The lateral area = 2640 cm²

∵ The area of the circle = π r²

∴ The area of the base = $\frac{22}{7}$ × (12)² = $\frac{22}{7}$ (144) = 452 $\frac{4}{7}$ cm²

→ By using the rule of the surface area above

∴ The surface area = 2640 + 2(452 $\frac{4}{7}$ ) = 3545 $\frac{1}{7}$ cm²

∴ The surface area of this cylinder is 3545 $\frac{1}{7}$ cm²

4 0

3 years ago

A. Complete the chart based on the initial conditions:

Nata [24]

Answer:

$Month\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Pop(whole \ ant)\\month1 => x_1=80\times0.94^1=1128\\month2=>x_2=1200\times0.94^2=1060\\month3=>x_3=1200\times0.94^3=996\\month4=>x_4=1200\times0.94^4=936$

$week Number\ \ \ \ \ \ \ \ \ \ \ \ \ \ Mass(g)\\week1 => x_1=80\times1.1^1=88g\\week2=>x_2=80\times1.1^2=96.8g\\week3=>x_3=80\times1.1^3=106.48g\\week4=>x_4=80\times1.1^4=117.128g$

Step-by-step explanation:

a. From the information provided, we can deduce that the population death's follows a Geometric sequence in the form $(a,ar,ar^2,ar^3...)$ where $a-first \ term$ and $r-common \ ratio$

#Since the population is reducing, $r$ can is obtained as $r=1-r=0.94$

#The $n^t^h$ term is obtained using the formula $x_n=ar^(^n^-^1^)$ , given a=1200

The number of ants alive after every month (in first 4 months)

The ant's alive after 4 months is obtained as the value of $x_5$

$x_n=ar^(^n^-^1^)\\1-x_5=1-1200\times 0.94^4=936.89\\\approx 936$

Hence, 936 ants are alive after 4 months.

b. As with the above question, the kitten population follows a geometric sequence: $(a,ar,ar^2,ar^3...)$ .

#Since it's a growing population , the common ration is the sum of 100% + the growth rate,

$r=1.1$ and $a=80$ and $x_n=ar^(^n^-^1^)$

The population after 4weeks will be:

$week Number\ \ \ \ \ \ \ \ \ \ \ \ \ \ Mass(g)\\week1 => x_1=80\times1.1^1=88g\\week2=>x_2=80\times1.1^2=96.8g\\week3=>x_3=80\times1.1^3=106.48g\\week4=>x_4=80\times1.1^4=117.128g$

8 0

4 years ago

Jessica Reads a story about a turtle that swam 16 feet in 24 seconds. She assumes that the time that it takes the turtle to swim

Zigmanuir [339]

Answer:

Time (secs) => distance (ft)

1 => ⅔

15 => 10

24 => 16

45 => 30

Step-by-step explanation:

Equation to represent this proportional relationship is $d = tk$ , where,

t = time

d = distance

k = constant of proportionality

To complete the table, let's find k given that the turtles swarm 16 ft (d) in 24 secs (t).

Substitute d = 16, t = 24 into the equation.

$d = tk$

$16 = 24k$

$\frac{16}{24} = k$ (division property of equality)

$\frac{2}{3} = k$

Let's complete the table by substituting the value of k and the other given value of t or d, as the case may be:

For 1 sec, let's find distance (d):

$d = tk$

$d = 1*\frac{2}{3}$

d = ⅔ ft

For 10 ft, let's find the time (t) taken:

$d = tk$

$10 = t*\frac{2}{3}$

Multiply both sides by 3

$10*3 = t*\frac{2}{3}*3$

$30 = t*2$

Divide both sides by 2

$\frac{30}{2} = \frac{t*2}{2}$

$15 = t$

t = 15 secs

For 45 secs, let's find distance (d):

$d = tk$

$d = 45*\frac{2}{3} = 15*2$

d = 30 ft

5 0

4 years ago

Write the following number in standard decimal form four tenths

Crazy boy [7]

0.4 is four tenths. 0.4 = 4/10=2/5

8 0

3 years ago

Read 2 more answers

Use the PACED decision-making process to _____.

Alex_Xolod [135]

Use the PACED decision-making process to make a decision or make a choice. The steps to follow when making a decision can be easily remembered when you use the word PACED:
P - What is the PROBLEM - Why is there a need to make a choice?
A - What are the ALTERNATIVES - What are the possible choices available?
C - Establish the CRITERIA - Why is one choice better than the other?
E - EVALUATE the alternatives - How well does each choice meet the criteria?
D - Make a DECISION - What is the best choice?

6 0

3 years ago