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3 years ago

The measure of minor arc JL is 60°.

Mathematics

2 answers:

Rama09 [41]3 years ago

7 0

Answer:

60+60= 120 is the answer

branly pls

MrRa [10]3 years ago

6 0

Answer:

Step-by-step explanation:

The lines form an equilateral triangle, and each angle in an equilateral triangle is 60.

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Find the measure of a positive angle coterminal with - 240°.

Irina18 [472]

-240+360=120
The answer is 120 degrees.

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vagabundo [1.1K]

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The lengths of two sides of a triangle are 5 inches and 16 inches find the range of possible lengths for the third side

Gnoma [55]

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3 years ago

Suppose a population of honey bees in Ephraim, UT has an initial population of 2300 and 12 years later the population reaches 13

Rama09 [41]

Answer:

common ratio: 1.155

rate of growth: 15.5 %

Step-by-step explanation:

The model for exponential growth of population P looks like: $P(t)=P_i(1+r)^t$

where $P(t)$ is the population at time "t",

$P_i$ is the initial (starting) population

$(1+r)$ is the common ratio,

and $r$ is the rate of growth

Therefore, in our case we can replace specific values in this expression (including population after 12 years, and initial population), and solve for the unknown common ratio and its related rate of growth:

$P(t)=P_i(1+r)^t\\13000=2300*(1+r)^{12}\\\frac{13000}{2300} = (1+r)^12\\\frac{130}{23} = (1+r)^{12}\\1+r=\sqrt[12]{\frac{130}{23} } =1.155273\\$

This (1+r) is the common ratio, that we are asked to round to the nearest thousandth, so we use: 1.155

We are also asked to find the rate of increase (r), and to express it in percent form. Therefore we use the last equation shown above to solve for "r" and express tin percent form:

$1+r=1.155273\\r=1.155273-1=0.155273$

So, this number in percent form (and rounded to the nearest tenth as requested) is: 15.5 %

6 0

3 years ago

This is the pond in a shape of a prism, it is completely full of water. Colin uses a pump to empty the pond. The level goes down

AnnZ [28]

Answer:

150 minutes

Step-by-step explanation:

P.S - The exact question is -

Given - This is the pond in a shape of a prism, it is completely full of

water. Colin uses a pump to empty the pond. The level goes

down by 20 cm in the first 30 min.

To find - Work put how many minutes Colin has to wait for the pond

to completely empty.

Proof -

Given that,

Height of prism = 1 m

Also,

Base of the prism is trapezium and

Sides of the trapezium are 0.6 m and 1.4 m

Height of trapezium is 2 m

We know that,

Area of trapezium = $\frac{1}{2}$ × (sum of sides)× height

= $\frac{1}{2}$ × (0.6 + 1.4)× 2

= $\frac{1}{2}$ × (2)× 2

= 2 m²

⇒Area of trapezium = 2 m²

Now,

Volume of prism = Area of trapezium × height of prism

= 2 m² × 1 m

= 2 m³

⇒Volume of prism = 2 m³

Now,

Given that the level goes down by 20 cm in the first 30 min

We know

100 cm = 1 m

⇒1 cm = $\frac{1}{100} m$ = 0.01 m

⇒20 cm = 20×0.01 m = 0.2 m

⇒The level goes down by 0.2 m in the first 30 min.

Also,

we know that height of water = height of prism = 1 m

So, the remaining water left in the pond = 1 m - 0.2 m = 0.8 m

Also,

Volume of Remaining water = Area of trapezium × height

= 2 m² × 0.8 m

= 1.6 m³

⇒Volume of Remaining water = 1.6 m³

Now,

Volume of emptied water = Total Volume - Volume of Remaining water

= 2 m³ - 1.6 m³

= 0.4 m³

⇒Volume of emptied water = 0.4 m³

Now,

0.4 m³ water will be empty in 30 minutes

⇒ 1 m³ water will be empty in $\frac{30}{0.4}$ = 75 minutes

⇒1.6 m³ water will be empty in 1.6 × 75 = 120 minutes

∴ we get

The remaining water is empty in 120 minutes

So,

Total pond is empty in 120 + 30 minutes

⇒Total pond is empty in 150 minutes

5 0

3 years ago