If someone could help me on this math problem and give answers and explanation would be great

Tony wants to estimate the number of bees in a beehive. He catches 100 bees from the hive and marks each one with a dye. He then

kotykmax [81]

Answer:

Number of total bees = 400

Step-by-step explanation:

He catches 100 bees from the hive and marks each one with a dye.

He later catches 60 and 15 were marked with the dye.

Its very to estimate from the data given.

I'll answer it with ratio.

We'll ratio number of bees with dye to total he caught the second day.

I.e 15:60 = 1:4

We'll multiply this ratio with the number he caught the first day to know the total.

1/4x =100

X = 100*4

X= 400

Where x is the total number of bees in the bee hive.

7 0

4 years ago

For the following amount at the given interest rate compounded continuously, find (a) the future value after 9 years, (b) the

Stella [2.4K]

Answer:

(a) The future value after 9 years is $7142.49.

(b) The effective rate is $r_E=4.759 \:{\%}$ .

(c) The time to reach $13,000 is 21.88 years.

Step-by-step explanation:

The definition of Continuous Compounding is

If a deposit of $P$ dollars is invested at a rate of interest $r$ compounded continuously for $t$ years, the compound amount is

$A=Pe^{rt}$

(a) From the information given

$P=4700$

$r=4.65\%=\frac{4.65}{100} =0.0465$

$t=9 \:years$

Applying the above formula we get that

$A=4700e^{0.0465\cdot 9}\\A=7142.49$

The future value after 9 years is $7142.49.

(b) The effective rate is given by

$r_E=e^r-1$

Therefore,

$r_E=e^{0.0465}-1=0.04759\\r_E=4.759 \:{\%}$

(c) To find the time to reach $13,000, we must solve the equation

$13000=4700e^{0.0465\cdot t}$

$4700e^{0.0465t}=13000\\\\\frac{4700e^{0.0465t}}{4700}=\frac{13000}{4700}\\\\e^{0.0465t}=\frac{130}{47}\\\\\ln \left(e^{0.0465t}\right)=\ln \left(\frac{130}{47}\right)\\\\0.0465t\ln \left(e\right)=\ln \left(\frac{130}{47}\right)\\\\0.0465t=\ln \left(\frac{130}{47}\right)\\\\t=\frac{\ln \left(\frac{130}{47}\right)}{0.0465}\approx21.88$

3 0

3 years ago

Grant simplified the expression 1.5(-3.2 + 2.5) His work is shown below explain the error in grants work

nata0808 [166]

Answer: (i think there was supposed to be a photo attached but ???)

-1.05

Step-by-step explanation:

1.5(-3.2 + 2.5)

1.5 x -3.2 = -4.8

1.5 x 2.5 = 3.75

(-4.8 + 3.75)

8 0

3 years ago

Prove that 16^4-2^13-4^5 is divisible by 11.

Nataliya [291]

You add all of that up and you will get 56320 and divided by 11 then u get 5120.

3 0

3 years ago

You can upgrade lighting at your factory to LED bulbs that cost $6.95 each and last an average of 5 years. It costs S3 in labor

marshall27 [118]

Answer:

11.95 dollars

Step-by-step explanation:

Cost of one LED bulb = 6.95 dollars

Cost of changing one bulb = 3 dollars

Life of each bulb = 5 years.

In 10 years, only one time after 5 years the bulbs would have been changed

Hence cost of 100 lamps = 695 and

cost of changing once = 500

Total cost = 1195 dollars for 11 years

Divide this by 10 years to get average cost per year

Cost of 100 lamps per year = 1195/100 = 11.95 dollars

8 0

3 years ago