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2 years ago

A coin was tossed 60 times and the coin landed on Heads 35 times. What proportion of the time did the coin land on Heads?

Mathematics

1 answer:

SVETLANKA909090 [29]2 years ago

4 0

Answer: Hence, the proportion of head lands obtained from the total number of tosses is 0.583

Step-by-step explanation:

Given the following :

Total number of coin tosses = 60

Total number of times coin landed on head = 35

Proportion of head landings obtained :

Total number of head landings obtained / total number of coin tosses

Proportion of head landing obtained :

= 35 / 60 = 7 / 12 = 0.5833

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A lake near the Arctic Circle is covered by a sheet of ice during the cold winter months. When spring arrives, the ice starts to

hichkok12 [17]

Answer: 1.5 meters

Step-by-step explanation:

Given: A lake near the Arctic Circle is covered by a sheet of ice during the cold winter months. S

S(t) models the ice sheet's thickness (in meters) as a function of time t (in weeks) $S(t)=-0.25t+4$

if we put x=0, then

$S(0)=-0.25(0)+4\\=4\ meters$

So 4 meters is the initial thickness

To find the thickness after 6 weeks, put x=6 we get

$S(6)=-0.25(6)+4\\=-1.5+4=2.5\ meters$

Decrease in thickness every 6 weeks= $4-2.5=1.5\ meters$

3 0

2 years ago

Read 2 more answers

To complete her holiday wrapping, Bella needs identical strips of ribbon measuring 3.5 feet each. She has 85 feet of ribbon in t

MA_775_DIABLO [31]

Bella can cut 24 pieces of ribbon from this long strip

Solution:

Given that Bella has 85 feet of ribbons in total

She needs identical strips of ribbon measuring 3.5 feet each

To find: Number of peices of ribbon can she cut from long strip

Number of peices of ribbon can she cut from long strip can be calculated by dividing the total feet of ribbon she has by length of identical strips she needs

Mathematically written as:

$\text { Number of Strip that can be cut }=\frac{\text { Total length of ribbon }}{\text { Length of each piece }}$

$\begin{array}{l}{\text { Number of Strip that can be cut }=\frac{85}{3.5}} \\\\ {\text { Number of Strip that can be cut }=24.28 \approx 24}\end{array}$

Hence , the number of strip can be 24 each of size 3.5 feet

6 0

2 years ago

Maxis taking a cross-country road trip. Gas prices vary as the friends travel across the US from $4 dollars per gallon on the ea

Zolol [24]

Answer:

A) The amount of gas they bought on each coast;

East Coast = 35 gallons

Mid-US = 100 gallons

West Coast = 15 gallons

B) The amount of gas they bought on each coast on the return journey;

East Coast = 37 gallons

Mid-US = 116 gallons

West Coast = 21 gallons

Step-by-step explanation:

Complete Question

Maxis taking a cross-country road trip. Gas prices vary as the friends travel across the US from $4 dollars per gallon on the east coast to $3 in the mid-US, to $5 on the west coast.

(a) If they used twice as much gas in the mid-US than on either coast combined, and they spend $515 on gas to purchased 150 gallons of gas, how many gallons of gas did they buy at each price?

The answer to this question is East Coast - 35 gal, Mid-US - 100 gal, West Coast - 15 gal.

(b) On their way back they had more baggage in the car and spend $601 for 174 gallons of gas. Based on the same ratio as in Part (a), how many gallons of gas did they buy at each price? I don't know the answer to this one

Solution

Let the amount of fuel bought on the east coast = x gallons

Let the amount of fuel bought on the mid-coast = y gallons

Let the amount of fuel bought on the west coast = z gallons

a) - They used twice as much gas in the mid-US than on either coast combined

y = 2(x + z) = 2x + 2z (eqn 1)

- They spend $515 on gas to purchase 150 gallons of gas.

Total gallons purchased = x + y + z = 150

Total amount spent = 4x + 3y + 5z = 515

From eqn 1, y = 2x + 2z, inserting this value for y in the 2 other equations

x + y + z = x + 2x + 2z + z = 150

3x + 3z = 150

Divide through by 3

x + z = 50 (eqn *)

4x + 3y + 5z = 4x + 3(2x + 2z) + 5z = 515

4x + 6x + 6z + 5z = 515

10x + 11z = 515 (eqn **)

x + z = 50

10x + 11z = 515

Solving the simultaneous equation,

x = 35 gallons

z = 15 gallons

y = 2x + 2z = 2(35 + 15) = 100 gallons

B) On the return journey, the ratio between x, y and z is still the same, but the total gallons and total amount spent is now different.

They used twice as much gas in the mid-US than on either coast combined

y = 2(x + z) = 2x + 2z (eqn 1)

- They spend $601 on gas to purchase 174 gallons of gas.

Total gallons purchased = x + y + z = 174

Total amount spent = 4x + 3y + 5z = 601

From eqn 1, y = 2x + 2z, inserting this value for y in the 2 other equations

x + y + z = x + 2x + 2z + z = 174

3x + 3z = 174

Divide through by 3

x + z = 58 (eqn *)

4x + 3y + 5z = 4x + 3(2x + 2z) + 5z = 601

4x + 6x + 6z + 5z = 601

10x + 11z = 601 (eqn **)

x + z = 58

10x + 11z = 601

Solving the simultaneous equation,

x = 37 gallons

z = 21 gallons

y = 2x + 2z = 2(37 + 21) = 116 gallons

Hope this Helps!!!

5 0

2 years ago

If leticia invested $12,000 in an account in which the interest earned is continuously compounded at a rate of %2.5 find the tot

Luda [366]

Given:

Principal value = $12000

Rate of interest = 2.5%

To find:

Total amount after 15 years.

Solution:

Formula for amount discontinuously compounded interest is

$A=Pe^{rt}$

where, P is principal, r is rate of interest and t is time in years.

Substitute P=12000, r=0.025 and t=15 in the above formula.

$A=12000e^{0.025(15)}$

$A=12000e^{0.375}$

$A=12000(1.45499141462)$

$A=17459.8969754$

$A\approx 17459.897$

Therefore, the amount after 15 years is $17459.897.

6 0

2 years ago

Now, solve this problem. 106% of $ _______ = $7.95

Alex787 [66]

Answer:

7.5

Step-by-step explanation:

106% of $x = $7.95

In other words,

$\frac{106}{100}$ of $x = 7.95

Multiplying both sides of the equation by $\frac{100}{106}$

$\frac{106}{100} * \frac{100}{106}$ of x = 7.95 * $[\frac{100}{106}]$

=> x = $[\frac{750}{100}]$

=> x = $[\frac{7.50}{1}]$

=> x = 7.5

Validation: 106% of 7.5 = 7.95

4 0

2 years ago