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suter [353]
2 years ago
6

Kevin and Randy Muise have a jar containing 80 ​coins, all of which are either quarters or nickels. The total value of the coins

in the jar is ​$11.80. How many of each type of coin do they​ have?
Mathematics
1 answer:
SCORPION-xisa [38]2 years ago
7 0

Answer:

  • 39 quarters and 41 nickels

Step-by-step explanation:

Let the number of quarters be x and nickels be y.

<u>Given:</u>

  • Quarter is 25 cents
  • Nickel is 5 cents
  • Number of coins is 80
  • Total amount is $11.80 = 1180 cents

<u>We have equations:</u>

  • x + y = 80
  • 25x + 5y = 1180

<u>Solve the system by elimination, subtract 5 times the first equation from the second one:</u>

  • 25x + 5y - 5x - 5y = 1180 - 80*5
  • 20x = 780
  • x = 780/20
  • x = 39

<u>Find the value of y:</u>

  • 39 + y = 80
  • y = 80 - 39y = 41

<u>Verify:</u>

  • 25*39 + 5*41 = 975 + 205 = 1180
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2w+w^3-1/2w^2 for w=2
mars1129 [50]

The required value is 8

How can we find value?

We will find the value by putting the value of w in the given function to get the required value.

We can find the value of given function foe w=2 as shown below:

Given, function is 2w+w^3-1/2w^2

Let A=2w+w^3-1/2w^2

for w=2

A=2(2)+(2)^3-1/2(2)^2

= 2+8-1/2(4)

=2+8-2

=8

Hence, the required value is 8.

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8 0
1 year ago
the brain volumes ​(​) of 50 brains vary from a low of to a high of . use the range rule of thumb to estimate the standard devia
Sloan [31]

The estimated standard deviation from the range rule is 145.5 cm3.As it is 29.8 cm3 smaller than the exact standard deviation, we consider that the estimation is not accurate enough.

Generally, brain volumes which are smaller than 921.1 cm3 can be considered significantly low and bigger than 1417.5 cm3 can be considered significantly high. Hence, brain volume of 1457.5 cm3 is bigger than the expected maximum, so it can be considered significantly high.

The calculation goes like this,

According to the range rule, the standard deviation and range, or the distance between the maximum and smallest value, are roughly inversely proportional:

s=R/4

If we have a sample of 50 brains volumes, and they range from 910 cm3 to 1492 cm3, we can estimate the standard deviation as:

s=max-min/4

s=1492-910/4=582/4=145.5

The exact standard deviation is 175.3 cm3.The difference is 175.3-145.5=29.8 cm3, so the estimation is not accurate enough.

The range rule of thumb states that we should anticipate a maximum value that is approximately two standard deviations above the mean and a lowest value that is approximately two standard deviations below the mean. The expected ranges are as follows given our mean volume of 1169.3 cm3 and standard deviation of 124.1 cm3:

Min= M-2s=1169.3-2*124.1=921.1

Max=M+2s=1169.3+2*124.1=1417.5

The brain capacity of 1457.5 cm3 can be regarded as significantly high because it is higher than the predicted maximum.

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5 0
1 year ago
The highest common factor (HCF) of 140 and x is 20
Zielflug [23.3K]

Answer:

x=60

Step-by-step explanation:

Given that ,

HCF of 140 and x=20,

LCM of 140 and x =420.

Solution:

It is known that the product of two numbers is equal to the product of their HCF and LCM, i-e:

140*x= HCF*LCM

Putting in the values provided,

140*x=20*420

140*x=8400

x=8400/140

x=60

Hence the variable x is 60.

5 0
3 years ago
29. March sales accounted for 1/7 of the total number of jazz records sold all year. About how many jazz records were sold all y
enot [183]

The March sales of Jazz records is an illustration of proportions, and the number of jazz records sold all year is 7x

<h3>How to determine the total number of sales?</h3>

The sales in March is given as:

Proportion = 1/7

Let the actual number of sales in the month of March be x, and the total sales in the year be y.

So, we have:

1/7 * y = x

Make y the subject

y =7x

Hence, the number of jazz records sold all year is 7x

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8 0
2 years ago
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