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Gwar [14]
4 years ago
12

A jar contains n nickels and d dimes. There is a total of 236 coins in the jar. The value of the coins is $15.75. How many nicke

ls and how many dimes are in the jar
Mathematics
1 answer:
just olya [345]4 years ago
6 0

The total if all 236 coins were nickels would be $11.80, which is $3.95 short of the actual amount.

Replacing a nickel with a dime adds $0.05 to the total value, so there must have been $3.95/$0.05 = 79 such replacements.

There are 79 dimes.

There are 236 -79 = 157 nickels.

_____

Using the given variables, the problem statement gives rise to two equations. One is the based on the number of coins. The other is based on their value.

  • n + d = 236
  • .05n +.10d = 15.75

Solving the first for n, we get

... n = 236 - d

Substituting that into the second equation, we have

... .05(236 -d) +.10d = 15.75

... .05d = 15.75 -236·.05 . . . . . collect terms, subtract .05·236

... d = 3.95/.05 . . . . . . . . . . . . . divide by .05

... d = 79

... n = 236-79 = 157

___

The solution should look familiar, as it matches the verbal description at the beginning.

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Matthew jogs 300 metres at 4m/s.<br> Work out how long it takes Matthew.
Aleks [24]

Answer:

75 seconds or 1 minute and 15 seconds

Step-by-step explanation:

300 meters/4 mps = 75 seconds

5 0
3 years ago
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If, for a random sample of 16 days, the sample mean ends up being exactly one standard deviation of x above the population mean,
Rudik [331]

Answer:

The answer to the question is

μx + (σx/4)

Step-by-step explanation:

The sample mean that is one standard deviations above the population mean  is given by

value = μx + (Number of standard deviations)

(σx/√n)

value = μx + 1 (σx/√16)=

=  μx + (σx/4) =

Where

μx = Population mean

σx = Population standard deviation

n = Sample size

The standard error of the mean is

σ/√n =σ/√16 = σ/4

The standard of error is an indication of the expected error in the mean of a sample from the mean of the population.

The above statements is based on the central limit theorem, which states that, in particular instances the normalized sum of independent random variables becomes closer and closer to those of  normal distribution regardless of the variation in the sample of the variables

8 0
3 years ago
A ball is thrown from an initial height of 2 feet with an initial upward velocity of 29 ft/s. The ball's height h (in feet) afte
Len [333]
H=14 for this particular instance so:
14=2+29t-16t²
14-2=2-2+29t-16t²
12=29t-16t²
0=-16t²+29t-12
that's as factored as possible so you should use the quadratic formula for the rest and check for extraneous answers
4 0
4 years ago
Please answer I need step by step explanation
olya-2409 [2.1K]

Answer:

10 cm

Simplified explanation/tl;dr: the small triangle is two thirds the size of the big triangle, so the missing side on the small triangle is two thirds the size of the same side on the big triangle

Long explanation/step by step:

It looks scary, but don't worry; for questions like this just find the ratio then multiply it by the similar side to find the missing side.

   This is what I mean: 8/12 simplified is 2/3 (4 is the common factor and 8/4 = 2 and 12/4 = 3). That's your fraction to multiply by.

   I chose 8 and 12 because look how the triangles are the same shape just different sizes, that means they're similar. the similar sides are just the same side on both triangles. (for this one, BC and GH are similar). to find how much smaller it is in fraction form, you just take two of the same sides and divide the small one by the big one. (big number becomes top, small becomes bottom)

   now just multiply 15 by 2/3 by using fraction multiplication. 15/1 x 2/3 = 30/3. Simplify that to 10/1 (3 is the common factor and 30/3 = 10 and 3/3 = 1). 10/1 = 10.

7 0
3 years ago
Solve the equation showing all work.<br><br> X²-4x+3=0
viktelen [127]

x2−4x+3=0

For this equation: a=1, b=-4, c=3

1x2+−4x+3=0

Step 1: Use quadratic formula with a=1, b=-4, c=3.

x=

−b±√b2−4ac

2a

x=

−(−4)±√(−4)2−4(1)(3)

2(1)

x=

4±√4

2

x=3 or x=1

5 0
1 year ago
Read 2 more answers
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