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IRINA_888 [86]
3 years ago
11

Keith has p pennies, n nickels, and d dimes in his pocket. The total number of coins is 9. The expression 0.01p+0.05n+0.10d repr

esents the value of the coins, which is equal to $0.44. He has one more dime than nickels. How many pennies does Keith have? Keith has _____ pennies.
Mathematics
2 answers:
IceJOKER [234]3 years ago
8 0

he  has 4 pennies

2 nickels=10 cents

3 dime=30 cents

             20 cents

40 +4 pennies =44 cents

Olenka [21]3 years ago
7 0

Answer:

Keith has 4 pennies, 3 dimes and 2 nickels.

Step-by-step explanation:

Let the pennies be = p

Let the nickels be = n

Let the dimes be = d

Total coins Keith has = 9

So, 1st equation form :

p+n+d=9     ....(1)

Keith has one more dime than nickels, means d=n+1   .....(2)

Total value of these coins is $0.44

So, third equation forms:

0.01p+0.05n+0.10d=0.44   .....(3)

Substituting (2) in (1)

p+n+n+1=9

p+2n=8     .....(4)

Similarly substitution (2) in (3)

0.01p+0.05n+0.10(n+1)=0.44

0.01p+0.05n+0.10n+0.10=0.44

0.01p+0.15n=0.34    ....(5)

Now multiplying (4) by 0.01 and subtracting by (5)

0.01p+0.02n=0.08 subtracting this from (5) we get

0.13n=0.26

So, we get n = 2

p+2n=8

p+2(2)=8

p+4=8

p = 4

p+n+d=9

4+2+d=9

6+d=9

d = 3

-------------------------------------------------------------------------------------

Therefore, Keith has 4 pennies, 3 dimes and 2 nickels.

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The mean of 100 observation is found to be 40. If at the time of compution two items were wrongly taken as 30 and 27 instead of
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Answer:

40.18

Step-by-step explanation:

According to this question, the mean of 100 observation is found to be 40. This means that the number of values in the set of data is 100. However, at the time of computation two items were wrongly taken as 30 and 27 instead of 3 and 72.

The mean is derived by dividing the sum of values in the data (Σx) by the number of observations (n) i.e.

Mean = Σx/n

For the computation error:

Mean = 40

Let x represent the sun of other 98 values except 30 and 27

n = 100

40 = x + 30 + 27/100

40 = 57 + x/100

Cross multiply

4000 = 57 + x

x = 4000 - 57

x = 3943.

Sum of other 98 values = 3943.

Now, let's find the correct mean with correct values of 3 and 72;

Mean = Σx/n

Mean = 3943 + 3 + 72/100

Mean = 4018/100

Mean = 40.18

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A school flag poll casts a 16 foot shadow on the lawn. A teacher stood at the shadows edge and measure the angle of elevation to
vovikov84 [41]

Answer:

30.1 feet.  

Step-by-step explanation:

We have been given that a school flag poll casts a 16 foot shadow on the lawn. A teacher stood at the shadows edge and measure the angle of elevation to the top of the poll at 62°. We are asked to find the height of the tall.

First of all, we will draw a diagram to represent our give scenario as shown in the attachment.

We can see that side length with 16 feet is adjacent side and height of the pole (h) is opposite side to angle of elevation.

We know that tangent relates opposite side of a right triangle to its adjacent side.

\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}

\text{tan}(62^{\circ})=\frac{h}{16}

h=16\cdot \text{tan}(62^{\circ})

h=16\cdot 1.880726465346

h=30.0916234\approx 30.1

Therefore, the poll is approximately 30.1 feet tall.

6 0
3 years ago
The proprietor of a boutique in New York wanted to determine the average age of his customers. A random sample of 25 customers r
jolli1 [7]

Answer:

28-2.064\frac{10}{\sqrt{25}}=23.872    

28+2.064\frac{10}{\sqrt{25}}=32.128    

So on this case the 95% confidence interval would be given by (23.9;32.1)  

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

\bar X=28 represent the sample mean

\mu population mean (variable of interest)

s=10 represent the sample standard deviation

n=25 represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

In order to calculate the critical value t_{\alpha/2} we need to find first the degrees of freedom, given by:

df=n-1=25-1=24

Since the Confidence is 0.95 or 95%, the value of \alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,24)".And we see that t_{\alpha/2}=2.064

Now we have everything in order to replace into formula (1):

28-2.064\frac{10}{\sqrt{25}}=23.872    

28+2.064\frac{10}{\sqrt{25}}=32.128    

So on this case the 95% confidence interval would be given by (23.9;32.1)    

7 0
3 years ago
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