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3 years ago

Sue has $1.15 in nickels and dimes, a total of 16 coins. How many nickels and how many dimes does Sue have?

2 answers:

7 0

Hey :)

Lets n be the number of nickels Sue has. Then the number of dimes is equal to (16-n). So, Sue has 5*n cents in nickels and 10*(16-n) cents in dimes. Since the total amount Sue has is $1.15, or 115 cents, it gives you an equation 5n + 10*(16-n) = 115.

Simplify this equation: 5n +160-10n = 115 (after opening parentheses) -5n = 115-160 (after collecting like terms at the left side and moving 160 to the right side with the opposite sign) -5n = -45 (after collecting like terms at the right side) n = 9 (after dividing both sides by -5). So, the number of nickels is equal to 9. The number of dimes is equal to 16 minus the number of nickels, that is 16-n = 16-9 = 7.

Check. The total number of coins is equal to 9 + 7 = 16. The total amount is equal to 9*5 + 7*10 = 45 + 70 = 115. The solution is correct.

Answer. Sue has 9 nickels and 7 dimes.

Hope this helps! :)

adell [148]3 years ago

6 0

0.05x+0.10y=1.15
x+y=16
solve the system

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Frank mary and seth shared some sweets in the ratio 4:5:7 seth got 18 more sweets than frank

Nimfa-mama [501]

Answer:

each number in the ratio 4:5:7 is worth 6 sweets. add 4,5, and 7 to get 16 then multiply it by 6 to get 96 sweets.

Step-by-step explanation:

add the ratios = 4+5+7= 16

1 number = 6 so

4x6= 24

5x6=30

7x6=42

Frank gets 24 sweets

Mary gets 30 sweets

Seth gets 42 sweets

The total number of sweets they shared is 24+30+42= 96

The share 96 sweets altogether.

The check your answer; do 42-24= 18

Therefore, now we know that the difference between Seth and Frank's amount of sweets is 18.

Therefore, this is correct.

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3 years ago

Suppose the national mean annual salary for a school administrator is $91,000 a year. A school official took a sample of 25 scho

Gemiola [76]

Answer:

H0 : μ = 91000

H1 : μ ≠ 91000

Test statistic = - 2.594

Pvalue = 0.016

|Tcritical | = 2.064

Reject H0. We can conclude that the mean annual administrator salary in Ohio differs significantly from the national mean annual salary.

Step-by-step explanation:

The hypothesis :

H0 : μ = 91000

H1 : μ ≠ 91000

From the data given :

77600 76000 90700 97200 90700

101800 78700 81300 84200 97600

77500 75700 89400 84300 78700

84600 87700 103400 83800 101300

94700 69200 95400 61500 68800

Using calculator :

Sample mean, xbar = 85272

Sample standard deviation, s = 11039.23

Sample size, n = 25

The test statistic :

(xbar - μ) ÷ (s/√(n))

(85272 - 91000) / (11039.23/√(25)

Test statistic = - 5728 / 2207.846

Test statistic = - 2.594

The Pvalue : df = n - 1 = 25 - 1 = 24

Pvalue(-2.594, 24) = 0.0159

Decision region :

Reject H0 ; If Pvalue < α ;

α = 0.05

Using the critical value :

Decision region :

Reject H0 ; If Test statistic > |Tcritical;

Tcritical value at df = 24 ; α = 0.05 ;

|Tcritical | = 2.064

Hence,

We Reject H0 ; Since, |Test statistic| > |Tcritical|and conclude that mean salary depends differs

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frutty [35]

Answer:

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Step-by-step explanation:

Given:

perimeter of the rectangle = 204 feet

Its length is six feet longer that twice its width

To Find:

The dimensions of the rectangle = ?

Solution:

Let the width of the rectangle be x

Then its length is six feet longer that twice its width.

That is length = 6 + 2x

Now we know that the perimeter of the rectangle is

perimeter = 2(length + width)

204 = 2(6+2x+x)

204 = 2(6+3x)

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x = $\frac{192}{6}$

x = 32

Thus the width is 32 cm

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=6 + 2x

=6 + 2(32)

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= 70 cm

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