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Question 1-
Super Sally works every day in the school office and earns $57 per day. Lazy Petunia shows up to work fewer than half as many days as Sally, and earns only $20 per day. At the end of the school year, their total earnings are $7733. The number of days that Petunia worked is closest to a) 20 b) 30 c) 40 d) 50 e) 60

Question 2-
How many 4 digit even numbers can be formed using 0,1 , 5,6, 7, 8 and 9 if repeats of digits are not allowed?
A) 120 B) 240 C) 320 D) 360 E)480

Question 3- The value of 28^983 x 98^984/14^2948
A) 98 B)392 C)784 D) 1372 E)2744
/=division
THANK YOU SO MUCH in advance!

Sagot :

MrRoyal

The number of days Super Sally and Lazy Petunia work are illustrations of simultaneous equations

(a) Super Sally and Lazy Petunia

Represent their earnings with the first letters.

So, we have:

[tex]\mathbf{L = \frac 12S}[/tex] -- number of days

[tex]\mathbf{20L + 57S= 7733}[/tex] --- the total earnings

Make S the subject in [tex]\mathbf{L = \frac 12S}[/tex]

[tex]\mathbf{S = 2L}[/tex]

Substitute 2L for S in [tex]\mathbf{20L + 57S = 7733}[/tex]

[tex]\mathbf{20L + 57 \times 2L = 7733}[/tex]

Expand

[tex]\mathbf{20L + 114L = 7733}[/tex]

Add

[tex]\mathbf{134L = 7733}[/tex]

Divide both sides by 134

[tex]\mathbf{L = 57.7}[/tex]

From the options, the closest to 57.7 is 60.

Hence, the number of days that Petunia worked is closest is 60

(b) 4 digit even numbers

The digits are given as: 0, 1, 5, 6, 7, 8 and 9

To create a 4-digit number, the first digit cannot be 0.

So, the first digit can be any of the remaining 6

Because, it is an even number, the number can only end with 0, 6 or 8

So, the last digit can be any of the 3

Since there is no repetition, the second and the third digits can be any of the remaining 5 and 4 digits, respectively.

So, the number of digits is:

[tex]\mathbf{n =6 \times 3 \times 5 \times 4}[/tex]

[tex]\mathbf{n =360}[/tex]

Hence, the number of digits is (d) 360

(c) The value of 28^983 x 98^984/14^2948

Rewrite the expression as:

[tex]\mathbf{\frac{28^{983} \times 98^{984}}{14^{2948}}}[/tex]

Express all number as a base of 14

[tex]\mathbf{\frac{14^{2 \times 983} \times 14^{7 \times 984}}{14^{2948}} }[/tex]

Apply law of indices

[tex]\mathbf{14^{2 \times 983+7 \times 984-2948}}[/tex]

Evaluate all products

[tex]\mathbf{14^{1966+6888-2948}}[/tex]

Evaluate the exponent

[tex]\mathbf{14^{5906}}[/tex]

Hence, the result of [tex]\mathbf{\frac{28^{983} \times 98^{984}}{14^{2948}}}[/tex] is [tex]\mathbf{14^{5906}}[/tex]

Learn more at:

https://brainly.com/question/16763389

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