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dalvyx [7]
3 years ago
10

A problem states that Ursula earns $9 per hour. To write an expression that tells how much money Ursula earns for h hours, Joshu

a wrote 9 divided by h. Sarah wrote 9h. Whose expression is correct and why?
Mathematics
1 answer:
LekaFEV [45]3 years ago
8 0
The correct one would by 9h because you are asking how much will Ursula make per hour. So let's say that h is 10, then in order to know how much Ursula makes per hour, you have to add 9 ten times. A short way to do that would be to simply multiply 9 with 10 so that you can get the answer of 90. It cannot be 9/h because then answer will be much lower than it is supposed to be. So the answer to the question is really 9h. 
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1) Omar has scored 85, 71, and 77 on the first three exams in his math class. If the standard 70,80,90 scale is used for grades
Rus_ich [418]

Answer:

a. 47

b. 87

c. 127

Step-by-step explanation:

Assume a total of 4 exams ( first 3 plus a final)

Let final score be X,

Hence,  average score = (85 + 71 + 77 + x) / 4 = (233 + x) / 4

a) to get a C, the average score must be 70

70 = (233 + x) / 4

(233 + x) = 70 (4) = 280

x = 280 - 233 = 47 (Ans)

b) to get a B, the average score must be 80

80 = (233 + x) / 4

(233 + x) = 80 (4) = 320

x = 320 - 233 = 87 (Ans)

c) to get a A, the average score must be 90

90 = (233 + x) / 4

(233 + x) = 90 (4) = 360

x = 360 - 233 =  127 (Ans)

6 0
3 years ago
Determine all prime numbers a, b and c for which the expression a ^ 2 + b ^ 2 + c ^ 2 - 1 is a perfect square .
kogti [31]

Answer:

The family of all prime numbers such that a^{2} + b^{2} + c^{2} -1 is a perfect square is represented by the following solution:

a is an arbitrary prime number. (1)

b = \sqrt{1 + 2\cdot a \cdot c} (2)

c is another arbitrary prime number. (3)

Step-by-step explanation:

From Algebra we know that a second order polynomial is a perfect square if and only if (x+y)^{2} = x^{2} + 2\cdot x\cdot y  + y^{2}. From statement, we must fulfill the following identity:

a^{2} + b^{2} + c^{2} - 1 = x^{2} + 2\cdot x\cdot y + y^{2}

By Associative and Commutative properties, we can reorganize the expression as follows:

a^{2} + (b^{2}-1) + c^{2} = x^{2} + 2\cdot x \cdot y + y^{2} (1)

Then, we have the following system of equations:

x = a (2)

(b^{2}-1) = 2\cdot x\cdot y (3)

y = c (4)

By (2) and (4) in (3), we have the following expression:

(b^{2} - 1) = 2\cdot a \cdot c

b^{2} = 1 + 2\cdot a \cdot c

b = \sqrt{1 + 2\cdot a\cdot c}

From Number Theory, we remember that a number is prime if and only if is divisible both by 1 and by itself. Then, a, b, c > 1. If a, b and c are prime numbers, then  2\cdot a\cdot c must be an even composite number, which means that a and c can be either both odd numbers or a even number and a odd number. In the family of prime numbers, the only even number is 2.

In addition, b must be a natural number, which means that:

1 + 2\cdot a\cdot c \ge 4

2\cdot a \cdot c \ge 3

a\cdot c \ge \frac{3}{2}

But the lowest possible product made by two prime numbers is 2^{2} = 4. Hence, a\cdot c \ge 4.

The family of all prime numbers such that a^{2} + b^{2} + c^{2} -1 is a perfect square is represented by the following solution:

a is an arbitrary prime number. (1)

b = \sqrt{1 + 2\cdot a \cdot c} (2)

c is another arbitrary prime number. (3)

Example: a = 2, c = 2

b = \sqrt{1 + 2\cdot (2)\cdot (2)}

b = 3

4 0
3 years ago
Please help I’m so close to passing math
kirill115 [55]

Answer:

$0.14 per ounce of salsa

Step-by-step explanation:

2.80/20

Move decimal to make the number a whole number

(Have to move the decimal the same amount of spaces)

28/200

0.14

Hope this helps. Have a nice day

8 0
2 years ago
Read 2 more answers
Amanda is a cabinetmaker. She makes cabinets using one of three types of wood: birch, maple, or cherry. She can finish each type
padilas [110]
Assume that each material in each category has an equal chance of being selected.

Categories:
(a) Type of wood used to make the cabinet: birch, maple, cherry.
     Each type of wood has a probability of 1/3 to be selected.
(b) Type of finish: transparent, semi-transparent.
    Each type of finish has a probability of 1/2 to be selected.
(c) Knob: bronze, steel, wood.
     Each material has 1/3 probability to be selected.

Each event (selecting material for the cabinet, for the finish, and for the knob) is an independent event.

Therefore
Probablity(birch wood AND bronze knob) = (1/3)*(1/3) = 1/9
Probability(wood knob) = 1/3
Probability(transparent stain) = 1/2
Probability(cheryy wood AND semi-transparent stain) = (1/3)*(1/2) = 1/6



6 0
3 years ago
Round to the nearest cent $6.51
son4ous [18]
Answer: $6.50
If the number is below 5 (so 1-4) you round down. If its above 5 (5-9), you round up.
E.G. 78.89 
Round this to the nearest 10th, you'll get 78.90

4 0
3 years ago
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