MATHEMATICS HIGH SCHOOL

A batch of cookies requires 1 1/2 cups of sugar. How many batches can Ty make with 7 1/2 cups of sugar?

Answers

Answer 1
Answer:

Answer:

5 batch of cookies.

Step-by-step explanation:

A batch of cookie requires  1(1)/(2) cups of sugar.

Ty has  7(1)/(2) cups of sugar.

He can make the total number of batches =  7(1)/(2) ÷  1(1)/(2)

=  (15)/(2) ÷  (3)/(2)

=  (15)/(2) ×  (2)/(3)

=  (30)/(6)

= 5 batches of cookies

Ty can make 5 batches of cookies.
Answer 2
Answer: Ty can make 5 because if you add 1 1/2 5 times it will add up to 7 1/2

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in a survey if 27.5 percent of those questioned chose swimming as their favorite. If 11 people chose swimming then how many people were surveyed

Answers

27.5% of x=11     x is the number of people  27.5%=.275     x=11/.275=40 people in the survey participated 

Final answer:

To determine the total number of people surveyed when given the number who preferred swimming and the percentage they represent, you set up an equation based on the percentage and then solve for the total. With this data, 40 people were surveyed.

Explanation:

The question pertains to the mathematical concept of percentages. You mention that 27.5 percent of the surveyed population favored swimming and this equaled to 11 people. To calculate the total number of people surveyed, we let the total number be 'x'. Therefore, the mathematical equation, based on the provided data, becomes 27.5% of 'x' = 11. In mathematical terms, it can be written as 0.275x = 11. For finding 'x', divide both sides of the equation by 0.275. Thus 'x' = 11 / 0.275 = 40. Therefore, based on the given percentages and data, it's inferred that a total of 40 people were surveyed.

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A newspaper carrier has $1.80 in change. He has two more quarters than dimes but three times as many nickels as quarters. How many coins of each type does he have?

Answers

1\ quarter=\$0.25\n1\ dime=\$0.10\n1\ nickel=\$0.05\n\nq\ \ \ \rightarrow\ \ \ the\ number\ of\ the\ quarters\nd\ \ \ \rightarrow\ \ \ the\ number\ of\ the\ dimes\nn\ \ \ \rightarrow\ \ \ the\ number\ of\ the\ nickels\n\nq=2d\ \ \ and\ \ \ n=3q\ \ \ \Rightarrow\ \ \ n=3\cdot 2d=6d\n\nq\cdot0.25+d\cdot0.10+n\cdot 0.03=1.80\n\n2d\cdot0.25+d\cdot0.1+6d\cdot0.05=1.8\n\n

0.5d+0.1d+0.3d=1.8\n\n0.9d=1.8\ \ \ \Rightarrow\ \ \ d=2\ \ \ \Rightarrow\ \ \ q=2\cdot2=4\ \ \ and\ \ \ n=6\cdot2=12\n\nAns.\ 4\ quarters,\ 2\ dimes,\ 12\ nickels

Cost of a dozen eggs depends on the size of the eggs. what is the dependent variable?

Answers

the cost of the eggs
cost (x) = x*price
this is an example of a proportional cost relation with the size been x 
Answer: the dependent variable is the cost of a dozen of eggs.

Explanation:

The cost is function of the size of the eggs, Cost = f (size).

That means that you introduce the size (this is the input) in the function an you obtain the cost (this is the output)

The input is the independent variable and the output is the dependent variable.

1)Which system of linear inequalities is graphed?A){x<−2y≤−x−1
B){x<−3y≤−x+1
C){x≤−3y≤−x−3
D){x<−3y≤−x−1

2)Which system of linear inequalities is graphed?

A) {y≤2x+1x+y≥−2
B) {y≥2x+1x+y≤−2
C) {y<2x+1x+y>−2
D) {y>2x+1x+y<−2

Answers

Answer:

1 ) D

2 ) D

Step-by-step explanation:

The general form of the straight line is given by y=mx+c, where m is the slope and c is y-intercept.

1 ) According to the graph, we get the co-ordinates (0,-1) and (-1,0).

Using these so-ordinates, we will find the equation of the line.

i.e. Slopem = (y_(2)-y_(1))/(x_(2)-x_(1))

i.e. m = (0-(-1))/(-1-0)

i.e. m = -1

Now, substituting m and (0,-1) in general form, we get c = -1.

So, the equation of this straight line is y = -x-1.

We will now use 'Zero Test' i.e. substitute (0,0) in the required equation and since the given regions are away from the origin, this pair of points will not satisfy the equation.

So, we get y < -x-1 and as the region is given to less than x= -3.

Hence, option D is correct.

2) Now, according to the second graph, we get the points (0,-2), (-2,0) and (0,1), (-1,-1) for two lines respectively.

Solving as in 1) we get that the equations of the lines are given by x+y = -2 and y = 2x+1 respectively.

Again using 'Zero Test', we see that these pair of points does not satisfy the equations.

So, we get x+y < -2 and y > 2x+1.

Hence, option D is correct.

Answer: C and B

Step-by-step explanation:

Draw a model to represent 3/4 divided by 3/12

Answers

The required model is attached in the image and the division of 3/4 by 3 /12 is 3.

Given that,
To draw the model to represent 3/4 divided by 3/12.

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements.

Model hs been attached below for the given problem of division,
= 3 * 4 / 3 * 12
For a rectangle space, drawing 4 column and 12 raws,
Now for 3 / 4 3 of the 4 column to be filled by red, for 3 / 12 every 3 cells in the row have been filled by red.
Calculating number of cells in 3 / 4 = 36
calculating number of cells in 3 / 12 = 12
Now ratio of the cells = 36 / 12 = 3

Thus, the required model is attached in the image and the division of 3/4 by 3 /12 is 3.

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The answer you are looking for is 1/3.

First, you must look at the denominators of each fraction, to see if you can simply divide straight across. In this case, you cannot, which means you must multiply by the reciprocal or "flipped" number. Generally when you multiply by the reciprocal, you flip the number with the smaller denominator to multiply.

So, you have 4/3 * 3/12. You then multiply straight across (4 * 3)/(3 * 12), to get an answer of 12/36, which simplified (divided by 3/3) gives you a final answer of 1/3.

I hope this helps!

What is 4.12 expressed as the quotient of two integers in simplest form

Answers

All you do is turn 4.12 into a whole, make it over 100 and simplify.

So, 4.12

= 412/100

Which simplifies to 103/25.
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