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2 years ago

What is made up of quantities and the operations performed on them

1 answer:

7 0

Algebra is made up of quantities and the operations performed on them are addition, subtraction, multiplication and division.
<span>Algebra is a branch of mathematics. It concerns itself with operations on sets of numbers or other elements. The sets of numbers and elements are represented by symbols. Algebra can be seen as a generalisation of arithmetic. Letters are substituted for numbers in Algebra. For example, x + 2x will always equal 3x no matter what values the symbol x represents. The algebraic can also include polynomial functions of one or more of the variables. </span>

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Sheila places a 54 square inch photo behind a 12-inch-by-12-inch piece of matting.

nata0808 [166]

The are of a rectangle is calculated by multiplying the length and the width of the shape. First, we determine the dimensions of this figure. We do as follows:

Width = 12 - 2x - 2x = 12 - 4x
Length = 12 - x - x = 12 - 2x

Area = (Length)(Width)
Area = (12 - 2x )(12-2x)

3 0

2 years ago

Suppose the area that can be painted using a single can of spray paint is slightly variable and follows a nearly normal distribu

Svetllana [295]

Answer:

Step-by-step explanation:

Hello!

You have the variable

X: Area that can be painted with a can of spray paint (feet²)

The variable has a normal distribution with mean μ= 25 feet² and standard deviation δ= 3 feet²

since the variable has a normal distribution, you have to convert it to standard normal distribution to be able to use the tabulated accumulated probabilities.

P(X>27)

First step is to standardize the value of X using Z= (X-μ)/ δ ~N(0;1)

P(Z>(27-25)/3)

P(Z>0.67)

Now that you have the corresponding Z value you can look for it in the table, but since tha table has probabilities of $P(Z$ , you have to do the following conervertion:

P(Z>0.67)= 1 - P(Z≤0.67)= 1 - 0.74857= 0.25143

There was a sample of 20 cans taken and you need to calculate the probability of painting on average an area of 540 feet².

The sample mean has the same distribution as the variable it is ariginated from, but it's variability is affected by the sample size, so it has a normal distribution with parameners:

X[bar]~N(μ;δ²/n)

So the Z you have to use to standardize the value of the sample mean is Z=(X[bar]-μ)/(δ/√n)~N(0;1)

To paint 540 feet² using 20 cans you have to paint around 540/20= 27 feet² per can.

P(X≤27) = P(Z≤(27-25)/(3/√20))= P(Z≤2.98)= 0.999

No. If the distribution is skewed and not normal, you cannot use the normal distribution to calculate the probabilities. You could use the central limit theorem to approximate the sampling distribution to normal if the sample size was 30 or grater but this is not the case.

I hope it helps!

4 0

2 years ago

Fredrick and Kate have 1713 cups of flour. They want to make loaves of banana bread for a bake sale. Fredrick has a recipe for b

Mariana [72]

Answer:

Fredrick's recipe will make 10 whole loaves.

There will be less flour left over if Frederick's recipe is used.

Step-by-step explanation:

Fredrick and Kate have 17 1/3 cups of flour. They want to make loaves of banana bread for a bake sale. Fredrick has a recipe for banana bread that calls for 1 5/8 cups of flour. Kate has a recipe that calls for 1 3/4 cups of flour. Select all the statements that are true about the recipes.

1. Fredrick's recipe will make 10 whole loaves.

2. Kate's recipe will make 11 whole loaves.

3. There will be less flour left over if Frederick's recipe is used.

4. There will be less flour left over if Kate's recipe is used.

5. More loaves of bread can be made using Frederick's recipe than Kate's recipe.

Solution:

Total cups of flour = 17 1/3

Fredrick recipe = 1 5/8 cups of flour

Kate = 1 3/4 cups of flour

Number of banana bread made with Fredrick's recipe = Total flour / flour per Fredrick's recipe

= 17 1/3 ÷ 1 5/8

= 52/3 ÷ 13/8

=52/3 × 8/13

= 416 / 39

= 10.67 loaves of banana bread

Number of banana bread made with Kate's recipe = Total flour / flour per Kate's recipe

= 17 1/3 ÷ 1 3/4

= 52/3 ÷ 7/4

= 52/3 × 4/7

= 216 / 21

= 10.29 loaves of banana bread

The true statements are:

Fredrick's recipe will make 10 whole loaves.

There will be less flour left over if Frederick's recipe is used

5 0

2 years ago

Diego has some money in his bank account before he starts a summer job. He deposits the money from the summer job in his bank ac

chubhunter [2.5K]

Answer:

it should be $23

Step-by-step explanation:

7 0

2 years ago

If each term in the sum a1+a2+a3+...+an is either 7 or 77 and the sum equals 350, which of the following could be equal to n?A.

Svetlanka [38]

Answer:

C. 40

Step-by-step explanation:

Let us say there are x 7's and y 77's.

We have been given that each term in the sum a1+a2+a3+...+an is either 7 or 77 and the sum equals 350. We are asked to find the value of n.

Since the sum of all numbers is 350, so we can represent this information in an equation as:

$7x+77y=350$

The only integer solutions for the equation $7x+77y=350$ are 10, 20, 30, 40, 50 .

So, there can be these many terms: 10 or 20 or 30 or 40 or 50 .

The given option only contains 40, so 40 would be the answer. For 40 terms to be there, there has to be 39 sevens and 1 seventy-seven.

Let us verify our answer.

$7x+77y=350$

$7(39)+77(1)=350$

$273+77=350$

$350=350$

Therefore, the total terms (n) could be equal to 40 and option C is the correct choice.

8 0

2 years ago