What does it mean to say that a number is a perfect square? Give on example of number that is a perfect square and of one that is not. Explain your examples.

The LCD of the fractions [tex]\frac{1}{3} ,\frac{11}{15}[/tex] is 15

"It is a part of a whole number and a way to split up a number into equal parts."

"The least common denominator (LCD) is the smallest number that can be a common denominator for a set of fractions."

For given question,

We have been given two fractions [tex]\frac{1}{3} ,\frac{11}{15}[/tex]

We need to find the least common denominator of [tex]\frac{1}{3} ,\frac{11}{15}[/tex]

The denominator of fraction [tex]\frac{1}{3}[/tex] is 3.

and the denominator of fraction [tex]\frac{11}{15}[/tex] is 15.

Multiples of 3 are 3, 6, 9, 12, 15, 18,...

Multiples of 15 are 15, 30, 45,...

The least common multiple of 3 and 15 is 15.

Therefore, the LCD of the fractions [tex]\frac{1}{3} ,\frac{11}{15}[/tex] is 15

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Solving the system of linear equations provided, we find that the cost of a can of orange is £0.85 and a chocolate bar costs £0.45. Therefore, three cans of orange and four chocolate bars would cost £4.35.

The student's question involves solving a system of linear equations to find the individual prices of a can of orange and a chocolate bar. Once the individual prices are determined, the student wants to know the total cost of three cans of orange and four chocolate bars. Here's a step-by-step approach to solve this problem:

Let the price of a can of orange be 'O' and the price of a chocolate bar be 'C'.

The first equation from the given information would be O + C = £1.30.

The second equation would be 2O + C = £2.15.

Subtract the first equation from the second to find the price of an additional can of orange, which gives us O = £0.85.

Substitute the value of O in the first equation to find C, which yields C = £0.45.

Now, calculate the cost of three cans of orange and four chocolate bars: 3O + 4C = 3(£0.85) + 4(£0.45) = £2.55 + £1.80 = £4.35.

So, three cans of orange and four chocolate bars would cost £4.35 together.

Answer:

Step-by-step explanation:

The standard form of fourteen thousand and two hundred eight thousandths is 1.4208 x 10⁴.

Standard form refers to any number that can be written as a decimal number between 1.0 and 10.0 multiplied by a power of ten. 1.23 108; If you look closely, 1.23 is a decimal number between 1.0 and 10.0, so the standard form of 123,000,000 is 1.23 108.

Given that the number is fourteen thousand and two hundred eight thousandths.

The standard form of the number will be written as,

14208 = 1.4208 x 10⁴

The standard form is 1.4208 x 10⁴.

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Answer:

The value of (F-G)(6) is -1.

Step-by-step explanation:

The given functions are defined as

[tex]F = \{(0, 1), (2, 4), (4, 6), (6, 8)\}[/tex]

[tex]G = \{(2, 5), (4, 7), (5, 8), (6, 9), (7, 5)\}[/tex]

We need to find the value of (F-G)(6).

Using subtraction of two function property, we get

[tex](F-G)(6)=F(6)-G(6)[/tex]           .... (1)

From the given functions it is cleared that the value of function F is 8 at x=6 and the value of function G is 9 at x=6. It means

[tex]F(6)=8[/tex]

[tex]G(6)=9[/tex]

Substitute F(6)=8 and G(6)=9 in equation (1).

[tex](F-G)(6)=8-9[/tex]

[tex](F-G)(6)=-1[/tex]

Therefore the value of (F-G)(6) is -1.

Answer:

35 smaller trucks.

Step-by-step explanation:

Given:

i) The larger truck with a 2.5-ton payload, and smaller trucks with 1.5-ton payload.

ii)  To unload a freight train 21 larger trucks are needed .

Total load of the freight train = 21 times 2.5 tons

= 21  × 2.5

= 52.5 tons

To find the number of small trucks needed, we need to divide 52.5 by 1.5

= 52.5 ÷ 1.5

= 35 small trucks needed.

So, to unload the freight, we need 35 smaller trucks.

Final answer:

Inno's solution of using the square root of 9 and 16 is the best estimate for the square root of ten, as it provides a narrower and more accurate range for the estimate.

Explanation:

To estimate a square root that is not a perfect square, one strategy is to find integers that the number falls between, and then those integers' respective square roots give us a range within which the square root of the number will fall.

Rosa and Inno's approaches are similar and most appropriate because they both use 9 and another square number that is close to 10.

Rosa uses the square roots of 9 and 25. Since the square root of 9 is 3, and the square root of 25 is 5, we know that √10 is a little more than 3, because 10 is closer to 9 than it is to 25. Inno uses the square roots of 9 and 16. Since the square root of 16 is 4, √10 is closer to 3 than 4 because 10 is closer to 9.

Therefore, Inno's solution gives a closer estimate of the square root of 10, as it falls between 3 and 4 (and closer to 3), and this is the best solution among those proposed.

Answer:

32x^4+32x^2y^6

Step-by-step explanation:

The root symbol was forgotten in the provided question. It should look like this:

Simplify the product. 8x^2(4x^2 + 4y^6)

The equation m/k = x solved for k will be k = m / x.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.

The equation is given below.

m/k = x

Simplify the equation for k, then we have

x = m / k

kx = m

k = m / x

The equation m/k = x solved for k will be k = m / x.

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Using the Pythagorean Theorem for the given right triangle, we calculated that the worker would need a ladder of at least 25 feet in length to reach the window.

The problem described can be solved by using the Pythagorean Theorem, which is appropriate for any right triangle. In the given problem, we have a right triangle - one side is the distance from the fence to where the ladder touches the building (12ft + 1ft + 9ft = 22ft), the other side is the height of the window from the ground (15ft), and the hypotenuse is the length of the ladder we need to find.

According to the Pythagorean theorem: [tex]A^2 + B^2 = C^2[/tex]. If we plug in our values, it would look like [tex]15^2 + 22^2 = C^2[/tex]. After carrying out the operations, we find that C^2 = 625.

To find the length of the ladder (C), we take the square root of 625, which is 25ft. So, the worker needs a ladder that is at least 25 feet long.

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Answer:

7/30

Step-by-step explanation:

Answer:

Part A: Marguerite rented a truck at $125 for 2 days. If she rents the same truck for 5 days, she has to pay a total rent of $275.

Write an equation in the standard form to represent the total rent (y) that Marguerite has to pay for renting the truck for x days. (4 points)

Part B: Write the equation obtained in Part A using function notation. (2 points)

Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)

(10 points)

Step-by-step explanation:

Answer:

Daniel will need [tex]19\frac{1}{2}[/tex] feet wood to complete his home project.

Step-by-step explanation:

We are told that Daniel needs 13 pieces of wood, each [tex]1\frac{1}{2}[/tex] feet long, to complete his home project.

To find total amount of wood needed we will multiply number of wood pieces by length of each wooden piece.

First of all we will convert our mixed fraction to improper fraction as: [tex]1 \frac{1}{2} =\frac{3}{2}[/tex]

Now let us multiply our values.

[tex]13*\frac{3}{2} =\frac{39}{2}[/tex]  

Now we will convert this improper fraction to mixed fraction to find our final answer.

[tex]\frac{39}{2}=19\frac{1}{2}[/tex]

Therefore, Daniel needs [tex]19\frac{1}{2}[/tex] feet wood to complete his home project.

Answer : The mean, median, and mode of the household pet data is, 1.4, 1 and 0 respectively.

Step-by-step explanation :

Mean : It is determine by adding all the numbers then divided by how many numbers there are.

[tex]Mean=\frac{\text{Sum of outcomes}}{\text{Number of outcomes}}[/tex]

Median : It is the middle term that is sorted by the list of numbers. It is determine by placing the numbers in increasing order.

For odd observations the formula will be: [tex]\frac{n+1}{2}[/tex]

For even observations:

First find the value at position [tex]\frac{n}{2}[/tex]

Second find the value at position [tex]\frac{n+1}{2}[/tex]

Then find that average of two values to get the median.

Mode : It is defined as the value that appears most in a set of data.

As we are given that the set of data:

1, 1, 0, 4, 1, 0, 1, 2, 3, 5, 2, 0, 2, 0, 3, 1, 2, 0, 0, 1, 0, 4, 0, 0, 3, 1, 0, 0, 2, 1, 0, 0, 4, 0, 1, 3, 5, 0, 2, 1

First we have to placing the numbers in increasing order.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5

Now we have to determine the mean.

[tex]Mean=\frac{\text{Sum of outcomes}}{\text{Number of outcomes}}[/tex]

Sum of outcomes = 1+1+0+4+1+0+1+2+3+5+2+0+2+0+3+1+2+0+0+1+0+4+0+0+3+1+0+0+2+1+0+0+4+0+1+3+5+0+2+1 = 56

[tex]Mean=\frac{56}{40}=1.4[/tex]

The mean of the household pet data is, 1.4

Now we have to determine the median.

For even data:

[tex]\frac{n}{2}[/tex] and [tex]\frac{n+1}{2}[/tex]

Here, n = 40

[tex]\frac{40}{2}[/tex] and [tex]\frac{40+1}{2}[/tex]

20 and 20.5

The number of pets at 20th position and 21th position is, 1 and 1 respectively.

Then we have to take an average of two values.

[tex]\frac{1+1}{2}=1[/tex]

The median of the household pet data is, 1

Now we have to determine the mode.

In the given set of data, 0 appears 15 times, 1 appears 10 times, 2 appears 6 times, 3 appears 4 times, 4 appears 3 times and 4 appears 2 times.

The value that appears most in a set of data is, 0

The mode of the household pet data is, 0

Answer:

160

Step-by-step explanation:

100 + 4 (15)

100 + 60

160