An acute triangle has sides measuring 10cm and 16 cm. The length of the third side is unknown. Which best describes the range of possible values for the third side of the triangle?

Final answer:

Atticus will spend $4.80 on the wrapping paper.

Explanation:

To find out how much Atticus will spend on the wrapping paper, we need to multiply the cost per square yard by the number of square yards desired.

Given that Atticus wants to buy a square yard, we multiply by to get.

Therefore, Atticus will spend $4.80 on the wrapping paper, which corresponds to option b.

Answer:

The correct option is 3.

Step-by-step explanation:

It is given that the Karolyn is arranging her art project, science project, and math project on her desk. The tree diagram below shows the sample space.

According to the tree diagram the elements of sample space are

1. art - math - science

2. art - science - math

3. science - art - math

4. science - math - art

5. math - art - science

6. math - science - art

Total number of possible outcomes is 6.

We need to find the probability that the science project is first. So, the favorable outcomes are

1. science - art - math

2. science - math - art

Total number of favorable outcomes is 2.

The probability of arranging the the science project first is

[tex]P=\frac{\text{Favorable outcomes}}{\text{Total possible outcome}}[/tex]

[tex]P=\frac{2}{6}[/tex]

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

The probability of arranging the the science project first is 2/6 or it can be written as 1/3. Therefore the correct option is 3.

Final answer:

To find the area of a window that measures 3 yards by 3/4 yard, multiply the length by the width. The area is 9/4 yd² or 2 1/4 yd², which corresponds to answer C.

Explanation:

The area of a rectangle is calculated by multiplying its length by its width. In this case, the window's dimensions are given in yards, and we need to find the area in square yards. We multiply the length (3 yards) by the width (3/4 yard) to find the area.

Area = length × width
Area = 3 yd × 3/4 yd
Area = 9/4 yd² or 2 1/4 yd²

So the correct answer is C. 2 1/4 yd².

The solution of the operations of the fractions are found as below.

Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.

4. [tex]\frac{3}{4}[/tex] + [tex]\frac{1}{2}[/tex]

Make the denominator equal.

1/2 is equal to (1×2) / (2×2) = 2/4

[tex]\frac{3}{4}[/tex] + [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{4}[/tex] + [tex]\frac{2}{4}[/tex] = [tex]\frac{3+2}{4}[/tex] = [tex]\frac{5}{4}[/tex]

5. 2 [tex]\frac{3}{8}[/tex] + 1 [tex]\frac{1}{8}[/tex]

This in the form of mixed fraction.

Convert it into improper fraction first.

2 [tex]\frac{3}{8}[/tex] = (2 × 8 + 3) / 8 = 19/8

1 [tex]\frac{1}{8}[/tex] = (1 × 8 + 1) / 8 = 9/8

2 [tex]\frac{3}{8}[/tex] + 1 [tex]\frac{1}{8}[/tex] = 19/8 + 9/8 = 28/8 = 7/2

6. 5 [tex]\frac{2}{5}[/tex] - 3 [tex]\frac{7}{10}[/tex]

5 [tex]\frac{2}{5}[/tex] = (5 × 5 + 2) / 5 = 27/5

3 [tex]\frac{7}{10}[/tex] = (3 × 10 + 7) / 10 = 37/10

5 [tex]\frac{2}{5}[/tex] - 3 [tex]\frac{7}{10}[/tex] = 27/5 - 37/10

              = 54/10 - 37/10

              = 17/10

7. 5 [tex]\frac{1}{2}[/tex] × [tex]\frac{3}{11}[/tex]

5 [tex]\frac{1}{2}[/tex] = 11/2

5 [tex]\frac{1}{2}[/tex] × [tex]\frac{3}{11}[/tex] = [tex]\frac{11}{2}[/tex] × [tex]\frac{3}{11}[/tex]

            = 3/2

8. [tex]\frac{5}{6}[/tex] ÷ [tex]\frac{1}{3}[/tex]

When dividing two fractions, the second term becomes reciprocal and the operation becomes multiplication.

[tex]\frac{5}{6}[/tex] ÷ [tex]\frac{1}{3}[/tex] =  [tex]\frac{5}{6}[/tex] × [tex]\frac{3}{1}[/tex] = 5/2

Hence the solutions are found.

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Answer:

6w

Step-by-step explanation:

They are basically asking you to multiply 6 and w, which is 6w

Curtis traveled at an average speed of 63 miles per hour on the first day of his road trip by dividing the total distance traveled, 693 miles, by the number of hours driven, which was 11.

To calculate the unit rate at which Curtis traveled in miles per hour on the first day, we divide the total distance traveled by the total time spent traveling. Curtis drove 693 miles in 11 hours, so the unit rate is 693 miles divided by 11 hours.

The calculation for miles per hour is as follows: 693 miles \/ 11 hours = 63 miles per hour (mph). Thus, Curtis traveled at an average speed of 63 mph on the first day of his road trip.

To find a fraction equivalent to 1/3 using the LCD, multiply the numerator and denominator by the same whole number that gives the LCD as the new denominator.

To find a fraction that is equivalent to 1/3 using the LCD (Least Common Denominator), we need to find a fraction with the same value but different numerator and denominator. The LCD of 1/3 is 3, so we can multiply the numerator and denominator by any whole number that gives us 3 as the new denominator. For example, multiplying both the numerator and denominator by 2, we get 2/6, which is equivalent to 1/3.

Final answer:

To find an equivalent fraction to 1/3 using the LCD, the fraction itself is already equivalent to 1/3.

Explanation:

To find a fraction equivalent to 1/3 using the least common denominator (LCD), we need to identify the LCD of 1/3. The LCD is the least common multiple of the denominators of the given fractions. In this case, the LCD is 3. Now, we need to express 1/3 with a denominator of 3. To do this, we multiply both the numerator and denominator by 1, resulting in 1/3 × 1/1 = 1/3. Therefore, 1/3 is already equivalent to 1/3.

The number one thousand less than 921,438 is 920,438.

Here's how we know:

Subtracting 1,000:

We want to find a number that is 1,000 less than 921,438. Subtracting 1,000 from 921,438 will give us the desired number.

921,438 - 1,000 = 920,438

Therefore, 920,438 is one thousand less than 921,438.

The explanation is as given:

We can think in terms of place values:

921,438 has a 1 in the thousands place.

Subtracting 1,000 (which has a 1 in the thousands place and zeros elsewhere) only affects the thousands place of 921,438.

The difference in the thousands place becomes 0(1 - 1), resulting in 920,438.

To write 0.45 as a fraction, express it as 45/100 then divide by the greatest common divisor, which is 5, to get 9/20 in simplest form.

To write 0.45 as a fraction in simplest form, we can start by recognizing that 0.45 means 45 hundredths, which is the same as 45 over 100. This can be written as:

\\[0.45 = \frac{45}{100}\\]

To simplify the fraction, we look for the greatest common divisor (GCD) that both the numerator (45) and the denominator (100) share. In this case, the GCD is 5. To get a fraction in simplest form, we divide both numerator and denominator by this number:

\\[\frac{45 \div 5}{100 \div 5} = \frac{9}{20}\\]

So, the fraction in simplest form of 0.45 is \(\frac{9}{20}\).

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since the fence will be 3 sides, the length would be length minus 2 widths

 so length = 1200 - 2x

 area = length x width

 width is x

area = (1200-2x)*x

= 1200x -2x^2

 after doing the calculations x = 600 meters, width = 300 meters

They would always be coplanar.

Hope this helps!

The question about the number of people who rode the train to work this morning is a statistical question, requiring data collection and analysis to reveal various statistics such as travel behaviors and the relation between ticket class and travel distance.

The question "How many people rode the train to work this morning?" represents a statistical question because it is likely to result in a variety of different answers and requires the collection and analysis of data to provide an accurate response. Statistical questions are concerned with understanding the distributions, trends, and patterns within collected data. In answering such a question, one would typically construct a table or a tree diagram to organize the data collected.

For example, if we wanted to know the percentage of commuters who travel alone to work, we would need to gather data on various modes of transportation, including trains, and analyze how many commuters use each mode alone. This situation could also relate to how many commuters decided to get on the train at each station on a given morning.

Answer:

708 Fahrenheit

Step-by-step explanation:

672 + 36 = 708

You add the 36 because it is a negative number and since you are trying to find the difference, for every negative number you have to add 1.

The difference between the melting and boiling points of mercury, -36 Fahrenheit and 672 Fahrenheit respectively, is 708 degrees Fahrenheit.

To find the difference between two temperatures, you simply subtract the lower temperature from the higher temperature. In this case, we have the boiling point of mercury at 672 degrees Fahrenheit and the melting point at -36 degrees Fahrenheit. So, we subtract -36 from 672 as follows:

672 - (-36) = 708 Fahrenheit.

The difference in temperature between the boiling and melting points of mercury is 708 degrees Fahrenheit.

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Answer:

None of them

Step-by-step explanation:

We have to find the irrational number

Rational number:

The number which can be expressed in [tex]\frac{p}{q}[/tex] form  are called rational number,where [tex]q\neq 0[/tex],p and q are integers are

Irrational number:

The number which can not be expressed in [tex]\frac{p}{q}[/tex] form  are called irrational number.

A)3.5

It can be written as

[tex]\frac{35}{10}[/tex]

Where 35 and 10 are both integers number

By definition of rational number

3.5 is a rational number

B)36

[tex]\frac{36}{1}[/tex]

36 and 1 are both integers number

By definition of rational number

36  is a rational number

C)48

[tex]\frac{48}{1}[/tex]

48 and 1 are both integers number

By definition of rational number

48  is a rational number

D)[tex]\frac{37}{100}[/tex]

37 and 100 are both integers number

By definition of rational number

[tex]\frac{37}{100}[/tex]  is a rational number

Calculating 1.5 to the third power involves multiplying the number by itself two additional times, which equals 3.375. This process of handling exponents applies to decimals just as it does for whole numbers, although additional rules apply when dealing with scientific notation involving powers of 10.

The question asks about calculating the value of 1.5 to the third power. To do exponents with decimals, the same rules apply as with whole numbers. We multiply the decimal number by itself for the number of times indicated by the exponent. Cubing, or raising a number to the third power, means multiplying the number by itself twice more (a total of three times).

Here's how it is done step by step for 1.5 to the third power (1.5³)

So, 1.5 to the third power equals 3.375.

If we are working with an exponent that includes a power of 10, such as 10², this indicates that the decimal is shifted two places to the right, making 1 × 10² equal to 100. However, in our case with 1.5³, we simply perform the multiplications as shown above without the need to shift the decimal place.

Another consideration in handling exponents with decimals is the application of rules for multiplying exponentiated quantities and shifting the decimal point based on the power of 10. This is particularly useful when dealing with scientific notation, which expresses large or small numbers in a more manageable format.