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Answer:The scale factor is  \frac{1}{5}

Step-by-step explanation:

Answer:

3/2

Step-by-step explanation

Final answer:

To convert 1/5 mile to other forms, it can be represented as 2/10 when the denominator is 10, 20/100 when the denominator is 100, and 0.2 as a decimal.

Explanation:

To convert 1/5 mile into a fraction with 10 in the denominator, multiply both the numerator and the denominator by 2 to get 2/10. To get a fraction with 100 in the denominator, multiply both the numerator and the denominator of 1/5 by 20 to get 20/100. As a decimal, 1/5 is equivalent to 0.2 because 1 divided by 5 equals 0.2.

The rectangular quilt has length 7 feet and width as 5 feet.

In order to find the perimeter, we have this formula:

[tex] P = 2(l+w) [/tex]

Plugging these values in the formula:

[tex] P = 2(7+5) [/tex]

Perimeter = 24 feet.

So 24 feet of lace are needed to cover the edges of the quilt.

Final answer:

Dennis's other number, considering the conditions of only having 1 and 3 as common factors and 18 as the least common multiple with 9, is 6.

Explanation:

To solve the problem regarding Dennis's numbers, it's crucial to understand the conditions provided: the numbers only share common factors of 1 and 3, one of the numbers is 9, and their first common multiple is 18. To find the other number, knowing one of the numbers allows us to apply the rule of least common multiples (LCM). Since 9's factors are 1, 3, and 9, and the LCM with the other number is 18, this other number must be divisible by itself and 3 but not be a multiple of 9 to maintain the unique common factors condition. The only number that satisfies the condition in which 18 is the LCM and shares only 1 and 3 as common factors with 9, would be 6, since 18 is the smallest number that both 9 and 6 can divide into without other common multiples.

There were 50 adult tickets and 20 children's tickets sold.

To determine the number of adult and children's concert tickets sold, we use a system of equations: x + y = 70 (total tickets) and 9x + 5y = 550 (total revenue). Solving these, we find 50 adult tickets and 20 children's tickets were sold.

To find the number of adult and children's concert tickets sold, given the total revenue and the price of each ticket, we can set up a system of linear equations. Let's define x as the number of adult tickets and y as the number of children's tickets. We are given that:

Now we have the following linear equations:

We can solve this system using either the substitution or elimination method. For simplicity, we'll use the elimination method.

Multiply the first equation by 5 to match the coefficient of y in the second equation:

Now subtract the new equation from the second equation given:

Using the value of x in the first equation, we find y:

Therefore, there were 50 adult tickets and 20 children's tickets sold.

The volume of the Jacksons' camping tent is 94.5 cubic feet. To calculate the volume, you multiply the dimensions: height (3.5 ft) by length (6 ft) by width (4.5 ft).

The formula for calculating the volume of a rectangular prism is V = lwh, where V is the volume, l is the length, w is the width, and h is the height.

The volume of the tent is determined by multiplying its length, width, and height. In this instance, the Jacksons' tent has a volume of 94.5 cubic feet, providing ample space for their camping needs. Understanding the volume of a three-dimensional object is essential for assessing its capacity and ensuring it meets the requirements of its intended use.

Complete Question:

The Jacksons went camping in a state park. One of the tents they took is shown, tent size in the attached picture 3.5 ft high, 6 ft long and 4.5 ft wide. What is the volume of the tent?

Final answer:

The factor that would scale up Wolfgang's picture the most is 1 4/9.

Explanation:

The factor that would scale up Wolfgang's picture the most is 1 4/9.

To find the scale factor, we compare the given factors: 7/8, 14/14, 1 4/9, and 3/2.

Out of these options, 1 4/9 would enlarge the picture the most when used to multiply its current dimensions.

Final answer:

You can tell that the first digit of the quotient of 2,874 divided by 3 is in the hundreds place by using estimation and recognizing that 287 (the first three digits) is greater than 3 multiplied by 100, thus ensuring the quotient reaches the hundreds place.

Explanation:

To determine if the first digit of the quotient of 2,874 divided by 3 is in the hundreds place before actually dividing, we can use an estimation technique. Estimation helps us to predict the placement of the quotient's digits without doing the full calculation. For the divisor 3 to produce a number in the hundreds place, it must be able to go into the first three digits of the dividend (here, 2,874).

We look at the thousands and hundreds places of the dividend. Since the number 2,874 has a 2 in the thousands place, we know 3 cannot be divided into 2 to give us a number in the hundreds place. But when we include the next digit in the hundreds place, we have 287, which is greater than 3 imes 100. Therefore, we can say that 3 will go into 287 at least 100 times, making the first digit of the quotient in the hundreds place.

This estimation is further validated by the recognition that the number in the hundreds place of 2,874 (which is 8) is more than twice 3, and therefore, dividing it by 3 will definitely yield a number greater than 100 but less than 1,000.

The function that describes a cell population of 100 cells tripling every hour is stated by the formula p(t) = 100(3)^t, which represents exponential growth.

This problem describes a phenomenon where the initial population experiences exponential growth in a way that it triples every hour. Exponential growth is typically represented by the function p(t) = p⁰×r^t, where:

- p(t) represents the final amount of entities (in this case, population) after time t,
- p0 is the initial amount of entities (in this case, initial population),
- r is the growth factor,
- and t is time.

In these types of problems, the base number of the exponent (in this case 3) represents the growth factor. This is based on the fact that every time period (in this case, every hour), the population triples, or in other words, gets multiplied by 3.

The initial population given is 100 cells. This is represented by p0 in our formula and is also the coefficient in our function.

By considering both the initial population and the rate at which it triples, we can construct the function as p(t) = 100 × 3^t.

Therefore, according to our built function, the correct choice is b. p(t) = 100 × 3^t.

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If a population of 100 cells triples every hour, which function represents p(t), the population after t hours?

a. p(t)=3(100)^t

b. p(t)=100(3)^t

c. p(t)=3t+100

d. p(t)=100t+3

Choose a number from 101 to 110, we selected 106. To represent it with tens and ones, draw ten groups of ten for 'ten tens' which equals 100, and then draw 6 individual objects depicting 'and more' to visually show that 106 is 100 plus 6.

To choose a number from 101 to 110 and represent it as ten tens and more, let's select the number 106. The number 106 can be broken down into ten tens (which is 100) and an additional 6 to make up the full number.

A visual representation of this could be:

For the ten tens, you can draw ten groups of ten sticks or circles together, which would represent 100.

For the additional 6, draw six more sticks or circles away from the groups of tens.

So the drawing will show ten sets of ten objects, such as sticks or dots for the tens, and then six individual objects for the ones, clearly indicating that 106 consists of 100 (ten tens) plus 6 more.