Two cyclists leave town at the same time on the same road going in  the same direction. Cyclist a is going 6 miles per hour faster than cyclist b. After 8 hours, cyclist a has traveled three times the distance as cyclist b. Use the equation 24x= 8(x+6) to find how fast cyclist b was traveling.

Answer:

As per the given statement: A forest ranger wants to determine the radius of the trunk of a tree. She measures the circumference to be 8.6 feet.

Shape of the trunk of a tree is circle.

Use the circumference formula:

[tex]C = 2\pi r[/tex]

where C is the circumference of a circle and r is the radius of a circle.

Solve for r;

Given: C = 8.6 feet and use [tex]\pi = 3.14[/tex]

Substitute the given value we get;

[tex]8.6 = 2 \times 3.14 \times r[/tex]

Simplify:

[tex]8.6 = 6.28r[/tex]

Divide both sides by 6.28 we get;

r = 1.6942675 feet

Therefore, the trunk's radius to the nearest tenth foot is, 1.4 ft

Answer:1.4

Step-by-step explanation:

that is it its not that hard

Answer:

You will need approximately 1.17 L of water with 3.5 L of glue.  This is a total of 4.67 L, which is NOT enough.

Step-by-step explanation:

Georgie has 3.75 litres of glue which is enough to make 5 litres of the mixture.

A ratio indicates how many times one number contains another. If a and b are to objects then ratio of a to the b is given as a : b.

Now it is given that,

Ratio of glue and water = 3 : 1

Amount of mixture = 5 litres

Georgie has glue = 3.5 litres

Now let x be the number,

So, Amount of glue in the mixture = 3x

and, amount of water in the mixture = x

⇒ Amount of mixture = 3x + x

⇒ 3x + x = 5

⇒ 4x = 5

⇒ x = 5/4

⇒ x = 1.25

Thus, Amount of glue in the mixture = 3*1.25 litres

⇒ Amount of glue in the mixture = 3.75 litres

So, Amount of glue in the mixture is greater than amount of glue Georgie has.

Thus, Georgie has 3.75 litres of glue which is enough to make 5 litres of the mixture.

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Jamaal spent x minutes on guitar and y minutes on homework, and the inequality representing his total practice time is x + y ≥ 45.

The student, Jamaal, spent x minutes practicing his guitar and y minutes on homework. The fact that he spent 45 minutes or more on both activities combined is represented by the inequality x + y ≥ 45. This inequality states that the sum of the time spent practicing guitar and the time spent on homework is equal to or greater than 45 minutes. To solve this inequality, you would ensure that when you add the minutes spent on each activity, the total does not fall short of 45 minutes, which is the minimum amount of time Jamaal has to spend on these activities.

The inequality representing Jamaal's total practice and homework time is x + y ≥ 45, meaning the total time spent on both activities is at least 45 minutes.

Jamaal spent x minutes today practicing guitar and y minutes on homework. If the total time he spent on both activities is at least 45 minutes, the inequality that best represents his practice time is x + y ≥ 45. This inequality indicates that when you add the minutes Jamaal spent practicing guitar and doing homework, the sum should be equal to or greater than 45 minutes.

There are 5 sides (a pentagon). The perimeter is the length of one side times the number of sides.

The polygon has 5 sides. The specific type of polygon with 5 sides is called a pentagon.

The perimeter of a polygon is the total length of all its sides. In a regular polygon, all sides are equal in length. So, if each side of the polygon is 2.5 cm and the perimeter is 12.5 cm, we can find the number of sides by dividing the perimeter by the side length:

Number of sides = Perimeter / Side length

Number of sides = 12.5 cm / 2.5 cm

Number of sides = 5

The mean absolute deviation of the set of data 3, 8, 10, 12, 15 is 2.4.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

To find the mean absolute deviation (MAD)

We have to find the mean (average) of the data set.

The mean is given by mean = (3 + 8 + 10 + 12 + 15) / 5

= 48 / 5

Mean= 9.6

Calculate the absolute deviation of each data point from the mean.

The absolute deviation of each data point from the mean is given by:

|3 - 9.6| = 6.6

|8 - 9.6| = 1.6

|10 - 9.6| = 0.4

|12 - 9.6| = 2.4

|15 - 9.6| = 5.4

The mean of the absolute deviations is given by:

MAD = (6.6 + 1.6 + 0.4 + 2.4 + 5.4) / 5

= 2.4

Therefore, the mean absolute deviation of the set of data 3, 8, 10, 12, 15 is 2.4.

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Option: C is the correct answer:

                   C. 2:3

The odds in favor of an outcome is the ratio of number of ways the outcome could occur to the number of ways it could not occur.

Here we are asked to find the  odds in favor of drawing a green marble.

Hence, it is the ratio of the number of ways the green marble will come up to the number of ways it could not come up.

The probability of drawing a green marble from a marble bag is 40%.

This means that the probability of not drawing a green marble from the bag is: 60%

( since, 100-40=60)

Hence, the odds in favor is: 40:60

i.e.

4:6=2:3

Answer:

D. Swordfish treat: 20%

Lizard Lollies : 50%

Puffer pops: 30%.      

Step-by-step explanation:  

We are told that Matrix is handing out treats at a local protest to promote his new detective agency.

Since he replaces the chosen treat each time with the same treat, so number of each treat remains same and it will not affect the probability for next person to choose the treat.  

We know that [tex]\text{Probability}=\frac{\text{The number of favorable outcomes}}{\text{Total number of possible out comes}}[/tex].

Let us find probability of choosing each type of treat one by one.

[tex]\text{Probability of choosing swordfish treat}=\frac{\text{Number of swordfish treat}}{\text{Total number of treats}}[/tex]

[tex]\text{Probability of choosing swordfish treat}=\frac{4}{4+10+6}[/tex]

[tex]\text{Probability of choosing swordfish treat}=\frac{4}{20}[/tex]

[tex]\text{Probability of choosing swordfish treat}=0.20[/tex]

Therefore, the probability of choosing swordfish treat is 0.20 or 20%.

[tex]\text{Probability of choosing lizard Lollies}=\frac{\text{Number of lizard lollis}}{\text{Total number of treats}}[/tex]    

[tex]\text{Probability of choosing lizard Lollies}=\frac{10}{20}[/tex]

[tex]\text{Probability of choosing lizard Lollies}=0.50[/tex]

Therefore, the probability of choosing lizard Lollies is 0.50 or 50%.

[tex]\text{Probability of choosing puffer pops}=\frac{\text{Number of puffer pops}}{\text{Total number of treats}}[/tex]

[tex]\text{Probability of choosing puffer pops}=\frac{6}{20}[/tex]

[tex]\text{Probability of choosing puffer pop}=0.30[/tex]  

Therefore, the probability of choosing puffer pops treat is 0.30 or 30%.

Upon looking at our given choices we can see that option D is the correct choice.

Answer: D

Step-by-step explanation:

Answer:

Step-by-step explanation:

Alright, lets get started.

The surface area of green solid is :

[tex]2 (3*3 + 3*3 + 3*3) = 2*27=54[/tex]

The surface area of orange solid is :

[tex]2(5*5 + 5*5 + 5*5) =2*75= 150[/tex]

So the ratios of their surface area will be :

[tex]\frac{54}{150}[/tex]

[tex]\frac{18}{50}[/tex]

[tex]\frac{9}{25}[/tex]

Hence the answer is 9:25   :  Answer Hope it will help :)

Final answer:

The population of Linton is 8,904 people, calculated by first finding the population of Elmore (x) and using the fact that Linton's population is 12 times that of Elmore's.

Explanation:

The question involves solving a proportion to determine the population of Linton, given that the population of Linton is 12 times as great as the population of Elmore and that their combined population is 9,646 people.

Let the population of Elmore be represented by x. Therefore, the population of Linton, which is 12 times greater than Elmore's, would be 12x. The combined population of Linton and Elmore, which is given as 9,646, can be represented by the equation:

x + 12x = 9,646

Simplify the equation:

13x = 9,646

Now, divide both sides of the equation by 13 to solve for x:

x = 742

Since we are looking for the population of Linton, we multiply x by 12

12 * 742 = 8,904

Therefore, the population of Linton is 8,904 people.

it would be C. Y=4X

Answer:

[tex] a_{n} = - 5 {( - 2)}^{n - 1} [/tex]

[tex]b = - 5[/tex]

[tex]c = - 2[/tex]

By converting mixed numbers to decimals and multiplying the total number of cups of flour by the cost per cup, we find out Maria will spend $3.80 on flour, which is option C.

To find out how much Maria will spend on flour to make her cookies, we need to calculate the total cost of white and whole wheat flour. Maria needs 3 1/10 cups of white flour and 4 1/2 cups of whole wheat flour. First, we convert the mixed numbers to decimal form: 3 1/10 cups is 3.1 cups, and 4 1/2 cups is 4.5 cups. Then we add them together to find the total number of cups Maria will use:

3.1 cups + 4.5 cups = 7.6 cups

Next, since flour costs $0.50 per cup, we multiply the total number of cups by the cost per cup:

7.6 cups × $0.50 per cup = $3.80

Therefore, Maria will spend a total of $3.80 on flour for her cookie recipe, making the correct answer C. $3.80.