On a recent trip, I took a cab from the airport to my hotel. These were the cab fares posted on the door of the cab: $2.20 for the first 1⁄2 mile and 30 cents for each additional 1/5 mile. How far did I travel if my fare was $17.20? What would my fare be if I were to travel 16.8 miles? What would my fare be if I were to travel n miles? What kind of relationship is this? Justify your response and provide a visual representation (a graph) of the relationship.

Answer:

Option (3) is correct.

(2,4) belongs to y ≥ 4x - 5

Step-by-step explanation:

Given : the point (2,4)

We have to find the equation of graph to which the point (2,4) belongs.

We will substitute the point in the  each given equation and for which the point satisfies will contain the point.

For 1) y ≥ x + 3

Put x = 2 and y = 4

⇒ 4 ≥ 2 + 3

⇒  4 ≥ 5 (false)

For 2) y ≥ -x + 8

Put x = 2 and y = 4

⇒  4 ≥ -2 + 8

⇒  4 ≥ 6 (false)

For 3) y ≥ 4x - 5

Put x = 2 and y = 4

⇒  4 ≥ 4(2) - 5 = 8 - 5

⇒  4 ≥ 3 (true)

For 4) y ≥ -2x + 9

Put x = 2 and y = 4

⇒  4 ≥ -4 + 9

⇒  4 ≥ 5 (false)

Since, the point (2,4) satisfies only inequality y ≥ 4x - 5.

Thus, (2,4) belongs to y ≥ 4x - 5

The answers are D:Rectangle, and B:Parallelogram

To calculate the percentage of dogs with a weight between 47.7 lbs and 54.9 lbs, we need to use the properties of the normal distribution. We can expect that around 82.7% of Mark's dogs would have a weight within this range.

To calculate the percentage of dogs with a weight between 47.7 lbs and 54.9 lbs, we need to use the properties of the normal distribution. We know that the mean weight is 52.5 lbs and the standard deviation is 2.4 lbs.

First, we need to standardize the lower and upper bounds of the weight range using the formula: z = (x - mean) / standard deviation. For the lower bound, z = (47.7 - 52.5) / 2.4 = -1.96. For the upper bound, z = (54.9 - 52.5) / 2.4 = 1.

Next, we can use a standard normal distribution table or calculator to find the percentage of values between -1.96 and 1. The percentage is approximately 82.7%. Therefore, we can expect that around 82.7% of Mark's dogs would have a weight between 47.7 lbs and 54.9 lbs.

Using the normal distribution, calculations of z-scores, and a z-table to determine probabilities, we can expect approximately 81.85% of Mark's Siberian Husky sled dogs to weigh between 47.7 lbs and 54.9 lbs.

To determine the percentage of Mark's Siberian Husky sled dogs that weigh between 47.7 lbs and 54.9 lbs, we need to use the properties of the normal distribution. The mean weight of the dogs is 52.5 lbs and the standard deviation is 2.4 lbs. We can calculate the z-scores for 47.7 lbs and 54.9 lbs:

Z = (X - μ) / σ

For 47.7 lbs:

Z1 = (47.7 - 52.5) / 2.4 ≈ -2.0

For 54.9 lbs:

Z2 = (54.9 - 52.5) / 2.4 ≈ 1.0

Using a z-table or a statistical software, we can find the probabilities corresponding to these z-scores. The probability between Z1 and Z2 is the area under the curve in this range.

The probabilities associated with the z-scores are approximately 2.28% for Z1 (< -2.0) and 84.13% for Z2 (< 1.0). To find the percentage between Z1 and Z2, we subtract the smaller percentage from the larger one:

Percentage between 47.7 lbs and 54.9 lbs = 84.13% - 2.28% = 81.85%

Thus, we would expect that 81.85% of Mark's dogs have a weight between 47.7 lbs and 54.9 lbs.

The total number of nickels that can be collected is 17 and this can be determined by forming the inequality.

Given :

A collection of quarters and nickels contains at least 42 coins and is worth at most $8.00.

The inequality can be formed in order to determine the total number of nickels that can be collected.

Let the total number of quarters be 'x' and the total number of nickels be 'y'. Then the inequality that represents the total number of quarters and nickels contained in the collection is at least 42 is given by:

x + y [tex]\geq[/tex] 42  --- (1)

The inequality that represents that the worth of the coins is at most $8 is given by:

0.25x + 0.5y [tex]\leq[/tex] 8   --- (2)

Now, according to the given data there are a total of 25 quarters in the collection, so, the number of nickels contained in the collection is:

x + y [tex]\geq[/tex] 42

25 + y [tex]\geq[/tex] 42

y [tex]\geq[/tex] 17

So, the total number of nickels that can be collected is 17.

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The collection can contain up to 35 nickels, given that it already includes 25 quarters and the total value does not exceed $8.00.

To determine how many nickels can be in the collection, we must first calculate the total value of the 25 quarters. Since each quarter is worth 25 cents, we multiply 25 quarters by 25 cents to get 625 cents, which is $6.25. The maximum value of the entire collection is $8.00. Thus, we subtract $6.25 from $8.00 to find the remaining value that can be occupied by nickels, which is $1.75. Each nickel is worth 5 cents, so we divide $1.75 by 0.05 (5 cents) to find the maximum number of nickels. $1.75 divided by 0.05 equals 35. Therefore, the collection can contain up to 35 nickels.

Iliana was part of a group that was working on changing 0.4 repeated to a fraction. The answer is 2.25.

Percentage counts the number compared to 100.

So, if we have a%, that means for each 100, there are 'a' parts. If we divide each of them with 100, we get:

For each 1, there are a/100 parts.

Iliana was part of a group that was working on changing 0.4 repeated to a fraction.

Each member of the group had a different answer.

Let x be 0.444444[tex]\bar 4[/tex]

So,

4 / 10 = 0.4

4 / 9 = 0.4444444...

9/ 4 = 2.25

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Answer:

500

Step-by-step explanation:

It is expected that approximately 500 students would finish the test in less than 40 minutes.

To determine the number of students who would be expected to finish the test in less than 40 minutes, we can use the concept of the standard normal distribution and the z-score.

The z-score measures the number of standard deviations an individual data point is from the mean. In this case, we want to find the proportion of students who finish the test in less than 40 minutes, which corresponds to finding the area under the curve to the left of the mean.

Using the z-score formula:

z = (x - μ) / σ

where x is the value (40 minutes), μ is the mean (40 minutes), and σ is the standard deviation (8 minutes).

Substituting the values into the formula:

z = (40 - 40) / 8

z = 0

A z-score of 0 indicates that the value is exactly at the mean.

Since we are interested in the proportion of students finishing in less than 40 minutes, we need to find the area under the curve to the left of the mean, which is represented by a z-score of 0.

By referring to a standard normal distribution table or using a statistical software, we find that the proportion of students finishing in less than 40 minutes is approximately 0.5000.

To find the expected number of students, we multiply the proportion by the total number of students:

Expected number of students = 0.5000 * 1000 = 500

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first equation y=1/2x +2

x=2 = 1/2(2) +2 =1+2 =3

x=4 = 1/2(4)+2 = 2+2 =4

first equation  is the answer

Answer:

[tex]y=\dfrac{1}{2}x+2[/tex]

A is correct

Step-by-step explanation:

Given: Table of x and y

 x  :  2    4     6     8

 y  :  3    4     5     6

Using two point find the slope:

(2,3) and (4,4)

[tex]Slope=\dfrac{4-3}{4-2}[/tex]

[tex]\text{Slope }=\dfrac{1}{2}[/tex]

Now we find slope using last two point

(6,5) and (8,6)

[tex]\text{Slope }=\dfrac{6-5}{8-6}[/tex]

[tex]\text{Slope }=\dfrac{1}{2}[/tex]

Slope is equal. Thus, The given relation is linear.

[tex]y-3=\dfrac{1}{2}(x-2)[/tex]

[tex]y=\dfrac{1}{2}x+2[/tex]

Hence, The relation represents a linear equation [tex]y=\dfrac{1}{2}x+2[/tex]

Answer:

[tex]sin x = \frac{11}{s}[/tex]

Step-by-step explanation:

[tex]Tan x = \frac{11}{r}[/tex]

[tex]Cos x = \frac{r}{s}[/tex]

Property : [tex]\frac{sin \theta}{cos \theta}=Tan \theta[/tex]

So, [tex]\frac{sinx}{cosx}=Tan x[/tex]

Substitute the values

[tex]\frac{sinx}{ \frac{r}{s}}=\frac{11}{r}[/tex]

[tex]sinx =\frac{11}{r} \times \frac{r}{s}[/tex]

[tex]sinx =\frac{11}{s}[/tex]

Hence the value of sin x° is [tex]\frac{11}{s}[/tex]

volume = PI * radius^2* height

3.14 x 1^2 x 1

v=3.14 cubic inches

Answer:

The correct answer is:

A) The food cans have a mean shelf life of 14 months.

Just took this quiz and this was the correct answer.

Step-by-step explanation:

Answer: Writting the equation and solving it, the answer is option D) .08c = .05c + 7.50; c = 250

Solution:

If the number of photocopies is c

Plan 1: Customers can pay $0.08 per page

The cost with plan 1 is: C1=0.08c

Plan 2: Customers can pay $7.50 for a discount card that lowers the cost to $0.05 per page.

The cost with plan 2 is: C2=7.50+0.05c

We want to find the number of photocopies for which the cost of each plan is the same, then we equal the cost of each plan:

C1=C2

Replacing C1 by 0.08c and C2 by 7.50+0.05c

0.08c=7.50+0.05c

Solving this equation for c: Subtracting 0.05c both sides of the equation:

0.08c-0.05c=7.50+0.05c-0.05c

Subtracting:

0.03c=7.50

Dividing both sides of the equation by 0.03

0.03c/0.03=7.50/0.03

c=250

Answer:

.08c = .05c + 7.50; c = 250

Step-by-step explanation:

i got a 100 on the test trust!

Answer:

C) 13.75 dollars per month

Step-by-step explanation:

i took the test and got it right

Answer:

Carmen's prediction is low because 200 times  is 50.

Step-by-step explanation:

First of all we are going to define the sample space for this exercise.

The sample space is Ω = {1,2,3,4,5,6,7,8}

Given the event A : ''Roll an 8-sided die an get a multiple of 4''

The probability for the event A is

Because they are two numbers (4 and 8) over a total of eight numbers (1,2,3,4,5,6,7,8) that are multiple of 4.

Now, given the random variable X : ''Total of numbers multiples of 4 If she rolls

an 8-sided die 200 times''

X can be modeled as a Binomial random variable.

X ~ Bi (n,p)

X ~ Bi (200,)

In which n is the total times she rolls the 8-sided die and p is the success probability. We define a success as obtain a number multiple of 4.

The mean for this variable is

We answer that Carmen's prediction is low because 200 times  is 50.

Final answer:

To achieve a 15 percent saline solution by mixing a 10 percent solution with a 25 percent solution, we calculate that we need to add 1.5 liters of the 25 percent saline solution to the initial 3 liters of the 10 percent solution.

Explanation:

To solve the problem, we need to calculate how much of a 25 percent saline solution should be added to 3 liters of a 10 percent saline solution to get a 15 percent saline solution. We'll use the concept of the conservation of mass of the solute (NaCl) and set up an equation to find the required volume of the 25 percent solution.

Let V be the volume of the 25 percent solution we need to add. The amount of NaCl in the 10 percent solution is (0.10)(3 L), and the amount of NaCl in the 25 percent solution is (0.25)(V). The resulting solution has a concentration of 15 percent, so the amount of NaCl in the final solution will be (0.15)(3 L + V).

Now we set up our equation based on the mass of NaCl being equal before and after the addition of the 25 percent solution:

(0.10)(3 L) + (0.25)(V) = (0.15)(3 L + V)

Solving this equation:

0.30 + 0.25V = 0.45 + 0.15V

0.25V - 0.15V = 0.45 - 0.30

0.10V = 0.15

V = 0.15 / 0.10

V = 1.5 L

Therefore, 1.5 liters of a 25 percent saline solution must be added to the initial 3 liters of a 10 percent solution to obtain a 15 percent saline solution.

Answer:

I'm a few years late, lol, but um the answer is 42 x [tex]10^{-3}[/tex] meters

For all the people who still need the answer.

Step-by-step explanation:

5 x [tex]10^{-11}[/tex] and 8.4 x [tex]10^{8}[/tex]

5 x 8.4 = 42  (multiply like terms)

[tex]10^{-11}[/tex] + [tex]10^{8}[/tex] = [tex]10^{-3}[/tex]  (add the exponents)

42 x [tex]10^{-3}[/tex]

The length in scientific notation is [tex]42\times10^{-7[/tex] meter.

Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as [tex]1.56\times10^7[/tex].

Given that, the diameter of a hydrogen atom is about [tex]5\times10^{-15}[/tex] meter. Suppose 8.4×10⁸ hydrogen atoms were arranged side by side in a straight line.

Now, multiply the numbers

[tex]5\times10^{-15}[/tex]×8.4×10⁸

= [tex]42\times10^{-7[/tex] meter

Therefore, the length in scientific notation is [tex]42\times10^{-7[/tex] meter.

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