Pepe is putting a fence in his backyard to enclose the garden in form of a triangle. The garden already has sides enclosed with 8 feet and 5 feet of fence, respectively. What can you say about the length of the third side?

Answer:

32 x^3 - y^3 + 42 x 2y + 11 xy^2 + 17

To find the common difference, subtract the first term from the last term and divide by the number of terms minus 1.

To find the common difference of an arithmetic sequence given the first and last term, you can use the formula: common difference = (last term - first term) / (number of terms - 1). First, subtract the first term from the last term. Then, subtract 1 from the number of terms. Finally, divide the result of the subtraction by the number of terms minus 1 to find the common difference.

Answer:

The Answer is Step 3. I took the test :)

Answer:

B. [tex]n(d-18)[/tex]

D. [tex]dn-18n[/tex]

Step-by-step explanation:

Let d represent the original price paid for the game.

We have been given that a local buys used video games. For each game bought, they will pay $18 less than the original price paid for the game.

The price of used video game would be original price minus 18. We can represent this information in an expression as:

[tex]d-18[/tex]

We have been given that Jordan sold n games, so the cost of n used games would be [tex]n(d-18)[/tex].

Using distributive property we will get,

[tex]n(d-18)=dn-18n[/tex]

Therefore, option B and D are correct choices.

Answer:

D

Step-by-step explanation:

Sam's gas usage is a proportional relationship because he gets a constant 25 miles per gallon in both given scenarios.

Yes, this is a proportional relationship. To determine proportionality, we can calculate the gas mileage for each scenario. Gas mileage is calculated by dividing the number of miles driven by the number of gallons used. For the first scenario, the gas mileage is 50 miles / 2 gallons = 25 miles per gallon. In the second scenario, the gas mileage is 100 miles / 4 gallons = 25 miles per gallon. Since the gas mileage is the same in both cases, it indicates a proportional relationship.

Answer:

Option A. July-August.

Step-by-step explanation:

Phillips family spent each month on groceries. The amount of money in each month is shown in a graph.

Approximate amount in each month was spent :

March : $450

April  : $400

May  :  $400

June  :  $500

July  :  $300

August : $ 500

Sep.  :  $480

Oct. : $420

From the graph given, there is a greatest month to month increase in spending occur in July to August (from $300 to $500).

So Option a. July-August is the correct answer.

Answer:

probability that a random draw is black = [tex]\frac{x}{x+y}[/tex].

Step-by-step explanation:

Given: A jar contains "x" black and "y" white balls.

To find: What is the probability that a random draw is black.

Solution: We have given that black balls  = x

                                                 white balls = y

                                     total balls = x + y

probability that a random draw is black = [tex]\frac{Number\ of\ outcome happen}{Total numer of outcomes}[/tex]

probability that a random draw is black = [tex]\frac{Ball\ drawn\ is\ black}{Total\ number\ of\ ball}[/tex].

probability that a random draw is black = [tex]\frac{x}{x+y}[/tex].

Therefore, probability that a random draw is black = [tex]\frac{x}{x+y}[/tex].

The final price that is paid for the jacket is:

                    $ 48

The actual cost of jacket was: $ 100

The cost of the jacket was reduced by 40%

This means that the after reduction of 40% the jacket will cost:

[tex]100-\dfrac{40}{100}\times 100\\\\\\=100-40\\\\=60[/tex]

This means that the cost of jacket after 40% reduction is: $ 60

Also, there was a coupon that contains 20% off.

This means that the jacket will actually cost:

[tex]60-\dfrac{20}{100}\times 60\\\\\\=60-12\\\\\\=48[/tex]

                    The final price of jacket is:

                              $ 48

To find the common ratio of the given sequence, divide each term by the previous term. The common ratio is 0.75.

The given sequence is: 128, 96, 72, 54, ...

To find the common ratio, we need to determine the ratio between consecutive terms. We can do this by dividing each term by the previous term.

Ratio between the 2nd and 1st terms: 96/128 = 0.75

Ratio between the 3rd and 2nd terms: 72/96 = 0.75

Ratio between the 4th and 3rd terms: 54/72 = 0.75

Since the ratio is the same for all consecutive terms, we can conclude that the common ratio of this geometric sequence is 0.75.

The correct common ratio for the given sequence is [tex]\(\frac{3}{4}\) or 0.75.[/tex]

To find the common ratio of the sequence, we divide each term by the previous term and look for a consistent value:

1. For the second term, \(96\), divided by the first term, [tex]\(128\)[/tex], we get:

[tex]\[ \frac{96}{128} = \frac{3}{4} = 0.75 \][/tex]

2. For the third term, [tex]\(72\),[/tex] divided by the second term, [tex]\(96\),[/tex] we get:

[tex]\[ \frac{72}{96} = \frac{3}{4} = 0.75 \][/tex]

3. For the fourth term, [tex]\(54\),[/tex] divided by the third term, [tex]\(72\)[/tex], we get:

[tex]\[ \frac{54}{72} = \frac{3}{4} = 0.75 \][/tex]

Answer: 48.7 degrees

Step-by-step explanation:

Let [tex]\theta[/tex] is the angle between the his sight line form with the side of the hotel,

Since, the building is of 5-story and a men having height 6 feet is in the fifth-story.

Thus, the total length from the eyes of the man and foot of the building = 6 + 12 × 5 = 6 + 60 = 66 feet

Also, the distance of the statue from the foot of the building = 75 feet.

Then by the below diagram,

[tex]tan\theta = \frac{75}{60+6}[/tex]

[tex]tan\theta = \frac{75}{66}[/tex]

[tex]\theta=48.6522227803\approx 48.7\text{ degree}[/tex]

The 95 percent confidence interval is wider than the 90 percent confidence interval because the 95 percent level of confidence includes more of the distribution. This means there is a greater level of certainty that the true value of the population mean is contained within the interval.

The 90 percent confidence interval is (67.18, 68.82). The 95 percent confidence interval is (67.02, 68.98). The 95 percent confidence interval is wider. If you look at the graphs, because the area 0.95 is larger than the area 0.90, it makes sense that the 95 percent confidence interval is wider. For more certainty that the confidence interval actually does contain the true value of the population mean for all statistics exam scores, the confidence interval necessarily needs to be wider.

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A trapezoid becomes an isosceles trapezoid when its non-parallel sides, or legs, are of equal length. Thus, for a given length x, an isosceles trapezoid requires both legs to be x in length.

A trapezoid is a geometric shape with one pair of parallel sides. A trapezoid becomes an isosceles trapezoid when the non-parallel sides (the legs) are equal in length. If we denote the length of the legs as x, then the trapezoid becomes an isosceles trapezoid when both legs are of equal length, meaning x equals x.

Without additional information such as the lengths of the base and height of the trapezoid or the angles within it, we cannot provide a specific numerical value for x. The key to remember here is that an isosceles trapezoid has equal length legs - so whatever value you have for one leg, the other leg must be the same for it to qualify as an isosceles trapezoid.

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Answer:

5.586

Step-by-step explanation:

The answer is 1/500 because it will always be the probability of the event occurring/total events

Answer:

The length of RO is 38.

Step-by-step explanation:

Given information: ROSE is trapezoid with median If MN = 24 and ES = 10.

Sufficient information is not given. This question can be solved if it is given that  [tex]RO\parallel ES[/tex].

According to the properties of trapezoid the length of the median is the average of length of parallel sides.

Let [tex]RO\parallel ES[/tex] and length of RO be x.

Since MN is median, therefore

[tex]MN=\frac{RO+ES}{2}[/tex]

[tex]24=\frac{x+10}{2}[/tex]

[tex]48=x+10[/tex]

[tex]x=38[/tex]

Therefore length of RO is 38.

To find out how much cement was delivered to each team, we can set up an equation based on the information provided and solve for the unknowns.

Let's denote the amount of cement delivered to the second team as x kg. According to the question, the first team received 50 kg less, so they received x - 50 kg of cement.

The first team used 150 kg of cement every hour for 3 hours, so they used a total of 150 * 3 = 450 kg of cement. Therefore, they had 1.5 times as much remaining cement as the second team, which means they had 1.5 * (x - 50) kg of cement remaining.

Since we know that the remaining cement of the first team is equal to 450 kg, we can set up the following equation: 1.5 * (x - 50) = 450. Solving this equation will give us the amount of cement delivered to each team.

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The first team received 750 kg of cement, and the second team received 800 kg of cement.

Let's denote the amount of cement delivered to the first team as [tex]\( x \)[/tex]kg and to the second team as[tex]\( y \)[/tex] kg. According to the problem, we have the following information:

1. The first team received 50 kg of cement less than the second team: [tex]\( x = y - 50 \)[/tex].

2. The first team uses 150 kg of cement per hour, and the second team uses 200 kg per hour.

3. After three hours of work, the first team has 1.5 times as much remaining cement as the second team.

Let's calculate the amount of cement used by each team after three hours:

- The first team uses [tex]\( 150 \times 3 = 450 \)[/tex] kg of cement.

- The second team uses [tex]\( 200 \times 3 = 600 \)[/tex] kg of cement.

Now, let's denote the remaining cement for the first team as [tex]\( R_1 \)[/tex] and for the second team as [tex]\( R_2 \)[/tex]. We can set up the following equations:

For the first team: [tex]\( R_1 = x - 450 \)[/tex].

For the second team: [tex]\( R_2 = y - 600 \)[/tex].

According to the problem, the remaining cement for the first team is 1.5 times that of the second team: [tex]\( R_1 = 1.5 \times R_2 \).[/tex]

Substituting the expressions for[tex]\( R_1 \)[/tex] and [tex]\( R_2 \)[/tex] into the equation, we get:

[tex]\( x - 450 = 1.5 \times (y - 600) \).[/tex]

Now, we can substitute[tex]\( x = y - 50 \)[/tex] into the equation:

[tex]\( (y - 50) - 450 = 1.5 \times (y - 600) \),[/tex]

[tex]\( y - 500 = 1.5y - 900 \),[/tex]

[tex]\( 0.5y = 400 \),[/tex]

[tex]\( y = 800 \).[/tex]

Now that we have [tex]\( y \)[/tex], we can find [tex]\( x \)[/tex]:

[tex]\( x = y - 50 \),[/tex]

[tex]\( x = 800 - 50 \)[/tex],

[tex]\( x = 750 \).[/tex]

To find the range of the function f(x) = 5x^2 + 4 for the given domain {-4, -2, 0, 1.5, 4}, evaluate the function for each value in the domain and find the minimum and maximum outputs. The range of the function is {4, 84}.

To find the range of the function f(x) = 5x^2 + 4 for the given domain {-4, -2, 0, 1.5, 4}, we need to evaluate the function for each value in the domain and find the minimum and maximum outputs.

The range of the function is the set of all possible outputs. In this case, the minimum output is 4 and the maximum output is 84. Therefore, the range of the function is {4, 84}.