One angle of a triangle measures 120°. The other two angles are in a ratio of 5:7. What are the measures of those two angles

Answer:

The interquartile range would be 6.

Step-by-step explanation:

3, 6, 8, 9, 10, 12, 13,

Median: 9

Lower quartile (Q1): 6

Upper quartile (Q2): 12

(IQR) Interquartile Range: 12 - 6 = 6

The interquartile range for the data set is, 6

We have to given that,

The data set is,

⇒ 10,3,8,6,9,12,13

We can arrange data set in ascending order,

⇒ 3, 6, 8, 9, 10, 12, 13

Hence, First quartile (Q₁) = 6

Second quartile (Q₃) = 12

Hence, The interquartile range for the data set is,

Interquartile range = 12 - 6

Interquartile range = 6

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To find the area of a square garden in square meters given its perimeter in yards, we first determine the side length by dividing the perimeter by 4, then convert this length into meters using the conversion rate, and finally square this metric side length to get the area in square meters.

The question you've asked involves calculating the area of a square garden in square meters given its perimeter in yards and a conversion factor between yards and meters. To solve this, we first determine the length of one side of the square garden using the given perimeter. The formula for the perimeter of a square is 4 × side length, so to find the side length, we divide the perimeter by 4. Given a perimeter of 60 yards, the side length is 15 yards.

To convert the side length into meters, we use the conversion factor that 1 yard is approximately 0.9 meters. Therefore, 15 yards × 0.9 meters/yard gives us 13.5 meters. Lastly, to find the area of the garden in square meters, we square the side length in meters, which is 13.5 meters × 13.5 meters = 182.25 square meters. This completes our calculation, showing that the area of the garden is approximately 182.25 square meters.

The proportion y/x = 7/2 indicates that the slope of the line is 7/2. Without additional information, we cannot determine the y-intercept from this proportion.

Pierce used the proportion y/x = 7/2 when deriving the equation of a line with similar triangles. This proportion suggests that for every 2 units of increase in x, y increases by 7 units. Therefore, the slope of the line, which is the ratio of the change in y (rise) to the change in x (run), would be 7/2. Thus, the correct answer is (c) the slope of the line is 7/2.

Because the question does not provide a specific point on the line, we cannot determine the exact y-intercept from the information given. However, since the proportion does not indicate any specific y-intercept value, we cannot conclude that it is 0, 2/7, or 7/2 without additional information. We only know the relationship between y and x given by the slope.

Answer:

10% or .1 or .10

Step-by-step explanation:

By comparing the theoretical probability of 1/6 with the experimental probability of 1/5, one can see that the experimental probability is one that is slightly higher.

Based on the question, to compare the theoretical and experimental probabilities of rolling the number 6, one have to calculate both probabilities.

The theoretical probability is seen as the expected probability according to the assumption of a fair six-sided number cube.

Based on the fact that there are six equally likely outcomes (numbers 1 to 6) on the cube, the theoretical probability of rolling a 6 is 1/6.

So, the experimental probability is based on the actual outcomes observed in Lavender's 90 rolls.

According to the given information:

Lavender rolled the cube 90 times and got the outcome of 6 in 18 of those rolls.

So: Experimental probability = Number of successful outcomes / Total number of outcomes

= 18 / 90

= 1/5

Hence, the experimental probability of rolling the number 6 is 1/5.

Since the experimental probability is slightly higher, one can say that it could be as a result of random variation or a biased number cube.

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Answer:

Option B. ΔABC ≅ ΔFGH

Step-by-step explanation:

In the given picture if we compare ΔFGH and ΔABC

side FG = BC

and AB = GH

and angle between them are equal

∠FGH = ∠ABC

Therefore SAS property of congruence is true for these triangles.

Option B. ΔABC ≅ ΔFGH

Answer:

C

Step-by-step explanation:

Final answer:

The student can fill up their gas tank up to 4 times within their $108 budget for gasoline. The inequality used to determine this is 27n ≤ 108, solved by dividing both sides by 27.

Explanation:

To solve the student's question regarding how many times they can fill up their gas tank within a $108 budget, we need to set up an inequality and solve it. Let's define the variable n as the number of times they can fill up their tank.

Step A: Write the Inequality

Since it costs $27 to fill up one tank, and the student has budgeted no more than $108 for gas, the inequality will be:

27n ≤ 108

Step B: Solve the Inequality

To find out how many times the student can fill up the tank, we divide both sides of the inequality by 27:

n ≤ [tex]\frac{108}{ 27}[/tex]

n ≤ 4

Therefore, the student can fill up their gas tank up to 4 times within their budget.

Answer:

Step-by-step explanation:

Let the cost of canvas be $x per sq inches.

Measurement of the canvas bought by the artist is

24 × 36 inches

Area of canvas = 24×36= 864 sq inches

Cost of canvas = 864x

New cost of canvas =x+5% of x

=x+0.05x

=1.05x

New Cost of canvas = 907.20x

Increase in price=907.20x-864x=43.2x

Percentage = [tex]\frac{43.2x}{864x}*100[/tex]

= 5%

Hence artist is going save 5% of cost by buying sheet today.