The chance that we picked 1 red and 1 blue is 0.2448 or 24.48%.
When we choose two balls at random without replacement, there are 50C2 = (50*49)/(2*1) = 1225 ways to choose two balls from 50 balls. Using the conditional probability formula, P(A and B) = P(A) * P(B|A), where A is the event of choosing a red ball and B is the event of choosing a blue ball.
P(A) = (20/50) = 0.4 (Probability of choosing a red ball at random from the bag)
P(B|A) = (15/49) = 0.306 (Probability of choosing a blue ball at random from the bag after choosing a red ball in the first trial)
Similarly, P(B) = (15/50) = 0.3 (Probability of choosing a blue ball at random from the bag)
P(A|B) = (20/49) = 0.408 (Probability of choosing a red ball at random from the bag after choosing a blue ball in the first trial)
Therefore, P(choosing one red and one blue) = P(A and B) + P(B and A) = P(A) * P(B|A) + P(B) * P(A|B)
= 0.4 * 0.306 + 0.3 * 0.408
= 0.1224 + 0.1224
= 0.2448 or 24.48%
Therefore, the chance that we picked 1 red and 1 blue is 0.2448 or 24.48%.
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McDoogles is expecting to sell 1,200 hamburgers in one day. Their actual total sales was 1,166 hamburgers. What is their percent of error, round to the nearest tenth of a percent?
The percent of error of Mc Doogles is 2.8%
What is the percent of error of McDoogles?To calculate the percent of error, we need to find the absolute difference between the expected value and the actual value, divide that by the expected value, and then multiply by 100 to get a percentage.
Given that:
Expected value = 1200Actual value = 1166Absolute difference = | 1200 - 1166 | = 34
Now:
Percent of error = (Absolute difference / Expected value) x 100
Percent of error = (34 / 1200) × 100%
Percent of error = 2.8%
Therefore, the percent of error is 2.8% (rounded to the nearest tenth of a percent).
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hello!! I NEED URGENT HELP!! PLEASE SHOW FULL SOLUTIONS FOR BOTH QUESTIONS AND ONLY ANSWER IF YOU KNOW! NO CALCULUS PLEASE! THAT WOULD BE VERY APPRECIATED!!
Step-by-step explanation:
sorry if answer is wrong
Solve this and show work
Answer:
see explanation below
Step-by-step explanation:
(secθ - cosθ)/secθ = (sinθ)^2
(secθ - cosθ)/secθ = (sinθ)^2
since secθ = 1/cosθ, you substitute
(secθ - cosθ)/(secθ)
= (1/cosθ - cosθ)/(1/cosθ)
= cosθ(1/cosθ - cosθ)
= 1 - cosθ^2
= sinθ^2
Use the Figure below to Answer this question
Answer:
y = 43
Step-by-step explanation:
Given AB is a straight line segment, and since angles on a straight line sum to 180°, we can construct the following equation:
⇒ 47° + y° + 90° = 180°
To find the value of y, solve the equation for y:
⇒ 137° + y° = 180°
⇒ 137° + y° - 137° = 180° - 137°
⇒ y° = 43°
⇒ y = 43
Therefore, the value of y is 43.
One - third of a number y is 14.
Answer:
42
Step-by-step explanation:
Answer:
Step-by-step explanation:
If one-third of a number y is 14, we can express this mathematically as:
1/3 y = 14
To solve for y, we can isolate y on one side of the equation by multiplying both sides by 3:
1/3 y * 3 = 14 * 3
Simplifying, we get:
y = 42
Therefore, the number is 42.
you have been tracking how long you spend on each course subject during your homework sessions. you want to see what percentage each subject represents. which type of chart would be best for this purpose?
a pie chart would be an effective way to quickly and easily understand the distribution of time spent on different course subjects.
For visualizing the percentage distribution of different course subjects, a pie chart would be the most suitable type of chart. Pie charts are ideal for displaying the relative proportions of different categories or groups as slices of a circular pie. Each slice of the pie represents a proportion of the whole, which in this case would be the total time spent on all course subjects during homework sessions. The size of each slice will correspond to the percentage of time spent on each course subject. Therefore, a pie chart would be an effective way to quickly and easily understand the distribution of time spent on different course subjects.
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every month, the number of friends max has on a social networking site increases by 21%. if he had 30 friends on 1 january, how many friends does he have on 1 january one year later? give your answer to the nearest integer. [answer format: integer, no units] g
Max has approximately 111 friends on January 1st of the next year.
Given that Max has 30 friends on January 1st, the number of friends increases by 21% every month.
We need to find out how many friends Max has on January 1st of the next year,
which is 12 months later.
First, we will calculate the number of friends Max has after one month: 30 + (21% of 30) = 30 + 0.21*30 = 36So, after the first month, Max has 36 friends.
Now, we will calculate the number of friends Max has after two months: 36 + (21% of 36) = 36 + 0.21*36 = 43.56 ≈ 44So, after the second month, Max has 44 friends.
Similarly, we can calculate the number of friends Max has after 12 months:30 + (21% of 30) + (21% of 30) + ... (12 times)≈ 30 + 6.3 + 7.65 + ... (12 terms)≈ 111.1
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PLEASE HELP <3 Kelly walks from the 1st floor to the 5th floor. Avery walks from the 8th floor to the 4th floor. Which best describes the distance Kelly and Avery walk?
Avery walks a greater distance than Kelly.
B Kelly walks a greater distance than Avery.
C Kelly walks at a slower speed than Avery.
D Kelly and Avery walk the same distance.
Answer:
D. Kelly and Avery walk the same distance.
Step-by-step explanation:
Kelly walked from the 1st floor to the 5th floor. That means she walked 4 floors.
Avery walked from the 8th floor to the 4th floor.
8 - 4 = 4.
They walked the same distance, except Avery went down, and Kelly went up, which is unrelated.
tabitha is renting a ballroom for an upcoming dinner reception. the rental fee for the ballroom includes a base price plus the cost of dinner per person. the table below shows the cost of the ballroom rental in relation to the number of people attending the dinner reception. no. of attendees 20 40 60 total rental cost $455 $615 $775 what is the base price for the ballroom rental?
The base price for the ballroom rental is $295.
Tabitha is renting a ballroom for an upcoming dinner reception. The rental fee for the ballroom includes a base price plus the cost of dinner per person. The table below shows the cost of the ballroom rental in relation to the number of people attending the dinner reception.
Table showing the relation between cost and attendee.The table shows that if 20 people attend, the total rental cost will be $455, and if 60 people attend, the total rental cost will be $775. Therefore, the increase in cost from 20 attendees to 60 attendees is $320. Thus, the difference between the cost for 20 attendees and the base price is $455 - (20 * cost of dinner per person), and the difference between the cost for 60 attendees and the base price is $775 - (60 * cost of dinner per person).Let b be the base price and c be the cost of dinner per person.
Therefore,
455 - (20c) = band775 - (60c) = b Subtracting the first equation from the second equation gives:
775 - (60c) - [455 - (20c)] = b320 = 40c, Therefore, c = 8.Substituting c = 8 into either of the equations above, we can find b:455 - (20c) = 455 - (20 * 8) = 295.
Therefore, the base price for the ballroom rental is $295.
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A house plan has concrete stairs leading down into the garage. How much concrete is needed to make the stairs? 3 ft 2 ft 8 ft 5 ft [? ] ft ³ 2 ft 8 ft 1 ft
The amount of concrete needed to make the stairs that leads to the garage is 64 cubic feet
Calculating the amount of concrete needed to make the stairs?The missing information is added as an attachment
The concrete needed to make the stairs is the volume of the stairs and this is calculated using
Volume = Base area * Height
Where
Base area = 3 * 2 + 2 * 1
Base area = 8
And
Height = 8
So, we have
Volume = 8 * 8
Evaluate
Volume = 64
Hence, the amount needed is 64 cubic feet
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A bank offers a CD that pays a simple interest rate of 11.0%. How much must you put in this CD now in order to have $2500 for a home-entertainment center in 6 years. The present value that must be invested to get $2500 after 6 years at an interest rate of 11.0% is $__?
you would need to invest $1506.02 in the CD now to have $2500 for a home-entertainment center in 6 years.
How to find the amount to be invest?The formula to calculate the future value of a simple interest investment is:
FV = P(1 + rt)
where FV is the future value, P is the principal (the initial amount invested), r is the annual interest rate (as a decimal), and t is the time period in years.
In this case, we want to find the principal that will result in a future value of $2500 in 6 years with an interest rate of 11.0% (or 0.11 as a decimal). So we can plug in the given values and solve for P:
2500 = P(1 + 0.11*6)
2500 = P(1.66)
P = 2500 / 1.66
P = $1506.02
Therefore, you would need to invest $1506.02 in the CD now to have $2500 for a home-entertainment center in 6 years.
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The Saad family is setting up for their annual New Year's party. There will be 143 adults and 62 children coming in the evening. Each table holds 15 people. How many tables will they need for all guests?
Answer:
There are a total of 143 + 62 = 205 people coming to the party.
To calculate the number of tables needed, we divide the total number of people by the number of people per table:
205 ÷ 15 = 13 with a remainder of 10
Since we can't have a fraction of a table, we need to round up to the nearest whole number, which means the Saad family will need 14 tables for all guests.
a pyrmid has a height of 5 in. and a surface area of 90 in square. find the surface area of a similar pyramid with a height of 10 in. round to the nearest tenth, if necessary
Check the picture below.
[tex]\cfrac{5^2}{10^2}=\cfrac{90}{A}\implies \cfrac{25}{100}=\cfrac{90}{A}\implies \cfrac{1}{4}=\cfrac{90}{A}\implies A=360[/tex]
A chain fits tightly around two gears as shown. The distance between the centers of the gears is 32 inches. The radius of the larger gear is 19 inches. Find the radius of the smaller gear. Round your answer to the nearest tenth, if necessary. The diagram is not to scale.
Answer:
The answer to your problem is, C.
Step-by-step explanation:
From the given figure it is noticed that the radius of a circle is 11 inches and the centers of two circles are 20 inches apart. The length of the direct common tangent between both circles is 19 inches.
If the centers of two circles of radius r₁ and r₂ are d units apart, then the length of the direct common tangent between them is
[tex]L = \sqrt{d^{2} - (r_{1} - r_{2} )^{2} }[/tex]
[tex]19 = \sqrt{20^{2} - (11-r_{2} )^{2} }[/tex]
Next, Square both sides.
[tex]361 = 400 - ( 11 - r_{2} )[/tex]
[tex]( 11 - r_{2} )^{2} = 400 - 361[/tex]
[tex]( 11 - r_{2} )^{2} = 39[/tex]
Change the square root both sides.
[tex]11-r = \sqrt{39}[/tex]
[tex]11- 6.245 = r[/tex]
[tex]4.775 = r[/tex]
[tex]R = 4.8ish[/tex]
Therefore the radius of second circle is 4.8 inches
Thus the answer to your problem is, C.
Edgar built a deck in his backyard with a section in the shape of a rectangle and a section in the shape of a square the model shows the dimensions of his deck in feet
From the given information provided, the area of the deck Edgar built in his backyard is 192 square feet.
The area of rectangular section is :
Area of rectangle = length x width
Substituting the given values, we get:
Area of rectangle = 16 ft x 8 ft
Area of rectangle = 128 square feet
The area of square section is :
Area of square = side x side
Substituting the given value, we get:
Area of square = 8 ft x 8 ft
Area of square = 64 square feet
Therefore, the total area of the deck is the sum of the area of the rectangular section and the area of the square section:
Total area of deck = Area of rectangle + Area of square
Total area of deck = 128 square feet + 64 square feet
Total area of deck = 192 square feet
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100 points
Michael has $16 and wants to buy a mixture of cupcakes and fudge to feed at least 4 siblings. Each cupcake costs $4, and each piece of fudge costs $2.
This system of inequalities models the scenario:
4x + 2y ≤ 16
x + y ≥ 4
Part A: Describe the graph of the system, including shading and the types of lines graphed. Provide a description of the solution set. (4 points)
Part B: Is the point (2, 3) included in the solution area for the system? Justify your answer mathematically. (3 points)
Part C: Choose a different point in the solution set and interpret what it means in terms of the real-world context. (3 points)
Source
StylesNormalFontSize
Answer:
Step-by-step explanation:
Part A:
The system of inequalities 4x + 2y ≤ 16 and x + y ≥ 4 can be graphed on a coordinate plane. To graph 4x + 2y ≤ 16, we can first graph the line 4x + 2y = 16. We can do this by finding the intercepts:
When x = 0, 4(0) + 2y = 16, so y = 8.
When y = 0, 4x + 2(0) = 16, so x = 4.
So, the intercepts are (0, 8) and (4, 0). We can connect these two points to graph the line.
To determine which side of the line to shade, we can test a point that is not on the line. For example, we can test the point (0, 0):
4(0) + 2(0) = 0 ≤ 16, so (0, 0) is in the shaded region.
Next, we can graph the line x + y = 4. This line passes through the points (0, 4) and (4, 0). To determine which side of the line to shade, we can test a point that is not on the line, such as (0, 0):
0 + 0 = 0 < 4, so (0, 0) is not in the shaded region. Therefore, we shade the region above the line.
The solution set for the system is the region that is shaded by both lines, which is the triangular region in the upper-left corner of the graph.
Part B:
To determine if the point (2, 3) is included in the solution area for the system, we can substitute x = 2 and y = 3 into both inequalities:
4(2) + 2(3) = 14 ≤ 16, so (2, 3) satisfies 4x + 2y ≤ 16.
2 + 3 = 5 ≥ 4, so (2, 3) satisfies x + y ≥ 4.
Therefore, the point (2, 3) is included in the solution area for the system.
Part C:
Let's choose the point (1, 3) as another point in the solution set. This means that Michael can buy 1 cupcake and 3 pieces of fudge, which would cost him:
1 cupcake * $4/cupcake + 3 pieces of fudge * $2/piece of fudge = $10
Since $10 is less than the $16 he has, he can afford to buy this combination of cupcakes and fudge. Therefore, the point (1, 3) represents a valid solution in which Michael buys 1 cupcake and 3 pieces of fudge to feed his siblings.
a hybrid vehicle has a mileage rating of 22 km/l. what is the gas mileage in miles per gallon? (given: 1 mi
To convert kilometers per liter to miles per gallon, we need to use conversion factors. There are approximately 3.785 liters in a gallon, and there are approximately 1.609 kilometers in a mile.
So, first we convert the fuel efficiency of the hybrid vehicle from kilometers per liter to kilometers per gallon:
1 km/liter * 3.785 liters/gallon = 3.785 km/gallon
Then, we convert kilometers per gallon to miles per gallon:
3.785 km/gallon * 1 mile/1.609 km = 2.35 miles/gallon
Therefore, the gas mileage of the hybrid vehicle is approximately 2.35 miles per gallon.
It's worth noting that the mileage rating of a hybrid vehicle can vary depending on factors such as driving conditions and habits, so the actual gas mileage may differ from the stated rating. Additionally, the conversion factors used here are approximate, so the exact gas mileage may vary slightly depending on the specific conversion factors used.
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A random group of adults was asked to complete a survey regarding the number of pets in their households. No two adults sur came from the same household. The number of households, , with no pets is one fourth of the number of households with multip Which of the following equations represents this situation if of the households have a single pet?
The equation representing the situation is 4x = y - 1, where x is the number of households with one pet and y is the total number of households. This can be answered by the concept of Simple equation.
Let's assume that there are x households with a single pet. The number of households with no pets is given as one-fourth of the number of households with multiple pets, which means there are 4 times as many households with multiple pets as there are households with no pets. Let's represent the total number of households as y.
Therefore, we can say that the number of households with no pets is (y - x)/4, and the number of households with multiple pets is 3(y - x)/4 since there are 4 times as many households with multiple pets as there are households with no pets.
Now, we can use the given information that the number of households with no pets is one-fourth of the number of households with multiple pets to write the equation:
(y - x)/4 = x/3
Solving for y, we get:
y = 4x + 3x/4 = 16x/4 + 3x/4 = 19x/4
But we are given that the total number of households y includes the households with one pet, so we can write:
y = x + (y - x)/4 + 3(y - x)/4 = x + y/4
Substituting the value of y from the previous equation, we get:
19x/4 = x + 19x/16
Solving for x, we get:
x = 16/3
Therefore, the equation representing the situation is 4x = y - 1, where x = 16/3 and y = 19x/4, which simplifies to:
4(16/3) = y - 1
y = 21
Therefore, there are 16 households with one pet and 5 households without any pets.
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A number is 12 greater than a second number. The sum of the two numbers is 66. What is the the smaller number?
Answer:
Step-by-step explanation:
The smaller number would be 27. If the first number is 12 greater than the 2nd number and we have to make it equal to 66. Our smaller number would be 27 becuase if we add 12 to 27 that gives us 39. 39+27= 66. Hopefully that makes sense.
I tried and it did not make sense help
Answer: D) -20.99
Step-by-step explanation:
-4.97-2.36+-5.19-8.47 = -20.99
When the temperature drops below 15°C in a building, the furnace turns on.
At what temperatures will the heater turn on? Write an inequality to represent
this situation, and graph the solution on a number line.
The inequality to represent this situation is T < 15°C, where T is the temperature.
What is inequality?Inequality is a statement that two values, expressions, or quantities are not equal. Inequality is usually represented by the symbols ">", "<", "≥", or "≤".
This inequality can be graphed on the number line by representing 15°C as a point on the number line. Any values to the left of 15°C, such as 14°C, 13°C, and so on, would be represented as points to the left of 15°C on the number line.
Less than inequality is used to compare two values to see if one is less than the other. In this case, the inequality T < 15°C states that the temperature T must be less than 15°C in order for the furnace to turn on.
Graphically, the solution to this inequality is represented by a number line with a point at 15°C and all points to the left of 15°C represented in the solution set.
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Determine the surface area of the cylinder. (Use π = 3. 14)
net of a cylinder where radius of base is labeled 5 inches and a rectangle with a height labeled 4 inches
157 in2
219. 8 in2
282. 6 in2
314 in2
The surface area of the cylinder with radius 5 inches and rectangle with height 4 inches is equal to 282.6 square inches.
Radius of the base = 5 inches
Height of the rectangle = 4 inches
Surface area of a cylinder
= area of the top and bottom circular faces + the area of the curved surface.
Here,
Rectangle represents the curved surface of the cylinder, with a height of 4 inches and a length equal to the circumference of the base.
Circumference of the base is equal to,
Circumference
= 2πr
= 2 x 3.14 x 5
= 31.4 inches (approx.)
Area of the curved surface of the cylinder is ,
Curved surface area
= Length x Height
= 31.4 inches x 4 inches
= 125.6 square inches
Area of each circular face of the cylinder is ,
Circular face area
= πr²
= 3.14 x 5²
= 78.5 square inches
Substitute the value to get total surface area of the cylinder we have,
Total surface area of the cylinder
= 2 x Circular face area + Curved surface area
= 2 x 78.5 square inches + 125.6 square inches
= 282.6 square inches (approx.)
Therefore, the surface area of the cylinder is approximately equal to 282.6 square inches.
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two angles are complementary. the measure of the larger angle is 26 degrees more than three times the measure of the smaller angle. what is the measure of each angle?
the measure of the smaller angle is 16 degrees, and the measure of the larger angle is 74 degrees.
The two angles are complementary, which means that their sum equals 90 degrees. Let x be the smaller angle, and y be the larger angle.
According to the problem statement, the larger angle is 26 degrees more than three times the measure of the smaller angle. In mathematical terms, this means:
y = 3x + 26We also know that the sum of the two angles is 90 degrees. In mathematical terms, this means:
x + y = 90 Substituting the expression for y from the first equation into the second equation,
we get: x + (3x + 26) = 90Simplifying this equation,
we get: 4x + 26 = 90 Subtracting 26 from both sides of the equation,
we get: 4x = 64Dividing both sides of the equation by 4,
we get: x = 16Substituting this value of x into the equation for y,
we get: y = 3(16) + 26 = 74
Therefore, the measure of the smaller angle is 16 degrees, and the measure of the larger angle is 74 degrees.
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Assume you are rolling two fair dice once. The probability of obtaining at least one 3 or one 4 equals
The probability of obtaining at least one 3 or one 4 when rolling two fair dice can be calculated using complementary probability. First, find the probability of not rolling a 3 or 4 on each die, and then use this to determine the probability of the desired outcome.
For a single die, the probability of rolling a 3 or 4 is 2/6 (since there are 2 favorable outcomes out of 6 possible outcomes).
Therefore, the probability of not rolling a 3 or 4 on one die is 1 - 2/6 = 4/6 or 2/3.
When rolling two dice, the probability of not rolling a 3 or 4 on both dice is the product of their individual probabilities, which is (2/3) * (2/3) = 4/9.
Now, to find the probability of obtaining at least one 3 or one 4, we use the complementary probability:
Probability(at least one 3 or one 4) = 1 - Probability(neither die shows 3 or 4) = 1 - 4/9 = 5/9.
So, the probability of obtaining at least one 3 or one 4 when rolling two fair dice is 5/9.
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in practice, the most frequently encountered hypothesis test about a population variance is a .
In practice, the most frequently encountered hypothesis test about a population variance is an F-test.
In statistics, hypothesis tests provide us with a tool to evaluate evidence about a population. Hypothesis testing is a crucial part of statistical inference, in which an analyst tests hypotheses using statistical methods such as t-tests, chi-squared tests, and analysis of variance (ANOVA).
In practice, the most commonly used hypothesis test for population variance is the F-test. This test can be used to test the null hypothesis that two population variances are equal. F-tests have a wide range of uses, including in quality control, financial analysis, engineering, and more. The F-test statistic is calculated by dividing the sample variance of one sample by the sample variance of another sample. The F-test requires that the data come from populations that follow normal distributions, and it is sensitive to outliers in the data.
Therefore, in practice, the most frequently encountered hypothesis test about a population variance is an F-test.
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.
Helpppp me Solve for x 3√x=10
Answer:
x = 100/9
Step-by-step explanation:
1) Square both sides.
[tex]9x=100[/tex]
2) Divide both sides by 9.
[tex]x = \frac{100}{9}[/tex]
Decimal Form: 11.111111
Check the answer:1) Let [tex]x = \frac{100}{9}[/tex].
[tex]3\sqrt{\frac{100}{9} } =10[/tex]
2) Simplify [tex]\sqrt{\frac{100}{9} }[/tex] to [tex]\frac{\sqrt{100} }{\sqrt{9} }[/tex].
[tex]3\times\frac{\sqrt{100} }{\sqrt{9} }=10[/tex]
3) Since 10 x 10 = 100, the square root of 100 is 10.
[tex]3\times\frac{10}{\sqrt{9} }=10[/tex]
4) Since 3 x 3 = 9, the square root of 9 is 3.
[tex]3\times\frac{10}{3} =10[/tex]
5) Cancel 3.
10 = 10
the problem I need help with asap is in the picture
Answer:
B. y less than or equal to - 2x + 1
please help with this congruent triangles
Step-by-step explanation:
75+42=117
180-117=63
Three of same angles makes the congruent triangles :)
grandma forgot how many raisins she put in a batch; you sample one loaf and count 40 raisins. how many do you estimate are in a batch? what is the the uncertainty in your estimate?
Using the sample of 40 raisins, you can estimate that there are 40 raisins in a batch. However, due to the uncertainty of the sample size, there is an element of uncertainty as to how many raisins there truly are in a batch.
Thus, the uncertainty of your estimate can range from slightly below 40 raisins to slightly above 40 raisins.
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solve the triangle PQR (find m
The length of r in the right triangle is 14.01 metres.
How to solve the side of a triangle?A right triangle is a triangle that has one of its angles 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, let's find the side r of the right triangle as follows:
using Pythagoras's theorem,
c² = a² + b²
where
c = hypotenusea and b are the other legsTherefore,
r² = 6.71² + 12.3²
r² = 45.0241 + 151.29
r = √196.3141
r = 14.0112133664
r = 14.01 metres
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