Can someone please explain this to me step by step? I am rather confused as to what to do.
Answers
The coordinate of P that divides line AB in the ratio 4:1 is (6.6, 3.8)
What is an equation?An equation is an expression that shows the relationship between numbers and variables.
If a point O(x, y) divides line segment AB with endpoints A(x₁, y₁) and B(x₂, y₂) in the ratio of n:m. The coordinates of O is:
[tex]x = \frac{n}{n+m}(x_2-x_1)+x_1 \\\\y = \frac{n}{n+m}(y_2-y_1)+y_1[/tex]
Given that P(x, y) divides line AB in the ratio 4:1. The coordinates are A(1, 3) and B(8, 4). Therefore:
[tex]x=\frac{4}{4+1}(8-1) +1=6.6\ unit\\\\y=\frac{4}{4+1}(4-3) +3=3.8\ unit[/tex]
The coordinate of P is (6.6, 3.8)
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Related Questions
The weight of an organ in adult males has a bell-shaped distribution with a mean of 330 grams and a
standard deviation of 50 grams. Use the empirical rule to determine the following.
(a) About 95% of organs will be between what weights?
(b) What percentage of organs weighs between 280 grams and 380 grams?
(c) What percentage of organs weighs less than 280 grams or more than 380 grams?
(d) What percentage of organs weighs between 180 grams and 430 grams?
Answers
According to the empirical rule -
a) About 95% of organs will be in range of weights of organs 230 grams and 430 grams.
b) 68% percentage of organs weighs between 280 grams and 380 grams.
c) 32% percentage of organs weighs less than 280 grams or more than 380 grams.
d) 97.35% percentage of organs weighs between 180 grams and 430 grams.
What is empirical rule?
The empirical rule 68-95-99.7 tells us that:
68% of the data is expected to be within 1 standard deviation from the mean.
95% of the data is expected to be within 2 standard deviation from the mean.
99.7% of the data is expected to be within 3 standard deviation from the mean.
There is a bell shaped distribution ( assume as approximately normal) with mean of 330 g and standard deviation of 50 g.
a) This happens for an interval with ±2 standard deviations from the mean.
That is:
X1 = μ + z1 × σ X2 = μ + z2 × σ
X1 = 330 - 2 × 50 X2 = 330 + 2 × 50
X1 = 330 - 100 X2 = 330 + 100
X1 = 230 X2 = 430
Therefore, the range of weights of organs is 230 grams and 430 grams.
b) Calculate the z-scores for each value to know how many standard deviations are from the mean.
z1 = (x1 - μ)/σ z2 = (x2 - μ)/σ
z1 = (280 - 330)/50 z2 = (380 - 330)/50
z1 = -50/50 z2 = 50/50
z1 = -1 z2 = 1
The values are 1 standard deviations from the mean each.
Therefore, the expected percentage is 68%.
c) This is the complementary of the point b.
Then, it is expected that (100 - 68)% = 32% of the organs weigh less than 280 grams or more than 380 grams.
d) Calculate the z-scores for each value to know how many standard deviations are from the mean.
z1 = (x1 - μ)/σ z2 = (x2 - μ)/σ
z1 = (180 - 330)/50 z2 = (430 - 330)/50
z1 = -150/50 z2 = 100/50
z1 = -3 z2 = 2
The values are 1 standard deviations from the mean each.
Therefore, the expected percentage is 68%.
The values are 3 standard deviations from the mean each. Between 180 and 330 there is 99.7%/2 = 49.85% of the data.
The values are 2 standard deviations from the mean each. Between 330 and 430 there is 95%/2 = 47.5% of the data.
Then, between 180 grams and 430 grams there is (49.85% + 47.5)% = 97.35% of the data.
Therefore, the expected percentage is 97.35%.
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Any one help me please the question is in the screenshot.
Answers
The answers include the following below:
The sale price is 85% of the regular price.The equation which can be used to find the sale price, s, of an oil change is s = 0.85(30).What is Sale price?This is referred to as the discounted price at which goods or services are being sold.
Since we were told that the discount is 15%, then the sale price will be (100-85)% of $30 which is 85% of $30.
This therefore means that the equation to find the sale price will be 85/100 × 30 = 0.85(30).
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(v) (5-6i)+(3+4i) - (5-7)
Answers
Answer:
Step-by-step explanation
In order to set premiums at profitable levels, insurance companies must estimate how much they will to pay in claims on cars of each make and model, based on the value of the car and how much damage it sustains in accidents. Let C be a random variable that represents the cost of a randomly selected car of one model to the insurance company. The probability distribution of C is given below C $0 $1000 $4000 $10,000 P(C) 0.60 0.05 0.13 0.22 The probability that the insurance company will have to pay a claim of at least $4000 for a randomly selected car is: a.0.05 b.0.13. c.0.22. d.0.35. e.0.406. The expected value of C is a.$0 b.$554 c.$2770 d.$3750 e.$40577. Which of the following is the best interpretation of expected value? (In the choices below,"Exp(C)" represents expected value you found in question 5). a.If the company insures 10 cars of this model, they know they will incur 10×Exp(C) in costs. b.The maximum cost to the company for insuring this car model is Exp(C) per car. c.The company must insure at least Exp(C) of these cars to make a profit. d.If the company insures a large number of these cars, they canexpect the cost per car to average approximately Exp(C). e.If the company insures a large number of these cars, they can expect the variability in cost per car to average approximately Exp(C).
Answers
The probability of a claim of at least $4000 is 0.35, option(d), the expected value of C is $2770 option (c), and the best interpretation is If the company insures a large number of these cars, they can expect the cost per car to average approximately Exp(C), option(d).
Given probability distribution
C $0 $1000 $4000 $10000
P(C) 0.60 0.05 0.13 0.22
The probability that the insurance company will have to pay a claim of at least $4000 for a randomly selected car is
= (1-0.60-0.05) = 0.35
so the expected value of C
= 0x0.60 + 1000x0.05 + 4000x0.13 + 10000x0.22
= 50+520+2200 = $2770
Now, the best interpretation of expected value:
If the company insures a large number of these cars, they can expect the cost per car to average approximately Exp(C).
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Exercise 2:
Identify the missing terms:
4a (-2a³+4__+3)+ 2a(__a³- 2a+_)= -2a*+12a²+26a
JE
Answers
The complete expression of the algebra is;
4a(-2a³ + 4a + 3) + 2a(3a³ - 2a + 7) = -2a⁴ + 12a² + 26a
How to expand algebraic expressions?We are given the expression as;
4a(-2a³ + 4__ + 3) + 2a(__a³ - 2a + _) = -2a* + 12a² + 26a
Expanding the left hand side gives;
-8a⁴ + __(16a) + 12a + __(2a⁴) - 4a² + __(2a)
Grouping like terms gives;
-8a⁴ + __(2a⁴) + 12a + __(2a) + __(16a) - 4a²
Factorizing out exponents gives;
a⁴(-8 + __(2)) + a(12 + __(2)) + a²((16/a) - 4)
Comparing this with the right hand side gives;
a⁴(-8 + __(2)) = -2a* -----(1)
((16/a) - 4)a² = 12a² -----(2)
(12 + __(2))a = 26a ----(3)
From eq 1, we can see that;
* = 4
From eq 2;
((16/a) - 4) = 12
16/a = 12 + 4
a = 16/16
a = 1
From eq 3;
(12 + __(2)) = 26
___ * 2 = 26 - 12
___ = 14/2
___ = 7
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Triangle AA'B'C" is the result of dilating AABC about point P by a scale factor of 2.
Answers
Answer:
FalseFalse==============================================
Explanation for problem 1
The center of dilation is point P, which is not located on line AB. This means line A'B' will move further away from P after applying the scale factor. It means segments AB and A'B' are not on the same line.
Side note: Side BC is through line P, so segment B'C' shares the same line with BC.
---------------------------
Explanation for problem 2
The scale factor enlarges the side lengths. In this case, the scale factor 2 will double each side. This in turn doubles the perimeter.
perimeter of A'B'C' = 2*(perimeter of ABC)
new perimeter = 2*(old perimeter)
Therefore, the perimeters are not the same.
Which figures have rotational symmetry?
Answers
consider the following argument, premise 1: if the sum of the digits in (student id) is divisible by 3 then (student id) is divisible by 3. premise 2: the sum of the digits in (student id) is divisible by 3. conclusion: (student id) is divisible by 3. substitute your eight-digit numeric student id for (student id) in the above argument and determine whether the argument, filled-in with your student id, is sound or unsound. justify your answer and include your student id in your explanation.
Answers
The argument, filled-in with the student ID 12345678, is sound because the two premises are true and the conclusion follows logically from them. The sum of the digits in 12345678 is 36, which is divisible by 3, so the first premise is true.
My student ID is 12345678.
The argument, filled-in with my student ID, is sound. This is because the two premises are true and the conclusion follows logically from them. The sum of the digits in 12345678 is 36, which is divisible by 3, so the first premise is true. The second premise is also true since it states that the sum of the digits in 12345678 is divisible by 3, which is the case. Therefore, the conclusion that 12345678 is divisible by 3 is logically valid from the two premises.
Student ID: 12345678
The argument, filled-in with the student ID 12345678, is sound because the two premises are true and the conclusion follows logically from them.
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Is x = 6 a solution to the equation 5(x – 3) = x + 13? Follow the steps to find out.
1. Rewrite the equation 5(x – 3) = x + 13 with 6 substituted for x. Write a question mark over the equal sign to show that you're testing to see if the equation is true.
2. Simplify both sides. Show your work.
3. Is x = 6 a solution to the equation? Why or why not?
4. Find a value of x that is a solution to 5(x – 3) = x + 13. Describe how you found the solution. (3 points)
Answers
Answer:
see below
Step-by-step explanation:
Step 1
5(x – 3) = x + 13
Step 2
See if x is a solution
5 (6-3) ?= 6+13
5 (3) ?= 19
15 ?= 19
Step 3
This is not true so it is not a solution
Step 4
5(x – 3) = x + 13
Distribute
5x-15 = x+3
Subtract x from each side
5x-x -15 = x+13-x
4x-15 = 13
Add 15 to each side
4x-13+13 = 15+13
4x =28
Divide each side by 4
4x/4 = 28/4
x = 7
7 is a solution
Answer:
First you substitute 6 for x!
5(6 - 3) = 6 + 13
6 - 3 = 3
The equation is now:
5 * 3 = 6 + 13
5 * 3 = 15
6 + 13 = 19
The result is:
15 = 19 which is not a true statement.
x is not equal to 6.
Now lets try 7.
5(7 - 3) = 7 + 13
7 - 3 = 4
7 + 13 = 20
5 * 4 = 20
Thus: x = 7
Step-by-step explanation:
Hope it helps! =D
(-1.2) (-3.5) (-2.7) (-0.4) a positive product?
Answers
We have the product of 4 negative numbers, by the rule of signs, we can see that the product is positive.
Is the product positive?Here we need to reember the rule of signs for the product, it is:
(-)*(-) = +
(+)*(+) = +
(+)*(-) = -
(-)*(+) = -
So the product between two negative numbers is positive, now let's look to our product.
(-1.2)*(-3.5)*(-2.7)*(-0.4)
We can rewrite this as:
(-1.2*-3.5)*(-2.7*-0.4)
The negative sings cancell, then we get:
(-1.2*-3.5)*(-2.7*-0.4)
(4.2)*(1.08)
Now we have the product of two positive numbers, this will be positive.
(4.2)*(1.08) = 4.536
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EACH COPAYMENT IS 20% OF THE COST FIND THE COPAYMENT AND BENIFIT AMOUNT 4,200,00+0=3,072.00
Answers
The copayment amount, given that it is 20 % of the amount is $ 840
The benefit amount is $ 3, 360
How to find the copayment amount ?A copayment for health insurance is a defined dollar amount that is determined by the insurance plan and used to divide the cost of covered treatments between the plan and the consumer.
The copayment amount is 20 % of the cost which is $ 4, 200 so the copayment is:
= 20 % x 4, 200
= $ 840
This then means that the benefit amount would be;
= Cost - copayment
= 4, 200 - 840
= $ 3, 360
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A biologist is studying the plant diversity in 15 million acres of the Sierra Nevada Mountains. He will count the number of species in 150 acres. Match the strategies to their corresponding sampling techniques.
The biologist goes to his 150 favorite hiking places and looks at an acres along each trail.
The biologist orders the 15 million acres by latitude and then surveys every 100000th acre on the list.
The biologist classifies the Sierras into 10 different ecological types and then makes sure that the proportion of each ecological type from the sample is the same as the proportion of that of the population.
The biologist goes to 15 diverse locations that have 10 acres each and surveys all 10 acres for each of these 15 locations.
The biologist enters the 15 million acres into a data base and had a computer randomly select 150 of these acres.
Cluster Sampling
Systematic Sampling
Convenience Sampling
Stratified Sampling
Simple Random Sampling
Answers
Answer:
The biologist goes to his 150 favorite hiking places and looks at an acre along each trail: Random Sampling.
The biologist orders the 15 million acres by latitude and then surveys every 100000th acre on the list: Stratified Sampling.
The biologist classifies the Sierras into 10 different ecological types and then makes sure that the proportion of each ecological type from the sample is the same as the proportion of that of the population: Stratified Sampling.
The biologist goes to 15 diverse locations that have 10 acres each and surveys all 10 acres for each of these 15 locations: Cluster Sampling.
The biologist enters the 15 million acres into a data base and had a computer randomly select 150 of these acres: Random Sampling.
give me brainiestGraph the inequality below on the number line.
y>-10
Answers
The graph of the inequality y > -10 is given by the image presented at the end of the answer.
What are the inequality symbols?The four inequality symbols, along with their meaning, are presented as follows:
> x: greater than x.< x: less than x.≥ x: at least x.≤ at most x.The inequality for this problem is given as follows:
y > -10.
Which means that the solution is the numbers that are greater = to the right of -10, with an open interval.
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In order to produce my movie, I need to shoot a scene for a high-speed chase and I need to shoot a scene for a bank robbery. The film production crew will be putting the movie together. I have the stunt crew for the chase scene from 10 am to 11 am and I have the stunt crew for the robbery from 6pm to 7 pm. Will the order I shoot the scenes in matter? What mathematical property did you use to answer this question?
Answers
The order in which you shoot the scenes will not matter in terms of the final outcome of the movie.
The mathematical property that one can use to answer this question is scheduling.
How to illustrate the information?From the information, in order to produce the movie, one needs to shoot a scene for a high-speed chase and need to shoot a scene for a bank robbery.
Here, the film production crew will be putting the movie together. However, it may impact the logistics of the production process and the scheduling of the crews. It is not a mathematical property that I used to answer this question. It is simply a matter of logistics and scheduling.
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PLEASE HELP!!!!! Complete the two-column proof.
Answers
The equation will be 5x + 7x = 180. Then the value of the variable 'x' will be 15.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
∠TSR = 5x and ∠UVW = 7x
Angle ∠TSR and angle ∠UVW are the supplementary angles. Then the equation is given as,
5x + 7x = 180
12x = 180
x = 180 / 12
x = 15
The equation will be 5x + 7x = 180. Then the value of the variable 'x' will be 15.
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Penny created a circle graph to show what percentage of students in her class walk to school, ride the bus, or ride in a car.
What percent of students in Penny’s class ride the bus to school?
HELPPPP ASAPPPPP
Answers
Answer:
45
Step-by-step explanation:
100-25-30=45
Round 11,900 to the nearest thousand.
Answers
Answer:
12,000
Step-by-step explanation:
How can we do this?
We can do this by taking the number 11,900,
11,900
looking at the hundredths place,
11,900
and figuring out if it is closer to 10, or 0. 9 is closer to 10, so we round up.
12,000
Therefore, 11,900 rounded to the nearest thousand is 12,000.
item 18 time remaining 4 hours 13 minutes 48 seconds 04:13:48 ebook item 18 time remaining 4 hours 13 minutes 48 seconds04:13:48 if bob can produce more donuts in one day, if
Answers
If Bob is able to produce more donuts than Sue in one day, that means that Bob has an absolute advantage in the production pf donuts.
Absolute advantage is when a particular person is able to produce more amount of product than the other with the same amount of input of resources, for example, time. Comparative advantage on the other hand is based on the opportunity cost.
Comparative advantage is basically the ability to produce a good or a service for an opportunity cost which is lower than that of a competitor. Since, Bob is able to produce more donuts than Sue, Bob has an absolute advantage over Sue.
--The given question is incomplete, the complete question is
If Bob can produce more donuts in one day than Sue can produce in one day, then:
a. Bob has a comparative advantage in the production of donuts.
b. Sue has a comparative advantage in the production of donuts.
c. Bob has an absolute advantage in the production of donuts.
d. Sue has an absolute advantage in the production of donuts."--
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The perimeter of a certain rectangle is 26 m. Also, the difference between the length of the rectangle and the breath is 3 m. Find the length and the breadth of the rectangle.
Answers
A rectangle having perimeter 26 m has a length of 8m and breadth of 5m.
What is perimeter?
The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.
The value for perimeter of a rectangle is - 26 m
Let x be the length of the rectangle and y be the breadth.
The formula for perimeter of rectangle is 2(l + b)
From the given information, it is known that -
Perimeter = 2(x + y) = 26 m...(1)
Difference between the length and breadth = x - y = 3 m....(2)
Use the first equation to solve for one of the variables in terms of the other -
2x + 2y = 26
x + y = 13....(3)
Add equation (2) and (3) -
x + y + x - y = 13 + 3
2x = 16
x = 16/2
x = 8 m
Now substitute the value of x in equation (2) -
x - y = 3
8 - y = 3
y = 8 - 3
y = 5 m
Therefore, the length is 8 m and the breadth is 5 m.
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mation.
2) (x-3)(x-8)= 0
Answers
Answer:
x-3 =0 or x-8 =0
x= +3 or x = +8
(x - 3)(x - 8) = 0
We will solve for x, this problem will have two solutions.
First, we will make both equations equal to 0:
x - 3 = 0
x - 8 = 0
Next, solve for x, add 3 and 8 to both sides:
x = 3
x = 8
There are your two solutions. Hope this step by step explanation helped!
A sample was taken of the salaries of four employees from a large company. The following are their salaries (in thousands of dollars) for this year. 33 31 24 36 The variance of their salaries is A. 5.1. B. 31. C. 26.
Answers
The variance of the four employees' salaries is 5.1, meaning that the difference in their salaries is 5.1 thousand dollars.
Step 1: Find the mean of the four salaries
33 + 31 + 24 + 36 = 124
124 ÷ 4 = 31
Mean = 31
Step 2: Find the difference between each salary and the mean
33 - 31 = 2
31 - 31 = 0
24 - 31 = -7
36 - 31 = 5
Step 3: Square each of the differences
2² = 4
0² = 0
(-7)² = 49
5² = 25
Step 4: Add up the squared differences
4 + 0 + 49 + 25 = 78
Step 5: Divide the sum by the number of salaries (minus 1)
78 ÷ (4 - 1) = 78 ÷ 3 = 26
Step 6: Take the square root of the variance
√26 = 5.1
Variance = 5.1
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In this diagram, circle A has radius = 11.5 and BC = 13.1. BC is a tangent line, calculate the distance of CD.
Answers
The distance of CD is 5.93.
What is Circle?Circle is a two dimensional figure which consist of set of all the points which are at equal distance from a point which is fixed called the center of the circle.
Given a circle.
Radius of circle = 11.5
AB = AD = 11.5
Since the tangent line is perpendicular to the radius of the circle at the point of tangency, ABC is a right angled triangle.
AC² = AB² + BC²
= 11.5² + 13.1²
= 303.86
AC = 17.432
CD = AC - AD
= 17.432 - 11.5
= 5.93
Hence the distance of CD is 5.93.
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Please helppp with this question
Answers
On solving the system of linear equations 3x + 3y = 45 and x + 2y = 24, the cost for each shirt is obtained as $6, and cost for each pair of pants is obtained as $9.
What is a linear equation?
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
Let the cost of shirts be x and the cost of pair of pants be y.
The number of shirts bought by person A = 3
The number of pair of pants bought by person B = 3
The total cost for person A = $45
The equation for person A is -
3x + 3y = 45....(1)
The number of shirts bought by person B = 1
The number of pair of pants bought by person B = 2
The total cost for person B = $24
The equation for person B is -
x + 2y = 24....(2)
Multiply equation (2) by 3 -
3(x + 2y) = 24 × 3
3x + 6y = 72....(3)
Subtraction equation (1) from equation (3) -
3x + 6y - (3x + 3y) = 72 - 45
3x + 6y - 3x - 3y = 27
3y = 27
y = 9
Substitute the value of y in equation (2) -
x + 2(9) = 24
x + 18 = 24
x = 24 - 18
x = 6
Therefore, the cost of shirts and pants is x = 6 and y = 9 respectively.
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What is the total area, in square inches, of the shaded sections of the trapezoid below? 5 in 6.3 in 8 in 5.4 in
Answers
The total area of the shaded sections of the trapezoid in square inches is 32.76 square inches.
What is area?An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely fill the entire surface of an enclosed figure. The square unit, which is frequently expressed as square inches, square feet, etc., is the accepted unit of area.
The shaded sections in the trapezoid are triangles.
The area of the triangle is given by the following formula:
A = 1/2 (b)(h)
For the first triangle, b = 5 and h = 6.3. Substituting the value in the formula we have:
A1 = 1/2 (5)(6.3)
A1 = 15.75
For the second triangle, b = 5.4 and h = 6.3. Substituting the value in the formula we have:
A2 = 1/2 (5.4)(6.3)
A2 = 17.01
The total area of the shaded region of the trapezoid is calculated by adding the area of the individual shaded portion:
A = A1 + A2
A = 15.75 + 17.01
A = 32.76
Hence, the total area of the shaded sections of the trapezoid in square inches is 32.76 square inches.
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The average pencil has 5,425 pencil shavings. How many pencils are found in 76,450 pencil shavings?
Answers
Answer:
14
Step-by-step explanation:
We can divide 76,450 shavings by the average shavings per pencil, 5,425 to get an answer of 14.09... This can be rounded to 14.
please help will mark BRAINLIEST
Answers
Answer:
100
Step-by-step explanation:
total angles of any triangle is 180
it tells you one of the base angles is 40, so 2 of them are 80
so the top one is 180-80 =100
Multiply mentally 70 • 100 • 400 = (Type a whole number)
Answers
big lake bob spends his time carving fishing lures and duck decoys. if big lake bob spends all of his time carving fishing lures he can carve 125 lures in a week. if he spends all of his time carving duck decoys he can carve 20 decoys in a week. for every 4 duck decoys big lake bob carves he must give up 25 fishing lures. Fill in the values in the table below to complete Big Lake Bob's production possibilities schedule. Fising Lures Duck Decoys 100 0 0 30
Answers
50 fishing lures are carved in a week.
A) Big Lake Bob
Production Possibilities Schedule:
Fishing Lures Duck Decoys
100 0
90 5
80 10
70 15
60 20
50 25
40 30
30 35
20 40
10 45
0 50
50 fishing lures are carved in a week.
25 duck decoys are crafted in a week.
This implies that Big Lake Bob forgoes 10 fishing lures for every 5 duck decoys he carves.
Large Lake Schedule of Bob's productivity potentials
B) Bob's potential for production The schedule is a table of numbers that shows the various combinations of two items that can be created using the restricted resources (labor hours, capital, materials, etc.) and technology in Bob's economy.
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Find the Area of the figure below, composed of a rectangle with a semicircle removed from it. Round to the nearest tenths place.
Answers
Answer:
39.9
Step-by-step explanation:
Rectangle: area = length × width
Semicircle: area = 0.5πr²
total area = 9 × 6 - 0.5 × 3.14159 × 3²
total area = 39.9
Use the theorems from Section 3.2 and the converses of those theorems in this section to write three biconditional statements about parallel lines and transversals.
Answers
The slopes of the two lines that form them must be equal (m1 = m2). This implies that the two lines are parallel.
1) Biconditional statement: If two lines are parallel, then the alternate interior angles formed by a transversal are equal.
Formula: m∠1 = m∠3 and m∠2 = m∠4
Calculation: If two lines are parallel with a transversal intersecting them, the slopes of the two lines must be equal (m1 = m2) and the alternate interior angles formed by the transversal must have the same measure (m∠1 = m∠3 and m∠2 = m∠4).
2) Biconditional statement: If two lines are parallel, then the corresponding angles formed by a transversal are equal.
Formula: m∠1 = m∠4 and m∠2 = m∠3
Calculation: If two lines are parallel with a transversal intersecting them, the slopes of the two lines must be equal (m1 = m2) and the corresponding angles formed by the transversal must have the same measure (m∠1 = m∠4 and m∠2 = m∠3).
3) Biconditional statement: If two angles are equal, then the lines that form them are parallel.
Formula: m1 = m2
Calculation: If two angles have the same measure, then the slopes of the two lines that form them must be equal (m1 = m2). This implies that the two lines are parallel.
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