Answers
Answer:
below
Step-by-step explanation:
To show that (AB)^-1 = B^-1A^-1, we need to show that:
(AB)(B^-1A^-1) = (B^-1A^-1)(AB) = I
where I is the identity matrix.
Using the associative property of matrix multiplication, we can simplify the left-hand side of the equation as:
(AB)(B^-1A^-1) = A(BB^-1)A^-1 = AIA^-1 = AA^-1 = I
Similarly, using the associative property of matrix multiplication, we can simplify the right-hand side of the equation as:
(B^-1A^-1)(AB) = B^-1(A^-1A)B = B^-1IAB = BB^-1 = I
Therefore, we have shown that (AB)^-1 = B^-1A^-1.
To show this identity, we need to demonstrate that:
(AB)^-1 = B^-1 A^-1
To do this, we start by multiplying both sides of the equation by (AB):
(AB)^-1 (AB) = B^-1 A^-1 (AB)
On the left side, we know that (AB)^-1 is the inverse of AB. So we can simplify to:
I = B^-1 A^-1 (AB)
Where I is the identity matrix. We can now simplify the right side by rearranging the terms:
B^-1 A^-1 (AB) = B^-1 (A^-1 A) B
Since A^-1 A = I, we can simplify further to:
B^-1 (A^-1 A) B = B^-1 IB = B^-1 B = I
Therefore, we have shown that:
(AB)^-1 = B^-1 A^-1
Q.E.D.
Related Questions
Find the volume of the two prisms.
someone pls help me I need to ace this test
Answers
Therefore, the total volume of the two prisms is 10,404 cubic inches.
What is volume?Volume is a measure of the amount of space occupied by a three-dimensional object. It is typically measured in cubic units, such as cubic meters (m³), cubic feet (ft³), or cubic centimeters (cm³). The volume of an object is calculated by multiplying its length, width, and height or by using an appropriate formula for the shape of the object.
Here,
The two prisms have the same dimensions of 17 inches in height, 18 inches in base, and 17 inches in length and width.
To find the volume of a prism, we multiply the area of the base by the height. The base of the prism is a rectangle with length 18 inches and width 17 inches, so the area of the base is:
Area of base = length × width
= 18 in × 17 in
= 306 in²
Therefore, the volume of one prism is:
Volume = area of base × height
= 306 in² × 17 in
= 5202 in³
The volume of the two prisms combined is simply twice the volume of one prism:
Total volume = 2 × 5202 in³
= 10404 in³
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The data represents the heights of eruptions by a geyser. Use the heights to construct a stemplot. Identify the two values that are closest to the middle when the data are sorted in order from lowest to highest. Which plot represents a stemplot of the data? * Height of eruption (in.) 66 32 50 900 50 40 70 70 59 61 60 88 80 50 63 54 62 73 70 49
Answers
The values closest to these middle elements are 60 and 61 inches.
How do we use stemplot to find the middle data?To construct a stemplot for the given data, we need to separate each observation into a stem and a leaf. The stem is the digit(s) on the left-hand side of the decimal point, while the leaf is the digit on the right-hand side. The stemplot for the given data is:
3 | 2
4 | 0 9 9
5 | 0 0 0 4 4 9
6 | 1 2 3
7 | 0 0 3 0
8 | 0 8
9 | 0
To find the two values that are closest to the middle, we need to sort the data in order from lowest to highest:
We have 19 observations, so the middle two observations are the 10th and 11th values, which are 60 inches and 61 inches, respectively. Therefore, the two values closest to the middle are 60 inches and 61 inches.
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The values closest to these middle elements are 60 and 61 inches.
How do we use stemplot to find the middle data?To construct a stemplot for the given data, we need to separate each observation into a stem and a leaf. The stem is the digit(s) on the left-hand side of the decimal point, while the leaf is the digit on the right-hand side. The stemplot for the given data is:
3 | 2
4 | 0 9 9
5 | 0 0 0 4 4 9
6 | 1 2 3
7 | 0 0 3 0
8 | 0 8
9 | 0
To find the two values that are closest to the middle, we need to sort the data in order from lowest to highest:
We have 19 observations, so the middle two observations are the 10th and 11th values, which are 60 inches and 61 inches, respectively. Therefore, the two values closest to the middle are 60 inches and 61 inches.
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The figure shows two parallel lines intersected by a transversal. One of the
angle measures is given. Find the measure of the indicated angle.
Find the measure of angle 5.
6
5
19°
4
3
2
Answers
Answer:
161
Step-by-step explanation:
angle 5 is supplementary to the given angle 180-1
Hi can i convert the binary number 1000000 to a hexadecimal number?
Answers
Answer: yes, the hex of the number 1,000,000 would be 40.
Help me solve this for class please
Answers
Answer:
Step-by-step explanation:
(a) π/4
(b) 0
(c) 1
(d) 1
(e) 2/3
(f) 1/2
Miller Toy Company manufactures a plastic swimming pool at its Westwood Plant. The plant has been experiencing problems as shown by its June contribution format income statement below:
Flexible
Budge
Actual
Sales (7,000 pools)
$265,000 $265,000
Variable expenses:
Variable cost of goods sold*
79,240
97,525
Variable selling expenses
19,000
19,000
Total variable expenses
98,240
116,525
Contribution margin
166,760
148,475
Fixed expenses:
Manufacturing overhead
Selling and administrative
Total fixed expenses
Net operating income (loss)
67,000
67,000
85,000
85,000
152,000
152,000
$ 14,760 $ (3,525)
Janet Dunn, who has just been appointed general manager of the Westwood Plant, has been given instructions to "get things under control. Upon reviewing the plant's income statement, Ms. Dunn has concluded that the major problem lies in the variable cost of goods sold. She has been provided with the following standard cost per swimming pool:
Direct materials
Direct labor
Variable manufacturing overhead
Total standard cost per unit
Standard
Quantity or
Hours
3.5 pounds
0.4 hours
0.3 hours
Standard Price or Rate
§ 2.10 per pound
$ 7.60 per hour
$ 3.10 per hour
Standard
Cost
$ 7.35
3.04
0.93
$ 11.32
During June, the plant produced 7,000 pools and incurred the following costs:
a. Purchased 29,500 pounds of materials at a cost of $2.55 per pound.
b. Used 24,300 pounds of materials in production. (Finished goods and work in process inventories are insignificant and can be ignored.)
c. Worked 3,400 direct labor-hours at a cost of $7.30 per hour.
d. Incurred variable manufacturing overhead cost totaling $8,400 for the month. A total of 2,400 machine-hours was recorded.
It is the company's policy to close all variances to cost of goods sold on a monthly basis
Required:
1. Compute the following variances for June:
a. Materials price and quantity variances
b. Labor rate and efficiency variances.
c. Variable overhead rate and efficiency variances.
2. Summarize the variances that you computed in (1) above by showing the net overall favorable or unfavorable variance for the month.
Answers
a. Materials price variance = (Standard price - Actual price) x Actual quantity
= ($2.10 - $2.55) x 24,300 pounds
= -$10,935 (Unfavorable)
b. Materials quantity variance = (Standard quantity - Actual quantity) x Standard price
= (3.5 pounds - 24,300 pounds) x $2.10 per pound
= -$48,465 (Unfavorable)
Labor rate and efficiency variances:
a. Labor rate variance = (Standard rate - Actual rate) x Actual hours
= ($7.60 - $7.30) x 3,400 hours
= $1,020 (Favorable)
b. Labor efficiency variance = (Standard hours - Actual hours) x Standard rate
= (0.3 hours - 3,400 hours) x $7.60 per hour
= -$23,600 (Unfavorable)
Variable overhead rate and efficiency variances:
a. Variable overhead rate variance = (Standard rate - Actual rate) x Actual hours
= ($3.10 - $8,400/2,400 hours) x 2,400 hours
= -$2,800 (Unfavorable)
b. Variable overhead efficiency variance = (Standard hours - Actual hours) x Standard rate
= (0.3 hours - 2,400 hours) x $3.10 per hour
= -$7,194 (Unfavorable)
Net overall favorable or unfavorable variance for the month:
To calculate the net overall variance, we sum up all the variances:
Overall Variance = Materials price variance + Materials quantity variance + Labor rate variance + Labor efficiency variance + Variable overhead rate variance + Variable overhead efficiency variance
= -$10,935 + (-$48,465) + $1,020 + (-$23,600) + (-$2,800) + (-$7,194)
= -$94,014 (Unfavorable)
For each triangle, calculate the ratio of the opposite side to the adiacent side to two decimal places. How do they compare?
Answers
Answer:
[tex]Triangle\: 1: } \dfrac{opposite}{adjacent} = \dfrac{16}{39.6} = \boxed{0.40404\cdots}[/tex]
[tex]Triangle\: 2: } \dfrac{opposite}{adjacent} = \dfrac{48}{118.8} = \boxed{0.40404\cdots}[/tex]
Choice C: The ratio is the same for both triangles
Step-by-step explanation:
[tex]Triangle\: 1: } \dfrac{opposite}{adjacent} = \dfrac{16}{39.6} = \boxed{0.40404\cdots}[/tex]
[tex]Triangle\: 2: } \dfrac{opposite}{adjacent} = \dfrac{48}{118.8} = \boxed{0.40404\cdots}[/tex]
So both ratios are the same. This is also because the ratios represent the tan of the angle that the adjacent side makes with the hypotenuse and this angle of 22° is same in both triangles
1. a gallon of water weighs 8 1/3 lbs.
a. what is the weight of 25
gallons of water?
b. If the weight of an empty 25 gallon tank is 1/10 of the water it can hold, what is the weight of the tank?
c. what is the weight of a 25 gallon tank filled with water?
Answers
B. ((8+1/3)25)/10
C. A+B
K
The reading speed of second grade students in a large city is approximately normal, with a mean of 88 words per
minute (wpm) and a standard deviation of 10 wpm. Complete parts (a) through (f).
(a) What is the probability a randomly selected student in the city will read more than 94 words per minute?
The probability is 0.2743.
(Round to four decimal places as needed.).
Interpret this probability. Select the correct choice below and fill in the answer box within your choice.
OA. If 100 different students were chosen from this population, we would expect
per minute.
OB. If 100 different students were chosen from this population, we would expect
minute.
OC. If 100 different students were chosen from this population, we would expect
per minute.
to read more than 94 words
to read exactly 94 words per
to read less than 94 words
Answers
If 100 different students were chosen from this population, we would expect approximately 27 of them to read more than 94 words per minute. Therefore, the correct choice is (A).
How to explain the probabilityThe probability that a randomly selected student in the city will read more than 94 words per minute is 0.2743.
z-score = (x - μ) / σ = (94 - 88) / 10 = 0.6
Therefore, the probability of a z-score being greater than 0.6 is:
P(Z > 0.6) = 1 - P(Z < 0.6) = 1 - 0.7257 = 0.2743
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1. If the gross domestic product of a country is significantly higher in one year than in another, what
might account for the difference
a. population growth
b. greater available resources and technological advances
Oc. inflation
C.
d. all of these
2. The Lorenz Curve for the United States indicates that the richest 20 percent of households have
what percentage of the nation's income
a. 20 percent
b. 3.8 percent
c. 90 percent
d. 46.8 percent
3. The economic condition most likely to be caused by a war affecting oil production in the
Mid East would be
a. demand-pull inflation
b. cost-push inflation
c. deflation
d. cost of living inflation
Answers
1. If the gross domestic product of a country is significantly higher in one year than in another, the factor that might account for the difference is d. all of these.
2. The Lorenz Curve for the United States indicates that the richest 20 percent of households have d. 46.8 percent of the nation's income.
3. The economic condition most likely to be caused by a war affecting oil production in the Mid East would be a. demand-pull inflation.
What is the gross domestic product?The gross domestic product or GDP refers to the total monetary value of goods produced and services provided in a country during one specific period.
What is the Lorenz Curve?The Lorenz Curve, developed by Max Lorenz measures income inequality or wealth inequality using a graphical representation.
What is demand-pull inflation?When there is a shortage in supply, pressure is mounted on the available quantity of an item, causing its price to increase.
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A rectangle has a height of 4x and a width of 3x +1. Express the area of the entire rectangle. Expression should be expanded. Area =
Answers
Answer:
12[tex]x^{2}[/tex]+4x
Step-by-step explanation:
area = width * height
substitution: area = (3x+1)*4x
distributive property: area = (4x*3x)+(4x*1)
simplify: area = 12[tex]x^{2}[/tex]+4x
Find the area of shaded region.
Answers
Answer: A is 36 cm^2
Step-by-step explanation:
In the diagram shown, Δ ABC is equilateral. AD is an altitude.
10). ∠ ABD = ______.
11). ∠ ADB = ______.
12). ∠ BAD = _____.
13). ∠ CAD = _____.
Suppose AB = 6. Find:
14). BD
15). AD
16). Area of Δ ABC
Answers
The missing sides of the triangle are
10). ∠ ABD = 60 degrees
11). ∠ ADB = 90 degrees
12). ∠ BAD = 30 degrees
13). ∠ CAD = 30 degrees
How to find the missing sides in the triangle14. BD is half of the length = BC / 2 = 6/2 = 3
15. AD is the height this is solved using Pythagoras theorem as below
AD^2 = AB^2 - BD^2
AD^2 = 6^2 - 3^2
AD^2 = 36 - 9
AD = sqrt (27)
16. Area of Δ ABC
= 1/2 * base * height
= 1/2 * 6 * sqrt (27)
= 9 sqrt (3)
= 15.59 square units
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a. Find angle x
b. What kind of angle is angle x ?
Answers
Answer: if the first angle is 61° then the angle x is 119°
but if the first angle is 67 then the angle x is 113°
Step-by-step explanation:
Line is 180° that means our formula will look like that 67 or 61 + x = 180 in that case we have to calculate x ⇒ 180 - 61 or 67 = x
The product of two numbers is 1296. If one number is16 times the other, find the number.
Answers
your aanswer is 9 ⚡
The value of numbers are,
⇒ 9 and 16
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
We have to given that;
The product of two numbers is 1296.
And, one number is 16 times the other,
Let first number = x
Hence, Second number is, 16x
So, We get;
⇒ 16x × x = 1296
⇒ 16x² = 1296
⇒ x² = 81
⇒ x = 9
Hence, first number = 9
And, Second number is,
= 16x
= 16 x 9
= 144
Thus, The value of numbers are,
⇒ 9 and 16
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What is (1/4) to the second power
Answers
Answer:
1/16
Step-by-step explanation:
(1/4)x(1/4)= 1/16
ANSWER THIS FIRST GET BRAINLESS W EXPLANATION!
3. Combine terms: 12a + 26b -4b – 16a.
(a) 4a + 22b,
(b) -28a + 30b,
(c) -4a + 22b,
(d) 28a + 30b.
Answers
To solve this equation by combining terms, the answer will be: (c) -4a + 22b.
How to solve the equationTo solve the equation, we need to combine like terms together. This means that the figures with the suffix, a will come together, while those with the suffix, b will also align themselves. Going by this rule, we will have:
12a -16a + 26b -4b.
= -4a + 22b
When a higher number is to be subtracted from a smaller number, the result will be a negative number as is the case with the terms that have the 'a' initials.
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How many bucket loads would it take to bucket out the world’s ocean
Answers
Answer:
Impossible to know, or best guess
Step-by-step explanation:
It is impossible to determine exactly how many bucket loads it would take to empty the world's ocean because the volume of the ocean is constantly changing due to factors such as tides, currents, and sea level rise. However, we can estimate the approximate volume of the ocean and calculate the number of bucket loads needed based on that estimate.
The approximate volume of the world's ocean is 1.332 billion cubic kilometers (km³) or 332.5 million cubic miles (mi³). Assuming that each bucket can hold 10 liters or 0.01 cubic meters (m³) of water, we can calculate the number of bucket loads needed to empty the ocean as follows:
1 km³ = 1,000,000,000 m³
1,332,000,000 km³ = 1.332 x 10¹⁸ m³
1.332 x 10¹⁸ m³ / 0.01 m³ per bucket = 1.332 x 10²⁰ bucket loads
Therefore, it would take approximately 1.332 x 10²⁰ or 133,200,000,000,000,000,000 bucket loads to empty the world's ocean. This number is so large that it is practically impossible to even visualize, let alone accomplish.
Another answer provided by our lord and savior (That one green ai)
A rectangle has perimeter 70 inches, and its area is 286 sq-inches. Find the dimensions of this
rectangle. (For purposes of this problem only, the width is shorter than the length.)
length =
width=
inches
inches
Enter your answers as numbers. If necessary, round to the nearest hundredths.
Answers
Thus, the dimensions of the rectangle are - length 22 inches and width 13 inches.
Explain about the rectangle:An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). The opposite sides of a rectangular are equal and parallel. A rectangle has two dimensions—length and width—because it is a two-dimensional form. The rectangle's longer side is its length, while its shorter side is its breadth.
Let the length of rectangle be 'l'
Let the width be 'w'.
Then,
Perimeter = 2(l + w)
70 = 2(l + w)
35 = l + w
l = 35 - w ...eq 1
Now,
Area = length * width
286 = l*w ...eq 2
Put eq 1 in eq 2
286 = (35 - w)*w
286 = 35w - w²
w² - 35w + 286 = 0
Solving the quadratic equation:
w² - 22w - 13w + 22*13 = 0
w(w - 22) - 13(w - 22)= 0
(w - 22)(w - 13) = 0
w = 22 and w = 13
As, length is greater than width-
width w = 13 inch
Length l = 35 - 13 = 22 inches.
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Approximately 8% of all people have blue eyes. A random sample of 20 people is selected, find μ. Round to one decimal place. Answer
Answers
Answer:
The mean of a binomial distribution is μ = np, where n is the sample size and p is the probability of success (having blue eyes).
μ = 20 x 0.08
μ = 1.6
Rounded to one decimal place, μ is 1.6.
Simplify using the vertical method
Answers
This method can be used to quickly obtain the product of two polynomials.A-6k²+25k²-16k-15.
What is expression?Expression in math is a combination of numbers, symbols and operators that represent a mathematical quantity or operation. It can be a single number, a single variable, or a combination of numbers, variables and symbols combined together to form a mathematical statement. An expression can also include functions, such as polynomials, exponential functions, or logarithmic functions.
The vertical method involves writing the terms of the two factors side by side and multiplying them together to get the product.
(3k+5) (2k²-5k-3)
6k³ + 0k² + 0k + -15
0k³ + 10k² + -15k + 0
0k³ + 5k² + -15k + 0
0k³ + 0k² + 15k + 0
Adding the terms in each column yields the product:
A-6k³+25k²-16k-15
Therefore, the correct answer is A-6k³+25k²-16k-15.
In conclusion, using the vertical method can simplify algebraic multiplication problems by breaking them down into columns and adding the terms in each column. This method can be used to quickly obtain the product of two polynomials.
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Two different functions are represented.
Function A:
X
0
1
2
3
4
f(x)
5
10
20
40
80
Function B:
Which statement best compares the two functions?
Neither function A nor function B has an x-intercept.
Neither function A nor function B has a y-intercept.
The domain and range of both functions contain only
positive numbers.
O The domain and range of both functions contain only
positive numbers and zero.
Answers
Okay, let's analyze the two functions based on the options:
Function A:
X f(x)
0 5
1 10
2 20
3 40
4 80
Options:
Neither function A nor function B has an x-intercept. - False, function A has an x-intercept at x=0.
Neither function A nor function B has a y-intercept. - False, function A has a y-intercept at f(x)=5.
The domain and range of both functions contain only positive numbers. - False, function A has values that include 0.
The domain and range of both functions contain only positive numbers and zero. - True, the domain and range of both functions contain only non-negative numbers including 0.
Therefore, the correct choice is:
O The domain and range of both functions contain only positive numbers and zero.
Let me know if you have any other questions!
Are the functions f(x) and g(x) inverses of each other? Use composition of functions to determine your answer.
f(x) = 7x-1
x+1
g(x)
O Yes
O No
Answers
Calculate the monthly finance charge for the credit card transaction. Assume that it takes 10 days for a payment to be received and recorded, and that the month is 30 days long. (Round your answers to the nearest cent.)
$500 balance, 16%, $50 payment
(a) previous balance method $
(b) adjusted balance method $
(c) average daily balance method
Answers
Interest charge for the month = 51.69 rounded to the nearest penny.
Here, we have,
The particular month in question is 30 days long.
Your balance at the start of the month is 3,000.
Annual interest rate = 21%.
Payment = 150.00.
When the payment is made in the month, it reflects on the tax amount you pay on both the average day balance.
YOU SEND THE PAYMENT IN ON THE FIRST DAY OF THE MONTH.
YOUR ACCOUNT IS CREDITED ON THE 11TH DAY OF THE MONTH.
Average daily balance is 3000 from day 1 until day 10 (10 days)
Average daily balance is 2850 from day 11 until day 30 (20 days)
Average daily balance for the month = 10 * 3000 + 20 * 2850
= 87000 / 30
= 2900
Interest charge for the month = 0.21 * 2900 * 30 / 365
Interest charge for the month = 50.05 rounded to the nearest penny
YOU SEND THE PAYMENT IN ON THE TWENTIETH DAY OF THE MONTH.
YOUR ACCOUNT IS CREDITED ON THE 30TH DAY OF THE MONTH.
Average daily balance is 3000 from day 1 until day 29 (29 days)
Average daily balance is 2850 from day 30 until day 30 (1 day)
Average daily balance for the month = 3000 * 29 + 1 * 2850
= 89850 / 30
= 2995
Interest charge for the month = 0.21 * 2995 * 30 / 365
Interest charge for the month = 51.69 rounded to the nearest penny
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Complete Question:
Calculate the monthly finance charge for the following credit card transaction. Assume that it takes 10 days for a payment to be received and recorded and that the month is 30 days long. Round your answer to the nearest cent.
3,000 balance, 21% rate, 150 payment, average daily method
help with calculus. determine wheter each labeled point is an absolute maximum or minumum OR a relative maximum or minimum or neither
Answers
The relative maximum and minimum point as well as the absolute maximum and minimum points based on labeled points on the graph are;
Points 1, 3, and 5 are relative maximum points
Points 2 and 4 are relative minimum points
Point 5 is an absolute maximum point
Point 2 is an absolute minimum point
What is a relative maximum point?A relative maximum is a point in which the maximum with regards to the immediate surrounding points.
Therefore, the relative maximum points are;
The points 1, 3, and 5
The relative minimum points are points that are the minimum points, when compared with the surrounding points
The relative minimum are the points 2 and 4
The absolute maximum is the point which is at the highest point on the graph
The absolute maximum on the graph is therefore, the [oint 5
The absolute minimum on the graph is the point which is the minimum point compared to all other points
Therefore, the absolute minimum point is the point 2
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Fill in the blanks.
The depth of the snow in my yard is normally distributed, with a mean of 2.5 inches and a standard
deviation of 0.25 inches.
What value is one standard deviation below the mean?
Hint: Read the section on the empirical rule.
inches
What value is one standard deviation above the mean?
I
What is the probability that a randomly chosen location will have a snow depth between 2.25 and 2.7
inches? 68
percent
Submit Question
inches
Answers
Where the above conditions existing, the probability that a randomly selected site will have a snow depth between 2.25 and 2.7 inches is 68.3 %.
What is the explanation for this ?t the value The value one standard deviation below the mean is 2.25 inches.
The value one standard deviation above the mean is 2.75 in.
To find the probability , calculate the z-scores for these values
z1 = (2.25 - 2.5 ) /0.25 = -1
z2= ( 2.7 -2.5 ) / 0.25 = 0.8
Using a standard normal distribution table ....
we can see that the probability of a z- score between -1 and 0.8 is approximately 0.683, or 68.3%.
Hence, the probability that a randomly chosen location will have a snow depth between 2.25 and 2.7 inches is 68.3%.
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Pedrobuysawheelbarrowpricedat$86.Shippingandhandlingareanadditional30%oftheprice.HowmuchshippingandhandlingwillPedropay?
Answers
The price of the wheelbarrow is $86, and Pedro will need to pay an additional 30% of the price for shipping and handling.
To calculate the shipping and handling cost, we can first find 30% of the price of the wheelbarrow:
30% of $86 = 0.3 x $86 = $25.80
Therefore, Pedro will need to pay $25.80 for shipping and handling.
line with slope m
below:
2|5
and containing the point (10,-5). Type your answer is slope-inte
Answers
Step-by-step explanation:
y=mx+b
y= -5 x= 10
-5 = 2/5 (10) + b
-5 = 4 + b
b= -9
the equation of aline is y = 2/5(x) -9
or 2x = 5y + 45
Using the parallel lines below determine the measure of the smaller angle.
-
x+114
x+72
▸
Answers
The measure of the smaller angle of the co-interior angles is 69°
What the measure of the smaller angle?Co-interior angles are simply angles that occur in between two parallel lines when they are intersected by a transversal.
The two angles add up to 180º as they occur on the same side of the transversal always.
From the image, the two co-interior angles are:
x + 114
x + 72
Since the two angles add up to 180º.
x + 114 + x + 72 = 180
Solve for x
2x + 186 = 180
2x = 180 - 186
2x = -6
x = -6/2
x = -3
Hence, the measure of the two angles are:
x + 114 = -3 + 114 = 111°
x + 72 = -3 + 72 = 69°
Therefore, the smallest angle is 69 degree.
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A wildlife group is trying to determine how many wild hogs are in a certain area. They trapped, tagged, and released 20 wild hogs. Later, they counted 8 wild hogs out of the 40 they saw.
What can the wildlife group estimate is the total population of wild hogs in that area?
A. 80
B. 90
C. 100
D. 16
Answers
Answer choice C is correct. That is the total population of wild hogs in that particular area is 100.
What do you mean by total population in a area?Total population in an area refers to the number of individuals of a particular species or group living in a specific geographical region or habitat. This can include both visible and hidden individuals, such as animals that are difficult to spot or track. Total population is an important measure for conservation and management efforts, as it helps determine the size of a population and whether it is growing or declining.
Given that 20 wild hogs were tagged and later they saw 8 tagged wild hogs out of 40 recaptured wild hogs. We need to find the total population of wild hogs in that area.
From the given information we can see,
(Number of hogs tagged) / (Total population) = (Number of tagged hogs recaptured) / (Number of hogs recaptured)
⇒ 20 / x = 8 / 40
⇒ 8x = 20 × 40
⇒ 8x = 800
⇒ x = 100
Therefore, the wildlife group can estimate that the total population of wild hogs in the area is 100.
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