3268760 different samples of size 10 people are possible to be selected.
15818400 different license plates are possible.
What is combination?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant.
The combination formula aids in determining the number of possible combinations that may be created by selecting a portion of a bigger collection of objects.
We need the number of possible combinations of choosing 10 people out of 25 (any order). The 25 binomial coefficient, (10) gives the number. Possible number of combinations are:
²⁵C₁₀ = 25! / (25-10)!(10!)
²⁵C₁₀ = 3268760
We want 3 letters and 3 digits but the first digit can't be zero. There are 26 alphabets and 10 digits. Since repetition is allowed we can use any of the 26 alphabets in place of all 3 letters.
This gives us 26 x 26 x 26 = 26³ ways to choose the first three letters.
For digits, since the first digit can't be 0, we can choose the rest 9 digits. For the next two digits, we can choose any one digit from 10. This gives us 9 x 10 x 10 ways to choose digits.
Finally, by law of multiplication, the total number of ways of choosing license plates is :
number of license plates = 26³ × 9 × 100
= 15818400
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3268760 different samples of size 10 people are possible to be selected.
15818400 different license plates are possible.
What is combination?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant.
The combination formula aids in determining the number of possible combinations that may be created by selecting a portion of a bigger collection of objects.
We need the number of possible combinations of choosing 10 people out of 25 (any order). The 25 binomial coefficient, (10) gives the number. Possible number of combinations are:
²⁵C₁₀ = 25! / (25-10)!(10!)
²⁵C₁₀ = 3268760
We want 3 letters and 3 digits but the first digit can't be zero. There are 26 alphabets and 10 digits. Since repetition is allowed we can use any of the 26 alphabets in place of all 3 letters.
This gives us 26 x 26 x 26 = 26³ ways to choose the first three letters.
For digits, since the first digit can't be 0, we can choose the rest 9 digits. For the next two digits, we can choose any one digit from 10. This gives us 9 x 10 x 10 ways to choose digits.
Finally, by law of multiplication, the total number of ways of choosing license plates is :
number of license plates = 26³ × 9 × 100
= 15818400
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Suppose the value of y and the value of x vary together at a constant rate of change (so that Δy=0.5⋅Δx), and y=2.5 when x=2.
a. Suppose the value of x
varies from x=2 to x=5.75.
What is the value of y when x=5.75?
Shown below are the steps of a proof by contraposition of the statement "If n is an integer and 5n + 3 is odd, then n is even." Match each step with its explanation.1. Assume n is not even, that is, it is odd. 2.Then n = 2k + 1 for some integer k. 3.5n + 3 = 5(2k + 1) + 3 = 10k + 8 = 2(5k + 4) 4. Hence, 5n + 3 is even. Negation of the conclusion Definition of an odd integer Definition of an even number Arithmetic
The correct explanation of each step is 1. Assume n is not even, that is, it is odd. - Negation of the conclusion. 2.Then n = 2k + 1 for some integer k. - Definition of an odd integer.
What is contraposition of the statement?When one is familiar with the inverse statement, it is simple to comprehend how to construct a contrapositive statement. Take the negation of the hypothesis and the conclusion to produce the conditional statement's opposite. Create the inverted statement first, then swap the hypothesis and conclusion to create the contrapositive of the conditional statement.
3.5n + 3 = 5(2k + 1) + 3 = 10k + 8 = 2(5k + 4) - Definition of an even number
1. Assume n is not even, that is, it is odd. - Negation of the conclusion.
2.Then n = 2k + 1 for some integer k. - Definition of an odd integer.
3.5n + 3 = 5(2k + 1) + 3 = 10k + 8 = 2(5k + 4) - Definition of an even number Arithmetic.
4. Hence, 5n + 3 is even.
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EASY POINTS!
At the local grocery store (Store A), the price of carrots is proportional to their weight, in
ounces. The equation representing this relationship is given by y = 0.40x.
Meanwhile, the market in the next town (Store B) sells their carrots by the pound,
represented in the table shown here:
Which store is currently selling their carrots at a cheaper unit rate?
Store A sells at cheaper rate.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
Store A: y= 0.40 x
so, the unit rate is 0.40.
Store B:
The cots of 3 pound carrot= 20.16
and, the cost of 48 ounce carrot = 20.16
and, cost per ounce= 20.16 /48= 0.42
So, the unit rate is 0.42.
Thus, store A sells at cheaper rate.
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The brain volumes (cm³) of 50 brains vary from a low of 906 cm³ to a high of 1498 cm³. Use the range rule of thumb to estimate the standard deviations and compare the result to the exact standard deviation of 171 cm³, assuming the estimate is accurate if it is within 15 cm³.
The estimated standard deviation is
Answer:
Step-by-step explanation:
The range of the brain volumes is:
Range = highest value - lowest value = 1498 cm³ - 906 cm³ = 592 cm³
According to the range rule of thumb, the standard deviation can be estimated as:
Standard deviation ≈ Range / 4
Standard deviation ≈ 592 cm³ / 4 ≈ 148 cm³
The estimate of the standard deviation is within 15 cm³ of the exact standard deviation of 171 cm³, so it can be considered accurate according to the given criteria. However, note that the range rule of thumb is a very rough estimate and may not be very accurate in all cases.
Answer:
The range rule of thumb suggests that the estimated standard deviation is approximately 18.2 cm³. This estimate is within 15 cm³ of the exact standard deviation of 171 cm³, indicating that it is accurate.
HELP ITS DUE BRO PLEASE SHOW WORK
By substituting the values and solving the equation for x, the value of x in both the subparts is as follows:
(A) x = 5/2
(B) x = 1
What are equations?They are connected by using the equal sign.
An example formula might be 3x - 5 = 16. We discover that the variable x has a value of 7 after solving this equation.
So, we have:
5x - 7
-3x + 3
(A) f(x) + g(x)
5x - 7 + -3x + 3
5x - 7 -3x + 3
2x - 5
2x = 5
x = 5/2
(B) g(x) - f(x)
-3x + 3 - (5x - 7)
-3x + 3 - 5x + 7
-8x + 8
-8x = -8
x = 1
Therefore, by substituting the values and solving the equation for x, the value of x in both the subparts is as follows:
(A) x = 5/2
(B) x = 1
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POD has a project with the following cash flows:
Year Cash Flows
0 −$ 249,000
1 147,100
2 164,600
3 129,700
The required return is 8.4 percent. What is the profitability index for this project?
Answer:
Step-by-step explanation:
The profitability index (PI) is a measure used in capital budgeting to evaluate the financial viability of an investment. It is calculated by dividing the present value of the future cash flows by the initial investment. The formula for calculating the profitability index is:
PI = Present value of future cash flows / Initial investment
To calculate the present value of the future cash flows, we need to discount each cash flow to its present value using the required return of 8.4 percent. The present value of each cash flow is as follows:
Year 0: -$249,000 (no discounting necessary for the initial investment)
Year 1: $147,100 / (1 + 0.084)^1 = $135,870.37
Year 2: $164,600 / (1 + 0.084)^2 = $137,672.76
Year 3: $129,700 / (1 + 0.084)^3 = $100,636.20
The present value of the future cash flows is the sum of the present values of each cash flow:
PV = $135,870.37 + $137,672.76 + $100,636.20 = $374,179.33
Now we can calculate the profitability index:
PI = $374,179.33 / $249,000 = 1.5035
Therefore, the profitability index for this project is 1.5035. This means that for every dollar invested in the project, the project is expected to return $1.50 in present value of future cash flows. A profitability index greater than 1.0 indicates that the project is expected to generate positive net present value and is therefore a good investment.
Rotate the figure shown 180° clockwise. Record the coordinates of the image.
What are the new coordinates for J'?
What are the new coordinates for L'?
What are the new coordinates for K'?
The coordinates of the figure after the rotation of 180° will result in a 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)
What is Rotation?The measure of the amount a figure is rotated about the center of rotation is called the angle of rotation. The angle of rotation is usually measured in degrees. We specify the degree measure and direction of a rotation.
90° clockwise rotation: (x,y) becomes (y,-x)
90° counterclockwise rotation: (x,y) becomes (-y,x)
180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)
270° clockwise rotation: (x,y) becomes (-y,x)
270° counterclockwise rotation: (x,y) becomes (y,-x)
Given data ,
Let the figure be represented as JKL
Now , the rotated figure be represented as J'K'L'
The coordinates of JKL be J ( x₁ , y₁ ) , K ( x₂ , y₂ ) and L ( x₃ , y₃ )
Now , let the rotation angle be d = 180°
For a rotation of 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)
Substituting the values in the equation , we get
The coordinates of J'K'L' is J' ( -x₁ , -y₁ ) , K' ( -x₂ , -y₂ ) and L' ( -x₃ , -y₃ )
Hence , the rotation is solved
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ind the area of the region enclosed by the curves yx and xy. question content area bottom part 1 set up the integral that gives the area of the shaded region. g
The area of the region enclosed by the given curves is 1/6.
The area of the region enclosed by a curve can be determined by doing a definite integral between the two points. The area under the curve y = f(x) is determined by integrating y = f(x) between the limits of a and b.
When the area of the region enclosed by two curves needs to be calculated the difference the function is integrated for the limits which are represented by the solution of the curves. The given curves are y = f(x) = x and y = g(x) = x^2. The solutions of the curves from the figure attached is (0,0) and (1,1).
Hence, the area is given as:
A = ∫_a^b▒〖((f(x)-g(x))〗 dx
A = ∫_0^1▒(x-x^2 ) dx
A = |1/2 x^2-1/3 x^3 |1¦0
A = 1/2 (1)^2- 1/3 (1)^3-(1/2 (0)^2- 1/3 (0)^3 )
A = 1/6
Note: The question is incomplete. The complete question probably is: Find the area enclosed between the curves y = x and y=x^2.
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PLEASE HELP!
Determine the terms and the coefficients of the terms for the
polynomial
x^2-3x+2
Complete the table for the polynomial
Terms Coefficients
X^2 ?
? -3
2 ?
Answer:
x^2=1
3x=+3
2=+2
Step-by-step explanation:
answers
1
3x
+2
hope it helps
Order of Operations with Decimals Consider this expression. 15.05 + (6.25 − 3.75) x 2.05
Question 1 When simplifying the given expression, which is the second operation to perform?
Responses
A 15.05 + 2.515.05 + 2.5
B 15.05 x 2.515.05 x 2.5
C 6.25 − 3.756.25 − 3.75
D 2.5 x 2.052.5 x 2.05
Question 2 Simplify 13.95 ÷ 5 x (8.34 − 6.09).
Responses
A 6.27756.2775
B 2.66952.6695
C 5.84355.8435
D 3.0375
15.05 + 2.5x 2.05 is the second operation and 13.95 ÷ 5 x (8.34 − 6.09) value is 6.2775, Option A is correct.
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is 15.05 + (6.25 − 3.75) x 2.05.
By using BODMAS rule we apply the operations.
15.05 + (6.25 − 3.75) x 2.05.
Firstly we solve the expression in parenthesis.
15.05 + 2.5x 2.05.
The other expression is 13.95 ÷ 5 x (8.34 − 6.09).
2.79 x (2.25)
6.2775
Hence, 15.05 + 2.5x 2.05 is the second operation and 13.95 ÷ 5 x (8.34 − 6.09) value is 6.2775, Option A is correct.
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A cyclist planned to ride 9 1/2 miles but only managed to travel 3 7/8 miles. What fraction of his planned trip did he travel?
Can anyone help with this please?
The fractional part that cyclist covered from his planned journey is 31/76.
What is fraction?
In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.
The total distance cyclist plans to travel in fraction is = 9(1/2) miles.
The distance cyclist covers in fraction is = 3(7/8) miles
The fraction of distance that cyclist travelled is -
Distance Travelled / Original distance planned
Substitute the value in the equation -
3(7/8) / 9(1/2)
Convert into improper fractions -
(31/8) / (19/2)
Use the arithmetic operation of division -
(31/8) / (19/2)
(31/8) × (2/19)
(31/4) × (1/19)
31/76
Therefore, the cyclist travelled 31/76 fraction of his planned journey.
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The bearing of a ship R from a lighthouse L is 220°
A canoe C is due North of R.
C is the same distance from the ship and the lighthouse.
What is the bearing of L from C?
The bearing of L from C is 50°.
How to solve for the bearing of lighthouse L from canoe CFirst we need to use the concept of transitive bearings. Given the bearing of the ship R from lighthouse L as 220°, and the fact that canoe C is equidistant from R and L,
we can set up a pair of complementary angles to find the bearing of L from C.
Since C is due North of R, the bearing of R from C is 90°. Then, the bearing of L from R is 90° + 220° = 310°.
To find the bearing of L from C, we subtract this angle from 180°.
Therefore, the bearing of L from C is 180° - 310° = 50°.
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what is the standard deviation of 5,7,9,11,13
Answer: √8
Step-by-step explanation:
Step 1: Find the mean.
(5+7+9+11+13)/5 --> 45/5 = 9
Step 2: Find each score's deviation from the mean.
5-9= -4
7-9= -2
9-9= 0
11-9= 2
13-9= 4
Step 3: Square each deviation from the mean.
-4^2 = 16
-2^2= 4
0^2 = 0
2^2 = 4
4^4 = 16
Step 4: Find the sum of squares.
16+4+0+4+16 = 40
Step 5: Find the variance.
40/5 = 8
Step 6: Find the square root of the variance.
the square root of 8 is √8
A manufacturing produces 931 units in 7 hours. The production rate is consistent each hour. How many hours does it take to produce 1,330 units?
A. 190
B. 133
C. 10
D. 14
Answer: C. 10
Step-by-step explanation:
931 / 7 = 133
so, 133 units per hour
133x = 1,330
1,330 / 133 = 10
Your answer is 10 hours, or option C
Question content area top Part 1 Suppose the average yearly salary of an individual whose final degree is a master's is $44 thousand less than twice that of an individual whose final degree is a bachelor's. Combined, two people with each of these educational attainments earn $121 thousand. Find the average yearly salary of an individual with each of these final degrees. Question content area bottom Part 1 The average yearly salary for an individual whose final degree is a bachelor's is $ enter your response here thousand and the average yearly salary for an individual whose final degree is a master's is $ enter your response here thousand.
The average yearly salary of an individual with each of these final degrees is,
Master's individual earns average of $66,000 while the Bachelor's individual earns $55,000.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The average yearly salary of an individual whose final degree is a master's is $44 thousand less than twice that of an individual whose final degree is a bachelor's.
And, Combined, two people with each of these educational attainments earn $121 thousand.
Now, The total amount earned by a Bachelor's person be $x:
And, amount earned by a masters person will be; $(2x - 44)
Hence, Total amount earned by the two individuals will be;
⇒ x + (2x - 44) = 121
Solve for x as;
⇒ x + 2x - 44 = 121
⇒ 3x - 44 = 121
⇒ 3x = 121 + 44
⇒ 3x = 165
⇒ x = 165/3
⇒ x = 55
And, (2x - 44) = 2 × 55 - 44
= 110 - 44
= 66
Therefore we conclude that; master's individual earns average of $66,000 while the Bachelor's individual earns $55,000.
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A map of the province of Québec has a scale of 1: 1 200 000. The distance between Trois Pistoles and Québec city is 125 miles. What is the distance on the map? Give your answer to the nearest sixteenth of an inch.
The answer is 9 11/16 inches.
What is distance?
Distance is the total movement of an object without any regard to direction.
To find the distance on the map, we need to convert the actual distance of 125 miles into the equivalent distance on the map, using the scale of 1:1 200 000.
Let's call the distance on the map d. Then, using the scale, we can write the relationship:
d = (1/1 200 000) * 125 miles
d = 0.0001041667 miles
Since one inch on the map represents 1/1 200 000 miles in real life, the distance on the map can be calculated as:
d (in inches) = 0.0001041667 miles * (1 inch/0.0001041667 miles)
d (in inches) = 9.672
Rounding to the nearest sixteenth of an inch, the answer is 9 11/16 inches.
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The government of Mexico declared blue sharks an endangered species.
They put tags on 36 blue sharks and release them. Later, they corral 130
blue sharks; among those blue sharks, 20 were tagged. Find the best
estimate for the blue shark population?
The best estimate for the blue shark population would be = 234.
How to calculate the estimate for blue shark population?The total number of blue sharks that was tagged and released = 36 blue sharks.
The total number of sharks that the government corral = 130.
The number of sharks among the corral sharks that are tagged = 20
Since 130 = 20
X. = 36
Make X the subject of formula;
X = 130× 36/20
= 468/20
= 234.
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A sales intern in a US metals company uses this graphic to follow industry trends and make informed business decisions. What graphic evidence best supports the claim that India is unlikely to be a strong competitor in the steel production industry in the future? India’s rate of steel production has gradually risen over China’s. India’s level of steel production in 2009 was much lower than that of all other countries. India’s total steel production and rate of production over a 30-year period has remained flat. China, Japan, and the US have had a much greater experience than India in producing steel
The graph backs up the assertion that India is unlikely to be a serious competitor in the steel production industry in the future because China, Japan, and the US have far more experience producing steel than India does.
What is an industry?A group of businesses or organisations that offer comparable goods or services is referred to as an industry. A few examples of the factors that can be used to define an industry include the kind of products or services they offer, their manufacturing procedures, the technology they use, or the customers they aim to serve. Development of industries was a result of the Industrial Revolution.
The graph shows that China, Japan, and the US all have a lot more experience making steel than India does, and India is not expected to become a significant competitor in the near future. Notwithstanding the nation's economic crisis, the industry—despite being one of the sectors that suffered the most—continues to play a vital role in the expansion of the economy.
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What is equivalent to 9+7x-3y
Answer:
16-3y
Step-by-step explanation:
9+7= 16
16-3y. first u do the ones that the same and don't have a letter after them. then you do the letter which in this case u just put the minus sign befor and it cokes out to 16-3y.
This table gives a few
(
x
,
y
)
(x,y)left parenthesis, x, comma, y, right parenthesis pairs of a line in the coordinate plane.
x
xx
y
yy
16
1616
44
4444
24
2424
64
6464
32
3232
84
8484
What is the
y
yy-intercept of the line?
Answer:
he y-intercept of the line is the point (0,-41)
Step-by-step explanation:
Hope this is right!
a) how far has the beam diverged from its assigned target when it reaches the moon? (the distance from the earth to the moon is 240,000 mi. round your answer to the nearest mile.)
The beam has diverged from its target by approximately 2097.80 miles when it reaches the moon.
What is the tangent function?
The tangent function is one of the main six trigonometric functions and is generally written as tan x. It is the ratio of the opposite side and the adjacent side of the angle in consideration in a right-angled triangle.
To calculate the distance the beam has diverged from its target, we need to find the horizontal distance the beam has traveled.
To do this, we'll use the tangent function:
tan(0.5°) = horizontal_distance / 240,000 miles
Rearranging the equation and solving for the horizontal distance, we get:
horizontal_distance = 240,000 miles * tan(0.5 degrees) = 240,000 miles * 0.008726646 = 2097.80 miles
Therefore, the beam has diverged from its target by approximately 2097.80 miles when it reaches the moon.
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Let give the number of liters of fuel oil burned in hours, and the number of gallons burned. Find a formula for by scaling the output of . Use the fact that 1 gallon equals 3.785 liters. You may enter the function verbatim, as you would for any other named function.
Answer: To convert liters of fuel oil burned in hours to gallons, we can use the conversion factor that 1 gallon is equal to 3.785 liters. The formula for the conversion can be represented as a function:
def liters_to_gallons(liters):
return liters / 3.785
Here, the input liters represents the number of liters of fuel oil burned in hours, and the output of the function is the equivalent number of gallons. The function performs the conversion by dividing the input value (in liters) by the conversion factor (3.785).
Question 5 of 21
****
This test: 100 point(s) possible
This question: 5 point(s) possible
An electrician purchased 9 dimmer switches at $30 each and received a $8 credit for each of the five duplex receptacles she returned. Write out a mathematical
statement that gives the amount of money she spent, then calculate this total.
Select the correct choice below and fill in the answer box to complete your choice.
(Simplify your answer.)
OA. 9×$30+5x$8=$
OB. 9x$30-5x$8=$
OC. (9-5) x ($30-$8)-$
OD. (9+5)×($30+$8) = $
Submit test
Answer:
B
Step-by-step explanation:
she purchased 9 units at $30 each (= she spent 9×$30), and she received $8 credits for each of 5 units she returned.
so, the total money spent was
9×$30 - 5×$8 = $270 - $40 = $230
because we are looking at the money spent, any credit is then entering the calculation as '-', because it reduces the amount of money spent.
Is he redoing the whole yard or just the front?
He's redoing the whole yard
How much topsoil does he need?
You will have to figure that out.
Remember he's putting a new 4 inch layer down over all the area currently covered by grass in the overhead picture above.
How big is the yard?
You can estimate it using the overhead schematic.
What kind of pickup truck does he drive?
A 2003 Ford F-150 XL.
How much can the pickup carry?
The truck bed is 80 inches long, 69
inches wide, and 20 inches tall.
How much is the delivery charge?
$30 per truckload on top of the soil cost. Each truckload can deliver up
to 18 cubic yards.
How much does the topsoil cost?
$18 per cubic yard (sold in 1/4 cubic
yard increments).
How far is the soil store?
It is 9 miles away. It takes about 20 minutes to drive there.
What gas mileage does the pickup truck get?
It averages 17 miles to the gallon.
What is the current gas cost?
Assume it's $3.79/gallon.
Using this information, figure out whether your neighbor will save money by picking up the soil himself. Use the results of your calculations to guide your decision: would you recommend that your neighbor pick up the soil himself, or pay for delivery?
Written Assignment: Write out your calculations with college level presentation and written statements that guide the reader through your process. Don't just fill the page with calculations. Label with headers what calculations you are performing for each part of your analysis. Clearly write out your final conclusions with your cost analysis using complete sentences. You need to submit your best work for evaluation, not a page of scratch paper.
1. How big is the area of the yard?
Area of the property:
Area of the house:
Area of the driveway:
Area of the yard (property – house – driveway):
2. How much topsoil will your neighbor need?
Convert 4 inches to feet:
Compute the cubic feet:
Convert cubic feet to cubic yards:
3. How much does the topsoil cost?
Amount of topsoil to be purchased:
Cost:
4. How much is the cost for delivery?
Number of truckloads:
Cost:
5. How much is the cost for your neighbor to pick up the topsoil himself?
Volume of the truck bed:
Convert cubic inches to cubic yards:
Number of trips:
Miles for number of trips:
Cost for gas:
He has to replace around 1775 square feet of yard, therefore after adding the 4 inches, he will require a total of 592 cubic feet of earth.
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 cover the surface of a closed figure. The square unit, which is frequently expressed as square inches, square feet, etc., is the accepted unit of area.
My calculations show that my Neighbour would save $20 by collecting the soil themselves. According to my calculations, he has to replace around 1775 square feet of yard, therefore after adding the 4 inches, he will require a total of 592 cubic feet of earth.
On the other hand, the man's truck can hold 110,400 cubic inches of dirt, and we know that we need 1,023,000 cubic inches of dirt, so we did a cubic feet to cubic inches calculation and found that it will take us 10 loads to get all the dirt. The shipping company charges $30 to deliver 18 cubic yards of dirt, but our neighbour needs about 22 cubic yards, so they will need to take 2 trips totaling $60 to get all the dirt. Since the store is 9 miles away, it will take 18 miles to transport each load of dirt.
With a total distance of 180 miles to travel and my neighbor's truck getting 17 miles per gallon, our estimated gas consumption is 10.6 gallons. At $3.79 per gallon, the 10.6 gallons of gas we'll need will cost us about $40. This indicates that we will save $20 by picking up the dirt ourselves rather than having it delivered.
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Linear equation that passes through the points of (-12,14) and (6,-1)
ASAP PLS
Answer:
y = -15/18 x - 12
Step-by-step explanation:
The linear equation that passes through the points (-12, 14) and (6, -1) can be found by using the point-slope form of a line. The point-slope form of a line is given by:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line, m is the slope of the line, and (x, y) are the coordinates of any other point on the line. To find the equation of the line passing through the points (-12, 14) and (6, -1), we can use either of the two points as (x1, y1) and find the slope m using the other point.
Let's use the point (-12, 14) as (x1, y1):
m = (y2 - y1) / (x2 - x1)
= (-1 - 14) / (6 + 12)
= -15/18
y - 14 = -15/18 (x + 12)
Simplifying the equation, we get:
y = -15/18 x - 12
This is the linear equation that passes through the points (-12, 14) and (6, -1).
Answer:
First you need to find the slope of the line joining the two points
Slope = [tex]\frac{(14-(-1))}{((-12)-6)}[/tex] =[tex]\frac{15}{-18}[/tex]
then find the equation
y-(-1) = 15/-18 (x-6)
y+1 = 15/-18 x +5
y = -15/18 x + 4
you can present the equation in the above way or multiply the whole equation by 18 if you do not want any fractions
A city engineer has estimated the annual toll revenues from a newly proposed highway construction over 20 years as follows: An ($2,000,000) (n) (1.06)" 1, n = 1,2, ..., 20. To validate the bond, the engineer was asked to present the estimated total present value of toll revenue at an interest rate of 6%. Assuming annual compounding, find the present value of the estimated toll revenue.
Answer:
get a life
Step-by-step explanation:
The present value of the estimated toll revenue for the proposed highway construction is approximately $31,333,333.33.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
To Calculate the percent of a number , divide the number by whole number and multiply by 100.
Now, Using the formula for the present value of an annuity, with a rate of 6% and 20 years, we get:
Present Value = $2,000,000 [ (1 - (1+0.06)⁻²⁰) / 0.06 ]
= $2,000,000 [ (1 - 0.312) / 0.06 ]
= $31,333,333.33
So, the present value of the estimated toll revenue for the proposed highway construction is approximately $31,333,333.33.
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2) If r=9, b=5, g=-6 , what does (r+b-g)(b+g) equal? A)-20 B) -8 C)8 D)19 E)20
Work Shown:
(r+b-g)(b+g)
(9+5-(-6))(5-6)
(9+5+6)(5-6)
(20)(-1)
-20
please help me with this question thank you
A store in Hampton bought a leather chair for $494.47 and marked it up 100% from the original cost. Later on, Sally purchased the leather chair and paid Hampton sales tax of 5.5%. How much, including tax, did she pay for the leather chair?
$
Answer: The markup percentage of 100% means the store added an amount equal to the original cost of the chair to its price, so the selling price of the chair before tax was 494.47 * 2 = $989.94.
The sales tax is calculated as 5.5% of the selling price before tax, which is 5.5/100 * 989.94 = $54.45.
The total amount paid by Sally for the leather chair, including tax, is 989.94 + 54.45 = $1044.39.
Step-by-step explanation:
The point A (2,1) has been marked.
(a) Mark the point B with co-ordinates (0,2)
(b) Mark the point C with co-ordinates (-1,1)
(c) There are three possible places for a fourth point D to make a parallelogram
using the four points A, B, C and D. Write down the coordinates of these three
points.
Take the vertices as A(2,1), B(0,2), C(-1,1) and D (x2,y2) The fourth coordinate is (1, 1)
How to find the fourth coordinate?Let the vertices ABCD represent the parallelogram.
The diagonals AC and BD bisect each other [property of parallelogram]
Mid point of AC = Mid point of BD ……….. 1
Mid point of AC = (x1+x2)/ 2 and (y1+y2) /2)
=(2-1)/2, (1+1)/2
=(1/2 , 1)
Mid point of BD= (x1+x2)/2, (y1+y2)/2
=(0+x2)/2, (2+y2)/2)
From equation 1
(1/2 , 1)=(0+x2)/2, (2+y2)/2)
{(1/2 , 1/1)} = {(0+x₂)/2 , (1+y₂)/2}
This implies that
1/2 = x₂/2 and 1/1 = (2+y₂)/2
Cross and multiplying we have
2x₂=2 and 2=2+y₂
Making x and y the subject of the relations
x₂=1 and y₂= 1
Therefore the fourth vertex D is (1,1)
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