The simplified expression of 100-3(4. 25)-13-4(2. 99) is 48.29.
What is PEMDAS?
PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). It is a mnemonic or acronym used to remember the order of operations when simplifying mathematical expressions.
To simplify the expression 100-3(4.25)-13-4(2.99), you can follow the order of operations (PEMDAS) which is:
Parentheses
Exponents
Multiplication and Division (from left to right)
Addition and Subtraction (from left to right)
Using this order, you can simplify the expression as follows:
100 - 3(4.25) - 13 - 4(2.99)
= 100 - 12.75 - 13 - 11.96 // multiply 3 and 4 with their respective numbers
= 62.29 - 13 - 11.96 // perform subtraction within parentheses
= 48.29 // perform final subtraction
Therefore, the simplified expression is 48.29.
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An electronics retailer offers an optional protection plan for a mobile phone it sells. Customers can choose to buy the protection plan for \$100$100dollar sign, 100, and in case of an accident, the customer pays a \$50$50dollar sign, 50 deductible and the retailer will cover the rest of the cost of that repair. The typical cost to the retailer is \$200$200dollar sign, 200 per repair, and the plan covers a maximum of 333 repairs.
Let X be the number of repairs a randomly chosen customer uses under the protection plan, and let F be the retailer's profit from one of these protection plans. Based on data from all of its customers, here are the probability distributions of X and F:
X=\# \text{ of repairs}X=# of repairsX, equals, \#, start text, space, o, f, space, r, e, p, a, i, r, s, end text 000 111 222 333
F=\text{ retailer profit}F= retailer profitF, equals, start text, space, r, e, t, a, i, l, e, r, space, p, r, o, f, i, t, end text \$100$100dollar sign, 100 -\$50−$50minus, dollar sign, 50 -\$200−$200minus, dollar sign, 200 -\$350−$350minus, dollar sign, 350
Probability 0. 900. 900, point, 90 0. 70. 070, point, 07 0. 20. 020, point, 02 0. 10. 010, point, 01
Find the expected value of the retailer's profit per protection plan sold
Note that the expected value of the retailers profit is - $114. This means he made a loss.
How did we arrive at this ?To find the expected value we must proceed as follows
Expected Value - E(F) is
Probability of F - P(F)
= 100 x ($100 - $200) + (P(F) = $50) x ($50 - $200) + (P(F) = $ -200) x ( $ - 200 - $200) + (P(F) = $- 350) x ($ -350 $ 200)
= (0.9) x (-100) + (0.07 ) x (-150) + (0.01) x (-550) + (0.02) x (-400)
= - 90 - 10.5 - 5.5 -8
E(F) = $ -114
So it is right to state that the expected value of the retailer's profit per protection plan sold is -$114, which is a loss.
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Full Question:
An electronics retailer sells mobile phones with an optional protection plan for $100. In case of an accident, the customer pays a $50 deductible and the retailer covers the rest of the repair cost, which is typically $200 per repair. The protection plan covers a maximum of 333 repairs.
Let X be the number of repairs a randomly chosen customer uses under the protection plan, and let F be the retailer's profit from one of these protection plans. The probability distributions of X and F are:
X = number of repairs: 0 1 2 3
Probability: 0.90 0.07 0.02 0.01
F = retailer profit: $100-$50-$200-$350
Probability: 0.90 0.07 0.02 0.01
The task is to find the expected value of the retailer's profit per protection plan sold.
a)cos 165 in terms of sine and cosine of acute angle
Cos 165 in terms of sine and cosine of acute angle would give cos(165) = -(1 + √3) / (2√2).
How to find the cosine ?To find the cosine of 165 degrees in terms of sine and cosine of an acute angle, we can use the cosine angle addition formula:
cos(A + B) = cos(A)cos(B) - sin(A)sin(B)
Since 120 degrees is in the second quadrant, the cosine is negative, and the sine is positive:
cos(120) = -cos(60) and sin(120) = sin(60)
cos(165) = -cos(60)cos(45) - sin(60)sin(45)
Now we can plug in the values of the trigonometric functions:
cos(165) = - (1/2) x (1/√2) - (√3/2) x (1/√2)
cos(165) = -(1 + √3) / (2√2)
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There are 50 athletes signed up for a neighborhood basketball competition. Players can select to play in the 6-player games ("3 on 3") or the 2-player games ("1 on 1").
All 50 athletes sign up for only one kind of game. Complete the table to show different combinations of games that could be played
If 13 matches are played in total then, 7 2-player matches and 6 6-player matches are played.
Here we see that the table has two columns- 6 player Athletes and 2 player athletes. It is given that no athlete participates in both the type of games. Hence we can say that
If one match for 2 player game is held then 2 players are employed there.
Hence we have 48 players left
hence we will have 48/6 = 8 6-player matches.
Similarly, if 1 6-player match is played then 44 players applied for the 2-player match, hence, we have 44/2 = 22 2-player matches
If 4 2-player matches are held then we will have 8 players booked. Hence 42/6 = 7 6-player matches were held.
If 4 6-player matches were held then, we have 26/2 = 13 2-player matches.
Hence the table will be
Number of 6 Player Games Number of 2-player games
8 1
1 22
7 4
4 13
b)
Let the total 2-player games played be x and 6-player games be y
we have,
x + y = 13
2x + 6y = 50
or, 2(x + y) + 4y = 50
or, 26 + 4y = 50
or, 4y = 24
or, y = 6
Hence x = 7
Therefore, in total 7 2-player matches and 6 6-player matches are played.
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Orlando wants to borrow $3,000 for the purchase of a used car. He has to pay back the loan after 4 years. The two loan options are simple interest at a rate of 5. 8% each year, or interest compounded annually at a rate of 5. 2% each year. Which method should he choose , simple or compound , and how much less will he owe using that method?
Orlando should consider using simple interest and the amount he will have to pay is $696, under the condition that he wants to borrow $3,000 for the purchase of a used car. He needs to clear the loan after 4 years.
Orlando should apply the simple interest method.
The amount of interest he will pay using simple interest is evaluated
I = P × r × t
Here
I = interest paid
P = borrowed principal amount
r = rate of annual interest
t = time
In this case,
P = $3,000
r = 5.8%
t = 4 years
Therefore,
I = $3,000 × 0.058 × 4
= $696
So Orlando will pay $696 in interest using simple interest.
The amount of interest he will pay using compound interest is calculated as follows:
[tex]A = P * (1 + r/n)^{(n*t)}[/tex]
I = A - P
Here,
A = end term amount
n = count of interest that is compounded each year
In this case,
P = $3,000
r = 5.2%
t = 4 years
Interest is compounded annually so n=1
Therefore,
A = $3,000 × (1 + 0.052/1)⁴
= $3,697.47
I = $3,697.47 - $3,000
= $697.47
So Orlando will pay $697.47 in interest using compound interest.
Therefore, Orlando should choose simple interest method and he will owe $1.47 less using that method.
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8 girls eat a total of 210 candies. after adding the number of candies eat by the ninth girl, the average number of candies eaten became 29. how many did the 9th girl eat?
The 9th girl ate 51 candies.
What is the number of candies eaten by the 9th girl, if the average number of candies eaten by 9 girls is 29 and the first 8 girls ate a total of 210 candies?Let the number of candies eaten by the 9th girl be x.
The average number of candies eaten by 8 girls is given as (210/x+210)/8, which simplifies to 210/8 + x/8.
After the 9th girl eats x candies, the total number of candies eaten becomes 210 + x.
The new average is given as (210 + x)/9 = 29.
Solving for x, we get:
210 + x = 261
x = 51
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Colin surveyed 12 teachers at his school to determine how much each person budgets for lunch. He recorded his results in the table. What does the relationship between the mean and median reveal about the shape of the data? the mean is less than the median, so the data is skewed left. The mean is more than the median, so the data is skewed right. The mean is equal to the median, so the data is symmetrical. The mean is equal to the median, so the data is linear.
The mean is equal to the median, so the data is symmetrical.
Given that :
Colin surveyed 12 teachers at his school to determine how much each person budgets for lunch.
The data is :
10 5 8 10 12 6 8 10 15 6 12 18
Mean is the average of these numbers.
Mean = (10 + 5 + 8 + 10 + 12 + 6 + 8 + 10 + 15 + 6 + 12 + 18) / 12
= 10
Now median is the element in the middle arranged in an order.
Arrange the data in ascending order.
5 6 6 8 8 10 10 10 12 12 15 18
The middle element is the average of the 6th and 7th elements.
Median = (10 10) / 2 = 10
So mean and the median is equal. So the data is symmetrical.
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You have decided to purchase a car for $25,625. The credit union requires a 10% down payment and will finance the balance with a 9% annual interest loan for 36 months. The sales tax in your city is 7. 5%, and the license and title charges are $175. 13. What is the total purchase price of the car including tax, license, and title? Round your answer to the nearest cent. A. $24,949. 80 c. $27,722. 01 b. $24,967. 32 d. $27,735. 14.
Answer is 27,529.82
To calculate the total purchase price of the car including tax, license, and title, we need to add the down payment, the financed balance, the sales tax, and the license and title charges.
First, we calculate the down payment:
10% of $25,625 = $2,562.50
Next, we calculate the financed balance:
$25,625 - $2,562.50 = $23,062.50
Then, we calculate the sales tax:
7.5% of $23,062.50 = $1,729.69
Finally, we add the license and title charges:
$1,729.69 + $175.13 = $1,904.82
So the total purchase price of the car including tax, license, and title is:
$2,562.50 + $23,062.50 + $1,904.82 = $27,529.82
Rounded to the nearest cent, the answer is option D: $27,735.14.
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Explain the role of the brackets, and how they effects the sum. Provide the answer for both sums. Sum 1 Sum 2 10 + 7 – 5 + 3 = 10 + 7 – (5 + 3) =
The role of the brackets, and how they effects the sum is given as the inside signs get changed after the opening of the bracket.
The associative property of addition is a mathematical statement that asserts that the arrangement of three or more integers does not affect their total. This indicates that no matter how the numbers are organised, the total of three or more integers remains the same.
The associative property of addition is a mathematical principle that asserts that when adding three or more integers, the amount obtained is constant regardless of how the numbers are grouped. Grouping here refers to where the brackets are positioned.
The sum for the 1st term is 10 + 7 – 5 + 3 = 15
The sum of the 2nd term is 10 + 7 – (5 + 3) = 17 - 8 = 9
Here, the bracket used made all the difference so after opening of the bracket the sign inside changed which impacted the summation of the terms above.
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Ink pens and pencils are substitutes. If demand of pen falls,what happens to demand, supply, quantity
Pen demand decrease reduces pen price, quantity supplied; increases pencil demand, price, and quantity supplied as a substitute.
How do pen demand changes affect supply?If the demand for ink pens falls, this would likely result in a decrease in the demand for pens and an increase in the demand for pencils, since they are substitutes.
As a result, the price of pens would likely fall, as producers try to entice buyers to purchase pens over pencils. This decrease in the price of pens would, in turn, lead to a decrease in the quantity supplied of pens, as producers shift their focus to producing other goods that are more in demand.
However, the quantity demanded of pencils would increase, leading to an increase in the price of pencils and an increase in the quantity supplied of pencils. Ultimately, the market for ink pens and pencils would adjust to reflect the changes in demand, resulting in changes in both price and quantity.
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What is the value of 1/4 (-4^3+10^2)
Answer:
The value of 1/4 (-4^3+10^2) is 9
The function f(t)=350(1. 2)^{365t}f(t)=350(1. 2)
365t
represents the change in a quantity over t years. What does the constant 1. 2 reveal about the rate of change of the quantity?
The constant 1.2 in the function represents the rate of change of the quantity per year.
Specifically, it represents the factor by which the quantity grows or decays over a year.
Since 1.2 is greater than 1, the function describes an exponential growth, where the quantity is multiplied by 1.2 each year.
For example, after one year, the quantity is multiplied by 1.2, after two years it is multiplied by 1.2 squared, and so on.
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Green Frog Convenience Store supplies two types of protein bars. One protein bar has 320 calories in the 2-ounce size. How many calories are in the 3-ounce size of the bar? *
The number of calories in the 3 ounce bar is 480.
To solve this problem, we can use a proportion. If the 2-ounce protein bar has 320 calories, then we can set up the following proportion:
2 oz / 320 cal = 3 oz / x cal
where x is the number of calories in the 3-ounce protein bar.
We can solve for x by cross-multiplying and simplifying:
2 oz * x cal = 3 oz * 320 cal
2x = 960x = 480
Therefore, the 3-ounce protein bar has 480 calories.
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Without using a protractor, estimate the measure of the angle below. Explain how you made your estimate.
Answer:
The approximated measure of this angle is 90°, so this may be a right angle.
Place a sheet of paper so that the corner corresponds to the angle. You will notice that the lines will closely align with the edges of the paper.
1. the elevation of death valley, california is - 282 feet. the elevation of tallahassee, florida is 203
feet. the elevation of westmorland, california is -157 feet.
compare the elevations of death valley and tallahassee using < or >
fill in the blank:
death valley (-282 feet)
tallahassee, florida (203 feet)
Based on the elevations given, Death Valley (-282 feet) < Tallahassee, Florida (203 feet).
To compare the elevations of Death Valley and Tallahassee, we'll use the inequality symbols i.e., "<" or ">" . The symbol "<" indicate less than and ">" indicate greater than.
Death Valley, California has an elevation of -282 feet, while Tallahassee, Florida has an elevation of 203 feet. Since -282 is less than 203, we use the "<" symbol.
So, the comparison is as follows:
Death Valley (-282 feet) < Tallahassee, Florida (203 feet)
This means that the elevation of Death Valley is lower than or less than the elevation of Tallahassee.
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PLS HELP FAST I ONLY HAVE A LIL TIME LEFT! WILL MARK BRAINLIEST
Answer:
DStep-by-step explanation:
In this set,
the maximum is 35
the minimum is 6
So, we can cross out options A, B
the median is 14
The only option that works for this set is option D
Question 4
Question
What does the y-intercept of this relationship represent?
the initial height of the plant
the height of the plant at the end of the experiment
the amount of plant food Ryan uses each day
the average amount the plant grows each day
Answer:
Step-by-step explanation:
The correct answer is:
the initial height of the plant
The y-intercept represents the point where the graph intersects the y-axis. In the context of a relationship between plant growth and time, the y-intercept would represent the initial height of the plant, which is the height of the plant at the start of the experiment, before any growth has occurred.
PLEASEEEE HELPPP ASAP 20 PTS
Use long division to determine the quotient of the following expression.
Write the quotient in standard form with the term of largest degree on the left. (10x^(2)+3x-77)-:(2x+7)
The quotient of the division 10x² + 3x - 77 ÷ 2x + 7 is 5x - 16
Evaluating the long division expressionsThe quotient expression is given as
10x² + 3x - 77 ÷ 2x + 7
The long division expression is represented as
2x + 7 | 10x² + 3x - 77
So, we have the following division process
5x - 16
2x + 7 | 10x² + 3x - 77
10x² + 35x
--------------------------------
-32x - 77
-32x - 112
-------------------------------------
35
Hence, the quotient of the long division is 5x - 16
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50 POINTS AND BRAINLYEST Triangle NMO has vertices at N(−5, 2), M(−2, 1), and O(−3 , 3). Determine the vertices of image N′M′O′ if the preimage is reflected over x = −1.
N′(5, −2), M′(2, 1), O′(3, 3)
N′(−5, 5), M′(−2, 3), O′(−3, 7)
N′(3, 2), M′(0, 1), O′(1, 3)
N′(−5, −2), M′(−2, −1), O′(−3, −3)
Answer:
N'(3, 2), M'(0, 1), O'(1, 3)
Step-by-step explanation:
Please sketch the graphs of the two triangles and the line of reflection to confirm my answer.
Since NMO is reflected over the line
x = -1, the y-coordinates of N'M'O' will remain the same. Since the x-coordinate of N is at -5, which is 4 units to the left of the line of reflection, the x-coordinate of N' is at -1 + 4 = 3. Since the x-coordinate of M is at -2, which is 1 unit to the left of from the line of reflection, the x-coordinate of M' is at -1 + 1 = 0. Since the x-coordinate of O is at -3, which is 2 units to the left of the line of reflection, the x-coordinate of O' is at -1 + 2 = 1. So the vertices of N'M'O' are at (3, 2), (0, 1), and (1, 3).
In Angle STU, the measure of U=90°, the measure of S=31°, and TU = 77 feet. Find the
length of US to the nearest tenth of a foot
If in Angle STU, the measure of U=90°, the measure of S=31°, and TU = 77 feet, then the length of US to the nearest tenth of a foot is approximately 39.4 feet.
In angle STU, we have a right triangle with U=90°, S=31°, and TU=77 feet. To find the length of US, we can use the sine function:
sin(S) = opposite side (US) / hypotenuse (TU)
sin(31°) = US / 77 feet
To find the length of US, multiply both sides by 77 feet:
US = 77 feet * sin(31°)
US ≈ 39.4 feet
Therefore, the length of US to the nearest tenth of a foot is approximately 39.4 feet.
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Daniel read 77 pages in \frac{2}{5}
of an hour. if he continues reading at the same rate, how many pages will he read in an hour?
Daniel will read approximately 193 pages in one hour if he continues reading at the same rate.
How many pages will Daniel read in an hour?Since Daniel read 77 pages in $\frac{2}{5}$ of an hour, we can set up the proportion:
$\frac{77}{\frac{2}{5}} = x$
where $x$ is the number of pages he would read in 1 hour.
To solve for $x$, we can simplify the left side of the equation by multiplying both the numerator and denominator by 5, which gives:
$\frac{77 \times 5}{2} = x$
Simplifying this expression gives:
$192.5 = x$
Therefore, if Daniel continues reading at the same rate, he will read 192.5 pages in one hour. However, since the number of pages must be a whole number, we can round this answer to the nearest whole number to get:
$x \approx 193$
So, Daniel will read approximately 193 pages in one hour if he continues reading at the same rate.
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A corporation earned a profit of $ 2.5 × 1 0 4 $2.5×10 4 for 200 days in a row. What was the corporation’s total profit during this time period? Express your answer in scientific notation.
Answer: hopefully the image helps
Step-by-step explanation:
Integrate the function. 「 dx ,X> 6. Give your answer in exact form. x2x² - 36
To integrate the function ∫(x² - 36) dx, we first need to factor out the expression inside the parentheses:
∫(x² - 36) dx = ∫(x - 6)(x + 6) dx
We can then use the power rule of integration to find the antiderivative:
∫(x - 6)(x + 6) dx = (1/3)x³ - 6x + C, where C is the constant of integration.
Since the original problem states X > 6, we can evaluate the definite integral using these limits:
∫(x² - 36) dx from 6 to X = [(1/3)X³ - 6X] - [(1/3)(6)³ - 6(6)]
= (1/3)X³ - 6X - 68
Therefore, the answer in exact form is (1/3)X³ - 6X - 68.
To integrate the given function, first note the correct notation for the function: ∫(x^2)/(x^2 - 36) dx for x > 6.
To solve this, we can use partial fraction decomposition. The given function can be rewritten as:
∫(A(x - 6) + B(x + 6))/(x^2 - 36) dx
Solving for A and B, we find that A = 1/12 and B = -1/12. Now we rewrite the integral as:
∫[(1/12)(x - 6) - (1/12)(x + 6)]/(x^2 - 36) dx
Next, separate the two terms and integrate them individually:
(1/12)∫[(x - 6)]/(x^2 - 36) dx - (1/12)∫[(x + 6)]/(x^2 - 36) dx
Now, notice that the integrals are of the form ∫u'/u dx. The integral of this form is ln|u|. So we have:
(1/12)[ln|(x - 6)| - ln|(x + 6)|] + C
Using the logarithm property, we can rewrite the answer as:
(1/12)ln|((x - 6)/(x + 6))| + C
That is the exact form of the antiderivative for the given function.
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You are going to run at a constant speed of 7.5
miles per hour for 45
minutes. You calculate the distance you will run. What mistake did you make in your calculation? [Use the formula S=dt
.]
The value of the distance you will run is 5.62500 miles
Calculating the value of the distance you will runFrom the question, we have the following parameters that can be used in our computation:
You are going to run at a constant speed of 7.5 miles per hour For 45 minutesThis means that
Speed = 7.5 miles per hour
Time = 45 minutes
The distance you will run is calculated as
Distance = Speed * Time
Substitute the known values in the above equation, so, we have the following representation
Distance = 7.5 miles per hour * 45 minutes
Evaluate the product
Distance = 5.62500 miles
Hence, the distance is 5.62500 miles
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I…. NEEDDDD… HELPPP
According to the information, the customer would save $492 in the first year by switching to Intellivision; the customer would save $207 in the second year by using Intellivision; ElectroniSource would be cheaper in the third year.
How to calculate the annual cost for both companies?a. To calculate the annual cost for ElectroniSource: $42/month for phone service x 12 months = $504/year, $35/month for internet service x 12 months = $420/year, and $59/month for cable television x 12 months = $708/year.
So the total annual cost with ElectroniSource would be $504 + $420 + $708 = $1,632.
With Intellivision, the flat monthly fee for all three services is $95, so the total annual cost would be $95 x 12 months = $1,140.
Therefore, the customer would save $1,632 - $1,140 = $492 in the first year by switching to Intellivision.
How to calculate the best rate for the second year?b. After the first year, Intellivision raises the rates by 25%, so the new monthly fee would be $95 x 1.25 = $118.75.
The total annual cost in the second year would be $118.75 x 12 months = $1,425.
Using the same services, the annual cost with ElectroniSource would still be $1,632.
Therefore, the customer would save $1,632 - $1,425 = $207 in the second year by using Intellivision.
How to calculate the best rate for the third year?c. If Intellivision raises the rates by 16% in the third year compared to the second year, the new monthly fee would be $118.75 x 1.16 = $137.95.
The total annual cost in the third year would be $137.95 x 12 months = $1,655.4.
The annual cost with ElectroniSource would still be $1,632.
Therefore, ElectroniSource would be cheaper in the third year.
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The radius of the moon is about 1. 738 mega meters. The formula for the volume of a sphere is v=4/3 nr3. Approximately what is the volume of the moon. Use 3. 14 as an approximation for pi
To calculate the volume of the moon, we can use the formula V = (4/3)πr^3, where r is the radius of the moon.
Given that the radius of the moon is about 1.738 mega meters (or 1,738,000 meters), we can substitute this value into the formula and simplify as follows: V = (4/3) × 3.14 × (1.738 × 10^6)^3 V ≈ 2.196 × 10^19 cubic meters Therefore, approximately, the volume of the moon is 2.196 × 10^19 cubic meters.
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Which unique sequence of rigid motions maps quadrilateral abcd to quadrilateral efgh?
s
а
ib
4
d
ll2_3 4 5 6
e
f
h
g
a a reflection over the x-axis followed by a translation of (,y) → (, y - 4).
b. a reflection over the y-axis followed by a translation of (1,y) → (, y-6).
c a translation of (+,y) → (2, y - 3) followed by a reflection over the y-axis.
a translation of (cv) (1-6, y) followed by a reflection over the x-axis.
d.
The correct answer is option B, a reflection over the y-axis followed by a translation of (1,y) → (1, y-6).
To solve this problem, we need to find the sequence of rigid motions (i.e., transformations that preserve distance and angle) that maps quadrilateral ABCD to quadrilateral EFGH.
First, we need to identify the corresponding vertices of the two quadrilaterals. Let's assume that vertex A maps to vertex E, vertex B maps to vertex F, vertex C maps to vertex G, and vertex D maps to vertex H.
Now, we can apply different transformations to map each vertex of quadrilateral ABCD to the corresponding vertex of quadrilateral EFGH. We can try each option provided and check if it maps all the vertices correctly.
Option A involves a reflection over the x-axis, followed by a translation of (0,y) → (0, y - 4). This transformation does not map vertex A to vertex E correctly.
Option B involves a reflection over the y-axis, followed by a translation of (1,y) → (1, y - 6). This transformation maps vertex A to vertex E, vertex B to vertex F, vertex C to vertex G, and vertex D to vertex H, which is the correct mapping.
Option C involves a translation of (+,y) → (2, y - 3) followed by a reflection over the y-axis. This transformation does not map vertex A to vertex E correctly.
Option D involves a translation of (1-6, y) followed by a reflection over the x-axis. This transformation does not map vertex A to vertex E correctly.
Therefore, the unique sequence of rigid motions that maps quadrilateral ABCD to quadrilateral EFGH is a reflection over the y-axis followed by a translation of (1,y) → (1, y-6), which is option B.
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You should always measure your following distance in.
You should always measure your following distance in seconds. The correct answer for measuring following distance is A.
It is important to keep a safe distance between vehicles on the road, which is known as following distance. Measuring following distance in seconds is a more reliable method than measuring it in car lengths or feet.
The recommended following distance is typically two to three seconds. This means that when the vehicle in front of you passes a fixed point on the road, you should not reach that same point before two to three seconds have elapsed.
Measuring in seconds is more effective as it takes into account the speed at which both vehicles are traveling. If you measure in car lengths or feet, it may not be accurate as the length of the cars may differ, and it does not account for the speed of the vehicles. By measuring in seconds, you can maintain a safe distance and reduce the risk of accidents or collisions.
The correct answer for measuring following distance is A.
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Complete question is:
You should always measure your following distance in __________
A. seconds. B. car lengths. C. feet.
A windshield wiper is 45 cm long and
creates a central angle of 120° in one
wipe. what is the sector area?
The windshield sector area is 706.86 cm².
To calculate the sector area of the windshield wiper, we need to use the formula for the area of a sector of a circle. The formula is:
A = (θ/360°) x πr²
where A is the area of the sector, θ is the central angle of the sector in degrees, and r is the radius of the circle.
In this problem, we are given that the windshield wiper has a length of 45 cm, which means that the radius of the circle traced by the wiper is 45 cm/2 = 22.5 cm.
We are also given that the wiper creates a central angle of 120° in one wipe. Substituting these values into the formula, we get:
A = (120°/360°) x π(22.5 cm)²
A = (1/3) x π x (22.5 cm)²
A ≈ 706.86 cm²
Therefore, the sector area of the windshield wiper is approximately 706.86 square centimeters.
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Solve for x and choose the correct solution: x-3<=-2
The solution of the given inequality, x - 3 ≤ -2, is solved as the possible value of x which is determined as: x ≤ 1.
How to Find the Solution of an Inequality?Given the inequality x - 3 ≤ -2, to find the solution, wr would have to solve for x as explained below:
x - 3 ≤ -2 [given]
Add 3 to both sides:
x - 3 + 3 ≤ -2 + 3 [addition property of equality]
x ≤ 1
This means that the values of x are less than or equal to 1, which is from 1 below.
Thus, the solution to the inequality is solved by finding the possible value of x, which is x ≤ 1.
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sets x y and z are defined below a number will be randomly selected from set x what is the probability that the selected number will be an element of set y and an element of set z.
x= (1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Y= (5, 10, 15, 20, 25)
Z= (1,5,25)
A. 0.1
B. 0.2
C. 0.5
D. 0.6
E. 0.8
When a number is chosen from set x, there is a 0.2 chance that the chosen number will also be found in sets y and z. The answer is option (B). 0.2.
What is Probability?The ratio of favourable outcomes to all possible outcomes of an event is known as the probability. The symbol x can be used to express the quantity of successful outcomes for a study with 'n' outcomes. The probability formula determines the likelihood that an event will occur.
It is the ratio of effective results to all effective results. The study of probability is a branch of mathematics that examines the likelihood that an event will occur. Probability, which expresses the likelihood that an event will occur, is calculated by dividing the total number of occurrences by the total number of positive events.
The number of elements of Both Y and Z answer is 5 and 25.
The probability of selecting a number from x that is an element of y and z
Intersection of y and z is (5, 25)
No.of elements in x is = 2/10
= 1/5
= 0.2
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