The vertices of the image triangle N′M′O′: N′(-1, 2), M′(-4, 1), O′(-3, 3).
What are vertices?
Vertices (singular: vertex) are the points where two or more straight lines or edges meet in a geometric shape such as a polygon, polyhedron, or graph. In two-dimensional shapes like polygons, a vertex is a corner where two sides intersect.
We can do this by finding the difference between the x-coordinate of the preimage vertex and -3, doubling this difference, and then subtracting this result from the x-coordinate of the preimage vertex. This will give us the x-coordinate of the image vertex.
For example, to find the x-coordinate of the image of vertex N, we have:
x-coordinate of N = -5
Difference between x-coordinate of N and -3 = -5 - (-3) = -2
Double the difference = -2 x 2 = -4
Subtract this result from the x-coordinate of N = -5 - (-4) = -1
Therefore, the x-coordinate of the image of vertex N is -1.
Using the same method, we can find the x-coordinates of the image vertices:
x-coordinate of N′ = -1
x-coordinate of M′ = -4
x-coordinate of O′ = -3
To find the y-coordinates of the image vertices, we don't need to do any calculations since the reflection is over a vertical line and does not affect the y-coordinates. Therefore, the y-coordinates of the image vertices are the same as the y-coordinates of the preimage vertices:
y-coordinate of N′ = 2
y-coordinate of M′ = 1
y-coordinate of O′ = 3
Putting it all together, we get the vertices of the image triangle N′M′O′:
N′(-1, 2), M′(-4, 1), O′(-3, 3)
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the price of firewood 4 years ago was $140 per cord. today, a cord of wood costs $182. what has been the annual rate of increase in the cost to the nearest tenth of a percent?
Using the formula for compound interest we find that the annual rate of increase in the cost of firewood is approximately 7.8%.
We can use the formula for compound interest to calculate the annual rate of increase:
A = P(1 + r)^n
where A is the final price, P is the initial price, r is the annual rate of increase, and n is the number of years.
We know that P = $140, A = $182, and n = 4, so we can solve for r:
182 = 140(1 + r)^4
(1 + r)^4 = 1.3
1 + r = 1.3^(1/4)
r ≈ 0.0777
The annual rate of increase is approximately 0.0777 or 7.8% to the nearest tenth of a percent.
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The point (−0.5, 4) is reflected across the y-axis and then across the x-axis. What are the coordinates of the reflected point?
Answer: The coordinates of the reflected point are (0.5, -4)
Step-by-step explanation: When a point is reflected across the y-axis, the x-coordinate changes sign while the y-coordinate remains the same. So the point (-0.5, 4) reflected across the y-axis will be (0.5, 4).When a point is reflected across the x-axis, the y-coordinate changes sign while the x-coordinate remains the same. So the point (0.5, 4) reflected across the x-axis will be (0.5, -4).
Answer:
(5,-4) because if the quadrant one is positive positive quadrant two is negative positive quadrant three is negative negative Quadrant four is positive negative
Step-by-step explanation: Hope this helps!! Mark me brainliest! :))
Describe some common or unique formulas that you use in your life.
Quadratic Fοrmula: This fοrmula is used tο find the rοοts οf a quadratic equatiοn. It is calculated as:
[tex]$ \rm x = \frac{(-b \pm \sqrt{(b^2 - 4ac)}}{ 2a}[/tex]
What is quadratic equatiοn?it's a secοnd-degree quadratic equatiοn which is an algebraic equatiοn in x. Ax² + bx + c = 0, where a and b are the cοefficients, x is the variable, and c is the cοnstant term, is the quadratic equatiοn in its standard fοrm.
1. Simple Interest Fοrmula: This fοrmula is used tο calculate the interest earned οr paid οn a lοan οr investment. It is calculated as:
[tex]\rm I = P \times r \times t[/tex]
Where I is the interest earned οr paid, P is the principal amοunt, r is the interest rate, and t is the time periοd.
2. Pythagοrean Theοrem: This fοrmula is used tο calculate the length οf οne side οf a right triangle given the lengths οf the οther twο sides. It is calculated as:
[tex]\rm a^2 + b^2 = c^2[/tex]
Where a and b are the lengths οf the twο legs οf the right triangle, and c is the length οf the hypοtenuse.
3. Quadratic Fοrmula: This fοrmula is used tο find the rοοts οf a quadratic equatiοn. It is calculated as:
[tex]$ \rm x = \frac{(-b \pm \sqrt{(b^2 - 4ac)}}{ 2a}[/tex]
Where a, b, and c are cοefficients οf the quadratic equatiοn ax² + bx + c = 0, and x is the sοlutiοn.
4. Bοdy Mass Index (BMI) Fοrmula: This fοrmula is used tο calculate a persοn's bοdy mass index, which is a measure οf bοdy fat based οn height and weight. It is calculated as:
BMI = (weight in kilοgrams) / (height in meters)²
A BMI οf 18.5 tο 24.9 is cοnsidered healthy, while a BMI οf 25 tο 29.9 is cοnsidered οverweight, and a BMI οf 30 οr higher is cοnsidered οbese.
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Complete question:
Describe some common or unique mathematical formulas that you use in your life.
Fred is a plant manager at Salem Construction Company. He has been employed there for 28
years and will be retiring at the end of this year. His pension is calculated on the average of
his last four years' salaries. In those years, he earned $82,000, $96,000, $105,000, and
$109,000. His employer will credit him 1.8% of that average for each year he worked.
a) Calculate Fred's annual pension.
B) Find his monthly p
ension.
Fred's Annual pension will be $603.
How to calculate Fred's annual pension, we first need to find the average of his last four years' salaries?Average salary = (82000 + 96000 + 105000 + 109000) / 4 = $100,500
Fred's employer will credit him 1.8% of that average for each year he worked, so we can calculate his annual pension as follows:
Annual pension = 0.018 * 4 * 100500 = $7,236
Therefore, Fred's annual pension will be $7,236.
How to find his Annual pension?We can simply divide his annual pension by 12:
Annual pension = 7236 / 12 = $603
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suppose the process mean shifts to 702.00 while the standard deviation remains constant. what is the probability of an out-of-control signal occurring on the first sample following the shift?
The probability of an out-of-control signal occurring on the first sample following the shift is approximately 0.0026 or 0.26%.
To determine the probability of an out-of-control signal occurring on the first sample following the shift, we need to calculate the probability of observing a sample mean or range value that falls outside the control limits.
For the X-bar chart:
New process mean (after the shift) = 702.00
Standard deviation (constant) = 1.738
Sample size (n) = 6
We can calculate the standard error (SE) for the X-bar chart using the formula:
SE = Standard deviation / √(sample size)
SE = 1.738 / √(6) ≈ 0.709
Next, we calculate the control limits for the X-bar chart based on the new process mean:
New UCL = New process mean + 3 × SE
= 702.00 + 3 × 0.709
= 704.127
New LCL = New process mean - 3 × SE
= 702.00 - 3 × 0.709
= 699.873
Now, we need to determine the probability of observing a sample mean outside the control limits, given that the process mean has shifted to 702.00. We can assume a normal distribution for the sample means.
To calculate the probability, we need to determine the z-scores for the new UCL and LCL using the formula:
z = (X - μ) / SE
where X is the value of interest (UCL or LCL), μ is the process mean, and SE is the standard error.
For the UCL:
z = (New UCL - μ) / SE
= (704.127 - 702.00) / 0.709
= 2.999
For the LCL:
z = (New LCL - μ) / SE
= (699.873 - 702.00) / 0.709
= -2.999
We can use a standard normal distribution table or a statistical calculator to find the probabilities associated with these z-scores.
Using a standard normal distribution table, the probability of observing a sample mean greater than the new UCL (2.999 z-score) is approximately 0.0013 (or 0.13%), and the probability of observing a sample mean lower than the new LCL (-2.999 z-score) is also approximately 0.0013 (or 0.13%). Since we are interested in either of these cases (an out-of-control signal), we add the probabilities:
Probability of an out-of-control signal = 0.0013 + 0.0013 ≈ 0.0026 (or 0.26%)
Therefore, the probability of an out-of-control signal occurring on the first sample following the shift is approximately 0.0026 or 0.26%.
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Complete question =
Control charts for x-bar and s have been maintained on a proces and have exhibited statistical control. The sample size is n=6. The control chart parameters are as follows:
X-bar: UCL = 708.20, Center line = 706.00, LCL = 703.80
R chart: UCL = 3.420, Center line = 1.738, LCL = 0.052
natural tolerance limits for the process are ±5.214.
the estimated standard deviation is 1.738.
d) Suppose the process mean shifts to 702.00 while the standard deviation remains constant. What is the probability of an out-of-control signal occuring on the first sample following the shift?
Land's Bend sells wide variety of outdoor equipment and clothing: The company sells both through mail order and via the internet: Random samples of sales receipts were studied for mail-order sales and internet sales, with the total purchase being recorded for each sale random sample of 17 sales receipts for mail-order sales results in mean sale amount of $70.60 with standard deviation of 521.75. A random sample of 9 sales receipts for internet sales results in mean sale amount of $87.30 with standard deviation of S18.75 . Using this data, find the 99 % confidence interval for the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases: Assume that the population variances are not equal and that the two populations are normally distributed.
Step of 3 : Find the point estimate that should be used in constructing the confidence interval:
16.70Therefore, the point estimate that should be used in constructing the confidence interval is -$16.70.
To find the point estimate that should be used in constructing the confidence interval, the formula for the point estimate can be used. The formula is as follows: Point Estimate = Sample Mean of Mail-Order Sales - Sample Mean of Internet Sales = $70.60 - $87.30 = -$16.70.How to find the point estimate?The point estimate is the best estimate of the unknown population parameter based on a given sample of data. In this case, the unknown population parameter is the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases.
To find the point estimate, we need to calculate the difference between the sample mean of mail-order sales and the sample mean of internet sales .The formula for the point estimate is given by :Point Estimate = Sample Mean of Mail-Order Sales - Sample Mean of Internet Sales= $70.60 - $87.30= -$
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10. 4 out of 5 students are going on the field trip tomorrow. If there are 400 students, how many
are going on the field trip?
The total students who are going on the field trip are 320 students out of 400 students which has been obtained by using the concept of fractions.
Define Fraction?A fraction represents a part of a number or any number of equal parts. There is a fraction, containing numerator(upper value) and denominator(lower value).
If 4 out of 5 students are going on the field trip, then the fraction of students going on the field trip is 4/5.
To find out how many students are going on the field trip, we can multiply this fraction by the total number of students:
Number of students going on the field trip = (4/5) x 400
Number of students going on the field trip = 320
Therefore, 320 students are going on the field trip.
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Mr. Johnson placed three desks together in his classroom. Each desk measures at 1.5 meters.
How many centimeters are all three desks?
Answer: 7.62
Step-by-step explanation:
Answer:
350 centimeters
Step-by-step explanation:
1.5 meters x 3 = 3.5 meters
There are 100 centimeters in one meter
So, 3.5 x 100 = 350
What is the equation of the line of reflection that reflects shape P into shape Q
The equation of the line of reflection that reflects shape P into shape Q is y = −2x + 12.
To find the equation of the line of reflection that reflects shape P into shape Q, we need to follow some steps:
Step 1: Draw the mirror line. To reflect a point or shape, we must have a mirror line. The mirror line is the line that passes through the reflection and is perpendicular to the reflecting surface. It serves as a reference for reflecting points or shapes.
Step 2: Find the midpoint of PQ. The midpoint of PQ is the point that lies exactly halfway between P and Q.
Step 3: Find the slope of PQ. The slope of PQ is the rise over run or the difference of the y-coordinates over the difference of the x-coordinates.
The slope formula is given by m = (y2 − y1) / (x2 − x1).
Step 4: Find the perpendicular slope of PQ. The perpendicular slope of PQ is the negative reciprocal of the slope of PQ. It is given by m⊥ = −1/m.
Step 5: Write the equation of the line of reflection. The equation of the line of reflection is given by y − y1 = m⊥(x − x1) or y = m⊥x + b, where m⊥ is the perpendicular slope of PQ and b is the y-intercept of the line. To find b, we substitute the coordinates of the midpoint of PQ into the equation and solve for b. Then we substitute m⊥ and b into the equation to get the final answer.
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What is the length of one side of the fenced-in garden? 12 ft 15 ft 21 ft 108 ft
Answer:
B. 15
Step-by-step explanation:
its right on edge
The expression the quantity secant of x plus 1 end quantity over tangent of x was simplified with the following steps:
Step 1: secant x over tangent x plus 1 over tangent x
Step 2: the quantity 1 over cosine x end quantity over tangent x plus 1 over tangent x
Step 3: the quantity 1 over cosine x end quantity over the quantity sine x over cosine x end quantity plus cosine x over sine x
Step 4: 1 over sine x plus cosine x over sine x
Step 5: cosecant x plus cosine x over sine x
Step 6: cosecant x plus cotangent x
Which identity/formula was used to simplify from step 2 to step 3?
The identity used to simplify from step 4 to step 5 is the definition of the cosecant function cosecant x = 1/sine x.
What is a mathematical expression?
A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. This mathematical operation may be addition, subtraction, multiplication, or division. An expression's structure is as follows: Expression is (Number/Variable, Arithmetic Operator, Number/Variable).
For instance, the expression x + y is an expression where x and y are terms with an addition operator between them. Mathematical expressions can be divided into two categories: algebraic expressions, which include both numbers and variables, and numerical expressions, which solely contain numbers.
= the expression 1/sine x
= 1/sine x + cosine x/sine x
= cosecant x + cosine x/sine x
= cosecant x + cotangent x.
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A little help :) Appreciated - 30 points (Reupload)
Answer:
See below!
Step-by-step explanation:
a) 1, 2, 3, 4, 5
The possible outcomes are all the options that there are on the spinner
b) 2
There are only 2 even numbers!
c) [tex]\frac{2}{5}[/tex] or 0.4
There are 2 out of 5 numbers are even on the spinner so that must be the solution!
d) 1
The spinner has only one multiple of 3, so the possible outcome should also be 1.
e) [tex]\frac{1}{5}[/tex] or 0.2
There are only 1 out of 5 options which are multiples of 3, so that would be our solution
f) 4
There are 4 prime numbers in the spinner (1, 2, 3, 5), so that would be a possible outcome.
g) [tex]\frac{4}{5}[/tex] or 0.8
The spinner has 4 out of 5 prime numbers, so our answer would be that!
Hope this helps, have a lovely day! :)
Help please, not sure how to solve this!!!
The exponential function for the Greenville's population so that the yearly growth rate is visible is given as follows:
G(t) = 24000(1.00124)^t.
How to define an exponential function?An increasing exponential function is modeled according to the rule presented as follows:
y = a(1 + r)^t.
In which:
a is the initial amount.r is the growth rate, as a decimal.The function for Greenville's population is given as follows:
G(t) = 24000(1.00496)^4t.
Which means that the population grows at a rate of 0.00496 = 0.496% every four years, hence the yearly growth rate is given as follows:
r = 0.00496/4
r = 0.00124.
Then the function is given as follows:
G(t) = 24000(1.00124)^t.
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the altitude of a triangle is increasing at a rate of centimeters/minute while the area of the triangle is increasing at a rate of square centimeters/minute. at what rate is the base of the triangle changing when the altitude is centimeters and the area is square centimeters?
The rate of change of the base of the triangle is (20 - 1/12 × base × b) cm/min when the altitude is h cm and the area is a sq cm. And this is solved by the concept of Differentiation.
The problem asks to find the rate of change of the base of a triangle when the altitude and area of the triangle are given.
Let's use the formula for the area of a triangle, which is A = 1/2 × base × altitude. Taking the derivative with respect to time, we get dA/dt = 1/2 × (d/dt)(base) × altitude + 1/2 × base × (d/dt)(altitude).
Now, we are given that dA/dt = the rate of change of the area = a constant value. Also, we know that (d/dt)(altitude) = the rate of change of the altitude = b cm/min.
Therefore, we can substitute these values into the formula above to get:
a = 1/2 × (d/dt)(base) × h + 1/2 × base × b
We want to find (d/dt)(base) when h and a are given. Since h is given, we can solve for (d/dt)(base) by isolating it in the equation above:
(d/dt)(base) = (2/a) × (a - 1/2 × base × b)/h
Substituting the given values of h and a, we get:
(d/dt)(base) = (2/60) × (120 - 1/2 × base × b)/6
where b is given in cm/min. Simplifying this expression, we get:
(d/dt)(base) = (20 - 1/12 × base × b) cm/min
Therefore, the rate of change of the base of the triangle is (20 - 1/12 × base × b) cm/min when the altitude is h cm and the area is a sq cm
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what is the modular inverse of $11$, modulo $1000$? express your answer as an integer from $0$ to $999$, inclusive.
The modular inverse of 11, modulo 1000 is 901. Expressing the answer in integer form.
To find the modular inverse of 11 modulo 1000, we need to find an integer x such that [tex]$11x\equiv1\pmod{1000}$[/tex].
One way to find the modular inverse is to use the extended Euclidean algorithm. Using this algorithm, we can find the greatest common divisor of 11 and 1000 and express it as a linear combination of 11 and 1000.
We can then use the coefficients of this linear combination to express 1 as a linear combination of 11 and 1000.
Applying the extended Euclidean algorithm, we have:
1000= 11 *90 + 10
11 = 10 *1 + 1
Working backward, we can express 1 as a linear combination of 11 and 1000:
1 =11 - 10* 1
= 11 - (1000 - 11*90)
= 901 * 11 - 1 *1000
Therefore, the modular inverse of 11 modulo 1000 is 901, since
11*901=1 mod{1000}.
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What’s 3.14 times six?
Answer:
18.84
Step-by-step explanation:
:)
In an arithmetic sequence, the tenth term is 28. The sum of term 5 and term 7 is 32. Calculate the sum of the first 50 terms
The sum of the first 50 terms is 3775. Let a be the first term and d be the common difference of the arithmetic sequence.
Then, the tenth term is a + 9d = 28, and the sum of the fifth and seventh terms is 2a + 12d = 32.
Solving these equations simultaneously, we get a = 2 and d = 3.
To find the sum of the first 50 terms, we use the formula for the sum of an arithmetic sequence:
S50 = (50/2)(2a + (50-1)d) = 25(2 + 49(3)) = 3775.
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in a class in which the final course grade depends entirely on the average of four equally weighted 100-point tests, brad has scored 87 , 89 , and 78 on the first three. what range of scores on the fourth test will give brad a c for the semester (an average between 70 and 79 , inclusive)?
Brad needs to score between 72 and 79 on the fourth test in order to get a C for the semester.
To explain why this is so, we need to first understand how the grade for the semester is calculated.Since the final course grade depends entirely on the average of four equally weighted 100-point tests, this means that each test will count for 25% of Brad’s final grade. Therefore, Brad needs to get an average score of 70-79 (inclusive) on the four tests combined in order to get a C for the semester.
In order to calculate what range of scores Brad needs to get on the fourth test in order to get a C for the semester, we need to look at the scores he has already obtained on the first three tests. Brad has scored 87, 89 and 78 on the first three tests. This gives him a total score of 254 (87+89+78=254). This means that Brad needs to get a score of between 70 and 79 on the fourth test in order to reach a total score of between 280-309 (inclusive), which will result in an average score of between 70-79 (inclusive), and give Brad a C for the semester.
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donica works at an electronics store. Her monthly pay is $1950. she also receives 4% commission on all her sales. she had $12,475 in sales last month. Her rent is 30% of her earnings last month.
how much does Donica pay for rent? round to the nearest whole number
Please explain how:)
Therefore , the solution of the given problem of percentage comes out to be Donica spends $735 in rent.
What exactly does a percentage mean?A statistic or measure that is stated as a percent of 100 is referred to as "a%" in statistics. The terms "pct," "pct," and "pc" are also uncommon. However, it is commonly denoted by the symbol "%". There are no measurements; the proportion of the total sum is flat. Because the numerator of percentages almost always equals 100, they are genuinely integers. Either the percent sign (%) or the word "fraction" must come before a number to indicate that it represents a percent.
Here,
Sales royalty for Donica is calculated as follows:
=> $12,475 * commission of 4%
=> $499 commission
Donica's overall earnings for the previous month after deducting the commission were:
Total income equals monthly salary plus commission.
=> Total income= $1950 + $499.
=> $2449 in total profits
We need to multiply Donica's total income by 30% to determine how much she spends in rent:
=> Rent is 30% of total income.
=> Rent = 0.3 * $2449 = $734.70.
When this is rounded to the closest whole integer, we obtain:
=> Rent = $735
Donica thus spends $735 in rent.
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The area of the given square is cot the power of 2
the area of a square is always the square of its side length, and if the area cannot be expressed as the square of an integer, then we can say that it is not the power of 2.
A square is a quadrilateral that has four equal sides and four right angles. The area of a square is the product of its length and width, which are equal in the case of a square. So, the formula for the area of a square is:
Area = side × side
or
Area = side²
In other words, the area of a square is the square of its side length.
Now, when we say that the area of a square is "not the power of 2," it means that the area cannot be expressed as a perfect square of an integer. For example, if the area of a square is 25, then it is the square of 5, which is an integer, and so the area is the power of 2.
However, if the area of a square is, say, 12, then it cannot be expressed as the square of an integer, since the square of any integer is always a whole number. Therefore, we can say that the area of the given square is not the power of 2.
In summary, the area of a square is always the square of its side length, and if the area cannot be expressed as the square of an integer, then we can say that it is not the power of 2.
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make x the subject of the formula
y = 7x + 4
|||
Calculator
Cone X has a diameter of 20 ft and a height of 16 ft. Cone Y is the same height as cone X, but its diameter is twice the diameter of
cone X
What is the difference in the volumes of the two cones?
Use 3.14
05.024 ft
15.072 ft
O 20.096 ft
3.01 Readiness Checkpoint: Volumes of Cylinders and Cones Di
I don't know
2 3
4 Finish
Answer:
(a) 5024 ft³
Step-by-step explanation:
You want the difference in volumes of two cones with height 16 ft, where the larger has diameter 40 ft and the smaller has diameter 20 ft.
VolumeThe volume of a cone is given in terms of its radius as ...
V = π/3(r²h) . . . . . . r=radius; h=height
The radius is half the diameter, so the formula with diameter is ...
V = π/3(d/2)²h = π/12d²h
DifferenceThe two given cones have the same height, but different diameters. The difference in volumes will be ...
V2 -V1 = (π/12)((d2)²h) -(π/12)((d1)²h) = (πh/12)((d2)² -(d1)²)
V2 -V1 = 3.14(16 ft)/12 × ((40 ft)² -(20 ft)²) = 3.14·16/12·1200 ft³
= 3.14·1600 ft³ = 5024 ft³
The difference in volumes of the two cones is 5025 cubic feet.
in a regression analysis, the coefficient of determination measures goodness of fit. independence of variables. economic plausibility. independence of residuals.
The coefficient of determination measures goodness of fit.
The coefficient of determination, often referred to as R-squared, measures the goodness of fit in a regression analysis. It does not measure the independence of variables, economic plausibility, or independence of residuals.
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the amount of time it takes john to wait in line at the bank is continuous and uniformly distributed between 7 minutes and 17 minutes. what is the probability that it takes john between 9 and 12 minutes to wait in line at the bank?
The probability of John waiting is
0.333.
The probability that it takes John between 9 and 12 minutes to wait in line at the bank is 0.333.
This is because the continuous and uniformly distributed time between 7 and 17 minutes is divided into 10 minutes, meaning each unit is equal to 0.1. Therefore,
the probability of John waiting between 9 and 12 minutes is 3 units of 0.1 which is 0.333.
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This figure consists of a rectangle and a quarter circle.
What is the perimeter of this figure?
Use 3.14 for π.
SOMEONE PLEASE HELP ME!! 40 POINTS
Answer:
61.27
Step-by-step explanation:
Circle perimeter formula: C=2πr
Quarter circle=2πr/4. Given r=11cm
2x3.14x11/4=17.27
Rectangle perimeter: C=2(a+b)
=2（2+20）=44
so, total: 17.27+44=61.27
Can someone pls help me (you are the best)
The answer is x=6x +2
2. The base of a right triangular prism has an area of 98 square units. If the total surface area of
the prism is 466 square units, which of the following are possible areas for the faces of the
prism?
O30, 110, and 190 square units
O 40, 80, and 120 square units
O 50, 100, and 150 square units
O 60, 90, and 120 square units
(1
Optiοn 2: 40, 80, and 120 square units, is the οnly set οf regiοns fοr the prism's faces that are viable.
Hοw is a triangular prism defined?A triangular prism is indeed a prism that has three rectangular sides and twο triangular bases. A pentahedrοn, that is. The rectangular base οf the supplied right triangular prism measures b and h and has an area οf bh = 98 square units. Let l stand in fοr the prism's height. The prism's entire surface area is calculated as fοllοws:
2bh + bl + lh
By simplifying and replacing the values οf bh, we οbtain:
2(98) + bl + lh = 466
bl + lh = 135
The areas οf the twο nοn-base sides οf a prism are each (1/2)bl since they are equivalent right triangle with legs b and l. Let's examine each οf the available respοnses tο see if it cοmplies with the requirements:
Optiοn 1: 30, 110, and 190 square units
If the area οf οne οf the nοn-base faces is 110 square units, then (1/2)bl = 110, sο bl = 220. But bl + lh = 135, sο this is nοt pοssible. This grοup οf lοcatiοns is therefοre nοt feasible.
Optiοn 2: 40, 80, and 120 square units
If the area οf οne οf the nοn-base faces is 80 square units, then (1/2)bl = 80, sο bl = 160. This means that lh = 135 - bl = 135 - 160 = -25, which is nοt pοssible. Sο this set οf areas is nοt pοssible.
Therefοre, this set οf areas is nοt pοssible. This grοup οf areas cannοt thus be achieved. If the area οf οne οf the nοn-base faces is 100 square units, then (1/2)bl = 100, sο bl = 200. But bl + lh = 135, sο this is nοt pοssible. Hence, it is impοssible tο cοver this grοup οf areas.
Optiοn 4: 60, 90, and 120 square units
If the area οf οne οf the nοn-base faces is 90 square units, then (1/2)bl = 90, sο bl = 180. This means that lh = 135 - bl = 135 - 180 = -45, which is nοt pοssible. Sο, this set οf areas is nοt pοssible.
Optiοn 2's range οf 40, 80, and 120 square units is the οnly set οf areas fοr the prism's faces that can be cοnsidered.
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a family trip to washington d.c considers the following scenarios: transportation (plane, car, train) and weather conditions (sunny, windy, rainy, cloudy). how many different combinations are possible?
There are 12 different combinations of transportation and weather conditions for the family trip to Washington D.C.
To find the total number of different combinations of transportation and weather conditions for the family trip to Washington D.C, we can use the multiplication rule of counting, which states that if there are m ways to do one thing and n ways to do another, then there are m x n ways to do both.
There are three different transportation options: plane, car, and train, and four different weather conditions: sunny, windy, rainy, and cloudy. To find the total number of different combinations, we simply need to multiply the number of transportation options by the number of weather conditions:
Total number of combinations = number of transportation options x number of weather conditions
Total number of combinations = 3 x 4
Total number of combinations = 12
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in the same room with a floor area that measures 15' x 10', how many feet of rubber wall base is required to cover the length of all four (4) walls, minus 3' for the door opening?
To cover the length of all four walls in a room that measures 15' x 10', minus 3' for the door opening, it would require 50 feet of rubber wall base.
A rubber wall base is a type of molding that is installed at the base of walls to protect the wall and add aesthetic appeal to the room. To calculate the amount of rubber wall base required for a room, we need to determine the perimeter of the room, which is the sum of the length of all four walls.
In this case, the room measures 15' x 10', which means that the length of the four walls would be (2 x 15) + (2 x 10) = 30 + 20 = 50 feet.
However, we need to subtract 3 feet for the door opening because the rubber wall base does not need to cover the area where the door is located. Therefore, the total amount of rubber wall base required for the room would be 50 - 3 = 47 feet.
But, we need to add some extra footage for corner pieces and cuts. Typically, it is recommended to add an extra 5% to 10% of the total length of the wall base to account for these additional pieces. So, adding 5% of 47 feet, we get an additional 2.35 feet, which we can round up to 3 feet.
Therefore, the final answer is 47 + 3 = 50 feet.
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Which expression is equivalent to 0.75a + 10b + a – 2b?
Answer:
1.75a + 8b
Step-by-step explanation:
0.75a + 10b + a - 2b ← collect like terms
= (0.75 + 1a) + (10b - 2b)
= 1.75a + 8b
Answer:
1.75a+8b
Step-by-step explanation:
Given here, 0.75a + 10b + a – 2b = 0.75a+a+10b-2b
=1.75a+8b
Hence, The required equivalent expression is 1.75a+8b