Answers
If the first, last, middle car in the parking-row are blue, then the total number of different arrangements are 144.
There are 7 different models of cars, out of which 3 are blue and 4 are red.
If the first, middle and last car in the row is blue, which means that the the position of blue cars is fixed and these 3 "blue-cars" can be arranged in 3! ways.
Now, only the 4 spots are left, so, the remaining 4 red-cars can be arranged in the remaining 4 spots in = 4! ways.
Therefore, the total number of ways is = 3! × 4! = 6 × 24 = 144.
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Related Questions
The Volume, V, in liters, of air in the lungs is approximated by the the model, V = -0.0374+3 +0.1525+2 +0.1729t, during a five second respiratory cycle. In here, t is measured in second
Answers
The model approximates the volume, V, in liters, of air in the lungs during a five-second respiratory cycle using the equation V = -0.0374t + 3 + 0.1525t^2 + 0.1729t.
The given equation represents a mathematical model for estimating the volume of air in the lungs during a respiratory cycle. It is a quadratic equation with three terms: -0.0374t, 0.1525t^2, and 0.1729t.
The term -0.0374t represents the linear decrease in volume over time, indicating that the volume decreases by 0.0374 liters for every second of the respiratory cycle.
The term 0.1525t^2 represents the quadratic relationship between volume and time squared, indicating that the rate of change of volume with respect to time is influenced by the square of time.
The term 0.1729t represents the linear increase in volume over time, indicating that the volume increases by 0.1729 liters for every second of the respiratory cycle.
Overall, this model provides an approximation of the volume of air in the lungs during a five-second respiratory cycle, taking into account both linear and quadratic relationships with time.
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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
When Ellen does 19 push-ups and 8 sit-ups, it takes a total of 43 seconds. In comparison, she needs 48 seconds to do 12 push-ups and 12 sit-ups. How long does it take Ellen to do each kind of exercise?
It takes Ellen _ seconds to do a push-up and _seconds to do a sit-up.
Thank you :
Answers
Answer:
push-up = 1 second
sit-up = 3 seconds
Step-by-step explanation:
let p represent the # of push-ups
let s represent the # of sit-ups
System of equations:
19p+8s=43
12p+12s=48
i'll eliminate s by multiplying the top equation by 3 and the bottom equation by -2
57p+24s=129
-24p-24s=-96
33p=33
p=1 second
now solve for s (i'll plug p into the 2nd equation)
12(1) + 12s=48
12s=36
s=3 seconds
I NEED HELP ON THIS ASAP!! IT'S DUE TODAY!!
Answers
The transformations performed on f(x) to create g(x) is a reflection over the y-axis and a translation 4 units up.
An equation for g(x) in terms of f(x) is g(x) = f(-x) + 4.
What is a reflection over the y-axis?In Mathematics and Geometry, a reflection over or across the y-axis or line x = 0 is represented and modeled by this transformation rule (x, y) → (-x, y).
By applying a reflection over the y-axis to coordinate A of the image ABCD, we have the following:
(x, y) → (-x, y)
Coordinate = (-1, 1/10) → Coordinate A' = (-(-1), 1/10) = (1, 1/10).
Furthermore, the transformation rule for the translation of a point by k units up is given by;
(x, y + k) → (x', y')
(1, 1/10 + k) → E(1, 4 1/10)
1/10 + k = 4 1/10
k = 4 1/10 - 1/10
k = 4.
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What is the surface area of the triangular prism?
6. 5 ft 8ft 6ft 2. 5ft
115
120
135
159
Answers
The surface area of the first triangular prism is 174.58 square feet and second triangular prism is 1721.6 square feet.
How to calculate the surface area?To calculate the surface area of a triangular prism, we need the measurements of the base and the height of the triangular bases, as well as the length of the prism.
For the first triangular prism with measurements:
Base: 5 ft
Height: 8 ft
Length: 6 ft
To calculate the surface area, we need to find the areas of the two triangular bases and the three rectangular faces. The formula for the surface area of a triangular prism is:
Surface Area = 2 * (Area of triangular base) + (Perimeter of triangular base * Length)
The area of a triangle can be calculated using the formula: Area = 1/2 * Base * Height.
Area of triangular base = 1/2 * 5 ft * 8 ft = 20 ft²
The perimeter of a triangle is the sum of its three sides.
Perimeter of triangular base = 5 ft + 8 ft + √(5 ft² + 8 ft²) = 5 ft + 8 ft + √89 ft ≈ 5 ft + 8 ft + 9.43 ft ≈ 22.43 ft
Surface Area = 2 * 20 ft² + (22.43 ft * 6 ft) = 40 ft² + 134.58 ft² = 174.58 ft²
Therefore, the surface area of the first triangular prism is approximately 174.58 square feet.
For the second triangular prism with measurements:
Base: 6 ft
Height: 2.5 ft
Length: 115 ft
Area of triangular base = 1/2 * 6 ft * 2.5 ft = 7.5 ft²
Perimeter of triangular base = 6 ft + 2.5 ft + √(6 ft² + 2.5 ft²) = 6 ft + 2.5 ft + √40.25 ft ≈ 8.5 ft + 6.34 ft ≈ 14.84 ft
Surface Area = 2 * 7.5 ft² + (14.84 ft * 115 ft) = 15 ft² + 1706.6 ft² = 1721.6 ft²
Therefore, the surface area of the second triangular prism is approximately 1721.6 square feet.
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The surface area of the triangular prism is x - 0 = -3
Find out the surface area of the triangular prism?If the solution to an absolute value equation is x = -3, then we know that the distance between x and 0 is 3 units. Since the absolute value of a number is the distance between the number and 0 on the number line, we can write the absolute value equation that corresponds to x = -3 as:
| x - 0 | = 3
To write this equation in the form x - b = c, we can simplify the absolute value expression by removing the absolute value bars. This gives us two possible equations:
x - 0 = 3 or x - 0 = -3
Simplifying further, we get:
x = 3 or x = -3
Therefore, the absolute value equation in the form x - b = c that has the solution set {x = -3} is:x - 0 = -3
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Refer to the data in exercise 2. should sarah use the mean or the median to show that she exercises for large amounts of time each day? explain
for exercise 2 this is what it says;
last week, sarah spent 34,30,45,30,40,38, and 28 minutes exercising. find the mean, median, and mode. round to the nearest whole number
Answers
The mean is 35 minutes and the median is 34 minutes.
let's first calculate the mean, median, and mode for Sarah's exercise times: 34, 30, 45, 30, 40, 38, and 28 minutes.
Step 1: Calculate the mean
Add up all the values and divide by the total number of values:
(34 + 30 + 45 + 30 + 40 + 38 + 28) / 7 = 245 / 7 = 35 minutes (rounded)
Step 2: Calculate the median
Arrange the values in ascending order: 28, 30, 30, 34, 38, 40, 45
There are 7 values, so the median is the middle value: 34 minutes
Step 3: Calculate the mode
Determine the value(s) that occur most often: 30 minutes (occurs twice)
Now, should Sarah use the mean or the median to show she exercises for large amounts of time each day? The mean is 35 minutes and the median is 34 minutes. Both values are close and represent the central tendency of the data. However, since the mean is slightly higher than the median, Sarah should use the mean (35 minutes) to show she exercises for a larger amount of time each day.
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The domain of g(x) = log 56 - x) can be found by solving the inequality
A. 6-x<0 ,B. 6-x>0,C. 6-x>=0, D. 6-x<=0
Answers
The inequality to solve is 56 - x > 0. The solution is x < 56. Therefore, the domain of the function g(x) is x < 56. So, the answer is option B.
The function is defined as g(x) = log(56 - x).
The domain of a logarithmic function is all the values that make the argument of the logarithm positive. In other words, the argument of the logarithm (56 - x) must be greater than 0.
So, we solve the inequality 56 - x > 0 for x
56 - x > 0
Subtract 56 from both sides
-x > -56
Divide both sides by -1, and remember to reverse the inequality
x < 56
Therefore, the domain of the function g(x) is all real numbers x such that x < 56. So, the correct answer is B).
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--The given question is incomplete, the complete question is given
" The domain of g(x) = log 56 - x) can be found by solving the inequality
A. 56-x<0 ,B. 56-x>0,C. 56-x>=0, D. 56-x<=0 "--
Kristen is trying to determine the x-intercepts of the graph of a quadratic function. Which form would be the most beneficial in order for Kristen to quickly identify the coordinates? A. Standard Form B. Intercept Form C. Vertex Form
Answers
The form in which is easier to identify the x-intercepts is the one in option B. Intercept form.
Which form would be the most beneficial in order for Kristen to quickly identify the coordinates?If a quadratic equation has a leading coefficient a and x-intercepts x₁ and x₂, then the quadratic equation can be written as:
y = a*(x - x₁)*(x - x₂)
That is called the factored form or the intercept form.
Notice that if the quadratic equation is written in that form, is really easy to identify the x-intercepts of the equation, then that would be the most beneficial form in order for Kristen to quickly identify the coordinates, the correct option is B.
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Menlo Company distributes a single product. The company's sales and expenses for last month follow:
Per Unit
$ 40
28
$ 12
Sales
Variable expenses
Contribution margin
Fixed expenses
Net operating income
Total
$ 600,000
420,000
180,000
Required:
1. What is the monthly break-even point in unit sales and in dollar sales?
2. Without resorting to computations, what is the total contribution margin at the break-even point?
3-a. How many units would have to be sold each month to attain a target profit of $70,800?
3-b. Verify your answer by preparing a contribution format income statement at the target sales level.
146,400
$ 33,600
4. Refer to the original data. Compute the company's margin of safety in both dollar and percentage terms.
5. What is the company's CM ratio? If the company can sell more units thereby increasing sales by $69,000 per month and there is no
change in fixed expenses, by how much would you expect monthly net operating income to increase?
Complete this question by entering your answers in the tabs below.
Req 1
Margin of safety
Req 3A
Req 3B
Req 2
Req 5
Refer to the original data. Compute the company's margin of safety in both dollar and percentage terms. (Round your
percentage answer to 2 decimal places (i.e. 0.1234 should be entered as 12.34).)
Dollars
Percentage
Req 4
%
Answers
If sales increase by 66,000, income will increase by 220,000.00
Net operating income 37,200.00
The margin of safety is 14.01%
How to solveStatement showing Computations
particulars Amount Per unit
Sales 628,000.00 40.00
Variable Expenses 439,600.00 28.00
Contribution Margin 188,400.00 $ 12.00
Fixed Expenses 151,200.00
Net operating income 37,200.00
'
1) BEP in unit sales = 151,200/12 12,600.00
.BEP in sales $ = 12,600 * 40 504,000.00
2) Total Contribution margin at BEP = Fixed costs 151,200.00
3)a Target Profit $ 64,800.00
Fixed Expenses 151,200.00
Desired Contribution 216,000.00
3b. No of units to be sold = 216,000/12 18,000.00
Sales 720,000.00
Variable Expenses 504,000.00
Contribution Margin 216,000.00
Fixed Expenses 151,200.00
Net operating income 64,800.00
4) Margin of safety = 628,000.00-540,000.00 88,000.00
MOS in % = 88,000/6280001 14.01%
5)CM Ratio = 188,400/628,000 0.3
If sales increase by 66,000, income will increase by 220,000.00
66,000/0.3
=220,000.
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You invest $5400 in an account that pays 7% compounded continuously, how many years would it take to reach $8000?
Answers
It would take approximately 7.62 years to reach $8000 if $5400 is invested in an account that pays 7% compounded continuously.
The formula for calculating the future value (FV) of an investment that is continuously compounded is FV = Pe^(rt), where P is the principal amount, r is the annual interest rate, and t is the time in years. In this case, P = $5400, r = 7% = 0.07, and FV = $8000. Substituting these values into the formula, we get:
$8000 = $5400e^(0.07t)
Dividing both sides by $5400 and taking the natural logarithm of both sides, we get:
ln(8000/5400) = 0.07t
Simplifying the left side of the equation, we get:
ln(4/3) = 0.07t
Solving for t, we get:
t = ln(4/3)/0.07 ≈ 7.62 years
Therefore, it would take approximately 7.62 years to reach $8000 if $5400 is invested in an account that pays 7% compounded continuously.
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PLS HELP ME WITH THIS!!!!
Answers
Answer:
g(x) = h(x -7) +5
Step-by-step explanation:
Given h(x) defines a parabola that opens upward with a vertex at (-2, -7) and g(x) defines the same parabola with its vertex at (5, -2), you want to express g(x) in terms of h(x).
TranslationThe graph of f(x) is translated right h units and up k units by ...
f(x -h) +k
We see that g(x) is a translation of h(x) right by 7 units and up by 5 units. This means (h, k) is (7, 5), and the translated function is ...
g(x) = h(x -7) +5
__
Additional comment
This is confirmed by the plots in the second attachment.
Answer: g(x)=h(x-7) +5
Step-by-step explanation:
The graph g(x) has been shifted up 5 (+5) and right 7
When shift a function, the y change, up/down, goes at end of function
When shift in x direction happens, you take opposite sign so we will do -7
g(x)=h(x-7) +5
Area The measurement of the side of a square floor tile is 10 inches, with a possible error of 1/32 inch.
(a) Use differentials to approximate the possible propagated error in computing the area of the square. (b) Approximate the percent error in computing the area of the square.
Answers
The possible propagated error in computing the area of the square is between 19/32 and 21/32 square inches.
How to calculate the error propagation?
(a) Let A be the area of the square tile. The differential of A with respect to the side length x is dA/dx = 2x.
dA ≈ (dA/dx)dx
At the lower end of the possible range for x, we have:
x = 9 31/32 inches
dx = 1/32 inch
dA = (2x)(dx) = (2(9 31/32))(1/32) = 19/32 square inches
At the upper end of the possible range for x, we have:
x = 10 1/32 inches
dx = 1/32 inch
dA = (2x)(dx) = (2(10 1/32))(1/32) = 21/32 square inches
Therefore, the possible propagated error in computing the area of the square is between 19/32 and 21/32 square inches.
(b) The percent error in computing the area of the square is given by:
(percent error) = (error / actual value) x 100
(percent error) = [(21/32 - 100) / 100] x 100% = -79/1600 x 100% ≈ -4.94%.
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145 student are in the auditorium. Of the students in the auditorium, about 86% of the students play a sport. About 45% of the students are in the school play. How many students play a sport? How many students are in the play? Round your answer to the nearest whole
Answers
About 125 students play a sport and about 65 students are in the play.
To find the number of students who play a sport and those who are in the play, we need to use the given percentages and round the answers to the nearest whole.
Find the number of students who play a sport:
Multiply the total number of students (145) by the percentage of students who play a sport (86%).
145 × 0.86 = 124.7
Round the answer to the nearest whole number:
Approximately 125 students play a sport.
Find the number of students who are in the play:
Multiply the total number of students (145) by the percentage of students who are in the play (45%).
145 × 0.45 = 65.25
Round the answer to the nearest whole number:
Approximately 65 students are in the play.
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I have some coins in my pocket. Nickles and pennies I have a total of $. 41 I have 21 coins in total. How many Nickles and pennies do I have?
Answers
The number of nickels and pennies in the pocket is 5 and 16 respectively.
How to find the number of coins?To find the number of coins, Let's assume the number of nickels is x and the number of pennies is y.
According to the problem, we have two equations:
The total value of the coins is $0.41:
0.05x + 0.01y = 0.41
The total number of coins is 21:
x + y = 21
Now we can solve this system of equations to find x and y. One way to do this is to use substitution.
Solving the second equation for y, we get:
y = 21 - x
Substituting this into the first equation, we get:
0.05x + 0.01(21 - x) = 0.41
Simplifying:
0.05x + 0.21 - 0.01x = 0.41
0.04x = 0.2
x = 5
So we have 5 nickels.
Substituting this into the equation y = 21 - x, we get:
y = 21 - 5 = 16
So we have 16 pennies.
Therefore, the number of nickels and pennies in the pocket is 5 and 16 respectively.
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Aleks and Melanie used a protractor to measure the angle below. Aleks thinks the angle measures 50° but Melanie says it is actually 130°. Their teacher confirms that Melanie has the correct answer. What mistake did Aleks make while measuring the angle?
Answers
The mistake, Aleks made, while measuring the angle is, he measure the angle from the wrong side of the line.
Angle is a dimensionless vector quantity, that is, it is very important, to take care of the directions, while measuring the angle.
That is, to measure the angle, say ∠ABC, the 0°(reference) line of the protractor, must be on one either AB or BC, to measure the angle rightly.
And since the angles between two lines are supplementary in nature, that is, the two angles will add up to make 180°, that is why, the angle measure by Alek and Melanie, add up to make 180°.
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Solve systems of equation by the substitution method.
a - 3 = 2b
4a + 5b- 8 = 0
Answers
The value of the variables are a = 1 and b = -1
How to solve the equationGiven that the equations are;
a - 3 = 2b
4a + 5b- 8 = 0
Using the substitution method, we have;
Make 'a' the subject of formula from equation (1)
a = 2b + 3
Now, substitute the value of the variable in the second equation
4(2b + 3) + 5b - 8 = 0
expand the bracket, we have;
8b + 12 + 5b - 8 = 0
collect the like terms, we get;
8b + 5b = 0 - 5
add or subtract the values
5b = -5
b = -1
Substitute the value of b as =-1
a = 2(-1) +3
expand the bracket
a = -2 + 3
a = 1
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What is the area of the following circle?
Either enter an exact answer in terms of π or use 3.14 for π and enter your answer as a decimal.
Answers
The area of the circle whose diameter is 14 is approximately 153.94 square units or 49π square units..
The area of a circle is given by the formula A = πr², where r is the radius of the circle. Since the diameter of the circle is given as d = 14, we know that the radius is half of the diameter, which is r = d/2 = 7.
Substituting the value of the radius in the formula, we get:
A = πr² = π(7)² = π(49) ≈ 153.94 (rounded to two decimal places using 3.14 for π)
Therefore, the area of the circle is approximately 153.94 square units. Alternatively, the exact answer can be left in terms of π, which would be A = 49π square units.
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Given that BC is tangent to circle A and that BC=3 and AB=5. Calculate
the length of the radius of circle A
Answers
The radius of circle A is 4.
From the given information, we can draw a right triangle ABC where BC is the tangent to circle A at point C, AB is the hypotenuse, and AC is the radius of the circle. By the Pythagorean theorem, we have:
AC² + BC² = AB²
Substituting the given values, we get:
AC² + 3² = 5²
AC² = 25 - 9
AC² = 16
Taking the square root of both sides, we get:
AC = 4
Therefore, the length of the radius of circle A is 4.
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GARDENING A gardener is selecting plants for a special display. There are 15 varieties of pansies from which to choose. The gardener can only use 9 varieties in the display. How many ways can 9 varieties be chosen from the 15 varieties?
Answers
Answer:
5,005
Step-by-step explanation:
This is a combination problem. The formula for combination is:
nCr = n! / (r!(n-r)!)
Where n is the total number of items, and r is the number of items to be selected.
Using this formula, we can calculate the number of ways to choose 9 varieties from 15:
15C9 = 15! / (9!(15-9)!) = 5005
Therefore, there are 5,005 ways to choose 9 varieties from 15 varieties of pansies.
A fair six-sided die will be rolled fifteen times, and the numbers that land face up will be recorded. Let x¯1 represent the average of the numbers that land face up for the first five rolls, and let x¯2 represent the average of the numbers landing face up for the remaining ten rolls. The mean μ and variance σ2 of a single roll are 3. 5 and 2. 92, respectively. What is the standard deviation σ(x¯1−x¯2) of the sampling distribution of the difference in sample means x¯1−x¯2?
Answers
The mean of a single roll is given as μ = 3.5, and the variance is given as [tex]σ^2[/tex] = 2.92.
The sample size for the first five rolls is n1 = 5, and the sample size for the remaining ten rolls is n2 = 10.
The mean of the sampling distribution of the difference in sample means x¯1−x¯2 is given as:
μ(x¯1−x¯2) = μ(x¯1) - μ(x¯2) = μ - μ = 0
The variance of the sampling distribution of the difference in sample means x¯1−x¯2 is given as:
σ^2(x¯1−x¯2) = (σ^2(x¯1)/n1) + (σ^2(x¯2)/n2)
where σ^2(x¯1) is the variance of the sample mean for the first five rolls and σ^2(x¯2) is the variance of the sample mean for the remaining ten rolls.
Since each roll of the die is independent, the variance of the sample mean for each sample is given as:
σ^2(x¯1) = σ^2/ n1 = 2.92/5 = 0.584
σ^2(x¯2) = σ^2/ n2 = 2.92/10 = 0.292
Substituting these values in the above equation, we get:
σ^2(x¯1−x¯2) = (0.584/5) + (0.292/10) = 0.1468
Therefore, the standard deviation of the sampling distribution of the difference in sample means x¯1−x¯2 is:
σ(x¯1−x¯2) = sqrt(σ^2(x¯1−x¯2)) = sqrt(0.1468) = 0.3835 (rounded to four decimal places)
Hence, the standard deviation of the sampling distribution of the difference in sample means x¯1−x¯2 is 0.3835.
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Can someone help me asap? It’s due today!!
Answers
John would have the option of taking 10 different cones
How to solve for the coneThe questions says that there is the option of having the flavors that are available ice cream flavors are: chocolate (C), mint chocolate chip (M), strawberry (S), rainbow sherbet (R), and vanilla (V).
The available flavors are then 5 in number
Then the number of scoops that he can have from each of the cone is said to be 2
Hence we would have 5 x 2
= 10
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The surface area of a rectangular prism is 335 ft2. If the area of the base is 21 ft2, and the perimeter of the base is 20 ft. What is the height of the prism? Round
your answer to the tenths.
Answers
2lw + 2lh + 2wh = 335
We also know that the area of the base is 21 ft^2, so lw = 21. Finally, we know that the perimeter of the base is 20 ft, so 2l + 2w = 20, or l + w = 10.
We can use these equations to solve for h. First, we can solve for l or w in terms of the other variable:
l = 21/w
w = 21/l
Next, we can substitute these expressions into the equation l + w = 10:
21/w + 21/l = 10
Multiplying both sides by wl, we get:
21l + 21w = 10wl
Substituting 21/w for l and 21/l for w, we get:
21(21/w) + 21(21/l) = 10(21)
Simplifying this equation, we get:
441/w + 441/l = 210
Multiplying both sides by wl, we get:
441l + 441w = 210lw
Substituting 21/w for l and 21/l for w, we get:
441(21/w) + 441(21/l) = 210(21)
Simplifying this equation, we get:
9261/w = 441
Solving for w, we get:
w = 9261/441
w ≈ 21
Substituting this value of w into the equation l + w = 10, we get:
l + 21 = 10
l = -11
This doesn't make sense, so we made a mistake somewhere. Let's go back and check our work.
We made an error in the equation 441l + 441w = 210lw. We should have multiplied both sides by 2 instead of by wl. So, let's start again:
441/w + 441/l = 210/21
Multiplying both sides by wl, we get:
441l + 441w = 210
Substituting 21/w for l and 21/l for w, we get:
441(21/w) + 441(21/l) =
In a 2 digit number the tens digit is 5 less than the units digit. The number itself is 5 more tha 3 times the sum of its digits. What is the number
Answers
Answer:
Step-by-step explanation:
(2-5)3=-9. (-9)5 =-45
Keisha's teacher gives her the following information: • m, n, p, and q are all integers and p = 0 and q + 0 m and B= 4 What conclusion can Keisha make? A + B = so the sum of two rational numbers is a rational number. AB= so the product of two rational numbers is a rational number. A + B = so the sum of a rational number and an irrational number is an irrational number. A. BE so the product of two irrational numbers is an irrational number.
Answers
Option C is correct i.e. A+B= (mp + nq)/pq, so the sum of two rational numbers is a rational number.
Given integers are m, n, p and q
And q ≠ 0 and p ≠ 0
A = m / p
B = n/ q
Adding A and B
A + B = m / p + n / q
A + B = (mq + np) / pq
as p ≠ 0 and q ≠ 0 so, pq ≠ 0
So, A + B = (mq + np) / pq is a rational number
Therefore, option C is correct i.e. A+B= (mp + nq)/pq, so the sum of two rational numbers is a rational number.
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Given question is incomplete, the complete question is below:
Keisha's teacher gives her the following information:
• m, n, p, and q are all integers, and p≠ 0 and q≠0
•A= m/q and B= n/p
What conclusion can Keisha make?
A: A +B = (mp + nq)/pq, so the sum of a rational number and an irrational number is an irrational number.
B: A•B= (mp + nq)/pq, so the product of two irrational numbers is an irrational number.
C: A+B= (mp + nq)/pq, so the sum of two rational numbers is a rational number.
D: A•B= (mp + nq)/pq, so the product of two rational numbers is a rational number.
Find the area of the surface obtained by rotating the curve of parametric equations x = 6 cos^3 θ, y = 6sin^3 θ, 0 ≤ θ ≤ π/2
Answers
The area of the surface obtained by rotating the curve of parametric equations x = 6 cos^3 θ, y = 6sin^3 θ, 0 ≤ θ ≤ π/2 is 96π/5 square units.
To find the area of the surface obtained by rotating the curve of parametric equations x = 6 cos^3 θ, y = 6sin^3 θ, 0 ≤ θ ≤ π/2, we can use the formula for surface area of revolution:
A = 2π ∫_a^b f(x) √(1+(f'(x))^2) dx
In this case, we need to first find the function y = f(x) that represents the curve. Using the given parametric equations, we can eliminate θ to get:
x = 6 cos^3 θ
x = 6 (1-sin^2 θ) cos^2 θ
y = 6 sin^3 θ
y = 6 (1-x/6)^(3/2)
So the function that represents the curve is y = 6 (1-x/6)^(3/2). Now we can use the formula for surface area of revolution:
A = 2π ∫_0^6 (6 (1-x/6)^(3/2)) √(1+(-3/4 (1-x/6)^(-1/2))^2) dx
A = 2π ∫_0^6 (6 (1-x/6)^(3/2)) √(1+9/16 (1-x/6)^(-1)) dx
A = 2π ∫_0^6 (6 (1-x/6)^(3/2)) √((25-9x)/(16(1-x/6))) dx
This integral can be evaluated using substitution and partial fractions. The final answer is:
A = 96π/5
Therefore, the area of the surface obtained by rotating the curve of parametric equations x = 6 cos^3 θ, y = 6sin^3 θ, 0 ≤ θ ≤ π/2 is 96π/5 square units.
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7z+9z+7-7 =180 How do
You solve this
Answers
The solution for the given linear expression is 11.25 (45/4).
Linear Expression
A linear expression can be represented by a line. The standard form for this equation is: y=mx+b , for example, y=11x+9. Where:
m= the slope.
b= the constant term that represents the y-intercept.
For the given example: m=11 and b=9.
The question gives the expression:7z+9z+7-7 =180. Then, you should find the variable z.
7z+9z+7-7 =180
16z+0=180
16z=180
z=180/16=90/8=45/4=11.25
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Please help :D
A. Explain how to make a prediction based on the probability of an event.
B. Then, give an example in which predictions are made based on probabilities
Answers
This prompt is about probability. The answers are given as follows;
Identifying the probability of an event is crucial to making predictions based on its likelihood. T his involves calculating the probability either through historical data or experimentation.
Once determined, utilizing this value enables one to make future predictions regarding the occurrence of such events; for instance, 80% probability of precipitation tomorrow implies an 80% chance of rain.
Calculating probabilities has proven essential to sports betting because it helps bookmakers given some degree of foresight on which teams are going to win specific games or tournaments. Operating under the premise that there will always be two probable outcomes (either one side wins while another loses), these bookmakers could assign numerical values on what percentage they deem worthy enough for each team's chances.
Subsequently, using precise mathematical formulas and equations, bettors assess wagering-related uncertainties based on these predetermined likelihoods before deciding whether or not they should place money bets.
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The final exam scores in a statistics class were normally distributed with a mean of
63 and a standard deviation of five.
find the score that marks the 11% of all scores.
Answers
The score that marks the 11% of all scores is approximately 56.875 .
To find the score that marks the 11% of all scores, we need to use the standard normal distribution table, also known as the Z-table, since the given distribution is a normal distribution.
The first step is to find the Z-score that corresponds to the 11th percentile, which is given by: Z = invNorm(0.11) ≈ -1.225
Here, "invNorm" represents the inverse of the standard normal cumulative distribution function, which can be computed using statistical software or a calculator.
The second step is to use the Z-score formula to find the raw score that corresponds to this Z-score:Z = (X - μ) / σ
where X is the raw score we want to find, μ is the mean of the distribution, and σ is the standard deviation. Plugging in the values we have:
-1.225 = (X - 63) / 5
Solving for X, we get:
X = -1.225 * 5 + 63 = 56.875
Therefore, the score that marks the 11% of all scores is approximately 56.875
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Assume there are 0. 9 U. S. Dollars in a Canadian dollar. If gasoline costs 1. 50 Canadian dollars per liter, how many U. S. Dollars does it cost to buy a gallon of gas in Canada? (1 gallon = 3. 8 liters)
a. $3. 28
b. $5. 13
c. $2. 95
d. $5. 68
Answers
5.13 U. S. Dollars will it cost to buy a gallon of gas in Canada. The correct answer to the question is A
Given in the question,
Cost of 1 liter gasoline = 1.50 Canadian dollars
1 gallon = 3.8 liters
Thus, to calculate the price of 1 gallon we multiply the cost of 1 liter by 3.8
Cost of 3.8 liters of gasoline = 1.5 * 3.8
= 5.70 Canadian dollars
1 Canadian dollar = 0.9 U. S. dollars
5.70 Canadian dollars = 5.70 * 0.9
= 5.13 U. S. dollars
That is the cost of 1 gallon of gas in Canada is 5 U S dollars and 13 cents.
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find the volume of the figure
Answers
Answer:
252 mi
Step-by-step explanation:
volume= L x W x H
9x 7 x 4 = 252 mi
What is the percent of change in 6 yards to 36 yards - - - 7th-grade math show the work
Answers
Answer:
Step-by-step explanation:
Rounded percent of change = 500.0% Therefore, the percent of change is an increase of 500.0%.
I think sorry if I’m wrong