Using the concept of arrangements, 720 days must pass before the class must repeat a seating arrangement
The class has 6 students and 6 desks and students change the seating arrangement each day. We are asked to calculate the number of days that must pass before the class must repeat a seating arrangement.
The number of days that must pass before the class must repeat a seating arrangement is equal to the total number of seating arrangements.
Person one has 6 positions to choose from, person 2 has 5 positions to choose from and so on.
Total number of seating arrangements = 6 × 5 × 4 × 3 × 2 × 1
= 720
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Each of four friends-Jennifer, Rebecca, Derek, and
Matthew-had the goal of raising $50. How much
money did each person raise? Show or explain your
answer
a. Jennifer raised 50% of her goal.
b. Rebecca raised 100% of her goal.
c. Derek raised 75% of his goal.
d. Matthew raised 150% of his goal.
Answer:
Jennifer raised $25
Rebecca raised £50
Derek raised $37.50
Matthew raised $75
Step-by-step explanation:
J: 50% = dividing by 2, 50/2= 25
R: 50 is 100%, because that was the total
D: 75% = dividing by 4, timsing by three, so 50/4 is 12.5 x 3 is 37.5, put it into currency $37.50
M: We add another 25% onto 50 so 25+50=75.
(hope this works!!)
Similar Triangles Question
Solve for the missing length, X.
The required value of the x for the missing lengths of the side triangle is given as 28.6 ft.
What are Similar triangles?Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.
here,
As the triangles are similar,
The ratio of corresponding sides is equal,
So
13/5 = x/11
x = 13 × 11 / 5
x = 28.6
Thus, the required value of the x for the missing lengths of the ais given as 28.6 ft.
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If x + y = 6 and 3x – y = 4 then x – y is equal to
Answer:
[tex]-1[/tex]
Step-by-step explanation:
[tex](x+y)+(3x-y)=4 \implies 4x=10 \implies x=2.5 \\ \\ 2.5+y=6 \implies y=3.5 \\ \\ \therefore x-y=2.5-3.5=-1[/tex]
Given f(x)=4x^2+9x+9, find f(−1)
The value of the function f(-1) is -4
What is a function?A function is simply described as an equation that explains the relationship between the independent variable and the dependent variable.
From the information given, we have the function;
f(x)=4x^2+9x+9
To determine the value of f(-1)
substitute the value of x as- 1, we get;
f(-1) = 4(-1)² + 9(-1) + 9
expand the bracket, we get;
f(-1) = -4 -9 + 9
Add or subtract the values, we have;
f(-1) = -4
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A line contains the points P (-1, 4) and Q (-4, -2). Write the equation of the line in the slope-intercept form.
A.y = 2x + 6
B.y = 6x + 2
C.y = 3x - 4
D.y =2x + 2
Answer:
Step-by-step explanation:
Given points are P(-1,4) and Q(-4,-2)
we know that slope m between two points (x1,y1) and (x2,y2) is m=y2-y1/x2-x1
so,slope m between points P and Q is m=-2-4/-4-(-1)
m=-6/-3
m=2
Now,we know that equation of line
with slope m having points (x1,y1) and (x2,y2) is y-y1=m(x-x1)
so equation of line between P and Q is y-4=2(x+1)
y-4=2x+ 2
y=2x+6
Too tired to do it. please answer it for me
Which angles are corresponding angles? Se
lect all that apply
The angles that are corresponding angles:
∠1 and ∠3
∠5 and ∠7
∠6 and ∠8
We know that when a transversal intersects parallel lines or non-parallel lines then the angles formed at the same relative position at each intersection are nothing but the corresponding angles.
If a transversal intersects parallel lines, then the corresponding angles formed have equal measure.
Wheras if a transversal intersects non-parallel lines, then the corresponding angles formed doesn’t have any relation with each other.
In the following figure we can observe that line p and line q are non-parallel lines and are intersected by transversal r.
From definition of corresponding angles, the pair of corresponding angles:
∠1 and ∠3
∠5 and ∠7
∠6 and ∠8
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Find the complete question below.
Part 4: Fill in the blank. cos (56°) = sin(°)
The complete expression in the blank is cos (56°) = sin(34°)
How to complete the blanksFrom the question, we have the following parameters that can be used in our computation:
cos (56°) = sin(°)
The blank expression can be calculated as
When x + y = 90;
sin(x) = cos(y)
Using the above as a guide, we have the following:
Blank + 56 = 90
Evakuate the like terms
Blank = 34
So, we have
cos (56°) = sin(34°)
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THERES A PICTURE
HELP ME PLEASEEEEE AND THANK YOUUUUU
The equation of the quadratic curve are:
Curve 1: y = -(x + 5)² + 4Curve 2: y = (x + 5)² + 4How to write the equation of parabolaQuadratic equation when the directrix is at y direction is of the form:
(x - h)² = 4P (y - k)
OR
standard vertex form, y = a(x - h)² + k where a = 1/4p
The vertex for curve 1
v (h, k) = (-5, 4)
h = -5
k = 4
substitution of the values into the equation gives
y = a(x - h)² + k
y = a(x + 5)² + 4
Using (-3, 0) to solve for a
y = a(x + 5)² + 4
0 = a(-3 + 5)² + 4
-4 = a (2)²
a = -1
The equation is y = -(x + 5)² + 4
The vertex for curve 2
v (h, k) = (5, -4)
h = 5
k = -4
substitution of the values into the equation gives
y = a(x - h)² + k
y = a(x - 5)² - 4
Using (3, 0) to solve for a
y = a(x - 5)² - 4
0 = a(3 - 5)² - 4
4 = a (-2)²
a = 1
The equation is y = (x + 5)² + 4
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A store pays $742 for a flute and marks the price up by 202%. What is the amount of the
mark-up?
Round your answer to the nearest dollar: $
a system if equations y=x-6 and y=-x-2 grap the sytsem then write the solution you can also awnser no soloution or infinite solutions.
the solution is where they intercept; (2,-4)
Which property of real numbers is shown below?
3 + ((-5) + 6) = (3 + (-5)) + 6
O commutative property of addition
O identity property of multiplication
associative property of addition
commutative property of multiplication
lThe table below shows the price of different quantities
of standard-sized lemons at Joe's Fruit Stand. What is the
least amount of money needed to purchase exactly 20
standard-sized lemons if the bags must be sold intact
and there is no tax charged for lemons?
Number of lemons:
Total price:
$3.60
1
$0.30
bag of 6
$1.20
bag of 12
$2.10
The least amount of money needed to purchase exactly 20 standard-sized lemons is $1.50, by buying three bags of 6 lemons each and two individual lemons.
What is Combination?
In mathematics, a combination is a way of selecting items from a larger set without regard to the order in which the items are selected. In other words, a combination is a selection of a subset of items from a larger set, where the order of the selected items does not matter.
The number of possible combinations of r items selected from a set of n items is denoted by the notation C(n, r), or sometimes written as nCr. The formula for calculating the number of combinations is:
C(n, r) = n! / (r! * (n - r)!)
To purchase exactly 20 standard-sized lemons at Joe's Fruit Stand, we need to find the combination of bags of lemons that adds up to a total of 20. We want to minimize the cost, so we should choose the combination of bags with the lowest cost.
One possible combination is to buy two bags of 12 lemons each, for a total of 24 lemons, and then discard 4 lemons. This would cost $2.10 x 2 = $4.20.
Another possible combination is to buy three bags of 6 lemons each, for a total of 18 lemons, and then buy two individual lemons for a total of 20 lemons. This would cost $0.30 x 3 + $0.30 x 2 = $1.50.
Therefore, the least amount of money needed to purchase exactly 20 standard-sized lemons is $1.50, by buying three bags of 6 lemons each and two individual lemons.
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consider the following regression model: which of the following is an algebraic property of ols estimates of this model and its associated statistics? group of answer choices the sum, and therefore the sample average of the ols residuals, is positive. the sum of the ols residuals is negative. the sample covariance between the regressors and the ols residuals is zero. ols sample regression line always passes through the sample average of x and sample average of y both a and b are correct both a and d are correct both c and d are correct none of the above
Option (c) is correct: the sample covariance between the regressors and the OLS residuals is zero. This is an important property because it implies that the OLS estimator is not biased and the estimated coefficients of the independent variables are consistent.
The algebraic property of OLS (Ordinary Least Squares) estimates is that the sample covariance between the regressors and the OLS residuals is zero. This means that the OLS estimates are unbiased and not correlated with the independent variables in the regression model.
Option (a) is incorrect: the sum, and therefore the sample average of the OLS residuals, can be either positive or negative depending on the distribution of the data and the fit of the model.
Option (b) is also incorrect: the sum of the OLS residuals can be either positive or negative depending on the distribution of the data and the fit of the model.
Option (d) is incorrect: the OLS sample regression line does not always pass through the sample average of x and the sample average of y. However, it does pass through the point of averages when the model includes a constant term (i.e., intercept).
Therefore, the correct answer is (c): the sample covariance between the regressors and the OLS residuals is zero.
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Which procedure correctly simplifies the expression 2(4x + 3) + (x - 3)?
To simplify the expression 2(4x + 3) + (x - 3), we need to use the distributive property of multiplication over addition, and then combine like terms.
The expression 2(4x + 3) + (x - 3) contains parentheses and addition and multiplication operations, so we need to follow the order of operations to simplify it. The order of operations is:
1. Simplify any expressions inside parentheses.
2. Evaluate any exponents.
3. Perform multiplication and division, from left to right.
4. Perform addition and subtraction, from left to right.
Let's follow these steps to simplify the expression,
1. Simplify any expressions inside parentheses.
There are two sets of parentheses in the expression: (4x + 3) and (x - 3).
We can use the distributive property of multiplication over addition to eliminate the parentheses:
2(4x + 3) + (x - 3) = 8x + 6 + x - 3
2. Evaluate any exponents,
There are no exponents in the expression.
3. Perform multiplication and division, from left to right.
There is no multiplication or division to perform.
4. Perform addition and subtraction, from left to right.
We can now simplify the expression by combining like terms:
8x + 6 + x - 3 = (8x + x) + (6 - 3) = 9x + 3
Therefore, the simplified expression is 9x + 3.
In summary, the correct procedure to simplify the expression 2(4x + 3) + (x - 3) is to use the distributive property to eliminate the parentheses, and then combine like terms to obtain the simplified expression 9x + 3.
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The function
y
=
f
(
x
)
y=f(x) is graphed below. Plot a line segment connecting the points on
f
f where
x
=
−
4
x=−4 and
x
=
1.
x=1. Use the line segment to determine the average rate of change of the function
f
(
x
)
f(x) on the interval
−
4
≤
x
≤
1.
−4≤x≤1.
The average rate of change of the function is 1.6
How to to determine the average rate of change of the functionFrom the question, we have the following parameters that can be used in our computation:
The graph
The interval is given as
−4≤x≤1.
From the graph, we have
f(-4) = -4
f(1) = 4
The average rate of change at this interval is calculated as
Rate = Change in function values/Change in x values
So, we have
Rate = (-4 - 4)/(-4 - 1)
Evaluate
Rate = 1.6
Hence, the rate is 1.6
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Kim bought a birdhouse that originally cost $36. She used a coupon that took 25% off the price. How much money did Kim save?
Kim saved $9 by using the coupon.
How to find Original price?
The MSRP (i.e., Manufacturer's Suggested Retail Price) set the original price, which is the cost. In the majority of cases, the original price would have been less expensive than the current price, though this is not always the case. Finding an item's original price and knowing the price after a discount are both made possible by original price.
Original price = Sales price/(100%-Discount%)
To find out how much money Kim saved, we need to first find out how much the birdhouse cost after the coupon was applied.
The coupon took 25% off the original price, so the birdhouse cost 100% - 25% = 75% of its original price.
So, the new price of the birdhouse would be:
36 * 75% = $27
Kim saved 36 - 27 = $9 by using the coupon.
Therefore, Kim saved $9 using the coupon.
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the tortoise and the hare are running a 1 km race. after running comfortably for 7 s, the hare is so far ahead that he decides to take a nap under a tree, 100 m away from the finish line. if the tortoise is moving constantly at a speed of 0.27 m/s, and the maximum speed of the hare is 15 m/s, how long can the hare afford to nap if he does not want to lose the race?
The hare can afford to nap for a maximum time of 3,690 seconds without losing the race if his speed is 15 m/s.
After running for 7 seconds, the hare has covered a distance of:
[tex]distance = speed \times time\\distance = 15 \times 7\\[/tex]
distance = 105m
The hare is now 895 m away from the starting line and 100 m away from the finish line.
The hare needs to cover a distance of 100 m to reach the finish line, while the tortoise needs to cover a distance of 895 m.
calculate the time it would take the tortoise to reach the finish line:
[tex]time = \frac{100}{0.27}[/tex] = 3704 seconds
The maximum speed of the hare is 15 m/s, which means the time it would take the hare to cover the distance is:
[tex]time = \frac{100}{15}[/tex] = 6.67 seconds
so, the time hare have to nap so that he does not lose race = 3704 - (7+6.67) ≅3690 seconds
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PROMPT: A spherical toy of diameter 75 cm must have a triangular sticker of height 12 cm and base of 10 cm. What is the surface area not covered by the sticker?
CLAIM:
EVIDENCE:
REASONING:
The surface area not covered by the sticker on the spherical toy is approximately 5614.1 cm².
CLAIM: The surface area not covered by the sticker on the spherical toy is approximately 5614.1 cm².
EVIDENCE: The total surface area of the spherical toy can be calculated using the formula A = 4πr², where r is the radius of the sphere. Since the diameter of the sphere is given as 75 cm, the radius is half of the diameter, which is 37.5 cm. Therefore, the total surface area of the spherical toy is:
A = 4π(37.5)²
A = 4π(1406.25)
A ≈ 17593.29 cm²
The surface area covered by the triangular sticker can be calculated by finding the area of the triangle, which is given by the formula A = 1/2 bh, where b is the base and h is the height. Therefore, the surface area covered by the sticker is:
A = 1/2 (10)(12)
A = 60 cm²
The surface area not covered by the sticker is the difference between the total surface area of the spherical toy and the surface area covered by the sticker:
A_not_covered = A - A_sticker
A_not_covered ≈ 17593.29 - 60
A_not_covered ≈ 17533.29 cm²
Therefore, the surface area not covered by the sticker on the spherical toy is approximately 5614.1 cm².
REASONING: By calculating the total surface area of the spherical toy and subtracting the surface area covered by the triangular sticker, we can determine the surface area not covered by the sticker. Since the sticker covers a relatively small area compared to the total surface area of the sphere, the surface area not covered by the sticker is almost equal to the total surface area of the sphere, minus the area of the sticker.
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x+1/x+4=3 find the value of x
PLEASE GIVE BRAINLIEST!
thank you and have a good day ;)
Answer:
-11/2
Step-by-step explanation:
Multiply both sides by a polynomial to clear functions
x + 1 = 3(x +4)
x + 1 = 3x + 12
x - 3x = 12 -1
-2x = 11
x = -11/2
I hope this helps
Answer:
The answer can be written in multiple forms
Fraction Form: [tex]x=-\frac{11}{2}[/tex]
Decimal Form: [tex]x=-5.5[/tex]
Step-by-step explanation:
Given
[tex]\frac{x+1}{x+4}=3[/tex]
Lets solve for [tex]x[/tex].
Eliminate the fraction by multiplying each side of the equation by [tex]x+4[/tex].
[tex]x+1=3(x+4)[/tex]
Simplify the right side by applying the distributive property.
[tex]x+1=(3*x)+(3*4)[/tex]
[tex]x+1=3x+12[/tex]
Subtract [tex]3x[/tex] from both sides of the equation.
[tex]x+1-3x=12[/tex]
Add [tex]x[/tex] and [tex]-3x[/tex].
[tex]-2x+1=12[/tex]
Subtract [tex]1[/tex] from both sides of the equation.
[tex]-2x=11[/tex]
Divide each side of the equation by [tex]-2[/tex].
[tex]x=-\frac{11}{2}[/tex]
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What’s the answer for this I’m not sure
Answer:
8√57/57
Step-by-step explanation:
a² + b² = c²
a² + 8² = 11²
a² + 64 = 121
a² = 57
a = √57
For angle Θ, opp = 8, adj = √57, hyp = 11.
tan Θ = opp/adj = 8/√57 = 8√57/57
3x - 5 = -3 is the answer positive or negative
Answer:
x = 2/3
0r 0.6(6)
both are positive
Step-by-step explanation:
3x - 5 = -3 is the answer positive or negative?
3x - 5 = -3
3x = -3 + 5
3x = 2
x = 2/3
0r 0.6(6)
x4-8x2y2+16y4-256 Factorise the equation
Answer:
it's like this the answer
Step-by-step explanation:
x⁴-8x²y²+16y²-256
(x²-8xy)²+(4y-16)²
Answer:
x⁴-8x²y²+16y²-256
(x²-8xy)²+(4y-16)²
Step-by-step explanation:
There are 4 grams of sugar in 1/2 of a liter of a new sports drink. How much sugar is in 3⁄4 of a liter of the sports drink?
There are 6 grams of sugar in 3/4 of a liter of the sports drink. when There are 4 grams of sugar in 1/2 of a liter of a new sports drink.
To find out how much sugar is in 3/4 of a liter of the sports drink, we need to first calculate the total amount of sugar in 1 liter of the drink. Since there are 4 grams of sugar in 1/2 of a liter, then in 1 liter, there would be 4 x 2 = 8 grams of sugar.
Now that we know there are 8 grams of sugar in 1 liter, we can calculate how much sugar there is in 3/4 of a liter: 8 x (3/4) = 6 grams.
Therefore, there are 6 grams of sugar in 3/4 of a liter of the sports drink.
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a certain species of virulent bacteria is being grown in a culture. it is observed that the rate of growth of the bacterial population is proportional to the number present. if there were 4000 bacteria in the initial population and the number doubled after the first 30 minutes, how many bacteria will be present after 3 hours?
For a certain species of virulent bacteria with the rate of growth of the bacterial population as proportional to the number the bacteria present after 3 hours is 256000.
What is exponential function?A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth.
When there is exponential growth, the quantity grows initially extremely slowly and subsequently quickly. Over time, the rate of change quickens. As time goes on, the rate of increase accelerates. It is intended for the quick growth to be a "exponential increase".
The species of bacteria follow an exponential growth pattern.
The exponential growth is given as:
[tex]A(t) = A_0e^{kt}[/tex]
Where, A₀ is the initial population = 4000
k = constant
t = time = 30 minutes = 1/2 hour.
The bacteria doubles in 30 minutes, thus A(t) = 2(4000) = 8000.
Substituting the values in the equation:
[tex]8000 = 4000e^{k(\frac{1}{2} )}\\\\2 = e^{k(\frac{1}{2} )}[/tex]
Takin ln on both sides of the equation:
ln(2) = 1/2 k
2(ln(2)) = k
k = 1.38
The number of bacteria present after 3 hours:
[tex]A(t) = 4000e^{(1.38)(3)}\\\\[/tex]
A(t) = 256000
Hence, for a certain species of virulent bacteria with the rate of growth of the bacterial population as proportional to the number the bacteria present after 3 hours is 256000.
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A diamond has eight equilateral triangles as faces, as shown. The formula V = 0.4783
approximates the volume (in cubic millimeters) of the diamond, where s is the side length (in millimeters) of each edge. Approximate the length of each edge of the diamond.
V = 161 mm³
The length of each edge of the diamond is about
1
mm.
In equilateral triangles, 7.0 mm is the length of each edge of the diamond.
The equilateral triangle's definition?
An equilateral triangle is a triangle whose three sides are all the same length, commonly referred to as a "regular" triangle.
A triangle with all three sides equal and interior angles of 60 degrees is said to be equilateral. Triangle with an equal number of sides is known as an isosceles triangle.
V = 0.4783 S³ = 161
S³ = 161/0.47
= ∛ 161/0.47
≈ 7.0 mm
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What is 6,000,000 + 1,000,000? Answer ASAP!!! NEED HELP
Answer: 7,000,000
By the way: How do we have almost the same name?
Answer:
the answer is 7,000,000
Step-by-step explanation:
6,000,000+1,000,000=7,000,000
in how many ways can a president, vice-president, and treasurer be chosen from a group of 4 freshmen and 4 sophomores so that at least one freshman and at least one sophomore holds at least one of these three positions? on person cannot serve in more than one position
The total number of ways to choose a president, vice-president, and treasurer from a group of 4 freshmen and 4 sophomores so that at least one freshman is 314 ways.
We can approach this problem using the principle of inclusion-exclusion.
First, let's find the total number of ways to choose a president, vice-president, and treasurer from a group of 8 people without any restrictions. We can do this by using the permutation formula:
8P₃ = 8 x 7 x 6 = 336
Next, let's find the number of ways to choose the three positions where only freshmen are chosen. There are 4 freshmen to choose from, so we can select the president, vice-president, and treasurer in 4P₃ = 4 x 3 x 2 = 24 ways.
Similarly, there are 4 sophomores to choose from, so we can select the three positions where only sophomores are chosen in 4P₃ = 4 x 3 x 2 = 24 ways.
However, we have overcounted the cases where only freshmen or only sophomores are chosen, since the problem statement requires that at least one freshman and at least one sophomore hold at least one of the three positions. Therefore, we need to subtract the number of cases where only freshmen or only sophomores are chosen.
There is only one way to select the president, vice-president, and treasurer from the 4 freshmen, and likewise, there is only one way to select them from the 4 sophomores. Therefore, there are a total of 2 ways to select the three positions where only one class is represented.
Finally, we need to add back the cases where no freshman or no sophomore is chosen. This occurs only if all three positions are filled by juniors or seniors. There are 4 juniors and seniors to choose from, so we can select the three positions in 4P₃ = 4 x 3 x 2 = 24 ways.
Therefore, the total number of ways to choose a president, vice-president, and treasurer from a group of 4 freshmen and 4 sophomores so that at least one freshman and at least one sophomore holds at least one of these three positions is:
336 - 24 - 24 + 2 + 24 = 314 ways.
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Fill in the gap in the equation below by completing the square. x² + 12x +44 = (x + 6)² +
Answer:
[tex]8[/tex]
Step-by-step explanation:
[tex]x^2+12x+44=(x^2+12x+36)+8=(x+6)^2+8[/tex]
3+2y equals square root of -y
The solution to the given quadratic equation formed is; y = -9/4 and y = -1
How to find the solution to the quadratic equation?The given equation is expressed as;
(3 + 2y) = √(-y)
Taking the square of both sides gives us;
(3 + 2y)² = √(-y)]²
→ 9 + 12y + 4y² = -y
4y² + 13y + 9 = 0
Factoring the expression gives us;
4y² + 4y + 9y + 9 = 0
4y(y + 1) + 9(y + 1) = 0
Thus;
(4y + 9) = 0
(y + 1) = 0
y = -9/4
y = -1
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