Answer:
120 possible arrangements.
It is a permutation
Step-by-step explanation:
Imagine that you are going to give the gold medal to any of the 6 runners. There would be 6 possibilities; now, imagine that you are going to give the gold and the silver medals random in the same way: you could give the gold medal to a person and you would have 5 possibilities to give the silver medal (you can't give both medals to the same person). So, note that for each possibility to give the gold medal there would be 5 possibilities to give the silver one.
Analogously, if you give the three medals random and supposing that you have already given the gold one, for each possibility to give the silver medal you would have 4 possibilities to give the bronze one. That is the reason for the calculation to be a multiplication:
N= Total number possibilities:
[tex]N=6*5*4=120[/tex]
This also can be seen as a permutation. A permutation is a reorganization of elements where the order matters. In this case, it is not just relevant who are the winners (who receive the medal), but their order. A combination just helps us to make groups without taking in mind the order, but the permutation does consider that.
The permutation can be learnt by the formula:
[tex]N=\frac{p!}{(p-n)!}[/tex]
where p is the total ef elements and n is the amount of elements of each subgroup that I want to built. In this case, our population 'p'=6, and we want to organize them in groups of 3 (n=3) where it is important for us the order:
[tex]N=\frac{6!}{(6-3)!}=6*5*4=120[/tex]
Helpp! -- A piece of wire 5 inches long is to be cut in two pieces. One piece is x inches long and is to be bent into the shape of a square. The other piece is to be bent in the shape of a circle. Find an expression for the total area made up by the square and the circle as a function of x.
The expression for the total area made up by the square and the circle as a function of x is f(x) = x^2/16 + (25 - 10x + x^2)/(4*Pi) square inches.
Explanation:To solve this problem, you need to know the formulas for the areas of a square (Area = side^2) and a circle (Area = pi * radius^2). If a piece of the wire with length x inches is to be bent into the shape of a square, then each side of the square will be x/4 inches long (since a square has 4 equal sides). Therefore, the area of the square = (x/4)^2 = x^2/16 sq.inches.
The remaining piece of the wire is 5-x inches long and is to be bent into the shape of a circle. The circumference of the circle is 5-x inches (since it uses the remaining wire), therefore the radius of the circle is (5-x)/(2*Pi) inches. Therefore, the area of the circle = Pi*((5-x)/(2*Pi))^2 = (25 - 10x + x^2)/(4*Pi) sq.inches.
The total area made up by the square and the circle is the sum of their areas, therefore the function representing the total area f(x) = x^2/16 + (25 - 10x + x^2)/(4*Pi) sq.inches.
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If 5x=17, what is the value of 15x-11
5x=17
x=17/5 = 3.4
15x-11 =
15(3.4)-11 = 51-11 = 40
someone please help me to find the answer to this geography problem please explain
Definition 7.1.1 laplace transform let f be a function defined for t ≥ 0. then the integral {f(t)} = ∞ e−stf(t) dt 0 is said to be the laplace transform of f, provided that the integral converges. to find {f(t)}. f(t) = cos t, 0 ≤ t < π 0, t ≥ π
A pizzeria owner wants to know which pizza topping is least liked by her customers so she can take it off the menu. She used four different methods to find this information.
Method 1: The owner asked every third customer to rate all the pizza toppings in order of preference.
Method 2: The owner gave all customers a toll-free telephone number and asked them to phone in their topping preferences.
Method 3: The owner asked the preferences of every other teenager who entered the pizzeria.
Method 4: The owner reviewed the pizzeria’s complaint cards and assessed all complaints related to pizza toppings.
Which method is most likely to give a valid generalization
The valid method is the owner asked every third customer to rate all the pizza toppings in order of preference. The correct option is A.
What is feedback?information that is utilized as a foundation for improvement, such as data on how people react to a product or how well someone performs a task.
I suggest method 1 because it is unbiased and systematic. The second method requires a lot of the initiative of customers and is likely to have extreme cases only (liked very much or disliked very much).
The third is biased towards teenagers, which may not be the only category of customers who ordered pizzas. Again, the fourth requires initiative from the customer, so biased towards customers who had something to say.
Therefore, the valid method is for the owner to ask every third customer to rate all the pizza toppings in order of preference. The correct option is A.
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is the graph of y=sin(x^6) increasing or decreasing when x=12
Derek and Mia place two green marbles and one yellow marble in a bag. Somebody picks a marble out of the bag without looking and records its color (G for green and Y for yellow). They replace the marble and then pick another marble. If the two marbles picked have the same color, Derek loses 1 point and Mia gains 1 point. If they are different colors, Mia loses 1 point and Derek gains 1 point. What is the expected value of the points for Derek and Mia?
Answer:
Thus, the expected value of points for Derek and Mia are [tex]\dfrac{-1}{9}[/tex] and [tex]\dfrac{1}{9}[/tex] respectively.
Step-by-step explanation:
Number of green marbles = 2 and Number of Yellow marbles = 1
Then, total number of marbles = 2+1 = 3
A person selects two marbles one after another after replacing them.
So, the probabilities of selecting different combinations of colors are,
[tex]1.\ P(GG)=P(G)\times P(G)\\\\P(GG)=\dfrac{2}{3}\times \dfrac{2}{3}\\\\P(GG)=\dfrac{4}{9}[/tex]
[tex]2.\ P(GY)=P(G)\times P(Y)\\\\P(GY)=\dfrac{2}{3}\times \dfrac{1}{3}\\\\P(GY)=\dfrac{2}{9}[/tex]
[tex]3.\ P(YG)=P(Y)\times P(G)\\\\P(YG)=\dfrac{1}{3}\times \dfrac{2}{3}\\\\P(YG)=\dfrac{2}{9}[/tex]
[tex]4.\ P(YY)=P(Y)\times P(Y)\\\\P(YY)=\dfrac{1}{3}\times \dfrac{1}{3}\\\\P(YY)=\dfrac{1}{9}[/tex]
Now, we have that,
If two marbles are of same color, then Mia gains 1 point and Derek loses 1 point.
If two marbles are of different color, then Derek gains 1 point and Mia loses 1 point.
Also, the expected value of a random variable X is [tex]E(X)=\sum_{i=1}^{n} x_i\times P(x_i)[/tex].Then, the expected value of points for Derek is,
[tex]E(D)= (-1)\times \dfrac{4}{9}+1\times \dfrac{2}{9}+1\times \dfrac{2}{9}+(-1)\times \dfrac{1}{9}\\\\E(D)= \dfrac{-5}{9}+\dfrac{4}{9}\\\\E(D)=\dfrac{-1}{9}[/tex]
And the expected value of points for Mia is,
[tex]E(M)= 1\times \dfrac{4}{9}+(-1)\times \dfrac{2}{9}+(-1)\times \dfrac{2}{9}+1\times \dfrac{1}{9}\\\\E(M)= \dfrac{5}{9}-\dfrac{4}{9}\\\\E(M)=\dfrac{1}{9}[/tex].
Thus, the expected value of points for Derek and Mia are [tex]\dfrac{-1}{9}[/tex] and [tex]\dfrac{1}{9}[/tex] respectively.
Answer: P(GG)= 4/9
P(GY)= 2/9
P(YG)= 2/9
P(YY)= 1/9
Derek, E(X) = -1/9
Mia, E(X) = 1/9
Step-by-step explanation: just did it on edge
Find the area of a square with radius 17√2 in. Round to he nearest whole number. Please help me!!
The area of the square with radius 17√2 is 1156 square inches.
What is area?The area is the amount of space within the perimeter of a 2D shape
What is the formula for the area of square?The formula for the area of square is
[tex]A = \frac{1}{2} d^{2}[/tex]
Where, d is the length of the diagonal of the square.
According to the given question.
The radius of the square is [tex]17\sqrt{2}[/tex] in.
⇒ Diameter or the length of the square = 2 × 17 √2 = 34√2
Therefore,
The area of the square
= [tex]\frac{1}{2}( 34(\sqrt{2)} )^{2}[/tex]
= [tex]\frac{2312}{2}[/tex]
=[tex]1156\ in^{2}[/tex]
Hence, the area of the square with radius 17√2 is 1156 square inches.
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Which of the following statements is true? A 6.75 < 6.759 < 6.751 < 6.85 B 5.55 < 5.559 < 5.65 < 5.69 C 4.11 < 4.12 < 4.17 < 4.15 D 7.42 < 7.41 < 7.40 < 7.39
The widrh of a rectangle is w yards and the length of a rectangle is (6w-4) yards. The perimeter of the rectangle is given by the algebraic expression 2w+2(6w-4). Simplify the algebraic expression 2w+2(6w-4) and determine the perimeter of a rectangle whose width w is 4 yards
p=2w+2(6w-4) can be simplified to:
p=2w+12w-8
p=14w-8
if w=4
p=14(4)-8
p=56-8 = 48 yards
check:
w = 4
length = 6w-4= 6(4)-4 = 24-4=20
perimeter = 4*2 + 20*2 = 8+40 = 48
it checks out, perimeter = 48 yards
Jane is going to walk once around the edge of a rectangular park. The park is 300 yards long and 200 feet wide. How far will Jane walk?
Jane will walk 733.34 yards around the edge of the rectangular park after converting the width from feet to yards and calculating the perimeter.
Jane is going to walk once around the edge of a rectangular park. The park is 300 yards long and 200 feet wide. To determine how far Jane will walk, we need to calculate the perimeter of the rectangle. First, let's convert all measurements to the same unit. Since the length is given in yards and the width in feet, we can convert the width to yards (1 yard = 3 feet).
Width in yards: 200 feet \/ 3 feet per yard = 66.67 yards.
Now that both measurements are in yards, we can calculate the perimeter:
Perimeter = 2 ×(length + width) = 2 × (300 yards + 66.67 yards) = 2 ×366.67 yards = 733.34 yards.
Therefore, Jane will walk 733.34 yards around the edge of the park.
Show that the series is convergent. how many terms of the series do we need to add in order to find the sum to the indicated accuracy? sum_(n=1)^(infinity) (-1)^(n+1)/( n^7)text( ) \(|text(error)| < 0.00005 \)
The series is convergent, but the number of terms needed to find the sum to a specific accuracy cannot be determined.
Explanation:To determine the convergence of the series sum_(n=1)^(infinity) (-1)^(n+1)/( n^7), we can use the Alternating Series Test. The Alternating Series Test states that if the terms of a series alternate in sign and decrease in absolute value, then the series is convergent. In this case, the terms of the series alternate in sign and decrease as n increases, so the series is convergent.
To find the number of terms needed to achieve a sum with an error less than 0.00005, we need to use the Remainder Estimation Theorem. However, this theorem requires that the terms of the series decrease in absolute value, which is not the case in this series. Therefore, we cannot determine the number of terms needed to reach the desired accuracy.
Overall, the series is convergent, but we cannot determine the number of terms needed to reach a specific accuracy.
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the longest runway at an airport has the shape of a rectangle with an area of 2181600sqft. this runway is 180 ft wide. how long is the runway
A carpenter is assigned the job of expanding a rectangular deck where the width is one-fourth the length. The length of the deck is to be expanded by 6 feet, and the width by 2 feet. If the area of the new rectangular deck is 68 ft2 larger than the area of the original deck, find the dimensions of the original deck.
If 2^m = 4x and 2^w = 8x, what is m in terms of w?
standard form of the equation of a hyperbola that has vertices at (-10, -15) and (70, -15) and one of its foci at (-11, -15).
Final Answer:
The standard form of the equation of the hyperbola with vertices at (-10, -15) and (70, -15) and one of its foci at (-11, -15) is (x - 30)^2 / 1600 - (y + 15)^2 / 81 = 1
Explanation:
To write the standard form of the equation of a hyperbola with the given vertices and a focus, we'll follow these steps:
1. Determine the center of the hyperbola.
2. Calculate the distance between the vertices and the center to find the length of the transverse axis (2a).
3. Calculate the distance between a focus and the center to find the focal distance (c).
4. Use the relationship c^2 = a^2 + b^2 to determine the length of the conjugate axis (2b).
5. Write the standard form equation based on the orientation of the hyperbola.
Step 1: Determine the center of the hyperbola.
The center of the hyperbola is the midpoint of the line segment joining the two vertices. Since the vertices are at (-10, -15) and (70, -15), the center (h, k) can be found as follows:
h = (-10 + 70) / 2 = 60 / 2 = 30
k = (-15 + (-15)) / 2 = -30 / 2 = -15
So, the center of the hyperbola is at (30, -15).
Step 2: Calculate the length of the transverse axis (2a).
The distance between the vertices is the length of the transverse axis. The vertices are 80 units apart because they are at (-10, -15) and (70, -15). This means:
2a = 80
a = 40
Therefore, the length of the semi-transverse axis a is 40 units.
Step 3: Calculate the focal distance (c).
The focal distance is the distance between the center and one of the foci. We were given one focus at (-11, -15). Since the center is at (30, -15), the focal distance c is:
c = |30 - (-11)| = |30 + 11| = 41
Step 4: Use the relationship c^2 = a^2 + b^2 to determine b.
We know that a = 40 and c = 41. Plugging these values into the relationship gives us:
41^2 = 40^2 + b^2
1681 = 1600 + b^2
b^2 = 1681 - 1600
b^2 = 81
b = 9
Therefore, the length of the semi-conjugate axis b is 9 units.
Step 5: Write the standard form equation.
Since the hyperbola is horizontal (the vertices have the same y-coordinate), the standard form of its equation is:
(x - h)^2 / a^2 - (y - k)^2 / b^2 = 1
Plugging in the values for h, k, a, and b, we get:
(x - 30)^2 / 40^2 - (y + 15)^2 / 9^2 = 1
Simplify further by squaring the values of a and b:
(x - 30)^2 / 1600 - (y + 15)^2 / 81 = 1
This is the standard form of the equation of the hyperbola with vertices at (-10, -15) and (70, -15) and one of its foci at (-11, -15).
What is the standard form of 8 hundreds + 2 hundreds
The standard form of 8 hundred + 2 hundred will be 1000.
What is the standard form of the number?A number can be expressed in a fashion that adheres to specific standards by using its standard form. Standard form refers to any number that may be expressed as a decimal number between 1.0 and 10.0 when multiplied by a power of 10.
Given that the number is 8 hundred + 2 hundred the standard form of the number will be:-
Standard form = 8 hundreds + 2 hundreds
Standard form = 800 + 200
Standard form = 1000
Therefore, the standard form of 8 hundred + 2 hundred will be 1000.
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What is the area of parallelogram ABCD in square units
13 square units
Further explanationConsider attachment for details.
We make a KLMN rectangle that touches all the vertices of the ABCD parallelogram. Consequently, the ABCD parallelogram is right inside the KLMN rectangle.
Let us take the following strategic steps:
Calculate the area of KLMN.Calculate the area of the triangles ABL, CDM, ADK, and BCN.Subtract the area of the KLMN rectangle with the area of all triangles.The difference in the area above is the area of the ABCD parallelogram.The Process:
The area of KLMN = 4 x 5 = [tex] \boxed{ \ 20 \ square \ units. \ }[/tex]The ADK triangle is congruent to the BCN triangle, and each area is [tex]\boxed{ \ \frac{1}{2} \times 4 \times 1 = 2 \ square \ units. \ }[/tex] Thus the total area of ADK and BCN is [tex]\boxed{ \ 2 + 2 = 4 \ square \ units. \ }[/tex]The ABL triangle is congruent to the CDM triangle, and each area is [tex]\boxed{ \ \frac{1}{2} \times 3 \times 1 = 1.5 \ square \ units \ }.[/tex] Thus, the combined area of ABL and CDM is [tex]\boxed{ \ 1.5 + 1.5 = 3 \ square \ units. \ }[/tex]Finally, the area of ABCD = 20 - 4 - 3 = 13.As a result, we get the area of the parallelogram ABCD is 13 square units.
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Evaluate the surface integral s f · ds for the given vector field f and the oriented surface s. in other words, find the flux of f across s. for closed surfaces, use the positive (outward) orientation. f(x, y, z) = x i + y j + 10 k s is the boundary of the region enclosed by the cylinder x2 + z2 = 1 and the planes y = 0 and x + y = 2
The price of an item has been reduced by 15% . The original price was $51 .
The question is about calculating the new price of an item after a discount. The original price of the item was $51.00, and it was reduced by 15%, making the new price $43.35.
Explanation:The subject of this question is Mathematics and it is looking for a solution to a percentage price reduction problem. The item had an original price of $51.00 and its price has been reduced by 15%. To find the new price after the discount, we have to calculate the amount of the reduction and subtract it from the original price.
First, let's calculate the amount of the discount: 15/100 * 51 = $7.65.}
Now, we subtract this amount from the original price: 51 - 7.65 = $43.35.
Therefore, the new price of the item after a 15% discount is $43.35.
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The manager at an ice cream shop keeps track of the number of deluxe cones and regular cones sold each day and the total money received. On Saturday, a total of 95 cones were sold, and the money collected was $628 . If deluxe cones are sold for $8 and regular cones are sold for $5 , how many deluxe cones and regular cones were sold?
Final answer:
By forming a system of equations and applying the elimination method, we conclude that the ice cream shop sold 51 deluxe cones and 44 regular cones on Saturday.
Explanation:
How to Solve for the Number of Deluxe and Regular Cones Sold
To solve for the number of deluxe cones and regular cones sold at the ice cream shop, we need to set up a system of equations. We are given that a total of 95 cones were sold and the total money collected was $628. Deluxe cones are sold for $8 and regular cones for $5. Let's define our variables:
x = number of deluxe conesy = number of regular conesNow, we can establish our equations:
The total number of cones sold is 95: x + y = 95The total money collected is $628: 8x + 5y = 628To solve the system, we can use the substitution or elimination method. Let's use elimination for this example.
Multiply the first equation by 5:
5x + 5y = 475Now subtract this from the second equation:
(8x + 5y) - (5x + 5y) = 628 - 4753x = 153x = 51With 51 deluxe cones sold, we can substitute that into the first equation to find y:
51 + y = 95y = 95 - 51y = 44So, 51 deluxe cones and 44 regular cones were sold on Saturday.
Select the correct inequality for the graph below: A solid line passing through points (1, 2) and (2, 5) has shading below. y < 3x − 1 y ≤ 3x − 1 y ≥ 3x − 1 y > 3x − 1
Here is your answer:
Solving the equation:
[tex] (5-2)\div(2-1)= 3 [/tex][tex] \frac{y - y1}{(x - x1) } [/tex][tex] y-5=3(x-2) [/tex][tex] y= 3x- 6+ 5 [/tex]" [tex] y= 3x-1 [/tex] " or option B.Hope this helps!
Step 1
Find the equation of the line that passes through points [tex](1, 2)[/tex] and [tex](2, 5)[/tex]
Find the slope of the line
The formula to calculate the slope is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values
[tex]m=\frac{5-2}{2-1}[/tex]
[tex]m=\frac{3}{1}[/tex]
[tex]m=3[/tex]
Find the equation of the line
The equation of the line into slope-point form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=3[/tex]
[tex](1, 2)[/tex]
substitutes
[tex]y-2=3(x-1)[/tex]
[tex]y=3x-3+2[/tex]
[tex]y=3x-1[/tex]
Step 2
Find the equation of the inequality
we know that
The solution is the shaded area below the solid line
therefore
the inequality is
[tex]y\leq 3x-1[/tex]
the answer is
[tex]y\leq 3x-1[/tex]
see the attached figure to better understand the problem
A section of land has an area of 1 square mile and contains 640 acres. determine the number of square meters in an acre
An acre, a unit of area commonly used in the Imperial and U.S. customary systems, is approximately 4047 square meters. This is calculable by using the known conversions between acres, square miles, and square meters.
Explanation:To determine the number of square meters in an acre, it's helpful to understand the relationship between these units. A square mile is equivalent to 640 acres. Therefore, the area of one acre is 1/640 of a square mile. However, these are both Imperial measurements, and we want to convert to a metric measurement - square meters.
To make this conversion, we need to identify the conversion factor between square miles and square meters. There are 2,589,988.11 square meters in a square mile.
Our starting point is that 1 acre = 1/640 square mile. Next, we substitute the number of square meters in a square mile:
1 acre = 1/640 x 2,589,988.11 square meters = 4046.86 square meters.
Therefore, there are approximately 4047 square meters in an acre.
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Two consecutive odd integers have a sum of 44 . Find the integers.
find the quotient of 0.34 and 0.2.
The formula can be used to find the velocity v in feet per second of an object that has fallen h feet. Find the velocity of an object that has fallen 23 feet. Round your answer to the nearest hundredth.
The Center of the Circle is at the origin on a coordinate grid. The vertex of a Parabola that opens upward is at (0,9). If the Circle intersects the parabola at the parabola's vertex, which Statement must be true?
The parabola and the circle have the same axis of symmetry, and can intersect at one point only.
The statement that must be true is; The maximum number of solution is one
Reason:
The given parameters are;
Location of the center of the circle = The origin (0, 0)
Location of the vertex of the parabola opening upwards = (0, 9)
Point where the circle intersects the parabola = The vertex
Required:
The statement that must be true
Solution;
The equation of the circle is x² + y² = r²
The vertex (0, 9) is a point on the circle, therefore;
0² + 9² = r²
The radius, r = 9
The highest point on the circle is the point with the maximum vertical
distance from the center, which is the point (0, 9), which is also the lowest
point on the parabola.
Therefore, the parabola and the circle can intersect at only the point (0, 9),
which gives;
The maximum number of solution is one.
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What is greater: a half dozen dozen pair of shirts or a half of two dozen dozen shirts
From the computation, a half of two dozen shirts will be greater.
A dozen = 12
It should be noted that a half dozen pair of shirts will be:
= 1/2 × 12
= 6 shirts
A half of two dozen shirts will be:
= 1/2 × (2 × 12)
= 12 shirts
Therefore, a half of two dozen shirts will be greater.
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In the first 120 miles over 240 mile journey a truck driver maintained an average speed of 50 mph what was his average featuring the next 120 miles if the average speed of the entire trip with 60 mph
James wants to tile his floor using tiles in the shape of a trapezoid. To make the pattern a little more interesting he has decided to cut the tiles in half along the median. The top base of each tile is 15 inches in length and the bottom base is 21 inches. How long of a cut will John need to make so that he cuts the tiles along the median?
Answer:18 inches
Step-by-step explanation:
The answer would be 18 inches.
What is the median of a trapezoid?The median of a trapezoid is the segment that connects the midpoints of the non-parallel sides.
The length of the median is the average of the length of the bases.
The top base of each tile is 15 inches in length and the bottom base is 21 inches,
Add the top base and bottom base,
So, 15+21=36
Now, divide that by 2
⇒ 18
Hence, the answer would be 18 inches.
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