Permutation formula:
\(P(n,r)=\frac{n!}{(n-r)!}\)In this case:
n is the nuber of woman in the race
r is the number of woman chosen (3 as you need to know the number of possibles 3 first places combinations)
\(\begin{gathered} P(6,3)=\frac{6!}{(6-3)!} \\ \\ =\frac{6!}{3!} \\ \\ =\frac{1\cdot2\cdot3\cdot4\cdot5\cdot6}{1\cdot2\cdot3} \\ \\ =4\cdot5\cdot6 \\ \\ =120 \end{gathered}\)Then, there are 120 first second and third place possibilities that can occur
In a lab experiment, 490 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 6 hours. How long would it be, to the nearest tenth of an hour, until there are 5210 bacteria present?
Answer:
20.5
Step-by-step explanation:
Which could be the dimensions of a rectangular prism whose surface area is greater than 140 square feet? Select
three options.
6 feet by 2 feet by 3 feet
6 feet by 5 feet by 4 feet
17 feet by 6 feet by 4 feet
8 feet by 3 feet by 7 feet
8 feet by 4 feet by 3 feet
Answer:
6 feet by 5 feet by 3 feet
17 feet by 6 feet by 4 feet
8 feet by 3 feet by 7 feet
hi I need help with my math
Step-by-step explanation:
heyy, what math do u need help with I can probably help
Answer:
bestie whats the question
The difference of F and 1/3 is 1/2
Answer:
f=5/6
Step-by-step explanation:
Answer: Are you giving us the answer?
Step-by-step explanation:
Are you giving us the answer.
Hep math math math math
Answer:
c
Step-by-step explanation:
basic theory, can't explain further.
Answer: y=6
Step-by-step: 2(−6)+3=18 distributed into 2−12+3=18
Next, Combine Like Terms.
2−12+3=18
5−12=18
Wait oh, you wanted the. Oh. Well the distribution of it is 2y-12+3y=18. Sorry!
Solve for x and show steps . Is the solution extraneous ? Check your work to show how you determined if the solution is extraneous or not
Square 4x-3=5
The solution of the equation 4x - 3 = 5 is not extraneous .
How to solve an equation?Extraneous solutions are values that we get when solving equations that aren't really solutions to the equation.
Therefore, let's solve the equation to know whether it is extraneous solution.
Hence,
4x - 3 = 5
add 3 to both sides of the equation
4x - 3 + 3 = 5 + 3
4x = 8
divide both sides of the equation by 4
4x / 4 = 8 / 4
x = 2
Therefore, it is not extraneous solution.
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the perimeter of a rectangle is 15x+17y. if the length is 7/2x+7y, then find the width of the rectangle
A.) 4x+3/2y
B.) 8x+3y
C.) 8x+10y
D.) 4x+3y
Answer:
A
Step-by-step explanation:
Length : \(\frac{7x}{2} + 7y\)
Perimeter: \(15x + 17y\)
Perimeter = 2(Length + Width)
15x + 17y = 2( \(\frac{7x}{2} + 7y\) + Width)
15x + 17y = 7x + 14y + 2(Width)
15x + 17y -7x -14y = 2(Width)
8x + 3y = 2(Width)
Width = \(\frac{8x + 3y}{2}\)
Width = 4x + 3y/2
simplify 3 x 5/6
A. 15/5
B. 23/6
C. 2 1/2
D. 3 5/6
Answer: 2 1/2, C
Step-by-step explanation:
Multiply 3 and 5 to get 15.
15/6
Reduce the fraction 15/6 to lowest terms by extracting and canceling out 3.
5/2 (improper fraction) or 2 1/2 (mixed number). They equal the same thing, just in different formats
Round 34,138 to the nearest thousand??
Answer:
34,138 to the nearest thousand is 34,000!
Step-by-step explanation:
Hope this helps! Good luck! <3
Answer:
0
Step-by-step explanation:
0.5 (-2 + 4d) -13 for d
Step-by-step explanation:
-13 x 4 = -52
-52 x 0.5 = -25
-2 x 0.5 = -1
-1 + -25 = -26
The area of a rectangular window is 3816 cm
If the length of the window is 72 cm, what is its width
Answer: The width of the rectangular window is 53 cm.
Step-by-step explanation:
We know that the area of a rectangle is given by the formula:
Area = Length x Width
Substituting the given values, we have:
3816 cm² = 72 cm x Width
To solve for the width, we can divide both sides by 72 cm:
Width = 3816 cm² ÷ 72 cm
Width = 53 cm
Therefore, the width of the rectangular window is 53 cm.
A diphosphonate kit contian 180 mCi of Tc99m in 30 ml when it is prepared at 8am. Immediately, a 20 mCi dose is withdrawn for a bone scan. if the patient arrives late at 9:30 and half the volume is accidentally discharged, how much volume from the kit must now be added to the syringe to correct the dose to 20 mCi? (no other doses have been withdrawn meanwhile, and the decay factor for 1.5 hrs is 0.841)
The remaining Kit volume in the syringe is sufficient to correct the dose to 20 mCi.
To solve this problem, we can use the concept of radioactive decay and the decay factor. Here's how we can calculate the required volume to correct the dose:
Determine the initial activity of the kit:
Initial activity = 180 mCi
Calculate the decayed activity at 9:30 (after 1.5 hours):
Decay factor = 0.841
Decay activity = Initial activity * Decay factor
Calculate the remaining activity after withdrawing 20 mCi at 8 am:
Remaining activity = Initial activity - 20 mCi
Calculate the remaining activity at 9:30:
Remaining activity at 9:30 = Remaining activity * Decay factor
Calculate the desired activity at 9:30 (20 mCi):
Desired activity at 9:30 = 20 mCi
Calculate the volume needed to achieve the desired activity:
Volume needed = Desired activity at 9:30 / Remaining activity at 9:30 * Volume at 9:30
Calculate the remaining volume at 9:30:
Remaining volume = Volume at 8 am - Volume withdrawn - Volume accidentally discharged
Calculate the volume that needs to be added:
Volume to be added = Volume needed - Remaining volume
Let's perform the calculations step by step:
Determine the initial activity of the kit:
Initial activity = 180 mCi
Calculate the decayed activity at 9:30 (after 1.5 hours):
Decay factor = 0.841
Decay activity = 180 mCi * 0.841 = 151.38 mCi
Calculate the remaining activity after withdrawing 20 mCi at 8 am:
Remaining activity = 180 mCi - 20 mCi = 160 mCi
Calculate the remaining activity at 9:30:
Remaining activity at 9:30 = 160 mCi * 0.841 = 134.56 mCi
Calculate the desired activity at 9:30 (20 mCi):
Desired activity at 9:30 = 20 mCi
Calculate the volume needed to achieve the desired activity:
Volume needed = (Desired activity at 9:30 / Remaining activity at 9:30) * Volume at 9:30
Volume at 9:30 = Remaining volume = 30 ml - (30 ml / 2) = 15 ml
Volume needed = (20 mCi / 134.56 mCi) * 15 ml = 2.236 ml
Calculate the remaining volume at 9:30:
Remaining volume = 30 ml - (30 ml / 2) = 15 ml
Calculate the volume that needs to be added:
Volume to be added = Volume needed - Remaining volume = 2.236 ml - 15 ml = -12.764 ml
Since the calculated volume to be added is negative, it means that no additional volume is required. The remaining Kit volume in the syringe is sufficient to correct the dose to 20 mCi.
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What is the value of 9 ÷ 0?
Answer: Undifined!
Step-by-step explanation: Division by zero is considered an invalid operation in mathematics because there is no number that can be multiplied by zero to produce the original number. In other words, there is no single valid answer to dividing by zero. Example: You have 0 cookies and you want to share them among 9 friends. There's no way to share, since you don't have cookies haha!
Answer:
UNDEFINED OR NO ANSWER.Step-by-step explanation:
An expression without a value is referred to as being undefined; it has an indeterminant form. When a number is divided by zero, it usually has no specified meaning. Mathematically, we can't divide by zero because the result is an equation we can't compute.
Hope it helps!NO LINKS!!!
Corresponding lengths in similar figures are given. Find the ratios (shaded to unshaded) of the perimeters and ares. Then find the unknown areas for each.
Answer:
Question 32
Scale Factor = 3/8Ratio of Perimeters = 8 : 3Ratio of Areas = 64 : 9Area of smaller figure = 144 mm²Question 33
Scale Factor = 10/7Ratio of Perimeters = 7 : 10Ratio of Areas = 49 : 100Area of smaller figure = 196 in²Step-by-step explanation:
Scale Factor: A number used as a multiplier when scaling an object.
Perimeter: The total distance around the outside of a 2D shape.
Area: The space occupied by a flat shape, measured in two dimensions.
Question 32Scale Factor
To find the scale factor from the shaded figure to the unshaded figure, divide the given side length of the unshaded figure by the given side length of the shaded figure:
\(\implies \sf \dfrac{unshaded}{shaded}=\dfrac{9}{24}=\dfrac{3}{8}\)
Ratio of Perimeters
Perimeters are measured in one dimension (length). To find the ratio of the perimeters, divide the given side length of one figure by the given side length of the other:
\(\sf \implies\dfrac{shaded}{unshaded}=\dfrac{24}{9}=\dfrac{8}{3}\)
Therefore:
\(\sf \implies shaded:unshaded=8:3\)
Ratio of Areas
Area is measured in two dimensions. To find the ratio of the areas, divide the square of the given side length of one figure by the square of the given side length of the other:
\(\sf \implies\dfrac{shaded}{unshaded}=\dfrac{24^2}{9^2}=\dfrac{64}{9}\)
Therefore:
\(\sf \implies shaded:unshaded=64:9\)
Area of the smaller figure (unshaded)
Area of shaded figure = 1024 mm²
Let x = area of unshaded figure
Use the ratio found above:
\(\begin{aligned}\implies \sf \dfrac{shaded\:area}{unshaded\:area} & =\sf \dfrac{64}{9}\\\\\sf \dfrac{1024}{x} & =\sf \dfrac{64}{9}\\\\\sf 1024 \cdot 9 & = \sf 64x\\\\\sf x & = \sf \dfrac{1024 \cdot 9}{64}\\\\\implies \sf x & = \sf 144\:\:mm^2\end{aligned}\)
Question 33Scale Factor
To find the scale factor from the shaded figure to the unshaded figure, divide the given side length of the unshaded figure by the given side length of the shaded figure:
\(\implies \sf \dfrac{ushaded}{shaded}=\dfrac{20}{14}=\dfrac{10}{7}\)
Ratio of Perimeters
Perimeters are measured in one dimension (length). To find the ratio of the perimeters, divide the given side length of one figure by the given side length of the other:
\(\sf \implies\dfrac{shaded}{unshaded}=\dfrac{14}{20}=\dfrac{7}{10}\)
Therefore:
\(\sf \implies shaded:unshaded=7:10\)
Ratio of Areas
Area is measured in two dimensions. To find the ratio of the areas, divide the square of the given side length of one figure by the square of the given side length of the other:
\(\sf \implies\dfrac{shaded}{unshaded}=\dfrac{14^2}{20^2}=\dfrac{49}{100}\)
Therefore:
\(\sf \implies shaded:unshaded=49:100\)
Area of the smaller figure (shaded)
Area of unshaded figure = 400 in²
Let x = area of shaded figure
Use the ratio found above:
\(\begin{aligned}\implies \sf \dfrac{shaded\:area}{unshaded\:area} & =\sf \dfrac{49}{100}\\\\\sf \dfrac{x}{400} & =\sf \dfrac{49}{100}\\\\\sf x& = \sf \dfrac{400 \cdot 49}{100}\\\\\implies \sf x & = \sf 196\:\:in^2\end{aligned}\)
Use the triangle shown on the right to complete the statement:
_____ (75*)=14.1/x
Answer: cos
2nd part: Use the equation shown to solve for the value of x. Round to the nearest tenth.
cos(75*)=14.1/x x=14.1/cos(75*)
Answer: 54.5 in
Answer:
Step-by-step explanation:
The answer is 54.5 on edg
For the triangle shown on the right, the term cos is used to complete the statement and the value of x is 54.5 degree for the triangle.
What is right angle triangle property?In a right angle triangle ratio of adjacent side to the hypotenuse side is equal the cosine angle between them.
\(\rm \cos=\dfrac{ adjacent}{hypotenuse}\)
Here, (a) is the adjacent side, (c) is the hypotenuse side and θ is the angle made between them.
The traingle is not provided in the image. Let the triangle for the given problem is similar to the attached image below.
Here the hypontenuse side is AC and adjacent side of triangle is 14.1 units. Thus by the property of right angle triangle,
\(\cos75=\dfrac{AB}{AC}\\\cos75=\dfrac{14.1}{x}\)
Now if we compare the above equation with the given statement __(75*)=14.1/x. The term cos is filled in the blank.
For the second part, we need to find the value of x. Thus solve the above equation further as,
\(\cos75=\dfrac{14.1}{x}\\x=\dfrac{14.1}{\cos75}\\x=\dfrac{14.1}{0.25882}\\x\approx54.5^o\)
Hence, For the triangle shown on the right, the term cos is used to complete the statement and the value of x is 54.5 degree for the triangle.
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can someone find the inverse and explain it step to step please!!!!!!! (FOR QUESTION 3)
Answer:
f^-1(x) = 4(x+5)/3
Step-by-step explanation:
Let f(x) = y
So, y = (3/4)x - 5
y + 5 = (3/4)x
4(y+5)/3 = x
The steps are first to make a variable that holds the same value as the function, then from there you simplify and eventually make x the subject of the equation.
A company sells widgets . The amount of profit ,y, made by the company ,is related to the selling price of each widget ,x, by the given equation.using this equation find out what price the widgets should be sold for , Greg nearest cent , for the company make the maximum profit y=-5x^2+222x-1510
Answer:
Each widget should be sold for $22.2.
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
\(f(x) = ax^{2} + bx + c\)
It's vertex is the point \((x_{v}, f(x_{v})\)
In which
\(x_{v} = -\frac{b}{2a}\)
If a<0, the vertex is a maximum point, that is, the maximum value happens at \(x_{v}\), and it's value is \(f(x_{v})\)
In this question:
The profit, y, is a quadratic function related to the price of widgets, x.
We want to find the price of each widget to generate maximum profit, that is, the x value of the vertex.
The profit function is:
\(y = -5x^2 + 222x - 1510\)
So \(a = -5, b = 222, c = -1510\)
The price for maximum profit is given by:
\(x_{v} = -\frac{b}{2a} = -\frac{222}{2(-5)} = -\frac{222}{-10} = 22.2\)
Each widget should be sold for $22.2.
Answer:
Guys its 22.20 not 22.2.
Step-by-step explanation:
Brainliest????
100 POINTSSSS!! I AM IN DESPERATE NEED OF HELP! so like help? i am struggling with the part where i make an equation for the blocks. i have a few more problems like this to do, so please give me a full explanation of how you solved it. thank you!!
Numbers 1 and 2 are correct.
Question 3:
We can see in each figure, the number of rows matches the figure amount. For example, figure 1 has 1 row, figure 2 has 2 rows, figure 3 has 3 rows, etc. Another thing we can see is that one block gets added to each column in every figure. If we count starting from 3 and keep adding 1 for each column, we get 22 blocks for one column. In figure 20, there will be 20 rows and 22 columns. We also have to keep in mind that they add 2 extra blocks at the top and bottom that stick out like the ones shown. In total, figure 20 will consist of 442 blocks.
Question 4:
[(2 + f) * (f)] + 2 = b
(2 + f) represents the number of blocks in each column.
(f) represents the number of blocks in each row.
2 represents the two extra blocks in each figure.
Note that f in this equation equals the number of the figure. For example, figure 3 is f = 3
We can test our equation with figure three.
[(2 + f) * (f)] + 2 = b
We have figure three so f = 3. Substitute and solve.
[(2 + 3) * (3)] + 2 = b
[5 * 3] + 2 = b
15 + 2 = b
17 = b
In the example, the number of blocks is 17. Therefore, this equation works for any figure.
Best of Luck!
Answer:
We will see that the number of rows in each figure corresponds to the figure amount. Figure 1 has one row, figure 2 has two rows, figure 3 has three rows, and so on. Another thing we can see is that in each diagram, one block is attached to each column. We get 22 blocks for one column if we count from 3 and keep adding 1 for each column. There will be 20 rows and 22 columns in Figure 20. We must also remember that they add two additional blocks at the top and bottom that protrude like the ones shown. Figure 20 will have a limit of 442 blocks.
4th question:
[(2 + f) * (f)] [(2 + f) * (f)] [(2 + f) 2 + 1 = b
The number of blocks in each column is represented by (2 + f).
The number of blocks in each row is represented by (f).
We will see that the number of rows in each figure corresponds to the figure amount. Figure 1 has one row, figure 2 has two rows, figure 3 has three rows, and so on. Another thing we can see is that in each diagram, one block is attached to each column. We get 22 blocks for one column if we count from 3 and keep adding 1 for each column. There will be 20 rows and 22 columns in Figure 20. We must also remember that they add two additional blocks at the top and bottom that protrude like the ones shown. Figure 20 will have a limit of 442 blocks.
4th question:
[(2 + f) * (f)] [(2 + f) * (f)] [(2 + f) 2 + 1 = b
The number of blocks in each column is represented by (2 + f).
The number of blocks in each row is represented by (f).
1 who staple food of the Vedic Aryan was ?
A) Barley and rice B) Milk and its products
C) Rice and pulses D) Vegetables and fruits
e) IAS CHINADU KUMAR KHAN f) IAS CHINADU
z
Answer: barley and rice
Step-by-step explanation:
Evaluate the definite integral of sin^5(x)dx from 0 to pi/2.
Step-by-step explanation:
The definite integral of sin^5(x)dx from 0 to pi/2 can be evaluated using the method of substitution.
Let u = sin(x), then du = cos(x)dx
The integral becomes:
∫sin^5(x)dx = ∫u^5du from 0 to sin(π/2)
= (u^6)/6 evaluated at sin(π/2) and 0
= (sin^6(π/2))/6 - 0
= (1^6)/6
= 1/6
So, the definite integral of sin^5(x)dx from 0 to pi/2 is equal to 1/6.
Please help due in 5 min!!!
Two cars leave Central Square. The first car drives north at 35 miles per hour (mph), and its distance to Central Square is A (here A is actually a function of time). The second car drives east at 50 mph and its distance from Central Square is B (here is also a function of time) The distance between the two cars is D. At a certain time, A = 20 miles and B = 40 miles. a. Sketch the general picture of what the cars and Central Square look like. Be sure to label the diagram with A, B, and D, representing the distances mentioned in the stem of the problem b. Give a general formula for D in terms of A and B. C. Find a formula for the derivative of D. with respect to time in terms of A. A, B, and B! d. Are the two cars getting closer or farther away from each other at the certain time? How fast is the distance between them changing at that time?
a. At the certain time, the two cars are located at points A and B on a coordinate plane, with Central Square at the origin. The distance between the two cars is represented by the length of line segment D connecting points A and B.
b. The general formula for D in terms of A and B is:
\(D = \sqrt{((A - 0)^2 + (B - 0)^2)}\)
c. The derivative of D with respect to time is:
\(\frac{dD}{dt} = (1/D)\frac{dA}{dt}(A - 0)+(1/D)\frac{dB}{dt}(B - 0)\)
d. At the certain time, the distance between the two cars is increasing because dD/dt is positive. The distance between the two cars is changing at a rate of,
\(\frac{dD}{dt} = (1/D)\frac{dA}{dt}(A - 0)+(1/D)\frac{dB}{dt}(B - 0)\\\\\frac{dD}{dt}= (1/D)(35)(20)+(1/D)(50)(40)\\\\\frac{dD}{dt}=35+50\\\\\frac{dD}{dt}=85 mph.\)
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figure below represents a floor covered with white tiles and gray tiles. KEY = 1 square unit Which expression could be used to find the area, in square units, of the entire floor? A (12+7) x (12+7) B (12 × 7) + (12 × 7) X (10+7) x (2+7) (10 × 7) + (2 × 7)
the area of the given fig will be (12 × 7) +(12 × 7)
What is square?
Having four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. Each square form may be recognized by its equal sides and 90° inner angles. A square is a closed form with four equal sides and interior angles that are both 90 degrees. Numerous different qualities can be found in a square.
a floor covered with white tiles and gray tiles.
the area of the given figure will be
(12 × 7) and another (12 × 7)
So the total area will be (12 × 7) +(12 × 7)
Hence the area of the given fig will be (12 × 7) +(12 × 7)
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Fencing costs 13.55 per foot. Jenny buys 15.25 feet of fencing. How much did Jenny spend for fencing?
Answer:
Jenny spent $206.63 for fencing.
Step-by-step explanation:
$13.55 x 15.25ft =$206.6375
Please help due tmr. Find c.
Round to the nearest tenth:
Answer:
c = 14.9 cm
Step-by-step explanation:
Applying the Law of Sines, we would have the following:
c/sin(C) = b/sin(B)
c = ??
C = 180 - (150 + 12) = 18°
b = 10 cm
B = 12°
c/sin(18) = 10/sin(12)
Multiply both sides by sin(18)
c = (10*sin(18))/sin(12)
c = 14.9 cm (nearest tenth)
y= -1/3x -9 written in standard form
Answer:
It would be x + 3y = -27.
in fair bankes alaska the tempreture the tempreture on that one day was -18f. on that same day the tempreture was 83 degrees higher than honolulu hawaii what was the temperature in honolulu hawaii on that day
Answer:
The answer is 65 degrees fahrenheit.
Step-by-step explanation:
i need to know the right answer
B. A secant line can intersect a circle at three points
Since in the case of a circle, a secant line intersects the circle at exactly two points (not three points). So this statement is untrue.
Need number 11 and 10 all parts
-16 - 5x = -5(x + 3)
Solve for X
Answer:
No solution
Step-by-step explanation:
There are no values of x that make the equation true.
The given expression has no solution at all because (-5x) on both sides get cancel out.
\( - 16 - 5x = - 5(x + 3)\)\( - 16 - 5x = - 5x + 3\)\( - 16 \neq3\)