Using the permutation formula, it is found that there are 840 possible arrangements of the 4 trophies.
The problem says the word "arrangements", which implies that the order matters, hence the permutation formula is used to solve this question.
What is the permutation formula?The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this problem, 4 elements from a set of 7 are arranged, hence:
[tex]P_{7,4} = \frac{7!}{3!} = 840[/tex]
There are 840 possible arrangements of the 4 trophies.
More can be learned about the permutation formula at https://brainly.com/question/25925367
Conner goes shopping for school supplies. He buys 3 notebooks that cost $4.50 each.
Conner also buys a pack of pencils for $2.50 and a large binder for $7.50. If there is a
6% sales tax applied to the total, what will be the total cost?
Answer:
but I think 2.39 but I know it
A lock has a 3-number code made up of 13 numbers. If none of the numbers are allowed to repeat, how many different ways can you choose three different numbers in order for a unique code?
Answer:
1716
Step-by-step explanation:
The first choice would be 1 of 13
The second choice would be 1 of 12 (it can't be the same as the first number since they don't repeat)
The third choice would be 1 of 11 (again, can't use the same number more than once)
That gives you 13*12*11=1716
The number of ways we can choose three different numbers in order for a unique code for this case is 2730.
What is combination?In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter.
here, we have,
We can use combinations for this case,
Total number of distinguishable things is m.
Out of those m things, k things are to be chosen such that their order doesn't matter.
This can be done in total of mCk ways.
If the order matters, then each of those choice of k distinct items would be permuted k! times.
So, total number of choices in that case would be:
mPk = m! / (m - k)!
This is called permutation of k items chosen out of m items (all distinct).
Given that:
The considered lock as a 3 number code
There are 15 numbers available.
None of the number can repeat.
In a lock, the order of the way numbers are arranged matters.
Because of no repetition allowed, we can simulate this situation as:
The number of ways we can choose 3 numbers out of 15 numbers with order = The number of different ways we can choose three different numbers in order for a unique code.
And we have:
The number of ways we can choose 3 numbers out of 15 numbers with order = 15P3 = 2730
Thus, the number of ways we can choose three different numbers in order for a unique code for this case is 2730
Learn more about combinations and permutations here:
brainly.com/question/16107928
#SPJ2
Find the area of the prism 14 in. 4 in. 9in.
Answer:
504 in cubed
Step-by-step explanation:
I am assuming this is a rectangular prism, since you did not show a picture.
l x w x h
14 x 4 x 9
14 x 36
504
492+817=492,817 is it correct
Answer:
I support, but this is actually the addition.
492+817 = 1309, yes :)
Step-by-step explanation:
please help me, thanks if you do
Answer:
Step-by-step explanation:
It represents the initial number of bacteria to start with. It can represent nothing else.
find an equation and the slope of the line that passes through (5,2) and is perpendicular to the x-axis
y=2; The slope is undefined.
x=5; The slope is 0.
y=2; The slope is 0.
x=5; The slope is undefined.
Solution: x = 5; The slope is undefined.
The slope that is perpendicular to the x-axis is undefined.
Explanation:
Given point: (5,2)
Since the line is perpendicular to the x-axis, then, the line is vertical.
Hence, x = 5
Answer:
x = 5, the slope is undefined
Step-by-step explanation:
Hello!
To be perpendicular to the x-axis, the line has to intersect at a 90° angle, causing it to be a vertical line with an undefined slope.
This removes the two middle options, as they have a slope of 0.
Consequently, looking at the two options, y=2, and x=5, y=2 would give us a parallel line to the x-axis, as we are drawing a line through all points with a y-coordinate of 2.
The correct option is x=5.
Which function has the greatest maximum range value?
The function f(x) is a sine graph, and the function with the greatest maximum range value is the function f(x)
How to determine the function with the greatest maximum range value?From the complete question (see attachment), the functions are given as:
Functions f(x) and g(x)
The maximum range value of these functions is their maximum output value
Function f(x) has a maximum range value of 3, while function g(x) has a maximum range value of -2
3 is greater than -2
Hence, the function with the greatest maximum range value is the function f(x)
Read more about maximum function values at:
https://brainly.com/question/5722003
#SPJ1
(50 points + Brainliest) Create an equivalent expression that includes a set of parentheses that make the value of the expression 13. Remember, you can have 2 or more numbers within the set of parentheses.
Answer:
1/2 x [(12/2)-6]+13
Step-by-step explanation:
something like that. hope it helped sista
Calculate the area of the red triangle to find the area of the garden. Show your work.
Side A is 90ft
Side B is 120
Side C is 150.
Pls Helo ASAP WILL GIVE BRAINLIEST and 100 points. Open the document below and answer all the questions.
Answer:
The third question is asking you to use the diamond method to solve. At the top of the x would be -16 and the bottom would be -6. The left side would have -8 and the right side would have 2. So the factored form would be (n-8)(n+2)
Step-by-step explanation:
The same thing applies to part b. The top of the x would be 15 and the bottom -8. The left would be -3 and the right would be -5. The factored from would be (x-3)(x-5)
Answer:
Wow! what a worksheet lol! I think I got all your answers here!
Step-by-step explanation:
Celeste took a taxi. The meter said $45. She tips the driver 15%. How much money did she pay the taxi driver?
Answer:
so I believe we can do 15% of 45, so that is 6.75.
so now we do:
45.00
+ 6.75
51.75 is your answer!
please mark brainliest if correct!
And that includes the point (-5’2) has a slope of -4. what is its equation in point slope form?
Answer:
The equation of the line in point-slope form is y - 2 = -4(x + 5).
Step-by-step explanation:
Use the point-slope equation: [tex]y-y_1=m(x-x_1)[/tex].
Substitute the point (-5, 2) and the slope m = -4 into the equation.
[tex]y-(2) = -4(x - (-5))[/tex][tex]y-2=-4(x+5)[/tex]If we stop here, this is the equation of the line in point-slope form.
What is 6 over 9 simplified
Answer:
2/3
Step-by-step explanation:
[tex] \frac{6}{9} [/tex]
[tex] \frac{6}{9} = \frac{2 \times 3}{3 \times 3} [/tex]
[tex] = \frac{2}{3} \times \frac{3}{3} [/tex]
[tex] = \frac{2}{3} \times 1 = \frac{2}{3} [/tex]
I hope it helped you
Answer:
531441
Step-by-step explanation:
im pretty sure this is it!
Question 14 of 15
Len wants to learn more about red kangaroos. Which of the following is a
statistical question Len could ask?
O A. How tall is a red kangaroo?
O B. Are there red kangaroos in Asia?
• C. Are red kangaroos an endangered species?
O D. What iS the tallest red kangaroo ever recorded?
Answer:
A statistical question Len could ask is "How tall is a red kangaroo?"
Step-by-step explanation:
A statistical question is something that we can ask and test hypotheses about using collected data. There will not be a specific answer, but rather multiple answers and we can average them in a sampling distribution.
Let's examine each question:
"How tall is a red kangaroo?"
There is not a specific height for each kangaroo, so we can take the averages of many different samples and find the "true mean" in the sampling distribution. This is a good example of a statistical question because data can be collected on red kangaroos and means can be calculated."Are there red kangaroos in Asia?"
"Are red kangaroos an endangered species?"
What is the tallest red kangaroo ever recorded?"
These are all examples of non-statistical questions. They are "yes" or "no" questions, and we cannot take multiple samples to determine the answer. Rather, there is a single answer that we do not need to test hypotheses or perform any statistical calculations.HELP!!! Solve the compound inequality.
x − 3 < 2 or x + 5 > 12
Answer:
Step-by-step explanation:
The compound Inequality is: 1. x -3 < - 9Adding 3 to both sidesx -3 + 3 < -9 + 3x < -6x ∈ (-∞,-6)2. x + 5 ≥ 12Subtracting ,5 from both sidesx +5 -5 ≥ 12 -5x ≥ 7x ∈ [7 , ∞)Combining , solution of inequality 1 and inequality ,2→→x ∈ (-∞,-6) ∪x ∈ [7 , ∞)Depicting on the number line ,the solution setOption C: A number line with an open circle on −6, shading to the left, and a closed circle on 7, shading to the right
In this diagram,
three concentric circles
rectangle. Point C lies on the middle
have their centers at O, and OABC is a
lies on the outer circle.
circle, point A lies on the inner circle, and point B
the smallest circle.
The intersection point of the rectangle's diagonals also lies on
1. If the radius of the smallest circle is 3, find its area.
2. Find the area of the yellow ring.
3. Find the area of the white ring.
I just need help on 2&3 i dont really know how to do that!
The area of the smallest circle with radius 3 is 28.27 unit². The area of the yellow ring and white ring is 28.27 unit² and 56.55 unit².
What is the area of the circle?The area of the circle is the space occupied by it. It can be given as,
[tex]A=\pi r^2[/tex]
Here (r) is the radius of the circle.
In this diagram, three concentric circles' rectangle.
Point C lies in the middle have their centers at O, and OABC is a lies on the outer circle. Point A lies on the inner circle, and point B the smallest circle. 1. The area of the smallest circle-The radius of the smallest circle is 3.
[tex]r_1=3\rm\unit[/tex]
Thus, the area of it is,
[tex]A=\pi (3)^2\\A=28.27\rm\; unit^2[/tex]
2. The area of the yellow ring.Let suppose the mid-point of the rectangle is D. Here, OB is the diagonal of the rectangle in which,
[tex]OD=BD[/tex]
The radius of the yellow ring's outer face from point O is,
[tex]r_3=OD+BD\\r_3=OD+OD\\r_3=2OD\\[/tex]
OD is the radius of the small circle, which is 3 units long. Thus,
[tex]r_3=2\times3\\r_3=6\rm\; units[/tex]
The line segment OC is the radius of the white circle from point O. In the triangle COB from the Pythagoras theorem, the radius r₂ of the middle circle is,
[tex]r_2=\sqrt{r_3^2-r_1^2}\\r_2=\sqrt{6^2-3^2}\\r_2=3\sqrt3[/tex]
Thus, the area of the yellow ring is,
[tex]A_y=\pi r_3^2-\pi r_2^2\\A_y=\pi (6)^2-\pi (3\sqrt{3})^2\\A_y=28.27\rm\; unit^2[/tex]
3. The area of the white ring.The area of white ring is,
[tex]A_w=\pi r_2^2-\pi r_1^2\\A_w=\pi (3\sqrt{3})^2-\pi (3)^2\\A_w=56.55\rm\; unit^2[/tex]
Hence, the area of the smallest circle with radius 3 is 28.27 unit². The area of the yellow ring and white ring is 28.27 unit² and 56.55 unit².
Learn more about the area of the circle here;
https://brainly.com/question/402655
#SPJ1
Please helppp!!!!!
Graph the following systems of equations. Then state the answer
Answer:
The y-intercept for the 1st one is (0, -3)
The y-intercept for the 2nd one is (0,3)
Step-by-step explanation:
I hope this helped you out. =)
who likes the hair. x2+5(7-6)=. 6÷2(1+2)=
Answer:
1. 2x + 5
2. 9
Step-by-step explanation:
1. x2+5(7-6)
2x+5(7-6)
2x+5·1
= 2x+5
2. 6÷2(1+2)
6÷2·3
= 9
f(x)=−2x+16
g(x)=4x+10
please give me the intersection points
Answer:
(1, 14)Step-by-step explanation:
The intersection is when both functions have same coordinates
f(x) = g(x)Substitute to get
- 2x + 16 = 4x + 104x + 2x = 16 - 106x = 6x = 1The y- coordinate is
y = - 2(1) + 16 = -2 + 16 = 14So the intersection point is (1, 14)
Answer:
(1, 14)
Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x)=-2x+16\\g(x)=4x+10\end{cases}[/tex]
Substitute the function notation for y to create a system of equations:
[tex]\begin{cases}y=-2x+16\\y=4x+10\end{cases}[/tex]
To find the points of intersection of the given functions, solve the system of equations.
Multiply the first equation (function f(x)) by 2:
[tex]\implies 2y=-4x+32[/tex]
Add this to the second equation (function g(x)) to eliminate x:
[tex]\begin{array}{r l}4x+10 & = y\\+ \quad -4x+32 & = 2y\\\cline{1-2} 42 & = 3y\end{array}[/tex]
Solve for y:
[tex]\implies 3y=42[/tex]
[tex]\implies y=14[/tex]
Substitute the found value of y into one of the equations and solve for x:
[tex]\implies 4x+10=14[/tex]
[tex]\implies 4x=4[/tex]
[tex]\implies x=1[/tex]
Therefore, the point of intersection of the given functions is (1, 14).
pls help me I don’t know how to do this!
Two tourist groups went to the local art museum. The admission for an adult ticket costs the same amount, and the admission for student ticket costs the same amount.
The first tourist group paid $46.90 for 3 adult and 5 student admission tickets.
The second tourist group paid $29.60 for 2 adult and 3 student admission tickets.
What was the cost in dollars of each adult admission ticket?
Group of answer choices
$6.25
$7.30
$7.75
$5.00
Answer:
the answer is going to be $5.00 cost dollar each adult
Step-by-step explanation:
because they pay the same money as students
Which numbers are not perfect squares?
24
25
14
36
18
20
16
Answer:
20, 18,14,24 are not perfect squares.
Answer:
24, 14, 18, 20
Step-by-step explanation:
A perfect square is a number that can be expressed as the product of two equal integers. Numbers 24, 14, 18, and 20 are not products of any equal numbers. The rest are.
5 x 5 = 25
6 x 6 = 36
4 x 4 = 16
hope this helps!
A biologist is studying the weights of female polar bears in the Arctic and finds that the mean weight is 179 kg with a standard deviation of 63 kg. Assume weights are normally distributed. What is the weight of a polar bear at the 30th percentile?
Answer:
294.1 pounds
Step-by-step explanation:
We find the z score for 90th percentile
= 1.282
Step 2
We solve using z score formula
z = (x-μ)/σ, where
x is the raw score ??
μ is the population mean = 230 pounds
σ is the population standard deviation= 50 pounds
1.282 = x - 230/50
Cross Multiply
1.282 × 50 = x - 230
64.1 = x - 230
x = 230 + 64.1
x = 294.1 pounds
In a survey of 200 employees, 65% agreed that the management of the cafeteria should be changed. if the confidence interval is 95%, the margin of error for this survey is %, and the maximum number of employees who could have agreed is about .
If the confidence interval is 95%, the maximum number of employees who could have agreed is about is 144.
Maximum number of employeeFirst step
Confidence interval=(Population±Margin of error)
Confidence interval=(0.65±0.0675)
Confidence interval=(0.65-0.0675); (0.65+0.0675)
Confidence interval=0.5825; 0.7175
Second step
Maximum number= 0.7175×200
Maximum number=143.5
Maximum number=144 (Approximately)
Therefore the maximum number of employees who could have agreed is about is 144.
Learn more about maximum number here:https://brainly.com/question/14927859
find the domain of this equation x+5/x+5
Will award brainliest BIG BOI POINTS
PLEASE HELPPPPPPPP!!!!
Answer:
See below ~
Step-by-step explanation:
1.
x² + y² + 14x - 2y = -1[x² + 14x + 49] - 49 + [y² - 2y + 1] - 1 = -1(x + 7)² + (y - 1)² = 49Centre = (x, y) = (-7, 1)Radius = √49 = 72.
x² + y² - 10x + 8y - 8 = 0[x² - 10x + 25] - 25 + [y² + 8y + 16] - 16 - 8 = 0(x - 5)² + (y + 4)² = 49Centre = (x, y) = (5, -4)Radius = √49 = 73.
Points are : (-2, 1) and (4, 3)D = √(4 + 2)² + (3 - 1)²D = √36 + 4D = √40D = 2√10whats a cooler number 86 or 42?
Answer:
86
Step-by-step explanation:
because 86 reminds me of 69
Find the measure of angle
Answer:
112 degrees
Step-by-step explanation:
180-68=112
Since they are supplementary they form a straight angle, or 180 degrees so the angle AED is 112
Answer:
112
Step-by-step explanation:
∠AED and 68 are Linear pair angles.
That is their sum will be equal to 180,
∠AED + 68 = 180
∠AED = 180 - 68
∠AED = 112
A train traveled at the same speed for 3 hours. It went 80.31 miles in all. How fast was the train going
Answer:
26.77 mph
Step-by-step explanation:
Formula for Avg. Speed = Distance/Time
80.31/3 = 26.77
Answer:
26.77 miles per hour
Step-by-step explanation:
Distance ÷Time
80.31 miles ÷3hrs
= 26.77 miles per hour
i will give Brainliest if half of the questions are answered
Answer:
Sorry I only know nuber 11 witch is 15
_
100
Step-by-step explanation: