Answer:
A)[tex]^{28}P_4}=491400[/tex]
Step-by-step explanation:
Total number of members = 28
We are supposed to find the no. of ways the four offices of chairman, vice chairman, secretary, and treasurer be filled from a club with 28 members
When 1 member is selected for Chairman position
So, 27 members will be left for the selection for the position of Vice chairman
When 1 member out of 27 is selected for Vice chairman position
So,26 members will be left for the selection for the position of secretary
When 1 member out of 26 is selected for secretary position
So,25 members will be left for the selection for the position of treasurer
Permutation relates to the act of arranging all the members of a set into some sequence or order,
The combination is a way of selecting items from a collection, such that (unlike permutations) the order of selection does not matter.
So, we will use permutation over here
Formula [tex]^nP_r=\frac{n}{(n-r)!}[/tex]
Substitute n = 28 and r = 4
So,[tex]^{28}P_4=\frac{28!}{(28-4)!}=491400[/tex]
So, Option A is true
A)[tex]^{28}P_4}=491400[/tex]
Hence There are 491400 ways the four offices of chairman, vice chairman, secretary, and treasurer be filled from a club with 28 members.
The number of ways the four offices of chairman, vice chairman, secretary, and treasurer be filled from a club with 28 members is 491,400.
The given parameters
Number of members = 28 Number of positions = 4Total arrangement of the different positions available[tex]nP_r =\frac{n!}{(n- r)!}[/tex]
[tex]28 P4 = \frac{28!}{(28-4)!} = \frac{28!}{24!} = 491,400[/tex]
Thus, the number of ways the four offices of chairman, vice chairman, secretary, and treasurer be filled from a club with 28 members is 491,400.
Learn more about permutation here: https://brainly.com/question/3086912
HELP ASAP PLEASE
Are the bases of the prism equilateral triangles? Why or why not? Note: The bases of a triangular prism are triangles.
For this prism to be a right prism, all the lateral faces must be rectangles. Is enough information given to prove the lateral faces are rectangles? Why or why not?
Answer:
Step-by-step explanation:
The bases of a triangular prism are equilateral triangles, since they have equal sides: 5, 5, and 5
yes, since if all lateral faces are rectangles, rectangles are formed from 4 perpendicular segments, thus, if all edges of the lateral faces are perpendicular, then they are rectangles
Answer:
yes
Step-by-step explanation:
i tried explaining it in a way that it wouldn't sound like I'm copying the answer above, but really, the answer above is correct and explains it well, refer to the answer above please
When the two crews start working together, what part of all
the garbage bins will the first garbage truck empty?
The crew of a garbage truck takes 5 hours to empty all the
bins in one neighborhood on pickup day. The city assigned
a second garbage truck to this neighborhood. During their
training, it took the crew from the second truck 8 hours to
empty all the bins.
0.6
0.5
0.7
Time
(hours)
t
Part of Bins
Emptied
Rate
(part/hour)
1
5
0.4
First Truck
500
(9
1
t
Second
Truck
1
8
8
This question is not properly written
Complete Question
When the two crews start working together, what part of all
the garbage bins will the first garbage truck empty?
The crew of a garbage truck takes 5 hours to empty all the bins in one neighborhood on pickup day. The city assigned a second garbage truck to this neighborhood. During their training, it took the crew from the second truck 8 hours to empty all the bins.
Options
• 0.6
• 0.5
• 0.7
Answer:
0.6
Step-by-step explanation:
Let us say that the total hours worked by both trucks = t hours
Number of hours worked by first truck = 5 hours
Number of hours worked by second truck = 8 hours
Let 1 = total number of bins.
For the 1st truck the rate at which work was carried out is
(1 ) ÷ (5 ) = 1/5
For the 1st truck the rate at which work was carried out is
( 1 ) ÷ (8 ) = 1/8
Then,
(1/5 + 1/8) × t =1
(1/5 + 1/8) × t= 1
(13/40)t = 1
t = 1÷ 13/40
t = 1× 40/13
t = 40/13 hours.
Hence, the total hours worked by both trucks = 40/13 hours
the part of all
the garbage bins that the first garbage truck will empty is calculated as:
1/5 × 40/13 hr
1/5 × 40/13
= 0.6153846154
Approximately = 0.6
Therefore, when the two crews start working together, the part of all
the garbage bins that the first garbage truck will empty is 0.6 of the total work done.
Answer:
A) 0.6
Step-by-step explanation:
3(x-1) - 8 = 4(1+x) +5. Too hard, i keep getting confused
3(x-1)-8=4(1+x)+5
One solution was found :
x = -20
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
3*(x-1)-8-(4*(1+x)+5)=0
Step by step solution :
Step 1 :
Equation at the end of step 1 :
((3•(x-1))-8)-(4•(x+1)+5) = 0
Step 2 :
Equation at the end of step 2 :
(3 • (x - 1) - 8) - (4x + 9) = 0
Step 3 :
Step 4 :
Pulling out like terms :
4.1 Pull out like factors :
-x - 20 = -1 • (x + 20)
Equation at the end of step 4 :
-x - 20 = 0
Step 5 :
Solving a Single Variable Equation :
5.1 Solve : -x-20 = 0
Add 20 to both sides of the equation :
-x = 20
Multiply both sides of the equation by (-1) : x = -20
One solution was found :
x = -20
hope this is wht u wanted
Is (0, 4) a solution to the equation y = x?
Answer:
No
Step-by-step explanation:
Plug x=0 and y=4 into y=x
4 doesn't equal 0
If anybody now this pls help my homework due TOMORROW
Answer:
Part A: D. [tex]y = (x + 1)(x+3)\\[/tex]
Part B: C. [tex]3x(x-3) = 0\\[/tex]
Step-by-step explanation:
For part A) we just have to plug in 0 for x and solve for y until we find the equation that says 3 is the value for y when x is 0. For purposes of speeding up the process the correct answer is D. I will show how to check for it now.
The equation: [tex]y = (x + 1)(x+3)[/tex]
Now plug in 0 for x.
[tex]y = (0 + 1)(0+3)\\[/tex]
Now solve.
y = (1)(3)
y = 3
This proves that this is the correct answer.
For part B) we just have to plug in the give values for x separately and check for each value of x that it equals 0. For the purpose of speeding up the process the correct answer is C. I will show how to check for it now.
The equation: [tex]3x(x-3) = 0[/tex]
Now plug in x for 0 and solve:
[tex]3* 0 (0-3) = 0\\[/tex]
[tex]0(-3) = 0\\[/tex]
[tex]0 =0\\[/tex]
This equation is true, now we check for the other value of x, 3.
[tex]3*3(3-3) = 0\\[/tex]
[tex]9(0) = 0\\[/tex]
[tex]0 =0\\[/tex]
This is also true so that means this is the correct answer.
NEED HELP ASAP
In the unit similar triangles and trigonometry, what is “ compass bearings ?”
Answer:
this is what I found "The bearing of a point is the number of degrees in the angle measured in a clockwise direction from the north line to the line joining the centre of the compass with the point. A bearing is used to represent the direction of one point relative to another point."
I can't really make sense of it though...
Answer:
What is the difference between constructing a square and constructing a regular hexagon?
The diameter of the circle is used for the square construction, but the radius of the circle is used for the regular hexagon construction.
The radius of the circle is used for the square construction, but the diameter of the circle is used for the regular hexagon construction.
The square will need two arcs along the circle, but the hexagon will need two arcs above and two arcs below the diameter of the circle.
The square will need six arcs along the circle, but the hexagon will need two arcs above and two arcs below the diameter of the circle.
Step-by-step explanation:
Jayne polled 50 students about their preferred after-school sport and then recorded the data in the table below. Which sport is more popular?
A. You can use a relative frequency table to examine how data sets are related by comparing percentages.
B. Row and column relative frequency tables tell you the same information as total relative frequency tables.
C. A column relative frequency table helps compare data in two different rows.
D. In a column two-way relative frequency table, each column totals 100%.
Step-by-step explanation:
D. In a column two-way relative frequency table, each column totals 100%.
Could anyone plz help me with this question ?
Answer:
45
Step-by-step explanation:
b and c are part of an 180 degrees angle.
You already have a 90 degrees angle
180-90=90
And since there are 2 angles
90/2=45
And b and c are vertical angles
How many degrees does the protractor show for the given angle
A. 35
B. 175
C. 175
D. 15
Please help with this I need help with it
Answer: 15 degrees
Step-by-step explanation:
180 degrees - 165 degrees = 15 degrees
Fill in the blanks. If the triangles cannot be shown to be congruent from the information given, leave the triangle's name blank and write CanNot Be Determined (CNBD) in the spot for rule.
GA ∩ TN = I
∆GIT ≅ ∆________
By rule _________
Answer:
GIT is congruent to AIN
By rule SAS
Step-by-step explanation:
welp hope this helps
A skier slides down a 750 m slope in 12.5 s. What is the average
velocity for the trip?
Answer:
The average velocity for the skier is exactly 60 meters per second.
Step-by-step explanation:
Divide the distance which is 750 meters and 12.5 seconds and you get 60 meters per second. Velocity formula --> 750 meters / 12.5 seconds = 60 m/seconds.
Plz mark brainliest if u r cool
Write an equation of the line in slope-intercept form.
The line passing through (0, 1) and (-4,5)
Answer:
y=-x+1
Step-by-step explanation:
solve for k. 2.5(4k+2) =12k
Answer:
2.5
Step-by-step explanation:
2.5(4k+2) =12k
2.5*6k=12k
Answer: 2.5
Step-by-step explanation:
3. Sophia had 1/4 of her birthday cake leftover. She split that cake
between her and her best friend. How much of the cake did they each
get?
Answer:
1/8 of the original cake.
1/8 = 0.125
Step-by-step explanation:
The easiest way to do this is with decimals.
1/4 = 0.25
Each of the girls gets 0.25/2 = 0.125
Each girl gets 1/8 of the cake or 0.125 of the cake.
Find the difference quotient of f; that is, find StartFraction f left parenthesis x plus h right parenthesis minus f left parenthesis x right parenthesis Over h EndFraction comma h not equals 0 comma for the following function. f left parenthesis x right parenthesis equals negative 4 x plus 6
Answer:
-4
Step-by-step explanation:
Given the following function:
f(x) = -4x + 6
We have to find the difference quotient of f(x); that is,
[f(x + h) - f(x)]/h
So, we ned to compute f(x + h) as follows:
f(x+h) = -4(x+h) + 6 = -4x - 4h + 6
Replacing into the difference quotient, we get:
[f(x + h) - f(x)]/h = [-4x - 4h + 6 - (-4x + 6)]/h
[f(x + h) - f(x)]/h = [-4x - 4h + 6 + 4x - 6)]/h
[f(x + h) - f(x)]/h = [- 4h)]/h
[f(x + h) - f(x)]/h = -4
What company should he rent from
HELP ASAP :(
How are the following three expressions different from each other, if indeed they are? do not just state the value of each but explain what may be the same or different. Be as specific as you can be in your response.
1.(-2)^2
2.-2^2
3. -(2)^2
Answer:
1. 4
2. -4
3. -4
Step-by-step explanation:
Let's look carefully at each problem and explain it.
1. (-2)^2
This means find the square of the number -2. Since the square of a number means multiplying the number by itself, then
(-2)^2 means the product (-2) * (-2),
and since the product of two negative numbers is positive, then
(-2)^2 = (-2) * (-2) = 4
Answer is 4.
2. -2^2
Here, the exponent applies only to the 2, not to -2. This problem means square 2 and then take the opposite of the product. This can be written as
-(2^2)
-2^2 = -(2^2) = -(2 * 2) = -(4) = -4
Answer is -4.
3. -(2)^2
This is the same as problem 2 above. You square the 2 first, then take its negative.
-(2)^2 = -(2^2) = -(2 * 2) = -(4) = -4
Answer is -4
Which number is a solution of the inequality −7x−3.5<−10.5
A. −3
B. −1
C. 1
D. 3
Answer: x > 1
Step-by-step explanation:
PLS HELP it is urgent and my homework due soon
Answer:
a) (1 , 4)
b) (-1 , 0) and (3 , 0)
Step-by-step explanation:
The turning point also call the vertex of the function is shown by in this case the maximum which is at the point (1 , 4). The roots, also known as zeros, are the values at which the graph crosses the x-axis. In this case it is at points: (-1 , 0) and (3 , 0)
Which of the following is the explicit rule for a geometric sequence defined by a recursive formula of an=5an-1 for which the first term is 23?
Answer:
D
Step-by-step explanation:
The explicit rule for a geometric sequence is
[tex]a_{n}[/tex] = a [tex]r^{n-1}[/tex]
where a is the first term and r the common ratio
Here a = 23 and from the recursive formula
[tex]a_{n}[/tex] = 5[tex]a_{n-1}[/tex] , then r = 5 , thus explicit formula is
[tex]a_{n}[/tex] = 23 × [tex]5^{n-1}[/tex] → D
The correct option is D.
The calculation is as follows:The explicit rule for a geometric sequence is
[tex]an = ar^{n-1}[/tex]
Here
a represents the first term
r represents the common ratio
So,
[tex]a_n = 5a_{n-1}[/tex]
So,
[tex]a_n = 23\times 5^{n-1}[/tex]
Learn more: brainly.com/question/17429689
What is the equation of the translated function, g(x), if
f(x) = x2?
g(x) = (x - 4)2 + 6
g(x) = (x + 6)2 - 4
g(x) = (x - 6)2 - 4
g(x) = (x + 4)2 + 6
Answer:
D. g(x) = (x + 4)2 + 6
Step-by-step explanation:
I just took the test and this was the correct answer
Determine the value of k. answers: A) 18° B) 180° C) 108° D) 97°
Answer:
C) 108°
Step-by-step explanation:
72°+k°=180° (straight line)
Subtract 72° from both sides
k°=108°
Our answer is C)108°.
Value of k = 108°
The correct option is C.
What is exterior angle?Exterior angles are angles that are parallel to the inner angles of a polygon but lie on the outside of it. The measure of an exterior angle is equal to the sum of the two internal opposite angles.
Given,
In a triangle,
Interior angles are
A = 72°,
B = 83° and
C = 25°
exterior angle A = k°
Exterior angle A = Interior angle B + Interior angle C
k = 83° + 25°
k = 108°
Hence, 108° is the value of k.
Learn more about exterior angle here:
brainly.com/question/28835566
#SPJ2
if F(x)=2x^2-5 and g(x)=3x+3, find (f-g)(x)
A.2x^2-3x-8
B.-x^2-8
C.3x-2x^2-2
D.2x^2-3x-2
Answer:
work is pictured and shown
Find f(2) and f(a + h) when f(x) = 3x^2 + 2x + 4
Answer:
[tex]f(2)=20\\f(a+h)=3a^2+6ah+3h^2+2a+2h+4[/tex]
Step-by-step explanation:
[tex]f(x)=3x^2 + 2x + 4[/tex]
[tex]f(2)=3(2)^2 + 2(2) + 4\\f(2)=3(4)+ 2(2) + 4\\f(2)=12+ 4+ 4\\f(2)=20[/tex]
[tex]f(a+h)=3(a+h)^2 + 2(a+h) + 4\\f(a+h)=3(a+h)(a+h) + 2(a+h) + 4\\f(a+h)=3a^2+3ah+3ah+3h^2+2a+2h+4\\f(a+h)=3a^2+6ah+3h^2+2a+2h+4[/tex]
Answer:
f(2) = 20
f(a+h) = 3a²+6ah+3h²+2a+2h+4
Step-by-step explanation:
f(x) = [tex]3x^2+2x+4[/tex]
A) Putting x =2
=> f(2) = 3(2)²+2(2)+4
=> f(2) = 12+4+4
=> f(2) = 20
B) Putting x = a+h
=> f(a+h) = 3(a+h)²+2(a+h)+4
=> f(a+h) = 3a²+6ah+3h²+2a+2h+4
Which is the best estimate for the sum 2/9 +10/11 ?
A. 0 + 0 = 0
B. 12+12=1
C. 1 + 1 = 2
D. 0 + 1 = 1
Answer:
D
Step-by-step explanation:
Beth traveled for 8 hours and arrived at her destination 480 miles away. How far would Beth have traveled if she had continued on her trip for 2 additional hours? Name two different rates that can used in solving this problem.
Answer:
She'd have travelled 120 extra miles, 600 miles in total.
Step-by-step explanation:
480 : 8 = 60 --> 60 miles per hour
60 x 10 = 600 --> 600 miles in 10 hours at that speed
600 - 480 = 120 --> extra miles in the extra two hours at that speed
the diagram shows a dilation of line AB about the origin O. Determine the scale factor of the dilation by following these steps.
Answer:
The scale factor is 1.5
Step-by-step explanation:
In the picture attached, the line AB is shown.
The first 3 steps are to measure some lengths
OA = 2 units OA’ = 3 units OB = 3 units OB’ = 4.5 unitsAB = 2.2 A’B’= 3.3The last 3 steps are to compute these ratios
OA'/OA = 3/2 = 1.5 OB'/OB = 4.5/3 = 1.5 A'B'/AB = 3.3/2.2 = 1.5Answer:
see explanation
Step-by-step explanation:
1. Measure these lengths:
OA - 2.0 units
OA' - 3.0 units
2. Measure these lengths:
OB - 3.0
OB' - 4.5
3. Measure these length's:
AB - 2.2
AB' - 3.3
4. Calculate the ration: OA' / OA = 1.5
5. Calculate this ratio: OB' / OB = 1.5
6. Calculate this ratio: A'B' / AB = 1.5
The heights of the sunflowers, in inches,
in Brittany's garden are shown below.
65 66 64 63 64
62. 65. 63, 64, 66
Brittany displayed the data in a dot pot
Which of the dot plots correctly displays
Brittany s dala?
Answer:
See picture attached
Step-by-step explanation:
The options are not provided, so I made my own dot plot. To did it, I ordered the set, and counted how many times each height appears, as follows:
62: once
63: twice
64: three times
65: twice
66: twice
Those are the numbers of dots you have to put over each height.
Which of the following is(are) the solution(s) to 8|x-3|=-24
O A. All values are solutions
O B. x= 6,0
C. No Solution
O D. x = 3,0
Question:
Consider the rectangle shown here.
A. State its area in square inches.
B. State its area in square feet, to the nearest tenth.
C. In general, A square inches equals how many square feet?
Answer:
A. Area in square inches = 1760 square inches
B. Area in square feet = 12.2 square feet
C. 1 square inch = [tex]\frac{1}{144}[/tex] feet
Step-by-step explanation:
Given,
Length of the rectangle (l) = 55 inches
Breath of the rectangle (b) = 32 inches
A. Area of the rectangle = length × breath
⇒ 55 × 32
⇒ 1760 square inches
Area in square inches = 1760 square inches
B. 1 foot = 12 inches
1 inch = [tex]\frac{1}{12}[/tex] feet
1 square inch = [tex]\frac{1}{144}[/tex] feet
∴ 1760 square inches = [tex]\frac{1760}{144}[/tex] feet
⇒ 12.2222 square feet
Area in square feet = 12.2 square feet
C. 1 square inch = [tex]\frac{1}{144}[/tex] feet
