Answer:
360 different permutations.
Step-by-step explanation:
It goes 6*5*4*3 because as you pick the pens the amount of pens in the jar would obviously decrease. Picking one leaves you with 5 new options. If you repeat that 4 times then you are left with 360 options.
The number of permutations of picking 4 pens from the box is 6P4, or 6!/(6-4)! = 654×3 = 360.
We have 6 pens and we are picking 4 of them. The order in which we pick the pens matters, so we are dealing with permutations.
The number of permutations of n objects is given by n!, or n factorial. So, the number of permutations of 6 objects is 6!.
However, we need to divide by the number of permutations of the 2 pens that we are not picking. There are 2 pens that we are not picking, so the number of permutations of those pens is 2!.
Therefore, the number of permutations of picking 4 pens from the box is 6!/(6-4)! = 654×3 = 360.
Learn more about permutations here: brainly.com/question/3867157
#SPJ2
What is the length of segment AB?
12
10-B
8-
6
А
2-
0
0
-10-8-6-4
- 2
2
4
6
8 10
--2-
<
05
06
O8
10
ous Question
Answer:
[tex]AB = 10 units[/tex]
Step-by-step explanation:
The line of segment AB can be calculated using distance formula, [tex] d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2} [/tex] , to calculate the distance between point A(6, 2) and point B(0, 10).
A(6, 2) can be (x1, y1),
B(0, 10) can be (x2, y2)
[tex] d = \sqrt{(0 - 6)^2 + (10 - 2)^2} [/tex]
[tex] d = \sqrt{(-6)^2 + (8)^2} [/tex]
[tex] d = \sqrt{36 + 64} [/tex]
[tex] d = \sqrt{100} [/tex]
[tex] d = 10 [/tex]
Simplify. Your answer should contain only positive exponents.
9) 3^-1 • 3^0
Answer:
1 / 3^1
Step-by-step explanation:
3^-1 • 3^0
When multiplying exponents with the same base, we add the exponents
3^ (-1+0)
3 ^-1
We know that a^ - b = 1/a^b
3 ^ -1 = 1/3^1
(1.6x+1.8)÷2.4−0.8=4.2
Answer:
x = 6.375
Step-by-step explanation:
Step 1:
4.2+0.8 = 5
(1.6x+1.8)÷2.4 = 5
Step 2:
5 · 2.4 = 12
1.6x + 1.8 = 12
Step 3:
12 - 1.8 = 10.2
1.6x = 10.2
Step 4:
10.2 ÷ 1.6 = 6.375
x = 6.375
A party rental company has chairs and tables for rent. The total cost to rent 9 chairs and 7 tables is $91. The total cost to rent 3 chairs and 5 tables is $59. What is the cost to rent each chair and each table? Costtorenteachchair:$ Costtorenteachtable:$
Answer:
cost to rent each chair=$1.75, cost to rent each tabble=$10.75
Step-by-step explanation:
Hello, I can help you with this
Step 1
Define
cost to rent a chair=x
cost to rent a table=y
9x=total cost for rent 9 chair
7y = total cost for rent 7 tables
a)The total cost to rent 9 chairs and 7 tables is $91.
in mathematical terms it is
9x+7y=91....equation 1
b) The total cost to rent 3 chairs and 5 tables is
3x+5y=59.... equation 2
and you have 2 equation and 2 unknown terms
let's solve this
from equation 1 isolate x
[tex]9x+7y=91\\9x=91-7y\\x=\frac{91-7y}{9}\\ \\[/tex]
from equation 2 isolate x
[tex]3x+5y=59\\3x=59-5y\\x=\frac{59-5y}{3}[/tex]
now, x= x, so
[tex]x=\frac{91-7y}{9}\\\\\\x=\frac{59-5y}{3} \ \\\ \frac{91-7y}{9}=\frac{59-5y}{3}\\ 3(91-7y)=9(59-5y)\\273-21y=531-45y\\273-531=-45y+21y\\-258=-24y\\y=\frac{258}{24}\\ y=10.75\\[/tex]
now, we know y, use it to find x
[tex]x=\frac{59-5y}{3}\\x=\frac{59-5(10.75)}{3}\\x=\frac{59-53.75}{3}\\\\x=\frac{5.25}{3}\\ x= 1.75\\[/tex]
Have a nice day
Please help find these angle for me plz!
Answer:
<DEF = 40°<EBF = <EDF = 56°<DCF = <DEF =40°<CAB = 84°Step-by-step explanation:
In triangle DEF, we have:
Given:
<EDF=56°
<EFD=84°
So, <DEF =180° - 56° - 84° =40° (sum of triangle angles is 180°)
____________
DE is a midsegment of triangle ACB
( since CD=DA(given)=>D is midpoint of [CD]
and BE = EA => E midpoint of [BA] )
According to midsegment Theorem,
. (DE) // (CB) "//"means parallel
. DE = CB/2 = FB =CF
___________
DEBF is a parm /parallelogram.
Proof: (DE) // (FB) [(DE) // (CB)]
AND DE = FB
Then, <EBF = <EDF = 56°
___________
DEFC is parm.
Proof: (DE) // (CF) [(DE) // (CB)]
And DE = CF
Therefore, <DCF = <DEF =40°
___________
In triangle ACB, we have:
<CAB =180 - <ACB - <ABC =180° - 40° - 56° =84° (sum of triangle angles is 180°)
[tex]HOPE \: THIS \: HELPS.. GOOD \: LUCK![/tex]
ASAP! I really need help with this question! Please do not send nonsense answers. Full solutions please!
Answer:
first option
Step-by-step explanation:
Given
[tex]\frac{15}{x}[/tex] + 6 = [tex]\frac{9}{x^2}[/tex]
Multiply through by x² to clear the fractions
15x + 6x² = 9 ( subtract 9 from both sides )
6x² + 15x - 9 = 0 ( divide through by 3 )
2x² + 5x - 3 = 0 ← in standard form
Consider the factors of the product of the coefficient of x² and the constant term which sum to give the coefficient of the x- term.
product = 2 × - 3 = - 6 and sum = + 5
The factors are + 6 and - 1
Use these factors to slit the x- term
2x² + 6x - x - 3 = 0 ( factor the first/second and third/fourth terms )
2x(x + 3) - 1(x + 3) = 0 ← factor out (x + 3) from each term
(x + 3)(2x - 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
2x - 1 = 0 ⇒ 2x = 1 ⇒ x = 0.5
Solution set is { - 3, 0.5 }
A circular table top has a radius of 24 inches.
What is the area of the table top, to the nearest square inch? Use 3.14 for n.
75 in.2
151 in.
1809 in.2
7235 in.2
Answer:
(C) 1809 in.2
Step-by-step explanation:
Took the test on edg :3
PLEASE HELP!
What is the length of the shortest altitude in a triangle, if the lengths of the sides are 15 cm, 17 cm, 8 cm. NO DECIMALS
Answer:
The shortest altitude = 8 cm
Step-by-step explanation:
Where we have the sides given by
15 cm, 17 cm, 8 cm
From cosine rule, we have;
a² = b² + c² - 2×b×c×cos(A)
We have
For the side 15 cm,
15² = 17² + 8² - 2×17×8 cos A
-388 = -612×cos×A
A = 61.93°
17² = 15² + 8² - 2×15×8 ×cos B
0 = -240·cos B
B = 90°
Therefore, 17 is the hypotenuse side and 15 and 8 are the legs, either of which can be the height which gives the shortest altitude as 8 cm
1. A box without a top is to be made from a rectangular piece of cardboard, with dimensions 8 in. by 10 in., by cutting out square corners with side length x and folding up the sides. (a) Write an equation for the volume V of the box in terms of x. (b) Use technology to estimate the value of x, to the nearest tenth, that gives the greatest volume. Explain your process.
Step-by-step explanation:
The dimensions are (8-2x) and (10-2x) We will say the depth of the box is x. The equation we use for the volume of the box is V=x(8-2x)(10-2x)
Answer:
part b of the answer is x=1.5 inches
Step-by-step explanation:
The solution for x2 + 2x + 8 ≤ 0 is
Answer:
Please use " ^ " for exponentiation: x^2 + 2x + 8 ≤ 0.
Let's solve this by completing the square:
x^2 + 2x + 8 ≤ 0 => x^2 + 2x + 1^2 - 1^2 + 8 ≤ 0. Continuing this rewrite:
(x + 1)^2 + 7 ≤ 0
Taking the sqrt of both sides: (x + 1)^2 = i*sqrt(7)
Then the solutions are x = -1 + i√7 and x = -1 - i√7
There's something really wrong here. I've graphed your function, x^2 + 2x + 8, and can see from the graph that there are no real roots, but only complex roots. Please double-check to ensure that you've copied down this problem correctly.
Answer:
B. The Empty Set
Step-by-step explanation:
Hope this helps!!! Have a great day!!!! : )
Graph this compound inequality: 2.5 < x < 4.5
-5 4
-3
-2
-1 0
+ ++ +
1 2 3 4 5
o
Drag a point to the number line.
Answer:
Please find the attached the required inequality graph
Step-by-step explanation:
Given that inequality is 2.5 ≤ x ≤ 4.5, we have;
The region in the given inequality is the region between 2.5 and 4.5 inclusive
Therefore, to represent 2.5 ≤ x ≤ 4.5 on the number line, we have;
A closed circle (representing the less than or equal to inequality symbol, showing inclusiveness) at 2.5, another closed circle at 4.5 (representing the less than or equal to inequality symbol, showing inclusiveness) and the region between 4.5 and 2.5 shaded.
Answer this question
Answer:
1.
a) exact form: -1 /14 or decimal form: -0.0714285
b) exact form: -23/120 or decimal form: -0.1916
2.
a) 89
b)98
c) 5.7
d) 4.8
3.
i) 2*2*2*2*2*2*3*3*3
ii) 3*3*3*5*5*5
iii) 2*2*2*2*2*2*2*2*2*2*2*2
iv) 2*2*2*2*2*2*5*5*5
9.
i) x = -9
ii) x + 1/7
I hope this helps get you started :)
If f(x) is the total cost, in dollars, of x candles, which of the following statements best describes the meaning of f(2)=6
Answer: A) The total cost of 2 candies is $6.00.
Step-by-step explanation:
Hi, the question is incomplete, options are :
A) The total cost of 2 candies is $6.00. B) The total cost of 6 candies is $2.00. C) The total cost of 2 candies is $3.00. D) The total cost of 3 candies is $2.00.
So, to answer this question we have to analyze the function given:
f(2)=6
Since the input value x (number of candles) is 2, and the output (cost in dollars ) is $6, the correct option is :
A) The total cost of 2 candies is $6.00.
Find the common ratio of the geometric sequence: 3,4,16/3,…
Answer:
4/3
Step-by-step explanation:
The common ratio is the number you multiply by 3 to get 4. This would be 4/3.
Answer:
4/3
Step-by-step explanation:
Well let's work backwards.
3 * what = 4
To figure out "what" we do,
4 ÷ 3
= 1.3333333333
As a fraction it is 4/3.
Thus,
the common ratio is 4/3.
Hope this helps :)
A circle has a radius of sqrt 45 units and is centered at -2.4, -4.8 write the equation of the circle
Answer:
(x+2.4)^2+(y+4.8)^2=2025
If you'd like additional help with math or another subject, check out growthinyouth.org!
Step-by-step explanation:
Find the value of x in the triangle
shown below.
X
85
67
Answer:
x = 28 degrees. 180 degrees in a triangle, 180-85-67=28
Answer:
28 degrees
Step-by-step explanation:
The interior angles of a triangle add up to 180 degrees.
The three angles given are: x, 85, and 67.
Therefore, these three angles must add to 180.
x+85+67=180
Combine like terms on the left. Add 85 and 67.
x+ (85+67)=180
x+152=180
We want to find x. We need to get x by itself. 152 is being added to x. The inverse of addition is subtraction. Subtract 152 from both sides.
x+152-152=180-152
x=180-152
x=28
x is 28 degrees.
If you get a penny a day from your uncle and each day he doubles the amount he gave you on the previous day how much would he give you on the twentieth day
Answer: On the 20th day, he will give $5242.88
Step-by-step explanation: This is a geometric series with elements:
initial value ([tex]a_{0}[/tex]) = 0.01
ratio = 2
At the twentieth day means the 20th term, i.e. n = 20.
To determine that term, use the formula: [tex]a_{n} = a_{0}.r^{n-1}[/tex]
Substituing terms:
[tex]a_{20} = 0.01.2^{20-1}[/tex]
[tex]a_{20} = 0.01.2^{19}[/tex]
[tex]a_{20} = 0.01.524288[/tex]
[tex]a_{20} = 5242.88[/tex]
Then, on the 20th day, your uncle gave to you $5242.88
A cylinder has a volume of 1200 meters cubed. What is the volume of a cone with the same radius and height? A. 400 m3 B. 900 m3 C. 1600 m3 D. 3600 m3
Hey there!
The volume of a cone is always 1/3 of that of a cylinder with the same except dimensions. You multiply the base by the height and then divide by three!
This means that if the cylinder has a volume of 1200 meters cubed, you simply divide by three, giving you 400 meters cubed !
The answer is A. 400 m³.
Have a wonderful day! :D
Answer:900
Step-by-step explanation:A cylinder has more volume considering because of the space but a cone simply has less
What system shows the correct numbers to multiply by the coefficients in order to eliminate y from the first two
equations when applying the linear combination method?
50+ 2 = 0
2x – 3y = -19
o
3 (5+2g = 0)
2 (2x – 3y = -19)
o
–3 (5x + 2y = 0)
12 (2x – 3y = –19)
-2 (5x + 2y = 0)
5 (2x – 3y = -19)
s -2(5x + 2y = 0)
1-5 (2x - 3y = -19)
Answer:
3 (5x+2y = 0)
2 (2x – 3y = -19)
Step-by-step explanation:
5x+2y=0 (1)
2x-3y=-19 (2)
To eliminate y from the first two equation when applying the linear combination method
We will multiply y Equation (1) and (2) with 3 and 2 respectively so that the coefficients of y in the two equations +6 and -6 respectively
3(5x+2y=0)
2(2x-3y=-19)
We have,
15x+6y=0 (3)
4x-6y= -38 (4)
Add Equation (3) and (4)
19x=-38
x= -2
Substitute x= -2 into (1)
5x+2y=0
5(-2)+2y=0
-10+2y=0
-10= -2y
y=-10/-2
=5
y=5, x=-2
Instructions: Find the missing side. Round your answer to the
nearest ten
Answer:
trig function is tangent
tan(63)=x/19
multiply each side by 19:
tan(63)19=x
x=37.3
Find the derivative of f(x) = negative 9 divided by x at x = -4. 4 divided by 9 16 divided by 9 9 divided by 16 9 divided by 4
Answer:
ﾠﾠﾠﾠﾠﾠﾠﾠ
Step-by-step explanation:
ﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠ
Answer:
9/16
Step-by-step explanation:
U
Which statements are true about x? Select three
options
B
XEBUC
Oxenc
OXEAUC
Oxeanc
ΕχεΑ
с
Answer:
A, B, C
Step-by-step explanation:
x is in the intersection of sets B and C, in set B, in set C, in the union of sets B and C, in the union of sets A and C
Answer: A, B, C
Answer:
[tex]\huge\boxed{x\in\bigg(A\cup C\bigg)}[/tex]
[tex]\huge\boxed{x\in\bigg(B\cup C\bigg)}\\\\\boxed{x\in\bigg(B\cap C\bigg)}[/tex]
Step-by-step explanation:
Look at the picture
Solve the equation for x.
Answer:
x = 27
Step-by-step explanation:
2/3x - 1/9x + 5 = 20
Subtract 5 from each side
2/3x - 1/9x + 5 -5= 20-5
2/3x - 1/9x = 15
Get a common denominator on the left side
2/3 *3/3 x - 1/9x = 15
6/9x - 1/9x = 15
5/9 x = 15
Multiply each side by 9/5
9/5 * 5/9x = 15 * 9/5
x = 15/5 *9
x = 3*9
x = 27
Answer:
x=27
Step-by-step explanation:
2/3 x -1/9 x+5=20
2/3x -1/9 x=20-5 common denominator
(6x-1x)/9=15 multiply each side by 9
(5x)=135
5x=135
x=135/5=27
x=27
Determine the equation of a line that passes through A(2,5) and is parallel to the line defined by 3x−y+12=0. State the equation in slope y-intercept form
Answer:
y = 3x - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
3x - y + 12 = 0 ( subtract 3x + 12 from both sides )
- y = - 3x - 12 ( multiply through by - 1 )
y = 3x + 12 ← in slope- intercept form
with slope m = 3
Parallel lines have equal slopes , thus
y = 3x + c ← is the partial equation
To find c substitute (2, 5) into the partial equation
5 = 6 + c ⇒ c = 5 - 6 = - 1
y = 3x - 1 ← equation of parallel line
There were some pieces of candy in a bowl. Shirley took half of them. Then Rose took half of the pieces left in the bowl. After that, Susan took half of the remaining pieces of candy. In the end there were 8 pieces of candy left in the bowl. How many candies were there in the bowl at the beginning?
Answer:
Number of pieces of candy in the bowl=64
Step-by-step explanation:
Let
x=number of pieces of candy in a bowl
Shirley took=1/2 of x
=1/2x
Remaining
x-1/2x
= 2x-x/2
=1/2x
Rose took half of the pieces left in the bowl=1/2 of 1/2x
=1/2*1/2x
=1/4x
Remaining
1/2x-1/4x
=2x-x/4
=1/4x
Susan took 1/2 of the remaining pieces of candy=1/2 of 1/4x
=1/2*1/4x
=1/8x
Remaining 8
1/8x=8
x=8÷1/8
=8*8/1
=64
x=64
HELP!! this is due today
Answer:
1
Step-by-step explanation:
If y=x, than the only way
y=rx can be possible is if r=1
Hope this helps!
Have a good day! :)
Answer:
1
Step-by-step explanation:
y = rx
Use any set of x and y-coordinates in the equation and solve for r.
For example, use (5.8, 5.8).
5.8 = r(5.8)
Divide both sides by 5.8:
r = 1
Answer: r = 1
Can anyone help me with this please? And QUICK!
Answer:
30.6
Step-by-step explanation:
The following data were obtained from the question:
Angle θ = 23°
Opposite = 13
Adjacent = y
The value of y can be obtained by using the following trig ratio:
Tan θ = Opposite /Adjacent
Tan 23° = 13/y
Cross multiply
y × Tan 23° = 13
Divide both side by Tan 23°
y = 13/Tan 23°
y = 30.6
Therefore, the value of y in the diagram above is 30.6
A family has two cars. The first car has a fuel efficiency of 20 miles per gallon of gas and the second has a fuel efficiency of 30 miles per gallon of gas. During one particular week, the two cars went a combined total of 1650 miles, for a total gas consumption of 65 gallons. How many gallons were consumed by each of the two cars that week? Firstcar:gallons= Secondcar:gallons=
Answer:
First car: 30 gallons
Second car: 35 gallons
Step-by-step explanation:
Hi, to answer this question we have to write a system of equations:
Total gas consumption was 65:
x+y=65
Where:
x = gallons consumed by the first car
y = gallons consumed by the second car
The first car has a fuel efficiency of 20 miles per gallon of gas and the second has a fuel efficiency of 30 miles per gallon of gas, the two cars went a combined total of 1650 miles:
x 20+y 30 = 1650
The system is:
x+y=65 (1)
x 20+y 30 = 1650 (2)
Isolating y on (1)
y = 65-x
Replacing y= 65-x on (2):
x 20+(65-x)30 = 1650
20x +1,950-30x= 1650
20x-30x= 1650-1950
-10x= -300
x= -300/-10
x = 30 gallons
Back to (1)
y =65-x
y =65-30
y= 35 gallons
Feel free to ask for more if needed or if you did not understand something.
Shelley and David have a sweet tooth. Shelley spent \$2.65 for 15 sour keys and 2 chocolate bars. David bought 3 chocolate bars and 10 sour keys for \$3.35 at the same store. Find the cost of each chocolate bar and each sour key at this store. If you need 8 chocolate bars and 24 sour keys to give to friends coming to your birthday party, how much will they cost you at this store?
Answer:
Chocolate bars: $0.95 each
Sour keys: $0.05 each
Total cost for 8 chocolate bars and 24 sour keys: $8.80
Step-by-step explanation:
sour keys=x
chocolate bars=y
15x+2y=2.65
10x+3y=3.35
multiply the second equation by 1.5
15x+4.5y=5.025
2.5y=2.375
y=0.95
Chocolate bars are $0.95 each.
Now substitute the y value in one of the equations
15x+2(0.95)=2.65
15x+1.9=2.65
15x=0.75
x=0.05
Sour keys are $0.05 each.
For the second part of the question, just multiply the number of chocolate bars by the cost and same thing with the sour keys and add them.
Final answer: $8.80
Please answer this in two minutes
Answer:
Step-by-step explanation:
In an isosceles trapezoid, two pairs of adjacent angles are supplementary. It means that the sum of the adjacent angles is 180°
Looking at the diagram, angle X and angle W are adjacent angles. It means that
X + W = 180
Since X = 105, then
105 + W = 180
W = 180 - 105 = 75°
Since W = b + 25°, then
b + 25° = 75
b = 75 - 25 = 50°
Answer: In an isosceles trapezoid, two pairs of adjacent angles are supplementary. It means that the sum of the adjacent angles is 180°Looking at the diagram, angle X and angle W are adjacent angles. It means that X + W = 180Since X = 105, then105 + W = 180W = 180 - 105 = 75°Since W = b + 25°, thenb + 25° = 75b = 75 - 25 = 50°
Step-by-step explanation:
