[tex]\text{The formula of a midpoint:}\\\\\left(\dfrac{x_1+x_2}{2};\ \dfrac{y_1+y_2}{2}\right)[/tex]
[tex]\text{We have}\\\\\text{endpoint}\ (-2,\ -14)\to x_1=-2,\ y_1=-14\\\\\text{midpoint}\ (-11,\ -20)\\\\\text{Therefore we have the equations:}\\\\\dfrac{-2+x_2}{2}=-11\qquad\text{multiply both sides by 2}\\\\-2+x_2=-22\qquad\text{add 2 to both sides}\\\\\boxed{x_2=-20}\\\\\dfrac{-14+y_2}{2}=-20\qquad\text{multiply both sides by 2}\\\\-14+y_2=-40\qquad\text{add 14 to both sides}\\\\\boxed{y_2=-26}\\\\Answer:\ \boxed{(-20,\ -26)}[/tex]
Final answer:
To find the other endpoint of a line segment when given the midpoint and one endpoint, use the formulas x2 = 2xm - x1 and y2 = 2ym - y1. For the given midpoint (-11, -20) and endpoint (-2, -14), the other endpoint is calculated to be (-20, -26).
Explanation:
To find the coordinates of the other endpoint of a segment when the midpoint and one endpoint are known, the midpoint formula can be used in reverse. For a line segment with endpoints (x1, y1) and (x2, y2) and midpoint (xm, ym), the coordinates of the midpoint are found by the formulas xm = (x1 + x2)/2 and ym = (y1 + y2)/2. If one endpoint is known, say (x1, y1) = (-2, -14) and the midpoint is (xm, ym) = (-11, -20), we can find the other endpoint (x2, y2) by rearranging the formulas: x2 = 2xm - x1 and y2 = 2ym - y1.
Calculating the values we get:
x2 = 2(-11) - (-2) = -22 + 2 = -20
y2 = 2(-20) - (-14) = -40 + 14 = -26
Therefore, the coordinates of the other endpoint are (-20, -26).
What is the value of x?
5
6
2
-2
Answer:
x= -2
Step-by-step explanation:
The distance from one end of the line to the other is -3x-1.
Counting on the number line we count 6 units. Setting them equal we get
-3x-1 = 5
Add 1 to each side
-3x-1+1 = 5+1
-3x = 6
Divide each side by -3
-3x/-3 = 6/-3
x = -2
What is the constant of proportionality for the relationship shown in this table?
x 3 6 9 12
y 1 2 3 4
1/6
1/3
3
9
Answer:
It is 1/3.
Step-by-step explanation:
The y values are 1/3 of the x values so the relation is
y = 1/3 x
Constant of proportionality = 1/3
The constant of proportionality for the given relationship y = 1/3x is (1/3).
What is proportionality?Proportionality are of two types one is direct proportion and another is inverse proportion. If two or more two quantities are in proportion they increase or decrease at a constant rate called the constant of proportionality.
We know two quantities are proportional if they increase or decrease by a certain constant rate.
Given when x = 3, y = 1 and when x = 9, y = 3.
∴ We can conclude that x = 3y or y = 1/3x.
So, the constant of proportionality is 1/3.
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Please help on this one ?
1 ║ 1 2 -3 2
1 3 0
--------------------------------------------------------------------
1 3 0 [tex]\boxed{2}[/tex]
⇒ The Remainder is 2
A scientist is testing a new antibiotic by applying the antibiotic to a colony of 10,000 bacteria. The number of bacteria decreases by 75% every two hours. How many hours will it take for the bacteria colony to decrease to 1000? Round your answer to the nearest tenth of an hour.
Answer:
3.3 hours.
Step-by-step explanation:
We have been given that a scientist is testing a new antibiotic by applying the antibiotic to a colony of 10,000 bacteria. The number of bacteria decreases by 75% every two hours.
Since number of bacteria is decreasing exponentially, so we will use exponential decay function.
[tex]y=a*b^x[/tex], where,
a= Initial value,
b = For decay b is in form (1-r), where r is rate in decimal form.
Let us convert our given rate in decimal form.
[tex]75\%=\frac{75}{100}=0.75[/tex]
As number of bacteria is decreasing every 2 hours, so number of bacteria decreased in 1 hour will be x/2.
Upon substituting our given values in above formula we will get,
[tex]y=10,000(1-0.75)^{\frac{x}{2}}[/tex]
To find the number of hours it will take to for the bacteria colony to decrease to 1000, we will substitute y = 1,000 in our equation.
[tex]1,000=10,000(0.25)^{\frac{x}{2}}[/tex]
Let us divide both sides of our equation by 10,000.
[tex]\frac{1,000}{10,000}=\frac{10,000(0.25)^{\frac{x}{2}}}{10,000}[/tex]
[tex]0.1=(0.25)^{\frac{x}{2}}[/tex]
Let us take natural log of both sides of our equation.
[tex]ln(0.1)=ln((0.25)^{\frac{x}{2}})[/tex]
[tex]ln(0.1)=\frac{x}{2}*ln(0.25)[/tex]
[tex]-2.302585=\frac{x}{2}*-1.386294[/tex]
[tex]x=\frac{-2.302585}{-1.386294}*2[/tex]
[tex]x=1.660964*2[/tex]
[tex]x=3.3219\approx 3.3[/tex]
Therefore, it will take 3.3 hours for the bacteria colony to decrease to 1000.
Final answer:
It will take 4 hours for the bacteria colony to decrease from 10,000 to 1,000, considering a 75% decrease every two hours.
Explanation:
To find out how many hours it will take for the bacteria colony to decrease from 10,000 to 1,000 with a 75% decrease every two hours, we can use the formula for exponential decay: [tex]N = N0(1 - r)^t[/tex], where N is the final amount, N0 is the initial amount, r is the rate of decrease (expressed as a decimal), and t is the time in units of the rate's period (in this case, every two hours).
Here, N0 = 10,000, N = 1,000, and r = 0.75. Plugging the values into the formula gives [tex]1,000 = 10,000(1 - 0.75)^t.[/tex]Simplifying, we find [tex](1 - 0.75)^t = 0.1.[/tex]
Solving for t, we find that t equals 2 cycles or 4 hours, because the bacteria population decreases by 75% every 2 hours, and it takes 2 cycles for the population to reach 1,000 from 10,000.
Please please please help!!!!
The two triangles below are similar.
What is the ratio of the corresponding side lengths?
A) 4:9
B) 4:2
C) 26:26
D) 4.5:2
Answer is 4:2 (choice B)
AB is 4 units while A'B' is 2 units. The ratio of the sides is simply gluing these two numbers together with a colon symbol in between to get 4:2. We can reduce this to get 2:1, but your teacher has decided not to do this.
Quentin has 6 5/8 feet of lumber but needs another 2 3/4feet to complete the project he's working on. How much total wood will the project have used when finished?
Answer:
Total wood required for the project will be 9 3/8 feet.
Step-by-step explanation:
As given in the question Quentin has lumber of length = 6 5/8
feet =53/8 feet.
Now Quentin needs more lumber = 2 3/4 feet =11/4 feet or 22/8 feet.
So we can get total wood required by adding these two figures
That is = 53/8 + 22/8
= (53 +22)/8
= 75/8
= 9 3/8 feet
Answer:
[tex]The\ total\ wood\ will\ the\ project\ have\ used\ be\ 9 \frac{3}{8}.[/tex]
Step-by-step explanation:
As given
[tex]Quentin\ has\ 6 \frac{5}{8}\ feet\ of\ lumber\ but\ needs\ another\ 2 \frac{3}{4}\ feet\ to\ complete\ the\ project\ he's\ working\ on.[/tex]
i.e
[tex]Quentin\ has\ \frac{53}{8}\ feet\ of\ lumber\ but\ needs\ another\ \frac{11}{4}\ feet\ to\ complete\ the\ project\ he's\ working\ on.[/tex]
[tex]Total\ wood\ will\ the\ project\ have\ used =\frac{53}{8} + \frac{11}{4}[/tex]
L.C.M of (8,4) = 8
Than
[tex]Total\ wood\ will\ the\ project\ have\ used =\frac{53 + 11\times 2}{8}[/tex]
[tex]Total\ wood\ will\ the\ project\ have\ used =\frac{53 + 22}{8}[/tex] [tex]Total\ wood\ will\ the\ project\ have\ used =\frac{75}{8}[/tex]
[tex]Total\ wood\ will\ the\ project\ have\ used = 9 \frac{3}{8}[/tex]
[tex]Therefore\ the\ total\ wood\ will\ the\ project\ have\ used\ be\ 9 \frac{3}{8}.[/tex]
Please help me with these problems
Answer:
1.a=2
2. C x=2 and x=-3
Step-by-step explanation:
The standard form for the quadratic function is
ax^2 +bx+c
so we need to rewrite the function to be in this form
2x^2 -10 = 7x
Subtract 7x from each side
2x^2 -7x-10 = 7x-7x
2x^2 -7x-10 = 0
a =2, b= -7 c=-10
2. The quadratic formula is
-b ± sqrt(b^2 -4ac)
----------------------------
2a
2x^2 + 2x=12
Lest get the equation in proper form
2x^2 + 2x-12 = 12-12
2x^2 +2x-12 =0
a=2 b=2 c=-12
Lets substitute what we know
-2 ± sqrt(2^2 -4(2)(-12))
----------------------------
2(2)
-2 ± sqrt(4+96)
----------------------------
2(2)
-2 ± sqrt(100)
----------------------------
4
-2 ± 10
----------------------------
4
-2 + 10 -2-10
----------- and --------------
4 4
8/4 and -12/4
2 and -3
Anfernee bought 4 umbrellas and 2 hats and spent between 40 to 60 dollars. Each hat cost the same amount. The price of a hat is 8 dollars. What is the least amount Anfernee could have spent on an umbrella and what is the most?
Answer:
Cheapest = $6
Most expensive = $11
Step-by-step explanation:
First we need to make an equation:
4u + 2h = 40 < x < 60
u is umbrellas and h is hats,
If a hat is 8, then this can be:
4u + 2(8) = 40 < x < 60
4u + 16 = 40 < x < 60
4u = 40 - 16
4u = 24
u = 6
So the cheapest an umbrella can be is $6.
The most expensive is:
4u = 60 - 16
4u = 44
u = 11
So the most expensive is $11
Function f, shown below, is translated down 3 units and left 4 units to create function g.
F(x)= 3|x-2|-5
Fill in the values of a, h, and I to write the function g.
G(x)= a|x-h|+k
Answer: G(x) = 3|x + 2| - 8
Step-by-step explanation:
"a" represents the vertical stretch (or shrink)
"h" represents the x-coordinate of the vertex
x-axis goes left and right"k" represents the y-coordinate of the vertex
y-axis goes up and downF(x) = 3|x - 2| - 5
G(x) = 3(x - 2 + 4| - 5 - 3
= 3|x + 2| - 8
Answer:
g(x)=3 lx+2l-8
:)
Scarlett sells designer ponchos. The revenue, RR, she makes from selling a batch of nn ponchos is given by the function R(n)=20nR(n)=20n, and the expenses, EE, that she incurs from producing a batch of nn ponchos is given by the function E(n)=10\cdot \sqrt{n}E(n)=10? n ? . Let PP be the total profit Scarlett makes from producing and selling a batch of nn ponchos
Answer:
Write a formula for P(n) in terms of R(n).
R(n) - E(n)
Write a formula for P(n) in terms of n.
20n - [tex]10\sqrt{n}[/tex]
Step-by-step explanation:
Please rate 5 stars and thanks if the answer is right :)
To calculate Scarlett's profit for selling ponchos, subtract her total expenses from her total revenue using the functions provided. For a specific number of ponchos, plug that number into both the revenue and expense functions and subtract the results.
Explanation:The student's question deals with the calculation of profit for a business venture, specifically for selling batches of designer ponchos. Given the revenue function R(n) = 20n and the expense function E(n) = 10 √{n}, the profit that Scarlett makes from producing and selling a batch of n ponchos can be calculated by subtracting the total expenses from the total revenue, which is P(n) = R(n) - E(n). To find Scarlett's profit for a specific number of ponchos, simply plug the value of n into both functions and perform the subtraction.
For example, if Scarlett wants to calculate the profit for selling 5 ponchos, the revenue would be R(5) = 20(5) = $100, and the expenses would be E(5) = 10√5. Scarlett's total profit for 5 ponchos would then be P(5) = $100 - 10√5.
1. What is the value of x? Show your work to justify your answer.
2. What is the value of the exterior angle? Show your work to justify your answer.
Answer:
see explanation
Step-by-step explanation:
the exterior angle of a triangle equals the sum of the 2 opposite interior angles, that is
2x + 4 = x + 60 ( subtract x from both sides )
x + 4 = 60 ( subtract 4 from both sides )
x = 56
exterior angle = 2x + 4 = (2 × 56) + 4 = 112 + 4 = 116°
Complex Roots #4 Problem
Find the missing value
8
14
45
15
Answer:
The correct option is B.
Step-by-step explanation:
From the given figure it is nices that the length of sides AB, BC and AC are 20, 22 and 35. The line AD is angle bisector.
Let the missing value be x.
The Triangle Angle Bisector Theorem states that the angle bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle.
Since AD is angle bisector, therefore
[tex]\frac{AB}{AC}=\frac{BD}{CD}[/tex]
[tex]\frac{20}{35}=\frac{22-x}{x}[/tex]
[tex]20x=35(22-x)[/tex]
[tex]20x=770-35x[/tex]
Add 35x both sides.
[tex]55x=770[/tex]
Divide both sides by 55.
[tex]x=\frac{770}{55}[/tex]
[tex]x=14[/tex]
Therefore, second option is correct.
A fruit punch recipe calls for 3/4 cup of pineapple juice and 1 1/2 cups of orange juice. I have 4 1/2 cups of pineapple juice and want to use all of it. How many cups of orange juice will I need?
Answer: If the recipe wants 3/4 cup of pineapple juice for every 6/4 cups of orange juice, 18/4 is 6x more than the recipe so 6/4 must be 6x larger too.
6 x 3/2 = 18/2 or 9 cups of orange juice. Hope this helps :) Please mark brainliest if you can ;)
2+2^2=???????????????????????????
Answer:
6
Step-by-step explanation:
First, you multiply 2 to the 2nd power, then add 2
Question
2+2^2
Answer:
6Step-by-step explanation:
2² = 2*2
----------------------
power first then sum
2 + 2² =
2 + 4 =
6
The coordinates of a point on a coordinate grid are (−2, 6). The point is reflected across the x-axis to obtain a new point. The coordinates of the reflected point are (4 points)
(2, 6)
(−2, 6)
(−2, −6)
(2, −6)
Answer:
its -2,-6 hope this helps ヾ(•ω•`)o o(*￣▽￣*)ブ
Step-by-step explanation:
In the diagram below, what needs to be labeled in order to prove triangle AHL and triangle EML are congruent by the SSS postulate
Answer:
Final answer is HL = LM.
Step-by-step explanation:
We have been given a diagram having two triangles in which sides AH= EM and AL=EL.
Now we need to find which statement is missing to prove that triangles AHL and EML are congruent using SSS.
SSS means (side - side - side)
Two pair of equal sides are already given so we have completed SS of SSS.
Last "S" means we need one more pair of equal sides so that must be using remaining sides HL and LM
Hence final answer is HL = LM.
In triangles AHL and EML, AH=EM, AL=EL. To prove congruence by SSS, it's concluded that D) HL=LM is required.
In the given problem, the conclusion is established by presenting a diagram containing two triangles, AHL and EML, with specified equal side lengths: AH = EM and AL = EL. The objective is to ascertain the missing statement required to demonstrate the congruence of these triangles through the Side-Side-Side (SSS) criterion.
The SSS criterion asserts that for two triangles to be congruent, the corresponding sides of the triangles must be equal in length. In this context, the sides AH and AL, as well as EM and EL, serve as two pairs of equal sides, satisfying the "SS" criteria of SSS. To complete the SSS congruence condition, it is necessary to establish the equality of the remaining sides, HL and LM.
Consequently, the final answer deduced from the step-by-step explanation is that HL equals LM. This signifies the fulfillment of the Side-Side-Side criterion, ensuring the congruence of triangles AHL and EML. The logical progression of the explanation elucidates the geometric relationships and justifies the conclusion that HL = LM is the missing statement essential for establishing the congruence of the two triangles.
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Based on the polynomial remainder theorem, what is the value of the function when x=-5
f(x)=x^4+9x^3+17x^2-8x+50
Answer: 15
Step-by-step explanation:
Using synthetic division:
-5 | 1 9 17 -8 50
| ↓ -5 -20 15 -35
1 4 -3 7 15 ← this is the remainder
Check:
f(x) = x⁴ + 9x³ + 17x² - 8x + 50
f(-5) = (-5)⁴ + 9(-5)³ + 17(-5)² - 8(-5) + 50
= 625 - 1125 + 425 + 40 + 50
= 15
Write an addition equation that will have a new thousand, a new hundred, and a new ten. Then solve. Explain how you chose your numbers.
Answer:
1987 + 1257 = 3247
Step-by-step explanation:
We are going to use a base number to start from. That number is 1,987 where the thousand is 1, the hundred is 9 and the ten is 8.
Then we are going to add 1,257 which will be 3,247. Thus we will have a new thousand which is 3 (formerly 1), a new hundred which is 2 (formerly 9), and finally, a new ten which is 5 (formerly 7).
1987 + 1257 = 3247 gives you a new thousand, a new hundred and a new ten.
Answer:
Step-by-step explanatcagion:
A car travels 54.9 miles in an hour.If the car continues at theach same speed for 12 hrs how many will it travel
Answer:
658.8 miles
Step-by-step explanation:
first divide 54.9 by 60. then multiply that by 12 times 60
The car will travel 658.8 miles if it continues at the same speed for 12 hours.
To find out how far the car will travel in 12 hours, we need to multiply the distance traveled in one hour by the number of hours the car will be traveling.
Given that the car travels 54.9 miles in one hour, we can represent this distance as [tex]\( \frac{549}{10} \)[/tex] miles per hour to avoid dealing with decimals. This fraction is equivalent to 54.9 miles.
Now, we multiply this distance by the time duration of 12 hours to find the total distance:
[tex]\[ \text{Total distance} = \text{Distance per hour} \times \text{Number of hours} \][/tex]
[tex]\[ \text{Total distance} = \frac{549}{10} \text{ miles/hr} \times 12 \text{ hr} \][/tex]
[tex]\[ \text{Total distance} = \frac{549 \times 12}{10} \text{ miles} \][/tex]
[tex]\[ \text{Total distance} = \frac{6588}{10} \text{ miles} \][/tex]
[tex]\[ \text{Total distance} = 658.8 \text{ miles} \][/tex]
Therefore, the car will travel 658.8 miles in 12 hours at the same speed.
Three ounces of cinnamon cost $2.40. If there are 16 ounces in 1 pound, how much does a cinnamon cost per pound?
Divide the cost for 3 ounces by 3, to find the cost per ounce:
2.40 / 3 = 0.80
It cost 80 cents per ounce.
Now multiply the cost per ounce by 16 ounces:
16 x 0.80 = 12.80
It will cost $12.80 for one pound.
Solve the system of equations by finding the reduced row-echelon form of the augmented matrix for the system of equations.
3x-4y-5z=-27
5x+2y-2z=11
5x-4y+4z=-7
A.(1,5,51)
B.(10,5,51)
C.(10,51,23)
D.(1,5,2)
Answer:
D. (1, 5, 2)
Step-by-step explanation:
It is convenient to let a graphing calculator do this. See the attachment.
Answer:
D.(1,5,2)
Step-by-step explanation:
Lets write the augmented matrix by writing the coefficients of all the variables
3 -4 -5 -27 Row 1
5 2 -2 11 Row 2
5 -4 4 -7 Row 3
WE need to get
1 0 0
0 1 0
0 0 1 then last column will be the value of x , y , z
To get identity matrix we use row operations
(R1=R1/3)
1 -4/3 -5/3 -9 Row 1
5 2 -2 11 Row 2
5 -4 4 -7 Row 3
Subtract row 1 multiplied by 5 from row 2 (R2=R2−(5)R1)
1 -4/3 -5/3 -9 Row 1
0 26/3 19/3 56 Row 2
5 -4 4 -7 Row 3
Subtract row 1 multiplied by 5 from row 3 (R3=R3−(5)R1)
1 -4/3 -5/3 -9 Row 1
0 26/3 19/3 56 Row 2
0 8/3 37/3 38 Row 3
Multiply row 2 by 326 (R2=(3/26)R2)
1 -4/3 -5/3 -9 Row 1
0 1 19/26 84/13 Row 2
0 8/3 37/3 38 Row 3
Add row 2 multiplied by 4/3 to row 1 (R1=R1+(4/3)R2)
1 0 -9/13 -5/13 Row 1
0 1 19/26 84/13 Row 2
0 8/3 37/3 38 Row 3
Subtract row 2 multiplied by 8/3 from row 3 (R3=R3−(8/3)R2)
1 0 -9/13 -5/13 Row 1
0 1 19/26 84/13 Row 2
0 0 135/13 270/13 Row 3
Multiply row 3 by 13/135 (R3=(13/135)R3)
1 0 -9/13 -5/13 Row 1
0 1 19/26 84/13 Row 2
0 0 1 2 Row 3
Add row 3 multiplied by 9/13 to row 1 (R1=R1+(9/13)R3)
1 0 0 1 Row 1
0 1 19/26 84/13 Row 2
0 0 1 2 Row 3
Subtract row 3 multiplied by 19/26 from row 2 (R2=R2−(19/26)R3)
1 0 0 1 Row 1
0 1 0 5 Row 2
0 0 1 2 Row 3
From the above matrix we can say that x=1 , y=5 and z= 2
Write an explicit formula for the sequence 2,-3,-8,-13,-18 then fin the 13th term
The given sequence is an arithmetic sequence with a common difference of -5. The explicit formula for the sequence is A_n = 2 + (n-1)*-5. Using this formula, the 13th term of the sequence is -58.
Explanation:The given sequence is 2, -3, -8, -13, -18. We find that the common difference of the sequence is -5 because each term subtracts 5 from the previous term. This is an arithmetic sequence. The explicit formula for an arithmetic sequence is given by A_n = A_1 + (n-1)*d where A_n is the nth term, A_1 is the first term, d is the common difference and n is the position in the sequence. So in this case, our formula becomes A_n = 2 + (n-1)*-5.
Now let's find the 13th term in the sequence. Substituting n=13 into the formula we get: A_13 = 2 + (13-1)*-5 = 2 - 60 = -58. Therefore, the 13th term of the sequence is -58.
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A public pool opened for summer. A total of 246 people came swimming over the first 3 days it was open on the first day79came to swim on the second day 104 people swam how many people swam on the third day
63 People came on the third day
Hi there!
So there was a public pool opened for summer and a total of 246 people came swimming over the first 3 days. On the first day 79 came to swim and on the second day 104 came to swim. To find how much people swam on the third day, we need to add 104 + 79 and subtract the answer with 246.
104 + 79 = 183
246 - 183 = 63
63 people came to swim on the third day.
Hope this helped!~
Find the equation of a line parallel to y = 3x - 6, passing through the point (-6, -7). options:
y = 3x + 11
y = 3x - 11
y = 3x - 7
y = -1/3x - 9
Parallel lines have the same a slope. Therefore if
k: y = 3x - 6 → slope = 3
and l: y = mx + b
l || k ⇔ m = 3
l: y = 3x + b
We have the point (-6, -7). Put the coordinates to the equation:
-7 = 3(-6) + b
-7 = -18 + b add 18 to both sides
11 = b → b = 11
Answer: y = 3x + 11Kwanzaa is an African American holiday celebrated December 26th through January 1st. The colors of Kwanzaa are red,green,and black, and the holiday has seven symbolic elements. Two of these elements are the mishumaa saba (the seven candles) and the kinara (the candle holder). Traditionally, the mishumaa saba are arranged in the kinara as shown, three identical red candles on the left, three identical green candles on the right and a black candle in the center. If, however, the candles could be arranged in any order, in how many different ways could the seven candles be arranged in the kinara?
Answer:
Step-by-step explanation:
Another very interesting problem
If the candles were all of a different color, then the first candle (randomly chosen) would be 7. The second candle would be any one of 6. Third would be any one of the remaining 5, then 4 then 3 then 2 then 1
The abbreviated way of writing that is 7! which means that the number of different ways would be
7*6*5*4 *3*2*1
However this problem is not that simple The complexity comes from the fact that there are colors that are duplicated.
That event is handled by dividing 7! /by 3! and another 3!
The result is 140
3! = 3*2*1 = 6
So you would take 7! and divide by 6*6
5040/36 = 140
This problem is much more difficult than any of the others.
There are 9 different ways the seven candles can be arranged in the kinara.
Explanation:The given problem is asking for the number of different ways that the seven candles can be arranged in the kinara for the celebration of Kwanzaa. Since there are seven candles, we can solve this problem by finding the number of permutations of seven objects. The formula for permutations is nPr = n! / (n - r)!, where n is the total number of objects and r is the number of objects we are arranging.
First, we calculate the number of ways to arrange the red candles. Since there are three identical red candles, this can be represented as 3P3 = 3! / (3 - 3)! = 3! / 0! = 3! / 1 = 3.Next, we calculate the number of ways to arrange the green candles. Similar to the red candles, this can be represented as 3P3 = 3! / (3 - 3)! = 3! / 0! = 3! / 1 = 3.Finally, we calculate the number of ways to arrange the black candle. Since there is only one black candle, there is only 1P1 = 1! / (1 - 1)! = 1! / 0! = 1! / 1 = 1.To find the total number of arrangements, we multiply the number of ways to arrange each set of candles together. Therefore, the total number of different ways the seven candles can be arranged in the kinara is 3 * 3 * 1 = 9.
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HELP PLEASE!!!
1. There are two bags of marbles. Bag A contains 9 red marbles and 3 green marbles. Bag B contains 9 black marbles and 6 orange marbles. Find the probability of selecting one Green marble from Bag A and one black marble from Bag B. These events are:
a. independent
b. dependent
c. neither
d. can not be determined
2. You are asked to find the probability of selecting two cards from a standard deck of cards. What is the probability that you select an Ace then a King? These events are:
a. can not be determined
b. independent
c. dependent
d. neither
Problem 1
Answer: Independent
The reason why is because each bag is separate from one another, so one event doesn't affect the other. If we know the result of what we pulled out of one bag, it doesn't change the probability of the other event.
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Problem 2
Answer: Dependent
Assuming you do not put the first card back, then the probability of picking a King on the second draw will be different than if you picked a King on the first draw. With all 52 cards in the deck, the probability of getting a king is 4/52 = 1/13. It changes to 4/51 after we picked out an ace for the first card (and didn't put that first card back).
The cost of stainless steel tubing varies jointly as the length and the diameter of the tubing. If a 5 foot length with diameter 2 inches costs $48.00 , how much will a 19 foot length with 3 inches diameter cost?
Answer:
$273.60
Step-by-step explanation:
The cost of stainless steel tubing varies jointly as the length and the diameter of the tubing.
i.e [tex]C\propto L\cdot D[/tex]
i.e [tex]C=k\cdot L\cdot D[/tex]
A 5 foot or 60 inches length with diameter 2 inches costs $48.00, so
[tex]\Rightarrow 48=k\times 60\times 2[/tex]
[tex]\Rightarrow k=\dfrac{48}{60\times 2}=0.4[/tex]
Now the equation becomes,
[tex]C=0.4\cdot L\cdot D[/tex]
So the cost of a 19 foot or 228 inches length with 3 inches diameter is,
[tex]C=0.4\times 228\times 3=\$273.60[/tex]
Which inequality corresponds with the graph?
A) x > -2
B) x < -2
C) x ≤ -2
D) x ≥ -2
Answer:
D
Step-by-step explanation:
An inequality is an expression which means more than one number is a solution. We graph the solutions on a number line to show all possible values. We graph using circles and arrows.
Equal to and less/greater than are graphed with filled in circles on the value.Only less/greater than (not equal to) are graphed with open (not filled in) circles on the value.We draw an arrow the direction the solutions satisfy the inequality. Generally this is the direction the inequality itself points.This is a filled in circle on -2 so this is [tex]\leq or \geq[/tex]. This means only answers C and D are options.
Answer D points to the right.
Peter has two coupons from Gussini's Department Store, one for $10 off and another for 10% off. Peter wants to purchase a shirt for $64. His friend Casey told him to use the 10% of coupon because it is the best deal and his friend Josue told him to use the $10 off coupon because it is the best deal. Which friend is correct?
Answer:
Josue is Write
Step-by-step explanation:
64 x .10 = 6.4 in savings while $10 off is better