Probability that he will choose debbie and esther as the two representatives is 1/20 .
What is the meaning of Probability ?Probability is the stream in mathematics in which likeliness of an event to happen is studied.
The range of probability lies between 0 to 1 , where 0 indicates uncertainty and 1 indicates certainty.
It is given that anna, becky, christina, debbie, and esther are the five candidates for student representative for the school board.
two students will be selected, and they will alternate attending the school board meetings.
all five students are equally well qualified, so the school superintendent decides to draw names at random.
probability he will choose debbie and esther as the two representatives = ?
Probability of chosing debbie is 1/5
Probability of choosing Esther is also 1/5
Either of them if chosen first the probability is 1/5
and the either of them chosen second the probability is 1/4
Probability that he will choose debbie and esther as the two representatives = (1/5)*(1/4) = 1/20 .
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Given that 2x³-5x² - 4x+8 = (Ax - 1)(x-B)(x + 1) + C for all values of x, find the
values of A, B and C.
Answer:
A=2, B=3, C=5
Step-by-step explanation:
Two polynomials are equal for all values of the variable if the corresponding coefficients are the same. The way to solve the problem is to multiply the RHS, rewrite it in a more orderly way
[tex](Ax-1)(x-B)(x+1)+C = \\Ax^3+(A-AB-1)x^2+(B-AB-1)x +B+C[/tex]
Now, for the two polynomials to be the same we need to have, at the same time
[tex]x^3: A=2\\x^2: A-AB-1= -5\\x:B-AB-1=-4\\1: B+C=8[/tex]
You might notice that we have more conditions than variables, but you can consider one of the two in the middle as a "check" option.
Now, grabbing the value from the first condition into the second we get B=3. Replacing both value in the third we see that the equality still holds, and replacing into the fourth we get C =5.
HELP PLS….Volume of cones
Find the volume of the cone.
Either enter an exact answer in terms of π or use 3.14 for and round your final answer to the nearest hundredth.
Answer:
20.93 units cubed
Step-by-step explanation:
[tex]V = \frac{3.14(2)^{2}(5) }{3} \\V = \frac{3.14(4)(5) }{3}\\V = \frac{62.8 }{3}\\V = 20.93[/tex]
What is 3.14 x 16
Can i have a step by step solution???
Answer:
3.14 × 16 is 18,84
Method in picture
[tex]{\color{aqua}{\boxed{\mathfrak{LordKeyarga23}}\:}}[/tex]
The value of the multiplication of the numbers 3.14 and 16 will be 50.24.
What is Algebra?Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.
The numbers are given below.
3.14 and 16
Then the multiplication of the numbers 3.14 and 16 will be given by putting a cross sign between them. Then we have
⇒ 3.14 x 16
⇒ 50.24
The value of the multiplication of the numbers 3.14 and 16 will be 50.24.
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Solve for the indicated operations.
1) 2/7 + 1/7 + 1/7
2) 4/8 - 3/10
3) 3.5 + 12.11 + 105.007
4) 1 275.25 − 97.75 431
5) 652.835 − 321.6571
Hello, the answer of each option is given below.
[tex]\frac{2}{7}+\frac{1}{7}+\frac{1}{7}=\frac{4}{7}[/tex][tex]\frac{4}{8}-\frac{3}{10}=\frac{(10.4)-(8.3)}{(8.10)}=\frac{16}{80}=\frac{16/16}{80/16}=\frac{1}{5}[/tex][tex]3.5+12.11+105.007=120.617[/tex]Missed equation that's why we can not solve effectively.[tex]652.835-321.6571=331.1779[/tex]Good luck! These are four-operation-equations. We should calculate by our hand or try to use calculator to get the result. Anyway, If you have any question(s), then feel free to ask in comments!
Help please
1.In ∆ABC, how many triangles are formed given: a=10 cm, b=18 cm, c=105°?
A. 1
B. 2
C. 3
D. None
2. In ∆ABC, if <A is obtuse and a<c, then how many triangle/s can be formed?
A. 1
B.2
C. 3
D. None
For questions 1 and 2 options, A and D are correct respectively.
What is the triangle?A triangle is a three-sided polygon. It is one of the most fundamental geometric forms.
1. In ∆ABC,
a=10 cm, b=18 cm, c=∠105°
For the given data only one triangle is formed. Option A is correct.
2. In ∆ABC, if <A is obtuse and a<c,
An obtuse angle is an angle more than the 90°.The given condition is wrong. None of the triangle is formed from the given options.
Hence for questions 1 and 2 options A and D are correct respectively.
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Sebastian swam laps every day in the community swimming pool. He swam an hour each day, 5 days each week, for 12 weeks. In
that time, he swam 1,800 laps. What was his average rate in laps per hour?
Answer:
0.25
Step-by-step explanation:
1,800 laps ÷ 12 weeks = 150 laps
150 laps ÷ 5 days each week = 30 laps per day
30 laps per day ÷ 120 hours per week = 0.25 per hour
Can someone give me the steps to solving this?
Answer:
[tex]\tan \theta = \dfrac{8}{15}[/tex]
Step by step explanation:
[tex]\text{Given that,}\\\\~~~~~~~\sin \theta = \dfrac{8}{17}\\\\\implies \sin^2 \theta = \dfrac{64}{289}\\\\\implies 1-\cos^2 \theta = \dfrac{64}{289}\\\\\implies \cos^2 \theta = 1-\dfrac{64}{289}\\\\\implies \cos^2 \theta = \dfrac{225}{289}\\\\\implies \cos \theta =\pm\sqrt{\dfrac{225}{289}}\\\\\implies \cos \theta = \pm\dfrac{15}{17}[/tex]
[tex]\text{In quadrant I, all ratios are positive, so,}~ \cos \theta = \dfrac{15}{17}\\\\\text{Now,}\\\\\tan \theta = \dfrac{\sin \theta }{\cos \theta}\\\\\\~~~~~~~~=\dfrac{\tfrac{8}{17}}{\tfrac{15}{17}}\\\\\\~~~~~~~~=\dfrac{8}{17} \times \dfrac{17}{15}\\\\\\~~~~~~~=\dfrac{8}{15}[/tex]
Please answer this question
[tex]\text{L.H.S}\\\\=\cot^2 \dfrac{\pi}6 -2\cos^2 \dfrac{\pi}{3}-\dfrac 34 \sec^2 \dfrac{\pi}4-4\sec^2 \dfrac{\pi}6\\\\\\=\cot^2 30^\circ -2 \cos^2 60^\circ- \dfrac 34 \sec^2 45^{\circ} -4 \sec^2 30^{\circ}~~~~~~~;[\pi= 180^{\circ}]\\\\\\=\left(\sqrt 3 \right)^2 -2 \left( \dfrac 12 \right)^2 -\dfrac 34 \left(\sqrt 2 \right)^2 -4 \left(\dfrac 2{\sqrt 3} \right)^2\\\\\\=3-2 \cdot \dfrac 14 - \dfrac 34 \cdot 2 -4 \cdot \dfrac 43\\ \\\\=3-\dfrac 12-\dfrac 32 - \dfrac{16}3\\\\\\[/tex]
[tex]\\=\dfrac{9-16} 3 - \dfrac 42 \\\\\\=\dfrac{-7}{3}-2\\\\\\=\dfrac{-7-6}3\\\\\\=-\dfrac{13}3\\\\\\=-4\dfrac 13 \\\\\\=\text{R.H.S}\\\\\\\text{Proved.}[/tex]
please help... Explain how you would find the volume of the octagonal prism.
Answer:
Formula for the volume id the octagonal prism .......
Step-by-step explanation:
To calculate the area of octagon ( base area) , multiply the perimeter of the octagon by its apothem and divide by 2 .Then, ti get the volume of the octagonal prism u need to multiply the result by the length of the.prism
Morgan wants to draw a right triangle two side lengths are 6 unites and 8 units. select all the possible dimensions of the third side
2 units 14 units
28units 10 units
√28 units
The possible dimension of the third side is 10 units.
What is the possible dimension of the third side?
A right triangle is a triangle that has three sides known as the opposite, adjacent and hypotenuse. The hypotenuse is the longest sides of the triangle. The opposite side is the side that faces an angle. The adjacent side is the third side.
If two side lengths are given, the third side can be determined using the Pythagoras theorem.
√a² + b ² = c
√6² + 8² = √36 + 64 = 10 units
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I'm struggling on finding a step-through for this question, can anyone help? (x+5)(2x+3)-3(x-2)(6x+5)
[tex]~~(x+5)(2x+3)-3(x-2)(6x+5)\\\\=2x^2 +3x + 10x +15 - (3x-6)(6x+5)\\\\=2x^2 +13x +15 - (18x^2 +15x -36x -30)\\\\=2x^2+13x+15-(18x^2 -21x-30)\\\\=2x^2 +13x+15-18x^2 +21x +30\\\\=-16x^2 + 34x+45[/tex]
The amount of parts, p, that a shop produced in d days is shown in the table below.
d
1 2 3 4 5
p(d) 66 132 240 326 455
Select the average rate of change for the number of parts that the company produced from day 1 to day 3.
87
91
66
146
Using it's concept, it is found that the average rate of change for the number of parts that the company produced from day 1 to day 3 is of 87.
What is the average rate of change?It is given by the change in the output divided by the change in input.
In this problem, in 2 days, from day 1 to day 3, the number of parts increased from 66 to 240, hence the rate of change is given by:
r = (240 - 66)/2 = 87.
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2x-16 in words phases
Answer:
16 less than two times a number "x"
Which ratio is equivalent to cos U?
SOMEONE PLEASE HELP ME ILL GIVE YOU BRAINLIST ANSWER
Answer:
(a) SW/VW
Step-by-step explanation:
In similar triangles ΔTUS and ΔVWS, corresponding angles are congruent. That means angle W will have the same measure and trig function values that angle U has.
The mnemonic SOH CAH TOA reminds you that the cosine ratio in this right triangle is ...
Cos = Adjacent/Hypotenuse
__
In ΔVWS, the side adjacent to angle W is side SW. The hypotenuse of the triangle is side VW. Then the cosine of interest is ...
cos(U) = cos(W) = SW/VW
Find 5-(-7).
5-(-7)=5+
Write as addition.
Answer: The answer is 5+28.
Step-by-step explanation:
First of all, you have to distribute the term in front of the parenthesis into the term(s) inside of it. In this case, “5-” is not a term because the “-” symbol is following it. However, we can distribute that particular symbol into the parenthesis. We then have 5+ 28 because - x - = +, and 5 x 7 - 5 = 28.
What is the ratio of no. lines of symmetry of an isosceles triangle to an equilateral
triangle
Which inequality is shown
Answer:
The choice A.
[tex]y > \frac{3}{2} x + 2[/tex]
Help please give a detailed answer!
Multiply.
31.2 x 10 x 3
Answer:
936
Step-by-step explanation:
You multiply 31.2 by 10, so you move the decimal one place to the right, so it's 312, And then, you multiply those numbers by 6 like 3, 1, and 2. For the ones digit 2 x 3 = 6, for the tens digit, 1 x 3 = 3, and for the hundreds digit, 3 x 3 = 9. Therefore, the answer is 936!
f(x) = 5 + 4x2, then f(3) =
Step-by-step explanation:
To answer this, we need to plug in 3 as x in the equation f(x) = 5 + 4x².
That would look like this: f(3) = 5 + 4(3)²
f(3) = 5 + 4(3)²
f(3) = 5 + 36
f(5)=41
Therefore, the answer is 41.
I hope this helps!! :)
please give me a good answer for 30 points
Answer:
[tex]measure \: [/tex]
ANSWER :3/50
Step-by-step explanation:
[tex] \sqrt{3 \: is \: a \: formula \: tht \: has \: equation} [/tex]
MEASURE:92-3 ) DEFIND THE "3"
ANSWER: 3/50
Solve 3-212.
OA. x≤-30
OB. xs-18
OC. x≥-30
OD. x2-18
The solution of the inequality 3-x/2≥12 is x≤-18
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
The given inequality is 3-x/2≥12
Three minus x by two greater than or equal to twelve
Subtract 3 from both sides
-x/2≥9
-x≥18
x≤-18
Hence, the solution of the inequality 3-x/2≥12 is x≤-18
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Divide 8,382 ÷ 7 please answer
Answer:
The answer is 1197.42
Step-by-step explanation:
Which set of values could be the side lengths of a 30-60-90 triangle?
OA. (6,6 2,12}
OB. (6,6√3, 12)
OC. (6, 12, 12√√3}
D. (6, 12, 12 √2)
The correct answer is option B which is the set of values that could be the side lengths of a 30-60-90 triangle are (6,6√3, 12).
What is the right-angled triangle?A triangle has three angles of 30-60 and 90 degrees in which the two sides are perpendicular to each other.
The three sides of the triangle will be calculated by applying the Pythagorean theorem:-
The sum of the square sides will be equal to the square of the third side.
For sides (6,6√3, 12)
12² = 6² + (6√3)²
144 = 36 + (36 x 3)
144 = 36 + 108
144 = 144
Therefore the correct answer is option B which is the set of values that could be the side lengths of a 30-60-90 triangle (6,6√3, 12).
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Your friend names a pair of supplementary angles. Is your friend correct? Explain.
Step-by-step explanation:
you must do it by step
Solution ,
here,
x+32=180 [Sum of straight angle]
x=180 - 32
x=148
ans
State the domain and range of the graph below
(01.01 LC)
Which of the following numbers is irrational?
√5.3√9
O
O √5
O
73
√9
An irrational number is the square root of 5 since it cannot be written as a ratio of two integers.
What are irrational numbers?Irrational numbers are number that cannot be written as a ratio of two integers.
Most irrational numbers are repeating decimals. From the given options, an irrational number is the square root of 5 since it cannot be written as a ratio of two integers.
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Lulu has 10 feet of ribbon. She uses 1 feet of ribbon for a project. She uses the
rest of the ribbon to make bows. She uses 8 inches of ribbon for each bow.
How many bows does Lulu make? Show your work.
10-1 = 9 feet left
9 x 12 = 108 inches
108 / 8 inches per bow = 13.5 bows
she can make 13 bows
A system of two linear inequalities is graphed as shown, where the solution region is shaded. Complete the sentences below by determining whether each point is, or is not. located in the solution region.
The point (-3.2)
The point (-7.5)
The point (2.-5)
The point (-14,6)
All the points The point (-3.2), The point (-7.5), Point (2.-5), and The point (-14,6) is located in the solution region.
What is a graph?A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
When we plot all the points on the graph we can see that all the points The point (-3.2), The point (-7.5), Point (2.-5), and The point (-14,6) are located in the solution region.
Therefore all the points The point (-3.2), The point (-7.5), Point (2.-5), and The point (-14,6) is located in the solution region.
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GEOMETRY Find the perimeter of the regular polygon. A regular polygon with three sides. The two sides are labeled 5 minus 2 x, and negative 4 x plus 9. The perimeter of the polygon is____units.
Answer:
19 units
Step-by-step explanation:
A regular polygon has equal-length sides. This fact can be used to solve for the value of x, and for the side length. Knowing the side length, we can find the perimeter.
__
side length5 -2x = 4x +9 . . . . . marked sides are the same length
-4 = 6x . . . . . add 2x -9
-2/3 = x . . . . . divide by 6
5 -2(-2/3) = 5 +4/3 = 6 1/3 . . . . length of one side
perimeterThe perimeter is the sum of the side lengths, or 3 times the length of one side.
P = 3s = 3(6 1/3)
P = 19 . . . . units
The perimeter of the polygon is 19 units.