The probability of answering all the question correctly is [tex]\boxed{\bf \dfrac{1}{256}}[/tex]
Further Explanation:
Given:
The total number of question is [tex]4[/tex].
Each question has [tex]4[/tex] options and one is correct.
Concept used:
Probability is defined as the ratio of number of favorable outcomes to number of total outcomes.
[tex]\boxed{\text{Probability}=\dfrac{\text{favorable outcomes}}{\text{total outcomes}}}[/tex]
Calculation:
The probability of getting the correct answer is calculated as follows:
[tex]\begin{aligned}P&=\dfrac{1}{4}\\&=0.25\end{aligned}[/tex]
The probability of getting the incorrect answer is calculated as follows:
[tex]\begin{aligned}P&=1-\dfrac{1}{4}\\&=1-0.25\\&=0.75\end{aligned}[/tex]
The formula for probability of answering all question correctly is as follows:
[tex]\boxed{P'=^nC_{r}P^{r}(1-P)^{n-r}}[/tex]
Here, [tex]n[/tex] is number of question and [tex]r[/tex] is number of correct answer, [tex]P'[/tex] is the probability of answering all question correctly.
Solve the above equation to obtain probability of answer all question correctly.
Substitute [tex]4[/tex] for [tex]n[/tex], [tex]0.25[/tex] for [tex]P[/tex] and [tex]4[/tex] for [tex]r[/tex] in above equation to obtain probability of answering all question correctly.
[tex]\begin{aligned}P'&=^4C_{4}(0.25)^{4}(1-0.25)^{4-4}\\&=\dfrac{4!}{(4-4)!\cdot 4!}\left(\dfrac{25}{100}\right)^{4}(0.75)^{0}\\&=\left(\dfrac{1}{4}\right)^{4}\\&=\dfrac{1}{256}\end{aligned}[/tex]
Therefore, the probability of the correct answer is [tex]0.25[/tex].
The probability of the incorrect answer is [tex]0.75[/tex].
The probability of answering all question correctly is [tex]\dfrac{1}{256}[/tex].
Thus, the probability of answering all question correctly is [tex]\boxed{\dfrac{1}{256}}[/tex].
Learn more:
1. Simplification: https://brainly.com/question/1602237
2. Quadratic equation: https://brainly.com/question/1332667
Answer details:
Grade: High school
Subject: Mathematics
Chapter: Probability
Keywords: Probability, Question, Richard, multiple choice, four answer, class, attend, guesses, correctly answer, favorable outcomes, total outcomes.
The probability that Richard will answer all four questions correctly is 0.004.
Explanation:The probability that Richard will answer all four questions correctly can be determined by multiplying the probability of getting one question correct by itself for each question. Since each question has four answer choices and only one is correct, the probability of guessing the correct answer for one question is 1/4.
Therefore, the probability of Richard answering all four questions correctly is (1/4) * (1/4) * (1/4) * (1/4) = 1/256. Rounded to three decimal places, this probability is approximately 0.004.
Thus, the probability that Richard will answer all questions correctly is 0.004.
?? Please help answer and solve, showing the steps you took
The following is a geometric sequence.
1, 2, 6, 24
TRUE
FALSE
given that (-2,7) is on the graph of f(x), find the corresponding point for the function f(x+4)
Answer:
CORRECT ANSWER ON PLATO: -6,7
Step-by-step explanation:
12.252525... is an example of a ___ decimal?
How do you write 12 hundreds
Two friends left school at the same time and drove in opposite directions. One friend averages 40 miles per hour and the other friend averages 35 miles per hour. when will they be 150 miles apart?
Answer:
The two friends will be 150 miles apart in 2 hours
Step-by-step explanation:
The two friends left the school at the same time and drove in opposite directions. One of them have a speed of 40 miles per hour while the other have a speed of 35 miles per hour .
The both of them are moving apart at the rate = 40 + 35 = 75 miles per hour
let
t = time at which they are 150 miles apart
speed = distance/time
time = distance/speed
time = 150/75
time = 2 hours
The two friends will be 150 miles apart in 2 hours
A building has an entry the shape of a parabolic arch 96 ft high and 18 ft wide at the base, as shown below. Find an equation for the parabola if the vertex is put at the origin of the coordinate system
The equation of the parabola if the vertex is put at the origin of the coordinate system is y =-32/27x^2
The height of the arch is given s:
height = 96 ft
The width of the base is given as:
width = 18 ft
A point on the building would be
(x,y) = (width/2, height)
So, we have:
(x,y) = (18/2, 96)
Simplify
(x,y) = (9, 96)
A parabola is represented as:
y = -a(x - h)^2 + k
The vertex of the parabola is at the origin.
So, we have:
y = -ax^2
Substitute (x,y) = (9, 96)
96 = -a * 9^2
This gives
96 = -81a
Divide both sides by 81
a= -96/81
So, the equation of the parabola is
y =-96/81x^2
Simplify
y =-32/27x^2
Read more about parabolas at:
https://brainly.com/question/24360143
A sequence has its first term equal to 8, and each term of the sequence is obtained by adding 6 to the previous term. If f(n) represents the nth term of the sequence, which of the following recursive functions best defines this sequence?
Answer:
f(1) = 8 and f(n) = f(n − 1) + 6; n > 1
Solve for h: a = 1/2bh
h = A over 2b
h = A/b (1 /2)
h = 2Ab
h = 2A/b
What is the perimeter of the nonagon below?
Answer:
Step-by-step explanation:
Alright, lets get started.
The sides of nonagon are given as below :
13
8
5
11
10
9
10
7
21
So, the perimeter will be addition of these sides.
Hence he perimeter is = [tex]13+8+5+11+10+9+10+7+21 = 94[/tex]
Hence the perimeter is 94 units (D) : Answer
Hope it will help :)
Two exterior angles of a triangle equal 100° and 150°. Find all the interior angles
The angles of the triangle will be 70°, 30°, and 80°.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
We know that the sum of the interior and the exterior angles is 180 degrees.
Two exterior angles of a triangle equal 100° and 150°.
The interior angle corresponding to the exterior angle of 100° will be
⇒ 180° - 100°
⇒ 80°
The interior angle corresponding to the exterior angle of 100° will be 80°.
The interior angle corresponding to the exterior angle of 150° will be
⇒ 180° - 150°
⇒ 30°
The interior angle corresponding to the exterior angle of 150° will be 30°.
Then the third angle of the triangle will be
⇒ 180° - 80° - 30°
⇒ 70°
The angles of the triangle will be 70°, 30°, and 80°.
More about the triangle link is given below.
https://brainly.com/question/25813512
#SPJ2
What is the area of triangle PQR?
Answer:
B. 2236square inches
Step-by-step explanation:
Formula for calculating the area of a triangle = 1/2 × base × height.
According to the triangle,
Base = QR = 86inches
Height = 52inches
Area of ∆PQR = 1/2 × 86 × 52
Area of ∆PQR = 43 × 52
Area of ∆PQR = 2236square inches
The value of a $225,000 house increases at a rate of 3.5% each year. Use a graph to predict the value of the house in 8 years.
A) ≈ $276,582
B) ≈ $286,263
C) ≈ $306,652
D) ≈ $296,282
Find the degree of the polynomial and indicate whether the polynomial is a monomial binomial trinomial or none of these 10x4-3w3+7w+5y5-4
The given polynomial 10x^4-3w^3+7w+5y^5-4 has a degree of 5 as the highest power of variable is 5. Also, it has five terms, hence it is neither a monomial, binomial nor trinomial.
Explanation:The polynomial in question is 10x4-3w3+7w+5y5-4. The degree of a polynomial is determined by the highest power of the variable in the polynomial. Here, the highest powers are 4 (from 10x4) and 5 (from 5y5). Since 5 is larger than 4, the degree of the polynomial is 5.
Furthermore, the given polynomial has five terms, so it is not a monomial, binomial or trinomial. These terms refer to polynomials with one, two, or three terms respectively. Therefore, the given polynomial does not fall under any of these categories.
Learn more about Degree of Polynomial here:https://brainly.com/question/29182596
#SPJ2
NEED HELP!!!!
Which of the following types of statement cannot be used to explain the steps of a proof? Check all that apply.
1.Postulate
2.Theorem
3.Conjecture
4.Guess
Choose more then 1
Answer:
Please don't use the answer that was given ,,, the correct answer is GUESS and Conjecture
Step-by-step explanation:
5. Given the following triangle side lengths, identify the triangle as acute, right or obtuse. Show your work. a. 3in, 4in, 5 in b. 5in, 6in, 7in c. 8in, 9in, 12in
The triangle with measures 3 in., 4 in. and 5 in. made up right angle triangle.
What is a triangle?A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.
a) Given that, 3 in., 4 in. and 5 in.
By using Pythagoras theorem, we get
5²=3²+4²
25=9+16
25=25
So, the triangle is right triangle.
b) The given sides of triangle measures 5 in., 6 in. and 7 in.
To determine whether the triangle is acute, right, or obtuse, add the squares of the two smaller sides, and compare the sum to the square of the largest side.
7²<5²+6²
49<25+36
49<61
So, the triangle is acute angle triangle.
c) The given sides of triangle measures 8 in., 9 in. and 12 in.
12²>8²+9²
144>64+81
144>125
So, the triangle is obtuse angle triangle.
Therefore, the triangle with measures 3 in., 4 in. and 5 in. made up right angle triangle.
Learn more about the triangle here:
brainly.com/question/2773823.
#SPJ7
someone answer and explain how to do this plz
area = the height times the base divided by 2
13*4=52
52/2 = 26
area = 26 sq. units
HELP ME!!!! PLEASE!!!! Ughhh
Suppose your walking rate is 4 feet per second. write that in miles per hour
Jorani flips two standard american quarters. how many ways can she get at least one head?
A barge that is used to transport bulk items is the shape of a rectangular prism and is 90 feet long, 35 feet wide, and 12 feet deep. If the barge can only be filled to a height of 75% of its depth, what volume of bulk items can the barge hold? ft3
Final answer:
The barge can hold 28,350 cubic feet of bulk items when filled to 75% of its depth, calculated by using the volume formula for a rectangular prism.
Explanation:
To calculate the volume of bulk items the barge can hold, we first determine the maximum height to which it can be filled. This is 75% of the barge's depth. Therefore, the fill height is 75% of 12 feet, which equals:
0.75 × 12 ft = 9 ft.
The volume V that the barge can hold is given by the formula for the volume of a rectangular prism:
V = length × width × height
Substituting the given dimensions and the fill height into the formula, we get:
V = 90 ft × 35 ft × 9 ft = 28,350 ft³.
So, the barge can hold 28,350 cubic feet of bulk items when filled to 75% of its depth.
Analyze the diagram below and complete the instructions that follow.
2004-04-02-05-00_files/i0370000.jpg
Find the area of triangle QRS. Round the answer to the nearest tenth.
A.
19.4 square units
B.
91.2 square units
C.
1,040.5 square units
D.
1,052.4 square unts
Choose the linear inequality that describes the graph. The gray area represents the shaded region
Answer:
y > -5x + 3
Step-by-step explanation:
one teaspoon equals 0.5 centimeters. how many liters equals 50 teaspoons? Round the answer to the nearest hundredth.
50 teaspoons would equal 50*0.5 = 25 centimeters
1 cm = 0.001 liter
25*0.001 = 0.025 liters
Algebraic expression for 5 times a number
Final answer:
The algebraic expression for 5 times a number is 5x.
Explanation:
The algebraic expression for 5 times a number is 5x.
The variable x represents the unknown number.
When you multiply 5 by any number, you can represent it as 5 times that number.
So, if the number is 10, the expression would be 5 times 10, which is equal to 50.
Read the following statement: x + 6 = 6 + x. This statement demonstrates:
the substitution property.
the reflexive property.
the symmetric property.
the transitive property.
Can someone help me please ? Thanks!
Find all the real zeros of the function.
Which number produces irrational number when added to 0.5
Answer with explanation:
The number in which we have to add a number to give irrational = 0.5
[tex]0.5=\frac{5}{10}\\\\=\frac{1}{2}[/tex]
is a Rational Number as the decimal expansion terminates or denominator contains the number in the form of [tex]2^n \text{or} 5^m \text{or} 2^n \times 5^m[/tex].
→Sum of two Rationals Can't be a Irrational Number.
→Sum of Rational And Irrational is Irrational.
So, if you add any Irrational number like √2,π,∛2 to , 0.5 , it will give an Irrational Number.
⇒0.5 +Irrational Number=Irrational Number
Find the surface area of a hemisphere with a diameter of 26 cm. Round your answer to the nearest tenth.