Answer:
a) 0.0031 = 0.31% probability of marking exactly 3 incorrect answers.
b) 0.0035 = 0.35% probability of passing.
Step-by-step explanation:
For each question, there are only two possible outcomes. Either the student chooses the correct answer, or he does not. Questions are independent of each other. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
10 multiple choice questions
This means that [tex]n = 10[/tex]
4 answers that are equally likely to be the correct one. The quiz taker selects the answers randomly.
This means that [tex]p = \frac{1}{4} = 0.25[/tex]
a) Probability of marking exactly 3 incorrect answers.
3 incorrectly = 7 correctly, so this is P(X = 7).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 7) = C_{10,7}.(0.25)^{7}.(0.75)^{3} = 0.0031[/tex]
0.0031 = 0.31% probability of marking exactly 3 incorrect answers.
b) Probability of passing
At least 7 correct, so
[tex]P(X \geq 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 7) = C_{10,7}.(0.25)^{7}.(0.75)^{3} = 0.0031[/tex]
[tex]P(X = 8) = C_{10,8}.(0.25)^{8}.(0.75)^{2} = 0.0004[/tex]
[tex]P(X = 9) = C_{10,9}.(0.25)^{9}.(0.75)^{1} \approx 0[/tex]
[tex]P(X = 10) = C_{10,10}.(0.25)^{10}.(0.75)^{0} \approx 0[/tex]
[tex]P(X \geq 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.0031 + 0.0004 + 0 + 0 = 0.0035[/tex]
0.0035 = 0.35% probability of passing.
If the Mustangs, the Braves, the Bulldogs, the Huskies, and the Vikings are playing in the same sports league,
in how many different orders can they finish their season?
Answer:
.
Step-by-step explanation:
-7z-2=12.
can u please show the work also
Answer:
z = -2
Step-by-step explanation:
-7z -2 = 12
-7z = 14 (add 2 on both sides)
z = -2 (divide -7 on boths sides)
z = -2
-7z = 12 + 2
-7z = 14
z = -14/7
z = -2
PLEASE HELP ITS URGENT
12. Carla is lying on the ground between two trees in her backyard. She is 67 feet from the tree to her left. The angle of elevation from her eyes to the top of the tree on the left is 50°. Carla is 75 feet from the tree to her right and the angle of elevation from her eyes to the top of that tree is 36°. a. Determine the height of each tree to the nearest foot. Show your work. b. State which tree is taller, and by how much.
Answer:
the left tree is taller
Step-by-step explanation:
shown in work above :)
The first tree is taller than the second tree by 25.3 ft.
We have to use the trigonometric ratios and angle of elevation to obtain the height of each tree as follows;
Let the height of the first tree be h1 and the height of the second tree be h2.
For the first tree;
tan 50° = h1/67
h1 = 67 tan 50° = 79.8 ft
For the second tree;
tan 36° = h2/75
h2 = 75tan 36°
h2 = 54.5 ft
The first tree is taller than the second tree by 25.3 ft.
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Which statement about the angles in the figure is true?
Helppp
9514 1404 393
Answer:
m∠1 +m∠8 = 90°
Step-by-step explanation:
There is no necessary sum relation between angles 3 and 5 or angles 7 and 10. The only thing you can say about those angle pairs is ...
∠3 + 90° = ∠5
∠10 +90° = ∠7
Angles 8 and 9 are congruent, so don't have any necessary sum.
Angle 1 is congruent with angle 3, which is complementary to angle 8, so we must have ...
m∠1 +m∠8 = 90°
If f(x) = (2x − 2)(x + 1)(x – 3) the lead term used to identify end behavior would be
A: 3
B: 2x
C: 4x
D: 2x^3
Construct a triangle with side lengths 6,6 and 6. what are the angle measures of a triangle
Answer:
60 degrees
Step-by-step explanation:
Hello! The side lengths of this triangle are all the same, so this is an equilateral triangle. These types of triangles have equal angles. A triangle equals 180 degrees so divide that by three. Each angle in this triangle is 60 degrees. Hope this helps :)
3. Which number is a natural number?
A-2.5
B 5-151
C-13+51
D|-81-2
Answer:
C
Step-by-step explanation:
A natural number is a number that you would use to count kids in a class for example. Like, 1,2,3,4 and so on. 2.5 is not a natural number since there cant be 2.5 of a student. 5-151 is a negative number and there cant be negative students. -13+51=38. 38 is a natural number. Now, in D it looks like there mightve been a absolute value sign but im not sure. If D has absolute value signs then D works too. Hope I could help.
I don't understand please help
Answer:
Step-by-step explanation:
the average rate of change is the same as
the slope of a line m = (y2-y1)/(x2-x1)
to find if is positive of negative look at the line between the years given (for example between 1930 and 1940)
if from left to right the line goes downward the rate of change is negative
if from left to right the line goes upward the rate of change is positive
Plzzz help mee
Which statement is best represented by the inequality p > 48?
A.The basketball team scored less than 48 points.
B.The basketball team scored 48 fewer points than last year's team.
C.The basketball team scored greater than 48 points.
D.The basketball team scored exactly 48 points.
Answer:
C
Step-by-step explanation:
the basketball team scored greater than 48 points.
f(x) = x^2 -2x -3 /x-3 identify the discontinuity
Answer:
Step-by-step explanation:
Again, parentheses would help with clarity. f(x) = (x^2-2x-3)/(x-3)
The denominator is x-3. Division by 0 is undefined, so x ≠ 3.
Challenge in a company, 95% of the workers are men. If 270people work for the company who
aren't men, how many workers are there in all? Use pencil and paper. Show two different ways that
you can solve this problem.
There are workers in all. (Type a whole num
Answer:
5,400
Step-by-step explanation:
5% = 270
270 ÷ 5 = 54
54 × 100 = 5400
Determine if the sequence is arithmetic or geometric.
3, 6, 9, 12, ....... when x = 0, 1, 2, 3, .....
Arithmetic
OR
Geometric
Answer:
arithmetic
Step-by-step explanation:
Equation in point slope form (5,-12);m=-2/3
Answer:
y + 12 = -2/3(x - 5)
Evaluate 2^x for (a) x = - 2 and (b) x = 3 3. Write your answers in simplest form
Answer:
a) 1/4
b) 8
Step-by-step explanation:
a) a negative exponent becomes positive if you take the reciprocal fraction
1 /2² = 1/4 when x = -2
b) x = 3
2³ = 2 x 2 x 2 = 8
The value of the expression as; a) 1/4 and b) 8
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
We are given that [tex]2^x[/tex] for (a) x = - 2 and (b) x = 3
a) Since negative exponent becomes positive if we take the reciprocal fraction
1 /2² = 1/4
when x = -2
b) x = 3
2³ = 2 x 2 x 2 = 8
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How would you graph
y = 2x - 1? , ILL MARK BRAINLIST
Answer:
Starts at negative 1 Y-axis, and then go yp 2 and 1 to the right
Is figure ABCD a translation of Figure ABCD
A. Yes it is translated 2 units left and 2 units up
B. Yes it is translated 1 unit left and 3 units up
C. Yes it is translated 3 units left and 1 unit up
D. No the two figures are oriented diferently
The sum of three decimal numbers is 6. Exactly one of the numbers is less than 1. What could the numbers be? Show your work.
Answer:
4, 1.6, .4
add them together
you get 6
what is 1 + 3s > 7 sadhfashdfajdfadfa
Answer:
4??????????????
Step-by-step explanation:
&÷&$^#£#*$,$
Compare and contrast the AA similarity criterion with the ASA congruence criterion. Choose the correct answer.
A. Both criteria require that two pairs of angles be congruent, but for congruence you also need to know that the included sides are congruent, so that the figures are the same size. The AA similarity criterion shows only that the two triangles are the same shape.
B. Both criteria require that two pairs of angles be congruent, but for congruence you also need to know that the non-included sides are congruent, so that the figures are the same size. The AA similarity criterion shows only that the two triangles are the same shape.
C. Both criteria require that two pairs of angles be congruent, but for congruence you also need to know that the included sides are congruent, so that the figures are the same size. The AA similarity criterion shows only that the two triangles are the same size.
D. Both criteria require that two pairs of sides be congruent, but for congruence you also need to know that the included angles are congruent, so that the figures are the same size. The AA similarity criterion shows only that the two triangles are the same shape.
Answer:
A
Step-by-step explanation:
Both criteria require that two pairs of angles be congruent, but for congruence, you also need to know that the included sides are congruent, so that the figures are the same size. The AA similarity criterion shows only that the two triangles are the same shape. Thus option A is correct.
What is AA similarity criterion?According to the Angle-Angle (AA) criterion, two triangle being considered comparable if "two angles from one triangle are equally equivalent to two angles of some other triangle."
According to the ASA congruence rule, two triangles are compatible when their two covered sides and two contained angles are equivalent to each other. However, thus according to AAS, if two triangles have two angles as well as one side that are identical to one another, then perhaps the triangles are congruent.
Because ASA and AAS are identical since it follows that if two images in one triangle are equal with two angles in another, therefore the third angles must likewise be identical. Therefore, option A is the correct option.
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The function f(x) = 400 * (1.2) ^ x models a population of mice after x years. What will the population be in 7 years ?
Answer:
Step-by-step explanation:
400×1.2⁷ ≅ 1433 mice
jack donates $X per month to charity. Ta the end if 10 months, he had 1250 donated in total. How much did he donate each month
Answer:
He donated $125 per month.
Step-by-step explanation:
$1250 divided by 10 months to figure out how much he payed each month.
In a sports meet, Sonam’s team completes the run at 40 seconds during heat events. On championship day, his team completes the same run at 45 seconds. What is the percentage difference in the completion time from the best completion time?
A. 10.5%
B. 12.5 %
C. 15.5 %
D. 20.5 %
Answer:
20.5
Step-by-step explanation:
The point M is the midpoint of LN where M(-12, 6) and N (-2,-5).
What are the coordinates of point L?
Answer:
(-22,17)
Step-by-step explanation:
Finding X co-ord for L:
M=x2-x1/2
-12=x2-2/2
-24=x2-2
-22=x2
Finding Y co-ord for L:
M=y2-y1/2
6=y2-5/2
12=y2-5
17=y2
Simplify.
−6x+86−32x−12+52x
Enter your answer in the box.
Do not use decimals in your answer.
Answer: 14x+74
Step-by-step explanation:
-6x+86-32x-12+52x=14x+74
-6x+86-32x-12+52x
=-6x-32x+52x+86-12
=14x+86-12
=14x+74
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The final expression after simplifying is 14x + 74.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example:
2 + 3x + 4y = 7 is an expression.
3x + 4 = 3 is an expression.
3 + 4x - 5 is an expression.
We have,
-6x + 86 - 32x - 12 + 52x
Add like terms.
-6x - 32x + 52x = 14x
Now,
14x + 86 - 12
14x + 74
Thus,
The final expression after simplifying is 14x + 74.
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Shaun's earnings at $12 per hour were less than $150. Write an inequality
Answer:
I think that the answer is 12x<150
Answer:
12x<150
Step-by-step explanation:
2.945 to the nearest hundredth
Answer:
2.95
Step-by-step explanation:
2.945 would round up to 2.95 because when a number is followed by 5 it rounds up.
this is confusing, i need help
Answer:
Step-by-step explanation:
2. SV ║TU
3. SV ≅TU
7. corresponding sides of congruent Δ are congruent
8. quadrilaterals that have one set of opposite sides ║ and ≅ are parallelograms
At Pizza Pi, 32% of the pizzas made last week had extra cheese. If 16 pizzas had extra cheese, how many pizzas in all were made last week?
Answer:
50
Step-by-step explanation:
you need to put first the 32 on top of 100 since it always goes over 100 then you put 16 over a blank and you divide 32 by 16 which equals 2 so since you divided at the top you need to divide at the bottom so you divide 100 by 2 and you get 50 so 50 is your answer
What is the y-intercept of the line given by the equation y = 8x + 75?
A. (0,75)
B. (0,-8)
C. (0, -75)
D. (0,8)
Answer:
The answer is A.
Step-by-step explanation:
In a linear equation, y = mx + b where b represent y-intercept.
y-intercept is the point where it touches y-axis, so the value of x is 0.
The y-intercept of the given equation is (0, 75). Therefore, option A is the correct answer.
What is a y-intercept?In Maths, an intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+c, where m is slope and c is the y-intercept.
The given equation of a line is y=8x+75.
To find the y-intercept, set x = 0 and solve for y.
Here, substitute x=0 in y=8x+75, we get
y=8(0)+75
y=75
So, the y-intercept is (0, 75)
Therefore, option A is the correct answer.
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Explain your answer !!
Have a great day
Will give brainlst
Answer:
Dang this looks hard
Step-by-step explanation:
Wish could help