Answer:
Approximately 0.0294.
Step-by-step explanation:
Assume that there's only one correct choice in each question.
The chance of getting a question correct by random guess is 1/4.The chance of getting a question wrong by random guess is 3/4.What's the probability that exactly 12 answers are correct?
12 out of the 28 answers need to be correct. [tex]\displaystyle \left(\frac{1}{4}\right)^{12}[/tex].The other 28 - 12 answers need to be incorrect. Multiply by [tex]\displaystyle \left(\frac{3}{4}\right)^{28 - 12}[/tex].There are more than one way of choosing 12 answers out of 28 without an order. Multiply by the combination "12-choose-28" [tex]\displaystyle \left(\begin{array}{c}12\\28\end{array}\right)[/tex].The probability of getting exactly 12 answers correct is:
[tex]\displaystyle \left(\frac{1}{4}\right)^{12} \times \left(\frac{3}{4}\right)^{28 - 12}\times \left(\begin{array}{c}28\\12\end{array}\right)\approx 0.0182[/tex].
With the same logic, the probability of getting [tex]x[/tex] ([tex]x\in \mathbb{Z}[/tex], [tex]12\le x\le 28[/tex]) correct out of the 28 random answers will be
[tex]\displaystyle \left(\frac{1}{4}\right)^{x} \times \left(\frac{3}{4}\right)^{28 - x}\times \left(\begin{array}{c}28\\x\end{array}\right)[/tex].
The probability of getting at least 12 correct out of 28 random answers is the sum of
the probability of getting exactly 12 correct out of 28, plusthe probability of getting exactly 13 correct out of 28, plusthe probability of getting exactly 14 correct out of 28, plusthe probability of getting exactly 15 correct out of 28, plusthe probability of getting exactly 16 correct out of 28, plus... all the way to the probability of getting exactly 28 correct out of 28.The Sigma notation might help:
[tex]\displaystyle \sum_{x = 12}^{28}{\left[\left(\frac{1}{4}\right)^{x} \times \left(\frac{3}{4}\right)^{28 - x}\times \left(\begin{array}{c}x\\28\end{array}\right)\right]}[/tex].
Evaluate this sum (preferably with a calculator)
[tex]\displaystyle \sum_{x = 12}^{28}{\left[\left(\frac{1}{4}\right)^{x} \times \left(\frac{3}{4}\right)^{28 - x}\times \left(\begin{array}{c}x\\28\end{array}\right)\right]} \approx 0.0294[/tex].
Which value of x makes the quotient of (5x^5+90x^2-135x)/(x+5) undefined?
Answer:
The value x=-5 makes the quotient undefined
Step-by-step explanation:
When we are looking for undefined values, we want values that make the denominator zero
x+5 =0
Subtract 5 from each side
x+5-5 =0-5
x=-5
The value x=-5 makes the quotient undefined
There are twelve shirts in your closet, five blue and seven green. Four of the blue shirts and one of the green shirts fit well. The others are too big. You randomly select a shirt to wear. It is blue or is too big. Find the probability of this occuring
Answer:
P (blue or too big) = 11 / 12Explanation:
A two way table permits to represent the situation clearly and find the answser is an easy way.
The two way table is that results from the given information is:
Initial information:
Blue Green Total
Fit well 4 1 ?
Too big ? ? ?
Total 5 7 12
Now by subtraction and addition you can fill the unknown fields:
Blue Green Total
Fit well 4 1 5
Too big 1 6 7
Total 5 7 12
Now, you can see that there are 5 blue and 7 too big shirts, but the total number of them is 5 + 7 - 1 (because one of the too big shirts is also blue).
Then, the number of shirts being blue or too big is 5 + 7 - 1 = 11.
And the probability is :
P(blue or too big) = number of blue or too big / total number of shirtsP (blue or too big) = 11 / 12 ← answerYou can also realize that there is only 1 green shirt that fits well, and that is the only option of not being blue of too big, so 1 /12 is the probability of not being blue or too big, and its complement (being blue or too big) is 1 - 1/12 = 11 / 12.
Write an equation of a line in point-slope form that is perpendicular to the line y=1/2x-7 and goes through the point (4,-3)
Answer:
y = - 2x + 5
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 )
y = [tex]\frac{1}{2}[/tex] x - 7 ← is in slope- intercept form
with slope m = [tex]\frac{1}{2}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{2} }[/tex] = - 2, hence
y = - 2x + c ← is the partial equation of the perpendicular line
To find c substitute (4, - 3) into the partial equation
- 3 = - 8 + c ⇒ c = - 3 + 8 = 5
y = - 2x + 5 ← equation of perpendicular line
What is the best definition of a triangle?
Answer:
A figure formed by 3 segments connecting 3 non-colinear points.
Answer:
Hi there!
The answer to this question is: C
A figure formed by three segments connecting three noncollinear points
Evaluate 12 sigma n=3 20(0.5)^n-1
9.99
19.95
29.98
39.96
Answer:
We have a geometric series in which:
a = 20
r = 1/2
Now, we know that: S2 = 20(1-r^2)/(1-r) and S12 = 20(1-r^12)/1-r
Therefore: sigma(3,12) = S12-S2 = 20[(1-r^12)/(1-r) - (1-r^2)/(1-r)] =5115/512 = 9.99023438
Therefore, the answer is: 9.99
Answer: Is D
Step-by-step explanation:
Of the following sets, which numbers in {1, 2, 3, 4, 5} make the inequality 3x + 1 > 4 true?
{1, 2}
{1, 2, 3}
{1, 2, 3, 4, 5}
{2, 3, 4, 5}
Answer:
{2, 3, 4, 5}
Step-by-step explanation:
3x + 1 > 4
3x > 3
x > 1.
If x = 1 the inequality is not true,
- but 2 3 4 and 5 will make the inequality true.
The numbers in 1, 2, 3, 4, 5} make the inequality 3x + 1 > 4 true is{2, 3, 4,5}
The answer is option D.
Which describes the solutions of the equation?The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.A system of equations is a collection of two or more equations with the same set of unknowns. In solving a system of equations, we try to find values for each of the unknowns that will satisfy every equation in the system.
⇒3x + 1 > 4
⇒ 3x > 3
⇒ x > 1.
If x = 1 the inequality is not true,
Therefore 2 3 4 and 5 will make the inequality true.
Learn more about inequality here:-https://brainly.com/question/24372553
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If f(x)=5x+40, what is f(x) when x=-5
Answer: 65
Step-by-step explanation:
F(x)=5x+40 and x=5
Enter 5 for x in the equation...
F(x)=5(5)+40
F(x)=25+40
F(x)=65
For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 15 N acts on a certain object, the acceleration of the object is 5 /ms2. If the acceleration of the object becomes 9 /ms2, what is the force?
Answer:
27 N
Step-by-step explanation:
Since force varies directly with acceleration, we can introduce a constant, k, and write [tex]F=ka[/tex]
When force is 15, acceleration is 5, so plug it into the equation and solve for k:
[tex]F=ka\\15=k(5)\\k=\frac{15}{5}\\k=3[/tex]
Now, to find force, we use a = 9 and k = 3, so
[tex]F=ka\\F=(3)(9)\\F=27[/tex]
The force is 27 N
the function f(x) = 3,005(1+0.03)^x represents the amount of money in a savings account where x represents time in years. what does 3,005 represent? a. the amount of money in the savings account after one year b. the amount of money added to the savings account each year c. the growth rate d. the initial amount of money placed in the savings account
Answer:
Option d. the initial amount of money placed in the savings account
Step-by-step explanation:
we have
[tex]f(x)=3,005(1+0.03)^{x}[/tex]
This is a exponential function of the form
[tex]f(x)=a(1+r)^{x}[/tex]
where
a is the initial value
r is the growth rate
(1+r) is the base
x is the number of years
f(x) is the amount of money in a savings account
In this problem we have
a=$3,005
r=0.03=3%
(1+r)=1.03
therefore
3,005 represent the initial value ( the amount of money for the value of x equal to zero)
Answer:
d. The initial amount of money placed in the savings account
Step-by-step explanation:
Given function that represents the amount of money after x years,
[tex]f(x)=3005(1+0.03)^x[/tex]
Which is an exponential growth function,
Since, in a growth function,
[tex]f(x)=ab^x[/tex]
a represents the initial value,
b is the growth rate per period,
x is the number of periods,
By comparing,
a = 3005,
Hence, 3005 must be represent the initial amount of money placed in the savings account,
Option 'd' is correct.
Can guys help me with question 4 and 5
Answer:
1. C.
2. $15.75
Step-by-step explanation:
To find the total cost of lures, multiply your cost of lures (4.25) against your total amount of lures (p).
[tex]4.25p[/tex]
To find the total cost of bobbers, multiply your cost of bobbers (1.50) against your total amount of bobbers (b).
[tex]1.5b[/tex]
To find the total cost of everything, add these two together and you'll have your equation.
[tex]4.25p+1.5b[/tex]
To find the cost given that Jake purchases 3 lures and 2 bobbers, simply plug in your numbers of lures and bobbers to the equation.
[tex]4.25(3)+1.5(2)\\12.75+3\\15.75[/tex]
Answer:
c. 4.25 *p + 1.50 b
15.75
Step-by-step explanation:
lures are 4.25 a pack and bobbers are 1.50
We want to buy p packers of lures and b bobbers
Take the cost per each item and multiply by the number of each item
Add them together to the total cost
4.25 *p + 1.50 b
This is the cost
Let p =3 and b=2
4.25 *3 + 1.50 (2)
12.75 +3
15.75
PLZ HELP WILL GIVE BRAINLIEST!!!
Type the correct answer in each BLANK. The line of best fit represents the number of miles Jean covered at different speeds during a trip. If the speed is represented by x and the distance covered is represented by y, the equation of the best line of fit is y =(BLANK) . She covered about (BLANK) miles at the speed of 50 miles per hour.
Answer:
y=2x
100 miles
Step-by-step explanation:
The slope is determined by change of y/ change of x
when using the points (0,0)-(50,100) is
100-0/50-0= 100/50=2
so the slope is 2.
Also there is no Y intercept on the equation bc it goes through the origin.
100 miles is the y point for 50 miles per hour
Answer:
The equation of the best line of fit is y = 2x
Step-by-step explanation:
The relationship between y and x is
y = mx + c
Where m = slope of the line
And c = intercept
At 50 miles per hour she has already covered a distance of 100 miles ---- from the graph
We can use this to calculate the slope of the line using the coordinates (0,0) (50,100)
Slope m is calculated as;
m = (y2 - y1)/(x2 - x1)
Where y2 = 100, x2 = 50
y1 = x1 = 0
Substitute these values
So m = (100 - 0)/(50 - 0)
m = 100/50
m = 2
Since there's no intercept, c = 0
The equation y = mx + c becomes
y = 2x + 0
y = 2x
The triangle below is classified as which of the following
This triangle has no sides which are the same, so this is classified as a scalene triangle.
After we have classified this triangle type, we look at the angles.
If you see the angles, all of the angles have no more than 90°. Acute is less than 90°, right is 90°, and obtuse if more than 90°.
All of the angles in this triangle is less than 90°. This means it's acute.
In conclusion, the triangle is scalene and it is acute, which means it is a scalene acute.
6. Find the sum of the arithmetic series.
∑_(n=1)^5▒〖(9-4n)〗
7. Find the first five terms of the sequence described.
a_1=3,a_(n+1)=a_n+5
Nicholas has a fish tank that is 12 inches high, 14.5 inches long, and 6.5 inches wide. If he fills the tank halfway with water, how many cubic inches of water are in the tank?
Answer:
565.5 in^3
Step-by-step explanation:
To find the full volume of the tank
V = l*w*h
We know 12 inches high, 14.5 inches long, and 6.5 inches wide.
Substituting in
V = 12 * 14.5*6.5
V =1131 in ^3
He is filling it 1/2 full, that would be 1/2 of the volume
1/2 V = 1131/2 = 565.5 in^3
Answer:
answer is 565.5 in^3
Step-by-step explanation:
The following set of coordinates most specifically represents which figure? (−5, 6), (−1, 8), (3, 6), (−1, 4) (6 points) Parallelogram Rectangle Rhombus Square
Answer:
Rhombus
Step-by-step explanation:
The given points are A(−5, 6), B(−1, 8), C(3, 6), D(−1, 4).
We use the distance formula to find the length of AB.
[tex]|AB|=\sqrt{(-1--5)^2+(8-6)^2}[/tex]
[tex]|AB|=\sqrt{16+4}[/tex]
[tex]|AB|=\sqrt{20}[/tex]
The length of AD is
[tex]|AD|=\sqrt{(-1--5)^2+(6-4)^2}[/tex]
[tex]|AD|=\sqrt{16+4}[/tex]
[tex]|AD|=\sqrt{20}[/tex]
The length of BC is:
[tex]|BC|=\sqrt{(-1-3)^2+(8-6)^2}[/tex]
[tex]|BC|=\sqrt{16+4}[/tex]
[tex]|BC|=\sqrt{20}[/tex]
The length of CD is
[tex]|CD|=\sqrt{(-1-3)^2+(6-4)^2}[/tex]
[tex]|CD|=\sqrt{16+4}[/tex]
[tex]|CD|=\sqrt{20}[/tex]
Since all sides are congruent the quadrilateral could be a rhombus or a square.
Slope of AB[tex]=\frac{8-6}{-1--5}=\frac{1}{2}[/tex]
Slope of BC [tex]=\frac{8-6}{-1-3}=-\frac{1}{2}[/tex]
Since the slopes of the adjacent sides are not negative reciprocals of each other, the quadrilateral cannot be a square. It is a rhombus
Answer:
answer is Rhombus
Step-by-step explanation:
(4x2 + 7x)(5x2 – 3x)
Multiply
Step-by-step explanation:
here is the answer for your question
Answer:
20x^4 + 23x^3 – 21x^2
Step-by-step explanation:
other answer was a bit hard to read, sorry
Which of the diagrams below represents the statement "If it is a square, then
it is a quadrilateral"?
A quadrilateral is a polygon with 4 number of sides and 4 vertices. The correct figure is figure B.
What is a quadrilateral?A quadrilateral is a polygon with 4 number of sides and 4 vertices. A few examples of a quadrilateral are square, rectangle, rhombus, parallelogram, etc.
For the above-given condition, "If it is a square, then it is a quadrilateral" figure B is correct because, as per the first diagram, not all the squares are quadrilateral, while as per the figure B every square is a quadrilateral.
Hence, the correct figure is figure B.
Learn more about Quadrilateral:
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Line m passes through the points (3.7) and (6, 12) while line n passes
through the points (-5, 1) and (-2, 6).
Which statement accurately describes the relationship between the two
lines?
Answer:
The line n is parallel to the line m.Step-by-step explanation:
Calculate slopes.
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Line m:
(3, 7), (6, 12)
[tex]m=\dfrac{12-7}{6-3}=\dfrac{5}{3}[/tex]
Line n:
(-5, 1), (-2, 6)
[tex]m=\dfrac{6-1}{-2-(-5)}=\dfrac{5}{3}[/tex]
The lines have the same slope. That is why they are parallel.
The normal pulse rate of a 13-year-old is between 70 and 100 beats per minute. As part of a health program, the medical staff at Grant Middle School measured the resting pulse rate of 12 randomly selected students in grades 7 and 8. The box plot shows the data for each group. Which statement correctly compares the data sets?
Answer:From the box plot, it can be seen that for grade 7 students,
The least value is 72 and the highest value is 91. The lower and the upper quartiles are 78 and 88 respectively while the median is 84.
Thus, interquatile range of the resting pulse rate of grade 7 students is upper quatile - lower quartle = 88 - 78 = 10
Similarly, from the box plot, it can be seen that for grade 8 students,
The least value is 76 and the highest value is 97. The lower and the upper quartiles are 85 and 94 respectively while the median is 89.
Thus, interquatile range of the resting pulse rate of grade 8 students is upper quatile - lower quartle = 94 - 85 = 9
The difference of the medians of the resting pulse rate of grade 7 students and grade 8 students is 89 - 84 = 5
Therefore, the difference of the medians is about half of the interquartile range of either data set.
Step-by-step explanation: i hope it helps it took a long time to write!
Answer:
I hope this helps
Step-by-step explanation:
what is the purpose of algebraic expressions?
Answer:
Algebraic expressions are useful because they represent the value of an expression for all of the values a variable can take on
100 PT QUESTION PLEASE HELP I WOULD REALLY APPRECIATE IT
Leo and Kamran go to high school together. There are a total of 1000 students in their grade. Out of the 6 periods they have, only 2 of their classes can be together. What is the percent probability that Leo and Kamran have a class together?
2/1000
0.002%
2/6
0.33%
0.002%×0.33%
The percentage of yall being in the same class is 0.00066%
I need help with 12.5•10•14 L•W•H
[tex]\huge{\boxed{\text{1750 units}^{3}}}[/tex]
Explanation:[tex]\begin{array}{cc}\text{First, multiply 12.5 by 10.}&125*14\\\text{Then, multiply 125 by 14.}&1750\end{array}[/tex]