A student is going to take a five-question, multiple-choice quiz. Each question has exact four choices for the answer, but only one of which is correct. The student forgets to study for the quiz and plans to randomly guess on each question. Let X be the number of correct answers he will obtains. Answer the following questions. Find the probability that he obtains at most one correct answer
Answer:
0.6328 = 63.28% probability that he obtains at most one correct answer
Step-by-step explanation:
For each question, there are only two possible outcomes. Either he obtains the correct answer, or he does not. The probability of obtaining the correct answer on a question is independent of any other questions, which means that the binomial probability distribution is used 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.
Five-question
This means that [tex]n = 5[/tex]
Each question has exact four choices for the answer, but only one of which is correct.
This means that [tex]p = \frac{1}{4} = 0.25[/tex]
Find the probability that he obtains at most one correct answer
This is:
[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{5,0}.(0.25)^{0}.(0.75)^{5} = 0.2373[/tex]
[tex]P(X = 1) = C_{5,1}.(0.25)^{1}.(0.75)^{4} = 0.3955[/tex]
[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.2373 + 0.3955 = 0.6328[/tex]
0.6328 = 63.28% probability that he obtains at most one correct answer
Select the correct answer.
What is this expression in simplified form?
5v2.9v6
OA. 45v3
OB. 90
O C. 90v3
OD. 45V2
Answer:
C. 90√3
Step-by-step explanation:
5√2 . 9√6 = 45√12 = 45×2√3
= 90√3
The simplified form is 90√3.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
Given expression is, 5√2×9√6
=5×9×√(2×6)
=45×√12
=45×2√3
=90√3
Hence, the simplified form is 90√3 .
To learn more on multiplication click:
https://brainly.com/question/5992872
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what are the adjectives in this sentence: the class cheered when Sonia had finished reading her funny poem.
Triangles A B C and A double-prime B double-prime C double-prime are shown. Triangle A double-prime B double-prime C double-prime is smaller and to the right of triangle A B C. Which transformations could have taken place to map △ABC to △A"B"C"? a reflection and a dilation a rotation and a dilation a translation and a dilation a reflection and a translation
C. a translation and a dilation
Step-by-step explanation:
the other person isn't wrong they just put it in the wrong order
Answer:c
Step-by-step explanation:took the test
How do you get total cost from price of $2.75 and qty demanded of 1250
Answer:
$3437.5
Step-by-step explanation:
Given data
Unit cost= $2.75
qty demanded= 1250
To get to the total, we have to multiply the quantity by the unity cost
=2.75*1250
=$3437.5
Hence the total cost is
$3437.5
What is the average rate of change for the function f(x) over the interval [0, 3]
Answer:
The average rate of change is 22
Step-by-step explanation:
Given
[tex]f(x) = x^4 - 5x[/tex]
Required
Average rate of change over [0,3]
This is calculated as:
[tex]Rate = \frac{f(b) - f(a)}{b - a}[/tex]
So, we have:
[tex]Rate = \frac{f(3) - f(0)}{3 - 0}[/tex]
[tex]Rate = \frac{f(3) - f(0)}{3}[/tex]
Calculate f(3) and f(0)
[tex]f(x) = x^4 - 5x[/tex]
[tex]f(3) = 3^4 - 5 * 3 =66[/tex]
[tex]f(0) = 0^4 - 5 * 0 = 0[/tex]
So, we have:
[tex]Rate = \frac{f(3) - f(0)}{3}[/tex]
[tex]Rate = \frac{66-0}{3}[/tex]
[tex]Rate = \frac{66}{3}[/tex]
[tex]Rate = 22[/tex]
Which of the following value are in the domain of the function graphed below?
Answer:
look at the domain, where the line is on the x-axis
Step-by-step explanation:
Eighty percent of one store’s customers paid with credit cards. Forty customers came in that day. How many customers paid for their purchases with credit cards?
Answer:
32
Step-by-step explanation:
40 = 100%
how many are 80% ?
well, 80% = 80× 1%
1% = 100% / 100
so, in our case
80% = 80×40/100 = 8×4 = 32
as a shortcut you consider a percentage x as a ratio factor of x/100 you multiply the 100% number with.
in our case
80% = 40 × 80/100 = 32
Helpppppppppppp pleaseeeeeeeeee
Answer:
it is b
Step-by-step explanation:
Answer:
B. [tex]x=24[/tex]
Step-by-step explanation:
We can start by isolating the square root by adding one to both sides:
[tex]-1+\sqrt{3x-8} =7\\\sqrt{3x-8}=8[/tex]
Now, we can square both sides and solve:
[tex]3x-8=64\\3x=72\\x=24[/tex]
a. Rewrite the equation 2x + y + 1 = 0 in slope-intercept form.
b. Give the slope and y-intercept.
c. Use the slope and y-intercept to graph the linear function.
If the coordinates of a point p(m-3, -6) = p(-7, -6), then find the value of m
Answer:
[tex]m =-4[/tex]
Step-by-step explanation:
Given
[tex]p(m-3 , -6) = p(-7 , -6)[/tex]
Required
Find m
[tex]p(m-3 , -6) = p(-7 , -6)[/tex]
By comparison:
[tex]m-3 = -7[/tex]
Add 3 to both sides
[tex]m = -7+3[/tex]
[tex]m =-4[/tex]
Plzzz help!!!!!!!!!!!!!!!!
Answer:
B) The function has a maximum value of (1)
Step-by-step explanation:
The given function has a maximum value, as its curve is inverted. The maximum value is the largest (y) value that a function can attain. As one can see, this value is (1), because the (y-coordinate) of the highest point on its curve is (1). This function has no minimum value, its endpoints go on infinitely in a negative direction.
Please help me
A. 7ft
B. 11ft
C. 15ft
D. 10ft
Answer:
A. 7ftStep-by-step explanation:
Have a good grades and study well sweetie
answered by: sugaxchimThe table below represents a linear function f(x) and the equation represents a function g(x):
x f(x)
−1 −9
0 −1
1 7
g(x)
g(x) = 3x − 2
Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x).
Part B: Which function has a greater y-intercept? Justify your answer.
Answer:
(a) The slope of f(x) is greater than the slope of g(x)
(b) f(x) has a greater y intercept
Step-by-step explanation:
Given
[tex]\begin{array}{cc}x & {f(x)} & -1&-9&0&-1&1&7 \ \end{array}[/tex]
[tex]g(x) = 3x - 2[/tex]
Solving (a): Compare the slopes
The slope (m) of f(x) is calculated as;
[tex]m = \frac{f(x_2) - f(x_1)}{x_2 - x_1}[/tex]
This gives:
[tex]m = \frac{f(0) - f(1)}{0 - 1}[/tex]
[tex]m = \frac{f(0) - f(1)}{- 1}[/tex]
Substitute values for f(0) and f(1)
[tex]m = \frac{-1 - 7}{- 1}[/tex]
[tex]m = \frac{-8}{- 1}[/tex]
[tex]m = 8[/tex]
The slope of g(x) can be gotten using the following comparison
[tex]g(x) = mx + b[/tex]
[tex]m \to slope[/tex]
So:
[tex]g(x) = 3x -2[/tex]
[tex]m = 3[/tex]
[tex]m_{f(x)} > m_{g(x)}[/tex]
Solving (b): Compare the y intercept
y intercept is when [tex]x = 0[/tex]
From the table of f(x)
[tex]f(0) = -1[/tex]
From the equation of g(x)
[tex]g(x) = 3x -2[/tex]
[tex]g(0) = 3*0-2[/tex]
[tex]g(0) =-2[/tex]
[tex]f(0) > g(0)[/tex]
A table represents the possibility of an association between eye color and hair color. Hair Color Eye Color Brown Black Green 22 15 Blue 18 19 In order to determine if there is a significant difference between eye color and hair color, the chi-square test for association and independence should be performed. What is the expected frequency of Blue Eyes and Black Hair?
Answer:
17
Step-by-step explanation:
_____________ Hair color
Eye color ___ Brown ___ Black ___ total
Green _____ 22 ________ 15 ____ 37
Blue _______ 18 ________ 19 ____ 37
Total _______40 ________34 ____ 74
Calculate the expected frequency of Blue Eyes and Black Hair?
The expected frequency Count ;
(row total * column total) / total number of observations
Expected frequency ;
Blue eye n black hair = (37 * 34) / 74
Expected frequency count = 1258 / 74 = 17
Expected count = 17
Answer:
The row total of blue eyes is 18 + 19 = 37.
The column total of black hair is 15 + 19 = 34.
The total of the whole table is 22 + 15 + 18 +19 = 74.
Step-by-step explanation:
E=(37)(34)/74=1258/74=17
If we know the values of the sine and cosine of x and y, we can find the value of cos(x - y) by using the ____ Formula for Cosine. State the formula: cos(x - y) = ____.
Answer:
[tex]\cos(x - y) = \cos(x)\cos(y) + \sin(x)\sin(y)[/tex]
Step-by-step explanation:
Given
[tex]\cos(x - y)[/tex]
Required
State the formula
From trigonometry identity, the formula of [tex]\cos(x - y)[/tex] is:
[tex]\cos(x - y) = \cos(x)\cos(y) + \sin(x)\sin(y)[/tex]
(Right angle Trigonometry) help me solve for X please!
Answer:
x = 52.0
Step-by-step explanation:
Reference angle = 68°
Length of side Opposite to reference angle = x
Adjacent length = 21
Apply the trigonometric function, TOA, which is given as:
Tan 68° = Opp/Adj
Substitute
Tan 68° = x/21
21 × Tan 68° = x
51.9768238 = x
x = 51.9768238 ≈ 52.0 (approximated to nearest tenth)
The cost of K-12 education per student was $2200 in 1978 and increased to $10,300 in 2008. (Source: Department of Education). (a) Find a linear equation that models these data. Let C represent the cost per student and x represent the number of years after 1978.
Answer: [tex]C=270x+2200[/tex]
Step-by-step explanation:
Given
Cost per student in the year 1978 is $2200
The cost increases to $10,300 in 2008
Suppose [tex]C=mx+a[/tex] is the linear equation defining the cost per student after x years
Substitute the value for 1978
[tex]\Rightarrow 2200=m(0)+c\\\Rightarrow c=2200[/tex]
After 30 years it becomes
[tex]\Rightarrow 10,300=m(30)+2200\\\Rightarrow 30m=8100\\\Rightarrow m=270[/tex]
Thus, the linear equation becomes
[tex]\Rightarrow C=270x+2200[/tex]
Cho S là ngoại diên của khái niệm con người, p(x,y) = x yêu thương y.
1) Viết các phán đoán sau đây dưới dạng công thức:
a) Nhiều người yêu thương A. (Thay A bằng chính tên của em).
b) A yêu thương nhiều người. (Thay A bằng chính tên của em).
2) Phủ định hai phán đoán ở phần 1) (viết dưới dạng câu văn hoàn chỉnh).
Answer:
Step-by-step explanation:
An assembly line consists of 21 tasks grouped into 5 workstations. The sum of the 21 task times is 85 minutes. The largest assigned cycle time is 20 minutes. What is the efficiency of this line
Answer:
The efficiency of this line is 0.85 = 85%.
Step-by-step explanation:
Efficiency:
The efficiency is given by the following formula:
[tex]E = \frac{T_t}{tn}[/tex]
In which [tex]T_t[/tex] is the total task time, [tex]t[/tex] is the largest assigned cycle time and n is the number of workstations.
5 workstations
This means that [tex]n = 5[/tex]
The sum of the 21 task times is 85 minutes.
This means that [tex]T_t = 85[/tex]
The largest assigned cycle time is 20 minutes.
This means that [tex]n = 20[/tex]
What is the efficiency of this line?
[tex]E = \frac{T_t}{tn} = \frac{85}{20*5} = \frac{85}{100} = 0.85[/tex]
The efficiency of this line is 0.85 = 85%.
Helppppo plsssssssssss I need helppp with thissss
Answer:
82 is what r equals
Step-by-step explanation:
So, lets go over what we know:
D equals rt, or r * t:
D=r*t
The table shows:
t=2 - d=164
t=3 - d=246
These are the only 2 values we need to look at.
We know that D= r*t, and we can just plug in the values found in the table for t and d to solve for r. So:
164= r * 2
Divide both sides by 2 to iscolate r:
82=r
So it seems like r is equal to 82, however this might be exponential or inaccurate, so lets double check witht the nexty values on the table:
246=r*3
Divide by 3 to iscolate the r:
82=r
So we know that r must equal 82.
Hope this helps!
Christen returned an overdue book to the library. Her fine was the same as the amount on the following day. Out of the fines shown below, which one would be closest to the number of days overdue?
Answer: 21 days overdue
Explanation: Since her fine was same as the amount on the following day. 21 will be closest to the number of day overdue so it is 21 days.
Answer:
22
Explanation:
They are saying that it has to be the closest number to the number of days overdue, cannot be neither 10 nor 14, and it cannot be 18 because that's one day from the days it's been overdue, and the question is saying: Her fine was the same as the amount on the following day. The graph shows us that it is about 1 more day than 18, so the only reasonable answer here is 22.
Also, I got it correct on edg =)
k+8
4) 3 =
3
Please help me
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{3 = \dfrac{k +8}{3}}[/tex]
[tex]\rightarrow\mathsf{\dfrac{k+8}{3}=3}[/tex]
[tex]\large\textsf{MULTIPLY by 3 to BOTH SIDES}[/tex]
[tex]\mathsf{3\times3=\dfrac{k+8}{3}\times3}[/tex]
[tex]\large\textsf{Work out the equation above to get to the next step}[/tex]
[tex]\large\textsf{We get: }\mathsf{k + 8 = 9}[/tex]
[tex]\large\textsf{SUBTRACT 8 to BOTH SIDES}[/tex]
[tex]\mathsf{k +8-8=9-8}[/tex]
[tex]\large\textsf{CANCEL out: 8 - 8 because that gives you 0}\\\\\\\\\large\textsf{KEEP: 9 - 8 because that gives you the value of k.}[/tex]
[tex]\mathsf{k = 9 -8}[/tex]
[tex]\mathsf{9-8=\boxed{k}}[/tex]
[tex]\mathsf{9-8=\boxed{\large\textsf{\bf 1}}}[/tex]
[tex]\boxed{\boxed{\large\textsf{Answer: \huge k = \bf 1}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
You have $45 to spend on notebooks and each one costs $5.
Write an inequality for the possible number of notebooks you
could buy, then find out the maximum number of notebooks
you could buy.
notebooks
Answer:
9notebooks
Step-by-step explanation:
5×y≤45( where y is number of notebooks)
$5=1notebook
$45=$45/$5x1
=9
therefore, you'll be able to buy nine notebooks with$45
Answer:
$5n = $45
n = 9
Step-by-step explanation:
Let n represent the amount of notebooks
$5n = $45
Divide each side by 5
$5n/5 = $45/5
n = 9
so the maximum number of notebooks you can buy is 9
Last question! Please show work. Really need to get this done in 1 hour
Answer:
x=1; y=2; z=3
Step-by-step explanation:
Rearrange for convince:
2y-4z+6x = -2
-4y+2z-3x=-5
-6y+3z+4x=1
Now we take to pairs and eliminate the same var.:
2y-4z+6x = -2 *2
-4y+2z-3x=-5
and
-4y+2z-3x=-5 *-3
-6y+3z+4x=1. *2
We get:
4y-8z+12y=-4
-4y+2z-3x=-5
= -6z+9x=-9
and
12y-6x+9x=15
-12y+6x+8x=2
= 17x=17
We now know x = 1, so z is:
-6z+9=-9
-6z=-18
z=3
Let’s grab the first formula and find y:
6+2y-12=-2
6+2y=10
2y=4
y = 2
Factor t^2 - 5t + 6. Type your answer in the space provided. Do not type spaces in your answer. Use only lowercase letters and include all necessary parentheses, variables and operation signs. For example, if the answer is (x +1)(x+2), type (x+1)(x+2).
Answer:
(x-3) * (x-2
Step-by-step explanation:
some 1 help me plz its algebra 1
Use roster notation to name the set of all letters in the word "more".
The set of all letters in the word "more" is { }
9514 1404 393
Answer:
{e, m, o, r}
Step-by-step explanation:
Perhaps most straightforward is the simple list in order of appearance.
{m, o, r, e}
Often, we prefer rostered sets to be in lexicographical order:
{e, m, o, r}
if 4 gallons of milk cost $11, how much would 7 gallons cost?
Answer:
$19.25
Step-by-step explanation:
11 ÷ 4 = $2.75 this is the cost per gallon of milk
2.75 * 7 = $19.25 this is the cost for 7 gallons of milk
Hope this helps
Answer:
$ 19.25
Step-by-step explanation:
Milk(gallons) Cost
4 11
7 x
[tex]\frac{4}{7} = \frac{11}{x}\\\\4 \times x = 11 \times 7\\\\4x = 77\\\\x = \frac{77}{4} = \$ 19.25[/tex]
You measure 37 dogs' weights, and find they have a mean weight of 69 ounces. Assume the population standard deviation is 9.2 ounces. Based on this, construct a 90% confidence interval for the true population mean dog weight.Give your answers as decimals, to two places_______ ± ________ ounces (Enter your answer as an integer or decimal number. Examples: 3, -4, 5.5172 ; Enter DNE for Does Not Exist, oo for Infinity)
Solution :
Given :
mean weight of the dogs, [tex]$\overline x$[/tex] = 69
Number of dogs, n = 37
Standard deviation, σ = 9.2
Confidence interval = 90%
At 90% confidence interval for the true population mean dog weight is given by :
[tex]$= \overline x \pm \frac{\sigma}{\sqrt n} \times z_{0.05}$[/tex]
[tex]$= 69\pm \frac{9.2}{\sqrt_{37}}} \times 1.64485$[/tex]
[tex]$=69 \pm 2.487799$[/tex]
= (66.5122, 71.4878)