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
HW HELP ASAP PLZZZZZ
Hello,
3x³a + 3x²a²
⇒ common factor : 3x²a
3x³a + 3x²a²
= 3x²a * x + 3x²a * a
= 3x²a(x + a)
:-)
Step-by-step explanation:
hope this will help you more
I don't know how to do this
Answer:
Step-by-step explanation:
yeah
Can someone please help me?
Answer:
y=3^(x-2) + 1
Step-by-step explanation:
When dealing with graphs I always use a graphing calculator or Desmos to graph and double check my answers especially when doing translations!
Charlene is a video game designer and wants to make sure that her games can be played on all types of screens. In order for the games to work on both devices with a standard aspect ratio and those with widescreen aspect ratios, the playable area of the games should have an aspect ratio of 3:2. This means that the width is equal to times the height. On one type of tablet, the playable area of the game on the screen is 54 square inches. Write and solve a system of equations to determine the dimensions of the playable area. A. The playable area has a width of 13.5 inches and a height of 9 inches. B. The playable area has a width of 6 inches and a height of 9 inches. C. The playable area has a width of 6 inches and a height of 4 inches. D. The playable area has a width of 9 inches and a height of 6 inches.
Answer:
The playable area has a width of 9 inches and a height of 6 inches.
Step-by-step explanation:
There are a number of ways you can get there.
1. Check the answers to see which have the right area and aspect ratio.
A: area = 24 in² — does not match 54 in²
B: area = 54 in², aspect ratio 6:9 = 2:3 — does not match 3:2 aspect ratio
C: area = 54 in², aspect ratio 9:6 = 3:2 — matches problem statement
D: area = 121.5 in² — does not match 54 in²
2. If the screen were 3:2 (inches), its area would be 6 in². The area of 54 in² is 9 times that value, so the actual screen dimensions are √9 = 3 times 3:2. That is, they are width:height = 9:6 inches — matches selection C.
3. You can write equations for width and height and solve.
w/h = 3/2
wh = 54
Substituting w=3/2·h into the second equation gives
... (3/2)h·h = 54
... h² = 36 . . . . . multiply by 2/3
... h = √36 = 6 . . . . square root, result in inches
Answer:
D. The playable area has a width of 9 inches and a height of 6 inches.
Step-by-step explanation:
if the playable area is 54 and that such ratio of dimensions is 3:2
Then we are basically being asked to find the factor of ratios below that also multiply to get 54
54 = 9 x 6 and this is also a ratio of 3:2
As 3(3 + 2) = 54
and as width was asked first when ratio was given 3:2
The width therefore is 9 and the height is 6
So answer is D
PLZZZZZZZZZZZZZZZZZZZZ HELPPPPPPPPPP MEEEEEEEEEE
Mariam makes $50 a week.
a) Show this relationship in a graph below. Try make graph or jus label the numbers
b) What is the unit rate of the line in the equation?
c) What is the connection between the unit rate and the amount of money Mariam makes per week?
d) Write the equation for this relationship.
e) Is this a proportional relationship? Justify your answer.
Answer:
b
Step-by-step explanation:
Graph the image of rectangle after a translation 6 units right and 1 unit down.
Answer:
see image
Step-by-step explanation:
one by one, move each point
Write equation for the line with a slope "undefined" and has the same x-intercept as x−y−1=0
Answer:
Step-by-step explanation:
Lines with undefined slopes are perfectly vertical, of the form "x = ". A line with "the same x-intercept" as the given line that has an undefined slope will be the line that we want. I know that sounds confusing; we'll work through it then I'll explain it better. In order to find the x-intercep of the given line, solving it for y will make it a bit easier to "see". Therefore,
-y = -x + 1 and
y = x - 1. The x-intercept exists when y = 0, so setting y equal to 0 and solving for x:
0 = x - 1 and
1 = x. That's the x-intercept. It's also the line that we want that has an undefined slope, because "x = " lines are lines vertical lines and vertical lines have undefined slopes.
x = 1 is the line you want.
1a. If an escape room party
has 16 participants and 4
escape puzzles:
• How many staff are
needed?
• Write an expression to
solve how many staff
are needed.
Answer:
2 staff members
Step-by-step explanation:
Given
See attachment for missing details
Let
[tex]s \to staff\ member[/tex]
[tex]p \to participant[/tex]
[tex]e \to puzzle[/tex]
Required
Staff members for 18 participants
From the attachment, we have:
[tex]1s \to 8p[/tex] ---- 1 staff member to 8 participants
[tex]s \to 8p[/tex]
Multiply both sides by 1
[tex]s * 2 \to 8p * 2[/tex]
[tex]2s \to 16p[/tex]
This means that 2 staff members are required for 16 participants
Select the correct answer.
On the curve y= x^2+ 1 point Q has the coordinates (1.3.2.69). Estimate the slope of the curve at point Q by taking values very close to the x-
coordinate of Q.
OA 2.5
OB. 2.6
OC. 3.3
OD 5.2
Answer:
I think No B
if wrong correct me pls
have a great day
20. The H.M. between 2 and 8 is
(1 marks )
Answer as an improper fraction = 16/5
Answer as a mixed number = 3 & 1/5
Answer in decimal form = 3.2
All of those values represent the same thing, but written in a different way.
=============================================================
Explanation:
I'm assuming HM stands for Harmonic Mean in this case.
If so, then we apply the reciprocal operation to each value to get 1/2 and 1/8 (from 2 and 8 respectively).
Add up those fractions:
1/2 + 1/8 = 4/8 + 1/8 = 5/8
Now we'll divide n = 2 over that result. The n = 2 refers to the number of items in the original set.
n divide over (5/8) = 2*(8/5) = 16/5 which is the answer as an improper fraction
-----------
To convert to a mixed number, we can do the following:
16/5 = (15+1)/5
16/5 = 15/5 + 1/5
16/5 = 3 + 1/5
16/5 = 3 & 1/5
Or if you need the answer in decimal form, then using a calculator would get you 16/5 = 3.2
which equation represents the graphed function
A. y=4x-2
B. y=-4x-2
C. y=1/4x-2
D. -1/4x-2
A review of combination
Answer:
What is a Combination? A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter. In combinations, you can select the items in any order. Combinations can be confused with permutations.
#happylearning
At midday the temperature in Moscow was 7°C.
At midnight it was -3°C.
By how many degrees did the temperature fall?
Answer:
10 degrees C
Step-by-step explanation:
the difference between both temperatures is expressed by a subtraction
7 - -3 = 7 + 3 = 10
you could also do the subtraction the other way around :
-3 - 7 = -10
but the negative sign has no meaning for a distance between two points (a distance itself has no direction).
so, we are always using the absolute value of such difference calculations (when it is about lengths, distances, and so on, where the direction had no meaning).
and so, also the -10 is actually simply 10 for our problem here.
the temperature fell by 10 degrees.
Score on last try: 0 of 8 pts. See Details for more.
Get a similar question
You can retry this question below
Five cards are drawn randomly from a standard deck of 52 cards
Determine the probability that exactly 3 of these cards are Aces. Write your answer in decimal form, rounded to 5 decimal
places
Answer
Answer:
there are 4 aces in the deck of 52 cards
so the probability to draw one ace is 4/52
if we draw an ace, there are 3 left in 51 cards.
so the next probability will be 3/51
we need to multiply probabilities to know how likely it is that this happens in a row.
for three in a row that's
[tex] \frac{4}{52} \times \frac{3}{51} \times \frac{2}{50} [/tex]
rewritten its:
[tex] \frac{4 \times 3 \times 2}{52 \times 51 \times 50} [/tex]
we'll see soon why this is easier to write.
we also have to account for the two cards that are no aces. it doesn't matter if the first two cards are no aces, the last two, or any rodney. just the ammount of non-aces is important.
there are 48 non-aces in the deck.
so the probability to draw one of them in the first step is 48/52.
wich each draw the number of cards left in the deck decreases by 1. and depending what we draw, that ammount also decreases.
we draw 5 cards, so we know what the denominators will be. the numerator will be the rest-ammounts of each event, like shown in the complicated fraction above.
let's write it most easily as this:
[tex] \frac{4 \times 3 \times 2 \times 48 \times 47}{52 \times 51 \times 50 \times 49 \times 48} [/tex]
this scenario looks like it only describes 3 aces, then two non-aces, but the order of multiplication isn't important. you could put the 48 and 47 to the left, same solution. so this expression represents all permutations of "3 aces when drawing 5 cards", including the two cards that are not aces.
that's why writing it as one convoluted fraction is indeed better and simpler than many fraction multiplied in row.
time to grap a calculator.
our probability for the event is
54144 possible valid outcomes out of
311875200 possible combinations.
luckily the calculator can reduce that to a simpler form of
[tex] \frac{47}{270725} [/tex]
(reduced with 2^6*3^, big number, but tried it out by hand stacking up prime factors until hittinga prime in the numerator)
written as a readable kind of number you probably know and like it's
0.0001736079047
in decimal form. now rounded as asked for:
0.00017
(as percentage: 0.017%)
hope the way how we got here is somewhat clear. feel free to ask any questions.
kind regards
Alex
Find angle X in the angle diagram.
Answer:
80*
Step-by-step explanation:
Angle x + 80* add up to the vertical angle of 160*
So, 160* = x + 80*
80* = x
Answer:
80°
Step-by-step explanation:
160 is vertically opposite the x and 80, which means they have the same value. This makes x+80=160.
This can be solved to x=80.
Find the value of -6 + 8(-3) ÷ 4
please help me .
Answer:
-12
Step-by-step explanation:
cause from the rule
we should always solve from bracket so -3×8= -24
and -24/4= -6
and -6-6
= -12
The Rockwell hardness of a metal is determined by impressing a hardened point into the surface of the metal and then measuring the depth of penetration of the point. Suppose the Rockwell hardness of a particular alloy is normally distributed with mean 70 and standard deviation 3. (Rockwell hardness is measured on a continuous scale.)a. If a specimen is acceptable only if its hardness is between 67 and 75, what is the probability that a randomly chosen specimen has an acceptable hardness?b. If the acceptable range of hardness is (70-c, 70+c) , for what value of c would 95% of all specimens have acceptable hardness?c. If the acceptable range is as in part (a) and the hardness of each of ten randomly selected specimens is independently determined, what is the expected number of acceptable specimens among the ten?d. What is the probability that at most eight of ten independently selected specimens have a hardness of less than73.84? [Hint: Y = the number among the ten specimens with hardness less than 73.84 is a binomial variable; what is p?]
Answer:
a) The probability that a randomly chosen specimen has an acceptable hardness is 0.7938.
b) If the acceptable range of hardness is (70-c, 70+c), then the value of c would 95% of all specimens have an acceptable hardness of 5.88.
c) Expected number of acceptable specimens among the ten is 7.938.
d) Binomial with n = 10 and p = P(X < 73.84)
[tex]p = P(Z <(73.84 - 70) / 3 ) = P(Z < 1.28) = 0.8997\\\\P(X <= 8) = 1 - P(X = 9) - P(X = 10)\\= 0.2650635[/tex]
Step-by-step explanation:
a )
[tex]P(67 < X< 75) = P( (67 - 70) / 3 < X < (75 - 70) / 3 )\\\\= P( - 1 < Z < 1.67) = 0.9525 - 0.1587 = 0.7938[/tex]
b )
[tex]c = 1.96 * 3 = 5.88[/tex] { Since Z = 1.96 for 95% CI refer table.}
c )
Expected number of acceptable specimens among the ten [tex]= 10 * P(67 < X< 75) \\\\= 10 * 0.7938 = 7.938[/tex]
d )
Binomial with n = 10 and p = P(X < 73.84)
[tex]p = P(Z <(73.84 - 70) / 3 ) = P(Z < 1.28) = 0.8997\\\\P(X <= 8) = 1 - P(X = 9) - P(X = 10)\\= 0.2650635[/tex]
Which equation can be simplified to find the inverse of y = 2x2
Answer: d
Step-by-step explanation:
edge 2020
The brain volumes (cm^3) of 50 brains vary from a low of 914 cm^3 to a high of 1492 cm^3. Use the range rule of thumb to estimate the standard deviation s and compare the result to the exact standard deviation of 186.4 cm^3, assuming the estimate is accurate if it is within 15 cm^3.
Answer:
[tex]X= 19.6 cm3[/tex]
Therefore
X is not Accurate as it Falls outside of the Volume 15cm^3
Step-by-step explanation:
From the question we are told that:
Sample size [tex]n=50[/tex]
Volume Range [tex]\triangle V= 914 cm^3 to 1492cm^3[/tex]
Exact standard deviation [tex]\sigma_E 186.4 cm^3,[/tex]
Generally the equation for range rule of thumb is mathematically given by
Where
[tex]\triangle V=1492cm^3- 914 cm^3[/tex]
[tex]\triangle V=578cm^2[/tex]
Therefore
Estimate Standard deviation
[tex]\sigma_e=\frac{578}{4}[/tex]
[tex]\sigma_e=144.5cm^3[/tex]
Since
Exact standard deviation is 186.4 cm^3
Comparing
[tex]X=\sigma_E- \sigma_e[/tex]
[tex]X= ( 164.1-144.5 ) cm3[/tex]
[tex]X= 19.6 cm3[/tex]
Therefore
X is not Accurate as is Falls outside of the Hallmark 15cm^3
Triangle ABC will be translated right 3 units and down 5 units to create triangle A'B'C'. What are the coordinates of B'?
Answer:
B'(4, 0)
Step-by-step explanation:
B (1, 5)
it translated right 3 units => x'=x+3
down 5 units => y'= y-5
plz help worth 50 points
Answer:
The answer is A
Step-by-step explanation:
Starting from -3 in the Y values of option A. If you subtract three from each value, you will get the next value to the right.
-3 minus -3 = -6-6 minus -6 = -9
Answer:
Someone already answered it but I won't let 50 points go to waste. !!!!!
Step-by-step explanation:
If $25,000 is borrowed with an interest of 8.0% compounded annually, what is the total amount of money needed to pay it
back in 10 years?
Round your answer to the nearest cent.
Do NOT round until you have calculated the final answer.
Answer:
[tex] \frac{8}{?100} \times 25000[/tex]
=2000
365×10=3650
2000×3650=7300000
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$25000\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &10 \end{cases} \\\\\\ A=25000\left(1+\frac{0.08}{1}\right)^{1\cdot 10}\implies A=25000(1.08)^{10}\implies A\approx 53973.12[/tex]
A student uses the ratio of 4 oranges to 6 fluid ounces to
find the number of oranges needed to make 24 fluid
ounces of juice. The student writes this proportion:
4 24
616
Explain the error in the student's work.
A student uses the ratio of 4 oranges to 6 fluid ounces to find the number of oranges needed to make 24 fluid ounces of juice. The student writes the proportion:4/6=24/16
plz answer I don't have a long time
Answer: x=52
Step-by-step explanation:
x+72=34+90
x+72=124
124-72=x
x=52
Henry signed up for a streaming music service that costs $14 per month. The service allows Henry to listen to unlimited music, but if he wants to download songs for offline listening, the service charges $1 per song. How much total money would Henry have to pay in a month in which he downloaded 50 songs? How much would he have to pay if he downloaded s songs?
Cost for 50 songs :
Cost for s songs :
Answer:
Cost for 50 songs: $64
Cost for s songs: s + 14
Step-by-step explanation:
Since it is $1 per song, if he downloaded 50 songs, it would be $50 extra dollars.
Add this to the monthly charge of 14:
50 + 14
= 64
So, the cost of 50 songs would be $64.
Now, find the cost for downloading s songs.
Each song is $1, so the cost can be represented by s + 14.
The answer is:
Cost for 50 songs: $64
Cost for s songs: s + 14
A random sample of 50 male employees is taken at the end of a year and the mean
number of hours of absenteeism for the years is found to be 63 hours. A similar sample of
50 female employees has mean of 66 hours. Could these samples be drawn from a
population with the same mean and standard deviation 10 hours?
Answer:
Yes the samples can be drawn from a population with the same mean and standard deviation 10 hours
Step-by-step explanation:
We are given;
Sample mean for male employees; x1¯ = 63
Sample mean for female employees; x2¯ = 66
Sample size = 50
Standard deviation; σ = 10
First,let's define the hypotheses of the question;
Null hypothesis; H0: μ1 = μ2
Alternative hypothesis; Ha: μ1 ≠ μ2
Now, let's find the test statistic from the formula;
z = (x1¯ - x2¯)/(σ√(2/n))
Thus;
z = (63 - 66)/(10√(2/50))
z = -3/2 = - 1.5
Now, we are not given the significance value but usually when it is not given, we can adopt α = 0.05.
Thus, from online p-value from z-score calculator using; z = -1.5; α = 0.05; two tailed test; we have;
p-value = 0.13364
The p-value is greater than the significance value and thus we will fial to reject the null hypothesis and conclude that these samples can be drawn from a population with the same mean and standard deviation
What is 5^-3?
Please I really need someone to explain to me what do you do when there is a negative sign in the exponent. Thank you :)
Answer: 1/125 or 0.008 (simplify 1.125 or should I do it?)
Step-by-step explanation:
Well, when there is a negative sign in the exponent you only move the negative exponents. Moving only negative exponents is recommended because using this rule, you multiply two exponents with the same base and add their powers.
3y - 2x = 9
2y - 2x = 7
Step-by-step explanation:
there is your answer in attachment
On each trial of an experiment, a participant is presented with a constant soft noise, which is interrupted at some unpredictable time by a slightly louder sound. The time it takes for the participant to react to the louder sound is recorded. The following list contains the reaction times (in milliseconds) for trials of this experiment.
170, 206, 218, 232, 238, 248, 254, 264, 268, 281, 281, 281, 316, 320, 320, 329, 336, 365, 399, 400, 438, 438, 452, 524, 724, 806
1. measures of central tendency do not exist for this data set?
a. Mean
b. Median
c. Mode
d. None of these measures
2. Suppose that the measurement 806 (the largest measurement in the data set) were replaced by 1169. Which measures of central tendency would be affected by the change? Choose all that apply.
Answer:
1.d. None of these measures (do not exist interpreted as all of these exist)
2.The mean is increased from 346.8 to 361.32
Step-by-step explanation:
After calculations we find that all the measures of central tendency exist for this data. The mean , median and mode can be easily calculated .
The mean is 346.8
The mode is 281
The median is 316
Suppose that the measurement 806 (the largest measurement in the data set) were replaced by 1169. The mean would be affected by the change.
The mean is 361.32
The mode is 281
The median is 316
The mean is increased from 346.8 to 361.32
WILL MARK BRAINLIEST TO THE FIRST PERSON OR WHO IS RIGHT!!!!
The work of a student to solve a set of equations is shown:
Equation 1: m = 8 + 2n
Equation 2: 6m = 4 + 4n
Step 1: −6(m) = −6(8 + 2n) [Equation 1 is multiplied by −6.]
6m = 4 + 4n [Equation 2]
Step 2: −6m = −48 − 12n [Equation 1 in Step 1 is simplified.]
6m = 4 + 4n [Equation 2]
Step 3: −6m + 6m = −48 − 12n + 4n [Equations in Step 2 are added.]
Step 4: 0 = −48 − 8n
Step 5: n = −6
In which step did the student first make an error?
Step 3
Step 5
Step 4
Step 2
Answer:
Step 3
Step-by-step explanation:
Step 3 should be:
−6m + 6m = −48 − 12n + 4n + 4
9514 1404 393
Answer:
Step 3
Step-by-step explanation:
When the equations are added in step 3, the result should be ...
-6m +6m = -48 -12n +4 +4n
In the work shown, the (+4) was left out in Step 3.
__
When the work is properly continued, it becomes ...
Step 4: 0 = -44 -8n . . . . [step 3 is simplified]
Step 5: n = -5.5 . . . . . . . [step 4 is divided by -8 and 5.5 subtracted]
Step 6: m = -3 . . . . . . . . . [n is substituted into Equation 1]
And the solution is (m, n) = (-3, -5.5).