Answer:
The probability that he answered neither of the problems correctly is 0.0625.
Step-by-step explanation:
We are given that a student ran out of time on a multiple-choice exam and randomly guess the answers for two problems each problem have four answer choices ABCD and only one correct answer.
Let X = Number of problems correctly answered by a student.
The above situation can be represented through binomial distribution;
[tex]P(X=r)=\binom{n}{r}\times p^{r}\times (1-p)^{n-r};x=0,1,2,3,....[/tex]
where, n = number of trials (samples) taken = 2 problems
r = number of success = neither of the problems are correct
p = probability of success which in our question is probability that
a student answer correctly, i.e; p = [tex]\frac{1}{4}[/tex] = 0.75.
So, X ~ Binom(n = 2, p = 0.75)
Now, the probability that he answered neither of the problems correctly is given by = P(X = 0)
P(X = 0) = [tex]\binom{2}{0}\times 0.75^{0}\times (1-0.75)^{2-0}[/tex]
= [tex]1 \times 1\times 0.25^{2}[/tex]
= 0.0625
Which side of the pentagon on the right corresponds to
side KJ on the pentagon on the left.
Answer:
side st.Step-by-step explanation:
st corresponds to kj since a it has five sides.If 6x + 5y = 10, what is y in terms of x?
Please include an explanation!
what you're trying to do is form an equation for y
6x + 5y = 10
5y = -6x + 10 we need y to be singular so divide by numeral before y
y = - 6x/5 + 10/5
y = - 6x/5 + 2
You work as an assistant to a carpenter who designed the tabletop below. He tells you that each shape is a right triangle, and each is the same size. You now need to calculate the area of one triangle so that you can begin building the tabletop. What is the area of each triangle in square inches? 28 1/4" and 20"
Answer:
282.5 inches squared
Step-by-step explanation:
A triangle is half the area of a square.
So we will solve the area as if we were finding the area for a square, and then we halve the result.
Length multiply by height to get the area:
28.25 × 20 = 565 inches squared
Now, half the answer to get the area of the triangle:
565/2=282.5 inches squared
Please help! Stuck on this question!!
Answer:
The 2 Gallon Tank is Enough
Step-by-step explanation:
A drink bottler needs to bottle 16 one-pint bottles. He has a 2 gallon tank and a 3 gallon tank.
There are 8 pints in a gallon. This means that 2 gallons would be 16 pints.
[tex]8 * 2 = 16[/tex]
So, the 2 gallon tank has 16 pints, which means that the 2 gallon tank should be enough to bottle all 16 bottles.
Answer:
2 gallon tank
Step-by-step explanation:
16 pints is the same as 2 US gallons
70 points! Please answer fast!
Answer:
slope = 2
Step-by-step explanation:
will make it so simple and short
slope = rise / run
slope = 6 / 3
slope = 2
Answer:
B
Step-by-step explanation:
The formula for slope is (y2-y1)/(x2-x1)
In this case it is (1+5)/(3-0)
6/3
2
Can I have help I am stuck on this problem It would mean the world if u helped me and tysm!! =-)
Answer:
8192
Step-by-step explanation:
2 cells at beginning, so the equation is (2)*(2^(4t)) where t is in hours. At the end of 3 hours, the cells will be 2*(2)^(12)=8192
what is the number if 4 is subtracted from the sum of one fourth of 5 times of 8 and 10
Answer:
Step-by-step explanation:
Lets, turn this into words and use order of operations, First, we look for multiplication and division.
the sum of one fourth of 5 times of 8 and 10 gets you 1/4(5*8) + 10 = 20
what is the number if 4 is subtracted from the sum
20 - 4 = 16
Perimeter =68 Length (L) is 4 less than twice the width (W)
Answer:
Length = 21.3333333333; Width: 12.6666666667
Step-by-step explanation:
Perimeter = 68
Perimeter of a rectangle:
2 (L +W)
Length (L) = 2W - 4
Width = W
2 ( 2W -4 +W) = 68
=> 2 (3W - 4) = 68
=> 6w -8 = 68
=> 6w = 76
=> w = 12.6666666667
Length = (12.6666666667 X 2) - 4
=> 21.3333333333
Kevin's total payroll deductions are 30% of his earnings. If his deductions add up to $369 for a two week period, how much were his earnings for the period?
Answer:
His earnings for the period= $123
Step-by-step explanation:
Kevin's total payroll deductions are 30% of his earnings. His deductions add up to $369 for a two week period.
If 30% of his earnings = $369
His earnings = x
30/100 * x= 369
X= 369*100/30
X= 123*10
X=$ 1230
His earnings for the period= $123
Which value is a solution to w∕18 ≥ –1?
Answer:
w ≥ -18
Step-by-step explanation:
Answer:
w is greater than or equal to-18
Let the following sample of 8 observations be drawn from a normal population with unknown mean and standard deviation:
21, 14, 13, 24, 17, 22, 25, 12
Required:
a. Calculate the sample mean and the sample standard deviation.
b. Construct the 90% confidence interval for the population mean.
c. Construct the 95% confidence interval for the population mean
Answer:
a
[tex]\= x = 18.5[/tex] , [tex]\sigma = 5.15[/tex]
b
[tex]15.505 < \mu < 21.495[/tex]
c
[tex]14.93 < \mu < 22.069[/tex]
Step-by-step explanation:
From the question we are are told that
The sample data is 21, 14, 13, 24, 17, 22, 25, 12
The sample size is n = 8
Generally the ample mean is evaluated as
[tex]\= x = \frac{\sum x }{n}[/tex]
[tex]\= x = \frac{ 21 + 14 + 13 + 24 + 17 + 22+ 25 + 12 }{8}[/tex]
[tex]\= x = 18.5[/tex]
Generally the standard deviation is mathematically evaluated as
[tex]\sigma = \sqrt{\frac{\sum (x- \=x )^2}{n}}[/tex]
[tex]\sigma = \sqrt{\frac{\sum ((21 - 18.5)^2 + (14-18.5)^2+ (13-18.5)^2+ (24-18.5)^2+ (17-18.5)^2+ (22-18.5)^2+ (25-18.5)^2+ (12 -18.5)^2 )}{8}}[/tex]
[tex]\sigma = 5.15[/tex]
considering part b
Given that the confidence level is 90% then the significance level is evaluated as
[tex]\alpha = 100-90[/tex]
[tex]\alpha = 10\%[/tex]
[tex]\alpha = 0.10[/tex]
Next we obtain the critical value of [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table the value is
[tex]Z_{\frac{ \alpha }{2} } = 1.645[/tex]
The margin of error is mathematically represented as
[tex]E = Z_{\frac{ \alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E =1.645 * \frac{5.15 }{\sqrt{8} }[/tex]
=> [tex]E = 2.995[/tex]
The 90% confidence interval is evaluated as
[tex]\= x - E < \mu < \= x + E[/tex]
substituting values
[tex]18.5 - 2.995 < \mu < 18.5 + 2.995[/tex]
[tex]15.505 < \mu < 21.495[/tex]
considering part c
Given that the confidence level is 95% then the significance level is evaluated as
[tex]\alpha = 100-95[/tex]
[tex]\alpha = 5\%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table the value is
[tex]Z_{\frac{ \alpha }{2} } = 1.96[/tex]
The margin of error is mathematically represented as
[tex]E = Z_{\frac{ \alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E =1.96 * \frac{5.15 }{\sqrt{8} }[/tex]
=> [tex]E = 3.569[/tex]
The 95% confidence interval is evaluated as
[tex]\= x - E < \mu < \= x + E[/tex]
substituting values
[tex]18.5 - 3.569 < \mu < 18.5 + 3.569[/tex]
[tex]14.93 < \mu < 22.069[/tex]
anybody know how to do this? if so, please explain!
Answer:
The x-intercepts are at (-4, 0) and (3, 0). The y-intercept is at (0, 1.2).
The graph is increasing at (-4, 0), (2.082, -0.604), (3, 0).
The graph is decreasing at (-2.082, 3.004), (0, 1.2), (1, 0)
Step-by-step explanation:
If you have a piece of glass that is 12in X 12in - how many square feet is it?
Answer:
1 square foot is the answer
Answer:
1 ft^2
Step-by-step explanation:
We know 12 inches = 1 ft
12 inches by 12 inches
1 ft by 1 ft
The area is 1 * 1 = 1 ft^2
Help me please thank y’all
x= 30 degrees
Step-by-step explanation:
there's 180 degrees in a triangle. You can see 60 degrees right there. Theres a 90 degree angle right next to it. 180-150=30
The lines shown below are parallel. If the green line has a slope of -1/2, what is the slope of the red line?
A.
2
B.
-
C.
-2
D.
Explanation: Parallel lines have the same slopes, but different y intercepts.
Answer:
the slope of the red line is also -1/2
Step-by-step explanation:
Which table has a constant of proportionality between 7 and x of 1/4? Choices are in the image
Answer:
A. has a constant proportion of 1/4.
Given that a random variable X is normally distributed with a mean of 2 and a variance of 4, find the value of x such that P(X < x)
Given that a random variable X is normally distributed with a mean of 2 and a variance of 4, find the value of x such that P(X < x)=0.99 using the cumulative standard normal distribution table
Answer:
6.642
Step-by-step explanation:
Given that mean = 2
standard deviation = 2
Let X be the random Variable
Then X [tex]\sim[/tex] N(n,[tex]\sigma[/tex])
X [tex]\sim[/tex] N(2,2)
By Central limit theorem;
[tex]z = \dfrac{X - \mu}{\sigma} \sim N(0,1)[/tex]
[tex]z = \dfrac{X - 2}{2} \sim N(0,1)[/tex]
P(X<x) = 0.09
[tex]P(Z < \dfrac{X-\mu}{\sigma })= 0.99[/tex]
[tex]P(Z < \dfrac{X-2}{2})= 0.99[/tex]
P(X < x) = 0.99
[tex]P(\dfrac{X-2}{2}< \dfrac{X-2}{2})=0.99[/tex]
[tex]P(Z< \dfrac{X-2}{2})=0.99[/tex]
[tex]\phi ( \dfrac{X-2}{2})=0.99[/tex]
[tex]( \dfrac{X-2}{2})= \phi^{-1} (0.99)[/tex]
[tex]( \dfrac{X-2}{2})= 2.321[/tex]
X -2 = 2.321 × 2
X -2 = 4.642
X = 4.642 +2
X = 6.642
An airplane has an air speed of 700 kilometers per hour at a bearing of 30 degrees The wind velocity is 40 kilometers per hour from the west Use vectors to find the art speed of the plane Round to the nearest hundredth
Answer:
The red arrow shows the resultant vector. We have a Side Angle Side triangle ABC so can use The Cosine Rule:
a2=b2+c2−2bccosA
This becomes:
R2=7002+402−(2×700×40×cos45)
R2=491,600−39,597.9
R=672.3xkm/hr
This is the groundspeed of the aircraft.
To find θ we can use The Sine Rule:
sinCc=sinAa
This becomes:
sinθ40=sin45672.3
sinθ=0.04207
θ=2.41∘
This is known as the drift angle and is the correction the pilot should apply to remain on course.
The heading is the direction the aircraft's nose is pointing which is 000∘.
The track is the actual direction over the ground which is 357.6∘
An alternative method to this would be to separate each vector into vertical and horizontal components and add.
The resultant can be found using Pythagoras.
9. Marvin Gate bought some fencing from a wholesaler for $6,000. The wholesaler offered a trade discount of 35%. What was the original price?
(Round to the nearest cent.)
A. $6,230.77
O B. $9.230.77
O C. $6,930.77
D. 55,930 77
Mark for review (Will be highlighted on the review page)
Answer:
B - %9230.77
Step-by-step explanation:
the original price of the fencing before the trade discount was approximately $9,230.77.
To find the original price of the fencing before the trade discount, we need to calculate the amount that corresponds to a 35% decrease from the discounted price.
Let's denote the original price as "P". The discounted price is given as $6,000.
The discounted price is calculated by subtracting the discount amount from the original price:
Discounted price = Original price - Discount amount
The discount amount is determined by multiplying the original price by the discount rate:
Discount amount = Original price × Discount rate
Given that the discount rate is 35% (or 0.35), we have:
Discount amount = P × 0.35
Substituting the discounted price of $6,000, we can write the equation as:
$6,000 = P - (P × 0.35)
Simplifying the equation:
$6,000 = P(1 - 0.35)
$6,000 = P(0.65)
To solve for P, we divide both sides of the equation by 0.65:
P = $6,000 / 0.65
P ≈ $9,230.77
Therefore, the original price of the fencing before the trade discount was approximately $9,230.77.
The correct answer is B. $9,230.77.
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Using the formula D = s:t where D equals distance traveled, r equals the average rate of
speed, and t equals the time traveled, choose the expression or equation that correctly
represents this information.
Mary drove 150 miles in three hours. What was her average rate of speed?
=
150 = 3
r = 3 = 150
O p + 150 · 3
Answer: r = 50 miles/h
Step-by-step explanation:
Let r be the rate of average speed.
Then
r = D/t
r = 150/3
r = 50 miles/h
please click thanks and mark brainliest if you like :)
An apartment building is infested with 6.2 X 10 ratsOn average, each of these rats
produces 5.5 X 10' offspring each year. Assuming no rats leave or die, how many additional
rats will live in this building one year from now? Write your answer in standard form.
Answer: 3.41x10^3
Step-by-step explanation:
At the beginning of the year, we have:
R = 6.2x10 rats.
And we know that, in one year, each rat produces:
O = 5.5x10 offsprins.
Then each one of the 6.2x10 initial rats will produce 5.5x10 offsprings in one year, then after one year we have a total of:
(6.2x10)*(5.5x10) = (6.2*5.5)x(10*10) = 34.1x10^2
and we can write:
34.1 = 3.41x10
then: 34.1x10^2 = 3.41x10^3
So after one year, the average number of rats is: 3.41x10^3
Among cases of heart pacemaker malfunctions, were found to be caused by firmware, which is software programmed into the device. If the firmware is tested in different pacemakers randomly selected from this batch of and the entire batch is accepted if there are no failures, what is the probability that the firmware in the entire batch will be accepted? Is this procedure likely to result in the entire batch being accepted?
Complete question is;
Among 8834 cases of heart pacemaker malfunctions, 504 were found to be caused by firmware, which is software programmed into the device. If the firmware is tested in three different pacemakers randomly selected from this batch of 8834 and the entire batch is accepted if there are no failures, what is the probability that the firmware in the entire batch will be accepted? Is this procedure likely to result in the entire batch being accepted?
Answer:
P(All three are not caused by firmware) = 83.84%
Probability that the entire batch will be accepted = 0.8384
Step-by-step explanation:
We are told that out of the 8834 cases of heart pacemaker malfunctions, 504 were found to be caused by firmware.
Thus,
Cases not caused by firmware = 8834 - 504 = 8330
So, probability of the first case not being affected by firmware is;
P(first case not caused by firmware) = 8330/8834
Also,
Probability of second case not being affected by firmware is given as;
P(second case not caused by firmware|first case not affected by firmware) = 8329/8833
Similarly,
Probability of third case not being affected by firmware is given as;
P(third case not caused by firmware|first and second not caused by firmware) = 8328/8832
Now, looking at the 3 Probabilities gotten, it is obvious that the events are not independent because the probability of occurence of one event depends on the probability of occurence of the other event.
Thus, we will make use of the general multiplication rule which is;
P(A & B) = P(B) × P(A|B)
Thus;
P(All three not caused by firmware) = P(first case not caused by firmware) × P(second case not caused by firmware|first case not affected by firmware) × P(third case not caused by firmware|first and second not caused by firmware)
Plugging in the relevant values, we have;
P(All three not caused by firmware) = (8330/8834) × (8329/8833) × (8328/8832)
P(All three are not caused by firmware) = 0.83840506679 ≈ 83.84%
Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. After 9 hours of burning, a candle has a height of 25.4 centimeters. After 23 hours of burning, its height is 19.8 centimeters. What is the height of the candle after 22 hours?
Answer:
Suppose that the height (in centimeters) of a candle is a linear function of
the amount of time (in hours) it has been burning.
After 11 hours of burning, a candle has a height of 23.4 centimeters.
After 30 hours of burning, its height is 12 centimeters.
What is the height of the candle after 13 hours?
:
Assign the given values as follows:
x1 = 11; y1 = 23.4
x2 = 30; y2 = 12
:
Find the slope using: m = %28y2-y1%29%2F%28x2-x1%29
m = %2812-23.4%29%2F%2830-11%29 = %28-11.4%29%2F19
:
Find the equation using the point/slope formula: y - y1 = m(x - x1)
y - 23.4 = -11.4%2F19(x - 11)
y - 23.4 = -11.4%2F19x + 125.4%2F19
y = -11.4%2F19x + 125.4%2F19 + 23.4
y = -11.4%2F19x + 125.4%2F19 + 23.4
y = -11.4%2F19x + 125.4%2F19 + 444.6%2F19
y = -11.4%2F19x + 570%2F19
y = -11.4%2F19x + 30, is the equation
:
What is the height of the candle after 13 hours?
x = 13
y = -11.4%2F19(13) + 30
y = -148.2%2F19 + 30
y = -7.8 + 30
y = 22.2 cm after 13 hrs
g If A and B are disjoint events, with P( A) = 0.20 and P( B) = 0.30. Then P( A and B) is: a. .00 b. .10 c. .50 d. 0.06
Answer: A) 0
P(A and B) = 0 when events A and B are disjoint, aka mutually exclusive.
We say that two events are mutually exclusive if they cannot happen at the same time. An example would be flipping a coin to have it land on heads and tails at the same time.
A researcher measures daily driving distance from college and weekly cost of gas for a group of commuting college students. What kind of correlation is likely to be obtained for these two variables?
Answer:
There is a positive correlation between these two variables.
Step-by-step explanation:
Positive correlation is an association amid two variables in which both variables change in the same direction.
A positive correlation occurs when one variable declines as the other variable declines, or one variable escalates while the other escalates.
As the distance covered by the vehicle increases the amount of gas consumed also increases. Thus, the weekly cost of gas will also increase.
Thus, there is a positive correlation between these two variables.
Will Give Brainliest Please Answer Quick
Answer:
Option (2)
Step-by-step explanation:
If a perpendicular is drawn from the center of a circle to a chord, perpendicular divides the chord in two equal segments.
By using this property,
Segment MN passing through the center Q will be perpendicular to chords HI ans GJ.
By applying Pythagoras theorem in right triangle KNJ,
(KJ)² = (KN)² + (NJ)²
(33)² = (6√10)² + (NJ)²
NJ = [tex]\sqrt{1089-360}[/tex]
NJ = [tex]\sqrt{729}[/tex]
= 27 units
Since, GJ = 2(NJ)
GJ = 2 × 27
GJ = 54 units
Option (2) will be the answer.
Which representation would be best for determining how many planes had an average cruising speed of 0.84 Mach?
Answer:
Question: 1
A dot plot shows individual values. So, we can most easily tell from the dot plot that 5 planes had an average cruising speed of 0.84 Mach
Question: 2
A box plot breaks data into quartiles, each representing 25% of the data. So to find the middle 50% of the data, look at the data that lies between the first and third quartiles of the box plot. The box plot shows that the first and third quartiles are 0.8175 and 0.85, respectively, so 50% of the data lies between 0.8175 and 0.85.
Question: 3
The histogram would be the best data representation for quickly determining how many planes had a speed less than 0.84 Mach. Adding the frequencies of the 3 bins less than 0.84 shows that 17 planes had a speed of less than 0.84 Mach. The dot plot could also be used to determine this, but it would take more time to count each individual dot.
Step-by-step explanation:
answer from plato
Thank me later
The graphical representation which would be best for determining the number of planes that had an average cruising speed of 0.84 Mach is a: histogram.
What is a histogram?A histogram can be defined as a type of graph (chart) that is used to graphically represent a data set (statistical information) into user-specified ranges through the use of rectangles.
Generally, the area of each rectangle of a histogram is directly proportional to the data frequency and its width is equal to the class interval.
In this scenario, a histogram is the graphical representation which would be best for determining the number of planes that had an average cruising speed of 0.84 Mach.
Read more on histogram here: brainly.com/question/21304143
IM GIVING BRAINLIEST TO THE FIRST PERSON TO ANSWER!
Show ALL work please! <3
Answer:
B
Step-by-step explanation:
What work is there to show? you basically isolate x. add 2 to both sides. and you get x is greater than or equal to 5. So the answer is B.
x-2[tex]\geq[/tex]3
+2 +2
x[tex]\geq[/tex]5
What is the smallest number that has both 6 and 9 as a
factor?
A 54
B 12
C 36
D 18
Answer:
yep it's D
Step-by-step explanation:
Find the slope of the line through the points (-4, 6) and (8,4).
I need help on this
Start with the slope formula.
m = y2-y1/x2 - x1
We take the second y minus the first y
over the second x minus the first x.
So we have 4 - 6/8 - -4.
This simplifies to -2/12 which reduces to -1/6.