Answer:
The mean and standard deviation of the number of questions that each student gets correct are 4 and 1.789 respectively.
Step-by-step explanation:
Let the random variable X be defined as the number of correct answers marked by a student.
It is provided that each question has 5 possible choices, 1 of the which is correct.
Then the probability of marking thee correct option is:
[tex]P(X)=\frac{1}{5}=0.20[/tex]
There are a total of n = 20 questions to be answered.
As the students does not the answer to any question, they would be guessing for each question. This implies that for a random question, all the five options has the equal probability of being correct and each of the five options can be correct independently from the other.
All these information above indicates that the random variable X follows a Binomial distribution with parameters n = 20 and p = 0.20.
The mean and standard deviation of a Binomial distribution are:
[tex]\mu=np\\\\\sigma=\sqrt{np(1-p)}[/tex]
Compute the mean and standard deviation of the random variable X as follows:
[tex]\mu=np=20\times 0.20=4\\\\\sigma=\sqrt{np(1-p)}=\sqrt{20\times 0.20\times(1-0.20)}=1.789[/tex]
Thus, the mean and standard deviation of the number of questions that each student gets correct are 4 and 1.789 respectively.
According to the question,
The probability of making 3 correct options will be:
→ [tex]P(X) = \frac{1}{5}[/tex]
[tex]= 0.20[/tex]
Total number of questions,
n = 20As we know,
The mean will be:
→ [tex]\mu = np[/tex]
By substituting the values, we get
[tex]= 20\times 0.20[/tex]
[tex]= 4[/tex]
and,
The standard deviation will be:
→ [tex]\sigma = \sqrt{np(1-p)}[/tex]
[tex]= \sqrt{20\times 0.20\times (1-0.20)}[/tex]
[tex]= 1.789[/tex]
Thus the responses above are correct.
Learn more about standard deviation here:
https://brainly.com/question/20896613
Please what is the length of AC? Please 1 day no answer.
Answer: AC = 2.33
Step-by-step explanation:
use tangent to find the missing side
Tangent = opposite/adjacent
tan B = ?/5
tan 25 = ?/5
multiply each side by 5
? = 2.33153829.....
so
AC = 2.33
Need Help ASAP !!!!!
Answer:
Luke worked 7 hours and Joshua worked 4 hours
Step-by-step explanation:
Let's call the number of hours that Luke worked l, and the number of hours that Joshua worked j. Since we know that Luke worked for 3 more hours than Joshua, we can express the amount of hours he worked as (j+3). Now, you can set up the following equation:
25j+35(j+3)=345
Expand parentheses:
25j+35j+105=345
Subtract 105 from both sides and combine like terms:
60j=240
j=4
Since Luke worked 3 more hours, he worked 7 hours. Hope this helps!
There were 208 tickets purchased for a major league baseball game. The lower box tickets cost $12.50 and the upper box tickets cost $10.00. The total amount of money spent was $2187.50. How many of each kind of ticket were purchased?
Answer:
so 189(from 189.66) lower box tickets are sold and 18 upper box tickets are sold
Step-by-step explanation:
lets take "x" as the # of lower box tickets
and "y" as the number of upper box tickets
so in total the number of tickets sold was 208
so x+y=208
next, we know that each lower box ticket costs 12.50 and each upper box tickets costs 10 and the total amount of money spent was $2187.50 so:
12.5x+10y=2187.50
lets subtract "x" from both sides in first equation to find value of y
y=208-x
now substitute y in equation number 2:
12.5x-10(208-x)=2187.5
12.5x-2080+10x=2187.5
22.5x-2080=2187.5
22.5x=4267.5
x=189.666
so 189 tickets lower box tickets were purchased now, substitute 190 in equation 1 to find value of "y"
y=208-190
y=18
so 189(from 189.66) lower box tickets are sold and 18 upper box tickets are sold
Find the area of the shape plssss help
ok so find the area of thesquare then triangles and then add them tiriange area is 1/2 times base times heightso 1/2 times 2 times 2 which is 4 divided by 2 which is 2 same with the other traingle so your total area for the traingles is 4. The area for the square is 2 times 2 which is 4. add them up yiouget the whole shape is 8 units squared Answer: 8 units squared
Step-by-step explanation:
What is the length of AC? PLEASE HELP ASAP WILL GIVE BRAINLIEST TY
Answer:
2.33 units
Step-by-step explanation:
[tex]\tan 25\degree =\frac{AC}{5}\\\\0.46630 = \frac{AC}{5}\\\\AC = 0.46630 \times 5\\AC =2.3315\\AC = 2.33 \: units[/tex]
Determine if the set of vectors shown to the right is a basis for IR3 If the set of vectors is not a basis, determine whether it is linearly independent and whether the set 311-4 spans R 12 Which of the following describe the set?
A. The set is a basis for R3
B. The set is linearly independent.
C The set spans R3
D. None of the above
Answer:
The problem is clearly solved in the attachment
A manufacturer of bolts has a quality-control policy that requires it to destroy any bolts that are more than 4 4 standard deviations from the mean. The quality-control engineer knows that the bolts coming off the assembly line have mean length of 13 13 cm with a standard deviation of 0.10 0.10 cm. For what lengths will a bolt be destroyed?
Answer:
13.4 centimeters
Step-by-step explanation:
In this case to calculate the distance we must take into account the data that they give us in the exercise.
The final length would be equal to the initial length added to the product of standard deviations from the mean and standard deviation given by the engineer, like this:
L = 13 + 4 * 0.10
L = 13 + 0.4
L 13.4
That means that lengths will a bolt be destroyed when the value is 13.4 centimeters
line s has a slope of 2/5. line t is perpendicular to s. what is the slope of line t
Answer:
-5/2
Step-by-step explanation:
In order to find the slope of a perpendicular line: negate the reciprocal of the original slope
Show steps how to solve for y!!!!!
2y+2=3y/2
Please help me
[tex]\text{Solve for y:}\\\\2y+2=\frac{3y}{2}\\\\\text{Multiply both sides by 2 to cancel the denominator}\\\\4y+4=3y\\\\\text{Subtract 3y from both sides}\\\\y+4=0\\\\\text{Subtract 4 from both sides}\\\\\boxed{y=-4}[/tex]
Answer:-4
Step-by-step explanation:
2y+2=3y/2
Cross multiply
2(2y+2)=3y
Open bracket
4y+4=3y
Collect like terms
4y-3y=-4
y=-4
find the second term in the sequence b(1)=16 b(n)=b(n-1)+1
Answer:17
Step-by-step explanation:
b(1)=16
b(n)=b(n-1)+1
b(2)=16(2-1)+1
b(2)=16(1)+1
b(2)=16+1
b(2)=17
OMG THIS QUESTION IS SO HARD WILL RATE IF U GET IT
These aren't too hard -- you should really try to do them yourself.
The upper triangle has base 2+2=4 and height 3.2. The lower one has base 4 and height 4. Of course the area of a triangle half base times height.
Area = (1/2) 4(3.2) + (1/2)(4)(4) = 2(7.2) = 14.4
Answer: 14.4 sq ft
Pls help with this one I will give brainliest thank you!
Answer:
B. 10 in.
Step-by-step explanation:
When you do length times width times height 10*10*10 equals 1000
10*10=100 and 100*10=1000
Answer:10 feet
Step-by-step explanation:
edge=[tex]\sqrt[3]{1000}[/tex]= 10 so the answer is B
Dixon and his little sister Ariadne stand next to each other on the playground on a sunny afternoon. Their mother measures their shadows. Ariadne’s shadow is 15 feet long and Dixon’s shadow is 18 feet long. If Ariadne is 5 feet tall , how tall is Dixon ?
Hey there! I'm happy to help you!
To solve this, we can set up a proportion below! I will put the data in table, fraction, and ratio form so you can see different ways to visualize it.
HEIGHT LENGTH OF SHADOW
DIXON ? 18
ARIADNE 5 15
or
[tex]\frac{height}{length} =\frac{5}{15} =\frac{h}{18}[/tex]
or
5:15= h:18
As we can see, we see that Ariadne's length of shadow is three times as large as her height. Therefore, that means that Dixon's height will be 1/3 of the length of his shadow!
18/3= 6
We can also use the cross multiplying method with our proportion and then solve for h!
h=5*18/15
h=90/15
h=6
Therefore, Dixon is six feet tall.
I hope that this helps! Have a great day!
A flagpole casts a shadow that is 36 feet long, while a yardstick casts a shadow of 48 inches long. About how tall is the flagpole?
Answer:
27 ft
Step-by-step explanation:
The object is 3/4 times as tall as the shadow it makes. (1 yd/48" = 3'/4') So, the flagpole will be 3/4 times 36 ft, or 27 ft high.
The flagpole is 27 ft tall.
FInd the permiter of a square with an area of 702.25 square yards
Answer:
The perimeter of the square is 106yd
Step-by-step explanation:
To solve this we first have to know the formula to calculate the area of a square
a = area = 702.25yd²
s = side
a = s * s
we replace the values
702.25yd² = s * s
702.25yd² = s²
√(702.25yd²) = s
26.5yd = s
The side of the square is 26.5yd
Now we have to use the formula to calculate the perimeter of a square
p = perimeter
s = side = 26.5yd
p = 4 * s
we replace with the known values
p = 4 * 26.5yd
p = 106yd
The perimeter of the square is 106yd
Answer:106 yards
Step-by-step explanation:
Length=L
Area=702.5
Area of square=L x L
702.5=L X L
702.5=L^2
L=√(702.5)
L=26.50
perimeter of square=4 x L
Perimeter of square=4 x 26.50
Perimeter of square=106
Perimeter of square=106 yards
Please help ASAP! I will mark Brainliest! Please answer CORRECTLY! No guessing! Show your work!
Answer:
All positive real numbers i think
Answer:
B
Step-by-step explanation:
4^x can never be 0 or negative, the graph has a horizontal asymptote at y = 0
So the range only includes positive values
In ΔPQR, the measure of ∠R=90°, RP = 9.9 feet, and QR = 3.2 feet. Find the measure of ∠P to the nearest tenth of a degree.
Answer:
17.9
Step-by-step explanation:
PLEASE ANSWER AS QUICKLY AS POSSIBLE
Answer: D
Step-by-step explanation: Both the Equality property and the Identity property
Question 11 of 15
Micah is filling up his cone-shaped cup with water. The cup (as shown) has a diameter of 72 millimeters and a slant height of 45
millimeters. How much water can Micah fill in his cup?
Answer:
36.644 mL . . . . depending on your value of π (see below)
Step-by-step explanation:
The height of Micah's cup is found from the radius and slant height. The radius is half the diameter, so is 36 mm. Then the height h is ...
45² = 36² +h²
h = √(45² -36²) = 27 . . . . . mm
The volume is given by the formula ...
V = (1/3)πr²h
V = (1/3)π(36 mm)²(27 mm) = 11664π mm³
For π = 3.14
11664(3.14) mm³ ≈ 36,625 mm³ = 36.625 mL
For π = 3.14159265
11665π mm³ = 36,644 mm³ = 36.644 mL
_____
Comment on units
A unit of measure used for relatively small volumes, especially of liquid, is milliliters (mL). 1 mL = 1000 mm³.
Answer:
The answer is 11664pimm^3
Step-by-step explanation:
Someone please help me with math. Thank You
Answer:
4) 64 cubic inches
Step-by-step explanation:
8x8 = 64
Please help ASAP! I will mark Brainliest! Please answer CORRECTLY! No guessing.
Answer:
27
Step-by-step explanation:
Input 5 for all x-values.
If that is an equal sign...
1/9*(3^5)
With PEMDAS, exponents are done before multiplication.
1/9*243
= 27
heeeeeeeeeeeeeeellllllllllllllllllllpppppppppp
Answer:
Keep the circle closed like it is and draw an incresing line (towards the positive numbers)(basically towards the right) with the arrow at the end of it
Step-by-step explanation:
Write the fraction from least to greatest: 1/8, 1/3, 1/8
Answer:
Start with making them equal.
1/8 --> 3/24
1/8 --> 3/24
1/3 --> 8/24
Now order them.
1/8, 1/8, 1/3.
Hope this helps ;)
Trina has a total of 32 crayons. How much boxes of crayons did she buy.
Answer:
Depends on the type of box, but most likely one box of crayons because 32 packs are sold.
Do you have answer choices?
how do u solve 3(1 - 3g) = -8g + 14 ?
Answer:
3 - 9g = -8g + 4
-9g + 8g = 4 -3
g = -1
Help timed test! At which root does the graph...
Answer:
x = -2
Step-by-step explanation:
The way you can tell if the graph is going to cross the x-axis or just touch the x-axis is by looking at the power of the factor.
(x - 5)^3 has a power of 3 which is an ODD number. An ODD power means that the graph will cross through the x-axis.
(x + 2)^2 has a power of 2 which is an EVEN number. An EVEN power means that the graph will touch the x-axis.
To find where it will touch the axis set the factor equal to zero and solve.
(x + 2) = 0
subtract 2 from both sides
x = -2
What is the estimated sum?
Round each number to the nearest hundred before adding.
521,370 + 26,839
A 548,100
B 548,200
C 548,000
D 547,000
Pls help
Answer:
B
Step-by-step explanation:
521,370 would round to 521,400
26,839 would round to 27,800
and adding them would be
548,200
Please Help!!!!!!! I am very confused. Can someone explain?
Answer:
1/6a-1/6, a=1
Step-by-step explanation:
Hey there! I can definitely explain :)
-2/3a+5/6a-1/6
Multiply the two terms (the first two), to have common denominators!
The common lowest (easiest to deal with) denominator is 18. So, multiply the first term (-2/3a) by 6/6 and the second term (5/6a) by 3/3!
-12/18a+15/18a-1/6
Now, add those together!
3/18a-1/6
Now simplify!
1/6a-1/6
If you want, you can solve for a!
1/6a=1/6
a=1
Hope this helps! Please mark brainliest :)
Simon is building a ramp in the shape of a triangular prism. He plans to paint each face of the ramp. What is the total surface area of the ramp?
A triangular prism. The base has a length of 8 feet and height of 4 feet. A rectangular side has a base of 8 feet and height of 5 feet. Another rectangular side has a base of 8 feet and height of 3 feet. The triangular sides have a base of 4 feet and height of 3 feet.
68 square feet
96 square feet
108 square feet
114 square feet
Answer:
108 square feet
Step-by-step explanation:
When you say "triangular prism" it means the base is a triangle and the lateral faces are all rectangles. It doesn't matter which side is lying on the ground.
So, we see this is a triangular prism with a 3-4-5 right triangle as a base, and a "height" of 8 feet.
Its total surface area is the area of the two triangle bases plus the area of the three rectangular faces:
A = 2(1/2)(4·3) +8(3 +4 +5) = 12 +96 = 108 . . . . . square feet
Answer:
its C
Step-by-step explanation:
Given two independent random samples with the following results: n1=8x‾1=186s1=33 n2=7x‾2=171s2=23 Use this data to find the 90% confidence interval for the true difference between the population means. Assume that the population variances are equal and that the two populations are normally distributed. Step 1 of 3: Find the point estimate that should be used in constructing the confidence interval.
Answer:
The point of estimate for the true difference would be:
[tex] 186-171= 15[/tex]
And the confidence interval is given by:
[tex] (186-171) -1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= -10.753[/tex]
[tex] (186-171) +1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= 40.753[/tex]
Step-by-step explanation:
For this case we have the following info given:
[tex] \bar X_1 = 186[/tex] the sample mean for the first sample
[tex] \bar X_2 = 171[/tex] the sample mean for the second sample
[tex]s_1 =33[/tex] the sample deviation for the first sample
[tex]s_2 =23[/tex] the sample deviation for the second sample
[tex]n_1 = 8[/tex] the sample size for the first group
[tex]n_2 = 7[/tex] the sample size for the second group
The confidence interval for the true difference is given by:
[tex] (\bar X_1 -\bar X_2) \pm t_{\alpha/2}\sqrt{\frac{s^2_1}{n_1} +\frac{s^2_2}{n_2}}[/tex]
We can find the degrees of freedom are given:
[tex] df = n_1 +n_2 -2 =8+7-2= 13[/tex]
The confidence level is given by 90% so then the significance would be [tex]\alpha=1-0.9=0.1[/tex] and [tex]\alpha/2=0.05[/tex] we can find the critical value with the degrees of freedom given and we got:
[tex] t_{\alpha/2}= \pm 1.77[/tex]
The point of estimate for the true difference would be:
[tex] 186-171= 15[/tex]
And replacing into the formula for the confidence interval we got:
[tex] (186-171) -1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= -10.753[/tex]
[tex] (186-171) +1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= 40.753[/tex]
