Answer:
Probability of rolling at least 4 sixes is 0.01696.
Step-by-step explanation:
We are given that an unbalanced die is manufactured so that there is a 20% chance of rolling a “six." The die is rolled 6 times.
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 trials (samples) taken = 6 trials
r = number of success = at least 4
p = probability of success which in our question is probability of
rolling a “six", i.e; p = 0.20
Let X = Number of sixes on a die
So, X ~ Binom(n = 6, p = 0.20)
Now, Probability of rolling at least 4 sixes is given by = P(X [tex]\geq[/tex] 4)
P(X [tex]\geq[/tex] 4) = P(X = 4) + P(X = 5) + P(X = 6)
= [tex]\binom{6}{4} \times 0.20^{4} \times (1-0.20)^{6-4}+\binom{6}{5} \times 0.20^{5} \times (1-0.20)^{6-5}+\binom{6}{6} \times 0.20^{6} \times (1-0.20)^{6-6}[/tex]
= [tex]15 \times 0.20^{4} \times 0.80^{2}+6 \times 0.20^{5} \times 0.80^{1}+1 \times 0.20^{6} \times 0.80^{0}[/tex]
= 0.0154 + 0.00154 + 0.000064
= 0.01696
Therefore, probability of rolling at least 4 sixes is 0.01696.
Using the binomial distribution, it is found that there is a 0.0086 = 0.86% probability of rolling at least 4 sixes.
For each roll, there are only two possible outcomes, either it is a six, or it is not. The result of a roll is independent of any other rolls, hence, the binomial distribution is used to solve this question.
Binomial probability distribution
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.In this problem:
The die is rolled 6 times, hence [tex]n = 6[/tex].There are six sides on the dice, one of which is 6, hence [tex]p = \frac{1}{6} = 0.1667[/tex].The probability is:
[tex]P(X \geq 4) = P(X = 4) + P(X = 5) + P(X = 6)[/tex]
In which:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{6,4}.(0.1667)^{4}.(0.8333)^{2} = 0.0080[/tex]
[tex]P(X = 5) = C_{6,5}.(0.1667)^{5}.(0.8333)^{1} = 0.0006[/tex]
[tex]P(X = 6) = C_{6,6}.(0.1667)^{6}.(0.8333)^{0} \approx 0[/tex]
Then:
[tex]P(X \geq 4) = P(X = 4) + P(X = 5) + P(X = 6) = 0.0080 + 0.0006 + 0 = 0.0086[/tex]
0.0086 = 0.86% probability of rolling at least 4 sixes.
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Identify the constant term in this expression.
7p − 3p + 9 + x
A)9
B) 3p
C) 7p
D) x
Answer:
The constant would be A) 9
Step-by-step explanation:
The Constant in a math expression is One number that is on its own or without a varialbe
Please find volume Of the 3D shape
Step-by-step explanation:
first you do 2x8x9=144
now you have to do 1x3x8=24
then you add them so it would be 168 and that is your answer
h(x) = -(x + 11)2 +1 what is the vertex
Answer:
with (-11, 1) as the vertex
Step-by-step explanation:
The vertex form of a parabola is given by
y = a (x-h) ^2 +k
where (h,k) is the vertex
h(x) = -(x + 11)^2 +1
is written in vertex form
h(x) = -(x - -11)^2 +1
with (-11, 1) as the vertex
Jane drives 63.84 miles in the morning and 45.9 miles in the afternoon.
How many miles did she drive in all?
Answer:
109.74 miles.
Step-by-step explanation:
Answer:
109.74 miles.
Step-by-step explanation:
jake went to the zoo
Answer:
i got u he was eaten by a bear.
Step-by-step explanation:
Answer:
to kiss the penguins
Step-by-step explanation:
The area of a rectangle whose perimeter is a fixed 80 feet is given by A=40w - w2 , where w is the width of the rectangle. Determine the width of the rectangle that gives the maximum area. What type of special rectangle is necessary to produce this maximum area? Justify.
Answer:
Width=20 feet
Since Length=Width=20 feet, the rectangle is a Square.
Step-by-step explanation:
Area, [tex]A=40w - w^2[/tex]
To determine the width of the rectangle that gives the maximum area, we take the derivative of A and solve for its critical point.
[tex]A'=40 - 2w\\$When A'=0\\40-2w=0\\40=2w\\w=20 feet[/tex]
The width of the rectangle that gives the maximum area =20 feet.
Perimeter of a rectangle=2(l+w)
Perimeter of the rectangle=80 feet
2(l+w)=80
2l+2(20)=80
2l=80-40
2l=40
l=20 feet
Since the length and width are equal, the special type of rectangle that produces this maximum area is a Square.
The area of the rectangle is the product of its dimensions
The width that gives the maximum area is 20 feetThe special rectangle is a squareThe area of the rectangle is given as:
[tex]\mathbf{A = 40w - w^2}[/tex]
Differentiate
[tex]\mathbf{A' = 40 - 2w}[/tex]
Set to 0
[tex]\mathbf{40 - 2w = 0}[/tex]
Add 2w to both sides
[tex]\mathbf{ 2w = 40}[/tex]
Divide both sides by 2
[tex]\mathbf{ w = 20}[/tex]
This means that, the width that gives the maximum area is 20 feet
The perimeter of a rectangle is:
[tex]\mathbf{P = 2(l + w)}[/tex]
So, we have:
[tex]\mathbf{80 = 2(l + 20)}[/tex]
Divide both sides by 2
[tex]\mathbf{40 =l + 20}[/tex]
Subtract 20 from both sides
[tex]\mathbf{l = 20}[/tex]
This means that, the length and the width are equal (i.e. 20 ft)
Hence, the special rectangle is a square
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0.5 + 6.38= 6.9 because 0.5 is precise to the tenth digit, so the answer must also be rounded to the nearest tenth.
True or false
Answer:
False
Step-by-step explanation:
0.5 + 6.38= 6.88
In general you'd round your answer to the greatest level of precision used in the question, not the least.
The statement is false. The explanation is given.
What is decimal?Decimals are numbers that have two components, a whole number component and a fractional component, which are separated by a decimal point.
Given:
A phrase: 0.5 + 6.38= 6.9 because 0.5 is precise to the tenth digit, so the answer must also be rounded to the nearest tenth.
0.5 + 6.38 = 6.88
To round the decimals:
Round the prior digit down if the final digit is less than 5. However, you should round the preceding figure up if it is 5 or above.
6.88 = 6.9.
Therefore, the statement is false.
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ANSWER ASAP! Thank you for your help! If you don’t see what it says on the end it says “A brick has a mass of”
Answer:
1.32
Step-by-step explanation:
.6*2.2
4. What is the next step if the data from an investigation do not support the original
hypothesis?
A The data are incorrect and the experiment is run again.
B The hypothesis is revised and another experiment is conducted.
OC The data are revised to support the hypothesis.
D The data are adjusted to match the observations.
Answer:
B: The hypothesis is revised and another experiment is conducted.
Step-by-step explanation:
If several different experiments all reveal that the hypothesis has not been confirmed, a revision of the hypothesis is in order. Perhaps it was the hypothesis all along that needed amendment.
sunscreen is priced at $10.00 per bottle,plus 8% tax. If Tonya purcheses a bottle of sunscreen with a $20.00 bill, then what is her change
Answer:
$9.20.
Step-by-step explanation:
For this question, you would have to figure out how much the total would be to get this answer.
Multiply 10 x .08 and you would get 0.8
Add those together and you would get 10.8.
Next you would subtract 20 - 10.8 and your answer is $9.20.
Feel free to let me know if you need more help. :)
Answer:$9.20
Step-by-step explanation
1.) 8/100 is .08
2.) Multiply 10 by .08 to find how much is 8% of $10. Which is $0.80
3.) The sunscreen costs $10.80. You subtract that amount from $20.
4.) The change would be $9.20
A circular tablecloth has a radius of 2.5 feet. Kyle is sewing a piece of ribbon around the edge of the tablecloth.
If Kyle has exactly enough ribbon, which measurement is closest to the length of the piece of nbbon in teet?
Answers:
A) 7.85 ft
B) 15.7 ft
C) 19.63 ft
D) 31.4 ft
Answer:
the answer is B
Step-by-step explanation:
because c=3.14 x diameter
diameter= 2.5+2.5=5
3.14 x 5 = 15.7ft
which equals B
Answer: 15.7
Step-by-step explanation: hope it helps
Find the relationship between the quantities in the table. Then use the relationship to calculate the missing values in the table. The relationship between the quantities in the table is x equals y. A = B = C =
Answer:
x 9 and 27
Step-by-step explanation:
hope this helps :)
Make a list of at least five words to match the following category.
Animal noises -- like "squeak"
Answer:
Meow
Squeak
bark
Caw
baa
Step-by-step explanation:
Brandon solved the following division problem: Mrs Stokes is taking the fourth
graders to the zoo in small vans. There are 67 total fourth graders that are
attending the field trip. The van can hold 7 students per van. How many vans
does Mrs. Stokes need to rent from the district? When Brandon finished the
division problem, he got the following results: 9 R 4 Which answer below should
Brandon choose?
The answer is 9 with a remainder of 2, he should use the remainder as part of his
answer
The answer is 10 he should round the quotient up by 1 because of the remainder
The answer is 9 he should just ignore the remainder
The answer is 2: he should use the remainder only
Answer:
10, he should round the quotient up by 1 because of the remainder
Step-by-step explanation:
Brandon did all of the math work correctly, but you can't over crowd the bus with 13 people. The 10th bus will not be filled to capacity but it would be enough for the 4 remaining fourth graders.
Find the volume of a right circular cone that has a height of 14.1 m and a base with a
radius of 17.6 m. Round your answer to the nearest tenth of a cubic meter.
Answer:
4573.8
Step-by-step explanation:
Jamie is painting her house. Each room takes 1/2 of a liter of paint.
If Jamie has 3 liters of paint, how many rooms can she paint
20 points for ANSWER.
Answer:
666 liters
Step-by-step explanation:
If each room takes 1/2, then 2 room takes 1 liter. So you would do 2•333=666
Find the selling price.
A store pays $8 for a pool noodle. The markup is 20%.
The selling price is $
Answer:
The selling price is $9.60.
Answer:
the selling price of the pool noodle is $9.60.
Step-by-step explanation:
The selling price of the pool noodle can be calculated by adding the markup to the cost price.
Step 1: Calculate the markup amount. The markup is 20% of the cost price of $8, which is calculated as: 20/100 * $8 = $1.60.
Step 2: Add the markup amount to the cost price to find the selling price. The selling price is $8 + $1.60 = $9.60.
Tim is building a model of a castle with small wooden cubes. So far Tim has constructed part of a security world castle,as shown below. Each wooden cube has a side length of 1/8ft
Based on the model,the length of the wall is ___ft, the width of the walk is 1/2 ft, and the height of the wall is ___. The volume of the portion of security wall that Tum has constructed so far is ___ cu ft.
Answer:
Based on the model,the length of the wall is 9/8 ft, the width of the walk is 1/2 ft, and the height of the wall is 11/8. The volume of the portion of security wall that Tim has constructed so far is 99/128 cu ft.
Step-by-step explanation:
In the picture attached, part of a security world castle is shown.
length: 9 blocks, which is equivalent to 9*(1/8) = 9/8 ft
height: 11 blocks, which is equivalent to 11*(1/8) = 11/8 ft
width: 1/2 ft
Volume: length*height*width = (9/8)*(11/8)*(1/2) = (9 * 11 * 1)/(8 * 8 * 2) = 99/128 cu ft
Based on the model, the length of the wall is 9/8 ft, the width of the walk is 1/2 ft, and the height of the wall is 11/8. The volume of the portion of security wall that Tim has constructed so far is 99/128 cu ft.
Tim is building a model of a castle with small wooden cubes. Each wooden cube has a side length of 1/8 ft. Given the following information, we will solve the problem step by step:
Length of the Wall
Assuming we know the total number of cubes used to form the length of the wall, we can multiply the number of cubes by the side length of each cube (1/8 ft) to obtain the length in feet.
Width of the Wall
We are given that the width of the wall is 1/2 ft.
Height of the Wall
If we assume that the wall height in the model is given in terms of the number of cubes stacked, we can multiply that number by 1/8 ft per cube to determine the total height in feet.
Volume of the Security Wall
To find the volume, we will assume there is a certain number of cubes used for the entire structure. The volume of a cube with side length 1/8 ft is:
Volume of one cube = (1/8 ft)³ = 1/512 cu ftThe total volume of the wall is then the volume of one cube multiplied by the total number of cubes used.
Therefore, to complete the details:
Length of the wall = Number of cubes in length direction [tex]\times[/tex] 1/8 ftWidth of the wall = 1/2 ftHeight of the wall = Number of cubes in height direction [tex]\times[/tex] 1/8 ftVolume of the security wall = Total number of cubes [tex]\times[/tex] 1/512 cu ftEnsure you have the number of cubes to accurately determine the final measures.
the length of a side of an equilateral triangle is 40cm. what is the length of the altitude of the triangle?
20√2 cm
20√3 cm
4√5 cm
6√5 cm
Answer:
20√3 cm
Step-by-step explanation:
Altitude of an equilateral triangle splits it into 2 equal right triangles, it bisects the base and the angle opposite to the base.
Let the altitude be x. Then as per Pythagorean theorem:
x² = 40² - (40/2)²x²= 1600 -400x²= 1200x= √1200x= 20√3 cmCorrect choice is the second one
a) 100 degrees
b) 50 degrees
c) 65 degrees
d) 30 degrees
Answer:
a) 100 degrees
Step-by-step explanation:
EFG + EGD + DGC = 180 since the form a straight line
EGD = 30 since it is a vertical angle to AGB = 30
DGC = 50
Substitute these values in
EFG +30 + 50 = 180
Combine like terms
EFG +80 = 180
Subtract 80 from each side
EFG +80-80 = 180-80
EFG =100
Consider rectangle ABCD with diagonals BD and AC intersecting at E.
Rectangle A B C D has diagonals B D and A C that intersect at the center of the rectangle at point E. Angles B C E is 52 degrees, angle C B E is 52 degrees, angle D E A is 104 degrees, and angle B E A is 76 degrees.
Which is true about the angle relationships in the rectangle? Check all that apply.
AngleBEA and AngleCED are vertical angles and equal 76°.
AngleABE and AngleCBE are complementary angles.
AngleBEC and AngleCED are vertical angles.
AngleBEA and AngleAED are supplementary angles whose sum is 180°.
AngleBEC and AngleAED are adjacent angles.
Answer:
A,B,D
Step-by-step explanation:
"The correct statements about the angle relationships in rectangle ABCD are:
- AngleBEA and AngleCED are vertical angles and equal 76°.
- AngleABE and AngleCBE are complementary angles.
- AngleBEC and AngleCED are vertical angles.
- AngleBEA and AngleAED are supplementary angles whose sum is 180°.
- AngleBEC and AngleAED are adjacent angles.
1. AngleBEA and AngleCED are vertical angles. Vertical angles are the angles opposite each other when two straight lines intersect. Since BD and AC intersect at E, angle BEC and angle AED are vertical angles and therefore equal. Given that angle BEC is 52 degrees, angle AED is also 52 degrees. However, the question states that angle DAE is 104 degrees, which means angle AED is 180 - 104 = 76 degrees (since angle DAE and angle AED are supplementary angles as they form a straight line). Therefore, angle CED is also 76 degrees, not 52 degrees as initially stated. This corrects the inaccuracy in the question.
2. AngleABE and AngleCBE are complementary angles. Complementary angles are two angles whose measures add up to 90 degrees. Since ABCD is a rectangle, angle ABE and angle CBE are right angles (90 degrees). Angle ABE is made up of angles ABE and BEC, and since angle BEC is 52 degrees, angle ABE is 90 - 52 = 38 degrees. Similarly, angle CBE is made up of angles CBE and BEC, so angle CBE is also 38 degrees. Therefore, angles ABE and CBE are complementary as their sum is 90 degrees.
3. AngleBEC and AngleCED are vertical angles. As previously explained, vertical angles are equal, so angle BEC and angle CED are equal, both being 52 degrees.
4. AngleBEA and AngleAED are supplementary angles. Supplementary angles are two angles whose measures add up to 180 degrees. Since angle BEC is 52 degrees and angle BEC and angle BEA are adjacent angles, angle BEA is 180 - 52 = 128 degrees. Angle AED is 76 degrees as previously calculated. Adding angle BEA and angle AED gives us 128 + 76 = 204 degrees, which is incorrect. The correct calculation should be that angle BEA is 76 degrees (as it is vertical to angle CED which is 76 degrees), and angle AED is 104 degrees (as given in the question). Therefore, angle BEA and angle AED are supplementary as their sum is 76 + 104 = 180 degrees.
5. AngleBEC and AngleAED are adjacent angles. Adjacent angles share a common side and a common vertex. In this case, angle BEC and angle AED share side AE and vertex E. This statement is true as they are indeed adjacent angles."
"Rule of law" refers to the
A. official name for the legislative branch of the national government of the united states
B. agencies such as the fbi, police department, or sheriffs department that make sure people obey the law
C. document that details the structure, function, and powers of the government of the united states
D. principle that both those who govern and those. who are governed must obey the law and are subjunctive to the same law
Answer:
I think it is d.
Step-by-step explanation:
Answer:
I'm pretty sure the answers D
Step-by-step explanation:
The perimeter of a certain square is 20 inches. Find the area of the square in square inches.
____ in.2
Answer:
25 in.2
Step-by-step explanation:
Because all sides of a square are equal, and the perimeter is 20 in. We divide 20 by 4. This gives us 5 in. for each side. The area of a square is length times width, so we do 5x5. This means the area of the square is 25 square inches.
Which angles are remote interior angles?
A 1 and 2
B 2 and 3
C 3 and 4
D 1 and 4
Answer:
A)
Step-by-step explanation:
1 and 2 are remote interior angles.
Remote interior angles does not share vertex of the triangle with the exterior angle.
Here 4 is the exterior angle.
Answer:
A) 1 and 2
Step-by-step explanation:
got it right
About 24% of people who get their feet examined are found to have bunions. What is the probability of a podiatrist examining six
people until he finds the first patient who has bunions?
(0.24)
(0.24)*(0.76)
(0.76) (0.24)
(0.76)
1 - (0.24)
Answer:
0.76)5(0.24)1
Step-by-step explanation:
The probability of a podiatrist examining six people until he finds the first patient who has bunions is [tex](0.76)^5[/tex] (0.24).
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
We have,
24% of people who get their feet examined are found to have bunions.
let p= 24%= 0.24
and, q= 1-p = 1-0.24 = 0.76
When he examines 6 people before he sees a patient with an bunions, the event is represented as:
P = ([tex]q^5[/tex]) p
= [tex](0.76)^5[/tex] (0.24)
= 0.2535525376 (0.24)
= 0.060852609024
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Henry knows that the circumference of a circle is 18 pie inches. What is the area of the circle?
O 36 x in 2
O 81x in 2
O 162 x in?
O 324 sin?
Answer:
81x in 2 (B)
Step-by-step explanation:
A = πr^2
Radius = 9
The Radius is 9 because you divide 18 by 2, the equation for Circumference is 2πr.
Answer: 81
Plug 9 into r in the Area equation.
π9^2
81π
The midpoint of a line segment partitions the line segment into a ratio of
The midpoint of a line segment partitions the line segment into a ratio of 1:1, meaning it divides the segment into two equal parts.
Explanation:In mathematics, a midpoint refers to a point that is exactly in the middle of a line segment. The definition of midpoint implies that it divides or partitions a line segment into two equal parts. Therefore, the ratio is 1:1.
Consider the given line segment AB with the midpoint M. If the length of the segment AB is L, then AM = MB = L/2. This shows that the line segment AB is divided into two equal parts by M, thus resulting in a 1:1 ratio.
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The correct answer is 1:1.
The midpoint of a line segment is the point that divides the segment into two equal parts. By definition, these two parts are of the same length, which means that the ratio of their lengths is 1:1. This is because the midpoint is equidistant from both endpoints of the line segment, effectively splitting the segment into two congruent segments.
To illustrate this with an example, let's consider a line segment AB with a midpoint M. The length of segment AM is equal to the length of segment MB. If we denote the length of AM as x and the length of MB as y, we have:
x = y
Expressing this as a ratio, we get:
x/y = 1/1
This ratio represents the division of the line segment by its midpoint, and it shows that the division is equal on both sides of the midpoint, hence the ratio of 1:1.
Over which interval is the graph of f(x) = –x2 + 3x + 8 increasing?
a.(–∞, 1.5)
b.(–∞, 10.25)
c.(1.5, ∞)
d.(10.25, ∞)
Answer:
c
Step-by-step explanation:
cause i said so!
Answer:
The correct answer is A) (-∞ , 1.5)
Step-by-step explanation:
Hope this helps! :)
Convert 163 into a hexadecimal
Answer:
A3
Step-by-step explanation:
Edit for clarification A means 10 and 3 is the remainder so 163/16=10 remainder 3 so the A is 10 and the 3 is the remainder so A3 means 10 remainder 3.
Answer:
A3.
Step-by-step explanation:
163 / 16 until ya get 0.
--> 163 / 16 = 10 with a remainder of 3
--> 10 / 16 = 0 with a remainder of 10
I then looked at a chart to see what this would mean if I was to turn it. It said A3.
Consider Circle Y with radius 4 m and m angle XYZ = 80 degrees
What is the approximate length of minor arc XZ? Round to the nearest tenth of a meter.
a. 3.7 m
b. 2.8 m
c. 5.6 m
d. 11.2 m
PLEASE HURRY!! I HAVE LIMITED TIME!! :)
Answer:
c. 5.6m
Step-by-step explanation:
pi x 8 x 80/360 = 5.58..
round to 1 d.p. = 5.6