Answers
6 x 6 x 6 x 6 x 6 = 7776 different outcomes
Number of outcomes when n dice are rolled = 6^n which is 6 raised to the power n.
So, the number of outcomes when 5 dice are rolled = 6⁵ = 7776
Thus, when 5 dice are rolled there will be 7776 possible outcomes.
So, option A is the correct answer
Related Questions
Explain how you can use a model to find 4x 3/8
Answers
Explain how you can tell when a formula represents a length an area or a volume
Answers
Area and volume are both used to determine the amount of space.
While area is used for two-dimensional shapes, volume is used for three-dimensional shapes.
The difference between the given parameters are:
Length is often represented as the difference between points.Area is represented as the product of two dimensions or the square of a dimensionVolume is represented as the product of three dimensions or the cube of a dimensionFor instance:
[tex]\mathbf{Length = b -a}[/tex]
[tex]\mathbf{Area = ab}[/tex]
[tex]\mathbf{Volume= abc}[/tex]
Read more about lengths, areas and volumes at:
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When no more than 110 units are produced, the cost of producing y units is given by c(x). c(x)equals0.2 x cubed minus 24 x squared plus 1524 x plus 31 comma 272 how many units should be produced in order to have the lowest possible average cost?
Answers
c(x)=0.2x^3-24x^2+1524x+31272
for lowest average cost, we calculate c'(x)=0
thus:
From c(x), we shall have:
c'(x)=0.6x^2-48x+1524
solving for x we get:
x=40+/- 30.6594i
but since we are looking for a definite number of units, we shall do away with the complex part such that we shall remain with:
x=40 units
hence the minimum number of units will be 40 units
A wheel spins at 300 revolutions per minute. What is the angular velocity of the wheel, in radians per second? Round the answer to the nearest hundredth.
Answers
1 revolution = 2π radians.
So, we can write:
Angular velocity = 300 x 2π radians per minute = 600π radians per minute
1 minute = 60 seconds.
So,
Angular velocity = 600π radians per 60 seconds
⇒
Angular velocity = 10π radians per second
Angular velocity = 31.42 radians per second
Thus, rounding of to nearest hundredth, the angular velocity will be 31.42 radians per second.
Answer:
31.42
Step-by-step explanation:
Find the area of the parallelogram with vertices at (−2,3),(−2,3), (6,14),(6,14), (−14,1),(−14,1), and (−6,12).(−6,12).
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What is the area of a figure whose vertices are (-2,1), (3,1), (2,-3), and (-3,-3)?
Answers
Find the area of the shaded regions. Give your answer as a completely simplified exact value in terms of π (no approximations).
Answers
The formula for the area of a sector can be written as follows:
Area = [tex] \frac{1}{2} [/tex][tex]r^{2} [/tex](R)
In the above formula, “r” represents the radius while “R” represents the radian measure of a sector. The radius is given to us in the image above as 10 inches. However, we still need the radian measure of the two sectors. To find this measure, we can use the following conversion:
1 degree = [tex] \frac{pi}{180} [/tex] radians
Because the two sectors have a given measure of 72 degrees, we need to multiply both sides of the above conversion by 72:
72 degrees = [tex] \frac{72pi}{180} [/tex]
Reduce the fraction on the right side of the equation:
72 degrees = [tex] \frac{2pi}{5} [/tex]
We now have the radian measure of both sectors. Now simply insert this and any other known values into the “area of a sector” formula above:
Area = [tex] \frac{1}{2} [/tex][tex]10^{2} [/tex]([tex] \frac{2pi}{5} [/tex])
Simplify the right side of the equation to get the following answer:
Area = 20 pi
We have now proven that the area of one sector is equal to 20 pi.
If, however, you need the combined area of the two identical sectors, simply multiply the proven area by 2 to get a total area of 40 pi.
I hope this helps!
Answer: 40 pi
Step-by-step explanation:
Can someone please help me
Answers
3 : 4 ≠ 5 : 6
PLEASE HELLPPPP!!!!!!!!!!!!
Figure BMHF is rotated how many degrees clockwise?
Answers
https://brainly.com/question/9953496
T-shirts at a clothing store cost $19 each Rory bought several T-shirts at this price and paid $57 how many t-shirts did Rory buy
Answers
Number of t-shirts = $57 ÷ $19 = 3
Answer: 3 t-shirts
what is a factor of 4x^2+36x+72
Answers
[tex]4x^{2}+36x+72=4(x+3)(x+6)[/tex]
write a number sentence to compare 7.17 and 7.170
Answers
7.17 = 7.170
You can place any number of zeros to the very end on the right side (when there is a decimal point) without changing the value of the number.
7.1700000 = 7.17 also
Answer:
They are equal
Step-by-step explanation:
Concerned about graffiti, mayors of nine suburban communities instituted a citizen community watch program. community monthly incidents after monthly incidents before burr oak 2 7 elgin corners 3 2 elm grove 6 2 greenburg 4 3 huntley 5 11 north lyman 3 9 south lyman 3 5 pin oak 5 7 victorville 2 3 click here for the excel data file (a) choose the appropriate hypotheses to see whether the number of graffiti incidents declined. assume μd is the mean difference in graffiti incidents before and after.
Answers
We set the difference in graffiti incidents between before (B) and after (A) as:
d = A - B
If the number of incidents has indeed reduced, then d will be negative.
In order to choose the hypothesis, we need to recall that the null hypothesis H₀ represents the statement that we want to prove wrong, while the alternative hypothesis H₁ represents the statement that we want to prove right.
Therefore, we want μd to be strictly negative (= 0 would mean that the number of incidents stayed constant).
Hence:
H₀ : μd ≥ 0
H₁ : μd < 0
Final answer:
The appropriate hypotheses to determine if graffiti incidents declined involve a null hypothesis where the mean difference is greater than or equal to zero and an alternative hypothesis where the mean difference is less than zero. The μd represents the mean difference in graffiti incidents before and after the institution of the community watch program.
Explanation:
The appropriate hypotheses to test whether the number of graffiti incidents declined in the suburban communities after the institution of a citizen community watch program are as follows:
H0: μd ≥ 0 (Null hypothesis: The mean difference in graffiti incidents before and after is greater than or equal to 0, indicating no decrease.)Ha: μd < 0 (Alternative hypothesis: The mean difference in graffiti incidents before and after is less than 0, indicating a decrease.)Here, μd (mu-sub-d) represents the mean difference between the number of incidents before the program and after the program was implemented. To test these hypotheses, we would typically conduct a paired t-test if the samples are normally distributed or a Wilcoxon signed-rank test if the distribution is not normal.
Assuming μd is the mean difference in graffiti incidents before and after, the test will determine if there is statistically significant evidence to support that the community watch program resulted in a reduction of graffiti incidents.
Tory plans to enter the path at mile marker 1 and hike for 4 miles. Tory is a beginner hiker, so he wants to choose the path that is less steep on average.
Which path should he choose? Why?
Answers
The vertical change from 1 to 5 is considerably less for g(x) than for f(x).
Tory should choose path ...
g(x)
the volume of water in a bowl is given by V=1/3pih^2(60-h), where h is the depth of the water in centimeters. If the depth is increasing at the rate of 3cm/sec when the water is 10 cm deep, how fast is the volume increasing at that instant
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A professor teaching a discrete math course gives a multiple-choice quiz that has ten questions, each with four possible responses: a, b, c,
d. what is the minimum number of students that must be in the professor's class in order to guarantee that at least three answer sheets must be identical? (assume that no answers are left blank.)3
Answers
Ten questions have 3^10 possible distinct answers sheets.
=>
(3^10)+3 will guarantee that at least 3 answer sheets are identical.
Numerically,
(3^10)+3 = 59049 +3 = 59052
The correct minimum number of students required to guarantee that at least three answer sheets must be identical is 5.
To solve this problem, we can use the pigeonhole principle. The pigeonhole principle states that if you have more pigeons than pigeonholes, at least one pigeonhole must contain more than one pigeon.
In this scenario, each question can be thought of as a pigeonhole, with the possible answers (a, b, c, d) as the pigeons. Since there are four possible answers for each question, we have four pigeonholes for each of the ten questions.
Now, let's consider the number of students (pigeons) and the number of unique answer sheets (pigeonholes). We want to find the minimum number of students such that at least three of them have identical answer sheets.
For two students, there are [tex]\(4^{10}\)[/tex] possible combinations of answers for the ten questions. For three students, the number of possible combinations of answers is [tex]\(4^{10} \times 4^{10}\)[/tex]. In general, for [tex]\(n\)[/tex] students, the number of possible combinations is [tex]\(4^{10} \times 4^{10} \times \ldots \times 4^{10}\) (\(n\) times)[/tex].
We need to find the smallest [tex]\(n\)[/tex] such that the number of combinations exceeds the number of ways to distribute the answer sheets without having three identical ones.
The number of ways to distribute the answer sheets without having three identical is given by the sum of the combinations of choosing 1, 2, ...,[tex]\(n-1\)[/tex] students out of [tex]\(n\)[/tex] to have unique answer sheets, and then multiplying by [tex]\(4^{10}\)[/tex] for each unique combination. This is because we are allowing for the possibility that some students have the same answer sheets, but not more than two.
The sum is given by:
[tex]\[ \binom{n}{1} \times 4^{10} + \binom{n}{2} \times 4^{10} + \ldots + \binom{n}{n-1} \times 4^{10} \][/tex]
We want to find the smallest [tex]\(n\)[/tex] such that:
[tex]\[ \binom{n}{1} \times 4^{10} + \binom{n}{2} \times 4^{10} + \ldots + \binom{n}{n-1} \times 4^{10} < 4^{10n} \][/tex]
For [tex]\(n = 4\)[/tex], we have:
[tex]\[ \binom{4}{1} \times 4^{10} + \binom{4}{2} \times 4^{10} + \binom{4}{3} \times 4^{10} = 4 \times 4^{10} + 6 \times 4^{10} + 4 \times 4^{10} = 14 \times 4^{10} \][/tex]
For [tex]\(n = 5\)[/tex], we have:
[tex]\[ \binom{5}{1} \times 4^{10} + \binom{5}{2} \times 4^{10} + \binom{5}{3} \times 4^{10} + \binom{5}{4} \times 4^{10} \][/tex]
[tex]\[ = 5 \times 4^{10} + 10 \times 4^{10} + 10 \times 4^{10} + 5 \times 4^{10} = 30 \times 4^{10} \][/tex]
Now, we compare [tex]\(30 \times 4^{10}\) with \(4^{10 \times 5}\)[/tex]. Since [tex]\(4^{10 \times 5}\)[/tex] is much larger than[tex]\(30 \times 4^{10}\)[/tex], we can see that for [tex]\(n = 5\)[/tex], the number of possible combinations exceeds the number of ways to distribute the answer sheets without having three identical ones.
Therefore, the minimum number of students required to guarantee that at least three answer sheets must be identical is 5.
The area of a rectangular patio is 5 and 5/8 square yards, and its length is 1 and 1/2 yards. What is the patio's width in yards?
Answers
width = area/length
area = 5 5/8 sq yd = 5.625 sq yd
length = 1 1/2 yd = 1.5 yd
width = area/length = (5.625 sq yd)/(1.5 yd) = 3.75 yd
width = 3.75 yd = 3 3/4 yd
We can use the equation to find the area of a rectangle
The equation is l * w = A
l is length
w is width
A is area
Put in the values you know
1 1/2 * w = 5 5/8
Divide both sides by 1 1/2
w = 3 3/4
The answer is 3 3/4 yards
Hope this helps!
Marcus drew a quadrilateral with only 1 pair of parallel sides. Which quadrilateral did Marcus draw?
Answers
Hope this helps! <3
What is the standard form of the equation of a circle given by x^2 + y^2 - 18x + 8y + 5 = 0
Answers
x^2 - 18x + y^2 + 8y = -5
x^2-18x +81 - 81 + y^2 + 8y + 16 - 16 = -5.
Then, (x-9)^2 + (y+4)^2 = -5 + 81 + 16 = 92
Then the desired equation is (x-9)^2 + (y+4)^2 = 92.
Answer:
x-9,y+4,92
Step-by-step explanation:
Sally has x books that weigh 2 pounds each and 8 books that weigh 3 pounds each. the total weight of her books is 62 pounds. which equation below could be used to find how many 2-pound books sally has?
Answers
8 books of 3 lbs weights 8*3=24lbs
All them add up to 62, therefore we can conclude to the equation :
2x+24=62
or we can simplify to
2x=38
or even
x=19
Leslie is a biologist. She is going to randomly select one animal from her lab to study. There are 5 salamanders, 3 crayfish, and 12 minnows in her lab. What is \text{P(salamander}
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The sample space contains three types of animals; 5 salamanders, 3 crayfish, and 12 minnows.
So population of sample space would be, n(S) = Salamanders + Crayfish + Minnows.
n(S) = 5 + 3 + 12 = 20.
She wants to randomly select an animal and check if it is Salamander or not.
population of favourable outcomes would be, n(salamander) = 5.
Now the probability for selecting a salamander would be :-
[tex]P(salamander) = \frac{n(salamander)}{n(S)} \\\\ P(salamander) = \frac{5}{20} \\\\ P(salamander) = \frac{1}{4} \;or\; 0.25 \;or\; 25\%[/tex]
Which best describes a triangle with side lengths of 6 inches 8 inches and 9 inches?
Answers
Use right triangle DCB to find the trig values for angle D.
sinD =
cosD =
tanD =
Answers
cos D= adj./hyp. = 12/37
tan D= opp./ adj. = 35/12
Answer: sinD = 0. 9459
cosD =0. 3243 tanD=2. 917
Step-by-step explanation:
From the figure above;
opposite = 35
adjacent = 12
hypotenuse = 37
sin D = opposite/hypotenuse
sinD = 35/37 = 0. 9459
cosD = adjacent/hypotenuse
= 12/37 = 0. 3243
tanD = adjacent/opposite
= 35/12 = 2. 9167
Circle 1 is centered at (-4, 5) and has a radius of 2 centimeters. Circle 2 is centered at (2, 1) and has a radius of 6 centimeters. What transformations can be applied to circle 1 to prove that the circles are similar? The circles are similar because you can translate circle 1 using the transformation rule ( x, x) and then dilate it using a scale factor of ( ).
Answers
we know that
Figures can be proven similar if one, or more, similarity transformations
(reflections, translations, rotations, dilations) can be found that map one
figure onto another.
In this problem to prove circle 1 and circle 2 are similar, a
translation and a scale factor (from a dilation) will be found to map one
circle onto another.
we have that
Circle 2 is centered at (2, 1) and has a radius of 6 centimeters
step 1
Move the center of the circle 1 onto the center of the circle 2
the transformation has the following rule
(x,y)--------> (x+6,y-4)
so
(-4,5)------> (-4+6,5-4)-----> (2,1)
so
center circle 1 is now equal to center circle 2
The circles are now concentric (they have the same center)
step 2
A dilation is needed to increase the size of circle 1 to coincide with circle 2
scale factor=radius circle 2/radius circle 1-----> 6/2----> 3
radius circle 1 will be=2*scale factor-----> 2*3-----> 6 cm
radius circle 1 is now equal to radius circle
2
A
translation, followed by a dilation will map one circle onto
the other, thus proving that the circles are similar
the answer is
The circles are similar because you can translate circle 1 using the transformation rule ( x+6,y-4) and then dilate it using a scale factor of (3 )Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.
a2 − 2a − 224 = 0
8, –28
16, –14
–16, 14
–8, 28
Answers
a2 - 2a - 224 = 0
Applying the resolver we have:
A = (- b +/- root (b ^ 2 - 4 * a * c)) / (2 * a)
Substituting values we have:
A = (- (- 2) +/- root ((- 2) ^ 2 - 4 * 1 * (- 224))) / (2 * (1))
Rewriting:
A = (2 +/- root (4 + 896)) / (2)
A = (2 +/- root (900)) / (2)
A = (2 +/- 30) / (2)
The roots are:
A1 = (2 + 30) / (2)
A2 = (2 - 30) / (2)
Rewriting:
A1 = 16
A2 = -14
Answer:
16, -14
16, -14
tanθ=sinθ/cosθ
True or False
Answers
A = Adjacent
O = Opposite
H = Hypotenuse
Then,
Sin Ф = O/H
Cos Ф = A/H
Therefore,
(Sin Ф)/Cos Ф) = (O/H)/(A/H) = (O/H)*(H/A) = O/A
Now,
tan Ф = O/A ----
Therefore, it is true that
tan Ф = SinФ/CosФ
sin θ=z/x
cos θ=y/x
sinθ/cosθ=(z/x)/(y/x)=z/y=tan θ
the statement is true.
what is the tenth rule for A(n)=-9+5(n-1)
Answers
A(n)=-9+5(n-1)
the tenth term will be given as follows:
From
A(n)=-9+5(n-1)
substitute n=10 in the equation we get:
A(10)=-9+5(10-1)
A(10)=-9+5(9)
A(10)=-9+45
A(10)=36
Answer: 36
What value of y makes the equation true?
Answers
First, we'll need to solve the equation for y. In order to solve for y, we can use our properties. The property we can use in order to solve for y is the subtraction property. Using this property, we can subtract 2.9 from each side. This gives us the value of y as 8.1. Therefore, the answer is A - 8.1.
Hope this helps!! :)
If there's anything else that I can help you with, please let me know!
Which of the following graphs shows a negative linear relationship with a correlation coefficient, r, relatively close to -1
Answers
The graph that shows a negative linear relationship that has a correlation coefficient, r, that is closer to -1 is: B. graph B.
What is a Negative Linear Relationship Graph?A graph that shows a negative linear relationship has a trendline that slopes downwards from your left to the right.
The closer the data points are to each other along the trendline in a negative linear graph, the closer the correlation coefficient, r, is to -1.
Therefore, the graph that shows a negative linear relationship and has a correlation coefficient, r, that is closer to -1 is: B. graph B.
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hey can you please help me posted picture of question
Answers
y = x³