Step-by-step explanation:
Step 1: Answer part a
He has 3.5 pounds of clay and each bowl is 0.5 pounds of clay. Therefore, 3.5 / 0.5 will give us the amount of bowls he can make.
3.5 / 0.5
7
Answer: He can make 7 bowls
Step 2: Answer part b
I don't really understand what the questions asking about how much clay does he need to make with all of his clay. If you explain what that means I can answer it.
If you meant how much mugs he is able to make → 14
If you meant how much clay he needs to have for each mug → 0.25
Answer & Explanation:
Part A
It gives us 2 numbers to determined how much bowls he can make.
He need 0.5 of clay to make 1 bowl and he has 3.5 pounds of clay.
[tex]3.5[/tex] ÷ [tex]0.5[/tex]
= [tex]7[/tex]
He can make 7 bowls out of the 3.5 pounds of clay that he has.
Part B
This question is very confusing...
He can make 1 mug with 0.25 pounds of clay.
[tex]3.5[/tex] ÷ [tex]0.25[/tex]
= [tex]14[/tex]
He can make 14 mugs if he uses all of his clay.
hope this helps
give brainliest if you please
One angle is twice its supplement increased by 36°. Find the measures of the two supplementary angles.
Answer:
48 and 132 degrees
Step-by-step explanation:
supplement=s
one angle=2s+36
2s+36+s=180
3s+36=180
3s=144
s=48
2(48)+36=132
Therefore, 48 and 132 degrees
I hope this helped and have a good rest of your day!
A bag contains 5 blue balls, 4 red balls, and 3 orange balls. If a ball is picked from the bag at random, what is the probability that it is a blue ball?
Answers have been rounded to the tenths place.
A
0.5
B.
0.4
O C.
0.3
OD. 0.2
Answer:
[tex] p =\frac{Possible}{Total}[/tex]
Where possible represent the possible cases on this case 5 since we have 5 balls and the total is the size of the sample space on this case 12. And replacing we got:
[tex] p =\frac{5}{12}= 0.417[/tex]
And rounded to the tenths place we got:
[tex] p=0.4[/tex]
And the best answer is:
B. 0.4
Step-by-step explanation:
For this case the size of the sampel space is 5+4+3= 12 representing the total of balls used.
We select a random ball from the total and we want to find the probability of selecting a blue ball. And for this case the can use the empirical definition of probability from Laplace given by:
[tex] p =\frac{Possible}{Total}[/tex]
Where possible represent the possible cases on this case 5 since we have 5 balls and the total is the size of the sample space on this case 12. And replacing we got:
[tex] p =\frac{5}{12}= 0.417[/tex]
And rounded to the tenths place we got:
[tex] p=0.4[/tex]
And the best answer is:
B. 0.4
What is the missing number in this sequence: –1, –2, –4, , –16, –32
Answer:-8
Step-by-step explanation: you add -1+ -1, to get -2, then -2+-2, to get -4 and so forth.
The missing term is -8.
The complete sequence is –1, –2, –4, -8, –16, –32.
What is geometric sequence?A unique kind of sequence called a geometric sequence has a constant ratio between every two succeeding terms. This ratio is regarded as one of the geometric sequence's common ratios.
aₙ=a₁(r)ⁿ⁻¹
Given:
–1, –2, –4, ?, –16, –32.
The sequence is a geometric sequence.
So, we will find the common ratio,
r = -2/-1 = 2
The general formula of geometric sequence,
aₙ = a₁(r)ⁿ⁻¹
a₄ = (-1)(2)⁴⁻¹
a₄ = (-1)(8)
a₄ = -8
Therefore, the missing term is -8.
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ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. Show your work OR give an explaination.
Answer:
5x -20
Step-by-step explanation:
p(x) = r(x) - c(x)
= 11x - (6x+20)
Distribute the minus sign
= 11x -6x -20
Combine like terms
= 5x -20
What is the radius of a sphere with a volume of
5044
m
3
,
5044 m
3
, to the nearest tenth of a meter?
Answer:
Radius, r = 10.64 m
Step-by-step explanation:
The formula of a spherical shaped object is given by :
[tex]V=\dfrac{4}{3}\pi r^3[/tex]
r is radius of a sphere
[tex]r=(\dfrac{3V}{4\pi })^{1/3} \\\\r=(\dfrac{3\times 5044}{4\times 3.14 })^{1/3} \\\\r=10.64\ m[/tex]
So, the radius of a sphere is 10.64 m.
The radius of a sphere is multiplied by . What effect does this have on the volume of the sphere? A. The volume of the sphere is multiplied by 1/343. B. The volume of the sphere is multiplied by 1/49. C. The volume of the sphere is multiplied by 1/7 . D. The volume of the sphere is multiplied by 1/21 . E. The effect on the volume of the sphere cannot be determined.
Answer:
Option A. The volume of the sphere is multiplied by 1/343.
Step-by-step explanation:
The volume of a sphere can be obtained by the following formula:
V = 4/3πr^3
Let the initial volume (V1) of the sphere be:
V1 = 4/3πr^3 = (4πr^3)/3
Now, if we multiply the radius by 1/7, then the new volume (V2) of the sphere will be:
V2 = 4/3 x π x (1/7r)^3
V2 = 4/3 x π x 1/343r^3
V2 = (4πr^3)/1029
Now we determine the ratio of V2 : V1 as shown below:
V2/V1 = (4πr^3)/1029 ÷ (4πr^3)/3
V2/V1 = (4πr^3)/1029 × 3/(4πr^3)
V2/V1 = 3/1029
V2/V1 = 1/343
V2 = 1/343 x V1
Therefore, the volume of the sphere is multiplied by 1/343.
the sum of four consecutive even integers is 68. what is twice the smallest among the integers?
Answer:4
Step-by-step explanation:
464565=753
Avoiding an accident while driving can depend on reaction time. Suppose that reaction time, measured from the time the driver first sees the danger until the driver gets his/her foot on the brake pedal, is approximately symmetric and mound-shaped with mean 1.9 seconds and standard deviation 0.12seconds. Use the 68-95-99.7 rule to answer the following questions.What percentage of drivers have a reaction time more than 2.14 seconds?%What percentage of drivers have a reaction time less than 1.78 seconds?%What percentage of drivers have a reaction time less than 2.02 seconds?%
Answer:
2.5% of drivers have a reaction time more than 2.14 seconds
16% of drivers have a reaction time less than 1.78 seconds
84% of drivers have a reaction time less than 2.02 seconds
Step-by-step explanation:
The Empirical Rule(68-95-99.7 rule) states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are above.
In this problem, we have that:
Mean = 1.9s
Standard deviation = 0.12
What percentage of drivers have a reaction time more than 2.14 seconds?
2.14 = 1.9 + 2*0.12
So 2.14 is two standard deviations above the mean.
Of the 50% of the measures above the mean, 95% are within 2 standard deviations of the mean, so, below 2.14. The other 5% is above.
0.05*0.5 = 0.025
2.5% of drivers have a reaction time more than 2.14 seconds
What percentage of drivers have a reaction time less than 1.78 seconds?
1.78 = 1.9 - 0.12
So 1.78 is one standard deviation below the mean.
Of the 50% of the measures that are below the mean, 68% are within one standard deviation of the mean, that is, greater than 1.78.
100 - 68 = 32
0.32*50 = 0.16
16% of drivers have a reaction time less than 1.78 seconds
What percentage of drivers have a reaction time less than 2.02 seconds?
2.02 = 1.9 + 0.12
So 2.02 is one standard deviation above the mean.
Of the measures that are below the mean, all are below 2.02.
Of those that are above, 68% are below 2.02.
0.5 + 0.68*0.5 = 0.84
84% of drivers have a reaction time less than 2.02 seconds
The percentage of drivers have a reaction is :
-2.5% of drivers have a reaction time more than 2.14 seconds
-16% of drivers have a reaction time less than 1.78 seconds
-84% of drivers have a reaction time less than 2.02 seconds
"68-95-99.7 rule"Answer 1:
The percentage of drivers have a reaction time more than 2.14 seconds is :2.14 = 1.9 + 2*0.12
So 2.14 is two standard deviations above the mean.Of the 50% of the measures above the mean, 95% are within 2 standard deviations of the mean, so, below 2.14. The other 5% is above.0.05*0.5 = 0.0252.5% of drivers have a reaction time more than 2.14 seconds
Answer 2:
The percentage of drivers have a reaction time less than 1.78 seconds is :1.78 = 1.9 - 0.12
So, 1.78 is one standard deviation below the mean.Of the 50% of the measures that are below the mean, 68% are within one standard deviation of the mean, that is, greater than 1.78.100 - 68 = 320.32*50 = 0.1616% of drivers have a reaction time less than 1.78 seconds.
Answer 3:
The percentage of drivers have a reaction time less than 2.02 seconds :2.02 = 1.9 + 0.12
So, 2.02 is one standard deviation above the mean.Of the measures that are below the mean, all are below 2.02.Of those that are above, 68% are below 2.02.0.5 + 0.68*0.5 = 0.8484% of drivers have a reaction time less than 2.02 seconds
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Help me with this and give the correct answer and get 25 points
Answer:
x =6.0
The base is 6x = 35.8
The side is 3x = 17.9
Step-by-step explanation:
We can use the pythagorean theorem
a^2 + b^2 = c^2
(6x)^2 +(3x)^2 = 40^2
36x^2 + 9x^2 = 1600
Combine like terms
45x^2 = 1600
Divide each side by 45
45x^2 /45 =1600/45
x^2 =35.555555555
Take the square root of each side
sqrt(x^2) = sqrt(35.555555555)
x =5.96284794 = 6.0
The base is 6x = 6*5.9628479 =35.77708 = 35.8
The side is 3x = 3*5.9628479 =17.88854382= 17.9
Answer:
x = 6.0
3x = 17.9
6x = 35.8
Step-by-step explanation:
Using pythagoras theorem
40² = (3x)² + (6x)²
1600 = 9x² + 36x²
1600 = 45x²
x² = 320/9
x = 5.96284794
3x = 17.88854382
6x = 35.77708764
what is the volume of a cylinder with a diameter of 8 name m and a height of 5.5
To begin, you must plug all the values you have into a formula, and also putting them in the right form.
The formula for the volume of a cylinder is: πr²h
FINDING RADIUS: With this in mind, now we know that, our diameter must be converted to a radius. To do this, you divide your diameter by two. This gives you, 4 as your radius.
FINDING HEIGHT: In the question you sent, you can tell they've given you, your height, so all you need to do is plug it into the equation.
PLUGGING IT IN:
Your pi, stays the same when using a calculator, just press your pi symbol depending on the calculator you are using. Your radius is 4, therefore it wants you to square it, which is 4x4, which equals 16. Next, you want to multiply it by the height, so just multiply it with your height, 5.5
YOUR ANSWER:
276.46m
Suppose that a college student is taking three courses: a two-credit course, a three-credit course, and a four-credit course. The expected grade in the two-credit course is 3.5, while the expected grade in the three- and four-credit courses is 3.0. What is the expected overall grade point average for the semester?
Answer:
The overall expected grade point average for the semester is 3.16/3.1 or 3.2 if you round it up.
Step-by-step explanation:
To get the average, you need to add up all the numbers then divide the sum by how many numbers you added.
3.5 + 3.0 + 3.0 = 9.5
9.5 / 3 = 3.16
Given Information:
expected grade in two-credit course = 3.5
expected grade in three-credit course = 3.0
expected grade in four-credit course = 3.0
Required Information:
Expected overall grade point average = ?
Answer:
The expected overall grade point average of this college student is 3.11
Step-by-step explanation:
The overall expected grade point average is given by
E(X) = Sum of grades/Total number of credit hours
Sum of grades = ∑ weightage*expected grades
Sum of grades = 2*3.50 + 3*3.0 + 4*3.0 = 28
Total number of credit hours = 2 + 3 + 4 = 9
E(X) = Sum of grades/Total number of credit hours
E(X) = 28/9
E(X) = 3.11
Therefore, the expected overall grade point average of this college student is 3.11 .
Ruth has 12 feet of ribbon.
She uses 7 feet of it for a craft project and gives 28 inches of it to her sister.
How many inches of ribbon does she have left?
Enter your answer in the box.
Answer:
See I don't know the answer but I did another one like this if it doesn't help you can report it no problem
Step-by-step explanation:
There are 2 different ways you can solve this problem and you'll get the same answer.
To help you visualize what you have to do, it might be easiest to translate your problem to a unit that easier to use.
Since you only have a ribbon 5 feet long, but you must cut it into 6 pieces, you know it won't even be 1 foot long.
One way to solve the problem would be to translate your 5-foot ribbon into a ribbon divided into inches.
1 foot = 12 inches
To find out how many inches long your ribbon is, you'll need to multiply the number of feet by 12.
Once you know that, then you can more easily divide it by 6. This will tell you how many inches each ribbon is.
Careful! the answer is to be put into feet so once you know how many inches long the ribbon is, you must then divide by 12 to get the correct answer in feet. Don't forget to round to the nearest tenth.
Another way to solve the problem is to simply divide the 5 feet by the number 6 and then round your number to the nearest tenth. It may be harder to visualize the answer this way, but you will get the same answer as if you translated your ribbon into inches and then divided by 12.
Good luck! I hope this helps!
32 inches of ribbon does she have left.
What is Unit Conversion?Unit conversion is a multi-step process that includes rounding, selecting the appropriate number of significant digits, and multiplying or dividing by a numerical factor.
We have,
Total length of Ribbon = 12 feet
After using 7 feet the remaining left
= 12 - 7
= 5 feet
Now, She gave 28 inches to her sister then the ribbon left
= 5 feet - 28 inches
= 60 inches - 28 inches
= 32 inches
= 2.66667 feet
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Fifthy-four times three
Answer:
162
Step-by-step explanation:
54 * 3 = 162
hope it's helpful
Answer:
162
Step-by-step explanation:
54 x 3 = 162
54+ 54+ 54= 162
Seth has a triangle that measures 20 inches by 20 inches
by 35 inches. What type of triangle does he have?
Answer:
Isosceles
Step-by-step explanation:
An isosceles triangle is a triangle in which the length of at least two sides are same.
The triangle which Seth has two sides of same length that is 20 inches.
Third side is different.
Hence. the triangle which Seth has is isosceles.
The difference of two supplementary angles is 24 degrees. Find the measure of the angles.
Answer:
102, 78
Step-by-step explanation:
angle 1= x
angle 2= x-24
x+x-24=180
x=102
x-24=78
102+78=180
The measure of the angles are 102 and 78 degrees
Let one of the angles be xLet the other angle be y.If the difference of two supplementary angles is 24 degrees, then;
x - y = 24
y = x - 24
Taking the sum of the angles and equating to 180 degrees since they are supplementary
x + y = 180
x + x - 24 = 180
2x = 180 + 24
2x = 204
x = 102
Since y = 180 - x
y = 180 - 102
y = 78 degrees
Hence the measure of the angles are 102 and 78 degrees
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Tristen is building 3 trophies using Legos. He needs 324 total Legos. Tristen uses 220 Legos for the largest trophy and 135 Legos for the smallest trophy. How many Legos will he use to build the final trophy
Answer:
166 legos are required
Step-by-step explanation:
In this case, let's analyze the data. We need 3 trophies, using at most 324 legos in total. The big trophy requires 220 legos, the smallest requires 135, so we need to know how much will be used in the medium trophy. This number should be 135 < X < 220
Now, if we know that the total legos to be used are 324, then, we can make a difference and sum for all the legos, and then, calculate the number of legos used.
Total legos = A + B + C
324 = 220 + 135 + C
324 = 355 + C
C = -31
This means that there is difference of 31 legos between the smallest and biggest trophy, therefore, this difference should be used and added to the smallest trophy and see how much Tristen use in the final trophy:
135 + 31
= 166 legos
So we need to use 166 legos to build the final trophy.
Answer:
he already used 355 so 166
Step-by-step explanation:
Indicate the general rule for this sequence. Find a1 and the common difference. a4 = 18 a7 = 9
Answer:
[tex]a_{n} = 27 - 3(n-1)[/tex]
Step-by-step explanation:
Arithmetic sequences concepts:
The general rule of an arithmetic sequence is the following:[tex]a_{n+1} = a_{n} + d[/tex]
In which d is the common diference between each term.
We can expand the general equation to find the nth term from the first, by the following equation:
[tex]a_{n} = a_{1} + (n-1)*d[/tex]
And also:
[tex]a_{n} = a_{m} + (n-m)*d[/tex]
In this question:
[tex]a_{4} = 18, a_{7} = 9[/tex]
Finding the common ratio:
[tex]a_{n} = a_{m} + (n-m)*d[/tex]
[tex]a_{7} = a_{4} + (7-4)*d[/tex]
[tex]9 = 18 + 3d[/tex]
[tex]3d = -9[/tex]
[tex]d = \frac{-9}{3}[/tex]
[tex]d = -3[/tex]
Finding the first term:
[tex]a_{4} = a_{1} + (4-1)*d[/tex]
[tex]18 = a_{1} + 3*(-3)[/tex]
[tex]a_{1} = 27[/tex]
General rule:
[tex]a_{n} = a_{1} + (n-1)*d[/tex]
[tex]a_{n} = 27 - 3(n-1)[/tex]
Find the midpoint of the line segment with end coordinates of: ( 0 , 2 ) and ( 8 , 8 )
Answer:
(4,5)
Step-by-step explanation:
To find the x coordinates of the midpoint, add the x coordinates together and divide by 2
(x1+x2)/2 = (0+8)/2 = 8/2 = 4
To find the y coordinates of the midpoint, add the y coordinates together and divide by 2
(y1+y2)/2 = (2+8)/2 = 10/2 = 5
The midpoint is (4,5)
Answer:
(4,5)
Step-by-step explanation:
Midpoint: (0+8)/2, (2+8)/2
8/2, 10/2
4,5
Find the mode of the data. Please :,(
Answer:
The mode is gymnastics
Step-by-step explanation:
The mode of a data set is the number that occurs most frequently in the set. To easily find the mode, put the numbers in order from least to greatest and count how many times each number occurs. The number that occurs the most is the mode!
hope his helps!!!!!!!!!!!!
Find the standard form equation
of the Hyperbola -2y-82+9x^2=y^2
Answer:
x²/9 − (y + 1)²/81 = 1
Step-by-step explanation:
-2y − 82 + 9x² = y²
9x² = y² + 2y + 82
9x² = y² + 2y + 1 + 81
9x² = (y + 1)² + 81
9x² − (y + 1)² = 81
x²/9 − (y + 1)²/81 = 1
What are the odds of winning a game, if the probability of winning the game is 3/11 ?
Step-by-step explanation:
We can express 3/11 as odds by saying "3 in 11". Therefore, you have a 3 in 11 chance of winning. Hope this helps!
the hiking club plans to go camping In a state park where the probability of rain on any given day is 0.7. which expression can be used to find the probability that it will rain on exactly 3 of the seven days they are there
Answer:
[tex]P(X = 3) = C_{7,3}.(0.7)^{3}.(0.3)^{4} = 0.0972[/tex]
Step-by-step explanation:
For each day there are only two possible outcomes. Either it rains, or it does not. The probability of rain on a day is independent of any other day. So we use the binomial probability distribution 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.
In a state park where the probability of rain on any given day is 0.7.
This means that [tex]p = 0.7[/tex]
Which expression can be used to find the probability that it will rain on exactly 3 of the seven days they are there
We have to find [tex]P(X = 3)[/tex] when [tex]n = 7[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{7,3}.(0.7)^{3}.(0.3)^{4} = 0.0972[/tex]
How many quarts of peanut oil worth 19 cents a quart must be mixed with 100 quarts worth 25 cents a quart to produce a mixture which will be worth 24 cents a quart?
Answer: 20 quarts of peanut oil worth 19 cents a quart must be mixed.
Step-by-step explanation:
Let x represent the number of quarts of peanut oil worth 19 cents a quart that would be in the mixture.
The total number of quarts in the mixture would be x + 100
The cost of the x quarts would be x × 19 = 19x cents
The cost of 100 quarts of the other peanut oil would be 25 × 100 = 2500 cents
The cost of the mixture would be
24(x + 100) = 24x + 2400
Therefore, the equation would be
19x + 2500 = 24x + 2400
24x - 19x = 2500 - 2400
5x = 100
x = 100/5
x = 20
Answer:
20 quarts
Step-by-step explanation:
Tom plants 3 seeds.
The probability that a seed will germinate is 4/5.
A) Calculate the probability that all 3 seeds will germinate.
B) Calculate the probability that at least one of the seeds will germinate.
Answer:
A. 64/125
B. 124/125.
Step-by-step explanation:
A). As the events ( germinate or not germinate) are independent we multiply the probabilities.
Prob(All seeds germinate) = 4/5*4/5*4/5 = 64/125.
B). Probability of at least one germinating = 1 - probability that none germinate
Probability of 1 seed not germinating = 1 -45 = 1/5.
So Prob(at least one germinating)
= 1 - (1/5 * 1/5 * 1/5)
= 1 - 1/125
= 124/125.
The probability that all 3 seeds will germinate is 64/125 and the probability that at least one of the seeds will germinate is 124/125.
What is probability?The probability of an event occurring is defined by probability.
Probability is also called chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.
(A)
The probability of all seeds will germinate will be the product of individual probability since all events are independent.
4/5 × 4/5 × 4/5 = 64/125.
B)
Probability of at least one germinating = 1 - the probability that none germinate
The probability of 1 seed not germinating will be given as,
1 -4/5 = 1/5
Thus, the probability of all three seeds not germinating = 1/5 × 1/5 × 1/5
Thus, the probability that at least 1 of the seeds will germinate.
⇒ 1 - (1/5 × 1/5 × 1/5)
⇒ 1 - 1/125
⇒ 124/125
Hence "The probability that all 3 seeds will germinate is 64/125 and the probability that at least one of the seeds will germinate is 124/125".
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Kim's softball team was playing in the championship game. When there were 4 innings left, the team was losing by a score of 17 to 6 points. In the last 4 innings, her team scored the same number of points per inning, and the other team did not score any more points. Kim's team won with the most points.
Find the minimum whole number of points per inning Kim's team could have scored.
Answer: I think the answer is 3.
Step-by-step explanation:
Kim's team scored the same number of innings to win the game and Kim's team already had 6 points so four times a number has to be greater than 17.
4* 3 + 6= 18
which means the minimum number can't be less than three so they may have scored three or more points in each of the four innings that was left.
Two men start at the same place walk rate of 5 km / hr and 5.6 km / hr respectively. What time will they take to be 3 km apart, the same direction as they walk?
A ) 3hrs B ) 4hrs C ) 5hrs D ) 6hrs
Answer:
5 hours
Step-by-step explanation:
5.6 all you have to use is .6 times 5hours to make 3kmapart
A fish bowl contains blue, green and red plastic fish. When a fish is picked out at random, the probability of it being blue is 0.7 and the probability of it being green is 0.2. A prize is given if a red fish is picked out. What is the probability of Matt picking a red fish? (Give your answer as a decimal.) There are 60 fish in the fish bowl. How many of the fish are red?
Answer:
0.1 probability of Matt picking a red fish
6 of the fish are red.
Step-by-step explanation:
We have these following probabilities:
70% = 0.7 probability that the fish is blue.
20% = 0.2 probability that the fish is green.
p probability that the fish is red.
The sum of all these probabilities is 100% = 1. So
0.7 + 0.2 + p = 1.
p = 0.1
0.1 probability of Matt picking a red fish
There are 60 fish in the fish bowl. How many of the fish are red?
n trials with p probability of sucess. The expected value is
[tex]E(X) = np[/tex]
Here we have [tex]n = 60, p = 0.1[/tex]. So
[tex]E(X) = np = 60*0.1 = 6[/tex]
6 of the fish are red.
The probability of Matt at the time of picking a red fish is 0.1.
And, The number of fish that should be red is 6.
Calculation of the probability:Since
There is a 70% probability when the fish is blue
And, 20% probability when the fish is green.
Now
Here we assume p be the probability in the case when the fish is red.
So,
Here the sum of probabilities should be 100% i.e. equal to 1.
Now
The following calculation is to be done
0.7 + 0.2 + p = 1
0.9 + p = 1
So,
p = 0.1
Now for the red one it should be
= 60 (0.1)
= 6
Hence, The probability of Matt at the time of picking a red fish is 0.1.
And, The number of fish that should be red is 6.
Learn more about probability here: https://brainly.com/question/10695144
find all local maximum and minimum points by the second derivative test when possible y=x^4-2×^2+3
Answer:
y = x^4 - 2x^2 + 3
y' = 4x^3 - 4x
y'' = 12x^2 - 4
To find local minimum and local maximum, we find solution of y' = 0
=> 4x^3 - 4x = 0
<=>4x(x - 1)(x + 1) = 0
<=> x = 0,
substitute into y => y(0) = 0 - 0 + 3 = 3 => A(0, 3)
substitute into y'' => y''(0) = 0 - 4 = -4 < 0 => A(0, 3) is a maximal
<=> x = 1,
substitute into y => y(1) = 1 - 2 + 3 = 2 => B(1, 2)
substitute into y'' => y''(1) = 12 - 4 = 8 > 0 => B(1, 2) is a minimal
<=> x = -1,
substitute into y => y(-1) = 1 - 2 + 3 = 2 => C(-1, 2)
substitute into y'' => y''(-1) = 12 - 4 = 8 > 0 => C(-1, 2) is a minimal
Hope this helps!
:)
Find the length of arc AB.
120
10
Step-by-step explanation:
the length s of the arc AC is given as :
s = r. 0
where
r = 10 is radius
0 = 90°
= π/2 rad is angle
s = 10. π/2
= 5π
= 5.3.14
= 15.7 ~ 16
the drama club is holding auditions for 5 different parts in a one-act play. if 9 people audition, how many ways can the roles be assigned?
Answer:
The roles can be assigned in 15120 ways.
Step-by-step explanation:
The parts, which means that the order in which the people are selected is important. So we use the permutations formula to solve this question.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this question:
5 people chosen from a set of 9. So
[tex]P_{(9,5)} = \frac{9!}{(9-5)!} = 15120[/tex]
The roles can be assigned in 15120 ways.