The probability of getting exactly 9 of them major in STEM is 0.139 or 13.9%.
The probability of getting at most 11 of them major in STEM is approximately 0.898 or 89.8%.
The probability of getting at least 11 of them major in STEM is approximately 0.318 or 31.8%.
a. Exactly 9 of them major in STEM.
In this case, the probability of success (a student majoring in STEM) is 0.27, and the number of trials is 35. The probability of exactly 9 students majoring in STEM is then given by the formula:
P(X = 9) = (35 choose 9) x (0.27)⁹ x (0.73)²⁶
where (35 choose 9) is the number of ways to choose 9 students out of 35, and (0.27)⁹ x (0.73)²⁶ is the probability of 9 successes and 26 failures. Evaluating this expression gives a probability of approximately 0.139 or 13.9%.
b. At most 11 of them major in STEM.
To calculate the probability that at most 11 students out of 35 major in STEM, we can use the cumulative binomial probability distribution. This distribution calculates the probability of at most X successes, where X is any number from 0 to the total number of trials.
The probability of at most 11 students majoring in STEM can be calculated as follows:
P(X <= 11) = P(X = 0) + P(X = 1) + ... + P(X = 11) = 0.898 or 89.8%.
c. At least 11 of them major in STEM.
The probability of less than 11 students majoring in STEM can be calculated using the cumulative binomial probability distribution, as in part (b). Specifically:
P(X < 11) = P(X = 0) + P(X = 1) + ... + P(X = 10)
Subtracting this probability from 1 gives the probability of at least 11 students majoring in STEM:
P(X >= 11) = 1 - P(X < 11) = 31.8%
Again, we can use the binomial distribution formula from part (a), or a binomial probability calculator or statistical software package to calculate this probability.
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what will be the answer
1) Using the Law of Syllogism, we can combine statement 1 and statement 3 to conclude that Sally weighs more than Jill's car:
If something weighs more than 2000 pounds, then it weighs more than Jill’s car.
Sally weighs more than 2000 pounds.
Therefore, Sally weighs more than Jill's car.
2) Using the Law of Detachment, we can apply statement 2 to our conclusion from the Law of Syllogism to conclude that Sally is too heavy for the bridge:
If something weighs more than Jill’s car, then it is too heavy for the bridge.
Sally weighs more than Jill's car.
Therefore, Sally is too heavy for the bridge.
What is the Law of Syllogism and the Law of Detachment?The Law of Syllogism opines that if two conditional statements have the same terms, then we can combine them to form a conclusion.
The Law of Detachment states that if a conditional statement is true and its hypothesis is true, then its conclusion is also true.
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please help me what to write in the boxes/answers
Answer:
There are no boxes bro so how can I answer you . I gonna get better to see your boxes but I can't see i think there is a attachment you forget to take with quest .Because this quest is not looking like Mathematics it's like English Grammar.If you didn't like my answer you will say anything you want . But in my decision you my bestfriend. I help others to give answers so I am trying my best.
-Thank You By MrIshaan
Select the correct sentences in the passage. Which statements are true? Any two squares are either similar or congruent. If two lines are parallel, they never intersect. If all the angles of a polygon are congruent, then it is a square. The intersection of two lines always forms 4 congruent angles. A line can be drawn through any two distinct points.
The correct sentences in the passage are option A, option B, and option E.
Any two squares are either similar or congruent. If two lines are parallel, they never intersect.A line can be drawn through any two distinct points.Let's check all the options, then we have
Any two squares are either similar or congruent. The statement is true.
If two lines are parallel, they never intersect. The statement is true.
If all the angles of a polygon are congruent, then it is a square. The statement is false because a regular polygon has an equal angle but it may be a pentagon, hexagon, etc.
The intersection of two lines always forms 4 congruent angles. The statement is false because opposite angles are the same. But if adjacent angles become the same, then the statement will be true.
A line can be drawn through any two distinct points. The statement is true.
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5. Lakita's test scores are 87, 96, 81, and 89.
What score does she need on the last test in
order to average 90 on her tests?
[5]
Answer: 97
Step-by-step explanation:
Average: All the numbers added divided by the number of numbers
Start adding the smallest grade in her notes: 87+96+81+89+81= 434/5= 86.8
Keep adding 1 to the last grade until you find a number that gives us an average of 90.
87+96+81+89+97+ 450
Then divide it by the amount of grades
450/5= 90
Which distribution is positively skewed?
O A.
OB.
O C.
ח
0 2
4
8 10
5
H
14
HHHH
24
6
8 10 12 14 16 18 20 22 24 26 28 30
The distribution that is positively skewed would be the Box plot in Option C.
What does a positive skew mean ?When discussing distributions, a positive skew refers to the tail being lengthier on the right side as opposed to the left. As such, more extreme values are located on the right-hand portion of said distribution.
To put it another way, there is a predominance of data clustering toward the left with only a handful of instances where extreme values are found further along the right-hand scale. This scenario would prompt an observer to note how the mean outstrips the median.
The box plot in option C has most of the data towards the left side which is the positive side so this is positively skewed.
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Robert has a pond in his backyard. How much land does the pond take up? if he were to put a fence around the pond, how much fencing would he need?
The requried amount of fencing needed t cover the pond in this backyard is 319.36 meters.
A figure of Robert's backyard has been shown, we have to determine the perimeter of his backyard,
The perimeter of backyard = 2L + 2[πw/2]
The perimeter of backyard = 2*78 + 2[π*52/2]
The perimeter of the backyard = 319.36 meters
Thus, the requried amount of fencing needed t cover the pond in this backyard is 319.36 meters.
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In ADEF, what is the length of segment DF?
F
60°
E
D
45
The calculated value of the length of segment DF is 51.96 units
Calculating the length of segment DF?From the question, we have the following parameters that can be used in our computation:
The right triangle
The length of segment DF is then calculated as
sin(60) = DE/DF
Substitute the known values in the above equation, so, we have the following representation
sin(60) = 45/DF
So, we have
DF = 45/sin(60)
Evaluate the quotient
DF = 51.96
Hence, the segment DF is 51.96 units
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Diagram NOT accurately drawn The radius of this circle is 8 cm. Work out the circumference of the circle. Give your answer correct to 2 decimal places. 8 cm (Total 2 ma
Step-by-step explanation:
If radius is 8cm then diameter = 16 cm
circumference of a circle = pi * d = pi * 16 cm = ~ 50.27 cm
HELPPPPPPPPPPP!!
The Jones family was one of the first to come to the U.S. They had 6 children. Assuming that the probability of a child being a girl is .5, find the probability that the Jones family had:
at least 4 girls?
at most 3 girls?
The probability that the Jones family had at least 4 girls is 0.5625 and the probability that the Jones family had at most 3 girls is 0.65625.
We can use the binomial probability formula to solve this problem. Let X be the number of girls in the Jones family, then X follows a binomial distribution with parameters n = 6 and p = 0.5.
The probability of having k girls in a family of 6 children is given by:
P(X = k) = (6 choose k) * [tex]0.5^{k}[/tex] * [tex]0.5^{6-k}[/tex]
where (6 choose k) is the binomial coefficient.
To find the probability of having at least 4 girls, we need to calculate the probability of having 4, 5, or 6 girls and add them up:
P(X >= 4) = P(X = 4) + P(X = 5) + P(X = 6)
= (6 choose 4) * [tex]0.5^{4}[/tex] * [tex]0.5^{2}[/tex] + (6 choose 5) * [tex]0.5^{0.5}[/tex] * [tex]0.5^{1}[/tex] + (6 choose 6) * [tex]0.5^{6}[/tex] * [tex]0.5^{0}[/tex]
= 0.234375 + 0.3125 + 0.015625
= 0.5625
Therefore, the probability that the Jones family had at least 4 girls is 0.5625 or 56.25%.
To find the probability of having at most 3 girls, we need to calculate the probability of having 0, 1, 2, or 3 girls and add them up:
P(X <= 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
= (6 choose 0) * [tex]0.5^{0}[/tex] * [tex]0.5^{6}[/tex] + (6 choose 1) * [tex]0.5^{1}[/tex] * [tex]0.5^{5}[/tex] + (6 choose 2) * [tex]0.5^{2}[/tex] * [tex]0.5^{4}[/tex] + (6 choose 3) * [tex]0.5^{3}[/tex] * [tex]0.5^{3}[/tex]
= 0.015625 + 0.09375 + 0.234375 + 0.3125
= 0.65625
Therefore, the probability that the Jones family had at most 3 girls is 0.65625 or 65.625%.
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A student ran a distance of 3 1/2 miles each day for five days the student ran a distance of 4 1/4 miles each day for the next five days what was the total distance in miles the student ran darrion is five days
Darrion ran a total distance of 38 3/4 miles in 10 days.
We have,
To find the total distance Darrion ran in 10 days, we need to add up the distance he ran in the first five days and the distance he ran in the next five days.
Distance ran in the first five days
= 3 1/2 miles per day x 5 days
= 17 1/2 miles
Distance ran in the next five days
= 4 1/4 miles per day x 5 days
= 21(1/4) miles
Total distance Darrion ran in 10 days
= Distance ran in the first five days + Distance ran in the next five days
= 17 1/2 miles + 21 1/4 miles
= 38 3/4 miles
Therefore,
Darrion ran a total distance of 38 3/4 miles in 10 days.
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A normally-distributed population has a mean μ = 32 and a standard deviation σ = 7. For a set of samples of size 8 taken from this population, about 99.7% of the means will be in what interval?
The standard error of the mean δ for a sample of size n is calculated as:
δ = σ / √(n)
where σ is the population standard deviation and n is the sample size.
For a sample of size 8 taken from a normally-distributed population with a mean of 32 and a standard deviation of 7, the δ is:
δ = 7 / √(8) ≈ 2.475
The 99.7% confidence interval for the sample mean is given by:
x ± 3 Substituting the values, we get:
32 ± 3(2.475)
where x is the sample mean.
Substituting the values, we get:
32 ± 3(2.475)
which simplifies to:
[24.575, 39.425]
Therefore, about 99.7% of the sample means taken from this population will fall within the interval [24.575, 39.425].
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Find the area of each figure. Round to the nearest hundredth where necessary.
Answer:
28(17) + π(7^2)
= 476 + 49π square meters
= 629.94 square meters
A manufacturing machine has a 2% defect rate.
If 7 items are chosen at random, what is the probability that at least one will have a defect?
Answer:7.02
Step-by-step explanation: cause im right
1. If AACB AEDF, what is the measure of ZEFD.
Answer:
Step-by-step explanation:
110
The pair of values below is from a direct variation. Find the missing value.
(3,8),(18,y)
y= ?
Answer:
the missing value is y = 48.
Step-by-step explanation:
In a direct variation, the ratio of the two variables remains constant. We can use this fact to find the missing value y:
y / 18 = 8 / 3
To solve for y, we can cross-multiply:
y = 18 * 8 / 3
y = 48
Therefore, the missing value is y = 48.
someone please help me
The linear equations and the values of the variables of the equations are;
(-2, 4)(0, 3)x = 1/3, y = 0x = 1. y = 5x = -2, y = -2x = 10, y = -3x = 8 GB, y = 88, B. Going with Company B is not a good ideax = 14, y = 42Cost of a shampoo = (147 - b·y)/x, cost of a conditioner = (147 - a·x)/yA linear equation is an equation that can be presented as; y = mx + c, where m is the slope and c is the y-intercept.
1. Please find attached, the graph of the equations y = 2x and y = 3x + 2, created with MS Excel, showing the solution point (-2, 4)
The solution is x = -2, y = 4
2. Please find attached, the graph of the equations y = 2x and y = 3x + 2, created with MS Excel, showing the solution point (0, 3)
The solution is x = 0, y = 3
3. The equations are solved using substitution as follows;
y = 2 - 6·x
9·x + 2·y = 3
Therefore;
9·x + 2×(2 - 6·x) = 3
4 - 3·x = 3
3·x = 4 - 3 = 1
x = 1/3
y = 2 - 6·x
y = 2 - 6 × 1/3 = 0
y = 0
4. 8·x + 7·y = 43
2·x + y = 7
Therefore;
y = 7 - 2·x
8·x + 7·y = 43
8·x + 7 × (7 - 2·x) = 43
49 - 6·x = 43
6·x = 49 - 43 = 6
x = 6/6 = 1
x = 1
y = 7 - 2·x
y = 7 - 2 × 1 = 5
y = 5
5. y = 8 + 5·x
Therefore where 7·x + 9·y = -32, we get;
7·x + 9 × ( 8 + 5·x) = -32
52·x + 72 = -32
52·x = -32 - 72 = -104
x = -104/52 = -2
x = -2
y = 8 + 5·x
y = 8 + 5 × (-2) = -2
y = -2
6. x = 4 - 2·y
x = 1 - 3·y
Therefore; 4 - 2·y = 1 - 3·y
3·y - 2·y = 1 - 4 = -3
y = -3
x = 1 - 3·y
x = 1 - 3 × (-3) = 10
x = 10
7. The cost for Company is C = 5·x + 48
The cost for Company 2 is C = 11·x
Therefore; 5·x + 48 = 11·x
11·x - 5·x = 48
6·x = 48
x = 48/6 = 8
The amount of data in GB at which the cost of both options are the same is 8 GB
y = 11 × 8 = 88
B. The amount of data at which the cost of both options are the same indicates that when using a small data amount, the cost of Company 2 is much more affordable, however, after 8 GB, the cost of using Company 1 becomes more affordable, hence going with Company 2 is not a good idea
8. Let x represent the number of students who can ride in a van and let y represent the number of students who can right in a bus, we get;
5·x + 3·y = 196
x + 6·y = 266
x = 266 - 6·y
Therefore;
5·x + 3·y = 196
5 × (266 - 6·y) + 3·y = 196
1330 - 27·y = 196
1330 -196 = 27·y
1134
y = 1134/27 = 42
y = 42
x = 266 - 6·y
x = 266 - 6 × 42 = 14
x = 14
9. Let x represent the number of bottles the shampoo and let y represent the number of bottles of the conditioner bought, therefore;
x + y = 19
Let a represent the cost of a shampoo and let b represent the cost of a conditioner
a·x + b·y = 147
The cost of a shampoo, a = (147 - b·y )/x
Cost of a conditioner, b = (147 - a·x )/y
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What is the volume of the solid?
A. 12 yd³
B. 14 yd³
C. 22 yd³
D. 5 yd³
Answer:
(1/2)(4)(3)(2) = 12 cubic yards
The correct answer is A.
What is the smallest whole number that rounds to 2,560 to the nearest ten?
The requreid smallest whole number that rounds to 2,560 to the nearest ten is 2,565. When we round 2,565 to the nearest ten, we get 2,570, which is the desired result.
When rounding a number to the nearest ten, look at the digit in the tens place. If that digit is 5 or greater, we round up by adding 1 to the digit in the hundreds place. If that digit is less than 5, round down by keeping the digit in the hundreds place the same.
In the given question, 2,560 rounded to the nearest ten would be,
2,560 rounded up to 2,560 + 10 = 2,570.
Therefore, the smallest whole number that rounds to 2,560 to the nearest ten is 2,565. When we round 2,565 to the nearest ten, we get 2,570, which is the desired result.
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(100 POINTS + BRAINLIEST) A box has 1 red marble, 1 blue marble, and 4 green marbles of the same shape and size. Dan draws a marble randomly from the box, replaces it, and then draws another marble randonmy What is the probability of drawing two green marbles in a row? Explain your answer.
The probability of drawing two green marbles in a row is 4/9.
Given that, a box has 1 red marble, 1 blue marble, and 4 green marbles.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.
Number of favorable outcomes = 4
Total number of outcomes = 6
Probability of drawing 1st green marble = 4/6
= 2/3
Probability of drawing 2nd green marble = 4/6
= 2/3
Probability of drawing two marbles = 2/3 × 2/3
= 4/9
Therefore, the probability of drawing two green marbles in a row is 4/9.
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Is 9/10 more than 78/100
The fraction 9/10 is more than 78/100.
In mathematics, an expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, division, and exponentiation) that are combined in a meaningful way.
To compare these two fractions, we can convert them to have a common denominator. In this case, the common denominator is 1000.
9/10 = (9/10) x (100/100) = 900/1000
78/100 = (78/100) x (10/10) = 780/1000
Now we can see that 900/1000 (which is equivalent to 9/10) is greater than 780/1000 (which is equivalent to 78/100).
Therefore, 9/10 is more than 78/100.
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Please answer the question I need this today
Answer:
C
Step-by-step explanation:
8 x 10^4 = 80,000
3 x 10^3 = 3,000
1 x 10 ^2 = 100
2 x 10^1 = 20
add it up
83,120
C is correct
Determine the approximate length of AC.
Answer:7 units
Step-by-step explanation:
What’s the probability that event A or B takes place?
The probability that event A or B takes place is P ( A ∪ B ) = 4/13
Given data ,
Let the probability of event A happening P ( A ) = 1/13
Let the probability of event B happening P ( B ) = 3/13
And , the probability of event A and B happening P ( A ∩ B ) = 0
So , from the probability rule ,
The probability that event A or B takes place is P ( A ∪ B ) and
P ( A ∪ B ) = P ( A ) + P ( B ) - P ( A ∩ B )
On simplifying , we get
P ( A ∪ B ) = 1/13 + 3/13 - 0
P ( A ∪ B ) = 4/13
Hence , the probability is 4/13
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Write a rational function with no vertical asymptotes and no holes. Explain.
The rational function f(x) = (x² + 1)/(x² + 2x + 2) has no vertical asymptotes and no holes.
We have,
A rational function is a function that can be expressed as the ratio of two polynomials.
It can have vertical asymptotes and/or holes in its graph, depending on the behavior of the denominator polynomial.
To construct a rational function with no vertical asymptotes and no holes, we need to ensure that the denominator polynomial does not have any real roots.
This means that the denominator polynomial should either have no roots or only complex roots.
One way to achieve this is to use a quadratic polynomial in the denominator that has no real roots.
For example, consider the function:
f(x) = (x² + 1)/(x² + 2x + 2)
The denominator polynomial x² + 2x + 2 has no real roots because its discriminant, 2² - 4(1)(2) = -4, is negative.
This means that the function f(x) has no vertical asymptotes.
To check if the function has any holes, we need to simplify the function by canceling out any common factors between the numerator and denominator.
However, since the numerator x² + 1 has no common factors with the denominator, there are no terms to cancel out.
Therefore, the function f(x) has no holes either.
Thus,
The rational function f(x) = (x² + 1)/(x² + 2x + 2) has no vertical asymptotes and no holes.
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Originally, a Petri dish contained 200,000 bacteria. After a scientist applied an antibiotic, the number of bacteria decreased by 75% per hour.
Which function could model this situation?
well, we know the number of bacteria is decreasing, so we can use a Decay equation for that, with a 75% rate of decay.
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &200000\\ r=rate\to 75\%\to \frac{75}{100}\dotfill &0.75\\ t=hours \end{cases} \\\\\\ A = 200000(1 - 0.75)^{t} \implies A = 200000(0.25)^t[/tex]
Find the slope of a line that is perpendicular to: x − y = 0
-1 is the value of the slope.
To find the slope of a line that is perpendicular to the line x - y = 0, we need to find the slope of the given line first.
To do this, we can rearrange the equation x - y = 0 to solve for y:
x - y = 0
y = x
So the given line has a slope of 1 since the coefficient of x is 1.
Since a line perpendicular to this line will have a slope that is the negative reciprocal of the slope of the given line, we can find the slope of the perpendicular line by taking the negative reciprocal of 1:
the slope of the perpendicular line = -1/1
the slope of the perpendicular line = -1
Therefore, the slope of a line that is perpendicular to the line x - y = 0 is -1.
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Consider the diagram.
Planes M and N intersect at line d. Lines a, b, and e are on plane M. Line a is vertical and forms a right angle with line d. Line b is diagonal and goes up and to the right. Line e is at the top of the plane and is close to being horizontal. Line c is on plane N and goes slightly up and to the right.
Lines a and d are
The line a and line d are perpendicular to each other.
How to identify a perpendicular line?Perpendicular lines and intersecting lines are the same because they both describe 2 lines that cross one another.
Perpendicular lines cross one another in a specific way. The intersection of perpendicular lines forms 90 degree angles.
Constructing lines a and d:
After constructing the two lines; line a and line intersect or meet each other at 90 degrees to the horizontal.
Thus, we can conclude that the line a and line d are perpendicular to each other.
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Answer:line a and line d are perpendicular
saw the answers
Find the average for the set of numbers 7, 6, 12, 5, 7, 6, 13.
Answer:
8
Step-by-step explanation:
To find the average of a set of numbers, you add up all the numbers in the set and then divide by the total number of numbers in the set.
So, to find the average of the set of numbers 7, 6, 12, 5, 7, 6, 13, you would first add up all the numbers:
7 + 6 + 12 + 5 + 7 + 6 + 13 = 56
Then you would divide the sum by the total number of numbers in the set, which is 7:
56 / 7 = 8
Therefore, the average of the set of numbers 7, 6, 12, 5, 7, 6, 13 is 8.
Answer:
the answer you are looking for would be 8
Your grandmother will be giving you $10,000 every year for the next five years, the first payment beginning at the end of the first year
A) If you invest these receivables in a bank at 6%, what is the total value at the end of 10 years if you make withdrawals of $3,000 in years 9 and 10?
B) An investor expects to receive $3,000 in year 2, $5,000 in year 5, and $7,000 in year 7. What is the present value of these payments if the interest rate is 8%?
Please also write the Excel formulas.
Answer:
a. The present value of these receivables is $42,123.64
b. The total value at the end of 10 years is $69,257.02
c. The present value of these payments is $10,059.37
Step-by-step explanation:
How do you complete these problems?
I just need help understanding how to get the answer. Thanks.
1. The area of the smaller rectangle is approximately 96 in².
2. The length of the hypotenuse of the smaller triangle is 32 units.
1. How to solve for the area of the smaller rectangleIf the scale factor of two similar rectangles is 4/7, then the ratio of their areas is (4/7)^2 = 16/49. This means that the area of the smaller rectangle is (16/49) times the area of the larger rectangle.
Let A be the area of the smaller rectangle. Then we have:
A = (16/49) * 294 in²
A = 96 in² (rounded to the nearest whole number)
Therefore, the area of the smaller rectangle is approximately 96 in².
2. 4/9, which simplifies to 2/3.
This means that the length of the hypotenuse of the smaller triangle is (2/3) times the length of the hypotenuse of the larger triangle.
Let x be the length of the hypotenuse of the smaller triangle. Then we have:
(2/3) * 48 = x
x = 32 units
Therefore, the length of the hypotenuse of the smaller triangle is 32 units.
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