Answer:
17/30
Step-by-step explanation:
Number of students = 30
Number of girls and A students = 13+4 = 17
Probability of a student being chosen at random being either a girl or an A student = Total Number of girls and A students/Total No of students = 17/30
Probably of a student chosen at random being either a girl or an A student would be 17/30
The probability of choosing a girl or an A student is 17/30 or 0.567.
There are a couple of ways to approach this problem, but one common method is to use the formula:
P(girl or A) = P(girl) + P(A) - P(girl and A)
where P(girl) is the probability of choosing a girl, P(A) is the probability of choosing an A student, and P(girl and A) is the probability of choosing a student who is both a girl and an A student.
To calculate each of these probabilities, we first need to find the total number of girls and A students in the class:
Total number of girls: 13
Total number of A students: 4 boys + 5 girls = 9
Now we can calculate each probability:
P(girl) = number of girls / total number of students = 13 / 30
P(A) = number of A students / total number of students = 9 / 30
P(girl and A) = number of girls who made an A / total number of students = 5 / 30
Plugging in the values, we get:
P(girl or A) = P(girl) + P(A) - P(girl and A)
= 13/30 + 9/30 - 5/30
= 17/30
Therefore, the probability of choosing a girl or an A student at random from the class is 17/30, or about 0.567.
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Data Classification For the given datasets, circle the data classification (categorical or quantitative) and type of data (Nominal or Ordinal or Continuous or Discrete). A. Height of sunflowers in a field. 1. Categorical or Quantitative 2. Nominal or Ordinal or Continuous or Discrete B. Jersey color of all the NCAA football teams.1. Categorical or Quantitative 2. Nominal or Ordinal or Continuous or Discrete
the data classification (categorical or quantitative) and type of data (Nominal or Ordinal or Continuous or Discrete)
A. Height of sunflowers in a field.
1.Quantitative
2.Continuous
B. Jersey color of all the NCAA football teams.
1.Categorical
2.Nominal
A. Height of sunflowers in a field.
1.Quantitative
2.Continuous
B. Jersey color of all the NCAA football teams.
1.Categorical
2.Nominal
Data classification is a process of organizing data into categories based on their characteristics, attributes, or features. There are two main types of data classification:
Categorical Data: Data that can be divided into categories or classes. For example, color, gender, and type of cuisine are all examples of categorical data. Categorical data can be further classified into two types:
a. Nominal Data: Data that does not have an inherent order or ranking. For example, hair color, eye color, and favorite movie are all examples of nominal data.
b. Ordinal Data: Data that has a natural order or ranking. For example, education level (high school, college, postgraduate), star rating (1 star, 2 stars, 3 stars), and satisfaction level (very unsatisfied, unsatisfied, neutral, satisfied, very satisfied) are all examples of ordinal data.
Quantitative Data: Data that can be measured and expressed as a number. For example, height, weight, and time are all examples of quantitative data. Quantitative data can be further classified into two types:
a. Continuous Data: Data that can take on any value within a specified range. For example, height, weight, and temperature are all examples of continuous data.
b. Discrete Data: Data that can only take on specific values. For example, number of children in a family, number of pets, and number of rooms in a house are all examples of discrete data
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Fran is decorating her bedroom.
She is going to put a border all around the bedroom.
This diagram shows a plan of the bedroom.
6 m
5m
2 m
5m
3 m
5 m
Border rolls are sold in 4 m lengths.
Work out the number of border rolls Fran will need to buy.
Diagram NOT
accurately drawn
Fran will have to buy 6.5 border rolls for the bedroom
How to work out the number of border rolls Fran will need to buy.The number of border rolls that Fran need to buy is compared with the perimeter of the bedroom
The perimeter of the bedroom is sum of the sides and this is solved as follows
= 6 m + 5m + 2 m + 5m + 3 m + 5 m
= 26 m
comparing for number of border rolls
1 border roll = 4 m
x border rolls = 26 m
cross multiplying
x * 4 = 26 * 1
x = 26 / 4
x = 6.5
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Equation h the number of times noah’s heart beats at this rate in minutes
Answer:
Step-by-step explanation:
Polk Elementary School was putting on its annual fall carnival. The school was selling 10 tickets for $1.00 or 2 tickets for 254. Which is the better buy? Explain why.
What is the quotient of 4 ÷ 4
Answer:
1 wow
Step-by-step explanation:
1. Let (X, d) be a metric space. Define e : X × X −→ R by
e(x, y) = min {1, d(x, y)}, ∀ x, y ∈ X
The function e is a metric on X, as it satisfies the properties of a metric:
Non-negativity: e(x, y) ≥ 0, for all x, y in X.Identity of Indiscernibles: e(x, y) = 0 if and only if x = y.Symmetry: e(x, y) = e(y, x), for all x, y in X.Triangle Inequality: e(x, y) + e(y, z) ≥ e(x, z), for all x, y, z in X.What is a Metric Space?A metric space in mathematics is a collection with a concept of distance between its components, which are typically referred to as points.
A metric or distance function is used to calculate the distance. The most universal context for learning many of the ideas of mathematical analysis and geometry is metric spaces.
Hence, the properties of a metric were satisfied in function e, so it has been defined.
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Find the magnitude and direction of -3i-4j
Answer:
MAGNITUDE AND DIRECTION OF A VECTOR
Given a position vector →v=⟨a,b⟩,the magnitude is found by |v|=√a2+b2. The direction is equal to the angle formed with the x-axis, or with the y-axis, depending on the application. For a position vector, the direction is found by tanθ=(ba)⇒θ=tan−1(ba)
Step-by-step explanation:
I NEED THIS ASAP PLS HELP AHH-
Two identical point charges of q = +1.75 x 10
−
8
C are separated by a distance of 0.30 m. How much work is done by the electric field force to move them away from each other so that they are 1.05 m apart?
The electric field force does 1.90 x 10⁻⁸ J of work to move the two point charges from 0.30 m to 1.05 m apart.
What do you mean by electric field?The electric field is a vector field that represents the force experienced by a charged particle due to an electric charge distribution. It is a measure of the electric force per unit charge at a particular point in space. The electric field is defined as the negative gradient of the electric potential, which is the energy per unit charge that a charged particle would have at that point in space. The electric field can be used to calculate the force experienced by a charged particle in the presence of other charges, and is a fundamental concept in the study of electromagnetism.
The electric field force between two point charges is given by Coulomb's law:
F = k * (q₁ * q₂) / r²
where k is the Coulomb constant (8.99 x 10⁹ N m²/C²), q₁ and q₂ are the magnitudes of the charges, and r is the distance between the charges.
To calculate the work done by the electric field force, we need to find the force at the initial distance (0.30 m) and the final distance (1.05 m), and then subtract the work done at the initial distance from the work done at the final distance.
At a distance of 0.30 m, the force is:
F = k * (1.75 x 10⁻⁸ C)² / (0.30 m)² = 4.02 x 10⁻⁸ N
The work done at this distance is:
W = F * 0.30 m = 1.21 x 10⁻⁷ J
At a distance of 1.05 m, the force is:
F = k * (1.75 x 10⁻⁸ C)² / (1.05 m)² = 1.33 x 10⁻⁸ N
The work done at this distance is:
W = F * 1.05 m = 1.40 x 10⁻⁷ J
Finally, to find the total work done, we subtract the work done at the initial distance from the work done at the final distance:
W total = W final - W initial = 1.40 x 10⁻⁷ J - 1.21 x 10⁻⁷ J = 1.90 x 10⁻⁸ J.
Therefore, the electric field force does 1.90 x 10⁻⁸ J of work to move the two point charges from 0.30 m to 1.05 m apart.
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Please help I need it ASAP
pls help!!! need some explanation
the measure of the side BD will be 5.
What is are of triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.
The sum of all angle of triangle = 180
From the ΔACE the sides BD║AE
Here given BC=4 and BA=5
BD+10/2 = BA
BD +10 = 2BA
BD = 10-5 = 5
Hence the measure of the side BD will be 5.
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You will be getting a loan for the full cost of the tractor.
The tractor will cost £64,950.
The compound interest rate is 4% per annum, which will be added to the total cost of the tractor up front.
You will pay back the loan in 36 equal monthly payments.
What will you pay each month?
Answer: £2,116.10 each month.
Step-by-step explanation:
To calculate the monthly payment, we first need to find the total amount owed after the compound interest has been added. The formula for compound interest is:
A = P * (1 + r/n)^(nt)
where:
A is the amount owed,
P is the initial principal (the cost of the tractor),
r is the annual interest rate,
n is the number of times interest is compounded per year, and
t is the number of years the loan is taken out for.
In this case:
P = £64,950
r = 4% = 0.04
n = 12 (the number of months in a year)
t = 3 (the number of years the loan is taken out for)
Plugging these values into the formula, we find that:
A = £64,950 * (1 + 0.04/12)^(12*3) = £76,079.69
To find the monthly payment, we divide the total amount owed by the number of payments:
Monthly payment = A / 36 = £76,079.69 / 36 = £2,116.10
So you will pay £2,116.10 each month.
A university president salary for the 2012-2013 academic year was $483,000. Calculate his 2013-2014 salary if he received a 3.1% raise. Show work please!
Answer: The 2013-2014 salary can be calculated as follows:
$483,000 + ($483,000 * 3.1%) = $483,000 + $14,973 = $497,973.
So, the university president's 2013-2014 salary was approximately $497,973 after receiving a 3.1% raise.
Step-by-step explanation:
Compute the sample variance and sample standard deviation in business contexts Question The following set of data represents stock prices of a pharmaceutical company, find the sample variance of the: 14, 7, 10, 9. Round your answer to ONE decimal place.
The sample variance is 14.67 and the sample standard deviation is 3.83.
To find the sample variance, we first need to find the sample mean of the data set. The mean of the data set is (14 + 7 + 10 + 9) / 4 = 10. The variance is the average of the squared differences between each data point and the mean. The sample variance is ((14 - 10)^2 + (7 - 10)^2 + (10 - 10)^2 + (9 - 10)^2) / (4 - 1) = 14.67. The sample standard deviation is the square root of the sample variance, which is 3.83.
These values give us an idea of the spread or dispersion of the data around the mean. In a business context, the sample variance and sample standard deviation can be used to determine the risk associated with a stock investment.
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We have a cohort of 100 cancer patients receiving various forms of treatment. Treatment can
be stand alone or combinations, the unique types of treatment are: surgery only, radiation
only, chemotherapy only, chemotherapy and radiation, surgery and chemotherapy, surgery
and chemotherapy and radiation, and no treatment. Our sample has the follow distribution of
treatments:
● 38 patients receiving surgery only
● 10 patients receiving radiation only
● 18 patients receiving chemotherapy only
● 17 patients receiving surgery and chemotherapy
● 6 patients receiving surgery, chemotherapy, and radiation
● 11 patients with no treatment (this does not count as a type of treatment)
If we randomly select one person from this sample, find the following probabilities:
a) P(any treatment)
Ans:
Answer:
89/100
Step-by-step explanation:
there were only 11 people without treatment so minus 11 from 100 which is 89
then just make it a probability by writing it out of 100.
hope this helps
Use the information about the graph of a polynomial function to determine the function. Assume the leading coefficient is 1 or -1
- The y - intercept is (0,-49)
- The x - intercepts are ( -7,0), (7,0)
- The degree is 2
- as x → - ∞, f(x) → ∞
- as x → ∞, f(x) → ∞
The polynomial function is f(x) = x² - 49 if the leading coefficient is 1 or f(x) = -x² - 49 if the leading coefficient is -1.
What is Polynomial?Polynomials are expressions of the form,
a₀ + a₁ x + a₂ x² + ................. + aₙ₋₁ xⁿ⁻1 + aₙ xⁿ
where a's are the coefficients, x is the variable and n is the number of terms.
Given that, the degree of the function is 2.
So the function is quadratic.
It is of the form f(x) = ax² + bx + c.
The y - intercept is (0,-49).
Substituting the point,
(a × 0²) + (b × 0) + c = -49
c = -49
Function is f(x) = ax² + bx - 49.
We have, the x - intercepts are ( -7,0), (7,0).
Substituting the points, we get two equations.
a (-7)² + b (-7) - 49 = 0 and a (7)² + b (7) - 49 = 0
49a - 7b - 49 = 0 and 49a + 7b - 49 = 0
Subtracting 49a - 7b - 49 = 0 from 49a + 7b - 49 = 0, we get,
14b = 0
b = 0
So the function is of the form f(x) = ax² - 49.
Given that, Assume the leading coefficient is 1 or -1.
Function is either f(x) = x² - 49 or f(x) = -x² - 49
Hence the required function is f(x) = x² - 49 or f(x) = -x² - 49.
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The store owner gave a 15% discount, yet Ty still had to pay $153 for the chess set. What was the original price of the chess set
Answer: $180
Step-by-step explanation:
180 x 15% = 27
27 - 180 = 153
What is the answer to 19-6(-k-2)
Answer:
6k + 31
Step-by-step explanation:
19 - 6(- k - 2) ← multiply each term in the parenthesis by - 6
= 19 + 6k + 12 ← collect like terms
= 6k + 31
Find the value of Y.
The value of the side y is 3√3. Option C
How to determine the value of the sideIt is crucial to note the different types of trigonometric identities.
They are;
sinetangentcotangentsecantcosecantcosineFrom the diagram shown, we have that;
The angle θ = 60 degrees
The opposite side = y
The adjacent side = 3
Let's use the tangent identity
tan 60 = y/3
Find the value
√3 = y/3
cross multiply
y = 3√3
Hence, the value is 3√3
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pls help overdue!!
REASONING You can paint 75 square feet of a surface every 45 minutes. Determine how long it takes you to
paint a wall with the given dimensions.
8 ft x 5 ft
Step-by-step explanation:
Let's find out the area of the given dimensions. In order to do that, we would just multiply 8 and 5, our given ft.
8 x 5 = 40
So if it takes 45 min for 75 feet, it takes x min for 40 feet. We can set up a ratio
[tex] \frac{45}{75} = \frac{x}{40} [/tex]
Next we cross multiply
[tex]75x = (45)(40) = 1800[/tex]
Now we divide by 75
[tex]x = 24 \: minutes[/tex]
I will give brainliest and ratings if you get this correct!
Depending on the data above,
find The arithmetic mean, median, mode and range
Mean = 31.333
Median = 30
Mode = 41
Range = 18
Mean
Determining the average can be done by adding up all the data values, then dividing by the amount of data.
Mean = [tex]\frac{30+25+23+41+39+27+41+24+32}{9}[/tex]
= [tex]\frac{282}{9}[/tex]
= 31.333
Median
The median is the middle value of a set of data after being sorted from smallest to largest data, and vice versa. If data has a median, then the median is single.
because the questions are not sequential, they must be sorted first from the smallest to the largest.
23 24 25 27 30 32 39 41 41
The median from this question is 30
Mode
The mode is the data that occurs most frequently.
23 24 25 27 30 32 39 41 41
And the mode of this problem is 41 because it appears two times
Range
the range is the difference between the highest value of a data set and the lowest value of a data set.
23 24 25 27 30 32 39 41 41
the range from 23 to 41 is 18
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The P(A)= 0.03 and the P(B) = 0.34. Events A and B are mutually exclusive. What is the P(A or B).
Answer:
Step-by-step explanation:
The probability of A or B occurring is the sum of the probabilities of A and B occurring, since they are mutually exclusive events.
Mutually exclusive events are events that cannot occur at the same time. In other words, if one event occurs, the other event cannot occur.
Therefore, the probability of A or B is:
P(A or B) = P(A) + P(B)
P(A or B) = 0.03 + 0.34
P(A or B) = 0.37
So, the probability of A or B is 0.37.
Geometry Help -- 30-60-90 and 45-45-90 triangles
Answer:
w = (10√3)/3
x = 5
y = 5√2
z = (5√3)/3
Step-by-step explanation:
→ The length of "x" is also 5 units because 45-45-90 triangles have the same leg lengths.
→ The length of "y" is 5√2 units because the hypotenuse of a 45-45-90 triangle is √2 times bigger than either leg length.
→ The length of "z" is 5/√3 or (5√3)/3 units because the longer leg length of a 30-60-90 triangle is √3 times bigger than the shorter leg length
→ The length of "w" is (10√3)/3 units because the longer leg length is 2 times bigger than the shorter leg length of a 30-60-90 triangle
See below for more information about general rules for 30-60-90 and 45-45-90 triangles!
Consider the following cash flows: 12/15/21-$1000 ，1/11/22 $300 ， 4/7/23 $600 ， 7/15/24 $925， If today is today’s date, and r = 0.15, what is the NPV of these cash f lows?
Given a discount rate of 0.15, the NPV of these financial movements is therefore $378.73.
What is cash flow, and how does it work?Spending that occurs in the normal run of business is included in cash flow from activities. Payroll, the cost of products sold, rent, and utility bills are a few examples of these cash withdrawals. When company activities are extremely seasonal, cash outflows can differ greatly.
Here's how to do the calculation:
We need to determine how many days passed between the first monetary influx of $-1000, which was received on 12/15/2021, and the present day (2/21/2023). It's been 432 days. Using the equation PV = FV / (1 + r)n, we can determine the current value (PV), the future value (FV), the discount rate (r), and the number of times (n). When the numbers are plugged in, we get PV = -1000 / (1 + 0.15)(432/365) = -845.67.
We must determine how many days passed between the second monetary influx of $300, which was received on January 11, 2022. It's been 406 days. We obtain PV = 300 / (1 + 0.15)(406/365) = 246.87 using the same method.
In order to determine the third financial movement, which is a $600 payment received on 4/7/2023, we must determine how many days have passed since that date. It's been 410 days. Using the same method, we get PV = 600 / (1 + 0.15)^(410/365) = 427.81.
We need to figure out how many days passed between the fourth financial transfer, which was $925 and was received on July 15, 2024. It has been 875 days. We obtain PV = 925 / (1 + 0.15)(875/365) = 548.72 using the same method.
Now we can add up the present values of all the cash flows to obtain the NPV:
NPV = -845.67 + 246.87 + 427.81 + 548.72 = 378.73
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How do you convert a Cartesian equation to a cylindrical equation?
To convert a point from Cartesian coordinates to cylindrical coordinates, use the formulae:
r²=x²+y² ,
tanθ=y/x, and z=z
What are coordinates?
A pair of numbers that use the separations between the two reference axes to define the location of a point on a coordinate plane. usually represented by the x- and y-values, respectively, (x, y).
The position of a point or a shape in a given space is determined by coordinates, which are numbers (a map or a graph ).
To convert a point from Cartesian coordinates to cylindrical coordinates, use the formulae:
r²=x²+y² ,
tanθ=y/x, and z=z
Cartesian coordinates are also called as rectangular coordinates
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To convert a point from Cartesian coordinates to cylindrical coordinates, use the formulae:
r²=x²+y² ,
tanθ=y/x, and z=z
What are coordinates?
A pair of numbers that use the separations between the two reference axes to define the location of a point on a coordinate plane. usually represented by the x- and y-values, respectively, (x, y).
The position of a point or a shape in a given space is determined by coordinates, which are numbers (a map or a graph ).
To convert a point from Cartesian coordinates to cylindrical coordinates, use the formulae:
r²=x²+y² ,
tanθ=y/x, and z=z
Cartesian coordinates are also called as rectangular coordinates
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PLEASE HELP I NEED IT PLEEASE.
A map of a farm is shown in a coordinate plane in which the coordinates are measured in yards. The map shows the barn at (-1, 2). A well is dug at (-1, y). What are two values of y such that the barn is 50 yards from the well?
Answer:
Values for y are y = 52 or y = -48
Step-by-step explanation:
No diagram was provided but the question had enough information to be answered
Since the x coordinates of both barn and well are the same, it means the well is either vertically north of the barn or vertically south.
Therefore y can be either 2 + 50 = 52 giving (-1, 52) as one coordinate
Also y can be 2 - 50 = -48 giving (-1, -48) as another coordinate
See attached figure
what comes next in the series 7,48,14,56,21,24
Consider the experiment of rolling fair six-sided die until a 5 is observed. Let A be the event that a 5 is observed on the first roll. Let B be the event that it takes at least two rolls for the first 5 to be observed. Find the following probabilities. (Round to nearest 4 decimal places)
P(A∩B)
P (A)
P(B)
Answer:
P(A∩B) = 0
P(A) = 0.1667
P(B) = 0.8333
=================================================
Explanation:
The events
A = a 5 is observed on the first rollB = it takes at least two rolls for the first 5 to be observedare mutually exclusive. There isn't any overlap. This is because event B involves "at least 2 rolls", meaning we cannot get 5 on the first roll. Either event A happens, or B does, but not both at the same time.
This allows us to say P(A∩B) = 0
In a venn diagram, the overlapped region between circles A and B would have probability 0 marked inside.
-----------------------
P(A) = 1/6 since there is exactly one side labeled "5" out of 6 sides total. This converts to the approximate decimal form 1/6 = 0.1667 when rounding to four decimal places. The 6's go on forever, but of course we have to round at some point.
------------------------
We found that P(A) = 1/6. The complement to this is 1-(1/6) = 5/6, which is the probability of rolling anything but a "5". This fraction represents the scenario "at least 2 rolls are needed for the 1st '5' to show up" since we forced the first roll to be anything but 5.
Put another way, we have two options:
Option 1: The first roll is "5". The probability is 1/6Option 2: The first roll is NOT "5" (so you'll need to do at least another roll to get "5"). The probability is 5/6.The two probabilities 1/6 and 5/6 add to 6/6, aka 1, to represent 100% of all possible cases. This means P(A)+P(B) = 1 for this scenario.
The fraction 5/6 converts to the approximate decimal form of 5/6 = 0.8333; use a calculator or long division to determine this value.
What type of function is S(x)? Years (input) 3,4,5,6,7 ; S(x) (output) 24,48,96,192,384
Answer:
S(x) = 3 × 2^x
Step-by-step explanation:
it is an exponential sequence
the common ratio is 2
Select the correct answer.
Four equivalent forms of a quadratic function are given. Which form displays the zeros of function h?
A. h(x) = -4(x − 2)(x + 2)
B. h(x) = -4(x2 − 4)
C. h(x) = -4x2 + 16
D. h(x) = -2(2x2 − 8)
In a random sample of 19 people, the mean commute time to work was 33.7 minutes and the standard deviation was 7.3 minutes. Assume the population is normally distributed and use a
1-distribution to construct a 80% confidence interval for the population mean μ. What is the margin of error of u? Interpret the results.
The confidence interval for the population mean u is D.
(Round to one decimal place as needed.)
The average confidence interval, according to our 80% level of confidence, falls between 31.54 and 35.86 minutes for the total population.
Why is there a 95% confidence interval?You only have a 5% probability of making a mistake with a 95% confidence interval. You have a 10% probability of being mistaken when the confidence interval is 90%. The difference between a 95 percent and 99 percent confidence interval is the width of the interval (for example, plus or minus 4.5 percent instead of 3.5 percent).
Why is a confidence interval important?Confidence intervals include details about the range in which the true value is likely to fall, as well as the kind and magnitude of the effect that has been proved. Conclusions concerning the can be made as a result of this.
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