The probability that Angela gets to go to the meeting is 2/5 or 0.4.
What is probability?
There are a total of 5 people in the club, and they need to pick 2 people to go to the meeting. The number of ways to pick 2 people out of 5 is given by the binomial coefficient:
C(5,2) = 5! / (2! (5-2)!) = 10
This means there are 10 equally likely outcomes, which can be represented by the following probability model:
Outcome Angela goes to meeting? Probability
A,B Yes 1/10
A,C Yes 1/10
A,D Yes 1/10
A,E Yes 1/10
B,C No 1/10
B,D No 1/10
B,E No 1/10
C,D No 1/10
C,E No 1/10
D,E No 1/10
The probability that Angela gets to go to the meeting is the sum of the probabilities of the outcomes where Angela goes to the meeting:
P(Angela goes to meeting) = P(A,B) + P(A,C) + P(A,D) + P(A,E)
= 1/10 + 1/10 + 1/10 + 1/10
= 4/10
= 2/5
Therefore, the probability that Angela gets to go to the meeting is 2/5 or 0.4.
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Eliana opened a savings account and deposited $700.00 as principal. The account earns 4%
interest, compounded monthly. What is the balance after 10 years?
Answer:
We can use the formula for compound interest to find the balance in Eliana's savings account after 10 years:
A = P(1 + r/n)^(nt)
where A is the balance, P is the principal (initial deposit), r is the annual interest rate as a decimal, n is the number of times interest is compounded per year, and t is the time in years.
Substituting the given values, we get:
A = $700(1 + 0.04/12)^(12*10)
Simplifying, we get:
A = $700(1.0033333)^120
Using a calculator, we get:
A ≈ $1,038.81
Therefore, the balance in Eliana's savings account after 10 years is approximately $1,038.81.
Can someone help
me?
Answer:
To find the real and imaginary parts of the complex number 26 = a + bi, we can use the fact that:
a + bi = 26
Taking the complex conjugate of both sides, we get:
a - bi = 26
Adding the two equations, we get:
2a = 52
Solving for a, we get:
a = 26
Substituting this value into one of the equations, we get:
26 + bi = 26
Therefore, b = 0.
Therefore, the real part of 26 is a = 26, and the imaginary part is b = 0.
Use graphical methods to solve this linear programming problem.
Maximize z = 3x + 4y
subject to 2x - 3y ≤ 12
x + y ≥ 3
3x + 4y ≥ 24
x ≥ 0
y ≥ 0
What is the maximum value of z? Select the correct choice below, and if necessary, fill in the answer box to complete your choice.
A. The maximum value is ___ (Simplify answer)
B. There is no maximum.
At what point(s) does the maximum value of z occur? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The maximum value of z occurs only at the point(s) ___
(Type an ordered pair. Use a comma to separate answers as needed.)
B. The maximum value of z occurs at the points ___ and at all points on the line segment connecting them. (Type an ordered pair. Use a comma to separate answers as needed.)
C. There is no maximum value of z.
Answer:
B. There is no maximum value.
C. There is no maximum value of z.
Step-by-step explanation:
To solve this linear programming problem using graphical methods, start by graphing the feasible region determined by the given constraints:
2x - 3y ≤ 12x + y ≥ 33x + 4y ≥ 24x ≥ 0y ≥ 0We can graph each of these inequalities by first plotting the corresponding boundary line, and then shading in the appropriate region.
Rearrange the first three inequalities to isolate y:
[tex]\boxed{\begin{aligned}2x - 3y & \leq 12\\2x - 12 & \leq 3y \\3y &\geq 2x - 12\\y& \geq \dfrac{2}{3}x-4\end{aligned}}[/tex] [tex]\boxed{\begin{aligned}x + y & \geq 3\\y & \geq -x+3\\ \phantom{w}\\\phantom{\dfrac12}\end{aligned}}[/tex] [tex]\boxed{\begin{aligned}3x + 4y & \geq 24\\4y & \geq -3x + 24\\y & \geq -\dfrac{3}{4}x + 6\\\phantom{w}\end{aligned}}[/tex]
Graph the inequalities.
If the inequality sign is ≥, draw a solid line and shade above the line.If the inequality sign is ≤, draw a solid line and shade below the line.The feasible region is the region that is shaded by all of the inequalities.
Please see the attached graph.
A bounded feasible region may be enclosed in a circle and will have both a maximum value and a minimum value for the objective function.
If a feasible region is unbounded, and the coefficients on the objective function are all positive, then an unbounded feasible region will have a minimum but no maximum, since there is no limit on how big it can get.
Therefore, as the feasible region for the given constraints is unbounded, and the coefficients of the objective function z = 3x + 4y are all positive, there is no maximum value.
Triangle ABC is rotated 180 degrees counterclockwise around vertex c. find the coordinates of B. B is (4,4) C is (3,1)
The image of the point B after the rotation by 180 degrees about point C is (0, 0)
How to determine the image of the point B after the rotationGiven that
B = (4, 4)
C = (3, 1)
The rotation rule is given as
Rotation by 180 degrees counterclockwise around vertex C
The rule of 180 degrees counterclockwise about the origin is
(x,y) = (-x,-y)
If the center of rotation is (a, b), then we have
(x,y) = (-(x - a) + b, -(y - b) + a)
So, we have
B' = (-(4 - 3) + 1, -(4 - 1) + 3)
Evaluate
B' = (0, 0)
Hence, the image of the point is (0, 0)
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[tex]8x ^{2} y + 12xy - 16xz[/tex]
Factorize the expression
The factοrs οf the expressiοn is 4x(2xy+3y-4z).
What is factοrizatiοn?Tο factοrise an algebraic statement, we first identify the terms' highest cοmmοn factοrs and then arrange the terms intο grοups in accοrdance with thοse grοups. In plain English, factοrizatiοn is the prοcess thrοugh which an algebraic expressiοn gets expanded in the οppοsite directiοn.
Here the given expressiοn is ,
=> [tex]8x^2y+12xy-16xz[/tex]
Nοw factοrizing the given expressiοn then,
=> 4×2×x×x×y+4×3×x×y-4×4×x×z
=> 4x(2xy+3y-4z)
Hence the factοrs οf the expressiοn is 4x(2xy+3y-4z).
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Can someone help me please
Answer: X=55 and Y=125
Step-by-step explanation:
y is an external angle
so according to external angle property sum of two angles is equal to external angle. two angles are given- 35 and 90
90+35=y
y=125
now with angle sum property
90+35+x=180
125+x=180
x=55
please mark it brainliest
Which fraction is not written in simplest form?
A. 35/84
B. 27/40
C. 18/65
D. 24/83
35/84
It can be simplified to 5/12 by dividing by 7.
solve for me please
(5xy+3x-7)+(3xy-xy+3y+4)
Answer:
Step-by-step explanation:
7xy+3x+3y−3
Easy simultaneous equation question - help me i cba :)
Answer:
Let x be the cost of 1 kg of mushrooms and y be the cost of 1 kg of turnips.
From the given information, we can form two equations:
2x + 2.5y = 8.55 (Equation 1)
3x + 4y = 13.10 (Equation 2)
To solve for x and y, we can use the method of elimination. Multiplying Equation 1 by 4 and Equation 2 by -2, we get:
8x + 10y = 34.20 (Equation 3)
-6x - 8y = -26.20 (Equation 4)
Adding Equation 3 and Equation 4, we get:
2x + 2y = 8
Simplifying this equation, we get:
x + y = 4 (Equation 5)
Now we have two equations: Equation 2 and Equation 5. We can solve for x and y using substitution or elimination. Here, we will use substitution.
From Equation 5, we can express x in terms of y as:
x = 4 - y
Substituting this expression for x into Equation 2, we get:
3(4 - y) + 4y = 13.10
Simplifying and solving for y, we get:
y = £1.50
Substituting this value for y into Equation 5, we can solve for x:
x + £1.50 = 4
x = £2.50
Therefore, the cost of 1 kg of mushrooms is £2.50 and the cost of 1 kg of turnips is £1.50.
a) The cost of 1 kg of turnips is £1.50.
b) The cost of 1 kg of mushrooms is £2.50.
Find the quotient. What is the remainder?
233 ÷ 6
Answer:
When you divide 233 by 6 using long division, you get:
38
---
6|233
216
---
17
Therefore, 233 ÷ 6 = 38 with a remainder of 17
Answer:
38.83 (the 3 goes on and on)
Question
Brian invests his money in an account paying 8% interest compounded semiannually. What is the effective annual yield on
this account? Enter your response as a percentage rounded to two decimal places and omit the percent sign (7.25%
should be input as 7.25.)
Step-by-step explanation:
Semi-annual means an interest period is 1/2 year
1/2 *8% = 4% = .04
effective annual interest rate is then
(1+ .04)^2 - 1 = .0816 or 8.16 (%)
please help me!
Mark reads 42 pages of a book every 3/4 hour. Write an equation that models the relationship between x, the number of hours Mark reads, and y, the number of pages of the book he reads.
The linear equation that models the number of pages that he reads is:
y = 56*x
How to write the equation?So we know that Mark reads 42 pages every 3/4 of an hour, and we want to write an equation that models the number of pages y that mark reads in x hours, to do so we needto get the unit rate.
Take the quotient between the number of pages and the time above to get:
u = (42 pages)/(3/4 hours) = 56 pages per hour.
Then the number of pages that he can read in x hours is modeled by the linear equation:
y = 56*x
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measure the diameter of the tin in mm and write down the real diameter in mm
The diameter of the tin is 2/5D and the circumference of the tin is 0.4πD
How to determine the circumference and the diameterGiven the the scale factor of dilation is
Container = 2/5 smaller than in reality
This means that
Scale factor = 2/5
So, we have
Diameter = 2/5D where D = diameter in reality
Also, we have
Height = 2/5H where H = height in reality
The circumference is then calculated as
C = πD
So, we have
C = π * 2/5D
Evaluate
C = 0.4πD
Hence, the circumference is 0.4πD
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Complete question
The Ricoffy tin container with no dimensions indicated.The container is 2,5 times smaller than what it is in reality
Diameter of the tin on the picture = ? Height of the tin on the picture = ? Actual weight of coffee = 750 g 1.1 Measure the diameter of the tin in mm and write down the real diameter in mm
Jacque bought 2.5 pounds of dark chocolate covered pecans at $0.30 per ounce. In dollars and cents, what was the cost of these pecans?
Answer:
$12.00
Step-by-step explanation:
We know that 1 pound = 16 oz. Thus, we can create a proportion to find how many ounces (x) is 2.5 pounds:
[tex]\frac{1}{16}=\frac{2.5}{x}\\ x=(2.5*16)\\ x=40[/tex]
Since 2.5 pounds = 40 oz, we can now multiply 40 by 0.30 to find the price of 40 ounces of peacans priced at $0.30/ounce:
40 * 0.30 = $12.00
An investor has an account with stock from two different companies. Last year, her stock in Company A was worth $5150 and her stock in Company B was worth $5250. The stock in Company A has increased 24% since last year and the stock in Company B has increased 20%. What was the total percentage increase in the investor's stock account? Round your answer to the nearest tenth (if necessary).
the total percentage increase in the investor's stock account is 22%.
How much is a percentage?In mathematics, a ratio or figure that can be expressed as a fraction of 100 is known as a percentage. If we want to calculate a percentage of a number, we should split it by 100 before multiplying it by the original number. Therefore, the percentage relates to a component per 100. The term percent means "per 100". It is represented by the symbol "%". In mathematics, a percentage is a number or ratio that is represented as a fraction of 100. Although "pct," "pct," and occasionally "pc" are also used as abbreviations, the percent symbol "%" is most commonly used to denote it. A percentage is a number that has neither measurements nor a defined unit of measurement.
In the given question,
Increase in stock A= 24% of $5150 = 1236
Increase in stock = 20% of $5250 = 1050
The total percentage increase in the investor's stock account= {(1236+1050)/(5150+5250)* 100=
= 21.98%
≈22%
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what is the value of 6(2b-4) when b =3
Answer: 12
Step-by-step explanation:
Use BODMAS, so first solve the inside of the bracket:
2*3= 6
6-4= 2
Now we can multiply that by the number outside the bracket. Why?
Because a number outside a bracket means to multiply that number by everything in the bracket. So:
6 * 2 = 12
Answer: 12
Step-by-step explanation:
2 x 3 = 6
6 - 4 = 2
6 x 2 = 12
B(t) = 100 · [tex]2^{\frac{t}{20} }[/tex]
How many minutes will it take for the culture to achieve 10,000 bacteria
Therefore, it will take about 46.5 minutes for the culture to achieve 10,000 bacteria.
What is expression?In mathematics, an expression is a combination of numbers, symbols, and operators (such as +, -, x, ÷, etc.) that represents a mathematical quantity or relationship. Expressions can be as simple as a single number or variable, or they can be complex and involve multiple terms and operations. Examples of expressions include 2x + 5, 3y - 7, and (a + b)(c - d).
Here,
We can set up an equation to solve for t:
B(t) = 100 ·[tex]2^{t/20}[/tex]
= 10,000
Dividing both sides by 100, we get:
[tex]2^{t/20}[/tex] = 100
Taking the logarithm of both sides with base 2, we get:
t/20 = log2(100)
t = 20 · log2(100)
Using a calculator, we can simplify this to:
t ≈ 46.5 minutes
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Assume lines n and m are parallel. If μ(∠1) =147°, find the following angle measures.
Hence, the angles' measurements are as follows: ∠1 = 147° , ∠2 = 33° and ∠3 = 147° as Interior angles on the same side of the transversal.
what is angles ?A geometric shape known as an angle is created by two rays or line segments that have a shared termination, or vertex. Angles, which express how much of a turn or rotation there is between two rays or line segments, are measured in degrees or radians. They are frequently employed in physics, engineering, geometry, trigonometry, and other disciplines.
given
The characteristics of parallel lines and transversals allow us to determine that:
Interior angles on the same side of the transversal: 1 + 2 = 180°; 2 + 3 = 180°.
We know that (1) = 147°, thus we can apply the first equation to determine 2:
∠1 + ∠2 = 180°
147° + ∠2 = 180°
∠2 = 33°
We can apply the second equation to determine 3 now that we know 2:
∠2 + ∠3 = 180°
33° + ∠3 = 180°
∠3 = 147°
Hence, the angles' measurements are as follows: ∠1 = 147° , ∠2 = 33° and ∠3 = 147° as Interior angles on the same side of the transversal.
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A soft drink company calls 500 people at random and asks, “Isn’t it true that our product is better than our rival’s product?” and 75% of the people respond, “Yes.” Is this an example of bias? Explain.
Yes, this is an example of bias, specifically, response bias.
What is probability?Probability is a measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain. Probability can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. It is an important concept in many fields, including mathematics, statistics, physics, and engineering, and is used to make predictions, analyze data, and make decisions under uncertainty.
Here,
Response bias occurs when the answers given by respondents in a survey do not accurately reflect their true opinions or beliefs. In this case, the question asked by the soft drink company is leading and suggestive, and it suggests that the company's product is superior to its rival's product. By framing the question in this way, the soft drink company is more likely to receive a positive response from respondents, even if they do not actually believe that the company's product is better than its rival's product.
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Solve the equation √y+3=√y +√ 3
Step-by-step explanation:
so, it is
sqrt(y + 3) = sqrt(y) + sqrt(3)
first we square both sides :
y + 3 = y + 3 + 2×sqrt(y)×sqrt(3) =
= y + 3 + 2×sqrt(3y) =
= y + 3 + sqrt(4×3y) = y + 3 + sqrt(12y)
0 = sqrt(12y)
we square again :
0² = 12y
0/12 = 0 = y
Identifying the values a, b, and c is the first step in using the Quadratic Formula to find solution(s) to a quadratic equation. What are the values a, b, and c in the following quadratic equation? -3x^2 -5x +9 =0
Answer:
The quadratic equation is in the standard form: ax^2 + bx + c = 0. To use the quadratic formula to find the solutions, we need to identify the values of a, b, and c in the equation:
a is the coefficient of the x^2 term, which is -3 in this case.
b is the coefficient of the x term, which is -5 in this case.
c is the constant term, which is 9 in this case.
Therefore, the values of a, b, and c in the quadratic equation -3x^2 - 5x + 9 = 0 are:
a = -3
b = -5
c = 9
What is the domain of the square root function graphed below?
A bag with 8 marbles has 8 blue marbles. A marble is chosen from the bag at random.
Translate the point (- 8, - 6) to the new origin given (h, k). Given center (h, k) = (5, 4), find point (x', y').
(13, 10)
(-13, -10)
(-3, -2)
Translation of the point (-8, -6) to the new origin (5, 4) is thus (-13, -10). Hence, the response is (-13, -10).
what is coordinates ?A sequence of numbers known as coordinates is used to describe the location of a point or object in space or on a plane. Coordinates in two-dimensional space typically have two values, which are typically written as (x, y), where x denotes the horizontal position and y denotes the vertical position. Coordinates in three dimensions can have three values, denoted as (x, y, z), where x, y, and z stand for the position along the x, y, and z axes, respectively. In many different fields, such as geometry, physics, and computer graphics, coordinates are used.
given
The coordinates of the new origin must be subtracted from the given point in order to translate the point (-8, -6) to the new origin (h, k) = (5, 4).
x' = -8 - 5 = -13
y' = -6 - 4 = -10
Translation of the point (-8, -6) to the new origin (5, 4) is thus (-13, -10). Hence, the response is (-13, -10).
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What is the volume of the prism?
Enter your answer, as a mixed number in simplest form, in the box.
cm³
Answer:
40 5/8
Step-by-step explanation:
6 1/2 × 2 1/2
13/2 × 5/2= 65/4
65/4 × 2 1/2
65/4 × 5/2 = 325/8
325/8= 40 5/8
Answer:
40 5/8
Step-by-step explanation:
6 1/2 × 2 1/2
13/2 × 5/2= 65/4
65/4 × 2 1/2
65/4 × 5/2 = 325/8
325/8= 40 5/8
The function f(x) is defined below. What is the end behavior of f(x)?
f(x) =-156x + 44x^2 - 4x^3 + 180
As x approaches negative infinity (i.e., x → -∞), the term -4x³ dominates the expression and becomes increasingly positive. Therefore, the end behaviour of f(x) as x → -∞ is f(x) → +∞.
What is behaviour of function?The behavior of a function refers to how the function changes or behaves as the input values (usually denoted as x) approach certain values, typically positive infinity, negative infinity, or a critical point.
According to question:To determine the end behaviour of the function f(x), we need to examine the highest-degree term of the polynomial, which is -4x³.
As x approaches positive infinity (i.e., x → ∞), the term -4x³ dominates the expression and becomes increasingly negative. Therefore, the end behaviour of f(x) as x → ∞ is f(x) → -∞.
Similarly, as x approaches negative infinity (i.e., x → -∞), the term -4x³ dominates the expression and becomes increasingly positive. Therefore, the end behaviour of f(x) as x → -∞ is f(x) → +∞.
In summary, the end behaviour of f(x) is:
As x → +∞, f(x) → -∞As x → -∞, f(x) → +∞To know more about behaviour of function visit:
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A survey was conducted that asked 1015 people how many books they had read in the past year. Results indicated that x=10.5 books and s=16.6 books. Construct a 95% confidence interval for the mean number of books people read. Interpret the interval.
Construct a 95% confidence interval for the mean number of books people read and interpret the result. Select the correct choice below and fill in the answer boxes to complete your choice.
A. There is a 95% probability that the true mean number of books read is between ? and ?
B. If repeated samples are taken, 95% of them will have a sample mean between ? and ?
C. There is 95% confidence that the population mean number of books read is between ? and ?
A 95% confidence interval that the t population mean number of books is between 9.89 and 11.11 books.
What is confidence interval ?
A confidence interval is a statistical range that provides an estimate of the likely range of values for a population parameter (such as a mean, proportion, or standard deviation) based on a sample of data. It is calculated using a specific level of confidence, which represents the probability that the true population parameter falls within the calculated range.
Confidence intervals are typically expressed as a range of values with a margin of error or standard error. The margin of error represents the amount of random variation that is expected due to sampling error, while the standard error reflects the variability of the sample data.
According to the question:
C. There is 95% confidence that the population mean number of books read is between a lower bound of approximately 9.89 books and an upper bound of approximately 11.11 books.
To construct the confidence interval, we can use the formula:
[tex]CI =\bar x \± z* (s/\sqrt{n})[/tex]
substitute the values, we get:
CI = 10.5 ± 1.96 * (16.6/√1015)
CI = (9.89, 11.11)
This means that we are 95% confident that the population mean number of books is between 9.89 and 11.11 books.
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Gianna is going to throw a ball from the top floor of her middle school. When she throws the ball from 48feet above the ground, the function h(t)=-16t^2+32t +48 models the height,h, of the ball above the ground as a function of time, t. Find the zero of this function that tells us when the ball will hit the ground.
What is the symbolic representation for this argument?
If a polygon has exactly three sides, then it is a triangle.
Jeri drew a polygon with exactly three sides.
Therefore, Jeri drew a triangle.p
The fact that Jeri drew a polygon with precisely three sides serves as the representation of this claim.
Describe a polygon.A polygon is a closed shape made of line segments rather than curves on a two-dimensional plane.
A minimum of three line segments need to be joined end to end to produce a closed figure. As a result, a triangle and a 3-gon are both terms for a polygon with at least three sides.
The polygons are divided into many categories based on the sides and angles, including:
Normal PolygonUneven PolygonPolygon Convexrounded polygonsIn this instance, Jeri's drawing of a polygon with precisely three sides serves as the symbolic expression of this argument.
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On New Year's Eve, the probability of a person having a car accident is 0.09. The probability of a person driving while intoxicated is 0.32 and probability of a person having a car accident while intoxicated is 0.15. What is the probability of a person driving while intoxicated or having a car accident?
Round to 2 decimal places
Answer:
Step-by-step explanation:
To calculate the probability of a person driving while intoxicated or having a car accident, we need to use the formula for the union of events:
P(A or B) = P(A) + P(B) - P(A and B)
where A and B are the events of driving while intoxicated and having a car accident, respectively.
Using the probabilities given in the problem, we can calculate:
P(intoxicated) = 0.32
P(accident) = 0.09
P(accident | intoxicated) = 0.15
To find P(intoxicated or accident), we first need to find P(intoxicated and accident). We can use the formula for the conditional probability as follows:
P(intoxicated and accident) = P(accident | intoxicated) x P(intoxicated)
P(intoxicated and accident) = 0.15 x 0.32 = 0.048
Now we can use the formula for the union of events:
P(intoxicated or accident) = P(intoxicated) + P(accident) - P(intoxicated and accident)
P(intoxicated or accident) = 0.32 + 0.09 - 0.048
P(intoxicated or accident) = 0.362
Therefore, the probability of a person driving while intoxicated or having a car accident is 0.362, or approximately 36.2%.