The probability of the student's name being drawn first is 1/3.
The probability that you and your two friends will be chosen, but your name will be drawn first is 1/3.The likelihood or chance of a specific event happening is referred to as probability. The probability of an event is represented by a number between 0 and 1, with 0 indicating that the event will never occur, and 1 indicating that the event will always occur.
Probability formula the probability of an event occurring is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability (P) = number of favorable outcomes/total number of possible outcomes.Probability of the scenario The total number of people who can be picked is three, with one of them being the student.
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In a certain school 41% of the students are senior form students. If its junior form students are 270 more than the senior form students, find the number of students of the senior form students and junior form students respectively.
Based on proportions, the numbers of students in the senior form and junior form are 615 and 885, respectively.
What is proportion?Proportion refers to the equation of two ratios.
Proportion is a fractional value depicted using ratios, percentages, fractions, and decimals.
The percentage of senior form students in the school = 41%
The percentage of junior form students = 59% (100% - 41%)
The additional percentage of junior over senior students = 18% (59% - 41%)
The additional number of junior form students over the seniors = 270
Proportionately, if 18% = 270, the total number of students (both junior and senior) = 1,500.
Therefore, the number of senior and junior students is as follows:
Senior = 615 (1,500 x 41%)Junior = 885 (1,500 x 59%).Check:
The difference in the numbers = 270 (885 - 615)
Thus, using proportions, we can state that there are 1,500 students in the school, consisting of 615 seniors and 885 juniors.
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suppose that inches 23 of wire costs 92 cents .at the same rate, how much (in cents) will 34 inches of wire cost?
The required cost of 34 inches of wire as per the cost of 23 inches of wire is 92 cents is equals to 136 cents.
Let x be the cost (in cents) of 34 inches of wire.
We know that 23 inches of wire costs 92 cents,
Use a proportion to solve this problem,
23 inches / 92 cents = 34 inches / x cents
To solve for x, apply cross-multiply and simplify,
⇒ 23 inches × x cents = 92 cents × 34 inches
⇒ 23x = 3128
⇒ x = 3128/23
⇒ x ≈ 136.00 cents
Therefore, the cost of 34 inches of wire will be approximately 136 cents.
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1. Explain how the expression 8-6x+x^2 is in standard form.
2. Is the expression equivalent to (x-4)(x-2)? Explain.
Answer:
1. It's a quadratic expression bcs the highest power in a quadratic expression is 2. Hence its in standard form. basically anything that follows ax^2 + bx + c
2. x^2-6x+8 (separate the coefficient into 2, where they add to get the coefficient number (-6), and multiply to get the number (8)
x^2-4x-2x+8 (separate it into 2 parts, and factorize each part)
x(x-4)-2(x-4)
(x-2)(x-4)
Hence, x^2-4x-2x+8 is equivalent to (x-2)(x-4)
How do i solve this??
The measure of angle x and y in the cyclic quadrilateral are 93 and 59 degrees.
How to solve cyclic quadrilateral?A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle. The sum of angles in a cyclic quadrilateral is 360 degrees.
The opposite angles in a cyclic quadrilateral add up to 180°. The opposite angles of a cyclic quadrilateral are supplementary.
Therefore, let's find the measure of x and y in the cyclic quadrilateral.
Hence,
x + 87 = 180
x = 180 - 87
x = 93 degrees
y + 121 = 180
y = 180 - 121
y = 59 degrees
Therefore,
x = 93°
y = 59°
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The cost per guest of catering an event of no more than 100 people is modeled by the
function fx=30+4x.The number of guests is modeled by the function g x = 100-x,
where x represents the number of guests fewer than 100 that attend.
Evaluate (f•g) (12) and interpret what it means in the context of the problem.
The result (f•g)(12) = 382 represents the overall cost of catering the event when 12 fewer guests than 100 attend.
what is function ?In mathematics, a function is a rule that gives each input value in a set a distinct output value. It is a relationship between a collection of inputs and a set of potential outputs, where each input has a single, precise counterpart in each possible outcome. f(x) = x2, where f is the function, x is the input, and x2 is the output, is a common function notation used to represent functions. Functions are used to model and analyse interactions between variables in many branches of mathematics as well as in many fields of science and engineering.
given
We must first locate the composite function f(g(x)) before substituting x = 12 to calculate (f•g)(12):
430 - 4x = f(g(x)) = f(100 - x) = 30 + 4(100 - x)
Thus, 430 - 4x = (f•g)(x) = f(g(x)).
If we replace x with 12, we get:
(f•g)(12) = 430 - 4
(12) = 382
Interpretation: Taking into account the cost per guest as modelled by f(x) = 30 + 4x and the number of attendees as modelled by g(x) = 100 - x, the result (f•g)(12) = 382 represents the overall cost of catering the event when 12 fewer guests than 100 attend.
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inequality and graph its solution 5< x -2 > 11
The solution of the inequality is 7 < x < 13 and graph is attached.
The inequality 5 < x - 2 < 11 represents a range of values for x that satisfy the inequality. To graph its solution, we can start by adding 2 to each part of the inequality:
5 + 2 < x - 2 + 2 < 11 + 2
This will be simplified to:
7 < x < 13
This solution represents all values of x that make the inequality true. To graph this on a number line, we can draw a line with a point at 7 and a point at 13, and shade in the region between them. The shaded region represents all values of x that satisfy the inequality.
In words, the solution can be described as follows: x is greater than 7 and less than 13. Alternatively, we can use interval notation to represent the solution as (7, 13).
It is important to note that the solution to the inequality is not a single value, but rather a range of values. The graph helps to visualize this range and make it easier to understand.
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Add and simplify.
3 ft. 9 in.
4 ft. 7 in.
+ 10 ft. 3 in.
-------------------
The sum of the units 3 ft. 9 in, 4 ft. 7 in. and 10 ft. 3 in. is 18 ft. 7 in.
Evaluating the sum of the unitsTo add these lengths, we need to first convert all the measurements to the same units.
Let's convert everything to inches.
3 ft. 9 in. = (3 x 12) + 9 = 45 in.
4 ft. 7 in. = (4 x 12) + 7 = 55 in.
10 ft. 3 in. = (10 x 12) + 3 = 123 in.
Now we can add the lengths:
45 in. + 55 in. + 123 in. = 223 in.
We have 223 inches in total.
To convert this back to feet and inches, we can divide by 12 to get:
18 ft. 7 in.
So the final answer is 18 ft. 7 in.
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Write equivalent expression using algebraic properties: 2x + 10 + 2(5y +3) and then find its value if x=1 and y=1.
Answer:
28
Step-by-step explanation:
2x+10+2(5y+3)
2×1+10+2(5×1+3)
2+10+10+6
28
x^2+4x-7=0
give answer to 2 decimal places
Answer:
Step-by-step explanation:
2. A baseball travels d meters 1 seconds after being dropped from the top of a building
The distance traveled by the baseball can be modeled by the equation d = 5t².
a. Complete the table and plot the data on the coordinate plane.
t (seconds) d (meters)
0
0.5
1
1.5
2
distance traveled (meters)
30
25
15
10
0.5
1.5 2 2.5 3 3.5
1
time (seconds)
Does anyone know the answer? Kendall Hunt High School Math, Algebra 1 in the unit 5 summary practice problems
The graph should show a parabolic shape, opening upwards. The points are (0,0), (0.5, 2.5), (1,5), (1.5, 22.5), and (2,20).
Define functionIn mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range) with the property that each input is related to exactly one output.
Using the table provided, we can fill in the values for distance traveled:
Given function d=5t²
Putting t=0, d=0
t=0.5, d=1.25
t=1, d=5
t=1.5, d=11.25
t=2, d=20
Hence, d(meters) are 0,1.25,5,11.25 and 20.
To plot this data on a coordinate plane, we can use the values of t as the x-coordinates and the values of d as the y-coordinates.
The graph should show a parabolic shape, opening upwards. The points (0,0), (0.5, 2.5), (1,5), (1.5, 22.5), and (2,20) should be plotted and connected with a smooth curve.
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select all angle measures for which cos 0 = 1/2
–120°
–60°
120°
600°
660°
The angle measures that satisfy cos theta = 1/2 are
-120° (or 240°)-60° (or 300°)660° (or 60°)How to find the angle measures of 1/2To find all angle measures for which cos theta = 1/2, we can use the unit circle and look for the x-coordinate of the point where the angle intersects the unit circle.
The x-coordinate (cosine) is equal to 1/2 at two points on the unit circle:
at 60 degrees (or pi/3 radians) and at 300 degrees (or 5pi/3 radians).However, the given angle measures are not all within one revolution (360 degrees or 2pi radians), so we need to find equivalent angles within one revolution.
To do this, we can add or subtract multiples of 360 degrees or 2pi radians from the given angles until they are within one revolution.
-120° = 360° - 120° = 240°
-60° = 360° - 60° = 300°
120° = 120°
600° = 600° - 1(360°) = 240°
660° = 660° - 2(360°) = 60°
So the angle measures that satisfy cos theta = 1/2 are -120° (or 240°), -60° (or 300°), and 660° (or 60°).
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can you please solve this
this is only 8th grade math
Answer:
second option: 6
Step-by-step explanation:
The general term of a geometric sequence is given by: [tex]a_{n} = a_{1} r^{n-1}[/tex]
∴ [tex]a_{1}[/tex] is the first term
[tex]a_{8} = a_{1} (3)^{8-1}[/tex]
13122 = [tex]a_{1}[/tex] [tex](3)^{7}[/tex]
13122 = [tex]a_{1}[/tex] x 2187
13122/2187 = [tex]a_{1}[/tex]
6 = [tex]a_{1}[/tex]
Someone already asked this question but wrong answer. PLS HELP!!!
[x/(y-1)](-4)-[xy+(-3)]/(-1) if x= -5 and y= -2
The worth of expression at x = - 5 and y = - 2 is,
⇒ 1/3
A numerical expression is characterized as the assortment of numbers factors and works by utilizing operations like expansion, deduction, multiplication, and division.
Considering that;
The expression is,
⇒ ([x/(y - 1)](- 4) - [xy + (- 3)]/(- 1)
Presently, We can place x and y in the above expression as;
⇒ ([x/(y - 1)](- 4) - [xy + (- 3)]/(- 1)
⇒ [- 5/(- 2 - 1) ] (- 4) - [-5×-2 + (- 3)]/(- 1)
⇒ [ - 5/ - 3 ] (- 4) - [10 - 3]/(- 1)
⇒ - 20/3 + 7
⇒ 1/3
In this way, The worth of expression at x = - 5 and y = - 2 is,
⇒ 1/3
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Please Help! Im confused!
Answer:<HBG
Step-by-step explanation:
Adjacent means next to in this situation so it would be the angle next to it.
Which expression is equivalent to sin(pi/12) cos(7pi/12) -cos(pi/12) sin(7pi/12)?
Step-by-step explanation:
Using the trig identity for sin ( a- b) , this reduces to
sin ( pi/12 -7 pi/12) = sin ( -6pi/12 ) = sin ( - pi/2)
A researcher’s hypothesis is that the average length of salmon returning to spawn from an Alaskan river is less than the historical average length of 24 inches. The researcher collects a random sample of 45 salmon, measures the length of each fish, and computes an average length of 22 inches, with a standard deviation of 3.1 inches. Which of the following is the appropriate test for the researcher’s hypothesis?A) A matched-pairs t-test for a mean differenceB)A two-sample t-test for a difference between meansC)A one-sample z-test for a population meanD)A one-sample t-test for a population meanE)A one-sample z-test for a population proportion
For this situation, the example size is 45 and the standard deviation is 3.1 inches, which is known. Hence, a one-example t-test is fitting for testing the scientist's hypothesis about the normal length of salmon getting back to generate from the Alaskan waterway.
The proper test for the scientist's hypothesis that the typical length of salmon getting back to generate from an Alaskan river is not exactly the verifiable normal length of 24 inches is a one-example t-test for a populace mean.
This is on the grounds that the specialist is looking at the example mean length (22 inches) to a realized verifiable populace mean (24 inches), and needs to decide whether the contrast between the two means is measurably huge. A one-example t-test is utilized to contrast an example mean with a realized populace mean and is suitable when the example size is little and the populace standard deviation is obscure.
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If (7,-4) is on the graph of F(x), which point must be on the
graph of the inverse function F¹(x)?
Point (D) (-7, 4) must be on the graph of the inverse function F¹(x) if point (7,-4) is on the graph of the function F(x).
What is an inverse function?If there is just one value of x in the domain where f(x)=y, then a function f does not have an inverse function.
The term "f inverse" is widely used to refer to this particular inverse function, which is singular.
A function's inverse will cause the input and output to be inverted.
If a function has an inverse, one can use algebra to find it by setting the function equal to y.
Then, swap x and y and solve for y in terms of x.
So, we have the coordinates:
(7, -4)
It lies in the 4th quadrant.
Then, its inverse would be in the 2nd quadrant.
Which would be:
(-7, 4)
Therefore, point (D) (-7, 4) must be on the graph of the inverse function F¹(x) if point (7,-4) is on the graph of the function F(x).
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Answer:
Step-by-step explanation:
it's (-4,7)
What critical value would you use for a 96% confidence interval from an SRS of 16 observations?
When creating a 96% confidence interval from a simple random sample (SRS) of 16 observations, the critical value to be used is 2.120.
What is a confidence interval?A confidence interval is a range of values for an unknown population parameter, such as the population mean or population proportion. Confidence intervals are usually stated as a range of values with a level of confidence that the population parameter is contained in the interval.
Let's examine the components of a confidence interval to understand what it is:
Upper Bound (UB) and Lower Bound (LB): The UB and LB are the endpoints of the confidence interval.Estimate (E): The estimate is the mean or proportion calculated from the sample.Standard Error (SE): The standard error of the mean (SEM) or the standard error of the proportion (SE) is the estimated standard deviation of the sampling distribution.Learn more about confidence interval at
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Anyone know how to do this?
An angle bisector theorem is used to determine AD = 4.68 as the length of the side of the triangle AD.
What is the angle bisector theorem explained?Vertex, the intersection of two lines, is used to measure angles. Internal angles are created by the sides of geometric shapes like triangles and rectangles.
Each geometric figure has a general dimension determined by the sum of its interior angles. Geometrical operations such as bisecting an angle are possible.Each angle that also is bisected is divided into two angles of equal size. The bisector is constructed from the vertex defining the principal angle.With the triangles that are presented, prove the angle bisector theorem:
There will be equality in the side ratios.
AB / BC = AD / DC
AB = 9 ; BC = 11.7 AD = 3.6
Put the values.
9/11.7 = 3.6 / AD
AD = 3.6*11.7 / 9
AD = 4.68
Thus, an angle bisector theorem is used to determine AD = 4.68 as the length of the side of the triangle AD.
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An airship flies 150km with the wind and then turns around and flies back, taking 6 hours and 15 minutes for the round trip. Find the speed of the wind if the speed of the airship in calm weather is 50 km/hr.
The speed of the wind is 10km/hr.
What is the speed?
A scalar quantity, speed is defined as the size of the change in an object's location over time or the size of the change in an object's position per unit of time.
Here, we have
Given: An airship flies 150km with the wind and then turns around and flies back, taking 6 hours and 15 minutes for the round trip.
We have to find the speed of the wind if the speed of the airship in calm weather is 50 km/hr.
150 = (50-c)(6.25-t)
6.25-t = 150/(50-c)
(6.25×50 - 6.25c -150)/(50-c) = t
t = (162.5 - 6.25c)/(50-c).....(1)
150=(50+c)t
t = 150/(50+c)
Now, we put the value of t in equation (1) and we get
150/(50+c) = (162.5 - 6.25c)/(50-c)
150 = (50+c) (162.5 - 6.25c)/(50-c)
150 = (50+c)(162.5 - 6.25c)/(50-c)
150 = (8125 - 312.5c +162.5c - 6.25c²)/(50-c)
7500 - 150c = 8125 - 312.5c + 162.5c - 6.25c²
7500 - 150c = 8125 - 150c - 6.25c²
7500 = 8125 - 6.25c²
8125 - 6.25c² - 7500 = 0
6.25c² - 625 = 0
c² = 100
c = 10
Hence, the speed of the wind is 10km/hr.
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I need to find the area
Answer:
9.9
Step-by-step explanation:
Turn Fractions into decimals. 3 3/5 turns to 3.6 and 5 1/2 turns to 5.5
Multiply them and get 19.8 and divide by 2 to get 9.9
Answer:
Step-by-step explanation:
Area = s x s. So 3 3/5 x 5 1/2 = 99/5 = 19 4/5
Please help me! This is due at 2:15 PM!!!! A game has 15 balls for each of the letters B, I, N, G, O. The table shows the results of drawing balls 1,250 times.
Letter Frequency
B 247
I 272
N 238
G 241
O 252
For which letter is the experimental probability closest to the theoretical probability? Explain please.
The experimental probability closest to the theoretical probability is O.
What is probability?
The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.
Here, we have
Given: A game has 15 balls for each of the letters B, I, N, G, O. The table shows the results of drawing balls 1,250 times.
Each letter should have the same probability of occurring since there are 15 of each.
There are 5 letters that can be drawn, so there is a total of 75 balls, and each letter has a probability of 15/75 = 1/5 of being drawn.
This means one would expect a theoretical frequency of 1250/5 = 250, i.e. any given letter should get drawn 250 times.
Hence, the experimental probability closest to the theoretical probability is O.
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What is 0. 1 , 0. 09 , 2% , 7/10 , 19/100 in ascending order
The correct order is: 2%, 0.09, 19/100, 7/10, 0.1. We can calculate it in the following manner.
First, we need to convert all the fractions and percentages to decimals, and then we can compare them in ascending order:
0.09, 0.1, 0.02, 0.7, 0.19
Therefore, the ascending order of the given numbers is:
0.02, 0.09, 0.19, 0.7, 0.1
So the correct order is: 2%, 0.09, 19/100, 7/10, 0.1
A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a measurement system.
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If a and y are in direct proportion and y is 35 when x is 7, find y when x is
10.
Answer: y =
Submit Answer
attempt 1 out of 4
Answer:
Step-by-step explanation you have to do this
Answer:
Saanvi recorded the number of math problems she did for homework each night for 10 days.
Step-by-step explanation:
(a)Work out the size of the angle marked y. L 40° y 160° 30⁰
A negative answer makes no sense because y is an angle and cannot be negative. As a result, we can conclude that there is no solution because the specified angles do not form a proper triangle.
What is a triangle?A triangle is a closed, double-symmetrical shape composed of three line segments known as sides that intersect at three places known as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all factions equal), isosceles, or scalene based on their sides. Triangles are classified as acute (all angles are fewer than 90 degrees), good (one angle is equal to 90 degrees), or orbicular (all angles are higher than 90 degrees) (all angles greater than 90 degrees). The region of a triangle can be calculated using the formula A = (1/2)bh, where an is the neighbourhood, b is the triangle's base, and h is the triangle's height.
The total of a triangle's angles is 180 degrees. As a result, we may begin by locating the missing angle in the triangle containing the angle denoted by y:
Angle missing = 180° - 40° - y = 140° - y
y + 160° + 30° = 180°
Mixing like terms and calculating y:
y = 180° - 160° - 30° = -10°
A negative answer makes no sense because y is an angle and cannot be negative. As a result, we can conclude that there is no solution because the specified angles do not form a proper triangle.
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Find the value of x in the triangle shown below.
X =
7
80°
9
7
To find the value of x in the triangle, we can use the law of sines, which states that in any triangle ABC, the following relationship holds:
a/sin A = b/sin B = c/sin C
where a, b, and c are the side lengths of the triangle opposite to the angles A, B, and C, respectively.
In this case, we can write:
x/sin 80° = 7/sin 50°
Using the properties of sines, we can simplify this expression to:
x = (7 x sin 80°) / sin 50°
Using a calculator, we can evaluate this expression to get:
x ≈ 9.05
Therefore, the value of x in the triangle is approximately 9.05.
What is the relationship between the angle of elevation and the angle of depression between two points?
The relationship between the angle of elevation and the angle of depression between two points is that they are alternate interior angles and are equal when measured from the same horizontal line.
The angle of elevation and the angle of depression are related to each other as follows. The angle of elevation is the angle between the horizontal line and the line of sight when an observer is looking upwards to an object. The angle of depression is the angle between the horizontal line and the line of sight when an observer is looking downwards to an object.
The two angles are complementary, which means that they add up to 90 degrees. This is because the horizontal line and the line of sight form a right angle.
So, if the angle of elevation is x degrees, then the angle of depression is (90 - x) degrees, and vice versa.
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What value of q makes the equation -0.5(3q+15) = 1.5(q+11) true?
Answer:
-8
Step-by-step explanation:
-0.5(3q+15) = 1.5(q+11)
3q + 15 = -3q - 33
6q = -48
q = -8
dentify the population and the sample in each exercise. The number of home runs hit during one week in July of the 2014-2015 baseball season.
In conclusion Sample: A subset of the population, which could be a randomly selected group of home runs hit during one week in July of the 2014-2015 baseball season, used to estimate the average number of home runs hit during that week.
What does average number mean?
Average number is a measure of central tendency that is calculated by adding up a set of numbers and dividing the sum by the total number of numbers in the set. It is also known as the mean.
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Complete question:
What is the population and sample in a study of the number of home runs hit during one week in July of the 2014-2015 baseball season?
Population: The population in this study would be all home runs hit during one week in July of the 2014-2015 baseball season by all players and teams in the league.
Sample: The sample in this study would be a subset of the population, such as the home runs hit during one week in July of the 2014-2015 baseball season by a specific team or a specific player.
What is the slope of the line that passes through (2, 5) and (−1, 5)? (1 point)
The slope of the line that passes through (2, 5) and (−1, 5) will be 0.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
The slope associated with two points (x₁, y₁) and (x₂, y₂) is given by
Slope = (y₂ - y₁)/(x₂ - x₁)
The slope of (2, 5) and (−1, 5),
Slope = (5 - 5)/(-1 - 2) = 0
Hence "The slope of the line that passes through (2, 5) and (−1, 5) will be 0".