The probability of at least one of them being a physics instructor is 120 ways to form the committee.
Probability of Independent Events: The 'At Least One' Rule?Sometimes, simply the occurrence of the event at least once matters when computing independent events. The "At Least One" Rule is used to describe this. The complement of the probability of the event never occurring will be used to calculate the probability of the event occurring at least once.
There are five chemistry instructors and six physics instructors at a college. If a committee of four instructors is selected.
Starting with 6, choose two because we require at least two professors. Let's move on to the remaining 8 individuals (there were initially 10, but now there are just 8): and select 3.
6 select 2; 8 select 3
15×56 =840
We then chose 5 individuals from a group of 10, at least 2 of whom were lecturers.
(9) = 20 options for selecting the professors. 3
(3) = 6 options for selecting the professors.
(9) (¹) = 20 × 6 = 120 ways.
Therefore, 120 ways to form the committee.
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Complete question:
There are five chemistry instructors and six physics instructors at a college. If a committee of four instructors is selected, find the probability of at least one of them being a physics instructor?
Identify the recursive formula for the sequence -3, 9, -27, 81, ....
Answer:
A
Step-by-step explanation:
there is a common ratio between consecutive terms , that is
9 ÷ - 3 = - 27 ÷ 9 = 81 ÷ - 27 = - 3
this indicates the sequence is geometric.
the recursive formula allows a term in the sequence to be found by multiplying the previous term by the common ratio r , that is
f(n) = - 3f(n - 1) if n > 1 : f(1) = - 3
Jenna collects stamps. She puts the same number of stamps on each page and then inserts each page into one of her two stamp books. One of her stamp books has a total of 840 stamps. The other has 1008. What is the largest number of stamps that Jenna could be putting on each page
168 is the largest number of stamps that Jenna could be putting on each page
What is the Greatest Common Factor?
The greatest common factor (GCF or GCD or HCF) of a set of whole numbers is the largest positive integer that divides evenly into all numbers with zero remainder. For example, for the set of numbers 18, 30 and 42 the GCF = 6.
So the largest number of stamps that Jenna could be putting on each page
would be gcd of 1008 and 840.
840 = 2 x 2 x 2 x 3 x 5 x 7
1008 = 2 x 2 x 2 x 2 x 3 x 3 x 7.
∴ The Gcd = 2 x 2 x 2 x 3 x 7 = 168.
Hence 168 is the largest number of stamps that Jenna could be putting on each page
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An interior wall is made up of metal studs with 5/8 gypsum board on each side if the actual width of a stud is 3 5/8 what is the total thickness of the wall
Which of the following ordered pairs is a solution of the system?
x + 3y = 12
y-x=12
Answer:
Step-by-step explanation:
please match the following pairs of lines with their descriptions:
The following pairs of lines should be matched with their descriptions as follows:
y = 2x/3 + 4 and y = -3x/2 + 9; perpendicular lines.y = 4x/5 + 8 and y = 5x/4 + 8; neither parallel nor perpendicular lines.y = 5x/6 + 8 and y = 5x/6 + 2; parallel lines.What are parallel lines?Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.
The condition for two parallel lines.In Geometry, two (2) lines are considered to be parallel if their slopes are the same (equal) and they've different y-intercepts.
This ultimately implies that, two (2) lines are parallel under the following conditions:
m₁ = m₂
Note: m is the slope.
What are perpendicular lines?Perpendicular lines can be defined as two (2) lines that intersect or meet each other at an angle of 90° (right angles).
The condition for two parallel lines.In Mathematics, the condition for perpendicularity of two lines is:
m₁ × m₂ = -1
Given the following equations:
y = 2x/3 + 4 and y = -3x/2 + 9; 2/3 × -3/2 = -1.
y = 4x/5 + 8 and y = 5x/4 + 8; neither parallel nor perpendicular lines.
y = 5x/6 + 8 and y = 5x/6 + 2; 5/6 = 5/6.
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Measure the length of AD & D B what is the ratio of AD to DB
Based on the calculations, the ratio of AD to DB is equal to 0.6.
What is a ratio?A ratio is a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.
From the graph, we have:
Length of AD = 1.5
Length of DB = 2.5
Ratio = AD/DB
Ratio = 1.5/2.5
Ratio = 0.6.
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The sine, cosine, cosecant, and secant functions have period _______; the tangent and cotangent functions have period _______.
The sine, cosine, cosecant, and secant functions have period 2π; the tangent and cotangent functions have period π.
Definition for Period of a Trigonometric Function :
The pause between any function's repetitions is known as the function's period. The duration of one complete cycle is the period of a trigonometric function. Trigonometric functions include three basic types: sin, cos, and tan, which have periods of -2π, 2π, and π respectively.
If a function repeats itself repeatedly at a predetermined frequency, it is said to be periodic. The formula for t is f(x) = f(x + p), where p is a real number that denotes the period of the function. Period is the interval between two occurrences of the wave.
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Joe needs to get to his house, which is 106 miles away in 2 hours. How fast does he need to drive? 48 mph 104 mph 0.019 mph 53 mph
Answer:
53 mph
Step-by-step explanation:
We need to give the answer in terms of miles per hour. This means that we need to find out how many miles Joe needs to travel in one hour. Therefore, this is a ratio problem.
We can set up a proportion where the unknown variable is the number of miles driven in one hour:
[tex]\frac{106}{2} =\frac{x}{1}[/tex]
x is just 106/2, or 53. Therefore, Joe needs to travel 53 mph
Which type of arc requires another entity to specify its start point?
Write an equation of the line passing through the point (8, 2) that is parallel to the line 6x - 9y = -7.
The equation passing through the point ()8, 2 and parallel to 6x - 9y = -7 is y = 6 / 7x - 2 / 7
How to find equation of a line?The equation of the line passes through the point (8, 2) and it is parallel to 6x - 7y = -7.
The equation of a line can be represented as follows;
y = mx + b
where
m = slope
b = y-intercept
Therefore, parallel line have the same slope.
6x - 7y = -7
7y = 6x + 7
y = 6 / 7 x + 1
m = 6 / 7
Hence, using (8, 2)
2 = 6 / 7 (8) + b
2 = 16 / 7 + b
b = 2 - 16 / 7
b = 14 - 16/ 7
b = - 2 / 7
Hence, the equation is y = 6 / 7x - 2 / 7
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1. What is the approximate area of circle A?
2. What is the approximate area of circle B?
3. What is the approximate area of the shaded region 1 (between the square and circle A)?
4. What is the approximate area of shaded region 2 (between circles A & B)?
The approximate area of circle A is π · 8² = 64π ≈ 201.062 square inches.
The approximate area of circle B is π · 4² = 16π ≈ 50.265 square inches.
The approximate area of shaded region 1 is 24² - 64π ≈ 374.938 square inches.
The approximate area of shaded region 2 is 64π - 16π = 48π ≈ 150.796 square inches.
How to estimate geometric areas
In this situation we have a square whose side length is known and two circles whose radii have to be estimated. By direct inspection we find that the diameter of circle A is two thirds of the length of the square side (l), in inches and the diameter of circle B is the half of the diameter of the former. Now we proceed to find the key dimensions of the figure:
Circle A
Diameter: 16 inches
Radius: 8 inches
Circle B
Diameter: 8 inches
Radius: 4 inches
The approximate area of circle A is π · 8² = 64π ≈ 201.062 square inches.
The approximate area of circle B is π · 4² = 16π ≈ 50.265 square inches.
The approximate area of shaded region 1 is 24² - 64π ≈ 374.938 square inches.
The approximate area of shaded region 2 is 64π - 16π = 48π ≈ 150.796 square inches.
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Identify the property being demonstrated for each expression.
3+ (5 + 7) = (3+5)+7
(3)[5(7)] = (3)[7(5)]
Intro
5+0=5
Dor
10 points please help me
a. Surface area = 172 cm²
Volume = 112 cm²
b. The surface area would be needed.
c. The volume would be needed.
How to Find the Surface Area and Volume of a Box?Surface area = 2(wl+hl+hw).
Volume = (length)(width)(height)
a. l = 7 cm
w = 2 cm
h = 8 cm
Surface area =2(wl+hl+hw) = 2·(2·7+8·7+8·2) = 172 cm²
Volume = (7)(2)(8) = 112 cm²
b. The surface area would be needed.
c. The volume would be needed to find the amount of juice the box will hold.
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A manufacturing firm has adopted a new layout for its production process, which is intended to increase worker productivity. With the old layout, mean daily output was 200 units. A manager wants to test the null hypothesis that with the new layout, mean daily output is no greater than 200, against the alternative hypothesis that it is greater than 200. Assume that daily output levels are approximately normally distributed, with standard deviation 18 units. Which sampling distribution is the basis for this hypothesis test? Letter (see multiple choices in the instructions)
Since the standard deviation for the population is known, the z-distribution is used as the sampling distribution basis for this hypothesis test.
When to use the t-distribution and the z-distribution?If the population standard deviation is known, the z-distribution is used.If the population standard deviation is not known, only the sample standard deviation, the t-distribution is used.In this problem, the standard deviation for the population is known, hence the z-distribution is used.
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Can someone please help me on this problem and show work pleasee I’m having trouble doing this!!!
Let’s start by stating the formula for the area of a rectangle,
A=LW
the letter a represents area, l represents length, and w represents width.
Next let’s substitute known values.
A=x(x+10)
Next let’s use the distributive property
A=(x(x))+(10(x))
Now simplify.
A=x^2 + 10x
So the equation for the area of this rectangle is A=x^2+10x
I believe this is the most simplified answer, please tell me if I am wrong and I will redo my work.
A recent survey at a local company showed that 300 employees, or 66⅔% of the company’s employees, carpool to work each day. How many employees work at this company?
I'm sorry for all this trouble just really need help I'm in summer school because I was gone most of the school year and its all online so i don't understand anything
Answer:
450 employees work at this company.
Step-by-step explanation:
300 = 2/3 of x
300 × 3 = 2x
900 = 2x
450 = x
Jasmine wants to buy a car marked at $5200 at a second hand car dealer. The deposit is two-fifth of the price of the car
for the next weck's delivery. Jasmine's father helped her in the deposit by paying 30% of the price. Will jasmine have
enough for her car deposit? If not, how much more does she need to add to get the deposit?
Jasmine will not have enough for the car. The amount more that she needs is $520.
Will Jasmine have enough for the car?
The first step is to convert the fraction that represents the amount needed as a deposit to percentage.
(2/5) x 100 = 40%
Difference in the deposit and the amount Jasmine's father deposited: 40% - 30% = 10%
Amount more that she needs : 10% x 5200 = $520
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Copy DEF to the line so that S is the
vertex.
This task will be complete when you have
constructed an angle with vertex S that is
congruent to ZDEF.
Estimate the distance between points G and I with a compass and sketch an arc from point V which bisects the earlier arc U.
How to construct an angle with vertex?
To copy an angle we observe the subsequent steps,
1). Mark a working line with the help of a straightedge.
2). Now we set a point S as the vertex of the angle.
3). Create an arc with a radius 'r' (any length ) from vertex S which bisects the working line V.
4). With the exact radius we mark an arc from point E which bisects the line ED and EF at G and H respectively.
5). Mark an arc from point G which bisects line EF at I.
6). Estimate the distance between points G and I with a compass and sketch an arc from point V which bisects the earlier arc U.
7). Now join the points S and U.
Therefore we copy any angle.
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Find the length of JN
The length of JN from the figure is 108
Measure of segment of a lineA line is the shortest distance between two points. Given the following parameters
Required
We need the length of JN
JN = JK + KN
JN = 59 + 49
JN = 108
Hence the length of JN from the figure is 108
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If a problem is 8(2x+4) = 2(1x+3) is the first step done of PEMDAS for THIS SPECIFIC PROBLEM parentheses or multiplication?
The first step is the parenthesis
How to determine the first step?The equation is given as:
8(2x+4) = 2(1x+3)
Using PEMDAS, the first step is to open the brackets by multiplication.
So, we have:
16x + 32 = 2x + 6
Hence, the first step is the parenthesis
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What ratios are equivalent to 12:9
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathsf{12:9}[/tex]
[tex]\huge\textbf{Simplifying:}[/tex]
[tex]\mathsf{12:9}[/tex]
[tex]\mathsf{= 12\div3 : 9 \div 3}[/tex]
[tex]\mathsf{= 4:3}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{4:3}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
What is the value of x? Show your work.
(Please hurry and see image for details.)
Answer:
7
Step-by-step explanation:
By the AA Postulate, triangles JKL and MNP are similar. Segment JK corresponds to segment MN, and segment JL corresponds to segment MP.
JK/MN = JL/MP
25/30 = 20/(4x-4)
25(4x-4) = 20*30
100x - 100 = 600
100x = 700
x = 7
HELP PLEASE!)
A square pyramid has surface that is covered in dark glass. The sides of the pyramid are 456 feet in length. The slant height of the pyramid is 185 feet.
Find the lateral surface area to determine the square feet of glass needed to cover the surface of the pyramid.
Answer choices
376,656 ft^2
42,180 ft^2
337,440 ft ^2
168,720 ft^2
The perimeter of a rectangle is 96 ft and the width is 22 ft what is the length of the rectangle
The length of the rectangle is 26ft.
What is the perimeter of a rectangle?
The sum of all sides of a rectangle is the perimeter of the rectangle.A rectangle has two equal lengths and two equal widths.Therefore, the perimeter 'P' of a rectangle is the sum of two equal lengths and two equal widths. That is, 'P=2l+2w' where 'l' is the length and 'w' is the width of the rectangle.What is the length of the rectangle with perimeter 96ft and the width 22ft?The perimeter of a rectangle is, P = 96 ft.
The width of the rectangle is, w = 22ft.
As we know the perimeter P of a rectangle is given by the formula, P=2l+2w
Therefore, substituting the values in the equation we get,
P = 2l + 2w
96 = 2l + 2*22
96 = 2l + 44
2l = 96 - 44
2l = 52
l = 52/2
l = 26
Hence, the length of the rectangle is 26ft.
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John's dad is 30 years old than john. if john were three times ad old as he is now,he would still be younger than his dad. what is the oldest that john could be right now
john could be right now 45
What is word problem in math?
A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world."
According to the question:
John's dad is 30 years old than john .In essence, x = y -30 .................equation 1And
john were three times ad old as he is now.y=3xSolution for the above equation:
[tex]x=y-30, y=3 x \quad\\ \quad x=15, y=45[/tex]
steps:
[tex]x=y-30 \\y=3 x[/tex]
Substitute :[tex]$y=3 x$[/tex]
[tex][x=3 x-30][/tex]
[tex]for $$x=3 x-30: \quad x=15[/tex]
For [tex]$y=3 x$[/tex]
Substitute: [tex]$x=15$[/tex]
[tex]y=3 \cdot 15[/tex]
Simplify:
[tex]y=45[/tex]
The solutions to the system of equations are: [tex]$x=15, y=45$[/tex]
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To solve the equation 1. 75n = 7 for n, what operation must be applied to both sides in order to isolate the variable n?
The line plot shows the prices of sunglasses at a department store.
a. Find the mean, median, and mode.
b. Which measure best describes the data? Why?
c. Which measure might be misleading in describing the average price of sunglasses? Explain your reasoning.
The measure that best describes the data is the median and the measure that might mislead the data is the mode
How to determine the mean, median and mode?The mean is calculated as:
[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]
So, we have:
[tex]\bar x = \frac{20* 2 + 50 * 3 + 60 * 6 + 70 * 3 + 80 * 4 + 90 * 4 + 100 * 2 + 130 * 1}{25}[/tex]
This gives
[tex]\bar x = \frac{1770}{25}[/tex]
[tex]\bar x = 70.8[/tex]
So, the mean is 70.8
The median is the middle number, and the position is calculated using
Median = (n + 1)/2 th
This gives
Median = (25 + 1)/2 th
Median = 13th
The 13th element is 70
So, the median is 70
The mode is the data element with the highest frequency.
So, the mode is 60
The measure that best describes the dataThe line plot has outliers at 20 and 130.
This is so because 20 and 130 are far from other data values
When a dataset has an outlier, the best measure is the median
Hence, the measure that best describes the data is the median.
The measure that might mislead the dataThe measure that might mislead the data is the mode
This is so the highest occurring value does not necessarily represent the dataset
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PLEASE HELP IM SO STUCK
Answer:
-4
Step-by-step explanation:
Slope = y/x
1. y=12 x=-3
12/-3=-4
2. y=8, x=-2
8/-2 = -4
3. y=4, x=-1
4/-1 = -4
4. 0/0 = 0
5. y=-4, x=1
-4/1 = -4
Hope it helps I had this question last year on Acellus.
Find the volume of the sphere.
Answer:
268.08 (268)
Step-by-step explanation:
The volume of a sphere is 4/3*pie*r^3
Find the value of cos F rounded to the nearest hundredth, if necessary. E 6 F 8 10 D
Answer:
cosF = 0.6
Step-by-step explanation:
cosF = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{EF}{DF}[/tex] = [tex]\frac{6}{10}[/tex] = 0.6
Answer:
Cos F = 0.6
Step-by-step explanation:
Trigonometry ratios:[tex]\sf \boxed{\bf \ Cos \ F = \dfrac{adjacent \ side \ of \ \angle F}{hypotenuse}}[/tex]
[tex]\sf =\dfrac{EF}{DF}\\\\=\dfrac{6}{10}\\\\= 0.6[/tex]