The number of different ways that the three positions can be filled is 504 ways.
How to calculate the value?From the information, there are 9 candidates for three positions at a restaraunt. Based on the data, one position is for a cook, the second position is for a food server and the third position is for a cashier.
Therefore, the number of ways will be:
= 9P3
= 9! / (9 - 3)!
= 9! / 6!
= 9 × 8 × 7
= 504
The number of ways is 504 ways.
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What is the net salary for someone with a gross of $150 000 a year if they must pay a tax of 30%?
Gross salary of an individual is $150 000 a year if they pay a tax of 30% then net salary is equal to $8750 per month and $105000 per year.
As given in the question,
Gross salary of an individual is $150 000 a year
Percentage of tax on gross salary =30%
Amount of tax is equal to
= 30% of $150 000
= (30/100)× 150 000
= $45000
Net salary per year
= $(150 000 - 45000)
= $105000
Net salary per month
= $(105000/12)
= $8750
Therefore, gross salary of an individual is $150 000 a year if they pay a tax of 30% then net salary is equal to $8750 per month and $105000 per year.
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How do you write 0.083 as a fraction?
Answer: 83/1000 should be the answer
Step-by-step explanation:
0.083 goes to the thousandths place. Which would mean the denominator would be 1000, and in the hundredths and thousandths place it says 83, so the numerator would be 83. Resulting in the answer, 83/100.
The solution of the expression 0.083 in form of fraction is,
⇒ 83/1000
We have to given that,
Write a number 0.083 as a fraction.
Here, The number is,
⇒ 0.083
⇒ 0.083 x 1000 / 1000
⇒ 83/1000
Therefore, The solution of the expression 0.083 in form of fraction is,
⇒ 83/1000
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Find the average rate of change of f(x)=x^2-4x+1 from x=2 to x=6
Answer:
The answer is 4
You invested $28,000 in two accounts paying 3% and 6% annual interest, respectively. If the total interest earned for
the year was $1590, how much was invested at each rate?
The amount invested at 3% is $
The mount invested at 6% is $
Answer: 6000 at 3% and 22000 at 6%
Step-by-step explanation:
x + y = 28,000
0.3x + 0.6y = 1500
multiply everything in the first equation by 0.3 since we want to be able to eliminate the variable x from both equations.
0.3x +0.3y = 840 then subtract second equation to just get one variable
0.3x + 0.6y =1500
-0.3y = -660
y = 22000
28000 - 22000 = 6000 which is x
So 6000 is invested at 3% and 22000 is at invested at 6%
You deposit $200 in an account earning 2% interest compounded annually. How much will you have in the account in 20 years?
Answer:
221
Step-by-step explanation:
Interest goes up 5 dollar each year
(2x+1)(3x+2)=6xsquare+7x+2
Factorization of the given equation : 6x² + 7x +2 is equal to
(2x +1 ) ( 3x +2 ).
As given in the question,
Given equation is
6x² + 7x +2
Using the sum and the product pattern we get
Product of extreme terms is 6 × 2=12
Factors of 12 are 1, 2, 3, 4, 6,12
4 ×3=12(product of extreme terms)
4 +3 = 7(middle term)
Factorize the equation by splitting middle term
6x² +7x +2
=6x²+ 4x +3x +2
=2x( 3x+2)+1(3x+2)
=(2x+1)(3x+2)
Therefore, factorization of the given equation : 6x² + 7x +2 is equal to
(2x +1 ) ( 3x +2 ).
The complete question is :
Factorize the given equation : 6x² + 7x +2 .
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Which calculation correctly uses prime factorization to write in simplest form?
if f(x)= 2x(1-x) ^2 then f(1)=
The value of f(1) is the value of function f(x) at x = 1 which is 0.
What is function?A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).
So,
We have given that the function
f(x)=[tex]2x(1-x)^2[/tex]
So, when x = 1
f(x)= [tex]2(1)(1-1)^2[/tex]
f(x)= 2(1)(0)
f(x)= 0
Therefore, The value of function f(x ) at x = 1 is f(1) 0.
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h(1) = -2
h(2) = 1
h(n) = h(n-2) + h(n-1)
Answer:
h(1)=h(1-2)+h(1-1)
h(1)=h(-1)+h(0)
h(-1)-h(-1)=0
h(0)=h(0)
f the gradient of a line is 3, what is the gradient of the line which is perpendicular to A
Answer:
-1/3
Step-by-step explanation:
gradients of perpendicular lines= m1 × m2=-1
hence , 3 × m2 = -1
m2 -1/3
Which inequality is represented by the number line below?
The inequality that is represented by the number line is C. x ≤ 7.
What is an inequality?An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The most frequent application is to size-compare two numbers on a number line. A difference between two values indicates whether one is smaller, larger, or simply not equal to the other.
It should be noted that from the number line, we can see that the arrow starts from -7 and then moves backwards. This shows that it's x ≤ 7.
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1. What is the value of 10/0?2. Which of the following fractions is equivalent to 3/4?
Answer:
1. Undefined
2. A
Explanation:
Part 1
[tex]\frac{10}{0}=\text{Undefined}[/tex]The value of 10/0 is undefined because you cannot divide by 0.
Part 2
From the given options:
[tex]\begin{gathered} \frac{-3}{-4}=\frac{3}{4}\text{ (Cancel the minus on both the top and bottom)} \\ -(\frac{3}{4})=-\frac{3}{4} \\ -(\frac{-3}{-4})=-\frac{3}{4} \\ \frac{-3}{4}=-\frac{3}{4} \end{gathered}[/tex]Therefore, A is the correct choice.
Please help I’ll mark you as brainliest if correct!!
The sequences are :
a. 2 , 16 , 18 , 54 , 162 is Geometric progression
Three terms : 486, 1458, 4374.
b. 1, 6 , 11, 16, 21 is arithmetic progression
Next three terms 26, 31., 36..
What is geometric progression?In a geometric progression, each element following the first is created by multiplying it by a number known as the common ratio, which is represented by the symbol r.You should be familiar with the following four main categories of sequences: arithmetic sequences, geometric sequences, quadratic sequences, and special sequences.An arithmetic progression is a set of integers with a fixed difference between any two succeeding numbers (A.P.).The terms in the sequence that result if the same number is added to or removed from each term of an A.P. are also in an A.P. with the same common difference.To learn more about : Progression
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Marked
Price
$320.00
Rate of
Discount
20%
Discount
Sale Price
$
$
(Simplify your answers. Type whole numbers or decimals.)
Answer: 64 is the answer
Step-by-step explanation:
I had a question like this and got it right! Hope this the correct answer for you!
well, we know that the regular price is 320 bucks, but is discounted by 20% so
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{20\% of 320}}{\left( \cfrac{20}{100} \right)320}\implies 64~\hfill \underset{\textit{discount price}}{\stackrel{320~~ - ~~64}{\text{\LARGE 256}}}[/tex]
I am a product of three different prime numbers, my largest factor is 13. I am between 185 and 200 who am I ?
The product of three different prime numbers that has largest factor is 13 and is between 185 and 200 is 195.
What are prime numbers?It should be noted that prime numbers are the numbers that can be divisible by only 1 and itself. They include 2, 3, 5, 7, 11, 13, etc.
It should be noted that the information illustrated that the prime numbers are 3, 5 and 13. The multiplication will be:
= 3 × 5 × 13
= 195
The number is between 185 and 200.
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How many feet of chain fence are necessary to
enclose a dog pen that is square and has an area of
144 square feet?
Answer:
48 feet
Step-by-step explanation:
Areas of a square is the length times the width. In a square the length and width are the same number because all the sides of a square have the same length.
12 x 12 = 144, so each side of the pen is 12 feet. We want to find the perimeter (the distance around the square). 4(12) = 48
Customers are charge a late fee of 20% of their bill . This person is a week late on a bill of 200$ what should we charge for late fee
Answer:
Step-by-step explanation:
20$
In the figure, m/RPZ= 95 and TU || RQ || VW. Find the measure of angle UZP.
The measure of the corresponding angle; ∠UZP = 95°.
What is defined as the term corresponding angle?The definition of corresponding angles states that when two parallel lines intersect with a third, the angles that take up its same relative position at every intersection are said to be corresponding angles to one another. The statement "If a line intersects parallel lines, therefore the corresponding angles with in two intersection regions are congruent" is true either way, based on the corresponding angles theorem.For the given question;
Lines TU || RQ || VW are parallel.
The measure of the ∠RPZ= 95.
Thus, from the diagram,
∠UZP = ∠RPZ= 95
As both angles are corresponding angle so equal.
Therefore, the measure of the ∠UZP = 95°.
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Mia used a pattern to create figures with building blocks. The first three figures are shown.
Figure 1
Mia needs
Assuming the building pattern continued, how many blocks would be needed to build the 6th figure?
Figure 2
AX blocks to build the 6th figure.
Figure 3
Answer:
I think the answer would be 33
What is the volume of this rectangular prism? 1/4 cm 1/2 cm 1/3 cm
The formula of the volume of a rectangular prism
[tex]V=l\times w\times h[/tex]we substitute the values given
l=length= 1/3cm
w=width=1/2cm
h=height=1/4cm
[tex]V=\frac{1}{3}\times\frac{1}{2}\times\frac{1}{4}=\frac{1}{24}cm^3[/tex]A school event requires 4 adults for every 35 kids. 12 adults are available. How many kids can attend?
Answer:
105 and five kids can attend
Step-by-step explanation:
12 divide by 4=3
this means that 3 groups of kids can go
so 35 x 3=105
therefore
Answer:
105 and five kids can attend
Step-by-step explanation:
12 divide by 4=3
this means that 3 groups of kids can go
so 35 x 3=105
So the answer is 105
10. Supose you bought a digital album from your favorite artist and set iTunes to play
the album in random order without repeats. The album has 10 songs and it turns
out you really like 5 of them. Find the following probabilities for the first 2 songs
played at random.
a) You like both of them 2
b) B) you like neither of the songs ,
c) C) you like at least one of the songs
Probability to like both of them is 0.02.
Probability to like neither of the songs is 0.62.
Probability to like at least one of the songs is 0.44
What is probability?
Probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
Given Data
The album has 10 songs and
it turns out you really like 5 of them.
a) You like both of them
P(like both of them )
= [tex]\frac{2}{10}[/tex] ×[tex]\frac{1}{9}[/tex]
= 0.02
Probability to like both of them is 0.02.
b )you like neither of the songs
P(like neither of the songs)
= [tex]\frac{8}{10}[/tex] ×[tex]\frac{7}{9}[/tex]
= 0.62
Probability to like neither of the songs is 0.62.
c) you like at least one of the songs
P( like at least one of the songs)
2 ×[tex]\frac{2}{10}[/tex] ×[tex]\frac{1}{9}[/tex]
= 0.44
Probability to like at least one of the songs is 0.44
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To rent a certain meeting room, a college charges a reservation fee of $19 and an additional fee of $6 per hour. The chemistry club wants to spend at most $67
on renting the room. What are the possible numbers of hours the chemistry club could rent the meeting room?
Use t for the number of hours.
Write your answer as an inequality solved for t.
By estimating the linear inequality, the possible numbers of hours the chemistry club could rent the meeting room exists 9 hours.
What is meant by Linear inequalities?In mathematics, an expression with uneven sides is referred to as an inequality. When a relationship leads to a non-equal comparison between two expressions or two numbers, it is referred to as an inequality in mathematics.
In this case, the equal sign "=" is replaced with any of the inequality symbols, such as greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), or not equal to symbol ().
Strict inequalities are denoted by the symbols "" and ">," whereas slack inequalities are denoted by "" and "". A linear inequality has the same appearance as a linear equation, but uses a different symbol to link the two expressions.
To rent a certain meeting room, a college charges a reservation fee of $19 - 16 and an additional fee of $6 per hour. The chemistry club wants to spend at most $67 - 70
Given that, college charges a reservation fee of $19 and an additional fee of $6 per hour.
The chemistry club wants to spend at most $67.
To estimate the possible numbers of hours the chemistry club could rent the meeting room:
The governing inequality is
19 + 6t < 67
The solution is
t < (67-19)/6
simplifying the above equation, we get
t = 8 hours.
Therefore, the value of t = 8 hours.
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Which equation shows a slope of -5 and a y-intercept of (0,1)?
Answer: second option
y= -5x +1
Find the contrapositive and determine if it is true or false.
Statement : Obtuse angles are not right angles.
The contrapositive statement is If an angle is a right angle, then is not an obtuse angle True. Option B
What is a contrapositive statement?
A contrapositive statement can be defined as a theorem created by contradicting the hypothesis and conclusion of a statement.
It involves exchanging both the hypothesis and conclusion of a given conditional statement and then negating both hypothesis and conclusion.
It is a combination of an inverse and converse statements.
The hypothesis and conclusion are interchanged or switched.
A contrapositive statement is written as;
a b is equivalent to b ~a
Given the statement;
Obtuse angles are not right angles.
The contrapositive statement is :
If an angle is a right angle, then is not an obtuse angle
Thus, the contrapositive statement is true
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Harlan is preparing a dip for a party the recipe calls for 4 cups of sour cream and three packages of onion soup mix he doesn’t want to prepare that my street decides to use only 2 cups of sour cream and one and a half packages of onion soup mix is this a proportional relationship
Yes!, This is a proportional relationship.
A proportional relationship means that the ratios of two variables are equal.
According to the question, the requirements of the recipe are
Number of cups of sour cream required be x1 = 4
Number of packages of onion soup mix required be y1 = 3
Used products by Harlan,
Cups used by Harlan of sour cream be x2 = 2
Packages of onion soup mix used by Harlan be y2 = 1.5
As we can see that,
x1/x2 = y1/y2
4/2 = 3/1.5
2 = 2
L.H.S = R.H.S ( ratio is same)
Therefore, we conclude that the above case is a proportional relationship.
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What’s the correct answer answer asap for brainlist
Answer:
answer a
Step-by-step explanation:
spongy bone in the center
4. In a school of 120 students, 41 studied Maths, 48 studied Chemistry and 42 studied Physics, 16 studied both Chemistry and Maths, 14 studied Maths and Physics, 18 studied Chemistry and Physics and 9 studied all the three subjects. Find how many of them studied:
(i) Exactly one subject.
(ii) At least one subject.
(iii) None of the subjects
Answer:
i) 62
ii) 92
iii) 28
Step-by-step explanation:
i) 19+23+20
=62
ii) 23+9+9+7+19+5+20
=92
iii) 120-23-9-9-7-19-5-20
or
120-92
=28
Help me solve this please
(a) 291/2020
Divide the total for the 10-14 year column by the total.
(b) 77/465
There are 465 people from the east, 77 of which were loyal for 10 to 14 years
(c) 437/1010
There are 291+583=874 people who were loyal for at least 10 years. Divide this by the total of 2020 people.
(d) 145/376
376 people are from the West, (45+100)=145 of which are at least 10.
(e) 32/157
157 people were loyal for less than a year, 32 of which were from the East.
(f) 53/157
157 people were loyal for less than a year, 53 of which were from the South.
(g) 433/465
465-32=433 people were loyal for at least 1 year out of the 465 people from the East.
(h) 335/376
376-41=355 people were loyal for at least 1 year out of the 376 people from the West.
Can someone help me with this geometry question?
4/5 is the probability that jack will win at least 30 points in a throw.
What do we mean by probability?The probability is the likelihood that something will happen, to put it simply.The likelihood or likelihood of various outcomes can be discussed when we don't know how an event will turn out.The study of events that fit into a probability distribution is known as statistics.The probability is determined by dividing the total number of outcomes by the total number of potential events.Odds and probability are two different concepts.Calculating odds involves dividing the probability of an event by the probability that it won't happen.So, the probability formula:
P = favourable events/Total number of eventsFavorable events: (At least 30 points) ⇒ 30 + 40 + 50Total events: (Sum of all points) ⇒ 150Now, insert values in the formula as follows:
P = favourable events/Total number of eventsP = 120/150P = 12/15P = 4/5Therefore, 4/5 is the probability that jack will win at least 30 points in a throw.
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