1 1 2 4 3 9 4 what is the next number
1) On average, Donna's Cafe has 42 customers, which represents 20% of the total approved occupancy by the fire department.
a) According to the fire department's occupancy approval, what percentage of the cafe is still available for customers?
b)According to the fire department's occupancy approval, how many seats are still available for customers?
State whether each situation involves a combination or a permutation.
4 of the 20 radio contest winners selected to try for the grand prize
5 friends waiting in line at the movies
6 students selected at random to attend a presentation
a) permutation, combination, permutation
b) combination, permutation, permutation
c) combination, permutation, combination
d) permutation, combination, combination
Answer:
4 of the 20 radio contest winners selected to try for the grand prize : C
5 friends waiting in line at the movies: C
6 students selected at random to attend a presentation: P
Final answer:
The scenarios illustrate combination when order does not matter (selecting contest winners and student attendees) and permutation when order matters (friends in line). The correct sequence is combination, permutation, combination.
Explanation:
In the context of the scenarios provided, we need to differentiate whether the situations are examples of combinations or permutations. A permutation is an arrangement of objects where order matters, while a combination is a selection of objects where order does not matter.
4 of the 20 radio contest winners selected to try for the grand prize - This is a combination, as the order in which the winners are selected is not relevant.5 friends waiting in line at the movies - This is a permutation, as the order in which the friends are lined up matters.6 students selected at random to attend a presentation - This is a combination, as the order of selection does not impact which students attend.Thus, the correct answer to the sequence of scenarios is: combination, permutation, combination, which correlates with option c.
2s + 5 greater than or equal to 49
The value of s is greater or equal to 22.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
2s + 5 greater than or equal to 49.
This can be written as,
(2s + 5) ≥ 49
Solve for s.
2s + 5 ≥ 49
2s ≥ 49 - 5
2s ≥ 44
s ≥ 22
Thus,
s is greater than or equal to 22.
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What is the value of 3×5+6×2+1
How much interest is gained if $250 is deposited in your bank account at the end of the year for each of the next 7 years? savings account pays 8% compounded annually?
The graph below shows the fine that a college student pays to the library based on the number of minutes a loaner laptop is overdue:
A graph is shown. The values on the x axis are 0, 2, 4, 6, 8. The values on the y axis are 0, 0.70, 1.40, 2.10, 2.80. Points are shown on ordered pairs 0, 0 and 2, 0.70 and 4, 1.40 and 6, 2.10. These points are joined by a line. The label on the x axis is Minutes Overdue. The title on the y axis is Fine.
Which statement best describes the point (0, 0) on the graph?
Answer:
So the answer would be No fine is paid if the laptop is returned exactly at the time at which it is due
What is the slope of a line that is perpendicular to the line whose equation is 0.5x−5y=9 0.5 x − 5 y = 9
What does the value of the LCM represent
Which algebraic expression shows the average melting points of helium, hydrogen, and neon if h represents the melting point of helium, j represents the melting point of hydrogen, and k represents the melting point of neon?
Final answer:
The algebraic expression for finding the average melting points of helium, hydrogen, and neon, using variables h, j, and k as their respective melting points, is (h + j + k) / 3.
Explanation:
The question asks for the algebraic expression that represents the average melting points of helium, hydrogen, and neon. The variables h, j, and k denote the individual melting points of these elements, respectively. To calculate the average melting point, you would add the melting points of each element and divide by the number of elements.
The algebraic expression for the average melting point is:
(h + j + k) / 3
Write an algebraic expression which represents the volume of a box whose width is 4y, height is 6y and length is 3y + 1.
David wishes to accumulate $1 million by the end of 20 years by making equal annual end-of-year deposits over the next 20 years. if david can earn 10 percent on his investments, how much must he deposit at the end of each year? $50,000 $17,460 $14,900 $117,453
David must deposit approximately $16,150.01 at the end of each year to accumulate $1 million by the end of 20 years at a 10 percent interest rate.
To calculate the equal annual end-of-year deposits that David must make to accumulate $1 million in 20 years at a 10 percent interest rate, we can use the formula for the future value of an ordinary annuity.
The formula for the future value of an ordinary annuity is given by:
[tex]FV = P * ((1 + r)^n - 1) / r[/tex]
where:
FV is the future value of the annuity (the desired $1 million in this case)
P is the annual deposit (what we need to find)
r is the annual interest rate (10% or 0.10 as a decimal)
n is the number of years (20 years in this case)
Substituting the known values:
[tex]$1,000,000 = P * ((1 + 0.10)^{20} - 1) / 0.10[/tex]
Now, we can solve for P:
$1,000,000 = P * (6.1917364224) / 0.10
$1,000,000 = P * 61.917364224
P = $1,000,000 / 61.917364224
P ≈ $16,150.01
So, David must deposit approximately $16,150.01 at the end of each year to accumulate $1 million by the end of 20 years at a 10 percent interest rate.
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If a boatman rows his boat 35km up stream and 55km downstream in 12 hours and he can row 30km upstream and 44 km downstream in 10hr , then the speed of the stream and that of the boat in still water
To answer this item, we let x be the speed of the boat in still water. The speed of the current, we represent as y.
When the boat travels upstream or against the current, the speed is equal to x – y and x + y if it travels downstream or along with the current.
The time it takes for the an object to travel a certain distance is calculated by dividing the distance by the speed.
First Travel: 35 / (x – y) + 55 / (x + y) = 12
Second travel: 30 / (x – y) + 44 / (x + y) = 10
Let us multiply the two equations with the (x-y)(x+y)
This will give us,
35(x + y) + 55(x – y) = 12(x-y)(x+y)
30(x + y) + 44(x – y) = 10(x-y)(x+y)
Using dummy variables:
Let a = x + y and b be x – y
35a + 55b = 12ab
30a + 44b = 10ab
From the first equation,
b = 35a/(12a – 55)
Substituting to the second equation,
30a + 44(35a/(12a – 55)) = 10a(35a/(12a-55))
The value of a is 11.
b = 35(11)/(12(11) – 55))
b = 5
Putting back the equations,
x + y = 11
x – y = 5
Adding up the equations give us,
2x = 16
x = 8 km/hr
The value of x, the speed of the boat in still water, is 8 km/hr.
speed of the stream = 3 km/hr
and speed of boat in still water= 8 km/hr
Step-by-step explanation:Let s be the speed of the boat upstream
and s' be the speed of the boat downstream.
We know that:
[tex]Time=\dfrac{distance}{speed}[/tex]
Hence, we get:
[tex]\dfrac{35}{s}+\dfrac{55}{s'}=12[/tex]
and
[tex]\dfrac{30}{s}+\dfrac{44}{s'}=10[/tex]
Now, let
[tex]\dfrac{1}{s}=a\ and\ \dfrac{1}{s'}=b[/tex]
Hence, we have:
[tex]35a+55b=12--------------(1)\\\\\\and\\\\\\30a+44b=10--------------(2)[/tex]
on multiplying equation (1) by 4 and equation (2) by 5 and subtract equation (1) from (2) we get:
[tex]a=\dfrac{1}{5}[/tex]
and by putting value of a in (2) we get:
[tex]b=\dfrac{1}{11}[/tex]
Hence, speed of boat in upstream= 5 km/hr
and speed of boat in downstream= 11 km/hr
and we know that:
speed of boat in upstream=speed of boat in still water(x)-speed of stream(y)
and speed of boat in downstream=speed of boat in still water(x)+speed of stream(y)
Hence, we get:
[tex]x-y=5\\\\\\and\\\\\\x+y=11[/tex]
Hence, on solving the equation we get:
[tex]x=8[/tex]
and y=3
Hence, we get:
speed of the stream = 3 km/hr
and speed of boat in still water= 8 km/hr
What the answer to this question?
volume = (1/3)*PI*(r1^2+r1*r2+r2^2)*h
h=10
r1=5
r2=2
= 408.41 cubic inches
round off answer as needed.
what is the gcf of 120 and 72
The circumference of a coin is 8π What is the radius? What is the diameter?
If thewronskian w of f and g is 3e4t,and if f(t) = e2t,find g(t).
please help me right now will give brainliest and offering 50 points
Above are two different models of the same hexagon. If the side length of the model on the left is in, what is the corresponding side length of the model on the right?
A. 10 1/4 in
B. 4 in
C. 5 in
D. 3 3/4 in
Answer:
The answer is 5 in.
Step-by-step explanation:
Since the scale for the model on the left is 1 in = 12 ft, and the scale for the model on the right is 1 in = 3 ft, the model on the right is 4 times larger than the model on the left.
Multiply the side length of the model on the left by 4 to find the side length of the model on the right.
A new bank account is opened on week 1 with a $200 deposit. After that first week, weekly deposits of $55 are made in the account. If y represents the total deposited into the account and x represents the number of weeks, which function rule describes this situation?
if the divisor is 40 what is the least 3 digit number dividend that would give a remainder of 4
A spring is oscillating so that its length is a sinusoidal function of time. Its length varies from a minimum of 10 cm to a maximum of 14 cm. At t=0 seconds, the length of the spring was 12 cm, and it was decreasing in length. It then reached a minimum length at time t= 1.2 seconds. Between time t=0 and t=8 seconds, how much of the time was the spring longer than 13.5 cm?
John’s gross pay for the week is $500. He pays 1.45 percent in Medicare tax, 6.2 percent in Social Security tax, 2 percent in state tax, 20 percent in federal income tax, and $20 as an insurance deduction. He does not have any voluntary deductions. What is John’s net pay for the week?
John's net pay is calculated by subtracting deductions for Medicare, Social Security, state and federal taxes, and insurance from his gross pay of $500. The total deductions amount to $168.25, resulting in a net pay of $331.75.
Explanation:Calculation of John's Net Pay
To calculate John's net pay, we need to subtract all the deductions from his gross pay. Since his gross pay is $500, we will apply the following deductions:
Medicare tax: 1.45% of $500 = $7.25
Social Security tax: 6.2% of $500 = $31.00
State tax: 2% of $500 = $10.00
Federal income tax: 20% of $500 = $100.00
Insurance deduction: $20.00
Add up all deductions: $7.25 (Medicare) + $31.00 (Social Security) + $10.00 (State Tax) + $100.00 (Federal Tax) + $20.00 (Insurance) = $168.25
John's net pay is therefore calculated by subtracting the total deductions from his gross pay: $500.00 - $168.25 = $331.75.
A stocker put 57 boxes of detergent on the shelves in 2 minutes. After 5 minutes, he had put 117 boxes on the shelves. How many boxes were on the shelves when he started?
A cone is placed inside a cylinder. The cone has half the radius of the cylinder, but the height of each figure is the same. The cone is tilted at an angle so its peak touches the edge of the cylinder’s base. What is the volume of the space remaining in the cylinder after the cone is placed inside it?
Answer:
Step-by-step explanation:
Given that A cone is placed inside a cylinder. The cone has half the radius of the cylinder, but the height of each figure is the same
Whatever position cone is placed, the space remaining will have volume as
volume of the cylinder - volume of the cone
Let radius of cylinder be r and height be h
Then volume of cylinder = [tex]\pi r^2 h[/tex]
The cone has height as h and radius as r/2
So volume of cone = [tex]\frac{1}{3} \pi (\frac{r}{2} )^2h\\=(\pi r^2 h)\frac{1}{24}[/tex]
the volume of the space remaining in the cylinder after the cone is placed inside it
=[tex]\pi r^2 h (1-\frac{1}{24} )\\=\frac{23 \pi r^2 h}{24}[/tex]
Answer:
11/12 pie r^2 h
Step-by-step explanation:
Find a rational zero of the polynomial function and use it to find all the zeros of the function. f(x) = x4 + 3x3 - 5x2 - 9x - 2
The rational zero -1 is a root of f(x). Synthetic division yields [tex]\(x^3 + 2x^2 - 7x - 2\)[/tex]. Further factorization or testing other rational roots finds the remaining zeros.
To find a rational zero of the polynomial function [tex]\(f(x) = x^4 + 3x^3 - 5x^2 - 9x - 2\)[/tex], we can use the Rational Root Theorem. According to this theorem, any rational zero of the polynomial function must be of the form ±p/q, where p is a factor of the constant term (-2 in this case) and q is a factor of the leading coefficient (1 in this case).
The factors of -2 are ±1, ±2, and the factors of 1 are ±1. Therefore, the possible rational zeros are:
±1, ±2
We can try these values to see if they are roots of the polynomial.
Let's start by trying x = 1:
[tex]\[f(1) = (1)^4 + 3(1)^3 - 5(1)^2 - 9(1) - 2\]\[= 1 + 3 - 5 - 9 - 2\]\[= -12\][/tex]
So, x = 1 is not a root.
Next, let's try x = -1:
[tex]\[f(-1) = (-1)^4 + 3(-1)^3 - 5(-1)^2 - 9(-1) - 2\]\[= 1 - 3 - 5 + 9 - 2\]\[= 0\][/tex]
Therefore, x = -1 is a root of the polynomial.
To find the other zeros, we can perform polynomial division or synthetic division by dividing f(x) by (x + 1). Let's use synthetic division:
-1 1 3 -5 -9 -2
1 2 -7 -2 ↓
The result is [tex]\(x^3 + 2x^2 - 7x - 2\)[/tex]. Now, we can factor this cubic polynomial or continue using the Rational Root Theorem to find additional roots. Let's try x = 1 again:
[tex]\[f(1) = (1)^3 + 2(1)^2 - 7(1) - 2\]\[= 1 + 2 - 7 - 2\]\[= -6\][/tex]
x = 1 is not a root, so we continue to try the other possible rational zeros. However, to save time, let's check if any of the values of [tex]\(x = \pm 2\)[/tex] are roots using synthetic division:
For x = 2:
2 1 2 -7 -2
1 4 1 ↓
For \(x = -2\):
-2 1 2 -7 -2
1 0 -7 ↓
Since none of these values result in a remainder of 0, [tex]\(x = \pm 2\)[/tex] are not roots.
Therefore, the zeros of the polynomial function [tex]\(f(x) = x^4 + 3x^3 - 5x^2 - 9x - 2\) are \(x = -1\),[/tex] and the other zeros can be found by further factoring the reduced cubic polynomial.
what is 1/3m-1-1/2n when m=21 and n=12
Answer:
Value of the expression is 0
Step-by-step explanation:
[tex]\frac{1}{3} m -1-\frac{1}{2} n[/tex]
Given the value of m and n
m= 21 and n= 12
We plug in the value of m and n in the given expression
[tex]\frac{1}{3} m -1-\frac{1}{2} n[/tex]
[tex]\frac{1}{3}(21) -1-\frac{1}{2}(12)[/tex]
[tex]\frac{21}{3} -1-\frac{12}{2}[/tex]
[tex]7-1-6= 0[/tex]
So the value of given expression is 0 when we plug in the values of m and n
Please hurry !!!
Which is an x-intercept of the graphed function?
A) 0,4
B)-1,0
C)4,0
D)0,-1
we know that
The x-intercept is the value of the coordinate x when the value of the function is equal to zero
so
In this problem we have that the x-intercepts of the graphs are the points
[tex](-2,0)\\(-1,0)\\(1,0)\\(2,0)[/tex]
therefore
the answer is the option
B)-1,0
A 31-m tall building casts a shadow. The distance from the top of the building to the tip of the shadow is 37 m. Find the length of the shadow. If necessary, round your answer to the nearest tenth.
A supply company manufactures copy machines. The unit cost C (the cost in dollars to make each copy machine) depends on the number of machines made. If x machines are made, then the unit cost is given by the function
C (x) = 0.8x ^ 2 - 256x +25,939 . How many machines must be made to minimize the unit cost? Do not round your answer.
Number of copy machines:
To minimize unit cost, 160 machines must be made.
Step-by-step explanation:
Find the first derivative of the cost function: C'(x) = 1.6x - 256.
Set the derivative equal to 0 and solve for x to find the critical point: 1.6x - 256 = 0. x = 160.
Check the nature of the critical point using the second derivative test to confirm that x = 160 gives the minimum cost.
Therefore, the number of machines that must be made to minimize the unit cost is 160 machines.
The number of machines that must be made to minimize the unit cost is 160.
To find the number of machines that must be made to minimize the unit cost, we need to find the minimum point of the function [tex]\(C(x) = 0.8x^2 - 256x + 25,939\).[/tex]
The function \(C(x)\) represents a quadratic equation, and the vertex of a quadratic equation represents its minimum or maximum point. The x-coordinate of the vertex of a quadratic function in the form [tex]\(ax^2 + bx + c\) is given by \(-\frac{b}{2a}\).[/tex]
[tex]For the function \(C(x) = 0.8x^2 - 256x + 25,939\), we have \(a = 0.8\) and \(b = -256\).Now, let's calculate the x-coordinate of the vertex:\[ x_{\text{vertex}} = -\frac{b}{2a} = -\frac{-256}{2 \times 0.8} = -\frac{-256}{1.6} = 160 \][/tex]
So, the number of machines that must be made to minimize the unit cost is 160.
A salesperson sold a total of $6,400.00.If her rate of commission is 6%, what is her commission?
multiply 6400 x 6%
6% = 0.06
6400 x 0.06 = 384
her commission was $384
Answer:
The commission amount of the salesperson is $384.
Step-by-step explanation:
A salesperson sold a total of $6,400.00.
The rate of commission is 6% or 0.06. Commissions are based on sales. These are some percentage of the sales amount.
So, here the amount will be = [tex]0.06\times6400=384[/tex] dollars
So, the commission amount of the salesperson is $384.