The seats are arranged in 5040 ways, if 7 people sit in seats labeled A, B, C, D, E, F, G.
Step-by-step explanation:
The given is,
7 people sit in seats labeled A, B, C, D, E, F, G.
Step: 1
No.of people = 7
No. of seats labeled = 7
Formula to calculate the number of ways to arrange,
[tex]P_{n} = n![/tex]...................................(1)
Where, n - Positive integer
Step: 2
From given, n = 7
Equation (1) becomes,
[tex]P_{7} = 7![/tex]
= 7 × 6 × 5 × 4 × 3 × 2 × 1
= 5040
= 5040 ways
Result:
The seats are arranged in 5040 ways, if 7 people sit in seats labeled A, B, C, D, E, F, G.
A diagram of a small shed is shown below, find the volume of the composite figure. 3m 6m 5m 5m 8m
Answer:
27
Step-by-step explanation:
You work 40 hours a week at a factory and make $2.00 per piece you create. It takes you
1 hour to create 5 pieces, how much money do you make per week?
I have to show work for the problem.
Answer:
400
Step-by-step explanation:
1 hour = 5 pieces • $2
1 hour = $10 bcas each piece you make is $2
40 hours = $400 because you get $10 per week
You earn $400 per week
Answer:
$400
Step-by-step explanation:
S x H = (1 x 5 x 2) x 40
S x H = (1 x 10) x 40
S x H = 10 x 40
S = 400
S = $400 H = 40
A town has a population of 17000 and grows at 3% every year. To the nearest year, how long will it be until the population will reach 20400
Answer:
The population will reach 20,400 after 6 years.
Step-by-step explanation:
Exponential function:
[tex]y(t)=y_0(1+r)^t[/tex]
y(t)= Population after t years
[tex]y_0[/tex] = initial population
r= rate of grow
t= time.
A town has a population of 17,000 and grows at a rate 3% every year.
y(t)= 20,400, [tex]y_0[/tex] = 17,000, r=3%=0.03, t=?
[tex]20,400=17,000(1+0.03)^t[/tex]
[tex]\Rightarrow \frac{20,400}{17,000}=(1.03)^t[/tex]
[tex]\Rightarrow \frac{102}{85}=(1.03)^t[/tex]
Taking ln function both sides
[tex]\Rightarrow ln|\frac{102}{85}|=ln|(1.03)^t|[/tex]
[tex]\Rightarrow ln|\frac{102}{85}|=t\ ln|(1.03)|[/tex]
[tex]\Rightarrow t=\frac{ln|\frac{102}{85}|}{\ ln|(1.03)|}[/tex]
⇒ t = 6 year.
The population will reach 20,400 after 6 years.
Answer:
6
Step-by-step explanation:
deltamath
(x2 + 5x – 3) + (3x2 – 4x + 5)
(6x-3)+(7x-7)
Hope I helped :d
Answer:
[tex]4x^{2} +x+2[/tex]
Use the distributive property to factor the expression below.
-15x²y² + 25xy²
[tex]-15x^2y^2+25xy^2=5xy^2(-3x+5)\:or\:-5xy^2(3x-5)[/tex]
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The average price of a gallon of milk is $3.31. If the price increases .88% each year , how much will a gallon of milk cost in 20 years?
Answer:
$3.94
Step-by-step explanation:
You will need to use the compound interest formula for this.
[tex]P(1+\frac{r}{n} )^{nt}[/tex]
P = initial balance
r = interest rate
n = number of times compounded annually
t = time
Your equation will look like this:
[tex]3.31(1+\frac{.0088}{1} )^{20}[/tex] = 3.94
The diagonal of a square measures 16 inches. What is the length of the sides?
Answer:
The length of the sides is 8[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Since the diagonal divide a square into 2 45-45-90 triangles:
The diagonal is the hypotenuse of the triangle
Divide 16 by [tex]\sqrt{2}[/tex] and you will get 8[tex]\sqrt{2}[/tex].
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If a taxi charges $0.68 per mile and $4 how far can you ride for $10? (round to 1 decimal
What is the first step in evaluating the expression 3 × (5 + 4) – 27 ÷ 9?
Step-by-step explanation:
According to BODMAS
the first way to evaluate the expression is starting from brackets.,
=3 * 9 -27 / 9
= 3 * 9 - 3
= 27- 3
=24
Answer:
Parenthesis.
Step-by-step explanation:
Parenthesis
Exponent
Multiply or
Divide
Add or
Subtract
PEMDAS is the order to solve expressions like so.
HELP ASAP
What are the square roots of 36 /100?
sqrt(36/100) = +-6/10
You find the square root of the numerator and the denominator.
HELP.The grades students scored on the most recent math exam are shown on the histogram below. How many students took the exam? A. 100 B. 85 C. 95 D. 90
Solve the system of equations
5x + 3y = -2
3x + 2y = -1
Answer:
Step-by-step explanation:
put the following equation of a line into slope-intercept form, simplifying all fractions. 4x + 3y = -3
The slope-intercept form of the equation 4x + 3y = -3 is y = -4/3x - 1. The slope of the line is -4/3 and the y-intercept is -1.
Explanation:The question asks to convert the equation 4x + 3y = -3 into slope-intercept form, and simplify all fractions. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.
To transform the given equation into this form, we need to express it in terms of y. Here are the steps:
Subtract both sides of the equation by 4x, we get: 3y = -4x -3.Next, divide each term by 3 to isolate y: y = -4/3x - 1. Therefore, the slope-intercept form of the equation is y = -4/3x - 1.In this equation, the term -4/3 is the slope and the -1 is the y-intercept. That means the line decreases for every 4 units in the y-axis when it increases 3 units in the x-axis.
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What number makes the equation true? Enter the answer in the box.
24-
=4
What is the area of the trapezoid? [A = 1/2(b1 + b2)h]
A) 1249.5 sq cm
B) 162.75 sq cm
C) 105 sq cm
D) 38.75 sq cm
We can see that b1 = 18, b2 = 24, and h = 5
So, we can just substitute these in.
A = 1/2(18 + 24)5
A = 1/2 * 42 * 5
A = 21 * 5
A = 105
So, the answer is C. 105 sq cm
Answer:
105
Step-by-step explanation:
you just have to plug in your variables
15. f(x) = (x - 2)
Find f(-2)
Answer:
f (-2)=(-2)-2
= -4
By putting value of x= -2 in f (x)
how do you write 2/16 as a percent?
Answer:
[tex]\huge\boxed{\dfrac{2}{16}=12.5\%}[/tex]
Step-by-step explanation:
[tex]p\%=\dfrac{p}{100}\to p=p\cdot100\%\\\\\dfrac{2}{16}=\dfrac{2:2}{16:2}=\dfrac{1}{8}\\\\\dfrac{1}{8}=\dfrac{1}{8}\cdot100\%=\dfrac{100}{8}\%=12.5\%\\\\\text{Other method.}\\\\\dfrac{1}{8}=\dfrac{1\cdot125}{8\cdot125}=\dfrac{125}{1000}=\dfrac{125:10}{1000:10}=\dfrac{12.5}{100}=12.5\%[/tex]
I need help plz only one question
Which is not equal to 400
Answer:
399
Step-by-step explanation:
The only expression that does not equal 400 is c. 500 - 200.
How to determine the expression that is not equal to 400From the question, we have the following parameters that can be used in our computation:
a. 2 * 200
b. 800/2
c. 500 - 200
d. 300 + 100
Evaluating each of the options, we have the following
a. 2 * 200 = 400
b. 800/2 = 400
c. 500 - 200 = 300
d. 300 + 100 = 400
Hence, the only option that does not equal 400 is c. 500 - 200.
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Question
Which is not equal to 400
a. 2 * 200
b. 800/2
c. 500 - 200
d. 300 + 100
The diameter of a circle is 7 feet. Find the radius
Answer:
3.5 feet
Step-by-step explanation:
Diameter = 7 feet
Radius = Diameter × [tex]\frac{1}{2}[/tex]
Radius = [tex]\frac{7}{2}[/tex] = 3.5 feet
A ranch experienced growth of its gopher population at a 1.5% annual rate, compounded continuously. At the end of a 3 year period, the population had reached a size of 78 gophers. How many gophers were on the ranch at the beginning of the 3 years according to the exponential growth function? Round your answer up to the nearest whole number, and do not include units.
Answer:
75 gophers (about)
Step-by-step explanation:
We will use continuous compounding interest formula:
[tex]P(t)=P_0e^{rt}[/tex]
Where
P(t) is final value (at time t)
P_0 is initial value
r is the compounding rate
t is the time period
Given:
P(t) = 78
r is 1.5% or 1.5/100 = 0.015
t is 3
We solve for P_0, what we want, using algebra as shown below:
[tex]P(t)=P_0e^{rt}\\78=P_0e^{(0.015)(3)}\\78=P_0e^{0.045}\\\frac{78}{P_0}=e^{0.045}\\\frac{78}{P_0}=1.0460\\P_0=74.57[/tex]
So, the initial population was 75 gophers.
The 75 gophers were on the ranch at the beginning of the 3 years according to the exponential growth function.
To solve this problem, we can use the following exponential growth function:
P(t) = P_0 * e^(rt)
where:
P(t) is the population at time t
P_0 is the initial population
r is the annual growth rate
t is the time in years
We know that the population after 3 years is 78 gophers, and the annual growth rate is 1.5%. We want to find the initial population, P_0.
So, we can plug in the following values into the exponential growth function:
P(3) = 78 = P_0 * e^(0.015 * 3)
Dividing both sides by e^(0.015 * 3), we get:
P_0 = 78 / e^(0.015 * 3)
Using a calculator, we can evaluate P_0 to be approximately 75.0.
Rounding up to the nearest whole number, we get an initial population of 75 gophers.
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a farmer is constructing a regular fenced in pen. there is 120m of fencing. determine the maximum area of the pen and the dimensions that result in maximum area
Answer: 900 square meters. 30x30
Step-by-step explanation: a square is the biggest area you can have, so 120 divided by 4 is 30, and then 30 times 30 is 900.
Put all the division problems that have an estimated quotient of 12 into the box.
8/0.95
18/2.2
47.6/3.9
10.6/1.89
71.9/6.5
123.4/9.2
157.4/16.4
The division problems 123.4/9.2 and 71.9/6.5 have an estimated quotient of 12 by considering 123.4 as 120, 9.2 as 10, 71.9 as 70, and 6.5 as 6.
Explanation:The division problems with an estimated quotient of around 12 will be the ones where you divide a number close to 120 by 10. In this case, it comes to be 123.4/9.2 and 71.9/6.5. To estimate the quotient, you can consider 123.4 as approximately 120 and 9.2 as approximately 10. Similarly, 71.9 can be considered as approximately 70 and 6.5 as approximately 6. When you divide these estimate numbers, both quotients are close to 12.
Estimation is a useful skill in Mathematics that allows you to simplify complex problems and get close to the exact answer. It's particularly helpful in situations where you only need a rough estimate and not the exact figure.
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Two hamburgers and three cokes cost $10.50. Four hamburgers and four cokes cost $18.00. Find the cost of a hamburger and a coke.
Answer: hamburger $3.00
Coke $1.50
Step-by-step explanation:
2hamburgers & 3cokes= $10.50
4hamburgers & 4cokes= $18.00
Let hamburger represent H
And coke represent C
2H +3C= 10.50.......equation 1
4H+4C= 18.00.......equation 2
2H =10.50 -3C...........equation 3
The 4H can be rewriting as
2(2H) right
So substitute for the 4H
So we have,
2(2H) +4C= 18
Substitute for 2H
2(10.50 -3C) +4C =18
Open the bracket
21 -6C +4C= 18
21-2C= 18
-2C = 18-21
-2C = -3
Minus cancel minus
C= 3/2 = $1.5
Substitute for c in equation 1
2H+3C =10.50
2H+3(1.5)= 10.50
2H+4.5=10.5
2H= 10.5-4.5
2H =6
H= 6/2
H=$3
So
An hamburger cost $3.00
A coke cost $1.50
Help me please!!....
Answer:
J
Step-by-step explanation:
As you can see, the peak occurs at (2,6). That means that all values below 6 are in the range.
5p coins weigh approximatly 3g wat would be the weight of £5 worth of 5p coins
Answer:
3g
Step-by-step explanation:
Since 5p=3g
5p=x
So let's solve by cross multiplying
5px=3g×5p
5px=15gp
Divide both sides by 5p
x=3g
Therefore the final answer is 3g
What is the value of y? PLEASE HELP ASAP!
Answer:
y = 40 degrees can i have branliest
Step-by-step explanation:
All angles in a triangle add up to 180
180 - 50 = 130
3y + 10 = 130
3y = 120
y = 40
Answer:
c
Step-by-step explanation:
suppose for everyone cup of rice I add 2 3/4 cups of water. If I add 2 1/2 cups of rice, how much cups of water do I add?
Answer:
6 7/8
Step-by-step explanation:
Since 1 cup of rice is added to 2 3/4 water
We are to determine the Amount of water to be to 2 1/2 cups of rice
Let the unknown number for water be x
So let's solve
1 cup of rice=11/4 water
5/2 cup of rice=x water
Cross multiply
x=5/2×11/4
x=55/8
X=6 7/8
Therefore,6 7/8 water is needed
Find the volume of a pyramid with a square base, where the side length of the base is
8.3 in and the height of the pyramid is 7.3 in. Round your answer to the nearest
tenth of a cubic inch.
The volume of the pyramid is 167.6 cube inch (approx).
Step-by-step explanation:
Given,
Each length (l) of the base of the pyramid = 8.3 in
Height(h) of the pyramid = 7.3 in
To find the volume of the pyramid.
Formula
Volume of the pyramid = [tex]\frac{1}{3}[/tex]×area of the base×height
Area of the base = l²
Now,
The volume of the pyramid = [tex]\frac{1}{3}[/tex]×l²×h
= [tex]\frac{1}{3}[/tex]×8.3²×7.3 cube inch = 167.6 cube inch (approx)
The volume of the pyramid is calculated using the formula for a pyramid's volume, V = (1/3)bh, with a base area of 68.89 in² and height of 7.3 in, which gives a volume of approximately 167.5 in³.
Explanation:To find the volume of a pyramid with a square base, we can use the formula V = (1/3)bh, where b is the area of the base and h is the height of the pyramid. First, calculate the area of the square base by squaring the side length: b = s² = 8.3 in × 8.3 in = 68.89 in². Next, use this base area in the formula to get the volume: V = (1/3) × 68.89 in² × 7.3 in.
Doing the calculation, we find that V = (1/3) × 68.89 in² × 7.3 in = 167.4757 in³. To round to the nearest tenth, the volume of the pyramid is approximately 167.5 in³.
The area of a circular window is 113.04 square inches. What is the diameter of the window? Use 3.14 for pi.
Answer: 12inches
Step-by-step explanation:
Area of a circle= 113.04square inches
Area of a circle =pir^2
Pi=3.14
R=?
So we are looking for the radius and from there we will get the diameter
Area=pir^2
113.04=3.14×r^2
R^2= 113.04/3.14
R^2=36
R=square root of 36
R= 6
Diameter =2r
Diameter = 2×6
Diameter = 12inches
Answer:
12 inches
Step-by-step explanation:
3.14 × r² = 113.04
r² = 36
r = 6
Diameter = 2r = 12