Step 1) : Based on the given conditions, formulate
[tex] \large\bf \longrightarrow \frac{510}{3000} [/tex]
Step 2) : Calculate
[tex] \bf \longrightarrow\frac{51 \cancel{0}}{{300 \cancel{0}} } \: = \frac{51 \div 3}{300 \div 3} = \frac{17}{100} [/tex]
Step 3) : Convert to percentage
[tex] \bf\longrightarrow{\frac{17}{100} = 0.17}[/tex]
Hence, the commission rate is 17%.Choose the number phrase that correctly matches the word phrase “18 less 6.”
18 x 6
18 + 6
6 – 18
18 – 6
Ay-Jiuan can buy 12 songs for $10, or she
can pay $0.85 per song. Which option has the lesser price per song?
Answer: The 12 songs for $10
Step-by-step explanation: 12 / 10 = 1.2 while 12 / 0.85 = 14.11
5/8 of the pens in a box are blue pens. 4/5 of the remaining are red pens.what fraction of the pens are red ?
the difference between compound interest and simple interest on the same sum of rupees 8000 for 2 year is rupees 20 find the rate of interest ?
Answer:
5%
Step-by-step explanation:
You want the interest rate that makes the difference between compound and simple interest on ₹8000 for two years be ₹20.
Interest formulasThe formula for the value of an account earning simple interest is ...
A = P(1 +rt) . . . . P earning interest rate r for t years
The formula for the value of an account earning compound interest is ...
A = P(1 +r)^t . . . . P earning interest rate r for t years
ApplicationWe want the difference in these amounts over 2 years to be ₹20.
8000(1 +r)^2 -8000(1 +2r) = 20
1 +2r +r^2 -(1 +2r) = 20/8000 . . . . . divide by 8000, expand the square
r^2 = 1/400 . . . . . . simplify
r = 1/20 = 5% . . . . . take the square root
The rate of interest is 5% per year.
A rain gauge collected 0.2 inches of
rain in 30 minutes. If it keeps
raining at the same rate, what is the
total time it will take to collect 1
inch of rain?
Answer:
you're answer will be 2 hours and 30 minutes
Step-by-step explanation:
i hope that helps you! :))
A gasoline tank contains 9.6 hectolitres (hL) when it is 60% full. What is the capacity of the tank (in hL)?
The capacity of the full tank is 16 hectolitre. percentage problem.
A gasoline tank contains 9.6 hectolitres (hL) when it is 60% full. when the tank is 100% full that is the capacity of the tank.
so, the capacity of the full tank is 9.6x(100/60) = 16 hL.
this a percentage problem. In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%". A percentage is a dimensionless number; it has no unit of measurement.
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List some TV shows or movies with permissive parents.
Answer: full house,fairly oddparents, the simsons
edit^^^ a movie is clueless or even mean girls
Step-by-step explanation:
The product of two consecutive even number is 12 more than the square of the smaller number. Find the smaller number
Answer:
Hello,
Step-by-step explanation:
Let's say 2x the smaller number,2x+2 the greater.
2x*(2x+2)=12+(2x)²
2x²+4x=12+4x²
4x=12
x=3
The smaller numbre is 2x=6 and the greater is 8
6*8=48 =12+6²
At a berry farm, Clayton picks 1 1/4
cups of blackberries and twice as many raspberries. He takes the berries home and uses them to make mixed-berry muffins. If Clayton needs 3/4
of a cup of mixed berries for each batch of muffins, how many batches can he make?
Write your answer as a whole number, fraction, or mixed number. Simplify any fractions.
Answer: 1 1/4 batches of muffins
Step-by-step explanation:
multiply 1 1/4 (5/4) by 2 and get 5/2 (2 1/2)next add 5/2 (10/4) and 5/4 and get 15/4divide 15/4 by 3 and get 5/4simplify that out into 1 1/4Answer this question please
Answer:
[tex] \sf (- \infty, 58] [/tex]
Step-by-step explanation:
Express as interval = [tex] \sf (- \infty, 58][/tex]
Robbie opens an account at a local bank by depositing $100. The account pays 2.4% interest, compounded weekly. He deposits $100 every week for 3 years.
b. Write the future value function if x represents the number of weeks.
c. Use a graphing calculator to graph the future value function.
d. Using the graph, what is the approximate balance after 2 years?
The equation of the future value function if x represents the number of weeks is [tex]= P((1+r/x)^{nt} - 1)/(r/x)[/tex].
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.
Given:
Robbie depositing= $100
Interest=2.4%
Time=3 years.
According to given question we have
P = periodic payment = $100 / week
r = interest rate = 2.4%, compounded weekly
t = 3 years
x = 52 weeks (# of times interest is compounded per year)
To write a equation we have
B = Future Value
[tex]= P((1+r/x)^{nt} - 1)/(r/x)[/tex]
Therefore, the equation of the future value function if x represents the number of weeks is [tex]= P((1+r/x)^{nt} - 1)/(r/x)[/tex].
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no the projvet iS 348
3=20
14. Model Real Life A self-balancing scooter travels 12 miles
per hour. An all-terrain vehicle can travel 6 times as
fast as the scooter. A go-kart can travel 67 miles
per hour. Which vehicle can travel the fastest?
An all-terrain vehicle can travel the fastest.
What is Speed ?Speed can be define as the time rate by which an object is moving or running along a path. A speed is the quantity which describes the moving rate of any object. We can define the speed with respect to distance and time . Or we can say speed is distance per unit of time . It is calculate in term of kilometers per hour.
Mathematically, we can write:
[tex]Speed = \frac{Distance}{Time}[/tex]
where, distance is measured in km
and Time is measured in hours
In the question, the distance for three different types of vehicles are given and we have to find fastest vehicle for which we need to find the speed.
For self-balancing scooter
Time = 1 hour
Distance = 12 miles
Therefore, Speed = 12 miles/h
For all-terrain vehicle
Time = 1 hour
Distance = 12 . 6 = 72 miles
Therefore, speed = 72 miles/h
For a go-kart
Time = 1 hour
Distance = 67 miles
Therefore, speed = 67 miles/h
Hence it is cleared that An all-terrain vehicle can travel the fastest.
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What is the next fraction in this sequence? Simplify your answer.
1/3, 1/9, 1/27, 1/81,
Submit
...
Answer:
1/243
Step-by-step explanation:
Each denominator is multiplied by 3 from the last one
3 x 3 = 9
9 x 3 = 27
27 x 3 = 81
81 x 3 = 243
Numbers that can be written as a power in more than one way
Numbers that can be written as a power in more than one way is known as exponents .
WHAT ARE EXPONENTS?A sign that denotes raising to a power that is placed above and to the right of a mathematical expression. for example , [tex]2^{a}[/tex].
The mathematical procedure known as exponentiation, abbreviated as bn, involves the base number (b) and the exponent (or power) number (n). In English, it is pronounced "b (raised) to the (power of) n." [1] Exponentiation is the process of repeatedly multiplying bases, where n is a positive integer, and the product is known as bn.
The exponent is typically denoted by a superscript to the right of the base. The term "b raised to the nth power," "b (raised) to the power of n," "the nth power of b," "b to the nth power," or, most simply, "b to the nth," is used to describe bn.
CALCULATIONNumbers that can be written as a power in more than one way is known as exponents .
These numbers are basically written to save time to multiply the same number multiple times .
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Order the list of numbers written in Scientific Notation from small to large.
4.5 x 10^4
1.9 x 10^7
7.6 x 10^-9
9.3 x 10^-15
5.7 x 10^13
solve for y : 3x-2y+12>0
Answer:
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
[tex]y < \frac{3x}{2} +6[/tex]
One pizza will feed 4 people. How many pizzas are needed for 36 people?
pizzas
Answer:
9 Pizzas
Step-by-step explanation:
The table lists the eight human blood types.
It also shows how blood types determine who a person can donate blood to and receive blood from.
Blood type
A+
B+
AB+
AB-
A-
B-
0+
0-
Can donate to
A+, AB+
B+, AB+
AB+
AB+, AB-
A+, A-, AB+, AB-
B+, B-, AB+, AB-
(a) X = 1
(b) x = 0
A+, B+, AB+, 0+
All blood types
Can receive from
A+, A-, 0+, 0-
B+, B-, 0+, 0-
All blood types
A-, B-, AB-, 0-
A-, O-
B-, 0-
0+, 0-
0-
Let U be the set of all eight human blood types.
U=(A-, B-, AB+, AB-, A-, B-, 0-,0-)
Let X be the set of blood types that type AB- cannot receive blood from.
Let I be the set of blood types that type B+ can donate blood to.
Find the sets below. Write each answer in roster form or as 2.
CE
D
AB-
0.0 Ø
8+
AB+
The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $6 and each adult ticket sells for $9. There was a total of $747 in revenue from the sale of 98 total tickets. Write a system of equations that could be used to determine the number of student tickets sold and the number of adult tickets sold. Define the variables that you use to write the system.
Answer:
x + y = 989x + 6y = 747==============================
Let the number of adult tickets be x and student tickets be y.
Set equationsNumber of tickets:Adult tickets + student tickets = 98x + y = 98Amount of revenue:Total of adult tickets = 9x, total of student tickets = 6y9x + 6y = 747The cold water tap can fill a container two hours faster than the hot water tap. The two taps together can fill a container in 80 minutes. How long does it take each tap to fill the container on its own?
Answer:
4 hours and 2 hoursStep-by-step explanation:
Let the time for cold tap be c and hot tap be h.
Convert2hrs = 120 minSet equationsThe cold water tap can fill a container two hours faster than the hot water tap:
c - h = 120The two taps together can fill a container in 80 minutes:
1/c + 1/h = 1/80Solve the system by substitutionc = h + 1201/c + 1/h = 1/801/(h + 120) + 1/h = 1/80(h + h + 120)/(h(h+120)) = 1/8080(2h + 120) = h(h + 120)160h + 9600 = h² + 120hh² - 40h - 9600 = 0h² - 40h + 400 = 10000(h - 20)² = 100²h - 20 = 100 (taking positive root only, since time is positive value) h = 120 min = 2 hrsFind cc = 120 + 120 = 240 min = 4 hrsFind the slope of a line that passes through (4.5,3.5) and (9.5,5.5)
M =
[tex](\stackrel{x_1}{4.5}~,~\stackrel{y_1}{3.5})\qquad (\stackrel{x_2}{9.5}~,~\stackrel{y_2}{5.5})~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5.5}-\stackrel{y1}{3.5}}}{\underset{run} {\underset{x_2}{9.5}-\underset{x_1}{4.5}}}\implies \cfrac{2}{5}[/tex]
First try was incorrect
Rew decided to purchase some dubbles (x) and totts (y). Altogether,
he planned to buy at most 7 items.
Write an inequality, in standard form, to model this relationship.
Answer:
x + y ≤ 7
(if that doesn't work, 0 ≤ x + y ≤ 7)
Rew wants to buy 7 items or less, so the number of dubbles and totts combined can't be bigger than 7, and is therefore less than or equal to 7.
Find the value of PT if
PT=4x+1 and 7x-8
Answer:
4x+8+7x-8
Step-by-step explanation:
4x+7x+8-8
11x+0
11x.
What is the solution to r/-3 = 12? A. r=-36 B. r= -4 C. r=4 D. r=36 (1 point)
Given g(x)=2x+3g(x)=2x+3, find g(0)
Answer:
G(0) = 3
Step-by-step explanation:
g(0) means what is the value of g(x) when x = 0
substitute x = 0 into g(x)
g(0) = 2(0) + 3 = 0 + 3 = 3
HELP
Graph the following system of inequalities on the coordinate plane. You will need to explain your
work. Each correct line graphed WITH the correct explanation and shading is worth 2 points.
> − −
+ ≤
> −
See attachment for the graphs of the inequalities
How to graph the system of inequalities?To do this, we analyze and plot each inequality at a time
Having said that, we have
Inequality 1: y > -3x - 2
Here, we have
y > -3x - 2
The inequality > implies that the right-hand side of the origin will be shaded
Also, it means that the line of the inequality will be a dotted line
Inequality 2: 4x + 5y ≤ 20
Here, we have
4x + 5y ≤ 20
The inequality ≤ implies that the left-hand side of the origin will be shaded
Also, it means that the line of the inequality will be a closed line
Inequality 3: y > -4
Here, we have
y > -4
The inequality > implies that the upper part of the origin will be shaded
Also, it means that the line of the inequality will be a dashed line
See attachment for the graphs of the inequalities
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Find the equation of the line with slope m=- 3 that contains the point (9, - 15) Use fractions in your response, not decimals
Answer:
y = - 3x + 12
Step-by-step explanation:
Slope intercept form of line
y = mx + b where m = slope, b = y-intercept
==> y = -3x + b is the equatin
To find b, plug in values for point x = 9, y =-15 and solve for b
-15 = -3(9) + b
-15 = -27 + b
Add 27 both sides
-15 + 27 = b
12 = b
b = 12
Equation is
y = - 3x + 12
At a point on the ground 15ft from the base of a tree, the distance to the top of the tree is 1 ft more than 2 times the height of the tree. Find the height of the tree.
At a point on the ground 15ft from the base of a tree, the distance to the top of the tree is 1 ft more than 2 times the height of the tree. Find the height of the tree.
The height of the tree is 8ft.
Given that,
A right triangle has two legs, which are height and (15 feet) from the base.
The hypotenuse is 15 feet from the base to the top of the tree.
or 2(height) + 1ft.
Let us take a as height of the tree; b=distance from base=15 ft; c=hypotenuse=2a+1ft
The area of the square created on the hypotenuse of any right triangle is equal to the sum of the areas of the squares formed on the triangle's legs:
[tex]a^{2} +b^{2} =c^{2}[/tex]
[tex]a^{2} +(15ft)^{2}=(2a+ 1ft) ^{2}[/tex]
[tex]a^{2} +225ft^{2}=4a^{2} +4a+1\\ 0=3a^{2}+4a-224\\ 0=(a-8)\times(3a+28)\\[/tex]
Now,
a-8=0 (or) 3a+28=0
a=8 (or) a=[tex]\frac{-28}{3}[/tex]
Therefore, The height of the tree is 8ft.
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Three angles add up to 180 degrees, angle one has a measure of 8x+8, angle two has a measure of 8x+8 and angle three has a measure of 2x+8.
Given that the sum of the angles is 180 degrees, what is the measure of angle one? Round your answer to the hundredths place IE 79.50.
The first angle will be 77.33°.
How to calculate the angle?It should be noted that the total angles will be 180°.
This will be illustrated as:
8x + 8 + 8x + 8 + 2x + 8 = 180
18x + 24 = 180
18x = 180 - 24
18x = 156
x = 8.667
The first angle will be
= 8x +8
= 8(8.667) + 8
= 77.33°
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(7m³ +8m²-m+2.8)-(-3m³ +9m+3.6)
Answer:
The correct answer would be,
= 10m^3 + 8m^2 - 10m - 0.8
Step-by-step explanation:
First you subtract the m^3 terms :
> 7m^3 + 3m^3
> 10m^3
Then you subtract m^2 , in this case we only have 1 m^2 :
> 8m^2
Then you subtract the m terms :
> -m - 9m
> -10m
The lastly you subtract the last terms :
> 2.8 - 3.6
> -0.8
= 10m^3 + 8m^2 -10m -0.8
(Make sure to distribute the negative before you solve it.) Just a point!!
Answer:
10m³+8m²-10m-0.8
Step-by-step explanation:
(7m³ +8m²-m+2.8)-(-3m³ +9m+3.6)
Use the sign to open the bracket we have;
7m³ +8m²-m+2.8+3m³-9m-3.6
bring like terms together
7m³+3m³+8m²-9m-m-3.6+2.8
Simplifying we have;
10m³+8m²-10m-0.8
hope it helps...
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