by dividing the equations we get, the simplified expression is (3y⁶) / (x⁵z*4).
What is an arithmetic operation?
Arithmetic operations is a branch of mathematics, that involves the study of numbers, the operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication, and Division.
To divide 15xy⁷z⁴ by 5x⁶yz*16, we can simplify the expression by canceling out common factors in the numerator and denominator.
First, we can simplify 15 and 5 by dividing both by 5:
15/5 = 3
5/5 = 1
Next, we can simplify x and x⁶ by dividing both by x⁶:
x/x⁶ = 1/x⁵
x⁶/x⁶ = 1
We can simplify y⁷ and y by dividing both by y:
y⁷/y = y⁶
y/y = 1
We can simplify z⁴ and z16 by dividing both by z16:
z^4/z16 = 1/(z4)
z16/z16 = 1
Putting it all together, we get:
(15xy⁷ z⁴) / (5x⁶yz16)
= (3 * y⁶) / (x⁵ * z4)
Therefore, by dividing the equations we get, the simplified expression is (3y⁶) / (x⁵z*4).
To learn more about the arithmetic operation visit,
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Nathan nets $680 every other week. How much does
Nathan earn per month on average? To be safe, how much
should Nathan estimate as income in a typical month?
A. Average: $1473.33: Safe: $1360
B. Average: $2946.67; Safe: $1360
C. Average: $2946.67; Safe: $1473.33
D. Average: $2946.67; Safe: $2720
in any circle, the ratio of the _ to the radius is 2.
a. diameter
b. radius
c. circumference
d. pi
PLEASE HURRY! 15 points
Answer:
The answer should be C
Step-by-step explanation:
Geometry Regents Cl-1 / Quarter 2 / Week 18:1/18 - 1/22 / Independent Learning Assign
7. What is the sum of the exterior angles of polygon QRST
Answer:
360°Step-by-step explanation:
The sum of the exterior angles of any polygon is 360 degrees and the QRST is not an exception.
A triangle has angles measuring 25° and 45°. What is the measure of the triangle's third angle?
Oa 90°
O b. 110°
Oc. 20°
Od 180°
to search
CAN SOMONE PLEASE HELP
Answer:
The answer to this question is B
Answer:
the answer for this question is 110°
Step-by-step explanation:
you have to add the angles first in this case 25 and 45
and then subtract the sum from 180.
so.... 25+45=70
180-70=110
hope its was helpful :)
PLEASE ANSWER QUICKLY I WILL GIVE YOU BRAINLIEST ANSWER
A boat rental company has two kinds of boats, rowboats and motorboats. The expressions below represent the cost, in dollars, for renting each kind of boat for x number of hours.
Cost of a rowboat rental: 8.5x+3
Cost of motorboat rental: 17.50x+25
Which expression shows how many more dollars it costs to rent a motorboat than a rowboat for x hours?
A. 8x+22
B. 9x+22
C. 9x+28
D. 26x+28
Answer:
The answer is B. 9x + 22
Step-by-step explanation:
17.50x + 25
- 8.5x + 3
= 9x + 22
Which graph represents the solution set of the system of inequalities? {y≥13x−3y<−3x−3
Answer:
see below
Step-by-step explanation:
Mango and her friends are running an 8 mile relay. Each friend will run 1/3 mile. How many friend will run with Mango?
Answer:
24
Step-by-step explanation:
Diego lives 1/2 from school. What is 50% of 1/2 mile?
Answer:
1/4 or .25
Step-by-step explanation:
In the right triangle, if a = 3 and b = 6, what is the value of c?
a 3 times the square root of 5
b 9
c 9 times the square root of 5
d 45
Answer:
A
Step-by-step explanation:
Using the pythagorean theorem, [tex]a^{2} +b^{2} =c^{2}[/tex]
we plug the numbers in; [tex]3^{2} + 6^{2} =c^{2}[/tex]
9+36=c^2
45=c^2
sqr root of 45 is [tex]\sqrt{45}[/tex]
next find the positive perfect sqr root of 45 which will be 9.
9 goes into 45 5 times so it will be [tex]\sqrt{9x5}[/tex]
Sqr root of 9 is 3 so it will be [tex]3 \sqrt{5}[/tex]
LAST ONE THEN IM GONE TILL NEXT YEAR
jk not really
Answer:
2) Quadrant IIis the right answer.
The Ratio of girls to boys in the art club of Wilson Middle School is 3 to 2. About what percent of the members in the art club are boys?
Answer:
i believe it's 20%
Step-by-step explanation:
girls: 3
boys: 2
ratio: 3:2
so, 20%
Consider the following sequence:
7, 11, 15, 19, 23, . . .
The common difference is ______
What is the Explicit equation for the sequence?
t(n) = ____n + ______
What is the 20th term?
Answer:
Common difference= 4, Equation; t(n)=4n+3, 20th= 83
Step-by-step explanation:
d=11-7=4
Equation
Recall, t(n)=a_1+(n-1)d
Replacing a_1 =7 and d=4
t(n)=7+(n-1)4
t(n)=7+4n-4
t(n)=4n+3
20th item
t(20)=4(20)+3=83
I hope that is helpful
Answer:
Step-by-step explanation:
This is an arithmetic progression.
It starts at 7 and keeps on adding 4.
The common difference is 4
The explicit equation is
t_n = a + (n - 1)*d
a = 7
d = 4
t_n = 7 + (n - 1)*4
t_n = 7 + 4n - 4
t_n = 4n + 3
t_20
t_20 = 4*20 + 3
t_20 = 83
Sarah mixes ⅓ cup of sugar with ½ cup of cream cheese to make a topping for cupcakes. Sarah uses 3/12 cup of the mixture to top each cupcake. How many cupcakes can Sarah top?
Answer:
thanks for the points
Step-by-step explanation:
Mark's football team has scored about 24 points each game. They played 12 games this season.
What is the best estimate for the total number of points they scored in the season?
Answer:
36
Step-by-step explanation:
well you could add 24+12 which equals 36
What is the equation for a line parallel to y=-4x-9 that passes through the point 0,8
One week gas was $1.25 per gallon. The next week gas was $1.50 per gallon. By what percentage did the price increase?
i really really need help with all of these you don't have to show your work but please help me with at least some or all of them pls i'm giving 50 points!!!!!
Answer:
Step-by-step explanation:
1. 24+9/2pi, 2. 51 3. 86. 4. 90 5. 56, all of these are done with the addition or subtraction of simple geometric formulas such as those for a rectangle,circle or triangle.
Answer:
Step-by-step explanation:
1. Rectangle + Semi-Circle
[tex]A = a*b + \frac{\pi r^{2}}{2}\\a=6, b=4, r=\frac{a}{2} = 3\\A = 24 + 4.5 \pi = 38.14 in^{2}\\[/tex]
2. Large Rectangle - Small Rectangle
[tex]A = 15 * 5 - 6*3 = 75 - 18 = 57 in^{2}\\[/tex]
3. Rectangle - Trapezoid
[tex]A = a * b - \frac{c+d}{2}h = 20*17 - 6 * \frac{6+12}{2} = 340 - 54 = 286 cm^{2}\\[/tex]
4. The composite figure is a rectangle if the triangle is moved to left and fills the missing part
[tex]A = a * b = 10 * 9 = 90 m^{2}\\[/tex]
5. Square - Triangle
A = [tex]A = a^{2} - \frac{b^{2}}{2} = 8 * 8 - \frac{4 * 4}{2} = 64 - 8 = 56 cm^{2}\\[/tex]
6. Circle - Square
[tex]A = \pi r^{2} - a^{2} = 64 \pi - 12 * 12 = 64 \pi - 144 = 57.06 m^{2}[/tex]
7. Square - Triangle
[tex]A = a^{2} - \frac{b*h}{2} = 15 * 15 - \frac{10 * 8}{2} = 225 - 40 = 185 sq.ft.[/tex]
8. Rectangle + Triangle
[tex]A = a *b + \frac{a*h}{2} = 9.5 * 9 + \frac{9.5*12}{2} = 85.5 + 57 = 142.5 in^{2}\\[/tex]
9. Triangle + Rectangle
[tex]A = \frac{a*b}{2} + c * d = \frac{12*10}{2} + 12 * 6 = 60 + 72 = 132 sq.ft.[/tex]
10. Rectangle + Quarter Circle
[tex]A = r * b + \frac{\pi r^{2}}{4} = 6 * 8 + \frac{36 \pi}{4} = 48 + 9 \pi = 76.27 in^{2}\\[/tex]
11. Square + Rectangle
[tex]A = a^{2} + b * c = 7 * 7 + 9 * 14 = 49 + 126 = 175 m^{2}[/tex]
12. Rectangle - 2 * Square
[tex]A = a * b - 2 * c^{2} = 25 * 18 - 2 * 8 * 8 = 450 - 128 = 322 sq.ft.[/tex]
13. Trapezoid
[tex]A = \frac{a+b}{2} * h = \frac{10+15}{2} * 15 = 12.5 * 15 = 187.5 sq.ft.[/tex]
14. Trapezoid - Rectangle
[tex]A = a * h - c * d = 12 * 7 - 9 * 5 = 84 - 45 = 39 in^{2}[/tex]
15. Rectangle - Triangle
[tex]A = a * b - \frac{a * b}{2} = \frac{a*b}{2} = \frac{10 * 20}{2} = 100 in^{2}[/tex]
16. Square + Trapezoid
[tex]A = a^{2} + \frac{a + b}{2} * h = 25 + \frac{5 + 9.5}{2} * 6 = 25 + 43.5 = 68.5 in^{2}[/tex]
If one factor of x2 + 2x – 24 is (x+6), what is the other factor?
(x+8)
(x–8)
(x+4)
(x−4)
Answer:
(x - 4)
Step-by-step explanation:
The other factor would be (x - 4)
You can use trial and error for this
Find the distance from point P to the given line
Answer:
The distance from point P, P(-2,4) to the given line y= 2x-2 is 1.56
Step-by-step explanation:
We need to find the distance from point P to the given line
P(-2,4) , y= 2x-2
The formula used is: [tex]Distance=\frac{|Ax_1+By_1+C|}{\sqrt{A^2+B^2} }[/tex]
Where A, B and C are points of line i.e Ax+By+C=0
and x_1 and y_1 are points of P
So, y=2x-2 in Ax+By+C=0 is:
2x-y-2=0
A=2,
B=-1
C=1
Point given is P(-2,4)
x_1=-2
y_1=4
Putting values and finding distance
[tex]Distance=\frac{|Ax_1+By_1+C|}{\sqrt{A^2+B^2} }\\Distance=\frac{|2(-2)+-1(4)+1|}{\sqrt{(-2)^2+(4)^2} }\\Distance=\frac{|-4-4+1|}{\sqrt{4+16} }\\Distance=\frac{|-7|}{\sqrt{20}}\\Distance=\frac{7}{\sqrt{20} }\\Distance=\frac{7}{4.5}\\Distance=1.56[/tex]
So, the distance from point P, P(-2,4) to the given line y= 2x-2 is 1.56
8y – 3(y – 2) >2y + 4(2y + 4)
Answer:
y<-2
Step-by-step explanation:
8y-3y+6>2y+8y+16
-3y-2y>16-6
-5y>10
y<-2
Answer:
y > -2
Step-by-step explanation:
Please look at the attachment:
can I get some help with changing the decimal 1.5 to a fraction please
Answer:
I do believe that 1.5 as a fraction is 3/2 or 1 and 1/2
Step-by-step explanation:
Hope this helps you:)
Answer:
1 ½ or 3/2
Step-by-step explanation:
Decimals can be written in fraction form. To convert a decimal to a fraction, place the decimal number over its place value. For example, in 0.6, the six is in the tenths place, so we place 6 over 10 to create the equivalent fraction, 6/10. If needed, simplify the fraction. - Khan Academy
Hope this helps :D
Allerga counted 7.5 red cards and 15 black cards in a deck of cards. What is the ratio of red cards to black cards
Answer:
7.5:15
It cannot be simplified further
Step-by-step explanation:
Hope this helps! Have a nice day!
Mae Ling earns a weekly salary of $325 plus a 7.5% commission
on sales at a gift shop. How much would she make in a work week if she sold
$5,800 worth of merchandise? Write in money format.
Answer:
$760
Step-by-step explanation:
Given data
weekly = $325
commission= 7.5%
if she sold $5,800 worth of merchandise
Her earnings will be
Week earning= base salary+ 7.5% of sales
Week earning= 325+ 7.5/100*5800
Week earning= 325+ 0.075*5800
Week earning= 325+ 435
Week earning= $760
A number x is less than 12.
Answer:
Step-by-step explanation:
Not completly sure what your looking for but it X would be any number lower then 12 (11,10,9,8,7,6,5,4,3.2,1)
Answer:
1-11
Step-by-step explanation:
its less than 12!
hope this is correct! c:
Prove: The difference of the cubes of two
successive integers is odd.
(n + 1)3-n3 = [ ? ]n2 + [ ]n + 1
= [ ](n + 1) + 1
= 6m + 1 (since n or n+1 is even)
= odd
(n + 1)³ - n³ = (n³ + 3n² + 3n + 1) - n³
… = 3n² + 3n + 1
… = 3n (n + 1) + 1
… = 6m + 1
where m is another integer. We can say this because, as the second-to-last step says, either n or n + 1 is even, which makes their product also even, so we can write it as a multiple of 2:
n (n + 1) = 2m
Then 6m is even, and adding 1 to it makes it odd.
Seventy-nine percent of products come off the line ready to ship to distributors. Your quality control department selects 12 products randomly from the line each hour. Looking at the binomial distribution, if fewer than how many are within specifications would require that the production line be shut down (unusual) and repaired?
a. Fewer than 7
b. Fewer than 9
c. Fewer than 6
d. Fewer than 10
Answer:
c. Fewer than 6
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
In the binomial distribution, an outcome is considered unusual if it is more than 2.5 standard deviations below the mean.
Seventy-nine percent of products come off the line ready to ship to distributors.
This means that [tex]p = 0.79[/tex]
Your quality control department selects 12 products randomly from the line each hour.
This means that [tex]n = 12[/tex]
Mean:
[tex]E(X) = np = 12*0.79 = 9.48[/tex]
Standard deviation:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{12*0.79*0.21} = 1.41[/tex]
Unusual:
[tex]9.48 - 2.5*1.41 = 5.96[/tex]
So fewer than 6 is considered unusual.
The graph below shows the solution set of which inequality
Answer:
D.
Step-by-step explanation:
A university conducted a study of whether running is healthy for men and women over age 50. During the first eight years of the study, 1.9% of the 457 members of a fitness association died. We are interested in the proportion of people over 50 who ran and died in the same eight-year period.
NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)
Define the Random Variables X and P', in words. which of the following?
a.) X is the proportion of people who ran and died in the eight-year period, and P' is the number of people who ran and died in the eight-year period.
b.) X is the proportion of all runners that die, and P' is the number of all runners that die.
c.) X is the number of people who ran and died in the eight-year period, and P' is the proportion of people who ran and died in the eight-year period.
d.) X is the number of all runners that die, and P' is the proportion of all runners that die.
Answer:
From given data, University conducted a study of whether running is healthy for men and women over age 50. During the first eight years of the study, 1.9% of the 454members of 50 plus fitn
Describe how to transform (^6 sqrt x^5)^7 into an expression with a rational exponent. Make sure you respond with complete sentences.
Answer:
[tex]x^{\frac{36}{5} }[/tex]
Step-by-step explanation:
The transformation is as follows:
As we know that
[tex]a^{\frac{m}{n} } \rightarrow\sqrt[m]{a^{n}} \\\\\sqrt[m]{a^{n}} \rightarrow a^{\frac{m}{n} }\\\\(\sqrt[6]{x^5})^7 \rightarrow (x^{\frac{5}{6} })^7 \rightarrow x^{\frac{5^\times 7}{6} }\\\\x^{\frac{36}{5} }[/tex]
In this way it would be transformed with a rational exponent
1. The perimeter of a sector of a circle of radius r is 8 metres.
(i) Express θ in terms of r, where is the angle of the sector
in radians, as shown.
Answer:
Step-by-step explanation:
s and r are the arc length and radius, respectively.
perimeter of sector = s+2r = 8
s = 8-2r
θ = s/r = (8-2r)/r
