Step-by-step explanation:
As a ream or
500
sheets of paper weigh
4.818
pounds
One sheet of paper weighs
4.818
500
=
0.009636
pounds.
It is apparent that pound is too big a unit for a sheet of paper.
As each pound has
16
ounces, one can say
one sheet of paper weighs
0.009636
×
16
=
0.154176
ounces.
If ounce is too big, as we have
1
pound equal to
28.34952
grams
one sheet of paper weighs
0.154176
×
28.34952
≈
4.371
grams
please mark as brainliest
In the expansion of (1/ax +2ax^2)^5 the coefficient of x is five. Find the value of the constant a.
Answer:
80x⁴
Step-by-step explanation:
[tex](\frac{1}{ax} + 2ax^2)^5 = 5C_0(\frac{1}{ax})^5(2ax^2)^0 + 5C_1(\frac{1}{ax})^4(2ax^2)^1 + 5C_2(\frac{1}{ax})^3 (2ax^2)^2[/tex]
[tex]+ 5C_3 (\frac{1}{ax})^2(2ax^2)^3 + 5C_4(\frac{1}{ax})^1(2ax^2)^4 + 5C_5(\frac{1}{ax})^0(2ax^2)^5[/tex]
[tex]5C_0(\frac{1}{ax})^5(2ax^2)^0 =1 \times (\frac{1}{ax})^5 \times 1 = \frac{1}{a^5x^5}\\\\5C_1(\frac{1}{ax})^4(2ax^2)^1 = 5 \times (\frac{1}{ax})^4 \times (2ax^2)^1 = 10 ax^2 \times \frac{1}{a^4x^4} = \frac{10}{a^3x^2}\\\\5C_2 (\frac{1}{ax})^3 (2ax^2)^2= 10 \times (\frac{1}{ax})^3 \times (2ax^2)^2 = 10 \times \frac{1}{a^3x^3} \times 4a^2x^4 = \frac{40x}{a}\\\\5C_3 (\frac{1}{ax})^2 (2ax^2)^3 = 10 \times (\frac{1}{ax})^2 \times (2ax^2)^3 = 10 \times \frac{1}{a^2x^2} \times 8a^3 x^6 = 80ax^4\\\\[/tex]
[tex]5C_4(\frac{1}{ax})^1(2ax^2)^4 = 5 \times \frac{1}{ax} \times 16a^4x^8 = 80a^3x^7\\\\5C_5(\frac{1}{ax})^0(2ax^2)^5 = 1 \times 1 \times 32a^5x^{10}[/tex]
The fourth term of the expansion has the constant a,
the coefficient of a is 80x⁴
In a class, three-fifths of 25 students are girls. What is the number of girls in the class?
Answer:
15
Step-by-step explanation:
3/5*25
Answer:
15 girls
Step-by-step explanation:
(3/5) x 25 = 15
What is the length of side a? Round to the nearest tenth of an inch. Enter your answer in the box.
9514 1404 393
Answer:
14.4
Step-by-step explanation:
The Pythagorean theorem tells you ...
7² +a² = 16²
a² = 256 -49
a = √207
a ≈ 14.4
There are 25 trees on the Jackson’s property. Twenty percent of the trees are oak trees. Which equation can be used to find the number of oak trees on the property?
StartFraction 25 divided by 1 Over 20 divided by 1 EndFraction = StartFraction 25 Over 20 EndFraction
StartFraction 100 times 5 Over 20 times 5 EndFraction = StartFraction 500 Over 100 EndFraction
StartFraction 20 times 4 Over 25 times 4 EndFraction = StartFraction 80 Over 100 EndFraction
StartFraction 20 divided by 4 Over 100 divided by 4 EndFraction = StartFraction 5 Over 25 EndFraction
Answer:
StartFraction 25 divided by 1 Over 20 divided by 1 EndFraction = StartFraction 25 Over 20 EndFraction
Step-by-step explanation:
Number of trees = 25
Percentage of aok trees = 20%
To obtain the Number of oak trees :
(Number of trees ÷ 1) ÷ (percentage ÷1)
(25 / 1) ÷ (20 / 1) = (25 /1) * (20 / 1) = 25 / 20
StartFraction 25 divided by 1 Over 20 divided by 1 EndFraction = StartFraction 25 Over 20 EndFraction
Question 20
A transformer has 500 turns in its primary coil and 200 in the secondary coil.
a) If an AC voltage of 220 V and frequency 50 Hz is established in the primary coil, find the voltage
and the frequency induced in the secondary coil. (2)
9514 1404 393
Answer:
88 V50 HzStep-by-step explanation:
The secondary voltage is proportional to the primary voltage. The constant of proportionality is the ratio of secondary turns to primary turns.
The secondary voltage is ...
(200/500)(220 V) = 88 V
__
A transformer does not change the frequency.* The voltage in the secondary coil is still 50 Hz.
_____
* Most transformers are designed to operate as linear devices. It is possible to design a transformer (with special core material) that operates non-linearly, and/or that is "tuned" to a frequency other than the one exciting the primary. That is, the secondary voltage may be some harmonic of the primary voltage. This would be a relatively unusual application of a transformer, beyond the apparent scope of the question here.
Kristin is saving up money to go on a trip around the world next year. In order to make enough to pay for her trip, Kristin has to work at least 260 days this year.
Which of the following inequalities represents Kristin's possible number of workdays, d
Answer:
A.
D needs to be equal or more to 260
Answer:
The correct option is A
Step-by-step explanation:
a trader borrowed 2500$ at a sumple interest at the end of 8 months he paid back $2500 find the rate
Answer:
8%
Step-by-step explanation:
Rate = 100×Interest ÷ Principal× Time
100× 2500/ 2500 × 8 = 800
800/100 = 8%
I hope this helps
3
5
6) through: (-3, -3), perp. to y=-**-4
5
A) y = 2x + B) y=--x+ 2
*
3
C) y=-x+2 D) y=-x+ 2
5
3
Step-by-step explanation:
answer in the image above
( 0 , -1 ) , ( 1,3)
Which equation is satisfied by BOTH of these pairs of numbers ( x , y ) ?
A. x + y = -1
B. 2x + y = 5
C. 3x - y = 0
D. 4x - y = 1
Answer:
D 4x-y=1
Step-by-step explanation:
4x-y=1. (x=0 ,y= -1)
4(0)-(-1)= 1
0+1= 1
4x-y=1 (x=1 y=3)
4(1)-3=1
4-3=1
what is the sum of the angles of a triangle
Answer:
Triangle has 180 degrees
Squares have 360 degrees
At a price of per ticket, a musical theater group can fill every seat in the theater, which has a capacity of . For every additional dollar charged, the number of people buying tickets decreases by . What ticket price maximizes revenue? Revenue is maximized when the price is
Answer:
The appropriate answer is "$12".
Step-by-step explanation:
As per the question,
Price per ticket,
= [tex]4+k[/tex]
Number of people,
= [tex]1800-90k[/tex]
Now,
The revenue (R) will be:
= [tex]Price \ per \ ticket\times Number \ of \ people[/tex]
By putting the values, we get
= [tex](4+k) (1800-9k)[/tex]
= [tex]-90k^2+1440k+7200[/tex]
or,
⇒ [tex]R'=1440-180k=0[/tex]
⇒ [tex]180k=1440[/tex]
⇒ [tex]k=\frac{1440}{180}[/tex]
[tex]=8[/tex]
hence,
The ticket price will be:
= [tex]4+k[/tex]
= [tex]4+8[/tex]
= [tex]12[/tex] ($)
What is the value of the expression 2x^2 + 3xy - 4y^2 when x = 2 and y = -4?
Answer:
-80
Step-by-step explanation:
2x^2 + 3xy - 4y^2
x = 2 | y = - 4
2(2)^2 + 3(2)(-4) - 4(-4)^2
2 * 4 + 3(2)(-4) - 4 * 16
8 - 24 - 64
-80
With the help of a diagram a boy starts at a and walks 3km east to b he then walk 4km north to c find the distance and bearing of c from a
Answer:
t=3
Step-by-step explanation:
sorry if its incorrect i got it right on edgy.
Given that 4x – 5y = 12 Find y when x = -3 Give your answer as an improper fraction in its simplest form.
Step-by-step explanation:
4(-3)-5y=12
-12-5y=12
-5y=12+12
-y= 24/5
y= -24/5
y= -4⅕
hope it helps
I got a 90% on my quiz. Thanks to everyone who helped me!
Also this is a really is question but I'm to lazy to do it. Can someone give me the answer to this? (Question in the picture)
Answer: The answer is A
Step-by-step explanation:
In the picture, model A shows 3 groups and in the 3 groups are 4 lines !
I'm bad explaining but I hope this helps .
Write an equation of a line that passes through (3,2) and (-5,6).
please help show steps thx
Answer:
1) P = 282m, A = 141m^2
2) P = 82.4in, A = 40in^2
3) P = 62.7m, A = 73.1m^2
Step-by-step explanation:
1) top:L=12m, W=3m, mid: l= 12m, w= 12-7 = 5m, bot: l=15m, w=3m
Perimeter= 2(lw)
P = 2(12x3) + 2(12x5) + 2(15x3)
P = 2(36) + 2(60) + 2(45)
P = 72 + 120 + 90
P = 282m
Area= lw
A = (12x3) + (12x5) + (15x3)
A = 36 + 60 + 45
A = 141m^2
2) Rectangle:l=7in, w=5in, Right Triangle:a=5-3=2in, b=12-7=5in
Perimeter= 2(lw) + (a+b+sqrt(a^2+b^2))
P = 2(7x5) + (2+5+sqrt(2^2+5^2))
P = 70 + 12.39
P = 82.4in
Area= lw + ((ab)/2)
A = (7x5) + ((2x5)/2)
A = 35 + 5
A = 40in^2
3) Semi-Circle: d=8m, r=8/2=4m, Right Triangle: a=8m, b=12m
Perimeter= pid + (a+b+sqrt(a^2+b^2))
P = 9pi + (8+12+sqrt(8^2+12^2))
P = 28.27 + 34.42
P = 62.7m
Area= (1/2)pir^2 + ((ab)/2)
A = (1/2)pir^2 + ((ab)/2)
A = (1/2)pi(4)^2 + ((8x12)/2)
A = 25.13 + 48
A = 73.1m^2
The bike you have been saving for is discounted 25%. You have $500 saved to purchase it. The original, non-discounted price of the bike is $575. There is a 5.60% sales tax added to the price of the bike. After you purchase the bike with the discount and sales tax, how much money will you have left over? Round your answer to the nearest dollar.
The telephone company charges $25 for a service call, and $15 for every 15 minutes the service representative works on repairs. Write an equation you could use to find the total cost of a repair visit.
Answer:
C=$25+$15m
Step-by-step explanation:
C is Cost
m is 15 minutes
The price for a visit would be $25 + $15 times the amount of time they work on repairs.
The equation you could use to find the total cost of a repair visit is C=$25+$15m.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
The telephone company charges $25 for a service call, and $15 for every 15 minutes the service representative works on repairs.
Let C is Cost and m be 15 minutes
From the data given in the question:
C = 25 + 15m
Thus, the equation you could use to find the total cost of a repair visit is C=$25+$15m.
Learn more about the linear equation here:
brainly.com/question/11897796
#SPJ2
20 men can do a piece of work in 24 days. After working for few days, 3 men are added and the work was finished 3 days earlier. After how many days if 4 men are added?
Answer: 17 and a half
Step-by-step explanation:
M D W
20 24 480
20 21 420
24 17 and a half 420
= 17 and a half
. year or once a year Your reading material illustrates a typical example of what happens if you pay just the minimum monthly payment every month on a credit card balance. In this example, approximately how long will it take to pay off the original debt completely? a. b. 2 years 5 years 12 years The debt will never be completely repaid. C. d.
A traingle has an area of 35cm2 ANSWER CORRECT WITH EXPLANATION PLEASE
GOOD POINTS UP FOR GRABS
What could its dimensions be?
Base = Height =
Answer:
Base=2 cm
Height=35 cm
or
Base=5 cm
Height=14 cm
Or
Base=7 cm
Height=10 cm
Or
Base=10 cm
Height=7 cm
Or
Base=14 cm
Height=5 cm
Or
Base=70 cm
Height=1 cm
Or
Base=35 cm
Height=2 cm
Or
Base=1 cm
Height=70 cm
Step-by-step explanation:
We are given that
Area of triangle=[tex]35cm^2[/tex]
We have to find the dimension of triangle.
We know that
Area of triangle=[tex]\frac{1}{2}\times base\times height[/tex]
Using the formula
[tex]35=\frac{1}{2}\times base\times height[/tex]
[tex]base\times height=35\times 2=70[/tex]
Factor of 70 :2,5,7,10,14,35,70
Therefore, the dimension could be
Base=2 cm
Height=35 cm
or
Base=5 cm
Height=14 cm
Or
Base=7 cm
Height=10 cm
Or
Base=10 cm
Height=7 cm
Or
Base=14 cm
Height=5 cm
Or
Base=70 cm
Height=1 cm
Or
Base=35 cm
Height=2 cm
Or
Base=1 cm
Height=70 cm
what is the value of x?
Answer:
46
ayo how r u doin siahsvsgshsgsgsgsg
The length of a rectangle is 5 inches longer than it is wide. If the area is 84 square inches, what are the
dimensions of the rectangle?
The width, or shorter side is i inches
Enter an integer or decimal number (more..
inches
The length, or longer side is
Answer:
b = 7 inches and l = 12 inches
Step-by-step explanation:
Given that,
The area of a rectangle, A = 84 sq inches
Let the width is b.
Length = (5+b)
The area of a rectangle is given by :
A = lb
So,
[tex]84=b\times (5+b)\\\\b^2+5b-84=0\\\\(b-7)(b+12)=0\\\\b=7\ in, b =-12\ in[/tex]
Neglecting negative value,
b = 7 inches
Length, l = 5+b = 5+7
l = 12 inches
Write two rational and three irrational number that are between 3and 4
a)rational number :
1)(3+4 )/2
=7/2 =3.5
2)(3.5+4)/2
=7.5/2 =3.25
b)irrational number :
1)10/3=3.33....
2)11/3=3.66....
......I hope it will help you. ..
Answer:
The real numbers, which can be represented by the ratio of two integer numbers, are called rational numbers, say P/Q where Q is not equal to zero.
The actual numbers that cannot be expressed as the two integer ratio are called irrational numbers.
Step-by-step explanation:
a)rational number :
1)
(3+4 )/2
=7/2 =3.5
2)
(3.5+4)/2
=7.5/2 =3.25
b)irrational number :
1)
10/3=3.33....
2)
11/3=3.66....
3)
√13
Help me outtttttttttto
Answer:
,
Step-by-step explanation:
hear is your answer please give me Some thanks
in the right triangle AB, mc=90, a=4, and sinA=1/2. what is the length of the hypotenuse?
Given:
In a right angle triangle ABC, [tex]m\angle C=90^\circ , a=4[/tex] and [tex]\sin A=\dfrac{1}{2}[/tex].
To find:
The length of the hypotenuse.
Solution:
It is given that [tex]m\angle C[/tex], so opposite side of this angle is the hypotenuse, i.e., c.
In a right angle triangle,
[tex]\sin \theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]
In the given triangle,
[tex]\sin A=\dfrac{a}{c}[/tex]
Substituting the given values, we get
[tex]\dfrac{1}{2}=\dfrac{4}{c}[/tex]
By cross multiplication, we get
[tex]1\times c=4\times 2[/tex]
[tex]c=8[/tex]
Therefore, the length of the hypotenuse is 8 units.
A distribution of values is normal with a mean of 232.4 and a standard deviation of 92.2. Find the probability that a randomly selected value is between 66.4 and 241.6. P(66.4 < X < 241.6)
Answer:
P(66.4 < X < 241.6) = 0.5039 = 50.39%.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
A distribution of values is normal with a mean of 232.4 and a standard deviation of 92.2.
This means that [tex]\mu = 232.4, \sigma = 92.2[/tex]
Find the probability that a randomly selected value is between 66.4 and 241.6.
This is the p-value of Z when X = 241.6 subtracted by the p-value of Z when X = 66.4.
X = 241.6
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{241.6 - 232.4}{92.2}[/tex]
[tex]Z = 0.1[/tex]
[tex]Z = 0.1[/tex] has a p-value of 0.5398
X = 66.4
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{66.4 - 232.4}{92.2}[/tex]
[tex]Z = -1.8[/tex]
[tex]Z = -1.8[/tex] has a p-value of 0.0359
0.5398 - 0.0359 = 0.5039
P(66.4 < X < 241.6) = 0.5039 = 50.39%.
The storage container below is in the shape of a rectangular prism with a height of 6 feet and a length that is 2 feet more than its width.
Recall that the formula for the volume of a rectangular prism is V = l · w · h, where l is the length, w is the width, and h is the height.
Write the equation that represents the volume of the storage container in terms of its width.
A.
V = 6w2 + 12w
B.
V = 6w2 - 12
C.
V = 6w2 + 12
D.
V = 6w2 - 12w
Answer:
A
Step-by-step explanation:
Step 1, setting variables:
We already know the exact height of the prism: 6 feet. We can set the unknown width as variable x, and length as x+2 (length is two feet more than width).
Step 2, writing equations:
Great! We have everything now. Let us write the equation by substituting our variables in:
[tex]V=l*w*h\\V=6w(w+2)\\[/tex]
Ok! Let us expand the equation:
[tex]V=6w^2+12w[/tex]
[tex]\fbox{A}[/tex]
I hope this helps! Let me know if you have any questions :)
Sima drinks 2.5 litres of water each day.
A full glass holds 125 mililitres of water.
How many full glasses of water does Sima drink each day?
Answer:
20 glasses a day
Step-by-step explanation:
2.5litres equals 2500millilitres
2500÷125=20