Answer:
$3600
Step-by-step explanation:
Given:
Total income T = $18,000
Fraction of income spent on house rent f1 = 1/5
Fraction of income spent on other expenditures f2 = 3/5
Fraction of income saved is;
f = 1 - (1/5+3/5) = 1 - 4/5
f = 1/5
The Amount he save is A;
A = fraction saved × total amount = f × T
Substituting the values
A = 1/5 × $18,000
A = $3,600
The Amount he save is $3,600
Answer: Varun saves 3,600 every month
Step-by-step explanation: Varun's income in the first instance is fixed at 18000, and out of this amount he spends 1/5 on house rent. We shall now determine the amount represented by 1/5 as follows;
Total income = 18000
House rent = 1/5
Rent expense = 1/5 of 18000
Rent expense = 1/5 * 18000
Rent expense = 3600
he also spends 3/5 on other expenditure
Other expenditure = 3/5 of 18000
Other expenditure = 3/5 * 18000
Other expenditure = (3 * 18000)/5
Other expenditure = 54000/5
Other expenditure = 10800
His expenses therefore have been derived as
Total expenditure = 3600 + 10800
Total expenditure = 14400
His savings per month therefore is derived as;
Total income - total expenditure = savings
18000 - 14400 = savings
3600 = savings
Therefore, Varun saves 3,600 every month
A classroom will be assembled so that the desks fit within an area that is 8 m by 12 m. The desks will be surrounded by a border that will be the same width on all sides of the rectangular room, to
allow for walking space. The area of the border will equal 20% of the area of the space that the desks
occupy. What is the width of the border, to the nearest hundredth of a meter?
Answer:
0.46 m
Step-by-step explanation:
area of desks: 8 m by 12 m = 8 m * 12 m = 96 m^2
20% of this area is 20% * 96 m^2 = 19.2 m^2
The area of the border is 19.2 m^2.
Let the path around the desks have width x.
The area of desks plus path is a rectangle 2x + 8 by 2x + 12.
area of desks plus path = (2x + 8)(2x + 12)
= 4x^2 + 24x + 16x + 96 = 4x^2 + 40x + 96
The area of the border is the area of the rectangle that includes the border minus the rectangle that has just the desks.
area of border = (4x^2 + 40x + 96) - (96) =
= 4x^2 + 40x
Above, we have the area of border = 19.2, so we get this equation:
4x^2 + 40x = 19.2
4x^2 + 40x - 19.2 = 0
x^2 + 10x - 4.8 = 0
We now use the quadratic formula to solve the equation for x.
[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
[tex] x = \dfrac{-10 \pm \sqrt{10^2 - 4(1)(-4.8)}{2(1)} [/tex]
[tex] x = \dfrac{-10 \pm \sqrt{100 + 19.2 )}{2} [/tex]
[tex] x = \dfrac{-10 \pm \sqrt{119.2 )}{2} [/tex]
[tex] x = 0.46 [/tex] or [tex] x = -10.46 [/tex]
We discard the negative solution.
Answer: the border is 0.46 m wide.
What is the surface area of the right cone below?
slanted height of 13 and radius of 4
A. 5277 units
B. 5477 units2
C. 687 units2
D. 104 units2
Answer:
213.69 units
Step-by-step explanation:
We have to first find the height of the cone.
We can use Pythagoras rule because the slant height, height and radius of a cone all form a right angled triangle:
[tex]h^2 = a^2 + b^2[/tex]
where h = hypotenuse
a and b = the other two sides of the triangle
The radius is 4 units and the slant height is 13 units:
[tex]13^2 = a^2 + 4^2\\\\169 = a^2 + 16\\\\a^2 = 169 - 16 = 153\\\\a = \sqrt{153}\\\\a = 12.37units[/tex]
The height of the cone is 12.37 units.
The surface area of a cone is given as:
SA = [tex]\pi r (r + \sqrt{h^2 + r^2} )[/tex]
[tex]SA = \pi * 4(4 + \sqrt{12.37^2 + 4^2} )\\\\SA = 12.57(4 + \sqrt{13^2} )\\SA = 12.57 (4 + 13)\\\\SA = 12.57(17)\\\\SA = 213.69 units[/tex]
The surface area of the cone is 213.69 units.
What is the probability brittnie gets at least 35 hits in her next 100 at bats? (round to 3 decimal places.)?
Answer:
0.350
Step-by-step explanation:
Probability is defined as the chances that an event will occur or not occur. The entire idea of probability has to do with 'chance' events. Thus, the probability that an event will surely occur is 1, while the probability that an event will never occur is zero. Probabilities range between 0-1.
Probability of an event is obtained from
Probability= expected outcome/total number of outcomes
In this case,
Expected outcome= 35
Total number of outcomes = 100
Probability= 35/100= 0.350
I need help with this ASAP, please thank you
Answer:
Option A is the correct answer.
Step-by-step explanation:
Line is passing through the point[tex] (2, - 6) = (x_1, \: y_1) [/tex] and its slope is - 3.
Equation of line in slope point form is given as:
[tex] y-y_1 = m(x-x_1) \\
\therefore y-(-6) = - 3(x-2) \\
\huge \red {\boxed {\therefore y + 6 = - 3(x-2)}} \\[/tex]
Answer: A
Step-by-step explanation:
Point-slope form is the following: y - y1 = m(x - x1). So all that is needed is to substitute y1 for -6, x1 for 2, and -3 for m(the slope).
y - y1 = m(x - x1)
y - (-6) = -3(x - (2))
y + 6 = -3(x - 2)
The price of a train ticket consists of an initial fee plus a constant fee per stop. The table compares the number of stops and the price of a ticket (in dollars). What is the initial fee?
Answer:
Initial Fee is $2.
Step-by-step explanation:
which equations are true identities
Answer:
C
Step-by-step explanation:
Both A and B are true identities.
See attachment.
a rectangle has a length that is 5 inches greater than its width, and its area is 104 square inches. The equation(x+5) x=104 represents the situation, where x represents the width of the rectangle. (x+5) x=104 x2+5x-104=0. Determine the solutions of the equation. What solution makes sense for the situation?
Answer:
x=8
Step-by-step explanation:
Area of a rectangle=length×width
Area=104
Width=x
Length=5+x
104=x*(5+x)
104=5x+x^2
104-5x-x^2=0
x^2+5x-104=0
Can also be written as
-x^2-5x+104=0
Solve the quadratic equation using formula
−x2−5x+104=0
using the Quadratic Formula where
a = -1, b = -5, and c = 104
x=−b±√b2−4ac/2a
x=−(−5)±√(−5)2−4(−1)(104)/2(−1)
x=5±√25−(−416)/−2
x=5±√441/−2
The discriminant b^2−4ac>0
so, there are two real roots.
Simplify the Radical:
x=5±21/−2
x=-26/2 or 16/2
x=-13 or 8
The value of x can't be negative
So, x=8 is the answer
Solve for x. 2x = 15 + x
A.) x = -15
B.) x = 15/2
C.) x = -15/2
D.) x = 15
Option D( X=15)
Solution,
2x=15+x
or, 2x-x=15
X=15
hope it helps...
Good luck on your assignment...
Answer:
[tex]x = 15[/tex]
Step-by-step explanation:
[tex]2x = 15 + x \\ 2x - x = 15 \\ x = 15[/tex]
Answer D is correct
solve the equation
7h-5(3h-8) = 72
Answer:
h = -4
Step-by-step explanation:
7h-5(3h-8) = 72
Distribute
7h - 15h +40 = 72
Combine like terms
-8h +40 = 72
Subtract 40 from each side
-8h+40-40 = 72-40
-8h = 32
Divide each side by -8
-8h/-8 = -32/-8
h = -4
Steps:
Step 1: Simplify both sides of the equation.
7h−5(3h−8)=72
7h+(−5)(3h)+(−5)(−8)=72(Distribute)
7h+−15h+40=72
(7h+−15h)+(40)=72(Combine Like Terms)
−8h+40=72 −8h+40=72
Step 2: Subtract 40 from both sides.
−8h+40−40=72−40
−8h=32
Step 3: Divide both sides by -8
Answer: h=−4
The answer for this question is h=-4
Please mark me brainliest
Hope this helps.
What is the inverse of the function f(x) = one-quarterx – 12? h(x) = 48x – 4 h(x) = 48x + 4 h(x) = 4x – 48 h(x) = 4x + 48
Answer:
h(x) = 4x+48Step-by-step explanation:
Given the function f(x) = 1/4x -12. To get the inverse of the function, first we will let y = f(x) to have y = 1/4x - 12.
Then we will make x the subject of the formula as shown:
y = 1/4x - 12
adding 12 to both sides we have;
y + 12= 1/4x - 12 + 12
y + 12 = 1/4x
Multiplying both sides by 4 we have;
4(y+12) = x
x = 4y + 48
Substituting y for x
y = 4x+48
f^-1(x) = 4x+48
h(x) = 4x+48
Thee final expression will give the inverse of the function
Answer:
h(x) = 4x+48
Step-by-step explanation:
Given the function f(x) = 1/4x -12. To get the inverse of the function, first we will let y = f(x) to have y = 1/4x - 12.
Then we will make x the subject of the formula as shown:
y = 1/4x - 12
adding 12 to both sides we have;
y + 12= 1/4x - 12 + 12
y + 12 = 1/4x
Multiplying both sides by 4 we have;
4(y+12) = x
x = 4y + 48
Substituting y for x
y = 4x+48
f^-1(x) = 4x+48
h(x) = 4x+48
Thee final expression will give the inverse of the function
1. Using the scale 1 in.: 4 ft, find the dimensions in a blueprint of an 8 ft-by-12 ft
room
Answer:
2 in by 3 in
Step-by-step explanation:
1 in = 4 ft Divide both sides with 4
0.25 in = 1 ft
0.25 * 8 = 2 in
0.25 * 12 = 3 in
2 in by 3 in
Answer: 2 in by 3 in
Step-by-step explanation:
1 in = 4 ft Divide both sides with 4 0.25 in = 1 ft 0.25 * 8 = 2 in 0.25 * 12 = 3 in 2 in by 3 in
PLLLSSSSSS HURRRYYYY To convert Celsius temperatures to Fahrenheit, you can use the expression 9/5 (C + 32). Tom says that another way to write this expression is 9/5 C + 32. What error did Tom make?
A. Tom did not make an error.
B. Tom should have simplified the fraction .
C. Tom did not distribute to both terms in parentheses.
D. Tom should have added inside the parentheses before multiplying.
Answer:
C.
Step-by-step explanation:
If you are distributing, you must distribute the outside to both terms in the inside.
I’ve been trying to figure this out all day and still can’t seem to figure it out
Answer:
(4x-1)(4x-1)
(x-6)(x+5)
(3x-7)(3x+7)
(3x-1)(x+6)
Step-by-step explanation:
yes
Ayuuuudeeeeen :')
t.t
Answer: a=4
Step-by-step explanation:
Es facil. La diagonales de un rectangulo se cortan en su punto medio por tanto la diagonal es 10 (el doble de 5).
Por pitagoras entonces:
[tex]a=\sqrt{10^2-8^2}=\sqrt{100-64}=\sqrt{36}=4[/tex]
Arturo, Pedro y Jorge son hermanos y duermen en la misma habitación. Su papá les compró una pintura para que entre los tres pinten su cuarto. Arturo como es el más grande tiene que pintar 1/2 del total de la habitación, Pedro 3/8 y Jorge como es el más pequeño pintará la última parte.
¿Que fracción de la habitación pintará Jorge?
Porfís ayudenme es para mañana
Answer:
1/8
Step-by-step explanation:
1/2= 4(1/2) = 4/8
4/8+3/8= 7/8
7/8 + 1/8 = 1
climate scientists use computer models to predict the likely change in global average temperature under various assumptions about CO2 production. What type of data source is this?
Answer:
[tex]\fbox{\begin{minipage}{10em}Option A: Simulation \end{minipage}}[/tex]
Step-by-step explanation:
The data is not collected from the world outside, but a computer.
=> The data can be generated under assumption from simulation only.
=> Option A is correct.
Hope this helps!
:)
Answer:
a. Simulation
Step-by-step explanation:
A computer model is generally a simulation of the real world. Certainly, a model of Earth's climate is a simulation.
__
In some cases, the data of interest is the performance of the computer itself (as opposed to some system outside the computer). In those cases, the running of the computer under different scenarios might be considered an experiment.
Simplify the Expression : -20 - (-5) * (-2^2)
Answer:
-40
Step-by-step explanation:
-20-(-5)*(-2^2)
- and a - = positive
-2^2 = -4 but if it was (-2)^2 then it would be 4
-20+5*(-4)
order of operations
-20-20
-40
hope this helps
An inspector checks 98 cell phones and finds 2 of them not working. If a company
has 850 of the phones, how many are likely to not be working?
Answer:
17
Step-by-step explanation:
Use ratio method
98:2
850:x
so, x = (850 x 2) divided by 98 = 17.3469388
Round it to nearest whole number = 17
Wht is the y-intercept of the line describes by the equation below?
Answer:
(0,7)
Step-by-step explanation:
This is in the form
y = mx+b where m is the slope and b is the y intercept
y = -5x +7
The slope is -5 and the y intercept is 7
(0,7)
Answer:
(0,7)
Step-by-step explanation:
y=mx+b
y=-5x+7
so y intercept is (0,7)
Let f(x) = ............
Answer:
So first lets find g(-1)
so we plug in the answers:
-2 * -1 ^2 -4
-2*1-4 = -2-4 =
-6
Now lets solve for f(-2)
-2^2-3
4-3=1
-6+1 = 5
3*5 = 15
Im getting answer of 15 but it shows -15 or something, so I dont know if I got it wrong or if its like a dash then the answer.
3(a-2/3)= 3/4a+2 1/4
Steps:
Step 1: Simplify both sides of the equation.
3(a−2/3)=3/4a+21/4
(3)(a)+(3)(−2/3)=3/4a+21/4(Distribute)
3a+−2=34a+2143a−2=3/4a+21/4
3a+−2=34a+2143a−2=3/4a+21/4
Step 2: Subtract 3/4a from both sides.
3a−2−3/4a=3/4a+21/4−3/4a
9/4a−2=21/4
Step 3: Add 2 to both sides.
9/4a−2+2=21/4+2
9/4a=29/4
Step 4: Multiply both sides by 4/9.
(4/9)*(9/4a)=(4/9)*(29/4)
Answer:
A=29/9
Please mark me brainliest
Hope this helps.
Solve the following system. x squared / 25 + y squared / 100 = 1 x squared + y squared = 25
Answer :
[tex] \frac{1}{100} (4 {x}^{2} + {y}^{2} )[/tex] [tex] \frac{dy}{dx} = \frac{ - x}{y} [/tex]Every 10 years the alumni have a reunion. Every 2 years the alumni have a soccer game. How often do the reunion and the soccer game fall in the same year?
Answer:
They would fall in the same year every 10 years
Step-by-step explanation:
Here in this question, we are interrelated in calculating the number of years it will take the alumni reunion and the alumni soccer game to fall in the same year.
Now looking at the number of years, we can see we have every 2 and every 10 years
To get the year in which they happen at the same time, we can simply find the lowest common multiple of 2 and 10 and that would be 10
This can be visualized in a way that;
The reunion has happened now, and will happen in the next 10 years.
Now since the soccer game has happened now, in the next 10 years, we shall be having 5 episodes. This means that it will take up to the 10th year before we have the soccer game and the alumni reunion occurring at the same time and the mathematical reason for this is that , 10 is the lowest common multiple of 10 and 2
Answer:
1 times
Step-by-step explanation:
Hello,
The alumni have reunions every 10 years
But also have football games every 2 years
We have to find how often do the football and reunion fall the same year.
Working with a space of 10 years
In 10 years, reunions happen only once
In 10 years, soccer games happen five times
Assuming we're in the year 2020,
The next reunion would likely occur in year 2030.
But soccer games will happen in year 2022, 2024, 2026, 2028 and finally 2030.
Checking both soccer and reunion coincidence, we can only find one which is in year 2030.
So, soccer games and reunions happen once in 10 years
Which multiplication expression is equal to 2/3 ÷ 1/2
2/3 ÷ 1/2 = 1.33333333333 or 1.3 for short
-Peter
Answer:
2*2/3 = 4/3
Step-by-step explanation:
2*2/3 = 4/3
PLEASE HELP!!!the pattern follows the rule, starting with a value of 4, every consecutive row has a value that is 2 less than twice the value of the previous row. What is the value of the fifth row
Answer:
34
Step-by-step explanation
1- 4
2- 4(2) - 2 = 6
3- 6(2) - 2 = 10
4- 10(2) - 2 = 18
5- 18(2) -2 = 34
what is 240:180 in its simplest form thanks
Answer:
4:3
Step-by-step explanation:
240:180=
60(4):60(3)=
4:3
Hope this helps!
Answer:
4:3
Step-by-step explanation:
24:18
4:3
What is the sum of the measures of the interior angles of a 12-gon?
1620°
O 1800°
O 1980°
O 2160°
Answer:
The answer is 1800!
Step-by-step explanation:
Answer:
B. 1800 degrees.
Step-by-step explanation:
Just took the quiz on Edg (2020-2021)!
Can someone please help with this answer
Answer:
16x9= 144 cm2
Step-by-step explanation:
There are 350 Families lives in the small town of America. A poll of 50 families revealed the mean annual church contribution is $550 with the standard deviation of $ 75.Construct the 95% confidence interval for the mean annual contribution
Answer:
$550+/-$20.79
= ( $529.21, $570.79)
Therefore, the 95% confidence interval (a,b) = ( $529.21, $570.79)
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean x = $550
Standard deviation r = $75
Number of samples n = 50
Confidence interval = 95%
z(at 95% confidence) = 1.96
Substituting the values we have;
$550+/-1.96($75/√50)
$550+/-1.96($10.60660171779)
$550+/-$20.7889393668
$550+/-$20.79
= ( $529.21, $570.79)
Therefore, the 95% confidence interval (a,b) = ( $529.21, $570.79)
∠A and \angle B∠B are complementary angles. If m\angle A=(2x+18)^{\circ}∠A=(2x+18) ∘ and m\angle B=(6x-8)^{\circ}∠B=(6x−8) ∘ , then find the measure of \angle B∠B?
Answer:
[tex]m\angle B=52^{\circ}[/tex]
Step-by-step explanation:
Two or more angles are said to be complementary if they sum up to 90 degrees.
Given that angles A and B are complementary, then:
[tex]\angle A+\angle B=90^\circ\\m\angle A=(2x+18)^{\circ}\\m\angle B=(6x-8)^{\circ}\\$Therefore:\\(2x+18)^{\circ}+(6x-8)^{\circ}=90^\circ\\2x+6x+18-8=90^\circ\\8x+10^\circ=90^\circ\\8x=90^\circ-10^\circ\\8x=80^\circ\\$Divide both sides by 8\\x=10^\circ\\$Therefore:\\m\angle B=(6x-8)^{\circ}\\m\angle B=(6(10)-8)^{\circ}\\=60-8\\m\angle B=52^{\circ}[/tex]
Answer:
56 :)
Step-by-step explanation: