Answer:
a
[tex]Y = \$ 30000[/tex]
b
[tex]Y = \$ 11250 [/tex]
c
[tex]X = \$ 36250 [/tex]
Step-by-step explanation:
From the question we are told that
The annual taxable income is [tex]A = \$ 300,000[/tex]
The tax rate for next year is [tex]r = 0.25[/tex]
The present tax rate is [tex]R = 0.35[/tex]
Generally the present amount of tax collected from Ms Benoit is
[tex]K = A * R[/tex]
[tex]K = 300000 * 0.35 [/tex]
=> [tex]K = \$105000 [/tex]
Generally the amount of tax collected from Ms Benoit nest year is
[tex]B = A * r[/tex]
[tex]B = 300000 * 0.25 [/tex]
=> [tex]B = \$75000 [/tex]
The reduction in the tax amount is mathematically represented as
[tex]Y = K - B[/tex]
=> [tex]Y = 105000 - 75000[/tex]
=> [tex]Y = \$ 30000[/tex]
Generally the tax amount of next year when the income is $375,000 is mathematically represented as
[tex]M = 375 000 * r[/tex]
=> [tex]M = 375 000 * 0.25[/tex]
=> [tex]M = \$ 93 750 [/tex]
The reduction in the tax amount is mathematically represented as when the income for next year is $375,000
[tex]Z = K - M[/tex]
=> [tex]Z = 105000 -93 750 [/tex]
=> [tex]Z = \$ 11250 [/tex]
Generally the tax amount of next year when the income is $275,000 is mathematically represented as
[tex]U = 275,000 * r[/tex]
=> [tex]U = 275 000* 0.25[/tex]
=> [tex]M = \$ 68 750 [/tex]
The reduction in the tax amount is mathematically represented as when the income for next year is $275,000
[tex]X = K - M[/tex]
=> [tex]X = 105000 -68 750 [/tex]
=> [tex]X = \$ 36250 [/tex]
How much greater is the product of 98 * 50 than the product of 97 * 50
Answer:
With 98x50 its like there are 98 fiveties. In 97x 50 there are 97 fiveties. There is one more 50 in 98x50.
Step-by-step explanation:With 98x50 its like there are 98 fiveties. In 97x 50 there are 97 fiveties. There is one more 50 in 98x50.
Answer:
duno
Step-by-step explanation: duno
An online music store is offering a promotion. When you spend $45 or more, you receive 3 songs for free. You buy an album for $15. Identify the inequality that represents how much more money m you must spend to receive the three free songs. 15+m≥45
15+m>45
45+m≥15
15+m≤45
Question 2 How much more must you spend to receive the three free songs? You must spend ____ more.
Answer:
When you spend $45 or more, you get 3 free songs.
You already spent $15.
Then, if we define m as the amount that you need to spend in order to get the 3 free songs, the minimum value of m will be such that you spend exactly $45 in total.
$15 + m = $45.
But if you spend more than $45 you also get the songs, so the inequality that represents this situation is:
$15 + m ≥ $45.
2)Solving the equation for m we have:
m ≥ $45 - $15 = $30
m ≥ $30.
So the minimum amount that you can spend in order to get the songs is when the equality is true, this means that:
m = $30 is the minimum that you must spend if you want the 3 free songs.
NEED THESE ASAP I have no idea what this is
Answer:
1) variables
2)26
3)8x+2y+2
4)38
How many units from zero is -253?
Answer:
253 units
Step-by-step explanation:
-253 is 253 units behind 0.
Please help on these questions ASAP!
I will give brainliest
J is the midpoint of CT
С
J
T
If:
CJ = 5x – 3 and
JT = 2x + 21
Find CT.
Answer:
CT=37
Step-by-step explanation:
5x-3 = 2x+21
-2x
3x-3 = 21
+3
3x = 24
÷3
× = 8
5(8) - 3 = 37
2(8) +21 =37
When r = 8 and s = 5, what is the value of r +2s
- 9?
Answer:
9
Step-by-step explanation:
If we substitute the variables for the numbers, the equation looks like this:
8+2(5)-9
Because 2s was multiplying 2 by s in the original equation, we can do that step first!
8+2(5)-9
8+10-9
Personally, I think it's a lot easier to subtract 9 from 10 first, but you can solve this part in any order.
8+10-9
8+1
This is the last part; we just have to add 8 and 1 now!
8+1=9
Hope this helps!!! Have a wonderful day C:
An object with mass of 1 kg, specific heat of 1000 J/kg°C, surface area of 0.01 m2, and initial temperature of 25°C is placed in a microwave oven with internal temperature of 25°C and heat transfer coefficient of 40 W/m2°C.If the microwave heat input into the object is 50 W,
a) Show that the differential equation that governs the temperature change forthis object is
dT/dt+0.0004T = 0.06
b) Solve this differential equation and find out what the temperature of this object is after 200 seconds heating inside the microwave.
Answer:
a) True. The differential equation is [tex]\frac{dT}{dt}+0.0004\cdot T = 0.06[/tex], where [tex]T[/tex] is measured in Celsius.
b) The temperature of the object after 200 second inside the microwave is approximately 34.611 ºC.
Step-by-step explanation:
a) The object is heated up by convection and radiation, from First Law of Thermodynamics we get that energy interactions on the object are represented by:
[tex]-\dot Q_{out} + \dot W_{in} = \frac{dU_{sys}}{dt}[/tex] (Eq. 1)
Where:
[tex]\dot Q_{in}[/tex] - Heat transfer rate to the object, measured in watts.
[tex]\dot W_{in}[/tex] - Electric power given by the microwave owen, measured in watts.
[tex]U_{sys}[/tex] - Internal energy of the object, measured in watts.
Then, we expand the expression by means of definition from Heat Transfer and Thermodynamics:
[tex]-h_{c}\cdot A_{s}\cdot (T-T_{\infty})+\dot W_{in} = m\cdot c\cdot \frac{dT}{dt}[/tex]
Where:
[tex]h_{c}[/tex] - Heat transfer coefficient, measured in watts per square meter-Celsius.
[tex]A_{s}[/tex] - Surface area of the object, measured in square meters.
[tex]T[/tex] - Temperature of the object, measured in Celsius.
[tex]T_{\infty}[/tex] - Internal temperature of the microwave oven, measured in Celsius.
[tex]m[/tex] - Mass of the object, measured in kilograms.
[tex]c[/tex] - Specific heat of the object, measured in joules per kilogram-Celsius.
After some algebraic handling, we get this non-homogeneous first order differential equation:
[tex]\frac{dT}{dt} = -\frac{h_{c}\cdot A_{s}}{m\cdot c} \cdot (T-T_{\infty}) + \frac{\dot W_{in}}{m\cdot c}[/tex]
[tex]\frac{dT}{dt}+\frac{h_{c}\cdot A_{s}}{m\cdot c}\cdot T =\frac{h_{c}\cdot A_{s}}{m\cdot c}\cdot T_{\infty}+\frac{\dot W_{in}}{m\cdot c}[/tex] (Ec. 2)
If we know that [tex]h_{c} = 40\,\frac{W}{m^{2}\cdot ^{\circ}C}[/tex], [tex]A_{s} = 0.01\,m^{2}[/tex], [tex]m = 1\,kg[/tex], [tex]c = 1000\,\frac{J}{kg\cdot ^{\circ}C}[/tex], [tex]T_{\infty} = 25\,^{\circ}C[/tex] and [tex]\dot W_{in} = 50\,W[/tex], the differential equation is:
[tex]\frac{dT}{dt}+0.0004\cdot T = 0.06[/tex]
b) The solution of this differential equation is:
[tex]T(t) = T_{o}\cdot e^{-0.0004\cdot t}+ \frac{0.06}{0.0004}\cdot (1-e^{-0.0004\cdot t})[/tex]
Where [tex]T_{o}[/tex] is the initial temperature of the object, measured in Celsius.
[tex]T(t) = T_{o}\cdot e^{-0.0004\cdot t}+150\cdot (1-e^{-0.0004\cdot t})[/tex]
[tex]T(t) = 150+(T_{o}-150)\cdot e^{-0.0004\cdot t}[/tex]
Where [tex]t[/tex] is the time, measured in seconds.
If we know that [tex]T_{o} = 25\,^{\circ}C[/tex], then:
[tex]T(t) = 150-125\cdot e^{-0.0004\cdot t}[/tex] (Ec. 3)
For [tex]t = 200\,s[/tex], we get that temperature of the object is:
[tex]T(200) = 150-125\cdot e^{-0.0004\times 200}[/tex]
[tex]T(200) \approx 34.611\,^{\circ}C[/tex]
The temperature of the object after 200 second inside the microwave is approximately 34.611 ºC.
Henry ran 5/6 of a mile this morning. Sharon only ran 2/3 of a mile. How much more did Henry run than Sharon?
Answer:
2 miles.
Step-by-step explanation: Hopefully this helped!
Answer:
1/6 more
Step-by-step explanation:
find the common denominator which gives you 4/6, rest is self explanatory, 5/6 is 1/6 more than 4/6
Divide. Write the quotient in lowest term 4 4/5 ÷1 1/2
Answer:
3 1/5
Step-by-step explanation:
24/5 ÷ 3/2
24/5 x 2/3
48/15
16/5
3 1/5
divede decimals by a whole number in this question 2.6÷2
Answer:
Step-by-step explanation:
2.6 ÷ 2 = 1.3
please helpppp
The length of a book (in pages) is a function of
the number of words in the book. This function
is written /(w). What is true about this function?
Circle the best answer.
Answer Choices:
(20,000) is the length of a book with 20,000
pages.
|(140) describes a book with 140 pages.
|(15,055) is the number of pages in a book with
15,055 words.
Answer:
|(15,055) is the number of pages in a book with
15,055 words.
Step-by-step explanation:
becuz the no of pages is a function to the words ..
I REALLY NEED HELP!!!
5^-3=
Answer:
[tex]\frac{1}{125}[/tex]
Step-by-step explanation:
whenever you see a negative exponenet, you should always write the reciprocal of it
[tex]5^{-3}[/tex] becomes [tex]\frac{1}{5^{3} }[/tex]
solve the denominator
[tex]5^{3}[/tex] = 125
therefore, your answer is [tex]\frac{1}{125}[/tex]
hope this helps!! :)
A submarine is positioned –1525 feet in relation to sea level. The submarine needs to be –1865 feet below sea level in 20 minutes. Which best represents the rate at which the submarine needs to travel?
–169.5 ft/min
–17 ft/min
17 ft/min
169.5 ft/min
An architect is building a scale model of an office building. The scale used to build the model is 1
120
.
HELP ME WILL GIVE BRAINLIEST, FIVE STARS ,AND THANK THEM. What is the equivalent decimal value for this scale?
0.008
0.008 ModifyingAbove 3 with bar
0.8 ModifyingAbove 3 with bar
0.00 ModifyingAbove 83 with bar
Answer:
0.008 3 with bar
Step-by-step explanation:
the line under 8 is supposed to be over 8
i know im late sorry
Answer:
0.0008 ModifyingAbove 3 with bar
Step-by-step explanation:
A birthday celebration meal is $49.20 including tax, but not the tip. Find the total cost if a 15% tip is added to the cost of the meal.
Answer:
$7.38
Step-by-step explanation:
multiply 49.20 by 15 percent.
Can you help me solve this problem please? Solve 6n = 2n – 8.
Find the equation of the linear function represented by the table below in slope-
intercept form.
Х
o
1
2
3
4
у
-1
3
7
11
15
Answer:
1y157
Step-by-step explanation:
An x-box cost $230 but is discounted 18%. What is the new cost of the x-box?
Answer:
41.4$
Step-by-step explanation:
10% of 230 is 23$
23/5=4.6
4.6$=2%
18.4$=8%
23+18.4$
41.4$
Answer:
41.4
Step-by-step explanation:
Hope this helped
5. Write a division number sentence
using 3,9,and 27
Answer:
27÷3 =9
Step-by-step explanation:
27 divided by 3 is 9
Answer: 3 * 9 = 27, 27 / 3= 9, 27/9 = 3
Step-by-step explanation:
3 being multiplied by 9 will give you 27.
27 divided by 9 will give you 3.
27 divide by 3 will give you 9.
Jane's flight to an all-star track meet was cancelled due to a storm. The airline gave Jane a
voucher for $10 to spend at any vendor in the airport. Jane can only use the voucher at one
vendor and, according to the voucher rules, no change will be given. Any money not spent on
the voucher is lost. If a bottle of soda costs $2.50 plus an additional 6% sales tax, how many
bottles of soda could Jane buy? *
Answer:
3
Step-by-step explanation
3 x 2.50 = 7.50
7.50 x 0.06 = 0.45
7.50 + 0.45 = 7.95
So, she would be able to buy 3 sodas and it would cost $7.95
PLEASE HELP!!! ILL GIVE BRANLIEST *EXTRA POINTS* dont skip :((
Answer:
2/9
Step-by-step explanation:
Any fraction in the form 0.n repeated is in the form n/9
Your percent grade varies directly with the number of correct answers. You got a
grade of 80 when you had 20 correct answers, What would your percent grade
be with 24 correct answers?
96%
help!!!
Answer:
96%
Step-by-step explanation:
20/ 0.80 = 25 (total number of questions)
24/25 = .96 x 100 = 96%
give three examples of turning force that we can see it our day to day life
Answer:
A person pushing a swing will make the swing rotate about its pivot.
A worker applies a force to a spanner to rotate a nut.
A person removes a bottle's cork by pushing down the bottle opener's lever.
A force is applied to a door knob and the door swings open about its hinge.
are the opposites of -6.5 and the absolute value of -6.5 the same?
Answer:
Yes
Step-by-step explanation:
the opposite of -6.5 is 6.5.
The absolute value of |-6.5| is 6.5.
Hope this helps.
please help as soon as you can
Answer:
FOR QUESTION 5
1. Angle 1 congruent to angle 4; given
2. Angle 1 supplementary to angle 2; assumed from diagram
3. Angle 4 supplementary to angle 3; assumed from diagram
4. Angle 2 congruent to angle 3; angles supplementary to congruent angles are congruent
5. Angle 3 congruent to angle 5; verticla angles are congruent
6. Angle 2 congruent to angle 5; substitution
FOR QUESTION 6
1. Angle 2 congruent to angle 3; given
2. Angle 2 congruent to angle 1; vertical angles are congruent
3. Angle 3 congruent to angle 4; vertical angles are congruent
4. Angle 1 congruent to angle four; substituiton (see statement #1)
Step-by-step explanation:
FOR 100 POINTS please answer asap and if you don't know plz don't answer. Thank you A scuba diver was exploring a reef 39.6 m below sea level. The diver ascended to the surface at a rate of 8.8 m/min. distance = rate(time)
a) How is 39.6 m below sea level displayed as rational number? ( 3pts)
b) How long did it take the diver to reach the surface? (4pts)
Answer:
A)
[tex]-39.6[/tex]
B)
[tex]4.5\text{ minutes}[/tex]
Step-by-step explanation:
We know that the scuba diver is exploring a reef 39.6 meters below the sea level.
Remember that sea level is always 0 meters in elevation.
We also know that the diver ascended to the surface at a rate of 8.8 meters per minute.
Part A)
Since sea level is the 0th meter, anything below this will be negative.
So, since the diver is 39.6 meters below sea level, we can express this as:
[tex]-39.6[/tex]
Part B)
We know that the diver ascends at a rate of 8.8 meters per minute.
The diver is currently at 39.6 meters.
Remember that the surface is the sea level. So, we want to find after how many minutes m does the diver reach the 0th meter.
So, we can write the following equation and solve for m:
[tex]-39.6+8.8m=0[/tex]
The -39.6 represents the diver's current altitude.
The 8.8m represents the diver's rate of ascending 8.8 meters per minute m. Notice that 8.8m is positive because we're ascending.
And the 0 represents the 0th meter or sea level or the surface.
So, solve for m. Add 39.6 to both sides:
[tex]8.8m=39.6[/tex]
Divide both sides by 8.8. So:
[tex]m=4.5[/tex]
So, it will take the diver 4 and a half minutes to reach the surface.
And we're done!
What is 2x(x-6) = 10 in standard form of quadratic equations
Step-by-step explanation:
2x(x-6)=10
use foil method so 2x times x-6 magiging 2x²-12x
tas yung +10 itratranspose mo magiging -10 kasi kapag nagtratranspose ang positive magiging negative and vice versa, so ang sagot ay
2x²-12x-10=0
a=2
b=-12
c=-10
On New year's Eve the times square ball is lowers 47 ft every 20 seconds how long does it take for the ball to be lower 141 ft
Answer:
1 minute
Step-by-step explanation:
141/47=3. then 3*20=60 which is equal to one minute
$16.20 per hour for 40 hours and time and a half for 8 hours. What is the total pay?
Answer:
Add 16.20+ 40+8
Step-by-step explanation: 16+20+40+8= 84