4) A teacher has an annual income of $51,750. The income tax the teacher has to pay is 7%. What is the amount of income tax in dollar and cents the teacher has to pay?
A) $3,448.25
B) $3,622.50
C) $3,891.10
D) $3,933.01

Answer:

y = -2x-1

Step-by-step explanation:

The formula for a line is [tex]y-y_{1} = m(x-x_{1})[/tex].

Plug in the information given in the problem: y-(-7) = -2(x-3)

So you get y+7 = -2x+6.

The final form you want needs to be equal to y (that means you want y by itself on the left side of the equals), so subtract 7 from both sides.  

You get y = -2x-1

[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{-7})~\hspace{10em} m = -2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-7)}=\stackrel{m}{-2}(x-\stackrel{x_1}{3}) \\\\\\ y+7=-2x+6\implies \blacktriangleright y=-2x-1 \blacktriangleleft[/tex]

[tex]n^{th}\textit{ term of a geometric sequence} \\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} a_7=\stackrel{7^{th}\ term}{192}\\ 7=\textit{term position}\\ a_1=\textit{first term}\\ r=\stackrel{\textit{common ratio}}{2} \end{cases} \qquad \qquad a_7=a_1\cdot 2^{7-1} \\\\\\ 192=a_1\cdot 2^6 \implies 192=64a_1\implies \cfrac{192}{64}=a_1\implies \boxed{3=a_1}[/tex]

Answer:

tag archives and records and counting the days

Answer:

1st number is 6

2nd number is 30

3rd number is 33

Step-by-step explanation:

Let x be the first number.

The second of three numbers is 5 times the first = 5x

The third number is 3 more than the second = 5x + 3

If the second is decreased by twice the third, the result is -21.

Multiply the third number by 2.

2(5x + 3)

= 10x + 6

Subtract the second number to it.

(5x)-(10x + 6) = -21

-5x - 6 = -21

Use APE or Addition Property of Equality

-5x = -21 + 6

-5x = -15

Use DPE or Division Property of Equality to get the value of x

[tex]\frac{-5x}{-5} = \frac{-15}{-5}[/tex]

x = 3

Now put the value of x in the equation

first number(x) = 6

second number(5x) = 5(6) = 30

third number(5x + 3)

5(6) + 3

30 + 3 = 33

[tex]\sf \longmapsto \frac{5}{8} \div6[/tex]

[tex]\sf \longmapsto \frac{5}{8} \times \frac{1}{6} [/tex]

[tex]\sf \longmapsto \frac{5 \times 1}{8 \times 6} [/tex]

[tex]\sf \longmapsto \frac{5}{48} [/tex]

Answer In DECIMAL:

[tex]\sf \longmapsto0.1041[/tex]

The stream gradient of a stream that drops 30 feet in elevation over a horizontal distance of 2640 feet is 0.01136363636.  

Stream gradient is the ratio of drop in elevation of a stream per units horizontal distance. Therefore,

stream gradient = vertical change in elevation / horizontal distance

where

vertical change in elevation = 30 feet

horizontal distance = 2640 feet

stream gradient = 30 / 2640

stream gradient  = 0.01136363636

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The volume of the solid obtained by rotating the region bounded by the given curves about [tex]y = 1[/tex] is [tex]\frac{11\pi}{30} [/tex] cubic units.

Let [tex]f(x) = 1[/tex], [tex]g(x) = x^{1/2}[/tex] and [tex]h(x) = x^{2}[/tex], both [tex]g(x) [/tex] and [tex]h(x)[/tex] have the following intersection points: [tex](x_{1}, y_{1}) = (0, 0)[/tex] and [tex](x_{2}, y_{2}) = (1,1)[/tex]. This means that the interval of x-coordinates for the solid of revolution is [tex]x \in [0, 1][/tex].

The integral formula for the volume of the solid of revolution ([tex]V[/tex]), in cubic units, is:

[tex]V = \pi \int\limits^{1}_{0} {[h(x)-f(x)]^{2}} \, dx - \pi \int\limits^{1}_{0} {[g(x)-f(x)]^{2}} \, dx [/tex] (1)

After substituting on each function and simplifying terms we get the following integral:

[tex]V = \pi \int\limits^{1}_{0} {(x^{2}-1)^{2}} \, dx - \pi \int\limits^{1}_{0} {(x^{1/2}-1)^{2}} \, dx [/tex]

[tex]V = \pi\left[\int\limits^{1}_{0} {x^{4}} \, dx - 2\int\limits^{1}_{0} {x^{2}} \, dx -\int\limits^{1}_{0} {x} \, dx + 2\int\limits^{1}_{0} {x^{1/2}} \, dx \right][/tex]

And the volume of the solid of revolution is:

[tex]V = \pi \cdot \left(\frac{1}{5}-\frac{2}{3} -\frac{1}{2}+\frac{4}{3} \right)[/tex]

[tex]V = \frac{11\pi}{30} [/tex]

The volume of the solid obtained by rotating the region bounded by the given curves about [tex]y = 1[/tex] is [tex]\frac{11\pi}{30} [/tex] cubic units. [tex]\blacksquare[/tex]

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Answer:

Hello! I know I am a bit late but for those who come here in the future,

This is the order (Least to Greatest)

1) 1,500 at 8% simple interest for 6 years

2) 1,500 at 6% simple interest for 10 years

3) 1,500 at 8% simple interest for 10 years

Hope this helps!

In situation 3, a person will earn the least simple interest in situation 1, a person will earn the most simple interest.

It is defined as the interest based on the principal amount, it does not include the compounded amount. The interest calculates on the initial amount or borrowed amount.

It is given for the three cases as,

P =$1500, R=8% , T = 10 years

P =$1500, R=8% , T = 6 years

P =$1500, R=6% , T = 10 years

The formula for the simple interest is,

Case 1,

SI = (P×R×T) / 100

SI = (1500×8×10)/100

SI = $ 1200

Case 2,

SI = (P×R×T) / 100

SI = (1500×6×10)/100

SI = $ 900

Case 3,

SI = (P×R×T) / 100

SI = (1500×8×6)/100

SI = $ 720

The simple interest for cases 1, 2, and 3 will be $ 1200, $ 900, and $ 720.

Thus, in situation 3, a person will earn the least simple interest in situation 1, a person will earn the most simple interest.

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We want to find different ways of selecting and ordering elements. The answers are:

A) C = 395

B) combinations = 479,001,600

C) combinations = 239,500,800

First, we know that Rebecca has 12 photos.

A) She wants to choose 8 of these 12 photos, we want to see in how many ways she can choose these 8 photos.

Remember that for a set of N elements, the number of different combinations of K elements (such that K is smaller than N) is given by:

[tex]C(N, K) = \frac{N!}{(N - K)!*K!}[/tex]

Here we have N = 12 and K = 8, then:

[tex]C(12, 8) = \frac{12!}{(12 - 8)!*8!} = \frac{12!}{4!*8!} = \frac{12*11*10*9}{4*3*2*1} = 495[/tex]

So there are 495 different ways of choosing 8 photos out of the 12.

B) Now we want to see in how many ways she can arrange all 12 photos.

The total number of combinations is just the product between the numbers of options, we got:

[tex]combinations = 12*11*10*9*8*7*6*5*4*3*2*1 = 479,001,600[/tex]

C) Now we must combine the two things we did before, first, we select 10 out of the 12 photos, and then we want to find in how many ways we can arrange these 10 photos.

[tex]C(12, 10) = \frac{12!}{(12 - 10)°*10°} = \frac{12*11}{2} = 66[/tex]

And we multiply this by the total number of arrangements of these 10 photos, that is just given by 10!, so we get:

[tex]c = 66*10! = 66*(10*9*8*7*6*5*4*3*2*1) = 239,500,800[/tex]

If you want to learn more, you can read:

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Answer:

1. M

2. H

3. A

4. K

5. B

6. C

7. G

8. E

and so on

Step-by-step explanation:

definitions to know:

same side interior/exterior angles

vertical angles

alternate interior/exterior angles

corresponding angles

The total available cash with Oscar will not be able to purchase the new Apple Watch Series 7 because the total cost of the watch is greater than available cash.

The given parameters;

The total cost of the new Apple Watch Series 7 is calculated as follows;

Total cost = 0.07(799)  +  799

Total cost = $854.93

Thus, we can conclude that the total available cash with Oscar will not be able to purchase the new Apple Watch Series 7 because the total cost of the watch is greater than available cash.

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mx + 5 = (x - 5) / m

mx + 5 = x/m - 5/mAnswer:

Step-by-step explanation:

first find the inverse equation

y = mx + 5

y - 5 = mx

(y - 5) / m = x

(x - 5) / m = f⁻ˣ(x)

The original function is a line with slope m and y intercept of 5

The inverse function is a line with a slope 1/m and x intercept of 5

so the common line is where m = 1/m

m = 1/m

m² = 1

m = ± 1

The only line with a common slope between these two options is when

m = -1 and y intercept is 5

Answer:

404 & 408

Step-by-step explanation:

Answer:

The area of a rectangle is A=l x w.

So, 200=10 x w

Divide both sides by 10.

20 = w

The width of the rectangle is 20 m.

:)

Answer: hi , b other one b too

Answer:

19) b

20) b

Step-by-step explanation:

Hello!

First, let's write our equation in point-slope form.

Point-Slope Form:

y-y1=m(x-x1)

y1= the y-coordinate of the point

m=the slope

x=the x-coordinate of the point

y-2=1/3(x-(-5)

y-2=1/3(x+5)

y-2=1/3x+5/3

y=1/3x+5/3+2

y=1/3x+3.7

Hope it helps.

~A smiley teen

#CarryOnLearning

[tex]MagicalNature[/tex] here to help

Answer:

Step-by-step explanation:

The numbers less or equal to 300 that are divisible by 3, 4, or both, but not by 9 are 142.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have a 3 - digit number as 300.

Assume that the numbers less or equal to 300 that are divisible by 3, 4, or both, but not by 9 are [x].

Sequence of numbers divisible by 3 -

3, 6, 9, 12, ...., 300

300 = 3 + (n - 1)3

297 = 3n - 3

n(3) = 100

Sequence of numbers divisible by 4 -

4, 8, 12, ..., 300

300 = 4 + (n - 1)4

296 = 4n - 4

n(4) = 75

Sequence representing numbers less than 300, divisible by 9 -

9, 18, 27, ..., 297

297 = 9 + (n - 1)9

n(9) = 33

So, the numbers less or equal to 300 that are divisible by 3, 4, or both, but not by 9 are -

[x] = n(4) + n(3) - n(9)

100 + 75 - 33

175 - 33

142

Therefore, the numbers less or equal to 300 that are divisible by 3, 4, or both, but not by 9 are 142.

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Answer:

A'(5,1)

B'(6,-3)

C'(2,3)

Step-by-step explanation:

assuming the translation is right 3, just add 3 to each x value

Answer:

it is 1.5

Step-by-step explanation:

if u do 4.50÷3 you will get 1.5 so the cost per jar is 1.5

40/20=2

So an opossum is 2 times as long as a bat

Answer:

4 1/4 is the answer u want

Answer:

61

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  Test 1                            Test 2                   Test 3                       Test 4

Answer: the test doesn't explain the order it was taken or dates. So it can be misleading

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

choose any point on the graph

Answer:

Step-by-step explanation:

Yo you man its 3

Answer:

a. negative eight times a number, the product of a number and negative eight

b. one less than a number, a number minus one

c. four less than the quotient of a number and two, half of a number minus four

d. nine more than the product of five and a number, five times a number plus nine

lemme know if this was a help :P

Step-by-step explanation:

30% × 390 = 117

= 390 - 117

= 507 kw/h

Answer is A. 101°

Step-by-step explanation:

Answer:

1  C

2  A

Step-by-step explanation:

1 C No it cannot be defined because A and B are not congruent

2  A Yes, the lines will remain parallel

PS. It's only 50 points because two answers are allowed. Each answerer gets half.

Answer: You have to get rid of the variables (the x's) so subtract 2x from 2x and 11x then go from there.

Step-by-step explanation:

Answer:

3 and 6

Step-by-step explanation:

11x - 53 = x^2 + 2x - 35

Subtract 11x - 53 on both sides,

0 = x^2 + 2x - 35 - ( 11x - 53 )

  = x^2 + 2x - 35 - 11x + 53

  = x^2 + 2x - 11x + 53 - 35

0 = x^2 - 9x + 18

x^2 - 9x + 18 = 0

Now this equation need to factorized.

x^2 - 9x + 18 = 0

x^2 - 3x - 6x + 18 = 0

x ( x - 3 ) - 6 ( x - 3 ) = 0

( x - 3 ) ( x - 6 ) = 0

x - 3 = 0

x = 3

x - 6 = 0

x = 6

The solutions to this system are 3 and 6.

we have (7 x 10^-6)(7 x 10^-6) = (7 x 10^-6)^2 = 49 x 10^-3 = 0.049

ok done. Thank to me :>