Janet is retiring after working for a major department store for 20 years. The company offered her a flat retirement benefit of $50 per year for each year of service. a. What was her monthly income in the fi rst year after retirement?​

Answer:

2 sqrt 74    

Step-by-step explanation:

d^2 = ( x1-x2)^2  + (y1-y2)^2

d^2 = ( 5 - -5 )^2  +  ( -10 -4)^2

       =   100 + 196

d^2 = 296

d = sqrt 296    =   2 sqrt (74)

Answer:

40a : 10b : 3c

Step-by-step explanation:

We can write this information more mathematically by saying:

[tex]a = \frac{1}{4} b[/tex]

[tex]b= \frac{3}{10} c[/tex]

This can be written as ratios as well by making them all integers so:

4a : b

10b : 3c

By making the b's in both equations the same, we can link all the ratios together so:

40a : 10b

10b : 3c

So,

40a : 10b : 3c

The equation of the function f  with solution 3, -9 is x²+6x-27 and the graph of this equation with the use of drawing tools is attached below.

A function assigns the value of each element of one set to the other specific element of another set.

A function has to be plot which has the value of f(x) as 3 and -9. Here, 3 and -9 are the solution of the function. Thus,

x=3

x-3=0

The second solution is,

x=-9

x+9=0

Multiply both factor for the function as,

f(x)=(x-3)(x+9)

f(x)=x²+9x-3x-27

f(x)=x²+6x-27

This is the required function. The graph of this function is attached below.

Thus, the equation of the function f  with solution 3, -9 is x²+6x-27 and the graph of this equation with the use of drawing tools is attached below.

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0.9947≅1  times you have to fill up the cylindrical beaker before the tank is full.

Volume is defined as the space occupied by any body in the three-Dimenions. All three parameters are required for the volume like length,width and hieght of cube or cubied.

here we have a beaker of cylindrical shape the volume of the shape will be calculated as:

[tex]\rm V=\dfrac{\pi}{4}\times d^2\times l=\dfrac{\pi}{4}\times (4)^2\times 8=100.53\ cubc\ inch[/tex]

We have a volume of rectangular prism = 100 cubic inches

So number of times the beaker fill the fluid will be calculated as:

[tex]=\dfrac { Volume \ of\ Prism}{Volume\ of\ beaker}=\dfrac{100}{100.53}=0.9947[/tex]

hence 0.9947≅1  times you have to fill up the cylindrical beaker before the tank is full.

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Step-by-step explanation:

Let p and h represent pay and hours worked respectively,

p = kh

k = p/h = 148.5/18 = 8.25

p= 8.25h

90.75 = 8.25h

h = 11 hours.

Hope it helps! :)

[tex]\Large\textsc{Answer\::}[/tex]

[tex]\Large\textsc{\textbf{Calculations\::}}[/tex]

First , notice that the equation of the second line , 6x=3y+5 , is not written in the same form as y=2x , so determining the slope is hard .

To determine the slope , we need to convert the first equation into slope intercept form .

Subtract 6x on both sides :

0 = 3y+5-6x

Now , subtract 3y on both sides :

-3y=-6x+5

Divide by -3 on both sides :

y=-6/-3x+5/-3

Which simplifies to :

y=2x-5/3 (remember , a negative divided by a negative results in a positive)

Put both equations together :

y=2x and y=2x-5/3

Notice that the slopes are the same . This indicates that the lines are parallel .

Now let's focus on the second maths problem :

Consider the equations below .

x=-4 and y=-2

Are the lines parallel or perpendicular?

The  slope of the first line is undefined , and the slope of the second line is zero .

Lines with undefined slopes are vertical , and lines with slopes of zero are horizontal .

Here's something you may have recalled from your Geometry class :

Is a vertical line parallel or perpendicular to a horizontal line ?

The ans is : perpendicular .

[tex]\footnotesize{\texttt{hope helpful~}[/tex]

Answer:

[tex]a_{5} = 22[/tex].

Step-by-step explanation:

In this recursive sequence, the value of the first term [tex]a_{1} = 2[/tex] is stated explicitly. The value of every other term of this sequence is given as an expression of the previous term.

For example, the value of the term [tex]a_{2}[/tex] ([tex]n = 2[/tex]) is given in terms of the value of [tex]a_{1}[/tex]:

[tex]\begin{aligned}a_{2} &= a_{(2 - 1)} + 5 \\ &= a_{1} + 5\end{aligned}[/tex].

Likewise, the value of [tex]a_{3}[/tex] ([tex]n = 3[/tex]) would be:

[tex]\begin{aligned}a_{3} &= a_{(3 - 1)} + 5 \\ &= a_{2} + 5 \\ &= (a_{(2-1)}+5) + 5 \\ &= (a_{1} + 5) + 5 \\ &= a_{1} + 2 \times 5 \\ &= a_{1} + (3 - 1) \times 5\end{aligned}[/tex].

In general, the value of [tex]a_{n}[/tex] (for integer [tex]n \ge 1[/tex]) would be:

[tex]\begin{aligned} a_{n} &= a_{1} + (n - 1) \times 5 \\ &= 2 + (n - 1) \times 5\end{aligned}[/tex].

Therefore, the value of [tex]a_{5}[/tex] ([tex]n = 5[/tex]) would be:

[tex]\begin{aligned}a_{5} &= a_{1} + (5 - 1) \times 5 \\ &= 2 + (5 - 1) \times 5 \\ &= 22\end{aligned}[/tex].

Answer:

[tex]-5B = \begin{bmatrix}-15&10\\ 20&40\end{bmatrix}[/tex]

Step-by-step explanation:

[tex]B=\begin{bmatrix}3&-2\\ -4&-8\end{bmatrix}[/tex]

[tex]\Longrightarrow -5B = -5 \times\begin{bmatrix}3&-2\\ -4&-8\end{bmatrix}[/tex]

[tex]\Longrightarrow -5B = \begin{bmatrix}-5 \times3&-5 \times-2\\ -5 \times-4&-5 \times-8\end{bmatrix}[/tex]

[tex]\Longrightarrow -5B = \begin{bmatrix}-15&10\\ 20&40\end{bmatrix}[/tex]

Answer:

one

Step-by-step explanation:

3x + 6 = -1 - 3 + 4x

Combine like terms

3x+6 = -4 +4x

Subtract 3x from each side

3x+6-3x = -4+4x-3x

6 = -4+x

Add 4 to each side

4+6 = -4+x+4

10 =x

There is one solution

Only one it's 10

Answer:

X=5

X=1

Step-by-step explanation:

2−6+5=0x

a = 1

b = -6

c = 5

=−(−6)±(−6)2−4⋅1⋅5√2⋅1

Answer:

A

Step-by-step explanation:

y + 3 = -6(x + 2)

y + 3 = -6x - 12

y + 3 = -6x - 12

y = -6x - 15

Answer:

216°..........................

Answer:

the answer is b , sub 2for x in each equ then whatever answer you get , use it to check is that what y is on grph

Answer:

right scalene

Answer:

When selecting a sample for a survey, the way you choose your sample: A) may lead to biased results.

Step-by-step explanation:

The way you choose your sample matters a lot in order to help limit the bias in sampling data.

There are four types of random samples: simple, stratified, cluster, and systematic.

There are two types of non-random samples: voluntary response and convenience.

You always want to have a random sample in order to have accurate, non-biased results. Therefore, A) May lead to biased results is the best answer.

well, if we take the whole area of the circle, including the trapezoid in it, and then we get the area of the trapezoid and subtract it from that of the circle's, what's leftover is what we did not subtract, namely the shaded area.  Let's notice the circle has a diameter of 20, thus a radius of half that, or 10.

[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ a=12\\ b=20\\ h=8 \end{cases}\implies A=\cfrac{8(12+20)}{2}\implies A=128 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\Large Areas}}{\stackrel{circle}{\pi (10)^2}~~ - ~~\stackrel{trapezoid}{128}}\implies 100\pi ~~ - ~~128~~\approx~~186.16[/tex]

Answer:

m<6 = 119°

Step-by-step explanation:

Two lines are parallel with each along a line.

m<4 and m<6 are supplementary angles which both angles add up to 180°.

m<4 + m<6 = 180°

61° + m<6 = 180°

m<6 = 180° - 61°

m<6 = 119°

Answer:

Step-by-step explanation:

m<6 + 61 = 180

m<6 = 139

Answer:

33.49 cubic inches

Step-by-step explanation:

Answer:

Step-by-step explanation:

Remark

To convert watts to amps, divide the watts by the amps

Givens

720 watts

8 amps (maximum safety of extension chord)

144 conversion factor

Solution

Amps = 720 watts / 144

Amps = 5

Answer

The iron uses 5 amps of current.

The extension chord is safe to use since 5 is less than 8

Answer:

720÷144=5 AMPS

Step-by-step explanation:

5ANSWER

Answer: Option #1: ( -2 , -1 )

Step-by-step explanation:

5(-2) - (-1) = 9

(-2) - (-1) = -1

The number of different strings that can be made from the letters in ORONO using some or all of the letters is 63

Suppose there are n items.

Suppose we have

[tex]i_1, i_2, ..., i_k[/tex]

sized groups of identical items.

Then the permutations of their arrangements is given as

[tex]\dfrac{n!}{i_1! \times i_2! \times ... \times i_k!}[/tex]

We're given the word ORONO.

3 ways: O, R, or N

Subcase: Consists O:

5 ways: OR, RO, ON, NO, OO

Subcase: Doesn't consist O:

2 way: RN, NR

Total permutation under this case = 5+2 = 7

Subcase: Consists 3 'O':

1 way: OOO

Subcase: Consists 2 'O':

6 ways: OOR, ROO, ORO, OON, NOO, ONO

Subcase:  Consists 1 'O':

6 ways: ORN, ONR, RNO, RON, NOR, NRO (or that there are 3 distinct letters to be arranged, which can be done in 3! = 6 ways)

Subcase: Doesn't consist O:

0 ways as only R and N cannot form three letter string.

Total permutation under this case = 1+6+6= 13

Subcase: Consists 3 'O':

So, we've got {O,O,O,R,N}

3 'O's are mandatory, so fourth letter is either R or N:

O, O, O, R can arrange themselves in : [tex]4!/3! = 4 \: \rm ways[/tex] (as total 4 words but 3 are identical)

Similarly, O, O, O, N can arrange themselves in 4 ways,

So when 4 letter string from ORONO consists of 3 'O's, then total 4+4=8 distinct strings can be made.

Subcase: Consists 2 'O':

So, we've got {O,O,R,N}

The total permuations of these 4 letters, of which 2 are identital is:

[tex]\dfrac{4!}{2!} = 12[/tex]

Subcase:  Consists 1 'O':

0 ways: Single 'O' and one-one R and N cannot form four letter string.

Subcase: Doesn't consist O:

0 ways as only R and N cannot form four letter string.

Total permutation under this case = 8+12 = 20

All 5 letters of ORONO would be used.

There are 3 identical objects, so total number of their permutation is:

5!/3! = 20

Thus, from all these cases, we conclude that:

Total permutations of string letters using some or all letters of ORONO is:

3+7+13+20+20 = 63

Thus,  the number of different strings that can be made from the letters in ORONO using some or all of the letters is 63

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Answer:

803.84, or C.

Step-by-step explanation:

If we know the circumference then we can use that to find the radius!

-

(π =pi)

Area of a circle formula: π · r^2

-

Let us plug in the circumference into the formula (not the area formula, the circumference one!)

c=2πr

100.48=2πr - 2*3.14 =6.28

100.48=6.28r

divide both sides by 6.28!
r= 16

Now, we plug that in the area formula.

π · r^2

3.14 * 16^2

3.14 * 256 =

803.84

Answer:

1702.45

Step-by-step explanation:

your welcome

1737.45 coupon not included

Answer: h = left or right, k = up or down

Step-by-step explanation:

h determines if the function is shifted left or right and k determines if the graph is shifted up or down

Answer: Heyaa! ~

Your Answers are... ±1,±2,±3,±4,±6,±12

Step-by-step explanation:

Find every combination of ± p/q, where p is a factor of the constant and

q is a factor of the leading coefficient.

Hopefully this helps you! ^^

- Matthew

Answer:

6

Divide the fractions.

3 / 1 = 3

4 / 8 = 2

Use the numerator as a multiplicand.

2 × 3 = 6

Answer:

Step-by-step explanation:

the marathon actual race distance is 26.2 now that Lin has already ran 19.6 miles so now we should subtract this two decimal numbers so that were get 6.6

Answer:

1. 0.4

2. 0.375

Step-by-step explanation:

All you gotta do is find how much does it cost for each slice for example 30/75=0.4 and decide which one is better

[tex]1.~\boxed{\sf0.55555555555}\boxed[/tex]

[tex]2.~\boxed{\sf 0.54545454545}\boxed[/tex]