In a certain company a salesman is paid a fixed salary for $3140 per month plus an annual commision of 2% on the TOTAL value of cars sold for the year. If the salesman sold cars valued at $720000 in 2009 calculate:
(i) his fixed salary for the year

(ii) the amount he recieved in commision for the year

(iii) his TOTAL income for the year​

Answer:

KL =9cm

Step-by-step explanation:

IL = KL {being corresponding side of congruent triangle}

or, 3x = x+6

or, 3x-x = 6

or, 2x = 6

or, x = 6/2

or, x = 3cm

Now,

KL = x+6

= 3+6

=9cm

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To find the inverse first we need to solve the equation for x ,

Then put x instead of y .

_________________________________

[tex]f(x) = 8x + 2[/tex]

[tex]y = 8x + 2[/tex]

[tex]8x + 2 = y[/tex]

Subtract sides 2

[tex]8x + 2 - 2 = y - 2[/tex]

[tex]8x = y - 2[/tex]

Divide sides by 8

[tex] \frac{8x}{8} = \frac{y - 2}{8} \\ [/tex]

[tex]x = \frac{y - 2}{8} \\ [/tex]

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Thus ;

[tex] {f}^{ - 1} (x) = \frac{x - 2}{8} \\ [/tex]

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Answer:

11000 meters

Step-by-step explanation:

1km=1000m

5km=5000m

5000+6000=11000m

Answer:

Let

the breadth =x

As we know that in a rectangle

[tex]{\boxed{\sf Area=lb}}[/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf 86\times x=6536[/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf 86x=6536 [/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf x={\dfrac{6536}{86}}[/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf x=76 [/tex]

[tex]\therefore[/tex][tex]Breadth=76m [/tex]

Answer:

-125

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

I am pretty sure its 14 if not im so sorry

Answer: 1750J

Step-by-step explanation:

The work done that will be used to loft the barbell and the hanging chain will be:

W1 = (1300 + (1/2 × 600))

= 1300 + 300

= 1600J

The work done that'll be used in lifting the upper part of the chain will be:

W2 = (1/2 × 600) × (1/2 × 1).

= 300 × 0.5

= 150J

Total work down will be:

=W1 + W2

= 1600J + 150J

= 1750J

Answer:

passed: 164

failed: 41

Step-by-step explanation:

Let the failed students be x, then the passed students will be 4x.

x + 4x = 205

x = 205/5 = 41

4x = 4*41 = 164

Answer:

The answer is y < 2x -3

Step-by-step explanation:

You can read this as all values on the graph will be the value of x times 2 minus 3..

For example, if we wanted to know what the value of y would be if x =2, we would plug in 2 and get 2(2) - 3 or just 1. We can see at the graph that when x = 2 y does equal 1. **In this situation we are pretending that the < symbol is the equal symbol..

To actually find the answer you can graph each equation until you find it or do it this way:

1) Find the slope and determine if it it works for the given graph.

We can see that the slope of the given graph is positive and if we look closer we can see that the slope is 2 over  and that we have a y-intercept of (0,-3).

2) We know that it is Option 2 instead of the first option because o the < sign. If it was option 1, then the shaded part of the graph would be on the other side of the line.

The inequality has the graph shown in the question. is to be considered as the  y < 2x -3.

Since

First determine the slope

So we can see that the slope of the given graph should be positive and then the slope should be 2 over and there is y-intercept of (0,-3).

So based on this, we can say that The inequality has the graph shown in the question. is to be considered as the  y < 2x -3.

Learn more about y-intercept here: https://brainly.com/question/15587122

Step-by-step explanation:

[tex]{:}\longrightarrow[/tex][tex]\sf 2x-10=3x+20 [/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf 3x+20=2x-10[/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf 3x-2x=-10-20[/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf x=-30 [/tex]

Answer:

D. [tex] = \frac{b}{a} [/tex]

Step-by-step explanation:

Given:

[tex] \frac{b^{-2}}{ab^{-3}} [/tex]

Required:

Assuming a ≠ 0, b ≠ 0, find the expression equivalent to the given expression.

SOLUTION:

[tex] \frac{b^{-2}}{ab^{-3}} [/tex]

Recall the exponent rule =>  [tex] \frac{x^{a}}{x^{b}} = x^{a - b} [/tex]

Applying the exponent rule, we would have:

[tex] \frac{b^{-2 -(-3)}}{a} [/tex]

[tex] = \frac{b^{-2 + 3}}{a} [/tex]

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

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

Thus, the equivalent expression of [tex] \frac{b^{-2}}{ab^{-3}} [/tex] = [tex] \frac{b}{a} [/tex]

Answer:

d

Step-by-step explanation:

Answer:

number cube

let even number= country

let odd number= not country

roll cube three times. repeat.

------------------------

Step-by-step explanation:

a p e x :))

The simulation design could she use to estimate the probability is;

C. Number cube

Let even number = rock

Let odd number = pop

Roll cube three times. Repeat

If she wants to estimate the probability that the next three songs are all rock songs, what she can do is to assign specific type of digits to each type of song.

The reason why I used even and odd numbers is because we are told that there are equal number of POP and rocks songs and from 0 to 9, we have equal number of even and odd numbers.

Looking at the options, the only one that corresponds to our simulation is option C.

Read more about probability simulation at; https://brainly.com/question/10333446

Answer:

[tex]y=7[/tex]

Step-by-step explanation:

First, let's use the two given points to find the slope. Remember the slope equation:

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

[tex]m=\frac{7-7}{0-4}[/tex]

[tex]m=\frac{0}{-4}[/tex]

[tex]m=0[/tex]

If we're following slope-intercept form, what we have so far is

[tex]y=0x+b[/tex]

Substitute one of the given points for the [tex]x[/tex] and [tex]y[/tex] values in order to find [tex]b[/tex]:

[tex]7=0(4)+b[/tex]

[tex]7=b[/tex]

Now, if we put that back into our slope-intercept equation we get

[tex]y=0x+7[/tex]

or,

[tex]y=7[/tex]

Right off the bat, we can see how we ended up with this equation because both points have the same y-values. This indicates a horizontal line.

I hope this helps!

Answer:

(1,1)

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Answer:

The answer is 6/25

Step-by-step explanation:

Both 24 and 100 are divisible by 4 so:

24/4 = 6 and 100/4 = 25

So, your final answer is 6/25

Step-by-step explanation:

1.2+2.3+3.4+⋯+n(n+1)=∑k=1nk(k+1)

=∑k=1n(k2+k)

=∑k=1n(k2)+∑k=1n(k)

=n(n+1)(2n+1)6+n(n+1)2

=n(n+1)6(2n+1+3)

=n(n+1)6(2n+4)

=n(n+1)6[2(n+2)]

=n(n+1)(n+2)3

Answer: 7.5 meters

Step-by-step explanation:

Answer:

a) 2211.6812281 rad/min

b) 352 rpm

Step-by-step explanation:

A bicycle with 24-inch diameter wheels is traveling at 16 mi/h. Find the angular speed of the wheels in radians per minute. ___ radians per minute

How many revolutions per minute do the wheels make? (Round your answer to three decimal places.) ___ revolutions per minute

truck with 24-in.-diameter wheels is traveling at 16 mi/h.

---------

1 mile per hour = 88 feet per minute

16 mi/hr = 1408ft/minute

----------

Each revolution = pi*d feet = 4pi feet

(b) How many revolutions per minute do the wheels make?

rev/min

-------------

Each revolution = pi*d feet = 4pi feet

rpm = 1408 ft/min / 4pi feet

=~ 352 rpm

---------------

(a) Find the angular speed of the wheels in rad/min.

rad/min

-------------

rad/min = rpm*2*pi

= 352 rpm × 2× π

= 2211.6812281 rad/min

So, the wheels make [tex]224.20 \ rev/min[/tex].

Angular speed measures how fast the central angle of a rotating body changes with respect to time. It is expressed as,

[tex]\omega=\frac{\theta}{t}[/tex]

Given that:

Diameter[tex]=24 \ in[/tex]

Radius[tex]=12 \ in[/tex]

First, we have to find the angular speed([tex]\omega[/tex]):

We use the formula,

[tex]v=\omega r[/tex]

Substituting,

[tex]16 \ mi/hr=\omega \times 12 \ in[/tex]   ([tex]\therefore[/tex] [tex]1mile=63360inches, \ and \ 1hour=60min[/tex])

[tex]=\frac{16 \ mi\times \left ( 63360 \ in/mi \right )}{\left ( 1 \ hr\times 60 \ min/hr \right )}[/tex]

[tex]=\omega \times 12 \ in[/tex]

[tex]\Rightarrow 15840 \ in/min=\omega \times 12 \ in[/tex]

[tex]\omega =16896/12\\w=1408 \ rad/min[/tex]

Now, we have to find rev/min:

([tex]\therefore \ 1 \ revolution=2\pi[/tex])

Thus,

[tex]1408 \ rad/min\times1 \ rev/2\pi \ rad=224.20 \ rev/min[/tex]..

Learn more about the topic Angular Speed: https://brainly.com/question/25648667

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[tex]f(x) = x + 3[/tex]

[tex]g(x) = {x}^{2} - 2[/tex]

_________________________________

[tex](f + g)(x) = f(x) + g(x)[/tex]

[tex](f + g)(x) = (x + 3) + ({x}^{2} - 2 ) \\ [/tex]

[tex](f + g)(x) = {x}^{2} + x + 3 - 2[/tex]

[tex](f + g)(x) = {x}^{2} + x + 1[/tex]

_________________________________

[tex](f + g)(t - 5) = ({t - 5})^{2} + (t - 5) + 1 \\ [/tex]

[tex](f + g)(t - 5) = {t}^{2} - 10t + 25 + t - 5 + 1 \\ [/tex]

Collect like terms

[tex](f + g)(t - 5) = {t}^{2} - 9t + 21 \\ [/tex]

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Answer:

n+8+n-12=

simplyfiy=2n+20

Step-by-step explanation:

Ya'll just have to simplify the expression and add the like terms together. hope I helped

Note: Your exponential expression seems a little unclear. Because 27 is not an exponential expression.

But, I am assuming that your exponential expression is:

The reason is that my solution would still clear your concept about this topic, no matter what the question is.

Answer:

The simplified value of the exponential expression is:

[tex]27^{\frac{1}{3}}=3[/tex]

Step-by-step explanation:

Assuming the exponential expression

[tex]\:27^{\frac{1}{3}}[/tex]

[tex]\mathrm{Factor\:the\:number:\:}\:27=3^3[/tex]

[tex]=\left(3^3\right)^{\frac{1}{3}}[/tex]

[tex]\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc},\:\quad \:a\ge 0[/tex]

[tex]\left(3^3\right)^{\frac{1}{3}}=3^{3\cdot \frac{1}{3}}[/tex]

[tex]=3^{3\cdot \frac{1}{3}}[/tex]

[tex]=3^1[/tex]

[tex]\mathrm{Apply\:exponent\:rule}:\quad \:a^1=a[/tex]

[tex]=3[/tex]

Therefore, the simplified value of the exponential expression is:

[tex]27^{\frac{1}{3}}=3[/tex]

Answer:

No solution

I hope this helps!

Answer:

B. [tex]-2\frac{1}{2}[/tex]

Step-by-step explanation:

First you need to get the least common denominator of the left

-7 3/4 and 1/2 the LCD is 4 so...

(1/1) 3/4 = 3/4 (This doesn't have to change since the denominator is already 4)

(2/2) 1/2 = 2/4

Let's make -7 3/4 into an improper fraction = -31/4

Let's make -2 1/4 into an improper fraction = -9/4

Plug back in

-31/4 - 2w + 2/4 [tex]\leq[/tex] -9/4 (collect like terms)

-29/4 - 2w [tex]\leq[/tex] -9/4 (add 29/4 on both sides)

-2w = 5 (divide by -2)

w = -5/2 or -2 1/2

Hope this helps!!

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[tex] \binom{ | - 18 \: \: \: \: \: - 8| }{ |10 \: \: \: \: \: \: \: \: \: \: \: \: \: \: 18| } = \\ [/tex]

[tex] - 18 \times18 - ( - 8 \times 10) = [/tex]

[tex] - 324 + 80 = - 244[/tex]

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Answer:

D

Step-by-step explanation:

Edge

Answer:

Angle 6

Step-by-step explanation:

Angles on opposite ends are congruent if they are formed by the same two lines or in other words, if the two angles are vertical angles.

Answer:

x = 19.8

Step-by-step explanation:

5x - 9 = 90

5x = 90 + 9

5x = 99

x = 19.8

Hope this helped!

Answer:

19.8

Step-by-step explanation:

5x-9=90

Cancel the 9 on both sides, so you get:

5x=90+9

5x=99

x= 19.8

Answer:

there are 5040 arrangements.

Step-by-step explanation:

i hope this works