shannon is paid £1150 a month after deductions.what is her net annual salary?(a year=12 months )

Answer:

a. €1200;$1667.70

Step-by-step explanation:

a. Number of euros

[tex]\text{euros} = \$1962 \times \dfrac{\text{1 euro}}{\text{\$1.635}} = \textbf{1200 euros}[/tex]

b. Dollars remaining

Dollars on hand                        = $1962.00

Less 15 % spent = 0.15 × 1962 =   -294.30

Balance remaining                   =  $1667.70

Answer:

36

Step-by-step explanation:

you know the number based on the sequence

the values increase in the form of x+2

e.g. 4-1=3

      9-4=5

      16-9=7

      25-16=9

you can see the number adds 2 for every increased number

and by following this sequence you will get the number 36

Answer:

by the square of 1, 2 ,3 the sequence has been made

Step-by-step explanation:

1 for 1²

4 for 2²

9 for 3²

16 for 4²

25 for 5²

so the later one will be 36 for 6²

so the answer is 36 thats all

Graph of increasing exponential function going through point (0, 2)

=======================================================

Explanation:

Assuming you meant to say f(x) = 2(1.5)^x, then we can see the equation is an exponential and it is increasing. It is increasing because the base b = 1.5 is larger than 1.

Plug in x = 0 to find y

y = 2(1.5)^x

y = 2(1.5)^0

y = 2(1)

y = 2

We have x = 0 and y = 2 pair up together meaning (0,2) is on the function curve. This is the y intercept.

Answer:

A.  graph of increasing exponential function going through point 0, 2

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\sqrt{x-3} +5=x\\\sqrt{x-3} =x-5\\squaring ~both~sides\\x-3=x^2-10x+25\\x^2-10x-x+25+3=0\\x^2-11x+28=0\\x^2-7x-4x+28=0\\x(x-7)-4(x-7)=0\\(x-7)(x-4)=0\\x=7,4[/tex]

put x=7 in the given equation

[tex]\sqrt{7-3} +5=7\\\sqrt{4} +5=7\\2+5=7\\7=7[/tex]

which is true .

∴ x=7 is a solution of the given eq.

now put x=4 in the given eq.

[tex]\sqrt{4-3} +5=7\\1+5=7\\6=7\\[/tex]

which is not true.

∴x=4 is an extraneous solution.

Answer:

A. R=0.86; strong correlation

Step-by-step explanation:

The correlation coefficient of 0.29 indicates that the correlation is a weak positive correlation. Thus option (D) is the correct answer.

"Correlation is a statistical tool that studies the relationship between two variables. Data sets have a positive correlation when they increase together, and a negative correlation when one set increases as the other decreases".

For the given situation,

Correlation coefficient = 0.29

Positive correlation: the two variables change in the same direction.

Negative correlation: the two variables change in opposite directions.

No correlation: there is no association or relevant relationship between the two variables.

The correlation coefficient lies between 0 to 0.3 indicating that the correlation is a weak positive correlation.

Hence we can conclude that option (D) weak positive correlation is the correct answer.

Learn more about correlation here

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Answer:Her score is 26

Step-by-step explanation:

To find the answer, we must deduct the total amount of points that are answered correctly

By the total amount of points that are answered incorrectly.

Because = 1 answered correctly = 4 points

= 1 answered incorrectly = deduct 7

points

So= 87 answered correctly × 4 points

= 348 points

So= 46 answered incorrectly × 7 points

=deduct 322 points

Then the answer will be= 348 - 322= 26

Hope this helps!

Answer:

66k+9

Step-by-step explanation:

Let's simplify step-by-step.

5(10k+1)+2(2+8k)

Distribute:

=(5)(10k)+(5)(1)+(2)(2)+(2)(8k)

=50k+5+4+16k

Combine Like Terms:

=50k+5+4+16k

=(50k+16k)+(5+4)

=66k+9

Answer:

=66k+9

HOPE THIS HELPS!!!!!! :)

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1 mile = 5,280 feet

1 hour = 3600 seconds

3600/5280 = 0.681818 feet per second

25 ft per second x 0.681818 = 17.045 miles per hour

Round the answer as needed.

Answer:

The correct answer is 17.045 miles per hour.

Answer:

The functions are [tex]f(x) = 7\cdot x+10[/tex] and [tex]g(x) = \frac{1}{x^{2}}[/tex], respectively.

Step-by-step explanation:

Let suppose that [tex]g(x) = \frac{1}{x^{2}}[/tex], then [tex]f(g(x))[/tex] is:

[tex]f(g(x)) = 7\cdot \left(\frac{1}{x^{2}} \right) + 10[/tex]

[tex]f(g(x)) = 7\cdot g(x) + 10[/tex]

Thus,

[tex]f(x) = 7\cdot x + 10[/tex]

The functions are [tex]f(x) = 7\cdot x+10[/tex] and [tex]g(x) = \frac{1}{x^{2}}[/tex], respectively.

Answer:

Combine numerators over the common denominator to make one term

Step-by-step explanation:

Answer:

D: Add the fractions together on the right side of the equation

Step-by-step explanation:

Let's finish this proof:

Add the fractions together on the right side of the equation

[tex]$x^2+\frac{b}{a} x+\left(\frac{b}{2a} \right)^2=\frac{b^2-4ac}{4a^2} $[/tex]

[tex]\text{Consider the discriminant as }\Delta[/tex]

[tex]\Delta=b^2-4ac[/tex]

Once we got a trinomial here, just put in factored form:

[tex]$\left(x+\frac{b}{2a}\right)^2=\frac{\Delta}{4a^2} $[/tex]

[tex]$x+\frac{b}{2a}=\pm\frac{\Delta}{4a^2} $[/tex]

[tex]$x+\frac{b}{2a}=\pm \sqrt{\frac{\Delta}{4a^2} } $[/tex]

[tex]$x=-\frac{b}{2a}\pm \sqrt{\frac{\Delta}{4a^2} } $[/tex]

[tex]$x=-\frac{b}{2a}\pm \frac{ \sqrt{\Delta} }{2a} $[/tex]

[tex]$x= \frac {-b\pm \sqrt{\Delta}}{2a} $[/tex]

[tex]$x= \frac {-b\pm \sqrt{b^2-4ac}}{2a} $[/tex]

Answer: Positive Charge

Answer:

negative

Step-by-step explanation:

When using the Right-Hand Rules, it is important to remember that the rules assume charges move in a conventional current (the hypthetical flow of positive charges).  In order to apply either Right-Hand Rule to a moving negative charge, the velocity (v) of that charge must be reversed--to represent the analogous conventional current.

The opposite charge is a negative charge.

Hi there! Hopefully this helps!

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

"Two more than five times a number x.​" means:

2 + 5 × x

Answer:

13/2 = a

Step-by-step explanation:

27 – 4 + 2a = 4a + 10

Combine like terms

23 +2a = 4a +10

Subtract 2a from each side

23+2a-2a = 4a-2a +10

23 = 2a+10

Subtract 10 from each side

23-10 = 2a+10-10

13 = 2a

Divide by 2

13/2 = a

Answer: a = 13/2

I assume you don't need a step - by - step, you're just asking for the answer. Hope this helps!

Answer:

Step-by-step explanation:

Given functions are

y = 5 cos ( 2π / 3 ) t

y = 5 cos ( 4π / 3 ) t

y= 10 cos ( 2π / 3 ) t

y = 10 cos ( 4π / 3 ) t

The pendulum half oscillation from left extreme to right extreme takes 1.5 s

So its time period of oscillation T = 1.5 x 2 = 3 s .

standard equation of oscillation is

y = A cos ω t where A is amplitude and ω is angular frequency .

Amplitude of oscillation A = 10 / 2 = 5 inch .

Among the given equation of motion only first two has amplitude equal to 5 . So both the last two are ruled out .

The angular frequency of first motion as per given equation

ω = 2π / 3

If time period is T

2π / T = 2π / 3

T = 3 s

So it matches with the time period of oscillation of pendulum .

Hence the first equation truly represents the oscillation of pendulum.

The function models the horizontal displacement as a function of time in seconds is  [tex]\rm y = 10 sin(\dfrac{2\pi}{3})t[/tex]  and this can be determined by using the given data.

Given :

It takes 1.5 seconds for a grandfather clock's pendulum to swing from left (initial position) to right, covering a horizontal distance of 10 inches.

For the oscillation the standard equation is given below:

[tex]\rm y = A\;cos \;\omega t[/tex]

where A is the amplitude, [tex]\omega[/tex] is the angular velocity, and t is the time.

Now, determine the time period that is:

T = 1.5 [tex]\times[/tex] 2

T = 3sec

Now, the angular frequency is given by:

[tex]\omega = \dfrac{2\pi}{3}[/tex]

So, the function models the horizontal displacement as a function of time in seconds is given below:

[tex]\rm y = 10 sin(\dfrac{2\pi}{3})t[/tex]

Therefore, the correct option is C).

For more information, refer to the link given below:

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Answer:

The correct option is;

(Choice C) Both angle measures and segment lengths

Step-by-step explanation:

The given transformations are;

The reflection over the line, [tex]\overleftrightarrow{PQ}[/tex], with, A rotation about the point P. Another reflection over [tex]\overleftrightarrow{PQ}[/tex]. A rotation about the point Q, we have;

The transformations involve changes only in the orientation and location of the pre-image, which remain rigid, therefore, there are no changes in the segment lengths or angle dimensions

Therefore, the correct option is,  both angle measures and segment lengths.

(Choice C) C Both angle measures and segment lengths

Part A

Her steps were

[tex]-2 \frac{5}{6} \div 1 \frac{1}{3}\\\\-\frac{17}{6} \div \frac{4}{3}\\\\-\frac{6}{17} \times \frac{3}{4}\\\\-\frac{6\times 3}{17\times4}\\\\-\frac{18}{68}\\\\-\frac{9}{34}\\\\[/tex]

Kelsey made a mistake on line 3. Note how the 17/6 flips to 6/17. This is not correct. You keep the first fraction the same, but you do flip the second fraction. This only applies when you divide two fractions.

The third step should look like [tex]-\frac{17}{6}\times \frac{3}{4}[/tex]

=======================================================

Part B

Here's what she should have written

[tex]-2 \frac{5}{6} \div 1 \frac{1}{3}\\\\-\frac{17}{6} \div \frac{4}{3}\\\\-\frac{17}{6} \times \frac{3}{4}\\\\-\frac{17\times 3}{6\times 4}\\\\-\frac{51}{24}\\\\-\frac{17}{8}\\\\[/tex]

If you want to convert that improper fraction to a mixed number, then you could do something like this

[tex]-\frac{17}{8} = -\frac{16+1}{8}\\\\-\frac{17}{8} = -\frac{16}{8}-\frac{1}{8}\\\\-\frac{17}{8} = -2 \frac{1}{8}\\\\[/tex]

Or you could divide 17 over 8 using long division to get 2 remainder 1. The 2 is the quotient that goes to the left of the 1/8. The remainder of 1 is the numerator of 1/8.

Answer:

Step-by-step explanation:

[tex]A=s^2\cdot \sin\alpha\\\\s=10\\\alpha=120^o\\\\A=10^2\cdot\sin(120^o)=100\sin(180^o-60^o)=100\sin(60^o)=100\cdot\frac{\sqrt3}2=50\sqrt3[/tex]

Answer:

87.6yd²

Step-by-step explanation:

Base: =1/2bh

=1/2(6)(5.2)=15.6

Sides: =1/2bh

=1/2(6)(8)=24 (3 of them)

15.6+24+24+24=87.6yd²

Answer:

number ten: x=5

number two: x=5³/5

Step-by-step explanation:

number ten:

4x + 3x - 9 = 26

4x + 3x = 26+9

7x = 35

x = 5

number two:

3x + 2x - 8 = 20

3x + 2x = 20+8

5x = 28

x = 5³/5

Answer:

the answer is 60.7

Step-by-step explanation:

60 to has a between numbers like given in the picture

so as number line it's

60.1 . 60.2 60.3 60.4 60.5 60.6 60.7 60.8 and continue

if u get any 3 digit number like 600 to 650 in number line

u do it like it the same 600.1 600.2.... and go on

Answer:

63½ or 63.5

Step-by-step explanation:

65-60=5

10points=5

1point=?

1×5/10= ½

that means the sequence continues after adding ½ i.e

60..60½...61...61½...62...62½...63...63½...64..64½...65

you have been asked the 8th number which is 63½

Answer:

uhfcytuyyytt ryffffffffgtgghhh

Changing the exponent by 1/2 ( going from x to 1/2x)

This does not change the y-intercept.

It does sharpen the curve, which means the y value does not increase as quickly when x is increased.

THe 3rd choice is correct.

Proof: make x=2

Y = 3^2 = 9

Y = 3^1/2(2) = 3^1 = 3

You can see y is smaller with the 1/2 included.

Answer:

  112

Step-by-step explanation:

To find the number of strides, divide the distance by the distance per stride:

  (98 m)/(7/8 m/stride) = (98)(8/7) strides = 112 strides

He takes 112 strides in walking 98 m.

Answer:

y=2x-5

Step-by-step explanation:

First simplify: y-1=2x-6

y-1=2(x-3)

First simplify and distribute everything.

y-1=2x-6

So, x equals 2 because it got distributed into the numbers inside the parenthesis.  Same with the 2 and -3.  They multiplied to become -6.

Since it's y-1=2x-6, you can simplify it even more so the -1 goes to the other side and turns into positive 1.

y - 1 (+ 1) = 2x -6 (+ 1)

-1(+1)=0 which leaves just the variable y on the left side.

-6(+1)=-5 which leaves 2x-5 on the right side.

This results in y=2x-5.  Hope this helped ;)

Answer:

y = 2x - 5

Step-by-step explanation:

y - 1 = 2(x - 3)

y - 1 = 2x - 6

y - 1 + 1 = 2x -6 + 1

y = 2x - 5

All of 4x+8 is under a cube root sign.

=====================================================

Work Shown:

To find the inverse, we swap x and y, then solve for y.

[tex]y = \frac{1}{4}x^3 - 2\\\\x = \frac{1}{4}y^3 - 2\\\\x+2 = \frac{1}{4}y^3\\\\4(x+2) = y^3\\\\4x+8 = y^3\\\\y^3 = 4x+8\\\\y = \sqrt[3]{4x+8}\\\\[/tex]

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

Side note:

If [tex]f(x) = \frac{1}{4}x^3 - 2[/tex] and [tex]g(x) = \sqrt[3]{4x+8}[/tex], then [tex]f(g(x)) = x[/tex] and [tex]g(f(x)) = x[/tex]for all x values in the domain. Effectively, you use function composition to confirm that we have the correct inverse equation.

Answer: x=-22

Step-by-step explanation:

    6x-4=-26+5x

6x-4-5x=-26+5x-5x ⇔ subtraction property of equality

       x-4=-26

  x-4+4=-26+4 ⇔ addition property of equality

         x=-22

Answer:

Step-by-step explanation:

6x - 4 = - 26 + 5x

First of all group like terms

Send the constants to the right side of the equation and those with variables to the left

That's

6x - 5x = 4 - 26

Simplify

We have the final answer as

Hope this helps you

Answer:

#3 would be the first one and #4 would be the third answer.

Step-by-step explanation:

i'm so sorry for the wait

Answer:

Step-by-step explanation:

Answer:

x=12

Step-by-step explanation:

To solve for the variable, we must isolate the variable, which is x.

[tex]\sqrt{x+4} -3=1[/tex]

3 is being subtracted from the square root of x+4. The inverse of subtraction is addition. Add 3 to both sides of the equation.

[tex]\sqrt{x+4} -3+3=1+3[/tex]

[tex]\sqrt{x+4} =1+3[/tex]

[tex]\sqrt{x+4} =4[/tex]

The square root of x+4 is being taken. The inverse of a square root is a square. Square both sides of the equation.

[tex](\sqrt{x+4})^2 =4^2[/tex]

[tex]x+4=4^2[/tex]

Evaluate the exponent.

4^2= 4*4=16

[tex]x+4=16[/tex]

4 is being added to x. The inverse of addition is subtraction. Subtract 4 from both sides of the equation.

[tex]x+4-4=16-4[/tex]

[tex]x=16-4[/tex]

[tex]x=12[/tex]

The solution to this equation is x=12.

Answer/Step-by-step Explanation:

12. A. (1,299 + 3,563) ÷ 22 = 221

4,862 ÷ 22 = 221

221 = 221 (TRUE)

B. 16*(132 + 34)*12 = 32,872

16*166*12 = 32,872

31,872 = 32,872 (NOT TRUE)

C. (65 + 78)*(45 - 29) = 2,188

143*16 = 2,188

2,288 = 2,188 (NOT TRUE)

D. (1,444 - 349) ÷ (457 - 238) = 6

1,095 ÷ 219 = 6

5 = 6 (NOT TRUE)

The answer is A.

13. Let the missing number = X

Thus,

i. 25*(157 + x) = 8,850

[tex] 157 + x = \frac{8850}{25} [/tex]

[tex] 157 + x = 354 [/tex]

[tex] x = 354 - 157 [/tex]

[tex] x = 197 [/tex]

ii. x ÷ (453 - 425) = 135

x ÷ (28) = 135

x = 135*28

x = 3,780

14. (56 + 69) * (268 - 137)

125*131 = 256

15. 9,144 ÷ (2,784 - 2,784)

9,144 ÷ 0 = cannot divide

16.  (72 + 126) ÷ (687 - 654)

198 ÷ 33 = 6

17. 22*(562 + 733)

22*1,295 = 28,490

18. Let the missing number be x

48*(x - 239) = 4,272

[tex] x - 239 = \frac{4,272}{48} [/tex]

[tex] x - 239 = 89 [/tex]

[tex] x = 89 + 239 [/tex]

[tex] x = 328 [/tex]

The missing number is 328.

19. (794 + 718) ÷ (68 - 41)

1,512 ÷ 27 = 56

20. (58*89) + (192 ÷ 16)

5,162 + 12 = 5,174

Answer:

Step-by-step explanation:

Using the equation A(t) = 400e-.032t

a) replace t with 4 so A(4) = 400e((-.032)(4))

The hardest part about this is making sure to use order of operations. Be certain it works like this:

A(4) = 400e-.128

A(4) = 400(.8799)

A(4) = 351.9 grams

b) A(8) = 400e((-.032)(8)) = 309.7 grams

c) A(20) = 400e((-.032)(20)) = 210.9 grams

Note here that even after 20 years, not quite half of the original amount is gone. So, we can anticipate that in finding the half life, that our answer should be slightly greater than 20 years.

d) 200 = 400e(-.032t)

Divide both sides of the equation by 400.

.5 = e(-.032t)

Change this to logarithmic form.

Ln .5 = -.032t

-.6931≈ -.032t

t ≈ 21.7 years

Hope this helps!

The amount of radioactive lead,

(a).After 3 years is 454.23 grams

(b).After 8 years is 387.07 grams

(c).After 10 years is 363.07 grams.

(d). half life is 21.66 years.

The decay of radioactive lead is given by function,

                          [tex]A(t)=500e^{-0.032t}[/tex]

The amount of radioactive lead After 3 years is,

             [tex]A(3)=500e^{-0.032*3}=0.908*500=454.23g[/tex]

The amount of radioactive lead After 8 years is,

            [tex]A(8)=500e^{-0.032*8}=500*0.774=387.07g[/tex]

The amount of radioactive lead After 10 years is,

            [tex]A(10)=500e^{-0.032*10}=500*0.726=363.07g[/tex]

Half life is defined as the interval of time required for one-half of the atomic nuclei of a radioactive sample to decay.

So,       [tex]250=500e^{-0.032t}[/tex]

            [tex]e^{-0.032t}=0.5\\\\-0.032t=ln(0.5)\\\\-0.032t=-0.693\\\\t=0.693/0.032=21.66 years[/tex]

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