A selection of staff wages is collected and shown below.

£254
£254
£310
£276
£116
£90
£312
£180
£180
£536
£350
£243
£221
£165
£239
£700

What is the mode of staff wages?

Answer:

[tex]\large\boxed{f(x)=5x}[/tex]

Step-by-step explanation:

[tex]\begin{array}{c|c}x&f(x)\\1&5\\2&10\\3&15\end{array}\\\\\\f(1)=5(1)=5\\f(2)=5(2)=10\\f(3)=5(3)=15\\\Downarrow\\f(x)=5x[/tex]

Answer:

x=35

Step-by-step explanation:

We have the two angles (6x -82)  and (3x + 23) that are equal. To find 'x' we need to solve the system of equations:

6x -82 = 3x + 23

Solving for 'x':

3x = 105

x = 35

[tex]6x-82=3x+23\\3x=105\\x=35[/tex]

Final Answer:

The derived relationship between p and q that is independent of y is: q = 1/2 * p

Explanation:

To find the relation between 'p' and 'q' that is independent of 'y,' we will combine the two given equations and eliminate 'y'.
The equations given are:
1) -2y² - 2y = p
2) -y² + y = q
First, we want to manipulate these equations to isolate similar terms. Notice that the first equation has -2y² and the second has -y². If we multiply every term in the second equation by 2, we will have a coefficient of -2y² in the second equation, which will help us cancel out the y² terms. Let's do that:
2(-y² + y) = 2q
-2y² + 2y = 2q
Now, let's subtract the second equation from the first equation:
(-2y² - 2y) - (-2y² + 2y) = p - 2q
On subtracting, -2y² will cancel out with -2y², and -2y will subtract 2y to give -4y:
-2y² + 2y² - 2y - 2y = p - 2q
0 - 4y = p - 2q
-4y = p - 2q
Since we want a relationship without 'y', we can't do much with this result directly, as it still contains 'y'. But let's look at the equations we've been given once more.
The goal is not to solve for 'y' but to find a relationship between 'p' and 'q'. To accomplish this, let's compare the two original equations and try to eliminate 'y' by dividing them. Divide the first equation by the second equation:
(-2y² - 2y) / (-y² + y) = p / q
Now, factor out -y from both the numerator and the denominator:
- y(2y + 2) / - y(y - 1) = p / q
Simplify the expression by canceling out the -y term:
(2y + 2) / (y - 1) = p / q
At this point, you can see that there is no straightforward way to solve this for a relationship that is completely independent of 'y' because the y's don't cancel out.
One method to proceed, since we must get rid of 'y', is to compare coefficients that correspond to the same powers of 'y' assuming p and q are related through such a power series.
We have from the first equation by rearranging:
y² + y = -p/2
Comparing coefficients to the second equation:
y² = -q
y = q
By matching coefficients for the same powers of y, we deduce:
y (from -y²) = -q (from -y² + y), so q = 1/2 * p
Thus, our derived relationship between p and q that is independent of y is:
q = 1/2 * p
This indicates that q is half of p.

Answer:

B- Mean

Step-by-step explanation:

When the variation is smaller it means that there are no large outliers. When there are large outliers the mean inctease. since you are decreasing the variation the mean would decrease.

Answer:

C (-1,6).

Step-by-step explanation:

This is a horizontal line segment since A and B have the same y-coordinate.  Point P will also have the same y-coordinate since P is suppose to be on line segment AB.

So the only choice that has the y-coordinate as 6 is C. So we already know the answer is C.  There is no way it can be any of the others.  

So we are looking for the x-coordinate of point P using the x-coordinates of A and B.

A is at x=-3

B is at x=0

The length of AB is 0-(-3)=3.

AP+PB=3

AP/PB=2/1

This means AP=2 and PB=1 since 2+1=3 and AP/PB=2/1.

So if we look at A and we know P is 2 units away (after A) then -3+2=-1 is the x-coordinate of P.

OR!

IF we look at B and we know P is 1 unit away (before B), then 0-1=-1 is the x-coordinate of P.

For this case we must resolve the following expression:

[tex]6 + 2 ^ 3 * 3 =[/tex]

For the PEMDAS evaluation rule, the second thing that must be resolved are the exponents, then:

[tex]6 + 8 * 3 =[/tex]

Then the multiplication is solved:

[tex]6 + 24 =[/tex]

Finally the addition and subtraction:

30

Answer:

30

Answer:

y=-(x-3)^2+2

Step-by-step explanation:

since the curve is convex up so the coefficient of x^2 is negative

and by substituting by the point 3 so y = 2

Answer:

B

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

here (h, k) = (3, 2), hence

y = a(x - 3)² + 2

If a > 0 then vertex is a minimum

If a < 0 then vertex os a maximum

From the graph the vertex is a maximum hence a < 0

let a = - 1, then

y = - (x - 3)² + 2 → B

Answer:

466.27$ APEX

Step-by-step explanation:

Answer:

We have ; p = 2050

r = [tex]12/12/100=0.01[/tex]

n = [tex]3\times12=36[/tex]

But we will take [tex]36-5=31[/tex]

EMI formula is :

[tex]\frac{p\times r\times(1+r)^{n}}{(1+r)^{n}-1}[/tex]

Substituting values in the formula we get;

[tex]\frac{2050\times0.01\times(1+0.01)^{31}}{(1+0.01)^{31}-1}[/tex]

= [tex]\frac{2050\times0.01\times(1.01)^{31}}{(1.01)^{31}-1}[/tex]

= $77.24

Now for further working you can see the sheet attached.

Total interest paid for the loan = $446.76

Answer:

2

Step-by-step explanation:

The diagonals of a parallelogram bisect each other. Since midpoints will be involved, use multiples of 2 to name the coordinates for B, C, and D.

Answer:

2

Step-by-step explanation:

Well by definition a Rhombus is an equilateral paralelogram, AB =BC=CD=DA with all congruent sides, and Diagonals with different sizes.

Also a midpoint is the mean of coordinates, like E is the mean coordinate of A,C, and B, D

[tex]\frac{B+D}{2}=E\\  \\ B+D=2E\\ and\\\\  \frac{A+C}{2} =E\\ A+C=2E[/tex]

So the sum of the Coordinates B and D over two returns the midpoint.

And subsequently the sum of the Coordinates B +D equals twice the E coordinates. The same for the sum: A +C

Given to the fact that both halves of those diagonals coincide on E despite those diagonals have different sizes make us conclude, both bisect each other.

Answer:

f(x)=-3x+4

(can't see some of your choices)

Step-by-step explanation:

We want x to be independent means we want to write it so when we plug in numbers we can just choose what we want to plug in for x but y's value will depend on our choosing of x.

So we need to solve for y.

9x+3y=12

Subtract 9x on both sides

     3y=-9x+12

Divide both sides by 3:

     y=-3x+4

Replace y with f(x).

    f(x)=-3x+4

Answer:

3(2x+3)=-3(-30+4)

6x+9=90+12

6x+9=102

6x=93

x=15.5

-please mark as brainliest-

Answer:

11½ = x

Step-by-step explanation:

6x + 9 = 78

- 9 - 9

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

6x = 69 [Divide by 6]

x = 11½ [3⁄6 = ½]

I hope this helps you out, and as always, I am joyous to assist anyone at any time.

Answer:

-10, -33, -125, -493, -1965

Step-by-step explanation:

a_1 = -10

a_n = 4a_(n - 1) + 7

The first five terms of the sequence are

a_1 =                                             -10

a_2 = 4(-10) + 7     =   -40 + 7 =    -33

a_3 = 4(-33) + 7    =  -132 + 7 =   -125

a_4 = 4(-125) + 7  = -500 + 7 =   -493

a_5 = 4(-473) + 7 = -1972 + 7 = -1965

[tex]\text{Hey there!}[/tex]

[tex]\text{a = m}^2[/tex]

[tex]\text{If m = -3 replace the m-value in the problem with -3}[/tex]

[tex]\text{a = -3}^2[/tex]

[tex]\huge\text{-3}^2\text{ = -3 * 3 = -9}[/tex]

[tex]\boxed{\boxed{\huge\text{Answer: a = -9}}}\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

20 feet wide, 24 feet long

Step-by-step explanation:

Let x - width, y - length.

The perimeter is given by the formula:

P = 2*(width + length) or using x, y

P = 2*(x + y) = 88

x + y = 44

And we know that the ratio between the sides is 5/6:

x/y = 5/6. x is on top because the length is bigger than the width

x = 5y/6

Plug this in the first expression:

y + 5y/6 = 44. Muliply by 6

6y + 5y = 264

11y = 264

y = 264/11 = 24.

So x = 5(24)/6  = 20

Answer:

[tex]1,207.6\ m[/tex]

Step-by-step explanation:

step 1

Find the perimeter of one lap

we know that

The perimeter of one lap is equal to the circumference of a complete circle (two half circles is equal to one circle) plus two times the length of 96 meters

so

[tex]P=\pi D+2(96)[/tex]

we have

[tex]D=35\ m[/tex]

[tex]\pi =3.14[/tex]

substitute

[tex]P=(3.14)(35)+2(96)[/tex]

[tex]P=301.9\ m[/tex]

step 2

Find the total meters of four laps

Multiply the perimeter of one lap by four

[tex]P=301.9(4)=1,207.6\ m[/tex]

Answer:

1207.6

Step-by-step explanation:

step 1

i got it right on the test

step 2

you get it right on the test

Answer: 1) (x - 7)(x - 8)

               2) 2x(2x-7)(x + 2)

               3) (4x + 7)²

               4) (9ab² - c³)(9ab² + c³)

Step-by-step explanation:

1) x² - 15x + 56  → use standard form for factoring

                    ∧

                -7 + -8 = -15

  (x - 7) (x - 8)

************************************

2) 4x³ - 6x² - 28x      → factor out the GCF (2x)

2x(2x² - 3x - 14)         → factor using grouping

2x[2x² + 4x    - 7x - 14]    

2x[ 2x(x + 2)   -7(x + 2)]

2x(2x - 7)(x + 2)

*************************************

3) 16x² + 56x + 49     → this is the sum of squares

√(16x²) = 4x      √(49) = 7

              (4x + 7)²

******************************************************

4) 81a²b⁴ - c⁶          → this is the difference of squares

√(81a²b⁴) = 9ab²       √(c⁶) = c³

       (9ab² - c³)(9ab² + c³)

It's false, trapezoids are not rectangles.

Answer:

y - 21 = 3(x - 5)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = 3 and (a, b) = (5, 21), hence

y - 21 = 3(x - 5) ← in point- slope form

The point slope form of an equation is y - y1 = m(x - x1). Substituting the given point (5,21) and slope 3 into the equation, we get y - 21 = 3(x - 5). To remove the parenthesis on the y side, we simplify the equation to be y = 3x + 6.

The question asks for the writing of a point-slope equation of a line with a given slope of 3 that passes through a point (5,21). The point-slope form of an equation is generally denoted as:

y - y1 = m(x - x1)

Here, (x1, y1) = (5,21) and m (slope) = 3. Hence, substituting these values yields the equation:

y - 21 = 3(x - 5)

The asked equation without parenthesis on the y side would be:

y = 3x - 15 + 21

So, the final equation is:

y = 3x + 6

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The intersection of the solution set consists of the elements that are contained in all the intervals. -8 ≤ x < 6.

Solving compound inequalities.

A compound inequality is the joining of two or more inequalities together and they are united by the word (and) or (or). In the given compound inequality, we have:

7x ≥ - 56 and 9x < 54.

Solving the compound inequality, we have;
7x ≥ - 56

Divide both sides by 7

[tex]\dfrac{7x}{7} \geq \dfrac{56}{7}[/tex]

x ≥ 8

Also, 9x < 54

Divide both sides by 9.

[tex]\dfrac{9x}{9} < \dfrac{54}{9}[/tex]

x < 6.

Therefore, the intersection of the solution set consists of the elements that are contained in all the intervals. -8 ≤ x < 6

Answer:

C 1 hours 12 minutes

Step-by-step explanation:

We know distance is equal to rate times time

d= r*t

We know the distance is 30 miles and the rate is 25 miles per hour

30 = 25 *t

Divide each side by 25

30/25 = 25t/25

30/25 =t

6/5 =t

1  1/5 =t

Changing 1/5 hour to minutes.   We know there is 60 minutes in 1 hours so 1/5 of an hour is 60*1/5

1/5 *60minutes = 12 minutes

1 hours 12 minutes

Answer:

[tex]\frac{3}{5}[/tex]

Step-by-step explanation:

To find the slope, all we need is to points on the line.

Judging by that graph, we can see a point at (0,1) and at (5,4).

Simply enter this into the slope formula and you'll have your slope.

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

Your y1 term is 1, your y2 term is 4.

Your x1 term is 0, your x2 term is 5.

[tex]\frac{4-1}{5-0} \\\\\frac{3}{5}[/tex]

Your slope is [tex]\frac{3}{5}[/tex].

Answer:

[tex]\large\boxed{\dfrac{3}{5}}[/tex]

Step-by-step explanation:

Look at the picture.

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

From the graph we have two points (0, 1) and (-5, -2).

Substitute:

[tex]m=\dfrac{-2-1}{-5-0}=\dfrac{-3}{-5}=\dfrac{3}{5}[/tex]

The given quadratic equation x² - 4x = -7 is rearranged into standard form and then solved using the quadratic formula -b ± √(b² - 4ac) / (2a). The roots of the equation are realized from solving this formula.

The subject of this problem is a quadratic equation in the form of ax²+bx+c = 0. The given equation is x² - 4x = -7, which can be rearranged into standard form as x² - 4x + 7 = 0. Thus, in this case, a=1, b=-4, and c=7.

The solutions or roots for this quadratic equation can be calculated using the quadratic formula, which is -b ± √(b² - 4ac) / (2a). Substituting the values of a, b, and c into the formula will give the roots of the given equation.

Doing that, we get: x = [4 ± √((-4)² - 4*1*7)] / (2*1)

The values that solve the equation are the roots of the quadratic equation.

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To solve the equation x^2 - 4x = -7 using the Quadratic Formula, we follow the steps of plugging the values of a, b, and c into the formula, evaluating the square root and simplifying to find the solutions.

To solve the equation x2 - 4x = -7 using the Quadratic Formula, we first need to make sure the equation is in standard form, which is ax2 + bx + c = 0. In this case, a = 1, b = -4, and c = 7. Plugging these values into the Quadratic Formula, we get:

x = (-(-4) ± √((-4)2 - 4(1)(-7))) / (2(1))

x = (4 ± √(16 + 28))/2

x = (4 ± √44)/2

x = (4 ± 2√11)/2

x = 2 ± √11

So the solutions to the equation x2 - 4x = -7 are x = 2 + √11 and x = 2 - √11.

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Answer:

The expression used to find of 75 and 60 is 45.

Step-by-step explanation:

To find expression of 75 and 60, multiply decimals from left to right.

0.75*0.60=0.45 =45%

.75*.60=.45=45

45=45

True

45, which is our answer.

Answer:

A. 18

Step-by-step explanation:

Median of a trapezoid: Its length equals half the sum of the base lengths.

So the sum of the lengths is 15 + 21 is 36 and half is 18.

18 inches long of a cut will John need to make so that he cuts the tiles along the median.

Given that, the top base of each tile is 15 inches in length and the bottom base is 21 inches.

The median of a trapezoid is the segment that connects the midpoints of the non-parallel sides.

The length of the median is the average of the length of the bases.

Now, add the top base and bottom base,

That is 15+21=36.

Now, divide that by 2

That is, 36/2= 18 inches.

Hence, the answer would be 18 inches.

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Answer:

(2p - 9)(3p + 5)

Step-by-step explanation:

We have the polynomial: 6p2 – 17p – 45

Rewrite the middle term as a sum of two terms:

6p2 + 27p - 10p - 45

Factor:

3p(2p - 9) + 5(2p - 9)

→ (2p - 9)(3p + 5)

For this case we must factor the following expression:

[tex]6p ^ 2-17p-45[/tex]

We must rewrite the term of the medium as two numbers whose product is [tex]6 * (- 45) = - 270[/tex]

And whose sum is -17

These numbers are: -27 and +10:

[tex]6p ^ 2 + (- 27 + 10) p-45\\6p ^ 2-27p + 10p-45[/tex]

We group:

[tex](6p ^ 2-27p) + 10p-45[/tex]

We factor the maximum common denominator of each group:

[tex]3p (2p-9) +5 (2p-9)[/tex]

We factor[tex](2p-9)[/tex] and finally we have:

[tex](2p-9) (3p + 5)[/tex]

Answer:

[tex](2p-9) (3p + 5)[/tex]

Answer:

7t^2 + 21t

Step-by-step explanation:

You have 7 tiles of each t by t+3.

One tile has an area of

t * (t+3) = t^2 + 3t

So in total the area is

7* (t^2 + 3t)

7t^2 + 21t

Answer:

D

Step-by-step explanation:

Given the 2 equations

y = x² - 2 → (1)

y = - 2x + 1 → (2)

Substitute y = x² - 2 into (2)

x² - 2 = - 2x + 1 ( subtract - 2x + 1 from both sides )

x² + 2x - 3 = 0 ← in standard form

(x + 3)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

x - 1 = 0 ⇒ x = 1

Substitute these values into (2) for corresponding values of y

x = - 3 : y = -2(- 3) + 1 = 6 + 1 = 7 ⇒ (- 3, 7 )

x = 1 : y = - 2(1) + 1 = - 2 + 1 = - 1 ⇒ (1, - 1 )

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y=x^2-2&(1)\\y=-2x+1&(2)\end{array}\right\\\\\text{substitute (1) to (2):}\\\\x^2-2=-2x+1\qquad\text{add 2x to both sides}\\x^2+2x-2=1\qquad\text{subtract 1 from both sides}\\x^2+2x-3=0\\x^2+3x-x-3=0\\x(x+3)-1(x+3)=0\\(x+3)(x-1)=0\iff x+3=0\ \vee\ x-1=0\\\\x+3=0\qquad\text{subtract 3 from both sides}\\x=-3\\\\x-1=0\qquad\text{add 1 to both sides}\\x=1\\\\\text{put the value of x to (1):}\\\\for\ x=-3\\y=(-3)^2-2=9-2=7\\\\for\ x=1\\y=1^2-2=1-2=-1[/tex]

Answer: B

Step-by-step explanation:

Division of components are consistent  - the same

Answer:

B. -3, 3, -3, 3...

Step-by-step explanation:

There's two types of sequences, arithmetic and geometric.

Arithmetic equations are sequences that increase or decrease by adding or subtracting the previous number.

For example, take a look at the following sequence:

2, 4, 6, 8, 10, 12, 14, 16, 18, 20...

Here, the numbers are increasing by +2. [adding]

So, this the sequence is arithmetic, since its adding.

Geometric sequences are sequences that increase or decrease by multiplying or dividing the previous number.

For example, take a look at the following sequence:

2, 4, 16, 32, 64, 128, 256, 512...

Here, the numbers are icnreasing by x2. [multiplying]

So, the sequence is geometric since its multiplying.

Based on this information, the correct answer is "B. -3, 3, -3, 3..." since its being multiplyed by -1.

Final answer:

Isabel's ride rotates 60° every two seconds. It takes 6 intervals (360° divided by 60°) to make a full rotation. Multiplying 6 intervals by 2 seconds gives us 12 seconds for Isabel to return to the starting position.

Explanation:

To determine how many seconds will pass before Isabel returns to her starting position on the ride, we need to establish the total degrees of rotation that equate to a full circle, which is 360°. Since the ride rotates 60° every two seconds, we can calculate the number of two-second intervals required to complete a full 360° rotation.

Firstly, divide 360° by 60° to find the number of intervals:

360° / 60° = 6 intervals

Since each interval takes 2 seconds, multiply the number of intervals by 2 to find the total time:

6 intervals × 2 seconds/interval = 12 seconds.

Therefore, it will take Isabel 12 seconds to return to her starting position on the amusement park ride.