Find unit rate $602 for 20 hours of work

The area of ΔQRS is 26.10 square units.

What is triangle?

A triangle is a closed, two-dimensional geometric shape with three straight sides and three angles.

To find the area of \($\triangle QRS$\), we can use the formula:

\($Area = \frac{1}{2} \times base \times height$\)

where the base and height are the length of two sides of the triangle that are perpendicular to each other. We can find these sides using trigonometry.

First, we need to find the length of side \($QR$\). We can use the Law of Cosines:

\($QR^2 = QS^2 + RS^2 - 2(QS)(RS)\cos(R)$\)

where \($R$\) is the angle at vertex \($R$\). Substituting the given values, we get:

\($QR^2 = 9^2 + 5^2 - 2(9)(5)\cos(57^\circ)$\)

\($QR \approx 8.02$\)

Next, we need to find the height of the triangle, which is the perpendicular distance from vertex \($R$\) to side \($QS$\). We can use the sine function:

\($\sin(R) = \frac{opposite}{hypotenuse}$\)

\($\sin(57^\circ) = \frac{height}{8.02}$\)

\($height \approx 6.51$\)

Now we can find the area of the triangle:

\($Area = \frac{1}{2} \times QR \times height$\)

\($Area = \frac{1}{2} \times 8.02 \times 6.51$\)

\($Area \approx 26.10$\) square units

Therefore, the area of \($\triangle QRS$\) is approximately \($26.10$\) square units.

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Using the constant of proportionality the value of x when y is 72 is 9.

What is a COP?

The ratio between two quantities that are directly proportional is the constant of proportionality. When two quantities grow and shrink at the same rate, they are directly proportional.

If y varies directly as x, it means that y can be expressed as a constant multiple of x, i.e., y = kx, where k is the constant of proportionality.

To find k, we can use the given information that y = 48 when x = 6 -

y = kx

48 = k(6)

k = 8

Now that we know k, we can use it to find x when y = 72 -

y = kx

72 = 8x

x = 9

Therefore, when x = 72, the value of x = 9.

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y=3x - 5....(i)

6x+3y=15.....(ii)

Then,

Keeping value of y in (ii)equation;

or,6x+3(3x-5)=15

or,6x+9x-15=15

or,15x=15+15

or,x=30/15

:x=2

Now, Keeping value of x in (i) equation;

y= 3x-5

or, y= 3×2 - 5

or,y= 6-5

: y=1

Answer:

- 1/64 (x+4)² (x-3) (x-4) = 0

Step-by-step explanation:

f(x) = a (x+4)²(x-3)(x-4)   ... curve touch (-4,0) and not cross x axis

x=0   f(x) = -3

a (4)² * (-3) * (-4) = -3

a = - 1/64

- 1/64 (x+4)² (x-3) (x-4) = 0

Answer:

30 days.

Step-by-step explanation:

27 ÷ 0.9 = 30.

Answer:

in 30 days she will reach 27 miles.

Step-by-step explanation:

27 miles / 0.9 miles = 30 days

Answer:

4 = 1x

Step-by-step explanation:

(3x)9 = (4x)5

9 = (1x) 5

4 = 1x

Answer:

The total cost of the ski hat and the ski boots is $112.35.

Step-by-step explanation:

First, we need to add the prices of the ski hat and the ski boots.

85.50 + 19.50 = $105

Now, we need to find 7% of $105, and then add it to the total.

105 x 0.07 = $7.35

105 + 7.35 = $112.35

Therefore, the total cost of the ski hat and the ski boots is $112.35.

Hope this helps! :D

The probability that;

i). two are red and 1 is blue is 0.0257

ii). at least 2 are white is 0.1144

iii). 1 of each colour is drawn is 0.0343

The probability of an event without replacement implies that once an item is drawn, then we do not replace it back to the sample space before drawing another item.

Total possible outcome = 3 + 7 + 8 = 18

i). probability that two are red and 1 is blue = 7/18 × 6/17 × 3/16

probability that two are red and 1 is blue = 7/272

probability that two are red and 1 is blue = 0.0257

ii). probability that at least 2 are white = 8/18 × 7/17 × 7/16 + 8/18 × 7/17 × 3/16

probability that at least 2 are white = 70/612

probability that at least 2 are white = 0.1144

iii). probability that 1 of each colour is drawn = 7/18 × 8/17 × 3/16

probability that 1 of each colour is drawn = 7/204

probability that 1 of each colour is drawn = 0.0343

Therefore, the probability that; two are red and 1 is blue, at least 2 are white and 1 of each colour is drawn are approximately 0.0257, 0.1144 and 0.0343 respectively.

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Answer:

outliner =211

Step-by-step explanation:

mean =71,84,85,85,91,211  

721 divided by 6= 1216 ( its going to keep on going)

median =3 bc (88-85=3)

mode=85

range=140

mean w/o outliner=102

Answer :

a) It is given that

Everyday a machine makes 500000 staples and puts them into the boxes.

The machine need 170 staples to fill a box

One box contans = 170 staples.

Total number of staples = 500000

Number of box required to fill 500000 staples = Total number of staples/No. of staples 1 box contains.

\( \: :\implies \) 500000 /170

\( :\implies \: \) 2941 (approx)

Therefore, 2941 boxes are required to fill with 500000 staples.

b) It is given that,

Each staple is made of 0.21 g of metal .

Total weight of metal = 1 kg = 1000 g

1 staple = 0.21 g

Number of staples = weight of metal/ Weight of 1 staple.

\( \: :\implies \) 1000/0.21

\( \: :\implies \) 4761 (approximately)

Therefore, 4761 staples can be made from 1 kg of the metal.

The value of n that satisfies the given polynomial expression is 10

From the question, we are to determine determine the corresponding value of n in the simplified expression.

The given expression is

(12x⁵ + 6x³ + x) - (x + 26)(2nx² + 1)

First, we will simplify this expression

(12x⁵ + 6x³ + x) - (x + 26)(2nx² + 1)

(12x⁵ + 6x³ + x) - (2nx³ + x + 52nx² + 26)

(12x⁵ + 6x³ + x - 2nx³ - x - 52nx² - 26)

Simplify further

(12x⁵ + 6x³ - 2nx³ - 52nx² - 26)

(12x⁵ + (6 - 2n)x³ - 52nx² - 26)

By comparison with (12x⁵ - 14x³ - 520x² - 26)

(6 - 2n)x³ = - 14x³

and

- 52nx² = - 520x²

Solve (6 - 2n)x³ = - 14x³ for n

(6 - 2n)x³ = - 14x³

6 - 2n = - 14

6 + 14 = 2n

20 = 2n

n = 20/2

n = 10

Similarly,

Solve - 52nx² = - 520x² for n

52n = 520

n = 520/52

n = 10

Hence, the value of n is 10

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The percent of the front page taken up by the prom story is 20%

From the question, we have the following parameters that can be used in our computation:

The front page

From the front page, we have

Area front page = 5 * 4

Area front page = 20

Also, we have

Prom = 2 * 2

Prom = 4

So, we have

Percentage = 4/20 * 100%

Evaluate

Percentage = 20%

Hence, the percent of the front page taken up by the prom story is 20%

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The numerical value of x in the similar pair of triangle is 10.

A ratio is simply the relation between two amounts showing how many times a value is contained within another value.

From the diagram,

Side A of the small triangle = 10

Side B of the small triangle = x + 2

Side A of the Big triangle = 10 + x

Side B of the big triangle = x + 14

Hence;

Ratio of Side A to Side B of the small triangle = 10 / x + 2

Ratio of Side A to Side B of the Big triangle = 10 + x / x + 14

Since the triangle area similar, equate the two ratio and solve for x.

10 / ( x + 2 ) = ( 10 + x ) / ( x + 14 )

Cross multiply

10( x + 14 ) = ( 10 + x )( x + 2 )

Expand using FOIL method

10x + 140 = 10x + 20 + x² + 2x

10x + 140 = x² + 12x + 20

x² + 12x + 20 = 10x + 140

x² + 12x + 20 - 10x - 140 = 0

x² + 2x - 120 = 0

Factor the left side of the equation

( x - 10 )( x + 12 ) = 0

Hence;

x - 10 = 0 and x + 12 = 0

x = 10 and x = -12

Since the dimension of the triangle cannot be negative,

x = 10

Therefore, the value of x is 10.

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If Gavin contributes towards a Pension fund (7,5% of his Basic Salary), then his net salary will be reduced by the amount he contributed towards pension fund i.e. R652.5.

1.1 Name of employee is Gavin Pillay. 1.2 UIF stands for Unemployment Insurance Fund. UIF is a benefit to provide short-term relief to workers who lose their jobs, or can't work due to illness, maternity or adoption leave. 1.3 The UIF paid by Gavin is calculated correctly.

Firstly, we need to calculate Gross Salary of Gavin, which is given as: Basic Salary + Overtime + M = R8700 + R1200 + R3201 = R13101Then, calculate total deductions from gross salary.

Total Deductions = PAYE + UIF = R1200 + 87 = R1287Hence, Gavin's net salary = Gross salary - Total Deductions = R13101 - R1287 = R11814Therefore, UIF paid by Gavin is calculated correctly as R87.1.4 This payslip is for the month of May i.e.

31/05/2023.1.5 Basic salary of Gavin = R8700. Deduct 7.5% of his basic salary to calculate his pension fund contribution. Pension Fund Contribution = 7.5/100 x R8700 = R652.5.1.6

Total deductions of Gavin includes PAYE, UIF and pension fund contribution.

Therefore, Total Deductions = PAYE + UIF + Pension Fund Contribution = R1200 + R87 + R652.5 = R1939.5.1.7

Gavin's age can not be determined as his date of birth is not provided.1.8 Address of Gavin's workplace is 21 Halsted Road, Pietermaritzburg?

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Answer: C

Step-by-step explanation:

Point D is at -14 on the number line.

In Mathematics, the midpoint of a line segment with two end points can be calculated by adding each end point on a line segment together and then divide by two (2).

Since E is the midpoint of line segment CD, we can logically deduce the following relationship:

Line segment CD = Line segment C + Line segment D

Midpoint E = (point C + point D)/2

By substituting the given points into the equation above, we have the following:

-3 = (8 + D)/2

-6 = 8 + D

D = -6 - 8

D = -14

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Lucille is being charged a simple interest rate of 0.4, or 40%.

To determine the simple interest rate Lucille is being charged, we can use the formula for simple interest:

Interest = Principal × Rate × Time

In this case, the principal (P) is $1500, the time (T) is 6 months (or 0.5 years), and the total amount to be paid back (A) is $1500 + $300 = $1800. We need to find the rate (R).

Interest = Principal × Rate × Time

$300 = $1500 × R × 0.5

Simplifying the equation:

$300 = $750R

To isolate R, we divide both sides of the equation by $750:

$300 / $750 = R

0.4 = R

Therefore, Lucille is being charged a simple interest rate of 0.4, or 40%.

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Assuming supply and demand are linear, the equilibrium price is equal to $252 and the equilibrium quantity is equal to 2,016 items.

A linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.

First of all, we would determine a linear function for both supply and demand by finding the slope using this formula as follows:

\(Slope,\;m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope,\;m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}\)

Note: price (p) in dollars would be the output and quantity (q) would be the input.

For supply, the points include the following:

Slope, m = (330 - 180)/(2640 - 1440)

Slope, m = 150/1200

Slope, m = 1/8.

Next, we would find the y-intercept at (1,440, 180):

p = qm + c

180 = 1/8(1440) + c

180 = 180 + c

c = 0.

Therefore, the supply equation is p = q/8.

For demand, the points include the following:

Slope, m = (330 - 180)/(1,470 - 2,520)

Slope, m = 150/-1,050

Slope, m = -1/7.

Next, we would find the y-intercept at (2,520, 180):

p = qm + c

180 = -1/7(2,520) + c

180 = -360 + c

c = 180 + 360.

y-intercept, c = 540.

Therefore, the demand equation is p = -q/7 + 540.

In order to find the equilibrium price and quantity, we would set the supply equal to the demand:

q/8 = -q/7 + 540

Multiplying all through by 56, we have:

7q = -8q + 30,240

15q = 30,240

q = 30,240/15

Equilibrium quantity, q = 2,016 items.

For the equilibrium price, we have:

p = q/8

p = 2,016/8

Equilibrium price, p = $252.

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Answer:

Step-by-step explanation:

volume = 34cm³

volume = 4/3×π×radius³

34cm³ = 4/3 × 3.14 × radius³

34cm³ = 12.56/3 × radius³

radius³ = 34×3/12.56

radius³ = 8

radius = ³√8

radius = 2cm

diameter = 2×radius

= 2×2

= 4cm

FOLLOW ME PLEASE

Answer:

3

Step-by-step explanation:

Answer:

x=3

Step-by-step explanation:

PLEASE MARK BRAINLIEST

Answer:

A=-8 and B=-2

Step-by-step explanation:

Answer: Equilateral

Step-by-step explanation:

It's equilateral because it says that each side of the triangle is 4cm. In simple words, all the sides of triangle are equal. Such a triangle is called an equilateral triangle.

Hope you understood.

Answer:

A TRANSLATION OF A GRAPH is its rigid movement, vertically or horizontally. On the left is the graph of the absolute value function. On the right is its translation to a "new origin" at (3, 4). y = |x|.

Answer:

Value of slope is -2 and y-intercept is 1

Step-by-step explanation:

We can see that the values in the table have a linear relationship.

A linear function is a straight line written as:

y = mx+b

Here,

m is the slope and b is the y-intercept

The slope is calculated by:

\(m = \frac{y_2-y_1}{x_2-x_1}\)

We can take any two consecutive pairs in the table to calculate the slope.

Taking first two input-output pairs.

(x1,y1) = (-3, 7)

(x2,y2) = (-2, 5)

Putting the values

\(m = \frac{5-7}{-2+3}\\m= -2\)

Putting the value of m in the general form

\(y = -2x+b\)

To find the value of b, we will put any pair of input-output (x,y) in the equation

Putting the first pair

\(7 = -2(-3) +b\\7 = 6 + b\\b = 7-6\\b = 1\)

Hence,

Value of slope is -2 and y-intercept is 1

9514 1404 393

Answer:

  (-6.5, -5)

Step-by-step explanation:

The first point is weighted by the length of the second segment, and vice versa.

  P = (3A +1B)/(3+1)

  P = (3(-7, -9) +(-5, 7))/4 = (-21-5, -27+7)/4 = (-6.5, -5)

Answer:

The top guy seems correct to me

Step-by-step explanation:

Answer:

The commission rate is 15%

Step-by-step explanation:

commission = commission rate x sales

where the commission rate is expressed as a decimal.

In this case, the salesperson earned a commission of $345 for selling $2,300 in merchandise. Therefore, we have:

345 = commission rate x 2300

To solve for the commission rate, we can divide both sides by 2300:

commission rate = 345/2300

Simplifying this expression, we get:

commission rate = 0.15

So, the commission rate is 15%

Answer:

No

Step-by-step explanation:

if your asking is 10 to the power of 4 is 1000000000000, it is not. 10 to the power of 4 is 10000

Answer:

  11

Step-by-step explanation:

The prime factorization of the given product is ...

  3 × 2^2 × 5 × 11 × 3·5 = 2^2 × 3^2 × 5^2 × 11

The factor required for this to be a perfect square is 11.

_____

Check

3·4·5·11·15 = 9900 ≈ 99.499^2

9900·11 = 108,900 = 330^2 . . . a perfect square number