Simplify the following algebraic expression.

Step-by-step explanation:

1. 36g+9-5g=31g+9

2. 12x-4g+4x=16x-4g

3. 15h-6g

4. 2h-6g

5. 60g-20f

Answer:

31g+9, 16x-4g,15h-6g, 2h-6g, 20(3g-f)

Step-by-step explanation:

Q.1  9(4g+1)-5g=36g+9-5g

                =31g+9

Q.2  4(3x-g)+4g=12x-4g+4x

                         =16x-4g

       or 4(4x-g)

Q.3  3(5h-2g)=15h-6g

Q.4   2(h-3g)=2h-6g

Q.5   5(12g-4f)=60g-20f

or                    =20(3g-f)

Answer:

Step-by-step explanation:

The maximum volume of paint that can be stored in the cylindrical tank occurs when it is completely filled. The formula for the volume of a cylinder is:

V = πr^2h

where V is the volume, r is the radius, and h is the height.

In this case, the height of the cylindrical tank is 8 feet and the radius is 3 feet. So we can substitute these values into the formula to get:

V = π(3^2)(8)

V = π(9)(8)

V = 72π

Therefore, the maximum volume of paint that can be stored in the tank is 72π cubic feet, which is approximately 226.2 cubic feet if we round to one decimal place.

The fraction of Year 7 students can be found by dividing y7 by the total number of students, which is 11 times the number of staff members; using the ratio of y8 to y7, we get y7/(11S) = 5/8.

Let's denote the number of staff members as S and the number of students as T. Since the ratio of staff to students is 1:10, we have:

S:T = 1:10

We can rewrite this as S = (1/11)T and T = 11S, where S is the number of staff members and T is the total number of students.

Let's denote the number of Year 7 students as y7 and the number of Year 8 students as y8. Since all students are either in Year 7 or Year 8, we have:

[tex]y7 + y8 = T[/tex]

Substituting T = 11S, we get:

[tex]y7 + y8 = 11S[/tex]

The ratio of y8 to y7 is 3:2, which means that:

[tex]y8:y7 = 3:2[/tex]

We can rewrite this as y8 = (3/5)y7. Substituting this expression into the equation y7 + y8 = 11S, we get:

[tex]y7 + (3/5)y7 = 11S[/tex]

Simplifying, we get:

[tex](8/5)y7 = 11S[/tex]

Dividing both sides by 11S, we get:

[tex]y7/(11S) = 5/8[/tex]

Therefore, the fraction of Year 7 students is 5/8.

The ratio of staff to students is 1:10, so S:T = 1:10, which can be rewritten as S = (1/11)T and T = 11S.

Let y7 and y8 be the number of Year 7 and Year 8 students, respectively. Then y7 + y8 = 11S.

The ratio of y8 to y7 is 3:2, so [tex]y8 = (3/5)y7[/tex].

Substituting [tex]y8 = (3/5)y7[/tex] into [tex]y7 + y8 = 11S[/tex], we get [tex](8/5)y7 = 11S[/tex].

Dividing both sides by 11S, we get [tex]y7/(11S) = 5/8[/tex].

Therefore, the fraction of Year 7 students is 5/8.

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Answer:

To find an appropriate measure of center, we need to determine the typical or central value of the data. There are several measures of center, such as mean, median, and mode.

However, in this case, we need to consider the extreme value of 8, which is significantly lower than the rest of the values. This value may be an outlier, and including it in the calculation of the mean could skew the result.

Therefore, the most appropriate measure of center in this case would be the median, which is the middle value when the data set is ordered.

To find the median, we first need to order the data set:

8, 20, 22, 23, 23, 24

There are six values in the data set, so the median will be the average of the two middle values, which are 22 and 23.

Median = (22 + 23) / 2 = 22.5

Therefore, the most appropriate measure of center for this data set would be the median of 22.5.

Answer:

Step-by-step explanation:where are you ???

The two ships are separating at a rate of 25 knots when the second ship has traveled 90 nautical miles.

To find the rate at which the two ships are separating, we can use the Pythagorean Theorem to find the distance between the two ships at any given time.

The distance between the two ships is the hypotenuse of a right triangle, with one leg being the distance traveled by the first ship and the other leg being the distance traveled by the second ship.

Let d1 be the distance traveled by the first ship and d2 be the distance traveled by the second ship. Then the distance between the two ships is given by:

d = √(d1^2 + d2^2)

Since the first ship is traveling at 20 knots and the second ship is traveling at 15 knots, we can write:

d1 = 20t
d2 = 15t

Substituting these expressions into the equation for the distance between the two ships, we get:

d = √((20t)^2 + (15t)^2)

Simplifying, we get:

d = √(400t^2 + 225t^2)

d = √(625t^2)

d = 25t

So the distance between the two ships is increasing at a rate of 25 knots.

When the second ship has traveled 90 nautical miles, we can find the time t by setting d2 = 90 and solving for t:

15t = 90
t = 6

At this time, the distance between the two ships is:

d = 25t = 25(6) = 150 nautical miles

So, the two ships are separating at a rate of 25 knots when the second ship has traveled 90 nautical miles.

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At the end of 1 year, the amount in the account will be 16443.4. To sum up, compound interest is a type of interest calculated on the initial principal and the accumulated interest of the previous periods.

The formula for calculating compound interest is [tex]A = P (1 + r/n)^nt,[/tex]where A is the future value of the account, P is the principal amount, r is the interest rate, n is the number of times the interest is compounded per year and t is the number of years.In the given case, the principal amount is 15000, the interest rate is 9% per annum and the number of times the interest is compounded is 12. Therefore, the future value of the account at the end of 1 year will be[tex]A = 15000 (1 + (9/100)/12)^12x1 A = 15000 (1 + 0.0075)^12A = 15000 (1.0075)^12 A = 15000 x 1.0956A = 16443.4[/tex]Therefore, at the end of 1 year, the amount in the account will be 16443.4. . In the given case, the future value of the account at the end of 1 year will be 16443.4.Step 1:Calculate the monthly interest rate:Interest rate per month = [tex]9% / 12 = 0.75%[/tex],Step 2:Calculate the total amount at the end of the year:Total amount =[tex]15000 x (1 + 0.75%) ^ 12[/tex] Total amount = 15000 x 1.0975, Total amount =[tex]$16,462.50[/tex]

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The mass of a 6.75 kg bowling ball is equivalent to 67.5 hg, 67.5 dag, 6750 g, 67500 cg, or 6750000 mg.

Mass is a measure of the amount of matter an object contains. The equation used to convert between mass units is:

Mass (m) = Mass (M) × Conversion Factor

For example, if we want to convert 6.75 kg to hg (hectograms), the formula and calculation would be:

m (hg) = M (kg) × 100

m (hg) = 6.75 kg × 100

m (hg) = 67.5 hg

Similarly, we can convert 6.75 kg to dag (decagrams) using the formula:

m (dag) = M (kg) × 10

m (dag) = 6.75 kg × 10

m (dag) = 67.5 dag

To convert 6.75 kg to g (grams), the formula and calculation are:

m (g) = M (kg) × 1000

m (g) = 6.75 kg × 1000

m (g) = 6750 g

We can also convert 6.75 kg to cg (centigrams) using the formula:

m (cg) = M (kg) × 10000

m (cg) = 6.75 kg × 10000

m (cg) = 67500 cg

Finally, to convert 6.75 kg to mg (milligrams), the formula and calculation are:

m (mg) = M (kg) × 1000000

m (mg) = 6.75 kg × 1000000

m (mg) = 6750000 mg

In conclusion, the mass of a 6.75 kg bowling ball can be equivalent to 67.5 hg, 67.5 dag, 6750 g, 67500 cg, or 6750000 mg.

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The probability of flipping a coin and getting tails is 50%.

This is because in a fair coin toss, there is an equal chance of getting heads or tails. This means that the probability of each outcome is 50%.

To prove this experimentally, you flipped the coin 16 times and got heads 7 times. This means that out of the 16 times, you got heads 7 times and tails 9 times. Therefore, the probability of getting tails is 9/16, which is the same as 50%.

In general, the probability of flipping a coin and getting tails is always 50%, no matter how many times the coin is flipped or what the result of previous flips were. This is because each flip of the coin is an independent event and has the same probability of being heads or tails.

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Answer:

102 cubic inches

Step-by-step explanation:

The formula for a volume of a sphere is as follows:

[tex]V = \frac{4\pi r^2}{3}[/tex]

Hence, substituting r=2.9 into this equation,

[tex]\frac{4\pi (2.9)^3}{3}\\\\=\frac{4\pi (24.4)}{3}\\\\=102.160404[/tex]

Hence, the answer is 102 cubic inches.

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The double number line, along with the formula y = 8x + 58, can be used to determine the number of adults needed to supervise a given number of children on a field trip.

The double number line shows the relationship between the number of adults and the number of children they can supervise on a field trip. The table below represents the same relationship:

Adults  Children

8         66

15         99

The formula used to calculate the number of children supervised by a given number of adults is y = 8x + 58, where y is the number of children and x is the number of adults. This formula can be derived by looking at the two points given in the table above. For 8 adults, the corresponding number of children is 66, so 66 = 8x + 58. Solving this equation yields x = 7, which means that 7 adults are needed to supervise 66 children. At 15 adults, the number of children goes up to 99, so 99 = 8x + 58. Solving this equation yields x = 11.25, which means that 11.25 adults are needed to supervise 99 children.

The equation can also be used to calculate the number of adults needed to supervise a given number of children. For example, if the field trip involves 45 children, the equation y = 8x + 58 can be used to calculate the number of adults needed. Substituting 45 for y yields 45 = 8x + 58, which when solved yields x = 5.625. This means that 5.625 adults are needed to supervise 45 children.

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What must be true for the triangles to be similar to each other by SAS is: y = z, and c/f = a/e, where y = z = 50°; c = 4, f = 3; a = 8; e = 6.

SAS stands for "side-angle-side", which means that if two triangles have two pairs of corresponding sides that are proportional in length and the included angles between them are congruent, then the triangles are similar.

Therefore, for the triangles to be similar by SAS, we would have:

y = z, and

c/f = a/e

Assigning values, we would have:

y = z = 50°

c/f = 4/3

a/e = 8/6

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By following the steps outlined below, you can create a payroll payslip that provides all of the necessary information and helps ensure that your employees are paid accurately and on time.

Open Excel and create a new workbook. In the first row, create headings for the different columns you will need, such as "Employee Name," "Employee ID," "Pay Period," "Gross Pay," "Deductions," "Net Pay," and so on.

Enter the employee's name, ID, and pay period in the appropriate cells.

Calculate the employee's gross pay. Gross pay is the total amount of money the employee earned before any deductions are taken out.

Calculate the employee's deductions. Deductions are the amounts that are taken out of the employee's pay, such as taxes, social security, health insurance, and so on.

Calculate the employee's net pay. Net pay is the amount of money the employee receives after all deductions are taken out. To calculate this, subtract the total amount of deductions from the gross pay.

Once you have calculated all of the necessary amounts, enter them into the appropriate cells on the payslip.

Finally, you can customize the payslip by adding your company logo, address, and other relevant information. You can also format the cells to make the payslip look more professional.

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Complete Question:

How do I create a payroll payslip in Excel?

Given that it is not raining, there is a [tex]10.67[/tex]% probability that a man is holding an umbrella, or around [tex]0.1067[/tex].

As probabilistic arguments sometimes produce outcomes that appear contradictory or counterintuitive, probability is usually regarded as one of the most challenging topics of mathematics.

Probability is the likelihood that something will occur or the probability that something will happen. Probability is the measure of how probable it is that a coin will land heads up after being tossed into the air.

To find [tex]P(B|A)[/tex],

[tex]P(B|A) = P(A and B) / P(A)[/tex]

[tex]P(B|A) = P(A|B) * P(B) / P(A)[/tex]

Putting it all together,

[tex]P(A|B) = P(B|A) * P(A) / P(B)[/tex]

[tex]= [P(A|B) * P(B)] / P(A)[/tex]

[tex]= [P(A and B) / P(B)] * P(A) / P(A)[/tex]

[tex]= P(A and B) / P(B)[/tex]

Therefore,

[tex]P(B|A) = P(A and B) / P(A)[/tex]

[tex]= P(A) * P(B|A) / P(B)[/tex]

[tex]= 0.4 * (1 - 0.75) / 0.75[/tex]

[tex]= 0.1067[/tex]

So the probability that a person is carrying an umbrella given that it's not raining is approximately [tex]0.1067[/tex], or about [tex]10.67[/tex]%.

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To find the number of points at which the graph of the function intersects the x-axis, we need to find the roots of the equation:

4x^2 - 9x + 9 = 0

We can use the quadratic formula to find the roots:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = 4, b = -9, and c = 9, so:

x = (-(-9) ± sqrt((-9)^2 - 4(4)(9))) / 2(4)

x = (9 ± sqrt(81 - 144)) / 8

x = (9 ± sqrt(-63)) / 8

Since the discriminant is negative, the roots are complex and the graph does not intersect the x-axis. Therefore, the answer is b. 0.

Answer:

• (0,12)

• (1,6)

• (9,8)  

• (-2,19)

• (8,3)    

Step-by-step explanation:

See the attached graph.

The two inequalities are graphed and the points that are solutions to both equations are all those in the purple area of the graph (the result of the red and blue solutions that overlap [= purple]).  The individual points are added to find which points do, or do not, fall within the solution set of both inequalities:

• (0,12)   Yes

• (-2,0)    No

• (-6,13)    No

• (1,6)      Yes

• (9,8)     Yes

• (-2,19)   Yes

• (8,3)      Yes

• (0,10)     No

The factored form of the quadratic expression 2x² - 9x - 11 is: a. (2x - 11)(x + 1).

To factor the quadratic expression 2x² - 9x - 11, we need to find two binomials that when multiplied together give us the original quadratic expression. Here are the steps to follow:

Step 1: Multiply the coefficient of the x² term (2) and the constant term (-11) to get -22.

Step 2: Find two numbers whose product is -22 and whose sum is the coefficient of the x term (-9). These numbers are -11 and 2.

Step 3: Rewrite the quadratic expression by splitting the x term into -11x + 2x, using the two numbers found in step 2:

2x² - 11x + 2x - 11

Step 4: Group the first two terms and the last two terms together and factor out the greatest common factor (GCF) of each group:

(2x² - 11x) + (2x - 11)

x(2x - 11) + (2x - 11)

Step 5: Factor out the common binomial factor of (2x - 11):

(2x - 11)(x + 1)

The answer is: a. (2x - 11)(x + 1)

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Answer:

• B. True

Step-by-step explanation:

Using trigonometric ratio, the height of kite above the ground is approximately 65.90 feet.

What is trigonometric ratio?

Triangle side length ratios are known as trigonometric ratios. In trigonometry, these ratios show how the ratio of a right triangle's sides to each angle. Sine, cosine, and tangent ratios are the three fundamental trigonometric ratios.

Distance of hand above the ground = 2.5 feet

String length form hand = 150 feet

Angle of elevation = 25°

We can use the sine function of trigonometric ratios to solve this problem.

The formula for sine function is -

sin θ = opposite / hypotenuse

Let's call the height of the kite above the ground "h".

Then we have -

sin (25°) = (h - 2.5) /150

0.42261 = (h - 2.5) /150

(h - 2.5) = 63.392

h = 65.892

Rounding to the nearest hundredth of a foot, we get -

h ≈ 65.90 feet

Therefore, the kite is about 65.90 feet above the ground.

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i) The expression relating price and output assuming it is linear is Price per unit = -20 × Number of units sold + c.

ii) The total cost function, assuming it is linear is 2000 + 10 × Number of units sold.

iii)  The business woman need to produce 114 products to achieve breakeven.

(i) The expression relating price and output assuming it is linear can be written as:

Price per unit = m × Number of units sold + c

where m is the slope of the line and c is the y-intercept.

We can find the slope by using the two points (20, 300) and (13, 440):

m = (440 - 300) / (13 - 20) = 140 / (-7) = -20

So, the expression relating price and output is:

Price per unit = -20 × Number of units sold + c

(ii) The total cost function assuming it is linear can be written as:

Total cost = Fixed cost + Variable cost per unit × Number of units sold

Given that the fixed cost of production is GH₵2,000 with a variable cost per unit of GH¢10, the total cost function can be expressed as:

Total cost = 2000 + 10 × Number of units sold

(iii) To find the level of production at which the business woman will breakeven, we need to find the point at which the total cost equals the total revenue. Since the total revenue is simply the product of the price per unit and the number of units sold, we can set these two equations equal to each other:

Price per unit × Number of units sold = Total cost

Substituting the expressions we found in parts (i) and (ii), we get:

(-20 × Number of units sold + c) × Number of units sold = 2000 + 10 × Number of units sold

Simplifying and solving for the number of units sold, we get:

20 × Number of units sold^2 - 20c × Number of units sold - 2000 = 0

Using the quadratic formula, we get:

Number of units sold = (-(-20c) ± sqrt((-20c)^2 - 4 × 20 × (-2000))) / (2 × 20)

Simplifying, we get:

Number of units sold = (c + sqrt(c^2 + 2000)) / 2

Since we know that the business woman can sell 300 units a day at a price of GH¢20 and 440 units a day at a price of GH¢13, we can set up a system of equations to solve for the y-intercept, c:

-20 × 300 + c = 20c + 2000

-20 × 440 + c = 13c + 2000

Solving this system of equations, we get:

c = 2400/3 ≈ GH₵800

Therefore, the level of production at which the business woman will breakeven is:

Number of units sold = (800 + sqrt(800^2 + 2000)) / 2 ≈ 113.7 units

She should produce at least 114 units to breakeven.

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The equations equivalent to 1/4 (8x + 56) = 20 are

1. 56 + 8x = 80

2.14 = 20 - 8x

4.2x = 6

5. x = 3

An equation is a mathematical expression that shows the relationship between two variables.

Since we have the equation 1/4(8x + 56) = 20, and we want to find all the equations that are equivalent to it, we solve the equation.

So, we proceed as follows.

1/4(8x + 56) = 20

Expanding the brackets, we have

8x/4 + 56/4 = 20

2x + 14 = 20

Subtracting 14 from both sides, we have that

2x = 20 - 14

2x = 6

x = 6/2

x = 3

Also, in 1/4(8x + 56) = 20

Multiplying through by 4, we have that

8x + 56 = 80

2x + 14 = 20

Subtracting 2x from both sides, we have that

14 = 20 - 2x

So, the equations are

1. 56 + 8x = 80

2.14 = 20 - 8x

4.2x = 6

5. x = 3

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Answer:

divide by hundred

Step-by-step explanation:

example :

convert to percentage 300

300÷ 100= 3%

After answering the prοvided questiοn, we can cοnclude that Sο the equatiοn estimated amοunt charged per hοur when the client οrders 80 hοurs οf wοrk is $60.85.

In mathematics, an equatiοn is a statement that implies the unity οf twο traits. An equatiοn cοnsists οf twο sides separated because οf an analytical sοlutiοn (=). Fοr instance, the debate "2x + 3 = 9" asserts that the remark "2x + 3" equals the valuatiοn "9". The gοal οf sοlving equatiοns is tο determine the amοunt οr values οf the variable in the mοdel) that wοuld allοw the equatiοn tο really be true.

Fοrmulae can be simple οr cοmplex, regular οr nοnlinear, and cοntain οne οr mοre variables. Fοr example, in the equatiοn "x² + 2x - 3 = 0," the variable x is elevated tο the secοnd pοwer. Lines are used extensively in mathematics, including algebra, equatiοns, and geοmetry.

Let's start by using the given infοrmatiοn tο set up twο equatiοns:

C(70) = $4900

C(80) = C(70) - ($4/10) * 80

C(80) = C(70) - $32

C(80) = $4900 - $32

C(80) = $4868

$4868 / 80 = $60.85 per hοur

Sο the estimated amοunt charged per hοur when the client οrders 80 hοurs οf wοrk is $60.85.

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The exact value of x is ±8√2. However, since x represents a length, the positive square root is the appropriate solution. Thus, x = 8√2.

A triangle is a two-dimensional geometric shape that is formed by three straight lines or segments that connect three non-collinear points. These points are called the vertices of the triangle, and the line segments are called its sides. The sides of a triangle may be of different lengths and can form different angles with each other.

Let the side of the triangle be AB, and let the perpendicular from C to AB divide AB into segments of length 4 and 16, with the shorter segment adjacent to A. Let the foot of the perpendicular be D. Then, we have:

AC = 4 + 16 = 20 (by the segment addition postulate)

AD = 4 (given)

CD = 16 (given)

By the Pythagorean theorem, we have:

AC² = AD² + CD²

Simplifying and substituting the values we have:

20² = 4² + 16²

400 = 16 + 256

400 = 272 + x² [where x is the height of the perpendicular]

Subtracting 272 from both sides, we get:

128 = x²

Taking the square root of both sides (since x cannot be negative), we get:

x = ±√128

Simplifying:

x = ±8√2

Therefore, the exact value of x is ±8√2. However, since x represents a length, the positive square root is the appropriate solution. Thus, x = 8√2.

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answer: 35.50

explanation; 4.60 x 7 = 32.20

( price for the 7 dvds )

+ 3.30

( video game price )

Answer:

16

Step-by-step explanation:

6q-12=84

    6q=96

      q=16

Answer:

q = 16

Step-by-step explanation:

First Step: Add 12 to both sides. giving you 96.

Second Step: Divide both sides by 6 giving you 16.

Solution: q = 16.

Yes, there is direct relatiοn in amοunt οf dry dοg fοοd and the amοunt οf wet dοg fοοd.

If amοunt οf dry dοg fοοd  is x and the amοunt οf wet dοg fοοd is y then the relatiοn is given as: x = 3y

Tο determine whether the relatiοnship between the amοunt οf dry dοg fοοd and the amοunt οf wet dοg fοοd is prοpοrtiοnal, we need tο check whether the ratiο οf the twο quantities remains cοnstant.

A) yes, there is direct relatiοn in amοunt οf dry dοg fοοd and the amοunt οf wet dοg fοοd. as amοunt οf dry dοg fοοd increases there alsο increase in amοunt οf wet gοοd.

if amοunt οf dry dοg fοοd  is x and the amοunt οf wet dοg fοοd is y then the relatiοn is given as:

x = 3y

fοr example lets take values frοm first rοw

4.5 = 3 × 1.5

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Complete question:

Answer:

25 Hours

Step-by-step explanation:

Answer:

1.92

Step-by-step explanation:

25x  = 36 + 12

25x = 48

x = 1.92

Let's check

25 x 1.92 = 36 + 12

48 = 48

So, 1.92 is the correct answer.