5.2. The entrance fee for adults was R50 each and that for children was R20. If the school raised
R31 400 in total, write an equation in x to determine how many adults and how many children
attended the performance. Then solve the equation and write down the number of adults and
(4)
children attended the performance.

Answer:

18 Bowls of Candy

Step-by-step explanation:

Camila has 6 bags of candy, and she can pour 1/3 of a bag into a bowl. To determine how many bowls of candy she can make in total, we need to divide the total amount of candy by the amount of candy per bowl.

Since Camila can pour 1/3 of a bag into a bowl, it means she can make 3 bowls of candy with a full bag.

Now, we can calculate the total number of bowls of candy:

Total bowls of candy = (Number of bags) x (Bowls per bag)

Total bowls of candy = 6 bags x 3 bowls per bag

Total bowls of candy = 18 bowls

Therefore, Camila can make a total of 18 bowls of candy with her 6 bags of candy.

The correct probability that either event will occur is 0.533.

A measure of the likelihood of an event to occur.

P(A or B) = P(A) + P(B).

Probability = Number of favorable outcomes/Total number of outcomes

P(A) = 1/5 = 0.3

P(B) = 1/3 = 0.33

P(A) + P(B) = 1/5 +1/3

                 = 0.533

Probability = 0.533.

Therefore, the probability that either event will occur is 0.533.

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The correct answer is A. a characteristic of the population.

A population parameter refers to a specific characteristic

A population parameter refers to a specific characteristic or numerical value that describes the entire population being studied. It is a fixed value that is typically unknown and estimated using sample data. Examples of population parameters include the population mean, population standard deviation, population proportion, etc.

Answer will be 27.

Given,

3√81

Now, to solve the expression the squares of whole numbers and square roots for some numbers must be known.

For example, squares of

1² = 1

2² = 4

3² = 9

4² = 16

5² = 25

6² = 36

7² = 49

8² = 64

9² = 81
10² = 100

Square roots,

√100 = 10

√81 = 9

√64 = 8

√49 = 7

√36 = 6

√25 = 5

√16 = 4

√9 = 3

√4 = 2

√1 = 1

Now ,

3√81 = 3× 9

= 27.

Thus the value is 27.

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Answer:

Multiply the number of yards by 3. Then multiply the number of feet by 12.

6 yards= 216 inches

8 yards= 288 inches

Step-by-step explanation:

Answer:

The equation for a parabola that opens down, translated to the right 3, and translated down 2 can be written in the standard form as:

y = a(x - h)^2 + k

where (h,k) represents the vertex of the parabola. Since the parabola opens down, the value of 'a' must be negative. The vertex is translated to the right 3 and down 2, so we have:

h = -3 and k = -2

Substituting these values in the standard form equation, we get:

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

This is the equation for a parabola that opens down, translated to the right 3, and translated down 2.

Answer:

Valerie's pay increased by 7.5%.

Step-by-step explanation:

The percent increase in Valerie's pay can be calculated as follows:

Percent increase = ((New pay - Old pay) / Old pay) x 100%

Substituting the given values, we get:

Percent increase = ((15.05 - 14) / 14) x 100%

Percent increase = (1.05 / 14) x 100%

Percent increase = 0.075 x 100%

Percent increase = 7.5%

Step-by-step explanation:

She now gets $1.05 per hour more .....1.05 is what percent of 14.00 ?

$ 1.05/ $ 14  x 100% = 7.5% increase

Based on the supply graph and demand graph shown above, the price at the point of equilibrium is $ 30.

Demand refers to quantity of a commodity that the consumers are willing to, able to purchase at a given price during a given period of time. Supply refers to quantity of a commodity that the producers are willing to, able to offer for sale at a given price during a given period of time.

Demand curve slopes downward due to inverse relationship between price and quantity demanded whereas supply curve slopes upward due to direct relationship between quantity supplied and price. When both demand and supply curve intersect with each other balance is achieved. Intersection point between demand and supply curve is known as equilibrium.

At this point when prices are equal is known as equilibrium price and when quantiy demanded or supplied are equal it is known as equilibrium quantity. When we combine the given graph. Equilibrium is achieved at a point when price is equal to $ 30 and quantity is equal to 20 units.

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Applying the properties of the diagonal of a rectangle, the value of x is calculated as: x = 37.

A rectangle is a quadrilateral that has two equal diagonals which bisect each other, to form equal segment. Rectangle RSTW has two diagonals RT and SW, therefore:

2(RZ) = SW

Given the following:

RZ = 2x + 7

SW = 5x - 23

Plug in the values:

2(2x + 7) = 5x - 23

4x + 14 = 5x - 23

4x - 5x = -14 - 23

x = 37

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The sale price of a pillow originally priced at 12 dollars is given as follows:

$9.

The sale price of a pillow originally priced at 12 dollars is obtained applying the proportions in the context of the problem.

The original price is given as follows:

$12.

The markdown rate for this problem is given as follows:

25%.

Hence the sale price of a pillow originally priced at 12 dollars is given as follows:

0.75 x 12 = $9.

(markdown of 25% means that 75% of the price is paid).

The complete problem is:

"A pillow was marked down at 25%. What is the sale price of a pillow originally priced at 12 dollars?"

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The area of a 135 slice of pizza be,

⇒ 6,782.41 inches²

We have to given that;

Recently they had a lunch special for a Personal Pie with a radius of 4 inches .

Since, WE know that;

Area of circle is,

A = πr²

Where, r is radius of circle

Here, Radius of circle = 4 inches

Hence, Area of pizza is,

⇒ A = 3.14 x 4²

⇒ A = 50.24 inches²

Hence, the area of a 135 slice of pizza be,

⇒ 50.24 × 135

⇒ 6,782.41 inches²

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Let x, xr , xr² be the terms of GP.

After the increase, the terms are : x+xr , xr+xr , xr²+xr

or in simplified manner : x(1+r), 2xr, xr (r+1) .

For these terms to be in Harmonic Progression, their reciprocals should be in Arithmetic Progression .

Thus,

Arithmetic mean of first and last terms should be equal to the middle term.

First term = 1/[x(1+r)] ; Middle term= 1/(2xr) ; Last term = 1/[xr(r+1)]

Assume,

A = Arithmetic mean of first and last term

A= [1/[x(1+r)]+[1/[xr(r+1)] /2

A= (1/2)[(r+1)/(xr(1+r))]

A= (1/2)(1/xr)

A= 1/(2xr)

A = Middle term

Thus, the reciprocals are in AP.

Hence x(1+r), 2xr, xr(r+1) in HP.

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The quadrant of the terminal side for 15) is fourth quadrant.

To change from radians to degrees, you need to the multiple the number of radians by 180/π.

Multiple the number of radians by 180/π.

15) 5 radians = 5 * (180/π)

16) 11π/6 = (11*180)/6 = 330.

19) 3.5 = 3.5*(π/180) degree.

20) 1 = 1*(π/180) degree.

therefore, terminal side for 15) is fourth quadrant.

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Reflect on what led to this situation and identify strategies to prevent it from happening again. This way, you can develop better time management skills and study habits for future assignments and tests.

Stay calm: It's important to remain calm and composed to think clearly and make the best use of your time.

Prioritize: Assess the situation and determine the importance of each task. Focus on completing the task that is past due first.

Communicate: If possible, reach out to your teacher or professor and explain the situation. Apologize for the delay and request an extension or an opportunity to make up the assignment or test.

Allocate time: Allocate dedicated time to work on the overdue task. Break it down into smaller, manageable parts to make it less overwhelming.

Seek help: If you're struggling with the task or need clarification, reach out to classmates, friends, or online resources for assistance. Don't hesitate to ask for help when you need it.

Plan your study time: Make a study schedule for the test that you have tomorrow. Allocate sufficient time for each subject or topic, focusing on areas that require more attention.

Review efficiently: Prioritize the key concepts, formulas, or theories that are likely to be covered in the test. Use active studying techniques such as summarizing, creating flashcards, or teaching the material to someone else.

Take breaks: While it's important to work efficiently, don't forget to take short breaks to rest and recharge. Breaks can help improve focus and prevent burnout.

positive: Maintain a positive mindset and believe in your ability to overcome challenges. Negative thoughts can hinder your productivity and performance.

Learn from the experience: Reflect on what led to this situation and identify strategies to prevent it from happening again. This way, you can develop better time management skills and study habits for future assignments and tests.

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The value of x is equal to 4 units.

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 H is the midpoint of line segment GI, we can logically deduce the following relationship:

Line segment GI = Line segment GH + Line segment HI

Line segment GH = Line segment HI

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

4x - 6 = 2x + 2

4x - 2x = 6 + 2

2x = 8

x = 8/2

x = 4 units.

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Answer:

Perimeter:[tex]4x+10[/tex] feet
Area:[tex]x^{2}+5x+6[/tex] feet

Step-by-step explanation:

The perimeter is equal to 2*width +2*length. The width is x+2 and the length is x+3, therefore the perimeter is equal to 2x+4+2x+6 which equals 4x+10.
The area is equal to width*length
(x+3)(x+2)=[tex]x^{2}+2x+3x+6=x^{2}+5x+6[/tex]

The angles of the triangle with sides 11, 12 and 20 are approximately 117.6 degrees.

We are given that;

The angles of triangle sides are 11, 12 and 20.

Now,

To find the angles of a triangle when its sides are given, we can use the law of cosines. The law of cosines states that c^2 = a^2 + b^2 - 2ab cos©, where a, b, and c are the sides of the triangle and C is the angle opposite to side c.

Using this formula, we can find the angle opposite to side 20 as follows: [tex]cos© = (a^2 + b^2 - c^2) / 2ab cos© = (11^2 + 12^2 - 20^2) / (2 * 11 * 12) cos© = -0.45 C = arccos(-0.45) C[/tex] = 117.6 degrees

Similarly, we can find the other two angles:[tex]cos(A) = (b^2 + c^2 - a^2) / 2bc cos(A) = (12^2 + 20^2 - 11^2) / (2 * 12 * 20) cos(A) = 0.25 A = arccos(0.25) A[/tex] = 75.5 degrees

[tex]cos(B) = (a^2 + c^2 - b^2) / 2ac cos(B) = (11^2 + 20^2 - 12^2) / (2 * 11 * 20) cos(B) = -0.55 B = arccos(-0.55) B[/tex]= 87 degrees

The triangle with sides 11, 12 and 20 are approximately 117.6 degrees, 75.5 degrees, and 87 degrees

Therefore, by the angle the answer will be 117.6 degrees.

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Answer: $45.31

Step-by-step explanation:

10*5*1.5=75

75/27 (formula)=2.77778

2.77778*16.31=45.31

Using calculator, the quadratic regression function that models the data is

f(x) = -290.6x² + 7127.4x - 43447.5.

the profit ≈  582.43

To find the profit for a selling price of $18.75, we substitute x = 18.75 into the equation.

f(18.75) = -147.30(18.75)² + 3231.00(18.75) - 8213.66

= -147.30 x 351.5625 + 60581.25  - 8213.66

=582.43375

f(18.75) ≈ 582.43

Therefore, the profit for a selling price of $18.75 is approximately $ 582.43

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Answer:

6650 cm³

Step-by-step explanation:

area of a circle = π r², where r is the radius

area =  π (46)²

= 2116 π

= 6650 cm³ to 3 significant figures

Answer:

6

Step-by-step explanation:

(3√3)^2/3 = (∛3)²  X ∛(√3)²  

= 3

27^2/3 = (∛27)²

= 3² = 9

9^-1/2 = 1/√9

= 1/3

so the answer is  3 + (9 X 1/3)

= 3 + 3

= 6

The expression to calculate the profit be,

⇒ P(x) = -2x² - 15x + 4,000

To calculate the profit of the company in a month,

we need to subtract the expenses from the revenue.

The profit equation (P) for the company in a month can be represented as,

⇒ P(x) = R(x) - E(x)

Substituting the given revenue and expense equations, we get,

⇒ P(x) = (5,000 - 2x²) - (15x + 1,000)

Simplifying the equation, we get,

⇒ P(x) = -2x² - 15x + 4,000

Therefore,

The profit of the company in a month can be calculated using the above equation,

where x represents the number of units sold or any other relevant variable.

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The surface area of the prism is S = 36 feet²

Given data ,

Let the surface area of the prism be represented as S

Now , the base of the prism is B

where B = l x w

And , length of prism = l and width of prism is = w

The formula for the surface area of a prism is SA=2B+ph, where B, is the area of the base, p represents the perimeter of the base, and h stands for the height of the prism

Surface Area of the prism = 2B + ph

The area of the triangular prism is A = ph + ( 1/2 ) bh

S = 2 ( 1/2 ) ( 3 x 4 ) + ( 4 x 2 ) + ( 3 x 2 ) + ( 5 x 2 )

On simplifying , we get

S = 12 + 8 + 6 + 10

S = 36 feet²

Hence , the surface area is S = 36 feet²

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Answer:

C=62.8

Step-by-step explanation:

1) In the formula C=πd, d represents the diameter, which is 20 inches. All you need to do is apply 20 into the equation and you get C=π20.

2) They said to use 3.14 instead of pi, so we are going to multiply 20*3.14, which is 62.8.

Answer: The value of P(2) is equal to 26

Step-by-step explanation:

To find P(2) for the given polynomial P(x) = -x^3 + 3x^2 + 6, we can use the remainder theorem by dividing the polynomial by (x - 2).

        -x^2 + 5x - 4

__________________________

x - 2 | -x^3 + 3x^2 + 0x + 6

        (x^3 - 2x^2)

        ___________

                5x^2 + 0x

                (5x^2 - 10x)

                ____________

                         10x + 6

                         (10x - 20)

                         __________

                                 26

The quotient is -x^2 + 5x - 4, and the remainder is 26.

Therefore, the value of P(2) is equal to the remainder, which is 26.

While these examples demonstrate some practical applications, divisibility rules are primarily mathematical tools that assist in simplifying calculations, verifying results, and understanding number properties.

Divisibility rules can be applied in various real-life scenarios, particularly in mathematics, finance, and everyday calculations. Here are a few examples:

Checking for even or odd numbers: The divisibility rule for 2 states that a number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8). This rule can be helpful when determining if a given quantity or count is even or odd. For example, in inventory management, you can quickly estimate the number of items in a collection by checking the parity of the count.

Divisibility by 3: The divisibility rule for 3 states that a number is divisible by 3 if the sum of its digits is divisible by 3. This rule can be useful when dealing with numbers or quantities that need to be evenly distributed or divided.

Divisibility by 9: The divisibility rule for 9 states that a number is divisible by 9 if the sum of its digits is divisible by 9. This rule can be applied in various financial calculations, such as checking if a large number is divisible by 9 to verify the accuracy of calculations involving money, invoices, or balances.

Divisibility by 10: The divisibility rule for 10 states that a number is divisible by 10 if its last digit is 0. This rule is often used in practical situations like determining if a given quantity can be divided evenly into groups of 10 or used in financial transactions involving rounding to the nearest multiple of 10.

Checking prime numbers: Divisibility rules can also help in determining whether a number is prime. For example, the rule that states a number is not divisible by any number greater than its square root can be used to quickly eliminate potential factors when checking for primality.

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Rounding up to the nearest cent, the present value that must be invested in the CD now is approximately $3333.34.

To calculate the present value required to have $4500 after 5 years with a simple interest rate of 7.0%, you can use the formula for simple interest:

Present Value = Future Value / (1 + (Interest Rate × Time))

In this case:

Future Value = $4500

Interest Rate = 7.0%

= 0.07

Time = 5 years

Substituting these values into the formula:

Present Value = $4500 / (1 + (0.07 × 5))

Present Value = $4500 / (1 + 0.35)

Present Value = $4500 / 1.35

Present Value ≈ $3333.33

You may use the simple interest calculation to get the present value necessary to have $4500 after five years with a simple interest rate of 7.0%:

Future Value / (1 + (Interest Rate Time)) = Present Value

In this instance

$4500 is the future value.

Rate of Interest = 7.0% = 0.07

t = 5 years

Substituting these values into the formula:

$4500 / (1 + (0.07 5)) = Present Value

$4500 / (1 + 0.35) equals the present value.

Present Value = $4500 / 1.35

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The present value that must be invested now in order to have $4500 for a home-entertainment center in 5 years at an interest rate of 7.0% is approximately $3333.33

Using the formula for calculating the future value of a single sum:

Future Value (FV) = Present Value (PV) + (PV * Interest Rate * Time)

We rearrange the formula to solve for the present value (PV):

PV = FV / (1 + Interest Rate * Time)

Plugging in the given values:

FV = $4500

Interest Rate = 7.0% = 0.07

Time = 5 years

PV = $4500 / (1 + 0.07 * 5)

PV = $4500 / (1 + 0.35)

PV = $4500 / 1.35

PV ≈ $3333.33

Therefore, the present value that must be invested now in order to have $4500 for a home-entertainment center in 5 years at an interest rate of 7.0% is approximately $3333.33 (rounded up to the nearest cent).

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Answer:

Step-by-step explanation:

See image below

Given statement solution is :- The average hotel room cost in 2012 would be $199.97, none of the provided options are correct.

To calculate the average hotel room cost in 2012, we can use the formula:

y = a(1 + r)^t

where:

y = future value (cost in 2012)

a = initial value (cost in 1980)

r = annual growth rate (5.1% or 0.051)

t = number of years (2012 - 1980 = 32)

Substituting the given values into the formula, we have:

y = $48.00(1 + 0.051)^32

Calculating the value:

y ≈ $48.00(1.051)^32

y ≈ $48.00(2.718282)^0.051(32)

y ≈ $48.00(2.718282)^1.632

y ≈ $48.00 * 4.171331

y ≈ $199.97

Rounding to the nearest cent, the average hotel room cost in 2012 would be $199.97.

Therefore, none of the provided options are correct.

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If Erin had 150m/ of buttermilk and recipe require 0.25 cups of buttermilk. Erin would  have enough buttermilk for the recipe (2).

1.2. Convert the units of measurement to a common unit.

Erin has:

150 ml of buttermilk

Recipe requires 0.25 cups of buttermilk.

1 cup=  236.59 ml

So,

0.25 cups = 0.25 * 236.59 = 59.15 ml

Therefore Erin has enough buttermilk for the recipe.

1.3. The cake recipe calls for the following ingredients:

0.8 kg of flour

650 g of sugar

900,000 mg of butter

Simplify the units by converting them to a common unit

0.8 kg = 0.8 * 1000 g = 800 g

650 g = 650 g (no conversion needed)

900,000 mg = 900,000 mg / 1000 = 900 g

Therefore the required amounts of the ingredients are: 800 g of flour, 650 g of sugar, 900 g of butter.

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