4+2(2-x)=3-2(5-x)


x ??​

The numbers sentence has an interpretation of  the square of a number n is added to 5

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

n² + 5​

The above sentence means that

The square of a number n is added to 5

Also, in the numbers sentence;

The variable is n

Hence, the interpretation is  the square of a number n is added to 5

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The 20th term of the sequence A(n) = [tex]4n^3 - 3[/tex]is 31997.

A sequence is an ordered set of numbers that is often produced using a formula or rule.

Terms refer to the individual numbers in a series. One infinite series of odd integers is the sequence 1, 3, 5, 7, 9,..., where each term is created by adding 2 to the term before it.

To find the 20th term of A(n) = 4n^3 - 3, we can substitute n = 20 into the equation:

[tex]A(20) = 4(20)^3 - 3[/tex]

[tex]= 4(8000) - 3[/tex]

[tex]= 32000 - 3[/tex]

[tex]= 31997[/tex]

Therefore, the 20th term of the sequence A(n) = [tex]4n^3 - 3[/tex]is 31997.

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Answer: 50

Step-by-step explanation:

Divide the amount of granola bars by 800

800dividedby16=50

Step-by-step explanation:

If A and B refuse to travel without each other, then we can treat them as a single unit. So, we only need to choose 4 people from the remaining 18. The total number of ways to do this is:

${18 \choose 4} = \frac{18!}{4!14!} = 3060$

Therefore, there are 3060 ways to choose 5 people from a group of 20 if A and B refuse to travel without each other.

Answer:

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According to given table the amount of monthly payment per $100, when APR is 11.5% and duration of loan 15 years is the intersection of the thrid row and first column. It is 1.168.

Find the amount of monthly payment by dividing the loan amount by 100 and multiplying by the amount mentioned above:

Threfore the montly payment amount is $182.68.

The answer of the given question based on hypothesis is ,(a)  the number of family is the sample size of 400 satisfies this requirement. (b) that the sample size should be sufficiently large.

In mathematics, a hypothesis is  statement or proposition that is assumed to be true for sake of argument or investigation, but has not been proven or demonstrated to be true. It is an educated guess or prediction that is based on previous observations or knowledge, and is used to guide further investigation or experimentation.

The other requirement that we need to meet to perform the hypothesis testing is that the sample size should be sufficiently large. A general rule of thumb is that the sample size should be at least 10 times larger than the number of successes and 10 times larger than the number of failures.

In this case, since we have 228 successes (families who want a condominium) and 172 failures (families who do not want a condominium), the sample size of 400 satisfies this requirement.

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The graph of the composition of functions is on the image at the end.

Here we want to graph the composition of the functions g(x) and f(x), where:

f(x) = -2x - 5

g(x) = x - 1

The composition:

g(f(x)) will give:

g(f(x)) = f(x) - 1 = -2x - 5 - 1 = -2x - 6

So it is just a linear function, basically it is a translation of 1 unit down of f(X), the graph of this composition is on the image at the end.

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using 12 mm marbles would be more cost-effective, with a total cost of $360 compared to $810 for 9 mm marbles.

How to solve?

To calculate the number of marbles needed per vase, we first need to calculate the volume of each vase. The volume of a cylinder can be calculated using the formula V = πr²2h, where r is the radius and h is the height.

V = π(6 cm)²2(28 cm) / 2 = 3,758.76 cm²3

Since Janine intends to fill each vase halfway, the volume of water needed per vase would be:

V_water = 3,758.76 cm²3 / 2 = 1,879.38 cm²3

To calculate the volume of marbles needed per vase, we can subtract the volume of water from the total volume of the vase:

V_marbles = 3,758.76 cm²3 - 1,879.38 cm²3 = 1,879.38 cm²3

We can now calculate the number of marbles needed per vase based on the size of the marbles:

For 9 mm marbles:

The radius is 0.9 cm (9 mm / 10)

The volume of one marble can be calculated using the formula V = (4/3)πr²3

V_marble = (4/3)π(0.9 cm)²3 ≈ 2.138 cm²3

Number of marbles needed = V_marbles / V_marble = 879.38 cm^3 / 2.138 cm²3 ≈ 826 marbles

Total cost = 30 tables × $3/bag × 9 bags = $810

For 12 mm marbles:

The radius is 1.2 cm (12 mm / 10)

The volume of one marble can be calculated using the formula V = (4/3)πr²3

V_marble = (4/3)π(1.2 cm)²3 ≈ 7.238 cm²3

Number of marbles needed = V_marbles / V_marble = 1,879.38 cm²3 / 7.238 cm²3 ≈ 260 marbles

Total cost = 30 tables × $4/bag × 3 bags = $360

Therefore, using 12 mm marbles would be more cost-effective, with a total cost of $360 compared to $810 for 9 mm marbles.

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Converting the sum to a percentage, we find that the sum of 2.3%, 3/4 and 0.01 equals 78.3%.

The first step is to add the numbers:

After the sum, we can convert this decimal to a percentage by multiplying by 100:

Therefore, to convert a sum of different units to a percentage, we need to first convert all the values to a common unit, then add them together, and finally multiply the sum by 100 to express it as a percentage. In this particular case, we converted the fraction 3/4 to a decimal, added all three values together, and then multiplied the result by 100 to obtain the answer of 78.3%.

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The purpose of headings in a table is option A. To help users understand the categories of information found in each column and row

A table is a method of classifying a given set of information into appropriate number of columns with respect to their individual class called headings.

Headings are used in the categorization of a set of information into a presentable form of columns called a table. It thus helps to identify a the source of an information as presented in the table.

Therefore, the purpose of headings in a table is that given in option A. That is; To help users understand the categories of information found in each column and row.

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22 inches is the measure of the unknown side ZW

Given a parallelogram WXYZ, since the opposite sides of a parallelogram is equal, hence WX = YZ

Given the following

WX = 8x + 2

YZ = 5x + 11

Substitute

8x + 2 = 5x + 11

8x - 5x = 11 - 2

3x = 9

x = 3

Determine the measure of ZW

ZW = XY = 6x + 4

ZW = 6(3) + 4

ZW = 18 + 4

ZW = 22

Hence the measure of the side ZW is 22 inches

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The value of the expression is 12.6.

Given is an expression, (12 × 1) + (1 × 6/10), we need to simplify it,

(12 × 1) + (1 × 6/10)

= 12 + 6/10

= 126 / 10

= 12.6

Hence, the value of the expression is 12.6.

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The total revenue over the project life of 3 years is $10,500, the total costs over the project life of 3 years is 111,750 birr and Net benefit of the project is  $4,107

The annual value of exports is $3,500.

Therefore, the total revenue over the project life of 3 years is 3 × $3,500 = $10,500.

The cost of investment has foreign components of $1,200, which is equivalent to 21,000 birr (1,200 × 17.5).

The non traded component of the cost of investment is 7,500 birr.

The total cost of investment is therefore 21,000 + 7,500 = 28,500 birr.

The annual cost of traded inputs is $900, which is equivalent to 15,750 birr (900 × 17.5).

The total cost of traded inputs over the project life of 3 years is 3 × 15,750 = 47,250 birr.

The annual cost of non traded inputs is 12,000 birr.

The total cost of non traded inputs over the project life of 3 years is 3 × 12,000 = 36,000 birr.

Therefore, the total costs over the project life of 3 years is 28,500 + 47,250 + 36,000 = 111,750 birr.

Net benefit = Total revenue - Total costs

= $10,500 - (111,750 ÷ 17.5)

= $10,500 - 6,393

= $4,107

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Answer:

The sequence is increasing by 5 at each step. So, we can write:

a1 = 30

a2 = 30 + 5 = 35

a3 = 30 + 25 = 40

a4 = 30 + 35 = 45

a5 = 30 + 4*5 = 50

We notice that the nth term is given by:

an = 30 + (n-1)5

So, the explicit formula for the nth term is:

an = 25n + 5

My scores were near the median for my team and my MAD was low.

Using multiplication, the total length of all the sunflowers in the garden is 1,260 inches.

Multiplication is one of the four basic mathematical operations, including addition, subtraction, and division.

Multiplication operation involves the multiplicand, the multiplier, and the product.

The total number of sunflowers in the garden = 210

The length of each sunflower = 6 inches

The total length of all the sunflowers = 1,260 inches (210 x 6)

Thus, based on multiplication operation, the total length of the sunflowers in the garden can be stated to be 1,260 inches.

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Assume that each sunflower measures 6 inches in length and there are 210 sunflowers in the garden.

In market 1, the quantity demanded will increase by 2.5% while in market 2, the quantity demanded will increase by 25%.

% Change in Quantity Demanded (Market 1) = (-) 0.25 * (-10%) = 2.5%

% Change in Quantity Demanded (Market 2) = (-) 2.5 * (-10%) = 25%

The negative sign for price elasticity of demand means that demand is inversely related to price.

For market 1:

Price = GH¢ 2

Quantity demanded = Q1

Change in price = -10% x GH¢ 2 = -GH¢ 0.20

Change in quantity demanded = 2.5% x Q1

Change in revenue = GH¢ 2.00 x 2.5% x Q1 = GH¢ 0.05 Q1

Marginal revenue = Change in revenue / Change in quantity demanded

Marginal revenue = (GH¢ 0.05 Q1) / (2.5% x Q1)

Marginal revenue = GH¢ 2.00

For market 2:

Price = GH¢ 1.50

Quantity demanded = Q2

Change in price = -10% x GH¢ 1.50 = -GH¢ 0.15

Change in quantity demanded = 25% x Q2

Change in revenue = GH¢ 1.50 x 25% x Q2 = GH¢ 0.375 Q2

Marginal revenue = Change in revenue / Change in quantity demanded

Marginal revenue = (GH¢ 0.375 Q2) / (25% x Q2)

Marginal revenue = GH¢ 1.50

iii. An alternative pricing strategy for the Kenkey seller could be to implement a tiered pricing system based on the price elasticity of demand in each market.

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Answer:

a) 29.0%

b) 25.2%

Step-by-step explanation:

denote T: total number of MM; G: green MM; R: red MM

a)

(G)/(T) * (G-1)/(T-1)

(32)/(27+32) * (32-1)/(27+32-1)

=(32/59) *(31/58)

=0.289888953

b)

(R)/(T) * (G)/(T-1)

(27)/(27+32) * (32)/(27+32-1)

=(27/59) * (32/58)

=0.252483927

The mean is equal to 17.8125.

The median is equal to 20.85.

The standard deviation is equal to 61.6386.

In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:

Mean = [F(x)]/n

25.8, 6.4, 21.4, 24, 3.2, 18.3, 20.3, 23.1

For the total number of data, we have;

Total, F(x) = 25.8 + 6.4 + 21.4 + 24 + 3.2 + 18.3 + 20.3 + 23.1​

Total, F(x) = 142.5

Mean = 142.5/8

Mean = 17.8125.

For the median, we have;

By sorting from least to greatest 3.2,6.4,18.3,20.3,21.4,23.1,24,25.8

Median = (20.3 + 21.4)/2

Median = 20.85

For the standard deviation, we have;

Standard deviation, S = √(1/n × ∑(xi - u₁)²)

Standard deviation, S = √(1/8 × (25.8 - 17.8125)² ..... + (23.1 - 17.8125)²)

Standard deviation, S = 493.10875/8

Standard deviation, S = 61.6386

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The distance from Point A to the directrix can be found to be 6.

For any point on a parabola, the distance to the focus is equal to the distance to the directrix. This property is what defines a parabola. This is the relationship between the distance from a point on a parabola to the focus and the distance from that point to the directrix.

So, if the distance between Point A on the parabola and the focus is 6, then the distance from Point A to the directrix is also 6.

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The speed of the plane in still air is 400 miles per hour and the speed of the wind is 100 miles per hour.

What is speed?

Speed is a measure of how quickly something moves or the distance covered per unit of time.

Let's assume that the speed of the plane in still air is denoted by "p" (in miles per hour) and the speed of the wind is denoted by "w" (in miles per hour).

When the plane flew into the wind, it was flying against the wind resistance which reduced its ground speed. Let's assume that the wind was blowing with a speed of "w" (in miles per hour) during the flight. Then the speed of the plane relative to the ground (i.e. ground speed) would be:

p - w

Similarly, when the plane was flying with the wind on its way back, the ground speed would be:

p + w

Now, we can use the given information to set up two equations:

Distance = Speed x Time

For the first part of the trip (against the wind), the equation becomes:

1500 = (p - w) x 5

Simplifying this equation, we get:

p - w = 300 (Equation 1)

For the second part of the trip (with the wind), the equation becomes:

1500 = (p + w) x 3

Simplifying this equation, we get:

p + w = 500 (Equation 2)

Now we have two equations with two variables. We can solve for "p" and "w" by adding Equations 1 and 2:

2p = 800

p = 400

Substituting this value of "p" into Equation 2, we get:

400 + w = 500

w = 100

Therefore, the speed of the plane in still air is 400 miles per hour and the speed of the wind is 100 miles per hour.

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The average rate of change of the function on the interval [0,3] is given as follows:

A. 7/3.

The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function. Hence we must identify the change in the output, the change in the input, and then divide then to obtain the average rate of change.

The numeric values for the function are given as follows:

Hence the average rate of change is given as follows:

r = (8 - 1)/(3 - 0)

r = 7/3.

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Answer: The estimated mean mathematics test score for the students is 685.7.

Step-by-step explanation: To estimate the mean mathematics test score, we can use the midpoint of each data class and the formula for calculating the weighted mean:

Midpoint of 550-599 class = (550 + 599) / 2 = 574.5

Midpoint of 600-649 class = (600 + 649) / 2 = 624.5

Midpoint of 650-699 class = (650 + 699) / 2 = 674.5

Midpoint of 700-749 class = (700 + 749) / 2 = 724.5

Midpoint of 750-799 class = (750 + 799) / 2 = 774.5

Weighted mean = (frequency of 550-599 class * midpoint of 550-599 class + frequency of 600-649 class * midpoint of 600-649 class + frequency of 650-699 class * midpoint of 650-699 class + frequency of 700-749 class * midpoint of 700-749 class + frequency of 750-799 class * midpoint of 750-799 class) / (total frequency)

Weighted mean = (6 * 574.5 + 10 * 624.5 + 15 * 674.5 + 12 * 724.5 + 8 * 774.5) / (6 + 10 + 15 + 12 + 8)

Weighted mean = 685.7 (rounded to one decimal place)

Therefore, the estimated mean mathematics test score for the students is 685.7

The supplier offering 2.00 a bag for 500 ml is offering the best price. This is because the cost per bag is lower than the cost of the 10000 ml bag, and the total cost for the hospital is significantly lower.

IV fluid is a sterile solution usually composed of water and electrolytes. It is administered intravenously, meaning it is delivered directly into a vein using a syringe or an IV bag.

To calculate this, divide the cost of the 10000 ml bag by the number of 500 ml bags it contains.

This can be done by dividing 64.20 by 20,i.e.,

64.20/20= 3.21

This means that the cost of one 500 ml bag is 3.21.

This is significantly lower than the 2.00 per bag offered by the other supplier.

To figure out the total cost for the hospital, multiply the number of bags needed by the cost per bag.

For the hospital, 10000 ml of IV fluid is used each month, so the number of bags needed would be 20.

Multiplying 20 by 2.00, 20*2= 40, gives a total cost of 40.00 per month. This is significantly lower than the cost of the 10000 ml bag at 64.20.

Therefore, the supplier offering 2.00 a bag for 500 ml is offering the best price.

This is because the cost per bag is lower than the cost of the 10000 ml bag, and the total cost for the hospital is significantly lower.

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The required function that describes the area A in terms of x is:

C.) A(x) = 2x² + 9x + 4

The area of a rectangle is given by the formula:

A = length x width

In this case, the length is x+4 feet and the width is 2x+1 feet. So, we have:

A = (x+4)(2x+1)

Expanding the expression on the right side, we get:

A = 2x² + 9x + 4

Thus, the function that describes the area A in terms of x is:

C.) A(x) = 2x² + 9x + 4

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The center of this circle is (0, 0) and the radius is 4 units

The equation x^2 + y^2 = 16 represents a circle centered at the origin (0, 0), since the x-coordinate and y-coordinate terms are squared and added together.

The center of the circle is therefore (0, 0), which we can plot on the graph

The radius of the circle is the square root of the constant term on the right-hand side of the equation,

Which in this case is 16.

So the radius is 4.

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