A group of students worked out the mean and range of their ages. The mean was 12 years and 3 months. The range was 2 years and 7 months. a) What was the mean of the ages of the same group of students exactly one year later? b) What was the range of their ages exactly one year later? Write a sentence to explain each of your answers.

An equation that can be used to determine the angle measure, in degrees, of angle DBC is 67 + n = 90.

The measure of n is equal to 23 degrees.

In Mathematics and Geometry, a complementary angle refers to two (2) angles or arc whose sum is equal to 90 degrees (90°).

By substituting the given parameters into the complementary angle formula, the sum of the angles is given by the following mathematical equation;

∠ABD + ∠DBC = 90

∠ABD + n = 90

67 + n = 90.

n = 90 - 67

n = 23°

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer: 6

Step-by-step explanation:

Therefore, area of the base 'B' of given rectangular prism is equal to 6 in².

Answer:

Step-by-step explanation:

B= area of the triangle 1+area of triangle 2

(1/2*3*1)+(1/2*2*1)

=1.5+1

=2.5

The value of b when the graph of function f(x) = a*bˣ passes through (2,54) and (5,16), is given by, b = 2/3.

Given the function of the graph is,

f(x) = a*bˣ

It is given that the graph of the function passes through the points with coordinates (2, 54) and (5, 16). So this points must satisfy the given function.

Substituting the point (2, 54) in the given function we get,

f(2) = 54

a*b² = 54 ..................... (i)

Substituting the point (5, 16) in the given function we get,

f(5) = 16

a*b⁵ = 16 ..................... (ii)

So dividing equation (ii) by equation (i) we get,

(a*b⁵)/(a*b²) = 16/54

b³ = 8/27

b³ = (2/3)³

b = 2/3

Hence the value of b is 2/3.

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Answer:

the price of each lemon bought by Encik Halim is RM1.45.

Step-by-step explanation:

Encik Halim bought 108 lemons and packed them into packets of 3 lemons each. So he made a total of 108/3 = 36 packets.

Let's assume that the cost of each lemon bought by Encik Halim is x RM.

The total cost of 108 lemons would then be 108x RM.

Encik Halim sold each packet at a price of RM6.80, so the total revenue he earned from selling 36 packets would be 36 x RM6.80 = RM244.80.

We are told that Encik Halim made a profit of RM88.20 from the sale of these packets, so his total cost would be:

Total cost = Total revenue - Profit

Total cost = RM244.80 - RM88.20

Total cost = RM156.60

We know that Encik Halim bought 108 lemons, so we can write:

Total cost = Number of lemons bought x Cost per lemon

RM156.60 = 108x

Therefore, the cost per lemon bought by Encik Halim is:

x = RM156.60/108

x = RM1.45

So the price of each lemon bought by Encik Halim is RM1.45.

Carolyn will need 15 square units of carpet to cover her front room. Carolyn will need 16 units of skirting board to go around the sides of her front room.

To find the area of Carolyn's front room, we need to multiply the length by the width. In this case, the dimensions are given as 5 x 3, so the area is:

Area = length x width = 5 x 3 = 15 square units

To find the perimeter of the room, we need to add up the lengths of all four sides. Since the room is rectangular, opposite sides are of equal length. So, we can find the perimeter by adding twice the length and twice the width, which gives:

Perimeter = 2(length + width) = 2(5 + 3) = 16 units

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The perimeter of rectangle RSTU is 21 cm.

The area of the rectangle RSTU is 27 cm².

A rectangle is a quadrilateral that has opposite side equal to each other and opposite side parallel to each other.

Therefore, let's find the perimeter of the rectangle RSTU and the area of RSTU.

Hence,

Let's find the width of the rectangle MNPQ

14 = 2(4 + w)

14 = 8 + 2w

14 - 8 = 2w

2w = 6

w = 6 / 2

w = 3 cm

Therefore, using similar ratio,

4 / 6 = 3 / RU

cross multiply

4RU = 18

RU = 18 / 4

RU = 4.5 cm

Therefore,

Perimeter of the rectangle RSTU = 2(6 + 4.5)

Perimeter of the rectangle RSTU = 2(10.5)

Perimeter of the rectangle RSTU =21 cm

Area of the rectangle RSTU = 4.5 × 6

Area of the rectangle RSTU = 27 cm²

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Answer:

[tex]x = \frac{(1 + \sqrt{11})( \sqrt{3 } - 1) }{2 } [/tex]

Answer:

The value of the account will be $5,628

Step-by-step explanation:

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have    

substitute in the formula above  

therefore

The value of the account will be $5,628

Given that a₁ = 9 and aₙ = aₙ₋₁ + 2 , we can find the value of a5 by repeatedly applying the recursive formula to find a₂, a₃, a₄, and a₅.Using this method, we get a₅ is 17.

The given sequence is not defined explicitly. However, we can use the recursive formula to find the value of a5.

a₁ = 9 and aₙ = aₙ₋₁ + 2 for n > 1

To find a₂, we use the recursive formula

a₂ = a₁ + 2 = 9 + 2 = 11

To find a₃, we use the recursive formula

a₃ = a₂ + 2 = 11 + 2 = 13

To find a₄, we use the recursive formula

a₄ = a₃ + 2 = 13 + 2 = 15

To find a5, we use the recursive formula

a₅ = a₄ + 2 = 15 + 2 = 17

Therefore, the value of a₅ is 17.

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According to Jean-Claude Maleuvre's book "Museum Memories: History, Technology, Art," Gauguin's views on Polynesian women were complex and contradictory. On the one hand, he was fascinated by their exotic beauty and saw them as a source of artistic inspiration. On the other hand, he objectified and exoticized them, portraying them as primitive and sexually available. Gauguin's depictions of Polynesian women have been criticized as perpetuating colonialist stereotypes and promoting a Westernized gaze.

Answer: To end up due north, the pilot will need to fly the plane 3.382 degrees east of north.

Step-by-step explanation:

don't know how to explain got it form chegg

An appropriate measure of center for the data, and its value include the following: D. The median is the best measure of center, and it equals 19.

In Mathematics and Statistics, a box plot is sometimes referred to as box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

Based on the information provided about the data set, the five-number summary for the given data set include the following:

Minimum (Min) = 12.

First quartile (Q₁) = 17.

Median (Med) = 19.

Third quartile (Q₃) = 20.

Maximum (Max) = 24.

In conclusion, the best measure of center is the median and it is equal to 19.

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Let H: X – Y be a mapping. The set Y is called the codomain of the mapping H: X – Y.

In mathematics, a mapping or function H: X – Y is a relation between two sets, where the set X is called the domain and the set Y is called the codomain.

The mapping H assigns each element in X to a unique element in Y. The codomain of the mapping H is the set Y, which contains all the possible outputs that can be obtained from the mapping.

It represents the range of the mapping H and provides a reference set for the outputs of the function. The actual range of the function may be smaller than the codomain, depending on the elements in X that are mapped to.

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The total amount withdrawn from the account after five years is $24,927.38.

The future value of a series of annual deposits of $2000) can be calculated using the following formula:

FV = [tex]PMT x (((1 + r)^n^-^ 1) / r)[/tex]

where FV = the future value, PMT= the payment amount =  $2000 r =  the interest rate per period = 4% n =  the number of periods = 5

the interest rate and the number of periods are the same.

[tex]FV1 = $2000 x (((1 + 0.04)^5^-^ 1) / 0.04) = $11,025.52[/tex]

This is the amount that the deposits will grow to one year after the last deposit, at an interest rate of 4% per year.

We use compound interest:

FV = [tex]PV x (1 + r)^n[/tex]

we apply this formula with a present value of $11,025.52, an interest rate of 6%, and 4 periods, we get:

FV2 = [tex]$11,025.52 * (1 + 0.06)^4 = $13,901.86[/tex]

Therefore the total amount withdrawn = FV1 + FV2 = $11,025.52 + $13,901.86 = $24,927.38

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Heracio used the computer 2 more hours to do homework than to shop online.

To solve the problem, we need to first calculate the number of hours Heracio spent on each activity:

Videos: 10% of 40 hours = 4 hours

Homework: 20% of 40 hours = 8 hours

Games: 20% of 40 hours = 8 hours

Social media: 25% of 40 hours = 10 hours

Shopping: 15% of 40 hours = 6 hours

To find out how many more hours Heracio used the computer to do homework than shop online, we need to subtract the number of hours spent shopping from the number of hours spent on homework:

8 hours (homework) - 6 hours (shopping) = 2 hours

Therefore, Heracio used the computer 2 more hours to do homework than to shop online.

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Answer: The graph that best represents the number of centimeters the toy car travels in x seconds would be a linear graph with a slope of 12. The equation for this graph would be y = 12x, where y represents the distance traveled in centimeters and x represents the time in seconds.

Step-by-step explanation:

Thee radius of the circle is 3. 696 feet

The formula that is used for calculating or determining the circumference of a circle is expressed as;

C = 2πr

Given that the parameters for the formula are expressed thus;

From the information given, we have that;

Radius = 23.21 feet

Substitute the values, we get;

23.21 = 2× 3.14r

Multiply the values

r = 23.21/6.28

Divide the values

r = 3. 696 feet

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The decimal 15.75 into a percentage is 1575%

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

Decimal = 15.75

This means that

Number = 15.75

Multiply the number by 1

so, we have the following representation

Number = 15.75 * 1

Express 1 as 100%

This gives

Number = 15.75 * 100%

Evaluate the products of 15.75 and 100

So, we have

Number = 1575%

Hence, the percentage is 1575%

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The correct statement is A) that is found by adding the data values and dividing the total by the number of data values

What is meant by adding?

Adding is an operation in which two or more numbers or quantities are combined to obtain a sum. It is represented by the symbol "+" and is one of the four basic arithmetic operations.

What is meant by dividing?

Dividing is an operation that separates a quantity or a number into equal parts or groups. It is represented by the symbol "÷" or "/" and is one of the four basic arithmetic operations.

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The factorization of the polynomial is determined as (x + 6)(x - 2).

The factorization of the polynomial is calculated as follows;

4x² + 10 + x - 50 - x² + 4 + 11x

collecting similar terms, we will have;

3x² + 12x - 36

divide through by 3;

x² + 4x - 12

Factorize the expression as follows;

x² + 6x - 2x - 12

x (x + 6) - 2(x + 6)

(x + 6)(x - 2)

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Answer:

(x+4)(x-9)!!!!!!!!!!!!!!!!!!

1.58 feet of coastline are found per person. To the nearest hundredth, we round to: 1.58 feet of coastline are found per person.

In statistics, the unitary approach is a way towards resolving proportional problems. It entails first determining the value of a single unit of either a statistic, and then applying that knowledge to determine the value of any other required number of units. Consider the scenario where we are aware that 5 bananas cost $2.50. We can employ the unitary technique to calculate the price of seven apples as follows: Determine the price of a single apple: 2.50 ÷ 5 = 0.50 .Divide the price of one banana by the quantity you want of apples. 0.50 × 7 = 3.50 .It follows that 7 bananas would cost $3.50. Additionally, this technique can be applied to more challenging issues requiring numerous ratios and proportions.

given

Divide the total number of feet of coastline by the state's population to get the amount of coastline per person in Oregon:

Total shoreline / Population equals coastline per person.

coastline divided by population (3,800,000) equals 6,000,000 feet.

1.58 feet of coastline are found per person. To the nearest hundredth, we round to: 1.58 feet of coastline are found per person.

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The solution to the given equation is ( 8 , 1 )

Given data ,

To determine whether (8, 1) is a solution to the system, we need to check whether it satisfies both equations:

x - 3y = 5: 8 - 3(1) = 5, which is true

y = x - 7: 1 = 8 - 7, which is true

Since (8, 1) satisfies both equations, it is a solution to the system. Therefore, the correct answer is:

Hence , (8, 1) is a solution to both equations, so it is a solution to the system

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The lateral and total surface area of the prism are 1000 square feet and 1120 square feet.

In this problem we need to determine the lateral and total surface area of a prism with a triangular base. The lateral surface area is the sum of the areas of the three rectangles and the total surface area is the sum of the lateral surface area and the areas of the two triangles.

The area formulas for the triangle and the rectangle are, respectively:

Triangle:

A = s · √[s · (s - a) · (s - b) · (s - c)]

s = 0.5 · (a + b + c)

Where:

Rectangle:

A = w · h

Where:

Now we proceed to determine each surface area:

Lateral surface area:

A = 2 · (20 ft) · (17 ft) + (20 ft) · (16 ft)

A = 1000 ft²

Total surface area:

s = 0.5 · (17 ft + 17 ft + 16 ft)

s = 25 ft

A = √[(25 ft) · (25 ft - 17 ft)² · (25 ft - 16 ft)] + 1000 ft²

A = 1120 ft²

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The mean amount of electricity generated in Texas by wind-powered turbines from 2007 to 2010 is 4,353 megawatts, to the nearest megawatt.

The data for this question can be found in the following table:

Year Electricity Generated (Megawatts)

2007 4,353

2008 7,113

2009 9,403

2010 10,089

To find the mean, we simply add up the values in the table and divide by the number of values, which is 4.

Mean = (4,353 + 7,113 + 9,403 + 10,089) / 4 = 4,353 megawatts

Therefore, the mean amount of electricity generated in Texas by wind-powered turbines from 2007 to 2010 is 4,353 megawatts, to the nearest megawatt.

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B = (715x) / (h^2)

Step 1: Get rid of the denominator by multiplying both sides by h^2

(B)(h^2) = 715x

Step 2: Isolate x by dividing both sides by 715

(Bh^2) / 715 = x

Answer: x = Bh^2 / 715

Hope this helps!

The function that has a greater slope and greater y-intercept than the linear function represented in the table is,

⇒ y = 3x + 7.5

We have to given that;

The table below represents a linear equation.

Now, The equation of line is,

Take two points (- 1, 5) and (1, 9)

⇒ y - 5 = (9 - 5) / (1 + 1) (x + 1)

⇒ y - 5 = 4/2 (x + 1)

⇒ y - 5 = 2 (x+ 1)

⇒ y - 5 = 2x + 2

⇒ y = 2x + 7

Hence, By options,

The function that has a greater slope and greater y-intercept than the linear function represented in the table is,

⇒ y = 3x + 7.5

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Answer:

The answer is 576

Step-by-step explanation:

the formula for a right rectangular prism is L*W*H. We know that the height is 4, and the base is 12^2. Which means that the length and width are both 12. So if ew do 12*12*4 you get 576.