Trundle wheels are used to measure distances along the ground.
The radius of the trundle wheel is 30 cm.
Jim wants to work out the distance between two junctions on a road.
He rolls the trundle wheel between the two junctions.
The trundle wheel rotates exactly 48 times.
Work out the distance between the two junctions.
Give your answer in metres correct to the nearest metre.

Answer:

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

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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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:

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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The matrix formed by performing the row operation 2R₁ + R₂ — R₂ on M will have a new R₂ = [ -8 -1 -3]

A rectangular array of numbers or mathematical objects which are arranged in rows and columns is called a matrix. Each row of a matrix is a horizontal sequence of numbers or objects that are separated by commas and enclosed within square brackets, and it represents a vector in the row space of the matrix.

performing the row operation 2R₁ + R₂ — R₂ on M, we have;

2(-3) + (-2) = -8 {row 2 column 1}

2(-1) + 1 = -1 {row 2 column 2}

2(-4) + 5 = -3 {row 2 column 3}

Therefore, the matrix formed by performing the row operation 2R₁ + R₂ — R₂ on M will have a new R₂ = [ -8 -1 -3]

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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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a) The transition matrix is  [tex]\left[\begin{array}{ccc} 0.3&0.7 \\ 0.6&0.4\end{array}\right][/tex]

b) After two years, brand A is expected to have 40.4% of the market share.

c) Brand A is expected to have 37.5% of the market share.

a) The transition matrix can be constructed using the probabilities provided in the problem. Let P be the matrix where the (i, j)-th entry represents the probability of transitioning from state i to state j. In this case, there are two states: using brand A (state 1) and not using brand A (state 2).

Using the information given in the problem, we can fill in the entries of the matrix as follows:

P = [tex]\left[\begin{array}{ccc} 0.3&0.7 \\ 0.6&0.4\end{array}\right][/tex]

b) To find the percentage of the market share that brand A gets after two years, we need to multiply the initial market share vector (40% for brand A and 60% for other brands) by the transition matrix twice:

| 0.4 0.6 | × P × P = | 0.404 0.596 |

Therefore, after two years, brand A is expected to have 40.4% of the market share.

c) To find the long-run market share for brand A, we need to find the steady-state vector of the transition matrix P. This is the vector π such that:

πP = π

and

π ₁+ π₂ = 1

where π₁ is the long-run probability of being in state 1 (using brand A) and π₂ is the long-run probability of being in state 2 (not using brand A).

Solving the equations above, we get:

π = | 0.375 0.625 |

This means that in the long run, brand A is expected to have 37.5% of the market share.

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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

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.

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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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

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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The measure of length of x of the parallelogram is x = 2.36 units

Given data ,

Let the parallelogram be represented as ABCD

Now , the measure of lengths of the sides are

The measure of AB = 13x - 20

The measure of CD = 2x + 6

The measure of BC = 5x + 4

Opposite sides are parallel

Opposite sides are congruent

So , AB = CD

13x - 20 = 2x + 6

Subtracting 2x on both sides , we get

11x = 26

Divide by 11 on both sides , we get

x = 2.36 units

Hence , the parallelogram is solved and x = 2.36 units

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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.

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 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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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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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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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.

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 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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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

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:

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

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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