A farmer wants to build a fence around the edge of a field shaped like a right-angled triangle, as shown below. The fence costs £1.26 per metre.
Calculate the total cost of the fence.
Give your answer to the nearest pound.

The distance between the points 3 and 18 is expressed as |3 - 18| and the absolute value of the expression is 15 units.

We are given two numbers 3 and 18 and we are asked to determine the distance between these two points using absolute value.

The distance between two numbers is equal to their difference and distance is always a positive quantity so the absolute value function is used over the distance to prevent a negative distance. The distance between points x and y is given by |x - y|

Put 3 and 18 in |x - y|

|x - y| = |3 - 18| = |-15|

The absolute value function is defined by |x| = x if x ≥ 0 or -x if x < 0

Here, -15 < 0. It can be concluded that |-15| = -(-15) = 15

The distance between the points 3 and 18 is expressed as |3 - 18| and the value of the expression is 15 units.

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It will take a total of 41.68 hours for 1/4 million species of beetles to embark.

A total of 250,000 species will embark (1,000,000/ 4 = 250,000)

Each pair of beetles will occupy 6 cm (one centimeter + space before the next pair). This means the space for all the beetles is 1500000 cm (250000*6 cm)

Now, their speed is 10 cm/per second, so at this speed,  it will take 150000 seconds to pass the bottom of the gang-plank (1500000/ 10) + 50 seconds to go up, which is equal to 150050 seconds. Based on this, let´s find out the time

15005/6 minutes

3001/72 hours

41.68 hours

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The coefficient in the expression is 5.

A coefficient is a numerical value that is multiplied by a variable in an algebraic expression.

In a polynomial expression, coefficients can be the numbers in front of the variables. The coefficient determines the size and direction of the variable's effect on the expression as a whole. For example, in the expression 2x, the coefficient is 2.

Therefore, the coefficient in the expression 10 – 6 + 5n is 5.

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Answer: 5

Step-by-step explanation:

Answer:14 cm

Step-by-step explanation:

Answer:

The power set of a set B = {a, b, c, d, e, f, g} is the set of all possible subsets of B.

In mathematical notation, the power set of B is represented as P(B).

The number of elements in the power set of B is 2^n, where n is the number of elements in B. In this case, n = 7, so the number of elements in P(B) = 2^7 = 128.

The power set of B is:

{{}, {a}, {b}, {c}, {d}, {e}, {f}, {g}, {a, b}, {a, c}, {a, d}, {a, e}, {a, f}, {a, g}, {b, c}, {b, d}, {b, e}, {b, f}, {b, g}, {c, d}, {c, e}, {c, f}, {c, g}, {d, e}, {d, f}, {d, g}, {e, f}, {e, g}, {f, g}, {a, b, c}, {a, b, d}, {a, b, e}, {a, b, f}, {a, b, g}, {a, c, d}, {a, c, e}, {a, c, f}, {a, c, g}, {a, d, e}, {a, d, f}, {a, d, g}, {a, e, f}, {a, e, g}, {a, f, g}, {b, c, d}, {b, c, e}, {b, c, f}, {b, c, g}, {b, d, e}, {b, d, f}, {b, d, g}, {b, e, f}, {b, e, g}, {c, d, e}, {c, d, f}, {c, d, g}, {c, e, f}, {c, e, g}, {d, e, f}, {d, e, g}, {e, f, g}, {a, b, c, d}, {a, b, c, e}, {a, b, c, f}, {a, b, c, g}, {a, b, d, e}, {a, b, d, f}, {a, b, d, g}, {a, b, e, f}, {a, b, e, g}, {a, c, d, e}, {a, c, d, f}, {a, c, d, g}, {a, c, e, f}, {a, c, e, g}, {a, d, e, f}, {a, d, e, g}, {b, c, d, e}, {b, c, d, f}, {b, c, d, g}, {b, c, e, f}, {b, c, e, g}, {b, d, e, f}, {b, d, e, g}, {c, d, e, f}, {c, d, e, g}, {a, b, c, d, e}, {a, b, c, d, f}, {a, b, c, d, g}, {a, b, c, e, f}, {a, b, c, e, g}, {a, b, d, e, f}, {a, b, d, e, g}, {a, c, d, e, f}, {a, c, d, e, g}, {b, c, d, e, f}, {b, c, d, e, g}, {a, b, c, d, e, f}, {a, b, c, d, e, g}​,{a, b, c, d, f, g}​,{a, b, c, e, f, g}​,{a, b, d, e, f, g}​,{a, c, d, e, f, g}​,{b, c, d, e, f, g}​,{a, b, c, d, e, f, g}​}

The reliability of each system can be calculated as follows:

(α) between A and B:

Reliability of A and B functioning together = Probability of both A and B functioning properly = 0.6 * 0.7 = 0.42

(β) between B and C:

Reliability of B and C functioning together = Probability of both B and C functioning properly = 0.7 * 0.8 = 0.56

(γ) between A and C:

Reliability of A and C functioning together = Probability of both A and C functioning properly = 0.6 * 0.8 = 0.48

Note: The calculations are based on the assumption that the components function independently and the failure of one component does not affect the functioning of another component.

The information provided is about the calculation of the reliability of different systems composed of components a, b, c, and d. The reliability is calculated based on the probability of each component functioning properly, which are given as 0.6, 0.7, 0.8, and 0.9 respectively. The reliability of each system (α between A and B, β between B and C, γ between A and C) is calculated as the product of the probabilities of the components composing the system functioning properly.

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Answer:

Step-by-step explanation:               I can't see what there  

The digit in the hundreds place is 4, the digit in the tenth place is 5, and the digit in the thousandth place is 1.

To find the digit in the hundreds place, you can simply divide the number by 100 and look at the hundreds place of the result. In this case, 401.5176 ÷ 100 = 4.015176, so the digit in the hundreds place is 4.

To find the digit in the tenth place, you can look at the first digit to the right of the decimal point. In this case, the digit in the tenth place is 5.

To find the digit in the thousandth place, you can look at the second digit to the right of the decimal point. In this case, the digit in the thousandth place is 1.

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The payment when you lease a new Toyota Corolla is 5935.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

From the information, you lease a new Toyota Corolla, the dealer is offering a 24 month deal where you pay 139 per month and a 2,599 down payment.

The total payment will be:

= 2599 + (139 × 24)

= 2599 + 3336

= 5935

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Complete question

If you lease a new Toyota Corolla, the dealer is offering a 24 month deal where you pay 139 per month and a 2,599 down payment. What is the total payment?

Answer:

The question is meaningless without the definition of the function g(x).

The probability that the selected joint was judged to be defective by inspector B but not by inspector A is 0.0695.

A. i. The probability that the selected joint was judged to be defective by Inspector A is 734/10000 = 0.0734.

ii. The probability that the selected joint was judged to be defective by Inspector B is 742/10000 = 0.0742.

iii. The probability that the selected joint was judged to be defective by Inspector A or B is 954/10000 = 0.0954.

iv. The probability that the selected joint was judged to be defective by both Inspectors A and B is the intersection of their judgments, which can be found by subtracting the defective joints found only by one inspector from the total defective joints found by both inspectors. The probability is (954 - (734 - 742))/10000 = 0.0478.

B. The probability that the selected joint was judged to be defective by neither of the two inspectors is (10000 - 954)/10000 = 0.9046.

C. The probability that the selected joint was judged to be defective by Inspector B but not by Inspector A is 742 - 0.0478 = 695/10000 = 0.0695.

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The only graph that has a function referred to as  many-to-one function  is; Graph A

A many-to-one function is defined as a function that have y-values associated to more than one x-value.

Graphically speaking, if a horizontal line is drawn through the graph, such horizontal line would cross the graph at least twice.

In the graphs, we can see that A is a parabola, and that if a horizontal line is drawn above y = 0, the line will go through the parabola twice. For example, in y = 10 it will cross the parabola at the point (-3, 10) and (3, 10). Therefore, this is a many-to-one graph.

The second graph is a one-to-one graph since there is only one y-value associated to each x-value.

The third graph is not even a function because by definition of function, each element of x should be associated with ONE element of y. In this case, x= 5 and x = 9 are associated to more than one y elements (the vertical lines that form two sides of the square) and therefore is not a function.

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Answer: $81.92

Step-by-step explanation:

First you must convert the 45% to a decimal.

0.45

You must multiply 0.45 by the total cost and then subtract what you get.

Answer: The machine packs 10 sandwiches in 3 minutes, so it packs 10/3 = 3.33 sandwiches per minute.

Step-by-step explanation:

The machine packs 10 sandwiches in 3 minutes, so it packs 10/3 = 3.33 sandwiches per minute.

To pack 100 sandwiches, it would take 100/3.33 = 30 minutes, or 30/60 = 0.5 hours.

Answer:

10:3

100:?

10*10=100

3*10=30

100:30

Step-by-step explanation:

Answer:

33.3%

Step-by-step explanation:

they're charging u 50 more

50 is 1/3 of 150 and 1/3 to percentage form is 33.3%

Answer:

33.3% I think

Step-by-step explanation:

Correct me if I'm wrong

200-150=50

150x33.3%=49.95

49.95+150=195.95

Close enough? nothing else works and 33.4% is over.

Answer:

A) The independent variable is the number of books (b) and the dependent variable is the total amount paid in fees (t).

Step-by-step explanation:

B) The input/output table for this function would be as follows:

b t

1 9

2 13

3 17

4 21

5 25

So some of the ordered pairs of the function are (1, 9), (2, 13), (3, 17), (4, 21) and (5, 25)

C) The domain of the function is discrete because it only includes specific values of b, the number of books. This is the only possible values of b are the natural numbers.

D) The domain of the function is all natural numbers b>=1, since it doesn't make sense for the number of books to be negative or zero. The range of the function is all natural numbers t>=5, since it doesn't make sense for the total amount paid to be negative or zero.

The correctly expresses that algorithm in pseudocode

numFreezing ← 0

numDays ← 0

FOR EACH temp IN temps

IF (temp ≤ 32)

{numFreezing ← numFreezing + 1}

{numDays ← numDays + 1}

DISPLAY(nonfreezing/numDays)

For this situation, Pseudocode B would be appropriate. Two variables are created by this code for the overall number of days (numDays) and the number of freezing days (nonfreezing). Then, it does a loop over the complete collection of data to determine whether each temperature is less than or equal to 32 degrees.

If so, it adds it to nonfreezing; otherwise, it skips the step while still increasing the number of days after each loop by 1. Contrary to answer A, which prints the ratio after each loop iteration, this answer only prints the ratio once the loop has been completed.

numFreezing ← 0

numDays ← 0

FOR EACH temp IN temps

IF (temp ≤ 32)

{numFreezing ← numFreezing + 1}

{numDays ← numDays + 1}

DISPLAY(nonfreezing/numDays)

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The full question:

A programmer for a weather website needs to display the proportion of days with freezing temperatures in a given month.

Their algorithm will operate on a list of temperatures for each day in the month. It must keep track of how many temperatures are below or equal to 32. Once it's done processing the list, it must display the ratio of freezing days over total days.

Which of these correctly expresses that algorithm in pseudocode?

Answer: I believe the answer is 60 square miles.

Step-by-step explanation:
Base = 8, height = 15

A= 15*8/2 = 60

There are two different combinations, these are:

We will use the variables:

x = number of 5¢ stamps used.

y = number of 3¢ stamps used.

z = number of 2¢ stamps used.

We can write this:

x*5 + y*3 + z*2 + 44 = 62

5x + 3y + 2z = 62 - 44

5x + 3y + 2z = 8

There are two ways in which we can do that, these are:

x = 1

y = 1

z = 0

5*1 + 3*y + 2*0 = 8

8 = 8

The other solution is:

x = 0

y = 0

z = 4

5*0 + 3*0 + 2*4 = 8

8 = 8

So there are two different ways.

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The salary after sixth year of employment will be $45918.34. The total compensation after six years are $250914.15.  

The amount raised over a period of time is given by the equation ,

Xₙ = X₀ (1+r)ⁿ

Xₙ is the final amount or number

X₀  is the initial amount or number

r is the rate

n is the number of years or period of time.

Here the annual rise is given as $1200. So we can calculate the rate.

r = 1200/36500 = 0.039

The salary rise during the sixth year, Xₙ = 36500 ×(1+0.039)⁶

                                                     = 45918.34

Total salary in all six years = 36500 + [36500×(1+0.039)¹] + [36500× (1+0.039)²] + [36500× (1+0.039)³] + [36500×( 1+0.039)⁴] +[36500×(1+0.039)⁵] + [36500× (1+0.039)⁶]

 =250914.15

So the 6th year salary is $45918.34 and total compensation for 6 years will be 250914.15.

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Answer:

$32,648

Step-by-step explanation:

1-  find 12% of 37,100         ( 37,100x12= 445,200  445,200/100= $4452)

2-  37,100- 4452= $32,648

(im not sure if its correct

The ordered pairs that are solutions of the given system of equations are:

(a) (0,−4)

The ordered pairs are a numerical value that occupies a specific position in the Cartesian plane, these pairs can have at least two components and these are:

P = (x, y)

First we will write the equations in a more organized way, then we will evaluate each of the pairs and validate that the equality is fulfilled.

[tex]y = -4e^{x}[/tex]

[tex]7x - y = 4[/tex]

(a) (−4,0)

y = -4e⁻⁴

y = -0.0732

Not true since the value of "x" does not make the value of "y" zero.

(b) (0,−4)

y = -4e⁰

y = -4

7(0) - y = 4

0 - y = 4

y = -4

If it complies

(c) (0,−2)

y = -4e⁰

y = -4  This pair is not a solution

(d) (−1,−3)

y = -4e⁻¹

y = -1.47    This pair is not a solution

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The required Number of months with the company recovery is investment and program x are 10.5.

Saving enhances emotions of stability and peace of mind and offers a financial "backstop" for life's uncertainties. Savings can serve as the "seed money" for higher-yielding assets like stocks, bonds, and mutual funds if an appropriate emergency fund has been developed.

This calculation can be used to determine the payback period

Payback of month = [tex]\frac{cost of invesment}{Saving during the year}[/tex] × months in year

= [tex]\frac{35000}{40000}[/tex] × 12

= 10.5 months

Thus, required number of months are 10.5 months.

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Answer:

width = 4.2 units

Step-by-step explanation:

Easy, if the length is 65 units

65 * width = 273

width = 273 / 65

width = 4.2

the answer is 4.2

if you have the lenght and area just divided both in the equation and then you will have the answer

An equation of the lines which pass through the point of intersection of the lines and are respectively parallel and perpendicular to the line 3x + 4y = 0 are as follows;

Parallel: y = -3x + 2.

Perpendicular: y = x/3 - 4/3.

Mathematically, the point-slope form of a line is modeled by this mathematical expression:

y - y₁ = m(x - x₁)

Where:

In order to determine the point of intersection of the lines, we would use an online graphing calculator to graph the given system of equations, and this is given by the ordered pair (1, -1).

Additionally, the slope of the given equation 3x + 4y = 0 in standard form is equal to -3. In Geometry, two (2) lines are parallel under the following conditions:

m₁ = m₂ (m represents the slope.)

At data point (1, -1), an equation of this parallel line can be calculated in point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-1) = -3(x - 1)

y = -3x + 3 - 1

y = -3x + 2.

In Mathematics, a condition that must be met for two lines to be perpendicular is given by:

m₁ × m₂ = -1

-3 × m₂ = -1

m₂ = 1/3

At data point (1, -1), an equation of this perpendicular line in point-slope form is:

y - y₁ = m(x - x₁)

y - (-1) = 1/3(x - 1)

y = x/3 - 1/3 - 1

y = x/3 - 4/3.

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The percent of change from 400 to 600 is 33.34%.

What is Percentage Increase?

It is given that the percent of change is from 400 to 600.

There is an increase from 400 to 600, so the percent of change is an increase.

[tex]\% \text Increase = \frac{\text FV - IV}{FV} \times 100[/tex]

Here, the final value (FV) = 600 and initial value (IV) = 400.

Substituting the given values in the above formula, we get

[tex]\% \text Increase = \frac{600-400}{600} \times 100\\\implies \% \text Increase = \frac{200}{600} \times 100\\\implies \% \text Increase = 33.34 \%[/tex]

Therefore, the percent of change from 400 to 600 is 33.34%.

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Linear inequalities in two variables are mathematical statements involving two variables, such as x and y, that are related to each other by a linear equation.

Variables are symbols or names used in programming or mathematics to represent a value that can change. They are typically used to store data that can be used in calculations, or to control the flow of a program. Variables can be declared and assigned a value, and the value can be changed at any time.

Linear inequalities in two variables are mathematical statements involving two variables, such as x and y, that are related to each other by a linear equation. A linear inequality in two variables is a mathematical statement that can be written in the form “ax + by < c” or “ax + by > c”, where Real numbers a, b, and c, as well as variables x and y, are used.. The inequality can be written in a number of different forms, including slope-intercept form, standard form, and point-slope form.

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The bond which has the most ionic character among the given answer choices as required is; Choice B; Li-F.

By definition, an ionic bond is one in which case, the bond is formed from the combination of highly electronegative and highly electropositive elements.

On this note, since the Lithium atom is the most electropositive metal and the Flourine ion is the most electropositive nonmetal, it follows that the bond which has the most ionic character is; Choice B; Li-F.

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[tex]\stackrel{f(x)}{500(0.97)^x}~~ = ~~\stackrel{g(x)}{20(1.03)^x}\implies \cfrac{500(0.97)^x}{20}=1.03^x\implies 25(0.97)^x=1.03^x \\\\\\ \cfrac{25(0.97)^x}{1.03^x}=1\implies \cfrac{0.97^x}{1.03^x}=\cfrac{1}{25}\implies \left( \cfrac{0.97}{1.03} \right)^x=\cfrac{1}{25}[/tex]

[tex]\log\left[ \left( \cfrac{0.97}{1.03} \right)^x \right]=\log\left( \cfrac{1}{25} \right)\implies x\log\left( \cfrac{0.97}{1.03} \right)=\log\left( \cfrac{1}{25} \right) \\\\\\ x=\cfrac{\log\left( \frac{1}{25} \right)}{\log\left( \frac{0.97}{1.03} \right)}\implies \boxed{x\approx 54}[/tex]