Peni needs $1.20 daily for bus
fares, 50 cents daily to spend at the school canteen and $1.00 per day for newspaper.​

Step-by-step explanation:

y-b=m(x-a)

y--8=1/4(x-6)

y+8=1/4(x-6)

4y+32=1(x-6)

4y+32=x-6

4y=x-38

y=1/4x-38/4

or -x+4y+38=0

or -×+4y= -38

Part (i)

Answer:  m/n

--------------------

Explanation:

You divide the total bill over the number of people at the dinner. This leads to the quotient and the amount each person pays (each person pays the same amount).

====================================================

Part (ii)

Answer:  80 dollars

--------------------

Explanation:

Plug in m = 400 and n = 5 to get

m/n = 400/5 = 80

====================================================

Part (iii)

Answer:  m = 7x

--------------------

Explanation:

x = m/n

x = m/7

7x = m ... multiply both sides by 7

m = 7x

The total bill is 7 times of what each person paid.

====================================================

Part (iv)

Answer:  7 people

--------------------

Explanation:

x = 20 is the amount each person paid

m = 140 is the total bill

n = number of people who went to dinner

x = m/n

20 = 140/n

20n = 140 ..... multiply both sides by n

n = 140/20 ..... divide both sides by 20

n = 7

Seven friends went to do dinner, splitting a $140 bill, paying $20 each

Answer:

m/n; $80; 7*x; 7 friends

Step-by-step explanation:

(I) $x=$m/n

(II) $x=400/5=$80

(III) $m=7*x

(IV) n=140/20=7

Answer:

21.16 m^2

Step-by-step explanation:

perimeter of square=4l

18.4/4=l

4.6=l

area of square=l^2

=4.6^2

=21.16 m^2

Answer:

10 miles

Step-by-step explanation:

The information given forms a right angled triangle ; hence, we can use Pythagoras rule to solve for the distance, x

Recall:

Hypotenus = sqrt(opposite ² + adjacent ²)

Hypotenus = x

Therefore,

x = sqrt(6² + 8²)

x = sqrt(36 + 64)

x = sqrt(100)

x = 10

Distance between tween my friends house and my house = 10 miles

The translated shape would have the vertices of :

Geometry employs translation to move a figure from a certain location to another while retaining its shape, size, and orientation. All points on the initial object are shifted equidistant in a unified direction. A vector showcases the magnitude and course of the movement.

The vectors of the original shape are:

U ( - 2 , 0 )

S ( -5 , - 4 )

T ( - 5, - 1 )

The translated vectors would be:

U' ( - 2 + 5, 0 + 5) = (3, 5)

S' ( -5 + 5, -4 + 5) = (0, 1)

T' ( -5 + 5, -1 + 5 ) = (0, 4)

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Answer:

3.5/100*8=.28

Step-by-step explanation:

Prior to placing an order to buy ABCD stock at a lower price, the investment adviser must conduct thorough research and analysis, set a target price, and determine an appropriate entry point for the purchase.

The investment adviser's primary responsibility is to act in the best interest of their client and make informed investment decisions. In this case, where the adviser believes ABCD stock is appropriate only if the price falls to $35 per share, several steps need to be taken before placing an order.

Firstly, the adviser should conduct comprehensive research on ABCD stock to understand its historical performance, financial health, industry trends, and any relevant news or events that might impact its future prospects. This research will help validate the adviser's belief that the stock is worth considering at a lower price.

Secondly, the adviser should establish a target price of $35 per share based on their analysis and the client's investment objectives. This target price serves as a reference point and provides a clear criterion for initiating the purchase.

Lastly, the adviser needs to identify an appropriate entry point for the purchase. This involves monitoring the stock's price movements and market conditions closely. The adviser may choose to set a limit order at $35 per share or implement a strategy to take advantage of potential price declines, such as dollar-cost averaging.

By following these steps, the investment adviser ensures that they have thoroughly evaluated the investment opportunity and have a plan in place before placing an order to buy ABCD stock for the client's account.

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The inverse of the bus-admittance matrix is the bus-impedance matrix.

What is a bus-impedance matrix?

The bus impedance matrix is a square matrix that represents the electrical circuit that connects the network nodes.

The values of this matrix are the impedances of the branches that join the nodes, and they are known as self-impedance (diagonal elements) and mutual impedance (non-diagonal elements).

What is the difference between the bus impedance matrix and the bus admittance matrix?

The difference between the bus impedance matrix and the bus admittance matrix is that the bus impedance matrix has all the elements non-zero, while the bus admittance matrix has most of the elements zero.

In power systems, the bus impedance matrix is preferable over the bus admittance matrix since the former is a dense matrix while the latter is a sparse matrix.

Hence, the computational cost required for carrying out power flow analysis using the bus impedance matrix is lower as compared to the bus admittance matrix.

The Jacobian matrix is a square matrix that represents the derivatives of a vector function with respect to another vector. It is used for performing Newton Raphson power flow analysis.

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Answer:

c: triangle ABC is congruent to DEF

Step-by-step explanation:

find the triangle with the same side lengths and angle measurements to the given triangle.

The true statement is DEF= ABC

Thus, option (C) is correct.

As, per the figure Triangle DEF.

<DFE= 23

<DEF = 67

<EDF = 90

ED= 5 unit

EF = 13 unit

DF = 12 unit

Now, to find the congruent triangle to DEF.

Look for the triangle which same angles and sides as triangle DEF.

So, In Triangle ABC.

<CBA= 23

<CBA = 67

<BAC = 90

AB= 5 unit

CB= 13 unit

CA= 12 unit

Therefore, the statement is DEF= ABC

Thus, option (C) is correct.

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Answer:

a) Revenue function = 1.299r + 1.379p

where: r = gallon of unleaded regular gasoline and p = gallon of regular unleaded premium gasoline

b) cost function = 1.219f + 1.289p

c) profit function = (1.299r + 1.379p) - (1.219f + 1.289p) = 1.299r - 1.219r + 1.379p - 1.289p = 0.08p + 0.09p

d) total profit = (0.08 x 100,000) + (0.09 x 40,000) = $8,000 + $3,600 = $11,600

Answer:

nonlinear

Step-by-step explanation:

sorry if im wrong

Answer:

Linear

Have a great day! :)

Since none of the 13 classmates had been given math homework between the original survey and Kelly's second survey, the sum of the values in the second data set is the same as the sum of the values in the original data set. Therefore, the change in the means can be determined without calculating the mean of either data set by considering the number of data points in each set.

Since both data sets have the same number of data points, the change in the means will be zero. This is because the mean is calculated by dividing the sum of the values by the number of data points, and since the sum of the values is the same in both data sets, the means will also be the same.

In other words, if the mean of the first data set is x, then the sum of the values in the first data set is 13x (since there are 13 classmates), and the sum of the values in the second data set is also 13x (since none of the values have changed). Therefore, the mean of the second data set will also be x, and the change in the means will be zero.

Answer: D

Step-by-step explanation:

20 x 2= 40

5/8 of 20 is 12.5

40+12.5= 52.5 or 52 1/2

Sorry I’m terrible at explaining

Answer:

LA = 720 , SA = 780

Step-by-step explanation:

find the missing length of the triangle using Pythagoras then use this value (8) to find the surface area of the sides and the triangle.Add up the values.

Answer:

Step-by-step explanation:

To find the lateral surface area of triangular prism, first we need to know the three sides of the triangle. Here, one side is missing and we have to find that using Pythagorean theorem. Let the unknow side of the triangle be 'c'

Pythagorean theorem,

15² + c² = 17²

225 + c² = 289

         c² = 289 - 225

         c² = 64 = 8*8

c = 8 in

a = 17 in & b = 15 in & h = 18 in

\(\boxed { \text{Lateral surface area = (a + b + c)*h }}\)

                                = ( 17 + 15  + 8 ) * 18

                                = 40 * 18

                                = 720 in²

\(\boxed { \text{total surface area = LSA + 2* area of base triangles}}\)

\(\text{ area of base triangles = 2* $ \dfrac{1}{2}*base*height $}\)

                                  = base * height

                                  = 8 * 15

                                   = 120 in²

Total surface area = 720 + 120

                                = 840 in²

Answer:

He would pay $62.10

Step-by-step explanation:

   $42.50

+  $25.00

   $67.50

-          8%

   $62.10

Using calculator, the value of  the angle 5 sin (20 +10°) -4 = 0​ where 0 <x<90 is 17.5 degrees

You should understand that the sine of an angle is the trigonometric ratio of the opposite side to the hypotenuse of a right triangle containing that angle

The given angle is 5 sin (20 +10°) -4 = 0

To find the angle, first open the bracket to have

5sin(30) - 4 = 0

Collecting like terms to have

5 sin 30 = 4

Dividing both sides by 5 we have

5 sin30/5 = 4/5

This means that sin30 = 0.8

⇒sin30 - 0.8 = 0

⇒ 0.5 -0.8 = 0

-0.3

Therefore sin⁻-0.3 = 17.5⁰

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The probability of getting purple or yellow on the spinner, and then rolling an even number on the dice is P = 1/4, so the correct option is B

First, we need to get the individual probabilities.

For the spinner, we can see 4 equal sections such that one is violet and one is yellow. So the probability of getting either violet or yellow is:

q = 2/4.

For the number cube we assume that we have a standard one of 6 sides, with outcomes {1, 2, 3, 4, 5, 6}

Such that 3 out of the 6 outcomes are even, then the probability of rolling an even number is:

p = 3/6 = 1/2.

Then the joint probability (that the two above things happen) is given by:

P  =p*q = (1/2)*(1/2) = 1/4.

The probability of getting purple or yellow on the spinner, and then rolling an even number on the dice is P = 1/4, so the correct option is B

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Answer:

B) 1/4

Step-by-step explanation:

Answer:

find the zeroes of the polynomial

Answer: -1

Step-by-step explanation:

f(-4)=4-5

Since your x is negative and this problem requires -x to find y, you switch the sign to positive.

Answer:

Step-by-step explanation:

The equation that Dimitri and Jillian were trying to solve is expressed as

(x+1)(x+3) = 12. They are both solving this equation to get the value of x.

Based on the their suggestion, Jillian strategy would have been the best and the only one that will work for us in solving the equation but he didn't take cognizance of 12 when using the formula in his second step hence None of them are correct. The following steps should have been taken;

Step 1: Multiply out the expression (x+1)(x+3)

= (x+1)(x+3)

= x(x)+ 3x+x+1(3)

= x² + 3x + x + 3

= x² + 4x + 3

He got x² + 4x + 3 on expansion

Step 2: He should have rewrote the equation as shown;

x² + 4x + 3 = 12

x² + 4x + 3 -12 = 0

x² + 4x -9 = 0

Step 3: He used the quadratic formula to factorize the expression x² + 4x + 3 where a = 1, b = 4 anad c = -9

x = (-b±√b²-4ac)/2a

x = (-4±√(4)²-4(1)(-9))/2(1)

x = -4±√16+36/2

x = (-4±2√13)/2

x = (-4+2√13)/2 or  (-4-2√13)/2

x = -2+√13 or -2-√13

Hence Neither of them is correct. Jillian is almost correct but he should have equated the equation to zero by taking 12 into consideration before factorizing.

The approximate volume of the pyramid when it's 75% full is 303.75 inches³.

The volume of a square base pyramid can be represented as follows:

volume of the square base pyramid = 1 / 3 Bh

where

Therefore, the square bas pyramid has a base side of 9 inches and height of 15 inches. Let's find the volume when it's 75% full.

B = 9² = 81 inches²

h = 15 inches

Therefore,

volume of the square base pyramid = 1 / 3 × 81 × 15

volume of the square base pyramid = 81 × 5

volume of the square base pyramid = 405 inches³

Therefore, when it's 75% full

volume  = 75% of 405

volume = 75 / 100 × 405

volume = 30375 / 100

volume = 303.75 inches³

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The normal distribution that best approximates X is N(42, 21).

In an accounting college class, 50% of students receive a B or above on the final exam. 84 students are randomly selected from an accounting class at a local college. Let X be the number of students who received a B or above on the final exam. The normal distribution that best approximates X is a normal distribution with mean µ = np and variance σ^2 = np(1 - p).

In this case, n = 84 and p = 0.5 since 50% of the students receive a B or above on the final exam, and we want to find the distribution of the number of students who receive a B or above on the final exam.X ~ N(µ, σ^2) = N(np, np(1 - p)) = N(84(0.5), 84(0.5)(0.5)) = N(42, 21)

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There are 1,280,240 different passwords that meet the criteria of containing at least one letter and at least one digit, and consisting of four alphanumeric characters (case insensitive).

To calculate the total number of different passwords, we can break the problem down into several steps:

Step 1: Calculate the number of possible characters for each position in the password. Since the password consists of four alphanumeric characters, there are 26 letters (A-Z) and 10 digits (0-9) for each position.

Therefore, there are 36 possible characters for each position.

Step 2: Calculate the total number of possible passwords without any restrictions.

Since there are 36 possible characters for each position and the password has four positions, the total number of possible passwords without any restrictions is:

36 x 36 x 36 x 36 = 1,679,616

Step 3: Calculate the number of passwords that do not contain at least one digit or at least one letter.

To do this, we can calculate the number of passwords that do not contain any digits and subtract it from the total number of possible passwords, and then do the same for passwords that do not contain any letters.

The number of passwords that do not contain any digits is:

26 x 26 x 26 x 26 = 456,976

The number of passwords that do not contain any letters is:

10 x 10 x 10 x 10 = 10,000

However, we have to be careful not to double-count the passwords that do not contain both letters and digits.

The number of passwords that do not contain both letters and digits is:

26 x 26 x 10 x 10 = 67,600

So the total number of passwords that do not contain at least one digit or at least one letter is:

456,976 + 10,000 - 67,600 = 399,376

Step 4: Subtract the number of invalid passwords from the total number of possible passwords:

1,679,616 - 399,376 = 1,280,240

Therefore, there are 1,280,240 different passwords that meet the criteria of containing at least one letter and at least one digit, and consisting of four alphanumeric characters (case insensitive).

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Answer:

2(3 + 8k)

Step-by-step explanation:

GCF of 6 and 16 is 2.

6 + 16k = 2(3 + 8k)

If we substitute t = 9 into the equation, we get P(9) = -8.81(9)^2 + 218.7(9) + 88,369, which gives the population in the year 1999.

The population of a certain country from 1999 through 2009 can be modeled by the equation P(t) = -8.81t^2 + 218.7t + 88,369, where t represents the year and t = 9 corresponds to 1999.

To understand the model, we can break down the equation:

-8.81t^2 represents the quadratic term, which indicates the curvature of the population growth or decline over time. It shows that the population changes at a decreasing rate as t increases or decreases.

218.7t represents the linear term, which represents the linear growth or decline component of the population over time. It shows a consistent increase or decrease in population as t increases or decreases.

88,369 represents the constant term, which is the initial population in the year 1999. It is the population value when t = 9.

By plugging in different values of t between 9 and 19, we can calculate the corresponding population values for each year within that range.

For example, if we substitute t = 9 into the equation, we get P(9) = -8.81(9)^2 + 218.7(9) + 88,369, which gives the population in the year 1999.

Using this model, we can estimate the population of the country for any year between 1999 and 2009 by substituting the corresponding value of t into the equation P(t) = -8.81t^2 + 218.7t + 88,369. The equation combines both quadratic and linear components to capture the population's growth or decline over time, with the constant term representing the initial population in 1999.

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The expression that fails to compute the area of a triangle correctly is option b: (1 / 2) * b * h.

The correct formula to compute the area of a triangle is one-half times the base multiplied by the height, which can be written as (1/2) * b * h. Option a, c, and d correctly represent this formula. However, option b is incorrect because it uses integer division instead of decimal division.

In option b, (1 / 2) is computed using integer division, which results in truncating the decimal part. Therefore, (1 / 2) evaluates to 0 instead of 0.5. As a result, the expression (1 / 2) * b * h would yield incorrect and significantly smaller results than the actual area of the triangle.

To accurately calculate the area of a triangle using this formula, it is essential to use decimal division or explicitly represent the fraction as a decimal. Options a, c, and d correctly account for this by using either 1.0/2.0 or 0.5, ensuring the proper calculation of the area.

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Let \(\(a\)\) and \(\(b\)\) be integers such that \(\(ab = 4\)\). We want to prove that \(\((a - b)^3 - 9(a - b) = 0\).\)

Starting with the left side of the equation, we have:

\(\((a - b)^3 - 9(a - b)\)\)

Using the identity \(\((x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3\)\), we can expand the cube of the binomial \((a - b)\):

\(\(a^3 - 3a^2b + 3ab^2 - b^3 - 9(a - b)\)\)

Rearranging the terms, we have:

\(\(a^3 - b^3 - 3a^2b + 3ab^2 - 9a + 9b\)\)

Since \(\(ab = 4\)\), we can substitute \(\(4\)\) for \(\(ab\)\) in the equation:

\(\(a^3 - b^3 - 3a^2(4) + 3a(4^2) - 9a + 9b\)\)

Simplifying further, we get:

\(\(a^3 - b^3 - 12a^2 + 48a - 9a + 9b\)\)

Now, notice that \(\(a^3 - b^3\)\) can be factored as \(\((a - b)(a^2 + ab + b^2)\):\)

\(\((a - b)(a^2 + ab + b^2) - 12a^2 + 48a - 9a + 9b\)\)

Since \(\(ab = 4\)\), we can substitute \(\(4\)\) for \(\(ab\)\) in the equation:

\(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 48a - 9a + 9b\)\)

Simplifying further, we get:

\(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 39a + 9b\)\)

Now, we can observe that \(\(a^2 + 4 + b^2\)\) is always greater than or equal to \(\(0\)\) since it involves the sum of squares, which is non-negative.

Therefore, \(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 39a + 9b\)\) will be equal to \(\(0\)\) if and only if \(\(a - b = 0\)\) since the expression \(\((a - b)(a^2 + 4 + b^2)\)\) will be equal to \(\(0\)\) only when \(\(a - b = 0\).\)

Hence, we have proved that if \(\(ab = 4\)\), then \(\((a - b)^3 - 9(a - b) = 0\).\)

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1. The values which the given number sentences true are:

a) 11 b) 5 c) 36

2. After substituting the value of  x we get the value for y as :

a) 6 b) 0 c) 7 d) 15

3. The number sentences are :

a) x ₋ y = 25

b) 5 × p = q ÷ 2

c) 2y ₋ 14 = 6

d) 15 × 4 = 4 ₋ (x₊y)

Given in the first bit we need to find the variables:

a) h ₊ 8 = 19

arrange the constants on one side.

h = 19 ₋ 8

h = 11

b) 2p ₋ 6 = 4

arrange the constants on one side.

2p = 4 ₊ 6

2p = 10

p = 10/2

p = 5

c) 1/3 y = 12

cross multiply.

y = 36

Now in the second exercise we are asked to substitute the x value and get the value of y.

a) y = 3x ₊ 2 if x =8

substitute x value in the equation.

y = 3(8) ₊ 2

y = 24 ₊ 2

y = 26

b) y = 4x ₋ 1 if  x = 1/4

y = 4(1/4) ₋ 1

y = 1 ₋ 1

y = 0

c) y = 0.2x ₊ 5 if x = 10

y = 0.2(10) ₊ 5

y = 2 ₊ 5

y = 7

d) y = 10x ₊ 12 if x = 0.3

y = 10(0.3) ₊ 12

y = 3 ₊ 12

y = 15

In the last third bit we need to frame equations for the given word problems.

a) The difference between two numbers is 25.

let the two numbers be x and y.

x ₋ y = 25.

b) The product of 5 and p is equal to quotient of q and 2.

5 × p = q ÷ 2

c) The difference between 14 and 2y is equal to 6.

2y ₋ 14 = 6

d) The product of 15 and 4 is equal to four less than the sum of x and y.

15 × 4 = 4 ₋ (x₊y)

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Answer:

5 cubed is 5 x 5 x 5 = 125.

10 squared is 10 x 10 = 100.

So, 5 cubed - 10 squared = 125 - 100 = 25.

We can also express 25 as a power of 5 by noting that 25 = 5 squared. Therefore:

5 cubed - 10 squared = 5 squared x 5 - 10 squared = 5^(2+1) - 10^(2) = 5^3 - 10^(2) = 125 - 100 = 25.

So, the answer is 5 squared or 5^2.

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

5 cubed - 10 squared

\(5^{3} - 10^{2} \\ = 125 - 100\\= 25\)

Hope this helps!

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1/3 is the probability of rolling either a 5 or a 6 using a normal six-sided die.

Probability can be defined as the ratio between the number of favorable outcomes and the total number of outcomes of an event.

Given:

Six-sided dice rolled once

Let n be the number of outcomes

let x be the number of favorable outcomes

We know that,

\(Probability=\frac{x}{n}\)

When the six-sided dice roll, The possible outcomes are,

\(\{1,\;2,\;3,\;4,\;5,\;6\}\)

Therefore,

\(Number\;of\;outcomes,\;n=6\)

\(Probability\;rolling\;5\;is\;\frac{1}{6}\)

\(Probability\;rolling\;6\;is\;\frac{1}{6}\)

Therefore, Probability of rolling either 5 or 6 is,

\(P(5\;or\;6)=\frac{1}{6} +\frac{1}{6}\)

\(P(5\;or\;6)=\frac{2}{6}\)

\(P(5\;or\;6)=\frac{1}{3}\)

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