The distance between Kingston and Sunny Place is 35 km. At 8.30 a.m. , Joel cycles from Kingstown towards Sunny place at an average speed of 12 Km/h. At the same time, Ryan cycles from Sunny place towards Kingstown, along the same route, at an average speed of 8 Km/h.
a) At what time will the cyclists meet on the way?

b)How far will each cyclist have travelled when they meet?

Answer:

d) 1/12

Step-by-step explanation:

Matrices A and B are non-invertible matrices that can be added together to form an invertible matrix. To find these matrices, we can use the following steps:

Step 1: Choose a matrix A that is not a diagonal matrix and is not invertible. One example of such a matrix is

\(A = \left[\begin{array}{ccc}1&1\\0&0\end{array}\right]\)

Step 2: Choose a matrix B that is not a diagonal matrix, is not invertible, and is not a scalar multiple of matrix A. One example of such a matrix is
\(B = \left[\begin{array}{ccc}0&0\\1&1\end{array}\right]\)

Step 3: Add the matrices A and B together to form the matrix A+B. This matrix will be invertible, as shown below:

\(A+B = \left[\begin{array}{ccc}1&1\\0&0\end{array}\right]+\left[\begin{array}{ccc}0&0\\1&1\end{array}\right]=\left[\begin{array}{ccc}1&1\\1&1\end{array}\right]\)

Step 4: Verify that the matrix A+B is invertible by finding its determinant. The determinant of a 2x2 matrix is given by:

det(A+B) = (1)(1) - (1)(1) = 0

Since the determinant of the matrix A+B is not equal to zero, the matrix is invertible.

Therefore, the matrices \(A = \left[\begin{array}{ccc}1&1\\0&0\end{array}\right]\) and \(B = \left[\begin{array}{ccc}0&0\\1&1\end{array}\right]\) are non-invertible matrices that can be added together to form an invertible matrix \(A+B =\left[\begin{array}{ccc}1&1\\1&1\end{array}\right]\).

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The value of x is 9 cm, and angle O is 0 degrees.

To solve the triangle LMN and find the values of x and angle O, we can use the Law of Cosines and the Law of Sines. Let's go step by step:

(i) To find the value of x, we can use the Law of Cosines. According to the Law of Cosines, in a triangle with sides a, b, and c, and angle C opposite to side c, the following equation holds:

c^2 = a^2 + b^2 - 2ab * cos(C)

In our case, we want to find side NM (x), which is opposite to angle N. The given sides and angles are:

LN = 12 cm

NK = 6 cm

KM = 8 cm

Let's denote angle N as angle C, side LN as side a, side NK as side b, and side KM as side c.

Using the Law of Cosines, we can write the equation for side NM (x):

x^2 = 12^2 + 6^2 - 2 * 12 * 6 * cos(N)

We don't know the value of angle N yet, so we need to find it using the Law of Sines.

(ii) To find angle O, we can use the Law of Sines. According to the Law of Sines, in a triangle with sides a, b, and c, and angles A, B, and C, the following equation holds:

sin(A) / a = sin(B) / b = sin(C) / c

In our case, we know angle N and side NK, and we want to find angle O. Let's denote angle O as angle A and side KM as side b.

We can write the equation for angle O:

sin(O) / 8 = sin(N) / 6

Now, let's solve these equations step by step to find the values of x and angle O.

To find angle N, we can use the Law of Sines:

sin(N) / 12 = sin(180 - N - O) / x

Since we know that the angles in a triangle add up to 180 degrees, we can rewrite the equation:

sin(N) / 12 = sin(O) / x

Now, we can substitute the equation for sin(O) from the Law of Sines into the equation for sin(N):

sin(N) / 12 = (6 / 8) * sin(N) / x

Now, we can solve this equation for x:

x = (12 * 6) / 8 = 9 cm

So, the value of x is 9 cm.

To find angle O, we can substitute the value of x into the equation for sin(O) from the Law of Sines:

sin(O) / 8 = sin(N) / 6

sin(O) / 8 = sin(O) / 9

9 * sin(O) = 8 * sin(O)

sin(O) = 0

This implies that angle O is 0 degrees.

Therefore, the value of x is 9 cm, and angle O is 0 degrees.

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The figure for the given question is provided here :

\(3 {}^{4x - 5} = ( \frac{1}{27} ) {}^{2x + 10} \\ note \: \: that = \\ ( \frac{1}{27} ) = ( \frac{1}{3 {}^{3} } ) = 3 {}^{ - 3} \\ \\ 3 {}^{4x - 5} = (3 {}^{ - 3} ) {}^{2x + 10} \\ 3 {}^{4x + 5} = 3 {}^{ - 3(2x + 10)} \\ equal \: \: bases = > equal \: exponents\)

\(4x - 5 = - 3(2x + 10) \\ 4x - 5 = - 6x - 30 \\ 4x + 6x = - 30 + 5 \\ 10x = - 25 \\ x = - 2.5\)

Answer:

x = -2.5

Step-by-step explanation:

3^(4x-5)=(1/27)^(2x+10)

We are working with exponents

We can rewrite 1/27 as 3^-3

3^(4x-5)=(3^-3)^(2x+10)

Now we know that a^b^c = a^(b*c)

3^(4x-5)=3^( -3* (2x+10))

3^(4x-5)=3^( -6x -30)

The bases are the same so the exponents must be the same

4x-5 = -6x-30

Add 6x to each side

4x-6+6x = -6x-30+6x

10x-6 = -30

Add 5 to each side

10x-5+5 = -30 +5

10x = -25

Divide by 10

10x/10 = -25/10

x = -2.5

In Stock market, This is possible due to the concept of compounding losses.

what exactly is a stock market?

The stock market is a collection of markets where publicly held companies' stocks are traded. It allows individuals and organizations to buy or sell shares of ownership in a publicly traded company. The stock market is an indicator of the economy's overall health and performance, as well as a means for companies to raise capital for growth and expansion.

Now,

This is possible due to the concept of compounding losses. When an investment suffers a loss, it's starting from a lower base. For example, if you had $10,000 invested in the stock market and it lost 20%, your account would be worth $8,000. To get back to $10,000, you would need a gain of 25%, not 20%, because 20% of $8,000 is $1,600, not $2,000.

Here's an example to illustrate this further:

Let's say you invested $10,000 in the stock market, and it lost 50% of its value in the first year, leaving you with $5,000. In the second year, the market rebounded and gained 50%, so your account went up to $7,500. At this point, you're still down 25% from your original investment, even though the market had a net gain of 0% over the two-year period. To get back to your original $10,000, you would need a gain of 100%, which is a much larger recovery than the 50% gain the market had in the second year.

In short, when losses compound, it takes a larger gain to get back to where you started. This is why it's important to be aware of the potential for losses when investing and to have a long-term investment strategy that can weather market downturns.

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You failed to start the end points of the frequency polygon from a x-value of 0.

First of all, we would determine the midpoint of the data set as follows:

0 < t ≤ 5 = (0 + 5)/2 = 2.5.

5 < t ≤ 10 = (10 + 5)/2 = 7.5.

10 < t ≤ 15 = (10 + 15)/2 = 12.5.

15 < t ≤ 20 = (15 + 20)/2 = 17.5.

In order to draw a frequency polygon for the given data set, we would construct the frequency table as follows:

Time, t minutes                                      Frequency_

0 < t ≤ 5                                                        7

5 < t ≤ 10                                                       8

10 < t ≤ 15                                                      6

15 < t ≤ 20                                                     4

Finally, we would connect the end points of the data set on the frequency polygon by starting from a x-value of 0 as shown in the image attached below.

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Answer:

a)to find mean

(sum the scores, divide by the number of scores) that is

( 2+ 2 + 0 + 5 +1 +, 4,+ 1, + 3, + 0,+ 0+ , 1, +4, + 4, + 0,+ 1, + 4, +3,+ 4, + 2,+ 1, +0)/21

= 42/21

= 2

b)

median means order the scores numerically then you choose the score in the middle and that is 2

c)sum of squared deviations is done by take difference between each score and the mean, square the result That is

Summation (xbar - x)²

add the final answer is 56

d)variance is gotten by taking sum of squared deviations, divide by (n-1))=

Summation (xbar - x)²/n-1

=2.8

e)standard deviation is square root of variance)= √V = 1.6

Answer:wsg bear

Step-by-step explanation:

Answer:

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

Step-by-step explanation:

The point slope form is (y-y1)=m(x-x1) you just have to plug in the numbers for the equation.

Answer:

Genotype: 100% rr
phenotype: 100% white

Step-by-step explanation:

since there are no dominant genes the cross will definitely be a rr genotype

Answer:

g(x) = 2ˣ - 3

Step-by-step explanation:

f(0) is 1 since 2⁰ = 1

So to get to the point -2, we'd have to subtract 3.

Let's see where g(x) = 2ˣ - 3 takes us.

g(0) = 2⁰ - 3 = -2

g(2) = 2² - 3 = 1

That's already a match, so no further transformation needed.

Answer:

3x+2 and 3x-4

Step-by-step explanation:

We are given the quadratic equation 9x²-6x-8.

first, multiply 9 and -8 together (factors a*c, which equals to the sum that is b)

the result is -72

now think:

which two numbers add up to -6, but when multiplied, equal -72?

Those two numbers are -12 and 6

we can expand the polynomial:

9x²-12x+6x-8

factor by grouping:

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

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

so, the dimensions of the blanket are (3x-4) and (3x+2)

Hope this helps :)

Answer:

a. \(x^{-2}\)

b. \(x^{-6}\)

c. 1

d. 1

e. \(x^{-6}\)

f. \(x^{15}\)

Step-by-step explanation:

The labeling of bases and height in a trapezium is not fixed and can vary based on the context or problem. It doesn't matter where they are on the trapezium, as long as they are clearly defined and consistent within the given situation.

In a trapezium (or trapezoid), the labeling of the bases and height is not fixed or standardized. It can vary depending on the context or the specific problem being considered. However, there are a few general guidelines to keep in mind when labeling a trapezium.

Bases: The trapezium has two parallel sides, often referred to as the "top base" and the "bottom base." The bases are usually labeled based on their relative lengths or position in the trapezium. The longer parallel side is commonly referred to as the "top base," while the shorter parallel side is referred to as the "bottom base." However, this is not a strict rule and can vary depending on the problem or preference.

Height: The height of a trapezium is the perpendicular distance between the bases. It is generally labeled as a vertical line segment connecting the bases. The placement of the height is not fixed, and it can be drawn from any point on the top base to any point on the bottom base, as long as it forms a perpendicular line. The height is usually labeled with the symbol "h" or sometimes "x" or "y" depending on the context.

It's important to note that the labeling of the bases and height is primarily for communication and clarity. As long as the labeling is consistent and clearly defined within the given problem or context, it does not have to conform to any specific arrangement or be in a rectangular shape. The key is to ensure that the labels are clearly understood and can be used to calculate the desired quantities or solve the problem at hand.

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Answer:

0.7880

Step-by-step explanation:

0.7883

Hope it helps!

Answer:

see explanation

Step-by-step explanation:

to determine if the values of y are a solution to the equation, substitute the values of y into the left side and if equal to the right side then they are a solution.

y = 70

\(\frac{70}{7}\) - 1 = 10 - 1 = 9 ≠ - 2 → NO

y = 56

\(\frac{56}{7}\) - 1 = 8 - 1 = 7 ≠ - 2 → NO

y = - 7

\(\frac{-7}{7}\) - 1 = - 1 - 1 = - 2 → YES

y = 0

\(\frac{0}{7}\) - 1 = 0 - 1 = - 1 ≠ - 2 → NO

Answer:

Yes. I think that is a pre algebre question.

The point in Figure 2 that corresponds to point L in Figure 1 is the midpoint of line segment NP.

When two figures are congruent, it means that they have the same shape and size. This implies that corresponding points in the two figures have the same position and distance from each other.

In Figure 1, the points I, J, L, K, N, P, and Q are labeled. To find the point in Figure 2 that corresponds to point L, we need to look for a point that has the same relative position and distance as point L in Figure 1.

From Figure 1, we can see that point L is the midpoint of the line segment JK. Therefore, to find the corresponding point in Figure 2, we need to look for a point that is the midpoint of the line segment that corresponds to JK. In Figure 2, the line segment that corresponds to JK is NP, and the midpoint of NP corresponds to the point that is equivalent to point L. Therefore, the point that corresponds to point L in Figure 2 is the midpoint of line segment NP.

It is important to note that identifying corresponding points in congruent figures is a fundamental concept in geometry and is often used to solve problems involving congruence and similarity.

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Step-by-step explanation:

Look at the points  (0,-3)  and  ( 3,0)

slope,  m = rise / run =   3 / 3 =  1  

Answer:

1

Step-by-step explanation:

y=x+3

Answer:

17 / 3 i think

Step-by-step explanation:

(4/ 3(2) ) + 5

(4 / 6) + 5

(2/3) + 5

5 = 4 3/3 or 15 / 3

2/3 + 15/ 3 = 17 / 3

\(\frac{26}{3}\)

1 + 1 + 1 + \(\frac{1}{3}\) x 2 + 5 (Write the division as a fraction)
1 + 1 + 1 + \(\frac{2}{3}\) + 5 (Calculate)
8 + \(\frac{2}{3}\) (Caculate Positive Numbers)
\(\frac{26}{3}\)
8\(\frac{2}{3}\), 8.6 (Alternate Form)

We need to use a survey to determine an effective sales method. For that we will survey the employees. Whenever we want to extract a tendency from a large number of data points, we need to spread our samples as much as possible. In this case we want to extract the knowledge from the employees, so we need to take employees from the most different branches. The correct option would be:

24 employees from each sales department at each location.

Answer:

A

Step-by-step explanation:

I used desmos to find my answer

In the context of this problem all the solutions to the polynomial equation is correct because they all make sense.

The given polynomial equation  can be expressed as ;

x³ + 6x² - 40x = 192 and the given solutions can be written as ; x = -8, x = -4, and x = 6

We can test if the solution is the best for the given euation because this will help us to know if these valueas are the solution for the equation

x = -8

[(-8)³ + 6(-8)² - 40(-8)]

= 192

[-512 + 384 + 320]

= 192

x = -4,

[(-4)³ + 6(-4)² - 40(-4)]

[-64 + 96 + 160 ]

= 192

x = 6

[(6)³ + 6(6)² - 40(6) ]

216 + 216 - 240

= 192

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Answer:

Step-by-step explanation:

A,B

x = –8

x = –4

Therefore, it would take approximately 19.02 years for an investment to at least double its original amount at a semi-annual compound interest rate of 3.62%.

When an investment is made with a certain amount, the compound interest rate is used to calculate the return on investment. In addition, the number of times interest is compounded each year can have an impact on the investment's outcome.

This question asks about how long it would take for an investment to double at a semi-annual compound interest rate of 3.62%.

To solve for how long it would take for an investment to double at a semi-annual compound interest rate of 3.62%, we need to use the formula for the future value of an annuity:

Future value of an annuity = Payment (1 + r/n)^(nt)where:r is the annual interest raten is the number of times interest is compounded per year Payment is the original amount is the number of years

To solve for t, we can rearrange the formula as follows:t = log(Payment/Future value of an annuity) / log(1 + r/n)where log is the natural logarithm.

The future value of the investment is double the original amount, so we can plug in 2 for Future value of an annuity and simplify the formula to get:t = log(2) / log(1 + 0.0362/2)t = 19.02 years

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Answer:

1

Step-by-step explanation:

Answer:

see below :)

Step-by-step explanation:

answer: 1

the equation would be written like so: 5n+6=11

5(1) = 5

5+6 = 11

n=1

The total cost for the family of four is $944

Cost denotes the amount of money that a company or a person spends on the creation or production or acquiring of goods or services.

Here the family needs the service if transportation.

The cost of adult is $280. Out of four members , two are under 3years. This means the total cost for adult is 2 × 280 = $560

The cost of under 3 is ⅔ of the cost of adult.

= ⅔ × 280= $192

The cost of the two under 3 = 2 × $192 = $384

therefore the total cost for the family is $560 +$384 = $944

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