The Grade 8 learners decided to start training more. They will either box or grid. There
are 125 Grade 8 learners, and they box and grid in the ratio 3:2. Calculate how many
learners participate in each sport?

The value of 'x' and 'y' in x + 1 : 3y = 1 : 7 and 2x : y + 3 = 2 : 5.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

We know, We can write a : b as, a/b.

Therefore, The given equations can be formed as,

(x + 1)/3y = 1/7 and 2x/(y + 3) = 2/5.

7x + 7 = 3y.

7x - 3y = - 7...(i)

And,

10x = 2y + 6.

10x - 2y = 6...(ii)

Now, Multiplying eqn(i) by 10 and (ii) by 7 we have,

70x - 30y = - 70...(iii) and 70x - 14y = 42...(iv)

Now, By Subtracting (iii) and (iv) we have,

- 16y = - 112

y = 7 and hence x = 2

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Answer:

y = -3/2x + 6

Step-by-step explanation:

Slope m = (y2 - y1)/(x2 - x1)

m = (6 - 0)/(0 - 4) = 6/-4 = -3/2

Slope-intercept form is y = mx + b

Substitue m = -3/2, y = 0, x = 4

0 = -3/2(4) + b

b = 6

y = -3/2x + 6

This size sample of this binomial distribution have:

P = 0.24
Mean = 50.4
Standard Deviation = 6.19

About 24% of a population are of a particular ethnic group. 210 people are randomly selected from this population.

First, we need to convert the percentage to a decimal by dividing by 100:

P = 24% / 100 = 0.24

Next, we can compute the mean and standard deviation of the binomial distribution for a sample size of 210 and probability of success of 0.24:

Mean = np = 210 * 0.24 = 50.4

Standard Deviation = √(np(1-p)) = √(50.4 * (1-0.24)) = √(38.304) = 6.19

So, the mean of this binomial distribution is 50.4 and the standard deviation is 6.19.

Therefore,
P = 0.24
Mean = 50.4
Standard Deviation = 6.19

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Kiara's rate is 4 miles per hour. Take note that this simply asks for her current rate, not an average rate.

To find Kiara's rate at the 9-hour mark, we can subtract the distance she has traveled so far (26 miles) from the total distance (38 miles) to get the distance she traveled in the last 3 hours, which is 12 miles.

Then, we can divide the distance she traveled in the last 3 hours by the time taken (9 - 6) to get her rate:

Therefore, Kiara's current rate is 4 miles per hour.

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The values of the variables are x = 23, y = 41/3, and z = -22/3.

The matrix equation Ax = b for the given set of linear equations is:

```
| -3 0 -6 |   | x |   | 11 |
|  5 -2  3 | * | y | = | 17 |
|  2 -1 -7 |   | z |   | -3 |
```

Where A is the coefficient matrix, x is the column matrix of variables, and b is the column matrix of constants.

To find the inverse of matrix A, we perform row operations on the augmented matrix [A|I]:

```
| -3 0 -6 | 1 0 0 |
|  5 -2  3 | 0 1 0 |
|  2 -1 -7 | 0 0 1 |
```

First, we divide the first row by -3:

```
| 1 0 2 | -1/3 0 0 |
| 5 -2 3 |  0   1 0 |
| 2 -1 7 |  0   0 1 |
```

Then, we subtract 5 times the first row from the second row, and 2 times the first row from the third row:

```
| 1 0  2  | -1/3  0  0 |
| 0 -2 -7 |  5/3  1  0 |
| 0 -1 -3 |  2/3  0  1 |
```

Next, we divide the second row by -2:

```
| 1 0  2  | -1/3  0   0 |
| 0 1 7/2 | -5/6 -1/2 0 |
| 0 -1 -3 |  2/3  0   1 |
```

And then we add the second row to the third row:

```
| 1 0  2  | -1/3  0   0 |
| 0 1 7/2 | -5/6 -1/2 0 |
| 0 0  1/2|  1/6 -1/2 1 |
```

Finally, we divide the third row by 1/2, and subtract 2 times the third row from the first row, and 7/2 times the third row from the second row:

```
| 1 0 0 |  0   1  -2 |
| 0 1 0 | -4/3 2  -7/2|
| 0 0 1 |  1/3 -1  2 |
```

So, the inverse of matrix A is:

```
|  0   1  -2 |
| -4/3 2  -7/2|
|  1/3 -1  2 |
```

Now, we can perform matrix multiplication A^-1b to get the values of the variables:

```
|  0   1  -2 |   | 11 |   | x |
| -4/3 2  -7/2| * | 17 | = | y |
|  1/3 -1  2 |   | -3 |   | z |
```

```
| x |   | 1(17) + (-2)(-3) |   | 23 |
| y | = | (-4/3)(11) + 2(17) + (-7/2)(-3) | = | 41/3 |
| z |   | (1/3)(11) + (-1)(17) + 2(-3) | = | -22/3 |
``

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They will be 72 km far apart after 2 hours. The solution has been obtained by using the concept of relative speed.

The speed of a moving body relative to another might be referred to as relative speed. The differential between two moving bodies is used to calculate their relative speed. Yet, the relative speed of two bodies travelling in opposition to one another is determined by summing their respective speeds.

We are given that the Serenity and the Mystic travels in the opposite direction at 16 mph and at 20 mph respectively.

So,

The relative speed = 16 + 20 = 36 mph

Now,

After 2 hours the distance between them will be as follows

36 × 2 = 72 mph

Hence, they will be 72 km far apart after 2 hours.

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Answer:

B

Step-by-step explanation:

I think so because the rise is going downward, which means it’s a negative number. Therefore m= -1/4

Answer:

because there was an issue the first time you did this for you can reach me by the researchers will ensure you have all available upon the first term or the receiver to the wrong I am not sure what is your educational sectors to be seen in this podcast encourage students and how to answer the questions know what they are doing for the study to be seen before turning in to a Research paper is the one that has been provided by a Goggle of a student who is known for its own thoughts on a great topic that will be implemented in a far way to encourage you and the effective to make my life easier reading a book english and a web page like that is always fighting for a free time and I mean the only thing I want do is make a essay My own and then I can Did it will also cause you to change your life

a) The expected payout for the insurance company is $182.

b) If the insurance company wants to charge 15% over the expected payout, the insurance company should charge the insured $27.30.

In a game of chance, the expected payout is the expected value of the game minus the cost.

For the insurance company, the expected payout is the probability-weighted value of the insurance undertaking.

The expected payout is the product of the amount to be paid to the insured family and the probability or chance of the insured dying.

The amount the insured family will receive = $130,000

The chance of the insured dying = 0.0014

The expected payout = $182 ($130,000 x 0.0014)

Charge over the expected payout = 15%

The amount the insurance company should charge the person = $27.30 ($182 x 15%)

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To set up the equation and solve for the 2 consecutive odd integers whose product is 195, we can follow these steps:

1. Let x be the first odd integer. 2.The next consecutive odd integer will be x+2. 3.The product of these two integers is 195, so we can set up the equation: x(x+2) = 195 4.Expand the equation: x^2 + 2x = 195

5.Rearrange the equation to get a quadratic equation: x^2 + 2x - 195 = 0 6. Use the quadratic formula to solve for x: x = (-2 ± √(2^2 - 4(1)(-195)))/(2(1)) 7. Simplify the equation: x = (-2 ± √784)/2 8. Solve for the two possible values of x: x = (-2 + 28)/2 or x = (-2 - 28)/2 9. Simplify the equations: x = 13 or x = -15 10. Since x is an odd integer, we can reject the solution x = -15. 11. The first odd integer is x = 13, and the next consecutive odd integer is x+2 = 15.

12. Therefore, the two consecutive odd integers whose product is 195 are 13 and 15.

The final answer is 13 and 15.

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Answer:30

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

18

The length of the segment indicated is 10.6.

Pythagoras discovered that the square of the hypotenuse in a right-angled triangle with a 90° angle is equal to the sum of the squares of the other two sides.

The triangle has three sides: the hypotenuse, which is always the longest, the opposite, which doesn't touch the hypotenuse, and the adjacent (which is between the opposite and the hypotenuse).

By Pythagoras' theorem;

a² + b² = c²

a= 16.4

b= 12.5

c =?

16.4² +  12.5² = c²

c² =  268.96 - 156.25 = 112.4

c² = 112.4

c = √112.4

c= 10.6

Therefore, the length of the segment indicated is 10.6.

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The events in terms of whether they are complimentary or not are:

The probability that it will not rain tomorrow is 2 / 3.

In probability theory, complementary events are two events that together cover all possible outcomes, meaning that if one event occurs, the other cannot occur. For example, in part (a) of the question, the events of getting an even number and getting an odd number when rolling a die are mutually exclusive, meaning that they cannot happen at the same time.

In part (b), the events of getting a prime number and getting an even number when rolling a die are not complementary events because the number 2 is both prime and even.

In parts (c) through (g), the events listed are complementary events. For example, in part (c), the events of all students attending class and no students attending class cover all possible outcomes, and only one of them can happen at a time.

If the probability of rain tomorrow is 1/3, the probability of no rain tomorrow is:

P(not raining) = 1 - P(raining)

P(not raining) = 1 - 1/3

P(not raining) = 2/3

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Jane deposits $1,250 quarterly into a retirement account that pays interest at the rate of 3.25% per year compounded continuously. At the end of 10 years, she will have $60,358.28 in her account. The correct answer is option 4

To solve the problem, we can use the formula for continuous compounding given by:[tex]A = Pe^{rt}[/tex], where,A is the amount at the end of the investment period, P is the principal (the initial amount deposited), e is Euler's number, which is approximately equal to 2.71828, r is the annual interest rate (expressed as a decimal), t is the time period in years

In this problem, P = $1,250, r = 0.0325 (3.25% as a decimal), and t = 10 years. We need to find A, the amount at the end of 10 years. Substituting the values in the formula, we get:

[tex]A = 1250e^{0.0325 × 10} ≈ $60,358.28.[/tex]

Therefore correct answer is option 4

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[2x^(2) + 7x + 6 = 0] has C. two real solutions

The quadratic equation 2[tex]x^{(2)}[/tex] + 7x + 6 = 0 has two real solutions. To solve, use the Quadratic Formula:

x = [-b ± √([tex]b^{2}[/tex] - 4ac)]/2a  

Where a = 2, b = 7, and c = 6.

So, x = [-7 ± √([tex]7^{2}[/tex]- 4(2)(6))]/2(2)  

x = [-7 ± √(49 - 48)]/4  

x = [-7 ± 1]/4  

x = -3/2 and x = 1/2  


Therefore, the equation has two real solutions: x = -3/2 and x = 1/2.

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Answer:

The answer for 17x10^8 is 1,700,000,000 and the answer for 4x10^8 is 400,000,000

subtract them.

Hope that helps you out!

The result of the given polynomial division (2x^(3)+4x^(2)+7x+5 divided by x+1) using long division method is 2x^(2) + 2x + 5.

To find the result of the given polynomial division using long division method, we need to follow the steps below:

Step 1: Write the dividend and the divisor in long division form.

        ______________________
x + 1  |  2x^(3) + 4x^(2) + 7x + 5

Step 2: Divide the first term of the dividend by the first term of the divisor. In this case, 2x^(3)/x = 2x^(2). Write the result above the dividend.

        2x^(2)  _______________
x + 1  |  2x^(3) + 4x^(2) + 7x + 5

Step 3: Multiply the result by the divisor and write the product under the dividend.

        2x^(2)  _______________
x + 1  |  2x^(3) + 4x^(2) + 7x + 5
        - (2x^(3) + 2x^(2))
        ---------------------

Step 4: Subtract the product from the dividend and bring down the next term.

        2x^(2)  _______________
x + 1  |  2x^(3) + 4x^(2) + 7x + 5
        - (2x^(3) + 2x^(2))
        ---------------------
                2x^(2) + 7x + 5

Step 5: Repeat the process until the degree of the remainder is less than the degree of the divisor.

        2x^(2) + 2x + 5  _______________
x + 1  |  2x^(3) + 4x^(2) + 7x + 5
        - (2x^(3) + 2x^(2))
        ---------------------
                2x^(2) + 7x + 5
        - (2x^(2) + 2x)
        ---------------------
                   5x + 5
        - (5x + 5)
        ---------------------
                   0

Step 6: Write the final result as the quotient plus the remainder over the divisor.

[tex](2x^{3} + 4x^{2} + 7x + 5)/(x + 1) = 2x^{2} + 2x + 5[/tex]

Therefore, the answer is 2x^(2) + 2x + 5

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The length of the dog run is 18.5 feet and the width is 14 feet. Micah can use his 65 feet of fencing to make a dog run with these dimensions.

To find the length of the dog run, we need to solve the equation for L. Here are the steps:

1. Start with the given equation: 2L + 2(L - 4.5) = 65
2. Distribute the 2 on the right side of the equation: 2L + 2L - 9 = 65
3. Combine like terms: 4L - 9 = 65
4. Add 9 to both sides of the equation: 4L = 74
5. Divide both sides of the equation by 4: L = 18.5

So, the length of the dog run is 18.5 feet. Since the length is 4.5 feet more than the width, we can find the width by subtracting 4.5 from the length:

W = L - 4.5
W = 18.5 - 4.5
W = 14

Therefore, the width of the dog run is 14 feet.

In conclusion, the length of the dog run is 18.5 feet and the width is 14 feet. Micah can use his 65 feet of fencing to make a dog run with these dimensions.

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Answer:

128688

Step-by-step explanation:

From function f(x)=x2−3andg(x)=−5x+2,The correct answer is A. (gf​)(52​)= -6.75

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between a variable quantity and another variable quantity.

To find (gf​)(52​), we first need to find f(52​) and then substitute that value into g(x).

First we need to Find f(52​)
f(x)=x2−3
f(52​)=(52​)2−3
f(52​)=52−3
f(52​)=1.75

Then we can  Substitute f(52​) into g(x)
g(x)=−5x+2
g(f(52​))=−5(1.75)+2
g(f(52​))=−8.75+2
g(f(52​))=−6.75

Therefore, (gf​)(52​)=−6.75

The final answer is A. (gf​)(52​)=−6.75

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Therefore , the solution of the given problem of probability comes out to be  the likelihood of obtaining a sum of 4 is about 8.3%.

Calculating the likelihood that a claim is true or that a specific event will occur is the primary objective of the branch of mathematics known as parameter estimation. Chance can be represented by any number between 0 and 1, at which 1 usually represents certainty and 0 typically represents possibility. A probability diagram shows the chance that a specific event will occur.

Here,

There are a total of 6 x 6 = 36 results when the spinner is spun twice because there are six sections on it, each with a number from 1 to 6.

We can make a list of every result and determine how many times the sum is 4:

=> 1, 3

=> 2, 2

=> 3, 1

There are three results, and their total is 4. As a result, 3/36 = 1/12 is the chance of receiving a sum of 4. We can multiply this by 100 and tenth it to represent it as a percentage:

=> 1/12 x 100 ≈ 8.3

In other words, the likelihood of obtaining a sum of 4 is about 8.3%.

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The values of x and y are 100 and 40, respectively

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

The circle

On the circle, we have the following congruent angles

ADC and ABC

Using the above as a guide, we have the following:

x = 100

The sum of angles in a triangle is 180

So, we have

y + y + x = 180

This gives

2y + 100 = 180

So, we have

y = 40

Hence, the value of y is 40

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Number of students that selected the elective subject of religion in 2014 is 1344

The problem tells us that in 2013, there were 1400 students who selected the elective subject of religion.

Then, in 2014, this figure decreased by 4%. This means that the new figure in 2014 will be 4 percentage less than the figure in 2013.

To calculate what 4% of 1400 is, we need to multiply 1400 by 4/100, which gives us 56. So, 56 students did not select the elective subject of religion in 2014 compared to 2013.

So, the number of students who selected the elective subject of religion in 2014 is

= 1400 - 56

= 1344

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Answer: 64.24 cm square

Step-by-step explanation:

length x width

11 x 7 = 77cm square

The radius of the circle is 2cm

The area of the circle = 

 r^2 = 2^2 12.57

Hence the area of the shaded region=

Area of rectangle – area of circle= 77 – 12.57= 64.43 cm2

Answer:

[tex]\large\boxed{\tt (3x+4)(x+7)=3x^{2}+25x+28}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to factor the given trinomial.}[/tex]

[tex]\large\underline{\textsf{What is a Trinomial?}}[/tex]

[tex]\textsf{A Trinomial is an expression that has 3 terms. No more, and no less.}[/tex]

[tex]\large\underline{\textsf{What is Factoring?}}[/tex]

[tex]\textsf{Factoring is a way to split a trinomial into 2 binomials. Binomials have 2 terms.}[/tex]

[tex]\textsf{Factoring helps us to find the possible values of x, setting the binomials equal to 0.}[/tex]

[tex]\textsf{We don't have to do this for our problem though.}[/tex]

[tex]\large\underline{\textsf{Factoring Looks Like;}}[/tex]

[tex]\tt x^{2} + x + 1 = (x+?)(x+?)[/tex]

[tex]\tt The \ 2 x's \ multiply \ to \ equal \ x^{2}.[/tex]

[tex]\textsf{The x's multiply with the whole numbers inside the opposite binomial.}[/tex]

[tex]\large\underline{\textsf{To Factor;}}[/tex]

[tex]\textsf{Factoring is a little tedious, we must be careful and make sure we are finding}[/tex]

[tex]\textsf{the correct factors for factoring to work out. Remember that the trinomial has to}[/tex]

[tex]\textsf{equal the 2 binomials being multiplied.}[/tex]

[tex]\large\underline{\textsf{Solving;}}[/tex]

[tex]\tt 3x^{2} + 25x + 28[/tex]

[tex]\textsf{3x can't be split apart in 2 whole numbers, so it remains 3 in one of the binomials.}[/tex]

[tex]\underline{\textsf{We should have;}}[/tex]

[tex]\tt (3x+?)(x+?)[/tex]

[tex]\textsf{We don't have to worry about} \ \tt 3x^{2} \ \textsf{anymore.}[/tex]

[tex]\textsf{Our goal is to find factors of 28 that multiply to get to 25x and 28.}[/tex]

[tex]\textsf{We might need to try many factor pairs before we have our factored expression.}[/tex]

[tex]\underline{\textsf{Factors of 28;}}[/tex]

[tex]\tt 28: 1, 2, 4, 7, 14, 28.[/tex]

[tex]\textsf{We should substitute the factor pairs in, then FOIL.}[/tex]

[tex]\textsf{Foiling is multiplying 2 binomials together.}[/tex]

[tex]\underline{\textsf{Substitute;}}[/tex]

[tex]\tt (3x+1)(x+28) = 3x^{2}+85x+28[/tex]

[tex]\textsf{Incorrect Factor Pair Whether Flipped or Not.}[/tex]

[tex]\tt (3x+2)(x+14)=3x^{2}+44x+28[/tex]

[tex]\textsf{Incorrect Factor Pair Whether Flipped or Not.}[/tex]

[tex]\large\boxed{\tt (3x+4)(x+7)=3x^{2}+25x+28}[/tex]

[tex]\textsf{Correct Factor Pair. If these factors were flipped it would be incorrect.}[/tex]

After solving the length of BM is 4 cm.

As we know from the question;

AB = 8cm

DL ⊥ AB

BM ⊥ AD

DL = 5cm

AD = 10cm

Think about the parallelogram ABCD now.

Here, let AB be the parallelogram's base and DL be its altitude (height).

The parallelogram's area is determined by: Base × Height

Area of ‖gm ABCD = AB × DL

Area of ‖gm ABCD = 8 × 5

Area of ‖gm ABCD = 40cm²

Now,

Think of AD as the parallelogram's base, and BM as its altitude (height).

area of ‖gm ABCD = AD × BM

10 × BM = 40cm²

Divide by 10 on both side,

BM = 40/10

BM = 4cm

length of BM = 4cm.

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The complete question is:

In ‖gm ABCD, it is given that AB = 8cm, DL ⊥ AB and BM ⊥ AD such that DL = 5cm and AD = 10cm. Then, BM = ?

The function that describes the profit earned from the sales of the bikes over a period of x years is: [tex]P(x) = 100x^3 + 6x^2 + 9x[/tex]. The Option A is correct.

The profit earned from the sales of the bikes can be calculated by subtracting the cost of manufacturing from the revenue earned. Therefore, the function that describes the profit earned can be represented as:

[tex]P(x) = S(x) - C(x)[/tex]

Substituting the given functions for S(x) and C(x), we get:

[tex]P(x) = (100x^3 + 6x^2 + 97x + 215) - (88x + 215)[/tex]

Simplifying this expression, we get:

[tex]P(x) = 100x^3 + 6x^2 + 9x.[/tex]

Full question "A company sells bikes that are light and fast. The revenue earned over a period of x years can be represented by the function, S(x) = 100x3 + 6x2 + 97x + 215. The cost of manufacturing the bikes can be represented by the function, C(x) = 88x + 215. Which function, P(x), describes the profit earned from the sales of the bikes over a period of x years?"

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The lateral surface and the total surface areas of the prism are 96 in² and 2304 in² respectively.

The surface area of a solid object is a measure of the total area that the surface of the object occupies.

Given is prism, we need to find the lateral surface and the total surface areas,

Lateral surface area = (perimeter of base) × length

Perimeter of base = 3 × 4 = 12 in

length = 8 in

The lateral surface area = 12 × 8 = 96 in²

Total surface area = (perimeter of base) × length × 2(base area)

= 96 × 2(3×4)

= 96 × 24

= 2304 in²

Hence, the lateral surface and the total surface areas of the prism are 96 in² and 2304 in² respectively.

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Answer:

3 pages per minuet 90pages/30min=3 pages per min

Step-by-step explanation:

Answer:

3 pages

Step-by-step explanation:

Create a ratio:

30 minutes is equal to 1 hour

90 pages/30 minutes

Divide 90/30

90/30=3

Alya reads 3 pages per minutes

Hope this helped you!

Stay safe and have a good day/night! :)