1|G9_ IGCSE1 - Chapter 14 Linear inequalities - Question 1 Solve the inequality. 3n-5> 17+8n Math​

Disjoint events are events that cannot happen at the same time. Two events A and B are independent if the occurrence of A does not affect the probability of B happening, and vice versa. Mathematically, this can be written as P(A and B) = P(A)P(B).

In the case of disjoint events, P(A and B) = 0 because they cannot occur at the same time. Therefore, the condition for A and B to be independent is that either P(A) = 0 or P(B) = 0, since any non-zero probability for either event would make the product P(A)P(B) also non-zero.

Two disjoint events are independent if and only if at least one of them has zero probability.

To learn more about probability : brainly.com/question/32004014

#SPJ11

Answer: 50°

Step-by-step explanation:

7 and 6 are vertical angles, which means they are equal. m<7 and m<6 are 130 degrees. Then. m<4 and m<6 are supplementary angles, and if m<6 is 130°, then you subtract that from 180 to get 50 = m<4. m<4 and m<1 are vertical angles, so that means m<1 is 50°.

The x-intercept for the given equation is x = -3.

Given is an equation 2x-y = -6, we need to find the x-intercept for the line,

So the x-intercept of a line is the point where it cuts the x-axis,

To find the x-intercept we will put y = 0,

So,

2x - 0 = -6

2x = -6

x = -3

Or, you can just see the points from which it is passing the x-values will be the x-intercept,

Hence the x-intercept of the line is x = -3.

Learn more about x-intercept click;

https://brainly.com/question/14180189

#SPJ1

Answer:

4(x+1)+5(5x-4)

=4x+4+25x-20

=29x-16

[tex]\stackrel{ \textit{\LARGE sum of all exterior angles} }{(6x+24)+(6x+26)+(4x+10)+(3x-22)+(5x-14)~~ = ~~360} \\\\\\ 24x+24=360\implies 24x=336\implies x=\cfrac{336}{24}\implies x=14[/tex]

The component form of the vector that describes the drummer's movement is <4, -3>.

The component form of a vector is given by the difference between the coordinates of the endpoints.

The initial point is (1, 4) and the final point is (5, 1).

Thus, the horizontal component is the difference between the x-coordinates, which is 5 - 1 = 4,

and the vertical component is the difference between the y-coordinates, which is 1 - 4 = -3.

Therefore, the component form of the vector that describes the drummer's movement is <4, -3>.

Learn more about Vector here:

https://brainly.com/question/29740341

#SPJ1

The input - output pairs of the linear function are given as follows:

The slope-intercept representation of a linear function is given by the equation shown as follows:

y = mx + b

The coefficients m and b have the meaning presented as follows:

From the table, when x increases by 8, y increases by 16, hence the slope m is given as follows:

m = 16/8

m = 2.

Hence:

y = 2x + b.

When x = 7, y = 16, hence the intercept b is given as follows:

16 = 14 + b

b = 2.

Hence the function is:

y = 2x + 2.

The output for an input of 25 is given as follows:

y = 2 x 25 + 2

y = 52.

The input for an output of 22 is given as follows:

22 = 2x + 2

2x = 20

x = 10.

The output for an input of 2x is given as follows:

y = 2(2x) + 2

y = 4x + 2.

The output for an input of x + 3 is given as follows:

y = 2(x + 3) + 2

y = 2x + 8.

More can be learned about linear functions at https://brainly.com/question/15602982

#SPJ1

The factored expression of the expression 4x³ - 6x² + 8x is 2x(2x² - 3x + 2)

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

4x³ - 6x² + 8x

The above expression is a polynomial expression

So, we have the following

4x³ - 6x² + 8x

Factor out x in 4x³ - 6x² + 8x

This gives

4x³ - 6x² + 8x = x(4x² - 6x + 8)

Factor out 2 in 4x² - 6x + 8

This gives

4x³ - 6x² + 8x = 2x(2x² - 3x + 2)

Hence, the factored expression is 2x(2x² - 3x + 2)

Read more about expression at

https://brainly.com/question/4344214

#SPJ1

The slope of the line that passes through the given points (2 12) and (6 11) is  -1/4.

Two points are given: (2, 12), (6, 11).

A line's "steepness" is quantified by a quantity called the slope, which is typically represented by the letter m. It is the adjustment of y for a unit adjustment of x.

We are aware that the formula for the slope of a line using two points is

m= y2 - y1 /x2 - x1

In this instance, x1 = 2, Y1 = 12, X2 = 6, Y2 = 11.

m = 11 - 12 / 6 - 2

m = -1/4

The slope is therefore -1/4.

To know more about  the Slope of a line

brainly.com/question/29775018?referrer=searchResults

Figure D, two lines that are the same distance apart :)

The area of the metal base for the water heater is approximately 452.2 square inches (rounded to the nearest tenth).

The radius of the hot water heater is 10 inches (half of the diameter). To find the radius of the base, we add the 2-inch overhang to the radius of the heater: 10 + 2 = 12 inches.

Now we can calculate the area of the base using the formula for the area of a circle: A = πr²

A = π(12)²  = 452.4 square inches (rounded to the nearest tenth).

Therefore, the area of the metal base for the hot water heater is 452.4 square inches.



To find the area of the metal base for the hot water heater, we need to calculate the area of a circle with a radius of 12 inches.

We get this radius by adding the 2-inch overhang to the radius of the heater, which is 10 inches. Using the formula for the area of a circle, A = πr² , we can plug in our value for r and solve for A.

After rounding to the nearest tenth, we get an area of 452.4 square inches. Therefore, the metal base needs to have an area of at least 452.4 square inches to properly support the hot water heater.


The area of the metal base for the hot water heater is 452.4 square inches, which was found by calculating the area of a circle with a radius of 12 inches (10 inch radius of the heater + 2 inch overhang). This information can be used to ensure that the base is the correct size and can properly support the hot water heater.

To know more about area of a circle visit:

brainly.com/question/28642423

#SPJ11

The measure of angles m∠QTR and m∠PTQ are 98.25° and 81.75° respectively, using the angle N between intersecting tangents.

The angle between two tangent lines which intersect at a point is 180 degrees minus the measure of the arc between the two points of tangency.

61.5 = 180 - arc PS

arc PS = 180 - 61.5

arc PS = 118.5

m∠QTR = 1/2 × (118.5 + 78) {intersecting chords}

m∠QTR = 196.5/2

m∠QTR = 98.25

m∠PTQ = [360 - 2(98.25)]/2 {one of the angles at a point}

m∠PTQ = 163.5/2

m∠PTQ = 81.75

Therefore, measure of angles m∠QTR and m∠PTQ are 98.25° and 81.75° respectively, using the angle N between intersecting tangents.

Read more about tangents here:https://brainly.com/question/9132922

#SPJ1

Answer:

The correct answer is 9%.

The correlation coefficient r is a measure of the linear relationship between two variables. It can range from -1 to 1. A value of 0 means that there is no linear relationship between the variables. A positive value of r means that the variables are positively correlated, i.e., as one variable increases, the other variable also increases. A negative value of r means that the variables are negatively correlated, i.e., as one variable increases, the other variable decreases.

The square of the correlation coefficient, r^2, is called the coefficient of determination. It is a measure of the percentage of variation in the dependent variable that is explained by the variation in the independent variable. In this case, r = 0.3, so r^2 = 0.09. This means that 9% of the variation in the dependent variable is explained by the variation in the independent variable.

The other answers are incorrect. 0.09% is too small, 3% is too large, and 30% is much too large.

Step-by-step explanation:

Brian orders 1000 t-shirts, and demand is 850, resulting in a $2200 profit after expenses and revenue.

To calculate the payoff for Brian if he orders 1000 t-shirts and the demand is 850, we need to consider the costs and revenues involved.

Costs:

Brian purchases each t-shirt for $6, so the cost of ordering 1000 t-shirts is 1000 * $6 = $6000.

Additionally, Brian incurs a service fee of $300.

Revenues:

Brian plans to sell each t-shirt for $10.

If the demand is 850, he will be able to sell 850 t-shirts.

Revenue from t-shirt sales:

Revenue = Selling price per t-shirt * Number of t-shirts sold

Revenue = $10 * 850 = $8500

Payoff:

The payoff is calculated by subtracting the costs from the revenues.

Payoff = Revenue - Costs

Payoff = $8500 - ($6000 + $300)

Payoff = $8500 - $6300

Payoff = $2200

Therefore, if Brian orders 1000 t-shirts and the demand is 850, his payoff would be $2200. This represents the profit he would make after accounting for the costs of purchasing the t-shirts and the service fee, and the revenue generated from selling the t-shirts.

To learn more about revenue from the given link

https://brainly.com/question/30495119

#SPJ4

Volume of cylinder is, V = 99π km³

And, Volume of sphere is, V = 457.3π meter³

Given that;

8) In cylinder;

Diameter = 18 km

Height = 11 km

9) In sphere,

Diameter = 14 m

Since, We know that;

Volume of cylinder is,

V = πr²h

V = π × 18/2 × 11

V = π × 9 × 11

V = 99π km³

And, We know that;

Volume of sphere is,

V = 4/3πr³

Hence, WE get;

V = 4/3 × π × (14/2)³

V = 4/3 × π × 7³

V = 457.3π meter³

Thus, We get;

Volume of cylinder is, V = 99π km³

And, Volume of sphere is, V = 457.3π meter³

Learn more about the circle visit:

https://brainly.com/question/24810873

#SPJ1

The total number of ways to assign employees to desks is 720 (6!), and the number of favorable outcomes is 144. Therefore, the probability is 144/720 = 1/5.

The total number of ways to assign six employees to six desks is 6! (6 factorial), which equals 720. Now we need to find the number of ways that the married couple will not have adjacent desks.

First, we can treat the married couple as one entity, which means we have 5 entities to assign to 6 desks. There are 6 possible ways to choose the position of the married couple in the row. For each of these positions, we can then assign the other 4 entities to the remaining 4 desks in 4! ways.

Therefore, the total number of ways to assign employees to desks without the married couple having adjacent desks is 6 x 4! = 144.

The probability of this happening is the number of favorable outcomes (144) divided by the total number of possible outcomes (720), which is 144/720 = 1/5.



The probability that the married couple will not have adjacent desks when six new employees are randomly assigned to six desks that are lined up in a row is 1/5.

We calculated this probability by first treating the married couple as one entity and then finding the number of ways to assign the remaining entities to the desks without the married couple being adjacent to each other. The total number of ways to assign employees to desks is 720 (6!), and the number of favorable outcomes is 144. Therefore, the probability is 144/720 = 1/5.

To know more about probability   visit:

brainly.com/question/32004014

#SPJ11

The statement which is true is (1) It is okay to use the median to estimate the mean since both are a measure of the center of a distribution.

While both the median and the mean provide information about the center of a distribution, they are not interchangeable. The median represents the middle value of a dataset, while the mean represents the average value. In some cases, the median may be a better estimate of the center, especially when dealing with skewed distributions or outliers.

The standard deviation and the interquartile range (IQR) are two different measures of variability. The standard deviation measures the dispersion of data around the mean, while the IQR measures the range between the first quartile (25th percentile) and the third quartile (75th percentile). They capture different aspects of the data's spread and are not interchangeable.

Point estimates based on a sample, such as the sample mean or proportion, are subject to sampling variability. These estimates may not perfectly match the true population parameter they aim to estimate. The difference between a point estimate and the true parameter is known as sampling error, and it can be substantial, especially for small sample sizes. It is important to acknowledge and consider this potential variability when interpreting point estimates.

Know more about standard deviation here:

https://brainly.com/question/29115611

#SPJ11

The sum of the lengths of the two parallel sides, a + b, is equal to 30 centimeters.

Let's denote the lengths of the two parallel sides of the trapezoid as a and b. The formula for the area of a trapezoid is given by:

Area = (1/2) * (a + b) * h

where h represents the height of the trapezoid.

We are given that the area is 120 square centimeters and the height is 8 centimeters. Substituting these values into the formula, we have:

120= 1/2*(a+b)*8  

Multiplying both sides of the equation by 2 and dividing by 8, we get:

240 = a + b

a+b = 120*2/8

= 30 cm

Therefore, the sum of the lengths of the two parallel sides, a + b, is equal to 30 centimeters.

For such more questions on parallel sides:

https://brainly.com/question/30719270

#SPJ11

a is correct

Step-by-step explanation:

The true statement is,

⇒ The joint frequencies is that twenty-three 9th graders and fifteen 11th graders prefer math.

Now, Based on the given table, the statement that is true about the joint frequencies is that twenty-three 9th graders and fifteen 11th graders prefer math.

Since, The given table shows that in the first column, under the ninth grade row, there are 18 students who prefer math and in the third column, under the 11th grade row, there are 15 students who prefer science.

Hence, There are no joint frequencies given that add up to 23, so the only true statement among the options is the first one.

Thus, The true statement is,

⇒ The joint frequencies is that twenty-three 9th graders and fifteen 11th graders prefer math.

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

Answer answer is b dont trust the otha dude

Step-by-step explanation:

The key feature that f(x) and g(x) have in common is that they both have a y-intercept of (0, 5). They differ in terms of their domain, range, and x-intercepts.

The function f(x) = -4^x + 5 is an exponential function, while g(x) = x^3 + x^2 - 4x + 5 is a polynomial function of degree 3.

To show that f(x) is an exponential function, we can observe that it has the form f(x) = a*b^x + c, where a = 5, b = -4, and c = 0. This function has a domain of all real numbers and a range of (0, 5). The x-intercept is not defined since the base of the exponential function is negative, and the y-intercept is (0, 1).

On the other hand, g(x) is a polynomial function of degree 3, which means that it has the form g(x) = ax^3 + bx^2 + cx + d. This function has a domain of all real numbers and a range of (-∞, ∞). The x-intercepts can be found by setting g(x) equal to zero and solving for x, while the y-intercept is (0, 5).

For such more questions on Key feature:

https://brainly.com/question/29195189

#SPJ11

The sales boy has a sale of $142.9.

Given that the commission given to a sales boy is 5%, he earns $150, we need to find the sale he did for the month,

So,

Let the sale be x,

Therefore,

x + 5% of x = 150

x of 105% = 150

x × 1.05 = 150

x = 142.9

Hence the sales boy has a sale of $142.9.

Learn more about commission click;

https://brainly.com/question/20987196

#SPJ1

Therefore, the control represented by the decimal value 15 is the one with all four bits set to 1.

In digital electronics, binary digits (bits) are used to represent numbers and control various devices. Each bit can have a value of either 0 or 1, and by combining multiple bits, we can represent larger numbers or control signals. The decimal system, which we are most familiar with, uses 10 digits (0-9) to represent numbers. In contrast, the binary system uses only 2 digits (0 and 1) to represent numbers or controls. To convert a decimal number to binary, we repeatedly divide the number by 2 and keep track of the remainders. The binary representation of a number is the sequence of remainders read in reverse order.

The decimal value 15 can be represented as a control with four binary digits (bits), as follows:

1 1 1 1

Each bit represents a power of 2, from right to left: 2^0, 2^1, 2^2, 2^3. Adding up the powers of 2 where there is a 1 in the binary representation gives us the decimal value.

So, in this case, we have:

1x2^0 + 1x2^1 + 1x2^2 + 1x2^3 = 1 + 2 + 4 + 8 = 15

To know more about decimal value,

https://brainly.com/question/31494892

#SPJ11

The rate at which the area of the circle is increasing at the moment when the circumference of the circle is 27/2 inches is 9 inches squared per second.

derivative of the circle's area with respect to time.

The area of a circle is given by the formula A = πr^2, where r is the radius of the circle.

Given that the radius is increasing at a constant rate of 2/3 inches per second, we can express this as dr/dt = 2/3.

We are also given that the circumference of the circle is 27/2 inches. The formula for the circumference of a circle is C = 2πr.

Plugging in the given circumference value, we have 27/2 = 2πr. Solving for r, we get r = (27/4π) inches.

Now, we can differentiate the area formula with respect to time:

dA/dt = d/dt (πr^2)

= 2πr(dr/dt)

Substituting the values, we have:

dA/dt = 2π(27/4π)(2/3)

= (27/2)(2/3)

= 9 inches squared per second

Know more about circumference of the circle here;

https://brainly.com/question/17130827

#SPJ11

A correlation of .9 indicates that 81% of the variance between two variables has been explained.

Correlation measures the strength of the relationship between two variables. A perfect positive correlation is 1.0, indicating that the two variables move in the same direction together. A perfect negative correlation is -1.0, indicating that the two variables move in opposite directions. A correlation of 0 indicates no relationship between the two variables.

To determine the proportion of variance explained by a correlation, you need to square the correlation coefficient (in this case, 0.9). This is called the coefficient of determination (R^2). So, you calculate:

R^2 = (0.9)^2 = 0.81

Thus, a correlation of 0.9 explains 81% of the variance between the two variables.

To know more about variables visit:

https://brainly.com/question/29583350

#SPJ11

These tests would allow us to determine if the observed sample mean of $934 is significantly different from the claimed average of $1250, providing evidence to support or reject the alternative hypothesis.

To test the claim made by the IRS representative that the average deduction for medical care is $1250, we can formulate the null and alternative hypotheses as follows:

Null Hypothesis (H0): The average deduction for medical care is $1250.

Alternative Hypothesis (H1): The average deduction for medical care is lower than $1250.

In this case, the taxpayer who believes that the real figure is lower has collected a sample of 32 random families. The sample mean is $934, and the sample standard deviation is $619. The null hypothesis assumes that the average deduction is $1250, while the alternative hypothesis suggests that it is lower than $1250.

To statistically test these hypotheses, we can use a one-sample t-test or a z-test, depending on the sample size and whether the population standard deviation is known.

Know more about alternative hypothesis here:

https://brainly.com/question/30404845

#SPJ11