Question 1
At the St. George's College bookshop, pens are sold at x dollars and rulers at
y dollars each. A student bought 4 pens and 5 rulers for $24 on Monday. He
then went back on Tuesday and bought 2 of the same pens and 7 of the same
rulers for $21.
i.
ii.
Write two equations in x and y to represent the information given above.
[2 marks]
Solve the equations for x and y.
[4 marks]
Calculate the total cost for one pen and one ruler.
ni.

Answer:

Step-by-step explanation:

6y-42=4y

2y=42

y=21

6x-12=2x+36

4x=48

x=12

Answer:

see the attachment!

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Answer:

x = 2, 6

Step-by-step explanation:

differentiate f(x) using the power rule

f'(a\(x^{n}\) ) = na\(x^{n-1}\) and f'( constant) = 0

given

f(x) = x³ - 12x² + 6x - 8

f'(x) = 3x² - 24x + 6

equate f'(x) to - 30

3x² - 24x + 6 = - 30 ( add 30 to both sides )

3x² - 24x + 36 = 0 ( divide through by 3 )

x² - 8x + 12 = 0 ← in standard form

(x - 2)(x - 6) = 0 ← in factored form

equate each factor to zero and solve for x

x - 2 = 0 ⇒ x = 2

x - 6 = 0 ⇒ x = 6

solution is x = 2, 6

angle has a measure equal to the sum of the the question is ∠DQS.


According to the problem, we need to find an angle whose measure is equal to the sum of the measures of ∠SQR and ∠QRS. We can use the angle addition postulate which states that the measure of an angle formed by two adjacent angles is equal to the sum of their measures.

Let's consider angle ∠DQS. This angle is formed by adjacent angles ∠SQR and ∠QRS. Therefore, according to the angle addition postulate, the measure of angle ∠DQS is equal to the sum of the measures of ∠SQR and ∠QRS.



Thus, we can conclude that the angle ∠DQS has a measure equal to the sum of the measures of ∠SQR and ∠QRS.

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Yes, If ABCD ≅ EFGH, are all corresponding parts congruent or same.

Congruent figures are identical in terms of both size and shape. Congruent figures have equal comparable sides and angles.

Congruent figures are identical copies of one another.

In other words, two figures are congruent if they can be converted into one another through a series of translations, rotations, and/or reflections.

Hence, Yes, If ABCD ≅ EFGH, are all corresponding parts congruent or same.

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An eating disorder characterized by bingeing and purging is called bulimia nervosa.

The minimum amount of body fat needed for good health is variable and can depend on factors such as age, gender, and individual circumstances. However, essential body fat is typically estimated to be around 3-5% for men and 8-12% for women.

The term used to describe a person who is very overfat is obese. Obesity refers to having excessive body fat, which can have negative effects on health.

People with anorexia nervosa, an eating disorder characterized by restrictive eating and an intense fear of gaining weight, often see themselves as too fat even when they are extremely thin. This distorted body image is a characteristic feature of anorexia nervosa.

A technique for assessing body fat levels that involves being weighed under water is called hydrostatic weighing or underwater weighing. It is considered one of the more accurate methods for determining body composition.

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Answer:

d =122.5 miles

Step-by-step explanation:

We know the formula is

d= rt

d is distance   r = rate and t is time

d = 35 miles per hour * 3.5 hours

d =122.5 miles

Answer:

122.5 miles traveled

Step-by-step explanation:

35 miles x 3.5 hours = 122.5 total miles traveled

Answer:

Yes, according to the angles and sides of the hills

Answer:

Answers

1.  40o, obtuse

2.  90o, right

3.  scalene

4a.  equilateral

4b.  isosceles

4c.  scalene

5.  An acute triangle has 3 acute angles, not just 1.  The figure contains a right angle and is therefore a right triangle.

6.  obtuse

7.  58o, acute

8.  Yes, because the measures add up to 180o.

9.  C

10.  The triangle would be isosceles, because isosceles triangles have two sides the same length.

Step-by-step explanation:

Answer:

Andre

7 p squared q + 7 p q squared minus 1 minus 2 p squared q minus 9

Step-by-step explanation:

5 p squared q + 7 p q squared minus 10.

5p²q + 7pq² - 10

7 p squared q + 7 p q squared minus 1 minus 2 p squared q minus 9

7p²q + 7pq² - 1 - 2p²q - 9

5p²q + 7pq² - 10

Jill

5 p squared q + 2 p q squared minus 6 + 5 p q squared minus 3

5p²q + 2pq² - 6 + 5pq² - 3

5p²q + 7pq² - 9

Anuj

4 p squared q + 7 p q squared minus 7 + 2 p squared q minus 3

4p²q + 7pq² - 7 + 2p²q - 3

6p²q + 7pq² - 10

Marsha

5 p squared q + 5 p q squared minus 10 + 3 p q squared

5p²q + 5pq² - 10 + 3pq²

5p²q + 8pq² - 10

The correct answer is:

Andre

7 p squared q + 7 p q squared minus 1 minus 2 p squared q minus 9

7p²q + 7pq² - 1 - 2p²q - 9

5p²q + 7pq² - 10

Answer:

Its andre, Plz give the other guys brainly

Step-by-step explanation:

There are two main subtypes of quantitative data, which are discrete data and continuous data. Each subtype has different techniques for analysis.

1. Discrete data: This type of data represents whole numbers or counts that can only take specific values. Examples include the number of students in a class or the number of cars in a parking lot. Techniques used to analyze discrete data include:
  a. Frequency distribution: A summary of the number of times each value appears in the dataset.

 b. Measures of central tendency: Calculating the mean, median, and mode of the dataset to understand its central point.

 c. Measures of dispersion: Assessing the range, variance, and standard deviation to understand the spread of the data.

2. Continuous data: This type of data represents measurements that can take any value within a range, such as height, weight, or temperature. Techniques used to analyze continuous data include:

 a. Histogram: A graphical representation of the distribution of the data, using bars to represent the frequency of values within specific intervals.

  b. Probability density function: A mathematical function that describes the probability of a continuous random variable falling within a specific range.

  c. Regression analysis: A statistical method for analyzing the relationship between a dependent variable and one or more independent variables.

Both discrete and continuous data can also be analyzed using inferential statistics, such as hypothesis testing and confidence intervals, to make inferences about a population based on a sample of the data.

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Answer:

135 cm

Step-by-step explanation:

Usually dilations have a center of dilation at the origin (0,0). When this occurs all we need to do is multiply each coordinate by the dilation scale. Unfortunately things get a little more complicated when the center of dilation is not at the origin.

In this case the center of dilation is located at F: (3,1)

The first step we must take is to find how many units point F is from vertex A.

In this case, F is 4 unit up and 8 units right of vertex A. (Reference the first image below to see how I found this)

Now we must multiply these dimensions (4 units and 8 units) by the factor of dilation (0.25)

4 * 0.25 = 1

8 * 0.25 = 2

This shows us how many dimensions away point \(A^{1}\) is from point F:

1 unit vertically

2 units horizontally

Now how do we know if \(A^{1}\) is above or below, left or right from point F? Easy! There has been no translations so the directions will be the same as the original:

Point F: (3, 1) ---> (3-2, 1-1) ---> (1, 0)

Reference the second image to see this

Hopefully this helps and makes sense. Let me know if you need further explanation or clarification.

~Just a girl in love with Shawn Mendes

Answer:

D 1,0

Step-by-step explanation:

credit to the one up above

The smallest base-10 positive integer greater than 5 that is a palindrome when written in both base 2 and 4 is 11.

To compute this, first convert 5 to binary and base-4:

5 in binary: 101

5 in base-4: 11

Since 11 is the same in both bases, the next number that would be a palindrome in both bases is 11.

To find the base 10 number of this palindrome, we convert 11 from binary and base-4 to base 10:

11 in binary: 1011

11 in base-4: 111

Therefore, the smallest base-10 positive integer greater than 5 that is a palindrome when written in both base 2 and 4 is 11.

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The length of the curve from t = 0 to t = 1 is given by option c, √(a² + b²).

The length of the curve defined by the parametric equations x(t) = at and y(t) = bt from t = 0 to t = 1 can be found using the following steps:

Compute the derivatives dx/dt and dy/dt:
  dx/dt = a (since x(t) = at)
  dy/dt = b (since y(t) = bt)

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Answer:

Divide both sides by V

Step-by-step explanation:

The equation is not well written.

Mariko needs to solve the equation below for D. Here is the equation:

M = DV

For Mariko to get D, he needs to make D the subject of the formula by dividing both sides of the equation by the coefficient of D i.e V as shown;

Divide both sides by V

M/V = DV/V

V at the denominator will cancel out the V at the numerator to have:

M/V = D

Rearrange

D = M/V

Therefore, the statement which correctly describes the step he should take is:

Divide both sides by V. Option B is correct.

Answer:

9x + 4.5 − 2x = 2.3 + 7x + 2.2

Step-by-step explanation:

if you simplify then you get 7x+4.5=7x+4.5 which mean 0=0

Answer:

x + 5

x + 2

Step-by-step explanation:

x2−25

x2−3x−10

Simplify the numerator.

(x+5)(x−5)

x2−3x−10

Factor x2−3x−10 using the AC method.

(x+5)(x−5)

(x−5)(x+2)

Cancel the common factor of x−5.

x+5

x+2

Just so you know its wrote in a fraction type way so that line is for the fraction line. Hope you know what I mean and I hope it helped.

Also use a website called math-way is you ever need help with your math

The acute angles in the triangle are 16.6 degrees and 73.4 degrees

From the question, we have:

Triangle type = Right triangle

Let the acute angles be x and y.

So, we have:

3/4x = 1/4 + 1/6y

Multiply through by 12

9x = 3+ 2y

The sum of acute angles in a right triangle is

x + y = 90

Rewrite as

y = 90 - x

Substitute y = 90 - x in 9x = 3+ 2y

9x = 3+ 2(90 - x)

Open the brackets

9x = 3+ 180 - 2x

Evaluate the like terms

11x = 183

Divide by 11

x = 183/11 = 16.6

Substitute x = 183/11 in y = 90 - x

y = 90 - 183/11

Evaluate

y = 807/11 = 73.4

Hence, the acute angles in the triangle are 16.6 degrees and 73.4 degrees

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The formula for the exponential function is V = 5000 (2)^(−t/4).

What is an exponential function?

A function whose value is a constant raised to the power of an argument is called an exponential function.

Here, we have

The value of an item initially worth $5000 loses half its value every 5 years.

V = V₀eˣⁿ

At t = 0,V = V₀

So, V = 5000eˣⁿ

At t = 4,V = V₀/2 = 2500

Substituting these into our equation, we have

5000e^(4k) = 2500

e^(4k) = 12

4k = −ln2

k = −ln2/4

Finally, we have our equation

V = 5000e^(−tln2/4 )

V = 5000(e^ln2)^(−t/4)

V = 5000 (2)^(−t/4)

Hence, the formula for the exponential function is V = 5000 (2)^(−t/4).

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9514 1404 393

Answer:

  -2

Step-by-step explanation:

The first two terms have a common factor of x. Taking that out gives ...

  (x² +5x -2) ÷ (x +5)

  = (x(x +5) -2) ÷ (x +5)

  = x -2/(x +5)

The remainder is -2.

_____

The remainder can also be found by evaluating (x² +5x -2) for x = -5:

  (-5)² +5(-5) -2 = 25 -25 -2 = -2

The remainder is -2.

Answer: I hope you feel better.

When drawing two slips of paper at random from a hat containing slips numbered 1 through 6, without replacing the first slip, there are 15 possible outcomes.

To determine the number of possible outcomes, we consider that when drawing the first slip, there are 6 options (numbers 1 through 6). After drawing the first slip, there are 5 remaining slips in the hat.

When drawing the second slip, there are 5 options available since the first slip is not replaced. Therefore, the total number of possible outcomes is the product of the number of options for each draw: 6 options for the first draw multiplied by 5 options for the second draw.

Thus, there are 6 x 5 = 30 possible outcomes. However, we need to account for the fact that the order of the slips does not matter. For example, drawing slip 1 and then slip 2 is the same as drawing slip 2 and then slip 1. Therefore, we need to divide the total number of outcomes by 2.

So, the final number of possible outcomes is 30 / 2 = 15.

In summary, when drawing two slips of paper at random from a hat containing slips numbered 1 through 6, without replacing the first slip, there are 15 possible outcomes.

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Answer:40

Step-by-step explanation:

their is 3 type of cheese and he buy 120

120/3=40

Answer:

bvhjk

Step-by-step explanation:

The prevalence rate per 100,000 is 99.8%

We know that the prevalence rate is the proportion of persons in a population who have a particular disease over a specified period of time.

In this question, we have been given a data on breast cancer for the past year:

number of new cases: 1,774;

number of total cases: 4,192;

population: 5,977,906

We need to find the prevalence rate per 100,000

The total number of infected people = 1,774 + 4192

                                                             = 5966

Chance of infection in the whole population would be,

5,977,906/ 5966 ≈ 1002

This means, chances of having breast cancer is 1 in every 1002 people.

A prevalence rate is calculated by dividing total number of infected people by the total population. The result is then multiplied by 100,000

Now we calculate the prevalence rate per 100,000

= (5966 / 5,977,906) × 100,000

= 0.000998 × 100,000

= 99.8 %

Therefore, the prevalence rate per 100,000 is 99.8%

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Answer:

3

Step-by-step explanation:

Therefore , the solution of the given problem of volume comes out to be false we must first know the cylinder's radius and height.

A three-dimensional object's volume, which is expressed in cubic units, indicates how much space it takes up. The symbols cm3 and in3 stand for cubic dimensions. However, you can use an object's bulk to estimate its dimensions. Usually, the weight of the item is converted into mass measures like kilograms and kilos.

Here,

The capacity of a cylinder and a cone that are the same height and radius are not the same.

The formula V = πr²h,

where r is the radius of the base and h is the height, determines the volume of a cylindrical. Contrarily, the equation

=> V = (1/3)r²h gives the volume of a cone.

To calculate the volume of a cone with the same measurements if the cylinder's volume is 99 cubic cm,

False we must first know the cylinder's radius and height.

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