Workers in an office of 40 staff were asked their favourite type of take-away. The results are summarised in the table. Take-away Frequency Angle Pizza 3 a Curry 12 b Fish & chips 7 c Kebab 3 d Other 15 e Work out the size of each angle to draw a pie chart.

Answer:

(2.57, -0.07)

Step-by-step explanation:

To solve the system of equations, we can substitute the expression for y in the second equation:

-5x + 4(1/8x - 1) = -13

We can then simplify and solve for x:

-5x + (1/2)x - 4 = -13

-3.5x = -9

x = 2.57

We can then substitute this value of x back into the first equation to find the value of y:

y = 1/8(2.57) - 1

y = -0.07

So the solution of the system of equations is (x, y) = (2.57, -0.07)

Answer:

6

Step-by-step explanation:

3/4 x 8 = 3 x 8 / 4 x 1 = 24/4 = 6

The parent function and transformed function will be y = ln x and y = ln (x + 8) + 12, respectively.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The function is given below.

y = ln x

The function is transformed by shifting 8 units left and 12 units up. Then replace x with (x + 8) and y with (y - 12). Then we have

y - 12 = ln (x + 8)

y = ln (x + 8) + 12

The parent function and transformed function will be y = ln x and y = ln (x + 8) + 12, respectively. The graph of the function is given below.

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For the given statement, the domain and range are - Domain : x ,Range : f(x)  40.

In mathematical notation, symbols are used in expressions and formulas to represent operations, unnamed numbers, relations, and any other mathematical objects. In mathematics, science, and engineering, mathematical notation is frequently used to communicate complicated ideas and properties in a clear, unambiguous manner.

A notation is a set of clear guidelines for using symbols to describe numbers and actions.

The sum of numerous linked terms is frequently represented by the sign (capital sigma) in shorthand notation. In statistics, sigma notation is frequently employed.

For each dividend number, the extended notation division method merely repeats the division, multiplication, and subtraction operations.

Given data :

x is the mass of the chicken (in kg)

f(x) : the cooking time ( in minutes )

Domain : x

Range : f(x)  40

f(x) = 15x + 40 - 15 minutes per kg (x) plus 40 more minutes

f (1) = 15 x 1 + 40 = 55

A 1 kg chicken needs 15 min + 40 min = 55 min

f (2) = 15 x 2 + 40 = 70

A 2 kg chicken needs 30min + 40 min = 70 min

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1 :1 is the blend as a ratio of corn oil to olive oil.

Now, According to the question:

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls)

"Information available from the question"

A chef made a blend of cooking oil.

1/5 of his mix was olive oil

and 4/5 was corn oil.

To find the blend as a ratio of corn oil to olive oil.

Now, Blend Ratio will be:

olive ratio + corn ratio

1/5 + 4/5

= 5/5 = 1/1

Hence, 1:1 is the blend as a ratio of corn oil to olive oil.

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If there is a 1/6 chance that a student will be in Miss Jones's math class, if there are 30 students in her class, then 180 students will be there at all.

Probability is a method to know how likely something is going to happen. Whenever we're uncertain about the outcome of an event, we can talk about the probabilities of certain outcomes. The analysis of events overseen by probability is called statistics.

Total number of students present in the miss jones class = 30

The chance that a student will be in Miss Jones's math class = 1/6

Let x be the students are there at all

According to the question,

1/6 × x = 30

⇒x = 30 × 6

⇒x = 180

Hence, 180 students are there at all.

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The given expression has sin A = BC/AC=36/85, cos A = AB/AC=77/85, tan A = BC/AB=36/77

In trigonometry, the values of sin, cos, and tan are the main functions we consider when solving trigonometric problems. Using these trigonometric values, the angles and sides of a right-angle triangle are calculated. In addition to sine, cosine, and tangent values, the other three significant values are cotangent, secant, and cosecant.

Normally, when calculating the sin, cos, and tan values for a triangle, the angles of 0°, 30°, 45°, 60°, and 90° are taken into consideration. These specific angles' values are easy to remember. What the trigonometric values are all about is knowing the standard angles for a specific triangle according to the trigonometric ratios (sine, cosine, tangent, cotangent, secant and cosecant).

We have, AB = 77 , BC = 36.and CA=85

When we consider the t-ratios of ∠A, we have

Base = AB = 77, Perpendicular = BC = 36, Hypotenuse = AC =85.

∴sin A = BC/AC=36/85 , cos A = AB/AC=77/85 , tan A = BC/AB=36/77

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The equation y+2 = 4(x-1) is already in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. In this equation, the slope is 4 and the y-intercept is -2.

For a line that is parallel to y+2 = 4(x-1), the slope (m) will be the same, which is 4.

To find the equation of a line that passes through a specific point (1,-3), we can use the point-slope form of a linear equation: y - y1 = m(x - x1)

So, using the point (1,-3) and the slope (4), we can write the equation as:

y - (-3) = 4(x - 1)

Simplifying this equation gives:

y + 3 = 4x - 4

Finally, we can write the equation in slope-intercept form by adding 4 to both sides and dividing both sides by 4:

y = 4x - 1

So the equation for the line that passes through (1,-3) and is parallel to y+2 = 4(x-1) is y = 4x - 1

When we simplify the expression (4x⁴y⁵ / 3xy²)⁵, the result obtained is 1024x¹⁵y¹⁵ / 243

To simplify the expression (4x⁴y⁵ / 3xy²)⁵, the laws of indices must be applied as illustrated below:

(4x⁴y⁵ / 3xy²)⁵

Recall

(Aᵐ)ⁿ = Aᵐⁿ

Thus,

(4x⁴y⁵ / 3xy²)⁵ = 1024x²⁰y²⁵ / 243x⁵y¹⁰

Recall

Aᵐ / Aⁿ = Aᵐ⁻ⁿ

Thus,

1024x²⁰y²⁵ / 243x⁵y¹⁰ = (1024 / 243)x²⁰⁻⁵y²⁵⁻¹⁰

1024x²⁰y²⁵ / 243x⁵y¹⁰ = (1024 / 243)x¹⁵y¹⁵

1024x²⁰y²⁵ / 243x⁵y¹⁰ = 1024x¹⁵y¹⁵ / 243

Therefore,

(4x⁴y⁵ / 3xy²)⁵ = 1024x¹⁵y¹⁵ / 243

From the above illustration, we can conclude that the simplified form of (4x⁴y⁵ / 3xy²)⁵ is 1024x¹⁵y¹⁵ / 243

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Answer:

13+15+17+19+21 = 85

Step-by-step explanation:

Hope you got it !

Answer:

The five consecutive odd integers whose sum will be 85 are 13, 15, 17, 19, and 21.

Step-by-step explanation:

To solve this problem, let's assume the first number is n.

Then the consecutive odd integers will be n+2, n+4, n+6, n+8

Thus we can write,

n+(n+2)+(n+4)+(n+6)+(n+8) = 85

In the next step add all the n's,

5n+20 = 85

Then transfer '20' from LHS to RHS,

5n = 85 - 20

5n = 65

Then in the next step '5' needs to be transferred to RHS,  

n = 65÷5

n = 13

Therefore, n = 13

n+2 = 15

n+4 = 17

n+6 = 19

n+8 = 21

Thus the five consecutive odd integers are 13, 15, 17, 19, and 21.

Answer:

4 2/9

Step-by-step explanation:

7 5/9 -3 1/3

68/9 -10/3

(68-30)/9

38/9

4 2/9

As the value of the ratio of both the quantities are NOT same so the given values .

No, The two rates not form a proportion.

Now, According to the question:

Two ratios are equivalent, if the fractions corresponding to them are equivalent. Four quantities are said to be in proportion, if the ratio of the first and the second quantities is equal to the ratio of the third and the fourth quantities.

A proportion is an equation that sets two ratios at the same value. For instance, you might express the ratio as follows:

1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls. 0.25 are male (by dividing 1 by 4)

Now,

0. 4 kilometer for every 15 minutes equals to (0.4/15) = 0.026

So for every minute they travel 0.026km.

0. 6 kilometer for every 20 minutes equals (0.6/20) =  0.03

So for every minute they travel 0.03km.

Here, as the value of the ratio of both the quantities are NOT same so the given values .

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The table for V* n and V/n shows the various answers as

Multiplication is when you take one number and add it together a number of times.

The table appears as follows

Volume(V)       Moles(n)          V*n               V/n

3                       0.145              0.435           20.7

4                        0.193             0.773            20.7

5                        0.242            1.210             20.7

6                       0.290             1.740             20.7

These figures are gotten by the multiplication and division of the numbers in the tables as given by the formulae

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There is sufficient evidence that the valve performs above the specifications.

Null Hypothesis (H0): The mean pressure of the valve is equal to 5.3 lbs/square inch

Alternative Hypothesis (H1): The mean pressure of the valve is greater than 5.3 lbs/square inch

To test whether the valve performs above the specifications, a hypothesis test can be used. The test statistic used will be a t-test since the sample size is below 30. The critical value at the 0.05 level is 1.645. The formula for the t-test is: t = (X-μ)/(s/√n) , where X is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size.

Plugging in the known values, the t-test is calculated as: t = (5.5-5.3)/(0.7/√100) = 2.571. Since this value is greater than the critical value at the 0.05 level (1.645), we can reject the null hypothesis and conclude that there is sufficient evidence that the valve performs above the specifications.

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Answer:

Classify the sequence {1, 6, 11, 16, 21, …}.

The pattern is +5:

1 + 5 = 6

6 + 5 = 11

11 + 5 = 16

16 + 5 = 21

21 + 5 = 26

And so on

Step-by-step explanation:

You're welcome

The required equation is y=3x-24, where x is the number of elementary school students and y is the number of middle school students.

An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =. In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the relationship between two expressions on opposite sides of the sign. It mostly consists of one variable and one equal to symbol. 2x - 4 = 2 is an example.

Here,

Let x be the number of students in elementary school and y be the number of students in middle school.

y=3x-24

The required equation is y=3x-24 where x be the number of students in elementary school and y be the number of students in middle school.

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The fraction of the circle that would represent food is given as 34.09

The data we have here is given as

Activities = 600

Food = 450

Souvenirs = 270

We would have to sum this up

600 + 450 + 270 = 1320

The proportion that represents food is given as 450

= 450 / 1320

= 0.3409

Then we would have to convert this to percentage

0.341 * 100

= 34.09

34.09 x 360 = 123 degrees

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The simplified form of the expression (3x² - 4xy + y²)(4x + 3y) is 12x³ - 7x²y + 8xy²  + 3y³.

Given the expression in the question;

(3x² - 4xy + y²)(4x + 3y)

To simplify, apply distributive property by multiplying each term in the first expression by each term in the second expression.

(4x + 3y)(3x² - 4xy + y²)

4x (3x² - 4xy + y²) + 3y(3x² - 4xy + y²)

3x² × 4x - 4xy × 4x  + y² × 4x  + 3x² × 3y - 4xy × 3y  + y² × 3y

12x³ - 16x²y + 4xy²  + 9x²y - 12xy²  + 3y³

Collect like terms

12x³ - 16x²y + 9x²y + 4xy²  - 12xy²  + 3y³

Add -16x²y and 9x²y

12x³ - 7x²y + 4xy² - 12xy²  + 3y³

Add 4xy²  and -12xy²

12x³ - 7x²y + 8xy²  + 3y³

Therefore, the simplified form is 12x³ - 7x²y + 8xy²  + 3y³.

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Based on the information provided, I have analyzed the three options for hosting a dance for the students of CISE, and have come to the following recommendations:

Ancient Abyss: This location charges a flat fee of $200 and $4 per person. This option may be suitable for smaller events with less than 50 attendees, as the flat fee is relatively high. However, for larger events with more than 50 attendees, the per person cost will become more significant and may make this option less cost-effective.

Beautiful Babylon: This location charges a flat fee of $99 and $6 per person. This option may be more cost-effective for larger events with more than 50 attendees, as the per person cost is lower than Ancient Abyss. However, for smaller events with less than 50 attendees, the flat fee may be relatively high.

Crazy Cleopatra: This location charges a flat fee of $280 and $3 per person. This option has the highest flat fee but the lowest per person cost. This option may be more cost-effective for larger events with more than 50 attendees, as the per person cost is lower than Beautiful Babylon. However, for smaller events with less than 50 attendees, the flat fee may be relatively high.

Based on the above analysis, I recommend that the student council consider Beautiful Babylon as the most cost-effective option for hosting the dance. However, I also recommend that the council consider the number of attendees expected at the event and adjust their decision accordingly.

In summary, The council should consider the number of attendees expected, Beautiful Babylon is a good option for larger events, for smaller events, Crazy Cleopatra is the better option.

Based on the information provided, the two numbers whose HCF is 101 are 1010 and 1313.

The HCF is the highest common factor or in other words, the highest number by which two numbers can be divided. Let's start by listing the four digits numbers that can be the HCF related to 101.

101 x 10 = 1010

101 x 11 = 1111

101 x 12 = 1212

101 x 13 = 1313

Now, from these numbers, there are two numbers whose difference is 303.

1313 - 1010 = 303

Based on this, the two numbers are 1010 and 1313

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A per the measurement, there is only form exactly 1 unique triangle.

The term triangle in math is known as a two-dimensional shape with three sides, three interior angles, and three vertices.

Here we have know that a rope 10 units in length, if side lengths must be in whole units.

And we need to find the number of different triangles can be made.

Here we know that length is 10 units, and the side length are whole units.

Which means that here we have 3 distinct value.

So as we all know that all of the triangles you make are the same triangle. Which means that if your three side lengths can form a triangle, then they can only form exactly 1 unique triangle.

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Answer:

milk

Step-by-step explanation:

milk store is where your dad went

The height of the figure is 66 m².

Finding the triangle's height can be done in a variety of ways. There are numerous other formulas, but the one that uses a triangle's area is the one that is most widely used. You can determine the triangle's area given its sides using an equation known as Heron's formula. Once you are aware of the region, you can use the fundamental equation to determine the triangle's altitude.

You multiply 27.5 and 4.8. Which gets you 132. And because your finding the area of a triangle you have to divide 132 by 2 which gets you 66.

27.5 × 4.8

= 132

132/2

= 66

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The account balance after five years will be $10355.

The interest that is paid on the principal and interest at regular intervals is known as compound interest. The difference between compound interest and simple interest starts to show after the first year, though.

The formula to calculate the compound interest is given below;-

[tex]A = P ( 1+\dfrac{R}{n})^{nt}[/tex]

Given that deposit at 7% annual interest compounded yearly to have $10,000 in the account at the end of 5 years.

The account balance after five years will be:-

[tex]A = P ( 1+\dfrac{R}{n})^{nt}[/tex]

[tex]A = 10000 ( 1+\dfrac{0.07}{1})^{5}[/tex]

A = 10000 x ( 1.07)⁵

A = $10355

Hence, the amount will be $10355.

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Answer:

I don't know

Step-by-step explanation:

Answer: 12.5%

(Don't worry!)

Total amount of fluid ounces of water used by Sofia to make proportionate amount of slime is equal to 4.8 fluid ounces.

Let us consider 'x' amount of salt solution.

Amount of glue used by Sofia = 7.5 fluid ounces

Amount of glue = 12.5 times of salt solution

⇒ 7.5 = 12.5x

⇒ x = 7.5 / 12.5

⇒ x = 0.6

Fluid ounces of water used by Sofia to make the required batch of slime is:

Now, Amount of salt solution = Fluid ounces of Water - 4.2

⇒Fluid ounces of Water = x + 4.2

⇒ Fluid ounces of Water = 0.6 + 4.2

⇒ Fluid ounces of Water = 4.8 fluid ounces

Therefore, the fluid ounces of water used by Sofia with salt solution and glue to make a slime is equal to 4.8 fluid ounces.

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