Svetlana has 1.2kg of apples and plenty of the other ingredients. She wants to make apple crumble for a maximum number of people. What is the maximum number of people she will be able to serve?
You must show your working

Answer:

78

Step-by-step explanation:

First we want 9 3/4 into an improper fraction.

(9 * 4) + 3 / 4 = 39 / 4

Then we want to change 39 / 4 into the same denominator as 1/8

39 / 4 * 2 = 78 / 8

And there is your answer, 78!

(hopefully this is correct, have a nice day!)

(a) Average-Value of "f" on [4, 7] is 1,

(b) The values of "c" such that f(average) = f(c), are c = 4 or c = 6.

Part (a) : To find the average value of "f" on the interval [4, 7], we need to calculate definite integral of f(x) over that interval and divide it by the length of the interval.

The definite integral of f(x) over the interval [4, 7] is calculated as :

∫₄⁷ (x - 5)² dx = [(x - 5)³/3] evaluated from 4 to 7

= [(7 - 5)³/3] - [(4 - 5)³/3]

= [2³/3] - [(-1)³/3]

= 8/3 + 1/3

= 9/3

= 3

The length of the interval [4, 7] is 7 - 4 = 3,

So, average value of "f" on interval [4, 7] is 3/3 = 1.

Part (b) : To find "c" such that f(average) = f(c), we equate "average-value" of "f" from part (a) equal to f(c) and solve for c.

f(average) = f(c)

1 = (c - 5)²

√1 = √((c - 5)²)

1 = |c - 5|

⇒ Case(i) : 1 = c - 5

c = 6

⇒ Case(ii): 1 = -(c - 5)

-1 = -c + 5

c = 4

Therefore, the two possible values for c are : c = 4 or c = 6.

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The given question is incomplete, the complete question is

Consider the given function and the given interval. f(x) = (x − 5)², [4, 7]

(a) Find the average value of f on the given interval,

(b) Find c such that f(average) = f(c).

The correct answer is In triangle ABC, the side lengths are AB = x inches, BC = 2x inches, and AC = 2x + 2 inches.

In a triangle ABC, let's assign the following variables to the lengths of the sides:

AB = x inches

BC = 2x inches (twice the length of AB)

AC = 2x + 2 inches (2 inches longer than BC)

To summarize:

AB = x

BC = 2x

AC = 2x + 2

These variables represent the lengths of the sides in the triangle.

In triangle ABC, we have three sides: AB, BC, and AC.

Side AB has a length of x inches.

Side BC is twice as long as AB, so its length is 2x inches.

Side AC is 2 inches longer than BC, meaning its length is 2x + 2 inches.

To summarize, the side lengths of triangle ABC are AB = x inches, BC = 2x inches, and AC = 2x + 2 inches.

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Step-by-step explanation:

[1+(1/Tan²θ)] + [ 1+(1/Cot²θ)]

[1+(1/Tan²θ)]+[1+(1/Cot²θ)] = 1/(Sin²θ-Sin⁴θ)

On taking LHS

[1+(1/Tan²θ)] + [ 1+(1/Cot²θ)]

We know that

Tan θ = 1/ Cot θ

and

Cot θ = 1/Tan θ

=> (1+Cot²θ)(1+Tan²θ)

=> (Cosec² θ) (Sec²θ)

Since Cosec²θ - Cot²θ = 1 and

Sec²θ - Tan²θ = 1

=> (1/Sin² θ)(1/Cos² θ)

Since , Cosec θ = 1/Sinθ

and Sec θ = 1/Cosθ

=> 1/(Sin²θ Cos²θ)

We know that Sin²θ+Cos²θ = 1

=> 1/[(Sin²θ)(1-Sin²θ)]

=> 1/(Sin²θ-Sin²θ Sin²θ)

=> 1/(Sin²θ - Sin⁴θ)

=> RHS

=> LHS = RHS

Hence, Proved.

[1+(1/Tan²θ)]+[1+(1/Cot²θ)] = 1/(Sin²θ-Sin⁴θ)

→ Tan θ = 1/ Cot θ

→ Cot θ = 1/Tan θ

→ Cosec θ = 1/Sinθ

→ Sec θ = 1/Cosθ

→ Cosec²θ - Cot²θ = 1

→ Sec²θ - Tan²θ = 1

→ Sin²θ+Cos²θ = 1

Hope this helps!!

Answer:

Step-by-step explanation:

Given the price of 5 units for $5.75

The unit rate is:

Correct choice is C

Answer:

Here you go! :]

Step-by-step explanation:

The terminal point determined by T is (4, 5).

To find the terminal point determined by T, we have to follow the below-given steps:Step 1: Identify the initial point, which is the point where we start from.Step 2: Consider the direction of the vector T, which can be left, right, up, down, or diagonal. We have to move in that direction.Step 3: Determine the magnitude of T, which is the distance that we move.Step 4: Once we have identified the direction and magnitude of T, we can add them to the initial point to determine the terminal point.The terminal point is the point that we reach after moving in the direction and for the distance specified by T. In other words, it is the point where we end up after starting from the initial point and moving in the direction and distance specified by T.For example, suppose the initial point is (1, 1), and we have a vector T = 3i + 4j. This vector has a magnitude of 5 and a direction that is up and to the right. We can add T to the initial point to find the terminal point as follows:(1, 1) + (3, 4) = (4, 5)So the terminal point determined by T is (4, 5).

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Answer:

980

Step-by-step explanation:

if you do 70×14 would equal 980

The perimeter of her garden is 4g² -34g - 2 cm.

It is important to note that the perimeter of a triangle is the addition of all its side. This will be illustrated thus:

In this case, Josh has a triangular garden with sides represented with 15g²- 6g + 8. The other sides are -17g² - 22g - 13 and the third side represented by 6g² - 6g + 3.

The perimeter will be:

= 15g²- 6g + 8 -17g² - 22g - 13 + 6g² - 6g + 3.

= 4g² -34g - 2

The perimeter is (4g² -34g - 2)cm.

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Answer:

-1/4x

Step-by-step explanation:

Step 1

State the for the sales tax rate

where

Step 2

Get the sales tax rate in percentage by substitution

that how its done in written way

Answer:

9

Step-by-step explanation:

put in order least to greatest

-9 -9 -7 -6 -5 -4 -3  0

9-0=9

range cannot be negative because it is the space between numbers and distance cannot be negative

Answer: The range is 9.

The Area of Trapezium is 50, 267 mm².

We have,

base 1 = 224 mm

base 2 = 77 mm

Height = 334 mm

Now, Area of Trapezium

= 1/2 (Sum of parallel side) x height

= 1/2 (224 + 77) x 334

= 1/2 x 301 x 334

= 50, 267 mm²

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We can see here that the relationship that exists between the triangular numbers and the rectangular numbers​ is that a doubling of the triangular number will give the rectangular number.

When dots or other items are placed in the form of a triangle, a triangular number is one that may create an equilateral triangle. It is a run of numbers that adheres to a particular pattern.

Beginning with 1, the series of triangular numbers continues by adding subsequent positive integers. The total of all positive integers up to a specific number makes up each triangular number.

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Answer:

2x+14

Step-by-step explanation:

Answer:

2x + 14

Step-by-step explanation:

Step 1:

2 × x + 2 × 14

Answer:

2x + 14

Hope This Helps :)

Answer:

Rosalita ran m miles yesterday, and 1.85 miles fewer today.

Step-by-step explanation:

The expression m - 1.85 is used to find how many miles Rosalita ran today. If she ran 1.85 miles less than yesterday, m, to find today's miles you would subtract 1.85 from m, which the expression does. The only scenario that makes sense is that Rosalita ran m miles yesterday and ran 1.85 fewer miles today.

Hope this helps :)

Answer:

\(\huge\boxed{A=6x^2-11x+3;\ \text{for}\ x>1.5}\)

Step-by-step explanation:

The formula of an area of a rectangle:

\(A=a\cdot b\\\\a,\ b-\text{sides of a rectangle}\)

We have:

\(a=2x-3\\b=3x-1\)

The domain:

\(2x-3>0\ \wedge\ 3x-1>0\\\\2x-3+3>0+3\ \wedge\ 3x-1+1>0+1\\\\2x>3\ \wedge\ 3x>1\\\\\dfrac{2x}{2}>\dfrac{3}{2}\ \wedge\ \dfrac{3x}{3}>\dfrac{1}{3}\\\\x>1.5\ \wedge\ x>\dfrac{1}{3}\Rightarrow\boxed{x>1.5}\)

Substitute:

\(A=(2x-3)(3x-1)\)

use FOIL: (a + b)(c + d) = ac + ad + bc + bd

\(A= (2x)(3x)+(2x)(-1)+(-3)(3x)+(-3)(-1)\\\\A=6x^2-2x-9x+3\)

combine like terms

\(A= 6x^2+(-2x-9x)+3\\\\A=6x^2-11x+3\)

Answer:

6x² - 11x + 3

Step-by-step explanation:

To find the area of a rectangle, we multiply the length by the width.

A = l • w

length: 2x-3

width: 3x-1

A = (2x-3) • (3x-1)

To multiply these two binomials, we must FOIL (first | outer | inner | last) them.

F: 2x • 3x = 6x²

O: 2x • -1 = -2x

I: -3 • 3x = -9x

L: -3 • -1 = 3

Combine the terms.

6x² - 2x - 9x + 3

Combine like terms.

6x² - 11x + 3

This is your area.

Hope this helps!

Answer:

  125

Step-by-step explanation:

Given 10 of 16 marbles in a bag are black, you want to know the expected number of times a black marble will be drawn if a marble is drawn and replaced 200 times.

The probability of drawing a black marble is the fraction of marbles that are black: 10/16 = 0.625. The expected number of draws of a black marble will be this value multiplied by the number of draws:

 times picking black = 200 · 0.625 = 125

You can expect to pick a black marble 125 times.

__

Additional comment

The usual caveats apply: each marble is equally likely to be drawn on any given draw. The draws are independent.

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Answer:

B i believe is your answer

Step-by-step explanation:

tell me if i'm right or wrong

The book is opened to pages 11 and 12.

How to get the product of the page

x * (x + 1) = 132

Expanding the equation, we get:

x² + x = 132

To solve for x, we need to rewrite the equation as a quadratic equation:

x²+ x - 132 = 0

Now, we can factor the quadratic equation:

(x - 11)(x + 12) = 0

This equation has two solutions for x:

x = 11

x = -12

Since page numbers cannot be negative, we discard the second solution. Thus, the left-hand page number is 11, and the right-hand page number is 11 + 1 = 12.

So, the book is opened to pages 11 and 12.

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Answer:7

Step-by-step explanation:

Answer:

C, D, F

Step-by-step explanation:

Anything to the power of 0 is equal to 1

C because 1=1

D because 1 multiplied by itself is 1

F because, just like what I said, anything to the power of 0 is equal to 1

Answer:

25/16

Step-by-step explanation:

5/8 divided by 2/5

= 5/8 times 5/2

= 25 / 16

Answer:

Step-by-step explanation:

Answer: area of the sector is 52.3m²

Step-by-step explanation:

The formula for determining the area of a sector is expressed as

Area = θ/360 × πr²

Where

θ represents the central angle which is formed by the two radii

r represents the radius of the circle.

π is a constant whose value is 3.14

From the information given,

θ = 60 degrees

r = 10 meters

Therefore,

Area = 60/360 × 3.14 × 10²

Area = 60/360 × 3.14 × 100

Area = 52.333

Rounding up to 1 decimal place, it becomes

52.3m²

9(5 - y)

EXPLANATION

Difference means subtraction.

This implies that the difference of 5 and y can be expressed as 5 - y.

Hence, nine times the difference of 5 and y can be represented as:

9(5 - y)

We use the chi-square distribution when making inferences about a single population variance.

Short Description of Chi-Square Distribution

The continuous probability distribution known as the chi-square distribution. The number of degrees of freedom (k) a chi-square distribution has determines its shape. This type of sampling distribution has a variance of 2k and a mean equal to its number of degrees of freedom (k). The range is of a chi-square distribution is from 0 to ∞.

Variance plays a key role in the analysis of risk and uncertainty. The sample variance, an unbiased estimator of population variance, is expressed by the following formula of core statistic for a sample size 'n' and Y' as the sample mean:

S² = ∑(Yₓ - Y') / (n-1)

The formula, (n-1)S² / σ² has the central chi-square distribution as χ²ₙ₋₁. Here (n-1) represents the degrees of freedom.

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