1.3 A cake recipe calls for 0.8 kg of flower, 650g of sugar and 900 000mg of butter. (2) 1.3.1 Determine the total mass of the ingredients. Give you answer in kilograms. 1.3.2 If sugar comes in 150g bags at cost of R5.95 per 150g, determine the total cost of the (2) sugar needed for this recipe.​

The area of the circle is 12.56 metres squared.

The circle has a diameter of 4 metres. The diameter of a circle is a line that passes through the centre and meets the circumference at opposite ends.  

Therefore, the area of the circle can be found as follows:

area of the circle = πr²

where

Hence,

r = 4 / 2

r = 2 metres

area of the circle =  3.14 × 2²

area of the circle =  3.14 × 4

area of the circle =  12.56 metres squared

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Answer:

We can compute this in 2 ways:

305 downwind - 260 still air = 45 mph wind velocity

260 still air - 215 downwind = 45 mph wind velocity

Step-by-step explanation:

3. The factored polynomial is p(x) = (x - 1)(x - 5)

4. The factored polynomial is p(x) = (x + 3)²

A polynomial is a mathematical expression in which the power of the unknown is greater than or equal to 2.

3. To factorize the polynomial using the graph, we see that the polynomial cuts the x - axis at x = 1 and x = 5.

This implies that its factors are (x - 1) and (x - 5)

So, the factored polynomial is p(x) = (x - 1)(x - 5)

4. To factorize the polynomial using the graph, we see that the polynomial touches the x - axis at only one point x = -3. So,it has repeated roots

This implies that its factors are (x - (-3)) = (x + 3) twice

So, the factored polynomial is p(x) = (x + 3)²

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Answer:

c

Step-by-step explanation:

the surface area for spheres is

4 × π × r²

4 × π × (7²) = 196 π

Answer:

2.7t5r

Step-by-step explanation:

Answer:

2 + 2 = 4

y tho

Step-by-step explanation:

The equation which describes the relationship between the side length and shaded area of the quilt is y=0.5x²

Side length, x = 1,3,4,5,8

Shaded Area, y = 0.5, 4.5, 8, 12.5, 32

The relationship can be modeled as a quadratic function. Using a graphing calculator for the quadratic function written in the form y = ax² + bx + c

a = 0.5 ; b = 0 ; c = 0

Therefore, the quadratic function can be written as y = 0.5x²

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Step-by-step explanation:

Given equation:

Simplify and convert into slope-intercept form (y = mx + b):

The slope is m = -3, the y-intercept is b = -1

See the graph below

Answer:

(x-8)(x-8) are the factors of the following biominals

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the product of the given fractions in lowest terms, we can multiply the numerators and denominators together, and then simplify the resulting fraction:

(24/18) * (2/17) * (34/3)

First, we can simplify the fractions by reducing any common factors in the numerators and denominators:

24/18 = (212)/(29) = 12/9 = 4/3

2/17 = 2/17

34/3 = (2*17)/3 = 34/3

Now we can multiply the simplified fractions:

(4/3) * (2/17) * (34/3) = (4234)/(3173) = 272/153

The product of the given fractions in lowest terms is 272/153.

The proportionality constant is 3.5.

The constant of proportionality is the ratio that relates two given values in what is known as a proportional relationship.

Given:

x          y

2         7

7        24.5

9        31.5

Now, using proportionality constant

y= kx

y/x= k

where if is proportionality constant

So, k= 7/2

k= 3.5

again, k = 24.5/7

K=3.5

Hence, the proportionality constant is 3.5.

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The sequence is decreasing as n increases and sequence converges to the value 0.

The given sequence is defined as aₙ = 1 / (7n + 3).

To determine if the sequence converges or diverges, we need to analyze its behavior as n approaches infinity.

As n increases, the denominator 7n + 3 also increases which means that the values of aₙ will get smaller and smaller, approaching zero as n becomes larger.

The sequence converges to the value 0.

The sequence is decreasing as n increases.

The sequence converges to the value 0.

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The total change in yards where the team started is 3x

The given parameters in the question are:

Yards per play = unknown

Number of plays = 3 consecutive plays

Represent the yards per play with x

So, we have

Yards per play = x

The total change in yards is the amount of yard per play multiplied by the number of plays

This is represented as

Total change = Yards per play * Number of plays

Substitute the known values in the above equation So, we have the following equation

Total change = x * 3

Evaluate

Total change = 3x

Hence, the total change is 36 yards

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The derivation of the critical radius(r*) as  and critical saturation(S*) as  is explained below .

To derive the critical saturation ratio (S*) and critical radius (r*),

We  use calculus to find the maximum value of the saturation ratio for a given radius on the Kohler curve.

First, let us consider the equation for the saturation ratio, S, as a function of radius, r:

that is : S = 1 + ar²/3b  ;

where a and b are constants.

Next, we find the derivative of S with respect to r:

On differentiating Curve "S" with respect to "r" ;

⇒ dS/dr = 2ar/3b  ;

Equating the derivative = 0 , we can find the critical points:

⇒ dS/dr = 0 = 2ar/3b  ;

On Solving for r, we have ;

⇒ r* = √(3b/a)

Next , to find the critical saturation ratio(S*) , we substitute r* back into the original equation for S:

⇒ S* = 1 + ar²/3b = 1 + a×(3b/a)/3b = 1 + √(4a³/27b)

Therefore , the critical saturation ratio and critical radius are written as r* = √(3b/a)  and  S* = 1 + √(4a³/27b)  .

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The given question is incomplete , the complete question is

Using your calculus skills derive the equations for the critical saturation ratio and the critical radius. (Hint: the critical point on the Kohler curve represents a maximum value).

The equations you should end up with are as follows:

r* = √(3b/a) and S* = 1 + √(4a³/27b) Where r* is the critical radius and S* is the critical saturation ratio .

Answer:

I NEED POINTS

Step-by-step explanation:

The probability to win 25$ and 2$ are 1/18 and 1/6

Probability is the ratio of favorable cases to total sample cases.

If two dice are rolled,

Total sample cases or combinations= 6x6=36

The favorable cases to get 2 or 12 ={1,2}{6,6}= 2 total cases

The favorable cases to get 7 ={1,6}{6,1}{2,5}{5,2}{3,4}{4,3}=6 cases

The probability to win 25$=2/36=1/18

The probability to win 2$=6/36=1/6

Thus the probability to win 25$ and 2$ are 1/18 and 1/6

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Main Answer: $1.27

Given data:

If you rolled two dice and got a sum of 2 or 12, you won $25. If you rolled a 7, you won $2. Any other roll was a loss. It cost $1 to play one game with one roll of the dice.

Solving part

Step-by-step explanation:

For 2 and 12

Number of possible outcomes = 2

Gain = 25 -1 = $24

For 7

Number of possible outcomes = 6

Gain = 5-1 = $4

For others

Number of possible outcomes = 36-(4+6) = 26

Gain = -$1

Expectation of the gain;

X= (2×$24 + 6×$4 - 26×1)/36

X = $46/36

X = $1.27

Final Answer: $1.27

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The digits after the decimal point repeat in a pattern of 6's. This is because 22/6 is a rational number,

A rational number is a number that can be expressed as a ratio or fraction of two integers (a numerator and a non-zero denominator).

We can see that the next three digits in the decimal points are 6, 6 and 6, respectively. Therefore, the decimal equivalent of 22/6 is:

22/6 = 3.666666...

We notice that the digits after the decimal point repeat in a pattern of 6's. This is because 22/6 is a rational number, which means that its decimal representation either terminates (ends) or repeats in a pattern. In this case, it repeats in a pattern of 6's.

Each of the digits after the decimal point will be 6 because this number is a rational number and repeating decimal with a repeating digit of 6.

The difference between 40 and the product of these digits and 6 is always 4.

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Answer:

1

Step-by-step explanation:

Multiply all of them together

The impact on Carns Company's income from eliminating the Small Tools Division would be a decrease of $1,209,000.

To determine the impact on Carns Company's income from eliminating the Small Tools Division, we need to consider the avoidable costs associated with the division.

The avoidable costs include all of the variable costs of the division and a portion of the fixed costs that are specifically related to the Small Tools Division. In this case, the variable costs of the division are $1,295,000, and $119,000 of the fixed costs are avoidable.

To calculate the impact on income, we subtract the avoidable costs from the loss reported by the division:

Impact on income = Loss - Avoidable costs

Impact on income = $205,000 - ($1,295,000 + $119,000)

Impact on income = $205,000 - $1,414,000

Impact on income = -$1,209,000

The negative sign indicates a decrease in income.

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\(5^2 - \left(\dfrac 14 \right)^2= 25 - \dfrac{1}{16} = \dfrac{400-1}{16} = \dfrac{399}{16}=24\dfrac{15}{16}\)

Answer:

\(S.E=1183.2\)

Step-by-step explanation:

From the question we are told that:

Population mean \(\mu=60000\)

Population standard deviation \(\sigma= 14,000 miles.\)

Sample size \(n=140\)

Generally the equation for Standard error  is mathematically given by

\(S.E=\frac{ \sigma}{ \sqrt n}\)

\(S.E= \frac{14000}{\sqrt 140}\)

\(S.E=1183\)

9514 1404 393

Answer:

  3.14^2 = 9.8596

Step-by-step explanation:

The way this question is written, f(r) is a constant equal to 3.14^2 = 9.8596. It is the same constant value regardless of the value of r.

  f(5) = 9.8596

_____

Additional comment

This looks suspiciously like the equation for the area of a circle:

  A = πr^2 = 3.14r^2

For r = 5, this is ...

  A = 3.14·5^2 = 3.14·25 = 15.7

Algebraically, the amount of money the insurance company will pay, represented as P, is equal to the total value of the stolen items (2b + t) minus the deductible (d).

Let's denote the amount of money the insurance company will pay as P. In this scenario, if the value of the stolen items is greater than the deductible, the insurance company will cover the loss, and Ron will receive compensation for the stolen items.

The total value of the stolen items can be calculated by adding the value of the bicycles (2b) and the value of the tools (t). So, the total value of the stolen items is 2b + t.

If the total value of the stolen items is greater than the deductible (d), then the insurance company will pay the difference between the total value and the deductible. Mathematically, this can be represented as:

P = (2b + t) - d

Therefore, algebraically, the amount of money the insurance company will pay, represented as P, is equal to the total value of the stolen items (2b + t) minus the deductible (d).

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Answer: $3703.70

Step-by-step explanation:

200x.054=$3703.70

9 gallons + 7 gallons = 16 gallons

1 qt + 2qt = 3 qts

Total = 16 gallons and 3 qts.