Here is a list of ingredients for making 16 flapjacks.
Ingredients for 16 flapjacks
120 g butter
140 g brown sugar
250 g oats
2 tablespoons syrup
jenny wants to make 24 flapjacks.
work out how much of each of the ingredients she needs.

butter
brown sugar
oats
syrup tablespoons â

Answer:

so i got x=-3 i didnt get any signs in between

Step-by-step explanation:

he required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

Let’s assume the general solution of the given differential equation is,

y=e^{mx}

By taking the derivative of this equation, we get

\(\frac{dy}{dx} = me^{mx}\\\frac{d^2y}{dx^2} = m^2e^{mx}\\\frac{d^3y}{dx^3} = m^3e^{mx}\\\frac{d^4y}{dx^4} = m^4e^{mx}\\\)

Now substitute these values in the given differential equation.

\(\frac{d^4y}{dx^4}-2\frac{d^2y}{dx^2}-8y\\=0m^4e^{mx}-2m^2e^{mx}-8e^{mx}\\=0e^{mx}(m^4-2m^2-8)=0\)

Therefore, \(m^4-2m^2-8=0\)

\((m^2-4)(m^2+2)=0\)

Therefore, the roots are, \(m = ±\sqrt{2} and m=±2\)

By applying the formula for the general solution of a differential equation, we get

General solution is, \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

Hence, the required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

Know more about constants here:

https://brainly.com/question/27983400

#SPJ11

Answer:

7

Step-by-step explanation:

CD is congruent to BC by CPCTC.

The ratio of corresponding sides for the given similar triangles is 2/5.

In the given options, the ratio of corresponding sides is provided for each set of similar triangles. Let's analyze each option to determine the correct ratio:

a. 10

This option only provides a single number and does not specify the ratio of corresponding sides. Therefore, it is not the correct answer.

b. 4/5

This option provides the ratio 4/5 for the corresponding sides of the similar triangles. However, the ratio can be simplified further.

To simplify the ratio, we divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 4 and 5 is 1.

Dividing 4 and 5 by 1, we get:

4 ÷ 1 = 4

5 ÷ 1 = 5

Therefore, the simplified ratio is 4/5.

c. 10/85

This option provides the ratio 10/85 for the corresponding sides of the similar triangles. However, this ratio cannot be simplified further, as 10 and 85 do not have a common factor other than 1.

Therefore, the correct ratio of corresponding sides for the given similar triangles is 2/5, as determined in option b.

For more such questions on triangles, click on:

https://brainly.com/question/17335144

#SPJ8

Answer:

-250

Step-by-step explanation:

Answer:

75

Step-by-step explanation:

9 + 9 + 9 + 9 + 9 + 30 = 75

Good luck on your assignment!

-1/7, since parallel lines have equal slopes.

Answer:

Surface area of cylinder = 2 π r ² +2 π r h

Step-by-step explanation:

Surface area of cylinder =

area of both circle ends + area of curved surface

= 2 π r ² +2 π r h

Given that \(\(T(n)\) = \(10n^2-3n\)\) if (\(\(n=1\)\)), you have to prove it by induction. So, we have proved it by induction that  \($$\(T(n)=10n^2-3n\)$$\)  if ( n= 1). The given statement is true for all positive integers n

Let's do it below: The base case (n=1) is given as follows: \(T(1)\) =\(10\cdot 1^2-3\cdot 1\\&\)=\(7\end{aligned}$$\). This implies that \(\(T(1)\)\) holds true for the base case.

Now, let's assume that \(\(T(k)=10k^2-3k\)\) holds true for some arbitrary \(\(k\geq 1\).\)

Thus, for n=k+1, T(k+1) = \(10(k+1)^2-3(k+1)\\&\) = \(10(k^2+2k+1)-3k-3\\&\)=\(10k^2+20k+7k+7\\&\) = \(10k^2-3k+20k+7k+7\\&\) = \(T(k)+23k+7\\&\) = \((10k^2-3k)+23k+7\\&\) =  \(10(k+1)^2-3(k+1)\).

Therefore, we have proved that the statement holds true for n=k+1 as well. Hence, we have proved it by induction that  \($$\(T(n)=10n^2-3n\)$$\)  if (n=1). Therefore, the given statement is true for all positive integers n.

For more questions on: integers

https://brainly.com/question/17695139

#SPJ8  

The ability to order items in a sequence, such as longest to shortest, is known as Seriation.

Seriation is a cognitive skill that involves arranging objects, events, or ideas in a particular order or sequence. It is a crucial aspect of cognitive development and is typically acquired during early childhood. Seriation is the ability to mentally order objects along a quantitative dimension, such as size, weight, or length.

Seriation involves comparing and ordering items based on specific criteria. For example, if given a group of objects of different lengths, a child who has developed seriation skills will be able to arrange the objects in order from shortest to longest. Similarly, if given a group of numbers, a child who has developed seriation skills will be able to arrange them in order from smallest to largest.

Seriation is an important cognitive skill that is used in various areas of life, including academic, professional, and personal domains. It allows individuals to organize information and ideas in a logical and meaningful way, which can facilitate more efficient processing and understanding of complex concepts.

Overall, seriation is a fundamental cognitive skill that plays a crucial role in various aspects of life, including problem-solving, decision-making, and organization. It is an essential skill that supports the development of higher-order thinking skills, such as analysis, evaluation, and synthesis.

To learn more about seriation refer below

https://brainly.com/question/13762666

#SPJ11

Answer:

\(\sqrt{3}\cdot\sqrt{6}=3\cdot\sqrt{2}\)

Step-by-step explanation:

Radicals

We have the expression:

\(\sqrt{3}\cdot\sqrt{6}\)

Since 6=2*3, it can be rewritten as:

\(\sqrt{3}\cdot\sqrt{6}=\sqrt{3}\cdot\sqrt{2}\cdot\sqrt{3}\)

Joining like radicals:

\(\sqrt{3}\cdot\sqrt{6}=\sqrt{3}\cdot\sqrt{3}\cdot\sqrt{2}\)

\(\sqrt{3}\cdot\sqrt{6}=\sqrt{9}\cdot\sqrt{2}\)

\(\boxed{\sqrt{3}\cdot\sqrt{6}=3\cdot\sqrt{2}}\)

This is the required form with b=2

The integer b for \(\rm b\sqrt{2}\) such as \(\rm \sqrt{3}\times \sqrt{6} = b\sqrt{2}\) holds good is 3 .

According to the property of square root for any  positive integer x

\(\rm \sqrt{x} \times \sqrt{x} = x....(1)\)

According to the  given condition

\(\rm \sqrt{3}\times \sqrt{6} = b\sqrt{2}\)

We can simplify the left hand side  of the equation as follows

\(\sqrt{3}\times \sqrt{6}\)

\(= \sqrt{3}\times \sqrt{2\times 3 }\)

\(= 3\sqrt{2}\)      ( By using equation (1))

So on comparing with right hand side of equation (1) we get

\(\rm 3\sqrt{2} = b\sqrt{2}\\hence \; on\; comparing\\b = 3\)

The integer b for \(\rm b\sqrt{2}\) such as \(\rm \sqrt{3}\times \sqrt{6} = b\sqrt{2}\) holds good is 3 .

For more information please refer to the link below

https://brainly.com/question/17309565

Answer:

34.65 mi²

Step-by-step explanation:

Area of parallelogramam = b · h

b = 6.3 mi

h = 5.5 mi

Let's solve

6.3 · 5.5 = 34.65 mi²

So, the area of the shape is 34.65 mi²

Answer:

The formula for the surface area of a sphere is:

Surface Area = 4πr^2

where r is the radius of the sphere and π (pi) is a mathematical constant approximately equal to 3.14159.

In this case, we are given that the radius of the sphere is 13 inches. So we can plug in the value of r into the formula to find the surface area:

Surface Area = 4πr^2

Surface Area = 4π(13^2)

Surface Area = 4π(169)

Surface Area = 676π

Therefore, the surface area of the sphere is 676π square inches.

Step-by-step explanation:

Answer:

Bdgetyeyreg2qqwwwe 32233

In this case, the likelihood function is the product of the Poisson probability mass function evaluated at each data point in the training data. To compute the log-likelihood, we take the natural logarithm of this product. To maximize the log-likelihood function, we take the derivative of it with respect to the parameter and set it equal to zero. Solving for the parameter gives us the maximum likelihood estimate.

To help you with your question, let's go through the process of using maximum likelihood estimation (MLE) for a Poisson distribution step by step.

1. Given training data drawn from a Poisson distribution, we have the probability mass function (PMF) as:
P(X=k) = (λ^k * e^(-λ)) / k!, where k is a non-negative integer and λ is the parameter we want to estimate.

2. The likelihood function, which is the joint probability of obtaining the sample given the model, is the product of individual probabilities:
L(λ) = Π P(X_i=k_i), for i = 1 to n, where n is the number of data points.

3. For MLE, we compute the log-likelihood function, which is the natural logarithm of the likelihood function:
log(L(λ)) = Σ log(P(X_i=k_i)), for i = 1 to n.

4. Plugging in the PMF, the log-likelihood becomes:
log(L(λ)) = Σ [k_i * log(λ) - λ - log(k_i!)], for i = 1 to n.

5. To maximize the log-likelihood function, we take its derivative with respect to λ and set it to 0:
d(log(L(λ))) / dλ = Σ [k_i/λ - 1] = 0.

6. Solve for the MLE estimate of λ:
λ_MLE = Σ k_i / n, where n is the number of data points.

The resulting estimate for λ, λ_MLE, is in accordance with the definition of λ in a Poisson distribution, as it represents the average number of events in the sample. The resulting estimate for the Poisson distribution parameter is the sample mean of the training data. This is in accordance with the definition of the Poisson distribution, where the mean and variance are equal to the parameter lambda.

Learn more about log-likelihood:

brainly.com/question/29646733

#SPJ11

The calculation section of the data sheet asks for both experimental and theoretical equations, with Equation 10-3 and Equation 10-4 provided as references. A more detailed explanation and analysis would require additional information and context.

Based on the given information, it seems that the question is related to an experiment involving standing waves on a string. The data sheet mentions the active length of a heavy string, the added mass of a light string, and the mass of a light weight-holder. The calculation section of the data sheet asks for both experimental and theoretical equations, with Equation 10-3 and Equation 10-4 provided as references.
To answer the question, more information is needed about the specific calculation or problem that needs to be solved. However, one possible approach could be to use the provided equations to determine the standing wave patterns on the string based on the given measurements. This could involve using the weight-holder mass, the active length of both the heavy and light strings, and the added mass of the light string to calculate the necessary variables for the equations.

Overall, the answer to the question will depend on the specific details and requirements of the experiment and the calculation being performed. A more detailed explanation and analysis would require additional information and context.

To know more about theoretical visit:

https://brainly.com/question/14966377

SPJ11

Answer:

the divisors of 63 are

Step-by-step explanation:

1,3,7,9,21,63

Answer:

Fraction Form: 2/6 or 1/3

or Decimal Form: .333

or Percent Form: 33.333?%

Step-by-step explanation:

The divisors of 63 that are 1-6 is 1 and 3

So there are TWO numbers out of SIX.

We would turn that into the fraction 2/6 and then simplify (optional) it to 1/3.

Then we use 2/6 to convert it to multiple forms if needed.

From the figure shown we notice that the angles 127° and 2 are supplementary, that means that:

We also notice that

and

furthermore

And

so we have the system of equations:

Solving for the angle 1 in the fourth equation we have

plugging this value in the second equation we have

Plugging this value in the third equation we have

Answer:

Step-by-step explanation:

We can defined the amplitude of a wave as the height of it, because it's the distance from the maxium point to the minimum point. In other words, it's the longest vertical displacement along the wave.

Additionally, amplitude represents power, when we apply waves to real phenomenons like the sound. So, greater grade of amplitude would represent louder sounds.

Therefore, the increase of amplitude would increase distance between the maximum and minimun point of the wave.

El ultimo numero son las unidades.

El numero anterior al ultimo (de izquierda a derecha) representa las decenas.

56 = 5 decenas , 6 unidades

Answer:

between 1 and 2.

Step-by-step explanation:

Answer:

{0, 1, -1}

Step-by-step explanation:

2x - 6 = 3x + 1 - x - 7

2x - 6 = 2x - 6

0 gives you -6 = -6

1 gives you -4 = -4

-1 gives you -8 = -8

Answer:

a= 7.4

Step-by-step explanation:

Answer:

7.4                                                                                                      

Step-by-step explanation:

Get the squares of the two given sides , subtract them , to get a squared.

square root the answer , which is 55 , to get the actual side , which is 7.416...

round off to 1 dp to get 7.4

The potato is in the air for approx. 1.0625 seconds.

The actual cost of manufacturing 24 coffee makers is $1,755.67.

a. To find the time that a potato is in the air, use the quadratic equation formula where a=-16,

b=34, and

c=42. `

t = (-b ± sqrt(b²-4ac))/2a`.

Let's start by finding the discriminant first. `b²-4ac = (34)²-4(-16)(42)

= 1156`.

Substitute the values of a, b, and c into the quadratic formula.

t = (-34 ± sqrt(1156))/-32

= (-34 ± 34)/-32`.

There are two solutions to the quadratic equation. Thus, we need to check if there are any negative values for time.

t = (-34 + 34)/-32

= 0.

t = (-34 - 34)/-32

= 1.0625`.

Therefore, the potato is in the air for 1.0625 seconds.

b. To find the actual cost of manufacturing 24 coffee makers, substitute x=24 into the cost function

C(x) = 155 + 66x + x²/36`.

C(24) = 155 + 66(24) + 24²/36

= 155 + 1584 + 16.67`. `

C(24) = 1755.67`.

Therefore, the actual cost of manufacturing 24 coffee makers is $1,755.67.

To know more about quadratic visit

https://brainly.com/question/18269329

#SPJ11

a. The probability that the six numbers chosen by a player match all six numbers in the state's sample is 1/273,765, a very low probability.  

b. The probability that five of the six numbers chosen by a player appear in the state's sample is 1/16,496.

c. The probability that at most four of the six numbers chosen by a player appear in the state's sample is (9,717,807/9,829,032) or 0.9886 (rounded off to four decimal places).

d. If a player enters one lottery each week, the expected number of weeks until a player matches all six numbers in the state's sample is approximately 273,765 weeks.

a. The formula for this probability is given as: (40 C 6)/((40 C 6)*(39 C 5)*(38 C 4)*(37 C 3)*(36 C 2)*(35 C 1)) = 1/273,765.

b. The formula for this probability is given as: ((6 C 5) * (34 C 1))/((40 C 6)*(39 C 5)*(38 C 4)*(37 C 3)*(36 C 2)*(35 C 1)) = 1/16,496.

c. he formula for this probability is given as: ((40 C 4) * (36 C 2))/((40 C 6)*(39 C 5)*(38 C 4)*(37 C 3)*(36 C 2)*(35 C 1)) = 0.9886.

d.  The formula for this expected value is given as: 1/p, where p is the probability of winning (found in part a). The expected number of weeks is therefore 1/((40 C 6)/((40 C 6)*(39 C 5)*(38 C 4)*(37 C 3)*(36 C 2)*(35 C 1))) = 273,765.

To know more about probability click on below link:

https://brainly.com/question/30034780#

#SPJ11

For the given equation which shows the relation of temperature in Celsius and Fahrenheit, the correct option is Option D.

What is meant by temperature?

Indicating the direction in which heat energy will naturally flow from a hotter body (one with a higher temperature) to a colder body(one at a lower temperature), the temperature is a measure of hotness or coldness defined in terms of any of several arbitrary scales.

The given equation is:

\(C = \frac{5}{9} (F- 32)\)

where C = temperature in Celsius

          F = temperature in Fahrenheit

The above equation can be rewritten as:

C = 5/9F - 160/9

Now, this is an equation of a straight line with a formula,

y = mx + c

Comparing,

m = 5/9 which is the slope of the equation.

This means that for a temperature increase of 1 degree Fahrenheit, the equivalent increase in temperature in Celsius is 5/9.

So the option I is true.

Similarly, an increase in 1 degree Celsius of temperature is equivalent to 9/5 = 1.8 degree increase in Fahrenheit.

So option II is true.

Option III is not true as is discussed above.

Therefore for the given equation of temperature, the correct option is Option D.

To learn more about temperature, follow the link.

https://brainly.com/question/30459660

#SPJ1

Answer:

D

Step-by-step explanation:

I have nothing else to say- lol

Answer:

Step-by-step explanation:

We know that

We also know that

Since 5! = 1*2*3*4*5 is divisible by 15:

We need to find the remainder when 1! + 2! + 3! + 4! is divided by 15 as all the rest are divisible by 15.

The sum is:

The remainder is:

As we see the remainder is 3

Answer:

Step-by-step explanation:

8 sqaure feet