The ratio of males to females is 2:3. there are 12 boys in class. How many females are in the class

If the triangle on the left had the same area as the circle on the right, it would require more resources and potentially be more unstable than the current configuration.

If the triangle on the left had the same area as the circle on the right, it would mean that the triangle would have to be larger than its current size. This is because the area of a circle is determined by the formula A=πr^2, where r is the radius of the circle.

Therefore, if the area of the circle is equal to the area of the triangle, the radius of the circle would have to be equal to the height of the triangle, and the base of the triangle would need to be wider.

This would result in a larger triangle with a greater surface area than the current triangle. The larger triangle would also have a longer perimeter, which would make it more difficult to enclose and would require more material to construct.

Additionally, the larger triangle would have a higher center of gravity, which could make it more difficult to balance and more prone to tipping over.

Overall, if the triangle on the left had the same area as the circle on the right, it would require more resources and potentially be more unstable than the current configuration.

It is important to consider both the area and the shape of an object when determining its practicality and effectiveness in a given situation.

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Answer:

Step-by-step explanation:

Answer:

You can drive at the most 150 miles per day

Step-by-step explanation:

Answer:

6.32455532034

is the square root of 40

A semicircle has been cut out of a rectangular paperboard that is 20 inches long and 12 inches broad, as seen below. After the semicircle is taken out, the paperboard's remaining perimeter is 34.58 inches.

The paperboard has a length of 20 inches and a width of 12 inches. A semicircle is cut out of it, which means we need to find the perimeter of the remaining part.

The diameter of the semicircle is equal to the width of the paperboard, which is 12 inches. So, the radius of the semicircle is half of the diameter, which is 6 inches.

The perimeter of the remaining part will be the sum of the length of the paperboard and the two straight sides of the semicircle.

The length of the paperboard is 20 inches, and the two straight sides of the semicircle are equal to the diameter of the semicircle, which is 12 inches. So, the perimeter of the remaining part is:

P = 20 + 12 + 12 = 44 inches

However, we also need to subtract the length of the curved part of the semicircle from the perimeter. The length of the semicircle can be found using the formula:

C = πr

where C is the circumference of the semicircle and r is the radius.

Since we have a semicircle, we need to divide the circumference by 2. So, the length of the curved part of the semicircle is:

C/2 = (π x 6) / 2 = 9.42 inches (rounded to two decimal places)

Therefore, the perimeter of the remaining part is:

P = 44 - 9.42 = 34.58 inches (rounded to two decimal places)

So, the perimeter of the remaining paperboard is 34.58 inches.

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Answer:

you can make 12 cans of them

Answer:

y intercept is 11 or (0,11)

Step-by-step explanation:

\(y = 2 {(x - 2)}^{2} + 3 \\ y = 2 {(0 - 2)}^{2} + 3 \\ y = 2(4) + 3 \\ y = 8 + 3 \\ y = 11\)

Answer:

13x^2+x-23

Step-by-step explanation:

(3x^2+7x-4)+(10x^2-6x-19)

3x^2+7x-4+10x^2-6x-19

3x^2+10x^2+7x-6x-4-19

13x^2+x-23

It will take approximately 25 hours and 1 minute for there to be 150mg of aspirin left in the bloodstream.

We have,

To determine how long it will take for there to be 150mg of aspirin left in the bloodstream, we can use the concept of half-life.

The half-life of aspirin is given as 6 hours, which means that after every 6 hours, the amount of aspirin in the bloodstream reduces by half.

Let's calculate the number of half-lives required to reach 150mg:

Initial amount of aspirin = 625mg

Final amount of aspirin = 150mg

625mg / 150mg = 4.17

This means it will take approximately 4.17 half-lives for the amount of aspirin in the bloodstream to reduce from 625mg to 150mg.

Since each half-life is 6 hours, we can calculate the total time it will take:

Total time = Number of half-lives * Half-life duration

Total time = 4.17 x 6 hours

Total time ≈ 25 hours and 1 minute

Therefore,

It will take approximately 25 hours and 1 minute for there to be 150mg of aspirin left in the bloodstream.

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The correct answer is B. The sample represents a proportion of the population.

A point estimate is a single value used to estimate a population's unknown parameter. The sample proportion (denoted by p), in the context of determining the population proportion, is a widely used point estimate. The sample proportion is determined by dividing the sample's success rate by the sample size.

The sample must be representative of the population for it to be a reliable point estimate of the population proportion. To accurately reflect the proportions of various groups or categories present in the population, the sample should be chosen at random.

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To get the Prime factorization of 3000 we need to multiply by 5.

When the number is factored using prime numbers, or primes, the process is known as prime factorization. The easiest method to determine the prime factors of a given number is to keep dividing the given number by the prime factors until we will get 1.

For example, the Prime factorization of 45 is given below

=> 45/5 = 9, 9/3 = 3,  3/3 = 1

=> 45 = 5 × 3 × 3

Here we have

The prime factorization of 600 is 2 x 2 × 2 × 3 × 5 × 5

Let us assume that on multiplying with p,

we will get the factorization of 3000

=> 2 x 2 × 2 × 3 × 5 × 5 × p = 3000

=> p = \(\frac{3000}{2\times 2 \times 2 \times 3 \times 5 \times 5}\)  

Her 2 x 2 × 2 × 3 × 5 × 5 = 600

=> p = \(\frac{3000}{600}\)

=> p = 5  

Therefore,

To get the Prime factorization of 3000 we need to multiply by 5.

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Answer:

- 32/21 or - 1 11/21

Step-by-step explanation:

It should be noted that the addition of the variables give in the expression will be 11✓2.

It should be noted that the information is incomplete. Therefore, an overview will be given. In this case, let a = ✓2, b = ✓8 and c = ✓128.

This can be illustrated as:

= a + b + c

= ✓2 + ✓8 + ✓128

= ✓2 + 2✓2 + 8✓2

= 11✓2

Therefore, it should be noted that the should be noted that the addition of the variables give in the expression will be 11✓2

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Answer:

\(\huge\boxed{\sf $1.25}\)$1.25

Step-by-step explanation:

Pizza = $2.50

Drink = $1.25

Total = $2.50 + $1.25

= $3.75

Paul has = $5

Change received = total money - money spent

= $5 - $3.75

= $1.25

\(\rule[225]{225}{2}\)

Hope this helped!

The equation of the perpendicular bisector of the line segment with endpoints (-7, 2) and (-1, -6) is y = (3/4)x + 1.

To find the equation of the perpendicular bisector of a line segment, we need to determine the midpoint of the line segment and the slope of the line segment. The perpendicular bisector will have a negative reciprocal slope compared to the line segment and will pass through the midpoint.

Given the endpoints (-7, 2) and (-1, -6), we can find the midpoint using the midpoint formula:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

Midpoint = ((-7 + (-1))/2, (2 + (-6))/2)

= (-8/2, -4/2)

= (-4, -2)

The midpoint of the line segment is (-4, -2).

Next, we need to find the slope of the line segment using the slope formula:

Slope = (y2 - y1)/(x2 - x1)

Slope = (-6 - 2)/(-1 - (-7))

= (-6 - 2)/(-1 + 7)

= (-8)/(6)

= -4/3

The slope of the line segment is -4/3.

Since the perpendicular bisector has a negative reciprocal slope, the slope of the perpendicular bisector will be 3/4.

Now, we can use the midpoint (-4, -2) and the slope 3/4 in the point-slope form of a line to find the equation of the perpendicular bisector:

y - y1 = m(x - x1)

y - (-2) = (3/4)(x - (-4))

y + 2 = (3/4)(x + 4)

y + 2 = (3/4)x + 3

y = (3/4)x + 1.

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We can use the logarithmic identity log_a(b) + log_a(c) = log_a(bc) to simplify the left side of the equation:

log_2(x) + log_4(x+1) = log_2(x) + log_2((x+1)^(1/2))

Using the rule log_a(b^c) = c*log_a(b), we can simplify further:

log_2(x) + log_2((x+1)^(1/2)) = log_2(x(x+1)^(1/2))

Now we can rewrite the equation as:

log_2(x(x+1)^(1/2)) = 3

Using the rule log_a(b^c) = c*log_a(b), we can rewrite this as:

x(x+1)^(1/2) = 2^3

Squaring both sides, we get:

x^2 + x - 8 = 0

This is a quadratic equation that can be solved using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = 1, and c = -8. Plugging in these values, we get:

x = (-1 ± sqrt(1^2 - 4(1)(-8))) / 2(1)

x = (-1 ± sqrt(33)) / 2

x ≈ -2.54 or x ≈ 3.54

However, we must check our solutions to make sure they are valid. Plugging in x = -2.54 to the original equation results in an invalid logarithm, so this solution is extraneous. Plugging in x = 3.54 yields:

log_2(3.54) + log_4(4.54) = 3

0.847 + 0.847 = 3

So x = 3.54 is the valid solution to the equation.

Answer:

1

The claim is that the mean amount of Walker Crisps eaten was significantly higher for the children who watched the sports celebrity- endorsed Walker Crisps commercial

2

The kind of test to use is a t -test because a t -test is used to check if there is a difference between means of a population

3

\(t = 3.054\)

4

The p-value  is   \(p-value = P(Z > 3.054) = 0.0011291\)

5

The conclusion is  

There is sufficient evidence to conclude that the mean amount of Walker Crisps eaten was significantly higher for the children who watched the sports celebrity- endorsed Walker Crisps commercial

The test statistics is  

Step-by-step explanation:

From the question we are told that

   The first sample size is  \(n_1 = 51\)

    The first sample  mean is \(\mu_1 = 36\)

    The second sample size is  \(n_2 = 41\)

    The second sample  size is  \(\mu_2 = 25\)

     The first standard deviation is  \(\sigma _1 = 21.4 \ g\)

    The second standard deviation is  \(\sigma _2 = 12.8 \ g\)

  The  level of significance is  \(\alpha = 0.05\)

The  null hypothesis is  \(H_o : \mu_1 = \mu_ 2\)

The  alternative hypothesis is  \(H_a : \mu_1 > \mu_2\)

Generally the test statistics is mathematically represented as

    \(t = \frac{\= x_1 - \= x_2}{ \sqrt{ \frac{s_1^2}{n_1} + \frac{s_2^2}{n_2} } }\)

=>   \(t = \frac{ 36 - 25}{ \sqrt{ \frac{ 21.4^2}{51} + \frac{ 12.8^2}{41} } }\)

=> \(t = 3.054\)

The  p-value is mathematically represented as

     \(p-value = P(Z > 3.054)\)

Generally from the z table  

             \(P(Z > 3.054) = 0.0011291\)

=>   \(p-value = P(Z > 3.054) = 0.0011291\)

From the values obtained  we see that \(p-value < \alpha\) so  the null hypothesis is rejected

Thus the conclusion is  

  There is sufficient evidence to conclude that the mean amount of Walker Crisps eaten was significantly higher for the children who watched the sports celebrity- endorsed Walker Crisps commercial

The value of the difference in the mean number of chips eaten can be used to test the hypothesis.

The correct responses are;

Reasons:

The given parameters are;

The amount of Walker Crisps potato chips children ate, based on commercial watched.

Celebrity endorsed food snack commercial mean, \(\overline x_1\) = 36 g

Sample size that watched the celebrity endorsed commercial, n₁ = 51

Alternative food snack commercial mean, \(\overline x_2\) = 25 g

Sample size that watched the other commercial = 41

Standard deviation, SD,  of the samples;

Sample that watched the celebrity endorsed commercial, SD₁ = 21.4 g

Sample that watched the other commercial, SD₂ = 12.8 g

Reasons:

1. The claim from the question is; The mean amount of Walker Crisp eaten was significantly higher for the children who watched the sports celebrity - endorsed Walker Crisps commercial.

The null hypothesis is, H₀; \(\overline x_1 = \overline x_2\) (There is no difference in the mean)

The alternative hypothesis is, Hₐ; \(\overline x_1\) > \(\overline x_2\) (The mean of the amount of Walker Crisps eaten is significantly higher for the children that watched the sports celebrity-endorsed commercial)

2. Given that the aim of the study is to determine if the mean of the first

sample is higher than the mean of the second sample, the kind of test to

be performed is the test of the difference in the mean of the two samples

based on specified hypothesis, (one sample is higher), which is done using

a t-test, given that the population mean is not specified (unknown).

The kind of test to use is a t-test

3. The test statistic is given by Welch's Test for unequal variance as follows;

\(\displaystyle t = \mathbf{\frac{\overline x_1 - \overline x_2}{\sqrt{\dfrac{s_1^2}{n_1} +\dfrac{s_2^2}{n_2} } }}\)

Which gives;

\(\displaystyle t = \frac{36- 25}{\sqrt{\dfrac{21.4^2}{51} +\dfrac{12.8^2}{41} } } = \frac{77500}{25379} \approx 3.054\)

The test statistic, t ≈ 3.054

4. From the above test statistic and by finding, degrees of freedom, df as follows, the p-value can be found.

\(\displaystyle df = \mathbf{\frac{\left(\dfrac{s_1^2}{n_1} +\dfrac{s_2^2 \righ}{n_2} \right)^2}{\dfrac{1}{n_1 - 1} \cdot \left( \dfrac{s_1^2}{n_1} \right)^2 + \dfrac{1}{n_2 - 1} \cdot \left( \dfrac{s_2^2}{n_2} \right)^2}}\)

Which gives;

\(\displaystyle df = \frac{\left(\dfrac{21.4^2}{51} +\dfrac{12.8^2 \righ}{41} \right)^2}{\dfrac{1}{51 - 1} \cdot \left( \dfrac{21.4^2}{51} \right)^2 + \dfrac{1}{41 - 1} \cdot \left( \dfrac{12.8^2}{41} \right)^2} \approx \mathbf{83.69}\)

From the t-test table, we have the p-value of the result as follows;

The p-value is; 0.001 < P(t > 3.054) < 0.0025.

5. The conclusion that can be made is; Given that the p-value of the test

statistic is less than the given alpha value of 0.05, we reject the null

hypothesis, given that there is significant statistical evidence to show that

the mean amount of Walker Crisp eaten was significantly higher for the

children that watch the celebrity-endorsed Walker Crisps commercial.

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By using trigonometry, the missing sides are

Example 1: x = 16.7

Example 2: x = 3.2

Example 3: x = 23.5

Example 4: x = 9.3

From the question we are to determine the value of the missing sides in the given triangles

We can determine the value of the missing sides by using SOH CAH TOA

Example 1

Angle = 42°

Opposite side = x

Hypotenuse = 25

Thus,

sin (42°) = x / 25

x = 25 × sin (42°)

x = 16.7

Example 2

Angle = 75°

Opposite side = 12

Adjacent side = x

Thus,

tan (75°) = 12 / x

x = 12 / tan (75°)

x = 3.2

Example 3

Angle = 36°

Hypotenuse side = x

Adjacent side = 19

Thus,

cos (36°) = 19 / x

x = 19 / cos (36°)

x = 23.5

Example 4

Angle = 53°

Opposite side = x

Adjacent side = 7

Thus,

tan (53°) = x / 7

x = 7 × tan (53°)

x = 9.3

Hence,

The missing sides are 16.7, 3.2, 23.5 and 9.3

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The equation of the relationship is f(200) = 0.75 * 200

From the question, we have the following parameters that can be used in our computation:

Total number of drinks = 200

Cost of each drink = 0.75

Using the above as a guide, we have the following:

f(x) = Cost of each drink * Total number of drinks

Where

f(x) = Total cost

Substitute the known values in the above equation, so, we have the following representation

f(200) = 0.75 * 200

Hence, the equation is f(200) = 0.75 * 200

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Answer:

303.61

Step-by-step explanation:

if you need explantion tell me and i will edit my answer

Answer:

24.4M

Step-by-step explanation:

hii!

Is there any more info? The question is a bit unclear!! Thank you! Repost with full questions thanks.

Brainliest??

Answer:

0.15m

Step-by-step explanation:

1m = 100cm

15/100

= 0.15m

a. there are three vectors in {a₁, a₂, a₃}.

b. There are infinitely many vectors in W = span {a₁, a₂, a₃} by definition.

c. we have that a₁ is in the W.

A matrix is a set of integers arranged in rows and columns. The rows and columns of integers are arranged in a rectangular matrix. The matrix A, for instance, contains two rows and three columns. The elements of the matrix, also known as the entries, are the integers. In addition to many areas of mathematics, matrices are widely used in the fields of engineering, physics, economics, and statistics.

a. The vector b is not in {a₁ ,a₂, a₃} since b is not equal to any of the column vectors of A. Clearly, there are three vectors in {a₁, a₂, a₃}.

b. Vector b is in W if the augmented matrix [a₁, a₂, a₃ b] is consistent.

The augmented matrix is:

\(\left[\begin{array}{cccc}1&0&-4&4\\0&3&-2&1\\-2&6&3&-4\end{array}\right] \sim \left[\begin{array}{cccc}1&0&-4&4\\0&3&-2&1\\0&6&-5&4\end{array}\right] \sim \left[\begin{array}{cccc}1&0&-4&4\\0&3&-2&1\\0&6&-1&2\end{array}\right]\)

Thus, since the system is consistent we have that b must be in W.

There are infinitely many vectors in W = span {a₁, a₂, a₃} by definition.

c. since   \(\left[\begin{array}{c}1\\0\\-2\end{array}\right] = 1. \left[\begin{array}{c}1\\0\\-2\end{array}\right] + 0. \left[\begin{array}{c}1\\0\\-2\end{array}\right] + 0. \left[\begin{array}{c}1\\0\\-2\end{array}\right]\) we have that a₁ is in the W.

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a. there are three vectors in {a₁, a₂, a₃}.

b. There are infinitely many vectors in W = span {a₁, a₂, a₃} by definition.

c. we have that a₁ is in the W.

A matrix is a set of integers arranged in rows and columns. The rows and columns of integers are arranged in a rectangular matrix. The matrix A, for instance, contains two rows and three columns. The elements of the matrix, also known as the entries, are the integers. In addition to many areas of mathematics, matrices are widely used in the fields of engineering, physics, economics, and statistics.

a. The vector b is not in {a₁ ,a₂, a₃} since b is not equal to any of the column vectors of A. Clearly, there are three vectors in {a₁, a₂, a₃}.

b. Vector b is in W if the augmented matrix [a₁, a₂, a₃ b] is consistent.

No, b is not in {a1, a2, a3}.

There are 3 vectors in {a1, a2, a3}.

Yes, b is in W.

There are infinitely many vectors in W.

Yes, a1 is in W because it can be expressed as a linear combination of the vectors in W. This is shown by the equation a1 = 1(a1) + 0(a2) + 0(a3).  The coefficients of the vectors in the linear combination are all integers and this equation shows that a1 is in the span of the vectors in W.

Thus, since the system is consistent we have that b must be in W.

There are infinitely many vectors in W = span {a₁, a₂, a₃} by definition.

c. since we have that a₁ is in the W.

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The probability that a randomly selected student will like pizza but not chicken nuggets is (28n - 8)/(28n + 7), where 28n is the students who like pizza and 8 is students who like both pizza and chicken nuggets.

To find the probability that a randomly selected student will like pizza but not chicken nuggets.

Let P = the number of students who like pizza but not chicken nuggets

Then, P = the number of students who like pizza - the number of students who like both pizza and chicken nuggets

P = 28n - 8

So, the probability that a randomly selected student will like pizza but not chicken nuggets is:

P(Pizza but not nuggets) = P/(Total number of students)

We can find the total number of students who like either pizza or chicken nuggets by adding the number of students who like pizza and the number of students who like chicken nuggets, and then subtracting the number of students who like both:

Total number of students = 28n + 15 - 8 = 28n + 7

So, the probability that a randomly selected student will like pizza but not chicken nuggets is:

P(Pizza but not nuggets) = P/(Total number of students) = (28n - 8)/(28n + 7)

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Answer:

−15x2+23x−6

Step-by-step explanation:

(3x−1)(−5x+6)

=(3x+−1)(−5x+6)

=(3x)(−5x)+(3x)(6)+(−1)(−5x)+(−1)(6)

=−15x2+18x+5x−6

=−15x2+23x−6

Check the picture below.

so following the template below, a shift 2 units to the left, means C=2

\(G(x)=\sqrt{x+2}\)

When rotated 90 degrees, counterclockwise direction the new coordinates will result in the attached image.

The old coordinate where were rotated are:

A(-5,8)

B (-1, 7)

C(-3, 5)

D(-4, 2)

To rotate a point counterclockwise about the origin, we switch the x and y coordinates and change the sign of the new x  -coordinate.

The new coordinates are after 90 degrees, counterclockwise  are

A' = (-8, -5)

B' = (-7, -1)

C' = (-5, -3)

D' = (-2, -4)

See attached image.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

See attached image.

he net income for the year is $16,550.

Calculation of the net income for the year:Retained earnings equation is:Beginning Retained Earnings + Net Income − Dividends = Ending Retained EarningsWhere, Beginning Retained Earnings = $0 (not given)Ending Retained Earnings = $16,550 (calculated from balance sheet)Dividends = $0 (not given)

Therefore,Net Income = Ending Retained Earnings - Beginning Retained Earnings + Dividends= $16,550 - $0 + $0= $16,550 Balance Sheet of Cole Valley Book Store as of December 31, current year:Current assets Cash on hand and in bank = $69,250 Amounts due from customers from sales of books = $43,500 Total current assets = $112,750 Property, plant, and equipment Unused portion of store and office equipment = $72,500

Total assets = $185,250Liabilities Amounts owed to publishers for books purchased = $12,400 One-year note payable to a local bank = $3,200 Total liabilities = $15,600 Stock holders' Equity Common stock, 5,600 shares at $71,500 = $400,400 Retained earnings, beginning = $0Net income = $16,550 Retained earnings, ending = $16,550 Total stockholders' equity = $416,950Total liabilities and stockholders' equity = $185,250 + $15,600 + $416,950= $617,800

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The value of x cannot be determined and the answer is undefined.

To find the value of x in this scenario, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, triangle ABC is a right triangle with AB as the hypotenuse. So, we can use the Pythagorean theorem to solve for AC, which is equal to the square root of (AB^2 - BC^2).

Using the given values, we have:
AC = sqrt(16^2 - 8^2)
AC = sqrt(256 - 64)
AC = sqrt(192)
AC ≈ 13.86

Now, we can use triangle ACD to solve for x. This triangle is also a right triangle with CD as the hypotenuse. So, we can use the Pythagorean theorem again to solve for AD, which is equal to the square root of (CD^2 - AC^2).

Using the given values, we have:
AD = sqrt(9^2 - 13.86^2)
AD = sqrt(81 - 192.23)
AD = sqrt(-111.23)

We can't take the square root of a negative number, so there is no real solution for x in this scenario.

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Answer: No. Don't look up here. Seriously. There is nothing here. LOOK AWAY! I WARNED YOU!!!!

Step-by-step explanation:

Cups of peanut butter: 1.5

Cups of vegetable oil: 0.5

Cups of light brown sugar: 2.5

Tablespoons of milk: 6

Teaspoons of vanilla extract: 5.5

Large eggs: 2

Cups of flour: 3

Teaspoons of baking soda: 1.5

Teaspoons of salt: 0.5

Just times 2 to all of them.