Tony is making a tiered cake for a party. He use 9 cups of butter from the refrigerator to make 4 cakes. We want to find how butter he needs to put in each cake. This situation can be represented by the expression -9 divided by 4. Find the solution, and explain what it means in the context of the problem.

Answer:

2 sq rt 33

Step-by-step explanation:

1st step:  subtract one, each side

(radical 2/3)r = 22

2nd step:  set up a proportion

(radical 2/3)r = 22

3rd step:  cross-multiply

radical 2*r = 66

4th step:  solve for 'r'

r = 66 / radical 2

5th step:  rationalize the denominator

multiply numerator and denominator by radical 2

6th step:  simplify

(66\(\sqrt{2}\)) / 2 = 33 \(\sqrt{2}\)

a) Since the triangles are congruent, and ΔABC is congruent to ΔDEF, segments AB and DE have the same value. Therefore, you can use algebra to solve for x when using the knowledge that (12 - 4x) is equal to (15 - 3x).

To solve:

12 - 4x = 15 - 3x

12 = 15 + x

-3 = x

Therefore, x is equal to -3.

b) To find the value of AB, plug in the value of x found in part a).

12 - 4x

12 - 4(-3)

12 - (-12)

12 + 12 = 24

Thus, segment AB is equal to 24.

c) As shown in part b), plug in the value of x found in part a) to find the value of segment DE.

15 - 3x

15 - 3(-3)

15 - (-9)

15 + 9 = 24

Thus, segment DE is also equal to 24.

We can confirm the knowledge of the equal side lengths because the triangle are congruent. This means that all the side lengths in the triangle are the same, which is confirmed when algebraically plugging in the value of x to solve for the values of the segments AB and DE.

I hope this helps!

The answer is P(>204.3) = 0.5000

There are an infinite number of real numbers > 204.3, but an equally infinite number of real numbers < 204.3

The chance of randomly selecting a number >204.3 is 1/2 or 50%

or for 4 decimals: 50.0000%

The probability of an event can be calculated via chance formula with the aid of truly dividing the favorable range of effects by means of the whole number of feasible effects.

Opportunity = the wide variety of ways of achieving fulfillment. The whole range of viable effects. As instance, the possibility of flipping a coin and it being head is ½, because there is 1 way of having a head and the whole range of viable effects is two (a head or tail).

Chance is the department of mathematics that research the possible outcomes of given occasions together with the outcomes' relative likelihoods and distributions.

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Answer:I think the answer is multiplication property of equality

Step-by-step explanation:

it is being multiplied to get the answer so that should be the answer

Answer:

the answer should be the multiplication property of equality

Step-by-step explanation:

because you're multiplying

Hope this helps! :)

Answer:

1. a+b 2.a-b. 3. ab 4. a/b

Answer:

Step-by-step explanation:

since there is no table included with the question I'm concluding that you need to find values of y using values of x, simply substitute the x values in the equation and you'll get the y value like this

if x = 1 y = 4

Answer:

x - 0 1 2 3 4 5

y - 3 4 5 6 7 8

It is very simple, all you have to do is add three to x every time, for example if x is 153, y will be 156. 3 should be the beginning, the y intercept in graphs, and the beginning means x should be 0.

Answer:

$4x

Step-by-step explanation:

$6 - $2 = $4

$4x

Answer:

X=6+2

Step-by-step explanation:

Answer:

-8.4 to 8.4 and 12.6

Step-by-step explanation:

Puedes separar los grupos en:

los que solo toman clases de piano; p

los que solo toman clases de violin: v

los que toman clases de piano y violin; 5

A) para determinar cuántos estudiantes no toman ni piano ni violin, podemos hallar el número total de estudiantes que toman clases solo de piano y los que toman solo de violín y los que toman ambas clases, de la siguiente forma:

Estudian solo piano, p = 14 - 5= 9

Estudian solo violín, v = 29 - 5 = 24

Estudian ambos: 5

Total de estudiantes que toman clases de esos instrumentos : 9 + 24 + 5 = 38

Por tanto, hay 40 - 38 = 2 estudiantes que no toman clases de piano ni violín.

B) ¿cuántos estudiantes toman clases de piano o violín?

Son los que tocan solo piano, o solo violín o ambos y los  hallamos arriba:  9 + 24 + 5 = 38.

Respuesta: 38

C) ¿Cuántos estudiantes tocan solo violín?

También lo encontramos arriba: son 29 - 5 = 24

Respuesta: 24

Answer:

GH = 4

Step-by-step explanation:

GH = AB due to congruency markings therefore

5y - 8 = 3y

-8 = =2y

4 = y

Answer:

GH=12

Step-by-step explanation:

You use what this other solution to the answer was. However, they did not include that GH is 3y, so while one y=4, 3y=12. Therefore, GH=12

Answer: 1 & 2 are congruent

Step-by-step explanation:

They both have the same amount of space to get to the other point .

1.  AC is congruent to BD.

2. BD and CE are not congruent.

3. AD and BE are not congruent.

4.  BC and CE are not congruent.

We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.

1. The segment AC is (1 - (-8)) = 9 units, and the line segment

BD is (3 -(-6)) = 9 units.

So, AC ≅ BD.

2. Line segment BD is 9 units and line segment CE is (7 - 1) = 6 units.

So, BD and CE are not congruent.

3. Line segment AD is (3 - (-8)) = 12 units and line segment BE is (7 - (-6)) = 13 units. (not congruent)

So, line segment AD and BE are not congruent.

4. Line segment BC is (1 - (-6)) = 7 units and line segment CE is (7 - 1) = 6 units.

So, Line segments BC and CE are not congruent.

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The perimeter of the square is 66.4 meters

The area is given as:

Area = 275.56m².

The perimeter of the rectangle is calculated using:

Perimeter = 4 * √Area

So, we have:

Perimeter = 4 * √275.56m²

Evaluate the exponent

Perimeter = 4 * 16.6m

Evaluate the product

Perimeter = 66.4 m

Hence, the perimeter of the square is 66.4 meters

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Answer:

350

175

x 2

-----

350

We need to prove that p→(p∧r) and ¬p∨r are logically equivalent.

Proof:

We know that:  p→q is logically equivalent to ¬p∨q

To prove that p→(p∧r) is logically equivalent to ¬p∨r, we need to convert the given statement p→(p∧r) into an equivalent statement in the form of p→q.

So, p→(p∧r) can be converted as: p→q ⇒ ¬p∨q

Step-by-step explanation:

In order to show that p→(p∧r) is equivalent to ¬p∨r, we will prove that p→(p∧r) is logically equivalent to ¬p∨r by checking whether they have the same truth values in all cases of p and r.

Table of truth:

p |r |p∧r |p→(p∧r) |¬p∨r
T |T |T |T |T
T |F |F |F |F
F |T |F |T |T
F |F |F |T |T

The two expressions have the same truth values in all cases. Therefore, we have proved that p→(p∧r) and ¬p∨r are logically equivalent.

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The group of volunteers can make a total of 200 masks out of 25 yards of fabric.

To calculate the number of masks that can be made, we divide the total amount of fabric (25 yards) by the amount of fabric required per mask (1/8 yard). To do this, we first convert the fraction 1/8 to decimal form, which is 0.125. Then, we divide the total fabric (25 yards) by the fabric required per mask (0.125 yards). This can be done by dividing 25 by 0.125, which equals 200. Therefore, the group of volunteers can make a total of 200 masks out of 25 yards of fabric. Each mask requires 1/8 yard of fabric, so dividing the total fabric by the fabric required per mask gives us the total number of masks that can be made.

Calculation steps:
1. Convert the fraction 1/8 to decimal form: 1/8 = 0.125.
2. Divide the total fabric (25 yards) by the fabric required per mask (0.125 yards):
  25 / 0.125 = 200.


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After installing three congruent triangular spaces with a base of 3 meters and a height of 3.5 meters, the total area left for the park can be calculated.

The area of a triangle can be calculated using the formula A = (1/2) * base * height. In this case, the base of each triangle is 3 meters, and the height is 3.5 meters. Substituting these values into the formula, we can find the area of one triangle:

A = (1/2) * 3 * 3.5

A = 5.25 square meters

Since there are three congruent triangles, the total area of the triangular spaces is 3 times the area of one triangle:

Total Area = 3 * 5.25

Total Area = 15.75 square meters

To find the area left for the park, we subtract the total area of the triangular spaces from the total area of the park. However, the size of the park is not provided in the question. Therefore, without knowing the dimensions of the park, it is not possible to determine the exact area left.

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Answer:

11.3

Step-by-step explanation:

To find mean: All values added together divided by amount of values:

X: 11+12+13+14 = 50

50 / 4 (amount of values) = 12.5 (mean of x)

F: 8+3+17+12 = 40

40/4 (amount of values) = 10 (mean of f)

To find mean of x and f combined:

10 + 12.5 = 22.5

22.5 / 2 (amount of values) = 11.25 (mean of x and f combined)

To 1 dec pl.

= 11.3

Hope that makes sense

Answer:

20

Step-by-step explanation:

If its is 2 to 8 you divide by 2 to get 1;5 which u multiply by 5 to get 5:20

Answer:20 chickens

Step-by-step explanation:if there are 2 roosters for every four chickens, then you do 4*5

The df value for the t-statistic in this independent-measures study with sample sizes of n = 6 and n = 8 is 12.

The degrees of freedom (df) value for the t-statistic in an independent-measures study depends on the sample sizes of the two groups being compared. In this case, one sample has a size of n = 6, and the second sample has a size of n = 8.

To calculate the df value, we need to consider the formula for calculating degrees of freedom in an independent t-test. The formula is given as:

df = (n1 + n2) - 2

where n1 and n2 are the sample sizes of the two groups being compared.

Applying this formula to the given sample sizes, we have:

df = (6 + 8) - 2

df = 14 - 2

df = 12

Therefore, the degrees of freedom (df) value for the t-statistic in this study is 12.

The concept of degrees of freedom is crucial in statistical analysis, particularly in hypothesis testing. In the context of an independent-measures study, degrees of freedom represent the number of values in the data that are free to vary. In this case, the df value of 12 suggests that there are 12 observations in the data that contribute to the estimation of population parameters.

The df value is important when determining critical values from t-distribution tables and calculating p-values. It affects the variability and precision of the t-statistic, influencing the decision to reject or fail to reject the null hypothesis.

Having a higher degrees of freedom value generally leads to narrower confidence intervals and more precise estimates. It also reduces the impact of random variability in the data. Conversely, a lower degrees of freedom value can result in wider confidence intervals and less precise estimates, increasing the likelihood of Type I or Type II errors.

In summary, the df value for the t-statistic in this independent-measures study with sample sizes of n = 6 and n = 8 is 12.

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The standard error of the mean for a simple random sample of 100 observations, with a sample mean of 80 and a standard deviation of 12, is 1.20 (option a).

The standard error of the mean measures the precision or variability of the sample mean estimate. It is calculated by dividing the standard deviation of the population by the square root of the sample size.

Given that the sample mean is 80 and the standard deviation is 12, we can calculate the standard error of the mean as follows:

Standard Error of the Mean = Standard Deviation / Square Root of Sample Size

Standard Error of the Mean = 12 / √100 = 12 / 10 = 1.20

Therefore, the standard error of the mean for this sample is 1.20. This value indicates the average amount of variability or uncertainty we can expect in the sample mean compared to the population mean. It represents the precision of the sample mean estimate and is an important measure in inferential statistics for making inferences about the population based on the sample.

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If you have a required return of 6% per year, compounded monthly, and you are offered an investment that will pay you $800 a month for 40 years, you would be willing to pay approximately $206,595.71 for this investment.

To determine the value you would be willing to pay for this investment, we can use the concept of present value. The present value of an investment is the current worth of the future cash flows it will generate. In this case, the investment will pay you $800 a month for 40 years.

To calculate the present value, we can use the formula:

\(PV = CF / (1 + r)^n\)

Where PV is the present value, CF is the cash flow, r is the required return per period, and n is the number of periods.

In this case, the cash flow is $800 per month, the required return is 6% per year (or 0.06/12 = 0.005 per month), and the number of periods is 40 years * 12 months = 480 months.

Plugging these values into the formula, we have:

PV = $800 / \((1 + 0.005)^(480)\)

Calculating this expression, we find that the present value is approximately $206,595.71. Therefore, you would be willing to pay approximately $206,595.71 for this investment to achieve your required return of 6% per year, compounded monthly.

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Answer:

1/6

Step-by-step explanation:

First, we'll simplify the inside portion of the question.

\(\frac{3^{3/4}}{3^{3/8}} =3^{3/4-3/8}=3^{3/8}\\\)

Next, we are raising this to the 4/9 power.

\((3^{3/8})^{4/9} = 3^{(3/8) * (4/9)} = 3^{1/6}\)

Thus, x = 1/6.

The action which best demonstrates the fairness is (c) manager hires an "older-woman" based on her "job-performance" for security position even though men have traditionally held this job.

This action demonstrates fairness because the manager made the hiring decision based on job performance, rather than on any gender or age biases.

The fact that the job was traditionally held by men, the manager recognized that the older woman was the best candidate for the position based on her qualifications and abilities.

This shows that the hiring-process was fair and unbiased, and that the manager was focused on selecting the most qualified candidate for the job, regardless of any stereotypes.

Therefore, the correct option is (c).

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The given question is incomplete, the complete question is

Which action demonstrates fairness?

(a) A referee position is opened at a sport organization but only men are told about the position since traditionally men perform the job.

(b) A man's application to work as a make-up artist at a department store is passed over even though he has more experience.

(c) A manager hires an older woman based on job performance for a security position even though men have traditionally held the job.

(d) A twenty-five-year-old with a strong Hispanic accent is told he is ineligible to apply for a public speaking position even though he is overqualified.

The Maclaurin series for f(x) converges absolutely for x within the interval (-2/3, 2/3).

To find the Maclaurin series for the function f(x) = (3cos(x))ln(1+x), we can use the standard formulas for the Maclaurin series expansion of elementary functions.

First, let's find the derivatives of f(x) up to the third order:

f(x) = (3cos(x))ln(1+x)

f'(x) = -3sin(x)ln(1+x) + (3cos(x))/(1+x)

f''(x) = -3cos(x)ln(1+x) - (6sin(x))/(1+x) + (3sin(x))/(1+x)² - (3cos(x))/(1+x)²

f'''(x) = 3sin(x)ln(1+x) - (9cos(x))/(1+x) + (18sin(x))/(1+x)² - (12sin(x))/(1+x)³ + (12cos(x))/(1+x)² - (3cos(x))/(1+x)³

Next, we evaluate these derivatives at x = 0 to find the coefficients of the Maclaurin series:

f(0) = (3cos(0))ln(1+0) = 0

f'(0) = -3sin(0)ln(1+0) + (3cos(0))/(1+0) = 3

f''(0) = -3cos(0)ln(1+0) - (6sin(0))/(1+0) + (3sin(0))/(1+0)² - (3cos(0))/(1+0)² = -3

f'''(0) = 3sin(0)ln(1+0) - (9cos(0))/(1+0) + (18sin(0))/(1+0)² - (12sin(0))/(1+0)³ + (12cos(0))/(1+0)² - (3cos(0))/(1+0)³ = -9

Now we can write the first three nonzero terms of the Maclaurin series:

f(x) = f(0) + f'(0)x + (f''(0)/2!)x² + (f'''(0)/3!)x³ + ...

f(x) = 0 + 3x - (3/2)x² - (9/6)x³ + ...

Simplifying, we have:

f(x) = 3x - (3/2)x² - (3/2)x³ + ...

To determine the values of x for which the series converges absolutely, we need to find the interval of convergence. In this case, we can use the ratio test:

Let aₙ be the nth term of the series.

|r| = lim(n->infinity) |a_(n+1)/aₙ|

= lim(n->infinity) |(3/2)(xⁿ+1)/(xⁿ)|

= lim(n->infinity) |(3/2)x|

For the series to converge absolutely, we need |r| < 1:

|(3/2)x| < 1

|x| < 2/3

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Answer:

y=-4

I think it helps you

Step-by-step explanation:

\(\tt{-y+6y-16y+15y=-16 }\)

\(\tt{ 21y-17y=-16 }\)

\(\tt{4y=-16 }\)

\(\tt{ y=\dfrac{-16}{4} }\)

\(\bold{ y=-4 }\)

Answer: In one simulated SRS of 100 students, the average GPA was x= 3.45

Step-by-step explanation:

Each dot in the dot plot in representation of one sample of 100 students, also I just turned it in

Answer:

A

Step-by-step explanation:

EDGE

Answer:

Y=6+5/12

Step-by-step explanation:

Move all terms containing "Y" to the right

Get rid of parenthesis and multiply all terms by the denominator

Add all numbers together and all the variables, then multiply

-12Y= -77

Y= -77/-12

Y= 6+5/12

The value of a for which v is a linear combination is given as follows:

a = -8.

v will be a linear combination of the set H if it can be obtained as the solution of a system of equations from the set H.

From the vectors, the system is defined as follows:

From the first equation, the value of x is obtained as follows:

-x = -1

x = 1.

From the second equation, the value of y is obtained as follows:

2x - y = 4

2 - y = 4

y = 2 - 4

y = -2.

From the third equation, the value of z is obtained as follows:

5x + 4y - 3z = -6.

5 - 8 - 3z = -6

3z = 3

z = 1.

Then the value of a needed for the linear combination is of:

a = -x + 3y - z

a = -1 - 6 - 1

a = -8.

The problem is given by the image shown at the end of the answer.

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The bottleneck time is 10, as this is the longest time for any station in the assembly line.

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Suppose A=BC, where B is invertible. Show that any sequence of row operations that reduces B to also reduces A to C. The zero matrix may be factored as 0= B.

To show that any sequence of row operations that reduces B to also reduces A to C, the following pieces of information in the problem statement are relevant:

A. The zero matrix may be factored as 0= B * 0. This is not relevant for showing that any sequence of row operations that reduces B to also reduces A to C.B. A=B.

This is not relevant for showing that any sequence of row operations that reduces B to also reduces A to C.C. B is invertible. This is relevant for showing that any sequence of row operations that reduces B to also reduces A to C.D. The converse not true. This is relevant for showing that any sequence of row operations that reduces B to also reduces A to C.

Given the relevant pieces of information from the previous step, there exist elementary matrices E1, ..., Ep  corresponding to row operations that reduce B to I, in the sense that Ep...E2E1B=I. Applying the same sequence of row operations to A amounts to left-multiplying by the product E1E2...Ep.

Therefore, A is transformed to C, since

C = IB = E1

E2...Ep

B = E1E2...EpA.

The proof is complete because C = IC = C.

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