Let p be a prime. Show that in the ring Zp we have (a+b)^p =a^p + b^p for every a, b element of Zp. [Hint:] Observe that the usual binomial expansion for(a+b)^n is valid in a commutative ring.] Is this result also true for Z6? Justify.

The area of the part of the plane 3x 2y z = 6 that lies in the first octant  is  mathematically given as

A=3 √(4) units ^2

Generally, the equation for is  mathematically given as

The Figure is the x-y plane triangle formed by the shading. The formula for the surface area of a z=f(x, y) surface is as follows:

\(A=\iint_{R_{x y}} \sqrt{f_{x}^{2}+f_{y}^{2}+1} d x d y(1)\)

The partial derivatives of a function are f x and f y.

\(\begin{aligned}&Z=f(x)=6-3 x-2 y \\&=\frac{\partial f(x)}{\partial x}=-3 \\&=\frac{\partial f(y)}{\partial y}=-2\end{aligned}\)

When these numbers are plugged into equation (1) and the integrals are given bounds, we get:

\(&=\int_{0}^{2} \int_{0}^{3-\frac{3}{2} x} \sqrt{(-3)^{2}+(-2)^2+1dxdy} \\\\&=\int_{0}^{2} \int_{0}^{3-\frac{3}{2} x} \sqrt{14} d x d y \\\\&=\sqrt{14} \int_{0}^{2}[y]_{0}^{3-\frac{3}{2} x} d x d y \\\\&=\sqrt{14} \int_{0}^{2}\left[3-\frac{3}{2} x\right] d x \\\\\)

\(&=\sqrt{14}\left[3 x-\frac{3}{2} \cdot \frac{1}{2} \cdot x^{2}\right]_{0}^{2} \\\\&=\sqrt{14}\left[3-\frac{3}{2} \cdot \frac{1}{2} \cdot x^{2}\right]_{0}^{2} \\\\&=\sqrt{14}\left[3.2-\frac{3}{2} \cdot \frac{1}{2} \cdot 3^{2}\right] \\\\&=3 \sqrt{14} \text { units }{ }^{2}\)

In conclusion,  the area is

A=3 √4 units ^2

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Answer:

\(\overline{TH}\)

Step-by-step explanation:

The diameter of a circle is a line that goes from one side to the other in a circle. It is the longest straight line that can be drawn in a circle. It also goes through the center of a circle.

That is the answer

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If I were to hypothesize that communication students will have a higher average score on the oral communication measures,

I would have a research hypothesis. A research hypothesis is a statement that is used to explain a relationship between two or more variables,

in this case, the relationship between being a communication student and having a higher score on oral communication measures.

The hypothesis can then be tested through research and analysis of data to determine if there is a significant correlation between the two variables. In order to fully test this hypothesis,

it would be necessary to gather data on both communication students and non-communication students and compare their scores on oral communication measures.

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\(\sf \bf {\boxed {\mathbb {ANSWER:}}}\)

(a) -3 \(\boxed{ > }\) -4

(b) 6 \(\boxed{ >}\) -20

(c) -8 \(\boxed{ < }\) -2

(d) 5 \(\boxed{ > }\) -7

\(\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{☂}}}}}\)

Answer:

minutes took to finish the race = 54 minutes

Step-by-step explanation:

It's known that:

\(speed = \frac{distance}{time}\)

then:

\(time = \frac{distance}{speed}\)

IN THE 1ST 10 MILES:

time = \(\frac{10}{25} = \frac{2}{5} = 0.4 hours\)

IN THE 2ST 10 MILES:

time = \(\frac{10}{20} = 0.5 hours\)

Hence, Overall time took to finish the race = 0.4 + 0.5 = 0.9 hours

time in minutes = 0.9 × 60 = 54 minutes


Another Solution:

Overall speed = \(\frac{S_1 + S_2}{2}\), Where: S1: 1st speed, S2: 2nd speed

then:

speed = \(\frac{25 + 20}{2}= 22.5 mph\)

Hence, time took = \(\frac{20}{22.5} = 0.9 hours = 54 minutes\)




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Answer:

1/8 kilgram of pasta. is how much each person will get.

Step-by-step explanation:

1/2 divided by four ... put bot into a common denomenator and then finish the problem. since they have same denomenator it should be easy

The area under the curve of f(x) is 57.

The Fundamental Theorem of Calculus states that if a function f(x) is continuous on the interval [a, b] and F(x) is an antiderivative of f(x) on that interval, then the definite integral of f(x) from a to b is equal to F(b) - F(a):

∫[a, b] f(x) dx = F(b) - F(a).

In this case, we are given the function f(x) = 2x + 10 and we want to find the area under the curve between x = 3 and x = 6.

To use the Fundamental Theorem of Calculus, we need to find an antiderivative of f(x). The antiderivative of 2x is \(x^2\), and the antiderivative of 10 is 10x. Therefore, an antiderivative of f(x) = 2x + 10 is F(x) = \(x^2\) + 10x.

Now, we can apply the Fundamental Theorem of Calculus:

∫[3, 6] (2x + 10) dx = F(6) - F(3).

Evaluating F(x) at x = 6 and x = 3, we have:

F(6) = \((6)^2\) + 10(6) = 36 + 60 = 96,

F(3) = \((3)^2\) + 10(3) = 9 + 30 = 39.

Substituting these values into the equation, we get:

∫[3, 6] (2x + 10) dx = F(6) - F(3) = 96 - 39 = 57.

Therefore, the area under the curve of f(x) = 2x + 10 between x = 3 and x = 6 is 57.

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The company survey 307 customers in order to get 98% confidence.

Sample proportion (p) = 0.5 (as no estimate is given)

α = 1 - 92% = 0.08.    Therefore, α/2 = 0.08/2 = 0.04

Z(α/2) = Z(0.04) = 1.751

Estimate = 5% = 0.05

Now, E = Z(α/2) * sqrt (p(1-p)/n)

n = (1.751/0.05)2 * 0.5 * (1-0.5)

n = 307

Hence, the company should survey 307 customers in order to be 98% confident that the estimated (sample) proportion is within 2 percentage points of the true population proportion of customers who are over the age of forty.

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The volume of one penny is 0.36 mL if the volume of 50 pennies is 18.0 mL.

To find the volume of one penny if the volume of 50 pennies is 18.0 mL, we use the concept of proportionality as follows:

We can find the volume of one penny by dividing the volume of 50 pennies by 50 since we know that 50 pennies occupy a volume of 18.0 mL.

Therefore, the volume of one penny can be calculated as:Volume of one penny = Volume of 50 pennies / 50= 18.0 mL / 50= 0.36 mL

Hence, the volume of one penny is 0.36 mL if the volume of 50 pennies is 18.0 mL.

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The line r has a slope 1/3 and y-intercept (0,5)

What is the Dilation?

Math definition of dilation Resizing an object is accomplished through a change called dilation. The objects can be enlarged or shrunk via dilation. A shape identical to the source image is created by this transformation. The size of the form does, however, differ.

Given

The slope of the line and its intercept (0,2)

The slope of the line r will not change.

And intercept is the addition of their ordinate will be.

Intercept = 2+3

Intercept = 5

So, the line r has slope 1/3 and y-intercept (0,5).

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Value of a  linear transformation T(1,0,-3) is (-2, 7, -5).

Given a linear transformation T from R³ to R³ such that T(1, 0, 0) = (4, -1, 2), T(0, 1, 0) = (-2, 3, 1) and T(0, 0, 1) = (2, -2, 0), we are required to find T(1, 0, -3).

Given a linear transformation T from R³ to R³ such that T(1, 0, 0) = (4, -1, 2), T(0, 1, 0) = (-2, 3, 1) and T(0, 0, 1) = (2, -2, 0), we know that every element in R³ can be expressed as a linear combination of the basis vectors (1,0,0), (0,1,0), and (0,0,1).

Therefore, we can write any vector in R³ in terms of these basis vectors, such that a vector v in R³ can be expressed as v = (v1,v2,v3) = v1(1,0,0) + v2(0,1,0) + v3(0,0,1).

From this, we know that any vector v can be expressed in terms of the linear transformation

                              T as T(v) = T(v1(1,0,0) + v2(0,1,0) + v3(0,0,1)) = v1T(1,0,0) + v2T(0,1,0) + v3T(0,0,1).

Therefore, to find T(1,0,-3),

we can express (1,0,-3) as a linear combination of the basis vectors as (1,0,-3) = 1(1,0,0) + 0(0,1,0) - 3(0,0,1).

Thus, T(1,0,-3) = T(1,0,0) + T(0,1,0) - 3T(0,0,1) = (4,-1,2) + (-2,3,1) - 3(2,-2,0) = (-2, 7, -5).

Therefore, T(1,0,-3) = (-2, 7, -5).

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Answer:

median= 1/3

Step-by-step explanation:

Answer: It's in the screenshot

Step-by-step explanation:

Using the t-distribution, as we have the standard deviation for the sample, it is found that the 95% confidence interval for the mean amount of liquid per bottle (in mL) in this production run is (500.39, 509.61).

The confidence interval is:

\(\overline{x} \pm t\frac{s}{\sqrt{n}}\)

In which:

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 9 - 1 = 8 df, is t = 2.306.

The other parameters are given as follows:

\(\overline{x} = 505, s = 6, n = 9\)

Hence:

\(\overline{x} - t\frac{s}{\sqrt{n}} = 505 - 2.306\frac{6}{\sqrt{9}} = 500.39\)

\(\overline{x} + t\frac{s}{\sqrt{n}} = 505 + 2.306\frac{6}{\sqrt{9}} = 509.61\)

The 95% confidence interval for the mean amount of liquid per bottle (in mL) in this production run is (500.39, 509.61).

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Answer:

\(f(x) = h(g(x))\)

Step-by-step explanation:

Given

\(f(x) = \sqrt{6x + 7}\)

Required

Write as simpler function

Let

\(h(x) = \sqrt x\)

\(g(x) = 6x + 7\)

Apply composite function rule:

\(h(x) = \sqrt x\)

\(h(g(x)) = \sqrt{g(x)}\)

Substitute: \(g(x) = 6x + 7\)

\(h(g(x)) = \sqrt{6x + 7}\)

By comparison:

\(f(x) = h(g(x)) = \sqrt{6x + 7}\)

So:

\(f(x) = h(g(x))\)

Where:

\(h(x) = \sqrt x\)

\(g(x) = 6x + 7\)

The natural numbers are "closed" under addition and multiplication. ... The subtraction of two natural numbers does NOT necessarily create another natural number (3 - 10 = -7). The division of two natural numbers does NOT necessarily create another natural number (1 ÷ 2 = ½). not closed under subtraction and division.

The amount of juice decreased by half, how much would remain is 2 pints. So, the correct answer is C.

The capacity of the container is 1 gallon, which is equivalent to 4 quarts, 8 pints, or 16 cups. If the amount of juice decreases by half, you would have 50% of the original amount remaining.

To calculate this, you can use the following conversions:

1 gallon = 4 quarts

1 gallon = 8 pints

1 gallon = 16 cups

Half of 1 gallon is:

0.5 * 4 quarts = 2 quarts

0.5 * 8 pints = 4 pints

0.5 * 16 cups = 8 cups

Since 2 quarts is equivalent to 4 pints and 8 cups, the correct answer is:

A) 1 quart (2 quarts remaining)

B) 1 pint (4 pints remaining)

C) 2 pints (4 pints remaining)

D) 4 cups (8 cups remaining)

The correct answer is C) 2 pints, as 4 pints of juice would remain in the container after decreasing the amount by half.

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Using the given ratios found the values of A, B and C, and completed the table as follows:

Black   9   18       45     72

White  13   26     65    104

What is meant by the ratio?

A ratio in mathematics demonstrates how many times one number is present in another. A ratio is what a fraction looks like when it is written as a:b. A ratio is the comparative or condensed version of two quantities of the same type.

Given the table:

Black   A   18   45   72

White  13   B    65    C

The table represents the ratios of black keys to white keys on pianos of various sizes.

The ratio of keys of the piano always remains constant.

So we can write as follows:

A/13 = 18/B = 45/65 = 72/C

To find A, we take the following ratios.

A/13 = 45/65

On solving, we get

A = 45 * 13 / 65 = 585/65 = 9

To find B, we take the following ratios.

18/B = 45/65

B = 18 * 65 / 45 = 1170/45 = 26

To find C,  we take the following ratios.

72/C = 45/65

C = 72 * 65 / 45 = 104

Therefore using the given ratios we can complete the table using the values of A, B and C,

Black   9   18       45     72

White  13   26     65    104

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The probability that the San Jose Sharks will win any given game is 0.3694 based on a 13-year win history of 382 wins out of 1,034 games played (as of a certain date).

An upcoming monthly schedule contains 12 games.a. Expected number of wins for the upcoming month:

Let X = number of games won in November 2005.The number of wins in a given game follows a Bernoulli distribution with probability of success p = 0.3694 and q = 1 - p = 0.6306.The expected number of wins in n Bernoulli trials is np.E(X) = npExpected number of wins for the upcoming month E(X) = 12 × 0.3694 = 4.4328

Therefore, the expected number of wins for the upcoming month is 4.4328.b. Suppose X = N(3, 2).What value of x is two standard deviations to the right of the mean? (Enter an exact number as an integer, fraction, or decimal.)

We have, μ = 3 and σ = 2Standard deviation is defined as the square root of the variance.The variance of the normal distribution is σ² = 2² = 4.Two standard deviations to the right of the mean means a z-score of 2.The z-score is calculated using the formula:

z = (x - μ) / σ2

= (x - 3) / 2x - 3

= 4x

= 7

Hence, the value of x is 7.c. Suppose X ∼ N(18, 3).

Between what x values does 68.27% of the data lie?We have, μ = 18 and σ = 3.68.27% of the data is within one standard deviation of the mean, which means the z-score is between -1 and 1.Using the formula: z = (x - μ) / σFor the lower limit, z = -1 -1 = (x - 18) / 3x = -3 + 18 = 15For the upper limit, z = 1 1 = (x - 18) / 3x = 3 + 18 = 21Hence, the data lies between x = 15 and x = 21.Therefore, the Answer is Option E: Between x = 15 and x = 21.

In summary, the expected number of wins for the upcoming month for San Jose Sharks is 4.4328. For X = N(3,2), the value of x is 7. For X ∼ N(18, 3), the data lies between x = 15 and x = 21.

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Marty's taxable income of $510,000 falls within the last tax bracket, his marginal tax rate would be 37%.

To determine Marty's marginal tax rate, we need to refer to the tax brackets for the given year. However, as my knowledge is based on information up until September 2021, I can provide you with the tax brackets for that year. Please note that tax laws may change, so it is always best to consult the current tax regulations or a tax professional for accurate information.

For the 2021 tax year, the marginal tax rates for individuals are as follows:

10% on taxable income up to $9,950

12% on taxable income between $9,951 and $40,525

22% on taxable income between $40,526 and $86,375

24% on taxable income between $86,376 and $164,925

32% on taxable income between $164,926 and $209,425

35% on taxable income between $209,426 and $523,600

37% on taxable income over $523,600

Since Marty's taxable income of $510,000 falls within the last tax bracket, his marginal tax rate would be 37%. However, please note that tax rates can vary based on changes in tax laws and regulations, so it's essential to consult the current tax laws or a tax professional for the most accurate information.

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Using the formula for volume and surface area of solids, we have the following:

1. 180 in.³; 258 in.²; $12.9

2. 144 in.³; 184 in.²; $9.2

3. 75 in.³; 228 in.²; $11.4

Volume of a rectangular prism = l × w × h

Surface area of a rectangular prism = 2(wl+hl+hw)

Volume of a square pyramid = 1/3 × a² × h

Surface area of a square pyramid = a² + 2al

Volume of a cylinder = πr²h

Surface area of a cylinder = 2πr( h + r)

1. Volume of the rectangular prism cereal box = 7.5 × 2 × 12 = 180 in.³

Surface area of the rectangular prism cereal box = 2(wl+hl+hw) = 2(2 × 7.5 + 12 × 7.5 + 12 × 2) = 258 in.²

Cost of material for the the rectangular prism cereal box = 258 × 0.05 = $12.9.

2. Volume of the square pyramid cereal box = 1/3 × a² × h = 1/3 × 6² × 12 = 144 in.³

Surface area of the square pyramid cereal box = a² + 2al = 6² + 2(6)(12.3) ≈ 184 in.²

Cost of material for the the square pyramid cereal box = 184 × 0.05 = $9.2.

3. Volume of the cylinder cereal box = πr²h = π(2.5²)(12) = 75 in.³

Surface area of the cylinder cereal box = 2π(2.5)(12 + 2.5) ≈ 228 in.²

Cost of material for the the cylinder cereal box = 228 × 0.05 = $11.4.

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On the arranged survey, the statistical margin of error is supposed to be 14.73 SEK.

In a large consumer survey, 610 randomly selected customers are interviewed in a large grocery store. They are asked, among other things, how much they have shopped for. On average, they have shopped for 412 SEK with a standard deviation of 181 SEK .

Estimate with a 95% confidence interval the average purchase amount in the entire population. The formula for finding the margin of error is given as;

Margin of Error = z * (σ/√n)

Where:

σ is the standard deviation

n is the sample size

z is the Z-score for the desired confidence level, which is 95%.

Z-score corresponding to 95% confidence level is 1.96

Margin of Error = 1.96 * (181/√610) = 14.73

The statistical margin of error is 14.73 SEK.

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Answer:

Mecury

Mars

Venus

Earth

Neptune

Uranus

Saturn

Jupiter

The correct expression in this case is |11.7−(−3.2)|.

Given that at 6 am, a meteorologist records the temperature as −3.2°F, and seven hours later, the meteorologist records the temperature as 11.7°F, to determine which expression represents the total temperature change, in degrees Fahrenheit, over the seven hours, the following reasoning must be carried out:

Therefore, the correct expression in this case is |11.7−(−3.2)|.

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Answer: 6 feet

Step-by-step explanation: 12 x6 =72 or 72/12 =6

Answer:

\(62.4$ cm^2\)

Step-by-step explanation:

The net of the triangular pyramid is attached below.

Since each of the faces is an equilateral triangle of side 6cm, the base of the pyramid will also be an equilateral triangle of side lengths 6cm .

In the equilateral triangles

Therefore, the surface area of the pyramid formed from the net shown

= 4 X Area of One Triangular Face

\(=4 (\frac12 \times bh)\\=4 (\frac12 \times 6\times 5.2)\\=4(15.6)\\=62.4$ cm^2\)

Gary podría recorrer 8,5 millas en 34 minutos a la misma velocidad.

Ver en españolGary está haciendo ejercicio en la bicicleta estática de su garaje. Pedalea 3,5 millas en 14 de una hora. ¿Cuántas millas podría pedalear Gary en 34 de una hora a la misma velocidad?

Gary bicicletas a 3.5 / 1 = 0.25 millas por minuto.La velocidad de

Gary en millas por minuto = (Distancia) / (Tiempo)Entonces,

la velocidad de Gary = 3.5 millas / 14 minutos= 0.25 millas por minutoPor lo tanto,

podemos encontrar la distancia que recorrerá Gary en 34 minutos usando la velocidad que se calculó anteriormente. La distancia que recorrerá Gary en 34 minutos es:

Distancia = Velocidad * Tiempo

Distancia = 0.25 millas / minuto * 34 minutos=

8.5 millasGary podría recorrer 8,5 millas en 34 minutos a la misma velocidad. Entonces, la respuesta es 8,5. Por lo tanto, podemos encontrar la distancia que recorrerá Gary en 34 minutos usando la velocidad que se calculó anteriormente.

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