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There are 15 questions, and John got an 84% on the quiz, how many questions did John get right and how many wrong?

The standard error of the proportion decreases as the sample size increases. This means that larger sample sizes provide more accurate estimates of the population proportion.

To calculate the standard error of the proportion, we can use the formula:
SE = √(p(1-p)/n)
Where:
SE = standard error
p = proportion of the population
n = sample size
For each sample size, we can plug in the values and calculate the standard error:
A. For a sample size of 30:
SE = √(0.39(1-0.39)/30) = 0.088
B. For a sample size of 60:
SE = √(0.39(1-0.39)/60) = 0.062
C. For a sample size of 90:
SE = √(0.39(1-0.39)/90) = 0.051

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Answer:

Step-by-step explanation:

\(\sqrt[3]{x+4}+\sqrt[3]{2x +8}=0\\\\\sqrt[3]{x+4}= -\sqrt[3]{2x + 8}\\\\(x +4)^{\frac{1}{3}}=-(2x+8)^{\frac{1}{3}}\\\\\)

Take cube,

\([(x+4)^{\frac{1}{3}}]^{3} =- [(2x +8)^{\frac{1}{3}}^{3}]\\\\(x+4)^{3*\frac{1}{3}}=-(2x + 8)^{3*\frac{1}{3}}\\\\\)

x + 4 = - (2x + 8)

x +4 = 2x *(-1) + 8 *(-1)

x+ 4 = -2x - 8

x +2x+4 = - 8

3x + 4 = - 8

      3x = - 8 -4

      3x = -12

        x = -12/3

x = -4

To determine the final temperature after mixing 10 grams of steam at 100 degrees Celsius with 50 grams of ice at 0 degrees Celsius, we need to calculate the amount of heat exchanged between the two substances.

First, we need to determine the heat absorbed or released during the phase change of ice to water at 0 degrees Celsius. This can be calculated using the equation:

\(\[ Q = m \cdot L \]\)

where \(\( Q \)\) is the heat absorbed or released, \(\( m \)\) is the mass of the substance, and \(\( L \)\) is the latent heat of fusion for ice. For water, the latent heat of fusion is approximately 334 J/g.

\(\[ Q_{\text{ice}} = 50 \, \text{g} \times 334 \, \text{J/g} = 16700 \, \text{J} \]\)

Next, we need to calculate the heat absorbed or released during the temperature change of water from 0 degrees Celsius to the final temperature. This can be calculated using the equation:

\(\[ Q = m \cdot C \cdot \Delta T \]\)

where \(\( Q \)\) is the heat absorbed or released, \(\( m \)\) is the mass of the substance, \(\( C \)\) is the specific heat capacity of water, and \(\( \Delta T \)\) is the change in temperature.

For water, the specific heat capacity is approximately 4.18 J/g°C.

\(\[ Q_{\text{water}} = 10 \, \text{g} \times 4.18 \, \text{J/g°C} \times (\text{final temperature} - 0°C) \]\)

Since the steam condenses into water, it releases its latent heat of vaporization. The latent heat of vaporization for water is approximately 2260 J/g.

\(\[ Q_{\text{vaporization}} = 10 \, \text{g} \times 2260 \, \text{J/g} = 22600 \, \text{J} \]\)

The total heat exchanged can be calculated by summing up the heat absorbed or released in each step:

\(\[ \text{Total heat exchanged} = Q_{\text{ice}} + Q_{\text{water}} + Q_{\text{vaporization}} \]\)

Now, we can set up an energy conservation equation:

\(\[ \text{Total heat exchanged} = 0 \quad (\text{since no energy is gained or lost in the system}) \]\)

\(\[ 16700 \, \text{J} + 10 \, \text{g} \times 4.18 \, \text{J/g°C} \times (\text{final temperature} - 0°C) + 22600 \, \text{J} = 0 \]\)

Simplifying the equation:

\(\[ 10 \, \text{g} \times 4.18 \, \text{J/g°C} \times (\text{final temperature} - 0°C) = -39300 \, \text{J} \]\)

\(\[ \text{final temperature} - 0°C = -3930 \, \text{J/°C} / (10 \, \text{g} \times 4.18 \, \text{J/g°C}) \]\)

\(\[ \text{final temperature} \approx -94°C \]\)

The negative value indicates that the final temperature is below 0 degrees Celsius, which means the mixture would still be in a frozen state.

Therefore, the approximate final temperature after mixing 10 grams of steam at 100 degrees Celsius with 50 grams of ice at 0 degrees Celsius is -94 degrees Celsius.

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Pythagorean theorem tells us how the side lengths of right triangles are related.

The Pythagorean theorem, also known as the Pythagorean identity, states that the sum of the squares of the lengths of the two sides forming the right angle is equal to the square of the length of the hypotenuse in any right triangle (the side opposite the right angle). In other words, the Pythagorean theorem can be used to calculate the length of the hypotenuse given the lengths of the two sides of a right triangle.

This relationship can be written as the equation:

\(a^2 + b^2 = c^2\)

where a and b are the lengths of the legs, and c is the length of the hypotenuse. The Pythagorean Theorem is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery.

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The polynomial is x⁹ - 23x⁷ - 6x³ + 2x² + 10 in the standard form, the degree of the polynomial is nine, and its leading coefficient is 1.

A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.

The polynomial below which is given in the question

-23x⁷ + x⁹ -6x³ + 10 + 2x²

To determine the polynomial in the standard form.

⇒ -23x⁷ + x⁹ -6x³ + 10 + 2x²

Rearrange the terms in the descending order of the degree of variables

⇒ x⁹ - 23x⁷ - 6x³ + 2x² + 10

This is the polynomial in the standard form

Here the degree of the polynomial is nine because nine is the highest degree in the above expression and its leading coefficient is 1.

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The question seems to be incomplete the correct question would be:

Write the polynomial in the standard form, and then identify the degree and leading coefficient

-23x⁷ + x⁹ -6x³ + 10 + 2x²

Answer:

6

Step-by-step explanation:

Right answer on acellus

If a power series matches a function f(x) exactly everywhere, then the radius of convergence is infinite.

This means that the power series converges for all values of x. In other words, the power series can be used to approximate the function f(x) with arbitrary accuracy for any value of x.

This is a very powerful tool in mathematics and has many practical applications in science, engineering, and other fields.

The proof that a power series with infinite radius of convergence matches a function f(x) exactly everywhere is based on the fact that a power series is a sum of infinitely many terms, each of which is a polynomial in x.

By adding up these polynomials, we can approximate any function f(x) to an arbitrary degree of accuracy. The only limitation is that we need to know the coefficients of the power series,

which can be obtained by differentiating or integrating the function f(x) or by using other mathematical techniques. Once we have the coefficients, we can plug them into the power series formula and get an exact match for the function f(x).

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Let's calculate the total cost of all the items purchased by the computer club:

Cost of 14 portfolios = 14 * $24.59

Cost of 14 binders = 14 * $12.92

Cost of 14 school sweatshirts = 14 * $14.00

Cost of 14 music cases = 14 * $1.25

Cost of 14 phone cases = 14 * $1.99

Cost of 14 mouse pads = 14 * $2.14

Total cost of all items = Cost of 14 portfolios + Cost of 14 binders + Cost of 14 school sweatshirts + Cost of 14 music cases + Cost of 14 phone cases + Cost of 14 mouse pads

Plugging in the given values:

Total cost of all items = (14 * $24.59) + (14 * $12.92) + (14 * $14.00) + (14 * $1.25) + (14 * $1.99) + (14 * $2.14)

Now, the computer club will pay for 40% of the total cost. To calculate this, we can multiply the total cost by 40% (or 0.40):

Club's payment = 0.40 * Total cost of all items

The remaining cost will be divided equally among the 14 members:

Remaining cost per member = (Total cost of all items - Club's payment) / 14

Plugging in the values and calculating:

Club's payment = 0.40 * ((14 * $24.59) + (14 * $12.92) + (14 * $14.00) + (14 * $1.25) + (14 * $1.99) + (14 * $2.14))

Remaining cost per member = ((14 * $24.59) + (14 * $12.92) + (14 * $14.00) + (14 * $1.25) + (14 * $1.99) + (14 * $2.14) - Club's payment) / 14

So, each member of the computer club will owe the calculated value for "Remaining cost per member".

Hope this is good

Volume of given figure is 90 cu.in

Total surface area of figure is 146 sq.in

Answer:

The other person is correct! Btw ty for answer all of those questions! They helped my a lot, can we be friends?

Step-by-step explanation:

The GCD of a and b in the ring of integers is the same as their GCD in the ring of Gaussian integers because both conditions of Gaussian integers are satisfied.

To show that the greatest common divisor (GCD) of integers a and b is the same in the ring of integers and the ring of Gaussian integers, we need to prove two things:

1. GCD(a, b) in the ring of integers divides both a and b.
2. Any common divisor of a and b in the ring of Gaussian integers also divides a and b in the ring of integers.

Let's start with the first point. If GCD(a, b) in the ring of integers divides a and b, it must also divide any linear combination of a and b. Since the ring of Gaussian integers is a subset of the ring of integers, any linear combination of a and b in the ring of Gaussian integers is also a linear combination of a and b in the ring of integers. Therefore, GCD(a, b) in the ring of integers divides any linear combination of a and b in the ring of Gaussian integers.

For the second point, any common divisor of a and b in the ring of Gaussian integers also divides a and b in the ring of integers because the ring of Gaussian integers is a subset of the ring of integers.

In conclusion, the GCD of a and b in the ring of integers is the same as their GCD in the ring of Gaussian integers because both conditions are satisfied.

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The average root mean square velocity of the gas molecules of ozone (O3) at 100K is approximately 341 m/s, and at 3000K it is approximately 1925 m/s.

The root means square velocity (v rms) of a gas molecule is given by the formula:

v rms = √(3kT/m)

where k is the Boltzmann constant, T is the temperature in Kelvin, and m is the mass of a single molecule. The mass of a single ozone molecule (O3) is approximately 48 g/mol or 4.8x10^-26 kg.

At 100K, the root mean square velocity is calculated as:

v rms = √(3kT/m) = √(3 x 1.38x10^-23 J/K x 100K / 4.8x10^-26 kg) = 341 m/s

At 3000K, the root mean square velocity is calculated as:

v rms = √(3kT/m) = √(3 x 1.38x10^-23 J/K x 3000K / 4.8x10^-26 kg) = 1925 m/s

Therefore, the average root mean square velocity of the gas molecules of ozone (O3) at 100K is approximately 341 m/s, and at 3000K it is approximately 1925 m/s.

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Answer:

Step-by-step explanation:

The reference angle for 3π/4 is π/4, and the quadrant of the terminal side is the second quadrant. In trigonometry, the reference angle is the positive acute angle between the terminal side of an angle and the x-axis. For the angle 3π/4, the reference angle is π/4.

The quadrant of the terminal side is determined by the sign of the trigonometric functions. In the case of 3π/4, it lies in the second quadrant where the cosine is negative and the sine is positive. Therefore, the cosine of 3π/4 is -√2/2, and the sine is √2/2.

Understanding the reference angle and the quadrant of the terminal side helps in analyzing and solving trigonometric problems accurately.

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To obtain the measure of the missing angle, subtract the measure of ∠ABD from the measure of ∠ABC. Note that m∠ABD + m∠DBC = m∠ABC.

Thus, we have:

Answer:

Step-by-step explanation:

common difference d=3-1=2

first term a=1

an=a+(n-1)d

2n-1=1+(l-1)2

2n-1=1+2l-2

2n-1=2l-1

l=n

(i used l for number of terms)

number of terms=n

\(S_{n}=\frac{n}{2} (first ~term+last~term)\\=\frac{n}{2} (1+2n-1)\\=n^2\)

Answer:

Step-by-step explanation:

Multiplying y by a value greater than 1 results in a vertical stretch. When the sign of it is negative there is a reflection over the x-axis. The appropriate choice is shown below.

__

The second attachment shows how the graph is flipped and stretched.

Answer:

13

Step-by-step explanation:

Answer:

5/8 × 4 = 5/8 × 4/1 = 20/8 = 5/2

Step-by-step explanation:

hope this helps

Answer:

The solution is 5/2

Step-by-step explanation:

\( \sf \frac{5}{8} \times 4 \\ = \sf \frac{5}{ \cancel8} \times \cancel4 \\ = \sf \frac{5}{2} \)

Answer:

9.296 x 10^7

Step-by-step explanation:

Answer:

9.296*10^7

Step-by-step explanation:

The scientific notation of 92960000 is 9.296 * 10 ^7

The answer is D. 95th percentile is not needed for constructing a box-plot.

A box plot, also known as a box-and-whisker plot, provides a visual representation of the distribution of a dataset. It consists of several key measures, including the following:

A. First quartile (Q1): This is the 25th percentile, which marks the lower boundary of the box.

B. 50th percentile: This is the median, which is the middle value of the dataset when it is ordered from smallest to largest. It is represented by a line within the box.

C. 75th percentile (Q3): This is the upper quartile, marking the upper boundary of the box.

D. 95th percentile: This measure is not typically used in constructing a box plot. It provides information about the value below which 95% of the data falls, but it is not necessary for constructing the basic elements of a box plot.

Therefore, the correct answer is D. 95th percentile.

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Step-by-step explanation:

THE SLOPE IS 0

HOPE THIS HELPS

Answer: Where is the triangle?

Step-by-step explanation: Brainliest pls:)

The correct answer is b. Expected value. The mean of a discrete random variable generalizes the concept of expected value. The expected value of a discrete random variable is the weighted average of all possible outcomes, where the weights are the probabilities associated with each outcome.

It represents the long-term average value that we would expect to observe if we repeated the random experiment multiple times.

In the context of a discrete random variable, the mean (or expected value) is calculated by multiplying each possible value of the variable by its corresponding probability and summing them up. It provides a measure of central tendency and represents the average value we would expect to obtain from the random variable over a large number of trials.

The population mean (mean of a variable) refers to the average value of a variable in the entire population, not specifically related to a random variable. The sample mean is the average value of a variable calculated from a sample of observations. The distribution of a discrete random variable refers to the pattern of probabilities associated with each possible outcome of the variable.

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Answer: y = -1/3(x + 1)² + 4

Step-by-step explanation:

First of all, we know that the graph is going to be a parabola

So we can start off with the parent function, y = x²

Using vertex form, y = a(x - h)² + k, where the vertex is point (h, k):

we have the formula: y = a(x + 1)² + 4

If the parabola must pass through the point (2,1), we can substitute these for x and y in our equation to find a, and finish the problem:

1 = a(2 + 1)² + 4

-3 = a(3)²

-3 = 9a

a = -1/3

based on this, our final formula will be y = -1/3(x + 1)² + 4

Answer:

3x+5x=40

=8x=40

=x=5

then no.of boys= 3×5 = 15

and no. of girls= 5×5=25

girls more than boys= 25-15=10

mark me brainliest

pls it takes too much time to solve this

Answer:

There will be 10 more girls than boys in the class.

Step-by-step explanation:

5x+3x=40

8x = 40

8x/8 = 40/8

x = 5

5*2 = 10

The population density of the neighborhood of 1250 people in people per square mile is 1534 people per square mile

Population density is the number of people per unit area of a location.

The population density is the number of people per square mile in the neighborhood

The population of the neighborhood = 1,250 people

The number of city blocks in the neighborhood = 30

The length of each city block = (1/16) mile

The width of each neighborhood = (1/8) mile

The area of each neighborhood = (1/16) × (1/8) = 1/128 square miles

The area of the whole neighborhood = 30 × 1/128 = 15/64 square miles

The population density = 1250/(15/64) = 16,000/3 ≈ 5334 people per square mile (rounding up)

The number of people per square mile, the population density, therefore is 5333 people per square mile

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Answer:

Step-by-step explanation:

It is assumed the interest is simple.

Use the interest formula:

We have:

Substitute values and solve for t:

Answer:

Reflection across x = -5

The circulation of F around C is -16. No, F is not equal to V f for some function f. The flux of F across C is -8. No, F is not equal to V x G for any vector field G.

(a) The circulation of F around C is -16.

Using Green's Theorem, we can write the circulation of F as the line integral around the boundary of D:

∮CF · dr = ∬D (∂Q/∂x - ∂P/∂y) dA

where P = 9x + 5y, Q = 2x - 7y, and dr = dx i + dy j.

Taking the partial derivatives, we get:

∂Q/∂x - ∂P/∂y = 2 - 9 = -7.

Thus, the circulation of F around C is:

∮CF · dr = ∬D -7 dA = -7(area of D) = -16.

(b) No, F is not equal to V f for some function f.

If F were equal to the gradient of some scalar function f, then the circulation of F around any closed path would be zero. However, we just calculated that the circulation of F around C is -16, which means F cannot be expressed as the gradient of any scalar function.

(c) The flux of F across C is -8.

Using Green's Theorem, we can write the flux of F across C as the line integral around the boundary of D:

∮CF · ds = ∬D (∂P/∂x + ∂Q/∂y) dA

Taking the partial derivatives, we get:

∂P/∂x + ∂Q/∂y = 9 - 7 = 2.

Thus, the flux of F across C is:

∮CF · ds = ∬D 2 dA = 2(area of D) = -8.

(d) No, F is not equal to V x G for any vector field G.

If F were equal to the curl of some vector field G, then the flux of F across any closed surface would be zero. However, we just calculated that the flux of F across C is -8, which means F cannot be expressed as the curl of any vector field.

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Answer:

B) \(y=x-5\)

Step-by-step explanation:

Because \(g(x)=\frac{x^2-3x-5}{x+2}\) simplifies to \(x-5+\frac{5}{x+2}\), we only care about the quotient, which will be our oblique asymptote equation. Therefore, the oblique asymptote for the function will be \(y=x-5\). See the attached graph for a visual.

Answer:

B

Step-by-step explanation:

Did it rn

39 subjects were tested in this simple one-way ANOVA.

The df for F distribution is (treatment df, error df)

Using given information

Treatment df = 7

Error df = 31

Total df= 7+31 = 38

Again, total df = N-1, N= number of subjects tested

Then, N-1 = 38

=> N= 39

One-way ANOVA is typically used when there is a single independent variable or factor and the goal is to see whether variation or different levels of that factor have a measurable effect on the dependent variable.

The t-test is a method of determining whether two populations are statistically different from each other, and ANOVA determines whether three or more populations are statistically different from each other.

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