If you roll two fair six-sided dice, what is the probability that the dice show the same number

To calculate the value that exceeds 5% of the samples, we need to find the corresponding z-score for a 5% one-tailed test.

There is a 5% chance that the mean reading speed of a random sample of 20 second grade students will exceed nothing wpm. This means that 95% of all random samples of 20 second grade students will have a mean reading speed of nothing wpm or less. Using a standard normal distribution table or calculator, we find that the z-score for a 5% one-tailed test is approximately 1.645. We can then use this z-score to find the corresponding raw score (reading speed) by using the formula: raw score = z-score * standard deviation + mean. However, we do not have the population standard deviation, so we will use the sample standard deviation as an estimate. Assuming the sample standard deviation is 10 wpm, and the mean reading speed for all second grade students is 100 wpm, the value that exceeds 5% of the samples can be calculated as: raw score = 1.645 * 10 + 100 = 116.45 wpm. Therefore, there is a 5% chance that the mean reading speed of a random sample of 20 second grade students will exceed 116.45 wpm.

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To practice adding mixed numbers with like denominators, you can use worksheets that include problems with varying variables.

Adding mixed numbers with like denominators. Since you mentioned worksheets, I'll explain the process step-by-step, and you can apply these steps to any worksheet problems you have.

Step 1: Identify the mixed numbers and their like denominators.
In a given problem, you'll be given mixed numbers (a whole number and a fraction combined) with like denominators (same number in the denominator).

Example: 2 1/4 + 3 3/4 (Both fractions have the denominator 4)

Step 2: Add the whole numbers.
Add the whole numbers of the mixed numbers together.

Example: 2 + 3 = 5

Step 3: Add the fractions with like denominators.
Add the numerators (top numbers) of the fractions and keep the denominators the same.

Example: 1/4 + 3/4 = (1+3)/4 = 4/4

Step 4: Simplify the fraction, if needed.
If the fraction is improper (numerator is equal to or greater than the denominator), simplify it to a mixed number.

Example: 4/4 = 1

Step 5: Combine the whole numbers and simplified fractions.
Add the whole numbers from Step 2 and the simplified fraction from Step 4.

Example: 5 (whole number) + 1 (simplified fraction) = 6

Final Answer: 2 1/4 + 3 3/4 = 6

Now, you can apply these steps to any problem in your adding mixed numbers with like denominators worksheets. Good luck!

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Answer: So after solving and simplifying terms equation is\(x^4+10x^3-47x^2-360x+1296\)

Step-by-step explanation: Given we have two equations f(x) =\(x^{2} +4x-32\) and g(x) = \(x-4\)

we have been asked to find ( f +g)(x) that is f(x)+g(x)

So first we add them \(x^{2} +4x-32 + x-4\)

So we have an equation that is: \(x^{2} +5x-36\)

Then we need to multiply both

\((x^2+5x-36)(x^2+5x-36)\)

So we get\(\left(x^2+5x-36\right)^2\)

Distribute parentheses

\(x^2x^2+x^2\cdot \:5x+x^2\left(-36\right)+5xx^2+5x\cdot \:5x+5x\left(-36\right)-36x^2-36\cdot \:5x-36\left(-36\right)\)

On simplifying

\(x^4+10x^3-47x^2-360x+1296\)

So standard form of result is \(x^4+10x^3-47x^2-360x+1296\) .

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Answer:

Step-by-step explanation:

You can see by the markings that ST is congruent to AY, and that TA is congruent to YS. Those are 2 sides, so so far we have SS. One important thing that comes up WAY TOO OFTEN IN GEOMETRY TO IGNORE is the fact that both of those triangles share the side SA. This is called the reflexive property. The theorem for congruency between these 2 triangles is SSS.

The 95% confidence interval for the proportion of people who prefer Candidate A is approximately 0.186 to 0.234.

To determine a 95% confidence interval for the proportion of people who prefer Candidate A, we can use the formula:

Confidence interval = p ± Z * √(p(1-p)/n)

Where:

p is the sample proportion (231/1100)

Z is the Z-score corresponding to the desired confidence level (95% confidence level corresponds to a Z-score of approximately 1.96)

n is the sample size (1100)

Calculating the confidence interval:

p = 231/1100 ≈ 0.210

Z ≈ 1.96

n = 1100

Confidence interval = 0.210 ± 1.96 * √((0.210 * (1-0.210))/1100)

Confidence interval = 0.210 ± 0.024

Confidence interval = (0.186, 0.234)

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To find dz/dt using the chain rule, we need to calculate the derivatives of z with respect to x and y separately, and then multiply them by the derivatives of x and y with respect to t.

Given:

z =  \(cosh^{2} (xy)\)

x = (1/2)t

y = \(e^{t}\)

Let's start by finding the partial derivatives of z with respect to x and y:

∂z/∂x = \(2cosh(xy) * sinh(xy) * y\)  (using the chain rule)

∂z/∂y = \(2cosh(xy) *sinh(xy)*x\)    (using the chain rule)

Next, let's find the derivatives of x and y with respect to t:

dx/dt = 1/2

dy/dt = \(e^{t}\)

Finally, we can use the chain rule to find dz/dt:

dz/dt = (∂z/∂x)(dx/dt) + (∂z/∂y)(dy/dt)

      = \(2cosh(xy) *sinh(xy)*y*(1/2) + 2cosh(xy)*sinh(xy)*x*e^{t}\)

Now, substitute the given expressions for x and y:

\(dz/dt = 2cosh((1/2)t*e^{t} * sinh((1/2)t*e^{t} *(1/2)* + 2cosh((1/2)t*e^{t} *sinh((1/2)t*e^{t} *((1/2)t)\)

Simplifying further, we have:

\(dz/dt = cosh((1/2)t*e^{t} *sinh((1/2)t*e^{t})* e^{t} + cosh((1/2)t* e^{t}*sinh((1/2)t*e^{t}* ((1/2)t)\)

This is the expression for dz/dt using the chain rule with the given values of x and y.

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Answer:

14 miles

Step-by-step explanation:

It's still 14 miles no matter which way you go.

(1, 0) is the solution of the line y = 3x - 3

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If \(\theta\)  is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m =  \(tan \theta\)

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.

Here,

The given line is

y = 3x - 3

To test whether (1, 0) is a solution of the line y = 3x - 3

Putting x = 1

y = 3\(\times\) 1 - 3 =

y = 3 - 3

y = 0

(1, 0) is the solution of the line y = 3x - 3

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Step-by-step explanation:

I would suggest that she studies or do a cost analysis of what it will cost her to transport to the library to request for the book and return it, if it is not expensive as compared to the cost of the book she should travel down to request for it. else she should purchase the book

Or

Fareeda can simply check if the second library has a distant library services so that the book can be either

1. Sent to her home or placement address, or

2.Scans of book chapters and articles be emailed to her.

The two column proof showing that m∠5 + m∠2 + m∠6 = 180°  is as detailed below.

A two-column proof is defined as geometric proof that consists of a list of statements, and then the reasons that we know those statements are true.

Thus, the two column proof is;

Statement 1: y || z

Reason 1: Given

Statement 2: m∠1 + m∠2 + m∠3 = m∠LAM

Reason 2: Angle addition postulate

Statement 3: m∠1 + m∠2 + m∠3 = 180°

Reason 3: definition of straight angle

Statement 4: ∠1 ≅ ∠5

Reason 4: Alternate interior angles theorem

Statement 5: ∠3 ≅ ∠6

Reason 5: Alternate interior angles theorem

Statement 6: m∠1 ≅ m∠5

Reason 6: Definition of ≅(congruency)

Statement 7: ∠3 ≅ ∠6

Reason 7: Definition of ≅(congruency)

Statement 8: m∠5 + m∠2 + m∠6 = 180°

Reason 8: substitution

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Answer:

check picture ..
edge 2023

Step-by-step explanation:

Answer:

3.30=90

17/1=17

90+17=107

Step-by-step explanation:

In the experiment, the subject whose behavior is being assessed are observational units. The observational unit in this instance is Harley (Dog).

We will first investigate if canines can comprehend both non-human and human gestures in this investigation. The dogs were placed around 2.5 meters apart from the experimenter so that the researchers could test this. Two glasses were placed one on either side of the experimenter.

A gesture would be made at one of the cups by either the experimenter (pointing, bowing, or staring) or by a non-human object (a mechanical arm pointing, a doll pointing, or a stuffed animal looking). After then, the scientists would observe whether the dog would approach the cup that was pointed out. Six dogs were put to the test. We'll focus on one of the dogs who participated in both of his trial sets.

The four-year-old mixed breed dog was given the name Harley. Each of the ten trials in a set consisted of one gesture and one pair of cups. In order to see if Harley would approach a particular cup, the experimenter bowed toward it during one round of experiments.

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The correct option is A. m ≤ (8)(20)

The inequality which gives the possible values of 'm' is m ≤ (8)(20).

A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.

An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.

According to the question;

Terrence's car contains 8 gallons of fuel.

Terrence can drive the car 'm' miles using the fuel currently in the car.

The car can drive 20 miles per gallon of fuel,(which is maximum fuel capacity of the car to drive).

Then,

The total miles 'm' covered by the car is 8×20 which is maximum capacity of the car to travel.

Thus, total miles covered by the car are less than the maximum value which is given by the inequality-

m ≤ (8)(20)

Therefore, the inequality which gives the possible values of 'm' is m ≤ (8)(20).

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The complete question is-

Terrence's car contains 8 gallons of fuel. He plans to drive the car 'm' miles using the fuel currently in the car. If the car can drive 20 miles per gallon of fuel, which inequality gives the possible values of 'm'?

answer choices

A. m ≤ (8)(20)

B. m ≥ (8)(20)

C. 8 ≤ 20m

D. 8 ≥ 20 m

We want to determine a property of a triangle's median.

The median is a line drawn from the vertex to the midpoint of the opposite side.

Thus, a median must always pass through a vertex and midpoint of the triangle

The value of the triple integral ∭\(e^{x^{2} y^{2} }\) dv in cylindrical coordinates is ∞ * (16 - 4(\(r^{2}\))) * 2π.

To evaluate the triple integral ∭\(e^{x^{2} y^{2} }\)dv in cylindrical coordinates, we need to express the differential volume element dv in terms of cylindrical coordinates.

In cylindrical coordinates, we have:

x = r * cos(θ)

y = r * sin(θ)

z = z

The differential volume element in Cartesian coordinates (dx * dy * dz) can be expressed in cylindrical coordinates as:

dv = r * dr * d(θ) * dz

Now, let's convert the integral limits and the integrand into cylindrical coordinates.

The solid e is bounded by the circular paraboloid z = 16 - 4(\(x^{2}\) + \(y^{2}\)) and the xy-plane. In cylindrical coordinates, the equation of the paraboloid becomes:

z = 16 - 4(\(r^{2}\))

The integral limits for cylindrical coordinates are:

r: 0 to ∞

(θ): 0 to 2π

z: 0 to 16 - 4(\(r^{2}\))

The integrand is: \(e^{x^{2} y^{2} }\)

Substituting the expressions in cylindrical coordinates, the triple integral becomes:

∭\(e^{x^{2} y^{2} }\) dv = ∫∫∫r * \(e^{r^{2} }\)* \(cos^{2}\)(θ) * \(sin^{2}\)(θ)) * r * dr * d(θ) * dz

Simplifying:

∭\(e^{x^{2} y^{2} }\) dv = ∫∫∫\(e^{2}\) * \(e^{r^{2} }\) * \(cos^{2}\)(θ) * \(sin^{2}\)(θ)) * dr * d(θ) * dz

Now, let's evaluate the triple integral using the provided limits.

∫∫∫\(r^{2}\) * \(e^{r^{2} }\) * \(cos^{2}\)(θ) * \(sin^{2}\)(θ)) * dr * d(θ) * dz

The innermost integral with respect to r:

∫\(r^{2}\) * \(e^{r^{2} }\) *\(cos^{2}\)(θ) * \(sin^{2}\)(θ)) dr = (1/2) * \(e^{r^{2} }\) * \(cos^{2}\)(θ) *\(sin^{2}\)(θ))

Integrating the above expression with respect to r from 0 to ∞, we get:

(1/2) * ∞ - (1/2) * 0 = ∞

Now, the remaining integral is:

∫∫∫∞ * d(θ) * dz

Integrating the above expression with respect to theta from 0 to 2π and z from 0 to 16 - 4(\(r^{2}\)), we get:

∫(0 to 2π) ∫(0 to 16 - 4(\(r^{2}\))) ∞ * d(theta) * dz = ∞ * (16 - 4(\(r^{2}\))) * 2π

Therefore, the value of the triple integral ∭\(e^{x^{2} y^{2} }\) dv in cylindrical coordinates, where e is the solid bounded by the circular paraboloid z = 16 - 4(\(x^{2}\) + \(y^{2}\)) and the xy-plane, is ∞ * (16 - 4(\(r^{2}\))) * 2π.

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Answer:

p=4

Step-by-step explanation:

because 5 is less than or equal to four!

another number grater than five no less than

so the answer is p=4

Answer:

\(\sqrt[8]{197^{7} }\)

Step-by-step explanation:

\(\sqrt[8]{197^{7} }\)

Answer:

(4, -5)

Step-by-step explanation:

Use the (y, -x) rule when rotating points 90 degrees clockwise on a graph.

LMNP is rotated 90° clockwise around the origin then, the coordinates of N will be (4, -5).

Let the point be having coordinates (x,y).

If the point is in the first quadrant:

Subcase: Clockwise rotation:

Then (x,y) → (y, -x)

Subcase: Counterclockwise rotation:

Then (x,y) → (-y, x)

On origin

No effect as we assumed rotation is being with respect to the origin.

LMNP is rotated 90° clockwise around the origin

In the given figure when we rotate it 90 degrees clockwise so the value as the rule

By Putting the value in x = 5 and y = 4

then, the coordinates of N will be (4, -5).

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Answer:

the answer is 44 cecaeuju

In summary, the Fourier coefficients for the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5 are:

c₀ = -3 (DC component)

cₙ = 0 for n ≠ 0 (other coefficients)

To find the Fourier coefficients of the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5, we can use the formula for Fourier series coefficients:

cn = (1/T) ∫[t₀-T/2, t₀+T/2] y(t) \(e^{(-i2\pi nt/T)}\) dt

where T is the period of the function and n is an integer.

In this case, the function y(t) is constant, y(t) = -3, and the period is T = 10 (since the interval -5 ≤ t ≤ 5 spans 10 units).

To find the Fourier coefficient c₀ (corresponding to the DC component or the average value of the function), we use the formula:

c₀ = (1/T) ∫[-T/2, T/2] y(t) dt

Substituting the given values:

c₀ = (1/10) ∫[-5, 5] (-3) dt

  = (-3/10) \([t]_{-5}^{5}\)

  = (-3/10) [5 - (-5)]

  = (-3/10) [10]

  = -3

Therefore, the DC component (c₀) of the Fourier series of y(t) is -3.

For the other coefficients (cₙ where n ≠ 0), we can calculate them using the formula:

cₙ = (1/T) ∫[-T/2, T/2] y(t)\(e^{(-i2\pi nt/T) }\)dt

Since y(t) is constant, the integral becomes:

cₙ = (1/T) ∫[-T/2, T/2] (-3) \(e^{(-i2\pi nt/T)}\) dt

  = (-3/T) ∫[-T/2, T/2] \(e^{(-i2\pi nt/T)}\) dt

The integral of e^(-i2πnt/T) over the interval [-T/2, T/2] evaluates to 0 when n ≠ 0. This is because the exponential function oscillates and integrates to zero over a symmetric interval.

all the coefficients cₙ for n ≠ 0 are zero.

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The 100 students from a large university represent a sample.

In statistics, a sample is a subset of individuals or observations taken from a larger group known as the population. The purpose of taking a sample is to make inferences and draw conclusions about the population based on the characteristics observed in the sample.

In this scenario, the 100 students from a large university who were asked about their opinion on the new health care program represent a sample. The sample is a smaller group of individuals selected from the larger population of all students at the university. The intention is to gather insights and information about the opinions of the broader population based on the responses obtained from the sample. Statistical inference techniques can be applied to analyze the data collected from the sample and make conclusions or predictions about the entire population.

It is important to note that the sample should be representative of the population to ensure that the conclusions drawn from the sample can be generalized to the larger population accurately. The process of selecting a sample and conducting statistical analyses is an essential part of studying and understanding populations using data and statistics.

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Answer:

x=6

Step-by-step explanation:

5*x+6=36

so 5*6=30

+6=36

Answer:

36

Step-by-step explanation:

If the distance to a star was suddenly cut in half, it would appear four times brighter.

The brightness of a star is directly proportional to the inverse square of its distance from us. This means that if the distance to a star is halved, its brightness will increase by a factor of four.

The relationship between brightness and distance can be expressed as follows:

B = k / d^2

where B is the brightness, k is a constant of proportionality, and d is the distance.

If the distance to the star is halved, it can be expressed as:

d' = d / 2

Plugging this into the equation for brightness, we get:

B' = k / (d / 2)^2

Expanding this and simplifying, we get:

B' = 4 * k / d^2

Since k is a constant, it cancels out and we are left with:

B' = 4 * B

This means that if the distance to a star was suddenly cut in half, it would appear four times brighter. In astronomical terms, this is equivalent to an increase of 2 magnitudes on the logarithmic magnitude scale.

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The value of the given expression [\(87^3+ 13^3/87^2 -87 * 13 + 13^2\)] by simplifying the numerator and denominator using suitable identities is 100.

We will first calculate the numerator:

As  (\(a^3\) + \(b^3\)) = (a + b)(\(a^2\) - ab + \(b^2\)) :

\(87^3\) + \(13^3\) = (87 + 13)(\(87^2\) - \(87 * 13\) + \(13^2\))

= 100(\(87^2\) - 87 * 13 + \(13^2\))

Now, calculate the denominator:

\(87^2 - 87 * 13 + 13^2\)

As,(\(a^2 -2ab +b^2\)) =\((a - b)^2\):

\(87^2 - 87 * 13 + 13^2 = (87 - 13)^2\)

\(= 74^2\)

So by solving the equation further:

\((87^3+13^3) / (87^2- 87 * 13+13^2) = 100*(87^2- 87 *13 + 13^2)/(87^2 - 87 * 13 + 13^2)\)

As we can see the numerator and denominator are the same expressions (\(87^2 - 87 * 13 + 13^2\)). so, they cancel each other:

\((87^3 + 13^3) / (87^2 - 87 * 13 + 13^2) = 100\)

So, the value of the given expression is 100.

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From the given information provided, for the given triangles, ∠G ≅ ∠I by cpctc. The correct answer is A) ∠G ≅ ∠I.

CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent". This means that if two triangles are congruent, then their corresponding parts (sides, angles) are also congruent.

In this case, the question states that ΔFGH is moved onto ΔIJK through a sequence of transformations. This implies that the two triangles are congruent. Therefore, their corresponding parts are congruent.

The sequence of transformations could involve translations, rotations, reflections, or a combination of these. However, since the question does not provide information about the specific transformations used, we cannot determine which parts of the triangles are congruent without additional information.

However, we can say that the corresponding angles that are part of the congruent triangles are congruent by CPCTC. Therefore, we can conclude that ∠G ≅ ∠I.

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Between Method A with a MAD(Mean Absolute Deviation) of 1.4 and Method B with a MAD (Mean Absolute Deviation) of 1.8, Method A performed better as it has a smaller MAD value.

To decide which estimating strategy performed the leading, we got to compare their Mean Absolute Deviation (Mad) values. Mad may be a degree of the average outright contrast between the genuine values and the forecasted values.

A little Mad esteem shows distant better; a much better; a higher; stronger; an improved" an improved forecasting accuracy, because it implies the forecasted values are closer to the real values.

Hence, between Strategy A with a Mad of 1.4 and Strategy B with a Mad of 1.8, Strategy A performed way better because it incorporates littler Mad esteem.

Be that as it may, it's vital to note that Mad alone does not allow a total picture of the determining execution. Other measurements, such as Mean Squared Blunder (MSE) or Mean Supreme Rate Blunder (MAPE) ought to too be considered to assess the exactness of the estimating strategies.

Furthermore, the setting and reason for the determining ought to too be taken under consideration when choosing the fitting estimating strategy. 

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Answer:

C 803.8 in2

Step-by-step explanation:

Answer:

the answer is C 803.8 in2

Step-by-step explanation:

Answer:

1587.6 m²

Step-by-step explanation:

\(A=\frac{1}{2} bh\) where b is the base length and h is the height (b and h on the triangle will always be perpendicular to each other)

Plug in 75.6 m as b and 42 m as h

\(A=\frac{1}{2} (75.6)(42)\\A=\frac{1}{2}( 3175.2)\\A=1587.6\)

I hope this helps!