Sarah rolls 2 fair dice and adds the results from each.
Work out the probability of getting a total that is a factor of 6.

The volume of the square pyramid-shaped roof with a height of 5 feet and a side length of 6 feet is 60 cubic feet.

A square pyramid has a square base and four triangular sides that come together to form a single point. To calculate the volume of a square pyramid, you can use the formula: 1/3 x Base x Height, where the base is the area of the square base and the height is the height of the pyramid.

In the given scenario, the rooftops of the village are shaped like square pyramids. The height of the roof is 5 feet and the length of the sides is 6 feet. Let us calculate the volume of the roof using the formula mentioned above:

The base of the square pyramid = side * side= 6 * 6= 36 sq. ft, Height of the square pyramid = 5 ft. Volume of the square pyramid= 1/3 * Base * Height= 1/3 * 36 sq. ft * 5 ft= 60 cubic feet. Therefore, the volume of the roof is 60 cubic feet.

Summary: A square pyramid has a square base and four triangular sides that come together to form a single point. The formula to calculate the volume of a square pyramid is 1/3 x Base x Height. The rooftops of the village are shaped as square pyramids with a height of 5 feet and the length of the sides is 6 feet. To calculate the volume of the roof, we can use the formula and find the volume of the roof. The volume of the roof is 60 cubic feet.

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Whether the data is normally distributed or not is determined by testing the skewness and kurtosis values of the sample. If the skewness and kurtosis are within the range of -2 to +2, the data is regarded to be normally distributed.

To determine if the data are from a population that is normally distributed, we'll compute the skewness and kurtosis for the given dataset. The formulas for calculating skewness and kurtosis are as follows:

Skewness = (3 * Mean – Mode) / Standard Deviation

Kurtosis = (Mean – Mode) / Standard Deviation

We will use the following steps to calculate skewness and kurtosis for the provided dataset:

Step 1: Calculate the mean (average) of the dataset.μ = (14 + 19 + 22 + 24 + 26 + 28 + 29 + 29 + 30 + 32) / 10

= 24.3

Step 2: Calculate the median (midpoint) of the dataset. The values in the data set are already in order, so we can find the median by simply taking the value in the middle of the data set. The median is 26.

Step 3: Calculate the mode (most frequently occurring value) of the dataset.There is no mode for this dataset as there are no repeated values.Step 4: Calculate the variance and standard deviation of the dataset.

Var(X) = [Σ (Xi – μ)2] / N

Var(X) = [(14-24.3)2 + (19-24.3)2 + (22-24.3)2 + (24-24.3)2 + (26-24.3)2 + (28-24.3)2 + (29-24.3)2 + (29-24.3)2 + (30-24.3)2 + (32-24.3)2] / 10

Var(X) = 27.01

SD(X) = √27.01

= 5.2

Step 5: Calculate the skewness of the dataset using the formula.

Skewness = (3 * Mean – Mode) / Standard Deviation

Skewness = (3 * 24.3 – 26) / 5.2

= 0.19

The skewness value of 0.19 is within the range of -2 to +2, indicating that the data is normally distributed. Similarly, the kurtosis value can be calculated using the formula.

Kurtosis = (Mean – Mode) / Standard Deviation

Kurtosis = (24.3 – 26) / 5.2

= -0.27

The kurtosis value of -0.27 is also within the range of -2 to +2. Therefore, we can conclude that the data is normally distributed.

In statistics, data are usually distributed in one of two ways: it is either normally distributed, meaning that the majority of values fall close to the mean, or it is skewed, meaning that a significant number of values fall in one direction of the mean or the other. It is important to know which of these distributions applies to a given data set so that you can make accurate predictions based on that data.

Normal distribution is a term used in statistics to describe a pattern of data that is symmetrical, meaning that the data values are equally likely to fall on either side of the mean. When the data is normally distributed, the majority of the data values fall close to the mean, with fewer values the farther away from the mean you go.

The normal distribution is useful for making predictions and understanding the likelihood of a particular outcome. This is because it is easy to see where the majority of the data falls on a normal distribution graph, and you can use that information to predict future outcomes.

Skewed distribution is a term used in statistics to describe a pattern of data that is asymmetrical, meaning that the data values tend to cluster on one side of the mean or the other. Skewed data can be difficult to interpret, and it may require special statistical methods to analyze.

This is because the data may be influenced by outliers, or extreme values, that skew the distribution. When the data is skewed, the median may be a better measure of central tendency than the mean.

We have calculated the skewness and kurtosis of the given data. The skewness value of 0.19 is within the range of -2 to +2, indicating that the data is normally distributed.

Similarly, the kurtosis value of -0.27 is also within the range of -2 to +2. Therefore, we can conclude that the data is normally distributed.

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The equations that have no solution are the third and fourth equations.

The equations that have one solution are the first, second and fifth equations.

There are three main methods of solving simultaneous equations as:

Elimination method

Graphical Method

Substitution method

The first two simultaneous equations clearly have one solution each because it is clear that when we subtract both, we can eliminate y and solve for x.

However, the third and fourth equations have no solution as the variables attached to both x and y in both cases are the same.

The fifth simultaneous equation has one solution because at least one of them with variable is different.

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Answer:

\(g^{-1} (7)=5\)

Step-by-step explanation:

We are asked to find \(g^{-1} (7)\).

One thing to remember about the inverse of a function is what exactly an inverse means.

If we have the ordered pair \((a,b)\) of function \(g\), then the corresponding ordered pair of \(g^{-1}\) would be \((b,a)\).

As we are asked to find \((7,b)\) of  \(g^{-1}\), we can instead find \((b,7)\) of \(g\).

This means that we are looking for where \(g(b)=7\).

From the graph, we can see that for this to be true, \(b=5\)

This means that \(g^{-1} (7)=5\)

The value of g^-1(7) is 5.

What is the value of g^-1(7)?

A function f from a set X to a set Y is said to be invertible if for every y in Y and x in X, there exists a function g from Y to X such that f(g(y)) = y and g(f(x)) = x. function is invertible only if each input has a unique output. That is, each output is paired with exactly one input. That way, when the mapping is reversed, it will still be a function.

Given that:

One thing to remember about the inverse of a function is what exactly an inverse means.

If we have the ordered pair (a, b) of function g , then the corresponding ordered pair of g^-1 would be (b, a).

As we are asked to find (7,b)  of  g^-1, we can instead find (b, 7) of g .

This means that we are looking for where  g(b)=7.

From the graph, we can see that for this to be true, b=5.

So, the value of g^-1(7) is 5.

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The given indefinite integrals are: ∫(60x - 5/4 + 18e²x - 1) dx = 30x² - 5/4x + 9e²x - x + C, where C is the constant of integration. ∫(252x¹² + 6x¹³) dx = 36x¹³ + x¹⁴ + C, where C is the constant of integration. ∫√(2x - 7)(x² + 3) dx = ∫[√2(x² + 3)] √(x - 7/2) dx

Substitute u = x - 7/2 to get,

dx = du √2.∫[√2(x² + 3)] √(x - 7/2) dx= √2 ∫[√(u² + 67/4)] du = (1/2) ∫[√(4u² + 67)] d(4u)= (1/8) ∫[√(4u² + 67)] d(4u) = (1/8)(1/2) [√(4u² + 67) (4u)] + C= (1/4) [√(4(x - 7/2)² + 67)] (2x - 7) + C

To find the indefinite integral, we need to use integration by substitution, which is a technique of integration that uses substitution to transform an integral into a simpler one. This process involves finding a function u(x) that, when differentiated, will yield the original function to be integrated. We then substitute u(x) for the original function and simplify the integrand by expressing it in terms of u(x).After this, we can use the power rule of integration to integrate the simplified expression with respect to u(x). Finally, we substitute the original function back in terms of x to obtain the desired answer. In summary, we can use integration by substitution to find indefinite integrals by using the following steps:Step 1: Identify a function u(x) and differentiate it to obtain du/dx.Step 2: Substitute u(x) for the original function and simplify the integral in terms of u(x).Step 3: Integrate the simplified expression with respect to u(x) using the power rule of integration.Step 4: Substitute the original function back in terms of x to obtain the final answer.

In conclusion, the given indefinite integrals have been evaluated using the appropriate integration techniques. We have found that the first integral is a simple polynomial function, while the second and third integrals require more advanced techniques, such as power rule of integration and integration by substitution. It is important to note that the constant of integration must be included in the final answer to account for all possible antiderivatives of the integrand.

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Answer- 9 shelves

In order to find out how many shelves are need we must divided 175 into 20. 175 divided by 20 is 8.75. But, because you cannot have have .75 of a shelf, you have to round this to a whole. This means that 9 shelves will be the least needed number of shelves need to store 175 books. To check this answer 20 books X 8 shelves is 160 books, which means eight shelves can only store 160 books, we will need and additional shelf to store the last 15 books.

HOPE THIS HELPS & GOOD LUCK!

As per the given image, the length of the hypotenuse (EC) is approximately 13.038 yards.

In a right-angled triangle, we will use the Pythagorean theorem to discover the length of the hypotenuse (EC).

The Pythagorean theorem states that during a right triangle, the square of the duration of the hypotenuse is identical to the sum of the squares of the lengths of the other  facets.

In this case, the bottom is 11 yards (eleven yd) and the height is 7 yards (7 yd).

\(EC^2 = base^2 + height^2\\\\EC^2 = 11^2 + 7^2\\\\EC^2 = 121 + 49\\\\EC^2 = 170\)

EC = sqrt(170)

EC = 13.038 yards.

Thus, the EC is 13.038 yards..

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Dario cuts the lasagna into 15 equal slices.

Given,

Quantity of Parmesan cheese = 2/3 pounds

Quantity of Ricotta cheese = 1 3/4 = 7/4 pounds

Quantity of Mozzarella cheese = 1 1/3 = 4/3 pounds

The quantity of cheese in each pieces when the lasagna is cut = 1/4 pounds

We have to find the number of slices of cheese.

Here,

Total quantity of cheese;

2/3 + 7/4 + 4/3 = 2 + 7/4 = 15/4 pounds

Number of slices = total cheese / quantity of cheese in pieces

= (15/4) / (1/4) = 15 slices

That is,

Dario cuts the lasagna into 15 equal slices.

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The evaluated expression is 9x^13y√x

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

\(x\2sqrt{x}9xx^{7}yx^{5}\)

Express properly

So, we have

x√x * 9x^7 * yx^5

Evaluate the products by applying the law of indices

So, we have the following representation

√x * 9* yx^13

This can be rewritten as

9x^13y√x

Hence, the solution is 9x^13y√x

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Answer:

x² - x - 12 = 0

Step-by-step explanation:

Given the x- intercepts are x = - 3 and x = 4 , then the factors are

(x + 3) and (x - 4)

Expressing as a zero product

(x + 3)(x - 4) = 0 ← expand using FOIL

x² - x - 12 = 0

Answer:

\((-4)\x^{\frac{2}{7} } =\sqrt[7]{(-4)^{2} }\)

Step-by-step explanation:

Hope this helps

Answer:

inconsistent, none

Step-by-step explanation:

Write both equations in slope-intercept form to see if the lines are parallel.

These two lines have slope m = −2 and different y-intercepts, therefore they are parallel.

Since the lines are parallel, the system is inconsistent and there are no solutions.

The system of equations  4x + 2y = −8 6x + 3y = 9 is inconsistent and has no solutions.

A system of equations is a collection of two or more equations with a same set of unknowns.

We need to write both equations in slope-intercept form to see if the lines are parallel.

4x+2y=-8

2y=-8-4x

y=-4-2x,

y=-2x-4, m₁=-2

and 6x+3y=9

3y=9-6x

y=-2x+3, m₂=-2.

So two lines have slope m = −2 and different y-intercepts,

It means two line are parallel.

Since the lines are parallel, the system is inconsistent and there are no solutions.

Hence 4x + 2y = −8 , 6x + 3y = 9 is inconsistent and has no solution.

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The cost of putting a new floor in Jordan's closet would be $84.00. To calculate the cost, we need to determine the area of the closet and multiply it by the cost per square foot of the flooring.

The closet in Jordan's house has dimensions of 4 feet by 3 feet. To find the area, we multiply the length (4 feet) by the width (3 feet), which gives us 12 square feet.

Next, we need to multiply the area (12 square feet) by the cost per square foot of the flooring, which is $7.00. Therefore, the total cost of putting a new floor in the closet would be $84.00.

This calculation assumes that the closet has a rectangular shape and that the entire floor area needs to be covered with new flooring. It's important to note that additional factors such as labor costs, preparation of the subfloor, and any other specific requirements or materials needed for the installation are not considered in this calculation.

The given answer only provides the cost based on the area of the closet and the cost per square foot of the flooring material.

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Answer:

a

Step-by-step explanation:

i just did it

Answer:

B. 1x-3

Step-by-step explanation:

slope is m = 1

y-int = (0, -3)

Multiplying ampere (amp) by ohm gives units of volt (V).

Therefore, the answer will be in volts (V). This is because ohm is the unit of electrical resistance, ampere is the unit of electrical current, and volt is the unit of electrical potential difference, which is calculated as the product of current and resistance according to Ohm's law: V = I × R.

Ohm is the unit of electrical resistance, which measures how much a material opposes the flow of electric current. One ohm (1 Ω) of resistance is defined as the amount of resistance that allows one ampere (1 A) of current to flow when a potential difference of one volt (1 V) is applied across it.

Ampere is the unit of electrical current, which measures the rate at which electric charge flows through a material. One ampere (1 A) of current is defined as the flow of one coulomb of electric charge per second.

Volt is the unit of electrical potential difference, which measures the amount of energy required to move a unit of electric charge from one point to another. One volt (1 V) of potential difference is defined as the amount of energy required to move one coulomb of electric charge across a circuit element that has one ohm of resistance.

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Pythagoras was an ancient Greek mathematician who founded the Pythagorean school of thought. The Pythagorean theorem is a fundamental concept in mathematics that is attributed to Pythagoras and his followers.

It states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. While this theorem is considered a cornerstone of mathematics today, it is important to understand that Pythagoras did not have access to the advanced mathematical tools and methods that we have today.

He had to rely on geometric constructions and reasoning to prove his theorem. Furthermore, Pythagoras believed that all numbers could be expressed as ratios of whole numbers, which is not always true in reality. Despite these limitations, the Pythagorean theorem has stood the test of time and continues to be a crucial tool in mathematics and other fields.

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Answer:

Step-by-step explanation:

\(log_{b}a=c = > b^c=a\\ln(a) = > log_{e}a=c = > e^c=a\\log(a) = > log_{10}a=c = > 10^c=a\)

\(log(1000) = 3 = > =10^3 =1000\\ log_{5}(25)=2 = > 5^2=25\\log_{12}144=x = > 12^x=144\\ln(12) =x = > e^x=12\)

Answer:

for the first one the answer is 28-9=18 and 30-13=17 are not the same but are close and for the second one the answer is $30 for the phone plan cause 200×0.15=30

If you use 50 minutes in a month, both plans will cost $32.50.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

2.

A. Let x be the number of minutes used in a month. Then, the cost of Plan A is given by:

Cost(A) = 0.09x + 28

The cost of Plan B is given by:

Cost(B) = 0.13x + 30

To find the number of minutes that will make the plans cost the same, we need to set Cost(A) equal to Cost(B) and solve for x:

0.09x + 28 = 0.13x + 30

0.04x = 2

x = 50

Therefore, the plans will cost the same if you use 50 minutes in a month.

B. If you use 50 minutes in a month, the cost of Plan A will be:

Cost(A) = 0.09(50) + 28 = 32.50

The cost of Plan B will also be:

Cost(B) = 0.13(50) + 30 = 36.50

Therefore, if you use 50 minutes in a month, both plans will cost $32.50.

3.

A. Let C be the monthly cost and t be the number of text messages sent. Then, the linear model that represents the monthly cost is:

C = 0.15t + base cost

The base cost is the cost for unlimited calling, which is not specified in the problem.

B. If you send 200 text messages, the monthly cost will be:

C = 0.15(200) + base cost

C = 30 + base cost

The total cost will depend on the base cost for unlimited calling.

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Hence, the required value of the line integral is\($\boxed{-84550}$\).

The given line integral is \($\int_{C}xyz ds$\), where the given curve C is \($x=8\sin t$, $y=t$, $z=-8\cos t$, $0\leq t\leq \pi$\).

Formula to evaluate line integral:\($$\int_{C}f(x,y,z)ds = \int_{a}^{b}f(x(t),y(t),z(t))\sqrt{\left(\frac{dx}{dt}\right)^2+\left(\frac{dy}{dt}\right)^2+\left(\frac{dz}{dt}\right)^2} dt$$Here, $f(x,y,z) = xyz$, $x(t)=8\sin t$, $y(t)=t$, $z(t)=-8\cos t$, $a=0$, $b=\pi$.\)

Hence, we have\($$\begin{aligned}\int_{C}xyz ds &= \int_{0}^{\pi} (8\sin t)(t)(-8\cos t)\sqrt{\left(\frac{dx}{dt}\right)^2+\left(\frac{dy}{dt}\right)^2+\left(\frac{dz}{dt}\right)^2} dt \\ &= \int_{0}^{\pi} (-64\sin t\cos t)(t)\sqrt{(8\cos t)^2+1^2+(-8\sin t)^2} dt \\ &= -64\int_{0}^{\pi} t\sin t\cos t\sqrt{64\cos^2t+64\sin^2t+1} dt\end{aligned}$$Let $u=64\cos^2t+64\sin^2t+1=65$, $du = 0$. When $t=0$, $u=65$, and when $t=\pi$, $u=65$\)

Hence, we have\($$\begin{aligned}& \int_{C}xyz ds = -64\int_{0}^{65} \left(\frac{t}{2}\right)\sqrt{u}\left(\frac{du}{32}\right) \\ &= -2\int_{0}^{65} t\sqrt{u}\ du \\ &= -2\left[\frac{2}{5}u^{\frac{5}{2}}\right]_{0}^{65} \\ &= -\frac{2}{5}(65)^{\frac{5}{2}} \\ &= -\frac{2}{5}(65)(65)^2 \\ &= \boxed{-84550}\end{aligned}$$\)

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The equation for traveling x miles in the cab can be written as:

Cost = $0.60 + $0.14 * x. The cab charges $0.88 for a ride of 2 miles. And the cab charges $1.72 for a trip of 8 miles.

a. The equation for traveling x miles in the cab can be written as:

Cost = $0.60 + $0.14 * x

b. To find the number of miles for a cab ride that costs $0.88, we can set up the equation:

$0.88 = $0.60 + $0.14 * x

Subtracting $0.60 from both sides, we get:

$0.88 - $0.60 = $0.14 * x

$0.28 = $0.14 * x

Dividing both sides by $0.14, we find:

x = $0.28 / $0.14

x = 2 miles

Therefore, the cab charges $0.88 for a ride of 2 miles.

c. To calculate the cost of a trip of 8 miles, we can substitute x = 8 into the equation:

Cost = $0.60 + $0.14 * 8

Cost = $0.60 + $1.12

Cost = $1.72

Therefore, the cab charges $1.72 for a trip of 8 miles.

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When a report card shows that a student has earned 21 points on a test with a total of 25 points, it can be concluded to state that the student has secured 84 percentage of the total points of the test.

The computation of the percentage of points secured by the student out of the total available points in a test can be done using the generalized formula and the use of provided information into the same as below,

Percentage = Scored Secured / Total Points x 100

Percentage = 21 / 25 × 100

Percentage = 0.84 × 100

Percentage = 84 percentage.

Therefore, the student has earned 84 percentage of total points on a test.

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Answer:

H and J

Step-by-step explanation:

Answer:

Like what king of range ? Like far range?

Step-by-step explanation:

Answer:

Interval

Step-by-step explanation:

Answer:

\(\huge\boxed{\sf Solution\ Set = \{5,-4\}}\)

Step-by-step explanation:

Given equation is:

\(x^2-x-20=0\)

Factoring it by mid-term break method.

+4x × -5x = -20x² (multiplication of side terms)

-5x + 4x = -x (Middle term)

Hence, we can split -x into -5 and +4

\(x^2-5x+4x-20=0\\\\x(x-5)+4(x-5)= 0\\\\Take \ (x-5)\ common\\\\(x-5)(x+4)=0\\\\\)

Either:

x - 5 = 0       OR       x + 4 = 0

x = 5             OR       x = -4

Solution Set = {5,-4}

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

Hope this helped!

\(Hiya!\)

I know, this is a late questions.. but, why not. answer it.

Here's a explanation!

\(x^2-x-20-0\)

\((x+4)(x-5)=0\)

\(x+4=0\)

\(x-5=0\)

There's a another answer too.

\(x=-4\)

\(x=5\)

ANSWER:

\(x=-4\)

\(x=5\)

Hopefully, this helps you!!

\(Sokka\)

Answer:

23.33%

Step-by-step explanation:

Let

x = percentage

Base = 30

Amount = 7

x% of 30 = 7

x/100 * 30 = 7

(x*30) / 100 = 7

30x / 100 = 7

Cross product

30x = 100 * 7

30x = 700

x = 700/30

x = 23.333333333333

Approximately,

x = 23.33%

The fraction in lowest terms is 2/3. Option C

First, we need to know that a fraction is described as the part of a whole variable, a whole number or a whole element.

The different  fractions in mathematics are listed thus;

From the information given, we have that;

a+1/b

Such that a = 5 and b = 9

Now, substitute the values, we get;

5 + 1/9

Add the values of the numerator

6/9

Divide the values

2/3

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Answer:

The rate of change is 9.5 ft/min

Step-by-step explanation:

every minute the balloon rises in 9.5 feet increments

Answer:

its 9.5

Step-by-step explanation: