What is the volume of a sphere whose radius is 6 yards?

Answer:

  A

Step-by-step explanation:

The solution matrices shown are the result of reducing the augmented coefficient matrix to "reduced row-echelon form". Many calculators and spreadsheets have functions specifically for that purpose.

The attachment shows the result of a TI-84 work-alike calculator's reduction of the coefficient matrix. It matches the first choice.

__

Additional comment

When the equations are written in the form shown here, with the variables in the same order, and the constant on the right side of the equal sign, the augmented matrix is simply the matrix of the numbers. It is shown as the argument of the RREF function in the attachment.

The left-right order of the variables on the left side of the equal sign matches the top-down order of the solution values in the rightmost column of the reduced matrix. That is, ...

  a = 2, b = -2, c = 0.

The radius of the circle is approximately 10.17 units (rounded to two decimal places).

To find the radius of the circle, we need to use the formula that relates the central angle to the length of the arc and the radius of the circle. The formula is given as:

arc length = radius x central angle

In this case, the arc length is given as 24.4 and the central angle is given as 2.4 radians. Substituting these values in the formula, we get:

24.4 = r x 2.4

Solving for r, we get:

r = 24.4 / 2.4

r ≈ 10.17

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J in 55min

J in 45min ( bigger hose)

Alternative method

The trick is to convert the numbers you are given to numbers that you can add together.

You have minutes per pool. You can’t work with that. But if you take the reciprocal of each you get pools per minute.

So if the first hose fills 1/55 = 0.01818 pools per minute and the second one fills 1/45 = 0.0222 pools per minute, then both of them will fill 0.1818 + 0.0222 = 0.04040 pools per minute. If we take the reciprocal of that we end up with 1/0.04040 = 24.75 minutes per pool.

The solution to the given differential equation is: x⁷ cos y = y + C

where C is the constant of integration

To solve the given differential equation:

\(\[7x^6\cos y dx - dy = 0\]\)

We can separate the variables and integrate both sides.

Separating variables, we can write the equation as:

\(\[7x^6\cos y dx = dy\]\)

Now, we can integrate both sides with respect to their respective variables:

\(\[\int 7x^6\cos y dx = \int dy\]\)

Integrating the left side:

\(\[\int 7x^6\cos y dx = 7 \int x^6 \cos y dx\]\)

To integrate \(\(x^6 \cos y\)\)with respect to x, we can use integration by parts.

Let's take u = x⁶ and \(\(dv = \cos y dx\)\).

Differentiating u with respect to \(\(x\) gives \(du = 6x^5 dx\).\)

Integrating dv with respect to x gives \(\(v = \int \cos y dx = \cos y \cdot x\).\)

Applying the integration by parts formula:

\(\[\int x^6 \cos y dx = u \cdot v - \int v \cdot du\]\)

Substituting the values:

\(\[\int x^6 \cos y dx = x^6 \cdot \cos y \cdot x - \int (\cos y \cdot x) \cdot (6x^5 dx)\]\)

Simplifying:

\(\[\int x^6 \cos y dx = x^7 \cos y - 6 \int x^6 \cos y dx\]\)

Moving the integral term to the left side:

\(\[7 \int x^6 \cos y dx = x^7 \cos y\]\)

Dividing both sides by 7:

\(\[\int x^6 \cos y dx = \frac{x^7 \cos y}{7}\]\)

Now, substituting this result back into our original equation:

\(\[7 \int x^6 \cos y dx = dy\]\)

\(\[\frac{7x^7 \cos y}{7} = dy\)

Simplifying:

x⁷ cos y = dy

Finally, the solution to the given differential equation is:

x⁷ cos y = y + C

where C is the constant of integration.

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The different possibilities of combinations of 4 are combinations of 4 distinct items, combinations of 4 items with replacement, combinations of 4 items without replacement and combinations of 4 items without replacement

It depends on what exactly you mean by "combinations of 4." Here are a few possibilities and the corresponding answers:

Combinations of 4 distinct items: If you have 4 distinct items and you want to know how many different ways there are to choose a group of 4 from among them, the answer is 4 choose 4, which is equal to 1.

Combinations of 4 items with replacement: If you have a set of items and you want to know how many different groups of 4 you can make if you're allowed to repeat items, the answer is the number of items raised to the 4th power

Combinations of 4 items without replacement: If you have a set of items and you want to know how many different groups of 4 you can make if you're not allowed to repeat items

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Answer:

$1620

Step-by-step explanation:

The volume (V) of a cube is calculated as

V = s³ ( s is the length of the side )

Here V = 5832 , then

s³ = 5832 ( take cube root of both sides )

s = \(\sqrt[3]{5832}\) = 18 ft

The area of the square floor is then

area = 18² = 324 ft²

cost = 324 × $5 = $1620

To evaluate \(8^{\frac{2}{3} }\) first find the square of 8 and then take the cube root.

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

Depending on the powers they possess, many rules of exponents are given.

Law of Multiplication: Exponents should be added while keeping the base constant when multiplying like bases.

Exponents should be multiplied while bases are kept constant when bases are raised by a power of two or more.

Division Rule: When dividing like bases, maintain the base constant and deduct the exponent of the denominator from the exponent of the numerator.

The given value can be written as:

\(8^{\frac{2}{3} } = \sqrt[3]{8^{2} }\)

Hence, to evaluate \(8^{\frac{2}{3} }\) first find the square of 8 and then take the cube root.

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Based on the given values, the function p(x) is not a probability mass function since it does not satisfy the requirement that the sum of probabilities equals 1.

To determine if the function p(x) is a probability mass function (PMF), we need to check if it satisfies the properties of a valid PMF.

1. Non-negativity: The values of p(x) must be non-negative. In the given function, p(x) takes the values 0, 0.3, 0.6, and 0.2, all of which are non-negative. So, the first property is satisfied.

2. Sum of probabilities: The sum of all probabilities p(x) must be equal to 1. Let's check if this property holds:

  p(1) + p(2) + p(4) + p(7) = 0 + 0.3 + 0.6 + 0.2 = 1.1

  Since the sum of probabilities is greater than 1 (1.1 in this case), the function p(x) does not satisfy the property of a valid PMF.

Therefore, based on the given values, the function p(x) is not a probability mass function since it does not satisfy the requirement that the sum of probabilities equals 1.

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Answer:

by adding 14581+418541=433,122

by adding 23427+23243=46,670

by substraction of both Numbers=

difference between both number is 386,452

Answer:

240

Step-by-step explanation:

Answer:

16 m^3

Step-by-step explanation:

Question:

"a regular square pyramid is 3m height and the perimeter of its base is 16m find the volume of the pyramid"

volume of pyramid = (1/3) * (area of base) * height

The perimeter of the base is 16 m, and the base is a square.

perimeter of square = 4 * side

4 * side = 16 m

side = 4 m

area of square = (side)^2

area of base = (4 m)^2 = 16 m^2

volume of pyramid = (1/3) * (area of base) * height

volume = (1/3) * (16 m^2) * 3 m

volume = 16 m^2

Answer: 72.5 degrees

Step-by-step explanation: Call smaller angle x, so larger angle is x+35, so 2x+35=180, subtract 35 from both sides, 2x=145, so x=72.5! I hope this helps you

Answer with step-by-step explanation:

The graph passes through both (1,4) and (2,0)

Thus it's slope is the difference of ordinates over difference of abscissae or -4

Thus the equation becomes y = -4x + b

This b is the required b

At x=2 ; y=0

Thus 0= -8 + b

b=8

The range at which Dan's car can go is 3.33 miles

A car's range is the distance it can travel with the current amount of fuel in the tank.

The vehicle calculates the range based on the amount of fuel, how the accelerator and brakes are used, and how quickly the car is travelling.

The range of a car can be measured in the unit of distance.

Therefore the range of a car can be calculated as;

R = distance per gallon/ number of gallon.

Dan's car is 40mpg and has 12 gallons in it's tank.

Therefore it's range = 40/12

= 3.33miles.

therefore the range of Dan's car is 3.33miles

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Answer:

f(8)=69

Step-by-step explanation:

f(X)= -3 (-3x) -3

f(8)= -3 (-3(8)) -3

= -3 (-24) -3

= 72-3

=69

If the school district surveyed 500 families to see if they were satisfied or not satisfied with the new district website. the maximum number of families who are satisfied with the new district website is approximately 130,771.

First, we need to calculate the confidence level, which is 1 minus the margin of error:

Confidence level = 1 - margin of error

Confidence level = 1 - 0.027

Confidence level = 0.973

Next, we can use the proportion of satisfied families in the sample to estimate the proportion in the population:

Proportion satisfied in population = Proportion satisfied in sample

Proportion satisfied in population = 480/500

Proportion satisfied in population = 0.96

Now we can use this proportion and the confidence level to calculate the maximum number of satisfied families in the population:

Maximum number of satisfied families = Proportion satisfied in population x Total number of families x Confidence level

Maximum number of satisfied families = 0.96 x 140,000 x 0.973

Maximum number of satisfied families ≈ 130,771

Therefore, the maximum number of families who are satisfied with the new district website is approximately 130,771.

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\( \huge \frak \green{question}\)

prove that √p is an irrational number , if p is not a perfect square.

\( \huge \frak \red{answer}\)

Let us assume, to the contrary, that √p is rational. So, we can find coprime integers a and b(b ≠ 0) such that :-

=> √p = a/b

=> √p b = a

=> pb² = a² ….(i) [Squaring both the sides]

=> a² is divisible by p

=> a is divisible by p So, we can write a = pc for some integer c.

Therefore,

a² = p²c² ….[Squaring both the sides]

=> pb² = p²c² ….[From (i)]

=> b² = pc²

=> b² is divisible by p

=> b is divisible by p

=> p divides both a and b.

=> a and b have at least p as a common factor.

But this contradicts the fact that a and b are coprime. This contradiction arises because we have assumed that √p is rational. Therefore, √p is irrational.

_____________________________________

\( \bold \green{i \: hope \: it \: is \: helpful}\)

________________________________

Answer:

11

Step-by-step explanation:

25-5.75=19.25

19.25÷1.75=11

Answer:

(-7,1) lies on the 2nd quadrant

(-7,-5) lies on the 3rd quadrant

Hope it helps:)

Answer: the first term in the sequence is 9.

Step-by-step explanation:

Let the primary term be x.

At that point the moment term is 2x + 4.

And the third term is 2(2x + 4) + 4 = 4x + 12.

Since the third term is given as 48, we will set up an condition and unravel for x:

4x + 12 = 48

4x = 36

x = 9

Answer:

4 minutes

Hope this helps!!! :)

Sabiendo que en la estrella la  suma de los cuatro  números de la línea  es la misma, la respuesta correcta es la opción c) los valores de b y c son 9 y 8 respectivamente.

En primer lugar, sabes que en la estrella la  suma de los cuatro  números de la línea  es la misma.

Por lo que es conveniente escoger aquella línea en donde todos los valores son conocidos, de manera de poder estimar el valor de la suma. De esta manera, se calcula:

12 +1 +2 +15= 30

Entonces la suma en todas las líneas debe dar como resultado 30.

Para calcular el valor de c y d, es preferible elegir aquellas líneas en donde solo aparezca b y donde solo aparezca c.

Entonces, escogiendo aquella línea donde se tiene como incógnita sólo el valor de b y sabiendo que debe sumar 30, se tiene:

12 + (8-3) + 4 + b= 30

Resolviendo:

12 + 5 + 4+ b= 30

21 + b=30

b= 30 - 21

b= 9

Por otro lado, eligiendo aquella línea donde se tiene como incógnita sólo el valor de c y sabiendo que debe sumar 30, se tiene:

15 + 3 +4 + c= 30

22 + c= 30

c=30 - 22

c= 8

Finalmente, se decide verificar en aquellas líneas donde aparecen ambos valores de c y d, o aquellas líneas que no se hayan utilizado previamente, de manera que sumen 30. Entonces:

Primera verificación: 2c +2 +3 +b= 2×8 +2 +3+ 9= 16 +2 +3+ 9= 30

Segunda verificación: 2c +1 +(8-3) +c= 2×8 +1 +5+ 8= 16 +1 +5+ 8= 30

De esta manera se comprueba que en todas las líneas de la estrella la suma de los cuatro números es la misma.

En resumen, la respuesta correcta es la opción c) los valores de b y c son 9 y 8 respectivamente.

Aprende más con este problema similar

Answer:

Thomas can choose any 4 out of 12 players, which is \($\binom{12}{4}$\) distinct possibilities for a team. Carrie can choose any 4 out of the remaining 8 players, which is \($\binom{8}{4}$\) distinct possibilities for a team. Lenny has only 1 choice for his team, whichever 4 have not yet been chosen. Combining all this yields

\(\frac{12\times11\times10\times9}{4\times3\times2}\times\frac{8\times7\times6\times5}{4\times3\times2} &= 11\times 10 \times 9 \times 7 \times 5 \\&= 99\times 35\times 10 \\&= (3500-35)\times 10 \\&= \boxed{34,650\text{ ways}}.\)

The residual plot tell you about the line of best fit, the closer a data point's residual is to 0, the better the fit.

A residual value is a measure of how much a retrogression line vertically misses a data point. Retrogression lines are the stylish fit of a set of data. You can suppose of the lines as pars; a many data points will fit the line and others will miss.

A residual plot has the Residual Values on the perpendicular axis; the vertical axis displays the independent variable.

A residual plot is generally used to find problems with retrogression. Some data sets aren't good campaigners for retrogression, including

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Answer:

3/2

Step-by-step explanation:

Using two points we can find the slope of a line

(0,1) and  (2,4)

The slope is given by

m= (y2-y1)/( x2-x1)

   = (4-1)/(2-0)

   = 3/2

Answer:

see explanation

Step-by-step explanation:

the nth term of an arithmetic sequence is

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

We require to find a₁ and d

given a₃ = 2 and a₅ = 32 , then

a₁ + 4d = 32 → (1)

a₁ + 2d = 2 → (2)

subtract (2) from (1) term by term to eliminate a₁

0 + 2d = 30

2d = 30 ( divide both sides by 2 )

d = 15

substitute d = 15 into (2) and solve for a₁

a₁ + 2(15) = 2

a₁ + 30 = 2 ( subtract 30 from both sides )

a₁ = - 28

Then

\(a_{n}\) = - 28 + 15(n - 1) = - 28 + 15n - 15 = 15n - 43

Explicit formula is \(a_{n}\) = 15n - 43

------------------------------------------------

A recursive formula allows a term in the sequence to be found by adding d to the previous term, that is

\(a_{n}\) = \(a_{n-1}\) + 15 ; a₁ = - 28

The probability that a randomly selected passenger has to wait for more than 4.25 minutes is 0.25, or 25%.

To calculate this probability, we can use the formula for the uniform distribution, which tells us that the probability density function (PDF) is given by:

f(x) = 1/(b-a)

where a and b are the endpoints of the interval (0 and 6 minutes in this case). This means that the probability of a waiting time between a and b is the area under the PDF curve between a and b, which is:

P(a < x < b) = ∫(a to b) f(x) dx = ∫(a to b) 1/(b-a) dx

In our case, we want to find the probability of a waiting time greater than 4.25 minutes, which means we need to calculate:

P(x > 4.25) = ∫(4.25 to 6) f(x) dx = ∫(4.25 to 6) 1/(6-0) dx

Simplifying this integral, we get:

P(x > 4.25) = ∫(4.25 to 6) 1/6 dx = [x/6] from 4.25 to 6

Evaluating this expression at the endpoints, we get:

P(x > 4.25) = [6/6] - [4.25/6] = 0.25

This means that there is a 1 in 4 chance that a passenger will have to wait longer than 4.25 minutes for their train to arrive.

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In a multiple regression ANOVA table, explained variation is represented by the regression sum of squares. The correct option is (A).

Regression sum of squares (also known as explained sum of squares or model sum of squares) is a measure of the amount of variance in the dependent variable that is explained by the regression model.

It is typically denoted as SSreg or SSmodel.

To calculate SSreg, we first calculate the predicted values of the dependent variable (y) based on the regression model, and then calculate the deviation of each predicted value from the mean of the dependent variable.

We then square these deviations and add them up to get the regression sum of squares.

Mathematically, the formula for SSreg is:

SSreg = Σ(yi - ŷi)^2

where yi is the actual value of the dependent variable for the ith observation, ŷi is the predicted value of the dependent variable for the ith observation based on the regression model, and Σ denotes the sum over all observations.

The regression sum of squares is an important component of the analysis of variance (ANOVA) table in linear regression, which is used to assess the overall fit of the model and the significance of the independent variables.

A larger SSreg indicates a better fit of the model to the data and a greater proportion of the variance in the dependent variable explained by the independent variables.

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The function y = 7|x + 1| - 5 can be written as a Piecewise Function as follows,

               7x + 2                for x > -1

y   =

              -7x - 12               for x < -1

Given, a function y = 7|x + 1| - 5

Now, we have to write the given function as a piecewise function

|x + 1| = (x + 1) for x > -1 and

|x + 1| = - (x + 1) for x < -1

So, the given function can be written as a piecewise function

               7(x + 1) - 5                for x > -1

y   =

              -7(x + 1) - 5                for x < -1

On simplifying, we get

               7x + 2                for x > -1

y   =

              -7x - 12               for x < -1

Hence, the given function y = 7|x + 1| - 5 can be written as a Piecewise Function as follows,

               7x + 2                for x > -1

y   =

              -7x - 12               for x < -1

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Answer:

3*4 is 12, 12*4 is 48, 48*4 is 192, so the answer is 192

If m=6, then 3×6= 18.

43-18=25

Your answer is 25.

Step-by-step explanation:

Can I have brainly please!

EVALUATE EXPRESSION

Step-by-step explanation:

43-3m=??             if m=6

substitute

43-3 * 6= 25