Which of the following is the radius of a sphere that has a volume of  32/3 π in³?
a. 1 in            
b. 2 in                 
c. 3 in                 
d. 4 in​

True

The statement "A system composed of two linear equations must have at least one solution if the straight lines represented by these equations are nonparallel," is true.

What is a system of linear equations?

In algebra, a system of linear equations is a collection of two or more linear equations with the same variables.

If these linear equations represent two or more lines that aren't parallel, the equations are said to form a system of equations with at least one solution.

The intersection of the lines is the location where an equation system has a solution.

Two lines are parallel if they have the same slope and never intersect.

If two lines have different slopes, they are nonparallel and intersect at a point.

How can one tell if a statement is true or false?

If a claim can be verified by evidence, logic, or reason, it can be considered true.

On the other hand, a statement is false if it is inaccurate or misleading, or if it contradicts existing facts, logic, or reason.

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Answer:

That state is Illinois.

Answer:

0.5kg/m

Step-by-step explanation:

The formula for acceleration is f/m = a

10/20 = a

0.5 = a

Best of Luck!

Answer:

diameter

Step-by-step explanation:

double the radius is the diameter

The unit rate here is also 8 cups of water per day.

We need to remember that in the unit rate we have as the denominator one unit of any quantity.

In this case, we have a day as the denominator one day, since:

In summary, therefore, the unit rate, in this case, is 8 cups of water per day:

Answer: $94.49

Step-by-step explanation:

125.99 x 25/100

125.99 x 0.25

you save = $31.50

final price = original price - discount

final price = 125.99 - 31.4975

final price = $94.49

Problem 1;

The set builder form of  {2,3,4}

⇒ {x | x is a member of the set {2, 3, 4}}

Problem 2:

The set {x: x ∈ R, x² = 4 or x² = 9}

In list form we can write,

{-2, 2, -3, 3}

Problem 3:

{1, 10, 100, 1000, 10000, ...} infinite

{1,3,5,7,9,.. 599} finte

The set of all real number solutions to: x + 3 + 2x = 3(x + 1): infinite set

The set of real number solutions to the equation x² = -4: finite set

problem 4:

The power set of s is,

p(s) = {Ф, a, b,  {a,b}}

problem 6:

A - B subset of AUB is Proved below

Problem 1;

The given set is {2, 3, 4}

The set builder form represents a set of elements using a rule or condition. For the set {2, 3, 4},

So we can write this in set builder form as,

⇒ {x | x is a member of the set {2, 3, 4}}

Problem 2:

The given set is {x: x ∈ R, x² = 4 or x² = 9}

Since,

x² = 4 ⇒ x = ± 2

x² = 9 ⇒ x = ± 3

In list form we can write,

{-2, 2, -3, 3}

The given set is {x|x E R; x is a solution to x² = -1}

Since there is no such real number for which x² = -1

Therefore it is a null set we can write it as Ф so

The given set is {x :x is an even positive integer and x ≤ 64}

Therefore in list form we can write,

{2, 4, 6, 8, 10, ............,64}

Problem 3:

For the set {1, 10, 100, 1000, 10000, ...}

Since there are no upper bound so it is infinite set.

For the set {1,3,5,7,9,.. 599}

It has both lower and upper bound hence this is a finite set.

The set of all real number solutions to: x + 3 + 2x = 3(x + 1).

⇒ 3x + 3 = 3x + 3

We can see that both sides of the equation are the same, so there are infinitely many solutions to this equation.

Therefore, the set of real number solutions is infinite

The set of real number solutions to the equation x² = -4

Since there is no such real number for which x² = -4

Therefore it is a null set we can write it as Ф so it is finite.

Problem 4;

The given set is S = {a,b}.

The power set of s is,

p(s) = {Ф, a, b,  {a,b}}

Problem 6:

We have to prove  A - B is subset of AUB,

To prove that A - B is a subset of AUB,

we have to show that every element of A - B is also an element of AUB.

Let x be an arbitrary element of A - B. By definition,

this means that x is an element of A, but x is not an element of B.

Since x is an element of A, we know that x is an element of A or B (by the definition of the union, denoted by the symbol U).

Therefore, x is an element of AUB.

So, we have shown that for any element x in A - B, x is also in AUB. Hence, we have proved that A - B is a subset of AUB.

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Answer:

$240

Step-by-step explanation:

30 (the weeks in 7 months) times 8 (his weekly savings) = 240

The Mean will decrease while the Median and the Mode will remain with the same amount.

For Central Measures, we have Median, Mode and  Mean. They try to describe the whole distribution by one value, in the center of it.

For this question, let's pick some examples from the Old Faithful, WY Station to the National Oceanic and Atmospheric Administration from 2015, January

1st Case Scenario:

For 7 days of precipitation, (Snow, ice pellets, etc. rain) in inches:

19 19 19 24 23 23 23 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Mean = 5

Median=0 (the sum of the 15th+16th position over 2)

Mode=0 (Most common observations)

2nd Case Scenario

For 3 days of precipitation, (Snow, ice pellets, etc. rain) in inches:

0 0 0 24 0 0 23 0 19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Mean = 2.2

Median =0

Mode=0

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Answer:

x=5

Step-by-step explanation:

Put everything on one side of the equation and have it equal to 180 degrees.

13x+3+72+8x= 180

Combine like terms

21x+75= 180

Subtract 75 on both sides

21x = 105

Divide by 21 on both sides

x= 5

hope this helped!

The average velocity from t = 2s to t = 4s would be - 48 ft/s.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that an object is thrown upward with initial velocity of 48 feet per second from a high of 120 feet. The height of the object t seconds after it is thrown is given by h(t) = - 16t² + 48t + 120.

Average rate of change of velocity with time is called average velocity. Mathematically -

v{avg.} = Δx/Δt                                                         .... Eq { 1 }

Δx = x(4) - x(2)

Δx = - 16(4)² + 48(4) + 120 - {- 16(2)² + 48(2) + 120}

Δx = - 96

Δt = 4 - 2 = 2

So -

v{avg.} = Δx/Δt = -96/2 = - 48 ft/s

Therefore, the average velocity from t = 2s to t = 4s would be - 48 ft/s.

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The verdict which is true about the radius of all three arcs when constructing an angle bisector is; - No; the second two arcs must have the same radius but it can be different from the first.

The correct answer option is option C.

Recall that an angle at point, O is formed by the intersection of two lines; say lines A and B.

Hence, in a bid to draw the Angie bisector of the angle; AOB, three arcs are needed.

The first arc is an arc drawn by placing the pivot of the compass at the point, O and drawing an arc which intersects lines A and B. The radius of this first arc in discuss can be any value.

Subsequently, the other two arcs are propagated using the points of intersection of the first arc with both lines such that the two arcs intersect.

It is however noteworthy to know that these two arcs must have the same radius.

Ultimately, the second two arcs must have the same radius but it can be different from the first.

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The value of the given integral ∫ x³dx +y²dy +z dz is 81.

What is line origin?

The point of departure. It is zero on a number line. Where the X and Y axes cross on a two-dimensional graph, like in the graph shown here: O is sometimes used as a symbol.

Here, we have

Given; x³dx +y²dy +zdz, where c is the line from the origin to the point (4, 3, 4).

Let x =4t , y =3t ,z =4t ,0≤t ≤1

dx =4dt , dy =3dt , dz =4dt

∫ x³dx +y²dy +zdz

=\(\int\limits^1_0 {x} \, dx\)[(4t)³4dt +(3t)²3dt +(4t)4dt]

=\(\int\limits^1_0 {x} \, dx\)[(256t³ +27t² +16t] dt

=\(\int\limits^1_0 {x} \, dx\)[([64t⁴ +(9)t³ +8t²]

= [64×1⁴ +(9)×1³ +8×1²​]  - [64×0⁴ +(9)×0³ +8×0²​]

= 81

∫ x³dx +y²dy +z dz = 81

Hence, the value of the given integral ∫ x³dx +y²dy +z dz is 81.

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Answer::

Explanation:

Let the number of lasagna cupcakes made = x

Let the number of Gorgonzola onion tarts made = y

0. It takes ,10 minutes, to assemble each pan of lasagna cupcakes.

1. It takes ,15 minutes, to roll out the Gorgonzola onion tarts and fill each pan.

2. She has a maximum of ,2 hours (120 minutes), to assemble the appetizers.

These translate to the inequality:

0. Each pan of lasagna cupcakes takes 20 minutes to bake.

1. Each pan of Gorgonzola tarts takes 6 minutes to bake.

2. She has 60 minutes to bake the appetizers.

These translate to the inequality:

Since she must bake either lasagna cupcakes or Gorgonzola tarts, we have that:

So the system of inequalities is:

The graph that bests represents this scenario is:

Answer:

(0,4)

Step-by-step explanation:

The answer is 0,4 because that's where both lines meet.

If you need further explanation let me know, hope this helps though, and have a great day!

Answer:

-7.8

Step-by-step explanation:

-7.8

Answer:

point D y F ese el la respuesta

Answer:

2x - (3 + 4x) = 12

x = -7.5

y = -27

Step-by-step explanation:

-4x + y = 3 (1)

2x - y = 12 (2)

From (1)

y = 3 + 4x

Substitute y = 3 + 4x into (2)

2x - y = 12 (2)

2x - (3 + 4x) = 12

2x - 3 - 4x = 12

2x - 4x = 12 + 3

-2x = 15

x = 15/-2

x = -7.5

Substitute x = -7.5 into (2)

2x - y = 12 (2)

2(-7.5) - y = 12

-15 - y = 12

-y = 12 + 15

- y = 27

y = -27

Given that Emma made 9 times as many goals as Vivian during soccer practice today.The main answer to the given question is that Emma made nine times as many goals as Vivian during soccer practice today.

We are given that Emma made 9 times as many goals as Vivian during soccer practice today. It is not specified about how many goals Vivian made during the practice session.Emma made 9 times as many goals as Vivian during soccer practice today.Meanwhile, the long answer to the given question is; we are given that Emma made 9 times as many goals as Vivian during soccer practice today.

Suppose the number of goals scored by Vivian during soccer practice today is x.Then the number of goals scored by Emma during soccer practice today would be 9x.In other words, the ratio of the number of goals scored by Emma to the number of goals scored by Vivian is 9:1.Therefore, the number of goals scored by Vivian and Emma could be any two numbers that are in the ratio of 1:9. Emma made nine times as many goals as Vivian during soccer practice today.

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The system of equations -2x + y = -3 in both choices has a solution of (-4, 5).

The two choices that have a solution of (-4, 5) when written as a system are:

1. A 2-column table with 4 rows. Column 1 is labeled x with entries -1, 2, 3, 5. Column 2 is labeled y with entries 2, -1, -2, -4.

  -2x + y = -3

2. A 2-column table with 4 rows. Column 1 is labeled x with entries -1, 2, 3, 7. Column 2 is labeled y with entries 0, -3, -4, -8.

  -2x + y = -3

In both cases, when we substitute x = -4 and y = 5 into the equations, we get:

-2(-4) + 5 = -3

8 + 5 = -3

-3 = -3

Therefore, the system of equations -2x + y = -3 in both choices has a solution of (-4, 5).

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Regular hexagon ABCDEF is inscribed in a circle with center H, the image of segment BC after 120 degree clockwise rotation about point H is the segment joining the points B' and C', which has endpoints (-0.5r\(\sqrt{3\), -0.5r) and (-0.5r, -0.5r).

Since the hexagon is inscribed in a circle with center H, we can conclude that H is also the center of the circle passing through vertices B, C, and D. Therefore, the circle passing through B, C, and D is also a 120 degree clockwise rotation of the circle passing through A, B, and C.

To find the image of segment BC after a 120 degree clockwise rotation about point H, we need to find the coordinates of B and C relative to H, and then apply a 120 degree rotation matrix to these coordinates.

Let the radius of the circle be r, and let the coordinates of H be (0,0). Then the coordinates of B and C are:

B: (r cos(60), r sin(60))

C: (r cos(0), r sin(0)) = (r, 0)

To apply a 120 degree clockwise rotation matrix, we can use the following matrix:

[ cos(-120) -sin(-120) ]

[ sin(-120) cos(-120) ]

Simplifying, we get:

[ cos(120) sin(120) ]

[ -sin(120) cos(120) ]

Applying this matrix to the coordinates of B and C, we get:

B': [ cos(120) sin(120) ][ r cos(60) ] = [ -0.5r \(\sqrt{3}\)]

[ -sin(120) cos(120) ][ r sin(60) ] [ -0.5r ]

C': [ cos(120) sin(120) ][ r ] = [ -0.5r ]

[ -sin(120) cos(120) ][ 0 ] [ -0.5r ]

Therefore, the image of segment BC after a 120 degree clockwise rotation about point H is the segment joining points B' and C', which has endpoints (-0.5r\(\sqrt{3}\), -0.5r) and (-0.5r, -0.5r), respectively.

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Answer:

\(diagonal \: of \: square = a \sqrt{2} \\ 12 = a \sqrt{2} \\ \frac{12}{ \sqrt{2} } = a \\ \: a = 6 \sqrt{2} \\ now \: area \: of \: square = {l}^{2} \\ = (6 \sqrt{2) {}^{2} } \\ = 72cm {}^{2} \\ again \: perimeter \: of \: square = 4l \\ = 4 \times (6 \sqrt{2} ) \\ = 33.94cm\)

The P-value is greater than the 1% level of significance. We fail to reject the null hypothesis at the 1% level of significance.

What is mean?

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.

Given that,
Sample size, n=24

5 4 5 4 4 3 6 4 3 3 5 6 3 3 2 7 4 5 2 2 2 3 5 2

Sample mean is defined as:
¯x=∑xin

Excel function for the sample mean:

=AVERAGE(5,4,5,4,4,3,6,4,3,3,5,6,3,3,2,7,4,5,2,2,2,3,5,2)

¯x = 3.83

Sample standard deviation is defined as:

s = ∑ ( x i − ¯ x ) 2 n − 1

Excel function for the sample standard deviation:

=STDEV(5,4,5,4,4,3,6,4,3,3,5,6,3,3,2,7,4,5,2,2,2,3,5,2)

s = 1.435 The null hypothesis is, H 0:μ =3.18

The alternative hypothesis is, H a : μ ≠ 3.18

t-test statistic is defiend as: t =
¯ x − μ s / √ n t = 3.83 − 3.18 1.435 / √ 24 t = 2.219

Excel function for the P-value:

=TDIST(2.219,23,2)

P-value = 0.0366

The P-value is greater than the 1% level of significance. We fail to reject the null hypothesis at the 1% level of significance.

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The probability that one of the scores in the sample is less than 1484 is 0.2437 .

a)Given that mean u = 1403

standard deviation σ = 200

sample size n = 32

P(x>1484) = P(X-u/σ > 1484-1403/200)

                = P (z > 0.405)

P(x>1484) = 0.2437 .

hence the probability that one score is greater than 1484 is 0.405 .

b) Now we have to find the average of the scores of 48 samples.

P(x>1484)

= P(x-μ/ σ/√n> 1484-1403 /200/√48)

= P(z>2.805.)

Now we will use the normal distribution table to calculate the p value to be 0.002516.

p-value = 0.0025

Normal distributions are very crucial to statistics because not only they are commonly used in the natural and social sciences but also to describe real-valued random variables with uncertain distributions.

They are important in part because of the central limit theorem. This claim states that, in some cases, the average of many samples (observations) of a random process with infinite mean and variance is itself a random variable, whose distribution tends to become normal as the number of samples increases.

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To solve the equation cos(θ) − sin(θ) = sqrt{2}sin(θ/2) in the interval [0, 2π), we can use the half-angle formula.
The half-angle formula for sine is: sin(θ/2) = ±sqrt{(1 - cos(θ))/2}.
cos^2(θ) + sin^2(θ) = 1, and rearrange the equation:
2cos(θ)sin(θ) = cos(θ)
Since we don't want cos(θ) = 0, we can divide both sides by cos(θ): 2sin(θ) = 1
Now, solve for θ:
sin(θ) = 1/2
Within the interval [0, 2π), the angles that satisfy this equation are:
θ = π/6, 5π/6
So, the solutions to the given equation are θ = π/6 and θ = 5π/6.

Using the double angle formula for sine, we can rewrite the right-hand side of the equation as:
sqrt{2}sin(θ/2) = sqrt{2}[2sin(θ/4)cos(θ/4)]

Then, using the identity cos(θ) - sin(θ) = sqrt{2}cos(π/4)(cos(θ - π/4)), we can rewrite the left-hand side of the equation as:
cos(θ) - sin(θ) = sqrt{2}cos(θ - π/4)

Substituting these expressions into the original equation, we get:
sqrt{2}cos(θ - π/4) = sqrt{2}[2sin(θ/4)cos(θ/4)]

Dividing both sides by sqrt{2} and simplifying, we get:
cos(θ - π/4) = 2sin(θ/4)cos(θ/4)

Using the half-angle formula for cosine, we can rewrite the left-hand side of the equation as:
cos(θ - π/4) = sin(π/4)cos(θ) + cos(π/4)sin(θ)
= (1/sqrt{2})cos(θ) + (1/sqrt{2})sin(θ)

Substituting this expression into the equation and simplifying, we get:
(1/sqrt{2})cos(θ) + (1/sqrt{2})sin(θ) = 2sin(θ/4)cos(θ/4)

Multiplying both sides by sqrt{2} and using the double angle formula for sine, we get:
sin(θ + π/4) = 2sin(θ/2)

Using the half-angle formula for sine, we can rewrite the right-hand side of the equation as:
sin(θ + π/4) = sin(π/4)cos(θ) + cos(π/4)sin(θ)
= (1/sqrt{2})cos(θ) + (1/sqrt{2})sin(θ)

Substituting this expression into the equation and simplifying, we get:
(1/sqrt{2})cos(θ) + (1/sqrt{2})sin(θ) = 2(1 - cos(θ))/2

Multiplying both sides by sqrt{2} and simplifying, we get:
cos(θ) + sin(θ) = 2 - 2cos(θ)

Rearranging, we get:
3cos(θ) + sin(θ) = 2

Solving this equation for cos(θ) using the quadratic formula, we get:
cos(θ) = (-1 ± sqrt{17})/6

Since we're only interested in solutions in the interval [0, 2π), we reject the negative root and get:
cos(θ) = (sqrt{17} - 1)/6

Finally, using the identity sin^2(θ) + cos^2(θ) = 1, we can solve for sin(θ) and get:
sin(θ) = ±sqrt{1 - cos^2(θ)}

Substituting the value of cos(θ) that we found, we get:
sin(θ) = ±sqrt{1 - [(sqrt{17} - 1)/6]^2}

Therefore, the solutions in the interval [0, 2π) are:
θ = arcsin[(sqrt{17} - 1)/6] and θ = π - arcsin[(sqrt{17} - 1)/6]

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The given function is solved using the power rule. The nth derivative of the given function f(x)=xⁿ is  \(f^{(n)}(x) = n!x^{n-n }= n!\).

The power rule instructs how to differentiate xⁿ. It is used to determine the slope of polynomial functions as well as any other function with a real number exponent.

The given function is considered a power function. This is because the x is raised to the power (n). This n is considered a real number. So the derivative of this function is derived using the power rule.

First, differentiating the given function as follows,

\(\begin{aligned}f'(x)&=nx^{n-1}\\f''(x)&=n(n-1)x^{n-2}\\f'''(x)&=n(n-1)(n-2)x^{n-3}\end{aligned}\)

So observing the pattern, the nth derivative is found as follows, \(f^{(n)}(x) = n!x^{n-n }= n!\)

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The complete question is -

Find the nth derivative of each function by calculating the first few derivatives and observing the pattern that occurs.

f(x)=xⁿ

Answer:

Tuesday

Step-by-step explanation:

by 0.18 2.24- 2.06

Answer:

62.5 miles per hour

Step-by-step explanation:

Answer:62.5 miles an hour

Step-by-step explanation: You would divide 250 by 4.

1. The probability of selecting exactly one tank with high-viscosity material is 0.

2. The probability of selecting at least one tank with high-viscosity material is 1.

3. The probability of selecting exactly one tank with high-viscosity material and exactly one tank with high impurities is 0.25.

1. The probability of selecting exactly one tank with high-viscosity material is calculated by the binomial distribution formula, P(X = n) = (nCx)p^x(1-p)^n-x, where n is the number of trials, x is the number of successes, and p is the probability of success. In this case, n = 4, x = 1, and p = 24/24 = 1. Therefore, P(X = 1) = (4C1)1^1(1-1)^4-1 = 0.

2. The probability of selecting at least one tank with high-viscosity material is calculated by the complement rule, P(X > 0) = 1 - P(X = 0). In this case, P(X > 0) = 1 - (4C0)1^0(1-1)^4-0 = 1.

3. The probability of selecting exactly one tank with high-viscosity material and exactly one tank with high impurities is calculated by the binomial distribution formula, P(X = n) = (nCx)p^x(1-p)^n-x, where n is the number of trials, x is the number of successes, and p is the probability of success. In this case, n = 8, x = 2, and p = 24/24 = 1. Therefore, P(X = 2) = (8C2)1^2(1-1)^8-2 = 0.25.

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