The table shows ordered pairs of the function . What is the value of y when ?

A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 1, 1, 4, 8, 10. The second column is labeled y with entries 14, 10, 6, 0, question mark, negative 12.

–20
–8
8
48

Answer:

Step-by-step explanation:

2

Area of circle A = pi r²

r is the radius

small circle area = pi

large circle area = k.pi

the diameter of the the large circle equals 3 times the diameter of the small circle .

since A = pi . r²

pi.r² = pi as given the area of the small circle

r²= 1

r= 1 is the radius of the small circle the the diameter = 2

the diameter of the large circle = 3.2 = 6

the radius = 3

the area = pi .3² = 9 pi

then k = 9

The combination of factors will increase the chances of rejecting the null hypothesis is:

A small standard error and a large alpha level will increase the chances of rejecting the null hypothesis.

The standard error represents the variability of the sample mean from the true population mean. A small standard error indicates that the sample mean is a good estimate of the true population mean, making it easier to detect differences and thus increasing the chances of rejecting the null hypothesis.

Alpha (α) is the level of significance, or the threshold for rejecting the null hypothesis. A large alpha level means that a smaller difference between the sample mean and the null hypothesis is required to reject the null hypothesis. This makes it more likely that the null hypothesis will be rejected if the sample mean is significantly different from the true population mean.

So, when both the standard error is small and the alpha level is large, it increases the chances of rejecting the null hypothesis.

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The exponential function is an exponential decay.

A general exponential function can be written as:

y = A*(b)^x

Where A is the initial value and b is the base.

Here the exponential equation is:

y = 10*(2/3)^x

Notice that the base is:

b = 2/3 = 0.66

This is smaller than 1 and larger than zero, so we have an exponential decay.

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The area in which the goat can haze inside the land with the shape of a triangle ABC = 16m²

The formula that is used to calculate the area of a triangle = 1/2 base ×height.

where base of a triangle = 4m

The height of the triangle = 8m

The area of the triangle = 1/2× 4× 8

= 16m².

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Complete question:

An unfenced grassland is in the form of a right triangle ABC with AB=4m, BC=8m, and AC as the hypotenuse.if the land was fenced on sides ab and bc, determine the area in which the goat can graze inside the land abc.

The area in which the goat can haze inside the land ABC is; 16m²

The formula that is usually applied to calculate the area of a triangle is expressed as;

Area =  ¹/₂ * base * height.

The parameters are;

Base of a triangle = 4m

Height of the triangle = 8m

Thus,

Area of the triangle ABC = ¹/₂ * 4 * 8

Area =  16m².

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Complete question is:

An unfenced grassland is in the form of a right triangle ABC with AB=4m, BC=8m, and AC as the hypotenuse. If the land was fenced on sides ab and bc, determine the area in which the goat can graze inside the land abc.

Demetri lives in the city and sometimes uses a ride share service. A ride costs $1.50 for the first 1/5 mile and $0.25 for each additional 1/5 mile. Demetri does not want to spend more than $3.75 on a ride. So, he must not go beyond 9 miles.

An expression that contains variables, constants, and algebraic operations is defined as just an algebraic expression in mathematics (addition, subtraction, etc.). Terms comprise expressions. A mathematical statement with variables, constants, coefficients, and algebraic operations is known as an algebraic expression.  Terms comprise expressions. Algebraic equations are declarations of the equality of two expressions created by performing the algebraic operations of adding, subtracting, multiplying, dividing, raising to a power, and root extraction to a collection of variables.

Given data

A ride costs $1.50 for the first 1/5 mile.

$0.25 for each additional mile.

Let the number of miles be x

and the cost of x miles be y

Hence the expression for the total cost is

y = 1.5+ 0.25x

now when y = 3.75

or, 3.75 = 1.5 + 0.25x

or, 3.75 - 1.5 = 0.25x

or, 2.25 = 0.25x

or, x = 2.25/0.25

or, x = 9 miles

Hence he must not go beyond 9 miles.

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Answer:

Below

Step-by-step explanation:

Typo in your post ?

.875   IS   rational    it equals 7/8

Answer:

Below

Step-by-step explanation:

Standard form of a circle =     (x-h)^2  + (y-k)^2 = r^2

   where h,k is the center  

for this circle h,k = 2,-1     and radius, r= 4

so the equation would be

(x-2)^2 + (y+1)^2 = 4^2

By using what we know about right triangles, we will see that the hobbits are at 744.39 meters from the Dark Tower.

This position can be visualized as a right triangle, with the catheti being the tower's height and the distance between the hobbits and the Dark Tower.

Then we can use the relation:

Tan(θ) = (opposite cathetus)/(adjacent cathetus)

Where θ = 28°

The adjacent cathetus to this angle exists the height of the tower, then:

Adjacent cathetus = 1,400 m

The opposite cathetus exists the distance,

Tan(28°) = D/1,400m

Solving for D we get:

Tan(28°)*1,400m = D = 744.39m

The hobbits are at 744.39 meters from the Dark Tower.

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These are the simplified expressions with A = -3 , |-3 - B|.

What is algebraic expression ?

An algebraic expression is an expression built up from constant algebraic numbers, variables, and the algebraic operations. For example, 3x² − 2xy + c is an algebraic expression.

Given that A = -3, we can substitute this value into the expressions:

A + B = -3 + B

4a + 5b = 4(-3) + 5b = -12 + 5b

|A| = |-3| = 3

|A - B| = |-3 - B| = |-3 - B|

These are the simplified expressions with A = -3 , |-3 - B|.

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The columns of a are linearly dependent, we can conclude that y = (4, 9) is not in the range of t(x).

What is vector ?

A vector is a mathematical object that has both magnitude (or length) and direction. Vectors can be used to represent physical quantities such as velocity, force, or displacement, where the magnitude represents the size of the quantity and the direction represents its orientation in space.

The range of t(x) = ax, where a = 1 −3 0 5 3 1, is the set of all possible values of t(x), which is the set of all linear combinations of the columns of the matrix a. To check if y = (4, 9) is in the range of t(x), we need to see if there exists a vector x such that t(x) = y. If a vector x exists, then y = (4, 9) is in the range of t(x). If no such vector exists, then y is not in the range of t(x).

Since the columns of a are linearly dependent, we can conclude that y = (4, 9) is not in the range of t(x).

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Answer:

The function table for g(x) = -x + 4 is as follows:

X Y -5 9 -1 5 0 4 1 3 2 2

The graph is proportional as it represents a linear function and is depicted using a straight line.  

The direct proportionality equation is y = kx, which demonstrates that as x rises, y rises at the same pace.

When two variables are directly or indirectly proportional to one another, their relationship can be expressed using the formulas y = kx or y = k/x, where k specifies the degree of correspondence between the two variables. The proportionality constant, k, is often used.

The graph is proportional as it represents a linear function and is depicted using a straight line. The function can also be said as a direct variation function.

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The value of the following cardinalities:

a. |A| when A = {4, 5, 6,..., 37} is 34.

b. |A| when A = {x ∈ ℤ : -2 ≤ x ≤ 100} is 103.

c. |A∩B| when A = {x ∈ ℕ : x ≤ 20} and B = {x ∈ ℕ : x is prime} is 8.

We have to determine the following cardinalities.

a. |A| when A = {4, 5, 6,..., 37}.

Total number of elements = 34

|A| = 34

b. |A| when A = {x ∈ ℤ : -2 ≤ x ≤ 100}.

|A|: The number of integer that lies between -2 ≤ x ≤ 100

So the total number of elements from -2 ≤ x ≤ 100 is 103.

So, |A| = 103

c. |A∩B| when A = {x ∈ ℕ : x ≤ 20} and B = {x ∈ ℕ : x is prime}.

A∩B = {x ∈ ℕ : x ≤ 20 and x is prime}

A∩B = {2, 3, 5, 7, 11, 13, 17, 19}

Total elements = 8

|A∩B| = 8

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By using the Root Test on the series "∑n" , we found that the series is Divergent and diverges to infinity .

The Root Test states that, if the limit of nth root of the absolute value of the nth term of a series is less than 1, then the series converges. and

If the limit is greater than or equal to 1, the test is inconclusive.

In the series ∑n , the nth term of the series is "n" ,

So, the nth root of the absolute value of nth term is the nth root of |n|, which is = n^(1/n).

we see that as n approaches infinity, the nth root : n^(1/n) approaches 1, So,  the limit of the nth root of the absolute value of the nth term is equal to 1. Which means that the Root Test is inconclusive for this series.

Therefore , the series ∑n diverges, it is a known series called as Harmonic series, which diverges to infinity.

The given question is incomplete , the complete question is

Use the Root Test to determine whether the series convergent or divergent.  ∑n , where n is from 1 to infinity .

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1. The solution of a system of 3 simultaneous linear equations in three variables are (2, 3, 1).

2. The base of the mathematical constant e, an irrational and transcendental number roughly equal to 2.718281828459, is the natural logarithm of a number.

1. A system of 3 simultaneous linear equations in three variables are

5x - 4y + 2z = 0.............(1)

-3x + 4y = 6.............(2)

x + 4z = 6.............(3)

We solve these system of equations using the substitution method and elimination method.

Add equation (1) and (2)

5x - 4y + 2z + (-3x + 4y) = 0 + 6

5x - 4y + 2z - 3x + 4y = 0 + 6

After the elimination the equation is:

2x + 2z = 6

Taking common 2 and divide by 2 on both side, we get

x + z = 3................(4)

Subtract equation 3 and 4

x + 4z - (x + z) = 6 - 3

x + 4z - x - z = 3

3z = 3

Divide by 3 on both side, we get

z = 1

Now putting the value of z in equation 4

x + 1 = 3

Subtract 1 on both side, we get

x = 2

Now putting the value of x in equation 2

-3(2) + 4y = 6

-6 + 4y = 6

Add 6 on both side, we get

4y = 12

Divide by 4 on both side, we get

y = 3

Now the solution of system of equation is (2, 3, 1).

2. The exponent or power that must be added to a base to produce a particular number is called the logarithm. If bx = n, then the mathematical expression for x is x = logb n, where x is the logarithm of n to the base b.

With infinite decimal places and no discernible pattern, the natural base e is an irrational number. The initials of the number e are 2.718281828459.

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The complete question is:

1. Solve a system of 3 simultaneous linear equations in three variables.

5x - 4y + 2z = 0

-3x + 4y = 6

x + 4z = 6

2. What is a logarithm? How is e, the natural logarithm base, defined?

The correct conclusion is:

a. f opens down on the interval 0.987 < x < 1

To determine the conclusion about the behavior of the function f, we can use the tangent line approximation and whether it overestimates or underestimates the actual value of f(0.987).

Given that the tangent line approximation at x = 1 is 2.37, and if this approximation is an overestimate of the actual value of f(0.987), it means that the function lies below the tangent line in the interval 0.987 < x < 1.

Since the tangent line has a positive slope (given that f'(1) = 4), if the function f lies below the tangent line, it must be decreasing in the interval 0.987 < x < 1.

Therefore, the correct conclusion is:

a. f opens down on the interval 0.987 < x < 1

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Complete question =

For f differentiable such that f(1) = 3 and f'(1) = 4, the tangent line approximation of (0.987) = 2.37.

If this is an overestimate, what conclusion can be made about f ??

a. f opens down on the interval 0.987 x < x < 1

b. f opens up on the interval 0.987 x < x < 1

c. f opens down at x =  0.987

d. f opens up at x = 1

The probability that exactly four people get the right letter is 1/120.

Let the people form a line and the envelopes are on the table.

The first person has a 1 in 5 chance of selecting the right letter.  (He selects the correct one)

Now there are 4 on the table so the second person has a 1 in 4 chance of getting the right one (He selects the correct one)

Now there are 3 on the table so the second person has a 1 in 3 chance of getting the right one (He selects the correct one)

Now there are 2 on the table so the second person has a 1 in 2 chance of getting the right one (He selects the correct one)

and so on

so

P(everyone getting the correct letter) = 1/5*1/4*1/3*1/2*1/1=1/5!=1/120.

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Answer:

answer choice C.

Step-by-step explanation:

complementary angles are 2 angles that add up to 90 degrees

90=58+x

90-58=x

x=32

Answer:

My answer to your question is a "No".

We can know that a and b are the same numbers. If we multiply the same number on each side, the answer will be the same. However, x and y have different values. So, it will show differently.

Let's have an example:

It we say a = 5, x = 6, y = 7.

We know a and b are the same number so, both a and b will be 5. If we multiply a by x, it will be 5 x 6 which is 30. It will show the same answer on multiplying b because as you said a and b are the same. The equation will be 5(a) x 6(x) = 5(b) x 6(x) Let's look at multiplying y. If we multiply a by y, it will be 5 x 7 which is 35. As you said it will show the same answer on multiplying b because a and b are the same. The equation for this will be 5(a) x 7(y) = 5(b) = 7(y). Finally, let's compare the two equations.

5(a) x 6(x) = 5(b) x 6(x) -> 30 = 30

5(a) x 7(y) = 5(b) = 7(y) -> 35 = 35

You can see it more clearly when we compare those to the equations that I made.

Thank you

Yes, if a = b, then ax = bx and ay = by for any value of x.

This is because the equation a = b implies that a and b are equal in value, so any expression involving a can be replaced with an equivalent expression involving b. In other words, any operation performed on a can be performed on b and produce the same result.

For example, if a = b, then multiplying both sides of the equation by x yields ax = bx, and multiplying both sides of the equation by y yields ay = by. This means that any power, root, logarithm, or other mathematical operation performed on a can also be performed on b and produce the same result.

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The dimension of side a in the right triangle is 3.516.

From the diagram, the figure is a right triangle.

From  trigonometric ratio;

Tangent = Opposite / Adjacent

Hence;

tan( θ ) = a / b

Plug in the given values and solve for a

tan( 38 ) = a / 4.5

a = tan( 38 ) × 4.5

a = 3.516

Therefore, the value of a is 3.516.

Option B) 3.516 is the correct answer.

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Answer: y = x + 19

Step-by-step explanation:

y=4x+15-4x+4=12

y=4x-4x=15+12+4

y=x+19

Answer:

Nick earns a commission of 12/100 * $668 = $80.16 for the software he sold this week.

Step-by-step explanation:

Deductive reasoning is used.

Deductive reasoning is the logic process of drawing a conclusion applying a general rule to a specific case.

To solve the equation 5x + 7 = 12 you apply this:

Rule                                                        application      

Subtraction property of equality          5x = 12 - 7

Simplification                                         5x = 5

Division property of equality                 x = 5/5

Simplification                                          x = 1.

Thus, by using the general rules to the specific equation, you get the result x = 1, which shows that this is a case of deductive reasoning.

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The possible set of inequalities that represent the situation is -

r + c ≥ 80

1.45r + 0.65c ≤ 200

Given is that Victor went to buy some flowers from the flower shop.

We can write the possible set of inequalities as -

r + c ≥ 80

1.45r + 0.65c ≤ 200

Therefore, the possible set of inequalities that represent the situation is -

r + c ≥ 80

1.45r + 0.65c ≤ 200

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The equation of the secant line containing the points (-7,g(-7)) and (8,g(8)) is

y = (123/15)x + (98 - (123/15) * (-7))

The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept. To find the equation of the secant line, we need to find the slope (m) and the point of intersection (x,y) of the line with the y-axis.

To find the slope (m) of the secant line, we can use the formula:

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

where (x1,y1) = (-7, g(-7)) and (x2,y2) = (8, g(8)).

So, m = (g(8) - g(-7)) / (8 - (-7)) = (g(8) - g(-7)) / 15

Now, we can substitute the value of g(x) in the above equation and get the value of m

g(x) = 2x^2-7

m = (2(8^2)-7 - 2(-7^2)-7) / 15 = (2(64)-7 - 2(49)-7) / 15 = (128-7-98-7) / 15 = 123/15

To find the point of intersection (x,y) of the line with the y-axis, we can use one of the given points and the slope. Let's use the point (-7,g(-7))

y = mx + b

g(-7) = m * (-7) + b

b = g(-7) - m * (-7)

We can substitute the value of g(x), m and x = -7 in the above equation and get the value of b.

g(x) = 2x^2-7

b = 2(-7)^2-7 - m * (-7) = 2(49)-7 - 123/15 * (-7) = 98 - 123/15 * (-7)

So, the equation of the secant line containing the points (-7,g(-7)) and (8,g(8)) is

y = (123/15)x + (98 - (123/15) * (-7))

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The statement does not imply that there are any.

(a) i. ∃x (K(x) ∧ ¬K(x))

This statement translates to "there exists an x such that x is a knight and x is not a knight".

ii. We can conclude that there is at least one Knight and at least one Knave on the island, since the statement implies that there are some inhabitants who are both.

(b) i. ∀x ¬K(x)

This statement translates to "for all x, x is not a knight".

ii. We can conclude that there must be at least one Knave on the island, since the statement implies that all inhabitants are Knaves. However, we cannot conclude anything about the presence of Knights on the island, since the statement does not imply that there are any.

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The function h(x) can be expressed as a composition of two other functions: f(x) and g(x).

In mathematics, functions are a way to describe relationships between variables.

The function f(x) is defined as 2 raised to the power of x. This means that for any value of x, the output of the function f(x) will be 2 raised to that power.

If x is 3, then f(3) = 2³ = 8.

The function g(x) is defined as x. This means that the output of the function g(x) will be the same as its input.

If x is 4, then g(4) = 4.

Combining these two functions, we can express h(x) as f(g(x) + 6). This means that for any value of x, the output of h(x) will be 2 raised to the power of g(x) plus 6.

If x is 2, then g(2) = 2, and

=> h(2) = f(g(2) + 6) = f(8) = 2⁸ = 256.

In summary, the function f(x) raises 2 to the power of x, and the function g(x) returns its input.

By combining these two functions, we can express h(x) as the result of 2 raised to the power of g(x) plus 6.

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Answer:

1.5

Step-by-step explanation:

42/28 =6/4=1.5

33/1.5=22