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Part 1
For the statement​ below, write the claim as a mathematical statement. State the null and alternative hypotheses and identify which represents the claim.
An amusement park claims that the mean daily attendence at the park is people.

To find the factors of the polynomial function g(x) = x^3 + 2x^2 - x - 2, we can use different methods such as long division, synthetic division, or grouping.

Using long division, we can divide g(x) by (x-1), which is a factor by the factor theorem:

            x^2 + 3x + 2

    ___________________________

x - 1 | x^3 + 2x^2 - x - 2

    - (x^3 - x^2)

      --------

          3x^2 - x

      - (3x^2 - 3x)

        ----------

                 2x - 2

        - (2x - 2)

          --------

                   0

Therefore, we have factored g(x) as:

g(x) = (x - 1)(x^2 + 3x + 2)

We can further factor the quadratic term using factoring or quadratic formula to obtain the complete factorization of g(x).

The factors of polynomial function g(x) = x³ + 2x² - x - 2 are (x-1), (x+1), and (x+2).

This can be obtained by factoring the polynomial using the grouping method.

Using this method, we group the first two terms together and the last two terms together, resulting in (x²{2 + 2)(x-1) = 0. This gives us two possible roots, x = 1 and x = ±√2i.

However, as we are only interested in real factors, we only consider the real root of x = 1.

G(x) can then be divided by (x-1) using linear long division, yielding the quotient x² + 3x + 2. This quotient can then be factored as (x+1)(x+2). Therefore, the factors are (x-1), (x+1), and (x+2).

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Answer:

A. They are one-dimensional

B. They connect two endpoints

Both statements A and B are true about line segments. Line segments are one-dimensional figures that have two endpoints and connect them with a straight path.

Statement C is not true. Line segments do not have a unit of measure on their own, but their length can be measured using a unit of measure such as inches, centimeters, or meters.

Statement D is not true either. Line segments are flat, one-dimensional objects and cannot grow to become three-dimensional objects. However, multiple line segments can be connected to form a three-dimensional object, such as a cube or pyramid.

The value of measure of ∠ RST is,

⇒ ∠ RST = 34°

We have to given that;

In circle S with m ∠RUT = 17°

Hence, We get;

⇒ ∠ RST = 2 × ∠ RUT

⇒ ∠ RST = 2 × 17°

⇒ ∠ RST = 34°

Thus, The value of measure of ∠ RST is,

⇒ ∠ RST = 34°

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Answer:

9/13

Step-by-step explanation:

P(odd or less than 5) = number of odd cards + number of cards less than 5 / total number of cards

P(odd or less than 5) = (20 + 16) / 52

P(odd or less than 5) = 36 / 52

P(odd or less than 5) = 9 / 13

Therefore, the probability of picking an odd card or a card less than 5.

Answer is 9/13

Answer:

C. 84.8 m

Step-by-step explanation:

Circumference of circle = D x 3.14

D = 27 m

Let's solve

27 x 3.14 = 84.78 m

So, the circumference of the circle is C. 84.8 m

Answer:

Option C) 84.8 is the correct answer.

Step-by-step explanation:

Here we have given that the diameter of circle is 27 m and we have to find the circumference of circle. The formula to find circumference of circle is :

[tex]\dashrightarrow\sf{C = \pi d}[/tex]

Where :

Thus, finding the circumference of circle by substituting the given values in the formula :

[tex]\dashrightarrow\sf{C = \pi d}[/tex]

[tex]\dashrightarrow\sf{C = \pi \times d}[/tex]

[tex]\dashrightarrow\sf{C = 3.14 \times 27}[/tex]

[tex]\dashrightarrow\sf{C = 84.78 \: m}[/tex]

[tex]\dashrightarrow\sf{C \approx 84.8\: m}[/tex]

Hence, the circumference of circle is 84.8 m.

The equation that represents a linear function is D 4x - 2 = 6.

A linear function is a function whose graph is a straight line. In general, the equation of a linear function can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Option A (x = 1) represents a vertical line passing through x = 1. Since the slope of a vertical line is undefined

Option B (y = 12²) represents a horizontal line passing through y = 144. Since the slope of a horizontal line is zero

Option C (y = 12-1) represents a horizontal line passing through y = 11. Since the slope of a horizontal line is zero

Option D (4x - 2 = 6) can be rewritten as 4x = 8 or x = 2. This is the equation of a vertical line passing through x = 2.

Therefore, the only equation that represents a linear function is D 4x - 2 = 6.

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Ian earned $500 in simple annual interest after 10 years, while Jackson earned $1,128.89 more in interest than Ian after 10 years due to compound interest.

Ian's account earns simple annual interest, which means that he earns 5% interest on his initial deposit every year. After 10 years, he will have earned

interest = principal x rate x time

interest = 1000 x 0.05 x 10

interest = $500

Jackson's account earns interest that is compounded annually, which means that he earns 5% interest on his initial deposit plus any interest that has already been earned every year. After 10 years, he will have earned

[tex]balance = principal x (1 + rate)^{time}[/tex]

balance = 1000 x (1 + 0.05)¹⁰

balance = $1,628.89

To find out how much more interest Jackson earned than Ian, we need to subtract the interest Ian earned from the balance in Jackson's account

$1,628.89 - $500 = $1,128.89

Therefore, Jackson earned $1,128.89 more in interest than Ian after 10 years.

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The x-intercept of the graph is (0,0).

On a graph, the x-intercept is the point at which a line crosses the x-axis. At that time, the y coordinate has no value. The y-intercept is the point where the line crosses the y-axis. The x coordinate has no value. For example, y = x + 5 would intersect the x-axis at (-5, 0), forming the x-intercept.

From the figure, it is clear that the line crosses the X-axis at the origin, which means that x - coordinate 0 keeping y -coordinate is also zero.

Which means that the x-intercept of the graph is (0,0).

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Answer:

691m^2

Step-by-step explanation:

This one is simpler than it looks. If you imagine the shape as a rectangle and two triangles, then move the triangle on the left over to the one on the right, the shape becomes a normal rectangle. Simply solve like your everyday quadrilateral.

area = base × height

a = 21m × 33m

a = 691m^2

Answer:

5 > [tex]\sqrt{18[/tex]

Step-by-step explanation:

The square root of 18 is approximately 4.24.

5 is greater than 4.24, so we can use the inequality sign >.

Because it gives exactly one output value for each input value, a(x) is a function, hence the answer is yes. Since several input values might result in the same output value, it is not a one-to-one function.

A mathematical item called a function accepts an input and creates an output. It looks like an apparatus with an input and an output. A formula or a graph can both be used to express a function. For instance, the function f(x) = x² returns the square of an input x as output.

Because it gives exactly one output value for each input value, a(x) is a function, hence the answer is yes. Since several input values might result in the same output value, it is not a one-to-one function. A(x) is not one-to-one, for instance, because a(1) and a(3) are both equal to 1.

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The correct option is- I, IV. Fixed Annuity and Traditional IRA are the plans are  not considered a defined contribution plan.

In contrast, a defined contribution plan does not guarantee a certain level of benefits at retirement. Under these plans, either the employee or even the employer (or both) may make contributions to the owner's individual account under the plan.

Traditional IRA:

An individual retirement account (IRA) of this type allows your income to increase tax-free. Only when you take withdrawals in retirement do you have to pay taxes on the investment earnings.

Fixed Annuity:

A fixed annuity is a financial contract that offers a retirement income stream and guarantees a certain rate of return, such as 2%. You can predict how much your annuity will increase and how much money it will produce by using a set interest rate.

Thus, Fixed Annuity and Traditional IRA are the plans are  not considered a defined contribution plan.

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Answer:

s^2+2s-8

Step-by-step explanation:

(s-2)(s+4)

=s^2+4s-2s-8

simplified= s^2+2s-8

Answer:

s^2+2s-8

Step-by-step explanation:

(s-2)(s+4)

=s^2+4s-2s-8

simplified= s^2+2s-8

The value of 5 cubic cm in liters, can be converted to be

To convert cubic centimeters (cm³) to liters (L), we can use the following conversion factor:

1 L = 1000 cm³

This means that 1 liter is equal to 1000 cubic centimeters. To convert cubic centimeters to liters, we can divide the number of cubic centimeters by 1000.

For example, to convert 5 cubic cm to liters:

5 cm³ ÷ 1000 = 0.005 L

Therefore, 5 cubic cm is equal to 0.005 liters (or 5 mL).

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Full question:

5 cubic cm to Liters

Answer:

Okay, based on your previous question and the analysis, the 3 statements that are true about the function f(x) = x2 – 5x + 12 and its graph are:

   The graph of the function is a parabola.

   The graph contains the point (0, 0).

So the options you should select are:

2) The graph of the function is a parabola.

   The graph contains the point (0, 0).

Let me know if selecting options 2 and 5 makes sense! I can provide any additional details or clarification if needed.

Please let me know if you have any other questions! I'm happy to help explain any other concepts related to this quadratic function and its graph.

Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 .The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).

Okay, just to reiterate, based on the previous analysis, the 3 statements that are TRUE about the quadratic function f(x) = x2 – 5x + 12 and its graph are:

   The graph of the function is a parabola. (true)

   The graph contains the point (0, 0). (true)

   The graph of the function opens down. (false, unknown without seeing graph)

   The value of f(–10) = 82 (false)

   The graph contains the point (20, –8). (false)

So you should select options:

2) The graph of the function is a parabola.

   The graph contains the point (0, 0).

Please let me know if selecting these 3 options makes sense and matches the analysis. I can re-explain anything if needed.

Your selected options should be:

2) The graph of the function is a parabola.

   The graph contains the point (0, 0).

   The graph of the function opens down.

Let me know if these look correct or if you have any other questions! I'm happy to help explain further or go over any part of the analysis.

Please select options 2, 5 and 3 as the statements that are true about the quadratic function and its graph.

Step-by-step explanation:

the criteria is required to ensure communication competence is The message achieves the intended effect. Option A

Communicative competence is simply described as the ability to achieve communicative goals in an appropriate and socially way.

It is well organized and goal-oriented, this means that it involves the ability to evenly select and apply skills that are appropriate and are also effective in a given context.

The different components of communication competence are;

Hence, the message should  always be effective for the context.

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The face value of the note is $9,000.

The face value of a note is the principal value mentioned or stated on the note.

The face value is different from the maturity value or the discounted value.

The maturity value refers to the face value plus accumulated interest.

The discounted value is a value less than the maturity value received for discounting the note before its maturity date.

The face value of the note = $9,000

Note period or maturity period = 60 days

Note interest = 8%

Note issuance date = April 15

Note maturity date = June 14

Maturity value = $9,120 ($9,000 + $9,000 x 8% x 60/360)

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The surface area is 653.1 square centimeters.

What is surface area?

A three-dimensional object's surface area is the space it takes up when viewed from the outside.

Here the given inner cylinder diameter d = 7m then

Radius r= d/2 = 7/2 = 3.5m

Now outer cylinder diameter = 9 cm then

Radius R= d/2 = 9/2 = 4.5 cm.

Height h = 26 cm.

Now using surface area of cylinder formula then,

=> Surface area A = [tex]\pi (R^2-r^2)h[/tex] square unit.

=> A = [tex]3.14(4.5^2-1.5^2)26[/tex]

=> A = [tex]3.14\times(20.25-12.25)\times26[/tex]

=> A = 3.14×8×26

=> A = 653.1 square centimeters.

Hence the surface area is 653.1 square centimeters.

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Answer:

  (a) ±{1, 2, 5, 10}

  (b) attached

  (c) {-2, -1, 5}

  (d) P(x) = (x +2)(x +1)(x -5)

Step-by-step explanation:

You want the possible and actual rational zeros for P(x) = x^3-2x^2-13x-10, and the factored form of the polynomial.

The rational root theorem tells you the possible rational zeros of a polynomial will be of the form ...

  ±(divisor of the constant)/(divisor of the leading coefficient)

The leading coefficient is 1, and the divisors of the constant are {1, 2, 5, 10}, so the possible rational zeros are ...

  {±1, ±2, ±5, ±10}

The attached graph shows the actual zeros of P(x) to be {-2, -1, 5}.

Each zero q corresponds to a factor (x -q). The factored form of the polynomial is ...

  P(x) = (x +2)(x +1)(x -5)

the scale factor used in the dilation of triangle D to create triangle D' is one-third. This means that every length in triangle D' is one-third the length of the corresponding length in triangle D.

How to solve the question?

To determine the scale factor used in the dilation of triangle D to create triangle D', we need to compare the corresponding sides of both triangles. The corresponding sides of two similar triangles are proportional, meaning that they have the same ratio.

In this case, we can see that the length of every side of triangle D' is one-third the length of the corresponding side of triangle D. For example, the length of the shortest side of triangle D is 18, while the length of the shortest side of triangle D' is 6. Similarly, the length of the longest side of triangle D is 30, while the length of the longest side of triangle D' is 10.

We can use this information to find the scale factor by dividing the length of any side of triangle D' by the length of the corresponding side of triangle D. Let's choose the shortest side for this calculation:

scale factor = length of corresponding side in D' / length of corresponding side in D

scale factor = 6 / 18

scale factor = 1/3

Therefore, the scale factor used in the dilation of triangle D to create triangle D' is one-third. This means that every length in triangle D' is one-third the length of the corresponding length in triangle D.

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Answer: 4

Step-by-step explanation:

The measure of the angle between the vectors is approximately 41.41 degrees.

When we join two line segments at a single point, an angle is formed, or we can say, an Angle is a combination of two line segments at a common endpoint. This common point is called Vertex of the angle and the two line segments are sides or arms of the angle formed.The sum of all the angles of a triangle (of all types) is equal to 180°. The sum of the length of the two sides of a triangle is greater than the length of the third side. In the same way, the difference between the two sides of a triangle is less than the length of the third side.

To find the angle between two vectors, we can use the dot product formula:

cos(theta) = (u · v) / (|u| |v|)

where u · v is the dot product of u and v, and |u| and |v| are the magnitudes of u and v, respectively.

First, let's calculate the dot product of u and v:

u · v = 3 × 4 + 4 × 3 = 24

Next, we need to calculate the magnitudes of u and v:

|u| = √(3² + 4²) = 5

|v| = √(4² + 3²) = 5

Now we can plug these values into the formula for cosine:

cos(theta) = (u · v) / (|u| |v|)

cos(theta) = 24 / (5 * 5)

cos(theta) = 24 / 25

To find the measure of the angle, we need to take the inverse cosine (or arccos) of this value:

theta = arccos(24/25)

theta ≈ 0.7227 radians or 41.41 degrees

So the measure of the angle between the vectors is approximately 41.41 degrees.

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The amount of insecticide that Vivian needs to purchase

for the control of pest in the lawn would be = 198.08 ounces

To calculate the area of the rectangular lawn, the formula for the area of rectangle should be used. That is ;

Area = Length× width

Length = 123.8 feet

width = 80feet

Area = 123.8× 80 = 9,904ft²

But 0.02 ounces of insecticide = 1 ft²

X ounces = 9,904ft²

Make X the subject of formula;

X = 9904×0.02

= 198.08 ounces.

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Answer:

Brother asked a very good question.

We can write the given arithmetic expressions into equations as follows:

70 + 15 = 85

This can be written as an equation: x + 15 = 85, where x is the unknown value that needs to be determined.

125 + 85 = 210

This can be written as an equation: y + 85 = 210, where y is the unknown value that needs to be determined.

These equations can be used to solve for the unknown values x and y by performing inverse operations (such as subtraction or division) to isolate the unknown variable on one side of the equation.

Applying the properties of a rhombus, we have:

AB = BD = CD = AC = 11

A rhombus is a type of quadrilateral, which is a four-sided polygon with four angles. A rhombus is a special type of parallelogram in which all four sides are equal in length.

Therefore, we would create an equation to find the value of  using the properties of rhombus:

2x - 3 = x + 4

2x - x = 3 + 4

x = 7

AB = 2x - 3 = 2(7) - 3 = 11

All sides are equal, therefore:

AB = BD = CD = AC = 11

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The value of D represents the vertical displacement or shift of the basic cosine graph. Therefore, the vertical displacement of the given graph is pi - 3.

What is Displacement?

In physics, displacement refers to the distance and direction of an object's change in position from its starting point. It is a vector quantity that measures the overall change in position of an object, regardless of the path it took to get there. Displacement can be positive, negative, or zero depending on the direction and distance of the movement.

To find the vertical displacement of the basic graph to produce a graph of y = pi - 3 cos(x - 2), we need to compare the given equation with the general cosine function y = A cos(Bx - C) + D.

Here, A = 3, B = 1, C = 2, and D = pi - 3.

The value of D represents the vertical displacement or shift of the basic cosine graph. Therefore, the vertical displacement of the given graph is pi - 3.

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Asnwer: 30 minutes

Explanation:

10 laps in 20 minutes is 1 lap every 2 minutes.

So we get this:

1 lap = 2 minutes

But we want 15 laps, so multiply both sides by 15 to get:

15 laps = 30 minutes

Answer:

[tex] \frac{w}{3} [/tex]