(sin alpha +cos alpha )2

The conclusion regarding the publisher's claim regarding the hypothesis is that have sufficient evidence to support the claim that the proportion is less than 30% of their readers own a Rolls Royce.

The null hypothesis is a statistical theory that suggests that no statistical relationship and significance exists in a set of given single observed variable, between two sets of observed data and measured phenomena.

Since we reject the null hypothesis , we have sufficient evidence to support the claim. In this case, we have sufficient evidence to support the claim that the proportion is less than 30% of their readers own a Rolls Royce.

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Complete question:

A newsletter publisher believes that less than 30% of their readers own a Rolls Royce. For marketing purposes, a potential advertiser wants to confirm this claim. After performing a test at the 0.02 level of significance, the advertiser decides to reject the null hypothesis. What is the conclusion regarding the publisher's claim?

Using the normal distribution, the value of z is of z = 1.5.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

For this problem, considering the symmetry of the normal distribution, the area above the mean is given by:

0.8664/2 = 0.4332.

Hence z has a p-value of 0.5  + 0.4332 = 0.9332, hence the value of z is z = 1.5.

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Using a calculator, the critical value for the t-distribution with a confidence level c=0.80 and sample size n=29 is of Tc = 1.3125.

It is found using a calculator, with two inputs, which are given by:

In this problem, the inputs are given as follows:

Hence, using a calculator, the critical value for the t-distribution with a confidence level c=0.80 and sample size n=29 is of Tc = 1.3125.

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Using the monthly payment formula, it is found that:

It is given by:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

In which:

Considering that she must pay 20% down, the parameters are given by:

P = 0.8 x 2900 = 2320, r/12 = 0.085/12 = 0.007083, n = 24.

Hence the monthly payments are found as follows:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]A = 2320\frac{0.007083(1.007083)^{24}}{(1.007083)^{24} - 1}[/tex]

A = $105.46.

The total finance charge is composed by the down payment plus the 24 monthly payments, hence:

F = 0.2 x 2900 + 24 x 105.46 = $3,111.04.

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The number of bars which can be cut for the 1" X 1" and 2" X 2" square bars are; 117 and 29 units respectively.

The total area of the given pan can be evaluated as follows;

Area = length × width

= 9 × 13

= 117 square units.

Hence, the number of 1" X 1" bars can be cut which can be cut from the pan;

= 117/(1×1)

= 117 1" X 1" bars.

For the 2" X 2" square bars, we have;

= 117/(2×2);

29 remainder 1 square unit.

Ultimately, one square unit of the pan is wasted for the 2" X 2" square bars.

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a) The factor form of the polynomial is f(x) = 4 · (x - 3) · (x + 5 / 4).

b) The values of the x-intercepts of the graph of f(x) are represented by the roots found in part a).

c) The function has a minimum and grows in the + y direction.

d) Marking the two x-intercepts, second, generating a line perpendicular to the x-axis that passes the midpoint of the line segment generated by the two intercepts and estimate the location of the vertex and, finally, creating a parabola with a minimum and growing in the + y direction by matching the points.

In this problem we have a quadratic function in standard form, that is, an equation of the form f(x) = a · x² + b · x + c, where a, b and c are real coefficients. a) First, we need to complete the square and find the roots to determine the factorized form:

4 · x² - 7 · x - 15 = 0

4 · [x² - (7 / 4) · x - (15 / 4)] = 0

x² - (7 / 4) · x - (15 / 4) = 0

x² - 2 · (7 / 8) · x - (15 / 4) + (289 / 64) = 289 / 64

x² - 2 · (7 / 8) · x + 49 / 64 = 289 / 64

(x - 7 / 8)² = 289 / 64

x - 7 / 8 = ± 17 / 8

x = 7 / 8 ± 17 / 8

Then, the factor form of the polynomial is f(x) = 4 · (x - 3) · (x + 5 / 4).

b) The values of the x-intercepts of the graph of f(x) are represented by the roots found in part a).

c) The end behavior of the graph is inferred from the lead coefficient. A positive coeffcient , which is the case of the function, indicates that vertex of the polynomial is a minimum and parabola grows in the + y direction.

d) In accordance with algebra, we can generate a quadratic equation by knowing three distinct points on Cartesian plane.

First, mark the two x-intercepts, second, generate a line perpendicular to the x-axis that passes the midpoint of the line segment generated by the two intercepts and, finally, generate a parabola with a minimum and growing in the + y direction.

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[tex]\frac{7}{4}[/tex] [tex]x\:-\:2\:=\:-5x\:+\:1[/tex]

[tex]\frac{7}{4}[/tex] [tex]x\:-\:2\:=\:-5x\:+\:1[/tex]

[tex]7x\: - \:8 \:=\: -20x\: + \:4 [/tex]

[tex]7x \:- \:8 \:+ \:20x \:= \:4[/tex]

[tex]7x\: + \:20x \:= \:4 \:+ \:8 [/tex]

[tex]27x\: = \:4\: + \:8[/tex]

[tex]x\:= [/tex] [tex]\frac{4}{9}[/tex]

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Answer:

x = 4/9

Step-by-step explanation:

Solve for x

7/4 x -2  = -5x +1

Add 5x to each side

7/4 x -2+5x  = -5x +1+5x

7/4 x  + 5x -2  = 1

Get a common denominator for the x terms

7/4x  +20/4x -2 = 1

Add 2 to each side

27/4 x -2+2 = 1+2

27/4 x = 3

Multiply each side by 4

27/4 x *4 = 3*4

27x = 12

Divide each side by 27

27x/27 = 12/27

x = 12/27

Simplify

x = 4/9

The number with the given characteristics is 17

Let the tens be x and the units be y.

So, the number is 10x + y

The relationship between the digits is

y = x + 6

The relationship between the number and the reverse is

2(10x + y + 10y + x) = 6 + 10 * (10x + y)

Simplify the second equation

2(11x + 11y) = 6 + 100x + 10y

Open the brackets

22x + 22y = 6 + 100x + 10y

Substitute y = x + 6

22x + 22(x + 6) = 6 + 100x + 10(x + 6)

Expand

22x + 22x + 132 = 6 + 100x + 10x + 60

Collect like terms

22x + 22x - 100x - 10x = 6 + 60 - 132

Evaluate the like terms

-66x = -66

Divide by -66

x = 1

Substitute x = 1 in y = x + 6

y = 1 + 6

y = 7

Recall that the number is 10x + y

So, we have

Number = 10 * 1 + 7

Evaluate

Number = 17

Hence, the number is 17

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By using an online graphing calculator, the overall equation represented by this scenario is plotted in the image attached below.

Based on the information provided about this company with respect to its delivery and total number of miles to be covered, we would assign variables as follows:

Next, we would translate the word problem into an algebraic equation by using an inequality:

y > x/2 - 3

Also, we would determine the intercepts as follows:

When x = 0, we have;

y = 0/2 - 3

y = -3.

y-intercept = (0, -3).

For the x-intercept, we have:

When y = 0, we have;

0 = x/2 - 3

x/2 = 3

x = 6.

x-intercept = (6, 0).

By using an online graphing calculator, the overall equation represented by this scenario is plotted in the image attached below.

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Answer:

c

Step-by-step explanation:

c is the answer

Answer:

2160°

Step-by-step explanation:

[tex]180(14-2)=2160^{\circ}[/tex]

[tex]number \: of \: performances = 9 \\ note = \\ one \: insists \: on \: being \: last \\ number \: of \: flexible \: performances = 9 - 1 = 8 \\ \\ c( \gamma ) = 8P8 \times 1 \\ c( \gamma ) = 8! \\ c( \gamma ) = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 \\ c( \gamma ) = 40320 \: ways[/tex]

Answer:i got 329

Step-by-step explanation:

The set of natural numbers greater than or equal to 6 will be 6, 7, 8, 9, 10, ....

It should be noted that the first information is about the set of natural numbers greater than or equal to 6. Therefore, they will be 6 and above.

It should be noted that the descriptive form simply states in words the elements that are in a set. It is the verbal description of the elements in the set. It is the determination of the elements that belong to a set and those that doesn't.

Also, the way that a set is described is known as the roster form. In this case, the contents of a set can be described by listing the elements that are in the set which are separated by a comma inside the bracket.

Also, the roster form: (5, 7, 9, 11) indicates odd natural numbers. The numbers that are given are odd.

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The two-column proof that shows that ΔEAB ≅ ΔDCB by SAS congruence theorem is explained below.

The Side-angle-side congruence theorem (SAS) that states that two triangles that are have two pairs of corresponding congruent sides and a pair of included corresponding congruent angles are congruent to each other.

Any triangle with two equal base angles is referred to as an isosceles triangle, The sides opposite these base angles are also congruent to each other.

Given the diagram below, the proof is expressed as follows:

Statement 1: ΔEAB and ΔDCB are two right triangles

Reason 1: Given

Statement 2: ∠EAB  ≅ DCB

Reason 2: Right angles

Statement 3: ∠BED ≅ BDE

Reason 3: Given

Statement 4: ΔBED is an isosceles triangle

Reason 4: Definition of isosceles triangle

Statement 5: BE ≅ BD

Reason 5:  Definition of isosceles triangle

Statement 6: ΔEAB ≅ ΔDCB

Reason 6: SAS

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Answer:

-2s-18 is the simplified answer

Step-by-step explanation:

s-3(s+6)

distributive property

s-3s-18

-2s-18

Answer:

(A)81/399

Step-by-step explanation:

The probability that the Principal selects a voyager on the first try is

82/400

Since another student is to be selected, the total population has reduced by 1 and the number of voyagers has been reduced by 1.

Probability that another voyager is selected on the second try is

81/399

The correct answer is A.

Answer:

Trapezoid

Step-by-step explanation:

One pair of parallel sides.

Answer:

4, 6, 4

6, 12, 8

8, 12, 6

Step-by-step explanation:

Tetrahedron:

4 faces, 6 edges, 4 vertices

Cube:

6 faces, 12 edges, 8 vertices

Octahedron:

8 faces, 12 edges, 6 vertices

you can also use the v - e + f = 2 to check

By using the PEMDAS order of operations, we get 3(6+7) = 39.

The equation be 3(6+7) then the correct answer is 34.

The order of operations exists as a law that describes the proper sequence of stages for estimating a math expression. We can recognize the order utilizing PEMDAS: Parentheses, Exponents, Multiplication, Division (from left to right), Addition, and Subtraction (from left to right).

Given: 3(6+7)

By using the PEMDAS order of operations, we get

(6+7) = 13

Then we get

3(6+7) = 3 [tex]*[/tex] 13

= 39.

Therefore, the value of 3(6+7) = 39.

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Answer:

5/16

Step-by-step explanation:

assuming you mean 5(1/2) = 8x

5(1/2) is the same as 5/2

so, 5/2 = 8x

5 = 16x

x= 5/16

Answer: 2.25 meters

Step-by-step explanation: 1 in = 2 meters. 0.75 is 75 percent of 1 so the length of the window is 75 percent of 2 which is 1.5. 1.5 squared is 2.25 so the length of the window is 2.25 meters

The three dimensional shape formed by the net shown below is a cube.

A three dimensional shape is a shape that has length, width and height. Examples of three dimensional shapes are cone, cylinder, prism and pyramid.

A two dimensional shape is a shape that have both length and width. Examples of two dimensional shape are circle, rectangle, square.

The cube is a a three-dimensional solid object bounded by six square faces.

The three dimensional shape formed by the net shown below is a cube.

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subtracting (c ^ 2 - 4c + 7) from (7c ^ 2 - 5c + 3) would give 6c² - 9c -4

Given the expressions as

(c ^ 2 - 4c + 7)

(7c ^ 2 - 5c + 3)

We are to substract expression 2 from expression 1

In doing this, we need to know the BODMAS rule ( bracket, of, division, multiplication, addition and subtraction). This would help in finding the solution

(7c ^ 2 - 5c + 3) -  (c ^ 2 - 4c + 7)

Expand the bracket

7c² - 5c + 3 - c² - 4c + 7

collect like terms

7c²- c² - 5c - 4c + 3 - 7

Add or substract the like terms

6c² - 9c -4

Thus, subtracting (c ^ 2 - 4c + 7) from (7c ^ 2 - 5c + 3) would give 6c² - 9c -4

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Answer:6c^2-c-4

Step-by-step explanation:

(7c^2-5+3)-(c^2-4c+7)

7c^2-5c+3-c^2+4c-7

Rearrange the terms

7c^2-c^2-5c+4c+3-7

Combine like terms

6c^2-c-4

Answer:

C. Subtract 4 from both sides.

Step-by-step explanation:

You need the equation in the form x² + ax + b = 0 to then either try factoring or use the quadratic formula.

In order to achieve that, you need to first:

Subtract 4 from both sides.

Hello and Good Morning/Afternoon:

Let's take this problem step-by-step:

When we expand a function, everything must be multiplied out evenly.

      [tex](x+6)*(x+6)\\=x*x +x*6+6*x+6*6\\=x^2 + 6x + 6x+36\\x^2 +12x+36[/tex]

Answer: x² + 12x + 36

Hope that helps!

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Polynomials are mathematical expressions made up of many terms.

To simplify the polynomial to the maximum, all like terms must be grouped together and rearranged from highest to lowest power.

Distribute

Combining like terms.

Answer:

38°

Step-by-step explanation:

EFGH is an isosceles trapezoid (a trapezoid with two congruent legs is isosceles)

∠HGF=70° (base angles of an isosceles trapezoid are congruent)

∠EGH=32° (angles in a triangle add to 180°)

∠FGE=38° (angle subtraction postulate)

The closest approximate average rate of change for Edna's profits from the 18th month to the 21st month is 14

From the question, we have the following ordered pairs

x intercepts = (6,0) and (18, 0)

Vertex = (12, -36)

Points (21, 41.25)

The closest approximate average rate of change for Edna's profits from the 18th month to the 21st month is the calculated using

m = [f(21) - f(18)]/[21 - 18]

This becomes

m = [f(21) - f(18)]/3

Substitute the known values in the above equation

m = [41.25 - 0]/3

Evaluate the difference

m = 41.25/3

Evaluate the quotient

m = 13.75

Approximate

m=14

Hence, the closest approximate average rate of change for Edna's profits from the 18th month to the 21st month is 14

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Complete question

The graph below shows the value of Edna's profits f(t), in dollars, after t months:

What is the closest approximate average rate of change for Edna's profits from the 18th month to the 21st month?

See attachment for graph

Answer:

A

Step-by-step explanation:

p = Pierre shells

Nardia shells = 3p

3p + p = 52

Answer:

a

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

3x + 3   =  6 + 6

3x + 3   =  12

3x         =  12 - 3

3x         =  9

   x        =  3

3 (3) + 3   =  6 + 6

   9  + 3   =  12

       12     =  12