angela is seeking a venue for her school’s athletic council banquet.Primo Banquet Hall charges $2000 plus $50 per person.The Lookout Banquet Hall charges $1500 plus $75 per person.
a)write an equation to represent each banquet hall
b)when do both halls charge the same amount
c)which hall should angela choose?explain indicating intervals

Answer:

b, c and e

Step-by-step explanation:

Given

See attachment for functions

Required

Select all statements that contain both functions

First, calculate the rate (slope) of both functions.

This is calculated as:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

For Alec's

[tex](x_1,y_1) = (0,3)[/tex]

[tex](x_2,y_2) = (2,9)[/tex]

So, the slope is:

[tex]m = \frac{9 - 3}{2 - 0}[/tex]

[tex]m = \frac{6}{2}[/tex]

[tex]m =3[/tex]

For Beth's

[tex](x_1,y_1) = (5,17)[/tex]

[tex](x_2,y_2) = (12,38)[/tex]

So, the slope is:

[tex]m = \frac{38 - 17}{12 - 5}[/tex]

[tex]m = \frac{21}{7}[/tex]

[tex]m =3[/tex]

Beth and Rec have the same slope. Hence, they save at the same rate.

Next, determine the amount they started with.

This implies that we calculate y when x = 0

From Alec's graph.

[tex](x,y) = (0,3)[/tex]

Alec's initial savings is 3

For Beth's savings, we make use of slope formula.

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex](x_1,y_1) = (5,17)[/tex]

[tex](x_2,y_2) = (0,y)[/tex]

So, we have:

[tex]3 =\frac{y - 17}{0 - 5}[/tex]

[tex]3 =\frac{y - 17}{ - 5}[/tex]

[tex]y - 17 = -15[/tex]

[tex]y = 17 -15[/tex]

[tex]y = 2[/tex]

Beth's initial savings is 2

Hence, Alec started with more money

Next, is to determine who has more money after 10 days.

Since they save at the same rate, the difference in their savings after any number of days will be the difference in their initial savings.

The difference (d) is calculated as:

[tex]d = 3 - 2[/tex]

[tex]d = 1[/tex]

Hence, Alec will have $1 more than Beth after 10 days

Answer:

its bc and e or Alec and Beth are saving at the same rate. Alec started with more money than Beth. and At 10 days, Alec will have $1 more than Beth in savings.

Step-by-step explanation:

(x + 5)^2 + (x/2 + 6)^2 = (30)^2

Take it from here.

Answer:

pole height = 29 ft

Step-by-step explanation:

x² = 30² - (1/2x + 6)² = 30² - (1/4x² + 6x + 36) = 900 - 1/4x² - 6x - 36

combine like terms:

x² = -1/4x² - 6x + 864

1 1/4x² + 6x - 864 = 0

divide both sides of the equation by 1 1/4:

x² + 4.8x - 691.2 = 0

(x - 24)(x + 28.8) = 0

x = 24 ft

pole height = 24 + 5 = 29 ft

Answer:

[tex]y = 2.096[/tex] or [tex]y = \frac{2\sqrt5+6}{5}}[/tex]

Step-by-step explanation:

Given

[tex]y = \frac{4}{x} + \sqrt x + 0.2 - 5x[/tex]

[tex]x = \frac{4}{5}[/tex]

Required

Find y

[tex]y = \frac{4}{x} + \sqrt x + 0.2 - 5x[/tex]

Substitute [tex]x = \frac{4}{5}[/tex]

[tex]y = \frac{4}{4/5} + \sqrt{4/5} + 0.2 - 5 * 4/5[/tex]

[tex]y = 5 + \sqrt{4/5} + 0.2 - 4[/tex]

Collect like terms

[tex]y = \sqrt{4/5} + 5 + 0.2 - 4[/tex]

[tex]y = \sqrt{\frac{4}{5}} + 1.2[/tex]

Split the surd

[tex]y = \frac{\sqrt4}{\sqrt5}} + 1.2[/tex]

[tex]y = \frac{2}{\sqrt5}} + 1.2[/tex]

Rationalize

[tex]y = \frac{2\sqrt5}{\sqrt5*\sqrt5}} + 1.2[/tex]

[tex]y = \frac{2\sqrt5}{5}} + 1.2[/tex]

Take LCM and add

[tex]y = \frac{2\sqrt5+1.2*5}{5}}[/tex]

[tex]y = \frac{2\sqrt5+6}{5}}[/tex]

or solve as:

[tex]y = \frac{2*2.24+6}{5}}[/tex]

[tex]y = \frac{10.48}{5}[/tex]

[tex]y = 2.096[/tex]

Answer:

20 Edges

Step-by-step explanation:

As this figure shows only 10 edges..so to meet the given condition (8 faces; 4 hexagons & 4 triangles) same figure is present at the back making total of 20 Edges.

Answer:

jkh and ihk

Step-by-step explanation:

Answer:

<JHK and IHK

Step-by-step explanation:

Answer:

the steady-state percentage of residents who are uninvolved is 0.5

Step-by-step explanation:

 Given the data in the question;

let N represent total number of people in the dormitory

I represent  people involved in a relationship

and U represent people uninvolved in a relationship.

so

N = I + U

I = N - U ------ let this be equation 1

Rate of Uninvolved = U/N

now, given that rate of break ups B = 15% every month = 0.15

rate of entering into relationship  R = 15% every month = 0.15

Now, the steady state condition is;

RU = BI ------- let this be equation 2

such that uninvolved rate is constant.

we input equation 1 into 2;

RU = B( N - U  )

we divide both sides by N

RU/N = B( N/N - U/N  )

RU/N = B( 1 - U/N  )

U/N = B / (B + R)

so we substitute

U/N = 0.15 / (0.15 + 0.15)

U/N = 0.15 / 0.3

U/N = 0.5

Therefore, the steady-state percentage of residents who are uninvolved is 0.5

Answer:

32 yd²

Step-by-step explanation:

because 8 • 4 is 32 so it's 32 yd²

Answer:

A = 32 yds^2

Step-by-step explanation:

We know the formula for the area of a rectangle is

A = lw  where l is the length and w is the width

A = 4 yds * 8 yds

A = 32 yds^2

Answer:

-5 9/40

Step-by-step explanation:

Answer:

2.250 feet thick

Step-by-step explanation:

hope it helps mark as brainliest

Answer:

Step-by-step explanation:

The outside diameter minus the inside diameter would leave a difference of TWICE the thickness of the pipe, so divide the difference by 2

Pipe Thickness =  (OD -  ID) / 2  

                           =  (1.275 - 0.975) / 2

                           =   0.3 / 2

                           =   0.15 feet

Answer:

A 0.014

Hope this helps!!!!

Answer:

false

Step-by-step explanation:

Answer:

C) x = 3.7

Step-by-step explanation:

sin 41° = x/5.6

0.6561 = x/5.6

x = 3.7

Answer:

C

Step-by-step explanation:

The net, if you imagine it folded up, will look like a long box.

Because all the dimensions are not equal, the figure cannot be a cube. Both square and rectangular pyramids have 5 faces, unlike this net.

A net of a rectangular prism, however, will have different dimensions for [tex]l[/tex] and [tex]w[/tex], and have 6 faces. So, the answer is C, rectangular prism.

Good luck ^^

The three-dimensional figure represented by the net shown below is a rectangular prism.

Option C is the correct answer.

A prism is a three-dimensional object.

There are triangular prism and rectangular prism.

We have,

From the figure,

We see that it is an open rectangular prism.

All the open sides are rectangular in shape.

If we fold all the sides it will form a rectangular prism.

Thus,

The three-dimensional figure represented by the net shown below is a rectangular prism.

Learn more about prism here:

https://brainly.com/question/12649592

#SPJ2

Answer:

Test statistic  Z = -1.0

 |Z| = |-1.0| < 1.96 at 0.05 level of significance.

The null hypothesis is accepted

The company that produces the drug test claims that less than 14% of the test results are wrong

Step-by-step explanation:

Step(i):-

Given that the population proportion P = 14% =0.14

Given that the sample size 'n' = 382 tests

Given that find a study where 47 out of 382 test results using this test were wrong (either a false positive or a false negative).

Sample proportion

                        [tex]p = \frac{x}{n} = \frac{47}{382} = 0.1230[/tex]

Null hypothesis: H₀ : P = 0.14

Alternative Hypothesis:H₁ : P≠ 0.14

Step(ii):-

Test statistic

              [tex]Z = \frac{p-P}{\sqrt{\frac{PQ}{n} } }[/tex]

         [tex]Z = \frac{0.1230-0.14}{\sqrt{\frac{0.14 X0.86}{382} } }[/tex]

       Z = - 1.0

     |Z| = |-1.0| < 1.96 at 0.05 level of significance.

Final answer:-

The null hypothesis is accepted

The company that produces the drug test claims that less than 14% of the test results are wrong

Answer:

x = -1/2y+2

Step-by-step explanation:

4x+2y=8

Step 1: Add -2y to both sides.

4x+2y+−2y=8+−2y

4x=−2y+8

Step 2: Divide both sides by 4.

4x/4 = -2y+8/4

x = -1/2y+2

Hope this helps!

Answer:

2.7

Step-by-step explanation:

the scale factor should be consistant as you scale up and down. So you can divide 4.59 by its corresponding side of 1.7 in order to get the scale factor of 2.7. When repeated with the other sides this number should remian consitant.  

Option C is correct. The law of cosines must be used to solve a triangle in the case of SAS rule (Side Angle Side Rule)

For a triangle, ABC with sides a, b, and c respectively, the law of cosines is used on such a triangle if there is a presence of an angle between any two sides.

[tex]c^2 = a^2 + b^2 + 2ab cos C[/tex]

Hence the law of cosines must be used to solve a triangle in the case of SAS rule (Side Angle Side Rule)

Learn more here: https://brainly.com/question/20880990

Answer:

105 mph = rate of first plane

130 mph = rate of second plane

Step-by-step explanation:

Let r = rate of first plane

then r + 25 = rate of second plane

2r = distance of first plane

2(r + 25) = distance of second plane

2r + 2(r + 25) = 470

2r + 2r + 50 = 470

4r = 420

r = 105 mph

r + 25 = 130 mph

Answer:

center:  (1, -2)

radius:  2

Answer

Sorry, I need points to ask more question.

Answer:

1 goes to 2

2 goes to 4

3-goes to 1

and 4 goes to 3

Step-by-step explanation:

[tex]\huge{\textbf{\textsf{{\color{pink}{An}}{\red{sw}}{\orange{er}} {\color{yellow}{:}}}}}[/tex]

a) 34°

b) 90°

c) 30°

Answer:

8h ≥ 154

Step-by-step explanation:

Mark me Brainllest

Answer: the fountain is located at point (-1,-0.5)

Step-by-step explanation:

Answer: (-1 , -0.5)

Step-by-step explanation:

Answer:

Measure of angle b is 42 degrees

Step-by-step explanation:

Since angle b is part of a right angle, we can see that part of the right and blue is 48 degrees, and the other part is b. So, we can do 90-48 to get 42 degrees.

Answer:

42

Step-by-step explanation:

since one of the lines for angle b makes a 90° angle all you have to do is subtract 48 from 90 and that is your answer

Integrating with shells is the easier method.

V = 2π ∫₁³ x (√x + 3x) dx

That is, at various values of x in the interval [1, 3], we take n shells of radius x, height y = √x + 3x, and thickness ∆x so that each shell contributes a volume of 2π x (√x + 3x) ∆x. We then let n → ∞ so that ∆x → dx and sum all of the volumes by integrating.

To compute the integral, just expand the integrand:

V = 2π ∫₁³ (x ³ʹ² + 3x ²) dx

V = 2π (2/5 x ⁵ʹ² + x ³) |₁³

V = 2π ((2/5 × 3⁵ʹ² + 3³) - (2/5 × 1⁵ʹ² + 1³))

V = 4π/5 (9√3 + 64)