28. Ashton is hosting a banquet. He plans to spend $400, plus/minus $50, at a
cost of $25 per guest,
a. Find the maximum and minimum number of guests.
b. If there can be up to 7 guests per table, what is the minimum number of
tables Ashton should reserve so everyone has a seat?

Answer:

Step-by-step explanation:

[tex]Let\ say\ r \ the \common\ ratio:\\a)a_4=r^2*a_2=9*a_2\Longrightarrow\ r=3\ (not\ -3\ since\ parts\ are\ positive)\\\\b)\\\displaystyle \sum_{i=1}^{n} a_i =a_1+a_2+a_3+...+a_n\\\\=a_1+a_1*r+a_1*r^2+a_1*r^3+...+a_1*r^{n-1}\\\\=a_1*(1+r+r^2+...+r^{n-1})\\\\=a_1*\dfrac{r^n-1}{r-1} \\\\147620=5*\frac{(3^n-1)}{3-1} \\\\3^n-1=\frac{2*147620}{5} \\\\3^n=59049 \\\\n*ln(3)=ln(59049)\\\\n=\dfrac{ln(59049)}{ln(3)} \\\\n=10\\\\a_n=5*3^{10-1}=5*19683=98415(cm)[/tex]

Answer:

b - a

Step-by-step explanation:

Given M and N are midpoints, let's find the coordinates of the midpoints first. Then we can use that information to find the length

The midpoint formula is

( (x1 + x2)/2, (y1 + y2) / 2 )

So M = ( (2a + 2c)/2, (0 + 2d)/2 ) = (a + c, d)

And N = ( (2c + 2b)/2, (2d + 0)/2 ) = (c + b, d)

Because the y-coordinates are the same (d), the distance from M to N is,

final x-coordinate minus initial x-coordinate

x-coordinate of N minus x-coordinate of M

(c + b) - (a + c)

Distribute the negative and remove the parentheses

c + b - a - c

Group the cs together

c - c + b - a

Cancel out the cs

b - a

Answer:

Daughter is 12 and mother is 48.

Step-by-step explanation:

Let the daughters age be x years now then the mothers age is 4x.

6 years ago the daughter was x-6 years  and the mother was 4x - 6.

So we have the equation:

x - 6 + 4x - 6 = 48

5x - 12 = 48

5x = 60

x = 12

So the daughter is 12 and the mother is 4*12 = 48.

Answer:

Last worked 39 hours and earned $553.22. Enter and solve an equation to find Julio's normal hourly rate,

Answer:

Step-by-step explanation:

The child graph is shifted 9 units to the right. That's what the nine does. The graph also shifts 3 units down when compared to g(x).

I have put a graph in so that you can see the shifts for yourself.

The red line is g(x) = x^4

The blue line is f(x) = (x - 9)^4 - 3

Answer:

5 Terms

Step-by-step explanation:

First we will count how many terms are there in this expression

a3

3a2b

-4ab

-11b

7

There are total 5 Terms in this expression

Answer:

[tex]herre \: total \: angle \: in \: circle = 360 \\ then \\ \: 6x + 1 + x - 19 + 35 = 360 \\ 7x - 18 + 35 = 360 \\ 7x + 17 = 360 \\ 7x = 343 \\ x = \frac{343}{7} = 49 \\ x = 49degree \\ thank \: you[/tex]

6x + 1° + x - 19° + 35° = 360°

6x + x + 1° - 19° + 35° = 360°

7x + 1° - 19° + 35° = 360°

7x + (-18)° + 35° = 360°

7x + 17° = 360°

7x = 360° - 17°

7x = 343°

x = 343° : 7

x = 49°

Step-by-step explanation:

It shows that the content of dietary fiber is negatively correlated to the blood cholesterol of college student, as the correlation coefficient is negative. However, the r=-0.45 shows the two factors are lowly correlated (absolute value of r between 0.3 and 0.5)

Answer:

see explanation

Step-by-step explanation:

6 × 24 ← replace 24 by 4 + 20

= 6(4 + 20) ← multiply each term in the parenthesis by 6

= 24 + 120

= 124

Answer:

First take 0.23 as 0.23/1

Then Multiply the numerator and denominator by any number, Let us say 100

So it becomes,

0.23 x 100/100

=> 23/100

Answer:

d ≈ 9.5

Step-by-step explanation:

Calculate the distance using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (8, 2) and (x₂, y₂ ) = (- 1, 5)

d = [tex]\sqrt{(-1-8)^2+(5-2)^2}[/tex]

   = [tex]\sqrt{(-9)^2+3^2}[/tex]

   = [tex]\sqrt{81+9}[/tex]

    = [tex]\sqrt{90}[/tex]

    ≈ 9.5 ( to the nearest tenth )

Answer:

0 and 2 s the answer

Answer:

formula= l³

Step-by-step explanation:

length of the cube =10mm

volume = l³

= 10³

=10×10×10

ans =1000mm

Answer:

20 seconds

Step-by-step explanation:

h(t) = -16t2 + 640t

to find the maximum value =>

h'(t) = 0

-32t + 640 = 0

-32(t -20)= 0

t-20 = 0

t = 20 seconds

Find derivative of h(t)

[tex]\\ \rm\longmapsto \dfrac{d}{dx}(-16t^2+640t)[/tex]

[tex]\boxed{\sf \dfrac{d(x^n)}{dx}=nx^{n-1}}[/tex]

[tex]\\ \rm\longmapsto -32t+640[/tex]

[tex]\\ \rm\longmapsto -32t+640=0[/tex]

[tex]\\ \rm\longmapsto -32t=-640[/tex]

[tex]\\ \rm\longmapsto t=\dfrac{-640}{-32}[/tex]

[tex]\\ \rm\longmapsto t=20s[/tex]

Answer:

x = 0, 2π/3, 4π/3, 2π.

Step-by-step explanation:

cos 2x = 2cos^2x - 1 so

2cos^2x - 1 = cos x

2cos^2x - cos x - 1 = 0

(2cosx + 1)(cos x - 1) =0

cos x = -1/2, 1.

When cos x = 1, x = 0, 2π

when cos x = -1/2, x = 2π/3, 4π/3.

Answer:

[tex] - 9 \sqrt{48} - 8 \sqrt{12} \\ = - 9 \times 4 \sqrt{3} - 8 \times 2 \sqrt{3} \\ = - 36 \sqrt{3} - 16 \sqrt{3} \\ = \sqrt{3} ( - 36 - 16) \\ = \sqrt{3} \times - 52 \\ = - 52 \sqrt{3} \\ thank \: you[/tex]

Answer:

It is 9000 cents or $90 total for 5 hours

Step-by-step explanation:

Answer: 7/64 inch is bigger by 1/64 inch difference

Step-by-step explanation:

STEP ONE: Convert the denominators into Least Common Multiple (LCM)

LCM of 32 and 64:

First 3 multiples of 32: 32, 64, 96

First 3 multiples of 64: 64, 128, 192

Since 64 overlaps in both terms, 64 is the LCM of 32 and 64.

STEP TWO: Convert the fractions

3/32 = (3 × 2) / (32 × 2) = 6/64

7/64 = 7/64

STEP THREE: Compare the numerator to define the size of fractions

6 < 7, therefore, 6/64 < 7/64

7/64 - 6/64 = 1/64 inch

Hope this helps!! :)

Please let me know if you have any questions

Answer:

8cm

Explanation:

If the 16 cm is the diameter then the radius is 8 cm

Answer:

[tex]x = 1[/tex]

Step-by-step explanation:

[tex]7(x+2)+34=55[/tex]

[tex]7(x+2)+34=55[/tex]

[tex](7)(x)+(7)(2)+34=55[/tex]

[tex]7x+14+34=55[/tex]

[tex]7x+48=55[/tex]

[tex]7x = 55 - 48[/tex]

[tex]7x=7[/tex]

[tex]x = 1[/tex]

Answer:x=1

Step-by-step explanation:

[tex]\\ \sf\longmapsto 3x+3=4x[/tex]

[tex]\\ \sf\longmapsto 4x-3x=3[/tex]

[tex]\\ \sf\longmapsto (4-3)x=3[/tex]

[tex]\\ \sf\longmapsto x=3[/tex]

Step-by-step explanation:

Solution,

According to figure

(3x+3)°=(4x)°

3x°+3°=4x°

3x°-4x°=-3

-x°=-3°

x°=3°

Answer:

[tex] \frac{3393939}{10000000} [/tex]

Step-by-step explanation:

[tex]0.(3)3(9) = \frac{3393939}{10000000} [/tex]

Answer:

six crore four lakh fifty seven thousand nine hundred eighty one

Answer:

x = 7

Step-by-step explanation:

Because the points are collinear:

AB + BC = AC

We'll plug in the expressions in terms of x.

(-1 + 2x) + (11) = (3x + 3)

And solve for x. Combine like terms on the left

2x + 10 = 3x + 3

Subtract 3 on both sides

2x + 7 = 3x

Subtract 2x on both sides

7 = x

Answer:

2

Step-by-step explanation:

first multiply everything by 6 to get rid of the fractions

then we get 5m-4 -6 = 24m -9m -30

simplify the equation 5m-10=15m-30

subtract 5m from both sides and add 30 to both sides 10m=20

divide by 10, m=2

Part A : D.)

Part B : Length of the sandbox is 10 feet.

Step-by-step explanation:

Given,

Perimeter = 29 ft

We need to find the equation for the perimeter and also the length of the sandbox.

Solution,

Let the width of the sandbox be 'w'.

Now as per question said;

The length of the sandbox is 1 foot longer than twice the width of the sandbox.

So we can say that;

Length =

Now we know that the perimeter is equal to the sum of twice of length and width.

framing in equation form, we get;

Perimeter =

we have given the perimeter, so on substituting the value, we get;

Hence The equation used to find the width is  .

Now we solve for 'w'.

Applying distributive property, we get;

Subtracting both side by '2' we get

Dividing both side by 6 we get;

Width of the sandbox = 4.5 ft

Length of the sandbox =

Hence Length of the sandbox is 10 feet.