HAPPY BIRTHDAY!
You have decided to give your best friend a bag of red
and green marbles for his birthday. Your friend likes
green marbles better than red ones, so the bag has
twice as many green marbles as red. The label on the
bag says it contains a total of 84 marbles.
How many green marbles are in the bag? Write a
system of equations for this problem. Then solve the
problem using any method you like. Be sure to check
your solution

The area of the shaded region is  [tex]\rm (150\sqrt{3} \ - 75\pi ) \ feet^2[/tex] option first is correct.

It is given that a circle is inscribed in a regular hexagon with sides of 10 feet.

It is required to find the shaded area (missing data is attached shown in the picture).

It is defined as the combination of points that and every point has an equal distance from a fixed point ( called the center of a circle).

We have a hexagon with a side length of 10 feet.

We know the area of the hexagon is given by:

[tex]\rm A = \frac{3\sqrt{3} }{2} a^2[/tex]  where a is the side length.

[tex]\rm A = \frac{3\sqrt{3} }{2} 10^2[/tex] ⇒ [tex]150\sqrt{3}[/tex] [tex]\rm feet^2[/tex]

We have the shortest length = x feet and from the figure:

2x = 10

x = 5 feet

The radius of the circle r = longer leg

[tex]\rm r = x\sqrt{3} \Rightarrow 5\sqrt{3}[/tex] feet

The area of the circle a = [tex]\pi r^2[/tex]  ⇒ [tex]\pi (5\sqrt{3} )^2 \Rightarrow 75\pi \ \rm feet^2[/tex]  

The area of the shaded region = A - a

[tex]\rm =(150\sqrt{3} \ - 75\pi ) \ feet^2[/tex]

Thus, the area of the shaded region is  [tex]\rm (150\sqrt{3} \ - 75\pi ) \ feet^2[/tex]

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Answer:

option A

Step-by-step explanation:

Answer:

f(-1)=2(-1)³-3(-1)²+7 = 2

f(1)=2(1)³-3(1)²+7 = 6

f(2)=2(2)³-3(2)²+7 = 11

I think the radius would be 13.9 ft

Answer: 1/6

Step-by-step explanation: I think you multiply 3 times 3 because the other circle circle has an option the first doesn't have have.

The function I = 19n is a linear function

The reasonable domain of the function is [0,21]

The function is given as:

I = 19n

The smallest value of n is 0 i.e. the smallest number of ticket sold is 0

The maximum capacity is 400.

So, we have:

19n = 400

Divide both sides by 19

n = 21.05

Remove the decimals

n = 21

Hence, the reasonable domain of the function is [0,21]

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Answer:

The answer is 21/40

Step-by-step explanation:

Hope that helps!

Using the t-distribution, as we have the standard deviation for the sample, it is found that the 99% confidence interval for the true mean number of visitors on summer days is given by:

c. 92.664 to 103.940 visitors

The confidence interval is:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which:

The critical value, using a t-distribution calculator, for a two-tailed 99% confidence interval, with 30 - 1 = 29 df, is t = 2.756.

The other parameters are given as follows:

[tex]\overline{x} = 98.3, s = 11.2, n = 30[/tex].

Hence, the bounds of the interval are given by:

[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 98.3 - 2.756\frac{11.2}{\sqrt{30}} = 92.664[/tex]

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 98.3 + 2.756\frac{11.2}{\sqrt{30}} = 103.94[/tex]

Hence option c is correct.

More can be learned about the t-distribution at https://brainly.com/question/16162795

Answer:

C

Step-by-step explanation:

Volume = bhd

Volume = (x + 3)(x + 8)(x²)

start with (x + 3) and (x + 8), factor:

x² + 8x + 3x + 24

x² + 11x + 24

now bring x² back:

(x² + 11x + 24)(x²)

x⁴ + 11x³ + 24x²

Answer:

x = 21.

Step-by-step explanation:

AS there are parallel lines:

4/12 = 7/x

4x = 84

x = 84/4 = 21.

The area of smaller square is 81

Answer:

  x = 3/8

Step-by-step explanation:

The difference of the two squares can be found several ways. One way uses the "difference of squares" special form.

  a² -b² = (a -b)(a +b)

For the given squares, this is ...

  (2x +3)² -(2x -3)² = ((2x +3)-(2x -3))((2x +3) +(2x -3)) = 6(4x) = 24x

We want to find x that makes this difference be 9:

  24x = 9

  x = 9/24 = 3/8

For the value x = 3/8, the difference between the squares of the binomials will be 9.

With one package (less actually) she can fill the 48ft^2 of the rectangular area.

We know that Sandy needs 7.8 square feet of space per hyacinth bulb, and the hyacinth bulbs are sold in packages of 8.

The rectangular region has a surface area of:

A = 8ft*6ft = 48 ft^2

The number of hyacinth bulbs that she can put in that surface is:

N = (48 ft^2/7.8 ft^2) = 6.15

So with 6 hyacinth bulbs, she can almost complete the rectangular area, and on each package there come 8 of them, so with one package she should be fine.

If you want to learn more about areas, you can read:

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Answer:

The answer is 7 PACKAGES

Step-by-step explanation:

I took the test!

The 7th term of the sequence to the nearest thousandth is 223.949

These are sequence that increases in an exponential form.

The formula for calculating the nth term of a geometric sequence is expressed as:

Tn = ar^n-1

Given the following parameters

a = 75

r = 1.2

n = 7

Substitute the given parameter into the formula

T7 = 75(1.2)^6
T7 = 223.949

Hence the 7th term of the sequence to the nearest thousandth is 223.949

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Collinear points: Three points A, B and C are said to be collinear if they lie on the same straight line.

There points A, B and C will be collinear if AB + BC = AC as is clear from the adjoining figure.

In general, three points A, B and C are collinear if the sum of the lengths of any two line segments among AB, BC and CA is equal to the length of the remaining line segment, that is, either AB + BC = AC or AC +CB = AB or BA + AC = BC.

In other words,

There points A, B and C are collinear if:

(i) AB + BC = AC i.e.,

Or, (ii) AB + AC = BC i.e. ,

Or, AC + BC = AB i.e.,

Answer:

a

Step-by-step explanation:

General equation of a circle : [tex](x-h)^2+(y-k)^2=r^2[/tex]

where (h,k) is at center and r = radius

Here, we want to find the equation of a circle with a given center at (3,4) and a given radius of 6

This is very simple, all we have to do is assign variables and then plug in the values of the variables into the general equation of a circle

First lets assign variables.

(h,k) is center and the circle has a given center at (3,4)

so (h,k) = (3,4) thus, h = 3 and k = 4

r = radius and the circle has a given radius of 6 so r = 6

now we plug this into the general equation of a circle.

recall equation : (x-h)² + (y-k)² = r²

h = 3, k = 4 and r = 6

plug in values

(x-3)² + (y-4)² = 6²

simplify exponent

(x-3)² + (y-4)² = 36

and we are done!

The answer is A

Answer:

2

Step-by-step explanation:

[tex]16^{\frac{1}{4} }[/tex] = [tex]\sqrt[4]{16}[/tex] = 2.  To find the fourth root, find the number that repeats itself four times using multiplication. 2 x 2 x 2 x 2 = 16

Call the two-digit number : ab

The new number formed : ba

We have : 10a + b + 10b + a = 143

11a + 11b = 143

a+b = 143 : 11 = 13

So, we have a few combinations for a and b : (4;9) , (5;8) , (6;7) , (7;6) , (8;5) , (9;4)

Out of all these, only 76 is the satisfied number, as the new number formed is 67, and 76 + 67 = 143 ; 76 - 67 = 9

Answer:

  6.03 years

Step-by-step explanation:

The value of the Range Rover decreases 25% per year, so its value "growth" factor is 1-25% = 0.75. The initial value is 60,000, so its exponential value function can be written ...

  r(x) = 60000(0.75^x)

The Honda has a "growth" factor of 18000/20000 = 0.90 and an initial value of 20,000, so its exponential value function can be written ...

  h(x) = 20000(0.90^x)

__

We want to find x such that h(x) > r(x).

  20000(0.90^x) > 60000(0.75^x)

  0.90^x > 3(0.75^x) . . . . . . . divide by 20000

  (0.90/0.75)^x > 3 . . . . . . . . divide by 0.75^x

  x > log(3)/log(1.2) . . . . . . . . take logs, divide by log(1.2)

  x > 6.025685

It will take about 6.03 years for the Honda to be worth more.

Answer:

Given equation: x + 2y = 7

Rearrange the given equation to make y the subject:

      [tex]\sf x + 2y = 7[/tex]

[tex]\sf \implies 2y=7-x[/tex]

[tex]\sf \implies y = \dfrac12(7-x)[/tex]

Now input the given x-values into the equation to determine the y-values:

[tex]\sf x=-2\implies y = \dfrac12(7-(-2))=4.5[/tex]

[tex]\sf x=-1\implies y = \dfrac12(7-(-1))=4[/tex]

[tex]\sf x=0\implies y = \dfrac12(7-0)=3.5[/tex]

[tex]\sf x=1\implies y = \dfrac12(7-1)=3[/tex]

[tex]\sf x=2\implies y = \dfrac12(7-2)=2.5[/tex]

[tex]\sf x=3\implies y = \dfrac12(7-3)=2[/tex]

As ordered pairs: (-2, 4.5)  (-1, 4)  (0, 3.5)  (1, 3)  (2, 2.5)  (3, 2)

Plot the endpoints on the graph (-2, 4.5) and (3,2), then connect with a line segment.

Answer:

A depreciation of 14.3% leaves you with 85.7%, right? Each year's value is 85.7% of the tear before.

So, 6500(0.857)3 = $4091.25

Answer:

73

Step-by-step explanation:

supplementary anges are equal to 180 so e is 180-107

Answer: 73∘.

Step-by-step explanation: With supplementary angles, the two angles have to add up to 180∘.  According to the question, the measure of <F is 107∘.  What we need to do is make <E and <F add up to 180∘.  To do this, we can subtract 107∘ from 180∘ to find <E:

180∘ - 107∘ = 73∘, which means that <F is 107∘ and <E is 73∘, which both make 180∘.

Therefore, <E is 73∘.

Have a great day! :)

X = 62.4

:)

to get X, i would subtract, 71.1 - 8.7, and the answer would be X, not %100 sure though sorry.

The volume of the fountain cup in gallons is 4775.2 gallons

Since the fountain cup is in the shape of a frustum, its volume is given by

V = πh/3(r² + rr' + r'²) where

So, substituting the values of the variables into th equation, we have

V = πh/3(r² + rr' + r'²)

V = π × 8 ft/3[(4 ft)² + 4 ft × 6 ft + (6 ft)²]

V = π × 8 ft/3[16 ft² + 24 ft² + 36 ft²]

V = π × 8 ft/3 × (76 ft²)

V = 608π ft³/3

V = 1910.088 ft³/3

V = 636.69 ft³

V ≅ 636.7 ft³

Since there are 7.5 gallons per cubic foot,

The volume of the fountain cup in gallons is V = 636.7 ft³ × 7.5 gallons/ft³ = 4775.2 gallons

So, the volume of the fountain cup in gallons is 4775.2 gallons

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Answer:

sqrt(37) = arpox 6.1

Step-by-step explanation:

sqrt(1^2+6^2) = sqrt(37)

Step-by-step explanation:

when we look at the triangle try to reposition it at least in your mind to make R to be the center of the circle. then RP (29) is the radius of the circle and the angle indication of the angle R in this circle.

then we see QP is the sine, and RQ is the cosine of the angle R. but don't forget : all are multiplied by the radius, because the pure sin and cos functions deliver the values for the standard circle with radius 1.

so,

QR = cos(R)×RP

21 = cos(R) × 29

cos(R) = 21/29

the fourth answer is correct.

Answer:

the answer is D I took the test

Answer:

3 tons per hour

Step-by-step explanation:

Since 0.5=1/6

you can multiply 0.5 by 6:

0.5x6= 3

With an ending result of 3 tons per hour