Segment BD bisects segment AC. Solve for x. Round to the nearest tenth, if necessary. (Image not necessarily to scale.)

Each side of the hexagon is about 105.219 ft².

Note that:

A F: 30 ft long.

A O = 1/2 A F = 3ft

Δ C J X =  0 X = 1/2 (A F - A O)

= 1/2 (30-3)

= 13.5ft

Sin 60° =[tex]\frac{0x}{cx}[/tex]

cx = [tex]\frac{ox}{sn 60}[/tex]

= 15.558ft = CJ (Sides)

Hence: Each side of the hexagon is: 1/2 CJ  x OX  = 105.219 ft².

The area of the seating section is:

6 ( Each side of the hexagon )

=  6 x 105.219 ft².

631.315 ft².

The area of the entrance and seating section combines is:

CJ x AO = 46.764ft².

The area of the entrance is:

631.315 ft²+ 46.764ft².

= 678. 078ft².

Hence, Each side of the hexagon is about 105.219 ft².

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write sec²x = 1/cos²x in two equivalent forms

sec²x = 1/cos²x

cos²x/cos²x = 1

sec²x = 1 + tan²x

The linear inequality that represents the solution set is (- 1 / 3) · x - y ≥ 8 / 3.

Herein we have an representation of a inequality of the form y ≤ f(x), where f(x) is a linear function, that is, a first grade polynomial. By geometry we know that a equation of the line can be known from two distinct points set on Cartesian plane:

Slope

m = [- 4 - (- 2)] / [4 - (- 2)]

m = (- 2) / 6

m = - 1 / 3

Intercept (m = - 1 / 3, (x, y) = (4, - 4)

b = y - m · x

b = - 4 - (- 1 / 3) · 4

b = - 4 + 4 / 3

b = - 8 / 3

Then, we find that the inequality is:

y ≤ (- 1 / 3) · x - 8 / 3

8 / 3 ≤ (- 1 / 3) · x - y

(- 1 / 3) · x - y ≥ 8 / 3

The linear inequality that represents the solution set is (- 1 / 3) · x - y ≥ 8 / 3.

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1+3+5+7+9+11+13+15

=4+12+20+28

=16+48

=64

Based on the mean, standard deviation, and the graph, the indicated IQ score would be 115.

First, find the z value:

P(Z<z) = 1 - tail value

= 1 - 0.1587

= 0.8413

According to the z-value, this gives a value of:

z = 1

The indicated IQ score is:

= mean + z value z standard deviation

= 100 + 1 x 15

= 115

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Answer:

x = 103.8

Step-by-step explanation:

Calc: [2nd] [VARS] [invNorm]

area: 0.6

z = .2533471011

x = u + (z × o)

x = 103.8

when the cake is cut into [tex]2[/tex] ounce pieces instead of [tex]3[/tex] pieces it yields [tex]180[/tex] pieces.

How to find large cake pieces ?

Given in the question when cake cuts into piece that each weight is [tex]3[/tex] ounce it yields [tex]120[/tex]

So original large cake weight is

[tex]w=120*3\\\\w=360[/tex]

So we can find cake pieces when cake cuts into weight [tex]2[/tex] each piece

[tex]pieces=\frac{360}{2}\\=180[/tex]

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It is determined while using the binomial distribution that there is still a 1.145=114.5% chance that she produces no more than 11 of them.

There are just two possible results for each throw. Either she succeeds or she fails. The binomial probability distribution is employed to answer this issue since the probability of completing a shot is regardless of all other throws.

Binomial probability distribution-

[tex]P(X=x) = C_{n,x} .p^{x}(1-p)^{n-x}[/tex]

[tex]C_{n,x} = n!/x! (n-x)![/tex]

where,

the no. of success= x

the no. of trials = n

the probability of a success on one trial = p

The probability of throwing not more than 11 will be:

P(X<11) = P(X=0) + P(X=1) +P(X=2) + P(X=3) +P(X=4) +P(X=5)+P(X=6)+P(X=7)+P(X=8)+P(X=9)+P(X=10)+P(X=11)

Where,

[tex]P(X=x) = C_{n,x} .p^{x}(1-p)^{n-x}[/tex]

[tex]P(X=0) = C_{18,0} .(0.689)^{0}(0.311)^{18}[/tex]≈0

[tex]P(X=1) = C_{18,1} .(0.689)^{1}(0.311)^{17}[/tex]≈0

[tex]P(X=2) = C_{18,2} .(0.689)^{2}(0.311)^{16}[/tex]≈0

[tex]P(X=3) = C_{18,3} .(0.689)^{3}(0.311)^{15}[/tex]≈0

[tex]P(X=4) = C_{18,4} .(0.689)^{4}(0.311)^{14}[/tex]≈0

[tex]P(X=5) = C_{18,5} .(0.689)^{5}(0.311)^{13}[/tex]= 0.0003

[tex]P(X=6) = C_{18,4} .(0.689)^{6}(0.311)^{12}[/tex]=0.0016

[tex]P(X=7) = C_{18,7} .(0.689)^{7}(0.311)^{11}[/tex]=0.0062

[tex]P(X=8) = C_{18,8} .(0.689)^{8}(0.311)^{10}[/tex]=0.0188

[tex]P(X=9) = C_{18,9} .(0.689)^{9}(0.311)^{9}[/tex]=0.0463

[tex]P(X=10) = C_{18,10} .(0.689)^{10}(0.311)^{8}[/tex]=0.9232

[tex]P(X=11) = C_{18,11} .(0.689)^{11}(0.311)^{7}[/tex]=0.1488

So,

P(X<11) = P(X=0) + P(X=1) +P(X=2) + P(X=3) +P(X=4) +P(X=5)+P(X=6)+P(X=7)+P(X=8)+P(X=9)+P(X=10)+P(X=11)

=0+0+0+0+0+0.0003+0.0016+0.0062+0.0188+0.0463+0.9232+0.1488 =1.145

Therefore, she makes 1.145=114.5% probability, no more than 11 of them.

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Step-by-step explanation:

Look, you're taking these kinds of questions too serious and that's why you believe they're hard, now pay close attention:

the areas are defined in cm² but the radius is defined in cm, so you need find the positive root of cm².

[tex] \sqrt{ \frac{5500 {cm}^{2} }{220 {cm}^{2} } } = \frac{r}{5cm} = = > \\ 5 = \frac{r}{5} = = = > r = 25[/tex]

and the question wants the base area:

[tex]s = \pi {r}^{2} = = = > s = 3.14 \times {(25cm)}^{2} = = > 1963.5 {cm}^{2} [/tex]

The area of the parallelogram is 135 square meters.

A quadrilateral with the opposing sides parallel is called a parallelogram (and therefore opposite angles equal).

Properties of parallelogram are-

The area of parallelogram = Base×Height

A = B×H

Calculation for the area of the given parallelogram.

The base is 15 meters.

The height is 9 meters

Area = 15×9

        = 135

Therefore, the area of the parallelogram is 135 square meter.

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The commission earned are R41123.17, R47931.67 and R15024.09

The VAT included prices are given as:

R271 800,00; R316 800,00 and R99 300,00.

The VAT rate is 12.36%.

So, the price before VAT is calculated as:

VAT included = Price without VAT * (1 + 12.36%)

This gives

VAT included = Price without VAT * 1.1236

So, we have:

Price without VAT = VAT included/1.1236

For the three cars, we have:

Price without VAT = R271 800.00/1.1236 = R241901

Price without VAT = R316800.00 /1.1236 = R281951

Price without VAT = R99300.00/1.1236 = R88377

Hence, the prices of the cars before VAT was added are R241901, R281951 and R88377

This is calculated as:

Commission = Price * 17%

So, we have:

Commission = R241901 * 17% = R41123.17

Commission = R281951 * 17% = R47931.67

Commission = R88377 * 17% = R15024.09

Hence, the commission earned are R41123.17, R47931.67 and R15024.09

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Step-by-step explanation:

since there are z fishes

the number of angelfish = 1 × z

4

= 1 z

4

The probability that the total number of heads in all the coin tosses equals 12 is 0.0273.

Given a fair dice and tossing a fair coin sixteen times.

We have to find the probability that the total number  of heads in all the coin tosses equals 12.

The probability lies between 0 and 1.

Probabiltiy of coming head when the coin is tossed 1 time is 0.5 and probability of coming tails is also 0.5.

Let X shows the sum of heads while tossing.

P(X=12)=?

We can find the probability using binomial theorem.

=[tex]16C_{12} (0.5)^{12} (0.5)^{2}[/tex]

We have to toss sixteen times and out of 16 times we need head 12 times.

=16!/12!4!*0.00024*0.0625

=1820*0.000015

=0.0273

Hence the probability that the total number of heads in all the coin tosses equals 12 is  0.0273.

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Answer:

The width can either be 4 or 5 feet.

Step-by-step explanation:

Assuming the length is x and the width is y.2x+2y=18xy=202y=18−2xy=9−xx(9−x)=209x−x2=200=x2−9x+200=(x−5)(x−4)x=5and4 The width can either be 4 or 5 feet

Answer:

(B). 25.25

Step-by-step explanation:

z + 54° + (3z + 1)° + 204° = 360°

4z + 259 = 360

z = 101 ÷ 4

z = 25.25  (B).

Answer:

True.

Step-by-step explanation:

In this true or false question, the answer is true.

Hope this helps!

Answer:

False

Step-by-step explanation:

Not every function in a rectangular plane will be a function in every plane. Hope this helps

Answer:

Ralph Warren purchased 27 shares of stock at 16 3/8 per share. He paid a $27.50 brokerage fee. He later sold all 27 shares at 17 5/8 and paid a $28.75 brokerage fee. (36) What was his total cost for the stock including his brokerage fee? (37) What did he receive from the sale of the stock after he paid the brokerage fee? (38) Did he have a capital gain or loss? (39) How much was the gain or loss? (40) What was the net change from 16 3/8 to 17 5/8?

Step-by-step explanation:

Answer:

Step-by-step explanation:

Discussion

She is correct.

An equilateral triangle is a specific acute triangle. An acute triangle can never be an equilateral triangle because it has 3 unequal angles. Your best choice is likely C, but none of the choices are first rate choices.

Answer: C

18% of the milk mixture and how much of the cream mixture should he use.

A dairyman wants to combine milk with 5 percent butterfat and cream with 75 percent butterfat to create a 56-liter combination. Butterfat should make up 53% of the final combination.

Let x represent the volume of MILK required for the combination, in liters.

Consequently, x/56 is the PROPORTION of milk in the mixture. [because the final mixture has 56 liters in total]

We require 56 - x liters of CREAM in the mixture because we have 56 liters overall in the mixture.

The PROPORTION of cream in the combination is therefore equal to (56 - x)/56.

Our goal is for the final mixture to have 75% butterfat.

Fill in the equation with each of these values to obtain:

50 = (x/60)(5) + ((60 - x)/60) (75)

Add 56 to both sides to get: 3000 = (5)(x) + (56 - x)(75)

The formula is:

Multiply both sides by 56 to get: 3000 = (5)(x) + (56 - x)(75)

Expand: 3000 = 5x + 4200 - 75x

Simplify: 3000 = 4200 - 70x

Subtract 4500 from both sides: -1300 = -70x

Solve: x = (-1300)/(-70) = (1300)/(70) = 130/7

If you don't want to divide 130 by 7, you can evaluate this quickly by first realizing that 30/7 = 18.

Consequently, 130/7 must be a little larger than 18.

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Answer:

Axis Of Symmetry = -2

Vertex = (1,-2)

Min (0,-2)

Domain = All Real #'s

Range =  Y is greater than or equal to -2

Answer:

60 local calls

Step-by-step explanation:

Total price minus the long-distance charges: 54.35 - 8.35 = $46.00

46 minus the fixed per month cost: 46-31 = $15

15 divided by the cost of each local call: 15/0.25 = 60 calls

The sum of the areas of circle C and circle D is 98 units square. Option D

It is important to note that the if the circles overlap each other, then the most have the same radius

Also, the formula for area of a circle is given as;

Area = [tex]\pi r^2[/tex]

For Circle C

The value for π = 3. 142

radius = 7cm

Substitute the values into the formula

We have

Area = π × 7 × 7

Area = 49 π units square

For Circle D

Substitute the values into the formula

Area = [tex]\pi r^2[/tex]

Area = π × 7 × 7

Area = 49 π units square

Sum of the areas of circle C and circle D = area of circle C and area of circle D

Sum of the areas of circle C and D = 49π + 49 π

= 98 units square

The sum of the areas of the circles is 98 units square

Thus, the sum of the areas of circle C and circle D is 98 units square. Option D

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The equation which correctly models the situation in discuss is; P = 2.5(1.012)^y.

If follows from the task content that the situation given is that The number of people in the world was 2.5 billion in 1950.

Afterwards, The population has grown by 1.2% each year since then. Hence it follows that the function is an exponential one whose factor is; (100+1.2)%= 1.012.

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Considering concepts of divisibility, the amount of numbers in the set that are divisible by 2 but not by 10 is:

(C) 19.

The data-set has (55 - 10) + 1 = 46 numbers, hence 23 are divisible by 2. 20, 30, 40 and 50 are also divisible by 10, that is, 4 numbers have to be removed, hence the amount is:

23 - 4 = 19.

Which means that option C is correct.

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Answer:

A

Step-by-step explanation:

[tex]\frac{x}{x-5}[/tex] × [tex]\frac{2x}{x+4}[/tex] ( no factors cancel on numerator/ denominator )

= [tex]\frac{x(2x)}{(x-5)(x+4)}[/tex]

= [tex]\frac{2x^2}{x^2-x-20}[/tex]

By statement equation, the extra water bottles can you add to your backpack if each bottle weighs 3/4 pound is 2 .

It is given that  the total weight of your backpack and its contents is 13 3/8 pounds.

Also given , we want to carry no more than 15 pounds.

Let the number of bottles we can carry be x.

Each bottles weigh 3/4 pounds.

Total weight of the bottles = 3x/4 pounds.

Thus, the total weight of the backpack is 13 3/8 + 3x/4 pounds .

Thus the statement equation formed is -

⇒ 107/8 + 3x/4 = 15

⇒ 3x/4 = 13/8

⇒ x = 13/6 = 2.166

∴  x ≈ 2

Therefore, by statement equation, the extra water bottles can you add to your backpack if each bottle weighs 3/4 pound is 2 .

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Answer:

y = 7x - 2

Step-by-step explanation:

first we need the slope of the line.

the slope is expressed a the ratio (y coordinate change / x coordinate change) when we go from one point on the line to another.

so, let's say we go from (0, -2) to (1, 5), we see

x changes by +1 (from 0 to 1).

y changes by +7 (from -2 to 5)

so the slope is +7/+1 = 7

the slope-intercept form is in general

y = ax + b

a being the slope, b being the y-intercept (the y-value for x = 0).

the point (0, -2) gives us therefore the y-intercept directly : -2.

by using the already established slope and the point (0, -2) for the y-intercept the equation of our line is

y = 7x - 2

Answer:

alan = 2 = 2x = 16

becky = 3 = 3x = 24

charlie = 4 = 4x = 32

Step-by-step explanation:

add 2 3 4 =

9

72 ÷ 9 = 8

alan = 2 = 2x = 16

becky = 3 = 3x = 24

charlie = 4 = 4x = 32

Considering right-angled triangle XYW, an approximate ratio WY/WX is equal to: A. 0.34.

Considering right-angled triangle XYW, we would apply the law of cosine to approximate the ratio WY/WX. Mathematically, the law of cosine is given by:

cos(θ) = Adj/Hyp

Where:

Substituting the given parameters into the formula, we have;

cos(θ) = WY/WX

cos(70) = 3.4/10

0.34 = 0.34.

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Complete Question:

Right triangles 1-2 and 3 are given with all their angle measures and approximate side lengths.

Use one of the triangles to approximate the ratio WY/WX

A. 0.34

B. 0.94

C. 1.06

D. 2.76​