In the diagram below, FG = 10.9, FH = 6.5, and GD = 9.1. Find the length Round your answer to the nearest tenth if necessary.

Answer:

m∠1 = 30°

m∠2 = 120°

m∠3 = 30°

w = 52

x = 104 (approximately)

y = 156 (approximately)

z = 180

Step-by-step explanation:

Step 1: Label your diagram with variables to make solving easier

Step 2: Solve for the missing degrees

Step 3: Solve for the missing side lengths

Answer:

convert the fractions to a common denominator of 90

5 1/6 , 5 13/30 , 5 68/90

The estimate should be 24 within a margin of error -4% with 90% confidence level.

In statistics, the margin of error is the degree of error in results from random sampling surveys. A wider margin of error in statistics suggests a reduced likelihood of relying on the results of a survey or poll, i.e. less trust in the results to represent a population.

A margin of error is a statistical parameter that compensates for the gap between actual and projected findings in a random survey sample. In layman's words, the margin of error measures the degree of unpredictability in data and research conclusions.

Given,

Confidence level=90%=0.90

Margin of error= -4%

α=1-0.9

α=0.1

α/2=0.05

P(z>[tex]z_{0.05}[/tex])=0.05

P(z>[tex]z_{0.05}[/tex])=1-0.05

P(z>[tex]z_{0.05}[/tex])=0.95

[tex]z_{0.05}[/tex])=1.96

Approximating P=0.5 and using E=0.2,

n=((1.96)²(0.5)(0.5))/(0.2)²

n=24.01

n=24

Therefore, the estimate should be 24 within a margin of error -4% with 90% confidence level.

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Answer: No, only Alex's solution is correct.

Step-by-step explanation:

Morgan's solution is incorrect because he subtracted 3 from the parentheses, which is illegal (in math, of course). This means that his answer is incorrect.

Answer: Alex is correct.

Step-by-step explanation:

Alex's steps are correct and are used properly, unlike Morgan, which did steps that aren't allowed and don't make sense. Alex's answer is correct.

If the perimeter of XYZ is 26 then the answer will be 6.5.

What is composition of transformation?

A composition of transformations combines two or more transformations that were separately applied to the prior image. The result of a composition of reflections along parallel lines is identical to that of a translation (twice the distance between the parallel lines).

What is Perimeter?

The perimeter of a form is the space surrounding its edge. Find the perimeter of various forms by summing the lengths of their sides.

Given;

The composition of transformations Ry=-5 r (90,A) maps ABC to XYZ .

the perimeter of XYZ is 26

ΔABC is the reflection of ΔXYZ which is transformed with angle 90°.

So,the answer will be [tex]26\div 4 = 6.5[/tex].

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The distance covered by gaby at a speed of 12 mph in 12 minutes is

2.4 miles.

Given,

Speed at which gaby is walking = 12 mph

we are asked to determine the distance covered by gaby at a given speed in 12 minutes = ?

We know, Distance = Speed × Time

speed = 12 mph

time = 12 minutes

= 12/60 hr

Distance = 12 × 12/60

= 5/2

= 2.4 miles

Hence gaby can cover 2.4 miles in 12 minutes.

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Answer:

120 ft²

Step-by-step explanation:

The length of each of the congruent sides is (50-16)/2 = 17 ft.

So, using the Pythagorean theorem, the altitude drawn from the vertex angle to the base has a length of 15 ft.

Thus, the area is (1/2)(15)(16) = 120 ft².

The number of pieces of tiles that are needed to pave a path 5 m long and 1 m wide is; 20 tiles

We are told that the size of each piece of tile is 50 cm by 50 cm.

Now, we are told that the area that needs to be paved with tiles measures 5 m by 1m. Thus;

Converting the area that needs to be tiles to cm, we have;

5m = 500 cm

1m = 100 cm

Thus;

Area to be tiled = 500 * 100 = 50000 cm²

Area of each tile = 50 cm * 50 cm = 2500 cm²

Thus;

Number of tiles that are required to pave the given path = 50000/2500 =20 tiles

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The cost of another 2 panes of glass cost = $5.90.

A nurery owner buy 7 pane of glass to fix some damage to his greenhoue.

The 7 pane cost = ​$20. 65

First find the cost of one pane of glass (the "unit cost")

7 panes of glass cost $20.65, so one pane of glass costs

= 20.65 ÷ 7

= $2.95 ← cost of one pane of glass

Then use that answer to find the cost of two panes of glass

If one pane of glass costs $2.95, then 2 panes cost

= 2 × $2.95

= $5.90 ← cost of two panes of glass

Hence the answer is the cost of another 2 panes of glass cost = $5.90.

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Answer:

12x² + 6xy - 30x

Step-by-step explanation:

Given expression,

→ 6x(2x + y - 5)

Simplifying the given expression,

→ 6x(2x + y - 5)

→ (6x × 2x) + (6x × y) - (6x × 5)

→ 12x² + 6xy - 30x

Thus, answer is 12x² + 6xy - 30x.

The values of x and y are 44.8 & 19.2 respectively.

What is the similarity theorem of the triangle?

According to the fundamental theorem of similarity, a line segment can divide two triangle sides into proportionate segments if and only if it is parallel to the third side of the triangle.

We have,

ΔABC ~ ΔAVW

We know the similarity theorem of triangle,

[tex]\frac{AC}{AW} = \frac{CB}{VW}[/tex]  

28/ x = 16/10

x = 1.6 * 28

x = 44.8

[tex]\frac{AB}{AV} = \frac{CB}{VW}[/tex]

y/12 = 16/10

y =  1.6 * 12

y = 19.2

The values of x and y are 44.8 & 19.2 respectively.

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The required price of one battery from the pack is   £0.465.

When we given a pack of objects with some cost, then to calculate the price of one object, divide the amount of pack by number of objects in the pack.

we have, price of 6 battery = £2.79

Then, the price of one battery = £2.79/6 = £0.465

Thus, the the price per battery is £0.465.

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Step-by-step explanation:

we have to mark the angles in the point denoted in the graph and connect it

The illustration of the dilated triangle has been shown.

The scale factor is defined as the ratio of the modified change in length to the original length.

Here,
The vertices of a triangle are A(-4, 6), B(6.4), and C(6. - 2).
The scale factor of 1/2.​,

Coordinates of the vertices of the triangle with scale factor,
A' = (-4 × 1/2 , 6 × 1/ 2)
A' = (-2, 3)

Similarly,
B' = (3, 2)
C' = (3, -1)

Thus, the illustration of the dilated triangle has been shown.

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Answer:

560 children tickets

540 adult

Step-by-step explanation:

560x6=3360

540x11=5940  

3360+5940 = 9300

The number of people that would have become sick in total over an indefinite period of time is of:

7500.

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q, meaning that each term is obtained by the multiplication of the previous term by the common ratio q.

The nth term of a geometric sequence is given by the rule presented as follows:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

The sum of an infinite sequence, as long as |q| < 1, is given by:

[tex]S = \frac{a_1}{1 - q}[/tex]

The first term and the common ratio in this problem are given as follows:

Hence the total number of people who got sick is obtained as follows:

S = 3000/0.4 = 7500.

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The coordinates of the endpoint A = (A, B) is (60, 9)

The midpoint of a line segment is given as,

x = (a + c)/2

y = (b + d) / 2

Where (x, y) is the midpoint and (a, b) and (c, d) are the two endpoints.

We have,

Midpoint = (31, -5) = (x, y)

Endpoints:

A = (a, b) and B = (2, -19) = (c, d)

The midpoint of a line segment is given as,

x = (a + c)/2

y = (b + d) / 2

Now,

31 = (a + 2)/2

31 x 2 = a + 2

62 = a + 2

a = 62 - 2

a = 60

-5 = (b - 19)/2

-5 x 2 = b - 19

-10 = b - 19

-10 + 19 = b

b = 9

Thus,

The coordinates of the endpoint A = (A, B) is (60, 9)

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The correct graph of the given information is given by (A).

Let the number of pounds is = x

Given that, Shipping company A charges a flat fee of $7 plus $0.50 for each pound.

So the suitable equation of the shipping A is when the total charge is y, is given by,

y = 7 + 0.50x

Again it is given that Shipping company B charges a flat fee of $11 plus $0.25 for each pound.

So the suitable equation of the Shipping B is when the total charge is y, is given by,

y = 11 + 0.25x

Hence the correct graph is (A).

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0.68 is the variable is normally distributed when standard deviation is r29. 44.

What is standard deviation in math?

μ = 146.21   σ = 23.44         x ~ n

P{ x < 160 } = ρ{ x - μ/σ < 160 - 146.21/29.44 }

                   = ρ{ z < 0.47 }

                    = 0.6808

                    ≈ 0.68

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the probablilty of p and k is 82.6%.

Given:

key club P(k) = 2.3%

physics P(p) = 8.6%

(p∩k) = 1.9%

formula:

P(p/k) = P(p∩k)/P(k)

putting the value,

P(p/k) = 1,9%/2.3%

= 0.019/0.023

= 0.826 = 82.6%

hence the probability of p given k is 82.6%.

#123

The probability of P given K is 0.826.

Given information;

The guidance department has stated that of the senior class, 2.3% are members of key club, K, 8.6% are enrolled in AP physics, P, and 1.9% are enrolled in both. This information is supplied in the question.

To get the probability of P given K [P(A)];

P(K) = 2.3

P(P) = 8.6

P(P ∩ K) = 1.9

P(A) = P(P ∩ K) / P(K)

       = 1.9/2.3

       = 0.826

Hence, the probability of P given K is 0.826.

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The distance between the base to the summit of the mountain is 300 meters.

Here Given that,

Person climbs a mountain road from the bas to the summit at a speed of 45 m/min.

And

descends the same road from top to bottom at a speed of 60 m/min

Now,

The time difference between the climbing and descending is 20 min.

So, we can say that

Velocity v₁=45 m/min

Velocity v₂=60 m/min

Time difference ∆t=20 min

We have to find the distance between the base to the summit.

As we know,

The formula for average velocity is

∆v=∆x/∆t

v₂-v₁=∆x/∆t

60-45=∆x/20

∆x=15×20

∆x=300 meter

Hence,

it is 300 meters from the base to the summit of the mountain.

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Answer:

Point Slope Form:  y - 0=2 (x - 0)

Simplified Form:  y=2x

Step-by-step explanation:

The point-slope form of line is given by:

y - y1=m(x - x1)

Where

m is the slope

 is the first x-coordinate

 is the first y-coordinate

Given slope is 2, thus we can say:

m = 2

Also, it says the line goes through the point (0,0), so:

and

Now, substituting, we get the point slope form to be:

y-y1=m(x - x1)

y-0=2(r-0)

y=2(x)

y=2x

The equation of line will be y = 2x

The slope of the equation m = 2 and the point P ( x₁ , y₁ ) = P ( 0 , 0 )

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation be represented as A

Let the point be represented as P

The value of P = P ( 0 , 0 )

The slope of the equation m = 2

Slope m = 2

Now , the equation of line in the slope intercept form is

y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 0 = 2 ( x - 0 )

On simplifying the equation , we get

y = 2x

Therefore , the value of A is y = 2x

Hence , the equation of line is y = 2x

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The 90th percentile with a mean of 392 hours and a standard deviation of 9 hours is  403.538.

Given:

The lifetimes of light bulbs of a particular type are normally distributed with a mean of 392 hours and a standard deviation of 9 hours.

P(z<=?) = 0.90

z = 1.282

1.282 = x - mean / standard deviation

1.282 = x - 392 / 9

1.282 * 9 = x - 392

11.538 = x - 392

x = 392 + 11.538

x = 403.538.

Therefore the 90th percentile with a mean of 392 hours and a standard deviation of 9 hours is 403.538.

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The solution of the system of equations y = -x + 6 and y = (1/2)x - 6 be

(8 , -2)

Given, two linear equations

y = -x + 6

y = (1/2)x - 6

Now, to plot the first equation i.e. y = -x + 6

first plot two points

(0 , 6) and (6 , 0)

Now, pass a straight line through these two points and we get the graph of the given equation.

Now, to plot the second equation i.e. y = (1/2)x - 6

first plot two points

(0 , -6) and (12 , 0)

Now, pass a straight line through these two points and we get the graph of the given equation.

Now, to get the solution Plot the point of intersection of these two lines i.e. (8 , -2)

Hence, the solution of the system of equations be (8 , -2).

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Answer:

(3, 2)

Step-by-step explanation:

4x + 5y = 22

2x + 3y = 12

4x + 5y = 22

-4x - 6y = -24

-y = -2

y = 2

4x + 5(2) = 22

4x = 12

x = 3

Answer: (3, 2)

The volume increase when the radius changes from 7 to 7.1 ft is 62.45 ft³ i.e. 4.34%. of the previous volume.

We know that the volume of the sphere is 4/3πr³.

So, here the radius of the sphere is 7 ft,

Therefore the volume of the sphere will be = 4/3π(7)³.

so, V1 = 4/3*3.14*(7)³.

V1 = 1436.76  ft³.

When the radius of the sphere will increase tp 7.1 feet then the volume will also increase which will be :

V2 = 4/3*3.14*(7.1)³.

V2 = 1499.21 ft³.

Now the increase in volume is V2- V1 .

which is , 1499.21 ft³ -  1436.76  ft³

i.e. 62.45 ft³ is the increase of the volume of the sphere.

This increased volume is the 4.34% of the previous volume of the sphere.

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Using the Pythagorean Theorem, 12² + 5² = 169 = ✓169 = 13

This is simply the way that one can find the missing length of a right angled triangle.

In this case, it should be noted that the theorem is in the form of:

a² + b² = c²

c = hypothenuse

a and b are the other sides

Based on the information given, this will be:

5² + 12²

= 25 + 144

= 169

Now the square root of 169 is ✓169 = 13.

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The length of the side AD is 24 inches

Consider the triangle ABC

The area of the triangle = 288 square inches

The length of the side CD = 9 inches

The length of the side DB = 15 inches

The length of the the base = The length of the side CD + The length of the side DB

Substitute the values in the equation

The length of the the base  = 9 + 15

= 24 inches

The area of the triangle = (1/2) × Base × Height

Substitute the values in the equation

288 = (1/2) × 24 × AD

288 = 12 × AD

AD = 288 / 12

AD = 24 inches

Hence, the length of the side AD is 24 inches

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Answer:If Giulio chooses the first option he will pay about 4,500

If he chooses the second option with the lower rate and compound interest, he will pay a total of about 3,000.

Step-by-step explanation: I dont have an explanation but I think I'm right