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By applying reflection theory and constructing a geometric system of two proportional right triangles, the height of the stainless steel globe is approximately 140 ft.

By physics we know that both the angle of incidence and the angle of reflection are same. Thus, we have a geometric system formed by two proportional right triangles:

5.6 ft / 4 ft = h / 100 ft

h = (5.6 ft × 100 ft) / 4ft

h = 140 ft

By applying reflection theory and constructing a geometric system of two proportional right triangles, the height of the stainless steel globe is approximately 140 ft.

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Answer:

Explanation -

In triangle SRT

angle R = 72°

angle T = 90°

angle S = 18° ( by angle sum property of a triangle)

in triangle VWU

angle W = 90°

angle V = 18°

angle W = angle T

side RS = side uv ( if two corresponding angles of two triangles are equal then their sides are also equal)

angle R = angle V

by angle side angle criteria both the triangles are congruent.

260 inches of trim are needed to surround the​ window.

The total land area of all the faces of a three-dimensional object is its surface area. When we wish to wrap something in real life, we employ the notion of surface areas of distinct things.

Actually, all we need is a trim that is the same size as our window and equal to the parallelogram's circumference, which is

The sum of the side is;

⇒Length of lower side + Length of the upper side

⇒ 90+90

⇒180 inches

The sum of adjacent sides;

Sum of adjacent sides  =  40+40

Sum of adjacent sides  = 80 inches

The length you should trim is needed to surround the​ window is found as;

⇒ 180 inches + 80 inches

⇒260 inches

Hence,260 inches of trim are needed to surround the​ window.

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Answer:

[tex]\boxed{\sf x= -29.5}[/tex]

Step-by-step explanation:

[tex]\sf \sqrt{-2x+5}-3=5[/tex]

[tex]\sf \sqrt{-2x+5}=8[/tex]

[tex]\sf -2x+5=64[/tex]

[tex]\sf -2x=59[/tex]

[tex]\sf \cfrac{-2x}{-2}=\cfrac{59}{-2}[/tex]

Therefore, x = -29.5.

Answer:

6 $50 bills and 9 $5 bills

Step-by-step explanation:

Let's let x = the number of $5 bills, and y = the number of $50 bills. With this, we can set up two equations:

5x + 50y = 345

x + y = 15

Because there is $345 total in the register, that means that 5 times the number of $5 bills plus 50 times the number of $50 bills would equal 345. And there are 15 bills total, so the numbers added is 15. Now, we can solve these equations through substitution:

x + y = 15

x = 15 - y

Now, plug in (15 - y) for x into the other equation, and solve for y:

5(15 - y) + 50y = 345

75 - 5 y + 50y = 345

75 + 45y = 345

45y = 270

y = 6

Since y is 6, that means we have 6 $50 bills. And there are 15 bills total, so there are 9 $5 bills. (15 - 6 = 9)

Option C. A 2-column table with 5 rows. Column 1 is labeled x with entries negative 9, negative 7, negative 5, negative 3, negative 1. Column 2 is labeled y with entries negative 25, negative 21, negative 17, negative 13, negative 9.  This labeled is correct.

According to the linear function,
Every linear function is characterized by a constant rate of change; the slope. The slope of a linear function is a measure of the “steepness” of the line. We use the symbols Δx and Δy which mean respectively the “change in x ” and the “change in y ”.

So Option C is correct after all assumptions.

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The image is attached with the answer.

A magic square is a 3*3 , 4*4 ,5*5 square in which the magic sum is constant for all the columns and rows and even diagonally the sum is same.

The empty squares have been filled and the image has been attached.

The magic sum is 0.81

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The labeled angles are both equal to c by the corresponding angles theorem.

Thus, a+b=c by the exterior angle theorem.

Answer:

<3 and <5<4 and <6

Step-by-step explanation:

Now that we know how to identify consecutive interior angles, let’s talk about the theorem. The consecutive interior angles theorem states that when the two lines are parallel, then the consecutive interior angles are supplementary to each other. Supplementary means that the two angles add up to 180 degrees.

We have that the ways 5-person committee such that exactly 2 local business owners are represented is mathematically given as

N=5940

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

The Probability that 2 local business owners are represented on the committee is given by finding the ways they can be seated amongst the 5

Generally, 2 local business owners are represented is mathematically given as

N=11C3 x 9C2

Therefore

N=165 x 36

N=5940

Therefore the way 5-person committee such that exactly 2 local business owners are represented is mathematically given as

N=5940

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Answer:

undefined

Step-by-step explanation:

Since line m passes through two points that have the same x-value but different y values, line m is horizontal to the y-axis which has an undefined slope.

Taking the change in y over the change in x. Then the correct option is A.

Suppose the given points are (x₁, y₁) and (x₂, y₂), then the equation of the straight line joining both two points is given by

[tex]\rm (y - y_1) = \left [ \dfrac{y_2 - y_1}{x_2 - x_1} \right ] (x -x_1)[/tex]

The equation of the line can be determined by the two known points.

Taking the change in y over the change in x.

Then the correct option is A.

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Differentiate both sides with respect to [tex]t[/tex], treating both [tex]x[/tex] and [tex]y[/tex] as functions of [tex]t[/tex].

[tex]x^3 + y^3 = 9 \implies 3x^2 \dfrac{dx}{dt} + 3y^2 \dfrac{dy}{dt} = 0[/tex]

Then when [tex]x=1[/tex], [tex]y=2[/tex] and [tex]\frac{dx}{dt}=-3[/tex], we get

[tex]3\times1^2\times(-3) + 3\times2^2\dfrac{dy}{dt} = 0 \implies \dfrac{dy}{dt} = \dfrac9{12} = \boxed{\frac34}[/tex]

The number of fowls is 9, and the number of goats is 12 if there were 42 eyes and 66 legs in her backyard.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Let x be the number of fowls and

y be the number of goats

Then total eyes = 2x + 2y  

Because both have two eyes

2x + 2y = 42 ..(1)

Total legs = 2x + 4y

fowl has two legs and a goat has 4 legs

2x + 4y = 66 ..(2)

After solving two linear equation:

-2y = -24

y = 12

x = 9

Thus, the number of fowls is 9, and the number of goats is 12 if there were 42 eyes and 66 legs in her backyard.

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Answer:

The smaller bottle holds 12.5 ml of perfume.

====================

Find the scale factor, the ratio of corresponding dimensions:

We know the volume is the function of three dimensions, therefore the ratio of volumes is the cube of the scale factor:

Substitute the known values and find the volume of small bottle:

The smaller bottle holds 12.5 ml of perfume.

The smaller bottle holds 12.5 ml of perfume.

I solved it and came with this result.

Answer:

to solve fractions such as

1 1/3

first multiple the denominator with the whole no.

and then add with the numerator

here 3 * 1 + 1 /3

= 4/3

1 2/3

= 3*1 + 2 /3

5/3

The sequence of transformations used to obtain figure A'B'C'D'from figure ABCD are a reflection across the y-axis followed by a horizontal translation 1 unit right

Figure ABCD is transformed to figure A'B'C'D', as shown below: (see attachment)

Which of the following sequences of transformations is used to obtain figure A'B'C'D'from figure ABCD?

From the attached figure, we can see that:

ABCD and A'B'C'D' are on either sides of the y-axis.

This means that ABCD is first reflected across the y-axis.

ABCD is 2 units from the y-axis, while A'B'C'D' is 1 unit from the y-axis.

This means that the reflection is followed by a translation.

The unit of translation is:

Unit = 2 - 1

Evaluate

Unit = 1

1 represents a right translation

Hence, the sequence of transformations are a reflection across the y-axis followed by a horizontal translation 1 unit right

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A mean is an arithmetic average of a set of observations. The correct option is B.

A mean is an arithmetic average of a set of observations. it is given by the formula,

Mean = (Sum of observations)/Number of observations

The average pay does not differ significantly since the average wage for subpopulations is not significant. As a result,  the subpopulations of mechanical and civil engineers are Not earning different salaries.

Hence, the correct option is B.

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Answer:

Linear Equations In One Variable =

[6(x-1)6] / 7 = 12

[(6x - 6)6] = 84

[36x - 36] = 84

36x = 84 + 36

36x = 120

x = 120/36

x = 10/3

equation solved (Answer : 10/3)

Answer:

D

Step-by-step explanation:

[tex]1200( {1.025}^{5} ) = 1357.69[/tex]

The probability that a single can will contain 11.6 ounces or less of soda is 0.2843

The given parameters are:

x = 11.6

Mean = 12

Standard deviation = 0.7

Calculate the z value using:

[tex]z = \frac{x - \bar x}{\sigma}[/tex]

This gives

[tex]z = \frac{11.6-12}{0.7}[/tex]

z = -0.57

The probability is then calculated as:

P(x ≤ 11.6) = P(z ≤ -0.57)

Using the z table of probabilities, we have:

P(x ≤ 11.6) = 0.2843

In (a), the probability that a can contains 11.6 ounces or less is 0.2843

The probability that all cans in a pack contains 11.6 ounces or less is

P(6) = 0.2843^6

P(6) = 0.00053

In (a), the probability that a can contains 11.6 ounces or less is 0.2843

The probability that all cans in a case contains 11.6 ounces or less is

P(36) = 0.2843^36

P(36) ≈ 0

See attachment for the normal distributions

The summary of the graph is that, as the sample size increases the probability decreases

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Answer:

600

Step-by-step explanation:

Because the tens digit is less than 5, round down to 600

Answer:

The rate at which the temperature drops.

Step-by-step explanation:

In science, the dependent variable is what you are measuring.
In math, the dependent variable is what you are evaluating.

Same idea, different topic.

Answer:

d=temp drop

t=hours

dependent variable is the temperature drops because the number of hours will tell you how much the temprature drops

this is the equation

total temp drops=t x 5

hope this helps!?

This shows that the greatest common factor is 8, Hence Venita's error is that she incorrectly determined the GCF.

Given the following expression

32ab - 8

Find the factors of each terms

32ab = 8 * 4. * a * b

8 = 8 * 1

Since 8 is common to both factors, hence

32ab - 8 = 8(4ab -1)

This shows that the greatest common factor is 8, Hence Venita's error is that she incorrectly determined the GCF.

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Answer:

the answer is B. 140 units²

Answer:

Y=72

Step-by-step explanation:

First we set up the equation which is (20-2) times 4=Y

Then we solve, 20 minus 2 is risk since it is in the parentheses. 20 minus 2 is 18.

After that 18 times 4 is 72

Y=72

The value of x for the missing lengths in the given chords in the circle is; x = 4

The intersecting chords theorem  is a statement in elementary geometry that describes a relation of the four line segments created by two intersecting chords within a circle.

Thus, for two chords AC and BD intersecting in a point S the following equation holds: AS * SC = BS * SD

Thus, for this question;

8(x + 2) = 12x

8x + 16 = 12x

12x - 8x = 16

4x = 16

x = 16/4

x = 4

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P(more than 1 hour of TV | 6th period class) is  0.352.

Probability determines the odds that a random event would happen. The odds of the random event happening lie between 0 and 1.

P(more than 1 hour of TV | 6th period class) = number of 6th period class students who watch tv for more than an hour / total number of students surveyed

12 / (12 + 9 + 5 + 8)

12 / 34 = 0.352

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From point (0, 9/2) and (-9, 0) we get a straight line.

A straight line is an infinite length line that does not have any curves on it. A straight line can be formed between two points also but both the ends extend to infinity.

Here, given equation:

    (y − 3) = 1/2(x + 3)

at x = 0,

    y - 3 = 1/2 (0 + 3)

    y - 3 = 1/2 X 3

     y = 3/2 + 3

    y = 9/2

at y = 0,

   0 - 3 = 1/2 (x + 3)

    -3 = 1/2 (x + 3)

    -6 = x + 3

    x = -6 - 3

   x = -9

Thus, from point (0, 9/2) and (-9, 0) we get a straight line.

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