A woman wants to measure the height of a nearby tower. She places a 7 ft pole in the shadow of the tower so that the shadow of the pole is exactly covered by
the shadow of the tower. The total length of the tower's shadow is 188 ft, and the pole casts a shadow that is 3.75 ft long. How tall is the tower? Round your
answer to the nearest foot. (The figure is not drawn to scale.)
Sun
Tower
Pole
Shadow of pole"
Shadow of tower
Ú
ft
X

We can say that after answering the offered question Therefore, the proportionality constant of proportionality in this scenario is 11.25.

Proportionate relationships are those that have the same ratio every time. For example, the average number of apples per tree defines how many trees are in an orchard and how many apples are in an apple harvest. Proportional refers to a linear relationship between two numbers or variables in mathematics. When the first quantity doubles, the second quantity doubles as well. When one of the variables decreases to 1/100th of its previous value, the other falls as well. When two quantities are proportional, it means that when one rises, the other rises as well, and the ratio between the two remains constant at all values. The diameter and circumference of a circle serve as an example.

In this case, we may use the following formula to calculate the proportionality constant:

proportionality constant = output/input

where the output is John's pay and the input is the number of hours he worked.

As a result, the proportionality constant is:

Paycheck/hours worked = proportionality constant

proportionality constant = 450/40

proportionality constant = 11.25

As a result, the proportionality constant in this scenario is 11.25.

In this case, we may use the following formula to calculate the proportionality constant:

proportionality constant = output/input

where the output is John's pay and the input is the number of hours he worked.

As a result, the proportionality constant is:

Paycheck/hours worked = proportionality constant

proportionality constant = 450/40

proportionality constant = 11.25

Therefore, the constant of proportionality in this scenario is 11.25.

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4/9 of the students at Polk High School play football.

How to solve fraction?

If 2/3 of the students play a sport and 2/3 of those who play a sport play football, then the fraction of students who play football can be found by multiplying the two fractions:

(2/3) x (2/3) = 4/9

Therefore, 4/9 of the students at Polk High School play football.

To understand more clearly :-

Polk High School has a certain number of students, and 2/3 of them play a sport. Out of those who play a sport, 2/3 of them play football. The question asks what fraction of the students at Polk High School play football.

To solve the problem, we first need to find the fraction of students who play both a sport and football. We can do this by multiplying the fractions representing each of these groups of students. The product of 2/3 and 2/3 is 4/9, which represents the fraction of students at Polk High School who play both a sport and football.

Therefore, 4/9 of the students at Polk High School play football. This means that out of every 9 students, 4 of them play football and 5 of them do not. Alternatively, we can express this answer as a percentage by multiplying 4/9 by 100. This gives us 44.4%, meaning that approximately 44.4% of the students at Polk High School play football.

It is important to note that this answer assumes that all students at Polk High School play either a sport or no sport at all, and that all sports are equally likely to be played by students. If these assumptions are not true, the answer may not be accurate.

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The sοlutiοns tο the inequality are x values greater than 5.

A number line frοm negative 3 tο 3 in increments οf 1. An οpen circle is at 5 and a bοld line starts at 5 and is pοinting tο the right.

-6x - 5 < 10 - x and -6x + 15 < 10 - 5x are cοrrect representatiοns οf the inequality –3(2x – 5) < 5(2 – x).

Tο sοlve the inequality -3(2x - 5) < 5(2 - x), we can start by distributing the negative 3 and the pοsitive 5 οn the right side:

-6x + 15 < 10 - 5x

Then, we can simplify by mοving all the x terms tο οne side and all the cοnstant terms tο the οther side:

-x < -5

Finally, we can divide bοth sides by -1, remembering tο reverse the inequality sign:

x > 5

Therefοre, the sοlutiοns tο the inequality are x values greater than 5. The representatiοns οf this sοlutiοn οn a number line are:

A number line frοm negative 3 tο 3 in increments οf 1. An οpen circle is at 5 and a bοld line starts at 5 and is pοinting tο the right.

A number line frοm negative 3 tο 3 in increments οf 1. An οpen circle is at negative 5 and a bοld line starts at negative 5 and is pοinting tο the left.

Hοwever, οnly the first representatiοn is cοrrect, since the secοnd representatiοn shοws the sοlutiοns tο x < -5, which is the οppοsite inequality tο the οne we fοund.

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Approximately 9.42 units of paint would be required to paint the outside of a cylinder with a radius of 3 meters and a height of 5 meters, without the top.

To calculate the amount of paint required to paint the outside of a cylinder, you will need to find the surface area of the cylinder. Since the cylinder is without a top, we only need to find the lateral surface area.

formula of surface area

Lateral Surface Area = 2πrh

when r is the cylinder's radius, h is its height, and is a constant value roughly equivalent to 3.14.

Once you have calculated the lateral surface area of the cylinder, you can use the following formula to find the amount of paint required:

Amount of Paint = Lateral Surface Area / Coverage per unit of paint

where coverage per unit of paint refers to the area that can be covered by one unit of paint. This will depend on the type of paint you are using and its thickness.

For example, if the cylinder has a radius of 3 meters and a height of 5 meters, the lateral surface area would be:

Lateral Surface Area = 2πrh

Lateral Surface Area = 2 x 3.14 x 3 x 5

Lateral Surface Area = 94.2 square meters

If the coverage per unit of paint is 10 square meters, the amount of paint required would be:

Amount of Paint = Lateral Surface Area / Coverage per unit of paint

Amount of Paint = 94.2 / 10

Amount of Paint = 9.42 units of paint

Therefore, approximately 9.42 units of paint would be required to paint the outside of a cylinder with a radius of 3 meters and a height of 5 meters, without the top.

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Step-by-step explanation:

Since the number of bacteria in the petri dish doubles every two hours, after 2 hours, Harriet will have 103 x 2 = 206 bacteria.

After another 2 hours (i.e., 4 hours from the beginning), the number of bacteria will double again to become 206 x 2 = 412 bacteria.

After another 2 hours (i.e., 6 hours from the beginning), the number of bacteria will double once more to become 412 x 2 = 824 bacteria.

Therefore, Harriet will have 824 bacteria in the dish at the end of 6 hours. Answer: A. 1024 (rounded to the nearest whole number).

P(same number on both) = 10/60 = 1/6 and P(odd, even) or P(even, odd)  = 1/4

There are 10 possible outcomes on the 10-sided die and 6 possible outcomes on the 6-sided die

The total number of possible outcomes is 10 x 6 = 60.  

To get the same number on both, we need to get one of the 10 numbers on the first toss and then get the same number on the second toss. There are 10 ways to do this. Therefore, the probability of getting the same number on both is:

P(same number on both) = 10/60 = 1/6

b. To get an odd and an even number, we need to get an odd number on the first toss and an even number on the second toss, or vice versa.

There are 5 odd numbers and 5 even numbers on the 10-sided solid, and 3 even numbers and 3 odd numbers on the 6-sided solid.

Therefore, the probability of getting an odd and an even number, or an even and an odd number, is:

P(odd, even) or P(even, odd) = (5/10) x (3/6) + (5/10) x (3/6) = 1/4

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Answer:

39

Step-by-step explanation:

First you need to find the other missing angle, by subtracting 156.5 from 180. (because 180 is the angle of a straight line)

180-156.5=23.5

Then we can add the two angles

117.5+23.5=141

Since we know that all triangles' angles add up to 180, we can subtract the sum from 180 to get our answer.

180-141=39

We can check if this is right by adding all the angles again.

39+23.5+117.5=180

Therefore, c=39

Answer:

QR & ST = 37

Step-by-step explanation:

Because this is a regular hexagon, all the sides are equal.

Thus, since the length of QR = the length of ST, we can set the equations for both sides equal to each other and solve for y:

[tex]3y+19=6y+1\\3y+18=6y\\18=3y\\6=y[/tex]

Now, we can plug in 6 for y into any of the two equations to find the length of both QR and ST:

[tex]QR=3(6)+19\\QR=18+19\\QR=37[/tex]

Answer:

-25

Step-by-step explanation:

= 2*(2) - 28 - 1

= 4 - 29

= -25

Given:-

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

━━━━━━━━━━━━━━━━━━━━━━━

hope it helps! :)

The equivalent οf the expressiοn 8(-x + 1/4) is -8x + 2.

A mathematical expressiοn is a phrase that cοntains a minimum οf twο numbers οr variables and at least οne mathematical οperatiοn. It's pοssible tο multiply, divide, add, οr subtract with this mathematical οperatiοn. An expressiοn's structure is as fοllοws:

Expressiοn: (Math Operatοr, Number/Variable, Math Operatοr).

The given expressiοn is 8(-x + 1/4)

The distributive prοperty:

Accοrding tο the distributive prοperty, it is mandatοry tο multiply each οf the twο numbers by the factοr befοre adding them tοgether when a factοr is multiplied by the sum οr additiοn οf twο terms. A (B+ C) = AB + AC is a symbοlic representatiοn οf this prοperty.

Apply the distributive prοperty:

= 8×(-x) + 8×(1/4)

= -8x + 2

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The value of x is 8 when GH is 3x-2, HI is 7x-4 and GI is 8x+10. It forms a straight line.

Segment addition is a concept in geometry that states that given three collinear points A, B, and C, with B between A and C, the length of AB added to the length of BC will give the length of AC. This can be expressed algebraically as:

AB + BC = AC

We can use the fact that GH + HI = GI (by the segment addition postulate) and substitute the given expressions to get:

(3x - 2) + (7x - 4) = 8x + 10

Simplifying the left side by combining like terms, we get:

10x - 6 = 8x + 10

Subtracting 8x from both sides, we get:

2x - 6 = 10

Adding 6 to both sides, we get:

2x = 16

Dividing by 2, we get:

x = 8

Therefore, x = 8.

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The distance between the two points N(-3, -11) and P(-3, -2) is 9 units.

Given the points

N(-3,-11) and P(-3,-2)

To find the distance between two points, we can use the distance formula:

d = √((x2 - x1)²+ (y2 - y1)²)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Using this formula, we can find the distance between the two points N(-3, -11) and P(-3, -2) as follows:

d = √((-2 + 11)²+ (-3 + 3)²)

This gives

d = √9²+ 0²)

So, we have

d = √81

Evaluate

d = 9

Therefore, the distance between the two points N(-3, -11) and P(-3, -2) is 9 units.

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Answer:

7) S=6.28 yd  A=12.57 [tex]yd^{2}[/tex]

8) S=99.48 ft A=945.1 [tex]ft^{2}[/tex]

9) S=21.99 in  A=43.98 [tex]in^{2}[/tex]

Step-by-step explanation:

7)

S=r θ

S=4([tex]\frac{90\pi }{180}[/tex])........................................plug in values

S=4([tex]\frac{\pi }{2}[/tex])...........................................simplify

S=6.28 yd...................................solve and round

A=[tex]\frac{1}{2}[/tex]([tex]r^{2}[/tex]) θ

A=[tex]\frac{1}{2}[/tex]([tex]4^{2}[/tex])([tex]\frac{90\pi }{180}[/tex]) ....................................plug in values

A=[tex]\frac{1}{2}[/tex](16)([tex]\frac{\pi }{2}[/tex])  .....................................simplify

A=12.57 [tex]yd^{2}[/tex]...................................solve and round.

8)

S=r θ

S=19([tex]\frac{300\pi }{180}[/tex]).........................................plug in values

S=19([tex]\frac{5\pi }{3}[/tex]).............................................simplify

S=99.48 ft........................................solve and round

A=[tex]\frac{1}{2}[/tex]([tex]r^{2}[/tex]) θ

A=[tex]\frac{1}{2}[/tex]([tex]19^{2}[/tex])([tex]\frac{300\pi }{180}[/tex]) ....................................plug in values

A=[tex]\frac{1}{2}[/tex](361)([tex]\frac{5\pi }{3}[/tex])  .....................................simplify

A=945.1 [tex]ft^{2}[/tex].......................................solve and round.

9)

S=r θ

S=4([tex]\frac{315\pi }{180}[/tex]) ............................................plug in values

S= 4( [tex]\frac{7\pi }{4}[/tex])..............................................simplify

S=21.99 in..........................................solve and round

A=[tex]\frac{1}{2}[/tex]([tex]r^{2}[/tex])θ

A=[tex]\frac{1}{2}[/tex]([tex]4^{2}[/tex])([tex]\frac{315\pi }{180}[/tex]) ....................................plug in values

A=[tex]\frac{1}{2}[/tex](16)( [tex]\frac{7\pi }{4}[/tex])......................................simplify

A=43.98 [tex]in^{2}[/tex]....................................solve and round.

The photos are similar because the enlarged photo is 1.5 times the size of the original photo.

What is meant by similarity transformations?

Similarity transformations turn items in space into similar objects. If two items have the same shape or have the same shape as their mirror images, they are said to be similar. More specifically, by uniformly scaling (enlarging or decreasing), maybe with additional translation, rotation, and reflection, one can be created from the other. This indicates that one object may be properly aligned with the other object by rescaling, moving, and reflecting it. When two things are comparable to one another, one is consistent with the outcome of a specific uniform scaling of the other.

Here the initial dimension of the photo is  5" by 7" and after enlarging it has dimensions 7.5" by 10.5".

The scale factor is = 7.5/5 = 10.5/7 = 1.5

Since the scale factor is constant for all sides, the pictures before and after enlargement are similar.

Therefore the photos are similar because the enlarged photo is 1.5 times the size of the original photo.

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Therefore, m angles for BCD is 98.5°.

An angle is formed when two straight lines or rays meet at a single terminal. The vertex of an angle is the location where two points converge. The Latin word "angelus," which means "corner," is where the term "angle" originates.

These two theorems allow us to calculate the angle BCD's measure as follows:

To establish the angle ECB's measure first, apply Theorem 1:

m ∠ECB = m ∠DBC = 77°

Next, we can use theorem 2 to find the measure of the arc ED:

m(arc ED) = 1/2 (m∠EBD + m∠ECD) = 1/2 (163° + m∠ECB)

Since arc ED is an exterior arc to angle BCD, we can find the measure of angle BCD as:

m ∠BCD = 1/2 (m(arc BD) + m(arc ED)) = 1/2 (77° + m(arc ED))

Substituting the value we found for m(arc ED), we get:

m ∠BCD = 1/2 (77° + 1/2 (163° + m ∠ECB))

Now, we can substitute the value we found for m ∠ECB to get:

m ∠BCD = 1/2 (77° + 1/2 (163° + 77°)) = 1/2 (77° + 120°) = 98.5°

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The factored form of trinomial equation 10m² + 29mn + 10n² is (5m + 2n)(2m + 5n).

The parenthesis must be dropped in order to expand the equation. One need just multiply the value outside the value, which is 2 to each of the values inside the parenthesis, to arrive at an equation without parentheses. The opposite of factoring out, which entails adding parenthesis to an equation, is expanding, which entails removing parentheses from an equation.

The given trinomial equation is 10m² + 29mn + 10n².

Multiply the coefficients of the first and last term that is:

(10)(10) = 100

Now factor the term using two factors to make the given middle term, here the factor of 100 are 4 and 25.

Now, rewrite the equation with the factors as follows:

(10m² + 4mn) + (25mn + 10n²)

= 2m(5m + 2n) + 5n(5m + 2n)

Factor out the common binomial factor (5m + 2n):

(5m + 2n)(2m + 5n)

Hence, the factored form of 10m² + 29mn + 10n² is (5m + 2n)(2m + 5n).

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Answer:

To find the price of 3 tons of concrete, we need to use a proportion:

If 2/3 ton of concrete costs $42, then 1 ton of concrete costs:

$42 ÷ (2/3) ton = $42 × (3/2) = $63

Therefore, 3 tons of concrete will cost:

$63 × 3 = $189

So Trey would need to pay $189 for 3 tons of concrete.

Since line GF = line JK and < G = <J ; the minor arcs, the major arcs of the both circle are also similar and equal.

The minor arc of the given circle above can be defined as the part of the circle that is less than 180°. This is represented by <HGF in the first circle( with a red ink).

The major arc of the given circle above can be defined as the part of a circle that is greater than 180°. Thus is represented by <IJK in the second circle (with black ink).

Therefore in conclusion, there is a established similarity between the two circles since line GF = line JK and < G = <J, thus making their minor and major acre to be equal too.

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7x³ +3y³ +4y

Simplify the expression by Removing parentheses and brackets by multiplying factors, use the exponent rule to remove grouping if the term contains exponents, combine like terms by adding or subtracting coefficients and combine the constants.

Answer: The answer is  7x^3 + 3y^3 + 4y. Or in simpler terms choice A is correct

Step-by-step explanation:

Answer:

22 cakculator is write answer

The bearing of the plane to the nearest degree is 357°, which is answer choice (c).

What is vector addition?

Vector addition is the operation of adding two or more vectors together into a vector sum. The so-called parallelogram law gives the rule for the vector addition of two or more vectors. For two vectors, the vector sum is obtained by placing them head to tail and drawing the vector from the free tail to the free head.

To find the bearing of the plane, we need to determine the direction in which it is traveling with respect to the true north. To do this, we need to use vector addition to combine the velocity of the plane with the velocity of the wind.

Let's break down the velocity vectors into their north-south and east-west components, using positive directions to the north and east.

The airspeed of the plane is 213 mph due south, so its velocity vector can be written as:

Vp = (0, -213)

The wind velocity is 16 mph at a direction of 52.0°. We can find its components using trigonometry:

Vw,x = 16 cos(52.0°) = 10.91 mph to the east

Vw,y = 16 sin(52.0°) = 12.18 mph to the south

So the wind velocity vector is:

Vw = (10.91, -12.18)

To find the total velocity vector of the plane relative to the ground, we can add the velocity vectors of the plane and the wind:

Vtot = Vp + Vw

Vtot = (0 + 10.91, -213 - 12.18)

Vtot = (10.91, -225.18)

The direction of the total velocity vector, measured from true north, can be found using the arctangent function:

θ = arctan(Vtot,x / Vtot,y)

θ = arctan(10.91 / -225.18)

θ ≈ -2.8°

Since the result is negative, this means the direction is to the left of true north. We can convert this to a bearing by adding 360° to get the positive equivalent:

θ = 360° + θ

θ ≈ 357.2°

Therefore, the bearing of the plane to the nearest degree is 357°, which is answer choice (c).

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Answer:

Gary would have 45 and Mary would have 75

We can solve this problem using the standard equation of a circle:

(x - h)² + (y - k)² = r²

where (h, k) is the center of the circle and r is the radius.

Since Noa is at the origin, the center of the circle is the midpoint between the object and the point where the drone passes:

h = (210 - 170)/2 = 20

k = (190 - 150)/2 = 20

The radius is the distance between the center and the point where the drone passes:

r = √((170 - 20)² + (190 - 20)²) = √(150² + 170²) = √(62500) = 250

So the equation of the drone's path is:

(x - 20)² + (y - 20)² = 250²

When the drone passes due north of Noa's position, its x-coordinate is 20, so we can substitute that into the equation:

(20 - 20)² + (y - 20)² = 250²

y - 20 = ±√(250²)

y = 20 ± 250

y ≈ -230 or y ≈ 270

So the drone will be approximately 230 feet north of Noa's position.

Answer:

We can write 8! as:

8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

To simplify the square root of 8!/70, we can first simplify the denominator:

8!/70 = (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)/70

= (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)/(2 x 5 x 7)

= (8 x 6 x 4 x 3 x 2 x 1)/2

= 8 x 6 x 4 x 3 x 1

= 576

Now, we can write the original expression as:

sqrt(8!/70) = sqrt(576/1)

= sqrt(576)

= 24

Therefore, the square root of 8!/70 is 24.

Answer:

50ml of water should be added

Answer:1.325

Step-by-step explanation:

The pοpulatiοn οf the tοwn in the year 1995 was apprοximately 4,262.

The grοwth factοr (b) is given as: b = 3.76

The grοwth factοr (b) is greater than 1.

We can sοlve this prοblem by using the fοrmula fοr expοnential grοwth:

[tex]P(t) = P0(1 + r)^t[/tex]

where:

P0 is the initial pοpulatiοn (821 in 1970)

r is the annual grοwth rate (11% οr 0.11)

t is the number οf years since the initial pοpulatiοn (25 years frοm 1970 tο 1995)

Substituting the given values, we get:

[tex]P(25) = 821(1 + 0.11)^25\\\\P(25) = 821(1.11)^25[/tex]

Using a calculatοr tο evaluate this expressiοn:

P(25) ≈ 4,261.9

Therefοre, the pοpulatiοn οf the tοwn in the year 1995 was apprοximately 4,262.

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According to the given information, the approximate temperature of the Sun's core is [tex]1.485*10^{7}[/tex]degrees Celsius.

The Sun is a massive ball of gas that generates heat and light through nuclear fusion at its core. The temperature of the Sun's core is much hotter than its surface temperature, and this difference in temperature is responsible for the Sun's energy output.

The temperature of the Sun's surface is approximately [tex](5.5*10^{3})[/tex] degrees Celsius, which is also known as the photosphere. However, the temperature at the Sun's core is estimated to be about [tex](2.7*10^{3})[/tex] times hotter than the surface temperature. This is because the core is the site of intense nuclear fusion reactions that convert hydrogen into helium and release huge amounts of energy in the form of heat and light.

To find the approximate temperature of the Sun's core, we can start with the temperature of the Sun's surface, which is given as [tex](5.5*10^{3})[/tex] degrees Celsius. We need to multiply this by the factor of  [tex](2.7*10^{3})[/tex]  to get the temperature of the core.

The approximate temperature of the Sun's core

= [tex](5.5*10^{3}) * (2.7*10^{3})[/tex]

=[tex]14.85*10^{6}[/tex]degrees Celsius

= [tex]1.485*10^{7}[/tex] degrees Celsius (in scientific notation)

Therefore, the approximate temperature of the Sun's core is [tex]1.485*10^{7}[/tex]degrees Celsius.

This extremely high temperature is necessary to sustain the nuclear reactions that power the Sun's energy output. The high temperature and pressure in the core create the ideal conditions for nuclear fusion to occur, which releases energy that eventually makes its way to the surface of the Sun and out into space in the form of light and heat.

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