Approximately how tall is the streetlight? Round your answer to the nearest tenth.

Part (i)

The square has area of 12*12 = 144 square meters. From that, we carve out four quarter-circles from each corner, as the diagram shows. Imagine that we rearranged the quarter circles so that they would then form a full circle. This circle would have radius 6 (half of the 12 meters), so the area of the circle is pi*r^2 = pi*6^2 = 36pi exactly

The four white sections combine to an exact area of 36pi, which approximates to 36*3.14 = 113.04 square meters. Use more decimal digits in pi to get a better approximation.

Exact answer: 36pi square meters

Approximate answer: 113.04 square meters (when using pi = 3.14)

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

Part (ii)

Once we know what the white sections combine to, we can subtract that area from the total overall area of 144 m^2

We end up with 144 - 36pi as the exact area of the red section

This approximates to 144 - 36*3.14 = 30.96 m^2

Exact answer:  144 - 36pi square meters

Approximate answer: 30.96 square meters (when using pi = 3.14)

The final answer after solving the given equation could be 14.

What is Linear Equation ?

Linear Equation can be defined as the equation in which the highest degree of the variable is one. Linear equations are generally three types , they are standard form , slope intercept form , point slope form and linear equation is also called as the equation of straight line.

Given,

Given equation,

2x + 6 = 3x -8

separating the value into a similar term:

2x-3x = -8 - 6

subtracting the equation:

-x = -14

remove negative sign:

x = 14

Therefore , the final answer could be 14.

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The probability of getting 2 blue is 1/9.

You are choosing replacement marbles. The trials (marble selections) are independent from one another and follow the binomial distribution.

1/3 of the time, a blue marble will be the first one chosen.

(This is due to the fact that 4 out of 12 marbles are blue, therefore 4/12 equals 1/3.

A blue marble is 1/3 more likely to be chosen the second time.

The two probabilities can be multiplied to obtain the following results because the marble selections are independent:

The likelihood of receiving two blues is (1/3)2 =1/9.

Therefore, there is a 1/9 chance of obtaining two blues.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

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Answer:

30° and 12

Step-by-step explanation:

The sum of the exterior angle and the interior angle = 180°

sum the parts of the ratio, 1 + 5 = 6 parts

Divide 180° by 6 to find the value of one part of the ratio

180° ÷ 6 = 30° ← value of 1 part of the ratio

(i)

The exterior angle = 30°

(ii)

The sum of the exterior angles of a polygon is 360°

To find the number of sides n divide 360 by 30 , that is

n = 360 ÷ 30 = 12

When solving the following system of equations,  the x in the first equation would be the easiest to solve for.

Systems of equations can be solved using one of three techniques: graphing, substitution, or elimination. Simply plot the provided equations on a graph and locate the point(s) where they all cross to solve a problem by graphing. You may find the values of the variables you are working for by finding the location of this point.

The result of the first equation is

x + 6y = 25

we can easily solve for x by subtracting 6y from both sides we have  

x + 6y - 6y = 25 - 6y

x - 25 - 6y

So, the first equation's x term can be simply solved.

When solving the following system of equations,  the x in the first equation would be the easiest to solve for.

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Answer:

x² + 7x + 5

Step-by-step explanation:

(- 3x² + 2x - 4) + (4x² + 5x + 9)

since both parenthesis are being multiplies by 1 , remove parenthesis

= - 3x² + 2x - 4 + 4x² + 5x + 9 ← collect like terms

= (- 3x² + 4x²) + (2x + 5x) + (- 4 + 9)

= x² + 7x + 5

Answer:

58 degrees

Step-by-step explanation:

The answer is 58 degrees.

180 degrees in a triangle, subtract the angles of 65 and 57, you get 58 degrees.

180 - 57 -65 = 58

David's deposit of $220 compounded continuously at a rate of 1.7% will become $260 after 10 years.

Here we have been given that David invested $220.

The interest rate was 1.7%

Since the amount was compounded continuously, there is no fixed date of when it was compounded, the whole process is taken as an exponential distribution.

There were no withdrawals or additional deposits to this, so our Principal is constant. Hence we can write the formula

Amount = Principal X eᵃˣ

where a = rate of interest/100

x = time

Therefore, we can say that

Ampunt after 10 years = 220 X e¹⁰ ˣ ⁰°⁰¹⁷

= $260.76707

rounding off to the nearest 10 dollars we get

= $260

Hence David's deposit of $220 compounded continuously at a rate of 1.7% will become $260 after 10 years.

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To verify the inverse we can use Horizontal Line Test.

Suppose F is a function.

F does not have an inverse if any horizontal line crosses the graph of f more than once. If no horizontal line crosses the graph of F more than once, then F does have an inverse. In mathematics, having an inverse is a very significant quality, and it has a name.

If and only if a function f has an inverse, then it is one-to-one. The following definition, which is also the one that is most frequently used, is equivalent. If f(a) = f(b) implies a = b for all a and b in its domain, then a function f is one-to-one.

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Answer:

B

Step-by-step explanation:

since the value is above 1 and your subtracting 1 to drop the value below the 0 point below making it negative.

Answer:

35 dimes and 65 nickels

Step-by-step explanation:

We will need use a system of equations to find the total number of nickels and dimes.

Because there are 100 dimes and there are only nickels and dimes, one equation is N + D = 100, where N is the total number of nickels and D is the total number of dimes.

Because a dime is worth $0.10, a nickel is worth $0.05, and the total change in the jar is worth $6.75, the second equation is 0.05N + 0.1D = 6.75

Substitution will be the easiest method to solve:

[tex]0.05N+0.1D=6.75\\N+D=100\\\\N=-D+100\\\\0.05(-D+100)+0.1D=6.75\\-0.05D+5+0.1D=6.75\\0.05D+5=6.75\\0.05D=1.75\\D=35\\\\N+35=100\\N=65[/tex]

Answer:

-1.256165295×10×10×10×10×10×10×10×10×10×10×10

Step-by-step explanation:

negative changes everything

'The leangth of the shortcut is: '

guessing- '75'

Hope this helps!

The point satisfies the equation ! 8 = 4 × (2)

Answer:

Yes

Step-by-step explanation:

If you plug in the numbers to the equation, you should get:

8 = 4(2)

Then,

8 = 8

therefore, (2,8) does satisfy the equation y = 4x.

Answer:

Q1 : [tex]\frac{5}{8}[/tex]

Q2: [tex]\frac{2}{3}[/tex]

Q3: [tex]\frac{11}{12}[/tex]

Q4: [tex]\frac{4}{5}[/tex]

Q5:  [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

Answer:

Q1. [tex]\frac{5}{8}[/tex]

Q2. [tex]\frac{2}{3}[/tex]

Q3. [tex]\frac{11}{12}[/tex]

Q4. [tex]\frac{4}{5}[/tex]

Q5. [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

Q1.

[tex]\sqrt{\frac{25}{64}}[/tex] ⇒ [tex]\frac{\sqrt{25}}{\sqrt{64}}[/tex] = [tex]\frac{5}{8}[/tex]

Q2.

[tex]\sqrt{\frac{36}{81}}[/tex] ⇒ [tex]\frac{\sqrt{36}}{\sqrt{81}}[/tex] = [tex]\frac{6}{9} = \frac{2}{3}[/tex]

Q3.

[tex]\sqrt{\frac{121}{144}}[/tex] ⇒ [tex]\frac{\sqrt{121}}{\sqrt{144}} = \frac{11}{12}[/tex]

Q4.

[tex]\sqrt{\frac{64}{100}}[/tex] ⇒ [tex]\frac{\sqrt{64}}{\sqrt{100}} = \frac{8}{10} = \frac{4}{5}[/tex]

Q5.

[tex]\sqrt{\frac{4}{9}}[/tex] ⇒ [tex]\frac{\sqrt{4}}{\sqrt{9}} = \frac{2}{3}[/tex]

Answer: Maisie walked 6.4 miles.

Step-by-step explanation:

Since Maisie is walking at a constant pace of 1.6 miles per hour we can set up the following equation:

y = 1.6(x)

In this equation, Y is the number of miles Maisie walked in total and X is the number of hours she walked. All we have to do is plug in 4 hours as x and solve.

y = 1.6(4)

y = 6.4 miles.

Answer: picture wont seem to load, maybe try again

Step-by-step explanation:

Answer:

x = 7.9

Step-by-step explanation:

Sin = Opposite over Hypotenuse

Thus,  [tex]sin(21)=\frac{x}{22}[/tex]

* multiply each side by 22 *

[tex]\frac{x}{22} *22=x\\22sin(21)=7.9[/tex]

we're left with x = 7.9 ( rounded )

Answer:

25.12 kilometers

Step-by-step explanation:

[tex]c = 2\pi \: r[/tex]

C = 2 × 3.14 × 4

C = 25.12

Answer: Choice 2

Step-by-step explanation:

The statement whether each data set is likely to be distributed nor not:

Number of minutes required to complete a marathon - Yes.

Number of miles in a marathon: - No.

Average age of a person who runs a marathon: No.

The distribution of values in a field is described by a statistical distribution, often known as a probability distribution. In other words, the statistical distribution identifies the typical and unusual values. The bell-shaped normal distribution is one of many varieties of statistical distributions.

Let n miles in marathon.

To normally distribute, number of minutes required to complete a marathon:

The number of minutes required to complete a marathon is likely to be normally distributed with small amounts in tails (very slow, very fast) and large amount in middle.

So, yes.

To normally distribute,  number of miles in a marathon:

The number of miles is a fixed number, not normally distributed.

So, no.

To normally distribute, average age of a person who runs a marathon:

The average age is a fixed number

Average age is not likely to be normally distributed.

So, no.

Therefore, the first one is yes, and the other two are no.

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The volume of the water walking ball is 43.71 m³

Surface Area of a Sphere. A = 4 π r2. The volume of a Sphere. V = (4 ⁄ 3) π r³. Where r is the radius of the circle

Given :

[tex]$V=\frac{1}{6\sqrt{\pi}}S^{3/2}$[/tex] and surface area of water walking ball is  60 m²

putting the values in the equation we get

V= 464.758/10.632

V=43.71

Hence, the volume of the water walking ball is 43.71 m³

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Answer:

25 [tex]cm^{2}[/tex]

Step-by-step explanation:

The others are squares as well, meaning each of the sides are equal.

The square root of 144 is 12, meaning the side of the red square is 12.

169's square root is 13, meaning the hypotenuse of the center triangle is 13.

Now that we have a side and the hypotenuse, we can use Pythagorean theorem to find out the final side.

12^2 + x = 13^2

[tex]12^{2} + x^{2} =13^{2} \\144 + x^{2} = 169\\x^{2} = 25\\x = 5[/tex]

Now that we have the side, let's just square it to find the area.

[tex]5 * 5 = 25[/tex]

For a house that have a height of 6 meters and length of 4.5 meters. On a scale drawing if the height of the house is 30 mm the length of the house will be 22.5 mm

In general, the term proportion refers to a part, share, or amount that is compared to a whole.

According to the definition of proportion, two ratios are in proportion when they are equal.

The length of the house on the map is calculated using equality in proportions as follows

The required proportion is

= height of the house / length of the house

= 6 / 4.5

= 4/3

Using this proportion, the length of the house in the drawing is

= 30 mm / 4/3

= 22.5

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Answer:

A fraction is a mathematical expression that represents the division of two numbers, called the numerator and the denominator. The numerator represents the number of parts being considered, while the denominator represents the number of parts in the whole. A fraction with a numerator of 6 and a denominator of negative 8 can be simplified to -3/4. To find an equivalent fraction, we can multiply or divide both the numerator and denominator by the same number without changing the value of the fraction. In this case, the fraction with a numerator of negative 8 and a denominator of 6 is equivalent to -4/3.

Step-by-step explanation:

The maximum possible value for the greatest common divisor (GCD) of 11n + 3 and 2n + 1 as n ranges over the positive integers is 1.

The GCD of two integers is the largest integer that divides both integers without leaving a remainder. We can use the Euclidean algorithm to find the GCD of two numbers.

The Euclidean algorithm states that for two integers a and b, we can find the GCD of a and b by repeatedly applying the following steps:

Divide a by b to get a quotient q and a remainder r

Replace a with b and b with r

Repeat the process until r is 0

If we apply this algorithm to 11n + 3 and 2n + 1, we get the following:

GCD(11n+3, 2n+1)

As 11n + 3 = 3(2n + 1) + 5n

= GCD(2n+1, 5n )

As 2n + 1 = (2/5)(5n) + 1

= GCD(5n, 1)

= GCD(1, 0)

= 1

So as n ranges over the positive integers, the maximum possible value for the GCD of 11n + 3 and 2n + 1 is 1.

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