Find the area of a regular hexagon with an apothem of 15cm

Answer:

yes

Step-by-step explanation:

since [tex]3^2=5+2^2[/tex]

Given a volume of 4500π cubic feet, the radius is found to be approximately 15 feet after solving the equation.

To find the radius of a sphere given its volume, we use the formula for the volume of a sphere: V = (4/3)πr³. In this case, the given volume is 4500π cubic feet. To solve for the radius, we can set up the equation as follows:

V = (4/3)πr³

4500π = (4/3)πr³

To isolate r³, we divide both sides by π and then multiply by 3/4:

4500 = (4/3)r³

(3/4) * 4500 = r³

3375 = r³

Now, we take the cube root of both sides to find the radius:

r = ³√3375

r ≈ 15 feet

Therefore, the radius of the sphere is approximately 15 feet.

the radius of the sphere is 15 feet.

The formula for the volume [tex](\( V \))[/tex] of a sphere in terms of its radius [tex](\( r \))[/tex] is:

[tex]\[ V = \frac{4}{3}\pi r^3 \][/tex]

Given that the volume of the sphere is [tex]\( 4500\pi \)[/tex] cubic feet, we can set up the equation:

[tex]\[ 4500\pi = \frac{4}{3}\pi r^3 \][/tex]

To find the radius [tex]\( r \)[/tex], we need to isolate it in the equation. First, let's cancel out [tex]\( \pi \):[/tex]

[tex]\[ \frac{4500\pi}{\pi} = \frac{4}{3} r^3 \][/tex]

[tex]\[ 4500 = \frac{4}{3} r^3 \][/tex]

Now, to solve for [tex]\( r \)[/tex], we'll multiply both sides by [tex]\( \frac{3}{4} \)[/tex] to isolate [tex]\( r^3 \):[/tex]

[tex]\[ r^3 = \frac{4500 \times 3}{4} \][/tex]

[tex]\[ r^3 = \frac{13500}{4} \][/tex]

[tex]\[ r^3 = 3375 \][/tex]

Now, to find ( r ), we'll take the cube root of both sides:

[tex]\[ r = \sqrt[3]{3375} \][/tex]

[tex]\[ r = 15 \][/tex]

So, the radius of the sphere is 15 feet.

Answer:

22.6 mi

Step-by-step explanation:

The shortest route is to go from bloomington to seaside to westminster. Simply add up the distances along this route.

Answer:

22.6

Step-by-step explanation:

13.2+9.4=22.6

Answer:

289

Step-by-step explanation:

Base of the square pyramid is square

Formula: Length × Width

17 × 17 = 289

Answer:

8000 litres

Step-by-step explanation:

⅓ (4 × 2.5 × 2.4)

= 8 m³

1 m² = 1000 litres

8 m³ = 8000 litres

The volume of water in the tank in litres can be found by calculating one third of the capacity of the tank in cubic metres and then multiplying that by 1000. We represent this as 1000X/3 litres, where X is the total capacity of the tank in cubic metres.

To solve this problem, we firstly need to know the total capacity of the tank in cubic metres. Since we don't have this specific information in the question, let's call this capacity as 'X' cubic metres.

One third of the tank is filled with water, so the volume of water in the tank is one third of X, which is (1/3) * X cubic metres. We know that 1 cubic metre is equivalent to 1000 litres, therefore, the volume of the water in the tank in litres is (1/3) * X * 1000, which simplifies to 1000X/3 litres.

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Given:

The graph shows the speed of a ball in free fall for 10 seconds.

We need to determine the constant of proportionality for the given graph.

Constant of proportionality:

The constant of proportionality can be determined using the formula,

[tex]\frac{y}{x}=k[/tex]

Where k is the constant of proportionality.

Let us consider any of the coordinate from the graph and substitute in the formula.

Consider the coordinate (4,40) and substitute in the above formula.

Thus, we have;

[tex]\frac{40}{4}=k[/tex]

[tex]10=k[/tex]

Thus, the constant of proportionality is 10 meters per second squared.

Answer:

10 meters per second squared

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

If the gardener bought more white than pink, that could mean he could have bought 12 white and one pink, 11 white and 2 pink, 10 white and 3 pink, 9 white and 4 pink, 8 white and 5 pink, or 7 white and 6 pink.

If you plug in the numbers, for example with 7 and 6, that would equal $53, which is not correct. Continue to do this with all of the answers.

With 8 white roses and 5 pink roses, this would equal $55 (40+15), which is the answer.

By solving form expressions the gardener bought 5 pink plants.

In mathematics, an expression is a combination of one or more numbers, variables, constants, and operators, which when evaluated, produce a value. Expressions can include mathematical symbols such as addition, subtraction, multiplication, division, exponents, roots, logarithms, and trigonometric functions.

Let's use algebra to solve this problem.

Let's assume that the gardener bought x pink plants and y white plants. We know that:

The gardener bought 13 plants in total: x + y = 13

The gardener spent $55: 3x + 5y = 55

The gardener chose more white plants than pink: y > x

We can use the first equation to solve for x in terms of y:

x = 13 - y

Now we can substitute this into the second equation:

3(13 - y) + 5y = 55

Simplifying and solving for y:

39 - 3y + 5y = 55

2y = 16

y = 8

So the gardener bought 8 white plants. To find out how many pink plants were bought, we can substitute this value into the first equation:

x + y = 13

x + 8 = 13

x = 5

So the gardener bought 5 pink plants.

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Answer:

2/5

Step-by-step explanation:

The theoretical probability of getting blue is TOTAL BLUE SPUN/ TOTAL SPINS

There were 12 blue spins out of 30 total spins, making the probability equal to 12/30 = 2/5

Answer:

Must determine the LCD.  Think:  what is the smallest (least) number divisible by both 30 and 20?  You could, of course, just multiply 30 and 20, obtaining 600, but that would not be the LCD.

Note that 30 and 20 share the common factor 10.  Multiplying 3 and 2 together produces 6.  The LCD is 10*6 = 60.  Note that both 30 and 20 divide into 60 with no remainder.

Then  19/30  = 2(19) / 2[30]  = 38/60, and 

13/20 = 3(13) / 3[20]  = 39/60.

Which is larger, 38/60 or 39/60?

Write the relationship between these 2 numbers using the appropriate inequality operator.

Step-by-step explanation:

The fractions 13/30 and 9/20, when rewritten with a common denominator, are 26/60 and 27/60, respectively.

To rewrite the fractions 13/30 and 9/20 with a common denominator, we need to find the least common multiple (LCM) of the denominators, which is the smallest multiple that both 30 and 20 share.

The prime factorization of 30 is 2 * 3 * 5, and the prime factorization of 20 is 2 * 2 * 5. To find the LCM, we take the highest power of each prime factor that appears in either number:

LCM(30, 20) = 2 * 2 * 3 * 5 = 60

Now, let's rewrite the fractions with the common denominator of 60:

13/30 = (13/30) * (2/2) = (13 * 2) / (30 * 2) = 26/60

9/20 = (9/20) * (3/3) = (9 * 3) / (20 * 3) = 27/60

So, the fractions 13/30 and 9/20, when rewritten with a common denominator, are 26/60 and 27/60, respectively.

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Answer: (f+g)(x)=5x2-x+6

Step-by-step explanation:

I hope this helps

Given:

Original figure and enlarged figure

To find:

Which ratios can be used to find the scale factor.

Solution:

Scale factor is the ratio of comparing the corresponding sides of two figures.

Option A:

[tex]$ \text {Scale factor} =\frac{\text { Enlarged }}{\text { Original }}=\frac{6.5}{3.25}$[/tex]

Length of enlarged side = 6.5

Length of original side = 3.25

It is correct.

Option B:

[tex]$\text {Scale factor}= \frac{\text { Enlarged }}{\text { Original }}=\frac{3.25}{6.5}$[/tex]

3.25 is the length of original figure. But here it is mentioned in enlarged.

So, it is not correct.

Option C:

[tex]$\text {Scale factor }=\frac{\text { Enlarged }}{\text { Original }}=\frac{3}{1.5}$[/tex]

Width of enlarged side = 3

Width of original side = 1.5

It is correct.

Option D:

[tex]$\text{Scale factor} =\frac{\text { Enlarged }}{\text { Original }}=\frac{1.5}{3}$[/tex]

1.5 is the width of original figure. But here it is mentioned in enlarged.

So, it is not correct.

Option E:

[tex]$\text{Scale factor}= \frac{\text { Enlarged }}{\text { Original }}=\frac{1.5}{3.25}$[/tex]

1.5 is the width of original figure. But here it is mentioned in enlarged.

So, it is not correct.

Therefore the ratios can be used to find the scale factor are:

[tex]$ \text {Scale factor} =\frac{\text { Enlarged }}{\text { Original }}=\frac{6.5}{3.25}\ \text{and }\ \text {Scale factor }=\frac{\text { Enlarged }}{\text { Original }}=\frac{3}{1.5}$[/tex]

Answer:

A C

Step-by-step explanation:

Using the cosine ratio, side BC in the right-angled triangle is approximately 19.4 cm when rounded to three significant figures.

In the right-angled triangle ABC, where angle A is 90 degrees, side AB is the base, side AC is the perpendicular, and side BC is the hypotenuse, we can use trigonometry to find the length of BC.

The cosine ratio (cos) relates the adjacent side to the hypotenuse in a right-angled triangle. In this case, cos(B) = AB/BC. To find BC, rearrange the formula to BC = AB/cos(B).

Given AB = 6.3 cm and angle B = 71 degrees, substitute these values into the formula:

[tex]\[ BC = \frac{6.3 \, \text{cm}}{\cos(71^\circ)} \][/tex]

Using a calculator, find that cos(71 degrees) is approximately 0.325. Now, divide 6.3 cm by this value:

[tex]\[ BC \approx \frac{6.3 \, \text{cm}}{0.325} \approx 19.385 \, \text{cm} \][/tex]

Rounded to three significant figures, the length of side BC is approximately 19.4 cm.

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Answer:

81

Step-by-step explanation:

18*9=162

162*[tex]\frac{1}{2}[/tex]=81

Answer:

81

Step-by-step explanation:

18 * 9 = 162

162 * 1/2 is 81

Also multiplying by 1/2 is the same as dividing by 2

Hope this helped!

The simplified form of the expression √(-16) + √(-25) + 5 is 5 + 9i, where i represents the imaginary unit.

The student has asked to simplify the expression Sq -16+sq-25+5. This appears to be a typo, and I believe they are referring to square roots. The correct mathematical expression to simplify should be √(-16) + √(-25) + 5. The simplification of the square roots involving negative numbers results in imaginary numbers because the square root of a negative number is not defined in the set of real numbers but rather in complex numbers. For the given expression, complex numbers and imaginary units ('i', wherein i^2 = -1) will be introduced in simplification:

When we add these results with 5, we obtain 5 + 4i + 5i, which simplifies to 5 + 9i.

Answer:16.97cm

Step-by-step explanation:

To find the hypotenuse side of an isosceles of side 12cm each

Using pythagoras theorem

hyp^2=opp^2+adj^2

hyp^2=12^2+12^2

Hyp^2=144+144

hyp=√288

Hyp=16.97cm

Answer:

The answer is 1

Step-by-step explanation:

The answer is 1

Hence Only 1 triangle can be drawn

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Answer:

The first term is 128

Step-by-step explanation:

The common ratio of the geometric series is given as:

[tex]r = \frac{1}{4} [/tex]

The sum of the first 4 term is 170.

The sum of first n terms of a geometric sequence is given b;

[tex]s_n=\frac{a_1(1-r^n)}{1-r}[/tex]

We put the common ratio, n=4 and equate to 170.

[tex]\frac{a_1(1-( \frac{1}{4} )^4)}{1- \frac{1}{4} } = 170[/tex]

Simplify:

[tex]\frac{a_1(1- \frac{1}{256} )}{ \frac{3}{4} } = 170[/tex]

[tex] \frac{255}{256} a_1 = \frac{3}{4} \times 170[/tex]

[tex]\frac{255}{256} a_1 = \frac{255}{2} [/tex]

[tex]\frac{1}{256} a_1 = \frac{1}{2} [/tex]

[tex] a_1 = \frac{1}{2} \times 256[/tex]

[tex]a_1 = \frac{1}{2} \times 256 = 128[/tex]

Answer:

128

Step-by-step explanation:

Answer:

2. (5/8)m - 3/8.

Step-by-step explanation:

(1/4)m + (3/4)m - (3/8)(m + 1)

=   m - (3/8)m - 3/8

= (5/8) m - 3/8.

Answer:

  4 units

Step-by-step explanation:

A function is periodic with period P when it can be shifted P units left or right and its graph will map to itself. Here, rising "edges" of the function cross grid lines that are 4 units apart, so the period is 4 units.

Answer:

See below in BOLD.

Step-by-step explanation:

Rearrange in ascending order of age:

11 11 11 12 12 13 14 15 15 16

1. The mean = (11 +11 +11 +12 +12 +13+ 14 +15+ 15+ 16) / 10

= 130/10

= 13 years.

2.  The median is the mean of the middle 2 numbers in the list:

= (12 + 13) / 2

= 12.5 years.

Answer:

G

Step-by-step explanation:

Range is the set of y values

Least function value is -3 and greatest is 4

The range of the function is -3 ≤ y ≤ 4, the correct option is G.

A function is a law that relates two variables namely, a dependent and an independent variable.

A function always has a defined range and domain.

Domain is all the value a function can have as an input

Range is all the value that a function can have as an output.

The function can be seen in the graph, it is a piecewise function

The range of the function has to be determined, all the possible value of y has to be noted from the graph.

The y has the value in the range of -3 to 4.

So, the range is -3 ≤ y ≤ 4.

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Answer:

1/3

Step-by-step explanation:

step-by-step explanation is three angles of triangle are cut off so 1/3

Answer:

3.5

Step-by-step explanation:

This is because 12 times 4 is 48 and if you divide 168 by 48 you get 3.5 . 3.5 times 12 times 4 is 168.

Answer:

16

Step-by-step explanation:

[tex] {x}^{2} - 8x + 16 = (x - 4) ^{2} \\ [/tex]

Answer:12.5h

Step-by-step explanation:

First, you would add 5+3+4.5. This equals 12.5. H represents her hourly pay rate. In order to find how much she earned, you would have to multiply 12.5(h).

Answer:12.5h

Step-by-step explanation:

Answer:

750 books

Step-by-step explanation:

10% .............75 books

100% .............x books

x = 100×75/10 = 7500/10 = 750 books

Answer:

70

Step-by-step explanation:

Dividing is multiplying by the reciprocal.

So 30 divided by 1/2

is like 30(2)=60

Then add 10 so 60+10=

70

The equivalent value of the expression "dividing 30 by half and adding ten"  is 70.

Given data:

Regarding step-by-step dissecting of "dividing 30 by half and adding ten"

Step 1 is to divide 30 in half.

A number is effectively divided by 1/2 when we divide it in half. A fraction's reciprocal is what you multiply by when you divide by it. 1/2 has a reciprocal of 2/1, or only 2.

As a result, multiplying 30 by 2 is equivalent to dividing it in half:

To make the equation simpler:

30 ÷ (1/2) = 30 × 2

= 60

Step 2: Ten-folding.

We obtain 60 by dividing 30 in half.

Now double the outcome by ten:

60 + 10 = 70

So, when you multiply 30 by half, add 10, and you get 70.

Hence, the equation is solved and the solution is 70.

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Answer:

[tex]\sqrt{8}[/tex] Is Correct!

The distance between (-5, -6) and (-3,-8) is [tex]\sqrt{8}[/tex].

Here we applied the distance formula

[tex]= \sqrt{(x_2 - x_1)^2 + (y_2 - y_2)^2} \\\\= \sqrt{(-3+5)^2 + (-8 + 6)^2}\\\\ = \sqrt{4 + 4} \\\\= \sqrt{8}[/tex]

Hence, we can conclude that The distance between (-5, -6) and (-3,-8) is [tex]\sqrt{8}[/tex].

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Answer:

13 and 8

Step-by-step explanation:

pls mark this brainliest im trying to lvl up

The two numbers that add up to 21 but subtract to 5 are 13 and 8.

The two numbers are 13 and 8.

To find the numbers, set up the system of equations:
x + y = 21 (Equation 1)
x - y = 5 (Equation 2)

Adding Equation 1 and Equation 2, you get 2x = 26, which means x = 13.

Substituting x back into Equation 1 gives y = 8.

Answer:

104

Step-by-step explanation:

180- 76 = 104

Answer:

104

Step-by-step explanation: