find the perimeter of a regular polygon with 15 sides each measuring 11cm and an apothem 18.4cm long

The volume of the rectangular prism is (867/20) cubic inches.

A volume is just the amount of space taken up by any three-dimensional solid. A cube, a cuboid, a cone, a cylinder, or a sphere are examples of solids. Volumes differ depending on the shape.

To find the volume of a rectangular prism, we need to multiply its length, width, and height. In this case, the length is 10 1/5 inches, the width is 4 1/4 inches, and the height is 2 inches. We can convert the mixed numbers to improper fractions and then multiply:

length = 10 1/5 inches = (51/5) inches

width = 4 1/4 inches = (17/4) inches

height = 2 inches

Volume = length x width x height

= (51/5) inches x (17/4) inches x 2 inches

= (867/20) cubic inches

Therefore, the volume of the rectangular prism is (867/20) cubic inches.

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Therefore, the Left Riemann Sum for this function, interval, and number of subintervals is 50.

The top-left corner of these rectangles touched the y=f(x) curve. In other words, the value of f at the subinterval's left endpoint determined the height of the rectangle over that subinterval. This technique is called the left-endpoint estimate because of this.

With left endpoints and n = 5 subintervals, we may use the Left Riemann Sum formula to approximate the area under the curve of f(x) = x2 + 4 over the range [0, 5]:

Left Riemann Sum = ∑[i=1 to n] f(x_i-1) Δx

In this case, a = 0, b = 5, n = 5, and we will use the left endpoints, so:

Δx = (5 - 0)/5 = 1

Using the left endpoints, the subintervals and their left endpoints are:

[0,1],[1,2],[2,3],[3,4],[4,5]

[tex]so,\; x_0 = 0, x_1 = 1, x_2 = 2, x_3 = 3, x_4 = 4.[/tex]

Now we can calculate the Left Riemann Sum:

Left Riemann Sum= [tex]f(x_0)\Delta x + f(x_1)\Deltax + f(x_2)\Deltax + f(x_3)\Deltax + f(x_4)\Deltax[/tex]

= f(0)×1+f(1)×1+f(2)×1+f(3)×1 + f(4)×1

= 4+5+8+13+20

= 50

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f(x)=2x+7

domain: x = {2, 3, 5, 9}

Replace each x value and solve for y

x=2

f(2)= 2(2) + 7 = 4 + 7 = 11

x=3

f(3)= 2(3) + 7 = 6 + 7 = 13

x=5

f(5)= 2(5) + 7 = 10 + 7 = 17

x=9

f(9)= 2(9) + 7 = 18 + 7 = 25

We can find the range of the function by plugging in each value in the domain into the function and listing the output values:

When x = 2, f(2) = 2(2) + 7 = 11

When x = 3, f(3) = 2(3) + 7 = 13

When x = 5, f(5) = 2(5) + 7 = 17

When x = 9, f(9) = 2(9) + 7 = 25

Therefore, the range of the function for the given domain is y = {11, 13, 17, 25}.

Hence, the correct answer is B. y = {11, 13, 17, 25}.

Answer:

Step-by-step explanation:

Let's denote the volume of the cube as V and the length of each edge as x. Given that the volume of a cube is V = x^3, we can find the rate at which the length of each edge is changing.

We're given that the rate of change of the volume is dV/dt = 56 in³/sec. We want to find the rate of change of the length of each edge, which is dx/dt, when the length of each edge is 6 inches.

First, we differentiate the volume equation with respect to time t:

V = x^3

dV/dt = d(x^3)/dt

Using the chain rule:

dV/dt = 3x^2 * (dx/dt)

Now, we know that dV/dt = 56 in³/sec and x = 6 in. Plugging these values into the equation, we get:

56 = 3 * (6)^2 * (dx/dt)

Solving for dx/dt:

56 = 108 * (dx/dt)

dx/dt = 56 / 108

dx/dt ≈ 0.5185 in/sec (rounded to four decimal places)

So, the rate at which the length of each edge is changing is approximately 0.5185 inches per second when the edges are 6 inches long.

Answer:

We can simplify the expression -8(2.5g-4.25)+5.25 by distributing the -8:

-8(2.5g-4.25)+5.25 = -20g + 34 + 5.25

Simplifying further, we can combine the constant terms:

-8(2.5g-4.25)+5.25 = -20g + 39.25

So the value of the constant term is 39.25.

The new triangle A'B'C' after the translation is A'(-3, 3), B'(4, -1), and C'(-2, 0).

A shape is translated when it is moved up, down, left or right without turning. They are congruent if the translated shapes (or the image) seem to be the same size as the original shapes. They have only changed their direction or directions.

To perform the given translation (x, y) → (x − 3, y - 4) on the triangle ABC with vertices A(0, 7), B(7, 3), and C(1, 4), we need to apply the same transformation to each vertex of the triangle and obtain their new coordinates.

For vertex A(0, 7), the transformation gives:

(x, y) → (x − 3, y - 4)

(0, 7) → (0 - 3, 7 - 4)

The new coordinates of A are (-3, 3).

For vertex B(7, 3), the transformation gives:

(x, y) → (x − 3, y - 4)

(7, 3) → (7 - 3, 3 - 4)

The new coordinates of B are (4, -1).

For vertex C(1, 4), the transformation gives:

(x, y) → (x − 3, y - 4)

(1, 4) → (1 - 3, 4 - 4)

The new coordinates of C are (-2, 0).

Therefore, the new triangle A'B'C' after the translation is A'(-3, 3), B'(4, -1), and C'(-2, 0).

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Answer:

To simulate the probable outcomes of this event with a six-sided number cube, you can place the numbers 1-6 on the faces in the following order: 1, 4, 3, 2, 5, 6. Then roll the cube and use the following outcomes:

a) Correct: a roll of 6 Incorrect: a roll that is not 6

b) Correct: a roll of an even number Incorrect: a roll of an odd number

c) Correct: a roll of a number less than 3 Incorrect: a roll of a greater than or equal to 3

d) Correct: a roll of a number that is not divisible by 3 Incorrect: a roll of a number that is divisible by 3

Step-by-step explanation:

Check the picture below.

so following the template below, a shift 2 units to the left, means C=2

[tex]G(x)=\sqrt{x+2}[/tex]

Answer:

x = 5

Step-by-step explanation:

given FH is a diameter , then

arc FH = 180°, that is

FG + GH = 180°

103° + GH = 180° ( subtract 103° from both sides )

GH = 77°

the central angle HIG is equal to the arc that subtends it GH , so

∠ HIG = 77°

∠ EIF and ∠ HIG are vertically opposite angles and are congruent , then

∠ EIF = 77°

the arc EF subtends the central angle EIF , so

EF = 77°

the sum of the 3 arcs = 180° , that is

HD + DE + EF = 180

15 + 18x - 2 + 77 = 180

18x + 90 = 180 ( subtract 90 from both sides )

18x = 90 ( divide both sides by 18 )

x = 5

then arc DE = 18x - 2 = 18(5) - 2 = 90 - 2 = 88°

Answer:

Step-by-step explanation:

answer 1,250

The given exponents term can be written in the form of [tex](a^{4})^{12}[/tex] .

What about exponents?

Exponents are a mathematical operation that involves multiplying a base number by itself a certain number of times. Exponents are often referred to as powers, and the base number is raised to a power, which is usually represented by a superscript number. For example, 2^3 means 2 raised to the power of 3, which is 2 x 2 x 2 = 8.

Exponents are commonly used in many areas of mathematics, including algebra, calculus, and geometry. They are used to represent very large or very small numbers, to simplify calculations, and to express repeated multiplication in a more compact form. Exponents can also be negative or fractional, allowing for the representation of roots and other mathematical concepts.

According to the given information:

In the given question [tex](a^{48} )[/tex] can be written as,

[tex](a^{4})^{12}[/tex] = [tex](a^{4})^{12} = a^{48}[/tex]

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Answer: To make soup for 4 people, Lori needs 1 1/4 cups of milk for every 3/4 cup of broth. Therefore, the ratio of milk to broth is:

(1 1/4 cups milk) / (3/4 cup broth) = (5/4 cups milk) / (3/4 cups broth) = (5/3) cups milk per cup of broth

To make soup for 120 people, Lori needs to multiply the ratio by 30 (120/4) to get the total amount of milk and broth needed:

(5/3 cups milk per cup of broth) * 30 = 50 cups of milk per 30 cups of broth

To convert cups to gallons, we divide by 16 (since there are 16 cups in a gallon):

50/16 = 3.125 gallons of milk

30/16 = 1.875 gallons of broth

Therefore, Lori needs a total of 3.125 + 1.875 = 5 gallons of milk and broth combined.

Step-by-step explanation:

Answer:

10 feet

Step-by-step explanation:

Let's start by finding the current area of the deck:

Area = length x width = 20 ft x 10 ft = 200 sq ft

If Ian increases each dimension by the same amount, let's call this amount "x", then the new dimensions of the deck will be:

Length = 20 ft + x

Width = 10 ft + x

The new area of the deck will be:

New Area = (20 ft + x) x (10 ft + x)

We know that Ian wants the new area to be triple the original area of 200 sq ft, so:

New Area = 3 x 200 sq ft

New Area = 600 sq ft

Substituting this into the equation above and solving for "x", we get:

(20 ft + x) x (10 ft + x) = 600 sq ft

200 + 30x + x^2 = 600

x^2 + 30x - 400 = 0

(x + 40) (x - 10) = 0

We discard the negative solution, and we get:

x = 10 ft

Therefore, Ian should increase each dimension by 10 feet to triple the area of his deck.

To confirm, we can check the original area of the deck which is 20 ft x 10 ft = 200 sq ft.

If Ian increases each dimension by 10 feet, the new dimensions of the deck will be 30 ft x 20 ft. The new area of the deck will be 30 ft x 20 ft = 600 sq ft. This is triple the original area of the deck (200 sq ft), which is what we wanted to achieve.

Therefore, increasing each dimension by 10 feet will triple the area of the deck as required.

Ian should increase both the sides by 10 feet each.

This is a simple mathematics problems related to the topic of mensuration.

Firstly we calculate the current area of the deck:

Area of the deck (rectangle) = l x b

Area of the deck (rectangle) = 20 x 10

Area of the deck (rectangle) =  200 square feet

Since Ian wants to triple the area of the deck, the required area is 600 square feet.

We now look at pairs of numbers multiplying which will give us 600:

(1,600) (2,300) (3,200) (4,150) (5,120) (6,100) (8,75) (10,60) (12,50) (15,40) (20,30) (25,24)

Out of the above pairs only one pair fulfils Ian's criteria to increase the length and breadth of the deck by equal measure, i.e., (20,30). So, Ian should increase the length and breadth of his deck by 10 feet each.

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Answer:-133.69

Step-by-step explanation:

5.96 x 106 -7.29 x 105

631.76 -7.29 x 105

631.76 - 765.45

= -133.69

The equation of the form y = c + b logₐX is y = -3 + 3 Log₃X

Recall that Slope-intercept form of a linear equation is where one side contains just “y”. It looks like y = mx + “b” where “m” and “b” are numbers. This form of the equation is very useful because the coefficient of "x" (the "m" value) is the slope of the line and the constant (the "b" value) is the y-intercept at (0, b)

The equation of the line is give as

y-y₁ = m(x-x₁) + c

Where m is the slope and c is the intercept

This implies that

y -3 = m(x -2)

But slope is given as  m = (y₂ - y₁)/(x₂-x₁)

m = (9-3)/ 4-2) = 6/2 = 3

Then, the equation is

y - 3 = 3x - 6

Collecting like terms we have

y = 3x -6+3

y = 3x -3

Writing this in the form y = c + b logₐX

y = -3 + 3 Log₃X

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The equation of the function in the form y = c + b log_a(x) is y = logₓ2

We can start by assuming that the equation is of the form y = c + b log_a(x), where c and b are constants and a is the base of the logarithm.

Using the point (2, 3), we get:

3 = c + b log_a(2)

Using the point (4, 9), we get:

9 = c + b log_a(4)

Simplifying the second equation using the logarithmic identity

loga(4) = 2 loga(2), we get:

3 +  2b loga(2) = 9

Substituting the first equation into this one, we get:

3 = 9 - 2b loga(2)

So, we have

-6 = - 2b loga(2)

Divide

bloga(2) = 3

So, we have

b = 3 / log_a(2)

Substituting this value of b into the first equation, we get:

3 = c + b log_a(2)

3 = c + 3 / log_a(2) * log_a(2)

So, we have

c = 0

Therefore, the equation of the curve is y = (2 / log_a(2)) log_a(x)

We can simplify this equation by using the logarithmic identity log_a(x^b) = b log_a(x):

y = 2 log_a(x) / log_a(2)

y = (2 / log(2)) log(x)

So the final equation is:

y = logₓ2

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The probability of drawing a vowel, placing it back in the bag, and then drawing a consonant is 0.1875 or 18.75%.

The probability of drawing a vowel from the bag of random letter tiles is 25%. Since the tile is replaced after drawing, the probability of drawing a vowel on the second draw is also 25%.

The probability of drawing a vowel and then a consonant can be calculated by multiplying the probabilities of each event:

P(vowel and consonant) = P(vowel) x P(consonant)

= 0.25 x 0.75

= 0.1875

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Check the picture below.

Make sure your calculator is in Degree mode.

[tex]\cos(25^o )=\cfrac{\stackrel{adjacent}{x}}{\underset{hypotenuse}{12}}\implies 12\cos(25^o)=x\implies \boxed{10.876\approx x} \\\\[-0.35em] ~\dotfill\\\\ \sin(25^o )=\cfrac{\stackrel{opposite}{z}}{\underset{hypotenuse}{12}}\implies 12\sin(25^o)=z \\\\[-0.35em] ~\dotfill\\\\ \sin(50^o )=\cfrac{\stackrel{opposite}{z}}{\underset{hypotenuse}{y}}\implies y=\cfrac{z}{\sin(50^o)}\implies y=\cfrac{12\sin(25^o)}{\sin(50^o)}\implies \boxed{y\approx 6.62}[/tex]

Hence, 30 inches deviate by 1.5 standard deviations from the 15-inch mean as the underlying data's standard deviation is 10 inches.

The standard deviation of statistics is a measurement of how much a group of data values deviate from their mean (average) value. While a significant standard deviation suggests that the pieces of information are dispersed throughout a broader range of values, a low standard deviation suggests that the data points are generally close to the mean.

given

a) If the sample's standard deviation is 3 inches, then the number of standard deviations from the mean of 15 inches that are 30 inches is:

z = (30 - 15) / 3 = 5

b) The context of the data and the standard deviation will determine whether 30 inches is distant from a mean of 15 inches.

A departure of 15 inches from the mean, meanwhile, can be viewed as being significantly off the mean if the standard deviation is minimal.

c) If the underlying data's standard deviation is 10 inches, then the number of standard deviations from the mean of 15 inches that are 30 inches is:

z = (30 - 15) / 10 = 1.5

Hence, 30 inches deviate by 1.5 standard deviations from the 15-inch mean as the underlying data's standard deviation is 10 inches.

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the price per cubic inch for the regular size popcorn is #29.85

You should understand that Price is what a buyer pays to acquire products from a seller.  It takes into account the overall value of the offering, including the value of all raw materials and service that went into making an offering, as well as its markup or margin

The popcorn has 6 faces and the area of the popcorn is given as

Area = LBH

Length

Bredth

Height

Area= 3*5*6 = 90 cm²

Therefore, Price is given as $1.99

This implies that 1.99*90 = $179.1

Therefore the price per inch is 179.1/6 = #29.85

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5.40 km is the distance Bokamoso ride on the way to school

What is speed, distance and time?

Speed is determined by dividing the distance travelled by the time taken to travel it. It gives the amount of time it took to travel a certain distance divided by the distance travelled.

Speed is inversely correlated with time and directly correlated with distance. As a result, distance equals speed times time, and time equals distance divided by speed; as speed rises, distance travelled will shorten, and vice versa.

Bokamosa rides at 16 km / hr

To get to school = 45 min

= 45 * 0.75 hour

= 0.3375 hr

Distance = Speed * Time

d = 16 * 0.3375

= 5.40 km

Hence, 5.40 km is the distance Bokamoso ride on the way to school.

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Answer:

Step-by-step explanation:

We need to find a number which increased by 3.5 of itself equals 621.

Let that number be x.

x increased by 3.5 of itself equals 621 implies x+ 3.5x = 621.

x(1+3.5) = 621

x(4.5) = 621

x = 621/4.5

x = 138

Therefore the required number is 138.

Answer: 138

Step-by-step explanation:

We need to find a number which increased by 3.5 of itself equals 621.

Let that number be x.

x increased by 3.5 of itself equals 621 implies x+ 3.5x = 621.

x(1+3.5) = 621

x(4.5) = 621

x = 621/4.5

x = 138

Therefore the required number is 138.

Answer:

center : (-3, -1) radius : 4

Answer:

FV ≈ $5,673.56

Step-by-step explanation:

To calculate the total amount that Matt will have saved after 2 years of saving $225 per month at an annual interest rate of 5%, we can use the formula for the future value of an annuity:

FV = P * (((1 + r/12)^(n*12) - 1) / (r/12))

where:

FV is the future value of the annuity

P is the periodic payment (in this case, $225 per month)

r is the interest rate per year (in this case, 5%)

n is the number of years (in this case, 2)

Substituting the given values, we get:

FV = $225 * (((1 + 0.05/12)^(2*12) - 1) / (0.05/12))

Using a calculator, we get:

FV ≈ $5,673.56

Therefore, after 2 years of saving $225 per month at an annual interest rate of 5%, Matt will have saved approximately $5,673.56.

Answer:

Whats the question?

Step-by-step explanation:

The absolute maximum value of f(x) is 4.5 and it occurs at x = -0.5, and the absolute minimum value of f(x) is -0.241 and it occurs at x = 0.833

To find the absolute maximum and minimum of the function f(x) = 4x^3 - 2x^2 - 5x + 3, we need to take the derivative of the function and set it equal to zero to find the critical points.

f(x) = 4x^3 - 2x^2 - 5x + 3

f'(x) = 12x^2 - 4x - 5

Setting f'(x) = 0, we get:

12x^2 - 4x - 5 = 0

Using the quadratic formula, we get:

x = -0.5 or x = 0.833

Now we need to check the values of f(x) at the critical points and the endpoints of the interval

f(-0.5) = 4(-0.5)^3 - 2(-0.5)^2 - 5(-0.5) + 3 = 4.5

f(0.833) = 4(0.833)^3 - 2(0.833)^2 - 5(0.833) + 3 = -0.241

So the absolute maximum it occurs at x = -0.5, and the absolute minimum occurs at x = 0.833

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The account has an annual interest rate of 6.80%, compounded continuously.

Interest is the cost associated with the boring money or to return on for lending money it is typically expressed as a percent of the principal amount borrowed or lent and usually the paid periodically over the life of loan interest can also be on from investment such as saving account bonds and the other financial instrument.

The interest rate of the account can be calculated as follows:

Rate = ln(1,698.49/1,051)/(8×ln(1))

Rate = 0.0680 or 6.80%

This means that the account has an annual interest rate of 6.80%, compounded continuously.

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The answer of the given question based on the Critical value is , , the critical value to for the confidence level c = 0.99 and sample size n = 22 is 2.819.

In statistics, the critical value is a value that is used to determine whether to reject the null hypothesis in a hypothesis test. It is based on the chosen level of significance, which is the maximum probability of making a Type I error (rejecting a true null hypothesis). The critical value is determined by the sampling distribution of the test statistic, which is often a t-statistic or z-statistic, depending on the test and the characteristics of the population being studied.

To find the critical value t for a 99% confidence level and a sample size of 22, we need to use a t-distribution table or a calculator.

Using a t-distribution table with 21 degrees of freedom (n-1), we find that the critical value for a 99% confidence level is approximately 2.819.

Therefore, critical value for confidence level c = 0.99 and sample size n = 22 is 2.819 (rounded to nearest thousandth).

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The mean number of bedrooms in a house in this neighborhood will be: 3.824.

In order to find the mean number of bedrooms in a house in the Belmont Neighborhood, we need to calculate the weighted mean by multiplying each number of bedrooms by their respective frequency.

Next, we will add the products, and then divide by the total frequency. So we can start as follows:

(2 * 7) + (3 * 35) + (4 * 56) + (5 * 27) = 14 + 105 + 224 + 135 = 478

Total frequency = 7 + 35 + 56 + 27 = 125

Therefore, the mean number of bedrooms = 478 / 125  approximately 3.824

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The equation of the circle is therefore: [tex](x + 4)^2 + (y + 7)^2 = 36[/tex]

What is circle?

A circle is a two-dimensional geometric shape that consists of all the points that are equidistant from a single fixed point called the center.

To find the equation of a circle with center (h, k) and radius r, the general equation is:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

In this case, the center of the circle is (-4, -7) and the circle is tangent to the vertical line x = 2. This means that the radius of the circle is the distance from its center to the line x = 2, which is 6 units.

The equation of the circle is therefore:

[tex](x - (-4))^2 + (y - (-7))^2 = 6^2\\\\(x + 4)^2 + (y + 7)^2 = 36[/tex]

Alternatively, we can also find the equation of the circle by using the fact that the line passing through the center of the circle and the point of tangency is perpendicular to the tangent line. Since the tangent line x = 2 is vertical, the line passing through the center (-4,-7) and the point of tangency must be horizontal, and its equation is y = -7.

The distance from the center (-4,-7) to the point of tangency on the line x = 2 is the radius of the circle, which is 6 units. The x-coordinate of the point of tangency is 2, so the distance from (-4,-7) to (2,-7) is 6 units. Therefore, the center of the circle (-4,-7) is 6 units away from the point (2,-7) along a horizontal line.

The equation of the circle is therefore:

[tex](x - (-4))^2 + (y - (-7))^2 = 6^2\\\\(x + 4)^2 + (y + 7)^2 = 36[/tex]

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