Evaluate the geometric series. Round to the nearest hundredth.
Please help me!!!

Given:

The height of the given fig = 7.5 unit

The radius of the given fig = 3.6 unit

To find the volume of the given composite figure.

Formula

The volume of the given fig

[tex]V = V_{1}+V_{2}[/tex]

where,

[tex]V_{1}[/tex] be the volume of the cone

[tex]V_{2}[/tex] be the volume of the semicircle

[tex]V_{1}=\pi r^{2} h[/tex], r be the radius and h be the height

[tex]V_{2} = \frac{2}{3} \pi r^{3}[/tex], r be the radius

Now,

Putting, r= 3.6, h = 7.5 and π = 3.14 we get,

[tex]V_{1} =(3.14)(3.6^{2} )(7.5)[/tex] cube in

or, [tex]V_{1}= 305.208[/tex] cube in

And,

[tex]V_{2} =\frac{2}{3} (3.14)(3.6^{3})[/tex] cube in

or, [tex]V_{2} = 97.67[/tex] cube in

So,

[tex]V = 305.208+97.67[/tex] cube in

or, [tex]V = 402.878[/tex] = 402.88 cube in

Hence,

The volume of the given figure is 402.88 cube in.

Answer:

(1,80)

Step-by-step explanation:

hope i am being a good help

Answer:

y = 1/2x - 3/2

Step-by-step explanation:

The easiest way to find the inverse is to switch x and y and solve for y.

y = 2x + 3

x = 2y + 3 (Switch)

x-3 = 2y (Subtract y from both sides)

x/2 - 3/2 = y (Divide both sides by 2)

Answer:

The inverse is 1/2x -3/2

Step-by-step explanation:

y = 2x+3

To find the inverse, exchange x and y

x = 2y+3

Solve for y

Subtract 3 from each side

x-3 = 2y+3-3

x-3 =2y

Divide each side by 2

x/2 -3/2 = 2y/2

1/2x -3/2 =y

The inverse is 1/2x -3/2

Final answer:

To convert 110 minutes to a fraction of 4 hours, we first turn both quantities into minutes and then form a fraction. Reducing this fraction to its lowest terms, 110 minutes to 4 hours can be expressed as the fraction 11/24.

Explanation:

To express 110 minutes in terms of hours, we need to divide the number of minutes by 60, since there are 60 minutes in an hour.

110 minutes ÷ 60 minutes = 1 hour 50 minutes

Now we have to represent 1 hour 50 minutes as a fraction of 4 hours. First, let’s convert 1 hour 50 minutes entirely to minutes to make it easier to compare. There are 60 minutes in an hour, hence:

1 hour = 60 minutes
50 minutes = 50 minutes
Total minutes = 60 + 50 = 110 minutes

Since we know 4 hours is the same as 240 minutes (4 hours x 60 minutes/hour), we can now write the fractional notation:

110 minutes / 240 minutes

Reducing this fraction to lowest terms by dividing both the numerator and the denominator by 10 yields:

11 / 24

Therefore, 110 minutes to 4 hours is expressed as the fraction 11/24 in lowest terms.

Answer:

66

Step-by-step explanation: What i did was take and figure out the pattern which is -7 every number. Then i went and multiplied 7 x 37 and got 259. Then I took 259 and subtracted that from 339 and got 66 which should be your answer.

Answer:

look it up on google if you havent tried already. also it doesn't hurt to ask for help from someone you know.

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

The inscribed angle ABD is on half the central angle ACD, that is

∠ ABD = 0. × 50° = 25°

The measure of arc AD is equal to the central angle it subtends, thus

arc AD = 50°

1. The measure of inscribed angle [tex]\( \angle ABD \)[/tex] is 25 degrees. 2. The measure of arc [tex]\( AD \)[/tex] is 50 degrees.

To solve this problem, we need to understand the relationship between central angles, arcs, and inscribed angles in a circle.

1. Measure of Arc AD:

The measure of an arc created by a central angle in a circle is equal to the measure of the central angle itself. Given that the central angle [tex]\( \angle ACD \)[/tex] is 50 degrees, the measure of arc [tex]\( AD \)[/tex] is also 50 degrees.

[tex]\[ \text{Measure of arc } AD = 50^\circ \][/tex]

2. Measure of Inscribed Angle ABD:

An inscribed angle that intercepts the same arc as a central angle will have a measure that is half the measure of the central angle. In this case, the inscribed angle [tex]\( \angle ABD \)[/tex] intercepts arc [tex]\( AD \)[/tex], which has a measure of 50 degrees.

[tex]\[ \text{Measure of } \angle ABD = \frac{1}{2} \times \text{Measure of arc } AD = \frac{1}{2} \times 50^\circ = 25^\circ \][/tex]

The complete question is:

Central angle ACD of circle C has a measure of 50 degrees. What is the measure of arc AD? What is the measure of inscribed angle ABD?

1. [tex]\( \angle ABD \)[/tex] = ______.

2. arc [tex]\( AD \)[/tex] = ______.

Answer:

9x(2x + 1)

Step-by-step explanation:

Looking at the two terms, notice that you can write the first term as:

18x² = 9x * 2x

Then, we can see that the first term and second term both have 9x in them. That means 9x is a common factor, so we can take it out from both of them ("take it out" basically means "divide"):

18x² + 9x = 9x * 2x + 9x = 9x * (2x + 1)

Thus, the factored form is 9x(2x + 1).

Hope this helps!

Answer:

5507.79 feet

Step-by-step explanation:

To find the height of the mountain, we can draw triangles as in the image attached.

Let's call the height of the mountain 'h', and the distance from the first point (31 degrees) to the mountain 'x'.

Then, we can use the tangent relation of the angles:

tan(34) = h/x

tan(31) = h/(x+1000)

tan(31) is equal to 0.6009, and tan(34) is equal to 0.6745, so:

h/x = 0.6745 -> x = h/0.6745

using this value of x in the second equation:

h/(x+1000) = 0.6009

h/(h/0.6745 + 1000) = 0.6009

h = 0.6009 * (h/0.6745 + 1000)

h = 0.8909*h + 600.9

0.1091h = 600.9

h = 600.9 / 0.1091 = 5507.79 feet

Answer:

x+5=12

x=7 aka D

Step-by-step explanation:

Hope it helps !

Final answer:

To solve the equation (x + 5) / 3 = 4 for x, multiply both sides by 3 and then subtract 5 from both sides, which yields the solution x = 7.

Explanation:

To solve the equation (x + 5) \/ 3 = 4 for x, we start by performing the inverse operation of the division by 3 to isolate x. We multiply both sides of the equation by 3:

3 * ((x + 5) \/ 3) = 3 * 4

Now, the equation simplifies to:

x + 5 = 12

Next, we subtract 5 from both sides of the equation to solve for x:

x + 5 - 5 = 12 - 5

Which gives us:

x = 7

So the answer to the equation is D) 7.

Final Answer:

After 5 years, the account balance would be approximately $11,541.20.

Explanation:

To calculate the account balance for a certificate of deposit that has an initial amount of $10,000.00, with an annual interest rate of 2.89% compounded monthly over 5 years, we must use the compound interest formula:

[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \][/tex]

where:
- A is the amount of money accumulated after t years, including interest.
- P is the principal amount, which is the initial amount of money ($10,000.00 in this case).
- r is the annual interest rate in decimal form (2.89% or 0.0289 in this case).
- n is the number of times that interest is compounded per year (12 times per year for monthly compounding).
- t is the time the money is invested for, in years (5 years in this case).

Firstly, we convert the annual interest rate from a percentage to a decimal by dividing by 100:

r = 2.89% = 0.0289

Now we substitute the given values into the formula:

[tex]\[ A = \$10,000.00 \left(1 + \frac{0.0289}{12}\right)^{12 \cdot 5} \][/tex]

We calculate the rate per period by dividing the annual interest rate by the number of compounding periods per year:

[tex]\[ \frac{0.0289}{12} = 0.00240833 \][/tex] (rounded to 8 decimal places for precision)

Now calculate the growth factor:

[tex]\[ \left(1 + \frac{0.0289}{12}\right) = 1 + 0.00240833 = 1.00240833 \][/tex]

This growth factor is raised to the power of 60 (since there are 12 months in a year and we are compounding for 5 years):

[tex]\[ (1.00240833)^{60} \][/tex]

Using a calculator, raise 1.00240833 to the power of 60 to get approximately:

[tex]\[ 1.00240833^{60} \approx 1.15412 \][/tex](rounded to 5 decimal places for simplicity)

Finally, multiply this result by the principal amount to find the accumulated amount:

[tex]\[ A = \$10,000.00 \times 1.15412 \approx \$11,541.20 \][/tex]

Therefore, after 5 years, the account balance would be approximately $11,541.20.

Answer:

0.1m/s²

Step-by-step explanation:

the explanation is in the picture

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Answer:

m/slope = -1.5

Step-by-step explanation:

Answer:

23/40 = as a decimal: 0.575   As a percentage 57.5%

Step-by-step explanation:

I know this because I used a online site to check my work.

I hope this helps you! :)

plz mark brainliest :)

Answer:

Step-by-step explanation:

Yes. n represents the number of week

Answer:

1: number of weeks

2. the payment amount for the end of week n

3: A

Answer:

c

Step-by-step explanation:

The deviation from the mean for the data point 27 in a data set with mean 30 is -3.

In mathematics, the deviation from the mean of a data set is a measure of the distance between each data point and the mean. It is obtained by subtracting the mean from the data point. In this case, the mean of the data set is given as 30. To find the deviation from the mean for the data point 27, you simply subtract 30 (the mean) from 27 (the data point).

So 27 - 30 = -3

This means the deviation from the mean for the data point 27 is -3 which corresponds to option b.

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Hey there,

The first step in solving this problem would have to be to add the two binomials together:

Knowing this now we find the GCF which would have to be 2x which goes into both terms.

The factored form would have to be 2x(5x - 2).

The GCF is 2x and the factored form is 2x(5x - 2).

Hope I helped,

Amna

The GCF for the expression (6x2 + 4x) + (4x2 - 8x) is 2x, and the expression in factored form is 2x(5x - 2).

To determine the greatest common factor (GCF) and write the expression in factored form for (6x2 + 4x) + (4x2 - 8x), we should first combine like terms:

6x2 + 4x + 4x2 - 8x = 10x2 - 4x

We can then identify that both terms have a common factor of 2x. Factoring that out, we get:

2x(5x2/2x - 4/2) = 2x(5x - 2).

Answer:

= -18/2.25

Step-by-step explanation:

We can find the slope by using the following

m = (y2-y1)/(x2-x1)

   = (-12-6)/(3.75 - 1.5)

   = -18/2.25

Answer:

The answer to your question is the letter D.

Step-by-step explanation:

Data

Point A = (1.5, 6)

Point B = (3.75, -12)

Slope measures the steepnees of a line.

Formula

slope = m = (y2 - y1) / (x2 - x1)

-Asign values to x1, y1, x2 and y2

    x1 = 1.5  y1  = 6  x2 = 3.75  y2 = -12

-Substitution

          m = (-12 - 6) / (3.75 - 1.5)

-Simplification

          m = -18 / 2.25

-Result

         m = 8

It is possible to simplify more the result so slope = 8.

Answer:

The third side is sqrt(5)

Step-by-step explanation:

This is a right triangle so we can use the Pythagorean theorem

a^2+b^2 = c^2  where a and b are the legs and c is the hypotenuse

We know the legs are 1 and 2 and we are looking for the hypotenuse.

1^2+2^2 = c^2

1+4 = c^2

5 =c^2

Take the square root of each side

sqrt(5) = sqrt(c^2)

sqrt(5) =c

The third side is sqrt(5)

Answer:

[tex]\sqrt{5}[/tex] or 2.236

Step-by-step explanation:

The pythagorem theorm states that side 1^2 + side^2 = hypotenuse^2

2^2 + 1^2 = h^2

4+1 = h^2

5 = h^2

[tex]\sqrt{5} = \sqrt{h^{2} }[/tex]

[tex]\sqrt{5} =h[/tex]

Answer:

C(3,3)

Step-by-step explanation:

Answer:

Answer is

Radius of a circle is 6 feet

Step-by-step explanation:

[tex]given \: diameter \: = 12 \: feet \\ d = 2r \\ radius = \frac{d}{2} \\ = \frac{12}{2} \\ = 6[/tex]

HAVE A NICE DAY!

THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION.

Answer:

6ft

Step-by-step explanation:

Answer: 978 in. squared

Step-by-step explanation:

area of the rectangle : 24 x 30 = 720

area of the two triangles combined : (9 x 12) ÷ 2 = 54 x 2 = 108

area of the triangle on top of the other triangle : (20 x 15) ÷ 2 = 150

720 + 108 +150 = 978

Answer:The correct answer is The spread is from 1966 to 1987

Step-by-step explanation:

Sam makes an error when recording by imputing the spread as being from 1966 to 1987 .If this happens ,then it will affect all other results such as the gap ,center and peak which will change

Answer:

A is the right answer

Step-by-step explanation:

I know this because i got it right on my test.

Answer:

19.6 gallons

Step-by-step explanation:

If 10 gallons of gas were used to drive 225 miles then If kareem drove on 1 gallon of gas would take 22.5 miles.

so 1 gallon=22.5 miles,441 miles=19.6 gallons because,441/22.5=19.6 gallons.

The Kareem 19.56 gallons of gas to drive 441 miles at the same rate.

To find the number of gallons Kareem to drive 441 miles at the same rate, set up a proportion based on the given information:

Miles driven / Gallons of gas = Miles to be driven / Gallons of gas

Using the values provided:

225 miles / 10 gallons = 441 miles / x gallons

cross-multiply to solve for x:

225x = 10 ×441

Dividing both sides of the equation by 225:

x = (10 ×441) / 225

Calculating the value:

x ≈ 19.56

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Answer:

C) translate horizontally 5 units left

Step-by-step explanation:

f(x + 5)

Is a change in domain

The graph of f(x) is shifted 5 units towards the left to obtain the graph of f(x+5)

Answer:

C

Step-by-step explanation:

When we only change the x part of the function (that is, we add, subtract, multiply, or divide something in relation to the x part of f(x)), that is called a horizontal transformation. When we change the entire function, that's a vertical transformation.

In this case, because we are only changing the x (we turn f(x) into f(x + 5)), this is a horizontal transformation. One thing to note about horizontal transformations is that they are "backwards", which means that if we add to the x, we actually move the graph in the negative direction (which is to the left), whereas if we subtract from x, we move the graph in the positive direction (which is to the right).

Here, we're adding 5 to x, which we know means that we are translating the graph of f(x) horizontally to the left 5 units.

Thus, the answer is C.

Hope this helps!

Step-by-step explanation:

The sum of the square of a number and 7 times a number

The phrase a number means an arbitrary variable, let's call it x.

x

Square the number:

x^2

7 times the number means we multiply x by 7:

7x

The sum means we add x^2 and 7x

x^2 + 7x

Answer:

The answer is x² + 7x + 10 = 0.

Step-by-step explanation:

First, you have to make an expression. By reading the question, we can make it :

Let number = x,

Square of a no,

x²

7 times a no,

7 × x

= 7x

And means ADD equals to -10,

x² + 7x = -10

x² + 7x + 10 = 0

(By forming an equation, you have to let expressions equals to 0, so I add 10 to both sides in order to get rid of -10)

Transformation involve moving a point away from its original location.

The vertices of the pre-image are (–1, 0) and (–1, –5).

The transformation of a function may involve any change.

Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.

The rule is given;

[tex]r_{y = x} T_{4,0(x,y)}[/tex]

The rule means that

ABCD was translated by 4 units to the right, then reflected over line y = x,

The rule of right translation by 4 units,

(x, y) --- (x+4, y)

The rule of reflection over,

(x, y) --- ( y, x+ 4)

The coordinates of A"B"C"D" are: (-4, 5), (-1, 5), (0, 3), (-5, 3).

Hence, the vertices of the pre-image are (–1, 0) and (–1, –5).

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