The circular base of a cone has a radius of 5 centimeters. The height of the cone is 12 centimeters, and the slant height is 13 centimeters. What is the approximate surface area of the cone? Use 3.14 for π and round to the nearest whole number. 267 cm2 283 cm2 456 cm2 487 cm2

present value of annuity = annual payment * [ 1 - (1+i)^-n ]/i

=>

12500 = 128.04 * [1-(1+9%/12^-n]/9%/12

=>n = 42 payments

Present value of annuity formula yields approximately 42 payments for $12,500, with $128.04 monthly payments at 9% interest.

Let's break it down:

[tex]\[PV = Pmt \times \left[1 - \frac{{(1 + i)^{-n}}}{i}\right]\][/tex]

Where:

[tex]- \(PV\) is the present value of the annuity.\\- \(Pmt\) is the amount of each payment in the annuity.\\- \(i\) is the interest rate per period, expressed as a decimal.\\- \(n\) is the total number of payments.[/tex]

Given your values:

- [tex]\(PV\)[/tex] is $12,500.

- [tex]\(Pmt\)[/tex] is $128.04.

- [tex]\(i\)[/tex] is the monthly interest rate, which is [tex]\(9\% / 12 = 0.09 / 12\)[/tex] since the annual rate is divided by 12 for monthly payments.

- [tex]\(n\)[/tex] is what we're solving for.

Substituting these values into the formula, we have:

[tex]\[12,500 = 128.04 \times \left[1 - \frac{{(1 + 0.09/12)^{-n}}}{0.09/12}\right]\][/tex]

Now let's solve for [tex]\(n\):[/tex]

[tex]\[12,500 = 128.04 \times \left[1 - \frac{{(1 + 0.0075)^{-n}}}{0.0075}\right]\]\[1 - \frac{{(1 + 0.0075)^{-n}}}{0.0075} = \frac{{12,500}}{{128.04}}\]\[\frac{{(1 + 0.0075)^{-n}}}{0.0075} = 1 - \frac{{12,500}}{{128.04}}\]\[ (1 + 0.0075)^{-n} = 0.0075 \times \left(1 - \frac{{12,500}}{{128.04}}\right)\]\[ (1 + 0.0075)^{-n} = 0.0075 \times \left(1 - \frac{{12,500}}{{128.04}}\right)\]\[ (1 + 0.0075)^{-n} = 0.9920\]Taking the natural logarithm of both sides:\[ -n \ln(1 + 0.0075) = \ln(0.9920)\][/tex]

Using a calculator:

n ≈ [tex]\frac{{-0.008025}}{{-0.007472}}\][/tex]

n ≈ [tex]41.961\][/tex]

So, rounding up, we get , n ≈ 42

Therefore, it would take approximately 42 payments to reach a present value of $12,500 given the annuity with an annual interest rate of 9% compounded monthly and a payment of $128.04 per month.

Final answer:

To find the number of miles Sara can drive on 12 gallons of gas, divide the total miles she drove by the total gallons of gas she used. Multiply this fuel efficiency by the number of gallons to get the result. (Option C)

Explanation:

To calculate the number of miles Sara can drive on 12 gallons of gas, we need to first find her fuel efficiency in terms of miles per gallon. To do this, we divide the total miles she drove (117 miles) by the total gallons of gas she used (5.2 gallons).

117 miles / 5.2 gallons = 22.5 miles per gallon

Next, we can use this fuel efficiency to calculate the number of miles Sara can drive on 12 gallons of gas. We multiply her fuel efficiency (22.5 miles per gallon) by the number of gallons (12 gallons).

22.5 miles per gallon * 12 gallons = 270 miles

Therefore, Sara can drive 270 miles on 12 gallons of gas.

The value of x is 17.

To find the value of x when (7x) and (2x+27) are the two angles made on a straight line, we can use the fact that the sum of the angles on a straight line is 180 degrees.

Let's set up an equation:

(7x) + (2x+27) = 180

First, we simplify the equation by combining like terms:

9x + 27 = 180

Next, we isolate the variable x by subtracting 27 from both sides of the equation:

9x = 180 - 27

9x = 153

Finally, we solve for x by dividing both sides of the equation by 9:

x = 153/9

Simplifying the division gives us:

x = 17

Therefore, the value of x is 17.

Complete question :-

Find the value of x, if (7x) and (2x+27) are the two angles made on a straight line?
A. 7
B. 49
C. 61
D. 17

So, the value of x is not one of the given options A, B, C, or D.

To find the value of x in the expression (7x)(2x+27), we need to simplify the expression and solve for x.

Step 1: Distribute the 7x to both terms inside the parentheses:

(7x)(2x+27) = 14x^2 + 189x

Step 2: Set the expression equal to 0 and factor out common terms, if possible:

14x^2 + 189x = 0

Step 3: Factor out x:

x(14x + 189) = 0

Step 4: Set each factor equal to 0 and solve for x:

x = 0 (from the first factor)

14x + 189 = 0

14x = -189

x = -189/14

So, the value of x is not one of the given options A, B, C, or D.

Answer:

New or current cost = 12 - 4.2 = $7.8

Step-by-step explanation:

Franco's Pizza is selling their pizzas 35% cheaper than usual. This is a discount on the normal cost. To get the amount it costs now, we will find the percentage of the discount on the original cost and subtract what we get from the original cost.

Discount = 35℅

Original cost of pizza is $12 (if a pizza normally cost $12).

So the discount in terms of dollars

= ℅ discount / 100 × normal cost of pizza

= 35 / 100 × 12 =0.35 × 12 = $4.2

New or current cost of pizza would be normal or original cost - the discount in dollars.

New or current cost = 12 - 4.2 = $7.8

The pizza is now $7.80.

If Franco's Pizza is selling their pizzas 35% cheaper than usual, we can calculate the new price by multiplying the original price by (1 - 0.35).

So, the new price of the pizza would be $12 * (1 - 0.35) = $7.80.

Therefore, the pizza is now $7.80.

Answer:

Carlos bought a new Mastercraft boat for $17,000. He made a $2,500 down payment on it. The bank's loan was for 60 months, and the finance charges totaled $4,900. What's his monthly payment?  

A. $323.33

B. $232.33

C. $313.33

D. $332.33

Step-by-step explanation:

1.- Carlos paid $ 2,500 of the $ 17,000 that Mastercraft costs and would be equal to: $ 17,000 - $ 2,500 = $ 14,500

2.- We have financial charges amounting to $ 4,900 to be added to the previous amount, and would be equal to: $ 14,500 + $ 4,900 = $ 19,400

3.- The bank loan is for 60 months, which would result in: $ 19,400 / 60 = $ 323.33

The answer is: A. $ 323.33

multiply Celsius by 9/5 then add 32 to get Fahrenheit

25 * 9/5 = 45

45 +32 = 77 degrees Fahrenheit

235.24 + 45.58 = 280.82

280.82/2 = 140.41

each check was 140.41

Answer:

Step-by-step explanation:

greder

Part 1: Q is less than P.

Part 2: The density of silver (Q) is higher than that of iron (P), indicating that silver has a greater mass per unit volume, making P greater than Q.

Part 1: The value of Q is less than the value of P.

Part 2: This conclusion can be drawn by comparing the densities of the two substances, iron, and silver. Density is calculated by dividing mass by volume (D = m/V), and since the mass of iron (100g) is equal to the mass of silver (100g), we can simplify the comparison by focusing on their densities.

The density of iron (7.8 g/cm^3) is significantly less than the density of silver (19.3 g/cm^3). Density is a measure of how much mass is packed into a given volume, so the higher the density, the more mass is concentrated in a smaller space. In this case, silver is much denser than iron, which means that for an equal mass, silver occupies a smaller volume compared to iron.

Since Q represents the density of silver and P represents the density of iron, and the density of silver (Q) is greater than the density of iron (P), we can conclude that Q is indeed less than P. The higher density of silver implies that it has a greater mass concentrated in the same volume. The value of Q is less than the value of p.

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Answer:

18

Step-by-step explanation:

Edge 2021 (^Just to back up the answer above, so nobody feels doubts^.)

We have that the sides of the polygon   is mathematically given as

n=20

Option C

From the question we are told

A regular polygon has possible angles of rotational symmetry of 20°, 40°, and 80°.

How many sides does the polygon have? 10 12 18 20

Generally the equation for the Polygon exterior angle  is mathematically given as

[tex]\theta=\frac{360}{n}\\\\18=\frac{390}{18}[/tex]

n=20

OptionC

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The width of the rectangular room is 6 meters.

A rectangle is one of the types of quadrilaterals in which all four angles are right angles or equal to 90 degrees. It is four-sided polygon in which the opposite sides are parallel and equal to each other.

For the given situation,

Let the width of the rectangular room, w = x

A rectangular room is twice as long as it is wide,

length of the rectangular room, l = 2x

The perimeter of the rectangle = 36 meters.

The formula of perimeter of rectangle is

[tex]P=2(w+l)[/tex]

⇒ [tex]36=2(x+2x)[/tex]

⇒ [tex]36=2(3x)[/tex]

⇒ [tex]x=\frac{36}{6}[/tex]

⇒ [tex]x=6[/tex]

Hence we can conclude that the width of the rectangular room is           6 meters.

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Final answer:

To find the number when decreased by 10%, set up an equation and solve for the number.

Explanation:

When a number decreased by 10% the result in 63. What is the number?

Let the number be x.

Equation: x - 0.10x = 63

Solve for x: 0.90x = 63 => x = 63 / 0.90 = 70

Final answer:

The number of scores in the sample is 4.

Explanation:

The question provided asks us to determine the number of scores in the sample based on the z-score of +1.00, given a population with a mean (μ) of 50 and a standard deviation (σ) of 12.

The z-score formula for a sample is

z = (M - μ) / (σ / √n),

where

We are given that M = 56, z = 1, μ = 50, and σ = 12.

To find the sample size (n), we use the formula and rearrange to solve for n:

Therefore, the number of scores in the sample is 4.

Answer:

4.5

Step-by-step explanation:

Answer:

The center is at (4, -6), and the length of the radius is 5.

Step-by-step explanation:

(x − 4)2 + (y + 6)2 = 25

(x − 4)2 + (y − (-6))2 = 52

When I compare my equation with the standard form, (x − h)2 + (y − k)2 = r2, I get h = 4, k = -6, and r = 5. The center is at (4, -6), and the length of the radius is 5.

plato answer

The reason that ship A is moving -35km/h is because ship B acts as an "origin" and as things move closer to the "origin" they become negative and as things move away from the "origin" they become positive.

We know that the rate of Ship A is expressed as dAdt=−35 and the rate of Ship B is expressed as dBdt=25

Step 2: We want to figure out how many km Ship A and Ship B traveled in 4 hours

ShipA:−35kmh⋅4hr=−140km

Now if we take this −140km and add it to the 150km we can see that Ship A is now only 10km away from where Ship B began

ShipB:25kmh⋅4hr=100km

This means that Ship B is now 100km from where it originally started

We can now redraw our information

Step 3: We must use the Pythagorean Theorem to find the third side of the triangle

x2+y2=z2→102+1002=z2

z=√102+1002

Step 4: Now that we know z, we must differentiate the original equation in order to find the rate at which z in changing

x2+y2=z2→2xdxdt+2ydydt=2zdzdt

We can simplify by canceling out the 2's

xdxdt+ydydt=zdzdt

Step 5: Write down all the information and then plug into equation

x=10anddxdt=−35
y=100anddydt=25
z=√102+1002anddzdt=?

Now plug in the information

xdxdt+ydydt=zdzdt

10(−35)+100(25)=√102+1002dzdt

−350+2500=√102+1002dzdt

2150=√102+1002dzdt

21.393=dzdt

The distance between the ships are increasing at a rate of 21.393 km/h

Answer:

C. 2+_ square root 10i / 2

Step-by-step explanation: