please help me with this. I know the answer for the first one, but I'm just confused about the second one.​

Answer: C. V ≈ 635.2 cm^3.

Explanation: The formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius and h is the height (or slant height in this case).

Using the given values, we have:

V = (1/3)π(4.25 cm)^2(12 cm)

V ≈ 635.2 cm^3 (rounded to the nearest tenth)

Therefore, the answer is C. V ≈ 635.2 cm^3.

The coordinates of point P are (-1, 1 8/11).

We have,

G(4, 4) and H(-7, 1)

m :n = 5:6

Using Section formula

x = (mx₂ + nx₁)/ (m+n) and y = (my₂ + ny₁)/ (m+n)

Here, x₁ = 4, y₁ = -7, x₂ = 4 and y₂ = -1

So, x = (5(-7) + 6(4))/ 11  and y = (5(-1) + 6(4))/ 11

x = -35+24/11 and y = -5 + 24/11

x = -11/11 and y = -19/11

x = -1 and y = 1 8/11

Learn more about Section Formula here:

https://brainly.com/question/30242630

#SPJ1

Answer:

1728 square ft²

Step-by-step explanation:

48x36=1728

Answer:

[tex]\large \boxed{\mathrm{Area}}[/tex] = [tex]\large \boxed{\mathrm{12 \ ft^2}}[/tex]

Steps:

12 inches = 1 foot

48 / 12 = 4 [tex]\meduim \boxed{\mathrm{feet}}[/tex]

36 / 12 = 3 [tex]\large \boxed{\mathrm{feet}}[/tex]

Answer:

3 x 4 = 12 ft²

Answer:

53

Step-by-step explanation:

20+8=28

90-28=62

62-9=53

90 angle!

The number of days required to complete the job in exponent form is 10¹ = 10.

The exponent form of the number of days is calculated as follows;

number of pages that can be printed by all machines = n x P

where;

N = 100 x 104

N = 10400 pages/day

However, the Ted's company needs 10 days to print 106 pages, our equation is formed as follows;

x = log(y)

where;

10ˣ = y

10ˣ = 10

x = 1

so the exponential form = 10¹ = 10

Learn more about exponent form here: https://brainly.com/question/23275698

#SPJ1

The magnitude of the speed of the particle is determined as √ (17), m/s.

option A.

The speed of a particle is defined as the rate of change of the particle's displacement with time.

Mathematically, the formula for the speed of the a particle is given as;

v = dx/dt

where;

The speed of the particle is calculated as;

v = u + at

where;

at time, t = 0, the equation for the speed of the particle becomes;

v = u

v = i + 4j

The magnitude of the speed is calculated as follows;

v = √ (1² + 4²)

v = √ (17), m/s

Learn more about speed of particles here: https://brainly.com/question/19661245

#SPJ1

Suppose [tex]f(x) =8^{3x[/tex] and [tex]g(x) =8^{4x[/tex], function operations that are correct include the following:

A. (f + g)(x) = [tex]8^{3x} + 8^{4x}[/tex]

B. (f × g)(x) = [tex]8^{7x}[/tex]

C. (f - g)(x) = [tex]8^{3x} - 8^{4x}[/tex]

In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

This ultimately implies that, an exponent is represented by the following mathematical expression;

bⁿ

Where:

By applying the division and multiplication law of exponents for powers of the same base to the functions, we have the following:

(f × g)(x) = [tex]8^{3x+ 4x}=8^{7x}[/tex]

(f ÷ g)(x) = [tex]8^{3x- 4x}=8^{-x}[/tex]

Read more on exponent here: brainly.com/question/27858496

#SPJ1

Answer:

To determine the monthly deposit that Sophia must make in order to reach her retirement goal, we can use the formula for the future value of an annuity:

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

where:

FV = future value of the annuity (which is Sophia's retirement goal of $1,600,000)

P = monthly deposit

r = annual interest rate (which is 9%)

n = number of times interest is compounded per year (which is 12 for monthly compounding)

t = number of years until retirement (which is 65 - 28 = 37)

Substituting the given values, we get:

1600000 = P * ((1 + 0.09/12)^(12*37) - 1) / (0.09/12)

Simplifying and solving for P, we get:

P = 1600000 * (0.09/12) / ((1 + 0.09/12)^(12*37) - 1)

P ≈ $524.79

Therefore, Sophia must make a monthly deposit of approximately $524.79 in order to reach her retirement goal of $1,600,000.

Step-by-step explanation:

Answer:

9 pounds/135 cubic inches

= 1 pound/15 cubic inches

= .07 pounds/cubic inch

The mistake is when you try to divide by X - 1, because you can't divide by zero.

Here we start by defining:

X = 1

The second step makes sense, we are adding the same value in both sides:

X + X = X + 1

2X = X + 1

Now subtract 2 in both sides:

2X - 2 = X + 1 - 2

2X - 2 = X - 1

Here is the mistake, you divide both sides by X - 1

But we already defined that X = 1

Then you are trying to divide by zero, and that opeartion is not defined, that is why you reach a false equation.

Learn more about divisions at:

https://brainly.com/question/25289437

#SPJ1

The most expensive car loan that Cindy can afford is $14,534.

The most expensive car loan is calculated by applying the following formula.

M.P = (Pr) / (1 - (1 + r)^(-n))

Where;

215 = (P x 0.00175) / (1 - (1 + 0.00175)^(-72))

215 = (P x 0.00175)/0.1183

(P x 0.00175) = 215 x 0.1183

P x 0.00175 = 25.44

P =  $14,534

Learn more about most expensive car loan here: https://brainly.com/question/12566025

#SPJ1

Check the picture below.

bearing in mind that a vertical line always has that slope.

Answer:

its not a function

Step-by-step explanation:

The exact value of tan2θ in simplest radical form is  -21/√7.

The value of tan2θ is calculated as follows;

From Pythagorean identity, we know that;

sin² θ + cos² θ = 1

cos² θ is calculated as follows;

(3/4)² + cos² θ = 1

9/16 + cos² θ = 1

cos² θ = 1 - 9/16

cos² θ = 7/16

cos θ = √(7/16)

tan θ = sin θ / cos θ = 3/4 x 4/√7 = 3/√7

Now, we will find tan 2θ;

tan 2θ = 2tan θ / (1 - tan² θ)

tan 2θ = 2(3/√7) / (1 - (3/√7)²)

tan 2θ = (6/√7) / (-2/7)

tan 2θ = -21/√7

Learn more about quadrant angle here: https://brainly.com/question/28587485

#SPJ1

The distance between Garret and Dino to the nearest yard is: 21 yds

The Law of Cosines is defined as a numerical formula that expresses the relationship between  the side lengths and points of any triangle. It usually expresses that the square of any particular side of a triangle is equal to the number of squares of the other different sides short two times the result of those sides and the cosine of the point between them.

Numerically, the Law of Cosines can be expressed as:

c² = a² + b² - 2abcos(C),

where c is the length of the side inverse to the point C, and an and b are the lengths of the other different sides.

Thus, the distance here is expressed as:

d² =  15² + 17² - 2(15 * 17)cos(81)

d = √434.218

d = 20.838 yds

Read more about Law of cosines at: https://brainly.com/question/4372174

#SPJ1

a)

The investment cost for replacing the 800 fixtures is $240,000.

b)

Annual utility cost savings is $57,600/year.

c)

Since the NPV is positive, the proposal should be accepted as it generates a positive return and is expected to be profitable.

We have,

a.

The investment cost for replacing the 800 fixtures is given as $300 per fixture, so the total investment cost would be:

Total Investment Cost = Number of fixtures x Investment cost per fixture

Total Investment Cost = 800 x $300

Total Investment Cost = $240,000

b.

To calculate the annual utility cost savings, we need to find the difference in the watt-hour consumption per fixture between HID and LED lighting, and multiply it by the number of fixtures, operating hours per day, operating days per year, and the metered utility rate per kilowatt-hour:

Energy consumption savings per fixture per hour = HID watt hour consumption - LED watt hour consumption

Energy consumption savings per fixture per hour = 500 watts/hr - 300 watts/hr

Energy consumption savings per fixture per hour = 200 watts/hr

Total energy consumption savings per hour for 800 fixtures:

= Energy consumption savings per fixture per hour x Number of fixtures

Total energy consumption savings per hour for 800 fixtures.

= 200 watts/hr x 800

Total energy consumption savings per hour for 800 fixtures.

= 160,000 watts/hr

Total energy consumption savings per year = Total energy consumption savings per hour x Operating hours per day x Operating days per year

Total energy consumption savings per year = 160,000 watts/hr x 10 hrs/day x 300 days/year

Total energy consumption savings per year = 480,000,000 watt-hours/year

Total energy consumption savings per year in kilowatt-hours (kWh):

= Total energy consumption savings per year / 1,000

Total energy consumption savings per year in kWh = 480,000,000 / 1,000

Total energy consumption savings per year in kWh = 480,000 kWh/year

Annual utility cost savings:

= Total energy consumption savings per year in kWh x Metered utility rate per kWh

Annual utility cost savings = 480,000 kWh/year x $0.12/kWh

Annual utility cost savings = $57,600/year

c.

To evaluate the proposal using net present value (NPV), we need to calculate the present value of the investment cost and the present value of the annual utility cost savings over a 15-year period.

Using the Present Value of the Ordinary Annuity formula with a 15-year life and 8% minimum rate of return, we get:

PV of Investment Cost = -$240,000 (negative because it's a cash outflow)

PV of Annual Utility Cost Savings = $514,883.81

NPV = PV of Annual Utility Cost Savings - PV of Investment Cost

NPV = $514,883.81 - (-$240,000)

NPV = $754,883.81

Therefore,

The investment cost for replacing the 800 fixtures is $240,000.

Annual utility cost savings is $57,600/year.

Since the NPV is positive, the proposal should be accepted as it generates a positive return and is expected to be profitable.

Learn mroe about investment costs here:

https://brainly.com/question/28462528

#SPJ1

Answer:5.08

4.34 are correct

Step-by-step explanation:We can solve this quadratic equation in sin(θ) by using the substitution u = sin(θ):

6u^2 - 3u - 8 = 0

We can use the quadratic formula to solve for u:

u = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 6, b = -3, and c = -8. Substituting these values, we get:

u = (3 ± sqrt(9 + 192)) / 12

u = (3 ± sqrt(201)) / 12

Therefore, either:

The three numbers are -2, 42 and 16 these we obtained by solving the equations

Let the three numbers x, y, and z. We know that:

x + y + z = 56 (Equation 1)

z - x = 44 (Equation 2)

x + y = 16 (Equation 3)

From Equation 3, we can solve for one of the variables in terms of the other:

y = 16 - x

Substituting this into Equation 1, we get:

x + (16 - x) + z = 56

Simplifying this equation, we get:

z = 40 - x (Equation 4)

Substituting Equation 4 into Equation 2, we get:

(40 - x) - x = 44

Simplifying this equation, we get:

40 - 2x = 44

Subtracting 40 from both sides, we get:

-2x = 4

Dividing both sides by -2, we get:

x = -2

z = 40 - (-2) = 42

Finally, using Equation 1, we can solve for y:

-2 + y + 42 = 56

y=16

Hence, the three numbers are -2, 42 and 16

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ1

Answer:

92.5

Step-by-step explanation:

First, we need to put the data in order from smallest to largest:

$71, 81, 89, 92, 93, 94, 94, 99$

There are 8 numbers in the data set, which is an even number. To find the median, we need to average the two middle numbers.

The middle two numbers are 92 and 93, so the median is:

$(92+93)/2 = 92.5$

Therefore, the median of the data is 92.5.

Answer: the answer is A=33∘, B=107.5∘, and C=39.5∘ is correct or c

Step-by-step explanation:

To find the angles of triangle ABC with side lengths a=12, b=21, and c=14, we can use the Law of Cosines and then apply the Law of Sines to find the remaining angles. Let's denote the angles as A, B, and C respectively.

According to the Law of Cosines:

c^2 = a^2 + b^2 - 2ab * cos(C)

Plugging in the given side lengths:

14^2 = 12^2 + 21^2 - 2 * 12 * 21 * cos(C)

196 = 144 + 441 - 504 * cos(C)

504 * cos(C) = 389

cos(C) = 389 / 504

C = arccos(389 / 504)

Using a calculator to find the approximate value of C, we get C ≈ 43.5°.

The probability that the sum of the numbers is even is,

⇒ P = 0.47

Since, We know that;

To have this kind of event you can have the following events, where

(d₁ ,d₂),  d1 is the number that appears uppermost on die 1 and d2 is the number that appears uppermost on dice 2:

(1, 1), (1, 3) , (1, 5), (2, 2), (2, 4) (2, 6) (3, 1) (3, 3) (4, 2) (4, 4) (4, 6), (5, 1) (5, 3), (5, 5) (6, 2) (6, 4) (6, 6)

And,  the total number of events is 36 since every dice have 6 numbers.

The probability is:

P(Event)=P(sum is even)/Total number of events

P = 17/36

P = 0.47

Thus, The probability that the sum of the numbers is even is,

⇒ P = 0.47

Learn more about the probability visit:

https://brainly.com/question/13604758

#SPJ1

The dimension of the rectangle is 50 meters by 10 meters

The perimeter of a figure is the sum of all the external sides of the figure

The formula for calculating the perimeter of rectangle [tex]= 2(\text{l}+\text{w})[/tex]

If the length is 40 meters longer than the width, then:

[tex]\text{l} = 40 + \text{w}[/tex]

Substitute

[tex]120 = 2(40+2\text{w})[/tex]

[tex]60 = 40 + 2\text{w}[/tex]

[tex]30 = 20+ \text{w}[/tex]

[tex]\bold{w = 10 \ meters}[/tex]

Since [tex]\text{l} =40 + \text{w}[/tex]

[tex]\text{l} =40 +10[/tex]

[tex]\bold{l=50 \ meters}[/tex]

Hence the dimension of the rectangle is 50 meters by 10 meters

Learn more on perimeter of figure here: brainly.com/question/22447290

Answer:

The angle of the intersection is 90 degrees

Step-by-step explanation:

How I know this is because EF is the diameter, which means that arc EF is equal to 180 degrees. Because we know this that means when it is spilt into two parts, the arc and angle measure has to be 90 degrees.

Another way to do this is to remember that a circle is 360 degrees and the circle is split into 4 parts. So all you have to do is divide 360/4 to get 90. Your answer.

Answer:

perimeter = 84 feet

Step-by-step explanation:

using Pythagoras' identity in the right triangle to find a

a² + 35² = 37²

a² + 1225 = 1369 ( subtract 1225 from both sides )

a² = 144 ( take square root of both sides )

a = [tex]\sqrt{144}[/tex] = 12

then

perimeter = 35 + 37 + 12 = 84 feet

Answer:

Step-by-step explanation:

the square base = 5 * 5 = 25

each of the triangular sides = 4*2.5=10

so… 25+(10*4)=25+40=65

The parent function is [tex]y = ab^x[/tex]

A function for the translation indicated is [tex]y = ab^{x+6} - 7[/tex].

In Mathematics and Geometry, the vertical translation a geometric figure or graph downward simply means adding a digit to the value on the y-coordinate of the pre-image or function.

In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x - N) while a vertical translation to the negative y-direction (downward) is modeled by this mathematical equation g(x) = f(x) - N.

Where:

In this scenario, we can logically deduce that the graph of the parent function  was translated or shifted to the left (horizontally) by 6 units and downward (vertically) by 7 units;

[tex]y = ab^x[/tex]

[tex]y = ab^{x+6} - 7[/tex]

Read more on translation here: brainly.com/question/4521517

#SPJ1