a 96 foot transmission tower casts a 72 foot long shadow. an anchor wire runs from the top of the tower to the tip of the shadow. a ladder is set up vertically 66 feet from the base of the tower so the top of the ladder touches the wire. what is the height of the ladder

x = 7

hope this helps!

Answer: The answer is 12 units I remember this question from school.

The answer is 12 units.

Hope this helps!

Answer:

1.57

it would be 1.57

Answer:

1.5651 to the nearest hundred would be 1.57

Step-by-step explanation:

For this case we have that by definition, the volume of a cylinder is given by:

[tex]V = \pi * r ^ 2 * h[/tex]

Where:

V: It's the volume

A: It is the radius of the cylinder

h: It is the height of the cylinder

We have to:

[tex]V = \pi * (7.2) ^ 2 * 12\\V = \pi * 51.84 * 12\\V = 1954.32195794513 \ m ^ 3[/tex]

On the other hand, the volume of the cone is given by:

[tex]V = \frac {\pi * r ^ 2 * h} {3}[/tex]

V: It's the volume

A: It is the cone radius

h: It is the height of the cone

We have:

[tex]V = \frac {\pi * (7.2) ^ 2 * 11} {3}\\V = \frac {\pi * 51.84 * 11} {3}\\V = 597.153931594347 \ m ^ 3[/tex]

Thus, the total volume is given by:

[tex]V = 2551.47588954 \ m ^ 3[/tex]

If we round up we have:

[tex]V = 2551.48 \ m ^ 3[/tex]

Answer:

[tex]V = 2551.48 \ m ^ 3[/tex]

It’s a great way to write numbers that are very big numbers or very small numbers.

Have a great day!

Answer:

75 in^3

Step-by-step explanation:

i know because i had the test, and the other persons answer is wrong :)

Answer:

The cost difference is $4.

Step-by-step explanation:

Consider the provided information.

I am paying $60 a month for my service.

I would like to upgrade to the $80.00 service package because my new employer offers a 20% discount with your company.

If i get 20% of discount that means i need to pay only 80% of the original amount.

80% of 80 can be calculated as:

[tex]\frac{80}{100}\times 80[/tex]

[tex]0.8\times 80=64[/tex]

Therefore, now i need to pay $4 extra for the upgrade service.

Hence, the cost difference is $4.

the cost difference would be $4 more per month if upgrade is done.

First, let's calculate the cost of the $80 service package with a 20% discount:

[tex]20\%\ of\ 80 = \frac{20}{100} \times 80 = 16[/tex]

Now we need to subtract the discount from the original price = [tex]\$80 - \$16 = \$64[/tex]

Now, let's find the cost difference between the current $60 service and the discounted $64 service. This can be done by subtracting 60 from 64 which gives:

[tex]\$64 - \$60 = \$4[/tex]

Therefore, the cost difference would be $4 more per month if upgrade is done.

9^2 + B^2 = 18^2

81 + B^2 = 324

B^2 = 243

Square root 243

B =15.59

9*3.14 = 28.26

(This solves for circumference)

300/28.26 = 10.6157

(This solves for rotations)

About 11 rotations.

Answer: Damien lived in his apartment longer.

Step-by-step explanation: Damien lived in his apartment longer because if you convert five years into weeks you get 260 weeks. 260 weeks is greater than 250 weeks.

Answer: Damien has lived in the apartment longer.

Step-by-step explanation: A year is aproxiamtely 52.1429 weeks long. Divide 250 by a years worth of weeks and you get 4.79 years. Damien has lived in the apartment 5 years making him live in the building longer.

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

y-x> 0 -----> inequality A

y> x

The solution of the inequality A is the shaded area above the dashed line y=x

x+1<0 ----> inequality B

x < -1

The solution of the inequality B is the shaded area at the left of the dashed line x=-1 (open circle)

therefore

The solution of the system of inequalities in the attached figure

Answer:

The first car travels at 60 mph and the second at 40 mph.

Step-by-step explanation:

Let's represent the speed of the first car as s1 and that of the second car as s1.  Then s1 = s2 + 20 reflects the fact that the speed of the first car is 20 mph faster than that of the second car.

The total distance traveled is 400 miles.  Since distance = rate times time,

time = distance / rate.

First car:  (s1*t) is the distance traveled;

Second car:  (s2*t) is the distance traveled.

Adding these two distances together results in 400 miles:

s1*t + s2*t = 400 miles, or

t(s1 + s2) = 400 miles.  Let's eliminate s1 by substituting s2+ 20 for it:

t(s2 + 20 + s2) = 400 miles.  But we know t:  the cars both travel 4 hours.

Thus,

(4 hr)(2s2 + 20) = 400 miles, or

(after dividing both sides by 4 hr)

(2s2 + 20) = 100 miles/hr

Subtracting 20 from both sides:

2s2 = 80, so that s2 = 40 mph.

If s2 = 40 mph, then s1 = s2 + 20 = 60 mph

The first car travels at 60 mph and the second at 40 mph.

Answer:

The first car travels at 60 mph and the second at 40 mph.

Step-by-step explanation:

hope this helps... :)

Answer:

2x+7

Step-by-step explanation:

Check the picture below.

Answer: 34

Step-by-step explanation: 34 answer

The answer is 35. This is because 62 - 27 = 35

Answer:

[tex]\large\boxed{x<4\to x\in(-\infty,\ 4)}[/tex]

Step-by-step explanation:

[tex]-4x+28>12\qquad\text{subtract 28 from both sides}\\\\-4x>-16\qquad\text{change the signs}\\\\4x<16\qquad\text{divide both sides by 4}}\\\\x<4[/tex]

These lines are only parallel lines because these lines don't touch each other and parallel lines don't touch each other.

Answer:

These lines are only parallel.

Answer:

  66 g

Step-by-step explanation:

You want the combined mass of pebbles that are 4.5 grams or more, given the histogram of masses.

Each dot in the diagram represents one pebble, so the 5 dots above the mass of 4.5 g mean there were 5 pebbles with that mass.

The total mass of pebbles with mass 4.5 g or more will be the sum of the masses of each of the pebbles located in that column, and the columns to its right. Of course, we can use multiplication to simplify the repeated addition:

  5×(4.5 g) +4×(5 g) +3×(5.5 g) +1×(7 g) = 66 g

The combined mass of the pebbles 4.5 g or more is 66 g.

I did this earlier for a senior but believed I got it wrong based on that I fixed it to this : 62.5 was the percentage so 6250% so 18x 62.5 1125 HEY that’s reasonable please keep in mind I’m in middle school and you should double check this

From conservation of angular velocity the larger pulley will rotate at a speed of 500 rpm.

The conservation of angular velocity states that the angular velocity for a conjugate system will be always equal to the angular velocity of a part of the same system.

Mathematically -

r1ω1 = r2ω2 = r3ω3 = ................. = rnωn

where r is the radius of the circular belts, ω is the angular velocity and n is the total number of segments in the conjugate system.

Given that a pair of belted pulleys have diameters of 18 in. and 12 in. Also given that the smaller pulley turns at 750 rpm.

The radius of the pulleys are 9 in. and 6 in. respectively.

Let x rpm be the speed of the larger pulley turn.

From conservation of angular velocity, we have

⇒ 6 * 750 = 9 * x

⇒ x = (6 * 750)/9

∴  x = 500 rpm

Therefore, from conservation of angular velocity the larger pulley will rotate at a speed of 500 rpm.

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Answer:

x = 5 and y = 2, or (5,2) (Whichever one you do in class)

Step-by-step explanation:

You should solve this problem using substitution!

First you want to solve for x on this equation, 3x + 2y = 19.

start by subtracting 2y on each side, 3x + 2y(-2y) = 19(-2y). 3x = -2y + 19

Then divide by 3, 3x/3 = (-2y + 19)/3, this would give you x = (-2y + 19)/3

Next you substitute (-2y + 19)/3 in for x in 4x + 3y = -14: 4(-2y/3 + 19/3) + 3y = -14

Then Solve: (See Math Papa Algebra Calculator if you want to know exactly how to solve.) This would give you y = 2

Then substitute the 2: giving you x = 5  

To solve the system of equations, use the method of elimination. Multiply both equations by suitable constants to eliminate one variable and then solve for the other variable. Substitute the value of one variable back into one of the original equations to solve for the other variable. The solution to the system of equations is obtained by finding the values of x and y that satisfy both equations.

The given question consists of a system of two linear equations:

3x + 2y = 19

-4x + 3y = -14

To solve this system, we can use the substitution or elimination method. Let's use the method of elimination:

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Answer:

C. 0.26

Step-by-step explanation:

If the student selected was a sophomore at the jazz concert, we'd use the table to find the student being out of 35 students in the same situation. To get the correct answer you must take 35 divided by the total number of students attended (137). Therefore, 35/137= 0.255 rounded to the nearest tenth would be 0.26

Hope this helps! :)

Answer:

C) 0.26

Step-by-step explanation:

35 sophomores attended the jazz concert out of 137 total students.

Divide 35 by 137, which is roughly 0.25547445...

Round two decimal places and you will get 0.26.

Answer:

2.5 m

Step-by-step explanation:

Consider the ramp, the ground and the back of the lorry to form a right triangle where the ramp is the hypotenuse and the distance from the back of the lorry is the adjacent side, x

Using the cosine ratio in the right triangle

cos32° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{3}[/tex]

Multiply both sides by 3

3 × cos32° = x, hence

x ≈2.5 m

ANSWER

[tex] \sum _{n = 1} ^{6} 2n[/tex]

EXPLANATION

The series is:

2 + 4 + 6 + 8 + 10 + 12

The first term is:

f(1)=2

The common difference is

[tex]d= 4 - 2 = 2[/tex]

The formula for the corresponding sequence is

[tex]f(n) = 2 + 2(n - 1)[/tex]

[tex]f(n) = 2 + 2n - 2[/tex]

[tex]f(n) = 2n[/tex]

The summation notation is:

[tex] \sum _{n = 1} ^{6} 2n[/tex]

The probability that the sum of the two resulting numbers is greater than 5 is 2/3

The probability that the product of the two resulting numbers is odd is 1/3

How to determine the required probabilities

From the question, we have the following parameters that can be used in our computation:

Die = {1, 2, 2, 4}

Spinner = {3, 4, 7}

The sample space is represented as

Space = {(1, 3), (1, 4), (1, 7), (2, 3), (2, 4), (2, 7), (2, 3), (2, 4), (2, 7), (4, 3), (4, 4), (4, 7)}

For the sum greater than 5, we have the following space

Space = {4, 5, 8, 5, 6, 9, 5, 6, 9, 7, 8, 11}

In the above, we have

Total = 12

Sum greater than 5 = 8

So, this probability is

P = 8/12 = 2/3

For the product resulting in odd numbers, we have the following space

Space = {3, 4, 7, 6, 8, 14, 6, 8, 14, 9, 12, 21}

In the above, we have

Total = 12

Odd results = 4

So, this probability is

P = 4/12 = 1/3

Hence, the probabilities are 2/3 and 1/3

Since there is no number line below I’m going to do this.

_________ __________ __________

Just split it into three ,’:b

Answer:

3. 2x - 1 = 4

4. x/6 = 1/2

The value of the solutions are,

3) x = 5/2

4) y = 3

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The algebraic expression is,

''One less than twice a number, x, is equal to four.''

And, ''A number divided by six is one-half.''

Now,

Since, The algebraic expression is,

''One less than twice a number, x, is equal to four.''

Hence, We can formulate;

⇒ 2x - 1 = 4

Solve for x;

⇒ 2x = 4 + 1

⇒ 2x = 5

⇒ x = 5/2

4) The algebraic expression is,

⇒ ''A number divided by six is one-half.''

Hence, We can formulate;

⇒ y/6 = 1/2

Solve for y as;

⇒ y = 6×1/2

⇒ y = 6/2

⇒ y = 3

Thus, The value of the solutions are,

3) x = 5/2

4) y = 3

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Answer:

Driveway is 36.57 meters long.

Step-by-step explanation:

We are given the length of a driveway to be 40 yards and we are to find its length in meters.

We know that 1 yard is equal to 0.914 meter long. So we will simply multiply 40 by 0.914 to find the length of the driveway in the meters.

Length of driveway in meters = [tex]40 \times 0.914[/tex] = 36.57 meters

The required, driveway is approximately 36.576 meters long.

To convert yards to meters, we can use the conversion factor: 1 yard = 0.9144 meters.

Given that the driveway is 40 yards long, we can calculate its length in meters by multiplying 40 yards by the conversion factor:

40 yards * 0.9144 meters/yard = 36.576 meters.

Therefore, the driveway is approximately 36.576 meters long.

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Answer:

Subtract 9x from both sides.

Step-by-step explanation:

Answer:

Subtract 9x from both sides

Answer:

if the federal reserve sells 50,000 in treasury bonds to a bank at 6% interest, the immediate effect on the money supply would be; the money supply would decrease by $50,000

Step-by-step explanation:

if the federal reserve sells 50,000 in treasury bonds to a bank at 6% interest, the immediate effect on the money supply would be; the money supply would decrease by $50,000.

The $50,000 will be transferred to the federal reserves and thus not available to be borrowed by the public.

When the Federal Reserve sells Treasury bonds to a bank, the money supply decreases. This is because the bank, having bought the bonds, will have to reduce its loans to maintain requisite reserves. This is a product of open market operations, a monetary policy tool active within the central banking system.

The question you're asking pertains to the field of macroeconomics, specifically monetary policy. You're curious about the effects on the money supply if the Federal Reserve sells $50,000 in Treasury bonds to a bank at 6% interest.

When the Federal Reserve sells these bonds to a bank, it effectively reduces the amount the bank can loan out to customers. The financial institution has to hold a certain amount in reserves, hence, by buying the bonds, it has to reduce its loans to fulfill this requirement. This, therefore, results in an immediate decrease in the money supply.

It's important to note that the Federal Reserve sells bonds to control the flow of money in the economy. This selling of bonds is a type of monetary policy tool called open market operations, which is used to influence the quantity of bank reserves and the level of interest rates.

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Answer: 2 2/5

Step-by-step explanation:

You can do 6 * 2/5 = 2 2/5

OR

You can do 2 + 2 + 2/5

6/5 = 1 1/5 * 2 = 2 2/5

Answer:Answer is 2 and 3

Step-by-step explanation:trust me