After a windstorm, a leaning pole makes a 75° angle with the road surface. the pole casts a 15-foot shadow when the sun is at a 45° angle of elevation. about how long is the pole?

Explanation:

We were given the equation:

The slope-intercept is represented by:

Rewriting the equation into its slope-intercept form, we have:

Therefore, the equation in slope-intercept is: y = -(8/3)x + 4

We will now input assumed values for "x" to obtain corresponding y-values. We have:

We will proceed to plot these points on the graph, we have:

Answer:

don't click that guy's link it's a virus

I'm pretty sure the answer if 50% chance

Step-by-step explanation:

I just combined the probabilities because it's for both lights

hope it helps <3

Answer:

x=14

Step-by-step explanation:

5x+3x+30 +2x+10 = 180 (angles on straight line add to 180)

10x+40 =180

10x=140

x=14

Answer:

A. 88

Step-by-step explanation:

A circle is 360 degrees right ? so, 136 cant be right since 136 is almost half of a circle and that angle doesn't look nearly half, 44 and 22 cant be right either since AB is 44 degrees and its growing outwards so it cant be exactly 44 and it cant be less 44 (22)

so your answer will be A. 88

The limit doesn't exist.

The value that a function (or sequence) approaches when the input (or index) gets closer to a particular value is known as a limit. Calculus and mathematical analysis are impossible without limits, which are also required to determine continuity, derivatives, and integrals.

In addition to being closely related to limit and direct limit in category theory, the idea of a limit of a sequence is further generalized to include the concept of a limit of a topological net.

A function's limit is typically expressed in formulas as

\(\lim_{x \to c } F(x) = L\)

It is typically used to assign values to specific functions at locations where none are defined while maintaining consistency with existing values.

\(F(x) = -x+8 ,x\leq 0\)

\(F(x) = 4x+9 , if x > 0\)

\(\lim_{x \to 0^{+} } F(x) = \lim_{n \to 0^{+} } (4x+9) = 9\)

\(\lim_{x \to 0^{-} } F(x) = \lim_{x \to 0^{-} } (-x+8) =8\)

\(\lim_{x \to 0^{+} } F(x) \neq \lim_{x \to 0^{-} } F(x)\)

So limit doesn't exist

For limit to exist

\(\lim_{x \to 0^{+} } F(x) = \lim_{x \to 0^{-} } F(x) = \lim_{x \to 0} f(x)\)

must be satisfied

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We know the value of x and y,

x = 6 and y = -1 [Given]

Substitute the value,

Answer:

6 minutes 8 balloon animals. 45 minutes 60 balloon animals!

Step-by-step explanation:

I divided 15 by 6 and got 2.5, so I then divided 20 by 2.5 and got 8 balloon animals! For the next one I divided 45 by 15 and got 3 then I multiplied 20 by 3 and got 60 balloon animals! Hope this helps!

Answer:

7.8

58.5

Step-by-step explanation:

You need to find the amount of minutes that your uncle needs to blow up one balloon, which is 1.3 minutes. Now multiply 1.3 and the other numbers in the table to get the answers above.

I hope this helps!

ANSWER:

$366.89

Given:

Cost of a gallon of paint = $29.95

x gallons of paint will cost: $29.95 * x gallons

Since Nikki needs 12.25 gallon of paints, the price she would spend on paint will be:

Nikki will spend $366.89 to complete the painting project

The probability of having a wireless mouse is 0.4 , the probability of not having a wireless keyboard is 0.3, and 0.2 is the probability of having both a wireless mouse and keyboard.

Using proper notation, we can denote the events as follows

Event A: Someone has a wireless mouse

Event B: Someone has a wireless keyboard

Then we have the following probabilities:

P(A) = 0.4 This signifies the probability that someone has a wireless mouse.

P(not B) = 0.3 This signifies the probability that someone does not have a wireless keyboard. Note that "not B" means the complement of event B, i.e., the event that someone does not have a wireless keyboard.

P(A and B) = 0.2 This signifies the probability that someone has both a wireless mouse and a wireless keyboard. The notation "A and B" means the intersection of events A and B, i.e., the event that someone has both a wireless mouse and a wireless keyboard.

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Answer:

78kg

Step-by-step explanation:

76×5= 380kg

380-72-74-75-81= 78kg

The expected number of boxes to be produced is given as 3,000 boxes. So, the correct answer is 0.3, indicating that the takt time in minutes is 0.3 minutes.

The production line operates for two eight-hour shifts each day, which means there are 16 hours of production time available. Since there are 60 minutes in an hour, the total available time in minutes would be 16 hours multiplied by 60 minutes, which equals 960 minutes.

The expected number of boxes to be produced is given as 3,000 boxes.

To calculate the takt time in minutes, we divide the total available time (960 minutes) by the expected number of boxes (3,000 boxes):

\(Takt time = Total available time / Expected number of boxes\)

\(Takt time = 960 / 3,000\)

By performing the calculation, we find that the takt time is approximately 0.32 minutes, which is equivalent to 0.3 minutes rounded to one decimal place.

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Answer:

x=2

Step-by-step explanation:

-1=3x-7

-1+7=3x

6=3x

x=6

3

x=2

hope it helps.

Answer:

x=2

Step-by-step explanation:

-1=3x-7

Add both sides by 7 to isolate 3x

-1+7=3x-7+7

6=3x

Divide both sides by 3 to isolate x

6/3=3x/3

2=x

I hope this helps!

Answer:

14.8cm

Step-by-step explanation:

d = l^2+w^2+h^2 = 14^2+3^2+4^2≈14.86607cm

Answer:

c

Step-by-step explanation:

The APR of a $200,000, 30-year loan (monthly payments) at 4% plus two points is 4.136%.

Given data:

Loan amount, P = $200,000

Interest rate, R = 4%

Points, P = 2 points

Total points paid, T = P * P = 2 * 2000 = $4000

Loan term, n = 30 years

Monthly payment, C = ?

First, find the monthly interest rate, r:

Monthly interest rate = (R/12) * 100 = (4/12) * 100 = 0.33%

Next, calculate the discount points:

Discount points = (P/100) * T = (4/100) * 4000 = $160

The effective loan amount = P - Discount points = 200,000 - 160 = $199,840

Now, find the monthly payment amount using the formula:

PV = C × [1 - (1 + r)^(-n)]/r [where PV is the present value of the loan]

C = PV × r/(1 - (1 + r)^(-n))

C = $199,840 × (0.0033) / [1 - (1 + 0.0033)^(-360)]

C = $950.75

Therefore, the monthly payment amount is $950.75.

Finally, compute the APR using the formula:

APR = [(Discount points + Interest) / Loan amount] × (12/n) × 100

Where Interest = Total interest paid over the life of the loan = C * n - P

Interest = 950.75 * 360 - 200,000 = $342,270

APR = [(160 + 342,270) / 200,000] × (12/360) × 100

APR = 0.04136 × 100

APR = 4.136%

Thus, the APR of a $200,000, 30-year loan (monthly payments) at 4% plus two points is 4.136%.

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Answer:

A) The number of wallpapers needed to cover the walls is 6 double roll wall papers

B) The number of wall paper border rolls needed is 3 rolls

Step-by-step explanation:

A) The given parameters are;

The dimensions of the room are 9 ft. by 12 ft. by 8 ft. high,

The area one double role wallpaper covers = 60 ft.²

Therefore, we have;

The area of the room wall = 12 × 8 × 2 + 9 × 8 × 2 = 336 ft²

The number of double rolls of wallpaper to be used = Area of wall/(area of wallpaper) = 336/60 = 5.6

Therefore, given that the wall papers are sold in single units, we round up to the next whole number of units to get;

The number of wallpapers needed to cover the walls = 6 double roll wall papers

B) The borders of a wallpaper are installed parallel (and installed along) to the ceiling line

Therefore, the amount of wallpaper border required is given as follows;

Wall paper border length required = 2 × Length of the room + 2 × Width of the room

∴ Wall paper border length required = 2 × 9 ft. + 2 × 12 ft. = 42 ft.

The size of each wall paper border sold = 5 yd. = 15 ft.

Therefore;

The number of wall paper border rolls required = 42 ft./(5 yd.) = 42 ft./(15 ft.) = 2.8 rolls

Therefore, we round up to get the number of wall paper border rolls needed as 3 rolls of wall paper borders.

Answer:

Answer: k = - 20

Step-by-step explanation:

Solution

115 = -6k - 5              Add 5 to both sides

115+5 = - 6k - 5+5     Combine

120 = - 6k                   Divide by - 6

120/-6 = -6k/-6

-20 = k    

Answer: -20

Step-by-step explanation:115 = -6k-5

Add5 to both sides

120= -6k

Divide both sides by 6

20= -k

K = -20

using standard z value, 20% of sandwiches are less than 10.58 inches.

In the given question,

Subway sells foot long sandwiches that have a mean of 11 inches and a standard deviation of 0.5 inches.

20% of sandwiches are less than...............inches.

The cumulative standardized normal distribution table indicates a z value of -0.84 for 20%.

From the question we know that

Mean(μ) = 11 inches

Standard Deviation(σ) = 0.5 inches

We have to find less than of 20% of sandwiches for z value of -0.84

P(ƶ<z) = 20%

We can write it as

P(ƶ<-0.84) = 20/100

P(ƶ<-0.84) = 0.20

Since z = -0.84

X-μ/σ = -0.84

Now putting the value

X-11/0.5 = -0.84

Multiply by 0.5 on both side

X-11/0.5 *0.5= -0.84*0.5

X-11= -0.42

Add 11 on both side

X-11+11= -0.42+11

X = 10.58

Hence, 20% of sandwiches are less than 10.58 inches.

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Right question is here

Subway sells foot long sandwiches that have a mean of 11 inches and a standard deviation of 0.5 inches. 20% of sandwiches are less than ................. inches. (The cumulative standardized normal distribution table indicates a z value of -.84 for 20%)

(a) 11.500

(b) 11.42

(c) 10.58

(d) cannot be determined from the information given

Step-by-step explanation:

y = (1 − 3x) / (x − 2)

Set the denominator to 0.

x − 2 = 0

x = 2

There is a vertical asymptote at x = 2.

Take the limit as x approaches ∞ and -∞.

lim(x→∞) y = -3

lim(x→-∞) y = -3

There is a horizontal asymptote at y = -3.

Plug in 0 for x and y.

y = (1 − 3(0)) / (0 − 2) = -1/2

0 = (1 − 3x) / (x − 2) → x = 1/3

There is a y-intercept at (0, -1/2) and an x-intercept at (1/3, 0).

Answer:

1 and 11.

Step-by-step explanation:

Because 11 is a odd number

Difference between the fees of Ahab and his sister is \(2.8*10^{3} -1.15*10^{3}=1.65*10^{3}\)

Review the following subtraction rules and properties:

Given: Ahab pays dollars for one year's tuition fees and his sister pays dollars fees in tuition for the first year

To find: Difference in tuition fees paid by Ahab and his sister?

Solution:

To find the difference in their fees we have to perform simply normal subtraction

Subtract the fees of his sister from Ahab's fees which is as follows:

\(2.8*10^{3} -1.15*10^{3}=1.65*10^{3}\)

Hence the difference between the fees of Ahab and his sister is \(2.8*10^{3} -1.15*10^{3}=1.65*10^{3}\)

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A useful graphical method of constructing the sample space for an experiment is a tree diagram that is option A.

A tree diagram is a useful graphical method of constructing the sample space for an experiment. It is a type of diagram used to represent the possible outcomes of an event. The diagram is structured in a way that each branch of the tree represents an event that can occur, and each level of the tree represents a stage in the experiment. By using a tree diagram, it is easier to visualize and understand all the possible outcomes of an experiment and the probabilities associated with each outcome. Therefore, option A is the correct answer.

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The mathematical expression y(x,t) = Asin(kx)sin(wt) provides a way to describe the behavior of a standing wave in terms of its amplitude, frequency, and location along the string.

At time t=0,

the standing wave can be mathematically expressed as

y(x,0) = Asin(kx)sin(w*0) = Asin(kx)sin(0) = 0.

This means that the displacement of the string is zero at time t=0.

However, it is important to note that this does not mean that the string is not moving at all. Rather, it means that the string is in a state of equilibrium at time t=0, with the maximum transverse displacement being A.

As time progresses, the standing wave will oscillate between the maximum positive and negative transverse displacement values, creating a pattern of nodes (points of zero displacements) and antinodes (points of maximum displacement).

The wave number k and angular frequency w are both constants that are dependent on the physical properties of the string and the conditions under which the wave is being produced.

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Answer:

first give options it is very hard to do

The original price of the radio is r112, and the VAT paid is r16.8.

To find the original price of the radio and the amount of VAT paid, we can use the formula:

Original price = Final price / (1 + VAT rate)

VAT paid = Final price - Original price

Given that the final price of the radio, including VAT, is r128.8 and the VAT rate is 15%, we can substitute these values into the formula:

Original price = 128.8 / (1 + 0.15)

VAT paid = 128.8 - Original price

Calculating the original price:

Original price = 128.8 / 1.15 ≈ r112

Calculating the VAT paid:

VAT paid = 128.8 - 112 ≈ r16.8

Therefore, the original price of the radio is approximately r112, and the VAT paid is approximately r16.8.

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It is known that all the gold ever mined is about 10 000 000 000 ounces (10 billion ounces). And, we need to find the length of one wall to fit it into a cubic shaped room.

Firstly, let's determine the volume of the gold. Since, we know that the gold would fill a cubic shaped room, thus its volume will be equal to the volume of the room. Therefore, the volume of the gold will be given by:

Volume of gold = Volume of the cubic room

                          = l³  (where l is the length of one wall)

Next, let's calculate the volume of 1 ounce of gold using the density of gold.

Density of gold is given as: 19.3 grams/cubic cm≈ 0.697 lb/ cubic in 1 ounce

                                                                                = 1/16 lb

Therefore, volume of 1 ounce of gold = 1/0.697

                                                              ≈ 1.43 cubic inches

Now, let's convert cubic inches to cubic feet.

1 foot = 12 inches

1 cubic foot = 12 x 12 x 12 cubic inches

                   = 1728 cubic inches

Therefore,1 cubic inch = (1/1728) cubic feet

Hence, the volume of 1 ounce of gold in cubic feet will be:

1.43 cubic inches = (1.43/1728) cubic feet

                             = 0.000827 cubic feet

Finally, substituting this value in the expression of the volume of the gold, we get:

l³ = Volume of the gold

Volume of the gold = 10 billion x 0.000827 cubic feet

                                = 8,270,000 cubic feet

So, the length of one wall to fit all the gold ever mined in a cubic shaped room would be:

l³ = 8,270,000 cubic feet

l = cube root (8,270,000)

  ≈ 200.5 feet (rounded to one decimal place)

To solve the given problem, we need to determine the length of one wall of a cubic shaped room to fit all the gold ever mined. We start with calculating the volume of the gold, which will be equal to the volume of the cubic room. We know that the volume of a cubic room is given by the cube of the length of one wall. So, we need to find the cube root of the volume of the gold. To calculate the volume of the gold, we need to first determine the volume of 1 ounce of gold using its density, and then multiply it by the total number of ounces of gold ever mined. We know that density of gold is approximately 19.3 grams/cubic cm. Thus, we can convert this density to pounds per cubic inch since we know that 1 cubic inch is equal to 0.0005787 cubic centimeters. 1 ounce is equal to 1/16 pound. We then convert cubic inches to cubic feet and get the value of the volume of 1 ounce of gold in cubic feet. Substituting the values of the volume of 1 ounce of gold and the total ounces of gold ever mined in the expression of the volume of the gold, we get the volume of the gold. Finally, we calculate the cube root of the volume of the gold to obtain the length of one wall of the cubic room.

Therefore, the length of one wall to fit all the gold ever mined in a cubic shaped room would be approximately 200.5 feet.

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Main answer:

She bought 5 coach tickets and 6 first class tickets.

Step-by-step explanation:

Given:

Total tickets = 11

Let's First class tickets =f, Coach tickets = c.

Total tickets = f + c

     f + c = 11  

⇒  f = 11 - c  →   equation 1

Cost she used to purchase coach tickets = $260

Cost she used to purchase First class tickets = $1130

Total budget for airfare = $8080

260c + 1130f = 8080  →  equation 2

Substitute equation 1 in equation 2;

260c + 1130(11-c) = 8080

260c + 12430 - 1130c = 8080

12430 - 8080 = 1130c- 260c

870c = 4350

c = 5 peoples

Now, Substitute c in equation 1;

f + c = 11

f = 11 - 5

f = 6 peoples

Hence, She bought 5 coach tickets and 6 first class tickets.

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Answer:261

Step-by-step explanation:

4x4x4x4=4x4=16\16x4=64x4=256\256+5=261

Answer:

90 or 270

Step-by-step explanation:

To determine the bearing of the tree from the student, we need to use the reference direction of North. Typically, bearings are measured in degrees clockwise from North.

If the student stands 15 meters away directly west of the tree, then we can draw a line connecting the student and the tree, which would be a line going directly east to west.

Since we want to find the bearing of the tree from the student, we need to measure the angle between the line connecting the student and the tree and the North direction. Since the line between the student and the tree is going directly east to west, this angle will be either 90 degrees or 270 degrees, depending on which direction we consider as North.

If we consider North to be directly above the student, then the bearing of the tree from the student would be 90 degrees, since the line connecting the student and the tree is perpendicular to the North direction.

If we consider North to be directly below the student, then the bearing of the tree from the student would be 270 degrees, since the line connecting the student and the tree is perpendicular to the South direction (which is opposite to North).

Therefore, depending on the reference direction of North that we choose, the tree's bearing from the student will be either 90 degrees or 270 degrees.

To find the series solution for the differential equation y'' + 2xy' + 2y = 0, we can assume a power series solution of the form:

Now, substitute y(x), y'(x), and y''(x) into the differential equation:

∑(n=0 to ∞) aₙn(n-1) xⁿ⁻² + 2x ∑(n=0 to ∞) aₙn xⁿ⁻¹ + 2 ∑(n=0 to ∞) aₙxⁿ = 0

We can simplify this equation by combining the terms with the same powers of x. Let's manipulate the equation step by step:

We can combine the three summations into a single summation:

∑(n=0 to ∞) (aₙ₊₂(n+1)n + 2aₙ₊₁ + 2aₙ) xⁿ = 0

Since this equation holds for all values of x, the coefficients of the terms must be zero. Therefore, we have:

This is the recurrence relation that determines the coefficients of the power series solution To find the series solution, we can start with initial conditions. Let's assume that y(0) = y₀ and y'(0) = y'₀. This gives us the following initial terms:

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