A man is carrying a pole of length 5m down a long corridor .the pole is measured to the nearest centimetre.at the end of the corridor is a right angled triangle corner. the corridor is 3 m wife and 3 m high, both measurements correct to the nearest 10 cm . will the pole be certain to get round the corner

Answer:

I think 5x is the answer

stay safe

The solution of the equation  e-²ˣ = 2x² using Newton's method with the initial guess x₁ = 5 is x ≈ 2.729

To use Newton's method to a solution of the equation e-²ˣ = 2x², starting with the initial guess x1 = 5, we first need to find the derivative of the function f(x) = e-²ˣ - 2approximate x².

f'(x) = -2e-²ˣ - 4x

Then we can use the Newton's method to obtain the next approximation x₂:

x₂ = x1 - f(x1)/f'(x1)

x₂ = 5 - (e-²⁵ - 25²)/(-2e-²⁵ - 45)

x₂ ≈ 3.235

We can continue to use Newton's method to obtain x₃, x₄, and so on until the desired level of accuracy is achieved. In this case, we find:

x₃ ≈ 2.744

x₄ ≈ 2.729

x₅ ≈ 2.729

So, the solution to the equation e-²ˣ = 2x² obtained by Newton's method with the initial guess x₁ = 5 is x ≈ 2.729 .

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b) It will take approximately 24.6 years to save $3,000 for your vacation by saving $100 each month with a 3% nominal interest rate compounded monthly.

c) equivalent effective interest rates are:

i. Semi-annually: 5.06%

ii. Quarterly: 5.11%

iii. Daily: 5.13%

iv. Continuously: 5.13%

EXPLANATION:

To calculate the time it will take for you to save $3,000 for your vacation, we can use the future value formula for monthly compounding:

\(Future Value = Principal * (1 + rate/n)^(n*time)\)

Where:

- Principal is the amount you save each month ($100)

- Rate is the nominal interest rate (3% or 0.03)

- n is the number of compounding periods per year (12 for monthly compounding)

- Time is the number of years we want to calculate

We need to solve for time. Let's substitute the given values into the formula:

\($3,000 = $100 * (1 + 0.03/12)^(12*time)Dividing both sides of the equation by $100:30 = (1.0025)^(12*time)\)

Taking the natural logarithm (ln) of both sides:

\(ln(30) = ln((1.0025)^(12*time))Using logarithmic properties (ln(a^b) = b * ln(a)):ln(30) = 12*time * ln(1.0025)\)

Solving for time:

\(time = ln(30) / (12 * ln(1.0025))\)

Using a calculator:

time ≈ 24.6

c)To calculate the equivalent effective interest rate for a nominal rate of 5% compounded at different intervals:

i. Semi-annually:

The effective interest rate for semi-annual compounding is calculated using the formula:

Effective Interest Rate = (1 + (nominal rate / number of compounding periods))^number of compounding periods - 1

For semi-annual compounding:

\(Effective Interest Rate = (1 + (0.05 / 2))^2 - 1\)

Calculating:

Effective Interest Rate ≈ 0.050625 or 5.06%

ii. Quarterly:

The effective interest rate for quarterly compounding is calculated similarly:

\(Effective Interest Rate = (1 + (0.05 / 4))^4 - 1\)

Calculating:

Effective Interest Rate ≈ 0.051136 or 5.11%

iii. Daily:

The effective interest rate for daily compounding is calculated using the formula:

Effective Interest Rate = (1 + (nominal rate / number of compounding periods))^number of compounding periods - 1

Since there are approximately 365 days in a year:

\(Effective Interest Rate = (1 + (0.05 / 365))^365 - 1\)

Calculating:

Effective Interest Rate ≈ 0.051267 or 5.13%

iv. Continuously:

The effective interest rate for continuous compounding is calculated using the formula:

\(Effective Interest Rate = e^(nominal rate) - 1\)

For a nominal rate of 5%:

\(Effective Interest Rate = e^(0.05) - 1\)

Calculating:

Effective Interest Rate ≈ 0.05127 or 5.13%

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Answer:

Hey there! The answer to your question is below.

Step-by-step explanation:

The answer would be f(4) = -11, g(x) = 2    x = 0

I attached a picture below, sorry for my bad handwriting.

By xBrainly

Of the top 10 cars and trucks based on gas mileage, 4 are Hondas, 3 are Toyotas, and 3 are Volkswagens. Therefore, The probability that the car is Japanese or German is 01.

Probability:

The probability of an event is a number that indicates the probability of the event occurring. Expressed as a number between 0 and 1 or as a percent sign between 0% and 100%. The more likely an event is to occur, the greater its probability. The probability of an impossible event is 0; the probability of an event that will definitely occur is 1. The probabilities of two complementary events A and B (A or B) add up to 1.

A simple example is tossing a fair (fair) coin. If a coin is fair, both possible outcomes ("heads" and "heads") are equally likely; since the two outcomes are complementary and the probability of "heads" is equal to the probability of "heads" Probability, so the probability of each of the two outcomes is equal to 1/2 (which can also be written as 0, 5 or 50%).

According to the Question:

Given that:

Total cars = 10

Honda cars = 04

Toyota Cars = 03

and, Volkswagens cars = 03

From the above list the Japanese cars are : Toyota

                                         German cars are: Honda and Volkswagens.

(a) Let P(J or G) = probability of getting Both Japanese and German car.

Probability of Getting Japanese or German car :

P(J or G) = Total number of Japanese and German car / Total number of   cars.

⇒ P(J or G) = 4 + 3 + 3/ 10

⇒ P(J or G) = 10/10

⇒ P(J or G) = 1

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Answer:

x ≈ 2.76

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan78° = \(\frac{opposite}{adjacent}\) = \(\frac{AB}{BC}\) = \(\frac{13}{x}\) ( multiply both sides by x )

x × tan78° = 13 ( divide both sides by tan78° )

x = \(\frac{13}{tan78}\) ≈ 2.76 ( to 2 dec. places )

The trig function that should be used to solve for x in the image is: C. Tangent (Tan).

We can correctly set up our trig equation to solve for x in the image as: 1. Tan37 = x/12.

The value of x is equal to: C. 9.04.

The trig function that should be used to solve for x in the image is: C. Cosine (Cos).

We can correctly set up our trig equation to solve for x in the image as: 2. Cos50 = 8/x.

From the image attached above, we can logically deduce that the triangle is a right-angled triangle with the following side lengths:

Opposite side = x.

Adjacent side = 12.

Therefore, we would determine the value of x by using Tan trigonometric function:

Tanθ = Opposite side/Adjacent side

Tan37 = x/12

x = 12Tan37

x = 9.04 units.

For the second image, we can logically deduce that the triangle is a right-angled triangle with the following side lengths:

Hypotenuse = x

Adjacent side = 8.

Therefore, we would determine the value of x by using Cos trigonometric function:

Cosθ = Adjacent side/Hypotenuse

Cos50 = 8/x

x = 8/Cos50

x = 12.45 units.

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Answer:

angle 1= 90° because the diagonals of rhombus are perpendicular to each other.

angle 2 = 31° alternate interior angles

angle 3+ angle 1+ angle 2= 180°

90+31+ angle 2= 180°

angle 2= 59°

The grocer should use x pounds of the $0.90 candy and y pounds of the $2.10 candy in the new mix.

To determine the quantities of each candy to use, we can set up a system of equations based on the given information. Let's denote x as the number of pounds of the $0.90 candy and y as the number of pounds of the $2.10 candy.

The total weight of the mix is 23 pounds, so we have the equation:

x + y = 23 (Equation 1)

The desired selling price of the mix is $1.90 per pound. Since the $0.90 candy and $2.10 candy are being mixed, we can calculate the average price per pound as follows:

(0.90x + 2.10y) / 23 = 1.90 (Equation 2)

We now have a system of two equations (Equations 1 and 2) that we can solve simultaneously to find the values of x and y.

To solve the system, we can start by multiplying Equation 1 by 0.90 to eliminate x's coefficient:

0.90x + 0.90y = 20.7 (Equation 3)

Next, we can subtract Equation 3 from Equation 2 to eliminate x:

(0.90x + 2.10y) / 23 - (0.90x + 0.90y) = 1.90 - 20.7

Simplifying this equation gives:

1.20y = 1.90 * 23 - 20.7

Solving for y, we find:

y = (1.90 * 23 - 20.7) / 1.20

y ≈ 11.5

Now that we have the value of y, we can substitute it back into Equation 1 to solve for x:

x + 11.5 = 23

x = 23 - 11.5

x ≈ 11.5

Therefore, the grocer should use approximately 11.5 pounds of the $0.90 candy and 11.5 pounds of the $2.10 candy in the new mix.

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Answer:

x=10 and y= 8.

Step-by-step explanation:

Given that the cost of 1 banana = $0.60

Cost of 1 mango = $1.50.

Total cost= $ 18  

Here, x be the number of bananas and y be the numbers of mangos,

As the number of bananas is 2 more than the number of mangos,

So, x=y+2

\(\Rightarrow y=x-2 \cdots(i)\)

Cost of x bananas \(=\$ 0.60 \times x\)

Cost of y mangos \(=\$ 1.50 \times y\)

Total cost = 0.6x+1.5y

\(\Rightarrow 18 = 0.6x+1.5y\\\\\Rightarrow 1.5y=18-0.6x\\\\\Rightarrow y= 12 - 0.4 x \cdots(ii).\)

Solving both the equations (i) as well as (ii), graphically as shown in the figure by plotting both the graphs.

Both the graphs intersect at the point (10,8) as shown in the graph.

So, the solution of both the equations is, (x,y)=(10,8). i.e

The number of bananas = x= 10 and

the number of mangos = y = 8.

Answer:

Brainliest if I am right? uwu

Answer:

The value of 7a - 9 is - 3

Step-by-step explanation:

Step 1:

7a + 9 = 15

Step 2:

7a = 15 - 9

Step 3:

7a = 6

Step 4:

a = 6/7

Step 5:

7 ( 6/7 ) - 9

Step 6:

6 - 9

Answer:

- 3

Hope This Helps :)

Answer:

-3

a = 6/7

Step-by-step explanation:

The answer is -3 because:

1) First, we have to isolate a

2) In order to isolate a, we have to -9 from 15 and +9

New equation: 7a = 6

3) We know that 6 + 9 equals to 15

4) In order to get 6 as a, we know that a has to equal a fraction

5) Then, we know that 7 x 6 equals 42 and 42/7 is equal to 6

6) Therefore, a is equal to 6/7

7) Now, 7 times 6 is 42. Then, 42 divided by 7 is 6.

8) Finally, 6 - 9 equals -3

Hope this helps!

Answer:

it is C

Step-by-step explanation:

it is c because all of the other answers are stated in the article, and a opinion is something you think

To solve this problem first we hace to name the variable so y will be the earnings and x will be the number of bracelets she sell so the equation will be:

So if y is equal to 101 we can solve the equation for x so:

Answer:

Step-by-step explanation:

where is the prism???

   i can't answer without seeing the question

Answer:

see below

Step-by-step explanation:

3, 12, 48, 192

We are multiplying by 4 each time  (12/3 =4)

The 5th term

192 *4 =768

The 6th term

768 *4 =3072

The th term

3072 *4 =12288

To find the common ratio, take the second term and divide by the first

2/4 = 1/2

The common ratio is 1/2

Problem 1

---------------------------

Explanation:

The first term is a = 3 and the common ratio or multiplier is r = 4. We start with 3 and multiply each term by 4 to get the next one. The nth term of this geometric sequence is

a(n) = a*(r)^(n-1)

a(n) = 3*(4)^(n-1)

Plug in n = 7 to get the seventh term

a(7) = 3*(4)^(7-1)

a(7) = 3*(4)^6

a(7) = 3*4096

a(7) = 12288

====================================================

Problem 2

----------------------

Explanation:

To find the common ratio, we pick any term but the first one and divide it over its previous term

r = common ratio

r = (second term)/(first term) = 2/4 = 1/2 = 0.5

r = (third term)/(second term) = 1/2 = 0.5

r = (fourth term)/(third term) = 0.5/1 = 0.5

Each term is cut in half to get the next one.

Answer:

i can agree to the answer that u have rn

Answer:

2/5x7

Step-by-step explanation:

Answer:

Graph 4

Step-by-step explanation:

The graph of f(x) = x^3 includes point (0, 0) since f(0) = 0^3 = 0.

The exponent of x is 3. This is not a linear function.

Negative values of x cubed are negative, and positive values of x cubed are positive.

For x < 0, f(x) < 0, and for x > 0, f(x) > 0.

Answer: Graph 4.

Using the 14c calibration on the x-axis, the approximate age of the neanderthal fossils is (C) 40,110 years old.

So, using calibration on the x-axis, the approximate age of the neanderthal fossils came out to be 40,110 years old.

Therefore, using the 14c calibration on the x-axis, the approximate age of the neanderthal fossils is (C) 40,110 years old.

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The correct question is given below:
Using the 14c calibration on the x-axis, what is the approximate age of the neanderthal fossil?

a. 5,730 years old

b. 34,380 years old

c. 40,110 years old

d. 45,840 years old

Answer:

piechart

tStep-by-step explanation:

Answer: Hello how r u.

Answer:

he made a good choice, the width is: 4 inches

Step-by-step explanation:

12 x 8 x _4_ = 384

The intersection of the two lines has a y-coordinate of 4. In the conventional (x,y) coordinate plane, the meeting point is at (2,4).

To find the point of intersection between the lines y = x/2 + 3 and y = 3x - 2, we can set their equations equal to each other and solve for x:

x/2 + 3 = 3x - 2

Simplifying this equation, we get:

5/2 x = 5

x = 2

Now that we have found the x-coordinate of the intersection point, we can substitute it into either of the two equations to find the corresponding y-coordinate. Let's use the equation y = 3x - 2:

y = 3(2) - 2

y = 4

Therefore, the y-coordinate of the point of intersection of the two lines is 4. The intersection point is (2, 4) in the standard (x,y) coordinate plane.

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The probability that Derek will draw out a pineapple candy is `1/8`.  Note: The answer is concise, clear, and provides an accurate solution.

Given a brown paper bag containing 4 lemon, 6 lime, 8 cherry, 2 pineapple, 5 orange, and 5 grape candies. All 14 students ahead of Derek have already selected a candy to eat, but no one got pineapple.

The probability that Derek will draw out a pineapple candy can be found using the formula; `P(pineapple) = (number of pineapple candies in the bag) / (total number of candies remaining in the bag)`.

Let’s consider the remaining candies in the bag after 14 students have picked out candies:

Total candies in the bag = 4 + 6 + 8 + 2 + 5 + 5 = 30 candiesCandies remaining in the bag after 14 students picked out candies = 30 - 14 = 16 candies No one got pineapple,

hence the number of pineapple candies remaining in the bag = 2  the probability that Derek will draw out a pineapple candy `P(pineapple) = 2/16 = 1/8` (as 2 is 1/8 of 16).

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It is divided into two sections, a 57-inch piece. The length of one component is double that of the other. The length of the shortest piece wound be 29.

Given that,

It is divided into two sections, a 57-inch pipe. The length of one component is double that of the other.

We have to calculate the shorter piece's length.

Let us take the length of shortest piece as x

The length of longest piece wound be 2x

We can write as,

x+2x=57

3x=57

x=57/3

x=29

The length of largest piece will be 2×29=58

Therefore, The length of the shortest piece wound be 29.

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Answer:

Its C

Step-by-step explanation:

It is C becuase when converting a fraction to a decimal, you just divide the numerator by the denominator

Basically solve the fraction

3/12=1/4

1/4 is a bencmark so right away you should know that should equal to 0.25 since its a quarter.

Or you can always look it like this

3 is the numerator

the “/“ between is basically ”divided by”

And the 12 is the denominator

Now read the equation in that order

3/12= 3 DIVIDED BY 12

There you go!

Leo's balance after 8 months will be $1723.05. The solution has been obtained by using geometric progression.

What is a geometric progression?

A geometric progression, also known as a geometric sequence in mathematics, is a set of non-zero numbers where each term comes after the first by multiplying the previous term by a fixed, non-zero number called the common ratio.

We are given that bank balances at the end of months 1, 2, and 3 are $1,500.00, $1,530.00, and $1,560.60, respectively.

From this, we get the common ratio to be 51/50 i.e. 1.02.

Now, using aₓ = a₁ r⁽ˣ⁻¹⁾ , we get

⇒a₈ = a₁ r⁽⁸⁻¹⁾

⇒a₈ = a₁ r⁷

⇒a₈ = 1500 (1.02)⁷

⇒a₈ = 1500 (1.1487)

⇒a₈ = $1723.05

Hence, Leo's balance after 8 months will be $1723.05.

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