Calculate the percentage error to the nearest 1 cm, if the footpath around a building is 400 m long

(a) The probability of a failure given there are more than 1,000 wells in a geological formation is 0.1001.

(b) The probability of a failure given there are fewer than 500 wells in a geological formation is 0.0852.

(a) We have to determine the probability of a failure given there are more than 1,000 wells in a geological formation.

P(B∣A) = Total number of failed wells more than 1000 wells/Total number of wells with 1000 failed wells

P(B∣A) = (180 + 443 + 60)/(1685 + 3733 + 1403)

P(B∣A) = 683/6821

P(B∣A) = 0.1001

(b) We have to determine the probability of a failure given there are fewer than 500 wells in a geological formation.

P(B∣C) = Number of failed well/Number of failed wells with total less that 500 wells

P(B∣C) = (2 + 14 + 44 + 3)/(28 + 363 + 309 + 39)

P(B∣C) = 63/739

P(B∣C) = 0.0852

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The complete question is:

Consider the well failure data in the table below. Let A denote the event that the geological formation of a well has more than 1000 wells, let B denote the event that a well failed, and let C denote the event that the geological formation of a well has fewer than 500 wells.

(a) What is the probability of a failure given there are more than 1,000 wells in a geological formation? Round your answer to four decimal places (e.g. 98.7654). P(B∣A)=

(b) What is the probability of a failure given there are fewer than 500 wells in a geological formation? Round your answer to four decimal places (e.g. 98.7654). P(B∣C)=

There are 20 marbles, and 12 of them are yellow; therefore, the number of yellow marbles does not equal the number of marbles, nor does the number of yellow marbles equal the number of yellow marbles because they are yellow.

I There can only be 31 marbles in the bag, since 30 marbles is the most number that each person can have equitably, plus one extra marble. As a result, the first response is A. Since 60 is divisible by 2, 3, and 5, plus 1 (leaving 1 remaining), 61 might also be a conceivable number of marbles in the bag.

The likelihood of selecting a ball from a bag is calculated by dividing the total number of balls by the quantity of that color. As a result, the likelihood of a red ball in the first case is 3/9, or 1/3. The likelihood of selecting a second ball if that ball is now eliminated is 2/8 or 1/4.

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Answer:

Below

Step-by-step explanation:

12/5  * 875 = R 2 100 000

to see how this works, set up a ratio

5 is to 875 000   as  12 is to x

5 / 875 000    = 12/x

x = 12/5 * 875 000

Answer:

R210,000

Step-by-step explanation:

875,00 : 5 days

x :12 days

cross multiply:

87500*12 = 1050000

5*x = 5x

divide:

1050000/5 = 210000

Answer:

737373

Step-by-step explanation:

You just add them together? Am I missing something?

The required volume of concrete in cubic yards to make the sidewalk is 124.4444 yards³

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

Given here: Dimensions of the side walk 4 ft. 140 and 6 feet.

We know the volume of the rectangular cuboid side walk will be given by

V= 4×140×6

 =3360 ft³

Thus the volume of concrete that will be required to make the side walk is 3360 ft³

In yards³ we know

1 cubic foot= 0.037037 yards cube

∴  3360ft³=124.4444 yards³

Hence, The required volume of concrete in cubic yards to make the sidewalk is 124.4444 yards³

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Answer:

165 of the animals at the shelter are cats.

Step-by-step explanation:

If one-fourth of the animals at the shelter are cats and there are 660 animals at the shelter, to get the number of cats you divide the total number of animals by the percentage of cats.

660 / 4 = 165

Answer:

y = 5

Step-by-step explanation:

3y - 7 = 8  Add 7 to both sides

3y - 7 + 7 = 8 + 7

3y = 15  Divide both sides by 3

y = 5

Answer:

0.0037

Step-by-step explanation:

Because 36/9643 cannot be simplified down any further, the only other way to describe it is as a decimal which is ~0.0037.

Answer:

To find out how much it would cost Suzie to lay the flooring so it fully covers the floor of room, you need to know the area of the room's floor and the cost per square foot of the flooring.

If the flooring will cost $2 per square foot, and if the area of the room's floor is x square feet. Then the total cost will be $2x.

Without knowing the area of the room's floor, it is impossible to determine the cost of the flooring.

Option D is the correct  Answer. A necessary and sufficient condition that the three triangles formed have equal areas, is that the point be the intersection of the medians​.

To divide a triangle into three triangles of equal area is to find the centroid the point where the medians intersect. After determining the centroid point G below, construct the segments connecting the vertices to the centroid. The three triangles created are of equal area.

So from a point within a triangle, line segments are drawn to the vertices. A necessary and sufficient condition that the three triangles thus formed have equal areas is that the point be the intersection of the medians of the triangle.

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Step-by-step explanation:

115 its rhe reuth i rhibk lol

Answer:

To find the cost of a hot dog and hamburger, we can set up a system of equations based on the information given. For example, let x be the cost of a hot dog and y be the cost of a hamburger. Then we have:

4x + 7y = 68 (equation 1)

7x + 3y = 67 (equation 2)

We can use substitution or elimination methods to solve the system of equations.

Substitution method:

Solve equation 1 for y in terms of x: y = (68 - 4x)/7

Substitute this expression into equation 2: 7x + 3((68 - 4x)/7) = 67

Simplifying and solving for x: 7x + 3(68 - 4x)/7 = 67

7x + 204 - 12x = 469

-5x = -401

x = 80

Substitute x = 80 back into equation 1: 4(80) + 7y = 68

320 + 7y = 68

7y = -252

y = -36

Therefore, the cost of a hot dog is $80, and the price of a hamburger is $-36 (which is not possible, it could be a typo or mistake in the given information)

Step-by-step explanation:

Answer: it would be B:log 5/log 7

Step-by-step explanation:

a) Assuming Christine makes no withdrawals, her $1,500 investment in a 5-year certificate of deposit with an annual interest rate of 1.44% compounded annually, will be worth (future value of) $1,611.16 after 5 years.

b) The total interest earned on Christine's investment after 5 years is $111.16.

The future value represents the compounded present value.

The future value can be computed using an online finance calculator.

N (# of periods) = 5 years

I/Y (Interest per year) = 1.44%

PV (Present Value) = $1,500

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $1,611.16

Total Interest = $111.16

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The measure of angle t is (d) 103 degrees

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

The triangle

Using the law of cosines, we have the following equation:

t² = x² + y² - 2xy * cos(T)

Substitute the known values in the above equation, so, we have the following representation

44² = 32² + 24² - 2 * 24 * 32 * cos(T)

Evaluate the products and exponents

1936 = 1600 - 1536 * cos(T)

So, we have

cos(T) = -336/1536

Divide

cos(T) = -0.21875

Take the arccos of both sides

T = 103

Hence, the angle is 103 degrees

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The answer to each part is given above.

Given are the functions as follows -

p(x) = - 5x + 5

q(x) = - 4x - 2

We can write -

(p о q)(5) = (- 5x + 5)(- 4x - 2)

(p о q)(5) = - 5x(- 4x - 2) + 5(- 4x - 2)

(p о q)(5) = 20x² + 10 - 20x - 10

(p о q)(5) = 20x² - 20x

(p о q)(5) = 20 x 25 - 20 x 5

(p о q)(5) = 500 - 100

(p о q)(5) = 400

(p о q)(5) = - 5x(- 4x - 2) + 5(- 4x - 2) = (q о p)(5) = 400

(q о p)(5) = 400

Therefore, the answer to each part is given above.

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Therefore , the solution of the given problem of slope comes out to be

line's equation is y =.1333 x + 1.55.

A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).If you look at the line from left to right, a line that is moving up will have a positive slope and a line that is moving down will have a negative slope.

Here,

Given : f(x) =4 +x

The line's "intercept" of the y-axis marks the location of the y-intercept. It also makes sense because a player with a 25 cm heel to toe measurement is about 1.55 metres tall. This is most likely.

Any line has the equation y=mx+b (m=slope, b=y-intercept).

Finding two spots on this line where it crosses will reveal the slope of the line. I'll use the numbers (25.5, 1.6) and (26.25,1.7).

=> (y(2)-y(1)) / (x(2)-x(1))

=> m 1.7 - 1.6 / 26.25 - 25.5

=>.1/.75 =.13333 is the formula to calculate the slope.

At roughly 1.55m, this line crosses the y-intercept.

This line's equation is y =.1333 x + 1.55.

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The mathematical expression, for the given statement is 20g/3

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given is a statement, two-thirds times g times 10.

Converting into mathematical expression,

2/3 of g = 2g/3

And,

2/3 of g of 10

= 2g/3 × 10

= 20g / 3

Hence, the mathematical expression, for the given statement is 20g/3

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The percentile of the top students will be 88%.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

The admissions index score is used to set eligibility standards intended to meet the goal of admitting the top 12% of high school students in the state.

The percentile of the top student is given as,

⇒ 100% - 12%

⇒ 88%

The percentile of the top students will be 88%.

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The equation y^2+4y represents a parabola that is open upward. The general form of a quadratic function is y = ax^2 + bx + c.

In this case, the coefficient of the x^2 term is 1, the coefficient of the x term is 4, and the constant term is 0.

This equation can be factored as y(y+4) = 0.

This equation is satisfied by y = 0 and y = -4.

Therefore, the solutions of y^2+4y = 0 are y = 0 and y = -4.

After taking the random sample, the following has the mean sample of (c) the sampling distribution of the sample mean.

A random sample is a group of people chosen at random, all with the same probability, from a larger group of people as mentionedinstatistics. It makes sure that the results you get from your sample should be close to what you would have gotten if you measured the entire population.

All units in the population have an equal chance of being chosen using the simplest random sample. Sampling should completely eliminate any signs of bias. Every person in the big population set has the same chance of being chosen because the people who make up the subset of the bigger group are selected at random.

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One less than the given number is known as preceding number whereas one more than the given number is the succeeding number.

The logics followed in order to find them:

Base numbers work exactly the same as base 10 numbers (the ones we use on a daily basis).

Take for example, in a decimal system, we have 10 digits available:

0,1,2,3,4,5,6,7,8,9.

When counting, when we get to the 9, we start over again, but writing a 1 to the left.

0,1,2,3,4,5,6,7,8,9,10,11,12....20,21,22,23....,90,91,92,93,94,95,96,97,98,99,10

When reaching 99, we have no more digits to use, so we start the count again and go from 99 to 100.

The same works with any other base number, take for example the base 7 number.

When counting in base 7, we only have 7 digits available: (0,1,2,3,4,5,6) So when 0_{7},each the digit 6, we go immediately to 10, like this:

It went from 6 to 10 and from 16 to 20. This is because in base 7, there is no digits from 7 to 9, so we have directly to 20.

So, if working with decimal numbers, the previous value for 640 would be 639, but notice that in base 7,

There is no such thing as the digit 9, so the greatest digit we can use there 6,

Therefore, the previous value for the number would be. The next number would be because the 1 does exist for a base 7 system.

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Complete question :-

What is the numeral preceding and succeeding each of the following.

A) 640 base 7

B) 100000 base 2

C) 555 base 6

D) 100 base 5

E) 10000 base 4

F) 405 base 6

Evaluating the composition of functions in x = 1 gives:

f(g(1)) = 28

Here we have the two functions:

f(x) = 4x

g(x) = 2x + 5

And we want to find to find the composition f(g(x)), we will get:

f(g(x)) = 4*g(x)

Replacing g(x) there we will get:

f(g(x)) = 4*(2x + 5)

         = 8x + 20

Now we can evaluate that in x = 1, then we will get:

f(g(1)) = 8*1 + 20 = 28

That is what we wanted to find.

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Answer:

8%

Step-by-step explanation:

We can start solving the problem by using the formula for compound interest:

A =[tex]P(1+\frac{R}{n})^{nt}[/tex]

Where A is the final amount, P is the initial principal, R is the interest rate, n is the number of times the interest is compounded in a year, and t is the number of years.

Given that the interest he earns during t = 0.5 to t = 1.5 is 1.0816 times the interest he earns during t = 0 to t = 1. We can use this information to set up an equation as follows:

[tex]P(1+\frac{R}{4})^{2}[/tex] = [tex]1.0816*P(1+\frac{R}{4})[/tex]

We can simplify this equation by canceling out the P and the (1+R/4) on the right side:

[tex](1+\frac{R}{4})[/tex] = 1.0816

We can then solve for R:

[tex]\frac{R}{4}[/tex]=[tex]\sqrt{(1.0816)-1}[/tex]

R = [tex]4(\sqrt{(1.0816)-1)}[/tex]

R ≈ 0.08, is the exact value of R.

So, Mr. Saver's nominal interest rate is 8%.

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Using a left-hand approximation means that we will use the left endpoint of each interval to approximate the area under the curve.

a) Using 4 boxes:

The interval from 0 to 2 can be divided into 4 equal parts, so each part has a length of 0.5.

The height of each box will be the value of y at the left endpoint of each interval.

The area of each box can be calculated as follows:

For the first box, the left endpoint is (0, 1) and the height is 2(0) + 1 = 1. The area is 0.5 * 1 = 0.5.

For the second box, the left endpoint is (0.5, 2) and the height is 2(0.5) + 1 = 2.5. The area is 0.5 * 2.5 = 1.25.

For the third box, the left endpoint is (1, 3) and the height is 2(1) + 1 = 3. The area is 0.5 * 3 = 1.5.

For the fourth box, the left endpoint is (1.5, 4) and the height is 2(1.5) + 1 = 4.5. The area is 0.5 * 4.5 = 2.25.

The total area is the sum of the areas of all the boxes, so the total area is 0.5 + 1.25 + 1.5 + 2.25 = 5.

b) Using 8 boxes:

The interval from 0 to 2 can be divided into 8 equal parts, so each part has a length of 0.25.

The height of each box will be the value of y at the left endpoint of each interval.

The area of each box can be calculated as follows:

For the first box, the left endpoint is (0, 1) and the height is 2(0) + 1 = 1. The area is 0.25 * 1 = 0.25.

For the second box, the left endpoint is (0.25, 2.5) and the height is 2(0.25) + 1 = 2.5. The area is 0.25 * 2.5 = 0.625.

For the third box, the left endpoint is (0.5, 3) and the height is 2(0.5) + 1 = 3. The area is 0.25 * 3 = 0.75.

And so on, for all 8 boxes.

The total area is the sum of the areas of all the boxes, so the total area is 0.25 + 0.625 + 0.75 + ... + 3.375 = 5.125.

So, the area between the x-axis and the curve y = 2x + 1 on the interval (0, 2) can be approximated as 5 or 5.125 depending on the number of boxes used.

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The value of ∠A in triangle ΔABC is 119° with ∠B = 44° and ∠C = 17° .

A polygon having three edges and three vertices is called a triangle. It is one of the fundamental geometric forms. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

The properties of a Triangle are :

The six types of triangles are: isosceles, equilateral, scalene, obtuse, acute, and right.

In triangle ΔABC

∠B = 44° and ∠C = 17°

So, The sum of angles of a triangle is 180°

Therefore,

∠A + ∠B + ∠C = 180°

⇒∠A + 44° + 17° = 180°

⇒∠A = 180° - 61°

⇒∠A = 119°

The value of ∠A in triangle ΔABC is 119° with ∠B = 44° and ∠C = 17° .

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The measure of the length of u for the condition is  1560 inches (approx).

The law of sines specifies how many sides there are in a triangle and how their individual sine angles are equal. The sine law, sine rule, and sine formula are additional names for the sine law.

The side or unknown angle of an oblique triangle is found using the law of sine. Any triangle that is not a right triangle is referred to as an oblique triangle.

Given ΔTUV

t = 820 inches

∠U = 132°

∠V = 25°

and ∠T = 180 - 132 - 25

∠T = 23°

so according to the law of sines

[tex]\frac{SinT}{t} = \frac{SinU}{u}= \frac{SinV}{v}[/tex]

so u = t*(SinU/SinT)

u = 820(Sin132/sin23)

u = 820(1.9019)

u = 1559.58 inches = 1560 inches (approx)

Hence the value of u is 1560 inches (approx).

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If Rahul is 1.45 meters tall. At 10 a.m., he measures the length of a tree's shadow to be 31.55 meters. He stands 26.7 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow.  the height of the tree is 9.43m.

Let x represent the height

x /1.45 = 31.55 -26.7

Cross multiply

x = 31.55 × 1.45 / 4.85

x = 45.7475 /4.85

x = 9.43

Therefore the height is 9.43.

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Answer:

a. To find out how much more expensive Plugged Pipes is than Pete's Plumbing, we need to subtract Pete's Plumbing's cost from Plugged Pipes' cost. The expression for the difference in cost is:

(50x + 75) - (25x + 50) = 25x + 25

This is the simplified form of the expression that represents the difference in cost.

b. If they each work for 2 hours, we can substitute x = 2 into the expressions for their costs and compare the results:

Plugged Pipes: 50(2) + 75 = 125 dollars

Pete's Plumbing: 25(2) + 50 = 100 dollars

So, Plugged Pipes is 25 dollars more expensive than Pete's Plumbing for 2 hours of work.

Step-by-step explanation:

Sure, here is a step-by-step explanation of how to find the difference in cost between Plugged Pipes and Pete's Plumbing for x hours of work:

To find out how much more expensive Plugged Pipes is for 2 hours of work we can substitute x = 2 into the expression for their costs and compare the results:

Plugged Pipes: 50(2) + 75 = 125 dollars

Pete's Plumbing: 25(2) + 50 = 100 dollars

So, Plugged Pipes is 25 dollars more expensive than Pete's Plumbing for 2 hours of work.