Mathematics/g12
nsc
march 2021
question1
a group of workers is erecting a fence around a nature reserve. they store their tools in a shed at
the entrance to the reserve. each day they collect their tools and erect 0,8km of new fence. they
then lock up their tools in the shed and return the next day.
1.1 if the fence takes 40 days to erect, how far would the workers have travelled in total?
(4)​

Answer:

5

Step-by-step explanation:

The  examples that would constitute a discrete random variable are;

I. Total number of points scored in a football game

III. Number of near collisions of aircraft in a year

A discrete random variable has only a countable number of different values that it can assume. Usually, but not always, discrete random variables are counts. A random variable is discrete if it can only take a finite number of different values. A variable whose value is determined by counting is referred to as a discrete variable.

A continuous variable is one whose value may be determined through measurement. A random variable is a variable whose value is the resultant number of an unpredictable event.

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Answer:

220

Step-by-step explanation:

If we take 20 common (as in we can take it out and group the rest) , we can say 20 (15 7/9-4 7/9) which is equal to 20 (11). 20x11 = 220.  

Based on the information provided, a test-taker who scores at the 5th stanine is scoring:
C. within the average range.

To better understand this, let's break down the terms and concepts involved:
Stanine: Stanine (short for "standard nine") is a method used to scale test scores on a nine-point scale.

The stanine scores range from 1 (lowest) to 9 (highest).

This method is typically used in educational assessments to categorize students' performance.
Average: In the context of test scores, the average score refers to the middle range of scores that is typical for the majority of test-takers.

In the case of stanine scores, the average range falls between 4 and 6.

This means that students scoring in stanines 4, 5, and 6 are considered to be within the average range.
Now, to answer your question, a test-taker who scores at the 5th stanine is considered to be within the average range of performance.

This is because their score falls between the 4th and 6th stanines, which, as mentioned earlier, encompass the average range.

It's important to note that this doesn't mean the student is performing poorly; rather, their performance is on par with the majority of other test-takers.

Option C. within the average range is correct.  

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The statement "The number to the left of the parentheses is -3. Example: -3(2x+3)" is true.

Why is this statement true?

To answer this question, we must first understand what the term "number to the left of the parentheses" refers to.

In an expression of the form nx, where "n" is a number, x is a variable, and there is no addition or subtraction, the number to the left of the parentheses is "n."This is true since (-3)(2x + 3) is a term of the form "nx," where n = -3 and x = (2x + 3).

Therefore, the statement is true: "The number to the left of the parentheses is -3. Example: -3(2x+3)."

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Answer: 23$ was in your pocket before u picked up 5$

Step-by-step explanation: Just subtract the total amount by hiw much u found...

Answer:

t - (-3)

or

t + 3

Answer:

I believe x would equal \(12\sqrt{2}\)

Step-by-step explanation:

using the properties of a 45 45 right angle.

Answer:

181 ÷ 2

= 90.5 feet

...........

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

Work Shown:

P(A) = 0.5

P(C given A) = 0.4 ... follow the uppermost branches.

P(A and C) = P(A)*P(C given A)

P(A and C) = 0.5*0.4

P(A and C) = 0.20

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

P(B) = 0.5

P(C given B) = 0.3 ... go from B to C

P(B and C) = P(B)*P(C given B)

P(B and C) = 0.5*0.3

P(B and C) = 0.15

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

There are two ways to get to C.

The first option will have us compute P(A and C). The second option will have us compute P(B and C). Both options are mutually exclusive (you can only pick one path), so that means we can add up the probabilities we found earlier

Therefore we can say....

getting to C = (take path A to C) OR (take path B to C)

P(C) = P(A and C) + P(B and C)

P(C) = 0.20 + 0.15

P(C) = 0.35

Answer:

They are 12, 13, 14 and 15.

Step-by-step explanation:

If the least integer is x, then:

x + x + 1 + x + 2 + x + 3 = 54

4x + 6 = 54

4x = 48

x = 12.

To determine the recommended sample size for estimating the proportion of American adults who decided not to go to college due to affordability, we can use the desired margin of error and confidence level. The point estimate for this proportion is 48%, and we want the margin of error to be approximately 1.5% at a 90% confidence level.

To calculate the sample size, we need to consider the formula for the margin of error:

Margin of Error = Critical value * Standard deviation

Given that we want the margin of error to be approximately 1.5% and a 90% confidence level, we can use a standard normal distribution table to find the critical value corresponding to a 90% confidence level.

By substituting the desired margin of error and critical value into the margin of error formula, we can solve for the standard deviation. Then, we can use the point estimate and the calculated standard deviation to calculate the recommended sample size using the formula:

Sample Size = (Z^2 * p * (1 - p)) / (E^2)

where Z is the critical value, p is the point estimate, and E is the desired margin of error.

By performing these calculations, we can determine the recommended sample size.

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Answer: Your answer is B! Hope you have an awesome day, and be kind be You!!! <3

Step-by-step explanation: Also, I'm 3D printing the Tesla Cyber truck, and this is the design I have so far. What do you think?

Answer:

it is a function a one to many function

Step-by-step explanation:

To solve the system of equations using the substitution method, we need to solve one of the equations for one of the variables, and then substitute that expression into the other equation.

Let's solve the first equation, x + y = 5, for y:

y = 5 - x

Now, substitute this expression for y in the second equation, x - y = 3:

x - (5 - x) = 3

Simplifying the left side of the equation:

2x - 5 = 3

Adding 5 to both sides:

2x = 8

Dividing both sides by 2:

x = 4

Now that we know x = 4, we can substitute this value back into either of the original equations to find y. Let's use the first equation:

x + y = 5

4 + y = 5

y = 1

Therefore, the solution to the system of equations is (4, 1).

So, the correct option is: The solution is (4, 1).

By the incenter property, this angle is half of the measure of ∠AEC Hence, the measure of ∠DEP is half of the measure of ∠AEC.

Since ΔDEP is congruent to ΔDCP by the SAS (Side-Angle-Side) postulate, the corresponding angles of these triangles are equal.

Therefore, the measure of ∠DEP is equal to the measure of ∠DCP.

Since P is the incenter of ΔAEC, ∠DCP is the angle formed by the bisector of ∠AEC.

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Given

The diagonals of a square is 12cm each calculate the area

Solution

From the properties of a square

All sides are equal

Let each side be x

Using pythagoras

Now

The final answer

The diagonals of a square is 12cm, the area will be

The length of a 16.9 fl. oz. water bottle cannot be determined without knowing its dimensions. Approximately 15,470,588 bottles, assuming an average length of 8.5 inches, would be needed to form a complete circle around the equator. Using all the bottles sold in the UK in 2016, the equator can be circled approximately 1,094 times. On average, around 46.3 million bottles were sold per day in the UK in 2016.

In 2016, a total of 16.9 billion plastic drinking bottles were sold in the UK. (a) To find the length of a 16.9 fl. oz. water bottle, we need to know the dimensions of the bottle. Without this information, it is not possible to determine the exact length.

(b) Assuming the average length of a water bottle to be 8.5 inches, and converting the equator's length of 25,000 miles to inches (which is approximately 131,500,000 inches), we can calculate the number of bottles that can circle the entire equator. Dividing the equator's length by the length of one bottle, we find that approximately 15,470,588 bottles would be required to form a complete circle.

(c) To determine how many times the equator can be circled using all the bottles sold in the UK in 2016, we divide the total number of bottles by the number of bottles needed to circle the equator. With 16.9 billion bottles sold, we divide this number by 15,470,588 bottles and find that approximately 1,094 times the equator can be circled.

(d) To calculate the average number of bottles sold per day in the UK in 2016, we divide the total number of bottles sold (16.9 billion) by the number of days in a year (365). This gives us an average of approximately 46.3 million bottles sold per day.

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5. The line that contains the circumcenter in ΔABC is: line k.

6. The line that contains the orthocenter in ΔABC is: line m.

7. The line that contains the centroid in ΔABC is: line l.

8. The line that contains the centroid in ΔABC is: line n.

Circumcenter is the point where all three perpendicular bisectors of the three sides of a triangle meet and they are of equal distance from the three vertices of the triangle.

Orthocenter is the point in a triangle where the three altitudes that are perpendicular to the opposite sides and connect with the vertices of the triangle intersect.

The centroid of a triangle is a the point of intersection where all three medians of a triangle. Medians of a triangle connects the vertices to the midpoints of the opposite sides of a triangle.

The incenter of a triangle is the point in a triangle where all three angle bisectors of the vertices of a triangle.

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\(\angle PYZ=116^{\circ}\) (angles on a line add to 180 degrees)

\(\angle ZYQ=58^{\circ}\) (angle bisector)

\(\angle XYQ=122^{\circ}\) (angle addition postulate)

\(\angle QYP=58^{\circ}\) (angle bisector)

Reflex \(\angle QYP=302^{\circ}\) (an angle and its reflex angle add to 360 degrees)

Theorem 10.18 states that the remainder R-Sn is bounded by the absolute value of the next term in the series, which is also the absolute value of the (n+1)th term. To determine how many terms of a given convergent series must be summed to ensure that the remainder is less than

\(10 { }^{ - 4} \)in magnitude.

We are given an alternating series, and we need to estimate the error in using the nth partial sum to approximate the sum of the series. This is a useful tool for estimating the error in approximating the sum of a series.

To apply Theorem 10.18, we need to evaluate the nth partial sum for the given value of n and find the absolute value of the (n+1)th term. We can use these values to estimate the error in approximating the sum of the series.

This is a common question in numerical analysis and involves estimating the error in approximating the sum of a series and then choosing the number of terms needed to achieve a desired level of accuracy.

These problems involve using techniques from calculus and numerical analysis to estimate errors in approximating the sums of series. These concepts are important in many areas of mathematics and science, including statistics, physics, and engineering.

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Answer:

The answer assumes that the density of glass is 3 g/cm^3, not 3 g/cm^2.

The mass of the paperweight is 270 grams.

Step-by-step explanation:

Lets calculate the volume of a sphere having a radius of 3.5cm, and then divide that by 2 to get the volume of the hemisphere (half a sphere).  The sphere has a diameter of 7cm (therefore, a radius of 3.5cm).

Vol (sphere) = (4/3)πr^3

Vol = (4/3)(3.14)(3.5cm)^3

Vol = 180 cm^3

Half of this (the hemisphere) will be 90 cm^3

We know the volume, and we know the density of glass (3 g/cm^3), so multiply the two to obtain the mass of the paperweight.

 (90 cm^3)*(3g/cm^3) = 270 grams

Let's assume her time for the third race is x seconds.which is 27.4 seconds.

We know that her fastest time was 26.3 seconds and her slowest time was 30.3 seconds. Therefore, we can set up the following inequalities:

26.3 < x < 30.3

Now, we know that Layla ran the 200-meter race 3 times, and her average time was 28.0 seconds. The average is calculated by summing the times of all races and dividing by the number of races:

(26.3 + x + 30.3) / 3 = 28.0

Let's solve this equation to find the value of x:

26.3 + x + 30.3 = 3 * 28.0

56.6 + x = 84.0

x = 84.0 - 56.6

x = 27.4

Therefore, Layla's time for the third race was 27.4 seconds.

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The expected number of minutes until the frogs stop jumping is 4, regardless of their initial positions.

Let's consider the probability that all three frogs are at different vertices at a given time. The first frog can land on any of the 12 vertices, the second frog can land on either of the two adjacent vertices to the first frog, and the third frog can land on either of the two adjacent vertices to the second frog that are not adjacent to the first frog. Therefore, the probability that all three frogs are at different vertices is:

\(P(all $ different) = 12 * 2/11 * 2/10 = 24/55\)

If all three frogs are at different vertices, then none of them can jump to the other two vertices adjacent to their current position, otherwise they will meet. Therefore, the next time they can meet is after the first jump of the frog that is alone, and this will happen with probability 1/3.

If two frogs meet, the expected number of minutes until the third frog joins them is just the expected number of minutes until two frogs meet, which is the same as the expected number of minutes until the frogs stop jumping. Therefore, it suffices to compute the expected number of minutes until the frogs jump to the same vertex for the first time, given that all three frogs are at different vertices.

Let T be the expected number of minutes until the frogs jump to the same vertex for the first time. Conditioning on the first jump, we have:

\(T = 1/3 * 1 + 2/3 * (T + 1)\)

The first term corresponds to the case where the frog that is alone jumps to one of the two vertices adjacent to one of the other frogs and they meet. The second term corresponds to the case where the frog that is alone jumps to the vertex adjacent to the other frog and the third frog jumps to the same vertex with probability 1/2, or they jump to different vertices with probability 1/2 and we are back to the starting position, but with one less frog being alone.

Solving for T, we get:

T = 4

Therefore, the expected number of minutes until the frogs stop jumping is 4, regardless of their initial positions.

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The two unit vectors that are orthogonal to both i −k and i − 3j + 2k are:i - j / √2- i + j / √2

Given i - k and i - 3j + 2k.

Find two unit vectors that are orthogonal to both i −k and i − 3j 2k.

The two unit vectors orthogonal to both i - k and i - 3j + 2k are as follows:

First we find the cross product between i - k and i - 3j + 2k.

(i - k) × (i - 3j + 2k) = i × i - i × 3j + i × 2k - k × i + k × 3j - k × 2k= 0 + 2j - 3j - 0 + 0 + i = i - j

The cross product is (i - j).

Let v be any vector orthogonal to (i - j).

Let v = ai + bj + ck where (a, b, c) is a non-zero vector such that ai + bj + ck is orthogonal to (i - j).

We know that the dot product of two orthogonal vectors is zero. i.e (ai + bj + ck) • (i - j) = 0

(ai + bj + ck) • (i - j) = ai + bj + ck - aj - bj= (a - c)i - (a + b)j + ck

So we need to have (a - c) = (a + b) = 0 since (a, b, c) is non-zero implies ai + bj + ck is non-zero.

Therefore a = c and a = - b and a ≠ 0.

So a = - b and c = a.

Thus v = ai - aj + ak or v = -ai + aj + ak, both of which are unit vectors.

The two unit vectors that are orthogonal to both i −k and i − 3j + 2k are:i - j / √2- i + j / √2

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Answer:

K = negative 1.7

Step-by-step explanation:

4.5- 13 = -8.5

-8.5/5 = -1.7

4.5 - 5(-1.7) = 13

Hope this helped

Answer:

[See Below]

Step-by-step explanation:

\(Hey~There!\)

____________________

➜ Turn each fraction into a decimal:

➜ Now divide:

____________________

So based on the work above we can conclude that your answer is:

____________________

\(Hope~this~helps~Mate!\\-Your~Friendly~Answerer,~Shane\) ヅ

Answer:

10. -x + y = 1.

Step-by-step explanation:

10. y + 1 = x + 2

y - x = 2 - 1

-x + y = 1.

Answer:

0.48

Explanation:

4.8 is greater than 0.48.