Thabo and his friend Amon shared a Job of cleaning Thabo's uncle yard He paid both of them R400. Thabo worked three hours and Amon worked for two hours. Use the information above to answer the questions that follow: 1.1 Determine the amount Thabo will receive, if they decide to share the R400 in a ratio of 3.2. 12 Thabo used 1/5 of his money towards a second hand video game. Calculate the cost of the video game. 13. Thibo's transport fare to school has increased from R800 to R1150. 1.3.1 Write R1150 in words. 1.3.2 Determine the percentage increase of the transport fare. You may use the formula: Percentage increase New amount-Old amount * 100% (2)​

The area of the given shape is 109.25 ft² .

What is Area?

Area is a measurement of the amount of space inside a two-dimensional figure or shape. It is the size of the surface of the shape, and it is measured in square units, such as square meters, square centimeters, or square inches.The area of a shape can be found by multiplying the length and width of a rectangle or the base and height of a triangle, or by using specific formulas for other shapes such as circles, trapezoids, or parallelograms

Given : height of triangle = diameter of semicircle = 10 ft

            radius of semicircle = 5 ft

           base of triangle = 14 ft

we know that, The area of given shape :

= area of given triangle + area of semi circle

=  1/2 × base × height  +   πr²/2

= 1/2 × 14 × 10 + (3.14 × 5²)/2

= 70 + 39.25

= 109.25 ft²                                  

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the prime factors of 24 are 2 and 3, which combine to give the unique prime factorization of 24 as 2^3 × 3.

There are no factors of 24 that are prime numbers. A factor of a number is a whole number that divides that number without leaving a remainder. Prime numbers, on the other hand, are numbers that are divisible only by 1 and themselves, and cannot be expressed as the product of any other numbers.

The prime factors of 24 are 2, 2, and 3. We can factorize 24 as 2 × 2 × 2 × 3 or 2^3 × 3. Here, 2 and 3 are both prime numbers, but they are not factors of 24 in isolation. They are only prime factors of 24 when combined in the manner shown.

This fact highlights an important concept in number theory: the uniqueness of prime factorization. Every composite number can be expressed as a unique product of prime numbers. This fundamental theorem of arithmetic is crucial in many areas of mathematics, including cryptography, where it is used to secure communications and protect sensitive information.

In summary, there are no factors of 24 that are prime numbers. However, the prime factors of 24 are 2 and 3, which combine to give the unique prime factorization of 24 as 2^3 × 3.

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Answer:

0.4

Step-by-step explanation:

Subtract 2.4m on each side

-1.2 = -3.0m

divide by -3.0

you get 0.4

U is a binomial random variable with n trials and probability of success given by 1 - p.

As Y is a binomial random variable with n trials and probability of success given by p. Using the moment-generating functions method, it can be shown that U = n - Y is a binomial random variable with n trials and probability of success given by 1 - p. The binomial distribution is described by two parameters: n, which is the number of trials, and p, which is the probability of success in any given trial. If a binomial random variable is denoted by Y, then:[tex]P(Y = k) = \binom{n}{k}p^{k}(1 - p)^{n-k}[/tex]

The method of generating moments can be used to show that U = n - Y is a binomial random variable with n trials and probability of success given by 1 - p. The moment-generating function of a binomial random variable is given by: [tex]M_{y}(t) = [1 - p + pe^{t}]^{n}[/tex]

The moment-generating function for U is: [tex]M_{u}(t) = E(e^{tu}) = E(e^{t(n-y)})[/tex]

Using the definition of moment-generating functions, we can write: [tex]M_{u}(t) = E(e^{t(n-y)})$$$$= \sum_{y=0}^{n} e^{t(n-y)} \binom{n}{y} p^{y} (1-p)^{n-y}[/tex]

Taking the summation of the above expression: [tex]= \sum_{y=0}^{n} e^{tn} e^{-ty} \binom{n}{y} p^{y} (1-p)^{n-y}$$$$= e^{tn} \sum_{y=0}^{n} \binom{n}{y} (pe^{-t})^{y} [(1-p)^{n-y}]^{1}$$$$= e^{tn} (pe^{-t} + 1 - p)^{n}[/tex]

Comparing this expression with the moment-generating function for a binomial random variable, we can say that U is a binomial random variable with n trials and probability of success given by 1 - p.

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a) Option A, A x2 statistic provides strong evidence in favor alternative hypothesis if its value is a large positive number.

b) Option B, The null hypothesis that sex and personal goals are not related vs. the alternative hypothesis that sex and personal goals are related.

c) Option B, The variables considered in a chi-squared test used to evaluate a contingency table B. are categorical.

(a) A x2 statistic provides strong evidence in favor of the alternative hypothesis if its value is a large positive number. The x2 statistic is used in hypothesis testing to determine whether there is a significant difference between observed and expected frequencies. A large positive value indicates that the observed frequencies are significantly different from the expected frequencies, which supports the alternative hypothesis.

(b) The hypotheses being tested in a chi-squared test on a contingency table are the null hypothesis that sex and personal goals are not related vs. the alternative hypothesis that sex and personal goals are related. This test determines whether there is a significant association between two categorical variables.

(c) The variables considered in a chi-squared test used to evaluate a contingency table are categorical. These variables cannot be averaged or assumed to be normally distributed. The chi-squared test is used to analyze the relationship between two or more categorical variables, where each variable has a discrete set of categories.

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Answer:

x² - 49

Step-by-step explanation:

(x - 7)² =

(x - 7) * (x - 7) =

x * x - 7 * 7 =

x² - 49

a.There is a 63.21% chance that the light bulb will have to be replaced within 500 hours.

The probability that the light bulb will have to be replaced within 500 hours can be calculated by finding the area under the exponential probability density function (PDF) from 0 to 500. Using the formula for the exponential PDF with a mean of 500, we get:

P(X ≤ 500) = 1 - e^(-500/500) ≈ 0.6321

Therefore, there is a 63.21% chance that the light bulb will have to be replaced within 500 hours.

b. There is a 39.35% chance that the light bulb will last between 200 and 800 hours.

The probability that the light bulb will last more than 1,000 hours can be calculated by finding the area under the exponential PDF from 1000 to infinity. Using the same formula, we get:

P(X > 1000) = e^(-1000/500) ≈ 0.1353

Therefore, there is a 13.53% chance that the light bulb will last more than 1,000 hours.

c. The probability that the light bulb will last between 200 and 800 hours is0.3935.

It can be calculated by finding the area under the exponential PDF from 200 to 800. Again, using the same formula, we get:

P(200 < X < 800) = e^(-200/500) - e^(-800/500) ≈ 0.3935

Therefore, there is a 39.35% chance that the light bulb will last between 200 and 800 hours.

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If the average of three numbers is 16 and one of the numbers is 18, then the sum of the other two numbers is option (d) 30

Let's use algebra to solve this problem. Let x and y be the other two numbers we are looking for. We know that the average of the three numbers is 16, so we can write:

(18 + x + y) / 3 = 16

Multiplying both sides by 3, we get,

[(18 + x + y) / 3] × 3 = 16 ×3

18 + x + y = 48

Subtracting 18 from both sides, we get,

18 + x + y - 18 = 48

x + y = 30

Therefore, the correct option is (d) 30

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The claim of the production manager is not true because more than 4000 insulating washers are defective per day.

The total amount of insulating washer for the electrical devices produced per day = 225,000.

The amount chosen at random for sampling = 200 washers.

The amount shown to be defective in the chosen sample = 4

If every 200 = 4 defective

225,000 = X

Make c the subject of formula;

X = 225000×4/200

X = 900000/200

X = 4,500.

This shows that the claim is wrong because more than 4000 insulating washers are defective per day.

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Answer:

Ans = 8

Step-by-step explanation:

because -- is + and  −−√70 is positive

so square root =8.366600265340757

and 8 is bigger as 8.366600265340757 is a decimal number.

The shortest distance from the origin to the curve x2 + xy + y2 = 3 is √(6-2√7) and the longest distance is √(6+2√7).

We have to find the shortest and longest distances from the origin to the curve x^2 + xy + y^2 = 3. This can be done using the Lagrange multiplier technique.

Given, x^2 + xy + y^2 = 3.

We have to minimize and maximize the distance of the origin from the given curve. The distance of the origin from the point (x, y) is given by √(x²+y²).

Therefore, we have to minimize and maximize the function f(x, y) = √(x²+y²) subject to the constraint x^2 + xy + y^2 = 3.

Now, we have to form the Lagrange function.

L(x, y, λ) = f(x, y) + λ(g(x, y))

where, g(x, y) = x2 + xy + y2 - 3L(x, y, λ) = √(x²+y²) + λ(x2 + xy + y2 - 3)

Now, we have to find the partial derivatives of L with respect to x, y, and λ.

∂L/∂x = x/√(x²+y²) + 2λx+y = 0 ............. (1)

∂L/∂y = y/√(x²+y²) + λx+2λy = 0 ............. (2)

∂L/∂λ = x² + xy + y² - 3 = 0 ............. (3)

Solving equations (1) and (2), we get x/√(x²+y²) = 2y/x.

Since x and y cannot be equal to 0 simultaneously, we can say that x/y = ±2.

Substituting x = ±2y in equation (3), we get y²(5±2√7) = 9.

Now, we can solve for x and y to get the values of (x, y) at which the minimum and maximum value of the distance of the origin occurs.

Using x = 2y, we get y²(5+2√7) = 9 ⇒ y = ±3/√(5+2√7)

Using x = -2y, we get y²(5-2√7) = 9 ⇒ y = ±3/√(5-2√7)

Therefore, the four points at which the distance is minimum and maximum are {(2/√(5+2√7), 1/√(5+2√7)), (-2/√(5+2√7), -1/√(5+2√7)), (2/√(5-2√7), -1/√(5-2√7)), (-2/√(5-2√7), 1/√(5-2√7))}.

To find the minimum and maximum distances, we can substitute these points in f(x, y) = √(x²+y²).

After substituting, we get the minimum distance as √(6-2√7) and the maximum distance as √(6+2√7).

Therefore, the shortest distance from the origin to the curve x^2 + xy + y^2 = 3 is √(6-2√7) and the longest distance is √(6+2√7).

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Answer:

[tex]\boxed{x=0}[/tex]

Step-by-step explanation:

We need solve for x

[tex]3=x+3-5x[/tex]

substract 3 to both sides of the equation:

[tex]3-3=x+3-5x-3\\0=-4x[/tex]

divide both sides of the equation by -4

[tex]\frac{0}{-4}=\frac{-4x}{-4}\\0=x\\\equiv x=0[/tex]

The value of "x" that satisfies the equation is x=0,

[tex]\text{-B$\mathfrak{randon}$VN}[/tex]

The probability of rolling one of these five numbers is 5/37.

Suppose you roll a special 37-sided die. The probability that one of the following numbers is rolled is as follows:

35 | 25 | 33 | 9 | 19.

The total number of sides of a die is 37. As a result, there are 37 numbers in the die.

Rolling one of the 5 given numbers implies that you can select either 35 or 25 or 33 or 9 or 19.

Therefore, the probability of rolling any of these numbers is:

1 / 37 + 1 / 37 + 1 / 37 + 1 / 37 + 1 / 37 = 5 / 37

So, the probability of rolling one of these five numbers is 5/37.

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The rate of change of the area of a square with respect to the length z, the diagonal of the square is  dA/dz = 2z; rate = 6. The correct answer is C.

We know that the area A of a square is given by A = s², where s is the length of the sides of the square. Also, we know that the diagonal of the square (z) is related to the sides by the Pythagorean theorem: s² + s² = z² or 2s² = z² or s² = z²/2.

Taking the derivative of both sides of the equation s² = z²/2 with respect to z, we get:

2s ds/dz = 2z/2

s ds/dz = z

Now, since the area A is given by A = s², we can take the derivative of both sides of this equation with respect to z:

dA/dz = d/dz (s²) = 2s ds/dz

Substituting the value of s ds/dz obtained earlier, we get:

dA/dz = 2s (z/s) = 2z

Therefore, the correct option is (c) dA/dz = 2z, and the rate of change of the area of the square with respect to the length z is 2z. When z = 3, the rate of change is 2(3) = 6. So, the answer is (c) dA/dz = 2z; rate = 6.

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In the case of the inequality w < 1, we found that the set of solutions is (-∞, 1), which represents all real numbers less than 1.

The inequality w < 1 means that w is less than 1. To identify all the numbers that satisfy this inequality, we need to look for values of w that are less than 1.

We can continue this process and substitute different values of w in the inequality w < 1 to find more solutions. For instance, if we substitute w = -1, we get -1 < 1, which is also true.

Therefore, -1 is a solution to the inequality w < 1. However, if we substitute w = 2, we get 2 < 1, which is false. This means that 2 is not a solution to the inequality w < 1.

Therefore, the set of all numbers that are solutions to the inequality w < 1 is the set of all real numbers that are less than 1. We can represent this set using interval notation as (-∞, 1), where (-∞) represents all numbers less than negative infinity and 1 represents the upper bound of the interval.

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Equation A is converted to equation B by multiplying or dividing both parts by a non-zero constant. Thus, option C is correct.  

If a function accepts more than one value, it is said to be nonconstant (if there is more than one element in its range).

As an illustration, a polynomial with real numbers as its domain and codomain becomes nonconstant. Just observing that and means the function accepts at least two distinct values allows us to demonstrate this.

Starting with the variable solely on a single side of the equation, we can start resolving equation A for x:

[tex]x/4 + 1 = -3\sx/4 = -3 - 1\sx/4 = -4[/tex]

We obtain x = -16 by multiplying both of the equation's sides by 4.

Starting with the variable with one of the equation's equations, we can solve equation B for x:

[tex]x + 4 = -12[/tex]

Therefore, We obtain [tex]x = -16[/tex] by deducting  [tex]4[/tex] from both of the equation's components.

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Answer:

see the answer and explanation in the attached figure below

Step-by-step explanation:

The corresponding sides and angles of two polygons ABCD and ZYXW must be proportionate if they are identical.

With straight sides around its perimeter, a polygon is really a circular, two-dimensional, flat of planar structure. Its sides are straight with no bends. Another term for a polygon's sides is its edges. The points at which two sides of a polygon converge are known as its vertices (or corners). These are numerous examples of polygonal geometry.

A closed polygon is a form with more than three sides. A quadrilateral is a 4-sided polygonal shape. A quadrilateral is any closed 4-sided form, however there are six particular quadrilaterals with distinctive characteristics that give them their own names.

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W in terms of t can be represented as W = 7.5t + 10.

When a baby weighs 10 pounds at birth and 40 pounds four years later, we must apply the linear equation to represent W in terms of t.

y = mx + b,

where

m indictaes the slope of the line while

b is the y-intercept.

The formula to find the slope of a line is as follows:

Slope (m) = (y2 - y1) over (x2 - x1)

Given that a baby weighs 10 pounds at birth, and four years later, the child's weight is 40 pounds, we can determine the slope of the line as:

Slope (m) = (40 - 10) over (4 - 0) = 30 / 4 = 7.5

Thus, the linear equation relating childhood weight W (in pounds) to age t (in years) is:

W = 7.5t + 10

Therefore, we can express W in terms of t as W = 7.5t + 10.

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The values of x such that the graph of f has a horizontal tangent are;x = 2π/3 + 2πn, 4π/3 + 2πn, where n is an integer.

1. The given derivative can be found by finding the first few derivatives and observing the pattern that occurs as shown below;Differentiating sin x with respect to x gives the derivative cos x. Continuing this process, the pattern that emerges is that sin x changes sign for every odd derivative, and stays the same for every even derivative. Therefore the 115th derivative of sin x can be expressed as follows;(d115/dx115)(sin x) = sin x, for n = 58 (where n is an even number)2. To find the values of x such that the graph of f has a horizontal tangent, we differentiate f with respect to x, and then solve for x such that the derivative equals zero. We have;f(x) = x + 2sin xDifferentiating f(x) with respect to x gives;f'(x) = 1 + 2cos xFor a horizontal tangent, f'(x) = 0, thus;1 + 2cos x = 02cos x = -1cos x = -1/2The solutions of the equation cos x = -1/2 are;x = 2π/3 + 2πn or x = 4π/3 + 2πnwhere n is an integer. Therefore the values of x such that the graph of f has a horizontal tangent are;x = 2π/3 + 2πn, 4π/3 + 2πn, where n is an integer.

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The probability that among 12 randomly selected flights, exactly 10 arrive on time is 0.1667

The probability that, among 12 randomly selected flights, exactly 10 arrive on time is 0.1667. This is calculated by using the binomial probability formula:

[tex]P(x) = nCx (p^x) (1-p)^{(n-x)}[/tex]

Where:

[tex]P(x) = 12C10 (0.815^{10}) (0.185)^2 = 0.1667[/tex]

The probability that among 12 randomly selected flights, exactly 10 arrive on time is 0.1667

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Answer:

y=2x+4

Step-by-step explanation:

m is slope.

Slope is change in y over change in x.

Line goes up (+y) two for every move to the right (+x), so the slope is 2.

B is the y-intercept, where the line crosses the y-axis. It crosses at 4, so B is 4.

Plug those into y=mx+b to get

y=2x+4.

(a) Starting with the 75% estimate for Italians, the sample you must collect in order to estimate the proportion of PTC tasters within ± 0.1 with 90 % confidence is n = 51.

(b) The sample size required if you made no assumptions about the value of the proportion who could taste PTC is n = 68.

(a) To estimate the sample size needed to find the proportion of PTC tasters within ± 0.1 with 90% confidence, we will use the formula for sample size estimation in proportion problems:
n = (Z² * p * (1-p)) / E²

Where n is the sample size, Z is the Z-score corresponding to the desired confidence level (1.645 for 90% confidence), p is the proportion of PTC tasters (0.75), and E is the margin of error (0.1).

n = (1.645² * 0.75 * (1-0.75)) / 0.1²
n = (2.706 * 0.75 * 0.25) / 0.01
n ≈ 50.74

Since we need a whole number, we round up to the nearest whole number:
n = 51

(b) If no assumptions were made about the proportion of PTC tasters, we would use the worst-case scenario, which is p = 0.5 (maximum variance):

n = (1.645² * 0.5 * (1-0.5)) / 0.1²
n = (2.706 * 0.5 * 0.5) / 0.01
n ≈ 67.65

Again, rounding up to the nearest whole number:
n = 68

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The angle of elevation of the sun is approximately 22.6 degrees.

The partnerships between the sides and angles of triangles are the subject of the mathematical discipline of trigonometry. It is used exhaustively in fields such as physics, engineering, and assessing.

In a right triangle, the side opposite the right angle is called the hypotenuse, while the other two sides are called the legs.

Given that, 7.6 m flagpole casts an 18.2 m shadow.

Using trigonometric ratio we have:

tan(θ) = h / s

Substituting the values:

tan(θ) = 7.6 / 18.2

tan(θ) ≈ 0.417

θ ≈ 22.6°

Hence, the angle of elevation of the sun is approximately 22.6 degrees.

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In the following question, among the conditions given, {q1, q2} is a basis for the vector space of polynomials p(t) of degree at most two that satisfy the constraint p(2) = 0. In this particular case, we must enter our basis as [[1,0,-4],[0,1,-2]], since q1(t) = t^2 - 4 and q2(t) = t - 2.

To find a basis for the vector space of polynomials p(t) of degree at most two which satisfy the constraint p(2)=0, we can take the following steps:
1. Rewrite the polynomials as linear combinations of the form a + bt + ct^2
2. Use the constraint p(2) = 0 to eliminate one of the coefficients a, b, or c
3. Normalize the polynomials so that they are unit vectors
For example, if your basis is 1 + 2t + 3t^2, 4 + 5t + 6t2 then you can enter it as [[1,2,3],[4,5,6]].

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Answer: Incorrect

Step-by-step explanation:

Your friend Frans' claim is incorrect. A row of zeros in the reduced matrix means that the corresponding equation in the system is redundant and does not provide any additional information. This does not necessarily mean that the system does not have a unique solution. In fact, a row of zeros in the reduced matrix is common when solving systems of linear equations using Gaussian elimination, and it can still lead to a unique solution or even an infinite number of solutions. Therefore, Frans' claim is wrong.

Answer:

n > 10

Step-by-step explanation:

2n > 20

2n/2 > 20/2

n > 10

The number of positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, are not divisible by either 5 or 7 is 4680.

Step by step explanation:
The number of positive integers with exactly four decimal digits between 1000 and 9999 inclusive can be obtained as follows:

Total number of four decimal digits = 9999 − 1000 + 1 = 9000
Numbers that are multiples of 5 are obtained by starting with 1000 and adding 5, 10, 15, 20, ..., 1995, that is, 5k, where k = 1, 2, 3, ..., 399.

Therefore, the number of positive integers with exactly four decimal digits that are multiples of 5 is 399.

Numbers that are multiples of 7 are obtained by starting with 1001 and adding 7, 14, 21, 28, ..., 1428, that is, 7m, where m = 1, 2, 3, ..., 204.

Therefore, the number of positive integers with exactly four decimal digits that are multiples of 7 is 204.

Note that some numbers in the interval [1000, 9999] are divisible by both 5 and 7. Since 5 and 7 are relatively prime, the product of any number of the form 5k by a number of the form 7m is a multiple of 5 × 7 = 35.

The numbers of the form 35n in the interval [1000, 9999] are

1035, 1070, 1105, 1140, ..., 9945, 9980.
We can check that there are 285 numbers of this form.

To find the number of positive integers with exactly four decimal digits that are not divisible by either 5 or 7, we will subtract the number of multiples of 5 and 7 and add the number of multiples of 35.

Therefore, the number of positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, are not divisible by either 5 or 7 is

9000 - 399 - 204 + 285 = 4680.

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Answer: (5a + 3)(b + 1)

Step-by-step explanation:

We can factor out the common factor of (b + 1) from both terms:

5a(b + 1) + 3(b + 1) = (5a + 3)(b + 1)

Therefore, the expression in complete factored form is (5a + 3)(b + 1).

Answer:

10. Other number is 12.

Explanation:

The prime factors of 120 are 2*2*2*3*5

To end up with even numbers, the odd numbers must be multiplied by even numbers. The only even numbers are 2s, while there are two odd numbers, 3 and 5.

So we MUST be talking about 2*3 and 2*5 with a 2 left over. That’s 6 and 10, which are by no stretch of the imagination consecutive. But we can either double the 10 (giving us 6 and 20, even less “consecutive”) or the 6.

Double 6 and we have 12. 10 and 12 are consecutive even numbers, because you can add two to get the next one.