Hanna, sarah and mthunzi bought a ticket for R60. Hanna contributed R15, Sarah R21 and mthunzi R24. They won R4000. Calculate the amount each will get? ​

Answer:

23

Step-by-step explanation:

We can think of (f o g)(-4) as f(g(-4)).

As you can see, we start with the inner function and the output of the inner function becomes the output of the outer function.

So we'll plug in -4 for x in g(x) and then the output of this becomes the input of f(x):

[tex]f(x)=2x-1\\g(x)=x^2-4\\f(g(-4))\\\\g(-4)=(-4)^2-4=12\\\\f(12)=2(12)-1=23[/tex]

The more money will be earned for job B.

Subtraction can be done for any numbers or algebraic expressions. It is the process of taking out certain value from a given amount of number.

For Job A :

Salary = $51,000

Distance = 9 miles from home

Total distance needed to travel to and back from job in a day = 18 miles

Number of working days in a year = 260

Number of working days in a year after vacation = 260 - (12% × 260) = 228.8 days

Total distance for working days in a year = 228.8 × 18 = 4118.4 miles

Mileage on his car = 24 miles per gallon

Amount of gas for 24 miles = 1 gallon

Amount of gas for 4118.4 miles = 171.6 gallon

Gas price for 1 gallon = $5.25

Gas price for 171.6 gallon = 171.6 × $5.25 = $900.9

Net salary after gas price = $51,000 - $900.9 = $50,099.1

For Job B :

Salary = $53,000

Distance = 22 miles from home

Total distance needed to travel to and back from job in a day = 44 miles

Number of working days in a year after vacation = 260 - (8% × 260) = $239.2 days

Total distance for working days in a year = 239.2 × 44 =  10,524.8 miles

Mileage on his car = 24 miles per gallon

Amount of gas for 24 miles = 1 gallon

Amount of gas for 10,524.8 miles = 438.533 gallon

Gas price for 1 gallon = $5.25

Gas price for 171.6 gallon = 438.533 × $5.25 = $2302.3

Net salary after gas price = $53,000 - $2302.3 = $50,697.7

The net salary after gas price is higher for job B.

Hence Net salary after gas price is higher for job B.

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Fractions of smallest to largest

Smallest to largest: 1/4, 1/3, 2/5, 2/3, 3/4

Smallest to largest: 1/5, 2/7, 3/5, 5/7, 31/35

Smallest to largest:  31/30, 23/20, 6/5, 13/10, 7/5

Smallest to largest:   13/10, 13/6, 11/5, 25/6, 21/5

An element of a whole is a fraction. The number is mathematically expressed as just a fraction, where the numerator and denominator are split. Both are integers in a simple fraction. A simple fraction contains a fraction in either the numerator or the denominator. A fraction consists of two components. The numerator seems to be the number which goes just at top of the line. 

Smallest to largest: 0.25, 0.33, 0.4, 0.67, 0.75

Smallest to largest: 0.2, 0.29, 0.6, 0.71, 0.89

Smallest to largest:  1.03, 1.15, 1.2, 1.3, 1.4

Smallest to largest:  1.3, 2.16, 2.2, 4.17, 4.2

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( 4x + 1 ) ° = ( 3x + 4 )°

Opposite side of parallelogram are always equal ...

4x + 1° = 3x + 4°

4x - 3x = 4° - 1°

x = 3°

The measure of angle R from the given parallelogram TPRS is 101°.

A parallelogram is a special kind of quadrilateral that is formed by parallel lines. The angle between the adjacent sides of a parallelogram may vary but the opposite sides need to be parallel for it to be a parallelogram. A quadrilateral will be a parallelogram if its opposite sides are parallel and congruent.

Given that, TPRS is a parallelogram.

Here, ∠T=(4x+1)° and ∠S=(3x+4)°

The sum of adjacent angles of a parallelogram is 180°.

∠T+∠S=180°

(4x+1)°+(3x+4)°=180°

7x+5=180

7x=175

x=175/7

x=25°

So, ∠T=(4x+1)°=4×25+1=101°

∠T=∠R=101° (Opposite angles of parallelogram are equal)

Therefore, the measure of angle R is 101°.

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The area of triangle FGH is given as follows:

15.05 units².

The area of a triangle is given by half the multiplication of the base length by the height.

The base length is given by the distance between points F and G, hence:

b = sqrt((-2 - (-4))² + (6 - 1)²)

b = 5.385.

The coordinates of the midpoint of segment FG are given as follows:

The distance between the midpoint and vertex H is the height, given as follows:

h = sqrt((-3 - 2)² + (3.5 - 6)²)

h = 5.59.

Hence the area of the triangle is given as follows:

A = 0.5 x 5.385 x 5.59

A = 15.05 units².

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Answer:

Step-by-step explanation:

A productive approach to identifying a research topic and subsequent research question can involve utilizing multiple sources, including:

Literature review: Reviewing existing research in the field can help identify gaps in knowledge and areas that need further investigation.

Personal interests and experiences: Consider your own experiences, interests, and expertise to identify a topic that you are passionate about and can contribute to.

News articles and current events: Stay up-to-date on current events and identify topics that are relevant and pressing in your field.

Professional associations and organizations: These organizations often have conferences and publications that highlight current research trends and topics.

Government reports and data sources: These sources can provide data and information on a wide range of topics and can serve as a starting point for identifying a research question.

Ultimately, a combination of these sources can be useful in identifying a research topic and subsequent research question. It's important to consider the feasibility, importance, and originality of the research topic, and to choose a topic that you can research thoroughly and effectively.

The insects population expected after 4 months is 414.

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

The standard form of an exponential function is:

y = abˣ

where a is the initial value and b is the multiplication factor.

An entomologist expects an insect population to increase by about 20% each month from may 1 to September 1.

Let us assume that the population of insect on May first was 200. If y represent the population of insects x months after May 1, hence:

y = 200(1.2)ˣ

At September 1; after 4 months:

y = 200(1.2)⁴ = 414

The insects population after 4 months is 414.

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Answer expressed in terms of pi: [tex]V=2304 \pi (m^{3})\\[/tex].

Answer rounded to the nearest whole number: [tex]V=7238(m^{3})[/tex].

Given figure: Sphere.

Given dimension: diameter (d)= 24m.

We're trying to calculate the volume of a sphere, here's the formula for that:

[tex]V=\frac{4}{3} \pi r^{3}[/tex]

There's something worth paying a bit extra ttention in this problem, and that is the fact that we were not given a value of radius (r) to use in the formula. Instead, we were given the diameter (d), which happens to be double of the radius, by definition. Hence, to find the radius we do the following:

[tex]d=2r\\\\ r=\frac{d}{2} =\frac{24m}{2} =12m[/tex]

Use the data in the volume formula:

[tex]V=\frac{4}{3} \pi (12m)^{3}[/tex]

[tex]V= \pi(\frac{4}{3} (12m)^{3})\\ \\V= \pi(2304m^{3} )\\ \\V=2304 \pi (m^{3})\\[/tex]

We were asked to express our answer in terms of pi. Therefore, let's isolate pi from the calculations for now:

[tex]V= \pi(\frac{4}{3} (12m)^{3})\\ \\V= \pi(2304m^{3} )\\ \\V=2304 \pi (m^{3})\\[/tex]

Answer expressed in terms of pi: [tex]V=2304 \pi (m^{3})\\[/tex].

The problem also asks to round to the nearest whole number. So, let's go ahead and calculate an approximate value and round it to the nearest whole number:

[tex]V=7238.229474 (m^{3})[/tex]

Since the first number after the dot (.) isn't 5 or greater, we may leave the whole part of the number as it is and delete the remaining decimal numbers.

Answer rounded to the nearest whole number: [tex]V=7238(m^{3})[/tex].

The answers for demand function are a) p(x) = -0.0006q + 15 and b) the price at which the demand will reach 20000 units put q = 20000, is $3

A demand function is a mathematical equation which expresses the demand for a product or service as a function of its price.

Given that, the demand function for a certain product is known to be linear.

When the price of the product is $12, the number of units sold is 5000.

But if the price of the product is $9, the number of units sold is 10000.

We need to find the demand function, expressed as price p in terms of quantity q and the price at which the demand will reach 20000 units.

a) P(x) can be calculated using point slope equation given:

Price is $12 for 5000 units sold. A decrease in price to $9 increases units sold to 10000.

Slope = Δ price / Δ units = 9-12 / 10000 - 5000

= -3 / 5000 = -0.0006

p(q) = m(q - x₁) + p₁

= -0.0006(q-5000) + 12

=  -0.0006q + 3 + 12

=  -0.0006q + 15

Therefore, the demand function is p(x) = -0.0006q + 15

b) To find the price at which the demand will reach 20000 units put q = 20000, put q = 20000

p(x) = -0.0006 × 20000 + 15

= -12 + 15

= 3

Therefore, the price at which the demand will reach 20000 units put q = 20000, is $3

Hence, the answers for demand function are a) p(x) = -0.0006q + 15 and b) the price at which the demand will reach 20000 units put q = 20000, is $3

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Consequently, when 3300 pounds are utilized, sand, gravel, and cement weigh 1800, 900, and 600 pounds, respectively.

In algebra, ratios display how infrequently one figure is contained in another. For instance, if there are 8- oranges and 6 citrus in a fruit dish, the percentage of oranges to oranges is 8 to 6. In a similar vein, lemons to whole fruit ratio is 8 to 1, whereas lemons to oranges rate is 6 to 8. A ratio is a non-zero ordered pair of numbers, x and y b, that is stated as a / b. A ratio is really an equation that joins two ratio. The ratio can be written as 1:3, signifying that if there 1 boy and (3) girls (she has 3 girls for every boy), 3/4 of the population is female and 1/4 is male.

given

the ratio of sans , gravel and sand is 6:3:2

total pounds needed = 3300

so 6x + 3x + 2x = 3300

11x = 3300

x = 300

6x = 6 * 300 = 1800

3x = 3* 300 = 900

2x = 2* 300 = 600

Consequently, when 3300 pounds are utilized, sand, gravel, and cement weigh 1800, 900, and 600 pounds, respectively.

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Answer:

325888899998898897879

The Cumulative Distribution Function (CDF) can be used to find the probability of a continuous random variable that is uniformly distributed between 3 and 8.

The formula for the CDF is F(x) = (x-a)/(b-a) where a is the lower bound of the distribution and b is the upper bound of the distribution. In this case, a = 3 and b = 8. Therefore, the CDF equation is F(x) = (x-3)/(8-3). The Cumulative Distribution Function (CDF) can be used to find the probability of a continuous random variable that is uniformly distributed between 3 and 8.As an example, let's find the probability of x being less than or equal to 5. The CDF equation would be F(5) = (5-3)/(8-3) = 2/5. Therefore, the probability of x being less than or equal to 5 is 2/5.

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Therefore , the solution of the given problem of test statistics comes out to be the p-value is 0.00052.

The Z-statistic, which demonstrates that the ordinary normal balanced hypothesis is true, has been used as the statistic for anything resembling a Z-test. Let's say you run two separate X-y tests with a 0.05 level of significance, and the results show that you got a 2.5 R t. (also referred as a Z-value). The p-value for this Z-value is 0.0124.

Here,

(a) State the null hypothesis [tex]H_{0}[/tex] and the alternative hypothesis H1.

The null hypothesis (H0) is that the population mean sodium level for healthy adults is equal to the textbook value of 141 Eq per liter of blood.

[tex]H_{0}[/tex]     : μ = 141

The alternative hypothesis (H1) is that the population mean sodium level for healthy adults differs from the textbook value.

H1: μ ≠ 141

(b) Determine the type of test statistic to use.

Since the sample size is greater than 30 and the population standard deviation is known, we can use a z-test to test the hypothesis.

(c) Find the value of the test statistic. (Round to three or more decimal places.)

The test statistic is calculated as:

z = (x'- μ) / (σ / √n)

Where x' is the sample mean, μ is the population mean under the null hypothesis, σ is the population standard deviation, and n is the sample size.

Substituting the given values, we get:

z = (149 - 141) / (13 / √21) = 3.464

Therefore, the value of the test statistic is 3.464.

(d) Find the p-value. (Round to three or more decimal places.)

Since this is a two-tailed test, we need to find the area under the normal curve beyond 3.464 in both directions. Using a standard normal table or calculator, we find that the area beyond 3.464 is 0.00026 in one direction. So, the p-value is:

p-value = 2 * 0.00026 = 0.00052

Therefore, the p-value is 0.00052.

(e) Can we conclude that the population mean adult sodium level differs from that given in the textbook?

Since the p-value (0.00052) is less than the level of significance (0.01), we can reject the null hypothesis and conclude that the population mean adult sodium level differs from that given in the textbook at the 0.01 level of significance.

Answer: Yes, we can conclude that the population mean adult sodium level

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The correlational hypothesis is a type of research hypothesis that proposes a relation between two variables.

Hypothesis proposes that there is a relationship or association between two variables, known as the independent and dependent variables.

The relation between the two variables can be positive or negative. A positive relation means that as the independent variable increases, the dependent variable also increases.

On the other hand, a negative relation means that as the independent variable increases, the dependent variable decreases.

The strength of the relation can be determined by calculating the correlation coefficient, which is a numerical representation of the strength of the relation between two variables.

In the mathematical representation of a correlational hypothesis, the equation

=> Y = mX + b

is used, where m represents the slope of the line and b represents the intercept. The slope of the line reflects the strength of the relation between the independent and dependent variables, while the intercept reflects the starting point of the relation.

Complete Question:

What is meant by the thing that it is stated in a question form it poses an expected relationship between variables it reflects a theory it is testable?

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The smallest angle is 5° when each of those angles was divided into 5 equal parts.

In Geometry, an angle is a figure which is produced by two rays, which share a common point called a vertex. The two rays stand in for the angle's two sides. The Roman word "Angulus," which means "corner," is where the term "angle" originates. The intersection of two curves in this plane results in the angles. Angles of several kinds can be generated on a planar surface. As follows:

Acute Angle

Obtuse Angle

Right Angle

Reflex Angle

Straight Angle

Full Angle

An angle greater than 90° but less than 180°  is referred to as a "obtuse angle."  An obtuse angle is between a right angle and a straight angle.

Now in this question,

Starting with an obtuse angle of 150°, bisecting it gives two angles of 75° each.

Trisecting each of these angles gives three angles of 25° each.

Dividing each of these angles into 5 equal parts gives angles of 5° each.

Therefore, the smallest angle is 5°.

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Answer:

x = 3

Step-by-step explanation:

A vertical line is drawn on a graph paper, which passes through points (3, 3) and (3, -3).  For a vertical line, slope or gradient is undefined.
Therefore, the equation of vertical line is the common x-coordinate of the points along the line. In this case, the common x-coordinate is 3

∴Equation of line

        x = 3

Answer:

Step-by-step explanation:

James is thinking of 6 miles as the total distance and 1/4 mile as one part of that distance. To find out how many parts of 1/4 mile he would have to walk to cover 6 miles, he needs to divide 6 by 1/4.

To perform this division, we need to remember that dividing by a fraction is the same as multiplying by its reciprocal.

The reciprocal of 1/4 is 4, so to divide 6 by 1/4, we multiply 6 by 4:

6 * 4 = 24

So, the quotient of 6 and 1/4 is 24.

The features of the sine function in this problem are given as follows:

The equation is given as follows:

y = 2sin(2πx/3) - 4.

The standard definition of the sine function is given as follows:

y = Asin(B(x - C)) + D.

For which the parameters are given as follows:

The function has a minimum value of -6 and a maximum value of -2, for a difference of 4, hence the amplitude is given as follows:

2A = 4.

A = 2.

Without vertical shift, a function with amplitude of 2 would oscillate between -2 and 2, while this one oscillates between -6 and -2, hence the vertical shift is given as follows:

D = -4.

The shortest distance between repetitions can be given by 2 - (-1) = 3, hence the period is of 3 units and the coefficient B is given as follows:

2π/B = 3

B = 2π/3.

The function is at it's midline at the origin, hence it has no phase shift, and thus the equation is given as follows:

y = 2sin(2πx/3) - 4.

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Answer:

12%

4.44 / 37

Step-by-step explanation:

Answer: 12%

Step-by-step explanation: 4.44 is 12% of 37.

To solve, use this example:

[tex]\frac{x}{100} = \frac{4.44}{37}[/tex]

First, divide the part percent by the whole percent. That'd be 4.44 / 37 which is 0.12. Now, we need to multiply 100 by 0.12 is 12. So, 4.44 is 12% of 37. I hope this helped!

X(t) = 2-t, Y(t) = 5-t, and Z(t) = 0 are the parametric equations for the line passing through (2, 5, 0) and being perpendicular to both i+j and j k. The line has symmetric equations x+2 = -(y + 5) and z = 0, or x+2 = -(y + 5) = z.

As x(t) = 2-t, y(t) = 5-t, and z(t) = 0, the parametric equations of the line passing through (2, 5, 0) and perpendicular to both i+j and j k can be written. The x, y, and z coordinates of the line are defined by these equations in terms of the parameter t. It is possible to write the line's symmetric equations as x+2 = -(y + 5) and z = 0, or as x+2 = -(y + 5) = z. These equations define the line as the collection of all points (x, y, and z) that concurrently meet both equations. The line goes through the point and is perpendicular to both i+j and j k. (2, 5, 0).

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Answer:

$16,050.00

Step-by-step explanation:

10[(40 x 30) + (9 x 45)]  

In one week, he works 40 hours (8 x 5) for $30 and 9 hours of overtime each week (one extra hour 5 days during a week week plus 4 hours on Sat.)

10(1200 +405)

10(1605)

$16,050.00

To calculate the carpenter's earnings, separate the regular work hours from the overtime hours. Compute earnings for both from their respective rates and add them together. Multiply by the number of days worked and finally, by the total number of weeks.

In order to calculate the earnings of a carpenter during a 10-week period, we must consider how many hours were worked at regular and overtime rates. During the weekdays, the carpenter worked 9 hours per day. The first 8 hours were paid at the regular rate, and the remaining 1 hour was considered overtime. On Saturdays, the carpenter worked 4 hours at the regular rate as it didn't supersede the 8-hour workday.

So, on weekdays, he earned: 8 hours * $30 + 1 hour * $45. On Saturdays, his earnings were 4 hours * $30. To find the weekly earnings we add weekday and Saturday earnings, then multiply by 5 (for weekdays) and add 1 Saturday, then multiply the total earnings by 10 weeks. Using these computations, we are able to find the total amount earned by the carpenter.

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Answer:

x(y/2 + z)

Step-by-step explanation:

There are two triangles here.

The small triangle which is bound by dotted lines has base = y and height = x

The height of the larger triangle is 2x and its base is y + z

Area of larger triangle = 1/2 ·  2x · (y + z)
= x(y + z) = xy + xz

Area of smaller triangle = 1/2 · x · y = xy/2

Shaded region area = Area of larger triangle - area of smaller triangle

= xy + xz - xy/2

= xy/2 + xz

= x(y/2 + z)

Answer: One way that Olivia might have found a combination of two transformations to move figure ABCDE onto figure A'B'C'D'E' is by using a combination of translations and rotations.

A translation is a type of transformation that moves a figure a certain distance in a specified direction, without changing its size or orientation. A rotation is a type of transformation that turns a figure about a fixed point, called the center of rotation, by a certain angle.

Olivia might have first translated figure ABCDE to a new location and then rotated it about a point to match the orientation of A'B'C'D'E'. For example, she could have translated figure ABCDE so that one vertex coincides with a corresponding vertex in A'B'C'D'E', and then rotated it about that common vertex so that the sides match up.

Alternatively, Olivia might have first rotated figure ABCDE to a new orientation and then translated it to the final position. The sequence of transformations could have been different, but the end result would still be figure ABCDE matching the orientation and position of A'B'C'D'E'.

Step-by-step explanation:

Answer:

The inverse tangent function, tan^-1, is continuous over its domain, which is the range of values from -π/2 to π/2. However, the function tan^-1 (xy^2/(x+y)) may not be continuous at all points in this domain, as the denominator (x + y) can be zero for some values of x and y.

Step-by-step explanation:

The change in electric potential is approximately 135.19 volts if you move from coordinate (-8.03, -4.24) to coordinate (7.02, 2.60)

What is a coordinate point?

Coordinates are a pair of numbers that are used to determine the position of a point or a shape in a 2-dimensional plane. We define the position of a point on a 2D plane using two numbers, called the x-coordinate and the y-coordinate.

The change in electric potential (ΔV) can be calculated using the equation:

ΔV = -∫ E dl

where E is the electric field and dl is an infinitesimal displacement along the path. We need to find the path integral of the electric field between the two coordinates.

Since the electric field is in the x-y plane, we can use the two-dimensional version of the equation:

ΔV = -∫ E * dx - ∫ E * dy

where dx and dy are the changes in x and y, respectively.

We can calculate the change in x and y as follows:

dx = 7.02 m - (-8.03 m) = 7.02 m + 8.03 m = 15.05 m

dy = 2.60 m - (-4.24 m) = 2.60 m + 4.24 m = 6.84 m

Next, we'll use the electric field equation to find the components of the electric field in the x and y directions:

Ex = -3.67 N/C

Ey = -4.359 N/C

Finally, we can use these values to calculate the change in electric potential:

ΔV = -∫ E * dx - ∫ E * dy = -Ex * dx - Ey * dy = -(-3.67 N/C) * (15.05 m) - (-4.359 N/C) * (6.84 m)

Converting from joules to volts:

ΔV = ΔV / (1.602 * 10^-19 C)

ΔV = (3.67 N/C * 15.05 m + 4.359 N/C * 6.84 m) / (1.602 * 10^-19 C) = 135.19 Volts

Hence, the change in electric potential is approximately 135.19 volts.

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The state space for the Markov chain {Xn} is {0, 1, 2}. At any time, Xn can only be 0, 1, or 2, depending on how many red balls are in the urn.

The transition probabilities for the Markov chain are as follows:

If Xn = 0, the next state Xn+1 can only be 1, with a probability of 1.0.

If Xn = 1, the next state Xn+1 can either be 0 or 2, with a probability of 0.5 each.

If Xn = 2, the next state Xn+1 can only be 1, with a probability of 1.0.

So, the transition probabilities can be represented in a transition matrix as follows:

P = [  [0, 1, 0],

 [0.5, 0, 0.5],

 [0, 1, 0]

]

This transition matrix represents the probabilities that the Markov chain will transition from one state to another in one step.

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The sum of cubes expression is a^3 + 8

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

The list of options

A sum of cube expression can be represented as

a^3 + b^3

From the list of options, we have

a^3 + 8

This can be expressed as

a^3 + 2^3

Hence, teh expression is a^3 + 8

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