Dumisani earn 42 480 per month. He splits his earnings in the ratio 7:5. And then saves the lesser amount. How much does he save

Answer:

34

Step-by-step explanation:

In all right triangles, the two shortest sides squared equals the longest side squared, given by the equation [tex]a^2+b^2=c^2[/tex].

We know the two shortest sides, so we can plug in

[tex]16^2+30^2=c^2\\256+900=c^2\\1156=c^2\\c=\sqrt{1156} \\c=34[/tex]

167.7 feet is the length of the zipline.

The angle of inclination is the angle formed between a horizontal line and a line or surface that is sloping or inclined. It is a measure of the steepness or slope of the line or surface and is typically expressed in degrees or as a trigonometric ratio.

We have a zipline that drops 30 feet from one treetop to a second treetop.

If the angle of inclination from the shorter tree to the taller tree is 10 degrees.

Let AB be the distance between two trees and BC be the drop in height from A to C. Then,

We have BC/AB = tan(θ)

Where θ = 10 degrees

We know BC = 30 feet.

So,

AB = BC/tan(θ) = 30/tan(10°) = 167.7 feet (rounded to one decimal place)

Therefore, the length of the zipline is 167.7 feet.

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Given:

Vince has 1/2 ton of gravel.

It is to be spread equally in 8 square yards.

To find:

How many tons of gravel will be spread in each square yard?

Solution:

Total gravel = 1/2 ton

To be spread equally in 8 square yards.

No. of tons of gravel will be spread in each square yard = (1/2) / 8 = 1/16 tons.

Therefore, 1/16 tons of gravel will be spread in each square yard.

Answer:

Given:

Vince has 1/2 ton of gravel.

It is to be spread equally in 8 square yards.

To find:

How many tons of gravel will be spread in each square yard?

Solution:

Total gravel = 1/2 ton

To be spread equally in 8 square yards.

No. of tons of gravel will be spread in each square yard = (1/2) / 8 = 1/16 tons.

Therefore, 1/16 tons of gravel will be spread in each square yard.

Step-by-step explanation:

Answer: a. The equation for the total expenses E for n bikers is:

E = 30n + 125n + 700

b. The equation for the total income I for n bikers is:

I = 350n

c. The equation for the profit P for n bikers is:

P = I - E = 350n - (30n + 125n + 700) = 195n - 700

Answer:

3

Step-by-step explanation:

HCF(a, b) x LCM(a, b) = a x b

We are given that LCM(18, 21) = 126. Let's use this to find the HCF:

HCF(18, 21) x 126 = 18 x 21

HCF(18, 21) = (18 x 21) / 126

HCF(18, 21) = 3

Therefore, the HCF of 18 and 21 is 3.

Answer:

3% of 600 is (3/100) x 600 = 18.

So, a number that is 3% larger than 600 would be:

600 + 18 = 618.

Therefore, the number that is 3% larger than 600 is 618

Answer:

618

Step-by-step explanation:

Let us first see what is 3% of the 600

3/100 x 600 = 18

a number that is 3% larger than 600 is 600+18 = 618.

Answer:

Step-by-step explanation:

For the second order differential equation, we find that Height = 1333.33 meters, Velocity = 240 meters/second.

The acceleration of a rocket fired vertically upwards t seconds after launch is given by a = 20 + 4t m/s². The second order differential equation for the height of the rocket is given by ℎ′′ = a.

The initial conditions for the rocket are:

ℎ(0) = 0 (the rocket starts from the ground) and ℎ′(0) = 0 (the rocket is not moving initially). For the differential equation, we integrate the acceleration once to obtain the velocity, and then integrate the velocity to obtain the height.

Integrating a = 20 + 4t gives v = 20t + 2t² + C1, where C1 is a constant of integration. Using the initial condition v(0) = 0, we get C1 = 0. Integrating v = 20t + 2t² gives ℎ = 10t² + 2/3 t³ + C2, where C2 is another constant of integration.  Using the initial condition ℎ(0) = 0, we getC2 = 0.

Therefore, the general solution for the height of the rocket is ℎ = 10t² + 2/3 t³.The velocity of the rocket is given by v = ℎ′.

At t = 10 s, the height of the rocket is ℎ(10) = 10 × 100 + 2/3 × 1000 = 1333.33 m. The velocity of the rocket at t = 10 s is v(10) = ℎ′(10) = 20 × 10 + 2 × 10² = 240 m/s.

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a) The probability is equal to the proportion of the range that lies below 17 minutes.P(X< 17) = (17 - 16) / (23 - 16) = 1/7

b) The probability is equal to the proportion of the range that lies above 22 minutes.P(X > 22) = (23 - 22) / (23 - 16) = 1/7

c)  The probability is equal to the proportion of the range that lies between 18 and 20 minutes.P(18 ≤ X ≤ 20) = (20 - 18) / (23 - 16) = 2/7

d) The mean and standard deviation of the download times are 19.5 and 1.4 minutes, respectively.

The probability that the download time will be less than 17 minutes.The probability is equal to the proportion of the range that lies below 17 minutes.P(X< 17) = (17 - 16) / (23 - 16) = 1/7

The probability that the download time will be more than 22 minutes.The probability is equal to the proportion of the range that lies above 22 minutes.P(X > 22) = (23 - 22) / (23 - 16) = 1/7

The probability that the download time will be between 18 and 20 minutes.The probability is equal to the proportion of the range that lies between 18 and 20 minutes.P(18 ≤ X ≤ 20) = (20 - 18) / (23 - 16) = 2/7

The mean and standard deviation of the download times.Using the formula for the mean and standard deviation for a uniform distribution with a range of [a, b],μ = (a + b) / 2 = (16 + 23) / 2 = 19.5σ = (b - a) / sqrt(12) = (23 - 16) / sqrt(12) ≈ 1.4 Therefore, the mean and standard deviation of the download times are 19.5 and 1.4 minutes, respectively.

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Answer:

5h

Step-by-step explanation:

300÷60=5

km÷km/h=h

=5h

Answer:

its bar graph

Step-by-step explanation:

thanks for the question

please mark me brainless

The respοnses fοr favοurite vacatiοn spοt can be described best by a pie chart.

One sοrt οf graph that illustrates the infοrmatiοn in the circular graph is a pie chart. It is a sοrt οf graphical representatiοn οf data where the slices οf pie depict the relative sizes οf the data. A list οf numerical and categοrical variables is necessary fοr a pie chart. Pie in this cοntext refers tο the entire thing, and slices tο its cοmpοnent pοrtiοns.

If yοu asked "What is yοur favοrite vacatiοn spοt?" tο a grοup οf peοple, the mοst apprοpriate type οf graph tο represent the respοnses wοuld be a pie chart.

A pie chart is a circular chart that is divided intο slices tο represent the prοpοrtiοn οf each categοry in a dataset.

In this case, each slice οf the pie chart wοuld represent a different vacatiοn spοt, and the size οf each slice wοuld cοrrespοnd tο the prοpοrtiοn οf respοndents whο selected that vacatiοn spοt as their favοrite.

Pie charts are useful fοr displaying categοrical data, where the categοries are mutually exclusive and add up tο 100%.

They are easy tο read and understand, and can quickly shοw the distributiοn οf respοnses amοng the different categοries.

On the οther hand, a bar graph οr a line graph wοuld nοt be apprοpriate fοr this type οf data since the respοnses are nοt numerical οr cοntinuοus.

A line plοt wοuld alsο nοt be apprοpriate since it is used tο display a series οf data pοints, and in this case, there is οnly οne data pοint per categοry.

Therefοre, a pie chart is the best chοice.

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The answer is no, you do not have enough time to climb all 3 walls within 7 1/2 minutes.

What is the conversion of the unit?

A conversion factor is a fraction equal to ' 1 '.  It has the same quantity in the numerator and denominator, but they're in different units.  You use it to convert a number from one unit to another unit.

There are different ways to approach this problem, but one possible method is to convert everything to a common unit, such as seconds.

First, convert 7 1/2 minutes to seconds by multiplying by 60:

7.5 minutes x 60 seconds/minute = 450 seconds

Next, multiply the time it takes to climb each wall by 3 to find the total time needed:

3 walls x 155 seconds/wall = 465 seconds

Comparing the total time needed (465 seconds) to the available time (450 seconds), we see that there is not enough time to climb all three walls.

Therefore, the answer is no, you do not have enough time to climb all 3 walls within 7 1/2 minutes.

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First vector v = [- 2 - 2 2] is in W and the second vector v = [6 - 1 - 3] is not in W.

W be the set of all vectors [x y x + y] with x and y real. To find: Whether each of the following vectors is in W. Let's check each vector whether it is in W or not: v = [- 2 - 2 2] To check the given vector is in W or not, we need to find the values of x and y such that the third component equals 2.So, x + y = 2 ⇒ y = 2 - x

The given vector can be written as v = [x y x + y]= [x, 2 - x, 2] Thus, given vector v is in W. v = [6 - 1 - 3]. To check the given vector is in W or not, we need to find the values of x and y such that the third component equals -3. So, x + y = -3 ⇒ y = -3 - x The given vector can be written as v = [x y x + y]= [x, -3 - x, -3]Thus, given vector v is not in W.

Moreover, Vectors, in Maths, are objects which have both, magnitude and direction. Magnitude defines the size of the vector. It is represented by a line with an arrow, where the length of the line is the magnitude of the vector and the arrow shows the direction.

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Simplified form of the algebraic expression (x^2 - x - 12) / (x^2 - 4) = (x + 3) / (x - 2)

To simplify the given algebraic expression (x^2 - x - 12) / (x^2 - 4), we first need to factor both the numerator and denominator as much as possible.

We can factor the numerator using the product-sum method or the quadratic formula, which yields:

x^2 - x - 12 = (x - 4)(x + 3)

Similarly, we can factor the denominator as a difference of squares, which gives:

x^2 - 4 = (x - 2)(x + 2)

Now, we can substitute these factorizations into the original expression:

(x^2 - x - 12) / (x^2 - 4) = [(x - 4)(x + 3)] / [(x - 2)(x + 2)]

At this point, we can simplify the expression by canceling out the factors that appear in both the numerator and denominator. Specifically, we can see that (x - 4) and (x + 2) appear in both the numerator and denominator, so they cancel out:

[(x - 4)(x + 3)] / [(x - 2)(x + 2)] = (x + 3) / (x - 2)

So the simplified expression is (x + 3) / (x - 2).

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The length of the ramp is approximately 16 meters.

Trigonometric ratios are ratios of the sides of a right triangle that relate the angles of the triangle to its sides.

There are 3 basic trigonometric ratios are given by

sin θ = opposite side /hypotenuse.

cos θ = adjacent side /hypotenuse.

tan θ  = opposite side /adjacent.

Here we have

The angle of the incline of the ramp is 32 degrees.

The height of the ramp is 10m.

Represent the following data as a right-angled triangle  

where the height of the ramp will be opposite side to the angle of the incline and the length of the ramp will be adjacent side

Let's assume the length of the ramp is "x".  

From the trigonometric ratios,

tan(32°) = 10/x

Multiply both sides by x:

x × tan(32°) = 10

Divide both sides by tan(32°):

x = 10 / tan(32°)

x = 10/0.62

x = 16.0033 meters

x = 16 meters

Therefore,

The length of the ramp is approximately 16 meters.

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Step-by-step explanation:

Let x be the number of suede coats and y be the number of cotton coats. Then, the system of inequalities representing the situation is:

150x + 69y ≥ 6200 (the total cost of the women's coats must be at least $6200)

x ≥ 0, y ≥ 0 (the number of coats cannot be negative)

Note that this system assumes that the store only sells suede and cotton coats for women, and that there are no other costs associated with these coats (such as shipping or storage costs).

Answer: 8

Step-by-step explanation:

Using SOHCAHTOA, we need TOA as we have the opposite (1) and the adjacent (7)

θ = [tex]tan^{-1}(\frac{1}{7} )[/tex] = 8.13 = 8

Answer:

The square root of 45 is approximately 6.708203932.

The required expression can express h in terms of A and b as [tex]$ h = \frac{2A - a}{b} $$[/tex]

Mathematical expressions consist of at least two numbers or variables, at least one math procedure, and a sentence. It's possible to multiply, divide, add, or subtract with this mathematical procedure. An expression's form is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

First, we can start by isolating the term that contains h on one side of the equation. To do this, we will first distribute the 0.5 term to get:

A = 0.5a + 0.5bh

Then, we can subtract 0.5a from both sides to get:

A - 0.5a = 0.5bh

Next, we can divide both sides by 0.5b to isolate h:

[tex]$ \frac{A - 0.5a}{0.5b} = h $$[/tex]

Simplifying the expression further, we can see that:

[tex]$$ \boxed{h = \frac{2A - a}{b}} $$[/tex]

Therefore, we can express h in terms of A and b as:

[tex]$ h = \frac{2A - a}{b} $$[/tex]

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The solution to the equation is (c) No, because there is only one real solution and the value is x = 4

The given equation is

(6 – 2x)(3 – 2x)x = 40

Next, we answer the question from the numbers given from the list of options

In option (c), we have

x = 4

By substitution, the equation becomes

(6 - 2 * 4)(3 - 2 * 4) * 4 = 40

Evaluate the product expression

40 = 40

The above equation is true

Hence, the solution is (c)

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Mode: The mode of this data is 8 hours. This is because 8 hours was the most frequently reported amount of time that the students watched TV during a school week.

Amount is a quantitative expression of magnitude, size, or degree of a particular quantity. It is typically used to describe an object, person, or an event. Amount is used to quantify something, to describe its size, duration, or extent. It can be used to measure a wide range of physical and abstract entities, such as money, time, energy, resources, and emotions. For example, you might say “there was a large amount of people at the event” or “I have a certain amount of money saved up.”

Range: The range of this data is 8 hours. This is because the difference between the highest amount of time reported (16 hours) and the lowest amount of time reported (8 hours) is 8 hours.

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The domain can be written as 3 <x < 81.75, which includes all x values that are feasible and fit within the constraints of the issue.

The most appropriate domain for this situation is (c) 3 < x < 81.75.

The reason for this is that the taxi charges $3 for the first mile, so x must be greater than 1. After that, the taxi charges $2.25 for every mile after the first, so the domain must exclude x = 0. Additionally, the problem states that the farthest the taxi will travel is 35 miles, so the domain must also include x < 35.

Therefore, the domain can be expressed as 3 < x < 81.75, which allows for all possible values of x that fall within the given parameters of the problem.

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The volume of small pyramid with base length 2, base width 2, and height 2. Its volume was 8/3π. We then scaled it by a factor of 2 and verified the formula V' = V × k3 holds true.

To create the smallest pyramid possible, we will use a tool such as a ruler or protractor to measure and construct the pyramid. Let's assume that we are using a ruler and that the smallest pyramid we can construct has a base length of 2 units, a base width of 2 units, and a height of 2 units.

To calculate the volume of the pyramid, we use the formula:

V = (1/3) × base area × height

The base area of the pyramid is:

A = base length × base width = 2 × 2 = 4 square units

Therefore, the volume of the pyramid is:

V = (1/3) × 4 × 2 = 8/3 cubic units (in terms of π, this is 8/3π cubic units)

Now, let's scale the original pyramid by a factor of k = 2. To find the new dimensions of the scaled pyramid, we multiply each dimension of the original pyramid by the scale factor k:

Base length = 2 × 2 = 4 units

Base width = 2 × 2 = 4 units

Height = 2 × 2 = 4 units

The base area of the scaled pyramid is:

A' = base length × base width = 4 × 4 = 16 square units

The volume of the scaled pyramid is:

V' = (1/3) × A' × height = (1/3) × 16 × 4 = 64/3 cubic units (in terms of π, this is 64/3π cubic units)

Now, we can verify that the formula V' = V × k3 holds true for the scaled pyramid:

V' = 64/3 cubic units

V = 8/3 cubic units

k = 2

V' = V × k3

64/3 = (8/3) × 23

64/3 = 8/3 × 8

64/3 = 64/3

Therefore, the formula V' = V × k3 holds true for a pyramid, and we have successfully verified it using the scaled pyramid.

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At the 1% level of significance, both the number of security guards (g) and the unemployment rate (u) have a significant effect on the dollar loss from theft each week (t). This is indicated by the p-values for both variables, which are both less than 0.01 (0.0012 for g and 0.0096 for u).

This means that there is less than a 1% chance that the observed relationship between these variables and the dependent variable (t) is due to chance. Therefore, we can reject the null hypothesis that there is no relationship between these variables and the dependent variable, and conclude that they have a significant effect on the dollar loss from theft each week.

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Answer:

The zeros of the polynomial function f(x) = x^4 - 2x^3 - 8x^2 + 10x + 15 are x = -1, x = 3 + √29/2, x = 3 - √29/2, and x = -0.4495 (approximately).

Step-by-step explanation:

To find all the zeros of the polynomial function f(x) = x^4 - 2x^3 - 8x^2 + 10x + 15, we can use the Rational Root Theorem and synthetic division.

Write the polynomial function in descending order of degree: f(x) = x^4 - 2x^3 - 8x^2 + 10x + 15.

Use the Rational Root Theorem to generate a list of possible rational zeros: ±1, ±3, ±5, ±15.

Use synthetic division to test each possible zero. We start with x = 1:

1 │ 1 -2 -8 10 15

│ 1 -1 -9 1

└───────────────

1 -1 -9 1 16

x = 1 is not a zero of the polynomial function.

We continue testing the remaining possible zeros:

-1 │ 1 -2 -8 10 15

│ -1 3 5 -15

└───────────────

1 -3 -3 15 0

Since the remainder is zero, we have found a zero of the polynomial function at x = -1.

We can use synthetic division to factor the polynomial function:

(x + 1)(x^3 - 3x^2 - 6x + 15)

Now we can solve for the remaining zeros of the polynomial function by factoring the cubic equation using the Rational Root Theorem and synthetic division:

3 │ 1 -3 -6 15

│ 3 0 -18

└─────────────

1 0 -6 -3

x = 3 is not a zero of the polynomial function.

-3 │ 1 -3 -6 15

│ -3 18 -36

└────────────

1 -6 12 -21

x = -3 is not a zero of the polynomial function.

The only remaining possible rational zeros are ±1/2 and ±5/2, but testing these values using synthetic division does not yield any more zeros.

However, we can see that the polynomial function can be factored as follows:

(x + 1)(x - 3)(x^2 - 3x - 5)

We can solve for the remaining zeros of the polynomial function by factoring the quadratic equation using the quadratic formula or factoring by grouping. Either way, we find that the remaining zeros are approximately x = (3 + √(29))/2 and x = (3 - √(29))/2.

Therefore, the zeros of the polynomial function f(x) = x^4 - 2x^3 - 8x^2 + 10x + 15 are x = -1, x = 3 + √29/2, x = 3 - √29/2, and x = -0.4495 (approximately).

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The radius is half that distance.r = 1/2(d) where d = distance between the endpoints of the diameter.

1. Writing the equation of the circle in standard formWe know that the endpoints of a diameter are (2,4) and (-14,-8) respectively, and that the midpoint of the diameter is the center of the circle. Therefore, let's begin by calculating the midpoint of the diameter using the midpoint formula:x = (x1 + x2)/2y = (y1 + y2)/2x = (2 + (-14))/2 = -6y = (4 + (-8))/2 = -2So, the midpoint is (-6,-2) which is the center of the circle. Now, we can use the distance formula to calculate the radius. Recall that the diameter is the distance between the two endpoints of the diameter, so the radius is half that distance.r = 1/2(d) where d = distance between the endpoints of the diameter.So, d = sqrt[(x2 - x1)^2 + (y2 - y1)^2]d = sqrt[(-14 - 2)^2 + (-8 - 4)^2]d = sqrt[(-16)^2 + (-12)^2]d = sqrt[256 + 144]d = sqrt[400] = 20So, r = 20/2 = 10. Now that we have the center and radius, we can use the standard form equation of a circle which is:(x - h)^2 + (y - k)^2 = r^2where (h,k) is the center and r is the radius.Substituting our values into the equation, we have:(x + 6)^2 + (y + 2)^2 = 100Expanding and simplifying, we can write the equation of the circle in standard form as:x^2 + 12x + y^2 + 4y + 20 = 0This is the equation in standard form.2. Graphing the circleTo graph the circle, we need to plot the center which is (-6,-2) and then draw the circle with radius 10 units. The circle will be a curve that is equidistant from all points on it to the center. Here's a sketch of the circle.
3. An equation of the circle in standard form is x² + 12x + y² + 4y + 20 = 0.

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You would need to deposit approximately $47.83 now to be able to withdraw $650 at the end of each year for 20 years, assuming an annual interest rate of 11% compounded annually.

It is typically expressed as an annual percentage rate (APR). Interest rates can be fixed, meaning they remain the same for the entire term of the loan, or variable, meaning they can change over time based on market conditions or other factors. The interest rate is an important factor to consider when borrowing money, as it affects the overall cost of the loan. It is also a key factor in investment decisions, as it determines the return on an investment.

To calculate the present value of an investment that will yield a future value of $650 for 20 years at 11% annual interest, we can use the formula for present value of an annuity:

PV = FV / (1 + r)ⁿ

where PV is the present value, FV is the future value, r is the interest rate per period, and n is the number of periods.

In this case, we want to find the present value of a 20-year annuity that pays $650 at the end of each year, with an annual interest rate of 11%. Plugging in the values, we get:

PV = $650 / (1 + 0.11)²⁰

PV = $650 / 13.584

PV = $47.83 (rounded to the nearest cent)

Therefore, you would need to deposit approximately $47.83 now to be able to withdraw $650 at the end of each year for 20 years, assuming an annual interest rate of 11% compounded annually.

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Answer:

First, let's simplify both sums by combining like terms:

3x + 5y - 2 + 2x - 3y + 1 = 5x + 2y - 1

4x - 8y + 3 - 5x + 6y + 7 = -x - 2y + 10

Now we can subtract the second sum from the first:

(5x + 2y - 1) - (-x - 2y + 10) = 5x + 2y - 1 + x + 2y - 10

Simplifying this expression, we get: 6x + 4y - 11

The sequence is 3, 9, 15, 21, 27, and the recursive formula for this sequence is a_1 = 3, a_n = a_{n-1} + 6, and the next term is 33.

The sequence is an arithmetic sequence with a common difference of 6, starting at 3. A recursive formula for this sequence can be written as:

a_1 = 3

a_n = a_{n-1} + 6, for n > 1

This formula means that the first term in the sequence is 3, and every subsequent term is found by adding 6 to the previous term.

To find the next term in the sequence, we can use this formula to compute a_6:

a_6 = a_5 + 6

a_6 = 27 + 6

a_6 = 33

Therefore, the next term in the sequence is 33.

The given sequence is an arithmetic sequence, where each term is 6 more than the previous term, starting at 3.

A recursive formula is a mathematical formula that is used to define a sequence in terms of its previous terms. In this case, we can use the recursive formula a_1 = 3 and a_n = a_{n-1} + 6 to define the given sequence. The formula says that the first term in the sequence is 3, and each subsequent term can be found by adding 6 to the previous term.

Using this recursive formula, we can find the next term in the sequence, which is 33. We can continue to apply the formula to find any term in the sequence.

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