3. Calculate the following- show all working out
a)7/8 of R60,00​

Step-by-step explanation:

let n be the number of working hour

so total income is 24n + 6

now 1/6 of the income will be into saving

so the saving is (24n + 6) /6

The expression representing the amount that will go into his savings each week is $4h + $1.

An expression is combination of variables, numbers and operators.

Mike's weekly pay is given by:

Pay = (hourly rate) x (hours worked) + sales bonus

Pay = $24h + $6

To find one-sixth of his weekly pay, we can multiply his pay by 1/6:

Savings = (1/6) x Pay

Savings = (1/6) x ($24h + $6)

Savings = $4h + $1

Therefore, the simplified expression representing the amount that will go into his savings each week is $4h + $1.

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Answer:

32

Step-by-step explanation:

The base angles of the triangle are the same since the sides are the same

<C = 74

A+B+C = 180 since the sum of the angles of a triangle = 180

74+B+74=180

Combine like terms

148+B =180

B = 180-148

B = 32

Answer:

[tex]\text{A. }32^{\circ}[/tex]

Step-by-step explanation:

From the Isosceles Base Theorem, the two base angles of a isosceles triangle are equal. Therefore, [tex]\angle A=\angle C=74^{\circ}[/tex].

Since the sum of the interior angles of a triangle is always equal to 180 degrees, we can write the following equation:

[tex]\angle A+\angle B+\angle C=180[/tex]

Substitute [tex]\angle A=\angle C=74^{\circ}[/tex] into this equation to solve for [tex]\angle B[/tex]:

[tex]74+\angle B+74=180,\\\angle B=180-74-74=\boxed{32^{\circ}}[/tex]

Answer:

This probability that the sample proportion is between 0.35 and 0.45 is the p-value of [tex]Z = \frac{0.45 - \mu}{\sqrt{\frac{p(1-p)}{160}}}[/tex] subtracted by the p-value of [tex]Z = \frac{0.35 - \mu}{\sqrt{\frac{p(1-p)}{160}}}[/tex]. These p-values are found looking at the z-table.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Estimate of the proportion:

This is p, and thus, we use [tex]\mu = p[/tex].

Sample of 160

This means that:

[tex]n = 160, s = \sqrt{\frac{p(1-p)}{160}}[/tex]

What is the probability that the sample proportion is between 0.35 and 0.45?

This probability that the sample proportion is between 0.35 and 0.45 is the p-value of [tex]Z = \frac{0.45 - \mu}{\sqrt{\frac{p(1-p)}{160}}}[/tex] subtracted by the p-value of [tex]Z = \frac{0.35 - \mu}{\sqrt{\frac{p(1-p)}{160}}}[/tex]. These p-values are found looking at the z-table.

Answer:

ans : it is order wise

a) 6/125 cm³

b) 8/125 cm³

c) 1/125 cm³

d) 36/125 cm³

Step-by-step explanation:

a)

for rectangular prism = length × width × height

= (1/5) × (2/5) × (3/5)

= 6/125 cm³

b)

for cube = length³

= (2/5)³

= 8/125 cm³

c)

for cube = (1/5)³

= 1/125 cm³

d)

for rectangular prism = (3/5) × (4/5) × (3/5)

= 36/125 cm³

Answer:

-240

Step-by-step explanation:

n = 5

a₅ = 30* (-2)(5 - 1)

   = 30 * (-2)*4

  = 30 * (-8)

  = - 240

Answer:

[tex] - \frac{9}{2} [/tex]

Step-by-step explanation:

Rate of change of y with respect to x

[tex] = \frac{60 - 96}{ - 12 - ( - 20)} \\ \\ = \frac{ - 36}{ - 12 + 20} \\ \\ = \frac{ - 36}{ 8} \\ \\ = - \frac{9}{2} [/tex]

Answer:

x=8

Step-by-step explanation:

the y-value in the first pair decreased by half, so the x-value must double due to inverse variation.

Answer:

6

Step-by-step explanation:

Answer:

[tex]10\\[/tex]

Step-by-step explanation:

[tex]7\frac{1}{2} =\frac{15}{2}[/tex]

[tex]\frac{15}{2}[/tex] ÷ [tex]\frac{3}{4}=[/tex]

[tex]\frac{15}{2} *\frac{4}{3}=[/tex]

you don't have to, but cross simplifying is better to do right now so that the answer you get will be simplified.

[tex]\frac{5}{1} *\frac{2}{1}=[/tex]

[tex]=\frac{10}{1}[/tex]

[tex]=10[/tex]

Hope this helps

Answer: I think the answer is 120

Step-by-step explanation:

I'm not sure tho

Answer:

10x +30

Step-by-step explanation:

2(3 + 5x) + 24

Distribute

2*3 + 2*5x+24

6+10x+24

Combine like terms

10x +30

Answer:

28.26

Step-by-step explanation:

The formula for calculating diameter is πd (pi times the diameter), so 3.14 times 9 is 28.26.

Answer:

fraction- 1/2

decimal- .5

percent 50%

Step-by-step explanation:

Answer:

P = 0, -5

Step-by-step explanation:

Answer:

p = 0

p = - 5

Step-by-step explanation:

3p(p + 4) = p(p + 2)​

3p² + 12p - (p² + 2p) = 0

3p² + 12p - p² - 2p = 0

3p² + 10p - p² = 0

2p² + 10p = 0

2p(p + 5) = 0

p = 0

p + 5 = 0

p + 5 - 5 = 0 - 5

p = - 5

but am not pretty sure

the volume of cone is =1/3 pie r² h

I think this is the formula to calculate it

Answer:

-x+y+6z=? You did not spcify so I just made it 0

x = -22/5, y = -4/5, z = -3/5

Step-by-step explanation:

Solve the following system:

{-x - 3 y - 2 z = 8 | (equation 1)

-x + y + 6 z = 0 | (equation 2)

x - 9 y - 2 z = 4 | (equation 3)

Subtract equation 1 from equation 2:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x+4 y + 8 z = -8 | (equation 2)

x - 9 y - 2 z = 4 | (equation 3)

Divide equation 2 by 4:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x+y + 2 z = -2 | (equation 2)

x - 9 y - 2 z = 4 | (equation 3)

Add equation 1 to equation 3:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x+y + 2 z = -2 | (equation 2)

0 x - 12 y - 4 z = 12 | (equation 3)

Divide equation 3 by 4:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x+y + 2 z = -2 | (equation 2)

0 x - 3 y - z = 3 | (equation 3)

Swap equation 2 with equation 3:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x - 3 y - z = 3 | (equation 2)

0 x+y + 2 z = -2 | (equation 3)

Add 1/3 × (equation 2) to equation 3:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x - 3 y - z = 3 | (equation 2)

0 x+0 y+(5 z)/3 = -1 | (equation 3)

Multiply equation 3 by 3:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x - 3 y - z = 3 | (equation 2)

0 x+0 y+5 z = -3 | (equation 3)

Divide equation 3 by 5:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x - 3 y - z = 3 | (equation 2)

0 x+0 y+z = -3/5 | (equation 3)

Add equation 3 to equation 2:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x - 3 y+0 z = 12/5 | (equation 2)

0 x+0 y+z = -3/5 | (equation 3)

Divide equation 2 by -3:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x+y+0 z = -4/5 | (equation 2)

0 x+0 y+z = -3/5 | (equation 3)

Add 3 × (equation 2) to equation 1:

{-x + 0 y - 2 z = 28/5 | (equation 1)

0 x+y+0 z = -4/5 | (equation 2)

0 x+0 y+z = -3/5 | (equation 3)

Add 2 × (equation 3) to equation 1:

{-x+0 y+0 z = 22/5 | (equation 1)

0 x+y+0 z = -4/5 | (equation 2)

0 x+0 y+z = -3/5 | (equation 3)

Multiply equation 1 by -1:

{x+0 y+0 z = -22/5 | (equation 1)

0 x+y+0 z = -4/5 | (equation 2)

0 x+0 y+z = -3/5 | (equation 3)

Collect results:

Answer: {x = -22/5, y = -4/5, z = -3/5

First let's understand the discriminant. Discriminant is an equation of D = b²-4ac. Discriminant is to find how many solutions do the equation have. In case for Quadratic Equation, there are 3 types of solutions which are:

To find discriminant graphically, we need to know that the x-axis plane represents the solutions to the equations. All equations can be drawn as a graph. Some graphs do not intersect x-axis while some graph do.

You may also notice that some graphs intersect x-axis more than one point. Like I said that the x-axis represents the roots or the solutions. Intersecting x-axis "n" times means that the equation has "n" roots.

For example, if a graph intersects x-axis 8 points - the equation has 8 roots or solutions.

From the graph, the parabola intersects on x-axis just only one point. That means there is only one solution. The question asks to find the discriminant of the function. Recall that if D = 0, there's only one real root. Therefore the discriminant for the function is zero.

Answer

Let me know if you have any doubts!

Answer:

????????????????????

Answer:

The surface area of the balloon is [tex]S(t) = \frac{100}{49} \pi t^8[/tex]

Step-by-step explanation:

Given;

S(r) = 4πr²

where;

S is the surface area of the balloon

r is the radius of the surface

The radius of the balloon at time "t" is given as;

[tex]r(t)= \frac{5}{7} t^4 \ \ \ t\geq 0[/tex]

The surface area of the balloon as a function of time "t" is calculated as;

[tex]S(t) = 4\pi (\frac{5}{7} t^4)^2\\\\S(t) = 4\pi (\frac{25}{49} t^8)\\\\S(t) = \frac{100}{49} \pi t^8[/tex]

Answer:

50%

Step-by-step explanation:

There are 12 months in a year.In the problem there are six months the number of cars his team sells more than 40%.=6/12x100%=0.5x100%=50%.Therefore his team sold 50%.

Hope this helped!

Answer:

0

Step-by-step explanation:

when the term has a coefficient of, it does not have to be written.

x- X/1

The sum of two opposites equals o

So the solution would be o

For initial 100 milligrams of a radioactive substance was if decreased by 2% in 8 hours, then half-life of the radioactive substance is 108.3 hours.

Rate of change is the change in one variable due to change in other.

Given the following:

Amount of a radioactive substance initially present=100mg

After 8 hours, mass decreased by 2%

Mass after 8 hours= 100-(2% of 100)

=100-(2*100/100)

=100-2

=98

The rate of decay is proportional to the amount of the substance present at time t.

Mathematically,

Let the amount of radioactive substance is A and at time t,

[tex]\dfrac d{dt}A\ \alpha\ A\\\\[/tex]

[tex]\dfrac d{dt}A= kA\\\\\\dA=kAdt[/tex]

On integrating both sides,

[tex]\int \frac {1}{kA}dA=\int dt\\\\[/tex]

[tex]\dfrac {ln A}{k}=t +ln \ c_1\\ln A =kt+k\ ln \ c_1\\[/tex]

On taking antilogarithm both sides,

[tex]e^{ln A} =e^{kt+k\ ln \ c_1\\A=e^{kt}e^{k\ ln \ c_1}\\A=e^{kt}e^{\ ln \ c_1^k}\\A=e^{kt}c_1^k \\[/tex]

Let, [tex]c_1^k=c[/tex]

[tex]A =e^{kt}c[/tex].................................1

At t=0, A=100

Substituting values in 1

[tex]100= e^0c\\c=100[/tex]

At t= 8, A=98

[tex]98=e^{k8}100\\0.98=e^{8k}\\8k=ln0.98[/tex]

k=-0.0064.

To determine the half time of the decay.

At half time A became A/2=50 mg

Substituting in 1.

[tex]50=e^{-0.0064t}100\\ln 0.5=-0.0064t\\t=\frac{ln 0.5}{-0.0064}\\t=108.3042\\t=108.3[/tex]....................................rounded to one decimal place.

Thus, The half-life of the radioactive substance is 108.3 hr.

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Answer:

An inscribed polygon might refer to any

polygon which is inscribed in a shape,

especially: A cyclic polygon, which is

inscribed in a circle

Answer:

A square

Step-by-step explanation:

Answer:

14+28

Step-by-step explanation:

Answer:

6x^{2}-54x=0

6x2−54x=0

Step-by-step explanation:

Answer:

41, 34, 105

Step-by-step explanation:

Given that :

Measure of angles :

6x -7; 3x +10; and 10x +25

Recall; sum of angles in a triangle is 180

(6x - 7) + (3x + 10) + (10x + 25) = 180

6x - 7 + 3x + 10 + 10x + 25 = 180

6x + 3x + 10x - 7 + 10 + 25 = 180

19x + 28 = 180

19x = 180 - 28

19x = 152

x = 8

Hence,

6x - 7 = 6(8) - 7 = 41

3x + 10 = 3(8) + 10 = 34

10x + 25 = 10(8) + 25 = 105

Answer:

A

Step-by-step explanation:

First you simplify both sides to get -2.4x+14.4 > 52.8

then you need to subtract the 14.4 from both sides giving -2.4x> 38.4

then divide both sides by -2.4 giving an answer of

x is less than or equal to -16 meaning you point to the left with a closed circle

Answer:

Step-by-step explanation:

1)

Three-Fourth

2)

Twelve Million One Hundred Thirty One Thousand Two Hundred Sixty Seven and Twenty Five Hundredths

3)

Seventy Five Percentage

4)

One Thousand Two Hundred and Fifty Six

5)

Twelve is to Twenty Six