Solve and classify the given system of linear equations. p=5(q+2) p=q-3

Janet's total tax allowances for the year are $27,200.

The first step is to convert the monthly gross salary to the annual gross salary by multiplying it by 12.

The insurance allowance is computed by applying the rate to the annual gross salary.

The personal and insurance allowances are added to determine the total tax allowances.

Generally, tax allowances reduce the taxpayer's taxable income.

Gross salary per month = $24,000

Annual gross salary = $288,000 ($24,000 x 12)

Personal allowances per year = $20,000

National insurance = 2¹/₂%

= $7,200 ($288,000 x 2¹/₂%)

Total allowances for the year = $27,200 ($20,000 + $7,200)

Thus, Janet is entitled to a total tax allowance of $27,200 for the year.

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If the town has a population of 20000 and grows at 5% every year , then the time required for the population to reach 41600 is 15 years .

To find out how long it will take for the town's population to reach 41600, we can use the formula :

⇒ A = P(1 + r)ⁿ

Where:

A = final population of town , P = initial population o town

r = percent increase (as a decimal)

let n = number of years for population to reach 41600 .

We know the final population is 41600, the initial population is 20000, the percent increase is 5% = 0.05  and we have to solve for n.

Substituting the values ,

we get ;

⇒ 41600 = 20000(1 + 0.05)ⁿ  ;

⇒ 41600 = 20000(1.05)ⁿ  ;

⇒ 41600/20000 = (1.05)ⁿ  ;

taking "log" on both sides ,

we get ;

⇒ log(41600/20000) = n × log(1.05)  ;

⇒ n = log(41600/20000)/log(1.05)  ;

⇒ n = 15.0105 ≈ 15

Therefore ,  it will take approximately 15 years for the town's population to reach 41600, to the nearest tenth of a year.

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The exact value of the sine of angle R is equal to 1 / 2.

In this problem we find the representation of a right triangle, where two side lengths are known and the exact value of a trigonometric function must be found. First, determine the length of side PR:

PR = 72 cm - PQ

PR = 72 cm - 24 cm

PR = 48 cm

Second, determine the length of side PQ by Pythagorean theorem:

RQ = √[PR² - PQ²]

RQ = √[(48 cm)² - (24 cm)²]

RQ = 24√3 cm

Third, determine the exact value of a trigonometric function of angle R by definition of sine:

sin R = PQ / PR

sin R = (24 cm) / (48 cm)

sin R = 1 / 2

Fourth, determine the exact value of a trigonometric function of angle R by definition of cosine:

cos R = RQ / PR

cos R = (24√3 cm) / (48 cm)

cos R = √3 / 2

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The quotient of 6y^4 + 10y³ - 8y² by 2y is given as follows:

6y³ + 10y² - 4y.

The dividend is given as follows:

6y^4 + 10y³ - 8y²

The common factors are given as follows:

Hence the dividend can be simplified as follows:

2y²(6y² + 10y - 4).

Simplifying by 2y, the result of the quotient is given as follows:

y(6y² + 10y - 4) = 6y³ + 10y² - 4y.

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Answer: The answer is 5

Step-by-step explanation:

-3-(-8)

-3+8

5

Answer: 5

Step-by-step explanation:

First the negative 3 adds to 8. Because if you see “- -“ it will be +. So we just have -3 + 8 = 5

The amount of commission that Joan earns this month on sales will be $480.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

Joan earns an 8% commission on her sales this month Joan had $6000 in sales.

Let 'x' be the commission. Then the equation is given as,

x / $6,000 = 0.08

x = 0.08 · $6,000

x = $480

The amount of commission that Joan earns this month on sales will be $480.

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Average rate of change of the function F (x ) = 9/ -2 (x)-7. Average rate is -3, 9

The average rate at which one quantity changes in relation to another's change is referred to as the average rate of change function. A method that determines the amount of change in one item divided by the corresponding amount of change in another is known as an average rate of change function.

Divide the change in y-values by the change in x-values to determine the average rate of change. In order to determine changes in measurable parameters like average speed or average velocity, finding the average rate of change is extremely helpful.

f (x ) = -2

f (x) = 9/ -2 (-2)-7

      = 9 / 4 - 7

      =9 / -3

      = -3

f (x ) = -4

f (x) = 9/ -2 (4)-7

      = 9 / 8 - 7

      =9 / 1

      = 9

Average rate is -3, 9

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The required distance travelled by Benita is calculated to be 11/6 miles when the relation between the distances travelled by Karis and Benita is given.

This problem is related to the chapter fractions. The relation between the distances travelled by both the people is given, so that we can calculate the actual distance travelled by the second person.

Karis ran 3 2/3 miles on Monday.

It is said that Benita ran half of the distance ran by Karis.

So, the distance ran by Benita would be,

⇒ 3 2/3 × 1/2

⇒ 11/3 × 1/2

⇒ 11/6 miles

Thus, the distance travelled by Benita is calculated to be 11/6 miles when the relation between the distances travelled by Karis and Benita is given.

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In a relay race each friend run a distance of 0.52 miles.

The distance of the race divided by the runners' times will give you their average velocities.

We are given that

Total distance covered in a race = 3.12 miles

Total number of persons = 6

Each person runs equal parts of the race.

We have to find the miles run by each person.

To find the distance covered by each person we will divide the total distance by total number of persons who took part in a race.

Each person runs = Total distance/ Total number of persons

Each person runs= 3.12 / 6 miles

Each person runs = 0.52 miles

Hence, each person runs 0.52 miles.

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There are two phrases for how many sweet Sue and Tony have: 13-x and

Equivalent refers to the mathematical notion of equality between several terms and expressions with a comparable value.

Equivalent vs. Equal. Equivalent and equal are distinct terms in mathematics.

Equal means identical in every respect, as opposed to equivalent, which is similar but not the same.

18 + x/ 2 is the equivalent.

Sue has 18 delicious.

Tony has 18 delicious.

Sue gives Tony some candy. Sue Sweet is going to

18 - x Sue consumes 5 candies, thus his sweet will be

18 - 5 - x = 13 - x

Sue gave Tony x candy to take. His sweetness will

18 + x

Tony consumed half of his candy. His final treat will be

18 + x / 2

The phrase for Sue candies is 13 - x.

18 + x / 2 is the equation for Tony Sweets.

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Radon-222 was initially present in a sample of 3.82 mg. Only 0.375 mg of the radon-222 in the sample were still present after 11.46 days, after which three half-lives had gone.

As per the data given in the above question are as bellow,

A material has a half-life when it takes a particular length of time for half of it to disappear or change.

11.46 days have 3 half lives because 11.46 x 3.82 Equals 3.

We thus split the 3 mg sample in half three times.

3 ÷ 2 = 1.5

1.5 ÷ 2 = 0.75

0.75 ÷ 2 = 0.375

After 11.46 days, there will only be 0.375mg of radon-222 left.

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Answer:

No, they are not proportional

Step-by-step explanation

50*2=100

32*2=64, not 60

The volume of One cone held 1.1017.36 inches3 of water when it was full.

A cone's volume is determined using the following formula:

V = 1/3πr²h

R is the radius, and H is the height.

the aforementioned conditions

A cone's volume is determined using the following ,

V = 1/3πr²h

R is the radius, and H is the height.

the aforementioned conditions

r = 12/2 = 6in

h =27in

Discover the volume V = 1/3(3.14)(6)2*27

V = 1.1017.36

In light of this, one cone held 1.1017.36 inches of water.

One cone held 1.1017.36 inches of water.

The complete question is,

Construction cones were soaked with water while a project was underway due to a strong downpour. A cone has a 12 inch diameter and a 27 inch height.

How much water was used to fill each cone?

Put a decimal in the box for your response. Pi is equal to 3.14; in3

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The domain and range for the function for the maximum height of the rockets Kate fires is; h = 70·t - 16·t² are;

Domain; 0 ≤ t ≤ 4.375

Range; 0 ≤ h ≤ 39.06

A function is a rule that defines the relationship between input variables and output variables, such that the each value from the set of input variables are assigned to exactly on variable from the set of output variables.

The possible specified function in the question is; h = 70·t - 16·t², and the possible required details is the domain and range that best represent the situation.

The domain of the above function is the set of possible input (t) values, which is found by the time it takes the rocket to land after flight as follows;

At ground level, h = 0, therefore;

h = 70·t - 16·t² = 0

(70 - 16·t)·t = 0

A possible solution is therefore, t = 0

The other solution is found as follows;

(70 - 16·t) = 0

70 = 16·t

16·t = 70

t = 70/16 = 4.375

The other solution or time at which the rocket is at ground level is t = 4.375

The range is the set of possible h values, which is obtained as follows;

The maximum point of the quadratic function, f(x) = a·x² + b·x + c, is the point, x = -b/2·a. Therefore, comparison between the function, f(x) = a·x² + b·x + c, and h = 70·t - 16·t², we get;

a = -16

b = 70

c = 0

The maximum height reached, therefore is obtained at the point, at which; t = -70/(2 × (-16)) = 2.1875

The maximum height, [tex]h_{max}[/tex], is therefore;

[tex]h_{max}[/tex] = 70 × 2.1875 - 16 × 2.1875² =  76.5625

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Answer:

b/w 19 & 55

Step-by-step explanation:

average of four equally weighted 100-point tests,

mark has scored 90, 86, and 85 on the first three.

C average = 70 and 79

90+86+85+x = 4*70 = 280, so x=19

90+86+85+x = 4*79 = 316, so x=55

60% of the pieces of candy in the bowl are chocolate.

(15/25)*100 = 60%

hmmm proofs like these can be a bit circular kinda, let's do some rigamarole on the equations and we'll see if that works for a definition

[tex]\stackrel{\theta \textit{ is always in radian unit}~\hfill }{s=r\theta\implies \cfrac{s}{\theta }=r \hspace{5em}v=\cfrac{s}{t}\implies t=\cfrac{s}{v}\hspace{5em}\omega=\frac{\theta }{t}} \\\\[-0.35em] ~\dotfill\\\\ \omega=\cfrac{\theta }{t}\implies \omega=\cfrac{\theta }{~~ \frac{ s}{v } ~~}\implies \omega=\cfrac{\theta }{1}\cdot \cfrac{v}{s}\implies \omega=\cfrac{\theta v}{s}\implies s\omega=\theta v \\\\\\ \cfrac{s\omega}{\theta }=v\implies \cfrac{s}{\theta }\cdot \omega=v\implies \boxed{r\cdot \omega=v}[/tex]

Answer:

68888jours 9999999888

If A1 and A2, are mutually exclusive and exhaustive with P(A1)>0 and P(A2) >0, and B is an event in S. then P(B) = P(A1 ∩B) + P(A2∩ B). [TRUE]

The sets A and B are the sets of all objects that are members of set A and members of set B. In written notation form:

A ∩ B = {x | x ∈ A and x ∈ B}

Here's how to determine the separation of two sets:

One set which is another subset if A ⊆ B then A ∩ B = A and vice versa.

The sets are equal if A = B, then A ∩ B = (A = B).

Sets are mutually exclusive if A // B, then A ∩ B = … and vice versa.

The sets are not mutually exclusive.

The union of sets A and B is the set of all objects that are members of set A or members of set B. In written notation form:

A ∪ B = {x | x ∈ A or x ∈ B}

Here's how to determine the union of two sets:

A set that is a set in other parts if A ⊆ B, then A ∪ B = B and vice versa.

The set is equal if A = B then A ∪ B = (A = B).

Sets are mutually exclusive if A // B, then A ∪ B = {x | x ∈ A or x ∈ B} and vice versa.

The sets are not mutually exclusive if A ⊃⊂ B, then A ∪ B = {x | x ∈ A, x ∈ B or x ∈ (A ∩ B)}.

Your question is incomplete but most probably your full question was:

If A, and A, are mutually exclusive and exhaustive with P(A)>and P(A2) >0, and B is an event in s. then P(B) = P(ALB) + P(ANB). True False

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The equation of the graphed function for this problem is given as follows:

y = x³ - 6x² - 7x - 6.

The function for this problem is obtained using the Factor Theorem, as a product of the linear factors of the function.

The zeros of the function are given as follows:

Hence the linear factors are given as follows:

Then the function is given as follows:

y = a(x - 1)(x - 2)(x - 3).

In which a is the leading coefficient.

The y-intercept is at y = -6, hence the leading coefficient is given as follows:

-6a = -6

a = 1.

Hence the function is:

y = (x² - 3x + 2)(x - 3)

y = x³ - 6x² - 7x - 6.

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Answer: 10. 3

Step-by-step explanation: 4x3=12, ad 3x3 is 9 so all the sides of the triangle are multiplied by 3

A graph of the solution to this inequality a > -3 is shown on the number line attached below.

In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:

In this exercise, we would use an online graphing calculator to plot the given inequality a > -3 as shown on the number line (graph) attached below.

In conclusion, the circle on the number line (graph) is open because of the greater than (>) symbol and it increases to the right of the number line.

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Complete Question:

Find the solution to this inequality a > –3.

Answer:

N(-21,-20)

Step-by-step explanation:

We can apply midpoint formula to solve for endpoint (N):

[tex]\displaystyle{\text{Midpoint}= \left(\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2}\right)}[/tex]

Let [tex]\displaystyle{x_1 = 1}[/tex], [tex]\displaystyle{y_1 = 12}[/tex] and Midpoint = (-10,-4). Therefore:

[tex]\displaystyle{\left(-10,-4\right)= \left(\dfrac{1+x_2}{2}, \dfrac{12+y_2}{2}\right)}[/tex]

Solve x with -10 and y with -4:

[tex]\displaystyle{\text{N}\left(x_2,y_2\right) = \left(\dfrac{1+x_2}{2}=-10, \dfrac{12+y_2}{2}=-4\right)}\\\\\displaystyle{\text{N}\left(x_2,y_2\right) = \left(1+x_2=-20, 12+y_2=-8\right)}\\\\\displaystyle{\text{N}\left(x_2,y_2\right) = \left(x_2=-20-1, y_2=-8-12\right)}\\\\\displaystyle{\text{N}\left(x_2,y_2\right) = \left(x_2=-21, y_2=-20\right)}\\\\\displaystyle{\text{N}\left(x_2,y_2\right)=\left(-21,-20\right)}[/tex]

Therefore, the coordinate of N is (-21,-20)

If the lamp is 3.6 m above the ground, the length of her shadow is 1.2 m.

In algebra proportionality is equality between two ratios. In the mathematical expression a/b = c/d, a and b are in the same proportion as c and d.

Height of the girl = 0.9 m.

Height of the lamp = 3.6 m.

Distance between the lamp and the girl = 4.8 m.

Let the length of her shadow = x m.

From proportionality relation:

3.6 : 4.8 = 0.9 : x

3.6/4.8 = 0.9/x

3.6x = 4.8 × 0.9

x  = (4.8 × 0.9) ÷ 3.6

x = 1.2

Hence, the length of her shadow is 1.2 m.

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A number line that models the expression 1/8 - (-3/4) is shown in the image attached below.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

Generally speaking, a number line primarily increases in numerical value towards the right and decreases in numerical value towards the left.

Next, we would evaluate and add the given numbers together as follows:

Number = 1/8 - (-3/4)

Number = 1/8 + 3/4

Number = 7/8

In conclusion, you would start at 1/8 on the number line and move 3/4 places to the right.

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In the essay “A Modest Proposal”, The author includes the quote to give the reader an objective summary of how dangerous the conditions were at Mauna Loa.

Jonathan Swift, a satirist, suggested jokingly in an essay titled "A Modest Proposal" from 1729 that the people of Ireland sell their children as food. A radical or shocking notion is frequently introduced in an ironic way using the term a modest suggestion.

Swift's essay, which is hailed as a masterwork of irony, is officially titled "A Modest Proposal for Preventing the Children of the Poor People in Ireland from Being a Burden to Their Parents or Country, and for Making Them Beneficial to Their Public."

When a proposal takes the form of an essay, it typically proposes a fix for a social or political issue. The adjective "modest" denotes reason or modesty. Because the idea is genuinely absurd, it is humorously used in the title of "A Modest Proposal."

A modest proposal is frequently used in jest to make a point by taking something to its logical conclusion, which highlights a problem. Swift's article, which at the time caused controversy, has since become a satirical mainstay and has influenced a lot of authors.

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Answer:

first hand account

Step-by-step explanation:

I got a 100 on the test

The increase in earnings brought on by producing one extra unit is known as the marginal profit. The proper domain for functions is the integers (0, 1, 2, ...).

By dividing marginal revenue by marginal cost, one can compute marginal profit. Because it can help determine whether to raise or lower the level of output, marginal profit analysis is useful.

Any quantity of output below the one at which marginal profit equals zero has a positive marginal profit, meaning that profit can be increased by producing more of that quantity. Conversely, any quantity of output above the one at which marginal profit equals zero has a negative marginal profit, meaning that profit can be increased by producing less of that quantity.

A company that manufactures and sells shirts. Daily profit of...

A company that manufactures and sells shirts. The daily profit the company makes depends on the number of shirts sold. The profit in dollars if a company sells x shirts can be found using the function f(x)=7x-40. Locates and interprets given function values ​​to determine the appropriate domain for the function.

f(-10) = -110, which means that if the company sells -10 shirts, it will make a profit of -$110. This interpretation makes no sense in the context of the problem.

f(10) = 26.5, so if the company sells 9.5 of his shirts, he makes a profit of $26.5. This interpretation makes no sense in the context of the problem

f(9.5) = 26.5, so if the company sells 9.5 shirts, it makes a profit of $26.5. This interpretation makes no sense in the context of the problem.

Therefore, based on the above observations, it is clear that the proper domain for functions is the integers (0, 1, 2, ...).

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By applying the Golden Ratio rule, the width of the painting is equal to 12.5 inches.

In Mathematics, a proportion simply refers to an equation which is typically used to represent the equality of two (2) ratios.

This ultimately implies that, proportions is a mathematical operation which can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.

By applying the Golden Ratio rule, the width of the painting can be calculated as follows;

20/x = 8/5

Cross-multiplying, we have the following:

8x = 20 × 5

8x = 100

x = 100/8

x = 12.5 inches.

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