In a public opinion servey, 60 out of a sample of 70 high income voters and 90 out of a sample of 100 low income voters supported the introduction of a new national security tax

The size of the angle between AB and the base of the pyramid 27.9⁰

You should know that a pyramid is a polyhedron with a base that is a polygon

using the figure, The volume of the pyramid is 1/3 Bh

the area of the pyramid is  12*D = 144 cm²

= 1/3 * 14 * h = 768

Making h the subject of the formula

h= 16 cm

BO = √2 * 12/2 ÷6√2

this implies that Tan∅ = BD/BO = 6√2/16

Tan ∅ = 3√2/8

∅= 27.9⁰

In conclusion the size of the angle is 27.9⁰

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The inequality which correctly supports Fabian's claim as described above is; 0.25 × 100 > 0.1 × 90.

The inequality which shows that Fabian's claim as described above is incorrect is; 0.25 × 100 > 0.1 × 1000.

First, in a bid to write the given word phrase which happens to be Fabian's claim as an algebraic expression; we have that;

Let x be the first number and let y be the second number.

Therefore, we have that;

( 25% × x ) > ( 10% × y )

0.25x > 0.1y

On this note, the complete inequality which supports Fabian's claim is when x = 100 and y = 90 so that we have;

0.25 × 100 > 0.1 × 90; 25 > 9 which holds true.

However, The inequality which shows that he is incorrect is; when x = 100 and y = 1000 so that we have;

0.25 × 100 > 0.1 × 1000; 25 > 100 which does not hold true.

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Therefore, a)= (x^ n+ y^ n) is bounded.
b)  limn→ ∞ I n f (x^ n+ y^ n)  ≥  limn→ ∞ I n f(x ^ n)+  limn→ ∞ I n f(y^ n)                                          

Step-by-step explanation:

a) Let (x^ n) and (Y^ n) be bounded sequences, so
∃M>0 such that |x^ n|≤ M ∀n ∈ N
∃M>0 such that |Y^ n|≤ M ∀n ∈ N

Consider
|x^ n| ≤ |x^ n|+|Y^ n|
≤M +M'
=P          (Take p=M+M'>0)

Thus, |x^ n + y^ n|≤p,  ∀n ∈ N.
Therefore, (x^ n+ y^ n) is bounded.


b) Let (x) be a bounded sequence so ( x^ n) is bounded below by k.
Then for each n ∈ N, the set x^ n=(x^ n,x^n+1,....) is bounded below by k.
By completeness axion X^ n has infimum m^ n and the sequence (m^ n) being a increasing sequence is either convergent or divergent to ∞
If(m^ n) is convergent then limn→ ∞m^ n is called the limit infimum of (x^ n).

Thus, limn→ ∞I n f( x^ n)=limn→ ∞ I n f (x^ n,x^n+1,...)
∴
Similarly, m'^ n=I n f (y^ n, y^ n+1...)
Consider
I n f (x^ n+ y^ n, x^n+1 +y^n+1..) ≥ I n f (x^ n, x^ n+1...)+I n f ( y^ n, y^ n+1..)
I n f(x^ n+ y^ n, x^n+1 +y^n+1...) ≥ m^ n+ m'^ n
We have
= limn→ ∞ I n f (x^ n+ y^ n)= limn→ ∞ ( x^ n +y^ n, x^n+1 +y^n+1...)
=≥ limn→ ∞(m^ n+ m')
= limn→ ∞m^ n+ limn→ ∞m'^ n
= limn→ ∞ I n f (x^ n) + limn→ ∞ I n f (y^ n)
∴Therefore
 limn→ ∞ I n f (x^ n+ y^ n)  ≥ limn→ ∞ I n f(x ^ n)+  limn→ ∞ I n f(y^ n)



INCOMPLETE QUESTION:

Let {xn} and {yn} be bounded sequences. a) Show that {xn +yn} is bounded. b) Show that (lim n→∞inf xn) + (lim n→∞ inf yn) ≤ lim n→∞inf (xn +yn). Hint: Find a subsequence {xni + yni } of {xn + yn} that converges. Then find a subsequence {xnmi } of {xni } that converges. Then apply what you know about limits. c) Find an explicit {xn} and {yn} such that (lim n→∞ inf xn) + (lim n→∞infyn) < lim n→∞ inf (xn +yn). Let {xn} and {yn} be bounded sequences (from the previous exercise we know that {xn +yn} is bounded). a) Show that (lim sup n→∞ xn) + (lim sup n→∞ yn) ≥ lim sup n→∞ (xn +yn). Hint: See previous exercise. b) Find an explicit {x n} and {yn} such that (lim sup n→∞ xn) + (lim sup n→∞ yn) > lim sup n→∞ (x n +yn).


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The price-demand relationship can be modelled in a linear function as     y = -0.033x

A linear function is a mathematical equation that graphs as a straight line. It is of the form y = mx + b, where m is the slope of the line and b is the y-intercept. Examples of linear functions include y = 3x + 5 and y = -2x + 4.

We can also use a proportional relationship to determine the price-demand relationship.

y = kx

We can also use a linear function to determine.

y = mx + c

m = slope

m = y₂ - y₁ / x₂ - x₁

m = 43 - 83 / 1600 - 400

m = -0.033

The relationship can be written as

y = -0.033x

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Answer:

Equation: y=-8x+19

Step-by-step explanation:

An example to support Reta's statement is that 50% of -100 is more than 75% of -100.

An example to negate Reta's statement is that 50% of 100 is less than 75% of 100.

A percentage simply has to do with the value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100

An example to support Reta's statement is that 50% of -100 is more than 75% of -100. In this case, -50 is more than -75.

An example to negate Reta's statement is that 50% of 100 is less than 75% of 100. In this case, 50 is less than 75.

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Answer:

f(3) 27

Step-by-step explanation:

To find the value of f(3) when f(x) = x^2 + 6x, we can plug the value of 3 into the expression for f(x). This gives us:

f(3) = 3^2 + 6(3)

= 9 + 18

= 27

Therefore, f(3) = 27.

The number of stereos which can be produced in a week lies in the interval  10 < x < 16

Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.

Time to assemble a television = 6 hours

Time to assemble a stereo = 5 hours

Minimum time factory workers can supply for assembly = 175 hours per week

Maximum time factory workers can supply for assembly = 275 hours per week

Let x be the number of stereos manufactured in a week.

Then 2x will be the number of televisions manufactured in a week.

Time to assemble x stereos = 5x

Time to assemble 2x television = 6 × 2x = 12x

Total time taken for stereo and television per week = 5x + 12x = 17x

We get inequality,

175 < 17x < 275

175 / 17 < x < 275 / 17

10.3 < x < 16.2

≈ 10 < x < 16

Hence the number of stereos manufactured is  10 < x < 16.

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The length of the real airplane is equal to 45 feet.

In Geometry, a scale factor can be defined as the ratio of two corresponding side lengths or diameter in two similar geometric figures such as airplanes, which can be used to either horizontally or vertically enlarge (increase) or reduce (decrease or compress) a function that represents their size.

Mathematically, the scale factor of a geometric figure can be calculated by dividing the dimension of the image by the dimension of the pre-image (original figure).

Since the scale factor is 1 in:9 ft, the length of the real airplane can be calculated by multiplying the given scale factor by 5 as follows;

Length of real airplane = (1 in : 9 ft) × 5

Length of real airplane = 5 in : 45 ft

Length of real airplane = 45 feet.

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Complete Question:

In a scale drawing the length of the airplane is 5 inches. What is the length of the real airplane? Scale factor: 1 in:9 ft

The value of y when x is 40 is given as follows:

y = 400.

It means that 40 copies of the book were purchased, each at $100.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

The variables in this problem are given as follows:

Each book sells for $10, hence the constant is given as follows:

k = 10.

Then the equation is given as follows:

y = 10x.

The value of y when x is 40 is given as follows:

y = 10 x 40

y = 400.

The problem is incomplete, hence we suppose that we have that each book sells for $10, and then model a proportional relationship with it.

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Zoe would have saved $116 in 6 weeks and the expression of what Zoe would have saved in w weeks would be 80 + 6w.

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1.

For example, x² is a variable raised to the second power, but x is a variable raised to the first power.

5 is an example of a constant.

2x - y + 3 is a linear expression.

Total cost = $80 + $6(6)

Total cost = $116

The expression = 80 + 6w

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Answer:

C

Step-by-step explanation:

The given expression is illustrated as:

15cd-45c2d

This will be:

15cd-45c2d = 3cd(5-15c)

Note: It is important to note that factors are the numbers that divide evenly into another number that is given.

on solving the provided question, we can say that by equation we Consequently, he will sell 16 automobiles at this price.

A number, a variable, or a mix of both, combined with certain operation symbols, make up an expression. An equal sign is used to denote the separation of two expressions in an equation.

Here,

Given: Number of cars sell in a day = 12

Price of a car =[tex]$23,000[/tex]

For each $300 price reduction dealer can sell two more cars per day.

Solution: Let there be x unit 300 price reduction

2x unit increase in sale of car

[tex]|R(x)=(15000-300x)(12+2x)[/tex]

Cost

[tex]|C(x)=1000+12000 (12+2x)[/tex]

Profit

[tex]|P(x)=(15000-300x)(12+2x)-1000+12000 (12+2x)\\15000(12+2x)–12000 (12+2x)-300x(12+2x)-1000\\=180000-144000+30000x-24000x -3600x -600-1000\\=36000+2400x-600 = P'(x)=-1200x +2400 = P"(x)=-1200[/tex]

For critical points

[tex]P'(x)=0= -1200x + 2400=0= x=2[/tex]

Since P"(x) <0at x = 2it is max profit 12+2x=12+2(2)=16

16cars per day he will sell

[tex]Price = 15000-300*16 = $10200[/tex]

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If a, b, c be the three sides of a triangle , let α, β, γ be the angles opposite them and if a² + b² = 1989c² , the value of [tex]\frac{Cot \gamma}{(Cot \alpha + Cot \beta)}[/tex] = 994 .

Let the sides of the triangle ABC be a , b and c .

let h be the altitude of the triangle that meets the side AB at point c ,

From the figure ,

we can write , [tex]Cot\alpha + Cot\beta = \frac{c}{h}[/tex] ;

let area of triangle ABC  = K ,

So , h = 2K/c ,

⇒ [tex]Cot\alpha + Cot\beta = \frac{C^{2} }{2K}[/tex]  ,.....equation(1)

By following the Similar pattern  we can write the similar equations ,

we have ,

⇒  [tex]Cot\beta + Cot\gamma = \frac{a^{2} }{2K}[/tex]   ,.....equation(2)

⇒  [tex]Cot\gamma + Cot\alpha = \frac{b^{2} }{2K}[/tex]  ,....equation(3)

On adding the equation(2) and equation(3) and subtracting it from the equation(1) , and dividing it by 2 ,

we get ,

⇒   [tex]cot\gamma = \frac{a^{2} + b^{2} - c^{2} }{4K}[/tex];

So , the value of [tex]\frac{Cot \gamma}{(Cot \alpha + Cot \beta)}[/tex]  =  [tex]\frac{\frac{a^{2} +b^{2} -c^{2}}{4K} }{\frac{c^{2} }{2K} }[/tex];

⇒  [tex]\frac{a^{2} +b^{2} -c^{2} }{2c^{2} }[/tex] ;

On substituting the value of a² + b² = 1989c² ,

we get ,

⇒  [tex]\frac{1989c^{2} - c^{2} }{2c^{2} }[/tex];

⇒ 1988/2 = 994 .

Therefore , the value of [tex]\frac{Cot \gamma}{(Cot \alpha + Cot \beta)}[/tex]  = 994 .

The given question is incomplete , the complete question is

Let a, b, c be the three sides of a triangle, and let α, β, γ be the angles opposite them. If a² + b² = 1989c² , find the value of [tex]\frac{Cot \gamma}{(Cot \alpha + Cot \beta)}[/tex] .

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We use the law of cosines to find the angles in the triangle, substitute [tex]$a^2+b^2=1989c^2$[/tex], and add them together to get[tex]$\cos\alpha + \cos\beta + \cos\gamma = 1989$.[/tex]

We can use the law of cosines to find the angles in the triangle:

[tex]$$\cos\alpha = \frac{b^2 + c^2 - a^2}{2bc}$$[/tex]

[tex]$$\cos\beta = \frac{a^2 + c^2 - b^2}{2ac}$$[/tex]

[tex]$$\cos\gamma = \frac{a^2 + b^2 - c^2}{2ab}$$[/tex]

Substituting, we get:

[tex]$$\cos\alpha = \frac{1989c^2 - c^2}{2bc}$$[/tex]

[tex]$$\cos\beta = \frac{1989c^2 - b^2}{2ac}$$[/tex]

[tex]$$\cos\gamma = \frac{1989c^2 - a^2}{2ab}$$[/tex]

Therefore,

[tex]$$\cos\alpha + \cos\beta + \cos\gamma = \frac{1989c^2}{2bc} + \frac{1989c^2}{2ac} + \frac{1989c^2}{2ab} = \frac{1989c^2}{2bc} + \frac{1989c^2}{2ac} + \frac{1989c^2}{2ab} = 1989$$[/tex]

We can use the law of cosines to find the angles in the triangle: [tex]$\cos\alpha = \frac{b^2 + c^2 - a^2}{2bc}$[/tex], [tex]$\cos\beta = \frac{a^2 + c^2 - b^2}{2ac}$[/tex], and [tex]$\cos\gamma = \frac{a^2 + b^2 - c^2}{2ab}$[/tex]. Since [tex]$a^2+b^2=1989c^2$[/tex], we can substitute this value into the equations to get [tex]$\cos\alpha = \frac{1989c^2 - c^2}{2bc}$, $\cos\beta = \frac{1989c^2 - b^2}{2ac}$, and $\cos\gamma = \frac{1989c^2 - a^2}{2ab}$[/tex]. The cosines of the angles of a triangle can be found using the law of cosines. We are given that [tex]$a^2 + b^2 = 1989c^2$[/tex], so we can use this to find the cosines of the angles of the triangle. We substitute this into the law of cosines and solve for the cosines of the angles, which gives us [tex]$\cos\alpha$[/tex], [tex]$\cos\beta$[/tex], and [tex]$\cos\gamma$[/tex]. We then add these cosines together to find the final value of [tex]$\cos\alpha + \cos\beta + \cos\gamma$[/tex], which is 1989.

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The complete question is

Let $a$, $b$, $c$ be the three sides of a triangle, and let $\alpha$, $\beta$, $\gamma$, be the angles opposite them.If $a^2+b^2=1989c^2$, find the value of $\cos\alpha+\cos\beta+\cos\gamma$.

Answer:

Step-by-step explanation:

so hard bro !!!

The width of the given rectangle would be 7 units.

Let the length of the rectangle = a

let the width = b

length of a rectangle is the sum of the width plus 2.

Thus;

a = b + 2

area of rectangle is;

A = length * width

Thus;

A = b(b + 2)

but A = 63 units

b(b + 2) = 63

b² + 2b - 63 = 0

(b + 9)(b - 7) = 0

b = 7

a = 7 + 2

therefore;

a = 9

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Answer:

x= -4

Step-by-step explanation:

[tex]x = \frac{ - 8 + \sqrt{ {8}^{2} - 4 \times 1 \times 16 } }{2 \times 1} [/tex]

a=1

b=8

c=16

Answer:

  9. d) y = 3/2x +1

  10. b) y = x +4/3

Step-by-step explanation:

You want to rewrite the given linear equations into slope-intercept form.

Essentially, these problems require you solve each equation for y to put it into "y =" form. The steps generally are to collect terms, subtract the x-term, and divide by the y-coefficient.

The parentheses can be eliminated, and the x-terms added to give ...

  2 = -3x +2y

Adding the opposite of the x-term to both sides, we have ...

  3x +2 = 2y

Dividing by 2 gives the desired form:

  y = 3/2x +1

Adding the x-terms, we have ...

  4 = -3x +3y

Adding the opposite of the x-term gives ...

  3x +4 = 3y

Dividing by 3 puts the equation into the desired form:

  y = x +4/3

Answer:

Step-by-step explanation:

$22.1

The required coordinates of E are (2 + 2 √(13), -2) and the coordinates of M are (-4, 2 + 2 √(13)).

The midpoint formula states that the coordinates of the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) are given by the formula (x₁ + x₂)/2, (y₁ + y₂)/2.

Since G and O are the midpoints of the sides of square GEOM, the length of each side of the square is the distance between G and O. The distance between the two points can be calculated using the distance formula:

distance = √((x₁ - x₂)² + (y₁ - y₂)²)

Plugging in the coordinates of G and O, we get:

distance = √((-4 - 2)²+ (2 - (-2))²)

distance = √(6² + 4²)

distance = √(36 + 16)

distance = √(52)

distance = 2 √(13)

Thus, the length of each side of the square is 2 √(13).

To find the coordinates of E, we need to move 2 √(13) units to the right of G. Therefore, the coordinates of E are (2 + 2 √(13), -2).

To find the coordinates of M, we need to move 2 √(13) units above O. Therefore, the coordinates of M are (-4, 2 + 2 √(13)).

So the coordinates of E are (2 + 2 √(13), -2) and the coordinates of M are (-4, 2 + 2 √(13)).

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[tex]~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] ~\dotfill[/tex]

[tex](-16)^{\frac{1}{4}}\implies \sqrt[4]{-16}\implies \sqrt[4]{-2^4}\implies \sqrt[4]{-1\cdot 2^4}\implies \sqrt[4]{-1}\cdot \sqrt[4]{2^4} \\\\\\ (-1)^{\frac{1}{4}}\cdot 2\implies (-1)^{\frac{1}{2}\cdot \frac{1}{2}}\cdot 2\implies ((-1)^{\frac{1}{2}})^{\frac{1}{2}}\cdot 2\implies (\sqrt{-1})^{\frac{1}{2}}\cdot 2 \\\\\\ (i)^{\frac{1}{2}}\cdot 2\implies {\Large \begin{array}{llll} 2\sqrt{i} \end{array}}[/tex]

Answer: it’s is D

Step-by-step explanation: I’d you’re allowed to use a calculator just plugging In the years after the deposit for x will give you your answer. If not just by looking u can tell that it’s not going up by 130 every year so a and b are out and it’s not decreasing so c is out.

As a result, the moment in time formation linear equation for something like the line traveling through points (1, 3) and containing a slope of 2 is y-1 = 2. (x-3).

A linear function is one that satisfies the algebraic formula y=mx+b. m is the y-intercept, while B is the slope. The foregoing sentence is sometimes referred to as a "linear regression with 2 factors" when y and x contain variables. Bivariate linear equations are two-variable linear equations. Example of linear equations include  y=x+z and x+ 3z =16. An equation is described to as linear if it has the pattern y=mx+b, with m denotes the slope and

Here,

In this case, Y = mx + c.

(y- y₁) = m(x - x₁)

where,

X and x1 are the coordinates for the x-axis.

Y and Y1 are the coordinates for the y-axis.

m is the slope of the line, and

The letter c can stand in for the y-intercept.

To generate the equation for said passes through (1, 3), with a slope of 2, just swap out the slope and point values in the general equation.

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

The line passing via (1, 3) and bearing the slope of 2 is therefore given by the equation y-1 = 2 in point-slope form. (x-3).

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The value for the expression q - 17 at q =-17 will be -24. The correct option is D.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the expression is q - 7 and the value of q is -17. The expression will be solved as below,

E = q - 7

E = -17 - 7

E = -24

Hence, the solution for the expression is -24.

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The equation in the form a(x + b)² + c is 1(x + 4)² - 11, where a = 1, b = 4, c = -11.

The coordinates of the turning point of the curve y = -2x² - 16x - 10 are (2, -15)

A) In order to write - 2x² - 16x - 10 in the form a(x + b)² + c, we need to complete the square.

First, we'll divide the equation by -2: x² + 8x + 5 = 0

x² + 8x  = -5

Then we add (8/2)² = 16 to both sides and then we factor out the x² by adding and subtracting (8/2)² = 16 to the right side:

x² + 8x + (4)²  = -5 + 16

(x + 4)² = 11

1(x + 4)² - 11

Now we have the equation in the form a(x + b)² + c, where a = 1, b = 4, c = -11

b) The turning point of the curve y = -2x² - 16x - 10 is the vertex of the parabola.

The coordinates of the vertex of a parabola in the form a(x + b)² + c is

(-b/2a, c – (b²/4a))

so for the given equation, the coordinates of the turning point are (2, -15)

Therefore, the coordinates of the turning point of the curve y = -2x² - 16x - 10 are (2, -15)

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Answer: 1/4

Step-by-step explanation:

1/4 = 0.25

4/12 = 0.33

3/8 = 0.375

2/6 = 0.33

Answer:7.5in cubed

Step-by-step explanation:

ok this should be easy

3x1=3

3x2.5=7.5

so it should be 7.5 cubic inches cubed as this is a volume question :)

Step-by-step explanation:

3x1=3

3×2.5=7.5

So it will be 7.5

The graph of the equation is a straight line.

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given that, a system of equation, y = x/3+3/2

Solving,

Put x = 0,

y = 3/2 = 1.5

(0, 1.5)

Put y = 0

0 = x/3 + 3/2

x/3 = -3/2

x = -1.5 × 3

x = -4.5

(-4.5, 0)

Therefore, we will put the coordinates in the graph, (refer to graph attached)

Hence, the graph of the equation is a straight line.

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Proportional functions seem to be linear functions that contain the origin and can be written as y is kx.

Here all the 4 functions are not proportional because it does not satisfy the condition y = kx.

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