Solve the math problem

Step-by-step explanation:

30 cal for 1 lb

x cal for 38.45 lbs

x = 38.45lbs × 30 cals

x = 1153.5 cals

a light is suspended at a height h above the floor. the illumination, i, at a point p is inversely proportional to the square of the distance, r, from the point p to the light and directly proportional to the cosine of the angle theta , I = k cos x / r² can be used to find the illumination at point p.

Light must be at the height of 7.07 for maximum illumination.

I = k cos x / r²

r² = h² + 10²

cos θ = h / [tex]\sqrt{h^{2} +10^{2} }[/tex]

then

I =  [tex]k \frac{h}{(h^{2} + 100)^{2/3}}[/tex]

on differentiating, we get,

[tex]\frac{dI}{dh} = k\frac{h^{2} + 100^{3/2 - 3h^{2}(h^{2} + 100 )^{1/2} } }{(h^{2} +100)^{3} }[/tex]

[tex]= k\frac{100 - 2h^{2} }{(h^{2} + 100)^{5/2} } \\\frac{dI}{dh} = 0\\ It gives that \\h = \sqrt{50} = 7.07\\on differentiating again,\\\frac{d^{2} I}{dh^{2} } = k \frac{(6h^{3} - 900h )}{(h^{2} + 100)^{7/2} }[/tex]

for h = 7.07,

[tex]\frac{dI^{2} }{dh^{2} } = -10267.6[/tex]

So , we can conclude that the light must be at the height of 7.07 for maximum illumination.

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The resultant of the parallel force passes, x=2.8888 in and y=-5.4444 in

Taking moment about 'y'

∈Mx=RXx

x=260/90

x=2.8888 in

Taking moment about 'x'

∈My=RXy

y= -490/90

y= -5.4444 in

When two forces of equal strength act in the same direction within the same plane, with the counterforce in the centre, this is known as a parallel force system.

A see-saw is an illustration of this. The fulcrum in the middle provides the counterforce to keep the seesaw in a neutral position while the children apply the two forces at the ends. The significant vertical forces on an aeroplane while it is in flight is another illustration (see image at right).

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Answer:

- 8 < x < - 4

Step-by-step explanation:

- 68 < 8x - 4 < - 36 ( add 4 to each interval )

- 64 < 8x < - 32 ( divide each interval by 8 )

- 8 < x < - 4

The zeroes of the polynomial functions are listed below:

Polynomials are algebraic constructions whose form is summarized by the following sum:

p(x) = ∑ cₙ · xⁿ, for n ∈ {0, 1, ..., m}

An alternative form to describe polynomials is using products of binomials of the form (x - r), where r is a root (zero) of the polynomial. The root of the polynomial is a value such that the result of the expression is equal to zero.

Then, we proceed to find the zeros of each polynomial function:

1) f(x) = 2 · x · (3 - x) · (x + 1). Roots: 2, 3, - 1.

2) f(x) = 2 · (x - 3) · (x + 2)² · (x - 1). Roots: 3, - 2 (multiplicity 2), 1

3) f(x) = x³ · (x - 2) · (x + 3). Roots: 0 (multiplicity 3), 2, - 3.

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[tex]110\cdot 10^{4x}=55\implies 10^{4x}=\cfrac{55}{110}\implies 10^{4x}=\cfrac{1}{2}\implies 10^{4x}=2^{-1} \\\\\\ \log\left( 10^{4x} \right)=\log\left( 2^{-1} \right)\implies 4x\log_{10}\left( 10 \right)=-1\log_{10}(2)\implies 4x(1)=-\log(2) \\\\\\ 4x=-\log(2)\implies x=-\cfrac{\log(2)}{4}\implies {\LARGE \begin{array}{llll} x\approx -0.08 \end{array}}[/tex]

The  total value of the uniform Aileen sold is x= 2260 on monthly Commission sells.

Given,

Let us assume the all little League uniform = x

Aileen first commission 10% of 2000$ in sales.

Aileen Second Commission 12% of (x-2000)$

Total Commission Aileen Earner = 10% ×2000 + 12% × (x-2000)

                                       231.2   = 0.1× 2000 + 0.12× (x-2000)

                                        231.2   = 200 + (0.12x - 240 )

                                        231.2   = 200 +  0.12x - 240

   After Transformation, we get

                                        0.12x = 231.2 - 200 +240

                                        0.12x = 271.2

                                               x = 271.2/.12

                                               x = 2260

Aileen Sell the total value of Lopez Sporting Goods Uniform is 2260.

So the final Answer is  x = 2260$.

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The word phrases given can be written in algebraic expressions as:

1. B. 4g

2. B. 6/(x + y).

"Product" means multiplication.

"The product of g and 4" can be written as an algebraic expression as: 4 × g = 4g.

"Quotient" means the result you get by dividing a number by another number.

"Sum" means addition, or what you get by adding two quantities together.

Therefore, "the sum of x and y" is written in algebraic expression as: x + y.

Thus, the quotient of 6 and (x + y) would be written in algebraic expression as: 6/(x + y).

Therefore, the word phrases given can be written in algebraic expressions as:

1. B. 4g

2. B. 6/(x + y).

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Wayne's actual act score is 18

A z-score tells you where the score lies on a normal distribution curve.

A standard deviation is a measure of how dispersed the data is in relation to the mean.

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

Given,

The mean = 21

Standard deviation =5

z-score = -0.6

We know z-score = (x-mean)/ Standard deviation

Substitute the values

-0.6 = [tex]\frac{x-21}{5}[/tex]

x-21 = -0.6 ×5

x-21 = -3

x=-3+21

x=18

Hence, the Wayne's actual act score is 18

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Answer:

volume of cylinder is πr²h so whatever your radius is then square it multiply by height. don't multiply by pi as it gives it to you in the answer

Answer:

1194 ....................... is the answer

The variables in the point-slope form of a line (x₁,y₁) is a given point on the line, m the slope of the line and (x,y) is any point on the line.

Given that the variables in the point-slope form of a line.

The general form of the equation of a line is y - y₁ = m (x-x₁) where  m is the slope of line, y₁ and x₁ is any point on the line

It is an equation of degree one x and y represent the coordinate of the point on the line represented in the coordinate plane

m = slope of the line

The general equation of a line is y = mx + c where

m = slope of line

(x₁ , y₁) = it is the given point on the line as data points are represented as (x₁,y₁) , (x₂,y₂) , (x₃,y₃) and so on

(x ,y) = it is any point line where x is any point on the x-axis and y is any point on y-axis

Hence, the variables in the point-slope form of a line where (x₁,y₁) is a given point on the line, m the slope of the line and (x,y) is any point on the line.

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Answer:

I think the answer is

Statement A

Step-by-step explanation:

Answer:

d. p+1

a negative 1 point something decimal plus one negative decimal.

gl sh awty

The temperature in degrees celcius in which bacteria cannot survive is greater than 3.66

This is a way of representing a variable with another

Given the inequality below;

q/5 C + 32 ≥ 120

Substitute C = 120oF

q/5(120) + 32  ≥ 120

24q + 32 ≥ 120

24q  ≥ 120 - 32

24q  ≥ 88

q ≥ 88/24

q ≥ 3.66

Hence the temperature in degrees celcius in which bacteria cannot survive is greater than 3.66

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The remainder theorem conclude given that F(-5)=17

When, x= -5

x+5=0

So, F(-5) = 17

According to the remainder theorem, the result of dividing p(x) by (x - a) is p. (a). According to the factor theorem, (x - a) can only be a factor of p(x) if f(a) = 0. It is used to locate the rest. A linear polynomial's status as a factor of the input polynomial is determined using this method.

The remainder theorem is used to calculate the remainder when a polynomial is split by a linear polynomial. We are aware that long division of polynomials can be used to find the remainder after dividing one polynomial by another. The remainder can instead be discovered using the remainder theorem.

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Answer:

Min = 0

Max = 51

M = 25.5

Q1 = 16.5

Q3 = 39

Hope this helps! <3

The algebraic expression that models the situation when Jenny had $105, but she is spending $13 per week is 105 - 13w.

Let the number of weeks be represented by x

Therefore, since Jenny had $105, but she is spending $13 per week, the appropriate expression will be:

= 105 - (13 × w)

= 105 - 13w

The expression is 105 - 13w.

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According to the question, to calculate break-even quantity with the given data. And the data is in dollars which is as follows:

Fixed cost (f(c)) = [tex]$1400[/tex] per week;

Variable cost (v(c)) = [tex]$2[/tex] per unit

Revenue = [tex]$6[/tex] per unit

Let us consider the break-even quantity to be ‘a’.

As per break-even point formula: Total costs = Total Revenue

And Total costs = Fixed cost + variable cost ;

      Total Revenue = (price per unit)(quantity sold)

Using above formulas, the above expression can be re-written as:

Fixed cost + variable cost = (price per unit)(quantity sold)

[tex]($1400)+($2a) = ($6a)[/tex]

[tex]4a = 1400[/tex]

[tex]a = 350[/tex]

Therefore, the break-even quantity is [tex]350[/tex] units.

What is the break-even quantity?

Break-even quantity in the firm is the incremental value which is used to sell in order to cover the cost of the marketing program or other companies investments. And in this, the total cost is equal to the total revenue.

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Answer: nice for her

Step-by-step explanation:

Answer:

(-5,5)

Step-by-step explanation:

Answer: y= 60x, y=50x

Step-by-step explanation:

Please Provide the whole question

Answer: [tex]\frac{3}{4s}[/tex]

Step-by-step explanation:

3s^2 / 4(s)^3=

3s^2 / 4s^3=

3/4 * s^2/s^3=

3/4 * s^(2-3)=

3/4 * s^(-1)=

3/4 * 1/s=

3*1 / 4s=3/(4s)

[tex] \large \bf \implies{32 {m}^{15} {n}^{10} }[/tex]

[tex]\bf \longrightarrow{(2m^{3}n^{2})^{5} } \\ \\ \bf \longrightarrow {2}^{5} \times ( {m}^{3})^{5} \times ( {n}^{2})^{5} \\ \\ \bf \longrightarrow32( {m}^{3})^{5}( {n}^{2})^{5} \\ \\ \bf \longrightarrow32 {m}^{15} {n}^{10} [/tex]

Note : We have used the two exponent rules:

[tex](1) \: \: \large \bf \boxed{ \bf \green{(ab)^{n} = {a}^{n} \times {b}^{n} }}[/tex]

[tex](2) \: \: \large \bf \boxed{ \bf \green{(a^{n})^{m} = {a}^{nm} }}[/tex]

Answer: -6.62 x 10^-8

Step-by-step explanation:

Answer:

4x + 3y = 6

A = 4

B = 3

C = 6

Step-by-step explanation:

A line have a function:

y = ax + b

Because the line has a slope of - 4/3

=> a = - 4/3

=> y = - 4/3 x + b

Because the line go through point (6; - 6)

=> - 6 = - 4/3 .6 + b

=> b - 8 = - 6

=> b = 2

=> The function of the line

y = - 4/3 x + 6

=> 3y = - 4x + 6

=> 4x + 3y = 6

Answer:

calculators are available

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

Without a graph, figure, or any other context the cost of grapefruit in 1995 in not related to the other years by any other facts or figures.

Answer: True, common sense dictates this.

Answer: true

Step-by-step explanation: