If one of the 255 subjects is randomly selected, find the probability that the person is over 40 and prefers cola.

Answer:

13

Step-by-step explanation:

We can multiply both the whole equation by [tex]c^2-7c-18[/tex]. This is the LCM of all of the denominators. Notice that when [tex]c^2-7c-18[/tex] is factored, we obtain [tex](c - 9)(c+2)[/tex].

[tex]\frac{5}{c-9}\times(c^2-7c-18)=\frac{5}{c-9}\times(c-9)(c+2)=5(c+2)=5(c)+5(2)=5c+10[/tex]

An easier approach is to multiply each individual fraction like so:

[tex]\frac{5c-2}{c^2-7c-18}\times(c^2-7c-18)=5c-2[/tex]

[tex]\frac{3}{c+2}\times(c^2-7c-18)=\frac{3}{c+2}\times(c-9)(c+2)=3(c-9)=3c-27[/tex]

Then, we add them:

[tex]5c-2+(3c-27)=5c-2+3c-27=8c-29[/tex]

Therefore the whole equation is now:

[tex]5c+10=8c-29[/tex]

Subtract 5c from both sides:

[tex]10=3c-29[/tex]

Add 29 to both sides:

[tex]39=3c[/tex]

Divide both sides by 3

[tex]c=13[/tex]

[tex]\frac{5}{13-9}=\frac{5(13)-2}{169-91-14}+\frac{3}{13+2}\\\\\frac{5}{4}=\frac{63}{60}+\frac{3}{15}\\\\\frac{5}{4}=\frac{21}{20}+\frac{1}{5}\\\\\frac{5}{4}=\frac{21}{20}+\frac{1}{5}\\\\\frac{5}{4}=\frac{21}{20}+\frac{4}{20}\\\\\frac{5}{4}=\frac{25}{20}\\\\\frac{5}{4}=\frac{5}{4}\Rightarrow Correct![/tex]

Therefore,

c = 13

Answer:

Step-by-step explanation:

1/3 + 1/3 x 1/3 / 1/3 - 1/3

= 1/3 + 1/3 x 1/1 -1/3

= 1/3 + 1/3 - 1/3

= 2/3 - 1/3

= 1/3

Answer:

5/9.

Step-by-step explanation:

1/3 + 1/3 * 1/3 / 1/3 - 1/3 * 1/3

= 1/3 + 1/3 * 1 - 1/3 * 1/3

= 1/3 + 1/3 - 1/3 * 1/3

= 2/3 - 1/9

= 5/9.

Step-by-step explanation:

that is a huge gas tank. that car is practically a tank.

the volume of the gas tank is

4×3×3 = 36 m³

I assume you use liters for liquid mass.

remember

1 meter (m) = 100 centimeter (cm)

10 cm = 1/10 m = 1 decimeter (dm)

1 liter = 10×10×10 cm³ = 1000cm³ = 1 dm³

1 m³ = 10×10×10 dm³ = 1000 dm³ = 1000 liters

so, his gas tank contained 36,000 liters.

he used the 36,000 liters in 45 hours.

his corresponding rate of gas consumption was

36,000 liters / 45 hours = 800 liters / hour

a) The coordinates of point A that meet the linear equation y = 2 · x + 7 are A(x, y) = (0, 7).

b) The equation of the line parallel to the line y = 2 · x + 7 is the line y = 2 · x + 3.

c) The coordinates of the midpoint of line segment BC is M(x, y) = (1, 7).

Herein we find three cases related to the linear equation y = 2 · x + 7. a) We need to determine the coordinates of point A, the y-coordinate can be determined by evaluating the function:

y = 2 · 0 + 7

y = 0 + 7

y = 7

The coordinates of point A that meet the linear equation y = 2 · x + 7 are A(x, y) = (0, 7).

b) Two lines are parallel to each other whether both have the same slope but different intercept. Then, the new line is of the form:

y = 2 · x + b

Now we proceed to find the intercept of the line:

b = y - 2 · x

b = 3 - 2 · 0

b = 3

The equation of the line parallel to the line y = 2 · x + 7 is the line y = 2 · x + 3.

c) The coordinates of point C is:

y = 2 · 2 + 7

y = 11

If we know that B(x, y) = (0, 3) and C(x, y) = (2, 11), then the coordinates of the midpoint of BC is:

M(x, y) = 0.5 · B(x, y) + 0.5 · C(x, y)

M(x, y) = 0.5 · (0, 3) + 0.5 · (2, 11)

M(x, y) = (1, 7)

The coordinates of the midpoint of line segment BC is M(x, y) = (1, 7).

The statement presents typing mistakes and omissions, complete form is shown below:

a) The line of y = 2x + 7 meets the y-axis at A, where x = 0. Write down the co-ordinates of A.

b) A line parralel to y = 2x + 7 passes through B(x, y) = (0,3) Find the equation of this line.

c) C is the point on the line y = 2x + 7 where x = 2. Find the the co-ordinates of the midpoint of BC.

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Answer:

3,500 people

Step-by-step explanation:

10% of 35,000 is the same as .10 × 35,000, or 3,500.

Answer: Reagan's pay was increased by 62%

Step-by-step explanation:

First, lets find the difference between the two pays:

$347,247 - $214,350 = $132,897

Let 214350 = 100%

Dividing 132,897 by 214350 to find the percent increase

[tex]\bold{\frac{132,897}{214,350} }=0.62\times100=62[/tex]

Therefore, Reagan's pay was increased by 62%

Answer:

40 + 5r

usually you put the one with the variable infront

so 5r+40

Step-by-step explanation:

5(8+r)

5*8 + 5*r

40 + 5r

Answer:

parallel

Step-by-step explanation:

//

Answer: these lines are parallel.

Step-by-step explanation:

[tex]\displaystyle\\\left \{ {{6x-2y=-2} \atop {y=3x+12}} \right. \\\\ \left \{ {{6x-2y+2=0} \atop {y=3x+12}} \right. \\\\ \left \{ {{6x+2=2y\ |:2} \atop {x=2}} \right. \\\\\left \{ {{3x+1=y} \atop {y=3x+12}} \right.\\ \\\left \{ {{y=3x+1} \atop {y=3x+12}} \right. \\So,\ these\ lines\ are\ parallel.[/tex]

Answer:

By definition, angles A and 1 are corresponding angles and angles B and 1 are consecutive angles. By the corresponding angles postulate, angles A and 1 are congruent, and by the consecutive angles theorem, angles B and 1 are supplementary. By the definition of supplementary angles, measures of angle B and 1 add up to 180 degrees (m<B + m<1 = 180). By definition of congruent angles, angles A and 1 have same measurement (m<A = m<1). By substitution property of equality, measures of angles A and B add up to 180 degrees (m<A + m<B = 180). By definition of supplementary angles, angles A and B are supplementary.

If the initial value problem is [tex]y^{11} -8y^{1} -15y=0[/tex] and [tex]y^{1}(0) =1[/tex],y(0)=0 then y(t)=[tex](e^{3t} -e^{5t} )/2[/tex].

Given the initial value problem be   [tex]y^{11} -8y^{1} -15y=0[/tex]and  [tex]y^{1}(0) =1[/tex],y(0)=0.

We are required to find the solution of the given initial value problem.

Laplace transform is an integral transformation that converts a function of a real variable to a function of a complex variable.

Take laplace on the DE, we get

[tex]s^{2}-sY(0)-y^{i}(0)-8[sY(s)-y(0)-15Y(s)]=0[/tex]

[tex]s^{2}Y(s)-s(0)-1-8{sY(s)-0)}+15Y(s)=0[/tex]

(Putting the values given in question)

Y(s)=([tex]s^{2} -8s+15)-1=0[/tex]

Y(s)=1/([tex]s^{2} -8s+15[/tex])

Simplifying the above:

=1/([tex]s^{2} -5s-3s+15)[/tex]

=1/[s(s-5)-3(s-5)]

=1/2 [1/(s-3)-1/(s-5)]

Taking inverse of the above we get,

y(t)=[tex](e^{3t} -e^{5t} )/2[/tex]

Hence if the initial value problem is [tex]y^{11} -8y^{1} -15y=0[/tex] and [tex]y^{1}(0) =1[/tex],y(0)=0 then y(t)=[tex](e^{3t} -e^{5t} )/2[/tex].

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The graph of the linear equation can be seen in the image below.

Here we have a linear equation:

y = -x

To graph it, we just need to find two points and the line, and then connect the points with a line.

Evaluating in x = 0, we get:

y = -0 = 0

Then we have the point (0, 0).

Evaluating in x = 1 we get:

y = -1

So we have the point (1, -1)

Now we just need to graph these two points and connect them with a line, the graph can be seen below.

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Answer:

20 lorries are needed to transport.

Mark brainliest

Answer:

14day

Step-by-step explanation:

lorries trip per day. crates

3. 5 2500

? 6 10000

(6×3×10000)÷(5×2500)=14days

There are 20! number of ways for everyone to do this so that at the end of the move, each seat is taken by exactly one person.

People are seated in a 2 by 10 rectangle grid. All 20 persons stand up from their seats and relocate to an orthogonally neighboring one upon the blowing of a whistle.

Now, we have to find the number of possible ways in which each seat is taken up by exactly one person after the move.

As the number of people is 20 and 20 seats are to filled exactly once.

So, the number of ways = 20!

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Así, concluimos que la liebre da un total de 38 saltos.

Notar que solo se nos pregunta cuantos saltos da la Liebre, no importa en que dirección son dichos saltos.

Entonces solo debemos sumar todos los números de saltos que se nos dan, esto es:

18 saltos + 5 saltos + 9 saltos + 6 saltos = 38 saltos.

Así, concluimos que la liebre da un total de 38 saltos.

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[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex] \qquad❖ \: \sf \: {b}^{2} - 9b + 14[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex] \qquad❖ \: \sf \:(b - 2) \sdot(b - 7)[/tex]

[tex] \qquad❖ \: \sf \:(b \sdot b) + (b \sdot - 7) - (2 \sdot b) - (2 \sdot - 7)[/tex]

[tex] \qquad❖ \: \sf \: {b}^{2} - 7b - 2b + 14[/tex]

[tex] \qquad❖ \: \sf \: {b}^{2} - 9b + 14[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

[tex] \sf \:(b - 2) \sdot(b - 7) = {b}^{2} - 9b + 14[/tex]

Answer:

b² - 9b + 14

Step-by-step explanation:

(b - 2) × (b - 7)

= b×b - 7b - 2b + 2×7  (Expand)

= b² - (7b + 2b) + 14  (gather like terms)

= b² - 9b + 14

Answer:

D

Step-by-step explanation:

An angle of depression is measured from the horizontal downwards.

this is angle D in the diagram

Answer:

  62.5 feet

Step-by-step explanation:

The markings on the angles in the figure tell you the triangles are similar. Similar triangles have proportional corresponding sides. This is used to write and solve an equation for x.

The angles in each triangle are marked with the following symbols:

The purpose of the marks is to signify that angles with the same mark are congruent. When the angles of one triangle are congruent to the angles of another triangle, the two triangles are similar.

Similar triangles have another feature: corresponding sides are proportional. That is, their ratios are identical.

This can be taken a couple of different ways:

In the given triangles, we can identify the corresponding sides as ...

  smaller triangle : larger triangle

  between right angle and double arc angle — 36 ft : 50 ft

  hypotenuse — 45 ft : x ft

Our description of similarity tells us we can write the statements of proportionality as either of ...

For proportions written in this way, the "outer" and "inner" products are the same. This is sometimes expressed by saying "the product of the means is equal to the product of the extremes."

  a : b = c : d   ⇒   ad = bc

When the ratios are written as fractions, this result is what you get from "cross multiplication":

  a/b = c/d   ⇒   ad = bc . . . . . the result of multiplying both sides by bd

Once the proportion is written in this product form, the value of any of the variables can be found by dividing both sides of the equation by the coefficient of that variable.

Using either of the proportions we wrote above, the product form is ...

  36x = 45·50

  x = (45·50)/36 . . . . . . divide by the coefficient of x

  x ≈ 62.5 . . . . feet

The distance from the playground to the swimming pool is 62.5 feet.

Answer:

20 cm

Step-by-step explanation:

When two triangles are similar, they're just dilated by a certain scale factor. In other words, each side is multiplied by the same value to create the similar triangle.

So to find this scale factor, we can use the two sides: 6 and 12, since we're going from the triangle with a 6 cm side to a 12 cm side, we divide 12 cm, by 6 cm to get a scale factor of 2

This means that the bottom side in the top triangle, which is 10 cm, is multiplied by a scale factor of 2, to get the new bottom side of x. So to find x, we simply multiply 10 cm by 2 to get 20 cm

Using the continuity concept, since the lateral limits and the numeric value of the function are equal at the point in which the definition changes, the function is continuous.

A function f(x) is continuous at x = a if it is defined at x = a, and:

[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]

The definition of the piecewise function is given by:

Since the definition of the function changes at x = 2, and the domain of the function has no restrictions, this is the only point in which there may be a discontinuity.

The lateral limits are:

The numeric value is:

f(2) = 1.5 x 2 = 3.

Since the lateral limits and the numeric value of the function are equal at the point in which the definition changes, the function is continuous.

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Answer:

70/29 or 2 12/29

Step-by-step explanation:

Answer:

length = 14 cm; width = 6.4 cm

Step-by-step explanation:

We can use proportions to find the length and width.

Thus, for length, l, we have:

[tex]\frac{1}{25}=\frac{l}{350} \\25l=350\\l=14[/tex]

For width, w, we have:

[tex]\frac{1}{25}=\frac{w}{160}\\ 25w=160\\ w=6.4[/tex]

Answer:

15 mister of cloths are needed to make 15 m if 1 puchu is 1 miter

Answer:15 meters

step by step explanation

The domain of f(x) is all set of real values while, the domain of g(x) is x ≤ -1 or x ≥ 2 and both functions have the same range

The functions are given as:

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

g(x) = √(x^2 - x - 2)

Domain

The polynomial function f(x) has no restriction on its input.

So, the domain of f(x) is all set of real values

Set the radical of g(x) = √(x^2 - x - 2) greater than 0

x^2 - x - 2 ≥ 0

Factorize

(x + 1)(x - 2) ≥ 0

Solve for x

x ≥ -1 and x ≥ 2

Combine both inequalities

x ≤ -1 and x ≥ 2

So, the domain of g(x) is x ≤ -1 or x ≥ 2

Range

Using a graphical calculator, we have:

Hence, both functions have the same range

We have:

h(x) = (-x^2 + x)/(x^2 - x - 2)

Set the denominator to 0

x^2 - x - 2 = 0

The above represents the radical of the function f(x)

This means that the breaks in the domain of h(x) and the zeros of f(x) are the same

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Complete question

Let f(x) = x^4 - 2x^3 - 3x^2 + 4x + 4, g(x) = √(x^2 - x - 2) and h(x) = (-x^2 + x)/(x^2 - x - 2)

Part A: Use complete sentences to compare the domain and range of the polynomial function f (x) to that of the radical function g(x). (5 points)

Part B: How do the breaks in the domain of h (x) relate to the zeros of f (x)? (5 points)

The value of 'a' closest to hundredths is 41.41

A triangle could also be  a polygon with three sides and three angles. The three sides for a triangle DEF shown above, written symbolically as △DEF, are line segments DE, EF, and DF

If three sides of a triangle are adequate to three sides of another triangle, then the triangles are congruent. (2) If three angles of a triangle are respectively  adequate to three angles of another triangle, then the 2 triangles are congruent.

Since this is often a right triangle, we'll  use trig functions:

cos theta = adjacent / hypotenuse;

cos a=FD/DE;

cos a=45/60.

Taking the inverse of each side:

cos-1(cos a) =cos-1(3/4);

a=41.40962211.

After Rounding to the closest hundredth:

The value of a is 41.41.

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The simplest form of the given expression ( x⁴ )⁸ exists x³².

Expression in Math exists described as the collection of numbers variables and functions by utilizing characters like addition, subtraction, multiplication, and division.

The given expression will be simplified as:-

( x⁴ )⁸ = x ⁴ ⁽⁸⁾

( x⁴ )⁸ = x ³²

Therefore the simplest form of the given expression exists as x³².

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Answer:

Step-by-step explanation:

Answer:

£13.75

Step-by-step explanation:

→ Call the charge x

x

→ Multiply by 16

16x

→ Equate to total

16x = 220

→ Divide both sides by 16

x = £13.75

Answer:

1/36

Step-by-step explanation:

Assuming the dice has 6 sides in total, we can set up a probability for each scenario.

The chances of the dice landing on 1 will be 1/6, since there are 6 total faces. Same goes for the second die and landing on 4.

Now that we have our 2 probabilities, we multiply them to get the final probability. 1/6 x 1/6 = 1/36.

Answer: B

Step-by-step explanation:

We can rearrange the equation to get [tex]x^2=-\frac{2}{3}[/tex], which clearly has complex roots.

Using a linear function, it is found that Company D would have given you the best deal for 7 hours of moving.

A linear function is modeled by:

y = mx + b

In which:

In this problem, we consider:

Hence the costs for x hours of moving from each company are given as follows:

For 7 hours, the costs are given as follows:

Due to the lower cost, Company D would have given you the best deal for 7 hours of moving.

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