Select the correct answer.
Consider the graph of rational function f.

Which graph represents function g if g(x) = f(2x)?

Answer:

number b is the write answer

Step-by-step explanation:

-2x²-3x+4-4x²+x-2

-2x²-4x²-3x+x+4-2

-6x²-2x+2

The set of whole numbers, the set of integers, and the set of rational numbers are closed under each of the four basic operations.

Whole numbers:

Addition: Yes

Subtraction: No (e.g. 5 - 7 = -2)

Multiplication: Yes

Division: No (e.g. 4 ÷ 2/3 is not a whole number)

Integers:

Addition: Yes

Subtraction: Yes

Multiplication: Yes

Division: No (e.g. 4 ÷ 1/2 is not an integer)

Rational numbers:

Addition: Yes

Subtraction: Yes

Multiplication: Yes

Division: Yes (provided the denominator is non-zero)

Polynomials:

Addition: Yes

Subtraction: Yes

Multiplication: Yes

Division: No (in general, polynomials cannot be divided by other polynomials)

Polynomials are like rational numbers with respect to closure under addition, subtraction, and multiplication.

However, they are not closed under division like rational numbers.

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x2 4x + 7 is an illustration of a polynomial with a single indeterminate x.

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Ordering the populations of the 6 different states, written in scientific notations, in order of the greatest to the least value is as follows:

Scientific notation is the standard way of writing very long or short numbers in their shorthand forms.

A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10, with the following parts: coefficient, base, and exponent.

For instance, New York's population is 19,700,000 and can be written in scientific notation as 1.97^7.

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The cost of car in the year 1983 is 2845

An equation is an expression that shows the relationship between two or more numbers and variables.

The CPI (consumer price index) is a measure of the overall change in prices of goods and services over a certain period of time. It is given by:

CPI = (cost of market basket in a given year / cost of market basket in base year) * 100

Given that:

CPI = 56.9 in 1976, cost of market basket in a given year = x, cost of market basket in base year = $5000

Hence:

56.9 = (x/ 5000) * 100

x = 2845

The cost of car is 2845

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The claim that the average of a random sample is the same as the average of the population from which it was taken is False.

The sample mean will, of course, differ from the population means. The sample mean, however, is a fair estimation of the population mean if the sample is a simple random sample.

Thus, neither the sample mean nor the population mean is statistically greater or lower. The sample mean will always have a mean that is identical to the mean of the original non-normal distribution. In other words, the population mean is the same as the sample mean.

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Step-by-step explanation:

we need to calculate the distances between the points as the side lengths of the triangle.

these side lengths must satisfy the Pythagoras principle :

c² = a² + b²

with c being the Hypotenuse (side opposite of the 90° angle) and the longest of the 3 sides, a and b being the legs.

the distance between 2 points is again calculated via Pythagoras, as the coordinate differences (= the legs) with the distance as Hypotenuse create right-angled triangles.

this is then caked the distance formula, but it is all Pythagoras again.

AB² = (xB - xA)² + (yB - yA)² = (6 - -2)² + (2 - 2)² =

= 8² + 0² = 8²

AB = 8

AC² = (0 - -2)² + (6 - 2)² = 2² + 4² = 4 + 16 = 20

AC = sqrt(20)

BC² = (0 - 6)² + (6 - 2)² = (-6)² + 4² = 36 + 16 = 52

BC = sqrt(52)

as sqrt(20) is a little bit more than 4, and sqrt(52) is a little bit more than 7, 8 is the longest side and Hypotenuse.

if this is a right-angled triangle, then

8² = sqrt(20)² + sqrt(52)²

must be true.

but

64 = 20 + 52 = 72

is wrong.

so, the segments do not form a right-angled triangle.

Answer:

125 million

Step-by-step explanation:

[tex]79.4 \times \frac{100}{63.5} = 125.03[/tex]

Answer:

Sweater: $26

Shirt: $5

Step-by-step explanation:

We can set up two linear equations to form a systems of equations which will allow us to solve for the price of a shirt and sweater.

The first step we want to take is assigning the shirt and sweater to an unknown, so I'll just refer to the price of a shirt as: [tex]S_h[/tex] with the little subscript "h" and I'll refer to the price of a sweater as: [tex]S_w[/tex] with the little subscript "w".

Now the next main thing to understand is we can calculate the total price of something by multiplying the price of an individual item by the quantity. So if I buy an apple for $10, but I buy 10 of them, then the total price would be 10 * 10 or $100. So when Andrea buys 6 shirts, the price of that can be represented as: [tex]6S_h[/tex] and when Anrea buys 7 sweaters the price of that can be represented as: [tex]7S_w[/tex], adding these together should equal 212, since it gives us that buying 6 shirts and 7 sweaters costs a total of $212.

Using this logic with the other case where she buys 10 shirts and 8 sweaters for $258, we can set up the two equations:

[tex]6S_h + 7S_w=212\\10S_h+8S_w=258[/tex]

From here we can use substitution to solve this equation. So let's solve for the [tex]S_h[/tex] on the top equation.

[tex]6S_h+7S_w=212[/tex]

Froom here subtract [tex]7S_w[/tex] from both sides and then divide by 6

[tex]S_h=\frac{212-7S_w}{6}[/tex]

Now we can plug this into the second equation:

[tex]10(\frac{212-7S_w}{6})+8S_2=258[/tex]

Simplifying the division and multiplication on the left side we get:

[tex]\frac{1060}{3}-\frac{70}{6}S_w+8S_w=258[/tex]

From here we can combine the like terms

[tex]\frac{1060}{3}-\frac{22}{6}S_w=258[/tex]

we can simplify the fraction a bit more

[tex]\frac{1060}{3}-\frac{11}{3}S_w=258[/tex]

Now subtract 1060/3 from both sides

[tex]\frac{-11}{3}S_w=\frac{-286}{3}[/tex]

Now divide both sides by -11/3

[tex]S_w=26[/tex]

Now from here we can substitute this back into any equation to solve for the shirt price. Let's use the equation where we solved for the price of the shirt but we just needed to know the price of the sweater.

[tex]S_h=\frac{212-7S_w}{6}[/tex]

Now let's plug in 26 for the sweater price.

[tex]S_h=\frac{212-7(26)}{6}[/tex]

Simplify this and we get:

[tex]S_h=5[/tex]

and now we know the shirt and sweater price!

For the function E(t) = 31 cos (0.11t), the rate at which the number of wolves in the forest is changing at time t = 7 is 22.2549.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The function to model the rate at which the number of wolves in a forest is changing is E(t) = 31 cos (0.11t)

Here t is the time measured in weeks.

The time value is given as t = 7

Substitute the value of t in the equation -

E(t) = 31 cos (0.11t)

Apply the arithmetic operation of multiplication -

E(7) = 31 cos (0.11 × 7)

E(7) = 31 cos (0.77)

E(7) = 31 × 0.7179

E(7) = 22.2549

Therefore, the rate value is obtained as 22.2549.

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Answer:

Below

Step-by-step explanation:

Put the numbers into the pythagorean theorem to see if true

12^2   + 15^2    =   18^2    ??????

144 + 225   =  324   ?????

369 = 324 ??????   <========= not true ....not a triple

Answer:

14ft

Step-by-step explanation:

Perimeter of a square = 4s where s = side length

Here, we are given the perimeter, and we want to find the side length. To do so we plug in the perimeter and solve for s

Perimeter = 56

So 56 = 4s

==> divide both sides by 4

14 = s

A square with a perimeter of 56 feet has a side length of 14 feet

Answer:

611.05

Step-by-step explanation:

To find the number of cubic feet of water needed to fill Fred's fish tank, we need to calculate the volume of the tank. The volume of a rectangular prism (such as a fish tank) can be found by multiplying the length, width, and height together. Using the given measurements, the volume of Fred's fish tank would be:

8.3 ft * 11.5 ft * 6 ft = 611.05 cubic ft

So, Fred will need 611.05 cubic ft of water to fill his fish tank.

By applying supply and demand concept, it can be concluded that:

a. Point of equilibrium for this market will be reached when p = 20 and q = 50

b. Consumers' surplus for this market when -150 < q < 50

c. Producers' surplus for this market when 50 < q < 130

Demand is the number of goods purchased or requested in the market at a certain price and time, while supply is the number of goods sold or offered in the market at a certain price and time.

Point of equilibrium will be reached when supply and demand are in balance.

We have the following supply and demand functions:

Supply: p = 15 + 0.1q

Demand: p= √(650- 5q)

A. The point of equilibrium occurs when supply and demand are in balance:

                                 15 + 0.1q = √(650- 5q)

                              (15 + 0.1q)² = 650 - 5q

                  225 + 3q + 0.01q² = 650 - 5q

0.01q² + 3q + 5q + 225 - 650 = 0

                    0.01q² + 8q - 425 = 0

                  q² + 800q - 42500 = 0

q² + 800q + 160000 - 202500 = 0

                 (q + 400)² - 202500 = 0

                                  (q + 400)² = 202500

                                     q + 400 = 450

                                                q = 50

As we know q, we can calculate the p:

p = 15 + 0.1q

  = 15 + 0.1 * 50

  = 20

B. The Consumers' surplus when demand > supply:

√(650- 5q) > 15 + 0.1q    ⇔    q < 50

which implies:

√(650- 5q) > 0                ⇔    q < 130

15 + 0.1q > 0                    ⇔    q > -150

So, the Consumers' surplus for this market when -150 < q < 50

C. The Producers' surplus when supply > demand:

15 + 0.1q > √(650- 5q)    ⇔    q > 50

which implies:

√(650- 5q) > 0                ⇔    q < 130

15 + 0.1q > 0                    ⇔    q > -150

So, the Producers' surplus for this market when 50 < q < 130

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Answer:

x ≥ 4

Step-by-step explanation:

Just treat the equation like you would a regular algebraic equation.

10 + x ≥ 14

10 + x - 10 ≥ 14 - 10

x ≥ 4

As for graphing it, I'm not really sure if you want a proper graph or a number line.

For a number line, put a closed dot on a 4

Answer:

f'(2) = 25

Step-by-step explanation:

differentiate f(x) using the power rule

[tex]\frac{d}{dx}[/tex] ( a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex] and [tex]\frac{d}{dx}[/tex] ( constant) = 0

f(x) = 2x³ + x² - 3x + 4

f'(x) = 3× 2x² + 2x - 3 = 6x² + 2x - 3 , then

f'(2) = 6(2)² + 2(2) - 3

      = 6(4) + 4 - 3

      = 24 + 1

      = 25

The closest value of x that would produce the box with the minimum surface area would be 117 ft.

The volume of a lidless box with height h and a square base with sides of length x is given by V = x^2 * h.

To have a volume of 117 ft^3, we have:

x^2 * h = 117

The surface area of a lidless box is given by:

A = 2x^2 + 4xh

We want to minimize this surface area while still keeping the volume of the box at 117 ft^3. To do this, we need to find an expression for h in terms of x, and then minimize A in terms of x.

From the volume equation, we can solve for h:

h = 117 / x^2

Substituting this expression into the surface area equation, we get:

A = 2x^2 + 4x * (117 / x^2)

= 2x^2 + 466 / x

Now, we can use calculus to find the minimum of A in terms of x.

The derivative of A with respect to x is:

dA/dx = 4x - 466 / x^2

Setting dA/dx equal to zero, we find the critical points:

4x - 466 / x^2 = 0

4x = 466

x = 116.5

We now need to check if x = 116.5 is a local minimum or maximum.

To do this, we need to examine the second derivative of A with respect to x:

d^2A/dx^2 = -932 / x^3

Since the second derivative is negative, this means that A has a local minimum at x = 116.5.

Hence, the value of x that produces the box with a minimum surface area is approximately 116.5 ft.

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The required solutions are as follows,

(a) The team has zero points in 1 minute of the competition.
(b) The team has two points in 5 minutes of the competition.
(c) After 8 minutes, the team has 3 points.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
From graph,
As at 0 seconds the race started and Monia finished eating a hot dog at 3 minutes. so 1 to 2.9 minutes of race point is zero.

Scorecard with time is given as
1 to 2.9-minute score = 0
3 to 4.9-minute score = 1
5 to 7.9 minutes score = 2

after 8 minutes score = 3

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Answer:

Step-by-step explanation:

Picture?

You didn’t give enough info. Are you able to provide more information? Or a picture?

The slope of the line describes by the table is 0.1.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

The table represents Bike ride, where x represents the number of minutes in 'x' and y represents the number of kilometers.

We know, slope(m) = (y₂ - y₁)/(x₂ - x₁).

Slope(m) = (1.0 - 0.5)/(10 - 5).

Slope(m) = 0.5/5.

Slope(m) = 0.1

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Answer:

To find the value of (a - 1/a)^2 and (a - 1/a), we can start by squaring the given equation:

a^2 + 1/a^2 = 18

(a^2 + 1/a^2)^2 = 18^2

a^4 + 2 + 1/a^4 = 324

a^4 + 1/a^4 = 322

Now, to find (a - 1/a)^2, we can square the difference of a and 1/a:

(a - 1/a)^2 = a^2 - 2 + 1/a^2

We can substitute the value of a^4 + 1/a^4 = 322 into this equation:

(a - 1/a)^2 = 322 - 2

(a - 1/a)^2 = 320

To find (a - 1/a), we can take the square root of (a - 1/a)^2:

(a - 1/a) = √320

And, a^2 + 1/a^2 = 18, we can solve for a,

a^4 - 18a^2 + 1 = 0

(a^2 - 1)(a^2 - 18) = 0

a^2 = 1 or a^2 = 18

a = 1 or a = ±√18

So, in this case, the value of (a - 1/a)^2 is 320 and (a - 1/a) is √320.

Step-by-step explanation:

The graph for the piecewise function f(x)={(1/3 x-1" if "x≤0 -1/2 x+6" if "0<x≤6 is attached in the solution.

A piecewise function is a function that is defined on a sequence of intervals.

Given is a piecewise function f(x)={(1/3 x-1" if "x≤0 -1/2 x+6" if "0<x≤6

Plotting the graph for:

f(x)={(1/3 x-1" if "x≤0 -1/2 x+6" if "0<x≤6

From the graph, we conclude that:

The graph of the given piecewise function is a straight line with two segments.

The first segment, which lies between x = 0 and x = 6, has a slope of -1/2 and a y-intercept of 6.

The second segment, which lies between x = 0 and x = -∞, has a slope of 1/3 and a y-intercept of -1.

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Answer:

15% tell me if im wrong

Step-by-step explanation:

The Percentage of bags with correct weight will be 84%

A percentage simply has to do with the a 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.

From the information, the following can be gotten:

Total number of bags = 2500

Bags with correct weight = 2100

Bags with lower weight = 275

Bags with higher rate = 125

Percentage of bags with correct weight will be:

= 2100 / 2500 × 100

= 84%

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Answer:

Below

Step-by-step explanation:

The equation you need to remember is:

rate X time = distance       re-arrange to

time = distance / rate         sub in the numbers given to get

time =   x / 15  hours

Answer:

Find the work required to pump the water out of the spout. (Use 9.8 m/s 2 for g. Use 1000 kg/m 3 as the weight density of water.

Step-by-step explanation:

The probability of 35 people being selected before the first person with a phobia being chosen does not provide sufficient evidence to suggest that the ADAA claim is false. To determine if the ADAA claim is false, we would need to perform a statistical hypothesis test to compare the sample proportion of adults with phobias to the ADAA estimate of 8.7%. This would involve collecting data on a random sample of adults, calculating the sample proportion of adults with phobias, and comparing it to the ADAA estimate of 8.7%.

If the sample proportion is significantly different from 8.7%, we can conclude that there is evidence to suggest that the ADAA claim is false. However, without performing a statistical hypothesis test, we cannot make a conclusion about the validity of the ADAA claim based solely on the probability of 35 people being selected before the first person with a phobia is chosen.

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Answer:

The correct solution is .54

Step-by-step explanation:

Think about this like counting change.

0.54 is the largest amount. Next would be 0.504 (which in change would be close to 0.50 rounded down), lowest amount would be 0.45

The equation cos (60°) = a/12 can be used to find one of the missing side lengths in the triangle.

Trigonometric identities are equations that are true for all values of the angles in a right triangle. They express the relationships between the angles and sides of a triangle and are used to simplify trigonometric expressions or to prove that two expressions are equal.

One of the trigonometric identities is the SOH CAH TOA.

SOH: sin θ = opposite/hypotenuse

CAH: cos θ = adjacent/hypotenuse

TOA: tan θ = opposite/adjacent

Since angle CBA is 60°, the adjacent side is a, the opposite side is b, and the hypotenuse is 12 units, then:

cos θ = adjacent/hypotenuse

cos (60°) = a/12

Rearranging the equation, we can solve one of the missing side lengths, which is a.

a = 12cos(60°)

Hence, we can use the equation cos (60°) = a/12 to find the length of side a.

The problem seems incomplete, it must have been...

"Which equation can be solved to find one of the missing side lengths in the triangle? Triangle A B C is shown. Angle A C B is 90 degrees and angle C B A is 60 degrees. The length of side C B is a, the length of C A is b, and the length of hypotenuse A B is 12 units.

cos(60°) = 12/a

cos(60°) = 12/b

cos(60°) = b/a

cos(60°) = a/12"

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The angle formed 28.42 degree between the slide and the drop.

The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

length of water slide is 42m. (Hypotenuse)

and length of drop = 20 m (Perpendicular)

Using Trigonometry

sin [tex]\theta[/tex] = P/ H

sin [tex]\theta[/tex] = 20 / 42

sin [tex]\theta[/tex] =  10 /21

sin [tex]\theta[/tex] = 0.476

[tex]\theta[/tex] = [tex]sin ^{-1[/tex] (0.476)

[tex]\theta[/tex] = 28.42 degree.

Hence, the angle is 28.42 degree.

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