For each pair of graphs in part C, what relationship do you notice for f(x) and f^-1 (x)?

Answer:

5x-4

Step-by-step explanation:

-(x+4)+6x           Hope this helps

-x-4+6x

       -1x

  5x-4

Regarding resolving the given issue, we have The sum of these probabilities is the likelihood of selecting a fidget and a piece of chocolate, which is (6/10) x (3/7) = 18/70 = 9/35.

A mathematical equation is a formula that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The symbol and the single variable are frequently the same. as in, 2x - 4 equals 2, for instance.

Esther has a total of 48 options available to her, which is equal to the product of her toy and candy options (6+2+2) x (4+3).

selecting a fidget from the reward box has a 6/10 chance of happening, while selecting a chocolate bar from the sweets bag has a 3/7 chance.

The sum of these probabilities is the likelihood of selecting a fidget and a piece of chocolate, which is (6/10) x (3/7) = 18/70 = 9/35.

Consequently, the response is (B) 9/35.

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The double integral  ∬D f(x, y) dxdy = -35²⁸/₃₀

Given the double integral ∬D f(x, y) dxdy where D: y = x, y = x², x = 3. and f(x, y) is (x - y)

First, we find the points of intersection.

So, y = x, y = x²

x = x²

x - x² = 0

x(1 - x) = 0

x = 0 or 1 - x = 0

x = 0 or x = 1

So, we integrate x on the interval [0,1] ∪ [1,3]

So, we have that

∬Df(x, y) dxdy = ∬(x - y) dxdy

= ∬x dxdy - ∬y dxdy

= ∫x dx∫dy - ∫ydy∫dx

= ∫xydx - ∫dxy²/2

= ∫x(x - x²)dx - ∫dx(x - x²)²/2

= ∫x(x - x²)dx - ∫dx(x - x²)²/2

= ∫₀¹x²dx - ∫₀¹x³dx - ∫₁³x²dx/2 - ∫₁³2x³dx/2 + ∫₁³x⁴dx/2

= [x³/3]₀¹ - [x⁴]₀¹ - [x³]₁³/6 - [x⁴]₁³ + [x⁵]₁³/10

= [1³ - 0³] - [1⁴ - 0⁴] - [3³ - 1³]/6 - [3⁴ - 1⁴] + [3⁵ - 1⁵]/10

= 1 - 1 - [27 - 1]/6 - [81 - 1] + [243 - 1]/10

= 0 - 26/6 - 80 + 242/10

= - 26/6 - 80 + 242/10

= (-130 - 2400 + 726)/30

= -1078/30

= -35²⁸/₃₀

So, the double integral is -35²⁸/₃₀

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The piecewise function in the graph is:

f(x) = -1  if x ≤ -5

f(x) = x - 1   if x > 3

First, on the left side we can see a constant function that ends at x = -5, so we can write that first part as:

f(x) = -1  if x ≤ -5

The second part is a line that starts at x = 3 (but does not contain it). It is a linear equation, and we can see the points (3, 2) and (4, 3), so the slope is 1.

y = x + b

To find the value of b, we can replace any of the points there:

2 = 3 + b

2 - 3  =b

-1 = b

Then the piecewise function is:

f(x) = -1  if x ≤ -5

f(x) = x - 1   if x > 3

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The system of linear equations that can be formed to find x and y is 3x + 2y = 15.12 and 2x + 4y = 19.36. Then one can of chili costs $2.37 and one jar of salsa costs $4.005.

Let us consider  x being  the cost of one can of chili and y be the cost of one jar of salsa.
Then we can write two equations
3x + 2y = 15.12
2x + 4y = 19.36

We can multiply the first linear equation by 2 and subtract it from the second  linear equation in order to  eliminate x
(2x + 4y = 19.36) - 2(3x + 2y = 15.12)
= -4x + 0y
= -9.48

Applying Simplification to this equation
-4x = -9.48
Dividing both sides by -4 gives us:
x = 2.37

Now we can place this value of x into either of the original equations to find y
3(2.37) + 2y = 15.12
7.11 + 2y = 15.12
Subtracting 7.11 from both sides
2y = 8.01
Dividing both sides by 2
y = 4.005
Then, one can of chili costs $2.37 and one jar of salsa costs $4.005.

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Answer:

= f / g^3.

Step-by-step explanation:

fg^-1 / g^2

= fg^(-1-2)

= fg^-3

= f / g^3.

Answer:

1014

Step-by-step explanation:

To get the area of ​​a rectangle we must multiply the length by the width.

So:

[tex]26*39=1014[/tex]

Hope This Helps :)

Pls Brainliest...

Answer:

Step-by-step explanation:

A polynomial function of degree n has at most n real zeros and at most n - 1 turning points.

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

Linear function is a function whose graph is a straight line

We are given that;

A polynomial function

Now,

Because of the Fundamental Theorem of Algebra states that a polynomial function of degree n has exactly n complex roots (or zeros), some of which may be repeated or non-real. The number of real roots is equal to or less than the number of complex roots.

A turning point is a point where the graph of the polynomial function changes direction from increasing to decreasing or vice versa. The number of turning points is equal to or less than one less than the degree of the polynomial function. This is because each turning point corresponds to a change in the sign of the first derivative of the function, and the first derivative is a polynomial function of degree n - 1.

Therefore, by the function the answer will be n - 1.

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The total actual area of the given logo is:  16.283 ft²

The given composite figure can be divided into a semi circle and a rectangle.

Formula for area of rectangle = length * width

Formula for area of semi circle = ¹/₂πr²

We are told that 1 inch on the printed copy actually represents 8 ft.

Thus:

¹/₂ inch = ¹/₂ * 8 = 4 ft

5/16 in = 5/16 * 8 = 2.5 ft

Thus:

Area of rectangle = 2.5 * 4 = 10 ft²

Area of semi circle = ¹/₂π * 2² = 6.283 ft²

The total actual area = 10 + 6.283 = 16.283 ft²

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The Amount of pepperoni used = 9 packages, Amount of sausage used= was 0.9375 packages of pepperoni, so the chef used 8.0625 more packages of pepperoni than sausage.

Multiplication is a basic arithmetic operation that involves combining or adding equal groups of numbers. It is represented by the symbol "x" or "*", and the result of multiplying two or more numbers is called the product. For example, 2 x 3 = 6, which means two groups of three (2 multiplied by 3) equals six.

The chef used 9 packages of pepperoni and 3/8 of a package of sausage. To compare the amount of pepperoni and sausage used, we need to express them in a common unit of measurement. We can do this by converting the 3/8 package of sausage to the equivalent amount in packages of pepperoni.

To do this, we can notice that 1 package of sausage is equivalent to 2.5 packages of pepperoni. Therefore, we can find the amount of sausage in packages of pepperoni as:

(3/8) package of sausage * 2.5 packages of pepperoni per 1 package of sausage = (3/8) * 2.5 packages of pepperoni = 0.9375 packages of pepperoni

Now, we can compare the amount of pepperoni and sausage used:

Amount of pepperoni used = 9 packages

Amount of sausage used = 0.9375 packages of pepperoni

To find the difference, we can subtract the amount of sausage used from the amount of pepperoni used:

9 packages of pepperoni - 0.9375 packages of pepperoni = 8.0625 packages of pepperoni

Therefore, the chef used 8.0625 more packages of pepperoni than sausage.

Therefore, the Amount of pepperoni used = 9 packages, Amount of sausage used= was 0.9375 packages of pepperoni, so the chef used 8.0625 more packages of pepperoni than sausage.

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Answer:

Step-by-step explanation:

The formula for the volume of a right circular cylinder is:

V = πr²h

where "r" is the radius of the base, "h" is the height, and π is the mathematical constant pi (approximately 3.14).

Substituting the given values, we get:

V = π(5)²(6)

V = 150π cubic inches

Since we are asked to give the volume in cubic inches and not in terms of pi, we can approximate π as 3.14 to get:

V ≈ 150(3.14) ≈ 471

Therefore, the volume of the cylinder is approximately 471 cubic inches, which is closest to option (d) 150.

Answer:

A 4-quart carton of yogurt costs $7.04. The price per cup is $0.44 per cup.

Step-by-step explanation:

What is the price?

A price is the sum of money that one party pays or receives in exchange for another's goods or services. The cost of production may go by another name in some circumstances.

If a product is classified as a "good" in a commercial exchange, its price is most likely to be referred to as such.

4 quarts equal one gallon.

That makes 8 quarts ½ a gallon and 4 cups make one quart, as seen by the gallon man in the attachments.

4 quarts equal 16 cups, because 4 x 4 is 16.

$7.04 is the price for a four-quart carton of it.

Now, divide 7.04 by that number to find the price per cup.

7.04 / 16 = 0.44.

Therefore, the price per cup is $0.44 per cup.

Answer:

We assume that A and B are independent events.

P(A) = .6, P(B) = .25

P(A and B) = P(A)P(B) = .6(.25) = .15

P(A or B) = P(A) + P(B) - P(A and B)

= .6 + .25 - .15 = .7

D is correct.

B. The probability of buying bread and cheese is 0.15

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one

Given Data;

The probability that a shopper buys bread, P(A) = 0.6

And, The probability that a shopper buys cheese, P(B) = 0.25

Now, If two events A and B are independent, then the probability that A and B occur is:

P(A∩B) = P(A) x P(B)

Now, Replacing with data:

P(A∩B) = 0.6 x 0.25

P(A∩B)  = 0.15

Thus, The probability of buying bread and cheese is 0.15

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The explicit rule to represent the arithmetic sequence of seats in the theater is aₙ = 8n + 12

The arithmetic sequence can be represented by the formula:

aₙ = a₁ + (n - 1)d

where an is the nth term of the sequence, a₁ is the first term, n is the position of the term, and d is the common difference between terms.

In this case, we know that the first term (a₁) is 20, and the common difference (d) is 8 (since each row has 8 more seats than the previous row).

Using the formula, we can write the explicit rule for this sequence as

aₙ = 20 + (n - 1)8

or

aₙ = 8n + 12

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Using the Alternate exterior angles theorem, the measure of angle QPN, m ∠QPN, is 113.8°

From the question, we are to determine the measure of angle QPN in the given diagram.

To determine m ∠QPN, we will use The Alternate exterior angles theorem

The Alternate Exterior Angles Theorem states that, when two parallel lines are cut by a transversal, the resulting alternate exterior angles are congruent.

In the given diagram,

Angle RSU and Angle QPN are alternate exterior angles.

Thus,

We can write that

m ∠RSU = m ∠QPN

From the given information,

m ∠RSU = 113.8°

Hence,

m ∠QPN = 113.8°

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Answer:

His speed is below the maximum speed llimit by 4960km/h

Step-by-step explanation:

elis drives at 40 mph the maximum is 50km/h

so, convert it into the same measurement and subtract

50 km is equal to 5000 miles

50-40 is 10

but if you subtract in is same measurement which is MOST LIKLEY TO BE CORRECT, THE AJSWER IS 4960 kmph

PLS MARK AS BRAINLIEST

According to the radius, the length of the sidewalk needs to be 62.8 feet to go around the pool.

In your case, the pool is circular, which means it has a center and a radius of 10 feet. Now, to find the length of the sidewalk, we need to know the circumference of the circle. The circumference is the distance around the circle and can be calculated using the formula:

circumference = 2 x π x radius

where pi is a mathematical constant that represents the ratio of the circumference of a circle to its diameter, approximately equal to 3.14.

Using the given radius of 10 feet, we can plug it into the formula:

circumference = 2 x 3.14 x 10 feet

which simplifies to:

circumference = 62.8 feet

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If we randomly select a student who works part-time, the probability of that student also driving themselves to school is 1 or 100%.

To find the probability of randomly selecting a student who drives and works part-time, we need to use the formula for conditional probability. This formula states that the probability of event A given event B is equal to the probability of both events A and B occurring together, divided by the probability of event B.

In this case, event A is selecting a student who drives to school, and event B is selecting a student who works part-time. To find the probability of both events occurring together, we need to find the intersection of sets A and B, which is the group of students who both drive and work part-time. According to the Venn diagram, this group has a size of 3.

Therefore, the probability of selecting a student who drives and works part-time is:

P(A|B) = P(A and B) / P(B)

= 3 / 3

= 1

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Answer:

Let's start with calculating how much money is raised in total:

- Let's assume there are x SUVs and y cars.

- The cost for one SUV is $10 and the cost for one car is $5.

- Therefore, the total cost for all SUVs is 10x and the total cost for all cars is 5y.

- The total cost is the sum of these: 10x + 5y.

Now we need to calculate how much money each team will get. We know that:

- 25% of the money goes to the football team. This can be written as 0.25(10x + 5y) or 2.5x + 1.25y.

- 30% of the money goes to the soccer team. This can be written as 0.3(10x + 5y) or 3x + 1.5y.

- The remaining percent goes to the basketball team. This is 100% - 25% - 30%, which is 45%. This can be written as 0.45(10x + 5y) or 4.5x + 2.25y.

Therefore, the expression to represent how much the soccer team and football team will receive is:

2.5x + 1.25y + 3x + 1.5y = 5.5x + 2.75y

The function represented by the graph in intercept form is:

f(x) = -0.00038(x + 5.8)(x + 5)(x + 2)(x - 1)(x - 4)

We have,

To write the function represented by the graph in intercept form, we need to find the x and y intercepts and write the function as a product of linear factors.

From the graph and the given points, we can see that the function has

4 x-intercepts at -5, -2, 1, and 4.

We can also see that the function has 3 turning points at (-3.8, 95), (-1.4, 35), and (2.5, 40).

To find the y-intercept, we can use the point (-5.8, -160), which the curve emerges from.

This means that the function can be written in the form:

f(x) = a(x + 5.8)(x + 5)(x + 2)(x - 1)(x - 4)

where a is a constant to be determined.

To find the value of a, we can use any of the given points that lie on the curve. Let's use the point (-3.8, 95):

95 = a(-3.8 + 5.8)(-3.8 + 5)(-3.8 + 2)(-3.8 - 1)(-3.8 - 4)

Simplifying and solving for a, we get:

a = -95/((5.8)(3)(0.8)(4.8)(7.8)) ≈ -0.00038

Therefore,

The function represented by the graph in intercept form is:

f(x) = -0.00038(x + 5.8)(x + 5)(x + 2)(x - 1)(x - 4)

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Answer:

Step-by-step explanation:

5(v+10) =

when sorting its  v+10

the common factors would be 5,1

4(x+6)=

when sorting it should be 4

the common factors are 4,2,1.

The area of the stained glass window is 156.56 in².

What is a rectangle?

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees.

To determine the area of the stained glass window, we can first calculate the area of the rectangle by multiplying its length and width, which is 16 in × 9 in = 144 in².

Next, we need to find the area of each semicircle. The diameter of each semicircle is 4 in, so the radius is 2 in. The area of a circle is given by the formula πr², so the area of each semicircle is (π × (2 in)²) ÷ 2 = 6.28 in².

Since there are two semicircles, their total area is 6.28 in² × 2 = 12.56 in².

To get the total area of the stained glass window, we add the area of the rectangle and the area of the semicircles, giving us a total of 144 in² + 12.56 in² = 156.56 in².

Therefore, the area of the stained glass window is 156.56 in².

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The solution is , f(x) = tan (x) the function is defined at 0≤x<90 is the domain of the function.

Given the function f(x) = tan (x)

From trigonometry identity, tan (x) = sin(x)/cos(x)

f(x) = sin(x)/cos(x)

Using the quotient rule to find the derivative of the function, we will have;

f'(x) = cos (x)cos (x) - sin (x)[-sin (x)]/ cos²x

f'(x) = cos²x - sin²x/ cos²x

Divide through by cos²x

f'(x) = cos²x/cos²x + sin²x/cos²x / cos²x/cos²x

f'(x) = 1 + sin²x/cos²x / 1

f'(x) = 1 + (sin²x/cos²x)

f'(x) = 1 + tan²x

From trig identity,  1 + tan²x = sec²x

Hence, f'(x) = sec²x

Hence the expression  f'(x)  in terms of the secant function is sec²x

f'(x) = 1/cos²x

For the function to be defined, it means that cos²x ≠ 0

cos²x ≠ 0

cos x ≠ 0

x ≠ cos⁻¹0

x ≠ 90⁰

Hence the value of x must not be equal to 90 for the function to be defined. x can be defined at when x = 0 since cos 0 = 1, the equation will  becomes f'(0) = 1/cos²0 = 1/1 = 1.

Hence the function is defined at 0≤x<90

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complete question:

Consider the function f ( x ) = tan ( x ) , and remember that tan ( x ) = sin ( x ) cos ( x ) . What is the domain of f ? Use the quotient rule to show that one expression for f ′ ( x ) is f ′ ( x ) = cos ( x ) cos ( x ) + sin ( x ) sin ( x ) cos 2 ( x ) . What is the Fundamental Trigonometric Identity? How can this identity be used to find a simpler form for f ′ ( x ) ? Recall that sec ( x ) = 1 cos ( x ) . How can we express f ′ ( x ) in terms of the secant function? For what values of x is f ′ ( x ) defined? How does this set compare to the domain of f ?

Answer: 4/5

Step-by-step explanation:

If each of the 100 people is asked to give one preference ballot for one of the five beverage choices, then the winner of the election will be the beverage with the most votes.

We have,

To determine the winner, we need to count the number of ballots for each choice and compare them.

For example, if we count 30 ballots for Coke, 20 for Diet Coke, 15 for Truly, 10 for Wine, and 25 for Beer, then the winner would be Beer, with 25 votes.

If there is a tie between two or more choices, we would need to have a run-off election or some other method to determine the winner.

Thus,

If each of the 100 people is asked to give one preference ballot for one of the five beverage choices, then the winner of the election will be the beverage with the most votes.

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Answer:

[tex]\text{Option F $\rightarrow | -8 - 7|$}[/tex]

Step-by-step explanation:

The difference between -8 and 7 on the number line is

- 8 - 7 = -15

However, as distance is always positive so we take the absolute value of |-8 - 7| = 15

Answer: Option F ==> |-8 -7|

The decimal form of 110% is 1.1

To find the length of the unknown leg of the triangle, we will need to use the Pythagorean Theorem.

Pythagorean Theorem: a^2 + b^2 = c^2

---a and b are the legs of the triangle

---c is the hypotenuse

a = 2

b = ?

c = 3

2^2 + b^2 = 3^2

4 + b^2 = 9

b^2 = 5

b = 2.236

b (rounded) = 2.2

Answer: 2.2 ft

Hope this helps!

The calculated height of the​ brace, h will be 5 ft

From the question, we have the following parameters that can be used in our computation:

Similar triangles

This means that

Ratio = Division or ratio of corresponding sides

So, we have

h : 9 = 10 : 18

So, we have the following representation

h/9 = 10/18

This gives

h = 9 * 10/18

By calculation, we have

height = 5 ft

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Cost of one egg is $1.85.

Assume,

X denotes the cost of 1 egg

Y denotes the cost of 1 sausage

According to question,

Cost equation for Hannah,

3X + 2Y = 7.13   ....(i)

Cost equation for Hannah,

5X + 3Y = 11.62  ....(ii)

Subtract 3x(i) from 2x(ii) we get

X = $1.85 is the cost of one egg.

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