That are a valid decomposition of c (x )such that c equals f ring operator g g (x )equals x squared f (x )equals cube root of x plus 1 end root g (x )equals x squared plus 1 f (x )equals cube root of x g (x )equals x plus 1 f (x )equals cube root of x squared end root g (x )equals cube root of x plus 1 f (x )equals x squared

Answer: The answers are both B and C

1. The amount of pizzas which the pizzeria must sell for employees to receive the bonus is 78.

2. The new number of pizzas sold is considered as percent increase of 20%.

The pizzeria sold 65 pizzas yesterday and the owner offers bonus if the number sold increases by 20% today. The number that must be sold, to receive a bonus is computed as follows:

= 65 pizza * (65 pizza * 20%)

= 65 pizza * 13 pizza

= 78 pizza.

It is a percent increase which is computed as follows. The formula for percentage increase is: ((Final value - Initial value)/Initial value * 100).

The Percent increase:

= (78 pizza - 65 pizza) / 65 pizza.

= 13 pizza / 65 pizza

= 0.2

= 20%

Full question "A local pizzeria sold 65 pizzas yesterday. (step 1) The owner offers the employees a bonus if the number of pizzas sold increases by 20% today. How many pizzas must the pizzeria sell for employees to receive the bonus? Explain your reasoning. (Part 2) Suppose the actual number of pizzas sold today was 60. Describe the number of pizzas sold as a percent increase or decrease, rounded to the nearest hundredth. Show your work. Answer:"

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Answer:

3 inches is approximately equal to 76.2 millimeters.

Step-by-step explanation:

Answer:

3 inches = 76.2 millimeters

Step-by-step explanation:

Answer:a

Step-by-step explanation:

The correct answer is

d) 4:16

Area and Perimeter of Similar Polygons:

Polygons are said to be similar when their corresponding angles are equal and their corresponding sides are in the same proportion. The perimeters and areas of identical polygons have a unique relationship, just as their corresponding sides do.

Perimeters: The scale factor and the perimeters ratios of perimeters are similar. In reality, the scale factor is identical to any ratio between any two similar forms (diagonals, medians, midsegments, altitudes, etc.).

Areas: If the scale factor of the sides of two similar polygons is [tex]\frac{m}{n}[/tex]

, then the ratio of the areas is [tex](\frac{m}{n} )^{2}[/tex].

(Area of Similar Polygons Theorem). Because area is a two-dimensional quantity, you square the ratio.

It is given that ,

the ratio of perimeters of two similar quadrilateral is 2:4.

now,

to find the ratio of area , we can take two quadrilaterals, say square.

Square ABCD of side 2 units and Square PQRS of side 4 units.

now ratio of areas,

[tex]=\frac{area of square ABCD}{area of square PQRS} \\\\=\frac{2*2}{4*4} \\\\=\frac{4}{16}[/tex]

If the given ratio of perimeters can be further solved as 1:2, then we can see that the ratio of areas can also be further solved as 1:4.

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The x- and y-components of the vector [tex]\mathbf{\hat a}}[/tex] are 8.9 m/s² and -6.4 m/s², respectively.

In mathematics, components are the parts or elements that make up a larger structure or object. In the context of vectors, components refer to the parts of a vector that describe its direction and magnitude in a particular coordinate system.

To find the x-components and y-components of the vector [tex]\mathbf{\hat a}}[/tex] = (11 m/s², 36 degrees left of -y-axis), we need to determine the direction of the vector. The notation "left of -y-axis" means that the vector makes an angle of 36 degrees with the negative y-axis, as measured counterclockwise from the negative y-axis.

The magnitude (or length) of the vector is given by the first component, which is 11 m/s².

The x-component of the vector can be found by multiplying the magnitude by the cosine of the angle:

x-component = magnitude x cos(angle) = 11 m/s² x cos(36°) = 8.9 m/s²

The y-component of the vector can be found by multiplying the magnitude by the sine of the angle:

y-component = magnitude x sin(angle) = 11 m/s² x sin(36°) = -6.4 m/s²

The negative sign indicates that the y-component is in the opposite direction of the negative y-axis.

Therefore, the x- and y-components of the vector [tex]\mathbf{\hat a}}[/tex] are 8.9 m/s² and -6.4 m/s², respectively.

Expressed as an ordered pair, the components are (8.9 m/s², -6.4 m/s²).

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The most specific name for the quadrilateral is trapezoid, the correct option is C.

A quadrilateral is defined as a two-dimensional shape with four sides, four vertices, and four angles. There are two main types: concave and convex. There are also various subcategories of convex quadrilaterals, such as trapezoids, parallelograms, rectangles, rhombi, and squares.

Given;

The figure with 4 sides and two opposite are equal

Now,

In the figure two opposite sides are equal in length

But they all are not parallel only on pair of opposite sides are parallel.

Also, the figure the adjacent angle are equal.

Therefore, the quadrilateral will be trapezoid.

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Answer:

The original price of the shoes was $53.

The discount percentage was 20%.

The discount amount was 53 * 0.2 = 10.6.

The sale price after the discount was 53 - 10.6 = 42.4.

The processing fee percentage was 20%.

The processing fee amount was 42.4 * 0.2 = 8.48.

The final price after the processing fee was 42.4 + 8.48 = 50.88.

Therefore, the discount was $10.60, and the final price was $50.88.

Step-by-step explanation:

Ordinal data can be ordered, as the naming implies. Both have "ord" to help remember the connection. An example of this would be something like small, medium, large. The items do not have to be numeric in nature.

Nominal data is any category or name. Order isn't present here. For example, if a survey asked about a person's favorite color, then there isn't any inherent order here.

Answer: The range of the tangent function is (-∞,∞). So the answer is A: All real numbers.

Step-by-step explanation:

The value of a, b, and c are 1, -2, and 6 respectively.

The y-intercept of this quadratic function is 6.

The axis of symmetry of this quadratic function is 1.

The vertex of this quadratic function is (1, 5).

Mathematically, the axis of symmetry of a quadratic function can be calculated by using this mathematical expression:

Axis of symmetry, Xmax = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

For the given quadratic function f(x) = x² - 2x + 6, we have:

Axis of symmetry, Xmax = -b/2a

Axis of symmetry, Xmax = -(-2)/2(1)

Axis of symmetry, Xmax = 2/2 = 1.

Vertex (h, k) = (1, 5).

In Mathematics, the y-intercept of any graph such as a quadratic function, generally occur at the point where the value of "x" is equal to zero (x = 0).

y-intercept = 6.

Lastly, we would create a table and then graph the quadratic function as follows;

x         y

0         6

2         2

5         11

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The correct answer is that the probability is 2/3. To see why, we can count the number of codes that do not have D in the first position, which is 6 (two options for the first position, and three options for the second position).

The size of the sample space is 4 options for the letter, 2 options for the first number, and 1 option for the second number, giving a total of 4x2x1=8 possible codes. To calculate the probability that a code has a letter that immediately follows an odd number, we first need to count the number of codes that meet this condition. There are two odd numbers to choose from (5 and 6), and two letters that can immediately follow an odd number (B and D). For each odd number, there is only one even number that can come before it, so there are 2x1x2=4 possible codes that meet this condition. Therefore, the probability that a randomly chosen code has a letter that immediately follows an odd number is 4/8, which simplifies to 1/2, or 0.5. To calculate the probability that D is in the code but is not in the first position, we need to count the number of codes that meet this condition. There are two places that D could appear (second or third), and three options for the first position (A, B, or C). Once the first position is chosen, there are two options for the remaining number (5 or 6). Therefore, there are 2x3x2=12 possible codes that meet this condition. The total number of possible codes is 8, so the probability that a randomly chosen code has D but not in the first position is 12/8, which simplifies to 3/2, or 1.5. However, probabilities must always be between 0 and 1, so this answer is not valid.

The correct answer is that the probability is 2/3. To see why, we can count the number of codes that do not have D in the first position, which is 6 (two options for the first position, and three options for the second

position). Of these 6 codes, 4 have D in the second position, and 2 have D in the third position. Therefore, the probability that a randomly chosen code has D but not in the first position is (4+2)/8, which simplifies to 2/3.

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Using matrix inversion, the value of x and y are 1.104 and 39.704 respectively

The system of equations can be written in matrix form as:

|  -650    1 |   | x |   |  175    |

|  120     1 |   | y |   |  25,080 |

To solve for x and y, we can use matrix inversion to get:

| x |   |  -650    1 |^-1   |  175    |

| y | = |  120     1 |     |  25,080 |

Using matrix inversion, we get:

| x |   |  -0.00016  0.00875 |   |  175    |    | 1.104 |

| y | = |  0.00476   0.00004 |   |  25,080 | =  | 39.704 |

Therefore, the solution to the system of equations is x = 1.104 and y = 39.704.

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Answer:

From the given information, we know that 2 red peppers produce a fire that is 25 meters long, and 10 green peppers produce a fire that is 15 meters long.

To find the length of the fire produced by the dragon eating 3 red peppers and 5 green peppers, we can use a proportion:

(3/2) * 25 + (5/10) * 15 = x

where x is the length of the fire produced by the dragon eating 3 red peppers and 5 green peppers.

Simplifying the equation, we get:

37.5 = x

Therefore, the length of the fire produced by the dragon eating 3 red peppers and 5 green peppers is 37.5 meters.

Step-by-step explanation:

The value of x found using the assumption, ΔABC is an isosceles triangle and the measure using the fact that ∠ABC > ∠ACB are;

a) x = 4.5

The assumption made is that the triangle is an isosceles triangle

b) {x ∈ Z| -6 ≤ x ≤ 8}

An isosceles triangle is a triangle that has a pair of congruent sides.

Let ΔABC be an isosceles triangle, we get;

∠ABC is congruent to ∠ACB, (∠ABC ≅ ∠ACB), therefore, by the definition of congruence triangles, we get;

m∠ABC = m∠ACB

The question indicates that the measure of the angles are;

∠ABC  = 100 - 12·x

∠ACB = 8·x + 10

Which indicates, by the substitution property, that we get;

100 - 12·x = 8·x + 10

100 - 10 = 8·x + 12·x = 20·x

100 - 10 = 90 = 20·x

20·x = 90

x = 90/20 = 4.5

The assumption made is that the triangle ΔABC is an isosceles triangle

b) ∠ABC > ∠ACB, therefore;

100 - 12·x > 8·x + 10

100 - 10 > 8·x + 12·x = 20·x

100 - 10 = 90 > 20·x

20·x < 90

x <  90/20 = 4.5

x < 4.5

The possible integer values of x can be found as follows;

100 - 12·x ≥ 0

100 ≥ 12·x

x ≤ 100/12 = 8.[tex]\overline{3}[/tex]

x ≤ 8.[tex]\overline{3}[/tex]

100 - 12·x ≤ 180

100 - 180 ≤ 12·x

12·x ≥ -80

x ≥ -80/12 = -6.[tex]\overline{6}[/tex]

x ≥ -6.[tex]\overline{6}[/tex]

Similarly, we get;

8·x + 10 ≥ 0

x ≥ -10/8 = -1.25x

x ≥ -1.25

8·x + 10 ≤ 180

x ≤ (180 - 10)/8 = 21.25

x ≤ 21.25

The possible integer value of x, using the interval, x ≥ -6.[tex]\overline{6}[/tex], x ≤ 8.[tex]\overline{3}[/tex] are therefore; -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, which can be expressed as; {x ∈ Z| -6 ≤ x ≤ 8}

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Answer:

Step-by-step explanation:

Here's a step-by-step explanation of the reflections:

Point R is located at (1, 1) on the coordinate plane.

Reflection over the y-axis: This reflection changes the sign of the x-coordinate. In other words, if the point (x, y) is reflected over the y-axis, the reflected point will be ( -x, y). So, for point R at (1, 1), the reflection over the y-axis creates R' at (-1, 1).

Reflection over the x-axis: This reflection changes the sign of the y-coordinate. In other words, if the point (x, y) is reflected over the x-axis, the reflected point will be (x, -y). So, for point R' at (-1, 1), the reflection over the x-axis creates R'' at (-1, -1).

So the final location of R'' is at the ordered pair (-1, -1).

The solution to the equation 4x² = 16 is x = 2.

Given the equation in the question;

4x² = 16

x = ?

To solve for x, first divide both terms by 4.

4x² = 16

4x²/4  = 16/4

x² = 4

Take the square roots of both sides

√x² = ±√4

x = ±2

x = -2 or 2.

Therefore, the value of x is 2.

Option D)2 is the correct answer.

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Answer:

D.2

Step-by-step explanation:

[tex]4 {x}^{2} = 16 \\ \frac{4 {x}^{2} }{4} = \frac{16}{4} \\ {x}^{2} = 4 \\ \sqrt{ {x}^{2} } = \sqrt{4} \\ x = \sqrt{4} \\ x = 2[/tex]

Answer:

The solution to the equation is **x = 3.24**. Here is how I solved it:

First, I isolated the square root term by subtracting 7 from both sides of the equation:

5 square root x = -9

Then, I divided both sides by 5 to get the square root of x alone:

square root x = -9/5

Next, I squared both sides to eliminate the square root:

x = (-9/5)^2

Finally, I simplified the right side by multiplying the fractions:

x = 81/25

x = 3.24

I checked my answer by plugging it back into the original equation and verifying that both sides are equal:

5 square root 3.24 + 7 = -2

-2.01 + 7 = -2

4.99 = -2

Since the difference is very small, I concluded that x = 3.24 is a valid solution.

Step-by-step explanation:

Answer:

5 seconds

Step-by-step explanation:

d = vt + 16t² , that is

vt + 16t² = d

substitute d = 480, v = 16 into the equation

16t + 16t² = 480 ( divide through by 16 )

t + t² = 30 ( subtract 30 from both sides )

t² + t - 30 = 0 ← in standard form

(t + 6)(t - 5) = 0 ← in factored form

equate each factor to zero and solve for t

t + 6 = 0 ⇒ t = - 6

t - 5 = 0 ⇒ t = 5

t > 0 , then t = 5

the object will hit the ground 5 seconds later

Answer:

-------------------------

As per given we have:

Substitute these into given equation and solve for t:

The first value of t is discarded as time can't be negative, so the answer is 5 seconds.

Answer:

After rounding the nearest tenth of a square foot, the surface area of the  circular cylinder is 131.88 feet^2.

Step-by-step explanation:

To find surface area of a right circular cylinder we can use the formula,

A = 2πrh + 2πr^2

Here A is surface area,

π is mathematical constant ,

r is radius, and h is the height of the cylinder.

We have

r = 3 ft

h = 4 ft,

Now we put the values to find the surface area,

A = 2π × 3 × 4 + 2π ×3^2

A = 24π + 18π

A = 42π

A= 42×3.14                             (we know π = 3.14 )

A = 131.88

After rounding the nearest tenth of a square foot, the surface area of the  circular cylinder is 131.88 feet^2.

The ratio of the number of sixth-graders who visited the science museum to the number of sixth-graders who visited the history museum is

10:39.

What is meant by the ratio of two quantities?

A ratio displays the multiplicity of two numbers. Mathematicians use the term "ratio" to compare two or more numbers. It serves as a comparison tool to show how big or tiny an amount is in relation to another. Two quantities are compared using division in a ratio. In this case, the dividend is referred to as the "antecedent" and the divisor as the "consequent." In general, a: b, which can be interpreted as "a is to b," is used to denote a ratio between two quantities, let's say "a" and "b."

Given,

  Number of students who picked the science museum = 10

Number of students who picked the history museum = 39

The ratio of students who visited the science museum to students who visited the history museum = 10:39.

Therefore the ratio of the number of sixth-graders who visited the science museum to the number of sixth-graders who visited the history museum is 10:39.

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The local maximums are at x = -4 and x = 4, and the value of the local maximum is f(x) = 1.

For a function f(x), we define a local maximum as a value of x = c such that:

f(c) ≥ f(x)

for any value of x in a given interval.

Here we can see two local maximums on the graph, and we can see that these are at:

x = -4 and x = 4

b) And the local maximum value of f is the value that the function takes in the maximum, we can see that:

f(-4) = f(4) = 1

The value of the local maximum is y = 1.

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The solution is the union of the solutions from both inequalities. That is, x is either greater than 3.2 or less than -0.75. So, the final solution is: -0.75 < x < 3.2.

What is  inequalities?

An inequality is a mathematical statement that represents a comparison between two values, and indicates the relationship of one value being greater than, less than, or equal to the other. It is usually represented using symbols such as ">" (greater than), "<" (less than), ">=" (greater than or equal to), "<=" (less than or equal to), and "≠" (not equal to). For example, the inequality "2x + 3 > 7" expresses that the value of the expression "2x + 3" is greater than 7 for some values of x.

Inequalities are used to describe a range of values that satisfy a certain condition. The solution to an inequality is a set of values that make the inequality true.

To solve the inequality "5x - 4 > 12 or 12x + 5 < -4", we can start by solving each inequality separately and then combining the solutions to find the final solution.

Adding 4 to both sides, we get 5x > 16

Dividing both sides by 5, we get x > 3.2

So, the solution to this inequality is x > 3.2

Subtracting 5 from both sides, we get 12x < -9

Dividing both sides by 12, we get x < -0.75

So, the solution to this inequality is x < -0.75

Final solution: Combining the solutions from both inequalities:

Since "or" is used in the inequality, the solution is the union of the solutions from both inequalities. That is, x is either greater than 3.2 or less than -0.75. So, the final solution is: -0.75 < x < 3.2.

So the solution to the inequality "5x - 4 > 12 or 12x + 5 < -4" is -0.75 < x < 3.2.

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On solving the provided question we can say that equations are = .60x + .85y = .75(180)

A mathematical equatiοn is a formula that joins two statements and uses the equal symbol (=) tο indicate equality. A mathematical statement that establishes the equality of twο mathematical expressiοns is known as an equation in algebra. Fοr instance, in the equatiοn 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart.

The relationship between the twο sentences on either side of a letter is described by a mathematical formula. Often, there is οnly one variable, which also serves as the symbοl. for instance, 2x – 4 = 2.

t x = the number of ounces of Sοlution A

y = the number of ounces of Sοlution B

x + y = 180    

y = 180 - x

Solving equation -

0.60 + 0.85y = 0.75(180)

0.60 + 0.85y = 135

60x + 85y = 13500

60x + 85(180-x) = 13500

60x + 15300 - 85x = 13500

-25x = -1800

x = 72ounces

y = 180 - 72

y = 108 ounces        

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Answer:

The greatest integer solution to the inequality 1 < (c - 1)^2 ≤ 36 is c = 6.

Step-by-step explanation:

The revenue corresponding to break even condition for selling x units is $4.28.

An evaluation of the model's accuracy in estimating the link between X and y is done using a cost function. In most cases, this is represented as a difference or distance between the projected value and the actual value. The price element (you may also see this referred to as loss or error.)

To break even (R = C) we have:

7.8 √x + 22,000 = 13.82x

Substitute the value of x = u² thus:

7.8u +22000 = 13.8u²

13.8u² - 7.8u - 22000 = 0

The quadratic formula is given as:

u = -b ± √b² - 4ac / 2a

u = -(-7.8) ± √(-7.8)²- (4)(13.82)(22000) / 2(13.82)

u = 7.8 ± 7.8 / 27.64

u = 7.8 + 7.8 / 27.64

u = 0.56

Back substituting the value of u:

x = u²

x = (0.56)²

x = 0.31

Substituting the value of x is R:

R = 13.82 (0.31)

R = 4.28

Hence, the revenue corresponding to break even condition for selling x units is $4.28.

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Answer:

Step-by-step explanation:

here's a more detailed explanation:

The assistant received a raise of 10%, which means that their salary increased by 10% of the original salary. The new salary after the raise is given as 47,585.

To find the original salary before the raise, we need to reverse the effect of the raise. To do this, we divide the new salary by the factor that represents the increase, which is 1 plus the raise as a decimal.

The raise as a percentage is 10%, which is equivalent to 0.10 as a decimal. Therefore, the factor that represents the increase is 1 + 0.10 = 1.10.

We can now use this factor to find the original salary by dividing the new salary by the factor:

Original salary = New salary / (1 + Raise as a decimal)

Original salary = 47,585 / (1 + 0.10)

Original salary = 47,585 / 1.10

Original salary = 43,259.09

So the salary before the raise was 43,259.09.

The value of AD is 26.

There are two circles with centers A and D.

The tangent line touches both points B and C.

The given measurements are enough to solve for the missing value and the solution is shown below:

Solve for the measurement of AC which the hypotenuse of legs AB and BC by Pythagorean theorem:

Solve for angle of A

sin A=26/27.51

A=70.93°

Finally, we solve for the length of AD using SOH

sin 70.93°=AD/27.51

AD=26

The answer is 26.

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The area of the given composite shape with two rectangles is 68 m²

What is a rectangle?

There are four right angles on the quadrilateral that forms the rectangle. Every corner or vertex has a right angle where the two sides meet. It differs from a square, which has all of its sides of equal length, in that the opposite sides of the rectangle are equal in length. Two dimensions and flatness combine to make a rectangle.

The figure can be divided into a rectangle with a length of 8m and breadth of 6m and another rectangle of length 5m and breadth = (10-6) = 4m.

To find the area of the whole figure, we first find the areas of small and big rectangles and sum their areas.

Area of small rectangle = length * breadth = 5*4 = 20 m²

Area of big rectangle = length * breadth  = 8 * 6 = 48 m²

Therefore the area of the given composite shape with two rectangles is 20+48 = 68 m².

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