Ethan works as a server in a restaurant. He gets a `15\%` tip on the cost of every order. What t

The missing side length is 22.6.

From the given figure, We can observe that it is a right-angled triangle.

We are provided with two angles in the triangles,

So, We can evaluate the third angle by the sum of the angles property of

a triangle.

∠ABC + ∠BAC + ∠ACB = 180°

90° + 37° + ∠ACB = 180°

∠ACB = 180° - 127°

∠ACB = 53°

By the property of the triangle,

tanα = Perpendicular/Base of the triangle

tanα = AB/BC

tan53° = x/17

x = tan53°×17

x = 22.6

Therefore, The missing side length is 22.6.

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The missing side length of right angled triangle is 22.6.

Given,

Right angled triangle

Here

Two angles in the triangles : 37 and 90 degrees .

So, We can evaluate the third angle by the sum of the angles property of a triangle.

∠ABC + ∠BAC + ∠ACB = 180°

90° + 37° + ∠ACB = 180°

∠ACB = 180° - 127°

∠ACB = 53°

By the property of the triangle,

tanα = Perpendicular/Base of the triangle

tanα = AB/BC

tan53° = x/17

x = tan53°×17

x = 22.6

Therefore, The missing side length is 22.6.

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The surface area of the triangular prism is, 178 cm²

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The triangular prism is shown in figure.

Now, We know that;

The surface area of the triangular prism is,

⇒ S.A = 2B + ph

Where, B stands for the area of the base, p represents the perimeter of the base, and h stands for the height of the prism.

Here, We have;

Height = 3 cm

Area of Base is,

⇒ B = 11 × 4

       = 44 cm²

Perimeter of base is,

⇒ p = 2 (11 + 4)

      = 2 × 15

      = 30

Hence, The surface area of the triangular prism is,

⇒ S.A = 2B + ph

          = 2 × 44 + 30 × 3

          = 88 + 90

          = 178 cm²

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First, we need to perform the calculation within the parentheses:

698347 + 2834619 = 3532966

Then, we can multiply the result by 3:

3532966 x 3 = 10598898

Therefore, 698347+2834619 times 3 is equal to 10598898.

Answer:

6,16

Step-by-step explanation:

To complete a ratio table, we need to find the missing values that would make the ratios equivalent. 82   19    4:1     164  38    4:1  57   13.5  4:1

328  76    4:1   410  95    4:1

To complete the given ratio table, we need to find the missing values that would make the ratios equivalent. Ratios are used to compare two or more quantities and are expressed in the form of a fraction, with the numerator representing one quantity and the denominator representing another.

Starting with the first row of the table, we can see that the ratio of the first two values is 82:19. To find the missing value in this row, we need to determine what value multiplied by 19 would give us 82. Using basic algebra, we can set up the equation

19x = 82

And solve for x, which gives us

x = 82/19.

= 4.32

This value is approximately 4.32. Therefore, the missing value in the first row is 82:19:4.32.

Moving on to the second row, we can see that the ratio of the first two values is 164:38. Similar to the first row, we can find the missing value by determining what value multiplied by 38 would give us 164.

Solving the equation

38x = 164

x = 164/38,

= 4.32.

Therefore, the missing value in the second row is 164:38:4.32.

In the third row, only one value is given, which means we need to determine the other value that would make the ratio equivalent to the previous rows.

Since the missing value in the first two rows is 4.32, we can set up the equation

57: x = 82/19

And solve for x.

This gives us x = 57 * (82/19), which is approximately 244.42. Therefore, the ratio in the third row is 57:244.42.

In the fourth row, we can use the same approach as the previous rows to find the missing value. Setting up the equation

76x = 328

x = 328/76,

which is approximately 4.32. Therefore, the missing value in the fourth row is 328:76:4.32.

Finally, in the last row, we are asked to explain the process of completing a ratio table. To complete a ratio table, we need to determine the missing values that would make the ratios equivalent. This involves setting up equations based on the given ratios and solving for the missing values. Once we have found the missing values, we can add them to the table and ensure that the ratios are equivalent across all rows

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The inequality that represents the greatest distance that can be driven while staying within the daily budget is:

0.18x + 40 ≤ 67

Solving for x, we get:

0.18x ≤ 27

x ≤ 150

Therefore, the greatest distance that can be driven in a day while staying within the daily budget is 150 miles.

Two other two-step inequalities with the same solutions are:

0.18x ≤ 28

x ≤ 155

The options that are not polynomials are:

A, B, C, and E.

A general polynomial on a variable x can be written as:

P(x) = aₙ*xⁿ + ... + a₁*x + a₀

The coefficients a are all real numbers, and all the exponents on the variable x must be integer numbers.

So:

We can't have square roots of the variable.

We can't have negative exponents on the variable.

With that in mind, the options that aren't polynomials are:

A: because there is an exponent of 2/3

B: There is an exponent of -3

C: there is an exponent of -2

E: There is an exponent of -2

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Answer:

Line Segment

Step-by-step explanation:

This is true because a probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.

The area under the probability distribution is a measure of the probability of all the possible outcomes. Since the sum of all the probabilities of all the possible outcomes must be 1, the total area under the probability distribution must also be 1. This is because the probability of an event happening is the area under the curve of the probability distribution at that event. Thus, the total area under the probability distribution must always equal 1.

This is true because a probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.

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The shape Miss Hodgman is describing a parallelogram.

A parallelogram is a two-dimensional flat shape with four sides. It has two pairs of opposite sides that are parallel and congruent, meaning they have the same length. Each pair of opposite sides is also parallel and has equal distance between them. The four interior angles of a parallelogram are all right angles or 90-degree angles.

The opposite angles of a parallelogram are also congruent, which means they have the same measure. The adjacent angles of a parallelogram are supplementary, which means they add up to 180 degrees. Therefore, each angle of a parallelogram measures 180 degrees divided by two, or 90 degrees.

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From the given data, we say a definite integral is improper if one endpoint is infinite, or if the integrand is infinite.

One endpoint is infinite, or if the integrand is infinite, the definite integral cannot be evaluated using the usual techniques. Instead, we must use the concept of a limit to find the value of the integral, if it exists. In the case where one endpoint is infinite, we take a limit as a variable approaches infinity. In the case where the integrand is infinite, we may need to split the integral into pieces or use some other method to deal with the singularity.

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For the given rectangle, the angles are:

1 = 72°

2 = 36°

3 = 18°

4 = 144°

What is a rectangle?

The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length. A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason.

Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.

The given figure is a rectangle.

The angle 3 = 18°

This is because they are alternate angles.

In triangle ADC,

 ∠DAC = 180 - ( 18 + 90) = 72°

The angles  ∠DAC and  ∠BCE are alternate angles.

∠BCE and 1 are congruent angles.

1 = 72°

2 = 180 - ( 72+72) = 36°

From triangle BDC,

∠CDE = 180 - (72+90) = 18

So 4 = 180 - ( 3+∠CDE ) = 180 - (18+18) = 144°

Therefore for the given rectangle, the angles are:

1 = 72°

2 = 36°

3 = 18°

4 = 144°

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If x is a rational number, then x = ab and x³ = a³b³, so both x and x³ are rational numbers. Considering the objection to this statement, we conclude that if x is irrational, then x³ is also irrational number.

This question is in the form p → q. Based on the Definition of a rational number is a ∈ Z, b ∈ Z ≥0, and  (a ≠ b) then a/b

Irrational Number:

All irrational numbers are real numbers that are not rational numbers. That is, an irrational number cannot be expressed as a ratio of two integers. A line segment is also said to be incommensurable if the ratio of the lengths of the two segments is irrational. That means there is no common "scale". That is, it can be used to express the length of two given segments as an integer multiple of itself.

Proof by inverse:

Inverse (q → p)

¬q≡ x is rational, and ¬p≡ x³ is rational.

∀x ∈ R:(x2∉Q)⇒(x∉Q) .

Using the method of proof by contradiction, let's try to prove that

∃x ∈ R: (x2∉Q) ∧(x∈ Q).

If  x is irrational, then we can represent it the next way:

x= pq, p∈ Z, q ∈N.

Let's raise  x to the 2nd power:

x³= (pq)³ = p³q³.

But  p³ is an integer and q³ is natural:

m = p³∈Z, n= q³∈N.

So we can say that

x³ =mn, m∈ Z, q∈ N,

which means that  x³ is irrational by definition

If x is a rational number, then x = ab and x³ = a³b³, so both x and x³ are rational numbers.

Considering the objection to this statement, we conclude that if x is irrational, then x³ is also irrational.

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Answer:

Option 2

 x     y

−3     0

−1      3

 0     4

 3     0

4 3

Step-by-step explanation:

For a relation x →  y to be a function, there can be one and only one value of y for a value of x

Looking at the tables we see that option 1 is out since all x values are 2 andthere are multiple values of y

The last option is out because for x = 0 there are two values of y=-2 and y = 2

Correct choice is the second option which has a unique y value for each value of x

Answer:

option 2 im doing it rn

Step-by-step explanation:

The  Ivan ran a total distance of 550 meters and the Ivan's displacement was 150 meters to the east.

1. To calculate the distance, we need to add up all the distances Ivan ran, regardless of the direction.

Total distance = 300 m + 200 m + 50 m = 550 m

2. To calculate the displacement, we need to find the net change in Ivan's position, which takes into account both distance and direction.

We can start by drawing a diagram to represent Ivan's motion:

      <--- 300 m --->  <--- 200 m ---> <--- 50 m --->

              East              West             East

                (+)               (-)              (+)

Here, the arrows represent the direction of Ivan's motion, and the symbols (+) and (-) represent the direction of his displacement.

To find the displacement, we can add up the individual displacements:

Displacement = +300 m - 200 m + 50 m = +150 m

The positive sign indicates that Ivan ended up 150 meters east of his starting position.

So Ivan's displacement was 150 meters to the east.

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So, the product of two irrational numbers may be rational or irrational, depending on the specific irrational numbers being multiplied.

A real number is said to be irrational if it cannot be expressed as the quotient of two integers, p/q, where p and q are both integers. The square root of two, for example, cannot be stated as an integer or a fraction.

No, that statement is not always correct.

In general, the product of two irrational numbers is not necessarily irrational. For example, consider the square roots of 2 and 8:

sqrt(2) * sqrt(8) = sqrt(2) * 2 * sqrt(2) = 2 * 2 = 4,

which is a rational number.

However, there are some cases where the product of two irrational numbers is irrational. For example, the product of the square root of 2 and the square root of 3 is irrational:

sqrt(2) * sqrt(3) = sqrt(6),

which is irrational.

So, the product of two irrational numbers may be rational or irrational, depending on the specific irrational numbers being multiplied.

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The result of the given expression of multiplication 4 x 2 is equal to 8.

Let us consider the expression of multiplication is represented by 'y' .

y = 4 x 2

We can solve above expression in two ways to get the result

1. Addition method.

2. Product method.

First method :

Addition method is explained as :

4 times 2 means :

Four is added two times

4 + 4 which is equal to 8.

or

2 + 2 + 2 + 2 = 8

Second method :

Product method :

Four times two means:

Fours two's are eight.

Therefore, the result value of the multiplication expression 4 x 2  is equal to 8.

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Work Shown:

a = change in distance = 492-300 = 192 miles

b = change in time = 12 weeks

c = a/b = rate of change of distance over time = speed of growth

c = (192 miles)/(12 weeks)

c = (192/12) miles per week

c = 16 miles per week

In other words, each time a week goes by, Ryan has walked another 16 miles.

For a related math concept, check out the slope formula. The slope represents the rate of change. It's useful for graphing linear equations.

Answer:

(D.) [tex]5x^{5} -5x^{3} +4[/tex]

Step-by-step explanation:

Adding Polynomials:

To add both of these two polynomials together, all we need to do is add like terms. All of the other options are wrong, since we do not add the exponents.

[tex]5x^{5} -5x^{3} +4[/tex]

The number of solutions in the equation is One solution

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

The graph

On the graph, we have two lines that intersect at a point

This means that the number of solutions is one

Here, the skills needed are:

The strategy to solve the problem is to use the graph method to solve the system of linear equations and check if the resulting solution satisfies all the equations in the system.

If it does, then the system has one unique solution.

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The indicated function values are If x = 0, then f(0) = 2,
If f(x) = 0, then x = - 1

To evaluate f(0), locate the point on the graph where x will be equal to '0' then find out the y-coordinate of that point where the value of f(0) will be equal to f(0).

Similarly, to find the x at f(x) = 0, take the y-coordinate as 0 and find the corresponding x - coordinate.  

Here we have

A graph that shows the function f(x)  

Given  x = 0  then f(0) will be equal to the y - coordinate at x = 1  

=> If x = 0 then f(0) = 2        

Given f(x) = 0 then x will be equal to the x - coordinate at y = 0

=> If f(x) = 0 then x = - 1    

Therefore,

The indicated function values are If x = 0, then f(0) = 2,
If f(x) = 0, then x = - 1

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Answer:

1. 2.25

2. -1

Step-by-step explanation:

right on edge

The rate of change of a circle's diameter with respect to its radius is a constant value of 2.

The diameter (d) of a circle is twice the radius (r), so we can write:

d = 2r

To find the rate of change of diameter with respect to radius, we can take the derivative of both sides of this equation with respect to r using the chain rule:

d/dx [d] = d/dx [2r]

d' = 2r'

Here, d' is the derivative of diameter with respect to radius, and r' is the derivative of radius with respect to some independent variable (e.g. time).

Since r' is simply equal to 1 (because the derivative of a variable with respect to itself is always 1), we have:

d' = 2

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The required number of pallets used to build one step of the mansion is 1/8 of a pallet of pavers.

In mathematics, the operation and interpretation of a function to make it simple or easier to grasp is known as simplifying, and the process is known as simplification.

Given:

Total number of pallets used = 3/4,

Number of steps = 6

pallet used to build one step = [3/4] / 6 = 3 / 24

                                               = 1 / 8

As a result, 1/8 of a paver pallet is what is needed to construct one step of the palace.

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The length of 164 centimeter after conversion to feet is equivalent to 5.38 feet .

The Units such as centimeter , meter , feet , inches , feet , are used to measure the distance between the two points .

We have to convert the length of 164 cm to feet ;

For conversion , we multiply the given length in centimeter by the conversion factor ;

The conversion factor to convert the length is 0.0328 ;

So , on multiplication ,

We get ;

⇒ 164 centimeter = 164 × 0.0328 feet ;

⇒ 164 centimeter = 5.3792 feet ≈ 5.38 feet .

Therefore , 164 centimeter is approximately equal to 5.38 feet .

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The probability of A given B is 0, and P(A | B) is not equal to P(A). Events A and B are mutually exclusive, meaning that they cannot both occur at the same time, and thus they are not independent. Mutually exclusive events are not necessarily independent and independent events may or may not be mutually exclusive.

P(A) = 0.30 and P(B) = 0.40, so P(A and B) = 0 because the events A and B are mutually exclusive. This means that the probability of A given B is 0, and P(A | B) = 0. P(A | B) is not equal to P(A).Events A and B are mutually exclusive, meaning that they cannot both occur at the same time, and thus they are not independent.The statement that mutually exclusive events and independent events are the same is not accurate. Mutually exclusive events are not necessarily independent and vice versa.Given the results of this problem, we can conclude that mutually exclusive events are not independent, and independent events may or may not be mutually exclusive. The two concepts are not necessarily related as mutually exclusive events do not necessarily need to be independent and independent events do not necessarily need to be mutually exclusive.

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If the recipe calls for 1 5/6 cups of flour, and Finn triples the recipe, he will need 3 times the amount of flour.

To find the total amount of flour Finn will need, we can first convert the mixed number 1 5/6 to an improper fraction:

Next, we can multiply this fraction by 3 to find the total amount of flour needed:

We can simplify this fraction by dividing both the numerator and the denominator by 3:

Therefore, Finn will need 11/2 cups of flour in total.

~ Zeph

Answer:

The area is one side times the other side

Make the other side x.

12x=42

x=42/12=3.5

The perimeter is 2x+2y where x and y are sides of the rectangle.

P= 2(3.5)+2(12)=7+24=31 inches

Hope this helps.

Answer: 3.5

Step-by-step explanation:

42/12 = 3.5

The minimum number of minutes that Lydia still needs to practice is 105 minutes to meet her coach's requirement.

To find the minimum number of minutes that Lydia still needs to practice, we first need to solve the inequality:

3.75 + h ≥ 5.5

Subtracting 3.75 from both sides, we get:

h ≥ 1.75

This means that Lydia still needs to practice for at least 1.75 hours to meet her coach's requirement of practicing for at least 5.5 hours per week.

To find the minimum number of minutes, we can multiply 1.75 by 60, since there are 60 minutes in an hour:

1.75 × 60 = 105 minutes

So, Lydia still needs minimum 105 minutes to practice.

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The coordinates of the figure are  A''(-3, 1),B''(2,2), C''(-2, -1).

What is the transformation of a point?

The transformation, or f: X →X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the image X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation. A function can be moved in one direction or another using translation, rotation, reflection, and dilation. A function can also be scaled using rotation around a point. Two-dimensional mathematical figures move about a coordinate plane according to transformations.

Given that the coordinates of the points A, B, C are A(-6,-3), B(-1,-4), C(-5,-1).

The rule of a reflection across the x-axis is (x,y)→(x,-y).

After reflection across the x-axis,

A(-6,-3)→ A'(-6,3)

B(-1,-4)→B'(-1,4)

C(-5,-1)→C'(-5,1)

A rule of translation of 3 units right and 2 units down is (x,y)→(x+3,y-2).

Thus the new coordinates are:

A'(-6,3)→ A''(-6+3,3-2)=A''(-3,1)

B'(-1,4)→ B''(-1+3,4-2)=B''(2,2)

C'(-5,1)→ C''(-5+3,1-2)=C''(-2,-1)

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Answer:

[tex]2x^{2}[/tex] + [tex]2x[/tex] + [tex]2[/tex]

Step-by-step explanation:

1. In the expression: C - 3D, we plug in the values of C and D

2. So we get the expression: [tex](2x^{2} + 5x -1) - 3(x - 1)[/tex]

3. Then we simplify this even more: [tex](2x^{2} + 5x -1) - (3x + 1)[/tex] by multiplying 3 to the numbers in the parentheses

4. Now we can remove the parentheses: [tex]2x^{2} + 5x - 1 - 3x + 3[/tex]

5. Now we can put the like terms next to each other: [tex]2x^{2} + 5x - 3x + 3 - 1[/tex]

6. FINALLY we simplify: [tex]2x^{2} + 2x + 2[/tex]

Hope this helps! <3