To which set(s) of numbers does √2 belong?
Select all that apply.

A. rational
B. irrational
C. integer
D. whole
E. natural
F. not rational

SOLUTION:

Step 1:

In this question, we are given the following:

Step 2:

he detiails of the solution are as follows:

sing the Laws of logarithm which says that:

Hence,

The height of the soccer ball after 1.8 seconds will be 372.47 feet.

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

An air kick is made with a soccer ball. The table displays the ball's height y (in feet) after x seconds.

The function is given as,

y = 0.06x² + 17.82x + 32.27

The height of the soccer ball after 1.8 seconds will be given as,

y = 0.06(18)² + 17.82(18) + 32.27

y = 19.44 + 302.76 + 32.27

y = 372.47

The height of the soccer ball after 1.8 seconds will be 372.47 feet.

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By definition, the work is given by:

Where W is the work in Joules (J), F is the force in Newtons (N) and d is the distance in meters (m).

In this problem we have:

• W = 280J,

• d = 35m.

We can find the force F in terms of W and d:

Replacing the values of W and d, we find that the force F is:

In the last step, we used that J = N m.

Answer: The force is F = 8N.

Answer: 50.24ft²

Step-by-step explanation:

Total area of square = 8 * 8 = 64 ft²

Diameter of circle = 8 ft

The formula of area of circle = π r²

(4 = r)

(r² = 16)

3.14 * 16

50.24ft²

The total number of 8780 minutes was spent on the assembly and packaging of the wagons in June at these two stores.

Matrix A shows the number of wagons sold at two different locations during the month of June.

[tex]A =\begin{bmatrix}50 & 90 & 30\\25 & 5 & 50\\\end{bmatrix}[/tex]

Matrix B shows the number of minutes required for the assembly and packaging of the three different-sized wagons.

[tex]B = \begin{bmatrix}15 & 5\\20 & 8 \\30 & 12 \end{bmatrix}[/tex]

We have to multiply Matrix A by Matrix B

[tex]AB =\begin{bmatrix}50 & 90 & 30\\25 & 5 & 50\\\end{bmatrix}\begin{bmatrix}15 & 5\\20 & 8 \\30 & 12 \end{bmatrix}[/tex]

[tex]AB =\begin{bmatrix}3450 & 1330 \\2875 & 1125 \\\end{bmatrix}[/tex]

So the time is 3450 + 1330 + 2875 + 1125 = 8780 minutes

Therefore, a total number of 8780 minutes was spent on the assembly and packaging of the wagons in June at these two stores.

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Answer:

Step-by-step explanation:

Took the quiz

Answer:

Step 1: DAB

Step 2: rotated triangle 180° using AC as center of rotation

Step 3: EAC

Step 4: now all 3 angles…

Step 5: a + b + c = 180°

Step-by-step explanation:

Answer:

yellow 75 gallons

white 45 gallons

red 15 gallons

Step-by-step explanation:

yellow (5) + white (3) + red (1) equal 9 total parts.

5/9 is yellow

3/9 is white

1/9 is read

5/9 x 135 = 75

3/9 of 135 = 45

1/9 of 135 = 15

We have following:

The sine of the angle is given by the quotient of the opposite side and the hypotenuse

replacing:

The answer is the option C. 0.38

It takes four (4) comedy routines to hear 360 jokes

A proportion can be defined as an equation which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.

By applying direct proportion, we have:

1 minute = 3 jokes

X minutes = 360 jokes

Cross-multiplying, we have:

3X = 360

X = 360/3

X = 120 minutes

Now, we can determine the number of comedy routines required for 360 jokes as follows:

Number of comedy routines = 120/35

Number of comedy routines = 3.42 ≈ 4 comedy routines.

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Find the inverse of:

a. To sketch f(x), we use the graph of the parent function

Translated 3 units to the left:

b. The part of the function f(x) that is one-to-one and non-decreasing is in the domain [-3, ∞). Expressing in inequality notation: x ≥ -3.

c. The function f(x) can be written as:

Applying square root on both sides:

Solving for x:

Swapping letters:

Since we have chosen only the non-negative part of the domain for f(x), we use only the positive sign:

Both functions, f(x) and its inverse are shown below:

Answer:

l=10.5 in , w=16.5 in

Step-by-step explanation:

p=2l+2w
54=2(w-6)+2(w)
54=2w-12+2w
54=4w-12
66=4w
w= 16.5
l=w-6
l=16.5-6

l=10.5 in
w=16.5 in

hope this helps

1. If Alex runs a mile in under 6 minutes, then he will have a new personal record. Alex ran a mile in 5 minutes and 45 seconds. Therefore, Alex set a new personal record. - law of Detachment

2. If you go to the water park, then you will need to bring sunscreen. If you do not bring sun screen, then you will burn. Therefore, when you go to the water park you will get a sunburn. - law of contrapositive

3. If two lines are parallel, then they never intersect. Line a and line b intersect. Therefore, line a and line b are not parallel - Law of Syllogism

4. If the measures of two angles in a triangle are 30° and 60°, then the third angle is 90°. If a triangle has a 90° angle, then it is a right triangle.  Therefore, if a triangle has two angles that measure 30° and 60°, then it is a right triangle. - Not a valid conclusion

According to the law of contrapositive, the initial assertion is accurate if and only if the contrapositive is accurate. The original assertion is untrue if the contrapositive is false. A conditional assertion that may or may not depend on another is a contrapositive.

Using deductive reasoning, a syllogism is a three-part logical argument in which two premises are joined to get a conclusion.

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Answer:

72 m

Step-by-step explanation:

We observe that 7y+6=18, and thus y=12/7.

So, the perimeter is:

[tex]2(18+7y+6) \\ \\ =14y+48 \\ \\ =14(12/7)+48 \\ \\ =72[/tex]

Answer:

  the slope is 3/4

  the y-intercept is 4

Step-by-step explanation:

You want the slope and y-intercept of the line defined by the equation 3x -4y = -16.

The values of interest can be found easily from the slope-intercept form of the equation of the line. Solving for y puts the equation in that form.

  3x -4y = -16 . . . . . . given

  -4y = -3x -16 . . . . . subtract 3x

  y = 3/4x +4 . . . . . . divide by -4

Compare this to the slope-intercept form equation:

  y = mx + b . . . . . . . line with slope m and y-intercept b

We see that ...

  m = 3/4, b = 4

  The slope is 3/4

  The y-intercept is 4

The degree of the polynomial is even.

Algebraic expressions called polynomials include indeterminates and constants. Polynomials can be considered a particular type of mathematics. In practically all areas of mathematics, including calculus, they are used to express numbers. They are also regarded as being crucial in several areas of mathematics. Examples of polynomials include 2x + 9 and [tex]x^{2}[/tex] + 3x + 11. The "=" sign is absent from all of these samples, as you may have observed.

The polynomial's degree is even since the final behavior is the same in both directions (for -x and for +x, y→∞).

The y-intercept is the fixed term. Since it is not an integer, evenness and oddness cannot be determined.

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If a monument in the form of a marble cylinder has a circular base with a radius 1.5 meters and the altitude of the monument is 3.5 meters. then the quantity of marbles contains in the monument is 24.74 meter cube

The shape of the monument  is cylinder

The base radius of the cylinder = 1.5 meter

The altitude of the monument = 3.5 meters

The volume of the cylinder = [tex]\pi r^{2}h[/tex]

Where r is the radius of the cylinder

h is the height of the cylinder

Substitute the values in the equation

The volume of the cylinder = [tex]\pi (1.5)^{2}(3.5)[/tex]

= 24.74 meter cube

Hence, If a monument in the form of a marble cylinder has a circular base with a radius 1.5 meters and the altitude of the monument is 3.5 meters. then the quantity of marbles contains in the monument is 24.74 meter cube

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Answer:

a) -2/9

Step-by-step explanation:

2/3 - 5/6, you would need to start by making the denominators the same, so 2/3 would become 4/6. 4/6-5/6 = -1/6.

-1/6 ÷ 3/4, use the keep change flip rule

-1/6 × 4/3 then multiply directly across:

-1×4=-4

6×3=18

-4/18 reduces to -2/9

Measure of the angle m ∠ RQS = 58 ° for the given circle with arc RS subtending m ∠RPS=14 x + 46 ° at the center P and m ∠ RQS = 3 x + 43 ° at Q, on the circumference.

As given in the question,

Measure of the angle is given by :

m ∠ RPS=14 x + 46 °                                  

m ∠ RQS=3 x + 43 °                                      

m ∠ RPS = twice m ∠RQS (angle subtended at center of the circle)

14 x +46 =2(3 x + 43)

⇒ 14x + 46 = 6x +86

⇒ 14x-6x=86-46

⇒8x=40

⇒ x=5°

m ∠ RQS = (3 x + 43) °  

                 =[3(5) + 43 ]°

                 = 58°

Therefore, measure of the angle in the given circle m ∠RQS is equal to the  58 °

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Answer:

You cannot multiply or divide for 4 and 3 so no false

Step-by-step explanation:

The required expression is  "8+x" .

When integer variables, constants, and algebraic operations are used to create an expression, it is said to be algebraic (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)

The required expressions are:

19) 8 + x

20) x - 10

21) 3 + x = 10

22) 4 > 6t

23) d > 3/2 p

24) 4s ≥ 70 + 5

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Answer:

3(2x+1)+2(x+4)

3x2x and 3x1

6x+3+2(x+4)

2xx and 2x4

6x+3+2x+8

and the like terms

6x+2x and 3+8

8x+11

Step-by-step explanation:

Answer:

8x +11

Step-by-step explanation:

3(2x+1)+2(x+4)

Use the distributive property to multiply 3 by 2x+1.

6x+3+2(x+4)

Use the distributive property to multiply 2 by x+4.

6x+3+2x+8

Combine 6x and 2x to get 8x.

8x+3+8

Add 3 and 8 to get 11.

8x+11

Answer:  x = 3

x = ± √3 = ± 1.7321

Step-by-step explanation:

those are 2 solutions

1) Using order of operations, the solution to the given expression is; 12

2) The estimated cost of groceries if the prices are estimated to the nearest dollar is; $42

In mathematics , the acronym for the right order of operations is PEMDAS which denotes;

P- Parentheses

E- Exponents

M- Multiplication

D- Division

A- Addition

S- Subtraction.

3) From the given statement, we are to add 6 to 12, then divide the sum by 4. Thereafter, we divide the quotient by negative nine and then multiply by twenty-four. This is expressed as;

[(6 + 12)/4] = 18/4 = 9/2

Then divide by -9 to get;

(9/2) ÷ 9 = 1/2

Then we multiply by 24 to get;

1/2 * 24 = 12

4) Let us first estimate each cost to the nearest dollar to get;

$6.47 ≈ $6

$14.72 ≈ $15

$7.99 ≈ $8

$9.40 ≈ $9

$2.79 ≈ $3

Total estimated cost = 6 + 15 + 8 + 9 + 3 = $42

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The surface area and volume of the polyhedron are mathematically given as

This is further explained below.

Generally, The surface area of a three-dimensional object is equal to the total of areas of all of its faces, also known as surfaces. A cuboid has six faces that are rectangular in shape.

Add together the areas of each of the cube's six sides to get the surface area of the cube. To get the surface area of the prism, we may additionally label its length (l), width (w), and height (h), and then use the formula surface area = length (l) times width (w) times height (h).

To refresh your memory, the surface area of an item is the entire area of the exterior surfaces of the three-dimensional object or the total sum of the area of the faces of the object.

In other words, the surface area of an object is its "face area." It is expressed in terms of square units as a measurement.

In conclusion, Generally, the Surface area is mathematically given as

SA= 9+35+35+33+36+12

SA=160 Sqr Units

Generally, the equation for Volume is mathematically given as

V=(11*9)+6

V=99+6

V=105 cubic units

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CQ is attached  surface area

Source of magnetic force - Nail

Source electric force - battery cell

We know that the electromagnet is a type of magnet whose magnetic property depends on the interaction of the magnetic material with an electric field. We can see in the image that the nail which serves as the magnetic material is connected to a cell which is the source of the given electric current.

It the follows that the nail above is the source of the magnetic force because the coils of wire while the battery cell is the source of the electrical force.

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Two different expressions that represent the total bill, including both tax and tip for the meal sold by the restaurant, are:

To arrive at the amount to be paid by the customer, we first have to get the original amount that they should pay for the meal. Next, they are meant to apply the 16% tip for the total meal and this is gotten by calculating 16% of the total meal.

Next, we ought to get 5% of the sales tax which will also be applied to the total bill. When all of these are summed up, we will arrive at the total amount to be paid by the customer. Another way will be, to sum up, all of the percentages and apply them to the total bill.

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Step-by-step explanation:

we have to find the equation, that's why we select the data

(t, n) = (50, 52) and (14,148)

we look as follows

n-52 = ((148-52) / (14-50)) * (t-50)

We perform the indicated operations

n-52 = (96/24) * (t-50)

n-52 = 4 (t-50)

finally we get the result

n = 4t-148

Answer:

Linear equation n = 4t-148

B)

Therefore,

Hence, the answer is 61degrees.

The expected number of the real workers in any sample of size 50 is 35

Algebra is a branch of mathematics that facilitates the description of problems or situations into mathematical statements. It involves variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division to generate a valid mathematical statement. All branches of mathematics, such as coordinate geometry, calculus, and trigonometry, employ algebra. An elementary algebraic formula is 2x + 4 = 8. Algebraic expressions serve as the mathematical statement when operations on variables and constants, such as addition, subtraction, multiplication, division, etc., are done. Assume James and Natalie had the notion to arrange the matchsticks into numerical patterns while they were fiddling with them.

Given that : A random sample of n = 50 teachers was selected from a Local Government and it has been established that 30% of the entire teachers are ghost workers and 70% are real workers.

n= 50

30 % are ghost workers

= 30% 0f 50

= 0.3×50

= 15 are ghost workers

50 - 15 = 35 are real workers

The expected number of the real workers in any sample of size 50 is 35

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Answer:

Monica sells one more book (12) than Carlos (11).

Step-by-step explanation:

Carlos: $60.50/$5.50 = 11

Monica: $57.00/$4.75 = 12

Monica sells one book more than Carlos.