Let U = {1, 2, 3, 4, 5, 6, 7, 8}, A = {6, 8, 10}, B = {5, 6, 9, 12}, and C = {1, 3, 7}

A ∪ B?

Yes!

[tex](2^{2} )^{3}[/tex] = 2^6 = 64

(8-4)^2 = 4^2 = 16

then for the last part

4^-4 is the same as [tex]1/4^{4}[/tex] or 1/256

Then it is order of operations:

do 16 x 1/256 first which is 1/16

and then 64 - 1/16 to get 63 15/16 :)

The amount paid to social security when Dr. Grumman earned $141,340 in 2020 is $8763.08.

A % in mathematics is a quantity or ratio that is stated as a fraction of 100 (from the Latin per centum, "by a hundred"). Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it.

We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.

Formula for percentages: (Value/Total value) * 100

Dr. Grumman earned $141,340 in 2020.

The social security he paid is:

(141340)(6.2/100) = 8763.08

Hence, the amount paid to social security when Dr. Grumman earned $141,340 in 2020 is $8763.08.

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Answer:

3:23

Step-by-step explanation:

The water fight ended at 4:28 and lasted for 32 minutes so

4:28 - 32 minutes = 3:56

3:56 - 33 minutes = 3:23

The instantaneous rate of change of R(t) at time t is the limit of the average rate of change of R(t) as h approaches 0. In this case, the instantaneous rate of change of R(t) at time t = 1 is R'(1) = 9000 dollars/day.

The average rate of change of a function is the ratio of how much the output of the function changes over a given period to the length of that period. We can calculate this for the function R(t) = 210 + 30t3 by considering the time intervals [t, t+h] at h = 1, 0.1 and 0.01 days.

For h = 1 day, the average rate of change of R(t) is 90 dollars/day. This can be calculated by dividing the difference in output of the function at t and t+h, i.e., 30t3+30(t+1)3 = 1080, by the length of the period, h = 1 day.

For h = 0.1 day, the average rate of change of R(t) is 900 dollars/day. This is calculated by dividing the difference in output of the function at t and t+h, i.e., 30t3+30(t+0.1)3 = 9, by the length of the period, h = 0.1 day.

For h = 0.01 day, the average rate of change of R(t) is 9000 dollars/day. This is calculated by dividing the difference in output of the function at t and t+h, i.e., 30t3+30(t+0.01)3 = 0.9, by the length of the period, h = 0.01 day.

The instantaneous rate of change of R(t) at time t is the limit of the average rate of change of R(t) as h approaches 0. In this case, the instantaneous rate of change of R(t) at time t = 1 is R'(1) = 9000 dollars/day.

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Answer:

y= -5/4x+

Step-by-step explanation:

find the gradient first ∆y/∆5x

-4-1/ 8-4

=-5/4

assume one of the points to be x, y

y-1/ x-4 =-5/4

cross multiply

4y-4=-5x+20

4y= -5x+20+4

divide both sides by 4

y= -5/4x+

Answer:

[tex]x = \frac{17}{3} = 5\frac23 = 5.\overline6[/tex].

Step-by-step explanation:

No idea what your question is, but [tex]x = \frac{17}{3} = {5\frac23} = 5.\overline{6}[/tex].

The missing side length is x = 30

What are basic Trigonometric functions?

The angles of sine,  cosine, and tangent are the primary classification of functions of trigonometry. And the three functions which are cotangent, secant, and cosecant can be derived from the primary functions. Basically, the other three functions are often used as compared to the primary trigonometric functions.

In a Right-angled triangle, the tan of an angle is equal to the opposite side/adjacent side

from the given figure,

tan 37° = x/40

0.75 = x/40

x = 30

Therefore, The missing side is 30.

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Note that the function takes the trapezoid's area as input and returns as output the length of the other base is A(x)/7-5=x.

Recall that the function for the trapezoid area is:

A(x)=(B+b)*h/2

where

B and b are the bases and

h is the height.

Thus, given a height of 14 and one base length of 5 with the length of its other base

With the given data: h=14 B and b =5 and x (it may vary which one is bigger)

So that function becomes:

A(x)=(5+x) * 14/2

A(x)=(5+x)*7

So if you want the inverse function, you have to operate to find x:

A(x)/7=5+x

A(x)/7-5=x

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Answer:

5 < x <  15

Step-by-step explanation:

The triangle inequality theorem states that the sum of the measures of any two sides of a triangle must be greater than the measure of the third side

In the given triangle we are provided measures of two of the sides as 10 and 5

Let the measure of the third side be x

So the three sides are 10, 5 and x

Then by the inequality theorem
10 + 5 > x

==>  15 > x or

x < 15    This is an upper bound for x

when we switch sides in an inequality > changes to < and < changes to >

We also have
x  + 5 > 10  ==> x > 10 - 5 ==> x > 5

and

x + 10 > 5 ==> x > -5

Since x > 5 is more restrictive than x > -5, we conclude that x > 5 or 5 < x is the lower bound on x

Combining all inequalities we get

5 < x <  15

Note

We could also state the lower and upper bound limits as

difference of two sides < x < sum of two sides
10 - 5 < x < 10 + 5

or

5 < x < 15

While this may seem easier to compute than the explanation given above, the derivation is left out and may confuse some students

The solution set to the inequality is w > 3

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

w+ 4<4 (w - 2)

Open the bracket

So, we have the following representation

w+ 4 < 4w - 8

Evaluate the like terms

So, we have the following representation

12 < 3w

Divide by 3

4 < w

So, we have

w > 4

See attachment for number line

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By applying standard deviation concept, it can be concluded that all the students had the same score.

The mean is the average of all the scores. It is calculated by adding up all the scores and dividing them by the number of scores.

The standard deviation is a measure of how spread out the scores are. It is calculated by finding the difference between each score and the mean, squaring those differences, finding the average of those squared differences, and then taking the square root of that average.

If all the scores are the same, then the difference between each score and the mean will be 0. This means that the standard deviation will also be 0. Therefore, the correct answer is "all the students had the same score."

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Answer:

4) 7 SqrRt( 5 )

5) 2 SqrRt( 10 )

6) 8 SqrRt( 6 )

Answer:

$115

Step-by-step explanation:

12 + 11 = 23

There are 23 students in the class.

Cost of supplies: $5 per student.

total cost = 23 × $5 = $115

The total cost to purchase the supplies is,

⇒ $115

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Given that;

There are 12 girls and 11 boys registered for the class.

And, You need to purchase supplies that will cost $5 per student.

Here, Total students = 12 + 11 = 23

Hence, The total cost to purchase the supplies is,

⇒ 23 x $5

⇒ $115

Thus, The total cost to purchase the supplies is,

⇒ $115

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Answer: 12

she has 15 cups of sugar and needs 1.25 cup for a batch so we say 15/1.25 to get 12

Answer:

12

Step-by-step explanation:

15 / 1.25 = 12 she can make 12 batches

Answer:

Step-by-step explanation:

4 x 6= 24

24+2=26

The value of x is approximately 0.8 cm when rounded to the nearest tenth.

A triangle is a two-dimensional geometric shape that has three sides and three angles. It is the simplest polygon and is a fundamental building block in many areas of mathematics and science.

The three sides of a triangle can have different lengths and can be of different types, such as equilateral, isosceles, or scalene. An equilateral triangle has three sides of equal length, while an isosceles triangle has two sides of equal length and a third side of a different length. A scalene triangle has all three sides of different lengths.

In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. Thus, we have:

sin(IHJ) = IJ/IH

Taking the sine of both sides and substituting the given values, we get:

sin(23°) = x/2

Multiplying both sides by 2, we have:

x = 2*sin(23°)

Using a calculator, we get:

x ≈ 0.83

Therefore, the value of x is approximately 0.8 cm when rounded to the nearest tenth.

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The measure of each interior angle of a regular polygon having 15 sides is equal to option B: 156°.

A polygon is an enclosed figure composed of more than three straight lines. To find the measure of each interior angle of a regular polygon having n sides, we would first find the total sum of interior angles of this polygon. The formula is:

(n-2) × 180°

= (15-2) × 180°

= 13 × 180°

= 2340°

We, here, found that the sum of all interior angles of a regular polygon having 15 sides is equivalent to 2340°. Now, to find the measure of each angle, we can divide this sum by the number of sides as:

2340/15 = 156°.

Therefore, the measure of each angle of a regular polygon having 15 sides is equivalent to 156°.

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Complete question is:

Find the measures of each interior angles of a regular polygon having 15 sides.

A. 106°

B. 156°

C. 206°

D. 256°

Answer:

22% = 163.63636364 litres.

50% = 409.090909 litres

Step-by-step explanation:

when 22% acid solutions = 180 litres

then 20% acid solutions = ?

therefore =

[tex] = \frac{20}{22} \times 180 \\ = \frac{3600}{22} \\ = 163.63636364.litres[/tex]

Also when 22% acid solutions = 180 litres

then 50% acid solutions = ?

therefore

[tex] = \frac{50}{22} \times 180 \\ = \frac{9000}{22} \\ = 409.090909.litres[/tex]

therefore 22% = 163.63636364 litres.

50% = 409.090909 litres.

Answer:

∴Sum of interior angles in ΔABC = 180°

∠A + ∠B + ∠C = 180°

2x° + 4x° + 6x° = 180°

              12x° = 180°

                = x =

                ∴x = 15

∴∠C = (6)×(15)

      = 90°

This means AC makes a 90° angle (i.e. ∠C) with BC.

∴AC is perpendicular to BC (Proved)

Also ΔABC is a right-angled triangle

Answer:

y = -17/18x + 5/18

Step-by-step explanation:

isolate the y so add five to the other side
18y = 5 + -17x

divide everything by 18

18y/18 -17x/18 5/18
y= -17/18x + 5/18

Answer:

(-1, 2)

Step-by-step explanation:

The solution to a system of equation will always intersect on a graph, which means that at a certain point, they will have the same x and y coordinate.

As we can see from the table, for both f(x) and g(x) when x = -1, y = 2, which is the intersection point.

Answer:

Center is (10, 3)

Radius = 6

Step-by-step explanation:

The standard equation of a  circle is

(x - a)² + (y - b)² = r²

where
(a, b) is the center of the circle and

r is the radius

Comparing (x - 10)² + (y - 3)² = 36

it is easy to  see that a = 10, b = 3 and r =√36 = 6
So center is(10, 3) and radius is 6

As per unitary method, Reeta's salary is 21,000 rupees.

The unitary method is a technique of solving problems by assuming a unit value and then finding out the required value in terms of that unit.

In this problem, we can assume Reeta's salary to be the unit value and then find out how much she spent on car repair work and how much money she has left using this unit value.

Let's assume Reeta's salary to be x rupees. Now, according to the problem, she has spent 2/7 of her salary on car repair work. So, the amount of money she spent on car repair work can be calculated as:

2/7 * x

Using the unitary method, we can now find out how much money she has left with her. We know that she has 15,000 rupees left. So, we can set up the following proportion:

2/7 * x = x - 15,000

Simplifying this equation, we get:

2x = 7(x - 15,000)

2x = 7x - 105,000

5x = 105,000

x = 21,000

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The integers 6,21 from the set will make the inequality 3(j-5)>3(7-2j) true.

An inequality response is defined?

An expression in mathematics where the sides are not equal is referred to as being inequal. A comparison of any two values, known as an inequality, demonstrates that one value is less than, larger than, or equal to the value on the opposite side of the equation.

The given inequality is 3(j-5)>3(7-2j). The given set is S:{−4, 4, 6, 21}.

First, we will simplify the given inequality.

3(j-5)>3(7-2j)

⇒j-5>7-2j

⇒3j>12

⇒j>4

It means that numbers greater than 4 will satisfy the given inequality.

Numbers greater than 4 in the given set are 6,21.

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It should be noted that the set of odd integers has the density property. The density property states that for every subset of the real numbers that contains an infinite number of points, the interior of that subset contains a non-empty open interval. This is true

The set of odd integers is a countable subset of the real numbers, meaning that it can be put into a one-to-one correspondence with the natural numbers. However, even though it is countable, it still has an infinite number of points.

Since the set of odd integers contains an infinite number of points, it must contain a non-empty open interval in its interior. To see this, consider the interval (2n-1, 2n+1) for any positive integer n. This interval contains the odd integer 2n and its endpoints are both odd integers, so it is completely contained in the set of odd integers.

Therefore, the set of odd integers has the density property and is a dense subset of the real numbers.

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The system of equations has infinite solutions.

Given:

y = -6x +2

-12x - 2y= -4

To solve for Equation 2,

The value of y is already given in equation 1,

Thus,

substituting the value of y in equation 2,

-12x -2(-6x +2) = -4

-12x - 12x = -4 +4

0=0

The solution of the two equations is 0. Also, we can see that both equations are in ratio.

Further, the image also shows that the line of the two equations are coinciding.

Hence, the system of equations has infinite solutions.

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How many solutions does this linear system have?

y = -6x +2

-12x - 2y= -4

one solution: (0, 0) one solution: (1, –4) no solution infinite number of solutions.

Answer:

20 boxes

Step-by-step explanation:

Each box ca hold 12 eggs

There are 230 eggs

So you will need 230/12 = 19 1/6 boxes =  19.167 boxes

Since you cannot get less than 1 box, round up to 20 boxes. There will be some empty spaces in one of the boxes

The value of the expression is 5.

What is order of operations?

The order of operations is a rule that specifies the correct sequence of steps to be taken when evaluating a mathematical equation.

To simplify this expression, we need to follow the order of operations, which is:

Exponents (powers, roots)

Multiplication and Division (from left to right)

Addition and Subtraction (from left to right)

So, we start with the exponents:

[tex]3^0+4^{-1} \\= 1 + 1/4 \\= 5/4[/tex]

Now we substitute this value back into the original expression:

[tex](3^0+4^{-1} )*2^2\\ = (5/4) * 2^2 \\= (5/4) * 4 \\= 5[/tex]

Therefore, the value of the expression is 5.

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