Fill in each going so that the resulting statement is true

The complement of A∪B is A′∩B ′.

A set of components in the universal set that are not a part of the initial set is known as the complement of a set in mathematics. Discover what a subset and its complement are, how to calculate a subset's complement, and the proper notation to use when writing a subset and its complement.

Given, universal set, U={1,2,3,4,5,6,7}

A={1,2,5,7}

B={3,4,5,6}

(A∪B) ′=U−(A∪B)

={1,2,3,4,5,6,7}−{1,2,3,4,5,6,7}=ϕ

A′∩B′=(U−A)n(U−B)

={3,4,6}n{1,2,7}=ϕ

Hence ( A∪B)′=A′∩B ′.

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Answer: 21:9 and 42:18

Step-by-step explanation:

14:6 at its most basic form is 7:3, so find anything that could be equal to this if a number is multiplied on both sides.

21:9 is our simplified ratio multiplied by 3 on both sides.

42:18 is our simplified ratio multiplied by 6 on both sides.

But, the final ratio doesn't work, because 7 and 3 respectively cannot multiply to 13 and 8 with the same value.

Answer:

Step-by-step explanation:

6x + 18 = 12x

=> 18 = 12x - 6x

=> 18 = 6x

\( = > x = \frac{18}{6} \)

=> x = 3 (Ans)

Step-by-step explanation:

6x+18=12x

18=12x-6x

collect liked terms

18=6x

divide both sides by 6

=3

The value of (fg)(x)= 3x³+ x²

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given:

f(x) = -3x+1

g(x) = \(x^{2}\)

Now, (fg)(x)

=f(x) * g(x)

=  (-3x+1) * (\(x^{2}\))

=-3x³+ x²

Hence, (fg)(x)= 3x³+ x²

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Answer:

The gcf of 16,48,72 is 4,12,18

Answer:

Using the law of sines and relations in a right triangle, the ground distance AB is of:

AB = 3745 ft.

The ratios between the sine of an angle and the length of the opposite side to the angle are the same in a triangle.

The sum of the measures of the internal angles of a triangle is of 180º, hence the missing angle is of:

180 - (74 + 49) = 57º.

Then the bottom side of the blue triangle is found as follows:

sin(57º)/3300 = sin(74º)/x

x = 3300sin(74º)/sin(57º)

x = 3782 ft.

The ground distance can be found considering that:

Hence the ground distance is calculated as follows:

cos(8º) = AB/3782

AB = 3782 x cos(8º)

AB = 3745 ft.

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A prime number is one where the only factors are one and itself. A composite number has other factors.

You'll have to look at the list of numbers from 1 to 50

In that list, 47 is the largest prime less than 50, and 12 is the smallest composite number greater than 10.

So 47-12 = 35

Answer:

The researcher cannot conclude that salary and gender are dependent.

Step-by-step explanation:

A dependent variable is a variable, for example "Salary" that depends on an independent variable, e.g. "Gender."  Salary is the dependent variable while gender is the independent variable.  This means that the value of salary changes in relation to the gender and not vice versa.  Two variables become dependent if they change based on another independent variable that is operating on them.  In this research, the researcher is not trying to measure gender but the relationship between salary and gender.  To achieve her purpose, she shows that salary depends on gender and not that gender depends on salary.

Answer:

B

Step-by-step explanation:

given scale is 1 inch represents 7.5 feet

then we require to calculate how many 7.5 feet there are in each dimension.

to obtain this divide each dimension by 7.5, that is

13 ÷ 7.5 ≈ 1.73 ( to 2 decimal places )

26 ÷ 7.5 ≈ 3.47 ( to 2 decimal places )

then dimensions are approximately 1.73 inches by 3.47 inches

9514 1404 393

Explanation:

Expand the right side using the distributive property, then collect terms.

  x² -y² = (x -y)(x +y)

  = (x)(x +y) -y(x +y)

  = x² +xy -yx -y²

  = x² +(xy -xy) -y²

  = x² -y² . . . . . . . . . . as required

Answer:

c StartFraction RootIndex 3 StartRoot 100 x EndRoot Over 5 EndFraction

Step-by-step explanation:

Answer:

Step-by-step explanation:

C. \(\sqrt[3]{100}\)x/5

Answer:

(1,2) (4,5)

Step-by-step explanation:

Answer:

Question: Q#01: [4] A police department believes that the number of serious crime which occur each month can be estimated by the equation C = 1200 - 12.5p Where c equals the number of serious crimes expected per month and p equal the number of officers assigned to preventive patrol.

Step-by-step explanation:

The correct answer is Graph 1: y = cos(x/4)Graph 2: y = cos(x/2)

Based on the given descriptions of the graphs and the patterns they follow, the correct pairs are:

Graph 1: y = cos(x/4) ⟶ This graph has a period of 8 units and matches the pattern described.Graph 2: y = cos(x/2) ⟶ This graph has a period of 4 units and matches the pattern described.

Graph 3: y = cos(x) ⟶ This graph has a period of 2π (or approximately 6.28 units) and matches the pattern described.

Graph 4: (Not used)

Graph 5: (Not used)

Please note that without visual representation, it's difficult to provide a definitive answer. The pairs are based on the descriptions provided and may vary depending on the actual shapes of the graphs.

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C. A changing amount of money spent on different categories each year

Amount is a term used to describe a quantity of something, typically money. It is often used to refer to the total value of a financial transaction or the sum of multiple payments. Amount can also refer to any other quantifiable measure, such as a number of items, units of time, or a volume or quantity of something.

Discretionary government spending is a type of government spending that is determined each year by the Congress, and typically includes funds for defense, education, infrastructure, and other government programs. The amount of money spent on each category can vary from year to year, making it a type of changing, or discretionary, spending.

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Answer:

A represents the amplitude of the graph

B represents provides the value for the period which is period= 2pi over B

C represents the phase shift or horizontal translation of the graph

D represents the vertical translation of the graph

Step-by-step explanation:

you're welcome

Based on the information provided, it is expected that after 18 months, the difference in the cost of the two plants is 240.

By following the sequence provided on the table, let's calculate the cost for each plant:

Plant A: 75, 110, 145, 180, 215, 250, 285, 320, 355, 390, 425, 460, 495, 530, 565, 600, 635, 670.

Plant B: 60, 110, 160, 210, 260, 310, 360, 410, 460, 510, 560, 610, 660, 710, 760, 810. 860, 910

Now, let's calculate the difference in cost:

910 - 670 = 240

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Answer:

57.02 dollars

Step-by-step explanation:

850 * 14/12 * .0575 =

The required, Jordan had to pay $53.03 in interest on her loan.

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan.

here,
To find the amount of interest Jordan had to pay, we can use the simple interest formula,

I = P  × r × t

Where I is the amount of interest, P is the principal (the initial amount of the loan), r is the annual interest rate as a decimal, and t is the time in years.

In this case, P = $850, r = 0.0575 (5.75% expressed as a decimal), and t = 14/12 (since the loan was for 14 months, which is 1 year and 2 months or 1.16667 years).

Substitute the value in equation 1.

I = $850 × 0.0575 × 14/12

= $57.02

Therefore, Jordan had to pay $53.03 in interest on her loan.

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The critical value (Using FDIST(0.05, 2,9)) = 3.356

Therefore F statistic should be \(\geq 3.356\)

(a) k = number of columns = 5, n = 3,. Therefore N = 15

df1 = k - 1 = 4

df2 = N - k = 15 - 4= 11

The critical value (Using FDIST(0.05, 2,9)) = 3.356

Therefore F statistic should be \(\geq 3.356\)

_________________________________________

(b) k = number of columns = 5, n = 5,. Therefore N = 25

df1 = k - 1 = 4

df2 = N - k = 25 - 4 = 21

The critical value (Using FDIST(0.05, 4,21)) = 2.758

Therefore F statistic should be \(\geq 2.758\)

_________________________________________

(c) k = number of columns = 5, n = 7,. Therefore N = 35

df1 = k - 1 = 4

df2 = N - k = 35 - 4 = 31

The critical value (Using FDIST(0.05, 4,31)) = 2.678

Therefore F statistic should be \(\geq 2.678\)

_________________________________________

(d) Summary:

(i) As the sample size increases, the critical value decreases, and therefore a smaller F statistic is required to reject the null hypothesis.

(ii) Keeping k constant and increasing n, decreases the critical value and

(iii) Keeping n constant and increasing k, will also decrease the critical value.

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The first and second lengths are not possible lengths of triangle.

The third and fourth lengths are possible lengths of triangle.

For the first case; 3 ft, 5 ft, 9 ft: Not possible. In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. However, in this case, 3 ft + 5 ft = 8 ft, which is less than 9 ft.

For the second case. 11 cm, 6 cm, 17 cm: Not possible. Using the same reasoning as above, we see that 6 cm + 11 cm = 17 cm, which means that the three sides cannot form a triangle.

For the third case. 4 in., 4 in., 6 in.: Possible. The sum of any two sides is greater than the third side, since 4 in. + 4 in. = 8 in., which is greater than 6 in. Therefore, these lengths can form a triangle.

For the fourth case. 16 yd, 10 yd, 12 yd: Possible. Again, we see that the sum of any two sides is greater than the third side, since 10 yd + 12 yd = 22 yd, which is greater than 16 yd. Therefore, these lengths can form a triangle.

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Answer:

−x2−6x+8

Step-by-step explanation:

1,Rearrange terms

2.Distribute

3.Add the numbers

4.combine like terms

hope this helps i lfet some steps for you!!!<3333

Answer:

-3 -12 -11

Step-by-step explanation

You need the total when added plus 2 to be less than 1 ,  the graphic is telling you 1 is the highest the answer could be.

Answer:

all of them..

Step-by-step explanation:

-3+2=-1

-12+2=-10

-11+2=-9

-2+2=0

which are all less than 1

The prove of the given trigonometric function is given below.

The given trigonometric function is,

(sin⁴(x) - cos⁴(x))/(sin²(x) - cos²(x))

Now proceed left hand side of the given expression:

We can write the expression  as,

⇒[(sin²(x))² - (cos²(x))²]/(sin²(x) - cos²(x))

Since we know that ,

Algebraic identity:

a² - b²  = (a-b)(a+b)

Therefore the above expression be

⇒(sin²(x) - cos²(x))(sin²(x) + cos²(x))/(sin²(x) - cos²(x))

⇒(sin²(x) + cos²(x))

Since we know that,

Trigonometric Identities come in handy when trigonometric functions are used in an expression or equation. Trigonometric identities hold for all values of variables on both sides of an equation. Geometrically, these identities include one or more trigonometric functions (such as sine, cosine, and tangent).

Then,

sin²(x) + cos²(x)² = 1 is an trigonometric identity

Hence,

(sin⁴(x) - cos⁴(x))/(sin²(x) - cos²(x)) = 1

Hence proved.

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The measure of each exterior angles of rectangle is 90°

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

A rectangle

A rectangle is a polygon with 4 sides

So, the measure of the exterior angle can be calculated using the formula for the exterior angles in a polygon

The exterior angles in a polygon are found by using:

Exterior of a rectangle in a polygon =  360°/Number of sides of the polygon

In this case,

The number of sides of the rectangle = 4

So, we have

Exterior of a rectangle =  360°/4

Evaluate

Exterior of a rectangle =  90°

Hence, the value of the measure of each exterior angles of rectangle is 90°

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Complete question

Find the measure of each exterior angles of rectangle?

Step by step​

The solution of the system of linear equations is (x, y, z) = (1, 1, - 3).

In this problem we find a system of three linear equations with three variables, which can be resolved by several methods. In this case, we shall use the method of substitution. First, clear the variable x in the third equation:

x = 4 - 3 · y

Second, substitute x in the first two equations:

3 · (4 - 3 · y) + 2 · y - z = 8

12 - 9 · y + 2 · y - z = 8

- 7 · y - z = - 4

2 · (4 - 3 · y) + 2 · z = - 4

8 - 6 · y + 2 · z = - 4

- 6 · y + 2 · z = - 12

Third, clear z in the first equation derived in the previous step:

z = 4 - 7 · y

Fourth, substitute z in the second equation derived in the second step:

- 6 · y + 2 · (4 - 7 · y) = - 12

- 6 · y + 8 - 14 · y = - 12

- 20 · y = - 20

y = 1

Fifth, calculate y and x:

z = 4 - 7 · 1

z = - 3

x = 4 - 3 · 1

x = 1

The solution of the system of linear equations is (x, y, z) = (1, 1, - 3).

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Answer:

..........................

Answer:

cube game

Step-by-step explanation:

one of them wins every time

A number cube is rolled. Player 1 gets a point for any number that is 3 or higher, and player 2 gets a point for any number less than 3

If a number cube is rolled and Player 1 gets a point for any number that is 3 or higher and Player 2 gets a point for any number less than 3 it wouldn't be fair to Player 2 because Player 1 has a higher chance of getting points because he/she has more opportunities.

I hope this is correct

Using simple percentage rule, the answer is 25%,52% and 16.67%.

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. The percent symbol, %, or the abbreviation "pct" are frequently used to indicate percentages. The term "percent" derives from "percent," a shortened form of "per centum," which meaning per hundred.

The required formula is:

percentage (%) = Change/total * 100

Percentage Decrease = \(\frac {80-60}{80} * 100\)

=25%

Percentage Decrease=\(\frac {500-240}{500} * 100\)

=52%

Percentage Decrease = \(\frac {144-120}{144} * 100\)

=16.67%

We calculated the percentage decrease using the above-mentioned formula.

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The function f(x) has five intercepts at -6 only, -2, -1, 1, and 3 only.

The correct answer is D.

The function f(x) has some specific characteristics as shown in the graph.

The graph of f(x) has five intercepts, as can be seen from the graph.

The intercepts of f(x) can be determined by observing where the graph of f(x) crosses the x-axis.

The function f(x) intercepts the x-axis at five different points: -6 only, -2, -1, 1, and 3 only.

At these points, f(x) = 0.
Furthermore, the graph of f(x) is increasing from -∞ to -6, then decreasing from -6 to -2.

The graph of f(x) then increases from -2 to -1, decreases from -1 to 1, increases from 1 to 3, and finally decreases from 3 to +∞.

Hence, we can deduce that the graph of f(x) has a local maximum point at x = -6, a local minimum point at x = -2, and another local minimum point at x = 3.
We can also conclude that f(x) is an odd function, meaning that f(-x) = -f(x).

This can be deduced from the symmetry of the graph about the origin.

Finally, we can see from the graph that the function f(x) is continuous everywhere except at x = -2 and x = 3.

At these points, f(x) is not defined.
The function f(x) has five intercepts at -6 only, -2, -1, 1, and 3 only.

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