Suppose A = {2, 5, 7, 9, 13, 25, 26}.
(a) Find n(A).
n(A) =

(b) T/F: 20 A
True
False

Answer:

8

Step-by-step explanation:

8 x 5 = 40

The simplified trigonometric expression [tex]\sqrt{(1 - \csc^2{(y)}){(\cos^2{y} - 1)}}[/tex] is given as follows:

[tex]\sqrt{(1 - \csc^2{(y)}){(\cos^2{y} - 1)}} = \cot{y}\sin{y}[/tex]

The trigonometric expression for this problem is defined as follows:

[tex]\sqrt{(1 - \csc^2{(y)}){(\cos^2{y} - 1)}}[/tex]

Then trigonometric identities are used to simplify the radicands of the rational expression.

The identity that uses the cossecant squared is given as follows:

csc²(y) = 1 + cot²(y).

Hence:

1 - csc²(y) = -cot²(y).

The identity that uses the cosine squared is given as follows:

sin²(y) + cos²(y) = 1.

Hence:

cos²(y) - 1 = -sin²(y).

Then the expression can be simplified as follows:

[tex]\sqrt{(1 - \csc^2{(y)}){\cos^2{y} - 1}} = \sqrt{-cot^2{y} \times -\sin^2{y}}[/tex]

As the product of two negative numbers is positive, we have that:

[tex]\sqrt{cot^2{y}sin^2{y}}

Taking the square root of each squared term, the simplified expression is given as follows:

cot(y)sin(y).

The problem asks for the simplified expression.

More can be learned about simplification of expressions at https://brainly.com/question/723406

#SPJ1

The total height of the building would be nh + 30.

Option (B) is correct.

What is a simplification in mathematics?

In mathematics, simplification refers to the process of making an expression or equation simpler or easier to understand or work with. This can involve combining like terms, removing unnecessary terms or factors, or rearranging the order of the terms.

The building's total height in feet is represented by the sum of the height of each floor plus the height of the spire.

So if the height of each floor is h, and there are n floors in the building and the building's spire is 30 feet, the total height of the building is:

= n * h + 30

=nh + 30

This is because the height of each floor is h, and there are n floors, so the total height of the floors is n * h. Adding the height of the spire, 30 feet, to the total height of the floors gives nh + 30.

Hence, the total height of the building would be nh + 30.

To learn more about the simplification, visit:

https://brainly.com/question/28595186

#SPJ1

On solving the provided question we can say that quadratic equation is  y = 3x + 2x^2 => y = 14

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

here,

quadratic equation is

y = 3x + 2x^2

y = 6 + 8

y = 14

as x = 2

To know more about quadratic equation visit:

https://brainly.com/question/30098550

#SPJ1

Answer:

Step-by-step explanation:

To calculate how long it will take John to recover his investment, we need to divide the cost of the degree by the difference in income between the two options.

$10,000 / ($35,000 - $20,000) = $10,000 / $15,000 = 0.67 years or 0.67*12 = 8 months.

So, it will take John 8 months to recover his investment if he goes to school.

Please note that this is a simplified calculation as it does not take into account the cost of living, taxes, and other expenses.

Answer:

(125, -312500)

C(x) = -312500

Step-by-step explanation:

use this equation into a graphing calculator and use the minimum function

We are aware that P = 2(a + b) units is the perimeter of a parallelogram.Consequently, the parallelogram's sides are 50 cm, 25 cm, 50 cm, and 25 cm.

We are aware that P = 2(a + b) units is the perimeter of a parallelogram.Adding up all four sides will reveal a parallelogram's perimeter.An area of a circle of radius r is known as r2 in geometry.

The circumference-to-diameter ratio, which is always the same and is roughly equivalent to 3.14159 in this context, is denoted by the Greek letter.

Let side a and the side next to it in the parallelogram be a and b, respectively.

The parallelogram's perimeter is equal to 2(a+b)=150, where a+b=75.

Since an is 25 cm taller than b, a=b+25.

By changing it in equation 1, b+25+b=75 2b=50 b=25 is obtained.

a+b=75\sa=75=25\sa=50

Consequently, the parallelogram's sides are 50 cm, 25 cm, 50 cm, and 25 cm.

To learn more about parallelogram refer

https://brainly.com/question/20526916

#SPJ1

Answer:

Step-by-step explanation:

Assuming that the same ratio of invitees to respondents holds true for the 30 additional HRDs, the best estimate of the number of people employed by the 30 organisations is 67.5 (30/45*100). This means that the total number of people employed by the 363 organisations represented by the 333 invited HRDs and the 30 additional HRDs is 5,475 (5,407.5 + 67.5).

i do not know the answer either

The acccceleration will be 1m/s² and the average speed is 47m/s.

For the acceleration problems, you must draw a tangent on curved velocity-time graphs. Since it requested acceleration at t = 10 seconds, we must create a straight line that only touches the graph once, at 10 seconds.

Now, when drawing tangents, you must be as precise as you can because they can only contact the line once.

Next, determine the gradient using the tangent. You can accomplish this by creating a triangle out of two additional lines drawn from the tangent, then dividing the rise by the run, or Y/X. The triangle that comes before the Y and the X simply denotes the Greek letter delta, which symbolizes change. Change in Y so prevails over Change in X. So 10/10 = 1. So 1m/s^2.

If we estimate the speed at 5 seconds intervals, then we have

Average speed = (36 + 46 + 49 + 50 + 50 +50 + 50) ÷ 7

Average speed = 331/7 = 47.29 m/s

Average speed = 47 m/s

Learn more about graph on:

https://brainly.com/question/16154358

#SPJ1

The profit for Mr Christopher is #1000.

Profit is the money that is earned in trade or business after paying the costs of producing and selling goods and services.

Given that, Mr. Christopher contributed #500 to a business, Miss Uche contributed #300 while Mrs. Amaka contributed #200, they share a profit #2000,

Let the ratio of their contribution = 5x : 3x : 2x

Therefore,

5x + 3x + 2x = 2000

10x = 2000

x = 200

Their profit share =

Mr. Christopher = 200 x 5 = 1000,

Miss Uche = 200 x 2 = 200

and

Mrs. Amaka = 200 x 3 = 600

Hence, the profit share of Mr. Christopher is #1000,

Learn more about profit, click;

https://brainly.com/question/23423917

#SPJ1

The area under the standard normal curve to the right of Z (3.15) = 0.0008

The total area under the standard normal curve happens to be 1 which is divided between two parts having an area under the curve = 0.5 on each side.

I.e. from 0 to the right side, the area under the curve = 0.5

Similarly, from 0 to the left side, the area under the curve = 0.5

Now, from the standard normal table,                                  

                                                          {the table is given in the attachment}

The area under the curve for the value of Z (3.15) = 0.4992

                                                                         {This value is the area under the curve from 0 to Z (=3.15)}

Hence, the Area under the curve to the right of Z (3.15) = 0.5 – 0.4992

                                                                                            = 0.0008

Learn more about the Standard Normal Curve:

brainly.com/question/29184785

For z = 3.15, the area under the standard normal curve is 0.99918365.

Normal distributions are symmetrical, bell-shaped distributions that are useful in describing real-world data.

The standard normal distribution, represented by the letter Z, is the normal distribution having a mean of 0 and a standard deviation of 1.

If {X} is a random variable from a normal distribution with mean {μ} and standard deviation {σ}, its Z-score may be calculated from X by subtracting μ and dividing by the standard deviation :

[tex]${\displaystyle Z={\frac {X-\mu }{\sigma }}}[/tex]

If {X} is the mean of a sample of size {n} from some population in which the mean is {μ} and the standard deviation is {σ}, the standard error is σ/√n :

[tex]${\displaystyle Z={\frac {{\overline {X}}-\mu }{\sigma /{\sqrt {n}}}}}[/tex]

If [tex]{\textstyle \sum X}[/tex] is the total of a sample of size {n} from some population in which the mean is {μ} and the standard deviation is {σ}, the expected total is nμ and the standard error is σ √n :

[tex]${\displaystyle Z={\frac {\sum {X}-n\mu }{\sigma {\sqrt {n}}}}}[/tex]

Given is the value of z = 3.15.

For z = 3.15, the area under the standard normal curve is 0.99918365.

Therefore, for z = 3.15, the area under the standard normal curve is 0.99918365.

To solve more questions on standard normal curve, visit the link below -

https://brainly.com/question/28971164s

#SPJ1

12 is the denominator because it represents the total number of times Nicanor selects a diving ring from the bag

Explaination:

Nicanor randomly selects a ring from the bag a total of 12 times. 3 times he selects a red ring, 4 times a yellow one, and 5 times a blue one.

When he selects a red ring, he selects it 3 times out of the 12 times total, which is represented as the fraction 3/12.

When he selects a yellow ring, he selects it 4 times out of the 12 times total, which is represented as the fraction 4/12.

When he selects a blue ring, he selects it 5 times out of the 12 times total, which is represented as the fraction 5/12.

Hope this helps you!

Answer:

The minimum length and width of the tarp would be the diagonal length of the café's piece of ground. To find this length, you can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. In this case, the café's piece of ground forms a right triangle, with one side measuring 6.0 m and the other side measuring 5.0 m. So, to find the length of the hypotenuse, we can use the formula: c = √(a^2 + b^2) where c is the length of the hypotenuse and a and b are the lengths of the other two sides. Plugging in the numbers, we get: c = √(6.0^2 + 5.0^2) = √(36 + 25) = √(61) = 7.81 m

So, the minimum length and width of the tarp would be 7.81 m.

Answer:

Step-by-step explanation:

36 percent can be written as 36/100. So now the question is 36/100 x 28.

Its easier if you simplify 100 and 28 by a common factor, which im going to use 4 for. So instead you get 36/25 x 7.

36x7=252

252/25=10.08

Answer:

46.08

Step-by-step explanation:

Remember that a percent is always a fraction out of 100, in this case 36/100, so it can also be written as a decimal number, in this case 0.36. Now all you need to do is multiply 128*0.36

Answer:

Step-by-step explanation:

24²=24×24

Which is 576

Answer: 844000

Step-by-step explanation:

843857 = 844000 because you round up

The number of terms (n) in the sequence = 10.

We know that,

                      S = [tex]\frac{n}{2\\}[/tex] {2a + (n-1)d}

Where,

            S = Sum of A. P. series

            n = number of terms in A. P. series

            a = first term of the series

            d = common difference

According to the question,

           Sum of the series, S = 340

                         First term,  a = 7

         Common difference, d = 6

                  S = [tex]\frac{n}{2\\}[/tex] {2a + (n-1)d}

                  340 =  [tex]\frac{n}{2}[/tex] {2*7 + (n-1)6}

                  340 =  [tex]\frac{n}{2}[/tex] {14 + 6n - 6}

                  340*2 = n( 6n + 8)

                   680   = 6n^2 + 8n

        6n^2 + 8n - 680 = 0

        2 (3n^2 +4n - 340) = 0

            3n^2 +4n - 340 = 0

        3n^2 + 34n - 30n - 340 = 0

        n (3n+ 34) - 10 (3n + 34) = 0

        (3n + 34) (n - 10) = 0

   if we take, 3n + 34 = 0

                         3n = - 34

                           n = -34/3

which is not possible, as the number of terms can not be negative

   if we take, n- 10 = 0

                       n = 10

Hence, the number of terms in the given A. P. series is 10.

Learn more about Arithmetic Progression (A. P.) Series:

https://brainly.com/question/20375979

Answer:

Step-by-step explanation:

Let the other diagonal be d.

From the Pythagorean theorem,

d2 = 82 + 1442

d2 = 64 + 20736

d2 = 20800

d = √20800

d = 144 cm

The integers that -3.425 lie between are -3 and -4.

The rational numbers  that -3.425 lie between to the nearest tenth are -3.4 and -3.5.

The rational numbers  that -3.425 lie between to the nearest hundredth are -3.42 and -3.43.

Integers are numbers without decimals and fractions. They are whole numbers. Integers can either be positive, negative or zero. Examples of integers are -5 and 10.

A rational number is a number that can be expressed as a fraction of two integers. Examples of rational numbers are 1/4, -2/3  

To learn more about integers, please check: https://brainly.com/question/21493341

#SPJ1

Answer:

a)  The product of any two odd integers is an odd integer.

b)  The sum of two negative integers is always smaller than the smallest negative integer.

Step-by-step explanation:

Given:

Carry out a few examples to find a pattern:

Pattern:

Write the conjecture based on the found pattern.

Conjecture:  

Test the conjecture for accuracy using at least three sets of numbers.

Test:

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

Given:

Carry out a few examples to find a pattern:

Pattern:

Write the conjecture based on the found pattern.

Conjecture:  

Test the conjecture for accuracy using at least three sets of numbers.

Test:

Step-by-step explanation:

Add

1/5+3/10=5/10

Find common denominator

1/5+3/10=1*2/5*3+3*1/10*1=2/10+3/10

10 is the least common multiple of denominators 5 and 10. Use it to convert to equivalent fractions with this common denominator.

Add

2/10+3/10=2+3/10=5/10

Simplify

5/10=1/2

5 is the greatest common divisor of 5 and 10. Reduce by dividing both the numerator and denominator by 5.

Answer:

Book: Library is most similar in relation to the following word pair Water: Ocean. Both pairs are closely related and are often found together.

The number of goodie  bags she will need to sell is 107.

Breakeven is when profit is zero. it is the point where total cost is equal to total revenue.

Breakeven: Total cost = total revenue

fixed cost + variable cost = price x quantity sold

fixed cost + (cost per unit  x quantity sold)

$250 + (1.25 x q) = 3.60 x q

$250 + 1.25q = 3.60q

In order to determine the value of q, take the following steps:

Combine and add similar terms :

$250 = 3.60q - 1.25q

$250 = 2.35q

Divide both sides o the equation by 2.35

q = 250/2.35

q =  106.3 = 107

To learn m8re about breakeven, please check: https://brainly.com/question/10190285

SPJ1

The total quantity of the three spices is 7/8

A recipe has three spices

1/8 teaspoon of turmeric

1/4 teaspoon of ginger

1/2 teaspoon of cumin

The total quantity of the three spices can be calculated as follows

1/8 + 1/4 + 1/2

= 7/8

Hence the total quantity of the three spices is 7/8

Read more on spices here

https://brainly.com/question/20221987

#SPJ1

Answer: [tex]x=0, -\frac{3}{2}[/tex]

Step-by-step explanation:

[tex]4x^2 +6x=0\\\\2x(2x+3)=0\\\\2x=0, 2x+3=0\\\\x=0, -\frac{3}{2}[/tex]

Answer:

Step-by-step explanation:

4(x-2)+11=3(x+3)

Use distributive property to get rid of the parentheses

4x-8+11=3x+9

Simplify the addition and subtraction

4x+3=3x+9

subtract 3 on both sides and 3x on both sides to isolate x

x=6

Answer:

5 people

Step-by-step explanation:

Relay race ---> 3/4 mile

Each runner runs 3/20 miles

3/4÷3/20

3/4×20/3=5

OR

3/4 --> 15/20

3/20 goes into 15/20 5 times

Answer:

5 runners

Step-by-step explanation:

Just multiply 3/20 by 3/4