Suppose that tan(theta)=-1/3 and pi/2 Find the exact values of sin (theta/2) and
tan(theta/2)

The domain of the piecewise function g of x is (–∞, 2) ∪ (2, ∞)

What are Functions?

A function is a mathematical rule that takes an input value and produces a unique output value. It can be thought of as a machine that transforms input values into output values.

The domain of the piecewise function g of x is (–∞, 2) ∪ (2, ∞), since the expression x squared plus 2 times x minus 8 is equal to zero when x is equal to negative 4 and 2, but the function is undefined at x equals negative 4 and x equals negative 5 due to the logarithmic function.

Therefore, the domain is all real numbers except for x equals negative 4 and x equals negative 5.

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Answer:

a) The minimum normal value of the platelet count of a healthy person in usual form is 105,000,000,000 per liter (or 105 x 10^9 per L).

b) The platelet count of Allen in the usual form is 65,000,000,000 per liter (or 65 x 10^9 per L).

c) Allen needs to gain 40,000,000,000 more platelets per liter (or 40 x 10^9 per L) to reach the normal value of a healthy person.

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here's your Answer ~

A.) minimum number of platelet count for a healty person :

[tex]\qquad \sf\dashrightarrow \:105000000000 \: \: per \: litre[/tex]

[ That's the usual form, you just need to add 9 zeros to the value ]

B.) The value of platelet count of Allen :

[tex]\qquad \sf\dashrightarrow \:65000000000 \: \: per \: litre[/tex]

C.) platelet count she should gain to be equal to the normal value :

[tex]\qquad \sf  \dashrightarrow \: 105 \times 10 {}^{9} - 65 \times 10 {}^{9} [/tex]

[ taking 10⁹ common ]

[tex]\qquad \sf  \dashrightarrow \: 10 {}^{9} (105 - 65)[/tex]

[tex]\qquad \sf  \dashrightarrow \: 40 \times 10 {}^{9} \: \: per \: \: litre[/tex]

In normal value, it will be :

[tex]\qquad \sf\dashrightarrow \:40000000000 \: \: per \: litre[/tex]

The statement that 35 percent of 150 is about 50  is completely false and hence unreasonable as 35 percent of 150 is exactly equal to 52.50.

In the given problem which is related to percentage of some specific number, the value is obtained by direct multiplication of percentage with the given number to get the answer. Percentage is defined as the ratio which is given with respect to number 100 or 100 units as a whole. Its symbol is %. It is a dimensionless quantity and hence has no units as ratios does not have units.

The given equation can be represented as follows to obtain the answer:

(35/100) × 150 = 52.50

Since 52.50 cannot be considered close to 50, hence the statement is u reasonable. Though 52.5 can be considered as about 52 or 53.

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Let's assume the number to be x.

According to the problem statement, the sum of a number and its reciprocal is 2 1/6 or 13/6.

So we can set up the equation:

x + 1/x = 13/6

Multiplying both sides by 6x, we get:

6x^2 + 6 = 13x

Bringing all the terms to one side, we get:

6x^2 - 13x + 6 = 0

We can solve for x using the quadratic formula:

x = [13 ± sqrt(13^2 - 4(6)(6))] / (2*6)

x = [13 ± sqrt(169)] / 12

x = [13 ± 13] / 12

So, x can be either 2/3 or 3/2. Therefore, the number is either 2/3 or 3/2.

In his bookshelf, Luke can arrange his textbooks in a total of six different ways.

Luke can line up his textbooks in 3! = 321 = 6 different ways. This is because for the first book, he has three choices, for the second book, he has two choices left, and for the third book, he has only one choice left.

Therefore, the number of different ways Luke can line up his textbooks on his bookshelf is 6.

The six possible ways are:

English, biology, history

English, history, biology

Biology, English, history

Biology, history, English

History, English, biology

History, biology, English

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Match the description with the step accordingly:

How many times larger is 2 × 10⁻² then 3 × 10⁻⁶: Divide the larger Scientific Notation by the smaller Scientific Notation - divide coefficients and subtract exponents.

Difference between 2 × 10⁻² and 3× 10⁻⁶: Subtract by getting the same exponent to be like terms.

400 times 2 × 10³: Multiply by changing the number to Scientific Notation - multiply coefficients and add exponents.

Scientific notation is a way of expressing numbers that are too large or too small (usually would result in a long string of digits) to be conveniently written in decimal form.

To find How many times larger is 2 × 10⁻² then 3 × 10⁻⁶. Divide the larger Scientific Notation by the smaller Scientific Notation - divide coefficients and subtract exponents. That is:

(3 × 10⁻⁶)/(2 × 10⁻²) = 3/2 × 10⁻⁶⁻⁽⁻²⁾ = 1.5×10⁻⁴

To find the difference between 2 × 10⁻² and 3× 10⁻⁶. Subtract by getting the same exponent to be like terms. That is:

2×10⁻² - 3×10⁻⁶ = (2 × 10⁻²) - (0.0003× 10⁻²)

                           = (2 - 0.0003) × 10⁻²

                           = (2 - 0.0003) × 10⁻²

                           = 1.9997× 10⁻²

For 400 times 2 × 10³. Multiply by changing the number to Scientific Notation - multiply coefficients and add exponents. That is:

400 × 2 × 10³ = 4 × 10² × 2 × 10³

                     = 4 × 2 × 10³ × 10²

                     = 4 × 2 × 10³⁺²

                     = 8 × 10⁵

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Answer:

V(t)= 900(0.8) ^t

Step-by-step explanation:

900[tex]x^{3}[/tex]=460.8

      [tex]x^{3}[/tex]=0.512

        x=0.8

Answer:

b

Step-by-step explanation:

The cost per square foot of the remaining sheet metal is $4.10.

To find the cost per square foot of the remaining sheet metal, we can first calculate how much sheet metal is remaining by solving the equation:

7.6X - 3.5X = 65.6

where X is the amount of sheet metal remaining in square feet.

Simplifying the left side of the equation gives:

4.1X = 65.6

Dividing both sides by 4.1 gives:

X = 16

Therefore, the amount of sheet metal remaining is 16 square feet.

To find the cost per square foot, we can divide the cost of the remaining sheet metal by the amount of sheet metal remaining:

$65.60 / 16 sq. ft. = $4.10 per square foot.

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The dimensions of the rectangle are: length: 20 units and width: 3 units.

To solve the problem, we can set up an algebraic equation using the formula for the area of a rectangle, which is A = length × width.

Let x be the length of the rectangle, and x - 17 be the width.

Then we can set up the equation:

60 = x(x - 17)

Simplifying the equation gives us:

x² - 17x - 60 = 0

Now we can factor the equation:

(x - 20)(x + 3) = 0

This gives us two possible solutions for x:

x = 20 or x = -3

However, since the length of a rectangle cannot be negative, we can disregard the second solution.

Therefore, the length of the rectangle is 20 units, and the width is 20 - 17 = 3 units.

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The factored form of the expression is 8(x+7).

The expression 8x+56 can be factored by finding the common factor of both terms. The common factor in this case is 8, since 8 can be evenly divided into both 8x and 56.

To factor the expression, we can use the distributive property to pull out the common factor of 8 from both terms:

8x+56 = 8(x+7)

Therefore, the factored form of the expression is 8(x+7).

Answer: 8(x+7)

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Step-by-step \frac{1}{2} x^{5} - 15x

Answer:

csc(0)= 25/7

sec(0)= 25/24

cot(0)= 24/7

Step-by-step explanation:

Answer:

csc Θ = 25/7

sec Θ = 25/24

cot Θ = 24/7

Step-by-step explanation:

csc Θ = 1/sin Θ

sin Θ = opp/hyp

csc Θ = hyp/opp

csc Θ = 25/7

sec Θ = 1/cos Θ

cos Θ = adj/hyp

sec Θ = hyp/adj

sec Θ = 25/24

cot Θ = 1/tan Θ

tan Θ = opp/adj

cot Θ = adj/opp

cot Θ = 24/7

The answer to this question is as follows Given that this is a equation contradiction, 4C(-3) = 8 cannot be satisfied for any value of C. As a result, this equation cannot be solved.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

4C(-3) = 8

The phrase 4C(-3), which calls for multiplying 4 by the value of C when it equals -3, has to be evaluated.

4C(-3) = 4 x C(-3) (-3)

We must now determine what C(-3) is. This requires entering -3 for the C expression:

C(-3)

By understanding that this phrase refers to the value of C when it is equal to -3, we can make it simpler. C(-3) thus equals 3.

When we add this value back into the formula, we obtain:

4C(-3) = 4 x C(-3) = 4 x (-3) = -12

But, because we were informed that 4C(-3) = 8, we have:

8 = -12

Given that this is a contradiction, 4C(-3) = 8 cannot be satisfied for any value of C. As a result, this equation cannot be solved.

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[tex] \frac{ {38}^{2} - {22}^{2} }{16} \\ [/tex]

The identity which can be used in this case is :

[tex] \boxed{ {a}^{2} - {b}^{2} = (a - b)(a + b)}[/tex]

Applying the above identity to the given equation , we get

[tex] \frac{ {38}^{2} - {22}^{2} }{16} \\ \\ \implies \: \frac{(38 - 22)(38 + 22)}{16} \\ \\ \implies \: \frac{(\cancel{16})(60)}{\cancel{16} } \\ \\ \implies \: \underline{\underline{60}}[/tex]

hope helpful! :)

Answer:

Neil:

Sima:

Step-by-step explanation:

Neil:

Sima:

Answer: There are 10 candidates for each position, and since a candidate can only hold one leadership position, the number of ways to fill the president position is 10. After the president position is filled, there are 9 candidates remaining for the vice president position. Finally, there are 8 candidates remaining for the secretary position.

The total number of ways to fill the three positions is the product of the number of ways to fill each position. Therefore, the number of ways to fill the three positions is:

10 x 9 x 8 = 720

So there are 720 different ways to fill the three leadership positions using the 10 possible candidates.

Step-by-step explanation:

the unlock code is: 54-575-26-12-7.5-36.

How to determine?

To find the area of each polygon, we need to use the formula for the area of each respective shape.

Assuming the polygons are rectangles, triangles, and trapezoids, we can find their areas as follows:

The area of the rectangle with length 9 ft and width 6 ft is A = length × width = 9 ft × 6 ft = 54 ft².

The area of the triangle with base 10 cm and height 115 cm is A = (1/2) × base × height = (1/2) × 10 cm × 115 cm = 575 cm².

The area of the trapezoid with bases 5 m and 8 m, and height 4 m is A = (1/2) × (base1 + base2) × height = (1/2) × (5 m + 8 m) × 4 m = 26 m².

The area of the triangle with base 3 cm and height 8 cm is A = (1/2) × base × height = (1/2) × 3 cm × 8 cm = 12 cm².

The area of the rectangle with length 1.5 m and width 5 m is A = length × width = 1.5 m × 5 m = 7.5 m².

The area of the trapezoid with bases 6 ft and 3 ft, and height 4 m is A = (1/2) × (base1 + base2) × height = (1/2) × (6 ft + 3 ft) × 4 m = 9 ft × 4 m = 36 ft².

Therefore, the unlock code is: 54-575-26-12-7.5-36.

Note that the areas are listed from left to right based on the order of the shapes in the original question. Also, the areas are separated by hyphens as requested.

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The area in square miles (rounded to the nearest integer) is:

area = 2,492 square miles.

Here we need to perform a change of units from acres to square miles. We know the relation:

1 square mile = 640 acres.

And we want to find the area of a park with 1,505,011 acres in square miles.

We can rewrite the relation above as:

1 acre = (1/604) square miles.

Then the area of the park will be:

Area = 1,505,011 acres  = 1,505,011*(1/604) square miles

Area = 2,491.74 square miles.

Rounding to the nearest integer we will get:

area = 2,492 square miles.

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Answer: The square root of 45 is a like radical to 3 x √5.

To see why, we can simplify each radical using the product rule of radicals:

3 x √5 = √(3^2 x 5) = √45

Similarly, we can simplify the square root of 45 using the prime factorization of 45:

√45 = √(3 x 3 x 5) = 3√5

Therefore, 3 x √5 is a like radical to √45, and vice versa.

Step-by-step explanation:

Answer:

its D

Step-by-step explanation:

TRUST ME BRO

Mohal would expect to earn $265 in a day when he waits on 16 tables, and he would expect to earn $15tt + $25 in a day when he waits on tt tables

Earnings or wages refer to the amount of money an individual receives in exchange for their work or services. This can include a regular salary or hourly wage, as well as bonuses, commissions, and other forms of compensation.

Earnings or wages are typically determined by a variety of factors, including the type of work being performed, the level of skill and experience required, the local job market, and the employer's policies and practices. In some cases, earnings may be negotiated between the employer and the employee, while in other cases they may be set by industry standards or government regulations.

To calculate Mohal's expected earnings in a day when he waits on 16 tables, we can use the formula:

Total earnings = Guaranteed wage + Tips

Guaranteed wage = $25

Tips = $15 x Number of tables

Number of tables = 16

So, Total earnings with 16 tables = $25 + ($15 x 16) = $265

To calculate Mohal's expected earnings in a day when he waits on tt tables, we can use the same formula:

Total earnings = Guaranteed wage + Tips

Guaranteed wage = $25

Tips = $15 x Number of tables

Number of tables = tt

So, Total earnings with tt tables = $25 + ($15 x tt) = $15tt + $25

Therefore, Mohal would expect to earn $265 in a day when he waits on 16 tables, and he would expect to earn $15tt + $25 in a day when he waits on tt tables.

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Answer:

Total earnings with 16 tables: 265

Total Earnings with t tables: 15t+25

Step-by-step explanation:

The slope of the line passing through the points (-5,5) and (5,8) is 0.3.

The slope of a line is the rate at which it rises or falls as it moves from left to right. It is defined as the change in the vertical distance divided by the change in the horizontal distance between any two points on the line.

The slope of a line passing through two points (x₁,y₁) and (x₂,y₂) can be calculated using the slope formula:

slope = (y₂-y₁)/(x₂-x₁)

Using the coordinates (-5,5) and (5,8), we can plug in the values to get:

slope = [tex]\frac{(8-5)}{(5-(-5))}[/tex]

slope = [tex]\frac{3}{10}[/tex]

slope = 0.3

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The value of x is 18.4.

Right angled triangle are those triangle for which one of the angle is 90 degrees.

Given that,

sin (2x + 7)° = cos (3x - 9)°  [Equation 1]

We have the trigonometric rule that,

cos (θ) = sin(90 - θ)

So, cos (3x - 9)° = sin (90 - (3x - 9))

So from equation 1,

sin (2x + 7)° = sin (90 - (3x - 9))

Equating,

2x + 7 = 90 - (3x - 9)

2x + 7 = 90 - 3x + 9

2x + 7 = 99 - 3x

5x = 92

x = 18.4

Hence the value of x is 18.4.

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(a) The probability that exactly one letter will be placed in the correct envelope is 1/2.

(b) The probability that exactly n−1 letters will be placed in the correct envelopes is 0.

(a) There are three possible ways that one letter can be placed in the correct envelope (A in A, B in B, or C in C) and six total possible arrangements of the letters (ABC, ACB, BAC, BCA, CAB, CBA).

Solving for the probability:

P = 3/6 = 1/2

(b) If n−1 letters are placed in the correct envelopes, then the remaining letter must also be placed in the correct envelope, resulting in all n letters being placed in the correct envelopes. Therefore, it is impossible for exactly n−1 letters to be placed in the correct envelopes.

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Answer:It is given that

In △ABC,

DE∥AC

What is similarity of triangles?

Two triangles are similar if corresponding angles are equal and corresponding sides are in proportion.

Let us consider △BDE and △ABC,

∠B=∠B.....common angles

∠BDE =∠BAC....corresponding angles

so, △BDE∼△ABC

Since △BDE and △ABC are similar so, corresponding sides will be in proportion,

Subtract 1 from both sides,

Thus, we proved   using the similarity of triangles.

Step-by-step explanation:

Answer:

Dear Mary,

I understand your concerns about the cost of attending college and how it might not be worth it in the end. However, earning a college degree can significantly increase your earning potential and lead to greater job opportunities. In fact, individuals with a bachelor's degree earn an average of $1 million more over their lifetime compared to those with only a high school diploma. Moreover, pursuing a degree in chemical engineering can open doors to highly rewarding and well-paying career paths.

I agree that the published costs of attendance on college websites can be overwhelming, but keep in mind that these figures are often the maximum amount and many students receive financial aid to reduce their expenses. Financial aid comes in many forms, including scholarships, grants, work-study programs, and loans. Scholarships and grants do not have to be repaid, so it's worth exploring those options first. Loans can be daunting, but they can also be manageable if you borrow responsibly and budget accordingly.

It's understandable that you may feel uncertain about whether you qualify for financial aid or not, but it's always worth applying. Many families are surprised to find out that they qualify for aid that they didn't expect. The Free Application for Federal Student Aid (FAFSA) is the form used to determine your eligibility for federal and state financial aid, and it's free to complete. Private institutions may also require additional forms, so make sure to check each college's financial aid website for more information.

As for student loans, there are many repayment plans available, and you can choose one that works best for your budget. If you're having trouble finding a job after graduation, you can apply for deferment or forbearance to temporarily suspend your payments. It's important to have a plan in place for repayment, but it's also important not to let the fear of repayment stop you from pursuing your dreams.

I hope this information helps you make a more informed decision about your college plans. Remember, investing in your education can have long-lasting benefits and lead to a brighter future.

Best regards,

[Your Name]

Step-by-step explanation:

Another inequality that describes the solutions would be: x ∈ (4, ∞)

What is inequality ?

In mathematics, an inequality is a statement that compares two values, expressions, or quantities, and asserts that they are not equal. Inequalities are often expressed using inequality symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

The inequality 3x > 12 can be solved by dividing both sides by 3:

3x/3 > 12/3

x > 4

This means that all values of x greater than 4 are solutions to the inequality 3x > 12.

This notation represents the interval of all real numbers greater than 4, including 4 itself. The symbol "(" means that 4 is not included in the interval, while "∞" indicates that the interval extends indefinitely to the right.

Therefore, Another inequality that describes the solutions would be: x ∈ (4, ∞)

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If f(x)=2x+1 and g(x)=x^2 +5, the value of  g(f(2)) = 30.

The question is asking to evaluate the composition of the two functions, g(f(2)). This means that first the innermost function, f(2), needs to be evaluated, and the result substituted in place of f(2) in the expression for g(f(2)).

First, evaluating f(2) yields f(2) = 2*2 + 1 = 5. Then, substituting 5 in place of f(2) in the expression for g(f(2)) yields g(f(2)) = g(5) = 5^2 + 5 = 30.

Therefore, the answer to the question is g(f(2)) = 30.

A composite function is a function evaluated on another function.

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The electric field outside the pipe is E(r) = σa² / ε_0r².

The electric field inside the pipe is E(r) = σa²/ ε_0r.

Assuming the metallic pipe is infinitely long, we can use Gauss's Law to determine the electric field both inside and outside the pipe.

Let's consider a cylindrical Gaussian surface of radius r and length L, with its axis coinciding with that of the pipe.

By Gauss's Law, the electric flux through the surface is given by:

Φ_E = ∫ E . dA = E x 2πrL

where;

The charge enclosed by the Gaussian surface is given by:

Q_enc = σ x π(2a)² x L

= 4πa²σL

where;

By Gauss's Law, the electric flux through the Gaussian surface is also given by:

Φ_E = Q_enc / ε_0

where;

Equating the two expressions for Φ_E, we get:

E x 2πrL = 4πa²σL / ε_0

Simplifying, we get:

E = σa² / ε_0r for r < a

E = σa² / ε_0r^2 for r > a

Therefore, the electric field inside the pipe (r < a) is inversely proportional to the distance from the axis, while outside the pipe (r > a) it is inversely proportional to the square of the distance from the axis.

To summarize:

Outside the pipe: E(r) = σa² / ε_0r²

Inside the pipe: E(r) = σa² / ε_0r

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