QUESTION IN ATTACHMENTS

We have to simplify the expression:

We could see it graphically:

We see that for any angle theta, the cosine of theta + pi/2 is equal to negative sin of theta.

Then we can write:

The answer is -sin(theta).

Explanation

Given the equation;

Using a graphing calculator, the graph of the circle becomes;

Answer:

Q.12 The polynomials are 2 and 3

What is polynomial ?

A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An example of a polynomial of a single indeterminate x is x² − 4x + 7.

Given, p(x) = -x² + x + 2

p has a degree 2

Let, a = 1 + i√2

      b = 1 - i√2

a + b = 1 + i√2 + 1 - i√2

        = 2

a * b = (1 + i√2) * (1 - i√2 )

        = 1 - (i√2)²

        = 1 - i²*2    (where, i² = -1)

        = 1 + 2

        = 3

Therefore, the polynomial are 2 and 3

Q.13 The polynomial is x³ + x

Given, Q(x) = x³ - 2x² - 1

Q has a degree of 3

=>(x - 0) (x - i) (x + i)

=>(x² - ix) (x + i)

=>x³ + x²i - ix² - i²x    (where i² = -1)

=>x³ + x

Therefore, the polynomial is x³ + x

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You have the following expression:

x² + 6x

In order to complete the square, take into account that 6 is two times the product of the first coeffcient by the second one in the binomial (a+ b)², then, you have:

6 = 2ab

a=1 because is the coeffcient of the term with x², then for b you obtain:

b = 6/2(1) = 3

the third term of the trynomial is the squared of b.

Answer:

55.17

Step-by-step explanation:

[tex]P(0)=0.023(0)^3-0.289(0)^2+3.068(0)+55.170=55.17[/tex]

1) Let's verify whether that's true or not, plugging in that point into the equa

(-4,2)

Since this is an identity, in other words, the left side is equal to the right side then we can say that's true.

So that's true y=-5/2x-8 is the equation of the line that has in one of its points the y-coordinate y=-8

Answer:

true

Step-by-step explanation:

it is true ........

Explanation:

A right triangle has exactly one angle that is 90 degrees. This is called a right angle.

The other two angles are acute, which means they are less than 90 degrees. An example would be 30 degrees and 60 degrees.

If 30 degrees is an interior acute angle, then 180-30 = 150 degrees is the exterior obtuse angle. Similarly, the adjacent angle to the 60 is 180-60 = 120 degrees.

This example shows we have two obtuse exterior angles. This applies to any right triangle, and not just this particular one.

ANSWER:

7

STEP-BY-STEP EXPLANATION:

We have the following data:

The median is the data value that separates the upper half of a data set from the lower half. Therefore:

In this case, being even, the two data are half, but since the value is the same, that is, 7, the median is equal to 7.

The interpretation of this value is in the middle of the 10 days (days 5 and 6), 7 would be the number of cars in a town given a a speeding ticket.

The Angle-Side-Angle (ASA) criterion states that any two angles and the side included between them of one triangle are identical to the corresponding angles and the included side of the other triangle if two triangles are congruent. One of the requirements for two triangles to be congruent is angle side angle.

When two parallel lines are intersected by another line, comparable angles are the angles that are created in matching corners or corresponding corners with the transversal.

If the three sides and the three angles of both angles are equal in any orientation, two triangles are said to be congruent.

Given,

M∠1 = M∠2

(On joining BD and CD)

M∠ADB = M∠ADC

In ΔABD and ΔADC

M∠ADB = M∠ADC  (Given)

M∠BAD = M∠DAC  (Given)

AD = AD  (Common Sides)

⇒ ΔABD ≅ ΔADC  (Angle Side Angle Property)

So, BD = CD  (Corresponding sides are equal to a Congruent Triangle)

Hence, proved that BD = CD.

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Answer:

24

Step-by-step explanation:

8y^0 + 2y^2 * x^-1

8(4)^0 + 2(4)^2 * 2^-1

8 + 2 * 16 * 2^-1

8 + 2 * 2^-1 * 16

8 + 2^1 - 1 * 16

8 + 16

24

Hope this helps! :)

Finding the ratio of

a)1:9

b)2 : 7

c) 2 : 5

What is Ratio?

A ratio indicates how often one number contains another number. For example, if a fruit bowl contains 8 oranges and 6 lemons, the ratio of oranges to lemons is 8 to 6. Similarly, the ratio of lemons to oranges is 6:8 and the ratio of oranges to whole fruit is 8:14.

Given,

Total no. of students =  42

a) Students who prefer punk to students who prefer hip-hop

  No. of students in punk = 2

  No. of students in hip-hop = 18

The Ratio will be,

punk : hip-hop = 2:18

                        = 1:9

b) Students who prefer rock to total no. of students that are surveyed

No. of students in rock = 12

Total no. of students =  42

The Ratio will be,

rock : total students = 12 : 42

                                 = 2 : 7

c) Students who prefer rock or classic rock to students who prefer all music

No. of students in rock = 12

Total no. of students who likes other music =  42 - 12

                                                                        = 30

The Ratio will be,

rock : total students with different music = 12 : 30

                                                                    = 2 : 5

Hence, The ratio comparison in three different way

a)1:9

b)2 : 7

c) 2 : 5

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The total yards gained or lost is the algebraic sum so the resultant yards is -15 yards thus they lose 15 yards.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Subtraction = Minus of any two or more numbers.

Summation = addition of two or more numbers or variable

Let's consider all gained yards by positive (+) and all lost yards by negative (-).

Given that,

In the first play = +8 yards (gain)

In second play = -12 yards (lost)

In the third play = 11 yards (Lost)

So total yards = +8 - 12 - 11 = -15 (Lost)

Therefore, the football team lost 15 yards.

Hence "The total yards gained or lost is the algebraic sum so the resultant yards is -15 yards thus they lose 15 yards".

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Using function concepts, it is found that:

a) The meaning of each expression is given as follows:

b) The expression is: A(4) = 1.3.

c) The expression is: A(2) = A(2.5).

In the context of this problem, the format of the function is:

A(t).

In which the meaning of each variable is given as follows:

Which gives the meaning of each expression in item a.

For item b, the expression is given as follows:

A(4) = 1.3.

As 4 hours after the episode premiered, the audience was of 1.3 million people.

For item c, the expression is given as follows:

A(2) = A(2.5).

As the audience after 2 hours = 120 minutes is the same as the audience half an hour = 30 minutes later.

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The Solution:

Given:

Required:

To find the value of V - W

Therefore, the correct answer is [option 3]

The  sample size should be taken as 545.6 to obtain a margin of error of 0.042 for the estimation of a population proportion.

What is sample size?

The process of deciding how many observations or replicates to include in a statistical sample is known as sample size determination. Any empirical study with the aim of drawing conclusions about a population from a sample must take into account the sample size as a crucial component. The sample size chosen for a study is typically influenced by the cost, convenience, or ease of data collection as well as the requirement that the sample size have adequate statistical power.

As given in the question,

Confidence level is 95% and the margin of error is 0.042

So,  

1 - α = 0.95,

α = 0.05,

E = 0.042

planning value (p) = 0.5

To calculate Sample size the formula is:

[tex]n = \frac{p(1-p)(Z_{a/2})^2}{E^2}[/tex]

From the table we can find that:

[tex]Z_{a/2} = 1.96[/tex]

Putting the values given in the question in formula:

[tex]n = \frac{0.5(0.5)(1.96)^2}{(0.042)^2}[/tex]

[tex]n = \frac{(0.25)(1.96)^2}{(0.042)^2}[/tex]

[tex]n = \frac{(0.25)(3.841)}{0.00176}[/tex]

n = 545.6

Hence the sample size is 545.6

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Consider that there are, generally, the following types of angles pairs,

1. Adjacent Angles: Angles that share a common side and are formed on the same vertex.

2. Complementary Angles: Angles that are adjacent and together form a right angle.

3. Supplementary Angles: Angles that are adjacent and whose sum of degree measures is 180 degrees.

a.

The adjacent angles to angle 4 are angles 1 and 3.

There are no complementary angles associated with angle 4.

The supplementary angles to angle 4, are angles 1 and 3.

Thus, the angle pairs that include angle 4 are,

b.

The adjacent angles to angle 5 are angles 6 and 7.

There are no complementary angles associated with angle 5.

The supplementary angles to angle 5, are angles 6 and 7.

Thus, the angle pairs involving angle 5 are,

The true equation is 5 + n = 6.2.

Here we have to find the equation for which n = 1.2.

So the first equation is

10n = 1.2

So for this, we get the value of n as:

n = 1.2/10

  = 0.12

which is not equal to 1.2.

So it is not correct

The second equation is:

n + 1 = 1.2

n = 0.2

which is not equal to 1.2

So it is also not correct.

The third equation is:

5 + n = 6.2

n = 6.2 - 5

  = 1.2

So it is correct.

The fourth equation is:

1.2n = 10

n = 10/1.2

  = 8.33

Here n is not equal to 1.2

So it is also correct.

Therefore the correct equation is 5 + n = 6.2.

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Answer:

[tex]5\%\text{ or }0.05[/tex]

Step-by-step explanation:

Simple interest rate means if I have "P" amount that I initially deposited, then every year this amount increases by "x% of P" or the original amount I deposited. So it's increasing by the same amount each year, unlike compound interest.

The formula for calculating the amount of interest is: [tex]I=P*r*t[/tex]

Where, r is the interest rate, t is the time unit, and P is the initial amount.

In most cases the t will be expressed in years, and one thing to note is the r is the interest rate in decimal form, so [tex]30\%=0.30[/tex], we want to convert it to decimal form by dividing by 100

We know the amount of interest, as it's given to us as 9,000, and the principle amount or initial amount, given to us as 60,000, and also the time which is given to us as 3 years.

So we know that:

[tex]I=9,000\\P=60,000\\t=3\\[/tex]

Plugging all these values into the equation we get:

[tex]9,000=60,000*3*r\\\\9,000=180,000*r\\\\\frac{9,000}{180,000}=r\\\\0.05=r[/tex]

as noted above, this interest rate, "r" is expressed in decimal form. Since we have to divide by 100 to convert from percentage to decimal, we have to multiply by 100 to convert from decimal to percentage.

this gives us: [tex]r=5\%[/tex]

N = Number of data

x1...xn = Samples

Let's calculate first:

Now:

So:

Answer:

14x+3 is the answer I think

The solution to the given equation would be [tex]14x+3[/tex].

Hope this helps!

There is a 5% chance that second graders will be faster than 94.597 wpm.

Sample size = 21

standard deviation = 10 wpm

SE = 10/sqrt(21) = 2.18 as a consequence.

Let X be the average reading speed of 21 second-grade students. z = (X - 91)/2.18 Normal(91,2.18) (91,2.18).

If the 95th percentile of a standard normal variable z is 1.65 [5% probability], the outcome is 91 + 1.65 x 2.18 = 94.597.

So there's a 5% chance that the average reading speed of a random sample of 21 second-graders will be faster than 94.597 wpm.

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Given:

the bearing of L from Q is 90°

Required:

what is the bearing of Q for L ​

Explanation:

There is a 180 degree difference in bearing between two location(L from Q, Q from L)

If L from Q is 90 degree then

Q from L is

180-90=90degree

Required answer:

90 degree

Given:

To find:

The root of 18 without using a calculator

There is a formula that gives an approximation of a square root without a calculator. This is given as:

12×(1/4+1/3)to the power of2+2/3 using PEDMASand INDICIES rule gives 7^8/3

 lndicies is expressed as Ax^n. Where A is the coefficient, x is the base and n is the power or index.

12×(1/4+1/3)to the power of2+2/3

Evaluating the expression

 = (12×( 1/4+1/3))^2+2/3

using PEDMAS

= (12× 7/12)^8/3

opening the bracket, we therefore have

= 7^8/3

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The probability that a randomly chosen applicant has a graduate degree, given that they are female is 0.236.

Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

Given that 249 are female and 59 are female and have a graduate degree out of 450 applicants.

We are given following in the question;

M: Applicant is male.

G: Applicant have a graduate degree

F : Applicant is female.

The Total number of applicants = 450

Number of female applicants = 249

Number of female applicants have a graduate degree = 59

Therefore,

P(G/F) = P([tex]G^F[/tex])/P(F)

= 59/207 or 0.236

Hence, the probability that a randomly chosen applicant has a graduate degree, given that they are female is 0.236.

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The area of the composite figure will be the sum of the area of the square and the area of the semicircle. The formula for determining the area of a square is expressed as

Area = length^2

From the diagram,

length = 12

Area of square = 12^2 = 144

The formula for determining the area of a semicircle is expressed as

Area = 1/2 * pi * radius^2

Radius = diameter/2

The diameter of the semicircle is 12. Thus,

radius = 12/2 = 6

pi = 3.14

Area of semicircle = 1/2 * 3.14 * 6^2 = 56.52

Area of composite figure = 144 + 56.52 = 200.52 in^2

The first option is the correct answer

The diagonal WY bisects the diagonal XV at point D, which means that XV is divided into two equal line segments XD and XV.

Replace the equation above with the given expressions for both line segments:

XD= 2x-6

XV= 3x-6

the maximum height is 254 feet.

Answer:

a)  0.5 seconds and 3.5 seconds.

b)  5.98 seconds (2 d.p.)

c)  No.

d)  254 feet at 2 seconds.

Step-by-step explanation:

Given equation:

[tex]h=-16t^2+64t+190, \quad t \geq 0[/tex]

where:

To calculate when the object will be 218 feet above the ground, substitute h = 218 into the equation and solve for t:

[tex]\begin{aligned}\implies -16t^2+64t+190 & = 218\\-16t^2+64t+190-218& = 0\\-16t^2+64t-28 & = 0\\-4(4t^2-16t+7) & = 0\\4t^2-16t+7 & = 0\\4t^2-14t-2t+7 &=0\\2t(2t-7)-1(2t-7)&=0\\(2t-1)(2t-7)&=0\\\implies 2t-1&=0\implies t=\dfrac{1}{2}\\\implies 2t-7&=0 \implies t=\dfrac{7}{2}\end{aligned}[/tex]

Therefore, the object will be 218 feet about the ground at 0.5 seconds and 3.5 seconds.

The object strikes the ground when h is zero. Therefore, substitute h = 0 into the equation and solve for t:

[tex]\begin{aligned}\implies -16t^2+64t+190 & = 0\\-2(8t^2-32t-95) & = 0\\8t^2-32t-95 & = 0\end{aligned}[/tex]

Use the quadratic formula to solve for t:

[tex]\implies t=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}[/tex]

[tex]\implies t=\dfrac{-(-32) \pm \sqrt{(-32)^2-4(8)(-95)} }{2(8)}[/tex]

[tex]\implies t=\dfrac{32 \pm \sqrt{1024+3040} }{16}[/tex]

[tex]\implies t=\dfrac{32 \pm \sqrt{4064} }{16}[/tex]

[tex]\implies t=\dfrac{32 \pm \sqrt{16 \cdot 254} }{16}[/tex]

[tex]\implies t=\dfrac{32 \pm \sqrt{16} \sqrt{254} }{16}[/tex]

[tex]\implies t=\dfrac{32 \pm 4 \sqrt{254} }{16}[/tex]

[tex]\implies t=\dfrac{8\pm \sqrt{254} }{4}[/tex]

As t ≥ 0,

[tex]\implies t=\dfrac{8+ \sqrt{254} }{4}\quad \sf only.[/tex]

[tex]\implies t=5.98 \sf \; s \; (2 d.p.)[/tex]

Therefore, the object strikes the ground at 5.98 seconds (2 d.p.).

To find if the object will reach a height of 300 feet above the ground, substitute h = 300 into the equation and solve for t:

[tex]\begin{aligned}\implies -16t^2+64t+190 & = 300\\-16t^2+64t+190-300 & =0\\-16t^2+64t-110 & =0\\-2(8t^2-32t+55) & =0\\8t^2-32t+55& =0\end{aligned}[/tex]

Use the quadratic formula to solve for t:

[tex]\implies t=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}[/tex]

[tex]\implies t=\dfrac{-(-32) \pm \sqrt{(-32)^2-4(8)(55)} }{2(8)}[/tex]

[tex]\implies t=\dfrac{32 \pm \sqrt{1024-1760} }{16}[/tex]

[tex]\implies t=\dfrac{32 \pm \sqrt{-736} }{16}[/tex]

[tex]\implies t=\dfrac{32 \pm \sqrt{16 \cdot -1 \cdot 46} }{16}[/tex]

[tex]\implies t=\dfrac{32 \pm \sqrt{16} \sqrt{-1} \sqrt{ 46}}{16}[/tex]

[tex]\implies t=\dfrac{32 \pm 4i\sqrt{ 46} }{16}[/tex]

[tex]\implies t=\dfrac{8\pm \sqrt{ 46} \;i}{4}[/tex]

Therefore, as t is a complex number, the object will not reach a height of 300 feet.

The maximum height the object can reach is the y-coordinate of the vertex.  

Find the x-coordinate of the vertex and substitute this into the equation to find the maximum height.

[tex]\textsf{$x$-coordinate of the vertex}: \quad x=-\dfrac{b}{2a}[/tex]

[tex]\implies \textsf{$x$-coordinate of the vertex}=-\dfrac{64}{2(-16)}=-\dfrac{64}{-32}=2[/tex]

Substitute t = 2 into the equation:

[tex]\begin{aligned}t=2 \implies h(2)&=-16(2)^2+64(2)+190\\&=-16(4)+128+190\\&=-64+128+190\\&=64+190\\&=254\end{aligned}[/tex]

Therefore, the maximum height of the object is 254 feet.

It takes 2 seconds for the object to reach its maximum height.

The formula to calculate the volume of a sphere is given to be:

where r is the radius.

From the question, we have the following parameters:

Therefore, the volume is calculated to be:

The volume is 463.0 cm³.

Solution:

Given the circle with center A as shown below:

The plane travels 120 feet counterclockwise from B to C, thus forming an arc AC.

The length of the arc AC is expressed as

Given that

we have

Hence, the length of the control line is 85.94366927 feet.