Find the three trigonometric function values for the angle ø shown.

sin ø =
cos ø =
tan ø =

​

Answer:

Step-by-step explanation:

When you work addition and subtraction problems, it is often easier to do them if you can "make a 10" or "make a 100", because adding or subtracting 10 or 100 is easier than with non-zero digits.

__

Here, you are steered toward noticing that there are two elements of the sum that have a total of -100. Those elements are -65 and -35. With the above in mind, you can use the commutative property to rearrange the sum to ...

  -65 +(-35) +(-150) . . . . . . . last two terms were swapped

Then the first step is to add -65 and -35:

  [tex]\text{It is easier to add }\boxed{-65}\,+\,\boxed{(-35)}\text{ first to get $-100$.}[/tex]

Now, the sum reduces to ...

  -100 +(-150) = -250

So, the final sentence becomes ...

  [tex]\text{Then add }\boxed{-100+(-150)}\text{ to get }\boxed{-250}\,.[/tex]

Answer:

Part A:

Probability that average single manager beat the index= [tex](0.5)^7=0.0078125=0.0078 (4\ decimals)[/tex]

Part B:

Fund Managers to beat index 7 years=78.125≅78 managers.

Step-by-step explanation:

Part A:

Given data:

Since there are equal chances for delivering equal better performance and of under performance so

Probability of better performance =0.5

Required:

Probability that the average single fund managers beats the index 7 years in a row (before fees)=?

Solution:

Since there is 7 year index:

Probability that average single manager beat the index= [tex](0.5)^7=0.0078125=0.0078 (4\ decimals)[/tex]

Part B:

Given Data:

Number of mutual fund managers=10,000

Probability that average single manager beat the index= 0.0078125 (Calculated in part A)

Required:

How many fund managers would you expect to beat the index 7 years in a row if only luck and no skill was involved?

Solution:

Fund Managers to beat index 7 years=Total number of managers*probability  average single member beat the index

Fund Managers to beat index 7 years=10,000*0.0078125

Fund Managers to beat index 7 years=78.125≅78 managers.

Answer:

[tex] x = \pm \sqrt{19} [/tex]

[tex] x = \pm 4.36 [/tex]

Step-by-step explanation:

[tex] x^2 = 19 [/tex]

[tex] x = \pm \sqrt{19} [/tex]

[tex] x = \pm 4.36 [/tex]

The exact solution is 4.36.

Squares are the numbers, generated after multiplying a value by itself. Whereas square root of a number is value which on getting multiplied by itself gives the original value. Hence, both are vice-versa methods. For example, the square of 2 is 4 and the square root of 4 is 2.

Given:

x² = 19

On taking root on both side

√x² = √19

x= √19

x = 4.3588

Hence, the exact solution and its approximation rounded to two decimal places is 4.36.

Learn more about square root here:

https://brainly.com/question/3120622

#SPJ2

Answer:

R(7a, 0 )

Step-by-step explanation:

R is on the vertical line RQ so will have the same x- coordinate as Q

R is on the horizontal line OR so will have the same y- coordinate as O

Thus coordinates of R = (7a, 0 )

Answer:

t^2 -4t + 4

Step-by-step explanation:

(2t-4)(2t-4) Use the FOIL Method (first, outside, inside, last)

2t*2t =4t^2 First

2t*-4 = -8t Outside

-4*2t = -8t Inside

-4*-4 = 16 Last

4t^2 -8t -8t + 16 (simplify/add like terms)

(4t^2 -16t + 16)/4 (you can further simplify by dividing each value by 4)

t^2 -4t + 4

Answer:

Step-by-step explanation:

The distance between two points can be found by using the formula

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(-3,1) and (1,-4)

The distance between them is

We have the final answer as

Hope this helps you

Answer:

2

Step-by-step explanation:

Pretend there is no decimal point. We can do this by multiplying both numbers by 10.

After that, it becomes 68/34. You then divide those two, and you get 2 as your answer.

Answer:

2

Step-by-step explanation:

its easy you can do it with calculator or paper -__-

Answer:

24

Step-by-step explanation:

Assuming you want to find a mean, the answer is: 24 (sum of all values/number of values)

Range is largest-smallest

Median is middle value

Answer:

26 and 36.

Step-by-step explanation:

Let the two whole numbers be a and b. Thus, the product of them is 936 while their sum is 62. In equations, this is:

[tex]ab=936\\a+b=62[/tex]

This is a system of equations. To solve, subtract either a or b from the second equation and substitute it into the first.

For instance, subtract b from both sides in the second equation:

[tex]a+b=62\\a=62-b[/tex]

Substitute this into the first equation:

[tex](62-b)(b)=936[/tex]

Distribute:

[tex]62b-b^2=936[/tex]

Rearrange:

[tex]-b^2+62b=936[/tex]

Divide everything by -1 to make the leading coefficient positive:

[tex]b^2-62b=-936[/tex]

Add 936 to both sides:

[tex]b^2-62b+936=0[/tex]

This is now a quadratic. Solve for b.

To do so, we can factor.

After a bit of testing, we can see that -36 and -26 are possible. Thus:

[tex](b-26)(b-36)=0[/tex]

For for b:

[tex]b=26\text{ or } b=36[/tex]

Thus, b is 26 or 36.

Now, plug these back into the isolated equation to solve for a:

[tex]a=62-b\\a=62-(26) \text{ or } a=62-(36)\\a=36\text{ or } a=26[/tex]

It doesn't really matter which one we choose since they're the same.

Thus, the answer is 26 and 36.

Answer : The polynomial in standard form is [tex]1a^2+9a+20[/tex]

Step-by-step explanation :

The polynomial in standard form means that the terms are ordered from highest exponent to lowest exponent.

Given: Subtract [tex]9a^2-6a+5[/tex] from [tex]10a^2+3a+25[/tex]

The expression will be :

[tex](10a^2+3a+25)-(9a^2-6a+5)[/tex]

Now open the bracket and change the sign.

[tex]=10a^2+3a+25-9a^2+6a-5[/tex]

Now we are adding or subtracting the like terms, we get:

[tex]=1a^2+9a+20[/tex]

Thus, the polynomial in standard form is [tex]1a^2+9a+20[/tex]

Answer:

24 - 16x

Step-by-step explanation:

8(3 - 2x)

Distribute

8*3 - 8*2x

24 - 16x

Answer:

[tex] \boxed{ \bold{ \huge{\boxed{ \sf{ \: 12.9 \: \: dollars}}}}}[/tex]

Step-by-step explanation:

Given,

Cost without tax = $ 12

Tax percent = 7.5 %

Cost including tax = ?

First, finding the tax amount :

[tex] \sf{tax \: amount \: = \: 7.5 \: \% \: of \: 12}[/tex]

⇒[tex] \sf{tax \: amount = \frac{7.5}{100} \times 12} [/tex]

⇒[tex] \sf{tax \: amount = 0.9}[/tex] dollars

Finding the total cost of the lunch including tax :

⇒[tex] \sf{total \: cost \: = \: 12 + 0.9}[/tex]

⇒[tex] \sf{total \: cost \: = \: 12.9}[/tex] dollars

Hope I helped!

Best regards ! :D

Answer:

x > 5

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Write out equation

8x - 6(x + 1) < 4(2x - 9)

Step 2: Distribute parenthesis

8x - 6x - 6 < 8x - 36

Step 3: Combine like terms

2x - 6 < 8x - 36

Step 4: Subtract 2x on both sides

-6 < 6x - 36

Step 5: Add 36 on both sides

30 < 6x

Step 6: Divide both sides by 6

5 < x

Step 7: Rewrite

x > 5

Answer:

-7/3

-3/4

0.5

2/3

1.2

You can get these numbers by sorting in your head. Think of a number line and that'll make things easier :)

Answer:

-7/3, -3/4, 0.5, 2/3, 1.2

Step-by-step explanation:

The larger the negative number is the smaller it's value is and its the complete opposite for positive numbers

The correct answer is D)  If a polygon is not a kite, then it is not a quadrilateral. FALSE

Explanation:

The statement "If a polygon is a kite, then it is a quadrilateral" as other statements is composed of two parts: the if statement or hypothesis and the conclusion. Additionally, to create the inverse of this statement it is necessary to negate both statements, this means the inverse is "If a polygon is not a kite, then it is not a quadrilateral" because this negates the hypothesis and the conclusion. Besides this, it can be concluded this inverse statement is false because the word "quadrilateral" describes all shapes with four sides, which include not only kites but squares, rectangles, trapezoids, etc. Therefore, a polygon can be quadrilateral without being a kite.

Answer: im pretty sure its exponential decay?

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\left(6^2\right)^x=1\\\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc}\\\left(6^2\right)^x=6^{2x}\\\\6^{2x}=1\\\mathrm{If\:}f\left(x\right)=g\left(x\right)\mathrm{,\:then\:}\ln \left(f\left(x\right)\right)=\ln \left(g\left(x\right)\right)\\\ln \left(6^{2x}\right)=\ln \left(1\right)\\\\\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)\\\ln \left(6^{2x}\right)=2x\ln \left(6\right)\\2x\ln \left(6\right)=\ln \left(1\right)\\[/tex]

[tex]\mathrm{Solve\:}\:2x\ln \left(6\right)=\ln \left(1\right):\\\quad x=0[/tex]

Answer:

x = 0

Simplified: [tex]36^{x} = 1[/tex]

Step-by-step explanation:

How to simplify:

Answer:

One brother says of his younger brother: “Two years ago, I was three times as old as my brother was. In three years’ time, I will be twice as old as my brother.” How old are they each now?

Step-by-step explanation:

Let us suppose two years ago my brother's age was x years

Then, my age was 3x

Three years from now, my brother's age will be (x +2+3) = (x+5) years

And my age will be (3x+2+3) = (3x+5) years

But it is given that i will be twice as old as my brother.

So, 2(x+5)= (3x+5)

or, x= 5 years

So my brother's present age is 5+2= 7 years

And my age is 5*3+2= 17 years

The age of the older brother is 13 and the age of the younger brother is 5.

Two simultaneous equations can be determined from this question:

y = 3x - 2 equation 1

y = 2x + 3 equation 2

Where:

y = older brother's age

x = younger brother's age

Equate equation 1 and equation 2

3x - 2 = 2x + 3

Combine similar terms

3x - 2x = 3 + 2

x = 5

Substitute for x in equation 1

3(5) - 2

15 - 2

y =13

To learn more about simultaneous equations, please check: https://brainly.com/question/25875552

Answer:

D.13-2x

Step-by-step explanation:

[tex]10-\left(2x-3\right)\\\\-\left(2x-3\right):\quad -2x+3\\=10-2x+3\\\\\mathrm{Simplify}\:10-2x+3:\\\quad -2x+13[/tex]

Answer:

13 -2x

Step-by-step explanation:

10-(2x-3)

Distribute the minus sign

10 -2x +3

Combine like terms

13 -2x

Answer:

A) ¬(¬q) ≡ q

B) ≡ ( эx) (¬p(x) ∧ ¬q(x)

C) ≡ ( зx ) (p(x) ∧ (¬ q(x) ∨ r(x)) )

Step-by-step explanation:

using De Morgan's law for quantified statements and the laws of propositional logic to show the equivalent of the following

from De -Morgan law

¬(A ∨ B ) = ¬ A ∧¬ B

ATTACHED BELOW IS THE COMPLETE SOLUTION

Answer:

i think b is answer. i think this is useful to you

Answer:

X= 60°

Y= 30°

Step-by-step explanation:

In triangle ABD, we have:

AB = BD = AD

Then triangle ABD is equilateral triangle.

Then, all its angles are equal to 60°.

=> X = 60°

____________________________________

ADC is right triangle at D.

So, X and Y are congruent angles (their sum is equal to 90°)

So, X + Y =90°

60° + Y = 90°

Y = 90 - 60

Y= 30°

[tex]hope \: this \: helps[/tex]

Answer:

L = A÷W

Step-by-step explanation:

The area of a rectangle (A) is related to the length (L) and width (W) of its sides by the following relationship: A = L ⋅ W. If you know the width, it's easy to find the length by rearranging this equation to get L = A ÷ W.

Answer:

1) W₁ is a subspace of Pₙ (R)

2) W₂ is not a subspace of Pₙ (R)

4) W₃ is a subspace of Pₙ (R)

Step-by-step explanation:

Given that;

1.Let W₁ be the set of all polynomials of the form p(t) = at², where a is in R

2.Let W₂ be the set of all polynomials of the form p(t) = t² + a, where a is in R

3.Let W₃ be the set of all polynomials of the form p(t) = at² + at, where a is in R

so

1)

let W₁ = { at² ║ a∈ R }

let ∝ = a₁t² and β = a₂t²  ∈W₁

let c₁, c₂ be two scalars

c₁∝ + c₂β = c₁(a₁t²) + c₂(a₂t²)

= c₁a₁t² + c²a₂t²

= (c₁a₁ + c²a₂)t² ∈ W₁

Therefore c₁∝ + c₂β ∈ W₁ for all ∝, β ∈ W₁  and scalars c₁, c₂

Thus, W₁ is a subspace of Pₙ (R)

2)

let W₂ = { t² + a ║ a∈ R }

the zero polynomial 0t² + 0 ∉ W₂

because the coefficient of t² is 0 but not 1

Thus W₂ is not a subspace of Pₙ (R)

3)

let W₃ = { at² + a ║ a∈ R }

let ∝ = a₁t² +a₁t  and β = a₂t² + a₂t ∈ W₃

let c₁, c₂ be two scalars

c₁∝ + c₂β = c₁(a₁t² +a₁t) + c₂(a₂t² + a₂t)

= c₁a₁t² +c₁a₁t + c₂a₂t² + c₂a₂t

= (c₁a₁ +c₂a₂)t² + (c₁a₁t + c₂a₂)t ∈ W₃

Therefore c₁∝ + c₂β ∈ W₃ for all ∝, β ∈ W₃ and scalars c₁, c₂

Thus, W₃ is a subspace of Pₙ (R)

Answer:

A month at the very least

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

√2 is irrational because radicals are irrational. π is also an irrational number. The third option, 1.3985624785461.... is obviously not a terminating decimal, hence, it is also irrational. Therefore, the answer is 1/3. We know this because 1/3 can be written in the form a / b where a and b are rational numbers, in this case, a = 1 and b = 3.

Answer:

The standard error is 0.033.

Step-by-step explanation:

We are given that Sukie interviewed 125 employees at her company and discovered that 21 of them planned to take an extended vacation next year.

Let [tex]\hat p[/tex] = proportion of employees who planned to take an extended vacation next year

[tex]\hat p[/tex] = [tex]\frac{X}{n}[/tex] = [tex]\frac{21}{125}[/tex] = 0.168

n = number of employees at her company = 125

Now, the standard error is calculated by the following formula;

       Standard error, S.E. =  [tex]\sqrt{\frac{\hat p(1-\hat p)}{n} }[/tex]

                                         =  [tex]\sqrt{\frac{0.168(1-0.168)}{125} }[/tex]

                                         =  [tex]\sqrt{\frac{0.168 \times 0.832}{125} }[/tex]  = 0.033

Hence, the standard error is 0.033.

Answer:

.10 - .23

Step-by-step explanation:

.168 +/- 1.96 ( sqrt ((.168 * .832)/125))

Answer:

Time travelled each day = 8 hours

Step-by-step explanation:

total distance of 2-day trip = 880 miles

half the distance each day = 880 ÷ 2 = 440 miles

velocity travelled each day = 55 miles per hour

time travelled each day = ???

velocity = (distance trvaelled) ÷ (Time)

55 = 440 ÷ Time

[tex]55=\frac{440}{Time} \\cross-multiplying\\55\ \times\ Time = 440\\Time = \frac{440}{55} \\Time = 8\ hours[/tex]

∴ Time travelled each day = 8 hours

Answer:

9 hours

Step-by-step explanation:

Total distance for the two days = 880 miles

If half of the distance is to be traveled each day, then;

distance each day = 440 miles

speed of the automobile = 55 miles per hour.

Now, let's calculate the number of hours that will be driven each day.

Remember that;

speed = distance / time

=> time = distance / speed           [substitute the values of distance and speed]

=> time = (440 miles) / (55 miles/hour)

=> time = 9 hours.

Therefore, the number of hours that will be driven each day is 9