You are out with friends. Half of you want to go bowling and the other half want to go to a movie. How will you make a fair decision about wether to go to a movie or go bowling using a fair coin and assuming that all of you want to go to either of the places together?

Answer:

angle JKL =  120 degrees

Step-by-step explanation:

Since arc JL is 60 degrees, the central angle is also 60 degrees.

Point K is the intersection of tanges at J and L, therefore KJM and KLM are 90 degrees.

Consider quadrilateral JKLM whose sum of internal angles = 360.

Therefore

angle JKL + angle KLM + angle LMJ + angle MJK = 360 degrees

angle JKL + 90 + 60 + 90 = 360

angle JKL = 360 - 90 - 60 -90 = 120 degrees

Answer:

120 degrees

Step-by-step explanation:

Since arc JL is 60 degrees, the central angle is also 60 degrees.

Point K is the intersection of tanges at J and L, therefore KJM and KLM are complementary or equal 90 degrees.

look at quadrilateral JKLM whose sum of internal angles = 360.

Therefore

angle JKL plus angle KLM plus angle LMJ plus angle MJK = 360 degrees

angle JKL + 90 + 60 + 90 = 360

Answer:

The probability of the event BC

= the probability of B * C = 48.6667% * 70%

= 34.0667%

Step-by-step explanation:

Probability of A, students with children = 44/150 = 29.3333%

Probability of B, students enrolled in at least 12 credits = 73/150 = 48.6667%

Probability of C, students working at least 10 hours per week = 105/150 = 70%

Therefore, the Probability of BC, students enrolled in 12 credits and working 10 hours per week

= 48.6667% * 70%

= 34.0667%

Answer:

-415

Step-by-step explanation:

first, add -395+-27+-95, which equals -517

then, add 102 to -517(all you do is subtract 102 from 517 and put a negative sign in front of that answer), in which you would get -415.

Answer:

500km

Step-by-step explanation:

add all the proportions and then divide by 3. with conversion.

Answer:

[tex]n >21[/tex]

Step-by-step explanation:

The number exceeds 21 or is greater than 21.

‘[tex]>[/tex]’ represents greater than.

Let the number be [tex]n[/tex].

[tex]n >21[/tex]

Answer:

Step-by-step explanation:

Given that :

A web page is accessed at an average of 20 times an hour.

Therefore:

a. he rate parameter λ of the distribution of the time until the first hit = 20

b.  What is the expected time between hits?

Let consider E(Y) to be the expected time between the hits; Then :

E(Y) = 1/λ

E(Y) = 1/20

E(Y) = 0.05 hours

E(Y) = 3 minutes

(c.)  What is the probability that there will be less than 5 hits in the first hour?

Let consider X which follows Poisson Distribution; Then,

P(X<5) [tex]\sim[/tex] G(∝=5,  λ = 20)

For 5 hits ; the expected time will be :

Let 5 hits be X

E(X) = ∝/λ

E(X) = 5/20

E(X) =1/4

E(X) = 0.25 hour

E(X) = 15 minutes

From above ; we will see that  it took 15 minutes to get 5 hits; then

[tex]P(\tau \geq 0.25) = \int\limits^{\alpha}_{0.25} \dfrac{\lambda^{\alpha}}{\ulcorner^{\alpha}} t^{a\pha-1} \ e^{-\lambda t} \, dt[/tex]

[tex]P(\tau \geq 0.25) = \int\limits^{5}_{0.25} \dfrac{20^{5}}{\ulcorner^{5}} t^{5-1} \ e^{-20 t} \, dt[/tex]

[tex]\mathbf{P(\tau \geq 0.25) =0.4405}[/tex]

Answer:

answer there

Step-by-step explanation:

hope it. was. helpful

Answer:

ƒ(x) = 3|x – 2| + 1

To find f(-2) substitute - 2 into f(x)

That's

f(-2) = 3| - 2 - 2 | + 1

= 3| - 4| + 1

But absolute value of any number is positive including negative numbers

That's

| - 4 | = 4

So we have

3(4) + 1

12 + 1

To find f(1) substitute 1 into f(x)

That's

f(1) = 3 | 1 - 2| + 1

= 3 | - 1| + 1

But | - 1| = 1

= 3(1) + 1

= 3 + 1

Hope this helps you

Answer:

f(-2) =13

f(-1) = 4

Step-by-step explanation:

ƒ(x) = 3|x – 2| + 1

Let x = -2

ƒ(-2) = 3|-2 – 2| + 1

       = 3 | -4| +1

Taking the absolute value

    = 3*4 +1

    = 12 +1 = 13

Let x = 1

ƒ(1) = 3|1 – 2| + 1

       = 3 | -1| +1

Taking the absolute value

    = 3*1 +1

    = 3 +1 = 4

Answer:

There is 90% confidence that the proportion of the adult citizens of the nation that dreaded Valentine’s Day is between 0.214 and 0.286.

Step-by-step explanation:

The summary of the statistics from the information given is ;

At 90% confidence interval, 25​% dreaded​ Valentine's Day and the margin of error for the survey was 3.6 percentage points

SO;

[tex]C.I = \hat p \pm M.O.E[/tex]

[tex]C.I = 0.25 \pm 0.036[/tex]

C.I = (0.25-0.036 , 0.25+0.036)

C.I = (0.214, 0.286)

The 90% confidence interval for the proportion of the adult citizens of the nation that dreaded Valentine’s day is 0.214 and 0.286.

There is 90% confidence that the proportion of the adult citizens of the nation that dreaded Valentine’s Day is between 0.214 and 0.286.

Answer:

C. Seasonal variation

Step-by-step explanation:

Distinct pattern around a trend line can be caused by seasonal variation.

Seasonal variation refers to a component of a time series which can be defined as the repetitive and predictable movement around the trend line in a year or less. It is caused by temperature, rainfall, public holiday and cycles of season

Seasonal variation can be detected by measuring the quantity of interest for small time intervals, such as days, weeks, months or quarters.

Firms affected by seasonal variation are usually interested in knowing their performance relative to the normal seasonal variation. They need to identify and measure this seasonality so as to help with planning.

Answer:

[tex]2(x^2+63)[/tex]

Step 1:

To solve this, we have to add the terms without any variables together.

[tex]2x^2+28+98\\2x^2+126[/tex]

Step 2:

To factor this, we have to find the multiples of 2x^2 and 126.

[tex]2x^2 = 2x, x\\126 = 63, 2[/tex]

Now, we can factor these numbers like this:

[tex]2(x^2+63)[/tex]

When we multiply the numbers, we get 2x^2 + 126, and when we separate 126, we get our original question, so that means our factoring is correct.

Answer:

x=2

Step-by-step explanation:

3(x-2)-6x=4(x-5)

Distribute

3x -6  -6x = 4x -20

Combine like terms

-3x-6 = 4x-20

Add 3x to each side

-3x-6+3x = 4x-20+3x

-6 = 7x-20

Add 20 to each side

-6+20 = 7x-20+20

14 = 7x

Divide by 7

14/7 =7x/7

2=x

Answer:

Step-by-step explanation:

[tex]3(x - 2) - 6x = 4(x - 5)[/tex]

Distribute 3 through the parentheses

[tex]3x - 6 - 6x = 4(x - 5)[/tex]

Distribute 4 through the parentheses

[tex]3x - 6 - 6x = 4x - 20[/tex]

Collect like terms

[tex] - 3x - 6 = 4x - 20[/tex]

Move variable to L.H.S and change it's sign

[tex] - 3x - 4x - 6 = - 20[/tex]

Move constant to RHS and change it's sign

[tex] - 3x - 4x = - 20 + 6[/tex]

Collect like terms

[tex] - 7x = - 20 + 6[/tex]

Calculate

[tex] - 7x = - 14[/tex]

Divide both sides of the equation by -7

[tex] \frac{ - 7x}{ - 7} = \frac{ - 14}{ - 7} [/tex]

Calculate

[tex]x = 2[/tex]

Hope this helps..

Best regards!!

Answer:

Option (B)

Step-by-step explanation:

Let the equation of the exponential function give in the graph is,

f(x) = a(b)ˣ

Since the given graph passes through two points (0, 3) and (-1, 1.5)

For (0, 3),

f(0) = a(b)⁰

3 = a(1) [Since b⁰ = 1]

a = 3

For (-1, 1.5),

f(-1) = a(b)⁻¹

1.5 = 3(b)⁻¹

1.5 = [tex]\frac{3}{b}[/tex]

b = [tex]\frac{3}{1.5}[/tex]

b = 2

Therefore, equation of the given function will be,

f(x) = 3(2)ˣ

Option (B) will be the answer.

Answer:

3/4

Step-by-step explanation:

3/4 is already in it's simplest form as you already know that consecutive numbers don't have anything in common to multiply.So, it is in it's simplest form.

Hope it helps u : )

The equivalent and the percentage form of 3/4 are 12/16 and 75% respectively.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given, the ratio of 3/4

Percentage of 3:4 = 34×100%=75%

the equivalent ratio of 3:4 is 12:16.

A ratio is a fraction that may compare part to whole or part to part. For example, suppose in a class, the ratio of boys to girls is 3 to 4. It means that the number of boys divided by the number of girls is a fraction that, in its simplest form, equals 3 over 4.

Learn more about ratios here:

https://brainly.com/question/13419413

#SPJ3

Answer:

(11π/9 )ft/s

Step by step Explanation

Let us denote the height as h ft

But we were told that The diameter of the base of the cone is approximately three times the altitude, then

Let us denote the diameter = 3h ft, and the radius is 3h/2

The volume of the cone is

V = (1/3)π r^2 h

Then if we substitute the values we have

= (1/3)π (9h^2/4)(h) = (3/4)π h^3

dV/dt = (9/4)π h^2 dh/dt

We were given as 22feet and rate of 8 cubic feet per minute

h = 22

dV/dt = 8

8= (9/4)π (22) dh/dt

= 11π/9ft/s

Therefore, the rate is the height of the pile changing when the pile is 22 feet is

11π/9ft/s

Answer:

13

Step-by-step explanation:

Divide:

27 ÷ 2 = 13 r1

So, he can buy 13 but has a dollar left.

Hope this helps you out! : )

Answer:

your answer is correct.

Answer:

What is the question?

Step-by-step explanation:

Answer:

$1.06 per share

Step-by-step explanation:

Calculation for dividend per share of common stock for board of directors of Midwest Foods

First step is to find the dividends due to the preferred shareholders

Dividends due to the preferred shareholders will be calculated as:

Using this formula

Total Dividend =Dividend- (Preferred stock *Per share of preferred stock )

Where,

Dividend=$3,500,000

Preferred stock =$300,000

Per share of preferred stock =$2.85

Let plug in the formula

Total Dividend =$3,500,000-($300,000*$2.85)

Total Dividend =$3,500,000-$855,000

Total Dividend =$2,645,000

The second step is to find Dividend per share of common stock

Using this formula

Dividend per share of common stock=Total dividend/Shares of common stock

Where,

Total dividend=$2,645,000

Shares of common stock=$2,500,000

Let plug in the formula

Dividend per share of common stock=$2,645,000/$2,500,000

Dividend per share of common stock=$1.06 per share

Therefore the dividend per share of common stock for board of directors of Midwest Foods will be $1.06 per share

Answer:

AC (b)

Step-by-step explanation:

Since 10 is half of 20, you have to find the variable closest to the middle. Which in this case, is C. So, your awnser is B. (AC)

Answer:

[tex]\boxed{\sf C}[/tex]

Step-by-step explanation:

The whole segment is [tex]\sf \sqrt {20}[/tex], we can see that AD is approximately 75% of the segment AE.

[tex]75\%*\sqrt{20} = 3.354102[/tex]

[tex]\sqrt{10}= 3.162278[/tex]

AC is almost half of AE.

[tex]\frac{\sqrt{20} }{2} = 2.2360679775[/tex]

[tex]\sqrt{10} = 3.16227766017[/tex]

It isn’t close to the option C.

Answer:

84%

Step-by-step explanation:

We find the z-score here

z= x-mean/SD = 32-40/8 = -1

So the probability we want to find is;

P(z>-1)

This can be obtained using the standard score table

P(z>-1) = 0.84 = 84%

Answer:

[tex]\angle AE = 32^{\circ}[/tex]

[tex]\angle EAD = 212^{\circ}[/tex]

[tex]\angle BE = 133^{\circ}[/tex]

[tex]\angle BCE = 227^{\circ}[/tex]

[tex]\angle AED = 180^{\circ}[/tex]

[tex]\angle BD = 79^{\circ}[/tex]

Step-by-step explanation:

The central angle of a circle is equal to 360º, whose formula in this case is:

[tex]\angle AB + \angle BC + \angle CD + \angle DE + \angle EA = 360^{\circ}[/tex]

In addition, the following conditions are known from figure:

[tex]\angle BC = 47^{\circ}[/tex], [tex]\angle DE = 148^{\circ}[/tex]

[tex]\angle DE + \angle EA = 180^{\circ}[/tex]

[tex]\angle CD + \angle DE = 180^{\circ}[/tex]

[tex]\angle AB + \angle BC + \angle CD = 180^{\circ}[/tex]

Now, the system of equations is now solved:

[tex]\angle EA = 180^{\circ}-\angle DE[/tex]

[tex]\angle EA = 180^{\circ}-148^{\circ}[/tex]

[tex]\angle EA = 32^{\circ}[/tex]

[tex]\angle CD = 180^{\circ}-\angle DE[/tex]

[tex]\angle CD = 180^{\circ}-148^{\circ}[/tex]

[tex]\angle CD = 32^{\circ}[/tex]

[tex]\angle AB = 180^{\circ} - \angle BC - \angle CD[/tex]

[tex]\angle AB = 180^{\circ}-47^{\circ}-32^{\circ}[/tex]

[tex]\angle AB = 101^{\circ}[/tex]

The answers are described herein:

[tex]\angle AE = 32^{\circ}[/tex]

[tex]\angle EAD = 212^{\circ}[/tex]

[tex]\angle BE = 133^{\circ}[/tex]

[tex]\angle BCE = 227^{\circ}[/tex]

[tex]\angle AED = 180^{\circ}[/tex]

[tex]\angle BD = 79^{\circ}[/tex]

Answer:

  SAS Postulate

Step-by-step explanation:

The contributors to the proof are listed in the left column. They consist of a congruent Side, a congruent Angle, and a congruent Side. The SAS Postulate is an appropriate choice.

Answer:

x = 26

Step-by-step explanation:

Since a triangle adds up to 180 degrees, we can do:

x + 4x - 5 + 55 = 180

5x + 50 = 180

5x = 130

x = 26

Answer: [tex]\dfrac{60}{143}[/tex]

Step-by-step explanation:

Given,  A class has five boys and nine girls.

Total students = 5+9=14

Number of ways to choose 6 students out of 14= [tex]^{14}C_6[/tex]  [Using combinations]

Number of ways to choose 4 girls out of 6 (4 girls + 2 boys = 6 ) = [tex]^{9}C_4\times\ ^{5}C_2[/tex]

If the teacher randomly picks six students, then the probability that he will pick exactly four girls:-

[tex]\dfrac{^{9}C_4\times \ ^{5}C_2}{^{14}C_6}[/tex]

[tex]=\dfrac{\dfrac{9!}{4!5!}\times\dfrac{5!}{2!3!}}{\dfrac{14!}{6!8!}}\\\\=\dfrac{1260}{3003}\\\\=\dfrac{60}{143}[/tex]

hence, the required probability = [tex]\dfrac{60}{143}[/tex] .

Answer:  C) $590

Step-by-step explanation:

Gene paid $1800 - $1800(0.2) = $1440 for Model Y

The store paid $850 for Model Y.

The profit was $1440 - $850 = $590

Answer:

D. [tex] lw = (x + 5)(x - 5) ; 119 ft^2 [/tex]

Step-by-step explanation:

Dimensions of the old square brick patio:

[tex] length (l) = x ft [/tex]

[tex] width (l) = x ft [/tex]

Note: a square has equal side measure

Dimensions of the new patio

[tex] length (l) = (x + 5) ft [/tex] ==> she increased length by 5 ft

[tex] width (l) = (x - 5) ft [/tex] she reduced width by 5 ft

Expression of the length and width of the new patio is: [tex] lw = (x + 5)(x - 5) [/tex]

Area of the new patio:

Dimension of original patio = x by x = 12 ft by 12 ft.

To find area of the new patio, replace x with 12 in the expression, [tex] lw = (x + 5)(x - 5) [/tex] , which gives you the area.

[tex] area = lw = (12 + 5)(12 - 5) [/tex]

[tex] area = (17)(7) [/tex]

[tex] area = 199 ft^2 [/tex]

Answer is D. [tex] lw = (x + 5)(x - 5) ; 119 ft^2 [/tex]

Answer: y = 90°

Step-by-step explanation:

55.30786941 = sin-1 (148/180)   round to 55.3°  angle x

34.69213059 = cos-1 (148/180) . round to 34.7°  "angle z" at right

34.7 +55.3 = 90

Sum of All angles of the triangle = 180°  180 -90 = 90

If angle x is 55.7 and angle z is 34.7° Angle y must be 90°

Ratio of inscribed arcs = ratio of chord to diameter

Answer:

As x → - ∞ , y → - ∞ and as x→ ∞ , y → -∞

Step-by-step explanation:

f ( x ) = - 5x⁴ + 7x² - x + 9

Here, dominating term is ( -5x⁴ ) which has even exponent.

Now, as x → ∞ ⇒ - 5x ⁴⇒ - ∞ [ x⁴ → ∞ ]

⇔ f (x) → - ∞ [ -5x⁴ is dominating term ]

x→ ∞ , y → -∞

as x→ - ∞ , ( -5x⁴ ) → - ∞ [ x⁴ → ∞ ]

as x→ - ∞ , y → -∞

Hence, Option B is the correct option.

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

You just have to focus on leading term, which is the term that has highest exponent of variable, as in our case , it is -5x⁴.

And then find leading coefficient, whether it is positive or negative degree ( power of variable) and whether it is even number or odd number)

Then, if leading coefficient is negative and degree is positive then always y will approach -∞ .

Hope this helps...

Best regards!!

Answer:

As x goes to negative infinity, y goes to  - ∞

As x goes to infinity, y goes to  - ∞

Step-by-step explanation:

We need to look at the dominate term

-5x^4

As x goes to negative infinity

-5 *(- ∞) ^ 4 = -5 * ∞ = - ∞

As x goes to negative infinity, y goes to  - ∞

As x goes to  infinity

-5 *( ∞) ^ 4 = -5 * ∞ = - ∞

As x goes to infinity, y goes to  - ∞

Answer:

(10, -29)

Step-by-step explanation:

I assume you are looking for the solution to this system of equations.

Plug them both into a graphing calculator. The point where they cross is:

(10, -29)

Answer:(10, -29)

Step-by-step explanation: