Please help
Trig: Laws of Cosines.
In Δ ABC , side a =3, side b =15 and m < C= 108* . Find side ' c' to the nearest integer.

Answers

Answer 1

Answer: 16

Step-by-step explanation:

law of cosines says that c^2 = a^2 + b^2 -2abcosC

so c^2 = 3^2 +15^2 - 2*2*15*cos108

c^2 = 234 -  (-27.8115294937 )

c^2 = 261.811529494

c = 16.18 rounds to 16

Answer 2

Answer:

16

Step-by-step explanation:

c² = a² + b² - 2(a)(b)cos(C)

c² = 3² + 15² - 2(3)(15)cos(108)

c² = 261.8115295

c = 16.18059114


Related Questions

George is 3 time as old as chun. Chun is 1/2 as old as elizabeth. Waneta is 4/7 as old as elizabeth. Waneta is 8 years old. How many years old is george

Answers

Answer:

21 years old.

Step-by-step explanation:

Given:

Waneta is 8 years old

Waneta is 4/7 as old as Elizabeth.

Chun is 1/2 as old as Elizabeth.

George is 3 time as old as Chun.

Question asked:

How many years old is George ?

Solution:

Let age of Elizabeth = [tex]x[/tex] years

Waneta is 4/7 as old as Elizabeth. ( given )

Age of Waneta = [tex]\frac{4}{7} \ of \ Elizabeth[/tex]

[tex]8=\frac{4}{7} \times x\\\\8=\frac{4}{7}x[/tex]

By cross multiplication:

[tex]4x=56[/tex]

By dividing both sides by 4

[tex]x=14\\[/tex]

Age of Elizabeth = [tex]x[/tex] = 14 years

Chun is 1/2 as old as Elizabeth. ( given )

Age of Chun = [tex]\frac{1}{2} \ of \ Elizabeth\\[/tex]

                     = [tex]\frac{1}{2} \times14= 7\ years[/tex]

George is 3 time as old as Chun.  ( given )

Age of George = [tex]3\ times \ of \ Chun\\[/tex]

                         [tex]=3\times7=21\ years[/tex]

Therefore, George is 21 years old.

Technician A says that a MAF sensor is a​ high-authority sensor and is responsible for determining the fuel needs of the engine based on the measured amount of air entering the engine. Technician B says that a cold wire MAF sensor uses the electronics in the sensor itself to heat a wire 20 degrees below the temperature of the air entering the engine. Who is​ right

Answers

Answer: Both Technicians are correct

Step-by-step explanation: Technician A talked about the functions of a MAF sensor which is to determine the fuel need of the engine based on the of air entering the engine.

Technician B talked about types of MAF sensor employed in vehicles and how they function

Bonita Industries sells radios for $50 per unit. The fixed costs are $645000 and the variable costs are 60% of the selling price. As a result of new automated equipment, it is anticipated that fixed costs will increase by $215000 and variable costs will be 50% of the selling price. The new break-even point in units is:

Answers

Answer:

The new break even point in units = 34400 units

Step-by-step explanation:

Fixed cost ( F ) = $ 645000

Selling price ( s )= $ 50

Variable Cost ( v ) = [tex]\frac{60}{100}[/tex] × 50 = 30

Break Even Quantity ( [tex]x_{BEP}[/tex] ) = [tex]\frac{F}{s - v}[/tex]

⇒ [tex]x_{BEP}[/tex] = [tex]\frac{645000}{50 - 30}[/tex]

⇒ [tex]x_{BEP}[/tex] = [tex]\frac{645000}{20}[/tex]

[tex]x_{BEP}[/tex] = 32250 units

Now the new fixed cost ( [tex]F_{1}[/tex] ) = $ 645000 + $ 215000 = $ 860000

Selling price ( s )= $ 50

Variable Cost ( v ) = [tex]\frac{50}{100}[/tex] × 50 = $ 25

Break Even Quantity ( [tex]x_{BEP}[/tex] ) = [tex]\frac{F_{1} }{s - v}[/tex]

⇒ [tex]x_{BEP}[/tex] = [tex]\frac{860000}{50 - 25}[/tex]

[tex]x_{BEP}[/tex] = 34400 units

Therefore, The new break even point in units = 34400 units

2)
What are the relative minimum and relative maximum values over the interval -3,3] for
the function shown in the graph? (4 points)
Minimum:
Maximum:​

Answers

Answer:

minimum: -9maximum: -6

Step-by-step explanation:

For a point to be a relative extreme, there must be points on both sides that are not as extreme. That is, the ends of the interval may be extreme values, but do not qualify as relative extrema, since there are not points on both sides.

In the interval [-3, 3], the relative extrema are the turning points.

The relative minimum is at y = -9 on the y-axis.

The relative maxima are at y = -6, between 1 and 2 on either side of the y-axis.

Answer:

minimum: -9

maximum: -6

Step-by-step explanation:

Let f(x)=15/(1+4e^(-0.2x) )

What is the point of maximum growth rate for the logistic function f(x)? Show all work.

Round your answer to the nearest hundredth

Answers

Answer:

6.93

Step-by-step explanation:

f(x) = 15 / (1 + 4e^(-0.2x))

f(x) = 15 (1 + 4e^(-0.2x))^-1

Taking first derivative:

f'(x) = -15 (1 + 4e^(-0.2x))^-2 (-0.8e^(-0.2x))

f'(x) = 12 (1 + 4e^(-0.2x))^-2 e^(-0.2x)

f'(x) = 12 (1 + 4e^(-0.2x))^-2 (e^(0.1x))^-2

f'(x) = 12 (e^(0.1x) + 4e^(-0.1x))^-2

Taking second derivative:

f"(x) = -24 (e^(0.1x) + 4e^(-0.1x))^-3 (0.1e^(0.1x) − 0.4e^(-0.1x))

Set to 0 and solve:

0 = -24 (e^(0.1x) + 4e^(-0.1x))^-3 (0.1e^(0.1x) − 0.4e^(-0.1x))

0 = 0.1e^(0.1x) − 0.4e^(-0.1x)

0.1e^(0.1x) = 0.4e^(-0.1x)

e^(0.1x) = 4e^(-0.1x)

e^(0.2x) = 4

0.2x = ln 4

x = 5 ln 4

x ≈ 6.93

Graph: desmos.com/calculator/zwf4afzmav

The point of maximum growth rate for the logistic function f(x) is at (7.5, 7.926).

What is exponential function?Exponential function → An exponential equation is given by - y = eˣ.Graph → The graph of  y = eˣ is upward-sloping, and increases faster as {x} increases

Given is the function f(x) as follows -

f(x) = 15/(1+4[tex]$e^{-0.2x}[/tex] )

The given logistic function is -

f(x) = 15/(1+4[tex]$e^{-0.2x}[/tex] )

The inflection point represents the time of most rapid growth. After the inflection point, the growth rate declines, reaches the limiting value. The inflection point occurs at half of the carrying capacity. This is the level of maximum growth.The equation for a logistic model is N = {K/1 + b[tex]$e^{-rt}[/tex]}. The constant {K} is the carrying capacity. It is the limiting value of N. The inflection point occurs at N = K/2.

So, we can say that at {x} = N = 15/2 = 7.5, the point of maximum growth exists. At {x} = 7.5, the value of {y} = 7.926. Refer to the graph of the function attached.

Therefore, the point of maximum growth rate for the logistic function f(x) is at (7.5, 7.926).

To solve more questions on exponential equations, visit the link below -

brainly.com/question/29506679

#SPJ3

Point w is located at -2 and 3 on a coordinate plane point w is reflected over the x axis to create point w point w is then reflected over the y axis to create point w what ordered pair describes the location of point w

Answers

Answer:

w(2,-3)

Step-by-step explanation:

the initial coordinates of point w are  w(-2,3), to differentiate the different coordinates of w we will place sub-indexes (according to the graph)

the point w is reflected over the x axis to create point w₁(-2,-3) point w is then reflected over the y axis to create point w₂(2,-3)

Marcus is working at a local pizzeria where he makes $12.50 per hour and is also working at the university bookstore where he makes $9.50 per hour. He must make at least $300 per week to cover his expenses but cannot work more than 30 hours per week in order to attend classes. Write a system of inequalities that models this situation where p represents the hours he works at the pizzeria and b represents the hours he works at the bookstore.

Answers

Answer: The system of inequalities that models this situation are

p + b ≤ 30

12.5p + 9.5b ≥ 300

Step-by-step explanation:

Let p represent the number of hours he works at the pizzeria.

Let b represent the number of hours he works at the bookstore.

He cannot work more than 30 hours per week in order to attend classes. This means that

p + b ≤ 30

Marcus is working at a local pizzeria where he makes $12.50 per hour and is also working at the university bookstore where he makes $9.50 per hour. He must make at least $300 per week to cover his expenses. This means that

12.5p + 9.5b ≥ 300

TRUE OR FALSE. if the slopes of two lines are negative reciprocals, the lines are perpendicular

Answers

Answer:

TRUE

Step-by-step explanation:

The voters of the city passed an ordinance to increase their sales tax by ¼ percent. The proceeds of the sales tax are to be used for culture and recreation. In the governmental activities journal, how would the ¼ percent sales tax revenue be recorded?

Answers

Answer:

General Revenue Sales Tax

Step-by-step explanation:

The ¼ percent would be recorded as general revenue sales tax in government activities journal.

This is because the revenue from the tax are categorised as the revenues generated from payrolls (which are imposed on employers), income and profits taxes, social security contributions, taxes levied on goods and services.

Options:

Program Revenue-Culture and Recreation-Sales Tax.

Program Revenue-Culture and Recreation-Operating Grants and Contributions.

General Revenue-Sales Tax.

General Revenue-Culture and Recreation-Sales Tax.

Answer:

General Revenue - Sales Tax

Step-by-step explanation:

General revenue is the income that is generated by the state which may be used to serve any administrative purpose by the state, and tax revenue is the income that is generated by the state through taxation.

Since the sales tax is a way of generating income by the state, it should be recorded as sales tax under general revenue.

A line segment that has both endpoints on the circumference

Answers

Answer:

A chord

Step-by-step explanation:

By the definition of a chord, it is a line segment whose endpoints lie on the circle, (and in this case circle is meant by the set of points equidistant from a center point, or as an algebraic term: circumference)

Kevin uses 84 fluid ounces of water to make an all-purpose cleaner. The directions call for 4 fluid ounces of concentrated soap for every 3 cups of water. How many fluid ounces of soap should he use? (1 cup 5 8 fl oz)

Answers

Answer: 28 fl oz

Step-by-step explanation:

84 fl oz. = 10.5 cups of water

10.5/3=3.5*8=28

why 3.5 times 8 is to get the exact amount of fluid ounces

Answer: he would need 14 fluid ounces of concentrated soap.

Step-by-step explanation:

The directions call for 4 fluid ounces of concentrated soap for every 3 cups of water.

1 cup = 8 fluid ounces

Converting 3 cups of water to fluid ounces, it becomes

3 cups = 3 × 8 = 24 fluid ounces

Kevin uses 84 fluid ounces of water to make an all-purpose cleaner. This means that the amount of concentrated soap that he would use is

(84 × 4)/24 = 336/24 = 14 fluid ounces of concentrated soap

Molly made 3,600 mL3{,}600 \text{ mL}3,600 mL3, comma, 600, start text, space, m, L, end text of tea for a party, and she served the tea divided equally in 12121212 cups. How many liters of tea did Molly put in each cup?

Answers

Answer:

0.3 liters

Step-by-step explanation:

Molly made 3600mL of tea for a party.

The tea was served equally in 12 cups.

We are to determine how many liters of tea Molly put in each cup.

Total Volume of Tea = 3600mL

Number of Cups=12

Volume Per Each Cup = 3600/12 = 300mL

Next, we convert our Volume Per Each Cup from mL to Liters

1000 Milliliter = 1 Liter  

300 Milliliter =[tex]\frac{300}{1000}[/tex] liters =0.3 liters

Molly put 0.3 liters of tea in each cup.

A plane can fly 520 miles in the same time as it takes a car to go 200 miles. If the car travels 80 mph slower than the plane, find the speed of the plane.

Answers

Answer: the speed of the plane is 130 mph

Step-by-step explanation:

Let x represent the speed of the plane. If the car travels 80 mph slower than the plane, then the speed of the car would be (x - 80) mph.

Time = Distance/speed

plane can fly 520 miles in the same time as it takes a car to go 200 miles. This means that the time it takes the plane to fly 520 miles is

520/x

Also, the time it takes the car to drive 200 miles is

200/(x - 80)

Since the time is the same, it means that

520/x = 200/(x - 80)

Cross multiplying, it becomes

520(x - 80) = 200 × x

520x - 41600 = 200x

520x - 200x = 41600

320x = 41600

x = 41600/320

x = 130 mph

Factor the expression. 100k^3 – 75k^2 + 120k – 90


5(5k^2 + 6)(4k – 3)

(25k^2 – 6)(20k + 3)

5(5k^2 – 6)(4k + 3)

(5k^2 + 30)(4k – 15)

Answers

For this case we must factor the following expression:

[tex]100k ^ 3-75k ^ 2 + 120k-90[/tex]

We take common factor 5:

[tex]5 (20k ^ 3-15k ^ 2 + 24k-18) =[/tex]

We have two groups within the parentheses:

Group 1: [tex]20k ^ 3-15k ^ 2[/tex]

Group 2: [tex]24k-18[/tex]

We factor each group:

Group 1: [tex]6 (4k-3)[/tex]

Group 2: [tex]5k ^ 2 (4k-3)[/tex]

Rewriting we have:

[tex]5 (5k ^ 2 (4k-3) +6 (4k-3)) =\\5 ((5k ^ 2 + 6) (4k-3))[/tex]

Answer:

[tex]5 (5k ^ 2 + 6) (4k-3)[/tex]

Having some trouble with this...pls help (in fraction form)

Answers

Answer:

[tex]\frac{17}{6}[/tex] or [tex]2\frac{5}{6}[/tex]

Step-by-step explanation:

1.Find the Least Common Denominator (LCD)

 LCD = 6

2.Make the denominators the same as the LCD.

   [tex]2+\frac{1*3}{2*3} + \frac{1*2}{3*2}[/tex]

3.Simplify. Denominators are now the same

   [tex]2+\frac{3}{6} + \frac{2}{6}[/tex]

4. Join the denominators

   [tex]2+\frac{3+2}{6}[/tex]

5.Simplify

   [tex]2\frac{5}{6}[/tex] = [tex]\frac{17}{6}[/tex]

Answer:

1 1/3

Step-by-step explanation:

Given function:

2y+xx= 1/3y= 1/2

Rewrite:

2·1/2+1/3

Find the solution:

[tex]2[/tex]·[tex]1/2=1[/tex] [tex]1+\frac{1}{3}=1\frac{1}{3}[/tex]

Therefore, 2y+x=1 1/3..

Point M is the midpoint of AC , find the coordinates of the missing endpoint when you are given one endpoint, and the coordinates of the midpoint. M(0, 5.5) and C(-3, 6).

Answers

The coordinates of the point A  is (3,5).

Step-by-step explanation:

Here, given the line segment is AC.

Let us assume the coordinates of the point A = (p,q)

The point M (0,5.5) is the mid point of line segment AC.

By Mid-Point Formula:

The coordinates of the mid  point M of segment AC is given as:

[tex](0,5.5) = (\frac{p + (-3)}{2} ,\frac{q+ (6)}{2})\\\implies \frac{p + (-3)}{2} = 0 , \frac{q+ (6)}{2} = 5.5\\\implies p = 0 + 3 = 3, q = 5.5 (2) - 6 = 11-6 = 5\\\implies p = 3, q = 5[/tex]

So, the coordinates of the point A  is (3,5)

Write an equation in​ slope-intercept form of the line satisfying the given conditions. The line passes through ​(minus1​,3​) and is parallel to the line whose equation is y equals 2 x plus 1.

Answers

Answer:

y = 2x + 5

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 2x + 1 ← is in slope- intercept form

with slope m = 2

Parallel lines have equal slopes, thus

y = 2x + ← is the partial equation of the parallel line

To find c substitute (- 1, 3) into the partial equation

3 = - 2 + c ⇒ c = 3 + 2 = 5

y = 2x + 5 ← equation of parallel line

Find v × w if v = 3i + 8j – 6k and w = –4i – 2j – 3k.

Answers

Answer:

[tex]vXw =-36i+33j+26k[/tex]

Step-by-step explanation:

v = 3i + 8j – 6k

w = –4i – 2j – 3k

The cross product

[tex]v X w=\left|\begin{array}{ccc}i&j&k\\3&8&-6\\-4&-2&-3\end{array}\right|[/tex]

[tex]=i\left|\begin{array}{cc}8&-6\\-2&-3\end{array}\right|-j\left|\begin{array}{cc}3&-6\\-4&-3\end{array}\right|+k\left|\begin{array}{cc}3&8\\-4&-2\end{array}\right|\\[/tex]

[tex]=i(-24-12)-j(-9-24)+k(-6+32)\\vXw =-36i+33j+26k[/tex]

There are twice as many flute players as there are trumpet players. If there are n flute players write an expression to find how many trumpet players there are.

Answers

Answer:

there are n flute players so that means that you have a n amount of flute players.

Step-by-step explanation:

You would need n flute players to play ou would have n trumpet players

i can't fail this class plz helppppppp

Which of the following are ordered pairs for the equation y = -1/3x - 6?


(0,-6) (3,-7) (-3,5)


(0,-6) (3,-7) (-3,-5)


(0,-6) (3,7) (-3,-5)


(0,6) (3,7) (-3,-5)

Answers

Answer:

2nd option (B)

Step-by-step explanation:

(0,-6) works

(3,-7) works

(-3,-5) works

This means the answer is B

School D has 880 boys to 200 girls The ratio of girls to all students is 5 to 27 22/27 of all students are boys idk how to get from 880 to 27 and do a proportion

Answers

Answer:

(i)Ratio of the Number of Girls in the School to the Total Population

=5:27

(ii)Ratio of the Number of Boys in the School to the Total Population=22:27

Step-by-step explanation:

Below is the steps on how the given ratio are derived

If the school has 880 boys and 200 girls

Total Population of the School=880+200=1080

Ratio of Girls to all Student is 5:27

Now, this is derived from this:

Ratio of the Number of Girls in the School to the Total Population

=200:1080[tex]=\frac{200}{1080} =\frac{5}{27}[/tex]

Which in reduced form is 5:27

You can do likewise for boys

Ratio of the Number of Boys in the School to the Total Population=880:1080[tex]=\frac{880}{1080} =\frac{22}{27}[/tex]

Which in reduced form is 22:27

A certain computer loses half of its value every two years. If the value of the computer after 3 years is 425, what was the initial value of the computer

Answers

To solve this problem, we can use the concept of exponential decay, where the value of the computer decreases by half every two years. Let's denote the initial value of the computer as [tex]\( V_0 \)[/tex]. After the first two years, its value will be [tex]\( \frac{1}{2}V_0 \)[/tex], after another two years (total of 4 years), its value will be [tex]\( \frac{1}{4}V_0 \)[/tex], and after three years, its value will be [tex]\( \frac{1}{8}V_0 \).[/tex]

Given that after three years its value is $425, we can set up the equation:

[tex]\[ \frac{1}{8}V_0 = 425 \][/tex]

Now, let's solve for [tex]\( V_0 \):\[ V_0 = 425 \times 8 \]\[ V_0 = 3400 \][/tex]

So, the initial value of the computer was $3400.

the area of a triangular flower bed in the park has an area of 120 square feet. The base is 4 feet longer than twice the height. What are the base and the height of the triangle

Answers

Answer: height = 10 feet

Base = 24 feet

Step-by-step explanation:

Let h represent the height of the triangular flower bed.

Let b represent the base of the triangular flower bed

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

Area = 1/2 × base × height

The area of a triangular flower bed in the park has an area of 120 square feet. This means that

1/2 × bh = 120

bh = 120 × 2

bh = 240- - - - - - - - - - - - - - - 1

The base is 4 feet longer than twice the height. This means that

b = 2h + 4

Substituting b = 2h + 4 into equation 1, it becomes

h(2h + 4) = 240

2h² + 4h = 240

2h² + 4h - 240 = 0

Dividing through by 2, it becomes

h² + 2h - 120 = 0

h² + 12h - 10h - 120 = 0

h(h + 12) - 10(h + 12) = 0

h - 10 = 0 or h + 12 = 0

h = 10 or h = - 12

Since the height cannot be negative, then h = 10

Substituting h = 10 into equation 1, it becomes

10b = 240

b = 240/10

y = 24

The answers are : (a) The height [tex]\( h \)[/tex] of the triangular flower bed is [tex]10\ feet[/tex]. (b) The base [tex]\( b \)[/tex] of the triangular flower bed is [tex]24 \ feet[/tex]

Let's denote the height of the triangular flower bed as [tex]\( h \)[/tex] feet.

According to the problem, the base of the triangle is [tex]4\ feet[/tex] longer than twice the height. Therefore, the base [tex]\( b \)[/tex] can be expressed as:

[tex]\[ b = 2h + 4 \][/tex]

The formula for the area [tex]\( A \)[/tex] of a triangle is given by

[tex]\[ A = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]

Given that the area [tex]\( A \)[/tex] of the triangular flower bed is [tex]120\ square\ feet[/tex], we can write the equation:

[tex]\[ \frac{1}{2} \times b \times h = 120 \][/tex]

Substituting [tex]\( b = 2h + 4 \)[/tex] into the area equation:

[tex]\[ \frac{1}{2} \times (2h + 4) \times h = 120 \][/tex]

Now, solve for [tex]\( h \)[/tex]

[tex]\[ (2h + 4) \times h = 240 \][/tex]

[tex]\[ 2h^2 + 4h = 240 \][/tex]

[tex]\[ 2h^2 + 4h - 240 = 0 \][/tex]

Divide the entire equation by [tex]2[/tex] to simplify:

[tex]\[ h^2 + 2h - 120 = 0 \][/tex]

Now, solve this quadratic equation using the quadratic formula, [tex]h = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 1 \), \( b = 2 \), and \( c = -120 \)[/tex]

[tex]\[ h = \frac{-2 \pm \sqrt{(2)^2 - 4 \times 1 \times (-120)}}{2 \times 1} \][/tex]

[tex]\[ h = \frac{-2 \pm \sqrt{4 + 480}}{2} \][/tex]

[tex]\[ h = \frac{-2 \pm \sqrt{484}}{2} \][/tex]

[tex]\[ h = \frac{-2 \pm 22}{2} \][/tex]

The solutions for [tex]\( h \)[/tex] are:

[tex]\[ h = \frac{20}{2} = 10 \][/tex]

[tex]\[ h = \frac{-24}{2} = -12 \][/tex]

So, the height [tex]\( h \)[/tex] of the triangular flower bed is [tex]10\ feet.[/tex]

Now, calculate the base [tex]\( b \)[/tex]

[tex]\[ b = 2h + 4 \][/tex]

[tex]\[ b = 2 \times 10 + 4 \][/tex]

[tex]\[ b = 20 + 4 \][/tex]

[tex]\[ b = 24 \][/tex]

The complete Question is

The area of a triangular flower bed in the park has an area of 120 square feet. The base is 4 feet longer than twice the height.

a. What is the base of the triangle ?

b. What is the height of the triangle ?

The idea in Exercise 3.51 generalizes to give a new formula for the expected value of any nonnegative integer-valued random variable. Show that if the random variable X takes only nonnegative integers as its values then E(X) = X[infinity] k=1 P(X ≥ k). This holds even when E(X) = [infinity], in which case the sum on the right-hand side is infinite. Hint. Write P(X ≥ k) as P[infinity] i=k P(X = i) in the sum, and then switch the order of the two summations.

Answers

Final answer:

The question asks to demonstrate that for a nonnegative integer-valued random variable X, the expected value E(X) equals the summation over all k of the probability P(X ≥ k). This is shown by expressing P(X ≥ k) as an infinite sum, switching the order of summation, and counting each probability P(X = i) exactly i times.

Explanation:

The student's question pertains to the calculation of the expected value (E(X)) of a nonnegative integer-valued random variable. Specifically, the question asks to show that for such a random variable X, the expected value can be expressed as E(X) = ∑₋∞ k=1 P(X ≥ k). To demonstrate this, we begin with the definition of expected value:

E(X) = μ = ∑ xP(x).

Next, we unpack P(X ≥ k) by writing it as an infinite sum of probabilities for all integers i starting from k:

P(X ≥ k) = ∑₋∞ i=k P(X = i).

To find the expected value, we consider the sum of all such probabilities over all k:

∑₋∞ k=1 P(X ≥ k) = ∑₋∞ k=1 ∑₋∞ i=k P(X = i).

We then switch the order of summation, so that we first sum over all possible values of i and then for each i, we sum over the corresponding k that contributes to P(X = i):

E(X) = ∑₋∞ i=1 P(X = i) ∑₉ i k=1.

By doing this, we count each P(X = i) exactly i times, which leads us to the initial definition of expected value, thus proving the given formula.

HL Theorem

ASA Postulate

SSS Postulate

SAS Postulate

Answers

Answer:

HL theorem.

Step-by-step explanation:

This states that if the hypotenuse (H) and  one leg (L) of one  right triangle are congruent to the hypotenuse and leg of another right triangle, then the triangles are congruent.

Answer:

ASA Postulate

Step-by-step explanation:

[tex] In \:\triangle QTS \:\&\:\triangle SRQ\\\\

QT || SR\\\\

\angle QTS \cong \angle SRQ... (each\: 90°)\\\\

TS \cong QR.... (given) \\\\

\angle QST \cong \angle SQR.. (alternate\:\angle s) \\\\

\therefore \triangle QTS \cong \triangle SRQ\\.. (By \: ASA \: Postulate) [/tex]

RHS Postulate can also be applied to prove both the triangles as congruent.

plz dont skip me help me

In which quadrant would point (12, 18) be located?


Quadrant IV


Quadrant II


Quadrant I


Quadrant III

Answers

Quadrant I is the answer. Both are positive coordinates

Answer:

it's Quadrant 1 because both of he cordnates

Step-by-step explanation:

Can someone please explain this problem to me idk what I am doing wrong and can you draw the problem for me thanks

Answers

Answer:

  you're not doing anything wrong

Step-by-step explanation:

In order for cos⁻¹ to be a function, its range must be restricted to [0, π]. The cosine value that is its argument is cos(-4π/3) = -1/2. You have properly identified cos⁻¹(-1/2) to be 2π/3.

__

Cos and cos⁻¹ are conceptually inverse functions. Hence, conceptually, cos⁻¹(cos(x)) = x, regardless of the value of x. The expected answer here may be -4π/3.

As we discussed above, that would be incorrect. Cos⁻¹ cannot produce output values in the range [-π, -2π] unless it is specifically defined to do so. That would be an unusual definition of cos⁻¹. Nothing in the problem statement suggests anything other than the usual definition of cos⁻¹ applies.

__

This is a good one to discuss with your teacher.

Simplify seven square root of three end root minus four square root of six end root plus square root of forty eight end root minus square root of fifty four.

Answers

[tex]7\sqrt{3}- 4\sqrt{6} + \sqrt{48} - \sqrt{54}[/tex] simplified as [tex]11\sqrt{3}- 7\sqrt{6}[/tex] or [tex]1.909[/tex] .

Step-by-step explanation:

We need to Simplify seven square root of three end root minus four square root of six end root plus square root of forty eight end root minus square root of fifty four. Which is equivalent to [tex]7\sqrt{3}- 4\sqrt{6} + \sqrt{48} - \sqrt{54}[/tex] :

[tex]7\sqrt{3}- 4\sqrt{6} + \sqrt{48} - \sqrt{54}[/tex]

⇒ [tex]7\sqrt{3}- 4\sqrt{6} + \sqrt{48} - \sqrt{44}[/tex]

⇒ [tex]7\sqrt{3}- 4\sqrt{6} + \sqrt{16(3)} - \sqrt{9(6)}[/tex]

⇒ [tex]7\sqrt{3}- 4\sqrt{6} + 4\sqrt{(3)} - 3\sqrt{(6)}[/tex]

⇒ [tex]11\sqrt{3}- 4\sqrt{6}- 3\sqrt{(6)}[/tex]

⇒ [tex]11\sqrt{3}- 7\sqrt{6}[/tex]

[tex]\sqrt{3} = 1.732 , \sqrt{6} = 2.449[/tex]

⇒ [tex]11(1.723)- 7(2.449)[/tex]

⇒ [tex]1.909[/tex]

Therefore, [tex]7\sqrt{3}- 4\sqrt{6} + \sqrt{48} - \sqrt{54}[/tex] simplified as [tex]11\sqrt{3}- 7\sqrt{6}[/tex] or [tex]1.909[/tex] .

Answer:

11√3 - 7√6

Step-by-step explanation:

I took the test and got it right.

Please assist me with these story problems.​

Answers

Answer:

  4. 16

  5. $88

  6. $687.50

Step-by-step explanation:

4. Let n represent the number.

An expression representing the number multiplied by 0.9 and 6.3 subtracted from the product is ...

  0.9n -6.3

We want that result to be 4.5, so we have the equation ...

  0.9n -6.3 = 4.5

Since all of the coefficients are divisible by 0.9, we can divide by 0.9 to get ...

  n -7 = 9

Adding 7 gives ...

  n = 16

The number is 16.

_____

5. For a problem like this, I like to work it backward. If Craig got an extra $18, then everyone's share was $32 -18 = $14. That was the share from a 5-way split, so the amount the friends split evenly was 5×$14 = $70. The total they started with must have been $70 +18 = $88.

The amount they split unevenly was $88. The amount they split evenly, after setting aside $18 for Craig's parents, was $70.

__

It is a bit tricky to write one equation for the amount the friends started with before they did any splits. Call that amount A. Then after setting aside $18, they split (A-18) five ways. Each of those splits was then (A-18)/5. When the $18 was added to one of those, the result was the $32 that Craig got. So, we have ...

  (A -18)/5 +18 = 32

and the solution process is similar to the "working backward" description above: subtract 18, multiply by 5, add back 18.

  (A -18)/5 = 14

  A -18 = 70

  A = 88 . . . . . . . . the amount the friends split unevenly

_____

6. Let P represent the original price of the laptop. We're told the price after all of the discounts was 500, so we have ...

  P -50 -(0.20P) = 500

  0.80P = 550 . . . . . add 50, collect terms

  P = 687.50 . . . . . . . divide by the coefficient of P

The original price was $687.50.

An ice cream shop serves small and large scoops of ice cream. Each scoop is sphere-shaped. Each small scoop has a diameter of approximately 6 centimeters. Each large scoop has a diameter of approximately 10 centimeters ​What is the difference, in cubic centimeters, between a large scoop of ice cream and a small scoop of ice cream? Round your answer to the nearest tenth.

Answers

Final answer:

The difference in volume between a large scoop and a small scoop of ice cream is approximately 410.5 cubic centimeters.

Explanation:

To find the difference in volume between a large scoop and a small scoop of ice cream, we need to calculate the volume of each scoop and then subtract the volume of the small scoop from the volume of the large scoop.

The volume of a sphere can be calculated using the formula V = (4/3)πr³, where r is the radius. Since the diameter of the small scoop is 6 cm, the radius is 3 cm. Plugging this into the formula, we get V = (4/3)π(3 cm)³. Evaluating this expression, we find that the volume of the small scoop is approximately 113.1 cm³.

Similarly, the diameter of the large scoop is 10 cm, so the radius is 5 cm. Using the same formula, we find that the volume of the large scoop is approximately 523.6 cm³.

To find the difference in volume, we subtract the volume of the small scoop from the volume of the large scoop: 523.6 cm³ - 113.1 cm³ = 410.5 cm³. Therefore, the difference in volume between a large scoop and a small scoop of ice cream is approximately 410.5 cubic centimeters.

Learn more about Volume here:

https://brainly.com/question/21623450

#SPJ12

The final answer is 410.5 cubic centimeters.

1. Calculate the volume of a small scoop:

- Given the diameter of the small scoop, [tex]\( d_{\text{small}} = 6 \) cm[/tex].

- Radius of small scoop, [tex]\( r_{\text{small}} = \frac{d_{\text{small}}}{2} = \frac{6}{2} = 3 \)[/tex] cm.

- Volume of a sphere [tex]\( V = \frac{4}{3} \pi r^3 \).[/tex]

- Substitute the radius into the volume formula: [tex]\( V_{\text{small}} = \frac{4}{3} \pi (3)^3 = \frac{4}{3} \pi (27) \)[/tex].

- Calculate:

[tex]\( V_{\text{small}} = 36 \pi \)[/tex] cubic centimeters.

2. Calculate the volume of a large scoop:

- Given the diameter of the large scoop,[tex]\( d_{\text{large}} = 10 \) cm[/tex].

- Radius of large scoop, [tex]\( r_{\text{large}} = \frac{d_{\text{large}}}{2} = \frac{10}{2} = 5 \) cm[/tex].

- Volume of a sphere [tex]\( V = \frac{4}{3} \pi r^3 \)[/tex].

- Substitute the radius into the volume formula:

[tex]\( V_{\text{large}} = \frac{4}{3} \pi (5)^3 = \frac{4}{3} \pi (125) \)[/tex].

- Calculate:

[tex]\( V_{\text{large}} = 166.7 \pi \)[/tex] cubic centimeters.

3. Find the difference:

- Difference in volume: [tex]\( V_{\text{large}} - V_{\text{small}} = 166.7 \pi - 36 \pi \)[/tex].

- Calculate: [tex]\( V_{\text{large}} - V_{\text{small}} = 130.7 \pi \)[/tex].

- Approximate [tex]\( \pi \)[/tex] to 3.14.

- [tex]\( 130.7 \times 3.14 = 410.498 \)[/tex].

- Rounded to the nearest tenth, the difference is approximately 410.5 cubic centimeters.

Other Questions
Who is the main character in the book speak When setting up a recurring appointment in an electronic scheduling system, the medical assistant should enter the information __________ and then indicate how often the appointment should recur. #3 only Fractions help GIVING BRAINLIEST A medical team has found that the blood concentration of a particular medicine has a decay rate of 40% in 24 hours. How much of an initial dose of 1,000 mg of the medicine will be detected after 48 hours? Round to the nearest mg920 mg200 mg449 mg360 mg600 mg More defective components: A lot of 1060 components contains 229 that are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective, and let B be the event that the second component drawn is defective. Write your answer as a fraction or a decimal, rounded to four decimal places.?Explain. how might Hammurabis code have prevented a single ruler from imposing or forcing his or her will on people? Find the area of the shaded region. With steps Name the piece of art above and its artist. What media did the artist choose for this piece and why? The owners equity isa. added to assets and the two are equal to liabilities b. added to liabilities and the two are equal to assets c. subtracted from liabilities and the net amount is equal to assets d. subtracted from owners equity and the net amount is equal to net income The author of the Declaration of Independence was:Benjamin FranklinGeorge WashingtonThomas Jefferson While traveling to and from a certain destination, you realized increasing your speed by 30 mph saved 3 hours on your return. If the total distance of the roundtrip was 560 miles, find the speed driven while returning. What is the fundamental frequency of a 0.003 kg steel piano wire of length 1.3 m and under a tension of 2030 N? Answer in units of Hz. 005 (part 2 of 2) 10.0 points What is the fundamental frequency of an organ pipe 1.38 m in length, closed at the bottom and open at the top? The speed of sound is 340 m/s. Answer in units of Hz. The expression 475 * 1.076 ^ t the average annual per capita health care costs, in dollars, in the US as a function of the number of years since 1970. What does 1.076 represent in this expression? "Comparing microwaves and visible light, which of the following is true? 1. Microwaves have higher frequency, same speed, and longer wavelength than visible light. 2. Microwaves have lower frequency, same speed, and longer wavelength than visible light. 3. Microwaves have lower frequency, slower speed, and longer wavelength than visible light. 4. Microwaves have lower frequency, faster speed, and shorter wavelength than visible light." Suppose that you are attempting to value an income-producing property using the direct capitalization approach. Using data from comparable properties, you have determined the overall capitalization rate to be 11.44%. If the projected first-year net operating income (NOI) for the subject property is $44,500, what is the indicated value of the subject using direct capitalization? Listed below are several terms and phrases associated with inventory measurement. Pair each item from the list below with the item of the following list that is most appropriately associated with it. 1. Perpetual inventory system 2. Periodic inventory system 3. F.o.b. shipping point 4. Gross method 5. Net method 6.Cost index 7. F.o.b. destination 8. FIFO 9. LIFO a. Legal title passes when goods are delivered to common carrier. b. Goods are transferred to another company but title remains with transferor. c. Purchase discounts not taken are included in inventory cost. d. If LIFO is used for taxes, it must be used for financial reporting. e. Assumes items sold are those acquired first. f. Assumes items sold are those acquired last. g. Purchase discounts not taken are considered interest expense. h. Used to convert ending inventory at year-end cost to base year cost. i. Continuously records changes in inventory. Which design principle refers to visual equilibrium? l mira a ________ que est en la tele todos los das. la bombera la vendedora la abogada la reportera A table has a square top. The area of the table top measures 18 square feet. Findthe length of one side of the table top Accountants and Economists differ in their calculations of profits in that; a. economists consider sunk costs b. accountants consider implicit costs only c. accountants consider explicit costs only d. all of the above