Geometry HW! PLS HELP!


If UVW =~(congruent symbol) EFC, what is the measure of

a) PMF of X(10) = C(10, 10) * (0.2)¹⁰ * (0.8)⁰

b) The probability of scoring no hits is the probability of X being 0.

c) The probability of scoring more hits than misses is the probability of X being greater than 5

d) E(X) = 10 * 0.2 and Var(X) = 10 * 0.2 * (1 - 0.2).

e) The expectation of Y: E(Y) = E(2X - 3) = 2E(X) - 3

The variance of Y: Var(Y) = Var(2X - 3) = 4Var(X)

f) The expectation of Z: E(Z) = E(X²)

What is probability?

Probability is a measure or quantification of the likelihood of an event occurring. It is a numerical value assigned to an event, indicating the degree of uncertainty or chance associated with that event. Probability is commonly expressed as a number between 0 and 1, where 0 represents an impossible event, 1 represents a certain event, and values in between indicate varying degrees of likelihood.

(a) To calculate the Probability Mass Function (PMF) of X, we can use the binomial distribution formula. Since the marksman takes 10 shots independently with a probability of 0.2 of hitting the target, the PMF of X follows a binomial distribution with parameters n = 10 (number of trials) and p = 0.2 (probability of success):

PMF of \(X(x) = C(n, x) * p^x * (1 - p)^{(n - x)}\)

Where C(n, x) represents the number of combinations or "n choose x."

Let's calculate the PMF for each value of X from 0 to 10:

PMF of X(0) = C(10, 0) * (0.2)⁰ * (0.8)¹⁰

PMF of X(1) = C(10, 1) * (0.2)¹ * (0.8)⁹

PMF of X(2) = C(10, 2) * (0.2)² * (0.8)⁸

...

PMF of X(10) = C(10, 10) * (0.2)¹⁰ * (0.8)⁰

(b) The probability of scoring no hits is the probability of X being 0. So we calculate PMF of X(0):

PMF of X(0) = C(10, 0) * (0.2)⁰ * (0.8)¹⁰

(c) The probability of scoring more hits than misses is the probability of X being greater than 5. We need to calculate the sum of PMF of X from X = 6 to X = 10:

PMF of X(6) + PMF of X(7) + PMF of X(8) + PMF of X(9) + PMF of X(10)

(d) The expectation (mean) of X can be found using the formula:

E(X) = n * p

where n is the number of trials and p is the probability of success. In this case, E(X) = 10 * 0.2.

The variance of X can be calculated using the formula:

Var(X) = n * p * (1 - p)

In this case, Var(X) = 10 * 0.2 * (1 - 0.2).

(e) To calculate the expectation and variance of Y, we need to consider the profit from each hit. Each hit earns $2, and since X represents the number of hits, Y can be calculated as:

Y = 2X - 3

The expectation of Y can be calculated as:

E(Y) = E(2X - 3) = 2E(X) - 3

To calculate the variance of Y, we can use the property Var(aX + b) = a²Var(X) when a and b are constants:

Var(Y) = Var(2X - 3) = 4Var(X)

(f) Similarly, for Z, each hit earns a dollar amount equal to the square of the number of hits:

Z = X²

The expectation of Z can be calculated as:

E(Z) = E(X²)

Hence, a) PMF of X(10) = C(10, 10) * (0.2)¹⁰ * (0.8)⁰

b) The probability of scoring no hits is the probability of X being 0.

c) The probability of scoring more hits than misses is the probability of X being greater than 5

d) E(X) = 10 * 0.2 and Var(X) = 10 * 0.2 * (1 - 0.2).

e) The expectation of Y: E(Y) = E(2X - 3) = 2E(X) - 3

The variance of Y: Var(Y) = Var(2X - 3) = 4Var(X)

f) The expectation of Z: E(Z) = E(X²)

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a) PMF of X(10) = C(10, 10) * (0.2)¹⁰ * (0.8)⁰

b) The probability of scoring no hits is the probability of X being 0.

c) The probability of scoring more hits than misses is the probability of X being greater than 5

d) E(X) = 10 * 0.2 and Var(X) = 10 * 0.2 * (1 - 0.2).

e) The expectation of Y: E(Y) = E(2X - 3) = 2E(X) - 3

The variance of Y: Var(Y) = Var(2X - 3) = 4Var(X)

f) The expectation of Z: E(Z) = E(X²)

What is probability?

Probability is a measure or quantification of the likelihood of an event occurring. It is a numerical value assigned to an event, indicating the degree of uncertainty or chance associated with that event. Probability is commonly expressed as a number between 0 and 1, where 0 represents an impossible event, 1 represents a certain event, and values in between indicate varying degrees of likelihood.

(a) To calculate the Probability Mass Function (PMF) of X, we can use the binomial distribution formula. Since the marksman takes 10 shots independently with a probability of 0.2 of hitting the target, the PMF of X follows a binomial distribution with parameters n = 10 (number of trials) and p = 0.2 (probability of success):

PMF of

Where C(n, x) represents the number of combinations or "n choose x."

Let's calculate the PMF for each value of X from 0 to 10:

PMF of X(0) = C(10, 0) * (0.2)⁰ * (0.8)¹⁰

PMF of X(1) = C(10, 1) * (0.2)¹ * (0.8)⁹

PMF of X(2) = C(10, 2) * (0.2)² * (0.8)⁸

......

PMF of X(10) = C(10, 10) * (0.2)¹⁰ * (0.8)⁰

(b) The probability of scoring no hits is the probability of X being 0. So we calculate PMF of X(0):

PMF of X(0) = C(10, 0) * (0.2)⁰ * (0.8)¹⁰

(c) The probability of scoring more hits than misses is the probability of X being greater than 5. We need to calculate the sum of PMF of X from X = 6 to X = 10:

PMF of X(6) + PMF of X(7) + PMF of X(8) + PMF of X(9) + PMF of X(10)

(d) The expectation (mean) of X can be found using the formula:

E(X) = n * p

where n is the number of trials and p is the probability of success. In this case, E(X) = 10 * 0.2.

The variance of X can be calculated using the formula:

Var(X) = n * p * (1 - p)

In this case, Var(X) = 10 * 0.2 * (1 - 0.2).

(e) To calculate the expectation and variance of Y, we need to consider the profit from each hit. Each hit earns $2, and since X represents the number of hits, Y can be calculated as:

Y = 2X - 3

The expectation of Y can be calculated as:

E(Y) = E(2X - 3) = 2E(X) - 3

To calculate the variance of Y, we can use the property Var(aX + b) = a²Var(X) when a and b are constants:

Var(Y) = Var(2X - 3) = 4Var(X)

(f) Similarly, for Z, each hit earns a dollar amount equal to the square of the number of hits:

Z = X²

The expectation of Z can be calculated as:

E(Z) = E(X²)

Hence, a) PMF of X(10) = C(10, 10) * (0.2)¹⁰ * (0.8)⁰

b) The probability of scoring no hits is the probability of X being 0.

c) The probability of scoring more hits than misses is the probability of X being greater than 5

d) E(X) = 10 * 0.2 and Var(X) = 10 * 0.2 * (1 - 0.2).

e) The expectation of Y: E(Y) = E(2X - 3) = 2E(X) - 3

The variance of Y: Var(Y) = Var(2X - 3) = 4Var(X)

f) The expectation of Z: E(Z) = E(X²)

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Answer:

B SSA

Step-by-step explanation:

Geometric proofs can be used to show that the two triangles are congruent using ASA, SAS and SSS.

However, there is no such thing as SSA in geometry because an angle and two sides can not show congruence of triangles. This is so because the angle is not an included angle.

Given a function of two variables, n and k, denoted as h(n, k), the function describes a mathematical relationship or operation that depends on the values of both n and k. Further details about the specific function, its definition, or purpose are required to provide a more comprehensive explanation.

A function of two variables, h(n, k), typically represents a mathematical relationship or operation that involves two independent variables, n and k. The specific form and purpose of the function can vary widely depending on the context or problem at hand.

To understand the behavior and properties of the function h(n, k), additional information is needed. This may include the mathematical expression defining the function, any constraints or conditions on the variables, and the intended interpretation or application of the function.

The function h(n, k) could represent various scenarios, such as a cost function in economics, a probability distribution in statistics, or a mathematical model in a scientific context. Without more details, it is challenging to provide a specific explanation or analysis of the function and its implications.

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Answer:

Step-by-step explanation:

To convert the value 1,000,000 to an exponential form means we are to write the value in multiples of 10.  Breaking down the values in multiples of 10 will give;

1,000,000 = 10 * 10 * 10 * 10 * 10 * 10 (it is broken down into 6 places because the value contains 6 zeros)

Express in exponential form

1,000,000 = (10 * 10 * 10) * (10 * 10 * 10)

1,000,000 = (10³) * (10³)

1,000,000 = 10³⁺³

1,000,000 = 10⁶

Hence the value 1,000,000 in exponential form is expressed as 1 * 10⁶

For 10 * 10:

10 * 10 = 10¹ * 10¹

10 * 10 = 10¹⁺¹

10 * 10 = 10²

10 * 10 = 1 * 10²

The value of the expression 10*10 in exponential form is 1 * 10²

For 10,000 * 10:

10,000 * 10 = (10*10*10*10) * 10

10,000 * 10 = (10⁴) * 10¹

10,000 * 10 = 10⁴⁺¹

10,000 * 10 = 1 * 10⁵

Hence, The value of the expression 10000*10 in exponential form is 1 * 10⁵

Answer:

The given statement is true. Reason: Area of a square = side × side Therefore, two squares that have the same area will have sides of the same lengths.

hop this helps

mark me brainliest

Step-by-step explanation:

To calculate the cash balance at the end of the period, we need to consider the cash inflows and outflows.

Starting cash balance: $4,520

Cash inflows: $1,654 (receivables collected)

Cash outflows: $1,961 (payments to suppliers) + $500 (cash expenses)

Total cash inflows: $1,654

Total cash outflows: $1,961 + $500 = $2,461

To calculate the cash balance at the end of the period, we subtract the total cash outflows from the starting cash balance and add the total cash inflows:

Cash balance at the end of the period = Starting cash balance + Total cash inflows - Total cash outflows

Cash balance at the end of the period = $4,520 + $1,654 - $2,461

Cash balance at the end of the period = $4,520 - $807

Cash balance at the end of the period = $3,713

Therefore, the cash balance at the end of the period is $3,713.

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well, from 1990 to 1998 is 8 years, and we know the amount went from $4800 to $6300, let's check for the rate of growth.

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6300\\ P=\textit{initial amount}\dotfill &\$4800\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{years}\dotfill &8\\ \end{cases} \\\\\\ 6300=4800(1 + \frac{r}{100})^{8} \implies \cfrac{6300}{4800}=(1 + \frac{r}{100})^8\implies \cfrac{21}{16}=(1 + \frac{r}{100})^8\)

\(\sqrt[8]{\cfrac{21}{16}}=1 + \cfrac{r}{100}\implies \sqrt[8]{\cfrac{21}{16}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[8]{\cfrac{21}{16}}=100+r\implies 100\sqrt[8]{\cfrac{21}{16}}-100=r\implies \stackrel{\%}{3.46}\approx r\)

now, with an initial amount of $4800, up to 2007, namely 17 years later, how much will that be with a 3.46% rate?

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &4800\\ r=rate\to 3.46\%\to \frac{3.46}{100}\dotfill &0.0346\\ t=years\dotfill &17\\ \end{cases} \\\\\\ A=4800(1 + 0.0346)^{17} \implies A=4800(1.0346)^{17}\implies A \approx 8558.02\)

The measure of angle a is 15 degrees and this can be determined by using the properties of the isosceles triangle.

In geometry, interior angles are formed in two ways. One is inside a polygon, and the other is when parallel lines cut by a transversal. Angles are categorized into different types based on their measurements.

Given:

The following steps can be used in order to determine the measure of angle a:

Step 1 - According to the given data, it can be concluded that triangle PQR and triangle PSR are isosceles triangles.

Step 2 - Apply the sum of interior angle property on triangle PQR.

\(\angle\text{Q}+\angle\text{P}+\angle\text{R}=180\)

\(\angle\text{Q}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-60\)

\(\angle\text{R}=60^\circ\)

Step 3 - Now, apply the sum of interior angle property on triangle PSR.

\(\angle\text{P}+\angle\text{S}+\angle\text{R}=180\)

\(\angle\text{S}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-90\)

\(\angle\text{R}=45^\circ\)

Step 4 - Now, the measure of angle a is calculated as:

\(\angle\text{a}=60-45\)

\(\angle\text{a}=15\)

The measure of angle a is 15 degrees.

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From the question, the sum of each of the geometric sequence are;

1)  31 3/4

2) 340

3) 11/16

4) -6, 12, -24

We have that;

Sn = a(1 -\(r^n\))/1 - r

Sn = 16(1 \(- (1/2)^7\))1 - 1/2

Sn = 16(1 - 1/128)/1/2

Sn = 16(127/128) * 2

Sn = 31 3/4

2) Un = a\(r^n\) -1

256 = \(4(4)^n-1\)

64 =\(4^n-1\)

\(4^3 = 4^n-1\)

n = 4

Sn= \(4(4^4 - 1)\)/4 - 1

Sn = 340

3) Since we have a5 then n = 5

Sn = 1(1 - (\(-1/2)^5\))/1 -(-1/2)

Sn = 33/32 * 2/3

= 11/16

4) 30= a(1 -\((-2)^4\))/1 - (-2)

30 = a(-15)/3

30 = -5a

a = 30/-5

a = -6

Then the first three terms are;

-6, 12, -24

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Given:

After 11 months, sumo wrestler weighed 140 kilograms.

He gained weight at a rate of 5.5 kilograms per month.

To find:

The y-intercept of the equation which represents y the  sumo  wrestlers  weight (in kilograms)  after x  months.

Solution:

Let y represent the sumo wrestlers weight (in kilograms) after x months.  

It is given that he gained  weight at a rate of  5.5 kilograms per month.

So, slope of the line is 5.5.

After  11  months,  sumo  wrestler weighed  140 kilograms. It means the line passes through the point (11,140).

The point slope form of the line is

\(y-y_1=m(x-x_1)\)

where, m is slope of the line.

\(y-140=5.5(x-11)\)

\(y-140=5.5x-60.5\)

Add 140 on both sides.

\(y-140+140=5.5x-60.5+140\)

\(y=5.5x+79.5\)

Therefore, the required equation is \(y=5.5x+79.5\).

Substitute x=0, to find the y-intercept of this equation.

\(y=5.5(0)+79.5\)

\(y=79.5\)

Therefore, the y-intercept is 79.5. It means initial weight of sumo is 79.5 kilograms.

Answer:

14.2

Step-by-step explanation:

6 + 6sin(30) + 6cos(30) = 14.2

Use the SOHCAHTOA, see below picture.

9514 1404 393

Answer:

Step-by-step explanation:

The zeros are the values of t that make the factors zero.

  1 -t = 0   ⇒   t = 1

  8 +16t = 0   ⇒   t = -8/16 = -1/2

The equation is used to model height after the ball is thrown. We don't expect it to be a good model before the ball is thrown (t < 0), so the zero in that region is extraneous.

Only the positive zero is in the function's domain, so that is the only one that is meaningful.

__

When t = 0 (at the time the ball is thrown), the function value is ...

  h(0) = (1 -0)(8 +0) = 8

The ball is thrown from a height of 8 feet.

Answer:

13

Step-by-step explanation:

Answer:

Option 1

Step-by-step explanation:

Arc MK is equal to the sum of arcs ML and LK.

The expected gain or loss is an illustration of mean and expected values.

The expected total gain is 83 points

The given parameters are:

The probability of rolling a 6 in a fair die is 1/6.

The probability of not rolling a 6 in a fair die is 5/6.

So, the expected gain in each game is:

\(\mathbf{E(x) = 20 \times \frac 16 - 3 \times \frac 56}\)

\(\mathbf{E(x) = \frac{20}6 - \frac{15}6}\)

Take LCM

\(\mathbf{E(x) = \frac{5}6}\)

\(\mathbf{E(x) = 0.83}\)

The number of games is 100.

So, the expected gain is:

\(\mathbf{Gain = 100 \times 0.83}\)

\(\mathbf{Gain = 83}\)

Hence, the expected total gain is 83 points

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1. In this scenario, the goalie saves 73% of the opponent's shots. Therefore, any digits from 00 to 72 represent shots that are saved, as they fall within the range of the goalie's saving ability.

2. To win the game, the Iceblades cannot let the other team score any goals. Therefore, the goalie needs to save all 5 shots taken by the other team for a group to be a success.

3. Group 1 is a success because the goalie saves all 5 shots taken by the other team. Since no goals are scored, the Iceblades maintain their one-goal lead and are on track to win the game.

4. In this simulation, the successes are the groups where the goalie saves all 5 shots. Based on the information given, Group 1 is the only success. Therefore, there is one success in the 10 groups.

5. Since there is only one success out of the 10 groups, the estimated probability of the Iceblades winning the game would be 1 out of 10, or 1/10. Expressed as a percentage, this is equal to 10%.

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Based on a scale factor of 3.75, the new statue that Jerry is making should be 30ft tall (height).

The scale factor is the ratio that compares the measurement of an object with its scaled down or scaled up model.

The scale factor compares the measurements of the model with the real object's.

The scaled down model:

Height = 8 inches

Width = 15 inches

The Statue:

Width = 4 ft

The scale factor = 3.75 (15 ÷ 4)

Therefore, the height of the statue, using the scale factor, should be = 30ft (8 x 3.75)

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The value οf x is 3

A variety οf issues are resοlved by algebraic calculatiοns that treat variables like explicit integers in a single cοmputatiοn. The quadratic fοrmula, fοr instance, can be used tο sοlve any quadratic equatiοn by exchanging the variables in the quadratic fοrmula fοr the numerical values οf the cοefficients in the equatiοn.

A variable in mathematical lοgic is either a symbοl fοr an undefined term οf the theοry (a meta-variable), οr it is a fundamental οbject οf the theοry that is changed withοut cοnsidering any pοtential intuitive meaning.

Given

8x+17 = 41

Sοlving fοr variable 'x'

Add '-17' tο each side.

17 + -17 + 8x = 41 + -17

Or, 8x=24

Divide each side by '8'

Or, x=3

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Hey there! I'm happy to help!

First let's find the radius. The radius is half of the diameter.

9/2=4.5

Here's how to find the volume of any sphere.

You cube the radius.

4.5³=91.125

You multiply by 3.14

91.125(3.14)=286.1325

And finally we multiply by 4/3.

286.1325(4/3)=381.51

We round to the nearest tenth, giving us a volume of 381.5 in^3.

Have a wonderful day! :D

9 in = 3 in

v = 3,14x 3 x 3

= 28,26

The teacher will have a total of 120 pens if 12 sets of pens are ordered.

To find the total number of pens a teacher will have if 12 sets of pens are ordered, we can start by finding the total number of pens in one set and then multiply it by 12.

In one set, there are 4 blue pens, 3 black pens, 2 red pens, and 1 purple pen. To find the total number of pens in one set, we can simply add the number of pens of each color:

Total pens in one set = 4 + 3 + 2 + 1 = 10

Therefore, the numerical expression to represent how many pens a teacher will have if 12 sets of pens are ordered is:

12 × 10 = 120

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Answer:

6p - 2

Step-by-step explanation:

The expression that needs to be made in this question refers to the total number of people that signed the petition. To calculate this we need to add the total number of signatures that both you and your friend were able to acquire. Once we do this we simply combine like terms in order to simplify the expression as much as possible.

4p + 5 + 2p - 3

4p + 2p + 5 - 3

6p - 2

Therefore, the total and simplified expression for the total number of signatures would be 6p - 2

Given:

The G.C.F of 2 numbers is 36.

The product of the 2 numbers is 23328.

To find:

The L.C.M. of the 2 numbers.

Solution:

If a and b are two numbers, then

\(L.C.M.(a,b)\times H.C.F.(a,b)=a\times b\)       ...(i)

We know that H.C.F. is equal to G.C.F.

Putting H.C.F. (a,b)= 36 and \(a\times b=23328\) in (i), we get

\(L.C.M.(a,b)\times 36=23328\)

Divide both sides by 36.

\(L.C.M.(a,b)=\dfrac{23328}{36}\)

\(L.C.M.(a,b)=648\)

Therefore, the L.C.M. of the 2 numbers is 648.

Answer:

$88

Step-by-step explanation:

Center : Mean  Before the introduction of the new course, center = average(121,134,106,93,149,130,119,128) = 122.5  After the introduction of the new course, center =  average(121,134,106,93,149,130,119,128,45) = 113.9  The center has moved to the left (if plotted in a graph) because of the low intake for the new course.  Spread before introduction of the new course :  Arrange the numbers in ascending order:  (93, 106,119, 121), (128, 130,134, 149) Q1=median(93,106,119,121) = 112.5 Q3=median(128,130,134,149) = 132  Spread = Interquartile range = Q3-Q1 = 19.5  After addition of the new course,

(45,93, 106,119,) 121, (128, 130,134, 149)

Q1=median(45,93,106,119)=99.5

Q3=median (128, 130,134, 149)= 132

Spread = Interquartile range = 132-99.5 =32.5

We see that the spread has increased after the addition of the new course.

Answer:

5.20

Step-by-step explanation:

48 / 9.23 = 5.20043336945

rounded to tenth is 5.20

Hope This Helped

Answer:5.20

Step-by-step explanation:

48 / 9.23 = 5.20

To find the remainder in the Taylor series centered at a=0 for f(x)=e^(-x), we start by finding the nth derivative of f(x). Differentiating f(x) repeatedly, we observe that f^n(x) = (-1)^n * e^(-x).

The formula for the remainder in the Taylor series is given by R_n(x) = (f^(n+1)(c) * (x-a)^(n+1))/(n+1)!, where c is some value between x and a.

For our function, f^(n+1)(x) = (-1)^(n+1) * e^(-x), so the remainder becomes R_n(x) = (-1)^(n+1) * e^(-c) * (x-0)^(n+1)/(n+1)!

To find a bound for |R_n(x)| that does not depend on c, we can use the fact that e^(-c) is always less than or equal to 1. Therefore, we have |R_n(x)| ≤ (x)^(n+1)/(n+1)!.

Based on this, the correct answer is A. |R_n(x)| ≥ 1/(n+1)!(x-θ)^(n+1), where θ is some value between x and 0.

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The corresponding point on the unit circle for the angle θ = 5pi/3  is given by: (0,5, -0.866).

What is the unit circle?

Basically, the unit circle is a circle with a radius of 1. It is used in trigonometry to help define and understand angles and their associated trigonometric values. The unit circle is centered at the origin (0, 0) of the coordinate plane, and each point on the circle is defined by its distance from the origin and its angle from the positive x-axis.

What is area of circle ?

The area of circle can be defined as the product of pi and square of radius of a given circle.

In this problem, we have that θ = 5pi/3 , hence:

cos θ = 0.5

sin θ = -0.866

Thus the point is (0,5, -0.866).

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