Find the standard deviation for the given probability distribution.

Probability Distribution
x P(x)
0 0.37
1 0.13
2 0.06
3 0.15
4 0.29

Sample space for the given experiment is:

OGRI, OGRS, OGII, OGIS, OPRI, OPRS, OPII, OPIS, GGRI, GGRS, GGII, GGIS, GPRI, GPRS, GPII, GPIS.

In probability theory, the sample space is the set of all possible outcomes of a random experiment or process. The sample space of an experiment refers to the set of all possible outcomes that can occur when the experiment is conducted. In this case, the experiment is choosing toppings for a salad at a restaurant. The sample space would consist of all possible combinations of the toppings and dressings that can be chosen.

There are two choices for the extra toppings: olives or garbanzo beans. There are also two choices for the meat: pepperoni or shrimp. Lastly, there are two choices for the dressing: ranch or Italian.

To find the sample space, we can list out all possible combinations of these choices. Using the given letters to represent each choice, the sample space would be:

{OGI, OGI, OPI, OPS, ORI, ORG, OGS, OPI, OPS, OSI, OSG, OSI, GGI, GPI, GPS, GRI, GRG, GGS, GGI, GPI, GPS, GSI, GSG, GSI}

This set contains all 24 possible outcomes that can occur when selecting toppings and dressing for the salad.

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Complete question:

Answer:

B. $436,72

Step-by-step explanation:

500,000 = R * ((1 - (1 + 0.02/12)^(-12*40)) / (0.02/12))

Resolviendo para R, obtenemos:

R = 436.72

Por lo tanto, Jesse necesitará invertir $436.72 en su IRA cada mes para alcanzar su meta de $500,000 en 40 años, suponiendo una tasa de interés del 2% compuesto mensualmente. La respuesta correcta es la opción B.

Joseph's mom was driving at a rate of 93.75 km/h.

Let's start by using the formula;

distance = rate × time

Let's call the distance that Joseph and his mom traveled "D". Let's also call the time that Joseph and his mom traveled before Joseph's dad caught up "T". Since Joseph's dad traveled for one hour less than Joseph and his mom, his travel time was "T - 1".

We know that Joseph's dad drove for four hours at 75 km/h, so he covered a distance of;

75 km/h × (T - 1) h = 75T - 75 km

We also know that Joseph and his mom traveled for T hours at some rate, which we'll call "R", so they covered a distance of;

R × T = D km

Since they ended up at the same place, we can set these two distances equal to each other;

75T - 75 = D

Rearranging, we get;

D = R × T

Substituting the expression for D, we get;

75T - 75 = R × T

Simplifying;

75 = R - 75/T

We know that R is the rate at which Joseph's mom was driving, and we want to find that rate. We also know that T is the time that she was driving before Joseph's dad caught up. We can solve for R by substituting the values we know;

75 = R - 75/T

75 = R - 75/4

R = 75 + 75/4

R = 93.75 km/h

Therefore, Joseph's mom was driving at 93.75 km/h.

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After factoring the given expression which is -2bk² - 4bk + 30b, we get -2b(k + 5)(k - 3). So, the correct answer is (a) .

To factor the expression -2bk² - 4bk + 30b, we first need to factor out the greatest common factor of -2b.

-2b(k² + 2k - 15)

Next, we need to factor the quadratic expression k² + 2k - 15.

We can find two numbers that multiply to -15 and add up to 2 by using trial and error or by using the quadratic formula. The two numbers are 3 and -5.

Therefore, we can write:

-2b(k + 5)(k - 3)

Therefore, the correct answer is (a) -2b(k + 5)(k - 3).

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Equation (12x² - 6x)(4x - 2) simplifies to 12x(2x - 1)².

We can start by factoring out the greatest common factor from both terms, which is 6x:

(12x² - 6x)(4x - 2) = 6x(2x - 1)(4x - 2)

Next, we can simplify the expression by factoring out the common factor (4x - 2) from the remaining terms (2x - 1):

6x(2x - 1)(4x - 2) = 6x(2x - 1) × 2(2x - 1)

Now we have two factors that are the same, (2x - 1), so we can combine them by multiplying them together:

6x(2x - 1) × 2(2x - 1) = 12x(2x - 1)²

Therefore, (12x² - 6x)(4x - 2) simplifies to 12x(2x - 1)².

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Given question is incomplete, the complete question is below

Assuming that x ≠ 1/2, simplify (12x² - 6x)(4x - 2).

The displacement over the interval is 0 and the distance over the interval is 27 meters

Given that

Velocity, v(t) = 3t² – 6t

Integrate to get the displacement function

So, we have

d(t) = t³ - 3t²

The interval is [0, 3]

So, we have

d(0) = 0³ - 3(0)² = 0

d(3) = 3³ - 3(3)² = 0

The displacement over the interval is 0

Recall that

v(t) = 3t² – 6t

So, we have

v(3) = 9

So, we have

distance = speed * time

This gives

distance = 9 * 3

Evaluate

distance = 27 meters

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Answer:

57

Step-by-step explanation:

We know that parentheses come first in the order of operations. Therefore, we will first evaluate (3 × 5).

3 × 5 = 15

↓ substituting this value back in for the parentheses

[tex]12+[15+2(15)][/tex]

Next, we will deal within the brackets, which act like parentheses. Multiplication comes before addition, so we will execute 2(15) first.

2(15) = 2 × 15 = 30

↓ substituting this value back in

[tex]12+[15+30][/tex]

Now, executing the addition:

15 + 30 = 45

↓ substituting this value back in for the brackets

[tex]12 + 45[/tex]

Finally, all there is to do is execute the addition.

12 + 45 = 57

[tex]\boxed{57}[/tex]

The area of the shaded region is given as follows:

0.0475.

Here, we have to obtain probabilities using the normal distribution:

The z-score of a measure X of a variable that has mean symbolized by  and standard deviation symbolized by  is obtained by the rule presented as follows:

Z = X - μ / σ

The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.

Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.

The mean and the standard deviation for the IQ scores are given as follows:

μ = 100, σ = 15

The shaded region is the area to the right of 125, hence it's area is one subtracted by the p-value of Z when X = 125, hence:

Z = (125 - 100)/15

Z = 1.67

Z = 1.67 has a p-value of 0.9525.

Hence:

1 - 0.9525 = 0.0475.

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Missing Information

The shaded region is the area to the right of 125.

Answer: 2

Step-by-step explanation:

Hace 2+3=5 collares. Para cada collar usa 2/5 por eso

5(2/5)=2

Answer: Donald and 2nd one A

Step-by-step explanation:

The price markup when we bought products for $50.00 and sold for $67.00 is c. 34%.

Price markup is the amount by which the selling price of a product is increased from its cost price.

It is expressed as a percentage of the cost price.

We would use the below formula to find out the price markup:

Markup = (Selling price - Cost price) / Cost price * 100%

Here,

cost price = $50.00

selling price = $67.00.

Markup = (67.00 - 50.00) / 50.00 * 100%

Markup = 17 / 50 * 100%

Markup = 0.34 * 100%

Markup = 34%

Therefore, the price markup is 34%.

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Answer:

216g³

Step-by-step explanation:

(6g)³

6³ = 216

g³ = g³

So, (6g)³ simplify will be 216g³

The only value of k that allows us to write √50 + √k as a single term is

k = 25.

What is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.

To be able to write the expression √50 + √k as a single term, we need to find a perfect square that is a factor of both 50 and k.

Prime factorizing 50, we get 50 = 2 * 5².

Since 50 contains a factor of 2, any perfect square factor of 50 must also contain a factor of 2. The only perfect square factor of 50 that contains a factor of 2 is 2*5² = 50 itself.

Now we need to find a perfect square that is a factor of k and contains a factor of 5. This can be done by prime factorizing k and seeing if any of the factors can be squared and still contain a factor of 5.

Let's try some values of k:

If k = 5, then √k = √5, which is not a perfect square, so it won't work.

If k = 25, then √k = 5, which is a perfect square that contains a factor of 5, so we can write √50 + √25 as 5√2 + 5 = 5(√2 + 1).

If k = 125, then √k = 5√5, which is not a perfect square, so it won't work.

Therefore, the only value of k that allows us to write √50 + √k as a single term is k = 25.

So, √50 + √25 can be written as 5(√2 + 1).

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Answer:

Step-by-step explanation:

−UPDATE!! The answer is 1/3 so harray

Answer:

area of the triangle BCD is

1/2.8.10 sq unit

=40 sq unit

BCD is a right angle triangle

so, BC^2+CD^2=BD^2

=> 8^2+10^2=BD^2

=> 64+100=BD^2

=> BD^2=164

=> BD=√164=2√41

BD=2√41 unit

1/2.BD.x=40

=> x=40.2/BD

=> x=80/2√41=40/√41

Stefanie bought 14 erasers.

Let's call the number of erasers Stefanie bought x.

We know that Stefanie paid $ 1.25 for the pencils, and she bought x erasers that each cost $ 0.50. So the total cost of the erasers is 0.5x.

Stefanie paid a total of $ 8.25, so we can write an equation:

1.25 + 0.5x = 8.25

1.25 + 0.5x - 1.25 = 8.25 - 1.25

Subtracting 1.25 from both sides, we get:

0.5x = 7

Dividing both sides by 0.5, we get:

x = 7 / 0.5

x = 7 × 2

x = 14

Therefore, Stefanie bought 14 erasers.

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Given question is incomplete, the complete question is below

Stefanie bought a package of pencils for $1.25 and some erasers that cost $0.50 each. She paid a total of $8.25 for these items, before tax. Exactly how many erasers did Stefanie buy?

Step-by-step explanation:

The domain of the new function remains the same as the domain of the original function because it only affects the coefficient of x, not the values of x itself.

However, the range of the new function changes because increasing the coefficient a shifts the entire graph of the function upwards. Specifically, the range of the new function becomes y ≥ 2 since the minimum value of the function is now 2, which occurs when x = 0.

Therefore, the correct answers are:

The domain stays the same.

The range becomes y ≥ 2.

Step-by-step explanation:

Monte answered 9 questions each worth 4 points =  9x 4 = 36 points

 the rest of the 87 points were three-pointers  ( 87-36) = 51 points

      51 points / ( 3points /question)  = 17 three pointers

Answer: I think the answer is 29 I hope this is helping you

Step-by-step explanation: Since 87 divided by 3 gives an integer which is 29 and 29 times 3 is 87 I think this is the answer I'm not entirely sure but that's what I think

The  n'th Taylor Polynomial centered at c is given as  f(z) = 21

An nth degree Taylor polynomial is a way of approximating a function with a partial sum of additions and multiplications.

the general formula for An nth degree Taylor polynomial is Function, f(x) = 1/x², n = 4, c = 5

Using the Taylor polynomial formula,

Pₙ(x) = (x) = f(a) + f′(a)(x − a) + f′′(a)/2! × (x − a)2 + f′′′(a)/3! × (x − a)3 + f(4)(a)/4! × (x − a)4 + ... + f(n) (a)/n! × (x − a)n

The function and its derivatives are:

f(x) =  1/x²

f′(x) = 4² + 5

f′′(x) = 21

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Answer:

B

Step-by-step explanation:

Using the data:

6 students sent 0-4 emails

4 students sent 5-9 emails

2 students sent 10 - 14 emails

3 students sent 15-19 emails

Option B graphs this data correctly

Answer:b

Step-by-step explanation:

have a nice day

Answer:

the train can travel 4/15 of the distance between two cities in one hour

The probability of opening to a page that is either 8 or 12 is 2/13.

The probability of opening to a page that is either 8 or 12 can be found by adding the individual probabilities of opening to page 8 and page 12. Since there are 13 pages in total, each page has a 1/13 chance of being opened. Therefore, the probability of page number 8 is 1/13, and the probability of opening to page 12 is also 1/13.

The probability of opening to page 8 or page 12 is the sum of the individual probabilities:

P(opening to page 8 or page 12) = P(opening to page 8) + P(opening to page 12)

P(opening to page 8 or page 12) = 1/13 + 1/13

P(opening to page 8 or page 12) = 2/13

Therefore, the probability of opening to a page that is either 8 or 12 is 2/13 or about 0.1538

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If the claim is approved, the homeowner's insurance policy will pay an amount of for the damages.

Given that,

Annual premium = $650

Deductible = $1,350 per claim.

Amount of damage formed in windstorm = $35,500

Amount of the damage that the insurance company will pay is the amount of the damage which deducts the deductible amount.

Amount insurance company pays = $35,500 - $1,350 = $34,150

Hence the amount paid by the company is $34,150.

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According to Amelia's results, 42% of students prefer coffee in the morning. If the margin of error is ±0.072, between 689 and 978 students at the school prefer coffee.

To calculate percentage;

total coffee takers/ total number of students surveyed x 100.

TCT= 63  TSS = 150 which then becomes 63/150x 100 = 42

To calculate margin of error;

TCT/TSS - ME  and TCT/TSS + ME, which becomes

63/150 + 0.072 = 0. 49

63/150 - 0.072 = 0.35

Next we calculate the the highest and lowest number by saying;

0.49 x total number of students in the school  1,981 =

0. 35 x total number of students in the school  1,981 =

The above answer is in response to the full question below;

There are a total of 1,981 students enrolled at Amelia's high school. Amella surveyed 150 of the students regarding their morning drink preference. Her results are recorded in the table.

Drinks                               number

Milk                                     45

Juice                                   18

Coffee                                 63

Smoothie                            11

Others                                 13

Complete the statement.

According to Amelia's results, [DROP DOWN 1] prefer coffee in the morning. If the margin of error is ±0.072, between [DROP DOWN 2] and [DROP DOWN 3) students at the school prefer coffee.

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The solution to the equation 3x² + x - 12 = 1 is x = -1/4; and x = 4

An equation is an expression that shows the relationship between numbers and variables using mathematical operators.

The polynomial is classified based on degree as linear, quadratic, cubic and so on.

Given the equation:

3x² + x - 12 = 1

subtracting 1 from both sides:

3x² - 11x - 4 = 0

3x² - 12x + x - 4 = 0

3x(x - 4) + 1(x - 4) = 0

(3x + 1)(x - 4) = 0

3x + 1 = 0; and x - 4 = 0

x = -1/4; and x = 4

The solution to the equation is x = -1/4; and x = 4

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[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=20\\ \theta =65 \end{cases}\implies a=\cfrac{(65)\pi (20)^2}{360} \\\\\\ A=\cfrac{650\pi }{9}\implies A\approx 226.89[/tex]

The quotient of the rational expression is [tex]A = \frac{4(x+2)}{(x-2)}[/tex]

Given data ,

Let the first expression be represented as p

Let the second expression be represented as q

And , A = p / q

[tex]p= {\frac{(x^{2}-4) }{(x+3)}[/tex]

[tex]q= {\frac{x^{2}-4x+4 }{4x+12} }[/tex]

where , [tex]A = \frac{\frac{(x^{2}-4) }{(x+3)} }{\frac{x^{2}-4x+4 }{4x+12} }[/tex]

On simplifying , we get

[tex]A = \frac{4(x^{2} -4)}{(x-2)^{2} }[/tex]

Now , taking the common terms in the equation , we get

[tex]A = \frac{4(x-2)(x+2)}{(x-2)(x-2)}[/tex]

[tex]A = \frac{4(x+2)}{(x-2)}[/tex]

Hence , the equation is [tex]A = \frac{4(x+2)}{(x-2)}[/tex]

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The single transformation that maps shape triangle a onto shape b is  [tex]\:\begin{pmatrix}-5\\ -5\end{pmatrix}[/tex]

From the figure, we have the following highlights

Both triangles are congruent

Triangle B is 5 units down from triangle A

Triangle B is 5 units left of triangle A

The above highlights mean that the triangle A must be translated 5 units left and 5 units down to get triangle B.

This is represented as (x,y) -> (x - 5, y - 5)

By vector representation, we have: [tex]\:\begin{pmatrix}-5\\ -5\end{pmatrix}[/tex]

Hence, the single transformation that maps shape a onto shape b is  [tex]\:\begin{pmatrix}-5\\ -5\end{pmatrix}[/tex]

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The main answer to the question "How many pounds of laundry detergent does Andrew make?" is 4.125 pounds.

he total amount of borax used to make 3 batches is:

8 ounces/batch x 3 batches = 24 ounces

The total amount of washing soda used to make 3 batches is:

10 ounces/batch x 3 batches = 30 ounces

The total amount of soap used to make 3 batches is:

6 ounces/batch x 3 batches = 18 ounces

To find the total weight of the laundry detergent, we need to add up the weight of each ingredient. Since 1 pound is equal to 16 ounces, we can convert the total weight from ounces to pounds by dividing by 16.

Total weight of laundry detergent = (24 + 30 + 18) ounces / 16 = 4.125 pounds

Therefore, Andrew makes 4.125 pounds of laundry detergent.