The student council is hosting a drawing to raise money for scholarships. They are selling tickets for $9 each and will sell 500 tickets. There is one $2,000 grand prize, four $400 second prizes, and sixteen $10 third prizes. You just bought a ticket. Find the expected value for your profit. Round to the nearest cent.

Answer:

The probability that the event will not happen is [tex]\frac{4}{17}[/tex]

Step-by-step explanation:

The occurrence of an event can be divided into two parts, the event would occur or the event would not occur. But the probability of an event is 1.

From the given question;

The probability of the event = 1

The probability that the event will happen, P = [tex]\frac{13}{17}[/tex]

Thus,

The probability that the event will not happen = probability of the event - probability that the event will happen

                                               = 1 - P

                                               = 1 - [tex]\frac{13}{17}[/tex]

                                               = [tex]\frac{17 - 13}{17}[/tex]

                                               = [tex]\frac{4}{17}[/tex]

Thus, the probability that the event will not happen is [tex]\frac{4}{17}[/tex].

Answer:

(a)[tex]\dfrac{2}{13}[/tex]

(b)[tex]\dfrac{3}{13}[/tex]

(c)[tex]\dfrac{4}{13}[/tex]

Step-by-step explanation:

In a standard deck, there are 52 cards which are divided into 4 suits.

(a)

Number of Seven Cards =4

Number of King cards =4

Probability of randomly selecting a seven or king

=P(Seven)+P(King)

[tex]=\dfrac{4}{52} +\dfrac{4}{52} \\=\dfrac{8}{52}\\=\dfrac{2}{13}[/tex]

(b)

Number of Seven Cards =4

Number of King cards =4

Number of Jack(J) cards =4

Probability of randomly selecting a seven or king

=P(Seven)+P(King)+P(Jack)

[tex]=\dfrac{4}{52} +\dfrac{4}{52}+\dfrac{4}{52} \\=\dfrac{12}{52}\\=\dfrac{3}{13}[/tex]

(c)

Number of Queen Cards =4

Number of Spade cards =13

Number of Queen and Spade cards =1

Probability of randomly selecting a seven or king

[tex]=P$(Queen)+P(Spade)-P(Queen and Spade Card)\\=\dfrac{4}{52} +\dfrac{13}{52} -\dfrac{1}{52} \\=\dfrac{16}{52} \\=\dfrac{4}{13}[/tex]

Answer:

2.964

Step-by-step explanation:

Question:

It is known that 20% of products on a production line are defective. Products are inspected until first defective is encountered. a) What is the probability that the experimenter must inspect six products to find a defective product?

Answer:

P(x = 6) = 0.0655

P(x = 6) = 6.55%

Step-by-step explanation:

It is given that 20% of products on a production line are defective.

p = 0.20

Then

q = 1 - p = 1 - 0.20 = 0.80

Which means that 80% of products on the production line are not defective.

We want to find out the probability that the experimenter must inspect six products to find a defective product.

Let x is the number of inspections to get a defective product.

P(x = 6) = ?

If out of 6 inspections 1 is defective then it means 5 are not defective

so the probability is

P(x = 6) = p¹ × q⁵

P(x = 6) = 0.20¹ × 0.80⁵

P(x = 6) = 0.20 × 0.32768

P(x = 6) = 0.0655

P(x = 6) = 6.55%

Therefore, there is 6.55% chance that the experimenter finds a defetive product in 6 inspections.

Answer:

R=9

Step-by-step explanation:

the formula for area of a circle is pi r squared

where r denotes the radius of the circle

equating the formula for area with the area of the circle provided

p\i r squared = 81 p\i

r squared = 81

r = radical 81

r =9 inches

Answer: 0.007

Step-by-step explanation:

Suppose that you have a ticket.

We have 3 prizes, and 300 tickets.

After the first tiket is drawn, someone win a prize, so now we have 299 tikets left and 2 prizes left.

Then, for the next draw, you have p = 1/299 of wining a prize.

If you did not win there, the probability for the third price is p = 1/298 (because there are 2 less tickets now)

Then the probability of winning at least one prize is:

P = 1/299 + 1/298 = 0.007

Answer:

y = -x + 2

Step-by-step explanation:

The slope intercept form equation of this line can be written like this :

y = my + p ; where m is the slope and p is the y intercept.

[tex]m = \frac{-1-4}{3-(-2)} = \frac{-5}{5} =-1[/tex]

then the equation becomes y = -x + p

(-2,4) is a point of the line means 4 = -(-2) + p

then p = 4 - 2 = 2

finally, y = -x + 2

Answer:

Hello! Here is your answer

Step-by-step explanation:

112=4(28)

a=4b

You can only have one variable so:

Combine b to a:

a-b=84

4b-b=84

Divide both sides by 3:

3b/3=84/3

b=28

But that is not it:

Sum of both cards:

a+b

a=112

b=28

112+28=140

          = 140

I hope I was of help.  If not please let me know! Thank you! Good luck!

Answer:

For this case we know that the confidence level is 89.48% or 0.8948 and the significance would be: [tex] \alpha=1-0.8948 = 0.1052[/tex] and the value of [tex]\alpha/2 =0.0526[/tex]

Now we need to find a quantile in the normal standard distribution who accumulate 0.0526 of the area on each tail of the normal standard distribution and we got:

[tex] z_{\alpha/2}= \pm 1.62015[/tex]

And we can use the following excel code for example:

"=NORM.INV(0.0526,0,1)"

Step-by-step explanation:

For this case we know that the confidence level is 89.48% or 0.8948 and the significance would be: [tex] \alpha=1-0.8948 = 0.1052[/tex] and the value of [tex]\alpha/2 =0.0526[/tex]

Now we need to find a quantile in the normal standard distribution who accumulate 0.0526 of the area on each tail of the normal standard distribution and we got:

[tex] z_{\alpha/2}= \pm 1.62015[/tex]

And we can use the following excel code for example:

"=NORM.INV(0.0526,0,1)"

Answer:

(–2, 5)

Step-by-step explanation:

I know its late now but here is the answer.

Answer:

The answer is a

Step-by-step explanation:

Answer:

B is the midpoint of line segment AC

Answer:

The number of computer is 5 and printer is 3

Answer:

d) −8

Step-by-step explanation:

x − 2+2 < −8+2

x < -6

The only number less than -6 is -8

Answer: The answer is 61

Step-by-step explanation: did it on 2020 edg pls mark me brainliest

Answer:

61

Step-by-step explanation:

answer is g(x)=|x+2|-1

[tex]answer \\ g(x) = - |x + 2| - 1\\ as \: we \: can \: see \: from \: the \: given \: graph \\ above \: that \: the \: graph \: of \: absolute \\ function \: has \: been \: reflected \: over \: the \\ x \: axis \: \: shifted \: 2 \: units \: left \: and \: 1 \: \\ units \: down. \\ due \: to \: reflection \: there \: is \: a \: negative \\ sign \: shift \: of \: 2 \: units \: left \: is \: given \\ by \: x + 2 \: and \: 1 \: units \: down \: is \: given \\ by \: - 1 \\ hope \: it \: helps[/tex]

Answer:

[tex]47\frac{5}{8}[/tex]

Step-by-step explanation:

Weight from before + Weight gained

[tex]46\frac{3}{8} +1\frac{1}{4}[/tex]

Convert to improper fractions.

[tex]371/8 + 5/4[/tex]

Find the common denominator.

[tex]371/8 + 10/8[/tex]

Add.

[tex]381/8[/tex]

Convert to a mixed fraction.

[tex]47\frac{5}{8}[/tex]

Answer:

47 5/8 kg

Step-by-step explanation:

Ealier weight + gained weight = Monday's weight

46 3/8 + 1 1/4

= 371/8 + 5/4

= 371/8 + 10/8

= 381/8

= 47 5/8 kg

Answer:

D

Step-by-step explanation:

Line 1: Since these angles are vertical, they are congruent

Line 2: We have 2 sides and an angle in between them so it is SAS

This means the answer is D.

Answer: The correct answer is this set:

1.) Vertical Angles are congruent

2.) SAS Congruence Postulate

Here is the full question.

The average finishing time among all high school boys in a particular track event in a certain state is 5 minutes 17 seconds. Times are normally distributed with standard deviation 12 seconds.

A.  The qualifying time in this event for participation in the state meet is to be set so that only the fastest 5% of all runners qualify. Find the qualifying time in seconds (round it to the closest second). (Hint: Convert minutes to seconds.)  

B. In the western region of the state the times of all boys running in this event are normally distributed with standard deviation 12 seconds, but with mean 5 minutes 22 seconds. Find the proportion of boys from this region who qualify to run in this event in the state meet. (Hint: normalcdf)

Answer:

a. x ≅ 337 seconds.

b. P(x > 337 )  = 0.1056

Step-by-step explanation:

A.

Given that ;

Mean [tex]\mu =[/tex] 5 minutes 17 seconds =( (60× 5)+17  ) seconds  = 317 seconds   ( since 60 seconds make 1 minute.

Standard deviation: [tex]\sigma[/tex] = 12 seconds.

Only the fastest 5% of all runners qualify

The objective is to determine the qualifying time in seconds

Let's look for the Z-score of 0.95;

The Z-score is 1.645 from the tables

[tex]x= ( \sigma * z ) + \mu[/tex]

[tex]x = ( 12 * 1.645 ) + 317 \\ \\x = 336.74[/tex]

x ≅ 337 seconds.

B. Given that the standard deviation = 12 seconds

Mean = 5 minutes 22 seconds = (5 × 60 + 22 )seconds = 322 seconds

he objective is  to find P(x > 337 )   i.e the proportion of boys from this region who qualify to run in this event in the state meet.

we are using command normalcdf   (SEE THE ATTACHED FILE BELOW FOR THE COMPUTATION)

we have  P(x > 337 )  = 0.1056

Answer:

220

Step-by-step explanation:

If we lost 12% we still have 100 - 12 = 88% of the employees left. 88% can be written as 0.88. 0.88 * 250 = 220 employees left.

Answer:

Step-by-step explanation:

a) The %tax comes from the "Rate" column on the line "up to $9525". It is 10%.

__

b) Simply compute the difference shown:

  $38,700 -$9,525 = $29,175

__

c) 22% of $9,300 is ...

  0.22 × $9,300 = $2,046

__

d) The total from the three previous calculations is ...

  $952.50 +3,501.00 +2,046.00 = $6,499.50

Answer:

10%

$29,175

$2,046

$6,499.50

got it right on ttm.  

Step-by-step explanation:

just believe me it works

Answer:  EF = 15

Step-by-step explanation:

The given description is that of an isosceles triangle. The base angles are congruent, therefore the sides opposite of those angles are also congruent.

The base angles are ∠E and ∠G and the vertex angle is ∠F.

The sides opposite to the base angles are EF and FG.

Thus, EF ≡ FG.

Since FG = 15 and FG = EF, then 15 = EF.

Based on the definition of an isosceles triangle, the length of EF in the triangle is: 15 units.

An isosceles triangle has two sides that are congruent. The angles opposite these congruent sides are also congruent.

ΔEFG is an isosceles triangle. The congruent sides are, FG and EF.

Therefore, EF = FG = 15 units.

Learn more about isosceles triangle on:

https://brainly.com/question/11884412

Answer:

Equilateral, acute

Step-by-step explanation:

Equilateral triangles have all sides the same length (all sides are 4 ft in this triangle, so it is equilateral).

Acute triangles have no angles that are greater than or equal to 90 degrees (all angles are 60, which is less than 90, so it is acute).

Answer:

When we talk about precision in measurements, we need to mention the significant figures, because that determines the precision.

Specifically, the more significant figures there are, more precise will be the number.

In this case, you can observe that both numbers have the same number of significant figures, which is 3, which means both numbers are equal in precision.

Answer:

A. V(t) = 40t + 250 B. (HoV)(t) = 24πt/5 + 30π C. The composition in B (above) can be described as the height of the wax in terms of time.

Step-by-step explanation:

A. Let the rate of change of volume V with respect to time be dV/dt = 40 ft³/min

Solving this, V = 40t + C. At the start of the day, that is t = 0, V = 250 ft³

Substituting these values, we have

250 ft³ = 40(0) + C

C = 250 ft³

So, V(t) = 40t + 250

B. Since H(V) = 3πV/25

(HoV)(t) = 3π(40t + 250)/25

= 24πt/5 + 30π

C. The composition in B (above) can be described as the height of the wax in terms of time.

Answer:

  12 cm

Step-by-step explanation:

The rule regarding secants and/or tangents is that the product of distances from their common point to the two intersection points with the circle is the same.

For the tangent the "two" intersection points with the circle are the same point, so ...

  product of tangent lengths = product of secant lengths

  (8 cm)(8 cm) = (4 cm)(4 cm +x)

Dividing by 4 cm gives ...

  16 cm = 4 cm + x

  12 cm = x

Answer:

(A)three eigenvalues, all of them real.

(D)one real eigenvalue and two complex eigenvalues.

(G)only one eigenvalue -- a real one.

Step-by-step explanation:

Given an [tex]n \times n[/tex] matrix, the characteristic polynomial of the matrix is the degree n  polynomial in one variable λ:

[tex]p(\lambda) = det(\lambda I- A)[/tex]

If such [tex]n \times n[/tex] matrix A has real entries, its complex eigenvalues  will always occur in complex conjugate pairs.

Therefore, for a [tex]3 \times 3[/tex] matrix with real entries, the following are possible:

(A)three eigenvalues, all of them real.

(D)one real eigenvalue and two complex eigenvalues.

(G)only one eigenvalue -- a real one.

A [tex]3 \times 3[/tex] matrix with real entries cannot have the following:

(B)three eigenvalues, all of them complex.

(C)two real eigenvalues and one complex eigenvalue.

(E)only two eigenvalues, both of them real.

(F)only two eigenvalues, both of them complex.

(H)only one eigenvalue -- a complex one.

Answer:

27/(4x^6y^8)

Step-by-step explanation:

Target the variables first. (x^a)^b is the same as x^(a x b).

In the numerator, it is x^(2 x 3) , which is x^6, and y^(4 x 3), which is y^12.

Same principle on the bottom. the denominator is x^12 and y^20.

In the numerator, the number 4 is alone so don't do anything to it. Cube 3. The coefficient of the numerator is 4 x 3^3 . The coefficient of the denominator is 2^4. Cancel like terms. when you divide same terms' exponents, you subtract the exponent on top by the exponent on the bottom. Remember that you can only simplify LIKE terms. (x with x, y with y, number with number.)

Answer:

Mega Gym charges a $384 registration fee and $2 each time the gym is used. Super Gym charges a fee of $6 every time the gym is used. What number of times, x, will Super Gym need to be used to exceed the cost of Mega Gym?

Step-by-step explanation:

Given: the inequality is [tex]384+2x<6x[/tex]

To find: the correct option

Solution:

Let x denotes number of times gym is used.

As Mega Gym charges a $384 registration fee and $2 each time the gym is used,

Total amount charged by Mega Gym = [tex]\$(384+2x)[/tex]

As Super Gym charges a fee of $6 every time the gym is used,

Total amount charged by Super Gym = [tex]\$\,6x[/tex]

In order to find number of times, x Super Gym is used such that cost of Super Gym exceeds the cost of Mega Gym,

Solve the inequality:

cost of Super Gym > cost of Mega Gym

[tex]6x>384+2x\\384+2x<6x[/tex]

So, the correct option is '' Mega Gym charges a $384 registration fee and $2 each time the gym is used. Super Gym charges a fee of $6 every time the gym is used. What number of times, x, will Super Gym need to be used to exceed the cost of Mega Gym? ''

Answer:

a) P(6) = 0.0097

b) P(More than 3) = 0.1611

Step-by-step explanation:

For each question, there are only two possible outcomes. Either it is guessed correctly, or it is not. Questions are independent of each other. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

A student takes a multiple-choice test that has 11 questions.

This means that [tex]n = 11[/tex]

Each question has five choices.

This means that [tex]p = \frac{1}{5} = 0.2[/tex]

(a) Find P (6)

This is P(X = 6).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 6) = C_{11,6}.(0.2)^{6}.(0.8)^{5} = 0.0097[/tex]

P(6) = 0.0097

(b) Find P (More than 3).

Either P is 3 or less, or it is more than three. The sum of the probabilities of these outcomes is 1. So

[tex]P(X \leq 3) + P(X > 3) = 1[/tex]

We want P(X > 3). So

[tex]P(X > 3) = 1 - P(X \leq 3)[/tex]

In which

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{11,0}.(0.2)^{0}.(0.8)^{11} = 0.0859[/tex]

[tex]P(X = 1) = C_{11,1}.(0.2)^{1}.(0.8)^{10} = 0.2362[/tex]

[tex]P(X = 2) = C_{11,2}.(0.2)^{2}.(0.8)^{9} = 0.2953[/tex]

[tex]P(X = 3) = C_{11,3}.(0.2)^{3}.(0.8)^{8} = 0.2215[/tex]

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0859 + 0.2362 + 0.2953 + 0.2215 = 0.8389[/tex]

Then

[tex]P(X > 3) = 1 - P(X \leq 3) = 1 - 0.8389 = 0.1611[/tex]

P(More than 3) = 0.1611