NO LINKS OR ELSE YOU'LL BE REPORTED! Only answer if you're very good at Math. No guessing please.

Julio takes a multivitamin and a calcium vitamin every day.One at a time,he randomly pulled 8 cherry, 5 grape,and 7 orange gummy vitamins out of the multivitamin container and put them back each time.He also randomly pulled 11 berry,3 lemon,and 6 pineapple gummy vitamins out of the calcium container and put them back each time.

Based on this information, what is the probability that Julio will select an orange multivitamin and a lemon calcium vitamin the next time he takes his vitamins?

Enter your answer in the box below as a fraction.​

Answer:

a)

X      P[X]

0       5/14

1        15/28

2       3/28

b)

The expected value is 0.75

Step-by-step explanation:

Ok, we know that out of 8 cameras, 3 are defective.

So first let's find the probability for a camera randomly selected to be defective.

This is just the quotient between the number of defective cameras and the total number of cameras.

p = 3/8

then the probability that a camera is not defective is:

q = 5/8.

Ok, now we draw 2 cameras at random from the box.

We can define X as the number of defective cameras in these two drawn, we can have 3 possible values of X.

X = 0  (neither of the cameras is defective)

X = 1 (one of the cameras is defective)

X = 2 (both of the cameras is defective).

Let's find the probabilities for each case.

X = 0.

In this case, we first draw a non-defective camera, with a probability of:

P = 5/8.

The second camera drawn must be also non-defective, but now there are 4 non-defective cameras in the box and a total of 7 cameras (because one was already drawn).

Then the probability now is:

Q = 4/7

The joint probability is the product of the two individual probabilities:

P[0] = P*Q = (5/8)*(4/7) = (5/14)

X = 1

Here we have two cases:

the first is defective and the second is non-defective

the first is non-defective and the second is defective

So we just have a factor of 2, to consider both cases

Assuming the first case

Probability of drawing first a defective camera is equal to the quotient between the number of defective cameras  and the total number of cameras:

P = 3/8

For the second draw we want to get a non-defective camera, here the probability is equal to the number of non-defective cameras remaining (5) and the total number of cameras (7, because we drawn one)

Q = 5/7

The joint probability, taking in account the permutation, is

P[1] = 2*P*Q = 2*(3/8)*(5/7) = (15/28)

finally, for X = 2

This is the case where we draw two defective cameras, we can use a similar approach as the one used in the first case:

For the first camera:

P = 3/8

For the second camera:

Q = 2/7

Joint probability:

P[2] = (3/8)*(2/7) = 3/28

then we have the table:

X      P[X]

0       5/14

1        15/28

2       3/28

b)

The expected value for an event that has the outcomes:

{x₁, x₂, ..., xₙ}

Each one with the correspondent probability

{p₁, p₂, ..., pₙ}

is defined as:

EV = x₁*p₁ + x₂*p₂ + ... + xₙ*pₙ

Then in our case, the expected value is just:

EV = 0*P[0] + 1*P[1] + 2*P[2]

EV = 0  + 15/28  + 2*3/28

EV = (15 + 6)/28 = 21/28 = 0.75

The  length of the hypotenuse of the triangle whose other two sides are of the length 5√2 units is given by: Option B: 10 units.

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

For this case, consider the figure attached below.

Then, we are given the facts that:

Using the Pythagoras theorem, we get:

[tex]|AC|^2 = |AB|^2 + |BC|^2\\\\h^2 = (5\sqrt{2})^2 + (5\sqrt{2})^2 \\\\h^2 = 2(5\sqrt{2}))^2[/tex]

Taking root, we get:

[tex]h = \sqrt{2 (5\sqrt{2})^2}[/tex] (only positive root since h is denoting length, which is a non-negative quantity).

Thus, we get:

[tex]h = \sqrt{2 (5\sqrt{2})^2} = \sqrt{(5\sqrt{2})^2} \times \sqrt{2} = (5\sqrt{2}) \times \sqrt{2} = 5 \times (\sqrt{2})^2 = 5 \times 2 \\\\h= 10 \: \rm units[/tex]

(square cancelled the square root).

Thus, the  length of the hypotenuse of the triangle whose other two sides are of the length 5√2 units is given by: Option B: 10 units.

Learn more about Pythagoras theorem here:

https://brainly.com/question/12105522

Answer:

10 units.

Step-by-step explanation:

just took the quiz

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Answer:

  a.  x + 4y = 160

  b.  160

  c.  40

Step-by-step explanation:

a. We can define the variables as ...

  x = number of 1/2-liter bottles

  y = number of 2-liter bottles

For the total number of liters to be 80, we require

  1/2x + 2y = 80

We can multiply this by 2 to eliminate the fraction.

  x + 4y = 160

__

b. The x-intercept is 160. It is the number of 1/2-liter bottles required when no 2-liter bottles are used.

__

c. The y-intercept is 40. It is the number of 2-liter bottles required when no 1/2-liter bottles are used.

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Answer:

  H. reflection, translation

Step-by-step explanation:

The order of vertices ABCD is clockwise. The order of vertices EFGH is counterclockwise, so a reflection must be involved.

The orientation direction of GH is nearly vertical. The corresponding direction of CD is up to the left. A reflection can make the directions be the same, but the reflection that gets the orientation correct may not put the figure in the correct location.

So, we choose the transformations ...

  H. reflection followed by translation

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Answer:

  $62.74

Step-by-step explanation:

The annuity formula can be used to find the payment needed. Fill in the known values and solve for the unknown.

The future balance due to a series of payments is given by ...

  A = P(n/r)((1 +r/n)^(nt) -1)

where A is the account balance P is the payment made each period, n is the number of periods per year, r is the annual interest rate, and t is the number of years.

You have A = $20,000, r = 0.041, n = 12, t = 18 and you want to find P

  P = A(r/n)/((1 +r/n)^(nt) -1)

  P = $20,000(0.041/12)/((1 +0.041/12)^(12·18) -1) ≈ $62.74

A monthly payment of $62.74 is required.

Step-by-step explanation:

answer is in photo above

Answer:

-2/5

Step-by-step explanation:

Answer:

Therefore, 7/4 simplified to lowest terms is 7/4.

Answer:

See below

Step-by-step explanation:

In #4, the angles are vertical because the angles are congruent to each other. Therefore, you would set up the equation x+8=120 where x=112.

In #5, the angles are complementary because their sum is 90°. Therefore, you would set up the equation 43+x+3=90 where x=44.

In #6, the angles are supplementary because their sum is 180°. Therefore, you would set up the equation 76+2x+4=180 where x=50.

Answer:

21 miles

Step-by-step explanation:

12 * 1.75

Answer:

In my choice yes, it helped me I mean snap showed me where I am.

Step-by-step explanation:

if you want to know how then just be online and turn on location

Answer:

if it says that your somewhere when you're not with someone or did not allow snap to know your location someone other than you may access to your account somehow.

id advise you to put extra security for your safety and your account.

Step-by-step explanation:

Answer:

the exact value is 1/4

Step-by-step explanation:

Mark as brainllest if helps!!!

Answer:

0.25

Step-by-step explanation:

cos 60° = 0.5

sin 30° = 0.5

cos 60° x sin 30° = 0.5 x 0.5 = 0.25

Answer:

b = 84 2/3.

Step-by-step explanation:

6 (b - 83) =10

6b - 6*83 = 10

6b - 498 = 10

6b = 508

b = 508/6

b = 84 2/3

[tex]\longrightarrow{\green{84.666}}[/tex] 

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex]6 \: (b - 83) = 10 \\ ➡ \: 6 \: b - 498 = 10 \\ ➡ \: 6 \: b = 1 0 + 498 \\ ➡ \: 6 \: b = 508 \\ ➡ \: b = \frac{508}{6} \\ ➡ \: b = 84.666 [/tex]

[tex]\boxed{To\:verify:}[/tex]

[tex]6 \:( b -83) = 10 \\ ➝ \: 6 \: (84.666 - 83) = 1 \\ ➝ \: 6 \times 1.666 = 10 \\ ➝ \: 9.996 = 10 \\ ➝ \:10 \: (round ing \: \: to \: \: closest \: \: whole \: \: number) = 10 \\ ➝ \: L. H.S.=R. H. S[/tex]

Hence verified.

[tex]\pink{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35}}}}}[/tex]

Answer:

1.632 ft^3

Step-by-step explanation:

3.4 times .8 times .6 = 1.632 ft.

therefore the volume of the rectangle is 1.632 ft^3

Answer:

1800

Step-by-step explanation:

First, you multiply 9 times 40 which is 360. So then since he worked for 5 more hours you multiply 360*5 which will give you 1800. :D

Answer:

I'm pretty sure they spent $22.50

Step-by-step explanation:

do (1÷6)×(90) then multiply 15 and 1.50

Answer:

16/3

Step-by-step explanation:

When multiplyin fractions by whole numbers, you can make the whole number a fraction by simply making the denominator 1, than you will multiply numerators by numerators and denominators by denominators, therefore

8 x 2 = 16

1 x 3 = 3

16/3

Answer:

We have:

R = (2, 2)

S = (5, 4)

RS is the segment that connects R with S.

So RS is just the distance between R and S.

Remember that the distance between two points (a, b) and (c, d) is given by:

[tex]distance = \sqrt{(a - c)^2 + (b - d)^2}[/tex]

Then the distance between S and R is

[tex]distance = \sqrt{(5 - 2)^2 + (4 - 2)^2} = \sqrt{3^2 + 2^2} = \sqrt{13}[/tex]

Then:

RS = √13

ii) Now we want to express RS in the form (K, Q)

where K is the magnitude (we already know that it is √13) and Q is the bearing, which is measured with respect to the horizontal axis.

To interpret the bearing, let's look at the image below:

We can use the relation:

Tan(θ) = (opposite cathetus)/(adjacent cathetus)

where the opposite cathetus is just the difference between the y-values:

Opposite cathetus = 4 - 2 = 2

And the adjacent cathetus is the difference between the x-values:

Adjacent cathetus = 5 - 2 = 3

Then we have:

Tan(θ) = 2/3

If we apply the inverse tangent equation to both sides, we get:

Atan(tan(θ)) = Atan(2/3)

θ = Atan(2/3) = 33.69°

The bearing is 33.69°

then:

RS = (√13, 33.69°)

Answer:

See solutions below

Step-by-step explanation:

For the set of datas

30, 12, 15, 14, 15, 24, 13, 18, 15, 27

Mean = 30+12+15+14+15+24+13+18+15+27/10

Mean = 183/10

Mean = 18.3

Median is the number at the middle after rearrangement

12,13,14,15,(15,15),18,24,27,30

Median = 15+15/2

Median = 30/2

Median = 15

Mode the value that occurs the most. According to the data since the number that occurs the most is 15, hence the mode is 15

b) For the set of datas

511, 503, 505, 505, 515, 491, 514

Mean = 511+503+505+505+515+491+514/7

Mean = 3,544/7

Mean = 506.3

Median is the number at the middle after rearrangement

491, 503, 505, (505), 511, 514, 515

Hence the median value is 505

Mode the value that occurs the most. According to the data since the number that occurs the most is 505, hence the mode is 505

Answer:

0.999945 = 99.9945% probability that at least two of the alarms are triggered.

Step-by-step explanation:

For each alarm, there are only two possible outcomes. Either it is triggered, or it is not. The probability of an alarm being triggered is independent of any other alarm, which means that the binomial probability distribution is used 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 home security system is designed to have a 90% reliability rate.

This means that [tex]p = 0.9[/tex]

Suppose that 6 home equipped with this system experience an attempted burglary.

This means that [tex]n = 6[/tex]

Find the probability that at least two of the alarms are triggered.

This is:

[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]

In which

[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]

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

[tex]P(X = 0) = C_{6,0}.(0.9)^{0}.(0.1)^{6} = 0.000001[/tex]

[tex]P(X = 1) = C_{6,1}.(0.9)^{1}.(0.1)^{5} = 0.000054[/tex]

[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.000001 + 0.000054 = 0.000055[/tex]

Then

[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.000055 = 0.999945[/tex]

0.999945 = 99.9945% probability that at least two of the alarms are triggered.

Answer:

x = 56°

Step-by-step explanation:

Applying,

Sum of the interior angles in a polygon = (n-2)180

Where n = number of sides.

From the question,

Given: n = 5 sides (Pentagon)

Therefore, sum up all the given interior angle of the polygon

(x-5)+(5x-6)+(2x-7)+x+(2x-2) = (5-2)180

10x-20 = 540

10x = 540+20

10x = 560

x = 560/10

x = 56°

Answer:

1.3kg

Step-by-step explanation:

Answer:

its 1.3kg

Step-by-step explanation:

to work out 10% of anything just divide it by 10.

e.g 13kg÷10=1.3kg

Answer:

its 2/3 because if u divied the width u get that

Step-by-step explanation:

you welcome i tried

Answer:

-6

Step-by-step explanation:

y-intercept of 3x – 4y = 24

=> x=0

3(0) -4y=24

-4y=24

y = 24/(-4) = -6

the point is (0, -6)

Answer:

En un comienzo habia dos bacteria.

Step-by-step explanation:

Answer:

BT=CT the first one because BAT=CAT and bc cut the similar vector between these two triangle

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Answer:

Step-by-step explanation:

You have not told us the scale factor for the readings. The answer choices seem to say it is 1. That is, the consumption in kWh is equal to the difference between the Present and Previous readings. Those differences are shown in the attachment.

__

A spreadsheet is a nice tool for doing repetitive calculations without error.

Answer:

28.45

Step-by-step explanation:

33.04-1.75=31.29

31.29/1.10=28.45