A basket of fruit contains 6 apples, 5 oranges, 3 bananas, and 2 limes.Which of the following statements about the fruits in the basket are true?Select the two correct statements.

Using the binomial distribution, it is found that there is a 0.8202 = 82.02% probability that the shipment will make it through the control check.

For each article, there are only two possible outcomes, either it meets the specifications, or it does not. The probability of an article meeting the specifications is independent of any other article, hence, the binomial distribution is used to solve this question.

Binomial probability distribution

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

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

The parameters are:

In this problem:

The probability is:

[tex]P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10)[/tex]

Then:

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

[tex]P(X = 8) = C_{10,8}.(0.85)^{8}.(0.15)^{2} = 0.2759[/tex]

[tex]P(X = 9) = C_{10,9}.(0.85)^{9}.(0.15)^{1} = 0.3474[/tex]

[tex]P(X = 10) = C_{10,10}.(0.85)^{10}.(0.15)^{0} = 0.1969[/tex]

[tex]P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) = 0.2759 + 0.3474 + 0.1969 =  0.8202[/tex]

0.8202 = 82.02% probability that the shipment will make it through the control check.

For more on the binomial distribution, you can check https://brainly.com/question/24863377

Answer:

42 ft

Step-by-step explanation:

2(L + W ) = P

2 (12 + 9) = P

2 (21) = P

42 = P

P = 42

Answer:

Step-by-step explanation:

12 cars in 15 hours how many cars is in 10 hours

12 : 15 = x : 10

x = 12 * 10 : 15

x = 8

-------------------

check

12 : 15 = 8 : 10

0.8 = 0.8

the answer is good

Answer:

223454353.000000000000000000

Step-by-step explanation:

A refrigeration system of 60 kW capacity at an evaporator temperature of – 40°C and a condenser temperature of 20°C is needed in a food storage locker. The refrigerant R134a is sub-cooled by 10°C before entering the expansion valve. The vapour is 0.98 dry as it leaves the evaporator coil. The compression in the compressor is of adiabatic type.

Answer:

The solution is in the photo

The least common multiple is the smallest expression that can be divided by both of the given expressions.

x^2 - 16 = (x - 4)(x + 4)

x^2 + 4x - 32 = (x + 8)(x - 4)

Both of the factored versions of the expressions have an (x - 4) in them. Thus, that will automatically be included in the LCM. Next, we have to include the (x + 4) and the (x + 8) in our LCM.

LCM = (x - 4)(x + 4)(x + 8)

Hope this helps! :)

Answer:

Step-by-step explanation:

Factorize the given expressions:

The LCM is the product of all unique  factors of both expressions:

answer: 60 × 100 = 600

Step-by-step explanation:

Answer:

$66

Step-by-step explanation:

Money saved after sale= 60% of $110

= 60/100 ×$110

= $66

Answer:

5

Step-by-step explanation:

Usually, the sequence is [tex]a_{1}, a_{2}, a_{3}, a_{4}, ..., a_{n}[/tex] where n is a postive number.

From the question,

[tex]a_{n} = a_{n-1} - 5[/tex]

if n = 2 ;  

[tex]a_{2} = a_{1} - 5[/tex]

[tex]a_{2} = 20 - 5 = 15\\[/tex]

Thus, we got [tex]a_{2} = 20[/tex].

if n = 3 ;  

[tex]a_{3} = a_{2} - 5[/tex]

[tex]a_{3} = 15 - 5 = 10[/tex]

Thus, we got [tex]a_{3} = 10[/tex].

if n = 4 ;  

[tex]a_{4} = a_{3} - 5[/tex]

[tex]a_{4} = 10 - 5 = 5[/tex]

Thus, we got [tex]a_{4} = 5[/tex].

***There are many ways to solve this question

example:

[tex]a_{n} = a_{n-1} - 5[/tex]

[tex]a_{n} - a_{n-1} = - 5[/tex]

Substitute n with 2, 3, 4

Then, we will get 3 equations.

Sum them up;

We will get

[tex]a_{4}-a_{3}+a_{3}-a_{2}+a_{2}-a_{1} = -15\\a_{4}-a_{1} = -15\\a_{4} = -15+20 = 5[/tex]

Answer:

8+15+4x and 3x+15+3x

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

Because OC biscts AOB, then COA=COB

Therefore AOB is twice COB

10x+4 = 2(6x-3)

10x+4 = 12x -6

2x = 10

x = 5

Therefore COA is 5x6-3 = 27

Answer:

9 degrees

Step-by-step explanation:

OK so we know that m<AOB is equal to the equation 10x+4. With this in mind, we also know that m<COB equals 6x-3. The ray OC intersects m<AOB, so this means that m<COB plus m<COA equals m<AOB.

First, we find m<COA by reversing the equation around to solve for m<COA.

m<AOB - m<COB = m<COA

Then, we Pug in the angles and solve.

m<AOB = 10x+4

m<COB = 6x-3

10x+4 - 6x-3 = 4x+1

Here is where things get interesting. See those 2 lines in each angle? That means they are equal in measure.

So what you do is simple, find what x equals in order to make this equation below true.

6x-3 = 4x+1

The answer for x is 2. So then just plug in to solve for m<COA and you're done!!

4(2)+1 =9

lil bonus: you can also get the same angle degree by plugging  2 into m<COB

Answer:

  1A: all real numbers

  1B: x = {-3, 0, +18}

  1C: (-3, 0) U [3, 18)

  2A: h(x) = -1/160x^2 +1/2x

  2B: focus: (40, -30); directrix: y = 50; axis of symmetry: x = 40

Step-by-step explanation:

The graph is attached. The domain is all real numbers.

__

The x-intercepts for x < 3 are the zeros of the quadratic:

  x^3 -9x = 0

  x(x^2 -9) = 0

  x(x +3)(x -3) = 0   ⇒   x = 0, -3, +3 . . . . x=3 is not in the domain of this piece

The x-intercepts for x ≥ 3 are the zeros of the log function:

  -log4(x -2) +2 = 0

  log4(x -2) = 2 . . . . . . add log4(x -2)

  x -2 = 4^2 . . . . . . . . . take the anti-log

  x = 2 +16 = 18 . . . . . . add 2

The x-intercepts of g(x) are x = {-3, 0, +18}.

__

The graph shows the function is positive on the intervals ...

  (-3, 0) U [3, 18)

__

The vertex of the curve is given as (40, 10). The vertical scale factor will make the function 0 at x=0.

  h(x) = a(x -40)^2 +10

  h(0) = 0 = a(-40)^2 +10 = 1600a +10

  a = -10/1600 = -1/160 = -1/(4·40)

The equation of the parabola is ...

  y = -1/(160)(x -40)^2 +10

In standard form, this is ...

  y = -1/160x^2 +1/2x

__

When we computed the leading coefficient (a) in Part A, we found it to be -1/(4·40). This corresponds to 1/(4p) where p=-40 is the focus to vertex distance. The negative sign means the focus is 40 units below the vertex, at (40, -30). The corresponding location of the directrix is 40 units above the vertex, at y=50.

Of course the axis of symmetry is the vertical line through the vertex: x = 40. These are shown in the second attachment.

The rates of change of points earned by both players tell us that;

Player A gains more point than Player B does for each correct answer in this round.

We are told that x is the number of

number ofquestions answered correctly and y is the score.

Now, for player B;

For 1 correct answer, he got a score of 4

For 2 correct answers, he got a score of 5

For 3 correct answers, he got a score of 6

For 4 correct answers, he got a score of 7

This means that rate of change of Player B is;

3 points for every extra question answered correctly. .

Now, the formula for player A's points is;

y = 4x + 3

Rate of change of points here is gotten by finding the derivative. Thus;

dy/dx = 4

This means player A earns 4 points for every extra question answered correctly.

In conclusion, it mean that Player A gains more point than Player B does for each correct answer in this round.

Read more on slope intercept form of equation at; https://brainly.com/question/19249035

Answer:

1 hour

Step-by-step explanation:

if he started at 12 pm, then in 1 hour he would finnish

Answer:

720 mi²

Step-by-step explanation:

The map has a scale of 1 in: 30 mi, meaning that for every inch you see on the map, in the real-life location, it will measure 30 miles. So we can find the area of the park on the map and then turn it into miles using the scale:

Area of a rectangle:

[tex]A=bh[/tex]

Replace the known values:

[tex]A=(4)(6)\\ A=24[/tex]

The area on the map is 24 mi², we can turn it to miles using the scale by multiplying our result with 30:

[tex]A=(24)(30)\\ A=720[/tex]

And last but not least, don't forget to put the unit!

Answer:

the measure of x is 38

Step-by-step explanation:

180-134=46 the value of one side of a line is 180 degrees so to find the vaule                of the inside angle we have to subtract 180 by the outside angle's

180-84=96

46+96=142 we then add the value's of both inside angles

180-142= 38

then we subtract that number by 180 because the total of all three angles of any triangle is always 180

Answer:

x = 38°

Step-by-step explanation:

Maths problem always go back to a number of foundational rules;

Once you recognise the ones that are relevant, you can then apply them to find the value or solution you want to find;

First thing is to look at the question and information provided in order to identify the relevant rules;

This question is asking for an angle and we can see a triangle (not a right-angle triangle) and line beneath it;

What rules should we think of with this in mind?

The following;

Using these rules, we can find x;

Firstly, according to rule 2, we can find angle OLM:

134 + OLM = 180

OLM = 180 - 134

OLM = 46

Secondly, also according to rule 2, we can find angle OML:

84 + OML = 180

OML = 180 - 84

OML = 96

Lastly, according to rule 1, we can find angle x:

OLM + OML + x = 180

46 + 96 + x = 180

x = 180 - 96 - 46

x = 38

Answer:

The equation of a line which contains the point (2, 5) and is parallel to the line y = 3x + 5 is

y = 3x - 1

A line is parallel to another when they both have the same slope.

The two equations above have a common slope of 3.

I hope this helped. Have a good new year!

x^2-10x+25

=x^2-5x-5x+25

x(x-5)-5(x-5)

=(x-5)(x-5)

x=5 , x=5

hope it's helpful to you

[tex]x^2 -10x +25\\\\=x^2 -2 \cdot 5 \cdot x +5^2\\\\=(x-5)^2\\\\=(x-5)(x-5)[/tex]

Answer:

[tex]{ \rm{5x - 8 < x + 10}} \\ \\ { \rm{5x - x < 10 + 8}} \\ \\ { \rm{4x < 18}} \\ \\ { \rm{x < 4.5}}[/tex]

Solving for x in the inequality gives us;

x < 4.5

We are given the inequality;

5x - 8 < x + 10

The first step is to use addition property of equality to add 8 to both sides;

5x - 8 + 8 < x + 10 + 8

5x < x + 18

Use subtraction property of equality to subtract x from both sides to get;

5x - x < x + 18 - x

4x < 18

Using division property of equality, we have;

x < 18/4

x < 4.5

Read more on inequalities at; https://brainly.com/question/25275758

Therefore, we found that x = -5/2.

Hoped this helped.

[tex]BrainiacUser1357[/tex]

Answer:

455554444444555556555555554444

Answer:

BRO BRING THE PHONE CLOSER TO THE SCREEN WE CANT SEE ANYTING

Step-by-step explanation:

The car overtakes the cyclist at a distance of 72 miles from the starting point.

,Speed is the ratio of distance travelled to time taken. It is given by:

Speed = distance / time

Let the car overtake the cyclist at distance d and time t.

For the car:

48 = d / t

d = 48t

For the cyclist:

16 = d / (t + 3)

d = 16t + 48

48t = 16t + 48

32t = 48

t = 1.5 hours

d = 48(1.5) = 72 miles

The car overtakes the cyclist at a distance of 72 miles from the starting point.

Find out more on speed at: https://brainly.com/question/3004254

Answer:

B (x-7<-6)

Step-by-step explanation:

x < 1

Answer:

[tex]3(3x-5)[/tex]

Step-by-step explanation:

First, you have to rewrite 9 as 3 * 3 and 15 as 3 * 5

Finally, you have to factor out the common term 3 to get [tex]3(3x-5)[/tex]

Hope this helps!

P.S next time list the answer choices it would help alot :)

is 1.25 because you just add them together

Answer:

11∑N=1 9000 (1.048)^n

Step-by-step explanation:

First month = a = 9,000burgers

Common ratio = r = 1 + 0.48 = 1.048

Total number of months = n = 11; from February to December.

Formula to determine the number of burgers the restaurant expects to sell this year:

       =   11∑N=1 9000 (1.048^n)

Answer:

a

Step-by-step explanation:

Answer:

click on image

Step-by-step explanation:

click on the image

Answer:

The slope is 1

Step-by-step explanation:

Notice that for every 2 unit increase in y, there's a 2 unit increase in x. This determines our slope, or rate of change. So, the slope is Δy/Δx=2/2=1.

Answer:

1

Step-by-step explanation: