Select the correct answer from each drop-down menu. a container holds 50 electronic components, of which 10 are defective. if 6 components are drawn at random from the container, the probability that at least 4 are not defective is . if 8 components are drawn at random from the container, the probability that exactly 3 of them are defective is .

Using the normal distribution and the central limit theorem, the probability the sample mean is more than 10 words is of 0.0210.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem, the parameters are given as follows:

[tex]\mu = 8.6, \sigma = 4.3, n = 39, s = \frac{4.3}{\sqrt{39}} = 0.6885[/tex]

The probability that the sample mean is more than 10 words is one subtracted by the p-value of Z when X = 10, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{10 - 8.6}{0.6885}[/tex]

Z = 2.03.

Z = 2.03 has a p-value of 0.979.

1 - 0.979 = 0.021.

The probability the sample mean is more than 10 words is of 0.0210.

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Answer:

[tex]\left(\dfrac{1}{4},\dfrac{49}{8}\right)[/tex]

Step-by-step explanation:

Turning points (stationary points) occur when the gradient of a graph is zero.

To find when the gradient of the graph is zero, differentiate the function, set it zero, then solve for x.

Given function:

[tex]f(x)=-2x^2+x+6[/tex]

Differentiate:

[tex]\implies f'(x)=(2)(-2)x^{2-1}+(1)x^{1-1}+6(0)[/tex]

[tex]\implies f'(x)=-4x+1[/tex]

Set the differentiated function to zero and solve for x:

[tex]\implies f'(x)=0[/tex]

[tex]\implies -4x+1=0[/tex]

[tex]\implies 4x=1[/tex]

[tex]\implies x=\dfrac{1}{4}[/tex]

To find the y-coordinate, input the found value of y into the given function:

[tex]\implies f\left(\dfrac{1}{4}\right)=-2\left(\dfrac{1}{4}\right)^2+\left(\dfrac{1}{4}\right)+6[/tex]

[tex]\implies f\left(\dfrac{1}{4}\right)=\dfrac{49}{8}[/tex]

Therefore, the turning point of the function is:

[tex]\left(\dfrac{1}{4},\dfrac{49}{8}\right)[/tex]

answers

f=1/4=49/8

Step-by-step explanation:

identify the coefficients

a=-2, b=1

substitute the coefficient into the expression

x= -1/((2x(-2))

then solve it out the equation

x=1/4

evaluate the function x =1/4

f(x) =-2x²+x+6(1/4)

f=1/4=49/8

Answer:

2 190km

Step-by-step explanation:

365×3= 1 095

1 095×2km= 2 190km

we have three sides, let's look at the two smaller sides first.

check the picture below atop

if we move the sides closer and ever closer to each other, to the extent that one is right on top of the other, what is the length of the red side?  Well, assuming the two smaller sides are one pancaked on top of the other, the red side will be as long as 9 - 4 = 5.  However, the sides can't be on top of each other, because if that's so, we have a flat-line, and thus we wouldn't have a triangle.  So whatever the third side may be, it must be greater than 5.

check the picture below at the bottom

Now, if we move the sides away from each other, farther and farther to the extent that one is parallel to the other, then the third side will just be as long as 4 + 9 = 13.  However, we can't do that, because if that were to happen, we again will have a flat-line and not a triangle.  So whatever the third side may be, it must be less than 13.

Answer:

7/2                

Step-by-step explanation:

3 hours and 30 minutes = 7/2 in improper fraction

1 hour = 60 minutes

30 minutes = 30 minutes * 1 hour/60 minutes =30/60 = 1/2 hour

3 hours and 30 minutes:

= 3 hours + 1/2 hour

= 3 1/2 hours

= [(2 * 3)+1]/2

= [6+1]/2

= 7/2

Answer:

Pay back  $ 67.79   in four weeks

Step-by-step explanation:

He will have to pay INTEREST FO

 59.99   x     .0325    x    4    = 7.7987  

     PLUS  the 59.99 that he borrowed

              = 67.79

Answer:

1 1/10

Step-by-step explanation:

1/2 + 3/5

1/2 = 5/10

3/5 = 6/10

6/10 + 5/10 =

1 1/10

Factors of 40: (1, 40) (2, 20) (4, 10) (5, 8)

---Using these factors will help us find a pair that adds up to -13 and multiplies to equal 40

-5 + -8 = -13

-5 x -8 = 40

(v - 8)(v - 5)

The trinomial can be factored into the following expression (v - 8)(v - 5).

Hope this helps!

The height of the shipping box in the shape of a rectangular prism is 15 inches

The given parameters are:

Volume = 9000 cubic inches

Base dimensions = 20 inches by 30 inches

The height of the prism is then calculated using:

Height = Volume/Base Area

So, we have:

Height = 9000/(20 * 30)

Evaluate

Height = 15

Hence, the height of the shipping box in the shape of a rectangular prism is 15 inches

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[tex]\text{Given that}~ x = 2,~ y = 3 ~ \text{and}~ z = -2\\\\\textbf{a)}\\\\2(x-y)=2(2-3) = 2(-1) = \boxed{-2}\\\\\textbf{b)}\\\\4x+3y-z = 4(2) +3(3) -(-2) = 8+9+2=\boxed{19}\\\\\textbf{c)}\\\\-2(3z+y) = -2[3(-2) +3] = -2(-6+3) = -2(-3) = \boxed{6}[/tex]

Answer:

median: 80

first q: 60

third q: 100

min: 40

max: 110

Step-by-step explanation:

The median is the middle (piece of data), the middle line in the box. Min is smallest number. Max is biggest number. First quartile is the left side of the box. Third quartile is right side of box.

Answer:

A.

Step-by-step explanation:

I believe it is A. because there are the numbers that equal all together to get that domain.

Step-by-step explanation:

X= -4x-4=-4(x+2)

X=-4x-4=-4x-8

X=-4x+4x=-8+4

X=-4

Answer:

so there is no x but it looks like it is undefined

Step-by-step explanation:

-4x - 4 = -4(x+2)  1. multiply -4 with x and 2

-4x - 4 = -4x - 8   2. + 4 on both sides

-4x = -4x - 4         3. +4x on both sides

0 = -4

Answer:

D. (2y - 7) units by (2y + 7) units

Step-by-step explanation:

Answer:

70= 5n+40

Step-by-step explanation:

(n=6 if you need it)

Hope this helps! ;-)

In order to find this answer, you will need to be able to make an inequality.

Step 1: Sophia makes $40 so start with that. 40

Step 2: Sophia also makes $5 per every outfit that she sells, so add that plus your variable (n). 40+5n

Step 3: Determine if Sophia wants to make more, equal to or more, less, or less than or equal to than what she wants to make per day. 40+5n *draw a greater than or equal to sign.

Step 4: Sophia wants to make more than or equal to what she makes per day. You will need to find what she wants to make more than. In this she wants to make more than or equal to $70.

Equation: 40+5n *greater than or equal to sign* $70

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Answer:

565.9.

Step-by-step explanation:

The second decimal place is 4 so the first one stays at 9.

Answer:

correct option is A i.e. 8/3

Answer:

120 meters

Step-by-step explanation:

The triangle area using Heron's formula

Heron's formula gives the area of a triangle when the length of all three sides is known. There is no need to calculate angles or other distances in the triangle first. Heron's formula works equally well in all cases and types of triangles.

[tex]T=\sqrt{s(s-a)(s-b)(s-c)} \\[/tex]

[tex]T=\sqrt{25(25-17)(25-17)(25-16)}[/tex]

[tex]T=\sqrt{14400} =120[/tex]

Answer

2 1/8

Step-by-step explanation 10–7 7/8=(10 – 7) + ( 0–7/8)= 3 +0 × 8 – 7/8= 3 + 08– 78=  3 + 0 – 78=  3 + -7/8 = 2 1/8

[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2 + b^2} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{7}\\ b=\stackrel{opposite}{4}\\ \end{cases} \\\\\\ c=\sqrt{7^2 + 4^2}\implies c=\sqrt{65}[/tex]

Linear function : y = x + 4

Exponential function : y = 4.5 e^(0.144 x)

Power function : y = 4.5 x^0.415

Answer:

10

Step-by-step explanation:

[tex]\frac{6}{2.5} =\frac{25}{x} \\6x=2.5*25\\6x=62.5\\x=10.417=10[/tex]

The Tree casts a height of 10.41 feet tall.

In general, the term "proportion" refers to a part, share, or amount that is compared to a total.

According to the concept of proportion, two ratios are in proportion when they are equal.

According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Given:

Connor is 6 feet tall and casts a shadow that is 2.5 feet long.

He stands next to a tree that is 25 feet tall.

let the shadow of tree is x feet long.

Using proportion

6/ 2.5 = 25/x

6x = 62.5

x= 10.41 feet

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Answer:

220 is ans by many hardworking But I don't knows which

Answer:

[tex]\huge{\boxed{\sf 55}}[/tex]

Explanation:

[tex]\sf Combination \ Formula = \ _n C_r=\dfrac{n !}{r ! (n-r) !}[/tex]

Here given:

Evaluate:

[tex]\rightarrow \sf \dfrac{11 !}{9 ! (11-9) !}[/tex]

[tex]\rightarrow \sf \dfrac{39916800}{ 362800 (2)}[/tex]

[tex]\rightarrow \sf \dfrac{39916800}{725760}[/tex]

[tex]\rightarrow \sf 55[/tex]

Answer:

(-1 , -5)

Hope this helped you! I would appreciate a Brainliest, if you wouldnt mind!

Answer:

Step-by-step explanation: