While conducting a test of modems being manufactured, it is found that 10 modems were faulty out of a random sample of 367 modems. The probability of obtaining this many bad modems (or more), under the assumptions of typical manufacturing flaws would be 0.013. Is this an unusually high number of faulty modems

Answer:

a = T - 4

Step-by-step explanation:

Simply just subtract 4 on both sides to get the answer!

Answer:

a=T-4

Step-by-step explanation:

subtract 4

Answer:

a. 0.4772 = 47.72 %

b. 0.7605 = 76.05 %

Step-by-step explanation:

What we must do is calculate the z value for each value and thus find what percentage each represents and the subtraction would be the percentage between those two values.

We have that z is equal to:

z = (x - m) / (sd)

x is the value to evaluate, m the mean, sd the standard deviation

a. ind the least proportion of data falls between 70 and 80 If the histogram is bell shaped:

So for 70 copies we have:

z = (70 - 70) / (5)

z = 0

and this value represents 0.5

So for 80 copies we have:

z = (80 - 70) / (5)

z = 2

and this value represents 0.9772

p (70 > x > 80) = 0.9772 - 0.5

p (70 > x > 80) = 0.4772 = 47.72 %

b.  Find the proportion of data between 65 and 77

So for 65 copies we have:

z = (65 - 70) / (5)

z = -1

and this value represents 0.1587

So for 77 copies we have:

z = (77 - 70) / (5)

z = 1.4

and this value represents 0.9192

p (65 > x > 77) = 0.9192 - 0.1587

p (65 > x > 77)  = 0.7605 = 76.05 %

f(x) = 6-5x

y = 6-5x .... replace f(x) with y

x = 6-5y .... swap x and y; solve for y

x+5y = 6

5y = 6-x

y = (6-x)/5

[tex]f^{-1}(x) = \frac{6-x}{5}[/tex] ... replace y with the inverse function notation

Answer:

The probability that none of the households are tuned to 50 Minutes is 0.04398.

Step-by-step explanation:

We are given that the television show 50 Minutes has been successful for many years. That show recently had a share of 20, meaning that among the TV sets in use, 20% were tuned to 50 Minutes.

A pilot survey begins with 14 households have TV sets in use at the time of a 50 Minutes broadcast.

The above situation can be represented through binomial distribution;

[tex]P(X = r)= \binom{n}{r} \times p^{r} \times (1-p)^{n-r} ;x = 0,1,2,3,.........[/tex]

where, n = number of samples (trials) taken = 14 households

r = number of success = none of the households are tuned to 50 min

p = probability of success which in our question is probability that households were tuned to 50 Minutes, i.e. p = 20%

Let X = Number of households that are tuned to 50 Minutes

So, X ~ Binom(n = 14, p = 0.20)

Now, the probability that none of the households are tuned to 50 Minutes is given by = P(X = 0)

               P(X = 0)  =  [tex]\binom{14}{0} \times 0.20^{0} \times (1-0.20)^{14-0}[/tex]

                              =  [tex]1 \times 1 \times 0.80^{14}[/tex]

                              =  0.04398

Answer:

36=2×3×3×3

Answer

[tex]36 = 2 \times 2 \times 3 \times 3 \\ \: \: \: \: \: \: \: \: = {2}^{2} \times {3}^{2} [/tex]

Step-by-step explanation:

First write the prime factors of 36 that you can see here

[tex]2 \: \: \: 2 \: \: \: 3 \: \: \: 3[/tex]

Now write 36 as a product of its prime factors.

[tex]36 = 2 \times 2 \times 3 \times 3 \\ \: \: \: \: \: \: \: \: = {2}^{2} \times {3}^{2} [/tex]

Answer:

Considering the audience helps a writer identify the types of details and language needed in the writing. Considering the audience helps the writer identify what is important to him or her. Considering the audience allows the writer to write about what he or she wants. Knowing the audience for a particular essay is important because it determines the content that will appear in the writing. If you are arguing for a change to occur, identifying the level at which you want this change to occur and/or the people you want to persuade to help create this change (audience) is important step by step

Answer:

30

Step-by-step explanation:

Answer:

It would decrease by 9.

Step-by-step explanation:

52 is the original mean or the initial mean.

43 is the final mean.  

52-43 = 9

So 9 is the difference.

Hope this helped!

The missing part in the question;

and the payoff is $2.20 won for every dollar bet. (As the player’s probability of winning in this case is [tex]\dfrac{1}{4}[/tex]........

Also:

For such a bet, the casino pays off as shown in the following table.

The table can be shown as:

Keno Payoffs in 10 Number bets

Number of matches        Dollars won for each $1 bet

0  -   4                                        -1

5                                                  1

6                                                  17

7                                                  179

8                                                 1299

9                                                 2599

10                                               24999

Answer:

Step-by-step explanation:

Given that:

Twenty numbers are selected at random by the casino from the set of numbers 1 through 80

A player can select from 1 to 15 numbers; a win occurs if some fraction of the player’s chosen subset matches any of the 20 numbers drawn by the house

Let assume X to represent the numbers of player chooses which are in the Casino-selected-set of 20.

Let assume the random variable X has a hypergeometric distribution with parameters  N= 80 and m =20.

Then, the probability mass function of a hypergeometric distribution can be defined as:

[tex]P(X=k)=\dfrac{(^m_k)(^{N-m}_{n-k})}{(^N_n)}, k =1,2,3 ... n[/tex]

Now; the probability that i out of  n numbers chosen by the player among 20  can be expressed as:

[tex]P(X=k)=\dfrac{(^{20}_k)(^{60}_{n-k})}{(^{80}_n)}, k =1,2,3 ... n[/tex]

Also; given that ; When the player selects 2 numbers, a payoff (of odds) of $12 won for every $1 bet is made when both numbers are among the 20

So; n= 2; k= 2

Then :

Probability P ( Both number in the set 20)  [tex]=\dfrac{(^{20}_2)(^{60}_{2-2})}{(^{80}_2)}[/tex]

Probability P ( Both number in the set 20) [tex]= \dfrac{20*19}{80*79}[/tex]

Probability P ( Both number in the set 20) [tex]=\dfrac{19}{316}[/tex]

Probability P ( Both number in the set 20) [tex]=\dfrac{1}{16.63}[/tex]

Thus; the payoff odd for [tex]=\dfrac{1}{16.63}[/tex] is 16.63:1 ,as such fair payoff in this case is $16.63

Again;

Let assume X to represent the numbers of player chooses which are in the Casino-selected-set of 20.

Let assume the random variable X has a hypergeometric distribution with parameters  N= 80 and m =20.

The probability mass function of the hypergeometric distribution can be defined as :

[tex]P(X=k)=\dfrac{(^m_k)(^{N-m}_{n-k})}{(^N_n)}, k =1,2,3 ... n[/tex]

Now; the probability that i out of  n numbers chosen by the player among 20  can be expressed as:

[tex]P(n,k)=\dfrac{(^{20}_k)(^{60}_{n-k})}{(^{80}_n)}, k =1,2,3 ... n[/tex]

From the table able ; the expected payoff can be computed as shown in the attached diagram below. Thanks.

Answer:

It is a probability sample because it utilizes some form of random selection. It is not a simple random sample because there is not an equal possibility of A, B, or C.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The question is incomplete and lacks the required diagram. Find the diagram attached. Here is also the complete question.

"The formula for the area of a parallelogram is A = bh, where b is the base and h is the height. Which simplified expression represents the area of the parallelogram? –4x3 + 14x – 24 square centimeters 2x3 – 6x2 – 14x + 24 square centimeters –4x3 – 14x + 24 square centimeters 2x3 + 6x2 + 14x + 24 square centimeters"

Area of a parallelogram = Base * Height.

Given the height of the parallelogram = (x-4)cm

Base = (2x² + 2x-6) cm

Area of the parallelogram =  (x-4)cm *  (2x² + 2x-6) cm

Area of the parallelogram = (x-4)(2x²+2x-6)

Area of the parallelogram = 2x³+2x²-6x-8x²-8x+24

= 2x³+2x²-8x²-6x-8x+24

=  (2x³-6x²-14x+24)cm²

Answer

option D

Step-by-step explanation:

The population of interest to the research is the set of all gun ownership status (yes/no) values for all adults in the country. Or all total adults in a country including those that own a gym or not. This is the population of interest. The sample is the 2550 individuals adults surveyed in the household telephone survey.

Answer:

third one

Step-by-step explanation:

when

x=0,      y=0

x=1,       y=8

x=2      y=0

and so on.

Answer:

C. f(x)= -2x^3 -2x^2 +12x

Step-by-step explanation:

edge 2020

Answer:

The formula is 1/2h(a+b)

h stands for the perpendicular height

a and b stand for the two horizontal lengths which are parallel to each other

Answer:

a) [tex]t = 1\,s[/tex], [tex]\dot A \approx 22619.467\,\frac{cm^{2}}{s}[/tex], b) [tex]t = 3\,s[/tex], [tex]\dot A \approx 67858.401\,\frac{cm^{2}}{s}[/tex], c) [tex]t = 5\,s[/tex], [tex]\dot A \approx 113097.336\,\frac{cm^{2}}{s}[/tex]. The rate at which the area within the circle is increasing linearly inasmuch as time passes by.

Step-by-step explanation:

The area of a circle is described by the following formula:

[tex]A = \pi \cdot r^{2}[/tex]

Where:

[tex]A[/tex] - Area, measured in square centimeters.

[tex]r[/tex] - Radius, measured in centimeters.

Since circular ripple is travelling outward at constant speed, radius can be described by the following equation of motion:

[tex]r (t) = \dot r \cdot t[/tex]

Where:

[tex]\dot r[/tex] - Speed of the circular ripple, measured in centimeters per second.

[tex]t[/tex] - Time, measured in seconds.

The rate of change of the circle is determined by deriving the equation of area and replacing radius with the function in terms of the speed of the circular ripple and time. That is to say:

[tex]\dot A = 2\cdot \pi \cdot r \cdot \dot r[/tex]

[tex]\dot A = 2 \cdot \pi \cdot \dot r^{2}\cdot t[/tex]

Where:

[tex]\dot A[/tex] - Rate of change of the circular area, measured in square centimeters per second.

[tex]\dot r[/tex] - Speed of the circular ripple, measured in centimeters per second.

[tex]t[/tex] - Time, measured in seconds.

If [tex]\dot r = 60\,\frac{cm}{s}[/tex], then:

a) [tex]t = 1\,s[/tex]

[tex]\dot A = 2\cdot \pi \cdot \left(60\,\frac{cm}{s} \right)^{2}\cdot (1\,s)[/tex]

[tex]\dot A \approx 22619.467\,\frac{cm^{2}}{s}[/tex]

b) [tex]t = 3\,s[/tex]

[tex]\dot A = 2\cdot \pi \cdot \left(60\,\frac{cm}{s} \right)^{2}\cdot (3\,s)[/tex]

[tex]\dot A \approx 67858.401\,\frac{cm^{2}}{s}[/tex]

c) [tex]t = 5\,s[/tex]

[tex]\dot A = 2\cdot \pi \cdot \left(60\,\frac{cm}{s} \right)^{2}\cdot (5\,s)[/tex]

[tex]\dot A \approx 113097.336\,\frac{cm^{2}}{s}[/tex]

The rate at which the area within the circle is increasing linearly inasmuch as time passes by.

Step-by-step explanation:

solve f(x) by supposing it has y and and then interchange it with x .

hope this is helpful

Answer:

See explanation below.

Step-by-step explanation:

Let's take P as the proportion of new candidates between 30 years and 50 years

A) The null and alternative hypotheses:

H0 : p = 0.5

H1: p < 0.5

b) Type I error, is an error whereby the null hypothesis, H0 is rejected although it is true. Here, the type I error will be to conclude that there was age discrimination in the hiring process, whereas it was fair and random.

ie, H0: p = 0.5, then H0 is rejected.

Answer:

The standard deviation of the amount of coffee dispensed per cup in ml is 3.91.

Step-by-step explanation:

Let the random variable X denote the amount of coffee dispensed by the machine.

It is provided that the random variable, X is normally distributed with mean, μ = 105 ml/cup and standard deviation, σ.

It is also provided that a sign on the machine indicates that each cup contains 100 ml of coffee.

And 10% of the cups contain less than the amount stated on the sign.

To compute the probabilities of a normally distributed random variable, first convert the raw score to a z-score,

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

This implies that:

P (X < 100) = 0.10

⇒ P (Z < z) = 0.10

The value of z for the above probability is, z = -1.28.

*Use a z-table

Compute the value of standard deviation as follows:

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

[tex]-1.28=\frac{100-105}{\sigma}[/tex]

     [tex]\sigma=\frac{-5}{-1.28}[/tex]

        [tex]=3.90625\\\\\approx 3.91[/tex]

Thus, the standard deviation of the amount of coffee dispensed per cup in ml is 3.91.

Answer:

9672 per year

Step-by-step explanation:

Take the amount he earns per week times the number of weeks he works

186* 52

9672 per year

Answer:

$9672

Step-by-step explanation:

Jack earns $186 in 1 week.

In 52 weeks,

186 × 52 = 9672

He earns $9672.

Answer:

The food would last 51 days

Step-by-step explanation:

After 15 days are over, you could say that the 16th day would be as follows -

80 soldiers, food finished in 60 - 15 = 45 days.

If 20 more soldiers arrive, there would be a total of 100 soldiers, so if  80 soldiers can finish their food in 45 days  - 1 soldier can finish = 45 * 80. Respectively,  100 soldiers can consume their food in ( 45 * 80 ) / 100  = 36 days.

As 15 days are already over, adding 36 more days = 51 days

The food would last 51 days if 20 more soldiers join after 15 days

There are several possible ways to answer this question, but I hope that explanation helps!

Answer:

A total of 51 days, or 36 days after the extra soldiers join in.

Step-by-step explanation:

Let's say a soldier eats 1 portion of food in 1 days. That portion may be divided into breakfast, lunch , and dinner, but it is still accounted as 1 portion per soldier per day.

There are 80 soldiers and enough food for 60 days.

The number of portions is

60 * 80 = 4800

The fort started with 4800 portions.

80 soldiers ate their portions for 15 days.

80 * 15 = 1200

After 15 days, they have

4800 - 1200 = 3600 portions left.

After 15 days, 20 more soldiers joined in.

Now there are 80 + 20 = 100 soldiers.

There are 3600 portions left for 100 soldiers.

3600/100 = 36

The food would last 36 days after the 15 days, or a total of 51 days.

Answer:

140$

Step-by-step explanation:

4 hours = 20

28 hours divided by 4 is 7

7 x 20 = 140

Answer: 41 candles

Step-by-step explanation:

Multiply the dimensions of the candle first.

V = l*w*h

7 * 2 = 14

14 * 10 = 140

Now, divide the total amount of wax used by the amount of wax used for one candle.

5,740 / 140 = 41

Answer:

The answer is A) -9.7 > -18.2

Step-by-step explanation:

This is because, when you are thinking about negative numbers, the closer they are to 0, the greater they are. So, it is warmer in Minnesota.

Answer:

A and A

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

Perpendicular ⇒ So the slope will be the negative reciprocal to this slope

Slope = m = 2

Point = (x,y) = (4,-8)

So, x = 4, y = -8

Putting in the slope-intercept form

[tex]y = mx+b[/tex]

-8 = (2)(4) + b

b = -8-8

b = -16

Now we'll put it in the slope-intercept form

y = 2x-16

=> y = 2x-8-8

=> y+8 = 2(x-4)

Answer:

Center: (1, 5)

Radius: r = 5

Step-by-step explanation:

Step 1: Rewrite equation

x² - 2x + y² - 10y = -1

Step 2: Complete the Square (x2)

x² - 2x + 1 + y² -10y + 25 = -1 + 1 + 25

(x - 1)² + (y - 5)² = 25

Step 3: Find answers

Center = (h, k)

(1, 5) as Center

Radius = r

r² = 25

r = 5

Answer: Center = (1, 5)

               Radius = 5

Step-by-step explanation:

The standard form for a circle is: (x - h)² + (y - k)² = r²     where

First, group the x's and group the y's in order to complete the square.

x² - 2x        + y² - 10y         = -1

     ↓                    ↓

   (-2/2)²=1         (-10/2)²=25

Add those values to BOTH sides:

x² - 2x + 1      +  y² - 10y + 25    = -1 + 1 + 25

Rewrite the left side as perfect squares and simplify the right side.

  (x - 1)²       +     (y - 5)²         = 25

We end up with (h, k) = (1, 5)   this is the center

        and r² = 25 --> r = 5         this is the radius

To graph the circle, place an x at the center (1, 5).  Plot a point 5 units (the radius) to the right of the center, another point 5 units up from the center, a third point 5 units left from the center, and a fourth point 5 units down from the center. "Connect the dots" to create a circle.

Answer:

t = 0

Before it starts rushing that's when it will be fastest

Step-by-step explanation:

For the water ib the tank to flow very fast it means that there is a big volume of water present.

And for volume of water to be present that much it means that the water must

have not leaked much or at all.

And for that it signifies large volume of water.

If we do the calculation we'd see that time will be actually equal to zero for the pressure and the volume of the water to be biggest.

V = 4500 (1 − 1 /50 t )^2

V = 4500

4500 = 4500(1- 1/50t)²

1 = 1- 1/50t

0 = -1/50t

t = 0

Answer:

[tex]\boxed{\df\ \dfrac{-19}{2}}[/tex]

Step-by-step explanation:

Hi,

x=-2

it gives

9*(-2)-4y=20

<=> -18-4y=20

<=> 18-18-4y=20+18=38

<=> -4y=38

<=> y = -38/4=-19/2

hope this helps

Answer:

x= -3 +√2 ≈ -0.1716,  and x = - 3 -2√2 ≈ -5.8284

Step-by-step explanation:

y= -1/2(x+3)² +4

For x -intercept, y = 0.

0 = - 1/2(x+3)² + 4 /*(-2)

0 = (x+3)² - 8

(x+3)² = 8

√(x+3)² = +/-√8

x+3 = +/-√8

x = - 3+/- 2√2

x= -3 +√2 ≈ -0.1716,  and x = - 3-2√2 ≈ -5.8284

Answer:

a. p=0.562

b. E = 0.0253

c. The 90% confidence interval for the population proportion is (0.537, 0.587).

d. We have 90% confidence that the interval (0.537, 0.587) contains the true value of the population proportion.

Step-by-step explanation:

We have to calculate a 90% confidence interval for the proportion.

The sample proportion is p=0.562.

[tex]p=X/n=583/1038=0.562[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.562*0.438}{1038}}\\\\\\ \sigma_p=\sqrt{0.000237}=0.0154[/tex]

The critical z-value for a 90% confidence interval is z=1.645.

The margin of error (MOE) can be calculated as:

[tex]MOE=z\cdot \sigma_p=1.645 \cdot 0.0154=0.0253[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=p-z \cdot \sigma_p = 0.562-0.0253=0.537\\\\UL=p+z \cdot \sigma_p = 0.562+0.0253=0.587[/tex]

The 90% confidence interval for the population proportion is (0.537, 0.587).

We have 90% confidence that the interval contains the true value of the population proportion.

Step-by-step explanation:

can u give image PlZzzzz ....

Answer:

Hey!

Your answer should be Y=2x+4

Step-by-step explanation:

Hope this helps!

Answer:

a) The volume of the wooden block is 240 cm^3.

b) The density of the wooden block is 0.7 g/cm^3.

Step-by-step explanation:

The volume of the rectangular wooden block can be calculated as the multiplication of the length in each dimension: length, wide and height.

With dimensions 10 cm x 3 cm x 8 cm, the volume is:

[tex]V=L\cdot W\cdot H = 10\cdot 3\cdot 8=240[/tex]

The volume of the wooden block is 240 cm^3.

If we know that the mass of the wooden block is 168 g, we can calculate the density as:

[tex]\rho = \dfrac{M}{V}=\dfrac{168}{240}=0.7[/tex]

The density of the wooden block is 0.7 g/cm^3.