Making handcrafted pottery generally takes two major steps: wheel throwing and firing. The time of wheel throwing and the time of firing are normally distributed random variables with means of 40 minutes and 60 minutes and standard deviations of 2 minutes and 3 minutes, respectively. Assume the time of wheel throwing and time of firing are independent random variables.
A) What is the probability that a piece of pottery will befinished within 95 minutes?
B) What is the probability that it will take longer than 110minutes?

Each side of the square would have to be 6 cm to have an area of 36 cm^2.  However, as a side can never be 0, and you never gave a starting size for the square, the question is unanswerable.

Answer:

-10 -24i

Step-by-step explanation:

Note : i=√-1 (imaginary number)

i² = -1

xy

= (−1−5i)(5−i)

= -5 +i -25i +5i²

=-5 +i -25i + 5(-1)

= -5 +i -25i -5

= -5 -5 +i -25i

= -10 -24i

A complex number is a number system that extends the real numbers with a particular element labelled "i" known as the imaginary unit. The value of x·y is (−10 −24i).

A complex number is a number system that extends the real numbers with a particular element labelled "i" known as the imaginary unit, and satisfies the equation i² = -1; every complex number may be represented as a + bi, where a and b are real numbers.

Given that x=−1−5i and y=5−i. Therefore, the value of x·y is,

x·y = (−1 −5i)(5-i)

     = −5 + i −25i +5i²

     = −5 −24i − 5

      = −10 −24i

Hence, the value of x·y is (−10 −24i).

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Answer:

This question is very simple,

Ok first you will need to find the x and y intercepts by letting y=0 and x=0

First let x=0

so, 0-y=1

y=-1

let y=0

x-0=1

x=1

now we know

x-intercept=(1,0)

y-intercept=(0-1)

Hence, find the graph that has the two corresponding points and that would be the graph you are looking for.

Step-by-step explanation:

Answer:

1/90 = 1.11%

Step-by-step explanation:

We have that the number of ways of total selections and assignments possible is a permutation.

We know that permutations are defined like this:

nPr = n! / (n-r)!

In our case n = 10 and r = 2, replacing:

10P2 = 10! / (10 - 2)! = 10! / 8!

10P2 = 90

In addition to this, there will only be one way to randomly select the two members currently holding the positions of President and Vice President and reassign them to their current positions. Thus,

Probability would come being the following:

P = 1/90 = 1.11%

Answer:

2{3[9+4(7-5)-4]}

2{3[9+4(2)-4]}

2{3[13(2)-4]}

2{3[26-4]}

2{3[22]}

2{66}

132

Step-by-step explanation:

Answer:

the value of x=12

Step-by-step explanation:

d) the answer is d on edg.

Answer:(x-5)(x+9)

Step-by-step explanation:

You want two numbers that can give you -45 in multiplication and two numbers that can add to 4 and that is -5 and 9.

Answer:  (x - 5)(x + 9)

If you have to solve, x=5 or x= -9

Step-by-step explanation: You need two numbers that multiply to be 45.

(could be 3 × 15 or 5 × 9) . The difference between the two factors needs to be 4, the coefficient of the middle term.

9 - 5 =4, so use those.  -45 has a negative sign, so one of the factors must be + and the other -  Since the 4 has the + sign, the larger factor has to be + so the difference will be positive.

So (x -5)(x + 9) are your factors. You can FOIL to be sure

x × x += x² . x × 9 = 9x .  -5 ×  x = -5x . -5 × 9 = -45 .

Combine the x terms: 9x -5x = +4x  

We assume that question b is asking for the distribution of [tex] \\ \overline{x}[/tex], that is, the distribution for the average amount of pollutants.

Answer:

a. The distribution of X is a normal distribution [tex] \\ X \sim N(8.6, 1.3)[/tex].

b. The distribution for the average amount of pollutants is [tex] \\ \overline{X} \sim N(8.6, \frac{1.3}{\sqrt{38}})[/tex].

c. [tex] \\ P(z>-0.08) = 0.5319[/tex].

d. [tex] \\ P(z>-0.47) = 0.6808[/tex].

e. We do not need to assume that the distribution from we take the sample is normal. We already know that the distribution for X is normally distributed. Moreover, the distribution for [tex] \\ \overline{X}[/tex] is also normal because the sample was taken from a normal distribution.

f. [tex] \\ IQR = 0.2868[/tex] ppm. [tex] \\ Q1 = 8.4566[/tex] ppm and [tex] \\ Q3 = 8.7434[/tex] ppm.

Step-by-step explanation:

First, we have all this information from the question:

a. What is the distribution of X?

The distribution of X is the normal (or Gaussian) distribution. X (uppercase) is the random variable, and follows a normal distribution with [tex] \\ \mu = 8.6[/tex] ppm and [tex] \\ \sigma =1.3[/tex] ppm or [tex] \\ X \sim N(8.6, 1.3)[/tex].

b. What is the distribution of [tex] \\ \overline{x}[/tex]?

The distribution for [tex] \\ \overline{x}[/tex] is [tex] \\ N(\mu, \frac{\sigma}{\sqrt{n}})[/tex], i.e., the distribution for the sampling distribution of the means follows a normal distribution:

[tex] \\ \overline{X} \sim N(8.6, \frac{1.3}{\sqrt{38}})[/tex].

c. What is the probability that one randomly selected city's waterway will have more than 8.5 ppm pollutants?

Notice that the question is asking for the random variable X (and not [tex] \\ \overline{x}[/tex]). Then, we can use a standardized value or z-score so that we can consult the standard normal table.

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]

x = 8.5 ppm and the question is about [tex] \\ P(x>8.5)[/tex]=?  

Using [1]

[tex] \\ z = \frac{8.5 - 8.6}{1.3}[/tex]

[tex] \\ z = \frac{-0.1}{1.3}[/tex]

[tex] \\ z = -0.07692 \approx -0.08[/tex] (standard normal table has entries for two decimals places for z).

For [tex] \\ z = -0.08[/tex], is [tex] \\ P(z<-0.08) = 0.46812 \approx 0.4681[/tex].

But, we are asked for [tex] \\ P(z>-0.08) \approx P(x>8.5)[/tex].

[tex] \\ P(z<-0.08) + P(z>-0.08) = 1[/tex]

[tex] \\ P(z>-0.08) = 1 - P(z<-0.08)[/tex]

[tex] \\ P(z>-0.08) = 0.5319[/tex]

Thus, "the probability that one randomly selected city's waterway will have more than 8.5 ppm pollutants" is [tex] \\ P(z>-0.08) = 0.5319[/tex].

d. For the 38 cities, find the probability that the average amount of pollutants is more than 8.5 ppm.

Or [tex] \\ P(\overline{x} > 8.5)[/tex]ppm?

This random variable follows a standardized random variable normally distributed, i.e. [tex] \\ Z \sim N(0, 1)[/tex]:

[tex] \\ Z = \frac{\overline{X} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex] [2]

[tex] \\ z = \frac{\overline{8.5} - 8.6}{\frac{1.3}{\sqrt{38}}}[/tex]

[tex] \\ z = \frac{-0.1}{0.21088}[/tex]

[tex] \\ z = \frac{-0.1}{0.21088} \approx -0.47420 \approx -0.47[/tex]

[tex] \\ P(z<-0.47) = 0.31918 \approx 0.3192[/tex]

Again, we are asked for [tex] \\ P(z>-0.47)[/tex], then

[tex] \\ P(z>-0.47) = 1 - P(z<-0.47)[/tex]

[tex] \\ P(z>-0.47) = 1 - 0.3192[/tex]

[tex] \\ P(z>-0.47) = 0.6808[/tex]

Then, the probability that the average amount of pollutants is more than 8.5 ppm for the 38 cities is [tex] \\ P(z>-0.47) = 0.6808[/tex].

e. For part d), is the assumption that the distribution is normal necessary?

For this question, we do not need to assume that the distribution from we take the sample is normal. We already know that the distribution for X is normally distributed. Moreover, the distribution for [tex] \\ \overline{X}[/tex] is also normal because the sample was taken from a normal distribution. Additionally, the sample size is large enough to show a bell-shaped distribution.  

f. Find the IQR for the average of 38 cities.

We must find the first quartile (25th percentile), and the third quartile (75th percentile). For [tex]\\ P(z<0.25)[/tex], [tex] \\ z \approx -0.68[/tex], then, using [2]:

[tex] \\ -0.68 = \frac{\overline{X} - 8.6}{\frac{1.3}{\sqrt{38}}}[/tex]

[tex] \\ (-0.68 *0.21088) + 8.6 = \overline{X}[/tex]

[tex] \\ \overline{x} =8.4566[/tex]

[tex] \\ Q1 = 8.4566[/tex] ppm.

For Q3

[tex] \\ 0.68 = \frac{\overline{X} - 8.6}{\frac{1.3}{\sqrt{38}}}[/tex]

[tex] \\ (0.68 *0.21088) + 8.6 = \overline{X}[/tex]

[tex] \\ \overline{x} =8.7434[/tex]

[tex] \\ Q3 = 8.7434[/tex] ppm.

[tex] \\ IQR = Q3-Q1 = 8.7434 - 8.4566 = 0.2868[/tex] ppm

Therefore, the IQR for the average of 38 cities is [tex] \\ IQR = 0.2868[/tex] ppm. [tex] \\ Q1 = 8.4566[/tex] ppm and [tex] \\ Q3 = 8.7434[/tex] ppm.

Answer:

b. 1.15

Step-by-step explanation:

The z statistics is given by:

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

In which X is the found proportion, p is the expected proportion, and s, which is the standard error is [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Out of 53 teachers who replied to the survey, 13 claim they are satisfied with their job.

This means that [tex]X = \frac{13}{53} = 0.2453[/tex]

She find that the proportion of satisfied teachers nationally is 18.4%.

This means that [tex]p = 0.184[/tex]

Standard error:

p = 0.184, n = 53.

So

[tex]s = \sqrt{\frac{0.184*0.816}{53}} = 0.0532[/tex]

Z-statistic:

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

[tex]Z = \frac{0.2453 - 0.184}{0.0532}[/tex]

[tex]Z = 1.15[/tex]

The correct answer is:

b. 1.15

Answer:

when a straight line cuts two or more parallel lines then the angles forming on the side of transversal line exteriorly opposite to eachother is called exterior alternative angle.

for eg if AB //CD and EF is a transversal line meeting the parallel lines at G abd H then the exterior alternative angle are angle EGB = angle CHF and angle AGE=angle DHF are two pairs of exterior alternative angle .

hope its helpful to uh !!!!!!

Step-by-step explanation:

input x , output y

if x= x1 then y=y1 and y1 is the only value then it is a function

if we get multiple values of y then it is not a function

Answer: 18 (b)

Step-by-step explanation:

3x6=18

Answer:

18

Step-by-step explanation:

you can use a visual for a short answer or organize 3 dots in six groups, count in total

Answer:

The critical value of  [tex]f(\theta) = 6\cdot \cos \theta + 3\cdot \sin 2\theta[/tex] are given by [tex]\theta \approx 0.091\pi \pm 2\pi\cdot n[/tex] or [tex]\theta \approx 0.909\pi \pm 2\pi \cdot n[/tex], [tex]\forall \,n \in \mathbb{N}[/tex]

Step-by-step explanation:

The function to be evaluated is [tex]f(\theta) = 6\cdot \cos \theta + 3\cdot \sin 2\theta[/tex], the first derivative of the function must be taken in order to determine the set of critical numbers. Each derivative are found by using the differentiation rule for a sum of functions and rule of chain and subsequently simplified by trigonometric and algebraic means:

First derivative

[tex]f'(\theta) = - 6 \cdot \sin \theta +6\cdot \cos 2\theta[/tex]

[tex]f'(\theta) = -6\cdot \sin \theta + 2\cdot (\cos^{2}\theta-\sin^{2}\theta)[/tex]

[tex]f'(\theta) = -6\cdot \sin \theta + 2\cdot [(1-\sin^{2}\theta-\sin^{2}\theta)][/tex]

[tex]f'(\theta) = -6\cdot \sin \theta + 2\cdot (1-2\cdot \sin^{2}\theta)[/tex]

[tex]f'(\theta) = -6\cdot \sin \theta + 2 - 4\cdot \sin^{2}\theta[/tex]

[tex]f'(\theta) = -4\cdot \sin^{2}\theta - 6\cdot \sin \theta +2[/tex]

The procedure to determine the critical number of the given function are described briefly:

1) First derivative is equalised to zero.

2) The resultant equation is solved.

Then,

[tex]-4\cdot \sin^{2}\theta - 6\cdot \sin \theta +2 = 0[/tex]

Whose roots are:

[tex]\sin \theta_{1} \approx 0.281[/tex] and [tex]\sin \theta_{2} \approx -1.781[/tex]

The sine function is a continuous function with a range between 1 and -1, so, only the first root offers a realistic solution. In addition, such function is positive at first and second quadrants and has a periodicity of [tex]2\pi[/tex] radians, the family of critical values are determined by the unse of inverse trigonometric functions:

[tex]\theta \approx \sin^{-1} 0.281[/tex]

There are two subsets of solutions:

[tex]\theta \approx 0.091\pi \pm 2\pi\cdot n[/tex] or [tex]\theta \approx 0.909\pi \pm 2\pi \cdot n[/tex], [tex]\forall \,n \in \mathbb{N}[/tex]

Answer:

1 or 9.

Step-by-step explanation:

A coefficient is "a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (e.g. 4 in 4xy)".

So, in this case, the coefficient of 9x would be 9.

The coefficient of x^2 would be 1.

Hope this helps!

In the given quadratic expression 9x - 20 + x, 1, 9, and -20 are the coefficients.

In a quadratic expression of the standard form ax² + bx + c, x is the variable and a, b, and c are the numeric coefficients.

In the question, we are asked to identify the coefficients from the given quadratic expression 9x - 20 + x².

First, we try to express the given quadratic expression, 9x - 20 + x², in the standard form of a quadratic expression, ax² + bx + c.

Therefore, 9x - 20 + x² = x² + 9x - 20.

Comparing the expression x² + 9x - 20 with the standard form of a quadratic expression ax² + bx + c, we get a = 1, b = 9, c = -20.

We know that in a quadratic expression ax² + bx + c, x is the variable and a, b, and c are the numeric coefficients.

Thus, we can say that in the given quadratic expression 9x - 20 + x², 1, 9, and -20 are the coefficients.

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The point that is a solution to the inequality shown in the graph is:

A. (0,5).

The points that are on the region shaded in blue are solutions to the inequality.

(3,2) and (-3,-6) are on the dashed line, hence they are not solutions. Point (5,0) is to the right of the line, hence it is not a solution, and point (0,5) is a solution, meaning that option A is correct.

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Answer: B. Sameer did not use the correct equation

Step-by-step explanation:

12 IS three-fourths OF x

IS: equals

OF: multiplication

[tex]12=\dfrac{3}{4}x[/tex]

48 = 3x

16 = x

Answer:

it's b in Edg

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

p^2 -4p +4

Let p = -1

(-1)^1 -4(-1) +4

1 +4+4

9

Answer:

216 cm³

Step-by-step explanation:

The volume of a cube is denoted by V = s³, where s is the side length.

Here, the side length is 6 centimetres, so plug this into the formula to find V:

V = s³

V = 6³ = 6 * 6 * 6 = 216

The answer is thus 216 cm³.

~ an aesthetics lover

Answer:

216

Step-by-step explanation:

6³ = 216

Answer:

$2.06

Step-by-step explanation:

$2.99 x 6 = $17.94

$20.00 - $17.94 = $2.06

Hope this helps

Answer: $0.26

Step-by-step explanation:

Cost of 6 pens

= 2.99 x 6

= 17.94

Add sales tax at 10%,

= 17.94 x 1.1

= 19.74

Change due to me

= 20 - 19.74

= 0.26

Answer:

p = 2

Step-by-step explanation:

p + 4/p - 4

multiplying through by p,

p×p + 4/p ×p - 4×p

p² + 4 - 4p = 0

p² - 4p + 4 = 0

factorizing,

p(p - 2) -2(p - 2) =0

(p -2)(p -2) =0

p-2 =0

p=2

Answer:

a) 32

b) none?

c) C & F

D) 9/5, 32?

Step-by-step explanation:

Answer:

a) [tex]P(X=2)=(4C2)(0.375)^2 (1-0.375)^{4-2}=0.330[/tex]  

b) [tex]P(X\geq 2)=1-P(X< 2)=1-[P(X=0)+P(X=1)][/tex]

[tex]P(X=0)=(4C0)(0.375)^0 (1-0.375)^{4-0}=0.153[/tex]  

[tex]P(X=1)=(4C1)(0.375)^1 (1-0.375)^{4-1}=0.366[/tex]  

And replacing we got:

[tex]P(X\geq 2)=1-P(X< 2)=1-[0.153+0.366]=0.481[/tex]

Step-by-step explanation:

Let X the random variable of interest, on this case we now that:  

[tex]X \sim Binom(n=4, p=0.375)[/tex]  

The probability mass function for the Binomial distribution is given as:  

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

Where (nCx) means combinatory and it's given by this formula:  

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]  

Part a

[tex]P(X=2)=(4C2)(0.375)^2 (1-0.375)^{4-2}=0.330[/tex]  

Part b

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

[tex]P(X=0)=(4C0)(0.375)^0 (1-0.375)^{4-0}=0.153[/tex]  

[tex]P(X=1)=(4C1)(0.375)^1 (1-0.375)^{4-1}=0.366[/tex]  

And replacing we got:

[tex]P(X\geq 2)=1-P(X< 2)=1-[0.153+0.366]=0.481[/tex]

Answer:

The answer to the best prediction is 115.04

Step-by-step explanation:

We have to:

x = 102

They also tell us that:

y = 5.9 + 1.07 * x

If we replace we have:

y = 5.9 + 1.07 * (102)

y = 115.04

Therefore, the best predicted value of ModifyingAbove and with caret given that the older child has an IQ of 102 is 115.04

Answer:

C

Step-by-step explanation:

The reason we can use this method is because we are given a composite figure with a house shape with one triangle on top. We can use the guidance of the dotted lines to make out that a rectangle can be used to find the figure. We can see that apart from the figure, there are two congruent triangles. To find the area we would do -

First find the missing height of the smaller triangles. We would use the pythagorean theorem to find that the missing height is√5

We could do 8(4) = 32 to find the area of the rectangle.

Then, we could do 2√5/2 to find one missing triangle. We could then add the triangles to find the measures of the combined triangles as 2√5. Then, we could do 32 - 2√5 to find the area as 27.5.

Hope this helps :)

Answer:

it is A,B,D

Step-by-step explanation:

i got it right on edge

Answer:

The solution:

X = 16 and Y = -6

Step-by-step explanation:

The equations to be solved are:

x+y = 10 ------- equation 1

x+2y = 4 ----------- equation 2

we can multiply equation 1 by -1 to make the value of x and y negative.

This will give us

-x- y = - 10 ------- equation 3

x+2y = 4 ----------- equation 2

We will now add equations 3 and 2 together so that x will cancel itself out.

this will give us

y = -10 +4 = -6

hence, we have the value of y as -6.

To get the value of x, we can put this value of y into any of the equations above.  (I will use equation 1)

x - 6 = 10

from this, we have that x = 4

Therefore, we have our answer as

X = 16 and Y = -6

Answer:

  82.5%

Step-by-step explanation:

It helps to start with the correct formula:

  f(x) = ((6)(1.0) +x(0.3))/(6 +x) . . . . parentheses are required

Then f(2) is ...

  f(2) = (6 +.3(2))/(6+2) = 6.6/8

  f(2) = 82.5%