A certain process for manufacturing integrated circuits has been in use for a period of time, and it is known that 12% of the circuits it produces are defective. A new process that is supposed to reduce the proportion of defectives is being tested. In a simple random sample of 100 circuits produced by the new process, 12 were defective. a. One of the engineers suggests that the test proves that the new process is no better than the old process, since the proportion of defectives in the sample is the same. Is this conclusion justified? Explain. b. Assume that there had been only 11 defective circuits in the sample of 100. Would this have proven that the new process is better? Explain. c. Which outcome represents stronger evidence that the new process is better: finding 11 defective circuits in the sample, or finding 2 defective circuits in the sample?

Answer:

0.5 is the probability that a randomly selected home will have a Jacuzzi given that it has a swimming pool.              

Step-by-step explanation:

We are given the following in the question:

S: Homes in Miami have a swimming pool

J: Homes in Miami have a jacuzzi

[tex]P(S) = 60\% = 0.6\\P(S\cap J) = 30\% = 0.3[/tex]

We have to find the probability that a randomly selected home will have a Jacuzzi given that it has a swimming pool.

Thus, we have to calculation the conditional probability of having a jacuzzi given the house has a swimming pool.

[tex]P(J|S) = \dfrac{P(J\cap S)}{P(S)}\\\\P(J|S) = \displaystyle\frac{0.3}{0.6} = 0.5[/tex]

0.5 is the probability that a randomly selected home will have a Jacuzzi given that it has a swimming pool.

Answer:

[tex]x + 3y -z - 3 = 0[/tex]      

Step-by-step explanation:

We have to find the equation of plane that is parallel to the vectors

[tex]\langle 3,0,3\rangle, \langle0,1,3\rangle[/tex]

The plane also passes through the point (2,0,-1).

Hence, the equation of plane s given by:

[tex]\displaystyle\left[\begin{array}{ccc}x-2&y-0&z+1\\3&0&3\\0&1&3\end{array}\right]\\\\=(x-2)(0-3) - (y-0)(9-0) + (z+1)(3-0)\\=-3(x-2)-9y+3(z+1)\\\Rightarrow -3x + 6 - 9y + 3z + 3 = 0\\\Rightarrow 3x + 9y -3z -9 = 0\\\Rightarrow x + 3y -z - 3 = 0[/tex]

It is the required equation of plane.

Answer:

a) a binomial distribution with mean 50

Step-by-step explanation:

Given that an  airplane has a front nad a rear door that are bother opened to allow passengers to exit when the plane lands. the plane has 100 passengers.

These 100 passengers can select either back door or front door with equal probability (assuming)

so probability for selecting front door = 0.5

No of passengers =100

Each passenger is independent of the other

Hence X no of passengers exiting through the front door is binomial with

p =0.5 and n =100

Mean of the variable X = np = 100(0.5) = 50

Variance of X = 100(0.5)(0.5)

Hence std dev = 10(0.5) = 5

So correct answers are

a) a binomial distribution with mean 50

Answer:

Step-by-step explanation:

Check the attachment for the solution

Answer:

Step-by-step explanation:

The objective is to determine which of the following matrices are in reduced echelon form and which others are only in echelon form. The given matrices are

                       [tex]\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0& 2 & 0 & 0 \\ 0& 0 & 1 & 1 \end{bmatrix}[/tex],  [tex]\begin{bmatrix} 1 & 0 & 1 & 1 \\ 0& 1& 1 & 1 \\ 0& 0 & 0 & 0 \end{bmatrix}[/tex]  and   [tex]\begin{bmatrix} 0& 0 & 0 & 0 \\ 1& 3 & 0 & 0 \\ 0& 0 & 1 & 0 \\ 0& 0 & 0 & 1 \end{bmatrix}[/tex].

First, recall what is an echelon and reduced echelon form of a matrix.

A matrix is said to be in a Echelon form if

A matrix is said to be in  a Reduced Echelon form if

A column that contains a leading 1 which is the only non-zero element is called a pivot column.

Now, let's have a look at the first matrix

                                 [tex]\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0& 2 & 0 & 0 \\ 0& 0 & 1 & 1 \end{bmatrix}[/tex]

As we can see, it doesn't have any zero rows. Each leading entry in a row is placed to the right of the leading entry from the row above and all elements below the leading entries in all columns are equal to zero. Therefore, this matrix is in an Echelon form.

In the second row, the leading entry is 2, not 1, so because of the first property of the Reduced Echelon form, it is not in a Reduced Echelon form.

Notice that it can be transformed to the Reduced Echelon form by multiplying the second row by [tex]\frac{1}{2}.[/tex]

The second matrix is

                                         [tex]\begin{bmatrix} 1 & 0 & 1 & 1 \\ 0& 1& 1 & 1 \\ 0& 0 & 0 & 0 \end{bmatrix}[/tex]

There is a zero row, and all non-zero rows are placed above it. Each leading entry in a row, which is the first non-zero entry, is placed to the right of the entry of the row above it and all elements below the leading entry are equal to zero in each column, so it is in the Echelon form.

It is also in the Reduced Echelon form, since all non-zero rows the leading entry is 1 and it is the only non zero element in each column.

The least given matrix is

                                        [tex]\begin{bmatrix} 0& 0 & 0 & 0 \\ 1& 3 & 0 & 0 \\ 0& 0 & 1 & 0 \\ 0& 0 & 0 & 1 \end{bmatrix}[/tex]

This matrix doesn't satisfy the condition that if there is any zero-row, it must be below all other non-zero rows, so it is not in Echelon form.

A matrix that is not in an Echelon form, it is not in an Reduced Echelon form either.

Therefore, this matrix is not in an Reduced Echelon form.

Answer:

The x-coordinate of the solution to this system of equations is 1.

Step-by-step explanation:

Given,

[tex]6x - 5y = 5\\\\3x + 5y = 4[/tex]

We have to find out the x-coordinate of the equation.

Solution,

Let [tex]6x-5y=5\ \ \ \ equation\ 1[/tex]

Again let [tex]3x+5y=4\ \ \ \ \ equation \ 2[/tex]

Now using elimination method we will solve the equations.

For this we will add equation 1 and equation 2 and get;

[tex](6x-5y)+(3x+5y)=5+4\\\\6x-5y+3x+5y=9\\\\9x=9[/tex]

Now on dividing both side by '9' we get;

[tex]\frac{9x}{9}=\frac{9}{9}\\\\x=1[/tex]

Hence The x-coordinate of the solution to this system of equations is 1.

1

ur welcome homie

poggers

Answer: Area of triangle is √3 / 2

Step-by-step explanation:

The explanation can be found in the attached in picture

Answer: You have only provided one Differential Equation (DE), it looks like you intended listing more.

The equation you wrote contains an incorrect d²x/dt, it is likely to be d²x/dt² + 5dx/dt + 10x = 0, which is linear. Unless it is (dx/dt)² + 5dx/dt + 10x = 0, then it is nonlinear.

Not to worry though, I will explain what linear and nonlinear DE's are.

Step-by-step explanation:

LINEAR DE: This is the kind of DE in which the functions of the dependent variable are linear. There are no powers of the dependent variable and/or its derivatives, there are no products of the dependent variable and its derivative, there are no functions of the dependent variable like cos, sin, exp, etc.

Example:

* 5d²x/dt² + dx/dt - x = 2t

This is linear, as it satisfies all the conditions.

NONLINEAR DE: If any condition explained for linear DE is not satisfied, then it is called nonlinear.

Example:

* d²x/dt² - sinx = 0

This is nonlinear because of the presence of sinx.

* d²x/dt² + xdx/dt = 0

This is nonlinear because of the product of the dependent variable, x, and its derivative, dx/dt.

* d²x/dt² + x² = 0

This is nonlinear because a function of the dependent variable is not linear. You shouldn't have x².

* (dx/dt)³ + 3dx/dt = 0 is equally nonlinear. You can't have nonlinear functions of the dependent variable or its derivatives.

I hope this helps answer the remaining parts of your question.

Answer:

For x=45

sample proportion=45/140=0.321

z=(0.321-0.30)/sqrt(0.3*(1-0.3)/140)

z=0.54

For x=47

sample proportion=47/140=0.336

z=(0.336-0.30)/sqrt(0.3*(1-0.3)/140)

z=0.93

Now,

P(0.54<z<0.93)=P(z<0.93)-P(z<0.54)

=0.8238-0.7054

=0.118

So,correct option is 0.119

If the coefficient matrix has a pivot in each column, it means that it is shaped like this:

[tex]A=\left[\begin{array}{cccc}a_{1,1}&a_{1,2}&a_{1,3}&a_{1,4}\\0&a_{2,2}&a_{2,3}&a_{2,4}\\0&0&a_{3,3}&a_{3,4}\\0&0&0&a_{4,4}\end{array}\right][/tex]

So, the correspondant system

[tex]Ax = b[/tex]

will look like this:

[tex]\left[\begin{array}{cccc}a_{1,1}&a_{1,2}&a_{1,3}&a_{1,4}\\0&a_{2,2}&a_{2,3}&a_{2,4}\\0&0&a_{3,3}&a_{3,4}\\0&0&0&a_{4,4}\end{array}\right]\cdot \left[\begin{array}{c}x_1\\x_2\\x_3\\x_4\end{array}\right] = \left[\begin{array}{c}b_1\\b_2\\b_3\\b_4\end{array}\right][/tex]

This turn into the following system of equations:

[tex]\begin{cases}a_{1,1}x_1+a_{1,2}x_2+a_{1,3}x_3+a_{1,4}x_4=b_1\\a_{2,2}x_2+a_{2,3}x_3+a_{2,4}x_4=b_2\\a_{3,3}x_3+a_{3,4}x_4=b_3\\a_{4,4}x_4=b_4\end{cases}[/tex]

The last equation is solvable for [tex]x_4[/tex]: we easily have

[tex]x_4=\dfrac{b_4}{a_{4,4}}[/tex]

Once the value for [tex]x_4[/tex] is known, we can solve the third equation for [tex]x_3[/tex]:

[tex]x_3 = \dfrac{b_3-a_{3,4}x_4}{a_{3,3}}[/tex]

(recall that [tex]x_4[/tex] is now known)

The pattern should be clear: you can use the last equation to solve for [tex]x_4[/tex]. Once it is known, the third equation involves the only variable [tex]x_3[/tex]. Once

Answer:

See the proof below.

Step-by-step explanation:

We can define a basis of V with the following elements:

[tex]X_1=\begin{matrix}1 & 0 \\0 & 0 \end{matrix} [/tex]

[tex]X_2=\begin{matrix}0 & 1 \\0 & 0 \end{matrix} [/tex]

[tex]X_3=\begin{matrix}0 & 0 \\1 & 0 \end{matrix} [/tex]

[tex]X_4=\begin{matrix}0 & 0 \\0 & 1 \end{matrix} [/tex]

So then if we define the basis X as following:

[tex] X = [X_1, X_2, X_3, X_4][/tex]

[tex]X =[\begin{pmatrix}1 & 0\\0 & 0\end{pmatrix},\begin{pmatrix}0 & 1\\0 & 0 \end{pmatrix},\begin{pmatrix}0 & 0\\1 & 0\end{pmatrix},\begin{pmatrix}0 & 0\\0 & 1 \end{pmatrix}[/tex]

We see the the dimension for X is 4 [tex] dim (V) = 4[/tex] since the basis have a dimension of 4 [tex] dim (X) =4[/tex]

Final answer:

The vector space V of all 2 x 2 matrices over a field F has a basis consisting of four matrices which are linearly independent and span V. This basis demonstrates that V has a dimension of 4.

Explanation:

In order to prove that the vector space V of all 2 x 2 matrices over a field F has dimension 4, we need to exhibit a basis for V that consists of four linearly independent elements, which also span V. Consider the following 2 x 2 matrices as the candidate basis elements:

These matrices are linearly independent and span the vector space of all 2 x 2 matrices. To show linear independence, assume that a linear combination of these matrices equals the zero matrix:

a ⬑ 1 0 ⬑ + b ⬑ 0 1 ⬑ + c ⬑ 0 0 ⬑ + d ⬑ 0 0 ⬑
⬑ 0 0 ⬑   ⬑ 0 0 ⬑   ⬑ 1 0 ⬑   ⬑ 0 1 ⬑
= ⬑ 0 0 ⬑
⬑ 0 0 ⬑

This equation leads to a = b = c = d = 0, which verifies the linear independence. Since we can represent any 2 x 2 matrix as a linear combination of these four basis matrices, they also span V, fulfilling both criteria for a basis. Hence, there are four basis elements, and therefore, the dimension of V is 4.

Answer:

I'm pretty sure it would be 345, just add the two 178 and 167

Answer:

A relationship is said to have direct variation when one variable changes and the second variable changes proportionally; the ratio of the second variable to the first variable remains constant. For example, when y varies directly as x, there is a constant, k, that is the ratio of y:x.

Answer:

For the set X = {a, b, c}, the following three relations satisfy the required conditions in (a), (b) and (c) respectively.

(a) R = {(a,a), (b,b), (c, c), (a, b), (b, a), (b, c), (c, b)} is reflexive and symmetric but not transitive .

(b) R = {(a, a), (b, b), (c, c), (a, b)} is reflexive and transitive but not symmetric .

(c) R = {(a,a), (a, b), (b, a)} is symmetric and transitive but not reflexive .

Step-by-step explanation:

Before, we go on to check these relations for the desired properties, let us define what it means for a relation to be reflexive, symmetric or transitive.

Given a relation R on a set X,

R is said to be reflexive if for every [tex]a \in X, (a,a) \in R[/tex].

R is said to be symmetric if for every [tex](a, b) \in R, (b, a) \in R[/tex].

R is said to be transitive if [tex](a, b) \in R[/tex] and [tex](b, c) \in R[/tex], then [tex](a, c) \in R[/tex].

(a) Let R = {(a,a), (b,b), (c, c), (a, b), (b, a), (b, c), (c, b)}.

Reflexive: [tex](a, a), (b, b), (c, c) \in R[/tex]

Therefore, R is reflexive.

Symmetric: [tex](a, b) \in R \implies (b, a) \in R[/tex]

Therefore R is symmetric.

Transitive: [tex](a, b) \in R \ and \ (b, c) \in R[/tex] but but (a,c) is not in  R.

Therefore, R is not transitive.

Therefore, R is reflexive and symmetric but not transitive .

(b) R = {(a, a), (b, b), (c, c), (a, b)}

Reflexive: [tex](a, a), (b, b) \ and \ (c, c) \in R[/tex]

Therefore, R is reflexive.

Symmetric: [tex](a, b) \in R \ but \ (b, a) \not \in R[/tex]

Therefore R is not symmetric.

Transitive: [tex](a, a), (a, b) \in R[/tex] and [tex](a, b) \in R[/tex].

Therefore, R is transitive.

Therefore, R is reflexive and transitive but not symmetric .

(c) R = {(a,a), (a, b), (b, a)}

Reflexive: [tex](a, a) \in R[/tex] but (b, b) and (c, c) are not in R

R must contain all ordered pairs of the form (x, x) for all x in R to be considered reflexive.

Therefore, R is not reflexive.

Symmetric: [tex](a, b) \in R[/tex] and [tex](b, a) \in R[/tex]

Therefore R is symmetric.

Transitive: [tex](a, a), (a, b) \in R[/tex] and [tex](a, b) \in R[/tex].

Therefore, R is transitive.

Therefore, R is symmetric and transitive but not reflexive .

Relation from the set of two variables is subset of certain product. The relation for the condition are,

[tex]R_1\;\;\;\;\ (1,1), (1,2),,(2,1), (2,2),(2,3)((3,2),3,3)[/tex]

[tex]R_2\;\;\;\;\ (1,1), (2,2),,(3,3)(1,3)3,1)[/tex]

[tex]R_3\;\;\;\;\ (1,2),,(2,1), ,(2,3)((3,2)[/tex]

Relation from the set of two variables is subset of certain product. Relation are of three types-

1) Reflexive and symmetric but not transitive -

Let a data set as,

[tex]X=1,2,3[/tex]

For the data set the relation can be given as,

[tex]R_1\;\;\;\;\ (1,1), (1,2),,(2,1), (2,2),(2,3)((3,2),3,3)[/tex]

[tex]R_1[/tex] is reflexive as it can be represent as [tex]R_1(a,a)[/tex] for,

[tex]a=1,2,3, \;\;\;\;\; [/tex]

[tex]a[/tex] ∈ [tex]X[/tex]

[tex]R_1[/tex] is symmetric as it can be represent as [tex]R_1(a,b)[/tex] for,

[tex]a,b \;\;\;\;(1,2) (2,1)[/tex]

[tex]a,b[/tex] ∈ [tex]X[/tex]

[tex]R_1[/tex] is not transitive as it can be represent as [tex]R_1\neq (a,c)[/tex] .

[tex]a,c\neq \;\;\;\;(1,3) (3,1)[/tex]

2)  Reflexive and transitive but not symmetric

Let a data set as,

[tex]X=1,2,3[/tex]

For the data set the relation can be given as,

[tex]R_2\;\;\;\;\ (1,1), (2,2),,(3,3)(1,3)3,1)[/tex]

[tex]R_2[/tex] is reflexive as it can be represent as [tex]R_2(a,a)[/tex] for,

[tex]a=1,2,3, \;\;\;\;\; [/tex]

[tex]a[/tex] ∈ [tex]X[/tex]

[tex]R_1[/tex] is transitive as it can be represent as [tex]R_1(a,c)[/tex] for,

[tex]a,c \;\;\;\;(1,3) (3,1)[/tex]

[tex]a,c[/tex] ∈ [tex]X[/tex]

[tex]R_1[/tex] is not symmetric as it can be represent as [tex]R_1\neq (a,b)[/tex] .

[tex]a,b\neq \;\;\;\;(1,2) (2,1)[/tex]

3) Symmetric and transitive but not reflexive

Let a data set as,

[tex]X=1,2,3[/tex]

For the data set the relation can be given as,

[tex]R_3\;\;\;\;\ (1,2),,(2,1), ,(2,3)((3,2)[/tex]

[tex]R_1[/tex] is symmetric as it can be represent as [tex]R_3(a,b)[/tex] for,

[tex]a,b=(1,2),(2,1) \;\;\;\;\; [/tex]

[tex]a,b[/tex] ∈ [tex]X[/tex]

[tex]R_3[/tex] is transitive as it can be represent as [tex]R_3(a,c)[/tex] for,

[tex]a,c \;\;\;\;(1,3) (3,1)[/tex]

[tex]a,c[/tex] ∈ [tex]X[/tex]

[tex]R_1[/tex] is not reflexive as it can be represent as [tex]R_3\neq (a,a)[/tex] .

[tex]a,a\neq \;\;\;\;(1,1) [/tex]

Thus the relation for the condition are,

[tex]R_1\;\;\;\;\ (1,1), (1,2),,(2,1), (2,2),(2,3)((3,2),3,3)[/tex]

[tex]R_2\;\;\;\;\ (1,1), (2,2),,(3,3)(1,3)3,1)[/tex]

[tex]R_3\;\;\;\;\ (1,2),,(2,1), ,(2,3)((3,2)[/tex]

Learn more about the Reflexive, symmetric and transitive relation here;

https://brainly.com/question/1581464

Answer:  (16.9914, 28.2286).

Step-by-step explanation:

The formula to find the confidence interval for population mean is given by :-

[tex]\overline{x}\pm z^*\dfrac{\sigma}{\sqrt{n}}[/tex]

, where [tex]\overline{x}[/tex] = Sample mean

[tex]\sigma[/tex]= Population standard deviation

n= Sample size.

z* = Critical value.

Let μ be the mean change in score  in the population of all high school seniors.

As per given ,  we have

n= 350

[tex]\overline{x}=22.61[/tex]

[tex]\sigma=53.63[/tex]

The critical z-value for 95% confidence interval is z*= 1.96 [From z-table]

Substitute all the value in formula , we get

[tex]22.61\pm (1.96)\dfrac{53.63}{\sqrt{350}}[/tex]

[tex]=22.61\pm (1.96)\dfrac{53.63}{18.708287}[/tex]

[tex]=22.61\pm (1.96)(2.8666)[/tex]

[tex]=22.61\pm (5.6186)[/tex]

[tex]=(22.61-5.6186,\ 22.61+5.6186) =(16.9914,\ 28.2286)[/tex]

Hence, the 95% confidence interval for [tex]\mu[/tex] is (16.9914, 28.2286).

Answer:

The answer is B

Step-by-step explanation:

Answer:

B. The second graph

Step-by-step explanation:

edge 2021 math assignment

Answer:

5

Step-by-step explanation:

Assuming both players can answer the same question, the minimum number of questions is the smallest number that when multiplied by either 0.60 or 0.80 yields a whole number.

Let x be the number of questions, solving by trial and error:

[tex]if\ x=2\\x*0.8=1.6\\x*0.6=1.2\\\\if\ x=3\\x*0.8=2.4\\x*0.6=1.8\\\\if\ x=4\\x*0.8=3.2\\x*0.6=2.4\\\\if\ x=5\\x*0.8=4\\x*0.6=3\\\\[/tex]

Therefore, the minimum number of questions in the game is 5.

To find the minimum number of questions in a game where one person answers 80% correctly and another answers 60% correctly, calculate the LCM of the fractions' denominators. The result is 5 questions.

You and your friend have different accuracy rates when answering questions in a game. You answer 80% of the questions correctly, while your friend answers 60% of the questions correctly. To find the minimum number of questions in the game, we need to ensure that both percentages can correspond to whole numbers of questions.

In a game with 5 questions:

Therefore, the minimum number of questions in this game is 5.

Answer:

The margin of error of the poll is 8%.

Step-by-step explanation:

This is a confidence interval. A confidence interval has both a lower end and an upper end.

The true proportion is the midpoint between the two ends.

The margin of error is the absolute difference between the proportion and the ends(which is the same, upper end - proportion = proportion - lower end),

In this problem, we have that:

The lower end is 52%.

The upper end is 68%.

The proportion is (52 + 68)/2 = 60%.

The margin of error is 60 - 52 = 68 - 60 = 8%.

Answer:

dont see much information here but as far as lawsuits go id aim for the highest answer

Step-by-step explanation:

_____________________________________

Answer:

2(x+6)(x-3)

Step-by-step explanation:

Factor the GCF out of the trinomial on the left side of the equation.

[tex]2x^2 + 6x - 36 =2(x^2 + 3x - 18)[/tex]

Greatest common factor of 2, 6, 18 is 2

so GCF is 2

divide each term when we take out GCF 2

so [tex]2(x^2 + 3x - 18)[/tex]

now factor the trinomial

product is -18 and sum is +3

6 times -3 is -18  and 6-3=3

[tex]2(x^2+3x-18)\\2(x+6)(x-3)[/tex]

Answer:

all work is shown and pictured

Answer:The total cost of the Sony Playstation is $179.9096

Step-by-step explanation:

The initial or regular cost of the Sony Playstation is $172.99.

The tax rate is 4%. Therefore, the value of the sales tax would be

4/100 × 172.99 = 0.04 × 172.99 = $6.9196

The total cost of the Sony Playstation would be the sum of the regular price and the sales tax. It becomes

172.99 + 6.9196 = $179.9096

Answer:

Central angle= 1.15 radians

Step-by-step explanation:

[tex]Arc\,\,length=s= 1.22\,m\\Radius=r=1.06\,m\\\\Central\,\, angle=\theta=?\\\\Using\\\\ s=r\theta\\\\\theta=\frac{s}{r}\\\\\theta= \frac{1.22}{1.06}\\\\\theta=1.15 \,rad[/tex]

Answer:

a) No it doesn't mean that linear model is inappropriate

b) No. The prediction using this model will not be accurate.

Step-by-step explanation:

a)

For answering this part, firstly consider the concept of [tex]R^{2}[/tex]

The [tex]R^{2}[/tex] also known as coefficient of determination is used to determine the amount of variability in dependent variable is explained by the linear model. Lower [tex]R^{2}[/tex] depicts that less variation of dependent is explained by the independent variable using the linear model. The linearity of model is determined by scatter plot. Thus, if the [tex]R^{2}[/tex] is lower, it doesn't mean that linear model is inappropriate.

b)

The predictions made by the model having lower [tex]R^{2}[/tex] value are erroneous. The model is used for prediction if the linear model explains the larger portion of variability in dependent variation. If the predictions made from the model that have lower [tex]R^{2}[/tex] value then the predicted values will not be close to the actual value and thus residuals will not be minimum as residuals are the difference of actual and predicted values.

Answer:

2.95 cent

Step-by-step explanation:

1 gallon = 231 cubic inches

1 litre = 1000ml = 61.0237 cubic inches

1 galloon = 231 / 61.0237 = 3.7854118 liters

if Carol paid $0.78 per litre

1 galloon = 0.78 x 3.7854118 = 2.952621204 ≅ 2.95 cent

Answer:

[tex] [tex] lim_{x \to 8} (1+3\sqrt{x})(1-6x^2 +x^3)[/tex]=[tex]1-384 +512+3\sqrt{8} -18(8)^{5/2} +3 (8)^{7/2} =1223.601[/tex]

And the limit on this case exists.

Step-by-step explanation:

We want to find the following limit:

[tex] lim_{x \to 8} (1+3\sqrt{x})(1-6x^2 +x^3)[/tex]

First we can distribute the polynomials like this:

[tex] lim_{x \to 8} (1-6x^2 +x^3+3\sqrt{x} -18 x^{5/2} +3x^{7/2})[/tex]

And Now we can use the distributive property for the limit and we got:

[tex] lim_{x \to 8} 1 - 6 lim_{x \to 8} x^2 + lim_{x \to 8} x^3 +3 lim_{x \to 8} \sqrt{x} -18 lim_{x \to 8} x^{5/2} + 3 lim_{x \to 8} x^{7/2}[/tex]

And now we can evaluate the limit and we got:

[tex] [tex] lim_{x \to 8} (1+3\sqrt{x})(1-6x^2 +x^3)[/tex]=[tex]1-384 +512+3\sqrt{8} -18(8)^{5/2} +3 (8)^{7/2} =1223.601[/tex]

And the limit on this case exists.

To solve limit problems in mathematics, limit laws are often very useful. In this specific case, as the function is a polynomial and defined for all real number values, a direct substitution of x=8 into the function is sufficient. Therefore, the limit as x approaches 8 for function 1 + 3x5 - 6x2 + x3 is calculable.

In the field of mathematics, limit laws are used quite frequently for evaluating limits. In this case, we want to calculate the limit as x approaches 8 for the function 1 + 3x5 - 6x2 + x3.

For a given polynomial function like this one, an easy and very straightforward approach is to substitute the value x is approaching (in this scenario, x = 8) directly into the polynomial function.

So, after substitution, our function becomes: 1 + 3*(8)^5 - 6*(8)^2 + (8)^3. Simplifying it further, the limit as x approaches 8 of this function gives us a definite numeric value.

Always remember while applying limit laws, you might at times need the limit laws to evaluate complex limit problems but in this given scenario, direct substitution works perfectly fine because this polynomial function is defined for all real number values of X.

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Answer:

Step-by-step explanation:

Since quality points to letter grades are A=​4; B=​3; C=​2; D=​1; F=0, weighted mean is the sum of the qulity points times corresponding credit hours divided by the total credit hours:

[tex]\frac{(4*4) + (1*2) + (4*2) + (2*3) + (3*1)}{12}[/tex] ≈ 2.92

Since 2.92<3.0, the student is not in Dean's list.

Answer:

There is a 40.96% probability that he answers exactly 1 question correctly in the last 4 questions.

Step-by-step explanation:

For each question, there are only two possible outcomes. Either it is correct, or it is not. This means that we use the binomial probability distribution to solve this problem.

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 combinatios 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.

In this problem we have that:

There are four questions, so n = 4.

Each question has 5 options, one of which is correct. So [tex]p = \frac{1}{5} = 0.2[/tex]

What is the probability that he answers exactly 1 question correctly in the last 4 questions?

This is [tex]P(X = 1)[/tex]

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

[tex]P(X = 1) = C_{4,1}*(0.2)^{1}*(0.8)^{3} = 0.4096[/tex]

There is a 40.96% probability that he answers exactly 1 question correctly in the last 4 questions.

Answer:

0.41

Step-by-step explanation:

kahn

The result is [tex]\frac{4}{7}[/tex]

Step-by-step explanation:

In this problem, we are asked to find how many 7/8 cup servings are in 1/2 of a cup of juice.

Mathematically, this is equivalent to divide 1/2 by 7/8. So we can write:

[tex]\frac{1/2}{7/8}[/tex]

This can be rewritten as a multiplication by reversing the denominator:

[tex]\frac{1}{2}\cdot \frac{8}{7}[/tex]

Now we can perform the multiplication of both the numerator and the denominator:

[tex]\frac{1\cdot 8}{2\cdot 7}=\frac{8}{14}[/tex]

And simplifying (dividing by 2),

[tex]\frac{8}{14}=\frac{4}{7}[/tex]

Learn more about  fractions:

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There are 4/7 servings of 7/8 cup in 1/2 cup of juice.

To determine the number of 7/8 cup servings in 1/2 of a cup of juice, divide the 1/2 cup of juice by 7/8 cup.

Now, the reciprocal of 7/8 and multiplying it by 1/2.

Reciprocal of 7/8 = 8/7

Now, perform the multiplication:

= (1/2 cup) * (8/7)

= (1 * 8) / (2 * 7)

= 8/14

= 4/7

Therefore,4/7 servings of 7/8 cup in 1/2 cup of juice.

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Answer:

D) 0.0902

Step-by-step explanation:

Data provided in the question:

Probability of burglary, p = [tex]\frac{661}{400,000}[/tex]

= 0.00165      

q = 1 - p                

or                    

q = 1 - 0.00165                      

or                    

q = 0.99835                              

Now,

P(r ≥ 2) = 1 - P(r < 2)

= 1 - [ P(0) + P(1) ]

= 1 - [  [tex]^{317}C_0(0.00165)^0(0.99835)^{317-0}+^{317}C_1(0.00165)^1(0.99835)^{317-1}[/tex] ]

[ as P(x) = [tex]^nC_rp^rq^{n-r}[/tex]]

= 1 - [ 0.593 + 0.3168]

= 1 - 0.9098

= 0.0902

Hence,

Option (D) 0.0902

Answer:its A

Step-by-step explanation:it was

Answer: a. 0.40   b. 0.23  c . 0.435   d . 0.25

Step-by-step explanation:

                                   melanin      content    Total

                                            high   low

moisture   high                     13      10                23

content    low                       47      30                77

 Total                                   60      40               100

Let A denote the event that a sample has low melanin content, and let B denote the event that a sample has high moisture content.

a) Total skin samples has low melanin content = 10+30=40

P(A)=[tex]\dfrac{40}{100}=0.40[/tex]

b) Total skin samples has high moisture content = 13+10=23

P(B) =[tex]\dfrac{23}{100}=0.23[/tex]

c) A ∩ B =  Total skin samples has both low melanin content and high moisture content =10

P(A ∩ B) =[tex]\dfrac{10}{100}=0.10[/tex]

Using conditional probability formula , [tex]P (A|B)=\dfrac{P(A\cap B)}{P(B)}[/tex]

[tex]P (A|B)=\dfrac{0.10}{0.23}=0.434782608696\approx0.435[/tex]

d)  [tex]P (B|A)=\dfrac{P(A\cap B)}{P(A)}[/tex]

[tex]P (B|A)=\dfrac{0.10}{0.40}=0.25[/tex]