Suppose that the number of a certain type of computer that can be sold when its price is P (in dollars) is given by a linear function N(P). (a) Determine N(P) if N(1000) = 10000 and N(1700) = 5800. (Use symbolic notation and fractions where needed.) N(P) = (b) Select the statement that gives the slope of the graph of N(P), including units and describes what the slope represents. 6 computers per dollar -6 dollars per computer computers per dollar -6 computers per dollar (c) What is the change AN in the number of computers sold if the price is increased by AP = 110 dollars? (Give your answer as a whole number.) AN = computers

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]

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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:

The world population in 2030 will be of 9.0062 billion.

The would population in 2060 will be of 13.71 billion.

Step-by-step explanation:

The exponential model for population growth is as follows.

[tex]P(t) = P(0)e^{rt}[/tex]

In which P(t) is the population in t years from now, P(0) is the population in the current year and r(decimal) is the growth rate.e = 2.71 is the Euler number.

If the world population is 7.0 billion in 2012.

2012 is the initial year, so P(0) = 7.

P(t) will be measured in billions of people.

The growth rate is constant at 1.4%.

This means that [tex]r = 0.014[/tex]

Calculate the population in 2030.

2030 is 2030-2012 = 18 years after 2012, so this is P(18).

[tex]P(t) = 7e^{rt}[/tex]

[tex]P(18) = 7e^{0.014*18} = 9.0062[/tex]

So the world population in 2030 will be of 9.0062 billion.

What will be the population in 2060.

This is 2060-2012 = 48 years after 2012. So this is P(48).

[tex]P(t) = 7e^{rt}[/tex]

[tex]P(48) = 7e^{0.014*48} = 13.71[/tex]

The would population in 2060 will be of 13.71 billion.

Answer:

1) The equation of a line is  [tex]y=-\frac{1}{2}x+\frac{17}{2}[/tex].

2) The equation of the line that passes through the points (2,4) and (3,7) is [tex]y=3x-2[/tex]

3) The equation of the line that has slope m = −2 and y-intercept equal to -1 is [tex]y=-2x-1[/tex]

4) The slope-intercept form of [tex]y-7=0[/tex] is [tex]y=7[/tex], where the slope is zero and the y-intercept is (0, 7).

Step-by-step explanation:

1) The equation of a line with slope m, passing through the point [tex](x_1,y_1)[/tex], is

[tex]y-y_1=m(x-x_1)[/tex]

We know that [tex]m = -\frac{1}{2}[/tex] and the point is (1,8). Therefore, the equation of the line is

[tex]y-8=-\frac{1}{2} (x-1)\\\\y-8+8=-\frac{1}{2}\left(x-1\right)+8\\\\y=-\frac{1}{2}x+\frac{1}{2}+8\\\\y=-\frac{1}{2}x+\frac{17}{2}[/tex]

2) The equation of a line is typically written as

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

where m is the slope and b is the y-intercept.

The slope of a line is a measure of how fast the line "goes up" or "goes down" and is given by

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

To find the equation of the line that passes through the points (2, 4) and (3, 7), the first step is to find the slope.

Applying the definition of the slope, we get that

[tex]m=\frac{7-4}{3-2}=3[/tex]

Now, we find the y-intercept with the help of point (2, 4) and the general form of the equation of a line

[tex]4=3(2)+b\\b=-2[/tex]

The equation of the line that passes through the points (2,4) and (3,7) is [tex]y=3x-2[/tex]

3) The equation of the line that has slope m = −2 and y-intercept equal to -1 is

[tex]y=-2x-1[/tex]

4) The slope-intercept form of [tex]y-7=0[/tex] is [tex]y=7[/tex], where the slope is zero and the y-intercept is (0, 7).

Final answer:

An equation of a line through the point (1, 8) with a slope of -1/2 is y - 8 = (-1/2)(x - 1). A line with a slope of -2 and a y-intercept of -14 is represented by y = -2x - 14. The equation y - 7 = 0 represents a horizontal line with a slope of 0 and a y-intercept of (0, 7).

Explanation:

Equations of Lines: Slope and Y-Intercept

To find an equation of a line that passes through the point (1, 8) with a slope m of -1/2, we use the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is the given point. Plugging in the values, we get:

y - 8 = (-1/2)(x - 1)

For a line with a slope m of −2 and a y-intercept b of −14, we can write the equation directly in slope-intercept form, which is y = mx + b. Therefore, the equation is:

y = -2x − 14

For the equation y − 7 = 0, this is a horizontal line where the slope is 0 because there's no change in y as x varies. The y-intercept of this line is (0, 7), as the line crosses the y-axis at y = 7.

Answer:

The answer is B

Step-by-step explanation:

Answer:

B. The second graph

Step-by-step explanation:

edge 2021 math assignment

Answer:

Step-by-step explanation:

The average of 2.605, 24.04, 13.3, and 201.64 is gotten by adding the values and dividing by 4 since we are dealing with 4 digits.

[tex]Average =\frac{2.605+24.04+13.3+201.64}{4}[/tex]

average = 241.585/4

average=60.39625

Answer:

The slope of the regression line is 0.01.

Step-by-step explanation:

The given regression equation for this bird is

[tex]DD=2.64+0.01D[/tex]        .... (1)

where, DD is dive duration measured in minutes, and D is depth in meters.  

The slope intercept form of a line is

[tex]y=mx+b[/tex]            .... (2)

where, m is slope and b is y-intercept.

On comparing equation (1) and (2), we get

[tex]y=DD,x=D,m=0.01,b=2.64[/tex]

Since, m=0.01, therefore the slope of the regression line is 0.01.

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: 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:

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: Area of triangle is √3 / 2

Step-by-step explanation:

The explanation can be found in the attached in picture

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:

a) 1820 ways

b) 43680 ways

Step-by-step explanation:

When the order of the choices is relevant we use the permutation formula:

[tex]P_{n,x}[/tex] is the number of different permutations of x objects from a set of n elements, given by the following formula.

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

When the order of choices is not relevant we use the combination formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

In this problem, we have that:

[tex]x = 4, n = 16[/tex]

(a) How many ways can this be done, if the order of the choices is not relevant?

[tex]C_{16,4} = \frac{16!}{4!(12)!} = 1820[/tex]

(b) How many ways can this be done, if the order of the choices is relevant?

[tex]P_{16,4} = \frac{16!}{(12)!} = 43680[/tex]

We can choose 4 objects from 16 in 1820 ways if order doesn't matter (combination), and in 43680 ways if order does matter (permutation).

The subject of this question is combinatorial mathematics. You're being asked to calculate combinations and permutations.

(a) If the order of the choices is not relevant, we are dealing with a combination. The formula for a combination is C(n, r) = n! / [r!(n-r)!], where n is the number of objects and r is the number of objects chosen. In this case, n = 16 and r = 4, so C(16, 4) = 16! / [4!(16-4)!] = 1820 combinations.

(b) If the order of the choices is relevant, we are dealing with a permutation. The formula for a permutation is P(n, r) = n! / (n-r)!. Again, n = 16 and r = 4, so P(16, 4) = 16! / (16-4)! = 43680 permutations.

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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

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] [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:

y = 0.0765x

Step-by-step explanation:

We have that:

y is the total taxes paid.

x is the total wages earned.

The total taxes paid is a function of the total wages earned.

For wages less than the maximum taxable wage base, Social Security contributions (including those for Medicare) by employees are 7.65% of the employee's wages.

So 7.65% of the total wages earned are paid in taxes. We write the percentage as a decimal, so 7.65/100 = 0.0765

So the answer for a) is:

y = 0.0765x

The relationship between the wages earned (x) and the Social Security taxes paid (y) can be expressed as a linear equation. The equation is y = 0.0765x, which means for every dollar earned, 7.65 cents are paid towards Social Security taxes.

The relationship between the wages earned (x) and the Social Security taxes paid (y) can be expressed as a linear equation. Since the contribution is 7.65% of the wages, the equation becomes y = 0.0765x, where x stands for the wages earned, and y represents the employee's Social Security taxes paid.

This equation means that for every dollar earned, 7.65 cents are paid towards Social Security taxes. So, if an employee earns $1000, you would substitute x with 1000 to find the taxes payable. That is y = 0.0765 * 1000, which equates to $76.50

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Answer:

Step-by-step explanation:

Hello!

Three samples of components manufactured are taken per day. They are classified as:

D: "Conforming (suitable for its use)"

E: "Downgraded (unsuitable for the intended purpose but usable for another purpose)"

F: "Scrap (not usable)"

This classification includes the three events that may occur in your sample space S. The experiment consists in recording the categories of the three parts tested in a day.

a. List the 27 outcomes in the sample space.

The possible outcomes in the space sample are the combinations of the three events. To avoid using the same letters as in the following questions I've named the evets as D, E, and F

S={DDD, DED, DFD, DEF, DFE, DEE, DFF, DDE, DDF , EDE, EEE, EFE, EED, EEF, EDF, EFD, EDD, EFF , FDF, FEF, FFF, FFE, FFD, FDE, FED, FDD, FEE}

b. Let A be the event that all the parts fall into the same category. List the outcomes in A.

A: "All the parts fall into the same category"

You have three possible outcomes for this event, that the three compounds are conforming, "DDD", that the three are unconforming, "EEE", or that the three compounds are scrap, "FFF". There are only three possible outcomes for this event.

S={DDD, EEE, FFF}

c. Let B be the event that there is one part in each category. List the outcomes in B.

B: "There is a part in each category"

This means, for example, The first one is conforming "D", the second one is unconforming "E" and the third one is scrap "F", then the first one may be unconforming "E", the second one is conforming "D" and the thirds one is scrap "F", and so on, you have 6 possible outcomes for this event:

S={DEF, DFE, EDF, EFD, FDE, FED}

d. Let C be the event that at least two parts are conforming. List the outcomes in C.

C: "At least two parts are conforming"

For this event, you can have two of the compounds to be considered conforming or the three of them.

S={DDD, DED, DFD, DDE, DDF , EDD, FDD}

A total of 7 combinations fit this event.

I hope you have a SUPER day!

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:  (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: 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]

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:

Step-by-step explanation:

A. Price is 1.75

Total revenue, if number of galsses equals X is 1.75X

Total cost function of X glasses of lemonade is 25+0.1X

Profit function is Revenue - Cost, P=1.75X-25-0.1X=1.65X-25

C. Marginal profit= d/dx(1.65x-25) = 1.65-0=1.65

X=300 glasses, P'(300)=1.65

X=700 glasses, P'(700)=1.65

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

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:

[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) FFFF, FVFF, FFVF, FFFV,

FVFV, FFVV,FVVF,VVFF,

VFVF, VFFF,VFFV,FFVV

VVVV, VFVV, VVFV, VVVF

b) FVFF, FFVF, FFFV,VFFF

c) VVVV or FFFF

d) FFFF, FVFF, FFVF, FFFV, VFFF

e) FFFF, FVFF, FFVF, FFFV ,VFFF, VVVV

Step-by-step explanation:

For this case we define some notation:

F= mortgage classified as fixed rate

V= mortgage classified as variable rate

We select a sample of 4 mortgages.

Part a

We have 2*2*2*2= 16 possible combinations defined below:

FFFF, FVFF, FFVF, FFFV,

FVFV, FFVV,FVVF,VVFF,

VFVF, VVFF,VFFV,FFVV

VVVV, VFVV, VVFV, VVVF

Part b

Which outcomes are in the event that exactly three of the selected mortgages are fixed rate

We need to see in the possible outcomes from part a) how many we have exactly three F's .If we analyze the possible options the possible combinations are:

FVFF, FFVF, FFFV, VFFF

Part c

Which outcomes are in the event that all four mortgages are of the same type?

For this case we have just two possible values: VVVV or FFFF

Part d

Which outcomes are in the event that at most one of the four is a variable ­rate mortgage?

We need to see in the possible outcomes from part a) how many have at least one V. After analyze we see that the possible values:

FFFF, FVFF, FFVF, FFFV, VFFF

Part e

The union represent all four mortgages are of the same type or outcomes are in the event that at most one of the four is a variable ­rate. So we are looking for the possible outcomes VVVV and FFFF and the outcomes with just one V ( FVFF, FFVF, FFFV ,VFFF) so then the union would be:

FFFF, FVFF, FFVF, FFFV ,VFFF, VVVV

Answer:

187 trees

Step-by-step explanation:

50 trees per acre in an orchard and

the orchard is 1.7 x 2.2 km,

we calculate the orchard dimension = 1.7 x 2.2km = 3.74

to calculate how many trees are in the entire orchard = 3.74 x 50 = 187 trees

The number of trees in the entire orchard will be 46,208.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

If there are 50 trees per acre in an orchard and the orchard is 1.7 x 2.2 km.

The area of the entire orchard will be

A = 1.7 x 2.2

A = 3.74 square km

We know that 1 square km = 247.105 acre

A = 3.74 x 247.105

A = 924.17

Then the number of trees in the entire orchard will be

⇒ 50 x 924.17

⇒ 46,208

The number of trees in the entire orchard will be 46,208.

More about the Algebra link is given below.

https://brainly.com/question/953809

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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:

3.2 pi

Step-by-step explanation:

Given 3 curves are:

y = square root ( x / 2)

y = 0

x = 2

Use washer method for hollow volumes.

Step 1: Compute A (y)

A ( y ) = pi * ( f_1 (y) ^2 - f_2 (y) ^2)

where,

f_1 (y) is the function further away from y axis

f_2 (y) is the function closer to y axis

f_1 (y) = 2

f_2 (y) = 2*y^2

A ( y ) = pi * ( 2 ^2 - (2*y) ^2)

A (y) = pi * (4 - 4*y^2)

A (y) = 4*pi * (1 - y^2)

Step 2: Compute V (y)

[tex]V = \int\limits^1_0 {A (y)} \, dy \\V = 4*pi\int\limits^1_0 {1 - y^2} \, dy\\\\V = 4 * pi* (y - 0.2 y^5) \limits^1_0\\\\V = 4*pi*(1 - 0.2)\\\\V = 3.2 pi[/tex]

Answer: V = 3.2 pi

The length of the angle bisector of angle ∠A is approximately 4.62 feet.

To find the length of the angle bisector of angle ∠A in triangle ΔABC, we can use the Angle Bisector Theorem, which states that in a triangle, the angle bisector of a vertex divides the opposite side into segments proportional to the adjacent sides.

In triangle ΔABC, let AD be the angle bisector of ∠A, where D lies on BC. According to the Angle Bisector Theorem:

AC/CD = AB/BD

Given AC = 5 ft and AB = 13 ft, we can plug in these values:

5/CD = 13/BD

To find BD, we use the Pythagorean theorem:

BD = √(AB² - AD²) = √(13² - 5²) = √(169 - 25) = √144 = 12 ft

Now, using the Angle Bisector Theorem:

5/CD = 13/12

Cross-multiply:

5 × 12 = 13 × CD

CD = (5 × 12) / 13 = 60 / 13 ≈ 4.62 ft