A report from the Center for Science in the Public Interest—a consumer group based in Washington, DC—released a study listing calories of various ice cream treats sold by six of the largest ice cream companies. The worst treat tested by the group was1,910 total calories. People need roughly 3,100 to 3,400 calories per day. Using a daily average, how many additional calories should a person consume after eating ice cream?

Answer:

d. 0.0213

Step-by-step explanation:

If a variable follow a poisson distribution, the probability that x events happens in a specific time is given by:

[tex]P(x)=\frac{e^{-a}*a^{x} }{x!}[/tex]

Where a is the mean number of events that happens in a specific time.

So, in this case, x is equal to 9 arrivals and a is equal to 16 customers per hour. Replacing this values, the probability is:

[tex]P(9)=\frac{e^{-16}*16^{9} }{9!}[/tex]

[tex]P(9)=0.0213[/tex]

Answer:

F(x)=[tex]\frac{3^x}{ln(3)}[/tex]+7cosh(x)+C

Step-by-step explanation:

The function is f(x)=3ˣ+7sinh(x), so we can define it as f(x)=g(x)+h(x) where g(x)=3ˣ and h(x)=7sinh(x).

Now we have to find the most general antiderivative of the function this means that we have to calculate [tex]\int\ {f(x)} \, dx[/tex] wich is the same as [tex]\int\ {(g+h)(x)} \, dx[/tex]

The sum rule in integration states that the integral of a sum of two functions is equal to the sum of their integrals. Then,

[tex]\int\ {(g+h)(x)} \, dx[/tex] = [tex]\int\ {g(x)} \, dx + \int\ {h(x)} \, dx[/tex]

1- [tex]\int\ {g(x)} \, dx =[/tex][tex]\int\ {3^x} \, dx = \frac{3^x}{ln(3)}+C[/tex] this is because of the rule for integration of exponencial functions, this rule is:

[tex]\int\ {a^x} \, dx =\frac{a^x}{ln(x)}[/tex], in this case a=3

2-[tex]\int\ {h(x)} \, dx =[/tex][tex]\int\ {7sinh(x)} \, dx =7\int\ {sinh(x)} \, dx =7cosh(x)+C[/tex] , number seven is a constant (it doesn´t depend of "x") so it "gets out" of the integral.

The result then is:

F(x)= [tex]\int\ {(h+g)(x)} \, dx=\int\ {h(x)} \, dx +\int\ {g(x)} \, dx[/tex]

[tex]\int\ {3^x} \, dx +\int\ {7sinh(x)} \, dx = \frac{3^x}{ln(3)} +7cosh(x) + C[/tex]

The letter C is added because the integrations is undefined.

Answer: a) The average of this set of numbers is 1.98 s. b) the standard deviation is 0.02 s.

Step-by-step explanation: The average is calculated by adding all numbers found in the experiment divided by the number of values. [tex]average = \frac{Sumxi}{n}[/tex]

The standard deviation is given by the square root of the squared sum of the difference between each number and the average divided by the total number of values. For instance, std deviation = [tex]\frac{sqrt{(1.94-1.98)^{2}+(1.96-1.98)^2+(2.01-1.98)^2...}}{11}[/tex] and that is done with all 11 terms of data minus the average to find the standard deviation.

In excel, the average of a certain set of numbers (displayed in cells A1 to A5) can be found by the commands =average(A1:A5). The standard deviation can be found by the commands =stdedv.p(A1:A5) in which p is the population. You can decrease decimals by clicking on the icon displayed in the Ribbon.

Answer:

[tex]y=11,600x+6,000[/tex]

Yearly sales in 1990: $98,800.

Step-by-step explanation:

We have been given that the sales of a certain appliance dealer can be approximated by a straight line. Sales were $6000 in 1982 and $ 64,000 in 1987.

If at 1982, [tex]x=0[/tex] then at 1987 x will be 5.

Now, we have two points (0,6000) and (5,64000).

[tex]\text{Slope}=\frac{64,000-6,000}{5-0}[/tex]

[tex]\text{Slope}=\frac{58,000}{5}[/tex]

[tex]\text{Slope}=11,600[/tex]

Now, we will represent this information in slope-intercept form of equation.

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

m = Slope,

b = Initial value or y-intercept.

We have been given that at [tex]x=0[/tex], the value of y is 6,000, so it will be y-intercept.

Substitute values:

[tex]y=11,600x+6,000[/tex]

Therefore, the equation [tex]S=11,600x+6,000[/tex] represents yearly sales.

Now, we will find difference between 1990 and 1982.

[tex]1990-1982=8[/tex]

To find yearly sales in 1990, we will substitute [tex]x=8[/tex] in the equation.

[tex]S=11,600(8)+6,000[/tex]

[tex]S=92,800+6,000[/tex]

[tex]S=98,800[/tex]

Therefore, the yearly sales in 1990 would be $98,800.

Answer:

1600 ml.

Step-by-step explanation:

Let x represent amount of tube-feeding formula.

We have been given that a tube feeding formula contains 6 grams of protein per each 80 ml of the formula.

To solve our given problem, we will use proportions as:

[tex]\frac{x}{\text{120 gram}}=\frac{\text{80 ml}}{\text{ 6 grams}}[/tex]

[tex]\frac{x}{\text{120 gram}}*\text{120 gram}=\frac{\text{80 ml}}{\text{ 6 grams}}*\text{120 gram}[/tex]

[tex]x=\text{80 ml}*20[/tex]

[tex]x=\text{1600 ml}[/tex]

Therefore, the patient should get 1600 ml of tube feeding formula every day.

Answer:

120cm = 46.8 inches

Step-by-step explanation:

This can be solved as a rule of three problem.

In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.

When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too.

When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease.

Unit conversion problems, like this one, is an example of a direct relationship between measures.

Each cm has 0.39 inches. How many inches are there in 120 cm?

1cm - 0.39inches

120cm - x inches

[tex]x = 120*0.39[/tex]

[tex]x = 46.8[/tex] inches

120cm = 46.8 inches

Answer:

x = 50

y = -10

Step-by-step explanation:

x + y = 40

x + 10 = 60

60 - 10 =x

60 - 10 = 50

x = 50

50 + y = 40

40 - 50 = y

40 - 50 = -10

y = -10

Hey!

------------------------------------------------

Solve for x:

x + y = 40

x + y - y = 40 - y

x = 40 - y

50 - 10 = 40

50 + (-10) = 40

x = 50

y = -10

------------------------------------------------

Solve for x:

x + 10 = 60

x + 10 - 10 = 60 - 10

x = 50

------------------------------------------------

Hope This Helped! Good Luck!

Answer:

Mean: 810.51

Standard deviation: 128.32

Step-by-step explanation:

First, we calculate the sample mean. We have 35 data samples, so we compute it as [tex]\displaystyle \frac{562 + .... + 753}{35}[/tex].

In general, given a set of n samples [tex]\{ X_1,...,X_n\}[/tex], we calculate the sample mean as

[tex]\displaystyle \bar{X} = \sum_{i=1}^n \frac{X_i}{n}[/tex].

For the standard deviation [tex]\sigma[/tex], we first begin by calculating it's square. It can be obtained from the formula

[tex]\displaystyle \sigma ^2 = \sum_{i=1}^{n} \frac{(X_i - \bar{X})^2}{n-1}[/tex]

By taking square root after computing the right hand side, we attain the desired value.

The attached image shows the dot diagram of this sample. The bottom pink vertical line shows the mean, and the two horizontal pink lines have a lenght of [tex]\sigma[/tex].

The standard deviation means "The average expected distance a new sample will be from the mean".  That's why usually, data samples which are denser around the mean have smaller standard deviations (as opposed to distributions who have a lot of values far away from the mean, which will make the standard deviation grow bigger).

Answer: There are 52223.18 AIDS death in 1995.

Step-by-step explanation:

Since we have given that

Number of AIDS deaths in 2003 = 18,017

Percentage of deaths of 1995 AIDS deaths =34.5%

Let the number of AIDS deaths in 1995 be 'x'.

According to question, it becomes ,

[tex]\dfrac{34.5}{100}\times x=18017\\\\x=18017\times \dfrac{100}{34.5}\\\\x=52223.18[/tex]

Hence, there are 52223.18 AIDS death in 1995.

Answer:

264,666.

Step-by-step explanation:

We have been given that a number has seven digits.

All digits are 6 except the hundred-thousands' digit.

Hundred thousands: 100,000.

The hundred thousand's digit is 2, so its value would be 200,000.

We have been given that thousands's digit is 4, so its value would be:

4 thousands: 4,000

The number with given hundred thousand's and thousands's digit would be 204,000.

Since all digits are 6 except the hundred-thousands' digit, therefore, our number would be 264,666.

Answer:

5.5 liters

Step-by-step explanation: there are 1000 milliliters in a liter, so divide 5,500/1000

Answer:

5.5 liters

Step-by-step explanation:

because 5500 millilitres is 5.5 liters

Answer:

Dependent variable: number of correct answers

Step-by-step explanation:

The dependent variable is the number of correct answers, because it is the variable that the researchers were recording as response in the experiment.

As it is a counting, it can only take finite values (0 correct answers, 1 correct answer, 2 correct answers and so on). Then, it can be classified as a discrete variable. Discrete values always represent exact quantities that can be counted. For example, number of passengers per car, or number of cows per acre.  

Discrete variables can be divided into nominal (they haven’t an order or a hierarchy, as in the example of cows/acre), ordinal (they follow a natural order or hierarchy), interval (they can be divided into classes) or ratio (they represent relative quantities).  

The number of correct answers is an ordinal variable, because they have a natural hierarchy. 1 correct answer it’ s better than 0, and 2 corrects answers are better than 1 and 0. Then, you can order your results: 0, 1, 2, 3, 4, etc.

The probability that no passenger is in their assigned seat is 0.6321.

Given data:

There are N passengers in a plane with N assigned seats (N is a positive integer), but after boarding, the passengers take the seats randomly.

The probability that no passenger is in their assigned seat is often referred to as the "surprising" or "paradoxical" result.

The problem is analyzed for a specific case with N = 3 passengers.

Passenger 1 sits in Seat 1: In this case, the remaining two passengers have a 1/2 chance of sitting in their assigned seats.

Passenger 1 sits in Seat 2: Again, the remaining two passengers have a 1/2 chance of sitting in their assigned seats.

Passenger 1 sits in Seat 3: In this case, the remaining two passengers will definitely sit in their assigned seats.

Now, calculate the probability for each scenario and find the overall probability that no passenger is in their assigned seat:

Scenario 1: Probability = 1/3 * 1/2 = 1/6

Scenario 2: Probability = 1/3 * 1/2 = 1/6

Scenario 3: Probability = 1/3

Overall Probability = Probability of Scenario 1 + Probability of Scenario 2 + Probability of Scenario 3

= 1/6 + 1/6 + 1/3

= 1/2

Thus, for N = 3, the probability that no passenger is in their assigned seat is 1/2.

Now, consider the case when N → ∞ (approaching infinity).

In this scenario, the probability can be calculated as follows:

Probability = 1 - 1/e

Hence, as N approaches infinity, the probability that no passenger is in their assigned seat approaches 1 - 1/e, or approximately 0.6321.

To learn more about probability, refer:

https://brainly.com/question/17089724

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Final answer:

The derangement problem questions the probability that no passenger sits in their assigned seat, which asymptotically approaches 1/e (approximately 0.3679) as the number of seats and passengers approaches infinity.

Explanation:

The student's question is about calculating the probability that no passenger is seated in their assigned seat on a plane where passengers sit randomly, especially when the number of passengers (and seats) approaches infinity. This is known as the derangement problem or a problem of calculating permutations where no element appears in its original position. A specific case of permutations without fixed points is termed as a derangement, and the probability of a derangement occurring in a permutation of N elements approaches 1/e where e is Euler's number, approximately equal to 2.71828. Through an approximation known as the asymptotic probability, when N → [infinity], this probability approaches 1/e, which is approximately 0.3679 or 36.79%.

Answer:

[tex]P \cap R=\{2,3,5,7\}[/tex]

Step-by-step explanation:

Given : Let P={ 1,2,3,5,7,9}, Q= { 1,2,3,4,5}, and R= {2,3,5,7,11}

To find : The value of [tex]P \cap R[/tex] ?

Solution :

The intersection of two sets is defined as the set of their common elements or the elements appear in both the sets.

The sets are P={ 1,2,3,5,7,9} and R= {2,3,5,7,11}

Common elements in P and R are {2,3,5,7}

So, [tex]P \cap R=\{2,3,5,7\}[/tex]

Therefore, The value of [tex]P \cap R=\{2,3,5,7\}[/tex]

Answer:

[tex]I=\frac{1000}{exp^{0,806725*t-0.6906755}+1}[/tex]

Step-by-step explanation:

The rate of infection is jointly proportional to the number of infected troopers and the number of non-infected ones. It can be expressed as follows:

[tex]\frac{dI}{dt}=a*I*(1000-I)[/tex]

Rearranging and integrating

[tex]\frac{dI}{dt}=a*I*(1000-I)\\\\\frac{dI}{I*(1000-I)}=a*dt\\\\\int\frac{dI}{I*(1000-I)}=\int a*dt\\\\-\frac{ln(1000/I-1)}{1000}+C=a*t[/tex]

At the initial breakout (t=0) there was one trooper infected (I=1)

[tex]-\frac{ln(1000/1-1)}{1000}+C=0\\\\-0,006906755+C=0\\\\C=0,006906755[/tex]

In two days (t=2) there were 5 troopers infected

[tex]-\frac{ln(1000/5-1)}{1000}+0,006906755=a*2\\\\-0,005293305+0,006906755=2*a\\a = 0,00161345 / 2 = 0,000806725[/tex]

Rearranging, we can model the number of infected troops (I) as

[tex]-\frac{ln(1000/I-1)}{1000}+0,006906755=0,000806725*t\\\\-\frac{ln(1000/I-1)}{1000}=0,000806725*t-0,006906755\\-ln(1000/I-1)=0,806725*t-0.6906755\\\\\frac{1000}{I}-1=exp^{0,806725*t-0.6906755}  \\\\\frac{1000}{I}=exp^{0,806725*t-0.6906755}+1\\\\I=\frac{1000}{exp^{0,806725*t-0.6906755}+1}[/tex]

Answer:

[tex]x=\frac{45}{4},  y=-\frac{201}{4}, z=-\frac{61}{2}[/tex]

Step-by-step explanation:

We start by putting our equation in a matricial form:

[tex]\left[\begin{array}{cccc}12&2&1&4\\3&3&-4&5\\2&-2&4&1\end{array}\right][/tex]

Then, we multiply the second row by 4 and substract the first row:

[tex]\left[\begin{array}{cccc}12&2&1&4\\0&10&-17&16\\2&-2&4&1\end{array}\right][/tex]

Now, multiply the third row by 6 and substract the first row:

[tex]\left[\begin{array}{cccc}12&2&1&4\\0&10&-17&16\\0&-14&23&2\end{array}\right][/tex]

Next, we will add [tex]\frac{7}{5}[/tex] times the second row to the third row:

[tex]\left[\begin{array}{cccc}12&2&1&4\\0&10&-17&16\\0&0&\frac{-4}{5}&\frac{122}{5}\end{array}\right][/tex]

Now we can solve [tex]\frac{-4}{5} z=\frac{122}{5}[/tex] to obtain

[tex]z=-\frac{61}{2}[/tex]

Then [tex]10y-17\frac{-61}{2}=16[/tex] wich implies that

[tex]y=\frac{16-\frac{17*61}{2}}{10} =\frac{\frac{32-17*61}{2}}{10}=\frac{-1005}{20}=\frac{-201}{4}[/tex]

Finally

[tex]x=\frac{4-2*\frac{-201}{4}+\frac{61}{2}}{12} =\frac{\frac{8+201+61}{2}}{12}=\frac{270}{24}=\frac{135}{12}=\frac{45}{4}[/tex].

[tex]z=-\frac{61}{2}\\ y=-\frac{201}{4} \\x=\frac{45}{4}[/tex]

Answer: The value of 100 th term is 298 and the value of n th term is 1+3n.

Step-by-step explanation:

Since we have given that

1,4,7,10............

Since it forms an A.P. in which

a = 1

d = [tex]4-1 =3[/tex]

So, the value of 100 th term is given by

[tex]a_{100}=a+(n-1)d\\\\a_{100}=1+(100-1)\times 3\\\\a_{100}=1+99\times 3\\\\a_{100}=1+297\\\\a_{100}=298[/tex]

And the value of n th term is given by

[tex]a_n=1+3n[/tex]

Hence, the value of 100 th term is 298 and the value of n th term is 1+3n.

Answer:

There is a 33% probability that this party was received from supplier Z.

Step-by-step explanation:

This can be formulated as the following problem:

What is the probability of B happening, knowing that A has happened.

It can be calculated by the following formula

[tex]P = \frac{P(B).P(A/B)}{P(A)}[/tex]

Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.

-In your problem, we have:

P(A) is the probability of a defective part being supplied. For this probability, we have:

[tex]P(A) = P_{1} + P_{2} + P_{3}[/tex]

In which [tex]P_{1}[/tex] is the probability that the defective product was chosen from supplier X(we have to consider the probability of supplier X being chosen). So:

[tex]P_{1} = 0.24*0.05 = 0.012[/tex]

[tex]P_{2}[/tex] is the probability that the defective product was chosen from supplier Y(we have to consider the probability of supplier Y being chosen). So:

[tex]P_{2} = 0.36*0.10 = 0.036[/tex]

[tex]P_{3}[/tex] is the probability that the defective product was chosen from supplier Z(we have to consider the probability of supplier Z being chosen). So:

[tex]P_{2} = 0.40*0.06 = 0.024[/tex]

So

[tex]P(A) = P_{1} + P_{2} + P_{3} = 0.012 + 0.036 + 0.024 = 0.072[/tex]

P(B) is the probability of the supplier chosen being Z, so P(B) = 0.4

P(A/B) is the probability of the part supplied being defective, knowing that the supplier chosen was Z. So P(A/B) = 0.06.

So, the probability that this part was received from supplier Z is:

[tex]P = \frac{0.4*0.06}{0.072} = 0.33[/tex]

There is a 33% probability that this party was received from supplier Z.

Answer:

B. 10n-207

Step-by-step explanation:

Given,

The average number of points of 9 games = 23,

∵ Sum of observations = their average × number of observations

So, the total points for 9 games = 9 × 23 = 207,

Now, if the average of 10 games is n,

Then the total points for 10 games = 10n,

Hence, the number of points earned in 10th game = the total points for 10 games - the total points for 9 games

= 10n - 207

i.e. OPTION B is correct.

The correct option is (B) 10n-207. To raise the average points per game to 'n' after the 10th basketball game, one would need to score '10n - 207' points in the 10th game, based on the previous average of 23 points in the first 9 games.

To solve the problem, we need to use the formula for calculating an average. The average score after 10 games would be the total points scored divided by 10. If the first 9 games had an average of 23 points, the total points from these games is 9 × 23 = 207.

To get an average of n after the 10th game, the total points should be 10× n. Therefore, the points needed in the 10th game would be the difference between 10 × n and the sum score from the first 9 games (207). That gives us the equation 10n - 207 for the number of points needed in the 10th game.

We have a vector [tex]\vec F[/tex] with a magnitude [tex]F[/tex] of 86.4 N.

a. Let [tex]\theta[/tex] be the angle [tex]\vec F[/tex] makes with the positive [tex]x[/tex]-axis. The [tex]x[/tex]-component of [tex]\vec F[/tex] is

[tex]F_x=(86.4\cos\theta)\,\mathrm N[/tex]

and has a magnitude of 72.3 N, so

[tex]72.3=86.4\cos\theta\implies\cos\theta=0.837\implies\theta=\boxed{33.2^\circ}[/tex]

b. The [tex]y[/tex]-component of [tex]\vec F[/tex] is

[tex]F_y=(86.4\cos33.2^\circ)\,\mathrm N=\boxed{47.3\,\mathrm N}[/tex]

a) The angle between the vector and the +x axis is approximately 33.196°.

b) The component of the force along the +y axis is approximately 47.304 newtons.

In this question we should apply the concepts of magnitude and direction of a vector to solve each part. The magnitude ([tex]\|\vec F\|[/tex]), in newtons, is a application of Pythagorean theorem and direction ([tex]\theta[/tex]), in degrees, is an application of trigonometric functions.

a) The angle between the vector and the component along the x axis ([tex]F_{x}[/tex]), in newtons, is found by means of the following expression:

[tex]\theta = \cos^{-1} \frac{F_{x}}{\|\vec F\|}[/tex] (1)

([tex]\|\vec F\| = 86.4\,N[/tex], [tex]F_{x} = 72.3\,N[/tex])

[tex]\theta = \cos^{-1} \left(\frac{72.3\,N}{86.4\,N} \right)[/tex]

[tex]\theta \approx 33.196^{\circ}[/tex]

The angle between the vector and the +x axis is approximately 33.196°. [tex]\blacksquare[/tex]

b) The magnitude of the +y component of the vector force ([tex]F_{y}[/tex]), in newtons, is determined by the following Pythagorean expression:

[tex]F_{y} = \sqrt{(\|\vec F\|)^{2}-F_{x}^{2}}[/tex] (2)

([tex]\|\vec F\| = 86.4\,N[/tex], [tex]F_{x} = 72.3\,N[/tex])

[tex]F_{y} = \sqrt{(86.4\,N)^{2}-(72.3\,N)^{2}}[/tex]

[tex]F_{y} \approx 47.304\,N[/tex]

The component of the force along the +y axis is approximately 47.304 newtons. [tex]\blacksquare[/tex]

To learn more on vectors, we kindly invite to check this verified question: https://brainly.com/question/13188123

Answer:

Values for each variable are:

x = 19

y = -4

z = -12

Step-by-step explanation:

As we can remember the Gauss-Jordan elimination method consists of creating a matrix with all the equations of the system.  Remember that, if a variable does not appear in one of the equations, we give a value of 0 to its coefficient .  Each equation will constitute a line of the matrix. So, the matrix will look like this:

2   2   1   18

1    0   1    7

0   4  -3  20

For the Gauss-Jordan elimination we can multiply lines, add or subtract one line to another or we can rearrange the order at any given time. The goal is to get only 1s in the matrix diagonal, to determine the value of each variable.

Since we already have a line with a 1, we'll take that line as our starting point, and we'll rearrange it as our 1st line. By multiplying the 1st line for  2 and then subtracting the result to the second line:

1   0   1   7

0   2  -1  4

0   4  -3  20

Now, we multiply the second line by 2 and subtract the result to the third line

1   0   1   7

0   2  -1  4

0   0  -1  12

In order to get the value of Z all we have to do is multiply the third line by (-1).

1   0   1   7

0   2  -1  4

0   0  1  -12

Now, we add the third line to the second line.

1   0   1   7

0   2  0  -8

0   0  1  -12

Then, multiply the second line by a fraction 1/2, to get the value for Y

1   0   1   7

0   1  0  -4

0   0  1  -12

Finally, we subtract the third line to the 1st line to get the value for X

1   0   0  19

0   1  0  -4

0   0  1  -12

All we got left is to prove our answer is correct by replacing the variables in the system with the values found:

First equation

2(19) + 2(-4) + (-12) = 18

38 - 8 - 12 = 18

38 - 20 = 18

Second equation

19 + (-12) = 7

19 -12 = 7

Third equation

4(-4) - 3(-12) = 20

-16 + 36 = 20

Annual is 1 year.

1 year has 12 months.

Multiply the monthly rate by 12:

3.15 x 12 = 37.80%

Answer:

The required value for the blank is 21.8696

Step-by-step explanation:

Consider the provided information,

4,275.50= 391/2 of ____

Replace blank with x.

4,275.50 = 391/2 of x

Use sign of multiplication for "of".

[tex]4,275.50 = \frac{391}{2} \times x[/tex]

Solve the above expression for x.

[tex]x=\frac{4,275.50\times 2}{391} [/tex]

[tex]x=21.8696 [/tex]

Thus, the required value for the blank is 21.8696

Answer:

Lady purchased 12 trinkets costing $0.30 each and 8 trinkets costing $0.65 each.

Step-by-step explanation:

A lady buys total number of trinkets = 20

Cost of each trinket is either $0.30 or $0.65.

Let the number of trinkets is x she purchased for $0.30 and y for $0.65

Then x + y = 20 --------(1)

Since she spends total amount = $8.80

Then the equation will be

0.30x + 0.65y = 8.80 ---------(2)

We replace x = (20 - y) from equation (1) to equation (2)

0.30(20 - y) + 0.65y = 8.80

6 - 0.30y + 0.65y = 8.80

0.35y + 6 = 8.80

0.35y = 8.80 - 6

0.35y = 2.80

y = [tex]\frac{2.80}{0.35}[/tex]

y = 8

Now we put y = 8 in equation (1)

x + 8 = 20

x = 20 - 8

x = 12

Therefore, lady purchased 12 trinkets costing $0.30 each and 8 trinkets costing $0.65 each.

Answer:

(a) 0.09 (b) 0.322 (c) 0.0966

Step-by-step explanation:

Let's define first the following events

M: an applicant is a male

F: an applicant is a female

A: an applicant is accepted

E: an applicant is enrolled

S: the sample space

Now, we have a total of 7500 applicants, and from these applicants 4200 were male and 3300 were female. So,

P(M) = 0.56 and P(F) = 0.44, besides

P(A | M) = 0.3, P(E | A∩M) = 0.3, P(A | F) = 0.35, P(E| A∩F) = 0.3

(a) 0.09 = (0.3)(0.3) = P(A|M)P(E|A∩M)=P(E∩A∩M)/P(M)=P(E∩A | M)

(b) P(A) = P(A∩S) = P(A∩(M∪F))=P(A∩M)+P(A∩F)=P(A|M)P(M)+P(A|F)P(F)=(0.3)(0.56)+(0.35)(0.44)=0.322

(c) P(A∩E)=P(A∩E∩S)=P(A∩E∩(M∪F))=P(A∩E∩M)+P(A∩E∩F)=0.0504+P(E|A∩F)P(A|F)P(F)=0.0504+(0.3)(0.35)(0.44)=0.0966

Answer:

Where are the sets of vectors?

Step-by-step explanation:

Which set of vectors?

Answer:

  P = (-18 5/9, 3 13/18, -17 2/3)

Step-by-step explanation:

The given point must satisfy both the equation of the line and that of the plane. We can substitute for x, y, and z in the plane's equation to get ...

  -7(-3-8t) +2(-6+5t) +8(-6-6t) = -4

  21 +56t -12 +10t -48 -48t = -4

  18t -39 = -4 . . . collect terms

  18t = 35 . . . . . . add 39

  t = 35/18 . . . . . .divide by the coefficient of t

The point is ...

  (x, y, z) = (-3-8(35/18), -6+5(35/18), -6-6(35/18))

  P = (x, y, z) = (-18 5/9, 3 13/18, -17 2/3)

Answer:

Step-by-step explanation:

We know that for two similar matrices [tex]A[/tex] and [tex]B[/tex] exists an invertible matrix [tex]P[/tex] for which

[tex][tex]B = P^{-1} AP[/tex][/tex]

∴ [tex]B^{T} = (P^{-1})^{T} A^{T} P^{T} \\[/tex]

Also [tex]P^{-1}P = I\\[/tex]

and [tex](P^{-1})^{T} = (P^{T})^{-1}[/tex]

∴[tex](P^{-1})^{T}P^{T} = I[/tex]

so, [tex]B^{T} = (P^{-1})^{T} A^{T} P^{T} = (P^{T})^{-1}A^{T} P^{T}\\B^{T} = A^{T} I\\B^{T} = A^{T}[/tex]

Answer:

Step-by-step explanation:

There are a total of 2+4+3 = 9 "ratio units", so each one is worth ...

  $8,280/9 = $920

Multiplying the ratio by $920, we get ...

  cook : custodian : bus driver = $920 × (2 : 4 : 3) = $1840 : $3680 : $2760

The monthly salaries for the school cook, custodian, and bus driver are $1,840, $3,680, and $2,760, respectively.

To find the monthly salary for each person, we need to first determine the common ratio between their salaries. The given salaries are in the ratio 2:4:3. We can assign a constant to the ratio, such as 2x:4x:3x.

Next, we can set up an equation using the given information that the combined monthly salaries total $8,280:

2x + 4x + 3x = 8,280

9x = 8,280

To solve for x, we can divide both sides of the equation by 9:

x = 920

Now, we can find the monthly salary for each person by substituting x back into the ratio:

School cook's monthly salary: 2x = 2(920) = $1,840

Custodian's monthly salary: 4x = 4(920) = $3,680

Bus driver's monthly salary: 3x = 3(920) = $2,760

Proof :

First, it is important to have in mind that a number [tex] m \in \mathbb{Z} [/tex] is a multiple of [tex]n\in\mathbb{Z} [/tex] iff there exists [tex]k\in\mathbb{Z}[/tex] such that  [tex] m = n \cdot k[/tex].

Also, you have to prove a logical equivalence. To this end, it is possible to prove two logical implications.

Step-by-step explanation:

1.) Let x, y be integers such that x + 3y is a multiple of 7. You have to prove that 3x +2y is a multiple of 7.

In effect, by hypothesis there exists k [tex]\in\mathbb{Z}[/tex] such that  x + 3y = 7 k .   So, you get  

[tex]\begin{equation*} 4(x+3y) + (3x + 2y) = 7x + 14y = 7 (x + 2y) \ \mbox{(direct computations and factoring)}\end{equation*} [/tex].

Therefore, 4(x +3y) + (3x +2y) is a multiple of 7. Then,

[tex](3x + 2y) = 7 (x + 2y) - 4(x + 3y) = 7 (x+2y) - 4 \cdot 7 k = 7 (x + 2y -4k) \ \mbox{(factoring)}[/tex].

Given that x,y,k are integers, then x + 2y - 4k is an integer  and hence, 3x + 2y is a multiple of 7.

To finish, it remains to prove its reciprocal statement.

2.) Let x, y be integers such that 3x + 2y is a multiple of 7. You have to prove that  x +3y  is a multiple of 7. Reasoining as before ,   there exists q [tex]\in\mathbb{Z}[/tex] such that 3x + 2y = 7 \cdot  q.  Thus,

 [tex]$$ \begin{equation*} 2(3x+2y) + (x + 3y) = 7x + 7y = 7 (x + y) \ \mbox{direct computations and factoring} \\\end{equation*} $$[/tex] Thus, [tex] 2(3x +2y) + (x +3y)[/tex] is a multiple of 7.

On the other hand,  using the hypothesis [tex] $$ \begin{equation*}   (x + 3y) = 7 (x + y) - 2(3x + 2y) = 7 (x+y) - 2 \cdot 7 q = 7 (x + y -2q) \ \mbox{(factoring)} \end{equation*} $$    [/tex] .

Finally, thanks that [tex]x,y,q [/tex] are integer numbers, then [tex] x + y - 2q[/tex] is a integer number and therefore, [tex] 3x + 2y [/tex] is a multiple of 7.