For the following linear system, put the augmented coefficient matrix into reduced row-echelon form.

x1 − 2x2 + 3x3 + 2x4 + x5 = 10

2x1 − 4x2 + 8x3 + 3x4 + 10x5 = 7

3x1 − 6x2 + 10x3 + 6x4 + 5x5 = 27

Answer:

4 units to the right

Step-by-step explanation:

Since all we know about function h(x) is that it has slope 2, we don't know its y intercept, so let's call it b and write the equation of that first line as:

[tex]h(x) = 2x + b[/tex]

Now, we translated that function up 8 units to get function d(x). This vertical displacement is expressed by adding 8 units to function h(x):

[tex]d(x) = h(x) + 8 = 2x+b+8[/tex]

We want to translate this last function d(x) either to the right or to the left in order to get the same expression as for function h(x).

Recall that translations to the right or left a fix number of units "c" affects the "x" coordinate of the function (by adding "c", we move to the left c units the graph of the function, and by subtracting "c" we move to the right the graph of the function).

So represent a generic shift for d(x) for example to the right in c units:

[tex]d(x) = 2(x-c)+x^{2} +b+8= 2x-2c+b+8[/tex]

Now we want this new shifted function to be EXACTLY as h(x) so we write the equality:

[tex]2x-2c+8+b=h(x)=2x+b\\2x-2c+8+b = 2x+b[/tex]

We can solve in the equation for the value "c" we need for the translation:

[tex]2x-2c+8+b = 2x+b\\-2c+8=0\\2c=8\\c=\frac{8}{2} = 4[/tex]

subtracting 2x from both sides, and also subtracting "b" from both sides.

This means that the translation to the right by 4 units will result on the exact same graph as for function h(x)

Answer:

The weighted mean of the number of t-shirts sold per week is 5.6.

Step-by-step explanation:

Given : The data below represents the number of T-shirts sold per week by a student who started his own online t-shirt business.

T-Shirt Sold per Week([tex]x_i[/tex]) Frequency([tex]w_i[/tex])

         2                                                          1

4                                                          4

6                                                          7

8                                                          3

To find : The weighted mean of the number of t-shirts sold per week ?

Solution :

The formula of weighted mean is

[tex]\text{Weighted mean}=\frac{\sum (x_i\times w_i)}{\sum w_i}[/tex]

Substituting the values in the formula,

[tex]\text{Weighted mean}=\frac{2(1)+4(4)+6(7)+8(3)}{1+4+7+3}[/tex]

[tex]\text{Weighted mean}=\frac{2+16+42+24}{15}[/tex]

[tex]\text{Weighted mean}=\frac{84}{15}[/tex]

[tex]\text{Weighted mean}=5.6[/tex]

Therefore, The weighted mean of the number of t-shirts sold per week is 5.6.

Final answer:

To find the weighted mean of T-shirts sold per week, you multiply each amount by its frequency, sum these products, and then divide by the total frequency. For this data, the weighted mean is 5.6 T-shirts per week.

Explanation:

To calculate the weighted mean of the number of T-shirts sold per week, we must multiply each number of T-shirts sold by its respective frequency and then divide the sum by the total number of observations.

We have the following data:

6 * 7 = 42

Add these products together:

2 + 16 + 42 + 24 = 84

Next, calculate the total frequency (total number of weeks):

1 + 4 + 7 + 3 = 15

Now, divide the sum of products by the total frequency to get the weighted mean:

84 / 15 = 5.6

Therefore, the weighted mean number of T-shirts sold per week is 5.6.

Answer:

151.

Step-by-step explanation:

50th or Fiftieth Ordinal numbers are just numbers that identify the order of things: Thus having 151 coming before 152.

The ordinal number just before 152nd is 151st.

The ordinal number just before 152nd is 151st. Ordinal numbers are used to indicate position or order, and they are formed by adding the suffix '-st' to the cardinal number. In this case, the cardinal number 152 is changed to the ordinal number 152nd by adding '-nd' suffix. To find the ordinal number just before 152nd, we go one step back and change the '-nd' suffix to '-st', resulting in 151st.

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Answer:

$13847.30, Option B

Step-by-step explanation:

sold toys = 4694

average profit on each toy = $2.95

total profit in the three months = $2.95 * 4694 = $13847.30

Answer:

The total cost is $3504.625

Step-by-step explanation:

1 inch = 0.0833333 feet

Height = 6 feet 6 inches =[tex]6+6 \times 0.0833333=6.5 feet[/tex]

Length = 90 feet

Breadth = 175 feet

Perimeter = [tex]2(l+b)=2(90+175) = 530 feet[/tex]

Cost of erecting the fence is $1.25 per linear foot .

So, Cost of erecting the fence of 530 feet = [tex]530 \times 1.25[/tex]

Cost of erecting the fence of 530 feet = [tex]662.5[/tex]

Area of fence = [tex]2(l+b)h=530 \times 6.5=3445 feet^2[/tex]

Cost of materials is $0.825 per square foot of fence

Cost of materials of 3445 square foot of fence = [tex]3445 \times 0.825[/tex]

                                                                             = [tex]2842.125[/tex]  

Total cost = $2842.125+$662.5

Total cost = $3504.625

Hence the total cost is $3504.625

Answer:

  5 5/12 pounds of nails

Step-by-step explanation:

  (3 1/3 boxes) × (1 5/8 pounds/box) = (10/3)(13/8) pounds = 65/12 pounds

  = 5 5/12 pounds

Mark used approximately 5.41 pounds of nails to build the tree house. This is found by converting the given fractions to decimal and then multiplying the weight of one box of nails by the number of boxes use

In the problem, we know that a box of 100 nails weighs 1 5/8 pounds. We are also told that Mark used 3 1/3 boxes of nails. Therefore, we first need to find out how much one box of nails weighs, and then multiply that weight by the number of boxes Mark used.

To convert 1 5/8 to a decimal, we know that 5/8 = 0.625, so 1 5/8 = 1.625 pounds. Mark used 3 1/3 boxes, and 1/3 converted to a decimal is approximately 0.33, so Mark used approximately 3.33 boxes. By multiplying 1.625 pounds by 3.33, we find that he used approximately 5.41 pounds of nails to build the tree house.

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Answer:

0

Step-by-step explanation:

4 - 2/2 - 3 =

Follow the correct order of operations. Start with the division.

= 4 - 1 - 3

Now do subtractions from left to right in the order they appear.

= 3 - 3

= 0

Answer: 0

Answer with Step-by-step explanation:

We have to find given length set form a triangle  and find the type of triangle acute, obtuse or right.

If sum of   length  of any two sides is greater than the length of third side then the given side length form a triangle otherwise not.

a.5 cm, 6 cm and 7 cm

[tex]5+6=11cm  > 7cm[/tex]

Hence, given set of side length form  a triangle.

[tex]5^2+6^2=25+36=61 >7^2=49[/tex]

Hence, given triangle is acute triangle.

b.2 cm,11 cm,15 cm

[tex] 2+15=17 cm > 11 cm[/tex]

Hence, given side length set form a triangle.

[tex]2^2+11^2=4+121=125 < (15)^2=225[/tex]

Hence, the triangle is an obtuse triangle.

c.10 cm,15 cm,20 cm

[tex]10+15=25 cm >20 cm[/tex]

Hence, given set of  length side form a triangle.

[tex](10)^2+(15)^2=225 >(20)^2=400[/tex]

Hence, the triangle is an acute triangle .

d.10 cm,24 cm,26 cm

[tex]10+24=34 cm > 26 cm[/tex]

Hence, given set  of side length form a triangle.

[tex](10)^2+(24)^2=676=(26)^2=676[/tex]

Hence, the triangle forms a right triangle.

e.1 cm,3 cm, 9 cm

[tex]1+9=10 cm > 3 cm[/tex]

Hence, the given set  of side length forms a triangle.

[tex]1^1+3^2=10<9^2=81[/tex]

Hence, the triangle is an obtuse triangle.

f.2 cm, 10 cm,11 cm

[tex]2+10=12 cm > 11cm[/tex]

Hence, the given set of side length set forms a triangle.

[tex]2^2+(10)^2=104<(11)^2=121[/tex]

Hence, the triangle is an obtuse triangle.

Answer:

  Integers are a subset of Rational Numbers because all Integers are Rational Numbers.

Step-by-step explanation:

A rational number such as 4/2 is also an integer: 2. A rational number such as 4/3 is not an integer. Hence, integers are a subset of rational numbers.

Answer:

Integers are a subset of Rational Numbers because all Integers are Rational Numbers.

Step-by-step explanation:

3 is integer but it can be written as [tex]\frac{3}{1} \ or \ \frac{6}{2},.. etc.[/tex] which is rational form. Hence every integer can be express as Rational Number.

Thus the last option is correct.

Further, Integers can be defined as the whole numbers including zero and positive whole numbers. i.e. ......,-3, -2, -1, 0, 1, 2, 3,.....

Example: -546, 87855889, 0, etc.

Rational Number is the number in the form [tex]\frac{p}{q}[/tex], where q≠0.

Example: [tex]\frac{2}{9}, \frac{-1}{267}, \frac{875}{2}, 3, etc.[/tex]

Answer:

Step-by-step explanation:

Given that *is the binary operation in the sets of integers.

[tex]a*b = a - b + ab[/tex]

closure: a-b+ab is again an integer belongs to Z.  Hence closure is true.

Associativity: [tex]a*(b*c) = a*(b+c-bc)\\= a-b-c+bc+ab+ac-abc\\= a-b-c +ab+bc+ca-abc[/tex]

[tex](a*b)*c=(a+b-ab)*c\\=a+b-ab-c+ac+bc-abc\\[/tex]

The two are not equal.  Hence this cannot be a group as associtiavity does not hold good.

Answer:

30

Step-by-step explanation:

I solved this question algebraically. First a variable (I used 'c') is introduced into the equation (for the number of correct answers). Thus we get the equation;

  2c - (40 - c) = 50

solving this...

  2c - 40 + c = 50

                3c = 90

                  c = 30

So the number of correct answers is 30. (30*2-10=50)

[Alternatively we can use a variable for the number of incorrect answers and get; 2* (40 - a) - a = 50, and solve this equation but this method is longer as you'll need to subtract this answer from 40 to get the number of correct responses.]

Answer:

The probability is 0.5086

Step-by-step explanation:

The probability P that at least one of these three modules will fail to work properly is calculated as:

P = 1 - P'

Where P' is the probability that all the modules works properly. So, P' os calculated as:

P' = 0.9 * 0.84 * 0.65

P' = 0.4914

Because 0.9 is the probability that module 1 works properly, 0.84 is the probability that module 2 works properly and 0.65 is the probability that module 3 works properly.

Finally, the probability P that at least one of these three modules will fail to work properly is:

P = 1 - 0.4914

P = 0.5086

Answer:

[tex]\begin{array}{ccc}\text{Stem}&|&\text{Leaf}\\ \\2&|&2,4,5,5,5,6,7\\3&|&2,2,2,3,3,3,4,5,5,7,7,7,8,9,9\\4&|&0,3,3,4,4,5,6,8,9\\5&|&1,2,2,3,4\\6&|&0,1,4\\7&|&0\end{array}[/tex]

Step-by-step explanation:

You are given the set of data

40 45 64 52 38 35 48 27 60 44 32 32 33 25 37 26 61 37 37 51 33 53 43 46 52 24 25 32 49 39 22 35 33 39 54 43 34 70 44 25 ​

First, rewrite it in ascending order:

22 24 25 25 25 26 27 32 32 32 33 33 33 34 35 35 37 37 37 38 39 39 40 43 43 44 44 45 46 48 49 51 52 52 53 54 60 61 64 70   ​

The first gigit of each number write into the stem column and the second digit of each number write into the leaf column. So, the stem-and-leaf display is

[tex]\begin{array}{ccc}\text{Stem}&|&\text{Leaf}\\ \\2&|&2,4,5,5,5,6,7\\3&|&2,2,2,3,3,3,4,5,5,7,7,7,8,9,9\\4&|&0,3,3,4,4,5,6,8,9\\5&|&1,2,2,3,4\\6&|&0,1,4\\7&|&0\end{array}[/tex]

Here is the back - to - back stem and leaf plot of the data :

LEAF ___________ stem _________ LEAF

Best actor age_____ | | ___ Best actress age

5, 6, 7 ___________| 2 | _______ 2, 4 5, 5

2, 2, 3, 5, 7, 7, 7, 8__ | 3 | __ 2, 3, 3, 4, 5, 9, 9

0, 4, 5, 8 _________| 4 | ______3, 3, 4, 6, 9

1, 2 _____________ | 5 | ___________ 2, 3

0, 1, 4 ___________ | 6 | ______________

________________ | 7 | _____________ 0

Given the data :

Best actor :

40 45 64 52 38 35 48 27 60 44 32 32 33 25 37 26 61 37 37 51

Best actress :

33 53 43 46 52 24 25 32 49 39 22 35 33 39 54 43 34 70 44 25.

Stem and leaf plot involves an ordered arrangement of values by seperating the the highest placed digit of each value into stems and the other digits into leaves.

Ordering the data :

Best actor :

25, 26, 27, 32, 32, 33, 35, 37, 37, 37, 38, 40, 44, 45, 48, 51, 52, 60, 61, 64

Best actress :

22, 24, 25, 25, 32, 33, 33, 34, 35, 39, 39, 43, 43, 44, 46, 49, 52, 53, 54, 70

The values range from :

22 to 70 ;

Hence, our stems will inculude : 2, 3, 4, 5, 6 and 7

LEAF ___________ stem _________ LEAF

Best actor age_____ | | ___ Best actress age

5, 6, 7 ___________| 2 | _______ 2, 4 5, 5

2, 2, 3, 5, 7, 7, 7, 8__ | 3 | __ 2, 3, 3, 4, 5, 9, 9

0, 4, 5, 8 _________| 4 | ______3, 3, 4, 6, 9

1, 2 _____________ | 5 | ___________ 2, 3

0, 1, 4 ___________ | 6 | ______________

________________ | 7 | _____________ 0

KEY : 2 | 2 = 22

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Answer:

2

Step-by-step explanation:

Rewriting the expression we have:

[tex]\dfrac{\dfrac{[(2\times 4)\times 3]}{12}\times(2\times 6)}{12}[tex]

Then we have the next step by step solution, starting by the insider parentheses:

[tex]\dfrac{\dfrac{[(2\times 4)\times 3]}{12}\times(2\times 6)}{12}=\dfrac{\dfrac{[8\times 3]}{12}\times(12)}{12}=\dfrac{\dfrac{24}{12}\times(12)}{12}=\dfrac{2\times(12)}{12}=\dfrac{24}{12}=2[/tex]

Answer:

V = 1.94 mi/h

Step-by-step explanation:

mark me brainliest plz

The speed of the current is approximately 0.5 mph.

Let's assume the speed of the current is "c" mph. Zene's upstream speed is (3 - c) mph and downstream speed is (3 + c) mph.

The time taken for the upstream trip is 7 / (3 - c) hours, and the time for the downstream trip is 7 / (3 + c) hours.

Since the total trip time is 8 hours, we can set up the equation:

7 / (3 - c) + 7 / (3 + c) = 8

Solving this equation, we find the speed of the current is approximately 0.5 mph.

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Answer:

Sample frame is the list of all counties in the U.S

Step-by-step explanation:

A sample frame refers to the set that lists all the individuals that could eventually be part of the selected random sample and, in fact, is used to make the selection of the sample units.

Taking into account the definition commented in the previous paragraph, in the situation described, the sample frame is the list of all counties in the U.S

Final answer:

To find the amount of Drug Z in the 50 ml injection, set up a proportion based on the known concentration (125 mg in 250 ml). Solving for the unknown quantity gives 25 mg of Drug Z in the injection.

Explanation:

To determine how much of Drug Z is in a 50 ml injection when 250 ml of the medication contains 125 mg of Drug Z, you can use a proportion. The proportion can be set up as follows:

(125 mg of Drug Z) / (250 ml of medication) = (X mg of Drug Z) / (50 ml of medication)

To solve for X, which represents the amount of Drug Z in the 50 ml injection, you cross-multiply and divide:

(125 mg) × (50 ml) = (250 ml) × (X mg)

6250 mg·ml = 250 ml·X mg

Divide both sides by 250 ml to isolate X:

X = (6250 mg·ml) / (250 ml)

X = 25 mg of Drug Z

Therefore, the 50 ml injection contains 25 mg of Drug Z.

Answer:

a.  [tex]\frac{dC(q)}{dq} = 0.000012q^2 -0.06q + 100[/tex]

b. [tex]\frac{dR(q)}{dq}=-0.01q+200[/tex]

c.

[tex]U'(2000)=-0.000012(2000)^2+0.05(2000)+100 = 152[/tex]

[tex]U'(7000)=-0.000012(7000)^2+0.05(7000)+100 = -138[/tex]

Step-by-step explanation:

a) The marginal cost function is given by the derivative of the total cost function, in this way the marginal cost function for this company is:

[tex]\frac{dC(q)}{dq} = \frac{dC(q)}{dq} (0.000004q^ 3 - 0.03q ^ 2 + 100q + 75000) = 0.000012q^2 -0.06q + 100[/tex]

b) The income function is given by the relation [tex]R (q) = P (q) q = -0.005q^2 + 200q[/tex].

The marginal revenue function for the company is given by the derivative of the revenue function, in this way the marginal revenue function is:

[tex]\frac{dR(q)}{dq}= -0.01q+200[/tex]

(c) The profit function of the company is given by the relation [tex]U (q) = R (q) - C (q)[/tex], and the marginal utility function is given by the derivative of the utility function, in this way , the marginal utility function is:

[tex]\dfrac{dU(q)}{dq}=R'(q) - C'(q) = -0.01q+200 - (0.000012q^2-0.06q+100) = -0.000012q^2+0.05q+100[/tex]

When q = 2000, the marginal utility is:

[tex]U'(2000)=-0.000012(2000)^2+0.05(2000)+100 = 152[/tex]

When q = 7000, the marginal utility is:

[tex]U'(7000)=-0.000012(7000)^2+0.05(7000)+100 = -138[/tex]

Answer:

A boxplot offers us information that can be used to compare two variables. In particular, if one variable is quantitative and the other variable is qualitative, a boxplot is generated for each category of the qualitative variable. Therefore, through this graph it is possible to analyze the relationship between the amount of money spent on food and the gender of the person.

A circular diagram offers information for a single variable, especially of a qualitative type.

A histogram offers us information for a single variable, especially quantitative type.

A relational analysis between two variables could be done using options (D) or (E), however one of the variables of interest is of qualitative type and the other is of quantitative type, so the scatterplot and the two-way table.

Step-by-step explanation:

If 57% of the houses take more than three months to sell, there is a 2.6% chance that a random sample proportion would be as high as or higher than the one they obtained.

The appropriate conclusion is that if 57% of the houses take more than three months to sell, there is a 2.6% chance that a random sample proportion would be as high as or higher than the one they obtained. This means that the result is statistically significant, indicating that the proportion of houses that take more than three months to sell is likely higher than 57%.

Answer:

a. 4536, b. 2500, c. 500, d. 1080

Step-by-step explanation:

for every question we can use the numbers 0 - 9, this is 10 numbers in total (0, 1, 2, ,3 , 4, 5, 6, 7, 8, and 9).

Fore every case we have to check how many numbers we are allow to use in each digit.

"The number cannot start with zero" this left us with 9 options of numers for the first digit.

"no digits can be repeated." So if we already use one numer for the first, we can't repeat this in the second, and so on. So for the second numer we have 9 numbers as option (now we can use 0), for the third, since we already use 2 digits, we have 8 options, and for the last, we have 7

that results in: 9*9*8*7 = 4536

"The number must begin and end with an odd digit. " for odd digits we have 1, 3, 5, 7, 9 --> 5 options for the fist and last digit, and for the two middle digits, we have 10 options for each since it is allowed to repeat numbers

that results in: 5*10*10*5=2500

"The number must be at least 5000" So the first digit can use 5, 6, 7, 8, or 9 -->5 options for the fist digit

"and be divisible by 10." so it has to end in a 0, --> 1 option fot the last numer

and for the middle digits there are no restrictions, so we use the 10 options for each.

that results in: 5*10*10*1=500

"The number must be less than 3000 and must be even" for it to be less than 3000 it has to start with 0, 1 or 2 -> 3 options for the first digit

"and must be even" so the number has to end in 0, 2, 4, 6 or 8 --> 5 options for the last number

"No digits may be repeated in the last 3 digits." So we can't repeat in the middle number the one we put in the last digit, this gives us 9 options for the fist middle number and 8 for the second middle number

that results in: 3*8*9*5 = 1080

Final answer:

A step-by-step calculation is conducted for each condition to find the number of 4-digit numbers that can be formed using the digits 0-9 without repetition with conditions such as starting digit restrictions, parity, and divisibility. In total, there are 4536, 2500, 500, and 900 possible numbers for each condition respectively.

Explanation:

To calculate the number of 4-digit numbers meeting various conditions using the digits 0 through 9, we must consider each condition separately.

Answer:

The minimum value of objective function is 5 at x=0 and y=5.

Step-by-step explanation:

The given linear programming problem is

Minimize [tex]z=4x+y[/tex]

Subject to  constraints

[tex]2x+4y\geq 20[/tex]         .... (1)

[tex]3x+2y\leq 24[/tex]          .... (2)

[tex]x,y\geq 0[/tex]

The related line of both inequalities are solid lines because the sign of inequalities are ≤ and ≥. It means the points lie on related line are included in the solution set.

Check both inequalities by (0,0).

[tex]2(0)+4(0)\geq 20[/tex]

[tex]0\geq 20[/tex]

This statement is not true. So, the shaded region of inequality (1) will not contain the origin.

[tex]3(0)+2(0)\leq 24[/tex]

[tex]0\leq 24[/tex]

This statement is true. It means the shaded region of inequality (2) will contain the origin.

[tex]x,y\geq 0[/tex] means first quadrant.

The common shaded region is feasible region. The vertices of feasible region are (0,5), (0,12) and (7,1.5).

Calculate the value of objective function at these vertices.

For (0,5)

[tex]z=4(0)+(5)=5[/tex]

For (0,12)

[tex]z=4(0)+(12)=12[/tex]

For (7,1.5)

[tex]z=4(7)+(1.5)=29.5[/tex]

Therefore the minimum value of objective function is 5 at x=0 and y=5.

Answer: The patient receives [tex]200\ \mu g[/tex] daily.

The  prescription will last 30 days .

Step-by-step explanation:

Given : Prescription= Two sprays into each nostril once daily.

That means total sprays for both nostrils = [tex]2\times2=4[/tex] [∵ 1 nostrils in each nose.]

If each spray contains [tex]50 \mu g[/tex] of drug, then the amount of drug received by patient daily :-

[tex]4\times50=200\ \mu g[/tex]

Thus , the patient receives [tex]200\ \mu g[/tex] daily.

Also, the container can deliver a  total of 120 sprays.

Then, the number of days of use will the  prescription last the patient will be:_

[tex]\dfrac{120}{4}=30[/tex]

Hence,  the  prescription will last 30 days of use .

Final answer:

The patient will receive 200 micrograms of mometasone furoate monohydrate daily, and the prescription will last for 30 days.

Explanation:

The question involves calculating the total dosage of mometasone furoate monohydrate received daily by a patient and determining how many days the prescription will last, based on the dose and the number of sprays available.

To find the daily dose, we can multiply the number of sprays per nostril by the dosage per spray and the number of nostrils:

2 sprays/nostril × 50 μg/spray × 2 nostrils = 200 μg/day

The patient receives 200 micrograms daily.

To find out how many days the prescription will last:

120 sprays/container ÷ (2 sprays/nostril × 2 nostrils) = 120 sprays/container ÷ 4 sprays/day = 30 days

The prescription will last the patient for 30 days.

Answer: a. 10.2 years

b. 12.6 years

c. 8.2 years

d. n = ln 4.1773/ln (1+r)

Step-by-step explanation:

$18,000 loan

annual​end-of-year installment payments of  ​$4,309

F = P(1+r)ⁿ

a. r = 15% = 0.15

18000 = 4309(1+0.15)ⁿ

18000/4309 = 1.15ⁿ

4.1773 = 1.15ⁿ

ln 4.1773 = ln 1.15ⁿ

ln 4.1773 = n*ln 1.15

n = ln 4.1773/ln 1.15

n = 10.2 years

b. r = 12% = 0.12

18000 = 4309(1+0.12)ⁿ

18000/4309 = 1.12ⁿ

4.1773 = 1.12ⁿ

ln 4.1773 = ln 1.12ⁿ

ln 4.1773 = n*ln 1.12

n = ln 4.1773/ln 1.12

n = 12.6 years

c. r = 19% = 0.19

18000 = 4309(1+0.19)ⁿ

18000/4309 = 1.19ⁿ

4.1773 = 1.19ⁿ

ln 4.1773 = ln 1.19ⁿ

ln 4.1773 = n*ln 1.19

n = ln 4.1773/ln 1.19

n = 8.2 years

d. The general relationship is  n = ln 4.1773/ln (1+r) r as a decimal

Answer:

1) 35 distinct groups can be formed.

2) 18  distinct groups can be formed containing 2 men and 1 woman.

Step-by-step explanation:

The no of groups of 3 members that can be chosen from 7 members equals no of combinations of 3 members that can be formed from 7 members.

Thus no of groups =

[tex]n=\binom{7}{3}=\frac{7!}{(7-3)!\times 3!}=35[/tex]

thus 35 distinct groups can be formed.

Part b)

Now since the condition is that we have to choose 2 men and 1 women to form the group

let A and B be men member's of group thus we have to choose 2 member's from a pool of 4 men which equals

[tex]\binom{4}{2}=\frac{4!}{(4-2)!\times 2!}=6[/tex]

Let the Woman member be C thus we have to choose one woman from a pool of 3 women hence number of ways in which it can be done equals 3.

thus the group can be formed in [tex]6\times 3=18[/tex] different ways.

Answer:

Step-by-step explanation:

We know that between 1 to 10 there are 5 even and 5 odd numbers.

We could get 4 even cards , 4 odd cards or 2 odd and 2 even cards

Let´s check all this combinations

Case 1: When all 4 numbers are even:  

We are going to take 4 of the 5 even numbers in the box so we have

[tex]5C4=5[/tex]

Case 2: When all 4 numbers are odd:  

We are going to take 4 of the 5 odd numbers in the box, so we have

[tex]5C4=5[/tex]

Case 3: When 2 are even and 2 are odd:

We are giong to take 2 from 5 even and odd cards in the box so we have

[tex]5C2 * 5C2[/tex]

Remember that we obtain the probability from

[tex]\frac{Number-of-favourable-Outcome}{Total-number-of-outcomes}[/tex]

So we have the number of favourable outcomes but we need the Total cases for drawing four cards, so we have that:  

We are taking 4 of the 10 cards:

[tex]10C_4=210[/tex]

Hence we have that the probability that their sum is even

[tex]\frac{5+5+100}{210}=\frac{11}{21}[/tex]

Final answer:

To find the probability that the sum of the four cards drawn is even, we can break down the problem into two cases: drawing all four even-numbered cards or drawing two even-numbered cards and two odd-numbered cards. Using the multiplication rule, we calculate the probability for each case and add them together to get the total probability.

Explanation:

Total Number of Possible Outcomes: If we draw four cards from a box containing cards numbered 1 to 10, the total number of ways to do this is given by the combination formula,

resulting in  10!/4!(10-4)! = 210 possible outcomes.

Number of Ways to Get an Even Sum:

For the sum of the numbers on the four drawn cards to be even, there are two cases to consider:

1. All four cards have even numbers: There are 5 even-numbered cards out of 10, and we need to choose 4 of them. The number of ways to do this is  =5.

2. Three cards have odd numbers, and one card has an even number:

   There are 5 odd-numbered and 5 even-numbered cards.

   We need to choose 3 odd-numbered cards out of 5 and 1 even-  numbered card out of 5.

  The number of ways to do this is =50

Total Number of Ways for an Even Sum:

Adding the possibilities from both cases, we have a total of 5 + 50 = 55 ways to get an even sum.

The probability is then calculated as the ratio of the number of ways to get an even sum to the total number of possible outcomes:

Probability = Number of Ways to Get an Even Sum/Total Number of Possible Outcomes = 55/210= 11/42

Therefore, the probability that the sum of the numbers on the four drawn cards is even is 11/42.

Answer:  5

Step-by-step explanation:

Let A denotes the number of major defects and B denotes the number of design defect.

By considering the given information, we have

[tex]U=28\ ;\ n(A)=14\ ;\ n(B)=8\ \ ;\ n(A^c\cap B^c)=1[/tex]

Now, the number of major defects or design defects:

[tex]n(A\cup B)=U-n(A^c\cap B^c)=28-11=17[/tex]

Also,

[tex]n(A\cap B)=n(A)+n(B)-n(A\cup B)\\\\\Rightarrow\ n(A\cap B)=14+8-17=5[/tex]

Hence, the number of  design defects were major=5

There are 5 design defects that are also classified as major defects.

To solve this problem, let's break down the information given and organize it in a systematic way using a Venn diagram and algebra.

Given data:

We need to find out how many of the design defects are also major defects.

Let's denote:

First, note that the defects that are neither major nor design are given as 11.

Therefore, the defects that are either major or design or both are:

[tex]28 - 11 = 17[/tex]

This tells us the total number of defects in sets A or B or both is 17.

Using the principle of inclusion-exclusion, the number of defects that are either major or design can be represented as:

[tex]|A \cup B| = |A| + |B| - |A \cap B|[/tex]

Where:
[tex]|A \cup B| = 17[/tex]
[tex]|A| = 14[/tex]
[tex]|B| = 8[/tex]

Now, substituting the values, we get:

[tex]17 = 14 + 8 - |A \cap B|[/tex]

Solving for [tex]|A \cap B|[/tex]:

[tex]17 = 22 - |A \cap B|[/tex]

[tex]|A \cap B| = 22 - 17 = 5[/tex]

So, the number of defects that are both design defects and major defects is 5.

Answer:

Hello, Your question is already answered but I wanted to add something else if you dont mind :) Inhalants can cause sudden death.

Step-by-step explanation:

Inhalants can kill you instantly. Inhalant users can die by suffocation, choking on their vomit, or having a heart attack. Most teenagers also consider Inhalants as relaxation, like when your stressed or if you've seen in most movies, people panic and then breath in paper bag. I'm not sure if those are the inhalers your talking about but It said 10 points so why not? Thank you, have a great day :)

The albuterol inhaler can deliver 200 inhalation-doses.

1 mg = 1000 μg

So, 18 mg = 18 * 1000 μg = 18000 μg

Number of inhalation-doses = Total albuterol / Amount per dose

Number of inhalation-doses = 18000 μg / 90 μg/dose

Number of inhalation-doses =  200 inhalation-doses

Therefore, the albuterol inhaler can deliver 200 inhalation-doses.

Read more about inhaler

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Let's suppose "good" here means that the amount a player can expect to win is positive.

The probability of drawing a heart from the deck is 13/52 = 1/4.

The probability of drawing a face card that is not a heart is 9/52.

The probability of drawing anything else is 30/52 = 15/26.

The expected winnings are then 10(1/4) + 8(9/52) - 6(15/26) = 11/26, meaning on average the player can expect to win about $0.42 per game, so by our definition this game is a "good" way to make money.

Statistically speaking, a player would gain 42 cents per game in the long run, making this gambling game potentially profitable.

This is determined by computing expected value, which takes into account the gains or losses for each possible outcome and the probability of each outcome.

The subject of this question is probability with reference to a game of cards. To evaluate whether or not the game is a good idea, we need to determine the expected value of the game, which is calculated by multiplying the value of each outcome by their probability and then summing these products. Here's how finances from the game might play out statistically:

The expected value of one round of the game is thus (0.25 x $10) + (0.173 x $8) + (0.577 x -$6) = $2.5 + $1.38 - $3.46 = $0.42. Therefore, statistically speaking, a player would gain 42 cents per game in the long run, making this gambling game potentially profitable.

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