Find the period and amplitude of the function. y-2sin 6x Give the exact values, not decimal approximations. Period: 2 Amplitude:

Answer:

ohhh you have the right time and I am so glad to see it in a better time and if it was not to do you have no doubt

Step-by-step explanation:

your body has to have your body to have the best results you need for kids in a group that can help with a lot to learn about it as you do so much of the time it works out to you to get the job you need for the next few years or 8īijjhguu is not just the best person but the meaning and skills of a person is the meaning of life and the meaning is the only 3AM in a school that you need a lot of a job 3to to do with you need to get your mind off to get your job done with your mind and then you have to do it right now and.

Answer:

1) Distance in feet equals 1640.4 feet

2) Distance in miles equals 0.3107 miles.

Step-by-step explanation:

From the basic conversion factors we know that

1 meter = 3.2808 feet

Thus by proportion we conclude that

[tex]500meters=500\times 3.2808feet\\\\\therefore 500meters=1640.4feet[/tex]

Similarly using the basic conversion factors we know that

1 mile = 1609.34 meters

thus we conclude that 1 meter =[tex]\frac{1}{1609.34}[/tex] miles

Hence by proportion 500 meters = [tex]500\times \frac{1}{1609.34}=0.3107[/tex] miles

Answer:

T={...,-3,-2,-1,0,1,2,3,4,....}

Step-by-step explanation:

We are given that T={5a+2b; a,b belongs Z}

We have to rewrite the given set T as  a list of its elements

Substitute a=0 and b=0

Then we get 5(0)+2(0)=0

Substitute a=-1 and b=2 then we get

5(-1)+2(2)=-1

Substitute a=2 and b=0

Then , 5(2)+2(0)=10

If a=0 and b=1

Then, 5(0)+2(1)=2

Substitute a=0 and b=2

Then, 5(0)+2(2)=4

If substitute a=1 and b=1

5(1)+2(1)=7

If substitute a=-1 and b=3

Then, we get 5(-1)+2(3)=1

Then, T={...,-3,-2,-1,0,1,2,3,4,....}

Answer:

Step-by-step explanation:

We know that multiplication product of two given positive real number will always be positive real number and if one of the real number is negative, the multiplication product will always be negative.

so for the given condition, if [tex]x > 0[/tex] and [tex]y > 0[/tex], [tex]x[/tex] and [tex]y[/tex] are both positive real numbers

hence their multiplication product [tex]xy[/tex] will also be a positive number.

∴ [tex]xy > 0[/tex]

Answer:

a) [tex]\neg \forall x :x>5 \equiv \forall x:x\leq 5[/tex]

b) [tex]\neg [x^2+2x+1=0]\equiv x^2+2x+1\neq0[/tex] or the set [tex]\{x:x\neq-1\}[/tex]

Step-by-step explanation:

First, notice that in both cases we have to sets:

a) is the set of all real numbers which are higher than 5 and in

b) the set is the solution of the equation [tex]x^2+2x+1=0[/tex] which is the set [tex]x=-1[/tex]

De Morgan's Law for set states:

[tex]\overline{\rm{A\cup B}} = \overline{\rm{A}} \cap \overline{\rm{B}}\\[/tex], being [tex]\overline{\rm{A}}[/tex] and [tex]\overline{\rm{B}}[/tex] are the complements of the sets [tex]A[/tex] and [tex]B[/tex]. [tex]\cup[/tex] is the union operation and [tex]\cap[/tex] the intersection.

Thus for:

a) [tex]\neg \forall x :x>5 \equiv \forall x:x\leq 5[/tex]. Notice that [tex]\forall x:x\leq 5[/tex] is the complement of the given set.

b) [tex]\neg [x^2+2x+1=0]\equiv x^2+2x+1\neq0[/tex] which is the set [tex]B = \{x:x\neq-1\}[/tex]

Answer: 120

Step-by-step explanation:

The total number of digits from 1 to 9 = 10

The number of digits from less than 5 (0,1,2,3,4)=5

Since repetition is not allowed so we use Permutations , then the number of 3-digit different codes will be formed :-

[tex]^5P_3=\dfrac{5!}{(5-3)!}=\dfrac{5\times4\times3\times2!}{2!}=5\times4\times3=60[/tex]

The number of digits from greater than 4 (5,6,7,8,9)=5

Similarly, Number of 3-digit different codes will be formed :-

[tex]^5P_3=60[/tex]

Hence, the required number of 3-digit different codes = 60+60=120

Answer:

To see the steps to the diagonal form see the step-by-step explanation. The solution to the system is [tex]x =  -\frac{1}{9}[/tex], [tex]y= -\frac{1}{9}[/tex], [tex]z= \frac{4}{9}[/tex] and [tex]w = \frac{7}{9}[/tex]

Step-by-step explanation:

Gauss elimination method consists in reducing the matrix to a upper triangular one by using three different types of row operations (this is why the method is also called row reduction method). The three elementary row operations are:

To solve the system using the Gauss elimination method we need to write the augmented matrix of the system. For the given system, this matrix is:

[tex]\left[\begin{array}{cccc|c}1 & 1 & 1 & 1 & 1 \\1 & 1 & 0 & -1 & -1 \\-1 & 1 & 1 & 2 & 2 \\1 & 2 & -1 & 1 & 0\end{array}\right][/tex]

For this matrix we need to perform the following row operations:

After this step, the system has an upper triangular form

The triangular matrix looks like:

[tex]\left[\begin{array}{cccc|c}1 & 0 & 0 & -0.5 & -0.5  \\0 & 1 & 0 & -0.5 & -0.5\\0 & 0 & 1 & 2 &  2 \\0 & 0 & 0 & 1 &  \frac{7}{9}\end{array}\right][/tex]

If you later perform the following operations you can find the solution to the system.

After this operations, the matrix should look like:

[tex]\left[\begin{array}{cccc|c}1 & 0 & 0 & 0 & -\frac{1}{9}  \\0 & 1 & 0 & 0 &   -\frac{1}{9}\\0 & 0 & 1 & 0 &  \frac{4}{9} \\0 & 0 & 0 & 1 &  \frac{7}{9}\end{array}\right][/tex]

Thus, the solution is:

[tex]x =  -\frac{1}{9}[/tex], [tex]y= -\frac{1}{9}[/tex], [tex]z= \frac{4}{9}[/tex] and [tex]w = \frac{7}{9}[/tex]

Answer: 29

Step-by-step explanation:

In statistics, the degrees of freedom gives the number of values that have the freedom to vary.

If the sample size is 'n' then the degree of freedom is given by:-

df= n-1

Given: The number of participants for the sample =30

Then the degree of freedom for this sample=30-1=29

Hence, The total degree of freedom= 29

In the context of the experimental design, the total degrees of freedom would be calculated based on the between-group and within-group variations. With three groups and three repeats, the total degrees of freedom would be 62.

When calculating the total degrees of freedom in an experiment where 30 participants each completed a memory task three times under different levels of caffeine, we can determine the degrees of freedom by considering the number of groups and the number of repeats within each group. Since there are three groups (no, moderate, and high levels of caffeine), and each participant completes the task three times, this setup hints at an Analysis of Variance (ANOVA) scenario with repeated measures. However, without the detailed design for the within-subject factors, we can only calculate the between-group degrees of freedom. For three groups, the between-group degrees of freedom would be the number of groups minus one, which would give us 2 degrees of freedom (dfbetween = number of groups - 1).

For within-group or repeated measures, you typically have dfwithin = (number of repeats - 1) × number of subjects. Since each participant repeats the task three times, and there are 30 participants, the calculation would be dfwithin = (3 - 1) × 30 = 2 × 30 = 60 degrees of freedom. Hence, the total degrees of freedom would be the sum of between-group and within-group degrees of freedom, which is 2 + 60 = 62.

Answer:

relative can take 2 tablets every six hours or 8 tablets a day without the amount being dangerous

Step-by-step explanation:

Given:

Amount of Tylenol per day that is dangerous = 2.3 g

1 g = 1000 mg

thus,

= 2.3 × 1000 mg

= 2300 mg

Amount of scored Tylenol tablets every six hours = 200 mg

Now,

for 6 hours intervals, total intervals in a day = [tex]\frac{\textup{24}}{\textup{6}}[/tex]  = 4

thus,

He takes Tylenol tablets 4 times a day

Now,

let x be the number of tablets taken in every interval

thus,

4x × 200 mg ≤ 2300

or

800x ≤ 2300

or

x ≤ 2.875

hence, relative can take 2 tablets every six hours or 8 tablets a day without the amount being dangerous

A person should take 2 tablets of 200mg Tylenol every six hours to keep the daily dose under the dangerous level of 2.3g.

The question is asking how many 200 mg tablets of Tylenol can a person consume every six hours (which is four times a day), while keeping the daily dose under 2.3g, to avoid a risk level that can be dangerous. The first step is to convert the maximum safe dose from grams to milligrams, because the dose per tablet is given in milligrams. 2.3 g equals 2300 milligrams.

Then, to find out the number of safe tablets per dose, you divide the total safe amount by the number of doses per day. So, 2300 milligrams divided by 4 equals 575 milligrams per dose. Last but not least, to find out the number of tablets, you should divide the amount per dose by the amount in each tablet: 575 divided by 200 equals about 2.875.

Since you cannot take a fraction of a tablet, the safest number of tablets to take every six hours would be 2.

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To find the probability, you need to calculate the number of ways to choose one Macintosh and one Windows computer from the given options and divide it by the total number of ways to choose two computers. The probability is 0.507.

To find the probability that the sample contains exactly one Windows machine and exactly one Macintosh machine, we can use the concept of combinations. There are a total of 30 computers, out of which 17 are Macintosh and 13 are Windows. The number of ways to choose one Macintosh and one Windows computer can be calculated by multiplying the number of ways to choose one Macintosh from 17 and the number of ways to choose one Windows from 13.

The number of ways to choose one Macintosh from 17 is C(17, 1) = 17 and the number of ways to choose one Windows from 13 is C(13, 1) = 13. Therefore, the total number of ways to choose one Macintosh and one Windows computer is 17 * 13 = 221.

The sample space is the total number of ways to choose two computers from 30, which is C(30, 2) = 435. So the probability of selecting exactly one Windows machine and exactly one Macintosh machine is 221 / 435 = 0.507.

Answer:

the correct answer is 2 blocks

Mario is 2 blocks away from his home after walking 7 blocks to a restaurant and then 5 blocks back towards home with help of subtraction.

The number of blocks that Mario is from his home can be calculated by finding the difference between the number of blocks he walked away from home and the number of blocks he walked back home. If Mario starts by walking 7 blocks from his home to a restaurant, he is initially 7 blocks away from home. If he then walks 5 blocks back toward home, he is effectively reducing the distance from his home by 5 blocks. You can calculate the new distance to his home by subtracting 5 from 7, which equals 2 blocks. Therefore, Mario is 2 blocks away from his home when he stops at the bookstore.

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Answer:

The horsepower required is 235440 watt.

Step-by-step explanation:

To find : What horsepower is required to lift an 8,000 pound aircraft six feet in two minutes?

Solution :

The horsepower formula is given by,

[tex]W=\frac{mgh}{t}[/tex]

Where, W is the horsepower

m is the mass m=8000 pound

g is the gravitational constant g=9.81

t is the time t= 2 minutes

h is the height h=6 feet

Substitute all values in the formula,

[tex]W=\frac{8000\times 9.81\times 6}{2}[/tex]

[tex]W=\frac{470880}{2}[/tex]

[tex]W=235440[/tex]

Therefore, The horsepower required is 235440 watt.

Answer:

602 tourists visited only the LEGOLAND.

Step-by-step explanation:

To solve this problem, we must build the Venn's Diagram of this set.

I am going to say that:

-The set A represents the tourists that visited LEGOLAND

-The set B represents the tourists that visited Universal Studios

-The set C represents the tourists that visited Magic Kingdown.

-The value d is the number of tourists that did not visit any of these parks, so: [tex]d = 58[/tex]

We have that:

[tex]A = a + (A \cap B) + (A \cap C) + (A \cap B \cap C)[/tex]

In which a is the number of tourists that only visited LEGOLAND, [tex]A \cap B[/tex] is the number of tourists that visited both LEGOLAND and Universal Studies, [tex]A \cap C[/tex] is the number of tourists that visited both LEGOLAND and the Magic Kingdom. and [tex]A \cap B \cap C[/tex] is the number of students that visited all these parks.

By the same logic, we have:

[tex]B = b + (B \cap C) + (A \cap B) + (A \cap B \cap C)[/tex]

[tex]C = c + (A \cap C) + (B \cap C) + (A \cap B \cap C)[/tex]

This diagram has the following subsets:

[tex]a,b,c,d,(A \cap B), (A \cap C), (B \cap C), (A \cap B \cap C)[/tex]

There were 1,107 tourists suveyed. This means that:

[tex]a + b + c + d + (A \cap B) + (A \cap C) + (B \cap C) + (A \cap B \cap C) = 1,107[/tex]

We start finding the values from the intersection of three sets.

The problem states that:

36 tourists had visited all three theme parks. So:

[tex](A \cap B \cap C) = 36[/tex]

72 tourists had visited both LEGOLAND and Universal Studios. So:

[tex](A \cap B) + (A \cap B \cap C) = 72[/tex]

[tex](A \cap B) = 72 - 36[/tex]

[tex](A \cap B) = 36[/tex]

79 tourists had visited both the Magic Kingdom and Universal Studios

[tex](B \cap C) + (A \cap B \cap C) = 79[/tex]

[tex](B \cap C) = 79 - 36[/tex]

[tex](B \cap C) = 43[/tex]

68 tourists had visited both the Magic Kingdom and LEGOLAND

[tex](A \cap C) + (A \cap B \cap C) = 68[/tex]

[tex](A \cap C) = 68 - 36[/tex]

[tex](A \cap C) = 32[/tex]

258 tourists had visited Universal Studios:

[tex]B = 258[/tex]

[tex]B = b + (B \cap C) + (A \cap B) + (A \cap B \cap C)[/tex]

[tex]258 = b + 43 + 36 + 36[/tex]

[tex]b = 143[/tex]

268 tourists had visited the Magic Kingdom:

[tex]C = 268[/tex]

[tex]C = c + (A \cap C) + (B \cap C) + (A \cap B \cap C)[/tex]

[tex]268 = c + 32 + 43 + 36[/tex]

[tex]c = 157[/tex]

How many tourists only visited the LEGOLAND (of these three)?

We have to find the value of a, and we can do this by the following equation:

[tex]a + b + c + d + (A \cap B) + (A \cap C) + (B \cap C) + (A \cap B \cap C) = 1,107[/tex]

[tex]a + 143 + 157 + 58 + 36 + 32 + 43 + 36 = 1,107[/tex]

[tex]a = 602[/tex]

602 tourists visited only the LEGOLAND.

Final answer:

To find the total kilograms of ibuprofen, multiply 36 tablets by 200 mg each to get 7200 mg, and then divide by 1,000,000 to convert to kilograms, resulting in 0.0072 kg.

Explanation:

To calculate the total amount of ibuprofen in kilograms, you start by finding the total amount in milligrams. Multiply the number of tablets (36) by the amount of ibuprofen per tablet (200 mg).

36 tablets × 200 mg/tablet = 7200 mg

Now, since there are 1,000,000 milligrams in a kilogram, you'll need to divide the total milligrams by 1,000,000 to convert it to kilograms.

7200 mg ÷ 1,000,000 mg/kg = 0.0072 kg

Therefore, the package contains 0.0072 kilograms of ibuprofen.

Answer:

R = {(10,2), (10,4), (10,6), (10,8), (2,10), (2,2), (2,4), (2,6), (2,4), (4,10), (4,2), (4,6), (6,10), (6,2), (6,4), (6,8)}

Step-by-step explanation:

A = (10, 1, 2, 3, 4, 5, 6)

B = (10, 1, 2, 3, 4, 5, 6, 7, 8)

R is a relation and defined as

R: A→B

R: The greatest common divisor of a and b is 2

To find the elements of R we need to find pair from A and B respectively.

R = {(10,2), (10,4), (10,6), (10,8), (2,10), (2,2), (2,4), (2,6), (2,4), (4,10), (4,2), (4,6), (6,10), (6,2), (6,4), (6,8)}

Now, these pairs were found by picking one element from A and checking with elements of B if they have a gcd of 2. If yes, they fall under the defined relation.

Answer:

Ans. Effective annual rate=1.8928%

Annual Compound semi-annually=1.8839%

Step-by-step explanation:

Hi, this is the formula to find the effective annual rate for this zero-coupon bond.

[tex]EffectiveAnnualRate=\sqrt[n]{\frac{FaceValue}{Price} } -1[/tex]

n= years to maturity

That is:

[tex]EffectiveAnnualRate=\sqrt[8]{\frac{50,000}{43,035} } -1=0.018928[/tex]

Means that the effective interest rate is 1.8928% effective annual

Now, let´s find the compound interest rate.

First, we have to turn this rate effective semi-annually

[tex]Semi-AnnualRate=(1+0.018928)^{\frac{1}{2} }  -1=0.00942[/tex]

0.942% effective semi annual

To turn this into a semi-annual, compounded semi-annually, we just have to multiply by 2, so we get.

1.8839% compounded semi-annually

Best of luck

Answer:

1) [tex]L(y)=\frac{2}{s^{3}}[/tex]

2) [tex]L(y)=\frac{6}{s^{4}}[/tex]

Step-by-step explanation:

To find : Calculate the Laplace transforms of the following from the definition ?

Solution :

We know that,

Laplace transforms of [tex]t^n[/tex] is given by,

[tex]L(t^n)=\frac{n!}{s^{n+1}}[/tex]

1) [tex]y=t^2[/tex]

Laplace of y,

[tex]L(y)=L(t^2)[/tex] here n=2

[tex]L(y)=\frac{2!}{s^{2+1}}[/tex]

[tex]L(y)=\frac{2}{s^{3}}[/tex]

2) [tex]y=t^3[/tex]

Laplace of y,

[tex]L(y)=L(t^3)[/tex] here n=3

[tex]L(y)=\frac{3!}{s^{3+1}}[/tex]

[tex]L(y)=\frac{3\times 2}{s^{4}}[/tex]

[tex]L(y)=\frac{6}{s^{4}}[/tex]

Answer:

The solutions of the quadratic equation are [tex]x_{1} = \frac{5 + \sqrt{13}}{6}, x_{2} = \frac{5 - \sqrt{13}}{6}[/tex]

Step-by-step explanation:

This is a second order polynomial, and we can find it's roots by the Bhaskara formula.

Explanation of the bhaskara formula:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = (x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]\bigtriangleup = b^{2} - 4ac[/tex]

For this problem, we have to find [tex]x_{1} \text{and} x_{2}[/tex].

The polynomial is [tex]3x^{2} - 5x +1[/tex], so a = 3, b = -5, c = 1.

Solution

[tex]\bigtriangleup = b^{2} - 4ac = (-5)^{2} - 4*3*1 = 25 - 12 = 13[/tex]

[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a} = \frac{-(-5) + \sqrt{13}}{2*3} = \frac{5 + \sqrt{13}}{6}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a} = \frac{-(-5) - \sqrt{13}}{2*3} = \frac{5 - \sqrt{13}}{6}[/tex]

The solutions of the quadratic equation are [tex]x_{1} = \frac{5 + \sqrt{13}}{6}, x_{2} = \frac{5 - \sqrt{13}}{6}[/tex]

Answer:

B. 4,200±CONFIDENCE.T(0.10,140,12)

Step-by-step explanation:

We are in posession's of the sample standard deviation, so the t-distribution is used.

The confidence interval is a function of the sample mean and the margin of error.

That is:

[tex]C.I = S_{M} \pm M_{E}[/tex]

In which [tex]S_{M}[/tex] is the sample mean, and the [tex]M_{E}[/tex] is the margin of error, related to the confidence level, the sample's standard deviation and the sample size.

So the correct answer is:

B. 4,200±CONFIDENCE.T(0.10,140,12)

Answer:

136 units

65x - 8840

Step-by-step explanation:

Given,

The production cost function is,

[tex]C(x) = 195x + 8840[/tex]

Revenue function,

[tex]R(x)=260x[/tex]

So, profit would be,

P(x) = Revenue - cost

= 260x - 195x - 8840

= 65x - 8840

In break even condition,

Profit, P(x) = 0

65x - 8840 = 0

65x = 8840

⇒ x = 136.

Hence, the break even quantity is 136 units.

The break-even quantity is 1360 units, where the revenue equals the cost. The profit function is given by P(x) = R(x) - C(x).

To find the break-even quantity, we need to find the point where the revenue function equals the production cost function. So we set R(x) equal to C(x) and solve for x:

260x = 195x + 88408

Simplifying the equation, we get:

65x = 88408

x = 1360

Now we analyze the break-even quantity. The break-even quantity is the point at which the firm's revenue equals its cost. In this case, it occurs at 1360 units. At this quantity, the firm's total revenue will equal its total cost, resulting in zero profit.

To find the profit function, we subtract the cost function C(x) from the revenue function R(x). The profit function can be expressed as:

P(x) = R(x) - C(x)

Answer:

Is needed 16 fluid oz of water to fill in 2 cups of water

Step-by-step explanation:

1 cup have 8 fluid oz

2 cups = 2 * 8 fluid oz = 16 fluid oz

Final answer:

The recipe requires 2 cups of water, which is equivalent to 16 fluid ounces since there are 8 fluid ounces in one cup.

Explanation:

To calculate how many fluid ounces of water is needed if a recipe requires 2 cups of water, you need to understand the unit equivalence between cups and fluid ounces. One cup is equivalent to 8 fluid ounces. Since the recipe requires 2 cups, you will multiply the number of cups by the unit equivalence to find the total number of fluid ounces.

Here is the calculation:

2 cups × 8 fluid ounces/cup = 16 fluid ounces

Therefore, the recipe requires 16 fluid ounces of water.

Answer:

[tex]8+27=17+18=35 cm=0.35 meter[/tex]

Step-by-step explanation:

[tex]8+27=35[/tex] cm

= [tex]17+18=35[/tex] cm as [tex]35-18=17[/tex] cm

Now as the final answer is in meters, so, we will convert 35 cm in meters.

100 cm = 1 meter

So, 35 cm = [tex]\frac{35}{100}=0.35[/tex] meters

Therefore, we can write the final expression as:

[tex]8+27=17+18=35 cm=0.35 meter[/tex]

Answer:

Step-by-step explanation:

Let A, B and C be square matrices, let [tex]D = ABC[/tex]. Suppose also that D is an invertible square matrix. Since D is an invertible matrix, then [tex]det (D) \neq 0[/tex]. Now, [tex]det (D) = det (ABC) = det (A) det (B) det (C) \neq 0[/tex]. Therefore,

[tex]det (A) \neq 0[/tex]

[tex]det (B) \neq 0 [/tex]

[tex]det (C) \neq 0[/tex]

which proves that A, B and C are invertible square matrices.

Answer:

a) Mode: 2 Median: 3 Mean: 4.6

b) Mode: 7 Median: 8 Mean: 9.6

c) Just added 5 to values. General below.

Step-by-step explanation: 2, 2, 3, 6, 10

a) Mode: 2 (Most apperances)

Median: 3 (odd data, middle number)

Mean: (2+2+3+6+10)/5 = 23/5 = 4.6

b) + 5

Data: 7,7,8,11,15

Mode: 7 (Most apperances)

Median: 8 (odd data, middle number)

Mean: (7+7+8+11+15)/5 = 48/5 = 9.6

c) The results from (b) is (a) + 5

In general: Let's add x to the same data provided:

2+x, 2+x, 3+x, 6+x, 10+x,

For the mode, it does not matter, the number with most apperances will continue to be the mode + x

For the median, same thing. It is just the median + x

For the mean, same thing. For the set of 5 numbers:

(2+x + 2+x + 3+x + 6+x + 10+x)/5 =

(23+5x)/5

23/5 + 5x/5 =

23/5 + x

For example, If it was 6 numbers, we would add 6 times that number and divide it by 6, adding x to the mean.

To compute the mode, median, and mean of a data set, count the frequency of each number, arrange the data in order, and find the middle value. Adding the same constant to each data value affects the mean but does not change the mode or median.

To compute the mode, median, and mean of the data set {2, 2, 3, 6, 10}, we can follow these steps:

After adding 5 to each data value, the new data set becomes {7, 7, 8, 11, 15}.

In general, when the same constant is added to each data value in a set, the mode remains unchanged, the median remains unchanged, and the mean is affected by adding the constant to each value. The mean increases when the constant is positive and decreases when the constant is negative.

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Answer:

In 17th year, his income was $30,700.

Step-by-step explanation:

It is given that the income has been increasing each year by the same dollar amount. It means it is linear function.

Income in first year = $17,900

Income in 4th year = $20,300

Let y be the income at x year.

It means the line passes through the point (1,17900) and (4,20300).

If a line passes through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the equation of line is

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

The equation of line is

[tex]y-17900=\frac{20300-17900}{4-1}(x-1)[/tex]

[tex]y-17900=\frac{2400}{3}(x-1)[/tex]

[tex]y-17900=800(x-1)[/tex]

[tex]y-17900=800x-800[/tex]

Add 17900 on both sides.

[tex]y=800x-800+17900[/tex]

[tex]y=800x+17100[/tex]

The income equation is y=800x+17100.

Substitute y=30,700 in the above equation.

[tex]30700=800x+17100[/tex]

Subtract 17100 from both sides.

[tex]30700-17100=800x[/tex]

[tex]13600=800x[/tex]

Divide both sides by 800.

[tex]\frac{13600}{800}=x[/tex]

[tex]17=x[/tex]

Therefore, in 17th year his income was $30,700.

Final answer:

Joe's annual income increases by approximately $55.81 each year, starting at $17,900 in the first year. By dividing the desired income minus the starting income by the annual increase, we find that Joe will reach an income of $30,700 in his 230th year.

Explanation:

To determine in which year Joe's income reached $30,700, we need to establish a pattern of how his income has increased over the years. Given that Joe's income started at $17,900 in the first year and was $20,300 in the 44th year, we can calculate the annual increase in his income.

The total increase over 43 years (from year 1 to year 44) is $20,300 - $17,900 = $2,400. To find the annual increase, divide this by the number of years the increase occurred over, which is one less than the total number of years, because the increase starts after the first year. That is:

Annual Income Increase = Total Increase / Number of Years
Annual Income Increase = $2,400 / 43
Annual Income Increase = approximately $55.81 (rounded to two decimal places)

Now we need to calculate the number of years it would take for his income to reach $30,700, starting from $17,900 and increasing at a rate of approximately $55.81 per year.

Years Needed = (Desired Income - Starting Income) / Annual Increase
Years Needed = ($30,700 - $17,900) / $55.81
Years Needed = approximately 229.84, which we round up to 230, because you can't have a partial year in this context.

Therefore, Joe will reach an income of $30,700 in his 230th year of work (adding 230 to the first year).

Answer:

Step-by-step explanation:

If we assume that [tex][(x \vee y) \wedge (x \rightarrow z) \wedge (\neg z)][/tex] is true, then:

[tex](x \vee y)[/tex] is true

[tex](x \rightarrow z)[/tex] is true

[tex](\neg z)[/tex] is true

If [tex](\neg z)[/tex] is true, then [tex]z[/tex] is false.

[tex](x \rightarrow z) \equiv (\neg x \vee z)[/tex], since [tex](x \rightarrow z)[/tex] is true, then [tex](\neg x \vee z)[/tex] is true

If [tex]z[/tex] is false and [tex](\neg x \vee z)[/tex] is true, then [tex]\neg x[/tex] is true.

If [tex]\neg x[/tex] is true, then [tex]x[/tex] is false, as [tex](x \vee y)[/tex] is true and [tex]x[/tex] is false, then [tex]y[/tex] is true.

Conclusion [tex]y[/tex] it's true.

I will only do the first-three. You can repost number 4.

Question 1

f(x) = -x^2 + 10x + 4

dy/dx = -2x + 10

Question 2

f(x) = 20 - x + 2

dy/dx = -1

Question 3

f(x) = ex^4 - 2x^2

dy/dx = e•4x^3 + x^4 - 4x

dy/dx = 4ex^3 + x^4 - 4x

Answer:

Johnny is wrong.

[tex]A \cup B = \left\{a,b,c,d,e,f,g,h\right\}[/tex]

Step-by-step explanation:

Johnny is wrong.

A better definition would be: [tex]A \cup B[/tex] is the set of all elements that belong to at least one A or B.

So, the elements that belong to both A and B, like c and d in this exercise, also belong to [tex]A \cup B[/tex].

So:

[tex]A \cup B=\left\{a,b,c,d,e,f,g,h\right\}[/tex]

Answer:

62 inches

Step-by-step explanation:

Let x be the height ( in inches ) of Ivan,

∵ Marcia is 5 inches shorter than Ivan,

height of Marcia = x - 5,

Marcia is  twice as tall as Sally-Jo,

height of sally-jo = [tex]\frac{x-5}{2}[/tex]

Mom is 2 inches taller than Ivan.

⇒ height of mom = x + 2,

Mom is 3 inches shorter than Dad,

height of dad = x + 2 + 3 = x + 5,

So, mean height of family is,

[tex]\frac{x+x-5+\frac{x-5}{2}+x+2+x+5}{5}[/tex]

[tex]=\frac{2x+2x-10+x-5+2x+4+2x+10}{10}[/tex]

[tex]=\frac{9x-1}{10}[/tex]

According to the question,

x + 5 = 74 ( 1 ft = 12 in )

x = 69

Hence, mean height of the family = [tex]\frac{9\times 69-1}{10}[/tex]

[tex]=\frac{620}{10}[/tex]

= 62 inches