52.25 is ___% of 1,1050.00

Answer:

Distance of the point from its image = 8.56 units

Step-by-step explanation:

Given,

Co-ordinates of point is (-2, 3,-4)

Let's say

[tex]x_1\ =\ -2[/tex]

[tex]y_1\ =\ 3[/tex]

[tex]z_1\ =\ -4[/tex]

Distance is measure across the line

[tex]\dfrac{x+2}{3}\ =\ \dfrac{2y+3}{4}\ =\ \dfrac{3z+4}{5}[/tex]

So, we can write

[tex]\dfrac{x-x_1+2}{3}\ =\ \dfrac{2(y-y_1)+3}{4}\ =\ \dfrac{3(z-z_1)+4}{5}\ =\ k[/tex]

[tex]=>\ \dfrac{x-(-2)+2}{3}\ =\ \dfrac{2(y-3)+3}{4}\ =\ \dfrac{3(z-(-4))+4}{5}\ =\ k[/tex]

[tex]=>\ \dfrac{x+4}{3}\ =\ \dfrac{2y-3}{4}\ =\ \dfrac{3z+16}{5}\ =\ k[/tex]

[tex]=>\ x\ =\ 3k-4,\ y\ =\ \dfrac{4k+3}{2},\ z\ =\ \dfrac{5k-16}{3}[/tex]

Since, the equation of plane is given by

x+y+z=3

The point which intersect the point will satisfy the equation of plane.

So, we can write

[tex]3k-4+\dfrac{4k+3}{2}+\dfrac{5k-16}{3}\ =\ 3[/tex]

[tex]=>6(3k-4)+3(4k+3)+2(5k-16)\ =\ 18[/tex]

[tex]=>18k-24+12k+9+10k-32\ =\ 18[/tex]

[tex]=>\ k\ =\dfrac{13}{8}[/tex]

So,

[tex]x\ =\ 3k-4[/tex]

   [tex]=\ 3\times \dfrac{13}{8}-4[/tex]

   [tex]=\ \dfrac{7}{4}[/tex]

[tex]y\ =\ \dfrac{4k+3}{2}[/tex]

   [tex]=\ \dfrac{4\times \dfrac{13}{8}+3}{2}[/tex]

   [tex]=\ \dfrac{19}{4}[/tex]

[tex]z\ =\ \dfrac{5k-16}{3}[/tex]

  [tex]=\ \dfrac{5\times \dfrac{13}{8}-16}{3}[/tex]

   [tex]=\ \dfrac{-21}{8}[/tex]

Now, the distance of point from the plane is given by,

[tex]d\ =\ \sqrt{(x-x_1)^2+(y-y_1)^2+(z-z_1)^2}[/tex]

   [tex]=\ \sqrt{(-2-\dfrac{7}{4})^2+(3-\dfrac{19}{4})^2+(-4+\dfrac{21}{8})^2}[/tex]

   [tex]=\ \sqrt{(\dfrac{-15}{4})^2+(\dfrac{-7}{4})^2+(\dfrac{9}{8})^2}[/tex]

   [tex]=\ \sqrt{\dfrac{225}{16}+\dfrac{49}{16}+\dfrac{81}{64}}[/tex]

   [tex]=\ \sqrt{\dfrac{1177}{64}}[/tex]

   [tex]=\ 4.28[/tex]

So, the distance of the point from its image can be given by,

D = 2d = 2 x 4.28

            = 8.56 unit

So, the distance of a point from it's image is 8.56 units.

Answer:

Her adjusted body weight is 78.26kg = 78.3kg, rounded to the nearest tenth.

Step-by-step explanation:

To find the Adjusted Body Weight(AjBW), first we have to consider the Ideal Body Weight(IBW).

We have the following formulas:

[tex]IBW = 45.5kg + 2.3kg*i[/tex], in which i is the number of inches that the woman has above 5 feet.

[tex]AjBW = IBW + 0.4*(ABW - IBW)[/tex], in which [tex]ABW[/tex] is her Actual Body Weight

So, in this problem:

Each pound has 0.45kg. So her weight is [tex]ABW = 220*0.45 = 99.8[/tex]kg.

The woman is 8 inches above 5 feet, so [tex]i = 8[/tex].

[tex]IBW = 45.5 + 2.3*8[/tex]

[tex]IBW = 63.9[/tex]kg

Her ideal body weight is 63.9kg. Her adjusted body weight is:

[tex]AjBW = IBW + 0.4*(ABW - IBW)[/tex]

[tex]AjBW = 63.9 + 0.4*(99.8-63.9)[/tex]

[tex]AjBw = 78.26[/tex]kg

Her adjusted body weight is 78.26kg = 78.3kg.

Final answer:

Jordan received 27 text messages this week, which is 3 times more than the 9 messages she got last week.

Explanation:

Jordan received 9 text messages last week and this week she received 3 times more. To find out how many text messages Jordan received this week, multiply the number of messages from last week by 3.

9 text messages (last week) × 3 = 27 text messages (this week)

Therefore, Jordan received 27 text messages this week.

Jordan received 27 text messages this week. The average number of texts received per hour by a user is approximately 1.7292, based on the daily average. Precise probabilities for receiving exact or more than two messages per hour cannot be calculated without additional data.

Jordan received 9 text messages last week and three times more this week. To calculate how many text messages Jordan received this week, we multiply 9 by 3, which is 9 × 3 = 27 text messages this week.

To calculate the average texts received per hour, we divide the daily average by the number of hours in a day:

41.5 texts / 24 hours ≈ 1.7292 texts per hour.

a. The probability that a text message user receives or sends exactly two messages per hour is not provided in the given information and would typically require more data to calculate, like the distribution type. However, we know the average is 1.7292, so two messages is a little above average.

b. The probability of receiving more than two messages per hour involves determining the proportion of time users receive more than two messages, based on the average rate. Again, more information is needed to provide a precise probability.

Answer:

[tex]x=\frac{\pi}{4}[/tex] and [tex]x=-\frac{3\pi}{4}[/tex]

Step-by-step explanation:

We are given that sin x+cos x=cos 2x

We have to solve the given equation for [tex]0\leq x\leq 2\pi[/tex]

[tex] sin x+cos x=cos^2x-sin^2x[/tex]

Because [tex]cos 2x=cos^2-sin^2[/tex]

[tex] sinx+cos x=(sinx +cos x)(sinx-cos x)[/tex]

[tex] 1 =sin x-cos x[/tex]

[tex] sin x=cos x[/tex]

[tex]\frac{sinx }{cos x}=1[/tex]

[tex]tan x=1[/tex]

[tex]tan x=\frac{sinx}{cos x}[/tex]

[tex]tan x=tan\frac{\pi}{4}[/tex]

[tex]x=\frac{\pi}{4}[/tex]

Tan x is positive in I and III quadrant

In III quadrant angle[tex]\theta[/tex]  replace by [tex]\theta -\pi[/tex]

Therefore, [tex]tan x=tan (\frac{\pi}{4}-\pi)=tan\frac{\pi-4\pi}{4}=tan\frac{-3\pi}{4}[/tex]

[tex]x=-\frac{3\pi}{4}[/tex]

Answer:

The amount of drug required = 44.44 mL

Diluent needed = 355.56 mL

Step-by-step explanation:

Data provided in the question:

Total volume of solution = 400 mL

Concentration of drug = 1 : 8

Now,

The ratio is interpreted as 1 part of drug and 8 part of diluent

Thus,

The amount of drug required = [tex]\frac{1}{1+8}\times\textup{Total volume of solution}[/tex]

or

The amount of drug required = [tex]\frac{1}{1+8}\times\textup{400 mL}[/tex]

or

The amount of drug required = 44.44 mL

and,

Diluent needed = [tex]\frac{8}{1+8}\times\textup{400 mL}[/tex]

or

Diluent needed = 355.56 mL

Final answer:

To make a 400mL solution with a 1:8 drug concentration, you need 44.4mL of the drug and 355.6mL of sterile water.

Explanation:

To prepare 400mL of a solution with a 1:8 concentration of a drug, using sterile water as the diluent, we should first calculate the amount of drug needed. A 1:8 concentration ratio means that for every 1 part drug, there are 8 parts diluent. Therefore, the total number of parts is 1 (drug) + 8 (diluent) = 9 parts.

To find the amount of drug needed:

To find the amount of diluent needed:

To summarize, you need 44.4mL of the drug and 355.6mL of sterile water to make a 400mL solution with a 1:8 drug concentration.

Answer:

7438.

Step-by-step explanation:

Let x be the attendance before the drop.

We have been attendance dropped 16% this year, to 6248. We are asked to find the attendance before the drop.

The attendance after drop would be 84% (100%-16%) of x.

[tex]\frac{84}{100}\cdot x=6248[/tex]

[tex]0.84x=6248[/tex]

[tex]\frac{0.84x}{0.84}=\frac{6248}{0.84}[/tex]

[tex]x=7438.095[/tex]

[tex]x\approx 7438[/tex]

Therefore, the attendance before the drop is 7438.

Answer:  374416

Step-by-step explanation:

Given : A test requires that you answer first Part A and then either Part B or Part C.

Part A consists of 4 true false questions, Part B consists of 6 multiple-choice questions with one correct answer out of five, and Part C consists of 5 multiple-choice questions with one correct answer out of six.

i.e. 2 ways to answer each question in Part A.

For 4 questions, Number of ways to answer Part A = [tex]2^4[/tex]

5 ways to answer each question in Part B.

For 6 questions, Number of ways to answer Part B = [tex]5^6[/tex]

6 ways to answer each question in Part C.

For 5 questions, Number of ways to answer Part C = [tex]6^5[/tex]

Now, the number of ways to  completed answer sheets are possible :_

[tex]2^4\times5^6+2^4\times6^5\\\\=2^4(5^6+6^5)\\\\=16(15625+7776)\\\\=16(23401)=374416[/tex]

Hence, the number of ways to  completed answer sheets are possible = 374416

Answer:

Step-by-step explanation:

You already have the answer.

1 [at] = 760 [mmHg]

1 [at] = 14,7 [psi]

1500 [mmHg] * 1 [at] / 760 [mmHg] * 14,7 [psi] / 1 [at] = 29.0 [psi]

To measure tartar emetic for the prescription, keep in mind the sensitivity of your balance and the acceptable weighing error. Tartar emetic of 15mg should be weighed as accurately as the balance allows and if the measurement falls within the acceptable error range, it can be dissolved in cherry syrup for uniform distribution.

The tartar emetic dose required by the prescription is 0.015 g. However, you're using a balance with a sensitivity of 4 mg (milligrams). Similar to procure the accurate tartar emetic measurement, you must take into account the balance's sensitivity and the acceptable weighing error of 5%.

0.015 g is equal to 15 mg. Our balance's lowest measurement is 4 mg, which is less than the 15 mg we need to weight accurately. When considering the acceptable weighing error of 5%, the actual amount of tartar emetic measured could range from 14.25 mg to 15.75 mg (15 mg ± 5%).

To solve with the stipulated constraints, you need to carefully weigh out the tartar emetic as close as the balance will allow, and if it does not reach the desired measurement but falls within the acceptable error range, you can dissolve it in the cherry syrup for uniform distribution within the medication. Always remember to mix well and be precise with measurements to ensure the correct strength of medicine.

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Calculate the acceptable error range for the weight of tartar emetic, then weigh it out on a balance with the specified sensitivity. Once within the error range, dissolve the tartar emetic in the cherry syrup.

The question asks how to obtain the correct quantity of tartar emetic given the equipment and accepted weighing error. To do this, first you must calculate the acceptable error range by multiplying the desired weight of the tartar emetic (0.015 g) by 5%, which yields an acceptable error of 0.00075 g. Since your balance has a sensitivity of 4 mg (0.004 g), it can accurately measure out this quantity. Then you would weigh out the tartar emetic on the balance until you are within this error range.

It's important to note that tartar emetic is fully soluble in water and so cherry syrup, which is water-based, can be used as the solvent for tartar emetic. After weighing, dissolve the tartar emetic into the cherry syrup before moving on to measure out the other ingredients for the prescription.

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Final answer:

There are 21 different sets of five marbles that can be made from one transparent, three yellow, and three orange marbles, with no red or green marbles included.

Explanation:

The student has asked how many possible sets of five marbles there are, with the restriction that none of the marbles in a set can be red or green. Considering the available marbles, the student can only choose from one transparent, three yellow, and three orange marbles.

Since there is no replacement and the colors do not matter beyond not being red or green, the student is creating combinations of seven unique marbles taken five at a time. This can be calculated using the combination formula C(n, k) = n! / (k!(n - k)!), where n is the total number of items to choose from, k is the number needed for the set, and ! denotes factorial.

For this problem, n is 7 (1 transparent + 3 yellow + 3 orange) and k is 5. So, we calculate C(7, 5) = 7! / (5!(7 - 5)!) = 7! / (5!2!) = (7 × 6) / (2 × 1) = 21. There are 21 different sets of five marbles where none are red or green.

The mean cost of repair is $391.75. The median cost of repair is $419.50. There is no mode for the repair costs.

To compute the mean, median, and mode cost of repair, we first need to list the repair costs in numerical order:

The mean is calculated by finding the average of the repair costs, which is the sum of the costs divided by the total number of costs. In this case, the mean is $(249 + 403 + 436 + 479)/4 = $391.75.

The median is the middle value of the data set once it is ordered. In this case, the median is $419.50, which is the average of $403 and $436.

The mode is the value that appears most frequently in the data set. In this case, there is no mode because none of the repair costs occur more than once.

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The mean cost of repair is $391.75, while the median cost is $419.50. Since there are no repeated repair costs, there is no mode.

To determine the mean, median, and mode repair costs of the four cars, follow these steps:

Mean

The mean (average) cost of repair is calculated by summing all the repair costs and then dividing by the number of cars.

Sum of costs = $436 + $403 + $479 + $249 = $1567

Number of cars = 4

Mean = $1567 / 4 = $391.75

So, the mean cost of repair is $391.75.

Median

To find the median, list the repair costs in ascending order: $249, $403, $436, $479.

Since there are four data points (even number), the median is the average of the two middle numbers.

Median = ($403 + $436) / 2 = $839 / 2 = $419.50

So, the median cost of repair is $419.50.

Mode

The mode is the number that appears most frequently in a data set.

In this case, each cost appears only once; therefore, no mode exists.

Answer:

x-intercept: (2,0)

y-intercept: (0,3)

Step-by-step explanation:

We are asked to graph our given equation [tex]\frac{1}{2}x+\frac{1}{3}y=1[/tex].

To find x-intercept, we will substitute [tex]y=0[/tex] in our given equation.

[tex]\frac{1}{2}x+\frac{1}{3}(0)=1[/tex]

[tex]\frac{1}{2}x+0=1[/tex]

[tex]2*\frac{1}{2}x=2*1[/tex]

[tex]x=2[/tex]

Therefore, the x-intercept is [tex](2,0)[/tex].

To find y-intercept, we will substitute [tex]x=0[/tex] in our given equation.

[tex]\frac{1}{2}(0)+\frac{1}{3}y=1[/tex]

[tex]0+\frac{1}{3}y=1[/tex]

[tex]3*\frac{1}{3}y=3*1[/tex]

[tex]y=3[/tex]

Therefore, the y-intercept is [tex](0,3)[/tex].

Upon connecting these two points, we will get our required graph as shown below.

Answer:

The sum of even numbers between 1 and 100 is 2550.

Step-by-step explanation:

To find : Add the even numbers between 1 and 100?

Solution :

The even numbers from 1 to 100 is 2,4,6,...,100  form an arithmetic progression,

The first term is a=2

The common difference is d=2

The last term is l=100

First we find the number of terms given by,

[tex]l=a+(n-1)d[/tex]

[tex]100=2+(n-1)2[/tex]

[tex]100=2+2n-2[/tex]

[tex]2n=100[/tex]

[tex]n=\frac{100}{2}[/tex]

[tex]n=50[/tex]

The sum formula of A.P is

[tex]S_n=\frac{n}{2}[a+l][/tex]

Substitute the values in the formula,

[tex]S_{50}=\frac{50}{2}[2+100][/tex]

[tex]S_{50}=25\times 102[/tex]

[tex]S_{50}=2550[/tex]

Therefore, The sum of even numbers between 1 and 100 is 2550.

Answer:

The next three terms are 1, 8 and 3.

Step-by-step explanation:

Consider the provided sequence,

2, 9, 4, 11, 6....

We need to find the next three terms.

It is given that we need to use a traditional clock face to determine the next three terms in the following sequence.

In the above sequence we are asked to add 7 hours to each time on the traditional clock face.

2 + 7 = 9

9 + 7 = 16 In traditional clock 16 is 4 O'clock

4 + 7 = 11

11 + 7 = 18 In traditional clock 18 is 6 O'clock

6 + 7 = 13 In traditional clock 13 is 1 O'clock

1 + 7 = 8

8 + 7 = 15 In traditional clock 15 is 3 O'clock

Hence, the next three terms are 1, 8 and 3.

Answer:  60

Step-by-step explanation:

5 shorts × 4 shorts × 3 socks = 60 different uniforms

Answer:

There is approximately 5.475 liters of blood in the body.

Step-by-step explanation:

At a resting pulse rate of 75 beats per minute, the human heart typically pumps about 73 ml of blood per beat.

73 ml in liters = [tex]73\times0.001=0.073[/tex] liters

Now, 75 beats/min x  0.073 liters/beat  = 5.475 liters/min

And 5.475 liters/min x 1 min/body = 5.475 liters/body

Hence, there is approximately 5.475 liters of blood in the body.

Answer:

For linear equations we use:

p=mx+b   ------  (1)

Now we have the following coordinates:

(x1,p1)= (1000,280) and (x2, p2)=(5000,400)

First we need slope (m)

m= [tex](400-280)/(5000-1000)[/tex]

= [tex]120/4000=0.03[/tex]

Now we will plug the value of m in the first equation

[tex]280=0.03(1000)+b[/tex]

=> [tex]280=30+b[/tex]

=> b = 250

Now plug into p=mx+b using only m=0.03 and b=250

[tex]p=0.03x+250[/tex]

When the unit price is $440, we can plug in 440 in for p;

[tex]440=0.03x+250[/tex]

=> [tex]0.03x=440-250[/tex]

=> [tex]0.03x=190[/tex]

=> x = 6333 refrigerators

The lowest price at which  a refrigerator will be marketed, we can find this by plugging x = 0 in p=mx+b.

[tex]p=0.03(0)+250[/tex]

=> p = $250

The linear equation relating the unit price p to the quantity supplied x is p = 0.03x + 250. When the unit price is $440, approximately 6333 refrigerators will be marketed. The lowest price at which a refrigerator will be marketed is $250.

To find the equation relating the unit price p of a refrigerator to the quantity supplied x when the relationship is known to be linear, we can use the two given points: (1000, 280) and (5000, 400).

First, we determine the slope (m) of the line:

m = (400 - 280) / (5000 - 1000) = 120 / 4000 = 0.03

Next, we use the point-slope form of the equation y - y₁ = m(x - x₁) where (x₁, y₁) is one of our points. We can use (1000, 280):

p - 280 = 0.03(x - 1000)

p = 0.03x + 250

Now, let's determine how many refrigerators will be marketed when the unit price is $440:

440 = 0.03x + 250

190 = 0.03x

x = 6333.33

So, approximately 6333 refrigerators will be marketed when the unit price is $440.

Lastly, we find the lowest price at which a refrigerator will be marketed by setting x to 0:

p = 0.03(0) + 250 = 250

The lowest price at which a refrigerator will be marketed is $250.

Answer:

$5250 net sales were generated by the sandals.

Step-by-step explanation:

Given :

The shoe department had yearly net sales of $375,000.

Sandals represented 1.4 % of the total net sales.

To Find : What net sales dollars were generated by the sandal ?

Solution:

The shoe department had yearly net sales of $375,000.

Sandals represented 1.4 % of the total net sales.

So,  net sales dollars were generated by the sandal = [tex]1.4 \% \times 375000[/tex]

Net sales dollars were generated by the sandal = [tex]\frac{1.4}{100} \times 375000[/tex]

                                                                              = [tex]5250[/tex]

Hence $5250 net sales were generated by the sandals.

Answer:

A) find its center  = (3, 2)

B) find the radius of the circle = √104

C) find the equation of the circle = x² + y² - 6x - 4y -91 = 0

Step-by-step explanation:

A)- The center must be the mid-points of (-2, 1) and (8, 3).

So, using the equation of mid-point,

[tex]h=\frac{x_{1}+x_{2}}{2}  and  k=\frac{y_{1}+y_{2}}{2}[/tex]

Here, (x₁, y₁) = (-2, 1) and (x₂, y₂) = (8, 3)

Putting these value in above equation. We get,

h = 3 and k = 2

Thus, Center = (h, k) = (3, 2)

B)- For finding the radius we have to find the distance between center and any of the end point.

Thus using Distance Formula,

[tex]Distance=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]

[tex]Radius =\sqrt{(8+2)^{2}+(3-1)^{2}}[/tex]

⇒ Radius = √104 = 2√26

C)- The equation of circle is determined by formula:

[tex](x-h)^{2}+(y - k)^{2} = r^{2}[/tex]

where (h, k ) is center of circle and

r is the radius of circle.

⇒ (x - 3)² + (y - 2)² = 104

⇒ x² + y² - 6x - 4y -91 = 0

which is the required equation of the circle.

Answer: 1/15 of all the workers invest the maximum allowable to the retirement plan.

Step-by-step explanation:

x = hourly workers

y = salaried workers

1/6 of the hourly workers invest the  retirement plan  = 1/6 * x = x/6

1/2 of the salaried workers invest in the same  plan. = 1/2 * y = y/2

1/5 of the hourly workers invest the maximum allowed = 1/5 * x/6 = x/30

1/3 of the  salaried workers invest the maximum allowed = 1/3 * y/2 = y/6

there are three times as many hourly workers as salaried  workers

x = 3y

Total workers: x + y = 3y + y = 4y

All workers that invest the maximum allowed: x/30 + y/6 = 3y/30 + y/6 =

3y + 5y = 8y = 4y

   30       30    15  

If all the workers are 4y, then 1/15 of all the workers invest the maximum allowable to the retirement plan.

Answer:

The answer is 36 degrees

Step-by-step explanation:

Lets call the variables X= Base Angle and Y= Vertix Angle and  X=2Y

As Isosceles triangle theorem "If two sides of a triangle are congruent, then the angles opposite those sides are congruent" We asume that the X value of each base angle is the same and the sum of the three angles are equal to 180 degrees, so we have:

1)X+Y+X=180

2) We know that X=2Y so we replace them in the below formula

3) 2Y+Y+2Y=180

4) 5Y=180

5) Then we resolve the variable Y and divide the 180 degrees by 5 Y=180/5

6)Then we have that Y=36 Degrees

Please see attachment to follow up the step by step

I hope that this answer finds you well

Answer:

Step-by-step explanation:

First, observe that:

[tex](n+1)^2(2(n+1)^2-1)=(n^2+2n+1)(2n^2+4n+1)=2n^4+8n^3+11n^2+6n+1[/tex]

We will prove by mathematical induction that, for every natural,  

[tex]1^3+3^3+5^3+......(2n-1)^3=n^2(2n^2-1)[/tex]

We will prove our base case (when n=1) to be true.

Base case:

[tex]1^3+3^3+5^3+......(2n-1)^3=1=n^2(2n^2-1)[/tex]

Inductive hypothesis:  

Given a natural n,  

[tex]1^3+3^3+5^3+......(2n-1)^3=n^2(2n^2-1)[/tex]

Now, we will assume the induction hypothesis and then use this assumption, involving n, to prove the statement for n + 1.

Inductive step:

[tex]1^3+3^3+5^3+......(2(n+1)-1)^3=1^3+3^3+5^3+......(2n+1)^3=\\=n^2(2n^2-1)+(2n+1)^3=2n^4-n^2+8n^3+12n^2+6n+1=2n^4+8n^3+11n^2+6n+1[/tex]

Then, by the observation made at the beginning of this proof, we have that

[tex]1^3+3^3+5^3+......(2(n+1)-1)^3=(n+1)^2(2(n+1)^2-1[/tex]

With this we have proved our statement to be true for n+1.  

In conlusion, for every natural n

,

[tex]1^3+3^3+5^3+......(2n-1)^3=n^2(2n^2-1)[/tex]

b)

Observe that [tex]3\mid (n^3-n+3) \iff 3\mid (n^3-n) \iff 3\mid n(n^2-1)[/tex]

Then,

Therefore, for every [tex]n\in \mathbb{N}), 3\mid (n^3-n+3)[/tex]  

c)

We will prove by mathematical induction that, for every natural n>3,

[tex](n-1)^2<2n^2.[tex]

We will prove our base case (when n=4) to be true.

Base case:

[tex](n-1)^2=(4-1)^2=9<32=2*4^2=2n^2 [/tex]

Inductive hypothesis:  

Given a natural n>4,  

[tex](n-1)^2<2n^2.[tex]

Now, we will assume the induction hypothesis and then use this assumption, involving n, to prove the statement for n + 1.

Inductive step:

[tex]((n+1)-1)^2=((n-1)+1)^2=(n-1)^2+2(n-1)+1<2n^2+2(n-1)+1=2n^2+2n- 1<2n^2+2n+1 =2(n+1)^2.[tex]

With this we have proved our statement to be true for n+1.    

In conclusion, for every natural n>3,

[tex](n-1)^2<2n^2.[tex]

Answer:

Timy earned $116.25 this week.

Step-by-step explanation:

Timy earns $7.75 from his part-time job at Walmart.

Let us suppose this is his hourly rate.

He worked 5 hours on Monday, 3 hours on Wednesday and 7 hours on Friday.

So, total hours he worked = [tex]5+3+7=15[/tex] hours

Now, his earnings will be = [tex]15\times7.75=116.25[/tex] dollars

Therefore, Timy earned $116.25 this week.

Answer:

$116.25

Step-by-step explanation:

Timy earns $7.75 from his part-time job at Walmart.

He worked on Monday = 5 hours

          On Wednesday  = 3 hours

            On Friday         = 7 hours

Total earning of this week = (7.75 × 5) + (7.75 × 3) + (7.75 × 7)

                                            = 38.75 + 23.25 + 54.25

                                            = $116.25

Timy earned $116.25 this week.

Answer:

See explanation below.

Step-by-step explanation:

To prove that the greatest common divisor of two numbers is 1, we use the Euclidean algorithm.

1. In this case, and applying the algorithm we would have:

(14a + 3, 21a + 4) = (14a + 3, 7a + 1)  = (1, 7a + 1) = 1

2. Other way of proving this statement would be that we will need to find two integers x and y such that 1 = (14a + 3) x + (21a + 4) y

Let's make x = 3  and y = -2

Then we would have:

[tex](14a+3)(3) + (21a+4)(-2)\\=42a+9-42a-8\\=1[/tex]

Therefore, (14a + 3, 21a + 4) = 1

Answer:

The angle is 28.

Step-by-step explanation:

If we consider the system below (were "A"is the angle):  

A   +  [(x/2)-14] = 90       (complement)

A   +   x   = 180                 (suplement)

We can isolate "X=180 - A"  and apply this in the first equation. This way we are able to have only one variable, and w'll see that A=28.

Answer:

The second one:

L∪J={i,j,k,l,m,n,o}

Step-by-step explanation:

The union is the elements listed in either set.

So since l,m,n, and o are elements of set L, they will also be elements of whatever it is "unioned" with.

Since i,j,k,l and m are elements of set J, they will also be elements of whatever it is "unioned" with.

When you write the union, just be sure to include each element that occurs in either set once.

So the union of L and J is {i,j,k,l,m,n,o}.

The answer is the second one.

The intersection would actually be that upside down U thing, the ∩ symbol. The intersection of two sets is a list of elements that both sets include.  So here the intersection would just consist of the elements l amd m.

The union of L and J is {i,j,k,l,m,n,o}. The correct option is the second option - L∪J = {i,j,k,l,m,n,o}

From the question, we are to determine the union of the sets

The union of two given sets is the smallest set which contains all the elements of both sets.

The given sets are

L= {l,m,n,o}

J= {i,j,k,l,m}

We are to determine the union of L and J, that is, L∪J

L∪J will be the set that contains all the elements of both L and J

Therefore

L∪J = {i,j,k,l,m,n,o}

Hence, the union of L and J is {i,j,k,l,m,n,o}. The correct option is the second option - L∪J = {i,j,k,l,m,n,o}

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Answer:

8

Step-by-step explanation:

Maximum amount of Acetaminophen that can be taken = 4 g per day

Weight of acetaminophen tablet = 500 mg

let the number of tablets that can be taken be 'x'

therefore,

x × 500 mg ≤ 4 g

also, 1 g = 1000 mg

thus,

x × 500 ≤ 4000

or

x ≤  8

hence,

the maximum numbers of tablets that can be taken per day is 8

Answer:

325/790 rounded to the nearest hundredths place is 0.41

Step-by-step explanation:

The given fraction is :

[tex]\frac{325}{790}[/tex]

Dividing by 5:

[tex]\frac{65}{158}[/tex]

= 0.41139

We can see that we have a 1 after the hundredth place, so we will not round the 41 as 42.

Now, rounding this to the nearest hundredths place, we get 0.41.

Answer:

[tex]angle = 0.24 rad = 14 °[/tex]

Step-by-step explanation:

The angle of depression is the angle formed by the horizontal at the camera position and the line formed by the camera and the objective, therefore it can be calculated from the information provided as shown in the attached file:

First, you draw f' and f" as parallel lines to the floor at the height of the objective and the height of the camera respectively. Then draw the line o between camera and objective.

the blue angle created by o and f" is the depression angle, which is the same as the angle created by o and f' because angles between parallel lines.

You need to calculate b, as:

b = h - a = 9 - 6 = 3

Then, for the trigonometric function tangent as we have a rectangle triangle:

[tex] Tan(angle)=\frac{b}{f'}[/tex]

therefore:

[tex]angle = Tan^{-1}(\frac{b}{f'} ) = Tan^{-1}(\frac{3}{12} )[/tex]

[tex]angle = 0.24 rad = 14 °[/tex]

There is a 99% likelihood that they will sell between 127.12 and 152.88 units.

There is a 95% likelihood that they will sell between 130.2 and 149.8 units.

There is a 68% likelihood that they will sell between 135 and 145 units.

Use the concept of the confidence interval of statistics defined as:

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts.

Given that,

The marketing team at Beth's Butter Works prefers the traditional plastic tub packaging.

They wanted a more refined estimate of potential sales.

They launched a third test at a regional level across 100 stores.

The average daily sales of these 100 stores during the test period was 140 units.

The standard deviation of daily sales across the 100 stores was 50 units.

To calculate the confidence intervals:

Consider the sample mean, sample standard deviation, and the desired level of confidence.

In this case,

Use the average daily sales of 140 units and the standard deviation of 50 units.

Now,

For a 99% confidence interval:

Use a z-score of 2.576 (corresponding to a 99% confidence level).

The formula for the confidence interval is:

Confidence Interval[tex]=\text{ Sample Mean} \pm (\text{Z-Score} \times (\text{Sample Standard Deviation} /\sqrt{\text{Sample Size}}))[/tex]

For a 99% confidence interval, the values are:

Lower bound [tex]= 140 - (2.576 \times (50 / \sqrt{100}))[/tex]

Lower bound = 127.12

Upper bound [tex]= 140 + (2.576 \times (50 / \sqrt{100}))[/tex]

Upper bound = 152.88

For a 95% confidence interval:

Use a z-score of 1.96 (corresponding to a 95% confidence level).

The values are:

Lower bound = [tex]140 - (1.96 \times (50 / \sqrt{100}))[/tex]

Lower bound = 130.2

Upper bound = [tex]140 + (1.96 \times (50 / \sqrt{100}))[/tex]

Upper bound = 149.8

For a 68% confidence interval:

Use a z-score of 1 (corresponding to a 68% confidence level).

The values would be:

Lower bound [tex]= 140 - (1 \times(50 / \sqrt{100}))[/tex]

Lower bound = 135

Upper bound [tex]= 140 + (1 \times(50 / \sqrt{100}))[/tex]

Upper bound = 145

Hence,

99% confidence interval:

There is a 99% likelihood that they will sell between 127.12 and 152.88 units.

95% confidence interval:

There is a 95% likelihood that they will sell between 130.2 and 149.8 units.

68% confidence interval:

There is a 68% likelihood that they will sell between 135 and 145 units.

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Final answer:

To calculate the confidence intervals for the average number of units sold by Beth's Butter Works, the formula for confidence intervals is used with a mean of 140 units and a standard deviation of 50 across 100 stores. The 99%, 95%, and 68% confidence levels correspond to confidence intervals of 127.12 to 152.88 units, 130.2 to 149.8 units, and 135 to 145 units, respectively.

Explanation:

To calculate the confidence intervals for the average number of units sold, we will use the formula for a confidence interval: mean ± (z * (standard deviation / √(sample size))). The mean daily sales are 140 units and the standard deviation is 50. Since the sample size is 100 stores, the standard error (standard deviation / √(sample size)) would be 50 / √(100) = 50 / 10 = 5. The z-scores for the different confidence levels are approximately 2.576 for 99%, 1.96 for 95%, and 1 for 68% (as this lies closest to one standard deviation from the mean).

For a 99% confidence interval, the calculation is:

140 ± (2.576 * 5) = 140 ± 12.88

The 99% confidence interval is therefore between 127.12 and 152.88 units.

For a 95% confidence interval, the calculation is:

140 ± (1.96 * 5) = 140 ± 9.8

The 95% confidence interval is therefore between 130.2 and 149.8 units.

To explain what a 95% confidence interval means for this study, it implies that, if we were to take many samples and build confidence intervals in the same way, 95% of them would contain the true average units sold across all possible stores.

For a 68% confidence interval, the calculation is:

140 ± (1 * 5) = 140 ± 5

The 68% confidence interval is therefore between 135 and 145 units.