For the equation below, determine its order. Name the independent variable, the dependent variable, and any parameters in the equation. (Enter your answers as comma-separated lists. If an answer does not exist, enter DNE.) mx'' + bx' + kx = 8t6, assuming x is a function of t

Answer:

The angle that the ramp makes with the ground is 11.54°

Step-by-step explanation:

From the image attached, we can see that the length of 17 1/2 ft corresponds to the hypotenuse in a right triangle, the length of 3 1/2 ft corresponds to the opposite side.

We can use the fact that the sin(θ) = [tex]\frac{Opposite}{Hypotenuse}[/tex] to find the angle that the ramp makes with the ground.

[tex]sin(\theta)=\frac{3.5}{17.5}[/tex]

The angle is equal to

[tex]\theta = sin^{-1}(\frac{3.5}{17.5} )\\\theta = 11.54\°[/tex]

The angle that the ramp makes with the ground can be found using the concept of tangent in trigonometry. By dividing the height of the loading platform by the length of the ramp and taking the inverse tangent of the result, we find the angle to be approximately 11.3 degrees.

This question can be solved by using trigonometric principles, specifically the tangent of an angle in a right triangle. The tangent of an angle θ (theta) can be defined as the ratio of the side opposite the angle to the side adjacent to it.

In this scenario, the ramp forms a right triangle with the ground and the vertical line from the loading platform to the ground directly below it. The height of the platform, or the 'opposite' side, is 3 1/2 feet, and the ramp, or the 'adjacent' side, is 17 1/2 feet.

Therefore, we can say that: tan θ = (3.5 / 17.5)

To find the value of θ, we take the inverse tangent (or arc tangent) of the quotient. Using a calculator to do this (remember to set your calculator to degree mode), we find θ to be approximately 11.3 degrees.

Thus, the angle that the ramp makes with the ground is about 11.3 degrees.

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Answer:

For a monthly cost of at least $7 and at most $8, you can have between 100 and 110 calling minutes.

Step-by-step explanation:

The problem states that the monthly cost of a celular plan is modeled by the following function:

[tex]C(x) = 4 + 0.10(x-70)[/tex]

In which C(x) is the monthly cost and x is the number of calling minutes.

How many calling minutes are needed for a monthly cost of at least $7?

This can be solved by the following inequality:

[tex]C(x) \geq 7[/tex]

[tex]4 + 0.10(x - 70) \geq 7[/tex]

[tex]4 + 0.10x - 7 \geq 7[/tex]

[tex]0.10x \geq 10[/tex]

[tex]x \geq \frac{10}{0.1}[/tex]

[tex]x \geq 100[/tex]

For a monthly cost of at least $7, you need to have at least 100 calling minutes.

How many calling minutes are needed for a monthly cost of at most 8:

[tex]C(x) \leq 8[/tex]

[tex]4 + 0.10(x - 70) \leq 8[/tex]

[tex]4 + 0.10x - 7 \leq 8[/tex]

[tex]0.10x \leq 11[/tex]

[tex]x \leq \frac{11}{0.1}[/tex]

[tex]x \leq 110[/tex]

For a monthly cost of at most $8, you need to have at most 110 calling minutes.

For a monthly cost of at least $7 and at most $8, you can have between 100 and 110 calling minutes.

Answer:

(A) No solutions regardless of values of a and b.

Step-by-step explanation:

Asumming that the system of equations is [tex]x+2y-3z=a\\ 2x+4y-6z=2a+2[/tex], the corresponding augmented matrix of the system is [tex]\left[\begin{array}{cccc}1&2&-3&a\\2&4&-6&2a+2\end{array}\right][/tex].

If two time the row 1 is subtracted to row 1, we get the following matrix

[tex]\left[\begin{array}{cccc}1&2&-3&a\\0&0&0&2a+2-2a\end{array}\right][/tex].

Then the system has no solutions regardless of values of a and b.

Answer: 15

Step-by-step explanation:

Given : The number of kinds of ice-cream cones ( sugar cones, cake cones and waffle cones)=3

The number of flavors of ice-creams =5

By using the fundamental principle of counting , we have

The number of possible cone/ice cream combinations can be ordered will be :-

[tex]5\times3=15[/tex]

Hence, the number of possible cone/ice cream combinations can be ordered =15

Answer:

Standard Deviation = 9.75        

Step-by-step explanation:

We are given the following data:

n = 25

Ages: 60, 61, 62, 63, 64, 65, 66, 68, 68, 69, 70, 73, 73, 74, 75, 76, 76, 81, 81, 82, 86, 87, 89, 90, 92

Formula:

For sample,

[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}[/tex]

where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.

[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]

Mean = [tex]\frac{1851}{25} = 74.04[/tex]

Sum of square of differences = 2278.96

S.D = [tex]\sqrt{\diplaystyle\frac{2278.96}{24} } = 9.74[/tex]

To calculate the standard deviation of the given ages, we find the mean, subtract it from each age to find deviations, square these, find their mean, and take the square root to get the standard deviation, which is 6.96.

The question is asking to calculate the standard deviation of the ages of 25 senior citizens. To find the standard deviation, we need to follow these steps:

Calculate the mean (average) age of the senior citizens.

Subtract the mean from each age to find the deviation of each value.

Square each deviation.

Calculate the mean of these squared deviations.

Take the square root of the mean of the squared deviations to get the standard deviation.

Performing these calculations, we find that the mean (average) age is 73.24. The sum of the squared deviations is 1210. After dividing this sum by the number of values (25), we get the variance, which is 48.4. Finally, taking the square root of the variance gives us the standard deviation, which to two decimal places is 6.96.

This measure of standard deviation is crucial in understanding the spread of ages among senior citizens in the sociologist's survey.

Answer:

PROPORTION.

Step-by-step explanation:

The relative frequency in a relative frequency histogram refers to                                  PROPORTION.

A relative frequency histogram uses the same information as a frequency histogram but compares each class interval with the number of items. The difference between frequency and relative frequency histogram is that the vertical axes uses the relative or proportional frequency rather than simple frequency

Answer:

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

Step-by-step explanation:

Given,

A = { 0, 1, 2, 3, 4, 5, 6 }

B = { 0,1, 2, 3, 4, 5, 6, 7, 8 }

Also, R is the relation from A to B as follows,

R = { (a, b) : HCF ( a, b ) = 2 ∀ a ∈ A, b ∈ B }

Since,

HCF ( 2, 2 ) = HCF ( 2, 4 ) = HCF ( 2, 6 ) = HCF ( 2, 8 ) = HCF ( 4, 2 ) = HCF ( 4, 6) = HCF ( 6, 4) = HCF ( 6, 2 ) =HCF ( 6, 8 ) = 2

Where, 2, 4, and 6 belong to A,

And, 2, 4, 6 and 8 belong to B,

Hence,

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

Consider the cubic polynomial,

[tex](x+a)(x+b)(x+c)[/tex]

Expanding this gives

[tex]x^3+(a+b+c)x^2+(ab+ac+bc)x+abc=x^3+x^2-4x-4[/tex]

We can factor this by grouping,

[tex]x^3+x^2-4x-4=x^2(x+1)-4(x+1)=(x^2-4)(x+1)=(x-2)(x+2)(x+1)[/tex]

Then letting [tex]a=-2[/tex], [tex]b=2[/tex], and [tex]c=1[/tex] gives [tex]a^3+b^3+c^3=-8+8+1=\boxed1[/tex]

Answer:

2/6 or 1/3 so color 2 out of the six squares

Step-by-step explanation:

1/2 - 1/6 is equal to 3/6 - 1/6 so 2/6

Answer:

[tex]x = 0[/tex] or [tex]x = \pi[/tex].

Step-by-step explanation:

How are tangents and secants related to sines and cosines?

[tex]\displaystyle \tan{x} = \frac{\sin{x}}{\cos{x}}[/tex].

[tex]\displaystyle \sec{x} = \frac{1}{\cos{x}}[/tex].

Sticking to either cosine or sine might help simplify the calculation. By the Pythagorean Theorem, [tex]\sin^{2}{x} = 1 - \cos^{2}{x}[/tex]. Therefore, for the square of tangents,

[tex]\displaystyle \tan^{2}{x} = \frac{\sin^{2}{x}}{\cos^{2}{x}} = \frac{1 - \cos^{2}{x}}{\cos^{2}{x}}[/tex].

This equation will thus become:

[tex]\displaystyle \frac{1 - \cos^{2}{x}}{\cos^{2}{x}} \cdot \frac{1}{\cos^{2}{x}} + \frac{2}{\cos^{2}{x}} - \frac{1 - \cos^{2}{x}}{\cos^{2}{x}} = 2[/tex].

To simplify the calculations, replace all [tex]\cos^{2}{x}[/tex] with another variable. For example, let [tex]u = \cos^{2}{x}[/tex]. Keep in mind that [tex]0 \le \cos^{2}{x} \le 1 \implies 0 \le u \le 1[/tex].

[tex]\displaystyle \frac{1 - u}{u^{2}} + \frac{2}{u} - \frac{1 - u}{u} = 2[/tex].

[tex]\displaystyle \frac{(1 - u) + u - u \cdot (1- u)}{u^{2}} = 2[/tex].

Solve this equation for [tex]u[/tex]:

[tex]\displaystyle \frac{u^{2} + 1}{u^{2}} = 2[/tex].

[tex]u^{2} + 1 = 2 u^{2}[/tex].

[tex]u^{2} = 1[/tex].

Given that [tex]0 \le u \le 1[/tex], [tex]u = 1[/tex] is the only possible solution.

[tex]\cos^{2}{x} = 1[/tex],

[tex]x = k \pi[/tex], where [tex]k\in \mathbb{Z}[/tex] (i.e., [tex]k[/tex] is an integer.)

Given that [tex]0 \le x < 2\pi[/tex],

[tex]0 \le k <2[/tex].

[tex]k = 0[/tex] or [tex]k = 1[/tex]. Accordingly,

[tex]x = 0[/tex] or [tex]x = \pi[/tex].

Answer:

Step-by-step explanation:

Let [tex]m,n[/tex] be any two integers, and assume [tex]m-n[/tex] is even. (This would mean either both [tex]m,n[/tex] are even or odd, but that's not important.)

We have

[tex]m^3-n^3=(m-n)(m^2+mn+n^2)[/tex]

and the parity of [tex]m-n[/tex] tells us [tex]m^3-n^3[/tex] must also be even. QED

Answer: 10gtt/ml means that in 10 drops there is a ml of the solution.

Now, you need 1000ml in 8 hours, and want to know the correct rate of flow in drops per minute.

first, 8 hours are 8*60 = 480 minutes.

then you need to infuse 1000ml in 480 minutes, so if you infuse at a constant rate, you need to infuse 1000/480 = 2.083 ml/min.

And we know that 10 drops are equivalent to 1 ml, then 2.083*10= 20.8 drops are equivalent a 2.083 ml, rounding it up, you get 21 drops for the dose.

So the correct rate of flow will be 21 drops per minute.

To find the correct rate of flow for an IV infusion, convert the time to minutes, divide the total volume by the total time to find the rate in ml/min, then multiply by the drip factor to convert to drops/min. Rounding to the nearest drop, we get 21 gtt/min.

To calculate the correct rate of flow for an IV infusion, we need to use the given information: the volume of the IV infusion (D5W 1000 ml), the time over which it must infuse (8 hours), and the IV tubing drip factor (10 gtt/ml).

First, convert the time from hours to minutes as we're interested in drops per minute: 8 hours * 60 minutes/hour = 480 minutes.

Next, we divide the total volume by the total time: 1000 ml / 480 minutes = ~2.08 ml/min. This is the rate in ml/min.

Finally, we multiply by the drip factor to get the rate in drops per minute: 2.08 ml/min * 10 gtt/ml = 20.8 gtt/min.

Rounding to the nearest drop gives us a rate of 21 gtt/min.

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Answer: The data are quantitative because they consist of counts or measurements.

Step-by-step explanation:

The definition of quantitative data says that if we can count or measure some thing in our data such as number of apples on each bag , length, width, etc then the data is said to be quantitative.

On the other hand  in qualitative data we can obverse characteristics and features but can't be counted or measured such as honesty , color, tastes etc.

Given : In studying different societies, an archaeologist measures head circumferences of skulls.

Since here we are measuring circumferences of skulls, therefor it comes under  quantitative data.

Hence, the correct answer is : The data are quantitative because they consist of counts or measurements.

The correct answer is D. The data are quantitative because they consist of counts or measurements. Quantitative data is numerical and can be measured and analyzed statistically.

Step by Step Solution:

When an archaeologist measures head circumferences of skulls, they are collecting quantitative data. Quantitative data consists of counts or measurements that are numerical in nature and can be subjected to statistical analysis. Examples of quantitative data in archaeology include measuring the length of projectile points, counting pollen grains, or recording quantities of animal bones at a site.

Therefore, the correct answer is:

D. The data are quantitative because they consist of counts or measurements.

Answer:

24.39mL of the solution would be given per hour.

Step-by-step explanation:

This problem can be solved by direct rule of three, in which there are a direct relationship between the measures, which means that the rule of three is a cross multiplication.

The first step to solve this problem is to see how many mg of the solution is administered per hour.

Each minute, 200 ug are administered. 1mg has 1000ug, so

1mg - 1000 ug

xmg - 200 ug

[tex]1000x = 200[/tex]

[tex]x = \frac{200}{1000}[/tex]

[tex]x = 0.2mg[/tex]

In each minute, 0.2 mg are administered. Each hour has 60 minutes. How many mg are administered in 60 minutes?

1 minute - 0.2 mg

60 minutes - x mg

[tex]x = 60*0.2[/tex]

[tex]x = 12mg[/tex]

In an hour, 12 mg of the drug is administered. In 250 mL, there is 123 mg of the drug. How many ml are there in 12 mg of the drug.

123mg - 250mL

12 mg - xmL

[tex]123x = 250*12[/tex]

[tex]x = \frac{250*12}{123}[/tex]

[tex]x = 24.39[/tex]mL

24.39mL of the solution would be given per hour.

Final answer:

Approximately 24.39 milliliters of the intravenous solution would be administered per hour to deliver an hourly drug rate of 12 milligrams based on the given concentration.

Explanation:

To calculate how many milliliters of the intravenous solution would be given per hour, first convert the rate of drug administered from micrograms to milligrams: 200 \5g is equal to 0.2 mg. Since the drug administration rate is 0.2 mg per minute, we need to multiply this by 60 minutes to get the hourly rate:

0.2 mg/minute x 60 minutes/hour = 12 mg/hour.

Next, we need to find out how many milliliters of the solution contain 12 mg of the drug. Since we have 123 mg in 250 mL, we can set up a proportion to solve for the volume needed:

(123 mg/250 mL) = (12 mg/V mL)

V = (12 mg x 250 mL) / 123 mg = 24.39 mL.

Therefore, approximately 24.39 mL of the solution would be administered per hour.

Answer:

P(cell has at least one of the positive nickel-charged options) = 0.83.

P(a cell is not composed of a positive nickel charge greater than +3) = 0.85.

Step-by-step explanation:

It is given that the Nickel Charge Proportions found  in the battery are:

0 ==> 0.17

.

+2 ==> 0.35

.

+3 ==> 0.33

.

+4 ==> 0.15.

The numbers associated to the charge are actually the probabilities of the charges because nickel is an element that has multiple oxidation states that is usually found in the above mentioned states.

a) P(cell has at least one of the positive nickel-charged options) = P(a cell has +2 nickel-charged options) + P(a cell has +3 nickel-charged options) + P(a cell has +4 nickel-charged options) = 0.35 + 0.33 + 0.15 = 0.83.

Or:

P(a cell has at least one of the positive nickel-charged options) = 1 - P(a cell has 0 nickel-charged options) = 1 - 0.17 = 0.83.

b) P(a cell is not composed of a positive nickel charge greater than +3) = 1 - P(a cell is composed of a positive nickel charge greater than +3)

= 1 -  P(a cell has +4 nickel-charged options)  '.' because +4 is only positive nickel charge greater than +3      

= 1 - 0.15

=  0.85

To summarize:

P(cell has at least one of the positive nickel-charged options) = 0.83!!!

P(a cell is not composed of a positive nickel charge greater than +3) = 0.85!!!

The probability of a cell having at least one positive nickel-charge is 0.83 and the probability that a cell is not composed of a positive nickel charge greater than +3 is 0.85; This was calculated based on probabilities of Nickel in different charge states.

For this problem, you're basically being asked to interpret a probability distribution of Nickel charge proportions, which involves summing probabilities.

(a) The probability that a cell has at least one of the positive nickel-charged options is the sum of the probabilities of Nickel in the +2, +3, and +4 states. From the given data, we simply add: 0.35 (for +2), 0.33 (for +3), and 0.15 (for +4). So, the total probability is 0.83.

(b) The probability that a cell is not composed of a positive nickel charge greater than +3 means we're looking for the probability of Nickel in the 0, +2, and +3 states. Here, we add: 0.17 (for 0 state), 0.35 (for +2 state), and 0.33 (for +3 state) to get a total probability of 0.85.

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Answer:

a) The set of solutions is [tex]\{(0,-3x_3,x_3): x_3\; \text{es un real}\}[/tex] y b) the set of solutions is [tex]\{(-6,\frac{-41}{17}-\frac{30}{17}x_4 , \frac{37}{17}+\frac{8}{17} x_4 ,x_4): x_4\;\text{es un real}\}[/tex].

Step-by-step explanation:

a) Let's first find the echelon form of the matrix [tex]\left[\begin{array}{ccc}5&2&6\\-2&1&3\end{array}\right][/tex].

The system has a free variable (x3).

       x1+[tex]\frac{2}{5}[/tex](-3x3)+[tex]\frac{6}{5}[/tex]x3=

      x1-[tex]\frac{6}{5}[/tex]x3+[tex]\frac{6}{5}[/tex]x3

     then x1=0.

The system has infinite solutions of the form (x1,x2,x3)=(0,-3x3,x3), where x3 is a real number.

b) Let's first find the echelon form of the aumented matrix [tex]\left[\begin{array}{ccccc}1&-2&1&-4&1\\1&3&7&2&2\\0&-12&-11&-16&5\end{array}\right][/tex].

The system has a free variable (x4).

      x2=[tex]\frac{-41}{17}-\frac{30}{17}[/tex]x4.

The system has infinite solutions of the form (x1,x2,x3,x4)=(-6,[tex]\frac{-41}{17}-\frac{30}{17}[/tex]x4,[tex]\frac{37}{17}[/tex]+ [tex]\frac{8}{17}[/tex]x4,x4), where x4 is a real number.

Answer:

You inject 60.9628 milliliters of dosage

Step-by-step explanation:

1 pound = 0.453592kg,

Patient's weight in pounds = 168

Patient's weight in kg = [tex]76.2035  kg[/tex]

Now we are given that The dosage is 0.4 mg per kilogram of bod

So, dosage = [tex]0.4 \times 76.2035 mg = 30.4814 mg[/tex]

1 microgram = 0.001 mg

Concentration of drug = [tex]500 micrograms/ml = 500 * 0.001 mg/ml = 0.5 mg/ml[/tex]

Now we are supposed to find How many milliliters (= cc) are you to inject?

So,milliliters of dosage required to inject = [tex]\frac{30.4814}{0.5} = 60.9628[/tex]

Hence you inject 60.9628 milliliters of dosage

Answer:

P= -0.05q+22

Step-by-step explanation:

To find the linear equation that relates price with quantity demanded, first we must find the slope. Because the independent variable is the quantity demanded and the dependent variable is the price, the slope represents how the price changes when there is an extra unit of quantity demanded. The problem gives this information: "for every additional card (extra unit) they need to drop the price by $0.05". The slope (m) in this case is negative because an extra unit, reduces the price: -0.05

The second step is to use this formula:

Y-y1= m*(X-x1)

y1 and x1 is a point of the demand curve, in this case it is y1= $7 and x1=300

Y-$7= -$0.05*(X-300)

Y-7=-0.05X+15

Y= -0.05X+15+7

Y= -0.05X-22

Price= -0.05 quantity demanded +22

Answer:

$64

Step-by-step explanation:

We have been given that a local food mart donates 20% of it's Friday's sales to charity. This Friday the food mart had sales totaling 320.00 dollars.

To find the the amount donated to the charity, we will find 20% of $320.

[tex]\text{The amount donated to the charity}=\$320\times\frac{20}{100}[/tex]

[tex]\text{The amount donated to the charity}=\$320\times0.20[/tex]

[tex]\text{The amount donated to the charity}=\$64[/tex]

Therefore, $64 were donated to the charity.

Answer:

Area: 180 units2 (units 2 is because since the are no specific unit given but every area should have a unit  of measurement)

Step-by-step explanation:

The area enclosed by the graph of the function, the horizontal axis, and vertical lines is the integral of the function between thos two points (x=2 and x=4)

So , let's solve the integral of f(x)

Area =[tex]\int\limits^2_4 3{x}^3 \, dx = 3*x^4/4[/tex]+C

C=0

So if we evaluate this function in the given segment:

Area= 3* (4^4)/4-3*(2^4)/4= 3*(4^4-2^4)/4=180 units 2

Goos luck!

a. As described in the problem you will be paying in the bill $0.15 per minute which means you have a linear relationship where both the total cost of the bill and the minutes will grow at the same rate (the price of the minute times the minutes) like this

[tex]C(t)=0.15t[/tex]

where C(t) is the total cost of the cell phone bill and t will be the time in minutes

b. The domain of the function will be the values that we can enter to the function. It is defined in the problem that this cost of the minutes its only up to 600 minutes so there is our limitation for the values that will enter the function. The domain will be between 0 and 600 both included because if he calls 0 minutes the bill will be 0 and if he calls 600 he would pay 0.15 for this last minute as well.

[tex][0,600][/tex]

Answer:

0.681

Step-by-step explanation:

Let's define the following events:

S: a Carter office worker is rated satisfactory

U : a Carter office worker is rated unsatisfactory

ND: a Carter office worker is placed by Nancy Dwyer

DN: a Carter office worker is placed by Darla Newberg

We have from the original text that

P(S | ND) = 0.8, this implies that P(U | ND) = 0.2.

P(S | DN) = 0.65, this implies that P(U | DN) = 0.35. Besides

P(DN) =  0.55 and P(ND) = 0.45, then we are looking for

P(DN | U), using the Bayes' formula we have

P(DN | U) = [tex]\frac{P(U | DN)P(DN)}{P(U | DN)P(DN) + P(U | ND)P(ND)}[/tex] = [tex]\frac{(0.35)(0.55)}{(0.35)(0.55)+(0.2)(0.45)}[/tex]=0.681

Final answer:

The probability that a Carter office worker rated unsatisfactory was placed by Darla is approximately 0.346.

Explanation:

To find the probability that a Carter office worker rated unsatisfactory was placed by Darla, we can use Bayes' theorem. Let's denote the event that the worker is placed by Darla as D and the event that the worker is rated unsatisfactory as U. We are given the following probabilities:

P(Darla places) = 55% = 0.55

P(Nancy places) = 45% = 0.45

P(Satisfactory | Nancy places) = 80% = 0.80

P(Satisfactory | Darla places) = 65% = 0.65

We want to find P(D | Unsatisfactory), which is the probability that the worker was placed by Darla given that they are rated unsatisfactory. Using Bayes' theorem, we have:

P(D | U) = (P(D) * P(U | D)) / (P(D) * P(U | D) + P(N) * P(U | N))

Substituting the given probabilities, we get:

P(D | U) = (0.55 * (1 - 0.65)) / (0.55 * (1 - 0.65) + 0.45 * (1 - 0.80))

P(D | U) ≈ 0.346

Therefore, the probability that a Carter office worker rated unsatisfactory was placed by Darla is approximately 0.346.

Answer:

the length PQ is 9 units,the length QR is 9 units,the length PR is 9.48 units,the triangle is not a right triangle,this is a isosceles triangle

Step-by-step explanation:

Hello, I think I can help you with this

If  you know two points, the distance between then its given by:

[tex]P1(x_{1},y_{1},z_{1} ) \\P2(x_{2},y_{2},z_{2})\\\\d=\sqrt{(x_{2}-x_{1} )^{2} +(y_{2}-y_{1}  )^{2}+(z_{2}-z_{1} )^{2} }[/tex]

Step 1

use the formula to find the length PQ

Let

P1=P=P(2, −3, −4)

P2=Q=Q(8, 0, 2)

[tex]d=\sqrt{(8-2)^{2} +(0-(-3))^{2}+(2-(-4))^{2}} \\ d=\sqrt{(6)^{2} +(3)^{2}+(6 )^{2}}} \\d=\sqrt{36+9+36}\\d=\sqrt{81} \\d=9\\[/tex]

the length PQ is 9 units

Step 2

use the formula to find the length QR

Let

P1=Q=Q(8, 0, 2)

P2=R= R(11, −6, −4)

[tex]d=\sqrt{(11-8)^{2} +(6-0))^{2}+(-4-2 )^{2}}  \\\\\\d=\sqrt{(3)^{2} +(6)^{2}+(-6 )^{2}}} \\d=\sqrt{9+36+36}\\d=\sqrt{81} \\d=9\\[/tex]

the length QR is 9 units

Step 3

use the formula to find the length PR

Let

P1=P(2, −3, −4)

P2=R= R(11, −6, −4)

[tex]d=\sqrt{(11-2)^{2} +(-6-(-3)))^{2}+(-4-4 )^{2}}  \\\\\\d=\sqrt{(9)^{2} +(-6+3)^{2}+(-4-(-4) )^{2}}} \\d=\sqrt{81+9+0}\\d=\sqrt{90} \\d=9.48\\[/tex]

the length PR is 9.48 units

Step 4

is it a right triangle?

you can check this by using:

[tex]side^{2} +side^{2}=hypotenuse ^{2}[/tex]

Let

side 1=side 2= 9

hypotenuse = 9.48

Put the values into the equation

[tex]9^{2} +9^{2} =9.48^{2}\\ 81+81=90\\162=90,false[/tex]

Hence, the triangle is not a right triangle

Step 5

is it an isosceles triangle?

In geometry, an isosceles triangle is a type of triangle that has two sides of equal length.

Now side PQ=QR, so this is a isosceles triangle

Have a great day

Answer:

10.022

Step-by-step explanation:

1. 49/9

2. 106/25

3. 10.022

4. When you add two rational numbers, each number can be written as a :

fraction

5. The sum of two fractions can always  be written as a : fraction

6. Therefore, the  sum of two rational numbers will always be : rational

Answer:

The value of q are 0.781,-1.281.

Step-by-step explanation:

Given : Two vectors [tex]A=i+j+kq[/tex] and [tex]B=iq-2j+2kq[/tex] are perpendicular to each other.

To find : The value of q ?

Solution :

When two vectors are perpendicular to each other then their dot product is zero.

i.e. [tex]\vec{A}\cdot \vec{B}=0[/tex]

Two vectors [tex]A=i+j+kq[/tex] and [tex]B=iq-2j+2kq[/tex]

[tex](i+j+kq)\cdot (iq-2j+2kq)=0[/tex]

[tex](1)(q)+(1)(-2)+(q)(2q)=0[/tex]

[tex]q-2+2q^2=0[/tex]

[tex]2q^2+q-2=0[/tex]

[tex]2q^2+q-2=0[/tex]

Using quadratic formula,

[tex]q=\frac{-1\pm\sqrt{1^2-4(2)(-2)}}{2(2)}[/tex]

[tex]q=\frac{-1\pm\sqrt{17}}{4}[/tex]

[tex]q=\frac{-1+\sqrt{17}}{4},\frac{-1-\sqrt{17}}{4}[/tex]

[tex]q=0.781,-1.281[/tex]

Therefore, The value of q are 0.781,-1.281.

The baseball team won 100 games and lost 28 games. We found the number of losses by solving the equation formed by the relationship between wins and losses, and the total number of games played.

To solve the problem, let's denote the number of games the baseball team lost as L, and hence, the games they won would be 3L + 16 as per the condition given. Considering that the team played a total of 128 games, the equation representing the total number of games played is:

L + (3L + 16) = 128

Combining like terms, we get:

4L + 16 = 128

Subtracting 16 from both sides, we have:

4L = 112

Dividing both sides by 4 yields:

L = 28

Now that we have the number of losses, we can calculate the number of wins by substituting L back into 3L + 16:

Wins = 3(28) + 16 = 84 + 16 = 100

Therefore, the team won 100 games and lost 28 games in the season.

Step-by-step explanation:

Perfect number is the positive integer which is equal to sum of proper divisors of the number.

Aliquot part is also called as proper divisor which means any divisor of the number which isn't equal to number itself.

Number : 6

Perfect divisors / Aliquot part = 1, 2, 3

Sum of the divisors = 1 + 2 + 3 = 6

Thus, 6 is a perfect number.

Number : 28

Perfect divisors / Aliquot part = 1, 2, 4, 7, 14

Sum of the divisors = 1 + 2 + 4 + 7 + 14 = 28

Thus, 28 is a perfect number.

Answer:

you need 100ml of 5X TAE and 400ml of water.

Step-by-step explanation:

You need to use a rule of three:

[tex]C_1V_1=C_2V_2[/tex]

where:

[tex]\left \{ {{C_1= 5X} \atop {C_2=1X}} \right.[/tex]

and

[tex]\left \{ {{V_1 = V_{TAE}} \atop {V_2=500ml}} \right.[/tex]

Therefore:

[tex]V_{TAE} = \frac{V_2*C_2}{C_1}[/tex]

[tex]V_{TAE} = 100ml[/tex]

Then just rest the TAE volume to the final Volume and you get the amount of water that you need to reduce the concentration.

Answer:

Step-by-step explanation:

It shall be 100xl times the number of 1x tae

Answer:

(B) 0.0588

Step-by-step explanation:

The probability is calculated as a division between the number of possibilities that satisfy a condition and the number of total possibilities. Then, the probability that the first card is diamonds is:

[tex]P_1=\frac{13}{52}[/tex]

Because the deck has 52 cards and 13 of them are diamonds.

Then, if the first card was diamonds, the probability that the second card is also diamond is:

[tex]P_2=\frac{12}{51}[/tex]

Because now, we just have 51 cards and 12 of them are diamonds.

Therefore, the probability that both cards are diamonds is calculated as a multiplication between [tex]P_1[/tex] and [tex]P_2[/tex]. This is:

[tex]P=\frac{13}{52}*\frac{12}{51}=\frac{1}{17}=0.0588[/tex]

Answer:

Ans. Joe will have $720,862.28 and Jill will have $819,348.90 after 30 years.

Step-by-step explanation:

Hi, since the interest is compounded with each payment, the effective rate of Joe is exactly equal to its compounded rate, that is 9.3%, but in the case of Jill, this rate is compounded weekly, this means that we have to divide 9.3% by 52 (which are the weeks in a year) in order to obtain an effective rate, in our case, effective weekly.

On the other hand, the time for Joe is pretty straight forward, he saves for 30 years at an effective annual interest rate of 9.3%, but Jill saves for 30*52=1560 weeks, at a rate of 0.1788% effective weekly.

They both have to use the following formula in order to find how much money will they have after 30 years of savings.

[tex]FutureValue=\frac{A((1+r)^{n}-1) }{r}[/tex]

In the case of Joe, this should look like this

[tex]FutureValue=\frac{5,000((1+0.093)^{30}-1) }{0.093} =720,862.28[/tex]

In the case of Jill, this is how this should look like.

[tex]FutureValue=\frac{96.15((1+0.001788)^{1560}-1) }{0.001788} =819,348.90[/tex]

Best of luck.