If km and np are parallel lines and m

The equation of the plane passing through the points P(-2,5,-4), Q(2,-5,-3), and R(-1,2,4) is -2x + 5y - 4z = 3.

To find the equation of a plane, we need to have a point on the plane and a normal vector to the plane. A normal vector is a vector that is perpendicular to the plane.

To find a normal vector, we can take the cross product of two vectors in the plane. Let's take the vectors PQ and PR, which lie in the plane

PQ = Q - P = (2, -5, -3) - (-2, 5, -4) = (4, -10, 1)

PR = R - P = (-1, 2, 4) - (-2, 5, -4) = (1, -3, 8)

Now we can take the cross product of these two vectors

N = PQ x PR = (4, -10, 1) x (1, -3, 8)

= (80, 33, 14)

This is a normal vector to the plane. We can use any of the three points given to write the equation of the plane. Let's use point P

-2(x + 2) + 5(y - 5) - 4(z + 4) = 0

Simplifying this equation, we get

-2x + 5y - 4z = 3

So the equation of the plane through the points P, Q, and R is

-2x + 5y - 4z = 3

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The correct value of the integral equation, considering the constant of integration \(\sqrt({x^2}+14x)\) will be equal to\(1/2(x+7)\sqrt({x^2}+14x)-[49/2ln(1/7\sqrt({x^2}+14x) + (x+7)] + C\).

Integration is a mathematical operation in which adding or summing up of some parts of an equation is done. It is opposite of differentiation. To solve the equation, first the knowledge about various trigonometric equations is very important. These are given below:

cosh²θ−sinh²θ = 1

cosh2θ = 2sinh²θ+1

sinh²θ = 1/2 (cosh2θ - 1)

sinh2θ = 2 sinhθcoshθ

arc cosh\(x\) = ln (\(\sqrt{x^2-1}\) + \(x\))

Substituting the values to simplify the equation:

\(x^{2} +14x = x^{2} +14x-49+49\\x^{2} +14x = (x+7)^{2} - 49\)

Now putting, x+7 = 7coshθ

dx = 7sinhθdθ

\(\sqrt{(x+7)^2-49} = \sqrt{49cosh^2\theta-49}\)

dx = \(7\sqrt{cosh^2\theta-1} = 7sinh\theta\)

\(sinh^2\theta=cosh^2\theta-1 = (\frac{x+7}{7})^2 - 1\)

\(\frac{x^2+14x-49+49}{49} = \frac{x^2+14x}{49}\\ sinh\theta = \frac{1}{7} \sqrt{x^2+14x}\)

\(\int\limits {\sqrt{x^2+14x} } \, dx =\int\limits {7sinh\theta*7sinh\theta} \, d\theta\)

\(= 49\int\limits {sinh^2\theta } \, d\theta\\=\frac{49}{2}\int\limits {(cosh2\theta -1)} \, d\theta\\= \frac{49}{2} (\frac{sinh2\theta}{2} -\theta)\\=\frac{49}{2}(sinh\theta cosh\theta - arc cosh(\frac{x+7}{7}))\)

Thus, on further solving, the final answer will be equal to \(1/2(x+7)\sqrt({x^2}+14x)-[49/2ln(1/7\sqrt({x^2}+14x) + (x+7)] + C.\)

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Answer:

Cost of the first house : $480,000

Cost of the second house : $320,000

Step-by-step explanation:

An estate agent has three houses for sale. The prices of the houses were

in the ratio 6:4:3 and the cheapest house was priced at $240 000. What

were the prices of the other two houses? (SHOW WORKING)​

The prices of the house has a ratio of

6:4:3

Sum total = 6 + 4 + 3 = 13

Cheapest house = $240,000

The sum total cost of the 3 houses = x

x is calculated as:

= 3/13 × x =$ 240,000

= 3x = $240,000 × 13

x = $240,000 × 13/3

x = $1,040,000

The Cost of the first house =

6/13 × $1,040,000

= $480,000

Cost of the second house

= 4/13 × $1,040,000

=$320,000

Therefore,

Cost of the first house : $480,000

Cost of the second house : $320,000

Answer:

12%

Step-by-step explanation:

3/25 = 0.12 * 100 = 12%

Answer:

Solution,

Lett handed men = 3

Total men = 25

Now,

percent of left handed men:

\( \frac{3}{25} \times 100 \: percent\)

\(12 \: percent\)

Hope this helps....

Good luck on your assignment...

Answer:

Step-by-step explanation:

w^3 + 4w^2 + 5w - 12

I WILL ANSWER SO TIMMY GET CROWN

The expected value in a binomial situation with n = 18 and π = 0.60 is E(X) = np = 18 * 0.60 = 10.8.

In a binomial situation, the expected value, denoted as E(X), represents the average or mean outcome of a random variable X. It is calculated by multiplying the number of trials, denoted as n, by the probability of success for each trial, denoted as π.

In this case, we are given n = 18 and π = 0.60. To find the expected value, we multiply the number of trials, 18, by the probability of success, 0.60.

n = 18 (number of trials)

π = 0.60 (probability of success for each trial)

To find the expected value:

E(X) = np

Substitute the given values:

E(X) = 18 * 0.60

Calculate the expected value:

E(X) = 10.8

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Force in member \(dc = (sqrt(3)/2)\) HIForce in member \(hc = HI * (2/3)\) Force in member \(hi = HI\)

Force in members dc, hc, and hi of the truss: Member hc: Member hc is subjected to compression forces.

Let the force in member hc be HC. By using the method of sections, the following forces can be calculated:

Sum of forces in the y direction = 0Sum of forces in the y direction\(= 0 \\= > HC + (sqrt(3)/2)*DC - (1/2)*HI = 0.HC + (sqrt(3)/2)*DC \\= (1/2)*HI\)

Taking moments about C, Hence,

 \(3/2 DC = HI \\= > DC = 2/3 HI\).

The sign convention for force in member hc would be compressive.

Member dc: Let the force in member dc be DC.

Apply the method of sections to calculate the forces in members dc and hi.

Sum of moments about

\(H = 0 \\= > DC*(1/2) - (sqrt(3)/2)*HI = 0 \\= > DC = (sqrt(3)/2)*HI.\)

The sign convention for force in member dc would be tensile.

Member hi: Let the force in member hi be HI.

Apply the method of joints to calculate the forces in members dc and hi.

The free body diagram for joint H can be drawn as follows: By using the method of joints,

Force balance in the y direction, \(HI - 2DC*sin(30) = 0 = > HI = sqrt(3) DC\)

. The sign convention for force in member hi would be tensile.

Therefore, Force in member \(dc = (sqrt(3)/2)\) HIForce in member \(hc = HI * (2/3)\) Force in member \(hi = HI\)

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Answer:

2 + sqrt(3)

Step-by-step explanation:

Roots that contain square roots come in pairs

If there is a root that is a- sqrt(b), there is a root that is a+ sqrt(b)

2 -sqrt(3) means there is a root 2 + sqrt(3)

Answer:

I'm gonna say false

GDP or Gross Domestic Profit is the money that is being spent/made inside the country. So it stands to reason that if people are spending more, the GDP would go up.

Hope this helps!

Answer:

\(3\frac{2}{3}\)

Step-by-step explanation:

Given the following question:

\(\frac{22}{6}\)

In order to convert a mixed number into an improper fraction we have to divide the numerator (in this case; 22) by the denominator (in this case; 6) to find your answer.

\(\frac{22}{6}\)
\(\frac{22}{6} \div2=\frac{11}{3}\)
\(\frac{11}{3}=11\div3=3\frac{2}{3}\)
\(=3\frac{2}{3}\)

Let three represent how many times 3 goes into 11, let 2 represent the remainder while of course keeping the denominator the same. Your answer is "3 2/3."

Hope this helps.

The prefix "kilo-" in the metric system means one thousand. Therefore, one kilometer equals 1000 meters.

The metric system is a decimal-based system that uses prefixes to denote multiples and submultiples of units. In this system, the prefix "kilo-" represents a factor of one thousand, which is equivalent to 10^3. For instance, one kilogram is equal to one thousand grams, and one kilometer is equal to one thousand meters. Similarly, other prefixes like "centi-" (one hundredth), "milli-" (one thousandth), and "mega-" (one million) are used in the metric system to denote different multiples and submultiples of units.

In conclusion, the prefix "kilo-" in the metric system represents a factor of one thousand. Therefore, when we use this prefix with the unit of length "meter," we get "kilometer," which is equal to 1000 meters.

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Answer:

x = 9

Step-by-step explanation:

This is a 45-45-90 right triangle so the sides are in the ratio x: x: \(x\sqrt{2}\)

Answer:

12

Step-by-step explanation:

(1/3) x  + 5 = 9

(1/3) x = 9 -5

(1/3) x = 4

Multiply both sides by 3

x = 12

Answer:

x = 12

Step-by-step explanation:

1/3x + 5 =9.

1/3x = 4,

x = 12

Answer:

third option

Step-by-step explanation:

Answer:

answer is 4.

Step-by-step explanation:

the difference between 5 and 9 is 4

9-5=4

and in 13 and 17 it's the same

17-13=4

so the common difference is 4

write 4️⃣is the answer

Answer:

The answer is A.

Step-by-step explanation:

The formula of discriminant is D = b² - 4ac using ax² + bx + c. In this question, a is 1, b is -4 and c is 4. Then substitute the values into the formula :

D = b² - 4ac

D = (-4)² - 4(1)(4)

= 16 - 16

= 0

Answer:

perpendicular

Step-by-step explanation:

the lines meet together

Answer:

See below

Step-by-step explanation:

Given there are 56 M&M's:

Remember to use \(np\) to calculate expected value! This will especially be helpful if you are conducting a chi-squared test of independence.

The complementary angle is 19 degrees and the supplementary angle is 109 degrees.

Complementary angles can be defined as the angles whose sum is 90 degrees.

The ‘c’ in complementary angle can be used to form 9 in 90 degrees. Supplementary angles are angles whose sum is 180 degrees. The ‘s’ in supplementary angle can be used to form 8 in 180 degrees

If the intersection of P and Q creates a 71 degree angle,

then 90 – 71 = 19 degrees is its complementary angle. Its supplementary angle is 180 – 71 = 109 degrees.

Therefore, The complementary angle is 19 degrees and the supplementary angle is 109 degrees.

So, The answer is D)

The complementary angle is 19 degrees and the supplementary angle is 109 degrees.

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Option C. is correct one, (1, 3) is a vertex (out of two) of the hyperbola.

In a hyperbola, the vertex refers to the point where the transverse axis intersects the hyperbola. The transverse axis is the axis that passes through the two vertices of the hyperbola, and it is perpendicular to the imaginary axis that separates the two branches of the hyperbola.

There are two vertices in a hyperbola, one on each side of the imaginary axis. The distance from each vertex to the center of the hyperbola is equal to the value of the constant.

The question specifies that the dot on the hyperbola denotes the vertices in both graph,

They are (1,3) and (1,- 7)

However, (1,3) is on the given option of possible answers, while (1,-7) is not,

Thus , (1,3) is a vertex (out of two) of the hyperbola.

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The proportion of people who were caught after being on the 10 10 most wanted list. The Lower Endpoint is 0.297 and the Upper Endpoint is 0.377.

Point estimate of proportion of people who get caught is,  p = 98/291 =  0.337

Standard error of sample proportion, SE = \sqrt{p(1-p)/n} = \sqrt{0.337 * (1 - 0.337)/291} = 0.02770928

Z value for 85% confidence interval is  1.44

Lower Endpoint = 0.337 - 1.44 * 0.02770928  = 0.297

Upper Endpoint = 0.337 + 1.44 * 0.02770928  = 0.377

Proportion refers to the relationship between two or more quantities, expressed in terms of a ratio or a fraction. It is a fundamental concept in mathematics that is used to compare the relative size of one quantity to another. In other words, it is a way of describing how much of one thing there is in relation to another.

Proportions can be expressed in different ways, depending on the context and the purpose of the comparison. For example, a proportion can be expressed as a percentage, a decimal, or a fraction. In everyday life, we encounter proportions in a variety of situations, such as when we measure ingredients for a recipe, calculate the percentage of people who voted in an election, or compare the sizes of objects.

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Complete Question: -

The FBI wants to determine the effectiveness of their 10 Most Wanted list. To do so, they need to find out the fraction of people who appear on the list that are actually caught

Step 1 of 2: Suppose a sample of 291 suspected criminals is drawn. Of these people, 98 were captured. Using the data, estimate the proportion of people who were caught after being on the 10 Most Wanted list. Enter your answer as a fraction or a decimal number rounded to three decimal places.

The code sorts the skill array in ascending order.

It then creates a HashMap to store the number of occurrences of each skill level. The left and right pointers are initialized to point to the first and last elements of the skill array. The result variable is used to store the sum of the effectiveness of all teams that can be created. The code then iterates through the skill array using the left and right pointers. If both pointers point to skills that have more than one occurrence, then two of each skill are used to create the team, and effectiveness is added to the result.

If only one pointer points to a skill with more than one occurrence, then one instance of that skill is paired with one instance of the other skill to form a team. Otherwise, if both pointers point to skills that have only one occurrence, then one instance of each skill is used to create the team. In any case, when a team is created, the HashMap is updated accordingly.

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\(7 \frac{5}{8} + 4 \frac{2}{3} \)

the simplest form.

\( \frac{61}{8} + \frac{14}{3} \)

\( = \frac{(61 \times 3) + (14 \times 8)}{8 \times 3} \)

\( = \frac{183 + 112}{24} \)

\( = \frac{295}{24} \)

\( = 12 \frac{7}{24} \)

hence, the correct answer is option D.

Answer:

s ≈ - 1.9 , s ≈ 11.9

Step-by-step explanation:

s² - 10s - 23 = 0 ( add 23 to both sides )

s² - 10s = 23

To complete the square

add ( half the coefficient of the s- term )² to both sides

s² + 2(- 5)s + 25 = 23 + 25

(s - 5)² = 48 ( take square root of both sides )

s - 5 = ± \(\sqrt{48}\) ( add 5 to both sides )

s = 5 ± \(\sqrt{48}\)

Then

s = 5 - \(\sqrt{48}\) ≈ - 1.9 ( to the nearest tenth ) ← smaller solution

s = 5 + \(\sqrt{48}\) ≈ 11.9 ( to the nearest tenth ) ← larger solution

The amount of aspirin that will be present in the patient's body after two hours is 281.25 milligrams.

You can simply replace those variables with the value you know of them and then operate on those values to get a final value. This is the result of that expression at those values of the considered variables.

For this case, we have:

Amount of aspirin in a person's body (in milligrams) after t hours of taking the medicine is:

\(a = 500\times(\dfrac{3}{4})^t\) (in milligrams)

For t = 2 hours, we get:

\(a = 500\times(\dfrac{3}{4})^2 = 281.25 \: \rm milligrams\)

Thus, the amount of aspirin that will be present in the patient's body after two hours is 281.25 milligrams.

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When palpating the abdomen, you should note whether the liver is enlarged in the right upper quadrant, option d.

The liver is the largest internal organ located in the upper right portion of the abdomen. When assessing for liver enlargement through palpation, healthcare professionals typically focus on the right upper quadrant of the abdomen.

By concentrating on the right upper quadrant during palpation, healthcare professionals can gather information about the size, tenderness, or abnormalities of the liver. This specific region provides the best access and proximity to assess the liver and detect any potential enlargement or abnormalities.

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Answer:

Rupees 891

Step-by-step explanation:

If you multiply 810 times 0.1 which is the decimal of 10%, you get 81 which you can add to 810 to get 891 which is the price the shopkeeper payed to buy the watch.

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