Find the measure of AEB

- already have answer just need the work

(a) A nonzero vector orthogonal to the plane through the points P, Q, and R is (9, -17, 35). (b) The area of triangle PQR is \(\sqrt\)(811) / 2.

(a) To determine a nonzero vector orthogonal to the plane through the points P, Q, and R, we can first find two vectors in the plane and then take their cross product. Taking vectors PQ and PR, we have:

PQ = Q - P = (5, 1, -2) - (-4, 0, 0) = (9, 1, -2)

PR = R - P = (6, 4, 1) - (-4, 0, 0) = (10, 4, 1)

Taking the cross product of PQ and PR, we have:

n = PQ x PR = (9, 1, -2) x (10, 4, 1)

Evaluating the cross product gives n = (9, -17, 35). Therefore, (9, -17, 35) is a nonzero vector orthogonal to the plane through points P, Q, and R.

(b) To determine the area of triangle PQR, we can use the magnitude of the cross product of vectors PQ and PR divided by 2. The magnitude of the cross product is given by:

|n| = \(\sqrt\)((9)^2 + (-17)^2 + (35)^2)

Evaluating the magnitude gives |n| = \(\sqrt\)(811).

The area of triangle PQR is then:

Area = |n| / 2 = \(\sqrt\)(811) / 2.

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The value of k such that P(Z > k) = 0.7291 is approximately -0.61. The value of x corresponding to a z-score of -1.2 is approximately 46.6.

Question 1: To find the value of k such that P(Z > k) = 0.7291, we need to look up the corresponding z-score for the given probability. In other words, we need to find the z-score that has an area of 0.7291 to its left.

Using a standard normal distribution table or a statistical calculator, we can find that the z-score corresponding to a left-tail probability of 0.7291 is approximately 0.610. However, since we want the probability of Z being greater than k, we need to take the complement of the given probability. Therefore, the value of k that satisfies P(Z > k) = 0.7291 is approximately -0.61.

Question 2: Given a normal random variable X with a mean of 50 and a standard deviation of 3, and a z-score of -1.2, we can use the z-score formula to find the corresponding value of x. The z-score formula states that z = (x - μ) / σ, where z is the z-score, x is the value of the random variable, μ is the mean, and σ is the standard deviation.

Rearranging the formula, we have x = z * σ + μ. Plugging in the values z = -1.2, σ = 3, and μ = 50 into the formula, we get x = -1.2 * 3 + 50 = 46.6. Therefore, the value of x corresponding to a z-score of -1.2 is approximately 46.6.

In summary, the value of k such that P(Z > k) = 0.7291 is approximately -0.61. The value of x corresponding to a z-score of -1.2 is approximately 46.6.

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Answer:

22.2

Step-by-step explanation:

48/13 ≈ 3.7

6 times 3.7 = 22.2

4 radians is equal to 299 degree after rounding it to the nearest degree.

Here we have to convert 4 radians into degree.

To convert radians to degrees,

We can use the formula:

degrees = radians x 180 /π

Where π is approximately 3.14.

So, if we substitute 4 radians into the formula, we get:

degrees = 4 x 180 / 3.14

degrees = 229.29

To round this to the nearest degree,

We look at the decimal part:

0.29 is less than 0.50, so we round down.

Therefore, the answer is 229 degrees.

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Answer:

D seems to be the best answer

Answer:

D

Step-by-step explanation:

Q1: A gold chain bought for Rs.50,000 is sold after two years at a profit of Rs.9,500 . The cost of this chain has increased by 15.8%.

To calculate the increase in the cost of the chain, the percentage increase should be determined which is carried out below. Thus;

The original price of gold chain = Rs. 60,000

The profit made after two years = Rs.9,500

The total amount of money made for selling the chain = 60,000+9500

= Rs. 69500

The increase in cost of chain;

= 9500/60000 × 100/1

= 950000/60000

= 15.8% increase in cost price.

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We have demonstrated using the Intermediate Value Theorem that the polynomial function has a real zero between 1 and 7.

To apply the Intermediate Value Theorem to the polynomial function f(x) = x^3 - x - 4 and show that it has a real zero between the integers 1 and 7, we need to verify that f(1) and f(7) have opposite signs.

Let's evaluate f(1) and f(7) to determine their signs:

f(1) = (1)^3 - (1) - 4 = 1 - 1 - 4 = -4

f(7) = (7)^3 - (7) - 4 = 343 - 7 - 4 = 332

From the calculations, we can see that f(1) = -4 and f(7) = 332.

Since f(1) is negative (-4) and f(7) is positive (332), they have opposite signs.

According to the Intermediate Value Theorem, if a continuous function changes sign between two points, then it must have at least one real zero between those points.

Since f(1) = -4 (negative) and f(7) = 332 (positive), the polynomial function f(x) = x^3 - x - 4 must have a real zero between the integers 1 and 7.

Therefore, we have demonstrated using the Intermediate Value Theorem that the polynomial function has a real zero between 1 and 7.

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Answer:

(x + 1)² = 4(y + 10)

Step-by-step explanation:

Equation of parabola:

(x - h)² = 4a(y - k)

with vertex(h, k) and focus (h, k + a)

vertex(h, k) = (-1, -10)

⇒h = -1 and k = -10

focus (h, k + a) = (-1, -9)

⇒ k + a = -9

⇒ -10 + a = -9

⇒ a = 10 - 9

⇒ a = 1

Equation of parabola:

(x - h)² = 4a(y - k):

(x - (-1))² = 4(1)(y - (-1))

= (x + 1)² = 4(y + 10)

Answer:

the answer is down below

Step-by-step explanation:

9 to 2

Answer:

78.5%

Step-by-step explanation:

Hope this helps ;) ❤❤❤

Answer:Fraction: 81/100      Decimal: 0.81         Percentage: 81%

Step-by-step explanation:

Answer:

The answer is D

Step-by-step explanation:

According to the Pythagorean Theorem, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs of a right triangle.

In other words, \(a^2 + b^2 = c^2\) for the triangle depicted below.

The right triangle's legs, a and b, are perpendicular sides, and the hypotenuse, c, is the side that faces away from the right angle.

Construction projects and almost anything involving right triangles, such as roofing for homes, are common uses for this application.

Hypotenuse² = Base² + Perpendicular²

The Pythagorean Theorem is used in a variety of computations. For instance, it may be used to determine the height and distance of straight and fallen trees, as well as the steepness of hills and mountains.

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Answer:

1. Positive, 2. negative, 3. 16.8-(-28.1), Final answer -44.9.

Step-by-step explanation

Tryna cheat off the I-ready diagnostics huh

Answer:

The answer to this question is that  1. Positive, 2. negative, 3. 16.8-(-28.1), Final answer -44.9.

Step-by-step explanation:

Good luck :)

Answer: Complex

Step-by-step explanation:

Answer:

I think the answer is complex number.

Step-by-step explanation:

The set of complex numbers is denoted by either of the symbols ℂ or C. Despite the historical nomenclature "imaginary", complex numbers are regarded in the mathematical sciences as just as "real" as the real numbers, and are fundamental in many aspects of the scientific description of the natural world.

Hope this helps!!

Answer:

  (a)  6√3, 6√7

Step-by-step explanation:

The right triangles shown are all similar, so corresponding sides are proportional. This gives rise to three "geometric mean" relations between the various lengths.

Using P, F, L, and H to represent the points marked Park, Football field, Library, and Home, the relations are ...

  PF/FH = FL/PF   ⇒   PF = √(FH·FL)

  PL/FL = HL/PL   ⇒   PL = √(FL·HL)

  PH/HL = HF/PH   ⇒   PH = √(HL·HF)

(a) The distance from the park to the library is ...

  PL = √(FL·HL) = √(12·9) = 6√3 . . . miles

(b) The distance from the football field to the park is ...

  PF = √(FH·FL) = √(21·12) = 6√7 . . . miles

Answer:

The next number in the sequence is 17/15.

Step-by-step explanation:

The perimeter of the rhombus is 4√117 feet.

What is rhombus?

A rhombus is a special type of quadrilateral (a polygon with four sides) where all four sides are equal in length. It is also known as a diamond shape because of its symmetrical appearance.

In a rhombus, the diagonals are perpendicular bisectors of each other. This means that they divide the rhombus into four congruent right triangles.

Let's denote the length of one diagonal as d1 and the length of the other diagonal as d2. In this case, d1 = 18 feet and d2 = 12 feet.

Each right triangle formed by the diagonals has legs equal to half the lengths of the diagonals. Therefore, the lengths of the legs are d1/2 = 18/2 = 9 feet and d2/2 = 12/2 = 6 feet.

Using the Pythagorean theorem, we can find the length of the hypotenuse of each right triangle, which is also a side of the rhombus.

\(h^2 = (leg1)^2 + (leg2)^2\\\\h^2 = 9^2 + 6^2\\\\h^2 = 81 + 36\\\\h^2 = 117\)

Taking the square root of both sides:

h = √117

Since the rhombus has four congruent sides, the perimeter is given by:

Perimeter = 4 * h = 4 * √117

Thus, the perimeter of the rhombus is 4√117 feet.

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Answer:

Sure, here are the numbers arranged from greatest to least

Step-by-step explanation:

Order from greatest to least

1.3, 4.5%, 1/3, -4/5, -0.04, -21.5%

Answer:

From the greatest to least

Step-by-step explanation:

1.3, 4.5%, 1/3, -4/5, -0.04, -21.5%

You can identify which number is greater than other by using a number line.

What is a number line?

A number line is what a math student can use to find the answer to addition and subtraction questions. A straight line, theoretically extending to infinity in both positive and negative directions from zero, that shows the relative order of the real numbers.

Hope this helps :)

Pls Brainliest...

Answer:

The answer is below

Step-by-step explanation:

A student on the cross- county team runs 30 minutes a day as a part of her training. Write an equation to describe the relationship between the distance she runs in miles, D, and her running speed, in miles per hour, when she runs at a constant speed of 5.4miles per hour for m minutes, and then at b miles per hour for n minutes

Solution:

Given that the student runs for a total of 30 minutes per day. He runs at 5.4 miles per hour for m minutes, and then at b miles per hour for n minutes.

Hence:

m + n = 30

60 minute = 1 hour. Therefore, m minute = m/60 hour, n minute = n/60 hour.

The distance traveled is the product the speed in miles per hour and the time taken to cover the distance. Distance = speed * time

The total distance ran (D) is:

D = 5.4(m/60) + b(n/60)

Answer:

1.55

Step-by-step explanation:

you just change the fractions to decimals

Answer:

slope = 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = x + 10 ← is in slope- intercept form

with slope m = 1

Answer:

Choice D

Step-by-step explanation:

The area can be found simply by multiplying the height by the base:

\((2y + 5)(y + 6)\\= 2y^2 + 12y + 5y + 30\\= 2y^2 + 17y + 30\)

So answer D is the correct one (note that they do not group like terms, leaving 12y + 5y in that form instead of adding them together).

The potential energy of the system of charges change as a result option (b) the potential energy decreases.

The potential energy of a system of charges depends on their relative positions and magnitudes. In this case, the system consists of three negative charges of equal magnitudes, and we are moving one of them away from the x-axis to a new position (0, +a).

Initially, the potential energy of the system can be calculated using the formula for the potential energy of a system of point charges

U = (1/4πε₀) × q₁q₂/r₁₂ + (1/4πε₀) × q₁q₃/r₁₃ + (1/4πε₀) × q₂q₃/r₂₃

where U is the potential energy of the system, q₁, q₂, and q₃ are the charges, r₁₂, r₁₃, and r₂₃ are the distances between the charges, and ε₀ is the electric constant.

Assuming that the charges are equal and using the distance formula for the distances, we get

U = (1/4πε₀) × q² [(1/|x+a|) + (1/|x|) + (1/|x-a|)]

When x=0, this simplifies to

U = (1/4πε₀) × (3q²/a)

When we move the charge at (0,0) to (0,a), we are effectively increasing the distance between this charge and the other two charges along the x-axis. This means that the distances r₁₃ and r₂₃ increase, while the distance r₁₂ remains the same.

As a result, the potential energy of the system decreases.

Therefore, the correct answer is (b) the potential energy decreases.

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x is the temperature and y is the number of swimmers. If there are 80 swimmers, then y = 80 instead of x = 80

This is how Corey should have solved

y = 1.505*x - 88.21

80 = 1.505*x - 88.21 <--- replace y with 80

1.505*x - 88.21 = 80

1.505*x = 80 + 88.21 <--- add 88.21 to both sides

1.505*x = 168.21

x = 168.21/1.505 <--- divide both sides by 1.505

x = 111.767

x = 111.8

If there are 80 swimmers at the pool, then the possible outside temperature is roughly 111.8 degrees F. This temperature seems awfully large, so it's possible that Corey's regression equation has limited scope; in other words, it isn't too useful if x is outside a given interval

PLEASE SEE THE ATTACHMENT

Answer:

A

Step-by-step explanation:

I got it right on Edge

Collecting gender information is an example of a nominal measurement, and the latitude coordinates are continuous.

Collecting gender information (male, female, or unspecified) is an example of a nominal measurement.

Nominal measurement involves categorizing data into distinct categories or labels without any inherent order or numerical value attached to them.

Your gas tank being at the halfway mark is an example of a continuous measurement. Continuous measurement refers to a scale where values can take on any numerical value within a given range.

In this case, the level of gas in the tank can be measured and represented as a continuous quantity.

The statement "The Equator is the line of 0 degrees latitude" indicates that latitude coordinates are continuous.

Latitude is a continuous measurement as it represents the angular distance from the equator, and the values can range from 0 degrees at the equator to 90 degrees at the North and South poles.

The latitude coordinates are continuous because they can take on any value within this range.

In summary, collecting gender information is a nominal measurement, the halfway mark of a gas tank is a continuous measurement, and latitude coordinates are continuous.

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Answer:

The answer is D; Hanna is not correct,. The fraction 1/4 is equal to 2/8, so you can graph it on the second tick mark to the right of zero.

Step-by-step explanation:

Because the number line is broken up into 8 parts, the points on the graph are, 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8, 8/8 (also known as one)

1/4 = 2/8. We know this because if we multiply 1/4 by 2, we get 2/8.

So, because 2/8 is the same as 1/4, we know that Hanna is not correct, and that you can graph 1/4 on this number line, because it is the same as 2/8.

I hope that this helps :)

Answer:D the last one.

Step-by-step explanation:

The greatest amount of sap collected from any one tree is two times.

The maximum amount of sap that can be gathered from a single tree is two times greater than the minimum amount. SAP enables businesses to innovate on anything from cancer therapies to flood mitigation. We support life-saving research and are deeply committed to social responsibility and sustainability. At SAP, we collaborate to create innovations.

Work in a stimulating and rewarding environment by joining us. Minerals and nutrients can be found in tree sap. In the spring, when new buds are growing, a sticky substance that travels through the tree and out onto the branches helps the tree produce energy. Sugars are created as a result of photosynthesis and sent back into the tree, where they serve as sustenance for the tree's growth.

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Correct Question:

The greatest amount of sap collected from any one tree is _____________

Answer:

y = 1.5

Step-by-step explanation: if u need the work lmk

Answer:

y = 1.5

Step-by-step explanation:

3.2y - 1.8 = 3

3.2y = 3 + 1.8

3.2y = 4.8

3.2y ÷ 3.2 = 4.8 ÷ 3.2

y = 1.5