The figure shows a right-angled triangle ABC, where the point A has coordinates (-4,2), the angle B is 90° and the point C lies on the x-axis. The point M(1.3) is the midpoint of AB. Find the area of the triangle ABC

answer:

50/50

step-by-step explanation:

hi there!

flip a coin a couple of times, most likely get the same number of heads then you will of tails, since a coin has 2 sides and only two equal sides the probability to flip that very coin and it landing on heads is 50 percent same as landing it on tails, we know its 50 percent because 100 percent is the full amount ( no matter how much the coin is worth ) and dividing that by 2 does indeed equal 50 or 50 percent.

i believe that is one of the reasons why before a lot of sport games start off with a coin toss to chose which team plays first because it is a 50/50 chance for each team, making it fair toss

i hope this helps you! i hope you have a good rest of your day! :)

Answer:

The area of the rectangle is 24.

Step-by-step explanation:

The given points:

a) (-2, 2)

b) (-2, -4)

c) (2, -4)

To complete the rectangle the other point must be (2, 2), so the rectangle formed has the following dimensions:

x: distance in the x-direction (from -2 to 2):

[tex]x = 2 - (-2) = 4[/tex]

y: distance in the y-direction (from -4 to 2):

[tex]y = 2 - (-4) = 6[/tex]

The area of the rectangle is:

[tex] A = x*y = 4*6 = 24 [/tex]

Therefore, the area of the rectangle is 24.

I hope it helps you!      

Minimizing curve C is a helix, described by the equation :

C(t) = (a cos(t), a sin(t), C exp(-cot(t)) + h)

To express the length L(p) of curve C in terms of p, we can use the formula for the length of a curve in cylindrical coordinates. In cylindrical coordinates, the arc length element ds can be given by:

ds² = dr² + r² dt² + dz²

Since dr = 0 (as r = a is constant along the curve C), and dt = -a sin(t) dt (from the parametrization), we have:

ds² = a² sin²(t) dt² + dz²

Integrating ds over the curve C from t = 0 to t = tmax, we get:

L(p) = ∫[0,tmax] √(a² sin²(t) + p'(t)²) dt

where p'(t) denotes the derivative of p(t) with respect to t.

To find the differential equation for the function p(t) that minimizes L(p), we can apply the Euler-Lagrange equation of the calculus of variations. The Euler-Lagrange equation is given by:

d/dt (dL/dp') - dL/dp = 0

Differentiating L(p) with respect to p' and p, we have:

dL/dp' = 0 (since p does not appear explicitly in L(p))

dL/dp = d/dt (dL/dp') = d/dt (a² sin²(t) p'(t) / √(a² sin²(t) + p'(t)²))

Using the chain rule, we can simplify the expression:

dL/dp = (a² sin²(t) p''(t) - a² sin(t) cos(t) p'(t)²) / (a² sin²(t) + p'(t)²)^(3/2)

Setting the Euler-Lagrange equation equal to zero, we get:

(a² sin²(t) p''(t) - a² sin(t) cos(t) p'(t)²) / (a² sin²(t) + p'(t)²)^(3/2) = 0

Simplifying further, we have:

p''(t) - (sin(t) cos(t) / sin²(t)) p'(t)² = 0

This is the differential equation that the function p(t) must satisfy to minimize L(p).

To solve this differential equation, we can make the substitution u = p'(t). Then the equation becomes:

du/dt - (sin(t) cos(t) / sin²(t)) u² = 0

This is a separable first-order ordinary differential equation. By solving it, we can obtain the solution for u = p'(t). Integrating both sides and solving for p(t), we get:

p(t) = C exp(-cot(t)) + h

where C is a constant determined by the initial condition p(0) = 0, and h is the value of p at t = tmax.

Therefore, the minimizing curve C is a helix, described by the equation :

C(t) = (a cos(t), a sin(t), C exp(-cot(t)) + h)

where C is a constant determined by the initial condition, and h is the value of p at t = tmax.

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The rancher can run approximately 19,425 mature 200 lb. ewes. To calculate the number of mature 200 lb. ewes the rancher can run on the remaining forage, we need to find the available forage after accounting for the 30 head of elk.

A rancher in Central California has a 5,000-acre BLM grazing allotment in the Oak Woodlands. Seventy percent of the allotment has loam soils producing 900 lbs. (DM) of forage per year, while the remaining 30% with sandy loam soil produces 500 lbs. of forage (DM) per year. The rancher must also account for 30 head of elk (500 lbs.). We need to determine how many mature 200 lb. ewes can be run on the remaining forage.

The total forage available from the loam soil is 70% of 5,000 acres, which is 3,500 acres. This amounts to 3,500 acres * 900 lbs./acre = 3,150,000 lbs. of forage (DM) per year.

Similarly, the total forage available from the sandy loam soil is 30% of 5,000 acres, which is 1,500 acres. This amounts to 1,500 acres * 500 lbs./acre = 750,000 lbs. of forage (DM) per year.

With the elk accounting for 30 * 500 lbs. = 15,000 lbs. of forage, the remaining available forage is 3,150,000 lbs. + 750,000 lbs. - 15,000 lbs. = 3,885,000 lbs.

Dividing the remaining forage by the weight of a mature ewe (200 lbs.), we get 3,885,000 lbs. / 200 lbs. = 19,425 ewes. Therefore, the rancher can run approximately 19,425 mature 200 lb. ewes on this allotment, considering the given forage production and the presence of elk.

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the solution to the equation log(a) + log(z - 6) = 2 is z = 100/a + 6.

We can simplify the equation using logarithmic properties. The sum of logarithms is equal to the logarithm of the product, so we can rewrite the equation as log(a(z - 6)) = 2.

Next, we can convert the equation to exponential form. In exponential form, the base of the logarithm becomes the base of the exponent and the logarithm value becomes the exponent. Therefore, we have a(z - 6) = 10^2, which simplifies to a(z - 6) = 100.

To solve for z, we need to isolate it. Divide both sides of the equation by a: (z - 6) = 100/a.

Finally, add 6 to both sides to solve for z: z = 100/a + 6.

So, the solution to the equation log(a) + log(z - 6) = 2 is z = 100/a + 6.

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Answer:

7/10

Step-by-step explanation:

Answer:

The last one is symmetrical.

The first one and the last one are correct.

Answer & explanation:

The student made an error by adding an r after removing the parentheses instead of subtracting an r.

Correct Steps:

(6b + 4r) – (2b + r)

6b + 4r - 2b - r

4b + 3r

Answer:

yo

Step-by-step explanation:

this was the sample response on edge

The student did not distribute the negative when subtracting. Distributing the negative, the expression is equal to 6b + 4r – 2b – r. Then use the commutative property to rewrite it as 6b – 2b + 4r – r. Then you can use the distributive property to write as (6 – 2)b + (4 – 1)r, which simplifies to 4b + 3r.

Answer:

a. 7% b. 1.4 inches

Step-by-step explanation:

(a)What is the probability that the diameter of a randomly selected tree will be at least 10 inches? Will exceed 10 inches.

Since our mean, x = 8.8 and standard deviation, σ = 2.8, and we want our maximum value to be 10 inches,

So, x + ε = 10 where ε = error between mean and maximum value

So,8.8 + ε = 10

ε = 10 - 8.8 = 1.2

Since σ = 2.8, ε/σ = 1.2/2.8 = 0.43

ε/σ × 100 % = 0.43 × 100 = 43%

Since 50% of our values are in the range x - 3σ to x and 43% of our values are in the range x to x + ε = x + 0.43σ, the probability of finding a value less than 10 inches is thus 50 % + 43% = 93%.

So, the probability of finding a value greater than 10 inches is thus 100 % -   93 % = 7 %.

(b) What is the value of c so that the interval (8.8-c, 8.8+c) contains 98% of all diameter values.

Since 98% of the values range from 8.8-c to 8.8+c, then half of the interval is from 8,8 - c to 8.8 or 8.8 to 8.8 + c. So, the number that range in this half interval is 98%/2 = 49%

So, c/σ × 100 % = 49%  

c/σ = 0.49

c = 0.49σ = 0.49 × 2.8 = 1.372 ≅ 1.37 inches = 1.4 inches to 1 d.p

Answer:

b,c,e

Step-by-step explanation:

Answer:3/5

Step-by-step explanation:when he takes one marble it’s 7/11 and when he takes another it’s 6/10 so simplify and you get 3/5

Answer:

Step-by-step explanation:

Answer:3/5

Answer:

Step-by-step explanation:

The square root of 16 and the square root of 17

Answer:

29 and 34

Step-by-step explanation:

cause

Answer: 19 mins

Step-by-step explanation:

hope this helps

Answer:

D

Step-by-step explanation:

lol this is a weird math question

jk

Hydrogen bonds occur only when hydrogen is covalently bonded to one of three elements: fluorine, oxygen, or nitrogen. Anything else isn't considered a hydrogen bond.

Answer:

zero point zero zero one two five

Step-by-step explanation:

Answer:

9 - 166.42m²

10 - 308.8cm²

Step-by-step explanation:

The first figure shown is a triangular prism

We can find the surface area using this formula

[tex]SA=bh+L(S_1+S_2+h)[/tex]

where

B = base length

H = height

L = length

S1 = base length

S2 = slant height ( base's hypotenuse )

The triangular prism has the following dimensions

Base Length = 4m

Height = 5.7m

Length = 8.6m

S1 = 4m

S2 = 7m

Having found the needed dimensions we plug them into the formula

SA = ( 4 * 5.7 ) + 8.6 ( 4 + 7 + 5.7 )

4 * 5.7 = 22.8

4 + 7 + 5.7 = 16.7

8.6 * 16.7 = 143.62

22.8 + 143.62 = 166.42

Hence the surface area of the triangular prism is 166.42m²

The second figure shown is a pyramid

The surface area of a pyramid can be found using this formula

[tex]SA = A+\frac{1}{2} ps[/tex]

Where

A = Area of base

p = perimeter of base

s = slant height

The base of the pyramid is a square so we can easily find the area of the base by multiplying the base length by itself

So A = 8 * 8

8 * 8 = 64

So the area of the base (A) is equal to 64 cm^2

The perimeter of the base can easily be found by multiplying the base length by 4

So p = 4 * 8

4 * 8 = 32 so p = 32

The slant height is already given (15.3 cm)

Now that we have found everything needed we plug in the values into the formula

SA = 64 + 1/2 32 * 15.3

1/2 * 32 = 16

16 * 15.3 = 244.8

244.8 + 64 = 308.8

Hence the surface area of the pyramid is 308.8cm²

The correct probabilities are 0.1017 and 0.2053.

Given:

P(c\NV)=0.139, P(C|V)= 1- 0.95 = 0.05

P(V) = 0.418

P(NV) = 1- 0.418 = 0.582.

(1). The probability of that person getting Covid? P CP(C) = P(C|NV)        P(NV)+P(C|V) P(V)

0.139*0.582+0.05*0.418

= 0.1017.

(2).  The probability that he or she was vaccinated with P fizer P(V|C).

   [tex]P(V|C) = \frac{P(V|C)P(V)}{P(C|NV)P(NV)+P(CV)P(V)}[/tex]

                        [tex]\frac{0.05\times0.418}{0.139\times0.582+0.05\times0.418} = 0.2053[/tex]

3). P(NV|C) = 1 - P(V|C) = 0.7946.

(4). The chances of Covid is decreased.

(5). A second paragraph using statistics to support someone choosing 0.1017 = 10% got Covid and 0.139 = 13% not vaccinate.

Therefore, the probability of that person getting Covid is 0.1017 and the probability that he or she was vaccinated with Pfizer is 0.2053.

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Answer:

x=6

Step-by-step explanation:

3x- 4=14

   +4 +4

    3x=18

      x=6

Answer:

The age of the boy is 15 years

Step-by-step explanation:

Let us assume a be the age of the boy

So, two-third of his age is 2 ÷ 3 × a

As the boy said that two-third minus 1 so it would be equivalent to

  2 ÷ 3 × to - 1

ANd, his current age is a and now if we deduct 6 so

a - 6

AFter this, two-third minus 1 is equivalent to a minus 6

So,  

 2 ÷ 3 × a - 1 = a - 6

- 1 + 6 = a -  2 ÷ 3 × a  

5 =  1 ÷ 3 × a  

a = 3 × 5

 = 15

Hence, The age of the boy is 15 years

The dimension of w is 1.

To find a basis for the subspace W = {(0, x, y, z) : x - 6y + 9z = 0} of R4, we can first find a set of vectors that span W, and then apply the Gram-Schmidt process to obtain an orthonormal basis.

Let's find a set of vectors that span W. Since the first component is always zero, we can ignore it and focus on the last three components. We need to find vectors (x, y, z) that satisfy the equation x - 6y + 9z = 0. One way to do this is to set y = s and z = t, and then solve for x in terms of s and t:

x = 6s - 9t

So any vector in W can be written as (6s - 9t, s, t, 0) = s(6,1,0,0) + t(-9,0,1,0). Therefore, {(0,6,1,0), (0,-9,0,1)} is a set of two vectors that span W.

To obtain an orthonormal basis, we can apply the Gram-Schmidt process. Let u1 = (0,6,1,0) and u2 = (0,-9,0,1). We can normalize u1 to obtain:

v1 = u1/||u1|| = (0,6,1,0)/[tex]\sqrt{37}[/tex]

Next, we can project u2 onto v1 and subtract the projection from u2 to obtain a vector orthogonal to v1:

proj_v1(u2) = (u2.v1/||v1||^2) v1 = (-6/[tex]\sqrt{37}[/tex]), -1/[tex]\sqrt{37}[/tex], 0, 0)

w2 = u2 - proj_v1(u2) = (0,-9,0,1) - (-6/[tex]\sqrt{37}[/tex]), -1/[tex]\sqrt{37}[/tex], 0, 0) = (6/[tex]\sqrt{37}[/tex]), -9/[tex]\sqrt{37}[/tex], 0, 1)

Finally, we can normalize w2 to obtain:

v2 = w2/||w2|| = (6/[tex]\sqrt{37}[/tex], -9/[tex]\sqrt{37}[/tex], 0, 1)/[tex]\sqrt{118}[/tex]

Therefore, a basis for W is {(0,6,1,0)/[tex]\sqrt{37}[/tex], (6/[tex]\sqrt{37}[/tex]), -9/[tex]\sqrt{37}[/tex], 0, 1)/[tex]\sqrt{118}[/tex]}.

For the subspace w = {(:a+2c = 0 and b – d = 0} of [tex]M_{2*2}[/tex], we can think of the matrices as column vectors in R4, and apply the same approach as before. Each matrix in w has the form:

| a b |

| c d |

We can write this as a column vector in R4 as (a, c, b, d). The condition a+2c = 0 and b-d = 0 can be written as the linear system:

| 1 0 2 0 | | a | | 0 |

| 0 0 0 1 | | c | = | 0 |

| 0 1 0 0 | | b | | 0 |

| 0 0 0 1 | | d | | 0 |

The augmented matrix of this system is:

| 1 0 2 0 0 |

| 0 1 0 0 0 |

| 0 0 0 1 0 |

The rank of this matrix is 3, which means the dimension of the solution space is 4 - 3 = 1. Therefore, the dimension of w is 1.

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Answer:

yuh, did you bestie

Step-by-step explanation:

≤))≥

_| \_

Answer:

-1 and I hope everyone reading this has a great day!

Answer:

I think the answer is 1/2 but dont take my word

Answer:

2.25kg

Step-by-step explanation:

500g+850g+900g=2250

2250/1000=2.25kg

Answer:

d

Step-by-step explanation:

Answer:

OE=53 and UH = 53

Step-by-step explanation:

Pythagoras theorem

Using the corrected linearized form a = c * A * B * log(x) - A * B * log(A) + A * B * log(B), solve for unknowns A, B, c, and x.

To solve the equation a = c * A * B * log(x) - A * B * log(A) + A * B * log(B) for unknowns A, B, c, and x, we need additional information or constraints.

Without specific values or relationships among the variables, it is not possible to provide a numerical solution. However, if you have specific values for any of the variables or if there are constraints or relationships among them, we can apply appropriate mathematical techniques, such as substitution or optimization methods, to find the values of A, B, c, and x that satisfy the equation.

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Answer:

The measure of the missing angle is 61

Step-by-step explanation:

Using the Consecutive Interior Angles theorem, you know that the angles are supplementary (meaning both angles combine to a 180* plane). Using that logic, you may subtract 119 from 180, and you get a 61* angle.

Answer: Question 1, debit card because debit cards are used for atms which requires a pin. A positive is that you’re using your own money for a debit card and not from another source, so you don’t have to pay extra frees

Step-by-step explanation: